question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>How do 3d <a href="http://en.wikipedia.org/wiki/Holography" rel="nofollow">holograms</a> work exactly? I read that there is a laser in use, but how are the multiple perspectives generated and how is the light <em>trapped?</em> in a certain area to create the effect?</p>
<p>Furthermore, how do you generate different colors? Is it still using multicolored projectors or is there something special? What kinds of lenses are used?</p>
| 930 |
[
-0.009717150591313839,
-0.056499842554330826,
0.022825274616479874,
-0.06249740719795227,
0.041137926280498505,
-0.013393196277320385,
-0.03870048001408577,
-0.025050662457942963,
-0.007146691903471947,
-0.0417768657207489,
0.01458932925015688,
0.06632658839225769,
0.02796371839940548,
0.0406968779861927,
0.013242390006780624,
-0.011534863151609898,
0.02171623706817627,
-0.009884821251034737,
-0.016916994005441666,
0.003936826251447201,
-0.035239193588495255,
0.02921352908015251,
-0.005742441397160292,
0.009125174954533577,
-0.030750399455428123,
0.017674660310149193,
0.047107890248298645,
0.02356031909584999,
0.04666540026664734,
0.036736950278282166,
-0.032189249992370605,
-0.00782821886241436,
-0.012159999459981918,
0.05168337747454643,
-0.0007671971688978374,
-0.03355187550187111,
-0.03413236513733864,
-0.024534350261092186,
-0.012453556060791016,
-0.0030046897009015083,
-0.025624137371778488,
0.009815515950322151,
-0.04308557137846947,
0.0774143636226654,
-0.01937982626259327,
-0.008338679559528828,
-0.04475314915180206,
-0.031411539763212204,
0.021826965734362602,
-0.07430583238601685,
0.05312589183449745,
0.00039062995347194374,
0.01741332747042179,
0.05486335977911949,
0.014076380990445614,
0.017790114507079124,
0.09308787435293198,
0.05880790203809738,
-0.014553731307387352,
-0.025200987234711647,
0.004987590946257114,
0.028568074107170105,
0.009738713502883911,
-0.04274197295308113,
-0.030944982543587685,
0.010838357731699944,
0.006358514539897442,
0.0017478493973612785,
0.036737192422151566,
-0.021835429593920708,
0.010467400774359703,
0.021401280537247658,
0.05802192538976669,
-0.0050140018574893475,
0.009286073036491871,
-0.042253054678440094,
0.011819289065897465,
0.0020837264601141214,
0.02392667904496193,
0.02269730716943741,
0.021279357373714447,
0.0017167739570140839,
-0.030100896954536438,
0.004141626413911581,
-0.00004231839920976199,
-0.0341305248439312,
0.10984300076961517,
0.0028077212627977133,
-0.01080239750444889,
-0.014359643682837486,
-0.02089625597000122,
0.024799762293696404,
0.01896061562001705,
0.014025328680872917,
-0.022260425612330437,
-0.000668450549710542,
0.0046440004371106625,
0.06463901698589325,
0.007261717692017555,
-0.029552336782217026,
0.008182854391634464,
0.020764408633112907,
-0.002459630137309432,
0.03542863577604294,
-0.03040515072643757,
0.0012884973548352718,
0.01067077275365591,
0.03955550864338875,
0.02254653535783291,
0.012576404958963394,
-0.05422353744506836,
0.01156829297542572,
-0.008049044758081436,
0.0048650894314050674,
-0.00023614478413946927,
-0.0024529038928449154,
0.017372937873005867,
-0.006544203031808138,
0.04442000761628151,
0.09972462803125381,
-0.011460809037089348,
-0.03273336961865425,
0.029053712263703346,
-0.009545771405100822,
-0.07317686080932617,
0.002915959805250168,
0.011000840924680233,
0.01250429917126894,
-0.05144360288977623,
0.05291479080915451,
0.00003901793388649821,
-0.017955301329493523,
-0.0025699890684336424,
0.007573610171675682,
0.005438067950308323,
0.0006215537432581186,
-0.13337332010269165,
-0.0358743742108345,
0.019144071266055107,
-0.015522516332566738,
-0.019628502428531647,
-0.05206836760044098,
0.027864428237080574,
0.038301628082990646,
0.07322877645492554,
-0.019904518499970436,
-0.016286229714751244,
0.01443418674170971,
0.041939590126276016,
0.0037545403465628624,
-0.0448610857129097,
0.011585261672735214,
-0.00006259476504055783,
-0.027977922931313515,
0.0209326334297657,
-0.08377649635076523,
0.019351085647940636,
0.03596113249659538,
0.012166662141680717,
-0.06747660040855408,
0.05355287715792656,
-0.006819803733378649,
-0.03492630273103714,
0.05081983283162117,
-0.020071256905794144,
-0.01851624995470047,
0.06287231296300888,
-0.011755417101085186,
-0.009276599623262882,
0.04212360829114914,
-0.03443339094519615,
0.05753166228532791,
-0.001787660177797079,
0.04234679415822029,
0.012226821854710579,
0.026382040232419968,
0.006457904819399118,
0.016568951308727264,
0.018658358603715897,
-0.007601255550980568,
-0.02890796586871147,
-0.028898442164063454,
0.026638586074113846,
0.0023518053349107504,
0.032551102340221405,
0.04789948835968971,
0.003419950371608138,
-0.018498437479138374,
-0.008018815889954567,
-0.04768020659685135,
0.01983977109193802,
-0.043132271617650986,
0.020329874008893967,
0.012439305894076824,
0.019596099853515625,
0.031415097415447235,
0.046434804797172546,
0.02902180328965187,
-0.0313631035387516,
-0.048979148268699646,
-0.020379189401865005,
0.044825732707977295,
0.02567032352089882,
0.006876186467707157,
0.028336817398667336,
0.0708453357219696,
0.02060490846633911,
-0.012026355601847172,
0.024540109559893608,
-0.0363924577832222,
0.0039845677092671394,
-0.013142481446266174,
0.005362781696021557,
0.02372847869992256,
-0.043201327323913574,
-0.005170656833797693,
0.0052881487645208836,
0.04223800450563431,
-0.02289632521569729,
0.01397036761045456,
-0.014966522343456745,
0.045231062918901443,
0.04962011054158211,
-0.030181368812918663,
0.012354670092463493,
0.025065787136554718,
-0.02173737995326519,
0.01326399389654398,
0.030416330322623253,
-0.03303475305438042,
-0.06027056276798248,
-0.010042382404208183,
0.016082027927041054,
0.03577544540166855,
-0.04149545356631279,
0.03772454336285591,
-0.010809983126819134,
0.04006095975637436,
0.0416746661067009,
0.019613167271018028,
-0.05230368673801422,
-0.00041758842417038977,
-0.008460926823318005,
0.005813094321638346,
0.009748564101755619,
0.04547933489084244,
0.023673204705119133,
0.020253462716937065,
-0.009217683225870132,
-0.01667545735836029,
-0.019297100603580475,
0.0583970881998539,
-0.05204683914780617,
0.0011642741737887263,
0.0015741452807560563,
-0.0259627066552639,
-0.010479668155312538,
-0.004704645834863186,
-0.021436376497149467,
0.011572787538170815,
0.010006411001086235,
-0.00788430031388998,
-0.03151227533817291,
-0.02699130028486252,
-0.005766010843217373,
0.05763297900557518,
0.002159303752705455,
0.011367752216756344,
0.016024939715862274,
-0.005934399086982012,
0.04627510905265808,
-0.027812521904706955,
0.03248104453086853,
-0.034607768058776855,
0.003291734494268894,
0.008927008137106895,
-0.00003641088551376015,
0.056340787559747696,
-0.049209173768758774,
-0.0651443675160408,
0.0005177883431315422,
-0.010216188617050648,
0.00957508571445942,
-0.014202075079083443,
-0.04279705882072449,
0.0013013751013204455,
-0.014228717423975468,
-0.02048955298960209,
0.02376476675271988,
-0.02803691290318966,
-0.00891112070530653,
-0.0018736132187768817,
-0.01349709928035736,
-0.06750448048114777,
0.006364653818309307,
0.0014217471471056342,
0.036439262330532074,
-0.01178532000631094,
-0.004667473025619984,
0.029873332008719444,
-0.01508986297994852,
-0.03283568099141121,
0.006264763418585062,
-0.030359890311956406,
-0.03253581002354622,
-0.005517361219972372,
0.03233848139643669,
0.008370514959096909,
-0.07263350486755371,
0.00524170370772481,
0.03989272192120552,
-0.04405967518687248,
0.03520522639155388,
-0.014459904283285141,
-0.012346583418548107,
0.029311563819646835,
-0.01641411893069744,
0.0386330783367157,
-0.029984934255480766,
-0.003595841582864523,
0.06321748346090317,
0.008904908783733845,
-0.03048214316368103,
-0.010791944339871407,
-0.0161435604095459,
-0.007397335022687912,
-0.035993076860904694,
0.05660503730177879,
0.027523593977093697,
-0.053833551704883575,
0.07105943560600281,
-0.004925507586449385,
-0.024206414818763733,
0.07694215327501297,
0.04944911226630211,
-0.006354361306875944,
0.0015677493065595627,
-0.0013786625349894166,
-0.020482590422034264,
0.04051396995782852,
0.033174119889736176,
-0.05361652746796608,
0.004592878744006157,
-0.005468121264129877,
0.010856308974325657,
0.013028351590037346,
-0.018677810207009315,
0.009333300404250622,
0.00752253457903862,
-0.012519938871264458,
-0.011454914696514606,
0.02051503397524357,
-0.022329946979880333,
0.006188603118062019,
-0.0011638879077509046,
-0.0002506321470718831,
0.03671900928020477,
-0.01242323312908411,
-0.01935807429254055,
0.007579597644507885,
0.04272504523396492,
-0.05194653570652008,
-0.029292328283190727,
-0.00464572012424469,
0.008292957209050655,
0.010904617607593536,
0.005491092801094055,
0.0014184319879859686,
0.050734855234622955,
0.03235092759132385,
0.0028698325622826815,
0.012712064199149609,
0.02232682891190052,
-0.0038763403426855803,
-0.049259040504693985,
0.023889577016234398,
-0.0015028608031570911,
0.048482172191143036,
-0.009019953198730946,
0.07401899993419647,
0.013059175573289394,
0.03081544302403927,
0.03334519639611244,
-0.03132776543498039,
-0.06890066713094711,
-0.0017492107581347227,
-0.024188194423913956,
0.0031363843008875847,
-0.024502983316779137,
-0.027293473482131958,
0.005986928008496761,
-0.028550175949931145,
-0.05259076505899429,
-0.035086747258901596,
-0.016832878813147545,
-0.042950041592121124,
-0.00031019552261568606,
-0.012431257404386997,
-0.003383287461474538,
-0.01823863759636879,
0.04773487523198128,
0.019525257870554924,
-0.002401394536718726,
0.03162430226802826,
0.029149606823921204,
-0.05442894995212555,
0.020262639969587326,
0.016804838553071022,
-0.016319582238793373,
0.011809763498604298,
0.046227846294641495,
0.03261271491646767,
0.03347768634557724,
0.021906783804297447,
-0.005424294620752335,
0.0007864522049203515,
0.05519482493400574,
-0.01880619116127491,
-0.019201748073101044,
-0.018732432276010513,
-0.026093820109963417,
-0.0023671446833759546,
-0.017780909314751625,
0.04644296318292618,
0.0008646923815831542,
0.01586417853832245,
0.026585659012198448,
0.00257860217243433,
-0.06102917343378067,
0.011779013089835644,
0.02230338752269745,
-0.02043377421796322,
-0.0038836372550576925,
-0.04566020891070366,
-0.026742178946733475,
-0.014630823396146297,
-0.01513820979744196,
0.051399074494838715,
0.011227894574403763,
-0.026607118546962738,
0.014551239088177681,
0.030118277296423912,
-0.028163760900497437,
-0.04260442405939102,
0.013934768736362457,
-0.0021768829319626093,
-0.014546869322657585,
-0.019687030464410782,
0.015267140232026577,
0.0002659390156622976,
0.05570172145962715,
0.02910871058702469,
0.019358688965439796,
-0.0515502505004406,
-0.07695890218019485,
-0.013027767650783062,
0.012242636643350124,
0.005000901874154806,
-0.007400018163025379,
-0.0010872813872992992,
-0.07196144759654999,
-0.02808506228029728,
0.02450624480843544,
-0.04316947981715202,
0.018021235242486,
-0.01622075028717518,
-0.0008182957535609603,
-0.027745306491851807,
0.020156409591436386,
0.005626116879284382,
-0.0004559980006888509,
-0.01001735869795084,
0.026238253340125084,
-0.011003251187503338,
-0.0004072108131367713,
-0.015583418309688568,
0.030338099226355553,
0.02654138021171093,
0.05652458593249321,
0.011389308609068394,
0.023976054042577744,
-0.008812512271106243,
0.037413500249385834,
-0.03693949431180954,
-0.06502258032560349,
0.011779463849961758,
0.029142359271645546,
-0.024846507236361504,
0.07179157435894012,
-0.03251938149333,
-0.029932789504528046,
-0.0018655925523489714,
0.018764277920126915,
0.001002524746581912,
0.002369624562561512,
-0.028897523880004883,
-0.009405558928847313,
-0.003129786578938365,
0.005871424451470375,
0.04870516061782837,
0.01374689768999815,
-0.03304612264037132,
0.010682342574000359,
-0.008571812883019447,
0.06646287441253662,
-0.002442101715132594,
-0.008184053003787994,
-0.0015655194874852896,
0.007541618309915066,
-0.045499518513679504,
0.054235298186540604,
0.0007513858727179468,
0.0007075523608364165,
0.004694650880992413,
-0.033620256930589676,
-0.011187789961695671,
0.02220921963453293,
0.008384644985198975,
0.010530736297369003,
0.015540115535259247,
-0.01019937265664339,
0.027082031592726707,
-0.018595367670059204,
-0.00022116283071227372,
0.014002511277794838,
0.010599992237985134,
0.012489965185523033,
0.004792237188667059,
0.017527472227811813,
-0.051158323884010315,
0.02176179178059101,
0.0006339302053675056,
-0.028185084462165833,
0.07342793047428131,
0.003486521542072296,
0.05810830742120743,
-0.0018574759596958756,
-0.08075429499149323,
-0.010269376449286938,
-0.04085611552000046,
-0.0521727129817009,
0.043462060391902924,
-0.0321471244096756,
0.058947306126356125,
-0.00834500603377819,
0.012946099042892456,
-0.0332941897213459,
-0.03093971684575081,
0.018429763615131378,
0.04452313482761383,
-0.0019906198140233755,
-0.0376601442694664,
0.019082317128777504,
-0.023028725758194923,
-0.03352252021431923,
-0.03370819240808487,
0.04507773742079735,
-0.012982570566236973,
0.0036456480156630278,
0.03018716536462307,
-0.01847328059375286,
0.03716999664902687,
0.007171548902988434,
-0.05110035836696625,
-0.009182436391711235,
-0.0032400693744421005,
-0.008865462616086006,
0.0066385772079229355,
0.0004630554176401347,
-0.017076166346669197,
-0.05681350827217102,
-0.019032416865229607,
0.012856366112828255,
0.019242731854319572,
-0.03815389424562454,
0.04147133231163025,
0.012261815369129181,
0.062222570180892944,
-0.02371862344443798,
-0.07112453877925873,
0.013333005830645561,
-0.02621099352836609,
0.01779540628194809,
-0.026429029181599617,
-0.0163071658462286,
-0.01943325437605381,
-0.03133678063750267,
0.025403112173080444,
0.02610628306865692,
0.020376713946461678,
-0.023404138162732124,
0.027324970811605453,
-0.007575330790132284,
0.0210733562707901,
0.01744226925075054,
-0.04233168438076973,
0.007635314948856831,
-0.038467492908239365,
0.01895121857523918,
0.044569212943315506,
0.03175244480371475,
-0.010798200964927673,
-0.02480340003967285,
-0.01616061106324196,
0.018185073509812355,
0.06904730945825577,
-0.043742790818214417,
0.06987979263067245,
0.03109813667833805,
-0.01450334396213293,
-0.004602558445185423,
-0.023519303649663925,
-0.009861642494797707,
0.01690378040075302,
-0.020489206537604332,
0.02531989850103855,
-0.003377723041921854,
0.02033526822924614,
-0.005478112027049065,
0.04804565757513046,
-0.004955066367983818,
0.018309777602553368,
0.024082597345113754,
0.019407758489251137,
-0.005788189359009266,
-0.027434518560767174,
-0.05485980212688446,
0.0684918686747551,
-0.03566470369696617,
0.03598478063941002,
0.017612287774682045,
-0.020843055099248886,
0.03968217968940735,
-0.01617525704205036,
0.004842666909098625,
-0.03483881801366806,
-0.05148522928357124,
-0.04623209685087204,
0.011462179943919182,
0.0006287673022598028,
0.03573131561279297,
-0.028446152806282043,
-0.017525548115372658,
0.023104621097445488,
-0.021465223282575607,
-0.0005541486898437142,
-0.004126720130443573,
-0.09794247895479202,
-0.046373091638088226,
-0.018920648843050003,
-0.031512826681137085,
0.03965931758284569,
0.007452101446688175,
-0.02198890782892704,
0.006903897039592266,
-0.03476284444332123,
0.009998205117881298,
0.003687133314087987,
0.04041556268930435,
-0.022833749651908875,
0.017691010609269142,
0.013112557120621204,
0.050762563943862915,
0.006610555574297905,
0.028625600039958954,
0.07854865491390228,
0.05931764096021652,
0.013110527768731117,
-0.0804448053240776,
0.03195735812187195,
-0.06254768371582031,
0.004085984546691179,
-0.047739654779434204,
0.06203367933630943,
-0.018236566334962845,
0.05340323597192764,
-0.015466989018023014,
0.04596118628978729,
0.019893674179911613,
-0.00627024145796895,
0.04180711507797241,
-0.014313302002847195,
-0.05128052085638046,
0.008865483105182648,
-0.024746540933847427,
-0.030153494328260422,
0.04217937961220741,
-0.06362617015838623,
0.0019758748821914196,
-0.021595045924186707,
-0.03407631441950798,
-0.016823986545205116,
-0.07443490624427795,
0.049369409680366516,
0.006265321746468544,
-0.01866639405488968,
-0.007354205008596182,
-0.014103265479207039,
-0.017974112182855606,
-0.035143136978149414,
0.026890680193901062,
-0.007861334830522537,
-0.03539744019508362,
0.005242654588073492,
0.017822835594415665,
0.006442107260227203,
-0.008236488327383995,
-0.0251949243247509,
0.012985612265765667,
-0.03251436725258827,
-0.010696916840970516,
-0.01112120971083641,
0.020690638571977615,
-0.04865119233727455,
-0.0025051042903214693,
-0.03398291766643524,
0.016494380310177803,
0.01655583456158638,
-0.04332748055458069,
-0.021467991173267365,
0.031017852947115898,
0.04012106731534004,
-0.013847927562892437,
-0.043267253786325455,
-0.017549611628055573,
0.010230076499283314,
-0.03245280310511589,
0.019622741267085075,
-0.00889347493648529,
0.022906584665179253,
0.018024949356913567,
-0.013266793452203274,
0.026001790538430214,
-0.0031516971066594124,
-0.007809571456164122,
-0.07549125701189041,
0.03178789094090462,
-0.009883644990622997,
-0.0067006186582148075,
-0.0027572796680033207,
0.031273145228624344,
-0.019221337512135506,
0.01687070168554783,
-0.03546016290783882,
0.0033120668958872557,
-0.03958695009350777,
0.0048975273966789246,
-0.01952732540667057,
-0.015154415741562843,
-0.010656331665813923,
0.007068634033203125,
0.08519377559423447,
0.0397241935133934,
0.015944398939609528,
0.02459682710468769,
-0.0329907163977623,
-0.017396308481693268,
0.04035945609211922,
-0.02393357828259468,
-0.007433883845806122,
0.009636265225708485,
-0.03663220629096031,
-0.03023267537355423,
-0.026658402755856514,
0.02478647045791149,
0.012463757768273354,
0.02772943116724491,
0.04594535753130913,
-0.0067258961498737335,
-0.03283151984214783,
-0.005166376009583473,
0.016520678997039795,
-0.011909381486475468,
0.03691953048110008,
0.007665691431611776,
0.012880501337349415,
-0.0011676778085529804,
-0.030124474316835403,
0.019634293392300606,
-0.000544699898455292,
-0.004629035945981741,
0.015058419667184353,
0.007803639862686396,
-0.013619461096823215,
-0.004896706901490688,
0.029685119166970253,
-0.016705799847841263,
-0.026509886607527733,
-0.036520589143037796,
0.038680266588926315,
-0.01500797551125288,
0.020473940297961235,
-0.014471597969532013,
-0.0040291487239301205,
-0.0009631900466047227,
-0.004207916092127562,
0.02260173298418522,
-0.02372685819864273,
0.002494166372343898,
0.02813376858830452,
0.038718242198228836,
0.012956767342984676,
0.03332551568746567,
0.01742042973637581,
-0.04520680010318756,
0.03906942531466484,
-0.013883243314921856,
-0.032480206340551376,
0.018496165052056313,
-0.004568302072584629,
0.03749464824795723,
0.05734538286924362,
-0.007684631273150444,
-0.0018765827408060431,
0.02687714621424675,
0.014349382370710373,
-0.010615166276693344,
-0.0130882877856493,
-0.018729260191321373,
0.01976904831826687,
0.015724562108516693,
0.02272977866232395,
-0.04827698692679405,
-0.04167278856039047,
0.05079661309719086,
0.008133036084473133,
0.02600405365228653,
0.010235247202217579,
0.0060182008892297745,
-0.004527431912720203,
0.02987552620470524,
0.021011214703321457,
-0.012810653075575829,
0.034046851098537445,
0.034024886786937714,
-0.004600290674716234,
0.041401457041502,
0.025074981153011322,
-0.011677470058202744,
-0.09348133951425552,
-0.005908373277634382,
0.013186225667595863,
-0.012188560329377651,
0.04016720876097679,
-0.042748820036649704,
-0.0008471502223983407,
0.03999628126621246,
-0.06371262669563293,
0.021387191489338875,
0.007434167433530092,
-0.025005217641592026,
-0.020664576441049576,
0.03348469361662865,
0.013113652355968952,
0.04002775996923447,
0.01961914449930191,
0.04153471440076828,
-0.00983845442533493,
0.016202980652451515,
-0.014149702154099941,
0.025452274829149246,
0.015730617567896843,
0.009885935112833977,
0.0010235037188977003,
0.0038101200480014086,
0.05469953641295433,
-0.02001969888806343,
-0.040366705507040024,
0.03179578483104706,
-0.0031406625639647245,
0.018242618069052696,
0.014126801863312721,
-0.02322561666369438,
-0.017820803448557854,
0.004167834762483835,
0.015677647665143013,
0.019739700481295586,
-0.02266613580286503,
0.0320054329931736,
0.02436739392578602,
0.017153896391391754,
0.006840283051133156,
-0.004722933284938335,
0.0179206021130085,
-0.04924986883997917,
0.00808236189186573,
0.03898748382925987,
0.00012858542322646827,
0.0036287016700953245,
0.016176294535398483,
-0.007683996576815844,
0.03140958771109581,
-0.030456773936748505,
0.012644853442907333,
-0.05454137921333313,
0.00022937325411476195,
-0.01873132400214672,
0.0016698368126526475,
-0.02326219156384468,
-0.003154039615765214,
-0.020833509042859077,
-0.021427685394883156,
0.0173161830753088,
-0.033402856439352036,
-0.01187452208250761,
-0.048226937651634216,
-0.0060363286174833775,
0.06093331053853035,
0.007665205281227827,
0.02058061957359314,
0.002334842225536704,
-0.016771109774708748,
0.02599591575562954,
-0.014269779436290264,
0.03387768939137459,
0.01751026138663292,
-0.04455681890249252,
-0.04402625933289528,
-0.04879925400018692,
0.051941968500614166,
0.00979703664779663,
-0.043677885085344315,
-0.10083679109811783,
-0.017148708924651146,
-0.010455753654241562,
0.07447346299886703,
0.0390523262321949,
-0.02998899109661579,
0.01136438362300396,
-0.006560074165463448,
0.03344603627920151,
0.04932844638824463,
-0.029979947954416275,
-0.030947914347052574,
0.0332205593585968,
-0.04231138154864311,
-0.046059902757406235,
-0.01849306933581829,
-0.05913008004426956,
0.024884283542633057,
0.02591712772846222,
-0.02363869734108448,
0.04806193336844444,
-0.009908509440720081,
-0.01738562621176243,
0.025251736864447594,
0.009548606351017952,
-0.030980950221419334,
0.06668844074010849,
-0.02107561007142067,
-0.017049597576260567,
0.010363483801484108,
-0.023542495444417,
-0.00759509252384305,
-0.004014247562736273,
-0.03732577711343765,
0.009227603673934937,
-0.010193178430199623,
-0.053724512457847595,
0.05143777281045914,
-0.06272934377193451,
0.016843656077980995,
0.03118855133652687,
-0.03179411590099335,
0.015871800482273102,
0.07841725647449493,
0.0020286040380597115,
0.0006179484189487994,
-0.03264669328927994,
-0.0016717750113457441,
-0.015648573637008667,
-0.01818843185901642,
-0.013259319588541985,
0.04906725138425827,
0.014675144106149673,
-0.0032425031531602144,
0.0265600997954607,
0.01779169775545597,
0.024670662358403206,
0.008159877732396126,
-0.0037962058559060097,
0.0454629622399807,
-0.02191055379807949,
-0.0177883580327034,
-0.0005668028607033193,
0.0006773407803848386,
0.01437707431614399,
0.022153984755277634,
-0.035536810755729675,
0.09845777601003647,
-0.03965882211923599,
0.003216736251488328,
-0.013520854525268078,
0.031847480684518814,
-0.02223697304725647,
-0.012672455981373787,
0.013555112294852734,
0.07310116291046143,
-0.0149224316701293,
0.006298135966062546,
-0.015973413363099098,
0.012392341159284115,
0.03948192298412323,
-0.014245991595089436,
0.04298769310116768,
0.0010932967998087406,
-0.03539247810840607,
-0.01105031743645668,
-0.01969161629676819,
-0.0447942391037941,
-0.01171740610152483,
0.007397610228508711,
0.009119278751313686,
-0.0018894107779487967,
0.033207155764102936,
-0.00952504388988018,
-0.06484355032444,
0.02118048630654812,
-0.0848858505487442,
-0.0010046646930277348,
-0.014581818133592606,
0.019954722374677658,
-0.014094294980168343,
0.022265205159783363
] |
<p>How would a society go about either preventing our sun in its primary sequence from going into a Red Giant a billion years from now? Or perhaps, accelerating the process of going from main sequence of our start to a red giant prematurely. </p>
<p>What catalysts would have to happen, implemented by humans, so no natural phenomenon could play a part in it, that would have an impact, even slight, on the future processes of the sun's lifecycle. </p>
<p>Any thoughts or help would be great!!!!</p>
| 8,434 |
[
-0.024819284677505493,
-0.05863653123378754,
-0.013993730768561363,
0.0014692256227135658,
0.05136830732226372,
0.004434195812791586,
-0.012695737183094025,
-0.03814408928155899,
0.004112451337277889,
-0.03160560503602028,
0.026626817882061005,
0.028145283460617065,
-0.00883039366453886,
0.039362333714962006,
0.03400154039263725,
-0.0173658337444067,
0.015017332509160042,
-0.016380250453948975,
-0.01352535281330347,
0.004504106938838959,
0.009446577169001102,
-0.03015545941889286,
0.007537458557635546,
0.03966040909290314,
-0.02997983805835247,
0.03956184536218643,
0.04089314490556717,
0.011706031858921051,
-0.018968934193253517,
0.044198427349328995,
-0.0058381687849760056,
-0.02953440137207508,
0.008871220052242279,
0.017756596207618713,
0.025866635143756866,
0.014318638481199741,
-0.01882869563996792,
-0.032973513007164,
-0.023602116852998734,
0.01275403518229723,
-0.05151323229074478,
-0.00003418681808398105,
0.002778018591925502,
0.028591705486178398,
0.020190661773085594,
0.02623947709798813,
-0.025422999635338783,
-0.01409677043557167,
0.05729087069630623,
-0.051723118871450424,
0.02723187580704689,
-0.009395038709044456,
0.004576710052788258,
0.006030041258782148,
-0.016667606309056282,
-0.030889330431818962,
0.060977134853601456,
0.07724438607692719,
0.03239772841334343,
-0.010861098766326904,
-0.0074483794160187244,
0.014603212475776672,
-0.024711262434720993,
-0.03313321992754936,
-0.0714031532406807,
0.03768143057823181,
-0.04463193565607071,
-0.011142382398247719,
0.05758973956108093,
0.0175512433052063,
0.018087049946188927,
-0.03140780329704285,
-0.015431315638124943,
0.013925015926361084,
0.011116697452962399,
-0.033323969691991806,
-0.005987491924315691,
-0.01142827607691288,
0.028754444792866707,
0.042124755680561066,
-0.009706571698188782,
-0.01783616654574871,
0.02833607792854309,
0.06560834497213364,
-0.008405143395066261,
0.027369791641831398,
0.06434851139783859,
-0.012496856972575188,
0.02273605205118656,
0.011736391112208366,
-0.007073783781379461,
-0.01795116998255253,
0.061401624232530594,
-0.02650299482047558,
-0.03567497804760933,
0.029598407447338104,
-0.010121354833245277,
0.022954406216740608,
0.0043255919590592384,
0.0127521101385355,
0.0336957611143589,
0.020726243034005165,
0.021187497302889824,
0.029698312282562256,
0.010911615565419197,
-0.05005618557333946,
-0.049971241503953934,
-0.02883663773536682,
0.008424317464232445,
-0.042958732694387436,
-0.03512600064277649,
-0.03751172125339508,
-0.0016930882120504975,
-0.015862422063946724,
-0.012441374361515045,
-0.04212772473692894,
0.017716873437166214,
-0.017010806128382683,
0.04260805994272232,
0.03872925415635109,
0.034701909869909286,
0.005607664119452238,
0.028558962047100067,
-0.00846688449382782,
-0.015882473438978195,
0.011028937064111233,
0.014460906386375427,
0.003690972225740552,
-0.0023658229038119316,
-0.01913697086274624,
0.0005322403740137815,
-0.03598292917013168,
-0.010188734158873558,
-0.03285863250494003,
0.06311933696269989,
0.007317882962524891,
-0.10798023641109467,
-0.042019519954919815,
0.05117258056998253,
-0.001704067108221352,
-0.00151225330773741,
-0.056480564177036285,
0.01992570050060749,
-0.0025218138471245766,
0.08016376197338104,
-0.012437940575182438,
-0.04364541172981262,
0.02023693546652794,
0.057506244629621506,
0.010854963213205338,
-0.01724950224161148,
0.010332532227039337,
0.002912712749093771,
-0.0017426934791728854,
-0.032399971038103104,
-0.07249423116445541,
0.009987592697143555,
-0.002630488481372595,
0.013896552845835686,
-0.03143998980522156,
0.05841827765107155,
-0.020976489409804344,
-0.011337632313370705,
0.01508686039596796,
0.0055333287455141544,
-0.021523071452975273,
0.08108066767454147,
0.04320528358221054,
-0.013093051500618458,
0.005241087172180414,
0.029927890747785568,
0.03602233901619911,
0.061223890632390976,
0.045010942965745926,
0.03722075745463371,
-0.047601621598005295,
-0.024734731763601303,
-0.003324502846226096,
-0.02025839500129223,
-0.04108254238963127,
-0.027419552206993103,
-0.03061485104262829,
0.007162270601838827,
-0.010142131708562374,
0.04938947409391403,
0.02265855297446251,
-0.03632121533155441,
0.010853344574570656,
0.025298185646533966,
-0.047459617257118225,
-0.0020548913162201643,
-0.052937425673007965,
-0.018550928682088852,
0.01841447316110134,
-0.00700382562354207,
-0.013471081852912903,
-0.020450888201594353,
0.030254101380705833,
-0.011310522444546223,
-0.05073142051696777,
0.0011796883773058653,
0.03409218415617943,
0.07143179327249527,
0.007930738851428032,
0.018677018582820892,
0.05706186965107918,
0.051239773631095886,
-0.035990551114082336,
0.005382533650845289,
-0.018936190754175186,
-0.04107140749692917,
0.016326649114489555,
-0.015345475636422634,
0.04746542125940323,
-0.045581236481666565,
0.04203896224498749,
0.018201809376478195,
-0.02012450620532036,
0.013412212021648884,
-0.013254838064312935,
-0.0333399623632431,
0.10000735521316528,
0.011107082478702068,
0.006138247437775135,
0.007078946102410555,
0.024540076032280922,
-0.01141616515815258,
-0.02461363933980465,
-0.03211798891425133,
-0.03257036954164505,
-0.04376756772398949,
0.002726515056565404,
0.031149836257100105,
0.02355700545012951,
-0.04693174734711647,
0.034612659364938736,
0.02661331743001938,
0.05091380700469017,
0.03066633641719818,
0.020495478063821793,
-0.02566378191113472,
-0.005091486498713493,
0.025867609307169914,
-0.002549950499087572,
-0.021285487338900566,
0.02688029780983925,
0.018934007734060287,
0.011488871648907661,
0.014434823766350746,
0.0034850710071623325,
0.0056955269537866116,
0.03241805359721184,
0.01722518727183342,
0.003205534303560853,
0.0038914349861443043,
-0.028737077489495277,
0.05150865390896797,
-0.03834154084324837,
-0.00579373212531209,
0.019533829763531685,
0.012429370544850826,
0.006577747408300638,
-0.03570510819554329,
0.00047952443128451705,
-0.04604027047753334,
0.012834100984036922,
-0.010057850740849972,
-0.0013886202359572053,
0.016826264560222626,
-0.027096424251794815,
0.01599830947816372,
-0.0012453320669010282,
-0.01541543286293745,
-0.0573759526014328,
-0.012496726587414742,
0.027612868696451187,
0.004476559814065695,
-0.014156712219119072,
-0.0005081099225208163,
-0.030609790235757828,
0.00601712241768837,
-0.025043653324246407,
0.010638548992574215,
0.007077643182128668,
-0.025395352393388748,
0.0029682472813874483,
0.03649980202317238,
-0.059707798063755035,
0.07777313143014908,
0.010724728927016258,
-0.011646842584013939,
0.047023363411426544,
0.006848671939224005,
-0.060897842049598694,
-0.007582372520118952,
-0.011994956992566586,
-0.014924561604857445,
0.00836322084069252,
-0.01641027443110943,
0.046645790338516235,
-0.014370358549058437,
-0.025787610560655594,
-0.012687700800597668,
-0.06508634984493256,
-0.03188199922442436,
-0.031805619597435,
-0.0011214398546144366,
-0.005185297690331936,
-0.02605283632874489,
0.06067195162177086,
0.016525128856301308,
-0.020345641300082207,
0.02515896037220955,
-0.02892344631254673,
-0.031074387952685356,
-0.007702122442424297,
0.011313318274915218,
0.041387032717466354,
-0.025753231719136238,
-0.009317679330706596,
0.026786725968122482,
0.05259013921022415,
-0.013438687659800053,
-0.039122965186834335,
-0.034303780645132065,
-0.04872652515769005,
-0.04457900673151016,
0.03304436802864075,
0.022251246497035027,
-0.03439825400710106,
-0.0021315801423043013,
0.019828522577881813,
-0.0022253498900681734,
0.035417694598436356,
-0.023384694010019302,
-0.008822889067232609,
0.022320374846458435,
-0.01805519498884678,
0.048002369701862335,
0.01377760898321867,
-0.007362702861428261,
-0.015860671177506447,
0.02520773373544216,
-0.023302314803004265,
0.03380073606967926,
0.004986186046153307,
-0.04967165365815163,
0.01487323734909296,
-0.017906436696648598,
0.009300154633820057,
-0.036409854888916016,
0.005750221200287342,
0.029247306287288666,
-0.002950676018372178,
0.010916651226580143,
-0.00471809646114707,
0.03598354011774063,
0.014098274521529675,
0.02029137685894966,
0.00203914288431406,
0.04674361273646355,
0.007668614387512207,
0.010582191869616508,
0.017718760296702385,
-0.001455466146580875,
0.00582414073869586,
-0.032279301434755325,
0.02588307112455368,
0.04135320335626602,
0.02568165585398674,
0.03912454470992088,
-0.021809831261634827,
-0.019685201346874237,
-0.026906199753284454,
-0.06843897700309753,
0.009403527714312077,
-0.026812264695763588,
0.028130309656262398,
-0.016108287498354912,
0.01974344626069069,
0.020898882299661636,
0.003526455955579877,
0.011162484996020794,
0.020548436790704727,
-0.08493083715438843,
0.019893961027264595,
-0.040973905473947525,
0.005244727246463299,
0.020261848345398903,
0.03455498814582825,
-0.03739147633314133,
-0.014081134460866451,
-0.034740149974823,
-0.04431626573204994,
0.024924343451857567,
0.0061573004350066185,
0.022290118038654327,
-0.04662759229540825,
-0.046698570251464844,
0.0023666962515562773,
-0.0012054609833285213,
0.05252855643630028,
-0.006971024442464113,
0.03544792905449867,
0.014671921730041504,
-0.03769613429903984,
0.009172950871288776,
-0.04021178558468819,
0.007378390058875084,
-0.0032538685481995344,
0.018385175615549088,
0.05544230714440346,
-0.00044238739064894617,
-0.04333563521504402,
-0.029756855219602585,
0.008811388164758682,
-0.02823028713464737,
0.03889231011271477,
0.02886209264397621,
-0.0037465288769453764,
-0.043817903846502304,
-0.0213666670024395,
0.01437598280608654,
0.026365602388978004,
-0.026930024847388268,
0.04225434735417366,
0.024729527533054352,
-0.025380698963999748,
-0.006007537245750427,
0.04189658537507057,
0.07994158565998077,
0.010902746580541134,
-0.04658073931932449,
-0.038922134786844254,
-0.04548971727490425,
-0.009715952910482883,
0.005761492531746626,
0.014761931262910366,
0.034915242344141006,
-0.033671002835035324,
-0.00935217086225748,
0.004867054987698793,
0.02518550679087639,
-0.02153930999338627,
0.007735843770205975,
-0.025965092703700066,
0.0730331689119339,
-0.0023473140317946672,
0.01923939399421215,
-0.0023223632015287876,
0.024762775748968124,
0.02816176228225231,
-0.035811420530080795,
0.03272407129406929,
-0.07309875637292862,
-0.0019825559575110674,
0.008060179650783539,
0.07837960869073868,
-0.051206182688474655,
-0.009864049032330513,
-0.09116961807012558,
-0.01809825748205185,
0.05318816006183624,
-0.028502918779850006,
0.024755116552114487,
-0.013094693422317505,
-0.029049944132566452,
0.024822521954774857,
-0.01567796804010868,
0.0013998362701386213,
0.017390506342053413,
-0.0065696570090949535,
0.035645466297864914,
0.013499172404408455,
0.012960688211023808,
-0.046394433826208115,
0.012903708033263683,
0.03265998139977455,
0.014749654568731785,
-0.0312654972076416,
-0.002484822180122137,
0.00867992453277111,
0.0289473794400692,
0.003258310491219163,
-0.06293876469135284,
0.011803507804870605,
0.014829212799668312,
-0.03258896619081497,
0.04903741180896759,
-0.03556368872523308,
-0.04741537570953369,
0.018797602504491806,
0.030404405668377876,
-0.06781228631734848,
-0.025970332324504852,
-0.045409783720970154,
0.011524559929966927,
0.039313409477472305,
-0.004967416170984507,
0.03837038204073906,
0.05509452894330025,
-0.05421708896756172,
0.01952945627272129,
-0.016445260494947433,
-0.01614183373749256,
-0.0229482538998127,
0.002966875210404396,
0.013880809769034386,
0.0069418614730238914,
0.0177677683532238,
0.032084669917821884,
0.010342434048652649,
-0.022702055051922798,
0.041720736771821976,
-0.041012249886989594,
0.0007324964390136302,
0.03326578810811043,
-0.027827173471450806,
-0.022833630442619324,
-0.042015425860881805,
0.05217424035072327,
-0.010965040884912014,
0.005827030632644892,
0.03656310215592384,
-0.02820081263780594,
0.013304146006703377,
-0.009434801526367664,
-0.01547233760356903,
-0.010170025750994682,
-0.022447362542152405,
-0.04264448583126068,
-0.010060162283480167,
-0.046737831085920334,
0.0812155157327652,
-0.01917806640267372,
0.05343829095363617,
0.015743089839816093,
-0.04345540702342987,
-0.014023939147591591,
-0.008569014258682728,
-0.03763803467154503,
0.0425521619617939,
0.009331410750746727,
0.0244995579123497,
-0.031546395272016525,
-0.01197029184550047,
-0.07521592825651169,
0.007834536023437977,
0.022696807980537415,
0.01409832015633583,
-0.034941669553518295,
-0.013035816140472889,
-0.005287982989102602,
-0.029602793976664543,
-0.009868552908301353,
0.015290183015167713,
0.0440048985183239,
-0.034547340124845505,
-0.003569437190890312,
-0.0006454740650951862,
0.01250640768557787,
0.05649518966674805,
-0.02153855375945568,
0.017067926004529,
0.02339821122586727,
-0.05015430599451065,
-0.01063612475991249,
-0.043891165405511856,
0.02775292657315731,
-0.015575939789414406,
-0.04454544559121132,
-0.033625464886426926,
0.02532384544610977,
0.014174067415297031,
-0.014852981083095074,
0.008181197568774223,
0.06000131368637085,
0.014338457025587559,
-0.0022243473213166,
-0.02553531900048256,
0.0713476836681366,
-0.013419699855148792,
0.04936949908733368,
0.030414476990699768,
0.024425843730568886,
0.020660260692238808,
-0.050598498433828354,
0.04900316521525383,
-0.025992777198553085,
0.013778984546661377,
0.016700662672519684,
0.01435134932398796,
-0.010084431618452072,
-0.00996751245111227,
0.0389472097158432,
-0.04039029777050018,
0.03238236531615257,
-0.005796808749437332,
0.017783652991056442,
-0.010692142881453037,
-0.0285080224275589,
-0.0363444909453392,
-0.054958317428827286,
0.002840285887941718,
-0.0214187353849411,
0.05356909707188606,
-0.05397302657365799,
0.04222334921360016,
-0.034439750015735626,
0.023622261360287666,
-0.010978341102600098,
-0.025234835222363472,
0.003451813943684101,
0.005750247277319431,
-0.007994619198143482,
-0.0016198199009522796,
-0.006908347364515066,
0.019383776932954788,
0.030588803812861443,
0.01639324612915516,
0.016073431819677353,
0.07196975499391556,
0.08403652906417847,
0.011834357865154743,
0.06590823829174042,
-0.0601980946958065,
-0.004281868226826191,
0.015716131776571274,
-0.036868397146463394,
0.01129809021949768,
0.010003888048231602,
0.021992908790707588,
0.048296354711055756,
-0.012205285020172596,
-0.0001224083680426702,
-0.02793106622993946,
-0.02138485386967659,
-0.014007697813212872,
0.0005397499189712107,
0.022324901074171066,
-0.0010121442610397935,
0.05306177958846092,
0.00648128055036068,
-0.011012592352926731,
0.002556117717176676,
0.030585257336497307,
-0.04523897543549538,
-0.04328278452157974,
-0.052612002938985825,
-0.036007653921842575,
-0.053983718156814575,
0.08609533309936523,
0.03361283242702484,
-0.04691969230771065,
-0.020009871572256088,
0.005165828857570887,
-0.0157516747713089,
0.005805817432701588,
0.04647854343056679,
-0.00023371601128019392,
0.05141308531165123,
0.004216375760734081,
0.030150478705763817,
0.006948358844965696,
0.02247140184044838,
0.11089387536048889,
0.0499110221862793,
0.027440907433629036,
-0.048191480338573456,
0.03315882757306099,
0.00576356565579772,
0.017159942537546158,
-0.0014842282980680466,
0.013332963921129704,
0.005520515609532595,
-0.016660738736391068,
0.0172931719571352,
0.009376546368002892,
0.01980009488761425,
0.013274582102894783,
0.03515541926026344,
-0.047835081815719604,
-0.02068861946463585,
0.0009861906291916966,
-0.002064409898594022,
0.0010603645350784063,
0.04626067355275154,
-0.03328923135995865,
0.0183054581284523,
-0.00015284788969438523,
-0.006600027903914452,
-0.01944163255393505,
-0.02866899035871029,
0.022594742476940155,
-0.010267667472362518,
-0.051341764628887177,
0.004098140634596348,
0.028217891231179237,
-0.015351209789514542,
-0.015500877983868122,
-0.0335763581097126,
0.01722317934036255,
-0.009727446362376213,
0.009637085720896721,
0.03040410205721855,
0.013315178453922272,
0.0678308755159378,
-0.022666113451123238,
0.030658036470413208,
-0.024662230163812637,
0.0025989683344960213,
-0.017238527536392212,
0.04069656506180763,
-0.00534092215821147,
0.011778376065194607,
0.001718175015412271,
0.03574727848172188,
-0.0010388013906776905,
-0.0056744227185845375,
-0.016460351645946503,
-0.015721354633569717,
0.03871598467230797,
-0.021602600812911987,
-0.03381168469786644,
0.012285725213587284,
0.050471141934394836,
0.00689855357632041,
0.044790711253881454,
-0.007680200506001711,
-0.006961902137845755,
-0.013465347699820995,
-0.056268878281116486,
0.019024470821022987,
-0.012332377955317497,
0.0073080225847661495,
-0.026328781619668007,
0.0409729965031147,
-0.029098864644765854,
0.011216308921575546,
0.019707633182406425,
0.04053880274295807,
0.007378228008747101,
-0.0014333532890304923,
0.009451099671423435,
-0.023502176627516747,
0.004138354677706957,
0.05246772617101669,
-0.00044814732973463833,
-0.0115357656031847,
-0.014270677231252193,
-0.038773681968450546,
0.0402371883392334,
0.020519740879535675,
-0.027270173653960228,
0.00019375799456611276,
-0.009211480617523193,
0.04171069711446762,
0.0216289721429348,
-0.004556562751531601,
-0.04302779585123062,
-0.001598929869942367,
-0.03365369886159897,
-0.011623752303421497,
-0.0022647869773209095,
0.07565530389547348,
0.019058814272284508,
-0.03581932187080383,
0.008314677514135838,
0.0017769037513062358,
-0.026743806898593903,
0.012124087661504745,
0.022662503644824028,
-0.021349605172872543,
-0.03662880137562752,
-0.0729532241821289,
0.0009113068808801472,
0.001553886104375124,
-0.018964603543281555,
-0.03987976163625717,
-0.023874687030911446,
-0.0021282790694385767,
-0.005173310171812773,
-0.041464902460575104,
0.07189896702766418,
-0.036522746086120605,
0.011344376020133495,
-0.03669387474656105,
-0.0018600900657474995,
-0.07823176681995392,
-0.017137208953499794,
0.005931835621595383,
-0.04130678251385689,
-0.004356551915407181,
0.0502740852534771,
-0.0027388855814933777,
-0.00861839484423399,
0.015437700785696507,
-0.014563442207872868,
0.013660719618201256,
-0.006024709437042475,
-0.01889442838728428,
-0.03167203813791275,
0.04963359236717224,
-0.02615329809486866,
-0.010430492460727692,
-0.013472524471580982,
-0.04313061758875847,
-0.07118634134531021,
0.010057579725980759,
-0.06257980316877365,
0.04370506852865219,
0.023720543831586838,
-0.02588736265897751,
0.007912207394838333,
0.04049832373857498,
-0.027664165943861008,
-0.036279331892728806,
0.03288494050502777,
0.05593135580420494,
-0.016923334449529648,
0.04966575652360916,
0.01809263974428177,
-0.03835785388946533,
-0.01781456544995308,
0.013495739549398422,
0.03546186536550522,
-0.04570981487631798,
-0.004253222607076168,
-0.034671247005462646,
-0.033258095383644104,
0.010593794286251068,
-0.027521373704075813,
-0.019576245918869972,
0.016706256195902824,
-0.0054704127833247185,
-0.024581367149949074,
0.029170431196689606,
0.02206745184957981,
-0.04947613552212715,
-0.07170897722244263,
0.008713001385331154,
-0.015407045371830463,
-0.014135926961898804,
0.04571116715669632,
-0.03933532163500786,
0.02169838175177574,
0.0210260096937418,
-0.0544024333357811,
0.06428048759698868,
-0.01532592810690403,
0.004782736301422119,
-0.037246350198984146,
-0.01872151903808117,
-0.043747276067733765,
0.05104289948940277,
-0.008234506472945213,
0.021328570321202278,
0.011648675426840782,
0.020124036818742752,
-0.0015923981554806232,
0.0019752494990825653,
-0.02210080251097679,
0.013254030607640743,
-0.0011212711688131094,
-0.008099386468529701,
0.06767198443412781,
-0.04887216165661812,
-0.0015651797875761986,
0.02111208066344261,
-0.005021484103053808,
0.08443690091371536,
-0.0015355537179857492,
0.002638044534251094,
0.015570715069770813,
0.021395782008767128,
0.0056912717409431934,
0.011293835937976837,
0.0032669513020664454,
0.013995202258229256,
0.0016347113996744156,
0.01570194959640503,
0.01158887054771185,
0.03156053274869919,
0.03870687261223793,
-0.0161785539239645,
0.0064391340129077435,
-0.009097428061068058,
-0.02767457254230976,
0.011890798807144165,
0.0035566731821745634,
0.011446830816566944,
0.027711128816008568,
0.003827192122116685,
-0.04402837157249451,
-0.024736398831009865,
0.010459743440151215,
-0.005054562818259001,
0.004251925274729729,
0.02380416728556156,
0.005344973411411047,
-0.020265720784664154,
-0.014049120247364044,
0.005099842790514231,
-0.03514885529875755,
-0.0028225018177181482,
-0.01034497283399105,
0.015611959621310234,
0.007126476150006056,
-0.008686602115631104,
-0.05394543707370758,
0.007020667195320129,
0.017393140122294426,
0.06983697414398193,
0.023210933431982994,
0.02479083091020584,
-0.018576476722955704,
-0.05393014848232269,
0.009841174818575382,
-0.02553618513047695,
0.013590428046882153,
-0.02132662758231163,
0.01747954823076725,
-0.015315777622163296,
-0.062350720167160034,
-0.016057712957262993,
-0.0031957682222127914,
0.06536811590194702,
-0.023793010041117668,
-0.022266777232289314,
0.0000883104803506285,
0.025676563382148743,
0.006754404865205288,
-0.07343394309282303,
0.03286179527640343,
0.017654210329055786,
-0.0046110074035823345,
-0.021043041720986366,
-0.008695088326931,
0.0033804643899202347,
-0.004458168055862188,
0.03489229455590248,
0.0404888391494751,
0.01576288416981697,
0.02948048524558544,
0.0040915473364293575,
0.0015317837242037058,
-0.023924749344587326,
0.017442747950553894,
0.03409070894122124,
-0.018002131953835487,
-0.022436320781707764,
0.044351086020469666,
-0.019809160381555557,
-0.034908659756183624,
0.028374454006552696,
-0.024672742933034897,
-0.015024032443761826,
-0.012173610739409924,
-0.04306816682219505,
0.011619696393609047,
-0.04555338993668556,
0.045456741005182266,
0.015267848037183285,
-0.025716645643115044,
0.018498169258236885,
0.04252288490533829,
0.004525397438555956,
0.018056971952319145,
-0.0025149027351289988,
-0.027808673679828644,
0.012070298194885254,
0.04209919646382332,
-0.053054481744766235,
0.03211553767323494,
0.03493398055434227,
0.0034159959759563208,
0.06466201692819595,
0.00610986165702343,
0.0057355179451406,
0.018805095925927162,
-0.012688661925494671,
0.024715689942240715,
-0.02786344103515148,
0.022150669246912003,
0.036891669034957886,
0.016982408240437508,
0.01753833331167698,
0.07905023545026779,
0.02304796315729618,
0.09294374287128448,
0.0024881837889552116,
0.005073326174169779,
0.014291604980826378,
-0.028924379497766495,
-0.05488372594118118,
0.0010563760297372937,
-0.007316924165934324,
-0.0016913370927795768,
-0.015430592000484467,
-0.013585902750492096,
-0.007479444146156311,
0.056687723845243454,
0.038366496562957764,
-0.023178651928901672,
0.04781084880232811,
0.02661001682281494,
-0.018449816852808,
0.004251028411090374,
-0.014669978991150856,
-0.03122982755303383,
-0.042228423058986664,
-0.013279294595122337,
0.058063529431819916,
0.007844610139727592,
0.02305649034678936,
0.010614916682243347,
-0.014116665348410606,
0.010489278472959995,
-0.06342210620641708,
-0.026851074770092964,
-0.04304836317896843,
0.0186732430011034,
-0.06179359182715416,
-0.022235099226236343
] |
<p>I googled the question and found no explanation. It seems that dog ears are inevitable (for paperbacks, notably) even if you've always been careful. From my experience, they are about equally likely to appear on the top corners as on the bottom corners (for both the beginning pages and the ending ones). Dog ears for the middle pages of the book are less likely but they can also appear in frequently used old books. Can someone explain why? </p>
<p><img src="http://i.stack.imgur.com/rw85F.jpg" alt="dog ears on the bottom corners for the beginning and ending pages"></p>
<p><img src="http://i.stack.imgur.com/bbpa6.jpg" alt="dog ears for the beginning pages of a book"></p>
<p>I apologize if this is not the right kind of question to post here. I can find no other sites on SE for it. </p>
| 8,435 |
[
-0.03167155757546425,
-0.08040205389261246,
0.04485273361206055,
-0.01250513456761837,
0.00946812517940998,
0.05148494243621826,
0.011777377687394619,
0.0013805866474285722,
-0.023013684898614883,
-0.024782715365290642,
0.026563577353954315,
0.05620723217725754,
0.03193697705864906,
0.022155672311782837,
0.016860198229551315,
0.003720706794410944,
-0.02051372267305851,
-0.022510796785354614,
-0.01245216466486454,
-0.027761204168200493,
0.019786065444350243,
0.05428832396864891,
-0.0015527016948908567,
0.01293722353875637,
-0.018827568739652634,
-0.012159302830696106,
0.03164634108543396,
0.00034656355273909867,
0.03551000356674194,
0.019196707755327225,
-0.06900524348020554,
0.0235277246683836,
0.050734277814626694,
-0.032485105097293854,
0.021199529990553856,
-0.01227472722530365,
0.003743021283298731,
-0.025974173098802567,
-0.036087241023778915,
0.005195123143494129,
-0.04086480662226677,
0.052988097071647644,
-0.011430910788476467,
0.05014512315392494,
-0.016774456948041916,
0.014221318066120148,
-0.013189698569476604,
-0.031470347195863724,
-0.013454974628984928,
-0.04701211303472519,
0.042265743017196655,
0.02125024050474167,
0.027072306722402573,
0.04630684107542038,
0.035671185702085495,
0.005868911277502775,
0.020373063161969185,
0.050845593214035034,
-0.013765075244009495,
-0.05452756956219673,
-0.014397588558495045,
-0.03448009490966797,
0.006944894324988127,
0.011122937314212322,
-0.009912625886499882,
0.023033391684293747,
-0.013477286323904991,
-0.005979085806757212,
0.037953756749629974,
-0.005139893852174282,
0.0016680120024830103,
0.020421022549271584,
0.06881671398878098,
0.009169211611151695,
0.01695689745247364,
-0.06689096987247467,
-0.009980212897062302,
0.05320931226015091,
0.061693012714385986,
0.03239859640598297,
-0.02790745347738266,
-0.0031279120594263077,
0.034216079860925674,
0.033069856464862823,
0.013429178856313229,
-0.006518814712762833,
0.08912673592567444,
-0.05064507946372032,
-0.0010882926872000098,
0.03963897377252579,
-0.026581211015582085,
0.014749311842024326,
0.023993302136659622,
-0.017807919532060623,
-0.026525432243943214,
0.028826043009757996,
0.0271027572453022,
0.039885226637125015,
-0.011468365788459778,
-0.02657591551542282,
0.04355501011013985,
-0.021089166402816772,
0.013890983536839485,
0.07505527883768082,
-0.029188022017478943,
-0.04456000402569771,
-0.06422099471092224,
0.01812221109867096,
0.02620798721909523,
-0.028939280658960342,
-0.046989209949970245,
0.008685639128088951,
-0.01770853064954281,
0.007063829340040684,
-0.008255795575678349,
0.01216043159365654,
-0.0092832762748003,
0.022940952330827713,
0.06271446496248245,
0.0473836325109005,
0.020708177238702774,
-0.02376296930015087,
0.015242758207023144,
-0.013524029403924942,
-0.08416684716939926,
0.014611683785915375,
0.04867146536707878,
-0.03225963935256004,
-0.03598320484161377,
0.053101491183042526,
-0.0065381587482988834,
0.007870851084589958,
0.051329948008060455,
0.00736320810392499,
0.05190339311957359,
0.014622661285102367,
-0.08216910064220428,
-0.05485941842198372,
0.057487256824970245,
-0.05028429627418518,
-0.0022161828819662333,
-0.09253605455160141,
0.035676971077919006,
-0.004887809045612812,
0.027808040380477905,
-0.010797335766255856,
-0.010665304027497768,
0.03436117246747017,
0.011987050995230675,
0.031904932111501694,
-0.01627836935222149,
0.0230237003415823,
-0.0081168282777071,
-0.02503482811152935,
-0.021654313430190086,
-0.06161293014883995,
0.031862881034612656,
0.024077892303466797,
0.01247263140976429,
-0.09543261677026749,
0.04752473905682564,
-0.020297683775424957,
-0.0016843635821714997,
-0.022456174716353416,
-0.026568101719021797,
-0.04559580981731415,
0.11686640232801437,
0.02904674783349037,
-0.02503836154937744,
0.017785003408789635,
0.023244990035891533,
0.060345347970724106,
0.015673721209168434,
-0.004820869769901037,
0.027102183550596237,
-0.02219943143427372,
0.018134133890271187,
-0.02185124158859253,
0.04717911034822464,
0.016148174181580544,
-0.0005288239917717874,
-0.033384934067726135,
0.01037486270070076,
-0.002581931883469224,
0.012702525593340397,
0.018869303166866302,
-0.030945148319005966,
-0.032404184341430664,
0.009500221349298954,
-0.007475113961845636,
0.033744994550943375,
-0.07894234359264374,
0.01532937865704298,
-0.019851036369800568,
-0.039815474301576614,
0.03476551175117493,
-0.044245000928640366,
-0.027227535843849182,
-0.027792342007160187,
-0.033704884350299835,
0.01616053842008114,
0.007172384764999151,
0.014308148995041847,
-0.07924763858318329,
0.0030616559088230133,
0.039738960564136505,
0.0035070625599473715,
-0.06528842449188232,
0.028810488060116768,
-0.07868388295173645,
-0.02782639116048813,
0.04525604844093323,
-0.03396223485469818,
-0.032559189945459366,
-0.019870715215802193,
-0.02162131480872631,
0.022047141566872597,
0.05458616465330124,
0.03427724540233612,
0.03208863362669945,
-0.011744175106287003,
0.012564226984977722,
0.010370418429374695,
-0.006147311069071293,
0.009676175191998482,
0.018015846610069275,
0.02532670460641384,
0.025398150086402893,
0.01363092940300703,
-0.03540575131773949,
-0.06912695616483688,
-0.034572117030620575,
0.05376603081822395,
-0.011439438909292221,
-0.0350714772939682,
0.0015326635912060738,
0.008714196272194386,
0.04411807283759117,
0.01964481733739376,
0.025556355714797974,
-0.007945901714265347,
-0.03386687487363815,
-0.04259352758526802,
0.016701940447092056,
0.01715901307761669,
0.044384121894836426,
0.044690970331430435,
0.0034305783919990063,
0.017443614080548286,
-0.02059597335755825,
-0.03895879164338112,
0.034750062972307205,
0.018250012770295143,
0.05074883624911308,
-0.002781315939500928,
-0.022388484328985214,
0.042078930884599686,
-0.04745571315288544,
0.00837753340601921,
0.00031224876875057817,
0.023645635694265366,
-0.015933340415358543,
-0.03107583522796631,
-0.011509419418871403,
0.001729145529679954,
0.04522566497325897,
-0.01510156411677599,
-0.015404648147523403,
0.01971297338604927,
-0.03485216200351715,
0.01540169958025217,
0.018605515360832214,
-0.0038981332909315825,
0.02446557581424713,
0.021991830319166183,
0.03176255151629448,
0.007619987707585096,
0.021633561700582504,
-0.003112226026132703,
-0.03914434462785721,
-0.026753731071949005,
-0.00659915991127491,
-0.01995808444917202,
-0.013265902176499367,
-0.016664378345012665,
-0.009990183636546135,
-0.01490843202918768,
0.027830706909298897,
0.03719821944832802,
0.042952559888362885,
0.029209710657596588,
0.006920924875885248,
-0.009674225933849812,
-0.028312278911471367,
-0.028000136837363243,
-0.03832152858376503,
0.02435602992773056,
-0.01777479238808155,
-0.01535843312740326,
0.03455665707588196,
0.006892777513712645,
0.0026536774821579456,
0.02978605590760708,
-0.00516429403796792,
-0.033786315470933914,
-0.013955867849290371,
-0.02546440251171589,
-0.026292771100997925,
0.011948993429541588,
-0.037882596254348755,
-0.01622823439538479,
-0.015144644305109978,
-0.0005134748644195497,
-0.051283545792102814,
-0.03186911344528198,
-0.03615407645702362,
0.006469224113970995,
0.012177656404674053,
-0.01230224221944809,
-0.009558162651956081,
0.06249472498893738,
0.012605438008904457,
-0.04359982907772064,
-0.012242894619703293,
-0.06007563695311546,
-0.030114734545350075,
-0.0532047376036644,
-0.037028197199106216,
0.06764310598373413,
0.0025002534966915846,
0.025360142812132835,
0.0018449084600433707,
0.0298475194722414,
0.03602336347103119,
0.02174544706940651,
-0.0016608318546786904,
0.015152105130255222,
-0.024477867409586906,
-0.029443828389048576,
-0.015579094178974628,
0.023412711918354034,
0.005193788092583418,
-0.02740888111293316,
0.01037962082773447,
0.04747714847326279,
0.02661353349685669,
-0.039934296160936356,
0.009974098764359951,
-0.007999727502465248,
0.019058572128415108,
-0.009200646542012691,
0.01830592378973961,
0.025131532922387123,
-0.04248645156621933,
-0.04156467691063881,
-0.006814633030444384,
0.06062878668308258,
-0.025603773072361946,
-0.020290140062570572,
0.027918564155697823,
0.013609698973596096,
-0.013419239781796932,
-0.0032132051419466734,
-0.019101304933428764,
0.005907987244427204,
0.03352096304297447,
-0.03157965838909149,
0.04780595377087593,
0.04284494370222092,
0.05475154146552086,
0.038290008902549744,
0.03043251857161522,
-0.0802697241306305,
-0.004680030979216099,
-0.0559132881462574,
-0.01591988280415535,
-0.03190720081329346,
0.03503510355949402,
-0.017501285299658775,
0.022401107475161552,
0.028216248378157616,
0.035013627260923386,
0.030225684866309166,
0.010512832552194595,
-0.07356372475624084,
0.00589712942019105,
-0.044030241668224335,
-0.005042462609708309,
-0.009094400331377983,
-0.007051937282085419,
-0.022576404735445976,
-0.008543393574655056,
-0.03134548291563988,
0.005823964718729258,
0.010154648683965206,
-0.034487564116716385,
0.027980420738458633,
-0.0030979725997895002,
-0.019149981439113617,
-0.019787831231951714,
0.0819062888622284,
0.01652384363114834,
-0.0101882703602314,
0.021981950849294662,
0.0013382838806137443,
0.003961628768593073,
-0.020291071385145187,
-0.03962203115224838,
0.028302326798439026,
0.006409501191228628,
0.03988802060484886,
0.021631717681884766,
-0.001992659643292427,
-0.027480725198984146,
0.01191908773034811,
-0.00404835119843483,
0.06888844072818756,
0.00790705718100071,
0.01421413104981184,
-0.010940037667751312,
-0.041346728801727295,
0.004877559840679169,
-0.016840685158967972,
0.00427632499486208,
-0.019952427595853806,
0.04835919290781021,
0.02505871281027794,
0.027911333367228508,
-0.04813000187277794,
0.0456753671169281,
0.05245170742273331,
0.021991534158587456,
-0.033624276518821716,
-0.0243675597012043,
-0.015412450768053532,
-0.05236482247710228,
-0.03327573090791702,
0.005649913102388382,
0.010667919181287289,
-0.032803334295749664,
-0.012387117370963097,
0.0046402872540056705,
-0.02759695239365101,
-0.014448446221649647,
0.005388003308326006,
-0.001992827979847789,
0.014915065839886665,
-0.0015330449678003788,
0.0026128841564059258,
0.05096442624926567,
0.010084418579936028,
0.05864996835589409,
0.004785917233675718,
-0.05212856084108353,
-0.0020217879209667444,
0.0028214394114911556,
0.015423709526658058,
0.035089071840047836,
-0.04595918953418732,
0.01285259798169136,
-0.04482901841402054,
-0.046908825635910034,
-0.00814048945903778,
-0.016550589352846146,
0.01619137078523636,
-0.03401988744735718,
0.002404428320005536,
-0.027239365503191948,
0.00400567939504981,
-0.012821396812796593,
-0.007215701509267092,
-0.008709581568837166,
0.02291940338909626,
-0.0291128009557724,
-0.0242887195199728,
-0.039369918406009674,
0.013018360361456871,
0.013250441290438175,
0.01860174536705017,
-0.00596782099455595,
0.008575841784477234,
-0.022717559710144997,
0.025496674701571465,
-0.058405403047800064,
-0.06016816571354866,
0.04088306054472923,
-0.08291446417570114,
-0.01763010025024414,
0.028722573071718216,
-0.02085953578352928,
-0.007272675633430481,
0.04286211356520653,
0.002722390927374363,
-0.025940246880054474,
-0.04318951070308685,
-0.01955016702413559,
-0.005914268083870411,
0.05474751442670822,
0.031406302005052567,
0.03187686949968338,
0.02115141972899437,
-0.002301402622833848,
-0.006831513252109289,
0.0030177272856235504,
0.048942841589450836,
-0.04714047536253929,
-0.005799960810691118,
-0.03896502032876015,
0.02718712016940117,
-0.047926463186740875,
0.0531427338719368,
-0.03434000164270401,
0.010389382019639015,
-0.025743653997778893,
-0.01521669514477253,
-0.03262368217110634,
-0.007828449830412865,
-0.016821080818772316,
0.015264349058270454,
0.03437527269124985,
0.03218343108892441,
-0.02204517275094986,
-0.02548607997596264,
0.0194527767598629,
-0.05194726958870888,
-0.0054545933380723,
0.05383426696062088,
-0.0006610851851291955,
-0.0076736267656087875,
-0.029888521879911423,
0.015586626715958118,
-0.004753724671900272,
-0.009612494148314,
0.01014716736972332,
-0.0460258349776268,
0.030654409900307655,
0.020008491352200508,
-0.04676895961165428,
0.0009888495551422238,
0.023065639659762383,
-0.019573405385017395,
0.06207018718123436,
-0.0550711490213871,
0.08056416362524033,
0.07101281732320786,
-0.01565348356962204,
-0.019997011870145798,
-0.020982934162020683,
0.036788567900657654,
0.02841896004974842,
-0.04512639716267586,
-0.01756359077990055,
-0.0046570864506065845,
-0.03463735058903694,
-0.02355917915701866,
-0.030792128294706345,
0.041761163622140884,
-0.04338350519537926,
-0.004989974666386843,
0.035466670989990234,
-0.011184205301105976,
0.06901684403419495,
0.00301649933680892,
-0.038116324692964554,
0.011268426664173603,
-0.009044667705893517,
-0.021998129785060883,
-0.0247552040964365,
0.04536497965455055,
-0.006518891081213951,
-0.014503389596939087,
0.01637754961848259,
0.00962862279266119,
0.01764470897614956,
0.011589610017836094,
0.020199507474899292,
0.024335920810699463,
-0.0020970029290765524,
0.02184179425239563,
-0.004842191468924284,
-0.011102921329438686,
0.0010536644840613008,
0.005532635375857353,
-0.00840749591588974,
0.013464787043631077,
-0.003831185633316636,
-0.02640475146472454,
-0.006789166945964098,
0.039426133036613464,
0.005722277332097292,
0.006417853757739067,
0.0800761952996254,
-0.04236770048737526,
-0.006453775800764561,
0.01105879619717598,
-0.073817677795887,
0.039109006524086,
0.03095368854701519,
0.013136343099176884,
0.032539255917072296,
0.01868937909603119,
-0.020122094079852104,
-0.020817173644900322,
-0.02097446471452713,
0.02111211232841015,
0.05966288968920708,
-0.0002967151813209057,
0.044812168926000595,
0.04912490025162697,
0.014306173659861088,
0.00926954485476017,
-0.03962154686450958,
-0.05307341739535332,
-0.019043566659092903,
-0.018771400675177574,
0.03614350035786629,
-0.02990707755088806,
0.005418125074356794,
0.01763882301747799,
-0.019559744745492935,
0.015919683501124382,
0.024067722260951996,
0.03374617174267769,
0.01012769527733326,
-0.020558428019285202,
0.03116036206483841,
-0.0032804140355437994,
0.057852938771247864,
-0.047299351543188095,
0.018221817910671234,
0.021975427865982056,
-0.03823700174689293,
0.03670867532491684,
0.030574701726436615,
0.005662163719534874,
-0.03257427737116814,
-0.02509082295000553,
-0.014205891638994217,
0.006462301127612591,
0.006665067281574011,
0.005057486239820719,
-0.024444665759801865,
0.006234044209122658,
0.011732113547623158,
-0.048662446439266205,
0.001652826787903905,
-0.00820849183946848,
-0.04508346691727638,
-0.012981452979147434,
-0.00515333004295826,
-0.012263600714504719,
0.044499047100543976,
-0.013091988861560822,
-0.023843958973884583,
0.023733779788017273,
-0.06792774796485901,
-0.01662134751677513,
0.012512050569057465,
0.029319319874048233,
-0.00805849302560091,
0.08858681470155716,
0.004731424152851105,
-0.007927224971354008,
0.005191139876842499,
0.0013596023200079799,
0.13945189118385315,
0.031108587980270386,
-0.0008559915004298091,
-0.07391437888145447,
0.0522155724465847,
-0.026413943618535995,
0.010553316213190556,
-0.003930548671633005,
0.006831115577369928,
-0.015639588236808777,
0.015432136133313179,
0.031117551028728485,
0.05894885212182999,
0.05668051540851593,
-0.016953442245721817,
0.03144348785281181,
-0.0828155130147934,
-0.043710868805646896,
0.011298446916043758,
-0.01820196583867073,
-0.03374111279845238,
-0.006699163932353258,
-0.03954004496335983,
-0.005337272770702839,
0.017446918413043022,
-0.003986042458564043,
-0.004670893773436546,
-0.034983716905117035,
0.0091581204906106,
0.024381015449762344,
0.006037464365363121,
-0.023950641974806786,
0.009112312458455563,
-0.001779005629941821,
-0.020100418478250504,
-0.020522568374872208,
0.015391668304800987,
0.02237178012728691,
0.023706721141934395,
-0.0025978735648095608,
0.03593785688281059,
-0.010274547152221203,
0.0032249093055725098,
0.021331388503313065,
-0.052524883300065994,
-0.04549834877252579,
0.0040408046916127205,
0.013381215743720531,
-0.007960466668009758,
-0.024698635563254356,
-0.02965850755572319,
0.018793510273098946,
0.03851354122161865,
-0.04662768170237541,
-0.014409838244318962,
0.007919304072856903,
-0.02090645767748356,
0.020711923018097878,
-0.04910830035805702,
-0.01940755918622017,
0.04024650156497955,
-0.004033288452774286,
0.029939843341708183,
0.016222096979618073,
-0.00972120650112629,
-0.011169113218784332,
-0.06692621856927872,
0.019546477124094963,
0.012086300179362297,
-0.005484868306666613,
-0.026896938681602478,
0.005836543161422014,
-0.07942574471235275,
0.029631348326802254,
-0.025025788694620132,
0.03127948194742203,
0.06278692185878754,
0.005330963525921106,
-0.042648401111364365,
0.0019037221791222692,
-0.01876005157828331,
0.04537107050418854,
0.030167169868946075,
-0.02238748036324978,
-0.07476775348186493,
-0.025990305468440056,
0.020517485216259956,
-0.016517654061317444,
0.005045904312282801,
0.0321856290102005,
-0.02017468959093094,
0.03712381049990654,
0.016333460807800293,
0.015588303096592426,
0.008101915940642357,
0.01111357007175684,
0.010843479074537754,
-0.011427058838307858,
0.0022401208989322186,
0.029210342094302177,
-0.016004296019673347,
0.012715881690382957,
0.05236818641424179,
0.02986046113073826,
0.002960266312584281,
-0.00652896985411644,
0.026991920545697212,
-0.016278404742479324,
0.026902489364147186,
0.041492510586977005,
-0.04696326330304146,
-0.026211516931653023,
0.009177032858133316,
-0.008627040311694145,
0.01509382389485836,
-0.007027284242212772,
0.029342714697122574,
-0.02943013422191143,
0.015297631733119488,
-0.06760433316230774,
0.0067499419674277306,
-0.019361576065421104,
-0.01555585116147995,
-0.07402724772691727,
0.008683529682457447,
0.019439296796917915,
0.039548296481370926,
-0.0025963473599404097,
0.05238499864935875,
0.0007496753823943436,
-0.032888706773519516,
0.0006049973308108747,
0.02008683979511261,
-0.005059452727437019,
0.03078855574131012,
-0.00032594165531918406,
-0.007972370833158493,
-0.0010163354454562068,
0.00004514495230978355,
-0.048415519297122955,
0.04302174225449562,
-0.053889788687229156,
-0.062486156821250916,
-0.01197692658752203,
0.008241699077188969,
-0.026391340419650078,
-0.03715592250227928,
-0.0053113955073058605,
-0.027094578370451927,
0.07552506029605865,
-0.015991181135177612,
-0.011698243208229542,
0.011857620440423489,
0.024042678996920586,
0.012352817691862583,
-0.001955724088475108,
-0.0009814559016376734,
-0.005711859557777643,
0.016979072242975235,
0.030570102855563164,
0.00421398039907217,
0.02752014994621277,
0.007757349405437708,
0.012172764167189598,
-0.0002677344309631735,
-0.0008354652090929449,
-0.022080987691879272,
0.01718616858124733,
0.0325159877538681,
0.011868037283420563,
-0.014144733548164368,
0.05166305974125862,
0.010420304723083973,
-0.020379111170768738,
-0.038646917790174484,
-0.027265924960374832,
-0.0043890406377613544,
0.03474517911672592,
-0.0027970660012215376,
-0.04820758104324341,
-0.006382819730788469,
0.03756089508533478,
-0.016411010175943375,
-0.006761219352483749,
0.018401166424155235,
-0.023608887568116188,
-0.06302868574857712,
-0.003898884169757366,
0.02004450000822544,
0.00843559205532074,
0.0007062524673528969,
0.018924947828054428,
0.03298136219382286,
-0.02030273526906967,
-0.0388500913977623,
-0.052451346069574356,
0.026239024475216866,
0.04404435679316521,
-0.045463964343070984,
-0.026788271963596344,
0.04421699792146683,
0.0010609958553686738,
-0.06536834686994553,
0.0366436131298542,
0.03316648676991463,
-0.017237184569239616,
0.010298439301550388,
0.019190464168787003,
0.030806398019194603,
-0.02538844756782055,
0.05480220913887024,
0.02180727943778038,
-0.03732389584183693,
0.03078196570277214,
0.003279286902397871,
0.006765947677195072,
0.024873752146959305,
0.03385000303387642,
0.0033117474522441626,
-0.01696685515344143,
-0.03321900963783264,
0.026433594524860382,
-0.029026813805103302,
0.0061996448785066605,
-0.012162196449935436,
0.049273137003183365,
0.04144668951630592,
-0.014760456047952175,
0.037769708782434464,
-0.06060977280139923,
0.016048764809966087,
-0.0028228415176272392,
0.003869554027915001,
0.022701522335410118,
0.05315006151795387,
0.008172190748155117,
-0.02979571931064129,
-0.004044247791171074,
0.01746276579797268,
-0.03702673688530922,
-0.022997746244072914,
0.023509373888373375,
-0.002962758531793952,
0.04711360111832619,
-0.01942591741681099,
-0.002141913864761591,
-0.014737186022102833,
-0.018648484721779823,
-0.016519274562597275,
0.008800562471151352,
-0.011042704805731773,
-0.005798113998025656,
0.014470824971795082,
-0.030595701187849045,
0.08401117473840714,
-0.01559407077729702,
-0.008792804554104805,
-0.0408720038831234,
-0.055169373750686646,
-0.026986632496118546,
0.04514738544821739,
0.037431295961141586,
-0.02163407765328884,
0.022068241611123085,
-0.01623314805328846,
0.013932409696280956,
-0.004878326319158077,
-0.020999625325202942,
0.003109077224507928,
0.03454917296767235,
0.012246964499354362,
0.019433068111538887,
0.041368767619132996,
-0.011903936043381691,
0.020238405093550682,
-0.0004595765785779804,
-0.01675107143819332,
0.01599237136542797,
-0.001748027978464961,
-0.00922661367803812,
0.003299920354038477,
0.03673708066344261,
0.013957303948700428,
0.07607904821634293,
0.00024172774283215404,
0.023197099566459656,
0.027521777898073196,
0.0014072617050260305,
-0.024540355429053307,
0.06800810247659683,
-0.004635103978216648,
-0.05273941531777382,
-0.0016899335896596313,
0.05575248971581459,
0.012904055416584015,
-0.017903048545122147,
0.014318879693746567,
0.024435188621282578,
-0.007654834073036909,
0.00991583801805973,
-0.024147793650627136,
0.02746391110122204,
0.0041005234234035015,
0.0053747231140732765,
-0.055231817066669464,
0.0324295349419117,
-0.0599246472120285,
-0.0230104923248291,
-0.00582069531083107,
0.028546329587697983,
0.02388390526175499,
0.0065894220024347305,
0.02048628404736519,
0.006157444324344397,
0.016045164316892624,
-0.021309418603777885,
0.03153413161635399,
-0.004330887459218502,
0.0034973532892763615,
0.02388528175652027,
-0.035590581595897675,
-0.009686359204351902,
-0.001489747315645218,
0.0027385149151086807,
0.032183967530727386,
0.011982342228293419,
0.031944964081048965,
0.017120346426963806,
-0.009041293524205685,
-0.034250255674123764,
0.0016324282623827457,
0.011393284425139427,
0.025764459744095802,
-0.0073228334076702595,
-0.02063494548201561,
0.012179303914308548,
-0.017742017284035683,
0.04138857498764992,
-0.03007282130420208,
0.010665996000170708,
-0.018978798761963844,
0.009634226560592651,
-0.03705202043056488,
-0.016823027282953262,
-0.035263314843177795,
-0.027653731405735016,
0.026127398014068604,
-0.0039277952164411545,
-0.0052550300024449825,
-0.02870444394648075,
-0.0016618025256320834,
-0.006913365796208382,
0.06060831621289253,
-0.048109788447618484,
-0.008173398673534393,
0.019210578873753548,
0.02611532434821129,
-0.023363592103123665,
0.009079883806407452
] |
<p>I am interested in (typically topological) field theories arising from Lagrangians of the form.</p>
<p>$f(\Phi) \lambda$,</p>
<p>where $\lambda$ is a Lagrange multiplier field not appearing in $f(\Phi)$. Perturbatively, the partition function just counts the solutions to $f(\Phi)=0$. What about nonperturbatively? Are there exponentially suppressed kinks that affect the partition function?</p>
<p>Has anyone considered these?</p>
| 8,436 |
[
0.019693143665790558,
-0.02196931093931198,
0.0025596036575734615,
-0.00794130191206932,
0.02007991634309292,
-0.009704269468784332,
-0.03094830922782421,
0.013485120609402657,
-0.019585177302360535,
-0.03665737807750702,
0.0068705384619534016,
0.0026539922691881657,
0.022031785920262337,
-0.0018052281811833382,
0.02426641806960106,
-0.022829074412584305,
0.004602122586220503,
-0.01093330793082714,
0.012049483135342598,
-0.002681564772501588,
-0.02302209846675396,
0.0455191545188427,
0.02150093950331211,
-0.007046704646199942,
-0.062293898314237595,
-0.015579544939100742,
0.020270969718694687,
0.03122895024716854,
0.005879209376871586,
0.10147242248058319,
-0.029994729906320572,
-0.021808061748743057,
-0.013491448014974594,
0.021275484934449196,
-0.0014337748289108276,
0.03073599748313427,
-0.03498312085866928,
-0.04548511281609535,
-0.032582029700279236,
-0.014833921566605568,
-0.04494410753250122,
-0.027383189648389816,
-0.026448199525475502,
0.032697539776563644,
0.008946800604462624,
0.018757246434688568,
-0.0020088788587599993,
-0.003477346384897828,
0.0805533230304718,
-0.04537937417626381,
0.029905082657933235,
0.046375878155231476,
0.03663402795791626,
0.014925838448107243,
0.025329485535621643,
-0.01783410646021366,
0.07061533629894257,
0.0620528981089592,
-0.00584749411791563,
-0.04933858662843704,
-0.04018238186836243,
-0.04206716641783714,
0.008809039369225502,
-0.047580085694789886,
-0.022175174206495285,
0.01609979383647442,
0.020750949159264565,
-0.04596157744526863,
0.041591577231884,
-0.007604079321026802,
-0.006932937540113926,
-0.01319257915019989,
0.051630038768053055,
-0.020461445674300194,
0.011481203138828278,
-0.005289393477141857,
0.02898409590125084,
-0.0011050923494622111,
0.002019393490627408,
0.050348274409770966,
0.013655177317559719,
0.032116636633872986,
0.004835241008549929,
0.024022847414016724,
0.012251963838934898,
-0.023591477423906326,
0.034266360104084015,
-0.008963195607066154,
-0.017812062054872513,
0.05653490498661995,
-0.053186532109975815,
-0.04074264317750931,
0.0385025292634964,
-0.055973924696445465,
-0.017611054703593254,
-0.002103509148582816,
0.012177316471934319,
0.04281068220734596,
-0.01154596358537674,
0.01465014647692442,
-0.044754352420568466,
-0.01080060750246048,
0.00977330468595028,
0.07247740030288696,
-0.0019119117641821504,
0.013615177012979984,
-0.03368261456489563,
0.01945333182811737,
-0.02386152744293213,
-0.0019755521789193153,
-0.042186394333839417,
-0.019440624862909317,
0.027179120108485222,
-0.01212227251380682,
-0.003911476582288742,
-0.019091876223683357,
-0.03635071963071823,
-0.04734219238162041,
0.03307388722896576,
0.09544798731803894,
0.03434237465262413,
-0.017561158165335655,
0.036767419427633286,
-0.023895997554063797,
-0.04655985161662102,
-0.0016182562103495002,
0.04025012254714966,
0.0027233848813921213,
-0.017873244360089302,
-0.026340007781982422,
-0.015606719069182873,
-0.016665052622556686,
0.029988305643200874,
0.007825483568012714,
0.04676808789372444,
-0.026826167479157448,
-0.03621802479028702,
-0.030726445838809013,
0.0072728367522358894,
-0.021911753341555595,
-0.028531331568956375,
-0.02022949606180191,
-0.03532330319285393,
0.007324770092964172,
0.06327478587627411,
0.0047577377408742905,
-0.021718356758356094,
0.010294949635863304,
0.07264608144760132,
0.017483090981841087,
-0.03681621700525284,
-0.01578708179295063,
-0.018184127286076546,
-0.05646849796175957,
-0.04242849349975586,
-0.0629611387848854,
0.021962806582450867,
0.04083302244544029,
0.010655977763235569,
-0.032095834612846375,
0.08075253665447235,
-0.01890915259718895,
0.003270207904279232,
-0.0019884570501744747,
-0.0056310915388166904,
-0.009195382706820965,
0.07689057290554047,
-0.02789081446826458,
0.05432860925793648,
0.02662527561187744,
-0.016174878925085068,
0.024140605702996254,
0.021248022094368935,
0.019472215324640274,
0.04125174134969711,
0.009096018970012665,
-0.009104329161345959,
-0.019147394225001335,
0.013135976158082485,
0.024432986974716187,
-0.003176057944074273,
-0.009745855815708637,
-0.014180226251482964,
-0.01347472332417965,
-0.03443419933319092,
0.009405821561813354,
0.007433149963617325,
-0.020749760791659355,
0.015901170670986176,
-0.05689156800508499,
-0.015899930149316788,
-0.041382864117622375,
0.007637116126716137,
0.01817561686038971,
0.005111116915941238,
0.07262585312128067,
0.018123336136341095,
0.005052115768194199,
-0.05009454861283302,
-0.07207614928483963,
0.012605255469679832,
0.03377041220664978,
-0.027808720245957375,
0.007181045599281788,
0.01699402928352356,
0.030390294268727303,
0.04987861588597298,
-0.013184028677642345,
0.04497288912534714,
-0.01632385514676571,
-0.055127277970314026,
-0.00816712062805891,
-0.04417835921049118,
0.04287169501185417,
-0.04557230696082115,
0.024188632145524025,
0.0011700434843078256,
0.009795955382287502,
-0.00487104058265686,
0.039863333106040955,
-0.01747109927237034,
0.0408930703997612,
0.06287802010774612,
0.02517220564186573,
0.0041993106715381145,
0.03468950837850571,
-0.02870204672217369,
0.007086669094860554,
0.009983755648136139,
-0.04717492684721947,
-0.06152070686221123,
-0.01417301595211029,
0.04415299743413925,
0.05523192882537842,
-0.007778877858072519,
0.001973863458260894,
0.024082759395241737,
0.00868387520313263,
0.019108420237898827,
0.035206638276576996,
-0.02664024382829666,
-0.0023837427143007517,
0.056782759726047516,
-0.0021063722670078278,
0.021790767088532448,
-0.0370204858481884,
0.06297525018453598,
-0.004736748989671469,
0.010987191461026669,
-0.02176993153989315,
-0.03488806262612343,
0.028508301824331284,
-0.01586899533867836,
0.006515166722238064,
-0.029406463727355003,
-0.0039058728143572807,
0.015442296862602234,
-0.01591654121875763,
0.04938648268580437,
0.026231111958622932,
0.011575729586184025,
0.0019909327384084463,
-0.02351165935397148,
0.003963606897741556,
0.02389424294233322,
-0.020817408338189125,
-0.03041969984769821,
-0.013063016347587109,
0.020477673038840294,
-0.03255029022693634,
-0.001474280608817935,
-0.008543606847524643,
0.02465711534023285,
-0.022451024502515793,
0.04056643322110176,
0.03979597985744476,
-0.033532049506902695,
0.043810389935970306,
-0.046660665422677994,
-0.011033430695533752,
0.05055583640933037,
-0.051353249698877335,
0.057783059775829315,
0.05414498969912529,
-0.015980228781700134,
0.015896545723080635,
-0.06741657853126526,
-0.03664198890328407,
0.039164841175079346,
-0.023869385942816734,
0.032181885093450546,
-0.022669702768325806,
-0.023794956505298615,
-0.019569575786590576,
-0.011869939044117928,
-0.011121204122900963,
0.022464722394943237,
-0.05710028111934662,
0.015723438933491707,
0.04516785964369774,
0.022753560915589333,
-0.01055254228413105,
0.004996071103960276,
-0.012749560177326202,
0.036915503442287445,
-0.027463573962450027,
0.01199228223413229,
0.018047355115413666,
-0.06459314376115799,
-0.0002571400546003133,
0.009469626471400261,
-0.032893404364585876,
0.06342609971761703,
-0.05747927725315094,
-0.027152102440595627,
-0.027310999110341072,
-0.01438906043767929,
0.032539840787649155,
-0.02546548657119274,
-0.0674305334687233,
0.06540434062480927,
0.05938643589615822,
-0.02742515131831169,
-0.005789816379547119,
-0.02181381545960903,
0.013279841281473637,
-0.009270532056689262,
-0.009145574644207954,
0.005644515622407198,
-0.0278975460678339,
0.05003485828638077,
-0.00204449612647295,
0.005667429883033037,
0.008469592779874802,
0.04372107982635498,
-0.022346781566739082,
0.03807811066508293,
0.012311358936131,
0.0023565057199448347,
0.08206918835639954,
0.024327343329787254,
-0.005231793504208326,
-0.0030435416847467422,
-0.024972928687930107,
-0.005915407091379166,
0.028611954301595688,
-0.06507551670074463,
0.06671623885631561,
0.034549713134765625,
0.009990973398089409,
0.011241828091442585,
0.016938423737883568,
0.011872301809489727,
-0.03349331393837929,
-0.019726771861314774,
0.01613452285528183,
0.022044749930500984,
-0.015951422974467278,
0.027562826871871948,
0.02756579779088497,
0.08271803706884384,
-0.05233190208673477,
-0.019664760679006577,
-0.026331614702939987,
0.015259427018463612,
0.039748549461364746,
-0.02425822615623474,
-0.02790825255215168,
0.036277689039707184,
0.01713273487985134,
-0.008255235850811005,
-0.0158584862947464,
-0.010811390355229378,
-0.0057770018465816975,
-0.06629209220409393,
-0.03725909814238548,
0.00028755617677234113,
0.04588061198592186,
0.007944080978631973,
0.018304241821169853,
-0.00497095100581646,
0.018323790282011032,
-0.0018152146367356181,
0.006944784428924322,
-0.06957397609949112,
0.02224116213619709,
-0.030450545251369476,
-0.001461604842916131,
-0.010474820621311665,
0.0073607442900538445,
0.04106495901942253,
0.0181902889162302,
-0.02271507866680622,
0.0003701883542817086,
-0.0073319380171597,
-0.06030464172363281,
0.003007190302014351,
-0.030115000903606415,
-0.05266826972365379,
-0.0042729913257062435,
0.02862839587032795,
0.049394991248846054,
-0.028068186715245247,
0.01567988656461239,
0.012181457132101059,
-0.03749717026948929,
0.0021962362807244062,
-0.026862850412726402,
0.018793629482388496,
0.0017177741974592209,
0.02619398944079876,
0.015060141682624817,
0.012801782228052616,
-0.010979793965816498,
0.026537712663412094,
0.05114724114537239,
0.09056112170219421,
-0.015096010640263557,
0.0023297597654163837,
0.023396160453557968,
-0.038316234946250916,
-0.049699705094099045,
-0.009924362413585186,
0.07349736988544464,
0.013189494609832764,
0.0064730774611234665,
0.041864022612571716,
0.018372096121311188,
-0.01739882305264473,
0.019392505288124084,
0.00032000982901081443,
0.024411261081695557,
-0.055211301892995834,
-0.03014267422258854,
0.018048405647277832,
0.01880066655576229,
0.02037961781024933,
-0.03912897780537605,
-0.01792583428323269,
0.014168523252010345,
0.028848763555288315,
0.010788735002279282,
-0.005629336461424828,
-0.007946430705487728,
-0.017684640362858772,
-0.008511068299412727,
0.018118135631084442,
-0.027443479746580124,
0.009876010939478874,
0.030013374984264374,
0.0788247138261795,
0.04252350330352783,
0.031284116208553314,
0.0010574795305728912,
-0.04341485723853111,
-0.009653974324464798,
0.038724154233932495,
0.012540880590677261,
0.04568883404135704,
-0.011660180985927582,
-0.04841376841068268,
0.008836859837174416,
0.0724204033613205,
-0.01302056573331356,
0.028745904564857483,
0.016654983162879944,
-0.031409237533807755,
-0.009759767912328243,
-0.012979797087609768,
-0.01686902530491352,
0.040132131427526474,
-0.016598666086792946,
-0.0025930162519216537,
-0.04715464264154434,
0.013132055290043354,
0.004139922559261322,
0.02170039899647236,
0.0044967373833060265,
0.053962137550115585,
0.011725632473826408,
0.012023293413221836,
-0.01545182429254055,
-0.012106252834200859,
-0.01106505561619997,
-0.06620007008314133,
-0.008001807145774364,
0.027429603040218353,
0.013361196964979172,
0.013305225409567356,
-0.042707137763500214,
-0.03860826790332794,
-0.01639850251376629,
-0.009378939867019653,
-0.014953961595892906,
0.040132008492946625,
-0.024153634905815125,
0.05821222439408302,
0.006155144888907671,
-0.0283530130982399,
0.03241230919957161,
0.09058940410614014,
-0.008768336847424507,
-0.010293186642229557,
0.01981678418815136,
0.010592490434646606,
-0.024190934374928474,
0.028569333255290985,
-0.0474696047604084,
-0.021549945697188377,
-0.06908080726861954,
0.03491190820932388,
-0.050627049058675766,
0.018705058842897415,
-0.010873737744987011,
-0.030902087688446045,
-0.005415291525423527,
0.025721251964569092,
0.03534848988056183,
0.004674728959798813,
0.03370889648795128,
0.01772947981953621,
0.0237555094063282,
-0.00246411026455462,
0.010546333156526089,
0.011841744184494019,
0.0003249495639465749,
0.011468421667814255,
-0.027554672211408615,
0.03687869384884834,
-0.022423075512051582,
0.004093697294592857,
0.010128392837941647,
-0.012194516137242317,
0.04347844049334526,
0.024166222661733627,
-0.022431274875998497,
-0.01255482342094183,
-0.03941991552710533,
-0.019564703106880188,
-0.00963995698839426,
-0.000772267987485975,
0.028798380866646767,
-0.016193751245737076,
0.03368755057454109,
0.01275169663131237,
-0.03158567473292351,
-0.05823349952697754,
-0.049375634640455246,
0.0004958753124810755,
-0.006772233173251152,
-0.01398229319602251,
-0.03305418789386749,
0.006219745147973299,
-0.058213215321302414,
-0.02372441254556179,
0.01683354377746582,
0.07446721941232681,
-0.025617554783821106,
0.01924832910299301,
0.03821289539337158,
0.042460791766643524,
0.013548795133829117,
0.022129392251372337,
-0.02599634975194931,
0.050159189850091934,
-0.0026094953063875437,
-0.002181119052693248,
0.0051877000369131565,
-0.0001979279040824622,
-0.02519414946436882,
-0.0009590144618414342,
0.016517672687768936,
-0.01845700293779373,
-0.008246458135545254,
-0.010698379948735237,
-0.013816874474287033,
0.04444615915417671,
0.024834640324115753,
0.052292823791503906,
-0.0020738202147185802,
-0.01854565739631653,
-0.011562841013073921,
0.02590441145002842,
-0.006304167676717043,
-0.01565004140138626,
-0.023453637957572937,
-0.04390762001276016,
0.025814441964030266,
-0.021885477006435394,
-0.004956623073667288,
0.019027400761842728,
0.03225332871079445,
0.006568665616214275,
-0.03851979598402977,
0.030717642977833748,
-0.018219484016299248,
0.01851082034409046,
0.0011161559959873557,
-0.00433730473741889,
-0.0008647574577480555,
0.03653606399893761,
-0.04067423194646835,
-0.05767760053277016,
-0.032642219215631485,
0.0038366378284990788,
0.03700387477874756,
0.011261658743023872,
0.005488111171871424,
-0.008545422926545143,
-0.012234187684953213,
-0.004277884028851986,
-0.020757878199219704,
-0.06698548048734665,
0.011573522351682186,
0.016933904960751534,
0.028507664799690247,
-0.028616737574338913,
0.05742548406124115,
0.041523709893226624,
-0.005864872597157955,
-0.03365657478570938,
0.0444471538066864,
0.02045302465558052,
0.015919269993901253,
0.05333595722913742,
-0.012445509433746338,
-0.037824828177690506,
0.03832855448126793,
-0.04913734272122383,
0.040938325226306915,
0.0009605116210877895,
-0.041233666241168976,
0.061113953590393066,
0.020018473267555237,
0.02529570832848549,
-0.016562068834900856,
-0.03029005602002144,
-0.016500461846590042,
0.043300434947013855,
0.013443500734865665,
0.029956107959151268,
0.03695015609264374,
-0.0012902281014248729,
0.039934828877449036,
0.0152321457862854,
-0.00834642443805933,
0.015547788701951504,
-0.02471395581960678,
-0.024700559675693512,
-0.07690883427858353,
-0.06615987420082092,
0.026062119752168655,
0.007888088934123516,
-0.030005713924765587,
-0.0008342684013769031,
0.010631713084876537,
0.0193317998200655,
-0.0025366460904479027,
0.035947322845458984,
-0.04736022651195526,
0.04859355092048645,
-0.009045815095305443,
0.031046075746417046,
-0.017517730593681335,
0.02172435075044632,
0.1163221076130867,
0.042670417577028275,
0.03307820111513138,
-0.09064832329750061,
-0.0014374617021530867,
-0.012982761487364769,
0.02199305035173893,
-0.04905933514237404,
0.022850560024380684,
0.020248204469680786,
-0.045981429517269135,
0.010192087851464748,
0.10760142654180527,
-0.014077974483370781,
-0.015051963739097118,
0.07893870025873184,
-0.017161257565021515,
-0.034295372664928436,
0.009013064205646515,
0.008586766198277473,
0.008227408863604069,
0.009343383833765984,
-0.042781416326761246,
0.02976551651954651,
0.011743499897420406,
0.00886420626193285,
-0.010206757113337517,
-0.047762978821992874,
0.011109978891909122,
-0.002440486801788211,
-0.0386536605656147,
-0.025701411068439484,
0.020926907658576965,
-0.015925748273730278,
-0.024898700416088104,
-0.006823330651968718,
0.02153407782316208,
-0.001906030811369419,
0.02657913789153099,
0.07976087182760239,
0.0057743308134377,
0.013511702418327332,
0.0046568866819143295,
0.009401373565196991,
-0.04298818111419678,
-0.03367162123322487,
-0.014827851206064224,
0.03985822573304176,
-0.028581077232956886,
0.019027765840291977,
-0.01805822178721428,
-0.01607009582221508,
0.032116733491420746,
-0.013885200954973698,
-0.042579472064971924,
-0.01688762754201889,
0.020331494510173798,
-0.01133900135755539,
-0.028044668957591057,
0.008411874994635582,
0.024175116792321205,
-0.0048299371264874935,
0.00883435271680355,
-0.011664580553770065,
-0.0048048109747469425,
0.0008046966977417469,
-0.00009228511044057086,
0.02034769579768181,
0.008940048515796661,
-0.030254799872636795,
-0.019087327644228935,
-0.013293866999447346,
-0.03155064210295677,
-0.007284719496965408,
-0.030737057328224182,
0.017047671601176262,
0.028214318677783012,
-0.0031028902158141136,
-0.01735432632267475,
-0.0025954917073249817,
-0.039855774492025375,
-0.011083695106208324,
-0.05933014675974846,
-0.012193265371024609,
-0.0038533201441168785,
-0.014869594015181065,
0.019441993907094002,
0.024712324142456055,
0.008554309606552124,
-0.029456662014126778,
0.010583721101284027,
0.032214224338531494,
-0.015243432484567165,
-0.03133441507816315,
-0.008553075604140759,
-0.013942544348537922,
-0.02804361842572689,
-0.023785891011357307,
-0.04153349623084068,
0.028631463646888733,
0.011667607352137566,
-0.0018177101155743003,
0.008483171463012695,
0.013045425526797771,
0.00259012496098876,
-0.01225439552217722,
0.020818185061216354,
-0.03883092477917671,
0.02441939152777195,
0.01952606625854969,
0.025053059682250023,
-0.05368273705244064,
-0.059103138744831085,
0.0023390173446387053,
0.004179316107183695,
-0.014888293109834194,
0.002507762983441353,
-0.052925389260053635,
-0.04446152597665787,
-0.004485574085265398,
0.02330332249403,
-0.05918359011411667,
-0.022074289619922638,
-0.030247610062360764,
0.01396955642849207,
-0.019872352480888367,
0.01442170049995184,
0.020985621958971024,
0.02966376766562462,
-0.04404435679316521,
-0.012249388732016087,
0.014329036697745323,
0.020976470783352852,
-0.01080464106053114,
-0.02018069662153721,
0.02658301219344139,
-0.006729105953127146,
0.005641590338200331,
0.030667925253510475,
-0.01920422352850437,
0.027597762644290924,
-0.0421992726624012,
-0.05102524161338806,
0.03433889523148537,
-0.026444407179951668,
0.01931144669651985,
0.03688245266675949,
-0.015391649678349495,
-0.05107332020998001,
-0.014472601935267448,
-0.01265476644039154,
-0.0037502197083085775,
0.0019130409928038716,
-0.025593597441911697,
-0.014969156123697758,
-0.01506668422371149,
0.016858385875821114,
-0.005504142958670855,
-0.0036203330382704735,
-0.023213373497128487,
0.01547926850616932,
-0.013052182272076607,
-0.01960224099457264,
-0.016295189037919044,
-0.0032006024848669767,
0.055037301033735275,
-0.03810819610953331,
-0.007153009530156851,
0.0002818381180986762,
0.054522134363651276,
-0.0014691852265968919,
0.016312843188643456,
-0.021338405087590218,
0.013943501748144627,
-0.07985909283161163,
-0.02003607712686062,
-0.00612957077100873,
0.013311383314430714,
0.061509981751441956,
-0.029869522899389267,
-0.005524303764104843,
-0.009306247346103191,
-0.04745051637291908,
0.04822221398353577,
-0.011681774631142616,
0.01059513445943594,
-0.06531992554664612,
-0.01508939266204834,
-0.005266363732516766,
0.05754761025309563,
0.07216348499059677,
0.048666901886463165,
-0.021964170038700104,
0.020264796912670135,
-0.03399818018078804,
0.006037033163011074,
-0.018791235983371735,
0.018152939155697823,
-0.0042003062553703785,
-0.02827538177371025,
0.041796281933784485,
0.0024619149044156075,
-0.06273078918457031,
-0.0055370088666677475,
-0.014055205509066582,
-0.031519144773483276,
-0.003126160940155387,
0.011231504380702972,
0.024575160816311836,
0.01893368735909462,
0.03087783232331276,
-0.0005860064411535859,
0.016475653275847435,
0.03170806169509888,
0.003533218754455447,
0.006457366514950991,
-0.06832034140825272,
0.033859893679618835,
0.043351806700229645,
-0.03267977759242058,
-0.015856850892305374,
0.0506804883480072,
0.005891312845051289,
0.007555900141596794,
-0.02381533943116665,
-0.017391663044691086,
0.014488514512777328,
0.013493359088897705,
0.0260301660746336,
-0.035816896706819534,
0.017524104565382004,
0.023211369290947914,
-0.012095971032977104,
0.006593689322471619,
0.0395486019551754,
-0.023746822029352188,
-0.006545830983668566,
0.006216331850737333,
0.017636459320783615,
0.02728532999753952,
-0.050753846764564514,
-0.00807445403188467,
-0.023959839716553688,
0.0004374768177513033,
-0.014829599298536777,
-0.05090118199586868,
0.012747623957693577,
0.03518931567668915,
-0.03126339986920357,
0.025453371927142143,
-0.004683929495513439,
-0.010606328025460243,
0.04045628383755684,
-0.05153433978557587,
0.02117793634533882,
0.009442118927836418,
0.04110916703939438,
-0.029590830206871033,
-0.040823809802532196,
0.023227758705615997,
0.0027595467399805784,
0.028458792716264725,
-0.008033348247408867,
-0.008708804845809937,
0.03581113740801811,
-0.007182739675045013,
0.008252688683569431,
0.004194529727101326,
-0.012101909145712852,
-0.036075007170438766,
0.028758611530065536,
-0.005922311916947365,
-0.008485926315188408,
-0.00798051431775093,
0.010786768980324268,
0.03844209760427475,
-0.022943608462810516,
-0.03184053301811218,
-0.017866171896457672,
-0.08862089365720749,
0.05799412354826927,
0.004813453182578087,
0.020671779289841652,
0.05367499962449074,
-0.01090127695351839,
0.05527440086007118,
-0.027441075071692467,
-0.02857762947678566,
-0.011594780720770359,
0.03064403496682644,
-0.06001731753349304,
-0.03822720795869827,
0.0004199219401925802,
0.008452902548015118,
0.0037372123915702105,
-0.03899135813117027,
0.015314589254558086,
0.05248906463384628,
-0.020627008751034737,
-0.02882308140397072,
0.0792754516005516,
0.023612432181835175,
0.05953742936253548,
0.010137566365301609,
-0.0047994814813137054,
0.004499605856835842,
0.014322280883789062,
0.0014899004017934203,
0.039237357676029205,
0.0019177529029548168,
0.023567406460642815,
0.03050961345434189,
-0.008718051016330719,
-0.048354532569646835,
0.036297984421253204,
0.013403266668319702,
0.04905681684613228,
-0.013878394849598408,
-0.009239856153726578,
0.026882965117692947,
-0.023287197574973106,
0.043103259056806564,
-0.014363237656652927,
-0.02658219262957573,
0.08116593956947327,
-0.022282421588897705,
0.017867546528577805,
-0.06377311050891876,
-0.0079538868740201,
0.0007276411633938551,
-0.0005707662203349173,
0.010300512425601482,
0.0823962613940239,
-0.04357895627617836,
0.016870763152837753,
-0.02488459274172783,
0.037340350449085236,
-0.002019433304667473,
-0.05242438241839409,
0.011726908385753632,
-0.013528827577829361,
-0.012855340726673603,
0.02089609019458294,
-0.03774857148528099,
-0.027759063988924026,
-0.007168593350797892,
-0.022378332912921906,
0.028461528941988945,
0.014898229390382767,
-0.016335824504494667,
-0.023449402302503586,
-0.032284073531627655,
0.039867233484983444,
-0.022897208109498024,
0.02015712484717369,
-0.02310960926115513,
0.008557428605854511,
-0.006700502242892981,
-0.009962256997823715
] |
<p>This problem is puzzling me.</p>
<p>Scenario 1:
A certain sphere is having an innelastic collision with a plane of a very large mass. Let the angle between the sphere's velocity and the surface be 90 degrees. The escape angle will be the same as the incident angle, therefore the sphere velocity will be 90 degrees from it's origin.</p>
<p>Scenario 2:
The same as above, but now the ball is static, and the surface is moving towards the sphere with the same speed.</p>
<p>I was expecting exactly the same result, since on my mind (and obviously wrong), the speeds were relative. The sphere in scenario 2 leaves the collision plane on a trajectory normal to the surface.
Note that I mention speed, because I have a gut feeling that the problem I'm having is with summing up the vectors.</p>
<p>I'm having problems visualizing and coming up with an intuitive explanation for why.</p>
| 8,437 |
[
-0.06868820637464523,
-0.037052299827337265,
-0.0526781789958477,
0.015696736052632332,
0.008246738463640213,
-0.009101097472012043,
-0.008338491432368755,
0.028052518144249916,
0.017085561528801918,
-0.002407369902357459,
-0.0007513365708291531,
0.06351309269666672,
0.07182475924491882,
0.01109378132969141,
0.027675261721014977,
-0.0006488797371275723,
-0.026498762890696526,
-0.007542716339230537,
0.010547012090682983,
-0.03144353628158569,
-0.024512531235814095,
-0.008684763684868813,
0.054812148213386536,
-0.032654523849487305,
0.023271581158041954,
0.04065970331430435,
0.026726169511675835,
-0.023187171667814255,
0.019105400890111923,
0.035113394260406494,
-0.0006527185905724764,
0.0009911733213812113,
0.010953843593597412,
0.0034260975662618876,
-0.008859452791512012,
0.03464873135089874,
-0.01221927348524332,
0.008772114291787148,
0.00152197212446481,
0.010631382465362549,
-0.041823212057352066,
-0.0029562462586909533,
-0.04034411534667015,
0.07346124947071075,
-0.05664607882499695,
0.023007012903690338,
0.005946346092969179,
0.013137073256075382,
0.06581443548202515,
-0.05403362214565277,
0.06957408785820007,
0.0077998340129852295,
0.028411196544766426,
0.03280158340930939,
-0.0031130057759582996,
-0.008906340226531029,
0.05878384783864021,
0.04570839926600456,
-0.012711518444120884,
-0.04246585816144943,
-0.005593643523752689,
-0.036749616265296936,
-0.0637250691652298,
0.000557019142434001,
0.004258592613041401,
0.035721536725759506,
-0.017567556351423264,
-0.03322024270892143,
0.00029833108419552445,
-0.026038775220513344,
-0.011092753149569035,
0.02803761512041092,
0.029572613537311554,
-0.07383030652999878,
0.03173064813017845,
-0.010424827225506306,
0.049123331904411316,
0.023921603336930275,
0.016565879806876183,
0.04815499484539032,
0.009603912942111492,
-0.0029750054236501455,
0.0903753861784935,
0.0649113655090332,
0.022748170420527458,
0.009042546153068542,
0.0358855240046978,
-0.00023429076827596873,
0.043806370347738266,
0.05904465913772583,
0.009026367217302322,
-0.009357286617159843,
0.02905823476612568,
0.0003516922297421843,
-0.021390145644545555,
0.037310514599084854,
-0.0013349674409255385,
0.06440595537424088,
0.011937093921005726,
-0.026986882090568542,
-0.04954688623547554,
-0.012670728377997875,
-0.006876373663544655,
0.05813762545585632,
0.024418188259005547,
0.026289308443665504,
-0.07944504171609879,
0.020720819011330605,
-0.029369447380304337,
-0.005291251931339502,
-0.043607816100120544,
0.03447791188955307,
-0.028908466920256615,
-0.008854036219418049,
-0.00448507210239768,
-0.034211765974760056,
-0.012328911572694778,
-0.004547633230686188,
0.03044816292822361,
0.037690527737140656,
0.05139382183551788,
-0.013080212287604809,
0.016377249732613564,
0.013972554355859756,
-0.020820554345846176,
0.0004878896870650351,
0.03391515836119652,
-0.01829257421195507,
-0.02810131199657917,
0.013064351864159107,
0.024649402126669884,
-0.029353652149438858,
-0.01449486892670393,
0.0016776766860857606,
0.008787003345787525,
-0.04268547520041466,
-0.07726873457431793,
-0.07900548726320267,
0.04467252269387245,
-0.01590980589389801,
-0.008508958853781223,
-0.0846630334854126,
-0.02255220338702202,
0.03645867109298706,
0.08175494521856308,
-0.022884618490934372,
0.015696652233600616,
-0.005739984102547169,
0.04863975942134857,
0.0099701639264822,
-0.006483534816652536,
-0.012185781262814999,
0.0036029352340847254,
-0.043819308280944824,
-0.00608587171882391,
-0.03902025893330574,
0.01438184455037117,
0.02640374004840851,
-0.0026871603913605213,
-0.032361146062612534,
0.031131772324442863,
-0.01626547798514366,
0.02460702881217003,
-0.0030495801474899054,
0.02725278027355671,
-0.020536912605166435,
0.042011890560388565,
0.014378758147358894,
-0.024878909811377525,
0.030801190063357353,
-0.0007109708967618644,
0.062033481895923615,
-0.008729975670576096,
0.02548404224216938,
0.052067067474126816,
-0.013298186473548412,
0.017231410369277,
-0.038547903299331665,
0.0020939966198056936,
0.002455751644447446,
0.0017375971656292677,
-0.058825310319662094,
0.02085721306502819,
-0.026918210089206696,
0.002706975443288684,
0.05205508694052696,
-0.003940918017178774,
-0.01289537362754345,
-0.01706213317811489,
0.019355859607458115,
-0.011203482747077942,
-0.07972761243581772,
0.05559861660003662,
0.002911857794970274,
-0.00961387436836958,
0.04394334927201271,
0.040027376264333725,
0.04491141065955162,
0.0020908282604068518,
-0.0005885019199922681,
-0.00664904760196805,
0.023454967886209488,
0.02005392126739025,
-0.01092459075152874,
-0.0049375747330486774,
0.05074673146009445,
0.06391705572605133,
0.018007908016443253,
-0.0015338835073634982,
-0.009950283914804459,
0.0012970012612640858,
-0.004084976390004158,
-0.013229596428573132,
0.0052675362676382065,
0.03040836565196514,
0.028063951060175896,
0.0052518839947879314,
0.01372557133436203,
-0.01541735976934433,
0.007478824816644192,
-0.05623665452003479,
0.08089425414800644,
0.04733125865459442,
0.006085292901843786,
-0.023695701733231544,
0.043394461274147034,
0.010941419750452042,
-0.007945098914206028,
0.01636592485010624,
-0.018767772242426872,
0.0032916644122451544,
0.012187602929770947,
0.005324673373252153,
0.03481738269329071,
-0.06835814565420151,
-0.007050563581287861,
0.0173869077116251,
0.02808605320751667,
0.028286950662732124,
0.04896404221653938,
0.009167815558612347,
-0.042054589837789536,
0.0483907014131546,
-0.0009167079697363079,
-0.009843941777944565,
-0.01580057106912136,
0.04849855601787567,
0.011230125091969967,
-0.0008798294584266841,
-0.007710509467869997,
-0.041648879647254944,
-0.0036027776077389717,
0.011728865094482899,
0.022807104513049126,
-0.011794096790254116,
0.00863438006490469,
0.011555304750800133,
0.0002806580741889775,
0.02473492920398712,
0.0339057557284832,
0.011306235566735268,
-0.012139730155467987,
-0.05908558890223503,
0.024905994534492493,
0.022926950827240944,
-0.010103682987391949,
0.015064900740981102,
0.023541796952486038,
0.030043555423617363,
-0.04235514625906944,
-0.0013930557761341333,
-0.004527000244706869,
-0.02520126663148403,
0.0002525451418478042,
0.007615531794726849,
0.0122791463509202,
0.023969508707523346,
0.028314145281910896,
-0.011854078620672226,
-0.05060809478163719,
0.01166192814707756,
-0.00989813357591629,
-0.008183886297047138,
0.02552984096109867,
-0.05078454688191414,
0.03350457921624184,
-0.058165404945611954,
-0.03437592089176178,
0.05143441632390022,
-0.014612830244004726,
-0.002215895801782608,
0.06850083917379379,
-0.0009240613435395062,
-0.05838572606444359,
-0.0012212926521897316,
-0.03360819071531296,
0.003122346242889762,
-0.028735723346471786,
0.01893971860408783,
0.03831186518073082,
-0.009342128410935402,
-0.030593689531087875,
0.0002303728979313746,
-0.022301143035292625,
-0.04765862599015236,
-0.027436017990112305,
-0.019976181909441948,
0.020599953830242157,
-0.010270290076732635,
-0.029663873836398125,
0.005086097400635481,
-0.04180077835917473,
-0.005916086956858635,
-0.04007076844573021,
-0.05672657489776611,
-0.017429867759346962,
-0.0028648509178310633,
0.04650747776031494,
0.004204295109957457,
-0.02178921177983284,
0.06205350533127785,
0.013700656592845917,
-0.015689130872488022,
-0.03948304057121277,
-0.0013693799264729023,
0.0002933394571300596,
-0.034844983369112015,
0.011729396879673004,
0.0208817757666111,
-0.02202547714114189,
0.02680477313697338,
0.0006821912829764187,
0.010190070606768131,
0.05774608999490738,
0.002316130790859461,
0.015806080773472786,
0.013004020787775517,
0.014411400072276592,
-0.006423877086490393,
0.019818978384137154,
-0.008128914050757885,
-0.051805056631565094,
0.003529095323756337,
0.04094866290688515,
0.06294471025466919,
0.027857348322868347,
-0.053009964525699615,
0.05449869856238365,
-0.02352098561823368,
0.021303435787558556,
-0.02464771643280983,
0.013210393488407135,
-0.004715587943792343,
-0.00012905705079901963,
-0.024344071745872498,
0.012240534648299217,
0.047066666185855865,
-0.047961924225091934,
0.0037079420872032642,
0.03160826489329338,
0.043531399220228195,
-0.028530968353152275,
-0.03400563821196556,
-0.03769771382212639,
0.008845088072121143,
0.0405324324965477,
-0.019404316321015358,
0.005491537041962147,
0.008580413646996021,
0.012419664300978184,
-0.0006799112306907773,
0.0229949988424778,
-0.03467853367328644,
0.016193203628063202,
-0.07342901825904846,
-0.0016938020708039403,
-0.021725943312048912,
0.045292969793081284,
-0.019865546375513077,
0.02522423304617405,
0.05550774931907654,
0.05410299077630043,
-0.0019016417209059,
-0.024632735177874565,
-0.0847025141119957,
0.035366471856832504,
-0.013230481185019016,
-0.04687345400452614,
-0.020741473883390427,
-0.016546202823519707,
-0.05117103457450867,
-0.0386824905872345,
0.0013881039340049028,
0.03997139632701874,
-0.0022249361500144005,
-0.059896595776081085,
0.025744253769516945,
-0.03460218012332916,
-0.04816807061433792,
-0.003338330192491412,
0.05607665702700615,
0.014856438152492046,
-0.01796925812959671,
0.041790250688791275,
0.05385463684797287,
-0.05963890999555588,
0.011372208595275879,
-0.03416437655687332,
0.02326418086886406,
-0.0031163052190095186,
0.024482361972332,
0.01897193305194378,
0.03012092225253582,
0.02535036951303482,
0.02010367251932621,
-0.015714285895228386,
0.01893596164882183,
0.0138996047899127,
0.005088040139526129,
-0.030917994678020477,
-0.09447484463453293,
-0.019974131137132645,
-0.034366264939308167,
0.03527778387069702,
-0.005536169279366732,
-0.021730784326791763,
0.026488713920116425,
0.02336183376610279,
0.014559485949575901,
0.013992843218147755,
0.03186291083693504,
0.013563044369220734,
0.02310323342680931,
-0.06655804067850113,
-0.028745152056217194,
-0.021195517852902412,
-0.030437029898166656,
0.040978893637657166,
-0.020302630960941315,
-0.025574849918484688,
-0.021783899515867233,
0.022388502955436707,
0.0017190788639709353,
-0.002648521214723587,
-0.010501970537006855,
-0.046131253242492676,
0.0140838623046875,
-0.01146478671580553,
-0.01310945674777031,
0.010447531007230282,
0.04572761058807373,
0.04331333935260773,
-0.00620377017185092,
0.00469606090337038,
-0.06243307143449783,
-0.025835052132606506,
0.00866791419684887,
0.03684619069099426,
-0.011053750291466713,
-0.016786973923444748,
-0.039284445345401764,
0.0035434593446552753,
0.028381535783410072,
-0.02108336240053177,
0.024539699777960777,
-0.01622014492750168,
0.00897041242569685,
-0.002061000093817711,
-0.0181866642087698,
-0.053640883415937424,
0.010730180889368057,
-0.01606936752796173,
0.021826710551977158,
-0.03207841143012047,
0.006212855689227581,
-0.019024387001991272,
-0.0010057908948510885,
0.014462503604590893,
0.02830437384545803,
0.017619740217924118,
-0.006924197543412447,
-0.0066875577904284,
0.013900681398808956,
-0.037073761224746704,
-0.055739276111125946,
0.0021046679466962814,
-0.01423587091267109,
-0.01975266821682453,
0.024772966280579567,
-0.03858237713575363,
0.004354717675596476,
0.027861926704645157,
0.0014998861588537693,
0.024789076298475266,
0.0010335012339055538,
0.0026170939672738314,
0.018932471051812172,
0.031121060252189636,
-0.005782119929790497,
-0.0032597011886537075,
-0.00900124292820692,
-0.009708164259791374,
-0.010221416130661964,
-0.026206230744719505,
0.02661081962287426,
0.000775351538322866,
-0.03178628534078598,
-0.032030027359724045,
0.003496781922876835,
-0.0005500686238519847,
0.02162444032728672,
0.01487853191792965,
0.0125116016715765,
-0.04452667012810707,
-0.02936069294810295,
-0.010403968393802643,
0.04409703612327576,
0.008547656238079071,
0.003216684330254793,
0.008247238583862782,
0.021497780457139015,
-0.008862330578267574,
-0.014881286770105362,
0.007854240946471691,
-0.004023687914013863,
-0.0010414507705718279,
0.025929005816578865,
0.01553222257643938,
0.043140459805727005,
-0.021795880049467087,
-0.008867251686751842,
0.0001816285657696426,
-0.0954248234629631,
0.0423661507666111,
-0.012600299902260303,
-0.00016903375217225403,
0.03536507114768028,
-0.057467665523290634,
-0.00030575040727853775,
0.00757179968059063,
-0.01965349353849888,
0.024888698011636734,
-0.060460224747657776,
-0.004952342249453068,
0.025054804980754852,
0.018071020022034645,
-0.06176793575286865,
-0.04509195312857628,
0.016743911430239677,
0.03174712881445885,
-0.044543031603097916,
-0.05028298869729042,
-0.02550595998764038,
-0.025124184787273407,
-0.016638420522212982,
0.005671559367328882,
0.048869866877794266,
-0.02297256514430046,
-0.05348619446158409,
0.02542232722043991,
0.007617331109941006,
0.047776076942682266,
-0.035741254687309265,
0.004605291876941919,
0.024509981274604797,
-0.006664135493338108,
-0.034366391599178314,
-0.010956999845802784,
0.07938492298126221,
-0.026280950754880905,
-0.03005940653383732,
-0.00040246814023703337,
-0.04858843982219696,
0.020874997600913048,
-0.03725998476147652,
0.02594178542494774,
0.011861061677336693,
0.01496477983891964,
0.0025944032240659,
-0.002475591143593192,
-0.013828935101628304,
-0.004229959566146135,
0.04922061413526535,
-0.00921586249023676,
-0.005845438688993454,
0.0012741244863718748,
-0.03640379384160042,
0.029577113687992096,
0.022184953093528748,
0.028884513303637505,
-0.00272282469086349,
0.037014175206422806,
-0.014758586883544922,
-0.014756935648620129,
-0.008721728809177876,
0.012274176813662052,
0.056715164333581924,
-0.020588373765349388,
-0.033811088651418686,
0.030033206567168236,
0.018233811482787132,
-0.024234728887677193,
-0.014447537250816822,
-0.05963464453816414,
0.035932719707489014,
0.0635179951786995,
-0.02682630345225334,
0.08476525545120239,
0.025856617838144302,
0.04409768804907799,
-0.01220414787530899,
-0.02809019200503826,
-0.0013941224897280335,
-0.019858919084072113,
0.009057839401066303,
0.009672335349023342,
-0.026766708120703697,
0.015158592723309994,
0.0016986895352602005,
0.041095346212387085,
-0.006695055402815342,
0.009117651730775833,
-0.005374771077185869,
-0.0074837119318544865,
0.052886951714754105,
0.02882259711623192,
-0.01824631169438362,
0.023696282878518105,
-0.003241021651774645,
0.05905991420149803,
-0.031666699796915054,
-0.04073704779148102,
0.07076416164636612,
0.04140004888176918,
-0.029450874775648117,
-0.04740006849169731,
-0.009305139072239399,
-0.007249089889228344,
-0.011950393207371235,
0.0195529256016016,
0.0007672618958167732,
-0.007023843005299568,
0.010430477559566498,
0.03045748546719551,
0.001368560129776597,
0.025052674114704132,
-0.04987899586558342,
-0.045080747455358505,
-0.04367237910628319,
-0.06361705809831619,
-0.022649867460131645,
0.01889055222272873,
0.012073208577930927,
0.0055973948910832405,
0.02554387040436268,
-0.052188824862241745,
0.006497226655483246,
-0.022890035063028336,
0.024919528514146805,
-0.02377874031662941,
0.0637485459446907,
0.009965159930288792,
0.014063985086977482,
-0.03427496924996376,
-0.017194245010614395,
0.0959855318069458,
0.06463341414928436,
-0.00846562534570694,
-0.030986666679382324,
0.016826018691062927,
-0.02350892871618271,
0.0002053643111139536,
-0.030792318284511566,
0.0073570446111261845,
0.039785683155059814,
0.010730392299592495,
0.032800767570734024,
0.06501919776201248,
0.0034927877131849527,
-0.007320130243897438,
0.025853173807263374,
-0.04120204970240593,
-0.025040216743946075,
-0.019053610041737556,
0.010659744963049889,
0.007543312385678291,
0.02211754024028778,
-0.019441187381744385,
0.04747671261429787,
-0.04400238022208214,
-0.012971460819244385,
-0.03704272583127022,
-0.028699593618512154,
-0.004874181468039751,
0.033786527812480927,
-0.05259554460644722,
0.03474809229373932,
0.012530087493360043,
-0.005594526417553425,
-0.042038071900606155,
0.030003739520907402,
0.03685459494590759,
-0.01868053525686264,
0.013775921426713467,
0.03009706363081932,
0.03431390970945358,
0.02959389053285122,
0.01062091626226902,
0.0056755985133349895,
-0.05163111537694931,
0.01578817516565323,
-0.05359119921922684,
0.08692332357168198,
-0.01776246353983879,
0.03319405019283295,
-0.02504492551088333,
0.005615048576146364,
0.02705060876905918,
-0.08333462476730347,
0.016789985820651054,
-0.03839739039540291,
0.029317358508706093,
0.02383177913725376,
0.01875554770231247,
-0.03164536505937576,
0.030962221324443817,
0.04239816218614578,
-0.004149722401052713,
0.0003031929663848132,
-0.005188493989408016,
-0.009899267926812172,
-0.021379925310611725,
0.06999780982732773,
-0.028704436495900154,
-0.042234428226947784,
-0.0051724608056247234,
-0.0032550091855227947,
-0.03880532085895538,
-0.0062992325983941555,
-0.003346398239955306,
0.024093424901366234,
0.022319257259368896,
0.009905370883643627,
-0.01247915904968977,
0.006169527303427458,
-0.052847396582365036,
0.004669338930398226,
-0.025583390146493912,
-0.0000594956218264997,
-0.04067600890994072,
-0.0016083980444818735,
0.001912086270749569,
0.02117214910686016,
-0.038209304213523865,
-0.0019318345002830029,
0.013302438892424107,
0.04488232359290123,
-0.014755980111658573,
0.005554854404181242,
-0.04823794960975647,
0.013281118124723434,
0.0019721088465303183,
0.022341638803482056,
-0.03147551789879799,
0.07130640000104904,
-0.007582678459584713,
0.009699944406747818,
0.0403224341571331,
0.021169790998101234,
-0.014911457896232605,
0.024075018242001534,
0.002424343256279826,
-0.020070265978574753,
-0.01965591125190258,
0.023268185555934906,
-0.00480413343757391,
-0.0011364133097231388,
0.021138537675142288,
-0.01581280678510666,
-0.01227855496108532,
-0.02863232046365738,
0.044186901301145554,
-0.039353903383016586,
0.020062437281012535,
-0.022952469065785408,
0.04185248166322708,
-0.018751246854662895,
-0.006800041999667883,
-0.04664333164691925,
0.0074353390373289585,
0.024989861994981766,
-0.006946314591914415,
-0.0372883565723896,
0.04405687749385834,
-0.04531331732869148,
-0.0037193584721535444,
0.0040742456912994385,
0.014525622129440308,
0.006464862264692783,
-0.014227197505533695,
0.007662682794034481,
-0.018961017951369286,
0.05713103711605072,
-0.02797960862517357,
-0.01773769222199917,
0.04542500898241997,
0.0014062791597098112,
-0.02975747548043728,
0.034853268414735794,
0.03689964860677719,
0.04836149141192436,
0.013417375274002552,
-0.017360003665089607,
-0.04086688533425331,
0.08655645698308945,
-0.015270554460585117,
-0.018656333908438683,
0.009307360276579857,
-0.03560219705104828,
-0.04343457147479057,
-0.04381179437041283,
0.035618580877780914,
-0.02882680483162403,
0.014352800324559212,
-0.005835925228893757,
-0.0070984577760100365,
-0.040250733494758606,
0.026032090187072754,
-0.02488788217306137,
-0.02010408043861389,
-0.02141183242201805,
0.03631008416414261,
-0.007033689878880978,
0.04767826572060585,
0.07246576994657516,
-0.016417140141129494,
-0.007574712857604027,
0.01988348364830017,
-0.012105748057365417,
-0.060242198407649994,
0.011637549847364426,
0.007549632340669632,
0.0027069919742643833,
0.030789097771048546,
-0.07209606468677521,
0.009201924316585064,
0.05513427034020424,
-0.09452180564403534,
0.014437268488109112,
-0.033325791358947754,
-0.028399623930454254,
-0.04858839139342308,
-0.021369334310293198,
0.030832407996058464,
0.022751400247216225,
0.021198229864239693,
0.02627224288880825,
0.05449961498379707,
-0.011317447759211063,
-0.014660855755209923,
-0.05443344637751579,
-0.01649935357272625,
0.01871686987578869,
-0.003528366796672344,
0.02256125956773758,
0.040338803082704544,
0.009372892789542675,
-0.022674299776554108,
-0.0018333438783884048,
-0.02512897178530693,
0.012087599374353886,
0.018815593793988228,
0.040438588708639145,
0.02790641412138939,
0.001102945301681757,
-0.0047474694438278675,
-0.0019921406637877226,
-0.0164838545024395,
-0.0036684442311525345,
0.04190826043486595,
-0.0030914193484932184,
-0.046978745609521866,
-0.010323924012482166,
0.032368388026952744,
-0.026971839368343353,
-0.0017496574437245727,
-0.007740444503724575,
-0.02900196611881256,
-0.03202608972787857,
-0.015977444127202034,
0.01698097586631775,
0.03686369210481644,
-0.027450261637568474,
0.01671680621802807,
-0.04692848399281502,
-0.006007643882185221,
0.03332620859146118,
0.0024401568807661533,
-0.007371748331934214,
0.019375545904040337,
-0.020766155794262886,
-0.010755953378975391,
-0.03170960769057274,
-0.006819927133619785,
0.020641323179006577,
-0.05711747705936432,
-0.04200070723891258,
0.02354210801422596,
-0.024771640077233315,
-0.01624767668545246,
-0.026172980666160583,
-0.01534492988139391,
0.017502497881650925,
0.009472995065152645,
0.01998470537364483,
-0.003385094925761223,
-0.03980004042387009,
-0.029705865308642387,
-0.07518365979194641,
0.015606521628797054,
0.024868151172995567,
-0.048991214483976364,
-0.0175432488322258,
-0.026789935305714607,
0.028704987838864326,
0.03046559914946556,
0.06027038395404816,
-0.03183623030781746,
-0.012870614416897297,
0.02330140769481659,
-0.025503698736429214,
0.041619036346673965,
-0.017443746328353882,
-0.001385976909659803,
-0.02023952081799507,
-0.01664988324046135,
0.04315977916121483,
0.024336781352758408,
-0.00045527314068749547,
0.005448422860354185,
-0.001635833759792149,
-0.016982359811663628,
0.005075962282717228,
0.013716106303036213,
-0.05801834166049957,
0.02514917217195034,
0.029281513765454292,
0.006735296919941902,
0.06957536935806274,
0.008599229156970978,
0.007194880396127701,
0.04131148010492325,
-0.060699839144945145,
-0.03672073036432266,
0.05818832665681839,
-0.016448084264993668,
-0.03140305355191231,
-0.0415816605091095,
0.00845924112945795,
0.024018729105591774,
-0.07803270220756531,
0.0016621735412627459,
0.016364872455596924,
-0.02501499466598034,
-0.035564083606004715,
0.0614948645234108,
0.0282943956553936,
0.021525518968701363,
0.008732147514820099,
0.055630382150411606,
0.014534788206219673,
-0.022291826084256172,
0.013410250656306744,
0.060806673020124435,
0.025334585458040237,
0.0061238911002874374,
-0.0034873471595346928,
0.03283348307013512,
-0.025507038459181786,
0.014131367206573486,
-0.005357866641134024,
0.03617491200566292,
-0.004148798529058695,
-0.00200563482940197,
-0.02081841230392456,
-0.013638424687087536,
0.016582118347287178,
0.00923940446227789,
0.008923234418034554,
0.030355216935276985,
-0.03510221838951111,
0.0027609344106167555,
0.009065413847565651,
0.019760506227612495,
-0.0471675768494606,
-0.014617863111197948,
-0.0006540237809531391,
0.022948602214455605,
0.006523676682263613,
-0.05116678401827812,
-0.012301179580390453,
0.004880669992417097,
0.030674269422888756,
0.018479403108358383,
0.028384871780872345,
-0.02398161217570305,
-0.004987322259694338,
0.0031087861862033606,
-0.02597624994814396,
-0.022021034732460976,
0.006592737045139074,
0.03461427614092827,
0.056662317365407944,
0.020634807646274567,
0.009766180999577045,
-0.014202723279595375,
-0.019880328327417374,
0.04595620930194855,
-0.081386499106884,
-0.006321786902844906,
-0.030019477009773254,
0.05059247091412544,
0.013783255591988564,
0.005763698369264603
] |
<p>This must be the first question everyone asks when starting to study field theory at finite density and zero temperature. </p>
<p>To introduce a finite density one adds a Lagrange multiplier which fixes the number of particles in a non-relativistic field theory or the number of particles minus the number of antiparticles in a relativistic field theories. To be concrete, in a non-relativistic field theory one has the Lagrangian density:
$$\mathcal L=i\psi ^*\partial _t \psi -{1\over 2m}\nabla\psi ^*\nabla\psi - V[\psi ^*\psi]$$
and then the same theory at finite density is described by:
$$\mathcal L=i\psi ^*\partial _t \psi -{1\over 2m}\nabla\psi ^*\nabla\psi - V[\psi ^*\psi]+\mu \psi ^*\psi \,\,\,\,\,\,\,\, [1]$$
where $\mu$ is the chemical potential and the number of particles is $N=\int \psi ^*\psi$.</p>
<p>What disturbs me is that one may redefine the field:
$$\chi\equiv e^{-i\mu t}\psi$$</p>
<p>with $t$ the time. And after replacing in [1]:</p>
<p>$$\mathcal L=i\chi ^*\partial _t \chi -{1\over 2m}\nabla\chi ^*\nabla\chi - V[\chi ^*\chi]$$
The "finite density term" disappears. Moreover, the path integral measure is invariant under this trivial field redefinition so that the finite density QFT seems equivalent to the zero density one. (Those who are familiarized with the non-relativistic limit of relativistic equation —such as Klein-Gordon or Dirac— will recognize this term and field redefinition.)</p>
<p>Something similar happens in the relativistic case. </p>
<p>What am I overlooking? </p>
<p>(Note that the theory is at zero temperature so I am in real time formalism and I don't have to impose periodic boundary conditions (I think). I am interested in time evolution, scattering, etc.)</p>
<p><strong>Reply to Ron's answer:</strong></p>
<p>(I here will overlook Thomas' comments, I will answer him tomorrow.)</p>
<p>Ron makes an interesting point, but I think his answer is not correct. The Hamiltonian density of the theory in the original fields is:$$\mathcal H={1\over 2m}\nabla\psi ^*\nabla\psi + V[\psi ^*\psi]-\mu \psi ^*\psi $$
What he correctly pointed out is that the Hamiltonian in the new fields is not just the previous Hamiltonian written in the new fields. This is right and in classical mechanics it is well-know that one has to add a piece to the Hamiltonian when one makes an explicit time dependent transformation. He pointed out the case of quantum mechanics, and the field theoretic version is:
$$i\partial _t \, \chi =i\partial _t \, (e^{-i\mu t}\psi )=i(-i) \mu \, e^{-i\mu t}\psi + e^{-i\mu t}[\psi , H]=[e^{-i\mu t}\psi ,\, \mu N + H] $$
And therefore the Hamiltonian for the field $\chi$ is:
$$H'=\mu N + H=\int {1\over 2m}\nabla\chi ^*\nabla\chi + V[\chi ^*\chi]$$
This is of course the Hamiltonian corresponding to the Lagrangian written in terms of $\chi$. In this way, one sees how the "standard" theory (without the $\mu$ term) is recovered in the Hamiltonian formalism as it was in path integral formalism. And this makes a lot of sense because the theory with $\mu = -m$ has to be equivalent to the theory with $\mu=0$ because we are just subtracting the rest energy.</p>
<p>Of course, this is true as long as one does not impose periodic boundary conditions. </p>
| 8,438 |
[
0.006452248431742191,
0.011131197214126587,
0.029452765360474586,
-0.03522615134716034,
0.022605180740356445,
0.015889091417193413,
-0.04871963709592819,
-0.04290159419178963,
-0.008580376394093037,
-0.021795758977532387,
0.024458836764097214,
0.007461907342076302,
0.055335912853479385,
0.010407883673906326,
0.01306493952870369,
0.012837732210755348,
-0.01508644875138998,
-0.017319699749350548,
-0.0015269170980900526,
-0.026887379586696625,
0.00278141419403255,
0.06499681621789932,
0.007525229826569557,
0.0026630577631294727,
-0.04942449927330017,
0.04626976326107979,
-0.04485499858856201,
0.006613487843424082,
-0.023862911388278008,
0.06371589004993439,
-0.009405162185430527,
-0.047392550855875015,
0.012195059098303318,
0.0003848591586574912,
0.010075136087834835,
0.032041680067777634,
-0.01885347068309784,
-0.03548330068588257,
0.020351460203528404,
-0.02491498924791813,
-0.06400598585605621,
-0.027107182890176773,
0.00017801146896090358,
0.005398573353886604,
-0.003379443194717169,
0.009916667826473713,
0.05275995284318924,
-0.02058887854218483,
0.05860576406121254,
-0.05173664912581444,
0.019300755113363266,
0.040347419679164886,
0.0408385805785656,
0.030843574553728104,
-0.008004654198884964,
-0.03628982976078987,
0.03570367023348808,
0.0665903389453888,
0.010284269228577614,
-0.0690625011920929,
-0.03417404741048813,
-0.007627478800714016,
0.01609361357986927,
-0.02632289007306099,
-0.01614874228835106,
0.031061170622706413,
0.04429972544312477,
-0.006640484090894461,
0.001722435699775815,
-0.007195000071078539,
-0.007410016376525164,
0.021615412086248398,
-0.023642495274543762,
-0.018716881051659584,
0.03197662532329559,
-0.00032607142929919064,
0.014990124851465225,
0.005176869686692953,
0.0006470473599620163,
0.03596843034029007,
-0.023671146482229233,
0.04555405676364899,
0.025557076558470726,
0.0019547841511666775,
0.017403313890099525,
-0.014272434636950493,
0.07907116413116455,
0.016093440353870392,
0.005678925197571516,
0.037434983998537064,
-0.017567923292517662,
0.029289672151207924,
0.03733828663825989,
-0.024943741038441658,
-0.0028361130971461535,
0.03649616613984108,
0.01344326976686716,
0.036583829671144485,
-0.0377558134496212,
-0.009924700483679771,
-0.04088872671127319,
-0.015287434682250023,
0.017437105998396873,
0.04584813490509987,
-0.012068078853189945,
-0.01444594468921423,
-0.04276105388998985,
-0.013187482953071594,
-0.013065175153315067,
-0.013601507991552353,
-0.04710688814520836,
0.0340111069381237,
-0.02584071271121502,
0.005149608477950096,
-0.01718728244304657,
-0.04571553319692612,
-0.0037224632687866688,
-0.015114054083824158,
0.054808780550956726,
0.08008231967687607,
0.0472751148045063,
-0.020658299326896667,
0.02117561735212803,
-0.011567066423594952,
-0.053052861243486404,
0.034133415669202805,
0.02878664806485176,
-0.003002048237249255,
-0.03248558193445206,
-0.014449826441705227,
0.019113099202513695,
0.0075100017711520195,
0.0347621813416481,
0.005818034056574106,
0.01883178949356079,
-0.03755870461463928,
-0.05399194359779358,
-0.02349812537431717,
0.05750493332743645,
-0.025512252002954483,
-0.029005445539951324,
-0.0672733411192894,
-0.019000591710209846,
0.017884818837046623,
0.09400695562362671,
-0.045345112681388855,
0.027679018676280975,
-0.0037855952978134155,
0.015159730799496174,
0.0009735106723383069,
-0.025581123307347298,
-0.017957227304577827,
-0.008374216966331005,
-0.02016596682369709,
-0.0011502268025651574,
-0.01923920400440693,
0.08255790174007416,
0.05746576189994812,
-0.0021903403103351593,
0.008371511474251747,
0.06974158436059952,
-0.01594684273004532,
0.0073819453828036785,
0.03240826725959778,
-0.015314274467527866,
-0.019506175071001053,
0.04791013151407242,
0.013236253522336483,
0.014795724302530289,
0.03349964693188667,
0.0048732636496424675,
0.020873669534921646,
0.019431354478001595,
0.0176759734749794,
0.069708913564682,
-0.028333140537142754,
0.005706080701202154,
-0.028829051181674004,
0.007701952010393143,
0.02013779990375042,
-0.019471779465675354,
0.006031487137079239,
-0.023790959268808365,
-0.0065388488583266735,
0.014881514012813568,
0.02492229826748371,
-0.019253021106123924,
-0.016648631542921066,
-0.011852371506392956,
-0.04692297801375389,
-0.042265791445970535,
-0.07732680439949036,
0.024411523714661598,
-0.010202285833656788,
-0.0023258584551513195,
0.022506242617964745,
0.020403966307640076,
-0.010172011330723763,
-0.004106119275093079,
-0.047260984778404236,
-0.00020557688549160957,
0.03645528480410576,
-0.007585921324789524,
-0.010898503474891186,
0.029629318043589592,
0.042372722178697586,
0.03493981808423996,
0.019482063129544258,
0.029453642666339874,
-0.03327703848481178,
-0.04996507614850998,
0.004681958816945553,
-0.004993482027202845,
0.05408715456724167,
-0.026137126609683037,
-0.056479617953300476,
-0.012838618829846382,
-0.016434332355856895,
-0.03992779180407524,
0.025729641318321228,
-0.017496779561042786,
0.027219705283641815,
0.04832693934440613,
0.0032755129504948854,
-0.011031988076865673,
0.03465905413031578,
-0.024039428681135178,
0.0035923763643950224,
-0.009335208684206009,
-0.016420191153883934,
-0.04106800630688667,
-0.01605319231748581,
0.058505717664957047,
0.06676942110061646,
-0.025328608229756355,
-0.0009609173284843564,
0.013124807737767696,
0.011013869196176529,
0.02101312018930912,
-0.0006688552093692124,
-0.04666993021965027,
-0.05145377665758133,
0.02333070896565914,
-0.0013531130971387029,
-0.008880749344825745,
-0.01981876976788044,
0.010839225724339485,
-0.030380472540855408,
-0.0017543265130370855,
-0.0280179250985384,
-0.06221974268555641,
0.016613489016890526,
-0.03874737396836281,
-0.0007400500471703708,
-0.00956420972943306,
-0.03369543328881264,
-0.006243717856705189,
0.005715097766369581,
0.041111163794994354,
0.02035398781299591,
-0.028306497260928154,
-0.017433442175388336,
-0.050368595868349075,
-0.024522531777620316,
0.035558659583330154,
-0.0020572044886648655,
0.002747174585238099,
-0.014753737486898899,
0.012623894028365612,
-0.019818073138594627,
-0.026259640231728554,
-0.002326423302292824,
-0.002691863803192973,
-0.009516675025224686,
0.0353391095995903,
0.035703130066394806,
-0.0022721567656844854,
-0.008603885769844055,
-0.01912541501224041,
-0.016154447570443153,
0.03207101300358772,
-0.007464038673788309,
0.025840604677796364,
0.06032935157418251,
-0.06056641414761543,
-0.011559355072677135,
-0.06584218889474869,
-0.07312766462564468,
0.027514532208442688,
0.019525153562426567,
0.03872019797563553,
0.02187890000641346,
-0.02149849385023117,
-0.061057593673467636,
-0.002883646637201309,
-0.010637744329869747,
-0.019510233774781227,
-0.02020280621945858,
0.018939625471830368,
0.029724562540650368,
0.0012957460712641478,
-0.0707654282450676,
0.006492357701063156,
-0.029285535216331482,
-0.036004938185214996,
-0.018125051632523537,
-0.01778835617005825,
0.03402308374643326,
-0.03161001205444336,
0.045456595718860626,
0.03380662947893143,
-0.05117408558726311,
0.0025606087874621153,
-0.050223227590322495,
-0.011210942640900612,
0.009385218843817711,
0.0058496915735304356,
0.02014215663075447,
0.03126388415694237,
-0.022925347089767456,
0.06563341617584229,
0.05118720233440399,
-0.012102802284061909,
-0.027843564748764038,
-0.005961715243756771,
-0.011778249405324459,
-0.030750064179301262,
-0.00817503035068512,
-0.007046990562230349,
-0.01721574366092682,
0.009746191091835499,
0.0025215090718120337,
0.01583293452858925,
0.011468678712844849,
0.01965055800974369,
0.018033519387245178,
0.027105940505862236,
0.0124960383400321,
0.009571980684995651,
0.042398758232593536,
-0.0032642087899148464,
-0.0002745042147580534,
-0.02284606546163559,
0.011987689882516861,
0.01999114267528057,
0.017037345096468925,
-0.0223554540425539,
0.08450739830732346,
0.023075785487890244,
0.016933729872107506,
-0.044865671545267105,
0.020496010780334473,
-0.018578309565782547,
-0.027885284274816513,
-0.00502695282921195,
-0.002087936270982027,
-0.01614469476044178,
-0.036685291677713394,
-0.006232780870050192,
-0.024738354608416557,
0.026624422520399094,
-0.037615664303302765,
-0.03143223002552986,
-0.01227391418069601,
-0.014856983907520771,
0.01575470343232155,
-0.029585305601358414,
-0.037007417529821396,
0.026608342304825783,
0.04194650426506996,
0.010724527761340141,
-0.025867925956845284,
-0.013109260238707066,
-0.009225625544786453,
-0.02933982014656067,
-0.04735416918992996,
-0.012556859292089939,
0.058660972863435745,
0.038193926215171814,
0.014158602803945541,
0.005908683408051729,
-0.0020720097236335278,
-0.003907766658812761,
0.0173263531178236,
-0.0748426541686058,
-0.0014508274616673589,
-0.022189993411302567,
-0.009341094642877579,
-0.019997425377368927,
-0.006639198400080204,
0.006782038137316704,
-0.03280617296695709,
-0.027230355888605118,
-0.02247956022620201,
0.007922348566353321,
-0.02197742648422718,
0.024980254471302032,
-0.030558021739125252,
-0.022342108190059662,
-0.050721269100904465,
0.050426386296749115,
0.05332288146018982,
0.005924939177930355,
0.030743323266506195,
0.024021480232477188,
-0.020232440903782845,
-0.005143740214407444,
-0.0274265818297863,
0.014498735778033733,
0.04429057985544205,
0.012504283338785172,
0.0230882428586483,
0.000015707057173131034,
-0.04445028305053711,
0.010746032930910587,
0.029340211302042007,
0.03689352050423622,
0.00999873224645853,
-0.0019871981348842382,
0.03769095987081528,
-0.060362692922353745,
-0.015456123277544975,
0.017972609028220177,
0.07876459509134293,
0.01520464476197958,
0.0018650323618203402,
0.04084421694278717,
0.007059391587972641,
0.004202126059681177,
0.02632078342139721,
0.016115140169858932,
-0.018520984798669815,
0.0019279816187918186,
-0.015075111761689186,
0.021023036912083626,
-0.025797614827752113,
0.04374683275818825,
-0.010011889971792698,
0.02428261935710907,
0.011335891671478748,
0.007952174171805382,
0.005827134475111961,
0.02191942185163498,
-0.055468931794166565,
-0.024102097377181053,
0.019316717982292175,
-0.001987670548260212,
0.02010665088891983,
-0.02787507325410843,
-0.0272282212972641,
0.06371862441301346,
0.03289703279733658,
-0.011522127315402031,
0.02170354686677456,
-0.059300076216459274,
-0.020006172358989716,
0.01583327166736126,
0.025617850944399834,
0.04027843475341797,
-0.00011408118734834716,
-0.040050651878118515,
-0.026415890082716942,
0.021327173337340355,
-0.010975160636007786,
0.007551250513643026,
-0.01736840233206749,
-0.0024531539529561996,
0.005358996335417032,
-0.05734089016914368,
-0.03192687779664993,
0.032792627811431885,
0.009191497229039669,
-0.021680839359760284,
-0.03511487692594528,
0.017055032774806023,
0.00340817729011178,
0.01224259752780199,
-0.028843045234680176,
0.027536598965525627,
-0.0074871014803647995,
0.02173246443271637,
0.023124458268284798,
0.019455257803201675,
-0.019317394122481346,
-0.07304934412240982,
-0.012502191588282585,
0.004179797135293484,
0.01349971629679203,
0.035833366215229034,
-0.02716974914073944,
-0.0743197500705719,
0.004600118845701218,
-0.012465204112231731,
-0.05036226287484169,
0.050763219594955444,
-0.0768108144402504,
0.059373337775468826,
-0.015299055725336075,
0.01789446920156479,
0.06591203808784485,
0.02137717790901661,
0.011749009601771832,
-0.017825307324528694,
-0.010230857878923416,
0.028998583555221558,
-0.04221707209944725,
0.023759035393595695,
-0.06054430082440376,
-0.016782639548182487,
-0.009301918558776379,
0.04383748769760132,
-0.029048413038253784,
0.002555666258558631,
0.011764014139771461,
-0.03454422205686569,
-0.04214033484458923,
0.01336677186191082,
-0.011263766326010227,
0.010743912309408188,
0.02575521357357502,
0.00030444114236161113,
0.038892656564712524,
-0.009235598146915436,
0.01866854727268219,
0.020088031888008118,
-0.01138457003980875,
0.043853309005498886,
-0.013422130607068539,
0.060400769114494324,
0.0031602061353623867,
-0.023420756682753563,
-0.013688314706087112,
-0.017136570066213608,
0.029881354421377182,
0.021379942074418068,
-0.00241876021027565,
-0.012497926130890846,
-0.029932081699371338,
-0.013718584552407265,
-0.02976400963962078,
-0.00932107213884592,
0.00016567340935580432,
0.006779133342206478,
-0.004005590453743935,
0.04378071054816246,
0.004268471617251635,
-0.0660424530506134,
-0.02931208163499832,
0.007342345081269741,
-0.04281461611390114,
-0.005290317349135876,
-0.016433412209153175,
-0.011915244162082672,
-0.012199166230857372,
-0.04317329451441765,
0.013035771436989307,
0.07852012664079666,
-0.0016831347020342946,
-0.006832690443843603,
0.022262677550315857,
0.06932111829519272,
-0.00015010162314865738,
-0.03810648247599602,
-0.028827114030718803,
0.003900810144841671,
-0.03521323204040527,
-0.00048628231161274016,
0.0022233708295971155,
0.032840002328157425,
-0.02558136358857155,
-0.018657704815268517,
-0.010796303860843182,
-0.04169683903455734,
0.0036301848012953997,
0.004756709560751915,
-0.022121720016002655,
0.027995603159070015,
-0.003315768437460065,
-0.03321881219744682,
-0.02164192497730255,
-0.027877673506736755,
0.015098679810762405,
0.029362685978412628,
0.00245298957452178,
-0.02709345333278179,
-0.003963496070355177,
-0.025533273816108704,
0.029144512489438057,
-0.027847981080412865,
0.009959083981812,
0.0022083537187427282,
0.03844286873936653,
0.0030702410731464624,
-0.02361607737839222,
0.01186133362352848,
-0.0018263614038005471,
-0.00735826650634408,
0.0010674530640244484,
-0.003563324920833111,
0.013098032213747501,
-0.023622244596481323,
-0.0240060705691576,
-0.009259289130568504,
-0.0440383218228817,
0.031574223190546036,
0.014052056707441807,
-0.009940680116415024,
0.017728693783283234,
-0.02463165670633316,
-0.040338173508644104,
-0.009607757441699505,
-0.011801346205174923,
-0.024635033681988716,
0.06141230836510658,
-0.02767902798950672,
0.01763695850968361,
-0.030962053686380386,
-0.019296156242489815,
0.0551861971616745,
0.045940861105918884,
-0.011934458278119564,
0.038554348051548004,
0.03401101008057594,
0.02416425570845604,
0.009848415851593018,
-0.0012757077347487211,
-0.04921138659119606,
0.06879962980747223,
-0.04191914200782776,
-0.005748334340751171,
0.007044125813990831,
-0.020970432087779045,
0.0020954099018126726,
0.035643234848976135,
0.046840742230415344,
-0.004863346926867962,
-0.01069777924567461,
-0.035668861120939255,
-0.023985546082258224,
0.02234167605638504,
-0.011569312773644924,
0.019743261858820915,
-0.0038562167901545763,
0.0186147503554821,
0.006830073893070221,
-0.002843958791345358,
0.032411232590675354,
-0.016813095659017563,
0.002852946287021041,
-0.051294099539518356,
-0.05450376868247986,
0.04531455039978027,
-0.030050991103053093,
-0.021454375237226486,
-0.004930926952511072,
0.009023450314998627,
0.023234358057379723,
0.02448956109583378,
0.013342242687940598,
-0.036143090575933456,
0.05312354490160942,
0.026066046208143234,
0.05040590837597847,
-0.010376044549047947,
-0.0019958193879574537,
0.14794844388961792,
0.03974739462137222,
0.0421043261885643,
-0.04351668059825897,
-0.009059755131602287,
-0.01736300252377987,
0.004971229005604982,
-0.02451094426214695,
0.03921102359890938,
-0.0160629041492939,
-0.024911342188715935,
-0.012793266214430332,
0.07603943347930908,
0.0040334961377084255,
0.0025005065836012363,
0.05173531547188759,
-0.03184327110648155,
-0.03856029361486435,
0.0034168632701039314,
0.03936668857932091,
-0.0049149636179208755,
-0.005586411338299513,
-0.03333909809589386,
-0.011298776604235172,
0.01674262061715126,
0.04112153872847557,
0.003000532742589712,
-0.025880921632051468,
0.02272936701774597,
0.0003520113241393119,
-0.07922889292240143,
-0.017081547528505325,
0.009913981892168522,
0.01013433188199997,
-0.04418464004993439,
-0.03832218796014786,
-0.0012518205912783742,
-0.022559741511940956,
0.021486662328243256,
0.06885416060686111,
-0.0023422541562467813,
0.025812240317463875,
0.0625859871506691,
0.008684182539582253,
-0.01605372503399849,
-0.016475001350045204,
-0.035560134798288345,
0.0809812918305397,
-0.031831759959459305,
-0.037845905870199203,
-0.010754446499049664,
-0.012379774823784828,
0.024744950234889984,
-0.020026447251439095,
0.001403021509759128,
-0.018201647326350212,
0.05251060426235199,
0.025334272533655167,
0.025447390973567963,
-0.03852544352412224,
0.01952117308974266,
0.014050805941224098,
0.010920844972133636,
-0.02199316956102848,
-0.02125237137079239,
-0.015215175226330757,
0.009085426107048988,
0.05051092430949211,
-0.015693167224526405,
-0.0011973625514656305,
-0.02369544841349125,
-0.008785325102508068,
-0.03848375752568245,
-0.02908514067530632,
-0.00316773378290236,
0.0003418860142119229,
0.08283538371324539,
0.0035572568885982037,
0.004673241171985865,
-0.021145785227417946,
-0.08762142807245255,
0.009887820109724998,
-0.028728898614645004,
-0.01194367278367281,
0.00964817963540554,
-0.014540158212184906,
-0.01366466749459505,
0.05058969557285309,
-0.03533697500824928,
-0.015646813437342644,
0.01525330450385809,
0.061338067054748535,
0.01190502755343914,
-0.003543039783835411,
-0.00771460123360157,
-0.006987673230469227,
-0.02647840790450573,
0.021170582622289658,
-0.017527209594845772,
-0.033365845680236816,
0.013667152263224125,
0.0027462770231068134,
-0.011910419911146164,
0.0409153550863266,
0.041538797318935394,
-0.006202174350619316,
-0.004817723296582699,
-0.0063004461117088795,
-0.0031309062615036964,
0.05218939483165741,
0.045382313430309296,
-0.04335879161953926,
-0.07476639002561569,
-0.013712989166378975,
0.011114059016108513,
-0.036673206835985184,
-0.002085400279611349,
-0.04264134541153908,
-0.056325823068618774,
-0.030172081664204597,
-0.011677965521812439,
-0.020222758874297142,
0.0007860013283789158,
-0.07444004714488983,
0.06597650796175003,
0.010622823610901833,
-0.013035359792411327,
-0.0011627841740846634,
0.03949826583266258,
-0.02391267940402031,
-0.021620679646730423,
0.011056138202548027,
-0.005198103375732899,
-0.02963794581592083,
-0.011850941926240921,
0.01347265299409628,
0.019507722929120064,
0.014885094948112965,
0.009460581466555595,
-0.018067510798573494,
0.028826195746660233,
-0.027516040951013565,
-0.0643903836607933,
0.037274718284606934,
0.02292804978787899,
0.0170963853597641,
0.06457506865262985,
0.025251656770706177,
-0.026415495201945305,
0.034252360463142395,
-0.017259079962968826,
-0.019307386130094528,
-0.01058563869446516,
-0.04958752542734146,
-0.022164691239595413,
-0.028185218572616577,
0.008892717771232128,
0.005241557490080595,
-0.007937265560030937,
0.02970629744231701,
0.02088182047009468,
-0.020023299381136894,
-0.00042241087066940963,
0.044454727321863174,
-0.04181501641869545,
0.01882733404636383,
0.04149841517210007,
0.004750865511596203,
-0.01613295078277588,
0.058805398643016815,
-0.02908952720463276,
-0.01972939632833004,
0.013921773992478848,
0.023913439363241196,
-0.10280188173055649,
-0.018610795959830284,
0.011520041152834892,
0.02221917174756527,
0.046688299626111984,
-0.04578491300344467,
0.016429776325821877,
0.010255497880280018,
-0.07018329203128815,
0.035379279404878616,
0.01113138161599636,
-0.026702383533120155,
-0.011852986179292202,
0.0063245841301977634,
-0.03313949331641197,
0.05157414823770523,
0.045192569494247437,
0.03637411445379257,
0.02211826667189598,
0.011212829500436783,
-0.012868638150393963,
-0.015835609287023544,
-0.015239790081977844,
0.04551819711923599,
0.003995770122855902,
-0.017108310014009476,
0.08813535422086716,
0.0013970982981845737,
-0.05765809491276741,
0.01640259474515915,
0.02535148337483406,
0.004104961175471544,
-0.008511761203408241,
0.020630154758691788,
0.026463693007826805,
0.03351880982518196,
0.019274452701210976,
-0.01176371332257986,
0.04553339630365372,
0.00911324005573988,
0.04699588567018509,
0.013256112113595009,
-0.04274240881204605,
0.01417842973023653,
0.025667734444141388,
-0.031928543001413345,
-0.024972138926386833,
0.08600685745477676,
-0.006661075633019209,
-0.04180021584033966,
0.017537210136651993,
-0.012886419892311096,
-0.007566167041659355,
0.020156433805823326,
0.029491128399968147,
-0.02448105625808239,
-0.016878405585885048,
-0.016987616196274757,
0.004849653225392103,
-0.0033615026623010635,
0.010844382457435131,
-0.008890949189662933,
-0.019551005214452744,
0.04464162513613701,
0.02084636129438877,
-0.02068975195288658,
-0.05225067958235741,
-0.02531089074909687,
-0.011578802019357681,
0.0046889870427548885,
0.015462473034858704,
-0.030648905783891678,
-0.05278518423438072,
0.03168807923793793,
0.005722116678953171,
0.04598020389676094,
-0.0670749619603157,
-0.009276050142943859,
0.03059149719774723,
-0.05992178991436958,
-0.0019235017243772745,
0.016298167407512665,
0.019456535577774048,
-0.02588619478046894,
-0.01258092187345028,
-0.01313671376556158,
-0.004630117677152157,
0.0745730921626091,
0.01643151231110096,
-0.00797492265701294,
0.02962520346045494,
-0.006678272504359484,
0.03475074842572212,
-0.03565613925457001,
-0.0369560681283474,
-0.020762784406542778,
-0.0009192384895868599,
0.015703096985816956,
0.01232913974672556,
-0.0062927487306296825,
0.037424713373184204,
0.02217995934188366,
-0.007910327985882759,
0.0009337036171928048,
0.04185765981674194,
-0.043201081454753876,
0.05894044041633606,
0.0036961562000215054,
0.00450202077627182,
0.04787196218967438,
-0.026694491505622864,
0.05116782337427139,
0.019683782011270523,
-0.018088558688759804,
-0.03135063499212265,
-0.000598837505094707,
-0.03146516904234886,
-0.0358823724091053,
0.005696714390069246,
0.002213457366451621,
-0.005818492267280817,
-0.013665340840816498,
0.028324980288743973,
0.069537453353405,
-0.022483617067337036,
-0.04301375523209572,
0.06711842864751816,
0.031355030834674835,
0.07765433937311172,
0.02430069074034691,
0.009141546674072742,
0.02795729599893093,
0.010491682216525078,
0.01144023984670639,
0.03749442100524902,
0.024021275341510773,
-0.016747383400797844,
0.025699278339743614,
0.0325072780251503,
-0.018957525491714478,
0.008393385447561741,
0.01741863042116165,
0.014761706814169884,
-0.03368900716304779,
-0.004304830450564623,
0.04223423823714256,
-0.052938755601644516,
0.03182680159807205,
0.02501572109758854,
-0.030734935775399208,
0.10145670920610428,
0.004759700503200293,
0.012032927013933659,
-0.0029001221992075443,
0.015513857826590538,
-0.012084621004760265,
0.02053770050406456,
-0.005039094015955925,
0.10146306455135345,
-0.00178188132122159,
-0.0002717545721679926,
-0.0325448140501976,
0.00854386668652296,
0.0019158796640112996,
-0.07622842490673065,
-0.037145763635635376,
0.05084022879600525,
-0.021285779774188995,
-0.0011416140478104353,
-0.040002960711717606,
0.018662871792912483,
-0.015849191695451736,
0.01945679448544979,
0.0253301914781332,
0.018130294978618622,
0.0066478680819272995,
-0.0007628920720890164,
-0.008165338076651096,
0.06616417318582535,
-0.01791517063975334,
-0.006982641760259867,
0.002468750812113285,
0.0020645391196012497,
-0.0003125979274045676,
-0.017632903531193733
] |
<p>Suppose I have an inertial frame with coordinate $\{q\}$. Now I define another reference frame with coordinate $\{q'(q,\dot q,t)\}$. I obtain the equation of motion in $\{q'\}$ in two different ways:</p>
<ol>
<li><p>First obtain the equation of motion in $\{q\}$ by the Euler Lagrange equation
$$\frac{d}{dt}\left(\frac{\partial L}{\partial \dot q}\right)-\frac{\partial L}{\partial q}=0$$
and then rewrite the equation in terms of $\{q'\}$.</p></li>
<li><p>First transform $L(q,t)$ to $L'(q',t)=L(q(q',t),t)$ and then obtain the equation of motion
$$\frac{d}{dt}\left(\frac{\partial L'}{\partial \dot q'}\right)-\frac{\partial L'}{\partial q'}=0$$</p></li>
</ol>
<p>Are the two answers just the same?</p>
| 8,439 |
[
-0.003116786479949951,
0.025492610409855843,
-0.002511520404368639,
-0.005584306549280882,
0.022684041410684586,
0.004515634849667549,
-0.019260119646787643,
-0.010031270794570446,
0.010677453130483627,
0.0065670255571603775,
-0.0048459190875291824,
0.016705790534615517,
0.053306031972169876,
0.001537826843559742,
0.029359741136431694,
0.011905799619853497,
-0.017930854111909866,
0.021490320563316345,
-0.006379472557455301,
-0.01793837919831276,
0.0005315936869010329,
0.0006666830740869045,
0.027345145121216774,
-0.011478880420327187,
-0.041334789246320724,
0.002112398389726877,
0.011887726373970509,
-0.04545171931385994,
0.000764118623919785,
0.06311361491680145,
-0.01203872263431549,
0.011767886579036713,
-0.027264639735221863,
0.029680946841835976,
0.01110120676457882,
0.046425409615039825,
-0.04614332690834999,
-0.01580674760043621,
0.015316820703446865,
0.015482746995985508,
-0.06668446958065033,
-0.0028855965938419104,
-0.004498031921684742,
0.07110154628753662,
0.022335944697260857,
0.04519230127334595,
0.044286392629146576,
0.0005782284424640238,
0.05363510921597481,
-0.037951838225126266,
0.0828067809343338,
0.0027969051152467728,
-0.013979085721075535,
0.015207781456410885,
-0.04046070575714111,
-0.010393423028290272,
0.0659903809428215,
0.028595509007573128,
-0.008551348932087421,
-0.0732898861169815,
0.004422035068273544,
0.007907852530479431,
-0.0040086484514176846,
-0.007155948784202337,
0.0004076954792253673,
-0.002374492585659027,
0.022497063502669334,
0.003276606323197484,
0.025280626490712166,
-0.03022846393287182,
0.01754424162209034,
0.019272636622190475,
0.032713938504457474,
-0.019450513646006584,
0.03874766454100609,
-0.030243225395679474,
0.012642599642276764,
0.025732027366757393,
0.010044810362160206,
0.029292238876223564,
0.004111335147172213,
-0.0012676698388531804,
0.04476548731327057,
0.027039818465709686,
-0.004923060070723295,
-0.050550106912851334,
0.06103803962469101,
0.016877977177500725,
-0.00048736928147263825,
0.03995278850197792,
0.0037048521917313337,
0.0008286787779070437,
0.008178048767149448,
-0.003347227117046714,
0.013715822249650955,
0.05626951903104782,
0.006322083063423634,
0.04307277128100395,
0.05229271575808525,
-0.04250297322869301,
-0.0022051138803362846,
-0.0582689605653286,
-0.004766216967254877,
0.04737855866551399,
0.0017596303950995207,
-0.01827285625040531,
-0.028389928862452507,
0.0028409042861312628,
-0.03389029949903488,
-0.02588353306055069,
-0.03052348643541336,
0.038387980312108994,
-0.0197905320674181,
0.03181864321231842,
-0.018166856840252876,
-0.015488746576011181,
-0.008207389153540134,
-0.02058509923517704,
0.04350091889500618,
0.04309733584523201,
0.014344132505357265,
-0.018889544531702995,
0.009255670942366123,
0.021298272535204887,
-0.031320903450250626,
0.0027309167198836803,
0.022959072142839432,
0.0008673710399307311,
-0.006327884737402201,
-0.008913944475352764,
-0.013957764953374863,
-0.005171699915081263,
-0.024656075984239578,
0.04040742293000221,
0.008609897457063198,
-0.010831191204488277,
-0.08879943937063217,
-0.04646844416856766,
0.03797092288732529,
0.008195323869585991,
-0.000028407317586243153,
-0.07690109312534332,
0.01919684000313282,
0.02157517336308956,
0.03918878361582756,
0.006942742969840765,
0.00008919477113522589,
0.011504081077873707,
0.028252698481082916,
-0.03451304882764816,
0.00749033410102129,
0.007583383470773697,
-0.032997678965330124,
-0.06604176014661789,
0.014162267558276653,
-0.06950442492961884,
0.004311125259846449,
0.031009675934910774,
-0.0005539077101275325,
0.004506056662648916,
0.09199075400829315,
0.011407519690692425,
0.0031480223406106234,
0.011004132218658924,
0.00026588162290863693,
-0.00725095858797431,
0.07315146178007126,
0.008168894797563553,
0.001955266809090972,
0.04636707901954651,
0.03878353163599968,
0.01738506369292736,
-0.018164290115237236,
0.00507487403228879,
0.04869341477751732,
-0.05081641301512718,
-0.04023142531514168,
-0.017359856516122818,
0.018180212005972862,
0.00820616539567709,
-0.05499914661049843,
-0.015370377339422703,
-0.005153539124876261,
-0.05350164696574211,
-0.0015511271776631474,
0.043951451778411865,
0.01150449551641941,
0.027736222371459007,
-0.014643222093582153,
-0.013547603040933609,
-0.01821621134877205,
-0.071540467441082,
0.028697039932012558,
-0.012365168891847134,
-0.01056321244686842,
0.03841637820005417,
0.02678067423403263,
0.013050578534603119,
-0.030359337106347084,
0.0062774489633738995,
0.013083661906421185,
0.03376614674925804,
-0.031139742583036423,
-0.015545491129159927,
0.012350648641586304,
0.06472444534301758,
0.032606229186058044,
0.015484006144106388,
0.008991165086627007,
-0.02466990239918232,
-0.004889850039035082,
0.02010040171444416,
0.0032350849360227585,
0.05290207639336586,
-0.01728108897805214,
-0.010892127640545368,
-0.012960921041667461,
0.00318716187030077,
-0.01947186142206192,
0.049225643277168274,
-0.04582446068525314,
0.06404057145118713,
0.08119214326143265,
-0.009487372823059559,
0.007059362716972828,
0.04810619726777077,
-0.011415465734899044,
0.02183745615184307,
0.014107044786214828,
-0.04787016659975052,
-0.011591071262955666,
-0.0025748866610229015,
0.025178074836730957,
-0.0024931880179792643,
-0.04467342048883438,
0.036900658160448074,
0.04494035243988037,
0.027714423835277557,
-0.013128276914358139,
0.014897766523063183,
-0.012580606155097485,
-0.061256758868694305,
0.035357728600502014,
0.017957167699933052,
-0.034060947597026825,
0.02301347255706787,
0.024450719356536865,
-0.014921429567039013,
0.01383073441684246,
-0.02325959876179695,
-0.03660808876156807,
0.07567334920167923,
-0.007214055396616459,
-0.015287942253053188,
0.04315105825662613,
-0.01911018230021,
0.043643027544021606,
-0.0036146752536296844,
0.034341245889663696,
0.015019724145531654,
-0.03162124380469322,
-0.047279030084609985,
-0.0037240050733089447,
0.044993311166763306,
-0.010409200564026833,
-0.0040060412138700485,
-0.0022337513510137796,
-0.010025025345385075,
0.026712238788604736,
-0.0448918454349041,
-0.001129385083913803,
-0.025613119825720787,
-0.034544844180345535,
-0.015293063595890999,
-0.015572827309370041,
0.012962298467755318,
0.03620859608054161,
0.008554698899388313,
-0.041011448949575424,
-0.029867758974432945,
-0.00919328723102808,
-0.0028860822785645723,
0.0011847886489704251,
0.0393524169921875,
-0.025896985083818436,
0.0321449339389801,
-0.04411708936095238,
-0.02528015337884426,
0.03899744153022766,
0.00837165117263794,
0.02071932703256607,
0.006654266733676195,
-0.03140636160969734,
-0.07918982952833176,
-0.043575216084718704,
-0.07227364927530289,
0.008465989492833614,
0.008707517758011818,
-0.009503060020506382,
0.06853844225406647,
-0.02440834417939186,
-0.03198676183819771,
-0.020718717947602272,
-0.06357018649578094,
-0.015032949857413769,
-0.018834711983799934,
0.025211863219738007,
0.028057649731636047,
-0.0070679024793207645,
0.01282847672700882,
0.005499477963894606,
-0.013645321130752563,
-0.014577244408428669,
-0.08699909597635269,
-0.0294693261384964,
0.04450342804193497,
0.020248297601938248,
0.032689888030290604,
0.008884798735380173,
-0.023717720061540604,
0.07569751888513565,
0.05747878551483154,
-0.01346917450428009,
-0.012974515557289124,
0.003924394957721233,
-0.008098604157567024,
-0.008485384285449982,
-0.01943804696202278,
0.0193093940615654,
-0.0381651446223259,
0.04173337668180466,
0.0055874064564704895,
0.03706924244761467,
0.010661059059202671,
0.010762056335806847,
0.02707522362470627,
-0.00657972227782011,
0.030934225767850876,
0.012868423014879227,
0.03974951431155205,
0.03150087594985962,
-0.0028053647838532925,
0.004937748424708843,
-0.004604383371770382,
0.04969869554042816,
-0.00816612970083952,
-0.06362780928611755,
0.032428938895463943,
0.030611108988523483,
-0.035057272762060165,
-0.019025558605790138,
0.04756787419319153,
-0.001753290300257504,
0.0066999755799770355,
-0.023897511884570122,
0.034774087369441986,
0.02444474771618843,
-0.00961308553814888,
-0.0032984199933707714,
0.028936920687556267,
0.04045451432466507,
-0.024232249706983566,
-0.016526104882359505,
0.002276855055242777,
-0.022545456886291504,
0.04502943530678749,
-0.01999066025018692,
-0.02193848416209221,
0.039274901151657104,
0.011246662586927414,
0.02581041306257248,
-0.0020640476141124964,
-0.03731831535696983,
0.017357204109430313,
-0.08489290624856949,
0.01834288239479065,
0.015139607712626457,
0.05412018671631813,
0.006863684393465519,
0.04411512613296509,
0.03203555569052696,
0.03745020925998688,
0.005015762057155371,
0.028369301930069923,
-0.08729303628206253,
0.05397719144821167,
-0.020084617659449577,
-0.01795107312500477,
0.0010020362678915262,
-0.002153391018509865,
0.04001991078257561,
-0.04357219114899635,
-0.020824376493692398,
-0.005675392225384712,
-0.012807405553758144,
-0.07378600537776947,
0.015270353294909,
-0.0428289994597435,
-0.04707276076078415,
-0.00959703978151083,
0.007518131285905838,
0.024184757843613625,
-0.008038555271923542,
0.016145506873726845,
0.05734511464834213,
-0.003826690139248967,
0.00683769304305315,
-0.013428720645606518,
-0.015669897198677063,
0.003857517149299383,
-0.020321566611528397,
-0.0028810384683310986,
0.039121199399232864,
0.0116902319714427,
0.0484013669192791,
0.011858627200126648,
0.04380270466208458,
-0.005972638726234436,
-0.03634354844689369,
-0.04193098098039627,
-0.06833623349666595,
-0.004550779704004526,
-0.018545476719737053,
0.05595262721180916,
0.0008398941135965288,
-0.020425163209438324,
0.026868700981140137,
0.040626443922519684,
0.043103840202093124,
0.053769584745168686,
0.01094133872538805,
0.018547814339399338,
-0.0028771355282515287,
-0.057528700679540634,
0.015263578854501247,
-0.022539271041750908,
-0.015238689258694649,
0.04533687233924866,
-0.003763222834095359,
-0.00969891157001257,
-0.011372564360499382,
-0.002132018329575658,
0.03268453851342201,
0.015773341059684753,
0.01348932832479477,
-0.013093792833387852,
0.02556179091334343,
0.01651526242494583,
-0.021629519760608673,
-0.006896567065268755,
0.012299918569624424,
0.04339209198951721,
-0.019142678007483482,
0.010163425467908382,
-0.06233849376440048,
-0.016220364719629288,
0.0002693151473067701,
0.01557101495563984,
-0.00936154555529356,
0.016711832955479622,
-0.07317694276571274,
-0.050873540341854095,
0.029092850163578987,
-0.04515552148222923,
0.036543551832437515,
0.0141712985932827,
0.003907719161361456,
-0.02022504433989525,
-0.039559200406074524,
-0.011500008404254913,
-0.022964105010032654,
-0.03006604127585888,
0.013570605777204037,
-0.010082563385367393,
0.014179776422679424,
-0.019454477354884148,
0.004675033502280712,
0.017717458307743073,
0.05422297492623329,
0.025363938882946968,
-0.005116199608892202,
-0.03185664489865303,
0.04406534135341644,
-0.04116130992770195,
-0.05807905271649361,
-0.021909762173891068,
0.03057343140244484,
0.0033308733254671097,
0.000016287245671264827,
-0.039467792958021164,
-0.06450580805540085,
0.06168712303042412,
-0.0159988384693861,
-0.006591359619051218,
0.02331848256289959,
-0.05731906369328499,
0.001708502066321671,
0.008562305942177773,
0.017998460680246353,
0.04258810356259346,
0.01978425495326519,
-0.010093849152326584,
-0.0335695818066597,
-0.018992092460393906,
0.0076535833068192005,
-0.021955756470561028,
-0.04990362748503685,
-0.040283381938934326,
0.03616292029619217,
-0.017740724608302116,
0.057665638625621796,
-0.021648172289133072,
0.034016016870737076,
-0.027212345972657204,
-0.03551379218697548,
-0.011104391887784004,
0.05650918558239937,
0.02554214559495449,
0.00785781629383564,
-0.009393864311277866,
0.02483505569398403,
0.0005844369297847152,
-0.03134620934724808,
0.0031727650202810764,
-0.017313161864876747,
0.009176326915621758,
0.05944577977061272,
-0.0002468079037498683,
0.059642624109983444,
0.00020223190949764103,
0.00035149481846019626,
0.026638345792889595,
-0.03581552952528,
0.011895469389855862,
0.024086300283670425,
0.009545630775392056,
0.03313346579670906,
-0.019259553402662277,
-0.05637691169977188,
-0.01824444904923439,
-0.029666567221283913,
0.010613596998155117,
-0.0641331821680069,
0.004686431493610144,
0.048194464296102524,
-0.016949962824583054,
-0.08842093497514725,
-0.048745837062597275,
0.009641306474804878,
-0.026625528931617737,
-0.010542899370193481,
-0.02659854292869568,
0.001928553101606667,
-0.03241429477930069,
-0.0328056700527668,
-0.012642204761505127,
0.0646616742014885,
-0.015662293881177902,
-0.030643435195088387,
-0.007683300878852606,
0.02586543746292591,
0.006019588094204664,
-0.026251841336488724,
0.015436230227351189,
-0.02699294686317444,
-0.017762353643774986,
0.0004276956315152347,
-0.002795314649119973,
0.06784258037805557,
-0.006312844809144735,
-0.012040242552757263,
-0.032759010791778564,
-0.014163153246045113,
0.04829024150967598,
0.010532121174037457,
-0.004011582117527723,
0.060741424560546875,
0.01794484443962574,
-0.013080475851893425,
-0.04493440315127373,
0.0014584624441340566,
0.012871148064732552,
0.02672950178384781,
0.012932904995977879,
0.020924339070916176,
-0.021747052669525146,
-0.038704849779605865,
-0.0019946773536503315,
-0.012391752563416958,
-0.006552814971655607,
-0.003013330278918147,
0.07490961253643036,
-0.04495593160390854,
0.012804153375327587,
0.03946148231625557,
0.014909831807017326,
0.042219460010528564,
-0.00583222508430481,
-0.0038762909825891256,
0.0132143534719944,
-0.0015342424158006907,
-0.037212926894426346,
-0.04548800364136696,
-0.019328666850924492,
0.016821634024381638,
0.060612164437770844,
-0.0062363967299461365,
0.03656986728310585,
0.02420107088983059,
0.020862504839897156,
0.012084582820534706,
0.0011408493155613542,
-0.020368630066514015,
-0.00012171873095212504,
-0.003977588843554258,
0.039230670779943466,
-0.026570815593004227,
-0.026575742289423943,
0.048563696444034576,
0.03716764971613884,
-0.029614433646202087,
-0.0015620333142578602,
0.019308175891637802,
0.0019423653138801455,
-0.016986176371574402,
-0.003113816026598215,
-0.02600470930337906,
0.013174561783671379,
-0.026488054543733597,
0.06802564114332199,
-0.015584524720907211,
-0.03613803908228874,
0.05712039768695831,
0.004707231651991606,
-0.009486006572842598,
-0.016869070008397102,
0.012602832168340683,
-0.04727077856659889,
0.0484711229801178,
-0.001410836004652083,
0.058777302503585815,
-0.005828095134347677,
-0.0005177753628231585,
0.06046868860721588,
0.0036720335483551025,
0.008200344629585743,
0.002004040405154228,
-0.03549908101558685,
-0.014847411774098873,
-0.016437316313385963,
-0.029120204970240593,
0.04279775172472,
-0.014079758897423744,
0.029709571972489357,
-0.010301665402948856,
-0.057362157851457596,
0.006263040471822023,
0.023383593186736107,
0.036334384232759476,
-0.05558060109615326,
0.09066963195800781,
0.021266194060444832,
-0.032931406050920486,
-0.03598429635167122,
0.013555150479078293,
0.09976311028003693,
0.04649743437767029,
0.01700575090944767,
-0.08094363659620285,
0.025625143200159073,
0.006991260685026646,
0.015255031175911427,
-0.018689781427383423,
0.033102408051490784,
0.007601823657751083,
0.023707687854766846,
0.017271850258111954,
0.03437662869691849,
-0.02106124721467495,
-0.009699977934360504,
0.018453093245625496,
-0.04884368181228638,
-0.0135198337957263,
0.012103195302188396,
0.004767008125782013,
-0.0010339359287172556,
0.014134041965007782,
0.01735122688114643,
0.0022279564291238785,
-0.018394162878394127,
0.0282759852707386,
-0.02433590032160282,
-0.06306484341621399,
-0.005729782395064831,
0.0002545813622418791,
-0.06164166331291199,
0.024501865729689598,
0.03982442989945412,
-0.021135518327355385,
-0.028014488518238068,
0.014474687166512012,
-0.012139164842665195,
-0.01335872057825327,
0.050257306545972824,
0.05155981332063675,
0.002813627477735281,
0.018188146874308586,
0.01315291691571474,
0.025464016944169998,
-0.0439462848007679,
0.023593446239829063,
-0.03460650146007538,
0.010264802724123001,
-0.005429243203252554,
0.040260519832372665,
-0.009157880209386349,
-0.01633634604513645,
-0.003537853481248021,
-0.06458010524511337,
-0.004307590890675783,
-0.0009766867151483893,
0.022131972014904022,
0.024811672046780586,
0.006194343324750662,
-0.02526363916695118,
0.006913464516401291,
-0.012640253640711308,
0.012942200526595116,
-0.01931375078856945,
0.01747235842049122,
-0.004101150203496218,
0.014505552127957344,
0.029123840853571892,
-0.048817817121744156,
0.02230638638138771,
-0.040420129895210266,
-0.03116418793797493,
-0.021502897143363953,
-0.02815910615026951,
0.007127872668206692,
0.01667214371263981,
0.03930075466632843,
-0.011806607246398926,
0.008366922847926617,
-0.04170175641775131,
-0.10428961366415024,
-0.002334475051611662,
0.021895280107855797,
0.006898618768900633,
-0.0013467053649947047,
0.021836625412106514,
-0.009984875097870827,
0.0412832647562027,
-0.03469211980700493,
0.030233848839998245,
0.028764590620994568,
0.022337598726153374,
-0.001840653596445918,
-0.02508685179054737,
-0.01839831843972206,
0.007132629863917828,
-0.0006062013562768698,
0.020412959158420563,
-0.05569290369749069,
0.015509078279137611,
0.012272263877093792,
0.052386995404958725,
-0.010179323144257069,
0.03504147008061409,
-0.005495601333677769,
-0.006567639298737049,
0.024552876129746437,
0.02255387231707573,
-0.000716445327270776,
0.053792454302310944,
0.04375984147191048,
-0.0477985255420208,
0.014306901022791862,
-0.028393248096108437,
-0.026180606335401535,
-0.007741149980574846,
0.014013833366334438,
-0.04641757532954216,
0.036188382655382156,
-0.027724605053663254,
0.0064617726020514965,
-0.04651379957795143,
0.007414055522531271,
-0.05756087601184845,
0.0342337042093277,
-0.006431105546653271,
-0.036642976105213165,
-0.05093961954116821,
0.04126911610364914,
-0.023987900465726852,
-0.017659008502960205,
0.003004108089953661,
0.03065495751798153,
-0.02293066866695881,
-0.02812870405614376,
0.012086636386811733,
-0.010979391634464264,
0.022382721304893494,
-0.03502581641077995,
-0.028056742623448372,
0.013896473683416843,
-0.007641837932169437,
-0.016693532466888428,
0.04824496805667877,
0.013673911802470684,
-0.0028769150376319885,
0.024222172796726227,
-0.04701485484838486,
0.014200452715158463,
0.0828622505068779,
-0.0023471142631024122,
0.001984694041311741,
-0.010009456425905228,
-0.06658051162958145,
-0.019977683201432228,
-0.012274319306015968,
0.004954168107360601,
-0.00677687069401145,
-0.0036085103638470173,
0.003865149337798357,
0.03656831756234169,
-0.027672305703163147,
0.012296946719288826,
0.027901001274585724,
0.012566358782351017,
0.010805032216012478,
0.007517319172620773,
-0.007248207461088896,
0.015303337946534157,
0.034096136689186096,
0.01029161550104618,
-0.013027237728238106,
0.007018286734819412,
0.013100855052471161,
-0.1151357889175415,
-0.008215718902647495,
-0.0010739334393292665,
0.011505135335028172,
0.028141070157289505,
-0.03565467149019241,
0.004897951148450375,
0.0259439367800951,
-0.07483521103858948,
0.00923556461930275,
-0.01298382319509983,
0.01739325374364853,
-0.027867695316672325,
0.006456528790295124,
-0.024449646472930908,
0.06500298529863358,
0.06734487414360046,
0.027889302000403404,
-0.011553863063454628,
0.013164234347641468,
0.01582801155745983,
0.013435899280011654,
0.005001663696020842,
0.034666385501623154,
0.026355769485235214,
-0.023608660325407982,
0.06694624572992325,
-0.012981241568922997,
-0.048681870102882385,
0.026707973331212997,
0.01851179078221321,
0.02360130287706852,
-0.016719745472073555,
0.016455356031656265,
-0.00033009739127010107,
0.0012569810496643186,
0.023037999868392944,
-0.004979437682777643,
-0.03491472080349922,
0.009759305976331234,
0.007812012918293476,
0.004259889014065266,
-0.04421200975775719,
-0.021120451390743256,
0.007847454398870468,
-0.029776789247989655,
-0.02705722115933895,
0.02033892832696438,
-0.005029964726418257,
0.02085818722844124,
-0.007827547378838062,
0.015700675547122955,
0.022941384464502335,
-0.02771082893013954,
-0.003516541561111808,
-0.0517948754131794,
-0.005446352064609528,
0.03414419665932655,
-0.04686208441853523,
-0.013836827129125595,
0.023770490661263466,
-0.016234727576375008,
-0.020559122785925865,
0.00970616564154625,
-0.018071874976158142,
-0.002064237603917718,
-0.08666344732046127,
-0.032907988876104355,
-0.015615984797477722,
-0.01664075441658497,
-0.02954954281449318,
-0.061596594750881195,
-0.021145399659872055,
0.05607321113348007,
0.04463277757167816,
0.01140645518898964,
-0.017921239137649536,
0.01442298199981451,
-0.0335610955953598,
-0.0612533874809742,
0.029091279953718185,
0.034420400857925415,
-0.04998182877898216,
-0.031445544213056564,
-0.021767104044556618,
-0.02416461892426014,
0.05804426968097687,
0.04057507589459419,
0.006170747801661491,
-0.03722837194800377,
0.05327998101711273,
-0.024490049108862877,
-0.005566860549151897,
-0.019644225016236305,
-0.029168464243412018,
-0.00875797774642706,
-0.005196030717343092,
0.016356028616428375,
-0.008884023874998093,
-0.033618468791246414,
0.0024682520888745785,
-0.0006651835283264518,
-0.017336126416921616,
0.06673861294984818,
0.008339096792042255,
-0.026818452402949333,
0.02192682772874832,
0.01831098459661007,
-0.0050902413204312325,
0.0488557443022728,
0.019723467528820038,
0.00991500448435545,
0.034417666494846344,
-0.07405003160238266,
-0.05533808097243309,
0.016816379502415657,
-0.043757904320955276,
-0.01906411536037922,
-0.04153173789381981,
-0.014530928805470467,
0.01749235764145851,
-0.0221804641187191,
0.0032094642519950867,
0.05728210508823395,
-0.016222164034843445,
-0.006653619464486837,
0.007200194057077169,
0.001499128993600607,
0.06268639862537384,
-0.004490443971008062,
0.03599352389574051,
0.024259623140096664,
-0.015424514189362526,
0.02226170524954796,
0.013441687449812889,
0.022544803097844124,
0.002278562868013978,
-0.02415088377892971,
0.04286056384444237,
-0.013663619756698608,
0.029181573539972305,
-0.014234742149710655,
0.028105411678552628,
-0.03184868395328522,
0.0006223558448255062,
0.02343931794166565,
-0.014723122119903564,
-0.012125334702432156,
0.02376352809369564,
-0.0207742340862751,
0.019710518419742584,
-0.031560588628053665,
0.022576548159122467,
-0.006424515973776579,
0.02914557233452797,
-0.026295552030205727,
-0.009705265052616596,
-0.020007135346531868,
0.06489408016204834,
0.0021257633343338966,
-0.03035801835358143,
-0.024049777537584305,
-0.05231902375817299,
0.00018402784189675003,
-0.01979478821158409,
-0.030995666980743408,
-0.008262972347438335,
-0.004250803962349892,
-0.00267320335842669,
-0.02754203975200653,
-0.05284024402499199,
-0.005173163954168558,
0.043246522545814514,
0.05430552363395691,
0.043441832065582275,
-0.0202338807284832,
-0.023119430989027023,
-0.02312113158404827,
0.057697683572769165,
-0.06200789287686348,
-0.0308771263808012,
0.01218394935131073,
0.01420271210372448,
0.022861579433083534,
-0.02664886973798275
] |
<p>I have seen on the internet that many times people assert that inside a cylindric <a href="http://en.wikipedia.org/wiki/Condenser" rel="nofollow">condenser</a> the electrostatic field is null due to the fact that the Gauss flux inside is null. But I wanted to make clear that this is not the reason. The reason lies on the symmetry of the condenser. Am I right?</p>
<p>If the electrostatic field was null inside the smaller radius conductor, it would mean that if we put a test particle there, it would not resist any force. However if I am right, this would not happen. The only thing that could happen so that the particle did not move, would be that the charge in the condenser could be reorganized in presence of that particle.
Do I have the concepts right? </p>
| 8,440 |
[
-0.05345385521650314,
0.013512324541807175,
0.023923659697175026,
-0.03356417268514633,
0.036455847322940826,
-0.013443505391478539,
-0.014461711049079895,
-0.0198805071413517,
-0.031689759343862534,
-0.0072732968255877495,
0.06130758672952652,
0.01582401432096958,
0.07060810923576355,
-0.02535928785800934,
-0.022009829059243202,
0.0014717831509187818,
-0.03088277019560337,
-0.012766835279762745,
0.014704377390444279,
-0.05621254816651344,
-0.03182974085211754,
0.021485229954123497,
-0.01726476103067398,
-0.014228825457394123,
-0.021591875702142715,
0.008921179920434952,
0.01133212260901928,
-0.011029982008039951,
-0.017658453434705734,
0.08196555078029633,
-0.02922985516488552,
-0.02018546126782894,
-0.027367379516363144,
0.0136781120672822,
0.0478597953915596,
0.010278676636517048,
-0.04687679186463356,
-0.0206507109105587,
-0.015114668756723404,
0.014281959272921085,
0.030346838757395744,
0.005315705202519894,
0.0033685180824249983,
0.04725907742977142,
-0.004735863301903009,
0.015971500426530838,
0.02663828246295452,
0.015886813402175903,
0.05363016575574875,
-0.10624229162931442,
0.006587784271687269,
-0.008007556200027466,
0.022174349054694176,
-0.010031343437731266,
0.03827369213104248,
-0.039922263473272324,
0.05145604908466339,
0.05513766407966614,
-0.03986155241727829,
-0.029668623581528664,
-0.03155531734228134,
-0.018150078132748604,
-0.010656141676008701,
-0.022798024117946625,
-0.01635339856147766,
0.04307438060641289,
0.03018830344080925,
-0.03234817832708359,
0.002547171665355563,
-0.03551283851265907,
0.006400547455996275,
0.020280318334698677,
-0.008470998145639896,
-0.019887493923306465,
0.019941575825214386,
0.01729942299425602,
0.025972073897719383,
0.007918882183730602,
-0.002977768424898386,
0.025918297469615936,
-0.01160523947328329,
0.019252965226769447,
0.006093209609389305,
0.02643544040620327,
0.01305256225168705,
-0.04206492379307747,
0.02809983491897583,
-0.03166556730866432,
0.006636469624936581,
0.018331021070480347,
0.006588071584701538,
-0.015207933261990547,
0.038557521998882294,
-0.0055003780871629715,
-0.029783932492136955,
0.020340103656053543,
0.027258457615971565,
0.04359026625752449,
-0.01387717667967081,
-0.003349686274304986,
-0.021565794944763184,
0.00968512985855341,
0.021202515810728073,
0.08561114221811295,
0.011018567718565464,
-0.028784355148673058,
-0.012160698883235455,
0.05440014600753784,
-0.01919504813849926,
-0.010112485848367214,
-0.06641100347042084,
0.002864841604605317,
0.027460690587759018,
0.019566096365451813,
0.02676696702837944,
-0.037095703184604645,
0.00336511735804379,
-0.01771307736635208,
0.03806805983185768,
0.05476251617074013,
0.022430628538131714,
-0.019816121086478233,
0.03125450760126114,
-0.05528290942311287,
-0.0409054234623909,
0.02993747591972351,
0.02202581986784935,
0.010858147405087948,
0.005591463763266802,
0.02042333409190178,
0.032298531383275986,
0.0264048520475626,
-0.008853391744196415,
-0.01023848820477724,
0.025394205003976822,
0.013090875931084156,
-0.09406837821006775,
-0.03855621814727783,
0.02629038877785206,
0.02016827091574669,
-0.004182659089565277,
-0.0891021266579628,
-0.027706759050488472,
0.028589284047484398,
0.09727588295936584,
-0.006060901563614607,
0.0029521482065320015,
-0.005162146408110857,
0.06360385566949844,
0.028189821168780327,
-0.0009599257609806955,
0.010075276717543602,
0.0016135849291458726,
-0.05972498655319214,
-0.04362354800105095,
-0.05205599218606949,
0.05133737623691559,
0.038278982043266296,
0.019866952672600746,
-0.022886481136083603,
0.03234165161848068,
-0.027302995324134827,
0.018317973241209984,
-0.00905554462224245,
-0.0056613446213305,
-0.023676162585616112,
0.08623568713665009,
0.03031136840581894,
-0.025977691635489464,
0.020689260214567184,
0.011966532096266747,
0.05370103940367699,
-0.01648573763668537,
0.015553716570138931,
0.05935465544462204,
-0.06538824737071991,
-0.011130601167678833,
-0.03929352015256882,
0.03605819121003151,
0.01792723685503006,
-0.03895154967904091,
-0.029496341943740845,
-0.002884459448978305,
0.016451774165034294,
-0.03977196291089058,
0.05344307795166969,
-0.013590431772172451,
0.01937180571258068,
-0.00827181339263916,
-0.05046830326318741,
-0.02247346192598343,
-0.02703690528869629,
0.019095540046691895,
-0.00022351161169353873,
-0.035684678703546524,
0.03391062095761299,
0.019339218735694885,
0.015120620839297771,
-0.04688902571797371,
-0.010572707280516624,
-0.011515268124639988,
0.008548557758331299,
-0.03632229566574097,
0.010300325229763985,
0.01692143641412258,
-0.006539746653288603,
0.030449924990534782,
-0.003322990844026208,
0.02649874985218048,
-0.005802415776997805,
0.009374781511723995,
-0.0084367785602808,
-0.007327479775995016,
0.005287433974444866,
0.05559670552611351,
-0.02327045239508152,
0.0284244567155838,
0.006803722586482763,
-0.01267747487872839,
0.05483454465866089,
-0.019066542387008667,
0.08339209109544754,
0.014465468935668468,
0.0015237791230902076,
-0.015181045047938824,
0.0314718522131443,
0.03433668985962868,
-0.01062309555709362,
0.02957327291369438,
-0.010994315147399902,
-0.06750782579183578,
-0.006731856614351273,
0.04609334468841553,
0.04823465272784233,
-0.03371597081422806,
0.017622480168938637,
0.012928968295454979,
0.02780546434223652,
0.02598240040242672,
-0.028259003534913063,
-0.03517615422606468,
-0.04869058355689049,
0.04318986088037491,
0.0041922833770513535,
0.026880759745836258,
-0.02822818048298359,
0.0672660693526268,
-0.0017815862083807588,
0.013672723434865475,
-0.014531977474689484,
-0.004079159814864397,
0.013945824466645718,
0.010215017944574356,
0.03213310241699219,
0.002859203377738595,
-0.04154416173696518,
0.014187540858983994,
0.01303097140043974,
0.052093274891376495,
0.0007914274465292692,
-0.024356989189982414,
0.008564600721001625,
-0.04169367253780365,
0.03062261827290058,
0.02937251888215542,
-0.01657283864915371,
-0.04271422699093819,
-0.031176229938864708,
0.03716225549578667,
-0.07888160645961761,
0.006229218095541,
-0.021731823682785034,
0.013143238611519337,
-0.05005575716495514,
-0.030623070895671844,
0.0028508633840829134,
0.022648153826594353,
0.048279497772455215,
-0.06334830820560455,
-0.03697342053055763,
-0.027552157640457153,
-0.02703053504228592,
-0.0051855118945240974,
0.062071237713098526,
-0.03076152503490448,
-0.0020157569088041782,
-0.024131396785378456,
-0.0025178445503115654,
0.04922407120466232,
-0.023796841502189636,
0.03784138709306717,
-0.015655947849154472,
-0.02086517959833145,
-0.03682194650173187,
-0.0027343914844095707,
-0.032457560300827026,
0.01983996480703354,
-0.04046962037682533,
-0.021497782319784164,
0.05352415144443512,
0.004591347649693489,
-0.05078878253698349,
0.02493719384074211,
-0.03662819042801857,
-0.04511705040931702,
0.013310151174664497,
-0.01861717365682125,
0.03371236473321915,
-0.03985743969678879,
0.04188006371259689,
0.026567645370960236,
-0.029669424518942833,
-0.002711075823754072,
-0.021789953112602234,
-0.04353607818484306,
0.00981262419372797,
-0.026639146730303764,
0.021729692816734314,
-0.03140958771109581,
-0.04608799144625664,
0.061489347368478775,
0.031512197107076645,
-0.039921265095472336,
-0.014319137670099735,
-0.01249642763286829,
-0.021189773455262184,
-0.01298545952886343,
-0.0011899338569492102,
0.055993884801864624,
-0.007639738265424967,
0.008406135253608227,
0.035130586475133896,
0.04217131808400154,
-0.004364009015262127,
-0.0057105328887701035,
-0.03654768317937851,
-0.011824656277894974,
0.03596395626664162,
0.019190004095435143,
0.07650643587112427,
-0.006444642320275307,
0.007739614229649305,
0.011009076610207558,
-0.007547485176473856,
0.039432793855667114,
0.04182877391576767,
-0.05821351706981659,
0.033450815826654434,
-0.012880251742899418,
0.04007995128631592,
0.014521440491080284,
0.006014357320964336,
-0.017824983224272728,
-0.010033843107521534,
0.00801309198141098,
-0.010951465927064419,
0.03519941493868828,
0.004115364979952574,
0.01847721077501774,
0.019646193832159042,
0.03511054068803787,
-0.024336976930499077,
-0.02170543745160103,
0.015177236869931221,
-0.018826641142368317,
0.0411529615521431,
-0.04294867068529129,
-0.03495340421795845,
0.037212688475847244,
0.03660454973578453,
0.029422996565699577,
0.041429147124290466,
-0.04250191152095795,
0.011971947737038136,
-0.027410635724663734,
0.0031726916786283255,
-0.0032910348381847143,
0.051857974380254745,
0.022974977269768715,
0.015262030996382236,
0.04884488880634308,
-0.004117283504456282,
-0.00008508768951287493,
-0.0018745082197710872,
-0.075283482670784,
-0.022730378434062004,
-0.020129356533288956,
0.006491793319582939,
-0.02374359965324402,
-0.012473619543015957,
-0.014379206113517284,
0.0001596201618667692,
-0.01733349822461605,
-0.0011415372136980295,
-0.0023111552000045776,
-0.06844031065702438,
0.015328130684792995,
-0.028971200808882713,
-0.04324484243988991,
0.008174768649041653,
0.03853803500533104,
0.04889344424009323,
-0.04330044239759445,
0.009188061580061913,
0.018411481752991676,
-0.04818429797887802,
0.006062116473913193,
-0.003409149358049035,
0.023314552381634712,
0.028225380927324295,
0.06040181592106819,
-0.004103252198547125,
-0.006809253711253405,
-0.04484697803854942,
-0.005540046840906143,
0.057791341096162796,
0.028928223997354507,
0.0033777758944779634,
0.0071550412103533745,
-0.019905628636479378,
-0.043550293892621994,
-0.042150627821683884,
-0.029110008850693703,
0.04710907116532326,
0.02023414894938469,
0.002536097541451454,
0.02017451636493206,
0.009270261973142624,
0.010681858286261559,
0.014763318933546543,
0.052653826773166656,
0.03572604060173035,
-0.017694944515824318,
-0.051813315600156784,
-0.006953412666916847,
-0.057309798896312714,
-0.004124716389924288,
0.010558162815868855,
-0.008163508959114552,
-0.046512775123119354,
-0.03503519669175148,
0.018526213243603706,
0.008974923752248287,
-0.03382422775030136,
0.027371171861886978,
-0.021207695826888084,
0.02311268076300621,
-0.004422883503139019,
-0.008919812738895416,
0.06739205121994019,
-0.0023291870020329952,
0.0385281965136528,
0.037172138690948486,
-0.0014048191951587796,
-0.06173611059784889,
-0.015333865769207478,
0.03823133930563927,
0.02439846470952034,
0.004215428605675697,
0.012160489335656166,
-0.04579100012779236,
-0.005129160359501839,
0.05779269337654114,
-0.020008375868201256,
0.023204337805509567,
-0.01372335571795702,
0.0008038412779569626,
-0.048576273024082184,
-0.023790055885910988,
-0.006895761005580425,
0.0036656430456787348,
-0.034377921372652054,
-0.005305280443280935,
-0.04857464134693146,
-0.030634967610239983,
-0.005666245706379414,
-0.013085360638797283,
-0.004134531132876873,
0.021710924804210663,
-0.022341476753354073,
0.03216921165585518,
0.026334248483181,
-0.007814865559339523,
0.018550192937254906,
-0.07355619966983795,
0.021250886842608452,
0.008795889094471931,
0.015875546261668205,
0.039761703461408615,
-0.02224254235625267,
0.005874451249837875,
0.00708476547151804,
0.0037648093421012163,
0.02312265895307064,
0.021799907088279724,
-0.04840216040611267,
0.027120089158415794,
0.014550228603184223,
-0.010071652010083199,
0.024334294721484184,
0.018498549237847328,
-0.008562209084630013,
0.0039912499487400055,
-0.02134762331843376,
0.009814271703362465,
-0.021292846649885178,
0.020254144445061684,
-0.02174467034637928,
0.02167487144470215,
-0.018840959295630455,
0.06253840774297714,
-0.005435940809547901,
0.04673372209072113,
-0.03740604966878891,
-0.0348878912627697,
0.018042786046862602,
0.0030688236001878977,
-0.00530156958848238,
-0.0006051818490959704,
-0.04355254024267197,
0.017625611275434494,
-0.014184612780809402,
-0.03808075562119484,
-0.018947625532746315,
0.004697720520198345,
0.002193468390032649,
0.022351179271936417,
0.019998135045170784,
-0.006568372715264559,
-0.014375519007444382,
-0.01418012473732233,
0.014417938888072968,
-0.040785882622003555,
0.05201323330402374,
-0.02697218954563141,
-0.022157499566674232,
0.05192601680755615,
-0.025718826800584793,
-0.036141104996204376,
0.03950048238039017,
-0.015511810779571533,
-0.0046664089895784855,
-0.07240274548530579,
-0.020838677883148193,
0.04025796800851822,
0.009721826761960983,
-0.08355657756328583,
-0.048389919102191925,
0.007333018351346254,
-0.017983200028538704,
-0.005746794864535332,
-0.03754796087741852,
-0.02489129826426506,
0.0029034276958554983,
-0.022284287959337234,
0.009036690928041935,
-0.002550592180341482,
-0.04392072558403015,
0.017844421789050102,
0.013604124076664448,
-0.009851962327957153,
0.07599518448114395,
0.009461703710258007,
0.0012888145865872502,
-0.0036587712820619345,
-0.03681473433971405,
0.0007662081625312567,
0.013356223702430725,
0.059740498661994934,
-0.019321177154779434,
-0.04117141291499138,
-0.01590995490550995,
-0.008058406412601471,
0.041402220726013184,
-0.009517727419734001,
-0.04763830453157425,
0.024333756417036057,
-0.003995155915617943,
-0.013264883309602737,
-0.00921208318322897,
0.025423001497983932,
-0.008643463253974915,
0.008197559043765068,
-0.025915754958987236,
0.031664684414863586,
-0.017969701439142227,
-0.058568812906742096,
0.00913643091917038,
0.012733608484268188,
-0.022535189986228943,
-0.01788695715367794,
0.08770684897899628,
0.0006350561743602157,
-0.004042530432343483,
0.020035577937960625,
-0.029724352061748505,
0.028011677786707878,
0.025851763784885406,
-0.018825873732566833,
-0.0012582053896039724,
0.009667351841926575,
-0.006717827171087265,
-0.016443612053990364,
-0.02189367264509201,
0.020088978111743927,
0.04134364426136017,
-0.016936838626861572,
0.03407607600092888,
0.01245792955160141,
-0.024026675149798393,
-0.00840842630714178,
-0.019060766324400902,
0.023548495024442673,
0.02650308795273304,
-0.012294702231884003,
0.006548549514263868,
-0.03169499710202217,
0.027938753366470337,
0.022721143439412117,
0.0712289959192276,
-0.021041853353381157,
-0.029276225715875626,
0.04154009371995926,
0.02931651845574379,
0.03615178167819977,
-0.03032539039850235,
-0.014493338763713837,
0.06855588406324387,
-0.0444415844976902,
0.08719384670257568,
-0.010055980645120144,
0.023965662345290184,
0.029060177505016327,
-0.02483430504798889,
0.008795665577054024,
-0.025324037298560143,
-0.02159702591598034,
-0.01562025211751461,
0.045403335243463516,
0.004272643011063337,
-0.00977930799126625,
-0.04271126165986061,
0.023887576535344124,
0.04980815574526787,
0.025151485577225685,
0.03129678592085838,
-0.00008279988105641678,
-0.0447983592748642,
-0.012002784758806229,
-0.04465392231941223,
0.003656867193058133,
0.03354165330529213,
-0.00420106528326869,
-0.032715000212192535,
-0.019488321617245674,
-0.009770828299224377,
0.04518377035856247,
0.05630585923790932,
0.021945783868432045,
-0.00785119365900755,
0.04445236176252365,
0.0033962461166083813,
0.015893172472715378,
-0.023362642154097557,
0.02148246206343174,
0.13649362325668335,
0.01707911677658558,
-0.012339281849563122,
-0.05277874320745468,
0.03350088372826576,
-0.012614482082426548,
0.017669999971985817,
-0.001433448982425034,
0.017431678250432014,
-0.042638517916202545,
0.009796452708542347,
0.0052872817032039165,
0.06595688313245773,
0.011190096847712994,
0.0034507405944168568,
0.008816419169306755,
-0.006105881650000811,
-0.03569676727056503,
-0.0022587492130696774,
0.032271355390548706,
-0.02033289521932602,
0.004791458137333393,
-0.07973930984735489,
0.047679703682661057,
0.00003020129952346906,
0.0006265922565944493,
-0.063738614320755,
-0.030809925869107246,
0.0387861542403698,
-0.019114593043923378,
-0.021057097241282463,
0.013030351139605045,
0.009554590098559856,
-0.00808111671358347,
-0.05557118356227875,
-0.009552269242703915,
0.0071225217543542385,
-0.004581905901432037,
0.024166230112314224,
0.04238040745258331,
-0.005893583409488201,
0.023052934557199478,
0.026631852611899376,
0.04320187121629715,
-0.0426616296172142,
-0.00637524900957942,
-0.02895401045680046,
0.062029991298913956,
-0.02456122823059559,
-0.0014686774229630828,
0.02679864503443241,
0.0007453300640918314,
0.032189346849918365,
-0.057523008435964584,
-0.07221489399671555,
-0.0246684942394495,
-0.029202209785580635,
0.020320238545536995,
-0.008194825612008572,
-0.010884538292884827,
0.03892723470926285,
-0.04999012127518654,
-0.0035833430010825396,
-0.007863937877118587,
0.008085732348263264,
-0.013486776500940323,
0.009479583241045475,
0.06772337853908539,
-0.010107316076755524,
-0.008142724633216858,
-0.03438849374651909,
-0.028261667117476463,
-0.0323665514588356,
-0.018466386944055557,
0.0058149369433522224,
0.024713193997740746,
0.03590385615825653,
-0.014575607143342495,
-0.003840136341750622,
-0.004432830028235912,
-0.05570552125573158,
0.020094120875000954,
0.010196881368756294,
0.01930220238864422,
-0.02949403040111065,
-0.032048359513282776,
0.026506870985031128,
0.050624437630176544,
-0.03856254741549492,
-0.0015946717467159033,
0.03752363473176956,
0.02621731534600258,
-0.01971648633480072,
-0.009874076582491398,
-0.050876837223768234,
0.00755148334428668,
-0.07032162696123123,
-0.0015510044759139419,
0.0015509057557210326,
0.008770886808633804,
0.03104539029300213,
0.017307858914136887,
-0.004774822387844324,
0.054714594036340714,
-0.039119116961956024,
-0.026475178077816963,
0.028270285576581955,
-0.0306206326931715,
0.004441374447196722,
0.02636655792593956,
-0.0013768259668722749,
-0.041895437985658646,
-0.027334757149219513,
-0.013898473232984543,
-0.00048578373389318585,
0.0058535500429570675,
0.01153402030467987,
-0.027359310537576675,
-0.00822095200419426,
-0.004756465554237366,
0.01754320040345192,
-0.023522624745965004,
0.008123757317662239,
-0.05935459956526756,
-0.031705863773822784,
0.018471725285053253,
-0.0018763908883556724,
-0.02774319052696228,
0.012544610537588596,
-0.039248619228601456,
0.00009995666914619505,
0.027225153520703316,
-0.011038064956665039,
-0.05774302035570145,
-0.0076148612424731255,
0.015154271386563778,
0.048569947481155396,
0.03280014544725418,
-0.015060767531394958,
0.010273953899741173,
0.03258579596877098,
-0.045438483357429504,
-0.026694143190979958,
0.00783669762313366,
-0.005902939010411501,
0.00041840720223262906,
-0.003515764605253935,
-0.0056319390423595905,
-0.001346556469798088,
0.061090074479579926,
-0.0011765634408220649,
0.03164083510637283,
-0.038836944848299026,
-0.04684196785092354,
0.05252203717827797,
-0.06139928475022316,
0.016881028190255165,
-0.002721494762226939,
-0.020732255652546883,
0.05408084765076637,
0.04802795872092247,
0.00010849047248484567,
-0.02845747582614422,
-0.01309839729219675,
0.04671391472220421,
-0.001795908436179161,
0.024634290486574173,
-0.00768956309184432,
-0.0019686506129801273,
0.06614577025175095,
-0.06108439713716507,
0.021643467247486115,
0.018320487812161446,
0.03914078697562218,
-0.08866754174232483,
-0.008345242589712143,
0.023188207298517227,
-0.026169979944825172,
-0.00035437021870166063,
-0.02152857556939125,
-0.018379544839262962,
0.023757698014378548,
-0.08412330597639084,
-0.0021034067030996084,
-0.015011448413133621,
-0.043350908905267715,
-0.03273295983672142,
-0.04470500349998474,
-0.03170277923345566,
0.044857122004032135,
-0.0019116445910185575,
0.03853346407413483,
0.009075427427887917,
0.0027565232012420893,
-0.0134211964905262,
-0.01584268920123577,
-0.02811398170888424,
0.044014036655426025,
0.0021722568199038506,
-0.0004426646919455379,
0.047732509672641754,
-0.025615524500608444,
0.010619777254760265,
0.024625778198242188,
-0.006595180369913578,
-0.005958437453955412,
-0.014815131202340126,
-0.005598839838057756,
0.000029348522730288096,
0.02755952626466751,
-0.002704985672608018,
0.04852662235498428,
-0.02609824389219284,
0.019728489220142365,
0.027835335582494736,
0.051929354667663574,
0.009314092807471752,
-0.025644611567258835,
0.03155360370874405,
0.000674839538987726,
0.003446093527600169,
0.01942422427237034,
-0.04482703655958176,
0.028076177462935448,
-0.03629982843995094,
0.012493482790887356,
0.033881474286317825,
0.02546367049217224,
-0.0007686326862312853,
-0.017560673877596855,
0.005064085125923157,
0.019467737525701523,
0.03641020134091377,
0.00599677162244916,
0.024534082040190697,
0.009427746757864952,
-0.02835770882666111,
0.052527304738759995,
0.023578930646181107,
0.0063361008651554585,
-0.022103609517216682,
-0.014282396994531155,
-0.013579519465565681,
-0.024405330419540405,
0.025290824472904205,
-0.02415422350168228,
-0.019366832450032234,
0.04222104698419571,
0.0559147372841835,
0.011552385985851288,
0.006782738026231527,
-0.026070598512887955,
0.02790995128452778,
-0.07784928381443024,
0.03236200660467148,
-0.016042888164520264,
-0.040743809193372726,
0.009392705745995045,
-0.026170654222369194,
-0.02978316694498062,
0.03172735124826431,
0.04305380582809448,
-0.018192531540989876,
0.0046546440571546555,
0.042520977556705475,
0.0027041970752179623,
0.001484517939388752,
-0.03514386713504791,
-0.00066570402123034,
0.03997945040464401,
-0.010967304930090904,
-0.0038479892536997795,
-0.0234425887465477,
-0.03865491971373558,
0.029002023860812187,
0.018566984683275223,
-0.008682441897690296,
0.005082104355096817,
-0.01288369856774807,
-0.05603524670004845,
0.004609358962625265,
0.02602086029946804,
-0.0022677744273096323,
0.04324129596352577,
-0.015477640554308891,
-0.006341585423797369,
-0.009459820576012135,
-0.031148144975304604,
-0.03875577077269554,
0.023119617253541946,
-0.07634139060974121,
0.038011081516742706,
-0.02630845084786415,
0.006866473238915205,
0.049049943685531616,
-0.0008408449357375503,
-0.00494910404086113,
0.04065999761223793,
-0.059126436710357666,
0.0020319418981671333,
0.062153179198503494,
0.03855929151177406,
0.041161373257637024,
-0.02662852220237255,
0.009693006984889507,
0.030255408957600594,
0.011315587908029556,
-0.004720109514892101,
0.05830506980419159,
-0.005329472478479147,
0.022224562242627144,
-0.014725208282470703,
0.07154983282089233,
0.00020078630768693984,
0.0021730330772697926,
-0.007198854349553585,
0.00798511877655983,
-0.02678687311708927,
0.018137525767087936,
0.03839443251490593,
-0.039912980049848557,
0.004851469770073891,
0.005020993296056986,
-0.005888098385185003,
0.08667025715112686,
-0.017146211117506027,
-0.010371671058237553,
0.010226164013147354,
0.016341421753168106,
0.018482692539691925,
0.006880820728838444,
-0.00048090709606185555,
0.021114753559231758,
-0.020070483908057213,
-0.031913984566926956,
-0.045159194618463516,
0.005741741042584181,
0.019224101677536964,
-0.024127574637532234,
-0.02994031272828579,
-0.043878473341464996,
0.024345381185412407,
0.011420183815062046,
0.012524220161139965,
-0.014359778724610806,
0.010723993182182312,
0.020831163972616196,
0.019798176363110542,
0.04276303946971893,
-0.00355082587338984,
0.004351336508989334,
-0.016679586842656136,
0.05676509067416191,
-0.02379251830279827,
-0.024196244776248932,
-0.012681248597800732,
0.01665051281452179,
-0.013414556160569191,
0.010174795053899288
] |
<p>I have a few questions about 3D waves:</p>
<ol>
<li>Are all 3D waves types of electromagnetic radiation?</li>
<li>Are all 2D waves mechanical?</li>
</ol>
| 8,441 |
[
-0.036185525357723236,
-0.010823949240148067,
-0.032985396683216095,
-0.05244935303926468,
0.03581205755472183,
0.01926491968333721,
-0.0510413832962513,
-0.05073351785540581,
0.011020967736840248,
-0.058805473148822784,
0.03297526761889458,
0.028503118082880974,
0.04866718873381615,
0.04673963040113449,
0.04225102812051773,
0.008861069567501545,
-0.005830220878124237,
-0.010509004816412926,
0.0019544002134352922,
-0.016964389011263847,
-0.034207090735435486,
0.002656544791534543,
-0.01154167577624321,
0.013958699069917202,
-0.03676038980484009,
0.024371644482016563,
0.06183675304055214,
0.0036558264400810003,
0.05395785719156265,
0.009789632633328438,
0.004164636135101318,
-0.02802974171936512,
-0.0048172688111662865,
0.02687070704996586,
0.0023266307543963194,
-0.03446388617157936,
-0.0525737963616848,
-0.006812287960201502,
-0.004456420429050922,
0.01132457796484232,
0.0024780617095530033,
0.011646401137113571,
-0.04571179300546646,
0.055150385946035385,
-0.019257688894867897,
0.012542951852083206,
0.003566234838217497,
-0.021676216274499893,
0.015285145491361618,
-0.0790971964597702,
0.08766423165798187,
-0.021504860371351242,
0.018155643716454506,
-0.00020758344908244908,
-0.009122919291257858,
-0.0010213812347501516,
0.07856863737106323,
0.048344746232032776,
-0.007959991693496704,
-0.05046173930168152,
0.009935191832482815,
0.009434807114303112,
-0.004355745390057564,
-0.03103063441812992,
-0.03312733769416809,
0.03884073346853256,
-0.01671525649726391,
-0.016733085736632347,
0.016582781448960304,
-0.012872525490820408,
0.0042040287517011166,
0.009961816482245922,
0.025649864226579666,
-0.03928697854280472,
-0.008901541121304035,
-0.02671055682003498,
0.013352490030229092,
0.027058569714426994,
0.04665476828813553,
0.01940862089395523,
0.0013779285363852978,
-0.015274666249752045,
-0.0033412370830774307,
0.009594383649528027,
-0.008097718469798565,
-0.02504974789917469,
0.09952601045370102,
0.019859440624713898,
-0.01658673770725727,
-0.008549475111067295,
-0.0014153550146147609,
-0.011254936456680298,
0.007950672879815102,
-0.005519429221749306,
-0.01908021792769432,
0.01999780908226967,
0.020527096465229988,
0.024581627920269966,
0.015511472709476948,
-0.05496736988425255,
0.016282573342323303,
0.010721579194068909,
0.03278150036931038,
0.07425441592931747,
-0.00394231453537941,
0.008092439733445644,
-0.0415412001311779,
0.04044432193040848,
-0.026040269061923027,
-0.00023255440464708954,
-0.030555007979273796,
0.020282547920942307,
-0.026668792590498924,
-0.0024903840385377407,
-0.01015927642583847,
-0.013095621950924397,
0.025702863931655884,
-0.03680979460477829,
0.025935692712664604,
0.12859992682933807,
0.0371716246008873,
-0.05144769325852394,
0.022483201697468758,
-0.0254156906157732,
-0.09107813239097595,
0.0031958853360265493,
0.017043337225914,
0.0035353689454495907,
-0.045454349368810654,
0.02941238135099411,
0.002685602055862546,
0.0007041675271466374,
0.012287754565477371,
-0.03037877194583416,
0.03239087387919426,
-0.03768936172127724,
-0.09156270325183868,
-0.06543222069740295,
-0.00411184411495924,
-0.009167495183646679,
-0.03217259421944618,
-0.06059990078210831,
-0.00028855112032033503,
0.03592827171087265,
0.05638742446899414,
-0.007958837784826756,
-0.006684976629912853,
-0.0037054854910820723,
0.06384412199258804,
-0.010989130474627018,
-0.023102959617972374,
0.009472875855863094,
-0.006036438979208469,
-0.04699677601456642,
0.016480619087815285,
-0.061425868421792984,
0.022982245311141014,
0.01521230861544609,
0.009590907022356987,
-0.017644692212343216,
0.05957501381635666,
-0.029802214354276657,
0.009503110311925411,
0.05138473957777023,
-0.03145625442266464,
-0.032382234930992126,
0.055343206971883774,
-0.002520590089261532,
0.03086877055466175,
0.03027857281267643,
-0.028767718002200127,
0.018161555752158165,
0.008358183316886425,
0.03256653994321823,
0.027053451165556908,
-0.006212451960891485,
-0.02049737609922886,
0.007130327634513378,
0.01835041120648384,
0.007769785355776548,
-0.045954130589962006,
-0.04313509911298752,
0.0103055564686656,
0.0229510385543108,
-0.0028182826936244965,
0.059777021408081055,
0.00041697261622175574,
-0.004602037835866213,
-0.0018236639443784952,
-0.04237772151827812,
0.013817149214446545,
-0.00651976652443409,
0.05398393049836159,
-0.019322922453284264,
0.010248668491840363,
0.0064689465798437595,
0.030221957713365555,
0.01382421050220728,
-0.037091441452503204,
-0.04211268946528435,
-0.007050652056932449,
0.07165978103876114,
0.017522143200039864,
-0.01696608029305935,
0.016926726326346397,
0.06805375963449478,
0.024229781702160835,
-0.02020912989974022,
0.012084039859473705,
-0.01695113070309162,
-0.01313006691634655,
0.0021462130825966597,
-0.029399171471595764,
0.01760537549853325,
-0.017680391669273376,
0.032318271696567535,
0.033080682158470154,
0.014763724990189075,
-0.05832548439502716,
0.02325589954853058,
-0.03751756623387337,
0.05896459147334099,
0.04342477768659592,
-0.0192398838698864,
0.008141126483678818,
0.026738561689853668,
-0.017760830000042915,
0.04005533456802368,
0.0370849072933197,
-0.008196650072932243,
-0.07120806723833084,
0.004819118417799473,
0.011195775121450424,
0.017030134797096252,
-0.055172067135572433,
0.02812681347131729,
0.009975215420126915,
0.04533698037266731,
0.05760427191853523,
0.013307142071425915,
-0.027595816180109978,
-0.04857494682073593,
0.016811251640319824,
-0.0025162184610962868,
0.015648964792490005,
0.038238927721977234,
0.030512379482388496,
0.03009100817143917,
0.009823069907724857,
-0.02262047864496708,
-0.019482512027025223,
0.061981286853551865,
-0.020006397739052773,
0.0017240046290680766,
0.03469086065888405,
-0.03817548230290413,
0.023458315059542656,
-0.024305760860443115,
-0.00540582463145256,
0.035782571882009506,
-0.027341758832335472,
-0.025075843557715416,
0.003966542426496744,
0.00853111781179905,
0.014688167721033096,
0.018209733068943024,
-0.010404807515442371,
-0.02806725725531578,
0.0358695462346077,
-0.030708307400345802,
-0.0031742812134325504,
-0.019195277243852615,
-0.021942805498838425,
-0.0033601250033825636,
-0.017422297969460487,
0.04184757545590401,
-0.009565466083586216,
0.059947606176137924,
-0.0531926304101944,
-0.048342566937208176,
0.009722874499857426,
-0.043003443628549576,
0.010596894659101963,
-0.004128025844693184,
-0.04853207990527153,
0.023960649967193604,
-0.042497675865888596,
-0.04923299700021744,
0.028730008751153946,
-0.03653896972537041,
-0.003540454199537635,
0.028766557574272156,
-0.03156137093901634,
-0.057612862437963486,
-0.0015760172391310334,
-0.020393749698996544,
0.05440624803304672,
-0.0027522780001163483,
-0.00506008742377162,
0.039385970681905746,
-0.016766490414738655,
-0.00936137791723013,
-0.0007464998634532094,
-0.005719583015888929,
-0.01972057670354843,
-0.020833438262343407,
-0.023831726983189583,
0.03441457822918892,
-0.03981776535511017,
0.00041642793803475797,
0.04132658243179321,
-0.06303779780864716,
0.0494513176381588,
-0.04014983028173447,
-0.06626127660274506,
0.02610640786588192,
-0.04202329367399216,
0.04443409666419029,
-0.0029622598085552454,
-0.040964383631944656,
0.05096264183521271,
0.0395229272544384,
-0.052013300359249115,
0.029161399230360985,
-0.022730853408575058,
-0.01933336816728115,
-0.02842654660344124,
0.033444542437791824,
0.023159099742770195,
-0.025882378220558167,
0.008871586993336678,
0.03370598703622818,
0.009790897369384766,
0.03753245994448662,
0.011620714329183102,
-0.006669718772172928,
0.01887085661292076,
0.02425013668835163,
0.0005899580428376794,
0.054518502205610275,
0.03531724959611893,
-0.03338218480348587,
0.024035971611738205,
-0.021023983135819435,
0.005925180856138468,
-0.001478775404393673,
-0.03247203305363655,
0.04911945387721062,
0.012250062078237534,
0.014500172808766365,
-0.02146451361477375,
0.05411454290151596,
0.02514929696917534,
-0.02703152224421501,
0.006804552394896746,
0.02385793626308441,
0.03577026352286339,
-0.008188094012439251,
0.011872589588165283,
0.0197185967117548,
0.03474951907992363,
-0.050147153437137604,
0.012390490621328354,
0.012537538073956966,
0.026129771023988724,
0.007786466274410486,
0.0040540508925914764,
-0.0268732700496912,
0.047212645411491394,
0.050278306007385254,
0.03234371915459633,
0.01419548224657774,
-0.02661995217204094,
-0.00015683671517763287,
-0.02575046196579933,
0.008772647008299828,
-0.006429529748857021,
0.0332377627491951,
0.0017962356796488166,
0.07755392044782639,
0.030835095793008804,
0.002082062652334571,
0.06721339374780655,
0.006830137688666582,
-0.0700569823384285,
-0.00506610469892621,
-0.029236845672130585,
0.01628243178129196,
-0.02597370557487011,
-0.01581418141722679,
-0.0355704240500927,
-0.025466345250606537,
-0.050200071185827255,
-0.03324202820658684,
-0.026231279596686363,
-0.060012634843587875,
-0.005990338511765003,
-0.028180966153740883,
-0.017127269878983498,
0.0073363883420825005,
0.045408379286527634,
0.004076950717717409,
-0.00838005542755127,
-0.006974427495151758,
0.06257042288780212,
-0.04515894874930382,
0.014561415649950504,
0.026669953018426895,
-0.005199654959142208,
-0.02103063277900219,
0.02401745691895485,
0.014135440811514854,
0.005882491823285818,
0.0009212190634571016,
0.005268831737339497,
0.015918930992484093,
0.04077845811843872,
0.0039059389382600784,
-0.010037941858172417,
-0.050387319177389145,
-0.031775396317243576,
-0.004582251887768507,
-0.009397991932928562,
0.0742456242442131,
0.02346089854836464,
-0.022192226722836494,
0.024876544252038002,
-0.018329409882426262,
-0.0234945397824049,
0.03858540207147598,
0.025491919368505478,
-0.015615895390510559,
-0.023337790742516518,
-0.04522617161273956,
-0.022288426756858826,
-0.026840779930353165,
-0.04213258996605873,
0.013658343814313412,
-0.01611269824206829,
-0.03961969539523125,
0.02814560942351818,
0.007521643303334713,
-0.00804166216403246,
-0.017465868964791298,
0.012793950736522675,
-0.004375946242362261,
-0.00721342209726572,
-0.009893734008073807,
-0.024101098999381065,
-0.018641291186213493,
0.0691254585981369,
0.05043337866663933,
-0.007397050969302654,
-0.05093727260828018,
-0.09626178443431854,
0.009180177003145218,
0.012003542855381966,
0.048014625906944275,
-0.011331427842378616,
-0.009214998222887516,
-0.044762905687093735,
-0.0391470305621624,
0.02385270781815052,
-0.015276908874511719,
0.010173123329877853,
-0.016810452565550804,
-0.025825951248407364,
-0.04659228399395943,
-0.005268633831292391,
-0.006698393728584051,
-0.0018593267304822803,
-0.01127025205641985,
0.025400059297680855,
-0.026991290971636772,
-0.0038190570194274187,
-0.003931110724806786,
-0.0048609534278512,
0.014871619641780853,
0.032952211797237396,
0.006449829787015915,
-0.006167029496282339,
0.004328242968767881,
0.01598808914422989,
-0.04615884646773338,
-0.04911119490861893,
-0.00699889799579978,
0.0413895808160305,
-0.01273617148399353,
0.062107477337121964,
-0.019807493314146996,
-0.04516003653407097,
0.01874392479658127,
0.01532900519669056,
0.007163663394749165,
0.01237678062170744,
-0.012239553965628147,
0.014992333017289639,
0.007243093103170395,
0.01026051677763462,
-0.0013682113494724035,
0.06329312175512314,
-0.03603439778089523,
-0.014601397328078747,
-0.012361166067421436,
0.060933444648981094,
-0.040999334305524826,
-0.030539490282535553,
-0.013023987412452698,
0.0011697339359670877,
-0.03440190479159355,
0.0535883791744709,
-0.0047664097510278225,
-0.00744972936809063,
-0.004557269625365734,
-0.023122692480683327,
-0.013000888749957085,
0.036694593727588654,
0.0009669721475802362,
-0.01751018315553665,
-0.027062319219112396,
0.0028219467494636774,
-0.015528809279203415,
-0.012500757351517677,
0.012449975125491619,
0.005668025463819504,
0.024822713807225227,
0.02576330304145813,
0.013365529477596283,
0.02055354416370392,
-0.050398655235767365,
0.02796625718474388,
-0.03157103434205055,
-0.06816356629133224,
0.02717215195298195,
0.0030007208697497845,
0.008865097537636757,
0.010120472870767117,
-0.04438334330916405,
-0.005401821341365576,
-0.007003533188253641,
0.0017812959849834442,
0.04217486456036568,
-0.023772021755576134,
0.05573849380016327,
0.019005104899406433,
0.03697402402758598,
-0.03737970441579819,
-0.053491417318582535,
0.01360411662608385,
0.042974650859832764,
-0.0041245026513934135,
-0.021287212148308754,
0.031493671238422394,
-0.0435897633433342,
-0.014533661305904388,
-0.005064824596047401,
0.057436052709817886,
-0.051062241196632385,
-0.024752605706453323,
0.04074043780565262,
0.00282116187736392,
0.05191875994205475,
0.0335879847407341,
-0.05594031512737274,
0.02500658482313156,
-0.00923607312142849,
0.024492822587490082,
-0.03191488981246948,
0.04842294007539749,
-0.013684113509953022,
-0.03755135461688042,
-0.0017632526578381658,
-0.0016869916580617428,
0.05317121744155884,
-0.03292826563119888,
-0.000007286984327947721,
0.03195726498961449,
0.015466089360415936,
-0.04491718113422394,
-0.03090461529791355,
0.04111669212579727,
-0.052490826696157455,
0.023135816678404808,
-0.030548768118023872,
0.011085848324000835,
-0.06398623436689377,
-0.026849966496229172,
0.020577015355229378,
0.0025782391894608736,
0.0055836564861238,
0.015393379144370556,
0.038688186556100845,
-0.006888658739626408,
0.025517597794532776,
-0.020498663187026978,
-0.017947515472769737,
-0.0022998214699327946,
-0.018731029704213142,
0.00943415705114603,
0.03241414204239845,
0.04355745017528534,
0.018932318314909935,
-0.026331963017582893,
-0.04244307428598404,
-0.0011713637504726648,
0.09156810492277145,
-0.03170301020145416,
0.05676833912730217,
0.029293734580278397,
0.014982471242547035,
0.012435889802873135,
-0.017377449199557304,
0.015704035758972168,
0.03250420466065407,
0.01156576070934534,
0.008205359801650047,
-0.01486814022064209,
0.03196800500154495,
0.0031584007665514946,
0.0335344560444355,
-0.019008586183190346,
-0.0011190164368599653,
0.025340184569358826,
0.016843358054757118,
-0.0004587255825754255,
0.001588406041264534,
-0.037823520600795746,
0.05446634441614151,
-0.030546965077519417,
0.019380996003746986,
0.004574949387460947,
-0.0098299290984869,
0.04362599179148674,
0.017243286594748497,
-0.014467562548816204,
-0.016933448612689972,
0.012580113485455513,
-0.050851065665483475,
0.023898623883724213,
0.01602252572774887,
0.024713926017284393,
0.002367365173995495,
-0.008801973424851894,
0.06721699982881546,
-0.008180840872228146,
0.005977738182991743,
0.02422267757356167,
-0.07054450362920761,
-0.004968253895640373,
-0.006300749257206917,
-0.035161472856998444,
0.06658454984426498,
0.02532406710088253,
-0.017939023673534393,
0.00016173013136722147,
-0.020808687433600426,
0.02884400449693203,
0.011167867109179497,
0.05125079303979874,
-0.026335209608078003,
0.023008204996585846,
-0.018343986943364143,
0.005918931216001511,
-0.018164988607168198,
-0.023732729256153107,
0.08898060023784637,
0.03877459838986397,
0.03315257281064987,
-0.03683203086256981,
0.012508627958595753,
-0.033202748745679855,
-0.0021026793401688337,
-0.03110954351723194,
0.009094730950891972,
-0.026475682854652405,
0.03347187489271164,
-0.00766559736803174,
0.052150025963783264,
-0.0038823194336146116,
0.0046141366474330425,
0.03973604366183281,
-0.02962644398212433,
-0.037930503487586975,
-0.004545124247670174,
0.032320357859134674,
0.008853161707520485,
0.04569627717137337,
-0.0534571148455143,
0.05167442187666893,
-0.04314305633306503,
-0.015452781692147255,
-0.029862547293305397,
-0.03380866348743439,
0.06870585680007935,
-0.0011443892726674676,
-0.05384214594960213,
-0.0035145620349794626,
0.009344522841274738,
-0.016297826543450356,
-0.05722418427467346,
0.03977063670754433,
0.023414120078086853,
0.0008297550375573337,
0.005405362695455551,
0.035572029650211334,
0.017531853169202805,
-0.01886715553700924,
-0.004213913809508085,
0.02799609676003456,
-0.06092469394207001,
0.00932266190648079,
-0.03295188769698143,
0.018965119495987892,
0.01377257052809,
0.017021119594573975,
-0.007992294616997242,
0.029848065227270126,
-0.00475667929276824,
-0.06491643190383911,
0.013012511655688286,
-0.014847799204289913,
0.05402028188109398,
-0.02355334535241127,
-0.02764369174838066,
-0.04891705513000488,
0.0060073561035096645,
-0.008461985737085342,
0.022406524047255516,
-0.017677592113614082,
-0.005086025223135948,
0.01079406775534153,
0.005298728123307228,
0.03207555040717125,
-0.012199428863823414,
-0.018618760630488396,
-0.041203904896974564,
-0.017365872859954834,
-0.010177313350141048,
0.002044734312221408,
0.011880584061145782,
0.032671503722667694,
0.029270268976688385,
0.032761432230472565,
-0.029148053377866745,
-0.014527981169521809,
-0.0660628154873848,
0.012666095048189163,
0.0004692254588007927,
0.006745775695890188,
-0.010758636519312859,
0.01758888177573681,
0.04344678670167923,
0.024258660152554512,
-0.005858045537024736,
0.05665689706802368,
-0.020610583946108818,
0.0050530158914625645,
0.00844807643443346,
-0.020794112235307693,
-0.03567272424697876,
0.014198336750268936,
-0.025678690522909164,
0.011251836083829403,
-0.01688665896654129,
0.013176977634429932,
0.043430134654045105,
0.010386877693235874,
0.009334967471659184,
0.023326927796006203,
-0.03694475069642067,
-0.006672673858702183,
0.018233267590403557,
-0.03131021186709404,
0.03767680376768112,
0.051002684980630875,
0.004532753489911556,
-0.025580337271094322,
-0.04075144976377487,
-0.02800731547176838,
0.021922556683421135,
-0.00863935798406601,
0.03220073878765106,
-0.0062022702768445015,
0.0035394623409956694,
-0.019830117002129555,
0.018417129293084145,
-0.049264077097177505,
-0.03430867940187454,
-0.030713025480508804,
-0.001152180484496057,
0.0005771172582171857,
-0.019360430538654327,
-0.01785215549170971,
0.025994708761572838,
-0.03972570598125458,
0.00443530036136508,
0.031367551535367966,
0.02275150828063488,
-0.03707268461585045,
0.0020338601898401976,
0.024180861189961433,
-0.004738174844533205,
0.050829898566007614,
0.01990383304655552,
-0.040774039924144745,
0.04213102161884308,
-0.01720648631453514,
-0.029269451275467873,
0.002582572866231203,
-0.032450105994939804,
0.044432830065488815,
0.04352841526269913,
-0.0339435450732708,
0.021349117159843445,
0.036778997629880905,
0.0010079307248815894,
0.014034982770681381,
-0.021268514916300774,
-0.045759640634059906,
-0.027816100046038628,
-0.013140909373760223,
0.0022721218410879374,
0.0005418469081632793,
-0.017040325328707695,
0.04819301515817642,
0.027456752955913544,
0.021410033106803894,
0.0019908687099814415,
0.005251792725175619,
-0.003051119390875101,
0.007922863587737083,
0.03331650048494339,
0.01149515900760889,
0.04190121591091156,
0.029389558359980583,
-0.013070492073893547,
0.05833376571536064,
0.023906638845801353,
-0.014010273851454258,
-0.11776576191186905,
-0.012073107995092869,
0.025603121146559715,
0.0019912091083824635,
0.026775654405355453,
-0.049875449389219284,
-0.014237022958695889,
0.02629578858613968,
-0.07863946259021759,
0.03347296640276909,
0.005640509072691202,
-0.016093578189611435,
-0.019673706963658333,
-0.004004975315183401,
-0.01206311583518982,
0.026012400165200233,
-0.011129355989396572,
0.059909671545028687,
0.0002755740424618125,
0.021202214062213898,
-0.0363706573843956,
-0.020315514877438545,
-0.0028807613998651505,
0.03730210289359093,
0.01238629873842001,
-0.01574261672794819,
0.033088307827711105,
-0.007816922850906849,
-0.02007453329861164,
0.025785507634282112,
0.0018289764411747456,
0.029535798355937004,
0.006646571680903435,
0.0034019474405795336,
0.019154775887727737,
0.004945297259837389,
0.027203325182199478,
-0.0037461803294718266,
-0.00997176207602024,
0.03464164957404137,
-0.004190337378531694,
0.018203286454081535,
0.006014718208462,
0.004695497918874025,
0.015895355492830276,
-0.06319118291139603,
-0.017929628491401672,
0.04308411851525307,
-0.02912908047437668,
-0.013316682539880276,
-0.024960245937108994,
-0.02836335264146328,
0.02257726714015007,
-0.017297735437750816,
0.010503903962671757,
-0.05163818597793579,
-0.013605288229882717,
0.006858232896775007,
-0.005185530986636877,
0.0018790200119838119,
0.01682189665734768,
0.01260277722030878,
-0.043007977306842804,
0.020572835579514503,
-0.0012782937847077847,
0.013671059161424637,
-0.060220737010240555,
0.03195780888199806,
0.03688294440507889,
0.02413116954267025,
0.004475760739296675,
-0.02463654987514019,
-0.027120787650346756,
0.032949626445770264,
0.007901986129581928,
-0.0062695713713765144,
0.002793736057356,
-0.04600692167878151,
-0.06305523216724396,
-0.08648905903100967,
0.03954337164759636,
0.008507484570145607,
-0.034664370119571686,
-0.06145268678665161,
-0.0009938357397913933,
-0.03212311863899231,
0.06717262417078018,
0.05631858855485916,
-0.018352601677179337,
0.015324164181947708,
0.02081906609237194,
0.004941239953041077,
0.04368393123149872,
-0.061583731323480606,
-0.030683297663927078,
0.020557450130581856,
-0.03131720796227455,
-0.015667585656046867,
-0.003255822230130434,
-0.031727638095617294,
0.0068459538742899895,
0.04138214886188507,
0.002368099754676223,
0.04077059030532837,
-0.026538090780377388,
-0.040560223162174225,
0.01013348437845707,
0.00024564057821407914,
-0.04575559124350548,
0.056628499180078506,
-0.05058657377958298,
0.0034196737688034773,
0.02231549471616745,
-0.04937637597322464,
-0.007884266786277294,
-0.003371849888935685,
-0.02500053308904171,
0.0244932658970356,
-0.008952747099101543,
-0.01621651090681553,
0.05412137135863304,
-0.038103047758340836,
-0.031072907149791718,
0.03258201852440834,
-0.036467425525188446,
0.008377389051020145,
0.05172397941350937,
0.03876609355211258,
0.00929045956581831,
-0.0011607162887230515,
0.032438408583402634,
0.021043436601758003,
-0.04643012210726738,
0.012364164926111698,
0.04460109770298004,
0.05158443748950958,
-0.009387130849063396,
-0.014913203194737434,
0.05233582481741905,
-0.014336558990180492,
-0.008659613318741322,
0.01754896715283394,
0.014198108576238155,
-0.025870410725474358,
-0.016916638240218163,
0.04216818884015083,
0.0166673231869936,
-0.02565484121441841,
0.03627869859337807,
-0.014590012840926647,
0.05992178991436958,
-0.018216636031866074,
0.016616232693195343,
-0.03758308291435242,
0.00429499289020896,
-0.00387719739228487,
0.015794476494193077,
0.027720650658011436,
0.04509599506855011,
0.007477279286831617,
0.009942814707756042,
-0.04084894806146622,
-0.0183496605604887,
0.04929495230317116,
-0.03861173987388611,
0.04142122343182564,
-0.022505320608615875,
-0.0014990001218393445,
-0.017961304634809494,
-0.005315779708325863,
-0.023164521902799606,
-0.004709300585091114,
0.02209809608757496,
0.0289135854691267,
-0.0017727629747241735,
-0.009999958798289299,
0.018056605011224747,
-0.05405142530798912,
0.028184253722429276,
-0.05959362909197807,
0.012579739093780518,
-0.017133943736553192,
0.02543579787015915,
0.017253195866942406,
-0.007748618256300688
] |
<p>I am approaching this from an intuitive perspective and I don't speak the language. However, I have been doing a lot of reading about Bell's Theorum and how invalidates either locality or counterfactual definiteness. </p>
<p>From my point of view, locality is the concept that there is no way that two particles can interact with each other "instantaneously" at a distance (i.e. faster than light.). Realism/counterfactual definitiveness is the concept that all particles have some true value for all variables at some instant regardless of whether or not that value was observed. Let's assume for the sake of this question that locality is true, which I believe is the current popular model in QM.</p>
<p>Assuming locality, why do Bell's Inequalities show that conterfactual definiveness must be false?</p>
<p><strong>Edit to respond to below post:</strong></p>
<p>This is crazy. Let me see if I am following you. I'll use your framework. </p>
<p>I'm not really sure what spin is but I'm seeing it as an observable phenomenon that exists as a function of a specific direction in a given particle at an instant of time, and the spin itself at any angle changes (randomly?) over time.</p>
<p>A and B are, we are assuming, perfectly correlated so so the spin at angle θ in A is definitely the same as the spin at angle θ in B. In any given electron (let's just take A) we can define some angle θ as the angle between two 'directions' on that electron that have an exactly 99% correlated spin. There's no way we can measure those two directions on the same particle at the same time, but since A and B are perfectly correlated, we can measure A at 0 degrees and B at θ degrees and experimentally we would see that they are the same spin This is crazy. Let me see if I am following you. A and B are, we are assuming, perfectly correlated so so the spin at angle θ in A is definitely the same as the spin at angle θ in B. In any given electron (let's just take A) we can define some angle θ as the angle between two 'directions' on that electron that have an exactly 99% correlated spin. There's no way we can measure those two directions on the same particle at the same time, but since A and B are perfectly correlated, we can measure A at 0 degrees and B at θ degrees and they will be the same spin 99% of the time.</p>
<p>Similarly, if we measure the spin at θ in A and at 2θ in B, we will see that these two values are the same spin 99% of the time. Assumingly, this will work for any two angles that are exactly θ apart -- with enough measurements they will be correlated exactly 99% of the time.</p>
<p>However, if we measure the spin at 0 in A and at 2θ in B, they are only correlated 96% of the time. If V0 is at most 1% off from V1, and V1 is at most 1% off from V2, V0 should be anywhere from 0-2% off from V2. But, we find, according to QM and experimentation, it is not! It is less heavily correlated than that.</p>
<p>This is where I lose you. Why does saying no to realism resolve this issue?</p>
| 8,442 |
[
0.005226712208241224,
0.0024363137781620026,
0.018621202558279037,
-0.060730814933776855,
0.06867379695177078,
0.007300578989088535,
-0.04489023610949516,
0.017079802230000496,
0.028364263474941254,
-0.031838309019804,
0.029975656419992447,
0.05018848553299904,
-0.016449017450213432,
0.01229330338537693,
0.010827919468283653,
0.02082810178399086,
0.026995712891221046,
-0.00455841887742281,
-0.01004769466817379,
-0.026597511023283005,
0.018724901601672173,
0.044620953500270844,
0.024071451276540756,
-0.0028535863384604454,
0.015021908096969128,
0.03829188272356987,
0.019100967794656754,
0.007576024625450373,
-0.0027730439323931932,
0.06602863222360611,
-0.021860269829630852,
-0.048592567443847656,
0.00958558265119791,
0.005782735534012318,
0.03057885728776455,
-0.027645815163850784,
0.0009744425187818706,
-0.015520118176937103,
-0.00463475938886404,
0.023462260141968727,
-0.04271366819739342,
-0.02111070603132248,
-0.014468714594841003,
0.06296780705451965,
-0.01691346801817417,
-0.007543927989900112,
-0.0012182985665276647,
0.013727875426411629,
0.06068764254450798,
-0.05429288372397423,
0.05481197312474251,
-0.023487882688641548,
0.028163593262434006,
0.006128709763288498,
-0.0063237822614610195,
-0.003452360862866044,
0.09203220903873444,
0.05663812905550003,
-0.00726786395534873,
-0.04307872802019119,
-0.028416156768798828,
-0.029098009690642357,
0.009682691656053066,
-0.002965001156553626,
-0.026597673073410988,
-0.004892943426966667,
0.008982415311038494,
0.0034680734388530254,
-0.008814379572868347,
-0.026962997391819954,
0.016286790370941162,
-0.013558484613895416,
0.027354668825864792,
-0.00039452992496080697,
0.0007832957780919969,
-0.04840731620788574,
0.0037325513549149036,
-0.005807031411677599,
0.010903971269726753,
0.03446559980511665,
-0.0470525361597538,
-0.0007187665905803442,
0.032918862998485565,
0.005413947161287069,
-0.012457010336220264,
-0.009851552546024323,
0.05611481890082359,
0.002610165858641267,
-0.02616184577345848,
0.05662938207387924,
-0.018971329554915428,
0.03432343900203705,
0.017740413546562195,
-0.003002908080816269,
-0.037530094385147095,
0.03683256357908249,
-0.010302995331585407,
0.0390826091170311,
-0.024824004620313644,
-0.044344332069158554,
-0.0006703737308271229,
-0.03803136944770813,
-0.009594661183655262,
0.07771550118923187,
-0.02997462823987007,
-0.0069734035059809685,
-0.020214416086673737,
0.029645422473549843,
0.003267320105805993,
-0.027626531198620796,
-0.026074470952153206,
0.03865450620651245,
-0.008260875009000301,
0.025428395718336105,
-0.014835644513368607,
-0.02707051672041416,
0.010105123743414879,
-0.01428475696593523,
0.09157557040452957,
0.06462519615888596,
0.022480931133031845,
-0.030259663239121437,
-0.014396866783499718,
-0.03040214627981186,
-0.04215225204825401,
-0.015984704717993736,
0.029208721593022346,
0.019753973931074142,
-0.029664896428585052,
0.023719819262623787,
0.034132327884435654,
-0.011932029388844967,
0.013922072015702724,
-0.005813359282910824,
0.02907394990324974,
-0.04743843898177147,
-0.1376463919878006,
-0.05770615115761757,
0.05781212076544762,
0.022915013134479523,
-0.025616483762860298,
-0.06770315021276474,
0.001293036388233304,
0.022097043693065643,
0.08379465341567993,
-0.013131215237081051,
0.025764966383576393,
-0.0024841867852956057,
0.0013401468750089407,
0.019924435764551163,
-0.006758817005902529,
0.0018328260630369186,
0.01605604961514473,
-0.022160427644848824,
-0.01581779308617115,
-0.04410376772284508,
0.006123068276792765,
0.021325325593352318,
-0.011365024372935295,
-0.012784406542778015,
0.05072290822863579,
-0.036445263773202896,
0.028831545263528824,
0.03377363458275795,
-0.007586440071463585,
-0.026055755093693733,
0.11819716542959213,
0.02769775316119194,
-0.009482976980507374,
0.03232135623693466,
0.002092910697683692,
0.010332814417779446,
0.008952287025749683,
-0.006745583843439817,
0.01847386173903942,
-0.03623703867197037,
-0.00798293948173523,
-0.0555482879281044,
0.008557853288948536,
-0.017910895869135857,
-0.048699717968702316,
-0.025839833542704582,
-0.04130168631672859,
0.014274666085839272,
-0.012020141817629337,
0.03848961740732193,
-0.03460947051644325,
-0.010196427814662457,
-0.013989017345011234,
-0.03851182386279106,
-0.011904234997928143,
-0.08093836903572083,
0.008398840203881264,
-0.004979017190635204,
-0.027140220627188683,
0.07572565227746964,
0.024471618235111237,
0.005360315088182688,
-0.02946164272725582,
-0.058339495211839676,
-0.04577423632144928,
0.03897895663976669,
0.012689455412328243,
-0.013606362044811249,
0.05328861251473427,
0.05261440947651863,
0.017181865870952606,
0.0015572905540466309,
0.013294776901602745,
0.031771764159202576,
-0.03704804927110672,
0.013348951004445553,
-0.019422810524702072,
0.00792402308434248,
0.03499958664178848,
0.007489015813916922,
0.0015793369384482503,
0.0018270853906869888,
-0.04769761860370636,
0.010595455765724182,
-0.022529594600200653,
0.0679013803601265,
0.003205373417586088,
0.010752823203802109,
0.004930721130222082,
0.04836171865463257,
0.021187985315918922,
0.0019934505689889193,
0.011634153313934803,
-0.0254477858543396,
-0.024810317903757095,
-0.0005809625145047903,
0.026644444093108177,
0.023452065885066986,
-0.014394735917448997,
0.024140961468219757,
-0.0022272916976362467,
0.04805583506822586,
0.011000899598002434,
0.025865783914923668,
-0.025169577449560165,
-0.035695865750312805,
-0.009288117289543152,
-0.004399240482598543,
-0.0026471076998859644,
0.03765961527824402,
0.02929774858057499,
-0.008783427067101002,
0.02096191793680191,
-0.03362386301159859,
-0.0009521999163553119,
0.01593833602964878,
-0.004749600775539875,
-0.007181178778409958,
-0.004899225663393736,
-0.038778550922870636,
0.03094770759344101,
0.020383182913064957,
0.021652422845363617,
0.00817695539444685,
-0.027250828221440315,
-0.017722129821777344,
-0.03417993709445,
-0.03742222115397453,
0.013681400567293167,
0.0018780090613290668,
-0.027336182072758675,
-0.021186258643865585,
0.008375531993806362,
-0.026209266856312752,
-0.008495403453707695,
-0.01425021979957819,
-0.022211872041225433,
0.00002851630597433541,
0.006335495505481958,
0.06033714488148689,
0.045575469732284546,
-0.0044487095437943935,
0.005296315997838974,
-0.033913884311914444,
0.026805680245161057,
-0.029158689081668854,
0.025928590446710587,
-0.002022167667746544,
-0.06355508416891098,
0.03385738655924797,
-0.03364669531583786,
-0.006943104322999716,
0.00836125947535038,
-0.009620947763323784,
0.032384417951107025,
0.007160589564591646,
-0.03011251799762249,
-0.03969739377498627,
-0.017046606168150902,
-0.0358467698097229,
-0.000619497790466994,
-0.030722258612513542,
0.0013320636935532093,
0.02195327915251255,
-0.021592602133750916,
-0.032536581158638,
0.0011836326448246837,
-0.004960627760738134,
-0.06311234086751938,
0.005348190199583769,
-0.039851509034633636,
0.01888815499842167,
-0.019931122660636902,
0.02915915660560131,
0.03284768387675285,
-0.04980427399277687,
-0.05713440477848053,
-0.05008197948336601,
-0.027989881113171577,
0.04808726906776428,
0.022513914853334427,
0.027777742594480515,
-0.01597195491194725,
-0.01690227910876274,
0.059857264161109924,
0.030022190883755684,
-0.03668460622429848,
-0.008733391761779785,
0.02062956430017948,
-0.035203706473112106,
-0.019453726708889008,
-0.007343250792473555,
0.019819868728518486,
-0.00785208959132433,
0.03768672049045563,
-0.00028110406128689647,
0.045973554253578186,
0.0056104157119989395,
0.033474236726760864,
0.0014068579766899347,
0.006898739840835333,
0.016877491027116776,
-0.004258725326508284,
0.04381752386689186,
0.03818646818399429,
-0.05483876168727875,
-0.025849254801869392,
0.02345483936369419,
0.03433144465088844,
0.005040745250880718,
-0.059834808111190796,
0.06449642777442932,
-0.009968006052076817,
0.04713554307818413,
0.001645607640966773,
0.018881574273109436,
-0.024903617799282074,
-0.025014212355017662,
-0.014905792661011219,
0.012400743551552296,
0.026961548253893852,
0.008092846721410751,
-0.011620784178376198,
0.07565540820360184,
0.007500895299017429,
-0.028576696291565895,
0.0021868033800274134,
0.0017632936360314488,
0.015463168732821941,
0.034910816699266434,
-0.02555057965219021,
-0.0398043654859066,
0.022457873448729515,
0.02976098097860813,
0.021459080278873444,
-0.016264311969280243,
-0.05684852600097656,
-0.027699731290340424,
-0.05264901742339134,
0.0209274273365736,
0.0006975615979172289,
0.037362825125455856,
0.022985003888607025,
0.06458384543657303,
0.035945240408182144,
-0.0043808892369270325,
-0.03245426341891289,
-0.005640984512865543,
-0.08350388705730438,
0.017402837052941322,
-0.024166978895664215,
-0.002494864398613572,
-0.00519012613222003,
-0.026368165388703346,
0.015149413608014584,
-0.02924576960504055,
-0.020989416167140007,
-0.028518380597233772,
-0.02023787796497345,
-0.051123179495334625,
0.013720707036554813,
-0.0409124381840229,
-0.015559843741357327,
-0.05108668655157089,
0.04640839993953705,
0.02168571762740612,
-0.013446963392198086,
0.033738214522600174,
0.025387834757566452,
-0.04942724481225014,
-0.003379357047379017,
0.001086171017959714,
0.017585156485438347,
0.027092643082141876,
0.029405180364847183,
0.06621340662240982,
-0.007806879002600908,
-0.022814711555838585,
-0.012016216292977333,
0.025151826441287994,
0.0824224129319191,
0.012750187888741493,
-0.02705039083957672,
-0.010699208825826645,
-0.052890218794345856,
-0.019386060535907745,
-0.018700474873185158,
0.07271482795476913,
0.013338940218091011,
-0.03467721492052078,
0.02661096677184105,
0.01758667454123497,
-0.000754122098442167,
0.008312877267599106,
0.04673657938838005,
0.009098083712160587,
-0.02000296674668789,
-0.014119981788098812,
-0.018870603293180466,
0.0009291574242524803,
-0.0053702788427472115,
0.027767155319452286,
-0.02427845075726509,
-0.01725294627249241,
-0.017176715657114983,
0.0226286631077528,
0.017601575702428818,
-0.046914536505937576,
0.02906079590320587,
-0.013107582926750183,
0.0033246269449591637,
0.005142477340996265,
0.006482723634690046,
-0.024060560390353203,
0.031348709017038345,
0.013357870280742645,
0.012058258056640625,
0.013623296283185482,
-0.04185638204216957,
0.020257215946912766,
0.030718524008989334,
0.03627708554267883,
-0.008277799934148788,
-0.0444236621260643,
-0.025171492248773575,
-0.045842744410037994,
0.045630063861608505,
-0.017542684450745583,
0.05184923857450485,
0.0020258391741663218,
-0.0011074363719671965,
-0.023914402350783348,
-0.061791613698005676,
-0.018508097156882286,
0.02473192848265171,
-0.009477289393544197,
0.02687588520348072,
-0.0405995137989521,
-0.022794395685195923,
-0.01753445528447628,
-0.021053548902273178,
0.01095998752862215,
0.030228769406676292,
0.002038202015683055,
0.01472205575555563,
0.01629842445254326,
-0.001990201883018017,
0.033291563391685486,
-0.10187233984470367,
0.02465890534222126,
-0.0028301235288381577,
-0.015398417599499226,
0.049947693943977356,
-0.03856984153389931,
-0.075467050075531,
0.0320621021091938,
-0.03054957091808319,
0.027866322547197342,
0.021962564438581467,
-0.04143243655562401,
0.08912055939435959,
-0.01072395034134388,
-0.012669438496232033,
0.016508618369698524,
-0.020693331956863403,
0.0016605212586000562,
-0.019046252593398094,
-0.017137935385107994,
0.026842230930924416,
-0.015025123953819275,
0.04006943851709366,
-0.09096693247556686,
0.004046784248203039,
-0.035819344222545624,
0.0175602026283741,
-0.005839547608047724,
-0.013095115311443806,
-0.004606525879353285,
-0.016036026179790497,
-0.03182011470198631,
0.01750950515270233,
0.005076387897133827,
-0.010953052900731564,
-0.023145414888858795,
-0.024036500602960587,
-0.009210542775690556,
-0.025602607056498528,
0.004108835477381945,
-0.010812360793352127,
-0.021209413185715675,
0.04975127801299095,
0.006741114892065525,
0.018026964738965034,
-0.021316304802894592,
-0.016897767782211304,
-0.011893543414771557,
-0.029519526287913322,
0.0040809097699820995,
-0.023077677935361862,
0.012696956284344196,
0.012826879508793354,
-0.07862205058336258,
-0.046918194741010666,
0.026179343461990356,
0.0007808706723153591,
0.045323196798563004,
-0.05191531777381897,
-0.0366307869553566,
0.010419555939733982,
-0.027513504028320312,
-0.05396387726068497,
-0.0458090640604496,
0.020975539460778236,
0.02296867035329342,
-0.019665051251649857,
-0.005332048051059246,
0.0025874748826026917,
-0.023216981440782547,
-0.0035103531554341316,
-0.007939852774143219,
0.050661537796258926,
-0.03194347769021988,
-0.007559850346297026,
0.02420618012547493,
0.017143234610557556,
0.037411000579595566,
-0.02143707312643528,
-0.022963840514421463,
-0.009091263636946678,
-0.017152121290564537,
0.021815333515405655,
0.04890591278672218,
0.03397178277373314,
-0.01855938881635666,
-0.029762757942080498,
-0.028216758742928505,
0.010180210694670677,
0.01835213601589203,
0.011147094890475273,
0.022377382963895798,
-0.024455025792121887,
-0.04923851415514946,
0.004837334621697664,
-0.002687765983864665,
0.011790783144533634,
0.003101583570241928,
0.018861347809433937,
0.002999925520271063,
0.00010027855023508891,
-0.018108628690242767,
-0.04680390655994415,
0.009080389514565468,
0.008280069567263126,
-0.00691855838522315,
-0.004710412584245205,
0.013457803055644035,
-0.016604453325271606,
0.0026138508692383766,
0.034743912518024445,
-0.017769522964954376,
0.013841638341546059,
-0.038227617740631104,
0.032135698944330215,
0.00011486979201436043,
-0.0014009271981194615,
-0.015196135267615318,
-0.0007419956964440644,
-0.027572397142648697,
0.012984832748770714,
0.06027347967028618,
0.030057547613978386,
0.05167728662490845,
0.029650840908288956,
0.013901217840611935,
-0.04477391391992569,
-0.0016998730134218931,
-0.014939842745661736,
0.006606424693018198,
0.016416169703006744,
0.022501053288578987,
-0.053443778306245804,
-0.02698647975921631,
0.04052643105387688,
0.05944971367716789,
-0.01146691758185625,
0.015822339802980423,
0.05538671463727951,
0.011066569946706295,
0.06189040094614029,
0.010339715518057346,
-0.033221643418073654,
0.05038813129067421,
0.0003252379538025707,
0.0296431053429842,
0.0006375394877977669,
-0.014624117873609066,
0.0346224419772625,
0.020227303728461266,
0.00871837604790926,
-0.008258285000920296,
-0.042066220194101334,
-0.06469585746526718,
-0.021655380725860596,
-0.009713392704725266,
0.004621789325028658,
-0.021592510864138603,
0.01653337851166725,
0.004858084488660097,
0.008201424963772297,
0.021499939262866974,
-0.02288990095257759,
-0.0812452882528305,
-0.011897820048034191,
-0.008536556735634804,
-0.023572588339447975,
0.060157276690006256,
-0.03382214531302452,
0.0033545640762895346,
0.026163693517446518,
-0.04485025629401207,
-0.00959724746644497,
-0.0010765136685222387,
0.014354068785905838,
-0.034363653510808945,
0.07285118103027344,
0.01939450390636921,
0.06009981781244278,
0.017494704574346542,
0.006887495052069426,
0.11091949790716171,
0.03319995477795601,
-0.023474834859371185,
-0.07059109956026077,
0.031935062259435654,
0.0029714987613260746,
0.051207706332206726,
-0.024779554456472397,
0.010208213701844215,
0.005650350358337164,
-0.012326297350227833,
0.026327405124902725,
0.01923934370279312,
0.057462550699710846,
-0.028366340324282646,
0.038768090307712555,
-0.04240930825471878,
-0.07505881041288376,
-0.018567416816949844,
0.06342583894729614,
0.04099378362298012,
-0.005417915061116219,
-0.04268098995089531,
-0.0198415108025074,
-0.010521878488361835,
0.028239477425813675,
-0.001673931605182588,
0.0025296935345977545,
0.014232555404305458,
0.023562364280223846,
-0.03525953367352486,
0.019154492765665054,
0.016063345596194267,
-0.013957679271697998,
-0.06398878991603851,
0.03682800754904747,
0.05676606297492981,
-0.020043930038809776,
0.033608924597501755,
0.02185315638780594,
-0.01961485855281353,
0.022076843306422234,
0.028402861207723618,
0.01910877227783203,
-0.03284164145588875,
-0.0015186163363978267,
-0.02444121614098549,
0.06594845652580261,
-0.008755935356020927,
-0.008860014379024506,
0.010586944408714771,
-0.020815877243876457,
0.01510435901582241,
-0.05002153664827347,
-0.010153266601264477,
-0.018918834626674652,
0.026398347690701485,
-0.00833870004862547,
0.02122299186885357,
-0.0061601209454238415,
0.05021332576870918,
0.0080863106995821,
0.023080311715602875,
0.004554621409624815,
-0.019672254100441933,
0.007276479620486498,
-0.015485326759517193,
0.05160381272435188,
0.008785441517829895,
-0.02562643215060234,
-0.020143039524555206,
-0.012032518163323402,
-0.04425317421555519,
0.0033569480292499065,
0.05031865835189819,
0.04404632747173309,
0.04775827378034592,
-0.006658151280134916,
0.0060447705909609795,
0.0010554080363363028,
-0.02336895279586315,
0.0018378766253590584,
-0.038573503494262695,
-0.025305233895778656,
-0.008764557540416718,
0.0335887148976326,
0.01900218240916729,
0.04889119043946266,
-0.040847428143024445,
-0.02548052929341793,
-0.01028380636125803,
0.005178993102163076,
0.03303777053952217,
-0.030246995389461517,
-0.030651938170194626,
0.012119817547500134,
-0.03155222535133362,
-0.013058315962553024,
-0.0022400508169084787,
0.000626717577688396,
0.03011849708855152,
-0.021870428696274757,
0.00863208994269371,
0.029025044292211533,
-0.0014210972003638744,
0.0001927717967191711,
0.0013385756174102426,
-0.027222130447626114,
0.005668250378221273,
0.03894690051674843,
0.01341235637664795,
-0.024271981790661812,
-0.012373012490570545,
-0.034672945737838745,
0.027704467996954918,
0.0036683217622339725,
0.0014155677054077387,
-0.020578725263476372,
-0.025124400854110718,
0.0022603466641157866,
0.03197650983929634,
-0.0056161112152040005,
-0.005481028463691473,
-0.0503375269472599,
0.004209124483168125,
0.013279941864311695,
-0.023470472544431686,
-0.001014316687360406,
0.0793101117014885,
0.031122062355279922,
-0.042200781404972076,
0.017367014661431313,
0.07627691328525543,
-0.028611082583665848,
-0.022556105628609657,
0.038060933351516724,
0.010963364504277706,
0.05048198252916336,
-0.01144784688949585,
-0.03438708186149597,
0.043793901801109314,
-0.011770548298954964,
-0.03750958666205406,
0.04161017760634422,
-0.017102180048823357,
-0.010143755935132504,
0.018345175310969353,
0.005969305522739887,
-0.007477435749024153,
0.03404443338513374,
-0.008814693428575993,
0.006922319997102022,
0.03480071201920509,
-0.01995454542338848,
-0.018284518271684647,
-0.04468664154410362,
0.03548203408718109,
0.014265930280089378,
-0.017363643273711205,
0.05719706043601036,
-0.003128571668639779,
0.005396752618253231,
0.02085929550230503,
0.0027626464143395424,
0.015883447602391243,
0.0324273519217968,
0.04122357815504074,
-0.02298770472407341,
-0.026351286098361015,
0.04899387061595917,
-0.05679929628968239,
0.03137308359146118,
0.016515448689460754,
0.0017069304594770074,
-0.07120469957590103,
-0.005000321194529533,
0.04229478910565376,
0.021472815424203873,
0.03484238311648369,
-0.022032056003808975,
0.03998569771647453,
0.03973913565278053,
-0.10408546775579453,
0.03412540629506111,
0.010591153055429459,
0.011684825643897057,
-0.0197896771132946,
-0.014282677322626114,
-0.04674177244305611,
0.044358883053064346,
-0.001332225278019905,
0.05532302334904671,
0.01380736194550991,
0.0295464675873518,
-0.014817768707871437,
-0.06997233629226685,
-0.039521683007478714,
0.015091201290488243,
-0.021442994475364685,
0.009945583529770374,
0.05633014813065529,
-0.03663655370473862,
-0.015540926717221737,
0.051798079162836075,
-0.026421554386615753,
0.015061981976032257,
-0.043343909084796906,
0.02119486592710018,
0.03239929676055908,
0.007953586988151073,
-0.008919069543480873,
-0.0022734911181032658,
0.007053270936012268,
-0.007623267360031605,
0.02448786236345768,
0.050292983651161194,
0.009317422285676003,
-0.01226030383259058,
-0.021160636097192764,
-0.051177069544792175,
-0.021419672295451164,
0.023868704214692116,
0.0003027122002094984,
-0.016772842034697533,
0.028409350663423538,
0.04212599992752075,
0.013585290871560574,
-0.02180338092148304,
0.008428005501627922,
-0.07348916679620743,
-0.005302468314766884,
0.03198030963540077,
0.024177225306630135,
-0.012136987410485744,
-0.014120158739387989,
-0.029331427067518234,
-0.013236204162240028,
0.06211558356881142,
-0.009954564273357391,
0.007920362986624241,
-0.0343024805188179,
-0.04586389288306236,
-0.006638909224420786,
0.029704660177230835,
0.04161713644862175,
-0.04308360069990158,
-0.030674559995532036,
-0.0009448514902032912,
-0.03645715489983559,
-0.01200124341994524,
-0.014231826178729534,
0.03103039786219597,
-0.02302119880914688,
-0.08297743648290634,
0.036703407764434814,
-0.005140652414411306,
0.026260780170559883,
-0.0525936596095562,
-0.014060130342841148,
-0.0037039995659142733,
0.02955547161400318,
0.0352594368159771,
0.027660243213176727,
0.005504431203007698,
0.05457913503050804,
-0.0033749716822057962,
0.0008230040548369288,
-0.05252348259091377,
-0.004080146085470915,
-0.014718681573867798,
-0.019366953521966934,
-0.0032970390748232603,
-0.022400572896003723,
-0.02974042482674122,
0.009714843705296516,
0.019969137385487556,
-0.0017867768183350563,
0.0219919104129076,
-0.0005455554346553981,
-0.06775142252445221,
0.06403586268424988,
-0.018260866403579712,
0.0013946346007287502,
0.05345228686928749,
0.04534948989748955,
0.017045091837644577,
0.020367015153169632,
-0.03415350988507271,
-0.030718348920345306,
0.023320456966757774,
-0.015679368749260902,
-0.0062620677053928375,
0.004165068734437227,
0.03940528631210327,
0.026811210438609123,
-0.0077251349575817585,
0.004885607864707708,
0.02839662693440914,
-0.04422663897275925,
0.01030681747943163,
0.03808782249689102,
-0.01618904061615467,
0.022213490679860115,
-0.009238597936928272,
0.02813250571489334,
0.000745226803701371,
0.014234602451324463,
0.01808024011552334,
0.03022969886660576,
0.038107797503471375,
-0.017734430730342865,
0.011386942118406296,
0.05585557967424393,
-0.021109359338879585,
0.016010364517569542,
-0.022199666127562523,
0.05344987288117409,
-0.006466171238571405,
0.008364984765648842,
0.02518780715763569,
-0.041462965309619904,
0.0138405067846179,
0.03404202312231064,
-0.03145569935441017,
0.06664025038480759,
-0.031742360442876816,
0.0028252180200070143,
-0.01093557383865118,
0.04185649752616882,
0.0024784125853329897,
-0.006995501462370157,
0.04172518476843834,
0.021261228248476982,
-0.018530191853642464,
-0.012991531752049923,
-0.0063917189836502075,
-0.023324517533183098,
0.023094121366739273,
-0.048672422766685486,
-0.0025948253460228443,
0.018307972699403763,
-0.027544597163796425,
-0.0223053228110075,
-0.021124979481101036,
-0.018502235412597656,
-0.018687084317207336,
0.05000036582350731,
0.007276872172951698,
0.02143676020205021,
-0.03608815744519234,
-0.0057101319544017315,
-0.015621899627149105,
0.03542018681764603,
-0.06211502477526665,
0.013298648409545422,
-0.013188847340643406,
0.016904326155781746,
-0.013351846486330032,
-0.0157088004052639
] |
<p>When we study the interaction of the electromagnetic radiation with free electrons we can find two different approaches in the literature: for low frequency (RF, light...) a classical view is used and it is said that the electrons oscillates due to the electric field of the wave, but for high frequency radiation (X-rays, gamma), the type of interaction seems totally different (Compton effect and the like) and radiation is usually modeled as "particles". For an radiation with "intermediate" frequency such as UV or very low energy X-rays, would interactions be "electric-like" or "compton-like"?. How is the transition between both regimens? </p>
| 8,443 |
[
-0.0059029837138950825,
-0.036545440554618835,
0.029138734564185143,
-0.03494184464216232,
-0.0010656329104676843,
0.02464485354721546,
-0.004249981604516506,
-0.0444071888923645,
0.029308637604117393,
-0.023595672100782394,
0.05818081647157669,
0.0068154726177453995,
0.0393809899687767,
0.005335325375199318,
0.029448697343468666,
0.01914617046713829,
-0.023750439286231995,
-0.018681757152080536,
-0.03402634710073471,
-0.006989520043134689,
-0.004668278619647026,
0.012146543711423874,
-0.01202747505158186,
0.03462991118431091,
-0.046943992376327515,
0.00492719653993845,
0.04012643173336983,
0.022477487102150917,
0.020409254357218742,
0.0387687161564827,
0.013752574101090431,
-0.014005923643708229,
-0.020139425992965698,
-0.02011590637266636,
0.010366586968302727,
-0.009310965426266193,
-0.029777929186820984,
-0.08323416858911514,
-0.003538950579240918,
-0.010365129448473454,
-0.03545722737908363,
-0.023415613919496536,
-0.0030262621585279703,
-0.0010167656000703573,
-0.04044870287179947,
-0.022771766409277916,
0.009000862948596478,
-0.02793007530272007,
0.05282970890402794,
-0.06723980605602264,
0.06122820824384689,
-0.007854554802179337,
0.03471764177083969,
0.012547226622700691,
-0.004760558716952801,
-0.002855275059118867,
0.09047535806894302,
0.06576834619045258,
-0.009806535206735134,
-0.05001964420080185,
-0.007877501659095287,
-0.04196071997284889,
-0.028066402301192284,
-0.004620581399649382,
-0.017951419577002525,
0.03422439843416214,
-0.036750875413417816,
-0.028177760541439056,
0.024853123351931572,
0.02556309662759304,
0.01638023369014263,
-0.005331899505108595,
0.04029363766312599,
-0.008907402865588665,
0.020099015906453133,
0.002793337218463421,
0.02752448432147503,
0.004188927821815014,
0.019870998337864876,
0.023643316701054573,
-0.026842957362532616,
-0.005780067760497332,
0.017082376405596733,
-0.011351687833666801,
0.0019898267928510904,
-0.022712014615535736,
0.0783059224486351,
-0.021392377093434334,
0.00039651538827456534,
0.015918947756290436,
-0.05551225319504738,
0.04040258377790451,
0.03459128737449646,
-0.020094748586416245,
-0.06465312093496323,
0.0377981923520565,
-0.013439805246889591,
0.0556771419942379,
0.017741652205586433,
-0.005610773805528879,
0.04954369738698006,
0.014389198273420334,
0.023207733407616615,
0.08684057742357254,
-0.0002462020784150809,
-0.03192486613988876,
-0.052348822355270386,
0.009046736173331738,
-0.03218820318579674,
-0.0395054966211319,
-0.02076292783021927,
0.027317509055137634,
-0.0005185339250601828,
0.029225371778011322,
0.01970849558711052,
0.012288657948374748,
0.030776219442486763,
-0.019398396834731102,
0.07401962578296661,
0.0938495621085167,
0.04107331112027168,
-0.05583755671977997,
0.05885131657123566,
0.016976865008473396,
-0.061407797038555145,
-0.023600822314620018,
0.03957849368453026,
-0.006033462937921286,
-0.04949742928147316,
0.016039038076996803,
-0.023791052401065826,
-0.016135558485984802,
0.01146763376891613,
-0.026529988273978233,
0.02199825830757618,
-0.020731594413518906,
-0.06760899722576141,
-0.03407829627394676,
-0.002992616267874837,
-0.024905340746045113,
-0.005392145831137896,
-0.06350400298833847,
-0.016136350110173225,
0.052869122475385666,
0.0637236014008522,
-0.003108254401013255,
-0.020118556916713715,
-0.016839416697621346,
0.044234100729227066,
0.01698780059814453,
0.016958272084593773,
-0.0064973728731274605,
0.01618647202849388,
-0.005534990690648556,
0.01960405334830284,
-0.0371362529695034,
0.026227541267871857,
0.036593589931726456,
0.014819985255599022,
-0.01178829837590456,
0.06232356280088425,
-0.03616483882069588,
-0.007304621394723654,
0.021174311637878418,
0.023694252595305443,
-0.01910337805747986,
0.0538240522146225,
0.041253432631492615,
0.018021931871771812,
0.04068766161799431,
0.008666765876114368,
0.039704520255327225,
0.014567160047590733,
0.021507401019334793,
-0.005073734559118748,
-0.04453832656145096,
-0.04049668461084366,
-0.04026228189468384,
0.009435179643332958,
-0.027660319581627846,
-0.04081800580024719,
-0.01718560978770256,
0.001257401774637401,
0.027391789481043816,
-0.000835029873996973,
0.0401138961315155,
-0.011078116483986378,
-0.011456556618213654,
-0.014230120927095413,
-0.042763251811265945,
-0.047264501452445984,
-0.05642706900835037,
0.025715600699186325,
0.006518428213894367,
-0.04067518934607506,
0.05561412498354912,
0.012448922730982304,
-0.011341962963342667,
-0.02416115254163742,
-0.038659047335386276,
-0.016720179468393326,
0.053649354726076126,
-0.015663936734199524,
-0.013071061111986637,
0.013056631200015545,
0.0728573203086853,
0.008437620475888252,
-0.01614605262875557,
0.008004797622561455,
-0.013778320513665676,
-0.05540091171860695,
0.0014051183825358748,
-0.049554191529750824,
0.04629913344979286,
0.028816919773817062,
0.002040702849626541,
-0.00013620055688079447,
-0.03218899294734001,
-0.018521839752793312,
0.05581951141357422,
-0.025998098775744438,
0.05554460734128952,
0.046285275369882584,
-0.0011205701157450676,
0.0063901799730956554,
0.05524526536464691,
-0.004853308200836182,
0.018734266981482506,
0.008858447894454002,
-0.04316788539290428,
-0.04490320757031441,
0.017774514853954315,
0.03221239149570465,
0.012925566174089909,
-0.03661419078707695,
-0.004709871951490641,
0.01020546443760395,
0.05484093725681305,
0.034502867609262466,
0.09105035662651062,
-0.024873442947864532,
-0.014784404076635838,
0.04256856068968773,
0.005270656663924456,
0.015226274728775024,
-0.015418053604662418,
0.01893397979438305,
-0.003595090936869383,
0.03507426008582115,
-0.024254050105810165,
-0.023407721891999245,
0.0305922981351614,
-0.007640801835805178,
0.003099513705819845,
-0.012095621787011623,
-0.055884044617414474,
0.018112007528543472,
-0.03918376937508583,
-0.020607981830835342,
-0.014361013658344746,
-0.035263702273368835,
0.00653564278036356,
-0.0036409220192581415,
0.0056564901024103165,
0.018203455954790115,
-0.03768859803676605,
-0.019712675362825394,
-0.030359523370862007,
0.017207782715559006,
-0.04398658871650696,
0.016585782170295715,
-0.0056870668195188046,
-0.04019254446029663,
-0.007092635612934828,
-0.008384473621845245,
0.03836280107498169,
0.009404407814145088,
0.04359724000096321,
-0.018638798967003822,
-0.06137225404381752,
-0.013909789733588696,
-0.054345060139894485,
0.011967817321419716,
0.0467948243021965,
-0.004355528391897678,
-0.005294408183544874,
-0.04970574378967285,
-0.017773859202861786,
0.032428547739982605,
-0.013372315093874931,
0.025923417881131172,
0.009168257005512714,
-0.03688086196780205,
-0.05144172161817551,
-0.01109233032912016,
-0.010660373605787754,
-0.011813928373157978,
0.0074142953380942345,
-0.002068714704364538,
0.042503293603658676,
0.00020403660892043263,
-0.015221022069454193,
0.022137682884931564,
-0.004980508703738451,
-0.05327259749174118,
-0.015544894151389599,
0.010696458630263805,
0.011977504938840866,
-0.034335654228925705,
0.002501386683434248,
0.03846586495637894,
-0.05993391200900078,
0.005877666641026735,
-0.041044387966394424,
-0.052204281091690063,
0.031632136553525925,
-0.02208046428859234,
0.03683250769972801,
-0.010163993574678898,
-0.03163493797183037,
0.05912347510457039,
-0.005546955857425928,
0.0010571038583293557,
-0.04585264250636101,
-0.023357940837740898,
-0.07851250469684601,
-0.0007564780535176396,
0.030412403866648674,
0.04710935428738594,
-0.002304414752870798,
-0.0009974677814170718,
0.0027763021644204855,
0.0038417428731918335,
0.010954378172755241,
0.0340176559984684,
0.009388861246407032,
0.005206342786550522,
0.0031385940965265036,
0.015597508288919926,
0.031455621123313904,
0.019539667293429375,
-0.04779573157429695,
0.03188268467783928,
-0.00730560626834631,
0.004454310052096844,
0.04553329944610596,
-0.03022424876689911,
0.02086995728313923,
0.03910963982343674,
0.02720685675740242,
-0.0174739807844162,
0.015554636716842651,
0.02104112133383751,
-0.022419223561882973,
0.006317198276519775,
0.04723648354411125,
0.02601449564099312,
-0.005445909686386585,
-0.025675250217318535,
0.018819089978933334,
0.08485865592956543,
-0.020452015101909637,
-0.02761635184288025,
0.024816786870360374,
-0.013808190822601318,
0.02001088671386242,
-0.029004357755184174,
0.0046234168112277985,
0.04818397015333176,
-0.025359518826007843,
0.034111764281988144,
0.02010592445731163,
-0.010289589874446392,
-0.025070741772651672,
-0.022639421746134758,
0.004520561080425978,
0.0012013660743832588,
0.04424596205353737,
0.010141114704310894,
0.06008211150765419,
0.03157300874590874,
0.022110406309366226,
0.017339499667286873,
0.010542288422584534,
-0.08348701149225235,
0.030165817588567734,
-0.008323905058205128,
0.0030784113332629204,
-0.03021465428173542,
0.0030665257945656776,
-0.04217453673481941,
0.011555862613022327,
-0.05153332278132439,
-0.021841639652848244,
-0.013206704519689083,
-0.03439013287425041,
0.04777304083108902,
-0.04144793003797531,
-0.03790780156850815,
-0.03137799724936485,
0.04815585911273956,
-0.004245419055223465,
-0.00831367913633585,
-0.01479077897965908,
0.046426352113485336,
-0.031201502308249474,
0.03222355619072914,
0.007944419980049133,
0.010245016776025295,
0.015795636922121048,
0.026127230376005173,
0.03854413330554962,
0.012390500865876675,
-0.017413709312677383,
0.007596248760819435,
0.048617031425237656,
0.06880795210599899,
0.029977615922689438,
-0.04492172226309776,
-0.020110974088311195,
-0.0582713708281517,
0.015926137566566467,
-0.03193360194563866,
0.06630953401327133,
0.007590922527015209,
-0.00599663145840168,
0.022442670539021492,
0.0012021500151604414,
-0.006757762283086777,
0.055168841034173965,
0.022912412881851196,
0.029496461153030396,
-0.031299736350774765,
-0.022709602490067482,
0.00992522668093443,
-0.014287791214883327,
0.008771930821239948,
0.019142303615808487,
-0.017244799062609673,
-0.007857096381485462,
0.010428366251289845,
0.03272738307714462,
-0.008693603798747063,
-0.029525764286518097,
-0.03214319422841072,
-0.019765250384807587,
-0.04184633120894432,
-0.021172471344470978,
-0.036245204508304596,
0.008203946985304356,
0.03806004300713539,
0.04329007863998413,
0.00917048193514347,
-0.014250199310481548,
-0.08871664851903915,
-0.007736983709037304,
0.05498388037085533,
0.03022143617272377,
0.014143073000013828,
-0.06205027922987938,
-0.038755711168050766,
0.025049224495887756,
0.02890550158917904,
-0.0016577272908762097,
0.009189716540277004,
-0.027988579124212265,
0.000407738727517426,
-0.006121648475527763,
-0.027037905529141426,
-0.01646025851368904,
0.013834967277944088,
-0.00834847055375576,
0.018214935436844826,
-0.04562734067440033,
-0.028787046670913696,
-0.007136033847928047,
0.05082740634679794,
0.03133393079042435,
0.06116785481572151,
-0.0014606043696403503,
0.007616330869495869,
0.01779184117913246,
0.01018497534096241,
0.003644425654783845,
-0.09168500453233719,
0.033409591764211655,
0.04489235207438469,
-0.009454426355659962,
0.04909341409802437,
-0.018593864515423775,
-0.015989456325769424,
0.020044837146997452,
0.0030425647273659706,
0.010472469963133335,
-0.011638246476650238,
-0.032115403562784195,
0.06631897389888763,
0.02751939184963703,
-0.027838028967380524,
0.07443301379680634,
0.04668353125452995,
-0.040882840752601624,
-0.013821412809193134,
-0.001103082438930869,
0.058775894343853,
-0.012992171570658684,
0.015000518411397934,
-0.019960762932896614,
0.022351857274770737,
0.019013473764061928,
0.08204281330108643,
-0.016682177782058716,
0.019352447241544724,
0.020635787397623062,
-0.0160809513181448,
-0.007107151206582785,
-0.002072960138320923,
-0.03098689392209053,
-0.034772686660289764,
-0.02937941625714302,
0.02607826702296734,
-0.0052313837222754955,
-0.022594112902879715,
0.013436390087008476,
-0.016744716092944145,
-0.006061631720513105,
0.031201858073472977,
-0.008429351262748241,
0.013578818179666996,
-0.04627096280455589,
0.005476492922753096,
0.011819089762866497,
-0.03735269606113434,
0.035388413816690445,
-0.019962197169661522,
-0.004239054396748543,
-0.012202959507703781,
-0.05855447053909302,
-0.03464079275727272,
0.001498525496572256,
0.009226243011653423,
0.05024553835391998,
-0.02900480106472969,
0.04855775088071823,
0.029351115226745605,
-0.01125574205070734,
-0.08754834532737732,
-0.07909779250621796,
0.023765655234456062,
0.02355390228331089,
-0.007356568239629269,
-0.0197434164583683,
0.05412713810801506,
-0.06404559314250946,
-0.028568148612976074,
0.028260033577680588,
0.03599820286035538,
-0.04337313771247864,
-0.014800327830016613,
0.005009819753468037,
0.004165904130786657,
0.019918587058782578,
0.0007422129274345934,
-0.04203002154827118,
0.020628906786441803,
0.010610710829496384,
0.018126072362065315,
-0.005730626173317432,
0.046669282019138336,
0.02364037185907364,
-0.036477603018283844,
0.0004160174576099962,
-0.0051227412186563015,
0.010128244757652283,
-0.029925113543868065,
-0.03525248542428017,
0.0997866690158844,
0.03630894422531128,
0.02641027234494686,
0.004523204639554024,
0.012723454274237156,
-0.01144762709736824,
0.03624327480792999,
0.011765128932893276,
-0.022709716111421585,
-0.04729459434747696,
-0.042153116315603256,
0.03724909946322441,
-0.002515567932277918,
0.026707598939538002,
0.02809114381670952,
0.03378857672214508,
-0.02056393399834633,
0.006509135942906141,
0.005081238225102425,
-0.021618638187646866,
0.0288403183221817,
-0.050910938531160355,
0.002547764452174306,
0.02350584976375103,
0.026965659111738205,
0.00006168049731059,
-0.016395356506109238,
-0.03609864041209221,
-0.026109803467988968,
0.04368661344051361,
-0.03867905214428902,
0.051173459738492966,
0.003296669339761138,
0.02314300648868084,
-0.0015551444375887513,
-0.04694018512964249,
0.005785593297332525,
-0.005024920217692852,
-0.013864056207239628,
-0.0005641566240228713,
-0.0044903503730893135,
0.01975197158753872,
0.018615707755088806,
0.05107768625020981,
0.009482329711318016,
0.03453629091382027,
0.029716109856963158,
0.03086869977414608,
0.013794021680951118,
-0.031234825029969215,
-0.03221674636006355,
0.036027926951646805,
-0.04532809928059578,
0.04845705255866051,
0.020008953288197517,
-0.01740000583231449,
0.020427104085683823,
0.018931426107883453,
0.024795670062303543,
-0.033493246883153915,
-0.007341154385358095,
-0.06679298728704453,
0.027673449367284775,
-0.015047987923026085,
0.0014188335044309497,
0.007419544737786055,
0.0175390113145113,
0.032716888934373856,
0.00452069379389286,
-0.0013586271088570356,
0.022026317194104195,
-0.03384113311767578,
-0.014037957414984703,
-0.04240914806723595,
-0.033448122441768646,
0.040539078414440155,
0.0015401046257466078,
-0.005182452965527773,
0.012766002677381039,
-0.022805819287896156,
0.007614733651280403,
0.025282200425863266,
0.03193480521440506,
-0.01765616051852703,
0.030145004391670227,
-0.03244585916399956,
0.01480968575924635,
-0.006590945180505514,
0.02310062013566494,
0.10315511375665665,
0.03769324719905853,
-0.012928860262036324,
-0.03109966591000557,
0.0067300437949597836,
-0.04784463718533516,
0.058524180203676224,
-0.01178035605698824,
-0.010330254212021828,
0.010788914747536182,
-0.010233192704617977,
-0.018765971064567566,
0.02346828207373619,
0.03470767289400101,
0.030693938955664635,
0.04210880398750305,
-0.058296896517276764,
-0.024754706770181656,
0.015693312510848045,
0.0009342339471913874,
0.016582397744059563,
0.052289046347141266,
-0.042668528854846954,
-0.0050054630264639854,
-0.047993164509534836,
0.006161232013255358,
-0.027026789262890816,
-0.03971116989850998,
0.03311403468251228,
-0.005483172833919525,
-0.07048287987709045,
0.0022660652175545692,
0.012513878755271435,
-0.004253423307090998,
-0.01217772625386715,
0.018179526552557945,
0.03556329384446144,
0.0019183818949386477,
0.006362223997712135,
-0.023091956973075867,
0.0347440242767334,
-0.022450853139162064,
0.0062903123907744884,
0.003998273052275181,
-0.038693055510520935,
0.00963118951767683,
-0.03119220957159996,
0.042822062969207764,
-0.01355744618922472,
0.017038380727171898,
-0.03820425271987915,
0.033627454191446304,
-0.010377113707363605,
-0.038012128323316574,
-0.033025648444890976,
-0.011211829259991646,
0.015967685729265213,
-0.03364073485136032,
0.003441903740167618,
-0.03877534717321396,
0.04597923904657364,
-0.010853305459022522,
0.04117989167571068,
0.027147553861141205,
-0.004365929402410984,
0.02561950497329235,
-0.00915614329278469,
0.034467149525880814,
-0.03034142777323723,
-0.025145594030618668,
0.00551078375428915,
-0.019886070862412453,
-0.029045848175883293,
-0.034458182752132416,
0.01962215080857277,
0.034407392144203186,
0.04672198370099068,
0.0004650508635677397,
-0.00669450219720602,
-0.035756826400756836,
-0.08847140520811081,
0.013756548054516315,
0.035203177481889725,
-0.00021333168842829764,
-0.004796389956027269,
-0.026050882413983345,
0.017140980809926987,
0.024953588843345642,
-0.038620591163635254,
0.011227089911699295,
-0.004822880961000919,
-0.010278322733938694,
0.019443299621343613,
-0.06133449822664261,
-0.01607823744416237,
0.003470916301012039,
0.02605418860912323,
-0.010409198701381683,
-0.040882475674152374,
0.03326825425028801,
-0.020830323919653893,
-0.008237496018409729,
-0.014892549254000187,
0.03491828963160515,
-0.0254142414778471,
-0.009069947525858879,
0.016611317172646523,
0.015866219997406006,
0.012523381039500237,
0.030228305608034134,
-0.0038963137194514275,
-0.04776764288544655,
-0.01964597776532173,
-0.0498989075422287,
0.019390080124139786,
0.0030265203677117825,
0.028080645948648453,
0.008266706950962543,
0.02149399183690548,
-0.014365021139383316,
0.03752288222312927,
0.007488503120839596,
-0.04392189905047417,
-0.03792347013950348,
0.04763521999120712,
0.01856136880815029,
-0.021717121824622154,
0.011881056241691113,
0.04171869158744812,
0.00535976467654109,
-0.03258964791893959,
0.0020784572698175907,
0.04734167456626892,
-0.03472084179520607,
0.017970554530620575,
0.0040140701457858086,
-0.0028812505770474672,
0.04340158402919769,
-0.025362687185406685,
-0.03031761199235916,
0.01961701735854149,
-0.05878356471657753,
-0.05667056143283844,
0.014659435488283634,
-0.004899943247437477,
0.014546379446983337,
0.05571352317929268,
-0.022314926609396935,
0.04293515160679817,
0.0565001405775547,
-0.013643410056829453,
0.016508491709828377,
-0.011481490917503834,
-0.03316078335046768,
-0.02891073003411293,
-0.01684953086078167,
0.028073810040950775,
-0.0004124278493691236,
-0.00692431814968586,
0.05945771187543869,
0.007117504719644785,
-0.010635146871209145,
-0.004947533831000328,
-0.013998824171721935,
-0.032771360129117966,
0.023412873968482018,
0.004651478957384825,
-0.004349608439952135,
0.04445115104317665,
0.04257528856396675,
-0.026654843240976334,
0.040052324533462524,
0.012323328293859959,
0.0010420671897009015,
-0.09261787682771683,
-0.04464663565158844,
0.01636246219277382,
-0.009527373127639294,
0.027295567095279694,
-0.046813033521175385,
-0.0174119770526886,
0.008118600584566593,
-0.0869186520576477,
-0.02773088775575161,
0.02404610812664032,
-0.002947201021015644,
-0.02544865384697914,
-0.011211930774152279,
-0.029159359633922577,
0.005135760176926851,
0.03246258571743965,
0.05123237520456314,
0.022904550656676292,
0.006888481788337231,
-0.01045135222375393,
-0.02936207689344883,
-0.021397532895207405,
-0.018210696056485176,
0.024758756160736084,
-0.018602656200528145,
0.07295829057693481,
-0.02696196548640728,
-0.0037751179188489914,
0.03941252827644348,
0.006166582461446524,
0.01205713115632534,
-0.013545660302042961,
-0.00012387361493892968,
0.00895798671990633,
0.019679291173815727,
-0.017017528414726257,
-0.03400224447250366,
-0.005642583593726158,
0.03187822923064232,
0.022843781858682632,
0.030725054442882538,
0.03713883087038994,
0.015696877613663673,
0.02221623621881008,
-0.03219309821724892,
-0.03435822203755379,
0.0329950675368309,
0.014197466894984245,
-0.022949371486902237,
-0.011734604835510254,
0.03142464905977249,
0.022382425144314766,
0.01607695408165455,
0.022853363305330276,
-0.06291139870882034,
-0.04531329870223999,
-0.024619150906801224,
0.03799333795905113,
0.018931487575173378,
-0.004393457435071468,
-0.03130634129047394,
-0.02172892913222313,
0.0027056699618697166,
0.014595484361052513,
0.004404240753501654,
-0.02604750543832779,
-0.007721853442490101,
0.004485586192458868,
0.015902765095233917,
-0.0022073169238865376,
-0.03669441491365433,
-0.05989549309015274,
0.02445962280035019,
-0.035078249871730804,
0.031841229647397995,
-0.019123565405607224,
-0.057335756719112396,
-0.015037989243865013,
-0.03878610208630562,
0.03277400881052017,
-0.0076792300678789616,
0.01925310678780079,
-0.04256609454751015,
-0.046968474984169006,
-0.02011938951909542,
0.018184097483754158,
0.04406199976801872,
0.00034917195443995297,
-0.03328481316566467,
-0.0071763149462640285,
0.00046462813043035567,
0.0179502684623003,
-0.05997264012694359,
-0.01643870212137699,
-0.030485693365335464,
-0.03330102935433388,
-0.007032967172563076,
0.0012172519927844405,
-0.04577192664146423,
0.04640408605337143,
0.004144241102039814,
0.0031485185027122498,
0.023461749777197838,
-0.024513229727745056,
-0.06057707592844963,
0.055838149040937424,
0.0490337535738945,
-0.031739428639411926,
0.03603874891996384,
-0.004945475608110428,
0.027880113571882248,
0.037313804030418396,
-0.021376606076955795,
-0.010047467425465584,
0.012215148657560349,
-0.01993211731314659,
0.020305100828409195,
0.011329996399581432,
-0.0018362677656114101,
-0.02146746776998043,
-0.05015056952834129,
-0.005341042764484882,
0.04067741334438324,
-0.046085525304079056,
0.011778953485190868,
0.06750009953975677,
0.02627822756767273,
0.003934942651540041,
0.03354892134666443,
-0.00005415678606368601,
0.014147917740046978,
0.02938610129058361,
-0.03252752125263214,
0.01866801828145981,
0.02573215402662754,
0.022649768739938736,
0.05267266929149628,
0.025964250788092613,
-0.00356311141513288,
0.0029391013085842133,
0.008048035204410553,
-0.012904609553515911,
-0.007611005567014217,
-0.007804385386407375,
0.014890381135046482,
0.022072819992899895,
-0.024554314091801643,
0.028352322056889534,
-0.025276556611061096,
0.063301682472229,
-0.04934274032711983,
-0.011862777173519135,
0.004482043907046318,
0.010852862149477005,
0.023526228964328766,
0.024893105030059814,
0.03203638643026352,
0.037125587463378906,
-0.02018560841679573,
-0.0068391188979148865,
-0.021443206816911697,
-0.017367679625749588,
0.05264825373888016,
-0.048678379505872726,
0.0028537949547171593,
-0.028606126084923744,
0.002469180151820183,
-0.012747340835630894,
0.009619789198040962,
-0.01451681088656187,
-0.017232542857527733,
0.0403163842856884,
0.034244604408741,
0.017586519941687584,
0.003700419794768095,
0.009268133901059628,
-0.032938502728939056,
0.019575905054807663,
-0.0501062273979187,
-0.001468308037146926,
0.0035901255905628204,
0.009117954410612583,
-0.01404916774481535,
0.022539649158716202
] |
<p>If we could irradiate a metal or a plasma with a coherent beam of hard X-rays, would the main effect be an ordered oscillation of the electrons like with a classical EM wave, or "compton-style" collisions?</p>
| 8,444 |
[
-0.04023293778300285,
-0.017015360295772552,
0.02380809374153614,
-0.04851241409778595,
0.042219530791044235,
0.03893754631280899,
-0.014696523547172546,
-0.022444959729909897,
0.008932001888751984,
-0.02164490334689617,
0.049385711550712585,
0.003199765458703041,
0.05508046597242355,
0.019570624455809593,
0.020600460469722748,
0.005771278869360685,
-0.0007311909575946629,
-0.02322801761329174,
-0.0022613934706896544,
-0.05582249164581299,
-0.007563539315015078,
-0.02171485871076584,
-0.030439764261245728,
0.027925943955779076,
-0.049023523926734924,
0.026925103738904,
-0.0018036955734714866,
-0.001483393250964582,
0.01890225149691105,
0.02014739252626896,
0.036648426204919815,
-0.009419562295079231,
0.011241049505770206,
-0.0025865035131573677,
0.05950837954878807,
-0.025297952815890312,
-0.009083111770451069,
-0.05744367092847824,
0.016857994720339775,
0.003704881062731147,
-0.024501340463757515,
-0.049548033624887466,
-0.001205321284942329,
0.007935883477330208,
-0.013589542359113693,
-0.020837411284446716,
-0.019918516278266907,
-0.020529206842184067,
0.019211551174521446,
-0.014751038514077663,
0.06321711838245392,
-0.033142391592264175,
0.018213791772723198,
0.006283512804657221,
-0.007454468868672848,
-0.012003631331026554,
0.0567469522356987,
0.06570684909820557,
0.01121261715888977,
-0.03555368259549141,
0.02420417033135891,
-0.006635934114456177,
-0.037924494594335556,
-0.0036315536126494408,
-0.0317634642124176,
0.040241993963718414,
-0.050983671098947525,
-0.01654379814863205,
0.020459279417991638,
0.036390941590070724,
-0.01647387631237507,
0.032867010682821274,
0.031767215579748154,
-0.022854138165712357,
0.0041342079639434814,
0.009516059421002865,
0.029641320928931236,
-0.04103546589612961,
0.020089810714125633,
0.028549829497933388,
-0.009610606357455254,
-0.008864477276802063,
0.022968241944909096,
0.04061200097203255,
-0.01792903058230877,
-0.0006759692914783955,
0.06404923647642136,
-0.03844718635082245,
-0.00021111691603437066,
0.04047931358218193,
-0.017401212826371193,
0.04046349599957466,
0.03794215992093086,
0.0004915996105410159,
-0.05305425822734833,
0.002018824452534318,
-0.017485877498984337,
0.08701629191637039,
-0.006461024284362793,
-0.014832132495939732,
0.048506494611501694,
0.015032347291707993,
0.005710715893656015,
0.05603431165218353,
0.027952177450060844,
-0.04676090180873871,
-0.00936866644769907,
0.036316338926553726,
-0.05883951857686043,
-0.036079179495573044,
-0.024573618546128273,
0.012732390314340591,
0.012517677620053291,
-0.005864001344889402,
0.030444540083408356,
-0.009524776600301266,
0.035615742206573486,
-0.011594187468290329,
0.048710476607084274,
0.12914228439331055,
0.020220661535859108,
-0.01827494613826275,
0.05896756798028946,
-0.0005521165439859033,
-0.05176959186792374,
-0.024699613451957703,
0.04018465802073479,
0.0019243680872023106,
-0.03943982720375061,
0.016026891767978668,
-0.04505467787384987,
-0.011018380522727966,
0.03240755572915077,
-0.050586801022291183,
0.03023097664117813,
-0.05191151052713394,
-0.060397520661354065,
-0.03199923411011696,
0.027681665495038033,
-0.00937124527990818,
-0.029148006811738014,
-0.053109727799892426,
-0.004075163975358009,
0.03138069435954094,
0.06714244186878204,
-0.003116905689239502,
-0.01874990016222,
0.0031945628579705954,
0.0592384897172451,
0.00838970486074686,
0.005865172948688269,
0.009320922195911407,
0.016026059165596962,
-0.04048454016447067,
-0.002625080058351159,
-0.059700705111026764,
0.02540646307170391,
0.03037397190928459,
0.030231760814785957,
-0.018153339624404907,
0.02262292429804802,
-0.021685170009732246,
0.02508626878261566,
0.007376437075436115,
0.013973284512758255,
-0.0020664974581450224,
0.050907958298921585,
0.0470828153192997,
0.016239210963249207,
0.03690365329384804,
0.01924571953713894,
0.026957722380757332,
0.02260790579020977,
0.02184668555855751,
-0.005569661036133766,
-0.0681980773806572,
-0.02270491048693657,
-0.04075790196657181,
-0.004793485626578331,
-0.034734759479761124,
0.0037935981526970863,
-0.018037432804703712,
0.014713871292769909,
-0.0029910311568528414,
-0.0023927080910652876,
0.05528971552848816,
-0.007401879411190748,
-0.02700558677315712,
-0.04480604827404022,
-0.054494164884090424,
-0.00951550155878067,
-0.04869956150650978,
0.05530008673667908,
-0.008008425123989582,
-0.022431230172514915,
0.014493865892291069,
0.019516896456480026,
0.010395941324532032,
0.02276340126991272,
-0.05225536972284317,
0.014091737568378448,
0.036466725170612335,
-0.02668258547782898,
0.01757272146642208,
0.0037170755676925182,
0.05707813426852226,
0.027147242799401283,
-0.03550751879811287,
0.030972795560956,
-0.012756329029798508,
-0.03694387525320053,
0.0006489789229817688,
-0.028932424262166023,
0.022703731432557106,
-0.004767734091728926,
0.0242704339325428,
0.023646758869290352,
-0.04491889104247093,
-0.007976249791681767,
0.024771330878138542,
0.006395857315510511,
0.062132030725479126,
0.04069865494966507,
0.009740188717842102,
0.007215708494186401,
0.031328726559877396,
0.029103880748152733,
0.003726677503436804,
0.02405007742345333,
-0.049725230783224106,
-0.05361635982990265,
0.005404450464993715,
0.04387772083282471,
0.04572833329439163,
-0.06148723140358925,
0.04380178451538086,
0.0038069651927798986,
0.04475988820195198,
0.05212279409170151,
0.06316404044628143,
-0.05507224053144455,
-0.0017541535198688507,
0.01649424061179161,
-0.016217408701777458,
-0.007813996635377407,
-0.038820769637823105,
0.028465980663895607,
0.018722539767622948,
0.01638629287481308,
-0.004882302600890398,
-0.0019093964947387576,
-0.0028912548441439867,
-0.017123505473136902,
-0.017834967002272606,
0.0014268506783992052,
-0.08929050713777542,
0.004838725086301565,
-0.01013109739869833,
0.012819482944905758,
-0.00018208575784228742,
-0.03101918287575245,
0.013884357176721096,
0.002367128385230899,
0.012895039282739162,
0.015267040580511093,
-0.022782649844884872,
-0.00016863617929629982,
-0.027720985934138298,
0.04485553130507469,
-0.042489901185035706,
0.00537900160998106,
-0.014447332359850407,
-0.006291024852544069,
0.00233931140974164,
-0.0034354780800640583,
0.026959942653775215,
0.028072604909539223,
0.01702314242720604,
-0.016932524740695953,
-0.04203794524073601,
-0.00010160404781345278,
-0.043277524411678314,
-0.011951637454330921,
0.03706389293074608,
-0.03731033205986023,
-0.011801612563431263,
-0.0013697623508051038,
-0.04269867017865181,
0.0389217846095562,
0.0024941617157310247,
0.013050565496087074,
0.040661413222551346,
-0.01883729174733162,
-0.04893333837389946,
0.009160111658275127,
-0.012666416354477406,
-0.0073087471537292,
-0.03183412551879883,
0.020893113687634468,
0.048585496842861176,
-0.015285497531294823,
-0.028967540711164474,
-0.014614236541092396,
0.008600507862865925,
-0.013808652758598328,
0.003915112931281328,
0.002353610238060355,
0.01798122376203537,
-0.010131875053048134,
0.02521236054599285,
0.04141879081726074,
-0.08609119057655334,
0.01213125605136156,
-0.012993598356842995,
-0.028127223253250122,
0.050383392721414566,
-0.05316024646162987,
0.0072566792368888855,
-0.007450267672538757,
-0.01814137026667595,
0.05166126787662506,
0.008203667588531971,
-0.022815292701125145,
-0.03580503910779953,
-0.048174403607845306,
-0.025702716782689095,
0.010294652543962002,
0.02953043207526207,
0.022705137729644775,
-0.0022367972414940596,
0.02377406135201454,
0.02512311562895775,
0.021352170035243034,
0.019501158967614174,
0.04721568152308464,
0.00857740268111229,
0.02299034781754017,
0.02747669443488121,
0.009859917685389519,
-0.01394477766007185,
0.004688630346208811,
-0.04697190970182419,
0.02349519357085228,
0.022735988721251488,
0.019633948802947998,
0.08548391610383987,
-0.07549768686294556,
0.03548424690961838,
0.047160401940345764,
0.005549238994717598,
-0.012852939777076244,
0.02703605778515339,
0.014317045919597149,
0.010724872350692749,
-0.033599160611629486,
0.05549890547990799,
0.023270258679986,
0.011912430636584759,
0.01846262626349926,
0.023098118603229523,
0.07817946374416351,
0.018701056018471718,
-0.01209422666579485,
0.013689501211047173,
-0.019531086087226868,
0.004282299894839525,
-0.020329564809799194,
-0.016693295910954475,
0.05472511798143387,
-0.013637622818350792,
0.03779899328947067,
-0.006962697021663189,
0.000059608184528769925,
0.027721259742975235,
-0.03134370222687721,
0.003156753722578287,
-0.017647167667746544,
0.017113935202360153,
0.031032105907797813,
0.0755636990070343,
0.05708286911249161,
0.02078750543296337,
-0.010210308246314526,
-0.013379552401602268,
-0.0478564016520977,
0.015306851826608181,
-0.02383081614971161,
0.011830983683466911,
-0.008720122277736664,
-0.0029805973172187805,
-0.0529557429254055,
-0.005998919252306223,
-0.025934768840670586,
0.005282966420054436,
-0.027806855738162994,
-0.03697044402360916,
0.017444927245378494,
-0.011024637147784233,
-0.07148508727550507,
-0.012982137501239777,
0.04399486631155014,
0.061444371938705444,
-0.017417896538972855,
0.03702589124441147,
0.0114436699077487,
-0.0145166777074337,
0.04837273061275482,
-0.017692329362034798,
0.05381172522902489,
-0.0119786923751235,
0.05978928133845329,
0.015135502442717552,
-0.0018810294568538666,
-0.032701525837183,
0.009187215939164162,
0.03494684398174286,
0.06623741239309311,
0.010869571007788181,
-0.024878187105059624,
-0.020953292027115822,
-0.04420698806643486,
-0.003465571440756321,
0.00984184443950653,
0.06388051062822342,
-0.0040938290767371655,
0.0069183846935629845,
0.020035644993185997,
0.002019363921135664,
-0.04525728151202202,
0.04002093896269798,
0.02347356453537941,
0.041168466210365295,
-0.01721249520778656,
-0.011184095405042171,
-0.023171745240688324,
-0.009685206227004528,
-0.014968108385801315,
-0.014188041910529137,
-0.006210559979081154,
0.00792105495929718,
0.013076753355562687,
0.007252527866512537,
0.02070990391075611,
-0.027387987822294235,
-0.054765485227108,
-0.06069077178835869,
-0.017528828233480453,
-0.006265370175242424,
0.015259540639817715,
-0.016537820920348167,
0.013653161004185677,
0.04261070862412453,
0.0162972304970026,
0.006832807790488005,
-0.12289638817310333,
0.001638990011997521,
0.03580800071358681,
0.037181369960308075,
0.017420684918761253,
-0.030853940173983574,
-0.03297507390379906,
-0.016256816685199738,
0.05587565898895264,
-0.0007814632263034582,
0.013957131654024124,
-0.06760942935943604,
-0.009435474872589111,
-0.011430847458541393,
-0.007905577309429646,
-0.050755575299263,
0.031076431274414062,
0.002304887166246772,
-0.026226794347167015,
-0.029473597183823586,
-0.019601093605160713,
-0.009626985527575016,
0.029199570417404175,
0.052371855825185776,
0.02763408049941063,
0.045533906668424606,
-0.009442627429962158,
-0.0019260896369814873,
0.03801813721656799,
-0.030180521309375763,
-0.0827508345246315,
0.03668101876974106,
0.025877002626657486,
-0.005509347189217806,
0.05336577445268631,
-0.008561769500374794,
-0.004321762826293707,
0.00547465356066823,
0.014753743074834347,
0.022245468571782112,
0.012353447265923023,
-0.007968726567924023,
0.06065008416771889,
0.01434833463281393,
0.005127199925482273,
0.06342615932226181,
0.04346907138824463,
-0.049003247171640396,
-0.0010692790383473039,
-0.00792000349611044,
0.07430391758680344,
-0.03939685970544815,
0.02363220602273941,
0.014586697332561016,
0.027859536930918694,
-0.021705755963921547,
0.06430342048406601,
-0.02597929909825325,
-0.013264328241348267,
0.04924430325627327,
0.00011601361620705575,
0.013019939884543419,
0.013333549723029137,
-0.02542346715927124,
-0.054550252854824066,
-0.01593799702823162,
0.034003160893917084,
-0.020158030092716217,
0.01047531794756651,
0.030237272381782532,
-0.0254011619836092,
-0.002613225718960166,
0.017353173345327377,
-0.01019915658980608,
0.006863714661449194,
-0.06392320990562439,
0.013350999914109707,
0.018826842308044434,
-0.04056956619024277,
0.0341089628636837,
0.014073928818106651,
0.007847427390515804,
-0.013051214627921581,
-0.04636269807815552,
0.019623378291726112,
0.013353831134736538,
-0.00890440121293068,
0.06039295345544815,
-0.004014519043266773,
0.046420108526945114,
0.013169488869607449,
-0.003441315609961748,
-0.09946487843990326,
-0.04110331833362579,
-0.015542292036116123,
0.024039624258875847,
-0.0008317769388668239,
-0.022896012291312218,
-0.00220599677413702,
-0.0384863018989563,
-0.020961176604032516,
0.007837746292352676,
-0.0051631866954267025,
-0.025629576295614243,
-0.0043214051984250546,
0.01818142831325531,
-0.03338533639907837,
0.017747817561030388,
0.017993619665503502,
-0.06554663181304932,
-0.005219147074967623,
-0.02599460817873478,
-0.003224289044737816,
-0.029285011813044548,
0.012619631364941597,
0.01378168910741806,
-0.033589620143175125,
-0.0511663481593132,
-0.018300505355000496,
0.019636867567896843,
-0.017715802416205406,
-0.010693030431866646,
0.0931830108165741,
0.034174248576164246,
0.0320003516972065,
0.0108364038169384,
-0.011082991026341915,
-0.03147086501121521,
0.023694349452853203,
0.011398609727621078,
-0.014226841740310192,
-0.05260508507490158,
-0.05581224709749222,
0.03452010825276375,
0.00702802324667573,
-0.0018816225929185748,
0.017398394644260406,
0.03740312159061432,
-0.007424196228384972,
-0.010761572979390621,
-0.00954347848892212,
-0.017108015716075897,
0.02417946420609951,
-0.07072167843580246,
-0.00136052374728024,
0.01942473277449608,
0.012458872981369495,
-0.008227669633924961,
-0.03029794991016388,
-0.025694431737065315,
-0.04575420543551445,
0.07522794604301453,
-0.05608297511935234,
0.03833293914794922,
-0.04671487584710121,
-0.002121393335983157,
-0.015436289831995964,
-0.031583160161972046,
0.018718726933002472,
0.004291685298085213,
-0.005436786450445652,
0.010266817174851894,
-0.006101315375417471,
0.007797104772180319,
0.0052113160490989685,
0.08201000839471817,
0.003796287579461932,
0.014219394885003567,
0.005882100202143192,
-0.00795377790927887,
0.026347441598773003,
-0.017726367339491844,
-0.051281072199344635,
0.061494678258895874,
-0.06852872669696808,
0.028363434597849846,
-0.008670930750668049,
-0.028857199475169182,
0.011965359561145306,
-0.008119288831949234,
-0.005247419700026512,
-0.0028475711587816477,
-0.01939147710800171,
-0.0738072618842125,
0.031010987237095833,
-0.02912251092493534,
0.002350185764953494,
-0.00578398397192359,
0.019594185054302216,
0.025206254795193672,
0.021459639072418213,
-0.02121182717382908,
0.00006306774594122544,
-0.06182730570435524,
-0.018822895362973213,
-0.010754416696727276,
-0.03156302869319916,
0.04285753518342972,
0.005993047263473272,
-0.01575976237654686,
0.012687074020504951,
-0.006438022945076227,
0.05564911291003227,
0.043210480362176895,
0.009879969991743565,
0.005822488572448492,
0.0503372997045517,
-0.02862066589295864,
0.021132588386535645,
-0.0048487065359950066,
0.010681617073714733,
0.11392776668071747,
0.04629599303007126,
0.03674653172492981,
-0.05334239453077316,
-0.01902155764400959,
-0.02528209611773491,
0.026222040876746178,
0.026065383106470108,
-0.0033106582704931498,
0.011554443277418613,
0.003894699737429619,
-0.012711765244603157,
0.042002011090517044,
0.031085072085261345,
0.03904313966631889,
0.04355689138174057,
-0.04619814455509186,
-0.015410074964165688,
0.02147914469242096,
-0.0005968139157630503,
0.04925721138715744,
0.043681800365448,
-0.06402084976434708,
-0.006812370382249355,
-0.05090145394206047,
-0.016256079077720642,
-0.03212323039770126,
-0.03051154688000679,
0.02025977522134781,
-0.008153044618666172,
-0.036750078201293945,
-0.004420633427798748,
0.0263863205909729,
-0.014231288805603981,
-0.027977880090475082,
0.015401569195091724,
0.022291719913482666,
0.01751096546649933,
0.01405296940356493,
-0.054147928953170776,
0.006067700684070587,
0.015237029641866684,
0.00263031548820436,
0.02648812346160412,
-0.03558404743671417,
0.011127588339149952,
-0.012221448123455048,
0.005034171976149082,
-0.022355522960424423,
0.00021745280537288636,
-0.03980906307697296,
0.027240686118602753,
0.018123362213373184,
-0.03265814483165741,
-0.019968166947364807,
-0.007560458965599537,
0.01811576820909977,
0.005287708714604378,
-0.0071242875419557095,
-0.033333949744701385,
0.03568422794342041,
-0.023571889847517014,
0.02186848782002926,
-0.012280088849365711,
-0.03595440462231636,
-0.021651247516274452,
-0.020190345123410225,
0.0564727857708931,
-0.011002646759152412,
-0.024584492668509483,
-0.055765025317668915,
-0.0258018858730793,
-0.0106679517775774,
-0.033559802919626236,
-0.0005707035888917744,
0.028884563595056534,
0.040083546191453934,
0.009508977644145489,
-0.012677707709372044,
-0.019781257957220078,
-0.06721910089254379,
0.03542527183890343,
0.008035290986299515,
-0.0029357222374528646,
-0.017798414453864098,
0.0013745413161814213,
0.028699947521090508,
0.04289386048913002,
-0.0013881446793675423,
0.00509220827370882,
0.012487445026636124,
0.021773234009742737,
0.0021163050550967455,
-0.04846857860684395,
-0.02322944812476635,
-0.001239874749444425,
-0.002244338858872652,
-0.0064903306774795055,
-0.025049734860658646,
0.052611496299505234,
-0.004184551537036896,
-0.022301753982901573,
0.025182656943798065,
0.07498855888843536,
-0.02826012670993805,
-0.02032211609184742,
0.03180026262998581,
-0.0035678495187312365,
0.003931861836463213,
0.012761181220412254,
-0.0025979855563491583,
-0.022940583527088165,
-0.02565147541463375,
-0.05870235338807106,
-0.012482170946896076,
0.006983940955251455,
0.01022731326520443,
-0.014458270743489265,
0.011876244097948074,
0.009140579029917717,
0.035493381321430206,
0.004810892976820469,
-0.02960004284977913,
-0.027422847226262093,
0.021118730306625366,
-0.023941531777381897,
-0.02955763228237629,
0.03223564475774765,
0.036772411316633224,
0.024774353951215744,
-0.0009827009635046124,
-0.009942082688212395,
0.02450566366314888,
-0.027233634144067764,
0.011607392691075802,
0.029161639511585236,
0.012738954275846481,
0.01982375793159008,
-0.010869091376662254,
-0.015145723707973957,
0.014023312367498875,
-0.045818571001291275,
-0.04275676608085632,
0.022174358367919922,
-0.02437935210764408,
0.001559590338729322,
0.06353439390659332,
-0.0092131607234478,
-0.003344713943079114,
0.061003826558589935,
0.0018324017291888595,
-0.017933135852217674,
-0.0002830947341863066,
-0.02552766725420952,
0.029339676722884178,
0.02466690167784691,
0.009024403057992458,
-0.01710282452404499,
-0.024422110989689827,
0.07077164202928543,
0.032313231378793716,
-0.009299356490373611,
0.03311348706483841,
-0.01629607565701008,
-0.020752929151058197,
0.01100436132401228,
-0.007202958222478628,
-0.02009635791182518,
0.008951735682785511,
0.039756596088409424,
-0.03191974014043808,
0.029360050335526466,
0.02069229632616043,
-0.01754423975944519,
-0.10538186132907867,
-0.0013833573320880532,
0.0067764753475785255,
0.000035831984860124066,
0.02345234528183937,
-0.00929559487849474,
0.03293025121092796,
-0.002907491521909833,
-0.06923152506351471,
0.010551190935075283,
0.008663596585392952,
-0.046549875289201736,
-0.04385301098227501,
0.014176912605762482,
-0.05341504141688347,
0.015191626735031605,
0.03948920592665672,
0.05342426523566246,
0.05016779527068138,
0.00862724520266056,
-0.001155232428573072,
0.008910460397601128,
-0.013442600145936012,
-0.014598301611840725,
0.018039312213659286,
-0.01989760436117649,
0.05200494825839996,
-0.022165711969137192,
-0.02953873574733734,
0.01160929910838604,
0.02230195328593254,
0.02610224485397339,
-0.011328257620334625,
0.04417860880494118,
-0.005718565545976162,
-0.00035986374132335186,
-0.03311803564429283,
-0.027560971677303314,
-0.011347244493663311,
0.011496600694954395,
0.0058469707146286964,
0.023398244753479958,
0.0037514055147767067,
0.022227659821510315,
0.033120471984148026,
-0.052532654255628586,
-0.02898922748863697,
0.02069244347512722,
-0.004497037269175053,
-0.0226699560880661,
-0.02793504297733307,
0.04212185740470886,
0.03864378482103348,
0.014247719198465347,
0.003757716855034232,
-0.062164414674043655,
-0.017791952937841415,
-0.03518516197800636,
0.030850373208522797,
-0.008870435878634453,
0.022587096318602562,
-0.012864911928772926,
-0.019991794601082802,
-0.01778450421988964,
0.015948696061968803,
-0.01079121045768261,
-0.03508874028921127,
-0.025125574320554733,
-0.010104585438966751,
0.004389431793242693,
-0.003666885895654559,
-0.02157381735742092,
-0.0172185767441988,
0.0319882333278656,
-0.026585618034005165,
0.06498690694570541,
0.026991624385118484,
-0.04666776955127716,
-0.04509010538458824,
-0.02010309509932995,
0.027970068156719208,
-0.002196087734773755,
0.008881554938852787,
-0.0301786158233881,
-0.0491676889359951,
0.007118307054042816,
0.02124932035803795,
0.021936021745204926,
0.019534017890691757,
0.00272749993018806,
-0.0021693315356969833,
-0.015434308908879757,
0.005841175559908152,
-0.057551369071006775,
-0.025659816339612007,
-0.02345186099410057,
0.006993025541305542,
-0.033213235437870026,
0.007455616258084774,
-0.03136615827679634,
0.01238219067454338,
0.010662011802196503,
0.020724501460790634,
-0.03331723436713219,
-0.03964833542704582,
-0.033732153475284576,
0.03564983233809471,
0.023640666157007217,
-0.06397054344415665,
0.06902533024549484,
-0.00648667523637414,
0.014718389138579369,
0.016001064330339432,
-0.02515195682644844,
-0.03089780919253826,
0.011130674742162228,
-0.037856247276067734,
0.024263575673103333,
0.002941112732514739,
-0.008266995660960674,
-0.0055679515935480595,
-0.03511877357959747,
0.03009892627596855,
0.004445378202944994,
-0.041291479021310806,
0.002092761918902397,
0.027234481647610664,
0.0005817333585582674,
0.009094721637666225,
0.021582482382655144,
0.009990772232413292,
-0.00356981810182333,
-0.022736364975571632,
-0.009669152088463306,
0.040854644030332565,
-0.004873535130172968,
0.04807246848940849,
0.02843359112739563,
0.008272260427474976,
-0.010050778277218342,
-0.04609483852982521,
0.020569896325469017,
0.006042227149009705,
-0.03174469247460365,
-0.010545065626502037,
0.013876940123736858,
-0.011810550466179848,
0.018096202984452248,
0.006309210322797298,
-0.012662192806601524,
0.06711456179618835,
-0.027900196611881256,
0.0011651425156742334,
-0.019287165254354477,
-0.02135792374610901,
0.025202171877026558,
0.006376342847943306,
0.007762813940644264,
0.05237709730863571,
-0.033025238662958145,
-0.019355468451976776,
0.0020559837576001883,
0.0013738442212343216,
0.07634090632200241,
-0.05835489183664322,
-0.027654802426695824,
-0.026379873976111412,
-0.005536175798624754,
0.02950957603752613,
-0.003430468263104558,
-0.050959616899490356,
-0.023644478991627693,
-0.0035869935527443886,
0.017317065969109535,
0.014027701690793037,
-0.008703014813363552,
0.0030264416709542274,
-0.032583512365818024,
0.02077229879796505,
-0.05617509037256241,
0.00556659372523427,
-0.031825341284275055,
0.028138943016529083,
-0.015107003971934319,
0.05547604337334633
] |
<p>Like any set of massive objects separated by distance, the Earth and Sun have a center of mass. How far in meters from the Sun's center is the Earth-Sun center of mass? Just curious? Also what percent of the Sun's radius is this distance?</p>
| 8,445 |
[
0.016642620787024498,
-0.007960427552461624,
-0.004739840980619192,
-0.012136226519942284,
0.04254736006259918,
0.010715010575950146,
-0.027012858539819717,
-0.05079348012804985,
0.012465691193938255,
-0.014031986705958843,
0.021892720833420753,
0.04655826836824417,
0.055882785469293594,
-0.015155010856688023,
0.0290131364017725,
0.00547516206279397,
-0.0011640972224995494,
0.00645799096673727,
0.014394580386579037,
-0.04059429466724396,
0.015158060938119888,
-0.02193835936486721,
0.009570525959134102,
0.02470100298523903,
-0.04246002808213234,
0.01923217624425888,
0.03020291030406952,
-0.0038029092829674482,
0.009567731991410255,
0.0698118507862091,
0.004085397347807884,
-0.030888954177498817,
0.024538151919841766,
0.04688815027475357,
0.04805566743016243,
-0.009488392621278763,
-0.007232716307044029,
-0.025942832231521606,
-0.03593195602297783,
0.04984153062105179,
-0.03832860663533211,
-0.029090983793139458,
0.0023311732802540064,
0.03072468936443329,
-0.019181346520781517,
-0.008002899587154388,
0.002223951043561101,
-0.04944299906492233,
0.05275882035493851,
-0.06658376008272171,
0.08605349808931351,
0.004734535235911608,
0.06126277148723602,
0.016371125355362892,
-0.0025145888794213533,
0.005869089160114527,
0.07578791677951813,
0.056410737335681915,
0.018544737249612808,
-0.0295396875590086,
-0.04379267245531082,
0.01634075678884983,
-0.01396239921450615,
-0.04860980808734894,
-0.02857065200805664,
0.027600305154919624,
-0.056452251970767975,
-0.0159236378967762,
0.04986104369163513,
0.027810974046587944,
-0.022174466401338577,
0.03639275208115578,
0.02969098463654518,
-0.022196626290678978,
0.009710777550935745,
-0.07480087876319885,
0.025058306753635406,
-0.0003426279581617564,
0.03378487750887871,
0.008704160340130329,
-0.0062964181415736675,
0.019770510494709015,
0.035812295973300934,
0.029940513893961906,
-0.003175696823745966,
-0.0099107651039958,
0.06807360798120499,
-0.0017463341355323792,
-0.004861477296799421,
0.028037190437316895,
-0.03410038724541664,
0.01142732985317707,
0.023808417841792107,
-0.002175271511077881,
-0.0099649578332901,
0.0524701327085495,
0.013166696764528751,
0.05137534439563751,
0.016875749453902245,
-0.02103884518146515,
0.021434122696518898,
0.007450048346072435,
0.03452348709106445,
0.05633056163787842,
0.038336075842380524,
-0.0218961201608181,
-0.02972489409148693,
0.0035960222594439983,
0.008512561209499836,
-0.026875318959355354,
-0.03567473590373993,
0.03280160576105118,
-0.004380664322525263,
-0.02180277556180954,
0.06447457522153854,
-0.03389187902212143,
0.007869752123951912,
-0.04969280958175659,
0.057547908276319504,
0.0019474454456940293,
0.04797516390681267,
0.0024586280342191458,
0.02542939968407154,
-0.039358384907245636,
-0.0363597497344017,
0.020314965397119522,
0.02376408688724041,
-0.0041096569038927555,
-0.024121463298797607,
0.010928522795438766,
-0.020359158515930176,
-0.009613148868083954,
-0.004336776211857796,
-0.027889415621757507,
0.02774599753320217,
-0.0022437970619648695,
-0.05959422513842583,
-0.053363192826509476,
0.04101536422967911,
-0.014398569241166115,
-0.03638264536857605,
-0.05843771621584892,
0.015242206864058971,
0.006538674235343933,
0.0586775466799736,
0.001982494257390499,
-0.008252848871052265,
0.000799570872914046,
0.044999416917562485,
-0.012102306820452213,
-0.017169611528515816,
-0.049261968582868576,
-0.005572811234742403,
-0.05223105102777481,
0.02590281516313553,
-0.07864480465650558,
-0.014772002585232258,
0.042126595973968506,
-0.005499603692442179,
-0.020675454288721085,
0.026613285765051842,
-0.014422563835978508,
-0.01726648397743702,
0.010130577720701694,
0.005395389162003994,
-0.037331473082304,
0.07105106115341187,
0.03741725906729698,
-0.030766066163778305,
0.03517506271600723,
0.027255378663539886,
0.03500313311815262,
0.05738824978470802,
0.011398984119296074,
0.05051026493310928,
-0.030553288757801056,
0.016557112336158752,
-0.004662540275603533,
0.01606708951294422,
0.01844344288110733,
-0.06097763776779175,
-0.023607900366187096,
0.013940501026809216,
0.027985859662294388,
0.01583622768521309,
0.07293698191642761,
-0.026810389012098312,
-0.02238355576992035,
-0.022210845723748207,
-0.011639773845672607,
-0.003797922283411026,
0.0110176308080554,
-0.0028276636730879545,
-0.01245610136538744,
0.0026301860343664885,
-0.011575836688280106,
0.030963776633143425,
0.010949385352432728,
-0.03943298012018204,
-0.0317358560860157,
0.021261468529701233,
0.048978012055158615,
0.013136191293597221,
-0.018279029056429863,
0.016569407656788826,
0.08982394635677338,
0.04170048609375954,
0.0033708768896758556,
0.01219484768807888,
-0.010587423108518124,
-0.05295925214886665,
-0.023808183148503304,
-0.0027357186190783978,
0.01617306098341942,
-0.0031009712256491184,
-0.002734158653765917,
-0.000535192375537008,
-0.007929197512567043,
-0.00168519071303308,
0.030177980661392212,
-0.008710266090929508,
0.11408895254135132,
0.011077613569796085,
0.029739150777459145,
-0.012679648585617542,
0.01286738645285368,
0.02055014856159687,
0.011122372932732105,
-0.005827095825225115,
-0.021039510145783424,
-0.028744803741574287,
-0.004371405579149723,
0.023988774046301842,
-0.00836592074483633,
-0.021998221054673195,
0.009644958190619946,
0.04189809411764145,
0.0669717937707901,
0.03122136741876602,
0.007236917968839407,
-0.041881971061229706,
-0.03304564207792282,
-0.016320116817951202,
0.007047244813293219,
-0.04093579947948456,
0.019695408642292023,
-0.0035992723423987627,
0.0312570221722126,
0.03239881247282028,
-0.00899806059896946,
-0.026161115616559982,
0.04916162043809891,
-0.008669179864227772,
-0.017333930358290672,
0.016127102077007294,
-0.003408458549529314,
0.055922433733940125,
-0.023031501099467278,
-0.013507582247257233,
0.017520813271403313,
-0.024893006309866905,
0.017816508188843727,
-0.01895374245941639,
-0.019470596686005592,
0.0029234837274998426,
0.009950290434062481,
-0.021482406184077263,
0.041418980807065964,
0.02310202270746231,
-0.04118017479777336,
0.018772702664136887,
-0.03833085298538208,
0.018890919163823128,
-0.011856003664433956,
-0.0029291545506566763,
0.04197150841355324,
0.012246130965650082,
0.004738254938274622,
-0.0036078302655369043,
-0.02228580228984356,
-0.013372428715229034,
-0.0433487668633461,
-0.019633792340755463,
-0.023424463346600533,
-0.0559886172413826,
0.03201284259557724,
-0.00025749794440343976,
-0.010775717906653881,
0.023284070193767548,
0.03955135866999626,
0.013830706477165222,
0.009027876891195774,
-0.0026674894616007805,
-0.05330013856291771,
0.0025359145365655422,
0.01451876387000084,
0.003397548571228981,
-0.023439211770892143,
0.020902929827570915,
0.030012477189302444,
-0.004822883754968643,
-0.013254381716251373,
0.0135289765894413,
-0.025699647143483162,
-0.060947030782699585,
-0.06459788233041763,
0.0339917428791523,
0.01771111600100994,
-0.06638528406620026,
0.01612211763858795,
0.0158305112272501,
-0.02456844039261341,
0.022508613765239716,
-0.024963511154055595,
-0.03563733771443367,
0.032369598746299744,
0.0003088367229793221,
0.013869363814592361,
0.004573253449052572,
-0.056904386729002,
0.07620767503976822,
0.022313563153147697,
-0.004948954563587904,
-0.017277739942073822,
0.019990697503089905,
-0.030478287488222122,
0.026770297437906265,
-0.00740515161305666,
0.012075035832822323,
-0.030040835961699486,
-0.019882887601852417,
0.031117983162403107,
-0.010936650447547436,
0.0024972916580736637,
-0.007485697511583567,
0.017554882913827896,
0.0038150486070662737,
-0.0314483717083931,
0.013319537974894047,
0.07469035685062408,
0.006708537694066763,
0.017900770530104637,
0.04268471524119377,
-0.009392427280545235,
0.057978734374046326,
-0.016406608745455742,
-0.03871437534689903,
0.026193222030997276,
-0.020001478493213654,
0.00394049845635891,
-0.00024384148127865046,
0.03438236936926842,
0.04896381497383118,
0.033994123339653015,
0.024055063724517822,
0.0006756584043614566,
0.03379492461681366,
-0.014207174070179462,
-0.06912876665592194,
0.04057827591896057,
0.04393358156085014,
-0.014672119170427322,
-0.024892453104257584,
-0.010389824397861958,
0.007895571179687977,
-0.008515949361026287,
-0.02021927572786808,
-0.05129972845315933,
0.04067979380488396,
0.04846879094839096,
0.02352822944521904,
-0.007716201711446047,
-0.02238745428621769,
-0.013959663920104504,
-0.09279563277959824,
-0.000995639362372458,
0.004273467697203159,
0.005025847814977169,
-0.01731755957007408,
0.07558911293745041,
0.022693948820233345,
0.004479947965592146,
0.01400433387607336,
0.027928346768021584,
-0.052109044045209885,
0.017874203622341156,
-0.06948646903038025,
-0.010042054578661919,
-0.01640191115438938,
0.010009242221713066,
-0.01312174741178751,
0.0000026772829642141005,
-0.025279168039560318,
-0.04250809922814369,
-0.02165866456925869,
-0.03816083446145058,
0.016515426337718964,
-0.030360793694853783,
-0.03195695951581001,
-0.02212291955947876,
0.020134437829256058,
0.01430541928857565,
0.014468626119196415,
0.03494994342327118,
0.05106040835380554,
-0.019777104258537292,
-0.02574349008500576,
-0.014806694351136684,
-0.0013561223167926073,
-0.02989346906542778,
0.03267933800816536,
0.06187526509165764,
0.0015734966145828366,
-0.06371011584997177,
-0.003908798564225435,
-0.009570824913680553,
0.03132256120443344,
0.02717350609600544,
-0.03668278083205223,
-0.021670039743185043,
-0.061365023255348206,
-0.025255734100937843,
-0.009030701592564583,
0.042651303112506866,
-0.052790671586990356,
0.004405141342431307,
0.0516388937830925,
0.012830959632992744,
-0.020748164504766464,
0.04903998225927353,
0.06294707208871841,
0.014751562848687172,
-0.02350383810698986,
-0.07755149155855179,
-0.0397430956363678,
-0.04015136882662773,
0.005427876021713018,
0.0007323144818656147,
-0.007839122787117958,
-0.009679131209850311,
-0.03346521779894829,
-0.008002319373190403,
0.007706317584961653,
0.0046484400518238544,
0.03395339846611023,
0.00494006322696805,
0.020733678713440895,
-0.036787889897823334,
-0.002504701493307948,
-0.011289604939520359,
0.003964104689657688,
0.06740553677082062,
-0.0204508975148201,
0.009573312476277351,
-0.0632784441113472,
-0.0012502060271799564,
0.003630821593105793,
0.03724585101008415,
-0.05263635143637657,
-0.0007805277709849179,
-0.04733527824282646,
-0.017257682979106903,
0.06036456674337387,
-0.02299675904214382,
0.027700692415237427,
-0.012661918066442013,
-0.008807106874883175,
0.01183787640184164,
0.0032122284173965454,
-0.001087991171516478,
-0.010586713440716267,
-0.00002624654553073924,
0.009935565292835236,
-0.00765532860532403,
-0.008885949850082397,
-0.0346483439207077,
0.04092366248369217,
0.05263587459921837,
0.042557135224342346,
0.07784169912338257,
-0.026768898591399193,
-0.013159970752894878,
0.008582639507949352,
-0.004012971185147762,
-0.06936255097389221,
-0.026400364935398102,
-0.0022521615028381348,
-0.044097092002630234,
0.0021813823841512203,
-0.034330520778894424,
-0.029877731576561928,
0.04297027364373207,
0.016157403588294983,
-0.02064882218837738,
-0.01674267277121544,
-0.023914888501167297,
0.015677006915211678,
0.02429818920791149,
-0.02674071490764618,
0.048545192927122116,
-0.005975071806460619,
-0.026511196047067642,
-0.01598244160413742,
-0.038541242480278015,
0.06022096797823906,
-0.000454293389339,
-0.03238464891910553,
0.021181678399443626,
-0.021302755922079086,
-0.03897927701473236,
-0.00040101134800352156,
-0.01826387643814087,
0.02755573019385338,
-0.013978797942399979,
-0.0633830800652504,
-0.0046926224604249,
0.027030998840928078,
0.020367169752717018,
0.012248554266989231,
0.037933897227048874,
0.04494345560669899,
-0.0010980074293911457,
-0.02076128125190735,
0.009708206169307232,
-0.023803945630788803,
0.00039700986235402524,
-0.023641202598810196,
-0.016454344615340233,
-0.007976035587489605,
-0.04349527880549431,
-0.009534267708659172,
-0.0051356893964111805,
-0.04508024826645851,
0.05412572994828224,
-0.05272330716252327,
0.006950021255761385,
0.016851896420121193,
-0.07258791476488113,
-0.07197374105453491,
-0.005797083023935556,
-0.001312927110120654,
0.08555450290441513,
-0.05928574874997139,
0.0026599003467708826,
-0.0037872553803026676,
0.01104145497083664,
-0.08068489283323288,
-0.021170012652873993,
0.0215428676456213,
0.03699861466884613,
0.0006757820956408978,
-0.03744862601161003,
-0.009023794904351234,
-0.02243523858487606,
-0.039369530975818634,
-0.0042491150088608265,
0.0608871728181839,
0.005947091616690159,
-0.014529951848089695,
-0.024976477026939392,
-0.010055068880319595,
0.04869149625301361,
-0.007455035578459501,
-0.00492393784224987,
-0.0008631875389255583,
0.020270725712180138,
-0.010956814512610435,
-0.01093081384897232,
0.09886253625154495,
-0.03299619257450104,
-0.034741587936878204,
-0.013791417703032494,
-0.017950940877199173,
0.006793322507292032,
-0.025493811815977097,
-0.010132191702723503,
0.06205892190337181,
0.04115653038024902,
0.011219890788197517,
-0.0018152367556467652,
0.052019599825143814,
0.007019483018666506,
0.0003633947344496846,
0.0013049528934061527,
0.011087545193731785,
-0.005508026573807001,
-0.026023847982287407,
0.039504069834947586,
-0.018990086391568184,
0.03730330616235733,
-0.02549133636057377,
0.06387276202440262,
0.0075040655210614204,
-0.0029693827964365482,
0.014302891679108143,
0.017625097185373306,
0.015787679702043533,
-0.016429681330919266,
-0.007104302290827036,
0.003291360568255186,
0.004312315955758095,
-0.02613908424973488,
0.010974693112075329,
-0.008243664167821407,
-0.019983092322945595,
0.07287365198135376,
-0.02217353880405426,
0.022898444905877113,
0.007250709924846888,
0.028639204800128937,
0.037732504308223724,
-0.015596183948218822,
-0.0066047413274645805,
0.008604754693806171,
0.005651845596730709,
0.01801341213285923,
-0.05213044583797455,
0.003318814793601632,
0.06789249181747437,
0.06058134883642197,
-0.01785772293806076,
0.026678254827857018,
0.009962248615920544,
0.02068086341023445,
0.03746123984456062,
0.005511818453669548,
-0.017198147252202034,
0.006164753343909979,
0.02431020885705948,
0.03018634207546711,
-0.006254967767745256,
-0.030466504395008087,
0.040822166949510574,
-0.020090103149414062,
0.008368050679564476,
0.009225038811564445,
-0.031200788915157318,
-0.01088214386254549,
0.015595562756061554,
0.01744556427001953,
-0.00006959661550354213,
-0.05633171647787094,
0.02123737335205078,
0.020320473238825798,
-0.010209848172962666,
-0.005383721087127924,
-0.023884905502200127,
-0.06538994610309601,
-0.054245855659246445,
-0.012140819802880287,
-0.08808115124702454,
0.03524288907647133,
0.023489661514759064,
-0.04579033702611923,
0.021747449412941933,
0.017299842089414597,
0.007901979610323906,
0.00443669781088829,
0.015646830201148987,
-0.04145502671599388,
0.05463775619864464,
0.004149830434471369,
-0.017589204013347626,
-0.0305611714720726,
-0.005716866813600063,
0.09193994849920273,
0.027554551139473915,
0.0027101468294858932,
-0.055414531379938126,
0.02070511318743229,
-0.01120243314653635,
-0.014559526927769184,
-0.04698773846030235,
0.004234071355313063,
-0.008890237659215927,
-0.002267999341711402,
0.036816321313381195,
0.05354666709899902,
0.02314479649066925,
-0.0027398597449064255,
0.049082200974226,
0.026087939739227295,
-0.04057128727436066,
0.013234199024736881,
0.02956341952085495,
-0.02485145814716816,
0.003980998881161213,
-0.022476384416222572,
0.011605743318796158,
-0.052353911101818085,
0.014663019217550755,
-0.03193848207592964,
-0.04294823482632637,
-0.0016364922048524022,
-0.021303288638591766,
-0.04209170117974281,
-0.008083410561084747,
-0.0036094062961637974,
-0.03618672117590904,
-0.04163377359509468,
0.023467211052775383,
0.03641820698976517,
-0.0020139191765338182,
-0.013923426158726215,
0.01811019890010357,
0.013961754739284515,
0.0392858050763607,
-0.003162599401548505,
0.007526000961661339,
-0.06142290309071541,
-0.012136063538491726,
-0.011870608665049076,
0.011334233917295933,
0.022999050095677376,
0.02632545679807663,
0.02639288641512394,
-0.002495940774679184,
-0.02786773070693016,
-0.011344402097165585,
0.014633378945291042,
0.00744329858571291,
0.04313843324780464,
-0.013890798203647137,
-0.02144947275519371,
-0.013467114418745041,
0.06092105060815811,
-0.013392792083323002,
0.021016031503677368,
-0.018932444974780083,
-0.004784150514751673,
-0.0024842736311256886,
-0.0021219567861407995,
0.025801734998822212,
-0.02986009232699871,
-0.03164955601096153,
-0.008882513269782066,
-0.029932528734207153,
-0.021848175674676895,
0.000023932321710162796,
0.01805453561246395,
0.016722088679671288,
0.03050772286951542,
0.018284538760781288,
0.00784663762897253,
-0.0026868581771850586,
-0.004131129011511803,
0.035617515444755554,
-0.026508215814828873,
-0.029966728761792183,
-0.046095941215753555,
-0.01844548061490059,
0.051909204572439194,
0.014125978574156761,
-0.027769865468144417,
0.025185614824295044,
-0.033567167818546295,
0.00977222342044115,
0.004494284279644489,
-0.038578253239393234,
0.01452894601970911,
0.042052436619997025,
-0.036028195172548294,
0.020039917901158333,
-0.023925311863422394,
0.029561148956418037,
0.05408397689461708,
0.015459949150681496,
-0.009782351553440094,
0.004468811675906181,
-0.028903162106871605,
0.00445572379976511,
-0.004164882469922304,
-0.05418996140360832,
-0.05027230456471443,
0.019304972141981125,
-0.013938811607658863,
-0.025715433061122894,
-0.007604275364428759,
-0.062412090599536896,
-0.027180146425962448,
-0.016753003001213074,
0.05908142030239105,
-0.060934748500585556,
0.04591483250260353,
-0.019507115706801414,
-0.012642194516956806,
-0.015725871548056602,
-0.0051692090928554535,
-0.04406141862273216,
-0.014906675554811954,
0.028862658888101578,
-0.02940576709806919,
0.0017509299796074629,
-0.0024651524145156145,
-0.013389094732701778,
0.007426898460835218,
0.0333436019718647,
-0.02885088138282299,
0.03993664309382439,
-0.0008274127612821758,
0.03690521791577339,
-0.01595834270119667,
0.0536993145942688,
-0.05303371325135231,
0.003468441544100642,
0.050528496503829956,
-0.036696113646030426,
-0.08025117218494415,
0.054188359528779984,
-0.02641730196774006,
0.06165735423564911,
0.00501404982060194,
-0.040835849940776825,
0.011103032156825066,
0.07237011939287186,
-0.006231871899217367,
-0.01069463137537241,
0.003106983844190836,
0.011614475399255753,
0.0035409776028245687,
0.03584733605384827,
-0.003742588683962822,
-0.04247231036424637,
-0.023647282272577286,
0.029940737411379814,
0.01861005648970604,
-0.04716247320175171,
0.0402565523982048,
0.0076139685697853565,
-0.02897876314818859,
-0.00012858171248808503,
0.03719855099916458,
0.020630331709980965,
0.03273820877075195,
0.027636395767331123,
-0.023637529462575912,
0.02299322746694088,
0.04348418116569519,
0.0004973247996531427,
-0.07595610618591309,
-0.026880653575062752,
-0.024291042238473892,
0.022452160716056824,
0.03179578483104706,
-0.0345580019056797,
-0.0012822971912100911,
0.05761944502592087,
-0.07255684584379196,
0.035745490342378616,
-0.04245544224977493,
-0.02315296232700348,
-0.002490145852789283,
-0.035632599145174026,
0.015261170454323292,
0.05980227142572403,
0.01843716949224472,
0.013609034940600395,
-0.024547776207327843,
0.013760842382907867,
-0.015855036675930023,
-0.03272198513150215,
-0.012102978304028511,
0.02586022950708866,
-0.01358821801841259,
-0.018997272476553917,
0.023886052891612053,
-0.008724172599613667,
-0.017358507961034775,
0.04460415616631508,
-0.013840568251907825,
0.019479697570204735,
-0.003808387089520693,
-0.00020260285236872733,
0.013817192055284977,
0.004549858625978231,
-0.0017309096874669194,
-0.0029259517323225737,
-0.013407398946583271,
0.012491580098867416,
0.005918244831264019,
0.03564392030239105,
-0.04710657149553299,
-0.014046675525605679,
0.049234796315431595,
-0.025856804102659225,
-0.02590179815888405,
0.02891247533261776,
-0.023759687319397926,
-0.0066886646673083305,
-0.0010569916339591146,
0.023148512467741966,
-0.004637543112039566,
-0.05882348120212555,
0.012306501157581806,
-0.055494002997875214,
-0.005096417851746082,
0.022055746987462044,
0.004665851593017578,
-0.009391951374709606,
0.013558018952608109,
0.04389039799571037,
-0.0019363200990483165,
-0.0010356692364439368,
-0.011436192318797112,
-0.014862185344099998,
-0.041779108345508575,
0.01487479917705059,
0.009340927936136723,
-0.0012443922460079193,
0.006815548520535231,
-0.03455778583884239,
-0.030355485156178474,
0.02916683442890644,
0.027718614786863327,
0.023238642141222954,
0.007982158102095127,
-0.013575239107012749,
-0.02556762844324112,
-0.05293583124876022,
0.007626908831298351,
-0.0010007728124037385,
0.0056715901009738445,
-0.020710516721010208,
-0.0071577089838683605,
-0.011660980992019176,
-0.024659911170601845,
0.03434397652745247,
0.044956061989068985,
-0.005202281288802624,
0.018807610496878624,
-0.023098303005099297,
0.019632481038570404,
-0.07344143837690353,
-0.011378178372979164,
0.005692442413419485,
-0.06468437612056732,
-0.005574760027229786,
-0.014262157492339611,
-0.007301317062228918,
0.0019908046815544367,
0.004335365258157253,
0.00412646122276783,
0.04516893997788429,
-0.005117008928209543,
-0.0015791886253282428,
0.04046563431620598,
0.01203983835875988,
0.0008882908150553703,
0.07867057621479034,
-0.0026670764200389385,
-0.003777432255446911,
0.05464167520403862,
-0.012810885906219482,
-0.03095998428761959,
0.011949227191507816,
-0.039115797728300095,
-0.019231591373682022,
0.0031545700039714575,
0.010486937128007412,
0.026618795469403267,
-0.06543450057506561,
0.013259983621537685,
0.039843056350946426,
-0.03131251782178879,
-0.01773340441286564,
0.026330135762691498,
0.00794743001461029,
0.035920675843954086,
0.0187749732285738,
0.025855759158730507,
0.038965705782175064,
-0.016079502180218697,
0.030076228082180023,
0.028510738164186478,
0.045583173632621765,
0.014531287364661694,
0.0032152337953448296,
0.004225137177854776,
0.008850090205669403,
0.03320813924074173,
-0.012878571636974812,
0.027810636907815933,
-0.015674278140068054,
-0.04536357894539833,
0.02025613561272621,
-0.014668110758066177,
0.029998453333973885,
0.020108003169298172,
-0.018146606162190437,
0.09320618957281113,
0.0002397128555458039,
0.0028060628101229668,
-0.0025934611912816763,
0.007962861098349094,
-0.003571375971660018,
0.009462021291255951,
-0.014083340764045715,
0.004354091361165047,
-0.033829204738140106,
-0.0020296243019402027,
0.014651102013885975,
-0.013883901759982109,
0.032263126224279404,
-0.019888490438461304,
0.04557957872748375,
0.01042043324559927,
0.009408591315150261,
-0.03573136404156685,
-0.003612436354160309,
-0.013632080517709255,
0.003361059818416834,
0.014643935486674309,
0.07402966916561127,
0.017648400738835335,
0.0067970831878483295,
0.017684154212474823,
0.02124517410993576,
0.027163760736584663,
-0.09897810965776443,
-0.0408608578145504,
-0.05409470945596695,
0.04146258905529976,
-0.020904412493109703,
-0.007216272410005331
] |
<p>Some of you may be familiar with the <a href="http://en.wikipedia.org/wiki/European_Union_energy_label" rel="nofollow">EU energy consumption classes</a> for domestic appliances (or equivalents in other areas).</p>
<p>Let's say we have a domestic appliance which was made before the energy directives were made active.</p>
<p>How can one measure (approximately) the energy consumption using whatever is available in one's kitchen or home and check which class the appliance could be put under?</p>
<p><strong>Clarification:</strong></p>
<p>Of course one can use a power meter an extract some results. The question is more precisely about what can one do using things (and methods) available in one's kitchen. It would be best to describe a mehod to implement this task and furthermore the method should be able to classify (approximately not laboratory precision required) the appliance in terms of the EU energy classes.</p>
<p>Answers that mention the power company power supply meter are in the spirit of what is asked.</p>
| 8,446 |
[
-0.022250311449170113,
-0.044652510434389114,
-0.01339448057115078,
-0.02076335810124874,
0.004764131270349026,
0.01491502020508051,
-0.03560160845518112,
-0.019584743306040764,
0.020585058256983757,
-0.015656059607863426,
0.013978245668113232,
0.03596906363964081,
0.049376230686903,
0.03933093696832657,
0.036867111921310425,
-0.005479561630636454,
0.004152167588472366,
0.023275796324014664,
-0.027995344251394272,
-0.03033060021698475,
0.01835363171994686,
-0.011336922645568848,
-0.0119923772290349,
-0.002400941215455532,
-0.010508866980671883,
0.019365640357136726,
0.014295628294348717,
-0.016890358179807663,
-0.009519261308014393,
0.021892093122005463,
0.009421699680387974,
-0.022696439176797867,
0.00237526698037982,
-0.00579458475112915,
0.03315216302871704,
0.010399844497442245,
-0.05818876624107361,
-0.027601094916462898,
0.013462414965033531,
0.05149197578430176,
-0.052579283714294434,
-0.01720072329044342,
0.043869420886039734,
0.02826371230185032,
0.004057828336954117,
0.02789263427257538,
-0.01437421515583992,
-0.019338427111506462,
0.007196913007646799,
-0.05265876278281212,
0.05155828222632408,
-0.007424766197800636,
0.044248566031455994,
0.02553332783281803,
-0.01468967366963625,
-0.01799180917441845,
0.05485792085528374,
0.035044122487306595,
-0.04103098064661026,
-0.044127486646175385,
-0.025959888473153114,
0.02483094111084938,
-0.0003037889546249062,
-0.055341705679893494,
-0.03687174618244171,
-0.003402376314625144,
-0.00780525291338563,
-0.028728637844324112,
0.06094648689031601,
0.017331652343273163,
0.023586424067616463,
0.0428597517311573,
0.014203167520463467,
-0.0002690272522158921,
0.034426249563694,
-0.02178283967077732,
0.02624538354575634,
0.05993879958987236,
0.02849639393389225,
0.025548521429300308,
-0.0005016206414438784,
0.004268009681254625,
0.0538925938308239,
0.07691348344087601,
0.031391121447086334,
-0.027455074712634087,
0.055716030299663544,
-0.026076382026076317,
-0.004916305188089609,
-0.009128233417868614,
0.022339249029755592,
0.015857327729463577,
0.033989522606134415,
-0.010629229247570038,
-0.011616392061114311,
0.026900729164481163,
-0.011633438989520073,
0.021938428282737732,
-0.00944786798208952,
-0.017270375043153763,
0.05432558432221413,
-0.011062699370086193,
0.02737005427479744,
0.032410357147455215,
-0.010618423111736774,
-0.016603469848632812,
-0.028938131406903267,
-0.02511666715145111,
0.01044619083404541,
-0.0035138381645083427,
-0.024265669286251068,
0.027324045076966286,
0.03217483311891556,
0.009490368887782097,
0.0008797944174148142,
-0.003607181366533041,
-0.01391951460391283,
-0.013079940341413021,
0.037096139043569565,
0.009011098183691502,
0.04758664593100548,
-0.0042206961661577225,
0.013001828454434872,
-0.06348563730716705,
-0.11758413910865784,
0.028507063165307045,
0.008650279603898525,
-0.0022247275337576866,
-0.05160834267735481,
0.030752047896385193,
-0.02741808071732521,
-0.018927808851003647,
0.009662068448960781,
-0.033282484859228134,
0.04301189258694649,
-0.006380549166351557,
-0.09618975222110748,
-0.04364732280373573,
0.018077174201607704,
0.013871673494577408,
-0.037775710225105286,
-0.08629953861236572,
-0.020897921174764633,
0.007824283093214035,
0.05243455618619919,
0.006992385257035494,
0.0022019431926310062,
-0.017977014183998108,
-0.014638726599514484,
-0.00723449420183897,
-0.02392655797302723,
-0.004454084672033787,
0.005964895710349083,
-0.028281504288315773,
0.03525441139936447,
-0.025338349863886833,
0.007305636070668697,
0.030147137120366096,
-0.018786121159791946,
-0.0008586772601120174,
0.041542042046785355,
-0.0018258881755173206,
-0.06406170129776001,
-0.006892167963087559,
-0.0221618190407753,
-0.018470343202352524,
0.07595746219158173,
-0.023618126288056374,
0.02399066835641861,
-0.012873212806880474,
0.038413334637880325,
0.018667759373784065,
-0.014375005848705769,
0.006338144186884165,
0.05843064934015274,
0.01008234266191721,
-0.04650038853287697,
-0.015454785898327827,
0.03969564288854599,
0.01003298070281744,
-0.0552654042840004,
-0.011060436256229877,
0.02398049272596836,
0.00466801505535841,
0.021542439237236977,
0.007847031578421593,
-0.0019966764375567436,
-0.04146168380975723,
0.03862087056040764,
-0.04879720136523247,
-0.0469733364880085,
-0.060459744185209274,
0.015209581702947617,
-0.03381858021020889,
-0.0054452307522296906,
0.011517928913235664,
-0.022548673674464226,
0.007534378673881292,
-0.032119281589984894,
-0.03430776298046112,
-0.0033447197638452053,
-0.007286855019629002,
0.026607679203152657,
-0.053021837025880814,
-0.004662429913878441,
-0.006214932072907686,
0.03617926314473152,
-0.03163065016269684,
0.04095284640789032,
-0.001946267089806497,
-0.044504858553409576,
0.002099451143294573,
-0.03258659318089485,
-0.002348746173083782,
0.0692291110754013,
-0.006523203570395708,
-0.007486064452677965,
-0.005061435047537088,
-0.01896372064948082,
0.04426702857017517,
0.031488824635744095,
0.04036521166563034,
0.05272280424833298,
-0.005415840074419975,
0.0038813846185803413,
-0.005516937468200922,
0.0007532369345426559,
0.02700328826904297,
-0.018745584413409233,
0.0016403167974203825,
-0.03513195365667343,
-0.01980477385222912,
0.03397471085190773,
0.025084877386689186,
-0.05461244285106659,
-0.014617634005844593,
0.0666370838880539,
0.008337217383086681,
-0.00020609654893632978,
0.009923599660396576,
0.006661911960691214,
0.0015959350857883692,
0.024416718631982803,
0.042386721819639206,
-0.009694435633718967,
0.04243388772010803,
-0.014301939867436886,
0.04003257676959038,
0.00870850495994091,
0.007784534711390734,
0.013783376663923264,
0.09532645344734192,
-0.008121146820485592,
0.0007233259966596961,
0.051906514912843704,
-0.01589709147810936,
0.02323736809194088,
-0.03673119470477104,
0.056112322956323624,
0.017627889290452003,
-0.017596518620848656,
0.02294858917593956,
0.01608525961637497,
-0.03303141891956329,
0.02343854308128357,
0.02763422764837742,
-0.015088480897247791,
-0.02868470549583435,
0.03454912453889847,
-0.04355931282043457,
0.04431631416082382,
-0.009383120574057102,
-0.023236483335494995,
-0.021991416811943054,
0.0025425537023693323,
0.041750717908144,
-0.008408314548432827,
0.029135366901755333,
-0.02211235836148262,
-0.03225823491811752,
-0.033071599900722504,
-0.013880476355552673,
0.022945083677768707,
0.01354441698640585,
-0.020258203148841858,
0.021601952612400055,
-0.0163761954754591,
-0.026795342564582825,
0.027667492628097534,
0.008488941937685013,
-0.008926640264689922,
0.034026555716991425,
0.0033573138061910868,
-0.03170439228415489,
0.0023986720480024815,
0.017899714410305023,
-0.005351541563868523,
0.011177070438861847,
0.012363319285213947,
0.03662433102726936,
0.00023440962831955403,
-0.06060497835278511,
-0.002970504341647029,
-0.045299235731363297,
-0.04300517216324806,
-0.01753365434706211,
-0.01864096336066723,
0.010406545363366604,
-0.01780346781015396,
0.013016053475439548,
0.03996758535504341,
-0.03964240103960037,
-0.031370509415864944,
-0.0601680725812912,
-0.06933004409074783,
0.025526219978928566,
0.02306438237428665,
0.040657658129930496,
0.03624303638935089,
-0.0052643874660134315,
0.06998175382614136,
0.03715848550200462,
-0.06361669301986694,
0.007133608218282461,
-0.03790155425667763,
0.03135531395673752,
-0.02469487302005291,
-0.012518908828496933,
0.05022797733545303,
-0.026295464485883713,
-0.00827829260379076,
0.029650822281837463,
0.016510970890522003,
0.023864204064011574,
0.005571842659264803,
-0.01645665057003498,
0.01829669624567032,
-0.015450987964868546,
0.013025266118347645,
0.04625868424773216,
0.01538360957056284,
-0.019116420298814774,
0.009615148417651653,
-0.038596171885728836,
0.01653454452753067,
0.06483863294124603,
-0.04239172860980034,
0.021219592541456223,
0.010078603401780128,
-0.014512129127979279,
-0.03911922499537468,
0.01893719844520092,
0.037395231425762177,
-0.02997242845594883,
0.03301162272691727,
0.019155748188495636,
0.01196853257715702,
0.009156814776360989,
-0.011380600742995739,
0.05847514048218727,
0.0815519317984581,
0.03588369861245155,
-0.031224271282553673,
-0.00076817482477054,
-0.003976793494075537,
0.010454429313540459,
-0.0007541655213572085,
-0.028848661109805107,
0.05390317738056183,
0.029890846461057663,
0.049222927540540695,
-0.015392513014376163,
-0.02201569639146328,
-0.01667305827140808,
-0.08663427084684372,
-0.041595667600631714,
-0.026030955836176872,
0.0562831275165081,
-0.00928175076842308,
0.020645420998334885,
0.005169004667550325,
-0.03235352039337158,
-0.000924022460822016,
0.005347464699298143,
-0.045870911329984665,
0.023524150252342224,
0.008928942494094372,
-0.0010993874166160822,
-0.006887014023959637,
-0.03002709522843361,
-0.0015516499988734722,
-0.029344914481043816,
0.0019884780049324036,
-0.018924934789538383,
-0.0035633009392768145,
-0.03637709841132164,
-0.009788241237401962,
0.01950903609395027,
-0.022130442783236504,
0.014449575915932655,
0.014217193238437176,
0.06069087237119675,
-0.001631974708288908,
-0.01419817004352808,
0.0445789210498333,
0.02045477367937565,
-0.03561321645975113,
0.008540096692740917,
0.004731953144073486,
-0.03383428975939751,
0.04736471548676491,
0.0008186562336049974,
0.051175571978092194,
-0.029467523097991943,
0.019609864801168442,
0.04934590309858322,
0.030288545414805412,
-0.023876067250967026,
-0.04286003112792969,
-0.04732685908675194,
-0.018140530213713646,
-0.018144842237234116,
0.030697623267769814,
0.06030861660838127,
-0.014219766482710838,
0.012420541606843472,
-0.009378946386277676,
0.034512802958488464,
-0.038712289184331894,
0.006397546268999577,
0.07281859219074249,
-0.004541471600532532,
-0.011963107623159885,
-0.03578531742095947,
-0.01882977969944477,
-0.021181786432862282,
-0.005609034560620785,
0.019258325919508934,
0.03357984498143196,
0.031225591897964478,
0.006540462840348482,
0.019773058593273163,
0.0001054693857440725,
-0.054017163813114166,
0.048738982528448105,
0.027843821793794632,
-0.022243982180953026,
0.030238712206482887,
-0.03687925264239311,
0.01826389692723751,
0.02384149096906185,
0.026515357196331024,
-0.006495989393442869,
0.012249113060534,
-0.16034908592700958,
-0.016786711290478706,
0.04928046092391014,
0.06886321306228638,
-0.014317032881081104,
-0.004304107278585434,
-0.03164773806929588,
0.0023005723487585783,
0.05323883518576622,
-0.03781060874462128,
0.05051334202289581,
-0.057336367666721344,
0.004532045219093561,
-0.03019757568836212,
-0.0066166534088552,
-0.01590239442884922,
-0.005009117070585489,
0.014025360345840454,
0.01570124179124832,
0.012124277651309967,
-0.011281528510153294,
-0.035910625010728836,
0.023822041228413582,
0.03301536664366722,
0.02539764530956745,
-0.034560754895210266,
-0.02605288103222847,
0.01842898316681385,
0.036405470222234726,
-0.008571239188313484,
-0.051816947758197784,
0.009354177862405777,
0.02840081974864006,
-0.016485778614878654,
0.055677320808172226,
-0.04361780732870102,
-0.04490499943494797,
0.006154278758913279,
-0.030426107347011566,
-0.01814131624996662,
-0.009071056731045246,
-0.04295129328966141,
0.06444859504699707,
0.0274068471044302,
-0.0156366266310215,
0.041390564292669296,
0.07853814959526062,
-0.021569807082414627,
0.0028276401571929455,
-0.012790627777576447,
-0.0401647575199604,
-0.037935785949230194,
-0.03862331435084343,
-0.026911824941635132,
0.0033940819557756186,
-0.030415954068303108,
0.03371225297451019,
-0.007351408712565899,
0.03704943507909775,
-0.025241008028388023,
-0.04807734861969948,
-0.041074734181165695,
0.01938505470752716,
-0.02021612413227558,
-0.015824921429157257,
-0.04992051050066948,
0.02630051039159298,
0.004688047803938389,
-0.008641061373054981,
-0.0135206189006567,
-0.02707061357796192,
0.05079352483153343,
-0.008490560576319695,
-0.006798147689551115,
0.038751743733882904,
-0.018142474815249443,
0.005484018940478563,
-0.009064767509698868,
0.01190976146608591,
0.03458334878087044,
-0.0016011761035770178,
0.03482735902070999,
0.02139599248766899,
-0.0441230908036232,
-0.030768781900405884,
-0.00039212178671732545,
0.023229455575346947,
0.017262011766433716,
0.009468396194279194,
0.02889832854270935,
0.012678045779466629,
-0.018424691632390022,
-0.05728006362915039,
-0.020840616896748543,
0.028887582942843437,
0.017996346578001976,
0.007760722655802965,
-0.007045342121273279,
-0.02280275523662567,
0.0021419392433017492,
-0.01591656170785427,
-0.02138884738087654,
0.037088263779878616,
-0.01686406135559082,
-0.003977299202233553,
-0.020583167672157288,
0.0212857685983181,
0.061987049877643585,
-0.041952505707740784,
-0.009685778059065342,
0.03882123902440071,
-0.015084278769791126,
-0.020459257066249847,
0.0017506048316136003,
-0.027628576382994652,
-0.032534729689359665,
-0.004345021676272154,
-0.014468963257968426,
0.015785956755280495,
0.034539613872766495,
-0.00761996628716588,
-0.0015645133098587394,
0.04103663191199303,
-0.038031626492738724,
-0.022072235122323036,
-0.021618256345391273,
0.05279500037431717,
-0.0032713680993765593,
-0.0036421166732907295,
0.0010049049742519855,
-0.021579883992671967,
0.005204516462981701,
0.013377757743000984,
0.024505615234375,
-0.04454481974244118,
-0.03273921087384224,
0.043486736714839935,
0.04884885251522064,
0.0011398635106161237,
-0.004521782975643873,
0.04870232939720154,
-0.013633968308568,
0.02233969233930111,
-0.011913420632481575,
0.006087861489504576,
-0.03294907510280609,
-0.023945676162838936,
-0.02244008705019951,
-0.01497279666364193,
-0.053631436079740524,
-0.06080310419201851,
0.0230264775454998,
0.0218878872692585,
0.06492481380701065,
0.023318160325288773,
-0.006667756009846926,
0.018110761418938637,
0.00021236820612102747,
0.004107506014406681,
0.010038938373327255,
0.008523117750883102,
0.04482745751738548,
-0.0009886868065223098,
-0.01586863212287426,
0.04187958315014839,
0.024378105998039246,
-0.019135991111397743,
-0.004496000241488218,
0.05116382613778114,
0.05120571330189705,
0.014345730654895306,
-0.05951199680566788,
-0.03279397636651993,
0.008567030541598797,
-0.04421970248222351,
-0.026993684470653534,
-0.009942691773176193,
-0.0320148691534996,
0.007808398455381393,
0.007458952255547047,
-0.05979658663272858,
-0.06831665337085724,
0.010909508913755417,
-0.08168001472949982,
0.034301791340112686,
0.01389412023127079,
0.009585324674844742,
0.010678725317120552,
-0.022245030850172043,
0.027316568419337273,
-0.024979285895824432,
0.021781202405691147,
0.017244696617126465,
-0.034427057951688766,
-0.008292975835502148,
-0.02653900720179081,
-0.05569394677877426,
0.06026053801178932,
0.006770291365683079,
0.010602736845612526,
0.002472100080922246,
-0.03076050616800785,
0.003839824814349413,
0.004835264757275581,
0.040894169360399246,
-0.015756910666823387,
0.06075414642691612,
-0.00740931648761034,
0.03264215216040611,
-0.008795698173344135,
0.00460104551166296,
0.1283455640077591,
0.007817618548870087,
0.004536888096481562,
-0.044182486832141876,
0.015038611367344856,
0.027296679094433784,
-0.006084604654461145,
-0.02512143738567829,
-0.01656346023082733,
-0.02091233804821968,
0.021517258137464523,
0.015829013660550117,
0.05991070345044136,
0.020361678674817085,
0.04831786826252937,
0.05362037941813469,
0.010039055719971657,
0.004044804256409407,
0.04984385520219803,
0.0482952743768692,
-0.010578547604382038,
0.0036083953455090523,
-0.04205554723739624,
0.024030983448028564,
0.04587242007255554,
-0.02954159863293171,
0.005757614970207214,
-0.023546848446130753,
0.0343804806470871,
0.0001644765434321016,
-0.05109494924545288,
0.052869077771902084,
0.0071350890211761,
0.002743001561611891,
-0.02793820947408676,
-0.02704755775630474,
0.0072946674190461636,
0.03100491315126419,
-0.008068306371569633,
0.04979269951581955,
0.04377026483416557,
-0.055380795150995255,
-0.0007464061491191387,
0.003304888727143407,
-0.055091891437768936,
-0.05243988335132599,
-0.03752659261226654,
-0.0004244630108587444,
0.016803652048110962,
-0.048957936465740204,
-0.0013774880208075047,
0.013004750944674015,
-0.008498480543494225,
-0.05859818682074547,
-0.04242875799536705,
-0.022352594882249832,
0.045529741793870926,
-0.04970771074295044,
-0.04996835067868233,
-0.022609105333685875,
0.02641425095498562,
-0.03841080144047737,
0.031513914465904236,
0.011331153102219105,
-0.022224856540560722,
-0.007769998628646135,
-0.025338787585496902,
0.009337696246802807,
0.05236968770623207,
-0.020397957414388657,
0.005819403100758791,
0.014387206174433231,
-0.027168944478034973,
0.0033313732128590345,
0.022015465423464775,
0.027749214321374893,
0.034386955201625824,
-0.018645023927092552,
0.02090519666671753,
-0.02675856649875641,
-0.0876818373799324,
0.04845501855015755,
-0.03421400487422943,
0.01603611372411251,
-0.025678783655166626,
-0.001810435438528657,
0.026865722611546516,
0.04542142525315285,
0.024561358615756035,
0.0264541395008564,
0.022905832156538963,
0.027886169031262398,
0.02500571496784687,
-0.017790453508496284,
-0.03733312338590622,
0.019289743155241013,
-0.05973101779818535,
0.009183457121253014,
0.003526207059621811,
0.04016554355621338,
0.02866838499903679,
-0.02274823747575283,
0.007431764621287584,
-0.014574156142771244,
-0.0030114941764622927,
0.005079702939838171,
-0.008943615481257439,
-0.02640126831829548,
-0.024412162601947784,
-0.0344507060945034,
0.008891057223081589,
-0.01924215257167816,
-0.03717077895998955,
-0.03740323334932327,
0.005720620043575764,
-0.03444288671016693,
0.037105485796928406,
0.0058720847591757774,
-0.004660462029278278,
-0.047628626227378845,
0.010379788465797901,
-0.013339227996766567,
0.0037954559084028006,
-0.029067890718579292,
-0.01706467941403389,
0.0145943071693182,
-0.034103915095329285,
-0.019316047430038452,
0.025881852954626083,
-0.01772836223244667,
-0.017064779996871948,
0.02968142181634903,
0.030945023521780968,
-0.00622628815472126,
-0.00860385037958622,
-0.024391254410147667,
-0.03175527974963188,
0.01468773651868105,
-0.021954122930765152,
-0.0327959805727005,
0.05816928297281265,
-0.018749356269836426,
-0.020146550610661507,
0.03450184315443039,
0.01294729020446539,
-0.0008238816517405212,
0.04336906969547272,
0.0180426687002182,
0.02326739951968193,
0.026314595714211464,
-0.03312191739678383,
0.014932740479707718,
0.014856896363198757,
0.025719355791807175,
-0.013043243438005447,
0.05902929976582527,
0.023823225870728493,
-0.0035043316893279552,
-0.012819782830774784,
0.04227820783853531,
0.072424978017807,
0.04691100865602493,
-0.030184000730514526,
0.00294678146019578,
0.010530168190598488,
0.008489672094583511,
0.014535957016050816,
0.05482430383563042,
-0.00488327257335186,
0.05015590786933899,
-0.05827523395419121,
0.009701711125671864,
-0.004040241707116365,
-0.009062891826033592,
-0.05571906268596649,
-0.015942521393299103,
-0.01236731931567192,
-0.003937967121601105,
0.02083706483244896,
-0.03880560025572777,
0.034170717000961304,
-0.0003338308597449213,
-0.04305870831012726,
0.00891094096004963,
0.0113529022783041,
-0.008552825078368187,
-0.009426064789295197,
0.04109697788953781,
-0.022294476628303528,
0.0417000949382782,
0.012605462223291397,
0.04616912826895714,
0.03209381923079491,
0.022801285609602928,
0.033301252871751785,
-0.04520006850361824,
0.011392918415367603,
0.0326315239071846,
0.006785470526665449,
-0.0044124554842710495,
0.02459467016160488,
-0.05187094584107399,
-0.018347756937146187,
0.011570289731025696,
-0.025283798575401306,
0.01657170243561268,
-0.002354840049520135,
-0.003313462482765317,
-0.029160592705011368,
0.035143934190273285,
0.06344378739595413,
-0.0266033373773098,
-0.05801492556929588,
0.01935356669127941,
0.009458605200052261,
0.02785797417163849,
-0.007764738518744707,
0.002409693319350481,
0.019262516871094704,
-0.0000661566955386661,
-0.01111555565148592,
0.005593125708401203,
-0.030227527022361755,
-0.019229203462600708,
0.034981679171323776,
-0.02050543949007988,
0.02186848409473896,
0.00410594092682004,
-0.01813153363764286,
-0.06166723743081093,
-0.027571003884077072,
0.034789614379405975,
0.019874952733516693,
0.025288181379437447,
-0.025377657264471054,
-0.030408840626478195,
-0.03042932227253914,
0.039785295724868774,
0.018099460750818253,
-0.06459705531597137,
-0.05150861665606499,
-0.00969651248306036,
0.0038402050267904997,
-0.010285068303346634,
-0.012320528738200665,
-0.014989537186920643,
-0.032640762627124786,
0.009982519783079624,
0.0011951447231695056,
-0.01872037909924984,
0.0028782575391232967,
-0.018808381631970406,
0.025346476584672928,
-0.035561058670282364,
0.03324385732412338,
0.03733469173312187,
-0.0055369543842971325,
-0.022714726626873016,
0.010422280989587307,
-0.026118962094187737,
0.010455025359988213,
0.05115003138780594,
-0.0194756630808115,
-0.03459068760275841,
-0.03369443863630295,
-0.011779731139540672,
0.025147700682282448,
-0.059800926595926285,
0.0840010792016983,
0.014891136437654495,
-0.02598409913480282,
-0.0029648381751030684,
-0.030552193522453308,
-0.04534362256526947,
0.006487405393272638,
0.04263445734977722,
0.012530726380646229,
-0.025913788005709648,
-0.022571872919797897,
-0.004282103385776281,
0.04216863587498665,
0.021588696166872978,
0.02124365232884884,
0.03666825219988823,
0.02077983319759369,
-0.01261727511882782,
0.026012029498815536,
0.007371522951871157,
-0.03963548690080643,
-0.012731146067380905,
-0.02265562303364277,
0.006809184327721596,
-0.015533494763076305,
0.007643449120223522,
0.02306046150624752,
-0.059514112770557404,
-0.04851797968149185,
0.0042631602846086025,
0.006339570973068476,
-0.018247835338115692,
0.020314397290349007,
0.02262195385992527,
0.011647057719528675,
-0.003615428227931261,
0.0045935786329209805,
-0.0058551449328660965,
0.01449511107057333,
-0.006341836415231228,
0.0570758581161499,
0.06613628566265106,
-0.03226465359330177,
0.03013189136981964,
0.022612789645791054,
-0.00234237895347178,
-0.0012552848784253001,
0.012783057056367397,
0.04250665009021759,
-0.0008264867356047034,
-0.021075503900647163,
0.018791059032082558,
0.003064253367483616,
-0.009540608152747154,
0.056816890835762024,
-0.02684503048658371,
0.04747198522090912,
0.011794733814895153,
-0.030746210366487503,
-0.04133576154708862,
-0.00606496399268508,
-0.004940959624946117,
-0.025454916059970856,
0.0403536781668663,
0.03132832795381546,
-0.01866762526333332,
0.04405812546610832,
-0.02828054688870907,
-0.01630091853439808,
0.0209366288036108,
-0.03676678240299225,
0.031687378883361816,
-0.015506434254348278,
0.0025453413836658,
-0.022472307085990906,
-0.001581992139108479,
-0.012314719147980213,
-0.013602318242192268,
0.0323958545923233,
0.06554284691810608,
0.04722737893462181,
-0.01815062016248703,
-0.01198335736989975,
-0.0006326804868876934,
0.05328386276960373,
-0.06263262033462524,
-0.009456210769712925,
-0.030129529535770416,
-0.03014083206653595,
-0.0014109694166108966,
-0.030085230246186256
] |
<p><strong>1. The problem statement, all variables and given/known data</strong></p>
<blockquote>
<p>Beam of electrons with energy $10eV$ hits the potential step
($8eV$ high and $0.5nm$ wide). How much of the current is
transmitted?</p>
</blockquote>
<p><strong>2. Relevant equations</strong></p>
<p>I know that energy mentioned in the statement is kinetic energy so keep in mind when reading that $E\equiv E_k$.</p>
<p>In our case the kinetic energy is larger than the potential energy $\boxed{E>E_p}$ and this is why stationary states for the regions 1, 2, 3 (picture) are as folows: </p>
<p>\begin{align}
\psi(x)_1 &=Ae^{iLx}+B^{-iLx} && L=\sqrt{\tfrac{2mE}{\hbar^2}}=1.619\times 10^{10}\tfrac{1}{m}\\
\psi(x)_2 &=Ce^{iKx} +De^{-iKx} && K=\sqrt{\tfrac{2m(E-E_p)}{\hbar^2}}=0.724\times 10^{10}\tfrac{1}{m}\\
\psi(x)_3 &=Ee^{iLx}
\end{align}</p>
<p><img src="http://i.stack.imgur.com/RbNgm.png" alt="enter image description here"></p>
<p><strong>3. The attempt at a solution</strong></p>
<p>I first used the boundary conditions for the border 1-2 and got a system of equations:</p>
<p>\begin{align}
A+B &= C+D\\
iLA-iLB&=iKC-iKD\\
&\downarrow\\
A+B &= C+D\\
A-B &= \tfrac{K}{L}(C-D)\\
&\left\downarrow \substack{\text{I used the assumption that}\\\text{$E \gg E_p$ and got the simplified}\\ \text{relation between L and K:}\\ \tfrac{L}{K}=\sqrt{E/E_p}\gg 1 \Longrightarrow L\gg 1\\ \text{and hence}\\ \tfrac{K}{L}=\sqrt{E_p/E}\ll 1 \Longrightarrow K\ll 1} \right.\\
A + B &= C+ D\\
A-D &= 0\\
&\downarrow~\Sigma\\
2A &=C+D\\
&\downarrow\\
C&=2A-D
\end{align}</p>
<p>Now i used the boundary conditions for the border 2-3 and got a system of equations in which i inserted the above result:</p>
<p>\begin{align}
Ce^{iKd} + De^{-iKd} &= Ee^{iLd}\\
iKCe^{iKd} -iK De^{-iKd} &= iLEe^{iLd}\\
&\downarrow\\
Ce^{iKd} + De^{-iKd} &= Ee^{iLd}\\
Ce^{iKd} -De^{-iKd} &= \tfrac{L}{K}Ee^{iLd}\longleftarrow\substack{\text{Things get weird}\\\text{when i insert }C=2A-D}\\
&\downarrow\\
2Ae^{iKd} -De^{iKd} + De^{-iKd} &= Ee^{iLd}\\
2Ae^{iKd}-De^{iKd} -De^{-iKd} &= \tfrac{L}{K}Ee^{iLd}\\
&\downarrow \substack{ \text{$L$ is very big while $K$ is very small}}\\
2A &= Ee^{iLd}\\
2A -2D &= \tfrac{L}{K}Ee^{iLd}
\end{align}</p>
<p>Now this result is what i don't understand. First equation gives me a ratio $E/A=2\exp[-iLd]$ which i think i need to calculate the transmissivity, but it is a complex exponential. Is this possible? How do i continue? Is this the way to solve this kind of case or did i go completely wrong?</p>
<p>This is my first finite potential well problem and i have been searching the web for a loong time to even find 2 videos (<a href="http://www.youtube.com/watch?v=vMndTqowzqU&list=FLUuDEwpR43gvcFvCBovHBUA&index=25" rel="nofollow">video 1</a> and <a href="http://www.youtube.com/watch?v=gwSBFZYfSCc&list=FLUuDEwpR43gvcFvCBovHBUA&index=24" rel="nofollow">video 2</a>) for a <strong>similar problem</strong> but for the case when $E<E_p$. The professor in the video allso uses similar approximation - but in his case $E \ll E_p$.</p>
<p>On this hyperlink there is allso a scan of the problem solved on the paper just in case anyone likes it this way. It is in Slovenian language but i added some headings to help you reading.</p>
| 8,447 |
[
-0.005888339132070541,
-0.026335351169109344,
0.009741605259478092,
-0.013259679079055786,
0.03521306812763214,
-0.041965316981077194,
-0.02283705398440361,
-0.005463666282594204,
0.017244543880224228,
0.002329234266653657,
0.07749771326780319,
-0.014282964169979095,
0.0199093297123909,
0.04511037468910217,
-0.013443084433674812,
0.06142263859510422,
-0.0009238420752808452,
0.0018826780142262578,
0.01567721739411354,
-0.05605025961995125,
0.022936256602406502,
0.03258861228823662,
0.0018969642696902156,
0.01857864484190941,
-0.029048923403024673,
0.029089588671922684,
0.03437058627605438,
-0.018459253013134003,
-0.009280065074563026,
0.0430525504052639,
-0.006072357762604952,
-0.023614434525370598,
0.03563039004802704,
0.018959151580929756,
-0.018088113516569138,
0.0034172043669968843,
-0.03554902225732803,
-0.06100987270474434,
0.023929772898554802,
0.023832131177186966,
-0.03974346071481705,
-0.0025632684119045734,
0.003818859811872244,
0.041631732136011124,
0.015711180865764618,
-0.039123278111219406,
0.006089186295866966,
-0.013074883259832859,
0.03302692994475365,
-0.06015974283218384,
0.06195526197552681,
-0.014729554764926434,
0.05035542696714401,
0.004397408105432987,
-0.0399656742811203,
-0.05650079622864723,
0.05806179344654083,
0.0992504209280014,
0.019830264151096344,
-0.013497056439518929,
-0.01725553721189499,
0.0001396937877871096,
-0.001737908460199833,
0.012947206385433674,
-0.025975052267313004,
0.03007388487458229,
0.01516632828861475,
0.0010718910489231348,
-0.006169512402266264,
-0.012490767985582352,
0.03284423425793648,
0.0030445281881839037,
0.0016257301904261112,
-0.0006471247179433703,
0.039182428270578384,
0.023864159360527992,
-0.030926479026675224,
0.04326758161187172,
0.02835201844573021,
0.06050249934196472,
-0.013988563790917397,
0.01731954514980316,
0.03797252103686333,
0.030698375776410103,
-0.013289517723023891,
-0.0267537459731102,
0.06275337189435959,
-0.022127816453576088,
-0.017010308802127838,
0.0194452702999115,
-0.009502533823251724,
0.03209763765335083,
0.013150242157280445,
-0.0008538442198187113,
-0.0047367038205266,
0.02070617489516735,
-0.012963552959263325,
0.05355086922645569,
0.004461049567908049,
-0.004780938848853111,
0.02503652311861515,
-0.04135715216398239,
0.025893839076161385,
0.06889200210571289,
0.045566607266664505,
0.02891126275062561,
-0.018490782007575035,
0.023228636011481285,
-0.013575280085206032,
0.009216753765940666,
-0.043152742087841034,
0.010257079266011715,
-0.003819297533482313,
0.020658425986766815,
-0.03606967255473137,
-0.05285189300775528,
-0.015306096524000168,
-0.02975435182452202,
0.022127972915768623,
0.00984219554811716,
0.003623889060690999,
-0.042588748037815094,
-0.006424256134778261,
0.012319025583565235,
-0.06592989712953568,
-0.009707783348858356,
0.01920091174542904,
-0.0006254282779991627,
-0.029007697477936745,
0.03988656774163246,
-0.0024213618598878384,
0.009837084449827671,
0.012727734632790089,
-0.013310221955180168,
-0.00258245668374002,
0.004809333011507988,
-0.10751686990261078,
-0.05720430612564087,
0.05802631378173828,
-0.022354014217853546,
0.01847681775689125,
-0.0790337398648262,
-0.04840253293514252,
0.058071110397577286,
0.06620746105909348,
-0.04363890364766121,
0.0030639327596873045,
-0.0020080520771443844,
0.03818388283252716,
0.010331081226468086,
-0.009543386287987232,
0.022680435329675674,
-0.017871065065264702,
-0.005930423736572266,
-0.002874459372833371,
-0.03944031521677971,
0.009692368097603321,
0.013784544542431831,
-0.04180050641298294,
0.004917213227599859,
0.0650855004787445,
-0.005732156336307526,
0.015886573120951653,
-0.008236884139478207,
-0.0278523787856102,
-0.021477723494172096,
0.07955984026193619,
0.04646367207169533,
0.01301334798336029,
0.05804271250963211,
-0.031092701479792595,
0.03182980418205261,
-0.038656312972307205,
-0.021396031603217125,
0.03023345209658146,
-0.01908506266772747,
0.011657889932394028,
-0.05678187310695648,
-0.006006981711834669,
0.02099732495844364,
-0.053878303617239,
-0.03396207466721535,
-0.035046495497226715,
0.0015599766047671437,
0.03947696462273598,
0.052368760108947754,
-0.01250309869647026,
-0.009158181957900524,
-0.017167603597044945,
-0.03832389414310455,
-0.05076337233185768,
-0.01857653446495533,
0.02219756320118904,
-0.0016740193823352456,
-0.014314373955130577,
0.04418151080608368,
-0.051911111921072006,
0.008538099937140942,
0.005555357318371534,
-0.03853803873062134,
0.00511756120249629,
0.032427795231342316,
0.009155666455626488,
0.016967544332146645,
0.03267602249979973,
0.047744497656822205,
0.026089685037732124,
-0.00024840488913469017,
0.03163699805736542,
-0.013661065138876438,
0.014669508673250675,
-0.008645331487059593,
-0.015085031278431416,
0.0745859444141388,
0.030518759042024612,
-0.02294573001563549,
-0.014058948494493961,
-0.005229305941611528,
-0.006618190091103315,
0.01827096752822399,
-0.033377740532159805,
0.060544829815626144,
0.0509897917509079,
0.020172791555523872,
-0.017697526142001152,
0.03504673391580582,
-0.005672459024935961,
0.049222443252801895,
-0.009382286109030247,
-0.0521707758307457,
-0.05888253450393677,
-0.01740482822060585,
0.017218396067619324,
0.02004779689013958,
-0.05683917924761772,
0.009487293660640717,
0.010232929140329361,
0.015361307188868523,
0.029183290898799896,
0.00022181720123626292,
-0.017632877454161644,
-0.031464945524930954,
0.048953112214803696,
0.021740945056080818,
-0.029591849073767662,
-0.0016538675408810377,
0.0420372411608696,
0.008544127456843853,
0.010614433325827122,
-0.016123002395033836,
-0.0029845719691365957,
-0.0028685203287750483,
-0.011861924082040787,
-0.004835562314838171,
-0.003643051255494356,
-0.038782574236392975,
0.05682642385363579,
-0.012390879914164543,
0.057435303926467896,
0.05578663945198059,
-0.05058756098151207,
0.038956597447395325,
-0.02323450706899166,
-0.01362626627087593,
0.00800970010459423,
-0.01606587879359722,
0.026913341134786606,
-0.005275540519505739,
0.014863718301057816,
-0.06308021396398544,
0.013838285580277443,
-0.03636076673865318,
-0.02469894476234913,
0.011410177685320377,
-0.02317572571337223,
0.053077854216098785,
0.01936742290854454,
0.002877947175875306,
-0.0679352879524231,
-0.00984257273375988,
0.010416869074106216,
-0.026541635394096375,
0.0480928048491478,
0.026512395590543747,
-0.055052731186151505,
-0.00887992326170206,
-0.02919674851000309,
-0.015969041734933853,
0.055169347673654556,
-0.0073267933912575245,
-0.018066171556711197,
0.022037625312805176,
-0.022109590470790863,
-0.037586599588394165,
-0.017604127526283264,
-0.034474510699510574,
0.004293503239750862,
-0.05790894478559494,
0.0045529757626354694,
0.058191411197185516,
0.020246945321559906,
-0.030908962711691856,
0.02214954048395157,
-0.009334711357951164,
-0.018824582919478416,
0.009947998449206352,
-0.018626587465405464,
0.009991932660341263,
-0.020350255072116852,
0.041969481855630875,
0.011567915789783001,
0.007323071826249361,
0.007503907196223736,
-0.03645746037364006,
-0.032623372972011566,
0.018980326130986214,
-0.021190375089645386,
0.021773867309093475,
-0.017005672678351402,
-0.020230760797858238,
0.09148461371660233,
0.02383773773908615,
-0.005624320823699236,
-0.015562346205115318,
-0.011493789963424206,
-0.024491168558597565,
-0.0427996926009655,
-0.005191880278289318,
0.06034097075462341,
-0.004074901342391968,
-0.008872642181813717,
-0.041939251124858856,
0.06807197630405426,
0.04341733455657959,
-0.03851450979709625,
-0.004569217097014189,
0.04433871805667877,
-0.02074603922665119,
-0.029108764603734016,
0.07011361420154572,
-0.0077390228398144245,
-0.012835868634283543,
0.003531036898493767,
0.024280814453959465,
0.017590317875146866,
0.027906058356165886,
-0.059955548495054245,
0.055185332894325256,
0.006851717829704285,
0.008619179017841816,
0.018804915249347687,
-0.00680358475074172,
0.008624149486422539,
-0.05702099949121475,
-0.0012004970340058208,
0.03819049522280693,
0.04295683279633522,
0.015182542614638805,
0.0012789724860340357,
0.03471190482378006,
0.024015873670578003,
0.03972707316279411,
-0.03487851098179817,
-0.03271232917904854,
-0.01675635389983654,
0.04533389210700989,
-0.02768023870885372,
-0.04765219986438751,
0.025617923587560654,
0.035742249339818954,
0.010414502583444118,
0.007761271204799414,
0.006070456933230162,
-0.04176771268248558,
-0.03327649086713791,
-0.021576479077339172,
-0.015154771506786346,
0.06853817403316498,
0.018410608172416687,
0.036440689116716385,
0.024726567789912224,
0.015204648487269878,
0.011232590302824974,
0.02817460522055626,
-0.05296432971954346,
-0.002284690970554948,
-0.009408876299858093,
0.005498207174241543,
-0.00011515156802488491,
-0.01509789563715458,
0.0009287455468438566,
-0.02428627572953701,
-0.009471528232097626,
0.008863593451678753,
0.025496946647763252,
-0.012226407416164875,
-0.012069319374859333,
-0.019915759563446045,
0.0046822321601212025,
-0.031919319182634354,
0.038122545927762985,
0.030238015577197075,
-0.008487081155180931,
-0.01457249466329813,
0.030555037781596184,
-0.03740956261754036,
-0.012120922096073627,
-0.012679077684879303,
-0.007505889981985092,
0.04694407433271408,
0.05012056604027748,
-0.00804858561605215,
-0.001956837484613061,
-0.029625363647937775,
-0.006035228259861469,
0.0036816068459302187,
0.03968629240989685,
0.00824678037315607,
-0.014670888893306255,
-0.02877596765756607,
-0.02301735430955887,
-0.0026130785699933767,
-0.021944256499409676,
0.05966740846633911,
-0.011996423825621605,
0.04907611012458801,
0.027192095294594765,
0.023400548845529556,
0.0032115881331264973,
0.034873101860284805,
0.018250714987516403,
0.010026181116700172,
0.00165275065228343,
-0.040707096457481384,
-0.005673518870025873,
-0.04804067686200142,
0.010119155049324036,
0.0263348575681448,
-0.014660610817372799,
-0.00010700432903831825,
0.03950194641947746,
0.045312996953725815,
0.03605347126722336,
-0.0049917795695364475,
0.0271174143999815,
-0.01963886246085167,
-0.03930029645562172,
-0.0068886904045939445,
-0.038301073014736176,
0.047897446900606155,
0.012570656836032867,
0.030008887872099876,
-0.00733046093955636,
0.013677389360964298,
-0.0957411527633667,
-0.027198147028684616,
0.051826491951942444,
0.07471920549869537,
0.014744090847671032,
-0.026766277849674225,
-0.08617878705263138,
-0.01949729584157467,
0.0034177827183157206,
-0.029144974425435066,
0.04293060675263405,
0.007205151487141848,
0.028111256659030914,
-0.03181484714150429,
-0.07993904501199722,
-0.029250074177980423,
0.00368654471822083,
0.004958271514624357,
0.009317489340901375,
-0.03401767089962959,
0.004474814515560865,
0.025550194084644318,
0.012675562873482704,
0.031321726739406586,
0.08262062817811966,
-0.0022461076732724905,
-0.01178719475865364,
0.019971555098891258,
-0.0021951610688120127,
-0.03305245563387871,
-0.06158324331045151,
0.03240134194493294,
-0.04698078706860542,
0.004968244582414627,
0.05606173351407051,
-0.0298078004270792,
-0.04168041795492172,
0.044701702892780304,
0.031937889754772186,
0.01997736655175686,
0.011356730945408344,
0.01586969941854477,
0.07885321229696274,
0.05333944782614708,
-0.01552208885550499,
0.05808202177286148,
0.019046630710363388,
-0.04872768744826317,
0.029180269688367844,
-0.03600238263607025,
-0.0002896932710427791,
-0.011620608158409595,
0.020079592242836952,
-0.034825459122657776,
0.044891081750392914,
-0.02966088242828846,
0.055805839598178864,
-0.04034744203090668,
0.03155865892767906,
-0.025149470195174217,
-0.02542797476053238,
0.017864983528852463,
-0.009190388023853302,
-0.041531454771757126,
-0.004599330481141806,
-0.034904636442661285,
0.007361917290836573,
0.007910994812846184,
-0.03004486672580242,
0.026013866066932678,
-0.010332219302654266,
0.03153093531727791,
-0.006003057584166527,
-0.04636827111244202,
-0.03120991215109825,
-0.05681542307138443,
0.0014640670269727707,
-0.031146857887506485,
-0.05410183221101761,
0.044762857258319855,
-0.00411474984139204,
0.0026807242538779974,
0.003406081348657608,
-0.022698748856782913,
-0.027439193800091743,
0.031714946031570435,
0.01475545670837164,
-0.012348291464149952,
-0.003085936652496457,
-0.001441200147382915,
-0.027917465195059776,
0.019393881782889366,
-0.06710810214281082,
-0.012691431678831577,
0.025208383798599243,
0.03610026091337204,
-0.01377816777676344,
-0.0018052482046186924,
-0.02930094115436077,
-0.015922855585813522,
-0.038645096123218536,
-0.0077206529676914215,
0.021835269406437874,
-0.04447385296225548,
-0.0016135695623233914,
-0.008897056803107262,
0.004407444968819618,
0.040540661662817,
0.0021994824055582285,
0.0010635033249855042,
0.01031454373151064,
-0.014654728583991528,
-0.035578299313783646,
-0.004581850953400135,
0.025786926969885826,
0.003567703999578953,
-0.03527846932411194,
-0.011414784006774426,
0.003976767882704735,
0.05563129484653473,
-0.02046271599829197,
-0.03345978260040283,
0.019509123638272285,
0.017470253631472588,
0.003607261460274458,
0.007535439450293779,
-0.003048524260520935,
-0.0019491370767354965,
0.04523709416389465,
0.00333334575407207,
0.011699491180479527,
-0.03888069465756416,
-0.02405671402812004,
0.04663718864321709,
-0.007770737167447805,
-0.021877529099583626,
-0.005290263332426548,
0.052697740495204926,
-0.013224429450929165,
0.03208642825484276,
-0.0015820447588339448,
0.0113347377628088,
0.033107489347457886,
-0.034521397203207016,
0.02018088288605213,
-0.003356869099661708,
0.015552953816950321,
-0.04390455037355423,
-0.06877020001411438,
-0.0666423887014389,
0.028350038453936577,
0.028526941314339638,
-0.012698735110461712,
0.004067581612616777,
-0.02059621922671795,
-0.015203982591629028,
0.02327338419854641,
-0.015882203355431557,
0.011888324283063412,
-0.007976147346198559,
0.020411312580108643,
0.0402257926762104,
-0.014069453813135624,
-0.023306753486394882,
0.01820734702050686,
0.02901136875152588,
-0.018522094935178757,
-0.043898988515138626,
0.05417477339506149,
0.006385119166225195,
-0.014952097088098526,
-0.029256679117679596,
-0.03389756381511688,
0.0373694933950901,
-0.03734399005770683,
0.043518852442502975,
0.021445337682962418,
-0.012748870067298412,
0.04876605048775673,
0.042954739183187485,
-0.0026235629338771105,
-0.050202757120132446,
-0.009972608648240566,
-0.046069566160440445,
0.008892744779586792,
0.020849790424108505,
-0.02685525082051754,
0.01812742091715336,
0.0439043827354908,
0.019099803641438484,
0.00947782676666975,
0.01428986992686987,
-0.010505187325179577,
-0.0353439524769783,
-0.010437537916004658,
-0.02621806226670742,
-0.06701668351888657,
0.03229016810655594,
-0.008515915833413601,
-0.002973351161926985,
0.0251508466899395,
-0.024061929434537888,
0.03476928919553757,
0.013906602747738361,
0.02716308832168579,
-0.011102640070021152,
0.03540920466184616,
-0.012800132855772972,
-0.001118674874305725,
-0.025175616145133972,
0.00830257497727871,
0.13717806339263916,
0.07807553559541702,
0.005484602879732847,
-0.04396333917975426,
0.04290461540222168,
0.013494186103343964,
0.006950140930712223,
-0.025101669132709503,
-0.0331093892455101,
0.009738332591950893,
-0.03109089657664299,
-0.013242616318166256,
0.020453685894608498,
-0.007499826606363058,
0.04401255398988724,
0.005821192637085915,
-0.05717327073216438,
-0.04709876328706741,
0.05024271830916405,
0.005545699968934059,
0.00978082325309515,
-0.011117401532828808,
-0.02768394537270069,
0.05256105586886406,
-0.053843144327402115,
0.0018774369964376092,
-0.049838773906230927,
-0.028571760281920433,
0.06197059527039528,
-0.006735947914421558,
-0.028411608189344406,
0.010588378645479679,
0.015627991408109665,
-0.029914384707808495,
0.012091701850295067,
0.023977110162377357,
0.0081513412296772,
-0.04611806198954582,
0.0619611032307148,
0.0029998256359249353,
-0.015904735773801804,
-0.01730153150856495,
0.004236488603055477,
0.016108158975839615,
-0.036316629499197006,
-0.04405350610613823,
-0.04212639853358269,
0.06800146400928497,
0.004090907052159309,
-0.036638904362916946,
0.011050201952457428,
0.014183404855430126,
-0.0020135552622377872,
-0.0004912576987408102,
-0.026710886508226395,
-0.009676188230514526,
0.0005564342718571424,
-0.01510175783187151,
-0.010844368487596512,
-0.036135636270046234,
0.025252345949411392,
0.03109806776046753,
-0.009139515459537506,
0.00219852477312088,
0.013706582598388195,
0.03301732987165451,
-0.018958209082484245,
0.03040255419909954,
0.0255372803658247,
0.0017258423613384366,
-0.023684130981564522,
-0.013479182496666908,
-0.005192190874367952,
-0.028488755226135254,
0.0006640761275775731,
0.013727528043091297,
0.026667874306440353,
0.011801155284047127,
-0.01622013933956623,
-0.04771273583173752,
-0.0692756250500679,
0.008828118443489075,
0.002331326249986887,
0.0007218761602416635,
-0.038655124604701996,
-0.013288747519254684,
-0.0036005331203341484,
0.030834166333079338,
-0.012908516451716423,
-0.029795803129673004,
0.03297824785113335,
0.05354688689112663,
-0.0056819915771484375,
-0.018713055178523064,
-0.045008014887571335,
-0.029634930193424225,
-0.01637965254485607,
0.039242636412382126,
-0.005437642335891724,
0.046647559851408005,
-0.03911053016781807,
0.026561731472611427,
0.031439997255802155,
0.03350691497325897,
-0.046526312828063965,
-0.02894367091357708,
0.0293376874178648,
-0.01577230542898178,
0.019133439287543297,
0.02029474265873432,
0.027167512103915215,
-0.029747765511274338,
0.010500194504857063,
-0.010023964568972588,
0.014926822856068611,
0.02665804699063301,
-0.006261774804443121,
-0.0016661512199789286,
0.023286767303943634,
-0.028048820793628693,
-0.01881473697721958,
-0.051490310579538345,
0.007975120097398758,
0.017270704731345177,
0.014843838289380074,
-0.027806127443909645,
0.0030249443370848894,
-0.009760407730937004,
0.024928193539381027,
0.002036085119470954,
0.00018532969988882542,
0.012760811485350132,
0.041820377111434937,
-0.01505625806748867,
-0.03201973810791969,
-0.00018578294839244336,
0.03459949418902397,
0.020731694996356964,
-0.01115503441542387,
-0.02462117187678814,
0.018850676715373993,
-0.01568497158586979,
-0.0020438972860574722,
-0.00014410974108614028,
0.03306910768151283,
0.003667086362838745,
0.03787326440215111,
-0.023839831352233887,
0.0020569839980453253,
0.030629470944404602,
0.0106742475181818,
-0.024913238361477852,
0.019525183364748955,
-0.052930980920791626,
0.02633914165198803,
-0.01704169437289238,
0.020674070343375206,
-0.006078469567000866,
0.038683757185935974,
0.03544418886303902,
-0.006856510881334543,
-0.017335593700408936,
-0.018882304430007935,
0.0091750742867589,
-0.023949915543198586,
-0.0036279696505516768,
0.013950402848422527,
0.0016388013027608395,
0.0028215963393449783,
0.05531356483697891,
-0.017667338252067566,
0.02109261229634285,
0.01183988805860281,
-0.007939011789858341,
-0.08677589893341064,
-0.0005059763207100332,
-0.013976676389575005,
-0.0075268372893333435,
0.051572445780038834,
-0.031408850103616714,
0.03589598834514618,
0.05327265337109566,
-0.05897877737879753,
-0.030393311753869057,
-0.006170686334371567,
0.018949586898088455,
-0.028173884376883507,
0.019052913412451744,
-0.05464547127485275,
0.023136921226978302,
0.026841232553124428,
0.05436697602272034,
0.0009451420046389103,
0.06996071338653564,
0.015463787131011486,
-0.05999195948243141,
-0.007303309161216021,
0.028917737305164337,
0.006650011986494064,
-0.018422961235046387,
0.04453121870756149,
-0.027684295549988747,
0.01633289083838463,
0.018272917717695236,
-0.01082815695554018,
-0.0318889319896698,
-0.025518886744976044,
0.008201785385608673,
0.0025334253441542387,
0.05788801610469818,
-0.005141130648553371,
0.016385558992624283,
0.027970103546977043,
-0.05985243618488312,
0.029145488515496254,
-0.021748028695583344,
0.00918757077306509,
0.0034289872273802757,
0.03200560063123703,
-0.007774333003908396,
-0.043629541993141174,
0.05598633363842964,
-0.03039570525288582,
-0.03340369835495949,
0.013487149961292744,
0.002560873981565237,
0.021111493930220604,
-0.04944407567381859,
-0.014498721808195114,
-0.03904886171221733,
-0.013813408091664314,
-0.02500317431986332,
0.025339527055621147,
0.0021647587418556213,
-0.012414753437042236,
-0.05354778841137886,
-0.054555464535951614,
0.0360582172870636,
0.005426325835287571,
-0.0005355557659640908,
-0.07421427965164185,
-0.015606469474732876,
-0.015517194755375385,
0.023787619546055794,
0.0015361024998128414,
-0.030120594426989555,
-0.07320285588502884,
0.01365494541823864,
-0.02019566111266613,
0.026378296315670013,
0.007441234774887562,
-0.01609889231622219,
-0.02038840390741825,
-0.060896847397089005,
0.010591133497655392,
0.0202657338231802,
-0.022133346647024155,
-0.033407457172870636,
-0.021030111238360405,
-0.00022417266154661775,
0.05451858788728714,
0.07254675775766373,
-0.004598586820065975,
-0.026437021791934967,
0.0341038852930069,
-0.025350555777549744,
0.01876957342028618,
-0.06418538838624954,
-0.02594960480928421,
0.013632173649966717,
0.006904758978635073,
0.008629457093775272,
0.01476723700761795,
-0.01448728609830141,
0.03970225527882576,
0.016010748222470284,
0.02771829068660736,
-0.000024601516997790895,
0.018322506919503212,
-0.011749392375349998,
0.006524180062115192,
-0.016552302986383438,
-0.028919508680701256,
0.0733049064874649,
-0.0034524002112448215,
0.008081461302936077,
-0.0026053311303257942,
-0.016121184453368187,
-0.018022870644927025,
0.0102986516430974,
-0.07848764955997467,
0.02252744697034359,
-0.010856281965970993,
-0.02864900976419449,
0.031051378697156906,
-0.05457489192485809,
-0.026652581989765167,
0.03420544043183327,
-0.05332168936729431,
-0.03815007954835892,
0.046983808279037476,
0.020782819017767906,
0.01814408414065838,
0.011859772726893425,
0.02469400130212307,
-0.01971137523651123,
0.014158027246594429,
0.023078836500644684,
0.006058123894035816,
0.026408515870571136,
0.01221055444329977,
0.027508558705449104,
0.023548375815153122,
-0.043912943452596664,
-0.0014601823640987277,
-0.01280305441468954,
-0.0016900412738323212,
0.00902416929602623,
-0.02855617366731167,
0.02061077579855919,
-0.007794650737196207,
-0.03676408529281616,
0.03176030516624451,
-0.020854350179433823,
0.08593636751174927,
-0.04211708530783653,
0.02042365074157715,
0.010521155782043934,
0.011646158993244171,
0.031030673533678055,
0.04789010435342789,
0.007616166491061449,
0.017839545384049416,
0.0050249905325472355,
-0.031130364164710045,
-0.037650901824235916,
0.02420099452137947,
-0.018923280760645866,
-0.05647396668791771,
0.005647195037454367,
-0.007130333222448826,
-0.009477238170802593,
-0.007637731730937958,
-0.020902080461382866,
0.024475175887346268,
-0.027279281988739967,
0.009997505694627762,
0.01417799573391676,
-0.02120801992714405,
0.009668444283306599,
-0.003994578495621681,
-0.0002963684964925051,
0.0490453764796257,
-0.029082993045449257,
-0.0008282744092866778,
0.0034586507827043533,
0.002664329716935754,
-0.012849382124841213,
0.050440430641174316
] |
<p>Only because</p>
<ol>
<li><p>Rep is unitary, so saves positive-definite norm (for possibility density),</p></li>
<li><p>Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and</p></li>
<li><p>It is the representation of the global group of relativistic symmetry, </p></li>
</ol>
<p>yes?</p>
| 8,448 |
[
0.027629029005765915,
-0.029099998995661736,
0.001293967361561954,
-0.05241619423031807,
0.02994995377957821,
0.014337149448692799,
-0.06172590330243111,
-0.048355791717767715,
-0.036376845091581345,
-0.08761587738990784,
0.013899235986173153,
0.008495690301060677,
0.06051955372095108,
0.0773324966430664,
-0.007233471609652042,
0.04871835932135582,
-0.001236235722899437,
-0.02578160911798477,
-0.0008872817270457745,
-0.02484660968184471,
-0.0019876614678651094,
0.043909382075071335,
-0.010458596982061863,
0.005631250329315662,
-0.02000805363059044,
-0.003311327425763011,
0.02130691520869732,
0.027710454538464546,
0.005769858602434397,
0.08886048197746277,
-0.05515787750482559,
-0.017213011160492897,
0.02777286246418953,
0.030183980241417885,
-0.007943357340991497,
0.0009270724258385599,
-0.017774002626538277,
-0.01103346236050129,
0.006596322637051344,
0.018313346430659294,
-0.0018141650361940265,
-0.02165537327528,
-0.0011664796620607376,
0.03706652298569679,
-0.008771887980401516,
0.055058613419532776,
-0.00801156461238861,
0.005841431673616171,
0.0288406852632761,
-0.024437658488750458,
0.07805142551660538,
0.012426676228642464,
-0.026844799518585205,
-0.032978229224681854,
-0.036707956343889236,
-0.003934871405363083,
0.042231034487485886,
0.06687375903129578,
0.027622012421488762,
-0.04193923994898796,
-0.029450789093971252,
-0.02376687526702881,
0.02364489994943142,
0.020430870354175568,
-0.002671297872439027,
0.001373097999021411,
0.041096653789281845,
-0.01425511110574007,
0.0016067271353676915,
0.03884965553879738,
0.010401071980595589,
0.010555349290370941,
-0.010307670570909977,
-0.05912765488028526,
-0.00538334995508194,
-0.010396245867013931,
0.015610959380865097,
0.01251121237874031,
0.033310629427433014,
0.02026692032814026,
-0.011356813833117485,
0.0018838292453438044,
0.01704627089202404,
0.0011270641116425395,
0.039980366826057434,
-0.0018712511518970132,
0.07957867532968521,
0.04007478058338165,
-0.0026664563920348883,
0.009886390529572964,
-0.006509459111839533,
-0.006459642201662064,
0.014843720011413097,
0.007245626766234636,
-0.022070448845624924,
0.01595214381814003,
0.009780786000192165,
0.02823142521083355,
-0.020439008250832558,
-0.010353288613259792,
-0.020228983834385872,
-0.011156358756124973,
-0.011439241468906403,
0.06560588628053665,
-0.004505672957748175,
0.012116576544940472,
-0.06002405658364296,
-0.025193946436047554,
-0.03408898040652275,
-0.017356691882014275,
-0.032232336699962616,
0.012866784818470478,
-0.05392122641205788,
-0.007146436255425215,
0.01733279600739479,
0.00016527825209777802,
-0.027345256879925728,
-0.031976934522390366,
0.035758864134550095,
0.07910578697919846,
0.029915668070316315,
-0.014346513897180557,
0.01627805083990097,
-0.027817724272608757,
-0.07146310806274414,
0.043196238577365875,
0.03696764260530472,
0.01628379337489605,
-0.028729548677802086,
0.02706207148730755,
0.005364058539271355,
-0.01962583139538765,
0.01860511489212513,
0.0022572947200387716,
0.030935823917388916,
0.0006833196384832263,
-0.09573335945606232,
-0.03702490031719208,
0.012942999601364136,
-0.015074256807565689,
-0.011695212684571743,
-0.0830686017870903,
0.03225823491811752,
0.02516217529773712,
0.08218517154455185,
0.0015388242900371552,
0.03202616423368454,
0.010053414851427078,
0.07423081248998642,
0.0034471580293029547,
-0.008483517915010452,
-0.037410106509923935,
-0.004524691496044397,
-0.05624854564666748,
-0.0013661399716511369,
-0.06967312842607498,
-0.0033855605870485306,
0.008463230915367603,
0.004805749747902155,
-0.016304366290569305,
0.05476986989378929,
-0.042928148061037064,
0.02679336816072464,
0.015201977454125881,
0.01670730486512184,
0.010974391363561153,
0.04732619971036911,
0.00381856900639832,
0.008026216179132462,
0.019728926941752434,
-0.018135104328393936,
0.015879809856414795,
0.01572086103260517,
0.033586543053388596,
0.04089375212788582,
-0.021070554852485657,
-0.0013254409423097968,
-0.00541668338701129,
0.015693403780460358,
-0.040625348687171936,
-0.04097985103726387,
-0.037296734750270844,
-0.02007346786558628,
-0.0039460319094359875,
-0.01620565913617611,
0.0201967004686594,
0.007977056317031384,
0.00506080174818635,
-0.00894563551992178,
-0.06265871226787567,
-0.023892639204859734,
-0.03605150431394577,
0.009060466662049294,
0.003639057744294405,
-0.0278058722615242,
0.004958317615091801,
0.026304610073566437,
0.00042654541903175414,
-0.010995285585522652,
-0.017311833798885345,
-0.04232525825500488,
0.028409436345100403,
-0.03594011440873146,
-0.012832224369049072,
0.005433090031147003,
0.02195041999220848,
0.05691505968570709,
-0.024652834981679916,
0.01627238281071186,
-0.002447974868118763,
-0.06308061629533768,
0.0024376928340643644,
0.015590086579322815,
-0.006999707315117121,
-0.0025098249316215515,
-0.016482338309288025,
0.029499603435397148,
0.019437074661254883,
-0.01297176443040371,
0.03183356299996376,
-0.03566322848200798,
0.03188420459628105,
0.013245892710983753,
0.03497074171900749,
0.02486526407301426,
0.0384666733443737,
0.0093843974173069,
0.02920139580965042,
0.012846277095377445,
-0.027281159535050392,
-0.06120371073484421,
-0.009960570372641087,
0.010091463103890419,
0.04562674090266228,
-0.026641972362995148,
0.060121800750494,
0.032809410244226456,
0.0215136855840683,
0.0021731508895754814,
-0.019294653087854385,
-0.02571704052388668,
-0.0399177223443985,
0.048144858330488205,
0.005943493917584419,
0.020642397925257683,
-0.00169353315141052,
-0.014598121866583824,
0.036122437566518784,
0.028379622846841812,
0.03257716819643974,
-0.006491618696600199,
0.06085076555609703,
-0.02382989414036274,
0.0001467497058911249,
0.015999797731637955,
-0.03618231415748596,
0.029522772878408432,
0.007796678692102432,
0.018850572407245636,
0.007736276835203171,
0.015976687893271446,
0.01778530515730381,
-0.04687798023223877,
-0.03076765686273575,
-0.002097082557156682,
-0.006822706665843725,
-0.018259873613715172,
-0.033318281173706055,
0.017617445439100266,
-0.04568203538656235,
0.008503631688654423,
-0.019214928150177002,
-0.01058457512408495,
-0.02490919828414917,
0.03465408831834793,
0.04208124428987503,
-0.004775856155902147,
0.009951290674507618,
-0.043972596526145935,
-0.018487289547920227,
0.015520392917096615,
-0.007667104713618755,
0.008586038835346699,
0.032834216952323914,
-0.04395443573594093,
-0.0008981701103039086,
-0.05707111954689026,
-0.041540127247571945,
0.015858693048357964,
-0.001277540111914277,
0.014701557345688343,
0.0012978761224076152,
-0.001965489238500595,
-0.03985806927084923,
0.002814278472214937,
-0.06166769936680794,
0.029977746307849884,
-0.04202267527580261,
0.002009958028793335,
0.036065056920051575,
0.005542804021388292,
-0.05307551845908165,
0.0033763356041163206,
-0.02508213371038437,
-0.0407111681997776,
-0.005250546615570784,
-0.0012816739035770297,
0.042512282729148865,
-0.02778574451804161,
0.04536481574177742,
0.018833868205547333,
-0.03632526472210884,
0.003680117893964052,
-0.0693804994225502,
-0.01717391237616539,
0.028702283278107643,
-0.006048610899597406,
0.03925951570272446,
0.007301912643015385,
-0.04002058506011963,
0.0748758465051651,
0.039766762405633926,
-0.017466239631175995,
-0.010991433635354042,
0.0051467763260006905,
-0.030057458207011223,
-0.026546631008386612,
0.011770115233957767,
0.010977369733154774,
0.017283042892813683,
0.024101652204990387,
0.029433568939566612,
0.02355874888598919,
-0.0018764747073873878,
-0.005552318412810564,
-0.03898194432258606,
-0.003669332480058074,
-0.026849696412682533,
-0.006110340356826782,
0.0525766983628273,
-0.008109427988529205,
-0.03368214890360832,
0.0010492063593119383,
0.012686585076153278,
0.018907686695456505,
-0.01188459899276495,
-0.06315869837999344,
0.01471687387675047,
0.008797421120107174,
0.055678609758615494,
-0.028801187872886658,
0.06843429803848267,
-0.008937552571296692,
-0.04784487187862396,
0.012789931148290634,
0.014164399355649948,
0.015836268663406372,
-0.0032029293943196535,
-0.012678290717303753,
0.006054959259927273,
0.028627648949623108,
0.0032661459408700466,
-0.014236660674214363,
0.015811776742339134,
-0.03985920175909996,
-0.006730871740728617,
-0.017061054706573486,
-0.04276305064558983,
-0.008847173303365707,
0.07226858288049698,
0.028865551576018333,
0.01966770738363266,
-0.05372358486056328,
-0.029305221512913704,
-0.03832576423883438,
-0.0032382626086473465,
-0.024951981380581856,
0.04216497391462326,
-0.01228219736367464,
0.05269700661301613,
0.03010246530175209,
-0.001415409380570054,
-0.03454883024096489,
-0.0060280426405370235,
-0.0684492439031601,
0.0194467231631279,
-0.014529310166835785,
0.026907559484243393,
0.00595337338745594,
-0.0022432708647102118,
0.01379889715462923,
-0.022622350603342056,
-0.017325008288025856,
0.0015583641361445189,
0.004038631916046143,
-0.06275419890880585,
-0.003360792063176632,
-0.029491007328033447,
-0.038366883993148804,
-0.0005574910901486874,
0.013817843981087208,
0.052618131041526794,
-0.043802473694086075,
0.03359384462237358,
0.05177842080593109,
-0.04196649044752121,
0.0022420650348067284,
0.00838484987616539,
0.004021735396236181,
0.05057113617658615,
0.0008915485232137144,
0.039418306201696396,
0.004958549980074167,
-0.03294345736503601,
-0.023264599964022636,
-0.01021686103194952,
0.043338168412446976,
0.030771326273679733,
-0.007099771406501532,
0.006094649434089661,
-0.004556277766823769,
0.011887460015714169,
0.017941027879714966,
0.05650472268462181,
-0.030323712155222893,
0.0012214083690196276,
0.050215065479278564,
-0.013918204233050346,
-0.004011831246316433,
0.04511156678199768,
0.04391026869416237,
-0.013263504020869732,
-0.03719712793827057,
-0.003318513510748744,
-0.006374804303050041,
-0.020750656723976135,
-0.02383534610271454,
0.018759289756417274,
0.010155357420444489,
-0.04214421659708023,
-0.008254543878138065,
-0.028173411265015602,
0.029832473024725914,
-0.07153386622667313,
0.008274409919977188,
0.031813811510801315,
0.028768472373485565,
-0.013766763731837273,
0.018567463383078575,
-0.02891474962234497,
0.049848057329654694,
0.041120804846286774,
0.01201326958835125,
-0.02416124753654003,
-0.03063887730240822,
0.007992449216544628,
0.0471898578107357,
0.036804743111133575,
0.011590949259698391,
-0.00993629451841116,
-0.043792787939310074,
0.01414019986987114,
0.04942099004983902,
-0.04857173189520836,
0.014383950270712376,
-0.007408114615827799,
-0.03481023386120796,
-0.005304819904267788,
-0.031381431967020035,
0.010494774207472801,
-0.0026003336533904076,
0.010704312473535538,
-0.023344779387116432,
-0.026710668578743935,
-0.005706286523491144,
-0.011545687913894653,
0.0016866351943463087,
-0.006886282470077276,
0.00809404905885458,
0.040630731731653214,
0.04096986725926399,
0.013342376798391342,
0.042759135365486145,
-0.03743031248450279,
-0.04605400934815407,
-0.01809726469218731,
0.023517493158578873,
0.005475388374179602,
0.036722391843795776,
-0.038909826427698135,
-0.0468721017241478,
0.012830468825995922,
-0.012971065007150173,
0.017720438539981842,
-0.03679415211081505,
-0.04199587181210518,
0.03377407789230347,
0.053367435932159424,
0.009705757722258568,
0.028982816264033318,
0.059354592114686966,
-0.003970231395214796,
-0.005041604395955801,
-0.03422056883573532,
-0.014513639733195305,
-0.05611087754368782,
0.004020228981971741,
-0.024426396936178207,
-0.0114517230540514,
-0.04807963967323303,
0.03389484062790871,
0.01043205987662077,
0.007793547585606575,
0.011029704473912716,
-0.008781938813626766,
-0.019014466553926468,
0.04170301556587219,
-0.02715793251991272,
0.012959089130163193,
-0.012147735804319382,
0.011368855834007263,
0.03236789256334305,
-0.01839233934879303,
0.030767027288675308,
-0.007418004330247641,
0.015725739300251007,
0.02554626576602459,
0.0035688327625393867,
0.0499713271856308,
0.00836069043725729,
0.024603258818387985,
0.007951932959258556,
-0.07311996072530746,
0.02980695851147175,
-0.0060095759108662605,
-0.0018794998759403825,
-0.003067463869228959,
-0.014830781146883965,
-0.044923100620508194,
0.008020229637622833,
-0.03949086740612984,
0.045205019414424896,
-0.020769594237208366,
0.035492975264787674,
0.06978414952754974,
0.008199864998459816,
-0.068852499127388,
-0.034890469163656235,
0.0035831001587212086,
0.021450424566864967,
-0.009482800029218197,
-0.005815198179334402,
0.0065736896358430386,
-0.04397541284561157,
-0.006475925445556641,
-0.00507744587957859,
0.07224525511264801,
-0.0034292396157979965,
0.007098622154444456,
0.0034875464625656605,
0.06216263398528099,
0.07484347373247147,
0.009636998176574707,
-0.008970619179308414,
0.029364842921495438,
-0.0203001257032156,
0.020741000771522522,
0.002236949047073722,
0.027698278427124023,
-0.022540424019098282,
-0.051062338054180145,
-0.0018768544541671872,
0.030864227563142776,
0.027118057012557983,
-0.01899917982518673,
-0.02390057034790516,
0.046159032732248306,
0.009073611348867416,
0.015937719494104385,
-0.046451929956674576,
0.013686394318938255,
-0.03847631812095642,
0.01506186556071043,
0.014676173217594624,
0.01540630217641592,
-0.042551714926958084,
-0.022272378206253052,
0.02264787256717682,
-0.024370620027184486,
-0.0285180676728487,
-0.0037101611960679293,
0.045465245842933655,
0.006805055774748325,
0.008611256256699562,
0.0036372754257172346,
-0.033235397189855576,
-0.019261660054326057,
-0.036428820341825485,
0.04286691173911095,
0.009636814706027508,
0.0059801614843308926,
-0.016737332567572594,
-0.0015123911434784532,
-0.027626236900687218,
-0.02374066784977913,
0.06545967608690262,
0.03753961995244026,
0.053741421550512314,
0.010133808478713036,
-0.016249876469373703,
-0.0017929751193150878,
0.0002559426357038319,
-0.02449582703411579,
0.001345217227935791,
0.012535621412098408,
0.040516797453165054,
-0.0286127757281065,
0.026468370109796524,
0.02737591601908207,
0.020204992964863777,
-0.02649679034948349,
0.0010414794087409973,
0.04417858645319939,
0.022227853536605835,
0.0057568857446312904,
0.009363614954054356,
-0.02731289528310299,
0.055844683200120926,
-0.04685034975409508,
0.010389701463282108,
-0.005105876363813877,
0.007333063520491123,
-0.03523716330528259,
0.018439797684550285,
0.0383632630109787,
-0.008791519328951836,
-0.012442408129572868,
-0.05454917252063751,
0.03182874992489815,
0.03140346333384514,
0.004589788615703583,
-0.0031878738664090633,
-0.00445354962721467,
0.0013725595781579614,
0.01649000495672226,
0.037081215530633926,
-0.007403876166790724,
-0.07562892138957977,
0.039172202348709106,
-0.03678248077630997,
-0.04858801141381264,
0.03595810756087303,
0.008415235206484795,
-0.022588396444916725,
-0.02368316799402237,
-0.02980465069413185,
0.026411661878228188,
0.04374757409095764,
0.04932243376970291,
-0.03768093138933182,
0.06576210260391235,
-0.0001963825197890401,
0.03229830041527748,
0.03244488313794136,
-0.026534289121627808,
0.14695604145526886,
0.014037362299859524,
0.026311304420232773,
-0.048846300691366196,
0.00892200879752636,
0.00012314518971834332,
-0.019487816840410233,
-0.0035527790896594524,
0.010686018504202366,
-0.039368368685245514,
0.011376261711120605,
0.006330897565931082,
0.04226719215512276,
-0.015370665118098259,
0.00459153251722455,
0.024089014157652855,
-0.048405442386865616,
-0.038586150854825974,
-0.005776884499937296,
0.03935282304883003,
0.02455613575875759,
0.021706828847527504,
-0.043095096945762634,
0.006359010469168425,
-0.027972480282187462,
0.01688886247575283,
-0.022333312779664993,
-0.030302589759230614,
0.01879388652741909,
-0.009161249734461308,
-0.027368875220417976,
-0.0036756659392267466,
-0.005209031049162149,
-0.022497547790408134,
-0.07381265610456467,
-0.022756468504667282,
0.01187631394714117,
-0.044490568339824677,
0.023310285061597824,
0.07649710774421692,
-0.01321931928396225,
-0.022474605590105057,
0.03107946738600731,
0.008508207276463509,
-0.05969838425517082,
0.01737285405397415,
-0.027698686346411705,
0.02652638591825962,
-0.03780944272875786,
0.005565921775996685,
0.031846217811107635,
-0.021687595173716545,
-0.000029781751436530612,
-0.06840252876281738,
-0.01704258844256401,
-0.03354913368821144,
0.04118770360946655,
-0.022828346118330956,
-0.03142479434609413,
-0.012103969231247902,
0.01898646540939808,
-0.03490659222006798,
0.030449943616986275,
-0.008101160638034344,
-0.04238443821668625,
-0.021901462227106094,
0.026992788538336754,
0.0013416096335276961,
-0.006605754606425762,
0.0024629037361592054,
-0.005725427996367216,
-0.057763684540987015,
-0.03343741595745087,
-0.013854161836206913,
0.00564786558970809,
0.02261812426149845,
0.03754691779613495,
0.011947044171392918,
0.000988901243545115,
-0.04832678288221359,
-0.07733675837516785,
0.02133902534842491,
-0.04509258270263672,
-0.03184705600142479,
0.009770621545612812,
-0.016464440152049065,
0.002440640702843666,
0.04713691771030426,
-0.059370920062065125,
0.006519852206110954,
0.023092934861779213,
0.04068181663751602,
-0.01561826653778553,
-0.014616253785789013,
0.011057808995246887,
0.015529170632362366,
-0.03816354274749756,
0.02495476044714451,
-0.013969128020107746,
-0.010503466241061687,
0.042215775698423386,
0.013822857290506363,
0.011260058730840683,
0.055170536041259766,
-0.03027869574725628,
-0.01632288284599781,
0.019331522285938263,
-0.05215800926089287,
0.02999822050333023,
0.035711828619241714,
-0.03832545876502991,
-0.02955709956586361,
-0.018606919795274734,
0.032253772020339966,
-0.002662496641278267,
0.012321810238063335,
0.010494030080735683,
-0.07086333632469177,
0.004903548862785101,
-0.028129901736974716,
0.023045659065246582,
-0.03302783519029617,
0.016551349312067032,
-0.04516126960515976,
0.006679598707705736,
0.00943398755043745,
-0.011066586710512638,
-0.012351849116384983,
0.003730913158506155,
0.008212805725634098,
-0.0074642072431743145,
0.03720582649111748,
0.016670778393745422,
-0.011972561478614807,
0.018142830580472946,
0.008651173673570156,
-0.002868770156055689,
0.037685152143239975,
-0.004562732297927141,
0.005645476281642914,
0.03416992723941803,
-0.04030238837003708,
-0.032528556883335114,
0.04414094239473343,
-0.0056811850517988205,
0.02896350994706154,
0.026215093210339546,
-0.015218746848404408,
-0.00443094689399004,
0.02039402164518833,
-0.05241282656788826,
-0.004225880838930607,
-0.010678209364414215,
-0.02881757542490959,
0.012340753339231014,
-0.03354450687766075,
-0.038265522569417953,
0.03422180190682411,
-0.05115998908877373,
0.01746147684752941,
0.002217025961726904,
-0.03047875314950943,
-0.006883989088237286,
-0.0014339379267767072,
-0.007367199752479792,
0.025732427835464478,
0.042565200477838516,
0.025317715480923653,
-0.009112470783293247,
0.011629854328930378,
-0.04356301203370094,
0.03236998990178108,
0.00165764638222754,
-0.03073997050523758,
-0.09357453882694244,
-0.016247324645519257,
0.006680316291749477,
-0.003787900321185589,
0.07452015578746796,
-0.03359958902001381,
0.024446897208690643,
0.007554119452834129,
-0.02665111795067787,
0.06874518096446991,
-0.0436704196035862,
-0.044922471046447754,
-0.008193993009626865,
-0.02572394162416458,
-0.02369036339223385,
0.05760033428668976,
0.03412388637661934,
0.0399860143661499,
0.04138729348778725,
-0.0012727045686915517,
-0.0010724154999479651,
0.004608861170709133,
0.0055391909554600716,
0.039031803607940674,
-0.01664622873067856,
-0.02160610444843769,
0.06636518985033035,
0.014097006060183048,
-0.02761176787316799,
0.01799180917441845,
0.028835410252213478,
0.002274774480611086,
-0.036676883697509766,
0.030480707064270973,
0.01500166580080986,
0.044817060232162476,
0.014411088079214096,
-0.017418989911675453,
-0.022142337635159492,
-0.009908434934914112,
0.011010452173650265,
0.0005959466798231006,
0.006217774469405413,
0.004428181331604719,
-0.015207593329250813,
-0.05077772215008736,
0.010729172267019749,
0.046083442866802216,
-0.01903083734214306,
-0.027999192476272583,
-0.005958665627986193,
-0.018770141527056694,
-0.0408950001001358,
-0.025176048278808594,
0.0070467665791511536,
-0.04806634783744812,
0.015830181539058685,
0.007864969782531261,
-0.000451316504040733,
-0.013333117589354515,
0.021808365359902382,
0.029241017997264862,
-0.05809035152196884,
-0.004124792758375406,
0.0017636844422668219,
0.004264726769179106,
-0.033921707421541214,
-0.006288365926593542,
0.04854607209563255,
0.027507701888680458,
0.011198073625564575,
-0.017742395401000977,
-0.04341238737106323,
0.062160924077034,
0.012453233823180199,
0.03755578026175499,
-0.02234989032149315,
-0.029917651787400246,
-0.0018359834793955088,
-0.04133430868387222,
0.03234298527240753,
0.043896716088056564,
-0.027119101956486702,
-0.03013421967625618,
-0.018067477270960808,
0.01906929537653923,
0.01864096336066723,
0.05903240293264389,
0.03199269622564316,
-0.003126757452264428,
0.03826246038079262,
-0.00247245654463768,
0.060938552021980286,
-0.0261471476405859,
0.01657295599579811,
-0.04869851842522621,
-0.024927107617259026,
-0.003081010654568672,
0.012595023959875107,
-0.022901112213730812,
0.020894303917884827,
0.025014040991663933,
-0.03197015821933746,
-0.007297102361917496,
0.033346906304359436,
-0.047789718955755234,
0.0526483915746212,
-0.02138744853436947,
-0.021473746746778488,
0.05005750432610512,
-0.0034725985024124384,
-0.00807515811175108,
0.011347491294145584,
-0.017370406538248062,
-0.03325353562831879,
0.008459524251520634,
0.008523773401975632,
-0.06922726333141327,
-0.0196766909211874,
0.0029888739809393883,
0.016367187723517418,
-0.038864754140377045,
-0.016445908695459366,
0.0855637714266777,
-0.03416513651609421,
-0.008485252968966961,
0.07662650942802429,
0.016968335956335068,
0.041305914521217346,
0.03072364814579487,
0.010759305208921432,
0.03950776904821396,
-0.025270773097872734,
0.03958693519234657,
0.07319355010986328,
0.019918354228138924,
-0.030202018097043037,
-0.021324647590517998,
0.006036571692675352,
-0.003828746499493718,
0.025007927790284157,
0.030189523473381996,
0.031015630811452866,
-0.0648653656244278,
0.016605090349912643,
0.05459573119878769,
-0.03731485456228256,
0.02980930544435978,
0.007949840277433395,
-0.023887624964118004,
0.12661850452423096,
-0.0039604236371815205,
0.018474049866199493,
-0.04285068064928055,
0.0004129390581510961,
-0.01924649067223072,
0.03377172723412514,
0.04429001361131668,
0.030547084286808968,
-0.007071116007864475,
0.0005091432831250131,
-0.0379994735121727,
-0.017703399062156677,
0.014137651771306992,
-0.04311298578977585,
-0.0028535088058561087,
0.020861098542809486,
-0.003954018000513315,
-0.023734306916594505,
0.0016638297820463777,
0.01358307246118784,
-0.02822052873671055,
-0.00031831496744416654,
0.05140109360218048,
0.03909139335155487,
-0.000799881003331393,
-0.014511116780340672,
-0.022246193140745163,
0.023218415677547455,
-0.03064652718603611,
-0.044950105249881744,
-0.02190054953098297,
-0.01742543652653694,
0.016820374876260757,
-0.00426476402208209
] |
<p>Assume we had an elevator shaft long enough for a free-falling elevator to reach terminal velocity.</p>
<p>As I understand it, when the elevator begins to fall a person inside would experiences weightlessness because they would be accelerating downward at the same rate as the elevator. The rate of downward acceleration for the elevator should reach a constant when air resistance equals gravity (right?). However, the person in the elevator would not be exposed to air resistance and should continue to accelerate downward. </p>
<p>So would they gradually sink back to the floor and experience gravity as though the elevator were at rest... at least until the inevitable termination of the experiment? </p>
| 8,449 |
[
-0.04673551023006439,
-0.041547540575265884,
-0.015295269899070263,
0.005309067200869322,
0.020293772220611572,
0.0017152026994153857,
-0.008586553856730461,
-0.03589441254734993,
0.007047670427709818,
-0.018216511234641075,
0.012942357920110226,
0.04532073810696602,
-0.0020436018239706755,
0.01918342337012291,
0.009189596399664879,
0.010239969938993454,
-0.024364538490772247,
0.0000975002913037315,
-0.007470681797713041,
-0.01738782227039337,
-0.01348879560828209,
0.011947596445679665,
-0.0063986144959926605,
0.015134732238948345,
-0.056824177503585815,
0.008135229349136353,
0.03039701282978058,
-0.05298945680260658,
-0.006112341303378344,
0.04358392953872681,
-0.020568029955029488,
0.026846813037991524,
-0.013953342102468014,
0.03905239328742027,
0.04261370003223419,
0.024258725345134735,
-0.05403316766023636,
-0.016097746789455414,
-0.022747663781046867,
0.04059808701276779,
-0.019911309704184532,
-0.02753978595137596,
-0.016474764794111252,
0.05020875483751297,
-0.024063026532530785,
0.0069517651572823524,
0.00477328896522522,
-0.01523845735937357,
0.022535867989063263,
-0.07169485092163086,
0.05653579160571098,
-0.024949289858341217,
0.026797104626893997,
0.015835914760828018,
0.0103811239823699,
-0.02212413400411606,
0.06739793717861176,
0.06863545626401901,
-0.012306339107453823,
-0.057025931775569916,
-0.0016130307922139764,
-0.052162010222673416,
-0.04531451687216759,
-0.03503388911485672,
-0.023526133969426155,
0.037822842597961426,
-0.03372419998049736,
-0.011923126876354218,
0.03739231452345848,
-0.030228758230805397,
0.012880412861704826,
0.014500750228762627,
0.00997005496174097,
-0.017967715859413147,
0.03366667032241821,
-0.005702787544578314,
0.04484214261174202,
0.032882608473300934,
0.025360312312841415,
0.03577708452939987,
-0.01542704738676548,
0.0020592433866113424,
0.07563919574022293,
0.037516120821237564,
0.015235332772135735,
-0.0008798301569186151,
0.06569412350654602,
-0.0025926281232386827,
-0.009012545458972454,
0.04804859310388565,
0.01216648705303669,
-0.019143972545862198,
-0.04786239564418793,
0.002835611579939723,
-0.030474983155727386,
0.039074596017599106,
0.008537025190889835,
0.07758309692144394,
-0.019023902714252472,
-0.03068789280951023,
0.0034897467121481895,
0.0013344535836949944,
0.0028451925609260798,
0.057828642427921295,
0.0007825673092156649,
0.0060165501199662685,
-0.027631418779492378,
0.013292570598423481,
-0.019595550373196602,
-0.03511890023946762,
-0.038289040327072144,
-0.024037307128310204,
-0.039329495280981064,
-0.03984132781624794,
0.027421215549111366,
-0.039120450615882874,
0.011200331151485443,
-0.007602936588227749,
0.06317318230867386,
0.03182394430041313,
0.06486616283655167,
-0.00239981128834188,
0.048009369522333145,
0.020120244473218918,
-0.04754341021180153,
0.009301707148551941,
0.015229515731334686,
-0.017951494082808495,
-0.04538263753056526,
0.037435926496982574,
0.031198648735880852,
-0.021727129817008972,
0.018033625558018684,
-0.014942034147679806,
0.08652234822511673,
0.0015919351717457175,
-0.08982384949922562,
-0.042090147733688354,
0.02949664741754532,
-0.005738905631005764,
-0.013543480075895786,
-0.07617457956075668,
-0.015087339095771313,
0.031145548447966576,
0.09577876329421997,
0.018412265926599503,
0.04413144662976265,
0.000013603854313259944,
-0.00760071724653244,
0.01940079964697361,
0.015370229259133339,
-0.006706079468131065,
-0.009522459469735622,
-0.04477599635720253,
-0.01380368135869503,
-0.07502707839012146,
0.011289635673165321,
0.026690734550356865,
0.007324437145143747,
-0.028336822986602783,
-0.0011299292091280222,
0.0005574838141910732,
0.007213322911411524,
0.005907622631639242,
-0.03781002014875412,
0.008290540426969528,
0.05501779541373253,
0.027863478288054466,
-0.03320958837866783,
0.022813789546489716,
0.04290756210684776,
0.04847760871052742,
-0.008937884122133255,
0.021777257323265076,
0.04419596493244171,
-0.04191519692540169,
-0.018996572121977806,
-0.0032298932783305645,
0.012415657751262188,
0.005032351706176996,
-0.021660279482603073,
-0.04048971086740494,
-0.018744956701993942,
0.019388075917959213,
0.01215849444270134,
0.029656952247023582,
0.03405461832880974,
-0.009584018029272556,
0.012994148768484592,
-0.04335000738501549,
-0.007802439387887716,
-0.09103111177682877,
0.014829915016889572,
0.0026217796839773655,
0.0006564679788425565,
0.0024882247671484947,
0.022828394547104836,
0.006990556139498949,
-0.06750855594873428,
0.008921286091208458,
0.0010600365931168199,
0.02562052011489868,
0.008016768842935562,
-0.019673509523272514,
0.0025898802559822798,
0.035068463534116745,
0.06232694908976555,
0.006838291883468628,
0.007901269942522049,
0.021572807803750038,
0.0036123257596045732,
-0.03226597234606743,
-0.012135940603911877,
0.02175435796380043,
-0.007202140521258116,
0.0391252338886261,
0.018753016367554665,
-0.019500160589814186,
-0.005184885114431381,
0.02978658303618431,
-0.027406349778175354,
0.08431801944971085,
0.05368760600686073,
0.008089033886790276,
0.027005529031157494,
0.0016143624670803547,
0.04384713992476463,
-0.006988243665546179,
-0.012645629234611988,
-0.018751677125692368,
-0.048270683735609055,
-0.003441723994910717,
-0.005329310428351164,
0.00021903357992414385,
-0.03198404982686043,
0.056024421006441116,
0.01933971792459488,
0.05966586992144585,
0.005739832762628794,
0.05537339299917221,
0.04026949405670166,
-0.03752071410417557,
0.016709767282009125,
0.021285761147737503,
0.02135189063847065,
0.004330113064497709,
0.02536918595433235,
0.04056170582771301,
0.01557015348225832,
-0.04104705527424812,
0.0017602923326194286,
0.008413049392402172,
0.013111282140016556,
0.03924589231610298,
-0.03882284462451935,
-0.04608790576457977,
0.015453321859240532,
0.0027489792555570602,
0.010496263392269611,
0.031234877184033394,
-0.017765961587429047,
0.007158790715038776,
-0.05640288442373276,
-0.01946449466049671,
0.01751069165766239,
0.02366206981241703,
-0.015460175462067127,
-0.03434047847986221,
0.01933424174785614,
-0.030766092240810394,
0.01401477213948965,
-0.059933919459581375,
-0.02649332955479622,
-0.04011526703834534,
0.004852249752730131,
0.01535875629633665,
0.011811299249529839,
0.03981746360659599,
-0.014425193890929222,
-0.0305012259632349,
-0.012600386515259743,
-0.07304871827363968,
0.000010465600098541472,
0.02248442731797695,
-0.02522171661257744,
0.03289037570357323,
-0.012016860768198967,
-0.0377313606441021,
0.0660790279507637,
0.02642216719686985,
0.01901761256158352,
0.06106110289692879,
-0.02888532541692257,
-0.022616678848862648,
0.010196728631854057,
-0.006975027732551098,
-0.04305560886859894,
-0.03390764445066452,
0.00469156913459301,
0.060217779129743576,
-0.021229524165391922,
-0.018280882388353348,
0.040312767028808594,
-0.07750631123781204,
-0.04011566936969757,
0.0025892811827361584,
0.021094106137752533,
0.00882535707205534,
-0.03810399770736694,
0.003818626282736659,
0.004944042768329382,
-0.047202203422784805,
-0.03222980350255966,
-0.05425344780087471,
-0.07332122325897217,
0.031100554391741753,
0.01618904620409012,
0.018890373408794403,
0.03277347609400749,
-0.027148766443133354,
0.09326977282762527,
-0.011375872418284416,
0.009639986790716648,
-0.06252779811620712,
-0.018569810315966606,
0.0039014790672808886,
0.005792461335659027,
0.016651121899485588,
-0.001237478805705905,
-0.029952334240078926,
-0.008274316787719727,
0.023994866758584976,
0.026323478668928146,
-0.0013099034549668431,
0.03033553436398506,
0.00103278539609164,
-0.001415371079929173,
0.052480075508356094,
-0.006626180373132229,
0.017443101853132248,
0.011002941988408566,
-0.007045436184853315,
-0.0012044885661453009,
-0.013058517128229141,
0.044046349823474884,
-0.018447082489728928,
-0.051901765167713165,
0.0693637803196907,
-0.019251739606261253,
0.007943082600831985,
-0.015130085870623589,
0.0017659226432442665,
-0.019570980221033096,
0.010748826898634434,
-0.027104536071419716,
0.0010417335433885455,
0.039127763360738754,
-0.013424011878669262,
-0.004640537314116955,
0.015426535159349442,
0.08487603813409805,
-0.05943571403622627,
-0.06931053847074509,
0.02320319227874279,
-0.0008692078408785164,
0.05568539351224899,
-0.04559142142534256,
-0.03126323223114014,
0.05016171932220459,
0.02879563346505165,
0.06534283608198166,
0.02434108592569828,
-0.03322509303689003,
0.020036861300468445,
-0.054152220487594604,
0.03287230804562569,
-0.0004511064325924963,
0.03538810461759567,
-0.004099927842617035,
0.05157052353024483,
0.06069493666291237,
0.04247095435857773,
0.03387640789151192,
0.021025944501161575,
-0.08880164474248886,
0.009333725087344646,
-0.05657964199781418,
-0.019992338493466377,
0.03520879149436951,
0.04819004610180855,
0.021900774911046028,
-0.02070404216647148,
-0.017151953652501106,
-0.0014689886011183262,
-0.017073342576622963,
-0.04415974020957947,
-0.00967987347394228,
-0.036110203713178635,
0.0014316592132672668,
-0.01853749342262745,
0.01545765995979309,
0.008645134046673775,
0.013149842619895935,
0.018159035593271255,
0.0126358512789011,
-0.007171377539634705,
-0.0002518644032534212,
0.018393144011497498,
-0.018121730536222458,
0.011690344661474228,
0.024505894631147385,
0.019565995782613754,
0.02933478355407715,
-0.024165885522961617,
0.023771699517965317,
0.02791070193052292,
0.026110485196113586,
-0.01769757643342018,
-0.015036090277135372,
-0.027796894311904907,
-0.04716905578970909,
-0.043949905782938004,
0.009376288391649723,
0.018238672986626625,
0.017903873696923256,
-0.014503025449812412,
0.016000032424926758,
0.033846866339445114,
0.024432726204395294,
0.05065823718905449,
0.07397834956645966,
0.018956901505589485,
0.024682948365807533,
-0.02933310717344284,
0.0025997532065957785,
-0.02064247615635395,
-0.03070467710494995,
0.0072313761338591576,
0.020048050209879875,
-0.05085306987166405,
0.0035552142653614283,
0.04219834506511688,
0.0258149616420269,
-0.022613316774368286,
0.00596434623003006,
-0.025102633982896805,
0.03140946850180626,
-0.012302391231060028,
0.016649169847369194,
0.008421773090958595,
0.03653419017791748,
0.022418467327952385,
0.03550947830080986,
-0.019590558484196663,
-0.07006639242172241,
-0.029604949057102203,
0.042573146522045135,
0.035424280911684036,
-0.023128194734454155,
0.0038740262389183044,
-0.04210854694247246,
-0.015016511082649231,
0.05372551828622818,
-0.022843297570943832,
0.03639762103557587,
-0.01736227422952652,
0.04497537389397621,
0.0026194362435489893,
-0.006896990817040205,
-0.03407449275255203,
0.004054296296089888,
-0.015430523082613945,
-0.02167620323598385,
0.012356783263385296,
0.007987688295543194,
0.032743293792009354,
-0.017666520550847054,
0.026833191514015198,
0.059952039271593094,
0.016327137127518654,
0.018241144716739655,
-0.02338608354330063,
-0.03285352513194084,
-0.06286907196044922,
-0.06530442833900452,
0.0015921633457764983,
0.025588812306523323,
-0.012768767774105072,
-0.02477319911122322,
-0.022591030225157738,
-0.06936036795377731,
0.01792026497423649,
0.006867145653814077,
0.017153264954686165,
0.002170381834730506,
-0.058361463248729706,
0.0238338652998209,
0.06788083165884018,
0.005300861783325672,
0.01645554229617119,
0.013975660316646099,
-0.013204683549702168,
-0.0009585031075403094,
0.01853914000093937,
0.04771443083882332,
-0.0265871062874794,
0.016039563342928886,
-0.025840753689408302,
0.012452500872313976,
0.009924739599227905,
0.06073557212948799,
-0.00007973924221005291,
0.019771693274378777,
-0.010561085306107998,
-0.03426452353596687,
-0.0040232217870652676,
0.010657970793545246,
0.03671445697546005,
-0.008873436599969864,
-0.007327570579946041,
-0.01385477278381586,
-0.019936056807637215,
-0.018987372517585754,
-0.017771469429135323,
-0.012847257778048515,
0.021682314574718475,
0.0467182956635952,
-0.02638915926218033,
0.002277308376505971,
-0.009648689068853855,
-0.03473025560379028,
0.027038224041461945,
-0.06867783516645432,
0.06210964173078537,
-0.025972915813326836,
-0.008255958557128906,
0.0446944423019886,
-0.02789493091404438,
0.013432452455163002,
0.03596784174442291,
-0.009706240147352219,
0.0046495976857841015,
-0.04481341689825058,
0.03734753653407097,
0.014347217977046967,
0.03174584358930588,
-0.06327711790800095,
-0.056303057819604874,
0.04583294317126274,
-0.004108504857867956,
-0.0043668546713888645,
-0.02265789918601513,
-0.009700600989162922,
-0.06014225259423256,
-0.03065025433897972,
-0.011593378148972988,
0.039923738688230515,
-0.011459925211966038,
0.0037574386224150658,
0.04237905144691467,
0.0035687393974512815,
0.04866170510649681,
0.010526476427912712,
-0.024736054241657257,
-0.010600789450109005,
0.0007618635427206755,
-0.01146285142749548,
-0.0077241589315235615,
0.0816359743475914,
-0.01080996636301279,
-0.03364245221018791,
-0.024832120165228844,
-0.03162483870983124,
0.03729310631752014,
-0.01843971572816372,
0.023984842002391815,
0.02614666149020195,
-0.007376016117632389,
0.013141943141818047,
0.0005862816469743848,
0.03182896226644516,
0.011409612372517586,
0.04394267499446869,
-0.0011396313784644008,
-0.021498970687389374,
0.020128600299358368,
-0.03734193742275238,
0.04310614615678787,
0.039726372808218,
-0.034991104155778885,
-0.004277929663658142,
0.04374651238322258,
-0.00016271663480438292,
-0.035679563879966736,
-0.005079806782305241,
-0.01770356297492981,
-0.002987270476296544,
0.022077610716223717,
-0.004372416529804468,
0.02640676684677601,
0.003206921275705099,
-0.024865565821528435,
-0.012143637053668499,
-0.03581932187080383,
-0.011844017542898655,
0.0776391327381134,
-0.014812835492193699,
0.04703070968389511,
0.0010210160398855805,
-0.008476453833281994,
-0.031969550997018814,
-0.01513807475566864,
0.009661146439611912,
0.01652361825108528,
-0.00974454078823328,
0.01861744001507759,
0.010607554577291012,
-0.044021569192409515,
0.008573723956942558,
0.05767567828297615,
-0.019413849338889122,
0.03815186023712158,
0.03627798706293106,
0.02254120446741581,
0.04347115010023117,
0.006109533831477165,
-0.015276746824383736,
0.0167382899671793,
-0.01166571956127882,
0.04742663353681564,
-0.019242670387029648,
-0.024968493729829788,
0.022971121594309807,
0.04738937318325043,
0.011307992041110992,
-0.03933938965201378,
-0.03267466649413109,
-0.05417182669043541,
0.005461026448756456,
0.013849642127752304,
0.011422589421272278,
-0.01233710814267397,
0.01480647549033165,
0.00519646517932415,
0.013846782967448235,
0.01903587579727173,
0.013666277751326561,
-0.025462154299020767,
-0.010470399633049965,
-0.0520760640501976,
-0.022620828822255135,
0.026162227615714073,
0.021391628310084343,
0.005258369725197554,
-0.015408811159431934,
-0.02761753462255001,
-0.007563624531030655,
0.0017679056618362665,
0.03937814384698868,
0.00204727821983397,
0.058827199041843414,
-0.016046935692429543,
0.0044822064228355885,
-0.0010549381840974092,
0.0131322480738163,
0.11024466902017593,
0.05686463415622711,
0.004820242058485746,
-0.050240408629179,
0.01335517130792141,
0.004579562693834305,
0.03542239964008331,
-0.01541273295879364,
0.007575912866741419,
-0.008470085449516773,
0.006795126013457775,
0.0007847297820262611,
0.02281806617975235,
-0.046538107097148895,
-0.033621061593294144,
0.06070718914270401,
-0.024806438013911247,
-0.012335369363427162,
-0.016820410266518593,
0.013564045540988445,
-0.048718784004449844,
0.015410903841257095,
-0.0019784814212471247,
0.024546893313527107,
-0.004050434101372957,
0.001265109982341528,
-0.0020069219172000885,
-0.02862018160521984,
0.0017398324562236667,
-0.007312994450330734,
-0.066169872879982,
-0.00032280245795845985,
0.02197452448308468,
-0.024130674079060555,
-0.0656464546918869,
0.028188785538077354,
0.013006160035729408,
-0.02617562562227249,
0.02227080427110195,
0.02699885703623295,
0.022515419870615005,
0.021673083305358887,
0.01348024606704712,
-0.001861839322373271,
-0.04554338753223419,
0.013514406979084015,
-0.007174946367740631,
0.03786418214440346,
-0.01828695647418499,
-0.028712833300232887,
-0.004752509295940399,
0.0016521454090252519,
0.02324608340859413,
-0.04979393631219864,
0.002534307772293687,
-0.044503554701805115,
0.011151360347867012,
0.010179265402257442,
0.016181955114006996,
0.02744412235915661,
-0.0011996191460639238,
0.019778942689299583,
-0.030651880428195,
0.02353120781481266,
-0.01926124282181263,
0.02545018121600151,
-0.008150838315486908,
0.015205473639070988,
-0.037598542869091034,
0.01315731555223465,
-0.02565584145486355,
0.003798670833930373,
-0.04709414765238762,
0.018071571364998817,
0.021917836740612984,
0.03528879955410957,
0.036463361233472824,
0.0010719436686486006,
0.0001891928113764152,
-0.020891550928354263,
-0.0409722775220871,
0.06899034976959229,
0.015980472788214684,
-0.028183281421661377,
-0.02358357049524784,
-0.0072719198651611805,
0.004598485771566629,
0.0667748749256134,
-0.05088695138692856,
-0.005693643819540739,
-0.011334424838423729,
0.02834174782037735,
-0.006749934516847134,
-0.02021118625998497,
0.013194674625992775,
0.01906287670135498,
-0.03825123608112335,
-0.009399673901498318,
-0.02163872681558132,
0.03401258587837219,
0.01838884875178337,
0.02246139757335186,
-0.019947532564401627,
-0.0017018761718645692,
-0.021215803921222687,
0.022513099014759064,
-0.0013075775932520628,
-0.0019268168834969401,
-0.0002773338637780398,
0.03403867408633232,
0.03820449858903885,
-0.061467964202165604,
-0.06201633810997009,
-0.04143809154629707,
-0.005845923442393541,
-0.029049331322312355,
0.024746468290686607,
-0.0038035274483263493,
0.042576197534799576,
-0.004886837676167488,
0.002254113322123885,
-0.043302442878484726,
0.025634873658418655,
-0.058138180524110794,
-0.008295876905322075,
-0.006940482184290886,
-0.007565201725810766,
-0.002150000771507621,
0.03132122755050659,
-0.06112464889883995,
0.009369481354951859,
0.0006616047467105091,
0.028456002473831177,
-0.03300629183650017,
-0.007914689369499683,
0.018690384924411774,
-0.00013365100312512368,
0.027910256758332253,
-0.00827023945748806,
-0.016184620559215546,
0.012151065282523632,
-0.0446343868970871,
-0.036572232842445374,
0.035195738077163696,
-0.0061814752407372,
0.0309486985206604,
0.013956926763057709,
-0.039162565022706985,
-0.014254857785999775,
0.019455935806035995,
-0.03919720649719238,
-0.0032412935979664326,
-0.016393667086958885,
-0.04259474202990532,
-0.03833878040313721,
0.010372709482908249,
0.029531428590416908,
-0.050529688596725464,
-0.02526702918112278,
0.028995966538786888,
0.051882315427064896,
-0.04673617333173752,
0.03469877317547798,
-0.010405356995761395,
-0.006636025849729776,
-0.040305737406015396,
0.017433231696486473,
-0.036256853491067886,
-0.0023827196564525366,
0.04903455078601837,
-0.023246074095368385,
0.023977145552635193,
-0.004767181351780891,
0.004563243128359318,
-0.12317666411399841,
-0.023673847317695618,
0.0022930456325411797,
0.01352186780422926,
-0.004801886156201363,
-0.029335346072912216,
-0.02151322364807129,
0.02732086181640625,
-0.0845361202955246,
0.014212106354534626,
-0.00793325062841177,
-0.015964198857545853,
-0.006686471868306398,
0.017512015998363495,
0.027471475303173065,
0.04279518872499466,
0.04838996008038521,
0.014204864390194416,
-0.0049822647124528885,
-0.01203060895204544,
0.011599901132285595,
-0.019870389252901077,
-0.007308810483664274,
0.03650791198015213,
-0.031362731009721756,
0.01036625262349844,
0.0747951939702034,
-0.020612703636288643,
-0.004230790305882692,
0.020466085523366928,
0.014324760064482689,
0.021319042891263962,
0.006301669869571924,
-0.006315522361546755,
-0.01657780259847641,
0.02947208099067211,
-0.01230206061154604,
0.03334982320666313,
-0.025682596489787102,
0.03791584447026253,
0.012994159013032913,
0.05419224128127098,
-0.05021658539772034,
0.011903680860996246,
-0.005626185797154903,
-0.024230435490608215,
-0.035679928958415985,
0.012675248086452484,
-0.03506425395607948,
0.01856125332415104,
-0.014720066450536251,
-0.011540829204022884,
-0.005390569102019072,
-0.01519768312573433,
-0.02147415094077587,
-0.050772249698638916,
-0.025376368314027786,
0.02010166458785534,
-0.024555960670113564,
-0.021194253116846085,
0.031253632158041,
-0.02117026410996914,
0.010047158226370811,
0.002299415646120906,
0.00693870335817337,
-0.02288641594350338,
-0.016610590741038322,
-0.009868581779301167,
-0.04350762814283371,
-0.009805160574615002,
-0.012020319700241089,
-0.06049889698624611,
-0.0064465985633432865,
0.026394151151180267,
0.02288895472884178,
0.01212958712130785,
0.00110096693970263,
-0.0320223905146122,
-0.012427449226379395,
-0.0921599268913269,
0.031727034598588943,
-0.00503392843529582,
-0.032735422253608704,
-0.03023705445230007,
-0.015739047899842262,
0.001645042560994625,
-0.010184370912611485,
0.05272991210222244,
-0.022412048652768135,
0.0220955703407526,
0.026638461276888847,
-0.014582638628780842,
-0.005015918985009193,
-0.05229141190648079,
0.006001098547130823,
0.010644170455634594,
-0.06926561892032623,
-0.01616331748664379,
0.019587146118283272,
-0.011181945912539959,
-0.005770920775830746,
0.019408036023378372,
-0.01648353785276413,
0.048203833401203156,
-0.015293221920728683,
-0.03602825850248337,
0.0413818359375,
0.04807896539568901,
0.007878326810896397,
0.04700668156147003,
-0.03340333700180054,
0.020302502438426018,
0.040262192487716675,
-0.03724626451730728,
-0.0243535153567791,
0.08052385598421097,
-0.02508692443370819,
0.023970024660229683,
-0.0032386058010160923,
-0.03826811537146568,
-0.003516606753692031,
-0.03579924628138542,
0.02608487382531166,
-0.01657736673951149,
-0.05069488659501076,
-0.016535544767975807,
0.05143775790929794,
0.034136995673179626,
-0.025136401876807213,
-0.03221818432211876,
-0.001962510170415044,
0.02641252987086773,
0.0071768625639379025,
0.0192736703902483,
0.02597920224070549,
0.016965100541710854,
-0.029442865401506424,
0.019065868109464645,
0.0382256805896759,
0.024597931653261185,
0.017741205170750618,
0.01520383171737194,
0.016076698899269104,
-0.04374086111783981,
-0.02190195582807064,
0.008139495737850666,
0.01706252247095108,
-0.005655696149915457,
0.0001695025566732511,
-0.01699219085276127,
0.06411140412092209,
0.0060358718037605286,
0.031862497329711914,
0.03580087050795555,
-0.016913000494241714,
0.0012384550645947456,
0.00878752302378416,
0.017771027982234955,
0.038454920053482056,
-0.007193149067461491,
0.005675450898706913,
-0.000997545663267374,
-0.02002102881669998,
0.015947990119457245,
0.009157776832580566,
0.011231508105993271,
-0.037664663046598434,
-0.006654778961092234,
-0.005681085400283337,
-0.019352350383996964,
-0.06519473344087601,
0.004848754499107599,
0.045506805181503296,
0.01266758143901825,
0.02232952043414116,
-0.022704536095261574,
-0.015406930819153786,
-0.03528781235218048,
0.060164351016283035,
-0.050659533590078354,
-0.023476354777812958,
-0.021257197484374046,
0.05288280174136162,
0.01120488066226244,
0.026531623676419258
] |
<p>I am trying to determine if a radiant barrier on the inside of a hot water tank would increase its insulating value. Normally radiant barriers are used in house construction to reduce heat loss by reflecting radiant heat back into the house. The reflective surface is placed against an air gap on the exterior wall facing inwards and the thermal radiation is reflected back across the air gap into the drywall and hence into the home. I am trying to determine if a radiant barrier placed directly against a liquid would have the effect of reducing heat loss from the liquid.</p>
<p>Lets say we have a tank designed to store hot water and keep it hot by reducing heat loss to the ambient surroundings. For example, the tank is metal and surrounded by a insulating layer of foam, fiber glass etc. with a high R value (A measure of resistance to heat transfer). Lets say there are two versions of this tank. The first tank has a grey or dark interior, similar to what would be found in a glass lined steel water tank commonly used a domestic water heater. The second tank is identical except that its interior is coated with a reflective silver surface facing towards the mass of hot water. Would the reflective surface increase the effective R value of the tank's walls and reduce heat loss from the tank? The possible effect is that thermal radiation emitted from the hot water molecules would reflect back from the silver surface and be reabsorbed by the hot water mass as it passes back into the body of the water.
This might seem similar to a thermos type vacuum flask, the main difference being that in a thermos flask there is a vacuum behind the radiant barrier so I don't know if their is difference in the radiant barrier effect between having a vacuum behind the radiant barrier and having solid conducting material behind it as we do in the water tank example. if their is any R value enhancement by virtue of the slivered lining of the water tank, how could we quantify it in terms of R value? Thanks.</p>
| 8,450 |
[
-0.044001903384923935,
-0.0027577851433306932,
0.004818164277821779,
-0.0002005894057219848,
0.026133809238672256,
0.02962690033018589,
-0.001236048643477261,
-0.04359206557273865,
0.009204579517245293,
-0.022037817165255547,
0.02730308473110199,
0.020560411736369133,
0.06522723287343979,
-0.024328192695975304,
0.037721604108810425,
0.0024327191058546305,
0.01728122867643833,
-0.010100265964865685,
0.043376170098781586,
-0.044906798750162125,
-0.009668058715760708,
0.02353072352707386,
-0.0033610665705055,
-0.013590180315077305,
-0.04349357262253761,
0.01621994562447071,
0.011101677082479,
-0.041695449501276016,
0.002984215971082449,
0.023879364132881165,
0.013442120514810085,
-0.03867075592279434,
-0.02723688632249832,
-0.007071400992572308,
0.0062631648033857346,
-0.022472374141216278,
-0.04300899803638458,
-0.007325548212975264,
-0.02969229407608509,
0.045264832675457,
0.0258420929312706,
-0.033486317843198776,
0.004475562367588282,
0.07152855396270752,
0.014154184609651566,
-0.03329673781991005,
0.004455719143152237,
-0.03794527053833008,
0.015503890812397003,
-0.07036091387271881,
0.01906290277838707,
0.011186112649738789,
0.044152893126010895,
0.06592755764722824,
-0.021030457690358162,
0.02912024036049843,
0.057920001447200775,
0.056099552661180496,
-0.004099272657185793,
-0.032158929854631424,
-0.016994658857584,
-0.01243327185511589,
-0.056098517030477524,
0.011736052110791206,
-0.02488788217306137,
-0.011520951986312866,
-0.02822251431643963,
-0.05647076666355133,
0.02214979939162731,
0.021147863939404488,
0.03410041332244873,
-0.005221720784902573,
0.016883205622434616,
-0.0070257834158837795,
0.040623992681503296,
-0.015710603445768356,
-0.005235964432358742,
0.048323288559913635,
0.004798795562237501,
0.009290981106460094,
0.016048088669776917,
-0.02154657617211342,
0.04719860851764679,
0.06925033032894135,
-0.010413477197289467,
0.008881832472980022,
0.0243715588003397,
-0.02411755733191967,
0.0194984283298254,
0.02217157371342182,
-0.011696888133883476,
0.012817395851016045,
0.036891527473926544,
0.053247299045324326,
-0.03360845893621445,
-0.011776485480368137,
0.000790561840403825,
0.07346532493829727,
-0.01438718568533659,
-0.032977283000946045,
-0.009280269034206867,
0.0205935537815094,
0.0038021118380129337,
0.0608297698199749,
0.009277396835386753,
-0.06841620802879333,
0.007957736030220985,
0.0034994054585695267,
0.020507607609033585,
-0.0035955356433987617,
-0.06113998964428902,
0.01931426301598549,
0.0085065932944417,
-0.05112948268651962,
0.04283858835697174,
-0.03949642926454544,
0.012757256627082825,
-0.010505198501050472,
0.04952380806207657,
0.060245439410209656,
0.038180798292160034,
0.042779311537742615,
-0.016226472333073616,
0.003463039407506585,
-0.051821909844875336,
0.03322296589612961,
-0.009748706594109535,
-0.002166726626455784,
-0.04585883393883705,
0.04105237126350403,
0.0009242534870281816,
-0.010744558647274971,
0.026520807296037674,
-0.03780624642968178,
0.05362675338983536,
-0.02674388885498047,
-0.07410229742527008,
-0.02973349578678608,
0.018211154267191887,
0.026594091206789017,
-0.014107397757470608,
-0.055106475949287415,
-0.0005880042444914579,
0.012453451752662659,
0.07518869638442993,
0.029659228399395943,
-0.019097117707133293,
-0.041456662118434906,
0.03260095790028572,
0.006137865129858255,
-0.053976964205503464,
0.0160928163677454,
0.023852095007896423,
-0.04662298411130905,
-0.009839843027293682,
-0.03234023600816727,
0.012046745046973228,
0.04128042235970497,
-0.029690992087125778,
-0.03899218142032623,
0.05479332059621811,
-0.03366410732269287,
0.013499053195118904,
0.04777975380420685,
0.01894775778055191,
-0.010369016788899899,
0.055235929787158966,
0.0035465084947645664,
0.015127190388739109,
0.018767934292554855,
0.03190968185663223,
0.03717579320073128,
0.016681093722581863,
0.013632033951580524,
0.02103075012564659,
-0.024776684120297432,
0.0015982050681486726,
-0.01329021155834198,
0.036851461976766586,
-0.006624588277190924,
-0.05988379940390587,
-0.007501872256398201,
-0.018770508468151093,
-0.017201527953147888,
0.0008195765549317002,
0.015393069945275784,
-0.034178826957941055,
-0.022986942902207375,
0.007512497715651989,
-0.0311996228992939,
-0.027982307597994804,
-0.05393259972333908,
0.015035049058496952,
-0.03999901935458183,
0.00004054659075336531,
-0.0074331206269562244,
0.030092349275946617,
0.030719924718141556,
0.014475003816187382,
-0.001645961543545127,
-0.014004749245941639,
-0.0010729337809607387,
0.047410544008016586,
-0.013422604650259018,
0.028606195002794266,
0.002719670068472624,
0.04732580855488777,
-0.03190091624855995,
0.02294503152370453,
-0.0580829419195652,
-0.025098945945501328,
-0.018819022923707962,
-0.014508784748613834,
0.014871960505843163,
-0.004850148689001799,
-0.03240485116839409,
0.0415169894695282,
0.003955220337957144,
0.03660853952169418,
0.02281973697245121,
-0.05515997111797333,
0.06038102135062218,
0.03028993122279644,
0.05513148009777069,
-0.025046158581972122,
-0.0014487653970718384,
0.01451772078871727,
-0.003050242317840457,
-0.02351938933134079,
-0.024538861587643623,
-0.034544214606285095,
0.009816614910960197,
0.04719197005033493,
0.0024585549253970385,
-0.08558978140354156,
0.009063184261322021,
0.020769938826560974,
0.02477685548365116,
0.021092023700475693,
0.008349365554749966,
-0.026131004095077515,
-0.007271099369972944,
0.04345026612281799,
0.0446428582072258,
0.001710690907202661,
0.005444484297186136,
0.0011566075263544917,
0.019208712503314018,
0.012005913071334362,
-0.03065597638487816,
0.01813378930091858,
0.05358128622174263,
-0.00724452268332243,
0.027650540694594383,
-0.055366333574056625,
-0.01866239495575428,
0.01324052456766367,
-0.05286727845668793,
-0.0014954389771446586,
0.042643047869205475,
0.013363336212933064,
0.037194058299064636,
-0.07653357833623886,
-0.006694816518574953,
0.027785800397396088,
-0.0010149066802114248,
-0.03205162286758423,
-0.011600718833506107,
0.020432917401194572,
-0.059370916336774826,
0.02467888779938221,
-0.021981634199619293,
0.032134149223566055,
-0.011297943070530891,
-0.006692198570817709,
0.0351162813603878,
0.024912172928452492,
0.010398452170193195,
-0.03386320546269417,
-0.025266291573643684,
-0.01512991264462471,
-0.012156088836491108,
-0.045156657695770264,
-0.00453169085085392,
-0.0324702225625515,
0.0148910628631711,
-0.041791319847106934,
-0.02991591766476631,
0.01580743119120598,
-0.02555781602859497,
-0.041494566947221756,
0.026296300813555717,
0.006253967061638832,
-0.0442671962082386,
-0.009748936630785465,
-0.02909671515226364,
0.03809415176510811,
-0.042710594832897186,
-0.012788076885044575,
0.038714539259672165,
-0.0032597139943391085,
-0.042727842926979065,
-0.008987468667328358,
-0.04425626993179321,
-0.022962398827075958,
-0.0018319380469620228,
-0.03218701854348183,
0.02137225680053234,
-0.020865051075816154,
0.02505815401673317,
0.031177423894405365,
-0.06024973839521408,
-0.006307695992290974,
-0.02791968733072281,
-0.05204475298523903,
0.028742369264364243,
-0.00492827920243144,
0.032948222011327744,
-0.01114887185394764,
-0.0012048506177961826,
0.04749971628189087,
0.03178008273243904,
-0.07135794311761856,
-0.02617310732603073,
-0.016509922221302986,
-0.0054000127129256725,
-0.032767172902822495,
0.01017634104937315,
0.04267029091715813,
-0.03160073608160019,
0.028974177315831184,
0.0018663628725335002,
0.008718384429812431,
0.014387126080691814,
-0.0030140329618006945,
-0.016279667615890503,
0.014707598835229874,
0.02217378094792366,
0.019891386851668358,
0.05838744342327118,
-0.012998276390135288,
-0.026286905631422997,
-0.006702230777591467,
-0.051642704755067825,
0.028330331668257713,
0.04220085218548775,
-0.072938933968544,
0.04605846479535103,
-0.0028543639928102493,
0.01071650255471468,
0.003543493803590536,
0.015214583836495876,
-0.03765453025698662,
0.017890101298689842,
-0.01877886801958084,
0.031937990337610245,
0.03279013931751251,
-0.022990286350250244,
0.0013187263393774629,
0.0406767874956131,
0.060902319848537445,
0.0032370907720178366,
0.0018946664640679955,
-0.0049338978715240955,
-0.03163231909275055,
-0.013758531771600246,
0.03215164691209793,
-0.03051658719778061,
0.04104166105389595,
0.04287048801779747,
0.04310576990246773,
0.0019319202983751893,
-0.019701620563864708,
-0.028693076223134995,
-0.0535462312400341,
-0.036636728793382645,
0.0009483551839366555,
0.055267397314310074,
-0.02972177229821682,
0.022234100848436356,
0.04648268222808838,
0.009354953654110432,
0.03178499639034271,
-0.022695491090416908,
-0.06754074990749359,
0.03861616179347038,
0.00048255716683343053,
0.014558600261807442,
-0.017609084025025368,
-0.010578622110188007,
-0.026521068066358566,
-0.05269566550850868,
-0.054803263396024704,
0.049852605909109116,
0.002407969906926155,
-0.045547813177108765,
0.010598459281027317,
0.0044156708754599094,
-0.04313070327043533,
-0.013659108430147171,
0.04912181198596954,
-0.0021905223838984966,
-0.04868486896157265,
0.002353100338950753,
0.00484891701489687,
-0.03347598388791084,
-0.001721360138617456,
-0.03566373512148857,
0.036811161786317825,
0.038371749222278595,
0.08005975186824799,
0.049231238663196564,
0.019842643290758133,
-0.03390514850616455,
0.0057799844071269035,
0.010240009054541588,
-0.002252438571304083,
-0.02907751128077507,
-0.020740501582622528,
-0.054287541657686234,
-0.04834841936826706,
-0.03123929724097252,
-0.0017624355386942625,
0.022055409848690033,
-0.0242985337972641,
-0.011176356114447117,
0.03757705166935921,
-0.011390622705221176,
-0.014682633802294731,
-0.016887418925762177,
0.050874385982751846,
0.0063376035541296005,
0.00007086180994519964,
-0.05393140763044357,
-0.02357889525592327,
-0.022133247926831245,
-0.015246176160871983,
0.028389213606715202,
0.029670892283320427,
-0.018669649958610535,
0.015058893710374832,
0.03503672033548355,
-0.006772530265152454,
-0.0050949170254170895,
0.009571587666869164,
-0.00024153444974217564,
0.021507468074560165,
-0.03235117346048355,
-0.010985749773681164,
0.028119124472141266,
0.0492340587079525,
0.04019865021109581,
0.0024014534428715706,
0.02608192153275013,
-0.06576009094715118,
-0.01749993860721588,
0.01466949749737978,
0.05583685636520386,
-0.015406183898448944,
-0.015548797324299812,
-0.05296960100531578,
-0.01174059696495533,
0.06377480179071426,
0.030284686014056206,
-0.002079514553770423,
-0.019647615030407906,
-0.012087104842066765,
-0.00044596969382837415,
0.010032078251242638,
0.04281685873866081,
-0.0036493679508566856,
0.015832651406526566,
0.030340442433953285,
-0.04066846892237663,
-0.029283974319696426,
0.02498719096183777,
0.005531989503651857,
0.02916106767952442,
0.005141052417457104,
0.009935179725289345,
0.03285208344459534,
-0.017411181703209877,
0.03992509841918945,
0.0023974901996552944,
-0.07104206085205078,
0.012033370323479176,
0.022192222997546196,
-0.002871677977964282,
0.02557796612381935,
-0.028474003076553345,
0.02300005964934826,
0.027503246441483498,
0.0211337860673666,
-0.0174765195697546,
0.0064133647829294205,
-0.02351086400449276,
0.046208757907152176,
0.023755624890327454,
0.012682471424341202,
0.06218186393380165,
0.04733112081885338,
0.012231865897774696,
-0.02141505666077137,
0.008523856289684772,
0.03459286689758301,
-0.009315052069723606,
-0.022754354402422905,
-0.012560619972646236,
-0.011196949519217014,
-0.04036989435553551,
0.03399305045604706,
-0.021788455545902252,
0.029705077409744263,
-0.023358086124062538,
-0.032705191522836685,
0.02489563636481762,
0.027559254318475723,
-0.034828901290893555,
-0.021542564034461975,
-0.022515492513775826,
0.036574166268110275,
0.005307616200298071,
-0.03203937038779259,
-0.0007377454894594848,
-0.02046242728829384,
-0.0000886870184331201,
-0.0001250886998604983,
-0.031639423221349716,
0.04529445618391037,
-0.02320089563727379,
-0.004395250231027603,
0.005417274311184883,
-0.026495307683944702,
0.02989586628973484,
-0.016186833381652832,
0.013206417672336102,
0.011469057761132717,
-0.048967961221933365,
0.0013052739668637514,
0.03730243816971779,
-0.016087409108877182,
0.028594089671969414,
-0.023635249584913254,
0.04734072834253311,
-0.0031181785743683577,
0.011797401122748852,
-0.061054814606904984,
-0.006447499617934227,
-0.004713595844805241,
0.028466716408729553,
-0.022300736978650093,
-0.04854528233408928,
-0.02802906185388565,
-0.04758588597178459,
-0.03697992488741875,
0.017943326383829117,
0.020664557814598083,
-0.019894592463970184,
-0.005189890973269939,
-0.005052924621850252,
0.015936842188239098,
0.057939313352108,
-0.020281322300434113,
-0.010575832799077034,
-0.005892275366932154,
-0.015638498589396477,
-0.028287502005696297,
0.0020117107778787613,
0.02488570660352707,
-0.025751570239663124,
-0.01658257283270359,
-0.005577196832746267,
0.02131718583405018,
0.06892190128564835,
-0.011960193514823914,
-0.015392535366117954,
0.009318535216152668,
0.026241788640618324,
-0.02131384052336216,
-0.053152598440647125,
0.05594601482152939,
0.005960346665233374,
0.007317958865314722,
-0.0009568586247041821,
0.02714725024998188,
-0.035304661840200424,
-0.00552488025277853,
0.002413566689938307,
-0.01578156091272831,
-0.012391505762934685,
-0.027600955218076706,
0.07754123955965042,
-0.015967948362231255,
-0.025848964229226112,
-0.02148563414812088,
-0.027893632650375366,
0.0306791290640831,
-0.03969575837254524,
0.03628836199641228,
-0.01642010733485222,
-0.0001394653954776004,
-0.014551730826497078,
-0.0627598986029625,
-0.06359941512346268,
-0.04342462494969368,
0.05165662243962288,
-0.06218471750617027,
0.05001240223646164,
0.003022425342351198,
-0.03611468896269798,
-0.006098528858274221,
-0.000348949950421229,
-0.006323283538222313,
0.022623715922236443,
-0.027729379013180733,
0.06781820207834244,
-0.02198842354118824,
0.0017155820969492197,
-0.017088549211621284,
0.03138413652777672,
-0.0003560456680133939,
0.041703496128320694,
0.03142284229397774,
0.06277278065681458,
0.014271813444793224,
-0.04865943267941475,
-0.018568232655525208,
0.02407047338783741,
-0.04736953228712082,
0.011381582356989384,
-0.021483419463038445,
0.02550644241273403,
0.028794722631573677,
0.011715139262378216,
0.007841778919100761,
-0.05522434040904045,
-0.016072522848844528,
-0.046878255903720856,
0.03233196958899498,
0.00021031325741205364,
0.03338238596916199,
-0.010719032026827335,
0.030290404334664345,
0.030809437856078148,
-0.017087049782276154,
0.0003221806255169213,
-0.002311654621735215,
-0.013434954918920994,
0.014612889848649502,
-0.013784467242658138,
-0.011686376295983791,
0.044148340821266174,
0.010032959282398224,
-0.03926587104797363,
-0.004708700813353062,
-0.027797020971775055,
0.0002180282463086769,
-0.0051163253374397755,
0.04110730439424515,
0.007879328913986683,
0.06780140846967697,
-0.018425902351737022,
0.05271907523274422,
0.05823048576712608,
0.03809836879372597,
0.10499736666679382,
0.04759574308991432,
0.000914325297344476,
-0.0336158461868763,
-0.02841014787554741,
-0.022319497540593147,
0.019233865663409233,
-0.018398432061076164,
0.028313061222434044,
-0.022929690778255463,
0.014177080243825912,
0.04316455498337746,
0.06867599487304688,
0.0031581218354403973,
0.012753422372043133,
0.03182785585522652,
-0.022029399871826172,
-0.008572660386562347,
-0.0009950961684808135,
0.005422062240540981,
-0.0006012474186718464,
0.00908270850777626,
-0.000831764773465693,
0.0006556865992024541,
0.007712601684033871,
-0.024773508310317993,
-0.034923311322927475,
-0.008572086691856384,
0.01805499568581581,
-0.01383762713521719,
-0.05512397363781929,
0.0351715087890625,
-0.02086425945162773,
0.02179902046918869,
-0.0485309474170208,
-0.018724102526903152,
0.0690995380282402,
0.0080103212967515,
-0.005405745003372431,
0.020214539021253586,
0.060285959392786026,
-0.035336196422576904,
0.023081708699464798,
0.0785360112786293,
-0.056045353412628174,
-0.009795255959033966,
-0.011891080066561699,
0.007169649470597506,
-0.0016381876775994897,
-0.0490424744784832,
-0.007508355658501387,
-0.007525463588535786,
0.015119565650820732,
-0.034397371113300323,
-0.031446654349565506,
-0.002527946839109063,
0.02686239592730999,
-0.004536190535873175,
-0.019360844045877457,
-0.004485555924475193,
0.04643182083964348,
-0.031731512397527695,
0.0016698481049388647,
0.010207203216850758,
-0.018547028303146362,
-0.02730928733944893,
-0.014475436881184578,
0.06511647999286652,
-0.008768456988036633,
-0.03846399113535881,
-0.04068957641720772,
-0.014120711013674736,
0.026021728292107582,
-0.026582278311252594,
-0.025056142359972,
0.02570212446153164,
0.03200200945138931,
-0.009316046722233295,
0.013834751211106777,
0.028151394799351692,
-0.06694123893976212,
0.01337827742099762,
-0.0325746014714241,
-0.03808160498738289,
-0.058744870126247406,
-0.01664895750582218,
0.034154199063777924,
0.02087584137916565,
-0.029232682660222054,
-0.0224042609333992,
0.0468105711042881,
0.031452905386686325,
0.02832936681807041,
-0.017751500010490417,
-0.027868663892149925,
0.005501231178641319,
-0.04022626951336861,
-0.0032353312708437443,
-0.03444937989115715,
0.02993975766003132,
0.019996052607893944,
-0.014565552584826946,
0.02961798757314682,
-0.003107698867097497,
-0.05264811962842941,
0.02202834002673626,
-0.017665041610598564,
-0.018133744597434998,
0.021398693323135376,
-0.028541693463921547,
0.015247688628733158,
-0.02166161499917507,
-0.039048876613378525,
-0.006499158684164286,
-0.026249457150697708,
-0.03814520686864853,
0.035606205463409424,
-0.018962036818265915,
0.003280647797510028,
-0.013315737247467041,
-0.0006866097683086991,
-0.02748749405145645,
0.0008466591825708747,
-0.04207189008593559,
-0.019194861873984337,
0.03994787484407425,
-0.005925511009991169,
-0.03288720175623894,
0.012559260241687298,
-0.01698479987680912,
-0.0224126148968935,
0.00621667318046093,
0.005241908133029938,
-0.02673196978867054,
-0.021793900057673454,
0.04115710407495499,
0.009486356750130653,
0.07461483031511307,
-0.043831173330545425,
-0.026829302310943604,
0.04075591266155243,
-0.04389980062842369,
-0.03863891214132309,
0.03547298163175583,
-0.007403054274618626,
0.0398067943751812,
-0.005173364654183388,
-0.004360409453511238,
-0.011911357752978802,
0.10740919411182404,
0.002617234829813242,
0.012230861000716686,
-0.02558496594429016,
-0.027773350477218628,
0.016434824094176292,
-0.03325042873620987,
0.029114319011569023,
-0.00840078480541706,
0.0036366365384310484,
0.03318294510245323,
0.038115520030260086,
-0.015280446968972683,
0.003306678729131818,
-0.028972145169973373,
-0.011133604682981968,
-0.04427603259682655,
-0.009532188065350056,
-0.014873212203383446,
0.01995089463889599,
0.04419886693358421,
-0.030956890434026718,
0.002967739012092352,
0.037595514208078384,
-0.016409408301115036,
-0.09864043444395065,
0.02871750481426716,
-0.028194472193717957,
0.019425973296165466,
-0.005216806195676327,
-0.04714376479387283,
0.05338853970170021,
-0.01384126115590334,
-0.027722159400582314,
0.021862152963876724,
-0.018380634486675262,
0.005359398201107979,
-0.07839776575565338,
0.02878115512430668,
-0.023292655125260353,
-0.005148150026798248,
0.027463270351290703,
0.02317233569920063,
0.023535002022981644,
0.04277409613132477,
-0.0028666446451097727,
0.00021442616707645357,
0.016454216092824936,
0.032233890146017075,
0.023775938898324966,
-0.023427452892065048,
0.08452150225639343,
-0.013279151171445847,
-0.022889526560902596,
-0.008050666190683842,
-0.012428788468241692,
0.025419261306524277,
0.0018047030316665769,
0.010616361163556576,
-0.02037765085697174,
0.030104469507932663,
0.015171858482062817,
0.017062285915017128,
-0.02023898810148239,
0.007974767126142979,
0.055730655789375305,
-0.02036331035196781,
0.0012737871147692204,
0.0070850239135324955,
0.076011061668396,
0.006739123724400997,
-0.0034202164970338345,
0.01924888975918293,
-0.01703791692852974,
0.00046227939310483634,
0.035007793456315994,
-0.01763572171330452,
0.06950703263282776,
-0.004843536298722029,
-0.005101575516164303,
-0.035998474806547165,
-0.03373658284544945,
0.02662038803100586,
0.0011324030347168446,
-0.007107902318239212,
-0.0014389397110790014,
-0.012156933546066284,
-0.03779159486293793,
0.017155474051833153,
-0.00955467764288187,
-0.03235951438546181,
-0.02512781322002411,
-0.02660234458744526,
0.004470081999897957,
-0.018683990463614464,
-0.019419759511947632,
0.0028292331844568253,
-0.023247480392456055,
-0.005361981224268675,
0.005907314829528332,
-0.0036223644856363535,
0.025327621027827263,
-0.00964096188545227,
-0.021793410181999207,
-0.028295159339904785,
0.044658415019512177,
-0.016948217526078224,
-0.03527408465743065,
-0.019664350897073746,
0.000560203508939594,
-0.009632879868149757,
0.031911712139844894,
0.07240565121173859,
-0.0068455105647444725,
-0.001318075810559094,
0.00006029987707734108,
0.02292836643755436,
0.01923184283077717,
-0.05675323307514191,
0.03254475072026253,
0.0019039383623749018,
-0.03551003709435463,
-0.011890433728694916,
-0.0001827348896767944,
0.003240227699279785,
0.008535089902579784,
0.05746840685606003,
-0.022923177108168602,
-0.0005149715580046177,
-0.008709193207323551,
-0.019057203084230423,
0.018516531214118004,
0.001624874654226005,
0.00240175798535347,
0.07548364996910095,
-0.003097002161666751,
-0.003969805780798197,
0.05003335326910019,
-0.022720104083418846,
-0.03521498665213585,
0.020447341725230217,
0.03250541538000107,
-0.010946765542030334,
0.038399823009967804,
-0.02564127743244171,
-0.018603820353746414,
-0.02965235710144043,
0.011998861096799374,
0.025023238733410835,
-0.03720462694764137,
-0.0338473878800869,
0.06769836694002151,
0.034824781119823456,
0.03141006454825401,
-0.002621034160256386,
0.03571125119924545,
0.02077280730009079,
0.045222438871860504,
-0.026712030172348022,
0.07692916691303253,
0.05335332080721855,
0.007861476391553879,
0.02572220377624035,
0.0491386316716671,
-0.017433125525712967,
0.024197781458497047,
0.03229796513915062,
0.015108445659279823,
-0.033403992652893066,
0.021538564935326576,
0.0515531525015831,
0.010908802039921284,
-0.024592703208327293,
0.019057132303714752,
-0.011418409645557404,
0.07479319721460342,
-0.03793254494667053,
-0.015411213040351868,
-0.023640001192688942,
-0.0057299332693219185,
-0.0029016113840043545,
0.026421641930937767,
0.03233826905488968,
0.03782473877072334,
-0.005706205498427153,
-0.0023671381641179323,
-0.00701058330014348,
-0.015451399609446526,
-0.009953790344297886,
-0.042573317885398865,
0.02702908031642437,
-0.011402911506593227,
-0.006948549300432205,
-0.029797304421663284,
-0.011163624934852123,
0.03539864346385002,
0.010155385360121727,
0.04560282453894615,
0.05758119001984596,
0.028044596314430237,
0.03771129623055458,
-0.045073043555021286,
0.0064355721697211266,
0.07812529057264328,
-0.08439318835735321,
-0.03190141171216965,
-0.010245958343148232,
0.005760932806879282,
-0.010398488491773605,
-0.030024215579032898
] |
<p>The photon has a mass of 0, but it has energy because of its motion. When it is sucked into the black hole and becomes a singularity, it loses its energy because it is no longer moving. It is not possible for something to be sucked out of a black hole, so it has no potential energy that the kinetic energy could have been transformed into. If I haven't missed a point, then energy has just been destroyed. Everyone knows that it isn't possible for energy to be destroyed because of the first law of thermodynamics a.k.a. the conservation law of energy. Therefore I must have missed a point, because I am not ready to criticize famous scientists that have indefinitely more knowledge then I do. Please tell me what I did wrong :)</p>
| 8,451 |
[
-0.03448743745684624,
-0.06273185461759567,
-0.035619646310806274,
-0.02748609520494938,
0.03244266286492348,
0.005958511494100094,
-0.04146769270300865,
-0.01735333912074566,
-0.04411615431308746,
-0.013149590231478214,
0.017214465886354446,
0.01547318510711193,
0.02973826788365841,
0.025130407884716988,
0.00402533495798707,
0.002564388560131192,
-0.023313632234930992,
-0.01721256598830223,
-0.006265664007514715,
-0.012767784297466278,
-0.007421864662319422,
0.021262435242533684,
-0.005521206650882959,
0.018367525190114975,
-0.03939853236079216,
0.008566823787987232,
0.01058996096253395,
0.022882236167788506,
0.01976281963288784,
0.05480973422527313,
-0.016228433698415756,
-0.03178960829973221,
0.009377943351864815,
0.02823653444647789,
0.012322046793997288,
0.01154819130897522,
-0.04415558651089668,
-0.033191949129104614,
-0.019435087218880653,
0.005551618058234453,
0.009867874905467033,
-0.03140838444232941,
0.0023686885833740234,
0.05159439146518707,
-0.03252504765987396,
-0.012261433526873589,
0.02133779227733612,
-0.010746411047875881,
0.06013287976384163,
-0.0510476753115654,
0.06732095777988434,
0.0021061834413558245,
0.01767433062195778,
0.023421015590429306,
-0.017680229619145393,
0.00010660892439773306,
0.07159373164176941,
0.08345427364110947,
-0.05394797772169113,
-0.058813922107219696,
-0.020626431331038475,
-0.0034106154926121235,
-0.03450711816549301,
-0.0019735153764486313,
0.006035283673554659,
0.025088144466280937,
-0.026027683168649673,
0.003767246613278985,
0.06083564832806587,
-0.020680636167526245,
0.027642911300063133,
0.015275009907782078,
0.009049435146152973,
0.006043768022209406,
-0.005827843211591244,
-0.02487970143556595,
0.018999336287379265,
0.011301637627184391,
0.0401785671710968,
0.048355791717767715,
-0.02334803156554699,
-0.007729583885520697,
0.0775221511721611,
0.057351868599653244,
0.00861450843513012,
0.009722605347633362,
0.08414822816848755,
-0.01591929979622364,
0.008236613124608994,
0.024550966918468475,
-0.0018888292834162712,
-0.005787400063127279,
-0.0009171765996143222,
-0.014892364852130413,
-0.019947359338402748,
0.03453051298856735,
-0.004663684871047735,
0.0628269612789154,
-0.006404341664165258,
-0.05042080581188202,
0.037983428686857224,
0.025401268154382706,
0.05542723089456558,
0.056496113538742065,
0.017836956307291985,
-0.037437520921230316,
-0.05227480083703995,
0.047237470746040344,
-0.002916423138231039,
-0.03729419410228729,
-0.05554686486721039,
0.01459550391882658,
-0.010077291168272495,
-0.027826344594359398,
0.025618301704525948,
-0.03948720544576645,
-0.011439015157520771,
-0.0004882020002696663,
0.0849544033408165,
0.06228579953312874,
0.043341316282749176,
-0.03349582478404045,
0.04318435490131378,
-0.01091101486235857,
-0.06270494312047958,
0.01849818415939808,
0.06268072873353958,
-0.021813809871673584,
-0.07583189010620117,
0.00821357499808073,
-0.03155889734625816,
0.00047507049748674035,
-0.00361350504681468,
0.0023013257887214422,
0.03689393773674965,
-0.03910910338163376,
-0.1067754253745079,
-0.05064360424876213,
0.0379483625292778,
-0.03258942812681198,
-0.032314833253622055,
-0.06168854236602783,
-0.015668228268623352,
0.018348321318626404,
0.09683240950107574,
-0.0038658753037452698,
-0.004549846053123474,
-0.028040673583745956,
0.04055022820830345,
-0.025961635634303093,
-0.01914001628756523,
-0.0044216881506145,
-0.01849846914410591,
-0.03873791545629501,
-0.011229133233428001,
-0.04505780339241028,
-0.007886904291808605,
0.04849722236394882,
0.022226883098483086,
-0.03271842747926712,
0.046525899320840836,
-0.027839262038469315,
0.026803188025951385,
0.019299589097499847,
-0.03702760115265846,
-0.02524390257894993,
0.07648126780986786,
0.02657248266041279,
0.004062994848936796,
0.01821066439151764,
0.03166724741458893,
0.043947167694568634,
-0.03290506452322006,
0.0031706569716334343,
0.02332446724176407,
-0.058418817818164825,
-0.01288980059325695,
-0.01837877370417118,
0.015119398944079876,
-0.016201280057430267,
-0.03083229809999466,
-0.04627242684364319,
0.010567049495875835,
-0.005996722728013992,
-0.01387295126914978,
0.06445763260126114,
-0.012864689342677593,
-0.030576659366488457,
-0.02582879550755024,
-0.0265202559530735,
-0.03633797541260719,
-0.05472452938556671,
0.02371041104197502,
0.011775119230151176,
0.010086682625114918,
-0.01058319304138422,
0.026929061859846115,
0.0423741340637207,
-0.06880160421133041,
0.0030251466669142246,
0.00478741992264986,
0.016585715115070343,
-0.04160279035568237,
0.012389731593430042,
0.005635316949337721,
0.05337996408343315,
0.06018463149666786,
0.001660024980083108,
0.0032977783121168613,
0.033829864114522934,
0.027107739821076393,
0.03455408290028572,
0.01754995994269848,
0.010858454741537571,
-0.02100260742008686,
-0.00492603424936533,
0.0063667600043118,
-0.002569477539509535,
0.018533723428845406,
0.03445862606167793,
-0.0010209436295554042,
0.08602160960435867,
0.009234706871211529,
-0.00039809392183087766,
-0.027239404618740082,
0.062416743487119675,
-0.002705164486542344,
0.026589075103402138,
-0.017413727939128876,
-0.022755799815058708,
-0.02822180837392807,
0.03552497178316116,
0.03470047190785408,
0.011651746928691864,
-0.04836615175008774,
0.007114765699952841,
0.03827957808971405,
0.015428042970597744,
0.016927408054471016,
0.008626679889857769,
-0.004644694272428751,
-0.007165542338043451,
0.016814498230814934,
-0.0068100495263934135,
0.011895823292434216,
-0.0006686667329631746,
0.026017528027296066,
-0.009832446463406086,
-0.005322248674929142,
0.005202643107622862,
0.006906992755830288,
0.0444825105369091,
-0.023012738674879074,
0.03794393688440323,
-0.00023353630967903882,
-0.025569356977939606,
0.03290925174951553,
-0.028649428859353065,
0.03681131824851036,
0.008382079191505909,
-0.01445006299763918,
0.013055025599896908,
-0.052516303956508636,
-0.0021803618874400854,
0.016187356784939766,
0.024565910920500755,
-0.007190129719674587,
0.009436513297259808,
0.0039213187992572784,
-0.027818718925118446,
-0.00569277536123991,
-0.017660699784755707,
-0.018002616241574287,
-0.04551691934466362,
-0.00035054865293204784,
0.01472950167953968,
0.008905375376343727,
0.026050183922052383,
-0.032896749675273895,
-0.020207658410072327,
0.0019516857573762536,
-0.030942196026444435,
-0.03102250024676323,
0.030299177393317223,
-0.043691687285900116,
0.0035423939116299152,
-0.020713776350021362,
-0.004559454042464495,
0.05186845734715462,
-0.02372317761182785,
0.04152786731719971,
0.03393682464957237,
-0.029620138928294182,
-0.0398322232067585,
0.013486758805811405,
-0.027864836156368256,
-0.0015863962471485138,
-0.007804251741617918,
0.005533074960112572,
0.0391349159181118,
-0.01464423630386591,
-0.0412895530462265,
0.05043988674879074,
-0.015820477157831192,
-0.062228504568338394,
-0.016197454184293747,
-0.019915008917450905,
0.012060546316206455,
-0.028575008735060692,
0.02391016110777855,
0.0005405814154073596,
-0.06589324027299881,
0.01243110466748476,
-0.044301822781562805,
-0.03273768350481987,
0.019978567957878113,
-0.005174457095563412,
0.009028514847159386,
-0.02259322814643383,
-0.03785832226276398,
0.03198884055018425,
0.006192435976117849,
-0.03272654488682747,
-0.009726452641189098,
0.003014648100361228,
-0.025247961282730103,
-0.0025750536005944014,
0.011365829966962337,
-0.007932696491479874,
0.012834254652261734,
0.015962934121489525,
-0.003946471493691206,
0.057666879147291183,
0.020923109725117683,
0.007537000812590122,
-0.055242810398340225,
-0.02332424186170101,
-0.008327662013471127,
0.00260912929661572,
0.016337012872099876,
0.002790868980810046,
-0.035156041383743286,
0.043472032994031906,
0.0012918015709146857,
0.043023861944675446,
0.006515814457088709,
-0.029811106622219086,
0.04453660547733307,
0.02433652989566326,
0.03769736364483833,
-0.03844955191016197,
0.01653170958161354,
-0.023647956550121307,
-0.017339516431093216,
0.027756307274103165,
0.0068174549378454685,
0.06536418944597244,
-0.021277664229273796,
-0.00548040634021163,
0.004236963111907244,
0.053852107375860214,
-0.0311663169413805,
-0.009050182066857815,
-0.009388773702085018,
-0.03456154093146324,
0.01083385106176138,
0.039334848523139954,
-0.0026796418242156506,
0.05600595474243164,
0.04148396849632263,
0.05546022579073906,
-0.00494731031358242,
-0.02937823161482811,
-0.02254195138812065,
-0.03633473813533783,
0.006362939719110727,
0.024565039202570915,
0.04838251322507858,
-0.00970188807696104,
0.039110928773880005,
0.05414819344878197,
0.009707340970635414,
0.038323719054460526,
-0.018615588545799255,
-0.09072720259428024,
0.049411095678806305,
-0.04294266551733017,
-0.010980808176100254,
0.004922161344438791,
-0.00434192456305027,
-0.022551534697413445,
-0.0316612683236599,
0.0031901223119348288,
0.030448928475379944,
0.0001744925248203799,
-0.06121452525258064,
0.00009291935566579923,
-0.0538935549557209,
-0.020774414762854576,
-0.008360662497580051,
0.018389277160167694,
0.05620855465531349,
-0.003271207446232438,
-0.01220663171261549,
0.054411571472883224,
-0.011903265491127968,
-0.010094046592712402,
0.005151762161403894,
-0.013155480846762657,
-0.007848694920539856,
0.0460285060107708,
0.021662916988134384,
-0.010635423474013805,
-0.003916199319064617,
0.010793227702379227,
0.029031218960881233,
0.020606158301234245,
0.011410060338675976,
-0.013596531003713608,
-0.011217758059501648,
-0.033338479697704315,
-0.011489911004900932,
-0.012174677103757858,
0.06300947815179825,
0.008642654865980148,
-0.010534469969570637,
0.012099712155759335,
0.03284439444541931,
0.027657629922032356,
0.040408965200185776,
0.08092876523733139,
-0.011649237014353275,
-0.02478024736046791,
-0.049505434930324554,
-0.009511149488389492,
-0.01827707327902317,
-0.02639857307076454,
0.000039588769141118973,
0.005142149981111288,
-0.060670703649520874,
-0.01789245568215847,
0.02022101730108261,
0.022153891623020172,
-0.021310392767190933,
-0.01266963966190815,
-0.010488930158317089,
0.0031586228869855404,
-0.009334135800600052,
0.016533594578504562,
0.003989978693425655,
0.010035153478384018,
0.0530172660946846,
-0.018342718482017517,
-0.01578206941485405,
-0.05990210548043251,
-0.016148727387189865,
0.037343189120292664,
0.04045945405960083,
0.009308183565735817,
-0.010696577839553356,
-0.04776100441813469,
0.002766610123217106,
0.025994636118412018,
-0.046388477087020874,
0.0380806028842926,
-0.0043205199763178825,
0.03236567974090576,
0.012331219390034676,
-0.02973354421555996,
0.013850984163582325,
0.03232496976852417,
-0.017921140417456627,
0.0460849367082119,
-0.026109391823410988,
-0.0027610836550593376,
-0.028117528185248375,
0.0009583146311342716,
0.013820772990584373,
0.08158842474222183,
0.026113836094737053,
-0.01478902529925108,
0.010634410195052624,
-0.009671141393482685,
-0.03687772527337074,
-0.0846790224313736,
-0.00033255675225518644,
-0.008802445605397224,
-0.03930193930864334,
0.02342996373772621,
-0.02262653224170208,
-0.0471385233104229,
0.024597065523266792,
0.03799949958920479,
-0.029926413670182228,
-0.01101850438863039,
-0.09824701398611069,
-0.016964679583907127,
0.007853159680962563,
0.022576669231057167,
0.04716134071350098,
0.00750240171328187,
-0.04484773799777031,
0.005489295814186335,
-0.04248500615358353,
0.023943211883306503,
-0.016955392435193062,
-0.011507311835885048,
-0.02766353078186512,
-0.006632267031818628,
-0.015273255296051502,
0.0433724969625473,
0.0034340200945734978,
0.010371987707912922,
0.003325696336105466,
-0.014159068465232849,
0.0013962187804281712,
-0.013259319588541985,
-0.001844902173615992,
0.021788157522678375,
-0.01378877554088831,
0.013351788744330406,
-0.03732495382428169,
-0.004035250749439001,
0.021441537886857986,
-0.008439121767878532,
-0.04684438183903694,
0.07567496597766876,
0.00019359208818059415,
0.02140047214925289,
0.010169458575546741,
-0.02317226305603981,
0.010504581965506077,
-0.027179008349776268,
0.044610340148210526,
-0.031115809455513954,
0.0024046222679316998,
0.003959106747061014,
-0.04938114807009697,
-0.040480416268110275,
-0.04249000549316406,
0.007822730578482151,
0.03703012689948082,
-0.07070940732955933,
0.03781621903181076,
0.03005632571876049,
0.03553415462374687,
-0.10075494647026062,
-0.04397272318601608,
0.04209336265921593,
0.014644656330347061,
-0.017863579094409943,
0.013244069181382656,
0.03255974128842354,
-0.037875715643167496,
-0.01545219961553812,
-0.015936708077788353,
0.011813097633421421,
-0.029637718573212624,
-0.00243047415278852,
-0.0017960781697183847,
0.017394952476024628,
0.029824404045939445,
-0.004866946022957563,
-0.034377217292785645,
0.02131601609289646,
0.00881033856421709,
-0.021403294056653976,
-0.01677636243402958,
0.07519619911909103,
0.0018046003533527255,
-0.046461816877126694,
-0.007147917989641428,
-0.005189770366996527,
0.004924273118376732,
0.0016312788939103484,
0.030943971127271652,
0.048854779452085495,
0.0191692803055048,
-0.019850078970193863,
-0.018744822591543198,
0.03440660610795021,
-0.01977834291756153,
0.013610472902655602,
0.0040390584617853165,
-0.008054202422499657,
0.006110247690230608,
-0.04755473509430885,
0.04804814234375954,
-0.0027515932451933622,
0.0276215560734272,
-0.0035585297737270594,
0.05687965080142021,
0.006502225063741207,
-0.02865254506468773,
0.012846197932958603,
-0.04987941309809685,
-0.003545320825651288,
0.014419419690966606,
0.025447269901633263,
-0.02287795953452587,
0.004765043500810862,
-0.018936913460493088,
-0.012063325382769108,
-0.028183136135339737,
0.004071048926562071,
0.08656959235668182,
0.002076004631817341,
0.012924152426421642,
-0.012421426363289356,
0.028280433267354965,
0.004499848000705242,
0.006628075614571571,
0.009681626223027706,
0.03266269713640213,
0.02085399068892002,
-0.015547375194728374,
0.02531798742711544,
0.004858765285462141,
0.032703470438718796,
0.06683716922998428,
-0.028751764446496964,
0.04754927009344101,
0.04137953370809555,
0.014236507005989552,
0.014246856793761253,
0.02096809819340706,
-0.03233540058135986,
0.019554859027266502,
-0.01858619786798954,
0.036453649401664734,
0.0030757649801671505,
0.006078988779336214,
0.02118203416466713,
-0.007043455261737108,
0.025302523747086525,
0.0004843835486099124,
-0.032625045627355576,
-0.03215642645955086,
0.0016867909580469131,
-0.02742411568760872,
0.017000362277030945,
0.03225760534405708,
0.042615894228219986,
0.020189490169286728,
0.03469937667250633,
0.004263845272362232,
-0.0004718635755125433,
-0.05421847477555275,
-0.047266699373722076,
-0.05594627931714058,
-0.06223844736814499,
0.04109774902462959,
-0.008703834377229214,
-0.012646473944187164,
0.008566026575863361,
0.0002776348264887929,
0.0014356563333421946,
0.014121901243925095,
0.044910017400979996,
0.009325448423624039,
0.029934002086520195,
0.008467034436762333,
-0.00288768601603806,
-0.031059257686138153,
0.02870831824839115,
0.1029491275548935,
0.059069354087114334,
-0.010662383399903774,
-0.06432636082172394,
0.008076059632003307,
-0.03490372747182846,
0.02685260958969593,
-0.05047990009188652,
0.04715016856789589,
-0.022189024835824966,
-0.0006029985961504281,
0.008489378727972507,
0.03319742903113365,
-0.010506265796720982,
-0.005547032225877047,
0.02485378086566925,
-0.03289979696273804,
-0.04532631114125252,
0.020249664783477783,
0.02736208401620388,
-0.014096152037382126,
-0.009012307971715927,
-0.02299179509282112,
0.007100604474544525,
-0.019255656749010086,
-0.01131054013967514,
-0.005660378374159336,
-0.04145960137248039,
0.014151018112897873,
-0.006456197239458561,
-0.03648735582828522,
0.01614510267972946,
0.029547661542892456,
-0.00233358982950449,
-0.033323731273412704,
0.00433875760063529,
0.051772478967905045,
-0.011418086476624012,
0.01034610066562891,
0.019783588126301765,
0.02559390477836132,
0.028424203395843506,
0.023753413930535316,
0.003184367436915636,
-0.03738953918218613,
-0.031622983515262604,
-0.00038217747351154685,
0.057855911552906036,
-0.02566305734217167,
0.022940104827284813,
-0.0064397710375487804,
-0.025995010510087013,
-0.03439999371767044,
-0.05898572877049446,
-0.0020305870566517115,
-0.017688225954771042,
0.001926466473378241,
0.0194062702357769,
-0.03452173247933388,
0.005299373064190149,
0.01696307584643364,
0.0007807419751770794,
0.025564206764101982,
-0.02088332362473011,
0.026843417435884476,
-0.0008878775988705456,
-0.02227192185819149,
0.022968769073486328,
-0.05664905533194542,
0.017725270241498947,
0.007612823508679867,
-0.036154769361019135,
-0.03305975720286369,
-0.026166647672653198,
0.005240910220891237,
0.03902319073677063,
0.013788832351565361,
-0.01598835363984108,
0.019099917262792587,
-0.033464472740888596,
-0.08071637898683548,
0.03902457281947136,
0.014583955518901348,
-0.06452559679746628,
-0.030610062181949615,
0.015808746218681335,
0.0008222513133659959,
0.051259785890579224,
-0.02462569996714592,
-0.010772679932415485,
0.01312904804944992,
0.012453564442694187,
0.0013147701974958181,
-0.002715073525905609,
-0.009445383213460445,
0.017679795622825623,
-0.02753436006605625,
-0.021940680220723152,
-0.030397482216358185,
0.026460280641913414,
0.023900045081973076,
-0.00336701818741858,
0.025494158267974854,
0.03336493298411369,
-0.04093898832798004,
-0.008230631239712238,
0.010506529361009598,
0.005145994946360588,
-0.02770833484828472,
0.02778446301817894,
0.011327256448566914,
-0.021565821021795273,
-0.07383210211992264,
-0.02681240439414978,
-0.008575869724154472,
-0.009153244085609913,
0.02614469639956951,
-0.0033905738964676857,
0.03722550719976425,
-0.020143834874033928,
0.04253459721803665,
-0.05374230071902275,
-0.012570416554808617,
-0.04834909364581108,
0.014295314438641071,
0.03244209662079811,
-0.015617409721016884,
-0.025668717920780182,
0.011711640283465385,
-0.005189462564885616,
-0.016725661233067513,
0.026376057416200638,
0.039949219673871994,
-0.028432808816432953,
-0.04584929719567299,
0.02859475649893284,
-0.004843104165047407,
0.061005618423223495,
0.00807968620210886,
0.0007807937217876315,
0.045037589967250824,
-0.051449138671159744,
-0.051697954535484314,
0.03573920950293541,
-0.014406573958694935,
0.009038090705871582,
-0.010013132356107235,
-0.026961054652929306,
-0.02148914523422718,
0.08374159038066864,
-0.009753086604177952,
0.023275453597307205,
0.013258662074804306,
-0.06441043317317963,
-0.04838075861334801,
0.03968684375286102,
0.01369338296353817,
-0.053991854190826416,
-0.017940787598490715,
0.02909689024090767,
0.012745704501867294,
0.016356678679585457,
-0.027141304686665535,
-0.017144786193966866,
0.028162166476249695,
0.014478439465165138,
0.0019694697111845016,
-0.005029098596423864,
0.01577790640294552,
0.07356000691652298,
-0.04906552657485008,
0.004445131868124008,
0.034643951803445816,
-0.007695381995290518,
-0.10874159634113312,
-0.009687846526503563,
-0.007589505519717932,
0.022980011999607086,
0.04597433656454086,
-0.039118800312280655,
0.037687115371227264,
0.043324656784534454,
-0.03283115103840828,
0.003197821555659175,
-0.030401887372136116,
-0.01103230845183134,
0.02924242615699768,
0.03329354524612427,
-0.011231034062802792,
0.03322065249085426,
0.05667302384972572,
0.06262434273958206,
-0.00670570507645607,
-0.010394190438091755,
-0.0008695017895661294,
-0.0155752282589674,
-0.024063825607299805,
0.04402368888258934,
-0.042874082922935486,
0.014125394634902477,
0.07206504046916962,
-0.014807582832872868,
-0.025367427617311478,
0.033734485507011414,
-0.009648812003433704,
0.003682068781927228,
0.025585871189832687,
0.027523906901478767,
0.018350517377257347,
0.030298609286546707,
0.009918928146362305,
0.0008710559923201799,
-0.008553226478397846,
0.025916781276464462,
0.03141433000564575,
0.02496461011469364,
-0.006498271133750677,
0.010089075192809105,
0.029469121247529984,
-0.041130345314741135,
-0.03458326309919357,
0.020798059180378914,
-0.0214129276573658,
-0.013017251156270504,
0.014309816993772984,
0.03382283076643944,
-0.009371213614940643,
-0.03588053211569786,
-0.0358838215470314,
-0.03676686808466911,
-0.04312657192349434,
0.0468435101211071,
0.005283192731440067,
0.01173405721783638,
-0.004105068277567625,
0.006130789872258902,
-0.021011918783187866,
0.027642514556646347,
-0.005512484814971685,
-0.004812854342162609,
-0.04609823226928711,
0.016131415963172913,
-0.016452884301543236,
0.00019933551084250212,
0.005504013504832983,
-0.06758131831884384,
-0.03627768158912659,
0.03646938130259514,
0.01700827106833458,
0.020894061774015427,
-0.008435073308646679,
-0.04508683830499649,
-0.03360765427350998,
-0.079121433198452,
0.0016840058378875256,
-0.015078644268214703,
0.01622055470943451,
-0.037465739995241165,
-0.00531748728826642,
0.0018092949176207185,
0.0191991925239563,
0.027336161583662033,
-0.06689581274986267,
-0.03705824539065361,
0.03500315919518471,
-0.03207000717520714,
0.020546728745102882,
-0.03759818151593208,
0.003698245622217655,
0.00887994933873415,
-0.04717656970024109,
0.0060832505114376545,
0.006220799870789051,
-0.017503108829259872,
0.023596979677677155,
0.012208078056573868,
-0.01949012652039528,
0.037200555205345154,
-0.00616103783249855,
-0.015303969383239746,
0.053169578313827515,
0.004059465602040291,
0.012965019792318344,
0.05154047906398773,
-0.0008062347187660635,
0.03850984573364258,
0.04499403014779091,
-0.01968841813504696,
-0.017189592123031616,
0.028828052803874016,
-0.019124532118439674,
-0.004449252970516682,
-0.00858636386692524,
-0.025529062375426292,
0.038899991661310196,
-0.027278490364551544,
0.005770809482783079,
0.059448909014463425,
-0.018915381282567978,
-0.0028167306445538998,
0.03755693882703781,
0.01574121229350567,
0.029611919075250626,
0.0055009666830301285,
0.030293866991996765,
0.008592718280851841,
0.02551187388598919,
0.01784655638039112,
0.06288853287696838,
0.02650870382785797,
0.00588085874915123,
0.006480935029685497,
0.010759169235825539,
-0.018935661762952805,
-0.022552192211151123,
-0.0014322581700980663,
0.038993097841739655,
-0.056871891021728516,
-0.049293700605630875,
-0.008860231377184391,
-0.007224962115287781,
-0.02561250701546669,
0.013751792721450329,
-0.025962570682168007,
0.062472276389598846,
-0.0032797204330563545,
0.020067056640982628,
0.00824595708400011,
-0.020965635776519775,
-0.015348659828305244,
0.04179050773382187,
0.008408169262111187,
0.08119882643222809,
0.013310033828020096,
-0.000655864248983562,
-0.020647035911679268,
0.009735041297972202,
0.029936904087662697,
-0.024389568716287613,
-0.008045986294746399,
-0.024187995120882988,
-0.016457365825772285,
-0.028783224523067474,
0.005667851306498051,
-0.006080613937228918,
-0.01495395228266716,
0.016897743567824364,
0.031492866575717926,
0.009019384160637856,
0.005164704751223326,
-0.004511021543294191,
-0.041003745049238205,
0.028463054448366165,
-0.04744746536016464,
0.010185646824538708,
-0.008704056032001972,
0.0427241325378418,
-0.023588865995407104,
-0.01155988872051239
] |
<p>I am a layman, so take this with a grain of salt.</p>
<p>I saw a TV show the other day which showed a Russian Cosmonaut who had spent more time in space than any other human. The relativistic effects of the low gravity and extreme speeds at which he had spent a decent part of his life had pushed him a small, but surprisingly non-trivial fraction of a second into the "future" as compared to the rest of us observers here on earth. I want to say it was something like a 50th of a second.</p>
<p>What, if any, are the relativistic effects all of us experience in an average lifespan simply by being on the earth as it travels through space in orbit and as the galaxy rotates and the universe expands. </p>
<p>By effects I mean as compared to a hypothetical observer who is able to remain completely motionless in space? Is it even measurable? </p>
<p>I know gravity is not being taken into account, so is this question even answerable?</p>
<p>Thanks for your patience with my question.</p>
| 8,452 |
[
-0.012214796617627144,
-0.07850278913974762,
-0.025170810520648956,
-0.05730891972780228,
0.032528106123209,
0.020305972546339035,
-0.03765203803777695,
-0.0396859273314476,
-0.0026205657050013542,
-0.04545649141073227,
0.003710032207891345,
0.04242972657084465,
0.03526034951210022,
-0.01413328479975462,
-0.005592371337115765,
0.003070381935685873,
-0.021879510954022408,
-0.02117146924138069,
-0.013551078736782074,
-0.0404779389500618,
0.025401681661605835,
0.021439053118228912,
0.03314139321446419,
-0.011401188559830189,
-0.06289669126272202,
0.013732821680605412,
0.058547113090753555,
0.004668517038226128,
-0.002838053973391652,
0.04965050891041756,
-0.01620888151228428,
-0.0019527493277564645,
-0.006874758750200272,
0.039257023483514786,
0.04371196776628494,
0.015040523372590542,
-0.06296997517347336,
-0.03211494907736778,
0.0040227207355201244,
0.020682644098997116,
-0.03684466332197189,
-0.0028849011287093163,
0.010051342658698559,
0.06327714771032333,
-0.03288362920284271,
0.011906584724783897,
-0.0013144300319254398,
-0.014394421130418777,
0.09477415680885315,
-0.03396516293287277,
0.056469693779945374,
-0.009057261049747467,
0.03784094378352165,
-0.019394924864172935,
0.001074463129043579,
-0.005013855639845133,
0.07897606492042542,
0.0857495442032814,
-0.027815381065011024,
-0.039719291031360626,
-0.028988344594836235,
0.0016624665586277843,
-0.011315076611936092,
0.0012528002262115479,
-0.006234500091522932,
0.01244704332202673,
-0.049590643495321274,
-0.03221854940056801,
0.040986038744449615,
0.010216695256531239,
0.013419047929346561,
0.016980456188321114,
0.025865083560347557,
0.014502943493425846,
0.016726640984416008,
-0.02305736020207405,
0.03367815911769867,
-0.008120388723909855,
0.027662910521030426,
0.039997655898332596,
-0.06271786242723465,
-0.025665543973445892,
0.04036223515868187,
0.046934694051742554,
0.027199016883969307,
0.025504780933260918,
0.06934227049350739,
-0.0073764207772910595,
0.02090904489159584,
0.03541162982583046,
-0.020170152187347412,
0.03675149381160736,
0.010030615143477917,
-0.0020386595278978348,
-0.04941020533442497,
0.06532611697912216,
-0.008172331377863884,
0.06254943460226059,
0.016064835712313652,
0.011445602402091026,
0.012082183733582497,
-0.019554462283849716,
0.016928639262914658,
0.06589465588331223,
0.013213492929935455,
-0.02943684160709381,
-0.029048031195998192,
-0.03533412516117096,
-0.0016902434872463346,
-0.015067916363477707,
-0.037176258862018585,
-0.0066424040123820305,
-0.02642006054520607,
-0.0024431750643998384,
0.016466747969388962,
-0.025271514430642128,
-0.02051422744989395,
0.0011808591661974788,
0.07504022866487503,
0.06300648301839828,
0.03055517189204693,
-0.01365615800023079,
0.017570624127984047,
-0.0033207584638148546,
-0.031257420778274536,
0.05396218225359917,
0.02276213839650154,
-0.023590700700879097,
-0.020648209378123283,
0.0198654904961586,
-0.01035190187394619,
-0.04127597436308861,
0.020248880609869957,
-0.0035926143173128366,
0.06472387909889221,
-0.014158113859593868,
-0.11256144940853119,
-0.0508195236325264,
0.031212028115987778,
0.011203715577721596,
-0.005959557835012674,
-0.07699838280677795,
0.031756188720464706,
-0.033394455909729004,
0.05023130774497986,
0.04378410428762436,
-0.010748244822025299,
-0.00473868427798152,
0.03237919881939888,
0.03601034730672836,
-0.048471733927726746,
0.027633994817733765,
-0.006420641206204891,
-0.05131499841809273,
0.015597052872180939,
-0.06372036039829254,
-0.038840748369693756,
0.04867060109972954,
0.008860653266310692,
-0.03388141095638275,
0.047201212495565414,
-0.003212455427274108,
0.007126129698008299,
0.018017524853348732,
0.01076290849596262,
-0.02398892678320408,
0.1017925888299942,
0.029156530275940895,
-0.014458325691521168,
0.03716406226158142,
0.035990651696920395,
0.039803504943847656,
0.01989869773387909,
0.014357054606080055,
0.04277711361646652,
-0.03178580850362778,
-0.011938923969864845,
0.011638087220489979,
-0.027248507365584373,
-0.03488690033555031,
-0.057546187192201614,
-0.034895606338977814,
-0.02564721181988716,
-0.037880729883909225,
0.013010566122829914,
0.04487692937254906,
0.003768028225749731,
0.014341117814183235,
-0.024801619350910187,
-0.014086352661252022,
0.011882911436259747,
-0.08362051844596863,
0.008726268075406551,
0.005200935062021017,
-0.008899777196347713,
-0.018251990899443626,
0.009873188100755215,
0.03584869205951691,
-0.05122401565313339,
-0.06454046815633774,
0.005093141924589872,
0.03118782490491867,
0.0025772210210561752,
-0.032890014350414276,
-0.002526002237573266,
0.07020772248506546,
0.015481865964829922,
-0.017777107656002045,
-0.01980637200176716,
0.002154055517166853,
-0.01912551186978817,
0.027103975415229797,
-0.024692663922905922,
0.027765728533267975,
0.016263706609606743,
0.004079060163348913,
0.005089486483484507,
-0.004006183706223965,
0.0154042923822999,
0.030358009040355682,
-0.018850240856409073,
0.08187421411275864,
0.006774899549782276,
-0.015333535149693489,
-0.0135417515411973,
0.014529958367347717,
0.02006339281797409,
-0.030165743082761765,
0.0020124909933656454,
-0.03978141024708748,
-0.04448136314749718,
-0.025462472811341286,
0.028281301259994507,
0.030305542051792145,
0.0055456506088376045,
0.010293669998645782,
0.035256531089544296,
0.030819587409496307,
0.024035068228840828,
0.003885502927005291,
-0.00504523329436779,
-0.040880873799324036,
-0.0030011169146746397,
0.0011171916266903281,
0.008091609925031662,
0.005489106755703688,
0.02762414515018463,
0.011750211007893085,
0.002826165873557329,
-0.024965357035398483,
0.015001315623521805,
0.02855973318219185,
-0.006010897923260927,
0.025009045377373695,
-0.0073676700703799725,
-0.036434024572372437,
0.03212413191795349,
0.005071200430393219,
-0.008035450242459774,
0.028929153457283974,
0.008227313868701458,
-0.002628420479595661,
-0.04221293702721596,
-0.03386726975440979,
-0.005582889076322317,
0.011957007460296154,
-0.0307499747723341,
-0.023861171677708626,
0.02734590321779251,
-0.032107893377542496,
-0.012379777617752552,
0.0005202568136155605,
-0.004865970462560654,
-0.019082002341747284,
-0.013857747428119183,
0.03044872358441353,
0.008986193686723709,
0.005111090373247862,
-0.018315719440579414,
-0.02599315159022808,
0.013209197670221329,
-0.041083306074142456,
-0.008039429783821106,
0.02621544897556305,
-0.030383465811610222,
0.062986820936203,
-0.0027481778524816036,
-0.06498836725950241,
0.023840902373194695,
-0.016072150319814682,
0.043463606387376785,
0.052968237549066544,
-0.015415719710290432,
-0.049324095249176025,
-0.0010005804942920804,
-0.011967083439230919,
-0.004915141500532627,
-0.05356903746724129,
-0.011642524972558022,
0.08181621134281158,
-0.005843303631991148,
-0.053835488855838776,
0.011652142740786076,
-0.03627520427107811,
-0.03141685202717781,
-0.01767907291650772,
0.007561821024864912,
0.020098958164453506,
-0.044767219573259354,
0.004994325805455446,
0.0003891057276632637,
-0.04694049432873726,
-0.004072277341037989,
-0.04648967832326889,
-0.04806601256132126,
0.07119004428386688,
0.01611107774078846,
0.034144703298807144,
-0.0015024958411231637,
-0.022677812725305557,
0.049879565834999084,
0.037317581474781036,
0.01600232534110546,
-0.06424911320209503,
0.003052300540730357,
0.03035811521112919,
0.01701987162232399,
0.009040477685630322,
0.0005263951607048512,
-0.02678709104657173,
0.0011991059873253107,
0.03960789740085602,
0.04410430043935776,
-0.029039334505796432,
-0.007861366495490074,
-0.02211606688797474,
0.005288018845021725,
0.011268720962107182,
0.011304189451038837,
0.012473712675273418,
0.02820730209350586,
-0.02715962752699852,
-0.02432810328900814,
-0.019542545080184937,
0.033327799290418625,
0.024608423933386803,
-0.06361199170351028,
0.061242975294589996,
-0.00013623143604490906,
0.005294375587254763,
0.008458408527076244,
-0.004533709492534399,
-0.03160422667860985,
0.016398075968027115,
-0.0041161044500768185,
-0.010738920420408249,
0.03015490248799324,
-0.009360273368656635,
0.00915222056210041,
0.020892461761832237,
0.06122608110308647,
0.023339644074440002,
-0.018638063222169876,
-0.00043508116505108774,
0.011293118819594383,
0.01512416172772646,
-0.04265769198536873,
-0.04849110543727875,
0.05210833624005318,
0.04919968917965889,
0.02268523909151554,
-0.0023321264889091253,
-0.048585470765829086,
0.010639267973601818,
-0.062449727207422256,
-0.010505177080631256,
-0.0036869957111775875,
0.06544404476881027,
0.01564548909664154,
0.019646190106868744,
0.009695729240775108,
-0.005724892485886812,
0.005663997959345579,
-0.008277504704892635,
-0.08034779876470566,
0.01450860220938921,
-0.04221298173069954,
-0.025038106366991997,
-0.020352637395262718,
0.046769704669713974,
0.010171116329729557,
-0.019307365640997887,
-0.018588285893201828,
-0.04100530594587326,
-0.0028852117247879505,
-0.07763326168060303,
-0.017183778807520866,
0.0009398344554938376,
-0.02390114963054657,
-0.028107335790991783,
0.009121685288846493,
0.042713381350040436,
-0.00023307498486246914,
0.008633523248136044,
0.025328511372208595,
-0.017190618440508842,
-0.016196612268686295,
-0.018441976979374886,
-0.0018180765910074115,
0.005579203367233276,
0.03309543430805206,
0.04228920862078667,
-0.01946537010371685,
-0.023837033659219742,
0.02593342214822769,
0.002669369103386998,
-0.004940562881529331,
0.0009187676478177309,
0.0036450934130698442,
-0.004631929565221071,
-0.03534654527902603,
-0.021255122497677803,
0.008292085491120815,
-0.003768221940845251,
0.03870680183172226,
0.05251511186361313,
0.04295460507273674,
0.01109035313129425,
-0.01004015002399683,
0.038533736020326614,
0.02164725586771965,
-0.03696748614311218,
-0.034353502094745636,
-0.03842257335782051,
-0.0205640010535717,
-0.03801359981298447,
0.0012283122632652521,
0.02681444212794304,
0.0012038969434797764,
-0.03349941596388817,
0.0017218616558238864,
-0.013402160257101059,
-0.011162592098116875,
-0.0022531067952513695,
0.009173312224447727,
0.012636573053896427,
0.038983236998319626,
0.0026264390908181667,
-0.005945523735135794,
0.005982577335089445,
0.02678084373474121,
0.06410128623247147,
0.009672091342508793,
0.02242964506149292,
-0.07104145735502243,
0.017334099858999252,
0.014421755447983742,
0.04149128869175911,
-0.003949265461415052,
-0.00624583987519145,
-0.016209358349442482,
-0.010429497808218002,
0.0455813854932785,
-0.023050831630825996,
0.0016986752161756158,
-0.0071526989340782166,
0.0011844781693071127,
-0.02135879173874855,
-0.0538388192653656,
-0.023197464644908905,
0.0166975948959589,
-0.02058812417089939,
-0.007909329608082771,
-0.014815261587500572,
0.006383287254720926,
0.024454688653349876,
-0.0012589795514941216,
0.027729175984859467,
0.05598876252770424,
0.03851240500807762,
0.0369853712618351,
-0.00937486533075571,
0.008285405114293098,
-0.005490383133292198,
-0.06971599906682968,
-0.0014951091725379229,
0.021419789642095566,
-0.02946457825601101,
0.03941750153899193,
-0.051864828914403915,
-0.04774562641978264,
0.03193946182727814,
0.01927710697054863,
-0.010343176312744617,
-0.020273998379707336,
-0.04910827800631523,
0.02484963834285736,
0.015095265582203865,
-0.0019888686947524548,
0.05367133766412735,
0.015768246725201607,
-0.0035652315709739923,
0.021359242498874664,
0.0524989552795887,
0.03890407830476761,
-0.04653126001358032,
-0.010926212184131145,
-0.004204283002763987,
-0.026940951123833656,
-0.01764826662838459,
0.0476468987762928,
-0.03841829299926758,
0.0012916927225887775,
0.046088285744190216,
-0.015241320244967937,
-0.019627448171377182,
0.036560796201229095,
0.022037385031580925,
0.008822737261652946,
-0.014826747588813305,
-0.03399156033992767,
0.015444517135620117,
-0.02849838137626648,
-0.005122327711433172,
0.03085746057331562,
-0.006865149829536676,
0.043430816382169724,
-0.039421238005161285,
-0.0015320783713832498,
0.0064864191226661205,
-0.01598605513572693,
0.032731104642152786,
-0.03206225857138634,
0.03575482219457626,
-0.035963963717222214,
0.00009578061872161925,
0.04387853667140007,
-0.06061315909028053,
-0.008664965629577637,
-0.004681413061916828,
-0.028621934354305267,
0.025732530280947685,
-0.021741217002272606,
0.02497086673974991,
0.005158334504812956,
0.015263116918504238,
-0.07738609611988068,
-0.05460137873888016,
0.052470315247774124,
-0.002208093646913767,
-0.008373379707336426,
-0.01342612225562334,
0.011315853334963322,
-0.0647638812661171,
-0.0017201300943270326,
-0.019735613837838173,
0.03819345682859421,
-0.027742687612771988,
-0.025046801194548607,
-0.004700520075857639,
0.0006461538723669946,
0.050856538116931915,
-0.012788765132427216,
-0.041134774684906006,
-0.008424927480518818,
0.0008140757563523948,
-0.02879919856786728,
-0.027608273550868034,
0.04976148530840874,
-0.028836868703365326,
-0.021921811625361443,
-0.013856476172804832,
-0.014129165560007095,
-0.03285086527466774,
-0.025287779048085213,
-0.020196886733174324,
0.0807606428861618,
-0.009137664921581745,
0.047326184809207916,
-0.020547932013869286,
0.02639015018939972,
-0.02826949954032898,
0.020317213609814644,
0.02326369099318981,
-0.0027963274624198675,
0.006870926357805729,
-0.012492787092924118,
0.052603255957365036,
0.025804603472352028,
-0.013887976296246052,
-0.013225110247731209,
0.03941263258457184,
0.037088215351104736,
-0.004805573262274265,
0.020768161863088608,
-0.016849948093295097,
0.03880971670150757,
-0.017706094309687614,
0.0019697085954248905,
0.033363934606313705,
-0.009144744835793972,
-0.04656162112951279,
-0.013295394368469715,
-0.026567595079541206,
-0.01622619479894638,
0.06029179319739342,
-0.04434332624077797,
0.03658968210220337,
0.007236089091747999,
0.007789510302245617,
-0.022361524403095245,
-0.02986343391239643,
-0.011426322162151337,
0.004450622946023941,
-0.03226890787482262,
0.010732151567935944,
-0.009458109736442566,
-0.012102102860808372,
0.032490991055965424,
0.05554409325122833,
-0.029578570276498795,
0.021832531318068504,
0.03302884101867676,
0.04000703990459442,
0.05188778042793274,
-0.016313450410962105,
-0.017591707408428192,
0.01916537620127201,
-0.027718763798475266,
0.015793580561876297,
0.0019563999958336353,
-0.013704422861337662,
0.04236017167568207,
-0.007902270182967186,
0.04421126842498779,
-0.021529532968997955,
-0.009739565663039684,
-0.04612220078706741,
-0.03833436593413353,
0.013372106477618217,
-0.0036113830283284187,
-0.009917224757373333,
-0.012025004252791405,
0.016620442271232605,
0.033395927399396896,
0.010834593325853348,
0.01426274236291647,
-0.05876868590712547,
-0.027446584776043892,
-0.06832356750965118,
-0.04788363352417946,
0.04801550135016441,
0.01934533566236496,
-0.029224378988146782,
-0.003816149430349469,
-0.02222410775721073,
0.011001518927514553,
0.006067928392440081,
0.06969701498746872,
-0.016630927100777626,
0.09783777594566345,
0.008618033491075039,
-0.0024367854930460453,
0.0045392983593046665,
0.02702786773443222,
0.0978049710392952,
0.03597626835107803,
-0.024320919066667557,
-0.013280303217470646,
0.02704797498881817,
-0.01741047203540802,
0.04021558165550232,
-0.002725703176110983,
0.00763182295486331,
-0.014876443892717361,
-0.01789254881441593,
0.04451024532318115,
0.04287272319197655,
0.012763679027557373,
-0.03316934406757355,
0.033991388976573944,
-0.027213938534259796,
-0.01852722093462944,
0.009980062022805214,
0.01747504435479641,
0.034271880984306335,
0.003848262829706073,
-0.020405743271112442,
0.03378598392009735,
-0.035273462533950806,
0.02936573512852192,
-0.000026545032596914098,
0.00857498962432146,
-0.02833661437034607,
-0.005676127038896084,
-0.051960065960884094,
0.000700566335581243,
0.023251134902238846,
-0.019479982554912567,
-0.05294967070221901,
0.0162099227309227,
0.023555254563689232,
0.003276300150901079,
0.006475741043686867,
0.024692311882972717,
-0.016212228685617447,
0.015247752889990807,
0.01373328547924757,
0.0037881440948694944,
-0.0788646787405014,
-0.00206550071015954,
-0.03738844767212868,
0.03996405005455017,
-0.03614446520805359,
-0.02329578809440136,
-0.018599027767777443,
0.004302774555981159,
-0.009114036336541176,
-0.054242853075265884,
-0.02154170349240303,
-0.007124520372599363,
0.007895341143012047,
0.032267820090055466,
-0.007131024729460478,
-0.01789727248251438,
0.006343274377286434,
0.012747918255627155,
0.03206794336438179,
-0.020395906642079353,
-0.002637810306623578,
0.01132262498140335,
-0.013995676301419735,
0.015309629030525684,
-0.04098120331764221,
-0.0010733635863289237,
-0.02924390323460102,
-0.022548843175172806,
-0.05306193605065346,
0.032821472734212875,
0.031335122883319855,
0.03149590641260147,
0.015536075457930565,
-0.020303858444094658,
-0.005625332240015268,
-0.036875344812870026,
-0.027658186852931976,
0.04471472650766373,
0.008658476173877716,
0.0010831780964508653,
-0.021648352965712547,
0.010887512005865574,
0.027040036395192146,
0.03539935499429703,
-0.049558479338884354,
0.031235454604029655,
-0.02514846995472908,
0.06049229949712753,
0.014840035699307919,
-0.017278891056776047,
0.010597909800708294,
0.009007133543491364,
-0.003077760571613908,
0.00919337384402752,
-0.03436644375324249,
0.0320589616894722,
0.02015724405646324,
-0.019411584362387657,
0.022755665704607964,
0.014918957836925983,
-0.023725349456071854,
0.017254628241062164,
0.01819588430225849,
-0.018292879685759544,
0.015351410023868084,
-0.002963114995509386,
0.02356858178973198,
-0.03262262046337128,
-0.002234353683888912,
-0.042157258838415146,
0.009512902237474918,
-0.023940958082675934,
-0.004974079318344593,
0.006121956277638674,
0.04959476739168167,
0.0074659688398242,
-0.011075656861066818,
-0.03602227941155434,
0.03898954018950462,
-0.0676950216293335,
0.05314677953720093,
0.035401564091444016,
-0.013218647800385952,
0.018932851031422615,
0.022116567939519882,
-0.027145640924572945,
-0.013825364410877228,
0.006006235256791115,
0.0022240635007619858,
-0.03027365729212761,
0.015227343887090683,
0.0175133366137743,
-0.011722159571945667,
0.032717056572437286,
-0.029669135808944702,
-0.05169828608632088,
0.016387028619647026,
-0.05553305149078369,
-0.04665312543511391,
0.06500089913606644,
-0.026179403066635132,
0.028924493119120598,
0.021335244178771973,
-0.026339013129472733,
-0.02720000594854355,
0.10090585052967072,
0.005557331722229719,
-0.007357866503298283,
0.0170834269374609,
0.013118093833327293,
-0.012236617505550385,
0.015673499554395676,
0.017343485727906227,
-0.03543317690491676,
-0.02114618383347988,
0.04597979038953781,
0.016218703240156174,
-0.03874192014336586,
0.037326931953430176,
-0.047955602407455444,
-0.030885115265846252,
-0.041907597333192825,
0.0018416019156575203,
-0.010453815571963787,
0.04654838517308235,
0.04586593434214592,
-0.05475688725709915,
0.021415138617157936,
0.0011978978291153908,
0.008984302170574665,
-0.08820325136184692,
0.019382324069738388,
-0.023849977180361748,
0.019463155418634415,
0.013728409074246883,
-0.03982924297451973,
0.0014892186736688018,
0.02295621484518051,
-0.059616729617118835,
0.03626515716314316,
-0.0000824346425361,
-0.024542830884456635,
-0.03287110477685928,
0.01309474278241396,
-0.002810821635648608,
0.04341281205415726,
0.06638412922620773,
0.041640810668468475,
-0.000009482824680162594,
0.04223145171999931,
0.0026859610807150602,
-0.059220507740974426,
-0.010392584837973118,
0.05468815192580223,
-0.017471708357334137,
0.014501801691949368,
0.06892823427915573,
-0.0073053776286542416,
-0.022609516978263855,
0.04604930430650711,
0.021367304027080536,
0.05980048328638077,
-0.012841934338212013,
0.027523227035999298,
0.0030995241831988096,
0.030520351603627205,
-0.0006092570256441832,
-0.04234064370393753,
0.008001438342034817,
0.03175804391503334,
-0.0057297442108392715,
0.020832082256674767,
-0.04652377590537071,
-0.0025170091539621353,
0.02403266914188862,
-0.0315130241215229,
-0.017584925517439842,
0.019031859934329987,
0.00750328041613102,
0.00039878010284155607,
0.013394832611083984,
0.003162964014336467,
0.014844591729342937,
-0.03838669881224632,
0.0022592907771468163,
-0.05003872513771057,
-0.01813615672290325,
-0.0039004224818199873,
-0.020814789459109306,
-0.03662533685564995,
0.014396854676306248,
-0.03259816765785217,
-0.008999074809253216,
-0.005943655967712402,
-0.008226821199059486,
-0.015392592176795006,
-0.02671503648161888,
-0.02793130837380886,
-0.002565938513725996,
0.020457539707422256,
0.00012998301826883107,
-0.043425045907497406,
-0.01815509982407093,
0.053199611604213715,
0.035645030438899994,
0.010388791561126709,
-0.004011540208011866,
0.0009214692981913686,
-0.0049589634872972965,
-0.08691579848527908,
0.011273928917944431,
-0.0031614205799996853,
0.01029669027775526,
-0.05351438373327255,
-0.02059379778802395,
0.003176705213263631,
0.0244931410998106,
0.04008716344833374,
-0.01150146871805191,
-0.009249105118215084,
0.029167501255869865,
-0.008235554210841656,
-0.0012341757537797093,
-0.08225777745246887,
0.015277460217475891,
-0.010754226706922054,
-0.036455266177654266,
-0.0011488376185297966,
-0.0337257944047451,
-0.024056022986769676,
-0.024281837046146393,
0.03450176864862442,
-0.017276274040341377,
0.027812762185931206,
0.0158368032425642,
-0.037387747317552567,
0.07264439761638641,
0.04527577757835388,
-0.005073565058410168,
0.04257943481206894,
0.021618200466036797,
0.034442611038684845,
0.053191717714071274,
-0.003621245501562953,
-0.03315597400069237,
0.037911366671323776,
0.005373845342546701,
0.020665975287556648,
0.0000011407670399421477,
-0.03365296870470047,
-0.022893190383911133,
-0.018437549471855164,
0.013330193236470222,
0.06440514326095581,
-0.00923872273415327,
-0.0028845623601228,
0.059089433401823044,
0.02830728329718113,
0.028573617339134216,
-0.013745005242526531,
0.0030822083353996277,
0.02849005162715912,
0.006915193982422352,
-0.012086690403521061,
0.02959909662604332,
0.018751224502921104,
-0.00800294242799282,
0.047343917191028595,
0.007107213139533997,
0.007214716169983149,
0.01647675782442093,
0.03478113189339638,
0.019768791273236275,
-0.059132661670446396,
-0.0002103685401380062,
0.006446084938943386,
-0.03144238889217377,
0.027606625109910965,
0.038322653621435165,
-0.02171744592487812,
0.06986971944570541,
-0.026629680767655373,
-0.015972785651683807,
-0.0028445087373256683,
-0.017521068453788757,
-0.03069467842578888,
0.019653737545013428,
0.02658172696828842,
0.050713177770376205,
-0.01757667027413845,
-0.004362920299172401,
-0.02348869852721691,
0.001123787835240364,
0.03803602233529091,
-0.03579171746969223,
0.0197165384888649,
-0.0032412162981927395,
-0.017898980528116226,
0.0018599547911435366,
0.004065636545419693,
-0.016654642298817635,
-0.015689317137002945,
0.01784258335828781,
0.025265134871006012,
0.020321529358625412,
-0.01844385825097561,
0.0008505641599185765,
-0.004888670053333044,
0.06036517769098282,
-0.06560786068439484,
-0.022032499313354492,
-0.03301845118403435,
0.014821160584688187,
-0.031659822911024094,
-0.01495277974754572
] |
<p>What is a good way to block neutrons and what is the mechanism that allows this? It's my understanding that polyethylene is somewhat effective. Why?</p>
| 8,453 |
[
-0.02726651169359684,
-0.03359227254986763,
-0.007335921283811331,
-0.05576416105031967,
0.00553370313718915,
0.02377820760011673,
0.008539391681551933,
-0.05059533193707466,
-0.011334139853715897,
-0.06277981400489807,
0.08639439195394516,
0.029810506850481033,
0.01603643409907818,
-0.012810783460736275,
0.006099926307797432,
-0.015389401465654373,
-0.004816759377717972,
-0.03454449400305748,
0.009311865083873272,
-0.05719700828194618,
-0.007333261892199516,
-0.03491458669304848,
-0.04154432937502861,
0.009624057449400425,
-0.019773082807660103,
0.03887329623103142,
0.03243211284279823,
0.024904396384954453,
0.0379241518676281,
0.031757112592458725,
0.032082363963127136,
-0.026732996106147766,
0.0351082868874073,
-0.00490157026797533,
0.0020033009350299835,
-0.019858572632074356,
-0.0334249772131443,
-0.015837593004107475,
-0.02498757280409336,
0.030135463923215866,
-0.03141270950436592,
-0.020871009677648544,
0.0008414908079430461,
0.008117512799799442,
-0.03454847261309624,
0.00268300692550838,
0.014666286297142506,
-0.018397366628050804,
0.058622606098651886,
-0.051776137202978134,
0.023597510531544685,
0.004190562758594751,
0.036954741925001144,
0.043414756655693054,
0.006449652370065451,
0.0020609982311725616,
0.09104892611503601,
0.07096850126981735,
-0.033116940408945084,
-0.024800943210721016,
-0.021442584693431854,
-0.006824027746915817,
-0.028200723230838776,
-0.006816502194851637,
-0.0038136187940835953,
0.03281577676534653,
-0.01895676553249359,
-0.02671237476170063,
0.012991301715373993,
-0.0090321721509099,
0.013973201625049114,
-0.010041460394859314,
0.020862819626927376,
0.022032398730516434,
0.004541055765002966,
-0.031974125653505325,
0.021818242967128754,
0.006064350716769695,
0.0653790608048439,
0.03605666756629944,
-0.010362998582422733,
-0.010735954158008099,
0.007327762432396412,
0.028814908117055893,
-0.00774234626442194,
-0.007332155015319586,
0.08383922278881073,
0.014397812075912952,
-0.00802656915038824,
0.04000260308384895,
-0.006277356296777725,
-0.013196787796914577,
0.06673797219991684,
0.008508478291332722,
-0.012328012846410275,
0.019738344475626945,
-0.00928802601993084,
0.06388450413942337,
0.03474295511841774,
0.01277694758027792,
0.011858874931931496,
0.015051673166453838,
0.034070856869220734,
0.10009703040122986,
0.04378720745444298,
-0.04272584244608879,
-0.05138181149959564,
0.020165039226412773,
0.008595459163188934,
0.0034343835432082415,
-0.020922040566802025,
0.009528391994535923,
-0.008856496773660183,
-0.0056776683777570724,
0.027788275852799416,
-0.02038370445370674,
-0.0032064386177808046,
-0.019253527745604515,
0.035025328397750854,
0.07646387070417404,
0.021854659542441368,
0.011294804513454437,
0.024391932412981987,
-0.04516012221574783,
-0.07170901447534561,
-0.024053368717432022,
0.0310744047164917,
-0.005234489683061838,
-0.04792003706097603,
0.02222839929163456,
0.023494556546211243,
-0.03718521445989609,
0.0475618802011013,
-0.025407355278730392,
0.06791288405656815,
0.008348846808075905,
-0.13430777192115784,
-0.07851135730743408,
0.054396890103816986,
0.0026705670170485973,
-0.045044515281915665,
-0.07230014353990555,
-0.0372774600982666,
-0.0006644288077950478,
0.0819256454706192,
-0.00599371874704957,
-0.03548756241798401,
0.0017484838608652353,
0.017426760867238045,
0.0018670071149244905,
-0.012275892309844494,
-0.02567368745803833,
0.01774781569838524,
-0.0007598492666147649,
-0.00025934178847819567,
-0.053341638296842575,
0.04321160912513733,
0.008629468269646168,
-0.006581908091902733,
-0.03262336179614067,
0.05830097571015358,
-0.05449914559721947,
0.0183815136551857,
-0.020912431180477142,
-0.048853661864995956,
-0.04883181303739548,
0.07382667809724808,
0.02667715959250927,
0.019223829731345177,
0.03395099937915802,
0.014398450031876564,
0.0578039325773716,
0.023447193205356598,
0.03473256528377533,
0.011635797098279,
-0.048064589500427246,
0.014490320347249508,
-0.043316252529621124,
0.0009353178320452571,
0.004274039063602686,
-0.06073814630508423,
0.00717084901407361,
0.021061234176158905,
0.013533171266317368,
0.004957482684403658,
0.028229612857103348,
0.0017125034937635064,
-0.007140681147575378,
0.021561764180660248,
-0.028192805126309395,
-0.02756628766655922,
-0.0755244717001915,
0.021016910672187805,
-0.0246427021920681,
-0.011732710525393486,
0.010978762060403824,
-0.00021248032862786204,
-0.003436935832723975,
-0.049450308084487915,
-0.02728455327451229,
-0.03697246313095093,
0.04729587212204933,
0.04422936961054802,
0.012764399871230125,
-0.001414007507264614,
0.007974574342370033,
0.026855437085032463,
-0.003258064156398177,
0.030371254310011864,
0.0016993734752759337,
0.009470922872424126,
-0.027898797765374184,
-0.045351944863796234,
0.005320058204233646,
-0.014137384481728077,
-0.05210408195853233,
0.016487495973706245,
-0.004369870759546757,
0.019220219925045967,
0.05206083878874779,
-0.0298300813883543,
0.12844198942184448,
-0.0015637308824807405,
0.004463765304535627,
-0.024428296834230423,
0.009545747190713882,
0.006199384108185768,
0.008868014439940453,
-0.0003111190162599087,
-0.050891149789094925,
-0.04416157305240631,
-0.006628955248743296,
0.029426708817481995,
0.006100637372583151,
-0.06751450151205063,
0.05223504826426506,
-0.030809683725237846,
0.022867927327752113,
0.021015314385294914,
0.031138665974140167,
-0.039843276143074036,
-0.009517865255475044,
0.031604595482349396,
0.011795112863183022,
-0.025598956272006035,
0.031577348709106445,
0.012036530300974846,
0.012685807421803474,
-0.0012816712260246277,
-0.029002700001001358,
-0.01950824446976185,
0.003262888640165329,
0.012928249314427376,
-0.0060899704694747925,
-0.007863164879381657,
-0.07252812385559082,
0.011634152382612228,
-0.009832768701016903,
-0.0016362364403903484,
-0.01308487355709076,
0.004995472263544798,
0.011264802888035774,
-0.03593924641609192,
-0.027330607175827026,
0.03339992091059685,
0.008992111310362816,
-0.03543214499950409,
0.007192809134721756,
0.03967500105500221,
-0.033346980810165405,
0.0006232949672266841,
-0.007511019241064787,
0.002833839738741517,
-0.0020251115784049034,
0.0054355948232114315,
0.030799780040979385,
-0.010817483067512512,
0.0446321927011013,
-0.043194010853767395,
-0.037045031785964966,
-0.011426783166825771,
-0.0323030911386013,
-0.01363504771143198,
0.0002622309257276356,
-0.03158128261566162,
0.015693502500653267,
-0.046356286853551865,
-0.002745679346844554,
0.024710822850465775,
-0.00418416503816843,
-0.0032582839485257864,
0.012155711650848389,
-0.0038079177029430866,
-0.03939708322286606,
-0.012730693444609642,
0.0037875892594456673,
0.0026785454247146845,
-0.02282271534204483,
-0.008685853332281113,
0.07244817167520523,
0.0112694650888443,
-0.014832104556262493,
0.0064612869173288345,
-0.06389698386192322,
-0.028863858431577682,
-0.0059445444494485855,
-0.0060384152457118034,
0.013254893012344837,
-0.0031488945242017508,
-0.0006048143259249628,
0.03351975232362747,
-0.05894404649734497,
0.03795793280005455,
-0.03192487731575966,
-0.024728145450353622,
0.008603307418525219,
-0.007922238670289516,
0.02558954246342182,
-0.007713416125625372,
-0.01676664873957634,
0.07527236640453339,
0.034365277737379074,
-0.015620210207998753,
-0.0040815225802361965,
-0.03628339245915413,
-0.04192302003502846,
-0.047126755118370056,
0.03649526834487915,
0.053482044488191605,
0.026531653478741646,
-0.0038828847464174032,
-0.0036106964107602835,
0.007739253342151642,
0.03727493807673454,
0.02110196463763714,
-0.02148929424583912,
-0.01743382215499878,
0.012568091973662376,
-0.016634082421660423,
0.030092526227235794,
0.019967474043369293,
-0.042710836976766586,
-0.011722470633685589,
0.027883650735020638,
0.03000267967581749,
-0.00690072774887085,
-0.027984807267785072,
0.03642427176237106,
0.0027205566875636578,
0.01555437408387661,
-0.02543916366994381,
0.04537924379110336,
-0.0163009874522686,
0.009599462151527405,
0.037396714091300964,
0.014881378971040249,
0.013744373805820942,
-0.005581285338848829,
0.036690711975097656,
0.018413787707686424,
0.10106512159109116,
-0.017476221546530724,
-0.01005055382847786,
-0.0076709953136742115,
-0.010305441915988922,
0.01011160109192133,
0.01471269503235817,
0.037455007433891296,
0.010899784043431282,
0.01656259596347809,
0.028254209086298943,
0.02812824584543705,
-0.0021644379012286663,
-0.006623202934861183,
-0.099173903465271,
0.003967341035604477,
-0.019143477082252502,
0.06490673869848251,
0.00017987083992920816,
0.02458231709897518,
0.026545774191617966,
0.0058670248836278915,
-0.007547407411038876,
-0.02152169868350029,
-0.039231136441230774,
0.03880922123789787,
-0.05139320343732834,
0.00014812609879299998,
-0.016262011602520943,
-0.004075905308127403,
-0.05575284734368324,
-0.006187955383211374,
-0.026445947587490082,
-0.001336778630502522,
0.028150586411356926,
-0.022112039849162102,
0.010804295539855957,
-0.029565755277872086,
-0.034096188843250275,
0.00424971291795373,
0.03221633657813072,
0.02635621465742588,
0.004808645695447922,
-0.008402617648243904,
0.006694221403449774,
-0.06681573390960693,
0.02092652954161167,
-0.0007763308240100741,
0.02983931452035904,
-0.005985404830425978,
0.039610810577869415,
0.015600833110511303,
0.015058865770697594,
0.017437834292650223,
-0.04377724602818489,
0.019407575950026512,
0.030652659013867378,
0.0009314825292676687,
-0.002092876471579075,
-0.011806180700659752,
-0.05141296237707138,
-0.027241164818406105,
-0.0003371942730154842,
0.0051457686349749565,
-0.048284322023391724,
0.028460098430514336,
0.016455385833978653,
-0.001815427211113274,
-0.057954929769039154,
0.00793285109102726,
0.08925621211528778,
0.02930270880460739,
-0.043179236352443695,
-0.043868083506822586,
-0.03478832542896271,
-0.006016677711158991,
0.02288171276450157,
0.013415682129561901,
0.006553552579134703,
-0.0015692145098000765,
0.015710359439253807,
0.04171646013855934,
-0.013624998740851879,
-0.02164345420897007,
0.010229116305708885,
0.002307683462277055,
-0.0029090032912790775,
-0.005999760702252388,
0.0016465283697471023,
0.027691179886460304,
0.023225657641887665,
0.0526510626077652,
0.005621824413537979,
0.0036930625792592764,
-0.050672709941864014,
0.007550119888037443,
0.047719910740852356,
0.03989029675722122,
-0.01842516101896763,
-0.009250035509467125,
-0.06118956580758095,
-0.010226575657725334,
0.04405660182237625,
-0.01602570340037346,
0.02071436122059822,
-0.04991880804300308,
-0.016352375969290733,
-0.034681692719459534,
-0.0012724347179755569,
-0.011399758979678154,
0.005640271119773388,
-0.0060872226022183895,
0.013405841775238514,
-0.02390432171523571,
-0.01713603548705578,
-0.03552794083952904,
0.042515743523836136,
0.018387751653790474,
0.023042889311909676,
0.007460332475602627,
0.014420618303120136,
0.024798082187771797,
0.027510005980730057,
-0.03111766278743744,
-0.07479958981275558,
0.011681118980050087,
0.01084801647812128,
-0.025235379114747047,
0.021427063271403313,
-0.03951222449541092,
-0.04445485398173332,
0.02403832972049713,
-0.010966631583869457,
-0.01642427407205105,
-0.044337138533592224,
-0.05241970345377922,
0.03650031238794327,
0.0444258376955986,
0.006293769460171461,
0.05308641120791435,
0.07837077230215073,
-0.024724995717406273,
0.008453329093754292,
-0.04439977556467056,
0.056882698088884354,
-0.01505875214934349,
0.021546587347984314,
-0.003836360527202487,
0.01826305314898491,
-0.021285956725478172,
-0.0048219733871519566,
-0.010688086040318012,
0.02105429396033287,
0.045469947159290314,
-0.049324095249176025,
-0.00020367238903418183,
0.019040482118725777,
0.0005300852353684604,
-0.024964608252048492,
0.0012399816187098622,
0.019832218065857887,
0.003366282442584634,
-0.029584959149360657,
0.03929742053151131,
0.016574976965785027,
-0.01174150686711073,
0.013553595170378685,
-0.022421734407544136,
-0.005104789976030588,
-0.041361160576343536,
-0.01987851969897747,
0.0023374094162136316,
-0.02061828412115574,
0.06347949057817459,
-0.015966664999723434,
-0.025491656735539436,
0.027279041707515717,
-0.07778744399547577,
-0.01447219867259264,
0.020823292434215546,
-0.03338675945997238,
0.029113532975316048,
-0.030788278207182884,
0.057640861719846725,
-0.017961975187063217,
0.0206459891051054,
-0.060387641191482544,
-0.06217734143137932,
0.04242429882287979,
0.0023593672085553408,
0.002175279427319765,
-0.0697934478521347,
-0.009988992474973202,
-0.001731831580400467,
-0.03275785222649574,
0.003420017659664154,
0.0176085252314806,
-0.038945410400629044,
-0.0029719844460487366,
0.016176827251911163,
0.026989690959453583,
0.04354451224207878,
-0.026860114187002182,
-0.05092311650514603,
0.02079988457262516,
-0.053713083267211914,
0.007268534507602453,
0.0009860366117209196,
0.027724018320441246,
-0.024957962334156036,
-0.007386702578514814,
0.0006618956685997546,
0.017586102709174156,
0.032127972692251205,
-0.010432898998260498,
0.051945414394140244,
0.052550315856933594,
0.011879167519509792,
-0.039168182760477066,
-0.03266461566090584,
0.006284728646278381,
-0.0017354724695906043,
0.05372892692685127,
0.0020532156340777874,
0.01422484777867794,
-0.035201139748096466,
-0.0538138709962368,
0.0588771253824234,
-0.002158444607630372,
-0.0146761704236269,
-0.027018079534173012,
0.03963013365864754,
-0.014973214827477932,
0.014869306236505508,
-0.011839739046990871,
-0.04225029796361923,
0.04036754369735718,
-0.012341097928583622,
0.01593279093503952,
0.0404592789709568,
-0.027733055874705315,
-0.013227798976004124,
-0.08324236422777176,
-0.0213761143386364,
0.004396489821374416,
0.017135176807641983,
-0.07875154167413712,
0.06728633493185043,
0.026517897844314575,
-0.016851969063282013,
-0.0137917036190629,
0.0016765811014920473,
-0.02921733818948269,
-0.012211708351969719,
-0.013113685883581638,
0.03829794004559517,
-0.004458315204828978,
0.013325979933142662,
0.012182989157736301,
0.04140102490782738,
0.005469765048474073,
0.03415733203291893,
0.04662105813622475,
0.01942644827067852,
0.050486329942941666,
-0.00932873971760273,
-0.0117316460236907,
0.027175631374120712,
-0.07164106518030167,
0.023763110861182213,
-0.010461398400366306,
-0.03494064509868622,
0.02856490947306156,
-0.03085293620824814,
0.045886535197496414,
-0.048236455768346786,
-0.02549907937645912,
-0.014029568992555141,
-0.005790310446172953,
0.016444485634565353,
-0.018167151138186455,
0.00041265549953095615,
0.008083436638116837,
0.03176697716116905,
0.015052554197609425,
0.028096910566091537,
-0.005116666201502085,
-0.08357241004705429,
-0.026054294779896736,
-0.002865781309083104,
-0.03076079487800598,
0.005922695621848106,
0.02511977031826973,
-0.05278816446661949,
0.02028222568333149,
-0.013362068682909012,
0.011701084673404694,
-0.0025938916951417923,
0.014478216879069805,
-0.004983557388186455,
0.00995146855711937,
-0.007565027102828026,
0.011770936660468578,
0.018256042152643204,
-0.012221288867294788,
0.10550083220005035,
0.026777615770697594,
0.003954142332077026,
-0.09685637801885605,
-0.027396827936172485,
0.017698338255286217,
0.021781854331493378,
-0.028714273124933243,
0.01655733771622181,
0.0011028703302145004,
0.035515397787094116,
-0.001594890607520938,
0.03561517596244812,
0.017996713519096375,
0.0330691933631897,
0.06070849299430847,
-0.07249126583337784,
-0.007283237297087908,
0.026508675888180733,
-0.025666000321507454,
-0.0034394701942801476,
-0.00199296441860497,
-0.03984178602695465,
0.039496734738349915,
-0.016009286046028137,
-0.03093864582479,
-0.02474001608788967,
-0.024879829958081245,
0.04600029066205025,
0.0374787263572216,
-0.004072539508342743,
-0.012213187292218208,
-0.005741685628890991,
0.005836918018758297,
0.002511173253878951,
0.0052210320718586445,
0.020065344870090485,
0.003391392296180129,
0.013210957869887352,
-0.02016034722328186,
0.03375657647848129,
0.016711991280317307,
-0.003760262858122587,
0.009979676455259323,
-0.033765628933906555,
-0.023903019726276398,
0.0008804627577774227,
0.018271582201123238,
-0.013373562134802341,
-0.002697681775316596,
0.017890114337205887,
0.004966984502971172,
0.024550452828407288,
0.0011448164004832506,
-0.02747214585542679,
-0.022515475749969482,
0.0038833944126963615,
-0.016869349405169487,
-0.02534552291035652,
0.001994118094444275,
0.03992430865764618,
-0.05302342027425766,
0.03295498341321945,
-0.01599276438355446,
-0.003768076654523611,
0.013951444998383522,
-0.012553539127111435,
-0.01295797061175108,
-0.013477533124387264,
-0.01738934963941574,
-0.04697853699326515,
0.0070180767215788364,
-0.0007087460835464299,
-0.00978348683565855,
0.014425573870539665,
0.02508021518588066,
0.033329322934150696,
-0.0058497595600783825,
0.012107900343835354,
0.007601186633110046,
-0.03667990863323212,
0.0706334039568901,
-0.042762428522109985,
0.007700726389884949,
-0.022562239319086075,
-0.025964809581637383,
0.0010447532404214144,
0.028666730970144272,
-0.0190585907548666,
-0.004027269314974546,
-0.016708988696336746,
-0.00852970965206623,
0.05127306282520294,
-0.009936286136507988,
-0.029478374868631363,
0.015358858741819859,
-0.010878827422857285,
0.04214497655630112,
-0.017743118107318878,
0.06736177951097488,
0.024366052821278572,
0.0038384879007935524,
0.042795706540346146,
0.006021698471158743,
-0.043138034641742706,
-0.02357463911175728,
-0.021262995898723602,
-0.043352656066417694,
-0.038448844105005264,
-0.0259792972356081,
-0.004788651131093502,
-0.0169209036976099,
-0.033561915159225464,
-0.005857763346284628,
-0.02330901101231575,
0.03390152007341385,
0.05338723957538605,
0.009519779123365879,
0.021721387282013893,
-0.046292614191770554,
0.0005273062852211297,
-0.02078731544315815,
0.008266457356512547,
-0.04377186670899391,
-0.007682436145842075,
0.028701063245534897,
0.019512580707669258,
-0.02201135829091072,
0.022507723420858383,
0.042910389602184296,
0.007414709310978651,
0.03248438611626625,
0.010693893767893314,
0.0005085628945380449,
0.03526650741696358,
0.04170987382531166,
0.030601564794778824,
0.0768982395529747,
-0.0012016124092042446,
0.006574271712452173,
0.05417678505182266,
-0.045238565653562546,
-0.06760682910680771,
0.004157364368438721,
-0.028198793530464172,
-0.0008661607280373573,
0.00379646266810596,
0.0038507969584316015,
0.013281013816595078,
0.07324697822332382,
-0.0273608211427927,
-0.03300171718001366,
0.002964808139950037,
-0.002264109207317233,
0.01531673688441515,
-0.0007659191032871604,
-0.008000410161912441,
-0.04516506567597389,
-0.012343272566795349,
0.032630037516355515,
-0.009775897487998009,
0.01756904274225235,
0.011276299133896828,
-0.03977381810545921,
0.0035310329403728247,
0.02043558657169342,
-0.001198028796352446,
0.03260673210024834,
-0.014577096328139305,
0.02565217949450016,
-0.01677856221795082,
0.05171128362417221,
0.01433672197163105,
-0.027323082089424133,
-0.08039993792772293,
0.006014948710799217,
-0.02460562065243721,
-0.02844131365418434,
0.018110226839780807,
-0.03592812642455101,
0.03553549200296402,
0.04227050393819809,
-0.07878798246383667,
0.01144402101635933,
-0.030621927231550217,
-0.04353056475520134,
-0.06490566581487656,
0.0005496505764313042,
-0.008741294965147972,
0.01737544685602188,
0.010558612644672394,
0.05468524992465973,
0.029673485085368156,
0.00023096243967302144,
-0.014257715083658695,
-0.00029364030342549086,
0.01012619212269783,
0.00787442084401846,
0.022033505141735077,
-0.02256118319928646,
0.03773874044418335,
-0.0053094313479959965,
-0.0012031588703393936,
0.005462096072733402,
-0.021028222516179085,
0.019452573731541634,
-0.015951190143823624,
0.033470820635557175,
0.008707902394235134,
0.029730308800935745,
0.00727333826944232,
-0.010484079830348492,
-0.016529636457562447,
0.013270478695631027,
0.012668013572692871,
0.026974262669682503,
0.0066900611855089664,
0.027541954070329666,
-0.005716848187148571,
-0.007328208070248365,
-0.010076712816953659,
0.015025234781205654,
0.017129570245742798,
-0.04359356313943863,
0.00922112911939621,
0.03487802669405937,
0.0669817253947258,
-0.018098054453730583,
-0.018404439091682434,
-0.04509202018380165,
-0.020498281344771385,
0.01751268468797207,
-0.0011866595596075058,
0.007143567781895399,
0.052100397646427155,
-0.03397204354405403,
0.0031776265241205692,
-0.020711394026875496,
0.03310701251029968,
-0.03357698768377304,
-0.008250094018876553,
0.01549174077808857,
0.042826905846595764,
0.03167654201388359,
-0.012638368643820286,
-0.03409840911626816,
-0.016670599579811096,
0.047082215547561646,
0.03298470377922058,
0.017309565097093582,
-0.005699585657566786,
-0.030260849744081497,
-0.010229459032416344,
-0.03477034717798233,
0.05324826389551163,
-0.023829469457268715,
0.008342623710632324,
-0.02692813239991665,
-0.04266158863902092,
-0.0037830902729183435,
0.0379776693880558,
0.06878656148910522,
0.012725189328193665,
-0.018298910930752754,
-0.017158709466457367,
0.01813580095767975,
0.009617230854928493,
-0.029794374480843544,
0.020087335258722305,
0.02298729680478573,
-0.042225055396556854,
-0.032497286796569824,
-0.005727673880755901,
-0.008463417179882526,
0.04289776831865311,
0.013717721216380596,
0.031445764005184174,
-0.0033815428614616394,
-0.011409095488488674,
-0.003217273624613881,
0.038248274475336075,
0.012023772113025188,
-0.003427737159654498,
0.032610487192869186,
-0.03351874649524689,
0.00315716746263206,
0.011358670890331268,
0.003938981797546148,
-0.06113873049616814,
0.033398572355508804,
-0.01474324893206358,
-0.0046666571870446205,
-0.0024469122290611267,
-0.0031885195057839155,
0.018494896590709686,
-0.04770757630467415,
0.03399873524904251,
0.04294312745332718,
-0.03344878554344177,
-0.0003261330130044371,
0.03609561175107956,
0.030751194804906845,
0.0147517379373312,
0.009881054051220417,
0.0404522679746151,
0.02236410789191723,
0.034782540053129196,
-0.028942525386810303,
0.05345738306641579,
0.03586843982338905,
-0.021375298500061035,
0.00973071251064539,
0.01927901990711689,
0.01058103982359171,
0.014298195019364357,
-0.004761234391480684,
0.041436150670051575,
-0.006018910091370344,
-0.027922147884964943,
-0.0019244813593104482,
-0.028673671185970306,
-0.02195516601204872,
0.01959257759153843,
-0.0073402393609285355,
0.0773032084107399,
-0.02484905533492565,
0.03863229602575302,
0.012518673203885555,
-0.015013307332992554,
-0.005577856674790382,
-0.015705808997154236,
0.031221214681863785,
0.025287142023444176,
-0.011377974413335323,
-0.022657938301563263,
-0.00457502668723464,
-0.005761453416198492,
0.02751735784113407,
-0.01733345165848732,
0.03455314412713051,
-0.0057707191444933414,
-0.02009282261133194,
-0.03261670097708702,
-0.040803711861371994,
-0.006476543378084898,
-0.0412769541144371,
0.026456395164132118,
0.033584706485271454,
0.005730251781642437,
0.035813331604003906,
-0.025681370869278908,
-0.013871386647224426,
0.06267040967941284,
-0.035855527967214584,
0.029400307685136795,
-0.023057276383042336,
0.0068462565541267395,
-0.059207603335380554,
0.034128282219171524
] |
<p>Assume that we have access to a computer with unlimited computing power.</p>
<p>As with the Lattice QCD can try to prove that we live in a simulated universe?</p>
<p>Apparently, one may use the issue of cosmic rays.</p>
<p><a href="http://www.wired.co.uk/news/archive/2012-10/11/universe-computer-simulation" rel="nofollow">Here is full article</a></p>
<p>Quote:</p>
<blockquote>
<p>If we were living in a simulator, we'd expect to find evidence of that lattice if we looked close enough to the edges of the observable universe - and that's what Silas Beane from the University of Bonn and colleagues have calculated, in a paper published in arXiv. As cosmic particles fly through the universe, they lose energy and change direction and spread out across a spectrum of energy values. There's a known limit is how much energy Those particles have, though, and Beane and his colleagues have calculated That this seemingly arbitrary cliff in the spectrum is consistent with the kind of boundary that you ''d find if there was an underlying lattice governing the limits of a simulator. It should also, if present, scatter the particles in a Certain Way as they come up against it, and the should be able it investigate Whether that's the case.</p>
</blockquote>
<p>Do you have any idea?</p>
| 8,454 |
[
-0.013628431595861912,
-0.03766420856118202,
0.011273575946688652,
-0.06527173519134521,
0.05507206544280052,
0.04146495461463928,
-0.0142626091837883,
-0.016738787293434143,
0.002287012292072177,
-0.023467672988772392,
0.02833031304180622,
0.032402243465185165,
0.03614113852381706,
0.038994040340185165,
0.004247076343744993,
0.017505137249827385,
-0.018868284299969673,
0.014321080408990383,
-0.023484639823436737,
-0.04294324293732643,
0.04645953327417374,
0.013377413153648376,
-0.011477396823465824,
0.001198037527501583,
-0.034938398748636246,
0.002223628107458353,
0.01567617803812027,
-0.003597848117351532,
-0.0049631246365606785,
0.0513218492269516,
-0.014924745075404644,
-0.027332808822393417,
0.040999770164489746,
0.025311578065156937,
0.03468664363026619,
-0.017856592312455177,
-0.025338586419820786,
-0.032024212181568146,
0.011854053474962711,
-0.025372888892889023,
-0.02980605512857437,
-0.010709763504564762,
-0.000044087108108215034,
0.0722726434469223,
-0.011200591921806335,
0.0011840115766972303,
-0.012354405596852303,
0.004843905568122864,
0.07465361803770065,
-0.0224295761436224,
0.03578576445579529,
-0.004640662577003241,
0.04774051159620285,
0.013925186358392239,
0.01871895045042038,
-0.04708293452858925,
0.061172645539045334,
0.04873190447688103,
0.006148214917629957,
-0.02393232472240925,
-0.0066841477528214455,
0.01268219668418169,
0.028473088517785072,
0.0003215682809241116,
-0.0015464404132217169,
0.020400669425725937,
0.01113864965736866,
-0.03897697106003761,
-0.024907955899834633,
0.008816182613372803,
0.0001774091215338558,
0.019925929605960846,
0.011852833442389965,
0.014662480913102627,
0.05444226786494255,
0.014898478984832764,
0.028332294896245003,
0.01842941716313362,
0.01822149008512497,
0.020560551434755325,
-0.020657138898968697,
-0.01202013622969389,
0.02568993717432022,
0.030057275667786598,
0.018302151933312416,
0.020730070769786835,
0.07808719575405121,
-0.03947486728429794,
-0.027855873107910156,
0.04680627956986427,
-0.002732963301241398,
0.01838768646121025,
0.046565745025873184,
0.0007977745844982564,
-0.057523585855960846,
0.011022052727639675,
0.01192240510135889,
0.02648998610675335,
-0.015209856443107128,
-0.05582278221845627,
-0.0012225047685205936,
0.0012818806571885943,
-0.007468486204743385,
0.03883723169565201,
-0.005799706093966961,
0.012032944709062576,
-0.04897906631231308,
-0.0034898524172604084,
-0.03310034051537514,
-0.010649275034666061,
-0.07287751883268356,
0.003956109285354614,
0.01708798296749592,
0.0368821881711483,
0.0023710685782134533,
-0.021575968712568283,
0.004077462945133448,
-0.04450332373380661,
0.04363260790705681,
0.03290027752518654,
0.03908922150731087,
0.016709890216588974,
-0.0027563958428800106,
-0.04617870971560478,
-0.0761851817369461,
0.010103357024490833,
0.0279372725635767,
-0.029000498354434967,
-0.08537507057189941,
0.006350986659526825,
0.010871400125324726,
0.003873310750350356,
-0.005784235429018736,
-0.02129087969660759,
0.04519875347614288,
-0.027325117960572243,
-0.09050498157739639,
-0.04603077471256256,
0.053924769163131714,
0.024564925581216812,
-0.0015124062774702907,
-0.05418431758880615,
-0.02256389521062374,
0.0384577251970768,
0.06604806333780289,
-0.017778625711798668,
0.01446456741541624,
-0.012827063910663128,
0.0463203527033329,
0.007355869747698307,
-0.016085024923086166,
0.024658655747771263,
-0.032442450523376465,
-0.0002864788693841547,
0.01645946130156517,
-0.0751461312174797,
0.012209208682179451,
0.029794156551361084,
-0.027215804904699326,
-0.03354010358452797,
0.05717315524816513,
-0.004237123299390078,
0.00024114851839840412,
-0.02534441277384758,
-0.025699498131871223,
-0.037301599979400635,
0.09710761904716492,
0.025583017617464066,
0.020260928198695183,
0.010685411281883717,
-0.042884740978479385,
0.0032240538857877254,
0.004315826576203108,
-0.0013596480712294579,
0.06742793321609497,
-0.04508328065276146,
-0.021615659818053246,
-0.01378287747502327,
-0.010098181664943695,
-0.04618491604924202,
-0.06248778477311134,
0.005171447992324829,
0.04533161222934723,
0.0011723849456757307,
0.002797306515276432,
0.03630151227116585,
-0.00288595724850893,
-0.03261781856417656,
-0.0013092930894345045,
-0.016170170158147812,
-0.03468286618590355,
-0.058733344078063965,
-0.01104208454489708,
0.012061677873134613,
0.008081731386482716,
-0.0072721331380307674,
0.028067301958799362,
0.016748566180467606,
-0.03168024122714996,
-0.058354638516902924,
0.009782013483345509,
0.04013684764504433,
0.029361702501773834,
0.018585385754704475,
-0.004372566007077694,
0.0535753108561039,
0.010760036297142506,
-0.012668698094785213,
-0.003522853832691908,
0.009007545188069344,
-0.05654461309313774,
-0.004462224431335926,
-0.04752802848815918,
0.026135647669434547,
0.023701583966612816,
0.001529463566839695,
0.04463505372405052,
0.004044340457767248,
0.015133313834667206,
0.024002304300665855,
0.02277768775820732,
0.016419759020209312,
0.028927939012646675,
-0.0004386626824270934,
-0.024898992851376534,
0.016294697299599648,
-0.020121058449149132,
0.012287640012800694,
-0.023354439064860344,
-0.02323160693049431,
-0.086891308426857,
-0.0475626140832901,
0.054055456072092056,
0.014092816039919853,
-0.014203661121428013,
0.028580056503415108,
0.0355919748544693,
0.021301234140992165,
0.022855019196867943,
0.026885757222771645,
-0.032251786440610886,
0.0001036664325511083,
0.018673570826649666,
0.02842205949127674,
0.014153331518173218,
0.032551590353250504,
0.03198147937655449,
-0.020617684349417686,
-0.044161491096019745,
-0.02714385651051998,
-0.025744279846549034,
-0.009553758427500725,
0.014291767962276936,
-0.0068039963953197,
0.0014088134048506618,
-0.055475641041994095,
0.012216063216328621,
0.011909011751413345,
0.01725924387574196,
-0.011464038863778114,
-0.01237926073372364,
-0.03749992698431015,
-0.03580281138420105,
0.00754292868077755,
-0.013527891598641872,
0.03209533914923668,
-0.02802199311554432,
-0.008077261038124561,
0.05815295875072479,
-0.03222113102674484,
0.05403174087405205,
-0.0054872725158929825,
-0.017328554764389992,
-0.019381193444132805,
0.015627218410372734,
0.049380045384168625,
0.02818155474960804,
0.008929764851927757,
-0.05162239819765091,
-0.03737594559788704,
0.021973256021738052,
-0.01024424284696579,
0.009757855907082558,
0.04826521873474121,
-0.02399839088320732,
0.033231690526008606,
-0.0449243001639843,
-0.04524776712059975,
-0.01506076380610466,
-0.022837253287434578,
0.025557084009051323,
0.028963783755898476,
-0.005872362293303013,
-0.028328105807304382,
-0.0005719228065572679,
-0.018741199746727943,
-0.01255663763731718,
-0.022638242691755295,
0.024148238822817802,
0.02826181799173355,
0.036469701677560806,
-0.08639529347419739,
0.004526643548160791,
-0.018259631469845772,
-0.03600279241800308,
-0.03542092815041542,
0.00034894782584160566,
0.01853654719889164,
-0.03227195516228676,
0.0278957337141037,
0.028730660676956177,
-0.028273826465010643,
-0.001712146564386785,
-0.0744597464799881,
-0.06057300418615341,
0.001165654044598341,
-0.03186974674463272,
0.04998230189085007,
-0.021831566467881203,
-0.0005986316245980561,
0.10626304894685745,
0.02663554437458515,
0.0033229629043489695,
0.026577498763799667,
-0.026224372908473015,
-0.0043996889144182205,
-0.05121149495244026,
0.0027048636693507433,
0.0030477733816951513,
-0.00471539655700326,
0.01692686602473259,
-0.028370611369609833,
0.05773567780852318,
0.00006414727977244183,
-0.004666982218623161,
-0.0034199212677776814,
-0.012180212885141373,
-0.04634209722280502,
0.004986397922039032,
0.05030030757188797,
-0.01376199908554554,
-0.026225456967949867,
0.011103951372206211,
-0.016041360795497894,
0.03292710334062576,
0.026136185973882675,
-0.05095374956727028,
0.06338480114936829,
0.003534681163728237,
0.036058105528354645,
-0.0202775988727808,
0.02680084854364395,
0.012823772616684437,
-0.02492794767022133,
0.022470727562904358,
0.0544387623667717,
0.034344132989645004,
0.04863446578383446,
-0.004492918029427528,
-0.010780589655041695,
0.07013674080371857,
-0.025617094710469246,
-0.028803184628486633,
-0.03011060133576393,
0.002417918760329485,
0.0006467004423029721,
-0.00868797767907381,
-0.0217768382281065,
0.03751910850405693,
0.029674027115106583,
0.03580613434314728,
0.023330116644501686,
-0.036866698414087296,
-0.04275878518819809,
-0.042604848742485046,
0.004671564791351557,
-0.057130273431539536,
0.04737749695777893,
0.043436892330646515,
0.014306709170341492,
0.006265990901738405,
0.010598993860185146,
-0.004016382619738579,
-0.02034885622560978,
-0.11500544846057892,
-0.025292707607150078,
-0.00425313226878643,
0.013148953206837177,
-0.02655741572380066,
-0.025837840512394905,
-0.028770718723535538,
-0.0023859627544879913,
-0.0003044172772206366,
0.0200852919369936,
-0.019159400835633278,
-0.05161091312766075,
-0.0028942786157131195,
-0.05326557904481888,
-0.04023732617497444,
-0.006046635564416647,
0.002502832328900695,
0.07579388469457626,
-0.03460756316781044,
0.009153450839221478,
0.00005360382056096569,
-0.019318552687764168,
-0.0424080453813076,
0.023743730038404465,
0.04967451095581055,
0.01196132879704237,
0.042454127222299576,
0.020181195810437202,
0.01853329688310623,
-0.046374741941690445,
0.003983994945883751,
0.025746667757630348,
0.03962847590446472,
-0.0003205821558367461,
-0.011222634464502335,
-0.006561466958373785,
-0.01492492388933897,
-0.021715285256505013,
0.043911874294281006,
0.015822850167751312,
-0.005618472117930651,
0.03921838849782944,
0.05247361212968826,
0.031397782266139984,
-0.05858877673745155,
0.04505864530801773,
0.04457581043243408,
-0.005640466697514057,
-0.02179643139243126,
0.004556457977741957,
-0.042938780039548874,
-0.0064910585060715675,
-0.01816108264029026,
-0.015274862758815289,
-0.007427882868796587,
-0.00034861257881857455,
0.04994969442486763,
0.024053147062659264,
0.014046669006347656,
-0.04621157422661781,
0.02792566455900669,
-0.023443829268217087,
0.024050524458289146,
-0.03742552548646927,
0.020950067788362503,
-0.009426052682101727,
0.022579481825232506,
0.03090149350464344,
0.032659102231264114,
-0.01927880570292473,
-0.05187460407614708,
-0.026289058849215508,
0.03542828932404518,
0.03734883666038513,
0.050927188247442245,
-0.023802010342478752,
-0.03321513906121254,
-0.03869900852441788,
0.030467307195067406,
-0.030519340187311172,
0.027042653411626816,
-0.04434812441468239,
0.009210026822984219,
-0.027368098497390747,
-0.015559672378003597,
0.014051780104637146,
-0.015269498340785503,
-0.0014938322128728032,
-0.02117406763136387,
-0.0049628084525465965,
-0.002799865324050188,
-0.013266773894429207,
0.04346184432506561,
0.01236080564558506,
0.023201238363981247,
-0.03317485749721527,
0.05188824236392975,
-0.013478194363415241,
-0.015061043202877045,
-0.02097088098526001,
-0.059586502611637115,
0.03164205327630043,
0.007658026181161404,
-0.023477086797356606,
0.05143439397215843,
-0.00958830676972866,
-0.02251885086297989,
0.0019689968321472406,
-0.00508869020268321,
0.010961499065160751,
-0.012205812148749828,
-0.05457949638366699,
0.05500977486371994,
0.015165502205491066,
0.022023547440767288,
0.044290609657764435,
0.03495301678776741,
-0.013576199300587177,
0.0010299945715814829,
-0.002354440512135625,
0.02529645338654518,
-0.0041726017370820045,
0.030025796964764595,
-0.0041895355097949505,
-0.0290539413690567,
-0.013156244531273842,
-0.0063420673832297325,
0.009738911874592304,
0.013346832245588303,
0.0013173993211239576,
-0.05235281214118004,
-0.0257553830742836,
-0.002521362155675888,
0.004231660161167383,
0.016325879842042923,
-0.03429926186800003,
0.012527740560472012,
0.010417728684842587,
-0.0067289345897734165,
0.03169739991426468,
-0.01166268065571785,
-0.006862544920295477,
0.02794141322374344,
-0.018497902899980545,
0.010286180302500725,
-0.05717935040593147,
0.006703482009470463,
-0.023382579907774925,
-0.04400111362338066,
0.05689696967601776,
-0.0183488130569458,
0.011827435344457626,
0.018348878249526024,
-0.017704034224152565,
-0.005990944802761078,
0.025293851271271706,
-0.020473871380090714,
-0.02512420527637005,
0.013164574280381203,
0.016273392364382744,
0.0032571607735008,
0.055153317749500275,
-0.0818900465965271,
-0.018799474462866783,
0.006694425828754902,
0.013579092919826508,
-0.025775296613574028,
-0.038968056440353394,
-0.03506474941968918,
-0.027377795428037643,
-0.008065097033977509,
-0.0011552522191777825,
-0.007420759182423353,
-0.048858288675546646,
-0.016314400359988213,
0.02901231124997139,
-0.016074443235993385,
0.017887786030769348,
0.024736857041716576,
-0.028939368203282356,
0.015476594679057598,
0.014754937961697578,
0.004710772540420294,
-0.011496859602630138,
0.02299453318119049,
-0.015580876730382442,
-0.022947877645492554,
0.008265036158263683,
0.017577366903424263,
0.025147225707769394,
-0.043568894267082214,
-0.0007454244769178331,
0.06107795983552933,
-0.017567461356520653,
0.021032163873314857,
0.002143860561773181,
-0.010219448246061802,
-0.01373149175196886,
0.05675208196043968,
-0.008054372854530811,
-0.012860498391091824,
0.0028294420335441828,
-0.00223521632142365,
0.043615538626909256,
0.007801446132361889,
0.016020378097891808,
0.04061330482363701,
0.07280687242746353,
0.007260740734636784,
-0.04647587984800339,
0.003272636793553829,
-0.022869613021612167,
0.00635081110522151,
-0.031000584363937378,
0.025025496259331703,
0.01827981509268284,
0.021590448915958405,
-0.009605594910681248,
-0.058864399790763855,
-0.04748792573809624,
-0.00011613405513344333,
-0.008023223839700222,
-0.0019385499181225896,
0.03785054013133049,
-0.0012483259197324514,
-0.007389947772026062,
-0.04753918573260307,
-0.03233424946665764,
0.01954592764377594,
0.013898852281272411,
0.0008471779874525964,
0.03979413956403732,
-0.032243698835372925,
-0.03272715583443642,
0.03117039054632187,
0.029748965054750443,
-0.018146906048059464,
0.05883825570344925,
0.013169410638511181,
0.02265147678554058,
0.042894113808870316,
-0.052849359810352325,
-0.018157027661800385,
0.03672769293189049,
-0.1018894761800766,
0.030644789338111877,
0.018863387405872345,
-0.013992123305797577,
0.01796538755297661,
0.0012449775822460651,
0.004323888104408979,
-0.014036821201443672,
0.0323500819504261,
-0.0701490044593811,
0.02155478298664093,
0.015497962012887001,
0.05294671654701233,
0.006849371828138828,
-0.00022565311519429088,
0.020883135497570038,
-0.0073377820663154125,
-0.0013086197432130575,
0.010339111089706421,
-0.05784336104989052,
-0.03277244791388512,
-0.05366478115320206,
-0.018123475834727287,
0.05030353367328644,
0.030882706865668297,
-0.014571210369467735,
-0.00024931595544330776,
-0.04045341536402702,
0.02165575511753559,
0.0036493991501629353,
0.030660543590784073,
-0.018133502453565598,
0.04375729709863663,
-0.0200627651065588,
0.05785936862230301,
-0.0352078452706337,
0.023172475397586823,
0.1337536722421646,
0.05001194402575493,
-0.020490363240242004,
-0.04264478757977486,
0.0023123188875615597,
-0.018467063084244728,
0.044609200209379196,
-0.01405020710080862,
-0.016984645277261734,
0.00491882162168622,
0.015579950995743275,
-0.0007534812903031707,
0.05548455938696861,
0.004400661215186119,
-0.017029551789164543,
0.03346754238009453,
-0.06371285021305084,
-0.02331254445016384,
0.024325121194124222,
0.02889535017311573,
-0.006972497794777155,
0.00048109018825925887,
-0.036164045333862305,
0.018121076747775078,
-0.02498573251068592,
0.009223154745995998,
-0.02402927540242672,
0.008282418362796307,
-0.007263914216309786,
0.0037118252366781235,
-0.0751468762755394,
-0.009086597710847855,
0.012092981487512589,
-0.042365867644548416,
-0.006635086610913277,
-0.007117846980690956,
0.0012737299548462033,
0.005230825860053301,
0.019603893160820007,
0.04532148316502571,
0.0036530587822198868,
-0.006616313010454178,
-0.0055904267355799675,
0.009662255644798279,
-0.0022550770081579685,
-0.0432230606675148,
-0.022099953144788742,
0.05164361745119095,
-0.052972063422203064,
-0.048080895096063614,
0.02016427554190159,
0.01483292318880558,
-0.008050805889070034,
-0.04710942879319191,
0.003854428417980671,
-0.025055265054106712,
0.02137347124516964,
-0.02902321144938469,
-0.005209602415561676,
0.012417426332831383,
0.011594591662287712,
-0.010637394152581692,
-0.007713723927736282,
0.0230844859033823,
-0.009273955598473549,
-0.004790386185050011,
-0.007472746539860964,
0.05461461469531059,
0.020725777372717857,
-0.011463410221040249,
-0.03301030769944191,
0.001997244544327259,
-0.06275811791419983,
-0.0010643862187862396,
0.002997328992933035,
0.004149863496422768,
0.018310701474547386,
0.044199809432029724,
0.008500260300934315,
0.01495001744478941,
0.00992408487945795,
0.015283197164535522,
-0.07505406439304352,
-0.03196817263960838,
-0.007710881531238556,
-0.026125432923436165,
0.053447216749191284,
0.022118058055639267,
-0.017514649778604507,
-0.02030912972986698,
0.01077750138938427,
0.023294173181056976,
0.03997734189033508,
0.019378570839762688,
-0.03354043886065483,
0.02826073206961155,
-0.04231493920087814,
0.07795777916908264,
-0.030615249648690224,
0.02580043487250805,
-0.013170244172215462,
-0.022846197709441185,
0.028792355209589005,
0.018612299114465714,
-0.037809766829013824,
0.016033248975872993,
0.05031157657504082,
-0.03114195354282856,
-0.02028709277510643,
0.01049948949366808,
-0.0012910767691209912,
-0.02253222092986107,
-0.01609412394464016,
-0.02631637454032898,
-0.004956610035151243,
0.015677371993660927,
0.009955431334674358,
-0.008373653516173363,
0.019645674154162407,
-0.008796568028628826,
0.0023741230834275484,
-0.05427704006433487,
-0.008407906629145145,
-0.0263401847332716,
-0.021830474957823753,
-0.0032732635736465454,
-0.014839810319244862,
-0.008434678427875042,
0.02693692222237587,
-0.01574105955660343,
-0.035419683903455734,
0.005629013292491436,
0.03227308392524719,
-0.04451211914420128,
0.017393140122294426,
0.017907921224832535,
0.05346184968948364,
0.02905196137726307,
-0.009679587557911873,
-0.019766660407185555,
0.030614113435149193,
-0.04616449400782585,
-0.07855097204446793,
0.00394818838685751,
-0.03861717879772186,
0.01014920324087143,
0.048145510256290436,
-0.02051801234483719,
-0.013202372007071972,
0.02866888977587223,
-0.03520561382174492,
-0.00400911970064044,
0.00372492172755301,
0.027761438861489296,
0.004434928297996521,
-0.016115203499794006,
0.05088202282786369,
0.0003466312191449106,
-0.012638874351978302,
0.02834411896765232,
0.0012361652916297317,
-0.015335052274167538,
-0.0014343049842864275,
-0.02304966375231743,
-0.05019119009375572,
-0.004551118705421686,
-0.002779907314106822,
0.033217206597328186,
0.000384982384275645,
0.05438670143485069,
-0.024647705256938934,
0.045544181019067764,
0.02911454066634178,
-0.049052558839321136,
-0.11055368930101395,
0.009739839471876621,
0.025778181850910187,
0.000804667011834681,
0.019275659695267677,
-0.04679054766893387,
0.05757571756839752,
0.016063757240772247,
-0.11294849961996078,
0.02017159014940262,
0.0015856693498790264,
0.006453803274780512,
-0.06124945357441902,
0.024318931624293327,
-0.02311941422522068,
0.017478272318840027,
0.05821109563112259,
0.05052917078137398,
0.012209613807499409,
0.02436981536448002,
-0.016227902844548225,
-0.01870035193860531,
-0.009635663591325283,
0.03751765191555023,
-0.047899674624204636,
0.03461141884326935,
0.043528612703084946,
-0.0015592919662594795,
0.027231955900788307,
0.0008504955912940204,
0.027119288221001625,
0.01385359838604927,
-0.04311923310160637,
0.005863570608198643,
0.00921593140810728,
0.04189346358180046,
0.026698321104049683,
-0.02580639347434044,
0.014349489472806454,
0.013985523022711277,
0.03188204765319824,
0.013833368197083473,
0.0011843052925541997,
0.007001121994107962,
0.024640757590532303,
-0.0021092977840453386,
-0.0035683412570506334,
0.048369988799095154,
0.03065921738743782,
0.0017565262969583273,
-0.012862901203334332,
0.039761487394571304,
0.027226176112890244,
-0.01760450191795826,
-0.010679677128791809,
-0.041028011590242386,
0.01762758195400238,
0.004457253962755203,
0.04687601700425148,
-0.021927159279584885,
-0.0026873250026255846,
-0.04509931430220604,
0.010369887575507164,
0.015810029581189156,
0.02874082326889038,
-0.041459012776613235,
-0.0032647207845002413,
0.0030236453749239445,
-0.028693174943327904,
0.04176797345280647,
0.04106840491294861,
-0.03910941630601883,
-0.03113851696252823,
0.014648379758000374,
0.042690958827733994,
0.03937770798802376,
0.0218641459941864,
-0.03515775501728058,
0.0001024687007884495,
-0.07164911925792694,
0.025608640164136887,
-0.009756692685186863,
0.0255306176841259,
-0.05753863975405693,
-0.036934807896614075,
0.006083074025809765,
-0.03449947014451027,
0.05018416792154312,
0.014628850854933262,
0.007840353064239025,
-0.008369989693164825,
-0.008697383105754852,
0.03662548214197159,
-0.006680608261376619,
-0.01226514670997858,
-0.02409190870821476,
-0.009624495171010494,
-0.002134814392775297,
-0.03379411995410919,
-0.030332885682582855,
0.025928329676389694,
0.05833674967288971,
0.03262164443731308,
-0.00723526393994689,
0.024876292794942856,
-0.05456148460507393,
0.07349038124084473,
0.006368555594235659,
0.014089318923652172,
0.06334720551967621,
0.007563019171357155,
0.005748133175075054,
0.018398640677332878,
-0.007557228207588196,
-0.0039211842231452465,
0.021180283278226852,
-0.030651165172457695,
-0.018441708758473396,
-0.010129746049642563,
0.015033215284347534,
0.018559005111455917,
-0.018182167783379555,
-0.024700162932276726,
0.031082764267921448,
-0.017246512696146965,
0.002566226292401552,
0.01019471324980259,
-0.008266586810350418,
0.022566765546798706,
-0.029005147516727448,
0.024507056921720505,
0.014814579859375954,
0.010081863962113857,
-0.027891650795936584,
0.05363979563117027,
0.03028418868780136,
-0.019613327458500862,
0.0201422069221735,
0.08183172345161438,
0.007343939505517483,
0.02027038298547268,
-0.007014340255409479,
0.02700025960803032,
-0.016902567818760872,
0.003911750391125679,
0.04664788767695427,
-0.011093142442405224,
-0.010843801312148571,
0.032585639506578445,
-0.000012284224794711918,
0.08996526896953583,
-0.009295005351305008,
0.016574906185269356,
-0.003054037457332015,
-0.03152434155344963,
-0.01100327167659998,
0.024463370442390442,
-0.015548821538686752,
-0.00996707659214735,
-0.014103304594755173,
-0.04784362390637398,
-0.003797337878495455,
0.044279418885707855,
0.021569417789578438,
-0.033169109374284744,
0.012024038471281528,
0.01934584230184555,
-0.004065752029418945,
-0.014998374506831169,
0.004800266586244106,
-0.01587498001754284,
-0.0287801381200552,
0.04018453508615494,
0.03076103888452053,
-0.016416173428297043,
0.010584338568150997,
-0.002940236357972026,
-0.022898204624652863,
0.04131428524851799,
-0.006210471969097853,
-0.01247542817145586,
-0.011476038955152035,
0.03466249257326126,
-0.02690018154680729,
-0.004046962596476078
] |
<p>I'm reading through Vol. 1 Chaper 18, and Feynman says that in the system:</p>
<p><img src="http://i.stack.imgur.com/G3AZG.png" alt="enter image description here"></p>
<p>(<a href="http://www.feynmanlectures.caltech.edu/img/FLP_I/f18-01/f18-01_tc_big.svg" rel="nofollow">See here</a> for a higher resolution copy - can't embed SVGs), the length of $PQ$ is equal to $r\Delta\theta$:</p>
<blockquote>
<p>If $OP$ is called $r$, then the length $PQ$ is $r\Delta\theta$, because of the way angles are defined.</p>
</blockquote>
<p>I'm probably being stupid, but surely this should be $r*\tan(\Delta\theta)$? Also, the diagram itself appears to depict an impossible figure. If the lengths of $OP$ and $OQ$ are equal, then the angle $OPQ$ cannot be 90 degrees. Like I said I'm probably being stupid, so hopefully someone can show me where I'm going wrong.</p>
| 8,455 |
[
-0.00532698817551136,
-0.009717438369989395,
-0.00017212436068803072,
-0.012396663427352905,
0.017588796094059944,
0.030997779220342636,
-0.020682768896222115,
-0.020134037360548973,
0.005311793182045221,
-0.02696686051785946,
0.02721375599503517,
0.003591320477426052,
0.08656062185764313,
0.05941152200102806,
-0.012688308022916317,
-0.0005982208531349897,
0.0033601573668420315,
0.01518633496016264,
0.010950542986392975,
-0.0262451209127903,
-0.01183970458805561,
0.03012968599796295,
0.03400473669171333,
-0.05309716612100601,
0.0016361098969355226,
0.04185869172215462,
0.04484935104846954,
0.00637833122164011,
-0.036084629595279694,
0.051257044076919556,
0.021762793883681297,
-0.05069829523563385,
0.04539436474442482,
0.017200838774442673,
-0.0014655839186161757,
-0.016594264656305313,
-0.009402715601027012,
-0.020398637279868126,
-0.00843831431120634,
-0.003651245729997754,
-0.005002986174076796,
0.020319778472185135,
-0.047249700874090195,
0.033125001937150955,
-0.04266619309782982,
0.017802970483899117,
-0.0243796706199646,
0.004467453807592392,
0.08604543656110764,
-0.043331079185009,
0.05341228097677231,
0.042574673891067505,
0.008946936577558517,
0.021607063710689545,
0.019773537293076515,
-0.041801195591688156,
0.05079516023397446,
0.04078492149710655,
-0.02741231583058834,
-0.05808047950267792,
-0.043030284345149994,
-0.028619365766644478,
-0.021263552829623222,
-0.005286828614771366,
-0.037541721016168594,
0.0005913129425607622,
0.011361304670572281,
-0.0199042409658432,
0.020995141938328743,
-0.011247033253312111,
0.018590833991765976,
0.0374780111014843,
0.013500148430466652,
0.019287854433059692,
0.013554711826145649,
-0.025559110566973686,
-0.00466330349445343,
0.006064500659704208,
0.05001912638545036,
0.032331403344869614,
-0.03772453963756561,
0.0019327430054545403,
0.03845867142081261,
0.060353491455316544,
-0.019093003123998642,
-0.027176667004823685,
0.031236061826348305,
0.009587905369699001,
-0.013057289645075798,
0.04589449241757393,
0.023791499435901642,
0.057382628321647644,
0.005272646434605122,
0.005533514078706503,
-0.007260805927217007,
0.04900886490941048,
0.0006750546162948012,
0.04326915740966797,
-0.012728352099657059,
-0.02788209356367588,
-0.0009984832722693682,
-0.031263019889593124,
-0.01937713287770748,
0.06660474836826324,
0.041193414479494095,
-0.0038186125457286835,
-0.018834443762898445,
0.023137319833040237,
0.02112550288438797,
0.004821013659238815,
-0.06514353305101395,
0.00038199409027583897,
-0.032611191272735596,
0.006578365806490183,
0.006884039379656315,
-0.020204508677124977,
-0.021136829629540443,
0.0051714531145989895,
0.07092104107141495,
0.03404541313648224,
0.045015014708042145,
-0.03187105432152748,
0.0195457823574543,
-0.050407540053129196,
-0.06277452409267426,
0.006188723258674145,
0.03845221549272537,
0.0061042169108986855,
-0.03518693521618843,
0.0149054741486907,
0.04295959323644638,
0.024874482303857803,
-0.015475002117455006,
0.0305082555860281,
0.012514295056462288,
0.01573343016207218,
-0.09652945399284363,
-0.05772287771105766,
0.02691081538796425,
0.02086794376373291,
0.02310311049222946,
-0.06958471238613129,
0.0023836244363337755,
0.04414396360516548,
0.07410131394863129,
-0.026893015950918198,
0.017899854108691216,
-0.0014534449437633157,
0.01508462056517601,
0.01409854181110859,
0.003994484897702932,
0.006808438338339329,
-0.02144339680671692,
-0.05601543188095093,
-0.011836673133075237,
-0.04759295657277107,
0.061125967651605606,
0.023178642615675926,
0.027532394975423813,
-0.03805544972419739,
0.05886276438832283,
-0.045807134360075,
0.057236820459365845,
0.01119285263121128,
-0.03609944134950638,
-0.04917468875646591,
0.09698006510734558,
0.03892183676362038,
0.010990386828780174,
0.010391896590590477,
-0.043373916298151016,
0.012135886587202549,
-0.0021299743093550205,
-0.002596355974674225,
0.03590851277112961,
-0.017664354294538498,
-0.021575355902314186,
-0.04044179618358612,
0.027058422565460205,
0.03459356352686882,
-0.023447202518582344,
-0.04609006643295288,
0.005028539802879095,
-0.011005174368619919,
-0.024420298635959625,
0.04069570451974869,
-0.020076094195246696,
0.005806369706988335,
-0.010871476493775845,
-0.022824466228485107,
-0.015154450200498104,
-0.040009185671806335,
0.012977744452655315,
0.05025169253349304,
-0.03138837218284607,
0.026056617498397827,
-0.0077414484694600105,
0.006428722757846117,
-0.008467148058116436,
-0.04553752392530441,
0.015197515487670898,
0.08029494434595108,
0.022568663582205772,
0.01179006788879633,
0.03228508681058884,
0.05523896962404251,
0.07280707359313965,
0.000778255402110517,
0.013061757199466228,
-0.012668251991271973,
-0.015804190188646317,
-0.017230959609150887,
-0.015547663904726505,
0.003871991764754057,
-0.0024866468738764524,
0.023533767089247704,
-0.013398920185863972,
0.03384651988744736,
0.01114357728511095,
0.024644993245601654,
-0.041212983429431915,
0.07242363691329956,
0.008451210334897041,
0.014048258773982525,
-0.00022686606098432094,
0.019061505794525146,
0.002908468944951892,
0.05113841965794563,
-0.007860314100980759,
-0.010717693716287613,
-0.023197529837489128,
0.017016688361763954,
0.03787295147776604,
-0.007866871543228626,
-0.02147478424012661,
0.028441131114959717,
-0.0071878815069794655,
0.03325139358639717,
-0.02288549207150936,
0.0024160374887287617,
-0.001778580597601831,
-0.03429185599088669,
-0.010708652436733246,
0.019593337550759315,
0.01473814807832241,
-0.009353707544505596,
0.012943758629262447,
0.010939015075564384,
0.02801317349076271,
0.0005092395003885031,
0.0022434222046285868,
-0.0033131048548966646,
-0.008019989356398582,
0.02293267473578453,
0.02142993174493313,
0.03779004141688347,
0.057240307331085205,
-0.012831690721213818,
0.02538025937974453,
0.02209656499326229,
-0.012529244646430016,
0.00675581581890583,
-0.02442919835448265,
-0.006150930654257536,
-0.00597767811268568,
-0.009246009401977062,
0.0015825150767341256,
-0.030190056189894676,
0.027067875489592552,
-0.029641801491379738,
-0.019941654056310654,
-0.03202127665281296,
-0.016382461413741112,
0.007194233126938343,
-0.005319150164723396,
0.017599420621991158,
0.0094941146671772,
0.013521663844585419,
-0.0038738898001611233,
-0.023922616615891457,
0.009372514672577381,
-0.0028033482376486063,
0.012864244170486927,
0.03489217534661293,
-0.03481413796544075,
0.0003624602104537189,
-0.028316106647253036,
-0.007806743960827589,
0.03459968417882919,
0.028962979093194008,
0.01989407278597355,
-0.009534367360174656,
-0.015918752178549767,
-0.018013708293437958,
-0.06799094378948212,
-0.007915806956589222,
0.0024411650374531746,
-0.04355102777481079,
-0.03831016644835472,
0.03859376162290573,
0.012477617710828781,
0.0014229173539206386,
0.04630577564239502,
-0.04102371633052826,
-0.042783964425325394,
-0.011991729959845543,
0.009331764653325081,
0.014781600795686245,
0.0027699528727680445,
0.0014178860001266003,
0.0071426937356591225,
-0.013816232793033123,
-0.03031131438910961,
-0.11567924171686172,
-0.0609598234295845,
-0.03829764947295189,
0.005517333280295134,
0.011618886142969131,
0.032778047025203705,
-0.05758710578083992,
0.0694338008761406,
0.012366830371320248,
-0.07198069989681244,
-0.027006248012185097,
0.030530592426657677,
-0.03555738180875778,
-0.04171791300177574,
0.003940528258681297,
0.030660590156912804,
-0.0005419866647571325,
0.03178102895617485,
0.01683252677321434,
0.024169720709323883,
0.04475463181734085,
0.0020396714098751545,
-0.004172374028712511,
0.006276906002312899,
-0.01834396831691265,
-0.021086374297738075,
0.035018112510442734,
0.024587316438555717,
0.012690731324255466,
0.0015292884781956673,
0.02761462889611721,
0.04606207460165024,
0.004859695211052895,
-0.08399464935064316,
0.0481470562517643,
-0.0016744181048125029,
0.040532853454351425,
-0.011949269101023674,
0.03118651919066906,
0.0012477615382522345,
-0.027275413274765015,
-0.028681403025984764,
0.036125726997852325,
0.05661635100841522,
-0.050152331590652466,
-0.01817025989294052,
0.019768711179494858,
0.03583900257945061,
-0.007217996753752232,
-0.02148370072245598,
-0.010625024326145649,
0.00192448019515723,
0.008130264468491077,
-0.015244630165398121,
-0.009209604933857918,
0.02610125206410885,
0.022313155233860016,
0.0384598970413208,
0.013975479640066624,
-0.026795564219355583,
-0.009856329299509525,
-0.05248311907052994,
0.0038232551887631416,
0.0024818533565849066,
0.0350743904709816,
0.027450362220406532,
0.05512062460184097,
0.021493464708328247,
0.02172207273542881,
-0.018157918006181717,
-0.019078833982348442,
-0.08502457290887833,
0.023251669481396675,
-0.020046565681695938,
-0.05440264567732811,
0.009016389958560467,
-0.03203975036740303,
-0.021052492782473564,
-0.008007965981960297,
0.015446566045284271,
-0.0036503130104392767,
-0.03056929260492325,
-0.017301004379987717,
0.007565012201666832,
-0.05417914688587189,
-0.030834095552563667,
-0.022722743451595306,
0.049776118248701096,
0.03820338845252991,
-0.051395054906606674,
0.0300686527043581,
0.07588765770196915,
-0.036770954728126526,
-0.0076454500667750835,
-0.004184425342828035,
0.033827755600214005,
0.002201734809204936,
-0.004201733041554689,
0.02586851827800274,
0.011085054837167263,
0.015433764085173607,
0.007972470484673977,
0.00821689423173666,
0.0481405146420002,
0.027212094515562057,
-0.04127771034836769,
-0.01197226345539093,
-0.03339625522494316,
-0.0442519374191761,
-0.013940073549747467,
0.05322100222110748,
-0.00046170668792910874,
0.0000979080650722608,
0.048822615295648575,
0.03879838436841965,
-0.03274815157055855,
0.04018993675708771,
0.06157288700342178,
0.027764292433857918,
-0.03673262149095535,
-0.052124422043561935,
-0.027366790920495987,
-0.023472577333450317,
0.027544330805540085,
-0.03384292870759964,
0.013643594458699226,
-0.03422272577881813,
-0.030367514118552208,
0.011793112382292747,
0.005629620980471373,
-0.026722462847828865,
0.023654788732528687,
0.0022362053859978914,
0.026136228814721107,
-0.027651192620396614,
0.01940825767815113,
0.020599599927663803,
0.036404650658369064,
0.04140153154730797,
-0.015878429636359215,
-0.029471492394804955,
-0.05736974626779556,
0.015375765971839428,
0.015604251064360142,
0.045021574944257736,
0.023050539195537567,
0.026027893647551537,
-0.058199238032102585,
-0.01597926765680313,
0.059089671820402145,
-0.020179472863674164,
0.04184193164110184,
-0.026477094739675522,
-0.05324844270944595,
-0.01836457848548889,
-0.05477607622742653,
-0.048038069158792496,
0.02103313058614731,
-0.0021829092875123024,
0.0290012676268816,
-0.009419737383723259,
-0.022708378732204437,
0.007053033448755741,
0.04355624318122864,
0.03495650738477707,
0.026546727865934372,
0.029590122401714325,
-0.012882699258625507,
0.02143167518079281,
0.016815105453133583,
-0.04142766818404198,
-0.07486362755298615,
0.04323291778564453,
-0.024383069947361946,
0.003976068459451199,
0.00672890106216073,
-0.01847631111741066,
-0.02583841234445572,
0.031492408365011215,
-0.006714268121868372,
0.052721668034791946,
0.013044193387031555,
-0.044355519115924835,
0.018416589125990868,
0.038451943546533585,
0.007759190630167723,
0.03909137099981308,
0.0003682012902572751,
0.01807221956551075,
0.005302701611071825,
-0.04429592937231064,
0.01441497728228569,
-0.0012210969580337405,
-0.003897386370226741,
-0.055411823093891144,
0.03522248566150665,
-0.028868375346064568,
0.0024616520386189222,
-0.020296379923820496,
0.01192973367869854,
-0.023507867008447647,
-0.03016825206577778,
-0.014834444969892502,
0.004255192819982767,
-0.015017376281321049,
0.0005020136013627052,
0.01621817611157894,
0.02423110231757164,
-0.002248773816972971,
0.0072312080301344395,
0.004314604680985212,
-0.041308701038360596,
0.00792104471474886,
-0.009636815637350082,
-0.02336900122463703,
0.013483745977282524,
-0.03284532576799393,
0.00015284419350791723,
0.014976524747908115,
-0.05687587335705757,
0.027549149468541145,
-0.01548917405307293,
0.004390850197523832,
-0.0013944661477580667,
-0.016397949308156967,
-0.01830996386706829,
0.007215884048491716,
-0.039543237537145615,
0.02527400478720665,
-0.021456342190504074,
0.01640981249511242,
0.019646283239126205,
-0.0027624936774373055,
-0.017511077225208282,
-0.03688029944896698,
0.026277294382452965,
0.011216907761991024,
-0.06883714348077774,
0.023876836523413658,
-0.029225438833236694,
-0.0006299524684436619,
-0.02759239822626114,
-0.037189509719610214,
0.03305637463927269,
-0.02637087181210518,
0.0004141026583965868,
-0.015111947432160378,
0.05063021928071976,
0.054586395621299744,
-0.005126591306179762,
0.02484641969203949,
0.047348495572805405,
-0.009158110246062279,
-0.010647949762642384,
-0.0030878079123795033,
0.04753287881612778,
-0.027476562187075615,
-0.04469768702983856,
-0.0016742195002734661,
0.0006599548505619168,
0.016741743311285973,
-0.024328770115971565,
0.005730480886995792,
-0.004855156410485506,
0.003350809682160616,
0.005031920969486237,
0.03379638493061066,
0.009769481606781483,
0.007440810091793537,
0.003787003690376878,
-0.004168437793850899,
0.01780192367732525,
-0.01770392619073391,
-0.06628409028053284,
0.017223414033651352,
-0.00043731776531785727,
0.02218669094145298,
0.00006492962711490691,
0.0730803832411766,
-0.03613650053739548,
-0.03967485949397087,
0.007948503829538822,
0.0065334150567650795,
0.03220655396580696,
0.02150294929742813,
0.018258364871144295,
0.01732141710817814,
-0.016088806092739105,
-0.042255137115716934,
-0.02469969168305397,
-0.05551114305853844,
0.010577809065580368,
0.07782913744449615,
0.007833353243768215,
0.027002349495887756,
-0.016149159520864487,
0.002617904916405678,
0.0019037349848076701,
-0.022227145731449127,
-0.034377291798591614,
-0.013066953979432583,
0.047043729573488235,
0.013807077892124653,
-0.046672429889440536,
-0.011295213364064693,
0.01041637733578682,
0.03493102639913559,
-0.02366015687584877,
-0.0019001234322786331,
0.05534708872437477,
0.009213492274284363,
0.019338220357894897,
0.005977248307317495,
-0.02581387758255005,
0.060114119201898575,
-0.011596976779401302,
0.05860499292612076,
-0.01272310595959425,
-0.02289816550910473,
0.010467426851391792,
0.020691370591521263,
0.02676004357635975,
-0.027063017711043358,
-0.03163900226354599,
-0.045579470694065094,
0.0018448602641001344,
0.03738340362906456,
0.018258649855852127,
-0.0028462426271289587,
-0.031190218403935432,
0.03627939149737358,
0.0257701575756073,
0.01035580225288868,
-0.052905723452568054,
-0.04337579011917114,
-0.06844054907560349,
0.004742763936519623,
-0.06807401776313782,
0.08127441257238388,
-0.011240622960031033,
-0.02260972186923027,
0.01067560724914074,
-0.03468216583132744,
-0.0015313971089199185,
0.028739338740706444,
0.01802023872733116,
-0.024200040847063065,
0.03157276287674904,
-0.024081258103251457,
0.05156712979078293,
-0.03203766420483589,
-0.03591557964682579,
0.10900680720806122,
0.037872426211833954,
0.012696739286184311,
-0.013318999670445919,
0.0690678283572197,
-0.02993379905819893,
0.009235971607267857,
-0.043939922004938126,
0.04584777355194092,
-0.030718160793185234,
-0.009171472862362862,
-0.03655382618308067,
0.06746267527341843,
0.01632797159254551,
0.010177726857364178,
0.05735145881772041,
-0.04662632569670677,
-0.05654122307896614,
0.013928588479757309,
-0.01590486243367195,
-0.01628814823925495,
-0.02448374591767788,
-0.035497330129146576,
-0.002583337714895606,
-0.04818514734506607,
0.030108699575066566,
-0.0045137000270187855,
-0.03324824199080467,
0.0190439373254776,
0.039097145199775696,
-0.03218329697847366,
-0.027421792969107628,
-0.02299787662923336,
-0.021958159282803535,
-0.013028084300458431,
0.029808465391397476,
0.026085322722792625,
-0.015216407366096973,
0.03954227641224861,
0.0703522115945816,
0.039212606847286224,
0.003986742347478867,
0.027962708845734596,
-0.006206799298524857,
-0.035119906067848206,
-0.040448058396577835,
-0.019280334934592247,
0.06422651559114456,
-0.025730764493346214,
0.011037524789571762,
-0.0206143856048584,
0.025620998814702034,
-0.009214610792696476,
-0.0646309107542038,
0.03969353437423706,
-0.021702313795685768,
0.013894971460103989,
0.008475469425320625,
0.008000271394848824,
-0.027678420767188072,
0.03935927152633667,
0.025876661762595177,
0.010615844279527664,
-0.021273966878652573,
0.007061406504362822,
0.04202058166265488,
-0.011830827221274376,
0.04132620990276337,
0.027934256941080093,
-0.013059776276350021,
-0.07032662630081177,
-0.0022123586386442184,
-0.020312931388616562,
0.037072230130434036,
0.027712320908904076,
0.04521315544843674,
-0.0011809783754870296,
-0.004583123605698347,
-0.007632764987647533,
-0.02257741428911686,
0.015123345889151096,
-0.006320711225271225,
-0.020978005602955818,
-0.07253026217222214,
-0.010674122720956802,
-0.017095107585191727,
0.01997474953532219,
0.02591526508331299,
0.011988532729446888,
0.0037903962656855583,
0.004343950189650059,
0.010950155556201935,
0.053200613707304,
-0.009820530191063881,
-0.04137502610683441,
-0.011783613823354244,
-0.010694443248212337,
-0.038928691297769547,
0.016248730942606926,
0.00938507355749607,
0.03983201086521149,
0.054629839956760406,
0.014535532332956791,
0.015610327012836933,
-0.019854754209518433,
-0.014543257653713226,
0.03867899626493454,
-0.010329986922442913,
0.004714571870863438,
-0.0011102051939815283,
-0.004224112723022699,
-0.056257788091897964,
-0.011482248082756996,
-0.04875878244638443,
-0.01807212084531784,
0.011806015856564045,
0.03414745628833771,
-0.05865870788693428,
-0.021920889616012573,
-0.04437632113695145,
-0.0021303407847881317,
-0.0067268782295286655,
0.02022469788789749,
-0.022617481648921967,
-0.006345308851450682,
0.0003037146816495806,
0.026608480140566826,
-0.0447123683989048,
0.04528714716434479,
-0.021850721910595894,
-0.02102396823465824,
-0.015587362460792065,
0.018080053851008415,
0.0068826377391815186,
-0.02912735566496849,
-0.03488021343946457,
0.020271990448236465,
0.0240740068256855,
-0.05839724838733673,
-0.055438823997974396,
0.03951817750930786,
-0.029566343873739243,
-0.021212488412857056,
0.023292621597647667,
0.015353421680629253,
0.0337604358792305,
-0.00040961819468066096,
-0.026594791561365128,
0.0053418041206896305,
0.03490478917956352,
-0.017714645713567734,
-0.03412926197052002,
0.010043692775070667,
-0.0307155828922987,
-0.015460215508937836,
-0.01764610968530178,
-0.02107967995107174,
-0.017116030678153038,
0.02963021770119667,
0.006388967856764793,
0.011869706213474274,
-0.009074350818991661,
-0.0019689472392201424,
-0.021908210590481758,
0.007304108235985041,
0.01919121854007244,
0.007857043296098709,
0.019266396760940552,
-0.024111632257699966,
0.015297142788767815,
0.007309149019420147,
0.04445798695087433,
0.013917489908635616,
-0.0030567380599677563,
-0.1047954186797142,
0.011233610101044178,
-0.0065101091749966145,
0.01596933603286743,
0.017179269343614578,
-0.05317823961377144,
-0.01646721549332142,
0.03155675157904625,
-0.07400732487440109,
0.006971166003495455,
-0.018119866028428078,
-0.007701984606683254,
-0.027490831911563873,
-0.007530187722295523,
-0.0378018282353878,
0.06598760932683945,
0.05177747458219528,
0.045341938734054565,
0.02490413747727871,
-0.026675688102841377,
-0.01270002406090498,
-0.05068027228116989,
-0.02868027240037918,
0.05599060654640198,
0.012898976914584637,
-0.006906145252287388,
0.04029512405395508,
-0.007818014360964298,
0.0028015675488859415,
0.035160016268491745,
-0.028457768261432648,
0.013911228626966476,
0.0073357513174414635,
-0.009883328340947628,
0.025637846440076828,
0.03037494607269764,
0.020587049424648285,
0.012433488853275776,
-0.025388432666659355,
-0.03314807265996933,
0.030476536601781845,
0.008918467909097672,
-0.03108607418835163,
-0.01553017646074295,
0.004702914971858263,
-0.05731818452477455,
-0.06876526027917862,
0.021415619179606438,
-0.029544509947299957,
-0.008333336561918259,
-0.018978673964738846,
0.008840763941407204,
-0.03207620605826378,
-0.056143101304769516,
0.018673235550522804,
-0.03697393834590912,
0.010052034631371498,
0.03892073780298233,
0.010877585038542747,
0.00983447302132845,
0.011429480277001858,
-0.0263129323720932,
-0.014731820672750473,
-0.011407601647078991,
0.01922474056482315,
-0.010976548306643963,
-0.04686206951737404,
0.015142629854381084,
-0.021898169070482254,
0.01591644622385502,
0.029921643435955048,
-0.014556561596691608,
-0.034315574914216995,
-0.004356025718152523,
0.012537595815956593,
0.02150525152683258,
0.0008902350091375411,
-0.03408024087548256,
-0.02309899590909481,
-0.0642722025513649,
0.036546286195516586,
0.009874911047518253,
-0.01588718593120575,
-0.027625882998108864,
-0.028467902913689613,
-0.003199261147528887,
0.02629557065665722,
0.048975102603435516,
0.012976394966244698,
-0.06042579561471939,
0.02506011724472046,
0.0020380609203130007,
0.00876166857779026,
-0.020430779084563255,
0.020663106814026833,
0.005494389217346907,
0.0355481319129467,
0.030652882531285286,
0.017903732135891914,
-0.0015029911883175373,
-0.025293877348303795,
0.0047103725373744965,
0.0017096849624067545,
-0.0014081199187785387,
0.0018402031855657697,
-0.07922494411468506,
0.012233470566570759,
-0.01590915583074093,
0.002197805093601346,
0.04826924577355385,
0.03807513788342476,
0.015654627233743668,
0.04585520923137665,
-0.05186527222394943,
-0.05248799920082092,
0.015016760677099228,
-0.05159012973308563,
-0.01670580543577671,
-0.03909078985452652,
-0.011674035340547562,
0.055549271404743195,
-0.012035851366817951,
0.013706699945032597,
0.05485792085528374,
-0.0010784340556710958,
-0.040920961648225784,
0.042399801313877106,
-0.01800399273633957,
0.014952220022678375,
0.009100212715566158,
0.006409811787307262,
0.035358671098947525,
-0.012831167317926884,
0.021035147830843925,
0.06373869627714157,
0.064228355884552,
-0.005951985251158476,
-0.013888062909245491,
0.05017472431063652,
0.0074415551498532295,
0.02167273871600628,
0.005894201807677746,
0.035947781056165695,
0.03090062364935875,
-0.0025326928589493036,
0.027091331779956818,
0.0012500020675361156,
-0.0030886526219546795,
0.022491225972771645,
-0.020330406725406647,
0.05547834932804108,
-0.0346807986497879,
0.04015272855758667,
-0.02156277745962143,
0.002706540282815695,
-0.057904746383428574,
0.02197526954114437,
0.01801704242825508,
0.019206149503588676,
-0.03112720139324665,
-0.04048414155840874,
-0.028531843796372414,
0.04042594134807587,
0.00036074608215130866,
-0.05053568631410599,
-0.0253362488001585,
0.030141258612275124,
-0.005663393530994654,
0.0018869716441258788,
-0.0065589104779064655,
0.000617984333075583,
-0.010072865523397923,
0.042497340589761734,
-0.0026674976106733084,
0.016894454136490822,
-0.008254372514784336,
0.006877340376377106,
-0.017133023589849472,
0.07500108331441879,
-0.033168647438287735,
-0.009158533066511154,
-0.007551086600869894,
0.019739024341106415,
-0.010739350691437721,
-0.02140931785106659
] |
<p>This is really a question to get a little more insight about a homework exercise.</p>
<p><strong><em>1.</em></strong> In my text book, the sum of multiplicities for all possible macrostates is given to be:</p>
<p>$$\sum \Omega_\mathrm{total}=\binom{N_A+N_B+q_\mathrm{total}-1}{q_\mathrm{total}}$$</p>
<p>For two Einstein solids $A$ and $B$ of $N_A$ oscillators in solid $A$, $N_B$ oscillators in solid $B$ and $q_\mathrm{total}$ units of energy in the system. I tried deriving this myself (which the text book doesn't require) but no dice there. How can I derive this myself?</p>
<hr>
<p><strong><em>2.</em></strong> The problem here is that the followup question pretty much defines the long term entropy of this system to be:</p>
<p>$$S=k\ln\left(\sum\Omega_\mathrm{total}\right)$$</p>
<p>Now there's confusion. I simply have no idea what I'm doing. Why is the sum of all the multiplicities together the long term entropy? How should I reason that this is the correct answer? Some explanation would be very, <em>very</em> welcome.</p>
| 8,456 |
[
-0.00132474722340703,
-0.0417071208357811,
-0.017721066251397133,
-0.006785915233194828,
0.03473386541008949,
-0.016486095264554024,
-0.024482116103172302,
-0.006126864813268185,
-0.021128922700881958,
-0.04072627052664757,
0.033198464661836624,
-0.01789397932589054,
0.03514711931347847,
0.01099531352519989,
0.014441381208598614,
-0.013406368903815746,
-0.009860441088676453,
-0.0004969749134033918,
0.007290893234312534,
-0.0223353523761034,
0.01750447042286396,
0.003046504221856594,
-0.016350869089365005,
-0.014017412438988686,
-0.018582407385110855,
0.06608797609806061,
0.017344310879707336,
-0.007315933704376221,
0.028978781774640083,
0.06585083156824112,
0.027440259233117104,
-0.04624707251787186,
0.030894724652171135,
0.0743146613240242,
0.03729970008134842,
-0.01574520580470562,
-0.06513096392154694,
-0.012811711058020592,
0.02247714251279831,
0.01735702157020569,
-0.07346071302890778,
-0.012674175202846527,
-0.0226465854793787,
0.012292953208088875,
-0.008055527694523335,
-0.00796743854880333,
0.025443704798817635,
-0.0069312117993831635,
0.02579011768102646,
-0.04257640242576599,
0.031623076647520065,
0.043914392590522766,
0.04117288067936897,
0.00470050610601902,
-0.016945336014032364,
-0.029288243502378464,
0.05984969437122345,
0.08346091955900192,
0.04168123006820679,
-0.06050539389252663,
-0.022215545177459717,
-0.003995262552052736,
-0.004212741274386644,
0.0010669976472854614,
-0.027364235371351242,
0.03697940334677696,
0.008840207010507584,
-0.02548184059560299,
0.042787615209817886,
-0.009586487896740437,
0.002545849187299609,
0.0036346139386296272,
0.028874453157186508,
-0.027190471068024635,
0.007614642381668091,
0.02748403511941433,
0.009896249510347843,
0.013088409788906574,
0.030717656016349792,
0.014906668104231358,
-0.019520042464137077,
0.006210563704371452,
0.032196417450904846,
0.03280937671661377,
0.007376472000032663,
-0.013417119160294533,
0.07239264249801636,
0.021442200988531113,
-0.013172694481909275,
0.03063807636499405,
-0.006364353001117706,
0.04205850884318352,
0.04038412123918533,
0.0033301201183348894,
-0.05808314308524132,
0.018425215035676956,
0.017314264550805092,
0.01917300932109356,
-0.0220030490309,
-0.030371351167559624,
-0.009073900058865547,
-0.07053130865097046,
0.03936881199479103,
0.059932492673397064,
0.006174389272928238,
-0.00363224558532238,
-0.03145100921392441,
0.007355928886681795,
-0.0018970411038026214,
-0.018511425703763962,
-0.010553449392318726,
0.020270029082894325,
0.01276008877903223,
-0.027501117438077927,
-0.0352916345000267,
-0.010400899685919285,
-0.015824206173419952,
0.009951765649020672,
0.0019123981473967433,
0.05014090612530708,
0.014991749078035355,
-0.004031561315059662,
0.031914494931697845,
-0.03922353684902191,
-0.09539102017879486,
0.014344745315611362,
0.04576767608523369,
-0.005884909071028233,
-0.06293328106403351,
0.026316160336136818,
0.03231336176395416,
-0.0004900963976979256,
-0.029337793588638306,
0.0198955275118351,
0.00992640946060419,
-0.011915617622435093,
-0.09175782650709152,
-0.06363064050674438,
0.04446105286478996,
-0.022958731278777122,
-0.034476738423109055,
-0.055946849286556244,
0.004859969951212406,
0.01851082593202591,
0.06376386433839798,
-0.02945951372385025,
0.006873635575175285,
-0.004313796292990446,
0.06669025868177414,
0.037872713059186935,
-0.055470872670412064,
-0.030025381594896317,
-0.029498349875211716,
-0.0041992743499577045,
0.011017943732440472,
-0.07580605149269104,
0.0355561226606369,
0.04991527646780014,
0.019657278433442116,
-0.00869172066450119,
0.04052010551095009,
-0.00600746925920248,
-0.005876899231225252,
0.011162394657731056,
-0.006724552251398563,
-0.03986401483416557,
0.07065122574567795,
0.024715935811400414,
0.033192962408065796,
0.01914806291460991,
0.0028603356331586838,
0.024713367223739624,
0.007486119866371155,
0.025406258180737495,
0.002772557083517313,
-0.040339481085538864,
0.036487825214862823,
-0.022136788815259933,
-0.0316103994846344,
-0.0038314396515488625,
-0.03135040029883385,
-0.05164816230535507,
-0.013418161310255527,
0.009732305072247982,
0.0008126858156174421,
0.021990535780787468,
0.002858932362869382,
0.006490998435765505,
-0.010254605673253536,
-0.03164839372038841,
0.0061727105639874935,
-0.05748171731829643,
0.011836372315883636,
-0.005139611195772886,
-0.056558556854724884,
0.021664271131157875,
0.007275363430380821,
0.0244938675314188,
0.02681852877140045,
-0.025675399228930473,
-0.007409872952848673,
0.020448286086320877,
0.010363814420998096,
-0.03952343761920929,
0.020117737352848053,
0.05387056991457939,
0.008949038572609425,
-0.006161731667816639,
0.02710856683552265,
0.013965546153485775,
-0.021050702780485153,
0.008031081408262253,
0.0005793592426925898,
0.047266267240047455,
-0.03741535544395447,
-0.04747786000370979,
-0.0043841395527124405,
-0.013094463385641575,
0.010421824641525745,
0.05494344234466553,
-0.02617473341524601,
0.04155462235212326,
0.07198206335306168,
0.01049164030700922,
-0.04038754478096962,
0.03378891572356224,
0.009382376447319984,
0.0628398135304451,
-0.024928519502282143,
-0.01671428792178631,
-0.07769351452589035,
0.014762071892619133,
0.009778418578207493,
0.05178823322057724,
-0.02859126590192318,
0.006242061965167522,
0.043763816356658936,
0.03658037632703781,
-0.005973245482891798,
-0.009136421605944633,
-0.0046319179236888885,
-0.011980235576629639,
0.04700298607349396,
-0.00029872043523937464,
-0.014734536409378052,
0.023598430678248405,
0.01563536562025547,
-0.01591762900352478,
-0.007319740019738674,
-0.009471429511904716,
-0.0038699915166944265,
0.011966872960329056,
0.020766107365489006,
-0.0072464849799871445,
-0.016244005411863327,
-0.007935874164104462,
0.03029944933950901,
-0.029981890693306923,
0.03579522669315338,
0.04233045503497124,
0.02459684945642948,
-0.03574851155281067,
-0.024919655174016953,
-0.02019495889544487,
-0.04326765611767769,
-0.0193119365721941,
-0.01628011092543602,
-0.028498336672782898,
0.008350438438355923,
-0.010286716744303703,
0.012775516137480736,
0.006259316578507423,
0.029373228549957275,
0.006283604074269533,
0.013009772635996342,
0.06249283626675606,
-0.014596505090594292,
0.0058784568682312965,
-0.027403954416513443,
-0.005892611108720303,
0.015453130938112736,
-0.02032696083188057,
-0.011292866431176662,
0.028053751215338707,
-0.08096563816070557,
0.0006158616743050516,
-0.011024861596524715,
-0.02841140702366829,
0.0469539649784565,
0.003594601061195135,
-0.019478492438793182,
0.010109995491802692,
-0.015326545573771,
-0.04764484614133835,
-0.01773606799542904,
-0.009327544830739498,
0.03457639738917351,
-0.06047659367322922,
0.003158220322802663,
0.07149159163236618,
0.014534356072545052,
-0.04092194885015488,
-0.01656581088900566,
-0.026095781475305557,
-0.03979485481977463,
0.01785930246114731,
-0.027934694662690163,
0.009753554128110409,
-0.00819359440356493,
-0.009306650608778,
0.03254394978284836,
-0.0028737050015479326,
-0.05656953528523445,
-0.07032622396945953,
-0.057372912764549255,
0.03031407669186592,
-0.025183049961924553,
0.045821305364370346,
-0.0032585638109594584,
-0.05202935263514519,
0.05317235738039017,
0.011643558740615845,
-0.016406575217843056,
-0.0235711969435215,
0.01051843911409378,
0.020531458780169487,
-0.038089778274297714,
-0.023598330095410347,
-0.002947675995528698,
-0.01261247880756855,
0.06974106281995773,
0.02971898950636387,
0.02069772221148014,
0.04007376357913017,
-0.021516483277082443,
-0.0234332587569952,
-0.0038737806025892496,
-0.01242148783057928,
0.005435433704406023,
0.05138180032372475,
0.021752163767814636,
0.013336182571947575,
0.01704288274049759,
-0.03300169110298157,
0.013183183036744595,
0.01925112120807171,
-0.0608612559735775,
0.043386250734329224,
0.014363614842295647,
-0.010996654629707336,
-0.057911913841962814,
0.04254401475191116,
-0.002774543594568968,
-0.022515907883644104,
0.020169179886579514,
0.00402534706518054,
0.025954928249120712,
-0.045775819569826126,
0.011656299233436584,
0.03225795924663544,
0.051087960600852966,
-0.002549585187807679,
-0.04380016773939133,
0.00006886367918923497,
0.010501816868782043,
0.015918297693133354,
-0.05196678265929222,
0.001801433158107102,
0.018818950280547142,
0.019278286024928093,
0.047049522399902344,
-0.026615697890520096,
-0.06785228848457336,
-0.009510395117104053,
-0.07253196090459824,
-0.02739744260907173,
-0.0002193304244428873,
0.05521267279982567,
-0.037434857338666916,
0.050101637840270996,
0.017673319205641747,
-0.008804157376289368,
0.03008325770497322,
0.00021064568136353046,
-0.048469893634319305,
0.05785354971885681,
-0.014040960930287838,
-0.02033378556370735,
0.06102888286113739,
0.007800516206771135,
0.03349865972995758,
-0.03382627293467522,
-0.015974825248122215,
-0.006207867991179228,
0.005206632893532515,
-0.0496106818318367,
-0.010293716564774513,
-0.061819251626729965,
-0.03305927664041519,
-0.012433924712240696,
0.024085111916065216,
0.04123516008257866,
-0.03792978450655937,
0.029262859374284744,
0.05169609561562538,
-0.03801335394382477,
0.044412966817617416,
-0.02296655997633934,
0.003902910742908716,
0.026167169213294983,
0.0035004890523850918,
0.04330531507730484,
0.022872868925333023,
-0.007383271120488644,
0.001895035500638187,
0.03647806867957115,
0.05389247089624405,
-0.009004278108477592,
-0.05080626904964447,
-0.006563061382621527,
-0.041485629975795746,
-0.0133970333263278,
-0.012099817395210266,
0.03792932629585266,
0.00371414958499372,
0.025830820202827454,
0.034164100885391235,
0.02089824341237545,
-0.00522310845553875,
0.022443443536758423,
0.04796478897333145,
-0.03242327645421028,
-0.02038317732512951,
0.007340379990637302,
-0.02568718232214451,
-0.020109985023736954,
-0.0020992623176425695,
0.025043606758117676,
0.006840219721198082,
-0.036982644349336624,
0.0144856758415699,
0.007103687152266502,
0.0191939864307642,
-0.023007407784461975,
-0.0020155420061200857,
-0.009418738074600697,
0.024601472541689873,
0.007496399339288473,
-0.011856808327138424,
-0.020576588809490204,
0.00621459586545825,
0.0360490046441555,
0.017861273139715195,
0.02467448264360428,
-0.06233919784426689,
-0.023525293916463852,
0.015821266919374466,
0.03583537042140961,
0.010671024210751057,
0.026485245674848557,
-0.059657830744981766,
-0.022233935073018074,
0.020269691944122314,
-0.01636344939470291,
0.050462137907743454,
0.030100122094154358,
0.026677850633859634,
0.026979321613907814,
-0.0480525903403759,
-0.0341944694519043,
0.030139915645122528,
0.006172495894134045,
0.0486784502863884,
-0.032148487865924835,
-0.01070081815123558,
0.00118201260920614,
0.02103695273399353,
0.030833689495921135,
0.03072711080312729,
-0.04235420376062393,
-0.01762901432812214,
-0.007348694838583469,
0.014760501682758331,
0.0036445055156946182,
-0.10768238455057144,
0.027290768921375275,
-0.015428743325173855,
-0.04950370639562607,
0.0166151225566864,
-0.05392482131719589,
-0.047105446457862854,
0.039328306913375854,
0.01285536028444767,
-0.0025942735373973846,
-0.006939678452908993,
-0.011712133884429932,
0.08077120780944824,
0.045884471386671066,
0.022670632228255272,
0.0345052070915699,
0.034564048051834106,
-0.006020702421665192,
0.03897546976804733,
0.0002827681601047516,
0.012227709405124187,
-0.031667761504650116,
0.03423961251974106,
-0.01613544300198555,
0.03520140424370766,
-0.030629882588982582,
0.03343360126018524,
-0.003092986298725009,
0.004037924110889435,
-0.003929139580577612,
-0.02921731397509575,
0.01410532183945179,
0.006543050520122051,
0.011881712824106216,
0.030297739431262016,
0.029999153688549995,
0.050047069787979126,
0.052820947021245956,
-0.016681231558322906,
0.03224963694810867,
-0.024030651897192,
-0.028547054156661034,
0.04579106345772743,
0.022582996636629105,
0.01579899527132511,
-0.044227682054042816,
0.0022587799467146397,
0.002364936051890254,
-0.01788756623864174,
0.04284512624144554,
-0.0030467193573713303,
0.014262771233916283,
0.024417361244559288,
-0.03107444755733013,
-0.028668677434325218,
-0.03129836544394493,
0.008044641464948654,
0.016649503260850906,
-0.012909640558063984,
-0.004798462614417076,
0.013476504012942314,
-0.012113546021282673,
-0.0686955377459526,
-0.030007105320692062,
0.027110720053315163,
0.03870132565498352,
-0.045483216643333435,
-0.017100883647799492,
-0.0010030970443040133,
-0.04429028183221817,
0.004815530031919479,
-0.009280444122850895,
0.026302900165319443,
-0.053310345858335495,
0.0010679611004889011,
0.04274619743227959,
0.06233853101730347,
0.03985055163502693,
-0.0011278280289843678,
0.0029737644363194704,
-0.008638528175652027,
0.020101768895983696,
-0.005150942597538233,
0.022502003237605095,
0.007236266043037176,
-0.02626444771885872,
-0.04984356462955475,
0.012046200223267078,
0.0036271116696298122,
0.02225758135318756,
0.0034961479250341654,
-0.036129992455244064,
0.013660379685461521,
-0.0018668476259335876,
0.009898231364786625,
-0.011411521583795547,
-0.008884990587830544,
-0.004043284337967634,
0.04252065345644951,
-0.022877134382724762,
0.02077905647456646,
-0.012236005626618862,
-0.026999523863196373,
-0.017160549759864807,
0.003984047099947929,
-0.010552404448390007,
0.0007159829838201404,
0.07370249181985855,
-0.009021652862429619,
-0.0016211005859076977,
0.025285974144935608,
-0.0027020517736673355,
0.03201373666524887,
-0.020064296200871468,
0.013314679265022278,
0.04049983248114586,
0.02863270230591297,
-0.0017317848978564143,
-0.02553628385066986,
-0.06621156632900238,
0.05580831319093704,
0.054739151149988174,
-0.026431117206811905,
-0.0037336181849241257,
0.036414552479982376,
-0.01806679368019104,
0.016075806692242622,
-0.034377679228782654,
-0.03790804743766785,
0.0353381521999836,
-0.007360082119703293,
0.03446464613080025,
-0.03749310225248337,
-0.03813683241605759,
0.02470339462161064,
0.022638773545622826,
-0.059545207768678665,
0.018408827483654022,
0.039670225232839584,
0.0017125393496826291,
-0.016891658306121826,
-0.010792397893965244,
-0.026209738105535507,
0.07817526906728745,
-0.035407792776823044,
0.03563988581299782,
0.0019864989444613457,
-0.03503960743546486,
0.019564801827073097,
0.03406618535518646,
0.040067631751298904,
-0.0690620094537735,
-0.03603193908929825,
-0.0038742111064493656,
0.012166634202003479,
0.03665115311741829,
0.010334523394703865,
0.04055989906191826,
-0.0072815027087926865,
0.028423471376299858,
0.035296760499477386,
-0.0026810807175934315,
0.017406370490789413,
-0.04028238728642464,
-0.002349614864215255,
0.002150583080947399,
-0.06994178891181946,
-0.027090655639767647,
-0.018228163942694664,
-0.03417598083615303,
0.058905165642499924,
-0.04199928045272827,
0.021578200161457062,
0.03490757197141647,
0.036292701959609985,
0.01584709621965885,
0.07868704199790955,
-0.0024514244869351387,
0.0479590967297554,
0.009967987425625324,
-0.004833003506064415,
0.11961384862661362,
0.03018411435186863,
-0.011690238490700722,
-0.04933907091617584,
0.027240479364991188,
0.017743244767189026,
0.008119272068142891,
-0.04495085030794144,
0.011362407356500626,
-0.010960888117551804,
0.0038266221527010202,
-0.009804094210267067,
0.036208879202604294,
-0.029972292482852936,
-0.010067312978208065,
0.008167841471731663,
-0.039785757660865784,
-0.03582668676972389,
0.023828057572245598,
-0.006361957173794508,
0.002118096686899662,
-0.022690126672387123,
-0.05296408385038376,
-0.00677925581112504,
0.023312311619520187,
0.002390165813267231,
-0.0347420759499073,
-0.036370910704135895,
0.028852304443717003,
0.024402758106589317,
-0.016738833859562874,
0.01921772211790085,
0.04017810896039009,
-0.020134134218096733,
-0.004119523800909519,
0.014590383507311344,
0.04288818687200546,
0.0022226108703762293,
0.015580378472805023,
0.03528149425983429,
0.028226520866155624,
-0.003994503524154425,
0.0021134456619620323,
-0.0038971430622041225,
-0.03882167860865593,
-0.015199428424239159,
-0.040793340653181076,
0.04642891511321068,
-0.03319818153977394,
0.00617355527356267,
-0.008431180380284786,
-0.009727568365633488,
-0.006907889153808355,
-0.022507941350340843,
-0.030552415177226067,
-0.018259141594171524,
0.02902112528681755,
-0.03970431908965111,
-0.03191928192973137,
-0.029511908069252968,
-0.0028228946030139923,
0.013257884420454502,
-0.011761518195271492,
-0.033418361097574234,
0.00020101593690924346,
0.028021367266774178,
-0.003598321694880724,
-0.014169184491038322,
0.012836427427828312,
0.016097618266940117,
-0.04536863788962364,
0.00039764121174812317,
-0.07372009009122849,
-0.008435750380158424,
-0.028554031625390053,
-0.005978511180728674,
0.03228094056248665,
0.019855119287967682,
-0.005505076143890619,
-0.013127491809427738,
-0.044522348791360855,
-0.00771004892885685,
0.006652278359979391,
-0.027636229991912842,
-0.02958090789616108,
-0.007318946998566389,
-0.03223339468240738,
0.05541742593050003,
-0.028060685843229294,
-0.014986131340265274,
0.017253626137971878,
0.018294187262654305,
0.006405620835721493,
-0.06631935387849808,
0.005383666604757309,
0.011649439111351967,
-0.032125603407621384,
-0.0031144528184086084,
0.000043331638153176755,
0.010532950051128864,
0.007897678762674332,
0.037259574979543686,
0.01884555071592331,
0.037972431629896164,
-0.011864331550896168,
-0.03125293552875519,
0.011524006724357605,
-0.013603575527668,
-0.008315450511872768,
0.04139581695199013,
-0.002559770131483674,
-0.011475668288767338,
-0.029697181656956673,
0.0033873242791742086,
0.008954389952123165,
0.02665151096880436,
0.0026463887188583612,
-0.0955929383635521,
-0.003714584279805422,
-0.02276676520705223,
0.007463839370757341,
-0.014318016357719898,
0.01565796509385109,
-0.01716824807226658,
0.0016674818471074104,
0.029821230098605156,
0.0385405458509922,
0.008298121392726898,
0.02043982222676277,
0.012255861423909664,
-0.047856882214546204,
0.0377800352871418,
0.04374915361404419,
0.036629728972911835,
-0.029383188113570213,
0.012134727090597153,
-0.011713427491486073,
0.04881420359015465,
-0.007421906106173992,
-0.040418609976768494,
0.02692418545484543,
-0.03681624308228493,
-0.05029921233654022,
0.010197697207331657,
0.01286236010491848,
0.012828671373426914,
0.05105973407626152,
-0.011607922613620758,
-0.03729964420199394,
0.022987021133303642,
-0.036779724061489105,
-0.00600385433062911,
-0.006926094181835651,
-0.01597524993121624,
-0.005059884395450354,
-0.0017892636824399233,
-0.01940630003809929,
0.021840346977114677,
0.03215084969997406,
0.009810307063162327,
0.039467766880989075,
-0.012831424362957478,
-0.024072926491498947,
0.002660038648173213,
0.009773039259016514,
0.02168041653931141,
0.006888873875141144,
0.032899826765060425,
0.018625928089022636,
0.06614740192890167,
0.012584519572556019,
0.048281557857990265,
0.0003566456725820899,
0.0017912726616486907,
-0.04255857318639755,
-0.03285689279437065,
-0.012194333598017693,
-0.02039441280066967,
0.04077568277716637,
-0.043060995638370514,
0.007391178514808416,
0.05035153776407242,
-0.05815347656607628,
0.04726964235305786,
-0.03170076757669449,
-0.004919596016407013,
-0.020714135840535164,
0.013791024684906006,
-0.05308055132627487,
0.028767429292201996,
0.04552816227078438,
0.017596475780010223,
0.03885963186621666,
0.04138025641441345,
0.011867169290781021,
-0.01725067012012005,
-0.01282219123095274,
0.012583241797983646,
0.03367859870195389,
-0.035736341029405594,
0.0468871109187603,
0.010581839829683304,
-0.045184679329395294,
0.02189083769917488,
-0.01773471012711525,
-0.03679141774773598,
0.004084853921085596,
0.032832421362400055,
0.002997023519128561,
0.03325221687555313,
-0.005638482980430126,
-0.03196633234620094,
0.003798831719905138,
0.041888970881700516,
0.013236845843493938,
-0.00287220673635602,
-0.035723429173231125,
0.0012400738196447492,
0.04053798317909241,
-0.014604427851736546,
-0.031204288825392723,
0.03616992011666298,
-0.018738187849521637,
0.019376659765839577,
0.005617770832031965,
0.017000798135995865,
-0.002804090268909931,
-0.02878369204699993,
-0.01914200559258461,
-0.07038574665784836,
-0.005340556148439646,
0.034514423459768295,
-0.003574409754946828,
-0.005838434677571058,
-0.026021353900432587,
-0.010767791420221329,
-0.02145243249833584,
-0.004238392226397991,
0.004354489967226982,
-0.024195553734898567,
-0.037778500467538834,
-0.04014565050601959,
-0.02390512079000473,
0.030095554888248444,
-0.05537727475166321,
-0.05165989696979523,
-0.055264897644519806,
0.0063562593422830105,
0.022106174379587173,
0.047704506665468216,
-0.012794372625648975,
-0.05879203975200653,
-0.006404995918273926,
-0.08600622415542603,
-0.00473368214443326,
0.029362257570028305,
0.00135410123039037,
-0.047145646065473557,
-0.027907388284802437,
-0.017354056239128113,
0.013963361270725727,
0.05336327478289604,
0.028412526473402977,
-0.00011535184603417292,
0.043067000806331635,
-0.014484305866062641,
0.07866327464580536,
0.0070128729566931725,
0.03630572184920311,
-0.027278900146484375,
0.015859270468354225,
-0.012888076715171337,
0.007264839485287666,
0.014857882633805275,
-0.006813515909016132,
0.056787360459566116,
-0.04486673325300217,
0.009610246866941452,
-0.009216626174747944,
-0.029523074626922607,
0.05350309610366821,
-0.05444147065281868,
-0.0039136032573878765,
0.06871138513088226,
0.009425838477909565,
0.016734980046749115,
0.021684177219867706,
-0.03099091909825802,
-0.02601618506014347,
0.02099427580833435,
-0.020045515149831772,
-0.04948429763317108,
0.00023507977311965078,
-0.002348558511584997,
0.005959241650998592,
-0.04049547389149666,
-0.031770773231983185,
0.04250435158610344,
-0.033779799938201904,
-0.02339758537709713,
0.04050640016794205,
0.01978376694023609,
0.05010739713907242,
0.005464368034154177,
0.014713017269968987,
-0.004719586111605167,
0.02081521973013878,
0.0002911974734161049,
0.06865130364894867,
0.05234810709953308,
-0.008238663896918297,
0.011334792710840702,
0.022799087688326836,
-0.021131381392478943,
-0.002838235581293702,
-0.011461257003247738,
0.033726051449775696,
-0.0563611164689064,
-0.02744787186384201,
0.021762745454907417,
-0.001890107523649931,
-0.023051682859659195,
-0.0023934480268508196,
-0.005000169854611158,
0.07651255279779434,
-0.04293329641222954,
-0.004225045442581177,
-0.03446478396654129,
0.005050908774137497,
-0.033938441425561905,
-0.002787970704957843,
0.007939326576888561,
0.041760969907045364,
-0.003735045902431011,
-0.005442886613309383,
-0.03597874194383621,
-0.018858322873711586,
0.044219035655260086,
-0.022817911580204964,
0.007501973304897547,
0.02494286559522152,
-0.02111140638589859,
0.021343551576137543,
0.01910734549164772,
-0.006090039387345314,
-0.049640823155641556,
0.016749849542975426,
0.03849717229604721,
0.015880882740020752,
-0.02057010680437088,
-0.032030023634433746,
-0.0023265923373401165,
0.07150308042764664,
-0.006450193468481302,
-0.018655993044376373,
-0.0659133568406105,
0.006132751237601042,
-0.017967063933610916,
-0.008068672381341457
] |
<p>Reading Landau's Statistical Physics Part (3rd Edition), I am trying to calculate the answer to Chapter 39, Problem 3.</p>
<p>You are supposed to calculate the total kinetic energy of the particles in an ideal gas hitting the wall of a vessel containing said gas.</p>
<p>The number of collisions per unit area (of the vessel) per unit time is easily calculated from the Maxwellian distribution of the number of particles with a given velocity $\vec{v}$ (we define a coordinate system with the z-axis perpendicular to a surface element of the vessel's wall; more on that in the above mentioned book):
$$
\mathrm{d}\nu_v = \mathrm{d}N_v \cdot v_z = \frac{N}{V}\left(\frac{m}{2\pi T}\right)^{3/2} \exp\left[-m(v_x^2 + v_y^2 + v_z^2)/2T \right] \cdot v_z \mathrm{d}v_x \mathrm{d}v_y \mathrm{d}v_z
$$</p>
<p>Integration of the velocity components in $x$ and $y$ direction from $-\infty$ to $\infty$, and of the $z$ component from $0$ to $\infty$ (because for $v_z<0$ a particle would move away from the vessel wall) gives for the total number of collisions with the wall per unit area per unit time:
$$
\nu = \frac{N}{V} \sqrt{\frac{T}{2\pi m}}
$$</p>
<p>Now it gets interesting:
I want to calculate the total kinetic energy of all particles hitting the wall, per unit area per unit time. I thought, this would just be:
$$
E_{\text{tot}} = \overline{E} \cdot \nu = \frac{1}{2} m \overline{v^2} \cdot \nu
$$
The solution in Landau is given as:
$$
E = \nu \cdot 2T
$$</p>
<p>That would mean that for the mean-square velocity of my particles I would need a result like:
$$
\overline{v^2} = 4\frac{T}{m}
$$
Now, I consider that for the distribution of $v_x$ and $v_z$ nothing has changed and I can still use a Maxwellian distribution. That would just give me a contribution of $\frac{T}{m}$ each. That leaves me with $2\frac{T}{m}$, which I have to obtain for the $v_z$, but this is where my trouble starts:</p>
<p>How do I calculate the correct velocity distribution of $v_z^2$?</p>
| 8,457 |
[
-0.011503256857395172,
-0.03314630314707756,
0.01007591187953949,
-0.06244395300745964,
0.05501360446214676,
0.02026122435927391,
-0.02581092156469822,
-0.007141426205635071,
-0.005984507035464048,
0.004428302403539419,
0.032601021230220795,
0.03282148018479347,
0.0934862494468689,
0.018591560423374176,
0.016978809610009193,
0.028440408408641815,
-0.03574315458536148,
0.007956274785101414,
0.022052645683288574,
-0.06595241278409958,
0.001723296009004116,
0.019047707319259644,
0.034662023186683655,
-0.021903768181800842,
-0.025901608169078827,
0.04636066406965256,
-0.025377118960022926,
-0.03148796036839485,
0.013328724540770054,
0.04279715567827225,
-0.04709465801715851,
-0.025452634319663048,
0.027288859710097313,
0.004562262445688248,
0.011802129447460175,
0.03486648574471474,
-0.00896294042468071,
-0.016286076977849007,
-0.024950740858912468,
0.00760640250518918,
-0.06663314998149872,
-0.003521229373291135,
-0.017023282125592232,
0.04550693556666374,
-0.024256285279989243,
-0.025423577055335045,
-0.018817119300365448,
-0.015078620985150337,
0.041478946805000305,
-0.05525878444314003,
0.05033114552497864,
0.0049871765077114105,
0.04186593368649483,
-0.019635194912552834,
0.0027961917221546173,
-0.020574072375893593,
0.05492011457681656,
0.062169354408979416,
0.00260250736027956,
-0.006679581478238106,
-0.03631783649325371,
-0.03535066172480583,
-0.0024062693119049072,
-0.05566871911287308,
-0.002271872479468584,
-0.004797765519469976,
0.014346880838274956,
-0.024858033284544945,
0.020838389173150063,
0.017138710245490074,
0.010671643540263176,
0.010788947343826294,
-0.007745808456093073,
-0.030990246683359146,
0.034491315484046936,
0.02166757918894291,
0.015268662013113499,
0.016721108928322792,
0.015106750652194023,
0.020497623831033707,
-0.025071850046515465,
0.02238454855978489,
0.08268822729587555,
0.02502533793449402,
-0.007952442392706871,
-0.018845779821276665,
0.07430768758058548,
0.0015428455080837011,
0.03160366415977478,
0.023179173469543457,
-0.013363149017095566,
0.034875016659498215,
0.027806106954813004,
-0.011670238338410854,
-0.009483487345278263,
0.037443842738866806,
0.003717432264238596,
0.05552813783288002,
-0.009301900863647461,
-0.03357290104031563,
-0.001135851489380002,
-0.0024875658564269543,
-0.012648212723433971,
0.06678678840398788,
-0.014143162406980991,
-0.01510891318321228,
-0.05598093569278717,
-0.002380696125328541,
-0.05275937542319298,
-0.029314404353499413,
-0.02544991858303547,
0.0250540804117918,
0.00011837638885481283,
-0.00555333960801363,
-0.04578889533877373,
0.013470448553562164,
-0.0018705625552684069,
-0.02626710757613182,
0.03821779042482376,
0.035331081598997116,
0.02623032033443451,
-0.024383272975683212,
-0.007336433511227369,
-0.030526112765073776,
-0.08403868228197098,
0.012186618521809578,
-0.00806718785315752,
-0.00256508425809443,
-0.008997641503810883,
0.011120027862489223,
0.031356342136859894,
0.007222420070320368,
-0.0008142514852806926,
-0.003406911389902234,
0.043612223118543625,
0.0030159687157720327,
-0.01483163982629776,
-0.03950083628296852,
0.04937006160616875,
-0.02432505413889885,
0.007573226001113653,
-0.06086081638932228,
-0.045831307768821716,
0.01763877645134926,
0.048379261046648026,
0.00815554428845644,
-0.000414007983636111,
-0.007381070405244827,
0.033474572002887726,
0.0018698893254622817,
-0.05390018969774246,
0.021353989839553833,
-0.054930489510297775,
-0.025127436965703964,
0.02162872813642025,
-0.016489604488015175,
0.06140056252479553,
0.03915645182132721,
0.0012144222855567932,
-0.017449717968702316,
0.07715371251106262,
-0.02514859102666378,
-0.022742820903658867,
0.012714271433651447,
0.01287877932190895,
-0.022395843639969826,
0.06436922401189804,
0.01597599685192108,
0.03127763047814369,
0.010807336308062077,
0.01308401022106409,
-0.010192383080720901,
0.0014579162234440446,
0.01432330347597599,
0.07294975221157074,
0.00010601682879496366,
-0.015957044437527657,
-0.02645847015082836,
-0.010103068314492702,
-0.000806895550340414,
-0.004457156173884869,
-0.06128726527094841,
0.003941365052014589,
-0.008055288344621658,
-0.009049443528056145,
0.034652143716812134,
0.00197966187261045,
0.018125614151358604,
-0.0390968844294548,
-0.025390582159161568,
-0.030029073357582092,
-0.04664992168545723,
0.025058981031179428,
-0.012611492536962032,
-0.025874800980091095,
0.030432213097810745,
-0.009126752614974976,
0.005539066158235073,
-0.018228305503726006,
-0.031265828758478165,
0.00987109076231718,
0.010102923028171062,
0.03767482191324234,
-0.021739736199378967,
0.0055731977336108685,
0.027749480679631233,
0.05148814618587494,
0.016145605593919754,
0.010904625989496708,
-0.030684035271406174,
-0.009239324368536472,
-0.03307531401515007,
-0.029444487765431404,
0.02224576845765114,
0.028387825936079025,
-0.06798707693815231,
0.04003879800438881,
-0.0026327921077609062,
-0.006600889377295971,
0.003624681616201997,
-0.028578007593750954,
0.05806689336895943,
0.05777754634618759,
0.024417079985141754,
-0.01575370691716671,
0.0052084303461015224,
-0.015875672921538353,
0.02690911665558815,
0.02213500253856182,
-0.03001062572002411,
-0.049941062927246094,
-0.02729041501879692,
0.042707834392786026,
0.040564000606536865,
-0.038662560284137726,
-0.017324067652225494,
0.05733301118016243,
-0.003913292195647955,
0.03955334797501564,
-0.009397151879966259,
-0.0100524527952075,
-0.05395198240876198,
0.029075875878334045,
0.040258411318063736,
-0.002785319462418556,
-0.008705413900315762,
0.031459759920835495,
0.01591872237622738,
0.004832006990909576,
0.027706647291779518,
-0.05676555261015892,
0.008937393315136433,
0.019501831382513046,
0.0027224156074225903,
-0.009950102306902409,
-0.020153429359197617,
-0.002619801787659526,
-0.0005426349816843867,
0.042037252336740494,
0.045829448848962784,
0.012286553159356117,
0.007552734576165676,
-0.01123183686286211,
0.0028006110806018114,
0.00656288955360651,
0.022682111710309982,
-0.009824436157941818,
0.0003884300822392106,
0.03250685706734657,
-0.010892932303249836,
0.020387792959809303,
-0.00019618423539213836,
-0.032832808792591095,
0.028808176517486572,
-0.009298832155764103,
0.013020460493862629,
0.06139849126338959,
-0.006957379635423422,
-0.05438496917486191,
-0.03366828337311745,
-0.007489362731575966,
-0.01864531822502613,
-0.003427457995712757,
0.04472508653998375,
-0.06132704019546509,
-0.010034396313130856,
-0.05877434462308884,
-0.03020162135362625,
0.004686072468757629,
0.01614905148744583,
-0.009249484166502953,
0.04352892190217972,
-0.002315892605111003,
-0.04892505332827568,
-0.0037274151109158993,
0.024716658517718315,
0.014834043569862843,
-0.04935530573129654,
0.016137748956680298,
0.05184004083275795,
-0.010053730569779873,
-0.03444104269146919,
0.019633110612630844,
-0.04441293329000473,
-0.05331636965274811,
-0.01871078833937645,
0.018543915823101997,
0.02223038114607334,
-0.028251582756638527,
0.009468798525631428,
0.02151702716946602,
-0.01760859601199627,
0.002469617873430252,
-0.04297028109431267,
-0.0301746167242527,
-0.03764747828245163,
-0.013881174847483635,
0.02382141537964344,
-0.026839593425393105,
-0.03070959448814392,
0.06314116716384888,
-0.01638181507587433,
-0.05349012091755867,
0.028875436633825302,
0.01520334742963314,
0.00878581590950489,
-0.025051578879356384,
0.04318050295114517,
0.007241973653435707,
-0.04574596509337425,
0.006742588244378567,
-0.029642434790730476,
0.041412435472011566,
0.04060724750161171,
-0.007737229578197002,
0.04037967696785927,
0.04255646839737892,
0.013164089992642403,
0.015351938083767891,
0.030793815851211548,
0.005237524397671223,
-0.0012508586514741182,
0.07158910483121872,
0.00908157229423523,
0.028172822669148445,
0.04814775660634041,
-0.08353765308856964,
0.07594525814056396,
-0.01870836690068245,
0.0020290850661695004,
-0.010761032812297344,
0.014245118945837021,
-0.0011295254807919264,
-0.04837155342102051,
-0.010997394099831581,
-0.004073240794241428,
0.04224530979990959,
-0.019069747999310493,
0.02611692063510418,
0.05999516695737839,
0.03451760485768318,
0.004072254989296198,
-0.03976990655064583,
-0.02666606195271015,
-0.0086361737921834,
0.01683376543223858,
-0.009548560716211796,
0.00883637648075819,
0.0008035560022108257,
0.05084321275353432,
-0.014912622049450874,
-0.03306291624903679,
0.006646576803177595,
-0.01067908015102148,
-0.015797417610883713,
-0.027257822453975677,
-0.021914945915341377,
0.02932455576956272,
-0.007998256012797356,
0.06273485720157623,
-0.036369118839502335,
0.032947760075330734,
0.024169716984033585,
-0.017835654318332672,
-0.11096644401550293,
-0.023650620132684708,
-0.0002252950653200969,
-0.04355514422059059,
-0.011772798374295235,
-0.011727999895811081,
0.02437382936477661,
-0.024720700457692146,
0.0021624721121042967,
0.01980944536626339,
0.001854986185207963,
-0.046697668731212616,
0.036329057067632675,
-0.03472215309739113,
-0.030734999105334282,
-0.00922758411616087,
0.06395062804222107,
0.04448676481842995,
-0.03330313041806221,
0.008303070440888405,
0.021159479394555092,
0.002465793862938881,
-0.001362049370072782,
0.002251157769933343,
-0.01356738805770874,
0.06115443632006645,
0.047521140426397324,
-0.005543041974306107,
0.01598154939711094,
-0.03902236372232437,
0.024941300973296165,
0.003284644801169634,
0.029162153601646423,
0.012907266616821289,
-0.027578061446547508,
-0.057178936898708344,
-0.01775878667831421,
0.0031699659302830696,
0.01190408319234848,
0.0741376131772995,
0.028714438900351524,
0.014959444291889668,
0.0485704131424427,
0.006922433618456125,
-0.0002277641906403005,
0.013325226493179798,
0.01679031178355217,
-0.010514101944863796,
0.006339999381452799,
-0.033626850694417953,
-0.004853095859289169,
-0.021157147362828255,
0.01860794425010681,
0.004718138836324215,
-0.002762048039585352,
-0.01839650608599186,
0.005102040246129036,
0.00861103180795908,
0.06401582062244415,
0.00937922578305006,
-0.01951071061193943,
0.012900053523480892,
0.011105567216873169,
0.017821773886680603,
-0.029605239629745483,
-0.010252525098621845,
-0.0006261698435992002,
0.0070559498853981495,
0.0038231804501265287,
-0.008448859676718712,
-0.05493694543838501,
-0.03528127074241638,
0.026485515758395195,
0.0468863919377327,
-0.005086606368422508,
0.009092281572520733,
-0.02163565345108509,
0.009403103031218052,
0.025330524891614914,
-0.008168908767402172,
-0.005539551377296448,
-0.023501303046941757,
-0.0015727417776361108,
-0.0165073424577713,
-0.08051864057779312,
-0.06850855052471161,
-0.026966549456119537,
0.01689957268536091,
0.017295949161052704,
-0.06732212752103806,
-0.015452654100954533,
0.002070893067866564,
0.01992502063512802,
0.03369266539812088,
0.02202935703098774,
-0.01248013973236084,
-0.0036316816695034504,
0.015254517085850239,
0.03671744838356972,
-0.02543550170958042,
-0.0835934579372406,
0.00009233270247932523,
0.004070750437676907,
0.04997393116354942,
-0.007743487134575844,
-0.04163801297545433,
-0.04204393923282623,
0.06863860040903091,
-0.01046831626445055,
0.024795325472950935,
0.003395632840692997,
-0.0023032028693705797,
0.07200413942337036,
0.045388203114271164,
0.0027008873876184225,
0.08116882294416428,
-0.00708284555003047,
-0.031721603125333786,
0.026924077421426773,
-0.04038243368268013,
0.029107095673680305,
-0.02421957068145275,
-0.03429226204752922,
-0.06300617009401321,
-0.0003968496748711914,
-0.001197940669953823,
0.05712193250656128,
-0.023960266262292862,
-0.006511242128908634,
-0.0497245118021965,
-0.026574794203042984,
0.012337131425738335,
0.009549995884299278,
0.003197306767106056,
-0.004389097914099693,
0.007375925313681364,
0.009160212241113186,
0.02309793420135975,
-0.04452257230877876,
0.010553490370512009,
-0.014492031186819077,
0.004262319300323725,
-0.003440392669290304,
-0.018353478983044624,
-0.023676931858062744,
-0.014215228147804737,
-0.00743746617808938,
0.04728284478187561,
-0.026139549911022186,
0.01965109258890152,
-0.027136821299791336,
-0.0006385219749063253,
0.022177275270223618,
-0.023357674479484558,
-0.06589661538600922,
0.00015618151519447565,
0.019874366000294685,
-0.005228574387729168,
-0.016112543642520905,
-0.01892717182636261,
-0.013744489289820194,
0.039662692695856094,
-0.05306848883628845,
0.007193268276751041,
0.006045896094292402,
-0.02698368765413761,
-0.05398046597838402,
-0.06149241328239441,
-0.06728075444698334,
-0.01452135480940342,
-0.048410817980766296,
0.01600426435470581,
0.03398203104734421,
-0.016053486615419388,
-0.009936220943927765,
0.0035469718277454376,
0.040873054414987564,
0.040945734828710556,
0.0010618588421493769,
-0.04427536949515343,
0.012614692561328411,
-0.02057730406522751,
-0.019633037969470024,
-0.0003627911501098424,
0.03174659609794617,
0.006455152295529842,
0.003270951099693775,
0.04115575924515724,
-0.021949399262666702,
0.03453141823410988,
-0.03929181024432182,
-0.0033569259103387594,
0.03236108273267746,
-0.010561186820268631,
-0.04531770199537277,
0.004252483136951923,
0.025775689631700516,
0.03796260431408882,
0.023077435791492462,
-0.00989402737468481,
-0.007594194728881121,
-0.02027588151395321,
0.01386705320328474,
0.003829302964732051,
-0.021862562745809555,
0.0033258020412176847,
0.006839840207248926,
0.05847639590501785,
0.042722053825855255,
0.011998974718153477,
-0.034175846725702286,
-0.00865362212061882,
0.040494926273822784,
-0.028849570080637932,
-0.01818956434726715,
0.014227519743144512,
-0.00882352888584137,
-0.01588522270321846,
-0.04216150566935539,
-0.07551386207342148,
0.033246513456106186,
0.04969214275479317,
0.00025862621259875596,
0.06579221785068512,
-0.02267063781619072,
-0.010962297208607197,
-0.007242905907332897,
-0.03064262680709362,
-0.013038567267358303,
0.042152028530836105,
-0.0018532504327595234,
0.03082704357802868,
-0.0022375620901584625,
-0.029196547344326973,
0.030720720067620277,
-0.017943210899829865,
-0.045554302632808685,
-0.013344049453735352,
-0.003164279041811824,
0.0037828346248716116,
0.004509530495852232,
-0.0009921054588630795,
-0.018470529466867447,
0.03794405236840248,
-0.04357164725661278,
0.03305889666080475,
-0.015711961314082146,
-0.014960836619138718,
0.03905922919511795,
0.04884292930364609,
-0.033767424523830414,
-0.05791400745511055,
0.04604373499751091,
-0.032763153314590454,
0.004237627610564232,
0.03507322445511818,
-0.00813448615372181,
0.028913190588355064,
0.01394393015652895,
0.035739365965127945,
-0.012437520548701286,
-0.001965395174920559,
0.018421418964862823,
-0.044548340141773224,
0.015262000262737274,
-0.030124571174383163,
-0.02677508443593979,
0.024473583325743675,
0.009634368121623993,
-0.014555959030985832,
-0.012106315232813358,
-0.04444344341754913,
0.029093926772475243,
0.012724851258099079,
0.02666059322655201,
0.012235174886882305,
0.0555771067738533,
0.00751383975148201,
0.041794877499341965,
-0.06630628556013107,
0.04111762344837189,
0.1373753845691681,
0.025630086660385132,
0.02331390418112278,
-0.017277605831623077,
-0.00663707684725523,
-0.018757691606879234,
-0.006284547504037619,
-0.05346439406275749,
0.028136495500802994,
0.0021271759178489447,
-0.043944407254457474,
0.006154450122267008,
0.07664407789707184,
-0.026438619941473007,
-0.0179862380027771,
0.006717294920235872,
-0.052204638719558716,
-0.047515273094177246,
-0.005601516924798489,
0.025766413658857346,
-0.003383257193490863,
0.009608503431081772,
-0.0033288090489804745,
0.005129911471158266,
-0.013524970971047878,
-0.02397013083100319,
-0.031190598383545876,
-0.05907543748617172,
0.013717732392251492,
-0.04021264240145683,
-0.06136927381157875,
0.004418408498167992,
-0.000060777863836847246,
-0.017198126763105392,
-0.009208929724991322,
-0.006704362109303474,
0.027156418189406395,
0.019654925912618637,
0.027023829519748688,
0.007275186944752932,
0.010644973255693913,
0.010728573426604271,
0.004495685920119286,
0.01948775351047516,
-0.03076333925127983,
-0.01241571269929409,
-0.0333685539662838,
0.07144482433795929,
0.00671998830512166,
0.015134502202272415,
-0.008031947538256645,
0.023638153448700905,
0.006013356614857912,
-0.023625539615750313,
0.017870716750621796,
-0.005649864207953215,
0.035303495824337006,
0.0002252864942420274,
0.017269229516386986,
-0.006138357799500227,
-0.00011508160241646692,
0.02033662237226963,
-0.0037122764624655247,
0.005092102102935314,
0.009268416091799736,
0.010374864563345909,
0.010731902904808521,
0.05084671452641487,
0.013087720610201359,
-0.01963026635348797,
-0.02147373929619789,
0.013341439887881279,
-0.05782909691333771,
-0.008017645217478275,
-0.020188555121421814,
0.008502330631017685,
0.03829256072640419,
0.005291585810482502,
-0.019525323063135147,
-0.02174176275730133,
-0.07084710150957108,
0.017792372032999992,
0.006518217269331217,
-0.011956826783716679,
-0.027078066021203995,
0.00001407868057867745,
-0.023897482082247734,
0.032802075147628784,
-0.015676314011216164,
0.004933016840368509,
-0.019188866019248962,
0.06658455729484558,
0.0048210094682872295,
0.018121913075447083,
-0.03748679906129837,
-0.005240004509687424,
-0.019223762676119804,
0.002326040295884013,
-0.010076839476823807,
0.0288804043084383,
0.019879676401615143,
0.03440437093377113,
0.0224690493196249,
0.04326227679848671,
-0.016134267672896385,
0.005887080915272236,
0.03305315598845482,
-0.039138004183769226,
-0.002876305254176259,
0.04799528419971466,
0.02736702188849449,
-0.03355861455202103,
-0.0011448179138824344,
0.0006579002365469933,
0.0006293115438893437,
-0.024518143385648727,
0.03033275716006756,
-0.020565927028656006,
-0.004624565131962299,
-0.019158417358994484,
-0.007483220659196377,
-0.006302754394710064,
-0.016362762078642845,
-0.011792517267167568,
0.04955243691802025,
-0.021396029740571976,
0.01152923982590437,
-0.03166782483458519,
0.023636799305677414,
-0.028138164430856705,
0.009375439025461674,
-0.005953688640147448,
0.012824833393096924,
-0.033225513994693756,
-0.061294618993997574,
0.06370159238576889,
-0.010095029138028622,
0.013525443151593208,
-0.0024426153395324945,
0.006807563826441765,
0.024678558111190796,
-0.03004753775894642,
-0.07313064485788345,
0.03037288412451744,
0.012223822064697742,
-0.0011316073359921575,
0.025695327669382095,
0.0020011127926409245,
-0.06479521095752716,
0.05846041440963745,
-0.04520837590098381,
-0.02086401917040348,
-0.06024574860930443,
-0.06302708387374878,
-0.027709275484085083,
-0.02396620810031891,
0.0679851695895195,
0.027328435331583023,
0.020362550392746925,
0.05413969233632088,
0.0405302569270134,
-0.020182201638817787,
0.031023966148495674,
-0.012772164307534695,
-0.04122801125049591,
0.019862284883856773,
0.01556264515966177,
-0.00021779554663226008,
0.05447236821055412,
0.09002528339624405,
0.007011893671005964,
0.007537142373621464,
-0.001431005191989243,
-0.021164800971746445,
-0.09552489221096039,
-0.018868422135710716,
-0.011155086569488049,
0.03389935940504074,
0.06266848742961884,
-0.07631829380989075,
0.0038307427894324064,
0.030586468055844307,
-0.07281536608934402,
0.026682298630475998,
-0.03581983223557472,
-0.0010856486624106765,
-0.06570176780223846,
-0.02590380609035492,
-0.012644993141293526,
0.027856310829520226,
0.02095932699739933,
0.01104809157550335,
0.03671548143029213,
0.05234808847308159,
-0.027602972462773323,
-0.03955565020442009,
-0.0034502141643315554,
0.04955822974443436,
-0.022730479016900063,
-0.02141484059393406,
0.07065452635288239,
-0.0007538061472587287,
-0.006104038562625647,
-0.004712763708084822,
0.006688951980322599,
0.02393941394984722,
-0.03308532014489174,
0.04016640782356262,
-0.00413889903575182,
0.031052827835083008,
0.02216492034494877,
0.04304679483175278,
0.03753548860549927,
-0.011164980009198189,
0.021303245797753334,
-0.019949408248066902,
-0.021420413628220558,
0.0034091435372829437,
0.012010236270725727,
0.01017831265926361,
-0.01766257733106613,
0.04113447293639183,
0.00573359802365303,
-0.0018982940819114447,
0.02716735564172268,
0.0018921301234513521,
0.011445261538028717,
-0.03375576436519623,
0.024411272257566452,
-0.028936145827174187,
0.016631295904517174,
0.03954022750258446,
0.020002583041787148,
0.009167075157165527,
-0.027708955109119415,
0.02174638770520687,
-0.029153229668736458,
0.014266138896346092,
0.0002544633753132075,
-0.0029456058982759714,
-0.045633506029844284,
-0.007938539609313011,
0.0049816761165857315,
-0.022888025268912315,
0.016653474420309067,
-0.024757441133260727,
-0.06063925847411156,
-0.022026846185326576,
0.0016524269012734294,
0.026067586615681648,
0.0008259259047918022,
-0.028962524607777596,
-0.006145931314677,
-0.054431408643722534,
0.008911645971238613,
-0.029882609844207764,
-0.04604363441467285,
-0.01554060634225607,
-0.04524487629532814,
0.009682152420282364,
0.02574898861348629,
0.06421064585447311,
0.032291144132614136,
0.012577153742313385,
0.008729924447834492,
0.01730942167341709,
0.0386313758790493,
-0.05815458670258522,
-0.0053140041418373585,
-0.018497411161661148,
0.0017847694689407945,
0.0199012141674757,
0.01066767517477274,
-0.004190194420516491,
0.002608489478006959,
0.0393306203186512,
-0.015109919011592865,
0.01765577122569084,
0.002044660272076726,
-0.021095819771289825,
0.01932208053767681,
-0.02437768131494522,
-0.018373074010014534,
0.04965304955840111,
-0.035485535860061646,
0.030314935371279716,
0.032764703035354614,
-0.008952358737587929,
-0.06057579070329666,
-0.034947555512189865,
-0.02763943374156952,
-0.012900818139314651,
-0.014141928404569626,
0.005592248402535915,
0.042877040803432465,
-0.053341373801231384,
0.030870182439684868,
0.03987469896674156,
-0.029591161757707596,
-0.03123786859214306,
0.0274798721075058,
0.029463432729244232,
0.03131354600191116,
-0.0048409076407551765,
0.011678765527904034,
0.019922491163015366,
0.009717869572341442,
0.013451144099235535,
0.06715305894613266,
0.03008970431983471,
0.017664609476923943,
0.004936254117637873,
0.0296311117708683,
-0.0437597930431366,
-0.0038894929457455873,
0.05066454038023949,
0.010641159489750862,
0.00488280551508069,
0.0006300705717876554,
0.02721717394888401,
-0.014830559492111206,
0.0008931942284107208,
0.04502105340361595,
0.0005740572232753038,
0.09122440963983536,
-0.017217937856912613,
0.03959580138325691,
-0.030605383217334747,
-0.01616004854440689,
-0.019895080476999283,
0.03440852835774422,
0.004985991399735212,
0.03798417001962662,
-0.03990967571735382,
0.012136286124587059,
-0.019252199679613113,
0.0059617008082568645,
-0.016244376078248024,
-0.049415916204452515,
-0.0013472175924107432,
0.031342413276433945,
0.014076320454478264,
-0.030896756798028946,
-0.042695920914411545,
-0.0024550792295485735,
-0.031721390783786774,
0.007217358332127333,
0.04470024257898331,
0.03393726795911789,
0.003394787898287177,
0.026630576699972153,
-0.043231695890426636,
0.053641293197870255,
-0.025676794350147247,
-0.022091424092650414,
0.006963190156966448,
0.04763404279947281,
0.0030650170519948006,
0.020390605553984642
] |
<p>Do we know exactly the difference between <a href="http://en.wikipedia.org/wiki/Particle" rel="nofollow">particles</a> and <a href="http://en.wikipedia.org/wiki/Quasiparticle" rel="nofollow">quasiparticles</a>? Is Higgs boson a particle or a quasiparticle? I ask this because if I understood well, Higgs boson created by a spontaneaous breaking symmetry and correspond to a Goldstone mode. Maybe I am wrong in my explication.</p>
| 8,458 |
[
-0.007917791604995728,
-0.026452189311385155,
0.04416496306657791,
-0.05043357238173485,
0.016057182103395462,
0.025488056242465973,
-0.025084013119339943,
-0.03064557909965515,
0.004783388692885637,
-0.007958028465509415,
0.05561923235654831,
0.0027614349965006113,
0.03830324858427048,
0.02029738947749138,
0.00930752232670784,
0.04069938510656357,
-0.0022866849321871996,
-0.010286095552146435,
-0.01653199829161167,
-0.004615957848727703,
0.0003169467381667346,
0.016078440472483635,
-0.011713787913322449,
0.0032991801854223013,
-0.011118408292531967,
0.018691638484597206,
0.02967427484691143,
0.04411391541361809,
0.009327325038611889,
0.038673046976327896,
0.008533126674592495,
-0.011814280413091183,
0.03448983281850815,
-0.012794743292033672,
0.012633733451366425,
-0.015165705233812332,
-0.009213131852447987,
-0.025653008371591568,
-0.017566943541169167,
0.007492566015571356,
-0.0411456823348999,
-0.029587332159280777,
-0.014064478687942028,
0.07153069972991943,
-0.026973934844136238,
-0.00973292626440525,
-0.003615564201027155,
-0.006644153501838446,
0.0403471514582634,
-0.08663259446620941,
0.05738244950771332,
0.04316556453704834,
0.021103085950016975,
0.0018751109018921852,
-0.0023320296313613653,
0.008029508404433727,
0.051372312009334564,
0.08739715069532394,
-0.03356471657752991,
-0.08961839228868484,
-0.013864326290786266,
-0.04544318839907646,
0.04806889593601227,
-0.02541358396410942,
-0.023205405101180077,
0.050366099923849106,
-0.012289635837078094,
-0.044630661606788635,
0.025829773396253586,
0.016963910311460495,
0.005294168367981911,
-0.000544006354175508,
0.02328275702893734,
0.01456854585558176,
0.04056067392230034,
-0.018838899210095406,
0.026814313605427742,
0.02883845567703247,
0.019465360790491104,
0.0365220382809639,
0.014261627569794655,
0.013672234490513802,
0.021659107878804207,
0.003870191052556038,
-0.009006593376398087,
-0.034418582916259766,
0.0916513130068779,
-0.050070274621248245,
0.005376959685236216,
0.05430036038160324,
-0.013109912164509296,
0.006765729747712612,
0.0872453972697258,
-0.0016545329708606005,
-0.021280188113451004,
0.01328500360250473,
0.01990222930908203,
-0.003864978440105915,
0.008521792478859425,
0.012229799292981625,
0.021271854639053345,
-0.016291968524456024,
0.054479438811540604,
0.059598613530397415,
-0.0020559022668749094,
-0.009168324060738087,
-0.022170603275299072,
-0.014006162993609905,
-0.062066834419965744,
-0.003906128229573369,
-0.017403090372681618,
0.013868511654436588,
-0.02382032200694084,
-0.006890943273901939,
0.01178741455078125,
-0.006609055679291487,
0.021969614550471306,
-0.01742756925523281,
0.10060682892799377,
0.04879075661301613,
0.05361950770020485,
-0.05212355777621269,
0.0011772798607125878,
-0.032677218317985535,
-0.08545603603124619,
0.003962554037570953,
0.030220575630664825,
0.006431280169636011,
-0.03843730315566063,
0.015823276713490486,
-0.010231024585664272,
0.002254494931548834,
0.03856365382671356,
-0.007137616164982319,
0.028525585308670998,
-0.02701515331864357,
-0.1158648133277893,
-0.06896521151065826,
0.0764215961098671,
0.03255651146173477,
-0.02517795003950596,
-0.08749056607484818,
0.003132987068966031,
-0.0007790903327986598,
0.06352926790714264,
-0.015942685306072235,
0.0443037673830986,
0.0013960881624370813,
0.027482375502586365,
0.00538370106369257,
0.0029044023249298334,
0.011362751014530659,
0.036573998630046844,
-0.03292249143123627,
0.0018245147075504065,
-0.04623384773731232,
-0.012466123327612877,
0.043474022299051285,
-0.01389042567461729,
-0.008199644275009632,
0.06499695777893066,
0.005368406418710947,
0.02291557937860489,
0.024798646569252014,
0.007734138984233141,
-0.01943850703537464,
0.061866022646427155,
-0.010862568393349648,
0.01594800129532814,
0.07305099070072174,
0.008846611715853214,
0.017836477607488632,
-0.003776128403842449,
0.026364203542470932,
0.028370946645736694,
-0.0358438715338707,
-0.06970096379518509,
-0.04107639193534851,
0.0048882667906582355,
-0.016093090176582336,
-0.0772772878408432,
-0.012746673077344894,
-0.0053665898740291595,
0.017746224999427795,
-0.008105624467134476,
0.02478025108575821,
-0.004392417147755623,
-0.036599304527044296,
0.008737885393202305,
-0.031581249088048935,
-0.07665238529443741,
-0.07354221493005753,
-0.010669875890016556,
-0.005589067470282316,
-0.023086540400981903,
0.03862616792321205,
0.0053399899043142796,
-0.015084631741046906,
-0.038910023868083954,
-0.006589767523109913,
-0.013998433016240597,
0.05651058256626129,
-0.015273385681211948,
0.004791766405105591,
0.003466360503807664,
0.023101966828107834,
0.004797180183231831,
-0.013853449374437332,
0.032672297209501266,
0.007571393623948097,
-0.049795377999544144,
-0.007173515856266022,
-0.027139797806739807,
0.03104487992823124,
-0.016702424734830856,
-0.012797772884368896,
0.021655874326825142,
-0.02041555382311344,
-0.050529275089502335,
0.06106875091791153,
-0.02171381562948227,
0.05115457996726036,
0.023780226707458496,
0.0012338112574070692,
-0.012205827049911022,
-0.015019059181213379,
-0.021180035546422005,
0.023505117744207382,
-0.02658708393573761,
0.008265533484518528,
-0.06361008435487747,
-0.009063356555998325,
0.016381505876779556,
0.008682523854076862,
-0.025641636922955513,
0.02050785720348358,
0.019585389643907547,
0.034848541021347046,
0.04631809517741203,
0.0008184700855053961,
-0.03981051594018936,
-0.03165502846240997,
0.02323518507182598,
0.03280974552035332,
-0.021138636395335197,
0.026879597455263138,
0.033485911786556244,
-0.02659190632402897,
0.007809171918779612,
-0.03416549041867256,
-0.032124634832143784,
0.0510852076113224,
-0.0007167484727688134,
-0.00825431477278471,
0.0010164526756852865,
-0.06797272711992264,
0.02808384597301483,
-0.005870846100151539,
0.04161201789975166,
0.003526488784700632,
-0.005138197913765907,
-0.019828185439109802,
-0.035677384585142136,
-0.01619233377277851,
-0.008451540023088455,
-0.002064997097477317,
-0.04375670477747917,
-0.03277062252163887,
0.020194614306092262,
-0.01574929617345333,
0.0211334265768528,
-0.018061405047774315,
-0.005316723138093948,
-0.017348982393741608,
0.02014893665909767,
0.006466865073889494,
-0.0026952726766467094,
0.07106758654117584,
-0.06243709847331047,
-0.022066336125135422,
0.01313287764787674,
-0.0418890155851841,
-0.010741823352873325,
0.019904552027583122,
-0.06992501020431519,
0.018305540084838867,
-0.08975431323051453,
-0.008039413020014763,
-0.013330461457371712,
-0.03322433680295944,
-0.005386956036090851,
-0.008665160275995731,
-0.01631888933479786,
-0.03133028745651245,
0.0031700634863227606,
-0.013499858789145947,
0.0046552675776183605,
-0.01649748906493187,
-0.01957372948527336,
-0.028828665614128113,
-0.013750135898590088,
0.0009354182402603328,
0.002370815956965089,
-0.049028430134058,
-0.05543099716305733,
-0.011228213086724281,
0.012608821503818035,
0.012287088669836521,
-0.006710920017212629,
0.0163981132209301,
0.08955483883619308,
-0.04697364941239357,
-0.011622699908912182,
-0.03473157808184624,
-0.029205234721302986,
0.035437095910310745,
-0.026804182678461075,
0.031044073402881622,
-0.02403884194791317,
-0.03870421275496483,
0.07358872890472412,
0.02382403425872326,
-0.046454548835754395,
0.0004135805065743625,
0.006112256087362766,
-0.009596801362931728,
-0.016469797119498253,
0.006063749548047781,
0.02790985070168972,
-0.009336083196103573,
0.02066921256482601,
0.021806128323078156,
0.027904365211725235,
0.007017897441983223,
0.029215138405561447,
-0.04209842160344124,
-0.04503525793552399,
0.012897377833724022,
0.01966833882033825,
0.043984103947877884,
0.004958495497703552,
-0.027535781264305115,
0.005130775272846222,
-0.03986877575516701,
0.046596821397542953,
-0.0169514287263155,
-0.004465234931558371,
0.06513918191194534,
0.011248922906816006,
0.021107390522956848,
-0.013190495781600475,
0.01644718647003174,
0.019386395812034607,
-0.01963743194937706,
0.007131333462893963,
0.00589341064915061,
0.013787264004349709,
0.0026614407543092966,
-0.009539904072880745,
0.03589871525764465,
0.04144113510847092,
-0.03895598277449608,
-0.023474853485822678,
-0.007974597625434399,
-0.020673900842666626,
0.02332248166203499,
0.010503807105123997,
-0.011323763057589531,
0.04175744205713272,
0.011892173439264297,
0.05354410037398338,
0.0032644812017679214,
0.0021000325214117765,
-0.056343186646699905,
-0.06672224402427673,
0.02400984615087509,
0.010227655991911888,
0.04181251302361488,
0.014859052374958992,
0.05562862008810043,
0.02773248590528965,
0.015085053630173206,
-0.009205120615661144,
-0.021791653707623482,
-0.08263101428747177,
0.01669446751475334,
-0.04663025960326195,
0.00570578221231699,
-0.015945330262184143,
-0.0351969376206398,
-0.005714897532016039,
-0.022905241698026657,
-0.010552048683166504,
-0.021704187616705894,
-0.004322568885982037,
-0.03380771726369858,
0.014749079011380672,
-0.021293962374329567,
-0.019470052793622017,
-0.011162159033119678,
-0.0018076400738209486,
0.0026401712093502283,
-0.03811585158109665,
0.010509990155696869,
0.04273185878992081,
-0.04105282574892044,
0.015947479754686356,
0.0140493493527174,
0.0162443108856678,
0.01855870895087719,
0.008538199588656425,
0.03880715370178223,
0.05094977840781212,
-0.023485999554395676,
0.02173856645822525,
0.025608625262975693,
0.05587901920080185,
-0.016118064522743225,
0.0028753310907632113,
-0.01343492791056633,
-0.04570651054382324,
-0.01744980178773403,
-0.002821940928697586,
0.04293268546462059,
-0.015816904604434967,
-0.015606746077537537,
0.04392550140619278,
0.010116398334503174,
-0.0057110232301056385,
0.05162256956100464,
0.05033912882208824,
0.011571268551051617,
-0.010241647250950336,
-0.0637655109167099,
-0.016691243276000023,
-0.018307283520698547,
-0.025208119302988052,
0.033679939806461334,
-0.009411996230483055,
-0.012741453014314175,
0.02944030798971653,
0.013576102443039417,
0.0032109629828482866,
-0.01044136006385088,
-0.014205456711351871,
-0.01760634407401085,
-0.0019379022996872663,
0.014087313786149025,
0.012409751303493977,
-0.03542688488960266,
0.05480072274804115,
0.03291575610637665,
-0.011759752407670021,
-0.01676981709897518,
-0.06257480382919312,
-0.0002520371344871819,
0.06321372836828232,
0.04400958493351936,
-0.03609466180205345,
-0.02828768827021122,
-0.03187965974211693,
-0.02376769296824932,
0.05003441125154495,
-0.015283152461051941,
0.018159164115786552,
-0.01794855110347271,
-0.0073937359265983105,
-0.005395122338086367,
0.026804449036717415,
-0.0010262029245495796,
0.04749813675880432,
0.006045742426067591,
0.024541644379496574,
-0.04064522311091423,
-0.015217079780995846,
-0.029311073943972588,
-0.015566345304250717,
0.01930011622607708,
0.03462032973766327,
-0.0024145597126334906,
0.03144175931811333,
0.009465519338846207,
0.0066759646870195866,
-0.0282580703496933,
-0.1067502424120903,
-0.01265603955835104,
0.02277289144694805,
-0.028104986995458603,
0.014963800087571144,
-0.025549113750457764,
-0.04315973073244095,
-0.006203072145581245,
0.005659759510308504,
0.026246780529618263,
-0.0035379468463361263,
-0.0519450344145298,
0.03727689012885094,
0.04156877472996712,
-0.0027810968458652496,
0.043217480182647705,
0.010745897889137268,
-0.029245790094137192,
-0.014628095552325249,
-0.03951262682676315,
0.0226751696318388,
-0.025261290371418,
0.0035850508138537407,
-0.016470197588205338,
0.008980204351246357,
-0.02192028984427452,
0.04338378831744194,
0.001419175649061799,
0.012918887659907341,
-0.013894780538976192,
-0.05052425339818001,
-0.045770153403282166,
0.005328475032001734,
0.00891012605279684,
-0.006527918856590986,
-0.03143599256873131,
0.03303670138120651,
0.01347651518881321,
-0.018982447683811188,
0.01699311099946499,
0.005244193132966757,
0.024733157828450203,
0.02154705300927162,
0.02130056917667389,
0.029395293444395065,
-0.016465842723846436,
-0.04305287450551987,
0.026018522679805756,
-0.05773722752928734,
0.0480697937309742,
-0.03807413950562477,
-0.004749867599457502,
0.007833576761186123,
-0.06311340630054474,
-0.04394928365945816,
0.0074170674197375774,
0.02366027981042862,
-0.007138677407056093,
-0.016270464286208153,
0.05817236751317978,
0.013622083701193333,
0.002771237399429083,
-0.06954270601272583,
-0.039041370153427124,
-0.006035500206053257,
0.005711346864700317,
-0.0032676467671990395,
0.020741911605000496,
0.04198537394404411,
-0.05293526127934456,
-0.022907542064785957,
-0.008417929522693157,
0.036990292370319366,
-0.0580112524330616,
-0.026936165988445282,
0.01587686501443386,
0.03304296359419823,
0.05280809476971626,
0.005579802673310041,
-0.017984766513109207,
-0.0020538424141705036,
0.02295919880270958,
0.003135380335152149,
-0.000477668916573748,
0.08189095556735992,
0.0005307436804287136,
-0.011286386288702488,
0.01762246899306774,
-0.011999234557151794,
0.03111077845096588,
0.0100656533613801,
0.028768446296453476,
0.03955159708857536,
-0.009766420349478722,
-0.007253704126924276,
-0.005217927508056164,
0.01195645984262228,
0.0164675060659647,
0.0151166757568717,
-0.025464989244937897,
-0.009851070120930672,
-0.010209403000772,
-0.014318769797682762,
0.025932760909199715,
-0.019907044246792793,
0.006392694544047117,
0.015134869143366814,
0.011048165149986744,
-0.026241274550557137,
0.008039836771786213,
0.04700890928506851,
-0.043344542384147644,
0.009132673032581806,
-0.02861688658595085,
0.03804710879921913,
0.001129516982473433,
0.011906208470463753,
0.007320270873606205,
-0.01655942015349865,
-0.059430476278066635,
-0.02164720743894577,
0.025328531861305237,
0.0023901904933154583,
0.02675100788474083,
0.004620268475264311,
-0.017924854531884193,
0.011490744538605213,
-0.03136862441897392,
0.023932065814733505,
0.030335968360304832,
0.011014205403625965,
0.011327797546982765,
-0.055155474692583084,
-0.01902068965137005,
0.03904996067285538,
0.031110253185033798,
-0.0332312285900116,
0.013534055091440678,
0.030157038941979408,
0.028986496850848198,
0.018028143793344498,
-0.013325127772986889,
-0.02713518775999546,
0.04336389899253845,
-0.02962413802742958,
0.03274836391210556,
-0.015041626058518887,
-0.011892066337168217,
0.04872508347034454,
0.01719256304204464,
0.016083214432001114,
-0.00029734938289038837,
0.003067129058763385,
-0.05452685430645943,
0.028426971286535263,
0.02487124875187874,
0.006609433796256781,
-0.02547718770802021,
0.01773933507502079,
0.025370923802256584,
0.030562642961740494,
0.016662638634443283,
0.022739548236131668,
-0.09562079608440399,
-0.016008779406547546,
-0.023317167535424232,
-0.06779054552316666,
-0.00436027254909277,
-0.019125616177916527,
-0.025940850377082825,
0.029212288558483124,
-0.004734184127300978,
0.024965643882751465,
0.01356407068669796,
0.04379930719733238,
-0.026951558887958527,
0.005067880731076002,
-0.03400148078799248,
0.027053283527493477,
-0.020571300759911537,
0.007038751617074013,
0.1101275086402893,
0.06722119450569153,
0.005578497890383005,
-0.051848653703927994,
0.021470362320542336,
-0.027844930067658424,
0.055832814425230026,
-0.02813698910176754,
0.014735422097146511,
-0.007056195754557848,
0.0020144921727478504,
-0.02313605323433876,
0.0627766102552414,
-0.012617603875696659,
0.007131602615118027,
0.038398098200559616,
-0.046727485954761505,
-0.053754400461912155,
-0.027114156633615494,
0.030690964311361313,
-0.019264591857790947,
0.0021003903821110725,
-0.022007351741194725,
0.010937140323221684,
-0.02317993901669979,
0.022145621478557587,
-0.04041426628828049,
-0.03822198510169983,
0.017393553629517555,
0.021369339898228645,
-0.04870942607522011,
-0.009133034385740757,
0.037768177688121796,
0.00533089367672801,
-0.030933436006307602,
-0.00725198071449995,
0.018253736197948456,
-0.013539590872824192,
0.03422617167234421,
0.05093909800052643,
0.02423231489956379,
0.0008486464503221214,
0.03072972409427166,
0.018393615260720253,
-0.05725877359509468,
-0.011248564347624779,
-0.014599828980863094,
0.05906207486987114,
-0.017152121290564537,
0.021783756092190742,
-0.02858850173652172,
0.0034994168672710657,
-0.004813056904822588,
-0.03566823527216911,
-0.014908735640347004,
-0.019882116466760635,
0.016529545187950134,
-0.0030383579432964325,
-0.025058533996343613,
-0.04639260843396187,
0.024005955085158348,
-0.042689282447099686,
0.024439020082354546,
-0.014812389388680458,
-0.0035945067647844553,
0.02789771929383278,
0.008712610229849815,
-0.008888712152838707,
-0.023571908473968506,
-0.018723225221037865,
-0.03207160159945488,
0.02694200724363327,
-0.05050709471106529,
-0.012733971700072289,
0.011314352974295616,
0.03574148565530777,
0.04674302414059639,
0.014005281031131744,
-0.0012469087960198522,
-0.016564982011914253,
-0.031011192128062248,
0.04738674685359001,
0.019469372928142548,
-0.013363026082515717,
0.004231741651892662,
0.014315484091639519,
0.035897333174943924,
0.04937425255775452,
-0.031360507011413574,
0.030422735959291458,
0.014085899107158184,
0.0036225751973688602,
0.005676937289535999,
-0.028157914057374,
-0.015447643585503101,
0.04517385736107826,
-0.01869436539709568,
0.014334460720419884,
-0.027771450579166412,
0.013669745065271854,
0.01060336921364069,
-0.0069619761779904366,
-0.012443505227565765,
0.0432451032102108,
0.012929166667163372,
-0.01416067872196436,
0.03813883289694786,
-0.0068883467465639114,
0.0014952413039281964,
0.031911831349134445,
0.012456429190933704,
-0.05332664027810097,
-0.03851683810353279,
-0.027247538790106773,
0.03089326061308384,
-0.022464869543910027,
0.0026134781073778868,
-0.03076540306210518,
0.0013778492575511336,
-0.013680297881364822,
0.029159042984247208,
-0.014286604709923267,
0.0069432626478374004,
-0.0378623865544796,
0.020989922806620598,
0.011853035539388657,
0.007438331842422485,
-0.005985776893794537,
0.04685741290450096,
-0.0006545255891978741,
-0.006719573866575956,
0.02432243898510933,
0.06409405916929245,
-0.01720944233238697,
-0.020310183987021446,
0.01593955047428608,
0.01462404802441597,
0.05424555018544197,
-0.006166398990899324,
-0.002252936363220215,
0.05328863859176636,
-0.02963009662926197,
-0.06306014209985733,
0.04255374148488045,
0.01932210475206375,
0.005809389054775238,
0.02521725557744503,
-0.019032107666134834,
-0.012171043083071709,
0.08353612571954727,
-0.019381342455744743,
0.008454466238617897,
0.02152382768690586,
-0.018901297822594643,
-0.07168640196323395,
-0.052775848656892776,
-0.0029534914065152407,
0.01568380557000637,
-0.03268355503678322,
0.04335944354534149,
0.01879228465259075,
-0.007657784968614578,
-0.015101267024874687,
-0.032415688037872314,
0.007062510121613741,
0.03130002319812775,
0.018234368413686752,
0.056269630789756775,
0.02058611437678337,
0.04325172305107117,
-0.03547360375523567,
0.05040237307548523,
0.01998506300151348,
0.01850009523332119,
-0.06124252453446388,
-0.05175285041332245,
-0.005815029144287109,
-0.0063371420837938786,
0.027554374188184738,
-0.04893594607710838,
0.022502398118376732,
0.024656658992171288,
-0.04164440557360649,
-0.022628776729106903,
-0.01943756639957428,
-0.010562838055193424,
-0.021548250690102577,
-0.002617516554892063,
-0.0046471343375742435,
0.0631895437836647,
0.01552008930593729,
0.03798510506749153,
0.021130895242094994,
0.03487986698746681,
0.0076912264339625835,
-0.03094599023461342,
-0.042914554476737976,
0.02295623905956745,
-0.002653868170455098,
-0.04968287795782089,
0.0943320021033287,
-0.018599212169647217,
-0.004115119576454163,
0.03720150142908096,
0.011809269897639751,
0.0019581702072173357,
-0.006683777552098036,
0.014409546740353107,
0.0060821278020739555,
0.018426228314638138,
0.0010974020697176456,
-0.03307728096842766,
-0.027462929487228394,
0.03571004793047905,
-0.019321633502840996,
0.03520315885543823,
0.041823580861091614,
-0.017230084165930748,
0.0022267112508416176,
-0.02194119244813919,
0.00047235246165655553,
0.018118971958756447,
-0.01967020146548748,
-0.00014993720105849206,
-0.015605478547513485,
0.009084959514439106,
0.013104506768286228,
-0.011609479784965515,
0.029191693291068077,
-0.0745377168059349,
0.007242475636303425,
0.0024400129914283752,
-0.011395972222089767,
-0.016127489507198334,
-0.0035391675774008036,
0.00009192414290737361,
-0.004203814547508955,
0.02266954630613327,
0.03989383205771446,
-0.037904635071754456,
-0.040553998202085495,
0.010440085083246231,
0.010802044533193111,
0.044182103127241135,
0.022913942113518715,
-0.05128597468137741,
-0.009322251193225384,
0.019109733402729034,
0.016413614153862,
0.03566987067461014,
-0.02864915318787098,
-0.008441775105893612,
-0.008566883392632008,
-0.03706470876932144,
0.01803414151072502,
0.026031343266367912,
0.01902206428349018,
-0.056295476853847504,
-0.008725259453058243,
-0.008174724876880646,
0.02254367806017399,
0.053757261484861374,
-0.017256544902920723,
-0.007476640399545431,
0.02246471308171749,
0.015065177343785763,
0.02216857299208641,
-0.03781985864043236,
-0.006601106841117144,
-0.0038832707796245813,
-0.018152909353375435,
0.021145008504390717,
0.003310042666271329,
-0.0357477180659771,
0.06160750240087509,
0.08141373842954636,
-0.016637280583381653,
0.0039458973333239555,
-0.030321303755044937,
-0.02807949110865593,
0.05985543876886368,
0.009735987521708012,
-0.0067964717745780945,
0.08415985107421875,
-0.013397672213613987,
0.028208347037434578,
0.05196259543299675,
-0.04214847832918167,
-0.003592949127778411,
-0.009231921285390854,
-0.0417119562625885,
-0.009584496729075909,
-0.005160809028893709,
-0.008399808779358864,
0.01937960647046566,
-0.026180213317275047,
-0.007622933015227318,
0.04001643508672714,
-0.02650442160665989,
-0.02564949356019497,
0.02941078133881092,
0.05116474628448486,
0.02039143070578575,
0.008414218202233315,
-0.008679373189806938,
0.02007288485765457,
-0.00885846372693777,
0.030912546440958977,
0.06140422821044922,
0.005141217727214098,
0.016799384728074074,
0.013865722343325615,
0.005823157262057066,
0.02225065603852272,
0.0025201519019901752,
0.01715364307165146,
0.01770789921283722,
-0.012594255618751049,
0.0010979905491694808,
0.008873053826391697,
-0.006127513479441404,
0.0022845936473459005,
0.02579635940492153,
-0.033866558223962784,
0.07515471428632736,
-0.04671190679073334,
-0.01870048977434635,
-0.00664169155061245,
-0.006951162125915289,
-0.007487019523978233,
0.0022164026740938425,
0.0179279837757349,
0.04542115703225136,
0.0017100619152188301,
-0.06493442505598068,
-0.02546822838485241,
0.0181208997964859,
0.027870191261172295,
-0.06773407012224197,
-0.013696960173547268,
-0.020726436749100685,
-0.004163854755461216,
-0.01704307086765766,
-0.00245691929012537,
-0.01232896838337183,
0.010249018669128418,
0.057886965572834015,
0.027205822989344597,
0.027925048023462296,
-0.030736759305000305,
-0.008674072101712227,
-0.03495616093277931,
0.0343925915658474,
-0.050642769783735275,
-0.007692168932408094,
-0.026620034128427505,
0.003288120962679386,
-0.04922852665185928,
0.004095602780580521
] |
<p><a href="http://en.wikipedia.org/wiki/Noether%27s_theorem">Noether's (first) theorem</a> states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.</p>
<p>Is the converse true: Any conservation law of a physical system has a differentiable symmetry of its action?</p>
| 740 |
[
-0.05948580056428909,
-0.008442901074886322,
-0.006726160179823637,
0.030069341883063316,
0.030209872871637344,
0.006431472487747669,
-0.060345277190208435,
0.0016379570588469505,
0.017528150230646133,
-0.04133470356464386,
0.0013878641184419394,
-0.022028546780347824,
0.05863001570105553,
0.023575065657496452,
0.023090042173862457,
0.027370620518922806,
-0.0025437769945710897,
0.009561832994222641,
-0.001117054489441216,
-0.027400759980082512,
-0.024335067719221115,
0.024723755195736885,
0.016154661774635315,
0.028051644563674927,
-0.021757248789072037,
0.010492262430489063,
-0.022508390247821808,
0.023492883890867233,
0.014042681083083153,
0.03983640298247337,
0.007097783964127302,
-0.0019077537581324577,
-0.02469516173005104,
0.0779714584350586,
0.005074465647339821,
0.03277916833758354,
-0.015870414674282074,
-0.023174013942480087,
0.009019535966217518,
-0.0066334460861980915,
0.015257764607667923,
-0.03129187598824501,
0.017035625874996185,
0.06514446437358856,
-0.04586711898446083,
0.030691735446453094,
-0.021801913157105446,
-0.014173651114106178,
0.033187687397003174,
-0.06524384766817093,
0.08530732244253159,
0.003201176645234227,
0.026712974533438683,
0.01745676063001156,
-0.020334826782345772,
-0.003182159038260579,
0.0482664629817009,
0.07089237123727798,
0.00918126292526722,
-0.04226887226104736,
-0.029901359230279922,
-0.010759368538856506,
-0.028942661359906197,
-0.011056941002607346,
-0.03438463434576988,
0.01706325262784958,
-0.005264733452349901,
-0.013379705138504505,
0.004256058018654585,
-0.012763266451656818,
-0.01258842647075653,
0.004986198619008064,
0.03237026184797287,
-0.023304371163249016,
-0.0033107472117990255,
0.01771704852581024,
0.01934206672012806,
-0.02662629634141922,
0.034001633524894714,
0.028427524492144585,
0.009136788547039032,
0.01804032176733017,
0.003101746551692486,
0.026933128014206886,
0.016938211396336555,
-0.014894086867570877,
0.055273182690143585,
0.003954832907766104,
0.007154610939323902,
0.036647066473960876,
0.038657378405332565,
-0.011521322652697563,
-0.0084755290299654,
-0.02953612431883812,
-0.01680777035653591,
0.02015065960586071,
-0.01095039863139391,
0.02386198565363884,
0.009148544631898403,
-0.027890659868717194,
-0.02359059453010559,
-0.01951359026134014,
0.025241220369935036,
0.024460433050990105,
0.015772772952914238,
-0.01995200850069523,
-0.025907285511493683,
0.022418871521949768,
-0.05903579294681549,
-0.001958893844857812,
-0.05386507883667946,
0.005373208783566952,
0.0059251682832837105,
-0.00457028578966856,
0.014728618785738945,
-0.017928658053278923,
-0.014719521626830101,
-0.01723313331604004,
0.03713173791766167,
0.07509290426969528,
0.08403920382261276,
-0.010978790000081062,
0.05100162699818611,
-0.0033967888448387384,
-0.07035663723945618,
-0.017385050654411316,
0.02786349318921566,
0.00889634620398283,
-0.030648620799183846,
-0.010809055529534817,
-0.0006309061427600682,
-0.002866901457309723,
-0.032795920968055725,
0.013138878159224987,
0.03509768843650818,
-0.019231503829360008,
-0.09099967032670975,
-0.06195806339383125,
0.014071979559957981,
0.015300873667001724,
-0.030691150575876236,
-0.0519610233604908,
0.023695440962910652,
0.015957655385136604,
0.0705208033323288,
-0.0026609194464981556,
0.0017562900902703404,
0.050064682960510254,
0.04087522253394127,
-0.01825602725148201,
0.007227405905723572,
-0.01761959120631218,
0.049213942140340805,
-0.053390491753816605,
-0.013341260142624378,
-0.07843274623155594,
0.0371348038315773,
0.0052890232764184475,
0.035786259919404984,
-0.00788831990212202,
0.06887976825237274,
-0.0198359414935112,
0.028318382799625397,
-0.015290282666683197,
-0.005741119384765625,
0.005576488561928272,
0.06328339874744415,
-0.014929618686437607,
0.017211006954312325,
0.015154552645981312,
0.02300739660859108,
0.03103823959827423,
-0.026956472545862198,
0.0332978293299675,
0.06779176741838455,
-0.031078485772013664,
-0.004071955569088459,
-0.0017938074888661504,
0.0022872742265462875,
0.0156948734074831,
-0.027061710134148598,
-0.006884455215185881,
-0.00875886995345354,
0.013049520552158356,
-0.018765652552247047,
0.03347938880324364,
0.017972828820347786,
-0.0020019521471112967,
0.0027579523157328367,
-0.03365924581885338,
-0.04830003157258034,
-0.0881194919347763,
0.023464305326342583,
-0.019480258226394653,
-0.04895478114485741,
0.024185366928577423,
0.03272382169961929,
0.042104411870241165,
-0.05040070042014122,
-0.004313578829169273,
0.026418473571538925,
0.02529808320105076,
-0.01060724537819624,
-0.02447069063782692,
0.010162129066884518,
0.05702834948897362,
0.044334691017866135,
0.02694603055715561,
0.0468464158475399,
0.017009161412715912,
-0.009800507687032223,
0.0039763483218848705,
-0.027277842164039612,
-0.0009304718114435673,
0.011657259427011013,
0.02559715136885643,
0.038133032619953156,
-0.0015506284544244409,
-0.011048714630305767,
0.05529920756816864,
-0.04733891040086746,
0.05031990259885788,
0.045466650277376175,
0.031949009746313095,
0.01118267048150301,
0.009521293453872204,
-0.0030835845973342657,
0.01309619564563036,
0.0021098912693560123,
-0.018230820074677467,
-0.026707105338573456,
0.012554917484521866,
0.02850072644650936,
0.04448525235056877,
-0.03800193592905998,
0.030453668907284737,
0.020378274843096733,
0.019638778641819954,
0.01289138663560152,
0.021671131253242493,
0.00499312486499548,
-0.03472979739308357,
0.03571845963597298,
0.0012655997416004539,
0.03011840023100376,
0.028440605849027634,
0.020510435104370117,
-0.011598484590649605,
0.03280350938439369,
0.007889661006629467,
-0.01786775141954422,
0.0008878385997377336,
-0.003131218021735549,
0.006952737923711538,
0.030185842886567116,
-0.022198155522346497,
0.010847107507288456,
0.002957525197416544,
0.0445953905582428,
0.03509681299328804,
-0.002007076982408762,
-0.016322685405611992,
-0.0021948020439594984,
0.00331089342944324,
0.01587691530585289,
-0.027256304398179054,
-0.046891406178474426,
-0.027122139930725098,
0.030562985688447952,
-0.02963094972074032,
-0.02710382640361786,
-0.02509985864162445,
-0.024804746732115746,
-0.027858760207891464,
-0.02712002396583557,
0.013433105312287807,
0.004338077735155821,
0.027505893260240555,
-0.03819945082068443,
-0.03298909589648247,
0.0014424137771129608,
-0.05416072532534599,
-0.01208436582237482,
0.027610396966338158,
-0.04252851754426956,
0.038525473326444626,
-0.05713067576289177,
-0.026100773364305496,
0.04159647598862648,
0.00400876346975565,
0.039762452244758606,
0.028338007628917694,
-0.0260639488697052,
-0.09014850854873657,
-0.014316190034151077,
-0.07067734748125076,
0.020481860265135765,
-0.019487638026475906,
0.00722234882414341,
0.0008883126429282129,
-0.023413825780153275,
-0.036722470074892044,
-0.012791227549314499,
-0.03154834732413292,
-0.06199216470122337,
-0.024834318086504936,
0.038501981645822525,
0.02361041121184826,
-0.027432963252067566,
0.019693439826369286,
0.027425235137343407,
-0.06562390923500061,
-0.027142537757754326,
-0.026110593229532242,
-0.030054546892642975,
0.02036559395492077,
-0.00421848613768816,
0.02579585462808609,
0.00420967536047101,
-0.07706081122159958,
0.07963566482067108,
0.037078309804201126,
-0.043912965804338455,
0.01976129226386547,
-0.02912144735455513,
-0.005076163448393345,
-0.029093120247125626,
-0.011523300781846046,
0.000864929985255003,
-0.024119967594742775,
0.02851199544966221,
0.03188386559486389,
0.05348072946071625,
-0.001839718664996326,
0.024656429886817932,
-0.03902357444167137,
-0.004769604653120041,
0.04118083044886589,
0.022009320557117462,
0.05204103887081146,
-0.01564684510231018,
-0.010338337160646915,
0.014179084450006485,
-0.0196822639554739,
0.046441614627838135,
0.03013046272099018,
-0.04498951882123947,
0.07043392956256866,
0.016948789358139038,
0.030083714053034782,
-0.04405464604496956,
0.04672113433480263,
-0.01699461042881012,
0.00389436399564147,
-0.013696367852389812,
0.048945553600788116,
0.031833089888095856,
-0.022372832521796227,
0.005499969702214003,
0.003935188986361027,
0.04033563658595085,
-0.03752610832452774,
-0.017801951617002487,
0.002615707227960229,
-0.005205376539379358,
0.040199752897024155,
-0.006756867282092571,
0.01783396117389202,
0.03440135717391968,
0.012352462857961655,
0.02258000522851944,
0.03232811391353607,
-0.030560612678527832,
0.027183212339878082,
-0.05130992829799652,
0.02081459015607834,
-0.008208097890019417,
0.03653740510344505,
-0.005376284476369619,
0.06255612522363663,
0.0002630104136187583,
0.027502672746777534,
0.002653972478583455,
-0.004218918737024069,
-0.08507566899061203,
0.047419171780347824,
-0.023391161113977432,
-0.006254676729440689,
-0.0025589773431420326,
-0.04003550857305527,
-0.009739145636558533,
-0.00047263718442991376,
0.0015746275894343853,
-0.026112370193004608,
0.0083489790558815,
-0.07834803313016891,
-0.013895127922296524,
-0.03910105675458908,
-0.06930902600288391,
-0.006249493453651667,
0.018551521003246307,
0.03507927060127258,
-0.04309486225247383,
0.03535189852118492,
0.02108686789870262,
-0.03477690741419792,
-0.024752242490649223,
0.004660369828343391,
0.025018231943249702,
0.0106757627800107,
0.006047796458005905,
0.005231142975389957,
0.009700050577521324,
-0.0013192975893616676,
0.014093390665948391,
0.024386437609791756,
0.06863095611333847,
0.007534694857895374,
0.02579590119421482,
-0.027381574735045433,
-0.0342886745929718,
-0.04579465091228485,
0.01721072942018509,
0.060645636171102524,
0.028794970363378525,
0.0031643796246498823,
0.015049206092953682,
0.019487181678414345,
-0.013113955035805702,
0.029390161857008934,
0.044703055173158646,
0.011469202116131783,
-0.022717293351888657,
-0.04473060369491577,
0.009293950162827969,
-0.05324213206768036,
-0.007877960801124573,
-0.004899113904684782,
0.011221370659768581,
-0.04821547120809555,
-0.003106888849288225,
0.001652624225243926,
0.037842098623514175,
-0.01035812683403492,
0.0031019377056509256,
0.018756480887532234,
-0.004667057190090418,
-0.006915666162967682,
0.00823131576180458,
0.021105023100972176,
0.03873676806688309,
0.03535802662372589,
-0.008398409932851791,
-0.015427954494953156,
-0.07426504045724869,
-0.006271393969655037,
0.0294325053691864,
0.012381166219711304,
-0.011022130958735943,
0.01890483684837818,
-0.06174914911389351,
-0.04398603364825249,
0.05206984654068947,
0.00016474130097776651,
0.028118601068854332,
-0.0012832110514864326,
-0.00047445407835766673,
0.011733334511518478,
-0.03178073465824127,
-0.015910256654024124,
0.016395583748817444,
-0.02121240645647049,
-0.003766341833397746,
-0.019910775125026703,
0.010752759873867035,
-0.028283966705203056,
0.027143850922584534,
0.007716342806816101,
0.060563813894987106,
0.03724338859319687,
0.02011658251285553,
-0.05147896707057953,
0.0054161641746759415,
-0.043126605451107025,
-0.04588860273361206,
0.01833219639956951,
0.04196974262595177,
-0.003342903684824705,
0.023653099313378334,
0.00858012679964304,
-0.03248472511768341,
0.01717533729970455,
-0.00319677428342402,
-0.0047798738814890385,
0.020617784932255745,
-0.024067731574177742,
0.027585119009017944,
0.03591910004615784,
0.018265750259160995,
0.0351032055914402,
0.048149194568395615,
-0.022412674501538277,
-0.025291167199611664,
-0.010572629049420357,
0.028201144188642502,
-0.0226640272885561,
-0.03164893016219139,
-0.024297300726175308,
-0.012686940841376781,
-0.011274038814008236,
0.028926603496074677,
-0.006862665060907602,
-0.003027599537745118,
-0.015593551099300385,
0.0053236414678394794,
0.006250131409615278,
0.018112512305378914,
0.019485536962747574,
-0.03515143692493439,
-0.0167681947350502,
0.04670125991106033,
0.016782648861408234,
-0.0029687255155295134,
0.021454503759741783,
0.002027725800871849,
-0.03497795760631561,
0.027029408141970634,
-0.002500037895515561,
0.040253233164548874,
-0.0188511423766613,
-0.03457149118185043,
0.0016047422541305423,
-0.010145695880055428,
0.020677823573350906,
-0.017002787441015244,
-0.008568727411329746,
0.053833965212106705,
-0.044654328376054764,
-0.0026607888285070658,
0.024668166413903236,
-0.026065392419695854,
-0.010254960507154465,
-0.07102030515670776,
0.02475966513156891,
0.036158882081508636,
0.01577833667397499,
-0.08346055448055267,
-0.04563663899898529,
-0.006701056845486164,
0.005618655122816563,
-0.04200425371527672,
-0.01596456952393055,
-0.04090822488069534,
-0.019821718335151672,
-0.059009455144405365,
0.004255699925124645,
0.03544829785823822,
-0.028245478868484497,
0.01721663773059845,
-0.00379135156981647,
-0.010137475095689297,
0.057231999933719635,
0.001687751617282629,
-0.002061612671241164,
-0.021295104175806046,
-0.012933335267007351,
-0.008876661770045757,
0.012923890724778175,
0.06289292871952057,
-0.010239611379802227,
0.019982269033789635,
0.0031860661692917347,
0.003799284575507045,
0.038584258407354355,
0.0037754687946289778,
0.00924772396683693,
0.031921468675136566,
0.003552188165485859,
-0.011576324701309204,
-0.04426727071404457,
0.008440605364739895,
-0.03995084762573242,
0.05343497917056084,
-0.0033485398162156343,
-0.010213496163487434,
-0.024650059640407562,
-0.018939465284347534,
-0.009488399140536785,
-0.001872809836640954,
0.021068882197141647,
-0.0022985597606748343,
0.07033940404653549,
-0.041606876999139786,
-0.018224287778139114,
0.009134282357990742,
-0.026354093104600906,
-0.004122721962630749,
-0.043211840093135834,
-0.0031586834229528904,
-0.00521129323169589,
0.004942195490002632,
-0.026056276634335518,
-0.021544095128774643,
-0.00952924694865942,
0.031058356165885925,
0.07954464107751846,
-0.00012877516564913094,
0.04481235146522522,
0.024472864344716072,
-0.012493308633565903,
0.015101446770131588,
-0.023891417309641838,
0.018016904592514038,
-0.014842011965811253,
0.056793514639139175,
0.029528556391596794,
-0.009926840662956238,
0.015638582408428192,
0.04652676358819008,
0.05292249098420143,
-0.033789489418268204,
0.01524229347705841,
0.02732594683766365,
-0.007291533052921295,
0.014365809969604015,
-0.021548647433519363,
-0.040148794651031494,
0.0342765711247921,
-0.04816332086920738,
0.06873166561126709,
-0.018439900130033493,
-0.017490534111857414,
0.03133213147521019,
0.003011145628988743,
0.008575277402997017,
-0.0018302121898159385,
-0.04699017480015755,
-0.01857290416955948,
0.051243577152490616,
-0.03728747367858887,
0.05909883230924606,
-0.026748256757855415,
0.01340546179562807,
0.053587231785058975,
-0.015217448584735394,
0.006770296022295952,
-0.007321174256503582,
-0.05418124049901962,
-0.012885193340480328,
-0.04072566330432892,
0.003983114846050739,
0.04976186156272888,
0.01931907795369625,
-0.027513334527611732,
-0.02296789363026619,
-0.0002709688851609826,
0.021275527775287628,
0.03574993461370468,
0.020954811945557594,
0.021514659747481346,
0.054401032626628876,
0.014842147938907146,
0.053422145545482635,
0.017006607726216316,
0.007987484335899353,
0.11278776079416275,
0.05049540475010872,
-0.028803423047065735,
-0.028421103954315186,
0.049560047686100006,
-0.03550371155142784,
-0.009198740124702454,
-0.012636066414415836,
0.023581862449645996,
0.01910955086350441,
-0.008041280321776867,
0.019485780969262123,
0.03755146637558937,
-0.034685347229242325,
-0.036457423120737076,
0.07627777010202408,
-0.03627712279558182,
-0.03321506083011627,
-0.015821609646081924,
-0.013901126570999622,
0.007915045134723186,
0.04250083118677139,
-0.03147849068045616,
-0.008857729844748974,
-0.00653078081086278,
-0.0019813603721559048,
-0.030573232099413872,
-0.06532984972000122,
0.027414314448833466,
0.015250098891556263,
-0.021863248199224472,
0.0019659854006022215,
0.024156656116247177,
-0.02076132223010063,
-0.08614044636487961,
-0.013626162894070148,
0.010758164338767529,
0.00509063433855772,
0.035605452954769135,
0.044769808650016785,
0.015028574503958225,
0.022896846756339073,
-0.0038920040242373943,
0.01602022908627987,
-0.06323132663965225,
0.054480865597724915,
-0.036366574466228485,
0.008395570330321789,
-0.013380651362240314,
0.056389451026916504,
-0.010931753553450108,
-0.03486248478293419,
0.0158876720815897,
-0.09737639874219894,
-0.03468715772032738,
0.01008265558630228,
0.011943740770220757,
-0.035549744963645935,
-0.014070510864257812,
-0.030452460050582886,
0.0022038931492716074,
-0.009679961949586868,
0.012385810725390911,
-0.05686555430293083,
-0.014195527881383896,
0.00006881034641992301,
0.01879771426320076,
0.03577302023768425,
-0.03363755717873573,
-0.015685979276895523,
-0.0179506316781044,
-0.030473535880446434,
-0.03511945903301239,
-0.04379219561815262,
-0.011777209118008614,
0.021907199174165726,
0.03500990942120552,
0.00858652126044035,
-0.024946171790361404,
0.00025716767413541675,
-0.06661809235811234,
0.026439368724822998,
-0.0016434519784525037,
-0.00496866088360548,
-0.014345436356961727,
0.02567301131784916,
0.017747964709997177,
0.03672031685709953,
-0.035628318786621094,
0.01983114518225193,
0.0007627387531101704,
0.008139264769852161,
0.04687235504388809,
-0.015209135599434376,
-0.004434838891029358,
0.009427045471966267,
-0.026207661256194115,
-0.024377023801207542,
-0.0057684434577822685,
0.01623743213713169,
0.04613005369901657,
0.026230748742818832,
-0.00928822997957468,
0.021031847223639488,
-0.01538371853530407,
0.012454363517463207,
0.004798853769898415,
-0.0057842968963086605,
0.036101166158914566,
0.02769208513200283,
0.014199895784258842,
-0.04254845157265663,
-0.023528805002570152,
-0.013029437512159348,
0.0003866013139486313,
0.02468372881412506,
-0.006620591972023249,
-0.027099505066871643,
0.006562507711350918,
-0.04041891172528267,
0.07386431843042374,
-0.04075269028544426,
-0.047928616404533386,
-0.04769010841846466,
0.013693471439182758,
0.04491763189435005,
-0.013917417265474796,
-0.01495317742228508,
0.02638068050146103,
-0.013800246641039848,
-0.025540338829159737,
0.028502171859145164,
0.03758838772773743,
-0.005897799041122198,
0.005834978073835373,
0.049283046275377274,
0.006348350550979376,
0.05694294348359108,
-0.011299584060907364,
-0.03451811894774437,
0.04975062981247902,
-0.03768743574619293,
-0.04618467018008232,
0.005729151889681816,
-0.018670227378606796,
0.006997697055339813,
0.005905694793909788,
-0.03388043865561485,
-0.015815632417798042,
0.03720536828041077,
-0.020646482706069946,
0.01956917531788349,
-0.006659390404820442,
-0.03155002370476723,
0.007401030510663986,
-0.05979439243674278,
0.0016590283485129476,
-0.010865817777812481,
-0.009218189865350723,
0.028994940221309662,
0.020846610888838768,
-0.008659299463033676,
-0.007564346771687269,
0.0061685130931437016,
-0.019040768966078758,
0.031993333250284195,
0.01497624907642603,
0.00963585264980793,
0.018307147547602654,
0.07478288561105728,
-0.03708804398775101,
0.020647108554840088,
0.004168996121734381,
-0.012429933995008469,
-0.11553417891263962,
-0.0077985068783164024,
0.009792164899408817,
-0.0031856177374720573,
0.03029981069266796,
-0.06267493963241577,
0.04358718544244766,
-0.00198652152903378,
-0.05147797241806984,
0.017689811065793037,
-0.03669816255569458,
-0.021058542653918266,
-0.03487830236554146,
0.006910810247063637,
-0.008070960640907288,
0.08693309128284454,
0.007001050747931004,
0.04122660309076309,
0.04658559709787369,
0.007992904633283615,
0.014832954853773117,
-0.03204666078090668,
-0.0236759502440691,
-0.0071985856629908085,
0.006512106396257877,
-0.020822327584028244,
0.03330892324447632,
-0.0008504409343004227,
-0.055891115218400955,
-0.0006620634812861681,
-0.017939656972885132,
0.009780973196029663,
-0.013022013939917088,
-0.00004286277908249758,
0.0327567383646965,
-0.006659328937530518,
-0.018231220543384552,
-0.004310087766498327,
-0.03522365540266037,
-0.004065301269292831,
0.019132131710648537,
0.025740621611475945,
-0.013610968366265297,
0.006121065467596054,
0.046243857592344284,
-0.043291784822940826,
-0.03373207524418831,
0.06154070422053337,
-0.014840885065495968,
-0.025927485898137093,
-0.030426185578107834,
-0.01830441690981388,
-0.0035971137695014477,
0.0015489187790080905,
0.026042567566037178,
-0.04290701076388359,
-0.01304609701037407,
0.03355998173356056,
-0.03297099098563194,
-0.018238747492432594,
0.024361232295632362,
0.01151643879711628,
-0.04063190519809723,
0.03121476247906685,
0.033225517719984055,
0.02716192975640297,
-0.052744582295417786,
-0.007618867326527834,
0.01243528351187706,
-0.01486140489578247,
-0.01909029670059681,
-0.06653783470392227,
-0.017077922821044922,
0.0290371123701334,
0.05551311746239662,
-0.0054392581805586815,
0.018057752400636673,
-0.04283325746655464,
-0.03138122707605362,
-0.06541652977466583,
0.0259025227278471,
0.017984658479690552,
-0.028242886066436768,
-0.03791728988289833,
0.0069039626978337765,
-0.010662308894097805,
0.0006047305068932474,
0.020949410274624825,
-0.016635512933135033,
-0.023140836507081985,
0.04893167316913605,
0.028334002941846848,
-0.011508390307426453,
-0.030308537185192108,
-0.0014684549532830715,
-0.0108103659003973,
-0.0005111916689202189,
-0.007013309746980667,
-0.015608866699039936,
-0.025846177712082863,
0.00981902051717043,
0.0048895906656980515,
-0.013963907957077026,
0.033346399664878845,
0.009923424571752548,
-0.05287700518965721,
0.06486522406339645,
0.0028177739586681128,
-0.009495429694652557,
0.04645306617021561,
-0.03498247638344765,
0.018202809616923332,
0.020813867449760437,
-0.04200053960084915,
-0.03362397477030754,
-0.009771956130862236,
-0.06230960413813591,
-0.04252392053604126,
-0.0037127570249140263,
-0.008226193487644196,
0.045803252607584,
-0.040062762796878815,
0.02404131554067135,
0.053309958428144455,
-0.041247982531785965,
-0.013926978223025799,
0.07100291550159454,
0.007475764956325293,
0.029616622254252434,
-0.028524864464998245,
-0.004944093991070986,
0.0222611241042614,
0.032945625483989716,
0.008866297081112862,
0.053751107305288315,
0.0015317702200263739,
-0.0186463613063097,
-0.03137684613466263,
0.035809680819511414,
-0.002207360928878188,
0.037757184356451035,
0.02950367145240307,
0.03486786037683487,
-0.01327031571418047,
-0.004645969718694687,
0.03507888689637184,
-0.001211098744533956,
0.00564727745950222,
0.005408266093581915,
-0.02863142266869545,
0.07316920161247253,
-0.01953403651714325,
0.014824630692601204,
-0.017631039023399353,
0.02837747149169445,
-0.027918342500925064,
-0.02142431028187275,
0.031614989042282104,
0.027795303612947464,
0.00096975511405617,
-0.0024676115717738867,
-0.03164887800812721,
0.017431775107979774,
-0.0267826858907938,
-0.052202265709638596,
0.03446781262755394,
-0.0007307576015591621,
0.008091442286968231,
0.0036859961692243814,
0.004211244639009237,
-0.02868422120809555,
-0.035527303814888,
0.01746639795601368,
0.022323794662952423,
0.06961692869663239,
0.0013726454926654696,
0.005221996456384659,
-0.04753528907895088,
0.04927481338381767,
-0.03445497900247574,
-0.05982436239719391,
-0.01878441870212555,
0.01465687993913889,
0.01703646034002304,
-0.016572492197155952
] |
<p>Good afternoon everybody.</p>
<p>I am reading on a book about semiconductor mobility. I have fully understood the definition, but I also noticed that often one talks about high or low mobility. My question is: what are the <strong>advantages</strong> of having a <strong>high</strong> mobility? I mean, in the technological applications or experimental uses of the semiconductor/etherojunction.
Do you know any main <strong>methods</strong> to improve mobility (in Si and/or Ge semiconductors for example)? Any <strong>bibliography</strong> about them?</p>
| 8,459 |
[
0.0020215599797666073,
-0.03801175579428673,
0.01387707982212305,
-0.030551094561815262,
0.00808230135589838,
0.024373721331357956,
-0.0052910554222762585,
0.0028575120959430933,
0.004059129394590855,
-0.04637029767036438,
0.030311232432723045,
0.043818939477205276,
0.018026700243353844,
-0.011068504303693771,
0.00924280472099781,
-0.003392185317352414,
0.010649760253727436,
-0.01851646974682808,
0.0003827526234090328,
0.002424505539238453,
-0.0007567697903141379,
0.014669008553028107,
0.024981742724776268,
0.02962636575102806,
-0.017425812780857086,
0.012329931370913982,
0.004826859571039677,
-0.0003620116040110588,
0.013734335079789162,
0.022292625159025192,
-0.03796197101473808,
0.0001870332780526951,
0.0009652772569097579,
-0.024978194385766983,
-0.004808786325156689,
-0.041431233286857605,
-0.02465108036994934,
-0.02734234184026718,
-0.0024090134538710117,
0.02320047654211521,
-0.04277321696281433,
0.004766677040606737,
0.008147663436830044,
0.022032901644706726,
0.004060933832079172,
0.010829390957951546,
0.019939009100198746,
-0.05796964094042778,
0.017944354563951492,
-0.0890376940369606,
-0.014785177074372768,
-0.0044395956210792065,
0.028380965813994408,
0.03261718526482582,
0.039112333208322525,
0.018289675936102867,
0.08137276023626328,
0.06990155577659607,
-0.034544337540864944,
-0.02823062054812908,
0.034738149493932724,
-0.060799043625593185,
0.03478587791323662,
-0.054932329803705215,
-0.027618803083896637,
0.04312325641512871,
0.019758552312850952,
-0.05839671194553375,
0.06306470930576324,
0.004728429950773716,
0.04192296043038368,
-0.0034255210775882006,
-0.0015380822587758303,
-0.018078887835144997,
0.025986377149820328,
-0.037462636828422546,
0.037315789610147476,
0.022414671257138252,
0.0478827990591526,
0.022566847503185272,
-0.005785518325865269,
-0.01345637533813715,
0.010946708731353283,
0.033849384635686874,
-0.02646929770708084,
-0.01815042272210121,
0.07755326479673386,
-0.0242686215788126,
0.000038477679481729865,
-0.004005120601505041,
-0.027209101244807243,
0.020068254321813583,
0.035719338804483414,
0.028709976002573967,
-0.03547515720129013,
0.0065084900707006454,
0.0033794832415878773,
0.05612947791814804,
0.02311098389327526,
-0.0012262719683349133,
0.004564599599689245,
-0.002719887997955084,
0.04874931275844574,
0.06865935772657394,
-0.001640769885852933,
-0.012932810932397842,
-0.02313857153058052,
0.003428487107157707,
0.002893497934564948,
-0.010940159671008587,
-0.018389511853456497,
0.0024521148297935724,
-0.016357524320483208,
0.008252687752246857,
0.015501638874411583,
-0.03754950687289238,
-0.032869789749383926,
-0.021173004060983658,
0.013395135290920734,
0.0984787568449974,
0.01894659921526909,
-0.051336899399757385,
0.010402530431747437,
-0.0035522051621228456,
-0.07268203794956207,
0.04480281472206116,
0.025427816435694695,
-0.0005917975795455277,
-0.011182261630892754,
0.01009729877114296,
0.03064686991274357,
0.0068891397677361965,
0.02393241599202156,
-0.026997476816177368,
0.052212342619895935,
0.003392380429431796,
-0.09339726716279984,
-0.032017070800065994,
0.08701610565185547,
-0.0043791476637125015,
0.0057456050999462605,
-0.09477662295103073,
0.002099586185067892,
-0.0005667837103828788,
0.07340577989816666,
0.013209344819188118,
0.010263188742101192,
-0.045516353100538254,
0.016931530088186264,
0.006878266576677561,
-0.040595971047878265,
-0.046817880123853683,
0.014431698247790337,
-0.004458015318959951,
0.03709402680397034,
-0.10093635320663452,
0.057236623018980026,
0.028988251462578773,
-0.004588489420711994,
-0.059214502573013306,
0.0564933717250824,
-0.005779048427939415,
-0.01764397695660591,
-0.03453170135617256,
-0.00801668968051672,
-0.011644969694316387,
0.07828482240438461,
0.012160437181591988,
0.025683294981718063,
0.023026524111628532,
0.0046519143506884575,
0.020059702917933464,
0.01177816279232502,
0.017861871048808098,
0.002436700975522399,
-0.013144130818545818,
0.008009389974176884,
-0.004223376978188753,
-0.0030979360453784466,
-0.020250780507922173,
-0.029389750212430954,
-0.037387553602457047,
-0.0017508051823824644,
0.028578350320458412,
-0.013860694132745266,
0.01950482279062271,
-0.001230926252901554,
0.01887666992843151,
0.037301529198884964,
-0.053933754563331604,
-0.028986850753426552,
-0.07492831349372864,
0.010190830565989017,
-0.010817626491189003,
-0.032670386135578156,
0.03347925469279289,
-0.024785006418824196,
0.013789907097816467,
-0.007744552567601204,
-0.025381257757544518,
-0.036684904247522354,
-0.022008715197443962,
0.017063666135072708,
-0.014450456015765667,
0.015395025722682476,
0.043722402304410934,
-0.013355571776628494,
-0.011739319190382957,
0.03049296885728836,
0.024761775508522987,
-0.017115868628025055,
0.008587856777012348,
-0.014886954799294472,
0.04002947360277176,
0.007787096314132214,
-0.05105248838663101,
-0.01766139082610607,
-0.022707099094986916,
-0.01518453098833561,
0.003121051238849759,
-0.015724675729870796,
0.10849939286708832,
0.06700506061315536,
0.01803227886557579,
0.0010402684565633535,
0.05969544127583504,
-0.007032936904579401,
-0.0380110964179039,
-0.00887585710734129,
-0.0013495597522705793,
-0.0625816360116005,
-0.027577154338359833,
0.06285122036933899,
0.023111984133720398,
-0.057978976517915726,
0.030720926821231842,
0.004873584024608135,
0.03689927980303764,
0.04840182512998581,
0.016983024775981903,
-0.018217165023088455,
-0.024959497153759003,
0.02725210413336754,
0.027897348627448082,
-0.015933359041810036,
0.029089070856571198,
0.01760992966592312,
0.02094554714858532,
0.0008614800171926618,
-0.01731574907898903,
-0.006272024009376764,
0.046378541737794876,
0.04773843660950661,
-0.012498543597757816,
0.006716784089803696,
-0.024650221690535545,
0.0022500830236822367,
-0.05293893814086914,
0.0157538503408432,
0.007860604673624039,
-0.017926689237356186,
0.04641181603074074,
-0.03302392363548279,
-0.0413987971842289,
0.05039044842123985,
-0.007134744431823492,
-0.01439071074128151,
0.0016039464389905334,
0.011187836527824402,
-0.06555639952421188,
0.018959490582346916,
-0.026039041578769684,
0.047570403665304184,
-0.02037530019879341,
-0.016489503905177116,
0.030993420630693436,
0.003713137935847044,
0.033320214599370956,
0.01594148389995098,
-0.01899084821343422,
-0.02229594811797142,
-0.021451575681567192,
0.024039261043071747,
0.02256477065384388,
-0.05718959495425224,
-0.007166050374507904,
-0.027883313596248627,
-0.07915996015071869,
0.047414425760507584,
-0.034733619540929794,
-0.009557832032442093,
-0.004898507613688707,
0.012339101172983646,
-0.047119755297899246,
0.005096779204905033,
-0.00048008805606514215,
0.02119358815252781,
-0.02090763859450817,
-0.014890615828335285,
0.029224013909697533,
-0.037790171802043915,
-0.007518064230680466,
0.013573367148637772,
-0.024177545681595802,
-0.07416492700576782,
0.0004889311385340989,
-0.007173299789428711,
0.014410031959414482,
-0.024666618555784225,
0.039963558316230774,
0.017572464421391487,
-0.03327792137861252,
-0.010151769034564495,
-0.05285629630088806,
-0.01633932814002037,
0.05862977355718613,
-0.02812449261546135,
0.0509178452193737,
-0.021655667573213577,
-0.03939144313335419,
0.05984024703502655,
0.029516924172639847,
-0.033865828067064285,
-0.018291153013706207,
-0.044749222695827484,
-0.04940900579094887,
-0.00792157556861639,
0.013146091252565384,
0.06936000287532806,
0.007887727580964565,
0.01654892973601818,
0.038471661508083344,
0.042314138263463974,
0.018804118037223816,
-0.032945264130830765,
-0.029512807726860046,
0.00943183246999979,
-0.019367089495062828,
-0.029406653717160225,
0.04210686683654785,
0.013273564167320728,
-0.06452586501836777,
0.022373922169208527,
-0.027066834270954132,
-0.001975428080186248,
-0.003397662891075015,
-0.03501248359680176,
0.03323571756482124,
0.003883772762492299,
-0.004118445795029402,
-0.004556628875434399,
0.0002098269760608673,
0.005715897772461176,
-0.019387733191251755,
0.02390480414032936,
0.044740695506334305,
0.018152086064219475,
-0.026176225394010544,
0.008948723785579205,
0.012517941184341908,
0.03834225982427597,
-0.009264268912374973,
0.00215255469083786,
0.014612169936299324,
-0.021636109799146652,
0.012883344665169716,
-0.03879720717668533,
-0.02722785249352455,
0.019989248365163803,
0.014456366188824177,
0.005254268180578947,
0.014704914763569832,
-0.05043327435851097,
-0.030153261497616768,
-0.0373142808675766,
0.013701200485229492,
0.012986638583242893,
0.06846945732831955,
-0.003922116477042437,
0.025630930438637733,
0.020777994766831398,
0.01183196809142828,
-0.02193761058151722,
-0.038251373916864395,
-0.08327653259038925,
0.011251697316765785,
-0.02214512787759304,
-0.017331229522824287,
0.007348545826971531,
-0.000055344975407933816,
0.013064797967672348,
-0.0315796360373497,
-0.031530432403087616,
-0.04803026095032692,
0.047977179288864136,
-0.030658584088087082,
0.03317243605852127,
-0.017398487776517868,
0.010364674963057041,
-0.04876018688082695,
0.026287470012903214,
-0.0025620372034609318,
-0.016164205968379974,
-0.018478820100426674,
0.028430171310901642,
-0.04088999703526497,
-0.03335244208574295,
-0.012245378457009792,
-0.0018182789208367467,
0.011640404351055622,
0.011681212112307549,
0.05022113770246506,
0.009264998137950897,
-0.0119994031265378,
-0.0015134295681491494,
0.00479091377928853,
0.0699070543050766,
-0.00882550235837698,
0.007552819326519966,
0.005170654039829969,
-0.01373473834246397,
-0.030539128929376602,
-0.03195272013545036,
0.05808698385953903,
0.007357294671237469,
-0.03277703747153282,
0.039380401372909546,
0.005250499118119478,
-0.013991089537739754,
0.03215566650032997,
0.015231057070195675,
0.030642757192254066,
0.007773443590849638,
-0.04826817661523819,
-0.019858064129948616,
-0.0011729559628292918,
0.003959981724619865,
0.0683702751994133,
0.002239095512777567,
-0.02362646348774433,
-0.018231721594929695,
0.03354701027274132,
0.011671599000692368,
-0.045835111290216446,
0.017451206222176552,
0.042591679841279984,
0.03801139444112778,
0.0023292084224522114,
-0.02586488425731659,
-0.03812165930867195,
0.005672776605933905,
0.018231436610221863,
0.005067718215286732,
0.0042691524140536785,
-0.08562446385622025,
-0.002496172906830907,
0.040581658482551575,
0.029594767838716507,
-0.027518216520547867,
0.029138196259737015,
-0.04925493523478508,
0.0058047231286764145,
0.008328127674758434,
-0.01832645945250988,
0.01361279096454382,
-0.049620091915130615,
-0.04559892788529396,
-0.05184107646346092,
-0.022862404584884644,
0.025006433948874474,
0.01608031801879406,
0.03243688493967056,
0.0045688762329518795,
-0.04425623267889023,
0.00066370889544487,
-0.028321584686636925,
-0.010387817397713661,
0.004685176070779562,
0.08399786055088043,
0.004941252525895834,
0.03423526883125305,
0.03827385976910591,
0.02661425806581974,
-0.031593747437000275,
-0.07950518280267715,
0.005029141902923584,
-0.0002817409986164421,
0.01934245228767395,
0.023490028455853462,
-0.026578793302178383,
-0.030952418223023415,
0.027905242517590523,
0.002171554835513234,
-0.047396253794431686,
-0.01176493614912033,
0.003054338740184903,
0.02503914386034012,
0.006055792327970266,
-0.02040867507457733,
0.044259387999773026,
0.013150460086762905,
-0.04480036348104477,
0.016677767038345337,
-0.016804834827780724,
0.034097086638212204,
-0.04635968804359436,
-0.015225126408040524,
0.009916480630636215,
-0.0033067441545426846,
-0.024174882099032402,
0.06511194258928299,
-0.014698892831802368,
0.058779068291187286,
0.02444535493850708,
-0.035440340638160706,
-0.016623402014374733,
0.055414341390132904,
-0.016697868704795837,
-0.005176714155822992,
0.008751856163144112,
0.03243738040328026,
-0.013708030804991722,
-0.0380607508122921,
0.01824106089770794,
0.05300423502922058,
0.005415374878793955,
0.03029688075184822,
0.0077069224789738655,
0.013919028453528881,
-0.03770320490002632,
0.009250680916011333,
0.0034716096706688404,
-0.0047408901154994965,
0.08198371529579163,
0.0021845276933163404,
-0.0014133600052446127,
0.025481177493929863,
-0.08789968490600586,
-0.03033597394824028,
0.03774247691035271,
-0.013356686569750309,
0.011918480508029461,
-0.03466934338212013,
0.03328308090567589,
-0.027640631422400475,
0.01462021004408598,
-0.07044228911399841,
-0.05112884193658829,
0.0193216260522604,
-0.015457898378372192,
0.000015417253962368704,
-0.021228421479463577,
-0.003493408439680934,
-0.0009239369537681341,
-0.06213192269206047,
0.03403284773230553,
0.04611871391534805,
0.024228472262620926,
-0.02792763151228428,
0.026103338226675987,
0.03744630888104439,
0.06262262910604477,
0.005890234839171171,
-0.0487913079559803,
0.0017511703772470355,
-0.017217077314853668,
0.02549218200147152,
-0.02419198863208294,
0.010513769462704659,
-0.023210598155856133,
-0.011924661695957184,
-0.0037722033448517323,
0.0078078522346913815,
0.02252255380153656,
0.004815482068806887,
-0.02203454077243805,
0.02658778615295887,
-0.011221729218959808,
0.0006248967838473618,
-0.04344257712364197,
0.01886668987572193,
-0.03457314148545265,
0.0454382449388504,
0.040060583502054214,
0.03149165213108063,
-0.047670282423496246,
-0.05009455978870392,
0.014155668206512928,
0.009223418310284615,
0.03747764974832535,
-0.0037434243131428957,
0.02331969514489174,
-0.014573661610484123,
0.02164280414581299,
0.051711712032556534,
0.01384628564119339,
0.06265310198068619,
-0.009231099858880043,
0.013016931712627411,
-0.023902636021375656,
0.036713454872369766,
-0.021966543048620224,
-0.019652752205729485,
-0.01813291572034359,
-0.0025516992900520563,
0.054164838045835495,
-0.04054531082510948,
0.02269621565937996,
0.00198356038890779,
-0.03555583581328392,
-0.01355832815170288,
0.00842403806746006,
-0.04001942649483681,
0.00989084504544735,
-0.04128846898674965,
0.030379610136151314,
-0.014545813202857971,
0.008324714377522469,
0.014428706839680672,
0.05335770547389984,
-0.01561329048126936,
0.023229185491800308,
0.0430821031332016,
0.046494897454977036,
-0.008810441941022873,
-0.015063086524605751,
-0.023852895945310593,
0.040594682097435,
-0.0242299847304821,
0.052023746073246,
-0.008385507389903069,
-0.013917987234890461,
0.04423561692237854,
-0.000995412701740861,
0.014767732471227646,
-0.014245772734284401,
-0.009631505236029625,
-0.06003452092409134,
0.02633936144411564,
0.03041752055287361,
-0.06557315587997437,
-0.005666370037943125,
0.0038420807104557753,
0.013879762962460518,
0.03329697251319885,
-0.0023700683377683163,
0.015033228322863579,
-0.04983414337038994,
-0.0472404845058918,
-0.004916056990623474,
-0.02909579686820507,
-0.014715413562953472,
-0.012955962680280209,
-0.03976587951183319,
0.012010486796498299,
-0.02179490216076374,
0.032924216240644455,
0.004834736697375774,
0.02680833451449871,
-0.014774270355701447,
0.08269480615854263,
0.013143494725227356,
0.05426895245909691,
-0.0036513032391667366,
-0.013332662172615528,
0.10960099846124649,
0.04133211448788643,
0.042338777333498,
-0.05519109219312668,
0.014246612787246704,
-0.01062480453401804,
0.043594688177108765,
-0.047639958560466766,
0.002502444665879011,
0.015138552524149418,
0.033427152782678604,
0.016556784510612488,
0.02894631400704384,
-0.0009926562197506428,
0.047600772231817245,
0.03769119456410408,
-0.03901565447449684,
-0.06748038530349731,
0.00805400125682354,
0.01693583093583584,
-0.02718948759138584,
0.0031109044793993235,
-0.03484748676419258,
0.0006969284149818122,
-0.02704058587551117,
-0.03468207269906998,
-0.00009409934864379466,
-0.025060158222913742,
0.05121250078082085,
0.019069937989115715,
-0.023887120187282562,
-0.008656210266053677,
0.005773449316620827,
0.005115962587296963,
-0.037529777735471725,
0.01019225362688303,
0.010912989266216755,
-0.01683933101594448,
-0.01546808797866106,
0.02981693483889103,
0.01636115089058876,
-0.015576020814478397,
0.01588141918182373,
0.025476332753896713,
-0.04785167798399925,
-0.004639248363673687,
-0.00515092583373189,
0.023782309144735336,
-0.0024920227006077766,
0.011870354413986206,
0.02707303874194622,
0.03573804348707199,
0.0002871645556297153,
-0.03130103647708893,
-0.056313227862119675,
-0.018356768414378166,
0.04197479784488678,
-0.03788025677204132,
-0.021088752895593643,
-0.02002616971731186,
0.04050006344914436,
0.015999095514416695,
0.013126577250659466,
-0.04575330391526222,
-0.004858600907027721,
0.007004658691585064,
-0.028552399948239326,
0.0015677972696721554,
-0.028678148984909058,
-0.0403633713722229,
-0.03893537446856499,
0.0030704308301210403,
-0.06834671646356583,
-0.017891600728034973,
0.018871529027819633,
0.0005457011866383255,
0.01045361626893282,
-0.021735621616244316,
-0.020520661026239395,
0.010809163562953472,
-0.03215322643518448,
0.023948153480887413,
-0.008705519139766693,
-0.005035726819187403,
-0.03445618599653244,
-0.0009416765533387661,
0.03544863685965538,
0.013952434062957764,
-0.0003411307989154011,
0.002654927084222436,
-0.06088210642337799,
0.01495015062391758,
0.01717524044215679,
-0.008153099566698074,
-0.006155095063149929,
-0.01106358878314495,
-0.03485523536801338,
0.009471964091062546,
-0.00804102886468172,
0.008772650733590126,
0.03202956169843674,
-0.02294153906404972,
-0.0314410999417305,
0.005469632335007191,
-0.01759699545800686,
0.010954434983432293,
0.03131034970283508,
0.003138215048238635,
-0.046671245247125626,
0.018118897452950478,
0.03241800144314766,
0.016218509525060654,
-0.0449686273932457,
-0.031649187207221985,
0.008987871930003166,
0.0041192262433469296,
0.023336688056588173,
0.013010945171117783,
0.053848493844270706,
-0.045729074627161026,
0.04921403154730797,
-0.04541028290987015,
0.014847318641841412,
-0.05038558691740036,
0.01611519791185856,
-0.01738940179347992,
0.028104526922106743,
0.02587779052555561,
-0.009490973316133022,
0.006431520450860262,
0.004948027897626162,
0.03363104537129402,
0.05273304134607315,
0.03509935736656189,
0.02146059460937977,
0.01722812093794346,
-0.05460772663354874,
0.06246889755129814,
-0.019599543884396553,
-0.0065543269738554955,
0.03388895466923714,
-0.030356820672750473,
-0.04562355950474739,
0.016241474077105522,
-0.040687646716833115,
0.014881306327879429,
-0.003332956228405237,
-0.0161572452634573,
-0.02532915212213993,
0.05704524740576744,
-0.003487578360363841,
-0.0045625632628798485,
-0.002316141501069069,
-0.03454321250319481,
0.000060614434914896265,
0.005826510488986969,
-0.032429423183202744,
-0.03642461821436882,
0.003074420616030693,
0.04127587750554085,
0.03987487778067589,
0.030202623456716537,
-0.011663481593132019,
0.015129432082176208,
0.020145252346992493,
0.0012235852191224694,
0.010667985305190086,
-0.013779718428850174,
0.04874656721949577,
0.05232620984315872,
-0.028475744649767876,
0.027995770797133446,
0.005042470525950193,
0.008340684697031975,
-0.036656055599451065,
-0.02287166751921177,
-0.019043099135160446,
-0.0021583368070423603,
0.03127172216773033,
-0.056140463799238205,
0.012205610051751137,
0.030821440741419792,
-0.07415848970413208,
0.014065034687519073,
-0.04862033203244209,
-0.001954520121216774,
-0.049070216715335846,
-0.023745819926261902,
-0.04007977247238159,
0.048532940447330475,
0.002420959295704961,
0.042113155126571655,
-0.012804443947970867,
0.03964303061366081,
0.01397443376481533,
0.004716030787676573,
-0.036010246723890305,
0.037602659314870834,
-0.02005748078227043,
-0.0481569878757,
0.043826472014188766,
0.0061788721941411495,
-0.0361299067735672,
0.03282729163765907,
-0.009521412663161755,
-0.011009595356881618,
0.011708836071193218,
0.0039021321572363377,
0.01931033283472061,
0.032869718968868256,
0.005768171511590481,
-0.027327634394168854,
-0.014615275897085667,
-0.010706366039812565,
0.021399030461907387,
0.02324264869093895,
0.018517283722758293,
0.01684635691344738,
0.006282528396695852,
-0.009415107779204845,
0.012910452671349049,
0.010977745056152344,
-0.020848173648118973,
-0.010600441135466099,
0.0038441403303295374,
0.02902039885520935,
0.03473425284028053,
-0.012248159386217594,
0.025500426068902016,
-0.02095777727663517,
-0.04934675991535187,
0.011906427331268787,
0.024441877380013466,
0.0458739697933197,
0.019659100100398064,
-0.006535533349961042,
-0.027965892106294632,
0.027908818796277046,
-0.01971818506717682,
0.017373405396938324,
-0.05753091722726822,
-0.04580580070614815,
0.02599824219942093,
0.020698461681604385,
0.006503761745989323,
-0.024376604706048965,
-0.035451922565698624,
0.05557902157306671,
0.007147578988224268,
0.040102966129779816,
-0.022733241319656372,
-0.03967864438891411,
0.0051703439094126225,
-0.01629847101867199,
0.012120328843593597,
0.007786633912473917,
0.01203958224505186,
-0.029244234785437584,
-0.023153280839323997,
-0.005250996444374323,
0.03075469471514225,
0.08599920570850372,
-0.019199859350919724,
-0.021187756210565567,
0.002049465198069811,
0.020115798339247704,
0.023379294201731682,
-0.02304847352206707,
0.004935958422720432,
-0.008729043416678905,
-0.05149850249290466,
-0.002544138114899397,
-0.00928003154695034,
-0.013897519558668137,
0.039380382746458054,
0.03213357552886009,
0.0000999136027530767,
0.0393226332962513,
-0.009555047377943993,
-0.013442455790936947,
0.015273728407919407,
0.041986145079135895,
0.002006225986406207,
0.06723874062299728,
-0.014999405480921268,
0.004360591527074575,
0.005592952948063612,
-0.0032918062061071396,
-0.035960711538791656,
0.03371850401163101,
-0.011944660916924477,
-0.018825413659214973,
-0.0012367760064080358,
-0.008519702591001987,
0.005769187118858099,
-0.038107872009277344,
0.010759830474853516,
0.017679624259471893,
-0.039627913385629654,
0.027990682050585747,
0.09177011996507645,
0.04159737005829811,
0.03324660286307335,
0.007538388017565012,
0.012649317272007465,
-0.016578886657953262,
-0.001579084899276495,
-0.008854038082063198,
0.0315614677965641,
0.017499122768640518,
-0.010704606771469116,
0.009626374579966068,
-0.0067784409038722515,
-0.0018148190574720502,
0.02698303572833538,
0.0020315132569521666,
0.01485662441700697,
-0.025776393711566925,
-0.0007454119622707367,
0.016153842210769653,
-0.010962926782667637,
0.008234802633523941,
0.04763393849134445,
-0.025747234001755714,
0.10595767945051193,
-0.055601831525564194,
-0.008071866817772388,
-0.0032011782750487328,
-0.024708064272999763,
-0.030260227620601654,
-0.016714761033654213,
-0.02023809403181076,
0.048350028693675995,
-0.01823626272380352,
0.019050998613238335,
-0.00813941191881895,
0.005846880376338959,
0.032148219645023346,
-0.01674104854464531,
0.027774745598435402,
0.009259018115699291,
-0.022230232134461403,
-0.010042410343885422,
-0.012373310513794422,
-0.026592304930090904,
0.01879599504172802,
-0.00977594405412674,
0.05876297503709793,
0.002988159656524658,
0.02034323662519455,
-0.05145285651087761,
0.010230419225990772,
0.03578430786728859,
-0.045683603733778,
0.0018456393154338002,
-0.03643651679158211,
-0.025888172909617424,
-0.05713488161563873,
0.014599104411900043
] |
<p>Recall the first law of BH thermodynamics</p>
<p>$ dM=\frac{\kappa}{8\pi} dA + \Omega dJ + \Phi dQ $</p>
<p>Now, let's consider the Reissner-Nordstrom solution $J=0$ such that $m>Q$ but only slightly greater. Suppose I have a small bit of charge $dQ$ which I bring in from infinity to the BH horizion. </p>
<p>1) Question: Is the extremal BH solution $m=Q$ possible? </p>
<p>I would think that if we consider the work to be done to bring $dQ$ from $\infty$ to BH horizon, this would blow up $\Phi$ and cause M to go to $\infty$ as well. Therefore, I would guess the extremal solution cannot be achieved in this scenario. </p>
<p>2) Now, this extremal solution DOES seem possible in the Kerr solution, but how would this affect $J$ and $\Omega$ ?</p>
| 8,460 |
[
0.008623829111456871,
-0.0018454089295119047,
-0.0025456829462200403,
0.003334809560328722,
0.04375159740447998,
-0.0009420369751751423,
-0.06794232875108719,
-0.03985456004738808,
-0.0066338470205664635,
-0.04193383827805519,
0.012147076427936554,
0.02536742016673088,
0.030678851529955864,
0.026673799380660057,
0.029241690412163734,
-0.008242812007665634,
-0.012278660200536251,
-0.019433975219726562,
0.009907565079629421,
-0.00953624863177538,
-0.00200800527818501,
0.06098276749253273,
0.014141147956252098,
0.016513455659151077,
-0.026423431932926178,
-0.005612615495920181,
0.007675359025597572,
0.016818229109048843,
-0.010907365009188652,
0.02333279699087143,
0.02438235655426979,
-0.010384163819253445,
0.008738135918974876,
0.023434098809957504,
0.021847253665328026,
-0.012325718998908997,
-0.041063521057367325,
-0.02523340843617916,
-0.020990414544939995,
-0.011884739622473717,
-0.03351140022277832,
-0.013197033666074276,
0.010390703566372395,
0.037132520228624344,
-0.003082107286900282,
-0.020703772082924843,
0.012854800559580326,
-0.006832086946815252,
0.021610544994473457,
-0.08200264722108841,
0.057043012231588364,
0.03860482946038246,
0.010720237158238888,
-0.0031843604519963264,
-0.005380121059715748,
0.005893956869840622,
0.06911835074424744,
0.08443820476531982,
0.0053513552993535995,
-0.012015980668365955,
-0.03572461009025574,
0.012272602878510952,
-0.037861112505197525,
0.010127026587724686,
-0.017743075266480446,
0.05916963890194893,
0.02174696885049343,
-0.004824124742299318,
0.018545377999544144,
-0.004505650606006384,
-0.008903364650905132,
0.030409444123506546,
0.031015945598483086,
-0.015791574493050575,
0.04589793086051941,
-0.0014280923642218113,
-0.005415373481810093,
-0.030535073950886726,
-0.0010971337324008346,
0.05787119269371033,
-0.005733080208301544,
0.004031293094158173,
0.04307204484939575,
0.07515795528888702,
0.0007718519773334265,
0.0030316186603158712,
0.046029262244701385,
-0.04169665277004242,
0.029866527765989304,
0.03803687170147896,
0.0008313054568134248,
0.010912035591900349,
0.028634088113904,
-0.020053522661328316,
-0.01698165014386177,
-0.017596082761883736,
0.015439478680491447,
0.04029141739010811,
0.005325343459844589,
-0.03664635866880417,
-0.01155465841293335,
0.0033126489724963903,
-0.009194440208375454,
0.04557172954082489,
0.056911367923021317,
-0.01634085550904274,
-0.01400848850607872,
0.021130118519067764,
-0.025722024962306023,
-0.01599959284067154,
-0.07196512818336487,
0.0006221377989277244,
-0.03083050064742565,
-0.03585212677717209,
0.006863723509013653,
-0.04883673042058945,
-0.00004245151285431348,
-0.06879975646734238,
0.02223152481019497,
0.05928708612918854,
0.05661751329898834,
0.012864829041063786,
0.00289751379750669,
-0.0221922155469656,
-0.05566095933318138,
0.022924745455384254,
0.03419770300388336,
-0.017733685672283173,
-0.03721332922577858,
-0.03950845077633858,
-0.03334943950176239,
0.01879010535776615,
0.003581882454454899,
0.024980539456009865,
0.006617820356041193,
-0.03914555162191391,
-0.05166514590382576,
-0.056558605283498764,
0.03915753588080406,
-0.010323124006390572,
-0.023439321666955948,
-0.07603546977043152,
0.022816676646471024,
0.04101647809147835,
0.06778736412525177,
0.00972590409219265,
-0.005701856687664986,
-0.0074936142191290855,
0.06227482855319977,
0.018015893176198006,
-0.022699005901813507,
-0.01045398972928524,
-0.024212270975112915,
-0.04537205770611763,
-0.01906748116016388,
-0.10868792235851288,
0.016399072483181953,
0.03621809557080269,
0.03786769136786461,
0.0006853509112261236,
0.061503324657678604,
-0.01773887313902378,
0.007457362487912178,
-0.0018179030157625675,
-0.0388045534491539,
0.025456000119447708,
0.08594634383916855,
0.008918109349906445,
0.03934193029999733,
0.013231029734015465,
0.023003611713647842,
0.05483545735478401,
0.027142146602272987,
0.019542399793863297,
0.010654664598405361,
-0.03391687572002411,
0.02858063206076622,
-0.04617858678102493,
0.01775973103940487,
0.008099786937236786,
-0.0002214264532085508,
-0.04006895422935486,
-0.010144389234483242,
-0.009846700355410576,
-0.005002286750823259,
0.020920922979712486,
-0.04934367910027504,
0.0023237941786646843,
0.00671915290877223,
-0.04173435643315315,
-0.006149583030492067,
-0.04542694613337517,
0.03184007480740547,
0.060306616127491,
-0.01284758560359478,
0.025080272927880287,
0.008069943636655807,
0.03400656580924988,
-0.05991610884666443,
-0.02290048450231552,
0.028086375445127487,
0.029183009639382362,
-0.0028672481421381235,
0.02026224508881569,
0.04859508201479912,
0.03652041777968407,
0.05626671761274338,
-0.008506400510668755,
0.023378849029541016,
-0.000109667336801067,
-0.03575696796178818,
-0.01811019703745842,
0.007592886220663786,
0.03710400313138962,
-0.01811627857387066,
0.010043024085462093,
0.03175744041800499,
-0.0008764032972976565,
-0.005510319955646992,
0.0037593641318380833,
-0.015188176184892654,
0.05910487100481987,
0.04538765549659729,
0.011294449679553509,
-0.030245080590248108,
0.03791385889053345,
0.013384131714701653,
0.001735921367071569,
-0.012578108347952366,
-0.012651090510189533,
-0.02029283531010151,
0.04116781800985336,
-0.007049816660583019,
0.02749234437942505,
-0.05936313048005104,
0.031858284026384354,
0.05172690004110336,
0.011215601116418839,
0.047995831817388535,
-0.01835910603404045,
-0.010624389164149761,
0.008336248807609081,
0.030354108661413193,
0.032082509249448776,
0.005839069839566946,
0.003436642000451684,
0.044941265136003494,
-0.016442889347672462,
0.01732799969613552,
-0.018669424578547478,
-0.008037176914513111,
0.012894295156002045,
-0.0024079428985714912,
0.01389184221625328,
0.009163825772702694,
-0.02924502082169056,
0.057260774075984955,
-0.013072832487523556,
0.025952497497200966,
0.06427954137325287,
0.005120506044477224,
-0.0009591517737135291,
-0.050778213888406754,
0.010625607334077358,
0.018986301496624947,
0.004264978691935539,
0.003179508028551936,
-0.03324078023433685,
0.007579389028251171,
-0.05534639582037926,
0.008105912245810032,
-0.01711810939013958,
0.007219748571515083,
-0.011871845461428165,
0.001395426457747817,
0.037334877997636795,
-0.0016389923403039575,
0.03212076798081398,
-0.027229195460677147,
-0.035735417157411575,
0.028993986546993256,
-0.003883786266669631,
-0.005581545177847147,
0.020862944424152374,
-0.03334631398320198,
-0.02171006053686142,
-0.053629983216524124,
-0.015138283371925354,
0.046062834560871124,
0.006119487341493368,
0.014501886442303658,
0.003478930564597249,
-0.008857285603880882,
0.007142782676964998,
0.02409963868558407,
0.011358209885656834,
0.010155406780540943,
-0.046417977660894394,
-0.002759139286354184,
0.028204815462231636,
0.019987570121884346,
-0.02153697982430458,
0.018145130947232246,
-0.023930983617901802,
-0.025577185675501823,
-0.010000081732869148,
0.0386352464556694,
-0.0016024371143430471,
-0.020247984677553177,
0.05050434172153473,
0.004661526996642351,
-0.017001325264573097,
0.014732513576745987,
-0.06905877590179443,
-0.04428745433688164,
0.05380357429385185,
0.0009458356071263552,
0.0017929773312062025,
-0.009705720469355583,
-0.07552915811538696,
0.054897163063287735,
0.032844141125679016,
-0.015307878144085407,
0.005390741862356663,
-0.01503310538828373,
-0.01800644025206566,
-0.002299961168318987,
-0.047321867197752,
0.03557379171252251,
-0.03392378240823746,
-0.01566343940794468,
0.028860511258244514,
0.04511148855090141,
0.02881522849202156,
-0.002937441924586892,
-0.0330619178712368,
0.027285261079669,
-0.007309773005545139,
0.05204683914780617,
0.05145131051540375,
0.015645170584321022,
0.03146401047706604,
0.021281078457832336,
0.0027293486054986715,
0.03976622223854065,
-0.003487741108983755,
-0.06468083709478378,
0.01604747772216797,
0.015957502648234367,
0.02187856286764145,
-0.008750961162149906,
0.02849843166768551,
-0.004727234598249197,
-0.03832013159990311,
-0.014489701949059963,
0.016679497435688972,
0.03014282137155533,
-0.03271416947245598,
-0.004610986448824406,
0.0097351660951972,
0.020850054919719696,
-0.032485898584127426,
-0.02661728486418724,
0.01441126223653555,
-0.022484637796878815,
0.031241292133927345,
-0.021200919523835182,
0.0026345783844590187,
0.02321917749941349,
0.011950207874178886,
-0.0014937532832846045,
0.0010692257201299071,
-0.012226210907101631,
0.016857698559761047,
-0.09412046521902084,
-0.056404996663331985,
-0.02606179751455784,
0.04706212133169174,
-0.00983815174549818,
0.04118160158395767,
0.04012911766767502,
0.008795976638793945,
0.02498146891593933,
0.0005177572602406144,
-0.09490444511175156,
0.03580605611205101,
-0.04528890177607536,
-0.003739953739568591,
0.00994400680065155,
-0.02822052128612995,
-0.019056320190429688,
-0.030072864145040512,
-0.01667216792702675,
0.003062525996938348,
0.01800651289522648,
-0.06084011122584343,
0.017713619396090508,
-0.042546313256025314,
-0.025831520557403564,
-0.0015454072272405028,
0.044722214341163635,
0.05805410444736481,
-0.018839385360479355,
0.003098556073382497,
0.05343791842460632,
-0.050445374101400375,
0.008455628529191017,
0.0006239648791961372,
0.01827302575111389,
0.0033432000782340765,
0.03885255381464958,
0.00929197482764721,
0.02192085236310959,
-0.014500275254249573,
-0.049623146653175354,
0.044108450412750244,
0.029895825311541557,
-0.006066587287932634,
-0.03225302696228027,
-0.05785834789276123,
-0.04731719195842743,
-0.003816615091636777,
-0.0042937146499753,
0.10807020962238312,
-0.006683405488729477,
0.011897798627614975,
0.00039203374763019383,
-0.011988157406449318,
-0.010250560007989407,
0.020060846582055092,
0.08466190844774246,
-0.0029210287611931562,
-0.03995852544903755,
-0.061089277267456055,
-0.058093734085559845,
-0.02297523058950901,
0.007332646753638983,
0.019274987280368805,
-0.0007657395326532423,
-0.045145198702812195,
-0.003162464825436473,
-0.0071626510471105576,
0.0017961878329515457,
0.0028119890484958887,
-0.01454888004809618,
0.016935329884290695,
0.027726124972105026,
0.022595448419451714,
0.02435239404439926,
0.018711090087890625,
0.03713716194033623,
0.061358146369457245,
-0.019766125828027725,
0.020144745707511902,
-0.04463377594947815,
-0.010291445069015026,
0.01777823269367218,
0.04901731386780739,
0.009552459232509136,
-0.00819355994462967,
-0.06745336204767227,
0.018290109932422638,
0.06283871829509735,
-0.05147259309887886,
0.0482834130525589,
0.03212882950901985,
0.014797871932387352,
-0.004888821858912706,
0.006186968181282282,
-0.05262488126754761,
0.02637130580842495,
0.0027732746675610542,
-0.003865670645609498,
-0.018684377893805504,
0.015258525498211384,
0.0011471171164885163,
0.053700320422649384,
0.013705982826650143,
0.028270388022065163,
-0.00038421989302150905,
-0.025493137538433075,
0.008389401249587536,
-0.0068361395969986916,
-0.0030874053481966257,
-0.05220279470086098,
0.0011647137580439448,
0.021140486001968384,
-0.02482672408223152,
0.03415592014789581,
-0.06392544507980347,
-0.038268350064754486,
0.06173353269696236,
0.012421759776771069,
-0.004534583073109388,
0.03128492832183838,
-0.05063287913799286,
0.031368616968393326,
0.0001687130716163665,
-0.024973317980766296,
0.03992101550102234,
-0.0003587304090615362,
-0.009920815005898476,
-0.008875644765794277,
-0.03248091787099838,
0.05607321858406067,
-0.0030488362535834312,
-0.025518644601106644,
-0.012495666742324829,
0.002954949392005801,
-0.04403313994407654,
0.050688736140728,
0.009104082360863686,
0.004257005173712969,
-0.004020877182483673,
-0.017717862501740456,
0.015963124111294746,
0.040353819727897644,
0.0021529176738113165,
-0.022703221067786217,
0.007770208176225424,
0.035618141293525696,
0.013496973551809788,
-0.004505316726863384,
0.029070215299725533,
-0.003683684393763542,
-0.010111967101693153,
0.0371348075568676,
-0.043157659471035004,
0.029915161430835724,
-0.0047291056253015995,
0.030625294893980026,
-0.008518810383975506,
-0.01150044146925211,
0.043028030544519424,
-0.024198004975914955,
-0.010302075184881687,
0.003353829961270094,
-0.03741619363427162,
-0.010680281557142735,
-0.026291102170944214,
-0.0232478529214859,
0.024437693879008293,
-0.03296753764152527,
0.004943914711475372,
0.06391773372888565,
0.0005019140080548823,
-0.07770755141973495,
-0.05037660524249077,
0.034922048449516296,
0.0019645732827484608,
0.01759810745716095,
-0.018046550452709198,
0.004338837694376707,
-0.0719476267695427,
-0.02779478020966053,
-0.035830624401569366,
0.06759585440158844,
-0.011049973778426647,
0.0031161243095993996,
-0.0293430183082819,
0.04110592603683472,
0.01680668257176876,
-0.008706964552402496,
-0.047075025737285614,
0.037221647799015045,
-0.017664233222603798,
-0.005337726324796677,
0.0036739776842296124,
0.036330223083496094,
-0.0033449626062065363,
-0.04498329386115074,
-0.052029263228178024,
-0.027105821296572685,
0.05637624114751816,
0.0009852474322542548,
-0.0036863021086901426,
0.03664181008934975,
0.0034131864085793495,
0.002978447824716568,
-0.030451267957687378,
0.014596153050661087,
-0.03799237683415413,
0.009711651131510735,
-0.01824653334915638,
-0.02229989692568779,
0.007735121063888073,
-0.05115942284464836,
0.03781939297914505,
-0.005613775458186865,
-0.019152987748384476,
-0.04025483503937721,
0.07421337068080902,
0.011763595044612885,
-0.035743724554777145,
-0.010310118086636066,
-0.01423817127943039,
0.01696823164820671,
0.005539776291698217,
0.012282362207770348,
0.028855564072728157,
0.025938719511032104,
-0.04632742702960968,
-0.05111950635910034,
-0.050175104290246964,
0.024585677310824394,
0.05894175171852112,
-0.006743512582033873,
0.024674978107213974,
0.01042722538113594,
-0.001138802501372993,
0.006786404177546501,
-0.04208635911345482,
-0.008276951499283314,
0.042836517095565796,
-0.008523987606167793,
0.029284022748470306,
-0.02373487316071987,
0.007039176300168037,
0.020808344706892967,
0.06890774518251419,
-0.017706865444779396,
-0.0368751659989357,
0.023864084854722023,
0.039475563913583755,
-0.01240632962435484,
-0.017859483137726784,
-0.02885969914495945,
0.043651461601257324,
-0.0602954626083374,
0.03824393451213837,
0.0066923052072525024,
0.001730429707095027,
0.0440482459962368,
0.021315721794962883,
0.042201440781354904,
-0.057826850563287735,
-0.03598114475607872,
-0.03175937384366989,
0.017087478190660477,
0.011027182452380657,
0.052005186676979065,
0.011807444505393505,
-0.017483381554484367,
0.02719409205019474,
-0.030055327340960503,
0.021245064213871956,
0.011920863762497902,
-0.04399772733449936,
-0.00926096923649311,
-0.012364602647721767,
-0.060551706701517105,
0.055595871061086655,
0.002741799456998706,
-0.015318474732339382,
0.043403010815382004,
-0.05121324583888054,
0.03762416914105415,
0.013909626752138138,
0.027585532516241074,
0.01602892018854618,
0.05025675147771835,
-0.019947826862335205,
0.0269833505153656,
-0.0006799640250392258,
0.032252758741378784,
0.1082507073879242,
0.06233152374625206,
0.015006482601165771,
-0.05849163979291916,
0.014610755257308483,
-0.017079466953873634,
0.012506947852671146,
-0.06643667072057724,
0.043899212032556534,
-0.012311072088778019,
-0.0010820594616234303,
0.02649657242000103,
0.04470399022102356,
-0.04016837105154991,
0.015263760462403297,
0.03568870201706886,
-0.04387424513697624,
0.003725898452103138,
0.051469653844833374,
-0.0034973309375345707,
0.011164478026330471,
0.008050923235714436,
-0.002876151818782091,
0.008365827612578869,
0.004033805336803198,
0.0073501416482031345,
-0.04988567903637886,
-0.02594173513352871,
-0.002835561754181981,
-0.03816341236233711,
-0.03811255469918251,
-0.004408464767038822,
-0.00824693962931633,
-0.012289372272789478,
-0.008312513120472431,
-0.006942917127162218,
0.006357428152114153,
-0.021714435890316963,
0.018985142931342125,
0.04391191899776459,
0.006689413916319609,
0.00810746755450964,
0.01255712192505598,
0.03281933441758156,
-0.016511358320713043,
0.019706903025507927,
-0.012758143246173859,
0.0397932268679142,
-0.0454057939350605,
0.008864638395607471,
0.01866266131401062,
-0.00904637947678566,
-0.016206245869398117,
-0.04989228770136833,
-0.04036498814821243,
-0.0007609665626659989,
-0.003835591021925211,
0.0026644461322575808,
-0.03704645484685898,
-0.009479640983045101,
0.029466312378644943,
0.039019014686346054,
0.013307997956871986,
-0.02177746780216694,
0.002341456711292267,
0.02296949364244938,
-0.016240157186985016,
0.03872572258114815,
0.0035273509565740824,
-0.026520147919654846,
-0.03793013468384743,
0.0006227861158549786,
-0.03676202893257141,
-0.01417720690369606,
-0.00040196324698626995,
-0.009716666303575039,
0.04457564651966095,
0.01736731454730034,
-0.019787535071372986,
-0.026515617966651917,
-0.01907249167561531,
-0.005395667627453804,
-0.004485676530748606,
-0.01366648729890585,
-0.02926088124513626,
0.020880870521068573,
-0.014618146233260632,
0.056452833116054535,
-0.004437005612999201,
-0.019553983584046364,
0.03491703048348427,
0.04488145560026169,
0.006531078368425369,
0.0037546074017882347,
-0.04694325476884842,
-0.03770137205719948,
-0.06032267585396767,
-0.000026405663447803818,
0.015683859586715698,
0.00038531963946297765,
-0.024537468329072,
-0.006441469304263592,
0.034303903579711914,
0.007814225740730762,
-0.03182335942983627,
0.011482840403914452,
0.027180934324860573,
-0.020033227279782295,
0.0032047457061707973,
0.022569023072719574,
-0.010141054168343544,
-0.0191410593688488,
-0.027026692405343056,
-0.04248780757188797,
0.01971207559108734,
-0.020132478326559067,
-0.010429685935378075,
-0.03721403330564499,
0.01619320921599865,
-0.009726391173899174,
-0.019185630604624748,
-0.044446591287851334,
-0.049116626381874084,
-0.024946605786681175,
0.036687467247247696,
-0.03342872112989426,
0.013775080442428589,
0.055329494178295135,
0.03840865194797516,
-0.00256549334153533,
-0.06259147822856903,
-0.00453819427639246,
0.009877456352114677,
-0.023210475221276283,
-0.01239154115319252,
0.013464882969856262,
0.039918314665555954,
0.02671525627374649,
-0.019981706514954567,
-0.04447252303361893,
0.0164627805352211,
-0.027836551889777184,
-0.0391603484749794,
0.014390341006219387,
-0.012236814014613628,
-0.0017654516268521547,
0.048321325331926346,
-0.018200745806097984,
-0.06137166917324066,
0.061676282435655594,
-0.000276355684036389,
-0.013589274138212204,
0.03274257481098175,
-0.030507449060678482,
-0.01600220613181591,
0.004008202813565731,
-0.007986483164131641,
-0.05544965714216232,
-0.005358709022402763,
0.010943111032247543,
0.009759864769876003,
-0.006227840669453144,
-0.030298754572868347,
0.011386806145310402,
0.036910280585289,
0.03109174780547619,
0.0083655109629035,
-0.025005878880620003,
0.029752034693956375,
0.0389302633702755,
-0.0526157021522522,
0.00965609960258007,
0.027323849499225616,
-0.012984306551516056,
-0.09027945250272751,
-0.043204184621572495,
0.013895002193748951,
-0.0013049596454948187,
0.058514222502708435,
-0.03151995688676834,
0.03694374859333038,
0.026843033730983734,
-0.07348870486021042,
0.020390963181853294,
-0.0002974056114908308,
0.00835438258945942,
-0.057553548365831375,
0.012928697280585766,
-0.03455989062786102,
0.062119029462337494,
0.06346967816352844,
0.04287022352218628,
-0.008522539399564266,
-0.02088024467229843,
-0.006036907434463501,
-0.03150530159473419,
0.012148275971412659,
0.04237581044435501,
0.0021184440702199936,
-0.05337543413043022,
0.07660363614559174,
-0.03789215907454491,
-0.045161668211221695,
0.0221698135137558,
-0.033148083835840225,
-0.028484772890806198,
0.028413020074367523,
0.017736058682203293,
0.01911761797964573,
0.007747101131826639,
0.05267646908760071,
0.0041037569753825665,
-0.03465328365564346,
0.009357774630188942,
0.019474122673273087,
0.035408858209848404,
-0.026059892028570175,
0.025231583043932915,
0.06051729619503021,
-0.015326597727835178,
-0.013965344987809658,
0.03266586735844612,
-0.05632973462343216,
-0.05260065197944641,
0.013394025154411793,
0.014760061167180538,
0.035172294825315475,
-0.01781580224633217,
-0.0019034467404708266,
-0.041232433170080185,
0.0033413474448025227,
0.01108911819756031,
0.0016244418220594525,
0.01621030457317829,
0.0004192835767753422,
0.01615975797176361,
-0.00782463513314724,
-0.008471911773085594,
0.011274163611233234,
-0.017393138259649277,
-0.054037027060985565,
0.009654772467911243,
-0.025041712448000908,
-0.001309013576246798,
-0.002840056549757719,
-0.03337318077683449,
-0.021049384027719498,
0.06687349826097488,
0.005642819683998823,
0.05157576501369476,
-0.021365953609347343,
-0.04116138070821762,
-0.023502783849835396,
-0.06174186244606972,
0.02641788125038147,
-0.017771268263459206,
-0.0015925801126286387,
0.001294528366997838,
-0.039897095412015915,
0.005987163633108139,
-0.008619709871709347,
0.056743867695331573,
-0.03174145892262459,
-0.023384328931570053,
0.046350423246622086,
-0.005082420073449612,
0.02012522518634796,
-0.003915941342711449,
0.0024196961894631386,
0.023749521002173424,
-0.017818333581089973,
-0.00976648647338152,
0.03073136880993843,
-0.02634935826063156,
0.02233116142451763,
0.034080300480127335,
-0.008875726722180843,
0.050925709307193756,
-0.013691808097064495,
-0.021553391590714455,
0.012035209685564041,
-0.02167704328894615,
0.0030689500272274017,
0.041189491748809814,
-0.014709233306348324,
0.019534671679139137,
0.028460007160902023,
-0.020967958495020866,
-0.045851439237594604,
0.012833771295845509,
-0.06485173106193542,
-0.0031988502014428377,
-0.014697332866489887,
0.008673680014908314,
-0.019155148416757584,
-0.046989742666482925,
0.006480233743786812,
0.04452543705701828,
-0.03553337603807449,
0.019973553717136383,
0.030104395002126694,
-0.00905262865126133,
0.0286884568631649,
0.005272059701383114,
-0.02169407717883587,
-0.006690391805022955,
0.012648177333176136,
-0.0063389320857822895,
0.040440816432237625,
0.059580594301223755,
-0.007444477640092373,
0.00710301985964179,
0.010867105796933174,
-0.03799466788768768,
-0.006290658377110958,
-0.02416067384183407,
0.004045219626277685,
-0.02883545495569706,
-0.05617937073111534,
0.05517231300473213,
0.005395699292421341,
0.02094392105937004,
-0.00026476479251869023,
-0.012062286026775837,
0.05310477688908577,
-0.019418813288211823,
0.03131962567567825,
-0.015873314812779427,
0.002437387825921178,
-0.021453650668263435,
0.03303838521242142,
-0.03589361160993576,
0.09528367966413498,
-0.021944068372249603,
-0.04804636538028717,
0.02004062570631504,
0.018853528425097466,
0.004074303898960352,
-0.015476944856345654,
-0.016405681148171425,
0.007726462557911873,
-0.01894499734044075,
-0.01328743901103735,
-0.018213098868727684,
-0.009321554563939571,
-0.013822096399962902,
-0.003121668007224798,
0.005964142736047506,
0.022079095244407654,
0.021591002121567726,
-0.014799845404922962,
0.007995647378265858,
0.024984387680888176,
-0.021971898153424263,
-0.02229914255440235,
0.0020702751353383064,
-0.005300450138747692,
-0.030821872875094414,
-0.021861402317881584
] |
<p><a href="http://en.wikipedia.org/wiki/Maxwell_equations" rel="nofollow">Maxwell's equations</a> allow for wave solutions via oscillations between electric and magnetic field content.</p>
<p>Couldn't we generate electric waves also if that solution didn't exists?
Imagine there was no magnetic field, only the electric field. If at one point in space we generated an electric field nicely varying in a sinus pattern of constant frequency, wouldn't this propagate with light speed, just like a plane EM-wave of that frequency, even though there was no magnetic field?</p>
| 8,461 |
[
-0.021755648776888847,
0.01343138050287962,
0.0009576654992997646,
-0.05104408785700798,
0.06584319472312927,
-0.0012040609726682305,
-0.04218878969550133,
-0.036973483860492706,
0.016354475170373917,
-0.03027990087866783,
0.01695837825536728,
0.02774115465581417,
0.018392590805888176,
0.02775636501610279,
0.02111591398715973,
-0.004373377189040184,
-0.0016189345624297857,
0.011406131088733673,
-0.04270218685269356,
-0.02866705320775509,
-0.031241854652762413,
0.019651679322123528,
-0.011374079622328281,
0.0314408577978611,
-0.041241999715566635,
0.0067621381022036076,
0.025127394124865532,
0.0340668149292469,
0.012545261532068253,
0.02878481335937977,
0.003851712681353092,
-0.023369640111923218,
0.005914486479014158,
0.04447212815284729,
0.019319331273436546,
0.0037803002633154392,
-0.041279856115579605,
-0.03314919024705887,
-0.004102576058357954,
-0.01905224099755287,
0.03539812192320824,
-0.02056606113910675,
-0.01490743551403284,
0.03741380199790001,
-0.053119875490665436,
-0.000522891350556165,
0.030897239223122597,
-0.016958076506853104,
0.049586012959480286,
-0.07313927263021469,
0.05115397274494171,
-0.021706992760300636,
0.029068194329738617,
0.007086634635925293,
-0.01636766456067562,
-0.02375018782913685,
0.09654215723276138,
0.05233843997120857,
-0.008676577359437943,
-0.03985271602869034,
-0.015000422485172749,
0.005686196964234114,
-0.003323860000818968,
-0.029721122235059738,
-0.038964834064245224,
0.07001698762178421,
0.010331844910979271,
-0.0065588816069066525,
0.021538054570555687,
-0.002547686453908682,
0.02213776670396328,
0.02096136473119259,
0.01809210516512394,
-0.008055350743234158,
0.002244454575702548,
-0.046604327857494354,
0.014788573607802391,
-0.015690745785832405,
0.05173804238438606,
0.04672301933169365,
0.0035685738548636436,
0.015055360272526741,
0.005791917443275452,
0.02033730410039425,
0.002534002996981144,
0.0028038504533469677,
0.05596163868904114,
-0.019110094755887985,
-0.006308883894234896,
0.004446284845471382,
0.0003367982862982899,
0.02033788524568081,
0.03486732020974159,
-0.0016177805373445153,
-0.01731153391301632,
0.014676190912723541,
-0.015905674546957016,
0.02956908382475376,
0.03437187522649765,
-0.036018695682287216,
0.03941436856985092,
0.00048287605750374496,
0.007605867926031351,
0.042513396590948105,
0.011868776753544807,
-0.04549890384078026,
-0.016312995925545692,
0.028685977682471275,
-0.06491392105817795,
-0.011517309583723545,
-0.028695745393633842,
0.03693438693881035,
0.02663387916982174,
0.006918019149452448,
0.013465224765241146,
-0.029422421008348465,
0.024255387485027313,
-0.05441485717892647,
0.05091382563114166,
0.10613304376602173,
0.03151779621839523,
-0.06603457778692245,
0.023923225700855255,
-0.02439264766871929,
-0.057330649346113205,
-0.043339867144823074,
-0.030962849035859108,
0.011944727972149849,
-0.03018113225698471,
0.0040614004246890545,
-0.052082885056734085,
0.004903202410787344,
-0.0035983421839773655,
-0.021790234372019768,
0.028114739805459976,
-0.01915854960680008,
-0.11277948319911957,
-0.07326450943946838,
0.001709765405394137,
-0.037912189960479736,
-0.021311359480023384,
-0.05882514268159866,
-0.001381038804538548,
0.0225001759827137,
0.07822732627391815,
-0.004994036629796028,
0.0023295830469578505,
0.015256043523550034,
0.05929536372423172,
0.012453229166567326,
-0.015734564512968063,
0.009910034947097301,
-0.029824987053871155,
-0.07300083339214325,
0.005912355147302151,
-0.06648217886686325,
0.017247982323169708,
0.022968856617808342,
-0.00035407900577411056,
-0.01957176998257637,
0.03966653719544411,
-0.032421160489320755,
0.004129419103264809,
0.0003260951489210129,
-0.025033308193087578,
-0.01297351811081171,
0.07991575449705124,
0.038497213274240494,
0.030338136479258537,
0.04330174997448921,
0.003934057429432869,
0.024593345820903778,
0.013073372654616833,
0.019590018317103386,
0.00009318831871496513,
-0.04480469599366188,
-0.010299930348992348,
-0.002818414941430092,
0.028298430144786835,
0.001360359019599855,
-0.011431886814534664,
-0.04075367748737335,
0.048714689910411835,
0.019878076389431953,
-0.0004843687638640404,
0.07814784348011017,
-0.01884082518517971,
-0.002914056181907654,
-0.0063254027627408504,
-0.046362776309251785,
-0.005540886428207159,
-0.023204054683446884,
0.05333561822772026,
0.04238269478082657,
-0.021662211045622826,
0.010003696195781231,
0.030226491391658783,
0.03247569873929024,
-0.058945491909980774,
-0.04909159988164902,
0.008626343682408333,
0.04768621549010277,
-0.0024941242299973965,
-0.01224038191139698,
0.018143299967050552,
0.043823689222335815,
0.028776347637176514,
-0.00855752732604742,
0.027337757870554924,
-0.0033148727379739285,
-0.06565575301647186,
0.014947639778256416,
-0.042441271245479584,
0.03567206487059593,
0.023373687639832497,
0.021284841001033783,
0.03140213340520859,
0.01896483637392521,
-0.029915904626250267,
0.04553001746535301,
-0.03579094260931015,
0.04713095352053642,
0.046513088047504425,
0.02501807175576687,
-0.009842145256698132,
0.0433487594127655,
0.0024869227781891823,
-0.006020716857165098,
0.003612599102780223,
-0.04029040038585663,
-0.053831133991479874,
0.018893295899033546,
0.07899586856365204,
-0.020440543070435524,
-0.03140878677368164,
0.03978901728987694,
0.03242100030183792,
0.04622206836938858,
0.05904826521873474,
0.07055819034576416,
-0.007022959645837545,
-0.015481516718864441,
0.016158035025000572,
0.009729423560202122,
0.009253809228539467,
0.028939705342054367,
0.04743826016783714,
0.028110390529036522,
-0.027173923328518867,
-0.01107910368591547,
-0.02340988628566265,
0.04691169410943985,
-0.017732135951519012,
-0.0043011438101530075,
0.007871889509260654,
-0.03153239190578461,
-0.003257971489802003,
-0.03394182771444321,
0.03445509448647499,
-0.014984112232923508,
-0.006759011652320623,
-0.008248639293015003,
-0.018114350736141205,
0.00010572308383416384,
-0.0022893694695085287,
-0.02079915814101696,
-0.0380219928920269,
-0.02608763985335827,
0.026186183094978333,
-0.04659690707921982,
0.004240998066961765,
-0.01392456330358982,
-0.0129163833335042,
-0.02154761739075184,
-0.025656355544924736,
0.03419000282883644,
0.02364984154701233,
0.034548815339803696,
-0.027152936905622482,
-0.048259761184453964,
0.010682492516934872,
-0.04254139959812164,
-0.007623294368386269,
0.024171441793441772,
-0.0027867057360708714,
0.018435828387737274,
-0.03644151613116264,
-0.0508420467376709,
0.0372098833322525,
0.009249009191989899,
0.01668175496160984,
0.024439537897706032,
-0.02969829924404621,
-0.054306767880916595,
0.01472452376037836,
-0.061411235481500626,
0.016568684950470924,
-0.002520232228562236,
0.0068407487124204636,
0.045714590698480606,
-0.008059603162109852,
-0.02665846049785614,
0.010722251608967781,
-0.03149851784110069,
-0.033348556607961655,
-0.0013510903809219599,
-0.016108253970742226,
0.04848095029592514,
-0.06081313639879227,
0.049322664737701416,
-0.00822389218956232,
-0.09322391450405121,
0.008504781872034073,
-0.043660372495651245,
-0.04525250568985939,
-0.005642485339194536,
-0.028176821768283844,
0.046810850501060486,
-0.006649894639849663,
-0.04679373279213905,
0.0553601011633873,
0.03958194702863693,
-0.023598648607730865,
0.0030255448073148727,
-0.04193572327494621,
-0.020387081429362297,
-0.028542017564177513,
0.010754880495369434,
0.04873459413647652,
0.0034548856783658266,
-0.015888551250100136,
0.011456677690148354,
-0.011977915652096272,
0.02205423265695572,
0.030431225895881653,
-0.004384457133710384,
-0.007164443843066692,
-0.007152109872549772,
0.01887434534728527,
0.05671010538935661,
0.008866763673722744,
-0.0360201857984066,
0.002043345710262656,
0.01315741240978241,
0.04767092317342758,
0.024206334725022316,
-0.017000872641801834,
0.02903449721634388,
0.0007699023699387908,
0.053251177072525024,
-0.05223645269870758,
0.03387250378727913,
0.0020855756010860205,
0.018617358058691025,
-0.020729849115014076,
0.005296205170452595,
0.033712420612573624,
0.010391458868980408,
-0.030714809894561768,
0.03265764191746712,
0.03448042646050453,
-0.015213469974696636,
-0.024410294368863106,
0.003528174012899399,
0.01673074997961521,
0.03313542157411575,
-0.010478055104613304,
-0.01381014660000801,
0.06632053852081299,
0.024053392931818962,
0.03888396546244621,
0.004040184430778027,
-0.026356486603617668,
-0.00650501623749733,
-0.02118055522441864,
0.028555065393447876,
-0.017370186746120453,
0.026610491797327995,
0.019207701086997986,
0.09149757772684097,
0.003775928867980838,
0.008886472322046757,
0.017305178567767143,
-0.0010786399943754077,
-0.08392337709665298,
0.02135905809700489,
-0.024608643725514412,
-0.04956625774502754,
-0.03418577462434769,
-0.028823019936680794,
-0.02415234036743641,
0.03297646343708038,
-0.023381931707262993,
-0.02189129963517189,
-0.031700875610113144,
-0.06895899027585983,
0.004857658874243498,
-0.026723036542534828,
-0.04791763052344322,
-0.03073994256556034,
0.0050749098882079124,
0.033080585300922394,
-0.00685354508459568,
-0.0046710181050002575,
0.026691611856222153,
-0.011700289323925972,
0.01393126230686903,
-0.016016056761145592,
-0.021571947261691093,
0.009302481077611446,
0.020788045600056648,
0.03350517526268959,
0.0002176495036110282,
0.007821474224328995,
-0.011505409143865108,
0.021524161100387573,
0.05202510952949524,
0.010473685339093208,
0.021069360896945,
-0.03334077075123787,
-0.01695181056857109,
-0.015360780991613865,
-0.003639986738562584,
0.04931434988975525,
-0.00695594260469079,
-0.011682652868330479,
0.01522474829107523,
-0.0017562329303473234,
0.005859608296304941,
0.05743611976504326,
0.026563478633761406,
0.02193521335721016,
-0.004017864819616079,
-0.033353809267282486,
0.010258606635034084,
-0.020826641470193863,
-0.03662103787064552,
0.0020217117853462696,
-0.011115658096969128,
0.005451390985399485,
-0.012503634206950665,
0.000027173335183761083,
0.02265285886824131,
0.02317422814667225,
-0.0004745903133880347,
0.0031227851286530495,
-0.015443620271980762,
-0.001598592847585678,
-0.014758449979126453,
0.002769565675407648,
0.034565407782793045,
0.02561679109930992,
-0.027053827419877052,
-0.026658538728952408,
-0.11405318230390549,
0.016176432371139526,
0.023683814331889153,
0.018257535994052887,
0.017373712733387947,
-0.02563893236219883,
-0.07825103402137756,
-0.021467356011271477,
0.021240459755063057,
-0.04985691234469414,
0.022952673956751823,
-0.007063953671604395,
-0.02509894222021103,
-0.03390374034643173,
-0.02776498906314373,
-0.005736486986279488,
0.040801696479320526,
-0.008318285457789898,
0.0016085641691461205,
0.006619374267756939,
-0.00014457361248787493,
0.03613744676113129,
0.037970419973134995,
0.03172391280531883,
0.06015622615814209,
-0.003728321520611644,
0.008920310065150261,
-0.004911078605800867,
0.005775624420493841,
0.002310714451596141,
-0.08766022324562073,
0.00020957902597729117,
0.017971433699131012,
-0.025126075372099876,
0.05948320031166077,
-0.022864634171128273,
-0.02829398214817047,
0.017148086801171303,
-0.0045314994640648365,
0.013964839279651642,
0.00392443360760808,
-0.03292582184076309,
0.019624384120106697,
0.014204014092683792,
0.023373184725642204,
0.05291034281253815,
0.03464467078447342,
-0.028271907940506935,
-0.03030954860150814,
-0.016189005225896835,
0.038080815225839615,
-0.006213592831045389,
-0.0208908561617136,
-0.00558376032859087,
0.009388971142470837,
-0.02078283578157425,
0.057290345430374146,
-0.011794941499829292,
-0.033761851489543915,
0.008101433515548706,
0.010407584719359875,
-0.014969553798437119,
0.02773110382258892,
-0.0019246675074100494,
-0.0008080957341007888,
-0.022385377436876297,
0.0390097051858902,
-0.013277649879455566,
-0.018158642575144768,
0.02613774873316288,
-0.001690360833890736,
0.015390598215162754,
0.04259590059518814,
0.022505853325128555,
0.012334810569882393,
-0.03461126610636711,
-0.0013374482514336705,
0.012687122449278831,
-0.07598903775215149,
0.053798019886016846,
-0.008466636762022972,
0.009726601652801037,
0.03142039105296135,
-0.057459112256765366,
-0.041398726403713226,
-0.011211485601961613,
-0.005718329921364784,
0.055951401591300964,
-0.04919319599866867,
0.02018718235194683,
0.026801396161317825,
-0.018603375181555748,
-0.07531571388244629,
-0.06165613979101181,
0.04475409910082817,
0.029288699850440025,
0.002073870971798897,
-0.01855303719639778,
0.0044088587164878845,
-0.03609786555171013,
-0.03183109313249588,
0.013573247008025646,
0.021553244441747665,
-0.023650361225008965,
-0.019385723397135735,
-0.014486649073660374,
0.01714767888188362,
0.04715043306350708,
0.008298296481370926,
-0.04752792418003082,
0.06047697737812996,
-0.030064599588513374,
0.022863002493977547,
-0.009480874985456467,
0.05677924305200577,
0.0008483437122777104,
-0.06234406307339668,
-0.008978544734418392,
0.005689326208084822,
0.00010727620974648744,
-0.030799973756074905,
-0.01829819194972515,
0.061516933143138885,
0.024487270042300224,
-0.007491531781852245,
-0.04310312122106552,
0.0240918081253767,
-0.02220815233886242,
0.011023666709661484,
-0.0038181375712156296,
-0.00635099969804287,
-0.03962819650769234,
-0.000642605300527066,
0.02186185121536255,
-0.0016399068990722299,
0.03802395984530449,
-0.014373654499650002,
0.0743425190448761,
-0.006920343730598688,
-0.010482659563422203,
-0.005055378191173077,
0.007578502409160137,
0.00525156082585454,
-0.015296382829546928,
0.017887447029352188,
0.008453738875687122,
0.023770049214363098,
-0.03741077706217766,
-0.01149667613208294,
-0.004710142966359854,
0.0013422860065475106,
0.07932529598474503,
-0.018965858966112137,
0.029602445662021637,
0.011160299181938171,
0.00048017397057265043,
0.00024455715902149677,
-0.01852402277290821,
0.010631521232426167,
0.008085068315267563,
-0.0011479679960757494,
0.005800627171993256,
-0.005360848270356655,
0.01741592213511467,
0.03528473898768425,
0.045757073909044266,
0.0026752592530101538,
-0.01615724340081215,
0.044735927134752274,
0.038996145129203796,
0.013925381936132908,
0.020507527515292168,
-0.049197494983673096,
0.010617184452712536,
-0.041370414197444916,
0.023357875645160675,
0.022706711664795876,
-0.009810484945774078,
0.03750554472208023,
-0.016202926635742188,
-0.0008682961924932897,
0.008601551875472069,
0.007333940360695124,
-0.031125925481319427,
0.008066529408097267,
-0.009619316086173058,
0.022811301052570343,
0.02190428599715233,
0.013955882750451565,
0.0011466469150036573,
0.02147846668958664,
-0.008674941956996918,
0.01320758368819952,
-0.07444046437740326,
-0.04592227563261986,
-0.04255720227956772,
-0.011429338715970516,
0.09070231765508652,
0.037048712372779846,
-0.02672790363430977,
0.012676049023866653,
-0.036950066685676575,
0.0652531310915947,
0.038841016590595245,
0.026044102385640144,
-0.05935169756412506,
0.04565379396080971,
-0.007926092483103275,
0.006339141633361578,
-0.02558537758886814,
0.016587931662797928,
0.1016036868095398,
0.05071999877691269,
0.03203843906521797,
-0.058446887880563736,
0.018255632370710373,
-0.07769269496202469,
-0.004066424444317818,
-0.024859754368662834,
0.034566786140203476,
-0.05505284294486046,
0.024308670312166214,
0.005180104169994593,
0.05539991334080696,
-0.02017877995967865,
0.03218482434749603,
0.04057636484503746,
-0.04547051340341568,
-0.0332241952419281,
-0.00972932018339634,
0.012354782782495022,
0.019024822860956192,
0.022089820355176926,
-0.051488541066646576,
0.03795293718576431,
-0.035880107432603836,
-0.01766045205295086,
-0.014982874505221844,
-0.03590904176235199,
0.02074112556874752,
0.015582178719341755,
-0.07366450130939484,
-0.03127940371632576,
0.025907086208462715,
-0.019258197396993637,
-0.026312146335840225,
0.006615147925913334,
0.03811119869351387,
0.010319272056221962,
0.020927278324961662,
0.021812258288264275,
0.01942336931824684,
-0.016611197963356972,
0.012884287163615227,
0.03897108882665634,
-0.040950946509838104,
0.05009964853525162,
-0.0603485107421875,
0.04511438310146332,
-0.017357083037495613,
0.006599342916160822,
0.01753830909729004,
0.013002511113882065,
-0.0187784843146801,
-0.04388129338622093,
-0.03125986456871033,
-0.03199773654341698,
0.01633981242775917,
0.012361961416900158,
0.015174686908721924,
-0.016312412917613983,
0.002816686173900962,
0.0026557622477412224,
0.01936296746134758,
-0.003235243959352374,
0.005072116851806641,
-0.010945127345621586,
0.021055346354842186,
0.046925485134124756,
-0.00036266795359551907,
-0.010021156631410122,
-0.017696956172585487,
-0.06182553619146347,
-0.0394209623336792,
0.005147747229784727,
0.03299553692340851,
0.03473106771707535,
0.021077102050185204,
-0.012978791259229183,
-0.025247294455766678,
-0.017099836841225624,
-0.04624655470252037,
0.012170860543847084,
0.025865960866212845,
-0.032342761754989624,
0.005236562341451645,
0.02871176041662693,
0.021666735410690308,
0.038377657532691956,
-0.027997776865959167,
0.003171789227053523,
0.013658992946147919,
0.009258688427507877,
0.015071826055645943,
-0.039132725447416306,
-0.029779888689517975,
-0.003708507167175412,
0.025396250188350677,
-0.0025880157481878996,
0.008803301490843296,
0.037554848939180374,
0.03285636752843857,
0.02666587568819523,
0.021204927936196327,
0.05111398920416832,
-0.014135940931737423,
-0.016001606360077858,
0.0010399953462183475,
-0.023349793627858162,
0.014815897680819035,
0.010343139991164207,
0.048667170107364655,
-0.0284735057502985,
-0.037083037197589874,
-0.014059730805456638,
0.008897527121007442,
0.02928079105913639,
0.019041692838072777,
-0.03527652099728584,
-0.012549353763461113,
0.007513202261179686,
-0.0008835835615172982,
-0.060512345284223557,
-0.030410852283239365,
-0.015806229785084724,
0.02972727082669735,
-0.02933032251894474,
-0.030036453157663345,
0.0030603434424847364,
0.031444232910871506,
-0.038653697818517685,
-0.005050495266914368,
0.028634047135710716,
0.049945998936891556,
-0.01103026419878006,
0.04101061075925827,
0.04519748315215111,
0.016031401231884956,
0.026605313643813133,
-0.019540533423423767,
-0.04340498521924019,
0.011762367561459541,
-0.036713868379592896,
-0.059462565928697586,
0.02013985626399517,
-0.0254899263381958,
0.022574972361326218,
0.034893251955509186,
-0.0482255183160305,
0.027804343029856682,
0.05759071186184883,
0.00401885062456131,
0.006826012395322323,
0.015906302258372307,
-0.011491844430565834,
-0.0021191234700381756,
0.0033863126300275326,
-0.008934070356190205,
-0.003250008448958397,
-0.029828794300556183,
0.05546250939369202,
0.02931293286383152,
-0.005014041904360056,
-0.01761733368039131,
0.011547856032848358,
-0.010417795740067959,
-0.0006090325769037008,
0.02900988981127739,
-0.00849668588489294,
-0.019188230857253075,
0.03400150686502457,
-0.00933649018406868,
0.023748820647597313,
0.045161258429288864,
0.007190752308815718,
-0.11664056777954102,
-0.015324000269174576,
0.0030879133846610785,
0.014406366273760796,
0.02574106492102146,
-0.019820228219032288,
0.007191671058535576,
0.016927914693951607,
-0.08034678548574448,
-0.001560270437039435,
-0.019429998472332954,
-0.020091025158762932,
-0.009553561918437481,
-0.012729433365166187,
-0.04503859952092171,
0.05791652575135231,
0.05914372205734253,
0.05762741342186928,
-0.0015938766300678253,
0.0019637485966086388,
-0.017963765189051628,
-0.005301498342305422,
-0.039271656423807144,
0.018694540485739708,
0.009251696057617664,
0.00851208996027708,
0.06711181253194809,
0.01203907560557127,
-0.014171353541314602,
0.011802216060459614,
0.019187865778803825,
0.0014296500012278557,
0.0033263321965932846,
0.004948107525706291,
0.03181510418653488,
0.001319220056757331,
-0.007654463406652212,
-0.025689678266644478,
-0.03822242468595505,
0.017719373106956482,
0.0012925313785672188,
0.015722256153821945,
-0.0030256870668381453,
-0.0025240997783839703,
0.027257950976490974,
-0.04704834520816803,
-0.01601257734000683,
0.02784840390086174,
-0.025036493316292763,
-0.0060800001956522465,
-0.003725145710632205,
0.043352626264095306,
0.0035458486527204514,
-0.0009666752303019166,
-0.012368275783956051,
-0.05944621562957764,
-0.022512786090373993,
0.019286463037133217,
0.020523276180028915,
0.0009718850487843156,
0.013379047624766827,
-0.015320847742259502,
-0.057343825697898865,
0.02796700783073902,
0.02742721512913704,
0.009981204755604267,
-0.05546850711107254,
0.0000025782942429941613,
0.014135041274130344,
0.00709493737667799,
0.023237312212586403,
-0.019896892830729485,
-0.03393205255270004,
0.04519256576895714,
0.01393961813300848,
0.02815236896276474,
-0.003677648724988103,
-0.052295245230197906,
-0.041713230311870575,
-0.03770950436592102,
0.06059941276907921,
-0.018952637910842896,
0.014068174175918102,
-0.057055771350860596,
-0.04404794052243233,
-0.014392552897334099,
0.04502734914422035,
0.05272987112402916,
-0.024601509794592857,
-0.009835033677518368,
0.03440764546394348,
-0.01269864197820425,
0.018864572048187256,
-0.04524219408631325,
0.0010565468110144138,
0.014676559716463089,
-0.036811042577028275,
-0.000522606133017689,
0.021115904673933983,
-0.015365997329354286,
0.015080442652106285,
0.0023322689812630415,
0.0003470090450718999,
0.018237512558698654,
-0.01970776356756687,
-0.05752508342266083,
0.028263641521334648,
0.03190455958247185,
-0.05395657196640968,
0.06761419773101807,
-0.025914808735251427,
0.016754960641264915,
0.01662144996225834,
-0.0013920082710683346,
-0.03257319703698158,
0.0008941502892412245,
-0.05530230328440666,
0.02070355787873268,
0.006589448545128107,
0.003086554119363427,
0.01941884122788906,
-0.025795351713895798,
-0.0010490163695067167,
0.051376793533563614,
-0.01727912575006485,
0.0013881385093554854,
0.05137503147125244,
-0.044711433351039886,
0.017981024459004402,
-0.00924851093441248,
-0.009002231992781162,
0.0020052031613886356,
0.0008314148290082812,
-0.029605679214000702,
0.01788012683391571,
-0.004566044546663761,
-0.022106751799583435,
0.02416585385799408,
0.027466818690299988,
-0.022291040048003197,
-0.008658141829073429,
0.02248571254312992,
0.03411370888352394,
-0.021309560164809227,
-0.023554684594273567,
0.005030530970543623,
-0.006415888201445341,
0.0034261448308825493,
0.013417694717645645,
-0.024302877485752106,
0.09456833451986313,
-0.005871083587408066,
0.03413324058055878,
-0.013605396263301373,
-0.0025488045066595078,
-0.003298644907772541,
0.02600288949906826,
-0.020158855244517326,
0.01959219016134739,
0.006377687212079763,
-0.018403906375169754,
-0.0183390025049448,
-0.003577294060960412,
0.021357284858822823,
-0.059945248067379,
-0.005881687626242638,
-0.027442121878266335,
-0.012550035491585732,
0.00247717322781682,
0.002024958375841379,
-0.019320914521813393,
-0.011119168251752853,
-0.00393521087244153,
-0.0005856846109963953,
-0.007180161774158478,
-0.04000229388475418,
0.006094820331782103,
-0.02523093856871128,
0.03193044289946556,
-0.03544018045067787,
0.00984068401157856,
-0.0012117630103603005,
0.017875120043754578,
-0.0245329849421978,
-0.019197706133127213
] |
<p>I'm pretty ignorant regarding neutron and nuclear transport modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like those required for NERVA-like rockets or <a href="http://path-2.narod.ru/design/base_e/nswr.pdf" rel="nofollow">this one</a>.</p>
<p>I would appreciate any references or some explanations of the required approximations for the models required to compute neutron transport that i would have to take in consideration for this exercise.</p>
| 8,462 |
[
0.015364743769168854,
-0.041010532528162,
-0.02075054496526718,
-0.0037857755087316036,
0.025844156742095947,
-0.004845131188631058,
-0.0052396259270608425,
-0.006797292269766331,
0.012403734028339386,
-0.08536700904369354,
0.05969338119029999,
0.012906934134662151,
0.03561977669596672,
-0.00829098280519247,
0.004093104507774115,
-0.0183256845921278,
-0.025241566821932793,
-0.031242964789271355,
-0.0030253231525421143,
-0.02765239030122757,
0.05206775292754173,
-0.006448604632169008,
-0.005776140373200178,
-0.022938493639230728,
-0.01552604604512453,
0.0296341460198164,
-0.0016424618661403656,
-0.007360995281487703,
0.0237213596701622,
0.053589243441820145,
0.015260236337780952,
-0.016202369704842567,
0.039112549275159836,
0.04174462705850601,
0.01293258462101221,
0.03687802329659462,
-0.03735626861453056,
-0.009346968494355679,
-0.028617477044463158,
-0.009401578456163406,
-0.026904361322522163,
-0.026296939700841904,
0.019656376913189888,
-0.016410863026976585,
0.02928508073091507,
0.005950091406702995,
0.022207094356417656,
0.00774692976847291,
0.047957342118024826,
-0.055893424898386,
0.007196148857474327,
0.03264295682311058,
0.03921462222933769,
0.03225018456578255,
0.018213804811239243,
0.0037313553038984537,
0.05614916607737541,
0.08023812621831894,
-0.0049912575632333755,
-0.045982178300619125,
0.002687692642211914,
-0.013439266942441463,
-0.010143926367163658,
-0.005954114254564047,
-0.0043906220234930515,
0.013230283744633198,
-0.027159003540873528,
-0.043024931102991104,
-0.011961891315877438,
0.04189600795507431,
0.01318485476076603,
-0.005384466610848904,
0.017603345215320587,
0.0015343539416790009,
0.025053570047020912,
0.01333829015493393,
0.016912812367081642,
0.023973064497113228,
0.02530064806342125,
0.056057222187519073,
-0.05364013835787773,
0.010809466242790222,
0.0034517222084105015,
0.009813047014176846,
-0.03485222905874252,
-0.017513297498226166,
0.031343478709459305,
-0.01876874826848507,
0.010556334629654884,
0.02062375470995903,
-0.0008175606490112841,
0.0005711038829758763,
0.047280728816986084,
0.010632872581481934,
-0.02815365605056286,
0.02564467489719391,
0.02016245760023594,
0.04431469365954399,
0.016355184838175774,
-0.00755707873031497,
0.012680193409323692,
-0.03258853033185005,
0.01928330399096012,
0.08360765874385834,
-0.004826986230909824,
-0.012993859127163887,
-0.04073847085237503,
0.014677220024168491,
-0.03342543542385101,
-0.018706485629081726,
-0.028118327260017395,
0.02223513275384903,
0.0032968190498650074,
0.001737757702358067,
-0.020327113568782806,
-0.029698967933654785,
-0.019688362255692482,
-0.05537308752536774,
0.040682293474674225,
0.05668910592794418,
0.017464371398091316,
-0.008737719617784023,
0.026679057627916336,
-0.017740437760949135,
-0.08820400387048721,
0.0017994203371927142,
0.048798151314258575,
-0.008929266594350338,
-0.03232856094837189,
0.03898301720619202,
0.00935168657451868,
-0.010917868465185165,
0.05066746845841408,
-0.0014456494245678186,
0.05772751197218895,
-0.016068531200289726,
-0.07633142918348312,
-0.06148235872387886,
0.0017726360820233822,
-0.007374183740466833,
-0.0221498254686594,
-0.0872800350189209,
0.013077612966299057,
0.04195723310112953,
0.033837441354990005,
-0.017950771376490593,
-0.016699399799108505,
0.004490387160331011,
0.0396069772541523,
-0.024038026109337807,
-0.06911110132932663,
-0.000546346593182534,
0.0087545495480299,
-0.030808109790086746,
-0.021019048988819122,
-0.08424635231494904,
0.05878930538892746,
0.023940542712807655,
-0.010568371042609215,
-0.02695334516465664,
0.04138167202472687,
-0.013263645581901073,
-0.002129937754943967,
-0.010205371305346489,
0.0027567786164581776,
-0.026778975501656532,
0.046225666999816895,
0.013492661528289318,
0.016514578834176064,
0.016520293429493904,
0.025076627731323242,
0.020192239433526993,
-0.01753023825585842,
0.013489671051502228,
0.051529429852962494,
-0.034842826426029205,
-0.009887841530144215,
0.004579197149723768,
-0.01855548284947872,
0.018724417313933372,
-0.025491373613476753,
-0.013520765118300915,
-0.005112426821142435,
0.030528521165251732,
0.01501659955829382,
0.024221722036600113,
0.007638882379978895,
-0.025684058666229248,
0.014875104650855064,
-0.02599284239113331,
-0.0038700250443071127,
-0.00798378698527813,
0.010147787630558014,
-0.06642734259366989,
-0.009636027738451958,
-0.0037854311522096395,
-0.03141946718096733,
0.00831521861255169,
0.022103412076830864,
-0.0668506771326065,
-0.02191491425037384,
0.008092760108411312,
0.013610168360173702,
0.016408143565058708,
0.007509192917495966,
0.05768009275197983,
0.001966865034773946,
-0.015760954469442368,
0.03126363456249237,
-0.02447723038494587,
-0.034879934042692184,
-0.04428352415561676,
-0.03259355574846268,
-0.011525273323059082,
0.029415935277938843,
-0.04425397142767906,
-0.0019682792481034994,
-0.027829499915242195,
0.02979360520839691,
0.02650315687060356,
-0.016008350998163223,
0.09884357452392578,
0.06812093406915665,
0.03926832228899002,
-0.014854300767183304,
0.008977691642940044,
0.02227988839149475,
0.01740221120417118,
-0.0023310529068112373,
-0.04405065253376961,
-0.033333972096443176,
-0.005156944040209055,
0.04857523366808891,
0.022834232077002525,
-0.057477205991744995,
0.011399276554584503,
0.04109141603112221,
0.025151394307613373,
0.052333470433950424,
0.025782467797398567,
-0.04519089311361313,
-0.01603008061647415,
0.003354057902470231,
0.021233592182397842,
-0.01904943771660328,
-0.018603147938847542,
-0.01616753078997135,
0.009334975853562355,
0.0016229781322181225,
-0.022552086040377617,
-0.045800019055604935,
0.0607181154191494,
-0.012407831847667694,
-0.037919044494628906,
-0.011881033889949322,
-0.04594728350639343,
0.0781370997428894,
-0.03302843123674393,
0.041638318449258804,
0.013916303403675556,
-0.024986492469906807,
0.015196518041193485,
0.015530094504356384,
0.0071794018149375916,
0.0064456528052687645,
0.038345739245414734,
0.0003240553487557918,
-0.018909957259893417,
0.024649616330862045,
-0.02280895970761776,
0.03625809773802757,
-0.015720540657639503,
0.01776309683918953,
-0.022733498364686966,
-0.012281355448067188,
0.026124732568860054,
0.011555868200957775,
0.004466015845537186,
-0.013163900934159756,
-0.03152601793408394,
-0.0038805766962468624,
-0.01815938577055931,
-0.021886464208364487,
0.005593971814960241,
-0.07873445749282837,
0.04503448307514191,
-0.020786933600902557,
-0.01980256848037243,
0.03013422340154648,
-0.020679116249084473,
-0.01497271005064249,
0.018743570894002914,
-0.014719483442604542,
-0.08423182368278503,
-0.023699425160884857,
-0.02463122084736824,
0.012183083221316338,
-0.04116063192486763,
0.02508620359003544,
0.07609831541776657,
0.013178888708353043,
-0.02868238091468811,
0.02468734048306942,
-0.04983377084136009,
-0.021927619352936745,
-0.007989341393113136,
0.02783523127436638,
-0.009390418417751789,
-0.023006819188594818,
0.03165268898010254,
0.029725657775998116,
-0.046653687953948975,
-0.012887959368526936,
-0.07429172098636627,
-0.024262990802526474,
0.027619943022727966,
0.016276927664875984,
0.029494935646653175,
-0.004046411719173193,
-0.036001455038785934,
0.09615444391965866,
0.02632465772330761,
-0.051797714084386826,
0.0030569189693778753,
0.015888966619968414,
-0.007574856281280518,
-0.016361091285943985,
0.043005991727113724,
0.029603075236082077,
0.0068296343088150024,
0.0021923554595559835,
-0.0014471689937636256,
0.015279382467269897,
0.040075309574604034,
0.0037575974129140377,
-0.0025179313961416483,
0.005276384297758341,
0.012827718630433083,
0.0030456907115876675,
0.0340457446873188,
-0.003717893734574318,
-0.056064996868371964,
0.0277305506169796,
-0.04502788558602333,
0.033266808837652206,
0.040987707674503326,
-0.04681982100009918,
0.030466994270682335,
0.007790259551256895,
-0.034050773829221725,
-0.03060128726065159,
0.014494997449219227,
-0.007325709797441959,
-0.030695470049977303,
0.0006570942350663245,
0.04981181025505066,
0.03812549263238907,
0.005498670041561127,
-0.0026514222845435143,
0.022614197805523872,
0.06325065344572067,
-0.017102427780628204,
-0.020402001217007637,
-0.016320673748850822,
-0.0012185749365016818,
-0.010162516497075558,
-0.0115432133898139,
0.01090166810899973,
0.055523015558719635,
0.03222372382879257,
0.022374281659722328,
0.0081776212900877,
0.023178543895483017,
0.004073541145771742,
-0.10676421970129013,
-0.011401558294892311,
-0.04822397977113724,
0.09352008998394012,
-0.009512963704764843,
-0.013603171333670616,
0.005012471694499254,
0.000539870117790997,
0.015370339155197144,
0.008378186263144016,
-0.06430818885564804,
-0.0004352858231868595,
-0.009772619232535362,
-0.06247466430068016,
0.02727808989584446,
-0.00478525273501873,
-0.07054872065782547,
-0.03136884793639183,
-0.04179106280207634,
-0.009771602228283882,
0.01674877293407917,
-0.039807435125112534,
0.050005193799734116,
-0.036370739340782166,
-0.050022613257169724,
0.014499210752546787,
0.04857287183403969,
0.03976631909608841,
-0.02223782055079937,
0.011224609799683094,
0.01780794933438301,
-0.05766604095697403,
-0.02961428090929985,
-0.028874406591057777,
0.04300118610262871,
-0.008532463572919369,
0.0637284442782402,
0.032923247665166855,
0.03912055492401123,
-0.05959949269890785,
0.030815886333584785,
0.0007150547462515533,
0.055435437709093094,
0.012716068886220455,
-0.03138408809900284,
-0.001805886160582304,
-0.053613267838954926,
-0.02272583171725273,
0.029359837993979454,
0.012206196784973145,
-0.007873508147895336,
0.031162654981017113,
0.026110470294952393,
-0.031725987792015076,
-0.030274784192442894,
-0.016834409907460213,
0.05605265498161316,
0.023404087871313095,
-0.0049571385607123375,
-0.029649026691913605,
-0.010697511956095695,
0.016622081398963928,
0.004075929056853056,
0.011464032344520092,
-0.009997600689530373,
-0.0035472391173243523,
0.002264393260702491,
-0.0008847698918543756,
0.012378271669149399,
-0.04132039472460747,
0.00490214116871357,
0.025891654193401337,
0.004194444976747036,
0.029281876981258392,
-0.007312162779271603,
0.04324514418840408,
0.02152482606470585,
0.03970194607973099,
-0.009338055737316608,
0.0011644134065136313,
-0.0907042920589447,
-0.016310807317495346,
0.04740181565284729,
0.015474772080779076,
0.0009331321343779564,
0.0029188483022153378,
-0.04043952748179436,
0.012933972291648388,
0.07386262714862823,
0.015896489843726158,
0.032538771629333496,
0.016935089603066444,
-0.0038906096015125513,
0.022812319919466972,
-0.028275083750486374,
-0.03734354302287102,
0.022152669727802277,
-0.026103025302290916,
0.020133228972554207,
-0.06316100805997849,
0.018547505140304565,
0.0007490725838579237,
0.022973427549004555,
0.05998792126774788,
0.06324247270822525,
0.0026042263489216566,
0.01945403218269348,
-0.010174214839935303,
0.02578026056289673,
-0.01578555442392826,
-0.06260943412780762,
0.001546761835925281,
-0.005256575997918844,
-0.005569573026150465,
0.01450413279235363,
-0.01792353019118309,
-0.023055095225572586,
0.024726031348109245,
0.03701343759894371,
0.005543178413063288,
-0.06267190724611282,
-0.05309033766388893,
0.07342777401208878,
0.033021580427885056,
-0.056514400988817215,
0.06046556308865547,
0.07901464402675629,
-0.00855276733636856,
-0.009314537048339844,
-0.05163303762674332,
-0.003058814909309149,
0.02104988694190979,
0.0479944571852684,
-0.027919385582208633,
0.02262771688401699,
0.010122949257493019,
0.06442408263683319,
-0.036389678716659546,
0.02312065102159977,
0.02052082121372223,
-0.009371028281748295,
-0.0033253799192607403,
0.015911823138594627,
0.000420199241489172,
-0.02245156280696392,
-0.008002507500350475,
0.0255566518753767,
0.018054846674203873,
-0.046363286674022675,
0.024061961099505424,
-0.005997273605316877,
-0.010216111317276955,
0.004831328056752682,
-0.03786759451031685,
-0.005499169696122408,
-0.015249130316078663,
-0.033458925783634186,
0.025966165587306023,
-0.029590362682938576,
0.05163908749818802,
-0.021062517538666725,
0.011073957197368145,
0.04583269730210304,
-0.03820163011550903,
-0.009348008781671524,
0.021011361852288246,
-0.026428069919347763,
0.01685711368918419,
-0.02058718353509903,
0.011038258671760559,
-0.02386416867375374,
0.021500973030924797,
-0.052113525569438934,
-0.07735340297222137,
0.050810590386390686,
-0.024515952914953232,
-0.024716859683394432,
-0.06754835695028305,
0.000726451282389462,
-0.029603196308016777,
-0.04957875236868858,
0.013431533239781857,
0.07210102677345276,
-0.0361391045153141,
-0.0259240809828043,
0.0009639392956160009,
0.029906872659921646,
0.06443485617637634,
0.0015609667170792818,
0.003693835809826851,
0.020064260810613632,
-0.014054730534553528,
-0.03783322125673294,
-0.0024972062092274427,
0.028417889028787613,
-0.0315580852329731,
-0.018955301493406296,
0.01297223661094904,
0.013796404004096985,
0.06889531016349792,
-0.026807626709342003,
0.010718446224927902,
0.03944259136915207,
-0.01608312875032425,
-0.026818983256816864,
-0.006382061168551445,
-0.0031340522691607475,
0.003312022192403674,
0.04444510117173195,
-0.03409235551953316,
-0.015575365163385868,
-0.02353067137300968,
-0.02530011348426342,
0.03566782921552658,
0.0019253616919741035,
0.00048188850632868707,
0.03540470078587532,
0.057144153863191605,
-0.0012635807506740093,
0.019115233793854713,
0.011522084474563599,
-0.019729426130652428,
0.004752902314066887,
-0.03342690318822861,
0.02137160301208496,
0.017275625839829445,
-0.03481753170490265,
-0.0466281957924366,
-0.040856532752513885,
-0.04997796565294266,
-0.01911940611898899,
0.02038767747581005,
-0.04320526123046875,
0.04789023473858833,
-0.007318262010812759,
0.04432743787765503,
-0.016817787662148476,
0.006180514581501484,
-0.046445995569229126,
-0.01848777011036873,
0.012401626445353031,
0.052852340042591095,
-0.0283647608011961,
-0.022085942327976227,
0.0013270340859889984,
0.05659249424934387,
0.020697740837931633,
0.02195296436548233,
-0.0034548952244222164,
-0.0014134927187114954,
0.003960642032325268,
-0.009107183665037155,
-0.0276037510484457,
-0.007136206142604351,
-0.037112172693014145,
0.03208165243268013,
0.0039445688016712666,
-0.03128189593553543,
0.05869185924530029,
-0.002841802081093192,
-0.013683157041668892,
-0.03006880357861519,
-0.03545906022191048,
-0.0355469211935997,
-0.011774221435189247,
-0.011731618084013462,
-0.020200075581669807,
-0.027546435594558716,
0.008144551888108253,
0.0359392985701561,
-0.026180962100625038,
0.023814888671040535,
0.00981301348656416,
-0.042567186057567596,
0.011764817871153355,
-0.0184270478785038,
-0.04639109969139099,
0.02010631561279297,
0.025188157334923744,
-0.011884094215929508,
0.0211546178907156,
-0.003165734000504017,
0.03702903166413307,
0.009268672205507755,
0.04733093082904816,
-0.02182135358452797,
0.09699166566133499,
-0.018381774425506592,
-0.00030535447876900434,
-0.008272936567664146,
0.02526930905878544,
0.11174821853637695,
0.037463098764419556,
0.00699025671929121,
-0.042250607162714005,
-0.0016344321193173528,
0.003693224396556616,
0.02350209839642048,
-0.02092486433684826,
0.041055601090192795,
0.045498065650463104,
0.01947338879108429,
0.046364471316337585,
0.03196614980697632,
0.004415974952280521,
0.019734272733330727,
0.03760237991809845,
-0.045735541731119156,
-0.056933991611003876,
0.05275977402925491,
-0.021634677425026894,
-0.0015049595385789871,
-0.0010953026358038187,
-0.03314581513404846,
0.04599284380674362,
0.012838602997362614,
0.016411880031228065,
-0.05017605796456337,
-0.013578920625150204,
0.0657736286520958,
0.004992749076336622,
-0.0543113648891449,
0.013426538556814194,
-0.005251778289675713,
-0.02093701995909214,
0.01544228196144104,
0.007167752832174301,
0.010201821103692055,
-0.020031049847602844,
0.004641701001673937,
0.012034369632601738,
0.026502123102545738,
0.005118725821375847,
-0.0045064520090818405,
0.04515182599425316,
-0.02052689902484417,
0.000948395929299295,
-0.020866645500063896,
0.03382229804992676,
-0.028280368074774742,
-0.016589805483818054,
0.00011695219291141257,
0.01938886195421219,
0.03565597906708717,
-0.07534965872764587,
-0.010139432735741138,
-0.004057134501636028,
0.008741326630115509,
-0.02513289824128151,
-0.009435882791876793,
-0.013071076944470406,
0.017666785046458244,
-0.01581825129687786,
0.03483807295560837,
-0.007798851002007723,
-0.0058617908507585526,
-0.010762116871774197,
-0.0565330907702446,
0.012477191165089607,
0.0021752193570137024,
-0.02394348755478859,
-0.027885213494300842,
0.015529432334005833,
-0.038464777171611786,
-0.03554049879312515,
0.03774738684296608,
0.032811105251312256,
0.05327101796865463,
0.010916872881352901,
-0.012512855231761932,
-0.003610469400882721,
-0.05553724244236946,
0.04000398516654968,
-0.005134487058967352,
-0.019833769649267197,
-0.034052103757858276,
-0.022739525884389877,
0.03156528249382973,
0.03881664201617241,
0.0188448466360569,
0.006853238679468632,
-0.06263993680477142,
-0.014991316944360733,
0.022612735629081726,
-0.028118867427110672,
0.005369406193494797,
0.013655874878168106,
-0.04718732461333275,
-0.014307684265077114,
-0.035653673112392426,
0.03740775212645531,
0.03564745560288429,
-0.005689682438969612,
-0.011277083307504654,
0.033562783151865005,
0.010036262683570385,
0.011391941457986832,
-0.024382177740335464,
-0.031249770894646645,
-0.016207588836550713,
-0.043744102120399475,
0.02472318522632122,
0.010718072764575481,
0.031118806451559067,
-0.005610159132629633,
-0.03067167103290558,
0.02431369200348854,
-0.026888635009527206,
-0.00384539389051497,
0.00024273009330499917,
-0.06693733483552933,
0.021106110885739326,
0.019156144931912422,
0.05403286591172218,
-0.0051611438393592834,
0.0365249328315258,
0.007560331374406815,
0.01495894230902195,
-0.05402049049735069,
-0.012116437777876854,
-0.03191553056240082,
0.009757766500115395,
0.030309529975056648,
-0.0019775312393903732,
0.005184409208595753,
0.0007004445651546121,
0.012215414084494114,
0.02684330940246582,
0.046440489590168,
-0.005076893139630556,
-0.014574848115444183,
0.01804925873875618,
-0.03459785506129265,
-0.02972782403230667,
0.00008795026951702312,
0.0035916785709559917,
0.024829966947436333,
0.021779794245958328,
-0.03360794484615326,
-0.017218584194779396,
0.0875818207859993,
-0.01761530712246895,
-0.037510551512241364,
0.015293680131435394,
0.002987715182825923,
-0.00349178584292531,
-0.0708886981010437,
0.038096848875284195,
0.003990987315773964,
0.022492026910185814,
0.02435271628201008,
0.010813397355377674,
-0.03591592609882355,
0.013070452958345413,
-0.038845982402563095,
-0.027533460408449173,
-0.009760708548128605,
-0.007564408238977194,
0.02031027525663376,
-0.013576900586485863,
0.041390273720026016,
-0.004905611276626587,
0.058202821761369705,
0.021247198805212975,
0.0007573792827315629,
-0.06775735318660736,
-0.01857658103108406,
-0.021837547421455383,
-0.03422732278704643,
0.030173441395163536,
-0.06669346988201141,
0.059789977967739105,
0.054447807371616364,
-0.029985273256897926,
0.0026242074090987444,
-0.010444235987961292,
-0.0331709161400795,
-0.04277869313955307,
-0.02398965321481228,
-0.005572356283664703,
0.025493508204817772,
0.021000314503908157,
0.04176836833357811,
0.005543255712836981,
-0.004852015059441328,
0.0170146431773901,
-0.0237750131636858,
0.017538301646709442,
-0.0314960777759552,
-0.020014315843582153,
-0.013380142860114574,
0.018219247460365295,
-0.007054497022181749,
-0.002429538406431675,
0.015980122610926628,
-0.01026697177439928,
0.021365776658058167,
-0.0026299022138118744,
0.03728579729795456,
0.014855900779366493,
0.039346784353256226,
0.021349787712097168,
0.010578962974250317,
0.013454324565827847,
0.01282083336263895,
-0.007980145514011383,
0.007914477027952671,
-0.03135335072875023,
0.05095459520816803,
0.008418189361691475,
0.0037315916270017624,
-0.01793770305812359,
0.05900052562355995,
0.029802097007632256,
-0.010644922964274883,
-0.0008388512069359422,
-0.03151831403374672,
0.0285594891756773,
-0.028201939538121223,
0.031851403415203094,
-0.04803076758980751,
0.03209083154797554,
-0.015911733731627464,
-0.0147816501557827,
-0.024289675056934357,
0.015696298331022263,
-0.014870216138660908,
-0.013844695873558521,
-0.024506865069270134,
-0.012923105619847775,
0.016092713922262192,
-0.023956356570124626,
0.0015410323394462466,
0.03304083272814751,
-0.007835998199880123,
-0.01091075036674738,
-0.023285172879695892,
-0.02300906367599964,
0.03974781185388565,
0.0004443524812813848,
0.037053655833005905,
0.017168372869491577,
-0.008292920887470245,
0.012361680157482624,
-0.0542612224817276,
0.0017576799727976322,
0.006901742424815893,
-0.02420872263610363,
-0.01667592115700245,
-0.023897990584373474,
0.002615705132484436,
0.03358979895710945,
0.03452000766992569,
-0.017740868031978607,
-0.0164449792355299,
0.017821764573454857,
-0.013207834213972092,
0.00480817724019289,
-0.06832600384950638,
0.006692363880574703,
-0.013305019587278366,
-0.025436514988541603,
-0.0164756178855896,
-0.02544245682656765,
-0.024716340005397797,
0.03275315836071968,
0.019947359338402748,
0.016437673941254616,
-0.020447656512260437,
0.01107905711978674,
-0.01179109700024128,
0.02556316927075386,
0.06523071229457855,
0.031437523663043976,
0.05918202921748161,
-0.005719600711017847,
0.0112331323325634,
-0.01642797701060772,
0.004733887035399675,
-0.000771215942222625,
0.01786666549742222,
-0.012892046943306923,
-0.011883137747645378,
-0.008698312565684319,
-0.03188551217317581,
0.01272592879831791,
-0.05656612664461136,
-0.006846614181995392,
0.041950661689043045,
-0.03240738436579704,
-0.015970775857567787,
0.043996937572956085,
0.0495917983353138,
0.011060507968068123,
-0.0017337535973638296,
0.012116797268390656,
0.04054006189107895,
0.013148992322385311,
-0.014258167706429958,
0.014426236040890217,
0.015495999716222286,
0.01574714295566082,
0.02107490412890911,
0.007913487032055855,
0.00880892388522625,
0.01036803051829338,
0.020664529874920845,
0.022458527237176895,
0.009747705422341824,
-0.017894677817821503,
0.0718158408999443,
-0.03989822044968605,
-0.021469585597515106,
0.03606218472123146,
-0.038149043917655945,
0.06798134744167328,
-0.019104808568954468,
0.016072504222393036,
-0.03956754878163338,
0.02392849512398243,
-0.0018675653263926506,
0.01114598661661148,
-0.032295141369104385,
0.027752794325351715,
0.004980466794222593,
-0.020003722980618477,
-0.007161236368119717,
-0.012441280297935009,
0.011161801405251026,
-0.055982813239097595,
0.007201725617051125,
-0.0026022151578217745,
0.0013469703262671828,
-0.018680233508348465,
-0.03695813938975334,
0.004666153807193041,
-0.014963550493121147,
0.005662974435836077,
0.0503731444478035,
0.03951677307486534,
-0.005937773268669844,
-0.01924622431397438,
-0.006016476545482874,
0.07860083132982254,
-0.05991099402308464,
-0.018353812396526337,
-0.002163537312299013,
-0.00902588665485382,
-0.04045012593269348,
0.024019531905651093
] |
<p>Water falling from a tap eventually breaks into droplets at a particular distance from the tap. The distance(from the tap) at which it breaks into droplets is observed to be an increasing function of the volume flux of the water flowing out of the tap. What is the valid explanation for this phenomenon?</p>
<p>My own line of reasoning is as follows : let $D$ be the critical distance measured from the tap, i.e. the distance at which the water breaks into droplets. At a distance $d<D$ the flow can be assumed to be streamlined to a good approximation; in which case the cross-sectional area of the stream goes on steadily decreasing down the flow. Due to this, the surface energy per unit volume associated with the surface of the water should go on increasing with the distance from the tap until it reaches a point where it becomes greater than/equal to the surface energy of the same volume of water as a water drop. At this distance, by minimisation of potential energy the water should break into droplets to minimise the surface energy. Let's say this happens when the cross section of the flow reaches a threshold value $A$. Now if the volume flux is low; it would mean that the cross sectional area at the tap is itself low. Due to that, the threshold area $A$ would be attained at a lesser distance from the tap. This probably explains the observation that the distance(from the tap) at which it breaks into droplets is observed to be an increasing function of the volume flux of the water flowing out of the tap. Am I right? Please correct/add to my explanation. </p>
| 8,463 |
[
-0.006901607848703861,
-0.002505022333934903,
-0.019908197224140167,
0.019187800586223602,
0.004339521750807762,
0.005112390499562025,
-0.034790776669979095,
-0.025004494935274124,
0.029509026557207108,
-0.017804067581892014,
0.007199774496257305,
0.009583557955920696,
0.0532601997256279,
0.0202987939119339,
0.04113946482539177,
0.02760942652821541,
0.003681750036776066,
-0.021704308688640594,
0.01880491152405739,
-0.020389486104249954,
0.008685014210641384,
0.04162146896123886,
0.00755035225301981,
-0.0014334100997075438,
-0.002493919339030981,
-0.017082344740629196,
-0.016943933442234993,
-0.014749723486602306,
-0.005365096498280764,
0.008812155574560165,
0.005270887166261673,
-0.04908781126141548,
-0.01109476387500763,
0.01826578564941883,
0.005976715590804815,
-0.006148536689579487,
-0.015034597367048264,
-0.036524880677461624,
-0.028935931622982025,
0.003060671966522932,
-0.029324814677238464,
-0.015258136205375195,
-0.01951313018798828,
0.0697816014289856,
-0.04918172210454941,
-0.01070837490260601,
0.024467816576361656,
-0.036909475922584534,
0.04627913236618042,
-0.06242524832487106,
0.0070024942979216576,
0.03260743245482445,
0.05106440931558609,
0.01883670873939991,
0.004341095685958862,
-0.025977158918976784,
0.07401063293218613,
0.056516166776418686,
-0.03445333614945412,
-0.04012489691376686,
-0.05385124683380127,
-0.0012231924338266253,
-0.0182531476020813,
0.001897272770293057,
-0.029382867738604546,
-0.006929631344974041,
-0.015747737139463425,
-0.02682577632367611,
-0.00403639767318964,
-0.028088748455047607,
0.013162813149392605,
0.007909724488854408,
0.012396672740578651,
0.02751760557293892,
0.025807004421949387,
0.03106461465358734,
0.04015328735113144,
0.003987877629697323,
0.02319144271314144,
0.05194694548845291,
0.02865484356880188,
0.017640305683016777,
0.024469856172800064,
0.056472353637218475,
-0.015566649846732616,
0.002310112351551652,
0.08252132683992386,
-0.03439956530928612,
0.03598165884613991,
0.03455129265785217,
0.003912393935024738,
0.002468009479343891,
0.019442830234766006,
-0.007302105892449617,
0.013700949028134346,
0.016720043495297432,
-0.018653394654393196,
0.026631828397512436,
0.025995807722210884,
-0.040727004408836365,
-0.015841791406273842,
-0.029581846669316292,
0.004842513240873814,
0.056429505348205566,
0.021529678255319595,
-0.017287174239754677,
-0.05801064893603325,
0.02998817339539528,
-0.01419849880039692,
-0.01656362973153591,
-0.04533350467681885,
-0.0031821143347769976,
0.012722373008728027,
0.007093971595168114,
-0.02002684958279133,
-0.017891936004161835,
0.012863271869719028,
-0.03636380657553673,
0.023938726633787155,
0.037434954196214676,
0.033803533762693405,
-0.029363056644797325,
0.022305762395262718,
0.0045646606013178825,
-0.05486932396888733,
0.06277810037136078,
0.015017317607998848,
-0.0297843124717474,
-0.047110915184020996,
0.012347416952252388,
-0.025810077786445618,
0.0177589301019907,
0.003930570557713509,
-0.00726171862334013,
0.018763456493616104,
-0.009456569328904152,
-0.08004181832075119,
-0.010663677006959915,
0.05545521527528763,
0.02120533585548401,
-0.022516757249832153,
-0.06437720358371735,
-0.003525407752022147,
0.02651597373187542,
0.08597135543823242,
-0.012417069636285305,
0.01905708760023117,
-0.006222820840775967,
-0.010707208886742592,
-0.007679479196667671,
-0.021143605932593346,
0.018128912895917892,
0.01603333093225956,
-0.04180581122636795,
-0.0008281272021122277,
-0.003788893111050129,
-0.005914935376495123,
0.07238399982452393,
-0.003437371924519539,
-0.03794734925031662,
0.051199521869421005,
-0.024193668738007545,
-0.0002322627551620826,
0.017372513189911842,
0.016531579196453094,
-0.03347659483551979,
0.07700792700052261,
0.007215715479105711,
0.045656073838472366,
0.01693163812160492,
0.034584663808345795,
-0.0006861544097773731,
-0.012111196294426918,
0.045510344207286835,
0.03178505226969719,
-0.03717892989516258,
0.0006505142664536834,
-0.02590012364089489,
0.038578350096940994,
0.007859421893954277,
-0.01832614094018936,
-0.021505510434508324,
-0.0667547881603241,
0.015216674655675888,
-0.007202645763754845,
0.02435665763914585,
-0.024073585867881775,
-0.050696101039648056,
-0.022475043311715126,
-0.02332661859691143,
-0.024444421753287315,
-0.047367777675390244,
0.0087790098041296,
-0.021804198622703552,
0.012094450183212757,
0.03669336065649986,
-0.028661873191595078,
0.014846784062683582,
-0.0256591085344553,
-0.009462105110287666,
-0.022349871695041656,
-0.01131978165358305,
0.009677841328084469,
-0.021392522379755974,
0.01805439405143261,
0.03291722387075424,
0.017683956772089005,
0.04091792181134224,
0.02490464597940445,
0.00408058799803257,
-0.0004075653268955648,
-0.004619285464286804,
0.006944017484784126,
0.0509464256465435,
-0.032462216913700104,
-0.021060993894934654,
0.018359167501330376,
-0.0015129128005355597,
0.04608091711997986,
0.03241109102964401,
-0.05854130908846855,
0.05861646682024002,
0.04702251777052879,
0.03854324668645859,
-0.015229071490466595,
0.0066477032378315926,
0.005967762786895037,
-0.006539144553244114,
-0.02549845725297928,
-0.048783861100673676,
-0.005194126628339291,
0.026880577206611633,
0.054037127643823624,
0.023752301931381226,
-0.01856025494635105,
-0.011672710999846458,
0.030590470880270004,
-0.011997436173260212,
0.029779601842164993,
0.01341491099447012,
0.0020725519862025976,
-0.007510038558393717,
0.028605187311768532,
0.06293147057294846,
-0.011829528957605362,
-0.005054489243775606,
0.013030171394348145,
0.0034467715304344893,
0.03116711974143982,
-0.012976217083632946,
-0.011423100717365742,
-0.00745415547862649,
-0.0006535035208798945,
0.026623418554663658,
-0.029022421687841415,
0.00658636586740613,
0.04965464398264885,
-0.04430403560400009,
0.0036621801555156708,
0.027754632756114006,
0.018317997455596924,
0.02715633250772953,
-0.08996175974607468,
-0.04122702032327652,
0.07397326081991196,
0.02428080327808857,
0.007783631794154644,
-0.012611789628863335,
0.01571432501077652,
-0.032776739448308945,
0.032370425760746,
-0.028857337310910225,
-0.03545275703072548,
0.003835058305412531,
-0.010782216675579548,
0.03851569443941116,
0.017891008406877518,
0.022251034155488014,
-0.027604537084698677,
-0.005586253944784403,
-0.007057159673422575,
0.015571155585348606,
0.001486712135374546,
0.016433831304311752,
-0.020621279254555702,
-0.03021186962723732,
-0.0001314726541750133,
-0.0014444824773818254,
0.0487716943025589,
-0.014299146831035614,
0.012954914942383766,
-0.01593148708343506,
0.01826111041009426,
-0.02438165433704853,
0.003003871999680996,
-0.043841518461704254,
0.0177542082965374,
0.0013632323825731874,
0.004445638507604599,
0.035415951162576675,
-0.008727231994271278,
-0.024905091151595116,
0.031784504652023315,
-0.027543723583221436,
-0.060783158987760544,
-0.03507331386208534,
-0.003739130450412631,
0.00035606141318567097,
-0.017730584368109703,
0.039843130856752396,
0.035714589059352875,
-0.03705378994345665,
-0.015092778019607067,
-0.07303779572248459,
-0.06548096239566803,
0.04064714536070824,
-0.029406288638710976,
0.04193924739956856,
0.0013800699962303042,
-0.039879851043224335,
0.06609083712100983,
0.017440171912312508,
-0.057782985270023346,
0.02123989723622799,
-0.006048991344869137,
0.011081361211836338,
-0.02041592262685299,
-0.02765791490674019,
0.03991378843784332,
-0.024930795654654503,
0.032738473266363144,
0.007123469840735197,
0.08841849118471146,
0.021484101191163063,
0.0020198861602693796,
-0.016329532489180565,
0.028289781883358955,
-0.0038977796211838722,
0.011506234295666218,
-0.007941788993775845,
-0.009962988086044788,
-0.0011105129960924387,
-0.014308763667941093,
-0.022230902686715126,
0.05343199893832207,
0.024556968361139297,
-0.042550839483737946,
0.043333057314157486,
-0.04434914141893387,
0.013225891627371311,
-0.036361660808324814,
-0.010477064177393913,
-0.007271838374435902,
-0.03879501298069954,
0.020196326076984406,
0.028466204181313515,
0.040161874145269394,
-0.04504993185400963,
-0.010070815682411194,
0.012087629176676273,
0.04154673591256142,
-0.016231847926974297,
-0.041504859924316406,
-0.01231122761964798,
-0.02596300281584263,
0.03257105126976967,
0.01953282579779625,
0.010386341251432896,
0.02785857766866684,
0.018665753304958344,
0.023463044315576553,
-0.00674034608528018,
-0.055889833718538284,
-0.005956314038485289,
-0.07250232249498367,
0.011545147746801376,
0.009114253334701061,
0.02203252911567688,
0.0021014423109591007,
0.032091401517391205,
0.047537755221128464,
0.027656663209199905,
-0.02487819455564022,
0.008190615102648735,
-0.07641559839248657,
-0.030239291489124298,
-0.04183865338563919,
-0.027627108618617058,
-0.029968775808811188,
-0.03453405946493149,
-0.013839563354849815,
-0.03225865587592125,
-0.019088927656412125,
0.011107129976153374,
0.02951013296842575,
-0.06804630905389786,
0.0108869643881917,
-0.02675016224384308,
-0.01843487098813057,
-0.037023723125457764,
-0.0014822309603914618,
0.041147101670503616,
-0.03714655339717865,
0.032062727957963943,
0.03833182528614998,
-0.008119871839880943,
-0.04837695136666298,
-0.0007690509082749486,
0.02739240787923336,
0.021566547453403473,
0.0075051262974739075,
0.054199256002902985,
0.003985102288424969,
0.018601059913635254,
0.0214092954993248,
0.00166776601690799,
0.031325746327638626,
-0.044610437005758286,
-0.012864507734775543,
-0.043829143047332764,
-0.041701365262269974,
-0.037176139652729034,
0.02825869806110859,
0.014349482953548431,
0.026800600811839104,
0.008346987888216972,
-0.0031512011773884296,
-0.009188559837639332,
-0.05693388730287552,
0.06774882227182388,
0.06974255293607712,
0.00308970152400434,
-0.029928194358944893,
-0.02801639586687088,
-0.016005080193281174,
-0.014902831055223942,
-0.01153460331261158,
0.061146534979343414,
-0.008036942221224308,
-0.009127086028456688,
-0.029070626944303513,
0.057873714715242386,
0.015172840096056461,
-0.03701138123869896,
-0.0011001360835507512,
0.03032723441720009,
-0.0015681384829804301,
-0.0159989632666111,
-0.023715557530522346,
0.01505310833454132,
0.0037904835771769285,
0.0016954767052084208,
0.029228786006569862,
0.010116718709468842,
-0.08942326158285141,
-0.04279569536447525,
0.03404183313250542,
0.048205018043518066,
-0.0211605504155159,
0.018906882032752037,
-0.03206416964530945,
-0.026099253445863724,
0.042231980711221695,
-0.031336478888988495,
0.03257826343178749,
-0.013870740309357643,
0.01868552155792713,
-0.030834315344691277,
-0.026114895939826965,
-0.00413548992946744,
0.003171553136780858,
-0.009999659843742847,
0.026919357478618622,
-0.013635522685945034,
-0.021447911858558655,
-0.03048059530556202,
0.009758899919688702,
-0.014354060404002666,
0.01921219192445278,
0.009404530748724937,
-0.006632186938077211,
-0.01564008556306362,
0.017559073865413666,
-0.027869248762726784,
-0.09533561021089554,
0.04567138850688934,
-0.03933851048350334,
0.017820483073592186,
0.016759619116783142,
-0.0022819405421614647,
-0.011935446411371231,
0.0803954154253006,
0.053956083953380585,
-0.02113468386232853,
0.0066023957915604115,
-0.006957691628485918,
0.06102987751364708,
0.024843277409672737,
-0.004169094376266003,
0.03712672367691994,
0.01042421068996191,
0.006307013798505068,
-0.012745353393256664,
0.005909447092562914,
0.06061963737010956,
0.003728416981175542,
-0.029681818559765816,
-0.03450525924563408,
-0.048917729407548904,
-0.0020171860232949257,
0.051258157938718796,
-0.019901033490896225,
-0.008261023089289665,
-0.05120847374200821,
-0.05394768342375755,
-0.013497927226126194,
-0.02919706515967846,
0.027964603155851364,
-0.021438980475068092,
0.03524934500455856,
0.0553906187415123,
0.015971556305885315,
0.020351918414235115,
0.016340510919690132,
-0.014760905876755714,
0.017236314713954926,
0.0061964234337210655,
-0.010079684667289257,
-0.014214660972356796,
-0.027245458215475082,
-0.043654896318912506,
0.058437272906303406,
-0.024914059787988663,
0.053085315972566605,
-0.022396905347704887,
0.001317333895713091,
-0.0005403488758020103,
-0.01688220351934433,
-0.008870863355696201,
0.0276067852973938,
0.005150615703314543,
0.021693767979741096,
-0.047879450023174286,
0.0013932513538748026,
-0.01131125446408987,
0.029410460963845253,
-0.08469751477241516,
-0.026376107707619667,
0.03588125482201576,
0.05795245245099068,
-0.026067432016134262,
-0.0273309163749218,
-0.024527382105588913,
-0.03876855596899986,
-0.03373619168996811,
0.02394854463636875,
0.017965035513043404,
-0.07179529964923859,
0.0035440402571111917,
0.009296692907810211,
0.044477008283138275,
0.027719827368855476,
-0.022739581763744354,
0.04028772935271263,
0.004076958633959293,
-0.02032979391515255,
-0.027962923049926758,
-0.017924653366208076,
0.06771145015954971,
-0.037249606102705,
0.011401486583054066,
0.01391381025314331,
-0.006636659149080515,
0.07274069637060165,
-0.06156381964683533,
-0.012858160771429539,
-0.021471839398145676,
-0.0037673150654882193,
0.027321472764015198,
0.022635752335190773,
-0.00002807888449751772,
0.02705475129187107,
0.04840247705578804,
0.006976057775318623,
-0.030598463490605354,
-0.018367035314440727,
-0.018188973888754845,
-0.008453791961073875,
-0.016029242426156998,
0.001120092929340899,
-0.01144777424633503,
0.06925907731056213,
-0.049697767943143845,
-0.005177921615540981,
0.0172447320073843,
0.0018946243217214942,
0.039513617753982544,
0.02074911817908287,
0.004633438307791948,
0.0019395097624510527,
-0.03450683131814003,
-0.010782623663544655,
-0.03883282095193863,
-0.04479741305112839,
0.025704246014356613,
0.036471616476774216,
0.019297851249575615,
0.030523084104061127,
-0.005526011344045401,
-0.01827068068087101,
0.028958432376384735,
-0.07150215655565262,
-0.02806084230542183,
0.02419714629650116,
-0.017507679760456085,
0.026336155831813812,
-0.02641313523054123,
-0.028367597609758377,
0.014583654701709747,
-0.005378798581659794,
-0.050171852111816406,
0.030313918367028236,
0.02465367503464222,
0.00006871212099213153,
0.04218415915966034,
-0.023892320692539215,
-0.02099011279642582,
0.018492817878723145,
-0.05379629507660866,
0.01808985136449337,
0.006992689799517393,
0.015639958903193474,
0.027835536748170853,
0.004289689008146524,
-0.004004534799605608,
-0.062158700078725815,
0.019794175401329994,
-0.05773497000336647,
0.018500378355383873,
0.007899693213403225,
0.013493739068508148,
-0.0012150630354881287,
0.0012891375226899981,
-0.015144912526011467,
0.0030899890698492527,
0.018638581037521362,
-0.011593993753194809,
0.0293046273291111,
-0.023831244558095932,
-0.05207597464323044,
-0.02528272569179535,
0.018553195521235466,
-0.002780752722173929,
-0.014016161672770977,
0.0016030577244237065,
-0.06528938561677933,
0.021757595241069794,
-0.009375354275107384,
0.0005315509624779224,
0.009005134925246239,
0.06811049580574036,
0.010442492552101612,
0.07043225318193436,
-0.007568322122097015,
-0.0006758516537956893,
0.13125447928905487,
0.06323755532503128,
-0.021237416192889214,
-0.051245205104351044,
0.04099426418542862,
0.003973106388002634,
0.015714874491095543,
-0.030444733798503876,
-0.00753671582788229,
0.00978196319192648,
-0.019301746040582657,
0.006320291664451361,
0.058051131665706635,
-0.006750313565135002,
0.024243706837296486,
0.0606238916516304,
-0.05886400490999222,
-0.03995199501514435,
0.046796463429927826,
0.027776366099715233,
-0.009794858284294605,
0.021497543901205063,
-0.014564129523932934,
0.0450226366519928,
0.01680462621152401,
-0.023473458364605904,
0.019255902618169785,
0.003049044171348214,
0.025041488930583,
-0.01468015369027853,
-0.021580923348665237,
0.0008968337206169963,
-0.004331880249083042,
-0.006902617868036032,
-0.019808629527688026,
-0.0011064136633649468,
0.018547018989920616,
0.008465724997222424,
-0.002675214782357216,
0.02446380816400051,
0.005185337737202644,
0.008874966762959957,
0.009540924802422523,
0.044090643525123596,
-0.06512748450040817,
-0.026964204385876656,
-0.029810260981321335,
0.05736570432782173,
-0.019618995487689972,
0.01754930056631565,
-0.027394860982894897,
-0.0372544601559639,
-0.007797458674758673,
-0.047206226736307144,
-0.026236122474074364,
-0.010657110251486301,
-0.002985230879858136,
0.02773364447057247,
-0.02251298911869526,
-0.037892404943704605,
0.024432852864265442,
-0.011838394217193127,
-0.0035473410971462727,
0.015230790711939335,
-0.012325657531619072,
-0.011505557224154472,
0.03136206418275833,
0.035904936492443085,
0.008479754440486431,
-0.015725264325737953,
0.00497671402990818,
0.013532751239836216,
-0.03783855959773064,
-0.009586970321834087,
-0.0089129488915205,
0.007630482781678438,
0.022524792701005936,
0.02405567653477192,
0.009280876256525517,
0.017486097291111946,
-0.05294796824455261,
0.029758475720882416,
-0.023857388645410538,
-0.017774684354662895,
-0.017302660271525383,
0.013295779004693031,
-0.05392206832766533,
0.043798159807920456,
-0.010838034562766552,
-0.019612694159150124,
0.012769808061420918,
0.0664396658539772,
0.03143532574176788,
-0.03195124492049217,
-0.01024519931524992,
-0.030160007998347282,
-0.013557308353483677,
0.0020331661216914654,
0.01555634569376707,
0.03756692260503769,
0.023006949573755264,
0.03243985027074814,
-0.0019267350435256958,
-0.009682695381343365,
-0.03338506445288658,
0.025496026501059532,
0.0032414935994893312,
-0.02487339824438095,
-0.012334725819528103,
0.0035499241203069687,
-0.04102305695414543,
-0.0005399155197665095,
-0.0016126023838296533,
0.013771540485322475,
0.015161209739744663,
0.0047194394282996655,
0.01474273856729269,
-0.011372438631951809,
0.010912979952991009,
-0.02345593273639679,
0.008691608905792236,
-0.04752105847001076,
-0.05577756091952324,
-0.0607069693505764,
-0.010853729210793972,
-0.0093965670093894,
0.007093092426657677,
-0.025213170796632767,
0.03958918899297714,
-0.008379647508263588,
-0.032215964049100876,
0.03177908435463905,
0.04023317992687225,
0.010623093694448471,
-0.01976093277335167,
0.04156394675374031,
-0.0049377563409507275,
0.06417527049779892,
-0.026690393686294556,
-0.04044358804821968,
0.05260502174496651,
-0.011093003675341606,
-0.05054755508899689,
0.026223987340927124,
-0.006952574010938406,
0.031389690935611725,
0.01865510269999504,
-0.01333501935005188,
-0.0034978478215634823,
0.07888075709342957,
0.007564295083284378,
0.0009074808331206441,
-0.013558915816247463,
-0.010715300217270851,
-0.00989552028477192,
-0.05498135834932327,
0.023574668914079666,
0.014093155972659588,
0.031442344188690186,
0.02894921973347664,
0.01446144375950098,
-0.0010562255047261715,
-0.013466913253068924,
0.015832444652915,
-0.04902458190917969,
0.026009773835539818,
0.012678860686719418,
0.03832858428359032,
0.01728292740881443,
0.05228567495942116,
-0.029060492292046547,
-0.025587579235434532,
-0.021087653934955597,
-0.013318597339093685,
-0.07832249999046326,
0.007435042876750231,
-0.013839995488524437,
0.019063197076320648,
0.0013244490837678313,
-0.06426812708377838,
0.032366350293159485,
0.05787322670221329,
-0.0708695575594902,
0.005366707686334848,
-0.021863078698515892,
0.02929401770234108,
-0.02646629326045513,
-0.017701035365462303,
-0.019515225663781166,
0.05220438167452812,
0.014805485494434834,
0.05696472153067589,
0.05676253139972687,
0.029069574549794197,
-0.037198543548583984,
-0.06269346177577972,
0.008314115926623344,
0.05071268603205681,
-0.03766000270843506,
-0.04149872064590454,
0.07211004942655563,
-0.0015353256603702903,
-0.011085139587521553,
0.0012410756899043918,
-0.06201746314764023,
-0.009821495972573757,
0.021784303709864616,
-0.007611703127622604,
0.021871834993362427,
0.020824093371629715,
0.013235493563115597,
0.029269255697727203,
0.04131773114204407,
0.007752573117613792,
-0.00024567171931266785,
-0.000473276391858235,
0.003388093551620841,
-0.029436251148581505,
0.036118440330028534,
-0.002786452416330576,
-0.08339404314756393,
0.023050593212246895,
-0.045096367597579956,
-0.025213276967406273,
0.024163134396076202,
-0.017234832048416138,
0.05394914746284485,
-0.04525752738118172,
0.010009841993451118,
-0.024922870099544525,
-0.037184275686740875,
0.05319433659315109,
0.01976732350885868,
0.013687606900930405,
0.007429732941091061,
-0.0002843359543476254,
-0.019531531259417534,
-0.03236265480518341,
0.002464973833411932,
-0.008539830334484577,
-0.04673692211508751,
-0.006220974959433079,
-0.0197994913905859,
-0.021741263568401337,
-0.020467737689614296,
-0.01400335319340229,
-0.045094769448041916,
0.0033099146094173193,
0.017652766779065132,
0.04122046008706093,
0.02037687972187996,
-0.001585838501341641,
-0.02780325897037983,
-0.09025893360376358,
0.05763405188918114,
-0.01258279662579298,
-0.005589429754763842,
-0.02619337849318981,
-0.006779486313462257,
0.0032606639433652163,
0.016871152445673943,
0.057999081909656525,
0.011184770613908768,
-0.0188751220703125,
0.018505839630961418,
0.01809089630842209,
0.037236277014017105,
-0.0038836882449686527,
-0.010993395000696182,
-0.041434939950704575,
-0.0006149332039058208,
0.009625755250453949,
-0.042897168546915054,
0.035677358508110046,
0.021273920312523842,
-0.016372859477996826,
0.002708755899220705,
-0.006696859374642372,
-0.014954930171370506,
-0.02693472057580948,
-0.00036222656490281224,
-0.0031001141760498285,
-0.005040672142058611,
0.0673675686120987,
-0.006360829342156649,
0.053645018488168716,
-0.011101310141384602,
-0.02504614368081093,
-0.03367678448557854,
0.023229403421282768,
-0.02557362988591194,
0.006357142236083746,
-0.039057739078998566,
0.0010655464138835669,
0.02341940999031067,
-0.016976026818156242,
-0.011488450691103935,
0.017834700644016266,
-0.02742929197847843,
-0.021118734031915665,
0.04381193965673447,
0.035121019929647446,
0.02523292414844036,
0.0011050272732973099,
0.023781079798936844,
0.04793676733970642,
0.04739831015467644,
-0.007801026105880737,
0.0644746869802475,
0.08193973451852798,
0.004673566669225693,
-0.0055477977730333805,
0.013345385901629925,
-0.012235243804752827,
0.030557341873645782,
0.020811889320611954,
0.01882566511631012,
0.011276429519057274,
-0.052587177604436874,
0.01590633951127529,
0.024948077276349068,
-0.006850298959761858,
0.021882936358451843,
-0.0015325029380619526,
0.07148802280426025,
0.03745584934949875,
0.01720665767788887,
-0.028398549184203148,
-0.03116685338318348,
0.020777495577931404,
0.008831328712403774,
0.017623944208025932,
0.02355489693582058,
-0.005487626884132624,
-0.0291284266859293,
-0.024494610726833344,
0.020767001435160637,
-0.027539782226085663,
0.011547715403139591,
0.034423019737005234,
-0.010130692273378372,
-0.005584049969911575,
-0.036311857402324677,
-0.00032349888351745903,
-0.003198605962097645,
-0.036052826792001724,
0.03648748621344566,
0.055510081350803375,
0.023611847311258316,
0.04349791258573532,
-0.038321591913700104,
-0.020778246223926544,
0.07179246097803116,
-0.04492232948541641,
-0.03152063488960266,
-0.011985797435045242,
-0.016310371458530426,
-0.0009534104028716683,
-0.024510879069566727
] |
<p>I'm learning quantum mechanics on my own. I've known that energy is quantized and I've started wondering about temperature. From thermodynamics we have:
$$U=\frac{3}{2}NkT $$
(for ideal gas, of course)<br>
Both U and N aren't continous, so i think T shouldn't be, too. Is that formula correct also for quantum mechanics?<br>
I'm really sorry because of my language, I'm still working on it.</p>
| 8,464 |
[
0.020211411640048027,
-0.05007626488804817,
-0.013957330957055092,
-0.026052679866552353,
0.029303334653377533,
-0.01960890181362629,
-0.04777159541845322,
-0.016448665410280228,
-0.0013359328731894493,
-0.020024722442030907,
0.031163867563009262,
0.021508626639842987,
0.04018136113882065,
-0.011908036656677723,
0.012616613879799843,
0.011882824823260307,
-0.013419459573924541,
-0.037313658744096756,
-0.006855532061308622,
-0.026814410462975502,
0.0017808993579819798,
0.04390852898359299,
0.013024702668190002,
-0.013815510086715221,
-0.016934864223003387,
0.08211351186037064,
-0.0035846803802996874,
0.02091480977833271,
0.050154879689216614,
0.0216065626591444,
0.0009774145437404513,
-0.038588035851716995,
0.055466651916503906,
0.014526915736496449,
0.03772611543536186,
0.02596396394073963,
-0.015716103836894035,
-0.005573666654527187,
-0.022619027644395828,
0.006702711805701256,
-0.040063414722681046,
-0.030266497284173965,
-0.016199469566345215,
0.005587228573858738,
-0.0315149687230587,
0.030859164893627167,
0.033327918499708176,
-0.018537120893597603,
0.008926094509661198,
-0.03964092954993248,
0.03338734060525894,
0.03202250972390175,
0.05263998359441757,
0.04487832263112068,
-0.03477207198739052,
0.021825557574629784,
0.08771288394927979,
0.05246273800730705,
-0.015466189943253994,
-0.023257222026586533,
0.011552578769624233,
-0.024972015991806984,
-0.01170832198113203,
-0.007880978286266327,
-0.010449079796671867,
0.028062785044312477,
-0.014139099046587944,
-0.031025700271129608,
-0.0019104115199297667,
-0.012727322988212109,
0.026679225265979767,
0.01009297464042902,
0.04708291217684746,
-0.04213649779558182,
-0.003992618527263403,
-0.03321217745542526,
0.03754068911075592,
-0.001921538496389985,
0.04807775467634201,
0.04203972965478897,
-0.008804037235677242,
0.020565273240208626,
0.03808898478746414,
0.02837260439991951,
-0.030475741252303123,
-0.005864697974175215,
0.06328141689300537,
-0.021144306287169456,
0.009340575896203518,
0.05995463207364082,
-0.02791580557823181,
0.03443460538983345,
0.03244205191731453,
-0.009446648880839348,
-0.012773096561431885,
0.018452951684594154,
0.004813778679817915,
0.028354797512292862,
-0.020048849284648895,
-0.032489292323589325,
0.010806284844875336,
0.018370429053902626,
0.02909304015338421,
0.08062779158353806,
-0.02503231354057789,
-0.04260578006505966,
-0.05328889191150665,
0.007955756969749928,
0.01862022466957569,
-0.013868690468370914,
-0.05731058493256569,
0.022103112190961838,
-0.04410959407687187,
-0.007152092177420855,
-0.016478577628731728,
-0.03630976751446724,
0.030535418540239334,
-0.010856305249035358,
0.02999480813741684,
0.04198888689279556,
0.04986341670155525,
-0.04742308333516121,
0.03211865946650505,
-0.0001755112170940265,
-0.06459057331085205,
0.02549101784825325,
0.030510887503623962,
0.00005251802213024348,
-0.04083586484193802,
0.0161854587495327,
-0.04024612531065941,
-0.045954667031764984,
0.02179417386651039,
-0.016621388494968414,
0.059682514518499374,
-0.03302435204386711,
-0.0881139487028122,
-0.06776708364486694,
0.01399501133710146,
-0.012332030571997166,
-0.05593135580420494,
-0.08196721225976944,
0.010768292471766472,
0.04496613144874573,
0.07783616334199905,
-0.018088890239596367,
-0.01078790333122015,
-0.045022185891866684,
-0.008991285227239132,
-0.0037525040097534657,
-0.03749920427799225,
-0.04347962513566017,
0.029040809720754623,
-0.049007534980773926,
0.03810890018939972,
-0.03342960774898529,
0.04216238856315613,
0.0324382446706295,
0.0005698042223230004,
0.008335152640938759,
0.07159579545259476,
-0.031562335789203644,
-0.007807524409145117,
0.005708984564989805,
-0.004427512641996145,
-0.04160527139902115,
0.09144582599401474,
0.0030052089132368565,
0.005897001828998327,
0.008972660638391972,
0.03436647355556488,
-0.00029455238836817443,
0.008774250745773315,
0.015178834088146687,
0.035442739725112915,
-0.029613839462399483,
-0.031959500163793564,
-0.0512404628098011,
0.013251887634396553,
0.007569146808236837,
-0.056622691452503204,
-0.025984033942222595,
0.02260618284344673,
0.026969831436872482,
-0.04542040824890137,
0.010487159714102745,
-0.0016491065034642816,
0.016432693228125572,
-0.0026241897139698267,
-0.013761392794549465,
-0.008176770992577076,
-0.04050714895129204,
0.016915490850806236,
0.013594446703791618,
0.009392212145030499,
0.01915227435529232,
0.01645125076174736,
0.02416485734283924,
-0.02030336856842041,
-0.03440621495246887,
0.019497321918606758,
0.06435137987136841,
0.004701378755271435,
-0.02138451673090458,
0.07145494967699051,
0.06689086556434631,
0.038873523473739624,
0.019104639068245888,
0.06122651696205139,
-0.04669301211833954,
-0.02512201853096485,
0.003825616789981723,
-0.008400548249483109,
0.02456335350871086,
-0.021211834624409676,
-0.010419570840895176,
0.02759671024978161,
-0.03104274533689022,
-0.03422071412205696,
0.025009747594594955,
-0.03951263800263405,
0.04322610795497894,
-0.01259562000632286,
-0.012689996510744095,
-0.02405923418700695,
0.057954415678977966,
0.012116601690649986,
0.05641055852174759,
-0.007086087483912706,
-0.031452249735593796,
-0.04474194720387459,
0.0009115635184571147,
0.04822282865643501,
0.022480711340904236,
-0.046273522078990936,
0.011307066306471825,
0.022014323621988297,
0.004242678638547659,
0.022499235346913338,
-0.00758295226842165,
-0.02343881130218506,
-0.033775102347135544,
-0.007978334091603756,
0.010696306824684143,
0.011675490066409111,
0.01610514707863331,
-0.0036175630521029234,
0.029575970023870468,
0.03536247834563255,
-0.0100519098341465,
-0.04245718941092491,
0.029221875593066216,
-0.00419061491265893,
0.03275396302342415,
0.005236069206148386,
-0.01307183038443327,
0.017385825514793396,
-0.015729479491710663,
0.030084921047091484,
-0.0023948336020112038,
-0.02021854557096958,
-0.00023750824038870633,
-0.009708575904369354,
-0.03011646680533886,
0.011873247101902962,
0.01950978860259056,
-0.02867964655160904,
0.024358754977583885,
0.020056938752532005,
-0.034809306263923645,
-0.003966429736465216,
-0.023882415145635605,
-0.009664446115493774,
-0.020954545587301254,
-0.011042077094316483,
0.046769239008426666,
-0.006437607575207949,
0.03853518143296242,
-0.0534832626581192,
-0.031863775104284286,
-0.0006637867772951722,
-0.03314594924449921,
0.012631464749574661,
0.00373368663713336,
-0.03633538633584976,
0.015889331698417664,
-0.039704401046037674,
-0.04609561711549759,
0.026583297178149223,
-0.035281699150800705,
0.034607868641614914,
0.029232263565063477,
-0.05030938237905502,
-0.049944788217544556,
-0.010108618065714836,
-0.008974972181022167,
0.0025964369997382164,
-0.024804480373859406,
0.013716801069676876,
0.04126495495438576,
-0.04743942990899086,
-0.0060416716150939465,
0.01148977316915989,
-0.0557287223637104,
-0.04745103418827057,
-0.043397922068834305,
0.012453901581466198,
0.03135557100176811,
-0.014218633063137531,
0.017171021550893784,
0.05742321163415909,
-0.07004439830780029,
-0.018754925578832626,
-0.04180852696299553,
-0.01998891867697239,
0.044947247952222824,
0.028732476755976677,
0.06066333130002022,
0.022968793287873268,
-0.010295323096215725,
0.06354504078626633,
0.02164052426815033,
-0.04717060178518295,
0.019582755863666534,
-0.018733391538262367,
-0.02310151793062687,
-0.047054219990968704,
0.019760746508836746,
-0.006786544807255268,
-0.02196909487247467,
0.015658164396882057,
0.010660389438271523,
0.03955001384019852,
0.039883092045784,
0.021791592240333557,
-0.009453529492020607,
0.041455019265413284,
0.01457088440656662,
0.023077167570590973,
0.08701106160879135,
0.006472356617450714,
-0.038608402013778687,
0.04275573417544365,
-0.005945797543972731,
0.020807920023798943,
0.018451057374477386,
-0.04843573644757271,
0.08188952505588531,
0.02286306768655777,
0.010421862825751305,
-0.053188543766736984,
0.060605112463235855,
0.0019038673490285873,
0.010342268273234367,
0.00826181285083294,
0.032229337841272354,
0.013773944228887558,
-0.016731727868318558,
0.017775367945432663,
0.042647238820791245,
0.02541384845972061,
-0.006638363003730774,
-0.022498920559883118,
0.007755745202302933,
-0.03034150041639805,
0.020354658365249634,
-0.0009040878503583372,
-0.03380999714136124,
0.036635871976614,
0.02815955877304077,
0.05320526659488678,
-0.010217959992587566,
-0.045773621648550034,
-0.01717742718756199,
-0.047093745321035385,
-0.01071314886212349,
-0.0024238931946456432,
0.0382339209318161,
0.00047271695802919567,
0.04693545401096344,
0.026821846142411232,
0.04597501829266548,
0.03783421963453293,
0.018913570791482925,
-0.05391314625740051,
-0.002357266843318939,
-0.03910399600863457,
-0.02755538932979107,
0.008083860389888287,
-0.012976620346307755,
-0.024943221360445023,
-0.035295069217681885,
-0.03200823441147804,
0.021100036799907684,
-0.02941046841442585,
-0.040810201317071915,
0.01947144791483879,
-0.03080594912171364,
-0.008908509276807308,
0.003862156067043543,
0.03997597470879555,
0.018715111538767815,
-0.029462020844221115,
-0.023100467398762703,
0.07428034394979477,
-0.03708089888095856,
0.0013941499637439847,
-0.0039655473083257675,
0.006589682772755623,
0.03262211009860039,
0.04065506532788277,
0.047206588089466095,
0.014367764815688133,
-0.012811733409762383,
0.012496257200837135,
0.016451315954327583,
0.062441080808639526,
-0.014707336202263832,
-0.04513036459684372,
-0.03535955771803856,
-0.03215458616614342,
-0.03346574679017067,
0.0018050884827971458,
0.06536972522735596,
0.0035209415946155787,
0.02931862883269787,
0.03329542279243469,
-0.003879871219396591,
-0.026790112257003784,
0.002976173534989357,
0.03677721694111824,
0.010277547873556614,
-0.04668485000729561,
-0.02577591873705387,
0.012088730931282043,
-0.011623803526163101,
-0.004678621422499418,
-0.014466848224401474,
0.01203557662665844,
-0.02430354245007038,
0.03093407116830349,
0.006611461751163006,
0.01736859790980816,
-0.02268936112523079,
-0.02737642452120781,
0.02443813718855381,
0.0423675961792469,
-0.02242346666753292,
-0.036108724772930145,
0.012459749355912209,
0.0006801063427701592,
-0.007696112152189016,
-0.009517713449895382,
0.0031887455843389034,
-0.05648088827729225,
0.01331301312893629,
0.019652212038636208,
0.020490208640694618,
0.00399178359657526,
-0.027445796877145767,
-0.035399891436100006,
-0.0065361810848116875,
0.05717651546001434,
-0.01616067625582218,
0.045535918325185776,
0.008039329200983047,
-0.02984555810689926,
0.03529907390475273,
-0.02695818804204464,
0.015613855794072151,
0.004099035635590553,
0.0041275667026638985,
0.03179711475968361,
-0.01409392524510622,
-0.027408378198742867,
-0.012106725014746189,
-0.0037093947175890207,
0.02885965071618557,
0.06377727538347244,
-0.028772838413715363,
-0.022446516901254654,
0.02492520958185196,
-0.008674036711454391,
-0.025266852229833603,
-0.0727522224187851,
-0.034321174025535583,
-0.005102555267512798,
0.01833275705575943,
0.013656729832291603,
-0.025384681299328804,
-0.054815199226140976,
0.009036985225975513,
0.005799721460789442,
-0.015234670601785183,
0.00436773058027029,
-0.016244204714894295,
0.07302925735712051,
-0.01364529225975275,
-0.009464729577302933,
0.012367124669253826,
0.032429441809654236,
0.020437272265553474,
-0.01592293754220009,
-0.05822506174445152,
0.063374824821949,
-0.029621196910738945,
0.02212928794324398,
-0.04001066833734512,
-0.04981459677219391,
-0.02637546882033348,
0.00793604925274849,
-0.03345225751399994,
0.0010832699481397867,
-0.015758473426103592,
-0.03618008270859718,
-0.01234824676066637,
-0.0198679119348526,
0.01458936557173729,
0.029978422448039055,
-0.004293262958526611,
-0.006421514321118593,
-0.008307763375341892,
-0.03227784484624863,
0.014175537042319775,
-0.005660456605255604,
-0.008945940993726254,
0.03932756185531616,
-0.007268414366990328,
0.03786433860659599,
-0.01770837791264057,
-0.0257369726896286,
0.021764378994703293,
-0.04067041724920273,
0.012637337669730186,
-0.005643256939947605,
0.003283934434875846,
-0.0015012490330263972,
-0.020793193951249123,
-0.013937675394117832,
-0.016578683629631996,
0.004448349587619305,
0.038637615740299225,
-0.042865775525569916,
0.037979450076818466,
0.0007516414043493569,
0.031604330986738205,
-0.0581466481089592,
-0.018755698576569557,
0.018706252798438072,
0.0007864179206080735,
-0.02071060985326767,
-0.01876872219145298,
0.01782679744064808,
-0.02316286414861679,
-0.03868651017546654,
0.020596973598003387,
0.055941492319107056,
0.00934506580233574,
-0.029592417180538177,
-0.015430280938744545,
0.04205929487943649,
0.014942692592740059,
0.019044796004891396,
-0.016009673476219177,
-0.011144282296299934,
0.0012001764262095094,
-0.04179801419377327,
0.02192198857665062,
0.05362248793244362,
-0.02410568855702877,
-0.02549854665994644,
-0.003544821636751294,
-0.02364194020628929,
0.028670798987150192,
-0.021140020340681076,
-0.009053011424839497,
0.0559222511947155,
0.022373884916305542,
-0.019347863271832466,
-0.02038515731692314,
0.06773966550827026,
0.028132321313023567,
0.015577304176986217,
-0.022709742188453674,
-0.020631218329072,
0.0016773520037531853,
-0.030123645439743996,
0.011532038450241089,
0.006287765223532915,
0.039691030979156494,
0.017420848831534386,
0.04269878938794136,
0.015023083426058292,
-0.005411198362708092,
0.01681492105126381,
-0.044185008853673935,
0.001025621546432376,
0.01732945814728737,
-0.0359540618956089,
-0.027033532038331032,
0.0004184484132565558,
-0.007782462053000927,
-0.05583115294575691,
-0.05135862156748772,
0.019247012212872505,
0.06367222964763641,
-0.027453787624835968,
0.05097170174121857,
0.013059268705546856,
-0.0076982975006103516,
0.030108079314231873,
-0.014141255989670753,
-0.04034515470266342,
0.007676229812204838,
-0.000713882502168417,
0.001331208972260356,
-0.015663761645555496,
0.005221444182097912,
0.016284644603729248,
0.056208524852991104,
-0.03999653831124306,
0.05048493668437004,
-0.004289753269404173,
0.004805955570191145,
-0.033152032643556595,
-0.0028395981062203646,
-0.0502074658870697,
0.04289577901363373,
-0.02627260982990265,
0.051227305084466934,
-0.009917933493852615,
-0.009374945424497128,
0.012308782897889614,
-0.012719317339360714,
-0.019003121182322502,
-0.030845170840620995,
-0.036514561623334885,
-0.04484046623110771,
0.00937234703451395,
0.010802940465509892,
0.0187697596848011,
-0.013394718989729881,
0.020039008930325508,
0.04949496313929558,
0.013645079918205738,
-0.004787456709891558,
0.005927537102252245,
-0.06708160042762756,
-0.014969642274081707,
-0.053333524614572525,
-0.05837598070502281,
0.022412430495023727,
-0.03325863182544708,
-0.025866709649562836,
0.013953547924757004,
-0.015491423197090626,
0.02492859959602356,
-0.001445614267140627,
0.0362723246216774,
0.0024224489461630583,
0.057063229382038116,
0.018962623551487923,
0.023302925750613213,
-0.023212628439068794,
0.050855595618486404,
0.11060468852519989,
0.0563027448952198,
0.015609283931553364,
-0.055186767131090164,
-0.0024445676244795322,
-0.044204048812389374,
0.00692151952534914,
-0.0006036927225068212,
0.009516826830804348,
-0.01983344554901123,
0.015678012743592262,
0.0005355299799703062,
0.05702032893896103,
0.0022732578217983246,
-0.007756512146443129,
0.049933332949876785,
-0.01153775304555893,
-0.05258641764521599,
0.02390371821820736,
0.028118310496211052,
0.016895785927772522,
0.007322956342250109,
0.005836968310177326,
0.00022473376884590834,
-0.026811400428414345,
0.03450312465429306,
-0.03435617312788963,
-0.024977941066026688,
0.06104704737663269,
0.006589619908481836,
-0.02564014121890068,
-0.00989468302577734,
0.006656802725046873,
-0.022957123816013336,
-0.041881971061229706,
0.00037335214437916875,
0.04120795056223869,
-0.003328962018713355,
0.0258481502532959,
0.012516343034803867,
-0.014206591062247753,
0.030207863077521324,
0.0054686604999005795,
0.0037431681994348764,
-0.03352900221943855,
-0.019255664199590683,
-0.003088099416345358,
0.027902770787477493,
-0.00587806012481451,
0.00836484506726265,
-0.001878248993307352,
0.013576403260231018,
0.020027533173561096,
-0.02660096436738968,
0.0017242287285625935,
0.021453795954585075,
0.052140187472105026,
-0.044548626989126205,
-0.010923818685114384,
-0.04511589556932449,
0.011860113590955734,
0.011715142987668514,
0.02243708446621895,
0.022553393617272377,
-0.005014082882553339,
0.03410058096051216,
0.018000178039073944,
0.02439899742603302,
-0.02102920226752758,
-0.020037544891238213,
-0.0003530268440954387,
-0.010253896936774254,
-0.050080835819244385,
-0.03869624063372612,
0.0419875904917717,
0.03243263065814972,
0.06977490335702896,
-0.0017529221950098872,
0.029924266040325165,
-0.00019904621876776218,
-0.09443045407533646,
0.028417835012078285,
-0.031101340427994728,
-0.009921378456056118,
-0.0034896780271083117,
0.007385748904198408,
0.01162730809301138,
0.0391206331551075,
-0.014065916649997234,
0.008034728467464447,
0.029085803776979446,
-0.01607317477464676,
0.05089929699897766,
-0.05025599151849747,
0.010305134579539299,
0.021780597046017647,
-0.07169142365455627,
0.009970507584512234,
-0.028036803007125854,
0.0023682890459895134,
0.03761860355734825,
0.017236221581697464,
-0.006846402306109667,
0.0029749462846666574,
-0.02629494108259678,
-0.009796633385121822,
-0.0029110133182257414,
-0.044813528656959534,
-0.008617673069238663,
0.00930202566087246,
-0.019345195963978767,
-0.016738353297114372,
-0.07764630019664764,
-0.035682499408721924,
0.034223757684230804,
-0.029425883665680885,
-0.00302555481903255,
-0.021610265597701073,
-0.001501671620644629,
0.012454858049750328,
0.030661163851618767,
-0.04215548187494278,
-0.0298891793936491,
-0.014876832254230976,
0.006609321106225252,
0.0009446508483961225,
0.014035675674676895,
-0.051603157073259354,
0.02675735391676426,
-0.02914997562766075,
-0.01808786951005459,
0.032620202749967575,
0.03440052270889282,
0.0014688438968732953,
-0.062338802963495255,
-0.005372124724090099,
-0.011057787574827671,
0.04990995675325394,
-0.015412556007504463,
-0.007686615455895662,
0.03087492287158966,
-0.02481619082391262,
-0.02377563901245594,
0.01994202844798565,
-0.0025499567855149508,
0.018415890634059906,
0.028027398511767387,
0.013460981659591198,
-0.014853950589895248,
0.0585402175784111,
-0.050473958253860474,
0.010006667114794254,
0.034880563616752625,
-0.05125633627176285,
0.0006041726446710527,
-0.04396490380167961,
-0.00405476288869977,
0.005394167732447386,
0.0011224638437852263,
0.05168405920267105,
0.03250592574477196,
-0.0037738929968327284,
0.0095755560323596,
0.011347057297825813,
0.007614961359649897,
0.026346547529101372,
0.07667194306850433,
0.015653513371944427,
0.013001038692891598,
0.031968243420124054,
-0.019312893971800804,
0.028189633041620255,
0.017646200954914093,
0.02822563797235489,
-0.10207100212574005,
-0.036186181008815765,
0.029515786096453667,
-0.016177726909518242,
0.0438813678920269,
-0.04335423931479454,
0.011193918064236641,
0.0012663339730352163,
-0.04022034630179405,
0.029255961999297142,
-0.03414391726255417,
-0.019824303686618805,
-0.012780781835317612,
-0.0027187170926481485,
-0.017170526087284088,
0.011056805960834026,
-0.003743840614333749,
0.03491606190800667,
-0.0022770280484110117,
0.02359127067029476,
-0.009836816228926182,
-0.01652071811258793,
-0.0057182698510587215,
0.032253947108983994,
-0.009220335632562637,
-0.024491244927048683,
0.037978701293468475,
-0.022089604288339615,
-0.00693987961858511,
0.03381206840276718,
-0.03827284276485443,
-0.006364204455167055,
-0.025427235290408134,
0.018515365198254585,
-0.02087160013616085,
0.03903929144144058,
0.06347619742155075,
-0.020386701449751854,
0.038873396813869476,
0.025892071425914764,
0.03270852193236351,
0.030925758183002472,
-0.011167898774147034,
-0.03635236993432045,
0.02270198054611683,
-0.055941104888916016,
-0.061842672526836395,
0.029879560694098473,
0.00359453447163105,
0.022382695227861404,
0.029100047424435616,
-0.009454621933400631,
-0.022888891398906708,
-0.05757055804133415,
0.016213374212384224,
-0.043840110301971436,
-0.0036782908719033003,
0.0460331104695797,
0.008472696878015995,
0.034690603613853455,
-0.02193273790180683,
0.003775204299017787,
0.002570348558947444,
0.03103184886276722,
0.0006143303471617401,
-0.013962113298475742,
-0.0558742955327034,
-0.006748996675014496,
0.03281521052122116,
0.011360648088157177,
-0.00981670618057251,
-0.060708627104759216,
-0.019059883430600166,
0.03190502151846886,
0.0035990665201097727,
-0.0008944280561991036,
-0.034631624817848206,
-0.008521324023604393,
-0.03401016443967819,
-0.059513747692108154,
0.00003730208845809102,
-0.0066106971353292465,
0.047034669667482376,
-0.051143232733011246,
0.02379106916487217,
-0.0006741704419255257,
0.007402751594781876,
0.08325440436601639,
0.029360849410295486,
-0.012673895806074142,
0.007578721269965172,
-0.03688204661011696,
0.006434559356421232,
-0.02361702173948288,
0.008743456564843655,
-0.028682556003332138,
0.006590625271201134,
-0.04440903291106224,
-0.012894967570900917,
-0.007321725133806467,
0.047580279409885406,
0.02894729934632778,
-0.019710062071681023,
-0.00973823107779026,
-0.007811756804585457,
0.0010948225390166044,
0.0571843720972538,
-0.019180962815880775,
0.011809791438281536,
0.05484722927212715,
-0.026968320831656456,
0.03982407972216606,
0.06468071043491364,
-0.02715553529560566,
-0.03944699466228485,
0.0069951219484210014,
0.008917657658457756,
-0.025467054918408394,
-0.0039251819252967834,
0.008504514582455158,
0.03644004091620445,
-0.021904826164245605,
-0.010269112884998322,
0.027305971831083298,
-0.03321382403373718,
0.002285352209582925,
0.007618371397256851,
0.023735735565423965,
0.05404430255293846,
-0.0210440494120121,
0.02347216010093689,
0.049026697874069214,
0.01917576603591442,
0.04416282847523689,
0.06367212533950806,
0.048120588064193726,
-0.0061395978555083275,
0.00961255468428135,
0.03595652058720589,
-0.04644377529621124,
0.00891729723662138,
0.01665359176695347,
0.01264701783657074,
-0.021066268905997276,
-0.03309335932135582,
0.028936069458723068,
-0.02667698822915554,
0.021393664181232452,
0.025012454017996788,
-0.02885039895772934,
0.07347986847162247,
0.000012245430298207793,
0.021233944222331047,
-0.04145708680152893,
0.03398066386580467,
-0.012009632773697376,
0.0033219419419765472,
0.019447755068540573,
0.015622490085661411,
-0.05260544270277023,
0.004028482362627983,
-0.02124655805528164,
-0.0076232473365962505,
0.010583381168544292,
-0.062332428991794586,
-0.016684526577591896,
-0.003618293209001422,
0.0033962479792535305,
-0.048577580600976944,
-0.02466263622045517,
-0.022743621841073036,
-0.022035347297787666,
0.009493627585470676,
0.023375937715172768,
0.03265359252691269,
-0.016025831922888756,
-0.010498227551579475,
0.004158189054578543,
0.05809859186410904,
-0.06634043157100677,
-0.012128706090152264,
-0.025218570604920387,
0.024418028071522713,
-0.013515649363398552,
-0.03176197409629822
] |
<p>I'm trying to program an $N$-body simulation and I'd like to be able to test it with a known solution to a simple, two-body problem. I've looked at multiple sources, but I just don't know how to apply it to my simple test case.</p>
<p>Two objects at rest placed 10 meters apart with mass of 1. The force between them is a modified gravitational force of F = 10 * m1 * m2 / r^2. How long will it take for each object to travel 4 meters?</p>
| 134 |
[
0.01663397066295147,
-0.01832016371190548,
-0.03650733456015587,
0.0023633127566426992,
0.01233638171106577,
-0.02150130458176136,
0.018274161964654922,
-0.023204032331705093,
0.00618709996342659,
0.0028586217667907476,
0.04220506176352501,
0.060520272701978683,
0.05486709251999855,
-0.01647142320871353,
0.020835217088460922,
-0.006214845925569534,
-0.03512900322675705,
-0.01955069601535797,
0.025490932166576385,
-0.015124518424272537,
-0.00005770985808339901,
-0.025313161313533783,
0.046097856014966965,
-0.04304874688386917,
0.02072833478450775,
0.024735605344176292,
0.02558836154639721,
-0.05274878814816475,
0.006108306813985109,
0.027957210317254066,
-0.01987219788134098,
-0.02359132096171379,
0.004059636499732733,
0.04871169850230217,
-0.00400837417691946,
0.023896045982837677,
-0.049395930022001266,
-0.014878672547638416,
0.0018120554741472006,
0.029091961681842804,
-0.04931144043803215,
-0.02951735071837902,
0.00969063863158226,
0.04578278213739395,
-0.009789464995265007,
0.004640229977667332,
0.03387899696826935,
0.003917792811989784,
0.06866073608398438,
-0.046464383602142334,
0.09949273616075516,
0.03293776884675026,
0.0423944853246212,
0.0011136069661006331,
-0.015505561605095863,
-0.022638393566012383,
0.06096856668591499,
0.07757335901260376,
-0.003962208051234484,
-0.03482483699917793,
-0.026803361251950264,
-0.020018182694911957,
-0.022087888792157173,
-0.03205752745270729,
-0.022727221250534058,
0.011358083225786686,
-0.02827143482863903,
-0.006395274773240089,
-0.013142897747457027,
-0.00998581200838089,
0.03255726397037506,
0.012802135199308395,
0.066559799015522,
-0.013248761184513569,
-0.00028926058439537883,
0.004642683081328869,
0.0278023611754179,
-0.009333046153187752,
0.030101681128144264,
0.04741014912724495,
-0.04919900745153427,
0.017132004722952843,
0.03667252138257027,
0.0631328821182251,
-0.03361150249838829,
-0.021660925820469856,
0.03618386760354042,
0.014177610166370869,
-0.0016287603648379445,
0.014413919299840927,
-0.030398879200220108,
0.02145349606871605,
0.06450363248586655,
0.04610954597592354,
-0.010512190870940685,
0.03961631655693054,
-0.01702968217432499,
0.06587943434715271,
-0.005242798011749983,
-0.027589984238147736,
-0.029374713078141212,
-0.04693939909338951,
0.015619488433003426,
0.034732066094875336,
-0.027608457952737808,
0.014532530680298805,
-0.020676618441939354,
0.0019446363439783454,
-0.04177088662981987,
0.011108520440757275,
-0.027822382748126984,
0.015366895124316216,
-0.0030328561551868916,
0.0109324399381876,
0.03645000606775284,
-0.0447348989546299,
0.00030799643718637526,
-0.03821537271142006,
0.0551740936934948,
0.025412458926439285,
0.06174813210964203,
-0.008099129423499107,
0.016548756510019302,
-0.029570447281003,
-0.019726529717445374,
-0.00577740091830492,
-0.010891278274357319,
-0.014168347232043743,
0.0004586674040183425,
0.046191804111003876,
-0.0054566338658332825,
-0.008713001385331154,
-0.011097390204668045,
-0.0036123080644756556,
0.030529383569955826,
-0.008473668247461319,
-0.07967740297317505,
-0.07588977366685867,
0.017269348725676537,
0.012836877256631851,
0.0062983231619000435,
-0.05695590376853943,
0.021637849509716034,
0.021016061305999756,
0.04816717654466629,
0.0012614025035873055,
-0.002940588863566518,
-0.005132084712386131,
0.053989559412002563,
-0.007611272856593132,
0.029485175386071205,
-0.016338780522346497,
-0.023103849962353706,
-0.0004846547089982778,
0.012548870407044888,
-0.08384674787521362,
0.012990893796086311,
0.03854125738143921,
-0.026642324402928352,
-0.015578318387269974,
0.061839036643505096,
0.002648602006956935,
0.03679617866873741,
0.0020545502193272114,
0.01022584643214941,
0.0050083063542842865,
0.06388889998197556,
0.013385034166276455,
-0.016224892809987068,
0.04124341905117035,
0.007414611056447029,
0.015271035023033619,
-0.004594126250594854,
0.01175234280526638,
0.03921074420213699,
-0.030011162161827087,
-0.016131684184074402,
0.007481426931917667,
0.0025548830162733793,
0.0055649010464549065,
-0.01150516141206026,
-0.04217640310525894,
0.017530623823404312,
-0.027230242267251015,
-0.016401249915361404,
0.023709475994110107,
0.016790172085165977,
0.035599734634160995,
0.0022531594149768353,
-0.02690504677593708,
-0.029867637902498245,
-0.074243925511837,
0.03333677351474762,
0.02182655595242977,
-0.014471933245658875,
0.017745984718203545,
0.007078587077558041,
0.039745934307575226,
-0.012103092856705189,
-0.04902380704879761,
-0.06202227249741554,
0.03041997365653515,
-0.015743056312203407,
-0.002564538735896349,
0.013884401880204678,
0.0840630829334259,
0.06070926785469055,
0.0025119364727288485,
0.02273895964026451,
-0.021475287154316902,
-0.024228833615779877,
-0.028442634269595146,
-0.016758762300014496,
0.014835895039141178,
0.035921361297369,
0.011361880227923393,
0.026371361687779427,
0.006317444611340761,
0.0036988556385040283,
0.0298125259578228,
-0.03070596233010292,
0.09895928204059601,
0.07606857270002365,
0.03503246232867241,
0.005191360134631395,
0.03255022317171097,
0.012143803760409355,
-0.010496898554265499,
0.0011859857477247715,
-0.04577649012207985,
-0.025528419762849808,
-0.036598190665245056,
0.02564532496035099,
0.0163654126226902,
-0.036573104560375214,
0.029876530170440674,
0.10090986639261246,
0.010718311183154583,
0.03816991671919823,
0.018617210909724236,
-0.0090481610968709,
-0.030232934281229973,
0.04960336908698082,
0.03741654381155968,
-0.014555909670889378,
0.024589145556092262,
0.02482604794204235,
0.05052761361002922,
-0.0071207270957529545,
0.01618894375860691,
-0.015620951540768147,
0.023254670202732086,
0.01564823091030121,
0.012718796730041504,
-0.004731133114546537,
-0.014637922868132591,
0.028681984171271324,
-0.014578953385353088,
-0.007907390594482422,
0.05382167175412178,
0.024134840816259384,
-0.009769147261977196,
-0.03200415521860123,
-0.03196844831109047,
0.02912130020558834,
0.017474738880991936,
0.01205203216522932,
-0.0013889529509469867,
0.028229180723428726,
-0.04495293274521828,
0.026691757142543793,
-0.03627655282616615,
-0.027295826002955437,
-0.03984463959932327,
0.01056757289916277,
0.02012987621128559,
0.03139127045869827,
0.0028631994500756264,
-0.0055361464619636536,
0.0012021021684631705,
0.01210998184978962,
-0.05069436877965927,
-0.016791600733995438,
-0.022734738886356354,
-0.05468393489718437,
0.02496204897761345,
-0.04376867413520813,
-0.044959843158721924,
0.03295845165848732,
0.021568799391388893,
-0.0027260391507297754,
0.03429717943072319,
-0.023868165910243988,
-0.020541757345199585,
-0.011958329938352108,
-0.01620110124349594,
-0.006634403020143509,
-0.0731031596660614,
0.0075479852966964245,
0.05028181150555611,
0.000979345990344882,
-0.0372869111597538,
0.0055830711498856544,
-0.06313914060592651,
-0.0024105117190629244,
-0.02365705370903015,
-0.005488820839673281,
0.027999909594655037,
-0.026347691193223,
0.01664864458143711,
0.006928286515176296,
-0.015671519562602043,
-0.0009533555130474269,
-0.046135492622852325,
-0.07257944345474243,
0.004575955215841532,
-0.013143634423613548,
0.05719372257590294,
0.002948831534013152,
-0.03895805403590202,
0.08592565357685089,
-0.007891486398875713,
0.02169937826693058,
-0.033290471881628036,
0.030460676178336143,
0.008497676812112331,
-0.03036591410636902,
0.040631432086229324,
0.004883528687059879,
-0.0175201166421175,
-0.03251966834068298,
0.013187258504331112,
-0.01143065094947815,
0.05018969997763634,
0.0043984646908938885,
0.0061388625763356686,
0.0021020162384957075,
0.021781597286462784,
-0.02003825455904007,
0.05037340894341469,
-0.008256248198449612,
-0.01838153973221779,
0.018279388546943665,
-0.034761007875204086,
0.027680259197950363,
-0.014541024342179298,
-0.06991256773471832,
0.04940992221236229,
-0.01940319314599037,
-0.028723880648612976,
0.021511660888791084,
0.04032932594418526,
-0.03344142809510231,
-0.050061892718076706,
0.016227323561906815,
0.032205648720264435,
0.07268106937408447,
-0.00841077882796526,
-0.00040595445898361504,
0.03746090084314346,
0.03273580223321915,
-0.023169206455349922,
-0.04028937593102455,
-0.0014485777355730534,
-0.028274724259972572,
0.027320371940732002,
0.0035638671834021807,
-0.025565622374415398,
0.046017687767744064,
0.03881486505270004,
0.043712664395570755,
0.003509864676743746,
-0.030251968652009964,
0.001727050170302391,
-0.06947170197963715,
-0.015449466183781624,
-0.01501535251736641,
0.060211945325136185,
0.007113430183380842,
0.044748853892087936,
0.03643925115466118,
-0.0019292909419164062,
0.0027810530737042427,
0.007087915204465389,
-0.0821138396859169,
0.041342467069625854,
-0.045214395970106125,
-0.05804494395852089,
0.015498950146138668,
-0.007499045692384243,
-0.03352978453040123,
-0.03453805297613144,
0.04720935970544815,
0.005956475622951984,
0.001606641337275505,
-0.041267476975917816,
-0.006891144905239344,
-0.04178904742002487,
-0.0458727665245533,
0.003980909939855337,
0.02146519161760807,
0.04995018616318703,
-0.017836758866906166,
0.00828727800399065,
0.04521608725190163,
-0.01716046780347824,
-0.005064209457486868,
-0.021396342664957047,
-0.017156682908535004,
-0.016364984214305878,
0.037061188369989395,
0.03608584776520729,
0.04655694216489792,
-0.060247693210840225,
0.029338475316762924,
-0.00208248826675117,
0.052993517369031906,
0.015060573816299438,
0.0017112062778323889,
-0.011711821891367435,
-0.04000413045287132,
0.018015826120972633,
-0.003436816856265068,
0.040024496614933014,
-0.00047036464093253016,
-0.024537237361073494,
0.015598542988300323,
0.035330433398485184,
-0.0005600800504907966,
0.014613610692322254,
0.07772397249937057,
0.008375591598451138,
-0.05451318249106407,
-0.027302905917167664,
-0.011965892277657986,
-0.03412545472383499,
0.014629886485636234,
0.03659806400537491,
0.002463150303810835,
-0.03150000050663948,
0.02106642536818981,
0.02791796252131462,
-0.009598118253052235,
-0.015078331343829632,
0.0034675230272114277,
-0.032500769942998886,
0.031135110184550285,
-0.02546972781419754,
0.012855377048254013,
0.004865739028900862,
0.033747535198926926,
0.013349007815122604,
-0.00476546585559845,
0.012983323074877262,
-0.06740520894527435,
0.01725137233734131,
0.03844579681754112,
0.014333602972328663,
-0.010779095813632011,
0.0043290420435369015,
-0.03403133526444435,
-0.03528190776705742,
0.0260614100843668,
-0.04731236770749092,
0.027179114520549774,
0.016616467386484146,
0.02057787775993347,
-0.015654463320970535,
0.01427159272134304,
-0.028811488300561905,
0.03346840292215347,
-0.03858904168009758,
0.007850084453821182,
-0.0023021234665066004,
-0.014041861519217491,
0.012362987734377384,
0.01234967540949583,
0.027229735627770424,
0.07007603347301483,
-0.0000333553871314507,
-0.03465191647410393,
0.00562070868909359,
-0.02703528292477131,
-0.03956519439816475,
-0.036096248775720596,
-0.008915913291275501,
-0.018017152324318886,
-0.03770105540752411,
0.027658885344862938,
-0.03409840539097786,
-0.04074271395802498,
0.0440782867372036,
-0.01811990700662136,
0.016136527061462402,
-0.025279972702264786,
-0.023328207433223724,
0.020473666489124298,
0.04148966073989868,
-0.03121555969119072,
0.042017169296741486,
0.0084640858694911,
-0.02032449096441269,
-0.0010197950759902596,
-0.020609531551599503,
0.03079674206674099,
-0.005914461333304644,
-0.011155573651194572,
-0.021152546629309654,
-0.019396787509322166,
-0.036982275545597076,
0.01720067858695984,
-0.007342428434640169,
0.04890136420726776,
-0.016384949907660484,
-0.027404166758060455,
0.005277694668620825,
0.04857584461569786,
0.017596298828721046,
0.05103067308664322,
0.013994845561683178,
-0.027648869901895523,
-0.004846872296184301,
-0.003059087321162224,
-0.003673572326079011,
-0.015921998769044876,
-0.00663491478189826,
-0.00748260784894228,
0.0009170837583951652,
0.008453965187072754,
-0.038205891847610474,
-0.03782568499445915,
0.03997962549328804,
-0.052126917988061905,
0.0670485571026802,
-0.013744205236434937,
0.0006989166140556335,
0.026675980538129807,
-0.051105957478284836,
-0.015066776424646378,
0.01744956523180008,
-0.0009470171644352376,
0.012293881736695766,
-0.04030685871839523,
-0.004013051278889179,
-0.006207128055393696,
0.04176454618573189,
-0.05899054929614067,
-0.0214679092168808,
0.028217557817697525,
-0.010798013769090176,
-0.0029309550300240517,
-0.049265056848526,
-0.04938264191150665,
-0.03305204585194588,
-0.011502201668918133,
-0.010532740503549576,
0.05343601852655411,
-0.02343802899122238,
-0.0018714083125814795,
-0.005441967863589525,
0.007468976080417633,
0.03876032307744026,
0.023873427882790565,
-0.0012617978500202298,
0.0021521314047276974,
-0.01562570594251156,
-0.004427813924849033,
0.0013426278019323945,
0.049008749425411224,
-0.034089960157871246,
-0.0405958853662014,
-0.05806220695376396,
-0.011967458762228489,
0.019791023805737495,
-0.03753107041120529,
0.028287621214985847,
0.056476425379514694,
0.005113760940730572,
0.04380442574620247,
-0.0044029103592038155,
0.028429770842194557,
-0.04473024606704712,
0.010163705796003342,
-0.041734252125024796,
0.011761048808693886,
0.024439649656414986,
-0.01628052070736885,
0.042374785989522934,
-0.006803205702453852,
0.02811005339026451,
0.013847354799509048,
0.0791834369301796,
-0.0032777665182948112,
-0.028321458026766777,
0.02332436852157116,
0.017768803983926773,
0.0118302833288908,
-0.012771175242960453,
-0.027207491919398308,
0.014950639568269253,
0.039056409150362015,
-0.02346496656537056,
-0.02187996543943882,
-0.014754200354218483,
-0.022948086261749268,
0.0751849040389061,
-0.035118959844112396,
0.06535230576992035,
0.019999386742711067,
0.010943169705569744,
0.005109029822051525,
-0.020222192630171776,
-0.0061833057552576065,
-0.005321464966982603,
0.018700461834669113,
0.05709570646286011,
0.0025918958708643913,
-0.00765187805518508,
0.011990581639111042,
0.05825287103652954,
-0.011220186948776245,
0.009216265752911568,
0.023900575935840607,
0.011534073390066624,
0.019994759932160378,
-0.0172060988843441,
-0.025039175525307655,
0.023159915581345558,
-0.04055707901716232,
0.032867275178432465,
-0.031537871807813644,
0.0029786184895783663,
0.038186877965927124,
0.03686901926994324,
0.02768769860267639,
-0.04614248126745224,
0.016128282994031906,
-0.02716517075896263,
-0.0005364003591239452,
0.0364110991358757,
-0.0007243784493766725,
-0.01775403507053852,
0.022247636690735817,
0.026351070031523705,
0.02387228049337864,
0.04288942366838455,
-0.021703269332647324,
-0.048417046666145325,
-0.06492649763822556,
-0.003542481455951929,
-0.04296962544322014,
0.033514540642499924,
0.032107286155223846,
-0.0316193513572216,
0.029225943610072136,
-0.008825661614537239,
0.02101857215166092,
0.012187088839709759,
0.007503123488277197,
-0.04450230672955513,
0.10724295675754547,
-0.008424783125519753,
0.012145809829235077,
-0.012858892790973186,
0.021734999492764473,
0.11491073668003082,
0.03348304703831673,
0.024032853543758392,
-0.0399923175573349,
0.021536855027079582,
-0.031744882464408875,
-0.0010755180846899748,
-0.026013001799583435,
0.002289125230163336,
0.03826053440570831,
-0.017377495765686035,
0.033842358738183975,
0.018515806645154953,
-0.0019898940809071064,
0.008173691108822823,
0.055768515914678574,
-0.0035548002924770117,
-0.05458085983991623,
0.016538003459572792,
0.008703540079295635,
-0.010813306085765362,
-0.02146572805941105,
-0.030437814071774483,
0.03483158349990845,
-0.057357244193553925,
-0.005263245664536953,
-0.03960617259144783,
-0.005240467377007008,
0.02886383607983589,
0.01100482139736414,
-0.020837483927607536,
0.03905964270234108,
0.0043008774518966675,
-0.0583457350730896,
-0.0057559506967663765,
0.03694557398557663,
0.009294083341956139,
-0.030336618423461914,
0.023604394868016243,
0.06798291951417923,
-0.01934841088950634,
0.014544449746608734,
-0.014606839045882225,
-0.011380690149962902,
-0.05417980998754501,
0.0061437711119651794,
-0.042894672602415085,
0.06444494426250458,
-0.022824879735708237,
-0.04205095022916794,
0.013937355019152164,
-0.005395751446485519,
-0.014595617540180683,
-0.05632339417934418,
0.019670292735099792,
0.021532660350203514,
0.05034482479095459,
-0.014961089938879013,
0.0008372493321076035,
-0.001140928128734231,
0.03732302039861679,
-0.01772536337375641,
-0.010061172768473625,
-0.004332204815000296,
0.010316427797079086,
0.009518522769212723,
-0.006588784512132406,
0.015762213617563248,
-0.0020586876198649406,
-0.02518339641392231,
-0.042199861258268356,
-0.028732135891914368,
-0.020914196968078613,
0.000447429803898558,
0.025404049083590508,
0.055044613778591156,
-0.013156061992049217,
0.003004282247275114,
0.00005162728120922111,
-0.019819680601358414,
-0.03604511916637421,
0.0006306009599938989,
0.007267797365784645,
-0.02678803540766239,
-0.03431369736790657,
-0.039944808930158615,
0.053530316799879074,
0.02905629761517048,
0.011240704916417599,
-0.002243244322016835,
-0.03285645321011543,
0.034975793212652206,
-0.006661887280642986,
-0.04545861482620239,
-0.031873758882284164,
0.017884181812405586,
-0.023939933627843857,
0.00849107000976801,
-0.045463766902685165,
0.01951555721461773,
0.027675729244947433,
-0.024791322648525238,
-0.02899283729493618,
0.014730855822563171,
-0.035382770001888275,
0.0397232249379158,
0.019201401621103287,
-0.05215141549706459,
-0.026942692697048187,
-0.0019045318476855755,
0.003694543382152915,
-0.03394560143351555,
-0.004131820984184742,
-0.0497242696583271,
-0.023250900208950043,
0.0045960452407598495,
-0.00040375121170654893,
-0.023273278027772903,
0.03627622127532959,
-0.02177792601287365,
-0.009636443108320236,
-0.038505490869283676,
0.03936319798231125,
-0.024169355630874634,
0.002767094410955906,
-0.02236774004995823,
-0.00004435995651874691,
-0.04016254469752312,
-0.006835997570306063,
-0.029032204300165176,
0.005550142377614975,
0.03785063326358795,
0.025854147970676422,
0.01732410304248333,
0.010399632155895233,
0.006635715253651142,
0.00162134796846658,
0.07350323349237442,
-0.01444842480123043,
-0.018953891471028328,
0.029457958415150642,
-0.05455215275287628,
-0.03210332244634628,
0.032244160771369934,
0.01550434809178114,
0.0641821101307869,
0.015376434661448002,
-0.01842467114329338,
-0.012736097909510136,
0.09428946673870087,
-0.05314554274082184,
-0.009215934202075005,
-0.008174867369234562,
-0.03237893432378769,
-0.018850743770599365,
-0.0005801498191431165,
0.009251512587070465,
-0.03197626397013664,
0.025851208716630936,
0.011816832236945629,
0.02158287912607193,
-0.04410572722554207,
0.0024135783314704895,
-0.001469722599722445,
0.02167462185025215,
-0.002944511827081442,
0.025263803079724312,
0.0038339493330568075,
0.011130326427519321,
0.056637953966856,
-0.0044476548209786415,
0.02120046876370907,
-0.025623207911849022,
-0.009790509007871151,
-0.09662877023220062,
-0.012275210581719875,
-0.006627507507801056,
0.011956465430557728,
0.056148018687963486,
-0.05763012543320656,
0.012225057929754257,
0.023823868483304977,
-0.047261592000722885,
0.031079616397619247,
-0.05550677701830864,
-0.024061618372797966,
-0.029782094061374664,
-0.04673844575881958,
0.027060354128479958,
0.054655760526657104,
0.01848258450627327,
0.005091778002679348,
-0.007173121441155672,
-0.007870876230299473,
-0.027480365708470345,
0.0012506745988503098,
0.03726474568247795,
0.024019578471779823,
0.004146346356719732,
0.019155370071530342,
0.009023962542414665,
0.009196965955197811,
-0.030649736523628235,
0.043023742735385895,
-0.027226585894823074,
0.027251409366726875,
-0.03055923990905285,
0.010913914069533348,
-0.013319259509444237,
0.051479119807481766,
0.02137507125735283,
-0.016278306022286415,
0.010338216088712215,
0.010967932641506195,
-0.02258279360830784,
0.02102353796362877,
-0.026880785822868347,
0.002014488447457552,
0.02947799116373062,
-0.022998549044132233,
-0.04870222881436348,
0.03690461069345474,
0.007417242042720318,
-0.005984122399240732,
-0.005041095428168774,
-0.008909589610993862,
0.027357080951333046,
-0.05830066278576851,
-0.000847629620693624,
-0.011601017788052559,
-0.011639977805316448,
0.05164286494255066,
-0.006303968373686075,
-0.02308855578303337,
0.013994243927299976,
-0.02148503065109253,
0.01607797108590603,
-0.007005095481872559,
-0.0015319915255531669,
-0.021411413326859474,
-0.04181281104683876,
-0.02362668514251709,
-0.028437256813049316,
0.008903425186872482,
-0.013597247190773487,
-0.03576793149113655,
-0.014590962789952755,
0.030270444229245186,
0.019885584712028503,
-0.004036440514028072,
-0.016441388055682182,
-0.0018739914521574974,
-0.01105450838804245,
-0.07128193229436874,
0.016560891643166542,
0.014888230711221695,
-0.017994262278079987,
-0.021387316286563873,
0.005161832552403212,
-0.01708339713513851,
-0.0320974625647068,
0.05100046843290329,
-0.018807098269462585,
-0.008655671961605549,
0.017102127894759178,
0.00815458595752716,
-0.008152684196829796,
-0.05365719273686409,
-0.003840074874460697,
-0.023161858320236206,
-0.03455279767513275,
-0.016468729823827744,
-0.00850591715425253,
0.020743923261761665,
-0.022400900721549988,
-0.029710877686738968,
-0.0022476166486740112,
-0.015645967796444893,
0.025694841518998146,
-0.060182150453329086,
0.03391857072710991,
0.01433521043509245,
0.02333562634885311,
0.041546858847141266,
-0.020259208977222443,
0.023138385266065598,
0.0068883271887898445,
-0.005059233400970697,
-0.010289110243320465,
0.014392253011465073,
-0.07431413978338242,
-0.030583474785089493,
-0.03062194585800171,
-0.03017481043934822,
0.0014050555182620883,
-0.07779984921216965,
-0.0259415153414011,
0.03244493156671524,
-0.010200191289186478,
-0.007069314364343882,
0.017595091834664345,
0.05123882740736008,
0.06331782042980194,
0.014189807698130608,
0.03727257251739502,
-0.019060228019952774,
-0.000350995542248711,
0.010468573309481144,
0.01555008627474308,
-0.00012511509703472257,
0.022810081019997597,
-0.007147167343646288,
0.05793248489499092,
-0.027475697919726372,
0.024926912039518356,
-0.013033908791840076,
0.03119695372879505,
0.030054563656449318,
-0.03737999498844147,
0.0199163518846035,
-0.02878100797533989,
0.017354782670736313,
0.01312513742595911,
-0.010504288598895073,
0.06934395432472229,
-0.05570322647690773,
0.0165567584335804,
-0.02987457439303398,
-0.00068266736343503,
-0.009449897333979607,
0.023408135399222374,
0.005785515531897545,
0.01471608504652977,
-0.02568584494292736,
-0.004861637484282255,
0.00223556743003428,
-0.020707065239548683,
0.05261734500527382,
-0.007480185013264418,
0.013603806495666504,
0.00984797440469265,
0.01852037012577057,
-0.029515227302908897,
-0.022767994552850723,
-0.04017363116145134,
-0.023584796115756035,
0.026120079681277275,
0.051897790282964706,
0.01309380866587162,
-0.05867328122258186,
-0.0010780028533190489,
0.019686562940478325,
0.038908544927835464,
-0.058605462312698364,
-0.05616968125104904,
-0.022451864555478096,
0.039802875369787216,
0.028170110657811165,
-0.013771146535873413
] |
<p>What is the Quantum Boltzmann equation and what does it describe? I think it describes the propagation of electrons and photons but I am not sure.</p>
| 8,465 |
[
-0.019979257136583328,
-0.021924160420894623,
-0.0006836586981080472,
-0.07032463699579239,
0.028022319078445435,
-0.0018309717997908592,
-0.014749420806765556,
-0.005880394019186497,
-0.0024430155754089355,
-0.01844741404056549,
0.05762244015932083,
0.060964860022068024,
0.05808380991220474,
0.00646002683788538,
0.00756000867113471,
-0.0005865981802344322,
0.01616508699953556,
-0.0020053121261298656,
-0.0005708129028789699,
-0.034644175320863724,
-0.0045235613361001015,
0.030590778216719627,
0.02313261479139328,
0.010606205090880394,
-0.006738642696291208,
0.03164347633719444,
0.0182795412838459,
0.0031164491083472967,
0.04590388387441635,
0.026223326101899147,
-0.012956195510923862,
-0.024059588089585304,
0.020973484963178635,
0.006862172391265631,
0.005147532559931278,
0.004844853188842535,
-0.024882197380065918,
-0.05384240299463272,
-0.02680915966629982,
-0.017219360917806625,
-0.04625779762864113,
-0.021639946848154068,
0.01058190781623125,
0.028893623501062393,
-0.04628811776638031,
0.010666955262422562,
0.006772782653570175,
-0.012358308769762516,
0.03804564103484154,
-0.08537521213293076,
0.05371931567788124,
-0.0014550270279869437,
0.05572539567947388,
0.025578869506716728,
-0.0150729576125741,
0.020485788583755493,
0.09133224189281464,
0.07820214331150055,
0.000496769673191011,
-0.04565849155187607,
0.009163309819996357,
-0.0016629493329674006,
0.027124889194965363,
-0.00804518349468708,
-0.003511528018862009,
0.06477120518684387,
0.025002039968967438,
-0.06209492310881615,
0.0052009341306984425,
0.013548231683671474,
0.023951642215251923,
0.0034309851471334696,
0.07645656913518906,
0.0005910132895223796,
0.02943146787583828,
-0.014225991442799568,
0.02870597504079342,
0.012288427911698818,
0.019139956682920456,
0.04646134003996849,
-0.030654296278953552,
0.0008371409494429827,
0.008185455575585365,
-0.017776446416974068,
-0.0311274416744709,
-0.007058813236653805,
0.1057954952120781,
0.0030744688119739294,
-0.01361300703138113,
0.012262433767318726,
-0.019818078726530075,
0.05104593560099602,
0.030180426314473152,
-0.01581905037164688,
0.015048029832541943,
0.024518799036741257,
0.01481303758919239,
0.04642751067876816,
0.01707025244832039,
-0.0251234732568264,
0.041588060557842255,
-0.008612924255430698,
0.0018992897821590304,
0.0640547126531601,
0.002176901325583458,
-0.014993736520409584,
-0.046047475188970566,
-0.0037228004075586796,
-0.03938216716051102,
0.012684189714491367,
-0.047070134431123734,
0.0067684645764529705,
-0.007203460205346346,
0.010512923821806908,
-0.011091851629316807,
-0.026417259126901627,
0.008739064447581768,
-0.01976643316447735,
0.03834884241223335,
0.074903205037117,
0.020079810172319412,
-0.03563845530152321,
0.020767981186509132,
-0.015292889438569546,
-0.04072585329413414,
0.020669808611273766,
0.02067839540541172,
-0.013350223191082478,
-0.03648209944367409,
0.025019172579050064,
-0.03746078163385391,
-0.03569561243057251,
-0.002306155161932111,
0.008070135489106178,
0.022680554538965225,
-0.055802732706069946,
-0.11190441250801086,
-0.07550521939992905,
0.03876053914427757,
-0.014828107319772243,
-0.012870723381638527,
-0.06970751285552979,
0.03063717484474182,
0.03708431497216225,
0.08363749831914902,
-0.01491543184965849,
-0.00395892234519124,
-0.03383724391460419,
0.008128968067467213,
-0.02038639411330223,
-0.03528358414769173,
0.0001402231864631176,
0.007984809577465057,
-0.0014231738168746233,
0.036974743008613586,
-0.06400448083877563,
0.019947096705436707,
0.04220808297395706,
-0.0188242606818676,
-0.03151819482445717,
0.0655752494931221,
-0.038727257400751114,
-0.020680757239460945,
0.013849436305463314,
-0.015100313350558281,
-0.0440652072429657,
0.04575280472636223,
0.02044736221432686,
0.01357106864452362,
0.05744767561554909,
0.010154154151678085,
0.009799046441912651,
0.01729164645075798,
0.017908215522766113,
0.0133743304759264,
-0.03864932060241699,
-0.013306296430528164,
-0.007900731638073921,
-0.01665632426738739,
0.003793547162786126,
-0.05054516717791557,
-0.028058921918272972,
0.010920295491814613,
0.017423035576939583,
-0.014914685860276222,
0.014464244246482849,
-0.0007099876529537141,
0.012357497587800026,
-0.01564072258770466,
-0.024449210613965988,
-0.02464400604367256,
-0.048678815364837646,
0.021394291892647743,
-0.021717138588428497,
0.017767006531357765,
0.01883416622877121,
0.041203293949365616,
0.013161205686628819,
-0.03142010420560837,
-0.029391949996352196,
-0.021289601922035217,
0.03002547100186348,
-0.024177802726626396,
0.002621451625600457,
0.028081368654966354,
0.04860718548297882,
0.03650691732764244,
0.006540962494909763,
0.03893968462944031,
-0.015044650994241238,
-0.00613747863098979,
-0.011412207968533039,
-0.0009454713435843587,
0.04086339473724365,
-0.014868787489831448,
-0.008777028881013393,
0.02228674106299877,
-0.040079452097415924,
-0.0067710839211940765,
0.003751847892999649,
-0.03124970756471157,
0.057695422321558,
0.022831832990050316,
0.027477867901325226,
-0.02987278439104557,
0.0417172834277153,
0.0032043750397861004,
-0.013505296781659126,
0.01583166792988777,
-0.03249810263514519,
-0.008920799009501934,
0.019882431253790855,
0.04539849981665611,
0.010339152999222279,
-0.013305864296853542,
0.020829183980822563,
0.008987043984234333,
0.013165874406695366,
0.03316792473196983,
0.02569763734936714,
-0.04687533527612686,
-0.0011501092230901122,
0.017234673723578453,
-0.02061423473060131,
-0.004449664149433374,
-0.008396366611123085,
0.03652810677886009,
0.010929374024271965,
0.042139988392591476,
-0.028272343799471855,
-0.05844685435295105,
0.03579207882285118,
0.0008965159067884088,
0.008810321800410748,
-0.004428875166922808,
-0.05325152724981308,
0.034932829439640045,
-0.022028829902410507,
0.01997789926826954,
-0.0018735910998657346,
-0.004406137857586145,
0.023250563070178032,
-0.003916681278496981,
-0.048216454684734344,
0.02126295678317547,
0.004321623593568802,
-0.009337123483419418,
-0.00514163076877594,
0.030612999573349953,
-0.04553089290857315,
0.01568204164505005,
-0.016228212043642998,
-0.009228589944541454,
-0.01625088043510914,
-0.025815511122345924,
0.010250164195895195,
0.014401312917470932,
0.036052633076906204,
-0.03831883519887924,
-0.08841823041439056,
-0.0012567895464599133,
-0.032554056495428085,
0.02832503616809845,
0.0179086085408926,
-0.019987424835562706,
0.028971605002880096,
-0.035597555339336395,
-0.06515496969223022,
0.04420360550284386,
-0.042794086039066315,
0.0015349102905020118,
0.022409887984395027,
-0.02576068788766861,
-0.027407733723521233,
0.002238689223304391,
-0.008160877972841263,
0.011109936982393265,
-0.029054000973701477,
0.01740843430161476,
0.05595676973462105,
-0.05006406828761101,
-0.015742013230919838,
0.0033452920615673065,
-0.029516205191612244,
-0.07254871726036072,
-0.017984019592404366,
0.006562604568898678,
0.04718148708343506,
-0.02183496206998825,
0.030611561611294746,
0.03949262946844101,
-0.06988932192325592,
-0.009903575293719769,
-0.03862937167286873,
-0.04875236004590988,
0.06288986653089523,
-0.01946929842233658,
0.03612079471349716,
-0.01895243674516678,
-0.029885394498705864,
0.06102132797241211,
0.011491131037473679,
-0.01820414885878563,
-0.0048287734389305115,
-0.012685304507613182,
-0.02522832341492176,
-0.03824063390493393,
0.022457145154476166,
0.007517809979617596,
-0.012130591087043285,
0.007505331188440323,
0.02061552181839943,
0.043285880237817764,
0.04637178033590317,
-0.0010146668646484613,
-0.029458854347467422,
0.011319630779325962,
-0.007325722835958004,
-0.002631879411637783,
0.03305104747414589,
0.016598396003246307,
-0.05096657946705818,
0.03106370009481907,
0.03191816806793213,
0.022457364946603775,
0.010090146213769913,
-0.029794976115226746,
0.04370438680052757,
0.02120753936469555,
0.004872488789260387,
-0.051048487424850464,
0.03728529065847397,
-0.045094091445207596,
-0.014649614691734314,
0.030696885660290718,
0.030770881101489067,
0.012710889801383018,
-0.010944148525595665,
0.026461154222488403,
0.011940684169530869,
0.048800598829984665,
-0.050054654479026794,
-0.02620617114007473,
0.02310062386095524,
-0.0190802663564682,
0.010159829631447792,
-0.0047353338450193405,
0.00359554891474545,
0.026571471244096756,
0.03341282531619072,
0.02632920816540718,
0.0028316995594650507,
-0.02723294496536255,
-0.03272870555520058,
-0.025593509897589684,
0.02199631743133068,
0.00331372139044106,
0.03587167710065842,
0.025634046643972397,
0.0842052772641182,
0.009413594380021095,
0.01822926662862301,
0.04383052513003349,
0.007432297337800264,
-0.08441580832004547,
-0.0015666455728933215,
-0.03533455729484558,
-0.032111022621393204,
-0.020288288593292236,
-0.0038932396564632654,
-0.022937554866075516,
-0.016238518059253693,
-0.05652548000216484,
-0.038315415382385254,
-0.012512710876762867,
-0.04036211222410202,
0.004473356995731592,
-0.011839617975056171,
-0.026509195566177368,
-0.014783831313252449,
0.001310968305915594,
0.04769382253289223,
0.002825650153681636,
0.021893542259931564,
0.06836594641208649,
-0.023809002712368965,
-0.0050186156295239925,
-0.009655410423874855,
-0.001272285240702331,
0.03158804401755333,
0.026641162112355232,
0.010482844896614552,
-0.008135366253554821,
-0.016793467104434967,
0.020657934248447418,
-0.0022925431840121746,
0.06513507664203644,
0.012020266614854336,
-0.012822833843529224,
-0.02228536643087864,
-0.036505457013845444,
0.0032973787747323513,
-0.02500680647790432,
0.03373897075653076,
-0.01275782659649849,
0.01323867216706276,
0.04575969651341438,
0.011969316750764847,
-0.0376950167119503,
0.006219788454473019,
0.0594363696873188,
0.008091052062809467,
-0.033177461475133896,
-0.025288807228207588,
0.010023773647844791,
-0.02345472201704979,
0.0030010982882231474,
-0.0016207888256758451,
0.001762382802553475,
-0.014456884935498238,
0.02528679370880127,
0.017799533903598785,
0.02339908853173256,
-0.018087508156895638,
-0.03499565273523331,
-0.003709368174895644,
-0.0067528970539569855,
-0.0059139309450984,
-0.003471218980848789,
-0.010130845010280609,
0.027990229427814484,
0.004547335673123598,
-0.01632797345519066,
-0.015885179862380028,
-0.05222450941801071,
0.0036297510378062725,
0.047835614532232285,
0.022312577813863754,
0.0006778723327443004,
-0.013344254344701767,
-0.06741277873516083,
-0.00918678566813469,
0.04363974928855896,
-0.018863093107938766,
0.04002534598112106,
-0.007442893926054239,
-0.0029928754083812237,
-0.013407590799033642,
-0.014704803004860878,
0.0247143916785717,
0.017229175195097923,
0.013772241771221161,
-0.01660207472741604,
-0.012347042560577393,
0.01828799955546856,
-0.014885925687849522,
0.015107850544154644,
0.0064767710864543915,
0.06387010961771011,
-0.0029874921310693026,
-0.017706720158457756,
0.009437787346541882,
0.009808403439819813,
-0.024697760120034218,
-0.09659057855606079,
-0.009118788875639439,
0.016211986541748047,
0.00656490633264184,
0.03376919776201248,
-0.03708287701010704,
-0.03867439180612564,
0.0017603066517040133,
-0.008091236464679241,
-0.01412288285791874,
-0.014167812652885914,
-0.02580401860177517,
0.04114872217178345,
0.007474768906831741,
-0.01663355901837349,
0.06660230457782745,
0.035467248409986496,
-0.055385176092386246,
-0.0021219030022621155,
-0.043346140533685684,
0.0531952790915966,
0.00284203770570457,
-0.007240061182528734,
-0.05065068230032921,
0.016256021335721016,
-0.023601070046424866,
0.04280417412519455,
-0.045282989740371704,
0.008204241283237934,
-0.006445765029639006,
-0.03857377544045448,
-0.012556827627122402,
0.015170513652265072,
-0.0025566837284713984,
-0.015047484077513218,
-0.03206753730773926,
0.0041973283514380455,
0.008297902531921864,
-0.040431637316942215,
0.041857413947582245,
0.020978884771466255,
0.0036787893623113632,
0.017565445974469185,
-0.0038046722766011953,
0.00003734390338649973,
-0.04533309489488602,
-0.03626938909292221,
0.023606132715940475,
-0.052939657121896744,
0.06035607308149338,
-0.0020184668246656656,
-0.016592901200056076,
0.029616788029670715,
-0.06199463829398155,
-0.0299563929438591,
0.00791080854833126,
-0.016678128391504288,
0.04838813096284866,
-0.020297111943364143,
0.019734427332878113,
-0.025260239839553833,
0.0029207125771790743,
-0.09098442643880844,
-0.03832829371094704,
0.01430675107985735,
-0.028226373717188835,
-0.00763325160369277,
-0.049142468720674515,
-0.003958527464419603,
-0.02604912966489792,
-0.03851258009672165,
0.04125339165329933,
0.05601012706756592,
-0.005908704362809658,
-0.0023665328044444323,
0.0043554361909627914,
-0.000793467101175338,
0.003474829951301217,
0.02868076227605343,
-0.0372038409113884,
-0.010873891413211823,
-0.02840535156428814,
-0.0024291113950312138,
0.041714172810316086,
0.06035620719194412,
-0.022960377857089043,
-0.008657296188175678,
-0.01144648902118206,
0.00921853631734848,
0.020646290853619576,
-0.04544798284769058,
0.019632481038570404,
0.014514562673866749,
0.029591571539640427,
-0.028103219345211983,
-0.04225178062915802,
0.030992884188890457,
-0.0017979618860408664,
0.05724623426795006,
-0.01781264692544937,
-0.031405624002218246,
-0.02746032364666462,
-0.029695745557546616,
0.03744593635201454,
-0.01490771770477295,
0.012795250862836838,
0.013567548245191574,
0.05813705176115036,
0.013029889203608036,
0.014650871977210045,
0.02144249528646469,
-0.022482283413410187,
0.03351786360144615,
-0.02445850893855095,
-0.005693077575415373,
0.03075007162988186,
0.018739378079771996,
-0.011961126700043678,
-0.04108615592122078,
-0.04429900273680687,
-0.018559293821454048,
0.07225064933300018,
-0.035976558923721313,
0.04032782092690468,
0.0072057414799928665,
-0.007616913877427578,
0.011171301826834679,
-0.024744650349020958,
-0.0036588425282388926,
0.03634698688983917,
0.0024374802596867085,
0.04770064353942871,
-0.014531750231981277,
0.024189194664359093,
0.012254180386662483,
0.07522544264793396,
-0.004530821926891804,
0.021112727001309395,
0.007746782619506121,
0.006381440907716751,
0.026280729100108147,
0.034468382596969604,
-0.05241595208644867,
0.05029330402612686,
-0.03961089998483658,
0.025034841150045395,
-0.016377417370676994,
-0.023894911631941795,
0.048874374479055405,
-0.00886073149740696,
-0.03526381030678749,
-0.014230535365641117,
0.013591393828392029,
-0.03140101581811905,
0.03928802162408829,
-0.01569346711039543,
0.020915968343615532,
-0.0028150160796940327,
0.03875923529267311,
0.020828573033213615,
-0.004709204193204641,
-0.010468610562384129,
-0.0019730895292013884,
-0.040772613137960434,
-0.004195906687527895,
-0.03315401449799538,
-0.04448070749640465,
0.020308921113610268,
0.030088044703006744,
-0.024344930425286293,
-0.0057882084511220455,
-0.026280125603079796,
0.04767405614256859,
-0.005734371021389961,
0.011674306355416775,
-0.013495109044015408,
0.057887107133865356,
-0.020665129646658897,
0.002807432319968939,
-0.022807611152529716,
0.03080681897699833,
0.1033768355846405,
0.0216887928545475,
0.037386540323495865,
-0.07527036219835281,
0.0012194477021694183,
-0.015366671606898308,
0.024723563343286514,
-0.007814787328243256,
0.01330571435391903,
-0.01999148540198803,
0.04328899085521698,
0.019123956561088562,
0.04481833428144455,
0.02388191781938076,
0.018915681168437004,
0.049187999218702316,
-0.051828544586896896,
-0.056185636669397354,
0.025531215593218803,
-0.005534448195248842,
-0.0047382572665810585,
0.040317416191101074,
-0.05102921277284622,
0.009418848901987076,
-0.04817559942603111,
-0.008892240934073925,
-0.03867620602250099,
-0.03571973741054535,
0.02567015029489994,
0.0056636822409927845,
-0.05629519745707512,
-0.0028183129616081715,
-0.01489670854061842,
-0.03260227292776108,
-0.005420590750873089,
0.0037486765068024397,
0.04375141113996506,
-0.02593926154077053,
0.03987791761755943,
0.00743220467120409,
0.02773658186197281,
0.014226242899894714,
0.002236969769001007,
0.029794538393616676,
-0.017522016540169716,
0.010444298386573792,
-0.02204267680644989,
0.01834106259047985,
-0.03277430683374405,
0.014920186251401901,
0.002589232288300991,
0.016852140426635742,
0.019961340352892876,
-0.05147562921047211,
-0.026160376146435738,
0.006960754282772541,
0.04300130903720856,
-0.033957868814468384,
-0.008133414201438427,
-0.05998309701681137,
0.02065269462764263,
0.0023814504966139793,
0.02199549600481987,
-0.009131005965173244,
-0.0022874579299241304,
0.01750078611075878,
-0.0061054350808262825,
0.000936057127546519,
-0.06009026989340782,
-0.024239370599389076,
-0.03354742005467415,
-0.017742929980158806,
-0.055933889001607895,
-0.062352489680051804,
0.05360336974263191,
0.024509266018867493,
0.04708775505423546,
-0.008748172782361507,
-0.007988514378666878,
-0.011292611248791218,
-0.08795098960399628,
0.032300326973199844,
-0.00696039292961359,
-0.014554503373801708,
-0.002248693723231554,
-0.008678357116878033,
0.044258225709199905,
0.052337344735860825,
-0.03694799914956093,
0.026628628373146057,
-0.00950300507247448,
-0.01325276680290699,
0.05122772231698036,
-0.02084481157362461,
0.008909766562283039,
0.030677706003189087,
-0.011429338715970516,
-0.020625039935112,
-0.019421568140387535,
0.025841375812888145,
0.02586999163031578,
0.00650194613263011,
0.009978778660297394,
0.02012927271425724,
-0.06084943190217018,
0.014604349620640278,
-0.0010001945775002241,
-0.01597471348941326,
0.004312466364353895,
0.012606347911059856,
0.02406211942434311,
-0.012108932249248028,
0.0005235578864812851,
-0.04565006494522095,
-0.018543869256973267,
0.013590754941105843,
0.021515442058444023,
-0.04463814198970795,
0.019129035994410515,
-0.0012345151044428349,
0.03740508109331131,
-0.04489610344171524,
-0.01134643517434597,
-0.027715738862752914,
0.043858498334884644,
-0.012041343376040459,
-0.006308951880782843,
-0.004138710908591747,
0.012218932621181011,
-0.0030183657072484493,
0.002128120744600892,
0.03135686367750168,
0.03002144768834114,
0.0197403896600008,
0.01648196578025818,
0.03752517327666283,
-0.008632602170109749,
0.04928398132324219,
-0.016031935811042786,
-0.005688662175089121,
0.03794464096426964,
-0.024135135114192963,
-0.04222928732633591,
0.025701172649860382,
-0.0015575246652588248,
0.015011022798717022,
0.05023052543401718,
-0.024731915444135666,
-0.029769310727715492,
0.06592103093862534,
-0.034396808594465256,
-0.02127879299223423,
-0.01585346646606922,
-0.05663631856441498,
-0.003457374172285199,
-0.019667649641633034,
-0.010085091926157475,
0.003010967280715704,
-0.007346581667661667,
0.04298516362905502,
0.04615160822868347,
-0.01855500414967537,
0.008907093666493893,
0.03880586475133896,
-0.010993625037372112,
0.013189238496124744,
0.04815487563610077,
-0.003938932437449694,
0.007461158093065023,
0.07259231060743332,
-0.018132269382476807,
0.047781605273485184,
0.010028606280684471,
0.009315511211752892,
-0.10638879984617233,
0.01854170300066471,
-0.006045958958566189,
-0.010446337051689625,
0.017568765208125114,
-0.04231790825724602,
0.03941354155540466,
0.04827887564897537,
-0.052859753370285034,
0.016012931242585182,
-0.0184797290712595,
-0.014375054277479649,
-0.01898069866001606,
0.03829639405012131,
0.002553715603426099,
0.06760884076356888,
0.01092508714646101,
0.03385751321911812,
0.029145196080207825,
0.01858452521264553,
-0.0004334797849878669,
-0.02393966168165207,
-0.004070422146469355,
0.009820808656513691,
-0.021785393357276917,
0.017322422936558723,
0.052948132157325745,
-0.025270629674196243,
-0.0008577420376241207,
0.0428464449942112,
0.020349683240056038,
0.03549237549304962,
-0.023828167468309402,
0.01815899834036827,
0.04617464542388916,
0.014366180635988712,
0.027890412136912346,
-0.02713855728507042,
0.03086751513183117,
0.025428438559174538,
0.01587679050862789,
0.042977821081876755,
-0.009192350320518017,
0.00580942677333951,
0.014344444498419762,
-0.029230546206235886,
-0.052904270589351654,
0.050961680710315704,
0.029002271592617035,
-0.00970113929361105,
-0.02596697025001049,
0.004739089403301477,
0.006375358905643225,
-0.016473986208438873,
0.012553093954920769,
-0.054449018090963364,
-0.006577222608029842,
0.026879938319325447,
-0.002741167787462473,
-0.01926131173968315,
0.02827855572104454,
-0.007708755787461996,
-0.029531672596931458,
0.012591909617185593,
0.007712755352258682,
0.016978364437818527,
-0.06714828312397003,
-0.017088627442717552,
0.022284582257270813,
0.0017720639007166028,
0.007480524480342865,
-0.04106349125504494,
-0.021634573116898537,
-0.000056944078096421435,
0.013314769603312016,
0.04512542858719826,
-0.002977358177304268,
-0.03653952106833458,
-0.028653696179389954,
-0.040612295269966125,
0.04198738932609558,
-0.030136017128825188,
-0.011179751716554165,
-0.04909829422831535,
-0.05911693349480629,
-0.007928849197924137,
0.024575838819146156,
0.09002010524272919,
0.003093267558142543,
-0.03640950098633766,
-0.01679977960884571,
0.006181646138429642,
0.007938397116959095,
-0.036684297025203705,
-0.015520334243774414,
-0.021107343956828117,
-0.00988458190113306,
-0.048802878707647324,
-0.006414825562387705,
-0.036096975207328796,
0.030476786196231842,
0.011914017610251904,
-0.017778165638446808,
0.03426551818847656,
-0.02917935885488987,
-0.05214853212237358,
0.028996983543038368,
0.030274298042058945,
-0.03799286484718323,
0.053087860345840454,
-0.05276509374380112,
0.015118442475795746,
0.04859883338212967,
-0.0005597511189989746,
-0.0456727109849453,
0.016034532338380814,
-0.01720344088971615,
-0.006590703502297401,
0.010883498936891556,
-0.013355927541851997,
0.05290067568421364,
-0.041269708424806595,
-0.006307405419647694,
0.033754825592041016,
-0.07423713803291321,
0.012937306426465511,
0.06121770292520523,
0.021703576669096947,
0.05973230302333832,
-0.014126143418252468,
0.0015426718164235353,
0.016990480944514275,
0.0006488041835837066,
-0.03111414983868599,
0.05788853019475937,
0.0421355701982975,
-0.0184769444167614,
0.025006111711263657,
0.00227714073844254,
-0.026573337614536285,
0.02319294400513172,
0.024310313165187836,
0.01254941988736391,
-0.03628472611308098,
-0.028014715760946274,
0.0007293762173503637,
-0.031614746898412704,
0.02035876177251339,
0.04192996025085449,
-0.027914656326174736,
0.08827272802591324,
-0.02675003744661808,
0.04432128742337227,
-0.02219855599105358,
0.03267920762300491,
-0.026982802897691727,
0.016795147210359573,
0.003668875666335225,
0.054277241230010986,
-0.0246978048235178,
-0.009627161547541618,
-0.00825303141027689,
-0.00460822181776166,
-0.009820913895964622,
-0.04430672526359558,
0.014350829645991325,
0.018706386908888817,
-0.003987976349890232,
-0.009516657330095768,
-0.0053972722962498665,
0.015894629061222076,
0.012446826323866844,
0.017595985904335976,
0.020418277010321617,
-0.007758708205074072,
0.0007723580929450691,
0.01734519563615322,
-0.013267258182168007,
0.03136560693383217,
-0.0780787542462349,
0.009438733570277691,
-0.01650458388030529,
0.03370111063122749,
-0.024882417172193527,
-0.0022271822672337294
] |
<p>Why will the resulting force lines of two positive point charges be like this:</p>
<p><img src="http://i.stack.imgur.com/3jnkx.jpg" alt="enter image description here"></p>
<p>I would expect this:
<img src="http://i.stack.imgur.com/KIltz.jpg" alt="enter image description here"></p>
| 8,466 |
[
-0.011015873402357101,
0.03701142594218254,
-0.01747981272637844,
0.01843693107366562,
0.007661452516913414,
0.0033535691909492016,
-0.006029085721820593,
-0.020584415644407272,
0.013107426464557648,
0.002974908798933029,
0.06658602505922318,
0.012233980000019073,
0.06491497904062271,
0.013476064428687096,
-0.00589884864166379,
-0.01084323599934578,
0.004014176316559315,
-0.007457158528268337,
0.00825434923171997,
-0.02574247494339943,
-0.017521604895591736,
0.005117634776979685,
0.01966133527457714,
0.02230156399309635,
-0.017203563824295998,
0.02336706593632698,
0.05781806260347366,
0.006225339602679014,
0.03937061131000519,
0.07621994614601135,
-0.029457394033670425,
-0.04155104234814644,
0.011852280236780643,
0.028422879055142403,
0.024180693551898003,
0.0015358485979959369,
-0.03357979282736778,
-0.03734815865755081,
0.011301952414214611,
0.02176482602953911,
-0.015912840142846107,
-0.0023767189122736454,
-0.0041016871109604836,
0.044252388179302216,
-0.02604692056775093,
0.013423369266092777,
-0.009052110835909843,
-0.014326846227049828,
0.07637310773134232,
-0.05361208692193031,
0.07329025119543076,
0.027702193707227707,
0.06823621690273285,
0.026773901656270027,
0.006073711905628443,
-0.009912888519465923,
0.06300313770771027,
0.07755853235721588,
-0.010414792224764824,
-0.041628919541835785,
0.014708691276609898,
-0.03797914832830429,
-0.040272265672683716,
-0.007179773412644863,
-0.04386404529213905,
0.06889232248067856,
-0.021500572562217712,
-0.05374205484986305,
0.030594857409596443,
0.010792579501867294,
0.04078312963247299,
0.022257596254348755,
0.020413585007190704,
-0.07499436289072037,
-0.0015339412493631244,
-0.03184710070490837,
0.03817746043205261,
-0.011023820377886295,
0.02967563457787037,
0.0595446452498436,
-0.04748540371656418,
0.02692355401813984,
0.029441630467772484,
0.04230169951915741,
0.012060597538948059,
-0.04587329924106598,
0.04889563471078873,
-0.022898806259036064,
0.010583771392703056,
0.010925062000751495,
-0.0006301320972852409,
0.014766615815460682,
0.018880469724535942,
-0.003058079397305846,
-0.008370941504836082,
0.006203404627740383,
0.00006691523594781756,
0.047116369009017944,
0.03127434849739075,
0.0033356244675815105,
0.015766281634569168,
-0.016597220674157143,
0.002273614751175046,
0.04776071384549141,
-0.003558814525604248,
-0.022915353998541832,
-0.01796765625476837,
0.006966406479477882,
-0.009928031824529171,
-0.006100610364228487,
-0.014115797355771065,
-0.006540008820593357,
-0.009072395972907543,
-0.0008824863471090794,
0.003846855368465185,
-0.05017789825797081,
0.0233404990285635,
0.004524290096014738,
0.03633788973093033,
0.035048216581344604,
0.035841673612594604,
-0.027811460196971893,
0.021576642990112305,
-0.023106945678591728,
-0.05648306757211685,
-0.01592663675546646,
0.017501259222626686,
-0.0010727543849498034,
0.015036283060908318,
-0.003050626954063773,
-0.01871134340763092,
-0.005350457038730383,
0.00889887660741806,
0.04236983880400658,
0.036197856068611145,
-0.004409880377352238,
-0.0910908654332161,
-0.06326327472925186,
0.025877291336655617,
-0.04360034689307213,
0.03067151829600334,
-0.08463267982006073,
0.0015885384054854512,
0.012568664737045765,
0.0653170645236969,
-0.02693476900458336,
-0.019914766773581505,
0.006502541713416576,
0.05713389068841934,
0.015007703565061092,
0.01267305575311184,
0.022578289732336998,
-0.024892380461096764,
-0.04141974821686745,
-0.03602801263332367,
-0.05808698385953903,
0.029080744832754135,
0.012915581464767456,
-0.004359758459031582,
-0.02442425675690174,
0.028357241302728653,
-0.02999277040362358,
0.007740559987723827,
0.007653804495930672,
-0.003961279988288879,
-0.0201595239341259,
0.06995034217834473,
0.02356143482029438,
-0.01847936399281025,
0.08726412802934647,
-0.012980571947991848,
0.03328462690114975,
0.01766081713140011,
0.038167811930179596,
0.04092416912317276,
-0.028918597847223282,
-0.02746720425784588,
-0.05086003616452217,
0.008406984619796276,
0.013471266254782677,
-0.054352737963199615,
-0.06364178657531738,
-0.019498296082019806,
0.008994006551802158,
-0.0015641591744497418,
0.06741990894079208,
-0.030854936689138412,
-0.002744294935837388,
-0.034650884568691254,
-0.035883136093616486,
-0.035197824239730835,
-0.0797264575958252,
0.0590977780520916,
0.0005331702996045351,
-0.04578422009944916,
0.010352755896747112,
0.017912607640028,
0.021919311955571175,
-0.013247686438262463,
-0.021485740318894386,
-0.009018517099320889,
0.028798440471291542,
-0.0175453070551157,
-0.009857004508376122,
0.02995346486568451,
0.06268032640218735,
0.048699554055929184,
0.01992146670818329,
0.02472289837896824,
-0.03849199414253235,
0.0007462367648258805,
0.02296457812190056,
-0.031499262899160385,
0.0033403479028493166,
0.014726837165653706,
-0.016029927879571915,
-0.005386018194258213,
0.015941878780722618,
0.007969497703015804,
0.02695258893072605,
-0.0198142658919096,
0.0840541198849678,
0.06877182424068451,
0.00490317540243268,
-0.018177935853600502,
0.026010600849986076,
-0.0283969733864069,
0.020950758829712868,
-0.008895576000213623,
-0.013661684468388557,
-0.015832599252462387,
-0.0051588271744549274,
0.02247173711657524,
0.057311639189720154,
-0.027034588158130646,
0.0038308780640363693,
0.033469825983047485,
0.014086644165217876,
0.002911642426624894,
0.028366344049572945,
-0.01493374165147543,
-0.0343996062874794,
0.03639698401093483,
0.039372820407152176,
-0.026165734976530075,
0.0020435622427612543,
0.022239143028855324,
0.018094606697559357,
0.019324030727148056,
0.02406579814851284,
-0.03174815699458122,
0.04100734740495682,
-0.03750796616077423,
0.017169762402772903,
0.0357247032225132,
-0.017110539600253105,
0.0393545962870121,
-0.003855103859677911,
0.019800469279289246,
0.030562615022063255,
0.009133017621934414,
-0.005771765485405922,
-0.01896556094288826,
0.03727925568819046,
0.018524182960391045,
0.0018495303811505437,
-0.007072931621223688,
-0.04108262062072754,
0.01618625782430172,
-0.06407127529382706,
0.006595569662749767,
-0.02505837194621563,
-0.030715040862560272,
-0.0100477896630764,
-0.00008302633068524301,
0.01880059763789177,
0.023612070828676224,
0.05955406278371811,
-0.019015302881598473,
-0.010542281903326511,
-0.011698164977133274,
-0.04645627364516258,
0.03954305499792099,
-0.002081772545352578,
-0.006888961419463158,
0.00195711525157094,
-0.06596671044826508,
-0.02253706008195877,
0.05163099616765976,
0.0027609739918261766,
0.008360135369002819,
0.0077871596440672874,
-0.036515310406684875,
-0.020390097051858902,
-0.03300071880221367,
-0.02829873561859131,
0.04102494195103645,
0.008218872360885143,
-0.01091066189110279,
0.060169998556375504,
-0.016237763687968254,
-0.015860620886087418,
0.029611919075250626,
-0.048065535724163055,
-0.0157401654869318,
-0.0059639448300004005,
0.007546751294285059,
0.03190267086029053,
-0.018450681120157242,
-0.014405220746994019,
0.024405676871538162,
-0.03537493571639061,
0.01667662337422371,
-0.05611400678753853,
0.0020360364578664303,
0.008428394794464111,
-0.011929558590054512,
0.05354030430316925,
-0.022715825587511063,
-0.06155732646584511,
0.06835705786943436,
-0.004912304226309061,
-0.0256089735776186,
-0.026336699724197388,
-0.03936266899108887,
-0.04392842948436737,
-0.013898373581469059,
0.008645953610539436,
0.045023806393146515,
-0.02946101315319538,
0.023994503542780876,
0.024864044040441513,
0.03125310316681862,
0.01954159326851368,
-0.008468400686979294,
0.03210310637950897,
0.013860245235264301,
0.019650643691420555,
-0.031676389276981354,
0.06413014233112335,
0.014866995625197887,
-0.025271987542510033,
-0.015417885966598988,
0.024482151493430138,
0.02485722489655018,
0.017394915223121643,
-0.03568492829799652,
0.025937288999557495,
0.004441059660166502,
0.02357315458357334,
-0.03654767945408821,
0.03576691076159477,
0.01762484200298786,
-0.01213483139872551,
-0.03965814411640167,
0.024035198614001274,
0.06935624778270721,
-0.07546272873878479,
-0.017943423241376877,
0.042607709765434265,
0.035895973443984985,
-0.023926271125674248,
-0.03143857419490814,
0.011638974770903587,
-0.0006115064024925232,
0.046244099736213684,
-0.016553077846765518,
-0.026971088722348213,
0.03997623547911644,
0.010957248508930206,
0.03078801929950714,
0.017532827332615852,
-0.01883980818092823,
0.017826983705163002,
-0.07485732436180115,
-0.005207401234656572,
0.014686946757137775,
0.06136460229754448,
-0.0017025322886183858,
0.09897951036691666,
0.005475751589983702,
0.027774065732955933,
-0.006734611466526985,
0.025116143748164177,
-0.07842081040143967,
0.032134611159563065,
-0.020943939685821533,
-0.042531270533800125,
-0.0011586283799260855,
-0.037569619715213776,
-0.005487441550940275,
-0.04285614192485809,
-0.03092293255031109,
-0.002310733776539564,
-0.012140006758272648,
-0.045130424201488495,
-0.0039601740427315235,
-0.041422661393880844,
-0.01632624678313732,
-0.03190542757511139,
0.03270629793405533,
0.013458341360092163,
-0.044833503663539886,
0.022214142605662346,
0.03675173223018646,
-0.02245219796895981,
-0.01739209145307541,
-0.028292251750826836,
0.017505694180727005,
0.0389150008559227,
0.00715457322075963,
0.002919440157711506,
0.03379371389746666,
0.005132332444190979,
-0.027445033192634583,
-0.020951176062226295,
0.04481909051537514,
0.03564886376261711,
-0.022453738376498222,
-0.028679709881544113,
-0.05821697786450386,
-0.015324418433010578,
-0.002650476060807705,
0.07263780385255814,
0.0032924788538366556,
0.01894863322377205,
-0.004138120450079441,
0.014252834022045135,
0.016918092966079712,
0.033093467354774475,
0.042716845870018005,
0.05735073238611221,
-0.011667612940073013,
-0.07709213346242905,
0.010399919003248215,
-0.028534337878227234,
0.0002444364072289318,
0.017261501401662827,
0.011133020743727684,
-0.029266338795423508,
0.00446968013420701,
0.035750359296798706,
-0.004601346328854561,
-0.0008470638422295451,
0.04837653785943985,
-0.049897268414497375,
0.02033885009586811,
-0.02371056191623211,
0.016588430851697922,
0.03251207619905472,
0.015520642511546612,
0.0505736880004406,
0.003987203352153301,
-0.009799327701330185,
-0.08961646258831024,
-0.014233062043786049,
0.0321245938539505,
0.00554393045604229,
-0.022244859486818314,
-0.025438889861106873,
-0.03866257146000862,
-0.004918022081255913,
0.04764499515295029,
-0.04981399327516556,
0.03946150839328766,
0.012371287681162357,
0.0070398165844380856,
-0.016670197248458862,
-0.0330246165394783,
-0.07789716124534607,
0.01817409135401249,
0.003771935822442174,
0.03676296025514603,
-0.009337094612419605,
0.007123701274394989,
0.02819962240755558,
0.03504562750458717,
0.043829724192619324,
0.06534779071807861,
0.007669012062251568,
-0.02008209004998207,
-0.01244906336069107,
-0.001702474313788116,
-0.016164347529411316,
-0.06594422459602356,
0.0252983495593071,
-0.00922379083931446,
0.005906373728066683,
0.04870903491973877,
-0.040419574826955795,
-0.05904974788427353,
-0.005862354300916195,
-0.005230668466538191,
0.03766876831650734,
-0.011333916336297989,
-0.024375788867473602,
0.0023665225598961115,
0.04819400608539581,
-0.017080068588256836,
0.06872817128896713,
0.02682686597108841,
-0.04194588214159012,
-0.03771604225039482,
-0.019045904278755188,
0.028787314891815186,
-0.002023732289671898,
-0.010718276724219322,
-0.045363783836364746,
0.0401618592441082,
-0.04158523678779602,
0.01592755876481533,
-0.0045442585833370686,
0.006713465787470341,
-0.04093487933278084,
-0.030242862179875374,
0.005111235193908215,
0.01979413814842701,
0.015326305292546749,
0.023967089131474495,
0.007096843793988228,
0.014299522154033184,
0.01785433664917946,
-0.02083621732890606,
0.013350265100598335,
-0.00934823788702488,
-0.016347264871001244,
0.019134175032377243,
-0.018375340849161148,
0.004277673549950123,
0.01611342281103134,
-0.006829948630183935,
-0.0033128196373581886,
-0.08374237269163132,
0.031165068969130516,
-0.010444866493344307,
0.0059721022844314575,
0.030089348554611206,
-0.05061616376042366,
-0.033647771924734116,
0.021914443001151085,
-0.02397955022752285,
0.03347685560584068,
-0.03755103051662445,
0.05384194850921631,
0.020195843651890755,
0.017859559506177902,
-0.02894236333668232,
-0.06734009832143784,
0.01602296344935894,
-0.0010912531288340688,
-0.011992158368229866,
0.0011380708310753107,
-0.017126167193055153,
0.009553804062306881,
-0.02444034069776535,
-0.005681603215634823,
0.06467593461275101,
-0.056710321456193924,
-0.048505235463380814,
0.017986709251999855,
-0.024969398975372314,
0.03543476015329361,
0.010802960954606533,
-0.005170383024960756,
-0.0024472454097121954,
-0.04183254390954971,
-0.03437144681811333,
0.0036700591444969177,
0.0490327924489975,
-0.028618814423680305,
-0.03409670293331146,
-0.012528493069112301,
-0.01874672621488571,
0.04641837626695633,
-0.031594645231962204,
0.029928823933005333,
-0.0021912322845309973,
0.02840137667953968,
-0.01728423312306404,
-0.013758428394794464,
0.01830132305622101,
-0.00839904323220253,
0.003553984686732292,
-0.0016919247573241591,
0.003540206700563431,
-0.0424966923892498,
-0.03374626114964485,
0.011045504361391068,
0.008517960086464882,
0.01826483942568302,
-0.017359759658575058,
0.03438420593738556,
-0.04533577337861061,
-0.02699493244290352,
0.018406420946121216,
-0.0038298387080430984,
0.05265621095895767,
0.029881710186600685,
-0.02931358478963375,
0.033061180263757706,
-0.0015543855261057615,
-0.04354005306959152,
0.003364111064001918,
-0.025469910353422165,
0.031471122056245804,
0.07417350262403488,
-0.023978406563401222,
0.08511800318956375,
0.015737146139144897,
-0.021404409781098366,
0.023434894159436226,
-0.01813298836350441,
-0.012228420935571194,
-0.022540751844644547,
0.007807545829564333,
0.026498498395085335,
-0.03772621229290962,
0.00795833207666874,
0.004513931460678577,
0.022350551560521126,
0.010447732172906399,
-0.020544691011309624,
0.018740050494670868,
-0.013550951145589352,
0.012572814710438251,
-0.006190157029777765,
-0.03478299826383591,
0.048394765704870224,
-0.028988100588321686,
0.04279192164540291,
0.03969216346740723,
-0.023706618696451187,
0.05450456216931343,
-0.017866870388388634,
-0.03136332705616951,
-0.05617833137512207,
-0.034960366785526276,
-0.019844483584165573,
0.023702599108219147,
0.010888840071856976,
0.00003611782085499726,
-0.01908082887530327,
0.006626062095165253,
0.02431226149201393,
0.03414933383464813,
0.03652563318610191,
-0.01319633424282074,
-0.05386944115161896,
-0.014891787432134151,
-0.027255725115537643,
-0.043368685990571976,
0.025933528319001198,
-0.0229214858263731,
-0.04534587636590004,
0.0334651879966259,
-0.031129393726587296,
0.06474617123603821,
0.007819870486855507,
0.005623461678624153,
-0.04126622527837753,
0.0822526067495346,
-0.024542830884456635,
0.019505688920617104,
-0.034046053886413574,
-0.010127559304237366,
0.12264885008335114,
0.038523994386196136,
0.02510915696620941,
-0.07762394100427628,
0.018419522792100906,
-0.020105255767703056,
-0.00559637788683176,
0.001732021919451654,
0.02610917016863823,
-0.015903480350971222,
0.018039675429463387,
-0.0031707119196653366,
0.0235076155513525,
0.017886338755488396,
0.0040958640165627,
0.05565743148326874,
-0.010302836075425148,
-0.03563813492655754,
0.011040635406970978,
0.01170733105391264,
-0.029178131371736526,
0.02911483310163021,
-0.019200189039111137,
0.02203785814344883,
-0.04075760394334793,
-0.008688290603458881,
-0.027780314907431602,
-0.015823202207684517,
0.01616368629038334,
0.028027383610606194,
-0.04421430453658104,
0.01381891779601574,
0.02027917467057705,
-0.01743033155798912,
-0.038390349596738815,
0.05033133178949356,
0.006242102477699518,
-0.01596607081592083,
-0.001392808393575251,
0.01577424257993698,
0.010822185315191746,
0.004093433730304241,
0.005100979469716549,
0.014771683141589165,
-0.04873280227184296,
0.015894144773483276,
-0.03940587118268013,
0.031003857031464577,
-0.019732527434825897,
-0.01806907169520855,
-0.043078962713479996,
0.018363215029239655,
0.011315988376736641,
-0.06181681156158447,
-0.03553757071495056,
-0.02752738445997238,
0.02616802603006363,
-0.017733436077833176,
-0.02227730117738247,
-0.040487390011548996,
-0.00955735333263874,
-0.016947655007243156,
0.01484210416674614,
0.007358267437666655,
0.014678443782031536,
0.01850622333586216,
0.006643070373684168,
0.0776408389210701,
-0.018076548352837563,
0.0024559604935348034,
0.009749931283295155,
-0.012580313719809055,
-0.05676553398370743,
-0.01581629551947117,
0.003375224769115448,
0.06831870973110199,
0.04912707954645157,
-0.0019144113175570965,
-0.013755830936133862,
-0.024296339601278305,
-0.04599624499678612,
0.041571445763111115,
-0.0037885119672864676,
-0.01057094894349575,
-0.01312182191759348,
0.0008849219302646816,
-0.006035196594893932,
0.02876339480280876,
-0.000919314450584352,
0.011935492046177387,
0.013112838380038738,
0.018138984218239784,
0.002796877408400178,
-0.05361403524875641,
-0.0502457432448864,
0.028239015489816666,
-0.039950042963027954,
-0.049243226647377014,
0.022419815883040428,
0.014925247058272362,
0.014780432917177677,
0.016866475343704224,
0.019682997837662697,
0.03724052384495735,
-0.02686341665685177,
-0.01149996742606163,
0.03373153135180473,
0.0013427435187622905,
0.0076266261748969555,
0.006103374529629946,
-0.03366396576166153,
-0.021668540313839912,
0.027442405000329018,
-0.011756284162402153,
-0.006996199954301119,
0.02679704688489437,
0.050377339124679565,
-0.02886592037975788,
-0.03309481590986252,
-0.023740289732813835,
-0.00007387997902696952,
-0.022469712421298027,
-0.02438371628522873,
-0.0612543560564518,
-0.00327442423440516,
0.0004284414171706885,
0.00621336605399847,
-0.04584534093737602,
0.02998093143105507,
-0.018490077927708626,
0.007879866287112236,
0.04398614168167114,
0.03251045197248459,
-0.004494964610785246,
-0.027148084715008736,
0.02732737548649311,
-0.003572187153622508,
0.031175129115581512,
-0.03078463487327099,
-0.061366621404886246,
0.007654950488358736,
-0.040322598069906235,
-0.03926548734307289,
-0.012371787801384926,
-0.0003078657609876245,
0.027475319802761078,
0.004246283322572708,
-0.006338144186884165,
-0.0038563814014196396,
0.08905735611915588,
-0.014758690260350704,
0.004744797479361296,
-0.0059470562264323235,
-0.02232443168759346,
0.018697110936045647,
-0.013873348943889141,
-0.025251740589737892,
-0.008814695291221142,
0.03746337071061134,
0.007014621514827013,
0.014293409883975983,
-0.019567439332604408,
-0.029448799788951874,
-0.002600168576464057,
0.018829692155122757,
0.0311404000967741,
0.05986356735229492,
0.010797981172800064,
0.0017770588165149093,
0.020501380786299706,
-0.030463803559541702,
-0.014525932259857655,
0.0024391841143369675,
0.025305386632680893,
-0.06980841606855392,
-0.0401216596364975,
-0.009595215320587158,
-0.019177794456481934,
0.0013899074401706457,
-0.047337573021650314,
0.0042135645635426044,
0.0207940973341465,
-0.048542119562625885,
-0.017045961692929268,
-0.018729710951447487,
-0.018275998532772064,
-0.03051089495420456,
-0.01701861061155796,
0.011064646765589714,
0.03646522015333176,
0.014385382644832134,
0.04916554316878319,
0.027372388169169426,
-0.002016661688685417,
-0.014185034669935703,
-0.017502736300230026,
-0.029402118176221848,
0.029802804812788963,
-0.004077801946550608,
-0.017344480380415916,
0.05031257122755051,
-0.003218341153115034,
-0.0036529831122606993,
0.02205384336411953,
-0.0017874558689072728,
0.013892329297959805,
0.013863474130630493,
0.03987862914800644,
-0.0013876102166250348,
0.012608190067112446,
0.0053331577219069,
-0.03117307275533676,
-0.02427355758845806,
-0.011120609007775784,
-0.0029313303530216217,
0.006193360313773155,
-0.0042486186139285564,
0.02741319313645363,
0.038274429738521576,
-0.022438082844018936,
-0.009834553115069866,
0.04478609189391136,
-0.017597787082195282,
-0.002359624719247222,
-0.03263091668486595,
0.024841630831360817,
0.03103041835129261,
-0.03337126225233078,
0.0038567325100302696,
-0.03737722337245941,
0.010759992524981499,
0.042044829577207565,
-0.02557981014251709,
0.02260744571685791,
0.005218053236603737,
-0.0018515975680202246,
-0.005172333214432001,
-0.02440164051949978,
-0.017278308048844337,
0.003876795992255211,
-0.06753277778625488,
0.011529103852808475,
0.016542349010705948,
0.00714116683229804,
-0.002679265569895506,
-0.04488562420010567,
-0.055996134877204895,
0.027134958654642105,
0.024778861552476883,
0.024385914206504822,
0.008295857347548008,
-0.05667895823717117,
-0.02736443467438221,
-0.08033875375986099,
0.04195290803909302,
-0.0039050141349434853,
-0.05919661372900009,
-0.02693852223455906,
-0.039836734533309937,
-0.02416548691689968,
0.026060840114951134,
0.043323054909706116,
0.0008079276885837317,
-0.026617683470249176,
0.006485259160399437,
0.010061475448310375,
0.019742628559470177,
-0.05404951050877571,
-0.024053744971752167,
0.026668235659599304,
0.01067222561687231,
0.04370006173849106,
-0.0032266629859805107,
-0.008946641348302364,
0.04328517988324165,
0.02297288179397583,
-0.012712339870631695,
-0.002212559338659048,
-0.04457486793398857,
-0.02383692003786564,
0.0004662478168029338,
0.005664519965648651,
-0.008706704713404179,
0.07724244147539139,
-0.00644137617200613,
0.031269583851099014,
-0.00048786785919219255,
-0.02870551310479641,
-0.019147902727127075,
0.011057548224925995,
-0.03815360739827156,
0.018259447067975998,
-0.028750943019986153,
-0.015969470143318176,
0.024995768442749977,
-0.0720161646604538,
0.023976262658834457,
0.018020249903202057,
-0.032739683985710144,
-0.03575212135910988,
0.04031255468726158,
0.02441883645951748,
0.018710840493440628,
0.0014943686546757817,
0.03370162844657898,
0.015957828611135483,
-0.03659190610051155,
0.00044723591418005526,
0.013550994917750359,
0.04307079687714577,
0.022924812510609627,
-0.0017854771576821804,
0.059316158294677734,
0.003697586478665471,
0.025140950456261635,
0.013158518821001053,
0.02915254607796669,
0.003533803392201662,
-0.015887262299656868,
0.008404274471104145,
-0.03393344208598137,
0.047634307295084,
0.012034231796860695,
-0.013523303903639317,
0.09992397576570511,
-0.05199122801423073,
0.044866569340229034,
0.0014150176430121064,
0.006351622287184,
0.01194410864263773,
0.00481024757027626,
0.00966213084757328,
0.03134237602353096,
-0.002545018447563052,
-0.02472245879471302,
-0.0059656105004251,
-0.018214026466012,
-0.00499248830601573,
-0.0029464729595929384,
0.022701121866703033,
-0.0013998104259371758,
0.012801182456314564,
-0.024514643475413322,
0.0007884699152782559,
-0.009507165290415287,
-0.019169894978404045,
0.028085198253393173,
0.02128855511546135,
0.0031852296087890863,
-0.01753929816186428,
0.009727275930345058,
-0.021933209151029587,
0.03791451081633568,
-0.037725139409303665,
-0.03202437609434128,
-0.019573833793401718,
0.02532820776104927,
-0.0028427953366190195,
0.00810193084180355
] |
<p>Approaching the following question</p>
<blockquote>
<p>Imagine we have a collection of $N = 100$ simple harmonic oscillators.
The total internal energy is $U = q \epsilon$ where $q$ is the number of energy
quanta. Assume $q >> N >> 1$. If we double the internal energy, by how
much will the entropy of the collection change?</p>
</blockquote>
<p>The question was originally found <a href="http://online.physics.uiuc.edu/cgi/courses/shell/phys213/practice.pl?exam1/su11" rel="nofollow">here</a> under <em>Question 5</em>.</p>
<p>The answer is $\sigma_{final} - \sigma_{initial} = 69.3$</p>
<p>How is this determined? </p>
<p>I know $S = k_b ln \Omega$, where $S$ is entropy, $\Omega$ is the number of micro-states, $\sigma = \frac{ 1}{ \Omega}$, $k_b$ is the Boltzmann constant.</p>
<p>I know $<energy> = 1/2 k T$ per quadradic term.</p>
<p>I know $\frac{ 1}{ T} \equiv \frac{ \partial S}{\partial U}$ </p>
<p>But how does doubling energy effect entropy? Specifically, what equation am I looking for to determine this?</p>
| 8,467 |
[
-0.02435636892914772,
-0.05934374779462814,
-0.004728802479803562,
-0.01195395179092884,
0.036546193063259125,
-0.010731021873652935,
-0.029764899984002113,
-0.02978985197842121,
0.0032958746887743473,
-0.03818744421005249,
0.06647010892629623,
0.0033155616838485003,
0.023960327729582787,
0.02339908666908741,
-0.0013783201575279236,
-0.017737098038196564,
0.00021832771017216146,
-0.026523154228925705,
-0.024561233818531036,
-0.027574265375733376,
0.002837305422872305,
0.013972747139632702,
0.034885525703430176,
-0.022188272327184677,
-0.028388135135173798,
0.05974763259291649,
0.03904806822538376,
0.0008610788499936461,
-0.004071587696671486,
0.04230596870183945,
0.01897946000099182,
-0.033556580543518066,
0.051713693886995316,
-0.006958337966352701,
-0.00140292476862669,
-0.01580212078988552,
-0.050157852470874786,
-0.03405139595270157,
-0.007109065540134907,
0.021264195442199707,
-0.07283370196819305,
0.0018909836653620005,
-0.020212465897202492,
0.01909702830016613,
0.0039885942824184895,
0.02011447586119175,
-0.015228549018502235,
-0.02727922797203064,
0.0341540165245533,
-0.02796524204313755,
0.0740416944026947,
0.0670466274023056,
0.046808741986751556,
0.007480544503778219,
-0.012239409610629082,
0.007265296299010515,
0.04393446445465088,
0.12085611373186111,
-0.0073592024855315685,
-0.050405994057655334,
0.012948213145136833,
-0.029628146439790726,
-0.03785302862524986,
-0.009050273336470127,
-0.008919044397771358,
0.015436227433383465,
0.03156878426671028,
0.001195326680317521,
0.02356225997209549,
-0.012377363629639149,
0.027640284970402718,
0.0003585592203307897,
0.06110108271241188,
-0.03577408567070961,
0.011926691979169846,
-0.02353643625974655,
-0.005164968781173229,
0.003794343676418066,
0.013908683322370052,
0.058028433471918106,
-0.018322017043828964,
-0.025513233616948128,
0.0142417186871171,
0.03818981721997261,
0.0021754184272140265,
-0.037040818482637405,
0.07626935094594955,
0.027267837896943092,
0.01695064827799797,
0.02217721939086914,
0.021412432193756104,
0.018490463495254517,
0.05834342911839485,
-0.043826065957546234,
-0.054452501237392426,
0.07831837236881256,
0.001570028834976256,
0.050787463784217834,
-0.011147971265017986,
-0.030695728957653046,
0.016868695616722107,
-0.02474874258041382,
0.05672425404191017,
0.09132713079452515,
-0.021466124802827835,
-0.009802388958632946,
-0.03657178953289986,
-0.010393901728093624,
-0.0065612345933914185,
0.001976107945665717,
-0.02287379652261734,
-0.00046096547157503664,
-0.005084971897304058,
0.0007774612167850137,
-0.015180932357907295,
0.0035197127144783735,
-0.02120116353034973,
-0.00443401699885726,
0.05542919412255287,
0.06361615657806396,
0.023798780515789986,
-0.009956239722669125,
0.02957363985478878,
-0.021674208343029022,
-0.059871312230825424,
-0.0016606281278654933,
0.0516846589744091,
0.021960003301501274,
-0.050126221030950546,
0.026000911369919777,
-0.028408730402588844,
0.00814915169030428,
-0.0361957810819149,
-0.018537446856498718,
0.003934551030397415,
0.007214323617517948,
-0.09078723192214966,
-0.07434786856174469,
0.06413210928440094,
0.01013875100761652,
-0.04875514283776283,
-0.060652293264865875,
0.00033566620550118387,
0.019697925075888634,
0.06551147252321243,
-0.027280578389763832,
0.008482251316308975,
-0.00862037017941475,
0.0327506847679615,
0.021706100553274155,
-0.04814205318689346,
-0.0029918979853391647,
-0.009604290127754211,
0.011224314570426941,
-0.001650570542551577,
-0.03736474737524986,
0.014380604028701782,
0.045128364115953445,
0.017074478790163994,
-0.028703711926937103,
0.023288927972316742,
-0.03565734252333641,
-0.006781555246561766,
0.006381991785019636,
-0.009751858189702034,
-0.038318902254104614,
0.05932629853487015,
-0.00006082239269744605,
-0.004877392202615738,
0.013926160521805286,
0.03458911553025246,
-0.004985347855836153,
-0.005437974352389574,
-0.024876978248357773,
0.02609989233314991,
-0.06172044947743416,
0.001432729884982109,
-0.038488008081912994,
-0.013175902888178825,
0.03256727755069733,
-0.0376148521900177,
-0.024070778861641884,
0.004783731419593096,
-0.01109562162309885,
0.044733673334121704,
0.02338680997490883,
0.020664485171437263,
-0.0011635218979790807,
-0.017945997416973114,
-0.05485699698328972,
-0.05422113090753555,
-0.0730699673295021,
0.043248552829027176,
-0.002670653397217393,
-0.005939112510532141,
0.034692876040935516,
0.015105986036360264,
0.04299071058630943,
-0.004896153230220079,
-0.016404207795858383,
0.015944870188832283,
0.04182693362236023,
0.03555748611688614,
-0.027228815481066704,
0.026246681809425354,
0.03756244480609894,
0.024159373715519905,
0.0024487506598234177,
0.04637617990374565,
-0.038894638419151306,
-0.027561819180846214,
0.001130314078181982,
-0.016092149540781975,
0.023142894729971886,
-0.025149662047624588,
-0.04090849682688713,
-0.0013684872537851334,
-0.0014239762676879764,
-0.005252793896943331,
0.010192587040364742,
-0.0389963798224926,
0.023737311363220215,
0.040750861167907715,
0.024821864441037178,
0.014765872620046139,
0.047143884003162384,
0.005174887832254171,
0.027305060997605324,
0.0028980097267776728,
-0.009260172955691814,
-0.033476460725069046,
-0.00017122556164395064,
0.04870424047112465,
0.03624546155333519,
-0.01326123159378767,
0.016815466806292534,
0.03596360981464386,
-0.023459184914827347,
0.007366427220404148,
-0.04665030539035797,
-0.022466149181127548,
-0.04538464918732643,
0.04175075516104698,
-0.0053872885182499886,
0.008827323094010353,
0.010757424868643284,
0.03259548544883728,
-0.007060110103338957,
-0.015223932452499866,
0.010928467847406864,
0.03453362360596657,
0.011461546644568443,
-0.014370722696185112,
-0.03133263438940048,
-0.004749751649796963,
-0.01731359399855137,
0.035963721573352814,
-0.02028137817978859,
0.013468781486153603,
0.021123023703694344,
-0.012431726790964603,
0.013701912946999073,
-0.02371472865343094,
-0.023907460272312164,
-0.03672979772090912,
-0.009810064919292927,
-0.003468380542472005,
-0.004418639466166496,
0.017473513260483742,
-0.04845051094889641,
0.021245373412966728,
0.02508818544447422,
0.02863200195133686,
0.0096405865624547,
-0.004537609405815601,
0.03368440270423889,
0.006563722621649504,
0.018509646877646446,
-0.07488430291414261,
-0.008987341076135635,
0.04450378194451332,
-0.008497790433466434,
0.014671167358756065,
0.007992525584995747,
-0.06414865702390671,
0.024017969146370888,
-0.01959923282265663,
-0.04050220176577568,
-0.001979834632948041,
-0.014684692956507206,
-0.0032968781888484955,
0.035658467561006546,
-0.012879240326583385,
-0.04348873719573021,
-0.013725165277719498,
-0.0181076992303133,
0.025667497888207436,
-0.03189294785261154,
0.004614141769707203,
0.07104729115962982,
-0.006069855764508247,
-0.03577689826488495,
-0.007029293570667505,
-0.019990483298897743,
-0.027173666283488274,
-0.007550819311290979,
-0.006455526687204838,
0.021554484963417053,
-0.004559946712106466,
0.03226085007190704,
0.036873627454042435,
-0.014405774883925915,
-0.03991521894931793,
-0.04934370517730713,
-0.04996839538216591,
0.013262179680168629,
-0.015739278867840767,
0.06883367896080017,
0.017238132655620575,
-0.03173551335930824,
0.07975039631128311,
0.03021981380879879,
-0.008125998079776764,
-0.0266221072524786,
-0.005332885310053825,
0.0018097630236297846,
-0.016364648938179016,
-0.007201706524938345,
0.010517691262066364,
-0.06283514201641083,
0.03671208769083023,
0.03570060431957245,
0.06770910322666168,
0.04196950048208237,
0.008017049171030521,
-0.025771591812372208,
-0.0015448256162926555,
-0.005809207912534475,
0.014536788687109947,
0.06557753682136536,
-0.010543887503445148,
-0.03150758892297745,
0.029590817168354988,
-0.0022510592825710773,
-0.004389195702970028,
0.04554019123315811,
-0.03881898894906044,
0.030824199318885803,
0.02602430246770382,
-0.013792150653898716,
-0.043109651654958725,
0.03694299980998039,
-0.0008292329730466008,
-0.03651753440499306,
0.0118945287540555,
0.034236159175634384,
0.041882507503032684,
-0.014588259160518646,
0.007234512362629175,
0.012296725064516068,
0.064104363322258,
-0.006744818761944771,
-0.025283485651016235,
-0.0012301813112571836,
0.018199559301137924,
0.0048548015765845776,
-0.029763532802462578,
-0.003693236503750086,
0.010325899347662926,
0.03173644468188286,
0.033318500965833664,
-0.03836137056350708,
-0.03581652790307999,
-0.001643268158659339,
-0.03246898576617241,
-0.04700881242752075,
-0.048728201538324356,
0.05417557805776596,
0.008748849853873253,
0.07552900910377502,
-0.013006865046918392,
0.014966455288231373,
0.018571704626083374,
0.022403176873922348,
-0.08693966269493103,
0.039243996143341064,
-0.0033691073767840862,
-0.013634645380079746,
0.044499676674604416,
0.006542638875544071,
0.030310269445180893,
-0.03158580884337425,
-0.02717120386660099,
-0.001007822691462934,
0.0014945637667551637,
-0.018845077604055405,
0.0006328934687189758,
-0.0365254245698452,
-0.014912307262420654,
0.004394063260406256,
0.021213876083493233,
0.026427626609802246,
-0.017344143241643906,
-0.013028022833168507,
0.04377211630344391,
-0.01583518087863922,
-0.006203305907547474,
-0.039914797991514206,
0.02607380412518978,
0.004580628126859665,
0.044074803590774536,
0.027289658784866333,
0.006280174478888512,
0.01240526232868433,
-0.0057495650835335255,
0.02479090727865696,
0.04074644669890404,
-0.007525463588535786,
-0.006502068135887384,
0.00009951132233254611,
-0.029692862182855606,
0.0037882202304899693,
0.011513636447489262,
0.04748835042119026,
-0.004580504260957241,
0.02802378125488758,
0.04221896454691887,
0.02175881899893284,
-0.03698238357901573,
0.0297732912003994,
0.024960985407233238,
-0.013952489010989666,
-0.03011973574757576,
-0.007400157395750284,
-0.00409166282042861,
-0.009430966340005398,
-0.022082220762968063,
-0.017330987378954887,
0.00945912767201662,
-0.01664177142083645,
0.044011570513248444,
0.011901846155524254,
0.01895667053759098,
0.005863947793841362,
-0.007680486422032118,
-0.0017670751549303532,
0.04402771219611168,
-0.0017708862433210015,
0.008569978177547455,
-0.03564084693789482,
-0.00995232816785574,
0.0647563487291336,
-0.021901840344071388,
0.012166894972324371,
-0.06175731495022774,
-0.012133059091866016,
0.02827216126024723,
0.04238663241267204,
-0.00545031763613224,
0.010717137716710567,
-0.03749465569853783,
-0.0006014953833073378,
0.031827252358198166,
-0.008527611382305622,
0.03959841653704643,
0.013710161671042442,
-0.008728362619876862,
0.0013475711457431316,
-0.05741500481963158,
-0.037349067628383636,
-0.000998199568130076,
0.006209466606378555,
0.007595319766551256,
-0.049374647438526154,
-0.04004168137907982,
-0.018559178337454796,
0.045332759618759155,
0.0061964476481080055,
0.07003872096538544,
-0.04923463240265846,
-0.016079483553767204,
-0.007815256714820862,
-0.0007273145020008087,
-0.01639557257294655,
-0.058568909764289856,
0.009149046614766121,
-0.02691003866493702,
0.005498387385159731,
0.0313626304268837,
-0.04116576164960861,
-0.04536420479416847,
0.04086454585194588,
0.04086881875991821,
-0.03885761275887489,
-0.01990065909922123,
-0.0012849332997575402,
0.05741795152425766,
0.013844640925526619,
0.004756440874189138,
0.05495257303118706,
0.043935954570770264,
-0.015189596451818943,
0.012771271169185638,
-0.049110934138298035,
0.029183337464928627,
-0.0094038350507617,
0.015783488750457764,
-0.01863514631986618,
0.04836780205368996,
-0.01266585011035204,
0.053914524614810944,
-0.0003179181949235499,
0.02295711450278759,
-0.010608555749058723,
-0.04397882893681526,
-0.0016437409212812781,
0.01827220804989338,
0.010927977971732616,
0.042346928268671036,
0.010197963565587997,
0.0226642657071352,
-0.006760101765394211,
-0.0029573843348771334,
-0.003056720830500126,
0.009607410058379173,
0.007109534461051226,
0.042359840124845505,
-0.005748089402914047,
0.04591408371925354,
-0.057914163917303085,
-0.029900280758738518,
0.03816445916891098,
-0.043112318962812424,
0.03588073328137398,
-0.011426462791860104,
-0.015103996731340885,
0.014278720133006573,
-0.025764118880033493,
-0.010436926037073135,
-0.015821287408471107,
-0.026545323431491852,
-0.01854565553367138,
-0.01989021711051464,
0.028199220076203346,
0.020341025665402412,
0.01653417944908142,
-0.0879037007689476,
0.00979530718177557,
0.02740662544965744,
-0.021634865552186966,
-0.004471445921808481,
-0.03596360608935356,
0.01194336824119091,
-0.04033641144633293,
-0.01985933817923069,
0.020494993776082993,
0.06755372881889343,
-0.031476445496082306,
-0.011332794092595577,
-0.0025616330094635487,
0.032644640654325485,
0.010130389593541622,
0.009968610480427742,
-0.029091395437717438,
-0.023256829008460045,
0.0018748975126072764,
-0.004621678031980991,
0.04874591529369354,
0.03723686560988426,
-0.031055260449647903,
-0.01120543759316206,
0.02325991913676262,
-0.009986656717956066,
0.04257496818900108,
-0.03886667639017105,
-0.007081042975187302,
-0.001308509032242,
-0.021688643842935562,
-0.01398862898349762,
-0.002682937541976571,
-0.002849696669727564,
-0.004680690821260214,
0.05643688887357712,
0.011132367886602879,
0.010744907893240452,
-0.05290788784623146,
-0.002742448356002569,
0.008511199615895748,
0.0032783704809844494,
0.01863030530512333,
-0.018641697242856026,
0.10835564136505127,
-0.021657248958945274,
-0.006172759458422661,
0.01354233268648386,
-0.034890830516815186,
0.041146744042634964,
-0.004345831461250782,
-0.0030749733559787273,
0.0074943131767213345,
-0.0024537250865250826,
-0.014483211562037468,
-0.038160938769578934,
-0.045048799365758896,
0.000018443586668581702,
0.03534094616770744,
-0.0033321715891361237,
0.041120488196611404,
0.01570782996714115,
0.008062279783189297,
0.049277257174253464,
-0.0018147516530007124,
0.02553262934088707,
0.008639962412416935,
0.014516935683786869,
0.032227784395217896,
-0.029130687937140465,
-0.03662266209721565,
0.031446587294340134,
0.035892054438591,
-0.014226716011762619,
0.050227079540491104,
0.005870177876204252,
0.009917358867824078,
0.03030271641910076,
-0.04936780780553818,
-0.04142981022596359,
0.05462832376360893,
-0.03223906457424164,
0.028818989172577858,
-0.013182555325329304,
0.004209334030747414,
0.04129841551184654,
0.022258831188082695,
-0.0032374055590480566,
-0.03922046720981598,
-0.004167528357356787,
-0.04833032935857773,
-0.00015319795056711882,
-0.006654145661741495,
-0.014637073501944542,
-0.006867014337331057,
0.0007108477875590324,
0.01644163206219673,
0.02798866666853428,
0.02470562607049942,
0.008555559441447258,
-0.035089343786239624,
-0.027132544666528702,
-0.0004331725649535656,
-0.09211041778326035,
0.002197220688685775,
0.008632274344563484,
-0.02171187475323677,
0.04501233249902725,
-0.03579619899392128,
0.04703288897871971,
0.02520347386598587,
0.01618807390332222,
-0.015375357121229172,
0.07943955808877945,
0.0024034634698182344,
0.045292846858501434,
-0.0006141073536127806,
0.024268019944429398,
0.12082921713590622,
0.06629319489002228,
0.02174314670264721,
-0.03513515740633011,
0.018129786476492882,
0.048760443925857544,
0.014519164338707924,
-0.012564366683363914,
0.003857784904539585,
0.014460457488894463,
0.00016015191795304418,
-0.014459127560257912,
0.05577269569039345,
-0.015217938460409641,
-0.0006779438117519021,
0.00631329882889986,
-0.0431029349565506,
-0.03863724693655968,
0.028644492849707603,
-0.020681973546743393,
0.0012411271454766393,
0.004581440705806017,
-0.03585848584771156,
-0.006308339536190033,
-0.021212110295891762,
0.028605075553059578,
-0.045276280492544174,
-0.0753239318728447,
0.02143985591828823,
-0.005212119780480862,
-0.01360852736979723,
0.03167099505662918,
-0.015058770775794983,
-0.013297772035002708,
-0.01090258825570345,
0.02458016946911812,
0.040313757956027985,
-0.0014176100958138704,
0.009641477838158607,
0.04036681354045868,
-0.008042164146900177,
0.026100046932697296,
0.029330478981137276,
0.06320852041244507,
-0.035665273666381836,
-0.02970181591808796,
-0.027899516746401787,
0.03225555643439293,
-0.05642041563987732,
0.0007953159511089325,
-0.006551057565957308,
-0.010758018121123314,
0.015233048237860203,
0.0002615389821585268,
-0.0261271670460701,
0.005525953136384487,
0.015016519464552402,
-0.02693316899240017,
0.003884888021275401,
-0.029422776773571968,
-0.009221159853041172,
0.006933568976819515,
0.04798559844493866,
-0.029993755742907524,
-0.005110772792249918,
-0.01635059341788292,
0.012139841914176941,
0.04601353406906128,
-0.031510233879089355,
-0.005890801548957825,
-0.024379560723900795,
-0.035669729113578796,
-0.05578235909342766,
-0.04236108809709549,
-0.004674730822443962,
-0.000882259220816195,
0.043861981481313705,
0.015190113335847855,
-0.00891948863863945,
-0.02947673201560974,
-0.06147794798016548,
-0.017214331775903702,
0.033938538283109665,
0.012989654205739498,
-0.02888226881623268,
0.01846635714173317,
-0.02172163687646389,
0.038065772503614426,
-0.03600700944662094,
-0.01646433398127556,
0.046706218272447586,
0.016382114961743355,
0.004433528520166874,
-0.01926170289516449,
-0.0360097736120224,
0.00015641917707398534,
-0.010511621832847595,
-0.01450091041624546,
-0.0026778390165418386,
0.02622283063828945,
-0.04072796180844307,
0.006596665363758802,
0.016079217195510864,
0.039388593286275864,
-0.0333055704832077,
0.0025877049192786217,
-0.0017134628724306822,
-0.029787447303533554,
-0.012133817188441753,
0.007107906974852085,
0.02953312173485756,
-0.010721569880843163,
-0.04247571527957916,
0.004135207273066044,
0.0035271882079541683,
0.0161537304520607,
0.009112201631069183,
-0.05555522441864014,
-0.002564078662544489,
-0.012673814781010151,
0.02821769379079342,
-0.034493401646614075,
-0.019111566245555878,
-0.0018658238695934415,
0.01629752852022648,
0.007547448854893446,
0.037588343024253845,
-0.011307192966341972,
0.025223903357982635,
0.004608849063515663,
-0.011729668825864792,
0.026823781430721283,
0.04966140538454056,
-0.012432476505637169,
-0.03450948745012283,
0.013458633795380592,
0.0034218968357890844,
0.03326338157057762,
-0.018652651458978653,
-0.04460785910487175,
0.08550835400819778,
-0.030010301619768143,
-0.0316653847694397,
0.023190537467598915,
-0.0027341407258063555,
0.016146469861268997,
0.01624603196978569,
-0.037877798080444336,
0.01606689766049385,
0.0364987850189209,
-0.015399503521621227,
0.002961846301332116,
-0.03094397485256195,
-0.0369916707277298,
-0.008740676566958427,
-0.026903411373496056,
-0.002710114698857069,
0.03555930778384209,
-0.005436264909803867,
0.03037566877901554,
0.027091875672340393,
-0.033617377281188965,
-0.03868431597948074,
0.035652413964271545,
-0.034096479415893555,
0.006056880112737417,
0.012661097571253777,
0.04186011105775833,
0.013720301911234856,
0.06835748255252838,
-0.02510864846408367,
0.030067138373851776,
-0.04248051717877388,
0.014802752062678337,
-0.06806949526071548,
-0.011392340064048767,
0.006337837316095829,
-0.010925281792879105,
0.018119370564818382,
-0.04169873893260956,
0.015033877454698086,
0.04574457183480263,
-0.03836413100361824,
0.03509197756648064,
-0.012009776197373867,
0.017760584130883217,
-0.04374326020479202,
0.03482453152537346,
-0.06315457075834274,
0.008236049674451351,
0.04904886335134506,
0.034063760191202164,
0.025709157809615135,
0.042140983045101166,
0.017168374732136726,
-0.045041412115097046,
-0.004768149461597204,
-0.0037847631610929966,
0.013142485171556473,
-0.017109118402004242,
0.03594379872083664,
-0.02247534692287445,
-0.0538373701274395,
0.014920786023139954,
-0.045995090156793594,
-0.01718446984887123,
-0.0369894802570343,
0.0325232557952404,
0.014470328576862812,
0.07228898257017136,
0.025025930255651474,
-0.019650569185614586,
0.017512904480099678,
0.012725344859063625,
0.008205577731132507,
0.013964589685201645,
0.0038098341319710016,
-0.029542816802859306,
0.031223146244883537,
0.025340504944324493,
-0.04148465022444725,
0.04536972567439079,
-0.03474538400769234,
-0.025680674239993095,
0.011832637712359428,
-0.006247245240956545,
-0.01411762647330761,
-0.04206951707601547,
0.018862761557102203,
-0.0402710996568203,
0.004668877925723791,
-0.011327343061566353,
0.005288665648549795,
0.010508416220545769,
0.0031692946795374155,
-0.0027540994342416525,
-0.019236693158745766,
0.0581660121679306,
-0.038105107843875885,
-0.02348296530544758,
-0.07939708232879639,
-0.013631296344101429,
0.006559687200933695,
0.03626638278365135,
-0.038629647344350815,
-0.062004391103982925,
-0.044925179332494736,
0.026718981564044952,
0.03169374540448189,
0.027586860582232475,
-0.04137508198618889,
-0.011229217983782291,
-0.024089163169264793,
-0.07735748589038849,
-0.04423847422003746,
0.016080325469374657,
-0.0003269812441430986,
-0.023339543491601944,
-0.00496908463537693,
-0.013327711261808872,
0.012908486649394035,
0.05961863324046135,
0.02992037869989872,
-0.0475543774664402,
0.04616868868470192,
-0.008237005211412907,
0.03763063624501228,
-0.025287585332989693,
0.004594745114445686,
-0.0499427430331707,
-0.03307972103357315,
-0.013912234455347061,
0.010307809337973595,
-0.008504302240908146,
0.027854306623339653,
0.02734638936817646,
-0.032136816531419754,
-0.028981026262044907,
-0.03288402780890465,
-0.013204928487539291,
0.031920425593853,
-0.008311930112540722,
-0.007913804613053799,
0.05677678808569908,
0.024781735613942146,
0.021586859598755836,
0.022398164495825768,
-0.008597863838076591,
-0.041691359132528305,
0.015796629711985588,
-0.028714429587125778,
-0.009611799381673336,
-0.03691340610384941,
-0.028149254620075226,
0.043459370732307434,
-0.03653433546423912,
-0.007225563749670982,
0.009845651686191559,
-0.05655641108751297,
-0.005376435816287994,
0.030479608103632927,
0.019496897235512733,
0.04851527884602547,
0.01201501302421093,
0.016348792240023613,
-0.003794159973040223,
-0.004628160502761602,
-0.02296251244843006,
0.07612434774637222,
0.037293482571840286,
-0.02194819226861,
0.011568943038582802,
0.04336513206362724,
-0.013800493441522121,
-0.011323848739266396,
-0.00966298021376133,
0.00804439652711153,
-0.009678277187049389,
-0.037698838859796524,
0.03356200084090233,
-0.04355030134320259,
-0.00874789897352457,
0.008821839466691017,
-0.009636782109737396,
0.055985815823078156,
0.011696179397404194,
-0.014550953172147274,
-0.042883388698101044,
0.01939322054386139,
-0.01702229678630829,
0.012726458720862865,
0.030283531174063683,
0.03312879055738449,
0.01925298012793064,
-0.025294408202171326,
-0.04730776324868202,
-0.004911357071250677,
0.010054290294647217,
-0.04125223681330681,
-0.019744884222745895,
0.019949201494455338,
0.023682821542024612,
0.005047691985964775,
-0.00877700187265873,
0.014865376055240631,
-0.06663962453603745,
0.04602412134408951,
0.03804134577512741,
0.01720905676484108,
0.012356380932033062,
-0.052841030061244965,
-0.02878728322684765,
0.08818966895341873,
-0.018157245591282845,
-0.032505813986063004,
-0.02995358780026436,
-0.006246258970350027,
-0.005436962470412254,
-0.06276388466358185
] |
<p>I would like to ask if there is any Nuclear process which can be used to produce a <a href="http://en.wikipedia.org/wiki/Wireless_power" rel="nofollow">wireless power</a> ? </p>
<p>Is there any nuclear process can be radiate to the environment with no harm to human beings?</p>
<hr>
<h1>How can I use the photo electric effect with some high Intensity radiation ?</h1>
| 8,468 |
[
-0.022484086453914642,
-0.07183845341205597,
0.010421560145914555,
-0.018289104104042053,
-0.02054845727980137,
0.002979160286486149,
-0.04461333155632019,
-0.03827882185578346,
0.019395774230360985,
-0.07789865881204605,
0.041550733149051666,
0.07651008665561676,
0.0326680988073349,
0.0022090496495366096,
0.01067758072167635,
0.007880523800849915,
0.019851384684443474,
-0.018892385065555573,
-0.0017235999694094062,
-0.029073523357510567,
-0.00525795528665185,
0.009862173348665237,
-0.022054485976696014,
0.015504727140069008,
-0.012616601772606373,
0.02945609949529171,
0.02031058259308338,
0.04968464374542236,
-0.006689405534416437,
0.04426918178796768,
0.0012821323471143842,
-0.042336806654930115,
0.0065893614664673805,
0.010026366449892521,
0.013359115459024906,
0.007018379867076874,
-0.030561858788132668,
-0.030676163733005524,
0.007596540730446577,
-0.006438630633056164,
0.031344782561063766,
-0.017996247857809067,
0.012817046605050564,
0.03289177641272545,
-0.02569102868437767,
-0.016607945784926414,
-0.017045604065060616,
-0.04403499513864517,
0.03808356821537018,
-0.06877675652503967,
0.04172980785369873,
0.007570977322757244,
0.01651586778461933,
0.001904516713693738,
0.013544510118663311,
0.0025121974758803844,
0.08278383314609528,
0.0784321203827858,
0.01027439534664154,
-0.04053874313831329,
0.014331437647342682,
0.004547419957816601,
-0.016219578683376312,
-0.03280683979392052,
-0.04624617472290993,
0.024562202394008636,
-0.0056639970280230045,
-0.002919611753895879,
0.029408562928438187,
0.024360939860343933,
0.05189228430390358,
0.018301423639059067,
0.015101902186870575,
0.006301333662122488,
0.02060488797724247,
-0.024429434910416603,
0.014858183450996876,
-0.011605523526668549,
0.03629836440086365,
0.03660619258880615,
-0.04279525950551033,
-0.000020321522242738865,
-0.015967773273587227,
0.015026906505227089,
-0.005707382690161467,
-0.004094922449439764,
0.05915944278240204,
-0.02779180184006691,
0.021641599014401436,
-0.011320522055029869,
0.012403300032019615,
-0.011424778029322624,
0.054852187633514404,
0.02979387529194355,
-0.0035189485643059015,
0.02355656400322914,
0.0053945668041706085,
0.060823407024145126,
0.013831976801156998,
-0.04846683517098427,
0.07745737582445145,
0.014717466197907925,
0.03192165866494179,
0.05064260959625244,
0.016307339072227478,
-0.05798498913645744,
0.0046446979977190495,
0.002896504709497094,
0.010015842504799366,
0.020537039265036583,
-0.06086086481809616,
0.000596501340623945,
0.005391022190451622,
-0.008629917167127132,
0.017035046592354774,
-0.019411617890000343,
-0.013585136272013187,
-0.0007395392749458551,
0.08108149468898773,
0.09771349281072617,
0.022984402254223824,
-0.0316111221909523,
0.05909954756498337,
-0.05545957013964653,
-0.06954950094223022,
0.012353431433439255,
0.01070035994052887,
0.014955079182982445,
-0.06470690667629242,
0.028044916689395905,
-0.01793874055147171,
0.0007739741704426706,
0.0007091584848240018,
-0.0355866439640522,
0.027534563094377518,
-0.019509755074977875,
-0.10892072319984436,
-0.0600941963493824,
0.009114869870245457,
-0.02623159997165203,
-0.002721720840781927,
-0.07254204154014587,
0.038079410791397095,
0.03471149504184723,
0.06353645771741867,
0.005078235175460577,
-0.04089444875717163,
-0.031240688636898994,
0.045680079609155655,
-0.005054988898336887,
-0.023214340209960938,
-0.028935464099049568,
0.032416731119155884,
-0.04358292743563652,
0.017630191519856453,
-0.054496653378009796,
0.03885187208652496,
0.0650632232427597,
0.014491025358438492,
-0.002927524270489812,
0.05496620759367943,
-0.017385466024279594,
0.013565669767558575,
0.01863080821931362,
-0.00009209124982589856,
-0.029242347925901413,
0.09694811701774597,
0.058703627437353134,
-0.0005391850718297064,
0.02825132943689823,
0.013613956049084663,
0.06235983595252037,
0.01123614702373743,
0.006421323399990797,
0.019670413807034492,
-0.0715377926826477,
0.0014575141249224544,
-0.010547482408583164,
0.04128469526767731,
0.01135138887912035,
-0.03997335955500603,
0.02101067267358303,
0.0039175888523459435,
0.02632998861372471,
0.007505142129957676,
0.03846123814582825,
-0.01770220324397087,
-0.010921628214418888,
0.043719831854104996,
-0.042116012424230576,
-0.009813886135816574,
-0.016937540844082832,
0.016015810891985893,
0.020038532093167305,
-0.016723396256566048,
-0.03109803982079029,
-0.01919334940612316,
-0.00603241752833128,
-0.05237426608800888,
-0.03169906139373779,
0.009558324702084064,
0.05244622752070427,
0.021947816014289856,
0.02136838808655739,
-0.022754410281777382,
0.05689394474029541,
0.007561740931123495,
-0.0022292346693575382,
0.019549768418073654,
0.0016192490002140403,
-0.022351261228322983,
-0.03643042594194412,
-0.042187802493572235,
0.02251814864575863,
0.035239774733781815,
-0.023112649098038673,
0.024028316140174866,
0.009345251135528088,
0.021149441599845886,
0.00731802498921752,
-0.016856035217642784,
0.07421348243951797,
0.05370312184095383,
0.02610684558749199,
0.018842104822397232,
0.012003733776509762,
0.007448379881680012,
-0.008434386923909187,
-0.03180302679538727,
-0.04282595217227936,
-0.08513681590557098,
0.013931668363511562,
0.01842903159558773,
-0.012876903638243675,
-0.07120037078857422,
0.04718021675944328,
-0.005836885422468185,
0.03872775658965111,
0.03339327126741409,
0.03445744886994362,
-0.031467463821172714,
0.009278354234993458,
0.03795044496655464,
0.024354584515094757,
-0.012472966685891151,
0.0292048379778862,
-0.018933050334453583,
0.019992200657725334,
0.008485722355544567,
-0.014279074035584927,
-0.0049939206801354885,
0.03443961963057518,
-0.05008706822991371,
-0.0041882931254804134,
-0.016378365457057953,
-0.03679993376135826,
0.042403340339660645,
-0.06519534438848495,
0.0041293129324913025,
-0.01314489170908928,
-0.02764931321144104,
0.009469983167946339,
0.022343812510371208,
-0.031347982585430145,
-0.0221247598528862,
0.016959406435489655,
-0.03125846013426781,
-0.009967449121177197,
0.033422037959098816,
-0.06492175906896591,
0.024911852553486824,
0.0025294949300587177,
0.03201759234070778,
-0.03907403722405434,
-0.004832202568650246,
0.04933501407504082,
0.0032470147125422955,
0.02957855723798275,
-0.029342763125896454,
-0.021595213562250137,
-0.004562499467283487,
-0.04409264400601387,
-0.019327286630868912,
0.028559310361742973,
-0.03960631042718887,
-0.004548690281808376,
-0.030752914026379585,
-0.013499361462891102,
0.04143520072102547,
-0.02805336005985737,
0.005928476341068745,
0.02430589310824871,
0.014321166090667248,
-0.07900082319974899,
0.00723101245239377,
-0.033131301403045654,
0.013029093854129314,
-0.0061968970112502575,
-0.02760971523821354,
0.046889737248420715,
0.024292491376399994,
-0.04448820278048515,
0.011948585510253906,
-0.042607877403497696,
-0.01900418847799301,
-0.010910136625170708,
-0.015981338918209076,
0.027146421372890472,
-0.030569126829504967,
0.055025864392519,
0.026314955204725266,
-0.056832365691661835,
0.0004646706802304834,
-0.0567135289311409,
-0.03733476251363754,
0.056301090866327286,
0.0036508135963231325,
0.04195773974061012,
-0.0010660146363079548,
-0.04805397242307663,
0.04194266349077225,
0.04231256991624832,
-0.02269601821899414,
-0.016831140965223312,
-0.028729546815156937,
-0.022079186514019966,
-0.02930184081196785,
-0.03517691045999527,
0.01683826372027397,
0.0026789994444698095,
0.004166987258940935,
-0.004458962939679623,
0.022701209411025047,
0.02516864985227585,
0.018252214416861534,
-0.03505038470029831,
-0.024029796943068504,
-0.024705292657017708,
0.021770311519503593,
0.026833847165107727,
-0.020578566938638687,
-0.06645676493644714,
0.00920463539659977,
0.0184954721480608,
0.0020882023964077234,
0.014861971139907837,
-0.04645060747861862,
0.0051503716967999935,
0.04317460581660271,
0.0036249372642487288,
-0.05265840142965317,
0.033716436475515366,
-0.002180122770369053,
-0.004671842325478792,
0.0041260370053350925,
0.021871261298656464,
0.04537006467580795,
-0.008609969168901443,
0.026633452624082565,
0.02905300445854664,
0.07627589255571365,
-0.013256492093205452,
-0.05874978005886078,
0.0039039545226842165,
0.005870939698070288,
-0.012959305197000504,
0.03452126681804657,
-0.005263342522084713,
0.03895684704184532,
0.01945655606687069,
0.03502703830599785,
0.019181502982974052,
0.030815184116363525,
-0.013618606142699718,
-0.0393083430826664,
0.0056224786676466465,
-0.0050969175063073635,
0.06910353899002075,
0.01843864843249321,
0.03856336325407028,
0.03266550973057747,
-0.007094775792211294,
0.041156601160764694,
-0.02501770108938217,
-0.07042162865400314,
0.037704505026340485,
-0.006055495236068964,
-0.0012925362680107355,
-0.002225198782980442,
-0.02379046007990837,
-0.045289814472198486,
0.007140030153095722,
-0.05413156747817993,
-0.008913865312933922,
0.009466113522648811,
-0.028131430968642235,
0.007122458890080452,
0.0023031476885080338,
-0.03164774924516678,
-0.03019671142101288,
0.027494724839925766,
0.017032137140631676,
-0.03538205102086067,
0.014697030186653137,
0.004023361019790173,
-0.03280052915215492,
0.016369175165891647,
-0.00704252440482378,
0.008964194916188717,
-0.010698121972382069,
0.05154772475361824,
0.04707842320203781,
0.01270344853401184,
-0.019424347206950188,
-0.0054824501276016235,
0.026074489578604698,
0.03820290043950081,
0.0034285879228264093,
-0.00024369548191316426,
-0.03279007598757744,
-0.023495612666010857,
-0.012317550368607044,
0.0028582292143255472,
-0.0005326240207068622,
0.02205883339047432,
0.027865951880812645,
-0.010868211276829243,
-0.023625396192073822,
-0.0307144857943058,
0.03119649551808834,
0.03627237677574158,
-0.00428342679515481,
0.00560277234762907,
-0.026013722643256187,
0.005465281195938587,
0.030642220750451088,
-0.006043808534741402,
0.023141654208302498,
0.006922272965312004,
-0.007008417509496212,
-0.032124463468790054,
0.031694263219833374,
0.04794309288263321,
-0.03368029743432999,
0.03207986429333687,
0.021751778200268745,
-0.018791116774082184,
0.002960412297397852,
-0.033438052982091904,
-0.009094172157347202,
0.03791669011116028,
0.011430404148995876,
-0.0001324318436672911,
-0.0143813481554389,
-0.07435821741819382,
0.02052321471273899,
0.021332997828722,
0.0774012953042984,
-0.024855677038431168,
0.0006216773763298988,
-0.03894089162349701,
0.012335741892457008,
0.026671256870031357,
-0.029411479830741882,
0.03244943544268608,
-0.024026034399867058,
-0.0005652732215821743,
0.015945427119731903,
-0.01272127777338028,
-0.013316536322236061,
0.010245213285088539,
0.010617847554385662,
-0.004254794679582119,
-0.025990774855017662,
-0.03459419310092926,
0.016830092296004295,
0.007102584931999445,
0.04895129054784775,
0.0623619519174099,
0.023906517773866653,
0.008575358428061008,
-0.012064202688634396,
0.04050913453102112,
-0.011157210916280746,
-0.06821606308221817,
0.014943571761250496,
-0.010724890045821667,
-0.033271901309490204,
0.050918761640787125,
-0.016561495140194893,
-0.03634410724043846,
0.024792978540062904,
0.021649906411767006,
-0.00867986399680376,
-0.056824129074811935,
-0.05154307186603546,
0.026461046189069748,
0.05353854224085808,
-0.003184044035151601,
0.056965410709381104,
0.08765622228384018,
-0.04976284131407738,
0.020824285224080086,
-0.01584271527826786,
0.018904568627476692,
-0.023051844909787178,
-0.003189481096342206,
0.023916317149996758,
0.02354981191456318,
0.006009989883750677,
0.015069291926920414,
-0.02703864499926567,
0.007826988585293293,
0.014603972434997559,
-0.010890448465943336,
-0.022388679906725883,
0.025194261223077774,
-0.0467279888689518,
-0.03058769181370735,
-0.061088282614946365,
0.01646515727043152,
0.0015533107798546553,
-0.037127379328012466,
-0.013846002519130707,
0.010980537161231041,
-0.004345970693975687,
0.007005893159657717,
-0.015537789091467857,
0.004249416291713715,
-0.0290046539157629,
0.02324173040688038,
0.014111573807895184,
-0.026481205597519875,
0.03283219411969185,
-0.012305086478590965,
0.026140645146369934,
0.019802965223789215,
-0.10210570693016052,
-0.04444994032382965,
0.024154050275683403,
0.013463485985994339,
0.020884279161691666,
-0.028047632426023483,
0.024225972592830658,
-0.021231751888990402,
-0.023459332063794136,
-0.03796956688165665,
-0.055634379386901855,
0.031005656346678734,
0.024945707991719246,
0.0023635972756892443,
-0.021077711135149002,
-0.029290370643138885,
-0.026146147400140762,
-0.043137408792972565,
-0.016796069219708443,
0.02916875295341015,
-0.04300079494714737,
0.00004782701944350265,
0.00995388813316822,
-0.0005187190836295485,
0.05273682251572609,
-0.00469615263864398,
-0.033630382269620895,
0.03014223277568817,
-0.005939646158367395,
0.007301183883100748,
-0.027724996209144592,
0.020347975194454193,
-0.017038585618138313,
-0.03635106608271599,
0.006713583134114742,
-0.027103841304779053,
0.031079282984137535,
-0.013252215459942818,
-0.019151853397488594,
0.04173211008310318,
0.04050438106060028,
-0.022280776873230934,
-0.0064663696102797985,
0.0346049964427948,
-0.006135552190244198,
0.010573343373835087,
-0.001018208684399724,
-0.009179544635117054,
-0.04949400946497917,
-0.034823741763830185,
0.020866340026259422,
-0.0036390386521816254,
-0.009642678312957287,
0.00027321139350533485,
0.03861724212765694,
-0.010876414366066456,
0.011540105566382408,
0.007719866931438446,
-0.034105706959962845,
0.007375755347311497,
-0.03533484786748886,
0.026683205738663673,
-0.018113967031240463,
0.007361751515418291,
-0.03339541703462601,
-0.013813633471727371,
-0.03091149404644966,
-0.03134875372052193,
0.05809442698955536,
-0.035999879240989685,
0.037268493324518204,
0.025922385975718498,
0.02421780675649643,
-0.0049233161844313145,
0.006704295985400677,
-0.00638334546238184,
0.0073326388373970985,
-0.017777882516384125,
0.021647362038493156,
0.02365773171186447,
-0.005208873655647039,
0.0193854458630085,
0.059186406433582306,
0.007976009510457516,
0.04912947118282318,
0.024596666917204857,
0.05830405652523041,
0.0005005234852433205,
-0.03734949231147766,
-0.06254390627145767,
0.02288035675883293,
-0.05147622153162956,
0.028769567608833313,
0.042479127645492554,
-0.05316561460494995,
0.023506643250584602,
-0.025015050545334816,
0.004448033403605223,
-0.03871757909655571,
-0.01303825806826353,
-0.058731090277433395,
0.04124721884727478,
-0.02733900211751461,
-0.0042565050534904,
-0.01627941243350506,
0.0022397562861442566,
0.029929781332612038,
-0.004176325164735317,
0.03054206632077694,
0.016500597819685936,
-0.05249888077378273,
-0.01772240549325943,
-0.04013979807496071,
-0.048559121787548065,
0.04639113321900368,
-0.02040228061378002,
-0.010475206188857555,
0.03143443539738655,
-0.018821900710463524,
0.029148424044251442,
0.0449649915099144,
0.05301212891936302,
0.031306833028793335,
0.02560391090810299,
-0.0052055181004107,
0.040598832070827484,
-0.00650379341095686,
0.010918042622506618,
0.12330418080091476,
0.024696435779333115,
0.02091623656451702,
-0.0263189896941185,
-0.01717977225780487,
-0.05126737430691719,
0.026088975369930267,
-0.006258473731577396,
0.008243752643465996,
-0.032536283135414124,
0.028216367587447166,
0.03315504267811775,
0.03168419748544693,
0.011196929030120373,
0.04661320894956589,
0.05089123919606209,
-0.034844085574150085,
-0.059867437928915024,
0.06979676336050034,
-0.02855159528553486,
-0.0209233146160841,
-0.0005893572233617306,
-0.057183846831321716,
-0.006107216235250235,
-0.047970037907361984,
-0.021036164835095406,
-0.023961136117577553,
-0.006941400468349457,
0.05760902538895607,
-0.0010153957409784198,
-0.04140104353427887,
-0.048276741057634354,
-0.02451941929757595,
-0.016178233548998833,
-0.025254102423787117,
-0.012591470032930374,
0.017811866477131844,
-0.020319832488894463,
-0.027291344478726387,
0.006638744845986366,
0.04554706811904907,
-0.03607318550348282,
0.021171994507312775,
0.02421504817903042,
-0.0389196053147316,
0.03235888481140137,
-0.004729066975414753,
0.02896578051149845,
-0.01383879967033863,
0.007411513011902571,
-0.015720857307314873,
0.005506398156285286,
0.023872429504990578,
-0.013103330507874489,
0.012844876386225224,
-0.0011554982047528028,
0.006484929472208023,
-0.010559982620179653,
-0.023213764652609825,
-0.03609257563948631,
0.02214954048395157,
-0.022185584530234337,
0.02197348140180111,
0.00982612930238247,
0.007613534107804298,
0.016443563625216484,
0.00979628972709179,
0.03354479745030403,
-0.009199507534503937,
-0.031384099274873734,
-0.060785721987485886,
-0.013555518351495266,
-0.027029648423194885,
-0.03525969386100769,
0.026897819712758064,
0.021566469222307205,
0.03371764346957207,
0.012436621822416782,
-0.029233770444989204,
-0.016914432868361473,
-0.04180140048265457,
0.06927322596311569,
-0.01760079525411129,
-0.027660338208079338,
0.006609285715967417,
-0.014889108948409557,
0.032837506383657455,
0.051368597894907,
-0.029142092913389206,
-0.022069575265049934,
-0.028322875499725342,
0.025288354605436325,
0.01981247402727604,
-0.04047460854053497,
-0.04252605885267258,
0.0008509785984642804,
0.012727945111691952,
0.0031790463253855705,
-0.03140312433242798,
0.02391805127263069,
0.028923438861966133,
-0.019703123718500137,
-0.022204440087080002,
-0.01400850247591734,
-0.03748476877808571,
-0.03228982910513878,
-0.003994518890976906,
0.0208964254707098,
-0.015037938952445984,
-0.009861798956990242,
0.014145071618258953,
-0.002129229251295328,
0.0013357086572796106,
-0.023189274594187737,
0.01430163811892271,
-0.004682105500251055,
0.01644643396139145,
0.010578898712992668,
0.020838195458054543,
-0.028487296774983406,
0.045941781252622604,
0.011937621980905533,
0.0034826542250812054,
-0.04282493516802788,
-0.01108555868268013,
0.022556155920028687,
0.02487627975642681,
-0.01207565888762474,
0.022953419014811516,
0.011080758646130562,
-0.002635295270010829,
0.04728441312909126,
0.027653178200125694,
-0.015869121998548508,
0.03042593225836754,
0.011631266213953495,
0.0019284080481156707,
0.05655907094478607,
-0.014482436701655388,
-0.01753510721027851,
0.06282314658164978,
-0.050287891179323196,
-0.03769741952419281,
0.022520726546645164,
-0.021279823035001755,
0.06393364071846008,
0.028647448867559433,
-0.021643931046128273,
-0.0035324960481375456,
0.046930912882089615,
0.030619826167821884,
0.024265332147479057,
0.020466430112719536,
0.019612137228250504,
-0.004419021774083376,
0.034323759377002716,
0.0011175880208611488,
-0.02324001118540764,
-0.026870641857385635,
0.006586792413145304,
0.043875761330127716,
0.03469206392765045,
-0.007285283412784338,
-0.024430541321635246,
-0.018973657861351967,
-0.029283881187438965,
0.025836840271949768,
0.007893091067671776,
0.014767291955649853,
0.018613623455166817,
-0.03300970792770386,
0.017538316547870636,
-0.003963557071983814,
-0.024833224713802338,
-0.0848030224442482,
-0.01735842414200306,
-0.008866265416145325,
-0.024845002219080925,
0.028727440163493156,
-0.043676409870386124,
0.04498835280537605,
0.004148504231125116,
-0.07537755370140076,
-0.016762124374508858,
0.044368475675582886,
-0.044805124402046204,
-0.008229054510593414,
0.044371429830789566,
-0.03467575088143349,
0.042222052812576294,
0.02078131213784218,
0.08475268632173538,
0.03075902722775936,
0.01696048118174076,
-0.00994376465678215,
-0.014573059044778347,
-0.018244998529553413,
-0.007868730463087559,
0.015423305332660675,
-0.02150668203830719,
0.05258122459053993,
-0.042210984975099564,
0.005457906052470207,
0.024163365364074707,
-0.037036556750535965,
0.028134316205978394,
-0.02920716628432274,
0.009365204721689224,
-0.019963044673204422,
0.047972358763217926,
0.027783114463090897,
-0.026772739365696907,
-0.0018410644261166453,
0.01531675923615694,
0.0302723478525877,
0.015310357324779034,
0.00286170095205307,
0.04457598179578781,
0.025961983948946,
-0.0181826613843441,
-0.015940653160214424,
0.046279970556497574,
-0.015931742265820503,
-0.0535556897521019,
0.002698552794754505,
0.023889878764748573,
0.009709903039038181,
-0.023735539987683296,
-0.014612602069973946,
-0.046306729316711426,
0.00027016320382244885,
-0.038303442299366,
-0.01826082356274128,
0.006481803022325039,
0.024520816281437874,
0.020187169313430786,
-0.026052704080939293,
0.033046476542949677,
-0.016560323536396027,
-0.03949858993291855,
-0.044785987585783005,
0.013004511594772339,
0.020411809906363487,
0.04105859622359276,
0.002330358140170574,
-0.04492928087711334,
-0.07116483896970749,
0.01725485920906067,
-0.007369815371930599,
0.025077298283576965,
0.03176251798868179,
0.012990573421120644,
-0.012592222541570663,
-0.008474729023873806,
0.035418134182691574,
-0.025278858840465546,
-0.00016817671712487936,
-0.034495268017053604,
-0.03661121428012848,
0.006415428593754768,
0.02820061706006527,
0.03796929493546486,
-0.026839714497327805,
-0.019506782293319702,
0.025407463312149048,
-0.0014860468218103051,
0.015281526371836662,
-0.05559879541397095,
0.03743833303451538,
-0.009808167815208435,
-0.042422182857990265,
-0.012054556049406528,
-0.005956243257969618,
-0.040049996227025986,
0.03262140229344368,
0.04094524681568146,
0.027337636798620224,
-0.02509959600865841,
-0.028536902740597725,
-0.03743128851056099,
0.05257393792271614,
0.009336389601230621,
-0.005764625500887632,
0.04641292616724968,
-0.03796854615211487,
0.011578187346458435,
0.00266720331273973,
-0.020539797842502594,
-0.011954235844314098,
0.02718840166926384,
-0.017447486519813538,
0.009629718959331512,
-0.0170003492385149,
-0.014451222494244576,
0.05898347124457359,
-0.0308054331690073,
-0.0003225476248189807,
0.017998313531279564,
-0.037851203233003616,
0.012007549405097961,
0.058766916394233704,
-0.011464007198810577,
-0.01756102778017521,
0.03139902651309967,
0.027850696817040443,
-0.03336002677679062,
-0.00514398654922843,
-0.023076286539435387,
0.02965947985649109,
0.023457854986190796,
-0.025088777765631676,
0.050346918404102325,
-0.007527835667133331,
0.03150429576635361,
-0.00943281315267086,
0.03186897188425064,
0.013287010602653027,
-0.024979179725050926,
-0.01609203964471817,
0.031085876747965813,
0.020261777564883232,
-0.01504484098404646,
0.012731450609862804,
-0.021603725850582123,
0.051683783531188965,
-0.028204279020428658,
-0.0025333778467029333,
-0.02170826680958271,
-0.013947773724794388,
-0.0013212194899097085,
0.002153304871171713,
-0.0023380129132419825,
0.06298085302114487,
-0.033668920397758484,
-0.014985974878072739,
0.007443752605468035,
0.014142959378659725,
-0.004039971623569727,
-0.04562116041779518,
0.004324126057326794,
-0.017367232590913773,
-0.024588176980614662,
-0.04845351725816727,
-0.020694421604275703,
0.014520740136504173,
-0.01646582968533039,
0.017627311870455742,
0.04480792582035065,
0.002513701794669032,
-0.0036440836265683174,
-0.02639169432222843,
-0.028103649616241455,
0.062278348952531815,
-0.014888335950672626,
0.01926388405263424,
0.00940969679504633,
-0.01496877335011959,
-0.01247597299516201,
0.007958998903632164
] |
<p>The Lagrangian density for QED is</p>
<p>$$ \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\bar{\psi}(i\gamma^{\mu}D_{\mu}-m)\psi $$</p>
<p>with</p>
<p>$$F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} $$
$$ \bar{\psi}=\gamma^{0}\psi^{\dagger}$$
$$D_{\mu}=\partial_{\mu}+ieA_{\mu}$$</p>
<p>$U(1)$ local gauge transformations are</p>
<p>$$\psi\rightarrow\psi^{'}=e^{-i\alpha(x)}\psi$$
$$A_{\mu}^{'}=A_{\mu}+\frac{1}{e}\partial_{\mu}\alpha(x)$$</p>
<p>I'm trying to see that $\mathcal{L}$ it is invariant under those $U(1)$ transformations, but I finish my calculation with</p>
<p>$$\mathcal{L}^{'}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+e^{-i\alpha(x)}\bar{\psi}[i\gamma^{\mu}D_{\mu}-m-\gamma^{\mu}\partial_{\mu}\alpha(x)]e^{i\alpha(x)}\psi $$</p>
<p>Any hint will be appreciated thanks</p>
| 8,469 |
[
-0.02782399207353592,
0.0223834291100502,
0.0046042390167713165,
0.00040257960790768266,
0.025087891146540642,
0.04023076221346855,
-0.03112245723605156,
-0.023217516019940376,
0.019612349569797516,
-0.031105000525712967,
0.05479620769619942,
-0.003586347447708249,
0.09013193100690842,
0.05676158890128136,
0.014312165789306164,
-0.0008160119177773595,
0.002779964590445161,
0.03391020745038986,
-0.006535535678267479,
-0.05128992721438408,
-0.027158547192811966,
0.032127685844898224,
0.010130801238119602,
-0.01120289508253336,
-0.05492553114891052,
0.0349547304213047,
-0.05005284771323204,
-0.01668701134622097,
-0.014643796719610691,
0.08128011971712112,
-0.010709856636822224,
-0.03435990959405899,
0.008734414353966713,
0.005475235637277365,
-0.015502769500017166,
0.023953724652528763,
-0.04200146719813347,
-0.039274025708436966,
-0.00004835733489017002,
0.02272237092256546,
-0.06251295655965805,
-0.04565592482686043,
-0.044261280447244644,
0.052348073571920395,
-0.0074597750790417194,
-0.0324379988014698,
0.018752779811620712,
0.02204379439353943,
0.08326045423746109,
-0.03491067513823509,
0.07425873726606369,
0.05033878609538078,
0.0196489579975605,
0.05135735869407654,
-0.0312652662396431,
-0.06101390719413757,
0.02065994031727314,
0.07796257734298706,
0.014096368104219437,
-0.04549499973654747,
-0.029580935835838318,
-0.07236815243959427,
0.0318649522960186,
-0.007199672516435385,
-0.002978521166369319,
0.015833711251616478,
0.01064233761280775,
0.02376658096909523,
0.02504909038543701,
-0.0034457400906831026,
0.002170845866203308,
0.004954102914780378,
0.013927578926086426,
-0.02981727384030819,
0.023070337250828743,
-0.007150330580770969,
-0.00044792582048103213,
0.020292656496167183,
0.003299514064565301,
0.030350536108016968,
0.004764811135828495,
0.026632795110344887,
0.0380418486893177,
-0.011191380210220814,
-0.023277658969163895,
-0.01876273937523365,
0.0765685886144638,
0.017391644418239594,
-0.00044955406337976456,
0.03931687772274017,
0.0026459600776433945,
-0.003422561101615429,
0.04113684222102165,
0.002760921837761998,
-0.020377781242132187,
0.029297219589352608,
0.032484591007232666,
0.05763371288776398,
-0.0013306153705343604,
0.001379347057081759,
-0.0280369333922863,
-0.01442914828658104,
-0.007101533003151417,
0.06944581121206284,
0.00489560654386878,
0.0009479490690864623,
-0.04249875620007515,
-0.024426599964499474,
-0.027933839708566666,
-0.03798456862568855,
-0.054012466222047806,
0.015888769179582596,
-0.052812010049819946,
-0.00892424862831831,
0.006894186604768038,
-0.07087752223014832,
-0.03339143842458725,
-0.003432074561715126,
0.03188401088118553,
0.060041412711143494,
0.018282510340213776,
0.026639537885785103,
0.022250672802329063,
0.00814251508563757,
-0.04997728019952774,
0.04267817363142967,
0.056965284049510956,
-0.009469274431467056,
-0.048216454684734344,
0.038292378187179565,
0.007576099131256342,
0.008207278326153755,
-0.007244643289595842,
0.0088515505194664,
0.01481588650494814,
-0.014824478887021542,
-0.0881025642156601,
-0.04094880819320679,
0.006866847164928913,
0.006086013745516539,
-0.027205437421798706,
-0.06579715758562088,
-0.032611094415187836,
0.03976969048380852,
0.08880917727947235,
-0.033254534006118774,
0.024468455463647842,
0.0065620108507573605,
-0.00633794954046607,
-0.003933957312256098,
0.012217161245644093,
-0.013616887852549553,
-0.008437657728791237,
-0.044576890766620636,
-0.00561519293114543,
-0.02500903233885765,
0.03580102697014809,
0.010086984373629093,
-0.008830178529024124,
0.01170862466096878,
0.08399145305156708,
0.007253764197230339,
0.023189125582575798,
0.025657061487436295,
-0.00937233492732048,
0.0029754380229860544,
0.06681843101978302,
0.035521697252988815,
-0.0008003830444067717,
0.014668536372482777,
0.0029161397833377123,
0.01807459443807602,
-0.03945248946547508,
0.004744359292089939,
0.03433748334646225,
-0.03154483810067177,
-0.043252330273389816,
-0.03611910715699196,
0.02284417301416397,
0.017343182116746902,
0.0002659431775100529,
-0.02814577892422676,
-0.03900305554270744,
-0.04101741313934326,
-0.01058531180024147,
-0.0009175129234790802,
0.009388478472828865,
-0.004770871251821518,
-0.004439205396920443,
-0.07152310013771057,
-0.05860787630081177,
-0.05021815374493599,
0.031447943300008774,
0.012504908256232738,
-0.029119202867150307,
0.04775262624025345,
0.004977731499820948,
0.004025040194392204,
0.006141630932688713,
-0.04359523206949234,
-0.016438789665699005,
0.0008579117711633444,
0.012443155981600285,
0.0002009199815802276,
0.018191378563642502,
0.016920503228902817,
0.00741085410118103,
-0.006835258100181818,
0.045679446309804916,
-0.04025683552026749,
-0.006853946018964052,
0.013856719247996807,
-0.0018451454816386104,
-0.010796690359711647,
-0.024968909099698067,
-0.013543159700930119,
-0.012550708837807178,
0.010628730989992619,
-0.011430115438997746,
0.01511200051754713,
-0.020502548664808273,
0.06974584609270096,
0.06481696665287018,
-0.014750823378562927,
0.020667431876063347,
0.0514233261346817,
-0.028009895235300064,
0.05912715569138527,
-0.018014665693044662,
-0.030348556116223335,
-0.019727718085050583,
0.001808859291486442,
0.011697686277329922,
0.025431644171476364,
-0.01928635686635971,
0.026683827862143517,
0.025567656382918358,
0.005075369030237198,
0.05182606726884842,
0.008592754602432251,
-0.017616620287299156,
-0.06128649786114693,
0.027388110756874084,
0.027619367465376854,
-0.009929941967129707,
-0.010697761550545692,
0.00460311584174633,
-0.021221155300736427,
0.007263488136231899,
-0.03007804974913597,
-0.024473054334521294,
0.041064050048589706,
-0.04776332527399063,
-0.004907097667455673,
-0.029914258047938347,
-0.016965143382549286,
0.04395180568099022,
-0.015514599159359932,
0.036616139113903046,
0.01750066503882408,
-0.011139579117298126,
0.005553464870899916,
-0.03350940719246864,
-0.005636787507683039,
0.035077545791864395,
-0.000052225805120542645,
0.011473980732262135,
-0.012168648652732372,
-0.000477504450827837,
-0.005949661135673523,
0.02436363324522972,
0.005444175563752651,
-0.007692018058151007,
-0.03365592285990715,
0.0003129978140350431,
0.03193286061286926,
0.016248099505901337,
-0.04657796025276184,
-0.0427926629781723,
-0.048522502183914185,
0.06405109912157059,
0.03216882422566414,
0.03117331862449646,
0.044346150010824203,
-0.05678786709904671,
-0.009699711576104164,
-0.052091702818870544,
0.0044209156185388565,
0.047658853232860565,
0.010139417834579945,
0.0016375088598579168,
0.030044041574001312,
-0.008390444330871105,
-0.05464722216129303,
-0.017459988594055176,
-0.009335042908787727,
-0.0074547394178807735,
-0.005396292544901371,
0.014387549832463264,
0.03047977201640606,
0.02057981863617897,
-0.020707527175545692,
-0.011886049062013626,
-0.02731694094836712,
-0.013341241516172886,
-0.005766053218394518,
0.022683031857013702,
-0.023282313719391823,
-0.02136288769543171,
0.06392258405685425,
0.028987187892198563,
-0.021713661029934883,
0.010509906336665154,
-0.05353908985853195,
-0.026701441034674644,
0.014553000219166279,
0.039852093905210495,
0.005723064299672842,
0.00997006706893444,
-0.048798978328704834,
0.10100117325782776,
0.0734114795923233,
-0.05823242664337158,
-0.00991574302315712,
-0.0009381970157846808,
-0.016300220042467117,
-0.039486534893512726,
0.014353498816490173,
-0.012242211028933525,
-0.0289917029440403,
0.036568690091371536,
0.015248420648276806,
0.0441562682390213,
-0.0052154818549752235,
0.0018279372015967965,
0.0034662235993891954,
0.07111760973930359,
-0.0016442942433059216,
0.007330428343266249,
0.07334376126527786,
-0.005937295034527779,
-0.007849199697375298,
-0.03226889297366142,
0.037805937230587006,
-0.018111925572156906,
-0.005261386279016733,
-0.04977221414446831,
0.07140961289405823,
0.01879679039120674,
-0.010151735506951809,
-0.028632139787077904,
0.047377023845911026,
0.018699437379837036,
-0.0522228442132473,
-0.04090513661503792,
0.00536787835881114,
0.03572941571474075,
0.0025873775593936443,
-0.004165916703641415,
0.04906373471021652,
0.028050074353814125,
-0.02848988212645054,
-0.042650554329156876,
-0.023657387122511864,
-0.029661349952220917,
0.05341203138232231,
-0.05661366134881973,
-0.05533547326922417,
0.04904155433177948,
0.029280290007591248,
0.021045314148068428,
-0.04979577660560608,
-0.050345826894044876,
0.0020833483431488276,
-0.05940326303243637,
0.030140018090605736,
0.007476109080016613,
0.04405121132731438,
0.05125357583165169,
0.023424655199050903,
0.04964260756969452,
0.03873717039823532,
-0.029805133119225502,
0.05158091336488724,
-0.060083504766225815,
0.01875227876007557,
-0.00033838985837064683,
-0.015413854271173477,
-0.014140178449451923,
-0.01653369516134262,
-0.018846428021788597,
-0.017222462221980095,
-0.027371680364012718,
-0.006209758576005697,
-0.02244444005191326,
-0.02178395353257656,
-0.006258737295866013,
-0.060837917029857635,
-0.015182944014668465,
-0.049175262451171875,
0.06455652415752411,
0.010615247301757336,
-0.017953909933567047,
-0.007547914050519466,
0.012080453336238861,
-0.02728760987520218,
-0.004006094764918089,
-0.019788146018981934,
0.012817634269595146,
0.022208821028470993,
0.019282225519418716,
0.020876791328191757,
-0.016415419057011604,
-0.01198346447199583,
0.01391991414129734,
0.04155999794602394,
0.0507202073931694,
0.017663542181253433,
-0.01977049745619297,
0.0012426634784787893,
-0.022055914625525475,
-0.03363782912492752,
0.051495518535375595,
0.06229206919670105,
0.03980398178100586,
0.008753297850489616,
0.03558940812945366,
0.0184897743165493,
-0.0058571635745465755,
0.04769441485404968,
0.04196678474545479,
0.01480751670897007,
-0.006292618811130524,
-0.0584104023873806,
0.02704584039747715,
0.0012078230502083898,
0.0018678545020520687,
-0.00722663477063179,
-0.013863625004887581,
-0.005565670784562826,
0.005077407695353031,
-0.021260941401124,
0.0205144751816988,
0.0008351066499017179,
0.0037142138462513685,
0.01488919835537672,
-0.004749896936118603,
0.03597114235162735,
-0.00379942380823195,
0.05439215153455734,
0.05102794989943504,
0.029178299009799957,
0.0076642828062176704,
0.018607541918754578,
-0.040765974670648575,
-0.012492557056248188,
0.025736438110470772,
0.05627691000699997,
0.01302454061806202,
0.012451411224901676,
-0.06392303854227066,
-0.025494705885648727,
0.02922327071428299,
-0.002987562445923686,
0.0634203553199768,
0.029218554496765137,
0.019306650385260582,
0.056228697299957275,
-0.04783151298761368,
-0.03792642056941986,
0.014678691513836384,
-0.007227085996419191,
0.006123697850853205,
-0.05022147670388222,
-0.005069376435130835,
-0.007203335408121347,
0.02292475290596485,
-0.01523053552955389,
0.07637505978345871,
0.009686756879091263,
0.001144319074228406,
-0.034649185836315155,
0.03730640187859535,
-0.017734482884407043,
-0.07704784721136093,
-0.006628262810409069,
-0.014508710242807865,
0.007787568960338831,
0.02401966229081154,
-0.02878331020474434,
-0.00979518610984087,
0.025360820814967155,
0.01577630825340748,
0.005034218542277813,
0.0013230788754299283,
-0.059366244822740555,
0.05030396953225136,
0.01347759272903204,
0.011637961491942406,
0.049307793378829956,
0.01898229494690895,
-0.012755811214447021,
-0.0220402292907238,
-0.018945949152112007,
0.021337201818823814,
-0.024156073108315468,
0.04010367766022682,
-0.012719721533358097,
0.02462025173008442,
-0.02128421701490879,
0.03254822641611099,
-0.053190186619758606,
0.013080391101539135,
0.00797209795564413,
0.003761261235922575,
-0.012325385585427284,
0.008562274277210236,
-0.008901345543563366,
-0.005129353143274784,
-0.0030470993369817734,
0.017726462334394455,
-0.005349707789719105,
-0.003674447303637862,
0.025388015434145927,
-0.025878017768263817,
0.0014140037819743156,
0.025022825226187706,
-0.023372214287519455,
0.00854379590600729,
0.013569673523306847,
-0.04539218544960022,
-0.019981984049081802,
-0.03230251744389534,
0.023187343031167984,
0.026927027851343155,
0.02271982468664646,
0.009268229827284813,
-0.028929075226187706,
-0.038354191929101944,
-0.018555214628577232,
-0.006637132726609707,
0.04988320916891098,
-0.048894938081502914,
0.03168810158967972,
0.0023301157634705305,
-0.007858352735638618,
-0.10219567269086838,
-0.03350698947906494,
-0.00037617009365931153,
-0.017305968329310417,
-0.023106910288333893,
-0.02813855931162834,
-0.006310474127531052,
-0.022417591884732246,
-0.01885993778705597,
0.003705308074131608,
0.020794376730918884,
-0.02273269183933735,
0.01877661794424057,
0.023088419809937477,
0.030038943514227867,
0.036867655813694,
-0.04036007821559906,
-0.00011629770597210154,
-0.030782418325543404,
-0.02374992147088051,
-0.01701403222978115,
-0.017690185457468033,
0.029622739180922508,
-0.019285771995782852,
-0.009141000919044018,
-0.011290457099676132,
-0.018459558486938477,
0.040245942771434784,
-0.0074048819951713085,
-0.035473015159368515,
0.017399001866579056,
0.0387277826666832,
0.014240057207643986,
0.009382358752191067,
-0.011987950652837753,
-0.012419652193784714,
0.01360936276614666,
-0.00030111175146885216,
-0.008482851088047028,
-0.016654226928949356,
-0.027082672342658043,
0.05794038623571396,
-0.03095175325870514,
0.008626630529761314,
0.022392841055989265,
0.08904927968978882,
0.016601700335741043,
-0.014814049005508423,
0.040634363889694214,
0.0009128386154770851,
-0.014987001195549965,
-0.013194582425057888,
0.018146542832255363,
-0.01466836966574192,
-0.005192687269300222,
-0.027234170585870743,
-0.02697581984102726,
-0.0029752517584711313,
0.01385862659662962,
0.04701093211770058,
0.011557426303625107,
0.02401183918118477,
0.04584905877709389,
0.009674816392362118,
0.01328989490866661,
0.0381099097430706,
-0.014856738969683647,
0.02130320481956005,
-0.006177709437906742,
0.03576996922492981,
-0.020028460770845413,
-0.03469819948077202,
-0.0019733442459255457,
0.03187042474746704,
-0.05595382675528526,
0.00683730049058795,
0.03124389983713627,
0.01830354705452919,
-0.000301623425912112,
0.010352852754294872,
-0.06803853064775467,
0.037859316915273666,
-0.03581831976771355,
0.046046532690525055,
-0.0030575282871723175,
-0.039023324847221375,
0.012661405839025974,
0.003440063213929534,
0.042269762605428696,
-0.002107033971697092,
-0.013668829575181007,
-0.017458323389291763,
0.04714631289243698,
0.02934926748275757,
0.020046798512339592,
0.00971580296754837,
0.035568077117204666,
0.05223085731267929,
-0.01982545293867588,
0.005201235879212618,
0.0034882575273513794,
-0.025843510404229164,
-0.022526321932673454,
-0.020375875756144524,
-0.04868550971150398,
0.06416436284780502,
-0.027201617136597633,
0.02396647445857525,
-0.0028930858243256807,
0.01435363944619894,
0.01801503449678421,
0.020325390622019768,
0.03643502667546272,
-0.006005538627505302,
0.06606829166412354,
0.010025162249803543,
0.040615856647491455,
-0.015207339078187943,
-0.012156094424426556,
0.1224384605884552,
0.04509473219513893,
0.04517374932765961,
-0.053816404193639755,
-0.03238359093666077,
-0.02050711214542389,
0.018549228087067604,
-0.03284289315342903,
0.025723149999976158,
-0.011337772943079472,
-0.019031917676329613,
-0.01982799917459488,
0.07713581621646881,
0.017475565895438194,
-0.0038480411749333143,
0.04657905921339989,
-0.014151977375149727,
-0.04538245126605034,
0.034478142857551575,
0.011853352189064026,
-0.043557312339544296,
0.014136039651930332,
-0.0698075219988823,
0.019001828506588936,
-0.00841016136109829,
0.014670513570308685,
-0.0624452568590641,
-0.05557728186249733,
0.02468772605061531,
-0.022557472810149193,
-0.006075579207390547,
-0.03441385552287102,
-0.023893458768725395,
-0.020458893850445747,
-0.03431922569870949,
-0.015433846041560173,
0.006853591185063124,
-0.01978544145822525,
0.06004326418042183,
0.0682050883769989,
-0.023081179708242416,
0.02039872296154499,
0.01947953552007675,
0.017913363873958588,
-0.02145586721599102,
-0.0005893630441278219,
-0.02821175754070282,
0.08395069092512131,
-0.014336252585053444,
0.0070800636895000935,
0.033658210188150406,
-0.0012228264240548015,
0.0101096136495471,
-0.02381868101656437,
0.007284156978130341,
-0.016431789845228195,
0.03664299473166466,
-0.013480900786817074,
0.007697140332311392,
-0.009333031252026558,
-0.011135033331811428,
0.013286586850881577,
-0.011542526073753834,
-0.04610930755734444,
0.008237066678702831,
-0.012779866345226765,
-0.005933837499469519,
0.0076040527783334255,
0.004530840087682009,
-0.018752049654722214,
-0.021538371220231056,
-0.02806629054248333,
-0.04165361449122429,
-0.028235679492354393,
0.0070667872205376625,
0.016754182055592537,
0.04782478138804436,
0.005850768648087978,
-0.01267531979829073,
-0.023762516677379608,
-0.0820898786187172,
-0.005370583385229111,
-0.02752002887427807,
0.00015528680523857474,
-0.03810262307524681,
-0.010437589138746262,
0.025724217295646667,
0.04425959661602974,
-0.02649770863354206,
-0.039494313299655914,
0.015002588741481304,
0.03312600404024124,
0.005346348043531179,
-0.034515753388404846,
-0.04246757924556732,
-0.0035619300324469805,
-0.01422915980219841,
0.022002123296260834,
-0.0080158282071352,
-0.0010374622652307153,
-0.007277076598256826,
0.0019081794889643788,
-0.008193141780793667,
0.04987052455544472,
-0.01482995692640543,
-0.007426294963806868,
-0.013251550495624542,
0.018720857799053192,
-0.001417373539879918,
0.043373096734285355,
-0.007115399930626154,
-0.014266871847212315,
-0.0521957091987133,
-0.022524293512105942,
-0.015380681492388248,
0.005149534437805414,
-0.01861133985221386,
-0.02562439814209938,
-0.04038173332810402,
0.03186819329857826,
0.029002545401453972,
-0.0033646984957158566,
0.01057974249124527,
-0.04290812835097313,
0.005546067375689745,
-0.024984372779726982,
-0.012816389091312885,
-0.040725938975811005,
0.03151702880859375,
-0.021060606464743614,
-0.043289583176374435,
0.008226223289966583,
0.02156708389520645,
-0.028644109144806862,
-0.0044466471299529076,
0.014885837212204933,
0.042160481214523315,
0.027256270870566368,
0.02126684971153736,
-0.02071589231491089,
0.022083917632699013,
-0.04064309224486351,
-0.027923395857214928,
0.06986529380083084,
0.014356723986566067,
0.013033285737037659,
0.04197688400745392,
0.0073073250241577625,
0.004080357030034065,
0.02123108133673668,
-0.008503914810717106,
-0.01637060008943081,
-0.042042121291160583,
-0.03190828114748001,
0.009926178492605686,
-0.017164085060358047,
-0.00934966467320919,
-0.006134557072073221,
0.017232049256563187,
-0.0126813855022192,
0.018947986885905266,
-0.02779710851609707,
0.0029968908056616783,
0.008169458247721195,
-0.022585555911064148,
0.013730257749557495,
0.010512451641261578,
0.008057592436671257,
-0.010931308381259441,
0.06041261926293373,
-0.003961081150919199,
0.001504441723227501,
-0.007507750764489174,
0.0011413336033001542,
-0.08701011538505554,
-0.016382426023483276,
0.014930756762623787,
0.031446464359760284,
0.0634935051202774,
-0.05688343942165375,
0.007982336916029453,
0.011135733686387539,
-0.03436246141791344,
-0.000258411921095103,
-0.027867717668414116,
-0.0072976392693817616,
-0.014005225151777267,
-0.005948455072939396,
-0.0003063589392695576,
0.07567037642002106,
0.009740510955452919,
0.04251713305711746,
-0.020386280491948128,
-0.0011315192095935345,
0.01785263977944851,
0.023460738360881805,
-0.05940108001232147,
0.0030120564624667168,
0.030565723776817322,
-0.01220639143139124,
0.05373601242899895,
-0.025828467682003975,
-0.05113421753048897,
0.019540438428521156,
-0.01283408422023058,
-0.01703612133860588,
0.0052394322119653225,
0.02632385678589344,
0.014949687756597996,
0.003037357237190008,
0.014857477508485317,
0.0022627152502536774,
0.03781314194202423,
-0.0031723773572593927,
0.03736235946416855,
0.038557540625333786,
-0.06264421343803406,
-0.001229890389367938,
0.0221728403121233,
-0.012185621075332165,
-0.030442044138908386,
0.035427067428827286,
-0.047529540956020355,
-0.009892097674310207,
-0.017558671534061432,
-0.012135724537074566,
0.011731106787919998,
-0.021089861169457436,
0.026666369289159775,
-0.01945105753839016,
-0.008940039202570915,
0.015522841364145279,
0.014018736779689789,
-0.001112143276259303,
0.03376835584640503,
0.01892074942588806,
-0.020275870338082314,
0.03983399644494057,
0.005766307469457388,
-0.021939564496278763,
-0.05661908537149429,
0.004584749229252338,
-0.034800413995981216,
-0.0033842117991298437,
0.01858227327466011,
-0.03802661970257759,
-0.04791343957185745,
-0.023700231686234474,
0.004438900854438543,
-0.027896178886294365,
-0.027865620329976082,
0.014369557611644268,
0.0034258386585861444,
-0.03978787735104561,
-0.01595642790198326,
0.0020666723139584064,
-0.043805081397295,
-0.005876403767615557,
-0.0002780215290840715,
-0.01690724492073059,
0.03013363480567932,
0.013063466176390648,
-0.004235627595335245,
-0.007479710038751364,
0.051426611840724945,
-0.005487548187375069,
0.009874805808067322,
-0.020990516990423203,
-0.008570694364607334,
-0.014093403704464436,
-0.009869229979813099,
0.013460534624755383,
0.028403587639331818,
-0.01855124905705452,
0.04296832159161568,
-0.001471873838454485,
-0.009884067811071873,
-0.006937848869711161,
0.001993262441828847,
-0.06013747304677963,
0.030412394553422928,
-0.03511064127087593,
0.011295445263385773,
0.04233524948358536,
0.04477515071630478,
0.02427125908434391,
0.028252262622117996,
-0.02838088944554329,
-0.0455365888774395,
0.031396448612213135,
-0.016384199261665344,
-0.019777651876211166,
-0.004040857311338186,
-0.0063489386811852455,
0.020655861124396324,
-0.04360385239124298,
0.004812720697373152,
0.017512613907456398,
-0.0325288325548172,
-0.04155691713094711,
0.05597216263413429,
-0.01137644611299038,
0.02149176225066185,
0.036252450197935104,
0.010743032209575176,
-0.00769687769934535,
-0.015120107680559158,
0.037212785333395004,
0.046129174530506134,
0.01673094742000103,
0.000618841324467212,
0.011886515654623508,
0.02569902315735817,
-0.03463567793369293,
0.00901472195982933,
-0.009727454744279385,
0.0279498640447855,
-0.014266650192439556,
-0.004980345256626606,
0.015601429156959057,
0.0004472454311326146,
-0.010885167866945267,
0.016201624646782875,
-0.038436468690633774,
0.03885376825928688,
-0.041475068777799606,
0.032554224133491516,
-0.009980589151382446,
0.0003610646817833185,
-0.04301224276423454,
0.01782771572470665,
0.03797774389386177,
0.09820416569709778,
0.012747145257890224,
-0.019943390041589737,
-0.04965570569038391,
-0.03913525864481926,
0.022176871076226234,
-0.061521660536527634,
-0.038394246250391006,
0.00900325458496809,
-0.0030043122824281454,
0.0147455595433712,
-0.024134114384651184,
-0.0022721467539668083,
-0.05835539847612381,
-0.020828334614634514,
0.02344576083123684,
0.028006458654999733,
-0.006853105966001749,
-0.03656908497214317,
-0.026236653327941895,
0.0948660597205162,
-0.01488457340747118,
-0.03284347429871559,
-0.012362977489829063,
-0.0036684207152575254,
0.0035766572691500187,
0.0377412773668766
] |
<p>Can someone kindly help me to know how can i get electron momentum density for one orbital like home?
what is the theory of electron momentum density? how can I derive electron momentum density from real electron density?
how can i use Fourier transform?</p>
| 8,470 |
[
-0.026552654802799225,
0.014138455502688885,
0.0027950704097747803,
-0.01959810219705105,
0.028174927458167076,
-0.02126682549715042,
-0.03794620931148529,
-0.026322627440094948,
0.035638146102428436,
-0.04428163170814514,
0.050513856112957,
0.04346252605319023,
0.03902582451701164,
0.021759115159511566,
0.008536331355571747,
0.006897445768117905,
0.0023762453347444534,
0.003592229913920164,
-0.009409436956048012,
-0.0064662969671189785,
-0.016348684206604958,
-0.0022644998971372843,
0.03132947161793709,
-0.0037808893248438835,
-0.021214375272393227,
0.03860000893473625,
0.0369110144674778,
0.0109052499756217,
0.04850633442401886,
0.07868102937936783,
-0.002006974769756198,
-0.039300695061683655,
0.03301076963543892,
0.013140755705535412,
0.032164208590984344,
-0.01459522545337677,
-0.00927854422479868,
-0.028617404401302338,
-0.013547772541642189,
0.05116156488656998,
-0.01968592032790184,
-0.048582930117845535,
-0.008416974917054176,
0.06093648821115494,
0.006542446091771126,
-0.002159950789064169,
0.01006308477371931,
-0.055665262043476105,
0.05358107388019562,
-0.0701274648308754,
0.0916561484336853,
-0.01674995757639408,
0.04070568457245827,
0.03287113457918167,
0.000775594380684197,
0.0052218628115952015,
0.05897412821650505,
0.07393105328083038,
-0.004950816743075848,
-0.03323190659284592,
-0.007710403297096491,
-0.024593308568000793,
-0.00017123224097304046,
-0.007842432707548141,
-0.013774387538433075,
0.033528368920087814,
-0.012716708704829216,
-0.03271116316318512,
0.045240387320518494,
0.0029594844672828913,
0.02060149796307087,
0.016123052686452866,
0.006799707189202309,
-0.035377226769924164,
0.004800870548933744,
-0.03615148738026619,
0.03429395705461502,
-0.007856984622776508,
0.03610631451010704,
0.03551604226231575,
0.000856748316437006,
0.008585491217672825,
0.020756680518388748,
0.020816879346966743,
0.008832129649817944,
-0.005738858599215746,
0.06415331363677979,
0.004257022403180599,
-0.03858371451497078,
0.04563550278544426,
-0.007081617601215839,
0.009099530056118965,
0.04980918765068054,
-0.0054098754189908504,
-0.029428256675601006,
0.03311638906598091,
-0.014606870710849762,
0.07068910449743271,
0.008656912483274937,
-0.02353040687739849,
0.02563554234802723,
-0.040150828659534454,
0.017929762601852417,
0.07539799064397812,
-0.012301991693675518,
-0.018590586259961128,
-0.02375420369207859,
0.006621662061661482,
0.0025889643002301455,
-0.01944032311439514,
0.012455425225198269,
0.03931209817528725,
-0.01627657376229763,
-0.0011932173511013389,
-0.00585763668641448,
0.008962162770330906,
0.014667727053165436,
-0.005482175853103399,
0.024623863399028778,
0.10035379976034164,
0.0052846260368824005,
0.004689101129770279,
0.02427218295633793,
-0.02032262086868286,
-0.0992363691329956,
0.013817664235830307,
0.009090949781239033,
0.026648234575986862,
-0.02972995676100254,
0.030618658289313316,
-0.009820840321481228,
-0.030450543388724327,
0.03858643397688866,
-0.010110250674188137,
0.042325459420681,
-0.005310018081218004,
-0.12504372000694275,
-0.0515512153506279,
0.01874377392232418,
-0.0429997518658638,
-0.016355833038687706,
-0.08722519874572754,
0.023035317659378052,
0.01912853680551052,
0.042269039899110794,
0.008626165799796581,
0.01037286315113306,
-0.04266315698623657,
0.037929244339466095,
0.020245779305696487,
-0.008502879180014133,
-0.017709989100694656,
-0.025325121358036995,
-0.04207257181406021,
0.007002105005085468,
-0.051046598702669144,
0.02330552414059639,
-0.004373951815068722,
-0.012055628001689911,
-0.02058751881122589,
0.08791104704141617,
-0.02262319065630436,
-0.005553058814257383,
-0.0052628587000072,
0.015580789186060429,
-0.03625543415546417,
0.05897507071495056,
0.023352809250354767,
-0.0017252517864108086,
0.062392957508563995,
-0.021005157381296158,
0.0019133280729874969,
-0.004645243752747774,
0.02039380371570587,
0.03309204429388046,
-0.03755978122353554,
-0.03730148449540138,
-0.06271675229072571,
0.05041278526186943,
-0.015268289484083652,
-0.01771249808371067,
-0.016048915684223175,
0.03362483158707619,
0.02457861602306366,
0.006164539605379105,
0.019994700327515602,
-0.0005146109033375978,
-0.013081864453852177,
-0.025338834151625633,
-0.0450923889875412,
-0.007789856754243374,
-0.05944528430700302,
0.03121538832783699,
-0.026122814044356346,
0.015470823273062706,
0.060642026364803314,
-0.0023847816046327353,
0.024394046515226364,
-0.036173973232507706,
-0.031288664788007736,
-0.034212931990623474,
0.029024364426732063,
0.015061860904097557,
-0.013343912549316883,
0.03806691616773605,
0.033464837819337845,
0.030801504850387573,
-0.00590889435261488,
0.014693394303321838,
-0.030271753668785095,
0.0037372540682554245,
-0.007522213738411665,
-0.0022183768451213837,
0.015780437737703323,
0.0038391314446926117,
0.011144201271235943,
-0.0038509198930114508,
0.018217783421278,
0.017052236944437027,
0.0047746701166033745,
-0.030391385778784752,
0.09245747327804565,
0.06350450217723846,
0.05828876793384552,
0.047947853803634644,
0.009976612403988838,
0.015820065513253212,
-0.00333723914809525,
0.03421079367399216,
0.0068903109058737755,
-0.017419127747416496,
0.023909302428364754,
0.04566492512822151,
0.02145310863852501,
-0.04632999747991562,
0.007978074252605438,
0.06591285765171051,
0.013416566886007786,
0.0637681856751442,
0.04605896398425102,
-0.044321004301309586,
-0.03588825464248657,
-0.005195343866944313,
0.0038828689139336348,
0.0066677541472017765,
0.010424897074699402,
0.03563370928168297,
0.026634475216269493,
0.0434250645339489,
-0.004562049638479948,
-0.046402979642152786,
0.05737484619021416,
-0.01766042970120907,
-0.032240282744169235,
-0.017956823110580444,
-0.042794954031705856,
0.01771310530602932,
-0.022653698921203613,
0.029965713620185852,
0.006810758728533983,
-0.04657557234168053,
0.028419073671102524,
-0.0345415398478508,
-0.03673378378152847,
0.02462562546133995,
0.009268282912671566,
-0.01679832860827446,
0.0018082121387124062,
0.007970261387526989,
-0.035398226231336594,
-0.00248505687341094,
-0.004377890378236771,
0.010040421970188618,
-0.007497265003621578,
0.016211437061429024,
0.04006959870457649,
-0.011971446685492992,
0.0010622055269777775,
0.010042324662208557,
-0.052140939980745316,
0.014485028572380543,
-0.020937271416187286,
0.019566763192415237,
-0.021037688478827477,
-0.07954875379800797,
0.007460417225956917,
-0.032522402703762054,
-0.0351298525929451,
0.04643332213163376,
0.028211722150444984,
0.00020119936380069703,
-0.0002470053732395172,
0.022008711472153664,
-0.03979315608739853,
-0.016801318153738976,
-0.015633996576070786,
0.007844082079827785,
-0.0017234962433576584,
0.008524483069777489,
0.041897013783454895,
-0.0486823208630085,
0.013466027565300465,
0.01915368251502514,
0.0021548201330006123,
-0.045797061175107956,
0.01584852859377861,
-0.002769161481410265,
0.00579610001295805,
-0.011554758064448833,
0.03553655743598938,
0.010586603544652462,
-0.04597334936261177,
0.008768084459006786,
-0.04192349687218666,
-0.019334066659212112,
0.01799722947180271,
0.005671342834830284,
0.028821298852562904,
0.005537714809179306,
-0.05780225992202759,
0.07999551296234131,
0.01536956150084734,
-0.04787479341030121,
-0.044938281178474426,
-0.0038964867126196623,
-0.03559121489524841,
-0.018514536321163177,
-0.003430401673540473,
0.0016860043397173285,
0.004572225734591484,
0.01810651458799839,
0.03021671622991562,
0.0019395877607166767,
0.03726409003138542,
0.020288633182644844,
-0.01449953019618988,
0.057312916964292526,
-0.0055245207622647285,
-0.025771694257855415,
0.06583492457866669,
-0.010877897031605244,
-0.023050054907798767,
0.015756037086248398,
0.020134273916482925,
0.013876031152904034,
0.008527985773980618,
-0.06612759083509445,
0.003091470105573535,
0.02843286842107773,
0.0009457819978706539,
-0.025754569098353386,
0.019081853330135345,
0.02495996467769146,
-0.00464296480640769,
0.0007710290374234319,
0.04077613726258278,
0.02647089771926403,
0.001304050674661994,
-0.025918640196323395,
0.04082009196281433,
0.0029331091791391373,
-0.00768562825396657,
-0.04828339442610741,
0.027314476668834686,
0.0043253907933831215,
-0.00039909809129312634,
-0.04576033353805542,
-0.07461751997470856,
0.03352122753858566,
0.027329986914992332,
0.054400112479925156,
-0.0259014330804348,
-0.023780403658747673,
0.030948687344789505,
-0.046244315803050995,
0.018804339691996574,
0.0060822078958153725,
0.07555980235338211,
0.01206118706613779,
0.07273100316524506,
0.04047556594014168,
0.025653740391135216,
0.002715986454859376,
0.01807444542646408,
-0.06279047578573227,
0.05405643209815025,
0.003354144049808383,
-0.0058538648299872875,
-0.040166910737752914,
-0.01312997192144394,
0.01397506520152092,
-0.05113448202610016,
-0.01366531290113926,
-0.019267525523900986,
0.0023599069099873304,
-0.033805739134550095,
0.010758115909993649,
-0.007899893447756767,
0.01704995706677437,
-0.046186693012714386,
0.07767952233552933,
0.00213765911757946,
-0.00963777955621481,
0.007374179549515247,
0.05377152934670448,
-0.022398004308342934,
-0.013127223588526249,
-0.04521986469626427,
0.031958773732185364,
-0.0262314286082983,
0.019275493919849396,
0.03555331379175186,
0.019943123683333397,
-0.016685372218489647,
-0.003398309927433729,
-0.005355468485504389,
0.08455228805541992,
0.040571365505456924,
0.00156483706086874,
-0.00708302715793252,
-0.01643502712249756,
0.02485901489853859,
-0.008758977055549622,
0.02161780372262001,
-0.02124820277094841,
0.017214113846421242,
0.02879898063838482,
-0.009652392938733101,
-0.010443181730806828,
0.036252811551094055,
0.05541452020406723,
-0.0015927967615425587,
-0.017820999026298523,
-0.0600232295691967,
0.018539555370807648,
-0.03398065268993378,
0.017884965986013412,
0.015945542603731155,
-0.002765335375443101,
-0.012817556038498878,
-0.005375626962631941,
-0.0009084700141102076,
0.0002647385699674487,
-0.01389383990317583,
-0.021607663482427597,
-0.01867755316197872,
0.01229427196085453,
-0.006109433714300394,
-0.006742368917912245,
-0.00594763970002532,
0.019437622278928757,
0.03783689811825752,
0.017279399558901787,
0.0022093048319220543,
-0.08210008591413498,
0.014552061446011066,
0.016539115458726883,
0.010898560285568237,
0.0012293043546378613,
0.000954562216065824,
-0.03671243041753769,
-0.014505087397992611,
0.03910119831562042,
-0.025719663128256798,
0.022526461631059647,
-0.02886057086288929,
0.023166721686720848,
-0.0029265540651977062,
-0.017057029530405998,
-0.02929498441517353,
0.0024841877166181803,
-0.018466686829924583,
-0.003536476753652096,
-0.05879976227879524,
0.028266556560993195,
-0.05748487263917923,
0.04825965687632561,
0.013889490626752377,
0.05555715039372444,
0.004924801643937826,
-0.0015425145393237472,
-0.005118802189826965,
0.052485935389995575,
-0.033429600298404694,
-0.08362863212823868,
-0.020195601508021355,
-0.011952066794037819,
0.020806126296520233,
0.02165033482015133,
-0.04510254040360451,
-0.058632198721170425,
0.03167639300227165,
-0.01553712785243988,
-0.027217186987400055,
-0.008228332735598087,
-0.029530225321650505,
0.050088439136743546,
0.011719929985702038,
0.0018162978813052177,
0.05140646919608116,
0.03505752608180046,
-0.0028856240678578615,
-0.0051156748086214066,
-0.05500254034996033,
0.03975425288081169,
-0.037209779024124146,
0.008758345618844032,
-0.035308632999658585,
0.024569332599639893,
-0.016927024349570274,
0.0446232408285141,
-0.040293075144290924,
0.047435443848371506,
0.00110454554669559,
-0.0279763862490654,
0.004762743134051561,
0.03786030411720276,
-0.009389840997755527,
0.0016207573935389519,
0.008253170177340508,
-0.030957737937569618,
-0.01404343731701374,
-0.022327572107315063,
0.004907991737127304,
-0.010486909188330173,
0.03450009226799011,
-0.021152541041374207,
-0.008438151329755783,
0.03767140209674835,
-0.02905656024813652,
-0.013237378560006618,
0.040502697229385376,
-0.036175794899463654,
0.03764737769961357,
-0.010754015296697617,
0.01632978394627571,
0.01079549640417099,
-0.08440882712602615,
-0.01890573278069496,
0.022820934653282166,
-0.008970142342150211,
0.06877095252275467,
-0.03088267147541046,
-0.0033484571613371372,
0.0072037517093122005,
0.013304103165864944,
-0.06637051701545715,
-0.010015836916863918,
0.01504848338663578,
0.010511990636587143,
-0.020874852314591408,
-0.030931953340768814,
0.0011348130647093058,
0.008535896427929401,
-0.004399978555738926,
0.01907307282090187,
0.02513662725687027,
-0.019555049017071724,
-0.032759133726358414,
0.009093549102544785,
-0.023788221180438995,
0.03716886043548584,
-0.00974209699779749,
-0.026648886501789093,
-0.018990235403180122,
-0.016133736819028854,
-0.0025703557766973972,
0.0051035392098128796,
0.023560741916298866,
-0.019704779610037804,
-0.016667358577251434,
-0.02644052729010582,
-0.016847586259245872,
0.028567150235176086,
-0.034273020923137665,
-0.009763224050402641,
-0.002144907834008336,
0.04774005338549614,
0.010309579782187939,
-0.032537203282117844,
0.022949328646063805,
-0.017227590084075928,
0.03709099069237709,
0.009118521586060524,
-0.0008055651560425758,
-0.05395996570587158,
-0.031707514077425,
-0.002352172276005149,
-0.009495578706264496,
0.026201710104942322,
0.020553914830088615,
0.04636715352535248,
0.02573009394109249,
0.01732739433646202,
0.038263123482465744,
0.0013133484171703458,
-0.028587210923433304,
-0.01232533622533083,
0.014470428228378296,
0.033478155732154846,
0.04080615192651749,
-0.019900668412446976,
-0.03466474637389183,
-0.02629905939102173,
0.004086545668542385,
0.04869557172060013,
-0.030030982568860054,
0.04062686115503311,
0.029257114976644516,
0.02725508250296116,
-0.037197310477495193,
0.02341529168188572,
-0.034791626036167145,
-0.01838335581123829,
-0.029871037229895592,
0.07290762662887573,
-0.00234321691095829,
-0.008654589764773846,
0.032209448516368866,
0.04500100016593933,
-0.031636398285627365,
0.03115185536444187,
0.028591332957148552,
0.021956348791718483,
0.013959546573460102,
-0.0035996423102915287,
-0.03558637946844101,
0.05100564286112785,
-0.0016989439027383924,
0.029631195589900017,
-0.02175118215382099,
0.014015182852745056,
0.04056653752923012,
0.03560718148946762,
-0.009365205653011799,
-0.027550900354981422,
-0.04870457574725151,
-0.002194344298914075,
0.029491817578673363,
0.041271086782217026,
-0.020648211240768433,
-0.027147386223077774,
0.043648187071084976,
0.0235589686781168,
0.006103630643337965,
0.014860996976494789,
0.013638120144605637,
-0.04219641909003258,
-0.019534632563591003,
-0.03875868022441864,
-0.06593156605958939,
0.015647556632757187,
-0.011237242259085178,
-0.017329251393675804,
0.02225147746503353,
0.01178645994514227,
0.038645848631858826,
0.02452736534178257,
0.003075822489336133,
-0.0026593999937176704,
0.0679541677236557,
0.00007055781316012144,
0.0022900039330124855,
0.018765205517411232,
-0.0028653941117227077,
0.10545766353607178,
0.064837746322155,
0.03521028161048889,
-0.0897783562541008,
-0.02848474308848381,
-0.03083363175392151,
0.02170179970562458,
-0.046789538115262985,
0.03333541750907898,
-0.014850523322820663,
0.0179128460586071,
-0.02013140358030796,
0.05757836624979973,
0.006295534782111645,
0.03057895600795746,
0.03422444686293602,
0.005786791909486055,
-0.05966497212648392,
0.0005032848566770554,
0.01313529908657074,
-0.023072727024555206,
-0.002873588353395462,
-0.04378814995288849,
0.0033730012364685535,
-0.05082681030035019,
0.004470130428671837,
-0.04970284923911095,
-0.045940324664115906,
0.029512004926800728,
-0.03806552290916443,
-0.026947494596242905,
-0.011104386299848557,
-0.010529180988669395,
-0.0032196911051869392,
-0.019431691616773605,
0.008731778711080551,
0.032392535358667374,
-0.006526558194309473,
0.024540552869439125,
0.02333306521177292,
-0.0073569598607718945,
0.004755895584821701,
-0.005441050976514816,
0.011229339055716991,
-0.02248576283454895,
-0.009604074992239475,
-0.02320183999836445,
0.04044349491596222,
-0.01866001822054386,
-0.012905368581414223,
-0.0074914805591106415,
0.009585131891071796,
0.007422429975122213,
-0.04086996987462044,
-0.019378481432795525,
-0.00273838359862566,
0.059255585074424744,
-0.025508852675557137,
-0.034031663089990616,
-0.041692908853292465,
0.02118329145014286,
-0.013225706294178963,
0.008850079961121082,
-0.03199796751141548,
-0.018803969025611877,
0.008417067117989063,
-0.02071097120642662,
0.04514532908797264,
-0.03349580988287926,
-0.03232146427035332,
-0.040781326591968536,
-0.024547604843974113,
-0.03813022002577782,
-0.031144650653004646,
0.03239108622074127,
-0.0009852075017988682,
0.06045965105295181,
-0.023565925657749176,
-0.011693623848259449,
-0.02469780296087265,
-0.08051347732543945,
0.017563294619321823,
-0.031243067234754562,
-0.01090188603848219,
-0.01123418565839529,
0.0114273177459836,
0.05121982842683792,
0.08324485272169113,
-0.007883560843765736,
0.015004857443273067,
0.024871382862329483,
-0.01728042960166931,
0.02010430581867695,
-0.06588513404130936,
-0.035167016088962555,
0.004695042967796326,
-0.004531161859631538,
-0.016489611938595772,
-0.04351142421364784,
0.0020520922262221575,
0.034287650138139725,
-0.026182930916547775,
-0.0009013889939524233,
0.022067921236157417,
-0.0500962920486927,
0.019612736999988556,
-0.025484275072813034,
-0.022106073796749115,
0.012176092714071274,
0.006397524382919073,
-0.0035495515912771225,
-0.01898261159658432,
-0.029072314500808716,
-0.02325204201042652,
-0.018594998866319656,
0.0158900935202837,
0.0321924090385437,
-0.015545503236353397,
-0.00043380449642427266,
0.008717191405594349,
0.018811652436852455,
-0.02370430715382099,
0.025103673338890076,
-0.0007653108914382756,
0.04511379450559616,
0.0006225408869795501,
-0.02705264464020729,
-0.03218788653612137,
0.04272032156586647,
0.012035041116178036,
-0.0120060620829463,
0.051897529512643814,
0.012160749174654484,
0.00720900297164917,
-0.0003614706511143595,
0.018026722595095634,
-0.01655445620417595,
0.0391496866941452,
-0.013017338700592518,
0.007813338190317154,
0.03755451366305351,
-0.055949531495571136,
-0.03819300979375839,
0.02718338742852211,
-0.005119129549711943,
0.02410162054002285,
0.044777508825063705,
0.0046602888032794,
-0.03007976897060871,
0.04612230136990547,
0.006262829527258873,
-0.001196154160425067,
0.012617639265954494,
-0.030740957707166672,
-0.0044358824379742146,
0.009069648571312428,
0.005332252476364374,
-0.029688365757465363,
-0.021369261667132378,
0.051353029906749725,
0.01820625364780426,
0.0205551590770483,
0.0317424051463604,
0.0158564280718565,
0.00857771560549736,
0.021333109587430954,
0.036470185965299606,
-0.015166018158197403,
0.01526042353361845,
0.03428889065980911,
-0.012209024280309677,
0.011781299486756325,
0.00436205230653286,
0.0037639669608324766,
-0.06749556958675385,
-0.0036545058246701956,
-0.01723512075841427,
-0.02095203846693039,
0.05289708822965622,
-0.048026714473962784,
-0.007849293760955334,
0.021800611168146133,
-0.06617796421051025,
0.002928647445514798,
-0.011769241653382778,
-0.029055384919047356,
-0.03493918105959892,
0.01544122863560915,
-0.009808999486267567,
0.05627838149666786,
0.009564569219946861,
0.05296234413981438,
0.03511190041899681,
0.013554032891988754,
-0.0003900045994669199,
0.0073329429142177105,
-0.014836933463811874,
0.027018116787075996,
-0.010273202322423458,
-0.0397026389837265,
0.0427020899951458,
-0.04623271897435188,
-0.038270894438028336,
0.03522329777479172,
0.005915567744523287,
0.005683936178684235,
-0.03113066591322422,
0.03007916547358036,
-0.022817669436335564,
0.013686850666999817,
0.011779099702835083,
-0.0247493889182806,
-0.020630590617656708,
0.020927540957927704,
0.015318835154175758,
0.014499954879283905,
-0.011538967490196228,
0.00023962935665622354,
0.011081776581704617,
-0.029743868857622147,
-0.04820924997329712,
0.05511460453271866,
-0.0038401782512664795,
-0.000324987166095525,
-0.007000960875302553,
-0.035184551030397415,
0.016047002747654915,
-0.03933390602469444,
0.01184762455523014,
-0.0511762760579586,
-0.012521250173449516,
0.0030485556926578283,
-0.0264148972928524,
-0.004343095701187849,
0.03954374045133591,
-0.014816861599683762,
-0.07040371000766754,
0.0600958950817585,
-0.0047062719240784645,
-0.027871016412973404,
-0.0758819431066513,
0.00942564383149147,
0.04204382002353668,
-0.003318656934425235,
0.01946241408586502,
-0.04973897337913513,
-0.024004420265555382,
0.04543688893318176,
-0.010426866821944714,
-0.021256566047668457,
-0.001018896815367043,
-0.015584620647132397,
0.017106810584664345,
-0.035248566418886185,
0.026232382282614708,
0.004137302748858929,
-0.015353841707110405,
0.002969390479847789,
-0.029524145647883415,
0.01325809396803379,
0.0040922206826508045,
0.0399269163608551,
-0.0018097752472385764,
0.011009649373590946,
-0.02549012005329132,
-0.014914972707629204,
-0.007845236919820309,
-0.06850925832986832,
0.00391815323382616,
-0.008208495564758778,
-0.05277963727712631,
-0.000270584860118106,
-0.013339443132281303,
-0.027166062965989113,
0.035700004547834396,
0.0014709084061905742,
0.025114011019468307,
-0.006024132948368788,
-0.008915161713957787,
-0.03609085828065872,
0.055005475878715515,
-0.01663065329194069,
-0.02265925705432892,
0.06213470175862312,
-0.019524939358234406,
-0.013093186542391777,
0.014123947359621525,
-0.01972915418446064,
-0.03253217414021492,
0.01087921392172575,
-0.04618590325117111,
-0.0354091078042984,
-0.033964455127716064,
-0.012269102036952972,
0.050826095044612885,
-0.04140629991889,
-0.008801675401628017,
0.051002465188503265,
-0.03508472815155983,
0.009499392472207546,
0.06999757140874863,
0.007378494367003441,
0.041419196873903275,
-0.005720698274672031,
0.011773769743740559,
-0.008523254655301571,
-0.02603522129356861,
0.008188006468117237,
0.012257690541446209,
0.03261991962790489,
-0.017952734604477882,
0.05332823097705841,
0.03541356697678566,
-0.002591292606666684,
0.009464765898883343,
-0.011487634852528572,
0.036493487656116486,
-0.048911791294813156,
-0.00395690044388175,
0.0061579979956150055,
-0.06303463876247406,
-0.011564993299543858,
0.019640294834971428,
-0.04087093099951744,
0.08722759783267975,
-0.030075782909989357,
-0.008124505169689655,
-0.0007432918064296246,
-0.024669788777828217,
-0.03859376162290573,
0.016160545870661736,
0.02941279672086239,
0.03672270476818085,
-0.007627104874700308,
-0.014584051445126534,
0.0034017821308225393,
-0.024719366803765297,
0.033727359026670456,
-0.04180188477039337,
0.017336342483758926,
-0.0012107950169593096,
-0.01749372109770775,
-0.0026874702889472246,
0.0023756667505949736,
-0.056962985545396805,
-0.03131803125143051,
-0.00022555433679372072,
0.028352070599794388,
0.03437313437461853,
0.006082836538553238,
-0.030611146241426468,
-0.016438886523246765,
0.063487708568573,
-0.038835227489471436,
-0.009758480824530125,
-0.020290199667215347,
0.0019212585175409913,
-0.02347598411142826,
-0.006158466916531324
] |
<p><strong>Can a student with a heavy math background start learning physics with Goldstein's "Classical Mechanics"?</strong></p>
<p>Or is the book too obtuse with basic physics that I need to start elsewhere?</p>
| 277 |
[
-0.004738819785416126,
-0.03288375958800316,
0.030701996758580208,
-0.030404476448893547,
0.01792590133845806,
0.027344100177288055,
-0.009030231274664402,
-0.04648137092590332,
-0.02200228162109852,
-0.008861960843205452,
0.030816378071904182,
0.02019542083144188,
0.04798734933137894,
0.040620554238557816,
0.022892843931913376,
0.0022901128977537155,
0.03310970216989517,
-0.030007079243659973,
-0.012946984730660915,
-0.031565699726343155,
-0.02697250247001648,
-0.017632320523262024,
-0.03011130355298519,
0.015108773484826088,
-0.014141486957669258,
0.03913987800478935,
0.027047790586948395,
-0.039020683616399765,
0.001574297551997006,
0.045257750898599625,
-0.00506986491382122,
0.044731173664331436,
0.011493504047393799,
-0.00203990051522851,
0.03852554038167,
0.015730392187833786,
-0.021697457879781723,
-0.011367573402822018,
-0.0024632031563669443,
-0.01820910908281803,
-0.032263800501823425,
0.0016306991456076503,
-0.011576388031244278,
0.05283097177743912,
-0.005922173149883747,
0.06892969459295273,
-0.0022636379580944777,
0.008263030089437962,
0.01880965568125248,
-0.03559368476271629,
0.0452413447201252,
0.02514832653105259,
0.03026069514453411,
0.030356207862496376,
-0.01824730634689331,
-0.031922683119773865,
0.07676858454942703,
0.04589753970503807,
-0.00657674903050065,
-0.038260191679000854,
-0.009037126787006855,
-0.008363048546016216,
-0.00656643183901906,
-0.039916444569826126,
-0.023599158972501755,
0.04949671030044556,
0.025006704032421112,
-0.03478958457708359,
0.047005411237478256,
-0.023188507184386253,
-0.010371563956141472,
0.029603859409689903,
0.057517632842063904,
-0.0026542237028479576,
0.011566259898245335,
-0.012490645982325077,
-0.0010732231894508004,
0.015940330922603607,
0.0001584856800036505,
0.0057857888750731945,
-0.003259336343035102,
0.00704905716702342,
0.051599420607089996,
0.06278347223997116,
0.02652784250676632,
-0.03748548775911331,
0.06766726821660995,
0.01633611135184765,
0.0024200405459851027,
0.023250948637723923,
-0.025935286656022072,
0.015051278285682201,
-0.008724376559257507,
0.004984414670616388,
-0.007662618067115545,
0.03241614252328873,
0.008309713564813137,
0.06333661824464798,
0.02282284013926983,
-0.017207350581884384,
0.028825193643569946,
-0.03883487358689308,
0.03706460818648338,
0.02987808547914028,
0.029798075556755066,
-0.013562013395130634,
-0.02579132653772831,
0.012666595168411732,
-0.044578906148672104,
-0.03954286500811577,
-0.016676703467965126,
0.026784537360072136,
-0.03313307836651802,
-0.006777223199605942,
0.0042355419136583805,
-0.037585530430078506,
-0.016255324706435204,
-0.011439465917646885,
0.05061645805835724,
0.02012835256755352,
0.06805960834026337,
-0.028047559782862663,
0.027085697278380394,
-0.028997987508773804,
-0.06290643662214279,
-0.023401014506816864,
0.030819501727819443,
-0.03941963613033295,
-0.04405137151479721,
0.0035952578764408827,
0.007122431881725788,
0.02400246448814869,
-0.042293086647987366,
0.019011324271559715,
0.01609189435839653,
-0.008509364910423756,
-0.05946608632802963,
-0.0754394456744194,
0.07559153437614441,
-0.008055889047682285,
-0.037121858447790146,
-0.05278143286705017,
0.011774619109928608,
0.03086368553340435,
0.03546791151165962,
0.007255622651427984,
0.02039417065680027,
0.00654491875320673,
0.03578492999076843,
-0.013719921931624413,
-0.02702890895307064,
-0.0004728160274680704,
-0.032742902636528015,
0.0021938197314739227,
0.012412614189088345,
-0.09351886063814163,
0.015071040950715542,
0.040326397866010666,
0.025004781782627106,
0.0007581948302686214,
0.02980172634124756,
-0.030229004099965096,
-0.002704736078158021,
0.03315208479762077,
-0.016237840056419373,
-0.028306279331445694,
0.058179643005132675,
0.03248719498515129,
0.03707998991012573,
0.0205614622682333,
-0.0008254151325672865,
0.07656040787696838,
-0.01887219026684761,
0.003666833508759737,
0.03852766379714012,
-0.018899688497185707,
-0.014919592998921871,
0.018931971862912178,
0.011165700852870941,
0.01657986268401146,
-0.0030027786269783974,
-0.04824959486722946,
-0.003784497734159231,
0.0343286357820034,
-0.04143514111638069,
0.0423651784658432,
0.03377119079232216,
0.056041717529296875,
-0.007614111062139273,
0.0017234798287972808,
-0.02777126245200634,
-0.030930813401937485,
0.051249582320451736,
-0.04608740657567978,
-0.013397891074419022,
0.03256388381123543,
0.0211537666618824,
0.03603074327111244,
-0.019758421927690506,
-0.031242799013853073,
-0.010239562951028347,
-0.00748625211417675,
-0.006838636007159948,
-0.0034834076650440693,
0.01778605580329895,
0.08258755505084991,
0.05789004638791084,
-0.028239166364073753,
0.00668718246743083,
-0.020205698907375336,
-0.011151131242513657,
-0.005364069249480963,
0.0008199299918487668,
0.019414229318499565,
0.023254578933119774,
0.03254857286810875,
0.015197898261249065,
-0.04346274212002754,
-0.022161517292261124,
0.03636641427874565,
-0.05241496115922928,
0.038708582520484924,
0.03474313020706177,
0.012992482632398605,
0.014840478077530861,
0.059190962463617325,
0.018841736018657684,
0.007641721982508898,
0.030978301540017128,
0.020763201639056206,
-0.015978455543518066,
-0.02184474468231201,
0.02658124640583992,
0.04454131796956062,
-0.03051966242492199,
0.06443096697330475,
0.04842386394739151,
0.025594979524612427,
0.035220518708229065,
0.005245860666036606,
-0.02697298303246498,
-0.06281855702400208,
0.03420086205005646,
0.019472315907478333,
-0.01436650287359953,
0.01289212517440319,
0.032863277941942215,
0.01852003112435341,
-0.02239994704723358,
0.015152898617088795,
-0.015945864841341972,
0.01458724495023489,
-0.001618646434508264,
0.019149553030729294,
0.025180475786328316,
-0.03442149609327316,
0.04147575423121452,
0.0007931159343570471,
0.032437946647405624,
0.01630328595638275,
-0.023332960903644562,
-0.0049742418341338634,
-0.037265896797180176,
-0.020767774432897568,
-0.05342867597937584,
0.003532429225742817,
0.005553844850510359,
-0.0165124349296093,
0.051086973398923874,
-0.08144966512918472,
-0.02880333736538887,
0.024231204763054848,
-0.044676680117845535,
-0.026803579181432724,
-0.02122483029961586,
0.01912948302924633,
-0.006155869457870722,
0.03135088458657265,
-0.08659446239471436,
-0.017633074894547462,
0.003226746106520295,
-0.030339395627379417,
-0.009447301737964153,
0.020831430330872536,
-0.028165994212031364,
0.001955070300027728,
-0.041947923600673676,
-0.01981406845152378,
0.044555842876434326,
-0.014563548378646374,
0.021761054173111916,
0.03832899406552315,
-0.013899181969463825,
-0.013489307835698128,
-0.010958177968859673,
-0.030329504981637,
-0.03258230537176132,
-0.05810470134019852,
-0.0301467664539814,
0.04458002373576164,
-0.03319511190056801,
-0.026542533189058304,
-0.03395848721265793,
-0.041394710540771484,
-0.07993898540735245,
-0.021358579397201538,
0.008170435205101967,
0.01626448892056942,
-0.021114638075232506,
-0.05517130345106125,
0.027206094935536385,
-0.05426839739084244,
0.0363733172416687,
-0.07097738981246948,
-0.05656241625547409,
0.04520290717482567,
0.008020074106752872,
0.026759643107652664,
0.0448007732629776,
-0.029266228899359703,
0.09220768511295319,
0.013545497320592403,
-0.04366180673241615,
-0.01987374760210514,
-0.017574399709701538,
-0.02203720435500145,
-0.02390221133828163,
0.007811693008989096,
0.02602475695312023,
-0.03531600162386894,
-0.015818847343325615,
0.01831728406250477,
0.019441887736320496,
0.040195755660533905,
0.002610105089843273,
0.010085584595799446,
0.023880282416939735,
-0.018554946407675743,
0.009280451573431492,
0.02219286374747753,
0.01583588495850563,
-0.044561441987752914,
-0.03308137133717537,
-0.025059271603822708,
0.032679397612810135,
0.010467837564647198,
-0.033725935965776443,
0.06832681596279144,
0.01887432299554348,
0.004005770199000835,
-0.011022966355085373,
0.02678166888654232,
-0.0061589679680764675,
-0.013720443472266197,
0.01619398407638073,
-0.018679115921258926,
0.009356323629617691,
0.01087099313735962,
-0.0014983300352469087,
0.03490106388926506,
0.03898575156927109,
-0.006582899484783411,
-0.005622350610792637,
0.02669382095336914,
-0.024247420951724052,
0.001955852610990405,
-0.013122121803462505,
0.03427170589566231,
0.0401853583753109,
0.005241739563643932,
0.036608655005693436,
0.032155852764844894,
-0.02992973104119301,
0.009575874544680119,
-0.060353975743055344,
0.006817810237407684,
0.01109192706644535,
0.019558658823370934,
-0.006454770918935537,
0.049038417637348175,
0.012702501378953457,
0.004744398407638073,
0.03217357397079468,
-0.011107955127954483,
-0.05720173195004463,
0.036306824535131454,
-0.0330871045589447,
-0.011240154504776001,
0.01602749526500702,
0.026313262060284615,
-0.0025782075244933367,
-0.024803414940834045,
-0.04319529980421066,
-0.03679724037647247,
-0.0004937800113111734,
-0.04558343067765236,
0.019494397565722466,
-0.044840436428785324,
-0.033029429614543915,
0.011716844514012337,
0.0032871458679437637,
0.046188462525606155,
-0.03816327080130577,
0.04035281389951706,
0.05060676485300064,
-0.030096663162112236,
0.01012752391397953,
-0.019351668655872345,
0.02241646684706211,
0.006191439460963011,
0.011637566611170769,
-0.007767510134726763,
0.047054223716259,
-0.008351732045412064,
0.022541599348187447,
-0.008709467947483063,
0.02693885564804077,
0.020272154361009598,
-0.02653706632554531,
-0.027039295062422752,
-0.05308784171938896,
-0.03926174342632294,
-0.011409400962293148,
0.0165695920586586,
0.0074886418879032135,
-0.007913053035736084,
0.06018440052866936,
-0.040551189333200455,
-0.02134929597377777,
0.045104291290044785,
0.025012735277414322,
0.013643343932926655,
-0.01559359859675169,
-0.031606435775756836,
-0.01727081835269928,
-0.05888599529862404,
0.001793628791347146,
0.030285267159342766,
-0.0033124724868685007,
-0.030130423605442047,
0.01409852597862482,
0.013105805031955242,
0.024549992755055428,
-0.055021464824676514,
-0.008894521743059158,
-0.02863900735974312,
0.031363263726234436,
-0.003010038984939456,
-0.013285432942211628,
0.04997171089053154,
0.03842375427484512,
0.039137452840805054,
-0.0061945924535393715,
-0.020585086196660995,
-0.05671427398920059,
-0.011745153926312923,
0.038921330124139786,
0.025008738040924072,
-0.006952669471502304,
0.05435551702976227,
-0.06984525173902512,
-0.02005303092300892,
0.06228030100464821,
-0.018706128001213074,
0.032116297632455826,
-0.04449149966239929,
0.008910511620342731,
-0.03250091150403023,
-0.059965599328279495,
-0.05069814249873161,
0.027735218405723572,
-0.012908429838716984,
0.019613228738307953,
-0.007777686230838299,
0.019825082272291183,
0.005586306564509869,
0.06547985970973969,
0.035768117755651474,
0.03738540783524513,
0.025082429870963097,
-0.02114948071539402,
-0.012180722318589687,
-0.013518565334379673,
-0.02244693599641323,
-0.07626587152481079,
-0.012189066037535667,
-0.045181285589933395,
-0.014236560091376305,
-0.00593503937125206,
-0.017295531928539276,
-0.043333638459444046,
-0.009733005426824093,
-0.021686751395463943,
0.012510397471487522,
-0.01892838440835476,
-0.04365826025605202,
0.004567118361592293,
0.014710078947246075,
0.007798667531460524,
-0.00036314286990091205,
0.042047545313835144,
-0.019820572808384895,
-0.0142184067517519,
-0.04495900869369507,
0.029206950217485428,
-0.03077942691743374,
0.005490518640726805,
-0.02281344123184681,
-0.021413451060652733,
-0.029246466234326363,
0.05620643496513367,
-0.018295614048838615,
0.0009888381464406848,
-0.024745233356952667,
-0.00967235304415226,
0.021007196977734566,
-0.00400206446647644,
0.00034404938924126327,
-0.00628644647076726,
-0.02193579636514187,
0.017314957454800606,
-0.007894620299339294,
0.006598080042749643,
0.01951741799712181,
-0.002419241238385439,
0.03900253772735596,
0.02046063542366028,
-0.012522285804152489,
0.011646191589534283,
-0.06704491376876831,
-0.005337180569767952,
-0.006530770566314459,
-0.06935101002454758,
0.08789709955453873,
-0.008041235618293285,
-0.006880301050841808,
0.04147215560078621,
-0.056420087814331055,
-0.02617417275905609,
0.01848013699054718,
-0.0026366938836872578,
0.009488120675086975,
-0.010401459410786629,
0.023308467119932175,
-0.006551710888743401,
0.000026532175979809836,
-0.011853193864226341,
-0.06583128869533539,
-0.0010308967903256416,
0.014556383714079857,
-0.006548670586198568,
-0.014789427630603313,
0.04035225883126259,
-0.01683952286839485,
0.008673994801938534,
-0.00959586538374424,
0.04387704282999039,
0.004752823151648045,
-0.003573950147256255,
0.032317765057086945,
0.003981630317866802,
0.04486117884516716,
0.00125521095469594,
-0.013007676228880882,
0.028697462752461433,
0.009026188403367996,
-0.0018513464601710439,
-0.016205307096242905,
0.08379465341567993,
-0.009011544287204742,
-0.05317991226911545,
0.0009094823035411537,
0.034914351999759674,
0.03184757009148598,
-0.03264620900154114,
0.013923720456659794,
0.04061099886894226,
0.001524861785583198,
-0.02514566294848919,
-0.017742743715643883,
0.004447140730917454,
0.002022723900154233,
0.025511808693408966,
0.013216853141784668,
0.031020501628518105,
0.00975658930838108,
-0.03773542493581772,
0.06384804099798203,
0.013930005952715874,
0.010875320062041283,
-0.014869708567857742,
0.06134355813264847,
0.0076034520752727985,
-0.01805177517235279,
0.012789924629032612,
-0.021088343113660812,
-0.01442501600831747,
-0.01056599896401167,
0.007985603995621204,
0.03149431571364403,
0.012374861165881157,
-0.027722027152776718,
-0.05492101609706879,
-0.04859233647584915,
0.03547762334346771,
0.0802081748843193,
0.011536505073308945,
0.046687379479408264,
0.015206532552838326,
0.003446414601057768,
0.032132066786289215,
0.00006492297688964754,
-0.011816834099590778,
-0.03376622498035431,
0.02014812082052231,
0.014527049846947193,
-0.04459170624613762,
0.006915878504514694,
0.022466279566287994,
0.01716465689241886,
-0.004771798849105835,
0.0076449355110526085,
0.029705878347158432,
0.010085280053317547,
-0.026400774717330933,
0.006732448469847441,
-0.050340685993433,
0.0371268168091774,
-0.04932893067598343,
0.042434122413396835,
-0.04833480715751648,
-0.0543380081653595,
0.04265264421701431,
0.0344119668006897,
0.009990782476961613,
0.0043349736370146275,
0.01601250469684601,
-0.04991737753152847,
0.01439984142780304,
0.023560291156172752,
0.03146001696586609,
-0.009150217287242413,
0.029729332774877548,
0.03762762248516083,
-0.020885447040200233,
0.0011934941867366433,
-0.004634069744497538,
-0.06865882873535156,
-0.03454722836613655,
-0.028674639761447906,
-0.045874640345573425,
0.04440414905548096,
0.008540399372577667,
-0.021500419825315475,
0.038142528384923935,
-0.018371213227510452,
0.052397698163986206,
0.015181880444288254,
0.04368951544165611,
-0.026686975732445717,
0.04276592284440994,
0.004843483213335276,
-0.02882574312388897,
-0.005883470177650452,
-0.007375702727586031,
0.14486649632453918,
0.04172568395733833,
-0.015016788616776466,
-0.07364068925380707,
-0.004842808470129967,
-0.04402072727680206,
0.023468317463994026,
-0.018378257751464844,
0.0013033094583079219,
-0.04732361063361168,
0.004152176436036825,
0.008309698663651943,
0.049901217222213745,
0.008330797776579857,
-0.0011675632558763027,
0.04328596964478493,
-0.07443106919527054,
-0.030390258878469467,
-0.0076671987771987915,
-0.0008478880627080798,
0.006201476790010929,
0.019854797050356865,
-0.0011875841300934553,
0.01352658774703741,
-0.03992735967040062,
-0.009368427097797394,
-0.013108239509165287,
-0.028645319864153862,
0.025235256180167198,
-0.02134588547050953,
-0.021896347403526306,
0.01594337448477745,
0.03669185936450958,
-0.035347435623407364,
-0.019868064671754837,
0.0408250130712986,
0.04111017659306526,
-0.018587704747915268,
0.021239055320620537,
0.01883130893111229,
-0.012893825769424438,
0.0019239612156525254,
-0.0041066729463636875,
0.0020963866263628006,
-0.023062855005264282,
0.03550276532769203,
-0.02588047832250595,
0.05069739744067192,
-0.003195511642843485,
0.033803608268499374,
0.009564918465912342,
-0.00505483103916049,
-0.0005050452309660614,
-0.08116762340068817,
0.016714971512556076,
-0.007665838114917278,
0.013617332093417645,
-0.03942739591002464,
-0.032143864780664444,
-0.05154766887426376,
0.008393852971494198,
-0.045066431164741516,
0.0065652234479784966,
-0.004145809914916754,
-0.03343501687049866,
0.02440924569964409,
0.000057043576816795394,
0.005013762041926384,
-0.022818055003881454,
-0.0181181188672781,
-0.06662917137145996,
0.01802155375480652,
-0.04803577437996864,
-0.018163172528147697,
-0.020883962512016296,
0.0191055741161108,
0.047309018671512604,
0.00359178869985044,
-0.03954918310046196,
-0.022773325443267822,
-0.047116607427597046,
0.042706068605184555,
-0.0017355415038764477,
0.02529853582382202,
-0.020650047808885574,
-0.02957606501877308,
0.04221103712916374,
0.05794334039092064,
0.02231973595917225,
0.012258718721568584,
0.021488768979907036,
0.03474089503288269,
0.03855050727725029,
0.029432352632284164,
0.012455659918487072,
0.021025246009230614,
-0.019543305039405823,
0.02247520349919796,
-0.021834511309862137,
0.012976127676665783,
0.022855669260025024,
0.008502916432917118,
-0.013524468056857586,
0.03140828385949135,
-0.0017203821334987879,
0.024351751431822777,
0.02451406605541706,
-0.04598550125956535,
-0.00735448906198144,
0.04844297468662262,
0.03527826815843582,
-0.04600758105516434,
-0.040136825293302536,
-0.026676887646317482,
-0.015042703598737717,
-0.03259008005261421,
0.057349469512701035,
-0.022990524768829346,
0.044778164476156235,
0.005680031608790159,
-0.009181474335491657,
-0.03849364444613457,
0.0108336815610528,
-0.054264768958091736,
-0.0007652428466826677,
0.006792528089135885,
-0.022095460444688797,
-0.01241510920226574,
0.04360513016581535,
0.01905044913291931,
0.0006898442516103387,
0.02893298678100109,
0.029673665761947632,
0.01957191526889801,
-0.029690256342291832,
0.028119441121816635,
-0.024638071656227112,
0.02837464213371277,
-0.001261505065485835,
-0.01761770248413086,
0.02207573503255844,
-0.03884424641728401,
-0.04285651817917824,
-0.021328995004296303,
-0.014251625165343285,
0.012084062211215496,
0.035010699182748795,
-0.04435979202389717,
-0.01017913967370987,
0.04669392853975296,
-0.007283448241651058,
-0.038485318422317505,
0.00887354090809822,
-0.06536068767309189,
-0.009607592597603798,
-0.03382173925638199,
-0.008906584233045578,
0.015768930315971375,
-0.026220954954624176,
0.03733067214488983,
0.05000137537717819,
0.007086413912475109,
0.004077283665537834,
-0.030261164531111717,
0.002353082876652479,
-0.023179879412055016,
0.011822869069874287,
-0.010204100981354713,
0.03155466914176941,
0.011004533618688583,
-0.01488169189542532,
0.015549353323876858,
0.0025821668095886707,
0.012101858854293823,
-0.1073586717247963,
-0.013839871622622013,
-0.0044563766568899155,
0.012043618597090244,
0.06016666442155838,
-0.07950994372367859,
0.015486543998122215,
0.008447504602372646,
-0.06154133751988411,
0.013031521812081337,
-0.0193690937012434,
-0.03155721351504326,
0.0026111097540706396,
-0.004961069207638502,
-0.005084856413304806,
0.031133081763982773,
0.015001784078776836,
0.02683626115322113,
0.014633855782449245,
0.017712848260998726,
0.012532759457826614,
-0.011236913502216339,
-0.006567695178091526,
0.013898278586566448,
-0.031017081812024117,
-0.0083927595987916,
0.022873878479003906,
0.010716251097619534,
-0.04529425501823425,
0.01972341537475586,
-0.009919298812747002,
0.025634557008743286,
0.01135994866490364,
0.03575862571597099,
0.024882443249225616,
0.023636143654584885,
0.030029816552996635,
-0.01459731999784708,
-0.030570296570658684,
0.00024409008619841188,
0.031479086726903915,
0.0216995682567358,
-0.03784552589058876,
0.013701600022614002,
0.022781023755669594,
-0.0388406403362751,
-0.054328713566064835,
0.032278984785079956,
0.008529569022357464,
0.007799293380230665,
-0.009315870702266693,
0.02900496870279312,
-0.023359021171927452,
0.015243243426084518,
0.028646264225244522,
-0.06044985353946686,
0.008486357517540455,
0.02905372902750969,
-0.002082523889839649,
-0.006772274617105722,
0.012589176185429096,
-0.031335752457380295,
-0.008776789531111717,
0.014985965564846992,
-0.005547925364226103,
0.011380146257579327,
-0.02600228041410446,
0.025400308892130852,
0.026788650080561638,
0.015562626533210278,
-0.016597481444478035,
-0.047402165830135345,
-0.002252551494166255,
0.026538655161857605,
0.0228058360517025,
0.031241165474057198,
0.021280117332935333,
-0.03216280788183212,
0.002400643890723586,
-0.09093628078699112,
0.02755150943994522,
0.03353385254740715,
-0.022183412685990334,
-0.02318248711526394,
-0.016813546419143677,
0.008636096492409706,
-0.027439435943961143,
0.038991350680589676,
-0.02960135042667389,
0.014098919928073883,
0.00667311018332839,
-0.0014749729307368398,
0.006385162007063627,
-0.05084628611803055,
0.001310032675974071,
-0.011907174251973629,
-0.018020857125520706,
0.022327180951833725,
0.0004061261424794793,
-0.01702442206442356,
-0.006879751570522785,
0.030524982139468193,
-0.01989728957414627,
0.017677998170256615,
0.01790512539446354,
-0.04585156962275505,
0.0550665482878685,
0.02340443804860115,
0.007161287125200033,
0.0462549664080143,
-0.03896482661366463,
0.01177770271897316,
0.05030316114425659,
-0.04265642166137695,
-0.03118300251662731,
0.030684592202305794,
-0.040689777582883835,
-0.04845256358385086,
0.003041050164029002,
-0.021097837015986443,
-0.015219572000205517,
-0.0334598645567894,
0.00395198492333293,
0.01616247184574604,
-0.014390075579285622,
0.02605455368757248,
0.022488482296466827,
0.0037026829086244106,
0.024886617437005043,
0.028535248711705208,
-0.04200705513358116,
0.06621873378753662,
-0.034452058374881744,
-0.021829649806022644,
0.029994137585163116,
0.03168991953134537,
-0.013225190341472626,
0.01141040213406086,
0.05039360001683235,
0.007848038338124752,
-0.026736708357930183,
0.036946751177310944,
0.05534755438566208,
-0.026195449754595757,
-0.042767010629177094,
-0.0004303349123802036,
0.031181655824184418,
0.008164146915078163,
0.03972858935594559,
-0.003979111090302467,
0.050184186547994614,
-0.032679975032806396,
0.013002240099012852,
0.0024134968407452106,
0.0006142139318399131,
-0.018916448578238487,
0.00276853796094656,
0.0021568583324551582,
0.04378889501094818,
-0.010040904395282269,
-0.004480408970266581,
-0.05062391236424446,
-0.011163479648530483,
0.002565392991527915,
-0.04435401409864426,
0.02318926341831684,
0.031992822885513306,
0.011442456394433975,
0.07119712233543396,
0.0036091154906898737,
-0.017142603173851967,
-0.04616672173142433,
0.023389173671603203,
0.034550558775663376,
0.013903218321502209,
-0.05341765657067299,
0.011939131654798985,
-0.034576933830976486,
0.040691979229450226,
-0.05180583521723747,
-0.014036670327186584,
-0.04407322779297829,
-0.026161814108490944,
-0.020447896793484688,
-0.012179257348179817
] |
<p>I want to know about the importance of the stability,
generally,why is stability important in super-gravity?
and why do we like these solutions?</p>
| 8,471 |
[
-0.016396235674619675,
-0.004732449539005756,
-0.018800443038344383,
-0.03694967180490494,
0.012644690461456776,
0.022721746936440468,
-0.00945527758449316,
-0.03466625139117241,
-0.007604240905493498,
-0.04671607166528702,
-0.0007084503886289895,
0.02211499772965908,
0.02168603613972664,
0.02055685594677925,
0.024233998730778694,
-0.025145994499325752,
0.018602704629302025,
-0.011684608645737171,
-0.025004230439662933,
-0.0221206396818161,
-0.0015116733266040683,
0.01157828513532877,
0.010035339742898941,
0.006468927022069693,
-0.02772868052124977,
0.016942759975790977,
0.011921683326363564,
0.008841283619403839,
0.035473037511110306,
0.05759558826684952,
-0.024314813315868378,
0.0039009456522762775,
-0.027325693517923355,
0.04255907982587814,
-0.0018087290227413177,
-0.005579146556556225,
-0.013476917520165443,
-0.009398892521858215,
-0.028505610302090645,
-0.006393723655492067,
-0.0606137178838253,
-0.016713757067918777,
-0.010455098934471607,
0.015903150662779808,
-0.01290161069482565,
-0.0018344421405345201,
0.0058240387588739395,
-0.009135594591498375,
0.06514056026935577,
-0.07652191072702408,
0.06996364146471024,
0.021182501688599586,
0.04150557145476341,
0.023640252649784088,
-0.005785724613815546,
-0.0026684252079576254,
0.06715148687362671,
0.06602907925844193,
-0.02718474715948105,
-0.030686751008033752,
-0.018205810338258743,
-0.013541181571781635,
0.009219068102538586,
-0.014684295281767845,
-0.0006900504231452942,
0.06343308836221695,
-0.007245669141411781,
-0.007012931630015373,
0.024952879175543785,
0.0024417273234575987,
-0.008614075370132923,
-0.004952118266373873,
0.006981601007282734,
-0.017297478392720222,
0.021120280027389526,
-0.020047005265951157,
-0.002394135110080242,
0.004909237381070852,
0.052961744368076324,
0.03426475077867508,
0.004035039339214563,
0.0044017513282597065,
0.04656156152486801,
0.05365787073969841,
-0.03452369198203087,
-0.01657145470380783,
0.0871545597910881,
0.00842740572988987,
0.020722635090351105,
0.049518898129463196,
0.011333582922816277,
0.006442439276725054,
0.05048615485429764,
-0.018067413941025734,
-0.017038406804203987,
-0.0013558651553466916,
0.028670739382505417,
0.04874369502067566,
0.0031406735070049763,
-0.009437085129320621,
0.004044866655021906,
-0.016835547983646393,
-0.00448118569329381,
0.0778704434633255,
0.024591559544205666,
-0.034843478351831436,
-0.06537730246782303,
0.013941838406026363,
-0.01409879419952631,
-0.007469235919415951,
0.0016441181069239974,
-0.026520026847720146,
-0.01904188096523285,
-0.024928700178861618,
0.0307068582624197,
-0.024454422295093536,
0.007785402704030275,
-0.034330472350120544,
0.06845783442258835,
0.08681324869394302,
0.04450732469558716,
-0.005285490304231644,
0.012888886034488678,
-0.003547607222571969,
-0.050220537930727005,
0.010484288446605206,
0.04041469842195511,
0.0018703468376770616,
-0.015876920893788338,
-0.005695327650755644,
0.011454344727098942,
-0.010892792604863644,
-0.01885375939309597,
0.0013813035329803824,
0.0325370654463768,
-0.011654761619865894,
-0.09275668114423752,
-0.06965383887290955,
0.049593616276979446,
-0.025095539167523384,
-0.01845940761268139,
-0.0517028272151947,
-0.0016410273965448141,
0.04953410103917122,
0.07167717069387436,
0.0026167139876633883,
0.010748428292572498,
0.028875423595309258,
0.052132442593574524,
0.0038804314099252224,
-0.04214030131697655,
-0.031252678483724594,
0.02893221750855446,
-0.04522423818707466,
-0.026576291769742966,
-0.0960349515080452,
0.006156293675303459,
-0.003004553960636258,
0.004814223852008581,
-0.04912051558494568,
0.05265915393829346,
-0.03736531734466553,
0.0035113543272018433,
-0.013304510153830051,
-0.013484891504049301,
-0.0004636181693058461,
0.058361370116472244,
0.012802292592823505,
0.029727917164564133,
0.022256992757320404,
-0.0293527003377676,
0.019058598205447197,
0.0388137586414814,
0.015434401109814644,
-0.010958613827824593,
0.0008760439814068377,
-0.010532672517001629,
-0.024075504392385483,
0.0060356417670845985,
-0.01340087503194809,
-0.01732838712632656,
-0.034813638776540756,
0.010620412416756153,
0.000407331099268049,
-0.023815490305423737,
0.04619521275162697,
-0.029504310339689255,
0.01976168528199196,
0.017288075760006905,
-0.06455160677433014,
-0.00548010878264904,
-0.0582590326666832,
0.015233194455504417,
0.02454209327697754,
-0.02553877793252468,
0.02863447740674019,
0.020583219826221466,
-0.014991632662713528,
-0.03462860733270645,
-0.018868984654545784,
0.0029542152769863605,
0.038680922240018845,
0.006511249579489231,
-0.01692299358546734,
0.041625674813985825,
0.044526707381010056,
0.018593261018395424,
-0.039553966373205185,
0.03406570851802826,
0.014664358459413052,
-0.033953361213207245,
-0.006552325561642647,
0.00745599577203393,
0.00815845187753439,
-0.010358360596001148,
-0.014474424533545971,
-0.003933412954211235,
0.0035887695848941803,
0.013109814375638962,
0.03517933562397957,
-0.052483364939689636,
0.0852610170841217,
0.039910558611154556,
0.02836792729794979,
0.010881131514906883,
0.04605405032634735,
-0.01109701581299305,
0.008610501885414124,
0.010918684303760529,
-0.024327078834176064,
-0.05766693130135536,
0.010977410711348057,
-0.0031420059967786074,
0.08889985084533691,
-0.03673272579908371,
0.020891154184937477,
0.031045865267515182,
0.018293019384145737,
0.025138039141893387,
-0.0028849123045802116,
-0.02648060768842697,
-0.045161694288253784,
0.06143110245466232,
0.0066312747076153755,
0.038532599806785583,
0.03717381879687309,
0.02942994423210621,
0.040237508714199066,
-0.03675031289458275,
-0.03107006661593914,
-0.03307655453681946,
0.0033509242348372936,
0.017343411222100258,
-0.011526286602020264,
0.0010681883431971073,
-0.017646610736846924,
0.00587808433920145,
-0.02209511585533619,
0.01736856810748577,
0.03564342483878136,
0.012070706114172935,
0.00017989962361752987,
-0.039505138993263245,
-0.008412528783082962,
0.016070645302534103,
0.008792699314653873,
0.0032789267133921385,
-0.03670577332377434,
0.022800056263804436,
-0.03942263126373291,
-0.011880082078278065,
-0.029076676815748215,
-0.007213272619992495,
-0.006304222159087658,
-0.010142910294234753,
0.026487555354833603,
-0.01984497904777527,
0.042051851749420166,
0.021538570523262024,
-0.019645612686872482,
0.007872296497225761,
-0.014503542333841324,
0.0022891522385179996,
-0.003656134707853198,
-0.03977978974580765,
0.03964456170797348,
-0.035835493355989456,
-0.01463318057358265,
0.0751391276717186,
0.008190368302166462,
0.04703286662697792,
-0.013061011210083961,
0.00029334481223486364,
-0.00873339083045721,
-0.02459612488746643,
-0.025259213522076607,
0.009619129821658134,
-0.02994825690984726,
0.012660051696002483,
0.08505385369062424,
-0.02258034236729145,
-0.0246660728007555,
0.025390218943357468,
-0.03818556293845177,
-0.0420096330344677,
-0.006497956812381744,
0.02196594327688217,
-0.009114883840084076,
-0.011536686681210995,
0.03358076885342598,
0.014018259011209011,
-0.02975604496896267,
0.01924276538193226,
-0.05041294917464256,
-0.05506449192762375,
0.0004022438661195338,
-0.013369793072342873,
0.047880202531814575,
-0.015564636327326298,
-0.06953222304582596,
0.11456054449081421,
0.0324472039937973,
-0.028892314061522484,
-0.01579497568309307,
-0.005683252587914467,
-0.024201249703764915,
-0.018167851492762566,
0.03484748676419258,
0.0387079156935215,
0.022546596825122833,
0.015384591184556484,
0.055303871631622314,
0.051094137132167816,
0.016852902248501778,
-0.005017321091145277,
-0.046342633664608,
-0.014545747078955173,
0.018594028428196907,
0.012042650952935219,
0.031466905027627945,
0.010494277812540531,
-0.045466627925634384,
-0.021493157371878624,
0.03149808570742607,
0.034546829760074615,
-0.00013057222531642765,
-0.05182066559791565,
0.03167015314102173,
-0.009622259996831417,
0.020665090531110764,
-0.0067447773180902,
0.022045111283659935,
-0.02059006690979004,
-0.025905823335051537,
0.02395058423280716,
-0.011704620905220509,
0.060350824147462845,
-0.02947208099067211,
-0.018954919651150703,
0.010985197499394417,
0.05667797476053238,
-0.027870548889040947,
-0.01996118575334549,
0.0151078375056386,
-0.018421834334731102,
0.02860254980623722,
-0.021995848044753075,
-0.021255770698189735,
0.030466189607977867,
0.0384233221411705,
0.013507068157196045,
-0.017398593947291374,
-0.036032117903232574,
-0.010985374450683594,
-0.08065721392631531,
-0.004124895203858614,
-0.012087270617485046,
0.06939370185136795,
0.0004052251169923693,
0.03505873307585716,
0.03150389716029167,
0.047263119369745255,
-0.016837522387504578,
-0.0050597041845321655,
-0.06553424149751663,
0.01744852401316166,
-0.04966963827610016,
-0.0030596978031098843,
-0.0031822919845581055,
0.014083800837397575,
-0.03657162934541702,
-0.015265360474586487,
-0.03367581218481064,
-0.028190964832901955,
0.019987450912594795,
-0.05324703827500343,
-0.004121514968574047,
-0.019471904262900352,
-0.016904933378100395,
-0.03455125167965889,
0.026036202907562256,
0.017317375168204308,
-0.0011818129569292068,
0.019068822264671326,
0.03399522975087166,
-0.03032691404223442,
0.005863986909389496,
0.006745561957359314,
0.008815771900117397,
0.012530744075775146,
0.00801379606127739,
0.02422758750617504,
0.018961701542139053,
-0.011290219612419605,
0.0014736700104549527,
0.034933578222990036,
0.03102346695959568,
-0.012654395774006844,
0.006044141948223114,
-0.007212682161480188,
-0.04147563502192497,
-0.029627148061990738,
-0.014519108459353447,
0.0244696456938982,
0.0007551192538812757,
-0.011473864316940308,
0.02573123201727867,
-0.007893713191151619,
-0.026857562363147736,
0.05685577541589737,
0.07234298437833786,
0.01864377222955227,
-0.04043903201818466,
-0.04587601497769356,
-0.03929469734430313,
-0.01868215575814247,
-0.006792712491005659,
0.03302410989999771,
-0.029591476544737816,
-0.05576898902654648,
0.005758974701166153,
0.023078324273228645,
0.025648083537817,
-0.038001105189323425,
-0.036797694861888885,
0.016214216127991676,
0.04796677455306053,
0.0038913714233785868,
0.030264919623732567,
-0.026804452762007713,
0.04563741013407707,
0.04160570725798607,
-0.003321027150377631,
-0.003782313084229827,
-0.040049463510513306,
0.00553118996322155,
0.027430474758148193,
0.015008049085736275,
0.0022478478495031595,
-0.021063875406980515,
-0.06915946304798126,
-0.012032021768391132,
0.0660383328795433,
-0.03645971789956093,
0.0446612648665905,
-0.0074701979756355286,
-0.002692110138013959,
-0.01561893243342638,
0.0078859468922019,
0.021054740995168686,
0.01715501770377159,
-0.0007235344382934272,
0.021142128854990005,
-0.02907702699303627,
0.026624735444784164,
-0.013333169743418694,
0.04580644890666008,
0.02652742713689804,
0.0776904970407486,
0.02987576462328434,
0.003616165369749069,
-0.003672601655125618,
0.01940503902733326,
-0.03288852050900459,
-0.1051386222243309,
-0.006892749108374119,
0.002693684073165059,
-0.03965432196855545,
0.014226953499019146,
-0.03732575476169586,
-0.05696628615260124,
-0.00196596747264266,
-0.0004207594902254641,
0.0027479759883135557,
-0.0034617851488292217,
-0.018945081159472466,
-0.009837571531534195,
0.053963471204042435,
0.007824132218956947,
0.024939246475696564,
0.025515170767903328,
-0.03816628456115723,
-0.035306040197610855,
0.020901992917060852,
0.012522224336862564,
-0.03109653852880001,
0.005857264623045921,
-0.0057417238131165504,
0.0027979169972240925,
-0.07449563592672348,
0.07460498064756393,
0.0033498848788440228,
0.011321461759507656,
0.01535174809396267,
-0.00851830281317234,
-0.01579994149506092,
0.053791843354701996,
0.04430244863033295,
-0.041430238634347916,
0.021187644451856613,
0.01376804243773222,
0.027324866503477097,
-0.04267058148980141,
0.017779715359210968,
-0.002292969962581992,
-0.023789387196302414,
0.0508890300989151,
-0.009069225750863552,
0.0314297080039978,
-0.020735764876008034,
-0.022099986672401428,
0.004190642852336168,
-0.038310013711452484,
0.04631764441728592,
0.03239760175347328,
-0.020099947229027748,
0.04153114929795265,
-0.077299103140831,
-0.013307273387908936,
-0.002812616527080536,
-0.017137348651885986,
0.02584809623658657,
-0.05599140003323555,
0.05103515088558197,
0.050460152328014374,
0.012967802584171295,
-0.11643905937671661,
-0.04141170158982277,
0.027020320296287537,
0.0007191320764832199,
-0.0265494491904974,
-0.002776260254904628,
0.03656677156686783,
-0.048012953251600266,
-0.03937600180506706,
-0.01714503765106201,
0.04087000712752342,
-0.044198568910360336,
-0.0010115746408700943,
0.014122596010565758,
0.01959049142897129,
0.00349052669480443,
-0.004354262258857489,
0.0004567487339954823,
0.014660781249403954,
0.001320975599810481,
0.028067266568541527,
-0.00540396710857749,
0.056898027658462524,
-0.020648682489991188,
-0.048116568475961685,
-0.013322251848876476,
-0.011465582996606827,
0.00512367207556963,
0.015803897753357887,
0.006376259494572878,
0.020473981276154518,
0.0411071851849556,
0.005232071503996849,
0.0027332743629813194,
0.013366598635911942,
-0.04583378881216049,
0.0401422493159771,
0.02255978249013424,
0.018851688131690025,
0.007095119450241327,
-0.04989778995513916,
0.0561947263777256,
0.004208834376186132,
-0.028339942917227745,
0.0002502057468518615,
0.0840204507112503,
-0.00022946830722503364,
-0.04232863709330559,
0.03210369870066643,
0.0031627800781279802,
0.011733355931937695,
0.020520096644759178,
-0.005495739635080099,
0.02412198856472969,
0.038361746817827225,
-0.011152135208249092,
-0.054121118038892746,
0.014411182142794132,
0.03359521925449371,
0.06329228729009628,
-0.059538740664720535,
0.0594649501144886,
0.01667196862399578,
-0.014567462727427483,
-0.023853614926338196,
-0.05073696747422218,
-0.032637275755405426,
0.0005147421616129577,
0.010371638461947441,
-0.0034123866353183985,
-0.024695711210370064,
0.017770476639270782,
0.01717904582619667,
0.04714073985815048,
0.0023308603558689356,
0.000665089872200042,
0.03124353475868702,
0.011092530563473701,
-0.005502411630004644,
-0.009638261049985886,
-0.061654143035411835,
0.049740079790353775,
-0.023469246923923492,
0.07127238810062408,
0.0009527089423500001,
-0.010868390090763569,
-0.0021162955090403557,
-0.01473089586943388,
0.03797058016061783,
-0.04042024910449982,
-0.03429564833641052,
-0.0318436436355114,
0.01948113553225994,
0.008837895467877388,
-0.019497394561767578,
0.0036640118341892958,
0.030319733545184135,
0.017457667738199234,
-0.00015049384091980755,
-0.02143038809299469,
-0.00029313936829566956,
-0.06758807599544525,
-0.04958200454711914,
-0.011362416669726372,
-0.06444051116704941,
0.03630490228533745,
0.019629552960395813,
-0.028841763734817505,
0.004664621315896511,
-0.022444913163781166,
-0.002161914249882102,
-0.005509661044925451,
0.022149711847305298,
-0.026779765263199806,
0.06830335408449173,
-0.01880190521478653,
0.03360866755247116,
0.014758548699319363,
-0.003371701342985034,
0.11641412228345871,
0.05242788419127464,
-0.0009642272489145398,
-0.05731302499771118,
0.03755543753504753,
-0.020071392878890038,
-0.006199931260198355,
-0.04821004718542099,
0.048817165195941925,
0.023194311186671257,
0.011721834540367126,
0.02240978740155697,
0.021285677328705788,
-0.006629657931625843,
-0.0065087201073765755,
0.030839579179883003,
-0.052562229335308075,
-0.03376523032784462,
-0.000018782529878080823,
0.001745037967339158,
-0.024899547919631004,
-0.009707480669021606,
-0.0070574008859694,
0.046470388770103455,
-0.02292747050523758,
-0.015105660073459148,
-0.009896031580865383,
-0.03556384518742561,
0.04402896761894226,
0.021239111199975014,
-0.02043924294412136,
0.007886315695941448,
0.007036358583718538,
-0.014580930583178997,
-0.0477401427924633,
0.03534865751862526,
-0.002859521424397826,
-0.04069608077406883,
0.023845918476581573,
0.018196791410446167,
-0.0009096989524550736,
-0.010535833425819874,
-0.014760544523596764,
0.016903359442949295,
-0.04305526986718178,
0.004367347341030836,
-0.04458320513367653,
0.03198058158159256,
-0.01631799340248108,
0.029290100559592247,
0.04775995761156082,
0.04634714126586914,
-0.003589670406654477,
-0.02579568699002266,
-0.04715902358293533,
-0.019371526315808296,
0.021034007892012596,
-0.02959793619811535,
-0.03885698318481445,
-0.000931810587644577,
0.012992936186492443,
0.004524874966591597,
0.025566643103957176,
-0.004568877164274454,
-0.0069865090772509575,
0.0053672934882342815,
-0.0186871737241745,
0.02031189203262329,
-0.014144410379230976,
0.011998617090284824,
-0.02657676488161087,
-0.006429180968552828,
-0.04578813537955284,
-0.0013005395885556936,
0.018534604460000992,
0.023891543969511986,
-0.02844914421439171,
0.011672928929328918,
-0.001256619580090046,
0.006182426121085882,
-0.01351971086114645,
0.017280155792832375,
-0.05172773078083992,
-0.020507648587226868,
-0.03445330262184143,
-0.007861902937293053,
0.013199650682508945,
0.016943426802754402,
0.008347888477146626,
0.009170089848339558,
-0.03468165174126625,
-0.02369431033730507,
-0.014875669032335281,
-0.0380241796374321,
-0.006460194941610098,
0.006919859908521175,
-0.0393599234521389,
-0.007927373982965946,
-0.012021265923976898,
0.015453426167368889,
0.00691626314073801,
-0.007381075993180275,
0.030116243287920952,
0.0319073386490345,
-0.027001334354281425,
0.025657374411821365,
0.02951814979314804,
-0.03356905281543732,
0.013422037474811077,
-0.0018961479654535651,
0.023538339883089066,
-0.0047593931667506695,
-0.01461907010525465,
-0.02953483909368515,
0.009853667579591274,
-0.006169586908072233,
0.02309979870915413,
-0.009276877157390118,
0.021648280322551727,
0.005915979854762554,
0.025878140702843666,
-0.06471430510282516,
0.011267626658082008,
-0.03277052566409111,
0.040616653859615326,
-0.02185378037393093,
-0.014751075766980648,
0.02815716341137886,
-0.009313371032476425,
-0.020950233563780785,
-0.03557801619172096,
0.004558656830340624,
0.009017588570713997,
-0.01841760240495205,
-0.020874327048659325,
0.03913462534546852,
0.000060345315432641655,
0.06307955831289291,
-0.0036757884081453085,
-0.030748458579182625,
0.017851464450359344,
-0.060185231268405914,
-0.04615984857082367,
0.010889907367527485,
0.0004727781633846462,
-0.016199791803956032,
0.008426644839346409,
-0.03429560363292694,
-0.020020605996251106,
0.03269924968481064,
-0.0014687924413010478,
-0.022547494620084763,
0.04261864349246025,
-0.042301543056964874,
-0.023529279977083206,
0.025657979771494865,
0.0015868707560002804,
-0.06887184828519821,
0.01914251409471035,
0.016637535765767097,
0.059142328798770905,
-0.022423043847084045,
-0.012433215044438839,
-0.0006400618585757911,
-0.006448415573686361,
-0.009862243197858334,
-0.010456087067723274,
0.005492381285876036,
0.005434423219412565,
0.03239935636520386,
-0.05135386064648628,
0.0004969471483491361,
0.02159981243312359,
0.03102410025894642,
-0.06895644962787628,
0.0033186848741024733,
0.026046959683299065,
-0.018531018868088722,
0.0288990531116724,
-0.0617142952978611,
0.023220926523208618,
0.049567412585020065,
-0.02202165126800537,
0.06083042174577713,
-0.07147160917520523,
-0.0016854932764545083,
-0.008337549865245819,
-0.027459563687443733,
-0.03037094697356224,
0.06974273920059204,
0.04869960620999336,
0.008502215147018433,
-0.008374089375138283,
-0.017380058765411377,
-0.01955009065568447,
0.008489338681101799,
-0.04089396074414253,
0.015560027211904526,
-0.027185197919607162,
0.011361949145793915,
0.06107379496097565,
0.036233335733413696,
-0.027802297845482826,
0.031288497149944305,
0.03048345260322094,
-0.03188662230968475,
0.0036629214882850647,
0.020399432629346848,
-0.005474920384585857,
0.042206522077322006,
0.002004558453336358,
-0.0011132553918287158,
-0.03915692865848541,
0.02277761697769165,
0.020579174160957336,
0.020375732332468033,
0.031150301918387413,
0.020021120086312294,
-0.03388429805636406,
-0.04282340034842491,
-0.018169395625591278,
0.014436447992920876,
-0.021312829107046127,
0.007451897952705622,
-0.033675290644168854,
0.005760896485298872,
0.0026720575988292694,
-0.030008481815457344,
0.00528875133022666,
-0.03464071452617645,
-0.03092934936285019,
0.02810835838317871,
0.022187719121575356,
0.018456632271409035,
0.06314361840486526,
-0.014676892198622227,
-0.01958065666258335,
0.010667728260159492,
0.002955758012831211,
0.009015845134854317,
-0.026777928695082664,
-0.012942017056047916,
-0.0019081050995737314,
-0.024831976741552353,
-0.03152252361178398,
-0.030408618971705437,
-0.005907499697059393,
0.061292197555303574,
0.011141805909574032,
0.031766146421432495,
-0.02902623824775219,
-0.06588730216026306,
-0.005563037935644388,
-0.059560295194387436,
0.04247607663273811,
-0.008522653952240944,
-0.0048851193860173225,
-0.014949786476790905,
-0.0297047421336174,
-0.02319968305528164,
-0.005631914362311363,
0.025818046182394028,
-0.014287053607404232,
-0.0019515209132805467,
0.03337198495864868,
-0.011933271773159504,
0.024426758289337158,
-0.01276884600520134,
-0.008079259656369686,
0.005114858970046043,
-0.03692572936415672,
-0.02221743017435074,
0.0003859537246171385,
0.05202556401491165,
0.004496762994676828,
0.007732907775789499,
-0.036289747804403305,
0.05828060582280159,
-0.009643767029047012,
-0.008708395063877106,
0.027053574100136757,
0.005994677543640137,
-0.04587620124220848,
0.09098347276449203,
-0.014930653385818005,
0.017415156587958336,
0.01981641910970211,
-0.007830988615751266,
-0.005663781892508268,
0.03176286816596985,
-0.009552489034831524,
-0.0017421976663172245,
-0.02040509320795536,
-0.03976215049624443,
-0.02230757474899292,
-0.05319010093808174,
-0.00803086906671524,
0.05642770603299141,
-0.05166611820459366,
-0.013146180659532547,
0.05402259901165962,
0.021595176309347153,
0.02304769679903984,
-0.010461356490850449,
-0.0038039220962673426,
0.019119199365377426,
0.035180509090423584,
-0.003801774699240923,
0.04993322491645813,
0.005543038249015808,
0.029078656807541847,
0.006650190334767103,
0.0036114032845944166,
-0.004024109803140163,
0.030736597254872322,
-0.006960017140954733,
0.048229578882455826,
-0.04783489927649498,
-0.02415701374411583,
0.010929101146757603,
-0.039002370089292526,
0.022691117599606514,
0.01581576094031334,
-0.01609480008482933,
0.08746763318777084,
-0.03900985047221184,
0.0050384001806378365,
-0.008569184690713882,
0.00687413988634944,
-0.025619780644774437,
-0.02248980663716793,
-0.014602708630263805,
0.07865834981203079,
0.009963936172425747,
-0.005398699082434177,
0.026960566639900208,
0.012742768973112106,
0.03285691887140274,
-0.024285493418574333,
0.046094466000795364,
-0.01677756756544113,
0.021232901141047478,
-0.023875346407294273,
0.007849439978599548,
-0.0059183151461184025,
-0.006783174816519022,
0.008937811478972435,
-0.00046422466402873397,
0.03703279048204422,
-0.004557555541396141,
-0.020709354430437088,
-0.029324663802981377,
0.056102216243743896,
-0.02888418734073639,
-0.0337127186357975,
-0.004163880832493305,
0.016372332349419594,
-0.027591796591877937,
0.01066640205681324
] |
<p>We know that nuclear magnetic moment can be expressed in terms of the expected value for nuclear spin as:</p>
<p>$$\langle\mu\rangle =[g_lj+(g_s-g_l)\langle s_z\rangle]\frac{\mu_N}{\hbar}$$</p>
<p>(Cf. Krane), where $\vec{j}$ is the <em>total</em> angular momentum, $\vec{l}+\vec{s}$.</p>
<p>How does the expected $\langle s_z\rangle$ value relate to the $\vec{j}$-component of spin, $\langle s_j\rangle$? Krane mentions that only that value is needed, given that it remains constant. </p>
| 8,472 |
[
-0.006991653237491846,
-0.0100401621311903,
-0.014454458840191364,
-0.026045460253953934,
0.058911971747875214,
0.036104392260313034,
-0.04231278598308563,
0.005756915081292391,
0.012995079159736633,
-0.07162642478942871,
0.05292796716094017,
0.062098827213048935,
0.07036565989255905,
0.022552818059921265,
-0.0025967243127524853,
0.011140565387904644,
-0.006828790530562401,
-0.02216283418238163,
-0.026550713926553726,
-0.020035626366734505,
0.010292554274201393,
0.04865961894392967,
-0.010426602326333523,
0.003008561674505472,
-0.014690429903566837,
0.037337929010391235,
0.022212151437997818,
0.004619079641997814,
0.024777192622423172,
0.054412294179201126,
0.006387523375451565,
-0.0451422855257988,
0.0325787179172039,
-0.0024613486602902412,
-0.0019875860307365656,
-0.04917488619685173,
-0.02529677003622055,
-0.03506513312458992,
-0.024034196510910988,
0.028211407363414764,
-0.07672592252492905,
-0.005583790596574545,
-0.03622015565633774,
0.006809949409216642,
-0.012065334245562553,
0.04330381006002426,
-0.028309974819421768,
-0.013522587716579437,
0.04309099540114403,
-0.04777216166257858,
0.04950561746954918,
0.0365774892270565,
0.021689068526029587,
-0.019931863993406296,
-0.0441279336810112,
0.015206186100840569,
0.07589709758758545,
0.06142488494515419,
0.007179763168096542,
-0.05313066393136978,
-0.0010907124960795045,
-0.026874911040067673,
0.013041432946920395,
0.009584558196365833,
0.03654514625668526,
0.00824536383152008,
0.01948121376335621,
-0.020280204713344574,
0.056871335953474045,
0.0192866288125515,
0.04128764569759369,
0.0263669416308403,
0.0360812209546566,
-0.03091594949364662,
0.01151557918637991,
-0.04713134095072746,
-0.0033579638693481684,
0.039166487753391266,
0.01585160568356514,
-0.013145019300282001,
0.0063071842305362225,
0.00015928495849948376,
0.007844246923923492,
0.021398108452558517,
-0.007421428337693214,
-0.010698679834604263,
0.03869406133890152,
0.012730012647807598,
0.03441761061549187,
0.03516129031777382,
0.026189547032117844,
0.02768063172698021,
0.05105771869421005,
-0.030062200501561165,
-0.061980634927749634,
0.045146647840738297,
-0.0009083625045605004,
0.031168153509497643,
-0.011174357496201992,
-0.010791436769068241,
0.024446900933980942,
-0.013601263053715229,
0.033567965030670166,
0.07092983275651932,
-0.006928363349288702,
0.017908619716763496,
-0.025794263929128647,
-0.019172165542840958,
-0.0030457547400146723,
-0.02415558136999607,
-0.015618161298334599,
0.04539619758725166,
-0.012714718468487263,
-0.004277724307030439,
-0.009061983786523342,
-0.0198808666318655,
0.03492047265172005,
-0.0038968571461737156,
0.03998664766550064,
0.044979553669691086,
0.01679365709424019,
-0.010673308745026588,
-0.02381196804344654,
-0.054586660116910934,
-0.07283386588096619,
-0.01840462163090706,
0.05254441872239113,
0.03009268082678318,
-0.0507100373506546,
0.006140746176242828,
0.030477607622742653,
0.01359270978718996,
0.0013264945009723306,
-0.009539632126688957,
-0.002376559656113386,
-0.023561179637908936,
-0.12301706522703171,
-0.07158967852592468,
0.028121795505285263,
-0.03702203929424286,
-0.013640720397233963,
-0.0945659652352333,
-0.020710723474621773,
0.05070384219288826,
0.06383926421403885,
0.00567966653034091,
0.026552366092801094,
-0.026323137804865837,
0.022435329854488373,
0.0019424123456701636,
-0.028018426150083542,
-0.024410651996731758,
-0.003705692943185568,
-0.028507979586720467,
-0.04490838199853897,
-0.07284034043550491,
0.011050717905163765,
0.03354246914386749,
-0.006919474340975285,
0.027640067040920258,
0.05755222216248512,
-0.045853644609451294,
-0.002218077424913645,
0.00042171802488155663,
-0.008699384517967701,
-0.036420054733753204,
0.06785810738801956,
0.02497517690062523,
0.019537292420864105,
0.05942675843834877,
0.01679384708404541,
0.013238147832453251,
0.029106393456459045,
0.049317941069602966,
0.050043050199747086,
-0.04920971766114235,
-0.0002817169879563153,
-0.03269881755113602,
0.027249854058027267,
-0.023372353985905647,
-0.044723838567733765,
0.02769649215042591,
0.012241841293871403,
0.025966988876461983,
-0.005240853875875473,
0.02228228561580181,
-0.009973263368010521,
0.00507297134026885,
-0.005663137882947922,
-0.04959854483604431,
-0.01542901061475277,
-0.06950405240058899,
0.027546372264623642,
-0.01995178312063217,
-0.030876128003001213,
0.03816315904259682,
0.012435736134648323,
0.013866961933672428,
0.014104437083005905,
-0.049377407878637314,
0.010985198430716991,
0.026825105771422386,
0.03705649822950363,
-0.0005874768830835819,
-0.02178194746375084,
0.04877875745296478,
0.004425675608217716,
-0.01328668650239706,
0.021154994145035744,
-0.02680574543774128,
-0.07562719285488129,
0.031207194551825523,
-0.023572111502289772,
-0.0021548739168792963,
0.06427878141403198,
-0.022003572434186935,
0.02225262112915516,
-0.00613671587780118,
0.03794532269239426,
0.02523350715637207,
-0.0274005439132452,
0.06248915195465088,
0.03398177772760391,
0.010935800150036812,
0.04148325324058533,
0.047769755125045776,
0.0003340361581649631,
-0.005861970130354166,
-0.010987655259668827,
-0.049997732043266296,
-0.04210103675723076,
-0.021264271810650826,
0.056179191917181015,
0.04274740070104599,
-0.030155688524246216,
-0.006708898115903139,
0.024585764855146408,
0.03532680496573448,
-0.01819300465285778,
0.011211780831217766,
-0.057598456740379333,
-0.02690327912569046,
-0.03653072193264961,
0.029643328860402107,
-0.0006790162879042327,
0.006924363784492016,
0.0060441517271101475,
0.024839242920279503,
-0.004880869761109352,
0.015301981009542942,
-0.013205359689891338,
0.0627584457397461,
-0.04013707488775253,
-0.025295423343777657,
0.011754573322832584,
-0.0665048286318779,
0.036563023924827576,
-0.030322164297103882,
0.019192922860383987,
0.01261543296277523,
-0.04237162321805954,
-0.02397189289331436,
-0.020025132223963737,
-0.016173530369997025,
-0.021851876750588417,
-0.023188941180706024,
-0.04407993704080582,
-0.02023126743733883,
0.019224300980567932,
-0.01824650913476944,
0.004048814065754414,
-0.030618388205766678,
-0.005898738279938698,
-0.011099549010396004,
-0.006828670855611563,
0.03165822848677635,
0.0020352713763713837,
0.014522905461490154,
-0.02019904926419258,
-0.044274453073740005,
0.008907615207135677,
0.009546227753162384,
0.021157993003726006,
0.025914369150996208,
-0.0393952950835228,
-0.021269265562295914,
-0.024854864925146103,
-0.006874267011880875,
-0.02226949669420719,
-0.008970274589955807,
0.0024814249482005835,
0.005214151926338673,
-0.020819514989852905,
-0.06991852074861526,
-0.037282783538103104,
0.025514202192425728,
0.0161672905087471,
-0.023379400372505188,
0.01082253735512495,
0.05194644257426262,
-0.010929446667432785,
0.0009999508038163185,
0.017563456669449806,
-0.02059672214090824,
-0.03486420214176178,
-0.022567301988601685,
-0.005773800425231457,
0.006572913844138384,
-0.019463254138827324,
-0.0012520907912403345,
0.05744728073477745,
-0.03181678056716919,
-0.025774464011192322,
-0.04478679224848747,
-0.03315984085202217,
0.03246788680553436,
0.002027014037594199,
0.06251969188451767,
0.03913789987564087,
-0.013445842079818249,
0.11491741240024567,
0.014745067805051804,
-0.013196257874369621,
0.016498152166604996,
0.014439749531447887,
-0.02473808452486992,
-0.05339275673031807,
0.02061564102768898,
0.05085761100053787,
0.04771643877029419,
0.058019742369651794,
-0.006515125744044781,
0.009949981234967709,
0.020062267780303955,
0.03442295640707016,
-0.017847638577222824,
-0.0009518840815871954,
-0.02161714993417263,
0.02005762793123722,
0.052194744348526,
-0.007436779327690601,
0.008878160268068314,
-0.0048647429794073105,
0.05415830388665199,
0.027127131819725037,
-0.012904951348900795,
-0.059552207589149475,
0.06467380374670029,
-0.009356881491839886,
0.0008198657305911183,
-0.017936550080776215,
0.09498981386423111,
-0.015873953700065613,
-0.005710249301046133,
0.017946885898709297,
0.021400894969701767,
0.03868431970477104,
-0.006731630302965641,
0.019397182390093803,
0.03239671513438225,
0.0017763900104910135,
-0.03233296051621437,
-0.003991224337369204,
-0.029916714876890182,
-0.050228286534547806,
0.006494952831417322,
-0.06615989655256271,
-0.03856318071484566,
-0.002843942027539015,
0.024700568988919258,
-0.024339700117707253,
-0.0364018976688385,
-0.03272431343793869,
-0.00694351177662611,
-0.06944852322340012,
-0.0075571187771856785,
0.01418236643075943,
0.03144886717200279,
0.02231743559241295,
0.03854638338088989,
0.028428031131625175,
-0.01523754745721817,
-0.010773937217891216,
-0.03589991480112076,
-0.09892317652702332,
0.007802682463079691,
-0.018213219940662384,
-0.0035980180837213993,
-0.011632363311946392,
-0.043372441083192825,
0.054202914237976074,
-0.025253167375922203,
-0.021815570071339607,
-0.04659361019730568,
-0.04411744698882103,
-0.0408816859126091,
0.043203141540288925,
-0.023760013282299042,
-0.03625498712062836,
-0.025904783979058266,
0.038418497890233994,
0.06826014816761017,
-0.015642259269952774,
-0.012872553430497646,
0.020194625481963158,
-0.028914611786603928,
-0.042176540940999985,
-0.010834373533725739,
0.018953684717416763,
-0.008315352723002434,
0.04720792546868324,
0.05961539223790169,
0.014797084033489227,
-0.035385340452194214,
-0.01767938770353794,
0.014360672794282436,
0.05398741364479065,
0.03412922844290733,
-0.0321480855345726,
0.012186452746391296,
-0.044475819915533066,
0.022788455709815025,
0.004419987555593252,
0.026482384651899338,
-0.0038276715204119682,
0.031637027859687805,
0.051204849034547806,
0.01893557794392109,
-0.03584085777401924,
0.023907359689474106,
0.04327503219246864,
0.028734231367707253,
-0.013363401405513287,
-0.05497818812727928,
0.020902082324028015,
-0.010850015096366405,
-0.021638011559844017,
0.019172126427292824,
-0.039851654320955276,
0.024662483483552933,
-0.001946129254065454,
-0.0061112442053854465,
-0.011824282817542553,
-0.00023943756241351366,
0.015148342587053776,
0.015694573521614075,
0.021144509315490723,
0.026336999610066414,
0.03523735702037811,
0.03355219587683678,
0.023027410730719566,
0.013603136874735355,
0.0034046764485538006,
-0.024111546576023102,
-0.04893767461180687,
0.003880075877532363,
0.00987088494002819,
0.053657110780477524,
-0.035480570048093796,
-0.03961295634508133,
-0.026816455647349358,
0.04381030052900314,
0.054498091340065,
-0.03663424402475357,
0.05118219554424286,
-0.017007650807499886,
-0.04378148913383484,
0.0049114651046693325,
-0.008245940320193768,
-0.036958884447813034,
0.03178228810429573,
-0.012875674292445183,
0.0012202445650473237,
-0.05165570601820946,
-0.007184250745922327,
-0.013353520072996616,
0.034369759261608124,
0.02675122208893299,
0.04808666557073593,
0.033937640488147736,
0.018246125429868698,
-0.019456934183835983,
0.04470350593328476,
0.013111470267176628,
-0.08551143854856491,
0.035169076174497604,
-0.01587701216340065,
-0.03395802155137062,
0.03223564848303795,
-0.04094899073243141,
-0.07633329182863235,
0.04042288661003113,
0.006303594913333654,
0.00018101994646713138,
-0.01807146519422531,
-0.01656319759786129,
0.05975634604692459,
0.04263729602098465,
-0.006322871893644333,
0.03990915045142174,
0.0022477698512375355,
-0.008600093424320221,
0.02196313813328743,
-0.02653481252491474,
0.05785989388823509,
-0.011609723791480064,
0.02832493558526039,
-0.04652213677763939,
0.018450351431965828,
0.022721070796251297,
0.026124656200408936,
0.000025664339773356915,
0.025070805102586746,
0.005982429254800081,
-0.025536954402923584,
-0.022994017228484154,
-0.012241335585713387,
-0.011944630183279514,
-0.03216635808348656,
0.01301245205104351,
0.019561074674129486,
0.026735808700323105,
0.011056588031351566,
0.04089372977614403,
-0.024164389818906784,
0.04119483008980751,
0.03201436996459961,
-0.020557139068841934,
-0.0004413704155012965,
-0.015313294716179371,
-0.008941850624978542,
0.02485336735844612,
-0.022974474355578423,
0.024060511961579323,
-0.02329087257385254,
-0.014155734330415726,
0.006937029305845499,
-0.006231701001524925,
-0.015909863635897636,
-0.001896215952001512,
-0.04209190979599953,
0.002902572276070714,
-0.04171587899327278,
0.007285956759005785,
0.029909204691648483,
0.0226190946996212,
-0.07226726412773132,
0.0030352582689374685,
0.011742617934942245,
0.03819770738482475,
0.005930174607783556,
-0.00688219117000699,
-0.019747493788599968,
-0.016052288934588432,
-0.027076922357082367,
0.016745299100875854,
0.05262678489089012,
-0.020709935575723648,
-0.02695108950138092,
0.011038445867598057,
0.04734879359602928,
0.06388095021247864,
-0.030374743044376373,
-0.023701148107647896,
0.0428067147731781,
-0.015456636436283588,
0.016376765444874763,
0.008680352941155434,
0.05713692680001259,
-0.03909751772880554,
-0.028047487139701843,
-0.010118121281266212,
0.02266072668135166,
0.03403250128030777,
0.013423774391412735,
0.00044751990935765207,
-0.024061433970928192,
-0.03843596950173378,
-0.013806884177029133,
-0.014513473026454449,
-0.025295618921518326,
0.01815718226134777,
0.04725542291998863,
0.015823757275938988,
0.007436432410031557,
0.0040396759286522865,
-0.011317051015794277,
0.02345006726682186,
0.02968306466937065,
0.04253731667995453,
0.011823682114481926,
0.06258990615606308,
0.010319218039512634,
-0.004038185812532902,
0.023341432213783264,
-0.002836184808984399,
0.024794206023216248,
-0.005476387217640877,
0.030193597078323364,
-0.0015166607918217778,
0.007224441971629858,
-0.022482451051473618,
-0.04477957636117935,
-0.02394309639930725,
0.041457295417785645,
0.046891968697309494,
-0.02394055761396885,
0.040524642914533615,
-0.011171369813382626,
-0.007453469093888998,
-0.03630564361810684,
-0.030349858105182648,
-0.04489416256546974,
0.010952230542898178,
-0.003088753903284669,
0.04273576661944389,
0.033509865403175354,
0.005031649023294449,
0.0036420775577425957,
0.05566192790865898,
-0.03369533270597458,
0.014488606713712215,
0.05539470538496971,
0.029158471152186394,
0.024656368419528008,
-0.0024396709632128477,
-0.06333547830581665,
0.05140106379985809,
-0.004134456627070904,
0.04915846884250641,
-0.009996422566473484,
0.010147955268621445,
0.0033012523781508207,
0.0060232216492295265,
-0.0005595575785264373,
-0.031188160181045532,
-0.004023456946015358,
-0.04529653862118721,
0.012857360765337944,
0.024697687476873398,
-0.04055095463991165,
-0.005590918939560652,
0.013283916749060154,
0.03220795467495918,
0.021840775385499,
0.011876360513269901,
0.012378554791212082,
-0.06504973769187927,
0.01586201600730419,
-0.024330807849764824,
-0.04353507608175278,
0.04810835048556328,
-0.03782079368829727,
-0.029247591271996498,
0.01725025847554207,
-0.0093075605109334,
0.020258339121937752,
-0.019411157816648483,
0.025747522711753845,
0.0038549804594367743,
0.08353163301944733,
0.03720472753047943,
0.006344616413116455,
-0.02167985402047634,
0.019008563831448555,
0.12583361566066742,
0.04372721165418625,
0.049620892852544785,
-0.05570344999432564,
0.00046631647273898125,
-0.025487668812274933,
-0.023620355874300003,
0.012251715175807476,
0.014279975555837154,
-0.0027588955126702785,
-0.001504138926975429,
-0.034616902470588684,
0.03935471549630165,
-0.02702413685619831,
-0.03587184101343155,
-0.0013069917913526297,
-0.05861717835068703,
-0.015296949073672295,
-0.002713477239012718,
0.015984976664185524,
-0.02153164893388748,
-0.00682472251355648,
-0.07103028148412704,
0.009507006965577602,
0.028591632843017578,
0.008050195872783661,
-0.02119038812816143,
-0.023455947637557983,
-0.019342439249157906,
-0.0009951443644240499,
-0.012786918319761753,
0.008267626166343689,
-0.011268277652561665,
0.003472997108474374,
-0.017589423805475235,
0.031049735844135284,
0.03662532940506935,
0.02234545163810253,
0.010546165518462658,
0.007640581578016281,
-0.010670602321624756,
-0.02115725725889206,
0.02253439649939537,
0.03325687348842621,
-0.03338053449988365,
-0.033929433673620224,
-0.007287922780960798,
0.06295114755630493,
-0.007482738699764013,
0.00259910780005157,
-0.010209131054580212,
-0.02279314585030079,
0.021357785910367966,
-0.029366109520196915,
-0.0060518234968185425,
0.01583848148584366,
0.007505349349230528,
-0.021586941555142403,
0.002055029384791851,
-0.008380469866096973,
0.023166848346590996,
-0.03105754405260086,
0.022250918671488762,
0.0028207350987941027,
-0.009329530410468578,
0.004819804336875677,
0.01932159811258316,
0.03141108155250549,
0.02364254742860794,
0.0020988306496292353,
-0.05040470510721207,
-0.015296705067157745,
-0.04598056152462959,
-0.009833264164626598,
0.014800578355789185,
-0.00202508014626801,
0.04002021253108978,
-0.006459131836891174,
0.005548028275370598,
0.007674189284443855,
-0.06434973329305649,
0.04561788961291313,
-0.023563235998153687,
-0.02865695394575596,
-0.0204208642244339,
-0.0008503924473188818,
0.004955232609063387,
0.014776787720620632,
-0.04769052937626839,
0.021419595927000046,
0.007576532196253538,
0.03689607232809067,
0.02485528402030468,
-0.023143000900745392,
-0.0011738985776901245,
0.01404828391969204,
0.0028597479686141014,
-0.00009142031922237948,
0.010760344564914703,
-0.003916262648999691,
0.0014107601018622518,
0.04471317678689957,
-0.008808513171970844,
0.04865873605012894,
0.03961658105254173,
-0.0065092649310827255,
0.04541574791073799,
-0.030352596193552017,
-0.004902147687971592,
0.014834064058959484,
-0.017548125237226486,
-0.042298685759305954,
-0.0030097090639173985,
-0.014296276494860649,
0.0028067482635378838,
0.030609091743826866,
-0.006547071039676666,
-0.022408422082662582,
-0.01820206828415394,
-0.02759304828941822,
0.008813879452645779,
-0.025377128273248672,
-0.017123067751526833,
-0.031250108033418655,
0.0371498204767704,
0.006159669253975153,
0.012504770420491695,
-0.0002487064339220524,
-0.006423339247703552,
-0.006845872849225998,
-0.014232299290597439,
0.02169334888458252,
0.0018991128308698535,
-0.015642328187823296,
-0.021066108718514442,
-0.029403945431113243,
-0.02830260992050171,
0.005680216941982508,
-0.0271348487585783,
-0.0190507173538208,
0.042917340993881226,
-0.01886080764234066,
-0.04382127895951271,
0.010575207881629467,
0.017983393743634224,
0.010472690686583519,
0.03360716998577118,
-0.02024178020656109,
-0.005481281783431768,
0.01671353541314602,
-0.05458857864141464,
0.0021534247789531946,
-0.007242596708238125,
0.008832820691168308,
-0.014666769653558731,
-0.046069011092185974,
0.010577595792710781,
0.038125138729810715,
0.001229375135153532,
0.03047514706850052,
-0.0014377470361068845,
-0.061753712594509125,
0.015293939039111137,
-0.027009496465325356,
0.01155069749802351,
-0.009350115433335304,
0.049009013921022415,
0.006721360608935356,
0.020261643454432487,
0.04485621303319931,
-0.020201751962304115,
0.03723140060901642,
-0.027480274438858032,
0.024346575140953064,
-0.058043401688337326,
-0.02704160287976265,
0.00400351220741868,
-0.048746149986982346,
0.011424348689615726,
-0.03870205581188202,
0.026020660996437073,
0.025717055425047874,
-0.09112855792045593,
-0.006284670438617468,
-0.0290441382676363,
-0.040264252573251724,
-0.032524432986974716,
-0.023687312379479408,
-0.015704337507486343,
0.018345071002840996,
-0.025381404906511307,
0.0069055017083883286,
0.008215159177780151,
-0.0017019008519127965,
0.0031179985962808132,
-0.016446150839328766,
-0.0358123742043972,
0.005062966141849756,
0.006881155539304018,
-0.04480208456516266,
0.05345012620091438,
0.002824384020641446,
-0.049329131841659546,
0.009020115248858929,
-0.006478579249233007,
0.011950567364692688,
-0.032020632177591324,
0.014079642482101917,
0.002759543713182211,
0.029332607984542847,
-0.01318723801523447,
-0.011404554359614849,
-0.010086597874760628,
-0.020346814766526222,
0.03765289857983589,
0.019998591393232346,
-0.02874852530658245,
-0.0030331299640238285,
-0.006505507975816727,
-0.01995786651968956,
-0.0105798514559865,
0.009691933169960976,
-0.011078550480306149,
-0.02762196585536003,
-0.0028577842749655247,
0.0014528686879202724,
-0.0037801554426550865,
-0.047109875828027725,
0.0327460914850235,
-0.029156628996133804,
0.007382901851087809,
0.016124337911605835,
-0.0034801724832504988,
0.0012102284235879779,
0.003308531828224659,
0.022722026333212852,
-0.006256043910980225,
-0.0015777726657688618,
0.02605704963207245,
-0.05587342381477356,
-0.04611852392554283,
-0.014480151236057281,
0.02741253934800625,
0.03532041609287262,
0.018395110964775085,
-0.04590979963541031,
-0.06751835346221924,
0.01922393962740898,
-0.007305975537747145,
0.04140597581863403,
-0.02221868932247162,
-0.04145115613937378,
0.026448048651218414,
-0.06088333949446678,
0.047517139464616776,
0.00931713916361332,
0.009211750701069832,
-0.03589664399623871,
-0.03518048673868179,
0.008104786276817322,
-0.012585548684000969,
0.05198560282588005,
0.05417967215180397,
-0.035941436886787415,
-0.013538535684347153,
0.020418893545866013,
0.02538110688328743,
-0.03595282882452011,
-0.0041906521655619144,
-0.017251940444111824,
0.00856783241033554,
-0.0033519749995321035,
-0.031992100179195404,
-0.044691991060972214,
0.015575354918837547,
0.02902819961309433,
0.007063252851366997,
0.005036625079810619,
-0.007017705589532852,
0.009620705619454384,
0.05669008567929268,
-0.004002104513347149,
-0.006909315474331379,
0.05915623530745506,
0.03591680899262428,
0.015555988065898418,
0.00025101436767727137,
0.015040155500173569,
-0.05067986994981766,
0.0017117805546149611,
-0.028266098350286484,
0.005530436988919973,
-0.036954961717128754,
-0.005310587119311094,
0.059781305491924286,
-0.04392329230904579,
0.002644724678248167,
0.029649149626493454,
-0.036490298807621,
0.005408098921179771,
0.018912820145487785,
0.03072945959866047,
0.046256162226200104,
0.03621663898229599,
0.010814808309078217,
0.0067896232940256596,
-0.0030992005486041307,
0.009120797738432884,
0.08326860517263412,
0.05698941648006439,
0.040249377489089966,
-0.00018346216529607773,
0.030299611389636993,
-0.044677507132291794,
0.03405749797821045,
0.042209167033433914,
-0.0006702564423903823,
-0.010552285239100456,
-0.023989353328943253,
0.008586680516600609,
0.00821398850530386,
0.009402679279446602,
-0.019401952624320984,
-0.026393530890345573,
0.06761416792869568,
-0.04831407219171524,
-0.01021980307996273,
-0.054517246782779694,
-0.005982786882668734,
-0.013952961191534996,
0.030656052753329277,
0.01889878325164318,
0.008060513064265251,
0.010583941824734211,
-0.00803479552268982,
0.002425162587314844,
-0.016172681003808975,
0.04511483386158943,
-0.017492113634943962,
0.008739005774259567,
0.02083578333258629,
0.022241754457354546,
-0.009387476369738579,
-0.04416084662079811,
-0.016660748049616814,
-0.054520878940820694,
0.01651063561439514,
0.037712570279836655,
0.020297175273299217,
0.006077867932617664,
-0.02017245627939701,
0.0009814322693273425,
0.03998636454343796,
-0.03353465721011162,
-0.018716683611273766,
-0.020648928359150887,
0.017284436151385307,
-0.021850965917110443,
-0.022853273898363113
] |
<p>How deep can I go if jumping from 50m?</p>
| 8,473 |
[
-0.01617346704006195,
0.00676123658195138,
-0.014424807392060757,
0.012671194039285183,
0.04836242273449898,
0.018504895269870758,
-0.005757168401032686,
-0.04931943491101265,
0.044117774814367294,
-0.04047098755836487,
0.04830051213502884,
0.042054105550050735,
0.0019544947426766157,
-0.010334683582186699,
0.0000778326575527899,
0.024465197697281837,
0.002796825719997287,
-0.03542536497116089,
0.010450301691889763,
-0.005622964818030596,
-0.018848348408937454,
0.018783047795295715,
-0.005318582523614168,
0.03148991987109184,
-0.04100535064935684,
0.009925877675414085,
0.04599277675151825,
0.011086540296673775,
-0.027151169255375862,
0.009332528337836266,
-0.0021537241991609335,
-0.02582547627389431,
0.04680875688791275,
0.01320612896233797,
0.048397041857242584,
-0.01434511598199606,
-0.034880977123975754,
-0.025378474965691566,
-0.04748521000146866,
0.01561562530696392,
0.021847562864422798,
-0.006488446611911058,
-0.0014750574482604861,
0.030558526515960693,
-0.018333666026592255,
0.04895692691206932,
-0.03006349876523018,
-0.028294740244746208,
0.048129837960004807,
-0.04506739228963852,
0.048346005380153656,
-0.004232774488627911,
0.04892376810312271,
0.021643398329615593,
0.021463235840201378,
0.03325769305229187,
0.08038514107465744,
0.05555184185504913,
-0.01787932775914669,
-0.0069625237956643105,
-0.014652205631136894,
-0.04381854832172394,
-0.020681098103523254,
-0.01985752582550049,
-0.032064370810985565,
0.029455212876200676,
-0.028537988662719727,
-0.0072181327268481255,
0.016452684998512268,
0.012236267328262329,
-0.02716321125626564,
0.006280564237385988,
0.040070634335279465,
0.020264172926545143,
0.05169497802853584,
-0.04099612683057785,
0.004187263548374176,
0.032165076583623886,
0.03406846150755882,
0.024161912500858307,
0.012160603888332844,
-0.004393036011606455,
0.028515348210930824,
0.009037134237587452,
0.030380943790078163,
-0.018695484846830368,
0.07874931395053864,
0.026966307312250137,
-0.024544689804315567,
0.02698359452188015,
-0.04011605679988861,
0.0011987702455371618,
-0.013622810132801533,
0.0036556844133883715,
0.017211036756634712,
-0.005381254479289055,
-0.002833615755662322,
0.05141229182481766,
-0.014831077307462692,
-0.013101073913276196,
-0.019677139818668365,
-0.03425809368491173,
0.013184493407607079,
0.040455467998981476,
0.02454764023423195,
0.026706982403993607,
0.007258057128638029,
0.0008353752200491726,
0.009675826877355576,
-0.020918766036629677,
-0.02859354391694069,
0.021395575255155563,
-0.01444322057068348,
-0.0220660213381052,
-0.009594399482011795,
-0.013030245900154114,
0.047099485993385315,
-0.031034912914037704,
0.024111004546284676,
0.03803092986345291,
0.022140104323625565,
-0.015305215492844582,
0.05907055363059044,
-0.059153348207473755,
-0.08023585379123688,
0.013538401573896408,
0.043652601540088654,
-0.01637660339474678,
-0.06594248861074448,
-0.00029460107907652855,
-0.012704338878393173,
-0.005068753845989704,
0.027751976624131203,
-0.012852522544562817,
0.02991531230509281,
0.00763332424685359,
-0.09021583199501038,
-0.08855520188808441,
0.042512375861406326,
0.0005583784659393132,
-0.043366193771362305,
-0.07120469957590103,
-0.003933296073228121,
0.03911697119474411,
0.054040051996707916,
0.015150112099945545,
0.05964302271604538,
0.013600891456007957,
-0.014664815738797188,
-0.019628621637821198,
-0.022084038704633713,
-0.03358926624059677,
-0.047529902309179306,
-0.009305867366492748,
0.02699189819395542,
-0.06480496376752853,
-0.00005514312579180114,
0.019214678555727005,
0.004696057178080082,
-0.022067846730351448,
0.01858634501695633,
-0.026464641094207764,
-0.007500428706407547,
-0.04109637811779976,
-0.026408659294247627,
-0.02944408357143402,
0.09273596107959747,
0.018627667799592018,
0.0028982292860746384,
0.02633332833647728,
-0.01397430244833231,
-0.019406065344810486,
0.004185035824775696,
-0.00971730425953865,
0.04965623468160629,
-0.017978930845856667,
0.028204619884490967,
-0.03141487389802933,
0.0029750920366495848,
0.020665764808654785,
-0.03501353785395622,
0.00590824568644166,
-0.0035076672211289406,
0.022735927253961563,
0.04469458386301994,
0.03725234419107437,
0.013129275292158127,
0.008982379920780659,
0.006919169332832098,
-0.008791285566985607,
-0.0018048265483230352,
-0.024770870804786682,
0.06771472841501236,
-0.0031865593045949936,
0.057920411229133606,
-0.0075164297595620155,
0.010323278605937958,
0.05431187525391579,
-0.07152368873357773,
-0.01930299773812294,
0.005563647020608187,
0.011388997547328472,
0.024472778663039207,
-0.002407383406534791,
-0.01719997450709343,
0.08381178230047226,
0.026558343321084976,
0.012659325264394283,
0.025946127250790596,
-0.0030566826462745667,
-0.0042960429564118385,
0.029000813141465187,
-0.0008652695105411112,
0.028386685997247696,
0.013485944829881191,
0.0009007427142933011,
0.018602585420012474,
0.006977612618356943,
-0.0350579172372818,
0.00037305394653230906,
-0.006422003265470266,
0.11286122351884842,
0.021215852349996567,
0.057507406920194626,
0.004527978133410215,
-0.01671658642590046,
0.015119737945497036,
-0.012669709511101246,
0.0246688611805439,
-0.0027042157016694546,
-0.05363709107041359,
-0.03197555989027023,
-0.026376238092780113,
0.020273976027965546,
-0.02789091132581234,
-0.028667446225881577,
0.030421635136008263,
-0.007596203591674566,
0.001262880745343864,
0.04785742610692978,
-0.026695122942328453,
-0.06029089167714119,
0.03641556575894356,
0.036475323140621185,
0.007871739566326141,
0.007189106196165085,
-0.007541243452578783,
0.043818436563014984,
0.0009063213947229087,
-0.08584362268447876,
0.012634815648198128,
-0.009503352455794811,
0.002204675693064928,
0.0015085545601323247,
0.031771570444107056,
-0.033525142818689346,
0.04548579826951027,
-0.045982759445905685,
-0.0017213246319442987,
0.03561151772737503,
-0.010305357165634632,
-0.013641106896102428,
-0.029455101117491722,
-0.005859109573066235,
0.054130736738443375,
0.04257382079958916,
0.0049108159728348255,
-0.0032650865614414215,
0.07666106522083282,
-0.03452884405851364,
-0.022584963589906693,
-0.04082992672920227,
-0.011080998927354813,
-0.01944117620587349,
0.0074336412362754345,
0.0051683406345546246,
-0.017546996474266052,
0.012578423134982586,
-0.01708231307566166,
-0.009823101572692394,
0.010167138651013374,
-0.004681970924139023,
0.040351979434490204,
-0.02405632846057415,
-0.03384321182966232,
0.037796661257743835,
-0.032356444746255875,
-0.0257369726896286,
0.05444583669304848,
0.007330500520765781,
0.022947927936911583,
0.00662705022841692,
-0.017823021858930588,
0.022030776366591454,
-0.013384460471570492,
0.015946311876177788,
0.026308953762054443,
0.012309858575463295,
-0.04659779369831085,
0.060216475278139114,
-0.006722796242684126,
-0.027980873361229897,
0.005089403595775366,
-0.037851057946681976,
-0.036729540675878525,
-0.03783740475773811,
0.01232793740928173,
0.015492074191570282,
-0.033744096755981445,
-0.009882400743663311,
0.012401423417031765,
-0.03925244137644768,
0.03552818298339844,
-0.010913318954408169,
-0.03692547231912613,
0.02528744377195835,
0.012240034528076649,
-0.010436671786010265,
0.013339902274310589,
-0.0212668739259243,
0.060874756425619125,
-0.013146594166755676,
0.005273101385682821,
-0.043135542422533035,
-0.046956077218055725,
-0.02075432799756527,
-0.0003996470186393708,
-0.037552762776613235,
0.0004310935328248888,
-0.041394948959350586,
-0.01395415049046278,
0.007436212617903948,
-0.0066859545186161995,
0.01471977774053812,
0.026208048686385155,
-0.02708740159869194,
0.0012999165337532759,
0.033245716243982315,
-0.0006095310673117638,
0.027345426380634308,
0.0323249027132988,
0.00007246778113767505,
0.012186983600258827,
-0.004401079844683409,
0.030679507181048393,
0.030519740656018257,
-0.03980138525366783,
0.06839114427566528,
-0.011128455400466919,
0.018004218116402626,
-0.004568401258438826,
0.030109718441963196,
0.0329507440328598,
-0.029037006199359894,
0.00679219514131546,
-0.000308397866319865,
0.05570423975586891,
-0.004704409744590521,
-0.033587709069252014,
0.033862046897411346,
0.05281803756952286,
0.032252516597509384,
-0.044636111706495285,
0.001960831694304943,
0.026332352310419083,
0.022274678573012352,
-0.001663288683630526,
-0.03332435339689255,
0.03617257624864578,
0.01699667051434517,
0.027334267273545265,
-0.0016923397779464722,
-0.02600652165710926,
0.010621888563036919,
-0.07981876283884048,
0.01952492445707321,
0.014791849069297314,
0.025696376338601112,
0.005336286034435034,
0.018123600631952286,
0.007482659537345171,
0.017031364142894745,
0.02595071867108345,
0.0185652244836092,
-0.08375424146652222,
-0.005842593498528004,
-0.053248390555381775,
0.01154416799545288,
-0.003184345318004489,
-0.007610105909407139,
-0.0024883083533495665,
-0.021473320201039314,
-0.012648040428757668,
-0.011870593763887882,
-0.006471575703471899,
-0.011136898770928383,
0.02193307876586914,
-0.006812647916376591,
0.0033703527878969908,
0.012869508937001228,
-0.0023720557801425457,
0.05987377464771271,
0.017665304243564606,
0.0656566470861435,
0.021263932809233665,
0.023821892216801643,
-0.0009094864944927394,
0.020779186859726906,
0.02667522057890892,
-0.04874006658792496,
0.02658410370349884,
-0.009899351745843887,
0.0038292710669338703,
0.007964408956468105,
0.01949862204492092,
-0.01537475548684597,
0.005923585034906864,
-0.010932552628219128,
-0.018608707934617996,
-0.0001002076460281387,
-0.02820359542965889,
-0.021483050659298897,
0.02030666545033455,
0.029135260730981827,
-0.04616200551390648,
0.00039588785148225725,
0.0332617424428463,
-0.027530986815690994,
-0.04693404212594032,
0.029613876715302467,
0.03701404854655266,
0.009096921421587467,
-0.020967796444892883,
-0.012373525649309158,
-0.03437451273202896,
-0.043925654143095016,
0.00034565114765428007,
-0.0010741838486865163,
0.00016487782704643905,
-0.015836462378501892,
0.007317340932786465,
0.08069607615470886,
0.009586533531546593,
-0.01836722157895565,
0.012634048238396645,
0.006007754243910313,
-0.007572952192276716,
-0.04559116065502167,
-0.015920132398605347,
-0.011792751960456371,
-0.0021274385508149862,
0.0389988012611866,
-0.031662993133068085,
-0.017235977575182915,
-0.10334120690822601,
-0.03041045367717743,
0.03227142244577408,
0.06717851758003235,
-0.00486782705411315,
-0.004470419604331255,
-0.06767559051513672,
-0.039330244064331055,
0.03840705752372742,
-0.003099942347034812,
0.025851968675851822,
-0.02596426010131836,
0.04752350226044655,
-0.008904770947992802,
-0.04929591342806816,
-0.02047565206885338,
-0.0236822422593832,
0.017587857320904732,
0.004075261298567057,
0.030555494129657745,
0.0184800922870636,
0.020565161481499672,
0.03034219518303871,
0.039871904999017715,
0.07083242386579514,
0.025911014527082443,
0.008276176638901234,
-0.055102646350860596,
-0.0074101886712014675,
-0.021698787808418274,
-0.058034367859363556,
-0.015749160200357437,
0.010885331779718399,
-0.027708875015378,
0.03485289216041565,
-0.006258491426706314,
-0.05210425704717636,
0.06020094081759453,
0.026200396940112114,
-0.01263281237334013,
0.011826599948108196,
-0.015432029962539673,
0.022776128724217415,
0.03528311848640442,
-0.009422321803867817,
0.05869781970977783,
0.007031620480120182,
-0.02936273254454136,
-0.02626156620681286,
-0.01603664457798004,
0.07065640389919281,
-0.06305970251560211,
-0.03377968817949295,
-0.009905247949063778,
-0.01706908456981182,
-0.04623827338218689,
0.02533235400915146,
-0.01671275869011879,
0.011751638725399971,
0.009980442933738232,
-0.03804585710167885,
0.012877266854047775,
0.05299165099859238,
0.058924540877342224,
-0.0022607059217989445,
0.038366202265024185,
-0.0008027502917684615,
0.013292279094457626,
-0.023712722584605217,
-0.0054842522367835045,
0.001139090396463871,
-0.001779917161911726,
0.017042839899659157,
-0.022834429517388344,
-0.023025132715702057,
-0.014228742569684982,
-0.015207398682832718,
-0.015402921475470066,
-0.019687600433826447,
0.07099057734012604,
-0.001815779716707766,
-0.018698759377002716,
0.0314079113304615,
-0.031066594645380974,
0.03943641856312752,
0.012807783670723438,
-0.010408887639641762,
0.00034531354322098196,
-0.0676170140504837,
0.03546493127942085,
-0.008983328007161617,
0.040027450770139694,
-0.04383258521556854,
-0.030925821512937546,
0.03365674614906311,
0.032080620527267456,
-0.02710689604282379,
-0.06384069472551346,
0.005685473792254925,
-0.018737278878688812,
-0.042807213962078094,
-0.020972076803445816,
0.046167463064193726,
-0.022794904187321663,
0.01838443987071514,
0.024795660749077797,
-0.013883979991078377,
0.05143684521317482,
0.05236564949154854,
-0.002043171087279916,
0.01801377348601818,
0.002289994852617383,
0.0017197149572893977,
-0.019773822277784348,
0.003396282671019435,
-0.02387981116771698,
-0.01885235868394375,
-0.02796071209013462,
-0.021999727934598923,
0.03130548074841499,
-0.032422713935375214,
0.010001369751989841,
0.024343322962522507,
0.010104180313646793,
0.003678686451166868,
0.0051766932010650635,
0.02374802716076374,
-0.03470572084188461,
0.03089279867708683,
0.011145088821649551,
-0.011255510151386261,
-0.03243831545114517,
-0.013666294515132904,
0.05887971445918083,
0.0020474714692682028,
0.041674308478832245,
-0.02477514185011387,
0.08148560672998428,
-0.04458213597536087,
-0.030853066593408585,
-0.007785987574607134,
0.006559223867952824,
0.03046373836696148,
-0.03434889018535614,
-0.04624861106276512,
0.04376178979873657,
0.018868446350097656,
-0.016248272731900215,
-0.02632952108979225,
-0.005473538767546415,
0.004566935356706381,
0.016195107251405716,
-0.014758819714188576,
-0.006672956515103579,
-0.017455779016017914,
-0.02299639582633972,
0.03064415045082569,
0.02114594355225563,
-0.005308041349053383,
0.0094075882807374,
-0.013522334396839142,
-0.005863779690116644,
-0.022778812795877457,
0.01280364952981472,
0.012088160961866379,
0.048476651310920715,
0.015264921821653843,
-0.008023638278245926,
0.029468372464179993,
0.000609467679169029,
0.021823611110448837,
-0.04896888509392738,
-0.03843861073255539,
0.03427207097411156,
-0.047627296298742294,
0.012160860002040863,
-0.030678559094667435,
-0.01842445880174637,
0.0427931472659111,
0.007670170161873102,
0.020078634843230247,
-0.014324959367513657,
0.0043600876815617085,
-0.02809637412428856,
-0.006847742944955826,
0.03242752328515053,
0.013033494353294373,
-0.01744796894490719,
-0.01847584918141365,
0.01419923547655344,
-0.03083694353699684,
-0.002976644318550825,
-0.018252912908792496,
-0.055898942053318024,
-0.06017109006643295,
-0.03271777555346489,
-0.049213238060474396,
0.04506582394242287,
-0.011010313406586647,
-0.005102763883769512,
0.03084917552769184,
-0.023558421060442924,
0.03134618699550629,
0.0036633757408708334,
0.030795300379395485,
-0.013389009051024914,
0.0352298840880394,
-0.02852698415517807,
-0.00726343085989356,
-0.016500510275363922,
-0.010307746939361095,
0.1278916597366333,
0.05148103088140488,
0.014554254710674286,
-0.011554545722901821,
-0.018224447965621948,
-0.027764983475208282,
0.02872566692531109,
0.005248112138360739,
0.010552765801548958,
-0.009723864495754242,
-0.007213728968054056,
0.027809811756014824,
0.027503876015543938,
-0.027788180857896805,
-0.011978666298091412,
0.03879057615995407,
-0.023204224184155464,
0.007456349674612284,
0.029518727213144302,
0.0026931718457490206,
-0.02700195275247097,
0.005891439039260149,
-0.010933564975857735,
0.029163908213377,
0.018182311207056046,
0.01421570498496294,
-0.04200785979628563,
-0.013615217991173267,
0.027316991239786148,
0.009638012386858463,
-0.06419306993484497,
-0.03158830851316452,
0.0015485582407563925,
-0.02652791328728199,
-0.03875536099076271,
0.058734796941280365,
0.014467377215623856,
-0.025492073968052864,
-0.020789286121726036,
0.02619718201458454,
0.02947058528661728,
0.016931632533669472,
-0.014017228037118912,
-0.002677126321941614,
-0.051214441657066345,
-0.029879869893193245,
0.0008105473243631423,
0.0027400569524616003,
-0.010915284976363182,
0.011064928025007248,
-0.014643304981291294,
0.020658671855926514,
0.01538144238293171,
-0.050331082195043564,
-0.028760885819792747,
-0.007313734386116266,
0.06042804569005966,
-0.018209252506494522,
-0.02026272937655449,
-0.014423996210098267,
-0.00461936742067337,
0.025568824261426926,
-0.005633327178657055,
-0.048153460025787354,
-0.00377641967497766,
-0.02468124032020569,
-0.01904023438692093,
0.04051625728607178,
-0.024503950029611588,
-0.020476138219237328,
-0.040551695972681046,
0.01185150258243084,
-0.0412418395280838,
-0.015407003462314606,
-0.005889715626835823,
0.010586097836494446,
0.026438431814312935,
0.0264580175280571,
-0.04895375296473503,
-0.028087453916668892,
-0.05047503858804703,
0.059979505836963654,
-0.027777263894677162,
0.019727924838662148,
-0.04321134462952614,
0.006064825691282749,
-0.001372911618091166,
0.019892150536179543,
0.008358262479305267,
0.037468425929546356,
-0.025543898344039917,
0.0521785169839859,
0.023474890738725662,
-0.05203556641936302,
-0.008084943518042564,
0.013412279076874256,
-0.042848873883485794,
0.02417909912765026,
0.008418763056397438,
0.04542642831802368,
0.0275425985455513,
-0.0023887353017926216,
0.02050486020743847,
-0.025454115122556686,
-0.036485593765974045,
0.008353723213076591,
-0.024645164608955383,
-0.03632759675383568,
-0.02461586892604828,
0.03266344219446182,
0.053725339472293854,
-0.02728373557329178,
-0.022722996771335602,
-0.042565517127513885,
-0.003172368509694934,
0.01969209685921669,
0.023547636345028877,
-0.02330648899078369,
0.040109045803546906,
-0.021784426644444466,
-0.012477022595703602,
0.009762519039213657,
-0.005002995952963829,
-0.01776489056646824,
0.024155346676707268,
0.009669589810073376,
-0.0101729491725564,
-0.0294907595962286,
-0.030941691249608994,
-0.06094749644398689,
0.014989791437983513,
0.00478740269318223,
0.0009398132679052651,
0.008208144456148148,
-0.025139303877949715,
0.04298935458064079,
-0.04037625715136528,
0.0413593128323555,
-0.0028632916510105133,
-0.0147023880854249,
0.025469258427619934,
-0.018076356500387192,
-0.05045769363641739,
0.02751895785331726,
-0.018070725724101067,
0.06288185715675354,
0.0026420012582093477,
-0.02894117310643196,
-0.048499781638383865,
0.07399110496044159,
0.017021283507347107,
-0.03505292907357216,
-0.0049089789390563965,
0.01223073061555624,
0.009475739672780037,
0.024337762966752052,
0.004096335731446743,
-0.06666667014360428,
-0.008985626511275768,
0.009764360263943672,
0.00621011620387435,
0.02458997443318367,
-0.005816617980599403,
0.03789251297712326,
-0.04782134294509888,
-0.012274356558918953,
-0.0013527480186894536,
-0.01887301169335842,
0.03483717516064644,
0.04754360020160675,
0.012576467357575893,
0.013100018724799156,
0.009574616327881813,
0.040062084794044495,
-0.13009101152420044,
0.0008065233123488724,
0.012311473488807678,
0.021257497370243073,
0.07288509607315063,
-0.07030011713504791,
0.039069175720214844,
0.0656060054898262,
-0.09275682270526886,
0.02415136620402336,
-0.0016717732651159167,
0.006791519001126289,
-0.022398408502340317,
0.01924712583422661,
-0.03022613376379013,
0.045726027339696884,
-0.0027350520249456167,
0.0716727077960968,
0.007404054515063763,
0.0011090651387348771,
-0.015736008062958717,
-0.0631532073020935,
-0.010876171290874481,
0.016695350408554077,
-0.02056632563471794,
0.015407910570502281,
0.04901347681879997,
-0.019899697974324226,
-0.04417124390602112,
0.007104057352989912,
-0.013763385824859142,
0.03461812809109688,
0.02007914148271084,
0.02523542195558548,
0.038332387804985046,
0.023286163806915283,
0.00024365361605305225,
0.016292301937937737,
-0.02538876049220562,
0.029244255274534225,
-0.039148781448602676,
0.02617023140192032,
-0.023314181715250015,
-0.002001232234761119,
0.002346613211557269,
-0.04837387055158615,
-0.028292153030633926,
0.04401368275284767,
-0.028276434168219566,
-0.001508922316133976,
0.03451171889901161,
-0.03114275634288788,
0.020490575581789017,
-0.024965843185782433,
-0.03296687453985214,
0.0025064952205866575,
0.035046931356191635,
0.010003190487623215,
-0.027520185336470604,
-0.011106188409030437,
0.03529668599367142,
-0.022204138338565826,
-0.0470585897564888,
-0.03787166625261307,
0.003462468972429633,
-0.07224903255701065,
-0.017543649300932884,
-0.0031215690542012453,
0.006273089908063412,
0.002938200021162629,
0.018030481413006783,
-0.028661184012889862,
-0.026882031932473183,
0.03663976863026619,
0.02581965923309326,
0.04491482675075531,
0.06278295814990997,
-0.020800191909074783,
-0.044652264565229416,
-0.07856566458940506,
0.044503066688776016,
-0.02235877513885498,
-0.024131983518600464,
-0.04147215560078621,
-0.03566353768110275,
0.039704177528619766,
-0.02019665762782097,
0.06067860126495361,
-0.036092404276132584,
0.0004092064336873591,
-0.01866603083908558,
0.046238187700510025,
0.02323227748274803,
0.009587510488927364,
-0.010025456547737122,
0.025412006303668022,
-0.023277441039681435,
-0.0018860818818211555,
-0.013292530551552773,
0.00603738147765398,
0.02544214576482773,
0.0049518090672791,
-0.014153559692203999,
0.027787597849965096,
-0.015113698318600655,
0.03802436217665672,
0.043307919055223465,
0.04060442000627518,
-0.02677459828555584,
0.059990037232637405,
-0.0028424260672181845,
-0.027693558484315872,
0.005759157706052065,
-0.03348372504115105,
-0.025863727554678917,
0.03645254671573639,
-0.02150198258459568,
0.017056826502084732,
0.010655684396624565,
0.0003542128251865506,
0.010605115443468094,
-0.04026336967945099,
-0.02790357917547226,
0.00956042017787695,
-0.018879422917962074,
-0.022682378068566322,
0.06258419156074524,
-0.006450864486396313,
0.02707141451537609,
-0.034569792449474335,
0.03797402232885361,
0.04386776313185692,
-0.03497399389743805,
0.005765498615801334,
0.012002510949969292,
0.052776165306568146,
-0.02843906357884407,
0.010898400098085403,
0.03294466808438301,
0.03118782304227352,
0.04371253028512001,
0.027940331026911736,
0.06481743603944778,
-0.005235403776168823,
-0.04541393741965294,
-0.01471524965018034,
-0.012522156350314617,
-0.02386963926255703,
0.0065268222242593765,
-0.04513942450284958,
0.04722042754292488,
0.01039955485612154,
0.004945825319737196,
-0.004646901972591877,
-0.030560871586203575,
0.013606577180325985,
-0.012620002031326294,
0.018153371289372444,
0.0006316051003523171,
-0.018383711576461792,
-0.025047611445188522,
-0.037643913179636,
0.00034869686351157725,
0.04655526205897331,
-0.013884475454688072,
0.03197763115167618,
0.011936919763684273,
0.04352477565407753,
-0.02476520463824272,
-0.008002081885933876,
-0.029624830931425095,
0.006951196119189262,
0.01788942888379097,
0.03682637959718704,
-0.002523263916373253,
-0.01044523622840643,
-0.016988513991236687,
-0.00979498028755188,
0.03267195075750351,
-0.06178387254476547,
0.0009785608854144812,
-0.03658481314778328,
-0.006914731115102768,
-0.008781914599239826,
0.0009012245573103428
] |
<p>The electric field of a point charge goes like $\displaystyle\frac{1}{r^2}$</p>
<p>The electric field of an infinite line goes like $\displaystyle\frac{1}{s}$</p>
<p>The electric field of an infinite plane is constant</p>
<p>Is there an intuitive way or some insight to understand such results and realize that they are expected?(One of my friends said that the electric field due to an infinite plane does not change at all because it looks infinite no matter how close or far from we are it. Is this argument correct? I am not convinced because we can say the same about the infinite line, it looks infinite no matter how close or far we are from it, yet it changes parametrically with the distance)</p>
| 8,474 |
[
-0.023215141147375107,
0.012877051718533039,
0.020383751019835472,
0.01579863205552101,
0.022058408707380295,
0.030214626342058182,
0.0014956165105104446,
-0.04329806566238403,
-0.00745209027081728,
-0.019786076620221138,
0.02242501825094223,
-0.0016531618312001228,
0.04899146407842636,
0.0006188020925037563,
-0.002102016704156995,
0.007284699939191341,
-0.0024920811410993338,
0.0007540492806583643,
-0.018614230677485466,
-0.03207904472947121,
-0.005500133149325848,
0.057940490543842316,
0.00640397472307086,
-0.006973667535930872,
-0.03307686001062393,
0.04522199556231499,
0.012940109707415104,
-0.003180897329002619,
0.03692379593849182,
0.05956060439348221,
-0.012233723886311054,
-0.03021666780114174,
0.010211601853370667,
0.02273583598434925,
0.012914425693452358,
-0.007292984984815121,
-0.00430121598765254,
-0.03594009950757027,
-0.009666159749031067,
0.011947105638682842,
-0.012696360237896442,
-0.025366827845573425,
-0.013775093480944633,
0.05514012649655342,
-0.023108337074518204,
0.0027891802601516247,
-0.013055599294602871,
-0.010998856276273727,
0.0399111844599247,
-0.057279109954833984,
0.05885846167802811,
0.019257472828030586,
0.04420365393161774,
0.04939693212509155,
0.03301458805799484,
-0.013338804244995117,
0.05797887220978737,
0.03708140179514885,
0.005211964715272188,
-0.0702175721526146,
0.0009299341472797096,
-0.02997455559670925,
-0.011579161509871483,
-0.03057742305099964,
-0.006333467084914446,
0.03449760749936104,
0.00468158395960927,
0.0018251471919938922,
-0.005621000658720732,
-0.030107636004686356,
0.01241032499819994,
0.051281772553920746,
0.007469074800610542,
-0.022667204961180687,
0.004875278566032648,
-0.004997034091502428,
0.01771872490644455,
0.020801983773708344,
0.06688707321882248,
0.039667993783950806,
-0.012742533348500729,
0.00266875047236681,
0.04956921562552452,
0.02595064416527748,
0.032311175018548965,
-0.019341273233294487,
0.04635251313447952,
-0.0017166142351925373,
0.010275840759277344,
0.03516542166471481,
-0.0004527866840362549,
-0.006623452994972467,
0.002927178516983986,
-0.021182330325245857,
-0.01023595966398716,
0.043059781193733215,
0.0060782344080507755,
0.02819840982556343,
0.019467780366539955,
-0.010831613093614578,
0.0007600708631798625,
-0.02618730068206787,
-0.027737194672226906,
0.03588639944791794,
0.02334604039788246,
-0.01959795318543911,
-0.024680783972144127,
0.030459998175501823,
-0.021010179072618484,
0.006023081950843334,
-0.027349168434739113,
0.055367518216371536,
0.03811245039105415,
0.03780744969844818,
0.0006307538133114576,
-0.04182913154363632,
0.05642617121338844,
-0.0342998243868351,
0.016771351918578148,
0.07865237444639206,
0.030141009017825127,
-0.05402142554521561,
-0.012729841284453869,
-0.018839707598090172,
-0.054866041988134384,
0.019641811028122902,
0.016548775136470795,
-0.011698459275066853,
-0.019802309572696686,
0.003150786506012082,
-0.025480743497610092,
0.014282787218689919,
-0.015126027166843414,
0.019226212054491043,
0.06939591467380524,
0.042562518268823624,
-0.09541137516498566,
-0.06492139399051666,
0.012938779778778553,
0.023593828082084656,
0.013396291062235832,
-0.060376059263944626,
-0.0031004040502011776,
0.004964562598615885,
0.041115809231996536,
-0.03138291463255882,
-0.00034831729135476053,
0.014042390510439873,
0.02958567813038826,
0.017059199512004852,
-0.013944071717560291,
-0.0015565966023132205,
-0.010549704544246197,
-0.03740258887410164,
0.0068705640733242035,
-0.06499195098876953,
0.023232651874423027,
0.037946462631225586,
0.0008120773127302527,
-0.04274258390069008,
0.050749827176332474,
-0.03213706612586975,
-0.028731973841786385,
0.016255080699920654,
-0.016437018290162086,
0.012986687943339348,
0.08403027802705765,
0.009548229165375233,
0.01574036292731762,
0.05747897922992706,
-0.0040586357936263084,
0.06086749956011772,
0.01660502515733242,
0.024434629827737808,
0.0604839064180851,
-0.015849081799387932,
-0.011258699931204319,
-0.0294138602912426,
-0.02414565719664097,
0.04781566560268402,
-0.045263733714818954,
-0.036094799637794495,
-0.02461943030357361,
0.024173496291041374,
-0.0013327780179679394,
0.038535043597221375,
-0.010318690910935402,
-0.009143940173089504,
-0.023787641897797585,
-0.03347792848944664,
-0.018413422629237175,
-0.0669013038277626,
0.06800077855587006,
0.04559032991528511,
-0.010670507326722145,
0.01756361685693264,
-0.005112168379127979,
-0.028479276224970818,
-0.08035354316234589,
-0.02982061170041561,
0.011197815649211407,
0.06944026052951813,
0.023136433213949203,
-0.038994260132312775,
0.022024059668183327,
0.023697109892964363,
0.057062819600105286,
0.041273269802331924,
-0.006119880825281143,
-0.04927680641412735,
-0.012676761485636234,
0.009066973812878132,
-0.04709833115339279,
0.027403591200709343,
-0.005858003161847591,
0.0006847366457805037,
-0.01658593863248825,
0.04683241620659828,
-0.02321389690041542,
0.06166652590036392,
-0.022907501086592674,
0.05718749761581421,
0.04764310643076897,
0.01284575555473566,
-0.04113294929265976,
0.05892878398299217,
-0.010466662235558033,
-0.004321859683841467,
-0.029578829184174538,
-0.05808533355593681,
-0.05483753979206085,
-0.0041128965094685555,
0.051498785614967346,
0.011395469307899475,
-0.004448675084859133,
-0.0063062021508812904,
0.0206057857722044,
0.049299705773591995,
0.011045508086681366,
0.005838572513312101,
-0.04100549966096878,
-0.04342322796583176,
0.008050881326198578,
-0.01059393584728241,
-0.0004274070670362562,
-0.006327337585389614,
0.03058721125125885,
-0.01734018884599209,
0.011026190593838692,
-0.0029873971361666918,
-0.007386475335806608,
0.023847971111536026,
-0.01844027079641819,
0.024595443159341812,
0.023153599351644516,
-0.02128218114376068,
0.01252670120447874,
-0.010502339340746403,
0.0008062688866630197,
0.006049780175089836,
-0.003920550458133221,
-0.007374652195721865,
-0.045017242431640625,
0.0136194359511137,
0.03153364732861519,
-0.021230822429060936,
-0.028425922617316246,
-0.015443539246916771,
0.01775774359703064,
-0.02729746326804161,
0.006740530487149954,
-0.004811151418834925,
-0.07287336140871048,
-0.021352652460336685,
-0.03614440932869911,
0.020873142406344414,
0.025139635428786278,
0.00946393795311451,
-0.047769784927368164,
-0.02196204848587513,
0.029085353016853333,
-0.025480372831225395,
0.029052231460809708,
-0.020314492285251617,
-0.015653882175683975,
0.015467715449631214,
-0.06379301846027374,
-0.010195384733378887,
0.04904879629611969,
-0.004758175928145647,
-0.0009057850111275911,
0.020593788474798203,
0.0022596463095396757,
-0.025220850482583046,
0.018908921629190445,
-0.05262868106365204,
0.04765832796692848,
-0.03091396577656269,
0.013851565308868885,
0.048872146755456924,
-0.03223835676908493,
-0.0358150489628315,
0.036585886031389236,
-0.05902949720621109,
-0.03643957898020744,
-0.015804806724190712,
0.012431474402546883,
0.00001740132756822277,
-0.012089397758245468,
0.01850844733417034,
-0.026361003518104553,
-0.06666784733533859,
-0.009753190912306309,
-0.03315875306725502,
-0.037273257970809937,
-0.0029516785871237516,
-0.017391139641404152,
0.060343701392412186,
-0.014001539908349514,
-0.07415705919265747,
0.06755457818508148,
0.031211890280246735,
-0.03706739842891693,
-0.02430097386240959,
-0.007091505918651819,
-0.006280766800045967,
0.010608491487801075,
-0.01718769408762455,
0.03070000372827053,
-0.031431376934051514,
-0.021047353744506836,
0.00737282307818532,
0.02924613654613495,
0.015104874037206173,
0.010904252529144287,
-0.01655549369752407,
0.006551168393343687,
0.0047912937588989735,
0.014848659746348858,
0.05927630141377449,
0.00200647278688848,
-0.019814383238554,
-0.00009517462603980675,
0.017053434625267982,
0.005529250018298626,
0.014423144981265068,
-0.0101523632183671,
0.05008240416646004,
-0.000025951840143534355,
0.019915195181965828,
-0.05107342451810837,
0.03677539527416229,
0.02414991892874241,
-0.002623938489705324,
-0.02004605531692505,
-0.008371071889996529,
0.026160648092627525,
-0.03214224427938461,
0.026598140597343445,
0.021463699638843536,
0.05815852805972099,
-0.0559440441429615,
-0.05276741459965706,
-0.004744193982332945,
0.02595113217830658,
0.04414839670062065,
-0.031049150973558426,
-0.047151241451501846,
0.030356837436556816,
0.05008005350828171,
-0.010157909244298935,
0.0003081173053942621,
-0.02494851127266884,
0.004197837319225073,
-0.055821750313043594,
-0.00582533935084939,
-0.0037999602500349283,
0.04900150001049042,
0.006902844645082951,
0.0652521550655365,
0.0008156435796990991,
0.023827286437153816,
0.011874410323798656,
0.034940823912620544,
-0.08290356397628784,
-0.020501043647527695,
-0.022381020709872246,
-0.029584389179944992,
-0.049211375415325165,
-0.015842227265238762,
-0.014953352510929108,
0.006236355751752853,
-0.00015753853949718177,
-0.010361390188336372,
-0.0417478047311306,
-0.06201108545064926,
-0.005282100290060043,
-0.03674127161502838,
-0.05781586468219757,
-0.07914451509714127,
0.029851702973246574,
0.024423856288194656,
-0.05461746081709862,
0.015069546177983284,
0.010667035356163979,
-0.029481200501322746,
-0.00736847473308444,
0.000214550324017182,
-0.01286771148443222,
0.023762322962284088,
0.03647061437368393,
-0.008899535983800888,
0.0029668863862752914,
0.0014688177034258842,
0.02111666277050972,
0.0176799725741148,
0.03226778283715248,
0.005551740527153015,
-0.018598446622490883,
-0.024844640865921974,
-0.06717292964458466,
-0.012025302276015282,
-0.026660924777388573,
0.061041537672281265,
-0.015120800584554672,
-0.01850336790084839,
0.032731328159570694,
0.008475130423903465,
-0.010231832042336464,
0.00651817349717021,
-0.02527492493391037,
0.026841968297958374,
-0.02986549586057663,
-0.057256799191236496,
0.005045139696449041,
-0.04718207195401192,
-0.007480763830244541,
0.015997711569070816,
-0.0008590925135649741,
-0.0005664935451932251,
-0.01934243179857731,
0.012462811544537544,
0.005250588990747929,
-0.02040429599583149,
-0.014230710454285145,
-0.02138413116335869,
-0.015291585586965084,
0.008250655606389046,
-0.012641770765185356,
0.04290590062737465,
0.04031363129615784,
0.0637241005897522,
-0.006280209869146347,
-0.04109900817275047,
-0.08847714960575104,
-0.022161372005939484,
0.03960828483104706,
0.012377440929412842,
0.012862199917435646,
-0.0022182990796864033,
-0.017631415277719498,
0.011065402068197727,
0.03435765579342842,
-0.0178799107670784,
0.010452528484165668,
-0.02015950158238411,
-0.028764547780156136,
-0.05038204416632652,
-0.027198798954486847,
-0.059794384986162186,
0.03741306811571121,
-0.019056685268878937,
0.04675669223070145,
-0.021767567843198776,
0.01981005072593689,
-0.0052129668183624744,
0.0358964167535305,
0.02847466804087162,
0.0806228294968605,
0.012630902230739594,
0.007931624539196491,
-0.0005987754557281733,
-0.024939602240920067,
-0.0032939957454800606,
-0.05420006439089775,
0.03879261016845703,
0.01954641193151474,
-0.0040837558917701244,
0.025403926149010658,
-0.019418973475694656,
-0.053739290684461594,
0.029467374086380005,
-0.023913627490401268,
-0.0001382515038130805,
0.011351016350090504,
-0.014825226739048958,
0.04538795351982117,
0.05227883160114288,
0.023868726566433907,
0.04058060050010681,
0.026317192241549492,
-0.0348052978515625,
-0.017076309770345688,
-0.004791093524545431,
0.03246211260557175,
-0.005885446444153786,
-0.01891040802001953,
-0.007083703298121691,
-0.010512636043131351,
-0.05319566652178764,
0.039675820618867874,
-0.021305955946445465,
0.010869254358112812,
-0.029703909531235695,
-0.03181308135390282,
0.012315932661294937,
0.021431053057312965,
-0.0011432874016463757,
0.04547903686761856,
-0.0447675846517086,
0.016336709260940552,
0.04012126103043556,
-0.026593919843435287,
0.001760129351168871,
0.02307036891579628,
0.010916795581579208,
0.011299969628453255,
0.011999501846730709,
0.039580896496772766,
-0.020615726709365845,
-0.011209096759557724,
0.006034127902239561,
-0.06435082852840424,
0.04277187958359718,
-0.03305913507938385,
-0.03463633731007576,
0.023286910727620125,
-0.05068086087703705,
-0.04061656445264816,
0.04180809110403061,
-0.030724765732884407,
0.018649926409125328,
-0.04646986722946167,
0.010429776273667812,
0.014354866929352283,
0.018704302608966827,
-0.0610094889998436,
-0.0436740517616272,
0.03397676721215248,
0.02062995731830597,
-0.0322752445936203,
-0.017330419272184372,
-0.00972633808851242,
-0.01466587744653225,
-0.024282848462462425,
0.019512899219989777,
0.011356702074408531,
-0.034257419407367706,
-0.01529038418084383,
-0.012607375159859657,
0.025523919612169266,
0.061891138553619385,
-0.03765452653169632,
-0.007288468070328236,
0.00534092728048563,
-0.03971479833126068,
-0.015366756357252598,
0.012364902533590794,
0.050574518740177155,
-0.019158558920025826,
-0.020853316411376,
-0.005023910664021969,
-0.00388749479316175,
0.02690989151597023,
-0.03208861127495766,
-0.002158692805096507,
0.04170709103345871,
-0.00834218692034483,
-0.02363738790154457,
-0.010049225762486458,
0.011093628592789173,
0.025273997336626053,
0.027759257704019547,
0.0006029653013683856,
-0.03363645449280739,
-0.012784642167389393,
-0.04908958822488785,
-0.014858359470963478,
0.029910258948802948,
0.017751455307006836,
-0.0040726689621806145,
0.03490331023931503,
-0.05358920991420746,
-0.021778235211968422,
0.039436668157577515,
-0.004472282715141773,
0.041937392204999924,
-0.0045098913833498955,
-0.014886381104588509,
0.03304373472929001,
0.022467661648988724,
-0.013038579374551773,
-0.010223934426903725,
-0.039232198148965836,
-0.007070413790643215,
0.03352575749158859,
0.01388629898428917,
0.03904157131910324,
0.02590712532401085,
-0.012431472539901733,
0.03506798297166824,
-0.025248365476727486,
-0.03366752341389656,
-0.03870562091469765,
0.005535132251679897,
0.013917435891926289,
-0.03681299090385437,
0.01185581088066101,
0.030026104301214218,
0.03457079082727432,
-0.02453020215034485,
0.006067393813282251,
0.016004499047994614,
0.005688265431672335,
0.05344315990805626,
-0.006678992882370949,
-0.025403713807463646,
0.04196280986070633,
-0.030941657721996307,
0.0005683844210579991,
0.009927173145115376,
-0.009468366391956806,
0.05184811353683472,
0.017639121040701866,
0.00333845685236156,
-0.04122918099164963,
-0.012706277891993523,
0.0012349362950772047,
0.003388822777196765,
0.037887800484895706,
0.027907447889447212,
-0.02724657580256462,
0.018843237310647964,
0.012321938760578632,
-0.033244162797927856,
-0.004693211521953344,
0.021538419649004936,
-0.013395505957305431,
-0.012218722142279148,
-0.027191713452339172,
-0.03903723880648613,
0.04690071567893028,
-0.0048804073594510555,
-0.03947177901864052,
0.011649140156805515,
-0.03788771852850914,
0.0220884308218956,
0.022789793089032173,
0.00107002560980618,
-0.0334240198135376,
0.02147858403623104,
-0.01070371363312006,
0.04815356433391571,
-0.062153492122888565,
-0.01900450512766838,
0.07829125970602036,
0.06460414826869965,
0.02527044713497162,
-0.031705450266599655,
0.04210570454597473,
-0.06210827827453613,
0.006800985895097256,
-0.033552393317222595,
0.0060661290772259235,
-0.026022059842944145,
0.022117625921964645,
0.02228565514087677,
0.03254304826259613,
0.00044759042793884873,
-0.005242393352091312,
0.03141150251030922,
-0.06157432869076729,
-0.03742559254169464,
-0.006800591945648193,
0.01666577160358429,
-0.017250655218958855,
0.06263498961925507,
-0.045025307685136795,
0.04629293829202652,
-0.03982330486178398,
0.017951516434550285,
-0.031772639602422714,
-0.053536076098680496,
0.031697724014520645,
-0.00726266298443079,
-0.0578092597424984,
0.006023259833455086,
0.026471348479390144,
-0.026387063786387444,
-0.06124017387628555,
0.024773987010121346,
0.05507880821824074,
0.008635629899799824,
-0.01161856297403574,
0.028822757303714752,
0.026401540264487267,
0.0018913567764684558,
0.009764688089489937,
0.02542162500321865,
-0.035085529088974,
0.004639888182282448,
-0.021352380514144897,
0.047573670744895935,
-0.005166436545550823,
0.02883375808596611,
-0.0001866936800070107,
0.04845834895968437,
0.009843878448009491,
-0.047337453812360764,
-0.021290533244609833,
-0.01143637578934431,
-0.021871473640203476,
0.025345394387841225,
-0.007096150889992714,
-0.0025982006918638945,
0.011031297966837883,
0.03556816652417183,
-0.010698415338993073,
0.03506797179579735,
-0.0013707784237340093,
0.0007716660620644689,
0.02321278303861618,
0.06154836714267731,
-0.002423826139420271,
-0.005147973541170359,
-0.006437814328819513,
-0.00735253794118762,
-0.032949067652225494,
-0.006580290384590626,
0.009205793961882591,
0.04437350854277611,
0.010416019707918167,
-0.0073290481232106686,
-0.0018764339620247483,
0.008747993968427181,
-0.07984068244695663,
0.02330181933939457,
-0.0010363367618992925,
0.005907034035772085,
-0.029136188328266144,
0.012223930098116398,
0.005908182356506586,
0.029858356341719627,
0.0024422139395028353,
0.010166316293179989,
0.028525780886411667,
0.02732139453291893,
0.014989935792982578,
-0.03280181437730789,
-0.0103866932913661,
-0.015864085406064987,
-0.042017266154289246,
0.015899548307061195,
0.02247709222137928,
0.016968555748462677,
0.026996852830052376,
0.029659466817975044,
0.015491282567381859,
0.04460122808814049,
-0.03571370244026184,
0.022137636318802834,
0.0053951190784573555,
-0.014035954140126705,
0.026274213567376137,
0.026777684688568115,
0.018280714750289917,
-0.02613634057343006,
0.028306247666478157,
0.0077995616011321545,
0.007206934038549662,
-0.03280745819211006,
0.012360303662717342,
0.008014525286853313,
-0.010328329168260098,
0.016583487391471863,
0.016903670504689217,
-0.039590392261743546,
-0.03136688843369484,
-0.05924282222986221,
-0.013710633851587772,
-0.00039180420571938157,
0.012667177245020866,
0.010157207027077675,
0.031223971396684647,
-0.02525632083415985,
-0.013391171582043171,
0.0505867600440979,
-0.017434844747185707,
-0.02346821315586567,
0.003099646884948015,
0.002821688773110509,
0.003014651592820883,
0.018008844926953316,
-0.05279387906193733,
-0.04561399295926094,
0.007448581513017416,
-0.019109250977635384,
-0.05339754372835159,
0.01585712656378746,
-0.01278594695031643,
0.03126613050699234,
0.023556428030133247,
0.008433575741946697,
-0.0012724713888019323,
0.04324993118643761,
0.004600932355970144,
0.015896650031208992,
-0.05036023631691933,
-0.04085526987910271,
0.026611309498548508,
-0.012936803512275219,
0.017047733068466187,
-0.021510889753699303,
-0.00010754696995718405,
0.025039762258529663,
0.010029872879385948,
-0.023658158257603645,
-0.0016160751692950726,
0.02217395044863224,
-0.010563015006482601,
-0.027647066861391068,
0.030285365879535675,
0.008137613534927368,
0.042205363512039185,
0.04742835834622383,
-0.029119202867150307,
0.03388866037130356,
0.009412946179509163,
-0.00003623421798693016,
-0.09326136857271194,
-0.042315367609262466,
0.034182824194431305,
0.017702708020806313,
0.033113062381744385,
-0.038540683686733246,
-0.03273378312587738,
0.037061043083667755,
-0.1041577085852623,
0.030355678871273994,
-0.00929926335811615,
-0.0033146345522254705,
-0.030137905851006508,
-0.010599296540021896,
0.031243745237588882,
0.05188697949051857,
0.045775774866342545,
0.07176264375448227,
-0.0049314252100884914,
0.012183884158730507,
-0.011046080850064754,
-0.029457729309797287,
-0.038464322686195374,
0.05972714722156525,
-0.013803146779537201,
-0.01959681510925293,
0.027420615777373314,
0.018714146688580513,
0.04061901941895485,
0.006625313777476549,
0.007614094763994217,
-0.00994196068495512,
-0.0026588793843984604,
0.03312191739678383,
0.028967328369617462,
0.03807180002331734,
-0.015363149344921112,
-0.009224776178598404,
-0.04999055340886116,
-0.022705888375639915,
0.011994445696473122,
-0.004387435503304005,
-0.024149082601070404,
-0.016721008345484734,
0.031134162098169327,
-0.05313578248023987,
0.0030583322513848543,
0.028361262753605843,
-0.02205096371471882,
-0.021398648619651794,
-0.0012230031425133348,
0.04471854120492935,
0.006046971306204796,
-0.012212187051773071,
0.01624915562570095,
-0.05846817418932915,
-0.026144223287701607,
0.03881688416004181,
0.00006244158430490643,
0.008855839259922504,
0.055151812732219696,
-0.009260247461497784,
-0.03277784213423729,
0.027452897280454636,
0.019963186234235764,
0.02244889922440052,
-0.056354597210884094,
0.007165927439928055,
0.003224517684429884,
-0.0018713751342147589,
0.048155248165130615,
-0.04793465510010719,
-0.055304136127233505,
-0.010608485899865627,
0.04679685831069946,
-0.004777299705892801,
-0.02730204164981842,
-0.053425997495651245,
-0.037565313279628754,
-0.06089485436677933,
0.06551932543516159,
-0.02236504852771759,
-0.04909742623567581,
-0.04531692713499069,
-0.030629273504018784,
-0.031415730714797974,
0.02933286502957344,
0.09252066165208817,
-0.0010622282279655337,
-0.012794677168130875,
0.024728884920477867,
0.006358184386044741,
0.042723629623651505,
-0.05630581080913544,
-0.02575664408504963,
0.04553258419036865,
-0.0017452134052291512,
0.004971804562956095,
0.0035198957193642855,
-0.00004723871825262904,
0.03311356529593468,
0.0015202380018308759,
-0.0071230377070605755,
0.02367859147489071,
0.02901403233408928,
-0.04998745024204254,
0.025557028129696846,
0.018774615600705147,
-0.02480410598218441,
0.0648927241563797,
-0.005336129572242498,
0.024331770837306976,
0.0061038159765303135,
-0.04084872454404831,
-0.008699730038642883,
0.0071466038934886456,
-0.04402393475174904,
-0.0027157808654010296,
-0.0343785360455513,
-0.0002279998589074239,
0.05130027234554291,
-0.04782695323228836,
0.010570850223302841,
0.05980144813656807,
-0.031922344118356705,
-0.012126607820391655,
0.07739897817373276,
0.01291658915579319,
0.027785280719399452,
-0.0009198838379234076,
0.00871339812874794,
-0.006240944843739271,
-0.012834837660193443,
0.01320869941264391,
-0.0013507279800251126,
0.03233475610613823,
0.01717548631131649,
0.04197654873132706,
0.05425200238823891,
0.010883182287216187,
0.020101012662053108,
0.0042462339624762535,
0.036254625767469406,
-0.034020472317934036,
0.015052545815706253,
0.015849685296416283,
-0.023547843098640442,
-0.013078328222036362,
0.002601170213893056,
-0.016244178637862206,
0.11138156801462173,
-0.022716498002409935,
0.037709228694438934,
0.010120970197021961,
0.005538839381188154,
-0.027285870164632797,
0.0017609748756513,
0.03868541494011879,
0.0234632957726717,
0.01657607965171337,
-0.013218955136835575,
-0.026803912594914436,
0.006048751994967461,
-0.0010530498111620545,
-0.0013826919021084905,
0.014032862149178982,
-0.008694425225257874,
-0.010596327483654022,
-0.012396940030157566,
-0.004856578074395657,
-0.014091448858380318,
-0.00398779334500432,
0.04069031402468681,
0.021610112860798836,
0.04121021926403046,
0.03288993984460831,
-0.009701564908027649,
-0.007630752865225077,
0.04555995762348175,
-0.08337372541427612,
0.0041274395771324635,
0.012861293740570545,
0.04097979888319969,
0.03558001667261124,
-0.0366332046687603
] |
<p>I'm very young so know no calculus whatsoever.</p>
<p>I want to be able to calculate uncertainties for a Physics course I'm doing online, but I believe you need to have knowledge of differentials to do this in some cases.</p>
<p>Do you need knowledge of calculus to be able to calculate with differentials?</p>
| 8,475 |
[
0.021344004198908806,
-0.020387498661875725,
-0.003611220745369792,
-0.0017498478991910815,
0.049098070710897446,
0.004380750935524702,
-0.030182700604200363,
-0.018278174102306366,
-0.0043793353252112865,
-0.03178061917424202,
0.016655465587973595,
-0.00455857627093792,
0.029054054990410805,
0.014771807007491589,
0.008821606636047363,
0.04233292117714882,
0.04377983137965202,
-0.017438078299164772,
0.009490187279880047,
-0.04742866009473801,
-0.019980885088443756,
0.007005299907177687,
0.0060643949545919895,
-0.02473449520766735,
-0.035604339092969894,
0.028300030156970024,
0.04215076193213463,
-0.01981300674378872,
-0.0005619210423901677,
0.06823768466711044,
-0.031486667692661285,
-0.011010528542101383,
0.011529357172548771,
0.0654299259185791,
0.03592922165989876,
0.0364600233733654,
-0.045515041798353195,
-0.021467946469783783,
-0.039055146276950836,
0.02888452634215355,
-0.02619067020714283,
-0.04007747769355774,
0.02744273841381073,
0.05198557674884796,
-0.0220099575817585,
0.029474180191755295,
0.002760490868240595,
-0.014110454358160496,
0.05725637450814247,
-0.04486532509326935,
0.08429081737995148,
0.005116676911711693,
0.06997337192296982,
0.036482274532318115,
-0.01648731157183647,
0.010083935223519802,
0.09211941063404083,
0.07140961289405823,
-0.030114250257611275,
-0.07501854747533798,
0.0029211477376520634,
-0.029099252074956894,
-0.007725214120000601,
-0.023798774927854538,
0.010189730674028397,
0.024476416409015656,
-0.0017415753100067377,
-0.027701586484909058,
0.0006924612098373473,
-0.010179017670452595,
0.003395756706595421,
0.015682028606534004,
0.0038114029448479414,
-0.002457439200952649,
0.033304255455732346,
-0.027392150834202766,
0.015601088292896748,
-0.007479197811335325,
0.04420444369316101,
0.0520855076611042,
0.008790077641606331,
0.0222280565649271,
0.029385222122073174,
0.006525770295411348,
0.025182275101542473,
-0.03984326124191284,
0.049860741943120956,
0.002092221286147833,
0.021734904497861862,
0.010213838890194893,
-0.011432982981204987,
0.0012856790563091636,
0.002467668615281582,
-0.024762580171227455,
0.017536791041493416,
-0.010545268654823303,
0.0039707752875983715,
0.02696617878973484,
0.017339078709483147,
-0.051824748516082764,
0.013238090090453625,
-0.021379414945840836,
0.031083213165402412,
0.06556390225887299,
0.02485192008316517,
-0.004378012381494045,
0.007594377733767033,
0.02473362162709236,
-0.013374654576182365,
-0.015563614666461945,
0.000973887974396348,
0.02250140905380249,
-0.015573164448142052,
0.028601842001080513,
-0.003680842462927103,
-0.01629350334405899,
-0.033587366342544556,
0.01353360339999199,
0.02365400828421116,
0.026133066043257713,
0.03212872892618179,
-0.010600241832435131,
0.028734715655446053,
0.015502442605793476,
-0.06877327710390091,
-0.015120062045753002,
0.027405625209212303,
0.002501208335161209,
-0.03771241754293442,
0.015865541994571686,
0.011544689536094666,
-0.008981838822364807,
0.023193933069705963,
0.04428208991885185,
0.004588387440890074,
0.012482636608183384,
-0.07815676182508469,
-0.06738032400608063,
0.013300281949341297,
0.008953972719609737,
-0.0372951477766037,
-0.04981232434511185,
0.01495334692299366,
0.06959088146686554,
0.03959202766418457,
-0.0228832196444273,
0.04591434448957443,
-0.02096656896173954,
0.024276724085211754,
-0.02909059077501297,
-0.025701966136693954,
-0.013608433306217194,
-0.0131961889564991,
-0.02572266384959221,
0.021740665659308434,
-0.03612830862402916,
0.05413678288459778,
0.030224891379475594,
0.004866471514105797,
-0.005466528236865997,
0.0628044605255127,
-0.0403258353471756,
0.006022022571414709,
0.02562902309000492,
-0.008974730037152767,
-0.020682120695710182,
0.06461477279663086,
0.0069635831750929356,
0.03905608877539635,
0.011184336617588997,
0.033232834190130234,
0.007041660603135824,
0.008669937960803509,
0.01267918385565281,
0.09072526544332504,
0.011991559527814388,
-0.04173295199871063,
-0.0460224412381649,
-0.002398807555437088,
0.004295157268643379,
-0.028478560969233513,
-0.028451399877667427,
-0.027948051691055298,
0.011583051644265652,
-0.01775837503373623,
0.03003498911857605,
0.07068661600351334,
-0.003468835260719061,
-0.016014419496059418,
0.01447331439703703,
-0.022598933428525925,
-0.05260537564754486,
0.029237685725092888,
-0.012849068269133568,
-0.004325983580201864,
-0.04662110656499863,
0.0043787662871181965,
-0.018307967111468315,
-0.03361443802714348,
-0.012684714049100876,
0.0009734731866046786,
0.022369980812072754,
0.013349493034183979,
-0.04092325270175934,
0.005343412980437279,
0.0561162531375885,
0.09359646588563919,
-0.02505296654999256,
0.027775589376688004,
-0.03350870683789253,
-0.011196480132639408,
-0.03619294986128807,
-0.033608630299568176,
0.021607041358947754,
0.005527840927243233,
-0.01100957952439785,
0.030428992584347725,
-0.015379847027361393,
-0.03900888189673424,
0.014145654626190662,
-0.033296138048172,
0.08460936695337296,
0.0658620074391365,
0.06161249428987503,
0.0025611596647650003,
0.03916095942258835,
0.04084254056215286,
0.025893520563840866,
0.023924164474010468,
0.004033468198031187,
-0.06444218009710312,
0.023939093574881554,
-0.009521890431642532,
0.022114435210824013,
-0.03676402568817139,
-0.0016038501635193825,
0.05514290928840637,
0.013776491396129131,
0.02149876393377781,
0.00030477732070721686,
0.013291009701788425,
-0.031506478786468506,
0.01043233834207058,
-0.027928687632083893,
0.05676662176847458,
0.03556837886571884,
0.01770171895623207,
0.03193052113056183,
0.009201902896165848,
-0.026555268093943596,
-0.0023791473358869553,
0.01608513854444027,
-0.021900387480854988,
0.023014768958091736,
0.015578705817461014,
-0.026203278452157974,
0.0430721640586853,
-0.006326143629848957,
-0.0003852227237075567,
-0.007277575321495533,
0.012483791448175907,
-0.0024648087564855814,
0.025074325501918793,
-0.01671733520925045,
0.016760610044002533,
0.003994070924818516,
-0.06483592092990875,
0.0064219217747449875,
0.047000981867313385,
-0.05248367413878441,
-0.019870700314641,
0.011318324133753777,
-0.0324341356754303,
-0.006263172719627619,
-0.010105726309120655,
0.043707676231861115,
0.00312904198653996,
0.03758324310183525,
-0.008496716618537903,
-0.02591162733733654,
-0.011274810880422592,
-0.008855760097503662,
-0.017385050654411316,
0.007577536627650261,
-0.060325585305690765,
0.030990438535809517,
-0.034336403012275696,
-0.06339319050312042,
0.0490003377199173,
-0.040084898471832275,
-0.0067704059183597565,
0.03092273138463497,
0.0008959835977293551,
-0.046059176325798035,
-0.03150017186999321,
-0.005500026512891054,
-0.04108637943863869,
-0.030620655044913292,
-0.017314663156867027,
0.014016138389706612,
-0.023089028894901276,
-0.03163537383079529,
0.013220959343016148,
-0.051615793257951736,
-0.016379186883568764,
-0.018063273280858994,
0.020479507744312286,
-0.005865678656846285,
-0.008003382943570614,
-0.027635816484689713,
0.011436183005571365,
-0.012123482301831245,
-0.006393544375896454,
-0.046107809990644455,
-0.09404898434877396,
-0.00579447764903307,
0.024272873997688293,
0.03285395726561546,
-0.015594106167554855,
-0.04089513048529625,
0.09052731841802597,
0.014129982329905033,
-0.034817565232515335,
0.013275052420794964,
-0.024781255051493645,
-0.003724784357473254,
-0.02736975997686386,
0.0037941960617899895,
-0.024326113983988762,
-0.005401189438998699,
-0.009934710338711739,
0.002141685225069523,
-0.018008491024374962,
0.015148856677114964,
-0.0021248124539852142,
0.028715698048472404,
0.014176416210830212,
-0.0028695601504296064,
0.0018747926224023104,
0.061111245304346085,
0.03472067043185234,
-0.038299474865198135,
0.0009078350267373025,
-0.0039742738008499146,
0.03190317004919052,
0.009603334590792656,
-0.03660184144973755,
0.04699934646487236,
0.000010367231880081818,
-0.02383246086537838,
0.004603078588843346,
0.04924451559782028,
-0.012397325597703457,
-0.01457876618951559,
0.021188298240303993,
-0.02286437153816223,
0.044275857508182526,
0.009597665630280972,
0.02360212430357933,
0.03111104853451252,
0.05351188778877258,
0.004694600123912096,
-0.001957239583134651,
0.0010321160079911351,
0.004438949748873711,
0.02657611109316349,
-0.03271401673555374,
0.015637783333659172,
0.047499556094408035,
0.04760256037116051,
-0.00201570731587708,
0.010528981685638428,
-0.02986426092684269,
-0.002515750238671899,
-0.10328302532434464,
0.015609524212777615,
-0.008427723310887814,
0.07100699096918106,
0.006911830045282841,
0.057667411863803864,
0.0142966965213418,
0.004436125047504902,
0.009675124660134315,
-0.008035100996494293,
-0.05885876715183258,
0.07583541423082352,
-0.009170408360660076,
-0.04526762664318085,
-0.04597482457756996,
-0.026904746890068054,
0.02268117293715477,
0.0067166914232075214,
-0.03394455090165138,
-0.059734828770160675,
0.023737255483865738,
-0.035346630960702896,
0.005606295075267553,
-0.002172528998926282,
-0.05369964614510536,
-0.005304134450852871,
0.025183716788887978,
0.017139248549938202,
-0.028048045933246613,
0.01812162436544895,
0.07632740586996078,
-0.017462337389588356,
-0.009600297547876835,
-0.03287682309746742,
0.026857204735279083,
0.022851204499602318,
0.04674164578318596,
-0.008302267640829086,
0.022191284224390984,
-0.01556004211306572,
0.015615819953382015,
0.024607839062809944,
0.08640410006046295,
0.006879687309265137,
-0.028190039098262787,
-0.019047914072871208,
-0.015459507703781128,
-0.00048533343942835927,
0.02016597054898739,
0.07192866504192352,
-0.026648547500371933,
-0.01031497772783041,
0.022866543382406235,
-0.01775803044438362,
-0.03862207382917404,
-0.008925968781113625,
0.03588803485035896,
-0.009716697968542576,
-0.02537716180086136,
-0.04878930374979973,
-0.009918417781591415,
-0.0663803368806839,
-0.0253025833517313,
-0.016596490517258644,
0.0722910463809967,
-0.013232454657554626,
-0.02395246922969818,
0.04050450399518013,
0.009152579121291637,
-0.014000858180224895,
0.030396196991205215,
-0.018168920651078224,
0.03279716148972511,
0.005817348137497902,
0.016109073534607887,
0.040459245443344116,
0.05092998594045639,
0.031760357320308685,
-0.022005928680300713,
-0.008558173663914204,
-0.09341274946928024,
0.0010177218355238438,
0.01707153208553791,
0.0740828886628151,
-0.023997578769922256,
-0.03868084400892258,
-0.022403059527277946,
-0.02215501479804516,
0.13583500683307648,
-0.011160100810229778,
0.026287425309419632,
-0.015711573883891106,
-0.01712469942867756,
-0.021636351943016052,
-0.04954429343342781,
-0.003844012040644884,
0.016385115683078766,
0.0008009322336874902,
0.0057270159013569355,
-0.03267950192093849,
0.008677909150719643,
-0.04868526756763458,
-0.006296682171523571,
0.046730875968933105,
0.07971436530351639,
0.007965629920363426,
-0.03678000345826149,
-0.03064662218093872,
0.005442060995846987,
-0.02418387681245804,
-0.053603846579790115,
0.012304859235882759,
-0.019002780318260193,
0.02273821458220482,
0.05250035226345062,
-0.0012869019992649555,
-0.03468010947108269,
0.014581077732145786,
-0.0156270619481802,
0.0017198451096192002,
-0.024699371308088303,
-0.029809650033712387,
0.03023822419345379,
0.05518519878387451,
0.05133707448840141,
0.03412332013249397,
0.06355325877666473,
-0.0293746180832386,
0.010476065799593925,
-0.019723132252693176,
0.003686817130073905,
-0.014715699478983879,
0.007907433435320854,
-0.01256611943244934,
-0.04373297467827797,
-0.03779012709856033,
-0.003487165318801999,
-0.023909814655780792,
0.006187546066939831,
0.0025586343836039305,
-0.037540365010499954,
-0.0008748842519707978,
0.009284050203859806,
0.027857329696416855,
-0.024953613057732582,
-0.024280564859509468,
-0.012699175626039505,
0.006823575124144554,
0.012468930333852768,
-0.0003843397134914994,
0.041897211223840714,
0.0257406085729599,
0.006341930944472551,
-0.05251508951187134,
-0.0020499250385910273,
-0.05205340310931206,
-0.01962234266102314,
0.0020562028512358665,
-0.05347341299057007,
0.026936162263154984,
0.015191166661679745,
-0.011313802562654018,
0.036279965192079544,
-0.028330877423286438,
-0.022873546928167343,
-0.01047456543892622,
-0.0006082727923057973,
0.03805577754974365,
-0.08937517553567886,
0.06053451821208,
-0.03625519201159477,
-0.006863577291369438,
-0.014701414853334427,
-0.0634123682975769,
0.007882412523031235,
0.033463142812252045,
-0.023383881896734238,
-0.024592246860265732,
0.007303686812520027,
-0.02323291078209877,
-0.019904186949133873,
-0.02087646909058094,
0.04065867140889168,
-0.0021501684095710516,
0.025299910455942154,
0.02971176989376545,
-0.01784506067633629,
0.04928211867809296,
-0.01662548817694187,
0.03255479410290718,
0.04538625851273537,
-0.03702569380402565,
-0.026964858174324036,
-0.03182576224207878,
0.04587589204311371,
-0.01986575499176979,
-0.015423242002725601,
-0.011901121586561203,
0.018096666783094406,
0.033322595059871674,
-0.019005699083209038,
-0.03640776872634888,
0.010930838994681835,
0.0028554550372064114,
-0.01950540393590927,
0.010091003961861134,
0.0030839843675494194,
-0.0248433668166399,
-0.027367819100618362,
0.005715412553399801,
0.035768717527389526,
-0.019116953015327454,
-0.003491088515147567,
-0.01886861026287079,
0.004580982495099306,
0.01678389497101307,
-0.006849762052297592,
0.05824323371052742,
-0.021541796624660492,
-0.02496013045310974,
0.007516921032220125,
-0.015241062268614769,
0.008182365447282791,
-0.034911271184682846,
0.010075531899929047,
0.013116736896336079,
-0.03307878598570824,
-0.013886362314224243,
-0.04221869260072708,
-0.04749831557273865,
-0.006156038027256727,
0.060538262128829956,
-0.022257324308156967,
0.05664941668510437,
0.02282998152077198,
0.00566538330167532,
-0.010062411427497864,
-0.007083100266754627,
-0.05959373712539673,
0.0147840715944767,
-0.004713012836873531,
0.033972688019275665,
-0.040327124297618866,
-0.006266172043979168,
-0.014024076983332634,
-0.0008326613460667431,
-0.020963158458471298,
0.014470761641860008,
-0.0015086751664057374,
-0.011214105412364006,
0.01530410721898079,
-0.001251022913493216,
-0.06962425261735916,
0.022377729415893555,
-0.04715702310204506,
0.009236197918653488,
-0.023167088627815247,
-0.01633673533797264,
0.06577636301517487,
0.01627838984131813,
-0.014040127396583557,
-0.00974951684474945,
0.016536187380552292,
-0.0009066583006642759,
0.015617793425917625,
0.021329794079065323,
0.009852305985987186,
0.0021479830611497164,
-0.012395117431879044,
0.06711819022893906,
-0.02123088575899601,
0.018053768202662468,
-0.04099785536527634,
-0.06229790300130844,
-0.023029325529932976,
-0.04508480802178383,
-0.047921810299158096,
0.059073831886053085,
-0.006914690602570772,
-0.027863983064889908,
-0.005168342497199774,
0.01898232102394104,
0.042757514864206314,
0.0011300280457362533,
0.015305742621421814,
-0.040472280234098434,
0.01674351841211319,
-0.022594664245843887,
0.0024757254868745804,
-0.054337408393621445,
0.01329109538346529,
0.13134624063968658,
0.038531627506017685,
0.02178327552974224,
-0.01733585074543953,
-0.025209704414010048,
-0.04547925665974617,
0.01925734058022499,
-0.0010304898023605347,
0.027871478348970413,
0.002621391788125038,
0.007160309236496687,
-0.003812301903963089,
0.030403982847929,
-0.01510123535990715,
-0.011469530873000622,
0.03337305784225464,
-0.026262449100613594,
-0.025809673592448235,
0.001020565046928823,
0.010400550439953804,
0.024349384009838104,
0.017928848043084145,
-0.04024992883205414,
0.01753113977611065,
-0.04303055629134178,
-0.012914909981191158,
-0.04412238672375679,
-0.03763734921813011,
0.022717121988534927,
0.011670468375086784,
-0.08029206097126007,
0.031238792464137077,
0.04963101074099541,
0.03171754255890846,
-0.033198282122612,
0.0330948606133461,
0.03473398834466934,
-0.010359147563576698,
-0.0031251811888068914,
0.036674585193395615,
0.02782057225704193,
-0.02588026225566864,
-0.02940652146935463,
0.01556243933737278,
-0.02810824103653431,
-0.0010649485047906637,
-0.04049764201045036,
0.018999718129634857,
-0.001858112053014338,
0.008456332609057426,
-0.008600207976996899,
-0.020032985135912895,
0.023882213979959488,
-0.0776781290769577,
-0.02146659977734089,
0.035913750529289246,
0.005242504645138979,
-0.018919581547379494,
-0.0097315339371562,
-0.0020921090617775917,
0.01477680541574955,
-0.021509205922484398,
-0.006664397660642862,
0.020869344472885132,
-0.03195055201649666,
-0.044532448053359985,
-0.012828212231397629,
0.029823968186974525,
-0.05652204528450966,
-0.012999983504414558,
-0.021184179931879044,
-0.0030685721430927515,
-0.021829940378665924,
0.01576315611600876,
0.027162835001945496,
0.011029137298464775,
0.03084806352853775,
-0.008782381191849709,
-0.006162784993648529,
0.009830870665609837,
-0.015981998294591904,
0.05518411099910736,
-0.04759823530912399,
0.030497921630740166,
-0.0074880183674395084,
-0.01235030684620142,
0.005837051663547754,
0.02335277758538723,
0.004008932039141655,
0.03881232067942619,
0.033189479261636734,
0.03075568936765194,
0.02536827325820923,
-0.006559606641530991,
-0.020483827218413353,
-0.00012383394641801715,
-0.03531276807188988,
0.02523498237133026,
-0.024483652785420418,
0.031700506806373596,
0.007174537051469088,
0.012249314226210117,
-0.015113737434148788,
0.04999568685889244,
-0.026555180549621582,
0.02528134174644947,
-0.017216257750988007,
-0.04474512115120888,
-0.007514498196542263,
0.03718187287449837,
0.06807509809732437,
-0.025520510971546173,
0.030075160786509514,
-0.014020539820194244,
-0.027725394815206528,
-0.019632825627923012,
0.0346163734793663,
-0.013943394646048546,
0.007466195151209831,
-0.002980558667331934,
0.03219543397426605,
-0.028205862268805504,
0.028283173218369484,
-0.055586062371730804,
-0.012678399682044983,
0.006782713811844587,
-0.01226208359003067,
-0.010084251873195171,
-0.004443162586539984,
0.0035248217172920704,
-0.0354154035449028,
0.036326825618743896,
-0.004444786347448826,
-0.013031039386987686,
-0.03061031363904476,
-0.007938042283058167,
-0.003829213324934244,
0.012660306878387928,
-0.029288053512573242,
-0.012295009568333626,
0.010442528873682022,
-0.004903131630271673,
-0.022715391591191292,
0.018573623150587082,
0.03544211760163307,
0.04298761859536171,
0.050452060997486115,
-0.031045429408550262,
-0.0038595786318182945,
0.06545550376176834,
0.004806166514754295,
0.011780442669987679,
-0.02262568660080433,
-0.01587083749473095,
0.004605643451213837,
-0.006036008708178997,
0.02546721324324608,
-0.00807251688092947,
0.009957998059689999,
0.004592554178088903,
-0.019046859815716743,
0.0019504587398841977,
-0.014645852148532867,
0.05782940611243248,
0.02045285888016224,
-0.0008383073727600276,
0.028719844296574593,
0.009044650010764599,
0.026577439159154892,
0.024811536073684692,
-0.024841776117682457,
0.0034363914746791124,
0.008514078333973885,
0.05116904526948929,
-0.09787775576114655,
-0.008665489964187145,
0.006317209452390671,
0.008926928974688053,
0.04123246297240257,
-0.05135616287589073,
-0.01297188363969326,
0.020035402849316597,
-0.00969510804861784,
-0.011172645725309849,
-0.031603068113327026,
-0.02793232351541519,
0.011725585907697678,
0.0008340367348864675,
0.004379672463983297,
0.039046235382556915,
0.03279193118214607,
0.04758826643228531,
0.0026493805926293135,
-0.023890400305390358,
-0.017693813890218735,
-0.02489451877772808,
0.005649780388921499,
0.011655069887638092,
0.004701647907495499,
-0.04066680371761322,
0.004534951876848936,
-0.027800822630524635,
-0.006521855015307665,
0.001993529498577118,
-0.013677970506250858,
0.010801768861711025,
-0.03185439854860306,
0.047123391181230545,
0.0678691491484642,
0.06413418054580688,
-0.0013479479821398854,
0.009797383099794388,
-0.0005189692601561546,
-0.004138213116675615,
0.027513960376381874,
0.02082146890461445,
-0.00942711066454649,
-0.004168801009654999,
0.050102196633815765,
-0.010139396414160728,
-0.04588894918560982,
0.02482125163078308,
-0.026928992941975594,
-0.01881345547735691,
-0.016526442021131516,
-0.02045550011098385,
-0.02398480661213398,
-0.02399655245244503,
0.0023528230376541615,
-0.023158598691225052,
-0.002618354745209217,
0.028230447322130203,
0.019814034923911095,
-0.017968380823731422,
0.022162681445479393,
-0.03411144018173218,
-0.05404070019721985,
0.02232578583061695,
0.010148164816200733,
-0.008835677057504654,
-0.034725021570920944,
0.01887906715273857,
0.011023270897567272,
-0.014497998170554638,
0.03911368176341057,
-0.026549091562628746,
-0.051972515881061554,
0.01752069778740406,
-0.010196483694016933,
-0.019159844145178795,
0.02470436692237854,
-0.03358062356710434,
0.0033974989783018827,
-0.06476254761219025,
0.047375235706567764,
0.04064681753516197,
-0.049527816474437714,
-0.04605431854724884,
-0.0111971665173769,
0.009491938166320324,
-0.018427805975079536,
0.05407797917723656,
-0.005570904817432165,
0.0009418115951120853,
0.04357276111841202,
-0.020543372258543968,
0.02493727020919323,
-0.021779915317893028,
0.013395561836659908,
-0.017304768785834312,
0.014461624436080456,
-0.012364132329821587,
0.016452139243483543,
0.011203181929886341,
0.029215270653367043,
0.018606649711728096,
-0.002539847744628787,
0.06964527070522308,
-0.020588364452123642,
-0.018773555755615234,
0.013210703618824482,
0.011765477247536182,
-0.03171263262629509,
0.04325157776474953,
0.005463477689772844,
-0.00005060584226157516,
0.004506472032517195,
0.004995285999029875,
-0.0165102519094944,
0.032895881682634354,
-0.015789780765771866,
-0.007001517806202173,
-0.025097539648413658,
-0.04563242569565773,
-0.01309814304113388,
-0.05886669456958771,
-0.01246616244316101,
0.0649188831448555,
-0.042656853795051575,
-0.04980118200182915,
0.06423017382621765,
-0.008715631440281868,
0.01229940727353096,
0.0021226892713457346,
0.015566996298730373,
0.03357359394431114,
-0.06131637468934059,
0.006578614469617605,
0.007658995222300291,
0.04614910110831261,
-0.016541944816708565,
0.0217867661267519,
0.04512351006269455,
-0.013476353138685226,
-0.0077500613406300545,
0.00567123806104064,
0.023358559235930443,
-0.012988065369427204,
-0.01935727894306183,
-0.008262435905635357,
0.00974859669804573,
0.028170542791485786,
0.015806078910827637,
-0.03225297853350639,
0.05868479236960411,
-0.013833118602633476,
0.003949721809476614,
-0.027218589559197426,
-0.012749969027936459,
-0.01988173834979534,
-0.020854273810982704,
0.04769023507833481,
0.023449601605534554,
-0.02389744110405445,
-0.013236037455499172,
-0.04403087869286537,
-0.004196112975478172,
0.02585161291062832,
-0.05581441894173622,
0.0547100231051445,
0.0029987278394401073,
0.04006797447800636,
-0.006229114253073931,
-0.0028038471937179565,
-0.036828603595495224,
-0.04089922457933426,
0.03848344460129738,
0.028714066371321678,
0.025554407387971878,
-0.007502181455492973,
-0.0037099760957062244,
-0.016051700338721275,
0.02234038896858692,
-0.03764624521136284,
0.00915784016251564,
-0.011086349375545979,
-0.011279895901679993,
0.025631465017795563,
-0.02497153915464878
] |
<p>I have earlier posted the same question <a href="http://math.stackexchange.com/questions/117876/conversion-of-motion-equation-from-cartesian-to-polar-coordinates-is-covariant">here</a> on <code>math stackexchange</code> but without any answer. As the question concerns tensors, I guess that I have come to the right place i.e. to physicists.</p>
<p>Say I have the following equation of motion in the <code>Cartesian</code> coordinate system for a typical mass spring damper system:</p>
<p>$$M \; \ddot{x} + C \; \dot{x} + K \; x = 0$$</p>
<p>where the dot $^\dot{}$ represents differentiation with respect to time.</p>
<p>Now I would like to convert this equation to <code>Polar</code> coordinates. So I introduce</p>
<p>$$x=r \; \cos{\theta}$$ to obtain</p>
<p>$$\dot{x}=\dot{r} \; \cos{\theta} - r \; \dot{\theta} \sin{\theta}$$</p>
<p>and
$$\ddot{x}=\ddot{r} \; \cos{\theta}-2 \; \dot{r} \; \dot{\theta} \; \sin{\theta}-r \; \dot{\theta}^2 \; \cos{\theta}- r \; \ddot{\theta} \; \sin{\theta}$$</p>
<p>I can insert $x, \; \dot{x} \; \text{and} \; \ddot{x}$ in my original equation in the <code>Cartesian</code> coordinate system to yield</p>
<p>$$M \; (\ddot{r} \; \cos{\theta}-2 \; \dot{r} \; \dot{\theta} \; \sin{\theta}-r \; \dot{\theta}^2 \; \cos{\theta}- r \; \ddot{\theta} \; \sin{\theta}) + C \; (\dot{r} \; \cos{\theta} - r \; \dot{\theta} \sin{\theta}) + K \; (r \; \cos{\theta}) = 0$$</p>
<p><strong>Note: I am just showing the equation and derivatives in the x-direction. But the full system has both $x$ and $y$ components.</strong></p>
<p>I wonder if the above way of thinking is right. I am <strong>very</strong> new to tensors and I after reading about <strong>covariant derivatives</strong>, I am now thinking that one should include consider the basis vectors of the <code>Polar</code>coordinate system (a <code>non-Cartesian</code>coordinate system) also since unlike the basis vectors of the <code>Cartesian</code> coordinate system which <em>do not</em> change direction in the 2D space, <code>Polar</code> coordinate basis vectors <em>change</em> direction depending on the angle $\theta$.</p>
<p>I am thinking about <code>covariant derivatives</code> as the conversion process includes differentiation with respect to the bases. For example if $x=r \; \cos{\theta}$, then</p>
<p>$$\dot{x}=\frac{dx}{dt}=\frac{\partial{x}}{\partial{r}} \cdot \frac{dr}{dt} + \frac{\partial{x}}{\partial{\theta}} \cdot \frac{d\theta}{dt}$$</p>
<p>So we have terms like $\frac{\partial{x}}{\partial{r}}$ and $\frac{\partial{x}}{\partial{\theta}}$ that concern basis vectors both in the <code>Cartesian</code> and in the <code>Polar</code> coordinate systems.</p>
<p>Hope that someone can shed some light on this.</p>
| 8,476 |
[
-0.0026299869641661644,
0.03535481169819832,
-0.021987473592162132,
-0.03866288810968399,
0.011712036095559597,
-0.01662677526473999,
-0.0578722283244133,
-0.022137660533189774,
0.036945175379514694,
-0.014716056175529957,
-0.0010366091737523675,
0.04982453212141991,
0.07348669320344925,
0.03022954799234867,
0.047445133328437805,
-0.004455144051462412,
-0.024353280663490295,
-0.0018326942808926105,
0.00019104735110886395,
-0.03629252687096596,
0.027078421786427498,
0.005318020470440388,
0.0024078309070318937,
-0.021548451855778694,
0.02596615068614483,
0.02679569646716118,
0.03323671966791153,
-0.04300135374069214,
-0.006758619099855423,
0.030782349407672882,
-0.028826722875237465,
-0.02161889523267746,
0.0032507481519132853,
0.011738847941160202,
0.020801294595003128,
0.018145225942134857,
-0.0193160530179739,
-0.019334010779857635,
0.026055578142404556,
0.0341779924929142,
-0.01728188619017601,
-0.003241242142394185,
-0.021539894863963127,
0.046809565275907516,
0.007770353928208351,
0.03262168914079666,
-0.004310044925659895,
-0.00447076465934515,
0.04433827102184296,
-0.012718182988464832,
0.09276055544614792,
-0.010281860828399658,
0.014039110392332077,
0.021826839074492455,
-0.06826808303594589,
-0.012636339291930199,
0.06847420334815979,
0.02881382405757904,
-0.013378959149122238,
-0.06701703369617462,
-0.015762099996209145,
-0.04008656367659569,
-0.014280642382800579,
-0.009348774328827858,
0.008396494202315807,
0.015723034739494324,
0.015705512836575508,
0.02405126392841339,
0.02595416270196438,
-0.04052773863077164,
0.01120147854089737,
-0.022013206034898758,
0.007586135063320398,
-0.01982816867530346,
0.005536091048270464,
-0.04391470551490784,
0.03150075674057007,
0.0016990541480481625,
-0.010718001052737236,
0.006480460520833731,
-0.028887150809168816,
0.013701106421649456,
0.022769182920455933,
0.026911651715636253,
-0.01667182520031929,
0.004708561114966869,
0.04077836126089096,
0.011895463801920414,
0.01815040223300457,
0.04911277815699577,
0.01857035979628563,
0.01528618298470974,
0.00559994438663125,
-0.007948421873152256,
0.010329770855605602,
0.01101774349808693,
0.0015576290898025036,
0.03543251007795334,
0.02472870983183384,
-0.027004951611161232,
-0.005762108135968447,
-0.0467560701072216,
0.004202596377581358,
0.0584937147796154,
0.02223467081785202,
-0.004148589447140694,
0.015203582122921944,
-0.02184596098959446,
-0.02066141553223133,
-0.05437255650758743,
-0.0693560466170311,
0.01043790765106678,
-0.001314525376074016,
-0.026052098721265793,
0.008424201048910618,
-0.05118328705430031,
-0.012273779138922691,
-0.01577058620750904,
0.04685944691300392,
0.046046435832977295,
0.07165361195802689,
-0.021144015714526176,
0.0423690490424633,
-0.04748764634132385,
-0.05361325293779373,
-0.01132182590663433,
0.021112916991114616,
-0.009611415676772594,
-0.011099538765847683,
-0.013023871928453445,
0.04672927036881447,
-0.04246656969189644,
-0.016904711723327637,
0.007520773913711309,
0.013428287580609322,
-0.009712733328342438,
-0.12025358527898788,
-0.05499667674303055,
-0.0123538076877594,
0.020995471626520157,
-0.0059296200051903725,
-0.0760854184627533,
0.012371351011097431,
0.04927748814225197,
0.06262896955013275,
0.03153442591428757,
-0.0009015656542032957,
0.07601719349622726,
0.04109124094247818,
-0.006569088902324438,
0.04742584004998207,
-0.007835988886654377,
-0.03313165158033371,
-0.039026129990816116,
0.0016048755496740341,
-0.045108597725629807,
0.0272379107773304,
0.018053900450468063,
-0.006204269360750914,
0.045539338141679764,
0.041388802230358124,
-0.012780790217220783,
0.002467487473040819,
0.021568017080426216,
-0.02322579361498356,
-0.05820648372173309,
0.05978373810648918,
0.01516658440232277,
0.016300255432724953,
0.008643911220133305,
0.006463575642555952,
-0.004794399719685316,
0.007080772891640663,
0.03274267539381981,
0.030849384143948555,
-0.04278644174337387,
0.002509528771042824,
-0.00833031814545393,
-0.012977832928299904,
-0.033269722014665604,
-0.04737533628940582,
-0.05056117847561836,
-0.01210622675716877,
-0.012270013801753521,
0.029030485078692436,
0.04477627947926521,
0.024158092215657234,
0.03201820328831673,
0.009979553520679474,
-0.024500396102666855,
0.027659758925437927,
-0.03689059987664223,
0.04561474174261093,
-0.03397539258003235,
-0.01554130669683218,
0.013723106123507023,
0.012273835949599743,
0.027564696967601776,
-0.024475928395986557,
-0.02544761262834072,
-0.002652843249961734,
0.016522293910384178,
-0.006113345269113779,
-0.01673649437725544,
0.021786758676171303,
0.048196930438280106,
0.049376629292964935,
0.03559775650501251,
-0.00699369003996253,
0.0004770145460497588,
0.005530146881937981,
-0.008335641585290432,
-0.010251098312437534,
0.02473074197769165,
0.005322448443621397,
0.008344381116330624,
-0.0024157853331416845,
-0.015440612100064754,
-0.015172528102993965,
0.0056611779145896435,
-0.03292112424969673,
0.061637844890356064,
0.08789778500795364,
0.0001481302606407553,
0.04636320099234581,
0.029985591769218445,
-0.00761569757014513,
0.04692424088716507,
0.0024200608022511005,
-0.028261765837669373,
-0.03679302707314491,
0.013189568184316158,
0.033216558396816254,
0.00186285434756428,
-0.07292928546667099,
0.021943112835288048,
0.029424037784337997,
0.0201919786632061,
0.010646460577845573,
0.015252978540956974,
-0.0034583676606416702,
-0.05343963950872421,
0.04696475714445114,
-0.004362102132290602,
0.00365432002581656,
0.007201183121651411,
0.018768401816487312,
-0.0245360154658556,
0.03375968337059021,
-0.009030759334564209,
0.0007406192598864436,
0.03872213885188103,
-0.014173797331750393,
-0.007117544300854206,
0.018981771543622017,
-0.010772721841931343,
0.058823488652706146,
0.009266454726457596,
0.022655917331576347,
0.06991930305957794,
0.008340328931808472,
0.006693874020129442,
-0.003589823842048645,
0.01561692077666521,
-0.023749452084302902,
0.004181884694844484,
-0.005131666082888842,
-0.03448832035064697,
0.012197387404739857,
-0.06329043209552765,
-0.03005053848028183,
-0.015785343945026398,
-0.06937170773744583,
-0.0024182028137147427,
0.0019178275251761079,
0.026328641921281815,
0.03231864795088768,
-0.003109529847279191,
0.007540356833487749,
0.0061678458005189896,
0.001653060782700777,
-0.03184264525771141,
0.0039974781684577465,
0.027162201702594757,
-0.049625810235738754,
0.030959200114011765,
-0.050949595868587494,
-0.006242807488888502,
0.05288830026984215,
-0.0002765733515843749,
-0.010079525411128998,
-0.0004265320603735745,
0.0018392384517937899,
-0.07174298167228699,
-0.025257166475057602,
-0.004888149909675121,
-0.003287428757175803,
-0.06630473583936691,
-0.0000463922624476254,
0.06613965332508087,
0.0053116572089493275,
-0.04365847259759903,
-0.026871658861637115,
-0.036389417946338654,
-0.0277043916285038,
0.005715934094041586,
-0.02855975739657879,
0.028568822890520096,
-0.025423461571335793,
0.014591420069336891,
0.025644080713391304,
0.01616641879081726,
0.027841338887810707,
-0.05890423431992531,
-0.03890799731016159,
0.015613904222846031,
0.008539662696421146,
0.06019330397248268,
0.010154517367482185,
-0.020354047417640686,
0.08717100322246552,
0.02533324435353279,
-0.02390650101006031,
0.01392791885882616,
0.017344307154417038,
-0.011720757931470871,
-0.054172080010175705,
-0.007873373106122017,
0.008752514608204365,
-0.01822769083082676,
-0.02135881781578064,
0.011151161976158619,
0.0031931225676089525,
0.015159763395786285,
-0.016801027581095695,
0.027271632105112076,
0.019077561795711517,
0.03081313520669937,
0.0019883757922798395,
0.05131196975708008,
0.03893570974469185,
0.003498553531244397,
0.017112530767917633,
-0.0033060256391763687,
0.030430909246206284,
-0.01755974441766739,
-0.08474498987197876,
0.022213652729988098,
-0.013990663923323154,
-0.001614373060874641,
0.011745935305953026,
0.03759526088833809,
0.0024197271559387445,
-0.045689526945352554,
-0.020860249176621437,
0.045285776257514954,
0.037739098072052,
-0.00547729292884469,
0.013499916531145573,
0.01600300893187523,
0.02119317464530468,
-0.002934063319116831,
0.014094740152359009,
-0.0078361127525568,
0.01353513915091753,
0.040533386170864105,
-0.032214075326919556,
-0.010559599846601486,
0.033173877745866776,
-0.00010438437311677262,
0.033597394824028015,
-0.0027511613443493843,
-0.018213458359241486,
0.012691814452409744,
-0.03629181906580925,
0.006271666847169399,
-0.015475873835384846,
0.03854990005493164,
0.010837702080607414,
0.0711689218878746,
0.03437730297446251,
-0.009165770374238491,
0.02977563627064228,
-0.01385512761771679,
-0.07419028133153915,
0.03401904180645943,
-0.0509650856256485,
-0.0218651182949543,
0.0278092622756958,
-0.03200270235538483,
0.006231904029846191,
0.01153659913688898,
-0.0007853854913264513,
0.007060145493596792,
-0.012819340452551842,
-0.05642455443739891,
0.025887858122587204,
0.006468567531555891,
-0.03952455148100853,
-0.020688114687800407,
0.05270789563655853,
0.03746585547924042,
-0.026491519063711166,
0.011196441948413849,
0.0714397057890892,
-0.016130825504660606,
0.008437919430434704,
-0.04223485663533211,
-0.00862178299576044,
0.019906053319573402,
0.00810054037719965,
0.0054114568047225475,
-0.005245970096439123,
0.027175836265087128,
0.017949538305401802,
0.0033428738825023174,
0.06358297169208527,
0.02639087103307247,
-0.018547935411334038,
-0.011353734880685806,
-0.05090602487325668,
0.006490272469818592,
0.012451454997062683,
0.057918816804885864,
-0.0049660587683320045,
-0.007857756689190865,
-0.0036326146218925714,
0.028470415621995926,
0.036438774317502975,
0.046387866139411926,
0.05948076397180557,
-0.0008292513084597886,
-0.041743163019418716,
-0.057042162865400314,
0.013203345239162445,
-0.005621293559670448,
0.005291183944791555,
-0.007052404806017876,
-0.015131116844713688,
-0.024263503029942513,
0.011479318141937256,
0.00900021381676197,
0.024648591876029968,
0.015024969354271889,
0.024345170706510544,
-0.002640796359628439,
0.040503665804862976,
-0.011571803130209446,
0.01808338798582554,
-0.012086089700460434,
0.01620372384786606,
0.04336017370223999,
-0.017533602192997932,
0.02824127860367298,
-0.06913745403289795,
-0.00971547607332468,
-0.011229214258491993,
0.04005486145615578,
-0.0029522425029426813,
-0.01870378851890564,
-0.04489884898066521,
-0.03609102964401245,
0.050855133682489395,
-0.014994233846664429,
0.0638941153883934,
-0.0016445476794615388,
0.02613287791609764,
-0.04221385717391968,
-0.018330464139580727,
-0.014200364239513874,
0.005657345987856388,
-0.019581060856580734,
0.034878648817539215,
0.00477393064647913,
0.005732697434723377,
0.02147095650434494,
-0.01587192714214325,
0.03712991252541542,
0.059310123324394226,
0.008681103587150574,
-0.07270298898220062,
-0.04513237252831459,
-0.0022573398891836405,
-0.010552587918937206,
-0.04619096592068672,
0.0059495712630450726,
0.020725877955555916,
-0.02677382156252861,
0.016969092190265656,
-0.04083903506398201,
-0.06297674775123596,
0.056877050548791885,
-0.0005609436193481088,
0.0391385592520237,
0.018417147919535637,
-0.04628775641322136,
0.020125828683376312,
0.04202446714043617,
-0.04439996927976608,
0.01031008455902338,
0.025150103494524956,
-0.005085785407572985,
-0.0019255627412348986,
-0.03005501627922058,
-0.004527081735432148,
-0.03324024751782417,
-0.013737916015088558,
-0.0462397038936615,
0.02129760943353176,
-0.02826523222029209,
0.02893160469830036,
-0.030968938022851944,
0.010592908598482609,
-0.06626474112272263,
0.00986533798277378,
-0.0013723165029659867,
0.029781581833958626,
-0.03163599595427513,
-0.015394064597785473,
0.0017099159304052591,
-0.016282670199871063,
-0.030245862901210785,
-0.0042517539113759995,
0.004128503147512674,
-0.04366980865597725,
-0.0020991635974496603,
0.022618373855948448,
-0.01717163436114788,
-0.011743757873773575,
-0.023577943444252014,
-0.013810104690492153,
-0.011715224012732506,
-0.0410785973072052,
0.042516399174928665,
-0.004408027045428753,
-0.001411575241945684,
0.032350052148103714,
-0.0506708025932312,
-0.058055613189935684,
0.03725595027208328,
0.005917077884078026,
0.021324658766388893,
-0.03406524285674095,
-0.03618406131863594,
0.03270222619175911,
0.02282155118882656,
-0.027163635939359665,
-0.06310013681650162,
0.00998661108314991,
-0.0326809398829937,
-0.012842519208788872,
0.004431476816534996,
0.005236290395259857,
-0.008528691716492176,
-0.022423839196562767,
0.017844272777438164,
0.06380823254585266,
-0.028593679890036583,
0.013848788104951382,
0.002757865935564041,
0.019298521801829338,
0.05524748936295509,
-0.01910453289747238,
0.004861351568251848,
0.03457488864660263,
-0.0003092638507951051,
-0.010637540370225906,
-0.0030799817759543657,
0.05226430296897888,
-0.022079739719629288,
-0.019995568320155144,
-0.04137437790632248,
0.0038446749094873667,
0.029131200164556503,
0.030273057520389557,
-0.03591109812259674,
0.009184258989989758,
0.0159201230853796,
-0.04475243762135506,
-0.06736719608306885,
0.0020411661826074123,
0.027662819251418114,
0.02571440115571022,
-0.023411976173520088,
-0.004291793331503868,
-0.02803092822432518,
-0.018834572285413742,
0.0018736590864136815,
0.0021742910612374544,
0.0022409914527088404,
-0.005027386825531721,
0.07547382265329361,
-0.029924843460321426,
0.008913462050259113,
0.03687431663274765,
0.012795370072126389,
0.013753633014857769,
0.023078972473740578,
-0.01816294714808464,
0.00035640891292132437,
-0.027158694341778755,
-0.03847184404730797,
-0.03238813206553459,
-0.06290866434574127,
0.002148878527805209,
0.10235030204057693,
-0.04303273186087608,
0.022676702588796616,
0.03593839704990387,
0.003213078947737813,
-0.0012055988190695643,
-0.00009630160639062524,
-0.04758637025952339,
-0.01910899393260479,
0.02972659282386303,
0.030441224575042725,
-0.03319477289915085,
-0.018431587144732475,
0.011382591910660267,
0.03722260892391205,
-0.03409513831138611,
0.0034523732028901577,
-0.03036617860198021,
0.030394837260246277,
-0.04680287837982178,
-0.014547663740813732,
-0.05144354701042175,
0.01030130498111248,
0.00017449875304009765,
0.04724159091711044,
-0.011347568593919277,
-0.03203500807285309,
0.013408289290964603,
0.017036883160471916,
0.019943730905652046,
-0.04210209101438522,
-0.00803744699805975,
-0.05372634902596474,
0.021951977163553238,
0.004019149113446474,
0.012491313740611076,
-0.01594800315797329,
0.029581548646092415,
0.08068588376045227,
-0.00557557912543416,
0.029952066019177437,
-0.019226083531975746,
-0.046674322336912155,
-0.03572788089513779,
-0.037491846829652786,
-0.057389527559280396,
0.0773872435092926,
0.01723923720419407,
0.004573708400130272,
0.012321293354034424,
-0.02992047555744648,
0.044063225388526917,
0.02035379782319069,
0.028230639174580574,
-0.025387324392795563,
0.10154815763235092,
-0.035436779260635376,
-0.027102861553430557,
-0.04428473860025406,
-0.01590694487094879,
0.12747319042682648,
0.020873937755823135,
0.020830603316426277,
-0.0209816861897707,
0.01169121265411377,
-0.0034978024195879698,
-0.0001901246141642332,
-0.0491405613720417,
0.013635930605232716,
0.020170608535408974,
-0.01343434676527977,
0.006161761935800314,
0.004468248691409826,
-0.02313198707997799,
-0.017987743020057678,
0.027840713039040565,
-0.027569163590669632,
-0.03872419148683548,
-0.04011784866452217,
0.012489127926528454,
-0.017362428829073906,
0.0201269518584013,
-0.0033773414324969053,
0.01222745981067419,
-0.032708022743463516,
0.018504440784454346,
-0.04878992587327957,
-0.009590919129550457,
-0.0016526272520422935,
-0.030280975624918938,
-0.04357706755399704,
0.033806703984737396,
-0.0013219976099207997,
-0.014924772083759308,
-0.030990147963166237,
0.04577726870775223,
0.017102031037211418,
0.007975436747074127,
0.04846876859664917,
0.029270783066749573,
0.009179195389151573,
-0.004352865274995565,
0.010807327926158905,
0.015434828586876392,
-0.0617230162024498,
0.025387920439243317,
-0.04790133237838745,
0.0491812489926815,
0.010610525496304035,
-0.00743980472907424,
-0.012216784060001373,
0.011185427196323872,
0.009795387275516987,
-0.04106703773140907,
0.01781228557229042,
-0.0003454661346040666,
0.04070202633738518,
-0.036097340285778046,
0.02786768041551113,
-0.0003324597200844437,
0.003956760745495558,
0.029264748096466064,
0.029698532074689865,
-0.05227304995059967,
-0.002655025804415345,
0.003387690521776676,
0.009595836512744427,
0.04594330117106438,
-0.013516278937458992,
0.008933722041547298,
-0.031793586909770966,
-0.0014568220358341932,
-0.017035791650414467,
-0.008306991308927536,
0.029896169900894165,
0.025888416916131973,
0.00007495511817978695,
0.017918605357408524,
-0.0008275267318822443,
-0.03930487856268883,
-0.04770209640264511,
0.015132268890738487,
0.03087598830461502,
0.0009624254889786243,
-0.02186105027794838,
-0.013532650656998158,
0.0033694016747176647,
0.03918470814824104,
-0.024028761312365532,
0.028145508840680122,
-0.002730247098952532,
0.035657741129398346,
0.03369063884019852,
-0.007161370012909174,
-0.022383932024240494,
0.04873080924153328,
-0.024286221712827682,
-0.015756729990243912,
-0.028251325711607933,
0.027420349419116974,
0.04242467135190964,
0.03350043296813965,
-0.003702530637383461,
0.025256142020225525,
-0.0014477825025096536,
-0.015194936655461788,
0.0476369708776474,
-0.004132790490984917,
0.007800974417477846,
-0.021460892632603645,
0.023346824571490288,
-0.03635875880718231,
0.0030148776713758707,
-0.020374834537506104,
-0.04165402054786682,
0.015409567393362522,
0.0006853699451312423,
-0.017780423164367676,
0.019502941519021988,
-0.07785679399967194,
-0.02165788598358631,
-0.023388393223285675,
0.024645162746310234,
-0.0036308481357991695,
0.01891324855387211,
-0.0047158049419522285,
-0.020690159872174263,
-0.03674536570906639,
0.04483205825090408,
-0.027918368577957153,
-0.001422290806658566,
0.01674438640475273,
0.051220476627349854,
0.005429152864962816,
0.013883382081985474,
0.009302311576902866,
0.01668151654303074,
0.02952101081609726,
-0.007955257780849934,
-0.017472900450229645,
-0.0008037015795707703,
-0.015319040976464748,
-0.006428966298699379,
0.031147943809628487,
0.0064336624927818775,
0.03191802278161049,
-0.0024094802793115377,
-0.024279534816741943,
0.005612675100564957,
0.057160671800374985,
-0.03944467753171921,
0.003185711335390806,
0.008764603175222874,
-0.03873632848262787,
-0.03542844206094742,
-0.03391779214143753,
0.03720973804593086,
-0.031036846339702606,
0.024814793840050697,
0.012647029012441635,
0.043042201548814774,
0.00901850126683712,
0.005464022047817707,
0.021510092541575432,
0.01355716586112976,
-0.012284822762012482,
0.007841634564101696,
0.016567831858992577,
0.01565553806722164,
0.025980688631534576,
-0.0207069031894207,
0.00503403740003705,
0.029116041958332062,
0.04153284803032875,
-0.12096098065376282,
-0.00815668050199747,
0.013256874866783619,
0.011073481291532516,
0.05431634187698364,
-0.050580743700265884,
-0.018581008538603783,
0.011933996342122555,
-0.07805489003658295,
0.029317788779735565,
-0.012901616282761097,
-0.025727707892656326,
-0.0017713423585519195,
-0.00899853091686964,
-0.030065901577472687,
0.059346169233322144,
0.029171166941523552,
0.04216853901743889,
0.02150188386440277,
0.025531116873025894,
-0.030302302911877632,
-0.021490542218089104,
-0.005709609482437372,
0.013168356381356716,
-0.002294087316840887,
-0.003451555036008358,
0.05807659775018692,
-0.01426362432539463,
-0.023336926475167274,
0.03422674164175987,
-0.009745924733579159,
-0.01670665480196476,
-0.012142366729676723,
0.02114190347492695,
0.016773395240306854,
0.022524943575263023,
0.047734349966049194,
-0.027020495384931564,
-0.01562756486237049,
-0.007945810444653034,
0.030263273045420647,
0.028894489631056786,
-0.03149430453777313,
0.020349688827991486,
0.014060748741030693,
-0.0377267561852932,
-0.0453135222196579,
0.017623990774154663,
-0.01968470774590969,
-0.0072621628642082214,
0.0046999105252325535,
-0.016728049144148827,
-0.010646633803844452,
-0.0481368713080883,
-0.0207491647452116,
-0.028366519138216972,
-0.006998917553573847,
0.029404012486338615,
-0.051616061478853226,
0.020636001601815224,
0.0460611954331398,
-0.030926765874028206,
-0.05550086870789528,
-0.00185215356759727,
0.003131299512460828,
-0.015089401043951511,
-0.07087554782629013,
0.006447681691497564,
0.009184684604406357,
-0.0039220754988491535,
-0.02528507076203823,
-0.007800326216965914,
-0.031219424679875374,
0.04141116887331009,
0.021389063447713852,
-0.006801729090511799,
0.007110131438821554,
-0.016670681536197662,
-0.0003124058712273836,
-0.06741677969694138,
-0.021197088062763214,
0.014293234795331955,
-0.05014999583363533,
-0.035907257348299026,
-0.018297092989087105,
-0.006972120609134436,
0.05014382302761078,
0.05703543871641159,
0.011555390432476997,
0.00806307140737772,
0.005284419283270836,
-0.0265307929366827,
-0.007890361361205578,
-0.05670483037829399,
0.006278336979448795,
0.008417360484600067,
0.0019573864992707968,
0.03049212135374546,
-0.012663627974689007,
-0.007882537320256233,
0.013147824443876743,
0.023064173758029938,
0.0050129881128668785,
0.06253873556852341,
0.007434877101331949,
-0.03826971724629402,
0.0071878330782055855,
-0.03902605175971985,
-0.006625244859606028,
0.0596824511885643,
0.000286329333903268,
-0.018942909315228462,
0.03556448593735695,
-0.03012906014919281,
-0.04493876174092293,
0.008760559372603893,
-0.07409123331308365,
-0.03364909440279007,
-0.014485380612313747,
-0.04493096470832825,
0.02914748154580593,
-0.061982784420251846,
0.017667271196842194,
0.05627606436610222,
-0.03450275957584381,
-0.006799365859478712,
0.03857196494936943,
0.0017229443183168769,
0.03610863909125328,
0.037338439375162125,
0.04841168224811554,
0.038435112684965134,
-0.021219389513134956,
0.03878617659211159,
-0.01675472781062126,
0.06365097314119339,
-0.01848505064845085,
-0.04081243649125099,
0.010511543601751328,
-0.034249864518642426,
0.04980714991688728,
0.006098640616983175,
0.03779619187116623,
-0.016783712431788445,
-0.0007528539281338453,
0.045515112578868866,
-0.022202616557478905,
-0.003124635200947523,
0.044620294123888016,
-0.02581085078418255,
0.04541214555501938,
0.017410961911082268,
-0.0018946918426081538,
-0.015257740393280983,
0.03521650284528732,
-0.041121650487184525,
0.002001377521082759,
-0.009230795316398144,
0.007979385554790497,
-0.012588982470333576,
0.0057976809330284595,
-0.0374552346765995,
-0.03425219655036926,
0.0009870273061096668,
-0.031230978667736053,
0.04041697457432747,
0.028442546725273132,
0.020909326151013374,
0.019488459452986717,
-0.042060211300849915,
-0.04935036227107048,
-0.044747959822416306,
0.06416734308004379,
0.005967311095446348,
0.02147328108549118,
-0.0368453785777092,
0.004205424804240465,
-0.047013748437166214,
0.05176080763339996,
-0.04148220270872116,
-0.011649060994386673,
0.03568583354353905,
0.03723267838358879,
0.020559297874569893,
0.0026558360550552607
] |
<p>When I first studied friction I faced f = $\mu$ N where f is force of friction, $\mu$ is coefficient of friction for the surface considered and N is the normal force for the body on surface. Now f is a force so it must be a vector which means it has a direction. N is normal force so it has direction too. But both f and N are mutually perpendicular to each other! And $\mu$ is a constant, so how can we write f and N in one equation? They do not have the same direction!</p>
<p>I think this is not clear to me because I have never read about the origin of this equation. From where do we get it?</p>
| 8,477 |
[
-0.026498766615986824,
0.013554384000599384,
-0.013236436992883682,
0.011603932827711105,
0.033813320100307465,
0.003174971556290984,
-0.025664495304226875,
0.006182234268635511,
-0.012623260729014874,
-0.036872487515211105,
-0.019393734633922577,
0.04727915674448013,
0.06963354349136353,
0.010683908127248287,
0.038813285529613495,
0.0033202951308339834,
-0.036031387746334076,
-0.000976257782895118,
-0.0024888929910957813,
-0.019462358206510544,
-0.018187128007411957,
0.024901870638132095,
0.030349206179380417,
-0.0028353948146104813,
0.02209148183465004,
0.03393300622701645,
0.021450096741318703,
-0.011893684975802898,
0.027708973735570908,
0.03279890865087509,
0.016278499737381935,
-0.03943072631955147,
-0.014541156589984894,
-0.010683641768991947,
0.0032590620685368776,
0.01245030015707016,
0.020421957597136497,
0.018000628799200058,
-0.0012670905562117696,
0.026523582637310028,
-0.03615923225879669,
-0.007018315605819225,
-0.019663268700242043,
0.040312573313713074,
-0.05862141400575638,
0.03756297007203102,
0.04073074460029602,
-0.0010082139633595943,
0.02687065489590168,
-0.05970321595668793,
0.07069118320941925,
0.011096558533608913,
0.0779673308134079,
0.021567489951848984,
-0.010851128026843071,
0.02591201290488243,
0.06726598739624023,
0.051255762577056885,
-0.016228491440415382,
-0.05436120927333832,
-0.003703663358464837,
-0.03927144035696983,
-0.010040109977126122,
-0.025522757321596146,
-0.011365010403096676,
0.011926054023206234,
-0.019609492272138596,
-0.023929394781589508,
0.02779276855289936,
0.018630966544151306,
-0.0021014870144426823,
0.027081811800599098,
0.041494328528642654,
-0.020139582455158234,
-0.0187999177724123,
-0.05556970834732056,
0.016140742227435112,
-0.03311097249388695,
-0.00757518270984292,
0.03588663786649704,
-0.014131082221865654,
0.017386605963110924,
0.03233720362186432,
0.03754017874598503,
0.01872553490102291,
-0.04081866145133972,
0.06853514164686203,
0.00715363584458828,
0.04937319830060005,
0.016428975388407707,
0.012311655096709728,
0.01734980009496212,
0.031123289838433266,
-0.0018574600107967854,
-0.004963486921042204,
0.019665498286485672,
0.013185217045247555,
-0.015580865554511547,
0.04249357804656029,
-0.03393940255045891,
0.002033363562077284,
-0.008987123146653175,
-0.008427256718277931,
0.037698112428188324,
0.0045099142007529736,
-0.003310038009658456,
-0.029986415058374405,
0.04055522009730339,
-0.03866241127252579,
0.001777916681021452,
-0.03479066118597984,
0.02925512194633484,
-0.020659275352954865,
0.019927818328142166,
0.01246869657188654,
0.014611058868467808,
0.03186465799808502,
-0.007239828817546368,
0.05986074358224869,
0.09674578160047531,
0.011905555613338947,
-0.05526048317551613,
0.015354486182332039,
-0.032992810010910034,
-0.056746792048215866,
-0.0035114057827740908,
0.028164092451334,
-0.0007633516797795892,
0.004542407114058733,
-0.006482495926320553,
0.009677821770310402,
-0.02030179463326931,
0.0015602749772369862,
0.03992573171854019,
0.005199531093239784,
0.008513770997524261,
-0.08051024377346039,
-0.06683383136987686,
0.06318068504333496,
-0.03788064047694206,
-0.01876174286007881,
-0.09221472591161728,
0.0029441621154546738,
0.009676968678832054,
0.05666004866361618,
-0.005308063235133886,
0.01416029129177332,
-0.0006946500507183373,
0.03437219560146332,
-0.013299867510795593,
0.02683344855904579,
-0.048378463834524155,
0.010469111613929272,
-0.06354807317256927,
-0.036261577159166336,
-0.05791721120476723,
0.04890735074877739,
0.010553239844739437,
0.005551123060286045,
-0.04516536369919777,
0.06079639866948128,
-0.021120542660355568,
-0.01278723031282425,
0.024644436314702034,
-0.01438820082694292,
-0.03089006431400776,
0.08255346119403839,
0.010844910517334938,
0.009807588532567024,
0.0464848130941391,
0.038317691534757614,
0.0008332304423674941,
0.015665829181671143,
0.06887187063694,
0.01571507193148136,
-0.04301447421312332,
-0.03035629913210869,
0.009390628896653652,
0.006720292381942272,
-0.022605979815125465,
-0.032344717532396317,
-0.01872917078435421,
0.01889048144221306,
0.009896809235215187,
-0.027466658502817154,
0.05415406823158264,
-0.016940061002969742,
0.0044157858937978745,
-0.025663306936621666,
-0.03395272418856621,
-0.004806173499673605,
-0.0875481516122818,
0.017668474465608597,
-0.019325098022818565,
-0.027640677988529205,
0.0351199135184288,
0.0009476219420321286,
0.02723688632249832,
-0.03734138607978821,
-0.029806630685925484,
-0.0070755393244326115,
0.056718453764915466,
0.004882164765149355,
-0.03167382627725601,
0.009524386376142502,
0.051108263432979584,
0.039138063788414,
0.015759741887450218,
0.024331387132406235,
-0.04203919693827629,
-0.01769285462796688,
0.03612884506583214,
-0.045877110213041306,
-0.005955174565315247,
0.02195010893046856,
-0.004983685445040464,
0.03797142952680588,
-0.018110577017068863,
-0.012864182703197002,
0.019369250163435936,
-0.037319038063287735,
0.033460572361946106,
0.03798894211649895,
0.024321842938661575,
0.013774658553302288,
0.03104408271610737,
0.0038209157064557076,
-0.014525785110890865,
-0.010479235090315342,
-0.031991444528102875,
-0.028921207413077354,
-0.0005584643804468215,
0.027336610481142998,
0.028809482231736183,
-0.03924832120537758,
-0.010505917482078075,
0.024050312116742134,
0.04089336097240448,
0.0380660742521286,
0.04157407581806183,
0.016980355605483055,
-0.04238618165254593,
0.009962065145373344,
0.0338904969394207,
-0.011305324733257294,
0.035720933228731155,
0.0043516503646969795,
0.0557437539100647,
0.02217908576130867,
-0.0008347140392288566,
-0.05446431413292885,
0.0742131769657135,
0.00803340133279562,
0.016831183806061745,
0.050479453057050705,
-0.002235791878774762,
0.03455600515007973,
-0.03833417594432831,
0.012808570638298988,
0.026030289009213448,
0.013567321002483368,
0.00805212277919054,
-0.01040200237184763,
-0.0009432893129996955,
0.036270055919885635,
-0.0237906314432621,
-0.023815087974071503,
-0.013090700842440128,
0.021902862936258316,
-0.008077708072960377,
0.0024876922834664583,
-0.01875990442931652,
-0.006616772618144751,
0.008685478940606117,
-0.01550648920238018,
0.025002896785736084,
0.018055222928524017,
0.0410819835960865,
-0.005200346000492573,
-0.0004540204827208072,
0.016135305166244507,
-0.059114597737789154,
0.015431826934218407,
-0.021065659821033478,
-0.04637047275900841,
0.023083144798874855,
-0.046948470175266266,
-0.037879232317209244,
0.03948977217078209,
-0.0064144921489059925,
0.03190753608942032,
0.03827935829758644,
-0.024352816864848137,
-0.07391852140426636,
-0.030600445345044136,
-0.04008859768509865,
-0.008474759757518768,
-0.01143755204975605,
0.005387037992477417,
0.04556780308485031,
-0.047616101801395416,
-0.008443139493465424,
0.030434809625148773,
-0.04518599435687065,
-0.06263583898544312,
-0.023433471098542213,
-0.038636818528175354,
0.03537864238023758,
-0.008221480064094067,
0.008546343073248863,
0.03702867031097412,
-0.07146952301263809,
-0.025830445811152458,
-0.04338660463690758,
-0.013480093330144882,
0.005560750607401133,
-0.022302567958831787,
0.0748538076877594,
-0.004689814522862434,
-0.0014484018320217729,
0.04817906394600868,
0.05740867555141449,
-0.026213036850094795,
-0.006875994615256786,
0.014918501488864422,
-0.020630797371268272,
-0.07273626327514648,
-0.0071736890822649,
0.04156968370079994,
-0.014541993848979473,
0.03926093503832817,
-0.013000023551285267,
-0.009489821270108223,
0.044246792793273926,
0.020434370264410973,
0.00813192967325449,
-0.031889475882053375,
-0.018722251057624817,
0.008070782758295536,
0.02754572592675686,
0.038368724286556244,
-0.01606101170182228,
0.017310956493020058,
0.03623005002737045,
0.062180016189813614,
0.0048207794316112995,
-0.03424711152911186,
0.035810112953186035,
0.006054210476577282,
0.0021567698568105698,
-0.05176372826099396,
0.010902765206992626,
0.0036226436495780945,
0.01031612791121006,
0.011630939319729805,
0.01654307171702385,
0.019564680755138397,
-0.05490924417972565,
-0.013032659888267517,
0.03129339963197708,
-0.02804253250360489,
-0.028456751257181168,
-0.055833443999290466,
-0.03072751685976982,
0.01950751431286335,
0.005627631209790707,
-0.025224510580301285,
0.007837161421775818,
0.022181754931807518,
0.033776815980672836,
0.03622179105877876,
0.00718357739970088,
-0.03623328357934952,
0.007042661774903536,
-0.05744273215532303,
-0.03961168974637985,
0.026231953874230385,
0.012134763412177563,
-0.0011620926670730114,
0.04570302739739418,
0.01421233918517828,
0.015832310542464256,
0.0034892389085143805,
0.004918217658996582,
-0.11609840393066406,
0.021773280575871468,
-0.0395047701895237,
-0.045457836240530014,
-0.015223948284983635,
-0.05105815455317497,
0.0030710760038346052,
-0.006916904356330633,
-0.009647976607084274,
0.029688309878110886,
-0.010611693374812603,
-0.07076169550418854,
0.029522357508540154,
-0.04234977066516876,
-0.03883690759539604,
-0.003568770596757531,
0.05359027907252312,
0.04554559662938118,
-0.027781713753938675,
0.004562068730592728,
0.04814724251627922,
-0.01243943627923727,
-0.012761574238538742,
-0.0154579384252429,
-0.02467758022248745,
0.03389638289809227,
-0.00415533222258091,
-0.000009944971679942682,
0.010404273867607117,
0.024104464799165726,
0.01660734787583351,
-0.006432376801967621,
0.07026737928390503,
0.056748680770397186,
0.0005008023581467569,
-0.05213136970996857,
-0.05565401539206505,
-0.006552537903189659,
-0.015546496957540512,
0.06484577059745789,
-0.001407344127073884,
0.0032816948369145393,
0.03118927590548992,
0.018596569076180458,
-0.03394520655274391,
0.038975827395915985,
0.02126922830939293,
0.036890868097543716,
-0.02562558464705944,
-0.05533432960510254,
-0.003680777968838811,
-0.017747653648257256,
0.005745612550526857,
0.009304970502853394,
-0.020668452605605125,
-0.044217683374881744,
-0.022247187793254852,
0.0378713458776474,
0.006584957242012024,
0.023417476564645767,
0.027513645589351654,
-0.023618051782250404,
0.03663216903805733,
-0.007304831873625517,
0.0017184505704790354,
-0.031689438968896866,
0.06851012259721756,
0.016423970460891724,
-0.02201898954808712,
-0.027869248762726784,
-0.05172887071967125,
0.019241586327552795,
-0.01632787473499775,
0.004883244168013334,
-0.02448182739317417,
0.013758448883891106,
-0.03894997015595436,
-0.00805565807968378,
0.04042099416255951,
-0.01793653517961502,
0.017772644758224487,
-0.002258638385683298,
-0.007317091803997755,
-0.009975455701351166,
-0.013859536498785019,
-0.032111577689647675,
0.02470102533698082,
-0.005977435037493706,
0.021902617067098618,
-0.005433184094727039,
-0.01750929467380047,
-0.02481403574347496,
0.0033863659482449293,
0.026395445689558983,
0.030842822045087814,
-0.00726755615323782,
-0.036366403102874756,
0.010105917230248451,
0.018302500247955322,
0.002597138984128833,
-0.09466100484132767,
0.0019009122624993324,
0.026292679831385612,
0.03592052683234215,
0.005188040900975466,
-0.029121965169906616,
-0.052373215556144714,
0.01078812312334776,
-0.018953068181872368,
-0.013376201502978802,
0.02123822085559368,
-0.02825978584587574,
0.04943275824189186,
0.015365904197096825,
-0.028118491172790527,
0.06179497390985489,
-0.004868030548095703,
-0.00505074905231595,
-0.02819415181875229,
-0.029006896540522575,
0.030614562332630157,
0.0005905005382373929,
-0.017355917021632195,
-0.04662051796913147,
0.026120560243725777,
-0.01916593872010708,
0.043388910591602325,
0.027288593351840973,
0.022149818018078804,
-0.04022889584302902,
-0.02697022818028927,
-0.05241331085562706,
0.015213091857731342,
0.03516048192977905,
-0.028703562915325165,
0.03312655910849571,
-0.006056959740817547,
0.022335683926939964,
-0.02191738784313202,
-0.01116117648780346,
-0.010823669843375683,
0.003455815138295293,
0.03155465051531792,
0.024766070768237114,
0.00975595973432064,
-0.00976006779819727,
-0.04462594538927078,
0.026843862608075142,
-0.04407680034637451,
0.020769041031599045,
0.0022846634965389967,
0.02375607378780842,
0.03633378446102142,
-0.05520356073975563,
-0.05406298488378525,
0.017573945224285126,
0.006706978194415569,
0.026650184765458107,
-0.06182603910565376,
-0.00866913702338934,
0.04012659192085266,
0.008312534540891647,
-0.03717304766178131,
-0.03978654742240906,
0.021018441766500473,
-0.047665975987911224,
-0.010607053525745869,
-0.01709439978003502,
-0.006030532997101545,
-0.026800572872161865,
-0.029925033450126648,
0.040367256850004196,
0.05505427345633507,
-0.0347558967769146,
-0.026572227478027344,
0.009188336320221424,
0.011242086067795753,
0.03095116838812828,
-0.022868052124977112,
-0.008152008056640625,
-0.015405653044581413,
-0.01091067399829626,
0.004953353200107813,
0.01904935948550701,
0.08145109564065933,
-0.014989062212407589,
-0.003597838571295142,
-0.007646366022527218,
-0.034754395484924316,
0.03904508799314499,
-0.0034341418650001287,
0.03136172890663147,
0.03356114402413368,
0.0124867158010602,
-0.03384388983249664,
-0.024876846000552177,
0.03269125893712044,
0.013087385334074497,
0.045657429844141006,
0.03354568034410477,
-0.0034243562258780003,
-0.02526615373790264,
-0.018567508086562157,
0.03431424871087074,
0.004391475114971399,
0.06602517515420914,
-0.003288985462859273,
0.05919002369046211,
-0.03267233446240425,
-0.0070020295679569244,
-0.0008318406180478632,
0.011609010398387909,
0.05940265581011772,
0.010300183668732643,
-0.006026970222592354,
0.002674760529771447,
-0.0032585994340479374,
-0.053015802055597305,
-0.020138340070843697,
-0.03740643709897995,
-0.0012198782060295343,
0.05691171810030937,
-0.04679218679666519,
0.06723813712596893,
0.036863502115011215,
-0.011718148365616798,
0.0014137199614197016,
0.0007932204171083868,
-0.020158883184194565,
-0.009705621749162674,
0.021439194679260254,
0.014023120515048504,
-0.028517751023173332,
0.018378719687461853,
0.03959295153617859,
0.02967189811170101,
0.010252319276332855,
-0.0192360058426857,
0.005979210138320923,
0.03954697400331497,
0.004423975478857756,
0.009738913737237453,
-0.03830119967460632,
0.047059763222932816,
0.0004974468611180782,
0.058999039232730865,
0.002677635755389929,
-0.023173218593001366,
0.043172795325517654,
0.032081134617328644,
-0.04115980491042137,
-0.06328848749399185,
0.014914657920598984,
-0.02328808605670929,
0.02149287238717079,
0.04224797710776329,
0.0013834998244419694,
-0.0038426786195486784,
0.02331417053937912,
0.044647231698036194,
-0.004469502251595259,
0.006896937265992165,
-0.01667800359427929,
-0.03889976441860199,
0.0018769754096865654,
-0.04254844784736633,
-0.013674333691596985,
0.03859061002731323,
-0.027561556547880173,
-0.03543723374605179,
0.007675579283386469,
-0.026938289403915405,
0.015384083613753319,
0.029127607122063637,
-0.009292042814195156,
-0.027625279501080513,
0.07646878063678741,
-0.011271725408732891,
0.006416205316781998,
-0.03695528581738472,
-0.006972275208681822,
0.110641710460186,
0.04691505804657936,
0.027571385726332664,
-0.02885282412171364,
-0.002637515077367425,
-0.0431421734392643,
-0.024250086396932602,
-0.025014417245984077,
0.07439316809177399,
0.00491558201611042,
0.03247266262769699,
0.025557441636919975,
0.04070999473333359,
0.022718632593750954,
-0.010465504601597786,
0.0355646125972271,
-0.005655077751725912,
-0.04394112899899483,
-0.021483030170202255,
0.015933463349938393,
0.0026189384516328573,
-0.00726470910012722,
-0.0006961534963920712,
0.013439690694212914,
0.0021151634864509106,
-0.004176595248281956,
-0.006503935903310776,
-0.03267909586429596,
0.01584322564303875,
0.00803056638687849,
-0.07589246332645416,
0.02793879248201847,
0.04468507319688797,
-0.018230367451906204,
-0.04147571697831154,
0.021458623930811882,
0.023570466786623,
-0.030453508719801903,
0.01945996843278408,
-0.014649845659732819,
0.01848679967224598,
0.012280168943107128,
0.02745332568883896,
-0.04093150049448013,
-0.03686046972870827,
0.006613307166844606,
-0.035862602293491364,
0.038100991398096085,
-0.009049898944795132,
0.057138871401548386,
0.009360559284687042,
0.014806694351136684,
-0.01497831754386425,
-0.01924094371497631,
-0.0028791700024157763,
-0.01693376526236534,
0.08063570410013199,
-0.04811929538846016,
0.016724271699786186,
-0.00475268205627799,
0.02426985092461109,
0.005993535276502371,
0.007379979360848665,
0.033526964485645294,
-0.013501327484846115,
0.018705444410443306,
-0.007522705476731062,
0.06287556141614914,
-0.02114645019173622,
-0.03746165335178375,
-0.019616415724158287,
-0.0146091403439641,
-0.049310825765132904,
-0.01434098556637764,
0.02384498529136181,
0.0196431465446949,
0.01818978413939476,
-0.007510069757699966,
-0.015230149962008,
-0.017813008278608322,
-0.04223712533712387,
0.037766773253679276,
-0.014748379588127136,
-0.005620891228318214,
-0.010722004808485508,
-0.029726233333349228,
0.020830292254686356,
0.027771491557359695,
-0.019837383180856705,
0.0180116705596447,
0.017447669059038162,
-0.0014732691925019026,
0.03395933285355568,
-0.007907173596322536,
-0.04669108986854553,
0.021007301285862923,
-0.027744652703404427,
0.007264724001288414,
0.009813588112592697,
-0.000008704717401997186,
0.03741583228111267,
0.02267647720873356,
-0.010759101249277592,
0.05005376785993576,
-0.024811165407299995,
-0.012815871275961399,
0.007535942830145359,
-0.04623739793896675,
0.04042111337184906,
0.049299340695142746,
0.006062142550945282,
-0.04843790829181671,
-0.04844002425670624,
-0.026181567460298538,
0.025762902572751045,
0.005655011162161827,
0.031010981649160385,
-0.03117271140217781,
-0.02137373946607113,
-0.04340582713484764,
0.07462333142757416,
-0.024125805124640465,
-0.03391997516155243,
-0.04187032952904701,
0.014882932417094707,
0.03824537619948387,
0.0023635048419237137,
-0.02777465432882309,
0.025164447724819183,
-0.006344205234199762,
0.008606115356087685,
-0.006201894488185644,
0.02218283899128437,
-0.007908174768090248,
0.00964389555156231,
0.02093777433037758,
-0.011597826145589352,
0.05390750989317894,
-0.0073609850369393826,
-0.02670116536319256,
0.029764261096715927,
-0.0190129354596138,
-0.06238950788974762,
0.0073581053875386715,
0.03996706008911133,
0.023732267320156097,
0.012736997567117214,
-0.0005993388476781547,
-0.007283950224518776,
0.06775902956724167,
-0.04711591452360153,
0.02255752682685852,
-0.006842179223895073,
-0.01958196796476841,
-0.054846543818712234,
-0.05600820481777191,
0.00619804160669446,
-0.018894126638770103,
0.017501257359981537,
0.028307311236858368,
0.011517400853335857,
-0.022272314876317978,
-0.02427365444600582,
0.04729405418038368,
-0.0037906726356595755,
-0.02842828631401062,
0.04351869970560074,
0.01848842017352581,
0.0002731649437919259,
0.03598082438111305,
-0.02897091768682003,
-0.0037701453547924757,
-0.002230995101854205,
0.03481007367372513,
-0.0944964811205864,
-0.017709579318761826,
0.034310586750507355,
-0.004866225644946098,
0.04685736447572708,
-0.06511962413787842,
-0.030948638916015625,
0.018509337678551674,
-0.06444456428289413,
-0.024520225822925568,
-0.039578698575496674,
-0.019215358421206474,
-0.0037038230802863836,
-0.010724417865276337,
0.02148127555847168,
0.03830399736762047,
0.014621746726334095,
0.02178720198571682,
0.034953437745571136,
0.010608669370412827,
-0.026105815544724464,
-0.01641947217285633,
0.009119205176830292,
0.02210960164666176,
-0.03089848719537258,
-0.031702976673841476,
0.05572770535945892,
0.015216846019029617,
-0.04312129691243172,
0.0321795679628849,
-0.024965111166238785,
-0.027143053710460663,
-0.023479118943214417,
0.040223635733127594,
-0.017677532508969307,
0.0007731980294920504,
-0.0003763399145100266,
-0.018022384494543076,
-0.024655314162373543,
0.01261158473789692,
-0.0001605935103725642,
0.032866742461919785,
0.0269145667552948,
-0.03365400806069374,
0.02176460437476635,
-0.044966477900743484,
-0.051954787224531174,
0.01588650792837143,
-0.04285035654902458,
-0.009359723888337612,
0.020715627819299698,
-0.020199423655867577,
0.01776718720793724,
-0.03614897280931473,
0.00005213993426878005,
-0.03734482079744339,
-0.0037283671554178,
0.011405047960579395,
-0.013606719672679901,
0.015666550025343895,
0.03194607049226761,
0.02834693342447281,
-0.02037547342479229,
0.007782468106597662,
0.0021852771751582623,
-0.010949719697237015,
-0.07138253003358841,
0.0003419922140892595,
0.02564045414328575,
-0.05831451714038849,
0.003258513519540429,
-0.030348140746355057,
-0.02001224458217621,
0.009584181942045689,
0.024109257385134697,
0.009420373477041721,
-0.02495127171278,
-0.06176905706524849,
-0.01590767875313759,
-0.02886911854147911,
0.02847559005022049,
0.026684049516916275,
-0.013843084685504436,
-0.02968982793390751,
-0.019467338919639587,
-0.0036917543038725853,
-0.019710488617420197,
0.042537886649370193,
-0.017783809453248978,
-0.003602353623136878,
0.006210173014551401,
0.021460162475705147,
0.03669314086437225,
-0.0162357185035944,
0.012086814269423485,
-0.019201260060071945,
-0.01212726067751646,
0.011643338948488235,
0.008353705517947674,
-0.008224567398428917,
-0.005126260686665773,
-0.014848882332444191,
-0.02489420212805271,
0.017066435888409615,
-0.02361128106713295,
-0.0068771266378462315,
-0.01120365783572197,
0.02691400982439518,
-0.034788791090250015,
0.05977058410644531,
-0.026322757825255394,
0.011956981383264065,
0.015064026229083538,
-0.010919847525656223,
-0.03815940394997597,
0.02168758027255535,
-0.016712090000510216,
-0.010083486326038837,
-0.01475975476205349,
0.007093050982803106,
0.0823100134730339,
-0.06639941036701202,
-0.01741158775985241,
0.024941951036453247,
-0.04294424131512642,
0.0001743004540912807,
0.03512297943234444,
0.012321282178163528,
0.012438838370144367,
-0.002913504373282194,
0.01980338990688324,
0.016521818935871124,
-0.006015207152813673,
0.015070663765072823,
0.028155013918876648,
0.026017632335424423,
-0.019783679395914078,
-0.0323353186249733,
0.04988337680697441,
-0.02727683074772358,
0.052437856793403625,
-0.0033756375778466463,
0.040799692273139954,
-0.011107394471764565,
-0.011673846282064915,
-0.0010846350342035294,
-0.008933023549616337,
0.015753399580717087,
0.020826468244194984,
-0.015087207779288292,
0.07838086038827896,
-0.01820342428982258,
0.013574729673564434,
-0.018299520015716553,
0.03842134401202202,
-0.028499698266386986,
-0.03464977815747261,
-0.007293574512004852,
0.03087819740176201,
-0.026716986671090126,
-0.029888629913330078,
0.01715557649731636,
0.00555803207680583,
0.02828228287398815,
-0.008519601076841354,
0.020245138555765152,
0.018250061199069023,
0.007765755522996187,
-0.020788075402379036,
-0.002231744583696127,
-0.027064865455031395,
-0.027274426072835922,
0.04548586532473564,
0.022780723869800568,
-0.004097664263099432,
0.0009290061425417662,
0.00002716130438784603,
-0.012609516270458698,
0.07756247371435165,
-0.08158256858587265,
-0.057883936911821365,
0.011821426451206207,
0.02697591297328472,
0.002085819374769926,
0.004801765084266663
] |
<p>Can you explain, please, <strong>step-by-step</strong> how an <a href="http://en.wikipedia.org/wiki/Electronic_filter" rel="nofollow">electronic filter</a> does work?
For example, high pass filter. I know It's a trivial things, but I can't get it completely. Don't bring me formula and etc. Just explanation in three words.</p>
| 8,478 |
[
-0.01555254403501749,
-0.02609097957611084,
0.01434374414384365,
-0.0012096741702407598,
0.035276517271995544,
-0.010196016170084476,
-0.0028359892312437296,
-0.005979997105896473,
0.038349349051713943,
-0.00791051797568798,
0.025175850838422775,
0.03957531973719597,
0.06024560704827309,
0.008116274140775204,
0.0019071055576205254,
0.006948784925043583,
-0.010439692996442318,
0.022402821108698845,
-0.010488561354577541,
-0.00020165542082395405,
-0.026251669973134995,
0.03809690102934837,
0.005023971199989319,
0.015265763737261295,
-0.0196361243724823,
-0.009012087248265743,
0.05639514699578285,
0.007435057312250137,
0.026435667648911476,
0.028163691982626915,
-0.016984177753329277,
-0.022296924144029617,
-0.01197903323918581,
0.020081905648112297,
-0.001064176089130342,
-0.010758680291473866,
-0.0374324694275856,
-0.01393960416316986,
-0.003079680958762765,
0.014492306858301163,
0.009006849490106106,
-0.014244608581066132,
-0.008333600126206875,
0.05413834750652313,
-0.03242439031600952,
0.015477639622986317,
0.0265222005546093,
-0.01964792050421238,
0.031234191730618477,
-0.0839349702000618,
0.05528908595442772,
-0.011514106765389442,
0.057797107845544815,
0.041656140238046646,
0.004288621712476015,
0.004853166174143553,
0.07581112533807755,
0.0716017633676529,
-0.05598243698477745,
-0.03709965944290161,
0.0014900426613166928,
-0.021496087312698364,
-0.015398203395307064,
-0.030186787247657776,
-0.02939954400062561,
0.02476351708173752,
0.0147379906848073,
-0.03306429088115692,
0.03694245591759682,
-0.002359568839892745,
-0.000788505538366735,
0.007456875406205654,
0.0016801541205495596,
-0.011469322256743908,
0.022634822875261307,
-0.04499107226729393,
0.01952637918293476,
0.017136283218860626,
0.04185542091727257,
0.05069625377655029,
-0.033735040575265884,
0.01151181198656559,
0.009260524995625019,
0.01535878237336874,
0.015897700563073158,
-0.0021919156424701214,
0.09297531843185425,
-0.02556067518889904,
0.007895656861364841,
-0.031023630872368813,
-0.042970988899469376,
0.017691144719719887,
0.016786515712738037,
0.00842249020934105,
-0.02097899653017521,
0.03515605628490448,
-0.012522369623184204,
0.02607029862701893,
0.03422883152961731,
-0.023523934185504913,
0.02093622088432312,
-0.019900469109416008,
0.04928911104798317,
0.03359583765268326,
-0.03834371641278267,
0.023801472038030624,
-0.04083448648452759,
0.024268485605716705,
-0.011346886865794659,
-0.005501836538314819,
-0.013080672360956669,
0.030242452397942543,
0.015693439170718193,
-0.004546463489532471,
0.021135400980710983,
0.011501794680953026,
-0.022213181480765343,
-0.03620213642716408,
0.02594265714287758,
0.04027140885591507,
0.05453834682703018,
-0.03927290439605713,
0.01151361595839262,
-0.015180188231170177,
-0.07100716233253479,
0.031765006482601166,
0.0028716493397951126,
0.01556022372096777,
-0.046471331268548965,
0.05366178974509239,
-0.0386204831302166,
-0.022500110790133476,
0.021007249131798744,
0.010154076851904392,
0.028449714183807373,
-0.020679662004113197,
-0.11962560564279556,
-0.024240916594862938,
0.026311729103326797,
-0.042543135583400726,
0.009225322864949703,
-0.07010527700185776,
0.022431518882513046,
0.02846003696322441,
0.06802423298358917,
-0.0012921153102070093,
-0.011892706155776978,
0.003144222544506192,
0.011981050483882427,
0.0346103236079216,
-0.033063411712646484,
-0.015195167623460293,
-0.0033696831669658422,
-0.0032815667800605297,
0.012781553901731968,
-0.04726306349039078,
0.03172013908624649,
0.01516446378082037,
-0.014787544496357441,
-0.05100323259830475,
0.04351413995027542,
0.007460171356797218,
-0.04386813938617706,
0.003591621993109584,
-0.011103260330855846,
-0.01583586446940899,
0.04148469120264053,
0.013466917909681797,
-0.006460233591496944,
0.03854270651936531,
-0.006828167475759983,
0.046455029398202896,
-0.016752716153860092,
0.015863601118326187,
0.018836135044693947,
-0.002768517006188631,
-0.008234787732362747,
-0.03031519614160061,
0.006044536363333464,
-0.015585161745548248,
-0.04119151085615158,
-0.05113673582673073,
0.04362497478723526,
0.04545774683356285,
-0.009183293208479881,
0.02972470410168171,
0.007108778227120638,
-0.018315644934773445,
-0.006559398025274277,
-0.03893455117940903,
-0.02112967148423195,
-0.09456732869148254,
-0.0006143786595202982,
-0.010972338728606701,
-0.02270578034222126,
-0.009828731417655945,
0.003663291223347187,
0.00103418726939708,
-0.03040388971567154,
-0.020052293315529823,
-0.005047990474849939,
-0.004937357734888792,
-0.009933085180819035,
-0.028311189264059067,
0.037656303495168686,
0.06306248158216476,
0.07108832150697708,
-0.0033050603233277798,
0.05792587623000145,
-0.015480042435228825,
0.0043698204681277275,
0.02653338573873043,
-0.02338838018476963,
0.03105008602142334,
-0.006076740566641092,
-0.05723633989691734,
-0.0019202018156647682,
0.011604197323322296,
0.0237737949937582,
0.029266711324453354,
-0.04918976128101349,
0.0902775451540947,
0.09132609516382217,
0.02645573951303959,
0.0035817441530525684,
0.035234060138463974,
0.028095273301005363,
-0.0036410491447895765,
-0.004319436382502317,
-0.0295138880610466,
-0.07035431265830994,
-0.0094857607036829,
0.030231628566980362,
0.012715963646769524,
-0.040757033973932266,
0.03288852050900459,
0.009776633232831955,
0.022365102544426918,
0.0504797138273716,
0.04886193946003914,
0.003826195141300559,
0.02761284075677395,
-0.0003920803137589246,
0.005630816798657179,
-0.018444526940584183,
0.022790001705288887,
-0.008200734853744507,
0.055198393762111664,
0.05228753387928009,
-0.008039148524403572,
-0.00853060930967331,
0.07329529523849487,
0.008906965143978596,
0.008795092813670635,
-0.011315287090837955,
-0.0058080097660422325,
0.00406179204583168,
-0.03644759953022003,
-0.019796565175056458,
0.010594114661216736,
-0.012475668452680111,
0.014305802062153816,
-0.010944795794785023,
0.009242900647222996,
-0.001179076381959021,
0.02720700204372406,
-0.02064851112663746,
-0.0019429267849773169,
0.019246388226747513,
-0.013588625937700272,
0.032966285943984985,
-0.04262394830584526,
0.026940681040287018,
-0.06319020688533783,
-0.014771120622754097,
0.00991004891693592,
0.023280784487724304,
0.04449215531349182,
-0.042323075234889984,
-0.05668008327484131,
-0.04549853503704071,
-0.04638313874602318,
0.025931481271982193,
0.0008283248171210289,
-0.006238067988306284,
0.008257278241217136,
-0.010839764960110188,
-0.013776354491710663,
0.04688845947384834,
-0.0009447055635973811,
-0.018194720149040222,
-0.02841402217745781,
-0.007612587884068489,
-0.06265902519226074,
-0.011329634115099907,
-0.029266489669680595,
0.020593397319316864,
-0.012918364256620407,
-0.02541043795645237,
0.05582511052489281,
-0.0015987110091373324,
-0.004736524540930986,
0.012540839612483978,
-0.017453843727707863,
-0.015907982364296913,
-0.004091156646609306,
-0.012406473979353905,
-0.006932990159839392,
-0.04487883672118187,
0.0035745666828006506,
-0.0006754794158041477,
-0.07540422677993774,
-0.0037907217629253864,
-0.025110293179750443,
-0.03101077303290367,
0.02543121576309204,
0.01150435395538807,
0.04341977462172508,
0.019201969727873802,
-0.03590549901127815,
0.07087608426809311,
0.003898753086104989,
-0.0680459663271904,
-0.001092602382414043,
-0.00810479186475277,
-0.02884102053940296,
-0.042987849563360214,
0.027916574850678444,
0.07673748582601547,
-0.015760080888867378,
0.03914957493543625,
0.006540881935507059,
-0.00901971384882927,
0.05458320677280426,
0.0020937861409038305,
-0.023778576403856277,
-0.006667232606559992,
-0.001044381526298821,
-0.019463250413537025,
0.04782445356249809,
0.021190907806158066,
-0.041852016001939774,
0.005832459777593613,
-0.008274698629975319,
0.04423275589942932,
0.02121048979461193,
-0.016131585463881493,
-0.004534436389803886,
-0.006477207876741886,
-0.04287750646471977,
-0.07729369401931763,
0.04010941460728645,
-0.00264084548689425,
0.01603221707046032,
0.005889369640499353,
0.02173168584704399,
0.03683806210756302,
-0.011345990933477879,
0.008408981375396252,
0.013072659261524677,
0.04730314761400223,
-0.07475931942462921,
-0.03733595460653305,
-0.00863971933722496,
-0.00898707751184702,
0.004350475501269102,
0.007041247561573982,
-0.017711874097585678,
0.03667072206735611,
0.04268448427319527,
0.015582387335598469,
0.020788896828889847,
-0.015877138823270798,
0.013298498466610909,
-0.06454803049564362,
0.0029028556309640408,
0.01631813682615757,
0.06182293966412544,
-0.014579398557543755,
0.09078862518072128,
0.0013733782107010484,
0.011112607084214687,
0.005292107351124287,
0.0053702048026025295,
-0.07215888798236847,
0.04798450693488121,
0.002547486452385783,
-0.0324753001332283,
-0.002817054046317935,
-0.0014414370525628328,
0.029505768790841103,
-0.015416216105222702,
-0.04406043887138367,
-0.04320567473769188,
0.00988906342536211,
-0.030935676768422127,
-0.010014851577579975,
0.01622684672474861,
0.012726438231766224,
-0.02371121197938919,
0.005044704768806696,
0.038331806659698486,
-0.03128087520599365,
-0.008935682475566864,
0.04442660138010979,
-0.05260235443711281,
0.01138991303741932,
-0.016486644744873047,
-0.014528085477650166,
0.02909085527062416,
0.008510751649737358,
0.029902052134275436,
0.028298627585172653,
-0.007731553167104721,
0.023143868893384933,
0.006379681173712015,
0.07913288474082947,
0.015865618363022804,
-0.002461241092532873,
-0.03503846004605293,
-0.035824667662382126,
-0.0163431316614151,
-0.015510160475969315,
0.019006898626685143,
0.009045232087373734,
0.02289016917347908,
0.043613675981760025,
0.011719528585672379,
-0.05605018511414528,
0.03407997637987137,
0.025927307084202766,
0.02129395864903927,
0.0008976341923698783,
-0.03382474184036255,
-0.02501622587442398,
-0.03709609434008598,
0.0002699840406421572,
0.04741217941045761,
0.018723296001553535,
-0.025231650099158287,
0.011834940873086452,
0.009978285990655422,
-0.004481285344809294,
-0.027242379263043404,
0.008870868012309074,
0.019891422241926193,
0.009340059943497181,
-0.015979021787643433,
-0.015194504521787167,
-0.011964017525315285,
0.0447160080075264,
0.06400495767593384,
-0.004818545188754797,
-0.03822201490402222,
-0.10269556194543839,
-0.010868264362215996,
0.022125352174043655,
0.04184260219335556,
-0.013076461851596832,
0.007550313603132963,
-0.07992617785930634,
-0.05046776309609413,
0.02184480056166649,
-0.03694628179073334,
0.020858580246567726,
-0.05064132809638977,
0.011619065888226032,
-0.03034982830286026,
-0.020625745877623558,
0.02910284884274006,
0.02536027505993843,
-0.008891678415238857,
-0.0025380654260516167,
-0.0022461481858044863,
-0.03528280183672905,
-0.03511255607008934,
-0.029171671718358994,
0.04091884568333626,
0.06750740855932236,
-0.008187895640730858,
0.012355518527328968,
0.006916416343301535,
0.017247570678591728,
-0.05103925243020058,
-0.03749798983335495,
0.0007399351452477276,
-0.009379139170050621,
0.022212546318769455,
0.040747594088315964,
-0.029841449111700058,
-0.014692912809550762,
0.005479827988892794,
0.016676731407642365,
-0.016070246696472168,
-0.006479012314230204,
-0.003820734564214945,
0.04026535153388977,
0.02784980647265911,
-0.017909688875079155,
0.06268147379159927,
0.033219434320926666,
-0.028362305834889412,
0.022081518545746803,
0.005821605678647757,
-0.021111896261572838,
-0.027062783017754555,
-0.0020127329044044018,
-0.03535720705986023,
0.014572402462363243,
-0.04046228900551796,
0.03594570234417915,
-0.012945481576025486,
0.014543579891324043,
-0.03019080124795437,
-0.03288128972053528,
0.0010093367891386151,
0.0505872406065464,
-0.05463094264268875,
-0.001195636810734868,
-0.0153824333101511,
0.0309689249843359,
0.01396632008254528,
-0.033712148666381836,
0.0010908906115218997,
-0.006245529744774103,
0.033239249140024185,
-0.003732479875907302,
-0.0063668545335531235,
0.018990954384207726,
-0.026391763240098953,
-0.006541040260344744,
0.0062483856454491615,
-0.05363196134567261,
0.06816796958446503,
-0.049562007188797,
-0.013956096954643726,
-0.006356676109135151,
-0.07070933282375336,
-0.03505512699484825,
-0.002063511870801449,
-0.0011919387616217136,
0.0013649355387315154,
-0.006391793955117464,
0.038199011236429214,
0.04267536476254463,
-0.019451195374131203,
-0.042509034276008606,
-0.07919805496931076,
0.06467653810977936,
0.033624615520238876,
0.002471033250913024,
0.00391159625723958,
-0.021323969587683678,
-0.006253635045140982,
-0.04965454712510109,
0.022989870980381966,
0.007512316107749939,
-0.027895694598555565,
-0.01529303565621376,
0.04474663734436035,
-0.014295748434960842,
0.079688161611557,
0.060364946722984314,
-0.023234611377120018,
0.020242583006620407,
-0.043302182108163834,
-0.005980007816106081,
-0.021246088668704033,
0.00556709012016654,
-0.0301566980779171,
-0.03027263656258583,
-0.014968504197895527,
0.007148334290832281,
0.05310242623090744,
-0.017941370606422424,
-0.015175249427556992,
-0.010667103342711926,
0.02431296557188034,
-0.004965334665030241,
-0.03992204740643501,
0.00766109861433506,
-0.0347696878015995,
0.025485774502158165,
0.00347421457991004,
-0.02178906835615635,
-0.04614035412669182,
-0.03457549959421158,
0.02984257973730564,
-0.0024357661604881287,
0.024402547627687454,
-0.019936252385377884,
0.05800020322203636,
-0.005410878919064999,
0.04418465495109558,
0.010863720439374447,
-0.026712501421570778,
0.03439227491617203,
-0.003254598006606102,
0.029303070157766342,
0.042832400649785995,
0.007320533972233534,
-0.017774010077118874,
-0.030029788613319397,
-0.05484098568558693,
-0.009707141667604446,
0.0570569783449173,
-0.04233108088374138,
0.021303517743945122,
0.02018127590417862,
-0.010156850330531597,
-0.03862538933753967,
-0.013340845704078674,
-0.018602611497044563,
0.01216098666191101,
-0.019886579364538193,
0.037673208862543106,
0.005015290342271328,
0.039032984524965286,
0.028752468526363373,
0.012922994792461395,
0.026365045458078384,
-0.00011657951108645648,
0.06205030530691147,
0.04264570772647858,
-0.008484342135488987,
0.018139846622943878,
-0.007790875155478716,
0.028075678274035454,
-0.01895585097372532,
0.02325025573372841,
0.029164014384150505,
0.005511059891432524,
0.02836024761199951,
0.005412037018686533,
0.0060770390555262566,
-0.06756286323070526,
-0.019779138267040253,
-0.04223011061549187,
0.02195490151643753,
-0.002359160454943776,
0.01678675413131714,
0.014443536289036274,
-0.009323114529252052,
0.0166215430945158,
0.020255332812666893,
0.037405915558338165,
0.007766765542328358,
-0.04027854651212692,
0.0025401152670383453,
-0.012919899076223373,
-0.004765266552567482,
0.029603077098727226,
0.053811829537153244,
-0.02916879579424858,
0.018949054181575775,
-0.005418097134679556,
0.035382431000471115,
0.045844629406929016,
0.03856140002608299,
-0.0416409969329834,
0.04167719557881355,
-0.0031603670213371515,
0.01657709665596485,
0.007382409181445837,
-0.024126553907990456,
0.10834551602602005,
0.04903355613350868,
0.004414959345012903,
-0.0815158411860466,
0.0154701117426157,
-0.01145899761468172,
0.008069710806012154,
-0.021845921874046326,
0.01297572162002325,
-0.00520473113283515,
0.061519794166088104,
-0.00039336204645223916,
0.01356284786015749,
0.009856363758444786,
0.032943032681941986,
0.06120141223073006,
-0.06261366605758667,
-0.031014880165457726,
-0.008449544198811054,
0.012255394831299782,
-0.009946372359991074,
0.012411494739353657,
-0.07887112349271774,
0.005389629863202572,
-0.029460681602358818,
-0.06212218478322029,
-0.057974521070718765,
0.004853914491832256,
0.061168402433395386,
-0.0070497202686965466,
-0.054152678698301315,
0.011677559465169907,
0.0061954353004693985,
-0.0383555069565773,
-0.006182732991874218,
0.032464154064655304,
0.041468121111392975,
-0.018040509894490242,
0.008328846655786037,
0.006623246241360903,
0.029537197202444077,
-0.0018279589712619781,
0.007631869520992041,
-0.007092370186001062,
-0.011130223050713539,
-0.017141057178378105,
-0.04517035558819771,
0.004398621153086424,
-0.011301452293992043,
-0.022894177585840225,
-0.030100589618086815,
0.030636608600616455,
0.0021083506289869547,
-0.0433000773191452,
0.0032256587874144316,
0.009249931201338768,
0.001230027643032372,
-0.01637130044400692,
-0.058681223541498184,
-0.026946550235152245,
0.03328139707446098,
-0.07020000368356705,
0.0067831180058419704,
0.004326230846345425,
-0.017916345968842506,
0.007059556432068348,
-0.028497537598013878,
-0.002023081062361598,
-0.0027774167247116566,
-0.012230339460074902,
-0.028235701844096184,
-0.015614832751452923,
-0.037588316947221756,
0.002003889298066497,
0.02996271476149559,
0.05991721525788307,
0.010428577661514282,
-0.004026657436043024,
-0.012301956303417683,
0.000986739993095398,
-0.06527934968471527,
0.025559552013874054,
0.003178430488333106,
-0.026668988168239594,
-0.01250580232590437,
-0.030192719772458076,
0.018137069419026375,
0.038749534636735916,
0.012196957133710384,
0.027047088369727135,
0.00595100549980998,
-0.010088399052619934,
0.05217410624027252,
-0.03339966759085655,
-0.023202987387776375,
0.04012485593557358,
-0.026823634281754494,
0.023805059492588043,
0.04023413732647896,
0.07490081340074539,
0.028333064168691635,
0.006634374149143696,
-0.033569809049367905,
0.007820460945367813,
-0.04612983018159866,
-0.009291189722716808,
-0.0038945775013417006,
-0.030704451724886894,
0.009898432530462742,
0.017183762043714523,
0.021188145503401756,
-0.030231667682528496,
-0.008056177757680416,
-0.023784231394529343,
0.014974252320826054,
0.005842165555804968,
0.032556574791669846,
0.010192309506237507,
0.018842244520783424,
-0.01028117910027504,
0.031200574710965157,
-0.049644965678453445,
0.0037939876783639193,
-0.0393630675971508,
0.013779540546238422,
0.03314078226685524,
0.013590759597718716,
-0.007384595461189747,
-0.00484951538965106,
-0.0013651689514517784,
-0.004399830941110849,
0.0374610610306263,
0.026934968307614326,
0.00987290684133768,
0.018845966085791588,
-0.001909926999360323,
-0.02386225014925003,
0.05698024109005928,
-0.03502870351076126,
-0.024254387244582176,
0.0600837767124176,
-0.050619907677173615,
-0.021664053201675415,
-0.0071746716275811195,
0.00375656527467072,
0.023319117724895477,
0.026814723387360573,
-0.035558998584747314,
0.015684906393289566,
0.039573971182107925,
0.018200308084487915,
0.006924794986844063,
-0.0020126267336308956,
-0.005854321643710136,
0.0024985307827591896,
0.001659251400269568,
0.012369908392429352,
-0.02652837336063385,
-0.000591915741097182,
0.034839555621147156,
0.04146924987435341,
0.022586826235055923,
-0.014009740203619003,
0.0014070677570998669,
-0.006456451490521431,
-0.0015631443820893764,
0.0255593154579401,
0.00423535006120801,
0.004417574033141136,
0.04002619534730911,
-0.015132295899093151,
0.01554363314062357,
-0.014232625253498554,
-0.024856746196746826,
-0.08404827862977982,
0.027512026950716972,
-0.0074326042085886,
-0.022853907197713852,
0.04121904447674751,
-0.04928344860672951,
-0.0027980299200862646,
0.050509627908468246,
-0.023071011528372765,
-0.027940398082137108,
-0.007477023173123598,
-0.03142865002155304,
-0.02473701536655426,
-0.01398226898163557,
0.0014104099245741963,
0.04520804062485695,
0.030085358768701553,
0.01872182823717594,
0.01098588202148676,
-0.03944987431168556,
0.0016289856284856796,
-0.014298954047262669,
0.003816725919023156,
0.026360847055912018,
-0.006215824745595455,
-0.01678856834769249,
0.03329028561711311,
-0.049282632768154144,
-0.005131480749696493,
0.049220647662878036,
-0.00617603724822402,
0.020909998565912247,
-0.0270207691937685,
0.010053262114524841,
0.009808013215661049,
0.02862112782895565,
-0.001075804466381669,
0.005312617402523756,
-0.020062293857336044,
0.03819258511066437,
0.021637700498104095,
0.031398940831422806,
0.014024847187101841,
-0.0031967752147465944,
0.05752874165773392,
-0.0010288764024153352,
-0.03701869398355484,
0.01808170974254608,
0.003111006459221244,
-0.0056357113644480705,
0.02376512996852398,
-0.006667909678071737,
0.03096959926187992,
-0.04036572575569153,
-0.0015447636833414435,
-0.014032961800694466,
-0.043492574244737625,
0.015853021293878555,
-0.01963777281343937,
-0.009177615866065025,
-0.008532105945050716,
-0.007074203807860613,
-0.04727998003363609,
0.06452668458223343,
0.018782278522849083,
-0.01966632902622223,
-0.05820828303694725,
-0.021960260346531868,
0.021981043741106987,
-0.011105897836387157,
0.002457486465573311,
-0.029110675677657127,
-0.01780727505683899,
0.021349595859646797,
0.02877614088356495,
-0.017747560515999794,
-0.0242778230458498,
-0.059353966265916824,
-0.036892518401145935,
-0.024826712906360626,
0.07721314579248428,
0.0169998686760664,
-0.03137315809726715,
-0.06501808017492294,
-0.03305431082844734,
0.005091263446956873,
0.05376339703798294,
0.054281264543533325,
-0.04098045080900192,
-0.02162400260567665,
-0.0016374799888581038,
0.019711101427674294,
0.02913377806544304,
-0.053596287965774536,
0.04567420482635498,
0.018868178129196167,
-0.031758617609739304,
-0.009904632344841957,
-0.008550811558961868,
-0.05198882520198822,
0.033557020127773285,
-0.007596632931381464,
0.005188513081520796,
0.032087717205286026,
-0.02619919553399086,
-0.003904930083081126,
0.016279542818665504,
0.06021376699209213,
-0.0019047579262405634,
0.07431584596633911,
-0.05437000095844269,
0.0019727530889213085,
0.009634826332330704,
-0.0018246237887069583,
-0.0408579520881176,
0.005984052084386349,
-0.021784750744700432,
0.03195013105869293,
-0.03272593766450882,
-0.03234173357486725,
0.030167987570166588,
-0.06772546470165253,
-0.02778083086013794,
0.030075235292315483,
-0.015577416867017746,
0.00008498437091475353,
0.07676530629396439,
-0.0006036937120370567,
0.0296859722584486,
-0.02021913230419159,
-0.009604096412658691,
-0.006037204992026091,
-0.0045848931185901165,
0.005731427576392889,
0.03402126580476761,
0.02804671600461006,
-0.005197944585233927,
0.04941515251994133,
0.005703875795006752,
0.0024309956934303045,
-0.0255750585347414,
0.01866012252867222,
0.015624803490936756,
-0.01881704293191433,
-0.01991610787808895,
0.008938298560678959,
-0.015417034737765789,
-0.0014649834483861923,
0.037363436073064804,
-0.03937964886426926,
0.07555283606052399,
-0.05036844313144684,
0.0131274638697505,
0.0233598779886961,
0.035698302090168,
-0.03158121183514595,
0.0031441552564501762,
0.0018479503924027085,
0.008053633384406567,
-0.021775366738438606,
-0.015805857256054878,
-0.009321973659098148,
-0.002935948548838496,
0.01991749182343483,
-0.020936813205480576,
0.05180187523365021,
0.015428237617015839,
-0.04479070380330086,
-0.027018673717975616,
0.022508909925818443,
-0.03562184050679207,
-0.03080054372549057,
0.002693419111892581,
0.03649023920297623,
-0.007128133904188871,
0.009748882614076138,
0.004057480953633785,
-0.025669222697615623,
0.05026043951511383,
-0.06652138382196426,
0.012434299103915691,
-0.019346849992871284,
-0.001721152919344604,
-0.020225562155246735,
0.017327439039945602
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2219/beginner-physics-resources">Beginner Physics Resources?</a><br>
<a href="http://physics.stackexchange.com/questions/12175/book-recommendations">Book recommendations</a> </p>
</blockquote>
<p>I'm wanting to learn physics. In fact i'm a software engineer and i find physics very fascinating. But everything I read things concerning physics, I don't understand many things. What are the books that can be helpful for someone who don't know physics but have a good foundation of mathematics??</p>
| 98 |
[
0.009767157025635242,
-0.0505293533205986,
-0.007541949860751629,
0.0012255855835974216,
0.03073829971253872,
0.013239804655313492,
-0.0005149840726517141,
-0.04450512304902077,
-0.02568904496729374,
-0.015228872187435627,
0.055784597992897034,
0.02056162990629673,
0.023157678544521332,
0.015134565532207489,
0.03043418936431408,
0.02192537672817707,
-0.006505810655653477,
-0.03308919444680214,
-0.008374551311135292,
-0.009211230091750622,
-0.009693339467048645,
-0.0030839284881949425,
0.011923357844352722,
0.03906361013650894,
-0.05274993181228638,
0.03535304591059685,
0.016305509954690933,
0.022921595722436905,
0.012335889041423798,
0.05377722159028053,
-0.007271219976246357,
-0.0012244423851370811,
-0.00040231403545476496,
0.01988203451037407,
-0.026509754359722137,
-0.009733217768371105,
-0.014220901764929295,
-0.00009650280117057264,
-0.03797595575451851,
-0.03031134605407715,
-0.030363718047738075,
-0.02757132425904274,
-0.011907960288226604,
0.05375256389379501,
-0.02209770306944847,
0.02735031396150589,
-0.00820255372673273,
-0.021753089502453804,
0.037015121430158615,
-0.05416277050971985,
0.04791025444865227,
0.013802362605929375,
0.05870359390974045,
0.0528976246714592,
0.0201152004301548,
-0.019153917208313942,
0.05679289624094963,
0.06435949355363846,
-0.036402229219675064,
-0.05330929532647133,
-0.021499861031770706,
-0.0435127392411232,
-0.013776950538158417,
-0.0341743566095829,
-0.02202954702079296,
0.08195200562477112,
-0.024448487907648087,
-0.022015664726495743,
0.023047247901558876,
-0.0013107830891385674,
-0.006501458585262299,
0.02312442660331726,
0.014042902737855911,
-0.006459114607423544,
0.0017295555444434285,
-0.025088975206017494,
-0.0012109550880268216,
0.008968050591647625,
0.0525023527443409,
0.0572354681789875,
0.0027931747026741505,
0.014411683194339275,
-0.00054816750343889,
0.02084459736943245,
0.01533618476241827,
-0.037917204201221466,
0.1146460548043251,
0.006717858836054802,
-0.03608502075076103,
-0.006526582408696413,
-0.031367216259241104,
-0.004459612537175417,
0.00939174648374319,
-0.011146082542836666,
-0.011987326666712761,
0.013582250103354454,
0.009650890715420246,
0.04145900532603264,
0.01667572185397148,
-0.04736827313899994,
-0.0013234695652499795,
-0.02246284671127796,
0.03307786211371422,
0.05354907736182213,
0.014800542034208775,
-0.03087524324655533,
-0.03215546905994415,
0.029767515137791634,
-0.02142970822751522,
-0.0208667553961277,
0.014165863394737244,
0.024801302701234818,
-0.0248554814606905,
0.00152344920206815,
-0.0012941601453348994,
-0.045398566871881485,
-0.0028925868682563305,
-0.011493572033941746,
0.037346042692661285,
0.06019093468785286,
0.039253730326890945,
-0.05145733058452606,
0.03345875069499016,
-0.01328139565885067,
-0.09313420206308365,
-0.033936165273189545,
0.03984551131725311,
-0.03263263404369354,
-0.034858815371990204,
0.02036098763346672,
-0.004952572751790285,
0.002218433655798435,
0.02213212102651596,
0.021836621686816216,
0.04631693288683891,
0.0117414565756917,
-0.09162534773349762,
-0.04989761486649513,
0.0555003359913826,
-0.04003983736038208,
-0.04630562290549278,
-0.0843745619058609,
0.03333881124854088,
0.01051201019436121,
0.06721185892820358,
0.00943714939057827,
0.015430624596774578,
-0.002234290586784482,
0.030650390312075615,
-0.020649466663599014,
-0.02862425707280636,
-0.004902660381048918,
-0.0357738621532917,
-0.018893040716648102,
0.03280329704284668,
-0.06736349314451218,
0.036353252828121185,
0.023399952799081802,
0.02880272828042507,
-0.031262170523405075,
0.06224115937948227,
-0.017425213009119034,
0.0019808209035545588,
-0.00169693015050143,
-0.022215301170945168,
0.0020732874982059,
0.08807101845741272,
0.010165803134441376,
0.027127407491207123,
0.04442230984568596,
-0.025943508371710777,
0.0014008332509547472,
-0.00538988970220089,
0.004740482196211815,
0.046013012528419495,
-0.008763933554291725,
-0.011736840009689331,
0.019705843180418015,
-0.003683937480673194,
0.0005686407093890011,
-0.029588624835014343,
-0.022925008088350296,
-0.003969285171478987,
-0.0021447225008159876,
-0.023300776258111,
0.07009366899728775,
0.035093434154987335,
0.02267322689294815,
-0.006898831110447645,
-0.024447666481137276,
-0.010480260476469994,
-0.05704803019762039,
0.011435069143772125,
-0.05094096064567566,
-0.010708389803767204,
0.057822342962026596,
0.029340703040361404,
0.0288704801350832,
-0.03711806237697601,
-0.03702663630247116,
-0.013486803509294987,
0.02182680368423462,
-0.0107027068734169,
0.00197990657761693,
0.014098258689045906,
0.061914969235658646,
0.04304172843694687,
-0.023221299052238464,
0.008420625701546669,
-0.005949363578110933,
-0.015980318188667297,
-0.008758378215134144,
-0.019314315170049667,
0.02393217757344246,
-0.0244586318731308,
-0.0005295667215250432,
0.00729905441403389,
0.022511286661028862,
-0.020108839496970177,
-0.002975991228595376,
-0.015696564689278603,
0.04393340274691582,
0.018494829535484314,
0.012880970723927021,
-0.0023086376022547483,
0.027423571795225143,
0.010720320045948029,
0.005086905788630247,
0.009278284385800362,
0.006755118723958731,
-0.040644869208335876,
0.014259501360356808,
0.050313882529735565,
0.00367094692774117,
-0.06830864399671555,
0.02633894793689251,
-0.017423240467905998,
0.020010309293866158,
0.027510451152920723,
0.026925310492515564,
-0.04210720211267471,
-0.07372263073921204,
0.03896937146782875,
0.004280918277800083,
-0.0023086247965693474,
0.035120632499456406,
-0.0022050843108445406,
0.02469288930296898,
-0.000016784439139883034,
-0.013166803866624832,
-0.026374462991952896,
0.034649886190891266,
-0.015866244211792946,
0.012204473838210106,
0.01456382591277361,
-0.053502604365348816,
0.04430833458900452,
0.0026317639276385307,
0.020613394677639008,
-0.005140496417880058,
-0.022753192111849785,
-0.0011215591803193092,
-0.033457640558481216,
-0.006239995360374451,
0.0107257179915905,
0.004151890520006418,
-0.016739321872591972,
-0.009650344960391521,
0.027636634185910225,
-0.05593055486679077,
-0.00491514103487134,
0.022168543189764023,
-0.01872548833489418,
-0.031094973906874657,
-0.020382553339004517,
0.018561959266662598,
0.008851373568177223,
0.03220577910542488,
-0.04406184330582619,
-0.019836505874991417,
0.01404425036162138,
-0.020586084574460983,
0.00253835110925138,
0.0014183257007971406,
-0.042763661593198776,
0.02576417848467827,
-0.04801586642861366,
-0.05274936184287071,
0.04728410765528679,
0.001957457512617111,
0.010563939809799194,
0.0050233579240739346,
0.0017222509486600757,
-0.007505255751311779,
0.004924634471535683,
-0.03399837389588356,
0.006201047450304031,
-0.03479417413473129,
0.0012518280418589711,
0.0323919951915741,
-0.024760020896792412,
-0.020894482731819153,
-0.006520361639559269,
-0.05103488638997078,
-0.05536719784140587,
-0.010495848022401333,
0.011753467842936516,
0.013179191388189793,
-0.03984332084655762,
-0.030117729678750038,
0.035283226519823074,
-0.04664672911167145,
0.012650027871131897,
-0.042984701693058014,
-0.03950333967804909,
0.006872087717056274,
0.03172210231423378,
0.02774844691157341,
0.017799068242311478,
-0.009730714373290539,
0.06811457127332687,
0.016796324402093887,
-0.02197635918855667,
-0.010466345585882664,
-0.02127155102789402,
-0.0009372838540002704,
-0.029445456340909004,
0.0023902361281216145,
0.04193810001015663,
-0.003377824556082487,
-0.01433792244642973,
0.03022691421210766,
0.01951349899172783,
0.012700563296675682,
0.03540440648794174,
0.003342703450471163,
0.0007990883314050734,
0.007941290736198425,
0.00759599544107914,
0.050576526671648026,
0.010338254272937775,
-0.037695784121751785,
-0.001688772113993764,
0.0028089650440961123,
0.021879911422729492,
-0.0051699853502213955,
-0.032044440507888794,
0.07542786002159119,
-0.00042826944263651967,
-0.011970988474786282,
-0.05569994077086449,
0.05116444081068039,
-0.0020474297925829887,
-0.03592865914106369,
0.03178573027253151,
0.02163488045334816,
0.018936000764369965,
0.016804222017526627,
0.03388749808073044,
0.04925616830587387,
0.031636469066143036,
-0.03830232843756676,
-0.02487393654882908,
-0.03586854785680771,
-0.008472491055727005,
0.012695319950580597,
0.0036249402910470963,
0.011736690998077393,
0.06099491938948631,
0.04617505893111229,
0.03624666854739189,
-0.002506641671061516,
-0.028060821816325188,
0.011586664244532585,
-0.06849334388971329,
-0.00039233421557582915,
-0.023367419838905334,
0.06834724545478821,
-0.012191369198262691,
0.0646304190158844,
0.013041079044342041,
0.023242689669132233,
0.017192723229527473,
-0.002039923332631588,
-0.10131160914897919,
0.027277950197458267,
-0.04819909483194351,
-0.002601275220513344,
-0.008298054337501526,
0.02472938597202301,
-0.012832105159759521,
-0.01631338708102703,
-0.015590611845254898,
-0.004757168237119913,
-0.004509372636675835,
-0.034257955849170685,
-0.009029733017086983,
-0.05220921337604523,
-0.005590570159256458,
-0.02414233610033989,
0.03644789755344391,
0.0222524031996727,
-0.025972284376621246,
0.023546796292066574,
0.040080759674310684,
-0.033024080097675323,
-0.03744664415717125,
0.00013759930152446032,
0.02304244600236416,
0.00038192307692952454,
0.014942947775125504,
0.02694527618587017,
0.015402078628540039,
-0.0040875389240682125,
-0.010905934497714043,
0.002913386095315218,
0.05556865781545639,
-0.028587624430656433,
-0.039018772542476654,
-0.006825524847954512,
-0.05299730598926544,
-0.008976607583463192,
-0.04664256051182747,
0.06348411738872528,
-0.004141474142670631,
-0.0029107495211064816,
0.0460604764521122,
-0.03385303169488907,
-0.03236204385757446,
0.028726477175951004,
0.049970295280218124,
-0.02457054890692234,
-0.015380381606519222,
-0.0067299227230250835,
-0.017612608149647713,
-0.06534849107265472,
0.016111303120851517,
0.00583368306979537,
0.005906556732952595,
-0.011080271564424038,
0.006787588354200125,
0.01131963450461626,
0.03406338021159172,
-0.021604567766189575,
0.0009465027833357453,
0.0012315468629822135,
0.041005734354257584,
0.008265739306807518,
-0.03462906554341316,
0.01442624069750309,
0.046004947274923325,
0.05122542753815651,
-0.009928163141012192,
-0.02615533396601677,
-0.0645861029624939,
-0.0007287689368240535,
0.017591513693332672,
0.048917338252067566,
-0.019346658140420914,
0.011339835822582245,
-0.04483239725232124,
-0.0571228452026844,
0.05441059172153473,
-0.03870781883597374,
0.027501564472913742,
-0.04163464903831482,
-0.018852023407816887,
-0.029112014919519424,
-0.03529271110892296,
-0.007694926578551531,
0.00415787473320961,
-0.0004237016837578267,
0.02893371880054474,
-0.0243638064712286,
0.015188370831310749,
-0.029770273715257645,
0.03526751324534416,
0.029879771173000336,
0.06818875670433044,
-0.006400917191058397,
0.019380882382392883,
0.006536535918712616,
0.020714836195111275,
-0.02873544581234455,
-0.08398829400539398,
-0.010226547718048096,
0.0020458889193832874,
-0.0018470613285899162,
-0.0012889342615380883,
-0.030040809884667397,
-0.0644400492310524,
0.03827865049242973,
-0.020946364849805832,
-0.026708312332630157,
-0.027954813092947006,
-0.04181530699133873,
-0.012692123651504517,
0.021528784185647964,
0.037113256752491,
0.025701278820633888,
0.033603914082050323,
-0.04908754676580429,
-0.018973616883158684,
-0.014470066875219345,
0.03867606446146965,
-0.023404214531183243,
-0.005587730091065168,
-0.037916041910648346,
-0.015153969638049603,
-0.0609157420694828,
0.07708404213190079,
-0.038723353296518326,
0.0029618320986628532,
-0.025112174451351166,
-0.012612663209438324,
-0.02868540957570076,
0.02295880764722824,
0.012672839686274529,
-0.0038041104562580585,
-0.0029183111619204283,
0.019605068489909172,
0.0055748457089066505,
-0.014116313308477402,
0.005786284804344177,
0.016629770398139954,
0.00184373720549047,
0.013049797154963017,
-0.011982119642198086,
0.03948989883065224,
-0.06392263621091843,
-0.023732410743832588,
-0.0024279761128127575,
-0.05815325677394867,
0.06913766264915466,
0.024185318499803543,
-0.014159869402647018,
0.02202628180384636,
-0.062153976410627365,
-0.04845927655696869,
0.03577185422182083,
0.00755374925211072,
0.04235454648733139,
-0.05200090631842613,
0.019912034273147583,
-0.005457301624119282,
0.00635031471028924,
-0.03184618800878525,
-0.08313561230897903,
0.008942747488617897,
0.010923455469310284,
-0.03221782296895981,
-0.04944821447134018,
0.05654185265302658,
-0.04685148224234581,
-0.024510474875569344,
-0.0017879789229482412,
0.024989893659949303,
-0.020603664219379425,
-0.008812402375042439,
0.02058003656566143,
-0.007058941759169102,
0.03825632110238075,
0.0019652533810585737,
-0.022842492908239365,
0.00478693563491106,
0.003464239649474621,
-0.025231599807739258,
-0.009015901014208794,
0.05814839527010918,
-0.008355420082807541,
-0.015032175928354263,
-0.007491787895560265,
0.0005966493627056479,
0.05419414862990379,
-0.046991415321826935,
0.03526991605758667,
0.024836929515004158,
0.026517296209931374,
-0.04586528241634369,
-0.03905463591217995,
-0.0049625118263065815,
-0.0011186548508703709,
0.04032875970005989,
-0.007353363558650017,
-0.012719133868813515,
-0.019639546051621437,
-0.04429500922560692,
0.0414687842130661,
0.004319464322179556,
0.0016056917374953628,
-0.007842233404517174,
0.06425847858190536,
-0.006864510010927916,
0.0021588474046438932,
0.02084759809076786,
-0.003307051258161664,
0.004095139447599649,
0.013487915508449078,
0.014473464339971542,
0.04955916106700897,
-0.005124814808368683,
0.006371818017214537,
-0.06369370222091675,
-0.04919165000319481,
0.007685334421694279,
0.07532458007335663,
0.005489014554768801,
0.06408977508544922,
0.04731330648064613,
-0.027600383386015892,
-0.00020459353982005268,
0.009714937768876553,
-0.019269729033112526,
-0.009030690416693687,
0.056191977113485336,
0.020677590742707253,
-0.05082414299249649,
0.006360409315675497,
0.0042478786781430244,
0.017500139772892,
-0.021541642025113106,
-0.00005346972102415748,
-0.01303157676011324,
0.04796556755900383,
-0.0017508389428257942,
-0.017569830641150475,
-0.021275324746966362,
0.04043836146593094,
-0.011999991722404957,
0.05961839482188225,
0.004306913819164038,
-0.01574529893696308,
0.045652762055397034,
0.01825799234211445,
0.014064256101846695,
-0.004170715343207121,
-0.013076224364340305,
-0.036766618490219116,
0.007830865681171417,
0.029018783941864967,
0.012455610558390617,
-0.015011933632194996,
0.04484666511416435,
0.013910562731325626,
-0.006734892725944519,
0.017270440235733986,
-0.009842555038630962,
-0.07339861989021301,
-0.04183868691325188,
-0.030463479459285736,
-0.04075515270233154,
0.046629950404167175,
0.01519988663494587,
-0.03984804078936577,
0.02716088481247425,
-0.05361742898821831,
0.038460858166217804,
0.008403670974075794,
0.04176129028201103,
-0.036565955728292465,
0.045178428292274475,
-0.030091822147369385,
-0.010294760577380657,
0.0008738941978663206,
0.008315647020936012,
0.11711787432432175,
0.05952530726790428,
-0.002369973575696349,
-0.0830230861902237,
0.01607871986925602,
0.000026591504138195887,
0.028783030807971954,
-0.05043995752930641,
0.039999861270189285,
-0.00041786552174016833,
0.04720107465982437,
-0.0009865047177299857,
0.06612035632133484,
0.00693892827257514,
0.01214561052620411,
0.05823035165667534,
-0.05236825719475746,
-0.0419057197868824,
-0.016828102990984917,
0.016546718776226044,
-0.0009427995537407696,
0.04174128174781799,
-0.028921224176883698,
0.0401548370718956,
-0.02826724946498871,
0.0035598769318312407,
-0.028391653671860695,
-0.033728886395692825,
0.02398853190243244,
-0.011247741058468819,
-0.019828613847494125,
-0.0017448088619858027,
-0.018829120323061943,
-0.018401948735117912,
-0.02548907697200775,
0.047293368726968765,
0.039190392941236496,
-0.020745722576975822,
0.021570393815636635,
0.0051657091826200485,
0.0008848842699080706,
-0.007227442227303982,
0.006913436576724052,
-0.0035547385923564434,
-0.05806766077876091,
-0.007610294967889786,
-0.042349349707365036,
0.03523983433842659,
-0.019621368497610092,
0.04013211280107498,
0.011838717386126518,
0.02347717434167862,
0.013227320276200771,
-0.03743353486061096,
0.00889241136610508,
0.02062770538032055,
0.02861650474369526,
-0.037120651453733444,
0.004987862426787615,
-0.05207854509353638,
0.05119289457798004,
-0.027251875028014183,
0.00593690387904644,
-0.009543364867568016,
-0.020489752292633057,
0.014052711427211761,
-0.006523663643747568,
0.004707856569439173,
-0.02213827520608902,
-0.005954870954155922,
-0.032193660736083984,
0.025177329778671265,
-0.038974158465862274,
-0.035237692296504974,
0.033150412142276764,
0.02772483229637146,
0.04781108349561691,
0.024777032434940338,
-0.01503843255341053,
0.005117801018059254,
-0.04568265378475189,
0.028204549103975296,
-0.007185474969446659,
0.0010834403801709414,
-0.006717576179653406,
-0.009104656986892223,
0.018989477306604385,
0.02314847521483898,
0.013683417811989784,
0.0021904355380684137,
-0.0031523059587925673,
-0.006796086207032204,
0.05517932400107384,
0.016352739185094833,
-0.02001226134598255,
0.004825538489967585,
-0.025149596855044365,
0.042218320071697235,
-0.005013276822865009,
0.022994445636868477,
0.03418813273310661,
0.010455871932208538,
0.04418085142970085,
0.045070432126522064,
-0.03741375729441643,
-0.009809563867747784,
-0.007674205116927624,
-0.04521899297833443,
-0.00020104035502299666,
0.045053791254758835,
0.03496422991156578,
-0.007554830051958561,
-0.04069456830620766,
0.026364650577306747,
-0.006342740263789892,
0.01076566707342863,
0.04114382341504097,
-0.01207257341593504,
0.036582160741090775,
-0.04431556537747383,
0.02254151552915573,
-0.027324844151735306,
-0.004633027594536543,
-0.06845737993717194,
-0.0033599664457142353,
0.009263807907700539,
-0.007994895800948143,
-0.017610272392630577,
0.03930794820189476,
0.0033220157492905855,
-0.007695387117564678,
0.02853373810648918,
0.0023171808570623398,
-0.009055783040821552,
-0.013154936023056507,
0.01679966039955616,
-0.03886766731739044,
0.02493830770254135,
-0.031320519745349884,
0.0073850261978805065,
0.07021460682153702,
-0.04422174021601677,
-0.062912218272686,
0.009697341360151768,
-0.0018506963970139623,
0.024485740810632706,
0.04174993559718132,
-0.028447749093174934,
-0.0007028349791653454,
0.08233623951673508,
-0.0011651908280327916,
0.010644526220858097,
-0.019117645919322968,
-0.014808598905801773,
-0.00879301130771637,
-0.0032447739504277706,
0.02772331051528454,
-0.019604517146945,
-0.022994287312030792,
0.04285549372434616,
0.03585262969136238,
0.011180100031197071,
-0.013750970363616943,
0.011794107966125011,
0.016380200162529945,
0.008134245872497559,
0.017235172912478447,
-0.008747794665396214,
0.04149281606078148,
0.023882417008280754,
-0.02685581147670746,
0.03089488483965397,
-0.016899488866329193,
0.01228441670536995,
-0.10801045596599579,
0.005148977041244507,
0.0018858471885323524,
0.02249603532254696,
0.03652514889836311,
-0.0705254003405571,
0.010587338358163834,
0.039064276963472366,
-0.047233134508132935,
0.037252310663461685,
-0.0043869344517588615,
-0.034157585352659225,
-0.005112201441079378,
-0.00587205495685339,
0.003862077370285988,
0.05782650038599968,
0.02555401436984539,
0.0709468200802803,
-0.004006047733128071,
0.01252865418791771,
-0.01654849573969841,
-0.007939969189465046,
0.0129734817892313,
0.0441410131752491,
-0.015140104107558727,
-0.024548053741455078,
0.030085580423474312,
0.013749435544013977,
-0.04391056299209595,
0.02496851235628128,
0.009062130004167557,
0.005336385685950518,
-0.004922786727547646,
0.027842778712511063,
-0.012000073678791523,
0.03899388387799263,
0.03175046294927597,
-0.010399478487670422,
-0.021765731275081635,
0.0278838612139225,
0.01227808278053999,
0.026911454275250435,
-0.002825395902618766,
0.001196429249830544,
0.014787252992391586,
-0.04668261855840683,
-0.05836827680468559,
0.03242836892604828,
-0.01694406569004059,
-0.02766837738454342,
-0.020475754514336586,
-0.02420847676694393,
-0.0023675516713410616,
-0.026820439845323563,
-0.02120593748986721,
-0.05566438287496567,
-0.005571335554122925,
0.024690264835953712,
-0.036195266991853714,
0.02416647970676422,
0.033474963158369064,
-0.01192430779337883,
-0.017270594835281372,
0.013871516101062298,
0.041018590331077576,
0.02896321378648281,
-0.023680245503783226,
0.010020612739026546,
0.03773798048496246,
-0.005910490173846483,
0.010531263425946236,
-0.0539233423769474,
-0.024697251617908478,
0.026658711954951286,
-0.009778894484043121,
0.010420029982924461,
0.019935529679059982,
-0.010914139449596405,
-0.019534733146429062,
-0.053865090012550354,
0.035747379064559937,
0.004959992598742247,
0.002350579248741269,
-0.04185221716761589,
0.019818246364593506,
0.02396119199693203,
0.01224689930677414,
0.006797598674893379,
-0.014523222111165524,
0.007787616457790136,
-0.0045421733520925045,
-0.01217731088399887,
0.028103582561016083,
-0.02353074587881565,
0.0101254777982831,
-0.008422979153692722,
-0.052654750645160675,
0.013310901820659637,
0.003975517116487026,
0.004804322496056557,
0.005834442097693682,
-0.0016944085946306586,
-0.0036443083081394434,
0.007230124901980162,
-0.01795901358127594,
-0.018139999359846115,
0.06701061129570007,
0.04128418490290642,
0.0006007085321471095,
0.038181617856025696,
-0.03350689262151718,
0.012063967995345592,
0.05202080309391022,
-0.03851766511797905,
-0.00328785739839077,
0.04728003218770027,
-0.04263662174344063,
-0.01793709397315979,
-0.009641401469707489,
-0.01307169534265995,
0.01424947939813137,
-0.06748387217521667,
0.008133089169859886,
0.041647717356681824,
-0.024302177131175995,
-0.005235439632087946,
0.05057520791888237,
0.0006430338835343719,
0.015805920585989952,
-0.0044575282372534275,
0.0013545724796131253,
0.03574317693710327,
-0.028066325932741165,
-0.0016786962514743209,
0.02639591693878174,
0.03250136598944664,
0.008868096396327019,
0.01722927950322628,
0.04972630739212036,
0.023547029122710228,
0.01314313244074583,
-0.0006435563554987311,
0.051157232373952866,
-0.004736179951578379,
-0.011666185222566128,
0.0049617053009569645,
-0.010493526235222816,
-0.035294003784656525,
0.01738138124346733,
-0.01997818425297737,
0.06571974605321884,
-0.05322660878300667,
0.029595334082841873,
0.0010755311232060194,
0.02141270600259304,
-0.010826699435710907,
0.0008367051486857235,
0.009947356767952442,
0.03311103582382202,
-0.02642960101366043,
-0.023527370765805244,
-0.025506319478154182,
-0.027099313214421272,
0.019431397318840027,
-0.061200182884931564,
0.04400425776839256,
-0.004888973198831081,
0.005294276401400566,
0.017808759585022926,
-0.015999596565961838,
-0.017646510154008865,
-0.03657497465610504,
0.027747957035899162,
0.057502590119838715,
0.008527103811502457,
-0.05040518194437027,
-0.00485864095389843,
-0.02378726564347744,
0.04517284408211708,
-0.04959084838628769,
0.023290351033210754,
-0.02073099836707115,
-0.013015088625252247,
-0.04249349609017372,
0.031074989587068558
] |
<p>When considering the 'Heisenberg' picture of the harmonic oscillator, I've come across the step:
$$\begin{align}
\left\langle n\left|(\hat{q_H}\hat{H}-\hat{H}\hat{q_H})\right|k\right\rangle &= (E_k-E_n)q_{nk}
\end{align}$$</p>
<p>where $\hat{q_H}$ is a position operator. I realise that this must be a pretty simple step for someone who is familiar with Dirac notation, but I'm not sure how the author has <em>unlocked</em> the $\hat{H}$ from the $\hat{H}\hat{q_H}$?</p>
<p>Any comments greatly appreciated as always.</p>
| 8,479 |
[
0.011952454224228859,
-0.026696160435676575,
0.04839206114411354,
-0.040164392441511154,
0.0343969464302063,
0.01094062440097332,
-0.02196100726723671,
-0.0032041522208601236,
0.01260866317898035,
-0.03965184465050697,
0.0005634422996081412,
0.04288972541689873,
0.0601467527449131,
0.015539479441940784,
0.0251828134059906,
0.04333370551466942,
-0.024060802534222603,
-0.020068183541297913,
-0.005305771250277758,
-0.06843092292547226,
0.03160911053419113,
0.0534917414188385,
-0.02613159269094467,
-0.007140508387237787,
-0.007313130423426628,
0.009766300208866596,
0.05531029775738716,
0.005025865975767374,
0.019550243392586708,
0.07088491320610046,
-0.01728304848074913,
-0.03756542503833771,
0.055106934159994125,
0.03169584274291992,
0.0009721385431475937,
-0.0288827046751976,
-0.004744182340800762,
-0.07029788196086884,
0.007325386628508568,
0.017167953774333,
-0.05886382982134819,
-0.008991512469947338,
-0.02781779132783413,
0.051733095198869705,
0.0015409857733175159,
0.04009655490517616,
-0.004037484992295504,
-0.036167483776807785,
0.04559802636504173,
-0.04322727024555206,
0.06996433436870575,
0.05307263880968094,
0.0019189136801287532,
0.007972472347319126,
-0.032274387776851654,
0.02235458232462406,
0.04223901405930519,
0.05384860187768936,
-0.005748028866946697,
-0.03184487670660019,
-0.027744727209210396,
-0.06672588735818863,
-0.026324164122343063,
-0.024750595912337303,
-0.0034527319949120283,
0.01743326149880886,
0.025682643055915833,
0.0009753647609613836,
0.01076120138168335,
-0.0022598453797399998,
-0.008277367800474167,
0.002028660150244832,
0.048778265714645386,
-0.048196665942668915,
0.030499013140797615,
-0.045120079070329666,
0.017000136896967888,
0.0018532807007431984,
0.025792133063077927,
-0.011603077873587608,
-0.009586951695382595,
-0.0015027744229882956,
0.011831972748041153,
0.05662178993225098,
-0.03557610884308815,
-0.018954766914248466,
0.03508175536990166,
0.010584058240056038,
0.01842682436108589,
0.05196991190314293,
-0.04052155464887619,
0.03751754015684128,
0.0476219616830349,
-0.014434983022511005,
-0.02796940878033638,
0.036209750920534134,
0.020168552175164223,
0.050767309963703156,
0.016259843483567238,
-0.03948357328772545,
0.03117278404533863,
-0.02217358909547329,
0.032191839069128036,
0.046762458980083466,
0.007409765385091305,
-0.012797003611922264,
-0.010535373352468014,
0.02106349542737007,
0.002800020622089505,
-0.0029613105580210686,
-0.06054188683629036,
0.0038567918818444014,
-0.013262851163744926,
0.0071075912564992905,
-0.009072254411876202,
-0.021391859278082848,
-0.028361819684505463,
0.020764803513884544,
0.06542740762233734,
0.061641477048397064,
-0.015500487759709358,
0.004380475729703903,
0.013377232477068901,
-0.04808860272169113,
-0.06822611391544342,
-0.006993497256189585,
0.05571519210934639,
-0.030948108062148094,
-0.03575064614415169,
0.029388949275016785,
0.006310304161161184,
-0.01485050842165947,
0.01735926978290081,
0.013895434327423573,
-0.005808756221085787,
-0.0035746637731790543,
-0.1104612648487091,
-0.05249791964888573,
0.01852739416062832,
-0.019008001312613487,
0.006628679111599922,
-0.07336416840553284,
0.030727865174412727,
0.041701339185237885,
0.0709134116768837,
0.024694494903087616,
0.016749640926718712,
0.002583260415121913,
-0.008251787163317204,
0.0202197078615427,
-0.00932456273585558,
-0.03144426271319389,
-0.0019676373340189457,
-0.03305097296833992,
-0.029052818194031715,
-0.028298746794462204,
0.012511584907770157,
0.03835773840546608,
0.014042288064956665,
-0.03806278854608536,
0.09334130585193634,
0.009514302015304565,
-0.015694856643676758,
0.022091437131166458,
-0.007706452161073685,
-0.040054455399513245,
0.09139245748519897,
-0.008736236952245235,
-0.01944781094789505,
0.05055645480751991,
0.011193721555173397,
0.015049834735691547,
0.007208157330751419,
0.04651729762554169,
0.01052855420857668,
-0.05071059986948967,
-0.00347707886248827,
-0.0669373944401741,
0.03058754839003086,
-0.033584535121917725,
-0.03171253204345703,
-0.03553448244929314,
0.011155043728649616,
0.03347666561603546,
0.015334326773881912,
0.018564941361546516,
0.010903964750468731,
0.014883387833833694,
0.02699611522257328,
-0.05593293160200119,
-0.015218560583889484,
-0.06538469344377518,
0.0366726890206337,
-0.015492645092308521,
-0.019043121486902237,
0.05944783240556717,
0.009586652740836143,
0.002818428911268711,
-0.010185005143284798,
-0.059843968600034714,
0.005993195343762636,
-0.005173313431441784,
0.013622439466416836,
-0.05133578181266785,
0.009885045699775219,
0.04267864301800728,
0.023254800587892532,
0.02834276296198368,
0.06913014501333237,
-0.04987858608365059,
-0.007442335598170757,
0.04130545258522034,
0.01369735598564148,
0.012878479436039925,
0.013718828558921814,
0.00047644891310483217,
0.005713493563234806,
-0.00875075813382864,
-0.016259431838989258,
0.009797527454793453,
-0.019888831302523613,
0.05815959349274635,
0.0195031575858593,
0.00633488642051816,
0.028707774356007576,
0.012293660081923008,
0.03483962267637253,
0.02606382593512535,
0.012694657780230045,
-0.026282260194420815,
-0.026830213144421577,
0.014976018108427525,
0.03966009244322777,
0.012896154075860977,
-0.04100343957543373,
-0.0184580460190773,
0.048301298171281815,
0.0307792779058218,
0.016125699505209923,
0.003282774705439806,
-0.049936000257730484,
0.001571274595335126,
-0.010243119671940804,
0.004156902898102999,
-0.025580603629350662,
0.009206441231071949,
0.032701168209314346,
-0.00622671190649271,
0.03326832503080368,
0.02629447542130947,
-0.05212373659014702,
0.029642384499311447,
-0.04633992910385132,
-0.010828894563019276,
0.0007231063791550696,
-0.04716421663761139,
0.03278234973549843,
-0.057430900633335114,
0.018726732581853867,
-0.015565549023449421,
-0.026161858811974525,
-0.024929070845246315,
-0.014280809089541435,
-0.02629886008799076,
0.014301897957921028,
-0.035001590847969055,
-0.042900390923023224,
0.004441862925887108,
0.00645089615136385,
-0.05149596557021141,
0.010233130306005478,
-0.051816005259752274,
-0.01635311357676983,
-0.002620568498969078,
0.0006625961977988482,
0.03851989656686783,
0.034547850489616394,
0.017497841268777847,
-0.04487422853708267,
-0.015077566727995872,
-0.017809538170695305,
0.0005846217973157763,
0.009283117949962616,
0.03242125362157822,
-0.024841874837875366,
-0.020255109295248985,
-0.04843933880329132,
-0.055965665727853775,
0.04335710033774376,
-0.014134707860648632,
-0.013348525390028954,
-0.008160501718521118,
-0.013024474494159222,
-0.01536948699504137,
-0.037615347653627396,
-0.028750816360116005,
0.036823820322752,
-0.03722957894206047,
-0.008431569673120975,
0.06518919765949249,
-0.01625324971973896,
0.0006394641823135316,
0.0163433775305748,
0.030322300270199776,
-0.04678061604499817,
-0.006305163726210594,
-0.022652382031083107,
-0.0017113457433879375,
-0.017620235681533813,
0.0369621179997921,
0.008198722265660763,
-0.017598813399672508,
-0.01239444687962532,
-0.051905885338783264,
-0.031082862988114357,
0.0386374294757843,
0.013764692470431328,
0.03388693183660507,
0.01190535444766283,
-0.004740527365356684,
0.09364134818315506,
0.00019853688718285412,
-0.008473179303109646,
-0.03675273805856705,
0.022243300452828407,
-0.029892774298787117,
0.009765982627868652,
-0.006052239332348108,
0.0518839955329895,
0.005747116170823574,
0.0630355179309845,
-0.011349949054419994,
-0.00816980842500925,
0.06392136961221695,
0.005055090878158808,
-0.022483723238110542,
-0.0010898697655647993,
-0.030875399708747864,
0.023640282452106476,
0.05257401242852211,
0.0029915280174463987,
-0.06339937448501587,
0.008383781649172306,
0.0004213712236378342,
0.02117648720741272,
0.01550029031932354,
-0.028679970651865005,
0.029369806870818138,
-0.004734588786959648,
-0.011003139428794384,
-0.006162379868328571,
0.046125780791044235,
-0.013804471120238304,
0.010578007437288761,
0.04018949344754219,
0.03511081263422966,
0.019247740507125854,
-0.029239481315016747,
0.00025386479683220387,
0.005492217373102903,
0.022015465423464775,
-0.04868943989276886,
0.009028945118188858,
0.013470698148012161,
-0.020383743569254875,
0.02594093605875969,
-0.04277832806110382,
-0.0172064658254385,
0.02362079545855522,
0.03184691071510315,
0.020589834079146385,
0.002330748364329338,
-0.057937752455472946,
0.006023169029504061,
-0.04642165079712868,
0.002224314259365201,
0.040655605494976044,
0.014023263938724995,
0.0009964549681171775,
0.06402797996997833,
0.03179376572370529,
0.01024247519671917,
0.02024080790579319,
0.0007492883014492691,
-0.040170859545469284,
-0.015252148732542992,
-0.019658448174595833,
-0.016385940834879875,
0.009493398480117321,
-0.03908074274659157,
0.03291742503643036,
-0.012816463597118855,
-0.03050023689866066,
-0.0086154630407691,
-0.042785897850990295,
-0.030306421220302582,
0.04267538711428642,
-0.027039669454097748,
-0.021795425564050674,
-0.012911834754049778,
0.01848292350769043,
0.04994653910398483,
-0.011464935727417469,
0.007131320424377918,
0.04478807374835014,
0.0014504074351862073,
0.013896804302930832,
-0.001812199829146266,
0.042404722422361374,
0.02875456213951111,
0.011380420066416264,
0.0027598885353654623,
0.03110824152827263,
-0.0018747191643342376,
-0.00653730658814311,
-0.04802796244621277,
0.06903029978275299,
0.015134249813854694,
-0.045364297926425934,
0.06121757999062538,
-0.02826923318207264,
0.0011367843253538013,
-0.031165504828095436,
0.05639106407761574,
-0.014527122490108013,
0.04164566472172737,
0.050759218633174896,
0.00594840245321393,
-0.04795681685209274,
0.021471071988344193,
0.06521185487508774,
0.005104128271341324,
-0.026025326922535896,
-0.059213414788246155,
0.02420692704617977,
-0.0010793430265039206,
-0.010344122536480427,
-0.018511183559894562,
-0.0012534164125099778,
-0.017574312165379524,
0.006028652656823397,
0.05392094701528549,
0.027733711525797844,
0.0043439604341983795,
0.039339277893304825,
-0.014861839823424816,
0.004765183199197054,
-0.01719098538160324,
0.01137930154800415,
0.007998133078217506,
-0.007801354397088289,
0.016977880150079727,
0.001966333482414484,
0.012374150566756725,
-0.07132167369127274,
-0.014719567261636257,
0.03382682427763939,
-0.0060427142307162285,
-0.0031157436314970255,
0.014336450956761837,
-0.05790169909596443,
-0.026159686967730522,
0.05266646295785904,
-0.02222766913473606,
0.03319622203707695,
-0.022866476327180862,
-0.03616267442703247,
-0.04349151626229286,
-0.023937297984957695,
-0.018094290047883987,
-0.0027347784489393234,
-0.0130632808431983,
0.01568016968667507,
-0.034678202122449875,
-0.014332086779177189,
-0.02637375146150589,
0.012166468426585197,
-0.0006440512952394783,
0.07412901520729065,
0.03454107046127319,
-0.04267604649066925,
-0.0008623316534794867,
0.03749489784240723,
-0.020080717280507088,
-0.10329713672399521,
0.008640932850539684,
0.012600868940353394,
0.010472173802554607,
0.044870249927043915,
-0.06303220242261887,
-0.03737005963921547,
0.009509710595011711,
0.018180537968873978,
-0.019289003685116768,
0.0028698977548629045,
-0.0311620831489563,
0.07021723687648773,
0.03834955021739006,
-0.017359493300318718,
0.04904346168041229,
-0.00039305814425460994,
-0.011484168469905853,
0.010557964444160461,
-0.006219767965376377,
0.026604223996400833,
-0.029526911675930023,
0.01340340357273817,
-0.028589807450771332,
0.021229950711131096,
-0.011797243729233742,
0.03583986684679985,
0.007065147627145052,
0.040759049355983734,
0.05236094817519188,
-0.02666638232767582,
-0.013915278017520905,
0.007229603826999664,
-0.024914955720305443,
-0.003226791275665164,
-0.0069803171791136265,
0.025743236765265465,
0.028567783534526825,
-0.032478347420692444,
-0.0046713571064174175,
0.027811795473098755,
0.012965668924152851,
0.027342230081558228,
0.002055645454674959,
0.036138780415058136,
-0.04874444380402565,
-0.008218771778047085,
0.009635345079004765,
-0.07038845866918564,
0.01590450294315815,
-0.03679933771491051,
-0.008062564767897129,
-0.0011980290291830897,
-0.018790384754538536,
-0.07023935765028,
-0.004564659669995308,
-0.045139506459236145,
0.023693911731243134,
-0.03073981963098049,
0.0009411221835762262,
0.03196866065263748,
0.00970330461859703,
-0.052070003002882004,
-0.008922337554395199,
-0.011252807453274727,
-0.01184476912021637,
-0.012761450372636318,
-0.007818917743861675,
0.017575601115822792,
-0.01342228427529335,
-0.02041901834309101,
0.032196443527936935,
0.04591597616672516,
-0.028175244107842445,
0.006777925882488489,
0.003727395785972476,
0.04239550232887268,
0.03682598099112511,
-0.014804800041019917,
-0.03480113297700882,
0.0032659098505973816,
-0.008657603524625301,
0.0025831882376223803,
0.035814762115478516,
0.03356917202472687,
-0.019176553934812546,
-0.033337533473968506,
-0.05466039851307869,
0.03750798478722572,
0.014313855208456516,
-0.026224706321954727,
-0.02633070759475231,
0.030851241201162338,
0.046562761068344116,
0.029652191326022148,
-0.047274865210056305,
-0.01505550928413868,
-0.014275451190769672,
0.03065592795610428,
-0.00446052523329854,
0.012799052521586418,
-0.00529074389487505,
-0.009021290577948093,
0.02421427145600319,
-0.004375542514026165,
0.03285194933414459,
-0.032044071704149246,
0.06534719467163086,
0.00023677856370341033,
0.016041206195950508,
0.06093310937285423,
-0.007079004310071468,
0.007058432791382074,
0.007140233647078276,
0.02026834338903427,
-0.014852789230644703,
-0.014873085543513298,
-0.019738828763365746,
-0.028310513123869896,
-0.043667081743478775,
0.019271381199359894,
0.03128112852573395,
-0.008569901809096336,
0.05335712805390358,
0.042758021503686905,
0.011997440829873085,
-0.03599344938993454,
-0.0010690420167520642,
-0.039690516889095306,
-0.021901892498135567,
-0.012975236400961876,
0.05899735167622566,
-0.005375775042921305,
0.012803160585463047,
0.05041728913784027,
0.030026983469724655,
-0.04012421891093254,
-0.0033863906282931566,
0.04281994327902794,
0.04303136095404625,
0.013178401626646519,
0.02301560528576374,
-0.054433442652225494,
0.04716207832098007,
-0.033732227981090546,
0.028857139870524406,
-0.008342817425727844,
-0.028520068153738976,
-0.010836770758032799,
0.04532596096396446,
-0.004909696988761425,
-0.015131033957004547,
-0.039651792496442795,
-0.02291923761367798,
0.02185925655066967,
0.013391198590397835,
-0.022511476650834084,
-0.023308025673031807,
0.026270058006048203,
0.02609897218644619,
0.02265116572380066,
0.01222017128020525,
0.03228561952710152,
0.003435272490605712,
0.0021344406995922327,
-0.043239206075668335,
-0.02701474167406559,
-0.02954949252307415,
-0.03798165172338486,
-0.03678305074572563,
0.03993551433086395,
-0.028267355635762215,
-0.01302661094814539,
0.020568571984767914,
0.018475012853741646,
-0.005825156345963478,
0.08705063909292221,
0.025143034756183624,
-0.025423351675271988,
0.011363510973751545,
0.0006942882318980992,
0.107422836124897,
0.057820383459329605,
0.025856930762529373,
-0.06002788245677948,
0.019384153187274933,
0.025869281962513924,
0.001207070774398744,
-0.033690545707941055,
0.006885441951453686,
-0.010531541891396046,
-0.01700519025325775,
-0.05500587821006775,
0.04911405220627785,
0.015938233584165573,
0.012016811408102512,
0.04338349774479866,
-0.03441726043820381,
-0.049660392105579376,
-0.00288401055149734,
0.027006017044186592,
-0.005547783337533474,
0.0019918896723538637,
-0.05197448655962944,
0.028679916635155678,
-0.010094672441482544,
0.021228328347206116,
-0.023172590881586075,
-0.03715229406952858,
0.0054356916807591915,
0.02934800647199154,
-0.050281234085559845,
0.0024796698708087206,
-0.017655856907367706,
-0.025127967819571495,
0.016496691852808,
0.037417493760585785,
0.0005955587839707732,
0.009084709919989109,
0.013320383615791798,
-0.005780920386314392,
0.02296460047364235,
-0.022513963282108307,
-0.01566765271127224,
-0.026155710220336914,
-0.028458941727876663,
-0.012720514088869095,
-0.015962786972522736,
0.0402650386095047,
-0.007780502550303936,
-0.01863076165318489,
0.012516719289124012,
-0.013835545629262924,
-0.01955224946141243,
-0.05195251852273941,
0.025119386613368988,
-0.005435757339000702,
0.025439215824007988,
0.0016122941160574555,
-0.012890821322798729,
-0.02503550797700882,
0.02377656288444996,
-0.006774022243916988,
-0.011789229698479176,
-0.040158916264772415,
-0.02437014691531658,
0.031091542914509773,
0.024498632177710533,
-0.012297483161091805,
0.00044238887494429946,
-0.027783649042248726,
-0.007887061685323715,
-0.024596964940428734,
-0.05401361733675003,
-0.0291872788220644,
0.0019902342464774847,
0.008231020532548428,
0.055997204035520554,
-0.00522127328440547,
0.0023058864753693342,
-0.020034752786159515,
-0.0914495661854744,
0.008670998737215996,
0.0009659407078288496,
-0.040894754230976105,
0.0077986991964280605,
-0.022448094561696053,
0.029993267729878426,
0.06085493415594101,
-0.03690280392765999,
0.00809964444488287,
0.017072021961212158,
0.005910799372941256,
0.017674261704087257,
-0.04532414674758911,
-0.004892343655228615,
0.0399513803422451,
-0.0385616235435009,
0.018610889092087746,
-0.045250363647937775,
-0.010751479305326939,
0.04722631350159645,
0.036153748631477356,
-0.005556376650929451,
0.03105117566883564,
0.0011971857165917754,
-0.023179451003670692,
-0.02700030617415905,
0.00020775511802639812,
0.00026823009829968214,
0.009912373498082161,
-0.00934465043246746,
-0.07597236335277557,
-0.04048028960824013,
-0.011963184922933578,
-0.004457392264157534,
-0.0043641673400998116,
0.04414673149585724,
-0.018413854762911797,
0.0023965034633874893,
0.0014573992229998112,
0.028975926339626312,
-0.026717402040958405,
0.02033941261470318,
-0.06063440442085266,
0.003209854708984494,
0.0003803629369940609,
0.02141711674630642,
-0.034572385251522064,
-0.0007836711592972279,
0.004881556611508131,
0.002958257682621479,
0.04720016568899155,
0.020061759278178215,
-0.004679179284721613,
-0.020050738006830215,
-0.017385538667440414,
-0.0013552795862779021,
0.005190384108573198,
-0.00844713393598795,
-0.02349461056292057,
0.02834887057542801,
-0.03642616048455238,
-0.025205355137586594,
0.03084230050444603,
0.0316799022257328,
0.013203772716224194,
0.05626155436038971,
-0.013422457501292229,
-0.014636576175689697,
0.024058662354946136,
-0.024446314200758934,
-0.011697234585881233,
0.020580483600497246,
-0.04927930608391762,
-0.025760332122445107,
-0.012663258239626884,
-0.0029923904221504927,
0.010982836596667767,
0.012651976197957993,
0.028547339141368866,
0.03574039414525032,
0.0011572531657293439,
0.0018037897534668446,
0.02900920994579792,
0.010242010466754436,
0.016268787905573845,
0.03624575957655907,
-0.02560179866850376,
0.017835721373558044,
0.04803226515650749,
-0.04478040710091591,
0.018449490889906883,
0.023134179413318634,
0.03297928720712662,
-0.08107437193393707,
-0.021871382370591164,
-0.010530497878789902,
-0.01407881360501051,
0.0694764107465744,
-0.04850952327251434,
0.007150677964091301,
0.02977030724287033,
-0.08302167057991028,
0.053097277879714966,
-0.0067152464762330055,
0.00537545420229435,
-0.033064473420381546,
0.01758098043501377,
-0.0053094495087862015,
0.043197400867938995,
0.015760313719511032,
0.04212017357349396,
-0.0015121811302378774,
0.019817683845758438,
-0.002535718260332942,
-0.035407450050115585,
-0.01578593999147415,
0.009189296513795853,
0.030014479532837868,
-0.051141880452632904,
0.058802198618650436,
-0.016360020264983177,
-0.059175197035074234,
0.04626654461026192,
-0.02464234083890915,
-0.036623213440179825,
-0.02227741852402687,
0.03319774568080902,
0.017644556239247322,
0.025741025805473328,
0.009960569441318512,
-0.02709215134382248,
-0.005604364909231663,
0.0005268516251817346,
0.033941593021154404,
0.025335578247904778,
0.03229625150561333,
-0.018890075385570526,
-0.006442100275307894,
-0.025606725364923477,
-0.04136212170124054,
0.06513777375221252,
-0.0027107864152640104,
0.009005141444504261,
0.013989770784974098,
-0.0005816479097120464,
0.014857211150228977,
-0.03625360131263733,
0.025564081966876984,
-0.046855390071868896,
-0.04054344817996025,
-0.007411004044115543,
-0.006188053637742996,
0.02119741588830948,
0.0010050201090052724,
-0.06861795485019684,
-0.052397388964891434,
0.05106159672141075,
0.039488907903432846,
-0.035783570259809494,
-0.057296618819236755,
-0.005322862416505814,
0.037706442177295685,
0.003603164106607437,
0.007717492058873177,
-0.035471685230731964,
-0.04815126955509186,
-0.002709421329200268,
0.0008471449255011976,
0.0074732499197125435,
-0.03666161373257637,
-0.009652286767959595,
0.008366101421415806,
-0.059245895594358444,
0.045537762343883514,
0.04585107043385506,
-0.018393173813819885,
0.011217079125344753,
-0.01706300862133503,
-0.0013176543870940804,
-0.010657879523932934,
0.06338227540254593,
-0.006241981405764818,
-0.052807167172431946,
-0.027767697349190712,
-0.029643790796399117,
0.017379676923155785,
-0.029709279537200928,
0.016583656892180443,
-0.012800686992704868,
-0.00843875017017126,
0.004766587633639574,
0.013978967443108559,
-0.022410260513424873,
0.033388737589120865,
0.01604399085044861,
-0.001393624464981258,
0.0072609917260706425,
-0.000052708302973769605,
-0.030782587826251984,
0.0049176630564033985,
-0.00863478984683752,
-0.033457763493061066,
0.03691292181611061,
0.023675622418522835,
-0.02058294042944908,
0.0319807343184948,
-0.019346440210938454,
-0.07468225806951523,
0.009097055532038212,
-0.02649458311498165,
-0.019607871770858765,
-0.03608762100338936,
0.002421427285298705,
0.029227912425994873,
0.012744459323585033,
-0.006358476355671883,
0.017576701939105988,
-0.009602271020412445,
0.012551258318126202,
0.029832417145371437,
0.0381995253264904,
0.06117543950676918,
0.02759966254234314,
-0.04573803022503853,
0.044600117951631546,
0.008982554078102112,
0.018548188731074333,
0.062310393899679184,
0.036059144884347916,
0.04507788270711899,
0.01601545698940754,
0.01301355566829443,
0.0031104530207812786,
0.017574407160282135,
0.029729535803198814,
0.035048071295022964,
-0.01980462856590748,
0.027870070189237595,
0.017270244657993317,
-0.009828307665884495,
-0.005367930047214031,
0.001905747689306736,
-0.03629551827907562,
0.08240042626857758,
-0.009549271315336227,
0.009780659340322018,
-0.027135798707604408,
0.035526569932699203,
0.0012289297301322222,
-0.009954380802810192,
0.0033182231709361076,
0.033878497779369354,
-0.050878919661045074,
-0.03105742856860161,
-0.050408363342285156,
0.01797677017748356,
-0.008438264019787312,
-0.03968627750873566,
-0.0012158784084022045,
0.04162731394171715,
-0.0034437840804457664,
-0.01493403036147356,
-0.01956397294998169,
0.012780934572219849,
-0.01426655612885952,
0.008952995762228966,
0.05992848053574562,
0.008702496998012066,
0.02103034220635891,
-0.008699925616383553,
-0.01942094787955284,
0.023641102015972137,
-0.033707987517118454,
-0.032563716173172,
-0.02596134878695011,
0.030765356495976448,
0.0002422229590592906,
-0.0021199712064117193
] |
<p>From Wikipedia (http://en.wikipedia.org/wiki/Water_electrolysis#Efficiency):</p>
<blockquote>
<p>The electrolysis of water requires a minimum of 237.13 kJ of electrical energy input to dissociate each mole.</p>
</blockquote>
<p>Each mole of water gives you 2 grams of Hydrogen and 16 grams of Oxygen (http://www.lenntech.com/calculators/molecular/molecular-weight-calculator.htm).</p>
<p>The energy density of the Hydrogen is 141.86 MJ/kg (http://en.wikipedia.org/wiki/Energy_density#Energy_densities_ignoring_external_components).</p>
<p>Calculation for 1 kg of water (55.55 moles):</p>
<blockquote>
<p>Energy for electrolysis: 237.13 kJ * 55.55 = 13.173 MJ</p>
<p>Energy released by Hydrogen combustion: 0.002 * 55.55 * 141.86 MJ = 15.76 MJ</p>
</blockquote>
<p>These calculations are not taking in account efficiency and energy loses, they are purely theoretical.</p>
<p>In various Wikipedia articles there are claims regarding to electrolysis similar to following:</p>
<blockquote>
<p>The energy required to generate the oxyhydrogen always exceeds the energy released by combusting it.</p>
<p>Electrolysis-based designs have repeatedly failed efficiency tests and <strong>contradict widely accepted laws of thermodynamics (i.e. conservation of energy)</strong></p>
</blockquote>
<p><strong>First Question:</strong> In theory (in practice we always have less efficiency and must take those in account), is there anything wrong with my calculation?</p>
<p><strong>Second Question:</strong> Can someone clarify to me the claims about laws of thermodynamics and conservation of energy - I do not see ANY CONNECTION between energy needed to electrolyze water and energy released by hydrogen combustion?</p>
| 8,480 |
[
-0.0864584818482399,
-0.009825587272644043,
-0.008002345450222492,
-0.001609372440725565,
0.029550058767199516,
-0.010355016216635704,
-0.072214275598526,
-0.04127058386802673,
0.035574205219745636,
-0.012159074656665325,
0.05519521236419678,
0.03534013032913208,
0.06584194302558899,
0.019876286387443542,
-0.001697647850960493,
-0.01569945178925991,
0.016036590561270714,
-0.026357581838965416,
0.01744026504456997,
-0.0021095171105116606,
-0.004059439990669489,
0.0011030393652617931,
-0.010393377393484116,
-0.0030092319939285517,
-0.044470082968473434,
0.03695144131779671,
0.03732715919613838,
-0.017443424090743065,
0.014440547674894333,
0.04149569943547249,
0.014445428736507893,
-0.027611369267106056,
0.00221846392378211,
0.0335855595767498,
0.02461567521095276,
0.03337116166949272,
-0.030173752456903458,
-0.031322963535785675,
-0.024599559605121613,
0.014591321349143982,
0.009383964352309704,
-0.007103124167770147,
-0.009285259060561657,
0.044282134622335434,
-0.011899225413799286,
0.03629244491457939,
-0.018499203026294708,
-0.050898775458335876,
0.01774601824581623,
-0.08115819841623306,
0.0436842180788517,
0.021290823817253113,
0.057962752878665924,
-0.0018010975327342749,
-0.015195198357105255,
0.025426790118217468,
0.07833756506443024,
0.06811656057834625,
-0.02329295128583908,
-0.03804360330104828,
-0.018318021669983864,
0.00251007336191833,
-0.0124922264367342,
0.01032554917037487,
-0.028148964047431946,
0.04761621356010437,
-0.008654986508190632,
-0.022816184908151627,
0.05756288021802902,
0.017380373552441597,
0.04601175710558891,
0.0036570492666214705,
-0.000991193694062531,
-0.010161635465919971,
0.016519350931048393,
-0.014213367365300655,
0.047193147242069244,
0.0020497599616646767,
0.0221745315939188,
0.0753108412027359,
-0.030895762145519257,
0.00097149598877877,
0.04992963373661041,
0.03394928202033043,
0.008253199979662895,
0.002591550350189209,
0.046572402119636536,
0.002062841784209013,
0.022247401997447014,
-0.005105890333652496,
0.03374442458152771,
0.01294942107051611,
0.022737562656402588,
0.021954506635665894,
0.019685793668031693,
0.02895415388047695,
-0.024257609620690346,
0.08636458963155746,
0.013002227991819382,
-0.021625293418765068,
0.012989131733775139,
0.0026610728818923235,
0.05858027562499046,
0.043786369264125824,
0.02516867220401764,
-0.0723545178771019,
-0.02400730550289154,
0.026154611259698868,
0.008117004297673702,
-0.0009022377780638635,
-0.023629335686564445,
0.021328739821910858,
0.0018115297425538301,
-0.02552323043346405,
0.00046019363799132407,
-0.0370916873216629,
0.022686488926410675,
0.017261922359466553,
0.05265986919403076,
0.03311556577682495,
0.016024770215153694,
-0.02712579257786274,
0.029669450595974922,
-0.030974050983786583,
-0.037817180156707764,
-0.018581775948405266,
0.0005652107065543532,
0.004589840769767761,
-0.006177126429975033,
0.03191649168729782,
-0.011345510371029377,
0.01752055622637272,
0.018578091636300087,
-0.028732044622302055,
0.048901595175266266,
-0.02359364554286003,
-0.058135952800512314,
-0.044947244226932526,
0.039687976241111755,
-0.0040093762800097466,
-0.01087147556245327,
-0.07180513441562653,
-0.012944727204740047,
0.015835415571928024,
0.04823586344718933,
-0.02056722529232502,
-0.0014335125451907516,
-0.028615284711122513,
0.047885484993457794,
-0.01567315310239792,
-0.03271691873669624,
-0.005869864020496607,
0.025174401700496674,
-0.05704183131456375,
-0.007802216801792383,
-0.04880387708544731,
0.02872934192419052,
0.009025364182889462,
0.03073226660490036,
-0.019926350563764572,
0.031158506870269775,
0.01137508638203144,
-0.03925658017396927,
-0.0023414460010826588,
0.020696453750133514,
-0.00832470040768385,
0.0630977526307106,
0.02354380674660206,
0.02467580884695053,
0.015214534476399422,
0.0035668008495122194,
0.007211293559521437,
-0.000749149126932025,
-0.0019498495385050774,
0.052653968334198,
-0.06028144806623459,
-0.004326986614614725,
-0.07612325251102448,
0.04787690192461014,
0.041332267224788666,
-0.04888095334172249,
-0.026205116882920265,
-0.015118202194571495,
-0.005119809880852699,
0.03600725531578064,
0.04365621507167816,
0.020486904308199883,
-0.022683365270495415,
-0.0066555337980389595,
-0.0332903116941452,
-0.04307350143790245,
-0.07028313726186752,
0.03524636849761009,
0.005897935479879379,
0.0061666881665587425,
0.004526333883404732,
-0.02153443917632103,
0.01267320942133665,
-0.05658373236656189,
-0.015529623255133629,
0.0020847064442932606,
0.034644510596990585,
0.011611181311309338,
0.023307442665100098,
0.006329984404146671,
0.06991823762655258,
0.020167816430330276,
-0.010182450525462627,
0.003314180299639702,
-0.0028591733425855637,
-0.024942222982645035,
-0.024165954440832138,
-0.041873108595609665,
-0.022216614335775375,
0.048825547099113464,
-0.032521191984415054,
0.026644600555300713,
-0.003297992516309023,
0.006541546434164047,
0.0286887064576149,
-0.011172358877956867,
0.0902748554944992,
0.04911479726433754,
0.03387237712740898,
-0.020354874432086945,
0.058100394904613495,
-0.01051529310643673,
0.0034523101057857275,
-0.0012215448077768087,
-0.006960152182728052,
-0.02085445076227188,
0.03386560454964638,
0.04024447128176689,
0.019491475075483322,
-0.06505314260721207,
0.013522032648324966,
0.018370818346738815,
-0.0016277877148240805,
0.019933436065912247,
-0.004811546765267849,
-0.020237546414136887,
-0.01091048214584589,
0.02648910880088806,
0.030897855758666992,
0.0031907290685921907,
0.04037833958864212,
0.014912279322743416,
0.026935821399092674,
-0.018733883276581764,
-0.03147261589765549,
-0.009428078308701515,
0.06350553035736084,
-0.027711570262908936,
0.027909792959690094,
-0.0015251998556777835,
-0.027336282655596733,
0.026482077315449715,
-0.04690025374293327,
0.01003983709961176,
0.0168157871812582,
0.0022902777418494225,
0.04441538825631142,
-0.028993919491767883,
-0.0003700125962495804,
-0.04077380895614624,
0.021628905087709427,
-0.014025446027517319,
-0.00988977774977684,
0.028618313372135162,
-0.0625513568520546,
0.00779859721660614,
-0.02570745348930359,
0.020449578762054443,
-0.0013064997037872672,
0.005415740422904491,
-0.012594670057296753,
-0.027389295399188995,
0.049033526331186295,
-0.028832770884037018,
-0.018790924921631813,
-0.03133855387568474,
-0.03157968074083328,
0.004663009196519852,
-0.019087813794612885,
-0.018668096512556076,
-0.035656169056892395,
-0.02139081247150898,
-0.006900120992213488,
0.033841345459222794,
-0.011401815339922905,
-0.034526631236076355,
0.014653568156063557,
0.02230919897556305,
-0.05750768259167671,
0.0014861804665997624,
-0.03826099634170532,
-0.00032837074832059443,
0.009055574424564838,
-0.015566501766443253,
0.04885391518473625,
-0.03521151468157768,
-0.0399622768163681,
0.04653910547494888,
-0.030345775187015533,
-0.027912013232707977,
0.0012362159322947264,
0.011552176438272,
-0.025427568703889847,
-0.0009768358431756496,
0.031675733625888824,
0.04234612360596657,
-0.06634838879108429,
-0.014327984303236008,
-0.05567009374499321,
-0.06471005827188492,
0.031923048198223114,
-0.017873942852020264,
0.06902345269918442,
-0.016718370839953423,
-0.06532104313373566,
0.03363998606801033,
0.018256530165672302,
-0.07927895337343216,
-0.014991234056651592,
-0.016819683834910393,
-0.015964064747095108,
0.014946024864912033,
-0.010272189974784851,
0.03469983860850334,
-0.01822826825082302,
-0.007643071934580803,
0.0006358249811455607,
0.028513962402939796,
0.013271831907331944,
-0.020037999376654625,
-0.0011145261814817786,
-0.0036657063756138086,
0.03056562878191471,
0.012803815305233002,
0.05554237216711044,
-0.012714838609099388,
-0.026547569781541824,
0.03547145798802376,
-0.025505082681775093,
0.04444025084376335,
0.04098065569996834,
-0.05728154629468918,
0.02882368117570877,
0.016819898039102554,
-0.010286850854754448,
-0.050928570330142975,
0.050255730748176575,
-0.021613385528326035,
-0.041872888803482056,
0.0545029453933239,
0.02560218796133995,
0.0579691044986248,
0.02521590143442154,
-0.022752687335014343,
0.0168609619140625,
0.06283573806285858,
-0.011814058758318424,
-0.04423194378614426,
0.0017650168156251311,
0.01296551525592804,
-0.008164986968040466,
0.03850904107093811,
-0.008364556357264519,
0.06577934324741364,
0.022475264966487885,
0.017884785309433937,
-0.005512816831469536,
-0.00802913960069418,
0.021639805287122726,
-0.10026685893535614,
-0.01805206947028637,
-0.012748691253364086,
0.07555557042360306,
-0.007313982117921114,
0.04952740669250488,
0.0008892274927347898,
-0.017524227499961853,
-0.016376687213778496,
-0.018130876123905182,
-0.06280967593193054,
0.02358071506023407,
-0.015600239858031273,
-0.02165122516453266,
0.010479564778506756,
-0.044021330773830414,
-0.02895861491560936,
-0.01628202013671398,
-0.02156953141093254,
-0.0034501608461141586,
0.006455606315284967,
-0.03901283070445061,
-0.00381670449860394,
-0.01587352342903614,
-0.018400222063064575,
-0.008417950011789799,
0.01334759034216404,
0.025120573118329048,
-0.007732914760708809,
0.03747108206152916,
0.03396240621805191,
-0.027766257524490356,
-0.013037332333624363,
-0.00885480921715498,
0.04773518815636635,
0.013188532553613186,
0.02767300419509411,
-0.012310616672039032,
0.034285131841897964,
0.033234186470508575,
-0.013997280038893223,
0.00800583977252245,
0.0057014417834579945,
-0.008692503906786442,
0.018549175933003426,
-0.05106920748949051,
-0.001306506572291255,
-0.017862241715192795,
0.060056090354919434,
0.03999415412545204,
-0.019860615953803062,
0.017654091119766235,
-0.02903261035680771,
-0.01677253469824791,
-0.0022176483180373907,
0.05748758465051651,
0.05654492974281311,
-0.00011181446461705491,
-0.00763211864978075,
-0.025432169437408447,
-0.020776968449354172,
-0.027441253885626793,
-0.020662816241383553,
0.016764499247074127,
-0.00976367387920618,
-0.013518144376575947,
-0.03813697397708893,
-0.001283050631172955,
0.0035297696013003588,
-0.010620137676596642,
0.05123249068856239,
0.007722070906311274,
0.013175072148442268,
-0.021093424409627914,
-0.0013955184258520603,
0.03818507492542267,
-0.015315637923777103,
0.02625122293829918,
0.0026722014881670475,
0.006085858214646578,
-0.08685936778783798,
-0.002566869370639324,
0.007807882037013769,
0.05802346393465996,
-0.01887197233736515,
0.0050112963654100895,
-0.06339998543262482,
0.017253315076231956,
0.01896941103041172,
-0.03154510632157326,
0.045304395258426666,
-0.021831529214978218,
0.035721804946660995,
-0.012936502695083618,
0.006154118571430445,
0.01402617059648037,
-0.024852614849805832,
0.028645606711506844,
0.022194044664502144,
-0.023088961839675903,
-0.0004286150506231934,
0.007481764070689678,
-0.00045524240704253316,
0.03617285564541817,
0.03480677306652069,
-0.017614571377635002,
-0.03141232207417488,
0.0049528335221111774,
0.02040706016123295,
-0.02206103503704071,
-0.06717691570520401,
-0.0014029750600457191,
-0.04923466593027115,
-0.011905351653695107,
0.03856493532657623,
-0.042921312153339386,
-0.05819499120116234,
0.029888322576880455,
0.03213634714484215,
-0.03189435228705406,
0.0010686737950891256,
-0.0356350839138031,
0.031993359327316284,
0.05482204258441925,
-0.0014668090734630823,
0.02579546347260475,
0.07099676132202148,
-0.04321477934718132,
0.0283038392663002,
-0.029976872727274895,
0.015681542456150055,
-0.023121068254113197,
0.0009104259661398828,
-0.03801826387643814,
0.028881357982754707,
0.0017598762642592192,
-0.001009649015031755,
-0.004950070288032293,
0.015276473015546799,
-0.04018806293606758,
-0.03560438007116318,
0.022735368460416794,
-0.017205944284796715,
0.010159363970160484,
-0.012669332325458527,
-0.007274382282048464,
0.06413961201906204,
-0.00875686202198267,
-0.0024548873770982027,
0.01567380502820015,
0.02607058174908161,
0.02249087207019329,
-0.0009378563845530152,
-0.01828581839799881,
0.013179806061089039,
-0.0049442811869084835,
-0.0029520071111619473,
0.04745292663574219,
-0.04065950959920883,
0.008097713813185692,
-0.025390632450580597,
0.021534455940127373,
0.010676920413970947,
-0.053085632622241974,
-0.040155790746212006,
0.03116430528461933,
0.02146661840379238,
0.02266913838684559,
-0.02138613536953926,
0.03252958133816719,
0.005453582387417555,
-0.019636718556284904,
-0.04493588209152222,
-0.03488049656152725,
0.054485127329826355,
0.027128780260682106,
-0.0181459691375494,
-0.04038158059120178,
-0.017368514090776443,
-0.015359963290393353,
-0.025111960247159004,
-0.02384110353887081,
0.016420947387814522,
-0.020810633897781372,
-0.0019423726480454206,
0.01462874747812748,
0.007978420704603195,
0.09120162576436996,
-0.00799503829330206,
-0.014118894934654236,
0.015855448320508003,
-0.025010045617818832,
-0.0346837192773819,
-0.0272823553532362,
0.01775943860411644,
-0.026068106293678284,
-0.011869585141539574,
0.00035410127020440996,
0.005326179787516594,
0.05368156358599663,
-0.020787453278899193,
-0.025332467630505562,
0.027498764917254448,
0.04080051928758621,
-0.031167779117822647,
-0.0273220706731081,
0.04152286425232887,
-0.019562674686312675,
0.04676448926329613,
-0.027406610548496246,
-0.010373031720519066,
-0.024301471188664436,
-0.016034940257668495,
-0.0210758987814188,
-0.01669379323720932,
0.01192475389689207,
-0.012155815958976746,
0.03277022764086723,
-0.0037992638535797596,
-0.012952981516718864,
0.004838965833187103,
-0.03952880948781967,
0.010702895931899548,
0.006465489976108074,
-0.015390467830002308,
-0.00027562942705117166,
-0.0023973919451236725,
-0.0320892333984375,
-0.05098123475909233,
-0.041331082582473755,
0.049098335206508636,
0.025346679612994194,
-0.009095367975533009,
0.029003731906414032,
0.012586552649736404,
0.002864306792616844,
0.022184059023857117,
-0.030874958261847496,
-0.025664275512099266,
0.003995547071099281,
0.013615952804684639,
0.02225727215409279,
0.027495795860886574,
-0.021668527275323868,
0.0674816146492958,
0.022946413606405258,
0.01719747856259346,
0.007069274317473173,
0.06757605820894241,
-0.009844309650361538,
0.019165514037013054,
-0.056841086596250534,
-0.061414964497089386,
-0.005738187115639448,
-0.052643075585365295,
0.031563300639390945,
-0.037894174456596375,
-0.010751702822744846,
0.032299213111400604,
-0.011680378578603268,
-0.00986709538847208,
-0.03580249845981598,
-0.03299492597579956,
-0.02733815833926201,
-0.0064109391532838345,
-0.01802315004169941,
0.0027611993718892336,
-0.023297186940908432,
0.025930708274245262,
0.026281287893652916,
0.017246192321181297,
0.04191772639751434,
-0.016653303056955338,
-0.05007893964648247,
-0.0037123423535376787,
0.006274288985878229,
-0.04236210882663727,
0.04474448412656784,
-0.00914875790476799,
-0.04915319383144379,
0.0014046787982806563,
-0.007269218564033508,
0.0180741548538208,
0.0012630426790565252,
0.038679879158735275,
-0.014308215118944645,
0.03452972322702408,
-0.015665685757994652,
0.016616936773061752,
-0.0007296623662114143,
0.00853805337101221,
0.11889724433422089,
0.06934254616498947,
0.021447734907269478,
-0.03403181955218315,
0.022111715748906136,
-0.020332427695393562,
-0.01011575385928154,
-0.010326983407139778,
0.015012177638709545,
-0.008616193197667599,
0.02842257171869278,
0.012797337956726551,
0.04063235595822334,
-0.004199412185698748,
0.0006214763270691037,
0.02909424714744091,
-0.009906237944960594,
-0.026342900469899178,
0.06427670270204544,
0.020752307027578354,
-0.03189975023269653,
-0.0017594302771613002,
-0.02891385927796364,
0.02947586588561535,
-0.045264001935720444,
-0.022761467844247818,
0.0201426949352026,
-0.016278641298413277,
0.015497091226279736,
0.032144829630851746,
-0.06349576264619827,
-0.012755000032484531,
-0.012987150810658932,
-0.02110530063509941,
-0.008501117117702961,
0.0032254140824079514,
0.02519145794212818,
0.010341398417949677,
-0.008997089229524136,
0.031729817390441895,
0.05277879536151886,
0.02458781749010086,
0.04127661511301994,
0.06470164656639099,
-0.05330211669206619,
0.015618911944329739,
-0.00989706814289093,
0.02155781351029873,
0.009829181246459484,
-0.004278433043509722,
0.003164983820170164,
-0.008416217751801014,
0.005441348534077406,
-0.05914262309670448,
-0.01946364715695381,
-0.013965586200356483,
0.018303539603948593,
-0.006726774852722883,
-0.06124319136142731,
-0.03984607383608818,
0.0130333686247468,
-0.03385975956916809,
0.00006610381387872621,
0.020600659772753716,
0.006418277975171804,
-0.03222152963280678,
-0.001419148058630526,
0.03461714833974838,
0.01715127006173134,
0.009398605674505234,
-0.032187994569540024,
-0.020389676094055176,
-0.024016480892896652,
-0.047887131571769714,
0.009450766257941723,
0.03357334062457085,
0.06921246647834778,
0.0005686760414391756,
0.016328496858477592,
0.009205632843077183,
-0.09253288805484772,
0.054229967296123505,
0.019865354523062706,
-0.03514141961932182,
-0.07278082519769669,
0.0176750048995018,
-0.01416811067610979,
0.02993636205792427,
-0.009087142534554005,
0.014451652765274048,
-0.0055990456603467464,
0.003538013668730855,
0.007379995658993721,
-0.037277042865753174,
-0.052491169422864914,
-0.009069091640412807,
-0.04224138706922531,
-0.050787534564733505,
0.028032202273607254,
0.016628947108983994,
-0.00019744719611480832,
0.008641746826469898,
0.013781423680484295,
-0.00006827526522101834,
0.02506275475025177,
0.0020954746287316084,
-0.001477076904848218,
-0.023836147040128708,
-0.03975962474942207,
-0.012260481715202332,
-0.0036153714172542095,
-0.013633971102535725,
0.0037464259658008814,
-0.06037985533475876,
0.012959619984030724,
0.020343998447060585,
0.021630924195051193,
-0.02314007468521595,
0.0025190715678036213,
-0.05851486697793007,
0.05081155523657799,
-0.006049043033272028,
-0.023759648203849792,
-0.008608805015683174,
-0.02730451337993145,
-0.01759994588792324,
-0.0009054234833456576,
-0.010393735952675343,
0.037456873804330826,
-0.007867954671382904,
-0.005017275922000408,
0.03675615414977074,
0.022628439590334892,
-0.043811943382024765,
-0.030603116378188133,
0.010493263602256775,
0.00465781195089221,
0.05489926412701607,
-0.06324467062950134,
-0.034978315234184265,
0.04184454306960106,
-0.023676034063100815,
-0.03582140430808067,
0.00511604268103838,
-0.044665250927209854,
0.020240550860762596,
0.05976049229502678,
-0.01268079038709402,
-0.018113750964403152,
0.07750594615936279,
-0.01988912560045719,
0.03098796121776104,
0.02034902200102806,
-0.005543754436075687,
0.016012126579880714,
0.026421621441841125,
-0.0042523834854364395,
-0.004111714195460081,
0.0030495987739413977,
0.039676062762737274,
0.037374347448349,
-0.0004033657314721495,
0.012945912778377533,
-0.0014465944841504097,
0.004108458757400513,
0.011171148158609867,
0.049950048327445984,
-0.010479972697794437,
0.0029861053917557,
0.03744284808635712,
-0.029760001227259636,
0.0053821285255253315,
-0.0020430907607078552,
-0.00503633264452219,
-0.08465695381164551,
-0.0005434404592961073,
-0.015708953142166138,
0.014187360182404518,
0.0016192026669159532,
-0.012644856236875057,
-0.008794481866061687,
0.02883075177669525,
-0.09259573370218277,
-0.03575612232089043,
-0.018538426607847214,
0.0032819616608321667,
-0.05772636830806732,
-0.01469553541392088,
-0.017278488725423813,
0.021107258275151253,
-0.004444561433047056,
0.07683566212654114,
0.017350349575281143,
0.026368161663413048,
-0.01497727818787098,
-0.016485853120684624,
0.008824153803288937,
0.023889178410172462,
0.0020312704145908356,
-0.021700549870729446,
0.029569081962108612,
-0.046699635684490204,
-0.03799182176589966,
0.006161052267998457,
-0.024690179154276848,
0.045484136790037155,
0.017500251531600952,
0.0034854384139180183,
-0.00103192834649235,
0.03788643702864647,
0.020102152600884438,
-0.033568818122148514,
-0.03637086600065231,
0.06506603211164474,
0.0017541350098326802,
0.015500516630709171,
0.008937317878007889,
0.03865217790007591,
0.0612003356218338,
-0.018261000514030457,
-0.024953752756118774,
0.02242852933704853,
-0.018106134608387947,
0.005914265289902687,
0.04468053579330444,
0.006790190003812313,
0.020042316988110542,
0.0008200132288038731,
-0.02471596747636795,
-0.03259210288524628,
0.0012343365233391523,
0.0352151058614254,
-0.004958776291459799,
0.020785098895430565,
0.02259090356528759,
-0.008140752092003822,
0.009037235751748085,
0.035849399864673615,
-0.027496209368109703,
-0.01530031394213438,
-0.04178595542907715,
0.015249796211719513,
0.020326465368270874,
-0.021737657487392426,
-0.01391096506267786,
-0.05531937628984451,
-0.02846102975308895,
0.08429477363824844,
-0.0013862084597349167,
0.003764828434213996,
0.037815626710653305,
-0.0354817733168602,
-0.019452115520834923,
-0.05266473442316055,
0.035230547189712524,
-0.040137335658073425,
-0.00040728735621087253,
-0.03468013182282448,
-0.05188557505607605,
0.014053136110305786,
0.03913702070713043,
0.03916992247104645,
-0.006811842322349548,
-0.046624064445495605,
0.009875761345028877,
-0.010859373956918716,
0.024013744667172432,
-0.04656294733285904,
0.014307483099400997,
0.01853169873356819,
-0.025742916390299797,
0.010755193419754505,
-0.03802911564707756,
-0.047157689929008484,
-0.01759941689670086,
0.048972271382808685,
-0.04928557574748993,
-0.027911504730582237,
-0.0026210977230221033,
0.015826983377337456,
0.029331551864743233,
-0.0016189917223528028,
-0.00441191578283906,
0.0899195447564125,
0.008546249009668827,
0.02713821828365326,
0.03391106054186821,
-0.002947835484519601,
-0.049420908093452454,
0.034120336174964905,
0.0006851318175904453,
0.016362247988581657,
0.002822170266881585,
-0.044897519052028656,
0.03646298870444298,
-0.0344710610806942,
0.010323282331228256,
0.03766452893614769,
-0.03330802172422409,
-0.014872625470161438,
0.0261357631534338,
0.04792080447077751,
0.017901672050356865,
-0.024658799171447754,
0.015324359759688377,
-0.027185671031475067,
0.02391793765127659,
-0.02476099133491516,
0.03038869984447956,
0.05458179488778114,
0.020304806530475616,
0.023929059505462646,
0.004435265902429819,
-0.020082972943782806,
0.017280152067542076,
0.05833638086915016,
-0.0022117237094789743,
-0.015582124702632427,
-0.02827385440468788,
0.018679434433579445,
0.012767098844051361,
0.004322931636124849,
-0.005213275086134672,
-0.027850424870848656,
0.06364355981349945,
0.019271057099103928,
0.02548104152083397,
-0.04197095334529877,
-0.0026111979968845844,
-0.021729527041316032,
0.010096896439790726,
-0.009665110148489475,
0.06645789742469788,
-0.010845327749848366,
0.0032336292788386345,
-0.009751768782734871,
0.023693997412919998,
0.020702475681900978,
-0.017022864893078804,
0.01580738089978695,
-0.02216615527868271,
-0.032020311802625656,
-0.045294929295778275,
-0.005988278426229954,
0.0032277412246912718,
-0.04078065976500511,
0.012416485697031021,
0.04781046882271767,
0.0007157315267249942,
0.0057854726910591125,
-0.06046822667121887,
0.009654952213168144,
0.057045020163059235,
-0.032049309462308884,
-0.0021075112745165825,
0.003997040446847677,
0.006752478890120983,
0.0039023433346301317,
-0.026281509548425674
] |
<p>Static electric fields are supposed to be conservative in nature and therefore give $0J$ work if traversed over a loop. However in the following problem I got non zero work by a static electric field. How can I explain this work ?</p>
<p><img src="https://lh4.googleusercontent.com/-S3oWGGy_30Y/UuLvVIXZnFI/AAAAAAAAAhE/kRutOGK9Q88/s1668-Ut/2014+-+2" alt="enter image description here"><br>
<strong>Note :</strong> This is done in field of line charge, diagram shows a cuboid type structure but that is just for differentiating between traversed path and line charge.</p>
<p>I am writing some of the important parts/equations here, but I have written the whole derivation <a href="http://thinklo.blogspot.in/2014/01/non-conservative-behaviour-of-static.html?m=0" rel="nofollow">here</a>.
$$W_{AB} = \frac{q\lambda}{4\pi\epsilon_0} [ln|\frac{(\sqrt{(L)^2+(r_1)^2}+L)(r_1)}{(\sqrt{(\frac{L}{2})^2+(r_1)^2}+\frac{L}{2})^2}|]$$</p>
<p>$$W_{BC} = \frac{q\lambda}{4\pi\epsilon_0}[ln|\frac{(\sqrt{(\frac{L}{2})^2+(r_1)^2}+(\frac{L}{2}))(r_2)}{(\sqrt{(\frac{L}{2})^2+(r_2)^2}+(\frac{L}{2}))(r_1)}|]$$</p>
<p>$$W_{CD} = \frac{q\lambda}{4\pi\epsilon_0} [ln|\frac{(\sqrt{(\frac{L}{2})^2+(r_2)^2}+\frac{L}{2})^2}{(\sqrt{(L)^2+(r_2)^2}+L)(r_2)}|]$$</p>
<p>$$W_{DA} = \frac{q\lambda}{4\pi\epsilon_0}[ln|\frac{(\sqrt{(L)^2+(r_2)^2}+(L))(r_1)}{(\sqrt{(L)^2+(r_1)^2}+(L))(r_2)}|]$$</p>
<p>$$W=W_{AB}+W_{BC}+W_{CD}+W_{DA}$$</p>
<p>$$W = \frac{q\lambda}{4\pi\epsilon_0} [ln|\frac{(\sqrt{(\frac{L}{2r_2})^2+1}+\frac{L}{2r_2})}{(\sqrt{(\frac{L}{2r_1})^2+1}+\frac{L}{2r_1})}|]$$</p>
<p>If field were to behave conservatively $W=0$ must have been satisfied, but unless $r_1 = r_2$, $W \neq 0$. Thus field is not behaving conservatively.</p>
<p>PS : This is not a homework question ! I am trying to explain the behaviour.</p>
| 8,481 |
[
-0.015141363255679607,
0.01912495493888855,
0.027435900643467903,
-0.003993104677647352,
0.03570052236318588,
-0.017976127564907074,
0.022259080782532692,
-0.03722962737083435,
-0.0056762248277664185,
-0.011758536100387573,
0.03051065281033516,
-0.008812219835817814,
0.050284408032894135,
0.023742005228996277,
0.02525646612048149,
0.010870127938687801,
0.016029996797442436,
-0.022052239626646042,
0.009417198598384857,
-0.011193492449820042,
-0.027901871129870415,
0.02166389860212803,
-0.004000554792582989,
-0.01798897236585617,
-0.020605994388461113,
0.03549257665872574,
-0.0010781176388263702,
-0.013225048780441284,
-0.03398126736283302,
0.03707200288772583,
-0.038337282836437225,
-0.009912949055433273,
-0.008475372567772865,
0.007706103380769491,
0.000772400526329875,
0.04018600285053253,
-0.04144761711359024,
-0.053242042660713196,
0.013075492344796658,
0.028578633442521095,
-0.027865901589393616,
-0.008353014476597309,
0.000139855474117212,
0.02416311763226986,
-0.0010792590910568833,
0.04771226644515991,
-0.018771765753626823,
-0.004670616239309311,
0.07678825408220291,
-0.04497572034597397,
0.043114833533763885,
0.03414775803685188,
0.06465962529182434,
0.018483687192201614,
-0.017517875880002975,
-0.00019377100397832692,
0.056692637503147125,
0.04785130172967911,
-0.013266106136143208,
-0.043433379381895065,
-0.037507764995098114,
-0.010508283972740173,
0.007718510925769806,
-0.029743939638137817,
-0.007482577580958605,
0.03244296833872795,
0.01975785382091999,
0.006021406035870314,
0.015197746455669403,
0.013884802348911762,
0.007650232873857021,
-0.0012829933548346162,
0.01254443172365427,
-0.05878276377916336,
0.009716600179672241,
0.028986340388655663,
-0.013265930116176605,
0.015736456960439682,
0.01528214756399393,
0.027712026610970497,
-0.02515225112438202,
-0.01533927209675312,
0.009211486205458641,
0.0606558658182621,
-0.01981094852089882,
-0.010665608569979668,
0.038463521748781204,
-0.004358222708106041,
-0.0044362498447299,
-0.005202914122492075,
0.02050803229212761,
0.010695169679820538,
0.030349334701895714,
0.0026189135387539864,
0.0021949787624180317,
0.055100973695516586,
-0.004784420598298311,
0.023258423432707787,
0.0024126542266458273,
-0.03124856762588024,
0.0029496168717741966,
-0.05469997972249985,
0.01222358737140894,
0.09661342948675156,
0.009975237771868706,
-0.022269543260335922,
0.024107182398438454,
0.02676091156899929,
-0.02618255838751793,
-0.015940740704536438,
-0.054026637226343155,
-0.00270659476518631,
0.04072432219982147,
-0.00005032594344811514,
-0.004474808927625418,
-0.06431140005588531,
-0.0073600048199296,
-0.014092008583247662,
0.020363494753837585,
0.0192826297134161,
0.00785115547478199,
-0.04004226624965668,
0.010879894718527794,
-0.016996029764413834,
-0.02628118172287941,
-0.00464623374864459,
0.03205502778291702,
-0.036329757422208786,
-0.05156445875763893,
-0.006384784821420908,
0.03301073983311653,
0.011937246657907963,
-0.020251715555787086,
0.013305362313985825,
0.03410596027970314,
-0.029655367136001587,
-0.07255516201257706,
-0.028622908517718315,
0.024842550978064537,
0.0031286203302443027,
0.04221896082162857,
-0.04995880275964737,
-0.029374588280916214,
0.025843609124422073,
0.10599806159734726,
-0.029206817969679832,
-0.025248952209949493,
0.048234883695840836,
0.01993122696876526,
0.0037683688569813967,
0.008065245114266872,
0.017304696142673492,
0.013041483238339424,
-0.04651820659637451,
0.022705424576997757,
-0.04696393385529518,
0.0067601329647004604,
0.01850275695323944,
-0.0024246282409876585,
0.010130779817700386,
0.05489761754870415,
-0.0046930438838899136,
0.04502361640334129,
0.010353018529713154,
-0.011914800852537155,
-0.01348729245364666,
0.07260435074567795,
0.019669577479362488,
-0.0023248810321092606,
0.03219226375222206,
0.010869304649531841,
-0.00430956669151783,
0.0027736476622521877,
0.0104247210547328,
0.06524251401424408,
-0.07799172401428223,
0.011111588217318058,
-0.060105763375759125,
-0.003383106552064419,
0.008766322396695614,
-0.06984482705593109,
-0.024327047169208527,
-0.012483648955821991,
0.01867363415658474,
0.009001243859529495,
0.07042448967695236,
-0.040457312017679214,
0.056157246232032776,
0.011767092160880566,
-0.002917370991781354,
0.007249950431287289,
-0.040965866297483444,
0.052721381187438965,
0.05459849163889885,
-0.051037441939115524,
0.008382806554436684,
-0.03165378421545029,
-0.009087631478905678,
-0.004992528818547726,
0.0004537012137006968,
0.0016043108189478517,
0.05589263513684273,
-0.006418868899345398,
0.002191490726545453,
0.025145849213004112,
0.02251579612493515,
0.03384923189878464,
0.05792762711644173,
0.01561907771974802,
-0.02319994568824768,
-0.018961157649755478,
0.009791484102606773,
-0.02374943345785141,
0.05410643666982651,
-0.0054920148104429245,
0.023248085752129555,
0.005139233078807592,
-0.016191432252526283,
-0.02235010638833046,
0.05118632689118385,
-0.021450763568282127,
0.03768225386738777,
0.05651743337512016,
0.001023691613227129,
-0.030773399397730827,
0.02984478324651718,
-0.04250752553343773,
0.027259066700935364,
-0.01035919040441513,
-0.032166488468647,
-0.0449337363243103,
0.005210841074585915,
0.05210987478494644,
0.03909464552998543,
-0.05226955935359001,
-0.0020567686296999454,
0.005351849365979433,
0.028532689437270164,
0.008578483946621418,
0.013774066232144833,
-0.017080463469028473,
-0.026982218027114868,
0.04675975441932678,
0.028136562556028366,
0.02561774291098118,
0.0017043096013367176,
0.010618236847221851,
-0.012067153118550777,
0.04203799366950989,
-0.004797393921762705,
-0.05966044217348099,
0.054451946169137955,
-0.012114609591662884,
0.02412249892950058,
0.014963656663894653,
-0.0014603066956624389,
0.03510533645749092,
-0.012281409464776516,
0.0440203994512558,
0.037898339331150055,
-0.023497654125094414,
0.0014549099141731858,
-0.02063942514359951,
0.0007208339520730078,
0.015230695717036724,
-0.02902376279234886,
0.004345910623669624,
-0.02823459543287754,
0.0143465306609869,
-0.02600296027958393,
-0.006092865020036697,
-0.002605502726510167,
-0.04956020042300224,
-0.004516724031418562,
-0.023984020575881004,
0.036163490265607834,
0.04090750962495804,
-0.02077450603246689,
-0.04504599794745445,
-0.018588440492749214,
-0.0045096720568835735,
0.001823680242523551,
0.04004225507378578,
0.007539504207670689,
0.007252965122461319,
-0.021259143948554993,
-0.04014355316758156,
-0.0028420104645192623,
0.07711374759674072,
0.026535775512456894,
-0.025895437225699425,
0.0644289180636406,
-0.006898838095366955,
-0.023579003289341927,
0.0021726381964981556,
-0.07433595508337021,
0.04064389690756798,
-0.04623626172542572,
-0.009747118689119816,
0.072148397564888,
-0.015400063246488571,
-0.06554986536502838,
0.007828472182154655,
-0.020405950024724007,
-0.01900399476289749,
-0.00041674001840874553,
-0.022426383569836617,
-0.0019775154069066048,
-0.009397830814123154,
0.07092907279729843,
-0.03852386027574539,
-0.04549602046608925,
0.012954850681126118,
-0.08028838783502579,
-0.016960298642516136,
-0.01862725429236889,
-0.00563253415748477,
0.04776734486222267,
-0.05439112335443497,
-0.06432173401117325,
0.07030629366636276,
0.02905450202524662,
-0.018392106518149376,
-0.006076517049223185,
-0.024662606418132782,
-0.026731327176094055,
-0.036110371351242065,
-0.04581255838274956,
0.02340167574584484,
-0.032920707017183304,
-0.0022208287846297026,
-0.013769662007689476,
0.07232852280139923,
0.021212691441178322,
0.015118354931473732,
-0.004377822391688824,
0.024835046380758286,
0.006030354183167219,
0.014610105194151402,
0.05375318601727486,
-0.0016193994088098407,
0.005078515037894249,
0.015505688264966011,
0.01392395794391632,
0.0006976375007070601,
0.020896730944514275,
-0.08575091511011124,
0.06239542365074158,
-0.0044298055581748486,
0.03312120586633682,
-0.03409745544195175,
0.044715967029333115,
0.010562499053776264,
-0.037939026951789856,
-0.01941615529358387,
0.001836681622080505,
0.039721082895994186,
-0.00670884782448411,
0.013527436181902885,
0.03982587903738022,
0.036500561982393265,
-0.021711932495236397,
-0.016915779560804367,
-0.012777330353856087,
-0.05247560515999794,
0.02742389217019081,
0.00639645429328084,
-0.057597432285547256,
-0.04907276853919029,
0.03861572593450546,
-0.02857031114399433,
0.007620025426149368,
-0.01244343165308237,
-0.016513224691152573,
-0.045706987380981445,
-0.02027956210076809,
-0.021066591143608093,
0.06831797957420349,
-0.004852629266679287,
0.029711250215768814,
0.018980547785758972,
-0.005993311293423176,
0.008332593366503716,
0.008408233523368835,
-0.045841626822948456,
0.04306044429540634,
-0.0028869269881397486,
-0.022891825065016747,
0.013133332133293152,
-0.021295711398124695,
-0.013863908126950264,
-0.006268762517720461,
-0.021518360823392868,
-0.01795298047363758,
0.010230612941086292,
-0.02855626679956913,
0.030092161148786545,
-0.016266845166683197,
-0.03898843750357628,
-0.057520635426044464,
0.02333633229136467,
0.0246236864477396,
-0.06554024666547775,
0.01465648040175438,
0.018063219264149666,
-0.018610671162605286,
0.007889516651630402,
-0.017939209938049316,
-0.004847462754696608,
0.02842673473060131,
-0.018090030178427696,
0.0010694523807615042,
0.007649660110473633,
0.012014721520245075,
-0.014240249991416931,
-0.006393963471055031,
0.041738614439964294,
0.017073649913072586,
-0.004423573613166809,
0.012854652479290962,
-0.0366823785007,
0.0088967839255929,
-0.012452192604541779,
0.06820899248123169,
0.00025862830807454884,
0.03883149102330208,
0.0036993606481701136,
0.0029909517616033554,
0.013892913237214088,
0.0015106688952073455,
0.0298785250633955,
0.03707012161612511,
-0.03856547176837921,
-0.028186459094285965,
-0.014204022474586964,
-0.032174885272979736,
-0.004304336383938789,
0.04576694965362549,
-0.04149007797241211,
-0.012092100456357002,
-0.014479534700512886,
0.038700856268405914,
0.03464893624186516,
0.011425009928643703,
0.01900041289627552,
-0.020578090101480484,
-0.008005206473171711,
-0.00990059319883585,
0.0016414261190220714,
0.05343620851635933,
0.01012928131967783,
0.02037997543811798,
-0.005170295014977455,
0.009853778406977654,
-0.062110207974910736,
-0.048384830355644226,
0.021167121827602386,
0.03437085077166557,
0.014137454330921173,
-0.022957060486078262,
-0.053209252655506134,
0.004871714394539595,
0.038923390209674835,
-0.03563590720295906,
0.05020841583609581,
0.013290020637214184,
0.03899827226996422,
-0.026648912578821182,
-0.0306946262717247,
-0.03475473076105118,
0.029252812266349792,
-0.014159595593810081,
0.024166902527213097,
-0.03678625077009201,
0.004105295520275831,
0.019285598769783974,
-0.021093731746077538,
-0.009313411079347134,
0.02992692030966282,
-0.013019101694226265,
-0.00024408292665611953,
-0.01388894859701395,
0.02771742083132267,
0.0005705339135602117,
-0.0594429075717926,
0.026711387559771538,
-0.0031251548789441586,
-0.007755224127322435,
0.02317807264626026,
-0.03287758678197861,
-0.052471935749053955,
0.011524937115609646,
0.005302131175994873,
0.04281870648264885,
0.004062204156070948,
-0.016123825684189796,
0.06306114047765732,
0.08048209547996521,
0.00496123731136322,
0.04923347011208534,
0.047351326793432236,
-0.07245896011590958,
0.016211796551942825,
-0.010995738208293915,
0.0346052460372448,
0.019354745745658875,
-0.01572386361658573,
-0.05846075713634491,
0.01729104109108448,
-0.044405944645404816,
0.0465078130364418,
-0.07186637073755264,
-0.00257684919051826,
-0.013569985516369343,
-0.020571062341332436,
0.030109556391835213,
0.018468331545591354,
-0.023889653384685516,
-0.020980602130293846,
-0.041343167424201965,
0.016519078984856606,
0.03125133737921715,
-0.025109438225626945,
-0.0040812729857862,
0.021525505930185318,
0.01046228501945734,
0.029000986367464066,
0.02221016399562359,
0.004746248014271259,
-0.03223932906985283,
0.00977171491831541,
-0.015572314150631428,
-0.053448572754859924,
0.038301754742860794,
0.006142658647149801,
-0.02102407068014145,
-0.03330013528466225,
-0.047135088592767715,
-0.03991882875561714,
0.03090689145028591,
-0.015957459807395935,
-0.021144229918718338,
-0.02089935727417469,
-0.03007565252482891,
0.061853159219026566,
0.0016470609698444605,
-0.04306039959192276,
-0.06367991119623184,
0.003726503113284707,
0.00212958175688982,
0.00914717372506857,
-0.031130176037549973,
-0.03532826527953148,
0.01590428128838539,
-0.07766462862491608,
0.042659174650907516,
0.05172210931777954,
-0.056297242641448975,
-0.006332244258373976,
0.04518112540245056,
0.012388392351567745,
0.021229637786746025,
-0.008383233100175858,
0.008199850097298622,
0.026649219915270805,
-0.04743102192878723,
-0.02424449659883976,
0.005097105633467436,
0.01986994408071041,
-0.0431516207754612,
-0.036886852234601974,
-0.006411640904843807,
0.017686478793621063,
0.034554317593574524,
-0.00011096805246779695,
-0.02628069370985031,
-0.0011563737643882632,
0.009537173435091972,
-0.019315361976623535,
0.0037024039775133133,
-0.003790559945628047,
0.03706401586532593,
0.04314962401986122,
-0.023943167179822922,
-0.021100187674164772,
-0.0606229230761528,
-0.054438985884189606,
0.014476964250206947,
0.0017170313512906432,
-0.01724347472190857,
-0.026400987058877945,
0.06471968442201614,
-0.02963758073747158,
-0.03468038886785507,
0.009140011854469776,
0.0018604849465191364,
-0.0035412285942584276,
0.0005604797624982893,
-0.0010735081741586328,
0.005185575224459171,
0.013295291922986507,
-0.01989954523742199,
0.015374805778265,
-0.0354117825627327,
0.006388755049556494,
0.07082479447126389,
0.00215066596865654,
0.04579862952232361,
0.02223948948085308,
-0.02831943705677986,
-0.011101746000349522,
-0.034074269235134125,
-0.016410890966653824,
-0.0007107356213964522,
0.019804008305072784,
0.016706056892871857,
-0.02610868401825428,
0.004935611970722675,
0.05489007756114006,
0.02008596993982792,
-0.033682987093925476,
-0.04981706291437149,
0.031279634684324265,
0.01718374527990818,
-0.017462190240621567,
0.0005624230834655464,
-0.040898289531469345,
0.038025859743356705,
-0.01443968340754509,
0.060199983417987823,
0.023034390062093735,
-0.01391636487096548,
0.05185322463512421,
0.006637632846832275,
-0.00031453551491722465,
0.0039747729897499084,
0.006528792437165976,
-0.025173883885145187,
0.01497106347233057,
-0.0062889158725738525,
-0.03788922727108002,
-0.020460929721593857,
0.04090866073966026,
0.011795184575021267,
-0.0032265023328363895,
0.033850185573101044,
-0.006202498450875282,
-0.003931669518351555,
0.009358054026961327,
-0.007204451598227024,
-0.01357798371464014,
0.07420752942562103,
0.02639687992632389,
-0.0031651705503463745,
0.024418905377388,
-0.019425975158810616,
0.059038516134023666,
0.04689847305417061,
0.01859854720532894,
-0.021516935899853706,
0.04115411266684532,
-0.01461835578083992,
0.007048225030303001,
-0.03115716204047203,
-0.0002122940495610237,
0.14250719547271729,
0.02759799361228943,
0.01989799737930298,
-0.063947394490242,
0.0022488445974886417,
-0.04643481597304344,
0.022707628086209297,
-0.0030451659113168716,
0.013148345053195953,
-0.04010538011789322,
-0.03092656284570694,
0.026972848922014236,
0.0036985892802476883,
-0.01945699192583561,
0.009306990541517735,
0.029649535194039345,
-0.03428871929645538,
-0.04661550000309944,
0.014657012186944485,
0.00048293755389750004,
-0.024382585659623146,
0.04352186247706413,
-0.01578461192548275,
0.02751997672021389,
-0.07018222659826279,
-0.011802823282778263,
-0.040401387959718704,
-0.03499846160411835,
0.01471570786088705,
-0.03880062326788902,
-0.04555434361100197,
0.0071216970682144165,
0.005341567099094391,
-0.02155454270541668,
-0.001402653637342155,
0.015772413462400436,
0.054507914930582047,
0.014466158114373684,
0.026348762214183807,
0.06460843235254288,
-0.013667291961610317,
-0.005649674218147993,
0.023826325312256813,
0.04513179510831833,
-0.04787084832787514,
-0.0025560033973306417,
-0.06274217367172241,
0.056322213262319565,
-0.01738368533551693,
0.0016243171412497759,
0.0007353168912231922,
-0.026476947590708733,
-0.006981394719332457,
-0.02865036204457283,
-0.004365295171737671,
0.008976875804364681,
0.01902979426085949,
-0.009466108866035938,
0.0038269534707069397,
-0.008580098859965801,
0.0019723495934158564,
0.03347358852624893,
-0.03016679175198078,
0.0025964053347706795,
-0.017456209287047386,
-0.03209309279918671,
0.025085987523198128,
0.046876031905412674,
-0.015725579112768173,
-0.02519623562693596,
-0.01348517369478941,
-0.026024172082543373,
0.0226729866117239,
0.022060498595237732,
-0.006549584213644266,
0.023724054917693138,
0.027311278507113457,
-0.01651306077837944,
-0.04779829457402229,
-0.0062021673657000065,
-0.10450038313865662,
0.040250666439533234,
0.012948337011039257,
-0.018016267567873,
-0.018831372261047363,
-0.022349925711750984,
-0.007761990185827017,
0.04392194002866745,
0.00350820180028677,
0.007548768073320389,
0.011757087893784046,
0.042682189494371414,
0.03388788923621178,
-0.008777854964137077,
-0.031450048089027405,
0.030017158016562462,
0.0034948985558003187,
0.012964658439159393,
-0.015633927658200264,
-0.011554854921996593,
0.011616205796599388,
0.020193077623844147,
-0.015413309447467327,
0.046890851110219955,
-0.013798761181533337,
0.012351227924227715,
0.034636013209819794,
0.006997068878263235,
0.013485348783433437,
0.026914197951555252,
0.03446318209171295,
-0.044973988085985184,
0.01431082934141159,
0.007368393242359161,
0.011480744928121567,
-0.01494888961315155,
0.028197340667247772,
-0.013570216484367847,
-0.036598339676856995,
-0.025687508285045624,
-0.007561243139207363,
-0.06121169403195381,
-0.025043131783604622,
-0.032162975519895554,
0.026226460933685303,
0.00005595430047833361,
0.03505293279886246,
-0.025401661172509193,
0.04921966791152954,
0.031231258064508438,
0.010149299167096615,
0.009033402428030968,
0.03790952265262604,
-0.028400525450706482,
-0.013888723216950893,
0.02528037130832672,
0.007407751400023699,
0.006029168143868446,
-0.00030912671354599297,
-0.03830912709236145,
-0.0018023655284196138,
0.007206653244793415,
-0.06627676635980606,
0.013333573006093502,
-0.016352325677871704,
0.0107533885166049,
0.0071020349860191345,
0.0038076029159128666,
0.0012193326838314533,
0.03646647557616234,
-0.006286261137574911,
-0.0036036751698702574,
-0.023634321987628937,
-0.04853052645921707,
-0.008043957874178886,
-0.06605669856071472,
0.0004484163655433804,
-0.019825104624032974,
0.023100556805729866,
0.008041836321353912,
0.005873212590813637,
-0.06517204642295837,
-0.003310678293928504,
0.026251500472426414,
-0.04045036807656288,
-0.0018904403550550342,
0.03627482429146767,
0.012782726436853409,
0.022137867286801338,
0.06352706998586655,
-0.01765168271958828,
-0.009320358745753765,
-0.010593480430543423,
-0.013092689216136932,
-0.06119723245501518,
-0.011790459975600243,
-0.022461602464318275,
0.019028909504413605,
0.017616763710975647,
-0.03804326802492142,
0.00560216186568141,
0.04781004413962364,
-0.08177779614925385,
0.008921349421143532,
-0.006368749774992466,
0.0036254299338907003,
-0.02457023784518242,
-0.056636057794094086,
-0.03608667850494385,
0.02535214275121689,
0.0003108812670689076,
0.07056394219398499,
0.0014405605616047978,
0.002928836503997445,
0.013167552649974823,
-0.026065466925501823,
-0.020582949742674828,
0.016102535650134087,
-0.00017252462566830218,
0.01583128795027733,
0.0491076223552227,
0.006446370854973793,
0.03096397966146469,
0.014702158980071545,
-0.014088382013142109,
0.014097718521952629,
-0.023798063397407532,
0.04778189957141876,
0.01973368227481842,
0.04635591059923172,
-0.001090930076315999,
0.00965395849198103,
-0.0031490917317569256,
-0.04997478798031807,
0.049367472529411316,
0.0010170798050239682,
-0.02320956625044346,
0.012791669927537441,
0.05517929792404175,
-0.03163687512278557,
-0.03748749569058418,
0.08292488008737564,
-0.02789088524878025,
-0.0022958419285714626,
0.028533637523651123,
0.0268482007086277,
0.03211182728409767,
-0.03485267609357834,
-0.012031542137265205,
-0.04394501820206642,
0.010904554277658463,
0.02335798181593418,
0.015984831377863884,
-0.015675637871026993,
0.002971653128042817,
-0.00943195540457964,
-0.019449740648269653,
0.011778095737099648,
0.018595336005091667,
-0.01729632169008255,
-0.08616894483566284,
-0.007358734495937824,
-0.03946954384446144,
0.001049949903972447,
0.010337786749005318,
-0.02046496607363224,
-0.02951919287443161,
0.008794071152806282,
0.007741475012153387,
0.005115250591188669,
-0.021067125722765923,
-0.014776897616684437,
-0.015445106662809849,
-0.06466422975063324,
0.06774555146694183,
0.015477550216019154,
-0.05389309301972389,
-0.008368243463337421,
-0.042423177510499954,
-0.01999874971807003,
0.0465804822742939,
0.06780081987380981,
0.012084423564374447,
-0.02864178828895092,
0.0334390290081501,
0.0018054429674521089,
0.015092316083610058,
-0.04617748782038689,
-0.011721260845661163,
-0.010493394918739796,
0.030204813927412033,
-0.007360828574746847,
0.012187318876385689,
-0.04646396264433861,
0.04218078404664993,
0.025814244523644447,
0.0007132031605578959,
-0.006382755469530821,
-0.014590987004339695,
-0.0552094504237175,
0.011002561077475548,
-0.03352881222963333,
-0.016816750168800354,
0.07424046844244003,
-0.0041154175996780396,
0.022930840030312538,
-0.006899592466652393,
-0.040341414511203766,
-0.028380123898386955,
0.02240210957825184,
-0.01837131939828396,
-0.0019006505608558655,
-0.03679785132408142,
-0.014305202290415764,
0.06282860785722733,
-0.034637730568647385,
-0.036996908485889435,
0.02508791722357273,
-0.020179491490125656,
-0.03634491190314293,
0.03766545653343201,
0.001161169377155602,
0.01799972727894783,
0.02173091471195221,
0.02223038300871849,
-0.0007692661602050066,
0.04467093199491501,
0.02619183622300625,
0.0071161058731377125,
0.015321450307965279,
0.023601075634360313,
-0.0016050091944634914,
0.05540012940764427,
-0.009026385843753815,
0.03813780099153519,
-0.013851032592356205,
0.010745115578174591,
-0.016992127522826195,
-0.023850617930293083,
0.03134174644947052,
-0.020835110917687416,
0.0008497012895531952,
-0.000010270728125760797,
-0.0109963184222579,
0.06163306534290314,
-0.031343284994363785,
0.06653809547424316,
0.002412875182926655,
-0.02563338354229927,
-0.0032333494164049625,
0.01319865882396698,
0.002916349796578288,
0.025069713592529297,
0.0001205723310704343,
-0.0005881108227185905,
-0.02660509943962097,
-0.01814299263060093,
0.014060386456549168,
-0.027815336361527443,
0.03921319171786308,
0.044333476573228836,
-0.02850385010242462,
0.003920596558600664,
-0.049848731607198715,
-0.00551257748156786,
-0.03209535777568817,
0.00847203005105257,
0.04550037160515785,
-0.003546354826539755,
-0.011760746128857136,
0.015102526172995567,
-0.024710150435566902,
0.05894576385617256,
-0.009009310975670815,
-0.013389085419476032,
0.03484896197915077,
0.029641617089509964,
0.026271028444170952,
-0.0027956306003034115
] |
<p>The question is to finde the initial horizontal velocity of the ball at end of the ramp, where it is released.</p>
<p>I know how to do this using gravitational potential energy and kinetic energy ($v=\sqrt{2gh}$), assuming all potential energy is converted into kinetic energy but the question is asking me to find the error in the experiment.</p>
<p>It gives me the values on $y$ as the ramp is lifted up (it is lifted up about 10 cm each time) and the corresponding values of $x^2$. I drew a graph of $x^2$ vs $y$ and found the gradient.</p>
<p>How can I use this to find the experimental initial horizontal velocity?</p>
<p>This sketch shows what the experiment looks like:
<img src="http://i.stack.imgur.com/RfGvy.png" alt="Experiment"></p>
| 8,482 |
[
-0.03831805661320686,
-0.015052100643515587,
-0.012638580054044724,
0.011574585922062397,
0.033910226076841354,
-0.0017193058738484979,
-0.023806771263480186,
-0.04722074046730995,
-0.012144875712692738,
-0.011633032001554966,
0.049185920506715775,
0.05156603083014488,
0.04050347954034805,
0.060340721160173416,
0.05076181888580322,
0.04107867553830147,
-0.02269897796213627,
-0.008542942814528942,
0.01890011690557003,
-0.015853913500905037,
-0.043582841753959656,
-0.005956665612757206,
0.007804339751601219,
0.02776811644434929,
0.003420609747990966,
-0.0203715693205595,
0.06945742666721344,
-0.020773407071828842,
-0.014295575208961964,
0.05848468467593193,
-0.010797390714287758,
-0.0010706232860684395,
0.021759476512670517,
0.004139793571084738,
-0.01396944746375084,
0.048859912902116776,
-0.035876404494047165,
-0.03131483495235443,
-0.03527329862117767,
0.021547209471464157,
-0.02463582530617714,
0.018389949575066566,
-0.00019139217329211533,
0.10681381821632385,
0.001842991216108203,
0.016362136229872704,
0.019859107211232185,
0.005475722253322601,
0.07189011573791504,
-0.03776223585009575,
0.05696733668446541,
0.014653422869741917,
0.009832269512116909,
0.03470643237233162,
-0.006345183588564396,
-0.0016681657871231437,
0.033627647906541824,
0.07246682792901993,
0.004717877600342035,
-0.04990388825535774,
-0.0035330462269484997,
-0.08370420336723328,
-0.027544263750314713,
-0.05192448943853378,
-0.016234830021858215,
0.018819360062479973,
-0.024420587345957756,
-0.011837197467684746,
-0.03762602433562279,
-0.029259387403726578,
0.02230066992342472,
0.010349273681640625,
0.024916872382164,
-0.003302647266536951,
0.028341997414827347,
-0.009547536261379719,
-0.017070889472961426,
0.03104858659207821,
0.004525868687778711,
0.04960131272673607,
0.0001556198112666607,
0.00027389926253817976,
0.07419612258672714,
0.04680776596069336,
0.0021189108956605196,
-0.01281063910573721,
0.03700390085577965,
-0.004637693986296654,
0.04006944224238396,
0.003465660847723484,
-0.004355811048299074,
-0.007938104681670666,
-0.011104630306363106,
-0.022944120690226555,
0.022237222641706467,
0.011351119726896286,
-0.0172408614307642,
0.030533647164702415,
0.01733691804111004,
-0.050004586577415466,
0.011400462128221989,
-0.047785598784685135,
0.037514809519052505,
0.08710424602031708,
-0.025129904970526695,
-0.03344633802771568,
0.0010420834878459573,
-0.005546194035559893,
-0.023374434560537338,
-0.019242459908127785,
-0.02462182193994522,
0.017379265278577805,
-0.0210425928235054,
0.016533169895410538,
0.0007631892221979797,
-0.02606835588812828,
-0.00599052757024765,
0.012830261141061783,
0.04797264188528061,
-0.03010413609445095,
0.031150825321674347,
-0.022376349195837975,
0.04333079978823662,
-0.002579191466793418,
-0.044076595455408096,
0.029774364084005356,
0.011586184613406658,
-0.024861443787813187,
-0.0270841121673584,
0.037080906331539154,
0.016745850443840027,
-0.020814860239624977,
-0.003796202130615711,
-0.004280066583305597,
0.016933567821979523,
0.008825773373246193,
-0.11271630227565765,
-0.07380307465791702,
0.05191783979535103,
0.006784503813832998,
-0.01380537636578083,
-0.07709900289773941,
-0.002893536351621151,
0.053087372332811356,
0.053326912224292755,
-0.003512437455356121,
0.044610653072595596,
0.004168258514255285,
0.027717629447579384,
0.003534669755026698,
0.0176090095192194,
-0.025408891960978508,
0.0020197464618831873,
-0.022232482209801674,
0.00473191449418664,
-0.04132484272122383,
-0.00043450796511024237,
0.0009428151533938944,
-0.007002703845500946,
-0.036113474518060684,
0.0257291067391634,
-0.042547427117824554,
-0.00289978738874197,
0.013955586589872837,
0.00001706273906165734,
0.009401988238096237,
0.08157554268836975,
0.05082370713353157,
-0.006972657982259989,
0.04126735404133797,
-0.00974305346608162,
0.04177544265985489,
-0.009604709222912788,
-0.00445821788161993,
0.045347701758146286,
-0.019367938861250877,
-0.022661548107862473,
-0.022079654037952423,
0.0009383124415762722,
-0.02117479406297207,
-0.02675466239452362,
-0.04189310595393181,
-0.004673297982662916,
0.0012758097145706415,
0.012139862403273582,
0.03778420388698578,
0.02794969454407692,
0.01092204824090004,
0.01371029019355774,
-0.031137896701693535,
-0.025474773719906807,
-0.08169480413198471,
0.020851893350481987,
-0.018697861582040787,
0.024066904559731483,
-0.014319878071546555,
0.005586634855717421,
0.029512831941246986,
-0.037796057760715485,
0.0326337069272995,
0.013204704038798809,
0.026588184759020805,
-0.01533246599137783,
0.019093643873929977,
0.020061293616890907,
0.03424805402755737,
0.04771267995238304,
0.030547332018613815,
0.008358238264918327,
-0.01201243419200182,
0.00846029818058014,
-0.009915069676935673,
-0.023632152006030083,
0.010947134345769882,
-0.048776887357234955,
0.02065698616206646,
-0.0026740669272840023,
-0.004443062469363213,
0.007245568558573723,
0.0019678580574691296,
-0.03154345601797104,
0.07035002112388611,
0.05943090096116066,
0.008556206710636616,
0.014551693573594093,
-0.00403849920257926,
0.006260131020098925,
0.039714958518743515,
0.00800181832164526,
-0.00788990966975689,
-0.04054199904203415,
0.017148373648524284,
0.0019144287798553705,
0.035939570516347885,
-0.018572241067886353,
-0.01416778564453125,
0.038590122014284134,
0.004062237683683634,
0.008186611346900463,
0.01738513633608818,
-0.0179587472230196,
-0.03650190308690071,
0.04630715399980545,
0.04291282221674919,
0.011204366572201252,
0.051686711609363556,
0.028566010296344757,
0.03248888626694679,
0.007357451599091291,
-0.004181108437478542,
0.014829270541667938,
0.000788658217061311,
-0.006271786987781525,
0.00577508145943284,
-0.005962137132883072,
-0.014531128108501434,
0.044467221945524216,
0.011411006562411785,
0.014139480888843536,
0.0620240643620491,
0.02508014254271984,
0.015094359405338764,
-0.042171746492385864,
-0.014589587226510048,
0.035036951303482056,
0.018531298264861107,
-0.009790253825485706,
-0.01147882267832756,
0.02198469638824463,
-0.033887166529893875,
-0.0029510543681681156,
0.003376533044502139,
-0.02489805407822132,
-0.020314930006861687,
-0.01242007501423359,
-0.015082812868058681,
0.012380012311041355,
-0.03038940764963627,
-0.0358988456428051,
-0.00739094614982605,
-0.016265444457530975,
-0.029215406626462936,
-0.008166885003447533,
-0.017218785360455513,
-0.02086050994694233,
0.031107822433114052,
-0.0420953705906868,
-0.0017491600010544062,
0.05275807902216911,
0.029454540461301804,
-0.01540070679038763,
0.06615817546844482,
0.010749390348792076,
-0.015932034701108932,
0.012566741555929184,
-0.02664387971162796,
0.004628982860594988,
-0.0036458312533795834,
0.007290150970220566,
0.04240491986274719,
0.025753997266292572,
0.003089377423748374,
0.05319780856370926,
-0.04949736222624779,
-0.01290829572826624,
-0.029247932136058807,
0.02778894081711769,
0.019325729459524155,
0.0009111382532864809,
0.02829548344016075,
0.0014364346861839294,
0.03453059121966362,
-0.011861634440720081,
-0.06984489411115646,
-0.06535903364419937,
-0.033112555742263794,
-0.01066809706389904,
0.019125917926430702,
-0.02089977078139782,
-0.016881845891475677,
0.09239662438631058,
0.016447406262159348,
0.0032522964756935835,
-0.03927401453256607,
-0.00782768428325653,
0.022072449326515198,
-0.005107062868773937,
-0.006650554947555065,
-0.00019118878117296845,
-0.01492282748222351,
-0.020386647433042526,
-0.02569427713751793,
0.022245556116104126,
0.05043492838740349,
0.038770146667957306,
0.027650674805045128,
0.0016965693794190884,
0.002645328873768449,
0.003930862993001938,
0.03340201824903488,
0.016104454174637794,
-0.034154124557971954,
-0.005614657420665026,
-0.0034647651482373476,
0.06381095200777054,
0.0013093807501718402,
-0.0409715361893177,
0.07210510969161987,
-0.04935367777943611,
-0.03201625123620033,
-0.02143305353820324,
0.02642446756362915,
-0.010432256385684013,
-0.01817449741065502,
0.020599381998181343,
-0.007651704363524914,
0.047118768095970154,
0.008363597095012665,
0.007090258877724409,
0.03392641991376877,
0.004293989855796099,
-0.028369059786200523,
-0.0530020147562027,
-0.012947105802595615,
0.0011604162864387035,
0.09659802913665771,
-0.014895951375365257,
-0.010141665115952492,
-0.02392636425793171,
0.02711072564125061,
-0.018440954387187958,
-0.004275718703866005,
-0.025361955165863037,
-0.0023210877552628517,
-0.030017727985978127,
0.036245331168174744,
-0.006175033748149872,
0.02895171009004116,
0.020625371485948563,
0.06657983362674713,
-0.00393492029979825,
0.021069010719656944,
0.025176024064421654,
0.0002554893144406378,
-0.11559323221445084,
-0.002261908259242773,
-0.03623432666063309,
-0.03725624084472656,
-0.007235469296574593,
-0.030213311314582825,
0.017143409699201584,
-0.04768291860818863,
0.020757198333740234,
0.0028885898645967245,
0.0011430170852690935,
-0.020084651187062263,
0.00440154317766428,
-0.023352425545454025,
-0.022981539368629456,
-0.022625572979450226,
0.01999538578093052,
0.02313629537820816,
-0.013469696044921875,
0.048028431832790375,
0.024210859090089798,
-0.04046867415308952,
-0.015657978132367134,
-0.03552871197462082,
-0.023283516988158226,
0.009480318054556847,
0.030241817235946655,
-0.007853418588638306,
0.052226465195417404,
0.01236504502594471,
0.011416137218475342,
-0.005153533536940813,
0.05908454582095146,
0.020137518644332886,
0.0053492081351578236,
-0.044533759355545044,
-0.01814112812280655,
0.008689820766448975,
-0.009295265190303326,
0.01253028865903616,
-0.005193690303713083,
-0.0029648232739418745,
0.03347842022776604,
0.012662049382925034,
-0.01358311902731657,
0.022979727014899254,
0.04711906984448433,
-0.016965532675385475,
-0.002765081124380231,
-0.03994924947619438,
-0.024301299825310707,
-0.05405900627374649,
-0.036410264670848846,
0.02354947105050087,
-0.012922011315822601,
-0.036449335515499115,
0.000043107276724185795,
0.05553590878844261,
0.05895679444074631,
-0.021648218855261803,
0.021630773320794106,
0.0015314981574192643,
0.04761122912168503,
-0.0010469274129718542,
-0.0031132427975535393,
0.015135916881263256,
0.03640857711434364,
0.020104829221963882,
-0.046691201627254486,
-0.005888423882424831,
-0.04043613374233246,
-0.025989925488829613,
0.012434465810656548,
0.06796726584434509,
-0.045491281896829605,
-0.003978469874709845,
-0.04858110845088959,
-0.012182220816612244,
0.060532983392477036,
-0.030678801238536835,
0.02370668575167656,
-0.01736690104007721,
0.05382964387536049,
-0.007573777809739113,
-0.023774730041623116,
-0.05471700057387352,
-0.00349682429805398,
-0.03178727626800537,
-0.005320606753230095,
-0.043823786079883575,
0.010645284317433834,
0.021046187728643417,
-0.0035540659446269274,
0.019830280914902687,
0.09012452512979507,
-0.01323521789163351,
0.01711198315024376,
0.006196990609169006,
-0.019285300746560097,
-0.04986361041665077,
-0.06681390851736069,
0.0015103102196007967,
-0.014760061167180538,
0.013504019938409328,
0.014637162908911705,
-0.010313941165804863,
-0.0744442492723465,
0.04596748948097229,
0.02262238599359989,
0.03916230425238609,
0.043633587658405304,
-0.020724700763821602,
0.008547812700271606,
0.06753819435834885,
-0.01034817099571228,
0.05864400789141655,
0.01784047856926918,
-0.01887250319123268,
-0.020104175433516502,
-0.005734073463827372,
0.041218291968107224,
-0.015474958345293999,
-0.01889563724398613,
-0.05250570923089981,
0.002052929252386093,
-0.010494137182831764,
0.05744463577866554,
0.0025482953060418367,
0.040951915085315704,
-0.02497527003288269,
-0.05796833336353302,
0.021279189735651016,
0.04423444718122482,
0.048951953649520874,
-0.010053226724267006,
-0.00317601440474391,
-0.012991489842534065,
-0.008452840149402618,
0.013604014180600643,
-0.018213795498013496,
0.008422641083598137,
0.013505742885172367,
0.006857038475573063,
-0.024110091850161552,
0.017946811392903328,
-0.046636663377285004,
-0.025541329756379128,
-0.01149925496429205,
-0.0275083277374506,
0.03645317256450653,
-0.016668926924467087,
0.0053631910122931,
0.006241811905056238,
-0.048966024070978165,
-0.039586421102285385,
0.02454766258597374,
0.035345252603292465,
-0.00382504565641284,
-0.030640337616205215,
-0.008495792746543884,
0.0162667166441679,
0.06776493042707443,
-0.034270189702510834,
-0.04806879907846451,
0.016242630779743195,
-0.03288756310939789,
-0.009162003174424171,
-0.014552121050655842,
-0.021810520440340042,
0.005665200296789408,
-0.029558250680565834,
-0.02210395038127899,
0.04645812511444092,
0.006552436854690313,
0.006786881014704704,
-0.005331485066562891,
-0.008261030539870262,
0.05659026652574539,
0.03156326338648796,
-0.00006869568460388109,
-0.005047155078500509,
0.000969704007729888,
-0.03009500540792942,
0.00409661466255784,
0.03705724701285362,
-0.025743916630744934,
-0.012635982595384121,
0.008593322709202766,
-0.02888849750161171,
0.04075481742620468,
-0.031549230217933655,
-0.006676817312836647,
0.030434085056185722,
0.02093055099248886,
-0.027689389884471893,
-0.03089984506368637,
-0.00006158888572826982,
-0.01571192406117916,
-0.029478998854756355,
-0.009516323916614056,
-0.0308391060680151,
-0.026231931522488594,
-0.03553087264299393,
0.025008978322148323,
-0.001064033480361104,
-0.048490241169929504,
-0.017728112637996674,
0.08247082680463791,
-0.033500541001558304,
-0.031685952097177505,
0.020591918379068375,
-0.017389245331287384,
-0.006589232012629509,
0.010709456168115139,
0.0023495398927479982,
0.028604602441191673,
-0.0077737546525895596,
-0.056662481278181076,
-0.017837760969996452,
-0.054521236568689346,
0.015956604853272438,
0.09633853286504745,
-0.0026126771699637175,
0.08453956246376038,
-0.012999840080738068,
0.006805858574807644,
0.00045422144467011094,
-0.0036308609414845705,
0.01235660258680582,
-0.021184317767620087,
0.0349261499941349,
0.0016683624126017094,
0.0027563157491385937,
-0.01036805845797062,
-0.007725345902144909,
-0.00431057671085,
-0.003099799854680896,
0.013604391366243362,
0.015406517311930656,
-0.0010726404143497348,
0.005393028259277344,
-0.052455220371484756,
-0.033635903149843216,
-0.0018622082425281405,
-0.011446477845311165,
0.05449981614947319,
-0.056526947766542435,
-0.04140794649720192,
0.06393101811408997,
0.03086373582482338,
-0.010348159819841385,
-0.03296021372079849,
0.025098253041505814,
-0.09137287735939026,
0.0010681792628020048,
0.012611621990799904,
0.004875278100371361,
0.018536455929279327,
0.0515521839261055,
0.017131386324763298,
0.009954509325325489,
0.06202905997633934,
-0.0756659135222435,
-0.07039490342140198,
-0.005872034467756748,
-0.025056051090359688,
-0.011195377446711063,
0.03832670673727989,
0.033466413617134094,
-0.04280254244804382,
0.020856427028775215,
-0.044648099690675735,
0.0009830869967117906,
-0.0006368941976688802,
0.025453029200434685,
-0.046568408608436584,
0.07246626913547516,
-0.028332974761724472,
0.006085435394197702,
-0.03381524980068207,
0.005540888756513596,
0.11622954159975052,
0.05582662671804428,
0.013984470628201962,
-0.03676816448569298,
0.025026457384228706,
-0.0024769199080765247,
0.008064357563853264,
-0.001964819384738803,
0.00123285420704633,
-0.006511972285807133,
-0.036027297377586365,
0.004213260021060705,
0.020595332607626915,
-0.03836290165781975,
-0.0006564112263731658,
0.02914964035153389,
-0.03871417045593262,
-0.035109832882881165,
-0.017464889213442802,
0.011675966903567314,
-0.0303047988563776,
0.023833004757761955,
0.019667314365506172,
0.04523906484246254,
-0.03425964340567589,
-0.025988277047872543,
-0.03326400741934776,
-0.046255141496658325,
0.009114176966249943,
-0.006416651885956526,
-0.04967914894223213,
0.03701447695493698,
0.004186068661510944,
-0.04621782526373863,
-0.055468134582042694,
0.020901378244161606,
-0.013977769762277603,
-0.026129906997084618,
0.022075122222304344,
0.03223889321088791,
0.02501998096704483,
0.009306739084422588,
0.001983894733712077,
0.012342793866991997,
-0.05299217253923416,
-0.029966704547405243,
-0.05482655018568039,
0.08972751349210739,
-0.01380537636578083,
0.0019319612765684724,
-0.03173429146409035,
0.021163692697882652,
-0.013897049240767956,
-0.0549250952899456,
0.005646781530231237,
0.00996199157088995,
0.04239936172962189,
-0.020804163068532944,
0.01328035444021225,
-0.018511781468987465,
0.0038520158268511295,
0.045936405658721924,
-0.018754668533802032,
0.024488190189003944,
-0.039797913283109665,
0.018887760117650032,
0.006689476314932108,
0.028269371017813683,
-0.036211006343364716,
-0.045049771666526794,
-0.0018505316693335772,
0.0025157383643090725,
-0.03764704614877701,
-0.0008528550970368087,
-0.019823549315333366,
0.009422652423381805,
0.011550795286893845,
0.019422173500061035,
-0.026158148422837257,
-0.013273132033646107,
-0.04889403656125069,
0.03411145135760307,
-0.005947757512331009,
-0.0010946858674287796,
-0.03803667798638344,
-0.018304184079170227,
0.008831032551825047,
0.050314608961343765,
0.015480749309062958,
-0.004833775572478771,
0.0015117645962163806,
0.03655818849802017,
0.003955489955842495,
0.006329766009002924,
-0.003316449001431465,
0.05272924527525902,
-0.029806947335600853,
0.001837155781686306,
-0.052537400275468826,
0.05688747763633728,
0.016606399789452553,
0.025705847889184952,
0.004489687737077475,
-0.010653994977474213,
-0.0027005686424672604,
0.023925354704260826,
0.013110348954796791,
-0.007397457491606474,
0.002119806595146656,
0.030126437544822693,
0.009482971392571926,
-0.01272883266210556,
-0.022517602890729904,
-0.020547155290842056,
-0.008494623936712742,
-0.013438893482089043,
-0.019137945026159286,
-0.0011132186045870185,
0.01607186533510685,
-0.025309331715106964,
0.027317659929394722,
-0.034945178776979446,
-0.017022669315338135,
-0.016866695135831833,
-0.019264522939920425,
0.005724200047552586,
-0.011573012918233871,
-0.010477929376065731,
0.041223492473363876,
-0.004828633274883032,
0.002727031707763672,
0.0033373208716511726,
0.0040935371071100235,
0.005692730657756329,
-0.022752253338694572,
0.03471793606877327,
-0.018824132159352303,
0.03119528293609619,
-0.027073213830590248,
-0.038046639412641525,
-0.002663516206666827,
-0.00962393544614315,
-0.030579062178730965,
0.05009359121322632,
0.054329752922058105,
0.03509518504142761,
0.018266011029481888,
-0.01862460933625698,
0.02255331352353096,
0.03177594766020775,
-0.022945526987314224,
-0.004086929373443127,
-0.009913665242493153,
-0.049162913113832474,
-0.01277237106114626,
-0.005530457943677902,
0.006706505548208952,
-0.018835611641407013,
0.020298738032579422,
0.030706606805324554,
-0.02263113483786583,
-0.0026217997074127197,
-0.0058556366711854935,
0.024242140352725983,
-0.014571517705917358,
-0.018660394474864006,
0.011348861269652843,
-0.019672563299536705,
0.018502987921237946,
0.049438051879405975,
-0.02364269271492958,
0.012128788977861404,
-0.005439100321382284,
-0.019121969118714333,
-0.11608927696943283,
-0.030037375167012215,
0.03139086812734604,
0.0474696047604084,
0.0469399094581604,
-0.06734172254800797,
0.042267825454473495,
0.051655177026987076,
-0.02653849869966507,
0.0015722207026556134,
-0.013837404549121857,
0.02873445302248001,
0.0006998321041464806,
-0.02290356159210205,
0.017010357230901718,
0.01627887599170208,
0.004104181192815304,
0.06183487921953201,
0.030708391219377518,
0.02191726304590702,
-0.025249160826206207,
-0.0235348641872406,
0.03188014030456543,
0.04175460338592529,
0.002560748951509595,
0.010249192826449871,
0.05774695798754692,
-0.015820376574993134,
-0.00947747565805912,
-0.006979216355830431,
-0.023771390318870544,
0.024461735039949417,
-0.009960279799997807,
0.01109470147639513,
-0.024591749534010887,
0.03987881913781166,
0.015382813289761543,
-0.004582943860441446,
-0.003394876606762409,
0.025451600551605225,
0.00752883730456233,
0.042115386575460434,
-0.027439845725893974,
-0.02362428978085518,
-0.000432261498644948,
-0.01205884013324976,
-0.028818195685744286,
0.06919624656438828,
-0.03699737414717674,
-0.005731766112148762,
0.04086129739880562,
-0.0217084102332592,
-0.0036983925383538008,
-0.04626937955617905,
-0.0077130855061113834,
-0.0018343280535191298,
-0.014046167023479939,
0.044054653495550156,
-0.04824782907962799,
-0.05397162213921547,
-0.004937903489917517,
-0.023531343787908554,
-0.0002615333069115877,
-0.0016394382109865546,
-0.009339619427919388,
-0.04922088235616684,
-0.048929303884506226,
-0.012694958597421646,
-0.023762881755828857,
-0.05073247849941254,
0.030749095603823662,
-0.023324839770793915,
-0.019810833036899567,
0.03839349001646042,
0.007283185143023729,
-0.0004603562119882554,
-0.003261132165789604,
-0.010840498842298985,
-0.016737578436732292,
-0.09087380021810532,
0.042495518922805786,
0.04754215478897095,
-0.06543475389480591,
0.0025698039680719376,
0.008710636757314205,
0.0037758825346827507,
0.0017388240667060018,
0.0596582368016243,
-0.019849330186843872,
-0.043038107454776764,
0.0308539979159832,
0.006998958066105843,
0.0180091243237257,
-0.061545055359601974,
0.0002378696226514876,
-0.0026769686955958605,
0.030962424352765083,
-0.0038671104703098536,
0.014277721755206585,
0.007273768540471792,
0.027858266606926918,
0.03616233542561531,
0.005827839951962233,
0.01424054242670536,
-0.0006017888663336635,
0.01105931680649519,
0.045241475105285645,
0.013137275353074074,
-0.03634534776210785,
0.07387219369411469,
-0.00990618858486414,
0.0029602195136249065,
0.02566254325211048,
-0.026536060497164726,
-0.042130328714847565,
0.026473859325051308,
0.003011244349181652,
-0.0042828721925616264,
-0.004798633977770805,
-0.02431042678654194,
0.004568540025502443,
-0.04851464927196503,
-0.0286042932420969,
0.01927727460861206,
-0.04373065382242203,
-0.006341414526104927,
0.0359782949090004,
0.05101544409990311,
0.032617684453725815,
0.0007615441572852433,
0.0021130701061338186,
-0.0004254779196344316,
-0.005650672595947981,
0.011832370422780514,
-0.006219475530087948,
0.028558380901813507,
0.009448789060115814,
-0.0088363541290164,
0.05024893581867218,
-0.0265834741294384,
0.010078472085297108,
0.06264559179544449,
0.017848599702119827,
-0.048057425767183304,
-0.017927516251802444,
-0.03666294366121292,
-0.028471695259213448,
-0.028453953564167023,
-0.017405103892087936,
-0.03995547071099281,
0.03780706971883774,
0.010000402107834816,
-0.00018256879411637783,
-0.005246012471616268,
0.008420445024967194,
-0.00041344997589476407,
0.02031032368540764,
0.007376756984740496,
0.03409324213862419,
0.021191518753767014,
-0.038975175470113754,
-0.01782645285129547,
0.022128963842988014,
-0.0069265952333807945,
0.015368717722594738,
0.04966447874903679,
0.022282255813479424,
-0.006679307669401169,
-0.006981863174587488,
-0.041930850595235825,
-0.018477752804756165,
-0.0372626855969429,
0.06924903392791748,
0.04356064647436142,
0.001902850577607751,
-0.01695001870393753,
0.005444319918751717,
-0.014301742427051067,
0.04508017376065254,
-0.0635983794927597,
-0.027269409969449043,
-0.012764881365001202,
0.0006484809564426541,
-0.006301529705524445,
0.027044987305998802
] |
<p>White light is always said to contain all the different wavelengths of light. Why, then, can we 'make' new colors simply by adding wavelengths? Is it just a matter of our perception, that, when two colors are added together, they appear to be the wavelength of another color. Or are the waves actually forming into another, differently 'waving' wave, with a different wavelength? </p>
| 8,483 |
[
-0.01808050647377968,
-0.0033704994712024927,
0.014041531831026077,
-0.02473767101764679,
0.041291020810604095,
0.008727865293622017,
-0.03965507075190544,
-0.04336933791637421,
0.005129374563694,
-0.03516293317079544,
0.003407840384170413,
0.04260845482349396,
0.020155148580670357,
0.0230836383998394,
0.026652520522475243,
0.028699684888124466,
0.012115908786654472,
0.006058808881789446,
-0.023501068353652954,
0.002813335508108139,
-0.024983111768960953,
0.021406257525086403,
-0.01039091870188713,
-0.0062277428805828094,
-0.042735569179058075,
0.011930272914469242,
0.048582352697849274,
0.014287608675658703,
0.06211000308394432,
0.04129677638411522,
0.028023332357406616,
-0.023638252168893814,
-0.023006785660982132,
0.06029476225376129,
0.02876777946949005,
-0.030054427683353424,
-0.03956272453069687,
-0.02779044397175312,
-0.017430655658245087,
0.0024467366747558117,
0.0014436711790040135,
-0.010352936573326588,
-0.02479577250778675,
0.006471784319728613,
-0.03177261725068092,
0.016584696248173714,
-0.032898902893066406,
-0.04230046272277832,
0.04718632623553276,
-0.04872598126530647,
0.07233414798974991,
-0.005331685300916433,
0.023950492963194847,
0.022134603932499886,
-0.003875049529597163,
0.040542904287576675,
0.09790707379579544,
0.056821826845407486,
-0.013911783695220947,
0.015076586045324802,
0.023258179426193237,
-0.005367211531847715,
-0.0046764579601585865,
-0.014402482658624649,
-0.03741490840911865,
0.04034348577260971,
-0.00009379521361552179,
0.013276509940624237,
-0.001225844956934452,
0.004310913383960724,
0.015152699314057827,
0.018702760338783264,
0.036435335874557495,
-0.02809741348028183,
-0.014273758977651596,
-0.04031671956181526,
0.0029652423691004515,
0.024586405605077744,
0.02707376517355442,
0.04030289500951767,
0.006461685057729483,
-0.00041914041503332555,
-0.014459121972322464,
-0.008235238492488861,
0.023554986342787743,
-0.026705630123615265,
0.10096202045679092,
-0.022983470931649208,
0.015607931651175022,
0.00027545291231945157,
-0.0005297430907376111,
0.006599766202270985,
0.029046591371297836,
0.0072651696391403675,
-0.010795068927109241,
0.01098671555519104,
-0.02970227785408497,
0.027762332931160927,
0.011482447385787964,
-0.018239807337522507,
0.05165959894657135,
0.0010548055870458484,
0.036875106394290924,
0.05509847775101662,
-0.03995569422841072,
-0.03538803383708,
-0.004341153893619776,
0.022279946133494377,
0.009471974335610867,
-0.006923746317625046,
-0.012808513827621937,
0.006978317629545927,
0.024832988157868385,
-0.007664517033845186,
-0.010028010234236717,
0.00012493605026975274,
0.010130198672413826,
0.014254757203161716,
0.07461784780025482,
0.11016258597373962,
0.010341368615627289,
-0.06203223392367363,
0.034068524837493896,
0.011986345052719116,
-0.05433300510048866,
-0.0024669840931892395,
-0.0344267264008522,
0.002537516178563237,
-0.03949209302663803,
0.020872056484222412,
0.004095627460628748,
-0.04137386009097099,
0.009794754907488823,
0.01216264721006155,
0.004782678093761206,
-0.028880562633275986,
-0.11924704909324646,
-0.06574062258005142,
0.0022647175937891006,
-0.02798421122133732,
-0.031206907704472542,
-0.06335308402776718,
0.021327612921595573,
0.004921176936477423,
0.0934339165687561,
0.007260637823492289,
-0.005728121846914291,
0.0038673372473567724,
0.02707863599061966,
-0.0027901011053472757,
-0.020046517252922058,
-0.03675583377480507,
0.0213208869099617,
-0.048728108406066895,
0.0192718543112278,
-0.07155138999223709,
-0.0025473618879914284,
0.032015059143304825,
0.017945021390914917,
-0.03059915453195572,
0.03364894539117813,
-0.034129898995161057,
0.0020579658448696136,
0.048975344747304916,
0.005913438741117716,
-0.024514315649867058,
0.08527134358882904,
0.017176087945699692,
0.001321701449342072,
0.04726988822221756,
-0.01675531454384327,
0.028075508773326874,
0.01005963422358036,
0.04969927296042442,
-0.01691940240561962,
-0.004591844510287046,
-0.012065116316080093,
-0.012640168890357018,
0.06838171929121017,
-0.01714520901441574,
-0.007308526895940304,
-0.024996981024742126,
0.010995513759553432,
0.031240958720445633,
0.03871966525912285,
0.05476782098412514,
0.013802848756313324,
-0.03407006710767746,
-0.001813923241570592,
-0.09299677610397339,
0.025685342028737068,
-0.042945049703121185,
0.010059191845357418,
0.01070923637598753,
-0.02312740869820118,
0.02412479557096958,
0.030357319861650467,
0.04337313026189804,
-0.030674900859594345,
-0.04541868343949318,
-0.02504606731235981,
0.05281072109937668,
0.014584780670702457,
-0.0038499117363244295,
0.02869640477001667,
0.0826796442270279,
0.0209647249430418,
-0.0008205764461308718,
0.03689973056316376,
-0.054474126547575,
-0.03792264312505722,
0.021302292123436928,
-0.01384198572486639,
0.04782700166106224,
-0.02210356295108795,
0.005639912094920874,
-0.0015705646947026253,
0.003875135211274028,
-0.00846918672323227,
0.031145866960287094,
-0.013013647869229317,
0.058601006865501404,
0.0355471633374691,
-0.03170960396528244,
0.0006471694214269519,
0.05569398030638695,
0.0031456209253519773,
0.007020271848887205,
0.009153520688414574,
-0.06162602826952934,
-0.05423586443066597,
0.0029548797756433487,
0.056862108409404755,
0.013087594881653786,
-0.021052148193120956,
-0.013152661733329296,
-0.02093876712024212,
0.06850492209196091,
0.026056669652462006,
0.06062295660376549,
-0.02666500024497509,
-0.02157130464911461,
0.002119079465046525,
0.045139461755752563,
0.053302280604839325,
0.007935011759400368,
0.03125404566526413,
0.014435254037380219,
0.01133364625275135,
-0.04060066491365433,
-0.014849572442471981,
0.01749453693628311,
-0.010746319778263569,
0.01504293642938137,
-0.016522904857993126,
-0.0043077245354652405,
0.011056000366806984,
-0.038027822971343994,
0.012427646666765213,
0.003213281976059079,
-0.0007695167441852391,
-0.020302848890423775,
-0.009864452295005322,
0.005137916188687086,
-0.0006739748641848564,
0.008377446793019772,
-0.04279782623052597,
-0.0030744748655706644,
0.021306969225406647,
-0.02735992893576622,
0.0144463200122118,
-0.009715104475617409,
-0.007785302586853504,
-0.04547075927257538,
-0.0007999319350346923,
0.015421739779412746,
0.01240765955299139,
0.0836295336484909,
-0.07735607773065567,
-0.05333989858627319,
-0.014501156285405159,
-0.02753615193068981,
-0.013052703812718391,
-0.0044100116938352585,
-0.025535859167575836,
0.043233275413513184,
-0.04237264394760132,
-0.0214556697756052,
0.023870250210165977,
-0.019899776205420494,
-0.0025478897150605917,
-0.006125668529421091,
-0.01168522983789444,
-0.06608007848262787,
-0.018493812531232834,
-0.03481961041688919,
0.04662197455763817,
0.02247048355638981,
0.00683639757335186,
0.015795625746250153,
-0.008855031803250313,
-0.06824629008769989,
-0.00007548382563982159,
-0.030711306259036064,
-0.044141996651887894,
-0.014274872839450836,
-0.0014794360613450408,
0.026088977232575417,
-0.05051504448056221,
-0.002948288805782795,
0.0007543088868260384,
-0.04038451984524727,
0.037190500646829605,
0.0019558006897568703,
-0.03856515884399414,
0.013473845086991787,
-0.025397930294275284,
0.057594411075115204,
-0.007330649066716433,
-0.00014544678560923785,
0.046370021998882294,
0.02023283764719963,
-0.03183839097619057,
-0.029404152184724808,
-0.0101166358217597,
-0.01055885385721922,
-0.03372527286410332,
0.047529108822345734,
0.055175844579935074,
-0.012413100339472294,
0.05420500040054321,
0.015720387920737267,
-0.0023170062340795994,
0.045691315084695816,
0.02662150375545025,
-0.023372268304228783,
0.02871018461883068,
0.010279062204062939,
-0.0038649130146950483,
0.011230159550905228,
0.029348690062761307,
-0.020471852272748947,
0.008642861619591713,
0.008387302048504353,
0.042346008121967316,
0.04512648656964302,
0.008075714111328125,
0.05462580546736717,
0.03913277015089989,
0.031142666935920715,
-0.035106971859931946,
0.05823035538196564,
-0.006575434468686581,
0.019294757395982742,
0.00023966545995790511,
0.010845562443137169,
0.026151716709136963,
-0.01024886779487133,
-0.010092806071043015,
0.006790244951844215,
0.02124042622745037,
-0.030052952468395233,
0.012753688730299473,
0.010453746654093266,
-0.0015557052101939917,
0.03264380246400833,
0.0043436624109745026,
0.008347774855792522,
0.05644575506448746,
0.03217436745762825,
0.014937237836420536,
0.01024097204208374,
-0.017488207668066025,
-0.0032740498427301645,
-0.04820328950881958,
-0.022696642205119133,
0.017496688291430473,
0.024103298783302307,
-0.002258855849504471,
0.08884446322917938,
0.006046931259334087,
0.040223173797130585,
0.014237397350370884,
-0.012165923602879047,
-0.07948695868253708,
0.004010148346424103,
-0.01972219906747341,
0.02275903895497322,
-0.05535555258393288,
-0.045984894037246704,
-0.0010699346894398332,
-0.0249162670224905,
-0.06479154527187347,
-0.04698347672820091,
-0.045491624623537064,
-0.0419926680624485,
0.013978580944240093,
-0.011327387765049934,
-0.031317491084337234,
-0.009251081384718418,
0.018238969147205353,
0.017705071717500687,
0.014014668762683868,
0.0001789447123883292,
0.0221176166087389,
-0.021467959508299828,
0.0001871707645477727,
-0.020891383290290833,
0.01802774891257286,
0.026468593627214432,
0.004728328436613083,
0.03787553310394287,
0.049682896584272385,
-0.05011716112494469,
0.019257841631770134,
0.02567015402019024,
0.05265092849731445,
0.000675432849675417,
-0.010103314183652401,
-0.018795298412442207,
-0.0601397268474102,
0.01025937870144844,
-0.021817075088620186,
0.0467391200363636,
-0.031068693846464157,
0.014798606745898724,
0.025316208600997925,
-0.017322584986686707,
-0.016449451446533203,
0.034798309206962585,
0.029975537210702896,
-0.013304394669830799,
-0.021924132481217384,
-0.02230822481215,
0.016983238980174065,
-0.02834056131541729,
-0.006117456592619419,
0.019949093461036682,
-0.015342989936470985,
0.011642000637948513,
0.006740771234035492,
0.025454184040427208,
-0.004117305856198072,
-0.017525920644402504,
-0.0193345807492733,
-0.04285423085093498,
-0.02412060834467411,
-0.010499165393412113,
-0.013990777544677258,
-0.02204040251672268,
0.05390005186200142,
0.023776540532708168,
-0.009377063252031803,
-0.0359451100230217,
-0.08527588099241257,
0.03453981876373291,
0.036868125200271606,
0.012064114212989807,
-0.017368845641613007,
-0.0014907310251146555,
-0.06949993968009949,
-0.040490247309207916,
0.021180277690291405,
-0.017032861709594727,
0.02728728950023651,
-0.040411513298749924,
-0.013456628657877445,
-0.013915405608713627,
-0.006835084408521652,
0.015751782804727554,
0.024289116263389587,
-0.011148557998239994,
0.0059640672989189625,
-0.00834091380238533,
0.01902453787624836,
-0.0064923688769340515,
0.04527130350470543,
0.039503782987594604,
0.05760932341217995,
-0.0006230345461517572,
-0.025585900992155075,
-0.005859460681676865,
-0.0017125318991020322,
-0.022743970155715942,
-0.06081942468881607,
0.004112548194825649,
0.022986795753240585,
-0.015524853020906448,
0.05732374265789986,
-0.02731960453093052,
-0.03574587404727936,
0.01627950742840767,
0.027278965339064598,
-0.001350471400655806,
0.0159281175583601,
-0.012070096097886562,
0.04542901739478111,
0.03614148125052452,
0.01737884059548378,
0.05544556304812431,
0.04636918753385544,
-0.03670914098620415,
0.003906761761754751,
-0.009234051220119,
0.06075313687324524,
-0.02555837295949459,
-0.0006772304768674076,
0.0018207088578492403,
-0.00995656754821539,
-0.00004637572783394717,
0.07143761962652206,
0.0052012181840837,
-0.041482143104076385,
-0.0037087430246174335,
-0.061422478407621384,
-0.011816899292171001,
0.010260176844894886,
0.011438938789069653,
-0.0171269029378891,
-0.002941740909591317,
0.04226714000105858,
0.01880238763988018,
-0.004864637274295092,
0.03179667145013809,
0.012223951518535614,
-0.008420147933065891,
0.0248601995408535,
0.019445952028036118,
0.029197772964835167,
-0.045232027769088745,
0.01590880937874317,
0.003571598557755351,
-0.013272300362586975,
0.04131315276026726,
-0.006258892361074686,
0.02963452786207199,
0.02050589956343174,
-0.08847009390592575,
-0.02696736715734005,
-0.026151131838560104,
-0.03783802315592766,
0.03492952510714531,
-0.043346237391233444,
0.060839373618364334,
0.033235665410757065,
-0.01133435033261776,
-0.06818642467260361,
-0.054091956466436386,
0.005289583466947079,
0.029849650338292122,
0.0018554501002654433,
-0.018494147807359695,
0.057628922164440155,
-0.036245591938495636,
-0.01234793197363615,
-0.027222899720072746,
0.03002196177840233,
-0.005597863346338272,
-0.003110085614025593,
0.011492755264043808,
0.0178554467856884,
0.013329189270734787,
0.011818149127066135,
-0.0332832969725132,
-0.014087557792663574,
-0.04191361740231514,
0.008011934347450733,
-0.008025151677429676,
0.026052266359329224,
-0.017230020835995674,
-0.03545864298939705,
0.003611438674852252,
-0.003135866019874811,
0.02219521999359131,
-0.04000719264149666,
-0.025714710354804993,
0.031086014583706856,
0.046684443950653076,
-0.023855220526456833,
-0.04922810196876526,
0.013779270462691784,
-0.0187984611839056,
-0.002093855058774352,
0.026384752243757248,
0.0011223034234717488,
-0.02616368606686592,
-0.03310747444629669,
0.02109997160732746,
0.0031069726683199406,
0.031955208629369736,
-0.026181142777204514,
0.060394395142793655,
-0.02224777638912201,
-0.01412997581064701,
0.007848100736737251,
-0.03623141348361969,
0.0013697129907086492,
-0.02580600418150425,
0.001635069027543068,
0.0021084833424538374,
0.0279031153768301,
-0.03264967352151871,
-0.018808525055646896,
0.01109115220606327,
0.0031539404299110174,
0.05503096804022789,
-0.05711929500102997,
0.047270938754081726,
0.03177143260836601,
-0.003614055225625634,
-0.017633846029639244,
-0.012908288277685642,
-0.009740972891449928,
0.003408726304769516,
-0.04464744031429291,
0.04314301908016205,
-0.008247047662734985,
-0.014012631960213184,
-0.01246986910700798,
0.03691387176513672,
0.02517884038388729,
-0.0025347915943711996,
0.04222346842288971,
0.019092988222837448,
-0.03026110678911209,
-0.0033674684818834066,
-0.06836666911840439,
0.014878547750413418,
-0.018009837716817856,
0.0029308348894119263,
0.024119310081005096,
-0.013961562886834145,
0.03666122257709503,
-0.012906904332339764,
-0.00905892625451088,
-0.02419181726872921,
-0.0352775938808918,
-0.005680538713932037,
0.002723468467593193,
-0.02642902359366417,
0.047935426235198975,
0.0035089689772576094,
-0.04716220125555992,
-0.0018784700660035014,
0.03168994560837746,
-0.006927387788891792,
-0.02583939954638481,
-0.06879967451095581,
-0.07649021595716476,
-0.04836267605423927,
-0.005800662562251091,
0.0454731322824955,
-0.006467853672802448,
-0.03667571395635605,
0.000019410181266721338,
-0.016016900539398193,
0.008267588913440704,
-0.008988285437226295,
0.03131910786032677,
-0.00963581632822752,
0.0033165556378662586,
0.013390923850238323,
0.0551702082157135,
-0.01742870733141899,
0.016273358836770058,
0.09940271824598312,
0.05260051041841507,
0.0040026092901825905,
-0.07013332098722458,
0.01465101633220911,
-0.06103042885661125,
-0.004803646821528673,
-0.016800573095679283,
0.030243966728448868,
-0.022831333801150322,
0.05923805758357048,
-0.04030214622616768,
0.06330176442861557,
-0.00822004396468401,
0.008383546024560928,
0.02712664008140564,
-0.020010145381093025,
-0.03495369851589203,
-0.008146058768033981,
-0.01625010371208191,
0.0070077646523714066,
0.04809865728020668,
-0.062111712992191315,
-0.019555771723389626,
-0.02754831314086914,
-0.009187066927552223,
-0.00047677429392933846,
-0.02316715382039547,
0.042022693902254105,
0.019288161769509315,
-0.04463436082005501,
-0.008041869848966599,
0.035516656935214996,
-0.0012781125260517001,
-0.0584581233561039,
0.0332186259329319,
0.05421287193894386,
-0.027157731354236603,
0.03133672848343849,
-0.0017421793891116977,
0.04935614764690399,
-0.008725135587155819,
-0.021753931418061256,
0.02831185795366764,
-0.029403524473309517,
0.0066957296803593636,
-0.008131150156259537,
0.0340302512049675,
-0.022509772330522537,
0.008019782602787018,
-0.017591919749975204,
-0.00287928176112473,
-0.008855286054313183,
-0.04424964264035225,
-0.015103382058441639,
-0.006910270545631647,
0.037926506251096725,
-0.005288311280310154,
-0.016983428969979286,
0.004766462836414576,
0.011190325021743774,
-0.009392287582159042,
0.03144179657101631,
0.015626130625605583,
0.0020773375872522593,
-0.011373610235750675,
0.031144756823778152,
0.00838709156960249,
0.03567895665764809,
-0.03830453380942345,
-0.05920710787177086,
-0.0029240876901894808,
-0.037401288747787476,
-0.041829850524663925,
0.0030453528743237257,
0.03272248059511185,
0.029527533799409866,
-0.03041529841721058,
-0.02883259765803814,
-0.025389857590198517,
-0.07205552607774734,
0.008417211472988129,
0.019244275987148285,
-0.02956676110625267,
-0.00020169564231764525,
0.003573731752112508,
0.05336500704288483,
0.043292418122291565,
-0.010070191696286201,
0.023220540955662727,
-0.004183674696832895,
0.0029791523702442646,
0.045608967542648315,
-0.023236481472849846,
0.008036848157644272,
0.026556864380836487,
-0.010548723861575127,
-0.016050178557634354,
-0.00940136518329382,
0.00911486241966486,
-0.0029732387047261,
0.039060141891241074,
0.017111169174313545,
0.030796971172094345,
-0.023581286892294884,
-0.011880949139595032,
0.0036614728160202503,
-0.02052682265639305,
0.017332235351204872,
-0.013167074881494045,
0.012201284989714622,
0.00026776076992973685,
-0.048431750386953354,
0.0017285047797486186,
-0.009115454740822315,
0.01493037212640047,
0.025961024686694145,
-0.0036028774920850992,
0.00768716586753726,
0.0035223765298724174,
0.039398327469825745,
-0.03434053063392639,
-0.03264192119240761,
-0.048180095851421356,
0.019688453525304794,
-0.01850464567542076,
-0.03916161507368088,
-0.004937267396599054,
0.03151804953813553,
-0.015814004465937614,
-0.031748805195093155,
0.04664812982082367,
0.06240306422114372,
-0.004801233299076557,
-0.0023054745979607105,
0.015950409695506096,
-0.011053934693336487,
0.027097566053271294,
0.003717681858688593,
-0.055387672036886215,
0.04574541375041008,
-0.041940588504076004,
-0.029283275827765465,
0.009826945140957832,
-0.022793009877204895,
0.04172331094741821,
0.0402289517223835,
-0.0146676916629076,
0.010452033020555973,
0.029613805934786797,
0.003640408394858241,
-0.025098828598856926,
0.0177321657538414,
-0.0006467622588388622,
0.006983370985835791,
0.00046175188617780805,
0.0022758147679269314,
-0.013696681708097458,
-0.013758023269474506,
0.04800994694232941,
-0.006493543274700642,
0.016498077660799026,
-0.030507536605000496,
0.005321783479303122,
-0.031912680715322495,
0.028325829654932022,
0.030970484018325806,
-0.017964934930205345,
-0.02007424086332321,
0.007718767039477825,
-0.0024339768569916487,
0.052697788923978806,
-0.00035320650204084814,
-0.01915852725505829,
-0.10852845013141632,
-0.0011041403049603105,
0.01966051198542118,
-0.025985686108469963,
0.024970846250653267,
-0.024053936824202538,
0.02585398592054844,
0.024383876472711563,
-0.09644992649555206,
-0.0006881979061290622,
-0.041486963629722595,
0.0001483011874370277,
-0.010459095239639282,
0.027176884934306145,
-0.04069766029715538,
0.023046500980854034,
0.04194219037890434,
0.07046052813529968,
-0.0008134401286952198,
-0.0064460807479918,
-0.024640707299113274,
-0.01151004433631897,
-0.013833269476890564,
0.02185264229774475,
-0.004030165728181601,
-0.0027205608785152435,
0.05603864789009094,
-0.008913438767194748,
-0.02423425391316414,
0.0029819272458553314,
-0.006975391414016485,
0.018013933673501015,
-0.016947967931628227,
-0.005449790973216295,
0.004947942215949297,
-0.00528758903965354,
-0.032852958887815475,
0.0026917376089841127,
-0.04630843177437782,
0.039769452065229416,
0.05190151184797287,
0.0013735848478972912,
0.00542478496208787,
-0.006234745495021343,
0.02682088315486908,
-0.06394707411527634,
-0.04452527314424515,
0.01124485395848751,
-0.01584818959236145,
0.009915819391608238,
0.017611201852560043,
0.03599962219595909,
0.03267011046409607,
-0.01432590652257204,
0.003265818115323782,
-0.041981473565101624,
-0.026680396869778633,
-0.023321926593780518,
0.03622124344110489,
0.0003102583868894726,
0.01660756580531597,
0.004703201819211245,
-0.01878475397825241,
0.013203202746808529,
-0.029000751674175262,
0.022672023624181747,
-0.0028721154667437077,
0.006337170489132404,
0.022974686697125435,
0.0003815688833128661,
0.014754501171410084,
-0.0020362157374620438,
-0.04782732203602791,
0.030763380229473114,
-0.027713751420378685,
0.015004967339336872,
-0.019365739077329636,
-0.0744425356388092,
-0.04463127255439758,
-0.0111845089122653,
0.07049838453531265,
0.016851477324962616,
-0.008218173868954182,
-0.06238000839948654,
-0.007269764319062233,
-0.008894695900380611,
0.05659322068095207,
0.07379777729511261,
-0.0168050155043602,
-0.02267286367714405,
-0.02669977955520153,
0.03864476457238197,
0.05367753654718399,
-0.04135121777653694,
-0.006793709937483072,
0.0121522918343544,
-0.016339121386408806,
-0.05161752179265022,
0.0056923129595816135,
-0.0270859207957983,
0.015810424461960793,
0.008669928647577763,
-0.01760839857161045,
0.015971796587109566,
-0.013506084680557251,
-0.029643375426530838,
0.0687825009226799,
-0.008478842675685883,
-0.03580553084611893,
0.07098791003227234,
0.0033932847436517477,
0.02128874510526657,
0.010655292309820652,
-0.02598847635090351,
-0.049274880439043045,
0.016324255615472794,
-0.02069447748363018,
0.011593963950872421,
-0.002413224196061492,
0.01800352893769741,
0.03442353010177612,
-0.022241340950131416,
0.016463302075862885,
0.028603915125131607,
-0.018352508544921875,
-0.0162169449031353,
0.0747792199254036,
-0.00686741853132844,
0.014752366580069065,
-0.009052080102264881,
-0.03203585371375084,
-0.01861242577433586,
0.025265954434871674,
-0.011983746662735939,
0.0336000882089138,
-0.003659291658550501,
0.02200215682387352,
0.041693512350320816,
0.022982370108366013,
-0.003944892901927233,
-0.006250157952308655,
-0.0005967426695860922,
0.028288673609495163,
-0.03571480140089989,
0.0005060528055764735,
-0.0021304881665855646,
0.0014339188346639276,
0.024069277569651604,
0.026802651584148407,
-0.038887377828359604,
0.09494924545288086,
-0.039249397814273834,
0.022385889664292336,
-0.011079173535108566,
0.016471441835165024,
-0.008518009446561337,
-0.0037939369212836027,
-0.007375967223197222,
0.04444081708788872,
0.005086421500891447,
-0.011792503297328949,
-0.04355042427778244,
-0.0007325728656724095,
0.021735193207859993,
-0.042641401290893555,
0.04045568034052849,
-0.011890697292983532,
-0.019033590331673622,
0.008619449101388454,
0.01156814955174923,
-0.004609681665897369,
-0.020039625465869904,
0.018028372898697853,
0.024267345666885376,
-0.003331417217850685,
0.010106275789439678,
-0.00575633067637682,
-0.04146712273359299,
0.04111991822719574,
-0.04135636240243912,
0.015060704201459885,
-0.009178496897220612,
0.010451162233948708,
-0.039709996432065964,
-0.026051083579659462
] |
<p>For the same speed and inclination, is the physics acting on the body equivalent? Lets assume the person keeps pace with something that moves perfectly uniformly.</p>
| 8,484 |
[
-0.015045145526528358,
-0.04679667577147484,
-0.027534842491149902,
-0.005479864310473204,
0.033637527376413345,
-0.0035334862768650055,
-0.01965588890016079,
0.004162945318967104,
-0.03626587986946106,
-0.006198178976774216,
-0.006616209167987108,
0.02629587985575199,
0.04976033791899681,
0.021221624687314034,
0.031916629523038864,
-0.0013412265107035637,
-0.011944659985601902,
0.032310567796230316,
-0.017685020342469215,
-0.04437580332159996,
-0.004833873361349106,
0.00384005275554955,
0.03917919844388962,
0.0032419010531157255,
-0.057150065898895264,
-0.0024417403619736433,
0.043148089200258255,
-0.052536480128765106,
-0.016103846952319145,
0.02684769406914711,
-0.02183198183774948,
0.0189363993704319,
-0.0008476165239699185,
0.03464978560805321,
0.024164045229554176,
0.01708449423313141,
-0.05712813884019852,
0.0024099969305098057,
-0.021563410758972168,
0.03981613367795944,
-0.048714570701122284,
-0.0059945411048829556,
0.003054333385080099,
0.05478627234697342,
-0.015604265965521336,
0.026059672236442566,
0.010633130557835102,
0.010974627919495106,
0.04744503274559975,
-0.03968539088964462,
0.08233507722616196,
0.006515925284475088,
0.04180740565061569,
0.01590152457356453,
0.011888837441802025,
-0.017052175477147102,
0.09120993316173553,
0.029140530154109,
0.010714598931372166,
-0.04196430370211601,
-0.01483834907412529,
-0.03660190477967262,
-0.019405126571655273,
-0.012366767972707748,
-0.017316048964858055,
0.016245603561401367,
-0.02750527113676071,
-0.043216314166784286,
0.04283386096358299,
0.017357459291815758,
0.01440439559519291,
0.04568662866950035,
0.04628612846136093,
-0.007898764684796333,
0.030209001153707504,
-0.014771653339266777,
0.027177201583981514,
0.014890765771269798,
0.017009802162647247,
0.019856061786413193,
-0.0256382804363966,
-0.030653664842247963,
0.053791921585798264,
0.06895861029624939,
0.013677411712706089,
-0.03190739452838898,
0.03423115611076355,
0.0012764810817316175,
0.02181161381304264,
0.04317252337932587,
0.013581535778939724,
0.02159990556538105,
0.009844985790550709,
-0.02274264581501484,
0.009962199255824089,
0.011177749373018742,
-0.0018543722108006477,
0.019564136862754822,
0.03175007924437523,
-0.026977460831403732,
0.011525478214025497,
-0.015892473980784416,
-0.011729223653674126,
0.05932815745472908,
0.04379112645983696,
-0.015216219238936901,
-0.02518792636692524,
0.0016960380598902702,
-0.033217888325452805,
0.006487446371465921,
-0.01359946746379137,
-0.018394896760582924,
-0.015610609203577042,
0.014831364154815674,
0.027254797518253326,
0.01357968244701624,
-0.021490806713700294,
-0.013671871274709702,
0.05713431537151337,
0.05651530623435974,
0.048407889902591705,
-0.019246963784098625,
0.017416445538401604,
-0.011658700183033943,
-0.015576174482703209,
0.03773244470357895,
0.007565272506326437,
-0.037935443222522736,
-0.032983601093292236,
-0.012540506199002266,
0.004498620983213186,
-0.005614646710455418,
0.01192439440637827,
0.010867330245673656,
0.031349651515483856,
0.004328316543251276,
-0.07269920408725739,
-0.054758358746767044,
0.03150930255651474,
0.020172590389847755,
0.0029091546311974525,
-0.10267911851406097,
-0.0059207165613770485,
0.014082442969083786,
0.051051974296569824,
0.005614854861050844,
0.028574081137776375,
0.03373651206493378,
0.014179637655615807,
0.007094317581504583,
0.007537116762250662,
-0.00537002133205533,
-0.02561412751674652,
-0.05286256596446037,
0.026411037892103195,
-0.07476527988910675,
0.007246918510645628,
0.05238836258649826,
0.0052797324024140835,
-0.03423064202070236,
0.014567743055522442,
-0.029558571055531502,
0.013854105025529861,
0.011246297508478165,
-0.015636038035154343,
-0.0006447876221500337,
0.045237068086862564,
-0.004912379663437605,
-0.019315050914883614,
-0.012147517874836922,
0.05838100239634514,
0.030176110565662384,
0.006510504055768251,
0.028964929282665253,
0.07483868300914764,
-0.060927774757146835,
-0.02238832786679268,
-0.003984399139881134,
-0.008414389565587044,
0.003952693194150925,
-0.04034370183944702,
-0.07043241709470749,
0.009814009070396423,
0.00872264988720417,
-0.014573568478226662,
0.02064037322998047,
0.000738704577088356,
0.01276271790266037,
-0.001973853912204504,
-0.030283354222774506,
0.00133183179423213,
-0.06082023307681084,
0.03647066280245781,
-0.003736906684935093,
0.0030587539076805115,
0.03448791429400444,
0.03175317123532295,
0.043968331068754196,
-0.05767017602920532,
-0.03289584815502167,
0.00344008463434875,
0.03693217411637306,
0.01249177847057581,
0.003086983459070325,
-0.0017714152345433831,
0.07203344255685806,
0.02790101058781147,
0.01725800894200802,
0.012949962168931961,
-0.004465720150619745,
-0.034744225442409515,
0.0063011543825268745,
-0.07017066329717636,
0.06371443718671799,
0.008996552787721157,
0.02789274975657463,
-0.005356290377676487,
-0.013328028842806816,
-0.018933651968836784,
0.05608581006526947,
-0.037105076014995575,
0.08445587754249573,
0.03776712715625763,
-0.030956754460930824,
-0.014997266232967377,
0.035899825394153595,
0.020088080316781998,
-0.023829350247979164,
0.003893199609592557,
-0.0674196183681488,
-0.015454253181815147,
-0.010460536926984787,
0.018688365817070007,
0.024597328156232834,
-0.023933211341500282,
0.013751165010035038,
0.033516086637973785,
0.06497244536876678,
0.03517598286271095,
0.022127702832221985,
0.010298257693648338,
-0.04723702371120453,
0.04195031896233559,
0.0006846936885267496,
0.029126964509487152,
-0.011721177957952023,
0.0028054395224899054,
0.03542432561516762,
-0.031966377049684525,
-0.013082779943943024,
-0.02848813869059086,
0.0021996013820171356,
0.04250074550509453,
0.03778190165758133,
-0.014403073117136955,
-0.045607976615428925,
0.024550404399633408,
-0.007931139320135117,
0.050798602402210236,
0.027249818667769432,
0.008817456662654877,
-0.021791143342852592,
-0.06606713682413101,
-0.029069460928440094,
0.025284329429268837,
0.03245443478226662,
0.0022281098645180464,
-0.05631488561630249,
0.03832711651921272,
-0.007775133475661278,
-0.000004548671313386876,
-0.015802884474396706,
0.010308572091162205,
0.008619861677289009,
-0.00970891211181879,
0.02007925510406494,
0.028061268851161003,
0.02953181602060795,
-0.030978020280599594,
-0.00450214883312583,
0.02271629124879837,
-0.02067195065319538,
-0.037769004702568054,
0.022251678630709648,
-0.05854543298482895,
0.013198397122323513,
-0.0013263728469610214,
-0.057826608419418335,
0.04035181179642677,
0.01647810824215412,
0.003061006311327219,
0.06111006811261177,
-0.008833426982164383,
-0.0569247268140316,
0.013573779724538326,
-0.023081811144948006,
-0.04498337581753731,
-0.01685391366481781,
0.034551411867141724,
0.052796028554439545,
-0.018606947734951973,
-0.024252446368336678,
0.009065911173820496,
-0.0550692193210125,
-0.032553452998399734,
0.009686076082289219,
-0.01387413777410984,
0.0357418991625309,
0.003463965142145753,
0.018755294382572174,
0.04068171605467796,
-0.06028752028942108,
-0.022107083350419998,
-0.05970759317278862,
-0.06179185211658478,
0.04049044847488403,
0.008361001498997211,
0.03746945783495903,
0.00940501969307661,
-0.0224065650254488,
0.05433288589119911,
0.032274819910526276,
-0.05589697137475014,
-0.0315728597342968,
-0.0058717927895486355,
0.00918596051633358,
-0.0014906693249940872,
0.003085881471633911,
0.06352774798870087,
-0.006231153849512339,
0.018125684931874275,
0.0428483746945858,
-0.010866136290133,
0.041952721774578094,
0.0013045076048001647,
0.008124156855046749,
-0.022927839308977127,
0.02803337387740612,
0.032980263233184814,
-0.007685308810323477,
0.015610318630933762,
-0.03936389833688736,
0.005861504469066858,
0.011872676201164722,
0.07522490620613098,
0.0036291489377617836,
-0.030932245776057243,
0.07062380015850067,
-0.0020647861529141665,
-0.0008329832344315946,
-0.032138895243406296,
0.03818964958190918,
0.012859665788710117,
0.008215440437197685,
-0.0345333106815815,
0.045348331332206726,
0.03690728545188904,
-0.012314753606915474,
0.0075481184758245945,
0.03588355332612991,
0.02724495902657509,
-0.010893958620727062,
-0.05671579763293266,
0.0042448812164366245,
0.016924016177654266,
0.017151635140180588,
-0.06156594678759575,
-0.03803008794784546,
0.030450526624917984,
0.0025216662324965,
0.02111135609447956,
0.020486975088715553,
-0.05458735302090645,
0.02819581888616085,
-0.08544198423624039,
0.005378278903663158,
0.009108607657253742,
-0.0026679399888962507,
-0.025447538122534752,
0.039457764476537704,
0.014354193583130836,
0.030920984223484993,
0.0083230622112751,
0.015468448400497437,
-0.06902062147855759,
0.011518287472426891,
-0.04642440378665924,
-0.02428101748228073,
-0.0019234290812164545,
0.011199908331036568,
-0.008890490047633648,
-0.052849285304546356,
-0.0025701848790049553,
-0.011625160463154316,
-0.010117773897945881,
-0.039789069443941116,
0.002631991868838668,
-0.0050617787055671215,
-0.06323474645614624,
0.009260021150112152,
0.014573984779417515,
0.005653697066009045,
-0.05382293090224266,
0.04318232089281082,
0.03092486597597599,
-0.01280210167169571,
-0.029964083805680275,
-0.042360853403806686,
0.03764504939317703,
-0.03074130043387413,
0.030214346945285797,
0.030898012220859528,
0.0009448535274714231,
0.005962601397186518,
0.0262617040425539,
-0.02884942665696144,
0.030857155099511147,
0.00867797527462244,
-0.03372329846024513,
-0.06739796698093414,
-0.04717206209897995,
-0.03725067898631096,
0.0002549735363572836,
0.014236790128052235,
0.0036439821124076843,
-0.005318149458616972,
0.030612997710704803,
0.02073424682021141,
-0.0007234608638100326,
0.060856111347675323,
0.061866410076618195,
0.011109966784715652,
-0.04673971235752106,
-0.043613698333501816,
-0.03081451915204525,
0.0044902111403644085,
0.0021187318488955498,
0.04431213438510895,
-0.012085623107850552,
-0.03316204622387886,
0.01318204402923584,
0.03437090665102005,
0.012248145416378975,
-0.012234807014465332,
-0.0035853690933436155,
-0.030148616060614586,
0.05305074155330658,
0.01214930322021246,
-0.008536606095731258,
-0.009589084424078465,
0.03191561996936798,
0.05174330621957779,
-0.016876906156539917,
-0.024381916970014572,
-0.07559220492839813,
0.0042073363438248634,
0.01080680638551712,
-0.012063064612448215,
-0.03817746788263321,
0.018508024513721466,
-0.007173977792263031,
-0.01384410448372364,
0.07329582422971725,
0.021667970344424248,
0.006832448299974203,
0.0043595111928880215,
-0.012041095644235611,
0.0010563894174993038,
-0.02283761091530323,
-0.03146478533744812,
0.024866854771971703,
-0.04213836044073105,
-0.03153056651353836,
-0.009117957204580307,
-0.00799214281141758,
0.006970804650336504,
0.007148931734263897,
0.03753974661231041,
0.02998529188334942,
0.019055865705013275,
0.016279812902212143,
-0.009149412624537945,
0.054154906421899796,
-0.04737462103366852,
-0.07902194559574127,
-0.00639851251617074,
0.024189162999391556,
-0.017013659700751305,
-0.02406962402164936,
0.001053944113664329,
-0.027574237436056137,
0.0366700142621994,
-0.027800075709819794,
-0.008704067207872868,
-0.007748899050056934,
-0.04398307949304581,
0.043005846440792084,
0.023794544860720634,
0.01147413533180952,
0.019892752170562744,
0.021003486588597298,
-0.04318555071949959,
-0.05257199704647064,
0.022742319852113724,
0.030609754845499992,
-0.04474436491727829,
0.0022947783581912518,
0.008195058442652225,
-0.007893791422247887,
-0.03606325015425682,
0.036975134164094925,
-0.007091654930263758,
0.02529889903962612,
-0.0027433871291577816,
-0.03129829093813896,
-0.053098633885383606,
0.012120249681174755,
0.03643798828125,
-0.017273906618356705,
-0.01842021755874157,
-0.004146004561334848,
-0.005455499514937401,
-0.01942959427833557,
0.009460791945457458,
-0.017781689763069153,
0.011888016946613789,
0.019733309745788574,
-0.008729230612516403,
0.005065068602561951,
-0.016028620302677155,
-0.016153467819094658,
-0.003869065083563328,
-0.03431373089551926,
0.03268229588866234,
-0.029595889151096344,
0.01772080361843109,
0.024884000420570374,
-0.04874550551176071,
-0.014877276495099068,
0.040109097957611084,
-0.01049923337996006,
0.04015744850039482,
-0.021021731197834015,
0.028549352660775185,
-0.0018360564718022943,
0.026812445372343063,
-0.05588373914361,
-0.03465842083096504,
0.03431624174118042,
0.02934405766427517,
0.0441884808242321,
-0.0335143581032753,
0.018504111096262932,
-0.06721524894237518,
-0.01980816200375557,
0.023445477709174156,
0.026080414652824402,
0.007262364029884338,
0.007336353417485952,
-0.028717147186398506,
0.01122729666531086,
0.06768190115690231,
0.0058698044158518314,
-0.018574120476841927,
0.044170036911964417,
-0.01879962719976902,
-0.007216483820229769,
-0.0503007136285305,
0.09795353561639786,
-0.0231173112988472,
0.013214233331382275,
-0.003804917214438319,
-0.022716175764799118,
0.05502009391784668,
-0.00042115600081160665,
-0.007413872517645359,
0.04094240441918373,
-0.01967499405145645,
-0.001363297225907445,
-0.01753031462430954,
0.020745866000652313,
0.005360372364521027,
0.04406619444489479,
0.002047197427600622,
-0.022730855271220207,
0.00040198935312218964,
-0.03723248839378357,
0.023685745894908905,
0.03063889592885971,
-0.030529534444212914,
-0.009250957518815994,
0.09154261648654938,
-0.0013260584091767669,
-0.010130776092410088,
0.005014611408114433,
0.021606434136629105,
0.023700794205069542,
-0.037768084555864334,
-0.00631312420591712,
0.010855762287974358,
-0.010966476052999496,
-0.004272616468369961,
-0.026028316468000412,
-0.02976330928504467,
-0.033205900341272354,
0.05669533833861351,
-0.03622689098119736,
0.06846718490123749,
0.02267717756330967,
0.03140249475836754,
0.006080842111259699,
-0.002324050525203347,
0.01202685758471489,
-0.01462181843817234,
-0.032532721757888794,
0.03612876310944557,
-0.010122859850525856,
-0.018888717517256737,
0.024921081960201263,
0.06233934685587883,
-0.023807445541024208,
-0.010417168959975243,
0.003940981812775135,
0.03928343951702118,
0.011262917891144753,
0.0347217358648777,
-0.02320881374180317,
-0.0018857853719964623,
-0.021560978144407272,
0.022325873374938965,
-0.05018573999404907,
-0.038877442479133606,
0.06657243520021439,
0.013704029843211174,
0.017307693138718605,
-0.027894750237464905,
-0.004656828008592129,
-0.010922711342573166,
0.01186191663146019,
0.015171310864388943,
0.0473245307803154,
0.008791322819888592,
-0.02359296754002571,
0.03383089229464531,
-0.011986562050879002,
0.003924164921045303,
-0.011089768260717392,
-0.07953821122646332,
-0.04231034591794014,
-0.010658510960638523,
-0.024270111694931984,
0.03973007574677467,
0.030621016398072243,
-0.002303906250745058,
0.025680989027023315,
-0.00700207008048892,
0.022827861830592155,
0.013308543711900711,
0.04250399395823479,
-0.0025536268949508667,
0.08340336382389069,
-0.0021210291888564825,
0.029560457915067673,
-0.03968745842576027,
0.015723729506134987,
0.11329071968793869,
0.022387443110346794,
0.02956385724246502,
-0.022544778883457184,
0.02105989307165146,
-0.026018355041742325,
-0.0038381749764084816,
-0.0060087754391133785,
0.017788248136639595,
0.04669414088129997,
-0.011299560777842999,
-0.0014542475109919906,
0.04849706590175629,
0.03509146720170975,
-0.05645120143890381,
0.051679447293281555,
-0.06483732163906097,
-0.036115407943725586,
-0.020685439929366112,
-0.01609024964272976,
-0.010964246466755867,
0.005402652081102133,
0.002438885159790516,
0.0030012663919478655,
-0.04237421229481697,
0.024417852982878685,
-0.017278848215937614,
-0.02487967349588871,
0.008354339748620987,
0.02105940878391266,
-0.05712873116135597,
0.01356008555740118,
-0.010914447717368603,
-0.03502823784947395,
-0.09124702960252762,
0.021654833108186722,
0.0005768954870291054,
-0.01722540892660618,
0.019006894901394844,
0.007722178474068642,
0.005949007347226143,
0.04084429889917374,
0.008585943840444088,
-0.03380527347326279,
-0.03542514517903328,
0.018361419439315796,
-0.04605786129832268,
0.024526037275791168,
-0.004319392144680023,
0.03896719589829445,
0.04244261234998703,
-0.009667133912444115,
-0.010191380977630615,
-0.07272401452064514,
-0.007443366106599569,
-0.04319983348250389,
-0.005153952166438103,
0.007647335529327393,
-0.0039110127836465836,
0.005345106590539217,
0.02585395611822605,
0.012201006524264812,
0.006953209172934294,
0.021941980347037315,
-0.018523000180721283,
-0.016253162175416946,
0.01836313121020794,
0.027035823091864586,
-0.04336942359805107,
-0.0208241268992424,
-0.029838301241397858,
0.006592203862965107,
-0.05234560742974281,
0.020558925345540047,
0.010613040067255497,
0.02122846432030201,
-0.008929150179028511,
-0.012233668006956577,
-0.02180934138596058,
-0.06372913718223572,
-0.01091859396547079,
0.03254630044102669,
-0.005680867470800877,
0.004989634267985821,
-0.005335763096809387,
-0.025397703051567078,
0.06009230762720108,
0.010889420285820961,
-0.042644649744033813,
0.013761766254901886,
-0.04853197559714317,
0.03839396312832832,
0.005828522611409426,
0.01929497718811035,
-0.03714434430003166,
0.013147681951522827,
-0.03282906487584114,
0.0442819707095623,
-0.005251175258308649,
0.0504021979868412,
0.01810111105442047,
-0.0038245688192546368,
-0.02921672910451889,
0.02044363133609295,
-0.008723679929971695,
0.03652330860495567,
0.006485355086624622,
-0.03908299282193184,
-0.021159129217267036,
0.020862312987446785,
0.003384874202311039,
-0.0268620103597641,
-0.03169054538011551,
-0.03031817264854908,
0.0030531224329024553,
-0.0188868697732687,
-0.013421213254332542,
-0.0063248188234865665,
0.03906434029340744,
-0.005720301531255245,
0.03296118602156639,
-0.037202559411525726,
0.003989743534475565,
-0.06477569788694382,
-0.011965607292950153,
0.037017010152339935,
0.01144322194159031,
-0.002094279509037733,
0.03954945504665375,
-0.022117450833320618,
-0.02838817611336708,
0.023632466793060303,
-0.014807820320129395,
0.0057000345550477505,
-0.019417669624090195,
0.019158827140927315,
-0.03539690375328064,
0.031195081770420074,
-0.033650267869234085,
-0.056476201862096786,
0.05419714376330376,
-0.04393046349287033,
-0.026141071692109108,
0.04373190924525261,
-0.02394195646047592,
0.015583346597850323,
0.016544120386242867,
-0.041743867099285126,
0.010408000089228153,
0.062423303723335266,
-0.018812013790011406,
0.011870522052049637,
0.014568818733096123,
-0.012039372697472572,
-0.06554386019706726,
-0.015663133934140205,
0.024653904139995575,
-0.013797227293252945,
-0.05292001739144325,
0.04279602691531181,
0.04769181087613106,
-0.04909694939851761,
0.026835927739739418,
0.00866474024951458,
-0.004575453698635101,
-0.03382726013660431,
0.010610159486532211,
0.008085419423878193,
0.014003624208271503,
0.0037653434555977583,
-0.021461309865117073,
0.007066155318170786,
-0.02568635158240795,
0.013585126958787441,
-0.07224132120609283,
0.01092667318880558,
0.013798151165246964,
0.01772432029247284,
0.011984637938439846,
-0.0752815455198288,
-0.029241900891065598,
-0.014376013539731503,
-0.0672941729426384,
0.008772126398980618,
-0.007145110052078962,
-0.01497969962656498,
-0.014129642397165298,
0.009829802438616753,
0.02236066199839115,
0.007327560801059008,
0.042313504964113235,
0.03583609312772751,
0.010202529840171337,
0.011172243393957615,
-0.004620274994522333,
-0.01930241473019123,
0.0057013812474906445,
0.009879117831587791,
0.01564057357609272,
-0.0010214259382337332,
0.03498999401926994,
-0.02600105106830597,
-0.053822919726371765,
-0.010363391600549221,
0.011126848869025707,
0.026261303573846817,
-0.030180344358086586,
0.0337609238922596,
0.03457353636622429,
0.023619072511792183,
-0.026166116818785667,
-0.005053685046732426,
-0.009341278113424778,
0.015904169529676437,
-0.013962511904537678,
0.0507582351565361,
-0.04930386692285538,
-0.005046742036938667,
0.03504132479429245,
-0.04036776348948479,
-0.02657492272555828,
0.014359919354319572,
-0.006951349787414074,
-0.030116437003016472,
-0.01585148274898529,
0.0045485906302928925,
0.05684121325612068,
-0.00032463378738611937,
0.015422062948346138,
-0.043646614998579025,
0.00524252699688077,
0.026032526046037674,
-0.0149582140147686,
0.01600889302790165,
0.029189635068178177,
0.00357999000698328,
0.008754846639931202,
-0.022547880187630653,
0.004689309746026993,
-0.02044016122817993,
-0.044091831892728806,
-0.004340554587543011,
-0.02610774151980877,
0.003500367281958461,
-0.016188863664865494,
-0.03767971321940422,
-0.013185442425310612,
0.028475230559706688,
0.031188922002911568,
0.0376879908144474,
0.02522006258368492,
-0.0194752998650074,
-0.04765079915523529,
-0.04622788727283478,
0.03643985092639923,
-0.004923728760331869,
-0.026271572336554527,
-0.04982374981045723,
0.01039233896881342,
-0.0022529985290020704,
0.01691449247300625,
0.0442018061876297,
-0.012025064788758755,
-0.014383753761649132,
0.02807736024260521,
-0.032415006309747696,
-0.0039917584508657455,
-0.020831238478422165,
0.007912672124803066,
-0.004691618494689465,
-0.038011204451322556,
0.015438559465110302,
-0.002401272300630808,
-0.03421150892972946,
-0.042290281504392624,
0.0006898751598782837,
-0.007975428365170956,
0.033265046775341034,
-0.002937126439064741,
-0.013111293315887451,
0.054874103516340256,
0.051816072314977646,
0.0010630283504724503,
0.0603998601436615,
0.005646059289574623,
0.02051025815308094,
0.01846918649971485,
-0.02704034559428692,
-0.045111071318387985,
0.05028506740927696,
-0.014835907146334648,
-0.007427566684782505,
-0.019857963547110558,
-0.007746905088424683,
0.0038907364942133427,
-0.0420190654695034,
-0.00309203309006989,
0.0263828057795763,
-0.01495024748146534,
-0.008778315037488937,
0.03405632823705673,
0.051104918122291565,
-0.018214048817753792,
-0.02707097679376602,
0.014127828180789948,
0.040395162999629974,
-0.009890429675579071,
-0.013842202723026276,
0.03374144062399864,
0.04109315574169159,
-0.020655009895563126,
0.008883110247552395,
0.038153667002916336,
0.0014073553029447794,
0.045893698930740356,
0.03366623446345329,
-0.0018896645633503795,
-0.02490273304283619,
-0.01444688905030489,
-0.005634959787130356,
-0.007453051395714283,
0.03915880247950554,
0.041438180953264236,
-0.0075760954059660435,
0.06758670508861542,
-0.05822579190135002,
-0.0033567806240171194,
-0.00901568029075861,
-0.011918570846319199,
-0.009996160864830017,
-0.014733248390257359,
0.060681261122226715,
-0.00008338627230841666,
0.006604116875678301,
-0.059730738401412964,
-0.022006502375006676,
-0.02652035281062126,
0.01361046638339758,
-0.050334393978118896,
0.03396114334464073,
-0.0011366172693669796,
-0.0255491491407156,
0.009473178535699844,
-0.02283015474677086,
-0.032583706080913544,
-0.03109721839427948,
0.008230851963162422,
0.02262146584689617,
0.036740340292453766,
0.006904962472617626,
0.01014962512999773,
-0.01776692271232605,
0.0606309249997139,
-0.0756368488073349,
-0.032787565141916275,
0.00006657833728240803,
0.0375414714217186,
0.03679751977324486,
-0.016602780669927597
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/21851/prove-that-negative-absolute-temperatures-are-actually-hotter-than-positive-abso">Prove that negative absolute temperatures are actually hotter than positive absolute temperatures</a><br>
<a href="http://physics.stackexchange.com/questions/28601/proof-of-existence-of-lowest-temperature-0-k">Proof of existence of lowest temperature $0 K$</a> </p>
</blockquote>
<p>On the Kelvin temperature scale, zero is the lowest possible temperature. Why there is no defined negative temperature?</p>
| 278 |
[
-0.04785335808992386,
-0.0624934621155262,
-0.0319078266620636,
0.015390428714454174,
0.022229954600334167,
-0.02124725468456745,
-0.039580389857292175,
-0.018119649961590767,
-0.030635319650173187,
-0.015991363674402237,
0.049786392599344254,
0.012973702512681484,
-0.0005625815247185528,
0.005928512662649155,
-0.002305337693542242,
-0.0025163982063531876,
-0.04298066347837448,
-0.009699284099042416,
-0.02453652210533619,
0.008268188685178757,
0.007574127521365881,
0.04249956086277962,
0.017516927793622017,
0.03541283309459686,
-0.04203752800822258,
-0.00789609458297491,
0.045158494263887405,
0.015378712676465511,
0.00012265749683137983,
0.06093158945441246,
-0.0016879988834261894,
0.022995686158537865,
0.022224118933081627,
-0.0008792190928943455,
0.04328599199652672,
0.015264603309333324,
0.004787018988281488,
0.017949353903532028,
-0.023902159184217453,
0.03337962552905083,
0.0033132850658148527,
-0.0420248843729496,
0.004926716443151236,
0.011336905881762505,
-0.009779046289622784,
-0.007480228319764137,
0.010817041620612144,
-0.003910989034920931,
0.022852003574371338,
-0.05617144703865051,
0.008120558224618435,
-0.019514579325914383,
0.07074487209320068,
0.0687006339430809,
0.005602376535534859,
-0.013798237778246403,
0.061255451291799545,
0.07578302919864655,
-0.026321975514292717,
-0.041440241038799286,
-0.01452245470136404,
-0.03495313227176666,
-0.0014248171355575323,
-0.0016136218328028917,
-0.012411531060934067,
0.03729429468512535,
0.019823191687464714,
0.016681691631674767,
-0.012110911309719086,
0.009079508483409882,
0.020421626046299934,
0.018384013324975967,
-0.005631063133478165,
-0.008221752010285854,
0.010600351728498936,
-0.010072211734950542,
-0.014383339323103428,
0.035567980259656906,
0.028048062697052956,
0.08738995343446732,
-0.015558291226625443,
0.026948539540171623,
0.03134980797767639,
0.01930077187716961,
-0.0025378090795129538,
-0.011499359272420406,
0.08938582986593246,
-0.00043770603951998055,
0.017894020304083824,
0.041824739426374435,
0.0050491285510361195,
-0.020448900759220123,
-0.0163295678794384,
0.009303899481892586,
-0.0014811190776526928,
0.013354571536183357,
0.005440705455839634,
0.030135134235024452,
-0.007406773045659065,
-0.040341783314943314,
0.0021777120418846607,
0.012026029638946056,
0.055198270827531815,
0.06726545095443726,
0.0013398322043940425,
-0.0315462127327919,
-0.01773037388920784,
0.02278505451977253,
-0.004661702550947666,
0.012865740805864334,
-0.022489234805107117,
0.009506593458354473,
0.010369233787059784,
-0.04222595691680908,
0.012046677991747856,
-0.051801856607198715,
0.01278688758611679,
-0.05396775156259537,
0.02445932663977146,
0.029386024922132492,
0.03532937169075012,
-0.008571011014282703,
0.0004895672900602221,
-0.011823419481515884,
-0.0580776184797287,
-0.0046909404918551445,
0.010983599349856377,
0.007223546039313078,
-0.014922657050192356,
0.0026597927790135145,
-0.030891433358192444,
0.02155926823616028,
-0.011605892330408096,
-0.007658639457076788,
0.04422524943947792,
-0.02606775425374508,
-0.0889376699924469,
-0.07519227266311646,
0.06008356809616089,
0.0025023906491696835,
-0.039146553725004196,
-0.04766245558857918,
0.013025800697505474,
0.015874283388257027,
0.03234875574707985,
-0.005535679403692484,
0.011805272661149502,
-0.02158173732459545,
-0.00012369036267045885,
0.009318282827734947,
-0.0010020978515967727,
-0.0028954632580280304,
-0.01579311490058899,
-0.03920847922563553,
-0.03667992725968361,
-0.058028608560562134,
0.011293233372271061,
0.005567615851759911,
-0.023559018969535828,
-0.007947628386318684,
0.04577198997139931,
-0.03186294808983803,
0.014769399538636208,
-0.002161653246730566,
-0.005801077000796795,
-0.01145386416465044,
0.107346311211586,
0.051132477819919586,
-0.0283000897616148,
0.013884901069104671,
-0.02193005196750164,
0.027673771604895592,
-0.024461250752210617,
0.017960723489522934,
0.021708287298679352,
-0.04035332426428795,
-0.015130363404750824,
-0.023791199550032616,
0.020373504608869553,
0.031369227916002274,
-0.072982057929039,
0.03466513380408287,
-0.004147726111114025,
-0.014456739649176598,
0.006065567955374718,
0.07337120175361633,
-0.02559039182960987,
0.008704027161002159,
0.03408217802643776,
-0.08400898426771164,
-0.003231405047699809,
-0.08173421025276184,
0.026444479823112488,
0.0505845844745636,
-0.024684451520442963,
0.021250439807772636,
0.023294957354664803,
0.018425317481160164,
-0.05583348497748375,
0.007691479288041592,
0.029537305235862732,
0.022587163373827934,
0.01871650665998459,
-0.013508021831512451,
0.04418813809752464,
0.06818734854459763,
0.08046691119670868,
-0.05487673357129097,
0.025616973638534546,
-0.03556192293763161,
-0.017243381589651108,
-0.006159714423120022,
-0.026332201436161995,
0.012227348983287811,
0.017737971618771553,
0.006031963042914867,
0.010029934346675873,
0.057740699499845505,
-0.01868526265025139,
0.023278120905160904,
-0.02670762501657009,
0.04870089143514633,
0.030309205874800682,
0.013131962157785892,
0.0046907104551792145,
0.009457048960030079,
0.03769615292549133,
0.012487202882766724,
-0.02475641667842865,
0.00884202029556036,
-0.05250262841582298,
-0.0017624212196096778,
0.05538303777575493,
0.044926710426807404,
-0.07676063477993011,
0.032604001462459564,
0.006494355853646994,
0.029715584591031075,
0.010815583169460297,
-0.014206946827471256,
0.017428241670131683,
-0.015992632135748863,
0.008959132246673107,
-0.02811047062277794,
0.006755663547664881,
0.04385934770107269,
0.03381852060556412,
0.01767902635037899,
0.027717797085642815,
0.007049906067550182,
-0.003124682232737541,
0.04366769641637802,
0.005433250218629837,
0.011263315565884113,
0.02388191595673561,
-0.01849810779094696,
0.029010502621531487,
-0.02719675935804844,
0.034435901790857315,
0.004731697496026754,
-0.014630916528403759,
0.044193901121616364,
-0.008476626127958298,
-0.010561719536781311,
0.01940278895199299,
0.009586499072611332,
-0.001372115220874548,
-0.0015966256614774466,
0.018297666683793068,
-0.04183698445558548,
0.0007124161929823458,
-0.014816108159720898,
0.00435218308120966,
-0.033705707639455795,
-0.005242825485765934,
0.055725883692502975,
0.009509466588497162,
0.0028175071347504854,
-0.05541849508881569,
0.0011432589963078499,
-0.0020839159842580557,
-0.013070396147668362,
0.046353813260793686,
0.044966619461774826,
-0.022994503378868103,
0.014851565472781658,
-0.01261930912733078,
-0.0384986475110054,
0.052370328456163406,
-0.04216790199279785,
-0.013401966542005539,
0.031111471354961395,
-0.02658149041235447,
-0.03632558882236481,
-0.0009216316975653172,
-0.06269583106040955,
0.01197934988886118,
-0.030968284234404564,
0.015373299829661846,
0.06382221728563309,
-0.006209008861333132,
-0.07112526893615723,
0.034227848052978516,
-0.05730810388922691,
-0.041995640844106674,
-0.014550893567502499,
-0.01900690421462059,
0.03874148055911064,
-0.02423813007771969,
0.047334715723991394,
0.014548790641129017,
-0.06084785237908363,
0.0033745993860065937,
-0.03808826580643654,
-0.02857360802590847,
0.017666460946202278,
-0.010499214753508568,
0.03094559907913208,
-0.018754903227090836,
-0.008138690143823624,
0.05371220037341118,
0.05212933197617531,
-0.014752274379134178,
-0.03126409277319908,
-0.004636131227016449,
-0.04043613374233246,
-0.01825479045510292,
-0.021563991904258728,
0.013415684923529625,
-0.02903270348906517,
0.010705317370593548,
0.039077892899513245,
0.03608032688498497,
-0.0005779439816251397,
0.008992938324809074,
-0.048832591623067856,
-0.007739506661891937,
-0.03174397721886635,
0.006326385773718357,
0.07037756592035294,
-0.01980479620397091,
-0.007245699875056744,
0.014731017872691154,
-0.003909577615559101,
0.049537379294633865,
0.01480140071362257,
-0.06566159427165985,
0.07215838879346848,
-0.00309753674082458,
0.010504699312150478,
-0.051779575645923615,
0.057989008724689484,
-0.011580153368413448,
0.0004659859696403146,
-0.006928848568350077,
-0.012339332140982151,
0.012312723323702812,
-0.004091151058673859,
0.002721285680308938,
0.012288461439311504,
0.07043825834989548,
-0.028121812269091606,
-0.022227123379707336,
-0.032861873507499695,
-0.027870476245880127,
0.01887362450361252,
-0.0021244296804070473,
0.0013779664877802134,
0.036438774317502975,
0.04080233722925186,
0.05065472424030304,
0.024062538519501686,
-0.022094491869211197,
-0.024083616212010384,
-0.05416111648082733,
-0.025965802371501923,
-0.049345649778842926,
0.05205601081252098,
-0.014331293292343616,
0.03390469402074814,
0.02052862010896206,
0.023136505857110023,
0.00016241312550846487,
0.009191921912133694,
-0.09485255926847458,
0.032144904136657715,
-0.04319798946380615,
-0.01735028252005577,
0.004265609662979841,
0.002293352736160159,
0.010080368258059025,
-0.019473442807793617,
-0.007327790837734938,
0.004394384566694498,
0.013775517232716084,
-0.035981178283691406,
0.0015871028881520033,
-0.005861120298504829,
-0.004930397029966116,
-0.007967350073158741,
0.023275883868336678,
0.08370110392570496,
-0.03761432319879532,
0.04556819051504135,
0.02317652478814125,
-0.033430613577365875,
0.011741416528820992,
-0.033369336277246475,
0.03417924419045448,
0.0625128448009491,
0.042143698781728745,
0.020643845200538635,
0.010826577432453632,
-0.003355520311743021,
-0.01004489790648222,
0.02334546111524105,
0.009795081801712513,
0.00986349955201149,
-0.02414989471435547,
-0.021558357402682304,
-0.031004900112748146,
-0.024635959416627884,
-0.011414501816034317,
0.05358031019568443,
-0.010806611739099026,
0.000023194381356006488,
0.02662593126296997,
-0.017953326925635338,
0.0010305042378604412,
0.04283354431390762,
0.03600217029452324,
-0.0316535122692585,
0.014393100515007973,
-0.020132292062044144,
-0.0579448863863945,
-0.04245618358254433,
0.002071013208478689,
0.029450254514813423,
0.009986493736505508,
-0.0044385092332959175,
0.013283240608870983,
0.031562093645334244,
0.010328126139938831,
-0.0019883131608366966,
0.02233032137155533,
0.0010684174485504627,
0.0502157062292099,
-0.03021068684756756,
-0.014732933603227139,
0.004743730649352074,
0.04262769594788551,
0.033072296530008316,
-0.03557996451854706,
-0.02878691628575325,
-0.07803752273321152,
-0.026504620909690857,
0.021480292081832886,
0.06804367899894714,
0.012579490430653095,
-0.02060483768582344,
-0.05838712677359581,
-0.02106364443898201,
0.05225153639912605,
-0.03622530400753021,
0.06253396719694138,
-0.0030968324281275272,
0.01121450960636139,
-0.018835660070180893,
-0.04568729177117348,
0.0264835637062788,
-0.0010176999494433403,
0.02179078757762909,
0.015473619103431702,
-0.01323775015771389,
0.024238836020231247,
0.00044392523705028,
-0.004157924093306065,
0.05261945724487305,
0.06285011768341064,
-0.04546572268009186,
0.009603353217244148,
0.007812067400664091,
-0.04795212298631668,
-0.0409671775996685,
-0.07254331558942795,
0.006500189658254385,
0.025960685685276985,
0.0008986784378066659,
0.0427834577858448,
-0.04979981482028961,
-0.028127286583185196,
0.025779446586966515,
-0.0053788661025464535,
-0.04199381545186043,
0.024982742965221405,
-0.052931927144527435,
0.035800281912088394,
0.03429827839136124,
0.01171871181577444,
0.03692033886909485,
0.03904034569859505,
-0.015414232388138771,
0.002029628260061145,
-0.029820378869771957,
-0.0009296905482187867,
-0.022797424346208572,
-0.0350848026573658,
-0.03299194574356079,
0.011544747278094292,
-0.038081761449575424,
0.012893703766167164,
-0.0243705902248621,
-0.0010512520093470812,
0.00221014441922307,
-0.020698901265859604,
0.0003370925842318684,
-0.0026795940939337015,
0.013891066424548626,
0.008992915973067284,
-0.006476417183876038,
-0.0009870075155049562,
0.016016308218240738,
-0.04695361107587814,
0.02481917291879654,
-0.003722206689417362,
-0.0012029513018205762,
0.008768461644649506,
-0.028681976720690727,
0.02590779773890972,
-0.020636452361941338,
-0.011077888309955597,
-0.03930506482720375,
-0.04714050143957138,
0.013577880337834358,
-0.006232245359569788,
-0.03437051177024841,
0.01460878737270832,
-0.06085202097892761,
-0.025023052468895912,
0.031729068607091904,
0.008740103803575039,
-0.000021080697479192168,
-0.029896382242441177,
0.03951069340109825,
0.05400904640555382,
-0.014337847009301186,
-0.09681861102581024,
-0.043007589876651764,
0.007931920699775219,
0.02448868378996849,
-0.007939680479466915,
-0.02450110949575901,
-0.008325591683387756,
-0.00006614754965994507,
0.009719436056911945,
-0.014961063861846924,
0.03775262460112572,
-0.017448341473937035,
-0.021039769053459167,
0.005828190129250288,
-0.0016784059116616845,
0.03037446364760399,
0.010862630791962147,
-0.020110532641410828,
0.009913026355206966,
-0.015935471281409264,
-0.04583243653178215,
0.040109783411026,
0.02266187034547329,
-0.025079548358917236,
-0.03253396600484848,
0.000907725072465837,
0.0035242377780377865,
0.008931433781981468,
0.032660435885190964,
-0.027302471920847893,
0.0178997740149498,
0.01057080551981926,
-0.03437534719705582,
-0.05180950090289116,
0.02754995971918106,
0.0027797380462288857,
0.005227952264249325,
-0.0006451148074120283,
-0.0321429967880249,
-0.013517576269805431,
-0.05006299540400505,
-0.0006395662203431129,
-0.021297650411725044,
-0.037434596568346024,
-0.0038192959036678076,
0.07717283070087433,
-0.012037863954901695,
-0.017345121130347252,
0.013569433242082596,
-0.015303329564630985,
0.018055180087685585,
0.017234550788998604,
-0.0015177675522863865,
-0.026864176616072655,
0.0029170052148401737,
-0.024352017790079117,
-0.017948172986507416,
-0.0457257442176342,
-0.006004254799336195,
0.038565218448638916,
0.042209237813949585,
0.06934627890586853,
-0.0052303289994597435,
-0.01298258826136589,
0.03291821852326393,
-0.03585865721106529,
0.034786418080329895,
-0.014556429348886013,
0.018227042630314827,
0.041179757565259933,
-0.05155797675251961,
0.03809716925024986,
0.04842575639486313,
0.019262870773673058,
-0.010245220735669136,
0.008326535113155842,
0.026191184297204018,
0.020438523963093758,
-0.00793057307600975,
-0.03638388216495514,
-0.029340099543333054,
0.04645514115691185,
-0.046922650188207626,
0.040762536227703094,
0.036083247512578964,
-0.024176228791475296,
0.016541676595807076,
-0.050152793526649475,
-0.0006046340567991138,
-0.055923596024513245,
-0.03444922715425491,
-0.039630986750125885,
0.021734928712248802,
0.011521082371473312,
0.04342242702841759,
0.01037593837827444,
-0.007686750032007694,
0.024655481800436974,
0.0038078012876212597,
0.024254996329545975,
-0.0033684123773127794,
-0.054652273654937744,
0.0036001824773848057,
-0.022081095725297928,
-0.061541348695755005,
0.05624068155884743,
-0.005842974409461021,
-0.04071617126464844,
0.021709389984607697,
-0.05796230956912041,
0.00385859003290534,
0.05901540070772171,
0.027062052860856056,
-0.013266363181173801,
0.028361449018120766,
-0.00806109607219696,
0.02448107674717903,
0.009168339893221855,
-0.009262274019420147,
0.1281067281961441,
0.07659705728292465,
0.017680732533335686,
-0.05815506353974342,
0.04475032910704613,
0.014520464465022087,
0.015969814732670784,
-0.043904077261686325,
0.02499329298734665,
-0.05340701341629028,
0.001522832433693111,
0.0016409800155088305,
0.066660575568676,
-0.001019144314341247,
-0.01646619290113449,
0.015123236924409866,
-0.0506289042532444,
-0.01928098127245903,
-0.010081262327730656,
-0.0042238240130245686,
-0.0003342946001794189,
0.014469722285866737,
-0.005586982239037752,
0.03182101994752884,
-0.027391012758016586,
-0.0042760311625897884,
-0.038046691566705704,
0.0007950735744088888,
0.034843605011701584,
0.011182114481925964,
-0.05303184688091278,
0.011427965015172958,
0.037058357149362564,
-0.02503383345901966,
-0.04154196381568909,
-0.028918089345097542,
0.042416930198669434,
0.0052179875783622265,
0.02651863358914852,
0.030181841924786568,
0.014359303750097752,
-0.015020296908915043,
0.020726049318909645,
0.03130964934825897,
-0.06039869785308838,
0.013956302776932716,
-0.055124618113040924,
-0.004484192933887243,
-0.021922336891293526,
-0.020155636593699455,
0.030734576284885406,
-0.017253698781132698,
-0.04484023153781891,
-0.014026151038706303,
-0.023485839366912842,
0.0018866840982809663,
0.055994912981987,
-0.047378890216350555,
-0.06264270842075348,
-0.010982654988765717,
0.052511874586343765,
-0.001874845940619707,
0.01870954968035221,
-0.005175922531634569,
-0.0031120057683438063,
0.002365852240473032,
0.004220237955451012,
0.019552303478121758,
-0.00016917198081500828,
0.00931012537330389,
0.00038205922464840114,
0.006886573508381844,
-0.03740581497550011,
-0.019155248999595642,
0.006183843594044447,
-0.004212460480630398,
0.05544118583202362,
0.027339449152350426,
0.019426582381129265,
-0.0007132099126465619,
-0.029798107221722603,
-0.02385558933019638,
-0.01268121600151062,
-0.017687806859612465,
-0.004936886020004749,
-0.0028522289358079433,
0.0054237875156104565,
0.03478388115763664,
-0.020535003393888474,
-0.012734905816614628,
0.01787721924483776,
0.04508349299430847,
0.034237708896398544,
-0.025952599942684174,
-0.013246028684079647,
-0.006789966952055693,
-0.0701260194182396,
0.023266656324267387,
0.015325563959777355,
0.049238529056310654,
0.041858796030282974,
0.044315118342638016,
0.029734577983617783,
0.015483187511563301,
-0.05901741608977318,
-0.01746341772377491,
0.01609218120574951,
-0.005327876657247543,
-0.0023176162503659725,
0.040423959493637085,
-0.002380200894549489,
-0.012698816135525703,
-0.08288151025772095,
-0.004454530775547028,
-0.007193578407168388,
0.04761100560426712,
0.020788833498954773,
-0.008542230352759361,
0.015207394026219845,
-0.02354891411960125,
-0.002789620775729418,
-0.07637584954500198,
-0.02789730206131935,
-0.014213897287845612,
-0.012483461759984493,
-0.02091330476105213,
-0.009780848398804665,
0.02115730196237564,
0.011484978720545769,
0.009800969623029232,
-0.005163161549717188,
0.04128079488873482,
0.05735461041331291,
-0.003004014492034912,
-0.021044088527560234,
0.012911103665828705,
0.007714994717389345,
0.04151400923728943,
-0.014540362171828747,
-0.0367988646030426,
0.03651827946305275,
-0.055390942841768265,
-0.01840408332645893,
0.0025855868589133024,
0.012846372090280056,
-0.005063039716333151,
0.015882527455687523,
-0.02386089228093624,
-0.0015402639983221889,
0.052170224487781525,
-0.021171577274799347,
-0.023561278358101845,
-0.0010558745125308633,
-0.004277691710740328,
-0.005675419699400663,
0.017155252397060394,
0.010910972021520138,
-0.010911209508776665,
-0.015084361657500267,
0.013147651217877865,
0.02325318567454815,
-0.010055731050670147,
-0.02284615859389305,
0.021562930196523666,
0.01627204567193985,
-0.004769064951688051,
0.03385421633720398,
0.011655444279313087,
0.004079099278897047,
0.01385562401264906,
-0.04584038630127907,
0.039321351796388626,
-0.036825284361839294,
0.011326785199344158,
-0.10880719870328903,
0.020434902980923653,
0.015835750848054886,
-0.00740760937333107,
0.03568942844867706,
-0.060423869639635086,
0.041007980704307556,
0.07424884289503098,
-0.051254402846097946,
0.0024750828742980957,
-0.014815869741141796,
0.029100440442562103,
-0.027273479849100113,
-0.0249999538064003,
-0.021852092817425728,
0.040360353887081146,
0.020951300859451294,
0.060403481125831604,
-0.013243798166513443,
0.036732710897922516,
-0.013482113368809223,
-0.030767500400543213,
-0.019527092576026917,
0.014830977655947208,
-0.005482984706759453,
-0.021062850952148438,
0.03443072736263275,
0.014125826768577099,
0.001010830863378942,
0.022089337930083275,
-0.01809035800397396,
-0.04235559329390526,
0.010125032626092434,
0.04246561974287033,
-0.01865088753402233,
0.046510081738233566,
0.010185420513153076,
0.015514825470745564,
-0.000012140563740103971,
0.027411067858338356,
0.005904892925173044,
0.03482012450695038,
0.001332474872469902,
0.01397491805255413,
0.03296351432800293,
-0.05247845500707626,
-0.02976207435131073,
0.056938864290714264,
-0.01034183707088232,
-0.014268106780946255,
0.018406588584184647,
0.00004536196502158418,
0.017927518114447594,
-0.0351644903421402,
-0.048730600625276566,
-0.01836160384118557,
-0.013890024274587631,
0.022160030901432037,
0.015008922666311264,
-0.015001161955296993,
-0.028387004509568214,
-0.002224522642791271,
-0.026063768193125725,
0.015676839277148247,
-0.013816667720675468,
0.018382398411631584,
-0.019822388887405396,
-0.02283630520105362,
-0.0020693824626505375,
0.03772405534982681,
-0.017367955297231674,
-0.053381383419036865,
-0.05618960037827492,
0.011083107441663742,
-0.015141296200454235,
0.018938900902867317,
-0.02753419242799282,
-0.03064865991473198,
-0.03178193420171738,
-0.06460554897785187,
0.0032402637880295515,
-0.02285628952085972,
0.03975943848490715,
-0.05447588488459587,
-0.024741748347878456,
-0.020821617916226387,
0.012070653028786182,
0.05441059172153473,
0.03144877776503563,
-0.02423599176108837,
-0.001134579419158399,
-0.010229509323835373,
0.023455679416656494,
-0.030525924637913704,
0.031480927020311356,
0.011344937607645988,
-0.03643994405865669,
0.04618147015571594,
-0.006565500516444445,
-0.024141505360603333,
0.03832319378852844,
0.03388439118862152,
0.0037195710465312004,
-0.009512487798929214,
-0.015067576430737972,
-0.01477066520601511,
0.07565490901470184,
0.00877806730568409,
-0.012497836723923683,
0.09145211428403854,
-0.0032326315995305777,
0.0024989512749016285,
0.015219250693917274,
0.015296022407710552,
-0.00897058192640543,
0.026690665632486343,
-0.03283120319247246,
0.0010240291012451053,
-0.01434019673615694,
-0.003513737116008997,
0.010261672548949718,
-0.029469234868884087,
-0.01020620483905077,
0.0417257659137249,
-0.03311780095100403,
-0.03026268258690834,
0.020293710753321648,
0.007613094989210367,
0.04512755945324898,
-0.02896682545542717,
0.009161590598523617,
-0.010586120188236237,
0.012330452911555767,
0.026576366275548935,
0.04342980310320854,
0.030184585601091385,
-0.022075507789850235,
0.018011586740612984,
0.024291183799505234,
0.010920020751655102,
0.022079871967434883,
-0.00028890816611237824,
0.03186769410967827,
-0.012160821817815304,
-0.01750492863357067,
0.04722066968679428,
-0.0016380976885557175,
-0.014702850952744484,
-0.0017915854696184397,
0.01521388441324234,
0.07161961495876312,
-0.0023907136637717485,
0.011538554914295673,
-0.010800881311297417,
-0.013437435030937195,
-0.010594122111797333,
0.03045952506363392,
0.005525870714336634,
0.017200183123350143,
-0.06292448937892914,
-0.002270443132147193,
0.011328913271427155,
-0.013682988472282887,
-0.0008180346339941025,
-0.05291666463017464,
0.014027598313987255,
-0.0006523734773509204,
0.001061145798303187,
-0.023689109832048416,
-0.00098919786978513,
-0.013775607571005821,
0.008662938140332699,
0.026575138792395592,
0.030289212241768837,
0.01130517479032278,
0.014630403369665146,
-0.04958780109882355,
-0.03012138605117798,
0.038333501666784286,
-0.01907305233180523,
-0.023269400000572205,
-0.007343364413827658,
0.007887529209256172,
-0.0026063737459480762,
-0.028795842081308365
] |
<p>I'm an aspiring physicist who wants to self study some Quantum Physics. My thirst for knowledge is unquenchable and I can not wait 2 more years until I get my first quantum physics class in university, so I want to start with a self study. I am enrolled in a grammar school and the most gifted among the gifted (not my description, mind you, I hate coming off as cocky, sorry) are enrolled in a special 'project'. We are allowed to take 3 school hours a week off in order to work on a project, which can be about anything you want, from music to mathematics. On the 4th of April we have to present our projects. Last year an acquaintance of mine did it about university level mathematics, so I thought, why not do it about university level physics? It is now the 3rd of October so I have half a year. My question is, where can I conduct a self study of quantum physics? Starting from scratch? And is it possible for me to be able to use and understand the Schrödinger equation by April? What are good books, sites, etc. that can help me? My goal is to have a working knowledge of BASIC quantum physics and I would like to understand and be able to use the Schrödinger equation. Is this possible? What is needed for these goals? </p>
| 1,004 |
[
0.0017009994480758905,
-0.018631426617503166,
0.00717414915561676,
-0.009168543852865696,
0.04568164423108101,
-0.02333766035735607,
-0.006062105763703585,
-0.05039992928504944,
-0.004117902833968401,
-0.05075332149863243,
0.022637158632278442,
0.04084355756640434,
0.03311745077371597,
-0.00011723884381353855,
0.0066517423838377,
0.020141296088695526,
-0.02621607854962349,
-0.039049603044986725,
-0.04211379215121269,
0.005622147582471371,
-0.002354995347559452,
-0.005563448183238506,
0.00018137191364075989,
0.03762529417872429,
-0.0462421253323555,
0.03372165560722351,
-0.008784490637481213,
0.014937492087483406,
0.016868842765688896,
0.035091884434223175,
0.026066673919558525,
-0.0188953448086977,
0.02846546284854412,
0.02792198397219181,
0.04047030210494995,
-0.005837742704898119,
-0.03521249070763588,
-0.01946829818189144,
-0.010977295227348804,
0.003291018772870302,
-0.0362451896071434,
-0.02502068504691124,
-0.013395918533205986,
0.013268550857901573,
-0.039471302181482315,
0.029969753697514534,
-0.001127839321270585,
-0.06457764655351639,
0.043973710387945175,
-0.04177023842930794,
0.04571962356567383,
0.05188971012830734,
0.03629176691174507,
0.023659953847527504,
0.01541096344590187,
-0.04443023353815079,
0.04581546410918236,
0.04068150371313095,
-0.004304650239646435,
-0.046546149998903275,
0.02412129007279873,
-0.0008073539938777685,
-0.01022901851683855,
-0.03605206683278084,
-0.05122503265738487,
0.026635877788066864,
-0.007253062445670366,
-0.009825780056416988,
0.02368197776377201,
-0.009114678017795086,
0.028698282316327095,
0.05979383364319801,
0.07678245007991791,
-0.01414398942142725,
-0.004861667286604643,
-0.045531488955020905,
0.006378623191267252,
-0.005164264235645533,
0.004075389355421066,
0.014740021899342537,
-0.013414228335022926,
0.030771883204579353,
-0.01848655380308628,
0.02259756810963154,
0.006820406764745712,
-0.0440077967941761,
0.06607476621866226,
-0.0016202118713408709,
-0.032717276364564896,
0.009245196357369423,
-0.018218383193016052,
0.010883364826440811,
0.029684390872716904,
-0.016879530623555183,
-0.030217688530683517,
0.03199450299143791,
0.014482660219073296,
0.06258998811244965,
-0.0016586999408900738,
-0.03353338688611984,
0.032994501292705536,
-0.019650092348456383,
-0.020890025421977043,
0.06598934531211853,
-0.00045832234900444746,
0.002122777048498392,
-0.013777758926153183,
0.03677305579185486,
0.011768882162868977,
0.0004773011023644358,
-0.008584724739193916,
0.029948396608233452,
0.008077125065028667,
0.002677549608051777,
-0.0035658497363328934,
-0.031251102685928345,
0.008717991411685944,
-0.016518954187631607,
0.04572605341672897,
0.06876397132873535,
0.03965440392494202,
-0.030047498643398285,
0.04812729358673096,
-0.036232706159353256,
-0.08565713465213776,
-0.012680944986641407,
0.025060463696718216,
-0.024110419675707817,
-0.04968474805355072,
0.039115145802497864,
0.01413129735738039,
-0.02033836580812931,
0.01918819360435009,
0.005880203563719988,
0.04072677344083786,
-0.008375534787774086,
-0.14330311119556427,
-0.022955626249313354,
0.0024290720466524363,
0.010891478508710861,
-0.027286747470498085,
-0.06623717397451401,
-0.002259687287732959,
0.018594374880194664,
0.09856577217578888,
-0.006678365636616945,
0.0368460975587368,
-0.018162954598665237,
0.007867374457418919,
0.029884200543165207,
-0.04111426696181297,
-0.018007587641477585,
0.007898884825408459,
-0.0005583920865319669,
0.04065214470028877,
-0.05395922064781189,
0.04763124883174896,
0.0007873511058278382,
0.018973499536514282,
-0.0503583699464798,
0.06863297522068024,
-0.006598618812859058,
-0.01427229680120945,
0.041509319096803665,
-0.027711713686585426,
-0.015742793679237366,
0.07302411645650864,
0.017860576510429382,
-0.007977154105901718,
0.02519771084189415,
0.02648327127099037,
0.056443940848112106,
-0.003668899182230234,
0.012606838718056679,
0.0037770597264170647,
-0.027339192107319832,
0.0017671153182163835,
0.02127140387892723,
-0.0001918479974847287,
-0.03137923404574394,
-0.00026653410168364644,
-0.028568139299750328,
-0.0035738619044423103,
0.05062326043844223,
-0.028858143836259842,
0.0629071295261383,
0.022812072187662125,
0.006753686815500259,
-0.011704406701028347,
-0.020831270143389702,
-0.055833421647548676,
-0.037511348724365234,
0.05017681419849396,
-0.03542837128043175,
-0.01002785935997963,
0.04812552034854889,
0.021956175565719604,
0.02059338614344597,
0.0033516574185341597,
-0.039634063839912415,
0.008425293490290642,
0.03019641898572445,
0.021231329068541527,
0.013136058114469051,
0.02863222546875477,
0.057187702506780624,
0.004873143043369055,
-0.0004320545122027397,
0.04470617696642876,
-0.02462518773972988,
-0.02285974659025669,
0.01910514384508133,
-0.022856393828988075,
0.04382191598415375,
0.003128283889964223,
0.0009180385386571288,
-0.014088161289691925,
-0.005938855931162834,
0.0017758477479219437,
0.02324162796139717,
0.0011503533460199833,
0.06071271374821663,
-0.00876084715127945,
0.005379684269428253,
0.006443389691412449,
0.058645740151405334,
0.03322197496891022,
0.04684942588210106,
0.030603954568505287,
-0.013685357756912708,
-0.02525971457362175,
0.03192541375756264,
0.026536671444773674,
-0.005817041732370853,
-0.0321461446583271,
0.008540982380509377,
0.007550149690359831,
0.017034338787198067,
0.046576619148254395,
0.020403876900672913,
-0.020945675671100616,
-0.011819818988442421,
-0.019167961552739143,
0.0028636965434998274,
-0.01836678758263588,
0.06839486956596375,
0.05788712203502655,
0.009771893732249737,
-0.018081724643707275,
0.008188923820853233,
-0.035191792994737625,
0.028294319286942482,
-0.01576254516839981,
-0.016404012218117714,
0.03202296793460846,
-0.038996439427137375,
0.011699562892317772,
-0.05025184154510498,
0.006825246848165989,
-0.007365841884166002,
-0.030244745314121246,
0.022914238274097443,
0.005021757911890745,
-0.035528797656297684,
-0.0018021445721387863,
-0.0030827075242996216,
-0.05056598410010338,
-0.002540258225053549,
0.017849726602435112,
-0.037033747881650925,
-0.012579604983329773,
0.01049903966486454,
0.010400055907666683,
-0.052741993218660355,
-0.02891869656741619,
-0.01020314171910286,
0.016960883513092995,
0.013211078941822052,
0.025105323642492294,
-0.048717811703681946,
0.02765709161758423,
-0.011399180628359318,
0.036187794059515,
-0.006550085265189409,
-0.04463797062635422,
0.039313867688179016,
-0.005745308473706245,
-0.05090076103806496,
0.08284226804971695,
-0.026759933680295944,
0.035101260989904404,
0.0008159676799550653,
0.0029331042896956205,
-0.01340579241514206,
0.01728653535246849,
-0.0058931615203619,
0.004792910534888506,
-0.022522684186697006,
0.0324396938085556,
0.037553660571575165,
-0.023809392005205154,
-0.01628878526389599,
-0.010916993021965027,
-0.03374861553311348,
-0.03880104050040245,
-0.040084317326545715,
0.0342145711183548,
0.010600452311336994,
-0.005561414640396833,
-0.005295097827911377,
0.002868492854759097,
-0.067598357796669,
-0.015051689930260181,
-0.057811055332422256,
-0.03576979413628578,
0.017337244004011154,
0.04554454982280731,
0.0192911047488451,
-0.002510092919692397,
0.0003553584683686495,
0.07055920362472534,
0.007104319054633379,
-0.06050148233771324,
-0.03289589285850525,
-0.003467779839411378,
-0.0012191440910100937,
-0.008284764364361763,
0.023954859003424644,
0.028093913570046425,
-0.021659864112734795,
-0.004597390070557594,
-0.0018022976582869887,
0.030551645904779434,
0.03603037819266319,
0.05226921662688255,
-0.05428910255432129,
0.005872733425348997,
-0.0025703345891088247,
0.01788240112364292,
0.027524705976247787,
-0.01118815690279007,
-0.0763944536447525,
-0.0036528734490275383,
-0.026645654812455177,
-0.006455725524574518,
0.04613800719380379,
-0.03059801645576954,
0.04932987317442894,
-0.004030367359519005,
0.0017366566462442279,
-0.017368990927934647,
-0.001533044152893126,
-0.013234148733317852,
0.015369707718491554,
0.03631875291466713,
0.02118086628615856,
0.018891815096139908,
0.0029478406067937613,
0.023555826395750046,
0.022392628714442253,
0.05271410197019577,
-0.01687801629304886,
-0.025143366307020187,
-0.01871247962117195,
-0.009337091818451881,
0.03068334236741066,
-0.034628234803676605,
-0.016988398507237434,
0.026652099564671516,
0.0419735386967659,
0.017703460529446602,
-0.042161062359809875,
-0.016659138724207878,
0.008335642516613007,
-0.07809524238109589,
0.014021840877830982,
-0.008590985089540482,
0.0645638108253479,
0.0022303895093500614,
0.05300607532262802,
0.0022103069350123405,
0.01521977223455906,
-0.000052796003728872165,
0.018814709037542343,
-0.07329177856445312,
0.023987162858247757,
-0.012261328287422657,
-0.011533583514392376,
0.019478576257824898,
0.012862632051110268,
-0.012369293719530106,
0.0005319042829796672,
-0.057824309915304184,
-0.02053060382604599,
-0.01578318513929844,
-0.042228423058986664,
-0.01149739883840084,
-0.050426218658685684,
-0.004187572281807661,
0.0030485182069242,
0.046344757080078125,
0.044556647539138794,
-0.032152000814676285,
-0.017584282904863358,
0.02557377517223358,
-0.047417379915714264,
-0.031173929572105408,
0.003969504497945309,
-0.0026861471123993397,
0.008107906207442284,
0.029928090050816536,
0.06651606410741806,
0.046468500047922134,
-0.037381306290626526,
0.021183237433433533,
-0.010090715251863003,
0.06802354007959366,
-0.013162389397621155,
-0.022870277985930443,
0.018754225224256516,
-0.05132438614964485,
0.003449926385655999,
0.02829444408416748,
0.05806101858615875,
0.039268288761377335,
0.029422521591186523,
0.021748429164290428,
-0.03035038337111473,
-0.059483353048563004,
0.012487992644309998,
0.10471083968877792,
-0.04533049091696739,
-0.023470431566238403,
-0.020416710525751114,
-0.01682817004621029,
-0.05217248573899269,
-0.006565059535205364,
-0.0054076556116342545,
0.03221159055829048,
-0.012095082551240921,
0.00988436583429575,
-0.007821394130587578,
0.04656151682138443,
-0.04836180433630943,
0.013244027271866798,
0.001220631180331111,
0.028608722612261772,
0.0023438401985913515,
0.0022404291667044163,
0.01315060444176197,
0.0007995283231139183,
0.0363672599196434,
-0.024681001901626587,
0.0022015213035047054,
-0.06741306185722351,
-0.0053774272091686726,
0.01602707803249359,
0.07340315729379654,
0.016374658793210983,
0.01578308641910553,
-0.04075242951512337,
-0.02612408995628357,
0.051193948835134506,
-0.021893328055739403,
0.01789451576769352,
-0.035433366894721985,
-0.04750419780611992,
-0.02280934900045395,
-0.002681240439414978,
0.015106278471648693,
0.02647838182747364,
-0.008111522532999516,
0.01399105042219162,
-0.028517408296465874,
-0.011956599541008472,
-0.010369992814958096,
0.024133924394845963,
-0.0016305863391608,
0.05978288874030113,
-0.004111107904464006,
-0.013387988321483135,
-0.0018396131927147508,
0.013375785201787949,
-0.03977116197347641,
-0.0714244395494461,
-0.009654202498495579,
0.013573545031249523,
-0.01754244975745678,
0.04051367938518524,
-0.04028581455349922,
-0.07606447488069534,
0.012125495821237564,
0.011272385716438293,
-0.018575213849544525,
-0.006341914646327496,
-0.04692050814628601,
0.00315621099434793,
0.02059035561978817,
0.008018868044018745,
0.04062289372086525,
0.07468940317630768,
-0.02098764292895794,
0.007106539327651262,
-0.030118677765130997,
0.018480334430933,
-0.013429480604827404,
0.019259484484791756,
-0.03141474351286888,
-0.041318800300359726,
-0.03563767299056053,
0.06972913444042206,
-0.05703260004520416,
-0.004730004817247391,
-0.04416640102863312,
0.005167469847947359,
-0.029853686690330505,
0.011595817282795906,
-0.0010281768627464771,
-0.0054563735611736774,
-0.012132778763771057,
-0.0010565005941316485,
0.0002839071094058454,
-0.020871030166745186,
0.00017123860015999526,
0.019149357452988625,
-0.010508490726351738,
0.008801774121820927,
0.0013172418111935258,
0.03306711092591286,
-0.04531269893050194,
-0.0443156398832798,
-0.006959153804928064,
-0.045320674777030945,
0.03979262709617615,
-0.021589649841189384,
0.022838830947875977,
0.04268256574869156,
-0.03775312006473541,
-0.03222271054983139,
0.006726385559886694,
-0.007744431030005217,
0.020907439291477203,
-0.01047041267156601,
0.009297897107899189,
0.003806985216215253,
0.0284791998565197,
-0.0688576027750969,
-0.06742841005325317,
0.05681465566158295,
-0.01113596186041832,
-0.022608928382396698,
-0.022604182362556458,
0.02439102716743946,
-0.001197866746224463,
0.005451181437820196,
0.0004589766904246062,
0.009647025726735592,
-0.028931742534041405,
0.0016789374640211463,
0.01370492484420538,
0.022705864161252975,
0.03942825272679329,
-0.00233322917483747,
0.009743787348270416,
-0.011652600951492786,
-0.0018029366619884968,
0.013870211318135262,
0.00035589898470789194,
0.012652561999857426,
-0.017594516277313232,
-0.034007780253887177,
-0.0271589532494545,
0.020550625398755074,
0.029116008430719376,
-0.07634641975164413,
-0.008668191730976105,
0.051444098353385925,
0.03866269066929817,
0.0012453298550099134,
-0.051596254110336304,
0.015941103920340538,
0.01935943216085434,
-0.012307373806834221,
-0.003606373444199562,
-0.003177258186042309,
-0.031394582241773605,
-0.05205988511443138,
0.04640014097094536,
0.018847862258553505,
0.021936992183327675,
-0.009147269651293755,
0.05899887904524803,
0.03509361669421196,
-0.02313550002872944,
0.03282899409532547,
0.007046244572848082,
-0.035254739224910736,
-0.03334035351872444,
0.03553541377186775,
0.019922146573662758,
-0.012731694616377354,
-0.0301026813685894,
-0.04244775325059891,
-0.042862631380558014,
0.021070696413517,
0.06798712909221649,
0.001354148262180388,
0.03658898174762726,
0.03553713858127594,
0.012986519373953342,
-0.0076568033546209335,
-0.010698792524635792,
-0.002137312199920416,
0.009164929389953613,
0.005273331888020039,
0.010920637287199497,
-0.013551140204071999,
-0.0015015077078714967,
-0.014627120457589626,
0.0728495866060257,
-0.02657938189804554,
0.04961954429745674,
0.06606155633926392,
0.034257881343364716,
0.005363682750612497,
-0.03213755786418915,
-0.011974289081990719,
0.03322893753647804,
-0.03746134415268898,
0.02897109091281891,
-0.000025336103135487065,
-0.012224145233631134,
-0.005986511707305908,
0.005776925478130579,
-0.0014690280659124255,
-0.033156123012304306,
-0.0424216128885746,
-0.05022271350026131,
0.038082268089056015,
0.005499092396348715,
-0.006432077847421169,
0.0002699668984860182,
0.010760214179754257,
0.021107416599988937,
0.03983182832598686,
0.03044012561440468,
-0.004443367011845112,
-0.04311966150999069,
-0.014457057230174541,
-0.02626855857670307,
-0.0628303810954094,
0.03068605810403824,
0.008679797872900963,
-0.04135551676154137,
0.006551681086421013,
-0.002785571152344346,
0.05616723373532295,
0.0006673940224573016,
0.018447499722242355,
-0.020350096747279167,
0.015938347205519676,
-0.018886471167206764,
0.01061469130218029,
-0.017316509038209915,
0.03248821943998337,
0.11627396941184998,
0.026967331767082214,
0.020940540358424187,
-0.05976322665810585,
0.011193935759365559,
-0.004739655647426844,
0.03386617451906204,
-0.023083623498678207,
0.010450693778693676,
-0.022289732471108437,
-0.012388413771986961,
-0.015430762432515621,
0.07233122736215591,
0.013052848167717457,
0.017229730263352394,
0.06659059971570969,
-0.038714539259672165,
-0.0660465732216835,
0.0026866754051297903,
0.0013127924175933003,
0.02772333286702633,
0.0360058955848217,
-0.057310689240694046,
0.049823563545942307,
-0.042130760848522186,
-0.006784916389733553,
-0.022075096145272255,
-0.035863231867551804,
0.05841352045536041,
0.005364203825592995,
-0.010526214726269245,
0.025957100093364716,
-0.019679144024848938,
0.01593119651079178,
-0.04830308258533478,
0.02483460120856762,
0.025661151856184006,
-0.024982191622257233,
0.02292403019964695,
0.017125695943832397,
0.006180722266435623,
-0.019995849579572678,
-0.01524327788501978,
0.018230648711323738,
-0.021804403513669968,
-0.009130396880209446,
0.01874191127717495,
0.044786106795072556,
-0.014666909351944923,
-0.027600858360528946,
-0.042277391999959946,
0.0078866733238101,
0.013927035965025425,
-0.018776847049593925,
-0.02603606879711151,
0.014266007579863071,
0.031498830765485764,
-0.061893969774246216,
0.025704234838485718,
-0.01542503573000431,
-0.0003202337247785181,
-0.011861582286655903,
0.001258289092220366,
-0.021436916664242744,
-0.03396306559443474,
0.009084388613700867,
0.01083430740982294,
-0.021830478683114052,
-0.022579994052648544,
-0.048095040023326874,
-0.019499463960528374,
0.01740030013024807,
-0.01944756880402565,
-0.029130853712558746,
0.0716671496629715,
0.011347528547048569,
0.023599309846758842,
0.0023141135461628437,
-0.020782826468348503,
-0.0026466662529855967,
-0.014218715950846672,
0.0199369378387928,
-0.004029233939945698,
-0.02585536241531372,
0.007660152390599251,
-0.004487793892621994,
0.031183065846562386,
0.03526558727025986,
0.01168548408895731,
0.053765956312417984,
0.031074216589331627,
-0.0017655990086495876,
0.04950270056724548,
-0.002558598993346095,
0.005034444388002157,
-0.010038517415523529,
-0.032606013119220734,
0.018022669479250908,
-0.02204657346010208,
-0.002079896628856659,
0.018430067226290703,
-0.018529538065195084,
-0.018334394320845604,
0.037399772554636,
-0.03480543941259384,
0.008308261632919312,
-0.032110586762428284,
-0.04222431406378746,
-0.010294594801962376,
0.024883942678570747,
0.03064895048737526,
-0.028250135481357574,
-0.0531107597053051,
-0.0015314520569518209,
0.03785892575979233,
-0.026238737627863884,
0.020686741918325424,
-0.020838869735598564,
0.06494917720556259,
-0.0011119869304820895,
0.04746818169951439,
-0.029805589467287064,
0.017038479447364807,
-0.0360812284052372,
0.023008638992905617,
0.009062434546649456,
0.002888993127271533,
-0.015981463715434074,
0.01145467720925808,
0.04100629687309265,
-0.056561361998319626,
0.010049604810774326,
0.008194556459784508,
-0.03722495958209038,
-0.019987033680081367,
0.003981827758252621,
-0.0014286765363067389,
0.04409974440932274,
0.006789296865463257,
-0.01757565326988697,
0.035999495536088943,
-0.06504513323307037,
-0.04565470665693283,
0.03711223974823952,
-0.033607907593250275,
0.024302562698721886,
0.033102039247751236,
-0.021763289347290993,
-0.005971717648208141,
0.05277010053396225,
-0.002641889499500394,
0.0006895037367939949,
0.017174724489450455,
-0.03827151283621788,
-0.014936178922653198,
0.03184641897678375,
-0.014710385352373123,
-0.05329221114516258,
-0.042593199759721756,
0.03652285784482956,
0.06287907063961029,
0.019729899242520332,
0.008301758207380772,
0.0018106072675436735,
0.01358026172965765,
0.012525209225714207,
-0.0038839003536850214,
-0.023044751957058907,
0.020565511658787727,
0.08060767501592636,
-0.032359927892684937,
0.03386727720499039,
0.01738319918513298,
0.021382011473178864,
-0.09913422167301178,
-0.012895775027573109,
0.017768368124961853,
-0.0030554612167179585,
0.03133286163210869,
-0.02377817966043949,
0.015842387452721596,
0.05254770442843437,
-0.056802261620759964,
0.04615604504942894,
-0.04683511704206467,
-0.016857758164405823,
0.013381910510361195,
0.012324456125497818,
-0.01342023815959692,
0.007384296040982008,
0.010196935385465622,
0.02943887934088707,
0.011462525464594364,
0.031146692112088203,
0.01590809039771557,
-0.018138015642762184,
0.010946331545710564,
0.034720443189144135,
-0.00890504289418459,
0.011801251210272312,
0.03722073882818222,
-0.06119361147284508,
-0.02178291045129299,
0.01468835212290287,
-0.050248295068740845,
-0.0021456757094711065,
-0.02482665702700615,
0.01058847177773714,
-0.06675118207931519,
0.0604393295943737,
0.06302597373723984,
-0.00557906087487936,
0.03167547285556793,
-0.007845228537917137,
0.028447376564145088,
0.039747416973114014,
0.012550781480967999,
0.01405903697013855,
0.012905243784189224,
-0.011253663338720798,
-0.056365180760622025,
0.062203578650951385,
0.033295273780822754,
0.025312095880508423,
0.03495600074529648,
0.009729619137942791,
-0.0006793427164666355,
-0.015486390329897404,
-0.0069157094694674015,
-0.06113513186573982,
-0.024759741500020027,
-0.018520688638091087,
-0.013054009526968002,
0.00617193104699254,
0.03224656358361244,
-0.04819808527827263,
-0.03711019083857536,
0.021555233746767044,
-0.017323346808552742,
-0.021479520946741104,
-0.05277552828192711,
-0.0035799124743789434,
0.007528192363679409,
0.01564035378396511,
0.020221387967467308,
-0.012929853983223438,
-0.008059732615947723,
0.023032069206237793,
-0.0058646672405302525,
-0.0013697573449462652,
-0.019498419016599655,
-0.014595544897019863,
-0.01697651855647564,
-0.03915803134441376,
0.03985504060983658,
0.01969221979379654,
0.024011801928281784,
-0.035707373172044754,
0.00293801655061543,
0.012444463558495045,
-0.001340184360742569,
0.02278440073132515,
-0.06391911953687668,
-0.015813888981938362,
0.0029369168914854527,
-0.01657463051378727,
0.010627035982906818,
0.005742775741964579,
-0.005650029517710209,
-0.016182634979486465,
-0.029284680262207985,
-0.03755796700716019,
0.011257600970566273,
-0.006345001980662346,
0.008095948025584221,
0.013211949728429317,
0.02316601760685444,
0.029296718537807465,
-0.027031032368540764,
-0.051629360765218735,
0.035845812410116196,
0.04846970736980438,
0.015103044919669628,
0.02545979619026184,
-0.016527503728866577,
0.011502704583108425,
0.031149089336395264,
-0.023758282884955406,
-0.036877673119306564,
0.04034942388534546,
-0.04841272905468941,
0.004329316783696413,
0.013736383058130741,
-0.04430960491299629,
0.003812336130067706,
-0.03451072797179222,
-0.009595271199941635,
0.018032509833574295,
0.0177962314337492,
0.0007872590213082731,
0.030269399285316467,
0.01533442921936512,
0.013610308058559895,
-0.024629583582282066,
-0.013191552832722664,
0.03807955980300903,
-0.009414697997272015,
0.015933407470583916,
0.03333552926778793,
0.01033865474164486,
0.0027672487776726484,
0.03578280657529831,
0.060675181448459625,
-0.005283788312226534,
-0.03193484991788864,
0.012870432808995247,
0.022238243371248245,
-0.015470101498067379,
-0.0180735494941473,
0.021596595644950867,
-0.007874811068177223,
-0.013069506734609604,
-0.009287434630095959,
-0.03389802575111389,
0.04528242349624634,
-0.0268123596906662,
0.01012131106108427,
-0.03640065714716911,
0.020925628021359444,
-0.0350891575217247,
0.002651819260790944,
-0.0015030987560749054,
0.02037276327610016,
-0.04439283534884453,
-0.023700818419456482,
-0.0831286609172821,
0.03739111125469208,
0.004125415813177824,
-0.003281214740127325,
0.03248579055070877,
0.0006111785187385976,
0.004112164955586195,
0.021576857194304466,
-0.0034948771353811026,
-0.02920529618859291,
-0.011771639809012413,
-0.004454868845641613,
0.02257479913532734,
-0.007323951460421085,
0.0010322406888008118,
-0.018173305317759514,
-0.038796115666627884,
0.046718087047338486,
-0.05647894740104675,
0.0027703556697815657,
-0.010995719581842422,
-0.005738465115427971,
-0.057286668568849564,
0.030946671962738037
] |
<p>I'd like answers both in the more intuitive side an on the more precise side. </p>
<p>Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a triangular prism, yield different results. Will this fact, then, be dependent on the format of the molecules of the liquid ?</p>
<p>I've heard of the rotational symmetry of liquids. What is its precise statement ? Why is it true ?</p>
| 8,485 |
[
-0.028874803334474564,
-0.012645180337131023,
-0.02823498658835888,
-0.05127723887562752,
0.05649113655090332,
0.004619913641363382,
-0.016962207853794098,
0.003341445466503501,
0.012201939709484577,
-0.0026450734585523605,
0.03930831328034401,
0.029444564133882523,
0.04230473190546036,
0.00756242498755455,
0.0176530871540308,
0.022075476124882698,
0.004437617491930723,
-0.0038529024459421635,
-0.010411204770207405,
0.003739567706361413,
0.009264609776437283,
0.021335382014513016,
-0.019684985280036926,
0.03542866185307503,
-0.030318301171064377,
0.08675455302000046,
0.0526457279920578,
0.009186677634716034,
0.04411298781633377,
0.04009687155485153,
-0.003489256137982011,
-0.034500960260629654,
0.02356460504233837,
0.017337022349238396,
0.046326033771038055,
-0.023941997438669205,
-0.009336329996585846,
-0.025478212162852287,
-0.02742353081703186,
0.025025563314557076,
-0.043140508234500885,
0.025893161073327065,
-0.022596510127186775,
0.03180563449859619,
-0.029545921832323074,
0.039370398968458176,
-0.01945873349905014,
-0.04359114542603493,
0.02413918450474739,
-0.06329820305109024,
0.03912241384387016,
0.01173000130802393,
0.012671036645770073,
0.03541216626763344,
-0.00859452597796917,
-0.006007439456880093,
0.05590924993157387,
0.038117244839668274,
-0.02102060243487358,
-0.07913871854543686,
0.027536628767848015,
0.023422272875905037,
0.010420440696179867,
0.009366513229906559,
-0.04445510730147362,
-0.01854434236884117,
0.013081202283501625,
-0.02195451222360134,
0.018676633015275,
-0.009717179462313652,
0.002853799145668745,
0.03577493503689766,
0.029411952942609787,
-0.02819279581308365,
0.019272226840257645,
-0.03364577516913414,
-0.006010074634104967,
0.040455956012010574,
0.01266555767506361,
0.01003354787826538,
0.007694342639297247,
0.006272491533309221,
0.029582839459180832,
0.01279690582305193,
-0.011264954693615437,
-0.005716347601264715,
0.0615047812461853,
0.0005592936649918556,
0.02445092983543873,
0.057619161903858185,
0.014691694639623165,
0.010624822229146957,
0.03109172359108925,
-0.014209345914423466,
-0.009343814104795456,
-0.028853323310613632,
-0.016024921089410782,
0.07119383662939072,
0.008996941149234772,
-0.024749096482992172,
0.003629827406257391,
-0.010976199060678482,
-0.006832688581198454,
0.09257657080888748,
-0.013569303788244724,
-0.016900300979614258,
-0.027744965627789497,
0.03759473189711571,
-0.012044085189700127,
-0.015100999735295773,
0.023152807727456093,
-0.016252528876066208,
-0.019665006548166275,
-0.024372365325689316,
-0.005821287166327238,
0.0044176955707371235,
0.009824520908296108,
-0.03370266407728195,
0.042372092604637146,
0.07849133759737015,
0.05219908803701401,
-0.030507957562804222,
0.013855647295713425,
-0.014653134159743786,
-0.06224476918578148,
0.012050659395754337,
-0.0084597859531641,
-0.003882521530613303,
-0.04887671768665314,
-0.0011395654873922467,
-0.0003687235584948212,
-0.0007663148571737111,
0.009310426190495491,
-0.00321431877091527,
0.04193565621972084,
-0.017765680328011513,
-0.08142359554767609,
-0.04727259650826454,
0.04350298270583153,
0.005607533268630505,
-0.07644294202327728,
-0.07043323665857315,
-0.0044942270033061504,
0.029729897156357765,
0.06776377558708191,
-0.03371626138687134,
0.03577820584177971,
-0.015396488830447197,
0.04422436282038689,
0.004006747156381607,
-0.017220646142959595,
-0.002663208404555917,
-0.0014951011398807168,
-0.07212941348552704,
-0.014950915239751339,
-0.031631190329790115,
0.005846844520419836,
0.0010574294719845057,
0.013568769209086895,
-0.02194962650537491,
0.036891233175992966,
-0.03411950543522835,
-0.01281309686601162,
0.02209310792386532,
-0.01248003076761961,
-0.014768208377063274,
0.06202024593949318,
-0.007296775467693806,
-0.0026930957101285458,
0.010745998471975327,
-0.011269684880971909,
0.02266477420926094,
0.017095010727643967,
0.023229502141475677,
0.07178401947021484,
0.013265805318951607,
-0.017634637653827667,
-0.02796464040875435,
0.037072110921144485,
-0.027646943926811218,
-0.03842560946941376,
-0.006080436520278454,
-0.013134746812283993,
-0.006338921375572681,
-0.025329560041427612,
0.051192186772823334,
0.005787272471934557,
-0.02573118358850479,
-0.009685194119811058,
-0.06310401856899261,
0.0006347561720758677,
-0.04083842784166336,
0.019296567887067795,
-0.031011242419481277,
-0.012255536392331123,
0.043296728283166885,
0.07390931248664856,
0.006295199505984783,
-0.018601534888148308,
-0.02642480470240116,
-0.0088282385841012,
0.02729165554046631,
0.033065393567085266,
-0.015130874700844288,
0.022849200293421745,
0.04052788019180298,
0.03081507235765457,
-0.03828679770231247,
-0.008174472488462925,
-0.0071870735846459866,
-0.0260725449770689,
-0.008489182218909264,
-0.02917957305908203,
0.016607703641057014,
-0.0023242379538714886,
-0.014162596315145493,
0.004140506032854319,
0.025571580976247787,
-0.004801627714186907,
0.0356825515627861,
-0.03765656054019928,
0.06598786264657974,
0.06058083102107048,
-0.011435933411121368,
0.03162246569991112,
0.03571581095457077,
0.015264284797012806,
0.00027592229889705777,
0.032798923552036285,
-0.034927014261484146,
-0.05732760578393936,
-0.00773831969127059,
0.0204369705170393,
0.03405030071735382,
-0.04949098825454712,
0.006055342499166727,
0.018587395548820496,
0.045911673456430435,
0.01393903698772192,
-0.009724908508360386,
-0.016855310648679733,
-0.04991533234715462,
0.005117902997881174,
0.02710665948688984,
0.050475575029850006,
0.020074350759387016,
0.029490066692233086,
0.020184477791190147,
0.03239646553993225,
-0.02027672529220581,
-0.03497224673628807,
-0.007011402864009142,
-0.013303456827998161,
-0.008145739324390888,
0.019926460459828377,
-0.014117571525275707,
0.025949178263545036,
-0.0333535373210907,
-0.026151029393076897,
0.029561107978224754,
0.003382845316082239,
-0.00943947583436966,
-0.07219430804252625,
0.027879249304533005,
-0.021983910351991653,
0.009134506806731224,
-0.008572082035243511,
-0.022268543019890785,
0.02877073548734188,
-0.03353627026081085,
-0.014173340983688831,
-0.030358819290995598,
0.0095574501901865,
0.00881847832351923,
-0.0047278511337935925,
0.026087883859872818,
-0.005787489004433155,
0.04334665834903717,
-0.0009665234829299152,
-0.030753809958696365,
0.0044688209891319275,
-0.012463290244340897,
-0.021456001326441765,
0.003342173993587494,
-0.02973291650414467,
-0.011292310431599617,
-0.046360064297914505,
0.004687887616455555,
-0.017513129860162735,
-0.03330747410655022,
0.0021952197421342134,
0.004196772351861,
0.00314904423430562,
-0.04764056205749512,
-0.03392345830798149,
-0.025989022105932236,
0.02812907099723816,
-0.03800591453909874,
-0.005763116292655468,
0.03579862415790558,
-0.047701288014650345,
-0.035512570291757584,
0.026407375931739807,
-0.03170682489871979,
-0.03547129034996033,
-0.01876913569867611,
0.003608344355598092,
0.005723109003156424,
-0.02303188294172287,
-0.010455502197146416,
0.04442121833562851,
-0.07463017106056213,
-0.0036177777219563723,
-0.024427102878689766,
-0.044639669358730316,
0.008814826607704163,
-0.023573799058794975,
0.06656276434659958,
0.030668780207633972,
-0.021536998450756073,
0.044076934456825256,
-0.010682475753128529,
-0.06315064430236816,
-0.025786953046917915,
0.005050948821008205,
0.002859615022316575,
-0.04990924894809723,
0.04550895839929581,
0.05173714458942413,
-0.040774159133434296,
0.020723873749375343,
0.03736809268593788,
0.04895450919866562,
0.0001500816288171336,
0.007029907777905464,
-0.0017840844811871648,
0.019365062937140465,
0.04461640119552612,
0.008947078138589859,
0.027521243318915367,
0.012766112573444843,
-0.019106758758425713,
0.007868625223636627,
-0.021931063383817673,
0.02401992492377758,
0.06941960006952286,
-0.07280129194259644,
0.05858347937464714,
0.005831723101437092,
0.02235434763133526,
-0.0005386230768635869,
0.04254037141799927,
-0.03591866046190262,
-0.009521888568997383,
0.03887814283370972,
0.05059492960572243,
0.04074620455503464,
-0.01367526687681675,
-0.019092492759227753,
0.036536380648612976,
0.05540155991911888,
-0.012371309101581573,
-0.029000984504818916,
0.011844722554087639,
-0.0073247794061899185,
0.06312599033117294,
-0.032328471541404724,
-0.018690411001443863,
0.07957162708044052,
0.021280406042933464,
0.00644620880484581,
-0.015649450942873955,
-0.03138086199760437,
0.018166033551096916,
-0.0868486687541008,
0.0069424863904714584,
-0.024621911346912384,
0.02777176722884178,
-0.0014184265164658427,
0.07721413671970367,
0.02576368674635887,
0.004847083240747452,
0.002225908450782299,
0.009576505981385708,
-0.0782061442732811,
0.015859264880418777,
-0.018557069823145866,
0.03823035955429077,
-0.018488168716430664,
-0.015961304306983948,
0.0058601838536560535,
-0.043768253177404404,
-0.02412250079214573,
-0.003299913601949811,
0.01411493681371212,
-0.04789310693740845,
0.033286742866039276,
-0.0025782245211303234,
-0.028210891410708427,
-0.016647160053253174,
0.06160148233175278,
0.010137208737432957,
-0.03771641477942467,
0.05668836832046509,
0.033019378781318665,
-0.002828035969287157,
0.03689160197973251,
0.013986113481223583,
0.06433708965778351,
0.013076269999146461,
0.04031581059098244,
0.014597433619201183,
-0.0231986865401268,
0.013463076204061508,
-0.0066718109883368015,
0.016220081597566605,
0.04887224733829498,
-0.016681713983416557,
0.003613221226260066,
-0.026965131983160973,
-0.03883049637079239,
0.01441396214067936,
-0.018681900575757027,
0.014684323221445084,
0.02327737770974636,
0.027453040704131126,
0.007892195135354996,
-0.01616387628018856,
-0.02763201668858528,
0.051960427314043045,
0.04834141582250595,
0.01455263327807188,
-0.03928186371922493,
-0.05882816016674042,
-0.016736464574933052,
-0.035448264330625534,
0.0042183599434792995,
0.030293984338641167,
0.019227175042033195,
-0.024219460785388947,
-0.0008791480795480311,
0.01428508386015892,
-0.030880743637681007,
-0.03103085234761238,
-0.020075544714927673,
-0.01641380786895752,
0.031830914318561554,
-0.0303889662027359,
0.03603381663560867,
0.03242344409227371,
0.05487053841352463,
0.03581824526190758,
0.03119444102048874,
-0.04087859392166138,
-0.061481229960918427,
0.005772109609097242,
0.02183384820818901,
0.029452582821249962,
0.012747646309435368,
-0.000710515130776912,
-0.03916802257299423,
-0.02100457064807415,
0.06655239313840866,
-0.01965116336941719,
-0.008980640210211277,
-0.02250799909234047,
0.008943791501224041,
-0.014801888726651669,
-0.006172065623104572,
-0.019825421273708344,
-0.020989306271076202,
0.0005767879774793983,
0.038249578326940536,
-0.024833055213093758,
-0.008003943599760532,
-0.04122988507151604,
0.0034239315427839756,
0.03282349556684494,
0.020989082753658295,
0.023631494492292404,
-0.010621368885040283,
0.00972360372543335,
0.01291662734001875,
-0.031454261392354965,
-0.08212259411811829,
-0.016818782314658165,
0.007568189408630133,
0.05478394776582718,
0.05178934335708618,
-0.013363415375351906,
-0.09452762454748154,
0.04251699149608612,
0.012165346182882786,
-0.018256783485412598,
0.02670866996049881,
-0.0177703108638525,
0.024763017892837524,
0.029972735792398453,
0.004945929627865553,
0.013538314960896969,
0.04621350020170212,
-0.012166677042841911,
-0.04865613952279091,
-0.044214602559804916,
0.03631052374839783,
-0.0177058856934309,
-0.002523438073694706,
-0.051384661346673965,
0.021988270804286003,
-0.02521738037467003,
-0.015472587198019028,
-0.018750065937638283,
0.013269267976284027,
-0.010285599157214165,
-0.040092695504426956,
-0.0013022723142057657,
0.023611560463905334,
0.02867567539215088,
-0.021592356264591217,
0.029097098857164383,
0.05782880634069443,
0.014762133359909058,
-0.014929900877177715,
0.007045984733849764,
-0.014549901708960533,
0.006069591268897057,
0.02208680473268032,
-0.018321087583899498,
0.02065756358206272,
-0.006680693477392197,
-0.012470558285713196,
0.011009838432073593,
-0.03632589429616928,
0.05857609212398529,
-0.018448228016495705,
0.022302867844700813,
0.02703756093978882,
-0.038319412618875504,
0.01867586188018322,
0.03048371896147728,
-0.01616288349032402,
0.034494027495384216,
-0.050213392823934555,
0.02748803235590458,
-0.012301314622163773,
-0.0036956481635570526,
-0.0668969601392746,
-0.043767884373664856,
0.007626850623637438,
0.02973128668963909,
-0.02080589346587658,
-0.023171037435531616,
0.003396078711375594,
-0.019091106951236725,
-0.03395477309823036,
0.006710782181471586,
0.022248394787311554,
-0.013932166621088982,
-0.04970543831586838,
0.050216030329465866,
0.025110678747296333,
0.06618796288967133,
-0.047737546265125275,
-0.032218147069215775,
-0.013041920959949493,
-0.033483345061540604,
-0.001400795648805797,
0.013931977562606335,
0.03302878513932228,
-0.025786207988858223,
-0.02143537811934948,
-0.012274951674044132,
-0.005918287672102451,
0.031346630305051804,
-0.018071318045258522,
0.04465246573090553,
-0.0019586633425205946,
-0.027756454423069954,
-0.03637714684009552,
-0.03973183035850525,
-0.016286242753267288,
-0.01997455582022667,
0.022919967770576477,
0.00611622491851449,
0.003702761372551322,
0.0028013684786856174,
-0.018633786588907242,
0.007500746753066778,
0.013862384483218193,
-0.011614118702709675,
0.013657763600349426,
0.052473798394203186,
0.016292618587613106,
-0.00043476957944221795,
-0.0023255504202097654,
-0.05515911802649498,
0.03495599329471588,
0.033990636467933655,
-0.04218246415257454,
0.006417966913431883,
0.029830267652869225,
-0.029384102672338486,
-0.058574531227350235,
-0.017802543938159943,
0.047210730612277985,
0.06020999327301979,
-0.013313633389770985,
0.0575520358979702,
0.04341168701648712,
-0.0012595333391800523,
-0.047326598316431046,
-0.050434522330760956,
0.0042700329795479774,
0.006903385277837515,
-0.02162436582148075,
0.03429415449500084,
-0.014178579673171043,
0.001427610986866057,
0.021544132381677628,
0.024180037900805473,
-0.026344189420342445,
0.006733615882694721,
0.0820859968662262,
-0.02187299355864525,
0.015508617274463177,
-0.018432743847370148,
-0.05371797829866409,
0.05955060198903084,
-0.04035133123397827,
0.0450194776058197,
-0.015051431022584438,
0.0122592868283391,
0.005252282600849867,
-0.007068476174026728,
0.01613415591418743,
-0.0619703009724617,
0.01802840456366539,
-0.02635212056338787,
0.018680507317185402,
0.01191316731274128,
0.014484062790870667,
-0.0007643962162546813,
0.0010600399691611528,
0.039384420961141586,
-0.004062966909259558,
-0.035464052110910416,
-0.001201061299070716,
-0.06788717210292816,
0.006872042082250118,
-0.0045954384841024876,
-0.04300875589251518,
0.02836047299206257,
0.022258464246988297,
-0.027738312259316444,
0.005442683584988117,
-0.01705469749867916,
0.008030042052268982,
0.00418748427182436,
0.02834000438451767,
-0.013462768867611885,
0.0367010235786438,
-0.003472418524324894,
0.015669453889131546,
-0.0041504669934511185,
-0.014667929150164127,
0.10165703296661377,
0.04122363403439522,
0.04556918144226074,
-0.038594190031290054,
0.012816759757697582,
-0.01406788919121027,
0.0076326229609549046,
0.004879090003669262,
0.02754932828247547,
-0.004145758226513863,
0.05838882923126221,
-0.011403030715882778,
0.06686138361692429,
-0.00360399903729558,
-0.0030740168876945972,
0.056223154067993164,
-0.04734103009104729,
-0.01293462049216032,
-0.03110465034842491,
0.029479429125785828,
-0.01054023765027523,
0.014954664744436741,
-0.056863658130168915,
0.027089450508356094,
-0.03546246513724327,
-0.03317614272236824,
-0.03388864919543266,
-0.03783086687326431,
0.028215426951646805,
0.007880426943302155,
-0.018276089802384377,
0.01399776991456747,
0.010769444517791271,
0.022630536928772926,
-0.07234898954629898,
0.04976852238178253,
0.028954973444342613,
-0.02353096939623356,
0.015508622862398624,
0.013326256535947323,
-0.00859653577208519,
0.0007707803160883486,
0.002053083386272192,
0.01841462031006813,
-0.06439471244812012,
-0.006923980079591274,
-0.026223216205835342,
0.0024362036492675543,
-0.0006398450932465494,
-0.03665929287672043,
0.0036433949135243893,
0.009613106958568096,
0.014336559921503067,
-0.07209379971027374,
-0.027513401582837105,
0.01165889110416174,
0.04607703164219856,
-0.0003741071850527078,
-0.03491893783211708,
0.004976854659616947,
0.026413697749376297,
-0.02360869012773037,
0.026840055361390114,
-0.0039000078104436398,
0.004965842701494694,
-0.0011148217599838972,
0.004888101480901241,
0.029517410323023796,
-0.013933496549725533,
-0.016571026295423508,
-0.027283750474452972,
0.004016026388853788,
-0.057968225330114365,
0.01489283051341772,
0.014900115318596363,
0.022427314892411232,
0.021537886932492256,
0.00411758478730917,
0.02442743629217148,
0.022099187597632408,
-0.04447438567876816,
0.04293845221400261,
-0.03390616178512573,
0.001314894761890173,
0.0018663115333765745,
0.027460187673568726,
0.03601574897766113,
0.019106583669781685,
-0.03479023650288582,
0.005045770201832056,
0.0118197500705719,
0.009576357901096344,
0.030133074149489403,
-0.007866797037422657,
-0.0661587193608284,
0.011153523810207844,
-0.06285697966814041,
0.004041293170303106,
0.009910352528095245,
0.04509766772389412,
0.0318322516977787,
0.024348950013518333,
0.0000479219997941982,
0.000807859527412802,
0.005650632083415985,
-0.013495168648660183,
-0.008006921969354153,
-0.03659043833613396,
-0.02043997123837471,
0.002298566047102213,
-0.012945124879479408,
-0.03760312497615814,
-0.024705486372113228,
-0.034724704921245575,
0.0021759367082268,
0.011352449655532837,
0.008382227271795273,
-0.014564596116542816,
0.002808817895129323,
-0.01068437285721302,
-0.009465999901294708,
-0.014485666528344154,
-0.010148567147552967,
-0.05583301931619644,
-0.021882446482777596,
0.030371755361557007,
0.009568816050887108,
0.012774103321135044,
0.024490289390087128,
-0.04187023267149925,
0.003784193191677332,
0.04129675030708313,
0.005779992789030075,
0.02350248396396637,
-0.01720166578888893,
0.05291702225804329,
0.005099136382341385,
0.04814651235938072,
-0.028002792969346046,
-0.05224468186497688,
0.019214607775211334,
0.011849003843963146,
-0.031539011746644974,
0.007087696809321642,
-0.03715141490101814,
-0.01638123393058777,
0.007009593304246664,
0.009874843992292881,
-0.02899010293185711,
0.060841046273708344,
-0.013026717118918896,
0.00845489650964737,
-0.012633534148335457,
-0.02112758532166481,
0.01114586554467678,
-0.00777487363666296,
0.043546613305807114,
-0.03364032506942749,
-0.010244900360703468,
0.05395166575908661,
0.02838256023824215,
0.0030160415917634964,
-0.0021684812381863594,
-0.008249768987298012,
0.003333884524181485,
0.019898265600204468,
0.036995626986026764,
-0.006172367837280035,
0.02560812048614025,
0.023419415578246117,
-0.05591510236263275,
0.05450604856014252,
0.05068589374423027,
0.015652336180210114,
-0.07951367646455765,
-0.005709935445338488,
0.025497911497950554,
-0.01291775330901146,
0.018408186733722687,
-0.054861970245838165,
-0.01245832908898592,
0.02924365922808647,
-0.07903175055980682,
-0.018678605556488037,
-0.04017964377999306,
-0.02854440174996853,
-0.03240102529525757,
0.0011477991938591003,
0.0027843390125781298,
0.06177400425076485,
0.02421710640192032,
0.015872811898589134,
0.042045410722494125,
0.003049319377169013,
-0.031158659607172012,
0.016303783282637596,
0.003924574702978134,
0.04701009765267372,
-0.005806018598377705,
-0.020619653165340424,
0.017606157809495926,
-0.024257436394691467,
-0.0702517032623291,
0.0008458257070742548,
-0.03171268850564957,
0.04039866104722023,
-0.0032595128286629915,
-0.021390123292803764,
-0.0315263606607914,
0.027654260396957397,
-0.013883697800338268,
-0.016675163060426712,
-0.03237071633338928,
0.0022647480946034193,
0.004876264370977879,
0.03435685858130455,
0.03308871388435364,
0.013791617006063461,
-0.024702852591872215,
-0.025956137105822563,
-0.012090965174138546,
0.03335065022110939,
-0.023475034162402153,
0.002248917706310749,
-0.009829926304519176,
0.01908617839217186,
0.03552396968007088,
0.002813147846609354,
0.03901916369795799,
-0.06630072742700577,
0.012182345613837242,
0.02672969177365303,
0.03249870613217354,
-0.022701449692249298,
0.023288603872060776,
0.03134727105498314,
-0.016815844923257828,
0.0036491304636001587,
-0.010337576270103455,
-0.031847935169935226,
-0.05232081934809685,
-0.015999678522348404,
-0.026194516569375992,
-0.03829197958111763,
-0.009962298907339573,
-0.031712424010038376,
0.0030265511013567448,
0.036227330565452576,
0.04291173070669174,
0.02689010091125965,
0.03338674455881119,
-0.056872252374887466,
-0.026474885642528534,
-0.06857695430517197,
0.047553900629282,
-0.003842534963041544,
0.01957656443119049,
-0.03775358572602272,
-0.004238642752170563,
-0.006469203624874353,
0.019486619159579277,
0.04705898463726044,
0.06454120576381683,
0.039918821305036545,
-0.029463009908795357,
-0.008808594197034836,
0.013817792758345604,
-0.03103748895227909,
-0.03508899360895157,
0.005075235851109028,
-0.04062003642320633,
0.04082038998603821,
-0.005421841982752085,
-0.009590398520231247,
-0.012524629011750221,
0.03496503829956055,
-0.043410222977399826,
0.03194665163755417,
0.011190395802259445,
-0.036541648209095,
0.016229193657636642,
-0.003014639485627413,
-0.02553441748023033,
0.08119072020053864,
-0.014858805574476719,
0.0037888791412115097,
0.012739039957523346,
-0.03692507743835449,
-0.05413395166397095,
0.029576824977993965,
-0.033736683428287506,
-0.03384798392653465,
-0.013234628364443779,
-0.02195562981069088,
0.024224525317549706,
-0.021565400063991547,
0.036932963877916336,
0.03212427720427513,
-0.04835807904601097,
0.012754028663039207,
0.053864505141973495,
0.04417974874377251,
0.01858559437096119,
-0.044332195073366165,
0.006809711456298828,
0.03305390104651451,
-0.013791551813483238,
0.0024790242314338684,
0.04710175469517708,
0.08304600417613983,
0.06380604207515717,
-0.001389670418575406,
-0.003605974605306983,
-0.010730493813753128,
0.0065837823785841465,
0.014395760372281075,
0.00257093389518559,
-0.015544909983873367,
-0.01807253435254097,
0.0443120002746582,
-0.012385002337396145,
0.033864669501781464,
-0.004189533181488514,
0.016835276037454605,
0.0675608366727829,
-0.005899303592741489,
-0.027716584503650665,
-0.0849880799651146,
-0.02364404872059822,
-0.018276352435350418,
-0.011444921605288982,
0.030045313760638237,
0.027256030589342117,
0.003193553537130356,
0.0032152049243450165,
-0.0065147122368216515,
-0.022151147946715355,
0.050430115312337875,
0.004003139678388834,
0.005243479274213314,
-0.0027927057817578316,
-0.009557262994349003,
-0.014049118384718895,
-0.009958084672689438,
-0.03187081590294838,
-0.001344253309071064,
0.02230381779372692,
0.009249558672308922,
0.005106145981699228,
0.029687777161598206,
-0.02129977010190487,
-0.029576340690255165,
0.037700068205595016,
-0.06144844740629196,
-0.04582529515028,
-0.009890373796224594,
0.03761283680796623,
-0.0006350770709104836,
-0.018867744132876396
] |
<p>I was trying to find out the cause behind the Explosion at petrol pump due to the Mobile phones but eventually it turns out it is not Radio Frequency which may cause the explosion rather it is totally the static electricity which may cause serious explosion and ignition of vapors,
The other reason I found is, due to the spark by the mobile phone battery in case the mobile has fallen out of your pocket and it seems more legit.
The second scenario, Its been said that Electromagnetic Waves absorb in liquid across a wide wavelength , is there any possibility that the absorption of radio Frequency in Petrol may cause any explosion ?</p>
<p>My question is,
anything can produce Static electricity then why mobile phones are prohibited ? Do they produce more Static Electricity than other equipments ? </p>
| 8,486 |
[
-0.05703175067901611,
-0.05205094441771507,
-0.002265241928398609,
0.0026096743531525135,
0.04488939791917801,
0.009743353351950645,
-0.025477919727563858,
-0.019903067499399185,
0.008598189800977707,
-0.020706048235297203,
0.026343828067183495,
0.044433098286390305,
0.017512541264295578,
-0.003995000850409269,
0.003094986779615283,
-0.012310539372265339,
0.04209241643548012,
-0.0036056446842849255,
0.0051557766273617744,
-0.03015073575079441,
-0.018194792792201042,
0.007578455377370119,
-0.007451758719980717,
-0.009290480986237526,
-0.05666553974151611,
-0.014436857774853706,
0.03663085773587227,
0.012107028625905514,
0.02320125326514244,
0.0023128085304051638,
-0.010619593784213066,
-0.020592281594872475,
-0.00014303484931588173,
-0.021709049120545387,
0.003738551866263151,
0.03206910938024521,
-0.0465567521750927,
-0.03941578418016434,
-0.05046620965003967,
-0.0453202985227108,
0.021444113925099373,
-0.008883033879101276,
0.016246573999524117,
0.04275239259004593,
-0.038233689963817596,
0.004906245041638613,
-0.021466264501214027,
-0.020228246226906776,
0.019219735637307167,
-0.07048233598470688,
0.05668547376990318,
-0.031077560037374496,
-0.0009897359414026141,
-0.0022233882918953896,
0.00007256834214786068,
0.03523053973913193,
0.06069354712963104,
0.030009500682353973,
-0.06195490434765816,
-0.05542467534542084,
0.00361358723603189,
0.018404562026262283,
-0.03552188724279404,
-0.023685242980718613,
-0.02152099274098873,
0.06430462002754211,
-0.002087763976305723,
-0.03789550065994263,
0.04559076204895973,
0.04587981849908829,
0.014311378821730614,
-0.03178337961435318,
0.020862137898802757,
0.017960606142878532,
0.03239445015788078,
-0.01999768428504467,
0.007286964450031519,
0.02362273819744587,
0.01983235776424408,
0.05741782486438751,
0.022644590586423874,
-0.004421761259436607,
-0.020194508135318756,
0.01105499267578125,
0.023564722388982773,
-0.03291403129696846,
0.05368175730109215,
0.012059557251632214,
0.022197915241122246,
0.0023862796369940042,
-0.003981757443398237,
0.0009998844470828772,
0.004250701051205397,
0.0370410792529583,
0.003978061024099588,
0.036276742815971375,
-0.019202977418899536,
0.05876200273633003,
0.014869460836052895,
-0.05620304495096207,
0.04179318994283676,
0.03695167601108551,
0.0853181779384613,
0.02924925647675991,
-0.005036960355937481,
-0.055701471865177155,
-0.03442498296499252,
0.010091427713632584,
-0.015046149492263794,
0.005486965179443359,
-0.02120538055896759,
-0.008711336180567741,
0.006129173096269369,
-0.0323784276843071,
0.011129997670650482,
-0.015113424509763718,
0.011890960857272148,
-0.03486111760139465,
0.05543447285890579,
0.09297630190849304,
-0.001230253605172038,
-0.015102334320545197,
0.007455835584551096,
-0.0003140396729577333,
-0.07941287755966187,
0.010821545496582985,
0.012851852923631668,
0.0018483512103557587,
-0.031612496823072433,
0.018084706738591194,
0.010050609707832336,
-0.004333386663347483,
0.0013180597452446818,
-0.0051660253666341305,
0.044578857719898224,
-0.021680686622858047,
-0.13072963058948517,
-0.07554700970649719,
0.013626537285745144,
-0.03577330708503723,
0.005228901747614145,
-0.054361291229724884,
-0.002280861372128129,
0.027206698432564735,
0.03601362928748131,
0.002699861768633127,
-0.004374556243419647,
-0.020685723051428795,
0.042484816163778305,
0.025240901857614517,
-0.014505482278764248,
-0.07457926869392395,
0.009704242460429668,
-0.004392705857753754,
0.02495061792433262,
-0.05617803707718849,
0.031191110610961914,
0.023916561156511307,
-0.009350771084427834,
-0.036285340785980225,
0.004886722657829523,
-0.014963511377573013,
-0.020444996654987335,
0.010703438892960548,
-0.02412400394678116,
-0.017365284264087677,
0.07576944679021835,
0.03286398574709892,
0.01494123600423336,
0.007668530102819204,
-0.012107038870453835,
0.08286502957344055,
0.015283796936273575,
-0.02905423939228058,
-0.013250582851469517,
-0.03519276902079582,
-0.006412535905838013,
-0.04232999309897423,
0.07353691011667252,
0.0075699337758123875,
-0.034810833632946014,
0.00000839509903016733,
-0.006232490297406912,
0.027385732159018517,
-0.014750163070857525,
0.015532821416854858,
-0.005882801953703165,
-0.037535976618528366,
0.010229809209704399,
-0.04108414798974991,
-0.03190043941140175,
-0.03148946166038513,
0.0674230083823204,
-0.021303359419107437,
-0.03464461863040924,
-0.012855082750320435,
-0.024073217064142227,
0.024673115462064743,
-0.0850830078125,
-0.012330370023846626,
0.01354015152901411,
0.010997110977768898,
0.00477558234706521,
-0.004899738822132349,
-0.017170095816254616,
0.03286908566951752,
-0.02735631912946701,
-0.0014123518485575914,
0.012522519566118717,
0.01931406557559967,
-0.04496126249432564,
0.019106410443782806,
-0.060608476400375366,
0.010874748229980469,
0.021904779598116875,
-0.038229577243328094,
0.038070738315582275,
-0.023394126445055008,
0.0023175382521003485,
0.0518413670361042,
-0.0380137637257576,
0.052794940769672394,
0.025360727682709694,
0.014446993358433247,
0.0017223895993083715,
0.03919797018170357,
-0.007734330836683512,
-0.013514864258468151,
0.014346444979310036,
-0.025512520223855972,
-0.043413907289505005,
-0.01074319425970316,
0.03101092204451561,
0.03380048647522926,
-0.05593639984726906,
0.00038747431244701147,
0.004406594671308994,
0.04697034880518913,
0.05379922315478325,
0.048008907586336136,
-0.012797828763723373,
-0.04348880797624588,
0.03717521205544472,
0.03922266513109207,
-0.01031487062573433,
0.021115640178322792,
0.008085856214165688,
-0.008472936227917671,
-0.01677042245864868,
-0.015361502766609192,
0.0002201741881435737,
0.0413416251540184,
-0.008991457521915436,
0.058565832674503326,
0.009315164759755135,
-0.018449701368808746,
0.017238331958651543,
-0.047434739768505096,
0.03565515950322151,
-0.019434554502367973,
-0.031589627265930176,
0.014034864492714405,
-0.0067213596776127815,
-0.0009041616576723754,
-0.0037254083435982466,
0.011505363509058952,
-0.06875414401292801,
-0.01845615543425083,
0.01872039958834648,
-0.06669431924819946,
-0.050934478640556335,
0.004221279639750719,
0.02276320941746235,
-0.007723414804786444,
-0.006176360417157412,
0.0441649965941906,
-0.01846993714570999,
0.04643000662326813,
-0.017845582216978073,
-0.0032997422385960817,
-0.015589104034006596,
-0.016671601682901382,
-0.006083871237933636,
-0.015128391794860363,
-0.022517118602991104,
0.014092275872826576,
-0.003936420660465956,
-0.03739488869905472,
0.08589180558919907,
-0.0362916924059391,
0.004271382000297308,
0.04305178299546242,
-0.02287925034761429,
-0.031092509627342224,
0.002290146891027689,
-0.022012392058968544,
0.027499893680214882,
0.009359709918498993,
-0.02474313974380493,
0.0102618969976902,
0.021742168813943863,
-0.027575615793466568,
-0.015245756134390831,
-0.043354734778404236,
-0.024370582774281502,
0.006713315844535828,
-0.02655971422791481,
-0.004753176122903824,
-0.028415510430932045,
0.018246663734316826,
0.01322441641241312,
-0.06772272288799286,
0.013987385667860508,
-0.02683315798640251,
-0.056026335805654526,
0.019163182005286217,
-0.017567163333296776,
0.08285587280988693,
-0.04143638163805008,
-0.04272934049367905,
0.030841277912259102,
0.042867302894592285,
-0.020138690248131752,
0.01613042689859867,
-0.044793352484703064,
-0.014531491324305534,
-0.05215359851717949,
0.008404400199651718,
0.08125875890254974,
-0.012150970287621021,
0.03584068641066551,
0.03645835816860199,
0.07130154222249985,
0.01988893933594227,
-0.013512878678739071,
-0.01338762603700161,
-0.0066070593893527985,
-0.03463750332593918,
-0.006562092807143927,
0.04180864617228508,
0.01461869291961193,
-0.028438623994588852,
-0.00981476716697216,
-0.013918528333306313,
0.022406907752156258,
0.020775146782398224,
-0.023347748443484306,
0.036385342478752136,
-0.0015775829087942839,
0.021360157057642937,
-0.027699140831828117,
0.03830451890826225,
0.012162850238382816,
-0.040989380329847336,
0.002551191719248891,
0.010057484731078148,
0.05632616579532623,
-0.03272813558578491,
0.009082235395908356,
0.02071489952504635,
0.0868082270026207,
-0.03420090675354004,
-0.031744979321956635,
0.03505057096481323,
0.018718117848038673,
0.0409366674721241,
-0.005572825204581022,
-0.00635065883398056,
0.057002052664756775,
0.015696078538894653,
0.04265470802783966,
-0.0013154743937775493,
0.016022931784391403,
-0.022957760840654373,
-0.050253137946128845,
-0.02810796909034252,
-0.01008645724505186,
0.05232280492782593,
0.024801012128591537,
0.05729043111205101,
0.009747468866407871,
-0.020086422562599182,
0.006837084889411926,
-0.019008059054613113,
-0.05914952978491783,
0.002631566720083356,
0.008970184251666069,
-0.01712818816304207,
-0.0011285979999229312,
-0.030977213755249977,
-0.05858580395579338,
0.012222188524901867,
-0.03168163076043129,
-0.016400307416915894,
-0.012562355026602745,
-0.0911494642496109,
0.0365685373544693,
-0.03085060976445675,
-0.06787656992673874,
-0.00488308584317565,
0.03442202880978584,
0.016164647415280342,
0.012501870281994343,
-0.004519595764577389,
-0.0004698510456364602,
-0.044146422296762466,
-0.01123647578060627,
0.004204493947327137,
-0.02606109529733658,
-0.010951453819870949,
0.037975095212459564,
0.0212120171636343,
-0.024446411058306694,
0.009605132974684238,
0.0016272998182103038,
0.027535319328308105,
0.02995859645307064,
0.01949862577021122,
0.019408391788601875,
-0.03924967721104622,
-0.01758907176554203,
-0.0233861543238163,
0.006506436970084906,
0.02649521455168724,
-0.015377617441117764,
0.01811457984149456,
-0.004649333655834198,
-0.043082207441329956,
0.012535041198134422,
0.01682554930448532,
0.05786909535527229,
0.0024214363656938076,
0.0276043564081192,
-0.009898647665977478,
-0.01008585374802351,
0.005184506066143513,
-0.025521833449602127,
0.04012037441134453,
0.018421368673443794,
-0.01692543737590313,
-0.02505612187087536,
0.04139023274183273,
0.030433574691414833,
-0.056248657405376434,
0.0616607628762722,
0.05352232605218887,
-0.03227418288588524,
-0.0008322526700794697,
-0.021509159356355667,
0.04095393046736717,
0.005679843481630087,
0.02497052401304245,
-0.014231248758733273,
-0.06314396113157272,
-0.10102739185094833,
0.029705913737416267,
0.02316601388156414,
0.053847603499889374,
-0.010743968188762665,
0.02034745179116726,
-0.05288034677505493,
0.014476875774562359,
-0.004784268792718649,
-0.06454633176326752,
0.0012987253721803427,
-0.03685429319739342,
0.010127486661076546,
0.0011840889928862453,
-0.009707261808216572,
-0.004102990962564945,
0.003953880630433559,
0.03398765251040459,
0.022508472204208374,
-0.028109975159168243,
-0.045400675386190414,
0.006924580316990614,
0.027489544823765755,
0.039406124502420425,
0.016208410263061523,
0.03945732116699219,
0.01101773139089346,
-0.04862748086452484,
0.027129754424095154,
-0.031237442046403885,
-0.028103703632950783,
0.01942487061023712,
-0.02166096493601799,
0.007450448349118233,
0.059377074241638184,
-0.024662943556904793,
-0.035553961992263794,
0.015130286104977131,
0.013736001215875149,
-0.012334955856204033,
-0.038155898451805115,
-0.03338455408811569,
0.007333457935601473,
0.041191212832927704,
0.003953843377530575,
0.0033067259937524796,
0.02940104529261589,
-0.04108569025993347,
0.026717185974121094,
0.005353511776775122,
0.021144689992070198,
-0.022911405190825462,
0.01190328598022461,
0.016641778871417046,
0.034534238278865814,
-0.017931168898940086,
0.06375239789485931,
0.024937331676483154,
0.012942553497850895,
-0.013650605455040932,
-0.04477700591087341,
-0.004370424896478653,
0.025461995974183083,
-0.034781891852617264,
-0.023984111845493317,
-0.05670960620045662,
0.019979719072580338,
0.02211434580385685,
-0.003019909607246518,
0.009370741434395313,
0.006044244859367609,
0.024333052337169647,
0.015497956424951553,
0.000026202436856692657,
0.01619492843747139,
-0.016004474833607674,
-0.003381192684173584,
0.012237141840159893,
-0.03755391016602516,
0.04819412901997566,
-0.03269881755113602,
-0.006587532814592123,
0.003475619712844491,
-0.0645410493016243,
-0.028359919786453247,
0.015080835670232773,
0.009118911810219288,
0.06405072659254074,
-0.04460020363330841,
0.05087224021553993,
0.007195385172963142,
-0.014055365696549416,
-0.05084914341568947,
-0.06029250845313072,
0.05998940393328667,
0.008698965422809124,
-0.026602454483509064,
-0.011066221632063389,
0.0032435995526611805,
-0.01106370147317648,
-0.025201745331287384,
0.007411251310259104,
0.009488610550761223,
-0.041158005595207214,
0.017273664474487305,
0.03816725313663483,
0.0020066152792423964,
0.07092000544071198,
0.012427229434251785,
-0.012723337858915329,
0.04436594992876053,
-0.02954244613647461,
-0.01501889992505312,
-0.027470862492918968,
0.028377322480082512,
0.0035393943544477224,
-0.06043839827179909,
-0.003891938365995884,
-0.02014094591140747,
0.02531294710934162,
-0.03690175712108612,
-0.0075622061267495155,
0.023302221670746803,
0.03885116055607796,
-0.005468633025884628,
-0.00845218263566494,
0.027313627302646637,
0.00827796384692192,
0.03932721167802811,
0.012045943178236485,
0.019690418615937233,
-0.0442756824195385,
-0.023162981495261192,
-0.020947523415088654,
-0.01020269375294447,
-0.009017666801810265,
0.019212666898965836,
0.03697064518928528,
0.0055138529278337955,
-0.002354065887629986,
0.03712008520960808,
-0.03732471168041229,
0.023353025317192078,
-0.03488323837518692,
0.01162988692522049,
0.013080877251923084,
0.027536416426301003,
0.03184858709573746,
-0.05357187241315842,
-0.03148982673883438,
0.009443950839340687,
0.01720629632472992,
-0.007851433008909225,
0.03743737190961838,
0.02231297641992569,
0.02519017457962036,
-0.02965809591114521,
-0.007586407009512186,
-0.005318285897374153,
0.02795155718922615,
-0.02885216474533081,
-0.00480375112965703,
0.00032328470842912793,
0.03480573371052742,
0.014164869673550129,
0.023998629301786423,
0.0332174226641655,
0.011710448190569878,
0.059835825115442276,
0.043761949986219406,
-0.008993846364319324,
-0.018107904121279716,
-0.05288591980934143,
-0.008873932994902134,
-0.036085836589336395,
0.028475740924477577,
0.02651098184287548,
-0.0016520241042599082,
0.0114098796620965,
-0.031697604805231094,
-0.013995938003063202,
-0.02199047990143299,
0.009836739860475063,
-0.04131385311484337,
0.009542247280478477,
-0.019289450719952583,
0.010651164688169956,
-0.0011669169180095196,
0.0004628240712918341,
-0.004523696843534708,
0.028825784102082253,
0.023065341636538506,
0.03541749715805054,
-0.06043201684951782,
-0.045698754489421844,
-0.0033355990890413523,
-0.030509045347571373,
0.04492180794477463,
-0.0044820657931268215,
-0.037970058619976044,
0.02140314318239689,
-0.05062108486890793,
0.03389935567975044,
-0.0073823463171720505,
0.02420806512236595,
-0.006739282980561256,
0.0777076780796051,
-0.003119340166449547,
0.011134359054267406,
0.010357851162552834,
0.009346088394522667,
0.11266181617975235,
0.016339030116796494,
0.03764653205871582,
-0.0378539115190506,
-0.01874273270368576,
-0.03958567976951599,
0.02334778569638729,
-0.04254535213112831,
0.011850399896502495,
-0.027429470792412758,
0.03374118730425835,
0.027944063767790794,
0.0411442369222641,
0.01372778695076704,
0.016370998695492744,
0.041498299688100815,
-0.010593115352094173,
-0.025780968368053436,
-0.006006891839206219,
0.05431258678436279,
0.0019276890670880675,
0.029005419462919235,
-0.05363836884498596,
0.032456155866384506,
-0.01971195638179779,
-0.009021583013236523,
-0.020853303372859955,
-0.028957681730389595,
0.037965647876262665,
0.004207123536616564,
-0.07108735293149948,
-0.028774801641702652,
-0.010945196263492107,
-0.021978123113512993,
-0.026120128110051155,
0.01971554383635521,
0.05238334834575653,
0.01965608447790146,
-0.03460563346743584,
0.04790983721613884,
0.03992178663611412,
-0.0496152900159359,
0.020241517573595047,
0.05876202881336212,
-0.056097377091646194,
0.020601851865649223,
-0.007961832918226719,
0.02480875328183174,
0.015646349638700485,
-0.0032798084430396557,
0.0022867980878800154,
0.015084640122950077,
-0.01758618652820587,
-0.00019080346100963652,
-0.0575840026140213,
-0.002013714052736759,
0.00018011571955867112,
0.0009296548087149858,
-0.01438912283629179,
-0.0691494271159172,
0.0268687941133976,
-0.015435833483934402,
0.037158168852329254,
0.01293368823826313,
0.016776299104094505,
-0.004825903568416834,
0.011181390844285488,
0.024602949619293213,
-0.03176978975534439,
-0.012009305879473686,
-0.01908382587134838,
-0.03748394921422005,
-0.04257550463080406,
-0.015104304999113083,
-0.010442052036523819,
0.061927132308483124,
0.03266448155045509,
0.017717383801937103,
-0.0023058780934661627,
0.011222580447793007,
-0.0380108579993248,
0.044454220682382584,
-0.008578144945204258,
-0.0387813001871109,
-0.012199162505567074,
0.02113613672554493,
-0.006938365288078785,
0.02437598817050457,
-0.04507894068956375,
-0.008227181620895863,
-0.0031197085045278072,
0.027798937633633614,
0.031536854803562164,
-0.021604733541607857,
-0.024548232555389404,
-0.023605044931173325,
-0.03281413018703461,
-0.0016391053795814514,
-0.00959800835698843,
0.011510277166962624,
0.00240022549405694,
-0.020307185128331184,
0.04415221884846687,
-0.011312447488307953,
-0.01095256581902504,
0.008566423319280148,
-0.0012766907457262278,
-0.0024638748727738857,
-0.044622402638196945,
0.01751629449427128,
0.051618486642837524,
0.02275206707417965,
-0.02346949465572834,
0.019744617864489555,
0.018917392939329147,
-0.0009115894790738821,
0.0420486219227314,
0.011168918572366238,
0.028108667582273483,
-0.029136309400200844,
0.01629817672073841,
-0.028025610372424126,
0.015872037038207054,
-0.047700367867946625,
-0.0015483167953789234,
-0.0008592820377089083,
-0.020984100177884102,
-0.032894812524318695,
0.05140458047389984,
-0.03957613557577133,
-0.0011811776785179973,
0.015173529274761677,
0.03067210502922535,
-0.03387363255023956,
-0.012668405659496784,
0.04842377081513405,
-0.005048278719186783,
0.05621863529086113,
-0.0471624918282032,
-0.006647627335041761,
0.04478950798511505,
-0.04248838126659393,
-0.019013047218322754,
0.05134935304522514,
-0.03807064890861511,
0.014221081510186195,
0.04079350456595421,
0.02409185655415058,
0.008467547595500946,
0.09601270407438278,
-0.013280893675982952,
0.001709245378151536,
0.0060211955569684505,
0.018211020156741142,
0.010607817210257053,
-0.009632918052375317,
-0.01437158789485693,
-0.014094882644712925,
-0.011393357068300247,
0.03283701464533806,
0.05904886871576309,
0.0196218304336071,
0.03127623349428177,
0.056647416204214096,
-0.012668715789914131,
0.008063381537795067,
-0.0033396976068615913,
0.008589467965066433,
0.052513208240270615,
0.032839640974998474,
-0.017013194039463997,
0.009832392446696758,
-0.014504275284707546,
-0.010849458165466785,
-0.09367703646421432,
-0.057320475578308105,
0.005274723283946514,
0.019636576995253563,
0.03223555162549019,
-0.02386101335287094,
0.028662536293268204,
0.02181118167936802,
-0.1001911386847496,
-0.0465223453938961,
0.007712841499596834,
-0.012995743192732334,
-0.010797563940286636,
0.007539927959442139,
-0.021331077441573143,
0.037727758288383484,
0.012230699881911278,
0.06785466521978378,
0.026013728231191635,
0.0030559804290533066,
-0.027098363265395164,
-0.0070832702331244946,
-0.0001243074075318873,
0.02746235951781273,
-0.01242453046143055,
0.031041130423545837,
0.08425511419773102,
-0.027661722153425217,
0.002836737083271146,
0.006514611653983593,
-0.02939092367887497,
0.013583377003669739,
0.020257581025362015,
0.01358039677143097,
0.019571805372834206,
0.04883761331439018,
0.007654293440282345,
0.004599046427756548,
-0.03825480490922928,
0.03070620633661747,
0.020783789455890656,
0.023613648489117622,
0.012332105077803135,
0.012188471853733063,
0.003599079791456461,
-0.03495626151561737,
0.009113597683608532,
-0.015464059077203274,
-0.01530255377292633,
-0.013371908105909824,
0.021110188215970993,
0.025507047772407532,
0.01904977858066559,
-0.025261612609028816,
-0.020335925742983818,
-0.04058018699288368,
-0.03052734211087227,
0.040728580206632614,
0.04665755107998848,
0.03645464405417442,
0.009883234277367592,
-0.015995778143405914,
-0.008822087198495865,
-0.00005342560325516388,
0.01467951387166977,
-0.02844739891588688,
-0.04597092792391777,
0.04695934057235718,
0.002083660801872611,
0.014782809652388096,
0.031025778502225876,
-0.04004930704832077,
-0.023499902337789536,
0.05615593120455742,
0.0017128381878137589,
0.0008680308819748461,
0.04205918312072754,
-0.031219065189361572,
-0.0157269649207592,
-0.04856608808040619,
0.026298249140381813,
-0.0091598154976964,
-0.00045492046047002077,
-0.03581647947430611,
-0.08421716839075089,
-0.005578093696385622,
0.025052357465028763,
0.02802155166864395,
-0.03128822520375252,
-0.025779375806450844,
0.007356894668191671,
0.006876974366605282,
0.0002976209216285497,
-0.01602567546069622,
0.016966262832283974,
0.02071436308324337,
-0.03454869985580444,
0.004731206223368645,
-0.014117707498371601,
-0.017777571454644203,
0.017293421551585197,
0.011393929831683636,
-0.004969749599695206,
0.008566167205572128,
-0.032839905470609665,
-0.04984554648399353,
0.02144162356853485,
0.031772512942552567,
0.01015628781169653,
0.05292665958404541,
-0.026369446888566017,
-0.014860116876661777,
0.008759711869060993,
-0.010275563225150108,
-0.03277634456753731,
0.020965905860066414,
0.008064446039497852,
0.03659970685839653,
-0.012976243160665035,
0.006431488785892725,
0.04452987015247345,
-0.01806964911520481,
0.01338773500174284,
-0.002647276734933257,
-0.002227283315733075,
-0.0030844409484416246,
0.07068634033203125,
0.004939371254295111,
-0.00956791266798973,
0.038314081728458405,
0.010172157548367977,
0.011179513297975063,
-0.018229681998491287,
-0.018734149634838104,
0.04879550263285637,
-0.006858564913272858,
-0.019588442519307137,
-0.011968632228672504,
0.05874921381473541,
0.0009556765435263515,
0.021087348461151123,
0.02663927897810936,
0.017384884878993034,
-0.009201918728649616,
-0.011949041858315468,
-0.001920085633173585,
0.013840718194842339,
-0.0040351334027945995,
0.029342301189899445,
-0.015284383669495583,
0.05784507840871811,
-0.003791975788772106,
0.012991570867598057,
-0.023563159629702568,
0.008074941113591194,
-0.012967501766979694,
0.0050159902311861515,
0.0007290930952876806,
0.010751770809292793,
-0.0031208929140120745,
-0.008330117911100388,
-0.018530884757637978,
0.02787288837134838,
0.02738252840936184,
-0.016936084255576134,
-0.004843901842832565,
-0.025379028171300888,
-0.012078000232577324,
-0.05500612035393715,
-0.02912576124072075,
0.00730351684615016,
0.020358705893158913,
0.033996231853961945,
0.062164057046175,
-0.020398152992129326,
-0.009804763831198215,
-0.020932430401444435,
-0.03934406861662865,
0.03806260973215103,
-0.042063646018505096,
0.01117237750440836,
-0.0065149301663041115,
-0.006684888154268265,
-0.027708502486348152,
-0.03667672351002693
] |
<p>How does <a href="http://en.wikipedia.org/wiki/Annihilation" rel="nofollow">annihilation</a> work? I'm wondering why matter and antimatter actually annihilates if they come into contact. What exactly happens? Is that a known process? Is it just because of their different charges? Then what about neutrons and anti-neutrons? I guess that would be about their quarks, but wouldn't it be very unlikely what all of their individual quarks would actually touch the anti-quarks of the other (anti-)neutron at exactly the same time?</p>
| 935 |
[
-0.01426426600664854,
-0.04761205613613129,
-0.010172019712626934,
-0.036770980805158615,
0.03030390292406082,
0.027045445516705513,
-0.051493898034095764,
-0.027027243748307228,
-0.0021524974144995213,
0.000014120917512627784,
0.041277751326560974,
0.03013380989432335,
0.04272795468568802,
-0.0037988717667758465,
0.014195927418768406,
0.004069026093930006,
0.0004620334948413074,
-0.05200061574578285,
0.014602705836296082,
-0.035642120987176895,
0.022176261991262436,
-0.019635727629065514,
-0.012736224569380283,
-0.0053014387376606464,
-0.027495423331856728,
0.04463927447795868,
0.030554398894309998,
-0.000999151961877942,
0.04184703528881073,
0.027678480371832848,
0.015850378200411797,
-0.04712639003992081,
0.020512733608484268,
0.006755910813808441,
0.017831454053521156,
-0.003375257831066847,
0.008806622587144375,
-0.0344952754676342,
-0.013764657080173492,
0.015556445345282555,
-0.027298618108034134,
-0.04868830367922783,
-0.011990610510110855,
0.035856593400239944,
-0.07383226603269577,
-0.004891475196927786,
0.006965636741369963,
0.0013272508513182402,
0.03235169127583504,
-0.0663653090596199,
0.029414856806397438,
0.053227756172418594,
0.06362645328044891,
0.004495905712246895,
-0.002092634327709675,
0.02356976456940174,
0.07123857736587524,
0.0620330311357975,
-0.012223823927342892,
-0.04244529828429222,
-0.01777595654129982,
-0.0058081913739442825,
-0.019674664363265038,
-0.00360287306830287,
-0.04775594547390938,
0.044701188802719116,
-0.0035248063504695892,
-0.0035413342993706465,
0.0056007979437708855,
0.01851191744208336,
0.018226759508252144,
0.02551841549575329,
0.03308919072151184,
0.015108498744666576,
-0.004744807258248329,
-0.030070532113313675,
0.06075098738074303,
-0.01783878728747368,
0.0298814307898283,
0.08319691568613052,
-0.023774482309818268,
0.029657404869794846,
-0.010424831882119179,
0.026319224387407303,
0.02406368963420391,
-0.023540981113910675,
0.07425608485937119,
0.009765248745679855,
-0.007832138799130917,
0.024099621921777725,
-0.0069836778566241264,
0.003556914394721389,
0.017146840691566467,
0.01649480126798153,
-0.013902825303375721,
0.050691526383161545,
0.008956165052950382,
0.05117237567901611,
0.010069762356579304,
-0.020808661356568336,
0.022449979558587074,
0.017822980880737305,
0.021149689331650734,
0.038047824054956436,
0.019196147099137306,
-0.03229920566082001,
-0.050392646342515945,
0.04073405638337135,
-0.024641629308462143,
-0.00035389262484386563,
-0.024665985256433487,
0.015905460342764854,
0.003451973432675004,
-0.023656409233808517,
0.02301836386322975,
-0.009123011492192745,
0.003673902014270425,
-0.017431041225790977,
0.06991646438837051,
0.05192771181464195,
0.030762378126382828,
0.0017468179576098919,
0.010494275949895382,
-0.05099138990044594,
-0.03313804045319557,
-0.011642864905297756,
0.02087988331913948,
0.00571531243622303,
-0.03755094110965729,
0.033032018691301346,
-0.028153030201792717,
-0.00011388926941435784,
0.014882342889904976,
-0.028475351631641388,
0.03346001356840134,
-0.028689030557870865,
-0.11803928017616272,
-0.0778968408703804,
0.029535042122006416,
-0.03843160718679428,
-0.06269842386245728,
-0.05279890075325966,
-0.01559400837868452,
0.02553429640829563,
0.06230287253856659,
-0.021921394392848015,
-0.05178237706422806,
0.01624692603945732,
0.006883845664560795,
0.01321140956133604,
0.0055719586089253426,
-0.023370465263724327,
0.024859776720404625,
-0.025806009769439697,
-0.006497915368527174,
-0.06047538295388222,
0.04072672128677368,
0.04412297531962395,
-0.002606248017400503,
-0.023333106189966202,
0.05904645100235939,
-0.005689512938261032,
-0.005540790501981974,
0.02638974040746689,
-0.014505895785987377,
-0.028735162690281868,
0.0813525915145874,
0.026770925149321556,
-0.032047856599092484,
0.055220235139131546,
0.03167146444320679,
0.050757866352796555,
0.009299343451857567,
0.0501776859164238,
0.0446467287838459,
-0.013042565435171127,
-0.008899643085896969,
-0.03647349774837494,
-0.00598731217905879,
-0.029452944174408913,
-0.04333747550845146,
-0.03238104283809662,
-0.024011533707380295,
0.04694492369890213,
0.0328679122030735,
0.04853964224457741,
-0.013442432507872581,
-0.023580504581332207,
-0.013073922134935856,
-0.048345133662223816,
-0.03784353286027908,
-0.08752892166376114,
0.020626427605748177,
-0.0359622947871685,
-0.0037379912100732327,
0.008802100084722042,
0.040794190019369125,
0.005480761174112558,
-0.043347153812646866,
-0.021480144932866096,
-0.0214578527957201,
0.04327838867902756,
-0.018794676288962364,
-0.001945266965776682,
0.01333946455270052,
0.04854781925678253,
0.02921278215944767,
-0.012875196523964405,
0.021242475137114525,
-0.004079072270542383,
-0.011909631080925465,
0.00017295160796493292,
-0.015506335534155369,
-0.025886230170726776,
0.014415929093956947,
-0.013264281675219536,
0.03267773985862732,
-0.0012409687042236328,
0.008404682390391827,
0.02329949475824833,
-0.0024646660313010216,
0.08497966080904007,
-0.008125205524265766,
0.009869556874036789,
-0.02808329649269581,
0.02301177754998207,
0.050904739648103714,
0.023195084184408188,
-0.00988006591796875,
-0.040316417813301086,
-0.05424037575721741,
-0.02283598855137825,
0.016898781061172485,
0.019272174686193466,
-0.010878762230277061,
0.024775398895144463,
-0.01504572480916977,
0.037370409816503525,
-0.0061680106446146965,
0.04003762826323509,
-0.019281547516584396,
-0.014758806675672531,
-0.0067930445075035095,
0.002825469011440873,
-0.000851518998388201,
0.0034677821677178144,
0.03327111154794693,
0.016250474378466606,
-0.0045098369009792805,
-0.011729489080607891,
-0.03931492567062378,
0.04558589309453964,
-0.02152579091489315,
-0.0038908624555915594,
-0.0006195320165716112,
-0.06776882708072662,
0.0006021857261657715,
-0.012258640490472317,
0.016353817656636238,
-0.005784451030194759,
-0.001784433494322002,
-0.0037067257799208164,
-0.02558540739119053,
0.006744715850800276,
0.004760582000017166,
0.0018917882116511464,
-0.009864631108939648,
-0.006095979828387499,
0.0048454394564032555,
-0.05408615618944168,
0.020806927233934402,
-0.00673937052488327,
0.0002552185032982379,
-0.02177891880273819,
-0.00006830988422734663,
0.03503589704632759,
0.04023604467511177,
0.0502144917845726,
-0.04236356541514397,
-0.07273802906274796,
-0.010472893714904785,
-0.05467262119054794,
0.012595545500516891,
0.04269024729728699,
-0.0325937420129776,
0.029417820274829865,
-0.06585671007633209,
-0.019155465066432953,
0.026708027347922325,
-0.029274113476276398,
0.009444008581340313,
0.03617675602436066,
-0.0355667807161808,
-0.07076390087604523,
-0.012799910269677639,
-0.0005618805298581719,
-0.0044897012412548065,
-0.033116526901721954,
0.05017996206879616,
0.04840695485472679,
0.002760109957307577,
-0.0348958857357502,
0.008534397929906845,
-0.058454882353544235,
-0.055293288081884384,
-0.006057157646864653,
0.007748511619865894,
0.05333610996603966,
-0.019254781305789948,
0.0077274092473089695,
0.05613844096660614,
-0.07327702641487122,
0.014802489429712296,
-0.04264485463500023,
-0.017728237435221672,
0.01625652052462101,
-0.011645037680864334,
0.02821383625268936,
0.015259196050465107,
-0.02490070089697838,
0.05251617729663849,
0.012499114498496056,
-0.04834916815161705,
0.0042562359012663364,
0.025360984727740288,
-0.022526919841766357,
0.007673099637031555,
0.03288034722208977,
0.03281060978770256,
-0.0007860275800339878,
0.010320751927793026,
0.028036711737513542,
0.06312493979930878,
0.01764642633497715,
0.020609209313988686,
-0.008275022730231285,
-0.03758089244365692,
0.030053626745939255,
-0.011050163768231869,
-0.0034054170828312635,
-0.0019901269115507603,
-0.012445206753909588,
0.004482520744204521,
0.029306795448064804,
0.0346192829310894,
0.00772306090220809,
-0.008615677244961262,
0.04221131280064583,
0.008341284468770027,
0.008682372979819775,
-0.029268167912960052,
0.028410937637090683,
-0.03626759722828865,
-0.0045083859004080296,
0.03496917709708214,
0.010919751599431038,
0.03697247430682182,
-0.01206528302282095,
0.006640242878347635,
0.018788279965519905,
0.03960511460900307,
-0.05706596374511719,
-0.04093264415860176,
0.003011781256645918,
0.0006717866635881364,
0.002701705554500222,
0.011231964454054832,
0.037369709461927414,
0.022910533472895622,
0.021070417016744614,
0.019001970067620277,
-0.013823376968502998,
-0.022495675832033157,
-0.012432034127414227,
-0.09708479046821594,
-0.00877179205417633,
0.000710907974280417,
0.03460558503866196,
-0.008810901083052158,
0.08991937339305878,
0.014629017561674118,
0.014189607463777065,
0.013248342089354992,
-0.027471620589494705,
-0.08503786474466324,
0.039643239229917526,
-0.05182049050927162,
-0.03402959182858467,
-0.023724811151623726,
-0.028367789462208748,
0.0010112059535458684,
0.008423378691077232,
-0.03537572920322418,
-0.02475571073591709,
-0.025386136025190353,
-0.03611522167921066,
0.031163781881332397,
-0.07144073396921158,
-0.025386808440089226,
-0.008194084279239178,
0.03475213050842285,
0.05722764879465103,
0.0024075014516711235,
-0.0015306234126910567,
0.03199847415089607,
-0.05909350514411926,
-0.00830311980098486,
-0.03719945624470711,
-0.0036959664430469275,
0.018422110006213188,
0.0464106909930706,
0.05361144244670868,
0.013010571710765362,
-0.023023277521133423,
-0.004315688740462065,
0.00960663240402937,
0.06619859486818314,
0.009164313785731792,
-0.0026405686512589455,
-0.007050775457173586,
-0.04292362555861473,
-0.016243167221546173,
-0.0026612989604473114,
0.02932572551071644,
-0.03319261223077774,
0.011808515526354313,
0.024317249655723572,
0.03718414902687073,
-0.03527652844786644,
0.06021038442850113,
0.059877414256334305,
0.011960615403950214,
0.0003123426577076316,
-0.03793300688266754,
-0.020123908296227455,
-0.004403218161314726,
0.013543604873120785,
0.013459320180118084,
-0.03440964221954346,
-0.02392934076488018,
0.0065868389792740345,
0.024752726778388023,
0.01693650893867016,
-0.059875015169382095,
0.02503291703760624,
-0.04179171845316887,
-0.01584307663142681,
-0.008069238625466824,
-0.0039010969921946526,
-0.006589279510080814,
0.03472201153635979,
0.03366325795650482,
-0.003722697263583541,
-0.002964095212519169,
-0.056982189416885376,
0.014702987857162952,
0.05002941936254501,
0.0529729463160038,
-0.00950226653367281,
-0.024761507287621498,
-0.06182227283716202,
-0.015384883619844913,
0.06334786862134933,
-0.03808728978037834,
0.005759244319051504,
0.004479025490581989,
-0.027154792100191116,
-0.022491009905934334,
-0.009961828589439392,
0.016077157109975815,
0.03380105644464493,
-0.009031271561980247,
-0.015457850880920887,
-0.024012967944145203,
-0.005581383127719164,
-0.03311796858906746,
0.014982410706579685,
0.039712775498628616,
0.024297548457980156,
-0.003007489023730159,
0.029407594352960587,
0.007016817573457956,
0.017851727083325386,
-0.015655631199479103,
-0.07243411988019943,
-0.005003160797059536,
0.000827068171929568,
-0.034876104444265366,
0.05473275110125542,
-0.021938133984804153,
-0.036384351551532745,
0.007535838522017002,
0.01114471722394228,
0.003039494389668107,
-0.03157487139105797,
-0.056024711579084396,
0.03175346553325653,
0.04055378958582878,
-0.03207819163799286,
0.04834701120853424,
0.02811138890683651,
-0.031314801424741745,
-0.021944507956504822,
-0.04040875285863876,
0.027670569717884064,
0.015448830090463161,
0.017039209604263306,
-0.02772793546319008,
0.011605004779994488,
-0.01912042871117592,
0.04515078663825989,
-0.027646968141198158,
0.013939937576651573,
-0.001678363885730505,
-0.027664372697472572,
-0.016054192557930946,
0.0025566548574715853,
0.017857445403933525,
-0.011964095756411552,
0.016676153987646103,
0.003241603961214423,
-0.018608301877975464,
-0.01911219209432602,
0.04260092228651047,
0.0031922687776386738,
0.007513204123824835,
0.0026348449755460024,
-0.014094293117523193,
0.02580811269581318,
-0.046269092708826065,
-0.03268309310078621,
0.040290240198373795,
-0.02538437396287918,
0.01997988298535347,
-0.017351383343338966,
-0.007276279851794243,
0.03130088746547699,
-0.0611836202442646,
-0.05657247081398964,
0.020328354090452194,
-0.019223036244511604,
0.040231794118881226,
-0.036340970546007156,
0.05970771983265877,
0.02977428399026394,
-0.0015428827609866858,
-0.07268672436475754,
-0.06071898713707924,
0.05777513235807419,
-0.013054956682026386,
-0.015006874687969685,
-0.043461449444293976,
-0.01000747550278902,
-0.0005794495227746665,
-0.0009582368656992912,
-0.003328596940264106,
0.02772221341729164,
-0.04176653176546097,
-0.031564850360155106,
0.03021426685154438,
0.003901589196175337,
0.03943457826972008,
0.005022166296839714,
-0.03438016399741173,
-0.002406988525763154,
-0.008228680118918419,
0.030264580622315407,
0.0282126571983099,
0.05403909459710121,
0.001163420733064413,
-0.06859147548675537,
-0.0026807442773133516,
0.009739471599459648,
0.02711963653564453,
-0.05237068235874176,
0.040109746158123016,
0.0006965931388549507,
0.025441255420446396,
0.00486037926748395,
0.019018683582544327,
0.03008389100432396,
-0.004928156267851591,
0.019042514264583588,
0.010125883854925632,
-0.026865845546126366,
-0.022052811458706856,
-0.04639565944671631,
0.02171584591269493,
-0.028876183554530144,
0.020020682364702225,
0.005838410463184118,
0.04161723330616951,
-0.021806279197335243,
0.010522069409489632,
0.0040712375193834305,
-0.019427942112088203,
0.05298282578587532,
-0.04993663728237152,
-0.004608234390616417,
0.018079189583659172,
-0.01890418864786625,
0.0025979396887123585,
-0.022039789706468582,
-0.03224778175354004,
0.002987438580021262,
0.02214941196143627,
-0.06667988747358322,
0.04795625060796738,
0.005169117823243141,
0.014650391414761543,
-0.00500946631655097,
-0.0155182471498847,
0.0028530561830848455,
-0.000006864263468742138,
0.007311341818422079,
0.01847809925675392,
-0.016307275742292404,
0.0031866375356912613,
0.03154519945383072,
0.06275814026594162,
-0.0010786636266857386,
0.001043311902321875,
0.03444790840148926,
0.01184146199375391,
0.012146668508648872,
0.010417541489005089,
-0.03690148517489433,
0.031144479289650917,
-0.03875790908932686,
0.004223483148962259,
0.006010726559907198,
-0.040808599442243576,
0.02963244915008545,
-0.007020351942628622,
0.031497132033109665,
-0.008628075011074543,
-0.022369075566530228,
-0.00395941361784935,
0.018593430519104004,
0.020484382286667824,
0.025245949625968933,
-0.024171089753508568,
0.04480791091918945,
0.035715632140636444,
0.016639020293951035,
0.017274057492613792,
0.006876797415316105,
-0.08010970056056976,
-0.03378736227750778,
-0.05083964392542839,
-0.026445504277944565,
0.007402482442557812,
-0.02540416270494461,
-0.009035267867147923,
0.0133615517988801,
-0.031844571232795715,
0.04684432968497276,
0.0071413093246519566,
0.021439049392938614,
-0.037776485085487366,
0.05823550000786781,
-0.018225790932774544,
0.025906499475240707,
0.006009148433804512,
0.009596827439963818,
0.09880190342664719,
0.028034210205078125,
-0.007123721297830343,
-0.07872217148542404,
-0.012034990824759007,
-0.008227820508182049,
-0.0010972595773637295,
-0.02883727103471756,
0.019732072949409485,
-0.000027084353860118426,
0.03571759909391403,
0.03174719214439392,
0.055931348353624344,
0.03586029261350632,
-0.0006054960540495813,
0.0660494789481163,
-0.0538904182612896,
-0.06879778206348419,
-0.015825659036636353,
-0.00298498896881938,
-0.008558371104300022,
0.006585064809769392,
-0.07558047026395798,
0.042324498295784,
-0.0019666021689772606,
0.011418069712817669,
-0.031286533921957016,
-0.019359862431883812,
0.020855462178587914,
0.03454386815428734,
-0.020270811393857002,
0.009918969124555588,
0.0215944591909647,
-0.01767268218100071,
-0.011798955500125885,
0.01898798905313015,
0.034171212464571,
-0.02309022843837738,
0.01954355649650097,
0.015030205249786377,
0.0347202867269516,
-0.0027573853731155396,
0.006393088959157467,
0.02484927512705326,
-0.053433626890182495,
-0.019780989736318588,
-0.007784901186823845,
0.028757058084011078,
-0.028717320412397385,
-0.0143797118216753,
-0.01067813765257597,
0.009940245188772678,
0.030779296532273293,
-0.006440167315304279,
-0.030175598338246346,
-0.00953089538961649,
0.004508950747549534,
-0.019441688433289528,
0.007091734558343887,
-0.03331216424703598,
0.03666886314749718,
-0.04504218325018883,
0.0447254478931427,
-0.015987489372491837,
0.0083547318354249,
0.00783899798989296,
-0.01668650470674038,
-0.0015575587749481201,
-0.023570261895656586,
-0.00019399505981709808,
-0.05135858431458473,
0.002118718344718218,
-0.03766703978180885,
-0.0154386842623353,
0.034270305186510086,
0.049363404512405396,
0.06065886467695236,
0.027716729789972305,
-0.009444939903914928,
-0.01723313517868519,
-0.026516906917095184,
0.05932546406984329,
-0.019449405372142792,
-0.03850056603550911,
0.0019430225947871804,
-0.013239879161119461,
0.013955233618617058,
0.0329500287771225,
-0.027798494324088097,
0.012462735176086426,
-0.01163040567189455,
0.00298606907017529,
0.03053140826523304,
0.012725839391350746,
0.004914800636470318,
0.010309692472219467,
-0.024822795763611794,
-0.0021546881180256605,
-0.03383500874042511,
0.05304333195090294,
0.03023514524102211,
0.0023210186045616865,
0.034471455961465836,
0.03265612944960594,
-0.008378550410270691,
-0.01910325139760971,
0.009529787115752697,
-0.02028404362499714,
-0.006465146783739328,
0.01535616721957922,
0.015298181213438511,
-0.010889304801821709,
-0.0038432267028838396,
0.0013205583672970533,
0.002045433036983013,
0.013581735081970692,
0.05088222026824951,
-0.02826804853975773,
0.010935463942587376,
-0.008564508520066738,
0.02312326617538929,
-0.009477585554122925,
-0.008389810100197792,
-0.06630206108093262,
-0.0035389666445553303,
-0.011663402430713177,
-0.015129750594496727,
-0.015888860449194908,
0.015212700702250004,
-0.003169373841956258,
0.0030599755700677633,
0.018429363146424294,
0.02296404168009758,
-0.03672218322753906,
-0.014759528450667858,
0.043947841972112656,
-0.011653522029519081,
0.04329594224691391,
-0.0067637222819030285,
-0.02125019207596779,
0.06897994875907898,
-0.035239413380622864,
-0.05499577894806862,
-0.0034778183326125145,
-0.025219300761818886,
0.02303275093436241,
0.002531000878661871,
-0.046697501093149185,
-0.04023640602827072,
0.08933422714471817,
-0.03295408934354782,
-0.013996814377605915,
0.0034111780114471912,
-0.005556934978812933,
-0.02588219754397869,
0.015154480002820492,
-0.019028378650546074,
-0.009373989887535572,
-0.031969089061021805,
0.044422026723623276,
0.009100721217691898,
-0.009954210370779037,
0.019537916406989098,
-0.027120836079120636,
0.005733289290219545,
0.03890816494822502,
0.031048355624079704,
0.007859159260988235,
-0.0003581205673981458,
0.05748192220926285,
-0.010532972402870655,
0.06777935475111008,
0.004703172016888857,
0.0013309657806530595,
-0.09043707698583603,
0.01814795844256878,
-0.011322145350277424,
-0.022540638223290443,
0.00863347202539444,
-0.03177208825945854,
0.020064646378159523,
0.05226055905222893,
-0.0364895835518837,
0.029810985550284386,
-0.04213573411107063,
-0.04571294039487839,
-0.020202623680233955,
-0.01708994060754776,
-0.00470017921179533,
0.0642084851861,
0.04236774146556854,
0.037951525300741196,
0.015825271606445312,
-0.016107816249132156,
-0.0326792448759079,
-0.015211755409836769,
-0.035074710845947266,
0.01144248154014349,
-0.02335921861231327,
-0.005326020065695047,
0.04835866391658783,
0.006057770922780037,
-0.0013369941152632236,
0.019416116178035736,
-0.04086323454976082,
-0.040434278547763824,
-0.001422312343493104,
0.02777605876326561,
0.0037055963184684515,
0.008126534521579742,
-0.009080994874238968,
0.013373945839703083,
0.008946683257818222,
0.0657181590795517,
0.015306148678064346,
0.025050487369298935,
0.006156557705253363,
0.003951242659240961,
0.021040333434939384,
-0.01237387116998434,
-0.0228259339928627,
0.02991541102528572,
0.0180081557482481,
-0.020725343376398087,
-0.017087973654270172,
0.032502513378858566,
0.03283350542187691,
-0.018038257956504822,
-0.0069833784364163876,
0.0022811987437307835,
0.021500397473573685,
0.021988121792674065,
0.0225985124707222,
0.031215859577059746,
0.026002751663327217,
-0.032040923833847046,
0.0025807649362832308,
-0.0028777816332876682,
0.0028202796820551157,
0.009870775043964386,
-0.01456382218748331,
-0.01146942563354969,
0.04281089827418327,
0.046696875244379044,
0.006254459265619516,
-0.06265249848365784,
-0.03683165833353996,
0.02748708240687847,
0.021156491711735725,
0.05094561725854874,
-0.008948341943323612,
-0.07422482967376709,
-0.017535049468278885,
-0.041817352175712585,
0.017296507954597473,
-0.023539571091532707,
0.014089057222008705,
-0.06509902328252792,
0.007871749810874462,
-0.002834605285897851,
0.0009434211533516645,
0.027506927028298378,
-0.0054315426386892796,
-0.02978769689798355,
0.00860907044261694,
-0.007580125704407692,
0.011360556818544865,
-0.017579231411218643,
-0.01755712926387787,
-0.010761065408587456,
-0.03717534989118576,
-0.021343830972909927,
0.004473171196877956,
-0.038953863084316254,
0.045633673667907715,
-0.0026554283685982227,
-0.04013466462492943,
-0.004225785844027996,
0.003536249976605177,
-0.0443451963365078,
0.0466819703578949,
-0.008314395323395729,
0.021158192306756973,
0.0795251652598381,
-0.0037319485563784838,
0.030537182465195656,
0.04014640673995018,
-0.005365295801311731,
-0.021514492109417915,
0.015437343157827854,
-0.029234088957309723,
0.003807068569585681,
-0.006912554614245892,
-0.02335410565137863,
0.05780462920665741,
-0.0412592776119709,
0.024618254974484444,
0.015635618939995766,
-0.028546232730150223,
-0.022694431245326996,
0.031135866418480873,
0.037680141627788544,
0.050889886915683746,
0.0005237692384980619,
0.015038268640637398,
0.013755321502685547,
0.04755198955535889,
-0.011483999900519848,
0.04376335069537163,
0.004059899132698774,
0.0428011491894722,
0.001749240793287754,
0.008063001558184624,
0.021108699962496758,
0.0062775076366961,
-0.006073531229048967,
0.05490078032016754,
-0.0032802764326334,
-0.03194836527109146,
0.001011646119877696,
-0.04499473422765732,
0.05392344295978546,
0.03015562891960144,
-0.028605040162801743,
0.09439126402139664,
-0.0463024377822876,
0.04462667554616928,
0.015190120786428452,
0.013506517745554447,
-0.012868067249655724,
0.01451647188514471,
-0.009049832820892334,
0.04015415906906128,
-0.04103388637304306,
-0.035308051854372025,
-0.025028951466083527,
0.020436210557818413,
0.0450725294649601,
-0.024124424904584885,
0.0371597483754158,
-0.001067653181962669,
-0.01024262048304081,
-0.03523671254515648,
-0.0067489491775631905,
-0.02406240813434124,
-0.04062189534306526,
0.02768850512802601,
0.025243869051337242,
-0.0047986782155931,
0.011032351292669773,
-0.00803160760551691,
-0.03436213359236717,
0.025474796071648598,
-0.04980994015932083,
-0.01774684339761734,
-0.05254652351140976,
0.01668262667953968,
-0.04588771238923073,
0.011667839251458645
] |
<p>I recently heard about the possibility of the creation of a "baby" universe or "pocket" universe from our space time,the theory says that concentrating enough mass into a tiny volume of space (like in black holes) a pocket of false vacuum would form e perhaps it'll continue to expand following it's own inflation period and go on forever completly disconnected from our space time without influencing it any way. Now my question is : supposing that we live in a metastable vacuum we know that true vacuum bubble could form via quantum tunnelling and begin to expand into our space time where these false vacuum bubble (or pocket/baby universe) are supposed to go and expand ?</p>
| 8,487 |
[
0.0032622874714434147,
-0.02404114231467247,
0.015069907531142235,
-0.028607435524463654,
0.04157338663935661,
-0.01015506498515606,
0.003961534239351749,
-0.06795503199100494,
0.013986503705382347,
-0.03646918013691902,
-0.020994141697883606,
0.023977363482117653,
0.002482267329469323,
-0.028687970712780952,
-0.01184100192040205,
0.016739683225750923,
-0.008803489618003368,
-0.03326673433184624,
0.0034159908536821604,
-0.04450015351176262,
0.03544281795620918,
0.03376984968781471,
-0.01496207807213068,
-0.00040867560892365873,
-0.02780861034989357,
0.02779165469110012,
0.01928936317563057,
0.01660054177045822,
-0.0033075250685214996,
0.039203476160764694,
-0.017987282946705818,
-0.01950460858643055,
0.004093253053724766,
0.0011542574502527714,
0.023380808532238007,
-0.042175985872745514,
-0.0444159135222435,
-0.027297409251332283,
-0.01001798827201128,
-0.015883859246969223,
-0.0477210208773613,
-0.010935881175100803,
-0.022569570690393448,
0.04287958890199661,
-0.023794014006853104,
-0.016491996124386787,
0.0057877120561897755,
-0.015558701939880848,
0.05387997254729271,
-0.049530986696481705,
0.0027403784915804863,
0.030734457075595856,
0.02264983579516411,
0.025618355721235275,
0.011130853556096554,
0.014979342930018902,
0.1194295734167099,
0.07536426186561584,
-0.021204378455877304,
-0.03541941195726395,
-0.021025145426392555,
0.005966329947113991,
-0.002850530669093132,
-0.02608577348291874,
-0.05009961128234863,
0.04954070225358009,
-0.02462311089038849,
-0.010197585448622704,
-0.019885044544935226,
-0.0021080675069242716,
0.03540946543216705,
0.006212588399648666,
0.02678338810801506,
-0.008263383992016315,
0.0010747574269771576,
-0.022152092307806015,
0.03453105315566063,
0.028085971251130104,
0.03817741945385933,
0.048951175063848495,
0.017751002684235573,
0.017902536317706108,
0.028994731605052948,
0.034220099449157715,
-0.007427084259688854,
0.03651827573776245,
0.059174295514822006,
-0.05390243977308273,
0.03168275207281113,
0.05276626721024513,
-0.011715970002114773,
-0.003498487640172243,
0.05708727985620499,
-0.017020152881741524,
-0.0396285243332386,
0.02663940005004406,
0.011961721815168858,
0.04726935550570488,
-0.014580218121409416,
-0.025427330285310745,
0.01591099053621292,
0.015167728066444397,
0.02406652830541134,
0.05547644570469856,
0.04572880268096924,
-0.059927262365818024,
-0.05143428593873978,
0.05171893909573555,
-0.008844648487865925,
-0.012548195198178291,
-0.026061758399009705,
0.011474024504423141,
0.004817728418856859,
-0.011574553325772285,
0.043048106133937836,
-0.03932927921414375,
0.0017552929930388927,
-0.07933496683835983,
0.025881139561533928,
0.06607133150100708,
0.06018121913075447,
-0.03783021867275238,
0.048456113785505295,
-0.012333308346569538,
-0.06940972805023193,
0.001114774844609201,
0.014490687288343906,
-0.02419855259358883,
-0.04264809936285019,
0.01884978823363781,
0.0017240793677046895,
-0.027508387342095375,
0.0219695083796978,
0.006330959498882294,
0.09587210416793823,
-0.024897657334804535,
-0.09268195927143097,
-0.04674528166651726,
0.026501791551709175,
-0.01171335019171238,
-0.004839030094444752,
-0.07084036618471146,
0.023214371874928474,
0.01288659032434225,
0.08046694844961166,
-0.01959151029586792,
-0.026962708681821823,
-0.0010685267625376582,
0.06066500395536423,
0.0347447544336319,
-0.04089495539665222,
-0.0027515538968145847,
-0.006330581847578287,
-0.04388778656721115,
0.023068377748131752,
-0.06812037527561188,
0.006467598490417004,
0.0319390632212162,
-0.016010401770472527,
-0.052285049110651016,
0.04047105833888054,
-0.026533080264925957,
-0.014208246022462845,
-0.0020072616171091795,
0.003351617371663451,
-0.02487012930214405,
0.08766243606805801,
0.0038966278079897165,
-0.05666074529290199,
0.059708353132009506,
-0.0027355835773050785,
-0.004509552847594023,
0.048232171684503555,
0.029690388590097427,
0.002667721826583147,
-0.046930860728025436,
0.006927148438990116,
-0.043263982981443405,
0.028743073344230652,
-0.011229847557842731,
-0.018035156652331352,
0.0016431716503575444,
-0.04459691047668457,
0.021194206550717354,
0.00486568920314312,
0.014206737279891968,
-0.020996537059545517,
-0.01729963906109333,
-0.014230815693736076,
-0.06764572858810425,
-0.02533518709242344,
-0.032289668917655945,
-0.01710069179534912,
0.028042053803801537,
0.006784349679946899,
0.0086752288043499,
0.019840098917484283,
0.03406703099608421,
-0.05758977308869362,
-0.04765389859676361,
-0.021043933928012848,
0.043477561324834824,
0.012697635218501091,
0.014815776608884335,
0.019767671823501587,
0.03593606501817703,
0.0036657180171459913,
-0.027229543775320053,
0.015331270173192024,
0.01523694396018982,
-0.012860310263931751,
0.01763073168694973,
0.0333779901266098,
0.024008020758628845,
-0.025511212646961212,
0.004946532659232616,
0.034350547939538956,
-0.0033986170310527086,
0.03430820256471634,
0.04747781157493591,
-0.04641488566994667,
0.06613840162754059,
0.01572856865823269,
0.02234743908047676,
-0.06651090830564499,
0.030715879052877426,
-0.0054274364374578,
0.01987389102578163,
-0.013348616659641266,
-0.038708604872226715,
-0.059434469789266586,
0.003959552384912968,
0.03492605686187744,
0.004717645235359669,
-0.020037196576595306,
0.03450932726264,
0.003975292667746544,
0.021751897409558296,
0.04254220053553581,
0.013096533715724945,
-0.01656711846590042,
-0.01976320706307888,
-0.0017286422662436962,
0.03762432560324669,
0.016630930826067924,
0.022331202402710915,
0.026285765692591667,
0.035616010427474976,
0.009562540799379349,
-0.03009685128927231,
-0.012202320620417595,
0.0019020651234313846,
0.01419745571911335,
0.009423274546861649,
-0.019055018201470375,
-0.01338836271315813,
0.012600935064256191,
-0.037978947162628174,
0.02307172864675522,
0.005050099920481443,
-0.001882093958556652,
-0.009080386720597744,
-0.036491941660642624,
0.0008291130070574582,
0.013629772700369358,
0.016936765983700752,
-0.0477515310049057,
-0.013514403253793716,
0.007695956155657768,
-0.02372760884463787,
0.023964285850524902,
-0.003927738405764103,
-0.007184652611613274,
-0.014467612840235233,
-0.02163512259721756,
0.02304629422724247,
-0.001814618706703186,
0.018139338120818138,
-0.0028476694133132696,
-0.0777323767542839,
-0.022454403340816498,
-0.024646146222949028,
0.011415215209126472,
0.011802107095718384,
-0.0379219613969326,
0.04249994829297066,
-0.022976988926529884,
-0.031213968992233276,
0.029140284284949303,
-0.03820977732539177,
0.03812327980995178,
-0.0007859262404963374,
-0.008147376589477062,
-0.0035974173806607723,
0.01889761909842491,
-0.04468736797571182,
0.014122867956757545,
0.005775115918368101,
0.018581541255116463,
0.040796954184770584,
0.013281182385981083,
-0.046371638774871826,
0.023108182474970818,
-0.03488399088382721,
-0.04737734794616699,
-0.0113845719024539,
0.0003645027754828334,
0.0023086094297468662,
-0.0411369614303112,
0.05267353728413582,
0.009980905801057816,
-0.07440357655286789,
0.022057723253965378,
-0.028452780097723007,
-0.048354726284742355,
0.03568924218416214,
-0.015080858953297138,
0.0440731905400753,
-0.007386198733001947,
-0.027704674750566483,
0.0675816684961319,
0.020665332674980164,
-0.010449729859828949,
0.008070158772170544,
0.0022858907468616962,
-0.015124397352337837,
0.0011603347957134247,
0.0036653855349868536,
0.019712883979082108,
0.004989112261682749,
0.009273513220250607,
0.06262806802988052,
0.04967697337269783,
0.002169686136767268,
0.008551206439733505,
-0.03372183442115784,
-0.017080368474125862,
-0.01959451287984848,
0.0030847054440528154,
0.022091686725616455,
-0.014931627549231052,
-0.011540700681507587,
0.004181781318038702,
-0.023670516908168793,
0.04955335333943367,
0.02969561144709587,
-0.042519792914390564,
0.017677824944257736,
0.02035442553460598,
-0.005185837857425213,
-0.01599147357046604,
0.024201635271310806,
-0.01749105006456375,
-0.009332546964287758,
-0.003572089597582817,
0.017728207632899284,
0.017652859911322594,
0.01261242013424635,
-0.02034742385149002,
0.02689136564731598,
0.03082852065563202,
-0.0016838645096868277,
-0.015759732574224472,
0.011059240438044071,
-0.0012594651198014617,
0.03470075502991676,
-0.013830076903104782,
-0.04238654673099518,
0.04746387153863907,
0.03794701397418976,
0.010807178914546967,
-0.015230214223265648,
-0.011029045097529888,
0.009198272600769997,
-0.045296359807252884,
-0.008312034420669079,
0.020445821806788445,
0.0035215301904827356,
0.003961635287851095,
0.014014734886586666,
0.026290498673915863,
-0.01606656238436699,
-0.010763255879282951,
-0.004600450862199068,
-0.05831519514322281,
-0.023974083364009857,
-0.049047403037548065,
-0.02422511763870716,
-0.023347001522779465,
-0.011325033381581306,
-0.01686033234000206,
-0.015104241669178009,
-0.020658042281866074,
-0.006737546529620886,
-0.011996437795460224,
-0.07480757683515549,
0.0022479884792119265,
-0.011978529393672943,
0.002477655652910471,
-0.0033428147435188293,
0.01800110749900341,
0.04432326927781105,
0.014850582927465439,
0.005493352189660072,
0.035003554075956345,
-0.008002321235835552,
0.00694311736151576,
-0.004034518729895353,
0.0014605185715481639,
0.011559493839740753,
0.012743665836751461,
0.05233938992023468,
-0.0076963892206549644,
-0.04975878447294235,
-0.024703120812773705,
0.03338916599750519,
-0.00812834408134222,
0.0008406192646361887,
0.006801807787269354,
-0.027678942307829857,
-0.048276692628860474,
-0.0062337457202374935,
-0.010070988908410072,
0.024658603593707085,
0.021277843043208122,
0.04733894392848015,
0.036810845136642456,
0.021601896733045578,
-0.022128595039248466,
0.03392251580953598,
0.11644739657640457,
-0.0046357279643416405,
-0.03568007051944733,
-0.027231652289628983,
-0.022331804037094116,
-0.04489283263683319,
-0.010539434850215912,
0.03611922636628151,
-0.00989923719316721,
-0.05771731585264206,
0.02876063622534275,
0.007649508770555258,
0.013712664134800434,
-0.030887171626091003,
0.014003822579979897,
-0.002094215713441372,
0.0252704955637455,
-0.0426333025097847,
0.016737759113311768,
0.00533072417601943,
0.027436470612883568,
0.046285226941108704,
0.011989980936050415,
-0.013452130369842052,
-0.07327892631292343,
-0.013842419721186161,
0.0069360495544970036,
0.022202037274837494,
0.027923818677663803,
-0.00712392944842577,
-0.07242205739021301,
-0.04223707318305969,
0.08682999759912491,
-0.05037063732743263,
0.03243107721209526,
-0.019537359476089478,
-0.005987866781651974,
0.0061830561608076096,
0.0040433467365801334,
0.005690502468496561,
-0.025172725319862366,
-0.040635544806718826,
-0.018430650234222412,
-0.007458197418600321,
0.012867753393948078,
0.0017067400040104985,
0.0014610327780246735,
0.013443723320960999,
0.0794021412730217,
-0.0014611525693908334,
0.0063393693417310715,
-0.016281630843877792,
-0.0045929173938930035,
-0.020786095410585403,
-0.055463142693042755,
0.024724258109927177,
0.01750684343278408,
-0.06920883059501648,
0.05547723174095154,
-0.036894720047712326,
-0.02999347820878029,
0.02392311580479145,
0.00333955860696733,
-0.031759653240442276,
-0.005026902537792921,
-0.023712899535894394,
0.029467714950442314,
0.010590984486043453,
0.01671142503619194,
0.01577969267964363,
0.03309530392289162,
-0.01125670038163662,
0.02629290148615837,
-0.022940896451473236,
0.01900349371135235,
-0.030771011486649513,
0.0024556326679885387,
-0.016798414289951324,
0.018471090123057365,
-0.0262780599296093,
0.05921104550361633,
-0.05469556897878647,
-0.028290633112192154,
0.0010989090660586953,
-0.008141664788126945,
0.011087561957538128,
0.03706267848610878,
0.0053508710116147995,
0.0120342206209898,
-0.025847265496850014,
0.01683499477803707,
0.022168023511767387,
-0.02636847272515297,
0.00560068991035223,
0.006101035978645086,
-0.012642117217183113,
0.055663857609033585,
-0.0215434730052948,
0.047918714582920074,
0.012843973003327847,
-0.00919498223811388,
0.031220994889736176,
-0.05769061669707298,
-0.004390685819089413,
-0.029899440705776215,
-0.01237897016108036,
0.03203028813004494,
-0.08115413784980774,
-0.0036890204064548016,
-0.01050802692770958,
-0.01767672784626484,
0.05498681217432022,
-0.048639725893735886,
0.025773432105779648,
0.028323886916041374,
0.027012385427951813,
-0.09890060871839523,
-0.03907134011387825,
0.026938848197460175,
0.019942646846175194,
-0.010628056712448597,
-0.035329923033714294,
0.028395986184477806,
-0.04752502217888832,
-0.02990766242146492,
-0.020275425165891647,
0.03402181342244148,
-0.026168007403612137,
0.0019186019198969007,
-0.0016084833769127727,
0.03286413103342056,
0.01742827147245407,
-0.00026504858396947384,
-0.008734428323805332,
-0.021482747048139572,
0.022718554362654686,
-0.004310073330998421,
0.02868412435054779,
0.03323984146118164,
-0.03512675315141678,
-0.03462236002087593,
-0.01002283114939928,
-0.021543193608522415,
0.01829121820628643,
-0.05410588160157204,
-0.02762366645038128,
0.04578621685504913,
0.03643186762928963,
0.023244142532348633,
-0.03592122346162796,
0.025592351332306862,
-0.006926814094185829,
0.010100632905960083,
0.007538497913628817,
-0.007092599291354418,
0.011703954078257084,
-0.04854918643832207,
0.04653112217783928,
-0.003489651018753648,
0.005633555352687836,
0.009437059052288532,
0.037093862891197205,
0.003435390768572688,
-0.029503213241696358,
0.007985012605786324,
-0.06504064798355103,
0.021951062604784966,
0.013401943258941174,
0.013765620067715645,
0.018793588504195213,
0.0155069874599576,
-0.026708947494626045,
-0.031204331666231155,
-0.02824385091662407,
-0.0019621506799012423,
0.05296669900417328,
-0.016645830124616623,
0.023836323991417885,
0.008621009066700935,
-0.03997505083680153,
-0.017552897334098816,
-0.02724280022084713,
-0.016887659206986427,
0.048682115972042084,
-0.008328450843691826,
0.0157245434820652,
-0.0316421240568161,
0.027539100497961044,
0.03296356648206711,
0.020000701770186424,
0.008522921241819859,
0.048809632658958435,
0.04299154877662659,
0.047334250062704086,
0.039024729281663895,
0.009009798057377338,
-0.04124315828084946,
0.041087556630373,
-0.044314466416835785,
0.026510726660490036,
0.003165861591696739,
0.010925468057394028,
0.011137227527797222,
-0.02192246913909912,
0.039196696132421494,
-0.0038958441000431776,
-0.05650859698653221,
-0.04483885318040848,
0.004261260852217674,
-0.010669201612472534,
0.03807107359170914,
0.019394448027014732,
0.029953762888908386,
-0.008282816037535667,
0.02426951378583908,
0.025777027010917664,
0.006652927026152611,
-0.08850827068090439,
-0.043828949332237244,
-0.03220273181796074,
-0.02280539646744728,
0.03743639588356018,
0.013877651654183865,
-0.030652526766061783,
0.009219232015311718,
-0.03300277516245842,
-0.008479507640004158,
-0.04071761295199394,
0.03677770122885704,
-0.032642338424921036,
0.07247740030288696,
0.00890425592660904,
0.04601234942674637,
-0.01487677451223135,
0.027053983882069588,
0.10008713603019714,
0.049616489559412,
-0.0025774440728127956,
-0.06256560236215591,
0.03692236170172691,
-0.05165757238864899,
-0.0068163787946105,
-0.04212580993771553,
0.03780157491564751,
-0.008267806842923164,
0.004917114973068237,
0.04421452432870865,
0.0602300763130188,
0.015877433121204376,
0.011088475584983826,
0.06300073862075806,
-0.02157280221581459,
-0.06857473403215408,
0.008594180457293987,
0.04853256046772003,
-0.007963438518345356,
0.0036279470659792423,
-0.020754801109433174,
0.053587984293699265,
-0.025569064542651176,
-0.0007550081936642528,
-0.011679073795676231,
0.0053928508423268795,
0.038451503962278366,
0.006261500064283609,
-0.05497641861438751,
-0.016830023378133774,
0.029268551617860794,
-0.06652624905109406,
-0.03979058936238289,
-0.012308339588344097,
-0.012110731564462185,
-0.01871511898934841,
0.023405272513628006,
0.01910017803311348,
0.01978825218975544,
0.015228306874632835,
0.005838329438120127,
0.03584419935941696,
-0.03391093760728836,
0.02942991442978382,
-0.00831377599388361,
0.049288276582956314,
-0.04066700115799904,
0.005994576495140791,
0.002092774026095867,
0.01992199569940567,
0.024335674941539764,
-0.03426484018564224,
-0.035546381026506424,
-0.007664995733648539,
0.019902074709534645,
-0.005146875511854887,
0.0020567341707646847,
-0.015510836616158485,
0.03342084959149361,
0.013853128999471664,
0.06038564443588257,
-0.038691215217113495,
0.014007781632244587,
0.015874963253736496,
-0.019384078681468964,
0.02298731543123722,
-0.026282956823706627,
-0.009493405930697918,
-0.009785959497094154,
0.0022114163730293512,
-0.05296871438622475,
0.01546195987612009,
0.04436182603240013,
0.009512174874544144,
0.06385895609855652,
0.006801729090511799,
0.020965375006198883,
-0.00555409537628293,
-0.017349932342767715,
0.030904674902558327,
-0.04087275266647339,
-0.003240629332140088,
-0.027032101526856422,
0.014772344380617142,
0.031915970146656036,
0.06833397597074509,
-0.05971900373697281,
-0.005631217733025551,
-0.0034759673289954662,
0.019515590742230415,
0.02922651916742325,
-0.027510330080986023,
0.00715705705806613,
-0.021347861737012863,
-0.033189207315444946,
-0.006921452470123768,
-0.02480934001505375,
0.011974189430475235,
0.020685337483882904,
0.0015577544691041112,
0.029404019936919212,
0.00009633659647079185,
-0.019872186705470085,
0.008782871067523956,
-0.0008531795465387404,
-0.05090045556426048,
-0.026867419481277466,
-0.007324972189962864,
0.0339619442820549,
0.015775570645928383,
-0.01164778508245945,
-0.002362069906666875,
0.003082167124375701,
-0.013067424297332764,
0.003054789500311017,
-0.04117892310023308,
0.054181985557079315,
0.0006903394241817296,
-0.00925436895340681,
-0.07630163431167603,
-0.0003448893839959055,
-0.04428327456116676,
0.023208647966384888,
0.013063829392194748,
-0.0031930338591337204,
0.02620091289281845,
0.022445641458034515,
-0.04580198600888252,
-0.03188006952404976,
0.008291196078062057,
0.016538329422473907,
-0.04401831701397896,
0.019226400181651115,
0.04445648193359375,
0.026184113696217537,
0.052500028163194656,
-0.010137478820979595,
-0.008120864629745483,
0.015643896535038948,
-0.05200708657503128,
-0.07988982647657394,
0.026873750612139702,
-0.03537629172205925,
0.02409946732223034,
0.01662876270711422,
-0.019212035462260246,
-0.051945168524980545,
0.05205376446247101,
-0.027919575572013855,
-0.027670633047819138,
0.035174958407878876,
-0.004909101873636246,
-0.023160910233855247,
-0.020421016961336136,
-0.004722651559859514,
0.008141443133354187,
-0.0005142194568179548,
0.01788836345076561,
0.030666442587971687,
-0.004242990631610155,
-0.02916637808084488,
-0.0008603938040323555,
-0.024487337097525597,
0.0206435639411211,
-0.02032291889190674,
-0.009139887988567352,
0.03862127289175987,
0.07134431600570679,
-0.03802524507045746,
0.02556266076862812,
0.05813738703727722,
-0.0221315436065197,
-0.11171141266822815,
-0.040213268250226974,
0.01954776793718338,
-0.03310348466038704,
0.009444009512662888,
-0.015460946597158909,
0.038166023790836334,
0.01939648762345314,
-0.05531223863363266,
0.03544165939092636,
-0.04517853632569313,
-0.006716701202094555,
-0.01684758812189102,
-0.007078940514475107,
-0.028717556968331337,
0.03055703639984131,
0.03393308445811272,
0.032767560333013535,
0.008334311656653881,
-0.006000650115311146,
-0.024733658879995346,
-0.021899458020925522,
-0.023709340021014214,
-0.0016867319354787469,
-0.005051337648183107,
-0.018269993364810944,
0.058913249522447586,
-0.01943828910589218,
-0.018535025417804718,
0.041438981890678406,
0.004428115673363209,
0.0014163934392854571,
-0.013884219340980053,
-0.006153826601803303,
0.015601292252540588,
-0.007675256114453077,
0.023546496406197548,
0.034662917256355286,
0.03850908949971199,
0.027945753186941147,
0.03152299299836159,
0.016870133578777313,
0.03638424351811409,
-0.002796525601297617,
0.0147392051294446,
-0.02700657956302166,
0.019603760913014412,
0.024159133434295654,
-0.006009435746818781,
0.049141671508550644,
-0.0019909238908439875,
0.013658806681632996,
-0.0042024352587759495,
-0.004138275980949402,
0.00001530371628177818,
-0.05902443826198578,
-0.0021153392735868692,
0.03718603402376175,
0.03245512768626213,
-0.005943173076957464,
0.02858542464673519,
-0.0010932685108855367,
-0.0072525981813669205,
0.006021177861839533,
0.0023063700646162033,
0.005769973620772362,
-0.035361722111701965,
-0.015941953286528587,
0.004749443382024765,
0.002901728730648756,
0.029359687119722366,
-0.046388331800699234,
-0.01940539851784706,
0.054720230400562286,
0.007129378151148558,
0.013511277735233307,
-0.01413758471608162,
-0.016720065847039223,
-0.013925003819167614,
-0.041286319494247437,
0.036403339356184006,
-0.04223942384123802,
0.008582741022109985,
-0.024953756481409073,
-0.04047990217804909,
0.003261435078456998,
-0.021454304456710815,
0.06450863927602768,
-0.029821546748280525,
-0.005453165154904127,
0.021218296140432358,
0.002883843146264553,
0.035486117005348206,
-0.03769214078783989,
0.00552032794803381,
-0.002882413798943162,
-0.05620700493454933,
-0.027410034090280533,
0.007898034527897835,
0.010179554112255573,
0.003154500387609005,
0.051505234092473984,
0.027092881500720978,
0.014052130281925201,
0.0014824371319264174,
-0.017815224826335907,
0.015126118436455727,
-0.008938235230743885,
0.022867945954203606,
0.0606677271425724,
-0.031041128560900688,
0.017096130177378654,
0.04599105194211006,
0.005128249526023865,
-0.025131715461611748,
0.015091192908585072,
-0.017975497990846634,
0.03949624300003052,
-0.021212369203567505,
-0.017980000004172325,
-0.01267233956605196,
-0.012684118002653122,
-0.028537485748529434,
0.05038845166563988,
-0.018762631341814995,
0.021119143813848495,
0.06892135739326477,
-0.0017752308631315827,
0.0504949726164341,
-0.02660146728157997,
-0.0011770558776333928,
0.023651355877518654,
0.0258109662681818,
0.003537622978910804,
0.028914636000990868,
0.0038225012831389904,
-0.01611214317381382,
0.03112475946545601,
0.017822545021772385,
-0.009745649993419647,
0.031991180032491684,
-0.010383279994130135,
0.05501016229391098,
-0.06776362657546997,
-0.01486851368099451,
0.008138789795339108,
-0.007708089426159859,
0.02130153775215149,
0.030672557651996613,
-0.0246217492967844,
0.09829267859458923,
-0.003939484246075153,
0.040161579847335815,
0.006423233542591333,
0.006046684924513102,
-0.022035161033272743,
0.013382822275161743,
-0.034796494990587234,
0.02798243798315525,
0.0067439572885632515,
-0.00890832394361496,
-0.013770232908427715,
0.040623899549245834,
-0.00905401911586523,
-0.030136851593852043,
-0.019262345507740974,
-0.03486023098230362,
-0.01868884079158306,
-0.019608724862337112,
0.021656105294823647,
-0.009739750064909458,
-0.007244022563099861,
0.032945115119218826,
0.04765261337161064,
0.03162294253706932,
-0.01276558917015791,
-0.0050083645619452,
-0.01042812317609787,
0.044339943677186966,
-0.04964340478181839,
-0.007635853718966246,
-0.015311754308640957,
0.0125785106793046,
-0.016375642269849777,
-0.0335446260869503
] |
<p>It seems impossible for an ice cube to contain bubbles. the ice should freeze far too slowly for a bubble to get trapped within it. However, virtually all ice (that I have seen in my freezer) contains gas bubbles. How is this possible? </p>
| 279 |
[
-0.028839733451604843,
-0.02381177432835102,
-0.00997989159077406,
-0.046173978596925735,
0.04128681495785713,
0.007842921651899815,
-0.038738690316677094,
-0.007484126836061478,
-0.01784556731581688,
-0.013512896373867989,
0.045754123479127884,
0.05136854201555252,
0.024967188015580177,
0.008230761624872684,
-0.010146696120500565,
-0.006373213138431311,
-0.01676050014793873,
-0.021968020126223564,
0.023243410512804985,
-0.008664967492222786,
-0.02628254145383835,
0.001550949178636074,
-0.006258216220885515,
0.032058365643024445,
0.000982498051598668,
0.01590176671743393,
-0.015575182624161243,
0.001275457558222115,
0.06305327266454697,
0.03300873562693596,
-0.0018454634118825197,
-0.013640932738780975,
0.00015443807933479548,
0.016071978956460953,
0.02792051061987877,
-0.034800127148628235,
-0.01140784565359354,
-0.00716726528480649,
-0.017138782888650894,
0.006406379863619804,
-0.05646195635199547,
-0.03493228554725647,
-0.004355479497462511,
0.035615406930446625,
-0.04093582555651665,
-0.0004376130527816713,
-0.009005239233374596,
-0.04905266314744949,
0.032062165439128876,
-0.07487794011831284,
0.03623640909790993,
0.007684575859457254,
0.079697385430336,
0.048927392810583115,
0.015132996253669262,
0.0336863212287426,
0.08801206946372986,
0.05652809143066406,
-0.029854940250515938,
-0.040641237050294876,
-0.014194111339747906,
-0.011649630032479763,
-0.04125995934009552,
-0.011216110549867153,
-0.025518331676721573,
0.04572854936122894,
-0.035221874713897705,
-0.020877564325928688,
0.012747549451887608,
0.024190079420804977,
0.026632044464349747,
0.005299674812704325,
0.023994484916329384,
-0.007546489592641592,
0.010565139353275299,
-0.02200685814023018,
0.007523892913013697,
-0.013015791773796082,
0.04079939424991608,
0.03405361250042915,
0.011112271808087826,
0.01972261443734169,
0.032370761036872864,
-0.0023060906678438187,
-0.008725387044250965,
-0.007640369236469269,
0.09330779314041138,
-0.03151043504476547,
0.004839578177779913,
0.04099298268556595,
-0.00365951145067811,
0.008743961341679096,
0.01646822690963745,
0.009629588574171066,
-0.005775583907961845,
-0.015197426080703735,
0.012008710764348507,
0.0717485174536705,
-0.0037759183906018734,
-0.037540242075920105,
0.013464611954987049,
0.01923822984099388,
0.030718065798282623,
0.08759425580501556,
-0.0021768512669950724,
-0.03143398463726044,
-0.059976208955049515,
0.05854649469256401,
0.011613494716584682,
-0.026907099410891533,
0.007774743251502514,
0.009264213033020496,
-0.01827496849000454,
-0.04213300347328186,
0.04447174444794655,
-0.010643063113093376,
-0.0011069385800510645,
-0.04909110441803932,
0.019319700077176094,
0.06275390088558197,
0.007958675734698772,
-0.032100751996040344,
0.01653912290930748,
-0.003656395012512803,
-0.06590442359447479,
0.01616644859313965,
0.024034274742007256,
-0.012833427637815475,
-0.0417725145816803,
0.020359989255666733,
0.00946373026818037,
0.00021393911447376013,
0.016475174576044083,
-0.004983049351722002,
0.06326406449079514,
-0.032876186072826385,
-0.09488209336996078,
-0.039960216730833054,
0.053712110966444016,
-0.0010706527391448617,
-0.034811098128557205,
-0.08306270837783813,
-0.009717945009469986,
0.0027746271807700396,
0.0589015819132328,
-0.017645204439759254,
0.000714943977072835,
-0.009245467372238636,
0.019708361476659775,
0.008654825389385223,
0.0015038077253848314,
0.007496902719140053,
0.0037650198210030794,
-0.04228324815630913,
0.04883845895528793,
-0.06584233045578003,
0.019972609356045723,
0.021861597895622253,
-0.009300915524363518,
-0.048767220228910446,
0.004339628852903843,
-0.025782303884625435,
-0.009962396696209908,
-0.01964235119521618,
-0.010394657962024212,
-0.051534973084926605,
0.05886640399694443,
-0.006017991341650486,
0.021505340933799744,
0.05581162869930267,
-0.018512191250920296,
0.03974737599492073,
0.023205319419503212,
0.03390917181968689,
0.0520499050617218,
-0.027025025337934494,
-0.0042573874816298485,
-0.004492593929171562,
0.032401375472545624,
0.029210980981588364,
-0.02770407684147358,
0.014169239439070225,
0.025041325017809868,
-0.0000017852423752628965,
0.013855122961103916,
0.054075706750154495,
0.008150093257427216,
-0.015374938026070595,
-0.030702678486704826,
-0.07703852653503418,
-0.0322764590382576,
-0.08439745008945465,
0.013171855360269547,
-0.022164681926369667,
-0.011614126153290272,
0.01525565329939127,
0.04732751101255417,
0.016690289601683617,
-0.039485860615968704,
-0.026786433532834053,
-0.010443488135933876,
0.04716065153479576,
0.02584141306579113,
-0.03087836503982544,
0.042077478021383286,
0.020858855918049812,
0.02588714100420475,
-0.007372088264673948,
-0.00035265740007162094,
0.023287586867809296,
0.0203059371560812,
-0.0025142135564237833,
-0.0021875302772969007,
-0.0061003766022622585,
-0.030722061172127724,
-0.03207127004861832,
0.042925700545310974,
0.008820144459605217,
-0.011533292941749096,
0.028375597670674324,
0.011071605607867241,
0.037987712770700455,
0.005424941424280405,
0.01286349631845951,
-0.006743006408214569,
0.005098878871649504,
0.03313875570893288,
0.009958452545106411,
0.025462336838245392,
-0.04693855345249176,
-0.03391442075371742,
-0.024852663278579712,
0.03898755833506584,
0.02617255039513111,
-0.05994812026619911,
0.033645905554294586,
-0.004565667826682329,
0.02937893196940422,
0.03330894932150841,
0.006070211995393038,
-0.020612075924873352,
-0.027526190504431725,
0.013888615183532238,
0.03182768449187279,
0.026793645694851875,
0.03403080999851227,
0.04056662693619728,
0.03016495890915394,
0.026321623474359512,
-0.040678512305021286,
-0.02519794926047325,
0.0068159266375005245,
-0.01201020646840334,
0.03644045069813728,
-0.006809836253523827,
-0.030504455789923668,
0.030583580955863,
-0.01981419324874878,
0.009637091308832169,
-0.008797630667686462,
0.020008932799100876,
0.003989914432168007,
-0.018823737278580666,
-0.011768707074224949,
0.021320650354027748,
0.02873196452856064,
-0.024229763075709343,
-0.0008947866735979915,
0.02751767635345459,
-0.01718875765800476,
0.03727182745933533,
-0.015357877127826214,
0.0017546165036037564,
-0.008075934834778309,
0.03837620094418526,
0.01588689535856247,
0.0013490011915564537,
0.0410112589597702,
-0.03608820587396622,
-0.03482842817902565,
-0.024834508076310158,
-0.05802421271800995,
-0.00983400084078312,
-0.007568688131868839,
-0.03270275518298149,
0.028355788439512253,
-0.0022708831820636988,
-0.018497999757528305,
0.016544220969080925,
-0.018200278282165527,
-0.021189536899328232,
0.024597033858299255,
-0.0033721928484737873,
-0.0018283582758158445,
0.01278669387102127,
-0.036020427942276,
0.011440036818385124,
-0.026442939415574074,
0.021462738513946533,
0.024157583713531494,
-0.028541775420308113,
-0.022366639226675034,
0.04130832105875015,
-0.0279016625136137,
-0.04828561842441559,
-0.034451037645339966,
-0.0260543841868639,
0.04676206409931183,
-0.06704439967870712,
-0.003315890906378627,
0.021023651584982872,
-0.05373311787843704,
-0.008971507661044598,
-0.019801830872893333,
-0.05896129459142685,
0.009825866669416428,
0.008375056087970734,
0.023723093792796135,
-0.039084285497665405,
-0.016828417778015137,
0.055640146136283875,
-0.024615954607725143,
-0.04098885878920555,
0.0033858248498290777,
-0.04121887683868408,
-0.019190562888979912,
-0.04058629646897316,
0.012685190886259079,
0.030527576804161072,
-0.029052458703517914,
0.012899852357804775,
0.027518752962350845,
0.04604315385222435,
0.007237157318741083,
0.0037439693696796894,
-0.05703384429216385,
-0.00028320454293861985,
0.036851972341537476,
0.009796232916414738,
0.031429141759872437,
-0.003407629206776619,
-0.031185973435640335,
0.015936031937599182,
0.01190900057554245,
0.03147897496819496,
0.06249832734465599,
-0.031119106337428093,
0.059178486466407776,
-0.04383939504623413,
-0.006060564890503883,
-0.04092284291982651,
-0.007815314456820488,
-0.016430992633104324,
0.01679738610982895,
0.06946512311697006,
0.015178244560956955,
0.020458471029996872,
0.013521077111363411,
-0.008609144017100334,
0.0285430196672678,
0.051938496530056,
-0.03377486765384674,
-0.017706073820590973,
-0.021377291530370712,
-0.017507420852780342,
0.056688953191041946,
0.023746559396386147,
0.003793960204347968,
0.054351091384887695,
0.003962528891861439,
0.019235027953982353,
-0.012515387497842312,
-0.01603332906961441,
0.0035715142730623484,
-0.05255112051963806,
0.0022669178433716297,
0.035742245614528656,
0.015539552085101604,
-0.002348735462874174,
0.06938978284597397,
0.02497868984937668,
0.0028850885573774576,
0.015646956861019135,
-0.0030555620323866606,
-0.048423442989587784,
0.008960261009633541,
-0.03728180378675461,
0.011432504281401634,
-0.03954470902681351,
-0.03183840215206146,
0.022051768377423286,
-0.027211425825953484,
0.004465162288397551,
-0.014578759670257568,
0.013959048315882683,
-0.0489984005689621,
0.005717772990465164,
0.009156783111393452,
0.012411345727741718,
-0.029936132952570915,
0.012770279310643673,
0.013703971169888973,
-0.001285501173697412,
0.02313595823943615,
0.019486119970679283,
-0.005697757005691528,
0.02859722077846527,
0.03645113855600357,
0.003028405597433448,
0.030310578644275665,
0.01755584217607975,
-0.0005793559830635786,
-0.0142591567710042,
0.008055335842072964,
-0.025375984609127045,
0.008493456989526749,
0.0308518148958683,
-0.013754460029304028,
0.016708023846149445,
-0.0335356779396534,
-0.046075835824012756,
-0.011814001947641373,
0.011926623992621899,
0.04920799285173416,
-0.01654580980539322,
0.03987392038106918,
-0.003190667601302266,
-0.00761994905769825,
-0.01685032993555069,
0.03837158530950546,
0.06956212967634201,
0.03578289598226547,
-0.016478246077895164,
-0.05806867033243179,
-0.05622224137187004,
-0.05885398015379906,
-0.002716559451073408,
0.03681707754731178,
0.027566812932491302,
-0.03469569981098175,
0.012382595799863338,
0.01244018692523241,
-0.019712425768375397,
0.0008585778414271772,
-0.029320305213332176,
0.008019213564693928,
0.023685874417424202,
-0.0453312024474144,
0.019262751564383507,
-0.0057608806528151035,
0.011443116702139378,
-0.0013193602208048105,
0.009425494819879532,
-0.022169295698404312,
-0.10422453284263611,
-0.009939380921423435,
0.026995237916707993,
0.0033089066855609417,
0.006949247792363167,
0.004755712114274502,
-0.08976712822914124,
0.012142990715801716,
0.04666358605027199,
-0.07057555764913559,
0.0031819306313991547,
-0.059345345944166183,
-0.013851940631866455,
0.0035849891137331724,
0.0013686070451512933,
0.05580206215381622,
-0.01547288242727518,
0.006656776648014784,
0.01238480769097805,
0.008057153783738613,
-0.01026530284434557,
-0.01379264984279871,
0.01347197126597166,
0.015957895666360855,
0.07024969905614853,
0.02608158066868782,
-0.0016186650609597564,
-0.03584090620279312,
0.018200058490037918,
-0.04059602692723274,
-0.07150111347436905,
0.013679045252501965,
-0.02388838864862919,
-0.006953050382435322,
0.03896036371588707,
-0.0224295686930418,
-0.0835510641336441,
0.02138305827975273,
-0.004387956578284502,
-0.006991448812186718,
-0.020191537216305733,
-0.06013188883662224,
-0.007548295892775059,
0.02089150808751583,
0.01783965900540352,
0.04324481263756752,
0.05805731192231178,
-0.034547243267297745,
-0.02377023547887802,
-0.04932677000761032,
0.04710707440972328,
-0.046874016523361206,
0.005063265562057495,
-0.006644918117672205,
0.01639600284397602,
-0.01235230267047882,
0.025780893862247467,
-0.022157713770866394,
0.004839757923036814,
0.03599793091416359,
-0.019031982868909836,
0.005310159642249346,
0.032227735966444016,
0.03770036995410919,
-0.01849028840661049,
-0.010481849312782288,
0.024433787912130356,
-0.015551352873444557,
0.0003776892845053226,
0.039373818784952164,
0.003972990904003382,
-0.02972608432173729,
0.02019418776035309,
-0.02586391754448414,
0.02715659700334072,
-0.023412784561514854,
-0.01060744933784008,
-0.014537086710333824,
-0.030829932540655136,
0.04730863869190216,
-0.0248405784368515,
-0.007779098115861416,
0.02251581661403179,
-0.07278116047382355,
0.02023729309439659,
0.004036237485706806,
0.006742351688444614,
0.0608256459236145,
-0.0574241578578949,
0.047046758234500885,
0.01019352674484253,
0.024791831150650978,
-0.08022088557481766,
-0.0602119080722332,
0.039629146456718445,
0.06277892738580704,
-0.007334697060286999,
-0.07109291851520538,
-0.00044720902224071324,
0.005804633721709251,
-0.016146071255207062,
-0.018221326172351837,
0.030816104263067245,
0.013981855474412441,
-0.021063046529889107,
0.062289346009492874,
0.027833594009280205,
0.06943210959434509,
0.005338209681212902,
-0.01322383526712656,
0.014917584136128426,
-0.018430056050419807,
-0.03851248323917389,
0.045900747179985046,
0.03341998532414436,
-0.027600450441241264,
-0.02342597022652626,
-0.0013488761615008116,
0.004529083147644997,
0.02665306068956852,
-0.02744929865002632,
0.0020634096581488848,
0.026244740933179855,
0.02234947681427002,
0.009535492397844791,
-0.02889867313206196,
0.025457940995693207,
0.005209699738770723,
0.0359172523021698,
-0.005893676541745663,
-0.013049821369349957,
-0.02648518793284893,
-0.032094556838274,
0.006007447373121977,
0.015666019171476364,
0.029370034113526344,
0.0007195290527306497,
0.06208299845457077,
-0.03166963905096054,
-0.027248520404100418,
-0.007144705392420292,
-0.045791227370500565,
0.05322989448904991,
0.019096480682492256,
0.0027484220918267965,
0.029155567288398743,
0.015392597764730453,
-0.007095538079738617,
-0.03579685464501381,
-0.016516104340553284,
0.019055703654885292,
0.04976271092891693,
-0.023543493822216988,
0.040879931300878525,
0.030516808852553368,
-0.05614690110087395,
-0.02791011519730091,
-0.03760373592376709,
0.0027105698827654123,
0.07437781989574432,
0.016603456810116768,
0.030222993344068527,
0.005892518442124128,
-0.0006079637096263468,
0.03624382242560387,
0.033591315150260925,
0.002471690298989415,
0.03352972865104675,
0.0380181185901165,
0.020426565781235695,
-0.022075409069657326,
0.012274441309273243,
-0.039853259921073914,
0.05698465555906296,
-0.018917042762041092,
0.03348191827535629,
-0.015847308561205864,
0.0010357294231653214,
0.05125517398118973,
-0.01746080443263054,
0.022353697568178177,
-0.033716026693582535,
-0.025309467688202858,
-0.007170751690864563,
0.025082409381866455,
-0.0003959798195865005,
0.009878129698336124,
0.019900420680642128,
0.0015697787748649716,
0.0006392044597305357,
0.01604248583316803,
0.011622910387814045,
0.0041059041395783424,
-0.08850788325071335,
0.00009172228601528332,
-0.011611643247306347,
-0.006440784782171249,
0.025627801194787025,
0.031084148213267326,
-0.035843029618263245,
-0.034671004861593246,
-0.025612561032176018,
-0.011848472990095615,
0.006666704546660185,
-0.0055786604061722755,
-0.028575487434864044,
0.061954159289598465,
0.016017360612750053,
0.025781508535146713,
0.01178109273314476,
0.018818290904164314,
0.10595584660768509,
0.05665693059563637,
-0.0020492949988693,
-0.06305868923664093,
0.011541427113115788,
-0.04423146694898605,
-0.01759459637105465,
-0.03914937749505043,
0.006643722765147686,
-0.020486658439040184,
0.020000040531158447,
-0.008971276693046093,
0.06629795581102371,
-0.0012197336181998253,
0.03161139786243439,
0.04246783256530762,
-0.04730101674795151,
-0.021924328058958054,
0.0022557831835001707,
0.03903035447001457,
-0.005163203924894333,
0.026405204087495804,
-0.022872325032949448,
0.01988501474261284,
0.0015060955192893744,
-0.017093459144234657,
-0.03321601450443268,
-0.025448456406593323,
0.022394409403204918,
0.010050979442894459,
-0.06895046681165695,
-0.01775076985359192,
0.03996703401207924,
-0.023063810542225838,
-0.03966642916202545,
0.003110595978796482,
0.02058187499642372,
-0.01106226909905672,
-0.013349100016057491,
-0.022885333746671677,
0.00793281476944685,
0.01903187297284603,
0.03473827615380287,
0.01578749530017376,
-0.03676504269242287,
-0.021060509607195854,
-0.017062999308109283,
0.009647618047893047,
-0.025645114481449127,
-0.03577357530593872,
-0.007343508303165436,
0.011948606930673122,
-0.026628240942955017,
-0.046482767909765244,
-0.02700996585190296,
-0.02100386843085289,
0.016910338774323463,
-0.00847900751978159,
-0.056268904358148575,
-0.026276875287294388,
0.019261982291936874,
-0.02679658867418766,
0.023359864950180054,
-0.001422383007593453,
-0.005801074206829071,
0.01596737653017044,
-0.024286417290568352,
0.022382725030183792,
-0.04859015345573425,
0.012416889891028404,
-0.039918188005685806,
-0.013112789951264858,
-0.055944476276636124,
0.008600564673542976,
0.008236365392804146,
0.027146730571985245,
0.022829139605164528,
-0.008454716764390469,
-0.016628850251436234,
0.028568968176841736,
-0.03890218213200569,
0.042459990829229355,
-0.02484646812081337,
-0.045477841049432755,
-0.04548386111855507,
-0.0008654545526951551,
0.03284700587391853,
0.040302447974681854,
-0.021886760368943214,
0.034334540367126465,
-0.013522515073418617,
0.013102945871651173,
0.0033284269738942385,
-0.01667254976928234,
-0.04115314036607742,
0.007430513855069876,
-0.043398432433605194,
-0.007870625704526901,
0.0033480438869446516,
0.027785683050751686,
0.036697305738925934,
0.012627585791051388,
0.05361451581120491,
-0.007037525996565819,
-0.053734008222818375,
0.006977816112339497,
0.015046282671391964,
-0.014990335330367088,
-0.05210739001631737,
0.014571668580174446,
-0.01718662865459919,
-0.03336825966835022,
-0.025642327964305878,
-0.0006029240321367979,
0.010744969360530376,
0.016121039167046547,
0.07717365026473999,
-0.03586607053875923,
0.008738425560295582,
-0.013209131546318531,
0.024606766179203987,
-0.03311636298894882,
-0.008869018405675888,
-0.0860329270362854,
-0.0036042705178260803,
0.013476453721523285,
0.002010370371863246,
-0.00235800095833838,
-0.00048539837007410824,
-0.01644701510667801,
0.02054014801979065,
0.01564941555261612,
0.040226951241493225,
-0.008634788915514946,
-0.0068137734197080135,
0.039448484778404236,
0.004976857919245958,
0.03769721835851669,
-0.060014400631189346,
-0.03177930414676666,
0.04561678320169449,
-0.043971411883831024,
-0.04739120602607727,
-0.00560689065605402,
-0.012045156210660934,
-0.01244941633194685,
0.024556195363402367,
0.011508774012327194,
-0.0317784920334816,
0.083028145134449,
-0.04426166042685509,
0.0019403460901230574,
-0.02808150090277195,
0.01399235799908638,
-0.012619627639651299,
0.009899762459099293,
0.002180333947762847,
-0.041373010724782944,
-0.010394677519798279,
0.0713331401348114,
0.009675134904682636,
0.006173981819301844,
-0.008661924861371517,
-0.019004615023732185,
0.02084379829466343,
0.03576911240816116,
0.03938787430524826,
0.01830066367983818,
0.012099186889827251,
0.05080277845263481,
-0.019662953913211823,
0.06094852462410927,
0.01640315353870392,
-0.016588089987635612,
-0.09331236779689789,
-0.004710185807198286,
-0.009702738374471664,
-0.0007483339286409318,
0.049645718187093735,
-0.007030097302049398,
0.04541720822453499,
0.063536137342453,
-0.061669785529375076,
-0.002335251308977604,
-0.057542331516742706,
-0.017418336123228073,
-0.03207588940858841,
-0.018878227099776268,
-0.012527423910796642,
0.052061527967453,
0.024127226322889328,
0.028561029583215714,
0.04236457869410515,
0.0024441261775791645,
-0.012685076333582401,
-0.005980530753731728,
0.005431074649095535,
0.044652391225099564,
0.015650419518351555,
0.012889755889773369,
0.0423743911087513,
-0.01717265136539936,
-0.012291772291064262,
0.020567134022712708,
0.0005791934090666473,
0.0007791228126734495,
0.0445462130010128,
0.0069196694530546665,
-0.0198303684592247,
0.011985762976109982,
0.015092500485479832,
0.005074802786111832,
0.01412806287407875,
0.06538496166467667,
0.024893619120121002,
0.03874602168798447,
0.02951188199222088,
-0.00747777009382844,
-0.0039431387558579445,
-0.049967799335718155,
-0.023165332153439522,
0.027404258027672768,
-0.030987605452537537,
0.00045911225606687367,
-0.002890057396143675,
0.013346740044653416,
0.05810109153389931,
-0.02318861521780491,
0.0007864086655899882,
-0.05333602428436279,
-0.012402985244989395,
0.04103192314505577,
0.023178957402706146,
-0.01536308042705059,
0.015620945021510124,
-0.02717703953385353,
0.0014751810813322663,
-0.005421571899205446,
0.017147772014141083,
-0.013547743670642376,
-0.015143821015954018,
-0.013541803695261478,
0.019061299040913582,
-0.02980181947350502,
-0.001696657040156424,
-0.021205328404903412,
-0.04246297478675842,
0.05357605218887329,
0.04554302990436554,
0.027527978643774986,
0.03537657856941223,
-0.03566962853074074,
-0.039911579340696335,
-0.049012888222932816,
0.03199990093708038,
-0.0439118817448616,
0.005120157264173031,
-0.027022114023566246,
-0.01755170151591301,
-0.0051030186004936695,
-0.00833173468708992,
0.060384638607501984,
-0.01991318352520466,
0.014977648854255676,
0.028100891038775444,
0.012898508459329605,
0.002377632539719343,
-0.021658778190612793,
-0.016016453504562378,
0.018233776092529297,
-0.026870490983128548,
0.02505815215408802,
0.011526868678629398,
-0.008068090304732323,
-0.011258899234235287,
0.02703021839261055,
-0.006112941075116396,
0.030698616057634354,
0.0067922803573310375,
0.004922983702272177,
0.0384635254740715,
-0.003355772700160742,
-0.05021679773926735,
0.048396095633506775,
-0.043109070509672165,
-0.0014574453234672546,
0.019223518669605255,
-0.027373962104320526,
-0.04360940679907799,
0.03417481109499931,
-0.014879084192216396,
0.01274727564305067,
-0.05228454992175102,
-0.030846089124679565,
0.015299743041396141,
-0.04317926988005638,
0.026990076526999474,
-0.024543559178709984,
-0.03315378725528717,
0.02674967050552368,
0.0454527884721756,
0.009909518994390965,
0.024680832400918007,
-0.007292641792446375,
-0.032173942774534225,
-0.016986459493637085,
0.026323558762669563,
-0.02567276731133461,
0.06956029683351517,
0.026395143941044807,
0.005747691728174686,
0.012532208114862442,
-0.005511260591447353,
0.015777401626110077,
0.03719456121325493,
0.02123427391052246,
0.03258621320128441,
0.011990503408014774,
-0.04665421321988106,
0.01786426082253456,
-0.03127307444810867,
0.02845396101474762,
-0.02791864424943924,
-0.006819321308284998,
0.05451622232794762,
-0.02839537151157856,
0.028090648353099823,
-0.03200714290142059,
-0.018334785476326942,
-0.0031235446222126484,
0.010585028678178787,
0.003020783420652151,
0.014182385988533497,
0.006783626042306423,
0.015542440116405487,
-0.03676711767911911,
0.009718083776533604,
0.021214907988905907,
-0.0027082902379333973,
0.015197006054222584,
-0.03004813753068447,
0.007025517988950014,
-0.02292007766664028,
0.015018231235444546,
-0.030129272490739822,
-0.016473298892378807,
0.008212514221668243,
0.015774745494127274,
-0.0012647627154365182,
0.018546072766184807,
-0.017207495868206024,
-0.02996688522398472,
0.07818426191806793,
-0.08018430322408676,
0.004860452841967344,
-0.02790592797100544,
0.05101006105542183,
-0.029264694079756737,
0.023914461955428123
] |
<p>In our quantum optics lecture we derived the formula for the <a href="http://en.wikipedia.org/wiki/Casimir_effect" rel="nofollow">Casimir force</a> between two plates (or at least the force per unit surface, since for two infinite plates we would have an infinite force). It was then said, that in experiments one often uses <a href="http://www.google.com/search?q=Casimir+plate+sphere" rel="nofollow">a sphere and a plate</a> to measure the force, where the small distance between the sphere and the plate is varied by a piezo.</p>
<p>I'm not particularly interested in how exactly the force is measured but rather how to theoretically calculate it in this case. Our professor said, the measured forces agree with the theory up to 1% so I guess, there is a way to calculate it.
Let's say I have a sphere of radius $R$ in a distance $d$ from a plate where $R\gg d$. How can I theoretically calculate the Casimir force between a plate and a sphere?</p>
| 8,488 |
[
0.03796117380261421,
-0.022707683965563774,
-0.004359587095677853,
-0.016003234311938286,
-0.007672343403100967,
-0.014711706899106503,
-0.0007792378310114145,
-0.019003545865416527,
0.0035935977939516306,
0.010879145935177803,
0.03822658583521843,
0.039366982877254486,
0.07159190624952316,
-0.009205947630107403,
0.005142074078321457,
0.0008024820708669722,
-0.02171461470425129,
-0.02333895117044449,
0.019652336835861206,
-0.05741414800286293,
-0.010501901619136333,
0.01091900747269392,
-0.0199283417314291,
0.01363062858581543,
0.015405211597681046,
0.004357377532869577,
0.004782011266797781,
-0.0020191858056932688,
0.04006738215684891,
0.042443208396434784,
0.0008406091947108507,
-0.023542454466223717,
0.016203099861741066,
0.006105833221226931,
0.009845713153481483,
-0.001429739873856306,
-0.05586986616253853,
-0.049949757754802704,
-0.014654886908829212,
0.007451939862221479,
-0.04695276543498039,
-0.0118801798671484,
-0.0031702874694019556,
0.047424811869859695,
0.016094854101538658,
-0.028865531086921692,
0.049564216285943985,
-0.01656419225037098,
0.047121383249759674,
-0.07012497633695602,
0.04024774581193924,
0.03279413282871246,
0.0820181742310524,
0.031014297157526016,
0.002292861230671406,
-0.0172733161598444,
0.07289152592420578,
0.050673384219408035,
-0.027552537620067596,
-0.05118716135621071,
-0.03800603747367859,
-0.021055957302451134,
-0.029345791786909103,
-0.05913582444190979,
-0.024744467809796333,
0.026134755462408066,
-0.027595924213528633,
-0.018161995336413383,
0.022602982819080353,
0.004074985161423683,
0.02834559604525566,
0.03921612724661827,
0.04006139189004898,
-0.0033838865347206593,
-0.0316266193985939,
-0.016313688829541206,
0.001686834846623242,
0.029869817197322845,
0.035739921033382416,
0.056471116840839386,
-0.014452919363975525,
0.03518807515501976,
0.04747885838150978,
0.05394213646650314,
0.01917540282011032,
-0.025550421327352524,
0.05865921452641487,
-0.013217653147876263,
-0.014956199564039707,
0.026339208707213402,
-0.01693175546824932,
-0.006233712658286095,
0.042467545717954636,
-0.000288434763206169,
-0.01727611944079399,
-0.0002193830005126074,
0.013520724140107632,
0.057703010737895966,
-0.02996937744319439,
-0.0417894683778286,
0.0023627192713320255,
0.006160628516227007,
-0.03154277056455612,
0.08642859011888504,
-0.008691594935953617,
-0.02347400039434433,
-0.01892792247235775,
0.022403502836823463,
0.008542981930077076,
-0.026246894150972366,
-0.051656585186719894,
0.04329119995236397,
-0.01306145265698433,
0.024552568793296814,
0.02187981829047203,
0.0021324155386537313,
-0.010363149456679821,
-0.04190916568040848,
0.03315112739801407,
0.041568323969841,
0.029410123825073242,
-0.028594283387064934,
-0.03299839422106743,
-0.05643612891435623,
-0.028396863490343094,
0.04605766758322716,
0.0417817123234272,
-0.005579857621341944,
-0.015281553380191326,
0.031804099678993225,
0.01122969575226307,
-0.02086331881582737,
-0.027333606034517288,
0.0015426501631736755,
0.013121267780661583,
-0.011446505784988403,
-0.09060820937156677,
-0.03358474746346474,
0.06263814866542816,
0.014048931188881397,
0.0014236331917345524,
-0.07106449455022812,
0.0011790395947173238,
0.024958983063697815,
0.06401944160461426,
0.018303295597434044,
-0.012384278699755669,
-0.034527137875556946,
0.045059751719236374,
0.015875065699219704,
-0.04150315746665001,
-0.011347129940986633,
0.009295429103076458,
-0.060172758996486664,
0.0005830769659951329,
-0.020374346524477005,
0.033416569232940674,
0.015667522326111794,
-0.005030678119510412,
-0.023251283913850784,
0.08071857690811157,
-0.014135774224996567,
-0.02567504532635212,
-0.014964327216148376,
0.009576101787388325,
-0.05330696329474449,
0.06352268904447556,
-0.015202038921415806,
-0.01568099856376648,
0.03491160273551941,
-0.027598688378930092,
-0.004433842375874519,
0.0032158028334379196,
-0.007351676933467388,
0.04322123900055885,
0.015075264498591423,
-0.0004976842901669443,
-0.04430919885635376,
0.01350934337824583,
0.00516526959836483,
-0.05372929200530052,
-0.009654281660914421,
0.012118671089410782,
0.01644057035446167,
-0.019536148756742477,
0.03359731659293175,
-0.024777313694357872,
-0.010105892084538937,
-0.044526584446430206,
-0.030110375955700874,
-0.036754757165908813,
-0.05516429990530014,
0.02395210787653923,
0.011363347992300987,
0.010093149729073048,
0.023998968303203583,
0.006485190242528915,
-0.02299608290195465,
-0.011563964188098907,
-0.06440862268209457,
-0.037236493080854416,
0.016426410526037216,
0.01649612933397293,
-0.02143936976790428,
0.027576729655265808,
0.03519653528928757,
0.036174897104501724,
-0.007959847338497639,
0.039318256080150604,
-0.04769357293844223,
-0.004140562377870083,
-0.0011768762487918139,
-0.024508807808160782,
0.005108099430799484,
0.016784431412816048,
-0.015828855335712433,
0.025114024057984352,
0.00013866597146261483,
-0.010731039568781853,
0.010944928973913193,
-0.019994303584098816,
0.06240369379520416,
0.049032729119062424,
0.038673195987939835,
-0.010218970477581024,
0.02373231202363968,
0.0317857600748539,
0.01499116886407137,
0.005721756257116795,
-0.04925474524497986,
-0.08484858274459839,
-0.016878722235560417,
0.04251423850655556,
0.03492655232548714,
0.008509592153131962,
0.008902334608137608,
0.029041392728686333,
0.027472250163555145,
0.026853259652853012,
0.00024947000201791525,
-0.016979588195681572,
-0.018725993111729622,
0.01824648678302765,
0.032235559076070786,
0.008274583145976067,
0.01529517862945795,
-0.005933780688792467,
0.03532491624355316,
0.022205667570233345,
0.04223458468914032,
-0.020134106278419495,
0.0018766107968986034,
-0.009600773453712463,
0.035184476524591446,
-0.0032005240209400654,
-0.007853595539927483,
0.010302895680069923,
-0.00047535920748487115,
0.040813904255628586,
0.010063298046588898,
0.017658010125160217,
0.02084052562713623,
-0.02234637923538685,
-0.009024537168443203,
0.025606535375118256,
0.0015416654059663415,
-0.04366617277264595,
0.01982930488884449,
0.007395806256681681,
-0.05568784102797508,
0.0032549374736845493,
0.002140456112101674,
-0.003319040173664689,
0.009679972194135189,
-0.013268416747450829,
-0.008115667849779129,
0.038511984050273895,
0.03953339159488678,
-0.015081893652677536,
-0.040655795484781265,
0.043914735317230225,
-0.0577397458255291,
-0.008523790165781975,
0.020246140658855438,
-0.029690569266676903,
0.02187470905482769,
-0.029439492151141167,
-0.013964135199785233,
0.023972027003765106,
-0.01199802104383707,
0.027635853737592697,
0.0002623619220685214,
0.011241014115512371,
-0.058315861970186234,
0.020531022921204567,
-0.00821718294173479,
-0.006031462457031012,
-0.03282565996050835,
0.029347611591219902,
0.012251797132194042,
0.0014097162056714296,
-0.031441375613212585,
0.038046661764383316,
-0.01648022048175335,
-0.05211353302001953,
-0.02463991567492485,
0.028939547017216682,
-0.0006767180166207254,
-0.046139176934957504,
0.012469019740819931,
0.014074577018618584,
-0.03460888937115669,
-0.027895232662558556,
-0.024413779377937317,
-0.04544849321246147,
0.04792221263051033,
-0.00846683420240879,
0.05202807858586311,
-0.018665924668312073,
-0.02520999312400818,
0.09893948584794998,
-0.0014734166907146573,
-0.029630472883582115,
0.00027962704189121723,
-0.02028067596256733,
0.009055293165147305,
0.009877688251435757,
-0.004193716216832399,
0.0415368378162384,
0.0033894293010234833,
0.013373632915318012,
0.014997527003288269,
-0.011298147030174732,
-0.009095096960663795,
0.02089281752705574,
0.009842767380177975,
-0.010106056928634644,
0.0078092231415212154,
-0.021077321842312813,
0.055695194751024246,
-0.015956096351146698,
-0.004756465088576078,
-0.010000919923186302,
0.00982169434428215,
0.015078862197697163,
0.011936518363654613,
-0.04515742138028145,
0.0172329843044281,
0.01672949455678463,
-0.031849104911088943,
-0.03299420326948166,
0.015020440332591534,
0.008751777932047844,
0.010938256047666073,
0.02585519291460514,
0.02023248001933098,
0.04634148254990578,
-0.021130571141839027,
-0.015322607941925526,
0.07115096598863602,
0.06938409805297852,
0.002441815799102187,
-0.025007743388414383,
-0.005687270779162645,
-0.005639196839183569,
0.03306356072425842,
-0.05079267546534538,
-0.013701708987355232,
0.022221140563488007,
0.04293002933263779,
0.02770509198307991,
0.0019092503935098648,
-0.023402130231261253,
0.004640507977455854,
-0.037011634558439255,
-0.017336536198854446,
-0.023986097425222397,
0.05712343752384186,
-0.012662775814533234,
0.053947813808918,
0.019184766337275505,
0.009452001191675663,
0.012379715219140053,
-0.016591044142842293,
-0.07023479789495468,
0.038327138870954514,
-0.020014159381389618,
-0.03224167600274086,
-0.02371387928724289,
-0.013819600455462933,
0.005289474502205849,
-0.02797090634703636,
-0.01719093881547451,
-0.053858060389757156,
-0.008231788873672485,
-0.03984647989273071,
0.027887091040611267,
-0.017328649759292603,
-0.050367582589387894,
-0.028871284797787666,
0.03224291279911995,
-0.013058321550488472,
-0.02522769197821617,
-0.01396115217357874,
0.042401134967803955,
-0.05468366667628288,
0.012771322391927242,
-0.02806905098259449,
-0.020686963573098183,
0.012663156725466251,
0.044697776436805725,
0.013241780921816826,
0.0405416376888752,
-0.030971437692642212,
0.011797240003943443,
0.0031268170569092035,
0.043748270720243454,
0.01826298236846924,
0.004027838818728924,
-0.046700574457645416,
-0.04099086672067642,
0.026007255539298058,
0.00958691630512476,
0.07125333696603775,
-0.059104423969984055,
-0.017063943669199944,
0.038850508630275726,
-0.009384911507368088,
-0.04811163246631622,
0.04211850091814995,
0.048895008862018585,
0.020100293681025505,
-0.00100658368319273,
-0.06774377822875977,
0.011137222871184349,
-0.021465841680765152,
0.0031732895877212286,
0.03862973675131798,
0.009965300559997559,
-0.02515031397342682,
0.001537420554086566,
0.0013178670778870583,
0.012349380180239677,
-0.007567914668470621,
0.0077448878437280655,
-0.010740164667367935,
0.008639435283839703,
-0.026553822681307793,
-0.025944983586668968,
0.013989746570587158,
0.05395146831870079,
0.04610152170062065,
0.0367623008787632,
-0.002433688146993518,
-0.06479978561401367,
-0.019703639671206474,
0.03440050408244133,
0.02139005810022354,
0.005389623809605837,
-0.007581278216093779,
-0.03669147565960884,
-0.02323528751730919,
0.04821673780679703,
-0.020161660388112068,
0.02960244007408619,
-0.005427934695035219,
0.00042266419040970504,
-0.04020320251584053,
0.007038693875074387,
-0.05134642869234085,
0.006224528420716524,
-0.01641761139035225,
-0.011732487007975578,
-0.043260037899017334,
-0.008147484622895718,
0.013754853047430515,
0.056893859058618546,
0.02312195859849453,
0.05939927324652672,
0.0047193849459290504,
0.009011365473270416,
0.01387922465801239,
-0.01686021313071251,
-0.03858823701739311,
-0.06221889704465866,
0.013817780651152134,
0.023867882788181305,
-0.0043604327365756035,
0.04076618328690529,
-0.01617337204515934,
-0.027740497142076492,
0.03908263519406319,
0.00020554446382448077,
0.009763563051819801,
-0.011839338578283787,
-0.013670441694557667,
0.048831261694431305,
0.04187257960438728,
0.01728627271950245,
0.0839875265955925,
0.046935711055994034,
-0.03680824860930443,
-0.00544709200039506,
0.0058794328942894936,
0.0286481324583292,
-0.02134215645492077,
-0.002137683564797044,
-0.0011004075640812516,
0.00569293275475502,
-0.04525446146726608,
0.03100886382162571,
0.021256327629089355,
0.027667110785841942,
-0.02410990186035633,
-0.03535575047135353,
-0.014585185796022415,
0.014551354572176933,
-0.006995704025030136,
0.022341832518577576,
0.013796981424093246,
0.023658666759729385,
0.03709248825907707,
-0.024777470156550407,
-0.014746157452464104,
0.02525290474295616,
0.02552294358611107,
-0.0038646478205919266,
-0.014342963695526123,
0.0474456250667572,
-0.03159407526254654,
-0.020120304077863693,
0.008780295960605145,
-0.0567125529050827,
0.0630001649260521,
-0.025078948587179184,
-0.01152280904352665,
-0.013498102314770222,
-0.07054697722196579,
-0.03816603496670723,
0.013368220999836922,
0.010482796467840672,
0.052625663578510284,
-0.054940614849328995,
0.011549440212547779,
0.03253595903515816,
0.007181363180279732,
-0.06694696843624115,
-0.029921403154730797,
0.055419012904167175,
0.040549565106630325,
-0.012506376020610332,
-0.05290571600198746,
-0.013849538750946522,
-0.021855171769857407,
-0.02518307790160179,
-0.006999578792601824,
0.014054910279810429,
-0.030911801382899284,
-0.004661513492465019,
-0.015160825103521347,
-0.0010870350524783134,
0.05602168291807175,
-0.01257476769387722,
-0.03753704950213432,
-0.008203770965337753,
-0.003142285393550992,
-0.02241881564259529,
0.01698707602918148,
0.0340406708419323,
-0.03129753842949867,
-0.0389101505279541,
0.0027607143856585026,
-0.011358869262039661,
0.016044065356254578,
-0.05952878296375275,
-0.025120215490460396,
0.02609829790890217,
0.011959312483668327,
-0.0007652746862731874,
-0.04470524564385414,
0.01999235525727272,
0.015454652719199657,
0.021048594266176224,
-0.018994389101862907,
-0.01163072045892477,
-0.05496559292078018,
-0.051271118223667145,
0.022976389154791832,
-0.0051774634048342705,
0.005300835240632296,
-0.013369147665798664,
0.05183503031730652,
0.017911192029714584,
0.002264557406306267,
0.019396254792809486,
-0.02793385274708271,
0.004418788477778435,
-0.008476756513118744,
0.013899398036301136,
-0.0021559493616223335,
0.007680418435484171,
-0.02482363022863865,
-0.02841121144592762,
-0.037119895219802856,
-0.01795203983783722,
0.07796972244977951,
-0.0008995664538815618,
0.06942294538021088,
0.014781393110752106,
0.0006540721515193582,
-0.028499610722064972,
0.023411815986037254,
-0.027213767170906067,
0.010273679159581661,
-0.01194846723228693,
0.034968625754117966,
-0.04504864662885666,
0.00861379038542509,
-0.0054648504592478275,
0.0356963574886322,
0.0009183511137962341,
0.02709556370973587,
0.015252649784088135,
0.060395218431949615,
0.03134585916996002,
-0.04276465252041817,
-0.020038248971104622,
0.03732871264219284,
-0.030934980139136314,
0.036040257662534714,
-0.00956600159406662,
0.0034177997149527073,
0.03417961299419403,
0.01908997632563114,
0.01712469570338726,
-0.031636424362659454,
-0.023766592144966125,
0.02182404138147831,
0.024252062663435936,
0.015924561768770218,
0.001955510349944234,
0.03036351315677166,
-0.015135861933231354,
0.005930568091571331,
0.010462984442710876,
0.00454054307192564,
0.001966083887964487,
-0.0659547820687294,
-0.005603841971606016,
-0.05001569166779518,
-0.057426825165748596,
0.0326126329600811,
0.0006726500578224659,
-0.06961557269096375,
0.027087446302175522,
-0.014089975506067276,
0.06150056794285774,
0.023818278685212135,
0.008788513951003551,
-0.042173732072114944,
0.07831858098506927,
-0.04032028093934059,
0.03524453938007355,
-0.005580100230872631,
0.022243725135922432,
0.09880869835615158,
0.026966024190187454,
-0.013099579140543938,
-0.06118238717317581,
0.0032418197952210903,
-0.04671667143702507,
-0.014048204757273197,
-0.05950865522027016,
-0.00408556405454874,
-0.05487113818526268,
0.00805271603167057,
0.040610410273075104,
0.0783928781747818,
-0.023861512541770935,
-0.01200858410447836,
0.05864519253373146,
-0.03291270509362221,
-0.02281944826245308,
0.015021074563264847,
0.021218573674559593,
-0.012381507083773613,
0.011238491162657738,
-0.023417305201292038,
0.04048686847090721,
-0.05367126315832138,
-0.026451265439391136,
-0.028926098719239235,
-0.0017651463858783245,
0.01595730148255825,
0.0023962603881955147,
-0.033523838967084885,
-0.011304105632007122,
-0.04498884081840515,
-0.030178945511579514,
-0.0375455766916275,
-0.006238394882529974,
0.028184209018945694,
-0.012242387048900127,
0.003223333042114973,
0.025976520031690598,
-0.016043629497289658,
0.023271694779396057,
0.016213813796639442,
-0.005043008364737034,
-0.02293611504137516,
0.013211327604949474,
-0.03657704219222069,
0.06648647785186768,
-0.013389259576797485,
0.020290382206439972,
0.01025334931910038,
-0.01127256266772747,
-0.020115092396736145,
-0.03676282614469528,
-0.03400453180074692,
-0.00848064012825489,
0.03271801769733429,
-0.03415844589471817,
-0.02234867587685585,
0.006994303781539202,
0.0480620451271534,
-0.002323311287909746,
0.038091544061899185,
-0.024728422984480858,
-0.027741342782974243,
0.00869088526815176,
0.03058505244553089,
0.060123562812805176,
-0.031132549047470093,
-0.026347381994128227,
-0.019198862835764885,
-0.03429883345961571,
-0.04046265035867691,
-0.008586762472987175,
0.01613255962729454,
0.0321725532412529,
0.05283615365624428,
0.010309992358088493,
-0.0055304323323071,
-0.04086366668343544,
-0.05922537297010422,
0.009874183684587479,
-0.06442666053771973,
-0.036945242434740067,
-0.01620909944176674,
-0.00931372120976448,
0.021542957052588463,
0.050326548516750336,
-0.027512701228260994,
-0.008847132325172424,
0.028857210651040077,
0.0034093984868377447,
0.05980025231838226,
-0.011163880117237568,
-0.013048561289906502,
-0.010926113463938236,
-0.0480646938085556,
-0.0021852219942957163,
-0.027288179844617844,
0.01395250391215086,
0.03962554410099983,
0.011466595344245434,
0.03898800536990166,
0.013416428118944168,
-0.04178064316511154,
0.0272856205701828,
-0.010495191439986229,
-0.01846836321055889,
-0.021506980061531067,
-0.009823410771787167,
-0.01756739802658558,
-0.04118439927697182,
-0.0021463497541844845,
-0.05056561902165413,
-0.012412391602993011,
-0.02308654971420765,
0.0254327654838562,
-0.039512258023023605,
-0.013374634087085724,
-0.011791547760367393,
-0.026790177449584007,
-0.041454609483480453,
-0.007089989259839058,
-0.02029101923108101,
-0.009991039521992207,
0.01675795577466488,
0.020862573757767677,
-0.020667485892772675,
0.03303923085331917,
-0.03474954888224602,
0.013170184567570686,
0.026920616626739502,
-0.021444261074066162,
0.013854214921593666,
0.02775803580880165,
0.0252017080783844,
-0.01632673107087612,
0.04933856800198555,
-0.012629435397684574,
-0.021992923691868782,
0.06379534304141998,
-0.05190581828355789,
-0.08320225775241852,
0.03942624107003212,
0.011531024239957333,
0.033912379294633865,
0.04532594978809357,
-0.011869962327182293,
-0.03229423239827156,
0.041880052536726,
-0.004053258802741766,
0.00006015279723214917,
-0.03851090371608734,
-0.009446782059967518,
-0.017327040433883667,
0.0017875577323138714,
0.011644747108221054,
-0.02601255290210247,
-0.016216877847909927,
0.05125168710947037,
0.002067995024845004,
-0.02865089848637581,
0.0064012170769274235,
0.009957671165466309,
-0.010091302916407585,
-0.002846058690920472,
0.017847081646323204,
0.02513842098414898,
0.04479902982711792,
0.09689345210790634,
-0.03533303365111351,
0.011492365971207619,
0.009393544867634773,
-0.006463704630732536,
-0.0828421339392662,
-0.02916557714343071,
-0.009357789531350136,
0.005810603033751249,
0.038801196962594986,
-0.06385038048028946,
0.025106774643063545,
0.0062673576176166534,
-0.05211513862013817,
0.03860541805624962,
-0.06155775859951973,
-0.00643228180706501,
-0.03569881618022919,
-0.018130935728549957,
0.019895510748028755,
0.034339118748903275,
0.0032583330757915974,
0.04354571923613548,
0.02040744759142399,
0.032479215413331985,
0.0037327713798731565,
-0.0019911674316972494,
0.029546814039349556,
0.0261617973446846,
0.002421426586806774,
-0.03361010178923607,
0.06739632040262222,
-0.010908922180533409,
-0.024828707799315453,
0.03301006183028221,
-0.0033502753358334303,
0.017806096002459526,
0.0038185198791325092,
0.02517491579055786,
-0.028947586193680763,
0.04134203866124153,
-0.005420764908194542,
0.0010251938365399837,
-0.026218151673674583,
0.03717408329248428,
0.024244681000709534,
0.006733483634889126,
-0.034403301775455475,
-0.005241958890110254,
0.01562717743217945,
-0.013128086924552917,
-0.010211963206529617,
0.0480520986020565,
-0.029414914548397064,
0.01456595677882433,
0.009174134582281113,
-0.01665502041578293,
0.00821908749639988,
-0.01315179094672203,
0.011028340086340904,
-0.06755819171667099,
-0.008976994082331657,
0.032796889543533325,
0.0176678616553545,
-0.035364363342523575,
0.02094338648021221,
0.012403495609760284,
-0.029714029282331467,
0.025318892672657967,
-0.006378370802849531,
0.0002736413152888417,
-0.04852551966905594,
-0.03671445697546005,
0.03050193563103676,
-0.014508143067359924,
0.027706203982234,
-0.02087053470313549,
-0.05042993277311325,
0.005785407032817602,
0.027194203808903694,
0.007863638922572136,
-0.020672576501965523,
-0.020794270560145378,
0.007528033573180437,
-0.06714650243520737,
0.01806929148733616,
0.014146973378956318,
-0.03588750585913658,
-0.002192265586927533,
-0.02618928626179695,
0.005755647551268339,
-0.03071063756942749,
0.058721873909235,
0.004786224104464054,
-0.02308071032166481,
0.010983138345181942,
-0.0030623399652540684,
0.035218529403209686,
-0.06296143680810928,
-0.004689658991992474,
0.002202997449785471,
-0.004171398933976889,
-0.017219066619873047,
0.01452441606670618,
-0.0012393663637340069,
0.010279770009219646,
0.02444012090563774,
0.012244061566889286,
0.02173943631350994,
0.017537914216518402,
-0.06520908325910568,
0.052802495658397675,
-0.002868127077817917,
0.04271959140896797,
0.07015001773834229,
-0.004892639350146055,
0.026306144893169403,
0.005852073896676302,
-0.011690657585859299,
-0.03364821895956993,
0.020591052249073982,
-0.030911890789866447,
0.0128622492775321,
-0.006584286689758301,
0.021745245903730392,
0.0016954134916886687,
-0.044464126229286194,
-0.012478552758693695,
0.041061416268348694,
-0.044163964688777924,
-0.005974804051220417,
0.020326219499111176,
0.011554652824997902,
0.03268834948539734,
0.010427119210362434,
0.021384550258517265,
0.0030833224300295115,
-0.0077346800826489925,
-0.005403186194598675,
0.05947861820459366,
0.02431339956820011,
0.0015801789704710245,
0.056205783039331436,
0.0498536042869091,
-0.012841595336794853,
0.013569069094955921,
0.03605533763766289,
0.01666928641498089,
-0.03300243616104126,
-0.04104367643594742,
-0.01050969585776329,
-0.004146404564380646,
-0.007339459843933582,
0.051709968596696854,
-0.004702959209680557,
0.1268893927335739,
-0.00016184020205400884,
-0.0007614432252012193,
-0.020381586626172066,
-0.0003931052633561194,
0.0010734276147559285,
0.05008694529533386,
0.019315164536237717,
0.0350077785551548,
-0.044069427996873856,
0.01950368657708168,
-0.005484499968588352,
0.009298568591475487,
-0.028116585686802864,
-0.01889503188431263,
0.023553920909762383,
-0.013758125714957714,
0.036422282457351685,
-0.0007103967946022749,
-0.0009385923040099442,
0.0020250980742275715,
0.0059545207768678665,
0.059862010180950165,
0.03555844724178314,
0.02934662066400051,
0.020931405946612358,
0.03792773559689522,
-0.005567746702581644,
0.0361967459321022,
-0.0727129727602005,
-0.02177167311310768,
-0.012231540866196156,
0.04626506567001343,
-0.026894288137555122,
0.005692388862371445
] |
<p>What what I understand, hydrostatic pressure is the "weight" of the water pushing against objects. But if this is true, why is hydrostatic pressure perpendicular to the surface it acts on instead of always going down?</p>
<p>For example, if you placed a book on a desk, the book's weight would push against the desk, but gravity is pulling it "down". But if you put another book beside this book the first book wouldn't apply any force on it. The weight exerted from the book always <em>goes down</em>.</p>
<p>Similarly, why doesn't hydrostatic pressure always go down? I understand that if you put a plate on the seabed, the weight of the water would push down on it, but if you just had a vertical plate standing on the bed, why would force push it from the sides?</p>
<p>To sum up, why does hydrostatic pressure act perpendicular to the object instead of always down?</p>
| 8,489 |
[
-0.037632349878549576,
-0.0219107735902071,
-0.005954505410045385,
-0.009042139165103436,
0.015502364374697208,
-0.02808259055018425,
-0.004002050496637821,
0.02986123599112034,
0.038850679993629456,
-0.010114751756191254,
0.008638717234134674,
0.057810284197330475,
0.042683981359004974,
-0.009232298471033573,
0.023175295442342758,
0.015168508514761925,
-0.0367928110063076,
-0.04495091363787651,
0.01977497711777687,
0.004980042111128569,
-0.03280618041753769,
0.032463815063238144,
0.01131467241793871,
0.03229605779051781,
-0.006276972126215696,
-0.014294267632067204,
0.02575061284005642,
-0.011097236536443233,
0.0623030923306942,
0.04416344314813614,
0.0023225934710353613,
-0.03631311655044556,
-0.02973845601081848,
0.009038614109158516,
0.027076516300439835,
0.017467904835939407,
-0.02895342744886875,
-0.02451365254819393,
-0.054304610937833786,
0.026408590376377106,
-0.005277200136333704,
-0.004697680938988924,
-0.025535836815834045,
0.0400453619658947,
-0.027100322768092155,
0.05091537907719612,
0.012913434766232967,
-0.00010566866694716737,
0.01177795510739088,
-0.08135475218296051,
0.026605429127812386,
-0.0022825137712061405,
0.05433346703648567,
0.04309072345495224,
0.03478537127375603,
-0.019356202334165573,
0.05296345055103302,
0.10231585055589676,
-0.03337746113538742,
-0.04611041769385338,
-0.038701023906469345,
0.006487551145255566,
-0.03458571434020996,
-0.02019471302628517,
-0.0095149464905262,
0.017594516277313232,
0.01362698059529066,
-0.006846087519079447,
0.014310752972960472,
0.025928637012839317,
0.012730607762932777,
-0.004152989014983177,
0.03178592398762703,
-0.022678308188915253,
-0.012612254358828068,
-0.026784710586071014,
0.0005539868725463748,
0.03519061207771301,
0.0032808473333716393,
0.020803801715373993,
0.010274305939674377,
0.01620837114751339,
0.02811228483915329,
0.05416779965162277,
0.016775846481323242,
0.00033241481287404895,
0.05845257267355919,
0.02885989472270012,
0.0035057691857218742,
0.03037104196846485,
-0.00989665649831295,
0.0015993514098227024,
-0.03315490484237671,
0.014700278639793396,
0.002631793264299631,
-0.01166532188653946,
-0.00034813766251318157,
0.021904101595282555,
0.019015813246369362,
0.020099839195609093,
0.02067176252603531,
-0.022270357236266136,
0.02326430380344391,
0.07997535914182663,
-0.006567998789250851,
-0.04865965619683266,
-0.048313457518815994,
0.030046360567212105,
-0.02378161996603012,
-0.00795698631554842,
-0.012357874773442745,
0.015607296489179134,
-0.022026417776942253,
-0.03775054216384888,
-0.0016996071208268404,
-0.0034070301335304976,
0.029540864750742912,
-0.01993473619222641,
0.046244747936725616,
0.019525691866874695,
0.03770245984196663,
-0.018143650144338608,
0.010561848990619183,
-0.05139631778001785,
-0.05172709375619888,
0.0004792761174030602,
0.04187930002808571,
-0.054301392287015915,
-0.009851394221186638,
0.024248549714684486,
0.01324145682156086,
0.01839553192257881,
0.0002889776951633394,
0.01241898164153099,
0.06245039403438568,
-0.004996068309992552,
-0.10619168728590012,
-0.05855622887611389,
0.05450698733329773,
0.0017641426529735327,
-0.021953731775283813,
-0.05832736939191818,
0.01975638046860695,
0.019401537254452705,
0.03747495636343956,
-0.020609155297279358,
-0.0013540007639676332,
-0.010246090590953827,
0.015222951769828796,
-0.021989548578858376,
0.008865803480148315,
0.016926903277635574,
0.004595845937728882,
-0.04527738317847252,
-0.03366087004542351,
-0.10961473733186722,
0.005139421671628952,
0.02146739698946476,
0.01479046419262886,
-0.04094927757978439,
0.059440627694129944,
-0.012775890529155731,
0.0000847068295115605,
-0.022982550784945488,
-0.0171749796718359,
-0.05347060039639473,
0.0663968101143837,
-0.007057763636112213,
-0.030692020431160927,
0.017459644004702568,
0.036263540387153625,
0.03454152122139931,
-0.02488946169614792,
0.020468026399612427,
0.0389542356133461,
-0.007308707106858492,
-0.005435848142951727,
-0.04102134704589844,
0.030059192329645157,
-0.016329409554600716,
-0.022184453904628754,
-0.009931549429893494,
-0.0022160904482007027,
-0.004412960726767778,
0.019238317385315895,
0.008982852101325989,
0.0014068970922380686,
-0.013446717523038387,
-0.023516841232776642,
-0.03782656788825989,
0.018417375162243843,
-0.04822893440723419,
0.033350199460983276,
-0.033781521022319794,
0.020066116005182266,
0.05407240614295006,
0.020889263600111008,
0.008144441992044449,
-0.040249742567539215,
-0.0062737963162362576,
-0.018433351069688797,
0.012466498650610447,
-0.014262448064982891,
-0.020115725696086884,
0.02600589580833912,
0.04355665668845177,
0.010098281316459179,
0.006503513548523188,
-0.00622539920732379,
-0.046836964786052704,
-0.027674023061990738,
0.018907444551587105,
-0.019895371049642563,
-0.015037518925964832,
-0.001340910093858838,
-0.0062386952340602875,
0.007906264625489712,
0.014615139923989773,
-0.0189119391143322,
0.033618900924921036,
-0.03651103004813194,
0.07161234319210052,
0.08342135697603226,
-0.0073189097456634045,
0.014013153500854969,
0.027156075462698936,
-0.007279376965016127,
-0.01179625652730465,
-0.005788388196378946,
-0.008143438026309013,
-0.042752478271722794,
0.0056483871303498745,
0.005613848101347685,
0.00779311079531908,
-0.006932821124792099,
0.011793890967965126,
0.019431812688708305,
0.048538804054260254,
0.028142808005213737,
0.03200513869524002,
0.0072291549295187,
-0.024207040667533875,
0.01964372955262661,
0.03649396821856499,
0.018535858020186424,
0.025264883413910866,
0.06740487366914749,
0.024696145206689835,
0.031026801094412804,
-0.010655241087079048,
-0.03132228925824165,
0.04749291017651558,
0.02112545818090439,
0.050193823873996735,
-0.009528360329568386,
-0.044330865144729614,
0.04223376139998436,
-0.02078310213983059,
0.035471729934215546,
0.011032262817025185,
0.028769472613930702,
0.005252600647509098,
-0.06592802703380585,
-0.00035186478635296226,
0.009737733751535416,
-0.019546348601579666,
0.0019119090866297483,
-0.010631772689521313,
0.023365605622529984,
-0.06262368708848953,
0.011712295934557915,
-0.01740075647830963,
0.001903249998576939,
-0.021862434223294258,
-0.03893998637795448,
0.020370149984955788,
0.02736620418727398,
0.0784578025341034,
-0.026636959984898567,
0.0007528550922870636,
0.008852685801684856,
-0.0363222174346447,
-0.03263457119464874,
-0.02517145872116089,
-0.03276481851935387,
0.003506813431158662,
-0.02636193111538887,
-0.005654305685311556,
0.036881592124700546,
0.0033699232153594494,
-0.0011244971537962556,
0.01057661883533001,
-0.005464155226945877,
-0.017607681453227997,
-0.03371688351035118,
-0.07482796907424927,
-0.019042879343032837,
-0.010633455589413643,
-0.012730701826512814,
0.05489754676818848,
-0.006224159151315689,
-0.013641844503581524,
0.017492925748229027,
-0.012222371995449066,
-0.051293015480041504,
-0.002043367363512516,
0.0011998163536190987,
-0.008828423917293549,
-0.008273047395050526,
0.0016349746147170663,
0.03387167304754257,
-0.08125405013561249,
-0.008831098675727844,
-0.02789919823408127,
-0.03897359222173691,
0.004236551001667976,
-0.019243702292442322,
0.030944809317588806,
-0.031528860330581665,
-0.04664723575115204,
0.08910995721817017,
0.0050880382768809795,
-0.03342382237315178,
0.01625990867614746,
-0.01060615386813879,
-0.012280050665140152,
-0.04690033942461014,
0.04249786585569382,
0.05522165447473526,
-0.027321241796016693,
0.04457731172442436,
-0.003030453808605671,
0.0102850291877985,
0.026883315294981003,
0.02300945855677128,
0.012775439769029617,
-0.03699886053800583,
0.035916347056627274,
0.025053026154637337,
0.040524810552597046,
-0.00045848978334106505,
-0.013206340372562408,
-0.0017607323825359344,
-0.021961400285363197,
0.01867426000535488,
0.0007066305261105299,
-0.01814677007496357,
0.053509488701820374,
0.01094982959330082,
-0.014209723100066185,
-0.06057390198111534,
0.02137354388833046,
-0.0001278037525480613,
0.0025125714018940926,
0.0293271541595459,
0.0009900310542434454,
0.05846411734819412,
-0.020938672125339508,
-0.034145601093769073,
0.0651584044098854,
0.04791492596268654,
-0.01717315800487995,
-0.05098354071378708,
-0.011451230384409428,
0.024958858266472816,
0.026781121268868446,
-0.0028494358994066715,
0.020958662033081055,
0.06486880779266357,
0.007102157920598984,
0.015894843265414238,
0.010141154751181602,
-0.0530887097120285,
-0.005793908145278692,
-0.06573782116174698,
0.018098384141921997,
0.03199777379631996,
0.04021196812391281,
-0.0037220565136522055,
0.028366250917315483,
0.0192439965903759,
0.009265612810850143,
0.013274772092700005,
0.019651737064123154,
-0.060679659247398376,
-0.0033751572482287884,
-0.02653178758919239,
0.004057965241372585,
0.0033802001271396875,
-0.02383701503276825,
-0.02253546379506588,
-0.022097177803516388,
-0.04898328706622124,
-0.009325802326202393,
-0.018966512754559517,
-0.0796779990196228,
0.0035028911661356688,
-0.006972289644181728,
-0.03873569145798683,
-0.016933344304561615,
0.020158423110842705,
0.006643817760050297,
-0.03955793380737305,
0.04314407333731651,
0.04236513003706932,
-0.025081923231482506,
0.004363285843282938,
-0.01870126836001873,
0.017857443541288376,
0.02168329618871212,
0.01297643594443798,
0.0153672955930233,
0.0272380281239748,
0.0042810277082026005,
0.004525751806795597,
0.0058068279176950455,
0.03652401268482208,
-0.004322076682001352,
0.0022968496195971966,
-0.035237427800893784,
-0.05053257197141647,
0.0027803811244666576,
-0.005646728444844484,
0.03200539946556091,
0.013212782330811024,
-0.023643579334020615,
0.017555059865117073,
-0.00740033620968461,
-0.003085683798417449,
0.0532173253595829,
0.03304116055369377,
0.022389153018593788,
0.02092491276562214,
-0.05007508769631386,
-0.01570364646613598,
-0.05110720917582512,
-0.0044866278767585754,
0.009561490267515182,
-0.023361563682556152,
-0.0377349890768528,
0.00002083654544549063,
0.008994107134640217,
-0.01884738728404045,
0.02156502567231655,
-0.011861015111207962,
-0.005353739019483328,
0.02438386157155037,
-0.026859471574425697,
0.021086543798446655,
0.05641039088368416,
0.026866985484957695,
0.07180177420377731,
-0.0039395904168486595,
-0.008775659836828709,
-0.044898759573698044,
-0.04050273075699806,
0.012572839856147766,
0.029287071898579597,
-0.01033759769052267,
0.0018066763877868652,
-0.04240930825471878,
-0.05600598827004433,
0.057320430874824524,
-0.022204013541340828,
-0.023826055228710175,
-0.0027511173393577337,
0.022559909150004387,
-0.01314125582575798,
0.0012317817891016603,
-0.020283067598938942,
-0.014719379134476185,
-0.007196156773716211,
0.030610885471105576,
-0.00693545863032341,
0.009310484863817692,
-0.029900608584284782,
0.008490019477903843,
0.006001760717481375,
0.031062649562954903,
-0.0003065353666897863,
0.026311688125133514,
0.003249304834753275,
0.02300398051738739,
-0.02300184592604637,
-0.06834287196397781,
-0.013291260227560997,
-0.01095917634665966,
0.0290045328438282,
0.034721698611974716,
-0.01771591417491436,
-0.052846942096948624,
0.025194523856043816,
-0.01030575018376112,
-0.04143963009119034,
-0.006099147256463766,
-0.014423388987779617,
0.018724730238318443,
0.0479925274848938,
-0.008862520568072796,
0.05950922146439552,
0.019249461591243744,
-0.046753332018852234,
-0.05017715319991112,
-0.044690314680337906,
0.022725556045770645,
-0.042544372379779816,
-0.01458664145320654,
-0.055322010070085526,
0.020461788401007652,
-0.031885527074337006,
0.034748826175928116,
0.012338745407760143,
-0.001971208956092596,
0.0009494210826233029,
-0.021243663504719734,
-0.024570565670728683,
0.021250175312161446,
-0.0011706389486789703,
0.006178563926368952,
0.02089436538517475,
0.02111007831990719,
0.01459984015673399,
-0.03624147176742554,
-0.005895472131669521,
-0.0008723954670131207,
-0.006544295698404312,
-0.013345352374017239,
0.017129933461546898,
-0.000017220572772203013,
0.020223399624228477,
-0.0021625198423862457,
0.02751684933900833,
-0.03023420460522175,
0.02471514418721199,
-0.02596398815512657,
-0.0021609198302030563,
0.02797655016183853,
-0.03031160868704319,
-0.021234281361103058,
0.008345157839357853,
-0.020852167159318924,
0.02144542895257473,
-0.02486393414437771,
0.02839806117117405,
0.04514818638563156,
0.0264594666659832,
-0.03761792927980423,
-0.04445234686136246,
0.04778043553233147,
-0.002877596067264676,
-0.015154070220887661,
-0.022105343639850616,
0.028934944421052933,
-0.0069247339852154255,
-0.02827955037355423,
-0.022408822551369667,
0.038566190749406815,
-0.048164039850234985,
0.0007593660848215222,
0.041116662323474884,
-0.019957587122917175,
0.06496337801218033,
-0.019037799909710884,
-0.022269366309046745,
-0.01223587803542614,
-0.024467017501592636,
-0.01743735931813717,
-0.04899696633219719,
0.0546846017241478,
0.0022932281717658043,
-0.011908936314284801,
0.00320445210672915,
-0.035530801862478256,
0.030892128124833107,
-0.011647531762719154,
0.03477088734507561,
0.007273067254573107,
0.02857307344675064,
-0.01853877678513527,
-0.006820920389145613,
0.0031797834672033787,
0.018132854253053665,
0.051767174154520035,
-0.0246383398771286,
0.001339988666586578,
-0.049441855400800705,
-0.04693732038140297,
0.011377101764082909,
0.0010670272167772055,
0.008137687109410763,
-0.017303500324487686,
0.060276422649621964,
-0.006712881848216057,
0.02259242534637451,
0.03624061867594719,
-0.026456518098711967,
0.024756522849202156,
0.04162899777293205,
-0.016406172886490822,
0.01347473543137312,
0.006862018257379532,
-0.04427209123969078,
-0.027311131358146667,
-0.00863285269588232,
0.021078940480947495,
0.06480507552623749,
-0.031043898314237595,
0.07561323046684265,
0.01003751065582037,
-0.029324285686016083,
0.009668486192822456,
-0.043466851115226746,
-0.026534881442785263,
0.00602740328758955,
-0.012855354696512222,
0.03734075650572777,
-0.056402042508125305,
0.05009332671761513,
0.019138777628540993,
0.04233231395483017,
0.003220632439479232,
0.0013606739230453968,
0.0458969920873642,
0.02524380572140217,
0.03152644261717796,
0.004204267170280218,
-0.0386507622897625,
0.037096623331308365,
-0.01815304346382618,
0.011584682390093803,
-0.01486185658723116,
-0.03629012405872345,
0.05002513900399208,
0.012269324623048306,
-0.011558924801647663,
-0.07358832657337189,
-0.006216350477188826,
-0.0240107960999012,
0.01601811684668064,
-0.0016914777224883437,
0.0497727245092392,
-0.025048570707440376,
0.04874705523252487,
0.050094377249479294,
0.0021152449771761894,
0.012941560707986355,
-0.015136197209358215,
-0.07055704295635223,
-0.024975432083010674,
0.011541509069502354,
-0.03568489849567413,
0.03830958530306816,
0.009061120450496674,
-0.02826518751680851,
0.0036170140374451876,
-0.027880463749170303,
0.027213722467422485,
0.011349150910973549,
0.015333653427660465,
0.002808499615639448,
0.07634051144123077,
0.0008054508944042027,
-0.002036390593275428,
-0.011066563427448273,
-0.01461614016443491,
0.1322142779827118,
0.030933622270822525,
0.04047605022788048,
-0.06352236866950989,
-0.010843916796147823,
-0.04099583998322487,
-0.03189000114798546,
-0.029383866116404533,
0.024215519428253174,
0.029352029785513878,
0.03633638098835945,
0.016467418521642685,
0.05614323914051056,
0.009687136858701706,
-0.021128922700881958,
0.06920628249645233,
-0.07545818388462067,
-0.03650442138314247,
-0.022603897377848625,
0.024601664394140244,
-0.03653498366475105,
0.05419425293803215,
-0.03301069140434265,
0.048243485391139984,
-0.027272650972008705,
-0.006987576372921467,
-0.0446937158703804,
-0.049644000828266144,
0.015340780839323997,
0.020995868369936943,
-0.06430484354496002,
-0.018057817593216896,
-0.02053515426814556,
-0.036659788340330124,
-0.04327700659632683,
0.051627613604068756,
0.021951280534267426,
-0.013011264614760876,
0.003937870264053345,
-0.039102599024772644,
0.0030677281320095062,
0.020847490057349205,
0.006847922690212727,
-0.00450789975002408,
-0.04472809657454491,
0.035724326968193054,
-0.021635262295603752,
0.037134960293769836,
-0.036155249923467636,
0.014799853786826134,
0.014377099461853504,
0.0101128239184618,
-0.006786762271076441,
-0.05214841663837433,
-0.022348131984472275,
-0.0036895989906042814,
0.05500884726643562,
0.017165526747703552,
-0.0633382648229599,
-0.0006700293160974979,
0.04901323840022087,
-0.03157420828938484,
0.014368451200425625,
0.020008543506264687,
0.002731592860072851,
-0.0023259459994733334,
-0.025984734296798706,
0.009219634346663952,
-0.01581125147640705,
-0.009678930975496769,
-0.017642907798290253,
0.011342865414917469,
-0.07129140198230743,
0.004297219216823578,
-0.019510187208652496,
0.010615576058626175,
0.051805317401885986,
0.026806678622961044,
-0.026523863896727562,
-0.022012049332261086,
-0.043081581592559814,
0.06494983285665512,
-0.06358134001493454,
-0.014856680296361446,
-0.03923054412007332,
-0.022241821512579918,
0.021652814000844955,
0.028321143239736557,
0.006604425143450499,
-0.003132237121462822,
0.0032850559800863266,
-0.017781099304556847,
0.02940528094768524,
-0.026937348768115044,
-0.05394987016916275,
0.021990284323692322,
-0.018689198419451714,
-0.016822565346956253,
0.0124191390350461,
-0.022970322519540787,
0.03558330237865448,
-0.006230965722352266,
-0.0038578775711357594,
0.013431873172521591,
0.006332444027066231,
-0.022701386362314224,
0.01750260218977928,
-0.006571485195308924,
-0.004939319100230932,
0.024450909346342087,
-0.0076230489648878574,
-0.044276706874370575,
-0.0003528475062921643,
-0.03525885194540024,
0.010479837656021118,
-0.0012879347195848823,
0.02617616578936577,
-0.016739917919039726,
0.014076444320380688,
-0.035773441195487976,
0.028125016018748283,
-0.02251218631863594,
0.001269159372895956,
-0.07087656110525131,
-0.01462920568883419,
0.020068522542715073,
0.006208185106515884,
-0.04281250759959221,
0.03164534643292427,
-0.06952530145645142,
-0.02312455140054226,
0.005633199121803045,
-0.025574343279004097,
0.015984000638127327,
0.02928438037633896,
0.06745827943086624,
-0.03525417298078537,
0.023173335939645767,
0.016321683302521706,
-0.022069048136472702,
0.04851894825696945,
-0.0025526925455778837,
-0.06876330077648163,
0.02875976264476776,
0.00006304879207164049,
0.012697038240730762,
0.040841151028871536,
-0.01764499954879284,
-0.030097944661974907,
0.06030293181538582,
-0.027032898738980293,
0.03199489042162895,
-0.0431724451482296,
-0.042312752455472946,
-0.018483752384781837,
0.008475475944578648,
0.03257095441222191,
-0.017930271103978157,
-0.0036989841610193253,
0.04747879505157471,
0.0032143201678991318,
0.013927467167377472,
0.012920767068862915,
0.0008917080122046173,
-0.018571581691503525,
0.015484270639717579,
0.02893625572323799,
-0.015050573274493217,
0.009318544529378414,
0.04346485435962677,
-0.055220913141965866,
0.041792865842580795,
0.03683793544769287,
-0.02045433782041073,
-0.0620446503162384,
0.008424497209489346,
-0.0192401222884655,
-0.03525456413626671,
0.02834208495914936,
-0.045255791395902634,
-0.05930393934249878,
0.018425723537802696,
-0.06366363167762756,
0.011996590532362461,
-0.06228155642747879,
-0.01005380880087614,
-0.03543868288397789,
-0.004881707020103931,
0.027871113270521164,
0.05186188966035843,
-0.03506381809711456,
0.02708757296204567,
0.02167043276131153,
-0.0026040319353342056,
0.01481487974524498,
-0.0027686781249940395,
0.004374718759208918,
0.026469290256500244,
0.009112400002777576,
0.02086932584643364,
0.04432430863380432,
-0.013286464847624302,
-0.026930710300803185,
0.028103908523917198,
-0.029754268005490303,
0.00975447241216898,
0.006400056183338165,
0.025002190843224525,
-0.018841560930013657,
0.0124193811789155,
0.0035626408644020557,
-0.005828428082168102,
-0.05410813167691231,
0.05492986738681793,
0.02349667437374592,
0.021015053614974022,
-0.010682305321097374,
0.005281921476125717,
0.0012941951863467693,
-0.03968880698084831,
-0.0021655792370438576,
0.03244995325803757,
-0.03467618301510811,
0.03008192591369152,
0.015577062964439392,
0.019564524292945862,
0.049785174429416656,
0.02209220454096794,
-0.01564866304397583,
-0.03202957659959793,
0.021166367456316948,
0.02037530019879341,
0.010866286233067513,
-0.020723477005958557,
0.019758913666009903,
0.05032140016555786,
-0.021874547004699707,
-0.00977692473679781,
0.010492371395230293,
-0.01827513426542282,
-0.08155733346939087,
-0.017057524994015694,
-0.027891986072063446,
-0.04078692942857742,
-0.011886350810527802,
-0.005806277506053448,
-0.027031803503632545,
0.03186040744185448,
0.05248109623789787,
0.017771856859326363,
-0.007733454462140799,
-0.0767453983426094,
-0.005789712071418762,
-0.02629905380308628,
0.07016096264123917,
0.019663704559206963,
-0.010350478813052177,
-0.01792011596262455,
0.00032214520615525544,
0.014549106359481812,
0.011770237237215042,
0.05401071906089783,
-0.0001565632119309157,
0.014231957495212555,
-0.00389618962071836,
-0.012530672363936901,
0.00008754608279559761,
-0.015072047710418701,
0.009861204773187637,
0.05622619017958641,
-0.06794662773609161,
0.051030416041612625,
0.0009470299701206386,
0.004079083446413279,
0.010839724913239479,
0.0008668367518112063,
-0.0212449561804533,
0.05351004749536514,
0.009709890931844711,
-0.021312851458787918,
0.029911110177636147,
0.012375922873616219,
-0.005857111420482397,
0.07425044476985931,
-0.018259180709719658,
-0.003635701024904847,
-0.008456778712570667,
-0.024012267589569092,
-0.02448587492108345,
0.029319623485207558,
-0.007287834770977497,
0.020991651341319084,
-0.01419838797301054,
0.018435319885611534,
0.038143858313560486,
-0.039794329553842545,
0.011719861067831516,
0.02966279909014702,
-0.05982812121510506,
0.003976461011916399,
0.06865983456373215,
0.010751651600003242,
0.013400429859757423,
-0.03307848423719406,
0.012380843050777912,
0.027261584997177124,
-0.01072226744145155,
0.03958239406347275,
0.0448521226644516,
0.0483010858297348,
0.04311911389231682,
0.0022582102101296186,
0.051870301365852356,
0.015821920707821846,
0.02978467009961605,
0.05437026917934418,
0.04400539770722389,
-0.018439993262290955,
-0.04562406986951828,
0.007449749857187271,
-0.0010000099427998066,
-0.03847247362136841,
0.014338864013552666,
-0.001683582435362041,
0.06633219867944717,
-0.010968905873596668,
-0.01519790105521679,
-0.03518010675907135,
-0.017423124983906746,
0.02741246297955513,
0.0002808483550325036,
0.0003872787347063422,
0.018168896436691284,
-0.018939891830086708,
-0.045534685254096985,
0.0026284148916602135,
0.014071136713027954,
0.01707930862903595,
0.023592786863446236,
0.029220007359981537,
0.004440837074071169,
0.001930131809785962,
-0.023572716861963272,
0.006312290672212839,
-0.0203749667853117,
-0.029813997447490692,
0.03680373728275299,
0.003787128021940589,
0.030389677733182907,
0.031156573444604874,
0.0004954145988449454,
-0.012406108900904655,
0.043242305517196655,
-0.08061670511960983,
-0.029667479917407036,
0.00497419573366642,
0.004128217231482267,
-0.013212870806455612,
-0.0057520377449691296
] |
<p>Actually I am not a physics student but I have to give a lecture about Fluorescence lifetime imaging(FLIM). I am thinking of comparing this techniques to another imaging techniques.
Does anyone know what is the best imaging techniques that is comparable to FLIM?
Thank you</p>
<p>Soha</p>
| 8,490 |
[
-0.001177532714791596,
-0.04500404745340347,
0.007871429435908794,
-0.025031881406903267,
0.028346402570605278,
0.0004950966103933752,
-0.008807683363556862,
-0.04360951855778694,
0.026423471048474312,
-0.02343170903623104,
0.027428539469838142,
0.0640222355723381,
0.026587948203086853,
0.010899053886532784,
0.027177486568689346,
-0.01050930842757225,
-0.013600838370621204,
-0.043250713497400284,
-0.00887191854417324,
-0.015728695318102837,
-0.0012127957306802273,
0.007849297486245632,
0.00318919587880373,
0.012170888483524323,
-0.023579897359013557,
0.01918322592973709,
-0.006743134465068579,
-0.021761557087302208,
-0.013873979449272156,
0.07962814718484879,
-0.016610996797680855,
0.0016937543405219913,
-0.013789546675980091,
0.02657344564795494,
0.0012290762970224023,
-0.014308163896203041,
-0.02677850052714348,
-0.05440107733011246,
-0.027518359944224358,
0.04951179027557373,
-0.048104628920555115,
0.0040349713526666164,
0.030437272042036057,
0.039708249270915985,
-0.02547820284962654,
0.031224289909005165,
-0.02770267426967621,
-0.051599424332380295,
0.027573388069868088,
-0.05505590885877609,
0.043820202350616455,
0.0012526146601885557,
0.04686504974961281,
0.021977128461003304,
-0.004234586842358112,
-0.013904085382819176,
0.05041714012622833,
0.1043468490242958,
-0.005959766451269388,
-0.06864895671606064,
-0.02860591746866703,
-0.01661614328622818,
0.0002577251580078155,
-0.02564355544745922,
-0.024811947718262672,
0.010812588036060333,
-0.011330057866871357,
-0.03373700752854347,
0.05404334515333176,
0.012278085574507713,
-0.024752827361226082,
0.0019915278535336256,
0.10792434960603714,
0.014560574665665627,
0.015016473829746246,
-0.016417836770415306,
-0.0009535140125080943,
0.001598581438884139,
0.0401478074491024,
0.03960369527339935,
-0.030029360204935074,
-0.007633294444531202,
-0.024146968498826027,
0.04512079060077667,
-0.01876320131123066,
-0.031002545729279518,
0.06204370781779289,
-0.02124313823878765,
-0.008481942117214203,
0.025045525282621384,
-0.04063329100608826,
0.0047408174723386765,
0.03277387097477913,
0.03265539929270744,
-0.02209584042429924,
0.04266415908932686,
-0.00468693021684885,
0.04712926596403122,
0.0009680931689217687,
-0.020085111260414124,
0.019681669771671295,
-0.06298033148050308,
0.03218018263578415,
0.0733780711889267,
0.016940830275416374,
-0.00036219446337781847,
0.007348611019551754,
0.0005360470968298614,
-0.01583169214427471,
0.03317011147737503,
-0.04254994913935661,
0.010450444184243679,
0.005048204213380814,
0.003946318291127682,
0.0049639297649264336,
-0.0023816602770239115,
-0.013033115305006504,
0.01808658242225647,
0.06956131011247635,
0.07862198352813721,
0.003071661340072751,
-0.03038698248565197,
-0.011948596686124802,
-0.017065243795514107,
-0.06054111570119858,
0.017434829846024513,
0.001607615384273231,
0.008894981816411018,
-0.043867118656635284,
0.03544485196471214,
0.02095218561589718,
-0.010730324313044548,
0.05118206888437271,
-0.02217763103544712,
0.04734353348612785,
-0.020051460713148117,
-0.0980457291007042,
-0.048860449343919754,
0.06244364380836487,
-0.01837215945124626,
0.027775811031460762,
-0.06290502101182938,
0.00782490149140358,
0.027009662240743637,
0.04985910281538963,
0.028684483841061592,
-0.007125815376639366,
-0.04229475557804108,
0.046583570539951324,
-0.008626972325146198,
0.000482422998175025,
-0.020745091140270233,
0.04873393848538399,
0.0058855959214270115,
0.035789940506219864,
-0.07327844947576523,
-0.0019835515413433313,
0.011633853428065777,
-0.013568221591413021,
-0.020953873172402382,
0.07760340720415115,
-0.027296654880046844,
0.008790187537670135,
0.004122360143810511,
0.0035507946740835905,
-0.00493202917277813,
0.09640680998563766,
0.02479803003370762,
0.030011052265763283,
0.016366442665457726,
-0.020623954012989998,
0.03418511897325516,
0.0032943421974778175,
0.020906690508127213,
0.03254540637135506,
-0.04542989283800125,
-0.00226743146777153,
0.020032551139593124,
0.019555257633328438,
0.027099324390292168,
-0.007846572436392307,
-0.03577735647559166,
0.01594577729701996,
0.010119912214577198,
-0.012812698259949684,
0.048436034470796585,
0.022932076826691628,
-0.023823710158467293,
0.03409803658723831,
-0.045036040246486664,
-0.02641056478023529,
-0.03440438210964203,
0.005149709060788155,
0.020586097612977028,
-0.039621949195861816,
0.03639305755496025,
0.00345959747210145,
0.005621320568025112,
-0.0323859266936779,
-0.03996007889509201,
-0.058092061430215836,
0.005842191632837057,
-0.006370057817548513,
-0.006814470514655113,
0.018966039642691612,
0.007845733314752579,
0.0023816898465156555,
-0.028134705498814583,
-0.0009897613199427724,
-0.05234295129776001,
-0.0251004695892334,
-0.02324366569519043,
-0.03579637035727501,
0.042036622762680054,
0.012921520508825779,
-0.019789710640907288,
-0.010450726374983788,
-0.0016298310365527868,
-0.013570652343332767,
0.02399287186563015,
-0.01015586405992508,
0.05744533613324165,
0.059184178709983826,
0.016501201316714287,
-0.027125878259539604,
-0.005677491892129183,
-0.009452778846025467,
0.018771616742014885,
0.007515139412134886,
-0.042255569249391556,
-0.05785509571433067,
-0.002472126856446266,
0.055513422936201096,
0.020831173285841942,
-0.02517399564385414,
0.04222704470157623,
0.02582649514079094,
-0.0019160605734214187,
0.07510776072740555,
0.005756495054811239,
-0.03178830444812775,
-0.05458422750234604,
0.002737130271270871,
0.04610934853553772,
-0.009248964488506317,
0.024566657841205597,
0.052019152790308,
0.014270222745835781,
0.04596313461661339,
0.0070350016467273235,
0.005190771073102951,
0.027040500193834305,
-0.04636114463210106,
0.009093046188354492,
-0.0035438379272818565,
-0.03752909228205681,
0.006952924188226461,
-0.0456661581993103,
0.014815928414463997,
0.02279854007065296,
-0.03835809975862503,
0.024745017290115356,
0.007197830826044083,
-0.03764355555176735,
0.031170308589935303,
-0.006160560064017773,
-0.02064937725663185,
0.011365369893610477,
0.01775149069726467,
-0.04224729537963867,
0.027871375903487206,
0.014982915483415127,
-0.01756727509200573,
-0.03709004446864128,
0.005395863670855761,
0.07453643530607224,
0.006869006901979446,
0.014171686954796314,
-0.019799362868070602,
-0.037450846284627914,
0.010346719063818455,
-0.022440562024712563,
0.006869821809232235,
0.008126825094223022,
-0.012091407552361488,
0.010221594013273716,
-0.0072446768172085285,
-0.02358500473201275,
0.011174380779266357,
-0.03348105400800705,
0.010065868496894836,
0.007654405664652586,
0.005119199398905039,
-0.0744200125336647,
0.005207419395446777,
0.022525930777192116,
-0.000871930387802422,
0.01635323464870453,
0.007563380524516106,
0.04879910871386528,
0.00045506650349125266,
-0.04285525158047676,
0.021398579701781273,
-0.045543916523456573,
-0.01006835326552391,
-0.012915100902318954,
0.002487955614924431,
0.029984818771481514,
-0.010047497227787971,
0.0196754802018404,
0.040543682873249054,
-0.01988251879811287,
0.005308821331709623,
-0.0224770475178957,
-0.026629645377397537,
0.05063255876302719,
0.023993803188204765,
0.005463221110403538,
-0.011301716789603233,
0.00035453421878628433,
0.011674859561026096,
0.0423557311296463,
-0.02967018634080887,
-0.049511391669511795,
-0.0026217990089207888,
0.0043534631840884686,
-0.012107479386031628,
0.014195237308740616,
-0.009881989099085331,
-0.012366102077066898,
0.014844520948827267,
0.006446920335292816,
0.007329369429498911,
0.07346514612436295,
0.025798730552196503,
0.01346517726778984,
-0.012402177788317204,
-0.034575849771499634,
-0.018388506025075912,
0.05118781328201294,
0.012484496459364891,
-0.03863310068845749,
0.0008520195260643959,
-0.013507938012480736,
-0.0020081899128854275,
0.03713338449597359,
-0.04413889721035957,
0.07099895179271698,
0.005885689053684473,
-0.011304999701678753,
-0.010164002887904644,
-0.009221733547747135,
-0.010917171835899353,
0.012627373449504375,
0.0012134467251598835,
0.03554724529385567,
0.015184774994850159,
0.01200563833117485,
0.02341783046722412,
0.040500394999980927,
0.05790536105632782,
-0.006875235587358475,
-0.009878247044980526,
-0.03214973956346512,
-0.009389371611177921,
0.020421022549271584,
-0.018586868420243263,
-0.05650515854358673,
0.0323149673640728,
0.02015308476984501,
0.007703080773353577,
-0.024049993604421616,
-0.0257734227925539,
-0.014969493262469769,
-0.05243498086929321,
0.018879126757383347,
-0.013163404539227486,
0.09347046911716461,
0.0609164834022522,
0.03302595019340515,
0.009819905273616314,
0.03301239758729935,
0.007684710901230574,
-0.011613855138421059,
-0.09263316541910172,
0.04686129093170166,
0.021586786955595016,
-0.009655511006712914,
-0.021376579999923706,
0.030673956498503685,
0.03581482544541359,
-0.010844866745173931,
-0.03250392526388168,
-0.021822761744260788,
0.005684806499630213,
-0.04465677961707115,
-0.022858718410134315,
-0.04234007000923157,
-0.018001064658164978,
-0.03259793296456337,
0.022931551560759544,
-0.008235487155616283,
-0.01856738142669201,
0.01303024310618639,
0.02817404642701149,
-0.039095111191272736,
0.006047895178198814,
0.029856206849217415,
0.0017818132182583213,
0.01857684552669525,
0.03677403926849365,
0.02918151766061783,
0.031876351684331894,
-0.07286129146814346,
0.0006760216783732176,
0.007158592343330383,
0.03391315042972565,
-0.004503310192376375,
-0.03487057238817215,
-0.023589974269270897,
-0.03315748646855354,
0.009689297527074814,
0.014352104626595974,
0.06331615895032883,
0.028243280947208405,
-0.017759541049599648,
-0.0007486160611733794,
0.021082818508148193,
-0.01637096516788006,
0.015561883337795734,
0.007506689988076687,
-0.012705229222774506,
0.0007638376555405557,
-0.044669125229120255,
-0.0291952695697546,
0.005134538747370243,
-0.016759706661105156,
0.03350897133350372,
0.029349839314818382,
0.0017212610691785812,
-0.005374454893171787,
0.013164954259991646,
0.007497700862586498,
-0.028238266706466675,
0.019318463280797005,
0.005226505920290947,
-0.007115819491446018,
-0.011918237432837486,
-0.03304711729288101,
-0.013808002695441246,
0.041757818311452866,
0.030613815411925316,
0.04750610888004303,
0.015304192900657654,
-0.08476682007312775,
0.015089782886207104,
0.03678559139370918,
0.013029424473643303,
-0.03639078885316849,
-0.006040522828698158,
-0.04394287243485451,
-0.04763493314385414,
0.06597589701414108,
-0.013412387110292912,
0.0011991526698693633,
-0.012533191591501236,
-0.019892258569598198,
-0.03141522780060768,
-0.0026253547985106707,
0.009840937331318855,
0.03412284329533577,
-0.004254682455211878,
0.018770527094602585,
-0.03794056177139282,
-0.0007175415521487594,
0.013736936263740063,
0.029368996620178223,
-0.010159247554838657,
0.061144836246967316,
0.019075846299529076,
0.02607688494026661,
0.027467522770166397,
0.051773011684417725,
-0.04274754226207733,
-0.07254047691822052,
0.03835158050060272,
-0.0022259997203946114,
-0.023951726034283638,
0.019113624468445778,
-0.0372355580329895,
-0.09951133280992508,
0.031454022973775864,
0.021675504744052887,
-0.027500580996274948,
0.01319190114736557,
-0.03634171932935715,
-0.01621132157742977,
0.011814139783382416,
-0.011475942097604275,
0.03607789799571037,
0.058785874396562576,
0.004735622555017471,
-0.009166097268462181,
-0.02416479028761387,
0.031282130628824234,
-0.02787853591144085,
-0.023447107523679733,
-0.027552740648388863,
0.014225100167095661,
-0.045123275369405746,
0.07232236862182617,
-0.05318458750844002,
0.02258259803056717,
-0.00009767617302713916,
-0.031350716948509216,
0.04197802022099495,
0.043497391045093536,
0.007631700485944748,
0.0020411470904946327,
0.0030626915395259857,
0.004726272542029619,
0.04131799936294556,
0.0226264838129282,
0.004669105634093285,
0.0033516071271151304,
-0.028382526710629463,
0.04197264835238457,
-0.004503678064793348,
0.024372991174459457,
-0.04673803597688675,
-0.0010269077029079199,
0.0026744420174509287,
-0.007912549190223217,
0.04446447268128395,
0.02770591527223587,
0.02377459965646267,
0.04373075067996979,
-0.07282114028930664,
-0.02549094520509243,
0.03861669823527336,
-0.011016419157385826,
0.06303253024816513,
-0.06980297714471817,
0.03484681248664856,
0.014360841363668442,
-0.031175151467323303,
-0.0665854960680008,
-0.08490502834320068,
-0.011602560058236122,
0.04374285787343979,
-0.026471348479390144,
-0.03174380585551262,
0.03224588930606842,
0.012907921336591244,
0.006271418649703264,
-0.0022387346252799034,
0.014256003312766552,
0.0315420962870121,
-0.0252058245241642,
-0.005533326882869005,
-0.001683418289758265,
0.04964987933635712,
0.021412963047623634,
0.03474954888224602,
-0.02285909838974476,
0.020036738365888596,
-0.016517331823706627,
-0.018709585070610046,
-0.006813711486756802,
-0.022509725764393806,
0.00772025715559721,
0.0038694085087627172,
0.03283809870481491,
0.03999173268675804,
-0.03670603409409523,
0.019140560179948807,
0.05091620609164238,
0.01485283114016056,
0.01307595893740654,
-0.047700200229883194,
0.023551685735583305,
-0.03960847482085228,
0.00595287187024951,
-0.0047377655282616615,
0.03643649071455002,
0.0056259711273014545,
-0.01586272567510605,
0.026872320100665092,
0.000994150061160326,
-0.01659872569143772,
-0.004780320450663567,
0.035570163279771805,
-0.026466963812708855,
0.02680499665439129,
0.02962564118206501,
-0.014117634855210781,
0.007852088660001755,
-0.010113400407135487,
0.042900338768959045,
0.017110932618379593,
0.045722849667072296,
-0.04563962295651436,
-0.03387966752052307,
-0.04231061413884163,
-0.014436045661568642,
0.0687529668211937,
0.006062651984393597,
0.04691433534026146,
0.03842959180474281,
0.001402205671183765,
-0.009202694520354271,
-0.014128160662949085,
-0.01896817237138748,
0.010931911878287792,
-0.01779174990952015,
0.06281286478042603,
-0.044735830277204514,
-0.026260098442435265,
0.02154255285859108,
0.022357430309057236,
-0.01109593641012907,
0.0488860197365284,
-0.0069418675266206264,
0.0547088086605072,
0.04838390275835991,
-0.038059301674366,
-0.06448449939489365,
0.052332207560539246,
-0.03443073108792305,
0.03656494617462158,
-0.02549140714108944,
-0.01818498969078064,
0.047590456902980804,
-0.031108401715755463,
0.008987817913293839,
-0.02068192884325981,
-0.0011598867131397128,
-0.043733078986406326,
0.014910346828401089,
-0.02790384739637375,
-0.009375013411045074,
0.0055375960655510426,
0.0382077656686306,
0.04479419067502022,
0.019004367291927338,
0.03375841677188873,
-0.0226482804864645,
-0.09063675254583359,
-0.020467417314648628,
-0.005402488633990288,
-0.04199955239892006,
0.032055582851171494,
-0.014897795394062996,
-0.033796362578868866,
0.016798513010144234,
-0.025291433557868004,
-0.0003751985204871744,
-0.028994999825954437,
0.04088299348950386,
-0.010803326964378357,
0.026829414069652557,
0.008013887330889702,
0.04489040747284889,
0.03396984934806824,
0.043644413352012634,
0.11156973242759705,
0.04008890315890312,
0.0216975137591362,
-0.04870633780956268,
-0.0032105003483593464,
-0.0023045437410473824,
0.027034981176257133,
-0.03136211261153221,
0.028359558433294296,
0.01707008294761181,
0.019245579838752747,
0.02098495326936245,
0.029323406517505646,
0.0176764614880085,
-0.01557185873389244,
0.0024294578470289707,
-0.027203692123293877,
-0.004876123741269112,
0.01356416754424572,
0.023918716236948967,
-0.012589066289365292,
0.015479139052331448,
-0.050392035394907,
0.04072389379143715,
-0.0022714915685355663,
-0.011442315764725208,
0.026542600244283676,
-0.04643378406763077,
0.049389392137527466,
-0.02037637308239937,
-0.01702025532722473,
0.0036898290272802114,
-0.016594627872109413,
-0.006631825584918261,
-0.03559378534555435,
0.02579568885266781,
-0.021930228918790817,
0.020137513056397438,
-0.004036862403154373,
0.019870135933160782,
0.013489129953086376,
-0.042831163853406906,
0.006835330277681351,
0.01902206987142563,
-0.010810568928718567,
-0.021668270230293274,
-0.06338117271661758,
0.04059301316738129,
-0.01100482139736414,
0.013778343796730042,
-0.011064348742365837,
-0.032116908580064774,
0.017554109916090965,
-0.04880797490477562,
-0.05633963271975517,
0.023180542513728142,
0.03970293328166008,
-0.021737227216362953,
0.03828452527523041,
-0.07233419269323349,
0.03741893917322159,
-0.0073653520084917545,
0.0438208281993866,
0.0008644933695904911,
-0.003997627180069685,
0.0092345355078578,
0.015275532379746437,
0.0007461511995643377,
-0.04456113278865814,
-0.030475476756691933,
0.0034447843208909035,
-0.005328926723450422,
-0.019283071160316467,
-0.016481691971421242,
0.026667039841413498,
0.005930113606154919,
0.019895100966095924,
-0.011071496643126011,
-0.006094194483011961,
0.003962238784879446,
-0.01777479611337185,
0.03317325934767723,
0.02561911568045616,
-0.029754741117358208,
0.024322768673300743,
0.004876331426203251,
0.08135305345058441,
0.032570209354162216,
-0.008108757436275482,
0.051846642047166824,
-0.024404015392065048,
0.008003076538443565,
0.040210455656051636,
-0.036556094884872437,
-0.03159026429057121,
-0.01170612033456564,
-0.014023038558661938,
0.00023107882589101791,
-0.05974467471241951,
0.021489014849066734,
0.022776881232857704,
-0.006791658699512482,
0.012816197238862514,
0.011134332977235317,
-0.017950160428881645,
-0.003428625874221325,
0.02372589521110058,
-0.04140475019812584,
0.005455025006085634,
-0.02107863873243332,
0.03529981151223183,
-0.02209850214421749,
-0.02898344397544861,
-0.02296719141304493,
0.011663984507322311,
-0.0032676008995622396,
-0.009516658261418343,
-0.0013262568973004818,
-0.0003954750718548894,
-0.020876992493867874,
0.020344538614153862,
-0.05288850516080856,
0.025145335122942924,
-0.051186975091695786,
0.026894181966781616,
0.00282010855153203,
-0.013735749758780003,
-0.013613804243505001,
0.020794302225112915,
0.0040936097502708435,
-0.028993062674999237,
0.037686049938201904,
0.015498078428208828,
0.0006875346298329532,
-0.004271355457603931,
0.011564566753804684,
-0.0030061237048357725,
0.04138243570923805,
-0.006235632114112377,
-0.00755684357136488,
0.027627788484096527,
-0.05337214469909668,
-0.04307163879275322,
0.039183780550956726,
-0.0183571670204401,
-0.03644387051463127,
0.04408613219857216,
-0.004725780803710222,
-0.03401118889451027,
0.049871932715177536,
-0.021603208035230637,
-0.05262957513332367,
-0.017048129811882973,
-0.0028946103993803263,
-0.0033682717476040125,
0.005010202061384916,
-0.014353361912071705,
-0.016474686563014984,
-0.020981330424547195,
-0.002422541845589876,
0.0047978502698242664,
-0.004798624664545059,
-0.012052522040903568,
-0.024918202310800552,
-0.009299980476498604,
0.027227219194173813,
-0.011856257915496826,
-0.004709389992058277,
0.05532895401120186,
0.05100091174244881,
-0.014245519414544106,
0.03404252976179123,
-0.015850456431508064,
-0.0017880722880363464,
-0.08634214848279953,
0.026707058772444725,
-0.011054059490561485,
0.024092281237244606,
0.000919699261430651,
-0.06434282660484314,
-0.008413217961788177,
0.0444491021335125,
-0.06953959167003632,
0.048835016787052155,
-0.05053126439452171,
0.0010703615844249725,
-0.025860965251922607,
0.011767947115004063,
-0.002171759493649006,
0.02675005793571472,
-0.005227568559348583,
0.01941804587841034,
0.015128189697861671,
0.01421799510717392,
-0.004198417998850346,
-0.004337176214903593,
-0.024893948808312416,
0.02069620043039322,
0.013070615008473396,
-0.03354598209261894,
0.0516081303358078,
0.005828597117215395,
-0.018238330259919167,
-0.006980271078646183,
-0.008802080526947975,
0.03508550673723221,
0.019043955951929092,
-0.014088189229369164,
-0.027273980900645256,
0.005893734283745289,
0.046363092958927155,
-0.03326822817325592,
0.00905793160200119,
-0.014631351456046104,
0.004151740111410618,
0.030730074271559715,
-0.0018558551091700792,
0.020602183416485786,
-0.0016200963873416185,
-0.00569769274443388,
-0.017828047275543213,
0.04701882600784302,
0.03204268589615822,
-0.03597095608711243,
0.026741335168480873,
-0.03171858191490173,
0.01163509115576744,
-0.016431467607617378,
-0.024945037439465523,
-0.05497495457530022,
0.0036082747392356396,
0.0065636602230370045,
0.02024943009018898,
-0.0005066648009233177,
0.016580726951360703,
-0.018147053197026253,
-0.049227580428123474,
0.012584546580910683,
-0.02987523563206196,
0.02326008677482605,
-0.004325091373175383,
-0.014660555869340897,
0.0342116616666317,
0.013689250685274601,
-0.029977595433592796,
-0.04429180547595024,
-0.05025719851255417,
0.04169486090540886,
-0.01726287044584751,
0.01786072924733162,
0.022207491099834442,
-0.007172081619501114,
-0.0296812541782856,
-0.0831475779414177,
0.03920844942331314,
-0.004434382077306509,
-0.00012052967940689996,
-0.03798176720738411,
0.002514713443815708,
-0.00577849755063653,
0.0302471611648798,
0.04375443607568741,
-0.011120359413325787,
-0.015268378891050816,
0.01525238435715437,
-0.010561604052782059,
0.01433983538299799,
-0.06021349877119064,
-0.012236256152391434,
-0.029057372361421585,
-0.022321060299873352,
-0.017472511157393456,
0.020666636526584625,
-0.03302674740552902,
-0.013796797953546047,
0.038287203758955,
0.01139894500374794,
-0.0055520907044410706,
-0.011407783254981041,
-0.018155153840780258,
0.05119483917951584,
-0.022007355466485023,
-0.009879399091005325,
0.040705665946006775,
0.010196293704211712,
0.02973395399749279,
0.008083531633019447,
-0.023555178195238113,
-0.03285403922200203,
0.02808889001607895,
-0.039595313370227814,
-0.009859925135970116,
-0.00819331780076027,
-0.07774852961301804,
-0.01438931841403246,
-0.06669525057077408,
0.006299132015556097,
-0.00652221217751503,
-0.04571337625384331,
0.0006960548926144838,
0.04049009829759598,
0.00466860830783844,
-0.003934565465897322,
-0.004072069656103849,
0.05110356584191322,
0.012182248756289482,
0.012620960362255573,
-0.06455793976783752,
0.0233775582164526,
0.001555068651214242,
-0.012599010020494461,
0.06996186822652817,
-0.010645243339240551,
-0.000052562922064680606,
0.0022759679704904556,
-0.0022246253211051226,
0.02286946214735508,
-0.04093027487397194,
0.0036972444504499435,
0.016387708485126495,
-0.012560531497001648,
-0.02373720146715641,
0.00923065934330225,
-0.015036205761134624,
0.06971018761396408,
-0.0680023580789566,
0.0037714424543082714,
-0.025317298248410225,
-0.015538430772721767,
-0.05388850346207619,
0.02300018072128296,
-0.008322532288730145,
0.061688654124736786,
-0.014214364811778069,
0.018931714817881584,
-0.01789805479347706,
-0.017795801162719727,
0.02642196975648403,
-0.04831123724579811,
0.014889185316860676,
-0.02737945131957531,
-0.021862786263227463,
0.0048937564715743065,
-0.007887656800448895,
-0.029704896733164787,
0.016047289595007896,
-0.02802327461540699,
0.02179560251533985,
0.017980756238102913,
0.026111632585525513,
-0.02911842055618763,
-0.020785298198461533,
0.06689644604921341,
-0.0642487183213234,
0.016068100929260254,
-0.01334458775818348,
0.005359053146094084,
-0.00507739745080471,
0.0010394228156656027
] |
<ol>
<li><p>What is the precise definition of <a href="http://en.wikipedia.org/wiki/Unified_field_theory">unification of fields</a> (in classical and quantum mechanics)?</p></li>
<li><p>In general, does unification of a field mean that we can write both of them at both sides of an equation (like Maxwell's laws)? Or does it mean that one of them can produce the other (like $E$ and $B$)?</p></li>
<li><p>Is there any intuitive explanation of how <a href="http://en.wikipedia.org/wiki/Electroweak_interaction">electroweak</a> unification works? Like an electric charge will feel a weak field or that a flavoured particle will produce a weak field?</p></li>
</ol>
| 8,491 |
[
-0.00864075031131506,
-0.025081166997551918,
-0.008202320896089077,
-0.021814337000250816,
0.0207778662443161,
0.030170971527695656,
-0.018452923744916916,
-0.02172224409878254,
0.022509319707751274,
-0.005121908616274595,
0.05449949577450752,
0.009951294399797916,
0.030983049422502518,
-0.021606747061014175,
0.032762981951236725,
0.02175939828157425,
0.03860193490982056,
-0.02650401182472706,
-0.017059126868844032,
-0.025254305452108383,
0.0015610806876793504,
0.010897306725382805,
-0.005403250455856323,
0.051216818392276764,
-0.006259934511035681,
0.026261109858751297,
0.03991864621639252,
0.021863479167222977,
0.030460521578788757,
0.06108357757329941,
-0.0004905686946585774,
-0.0639648512005806,
0.021076859906315804,
0.024952445179224014,
0.005946332588791847,
0.0008538459078408778,
0.010337091982364655,
-0.02997548319399357,
0.002335070166736841,
-0.009532982483506203,
-0.011174854822456837,
-0.004302915185689926,
-0.042345333844423294,
0.046489033848047256,
-0.031138552352786064,
0.005853571929037571,
-0.012463650666177273,
0.007219561375677586,
0.02867349237203598,
-0.0508016012609005,
0.04281497374176979,
0.02472470887005329,
0.0362560898065567,
0.005425591487437487,
-0.011506648734211922,
-0.01960683800280094,
0.07839982956647873,
0.05619106441736221,
0.029489004984498024,
-0.07889356464147568,
-0.018889715895056725,
-0.013830122537910938,
0.016244400292634964,
-0.028574848547577858,
-0.041580501943826675,
0.0996893048286438,
-0.0005602688761427999,
0.012716020457446575,
0.017356056720018387,
-0.015808604657649994,
0.01084176916629076,
0.00445288373157382,
0.04095166176557541,
-0.018374785780906677,
0.04377643018960953,
-0.057371072471141815,
0.019422227516770363,
0.02130739577114582,
0.030435454100370407,
0.048984892666339874,
-0.03065904602408409,
0.027581913396716118,
0.033232010900974274,
0.015174956992268562,
0.015092260204255581,
-0.00573127344250679,
0.08660898357629776,
0.00004574745616992004,
0.004106916021555662,
0.0069430069997906685,
-0.006387101486325264,
0.014087894931435585,
0.03582685813307762,
-0.021976236253976822,
-0.017952879890799522,
0.043480001389980316,
0.015074429102241993,
0.020290527492761612,
0.017161428928375244,
-0.026174239814281464,
0.019109075888991356,
0.006611107382923365,
0.010033754631876945,
0.07437669485807419,
0.0049330322071909904,
-0.008934489451348782,
-0.0332355722784996,
0.02064002864062786,
-0.036024924367666245,
-0.00404794467613101,
-0.01467944122850895,
-0.01672823168337345,
-0.026726488023996353,
0.009896568022668362,
0.012622836977243423,
-0.027393845841288567,
0.008962181396782398,
-0.017733002081513405,
0.06937254965305328,
0.05078883469104767,
0.08199756592512131,
-0.05241842195391655,
0.011996826156973839,
-0.022206060588359833,
-0.09529348462820053,
-0.01577197201550007,
0.007998298853635788,
0.02558402344584465,
-0.041328269988298416,
0.02823086641728878,
-0.02246912382543087,
-0.02034681849181652,
-0.030758405104279518,
0.045917823910713196,
0.013960718177258968,
-0.013308447785675526,
-0.12505050003528595,
-0.0809222161769867,
0.0456136129796505,
-0.03398023173213005,
-0.042465146631002426,
-0.06024942174553871,
0.0037226376589387655,
0.023507922887802124,
0.07311782240867615,
0.011241902597248554,
-0.016949372366070747,
0.007654460612684488,
0.038730327039957047,
0.026751907542347908,
-0.005550078582018614,
-0.009542378596961498,
-0.004342756234109402,
-0.008228974416851997,
0.027008263394236565,
-0.07328194379806519,
-0.005112791433930397,
0.015923555940389633,
-0.021146757528185844,
-0.01563853956758976,
0.10484424233436584,
-0.00008579396671848372,
0.011194974184036255,
0.01304614171385765,
-0.0026829137932509184,
-0.0036450212355703115,
0.05266812443733215,
0.010070747695863247,
0.011265227571129799,
0.07605302333831787,
-0.02078203298151493,
0.013184179551899433,
0.004431548528373241,
0.04136086627840996,
0.004248996265232563,
-0.021372569724917412,
-0.027012934908270836,
-0.013396491296589375,
-0.01423508021980524,
-0.021906526759266853,
-0.08071158081293106,
-0.06429439783096313,
-0.009712615050375462,
0.022048773244023323,
-0.0014735370641574264,
0.03003048710525036,
-0.013599437661468983,
-0.013032414019107819,
0.0035127850715070963,
-0.0491449199616909,
-0.04311323165893555,
-0.07726289331912994,
0.011375228874385357,
-0.015616221353411674,
-0.02353278361260891,
0.025289807468652725,
-0.009621093049645424,
0.03551920875906944,
-0.07930309325456619,
-0.03950497508049011,
-0.013775509782135487,
0.05677783116698265,
-0.02017820253968239,
0.0017062731785699725,
0.010058339685201645,
0.06743697822093964,
0.04152202978730202,
-0.008293049409985542,
0.03329086676239967,
-0.010346373543143272,
-0.06307002156972885,
0.019485777243971825,
-0.026011239737272263,
0.00808717217296362,
0.00731894513592124,
0.025170322507619858,
-0.0034201061353087425,
0.004337214399129152,
-0.002455094363540411,
0.024609794840216637,
-0.03697214275598526,
0.07615116983652115,
0.014631026424467564,
0.02552703768014908,
0.021652232855558395,
0.06684821099042892,
0.022684844210743904,
0.043320875614881516,
0.000950201996602118,
-0.014320572838187218,
-0.05682116001844406,
-0.01857033558189869,
0.039585601538419724,
0.019241001456975937,
-0.020244140177965164,
0.050464119762182236,
-0.007677991408854723,
0.025456007570028305,
-0.0055787814781069756,
0.013859138824045658,
-0.021176474168896675,
-0.03385812044143677,
0.007783195935189724,
-0.0007405719952657819,
-0.008943431079387665,
0.049419235438108444,
-0.011724499985575676,
0.002366303466260433,
0.026025639846920967,
0.008965689688920975,
-0.05062773451209068,
0.0563955195248127,
-0.020815972238779068,
-0.007660536095499992,
-0.011185850948095322,
-0.020716741681098938,
0.02175525389611721,
-0.016518818214535713,
0.05997905507683754,
-0.012481886893510818,
-0.01153507735580206,
-0.006264063064008951,
-0.007925628684461117,
-0.009332441724836826,
-0.004506899509578943,
-0.003727732924744487,
-0.00309532368555665,
-0.03078303672373295,
0.0032624283339828253,
-0.04427579790353775,
-0.0009418658446520567,
-0.009530985727906227,
-0.013095157220959663,
-0.025309542194008827,
-0.011173256672918797,
0.03890933096408844,
-0.010260236449539661,
0.04847239702939987,
-0.042839448899030685,
-0.03453098237514496,
-0.00615046638995409,
-0.052626341581344604,
0.014948228374123573,
0.006964146159589291,
-0.018238143995404243,
0.013982492499053478,
-0.07995768636465073,
-0.013059299439191818,
0.03186596557497978,
-0.009766916744410992,
0.011454823426902294,
0.011417564935982227,
-0.01833813451230526,
-0.04614564776420593,
-0.054869040846824646,
-0.03118542768061161,
0.039431001991033554,
0.00850381888449192,
-0.008248696103692055,
0.03780541941523552,
-0.005848690401762724,
-0.025726186111569405,
-0.0011542998254299164,
-0.03426468372344971,
-0.04209144786000252,
-0.024227872490882874,
-0.0031245467253029346,
0.002046945970505476,
-0.03875886648893356,
0.021920332685112953,
0.009452423080801964,
-0.054547421634197235,
-0.006186192389577627,
-0.04542550444602966,
-0.030924085527658463,
0.0241128858178854,
-0.02661142311990261,
0.03560583293437958,
0.02011336386203766,
-0.05504195764660835,
0.05613061785697937,
0.028744209557771683,
-0.02525199018418789,
-0.012574328109622002,
0.014002451673150063,
-0.014730023220181465,
-0.025972973555326462,
0.012351680546998978,
0.01645282469689846,
-0.003068736521527171,
0.015713775530457497,
0.052159976214170456,
0.029162075370550156,
-0.00488807400688529,
0.025551944971084595,
-0.014881374314427376,
-0.01874312199652195,
-0.0038798144087195396,
-0.01879429817199707,
0.02153477631509304,
0.0009749347809702158,
-0.02097695879638195,
-0.006884071510285139,
-0.013447876088321209,
0.035413824021816254,
0.02261868305504322,
-0.0038896938785910606,
0.06689352542161942,
0.03008526936173439,
0.009346901439130306,
-0.042475052177906036,
0.04089904949069023,
-0.0018218199256807566,
-0.015808306634426117,
0.013093912042677402,
-0.02533014863729477,
0.021943870931863785,
-0.013866846449673176,
-0.03219251707196236,
0.02459532953798771,
0.04715415835380554,
-0.07295458763837814,
-0.03532283380627632,
-0.017461156472563744,
0.012167790904641151,
0.01652468740940094,
-0.02068837359547615,
-0.006728028878569603,
0.040042899549007416,
0.05872739106416702,
0.03395327180624008,
0.007926239632070065,
-0.04725411906838417,
-0.042180947959423065,
-0.07071679085493088,
0.009587567299604416,
0.023406583815813065,
0.04815744608640671,
0.019677981734275818,
0.09319744259119034,
0.01640961319208145,
0.0046920860186219215,
-0.0016343810129910707,
0.0025205607526004314,
-0.08676501363515854,
0.04640478268265724,
-0.03711310401558876,
-0.01087295264005661,
-0.026863474398851395,
-0.024072151631116867,
0.0014116442762315273,
0.0006579651962965727,
-0.050317127257585526,
-0.03584142401814461,
0.019277984276413918,
-0.02503286302089691,
0.017452675849199295,
-0.02961002103984356,
-0.030414007604122162,
-0.003439277643337846,
0.026451025158166885,
0.04033656790852547,
-0.043017808347940445,
0.014126219786703587,
0.033631954342126846,
-0.04380470886826515,
-0.017083099111914635,
-0.004297376144677401,
0.014161805622279644,
0.008776168338954449,
0.018518175929784775,
0.03668389096856117,
0.03730292245745659,
-0.027944320812821388,
0.013066556304693222,
0.04733732342720032,
0.10232589393854141,
0.011308286339044571,
-0.00993314664810896,
-0.019834106788039207,
-0.0495377741754055,
-0.0077610621228814125,
-0.0069853197783231735,
0.06468501687049866,
0.0017058085650205612,
0.01837502233684063,
0.03350706771016121,
0.008175217546522617,
-0.03146975487470627,
0.05765139311552048,
0.03978011757135391,
-0.00971659179776907,
-0.03656536713242531,
-0.02890525385737419,
0.0023709889501333237,
-0.013085667975246906,
-0.0018898685229942203,
0.0030140422750264406,
0.008520764298737049,
-0.027512872591614723,
-0.024061542004346848,
0.009032497182488441,
0.020544594153761864,
-0.06496154516935349,
-0.01782592013478279,
0.003892705077305436,
-0.005892210640013218,
-0.009453329257667065,
-0.03347558528184891,
-0.029808849096298218,
0.0667099878191948,
0.05797110125422478,
-0.0032330541871488094,
-0.015094761736690998,
-0.0595543310046196,
0.019507335498929024,
0.043940816074609756,
0.06186093017458916,
-0.015366782434284687,
-0.006764983758330345,
-0.053552135825157166,
-0.01030476950109005,
0.019060809165239334,
-0.01721195876598358,
0.014491936191916466,
0.0029421281069517136,
0.03309452161192894,
-0.02814045362174511,
-0.01979675516486168,
0.002273153280839324,
0.058214522898197174,
0.0014559770934283733,
0.007869363762438297,
-0.029225770384073257,
0.004668804816901684,
-0.0022741626016795635,
0.03389473631978035,
0.0163674708455801,
0.022251278162002563,
-0.023244040086865425,
0.023678937926888466,
0.005986005533486605,
0.008137678727507591,
-0.025992125272750854,
-0.10211516916751862,
-0.015482121147215366,
0.01531586516648531,
-0.03243119642138481,
0.03565126657485962,
-0.017732923850417137,
-0.0351497158408165,
0.010103539563715458,
0.020715035498142242,
0.016869323328137398,
-0.021499332040548325,
-0.04019612818956375,
0.04318424314260483,
0.03620053455233574,
0.006814972963184118,
0.039518751204013824,
0.0150455879047513,
-0.06625209748744965,
-0.020948166027665138,
-0.02536548301577568,
0.028433730825781822,
-0.004935010336339474,
0.009453034028410912,
-0.019647594541311264,
-0.001563736004754901,
-0.05263848975300789,
0.050323016941547394,
-0.025166962295770645,
0.010334663093090057,
-0.018856115639209747,
-0.042293764650821686,
-0.05512763559818268,
0.016028009355068207,
0.006927445065230131,
0.009914244525134563,
0.01407101470977068,
0.014957602135837078,
-0.006700696423649788,
-0.030145633965730667,
0.00582756195217371,
0.019880445674061775,
0.010299522429704666,
-0.02295786142349243,
-0.011365479789674282,
0.039480000734329224,
0.004527118988335133,
-0.010156138800084591,
0.02683725208044052,
-0.056753452867269516,
0.04003802314400673,
-0.0265215877443552,
0.004458142444491386,
0.01813563145697117,
-0.04861469566822052,
-0.040123701095581055,
-0.00034090844565071166,
0.006252785213291645,
0.014352845959365368,
-0.028670480474829674,
0.017093367874622345,
0.022877966985106468,
-0.002334958640858531,
-0.038605231791734695,
-0.0613248310983181,
0.019376743584871292,
-0.003836063202470541,
-0.00198911945335567,
-0.01112378854304552,
0.004601157736033201,
-0.041763488203287125,
-0.03339889273047447,
-0.017346488311886787,
0.0719737783074379,
-0.045231837779283524,
-0.010011591948568821,
0.006208860781043768,
0.00975844170898199,
0.027720345184206963,
0.039114393293857574,
-0.009583785198628902,
0.016539139673113823,
-0.012089294381439686,
0.013310299254953861,
0.017217574641108513,
0.05767776444554329,
-0.006913277320563793,
-0.04786380007863045,
-0.011721532791852951,
0.004113071132451296,
0.014790356159210205,
-0.025575099512934685,
-0.010065174661576748,
0.03917285054922104,
0.026545874774456024,
-0.032297130674123764,
-0.0159299336373806,
0.0208333320915699,
-0.0008789552957750857,
0.04511609673500061,
-0.010854185558855534,
0.02270771563053131,
0.018062621355056763,
-0.05186505988240242,
0.03480575606226921,
-0.04402594268321991,
-0.003552346723154187,
0.006791388150304556,
0.03120984137058258,
-0.005090702325105667,
0.026277337223291397,
0.008266291581094265,
-0.026684194803237915,
0.017074620351195335,
-0.01127228420227766,
0.02460310608148575,
0.025732150301337242,
0.007492312230169773,
-0.013775723986327648,
0.004859112203121185,
-0.031907618045806885,
-0.016871817409992218,
0.04730224609375,
-0.035298630595207214,
0.03731585666537285,
0.06706670671701431,
-0.01645103096961975,
0.007125933654606342,
-0.03304191678762436,
-0.008502505719661713,
-0.008422083221375942,
0.0406925268471241,
0.006485336925834417,
-0.01901359297335148,
-0.016707494854927063,
0.05394510552287102,
0.03871196135878563,
-0.013097720220685005,
-0.014121895655989647,
0.03326987102627754,
0.03594603016972542,
-0.010260465554893017,
-0.017983954399824142,
-0.06037268042564392,
0.0519871786236763,
-0.026212094351649284,
0.0009857433615252376,
0.03047223947942257,
-0.009529114700853825,
0.03722505271434784,
0.026881499215960503,
0.008302460424602032,
0.011323466897010803,
-0.01253119669854641,
-0.05542125552892685,
0.026269439607858658,
0.008734873495995998,
0.021699974313378334,
-0.006002509035170078,
0.022138481959700584,
0.02100105583667755,
0.006856462452560663,
0.006855976302176714,
0.016116442158818245,
-0.0778462216258049,
-0.03849814832210541,
-0.02958499826490879,
-0.028798222541809082,
0.05337483063340187,
-0.013834488578140736,
-0.02176935411989689,
0.012527849525213242,
-0.004702653735876083,
0.0276357252150774,
0.015735967084765434,
0.03619026392698288,
-0.048618853092193604,
0.029490258544683456,
-0.003732898272573948,
0.03881068155169487,
-0.02118852734565735,
-0.0067290798760950565,
0.10984534025192261,
0.04554818943142891,
0.014634092338383198,
-0.05492796748876572,
0.009570867754518986,
-0.02630707062780857,
0.00506388396024704,
-0.009894434362649918,
0.018863966688513756,
-0.03129976987838745,
0.03586670756340027,
0.00395843805745244,
0.050959911197423935,
0.022625474259257317,
-0.049604665488004684,
0.06172725558280945,
-0.04552644118666649,
-0.058689385652542114,
-0.02115917019546032,
0.051207222044467926,
-0.029966061934828758,
0.004330769181251526,
-0.043754104524850845,
0.02404184453189373,
-0.020097944885492325,
-0.0011967382160946727,
-0.031245073303580284,
-0.02559009939432144,
0.027791226282715797,
-0.01519138552248478,
-0.0357387512922287,
0.014614924788475037,
0.005441003013402224,
-0.006948902737349272,
-0.03607599064707756,
0.021949509158730507,
0.03270765766501427,
-0.008570578880608082,
0.017642127349972725,
0.03655056282877922,
0.018083063885569572,
-0.017392020672559738,
0.001983222784474492,
0.03157304599881172,
-0.03924768790602684,
-0.006397533696144819,
-0.012132523581385612,
0.05449949577450752,
0.005482400301843882,
0.003080562688410282,
-0.024504706263542175,
0.015417030081152916,
0.023216422647237778,
-0.0390988290309906,
0.0031825199257582426,
0.011933880858123302,
0.021116644144058228,
-0.029540374875068665,
-0.014509100466966629,
-0.029569093137979507,
0.06266401708126068,
-0.023949608206748962,
-0.0021149974782019854,
0.00019605348643381149,
-0.006761237978935242,
0.013329020701348782,
-0.015498767606914043,
0.011645453050732613,
0.020323602482676506,
-0.012111273594200611,
-0.031865958124399185,
-0.027754466980695724,
-0.02995157614350319,
0.005272622220218182,
0.02653161808848381,
0.028694750741124153,
0.04993866756558418,
0.006390767637640238,
0.0016011701663956046,
-0.017411697655916214,
-0.06663955748081207,
0.07758068293333054,
-0.004362490028142929,
-0.013374697417020798,
-0.012475267983973026,
0.009106087498366833,
0.031179284676909447,
0.02287386730313301,
-0.0017759683541953564,
0.019153939560055733,
0.000870487536303699,
0.0006261293310672045,
0.016757477074861526,
-0.021165955811738968,
-0.02924812212586403,
0.0059046437963843346,
-0.0005169468931853771,
-0.02869359403848648,
-0.04592418670654297,
0.015374654904007912,
0.04786686971783638,
0.01777581311762333,
0.0053215124644339085,
0.030034154653549194,
-0.011915009468793869,
-0.02123461663722992,
0.028871750459074974,
-0.005568488035351038,
0.01214528176933527,
0.03154477849602699,
0.0067488146014511585,
-0.015690350905060768,
-0.0045592146925628185,
0.0034794171806424856,
0.004130109678953886,
0.028355062007904053,
0.015812546014785767,
-0.044669292867183685,
0.01776730827987194,
-0.02379993349313736,
0.032963234931230545,
-0.04201699048280716,
-0.040196169167757034,
-0.046504464000463486,
-0.009832607582211494,
0.00355902430601418,
-0.05289924889802933,
0.009098883718252182,
0.026302507147192955,
0.001510879141278565,
-0.03397536277770996,
-0.003679782385006547,
0.04063229635357857,
-0.02797105349600315,
0.008249644190073013,
0.02396359294652939,
-0.0166785828769207,
0.02138560824096203,
0.031219664961099625,
-0.04313273727893829,
0.03361652418971062,
-0.028426915407180786,
-0.034761928021907806,
0.036665551364421844,
-0.006438495125621557,
0.03165358304977417,
0.04669315740466118,
-0.032156169414520264,
-0.03158501163125038,
0.04341893643140793,
-0.013379093259572983,
0.007331987842917442,
0.007253110874444246,
-0.03922530636191368,
-0.0009167995303869247,
-0.001397395390085876,
0.0014594995882362127,
0.029340695589780807,
-0.03451751545071602,
0.024840904399752617,
0.023632008582353592,
-0.013852584175765514,
-0.02326332964003086,
0.013783741742372513,
-0.013545377179980278,
0.04504220187664032,
0.031761761754751205,
0.002329243579879403,
-0.007864654995501041,
0.06084608659148216,
-0.0075796120800077915,
0.018746759742498398,
0.017509039491415024,
0.021107370033860207,
-0.09812183678150177,
-0.028759151697158813,
0.012182878330349922,
-0.00424176175147295,
0.04562758654356003,
-0.06227436661720276,
0.00585477240383625,
0.018481582403182983,
-0.02427659183740616,
0.013378296047449112,
-0.0031203755643218756,
-0.028190670534968376,
-0.0014428076101467013,
-0.019515352323651314,
0.0005201419699005783,
0.07906802743673325,
0.009673787280917168,
0.05537686496973038,
-0.015402736142277718,
0.00565582700073719,
0.005629854742437601,
-0.03541519120335579,
-0.0581839345395565,
0.033925604075193405,
-0.004805899690836668,
-0.0382753349840641,
0.07499922066926956,
-0.001270062173716724,
-0.0369085818529129,
0.02667403407394886,
-0.005749511532485485,
0.0069710793904960155,
-0.0012081624008715153,
-0.0009489808580838144,
0.023369058966636658,
-0.003298927564173937,
0.009043295867741108,
-0.01802213303744793,
-0.024868927896022797,
0.03196043521165848,
0.024593036621809006,
0.028300752863287926,
-0.0033460536506026983,
0.01723988726735115,
-0.012832161039113998,
-0.015644868835806847,
-0.03387127444148064,
0.04469535872340202,
-0.04800103232264519,
-0.03137675300240517,
-0.022410733625292778,
-0.0009995928267017007,
-0.014944780617952347,
-0.01900724321603775,
-0.008492214605212212,
-0.018976708874106407,
-0.007785124704241753,
0.04508277028799057,
0.02049899473786354,
0.01577376388013363,
0.03190632537007332,
0.007166924420744181,
0.008395042270421982,
0.03747863695025444,
0.01568092219531536,
0.007211053278297186,
-0.034827981144189835,
0.002689614426344633,
0.02328166924417019,
0.018857769668102264,
0.02807396464049816,
-0.050837330520153046,
-0.05044642463326454,
0.010372010990977287,
0.019256947562098503,
-0.006188933737576008,
-0.0020114497747272253,
-0.07207503914833069,
-0.003670038655400276,
-0.030543407425284386,
0.016948344185948372,
0.023816626518964767,
0.015376138500869274,
-0.04293603450059891,
-0.029660016298294067,
0.006844848394393921,
0.021506333723664284,
0.03697486221790314,
0.017461609095335007,
-0.005013484973460436,
0.009444029070436954,
0.02037445828318596,
0.029814444482326508,
-0.02311144769191742,
-0.0004723377351183444,
-0.03765663504600525,
-0.02128737047314644,
0.0013877475867047906,
-0.010031835176050663,
0.0034327819012105465,
0.026816710829734802,
0.04745659604668617,
-0.041048016399145126,
0.026668552309274673,
0.0038169273175299168,
-0.04625103250145912,
0.06646908819675446,
-0.001546552055515349,
-0.018228666856884956,
0.05901969224214554,
-0.012528149411082268,
0.027435749769210815,
0.022796954959630966,
-0.005897107068449259,
-0.0026922032702714205,
-0.011222193948924541,
-0.04422498494386673,
-0.020311977714300156,
-0.00167578284163028,
-0.015166926197707653,
0.02794925682246685,
-0.06900690495967865,
-0.019047964364290237,
0.022230105474591255,
-0.037265390157699585,
-0.021240385249257088,
0.06449099630117416,
-0.0009087530197575688,
0.03579819202423096,
0.011869468726217747,
-0.03241213411092758,
0.018693707883358,
-0.03371337056159973,
0.011671715416014194,
0.023095648735761642,
0.047733306884765625,
-0.0015611638082191348,
-0.011368641629815102,
0.015253954567015171,
0.02021896094083786,
0.0031280023977160454,
-0.014794680289924145,
0.04232123866677284,
-0.0384167805314064,
-0.018162786960601807,
0.023209761828184128,
-0.00014540564734488726,
0.042048532515764236,
0.03130028769373894,
-0.014889184385538101,
0.07750260084867477,
-0.055248480290174484,
0.0079044159501791,
-0.012600108049809933,
0.029596466571092606,
-0.0056585948914289474,
0.008250469341874123,
0.016434945166110992,
0.03385442495346069,
0.021318525075912476,
-0.009706508368253708,
-0.031018951907753944,
0.02259584702551365,
0.019411446526646614,
-0.04995899274945259,
0.01609286665916443,
0.00861878041177988,
-0.019398830831050873,
-0.0000740768518880941,
-0.0083044758066535,
-0.006133406888693571,
-0.04188232496380806,
0.033429019153118134,
0.023291463032364845,
0.022467831149697304,
-0.03418981656432152,
-0.012484630569815636,
-0.03642944246530533,
0.0217996034771204,
-0.031139057129621506,
-0.028002895414829254,
-0.030600935220718384,
-0.008651107549667358,
-0.03846744820475578,
-0.011980779469013214
] |
<p>I've spent some time reading wiki etc. What I get now is that apart from the normal light amplitude information, <a href="http://en.wikipedia.org/wiki/Holography" rel="nofollow">holograms</a> also record the phase information of light. But this is so difficult for me to understand. In my understanding to display the 3D objects you have to reconstruct the 3D object field; the light source and exact light field at that moment, what does the phase mean here? why phase alone makes all these happen?</p>
<p>Apart from the principles, what is restraining holography display from being popular at the moment? </p>
| 8,492 |
[
-0.01694387197494507,
-0.03169332072138786,
-0.0036683862563222647,
-0.04532181844115257,
0.042962491512298584,
-0.0007045971578918397,
-0.04516735300421715,
-0.011022156104445457,
-0.014207902364432812,
-0.02833133563399315,
0.022186269983649254,
0.029102742671966553,
0.02759905904531479,
0.05866112932562828,
0.020288079977035522,
-0.014430842362344265,
0.0042129699140787125,
-0.019473373889923096,
-0.04336114972829819,
-0.029636556282639503,
-0.041439954191446304,
0.0466049462556839,
-0.006311897654086351,
-0.01109360158443451,
-0.014779441989958286,
0.0189870186150074,
0.051122136414051056,
0.041344307363033295,
0.05717826262116432,
0.06706562638282776,
-0.010873976163566113,
-0.023450935259461403,
-0.015456913970410824,
0.039254751056432724,
-0.01392365526407957,
-0.024904675781726837,
-0.02535276859998703,
-0.016795743256807327,
0.016323816031217575,
-0.009591485373675823,
-0.050581447780132294,
0.010625598952174187,
-0.03569885343313217,
0.08202344924211502,
-0.009073862805962563,
-0.021340932697057724,
-0.016174720600247383,
-0.02159162051975727,
0.012362166307866573,
-0.056633107364177704,
0.06036629527807236,
-0.02006172016263008,
0.027468640357255936,
0.014909966848790646,
0.007897130213677883,
0.0013591517927125096,
0.08506981283426285,
0.04460711404681206,
-0.01042863354086876,
-0.045151788741350174,
-0.01908026449382305,
0.007555956952273846,
0.003968243487179279,
-0.03996451944112778,
-0.02915523201227188,
0.024240711703896523,
-0.007996194064617157,
-0.0030048012267798185,
0.04947414994239807,
0.0072371927089989185,
-0.016784826293587685,
0.010147146880626678,
0.050383348017930984,
0.0012700462248176336,
0.013811251148581505,
-0.03434839844703674,
0.02273396961390972,
-0.009333539754152298,
0.023066578432917595,
0.016669252887368202,
0.007083776872605085,
0.012902813032269478,
0.0027514419052749872,
0.023493623360991478,
-0.004331917967647314,
-0.00971256848424673,
0.09287262707948685,
0.010251158848404884,
0.0027192500419914722,
-0.005382504779845476,
-0.020751651376485825,
0.03159573674201965,
0.03804994747042656,
0.00011797273327829316,
-0.03142271935939789,
-0.007324562408030033,
0.015563739463686943,
0.045014455914497375,
-0.015364861115813255,
-0.03645409271121025,
-0.013140666298568249,
0.02550327032804489,
0.0015595598379150033,
0.04519108310341835,
-0.03402665629982948,
-0.010611375793814659,
-0.01211690902709961,
0.02062400057911873,
0.006306675262749195,
-0.01032538153231144,
-0.006350611802190542,
0.017909135669469833,
0.008021797984838486,
0.022389933466911316,
0.00031039456371217966,
-0.01523706316947937,
0.016913389787077904,
0.00010823299817275256,
0.07129811495542526,
0.09097632765769958,
-0.0005976932588964701,
-0.012158690951764584,
0.009111056104302406,
-0.02021006867289543,
-0.10771538317203522,
0.00322723132558167,
0.0245369803160429,
-0.01892022229731083,
-0.056633360683918,
0.048217903822660446,
0.003919863607734442,
-0.0010371302487328649,
0.036348942667245865,
-0.011119133792817593,
0.018375786021351814,
-0.01010065246373415,
-0.11728058010339737,
-0.027474716305732727,
0.02555638924241066,
-0.01945635676383972,
-0.02581986039876938,
-0.07026409357786179,
0.032910414040088654,
0.03712143376469612,
0.09144270420074463,
-0.009081645868718624,
-0.00940712634474039,
0.000031173905881587416,
0.03962712362408638,
0.01655312441289425,
-0.027458928525447845,
-0.017297130078077316,
0.017957797273993492,
-0.032628126442432404,
-0.0193158071488142,
-0.052640557289123535,
0.010476276278495789,
0.060501761734485626,
-0.005302721168845892,
-0.06686482578516006,
0.05028555914759636,
-0.01840519905090332,
-0.02104293368756771,
0.04343680664896965,
-0.015656594187021255,
-0.054197367280721664,
0.05814957991242409,
-0.018617933616042137,
0.030669286847114563,
0.04921041429042816,
-0.01894962228834629,
0.06927040964365005,
-0.004395230673253536,
0.027371739968657494,
0.03786626085639,
0.009886827319860458,
-0.020221121609210968,
0.016820799559354782,
0.016819912940263748,
-0.01465565711259842,
-0.0100071607157588,
-0.026596102863550186,
0.020339272916316986,
0.0244300439953804,
0.016710177063941956,
0.02964121848344803,
-0.02006254345178604,
-0.01349691953510046,
0.020564986392855644,
-0.04307863116264343,
-0.009446480311453342,
-0.06778231263160706,
0.05091042071580887,
0.006455776281654835,
0.01496703177690506,
0.039055366069078445,
0.029169393703341484,
-0.00923047587275505,
0.0023395598400384188,
-0.03473738953471184,
-0.004909663926810026,
0.02719409577548504,
0.029891228303313255,
-0.017306223511695862,
0.044335249811410904,
0.05385090783238411,
0.012166420929133892,
0.0006969448295421898,
0.022191764786839485,
-0.01682053692638874,
-0.020059293136000633,
-0.024965178221464157,
-0.006470161024481058,
0.009502265602350235,
-0.04401431977748871,
-0.024383727461099625,
0.005699752829968929,
0.02791239507496357,
-0.03326018154621124,
0.022328194230794907,
-0.042072419077157974,
0.0645730271935463,
0.05717043578624725,
-0.01648707129061222,
-0.007053874898701906,
0.02666250430047512,
0.00458099227398634,
-0.00047937632189132273,
0.0030684832017868757,
-0.019968409091234207,
-0.04859476163983345,
0.01090402714908123,
0.03469902276992798,
0.04547290503978729,
-0.050233252346515656,
0.03788222745060921,
0.016801618039608,
0.04773222282528877,
0.047842491418123245,
0.03110620006918907,
-0.034803908318281174,
-0.016706403344869614,
-0.005424529779702425,
0.007020725402981043,
-0.007960510440170765,
0.02123863995075226,
0.022239727899432182,
-0.001842421479523182,
-0.014431525021791458,
-0.017733054235577583,
-0.05431961268186569,
0.04780343919992447,
-0.04399487003684044,
0.013031872920691967,
0.013113058172166348,
-0.020231982693076134,
-0.009546040557324886,
-0.019878409802913666,
0.0031594194006174803,
-0.0073239472694695,
-0.015919838100671768,
-0.007064780220389366,
-0.05788068845868111,
-0.011950720101594925,
0.021787326782941818,
0.0414927713572979,
-0.039471130818128586,
-0.016672246158123016,
0.007994488812983036,
-0.002443632809445262,
0.01838824525475502,
-0.022754879668354988,
0.003108975477516651,
-0.05145436152815819,
-0.00828363187611103,
0.033271726220846176,
-0.020128943026065826,
0.06759915500879288,
-0.017906084656715393,
-0.06910532712936401,
0.0053177508525550365,
-0.0051855361089110374,
0.011742700822651386,
0.013450580649077892,
-0.06069698557257652,
-0.03631826117634773,
0.0006418285192921758,
-0.02459629997611046,
0.033948864787817,
-0.008314856328070164,
0.02163727581501007,
-0.017917968332767487,
-0.015612572431564331,
-0.05366647616028786,
-0.00631468091160059,
0.002363944426178932,
0.029774945229291916,
-0.009001553058624268,
0.008127212524414062,
0.005246402695775032,
-0.018854543566703796,
-0.04243054986000061,
0.009811852127313614,
-0.013784622773528099,
-0.03323328495025635,
-0.004757648333907127,
0.020687295123934746,
0.0013118248898535967,
-0.07350766658782959,
0.03457879275083542,
0.026980215683579445,
-0.06188243627548218,
0.01651889458298683,
-0.019705286249518394,
-0.035334907472133636,
0.0068736025132238865,
-0.02015482261776924,
0.027714360505342484,
-0.025639019906520844,
-0.02210894040763378,
0.0806649699807167,
0.0076522380113601685,
-0.03227512165904045,
-0.019771119579672813,
0.002889020834118128,
-0.0058133406564593315,
-0.03538213670253754,
0.01704799197614193,
0.019503261893987656,
-0.0077507030218839645,
0.09062610566616058,
-0.023795507848262787,
-0.03813838213682175,
0.05419612675905228,
0.055954448878765106,
-0.009677127003669739,
-0.01434090081602335,
-0.009577149525284767,
-0.009368759579956532,
0.0206406582146883,
0.02663647197186947,
-0.06347323954105377,
-0.0024287602864205837,
0.0058841342106461525,
0.02084418386220932,
0.02376873791217804,
-0.024979164823889732,
0.011477936059236526,
-0.020343521609902382,
-0.000984984333626926,
-0.006907214876264334,
-0.0003652183513622731,
-0.0335325263440609,
0.004303011577576399,
-0.02207930199801922,
-0.003854412119835615,
0.03252611309289932,
0.01252406183630228,
-0.04110818728804588,
0.003332595806568861,
0.02224762737751007,
-0.027608748525381088,
-0.008690474554896355,
0.0027496733237057924,
-0.009916855953633785,
0.0045991213992238045,
0.0010839696042239666,
-0.03503171354532242,
0.052632417529821396,
0.04408251494169235,
0.000646013009827584,
-0.013237347826361656,
0.03805354982614517,
-0.034628305584192276,
-0.036596450954675674,
0.01590101234614849,
0.008300606161355972,
0.05163542181253433,
0.00042187180952169,
0.08975578844547272,
0.04116324335336685,
0.0012846313184127212,
-0.006661572959274054,
0.009964081458747387,
-0.054856326431035995,
-0.007697541266679764,
-0.02113434113562107,
0.01574213244020939,
-0.019082453101873398,
-0.0009262174135074019,
-0.01750229299068451,
-0.03047746606171131,
-0.04525494575500488,
-0.03795085847377777,
-0.007488162722438574,
-0.054921746253967285,
-0.016322582960128784,
-0.0028665107674896717,
0.0067495848052203655,
-0.030138550326228142,
0.05295126512646675,
0.006198954302817583,
-0.010813489556312561,
0.013372140936553478,
0.04370776191353798,
-0.05588285252451897,
0.004760527051985264,
0.0010618448723107576,
-0.0018724503461271524,
0.024114081636071205,
0.05510324239730835,
0.042885273694992065,
0.01712125353515148,
-0.0020891239400953054,
-0.00031067803502082825,
0.02329864725470543,
0.05980616807937622,
0.0032491127494722605,
0.010006279684603214,
-0.0026798751205205917,
-0.028003990650177002,
0.006642261520028114,
-0.012354003265500069,
0.05300367996096611,
0.012546957470476627,
0.00414280267432332,
0.009534316137433052,
-0.013906092382967472,
-0.015560087747871876,
0.02025100588798523,
0.03714914992451668,
-0.004818496759980917,
0.015429718419909477,
-0.07012665271759033,
-0.02023259922862053,
-0.011107375845313072,
-0.02207045815885067,
0.04932147264480591,
0.006289597600698471,
-0.023095034062862396,
-0.01104260329157114,
0.01540714967995882,
-0.028899701312184334,
-0.030390605330467224,
0.0004821812326554209,
0.0012485429178923368,
-0.0006505372002720833,
-0.008559326641261578,
0.02129119262099266,
0.016549168154597282,
0.05940045788884163,
0.04503452777862549,
0.04302528500556946,
-0.03057800605893135,
-0.07129944860935211,
-0.01822471432387829,
0.015087056905031204,
-0.006007443182170391,
0.010593592189252377,
-0.02290777489542961,
-0.041542958468198776,
-0.026745473966002464,
0.006312948185950518,
-0.05474136769771576,
0.030252503231167793,
-0.02446991764008999,
-0.012346080504357815,
-0.017952794209122658,
0.014718505553901196,
0.003426608629524708,
0.011714683845639229,
-0.012983233667910099,
0.030300529673695564,
-0.030202463269233704,
-0.0005129438359290361,
0.016746360808610916,
0.01255174819380045,
-0.0334070585668087,
0.024773266166448593,
0.01020746398717165,
-0.0005508824251592159,
-0.010345835238695145,
0.0389118418097496,
-0.05480600893497467,
-0.06511552631855011,
0.015576649457216263,
0.016972457990050316,
-0.011049495078623295,
0.05267577990889549,
-0.042698051780462265,
-0.021659303456544876,
-0.0001169999668491073,
0.007256331853568554,
-0.009321426972746849,
0.004444777499884367,
-0.04981806129217148,
0.017861943691968918,
-0.00750842085108161,
0.004711663816124201,
0.06410666555166245,
0.01938951388001442,
-0.009447697550058365,
0.004386332351714373,
0.017356978729367256,
0.05084962025284767,
-0.02103462815284729,
0.029013486579060555,
-0.0033205258660018444,
0.012073327787220478,
-0.04314802959561348,
0.0830877497792244,
0.007642545737326145,
0.012809923849999905,
0.012012988328933716,
-0.004451792687177658,
-0.006887017283588648,
0.02232421189546585,
-0.0012773494236171246,
-0.002974424045532942,
0.007597632706165314,
0.015284803695976734,
0.02882177010178566,
-0.013765375129878521,
-0.006492881570011377,
0.007421424146741629,
0.006467899307608604,
0.015719737857580185,
0.04307451471686363,
0.011824829503893852,
-0.04658067971467972,
0.004390521440654993,
-0.0002659267629496753,
-0.02293064258992672,
0.03938862308859825,
-0.008401074446737766,
0.045412804931402206,
0.010977701283991337,
-0.10081997513771057,
0.0014197803102433681,
-0.04091755673289299,
-0.03484315052628517,
0.060869645327329636,
-0.029175730422139168,
0.016233621165156364,
0.01755383051931858,
0.03179870918393135,
-0.04353306069970131,
-0.07298983633518219,
0.038355711847543716,
0.03849836811423302,
-0.01421797089278698,
-0.00576090719550848,
0.02269497886300087,
-0.019460618495941162,
-0.04113364219665527,
-0.025415493175387383,
-0.0029356053564697504,
-0.008757148869335651,
-0.01721377484500408,
0.03631201758980751,
-0.007425739895552397,
0.03252540901303291,
-0.014836900867521763,
-0.03707445412874222,
0.027688849717378616,
0.0076837618835270405,
-0.0002276233135489747,
0.004580939654260874,
0.024973314255475998,
-0.013079026713967323,
-0.061312370002269745,
-0.03632888197898865,
-0.01963985338807106,
0.015229977667331696,
-0.02183438278734684,
0.025876037776470184,
0.017063317820429802,
0.04930959269404411,
-0.025291254743933678,
-0.04265151917934418,
0.007507100235670805,
-0.008479490876197815,
0.043151888996362686,
-0.003393137129023671,
-0.02566641755402088,
-0.009371018968522549,
-0.01651148870587349,
0.038066912442445755,
0.03043546713888645,
0.010898570530116558,
-0.017131561413407326,
0.009792421944439411,
-0.006868506781756878,
-0.009859628044068813,
0.008171219378709793,
-0.024189544841647148,
-0.006534635554999113,
0.004884206224232912,
0.03992766514420509,
0.06673015654087067,
0.04000820592045784,
-0.024512531235814095,
-0.01715928688645363,
-0.032040685415267944,
0.0221157968044281,
0.08306796103715897,
-0.01930493488907814,
0.058907318860292435,
0.009951173327863216,
0.0012613415019586682,
-0.02506704442203045,
0.0014331029960885644,
-0.00987681932747364,
0.04412754997611046,
-0.03447294235229492,
0.009263806976377964,
-0.029174083843827248,
-0.022230239585042,
0.002901182509958744,
0.03754883259534836,
-0.02784712240099907,
0.03421138599514961,
0.02528822049498558,
0.03234235197305679,
-0.003649600315839052,
-0.004726238548755646,
-0.04274580627679825,
0.06057572737336159,
-0.05088600888848305,
0.034759651869535446,
0.01392363291233778,
0.019852766767144203,
0.03842107579112053,
-0.018768247216939926,
0.017801819369196892,
-0.05131404846906662,
-0.04340967908501625,
-0.04165266081690788,
-0.0014700943138450384,
0.00947772990912199,
-0.001264057820662856,
-0.0014941623667255044,
-0.02045147493481636,
0.02295593172311783,
-0.0016820825403556228,
0.009086862206459045,
0.02766389213502407,
-0.0987323597073555,
-0.0629044845700264,
-0.006231600418686867,
-0.0382160060107708,
0.054407183080911636,
0.006703874561935663,
-0.0016988704446703196,
-0.0005283193895593286,
-0.03283270075917244,
0.01805136725306511,
-0.006361956708133221,
0.055113911628723145,
-0.0425533726811409,
0.011696750298142433,
0.01410507783293724,
0.053010497242212296,
0.0007554657058790326,
0.029871439561247826,
0.10598307102918625,
0.048851434141397476,
0.011403726413846016,
-0.055168598890304565,
0.034298330545425415,
-0.030592557042837143,
0.014615822583436966,
-0.045271649956703186,
0.07060116529464722,
0.008657978847622871,
0.023846179246902466,
0.008574982173740864,
0.05854424461722374,
0.03424609825015068,
0.002942664548754692,
0.032806526869535446,
-0.04857730120420456,
-0.054614368826150894,
-0.0038872677832841873,
0.014286349527537823,
-0.02300180308520794,
0.030903074890375137,
-0.049276530742645264,
-0.010432107374072075,
-0.0015439159469678998,
-0.032546356320381165,
0.0036915470845997334,
-0.050883132964372635,
0.02143770642578602,
0.006604162510484457,
-0.0264597088098526,
-0.002571738325059414,
0.011755666695535183,
-0.022117329761385918,
-0.06106957048177719,
0.0018969002412632108,
-0.012465571984648705,
-0.0015755649656057358,
0.0038577436935156584,
0.025550464168190956,
-0.016909779980778694,
-0.027129728347063065,
-0.00845272559672594,
0.0003472234238870442,
-0.0390004888176918,
-0.025122465565800667,
-0.036691851913928986,
0.038688212633132935,
-0.05256287753582001,
0.01985592022538185,
-0.0007364812190644443,
0.003167080460116267,
0.02404065802693367,
-0.04202728718519211,
-0.014213222078979015,
0.012537255883216858,
0.01902385614812374,
-0.0129131143912673,
-0.051074180752038956,
-0.013048087246716022,
0.015223103575408459,
-0.02519172988831997,
0.03601662442088127,
0.0033795961644500494,
0.014599227346479893,
0.005333100911229849,
-0.0011078143725171685,
0.04023865610361099,
0.01597367599606514,
-0.007902493700385094,
-0.03162265941500664,
0.03909577056765556,
-0.0011448602890595794,
0.005164331756532192,
0.002220942871645093,
0.03387037664651871,
-0.007607043255120516,
0.01807844080030918,
-0.015308534726500511,
0.019338104873895645,
-0.03406485170125961,
0.0007947917329147458,
-0.03140817955136299,
-0.05274345725774765,
-0.033266332000494,
0.037733543664216995,
0.08010560274124146,
0.057835500687360764,
-0.0110936826094985,
0.009588812477886677,
-0.022393621504306793,
-0.01265157200396061,
0.03972841799259186,
-0.012055253610014915,
-0.03929484263062477,
0.025179395452141762,
-0.012678487226366997,
-0.02913997881114483,
-0.0212243665009737,
0.009608709253370762,
0.029869617894291878,
0.02934129908680916,
0.05389904975891113,
0.029763221740722656,
-0.03086790442466736,
-0.00902464147657156,
0.0006538564339280128,
0.015031483955681324,
0.01582723669707775,
0.009693318046629429,
0.01520830299705267,
-0.017317548394203186,
-0.0633908063173294,
-0.0036799649242311716,
-0.012134337797760963,
-0.006378932390362024,
0.019669298082590103,
0.01819201000034809,
-0.02403055503964424,
0.009832358919084072,
0.0316508449614048,
-0.030403470620512962,
-0.021208852529525757,
-0.04187667369842529,
0.03168024495244026,
-0.022519709542393684,
-0.0035501879174262285,
-0.01923937164247036,
0.017478378489613533,
0.014590729959309101,
-0.019820718094706535,
-0.006228139623999596,
-0.00020078342640772462,
-0.03100414387881756,
-0.0011803656816482544,
0.030529415234923363,
-0.0018968862714245915,
0.027269329875707626,
0.018010292202234268,
-0.032454993575811386,
0.03742978349328041,
-0.021138740703463554,
-0.062186915427446365,
0.03104270249605179,
-0.013408094644546509,
0.03715382516384125,
0.03916057571768761,
0.030083488672971725,
-0.012258141301572323,
0.026183266192674637,
-0.0035304322373121977,
-0.0024612760171294212,
0.024380769580602646,
-0.009106180630624294,
0.0024977365974336863,
0.04079741612076759,
0.012367145158350468,
-0.066477470099926,
-0.018139949068427086,
0.07156931608915329,
0.026554863899946213,
0.03932291269302368,
0.011196371167898178,
0.012108363211154938,
0.020974615588784218,
0.017891038209199905,
0.01905656047165394,
-0.0019355126423761249,
0.03339526057243347,
0.03464411571621895,
-0.02175888791680336,
0.03334547579288483,
0.042017146944999695,
0.001642510760575533,
-0.07944265007972717,
0.0038174036890268326,
0.016272513195872307,
0.005380723159760237,
0.053819239139556885,
-0.024393418803811073,
-0.0027910550124943256,
0.0074845124036073685,
-0.06750284135341644,
0.03226831555366516,
-0.0169789157807827,
-0.05016415938735008,
-0.015310467220842838,
-0.00476157758384943,
0.004578274674713612,
0.06844247877597809,
0.03958355262875557,
0.01628636196255684,
-0.006316674407571554,
-0.0030363663099706173,
-0.007607001345604658,
0.017443351447582245,
-0.006153159774839878,
0.014284603297710419,
-0.02655121311545372,
-0.01123722456395626,
0.08252327144145966,
-0.011338085867464542,
-0.04503101855516434,
0.012856189161539078,
-0.0027630487456917763,
-0.0000966145598795265,
0.018004875630140305,
-0.006385070271790028,
-0.024528812617063522,
0.018886446952819824,
0.013966165482997894,
-0.00573975732550025,
-0.0469999723136425,
0.010872216895222664,
0.0468812994658947,
0.013048849068582058,
0.005755544640123844,
-0.019465487450361252,
-0.012133902870118618,
-0.049187298864126205,
-0.01860790140926838,
0.02685438096523285,
-0.005347974598407745,
-0.005141852423548698,
0.010399611666798592,
0.01840367540717125,
0.018121853470802307,
-0.02472754381597042,
0.03141629695892334,
-0.05404702574014664,
-0.02370074950158596,
-0.018470335751771927,
0.006501271855086088,
-0.00949077494442463,
-0.008660699240863323,
-0.030898958444595337,
-0.05192550644278526,
0.03445902466773987,
-0.003741280175745487,
-0.024309689179062843,
-0.044983308762311935,
0.006885217037051916,
0.03181154280900955,
-0.01930565945804119,
0.029050320386886597,
-0.013666743412613869,
-0.039012566208839417,
0.05276787281036377,
0.007215534802526236,
0.0326952300965786,
-0.014794431626796722,
-0.050464171916246414,
-0.05035261809825897,
-0.0681469514966011,
0.03934767469763756,
0.020648673176765442,
-0.03230545297265053,
-0.050095923244953156,
-0.0065128686837852,
-0.0040915473364293575,
0.040143873542547226,
0.016776353120803833,
-0.03355410695075989,
-0.011585185304284096,
0.002604364650323987,
0.025910677388310432,
0.025761285796761513,
-0.0227566696703434,
-0.03699247166514397,
0.01635052263736725,
-0.02838163822889328,
-0.02726869098842144,
-0.04004247859120369,
-0.028661927208304405,
0.017509838566184044,
0.031367555260658264,
-0.019129125401377678,
0.039755433797836304,
-0.0003778789541684091,
-0.03412805125117302,
0.025527847930788994,
-0.0053041004575788975,
-0.014578943140804768,
0.08447016030550003,
-0.02765798196196556,
-0.021063590422272682,
0.020392049103975296,
-0.013492001220583916,
-0.005572475492954254,
-0.004656392615288496,
-0.03883303329348564,
-0.006651711650192738,
-0.008863165974617004,
-0.006575171835720539,
0.04927380755543709,
-0.040979769080877304,
-0.008037267252802849,
0.040702689439058304,
-0.022119561210274696,
0.028773952275514603,
0.08749394863843918,
0.002019628882408142,
0.006751806940883398,
0.0013776582200080156,
0.04180598258972168,
-0.024552857503294945,
-0.011093982495367527,
-0.0068353209644556046,
0.04791684076189995,
0.030780307948589325,
0.012332543730735779,
0.029438570141792297,
0.03711707890033722,
-0.011627459898591042,
-0.007229408249258995,
-0.010938586667180061,
0.08403856307268143,
-0.03261687606573105,
-0.014742908999323845,
-0.017154401168227196,
-0.005444671493023634,
0.012928429991006851,
0.036742422729730606,
-0.00541527708992362,
0.10208620876073837,
-0.02953214757144451,
-0.01078529842197895,
-0.012491470202803612,
-0.008388124406337738,
-0.02103359065949917,
-0.005008876323699951,
0.036653343588113785,
0.06707704812288284,
0.00811651162803173,
0.015120740979909897,
-0.02329857088625431,
-0.018138322979211807,
0.032673414796590805,
-0.0026449328288435936,
-0.0047750030644237995,
-0.017828725278377533,
-0.055769775062799454,
-0.001343218027614057,
-0.03168037533760071,
-0.05172940716147423,
-0.02156902104616165,
0.009411513805389404,
-0.009044709615409374,
0.003153207479044795,
0.043236780911684036,
-0.0236255694180727,
-0.033853791654109955,
0.03461844101548195,
-0.07666260004043579,
0.00821080431342125,
-0.008874785155057907,
0.028249917551875114,
0.0081375977024436,
0.0033060775604099035
] |
<p>I am a physics enthusiast and I have a question: Why is it meaningless to express the '$\pm$' (standard deviation) value as a percentage?</p>
| 8,493 |
[
0.003264291910454631,
-0.008307328447699547,
-0.007386107929050922,
-0.059192948043346405,
0.03247996047139168,
0.03746320307254791,
-0.01792815700173378,
-0.02590084634721279,
-0.02674628049135208,
0.004774500150233507,
0.022310536354780197,
0.03328080475330353,
0.060449592769145966,
-0.004739403259009123,
0.03703854978084564,
0.032703790813684464,
-0.005831659771502018,
0.01982167549431324,
-0.011430725455284119,
0.02550021931529045,
-0.020401468500494957,
0.002371123991906643,
-0.008707948960363865,
-0.0018809038447216153,
-0.02371905744075775,
0.01714419387280941,
0.027402320876717567,
0.0069716996513307095,
0.04384015500545502,
0.05575799569487572,
-0.015536865219473839,
-0.029543085023760796,
0.049234822392463684,
0.039353206753730774,
0.04169841110706329,
-0.01732197217643261,
-0.022863904014229774,
-0.011809219606220722,
-0.033120959997177124,
0.03643026947975159,
-0.06652873754501343,
0.017722606658935547,
0.013132092542946339,
-0.000239098648307845,
-0.04347012937068939,
0.03913184627890587,
0.021336058154702187,
-0.04116617888212204,
0.0441327728331089,
-0.02681923098862171,
0.05388525873422623,
0.00610478175804019,
0.05968855693936348,
0.028279045596718788,
0.0024379813112318516,
0.023535888642072678,
0.0902094617486,
0.0428033247590065,
-0.027132080867886543,
-0.06201358884572983,
-0.00879207905381918,
-0.006908840034157038,
0.001623656484298408,
-0.01482870802283287,
0.016128340736031532,
0.014199608005583286,
-0.006681997794657946,
-0.016213322058320045,
0.0789940282702446,
0.001457464648410678,
0.00283703301101923,
0.02416054718196392,
0.017006518319249153,
-0.02898883819580078,
-0.006575694773346186,
-0.05734977871179581,
0.03911618888378143,
0.009120115078985691,
0.009491084143519402,
0.02945639379322529,
-0.0005238474113866687,
-0.033343974500894547,
0.07818777114152908,
0.0009609176777303219,
0.020817529410123825,
-0.028103375807404518,
0.03958970680832863,
-0.011378996074199677,
0.026325363665819168,
0.010319114662706852,
-0.02007785253226757,
0.0049715545028448105,
0.05341534689068794,
0.001798928831703961,
-0.027000145986676216,
0.04521069675683975,
-0.005949273705482483,
0.032636623829603195,
0.011316612362861633,
-0.022111792117357254,
0.004034124780446291,
-0.015325975604355335,
0.03630674630403519,
0.03748193010687828,
-0.02608747035264969,
-0.011020070873200893,
-0.014892097562551498,
-0.002380299149081111,
-0.0020553318317979574,
-0.017327701672911644,
-0.014313159510493279,
0.020065374672412872,
0.02100646123290062,
0.02135634981095791,
0.03240473195910454,
-0.01298567559570074,
-0.006392600014805794,
-0.024041032418608665,
0.04669889807701111,
0.054242927581071854,
0.033035941421985626,
-0.025042500346899033,
0.010034414939582348,
-0.02088351733982563,
-0.035321176052093506,
0.03522011265158653,
0.020679045468568802,
-0.014245565049350262,
-0.05113983899354935,
0.007508606184273958,
-0.0050394912250339985,
-0.010202127508819103,
0.052585892379283905,
0.012789741158485413,
0.02172640711069107,
-0.02758430875837803,
-0.09093724936246872,
-0.05597050487995148,
0.04578740522265434,
-0.0043700519017875195,
-0.015632404014468193,
-0.08675634860992432,
0.0029756592120975256,
0.029814356938004494,
0.06282525509595871,
0.03380345180630684,
0.021358858793973923,
-0.011545236222445965,
0.032609887421131134,
0.01983404904603958,
0.0009103884804062545,
-0.009171943180263042,
0.009024872444570065,
-0.043388731777668,
0.01763617992401123,
-0.04919042810797691,
0.004507843405008316,
0.034710709005594254,
0.0017857854254543781,
-0.03257608413696289,
-0.013117523863911629,
-0.032073818147182465,
-0.012859191745519638,
0.008726853877305984,
0.01683579571545124,
-0.026457685977220535,
0.06796011328697205,
0.01651448756456375,
-0.004985395353287458,
0.016399657353758812,
0.019391914829611778,
0.01058452483266592,
0.019000021740794182,
0.025426145642995834,
0.04297912120819092,
-0.03810533508658409,
0.006884307134896517,
0.0017550713382661343,
0.011232043616473675,
-0.018194250762462616,
-0.08392327278852463,
-0.0205501988530159,
0.008090087212622166,
0.01679828390479088,
-0.01567818596959114,
0.03605789318680763,
0.014180809259414673,
-0.0031041246838867664,
0.01461225375533104,
-0.025168877094984055,
-0.026746582239866257,
-0.07885587215423584,
0.011357473209500313,
-0.032101377844810486,
-0.017235584557056427,
0.004000072833150625,
0.027265390381217003,
0.015006249770522118,
-0.029313061386346817,
-0.011651643551886082,
0.01997845619916916,
0.01522893738001585,
0.012851827777922153,
-0.05569225922226906,
0.006236049346625805,
0.051063284277915955,
0.047403015196323395,
0.013044867664575577,
0.007466730661690235,
-0.0017650111112743616,
-0.053027912974357605,
-0.02562745288014412,
-0.018228592351078987,
0.009273093193769455,
0.004517054185271263,
-0.052779797464609146,
0.016689425334334373,
-0.019591212272644043,
-0.01458242442458868,
0.05545347183942795,
-0.03680814057588577,
0.08491557091474533,
0.03396930918097496,
0.00003028003811778035,
-0.018511153757572174,
0.001303558237850666,
0.03005014732480049,
0.012576489709317684,
0.013451206497848034,
-0.040654316544532776,
-0.03448370844125748,
0.026402732357382774,
0.033336490392684937,
0.0031205068808048964,
-0.04416247084736824,
-0.0009985247161239386,
0.04269813373684883,
0.029983120039105415,
0.034848470240831375,
0.046216342598199844,
-0.008216183632612228,
-0.04900013655424118,
0.0024049030616879463,
0.015436484478414059,
0.0006468184292316437,
0.00578742939978838,
0.005538381636142731,
0.031931377947330475,
0.009087968617677689,
0.043984223157167435,
-0.010075097903609276,
0.04208979383111,
-0.016239646822214127,
0.012253966182470322,
0.02573515474796295,
-0.009582139551639557,
0.02331848442554474,
-0.02752649411559105,
0.02409004420042038,
0.016357913613319397,
0.005659195128828287,
0.0007587500149384141,
-0.029964778572320938,
-0.05331272631883621,
-0.0010673323413357139,
0.028499282896518707,
-0.032472819089889526,
-0.021273495629429817,
0.02244972251355648,
-0.021744344383478165,
-0.008719425648450851,
-0.05194216966629028,
-0.020982246845960617,
-0.021090352907776833,
-0.01788145862519741,
0.07238650321960449,
0.0308056827634573,
0.04260215163230896,
-0.0014183425810188055,
-0.031046828255057335,
0.02908698096871376,
-0.017749302089214325,
-0.022521449252963066,
-0.00026744467322714627,
-0.047125574201345444,
0.005727039650082588,
0.02108439803123474,
-0.05361640825867653,
-0.006051693577319384,
-0.024921104311943054,
0.02944040857255459,
0.0035762153565883636,
-0.001296565867960453,
-0.04294780641794205,
-0.006837611086666584,
-0.021034924313426018,
-0.02236608974635601,
-0.021945344284176826,
-0.016165297478437424,
0.02468700334429741,
-0.042834147810935974,
-0.01538269966840744,
0.049112606793642044,
-0.059910066425800323,
-0.041009046137332916,
-0.05535461753606796,
-0.016569338738918304,
0.005882658064365387,
-0.029830679297447205,
-0.026372436434030533,
0.033143896609544754,
-0.0430474728345871,
-0.04379481449723244,
-0.02269572950899601,
-0.0461818128824234,
-0.01397396344691515,
0.009416206739842892,
0.042557574808597565,
-0.01835780031979084,
-0.04526790976524353,
0.08967796713113785,
0.05074121057987213,
-0.02620588429272175,
0.02320871315896511,
0.012117893435060978,
-0.012275912798941135,
-0.0497458353638649,
0.0077500431798398495,
0.02060515806078911,
-0.004901546519249678,
0.023692073300480843,
0.01773381046950817,
0.02660392038524151,
0.023459821939468384,
0.022279053926467896,
0.007088433485478163,
-0.015136320143938065,
-0.024401728063821793,
0.0028691773768514395,
0.029194701462984085,
0.021622449159622192,
-0.03941638767719269,
0.019001584500074387,
0.021258536726236343,
0.059610914438962936,
0.026739908382296562,
-0.04118812084197998,
0.06012363359332085,
0.004342838190495968,
0.024755006656050682,
-0.05676443502306938,
0.04191478714346886,
0.020615089684724808,
-0.0015234730672091246,
0.017988082021474838,
-0.00828144233673811,
-0.0017025767592713237,
-0.024735428392887115,
-0.010293781757354736,
0.04548778757452965,
0.010127007029950619,
-0.041244979947805405,
-0.033061858266592026,
-0.018747715279459953,
0.007023250218480825,
-0.004087325185537338,
0.022816486656665802,
-0.05076882243156433,
0.060194097459316254,
0.07644352316856384,
0.04091445356607437,
-0.03402966633439064,
-0.025211390107870102,
-0.000396983465179801,
-0.07235715538263321,
-0.023345747962594032,
-0.008757336065173149,
0.01824612356722355,
-0.01892111264169216,
0.0966888815164566,
0.026901425793766975,
-0.0013992153108119965,
-0.004366307985037565,
-0.0018108290387317538,
-0.04930306598544121,
0.03308762237429619,
-0.022526968270540237,
-0.01861521787941456,
-0.03505207225680351,
-0.034301768988370895,
-0.012400653213262558,
-0.042641665786504745,
-0.00426239799708128,
-0.020933927968144417,
0.015531644225120544,
-0.018584057688713074,
-0.01786571554839611,
0.008615435101091862,
-0.03514370322227478,
-0.05012894794344902,
0.033441755920648575,
0.018452761694788933,
-0.0271212849766016,
0.018969103693962097,
0.06212391331791878,
0.0014003549003973603,
-0.04606793448328972,
-0.0346691869199276,
0.0013412003172561526,
0.012584386393427849,
0.028511114418506622,
0.052057091146707535,
0.005842168815433979,
-0.058823972940444946,
0.03779463469982147,
0.029500871896743774,
0.053420793265104294,
0.017861345782876015,
-0.0008477555820718408,
-0.05153319612145424,
-0.030848687514662743,
-0.011374426074326038,
0.026774385944008827,
0.020531509071588516,
0.006556074600666761,
0.0032126300502568483,
0.025920547544956207,
0.0048158722929656506,
-0.022610483691096306,
0.010813127271831036,
0.03440463915467262,
-0.02774156630039215,
-0.02467520162463188,
-0.05411628261208534,
0.023282794281840324,
-0.035307496786117554,
-0.018153689801692963,
0.009288090281188488,
0.02937127836048603,
0.0055952370166778564,
-0.004931745585054159,
0.004157241899520159,
-0.0031039747409522533,
-0.010719092562794685,
0.019270414486527443,
-0.01631724275648594,
0.026475511491298676,
0.007182231638580561,
0.0006872694357298315,
0.02013452723622322,
0.046797532588243484,
0.035372294485569,
0.01738327369093895,
-0.010502881370484829,
-0.05589578300714493,
0.012131033465266228,
0.0048025804571807384,
0.044856585562229156,
-0.042427755892276764,
-0.005515017081052065,
-0.015705933794379234,
-0.015221606940031052,
0.03870329260826111,
-0.020196665078401566,
-0.011495494283735752,
-0.018591925501823425,
0.01996752992272377,
-0.029297038912773132,
-0.019900565966963768,
-0.019458219408988953,
0.024594834074378014,
-0.009869732894003391,
0.009584460407495499,
-0.010445277206599712,
-0.02702810801565647,
-0.012054691091179848,
0.002097565680742264,
0.036237526684999466,
0.08056880533695221,
-0.0013524112291634083,
-0.008961770683526993,
-0.022061318159103394,
0.03187050297856331,
-0.01484624668955803,
-0.07045669108629227,
-0.018010379746556282,
-0.0011511152843013406,
0.0027380448300391436,
0.020290544256567955,
-0.02158481441438198,
-0.07711101323366165,
0.04015343636274338,
0.01798587664961815,
-0.021553367376327515,
-0.006209852639585733,
-0.037033502012491226,
0.01551214512437582,
0.03369864821434021,
-0.0051745218224823475,
0.050121862441301346,
0.01508111972361803,
-0.012444610707461834,
-0.003079204587265849,
-0.025674568489193916,
0.0482625775039196,
-0.038289181888103485,
-0.01039956696331501,
-0.03764679282903671,
-0.006599067710340023,
-0.04096100479364395,
0.015812143683433533,
-0.01868458278477192,
0.037206750363111496,
0.00034095917362719774,
-0.023481030017137527,
-0.009916389361023903,
0.007721027359366417,
0.028643663972616196,
-0.01049018744379282,
-0.00031475111609324813,
0.01466267742216587,
-0.026432473212480545,
-0.026375286281108856,
0.019156692549586296,
-0.0273624025285244,
-0.012806760147213936,
0.015749618411064148,
-0.015272056683897972,
0.01250903494656086,
-0.05231034755706787,
-0.009132296778261662,
0.02788747474551201,
-0.047406330704689026,
0.00679586548358202,
-0.039770063012838364,
0.0021858455147594213,
-0.00536322221159935,
-0.07493208348751068,
-0.07326942682266235,
0.01749025471508503,
0.010910103097558022,
0.057752564549446106,
-0.05302064120769501,
0.024977516382932663,
-0.006296353414654732,
0.044345248490571976,
-0.05556384474039078,
-0.04972599819302559,
0.014706199057400227,
0.004100787919014692,
-0.015721116214990616,
-0.005330293904989958,
-0.004416456446051598,
-0.015400320291519165,
-0.04025036469101906,
-0.0008610595250502229,
0.03406575694680214,
-0.011060415767133236,
-0.01228207629173994,
-0.013150251470506191,
-0.008103478699922562,
0.08414264768362045,
-0.02232355996966362,
-0.019140811637043953,
0.020117301493883133,
0.024432994425296783,
-0.016117999330163002,
0.002470952458679676,
0.0562419593334198,
-0.03791651874780655,
0.006121501792222261,
0.010036388412117958,
-0.05894925445318222,
0.01651771180331707,
-0.009744202718138695,
0.00913198385387659,
0.036665670573711395,
0.029729396104812622,
0.021651387214660645,
-0.002868560142815113,
0.035041745752096176,
0.017208624631166458,
0.00398202333599329,
0.014839707873761654,
-0.011591952294111252,
-0.04088087007403374,
-0.008184690959751606,
0.06383912265300751,
0.029672710224986076,
0.01930604875087738,
-0.019481629133224487,
0.0819828137755394,
0.006008183117955923,
-0.01326395571231842,
0.009340067394077778,
-0.00811367854475975,
-0.0007617827504873276,
0.02757231332361698,
0.0006008955533616245,
0.02536615915596485,
0.011667801067233086,
-0.015492936596274376,
-0.004815796855837107,
-0.03369239345192909,
-0.003996902611106634,
0.09592390805482864,
-0.02300325408577919,
0.06165548786520958,
-0.016070440411567688,
-0.01010329369455576,
0.001821919926442206,
-0.027033772319555283,
-0.027801334857940674,
0.011478451080620289,
0.00019916605378966779,
0.0055303554981946945,
-0.009046933613717556,
0.008555281907320023,
0.01726105436682701,
0.037170249968767166,
-0.01742861419916153,
0.03250395879149437,
0.013789685443043709,
0.031575512140989304,
0.00797162763774395,
0.007117042317986488,
-0.03464391827583313,
0.03416288271546364,
-0.024894172325730324,
0.03607986867427826,
-0.03541678190231323,
-0.02943265251815319,
0.05181751772761345,
-0.04542630538344383,
-0.041960135102272034,
-0.041870176792144775,
0.019628921523690224,
-0.01903354935348034,
0.004443463869392872,
0.009930606000125408,
-0.007930626161396503,
0.01875540241599083,
-0.0066844322718679905,
0.029439400881528854,
-0.014382254332304,
-0.00018334717606194317,
-0.0118424566462636,
-0.08653918653726578,
-0.03903189301490784,
-0.030266011133790016,
-0.06617075949907303,
0.047404561191797256,
-0.005495260003954172,
-0.013724935241043568,
-0.002107304986566305,
0.004110113717615604,
0.039002999663352966,
-0.0035867500118911266,
0.02115972340106964,
-0.03976547345519066,
0.039231784641742706,
0.026869678869843483,
-0.003477109130471945,
-0.012337957508862019,
-0.01043307688087225,
0.12273376435041428,
0.03090618923306465,
0.0367022268474102,
-0.028293738141655922,
0.039855748414993286,
-0.03448793664574623,
0.017834777012467384,
-0.012056011706590652,
0.04206346347928047,
0.012278920970857143,
0.028496770188212395,
0.03574080020189285,
0.054612502455711365,
0.0454179011285305,
-0.0014137695543467999,
0.05576494708657265,
-0.023372195661067963,
-0.04675374925136566,
-0.009508145973086357,
0.013015517964959145,
0.0021338684018701315,
0.00044428984983824193,
-0.03553043305873871,
0.00255002873018384,
-0.026532290503382683,
0.01687737926840782,
-0.0017568268813192844,
-0.01809680461883545,
-0.011953305453062057,
-0.0057662599720060825,
-0.026358112692832947,
0.0017842784291133285,
0.026125647127628326,
0.022962260991334915,
-0.06520752608776093,
-0.007655756082385778,
0.0521421879529953,
-0.03449959680438042,
-0.004353756085038185,
0.009401190094649792,
0.01427759975194931,
0.008407168090343475,
0.00439012935385108,
0.0012102979235351086,
-0.05729208141565323,
-0.0081305131316185,
-0.05383693054318428,
0.044841304421424866,
-0.022583698853850365,
0.023061012849211693,
-0.007822616025805473,
-0.004462630487978458,
-0.05001281201839447,
-0.0270058773458004,
-0.0037483018822968006,
0.0028246864676475525,
0.02128705196082592,
-0.003729725955054164,
-0.005494335666298866,
-0.01680089347064495,
0.0023445747792720795,
-0.02397136017680168,
0.03652535751461983,
0.043620940297842026,
-0.00005015577335143462,
-0.016272228211164474,
0.04376992583274841,
-0.002731331856921315,
-0.026330899447202682,
-0.010128391906619072,
0.023621829226613045,
-0.006198288407176733,
-0.04633611813187599,
-0.012531203217804432,
0.014470851048827171,
0.012446590699255466,
0.017679493874311447,
-0.008622648194432259,
0.02844998426735401,
0.011669417843222618,
-0.038973793387413025,
0.0679486021399498,
0.0028259025420993567,
-0.02108031138777733,
-0.009833147749304771,
0.02350783534348011,
0.014508849941194057,
0.04627581313252449,
-0.03486562892794609,
0.003332027466967702,
-0.02303035371005535,
0.061090487986803055,
0.006283652037382126,
-0.04478912055492401,
-0.023040156811475754,
0.02890787459909916,
-0.018802346661686897,
0.025898946449160576,
0.024831658229231834,
0.04276413097977638,
0.05581638216972351,
0.012855726294219494,
0.01190274115651846,
0.017071953043341637,
-0.008811566978693008,
0.0005729389376938343,
0.024959949776530266,
-0.03843167424201965,
0.0026090152096003294,
0.04900120571255684,
-0.00635943841189146,
-0.01462595909833908,
-0.00654588034376502,
-0.036257240921258926,
0.009460833854973316,
0.026727937161922455,
0.0320046991109848,
-0.00008813790191197768,
0.0018511587986722589,
-0.001401663525030017,
-0.035369016230106354,
-0.008102294988930225,
-0.013772240839898586,
-0.06606011092662811,
-0.014306553639471531,
0.007659288588911295,
-0.03443653881549835,
-0.016740083694458008,
0.010255257599055767,
0.012285871431231499,
0.007251170463860035,
0.05157720297574997,
-0.0017283788183704019,
0.02266693115234375,
-0.01314440555870533,
0.06159472092986107,
-0.0088565768674016,
0.03564869612455368,
-0.0552438460290432,
-0.016802072525024414,
0.06714557111263275,
-0.03992750123143196,
-0.0879867747426033,
0.022881068289279938,
0.012939997017383575,
0.04052233323454857,
0.017911551520228386,
0.00740246893838048,
-0.008601749315857887,
0.05892915651202202,
-0.053157806396484375,
-0.009112302213907242,
-0.0013788219075649977,
0.005079398863017559,
0.0063581387512385845,
-0.010631602257490158,
-0.009245887398719788,
-0.021896807476878166,
0.012381219305098057,
0.028506159782409668,
0.037234678864479065,
-0.0028435473795980215,
-0.0003510753158479929,
0.011530045419931412,
0.00033187339431606233,
0.022029314190149307,
0.06026608869433403,
0.04035510867834091,
-0.006371738854795694,
0.03735782578587532,
-0.051516998559236526,
0.015474440529942513,
-0.009304092265665531,
0.004648065660148859,
-0.07171901315450668,
-0.028151575475931168,
0.0005489104078151286,
0.003840372432023287,
0.003065976779907942,
-0.037898775190114975,
0.018716637045145035,
0.03458002954721451,
-0.07271511107683182,
0.028449546545743942,
-0.03737141564488411,
-0.07615391910076141,
-0.011198841966688633,
-0.019834529608488083,
0.011855675838887691,
0.07308204472064972,
0.03951304778456688,
0.00370754930190742,
0.03504582494497299,
0.0017501505790278316,
0.02868710085749626,
-0.011949299834668636,
-0.02141960896551609,
0.032773833721876144,
-0.023101458325982094,
-0.029940398409962654,
0.03885636106133461,
-0.020202575251460075,
-0.04331132397055626,
0.04759826511144638,
-0.012781999073922634,
-0.0031581365037709475,
-0.01239328645169735,
0.046689677983522415,
-0.017262598499655724,
0.01623927801847458,
0.046421609818935394,
-0.018027231097221375,
-0.022244278341531754,
-0.026048224419355392,
0.022963933646678925,
0.025328516960144043,
-0.015656594187021255,
0.001296882750466466,
0.03616560995578766,
-0.046909186989068985,
-0.08333873748779297,
-0.013533416204154491,
0.001908712089061737,
-0.01568104699254036,
0.014313047751784325,
-0.0013758172281086445,
0.024052998051047325,
-0.07631560415029526,
0.03524846211075783,
-0.0548626184463501,
0.028122134506702423,
0.02612842246890068,
0.009794353507459164,
-0.022878361865878105,
-0.009105445817112923,
0.0075731296092271805,
-0.021350665017962456,
0.005499834194779396,
0.025303397327661514,
-0.022223353385925293,
-0.05751286819577217,
0.009191051125526428,
0.008881581015884876,
-0.012436091899871826,
0.00363272987306118,
-0.03445009887218475,
-0.043071944266557693,
0.03328879922628403,
0.01495313923805952,
0.020336251705884933,
0.002347140572965145,
-0.03797513619065285,
-0.01038418710231781,
-0.09424564242362976,
0.056299712508916855,
-0.008639036677777767,
0.015272418968379498,
-0.07580465078353882,
-0.015007484704256058,
-0.022130809724330902,
0.02052345499396324,
0.03627701476216316,
0.027954041957855225,
0.009485909715294838,
0.015874817967414856,
0.003269706852734089,
0.03470286726951599,
-0.04248465597629547,
0.006362730637192726,
-0.05064404755830765,
-0.046253301203250885,
-0.019157851114869118,
-0.01913563907146454,
-0.017016712576150894,
0.010538505390286446,
-0.0013929135166108608,
0.004796462599188089,
0.04570312798023224,
-0.01108583528548479,
0.0053648692555725574,
0.06117409095168114,
-0.0015986913349479437,
-0.059667013585567474,
0.046846892684698105,
-0.01839286834001541,
-0.000038251804653555155,
0.04025408253073692,
-0.02101520635187626,
-0.05263389274477959,
0.013220628723502159,
-0.00027452525682747364,
-0.031374603509902954,
-0.004652701318264008,
0.025587916374206543,
0.030009374022483826,
-0.04515959322452545,
-0.01454447116702795,
0.03059222362935543,
-0.04585401341319084,
-0.004048166796565056,
0.030382517725229263,
0.04035196453332901,
0.015724319964647293,
0.02214210294187069,
0.007239424157887697,
-0.000011772758625738788,
-0.026343364268541336,
0.01897658035159111,
0.033410411328077316,
0.01603974588215351,
-0.005613336339592934,
0.03930201008915901,
0.016292531043291092,
-0.012463631108403206,
0.0043886746279895306,
0.0494791641831398,
0.05228088051080704,
-0.04748775064945221,
-0.03666029870510101,
-0.01448009256273508,
-0.033621907234191895,
0.039258647710084915,
0.01677551679313183,
-0.0028705252334475517,
0.06788933277130127,
-0.02107238955795765,
0.01086443942040205,
-0.007413683924823999,
-0.001987854717299342,
-0.0026197193656116724,
-0.033322181552648544,
0.019272051751613617,
0.024343732744455338,
-0.008078404702246189,
-0.0500158965587616,
-0.0023127098102122545,
0.0220288448035717,
0.018793586641550064,
-0.03578028455376625,
0.034764841198921204,
-0.0009325282881036401,
-0.025022434070706367,
-0.0555589497089386,
0.015314347110688686,
-0.021621771156787872,
-0.001370924524962902,
0.04270968586206436,
0.0477970615029335,
0.034390028566122055,
0.009301753714680672,
-0.018278269097208977,
-0.030976299196481705,
0.05959649384021759,
-0.04931631311774254,
-0.015449348837137222,
-0.035088084638118744,
0.01439221203327179,
-0.003667410695925355,
-0.019869046285748482
] |
<p>let $|\psi\rangle = a_0|0\rangle + a_1|1\rangle \in H$. Show that there are 3 real $r_x,r_y,r_z$ s.t. $$|\psi\rangle \langle\psi|= \frac{1}{2}(I + r_x\sigma_x + r_y\sigma_y + r_z\sigma_z.)$$</p>
<p>Any suggestions on where to start with this?</p>
| 280 |
[
-0.015789136290550232,
-0.03212447091937065,
0.004611032083630562,
-0.03121492639183998,
0.05954646319150925,
-0.007045238744467497,
-0.054038602858781815,
-0.023308491334319115,
0.010297158733010292,
-0.03355765715241432,
0.05431237071752548,
-0.002740317489951849,
0.03770819306373596,
0.04388001933693886,
0.016357939690351486,
-0.006580284330993891,
-0.014241406694054604,
-0.015230138786137104,
-0.01491404976695776,
0.001877903356216848,
0.014911658130586147,
0.02324005216360092,
0.03234952688217163,
-0.00880134105682373,
-0.01957826316356659,
0.03596086800098419,
0.025311527773737907,
0.02286561392247677,
0.015398481860756874,
0.056692857295274734,
-0.05629017949104309,
-0.028018733486533165,
0.00233488529920578,
0.02271146886050701,
0.021318921819329262,
-0.005408568773418665,
-0.031815122812986374,
-0.0198343638330698,
-0.012062539346516132,
-0.005797215737402439,
-0.04656631872057915,
0.0038926550187170506,
-0.0035637018736451864,
0.0388299897313118,
-0.01278003491461277,
-0.03566298633813858,
-0.025284333154559135,
-0.051418449729681015,
0.0395684540271759,
-0.03871225565671921,
0.06066116318106651,
-0.014866147190332413,
0.03145092353224754,
0.0015916855772957206,
0.011250149458646774,
-0.009864045307040215,
0.024593347683548927,
0.0815340131521225,
0.028025029227137566,
-0.011831274256110191,
-0.007729628589004278,
-0.029978523030877113,
-0.0035790610127151012,
-0.04933968186378479,
-0.04586021974682808,
0.014363475143909454,
0.003078008536249399,
0.0035864736419171095,
0.008470047265291214,
-0.015167380683124065,
-0.010394452139735222,
0.0021351382602006197,
0.029269667342305183,
-0.022376669570803642,
0.033246759325265884,
0.0003115140425506979,
-0.02025626040995121,
-0.0019659060053527355,
0.035293273627758026,
-0.001531164045445621,
0.021336127072572708,
0.009298156946897507,
0.012827112339437008,
0.025189625099301338,
0.024379223585128784,
-0.010408496484160423,
0.05235520750284195,
0.005416512954980135,
-0.011006849817931652,
0.03270777687430382,
-0.006865296047180891,
0.005053297150880098,
0.058718401938676834,
0.030397217720746994,
-0.026196317747235298,
0.05917326360940933,
0.009160937741398811,
0.043319422751665115,
-0.011032415553927422,
-0.0056396848522126675,
0.003726259106770158,
-0.07165264338254929,
0.022397074848413467,
0.07556851208209991,
-0.004655829630792141,
0.024329068139195442,
-0.03727945312857628,
0.02639724686741829,
-0.0235334150493145,
-0.029442809522151947,
-0.033698391169309616,
0.045377738773822784,
-0.002767772413790226,
0.025388166308403015,
-0.03561243787407875,
-0.008266479708254337,
0.03098955564200878,
-0.023218652233481407,
0.04940233379602432,
0.08262614905834198,
0.042766861617565155,
-0.021568382158875465,
-0.006614903453737497,
0.012618791311979294,
-0.08733777701854706,
0.042130108922719955,
0.0028947838582098484,
-0.0031326247844845057,
-0.062389492988586426,
0.041085150092840195,
0.024397186934947968,
-0.0014740105252712965,
0.016653865575790405,
-0.01952757127583027,
0.028719868510961533,
-0.021901655942201614,
-0.09123795479536057,
-0.05158041790127754,
0.0031083249486982822,
-0.02816358581185341,
-0.024621643126010895,
-0.055395908653736115,
0.024596763774752617,
0.04575134068727493,
0.0880226269364357,
-0.03775718808174133,
0.012785987928509712,
0.01731875166296959,
0.02070019021630287,
0.03768292814493179,
-0.01089438982307911,
-0.03600447624921799,
-0.026163756847381592,
-0.02265477180480957,
-0.004125415347516537,
-0.021302057430148125,
0.0582863874733448,
0.009555730037391186,
-0.020869281142950058,
-0.013319749385118484,
0.08621661365032196,
0.022010501474142075,
0.010381569154560566,
0.04160437360405922,
-0.0420989952981472,
-0.0066388980485498905,
0.05677807703614235,
-0.010801042430102825,
0.0074518052861094475,
-0.003400153247639537,
-0.04683046042919159,
0.03696828335523605,
0.0042108637280762196,
0.04303605854511261,
0.015508812852203846,
-0.03156935051083565,
-0.027805346995592117,
-0.018763896077871323,
-0.02137889713048935,
0.012226051650941372,
0.006382873747497797,
-0.040832776576280594,
-0.0045721279457211494,
0.024943450465798378,
0.016147775575518608,
0.008401896804571152,
-0.001766276080161333,
-0.030470238998532295,
0.012371945194900036,
-0.04011361673474312,
0.02060665562748909,
-0.06392364203929901,
0.0316966287791729,
0.03295096382498741,
-0.03271927684545517,
0.04237132892012596,
0.02996143139898777,
-0.019366970285773277,
-0.003917116206139326,
-0.02708829753100872,
-0.013010768219828606,
0.025028306990861893,
0.05411246791481972,
-0.01977454498410225,
0.04113426432013512,
0.050609614700078964,
0.04589423909783363,
0.017960725352168083,
0.021335313096642494,
-0.015295500867068768,
0.003169116796925664,
-0.012810925021767616,
0.0034182562958449125,
0.013347701169550419,
-0.001035649562254548,
0.016973722726106644,
-0.007474976126104593,
0.016045384109020233,
-0.0015188433462753892,
0.022370241582393646,
-0.03513403236865997,
-0.0024517206475138664,
0.01977226324379444,
0.009535558521747589,
0.003021780401468277,
-0.014791191555559635,
0.01841576397418976,
0.004515341017395258,
0.006639681290835142,
0.015687113627791405,
-0.05277906358242035,
0.020729240030050278,
0.047307346016168594,
0.04359614476561546,
-0.053698353469371796,
0.023178638890385628,
0.00992587674409151,
0.06110968068242073,
0.026005689054727554,
0.019353097304701805,
-0.015228205360472202,
0.01069594081491232,
-0.007458869833499193,
-0.006645809393376112,
0.012410315684974194,
0.029385240748524666,
0.021893447265028954,
-0.009538721293210983,
0.011644627898931503,
0.0013276609824970365,
-0.0030731495935469866,
0.03790297731757164,
-0.04867202788591385,
0.0214846134185791,
-0.017259784042835236,
-0.030062399804592133,
-0.005247269291430712,
-0.03351379930973053,
0.022238409146666527,
0.013047962449491024,
-0.010365771129727364,
-0.037437837570905685,
-0.009587560780346394,
-0.03160283714532852,
-0.03004961647093296,
-0.00734848715364933,
-0.005574245937168598,
-0.02633986808359623,
0.03226114809513092,
-0.04676930978894234,
-0.003857583273202181,
-0.03195999935269356,
0.0014477986842393875,
-0.04736900329589844,
-0.04376748576760292,
0.010705403983592987,
0.01734522171318531,
0.006400164216756821,
-0.022058336064219475,
-0.014370749704539776,
0.04296131432056427,
0.011502214707434177,
0.028292635455727577,
0.0030828281305730343,
-0.04267570748925209,
0.01832781545817852,
-0.054070845246315,
-0.03981107473373413,
0.017075352370738983,
0.00171007274184376,
-0.02416977472603321,
0.02286567911505699,
-0.0032365801744163036,
-0.0648188665509224,
0.002896540332585573,
-0.043972425162792206,
0.05100617557764053,
-0.07465970516204834,
0.031941138207912445,
0.035730861127376556,
-0.016835128888487816,
-0.06884196400642395,
0.01711430586874485,
0.03096682019531727,
-0.03820975497364998,
0.005054071545600891,
-0.03386625275015831,
-0.023615919053554535,
-0.028922973200678825,
0.037363141775131226,
-0.0025876290164887905,
-0.041093312203884125,
0.02931124158203602,
-0.04709448665380478,
-0.058662451803684235,
-0.02807682938873768,
0.023271242156624794,
0.04157979413866997,
-0.01382421888411045,
-0.010123459622263908,
0.08256731927394867,
0.025859037414193153,
-0.03629155829548836,
-0.007480482570827007,
0.03208991885185242,
0.02620498649775982,
-0.04795527830719948,
0.04437563568353653,
0.047114890068769455,
-0.019025763496756554,
0.03519773110747337,
0.023290446028113365,
0.02128191851079464,
0.05644850432872772,
0.014070254750549793,
-0.03503726050257683,
0.04139723628759384,
-0.0021594029385596514,
-0.006061693653464317,
0.09952397644519806,
0.000488186749862507,
-0.02159024588763714,
0.0024188910610973835,
0.003212655195966363,
-0.012557088397443295,
0.01391687337309122,
-0.03884873539209366,
0.0431784987449646,
-0.01828870177268982,
0.021841561421751976,
0.01873369887471199,
0.046160150319337845,
0.025259127840399742,
-0.05492102727293968,
-0.00784955732524395,
0.029277363792061806,
0.001411961275152862,
-0.045661505311727524,
0.013941333629190922,
0.04616778716444969,
-0.034465398639440536,
-0.06323636323213577,
0.0013055027229711413,
-0.03642212226986885,
-0.007379213813692331,
0.014220545999705791,
-0.013578414916992188,
-0.09268926084041595,
0.018177103251218796,
0.007415305357426405,
0.018986817449331284,
-0.014383772388100624,
-0.042834095656871796,
-0.03163169324398041,
-0.01640462502837181,
-0.006324787624180317,
-0.013773558661341667,
0.05918369069695473,
-0.02787209115922451,
0.03811921551823616,
-0.01327111292630434,
-0.010316459462046623,
0.0022480515763163567,
-0.0508544035255909,
-0.002845457987859845,
-0.01458591315895319,
-0.03179692476987839,
-0.0006223614909686148,
0.02023511379957199,
-0.01998598501086235,
0.011288633570075035,
-0.06186332181096077,
-0.00660060765221715,
-0.016809048131108284,
-0.06339021772146225,
-0.013387080281972885,
0.024436291307210922,
-0.03209170699119568,
-0.037642620503902435,
-0.00925800297409296,
0.04329153522849083,
0.04836459085345268,
0.03635214641690254,
0.023729508742690086,
0.04827982187271118,
-0.026426240801811218,
0.011764205992221832,
-0.026841621845960617,
-0.004699142649769783,
0.00812823511660099,
0.031666964292526245,
0.05119329318404198,
0.013524593785405159,
0.02057139202952385,
-0.032879024744033813,
-0.06139668449759483,
0.04222767800092697,
-0.002402352634817362,
0.006742734927684069,
0.03336736187338829,
0.0032427951227873564,
-0.019296573475003242,
-0.007670174352824688,
0.08222455531358719,
-0.006927597336471081,
0.016817839816212654,
0.011363104917109013,
-0.010216685943305492,
-0.031894750893116,
0.01569366827607155,
0.04422638937830925,
-0.017097152769565582,
-0.03554209694266319,
-0.03570561856031418,
-0.03849273547530174,
0.0027114353142678738,
-0.007053784094750881,
-0.009862059727311134,
-0.001901009469293058,
-0.011726266704499722,
0.009011340327560902,
0.019279859960079193,
0.04602282494306564,
0.011378524824976921,
0.02680359035730362,
-0.005932989064604044,
-0.010983727872371674,
0.014473755843937397,
-0.029233913868665695,
-0.00580902025103569,
0.018893610686063766,
0.01096559688448906,
-0.013785215094685555,
-0.010957625694572926,
-0.05704265460371971,
0.0029475055634975433,
0.02933991514146328,
0.04088670387864113,
0.02448543906211853,
0.02990405075252056,
-0.02417062409222126,
-0.03630192577838898,
0.05650535225868225,
-0.038959067314863205,
0.04600602388381958,
-0.0291023887693882,
-0.011106611229479313,
0.0009215583559125662,
-0.06287655234336853,
-0.050345003604888916,
0.02776861935853958,
0.0005668603116646409,
0.026945950463414192,
-0.05654650554060936,
0.027188172563910484,
-0.0204500500112772,
0.02008383348584175,
0.05515393242239952,
0.041358787566423416,
-0.006371158175170422,
0.034595124423503876,
-0.01974891498684883,
0.04902298375964165,
-0.016470709815621376,
-0.0552087277173996,
0.03591994568705559,
-0.012103424407541752,
-0.013317727483808994,
0.04852551966905594,
-0.05863563343882561,
-0.012042932212352753,
-0.013205691240727901,
0.055669963359832764,
-0.028385162353515625,
0.05959906801581383,
-0.03365598991513252,
0.050596121698617935,
0.05539773777127266,
0.01650827005505562,
-0.007947844453155994,
0.0024091775994747877,
-0.00881646852940321,
0.017270103096961975,
-0.027708925306797028,
-0.004780934192240238,
-0.021683797240257263,
0.013472487218677998,
-0.023316940292716026,
-0.003354937769472599,
-0.007920426316559315,
0.027796441689133644,
0.003994185011833906,
0.008194704540073872,
-0.009603088721632957,
-0.023117678239941597,
-0.019317369908094406,
-0.026876505464315414,
-0.06473109871149063,
0.029501283541321754,
0.0016115456819534302,
0.04990449175238609,
0.006978305522352457,
-0.02964361384510994,
-0.005642549600452185,
-0.03487659618258476,
0.01239586342126131,
0.045578036457300186,
-0.028736090287566185,
0.09976384043693542,
-0.045088913291692734,
-0.01918398216366768,
-0.0019282246939837933,
-0.0957801565527916,
0.020296650007367134,
-0.034048739820718765,
0.03442872315645218,
-0.016027696430683136,
-0.01751081272959709,
-0.04276527836918831,
0.0038414429873228073,
-0.024427862837910652,
-0.0042569334618747234,
-0.015365269035100937,
0.0026659537106752396,
-0.000780432135798037,
0.007551273796707392,
-0.07658524811267853,
-0.050213273614645004,
-0.01354222185909748,
0.040459562093019485,
-0.027900876477360725,
-0.022576497867703438,
0.0017075202194973826,
-0.010403184220194817,
-0.013904520310461521,
-0.02706991881132126,
0.017230968922376633,
-0.03582567349076271,
-0.004287831485271454,
0.014507216401398182,
0.02071181870996952,
0.009441488422453403,
0.017043031752109528,
-0.0165118295699358,
0.010062954388558865,
0.006852749735116959,
-0.022840559482574463,
-0.01472983043640852,
0.00655309297144413,
-0.0077099367044866085,
-0.02737920917570591,
0.0028610113076865673,
-0.005435765255242586,
0.011447214521467686,
-0.04087018594145775,
-0.011756950989365578,
-0.005594880320131779,
-0.005620519630610943,
0.0010489794658496976,
-0.056138794869184494,
-0.0021085322368890047,
0.012658427469432354,
0.006247180979698896,
-0.022388838231563568,
0.0028020453173667192,
-0.014137501828372478,
-0.03327212482690811,
0.008541597984731197,
0.02335941605269909,
-0.010999473743140697,
0.004704883322119713,
0.03149767965078354,
0.03673640266060829,
0.017129680141806602,
0.031922049820423126,
0.014685909263789654,
-0.002688890090212226,
-0.03554467111825943,
0.027211369946599007,
-0.008022834546864033,
0.015281300991773605,
-0.03691161796450615,
-0.01210660208016634,
-0.044821105897426605,
0.05836616829037666,
0.05220750346779823,
0.03446464240550995,
0.057072561234235764,
0.01638960652053356,
0.002180392388254404,
-0.037881188094615936,
0.021820195019245148,
-0.015593437477946281,
0.022617308422923088,
0.015067779459059238,
0.04905451834201813,
-0.0229068361222744,
0.014568502083420753,
0.036913514137268066,
0.04572641849517822,
-0.025992736220359802,
0.012507976964116096,
0.019814882427453995,
0.008835917338728905,
0.0020172097720205784,
-0.016244247555732727,
-0.0395096056163311,
0.03923822194337845,
-0.03637642785906792,
0.02582087181508541,
0.005422407761216164,
-0.005014749243855476,
0.013633351773023605,
0.045762110501527786,
-0.006683329585939646,
-0.025815846398472786,
-0.03507448360323906,
-0.046986959874629974,
-0.0008899937965907156,
0.004462654702365398,
0.025220384821295738,
-0.015728136524558067,
0.014613114297389984,
0.026888923719525337,
0.0038609846960753202,
0.02241574041545391,
0.018178222700953484,
-0.057424865663051605,
-0.006570589262992144,
-0.03225970268249512,
-0.02368193119764328,
0.03673731908202171,
0.006985264364629984,
-0.021964330226182938,
0.011989662423729897,
-0.01841140165925026,
-0.002729634987190366,
0.0215965174138546,
0.010361237451434135,
0.006792796775698662,
0.03671332821249962,
0.0008495322545059025,
0.048126447945833206,
0.02123630791902542,
0.017014674842357635,
0.12115072458982468,
0.06134546548128128,
0.020107382908463478,
-0.04133985936641693,
0.015232618898153305,
-0.020777305588126183,
-0.0063056331127882,
-0.04846688732504845,
0.06304513663053513,
-0.018377143889665604,
0.03890789672732353,
-0.010492799803614616,
0.035525545477867126,
-0.024224156513810158,
0.02423393353819847,
0.0223790742456913,
-0.03732635825872421,
-0.04749353975057602,
-0.0447816327214241,
0.048761434853076935,
0.02780298702418804,
0.026670081540942192,
-0.039997201412916183,
0.05197282135486603,
-0.0363917201757431,
-0.02548186294734478,
-0.028605373576283455,
-0.02739095687866211,
0.04238041490316391,
-0.03017013520002365,
-0.005619869567453861,
0.020319340750575066,
-0.021959714591503143,
-0.006260525435209274,
-0.024850279092788696,
-0.004122395534068346,
0.036295004189014435,
-0.020282858982682228,
0.008470444008708,
0.0279470793902874,
0.02495831996202469,
-0.00935197714716196,
-0.029106872156262398,
-0.0033501896541565657,
-0.027909789234399796,
-0.01848287507891655,
-0.0280293095856905,
0.06543117761611938,
-0.04554170370101929,
-0.02776201255619526,
0.006358795333653688,
0.0026602470315992832,
-0.010365000925958157,
-0.04093347489833832,
-0.034738797694444656,
0.008019167929887772,
0.010550382547080517,
-0.008956411853432655,
0.004712473601102829,
0.02045217715203762,
0.03211694583296776,
-0.02514813467860222,
0.01932615600526333,
-0.017431896179914474,
-0.027645841240882874,
-0.016949377954006195,
0.004953423514962196,
0.03467624634504318,
0.028896287083625793,
-0.0019246102310717106,
-0.011097235605120659,
-0.007511059753596783,
-0.019808784127235413,
-0.024039003998041153,
0.025505514815449715,
0.02719484642148018,
0.05836179852485657,
0.04420631378889084,
-0.02801450900733471,
0.0013303146697580814,
-0.04777303338050842,
-0.016949456185102463,
-0.017315682023763657,
0.009471097029745579,
0.006611534394323826,
-0.040904175490140915,
0.026902802288532257,
0.06670695543289185,
-0.023794032633304596,
-0.035519007593393326,
0.013642857782542706,
0.0633094534277916,
0.05993323773145676,
-0.03142301365733147,
0.010954558849334717,
-0.012380455620586872,
-0.06530970335006714,
0.0075723701156675816,
-0.025336282327771187,
0.013157816603779793,
0.03828366845846176,
0.0324954017996788,
0.029706723988056183,
0.0446072556078434,
-0.017563514411449432,
0.026412544772028923,
0.04271848872303963,
-0.023731403052806854,
-0.011933057568967342,
0.021090740337967873,
0.01696927472949028,
-0.05036301910877228,
-0.03667193278670311,
0.019676702097058296,
0.0164608433842659,
0.006488552317023277,
-0.012217998504638672,
-0.016005203127861023,
0.007241099141538143,
-0.00045903990394435823,
0.017488885670900345,
-0.05145043134689331,
-0.008045155555009842,
-0.0008914258214645088,
0.016792887821793556,
-0.0027908547781407833,
-0.0008891192264854908,
-0.03572119399905205,
-0.02884998545050621,
0.041909970343112946,
-0.010720090940594673,
0.05748726800084114,
-0.003783163847401738,
-0.0418194904923439,
-0.001997521612793207,
-0.00811535120010376,
0.004362090025097132,
-0.020837338641285896,
0.005873201414942741,
0.009836092591285706,
-0.001772888470441103,
-0.03863915428519249,
-0.008188036270439625,
-0.013779588975012302,
0.0004038293845951557,
0.025087324902415276,
0.03311280533671379,
-0.03909308463335037,
-0.03336257487535477,
0.015403191559016705,
-0.011996741406619549,
-0.017556732520461082,
-0.006095122545957565,
0.023323439061641693,
0.0012122290208935738,
-0.0035689708311110735,
0.032339680939912796,
0.00312807341106236,
0.003842688165605068,
0.025386150926351547,
0.02482646517455578,
-0.03627263382077217,
0.017470194026827812,
-0.015846973285079002,
-0.0004929763381369412,
0.03466178476810455,
0.019446557387709618,
-0.005355292931199074,
0.061266276985406876,
-0.0007734006503596902,
-0.06602731347084045,
0.06034905090928078,
0.04372707009315491,
0.013334142975509167,
-0.0556861087679863,
-0.03375844284892082,
0.01854822225868702,
-0.008716083131730556,
0.05095851048827171,
-0.04590983688831329,
-0.008799424394965172,
0.039172980934381485,
-0.07872597128152847,
-0.00501804007217288,
-0.02730565331876278,
-0.0106956260278821,
-0.04785611480474472,
0.0015637289034202695,
-0.03377344459295273,
0.03461610898375511,
-0.051358189433813095,
0.04609266296029091,
0.008800347335636616,
0.028376003727316856,
-0.009400074370205402,
-0.05600188672542572,
-0.004293817561119795,
0.020651791244745255,
0.01805092766880989,
-0.015609336085617542,
0.052163492888212204,
-0.03079293668270111,
-0.022126667201519012,
0.000765003205742687,
0.010940519161522388,
0.0017120866104960442,
-0.020397182554006577,
0.03642602637410164,
0.018625469878315926,
0.06635989993810654,
0.009377333335578442,
-0.0007006330997683108,
0.034116607159376144,
-0.03752638399600983,
0.06044049188494682,
0.006639204453676939,
-0.010997314937412739,
-0.036694228649139404,
0.05055517330765724,
-0.02097431756556034,
-0.04619818553328514,
0.03932666778564453,
0.03657216578722,
0.0076567260548472404,
-0.0023040107917040586,
-0.030729496851563454,
-0.009086105972528458,
-0.019827354699373245,
0.0035927463322877884,
-0.015537825413048267,
0.005996557883918285,
0.02440439723432064,
0.05383401736617088,
-0.020334957167506218,
0.021518124267458916,
-0.02717016637325287,
-0.05887991189956665,
0.022494984790682793,
-0.013978848233819008,
-0.002622727071866393,
-0.05883200839161873,
-0.007135541178286076,
0.02983066812157631,
0.039003998041152954,
0.007460407447069883,
0.0048350803554058075,
-0.013761543668806553,
0.008509613573551178,
0.00936072040349245,
-0.0015228879638016224,
-0.003792290575802326,
-0.036874640733003616,
-0.04904177039861679,
-0.05255715548992157,
0.041204068809747696,
0.0703030675649643,
0.008124567568302155,
-0.005647082347422838,
-0.046280547976493835,
-0.03261759504675865,
0.007974130101501942,
0.060925859957933426,
-0.008834869600832462,
-0.005450828932225704,
-0.023222941905260086,
0.010926672257483006,
0.029017677530646324,
-0.054214444011449814,
0.014609306119382381,
-0.010589396581053734,
-0.02604013867676258,
-0.012411274015903473,
0.017478717491030693,
-0.01129233743995428,
-0.010081624612212181,
0.022062484174966812,
0.017454663291573524,
0.004379899241030216,
0.008631715551018715,
-0.08321123570203781,
0.0023022114764899015,
-0.018233178183436394,
-0.022954637184739113,
0.0683569684624672,
0.0017010930459946394,
0.008223650977015495,
0.014419917948544025,
-0.02592112496495247,
-0.017457079142332077,
0.01996389776468277,
-0.013528063893318176,
-0.0016247897874563932,
-0.009856808930635452,
-0.014332828111946583,
0.018900102004408836,
-0.03251470625400543,
0.025271663442254066,
0.05241788551211357,
-0.03284529596567154,
0.00029888932476751506,
0.042441803961992264,
0.004269955679774284,
0.05895739048719406,
0.005668713245540857,
-0.0045035346411168575,
0.0013683183351531625,
-0.024627026170492172,
0.03997558727860451,
0.04328037425875664,
-0.009887815453112125,
-0.00011764220835175365,
0.020717034116387367,
0.0729455053806305,
-0.020478172227740288,
0.005522026680409908,
-0.011427752673625946,
0.0190572552382946,
-0.030479352921247482,
0.023096593096852303,
0.06021897494792938,
-0.06713841110467911,
-0.0018236840842291713,
0.026835501194000244,
-0.00847670529037714,
0.09702058136463165,
-0.010567993856966496,
0.015710987150669098,
-0.04126877710223198,
0.02225549705326557,
-0.022916363552212715,
0.011487578973174095,
0.046383120119571686,
0.05864453688263893,
-0.06636302918195724,
-0.002359738340601325,
-0.0058874404057860374,
0.007593899499624968,
0.02318475767970085,
-0.054879080504179,
0.009423797950148582,
0.029103418812155724,
0.005704277195036411,
-0.0014701010659337044,
-0.004175588022917509,
-0.0012848989572376013,
-0.013524663634598255,
0.028468245640397072,
0.04491889849305153,
0.00006674809264950454,
-0.02273504063487053,
-0.036172054708004,
-0.03051287680864334,
0.00922123622149229,
-0.016379816457629204,
-0.017530065029859543,
-0.009881410747766495,
0.015492256730794907,
-0.015339134261012077,
-0.006907057017087936
] |
<p>I have an idea of making a tennis serving machine. I will briefly describe what it is:</p>
<ul>
<li>The machine is configured to serve the ball at a fixed speed to the center of the left (or right) service court</li>
<li>Based on the rotation in 3 directions (X,Y,Z) of the ball, the machine would let the ball land in various positions in the left service court.</li>
</ul>
<p>How can I determine the relationship between the angular velocity of the ball and the location where it lands?</p>
| 8,494 |
[
-0.05445197597146034,
-0.03477020934224129,
-0.02164899930357933,
-0.01049503032118082,
0.04077841341495514,
0.00011179108696524054,
-0.008095016703009605,
0.016518540680408478,
0.014971625991165638,
0.0027614538557827473,
0.029497241601347923,
0.050929851830005646,
0.035794321447610855,
0.047040823847055435,
0.026919031515717506,
-0.0002433994523016736,
-0.004473200533539057,
0.0015277824131771922,
0.0055310726165771484,
-0.018309352919459343,
0.026583261787891388,
-0.02096356637775898,
0.0032793611753731966,
0.015423595905303955,
-0.007561752572655678,
0.01673194207251072,
0.043790560215711594,
-0.06647197157144547,
0.004622107837349176,
0.034540098160505295,
-0.036173511296510696,
0.00041720832814462483,
0.007421398069709539,
0.046469490975141525,
0.03850453346967697,
-0.0058629619888961315,
-0.04540989547967911,
-0.021824553608894348,
0.008000994101166725,
0.026626696810126305,
-0.001346040633507073,
0.011015225201845169,
-0.04958518221974373,
0.04925818368792534,
-0.018783481791615486,
0.047247160226106644,
-0.04053543508052826,
-0.005937353707849979,
0.06230412796139717,
-0.06447675824165344,
0.07038112729787827,
0.012863071635365486,
0.0017361012287437916,
0.014442184939980507,
0.001398942549712956,
-0.018365195021033287,
0.0855751484632492,
0.07225901633501053,
0.04244918376207352,
-0.06967462599277496,
0.000009370080078952014,
-0.03202536702156067,
-0.014168135821819305,
-0.05900297686457634,
-0.02694021537899971,
0.03343978524208069,
0.017849719151854515,
-0.021348193287849426,
0.03298762068152428,
-0.021885477006435394,
0.008553856983780861,
0.04480384290218353,
0.03264438733458519,
-0.02340235747396946,
0.007959563285112381,
-0.05321722850203514,
0.01530903298407793,
0.0017140009440481663,
-0.013001574203372002,
-0.02103324979543686,
0.006499199662357569,
-0.014591912738978863,
0.032359782606363297,
0.022268516942858696,
0.0017053434858098626,
-0.002328508999198675,
0.036840297281742096,
0.014800612814724445,
0.005229579750448465,
0.02962387539446354,
0.019107690081000328,
0.010040043853223324,
0.017114991322159767,
-0.009736745618283749,
-0.02441711723804474,
0.016219468787312508,
-0.0017443564720451832,
0.04264156520366669,
0.01221443247050047,
-0.022205661982297897,
-0.015329651534557343,
-0.02570171467959881,
-0.003964074421674013,
0.06921055912971497,
-0.029857438057661057,
-0.017353175207972527,
-0.00856650061905384,
0.0010386293288320303,
-0.038240302354097366,
-0.00010465536615811288,
-0.03525347635149956,
0.0038416460156440735,
-0.005893897730857134,
0.050373077392578125,
0.004377109929919243,
0.005106968805193901,
-0.02497042529284954,
-0.014046608470380306,
0.024523302912712097,
0.01925811357796192,
0.040588073432445526,
-0.03327811509370804,
-0.023130804300308228,
-0.04594280570745468,
-0.05108308792114258,
0.01063734944909811,
0.01294748019427061,
-0.019564269110560417,
-0.027647478505969048,
0.002023653592914343,
0.008358658291399479,
0.005755977239459753,
-0.006941909436136484,
0.024651437997817993,
0.014442826621234417,
-0.024511203169822693,
-0.0780690386891365,
-0.05730385333299637,
0.0709681361913681,
0.02123974822461605,
-0.008349037729203701,
-0.08216261863708496,
-0.0150502510368824,
0.055278509855270386,
0.08573576807975769,
0.013316045515239239,
0.013158547692000866,
0.018142003566026688,
0.03776629641652107,
-0.0008359216153621674,
0.006072644144296646,
-0.00811492744833231,
-0.032406482845544815,
-0.04023553058505058,
0.035173449665308,
-0.016014644876122475,
0.027798917144536972,
0.03406960144639015,
-0.011506128124892712,
-0.05195748805999756,
0.0018381085246801376,
-0.020258015021681786,
-0.007162763737142086,
0.02248387038707733,
-0.006474536843597889,
-0.024684438481926918,
0.05304782837629318,
0.01506207138299942,
0.01144040934741497,
0.01320748869329691,
-0.04308740422129631,
0.0034897413570433855,
0.007762479595839977,
0.019712302833795547,
0.06076408922672272,
-0.03705945983529091,
-0.02929115667939186,
0.013358870521187782,
-0.008726751431822777,
-0.03792332485318184,
-0.028355000540614128,
-0.04040888324379921,
0.00652510579675436,
0.04229481518268585,
-0.0034143130760639906,
0.052325960248708725,
0.0016529622953385115,
0.026599757373332977,
0.011123118922114372,
-0.029380226507782936,
0.020712435245513916,
-0.03957468271255493,
0.02090701274573803,
-0.007684724405407906,
-0.008769465610384941,
-0.0002611344098113477,
0.005400196649134159,
0.02429274097084999,
-0.006964912172406912,
-0.006105819717049599,
0.01824137195944786,
0.00487752677872777,
0.02937609888613224,
-0.01061607338488102,
0.00009747379226610065,
0.0739607885479927,
0.03929777815937996,
-0.042755935341119766,
0.009423221461474895,
0.008710911497473717,
-0.013324196450412273,
-0.022067956626415253,
-0.010489990934729576,
0.011305220425128937,
0.03503132238984108,
0.001057973480783403,
0.014866712503135204,
0.011679934337735176,
-0.019236033782362938,
-0.0034068883396685123,
-0.015605777502059937,
0.07502894103527069,
0.0821428894996643,
-0.014834932051599026,
0.04324769228696823,
-0.009118597954511642,
-0.016948558390140533,
-0.0062867989763617516,
0.0038189426995813847,
-0.02826683782041073,
-0.058207690715789795,
-0.04063013941049576,
0.03464595973491669,
0.05185985192656517,
-0.03979121148586273,
-0.002615872072055936,
0.05764806643128395,
0.023354310542345047,
-0.005837133154273033,
0.0021894925739616156,
-0.041770532727241516,
-0.025427483022212982,
0.03292962908744812,
0.011516647413372993,
0.01189419161528349,
0.006933007854968309,
-0.009010128676891327,
0.0261201374232769,
0.0026255459524691105,
0.01777493581175804,
-0.027894744649529457,
0.03802238777279854,
0.03256151080131531,
0.018605615943670273,
0.019785473123192787,
-0.009365230798721313,
0.030311618000268936,
-0.01427825540304184,
0.010621577501296997,
0.02974606491625309,
0.004477031994611025,
0.03547729179263115,
-0.006867785472422838,
-0.010944043286144733,
0.0004704169405158609,
0.037569817155599594,
0.030641430988907814,
-0.014401687309145927,
0.02591036818921566,
-0.04039229080080986,
-0.013817750848829746,
0.011468200013041496,
-0.011016973294317722,
-0.03229660913348198,
0.016333576291799545,
0.0025497220922261477,
0.014521921053528786,
0.00383912306278944,
0.006168228108435869,
-0.021958110854029655,
0.024379421025514603,
0.009510950185358524,
-0.011943880468606949,
0.030716408044099808,
-0.061849161982536316,
-0.00046844762982800603,
-0.01435218844562769,
-0.022983256727457047,
0.010697164572775364,
-0.0020545327570289373,
-0.006001880392432213,
0.02749311923980713,
0.029064632952213287,
-0.06239321455359459,
-0.03725896030664444,
-0.01848546415567398,
0.030139340087771416,
-0.02153054066002369,
0.003190527204424143,
0.038878053426742554,
-0.001729226903989911,
-0.030960045754909515,
0.03175114840269089,
-0.04543396458029747,
-0.04814109578728676,
-0.020122738555073738,
0.001178853795863688,
0.05750702694058418,
-0.04411013051867485,
-0.001379948342218995,
0.030071454122662544,
0.011969111859798431,
-0.02431468665599823,
-0.07147768139839172,
-0.05332046002149582,
-0.00011452901526354253,
0.009624645113945007,
0.07352166622877121,
0.019418839365243912,
-0.017326708883047104,
0.08383328467607498,
0.017038913443684578,
-0.049608681350946426,
-0.02106439881026745,
-0.022618314251303673,
-0.0039104581810534,
-0.0831812173128128,
0.03142186999320984,
0.02770955115556717,
-0.07899437844753265,
0.03101038560271263,
-0.01322221476584673,
-0.0015116081340238452,
0.02883763238787651,
0.013674805872142315,
-0.014229847118258476,
-0.005751367192715406,
-0.013886325061321259,
-0.018505467101931572,
0.04358963668346405,
0.003491638693958521,
-0.02807692065834999,
-0.010926051065325737,
-0.006724780425429344,
0.033380839973688126,
0.023925628513097763,
-0.0694957822561264,
-0.001977642998099327,
-0.03146076574921608,
-0.044337354600429535,
-0.002541698981076479,
0.03656607121229172,
0.029504939913749695,
-0.018202893435955048,
0.00705762067809701,
0.04480233043432236,
0.04611531272530556,
0.014840398915112019,
-0.002035731915384531,
0.060089774429798126,
0.006923446897417307,
-0.06990372389554977,
-0.03441637009382248,
-0.025008440017700195,
0.005324248224496841,
0.020375249907374382,
-0.031217902898788452,
-0.030829984694719315,
0.006979183293879032,
-0.0003990286495536566,
0.005826403386890888,
0.03701929748058319,
-0.020645974203944206,
-0.007862983271479607,
-0.039319392293691635,
0.03452296927571297,
0.0165823046118021,
0.04598114266991615,
0.03221902251243591,
0.0654895007610321,
0.01622890867292881,
-0.016847774386405945,
0.007206992711871862,
0.017525989562273026,
-0.06613866239786148,
0.02436234802007675,
-0.030740953981876373,
-0.020661916583776474,
-0.025902574881911278,
-0.03910353034734726,
0.009430200792849064,
-0.05036241561174393,
-0.015348318964242935,
-0.008131283335387707,
-0.02175993286073208,
-0.02475477010011673,
0.037821706384420395,
-0.05795939639210701,
-0.022361289709806442,
0.018745258450508118,
0.03339328616857529,
-0.004404260776937008,
-0.025598837062716484,
0.038916509598493576,
0.03825483098626137,
-0.01955849677324295,
-0.024052191525697708,
-0.032343048602342606,
-0.007347830105572939,
-0.023973921313881874,
0.03276209905743599,
0.011309580877423286,
0.008996454998850822,
-0.006787786725908518,
0.014965478330850601,
-0.02373940870165825,
0.015204034745693207,
0.04138439893722534,
-0.006545669864863157,
-0.049478232860565186,
-0.04172143712639809,
-0.021990859881043434,
0.008752546273171902,
0.05573936924338341,
0.015196656808257103,
-0.025178957730531693,
0.05695796012878418,
-0.0036308097187429667,
-0.020740317180752754,
-0.012019562534987926,
0.017074190080165863,
0.025702930986881256,
-0.005780491977930069,
-0.07081618905067444,
-0.03619152680039406,
0.0012929708464071155,
0.005486398469656706,
0.01866314187645912,
-0.004024098627269268,
0.0066456543281674385,
-0.009313787333667278,
0.03592751547694206,
0.012886437587440014,
-0.009543392807245255,
0.03910957649350166,
-0.020276831462979317,
0.04216481000185013,
-0.012470428831875324,
-0.0062089283019304276,
-0.00023604439047630876,
0.056792352348566055,
0.016911301761865616,
0.008339243941009045,
-0.03354576602578163,
-0.09331768751144409,
-0.02987360954284668,
0.04866304248571396,
0.006997487973421812,
-0.025472154840826988,
-0.005952195730060339,
-0.021540923044085503,
-0.006373342126607895,
0.019927876070141792,
-0.05503407493233681,
0.06896660476922989,
-0.008423082530498505,
0.012831034138798714,
-0.024630539119243622,
-0.06225590780377388,
-0.06997187435626984,
0.039602745324373245,
-0.032575566321611404,
0.01623917557299137,
-0.046335428953170776,
-0.013964954763650894,
-0.03827846050262451,
0.016904640942811966,
0.06085763871669769,
0.047049857676029205,
0.026098156347870827,
0.019597196951508522,
-0.005307652987539768,
0.01824772171676159,
-0.0013036192394793034,
-0.0890531837940216,
-0.004434914328157902,
0.0043223537504673,
0.027806488797068596,
0.05096637085080147,
-0.038251977413892746,
-0.005794805940240622,
0.025328563526272774,
0.012778142467141151,
-0.01895001530647278,
0.028453027829527855,
-0.03158679977059364,
-0.01548092532902956,
0.019737280905246735,
0.010553206317126751,
0.012681065127253532,
0.0035272142849862576,
-0.036925796419382095,
-0.024604130536317825,
-0.009623564779758453,
0.020684175193309784,
0.01168762519955635,
0.007258906029164791,
-0.026761243119835854,
0.0209608543664217,
-0.019617974758148193,
0.024792388081550598,
-0.002786794677376747,
0.03074011392891407,
-0.03217281773686409,
-0.04487650468945503,
-0.07095412164926529,
0.01997079700231552,
-0.0008495623478665948,
-0.01799413189291954,
-0.013843143358826637,
0.022532343864440918,
-0.02225058153271675,
0.007269089110195637,
0.029238762333989143,
-0.02316955476999283,
0.043069709092378616,
0.01751832477748394,
-0.0017713289707899094,
0.04897960647940636,
-0.047095924615859985,
-0.021593967452645302,
-0.013007167726755142,
-0.07285531610250473,
0.04384707659482956,
0.004953359719365835,
0.0012989810202270746,
0.07028517127037048,
-0.06379625201225281,
-0.022075669839978218,
0.01911194436252117,
0.003196735167875886,
0.02038506232202053,
-0.017291171476244926,
-0.05158175900578499,
-0.025324856862425804,
0.02732708491384983,
-0.003266749670729041,
-0.028648845851421356,
-0.006800799630582333,
0.006474926136434078,
-0.003636914538219571,
-0.02970960922539234,
0.001680319313891232,
-0.005128422286361456,
-0.028861824423074722,
0.046116869896650314,
0.04066772386431694,
-0.008756895549595356,
-0.015283982269465923,
0.033303674310445786,
-0.007972697727382183,
0.0443301722407341,
0.006358277052640915,
-0.0017477155197411776,
0.02761947736144066,
-0.011058706790208817,
-0.02370758354663849,
-0.009691153652966022,
0.06466229259967804,
-0.029827117919921875,
-0.024116260930895805,
-0.01261775754392147,
0.05331210792064667,
0.06077815219759941,
-0.01690230891108513,
-0.02478484995663166,
-0.020737996324896812,
0.036224499344825745,
-0.020777517929673195,
-0.024512050673365593,
0.03529767692089081,
0.04838741198182106,
0.008101548068225384,
0.006181675009429455,
-0.0007339543662965298,
-0.025557134300470352,
-0.017280124127864838,
0.025182876735925674,
0.008945656940340996,
0.01973826251924038,
0.007401202339679003,
0.04284366965293884,
-0.01831093803048134,
0.003531233873218298,
0.006775281857699156,
0.023548591881990433,
0.06702640652656555,
0.005546842236071825,
-0.013842005282640457,
0.009936145506799221,
0.04272347688674927,
-0.016573648899793625,
-0.015439536422491074,
-0.014757167547941208,
0.00715688755735755,
0.07996577024459839,
-0.024595575407147408,
0.07494251430034637,
0.048345424234867096,
0.018262343481183052,
-0.02657199092209339,
0.003504117950797081,
0.01334270741790533,
-0.004965437576174736,
0.00229381094686687,
0.03410208225250244,
-0.026545362547039986,
-0.001483180676586926,
0.030851591378450394,
0.014966768212616444,
0.008159950375556946,
0.004180464427918196,
0.02145824395120144,
-0.002819253597408533,
0.04049398750066757,
-0.024341987445950508,
-0.04516388848423958,
0.02976546250283718,
-0.024867044761776924,
0.07608848065137863,
-0.010135895572602749,
0.008312809281051159,
0.06343074887990952,
0.03089962899684906,
0.010727561078965664,
-0.04572675749659538,
0.02661518193781376,
-0.05559542402625084,
-0.0061787692829966545,
0.009143371134996414,
-0.008559571579098701,
-0.018049342557787895,
0.034008514136075974,
0.05650942400097847,
-0.010198581963777542,
0.031014256179332733,
-0.03902677819132805,
-0.057349637150764465,
-0.002380148507654667,
-0.06409536302089691,
-0.04308803752064705,
0.05403681471943855,
0.0016701052663847804,
-0.011506566777825356,
0.018662242218852043,
-0.004524545278400183,
0.03468530252575874,
0.006745113525539637,
0.02212660014629364,
-0.02898651920258999,
0.06963314116001129,
0.019731430336833,
-0.007277666125446558,
-0.008557325229048729,
0.0014341446803882718,
0.1260206550359726,
0.022670214995741844,
0.0016450119437649846,
-0.039609383791685104,
0.009405473247170448,
-0.02497720532119274,
0.010277202352881432,
-0.024318356066942215,
-0.0030753277242183685,
0.02036699838936329,
0.021336108446121216,
0.0058925761841237545,
-0.00527947535738349,
-0.043527159839868546,
-0.018715808168053627,
0.0562937967479229,
-0.04104670509696007,
-0.019705254584550858,
-0.0053283278830349445,
0.030024249106645584,
0.01805400662124157,
0.01895924098789692,
-0.05648425221443176,
0.022531460970640182,
-0.04091998189687729,
-0.05095019191503525,
0.0007972363382577896,
-0.04757004231214523,
0.012284197844564915,
-0.010333661921322346,
-0.05126762390136719,
0.0061312043108046055,
0.044214826077222824,
-0.0052191223949193954,
-0.03598641976714134,
0.035543106496334076,
0.005369329825043678,
-0.024821056053042412,
0.020648200064897537,
0.01128335576504469,
0.0161978080868721,
0.007557450793683529,
0.038166508078575134,
-0.010054484009742737,
-0.07403961569070816,
-0.02314716950058937,
-0.05570526793599129,
0.02260601706802845,
-0.0047469595447182655,
0.03477414697408676,
-0.03403683006763458,
-0.006833819672465324,
0.01606225036084652,
-0.05204806476831436,
0.013678032904863358,
0.015326530672609806,
0.012054594233632088,
-0.04423960670828819,
0.0070429155603051186,
-0.027494030073285103,
0.007554053328931332,
0.02733187936246395,
-0.012766634114086628,
0.007572455331683159,
0.0047934758476912975,
-0.012534950859844685,
0.023068392649292946,
0.060401979833841324,
-0.01821104995906353,
-0.05510811135172844,
-0.03586355224251747,
-0.010034049861133099,
-0.01180038321763277,
0.050871316343545914,
0.02746129222214222,
-0.0065092723816633224,
-0.018271705135703087,
0.00997571274638176,
-0.01591118611395359,
-0.010021575726568699,
-0.08297348022460938,
-0.000413805537391454,
-0.04540747031569481,
0.00006499167648144066,
-0.03059595450758934,
-0.01135221030563116,
0.04535895586013794,
0.04998687654733658,
-0.009336973540484905,
-0.005198789294809103,
-0.013273131102323532,
0.02048891969025135,
0.014443004503846169,
-0.001901380019262433,
-0.022051947191357613,
0.03416453301906586,
-0.07601696252822876,
-0.0022626384161412716,
-0.021104877814650536,
0.06758340448141098,
0.03487246111035347,
0.02222432941198349,
0.016582559794187546,
-0.024441814050078392,
-0.022602908313274384,
0.028915362432599068,
0.02933327667415142,
-0.02346840314567089,
-0.02891186624765396,
0.011658650822937489,
0.019864190369844437,
-0.050822850316762924,
0.002319855848327279,
-0.02357982099056244,
-0.041559889912605286,
-0.01710558868944645,
0.02175004594027996,
0.00905825849622488,
0.0003406079194974154,
-0.0427156426012516,
0.0022395001724362373,
-0.031989868730306625,
0.02953994646668434,
-0.032261744141578674,
-0.014915568754076958,
-0.0013460436603054404,
0.0025045203510671854,
-0.015299573540687561,
0.031196031719446182,
-0.023036524653434753,
-0.004952964372932911,
0.01118616946041584,
0.016257332637906075,
0.037864889949560165,
-0.017208393663167953,
0.012052005156874657,
-0.010160945355892181,
0.05327209457755089,
-0.031024284660816193,
-0.0397975817322731,
0.02322522923350334,
-0.029060671105980873,
-0.0007705168100073934,
0.04520867019891739,
-0.01542519312351942,
0.03680357709527016,
0.015072737820446491,
-0.02566387504339218,
0.0027107284404337406,
0.0022630905732512474,
0.0023112136404961348,
-0.020643584430217743,
-0.0031160295475274324,
-0.017154550179839134,
0.038606442511081696,
-0.00044365221401676536,
0.036337319761514664,
-0.025636544451117516,
-0.025943709537386894,
0.020911013707518578,
0.019306380301713943,
-0.009629021398723125,
0.011216863058507442,
0.015848491340875626,
0.01157073862850666,
0.001505194348283112,
0.005936062894761562,
-0.008852632716298103,
0.047880034893751144,
0.04129635542631149,
-0.023239634931087494,
0.03018186241388321,
-0.0016678330721333623,
0.002057655481621623,
-0.08740166574716568,
0.025061726570129395,
0.010817017406225204,
0.0005148741183802485,
0.05722757428884506,
-0.055976301431655884,
-0.020909568294882774,
0.028411805629730225,
-0.05308304727077484,
0.04220908135175705,
-0.013922564685344696,
-0.006943888496607542,
-0.06068309769034386,
-0.008635120466351509,
0.020045997574925423,
0.03652216121554375,
0.03477850928902626,
0.028885403648018837,
0.048005711287260056,
0.02310028113424778,
-0.007024246733635664,
-0.003777015721425414,
0.023036181926727295,
0.0580647774040699,
-0.02303205244243145,
-0.030169568955898285,
0.026726236566901207,
-0.03641584888100624,
-0.03949347138404846,
0.03186827525496483,
-0.031755231320858,
0.03357527032494545,
-0.01154235191643238,
-0.012378041632473469,
-0.015038378536701202,
0.028710614889860153,
0.0228519719094038,
0.020096443593502045,
0.019293513149023056,
0.003483134787529707,
0.023074988275766373,
0.03375167027115822,
-0.03522060066461563,
0.009452292695641518,
0.006469255313277245,
-0.03268885985016823,
-0.03538065031170845,
0.029250748455524445,
-0.048541031777858734,
-0.0067769428715109825,
0.019317874684929848,
0.011256853118538857,
-0.010452143847942352,
-0.024233032017946243,
-0.016074735671281815,
-0.040587786585092545,
-0.003977608866989613,
0.032707955688238144,
-0.027491502463817596,
-0.009477752260863781,
-0.00824452843517065,
-0.01946250908076763,
-0.015696600079536438,
0.013012388721108437,
-0.026823043823242188,
-0.0011357011971995234,
-0.046358659863471985,
0.0032571954652667046,
0.014131267555058002,
-0.020578831434249878,
-0.03475299850106239,
-0.02464776486158371,
0.00875317957252264,
0.031307876110076904,
0.0177902914583683,
0.023459454998373985,
0.04375719279050827,
0.009918548166751862,
0.00784189160913229,
-0.06791706383228302,
0.019444424659013748,
0.05307554081082344,
-0.05454366281628609,
-0.012158806435763836,
-0.05110976845026016,
0.031907882541418076,
0.010588586330413818,
0.06330762058496475,
-0.011765876784920692,
-0.017222214490175247,
-0.0014049799647182226,
0.010124754160642624,
0.035450831055641174,
-0.013757689855992794,
0.011593683622777462,
-0.02880311943590641,
-0.044106073677539825,
0.014787532389163971,
-0.02698431722819805,
-0.0328393280506134,
-0.018510986119508743,
0.03898110240697861,
-0.016541115939617157,
-0.009593629278242588,
-0.023625006899237633,
-0.057954996824264526,
0.008866866119205952,
0.0015955219278112054,
0.006648349575698376,
0.08437585830688477,
0.009231600910425186,
-0.01709704101085663,
0.03353506699204445,
-0.018782326951622963,
-0.02952018566429615,
0.033936306834220886,
-0.04758523032069206,
0.0006367868045344949,
-0.030001623556017876,
-0.030913468450307846,
0.05991547927260399,
-0.05945903807878494,
-0.023886894807219505,
0.04624919220805168,
-0.015273182652890682,
-0.005653671454638243,
0.018077539280056953,
0.003690023673698306,
0.023018358275294304,
-0.014209659770131111,
0.020635217428207397,
0.015553127974271774,
-0.050251975655555725,
-0.043915435671806335,
0.03292132541537285,
0.040145114064216614,
-0.018702568486332893,
-0.013601312413811684,
0.05909426882863045,
0.002265837974846363,
0.007645657751709223,
-0.0024890222121030092,
0.07451092451810837,
0.012304369360208511,
0.028904689475893974,
-0.014314327389001846,
0.004282306879758835,
0.027101466432213783,
0.037389665842056274,
-0.008603708818554878,
0.041809674352407455,
-0.026680216193199158,
-0.026371994987130165,
-0.05358687788248062,
-0.006899472326040268,
-0.021914510056376457,
0.004949355963617563,
0.018202058970928192,
0.00024746498093008995,
0.009355796501040459,
-0.0025631075259298086,
0.013483673334121704,
-0.0034920067992061377,
0.041097402572631836,
-0.00599866546690464,
0.03322424367070198,
0.018992768600583076,
0.009725750423967838,
0.0031310187187045813,
-0.04502222314476967,
0.004264389630407095,
-0.013635753653943539,
0.05980083718895912,
0.02347681298851967,
0.028623336926102638,
-0.021124983206391335,
0.004836792591959238,
-0.04032503068447113,
0.04138803854584694,
-0.0828627422451973,
-0.05066290870308876,
-0.051911789923906326,
0.03342439979314804,
0.022466329857707024,
0.015957748517394066
] |
<p>What really is <a href="http://en.wikipedia.org/wiki/Reflection_%28physics%29" rel="nofollow">reflection</a>? Is it just the reemission of EMR? I asked my teacher, he said in quantum sense, it is true. But when I read something about emissivity in Stefan Boltzmann's equation, it states that if an object reflects most light, then it absorbs and reemits less. So what it said means reflection and absorption and reemission are different concepts.</p>
| 92 |
[
-0.027813399210572243,
-0.05274028331041336,
0.02250511199235916,
-0.026850711554288864,
0.027701258659362793,
0.04588138684630394,
-0.004926552064716816,
-0.02311103790998459,
-0.032995373010635376,
0.006096920929849148,
0.028106527402997017,
0.04709561914205551,
0.03773963823914528,
0.020786279812455177,
-0.005504160188138485,
0.002177818911150098,
0.022311044856905937,
0.024981090798974037,
0.00635859090834856,
-0.021864978596568108,
-0.0046450477093458176,
0.03719870001077652,
0.028159601613879204,
0.005182967521250248,
-0.033968254923820496,
0.019907789304852486,
0.026787294074892998,
-0.013065800070762634,
0.05033291503787041,
0.02269320748746395,
0.011452442966401577,
0.0042701605707407,
-0.0026572502683848143,
-0.05359252169728279,
0.008899456821382046,
-0.008102870546281338,
-0.011967755854129791,
-0.0011151793878525496,
-0.038494087755680084,
0.03865118697285652,
-0.0002359927020734176,
-0.004853131249547005,
-0.007531830575317144,
0.03361498564481735,
-0.003899327479302883,
-0.0286701750010252,
-0.013877397403120995,
-0.030020203441381454,
0.03001663088798523,
-0.06503600627183914,
0.03725401684641838,
-0.0012696732301265001,
0.024028940126299858,
0.012034597806632519,
0.01606481894850731,
-0.003142766887322068,
0.07924938201904297,
0.06929197162389755,
-0.02759717032313347,
-0.016017505899071693,
-0.010298578068614006,
-0.02152326889336109,
-0.009188578464090824,
0.010010723024606705,
-0.013307144865393639,
0.011702240444719791,
0.04761509969830513,
-0.04320712760090828,
0.04471511393785477,
0.05075262859463692,
-0.006619117688387632,
0.016260085627436638,
0.047705117613077164,
-0.004226016346365213,
0.04119346663355827,
-0.03852203115820885,
0.021600672975182533,
0.014681658707559109,
0.043258246034383774,
0.034899886697530746,
0.0022936579771339893,
0.0038680133875459433,
0.013619634322822094,
0.015278566628694534,
0.012471797876060009,
-0.01416613906621933,
0.07637560367584229,
0.03288659825921059,
0.014483905397355556,
0.0018482910236343741,
-0.003371091093868017,
0.012504246085882187,
0.007681064773350954,
0.006209368817508221,
-0.04160134121775627,
0.023052748292684555,
0.012313127517700195,
0.07499568909406662,
-0.024477604776620865,
-0.04991533234715462,
-0.01365652121603489,
0.038787003606557846,
0.022361548617482185,
0.035871680825948715,
-0.01311987079679966,
-0.016904909163713455,
-0.029515285044908524,
0.017614688724279404,
-0.02228185161948204,
-0.00004172283661318943,
-0.019306855276226997,
0.012933806516230106,
-0.004182146396487951,
0.0239403173327446,
-0.003629528684541583,
-0.025538969784975052,
0.024459855630993843,
-0.009912671521306038,
0.04318476468324661,
0.076386459171772,
-0.0013260741252452135,
-0.013138769194483757,
-0.00001774276461219415,
-0.002319403225556016,
-0.09049540758132935,
0.024855833500623703,
0.020574843510985374,
-0.007809592876583338,
-0.03780612349510193,
0.0374055840075016,
-0.008555715903639793,
-0.03207898512482643,
0.0019174490589648485,
-0.0006281837122514844,
0.00793907605111599,
-0.03723005950450897,
-0.09954601526260376,
-0.02967112325131893,
0.030686113983392715,
0.008264404721558094,
-0.049695439636707306,
-0.07530437409877777,
0.02443755604326725,
0.03112824074923992,
0.10583947598934174,
0.01788855344057083,
0.016351254656910896,
-0.018034493550658226,
0.007469294127076864,
0.0005450063617900014,
-0.011553340591490269,
-0.024102218449115753,
0.005380566231906414,
-0.027195386588573456,
0.0050432453863322735,
-0.06379851698875427,
0.006872185040265322,
0.07708228379487991,
-0.04620278254151344,
0.0036471846979111433,
0.051772329956293106,
-0.05235949531197548,
-0.022747870534658432,
0.012167626060545444,
-0.022455474361777306,
-0.045103177428245544,
0.07825438678264618,
0.027760298922657967,
-0.01725836843252182,
0.010326419025659561,
0.024949830025434494,
0.01583953946828842,
0.012603591196238995,
0.04893863573670387,
0.011373092420399189,
-0.02949245646595955,
-0.01939382031559944,
0.0018194537842646241,
0.019109541550278664,
0.028928883373737335,
-0.044853728264570236,
-0.031173987314105034,
0.04244465008378029,
-0.0066749332472682,
-0.0092720752581954,
0.005718871019780636,
-0.0021157492883503437,
-0.01703464798629284,
0.027170337736606598,
-0.02456061914563179,
-0.029392099007964134,
-0.020828554406762123,
0.007569897919893265,
-0.020513389259576797,
0.012871106155216694,
-0.009626451879739761,
0.011147314682602882,
-0.027902446687221527,
-0.05973173305392265,
-0.06261932849884033,
0.019230589270591736,
0.03630754351615906,
-0.005140134133398533,
0.006608637981116772,
-0.01589469239115715,
0.045993417501449585,
0.03247020021080971,
-0.0007352484972216189,
0.011847056448459625,
-0.046284500509500504,
-0.017342742532491684,
-0.014070536941289902,
-0.009583273902535439,
0.017906278371810913,
0.014300493523478508,
-0.046965841203927994,
0.022142799571156502,
0.013309421949088573,
0.00010979235958075151,
0.014167808927595615,
-0.016826005652546883,
0.0348835363984108,
-0.006995776668190956,
0.003771503921598196,
-0.013811769895255566,
0.03454137220978737,
-0.012679480016231537,
-0.00011554142110981047,
-0.004913949873298407,
-0.017996763810515404,
-0.018944641575217247,
-0.011282469145953655,
0.04160868749022484,
-0.01682618074119091,
-0.06954752653837204,
0.02437267079949379,
-0.031646061688661575,
0.02790827676653862,
0.041791051626205444,
0.015243040397763252,
-0.04515864700078964,
-0.01508881151676178,
0.02206358127295971,
-0.011263030581176281,
0.014061092399060726,
0.045697085559368134,
0.013940812088549137,
0.01552822906523943,
0.05746418982744217,
-0.06857260316610336,
-0.009406357072293758,
0.0653613954782486,
0.0190195981413126,
0.023021243512630463,
-0.0010022551286965609,
-0.02721899189054966,
0.012411379255354404,
-0.03249514847993851,
0.03237302601337433,
0.008262725546956062,
-0.026193877682089806,
0.01311358343809843,
-0.06411523371934891,
-0.02214796654880047,
0.0061771138571202755,
0.007731648627668619,
-0.0350920744240284,
-0.008039740845561028,
0.02787099778652191,
-0.033713798969984055,
-0.0017549064941704273,
-0.02369447983801365,
-0.0013800736051052809,
-0.03135578706860542,
-0.021013133227825165,
-0.007515839301049709,
-0.023756779730319977,
0.015267233364284039,
-0.04599780961871147,
-0.05772510543465614,
-0.02349073253571987,
-0.04440269246697426,
0.028579307720065117,
-0.00019453086133580655,
-0.037404969334602356,
0.04742397740483284,
-0.054951783269643784,
-0.04508638754487038,
0.004440128803253174,
0.0015073606045916677,
0.02403969317674637,
0.01765841618180275,
0.0009540247265249491,
-0.06820405274629593,
-0.011586003005504608,
0.0060583800077438354,
-0.018725616857409477,
-0.031159505248069763,
-0.013026895001530647,
0.04406764358282089,
-0.07353450357913971,
-0.0164649598300457,
-0.026527488604187965,
-0.029423996806144714,
-0.07163646817207336,
-0.025462981313467026,
-0.054110512137413025,
0.009698509238660336,
-0.015167186968028545,
0.028662435710430145,
0.05347886681556702,
-0.05503455922007561,
-0.011530764400959015,
-0.019519519060850143,
-0.06996791064739227,
0.0562632754445076,
-0.02959379181265831,
0.023909159004688263,
0.008794009685516357,
-0.005534396506845951,
0.033958904445171356,
0.03104798123240471,
-0.02955024130642414,
-0.008313440717756748,
0.03567490354180336,
0.0028054292779415846,
-0.04197897017002106,
-0.024178756400942802,
0.05238526314496994,
-0.02122454158961773,
0.01313238125294447,
-0.01631101407110691,
0.02189105562865734,
0.020642297342419624,
0.019183209165930748,
-0.03627564013004303,
0.002775405766442418,
-0.007464911788702011,
0.01107904501259327,
0.048209141939878464,
-0.00222192145884037,
-0.05329620838165283,
0.043125782161951065,
0.004196899477392435,
0.028685346245765686,
0.033583857119083405,
-0.04130818694829941,
0.051552243530750275,
0.013127632439136505,
0.020861737430095673,
-0.02488608844578266,
0.018055608496069908,
-0.0238278117030859,
0.005942994728684425,
0.02883155085146427,
0.04473545029759407,
0.009415745735168457,
-0.014878816902637482,
0.011991027742624283,
0.022345826029777527,
0.05277605354785919,
-0.003938619047403336,
0.006576004438102245,
-0.014896633103489876,
-0.016550051048398018,
-0.0020681212190538645,
0.007205888628959656,
-0.011050709523260593,
0.04951319843530655,
0.043747760355472565,
0.03861473500728607,
0.010111449286341667,
-0.06408466398715973,
-0.04031932353973389,
-0.04478845372796059,
0.0026278633158653975,
0.014210567809641361,
0.05141383409500122,
0.014105875045061111,
0.02656741626560688,
0.004030540585517883,
0.02650323323905468,
0.005636734422296286,
0.007447080221027136,
-0.10671043395996094,
-0.004771705251187086,
-0.03285561129450798,
0.012154879048466682,
-0.017778154462575912,
0.010053603909909725,
0.005962105002254248,
-0.027225349098443985,
-0.03455597907304764,
0.0007065844838507473,
0.007447421550750732,
-0.05514385551214218,
-0.00574368005618453,
-0.046658843755722046,
-0.0332038551568985,
-0.03727266192436218,
0.037054527550935745,
0.032137658447027206,
-0.02274337038397789,
0.03865330293774605,
0.06534454226493835,
-0.05878768116235733,
0.019581981003284454,
-0.020207570865750313,
-0.009205219335854053,
0.051175981760025024,
0.03968360275030136,
0.03399212658405304,
-0.0027607835363596678,
-0.013361391611397266,
0.04152859374880791,
0.0341438427567482,
0.02058561146259308,
-0.012181982398033142,
-0.03340042009949684,
-0.03288298845291138,
-0.03250719606876373,
-0.025062575936317444,
-0.03757587820291519,
0.03480605036020279,
-0.04050402715802193,
0.010536400601267815,
-0.000013480597772286274,
-0.007345017045736313,
-0.014219634234905243,
0.008714687079191208,
0.032886773347854614,
0.019238440319895744,
-0.0021245512180030346,
-0.04494782164692879,
0.0005387379205785692,
-0.03671703860163689,
0.010640681721270084,
0.007612999994307756,
0.021571384742856026,
-0.007722174283117056,
0.0057167774066329,
-0.002619195729494095,
0.03465856611728668,
0.016570881009101868,
-0.014147218316793442,
0.014465028420090675,
-0.006805895362049341,
-0.018202675506472588,
0.004040732514113188,
-0.017436446622014046,
0.056132104247808456,
0.043240562081336975,
-0.0011245454661548138,
-0.027174774557352066,
-0.06894350796937943,
0.011573398485779762,
0.03957081958651543,
0.026762191206216812,
-0.013630719855427742,
0.010321399196982384,
-0.03469037637114525,
-0.0055842651054263115,
0.052883218973875046,
-0.026419930160045624,
0.027196824550628662,
-0.0397295206785202,
0.01315851416438818,
-0.038666609674692154,
-0.021745799109339714,
0.021130530163645744,
0.018569421023130417,
0.003520262660458684,
0.002747009042650461,
0.002905359258875251,
-0.018567180261015892,
0.014156227000057697,
0.004255852662026882,
0.005427032709121704,
0.039766084402799606,
-0.019189970567822456,
0.008142783306539059,
0.0107724042609334,
0.021808790042996407,
-0.003164393361657858,
-0.0878114253282547,
-0.016454581171274185,
0.010497515089809895,
0.008074193261563778,
0.037716254591941833,
-0.015898317098617554,
-0.04240529239177704,
0.04374656081199646,
0.00852258875966072,
-0.039717741310596466,
-0.004565875977277756,
-0.07270026206970215,
0.042332958430051804,
-0.0003526929358486086,
-0.06719671189785004,
0.043687693774700165,
0.05153455585241318,
0.0018853186629712582,
-0.0003241662052460015,
-0.01621566340327263,
0.030542731285095215,
-0.033787619322538376,
-0.012883509509265423,
-0.003745481139048934,
-0.01611870713531971,
-0.0622856542468071,
0.057510003447532654,
-0.00388129404745996,
0.0029944514390081167,
-0.028387105092406273,
-0.025094345211982727,
-0.030463071539998055,
0.022058924660086632,
-0.036611057817935944,
0.021290773525834084,
-0.014858406968414783,
0.013194349594414234,
-0.00031589283025823534,
-0.01905878446996212,
-0.008429398760199547,
0.02473265677690506,
0.0029447900597006083,
0.03198307752609253,
0.010755137540400028,
0.05209237337112427,
-0.012811937369406223,
-0.002686471911147237,
0.02466520667076111,
-0.012501824647188187,
0.04715006425976753,
-0.023076632991433144,
0.00957147590816021,
0.04748355597257614,
-0.059331245720386505,
0.004184462130069733,
0.009173608385026455,
-0.019217289984226227,
0.02037474513053894,
-0.05793725699186325,
0.03826780989766121,
0.036366865038871765,
0.024529723450541496,
-0.04361570626497269,
-0.03725374490022659,
0.008142765611410141,
0.0007233805954456329,
-0.03473113849759102,
-0.013650131411850452,
-0.044069647789001465,
-0.02094823122024536,
-0.06277299672365189,
0.04514896497130394,
0.03019176609814167,
-0.008618230931460857,
-0.015176443383097649,
0.019618337973952293,
0.03330974653363228,
0.02170240879058838,
-0.008043384179472923,
-0.02450626902282238,
-0.029826870188117027,
-0.017910724505782127,
0.012073480524122715,
0.014081028290092945,
0.06121312454342842,
0.0027871315833181143,
-0.040951021015644073,
-0.035503000020980835,
0.004149267449975014,
0.06328199803829193,
-0.01589561067521572,
0.037541452795267105,
0.03939308226108551,
0.02018018439412117,
-0.007573170121759176,
-0.0312536396086216,
0.02473401091992855,
0.033892109990119934,
0.02909889817237854,
-0.0007153049227781594,
0.009148972108960152,
-0.0033610984683036804,
-0.034336771816015244,
0.029831718653440475,
-0.012288088910281658,
0.04292982816696167,
-0.011283271946012974,
0.08968120813369751,
-0.03567865118384361,
0.0116189606487751,
-0.02338906191289425,
-0.020754467695951462,
0.014078767038881779,
-0.0226377435028553,
0.011633196845650673,
0.026160473003983498,
0.033939212560653687,
0.00006382522406056523,
-0.04480919614434242,
-0.03772254288196564,
-0.013920503668487072,
0.029921621084213257,
-0.022720713168382645,
0.040022287517786026,
0.009519945830106735,
-0.007480783388018608,
0.01206756941974163,
-0.0016755511751398444,
-0.02939622662961483,
0.02297966182231903,
-0.03297927975654602,
0.03732018917798996,
-0.05612045153975487,
-0.001639307476580143,
0.001027813646942377,
0.05719577521085739,
-0.008235943503677845,
0.0011258290614932775,
0.002046294277533889,
0.06808403879404068,
-0.007365977391600609,
-0.014544988051056862,
-0.01856003701686859,
0.06204623728990555,
-0.024482056498527527,
0.0503590889275074,
0.02026251144707203,
-0.02310374565422535,
0.03885477036237717,
-0.025757761672139168,
0.022412123158574104,
-0.07535813748836517,
0.006055631209164858,
-0.0621175691485405,
0.008100910112261772,
-0.009847146458923817,
0.04286777228116989,
-0.011265500448644161,
-0.02297905460000038,
0.008462431840598583,
-0.0021447185426950455,
0.005105596501380205,
-0.00258209859021008,
-0.07828646898269653,
-0.00970123615115881,
-0.040675461292266846,
-0.026711994782090187,
0.039782267063856125,
-0.0028397205751389265,
-0.02177310176193714,
0.01742762140929699,
-0.03104574792087078,
0.027422405779361725,
0.02189738303422928,
0.02617706172168255,
-0.019175339490175247,
0.005325913429260254,
-0.0005139013519510627,
0.026125552132725716,
-0.004632093012332916,
0.02162688970565796,
0.12481963634490967,
0.03706374764442444,
0.007489536423236132,
-0.04412942752242088,
0.021076645702123642,
-0.04217490926384926,
0.011088738217949867,
-0.010352215729653835,
-0.007064692676067352,
-0.02139352262020111,
0.08239496499300003,
0.019222980365157127,
0.04580669105052948,
0.03660611808300018,
-0.0011549617629498243,
0.002087503671646118,
-0.04796827957034111,
-0.008861281909048557,
0.010505465790629387,
0.011441642418503761,
-0.03198482468724251,
0.03837922587990761,
-0.052751246839761734,
-0.008191734552383423,
-0.004113170318305492,
0.017571885138750076,
-0.028942737728357315,
-0.007491154596209526,
-0.0045630838721990585,
-0.0007602385594509542,
0.00012435841199476272,
0.023653585463762283,
-0.013837415724992752,
-0.023314958438277245,
-0.016795461997389793,
0.059085775166749954,
0.06725116819143295,
-0.0016359520377591252,
0.015068716369569302,
0.016791656613349915,
0.0347038172185421,
-0.012583889998495579,
0.020222796127200127,
0.039816711097955704,
-0.036575447767972946,
-0.00586002878844738,
-0.015967952087521553,
0.04535949230194092,
-0.03595690801739693,
-0.012232991866767406,
0.009027643129229546,
-0.027231484651565552,
0.014711636118590832,
-0.06020765006542206,
0.014441214501857758,
0.011245492845773697,
0.013004777021706104,
-0.013658372685313225,
-0.032798707485198975,
-0.025929870083928108,
0.045522645115852356,
-0.015922892838716507,
0.018885338678956032,
0.004870570730417967,
-0.007847094908356667,
-0.012540735304355621,
-0.00013504225353244692,
0.024376114830374718,
-0.010539816692471504,
-0.021562431007623672,
-0.048599470406770706,
-0.00582423759624362,
-0.017024969682097435,
-0.042587727308273315,
0.016738878563046455,
0.004888462368398905,
0.03098003938794136,
-0.0162847638130188,
0.0032130982726812363,
-0.013567340560257435,
-0.07365930080413818,
0.02453691139817238,
-0.02167949639260769,
-0.02970554493367672,
-0.006537472829222679,
0.0013919469201937318,
0.043215394020080566,
0.04862278699874878,
-0.01879134215414524,
0.018435435369610786,
0.04738700017333031,
-0.010664066299796104,
0.00942195300012827,
-0.014294181950390339,
0.006721009965986013,
0.02013043500483036,
0.010512975975871086,
0.018397808074951172,
-0.015450532548129559,
0.05610010772943497,
-0.0037184699904173613,
0.01459849625825882,
-0.009615977294743061,
0.02736918441951275,
-0.053895507007837296,
0.018499404191970825,
-0.024551093578338623,
-0.017786048352718353,
0.003402059432119131,
-0.018777677789330482,
-0.024400759488344193,
-0.031677667051553726,
-0.02215137891471386,
-0.042427606880664825,
0.015245368704199791,
-0.02537955343723297,
0.00341075100004673,
-0.0201182272285223,
0.020187856629490852,
-0.017272168770432472,
0.045704081654548645,
-0.02851002663373947,
-0.013597865588963032,
-0.0423724465072155,
0.020174235105514526,
0.01919337920844555,
0.0028938869945704937,
-0.040912650525569916,
0.01487769652158022,
0.018233561888337135,
-0.009737365879118443,
0.02353796735405922,
0.049437515437603,
0.0019121540244668722,
-0.004992654547095299,
0.051242418587207794,
-0.014125149697065353,
0.03367628529667854,
-0.032858531922101974,
-0.04123780131340027,
0.05778812617063522,
-0.028338074684143066,
-0.019981903955340385,
0.020131295546889305,
-0.019556814804673195,
0.02428182028234005,
0.023372536525130272,
0.01762743666768074,
-0.00019646843429654837,
0.07789438217878342,
-0.003638197435066104,
-0.015973903238773346,
-0.0375308059155941,
-0.04218776524066925,
0.004985432606190443,
-0.042987383902072906,
0.02400428056716919,
-0.0026243047323077917,
0.00393742835149169,
0.05350012704730034,
0.01886645331978798,
-0.018246488645672798,
0.008013587445020676,
-0.013711108826100826,
0.012587239034473896,
-0.01012940239161253,
0.038538314402103424,
0.0010105242254212499,
0.014841988682746887,
0.025869611650705338,
-0.027104122564196587,
0.06627114862203598,
0.0055989897809922695,
-0.01013265922665596,
-0.047895047813653946,
0.032309748232364655,
-0.011631250381469727,
-0.03623846545815468,
0.031080784276127815,
-0.023993592709302902,
0.034467875957489014,
0.034892115741968155,
-0.042860228568315506,
0.023521358147263527,
-0.004668948706239462,
-0.017197387292981148,
-0.013594566844403744,
0.034052927047014236,
-0.0065985992550849915,
0.052185703068971634,
0.029169343411922455,
0.04397289454936981,
0.007841374725103378,
0.018712161108851433,
0.010694830678403378,
-0.05124553292989731,
-0.04667272791266441,
0.034007780253887177,
-0.04477928206324577,
0.008933107368648052,
0.0950588509440422,
-0.02470346912741661,
-0.012403706088662148,
0.047278691083192825,
0.008194033056497574,
0.015804383903741837,
-0.0016437337035313249,
-0.009303707629442215,
0.0006201908108778298,
0.02850787155330181,
0.032735683023929596,
-0.020546961575746536,
-0.0030817948281764984,
0.030002867802977562,
0.05305659398436546,
0.04738415777683258,
0.012247494421899319,
-0.021292420104146004,
0.027439827099442482,
-0.043133001774549484,
-0.030501797795295715,
0.004943717271089554,
0.02137664519250393,
-0.009949627332389355,
0.0035490954760462046,
0.03477683290839195,
0.030270546674728394,
-0.01879185065627098,
0.008364093489944935,
-0.0706566646695137,
-0.021116124466061592,
0.012971130199730396,
0.01176430843770504,
-0.005008338950574398,
0.022413838654756546,
0.001994687132537365,
-0.021217044442892075,
0.0472741425037384,
-0.020883051678538322,
-0.03870271146297455,
-0.022703466936945915,
-0.002896431367844343,
0.028014935553073883,
-0.03692133352160454,
-0.026273248717188835,
-0.01983366347849369,
-0.05345158278942108,
0.01620553806424141,
0.020666733384132385,
0.02909044921398163,
-0.0070104035548865795,
-0.052563659846782684,
-0.024775724858045578,
-0.07650408148765564,
0.0618363656103611,
-0.0459967665374279,
-0.018632536754012108,
-0.07001956552267075,
-0.03451421484351158,
0.004995719995349646,
0.0072093927301466465,
0.06318099051713943,
0.0070556639693677425,
-0.0005383352399803698,
-0.054063498973846436,
0.014349319972097874,
0.0367375910282135,
-0.04199468344449997,
0.009086061269044876,
0.0006567874224856496,
-0.025780336931347847,
-0.003124069422483444,
0.012958869338035583,
-0.03494996577501297,
-0.004160911310464144,
0.02562161348760128,
-0.03616135194897652,
0.020093290135264397,
-0.017295273020863533,
-0.01941135711967945,
0.05093972012400627,
0.01645328290760517,
-0.012401984073221684,
0.04146432876586914,
-0.05667760595679283,
0.01726522669196129,
0.03273865580558777,
-0.03548097610473633,
-0.025579670444130898,
0.021920831874012947,
0.013629043474793434,
-0.019236864522099495,
0.013993180356919765,
0.002141687786206603,
0.04750405251979828,
-0.018957559019327164,
0.005017691291868687,
0.03430520370602608,
-0.03322120010852814,
-0.021036367863416672,
0.0648769736289978,
0.0171176977455616,
0.03589006885886192,
-0.0027796179056167603,
0.03486400842666626,
0.0013955153990536928,
-0.03376046195626259,
-0.025811554864048958,
0.07997915148735046,
0.03499079495668411,
-0.045928698033094406,
0.028121529147028923,
0.031121421605348587,
0.015061466954648495,
0.015446779318153858,
-0.0048039318062365055,
0.025558138266205788,
-0.04003458097577095,
-0.015523377805948257,
0.03237050399184227,
-0.014395525678992271,
0.0011815184261649847,
0.04665406420826912,
-0.02052374742925167,
0.08877046406269073,
-0.02173987776041031,
0.01940120942890644,
-0.0020737566519528627,
0.0035679046995937824,
-0.006126879248768091,
0.005772903095930815,
0.03184313699603081,
0.03186696022748947,
-0.010142968967556953,
-0.02594190649688244,
-0.051243510097265244,
0.02031530998647213,
0.034378938376903534,
-0.019986754283308983,
0.021234095096588135,
-0.024801256135106087,
-0.009888487868010998,
-0.015589919872581959,
-0.002888105809688568,
0.036068107932806015,
-0.010298006236553192,
0.025539366528391838,
0.036403682082891464,
0.014378190040588379,
0.02606889046728611,
-0.014555644243955612,
-0.017338134348392487,
0.01818356290459633,
-0.08561565726995468,
0.0022281871642917395,
-0.006800389848649502,
0.026594562456011772,
0.010995358228683472,
-0.047255925834178925
] |
<p>The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be $I_{ii}=\frac{2}{5}mR^2$, where $m=\frac{M}{2}$ is the mass of the hemisphere? Is it because the tensor of inertia of each hemisphere would be expected to be $I_{ii}=\frac{1}{5}MR^2$, but then $M = 2m$, hence $I_{ii}=\frac{2}{5}mR^2$?</p>
| 8,495 |
[
-0.023733900859951973,
0.012598582543432713,
-0.024249523878097534,
-0.02576143480837345,
0.03599230572581291,
0.019311828538775444,
-0.027255479246377945,
-0.020502062514424324,
0.026600394397974014,
-0.018866118043661118,
-0.0001462045474909246,
-0.006490620318800211,
0.10157717019319534,
0.03051239810883999,
0.03185092285275459,
0.00011351284047123045,
-0.007450517266988754,
0.009287204593420029,
-0.008193658664822578,
-0.027167223393917084,
0.005367627367377281,
0.04513895511627197,
0.03901807963848114,
-0.0398002527654171,
-0.00801580585539341,
0.03314200043678284,
0.011840291321277618,
-0.04208634793758392,
0.010149307548999786,
0.058123879134655,
-0.007395351305603981,
0.008092759177088737,
0.038443777710199356,
-0.0021827826276421547,
-0.0007171222823671997,
-0.020915009081363678,
-0.007921154610812664,
-0.0023518528323620558,
0.026076488196849823,
0.03482535481452942,
-0.06282626837491989,
0.0031438583973795176,
-0.03235927224159241,
0.03781215101480484,
0.017128441482782364,
0.012665308080613613,
0.02223391644656658,
-0.01442425325512886,
0.014751531183719635,
-0.04438433051109314,
0.09528174996376038,
0.007928798906505108,
0.025572175160050392,
0.0024731254670768976,
-0.018454959616065025,
-0.005980353336781263,
0.07341892272233963,
0.06602074950933456,
-0.010723511688411236,
-0.06621172279119492,
-0.02120848186314106,
-0.0449528843164444,
-0.021441804245114326,
-0.03448314592242241,
-0.009622366167604923,
0.03384250029921532,
-0.01855725422501564,
-0.00020987687457818538,
0.014682422392070293,
0.014622179791331291,
0.018390418961644173,
-0.011503195390105247,
0.012840845622122288,
-0.06523243337869644,
0.009889192879199982,
-0.03389589115977287,
0.05815502256155014,
0.010799983516335487,
0.016121938824653625,
0.013727441430091858,
0.00824536569416523,
-0.009617866948246956,
0.06003638356924057,
0.012530150823295116,
-0.0037772308569401503,
0.02206967957317829,
0.04641422629356384,
-0.0025206406135112047,
0.022904619574546814,
0.03908047080039978,
-0.0025256392545998096,
-0.015212155878543854,
0.013420293107628822,
-0.030926639214158058,
-0.014645312912762165,
0.013309462927281857,
-0.012507065199315548,
0.04360978305339813,
-0.02799038402736187,
-0.028586868196725845,
-0.037653226405382156,
-0.015533685684204102,
-0.020146507769823074,
0.05515815317630768,
0.025260943919420242,
0.009206464514136314,
-0.03982774540781975,
-0.028460370376706123,
-0.026100080460309982,
-0.024491919204592705,
-0.044136375188827515,
0.013985204510390759,
-0.014371608383953571,
-0.038325775414705276,
-0.0004059529455844313,
-0.009465867653489113,
0.01673596352338791,
-0.013978669419884682,
-0.019686009734869003,
0.039212118834257126,
0.000401977013098076,
-0.01803511567413807,
-0.01612590253353119,
-0.02035827375948429,
-0.04468409717082977,
0.035826921463012695,
0.011608184315264225,
-0.026487622410058975,
-0.01269298605620861,
-0.014749863184988499,
0.04795841872692108,
-0.0374017171561718,
0.000022802953026257455,
0.021899744868278503,
0.011520658619701862,
-0.017384110018610954,
-0.08942911028862,
-0.06404249370098114,
0.050621699541807175,
-0.00029136022203601897,
0.008854012936353683,
-0.07658442109823227,
0.0014666346833109856,
0.018523233011364937,
0.060499824583530426,
0.0036265889648348093,
0.03451257571578026,
0.0065698279067873955,
0.0698113963007927,
-0.004621025174856186,
-0.010816987603902817,
-0.019392408430576324,
-0.019222598522901535,
-0.033376701176166534,
0.0050497474148869514,
-0.07591355592012405,
0.010189859196543694,
0.002826705342158675,
0.005498839542269707,
-0.015549113973975182,
0.03747529909014702,
0.009339510463178158,
0.02657853439450264,
0.03014046512544155,
0.027059761807322502,
-0.0241088829934597,
0.03947380930185318,
-0.0006018573185428977,
0.029041875153779984,
0.023761307820677757,
0.02992849051952362,
0.019536742940545082,
0.0072927651926875114,
0.05193304643034935,
0.04689299315214157,
-0.010730172507464886,
-0.015245194546878338,
-0.006232292857021093,
0.024202967062592506,
0.0069524021819233894,
-0.041777726262807846,
-0.017143143340945244,
-0.004004379268735647,
-0.022517718374729156,
-0.01602119207382202,
0.03751005977392197,
0.0018314637709408998,
-0.008089383132755756,
-0.00533200753852725,
-0.06406538933515549,
0.01531616784632206,
-0.04189398139715195,
0.02359042316675186,
-0.004110738635063171,
-0.023044122382998466,
0.045405931770801544,
0.0027987153735011816,
0.035660888999700546,
0.026654498651623726,
0.001046220539137721,
-0.020328115671873093,
0.027705775573849678,
-0.0017490689642727375,
-0.009018657729029655,
0.024182001128792763,
0.038042448461055756,
0.026222804561257362,
0.05863208323717117,
0.036054063588380814,
-0.016338767483830452,
-0.0074705276638269424,
-0.00046744191786274314,
0.01652311347424984,
0.007613094989210367,
-0.016078153625130653,
-0.0007669650367461145,
-0.025005243718624115,
0.018239952623844147,
-0.006902420427650213,
0.05368712171912193,
-0.02763519249856472,
0.10200679302215576,
0.06702835112810135,
-0.018741561099886894,
0.03897114098072052,
0.02342813089489937,
0.026724403724074364,
-0.0010885600931942463,
0.004533049650490284,
-0.05998948961496353,
-0.049347639083862305,
-0.006409419700503349,
-0.016988521441817284,
0.04245217517018318,
-0.07542593032121658,
0.021586162969470024,
0.032426636666059494,
0.05523030087351799,
0.009379777126014233,
-0.0021392053458839655,
0.014216998592019081,
-0.0713016465306282,
0.0180224422365427,
-0.010656683705747128,
-0.0054085818119347095,
0.022257136180996895,
0.014429783448576927,
0.02249705046415329,
0.03364570438861847,
0.006466500461101532,
0.014808001928031445,
0.04688626527786255,
-0.0012153586139902472,
0.024378301575779915,
0.023081529885530472,
0.010967674665153027,
0.03637766093015671,
-0.010281805880367756,
0.02215442806482315,
0.054201316088438034,
0.05110761523246765,
-0.02921264059841633,
-0.03751800209283829,
0.007189498748630285,
0.018540916964411736,
-0.006710290443152189,
0.015721246600151062,
-0.009258842095732689,
0.004363443702459335,
-0.04661855474114418,
-0.006674120202660561,
0.007704117335379124,
-0.011623824946582317,
0.026751551777124405,
0.006652877200394869,
0.02144409716129303,
0.01679662987589836,
0.0434834361076355,
0.003240328747779131,
-0.01994464360177517,
-0.003832821501418948,
-0.03380848094820976,
0.003516826778650284,
-0.007050266023725271,
-0.06219640001654625,
0.036993544548749924,
-0.03526954725384712,
-0.003461795160546899,
0.019242597743868828,
-0.01348812784999609,
-0.009522976353764534,
0.018865525722503662,
0.012346521019935608,
-0.024218056350946426,
-0.004332903306931257,
-0.01946689561009407,
0.018204858526587486,
-0.02491164021193981,
0.03836112469434738,
0.04477774351835251,
-0.033256690949201584,
-0.008950249291956425,
-0.03638816997408867,
-0.03490486368536949,
-0.07553558796644211,
-0.04162625968456268,
-0.01582413911819458,
0.021831898018717766,
-0.03993765264749527,
0.011196376755833626,
0.04490951821208,
-0.012442918494343758,
-0.010618523694574833,
-0.04252006113529205,
-0.041210372000932693,
0.022362789139151573,
0.003984495997428894,
0.0518839992582798,
0.023349212482571602,
-0.026650073006749153,
0.08615511655807495,
0.02733701281249523,
-0.055010050535202026,
-0.02087189443409443,
-0.006421463098376989,
0.019105825573205948,
-0.039390720427036285,
0.004799765069037676,
0.01971944235265255,
-0.028676806017756462,
0.01395314559340477,
0.0673682764172554,
-0.015683185309171677,
0.03880994766950607,
-0.017975015565752983,
0.004695611540228128,
0.0020754272118210793,
0.03171934187412262,
-0.0018350576283410192,
0.02748003415763378,
-0.009239432401955128,
-0.0000020232805582054425,
-0.011257447302341461,
-0.009195992723107338,
0.04228905215859413,
0.00972706452012062,
-0.06280943006277084,
0.0061705284751951694,
-0.07389996200799942,
0.0011927996529266238,
-0.03312540054321289,
0.03640753775835037,
-0.00043673484469763935,
0.004176600370556116,
0.03009006194770336,
0.02556937001645565,
0.02860347367823124,
-0.048709385097026825,
0.00887366198003292,
0.034003905951976776,
-0.04638592153787613,
-0.001997921848669648,
0.007929856888949871,
-0.019740046933293343,
0.005421916954219341,
-0.0016166276764124632,
-0.019486814737319946,
-0.01614529639482498,
0.03318868204951286,
0.0345294363796711,
0.027064261958003044,
0.0021752072498202324,
-0.018467308953404427,
0.009618625044822693,
-0.06347042322158813,
-0.01711895875632763,
0.0016162972897291183,
0.012113077566027641,
-0.028869038447737694,
0.03699130937457085,
0.025828909128904343,
0.028833411633968353,
-0.013313313946127892,
-0.0025697583332657814,
-0.07319209724664688,
0.02922268584370613,
-0.039186328649520874,
-0.018024563789367676,
0.01013448927551508,
-0.027201883494853973,
0.020969795063138008,
-0.02929168939590454,
-0.016285767778754234,
-0.0117567777633667,
-0.0034477657172828913,
-0.04990505054593086,
0.03808441013097763,
0.003710622899234295,
-0.020539093762636185,
-0.0009607063257135451,
0.032390303909778595,
0.019307008013129234,
-0.04905325174331665,
0.03926003351807594,
0.045831672847270966,
-0.009099064394831657,
0.020177995786070824,
-0.016456065699458122,
-0.007006207015365362,
0.009635779075324535,
-0.030845796689391136,
0.013901498168706894,
0.014069640077650547,
-0.023673273622989655,
0.03132551908493042,
-0.005976635962724686,
0.07579945772886276,
-0.00010417499288450927,
-0.028544986620545387,
-0.04001588374376297,
-0.06513304263353348,
-0.01784113422036171,
-0.005783319938927889,
0.050809670239686966,
-0.03226032480597496,
-0.02022870071232319,
0.039012350142002106,
-0.020702937617897987,
0.02604944258928299,
0.04081977903842926,
0.07084342837333679,
0.0008591912919655442,
-0.026167133823037148,
-0.05474797263741493,
-0.04425378516316414,
-0.03863807022571564,
-0.013787000440061092,
0.0367685966193676,
-0.024429021403193474,
-0.027844106778502464,
-0.0021649613045156,
0.012550944462418556,
0.016908058896660805,
0.010985261760652065,
-0.00005922038326389156,
-0.010038617067039013,
0.06786112487316132,
0.003760701045393944,
-0.001800741534680128,
0.007272843737155199,
0.014562143012881279,
0.07376398146152496,
-0.011745300143957138,
-0.02946918085217476,
-0.06857778877019882,
-0.00020465994020923972,
-0.03691515326499939,
0.009568934328854084,
-0.03138098865747452,
0.019469663500785828,
-0.064436174929142,
-0.0007592025795020163,
0.07320081442594528,
-0.026288988068699837,
0.012055792845785618,
-0.010862741619348526,
-0.0020735885482281446,
0.002302782377228141,
0.024693820625543594,
-0.020636649802327156,
-0.007535113021731377,
0.02478000894188881,
0.015549885109066963,
-0.01628286764025688,
0.0051266904920339584,
-0.027194157242774963,
0.014195606112480164,
0.03247670456767082,
0.0242331400513649,
0.03502781689167023,
0.004544781520962715,
-0.0053848568350076675,
0.04905702546238899,
-0.04469911381602287,
-0.06549480557441711,
-0.010362244211137295,
-0.00021453907538671046,
-0.029578791931271553,
0.017153458669781685,
-0.04425041005015373,
-0.0962778776884079,
0.04076741635799408,
0.02580314874649048,
0.01966552622616291,
0.004989463370293379,
-0.023031607270240784,
0.031866755336523056,
-0.007224980741739273,
-0.034900497645139694,
0.03564317896962166,
0.025523122400045395,
-0.014423864893615246,
-0.038286495953798294,
-0.04531628638505936,
0.044891733676195145,
-0.04303663596510887,
-0.017378153279423714,
-0.015483934432268143,
0.020827578380703926,
-0.04005728289484978,
0.02951974608004093,
-0.005992758087813854,
0.0315404087305069,
-0.015077703632414341,
-0.030701840296387672,
0.0025655252393335104,
0.062083542346954346,
0.03166206181049347,
0.004645693115890026,
-0.022868908941745758,
0.045047808438539505,
0.015848515555262566,
-0.040979623794555664,
0.023753227666020393,
-0.00013664111611433327,
0.012781335040926933,
0.001747957314364612,
0.009238207712769508,
0.0328131727874279,
-0.027282368391752243,
-0.019648374989628792,
0.0006815061205998063,
-0.050092000514268875,
0.03655856102705002,
-0.0012489325599744916,
-0.02678290195763111,
0.016597583889961243,
-0.04795895889401436,
-0.011370356194674969,
0.01199057511985302,
-0.00210101087577641,
0.037273503839969635,
-0.003962476272135973,
-0.001378126791678369,
0.03316987678408623,
0.02227385714650154,
-0.0638047382235527,
-0.025728022679686546,
0.007400769740343094,
0.018624423071742058,
-0.005614571273326874,
-0.030111243948340416,
-0.006142948754131794,
-0.013551801443099976,
-0.05598431080579758,
-0.018062273040413857,
0.07082876563072205,
-0.043777573853731155,
-0.022189833223819733,
0.03287515044212341,
0.013529053889214993,
0.0335569754242897,
-0.03549308702349663,
-0.006543733179569244,
0.008884262293577194,
-0.012639688327908516,
-0.005923544988036156,
0.0021768370643258095,
0.05608942732214928,
-0.006070305127650499,
-0.035944148898124695,
0.009776719845831394,
-0.00773709686473012,
0.017099743708968163,
0.0036046297755092382,
-0.008010203018784523,
0.03249896690249443,
-0.025049526244401932,
-0.0010869833640754223,
-0.03850673884153366,
0.011416211724281311,
-0.01946035400032997,
0.043108340352773666,
-0.030245576053857803,
-0.00941985473036766,
-0.0019093923037871718,
-0.036388881504535675,
0.021999318152666092,
0.005165012553334236,
0.026246214285492897,
0.03246099874377251,
0.0671338215470314,
-0.01752207800745964,
0.012447523884475231,
0.0003941674658562988,
-0.001955221174284816,
0.023045964539051056,
0.02129124291241169,
-0.039734676480293274,
0.0007064678356982768,
0.02054516039788723,
-0.02867485210299492,
-0.018578127026557922,
-0.025990979745984077,
0.04754597693681717,
0.09422152489423752,
-0.02848285622894764,
0.03434563800692558,
0.02876959927380085,
-0.027486132457852364,
-0.0023853301536291838,
-0.03168288990855217,
-0.011009425856173038,
0.0064628589898347855,
0.010000646114349365,
0.0401129312813282,
-0.03696582838892937,
-0.008839313872158527,
0.03717014193534851,
0.05120839551091194,
-0.03450793772935867,
0.027775650843977928,
0.01209060288965702,
0.028276270255446434,
0.001262754900380969,
0.018942566588521004,
-0.018850678578019142,
0.005512458272278309,
0.02807353436946869,
0.04159742593765259,
-0.02706843614578247,
-0.007887644693255424,
0.036652542650699615,
0.023948121815919876,
-0.013089713640511036,
-0.05125182121992111,
0.005053490400314331,
-0.01758219487965107,
0.05184156820178032,
0.04345445707440376,
0.013177266344428062,
-0.002604990266263485,
0.006843374576419592,
0.021714499220252037,
-0.002411757130175829,
-0.005888528656214476,
-0.030829310417175293,
-0.0542316734790802,
-0.019654715433716774,
-0.020025385543704033,
-0.03583674132823944,
0.03757501393556595,
-0.0013538143830373883,
-0.01313685066998005,
0.007293436210602522,
-0.03106902539730072,
0.0415310263633728,
0.007818886078894138,
0.04339790344238281,
-0.00038077880162745714,
0.0955849289894104,
-0.015979228541254997,
-0.0064462474547326565,
-0.005186604335904121,
0.023437894880771637,
0.10805245488882065,
0.040835920721292496,
0.030657103285193443,
-0.04849424213171005,
0.04096323251724243,
-0.0006454313988797367,
-0.01573288068175316,
-0.045416928827762604,
0.020900167524814606,
-0.02795935794711113,
0.009947395883500576,
0.01275964081287384,
0.06979931890964508,
-0.0094158835709095,
0.007643863093107939,
0.029382869601249695,
-0.016409127041697502,
-0.03416316211223602,
-0.04344923049211502,
0.017564743757247925,
-0.017451975494623184,
0.024986080825328827,
0.005179054103791714,
0.05073927342891693,
-0.06488322466611862,
0.013259639032185078,
-0.014256798662245274,
-0.01909734681248665,
-0.02000873163342476,
0.05333610624074936,
-0.07767505943775177,
0.031301554292440414,
0.014231612905859947,
-0.008897194638848305,
-0.04433814063668251,
0.03831237554550171,
0.017055919393897057,
-0.0308295339345932,
0.022552330046892166,
-0.018638238310813904,
-0.03782487288117409,
0.041827619075775146,
0.04209550842642784,
0.020978476852178574,
-0.050174642354249954,
0.010633505880832672,
-0.04091370105743408,
0.04679366573691368,
-0.00955991167575121,
0.002180173760280013,
-0.003442626679316163,
-0.03181514889001846,
-0.025340188294649124,
-0.04777110740542412,
0.01058051735162735,
-0.01364112924784422,
0.024925565347075462,
-0.03327658399939537,
0.011289507150650024,
-0.018192091956734657,
0.020675525069236755,
0.035344112664461136,
0.03349147364497185,
-0.028471289202570915,
0.002570306183770299,
-0.029648713767528534,
0.011619551107287407,
0.054874252527952194,
-0.02378155291080475,
-0.01487743854522705,
-0.006824911572039127,
-0.003495562821626663,
-0.030093641951680183,
-0.04497581720352173,
0.020127736032009125,
0.017579808831214905,
0.04811142757534981,
0.007989592850208282,
-0.03546300530433655,
-0.016763918101787567,
-0.04547115042805672,
0.005341551266610622,
-0.006935812532901764,
0.0014968671603128314,
-0.02124282717704773,
-0.004941408522427082,
0.03079516813158989,
0.010815877467393875,
-0.04600541293621063,
0.03664667531847954,
-0.013297916390001774,
0.01842414401471615,
0.01088694203644991,
0.017071252688765526,
-0.0033436014782637358,
0.027660474181175232,
-0.023799262940883636,
0.00438885111361742,
-0.023895693942904472,
0.027208231389522552,
0.04081791266798973,
0.03570609912276268,
0.015320474281907082,
0.040921375155448914,
-0.0347636379301548,
0.00025930182891897857,
0.0038066054694354534,
-0.023306861519813538,
0.009590030647814274,
0.06661733239889145,
-0.029199542477726936,
-0.051784053444862366,
0.0037717819213867188,
-0.029311195015907288,
-0.025265049189329147,
-0.005217621102929115,
0.04221334680914879,
-0.053266387432813644,
0.0014658750733360648,
-0.03449074551463127,
0.01889137178659439,
-0.02801336906850338,
0.019980356097221375,
-0.0597141869366169,
0.014835599809885025,
0.02307082712650299,
-0.022256571799516678,
-0.02465709112584591,
0.024850904941558838,
-0.06150668114423752,
-0.00669911177828908,
0.02336146868765354,
0.012960744090378284,
-0.008208876475691795,
-0.020625784993171692,
0.046170931309461594,
0.007070485036820173,
0.05229676514863968,
-0.019035635516047478,
-0.02286657691001892,
0.04369974136352539,
-0.008258936926722527,
-0.05075494572520256,
0.03610503301024437,
0.003892851062119007,
0.031435247510671616,
0.021232416853308678,
-0.026442432776093483,
-0.01234192680567503,
0.07662927359342575,
-0.06260713934898376,
0.006721875164657831,
-0.04221431538462639,
-0.02618219517171383,
-0.016206832602620125,
-0.021097738295793533,
-0.0051437565125525,
-0.014100474305450916,
-0.0036409583408385515,
0.06944023817777634,
0.02800973877310753,
-0.012168478220701218,
-0.0037220490630716085,
0.007072906009852886,
-0.012601225636899471,
0.011378318071365356,
0.015241307206451893,
0.039436452090740204,
0.024464480578899384,
0.0443045049905777,
-0.027884995564818382,
0.026869773864746094,
0.014340288005769253,
0.019175872206687927,
-0.08080675452947617,
-0.03527658060193062,
-0.005298334173858166,
0.021548036485910416,
0.058167167007923126,
-0.06697658449411392,
0.030656514689326286,
0.02446836046874523,
-0.06758472323417664,
-0.006434152834117413,
-0.05184545740485191,
-0.07797190546989441,
-0.01765289157629013,
-0.03182812035083771,
0.0018823996651917696,
-0.004217363893985748,
0.025421125814318657,
0.004426067695021629,
0.03937077894806862,
0.013093375600874424,
-0.02601553313434124,
-0.02093389257788658,
-0.02500239759683609,
0.04241658374667168,
-0.012211640365421772,
-0.03308000788092613,
0.05893116816878319,
0.007629518862813711,
-0.027018340304493904,
0.026124997064471245,
-0.036839671432971954,
0.0138390576466918,
0.0015456863911822438,
0.034635480493307114,
-0.0018333100015297532,
0.016163010150194168,
-0.006038781721144915,
-0.01798343099653721,
-0.002185236196964979,
0.016576871275901794,
0.05001211166381836,
0.009736929088830948,
-0.015602482482790947,
-0.00080998579505831,
0.02021019347012043,
-0.03770358860492706,
0.016969256103038788,
0.01131815742701292,
-0.019752081483602524,
-0.029800662770867348,
0.014332414604723454,
-0.001722770044580102,
0.02315658889710903,
-0.028224758803844452,
0.050517961382865906,
-0.07120972871780396,
-0.0022338421549648046,
0.022621886804699898,
-0.012111324816942215,
-0.013430705294013023,
0.012638844549655914,
-0.0004902636865153909,
-0.03496021777391434,
0.01618485525250435,
-0.0024017125833779573,
-0.04195260629057884,
-0.04194779321551323,
-0.025879180058836937,
0.025030208751559258,
-0.03994719311594963,
-0.005088841076940298,
-0.0370844267308712,
-0.018944596871733665,
0.04611630365252495,
0.036733757704496384,
0.019941022619605064,
-0.013405773788690567,
-0.00695256981998682,
-0.05525834113359451,
-0.05295826494693756,
0.017612259835004807,
-0.011915298178792,
-0.0458579882979393,
0.00011321126658003777,
-0.011331424117088318,
-0.015443967655301094,
0.00016971543664112687,
0.040205515921115875,
0.044060952961444855,
0.0022368337959051132,
0.03722717612981796,
-0.004723072052001953,
-0.008990375325083733,
-0.07547879964113235,
0.012609349563717842,
0.0033688063267618418,
-0.0019927506800740957,
0.033718496561050415,
-0.005616957787424326,
-0.0040244460105896,
-0.009111701510846615,
-0.011853447183966637,
0.015832984820008278,
0.0785461962223053,
0.05831889808177948,
0.008230981417000294,
0.005945938173681498,
-0.013480816036462784,
-0.01213745679706335,
0.06747321784496307,
-0.00026109046302735806,
-0.013888396322727203,
0.012354674749076366,
-0.05286487936973572,
-0.05432535707950592,
0.0229524876922369,
-0.010524249635636806,
-0.030843906104564667,
-0.04134169593453407,
-0.009650717489421368,
0.005253977607935667,
-0.025537624955177307,
0.005452630575746298,
0.03701670467853546,
-0.032862745225429535,
-0.003379818983376026,
0.04151370748877525,
0.02588311955332756,
0.037219032645225525,
0.025396712124347687,
0.02776840329170227,
0.040375471115112305,
-0.040141183882951736,
0.034054774791002274,
0.017984390258789062,
0.00691938167437911,
0.024275019764900208,
-0.012332506477832794,
0.014906344935297966,
-0.0415651760995388,
0.00944559182971716,
-0.021750329062342644,
0.037580788135528564,
-0.024075321853160858,
-0.08402880281209946,
-0.023783545941114426,
-0.03752673789858818,
0.038745537400245667,
0.0022261356934905052,
-0.014653974212706089,
0.06941696256399155,
0.0006537058507092297,
-0.0058917272835969925,
-0.024071678519248962,
0.019394025206565857,
-0.004650989081710577,
0.025732560083270073,
0.008631639182567596,
0.04836932569742203,
0.004080537706613541,
-0.013741620816290379,
-0.011941191740334034,
-0.05078495666384697,
0.02070450969040394,
-0.031155893579125404,
0.0000700904056429863,
0.014276313595473766,
0.02320173569023609,
0.003527793101966381,
-0.0254654698073864,
-0.013734204694628716,
-0.021434783935546875,
0.024747872725129128,
0.035534631460905075,
0.03928859904408455,
-0.02287534810602665,
-0.033231861889362335,
-0.030500520020723343,
0.04708341136574745,
-0.06693518906831741,
-0.01679099351167679,
-0.009161711670458317,
0.01560697890818119,
0.014175779186189175,
-0.000369987275917083
] |
<p>The escape velocity of Earth is $v=\sqrt{\frac {2GM}{R}}$, where $M$ is the mass of the Earth and $R$ it's radius (approximating it as a sphere), and is much less than light speed $c$.</p>
<p>But I want to know the escape velocity of black holes. Is it much more than light speed?</p>
| 281 |
[
-0.028635993599891663,
-0.06305138021707535,
-0.006325968075543642,
-0.0474550686776638,
0.023632168769836426,
-0.003650709055364132,
-0.05195600911974907,
-0.046138085424900055,
-0.024628233164548874,
-0.02229239232838154,
0.021051721647381783,
0.05676689371466637,
0.06355249136686325,
0.009114748798310757,
0.0020331540144979954,
0.012080785818397999,
-0.028853563591837883,
0.01787206158041954,
0.007407798897475004,
-0.04181225225329399,
0.007715031038969755,
0.02936241403222084,
0.01942206360399723,
0.013830692507326603,
-0.017368579283356667,
0.020253514871001244,
0.04061312973499298,
0.00639829458668828,
0.02889532968401909,
0.05006052553653717,
0.0043128482066094875,
-0.001542017562314868,
0.027848420664668083,
0.04203430563211441,
0.005285431165248156,
0.01625441014766693,
-0.020741527900099754,
-0.03234080597758293,
-0.014611687511205673,
0.0315222404897213,
-0.03954301029443741,
-0.06648058444261551,
0.011414957232773304,
0.027363229542970657,
-0.007036148104816675,
0.0077178869396448135,
0.011692438274621964,
-0.045374393463134766,
0.0467977300286293,
-0.057761307805776596,
0.05650067701935768,
-0.011439136229455471,
0.034967340528964996,
0.004362065810710192,
0.002138629788532853,
0.015508853830397129,
0.09803251177072525,
0.06030799075961113,
-0.04448828101158142,
-0.03209199011325836,
-0.011286450549960136,
-0.010807521641254425,
-0.000496510649099946,
-0.01802668161690235,
-0.005382775329053402,
0.05662428215146065,
-0.030569525435566902,
-0.020616985857486725,
0.021081140264868736,
0.010312744416296482,
0.0007621516124345362,
0.011568652465939522,
0.005829754751175642,
0.016174975782632828,
-0.008645734749734402,
-0.047210101038217545,
-0.015586825087666512,
0.0063306959345936775,
0.020360136404633522,
0.07236973941326141,
-0.026696039363741875,
0.013158444315195084,
0.062279488891363144,
0.012103840708732605,
-0.006925888825207949,
0.046538591384887695,
0.07811222225427628,
0.014810650609433651,
0.0046867504715919495,
0.0160210058093071,
-0.00874700304120779,
-0.022047175094485283,
-0.0019311810610815883,
-0.03482932224869728,
-0.019464775919914246,
0.022764606401324272,
0.0032639421988278627,
0.05394289270043373,
0.0016761402366682887,
-0.043148960918188095,
-0.013441667892038822,
0.0000446944213763345,
0.013210885226726532,
0.07065530121326447,
0.053763497620821,
-0.025243761017918587,
-0.0680205449461937,
0.004926642403006554,
-0.03787553682923317,
-0.02268592081964016,
-0.03236522153019905,
0.014173316769301891,
-0.007966235280036926,
-0.04479273408651352,
0.01421215757727623,
-0.016515791416168213,
-0.009726849384605885,
-0.02241666615009308,
0.05504937842488289,
0.0575079508125782,
0.02751154452562332,
-0.005409850273281336,
0.017871418967843056,
-0.02739729918539524,
-0.04180346056818962,
0.017671456560492516,
0.046759236603975296,
-0.019350282847881317,
-0.031594518572092056,
0.01599656417965889,
-0.009295723401010036,
-0.02471676655113697,
-0.008710144087672234,
-0.010123899206519127,
0.03600076213479042,
-0.03274596109986305,
-0.10562457144260406,
-0.0655132606625557,
0.03082822635769844,
-0.016085494309663773,
-0.006639091297984123,
-0.05729956179857254,
0.026138702407479286,
0.027964022010564804,
0.08164537698030472,
0.011721335351467133,
0.003632636507973075,
-0.010957335121929646,
0.011060567572712898,
-0.012532327324151993,
-0.023826822638511658,
0.0038011318538337946,
0.012889211997389793,
-0.019810577854514122,
0.049734052270650864,
-0.06901876628398895,
-0.002127583371475339,
0.03548124432563782,
0.0034551373682916164,
-0.02850204147398472,
0.07055265456438065,
-0.036218732595443726,
0.0058160340413451195,
0.008646078407764435,
0.003757656319066882,
-0.007602934259921312,
0.08411841839551926,
0.02150863967835903,
-0.015591942705214024,
0.0398518405854702,
0.017849452793598175,
0.03265789523720741,
0.04934085160493851,
0.0028279589023441076,
0.032449640333652496,
-0.03180903196334839,
-0.007645956240594387,
-0.025220362469553947,
0.006788111757487059,
0.0064500467851758,
-0.03997498005628586,
-0.04349512979388237,
0.003984331153333187,
-0.008958172053098679,
0.015923621132969856,
0.04350381717085838,
-0.022811900824308395,
-0.022920845076441765,
-0.028954941779375076,
-0.025083526968955994,
-0.01175426784902811,
-0.06371591240167618,
0.0457276925444603,
0.03644239157438278,
0.01135676447302103,
-0.013153347186744213,
0.022350264713168144,
0.039615727961063385,
-0.029722411185503006,
0.017180299386382103,
0.008400935679674149,
0.07760367542505264,
-0.033202964812517166,
-0.02440263330936432,
-0.0017423572717234492,
0.056888747960329056,
0.04357229918241501,
-0.02096521481871605,
0.012284155935049057,
0.02339775674045086,
-0.029041172936558723,
-0.013596724718809128,
-0.011910203844308853,
-0.0021765248384326696,
-0.025069860741496086,
0.0029370952397584915,
0.02436990849673748,
0.006943135056644678,
0.027777863666415215,
0.04538559913635254,
-0.001117974636144936,
0.0748455673456192,
0.029207350686192513,
0.03826563060283661,
-0.006770179606974125,
0.02168171852827072,
0.017612271010875702,
-0.008792939595878124,
0.0025523214135318995,
0.000044568841985892504,
-0.025409508496522903,
0.010830962099134922,
0.03338988870382309,
0.018387602642178535,
-0.053559061139822006,
0.012035274878144264,
0.051979053765535355,
0.036713313311338425,
0.02235044725239277,
0.03625958785414696,
-0.032937806099653244,
-0.044672273099422455,
0.013042108155786991,
-0.006230623461306095,
0.017289413139224052,
0.015549329109489918,
0.043812017887830734,
0.01751399226486683,
-0.008953954093158245,
-0.02819894626736641,
0.0015969284577295184,
0.01817356050014496,
-0.015910780057311058,
-0.007431349251419306,
0.006789044011384249,
-0.030179988592863083,
0.00027690193383023143,
-0.024910278618335724,
0.0026132846251130104,
0.012989016249775887,
0.009928088635206223,
0.02529129758477211,
-0.05331915244460106,
0.00003209057103958912,
0.03059796802699566,
-0.0010570886079221964,
-0.0017599444836378098,
-0.024873849004507065,
0.018764277920126915,
-0.07436468452215195,
0.01823980174958706,
-0.0313960462808609,
-0.002767335157841444,
-0.02699601650238037,
0.024443574249744415,
0.0019652422051876783,
0.020715370774269104,
0.03292490914463997,
-0.0061300466768443584,
-0.058474957942962646,
0.027071144431829453,
-0.034168824553489685,
-0.019421515986323357,
0.005703166592866182,
-0.02564743533730507,
0.039805810898542404,
-0.0383555069565773,
-0.05104340612888336,
0.07218141853809357,
-0.021388862282037735,
0.02226731739938259,
0.04398937523365021,
-0.01601875014603138,
-0.02845994010567665,
0.03265588730573654,
-0.0070772236213088036,
0.005857131443917751,
-0.017999829724431038,
0.009709120728075504,
0.03952391445636749,
-0.013449366204440594,
-0.029470399022102356,
0.008984970860183239,
-0.02739238366484642,
-0.048055052757263184,
-0.009008977562189102,
0.019709080457687378,
0.014238317497074604,
-0.030576443299651146,
-0.006037131883203983,
0.021707233041524887,
-0.06393969058990479,
0.015150601044297218,
-0.03319865092635155,
-0.028830774128437042,
0.034714650362730026,
0.0012216375907883048,
0.018920473754405975,
-0.006600725464522839,
-0.04656081646680832,
0.06832795590162277,
0.02902267873287201,
0.0029144908767193556,
-0.02999802865087986,
-0.01993706077337265,
0.004549073986709118,
-0.011732276529073715,
-0.011964749544858932,
0.02490536868572235,
-0.0015569457318633795,
-0.0388617217540741,
0.03058398887515068,
0.03875090926885605,
0.01606622524559498,
-0.022677579894661903,
0.015326017513871193,
-0.0009497547871433198,
-0.00930052250623703,
-0.008388266898691654,
0.041678328067064285,
0.0010412621777504683,
-0.03853633254766464,
0.034724779427051544,
0.00998416543006897,
0.05207730829715729,
0.020431775599718094,
-0.05089905485510826,
0.049294695258140564,
-0.010651947930455208,
0.016875727102160454,
-0.008590235374867916,
0.018805090337991714,
0.008181100711226463,
-0.01838771067559719,
0.026201417669653893,
-0.010083319619297981,
0.06442876905202866,
0.014722881838679314,
-0.0041430070996284485,
-0.006948156747967005,
0.05416805297136307,
-0.027745917439460754,
-0.007093041203916073,
-0.0351138673722744,
-0.012941033579409122,
0.022414755076169968,
-0.0003344691649544984,
-0.019350916147232056,
0.031131569296121597,
0.03302232548594475,
-0.018030716106295586,
-0.006669491529464722,
-0.009023723192512989,
-0.001668846351094544,
-0.088605597615242,
-0.02077137492597103,
-0.0004906356916762888,
0.035168156027793884,
0.00412965239956975,
0.038605839014053345,
0.013971379958093166,
0.008300296030938625,
0.026501614600419998,
-0.013148208148777485,
-0.08924435824155807,
-0.0010307139018550515,
-0.06609755754470825,
-0.03612430393695831,
-0.014734611846506596,
-0.0285862497985363,
-0.029295647516846657,
0.0018168364185839891,
0.0006705446867272258,
-0.004589594900608063,
-0.00014141130668576807,
-0.05795297771692276,
0.017591483891010284,
-0.020924951881170273,
-0.008379515260457993,
0.0016326960176229477,
0.060168955475091934,
0.019892994314432144,
0.0002401993697276339,
-0.0030198481399565935,
0.042315758764743805,
-0.04664890095591545,
-0.006910756696015596,
0.018527794629335403,
-0.0032584993168711662,
-0.006030370481312275,
0.025705179199576378,
0.023678313940763474,
-0.027111083269119263,
-0.01612706296145916,
-0.019502388313412666,
0.03228504955768585,
0.01977613754570484,
-0.005080055445432663,
-0.00652733538299799,
-0.04284143075346947,
-0.06401420384645462,
-0.010553083382546902,
-0.009673146530985832,
0.053359441459178925,
-0.029823392629623413,
-0.00336993089877069,
0.03646088019013405,
-0.006980347912758589,
-0.015266014263033867,
0.0219272430986166,
0.03348732367157936,
-0.021626746281981468,
-0.029333293437957764,
-0.0545932911336422,
-0.05860117822885513,
-0.03399261459708214,
-0.012358571402728558,
0.007868635468184948,
0.010861887596547604,
-0.0538259856402874,
-0.0003222631348762661,
0.020690372213721275,
0.004392439033836126,
-0.04714266210794449,
-0.038235124200582504,
0.02019922249019146,
0.03509273752570152,
-0.03034481219947338,
0.013761330395936966,
0.009267440065741539,
0.044259533286094666,
0.02853766642510891,
-0.005907868500798941,
0.004968571476638317,
-0.05120512843132019,
-0.01976984366774559,
0.02470715343952179,
0.04817298799753189,
0.01693965680897236,
-0.022235626354813576,
-0.07827439904212952,
0.03228587284684181,
0.04354768246412277,
0.0011629724176600575,
0.007091299630701542,
0.011735904030501842,
0.0013568623689934611,
0.003214634023606777,
-0.02648172900080681,
0.011572112329304218,
0.025733329355716705,
0.009340628050267696,
-0.005913206841796637,
-0.03109053522348404,
0.04651837795972824,
-0.0003812015347648412,
0.021842248737812042,
0.028465772047638893,
0.07033094763755798,
0.020600920543074608,
0.017741229385137558,
0.0023306705988943577,
-0.010545340366661549,
-0.022184280678629875,
-0.062856525182724,
-0.01548426877707243,
0.000267017021542415,
-0.03642508015036583,
0.020199675112962723,
-0.039227139204740524,
-0.041566167026758194,
0.028903594240546227,
0.009690645150840282,
-0.00870550237596035,
0.004359120037406683,
-0.05888522043824196,
-0.015407980419695377,
0.00924832746386528,
0.005221090745180845,
0.04356680065393448,
-0.0036435755901038647,
0.007285318337380886,
0.0018432533834129572,
-0.027088476344943047,
0.049470093101263046,
-0.06509397178888321,
-0.04909439757466316,
0.005443126894533634,
-0.004569364245980978,
-0.05865960940718651,
0.057728126645088196,
-0.008244721218943596,
0.030132092535495758,
-0.0035024876706302166,
-0.0358940064907074,
-0.013892783783376217,
0.02649834007024765,
0.04443763941526413,
0.023935357108712196,
0.018373236060142517,
0.003451400902122259,
0.011621059849858284,
-0.0163726843893528,
0.005442502908408642,
0.0209709033370018,
0.011980668641626835,
0.044724296778440475,
-0.005726945586502552,
-0.008322770707309246,
-0.02263307385146618,
-0.008496862836182117,
0.023700186982750893,
-0.04533519595861435,
0.05049245059490204,
-0.00763222249224782,
-0.02845764346420765,
0.020372025668621063,
-0.04704546555876732,
-0.005875558126717806,
-0.0005923574790358543,
0.00920417346060276,
0.023953091353178024,
-0.08378838747739792,
0.04494677111506462,
0.04538041353225708,
0.02880372665822506,
-0.09240454435348511,
-0.022797226905822754,
0.056810569018125534,
0.014149119146168232,
-0.01608871854841709,
-0.011537699028849602,
0.02238948456943035,
-0.05358890816569328,
-0.029634889215230942,
-0.02725738100707531,
0.04820782318711281,
-0.013190285302698612,
0.008801866322755814,
-0.025164354592561722,
0.02252878062427044,
0.020489247515797615,
0.013946541585028172,
-0.024734988808631897,
0.012078531086444855,
0.015313700772821903,
0.004684960935264826,
-0.009573247283697128,
0.056670017540454865,
-0.01590530015528202,
-0.0414377897977829,
-0.03770092874765396,
-0.03682682663202286,
-0.013827856630086899,
-0.010997416451573372,
0.022319236770272255,
0.04988556355237961,
0.01271749846637249,
-0.0052993763238191605,
-0.010802443139255047,
0.03765629976987839,
-0.021782660856842995,
0.024295669049024582,
-0.027427759021520615,
-0.003876845818012953,
-0.024617614224553108,
-0.025109238922595978,
0.024150829762220383,
0.02833111584186554,
0.008985023014247417,
-0.028357993811368942,
0.04154425114393234,
0.01661437563598156,
-0.03751777112483978,
-0.018077997490763664,
-0.02519054524600506,
0.017050152644515038,
0.014013692736625671,
-0.01922518201172352,
0.028732435777783394,
0.008638604544103146,
-0.01697443053126335,
-0.016307516023516655,
-0.027035662904381752,
-0.010023259557783604,
0.08007661998271942,
-0.0006331822369247675,
0.03189455345273018,
0.026765309274196625,
0.0021557193249464035,
-0.0038550368044525385,
-0.05972133204340935,
0.005734535399824381,
0.0339076928794384,
0.010691271163523197,
0.012369710952043533,
-0.0008329725824296474,
-0.00018934006220661104,
0.042519453912973404,
0.02974536642432213,
-0.01947210542857647,
0.02151551842689514,
0.0013759250286966562,
0.006484969984740019,
-0.020402858033776283,
-0.009879041463136673,
-0.01920994184911251,
0.038673073053359985,
-0.03609129413962364,
0.040018871426582336,
-0.014074502512812614,
0.007079015020281076,
0.039025627076625824,
-0.005615453701466322,
0.03732248768210411,
-0.010868237353861332,
-0.027955835685133934,
-0.04267304390668869,
0.00108700233977288,
0.006535383407026529,
-0.01183945033699274,
-0.0015338105149567127,
0.010392841883003712,
0.0203836839646101,
-0.006296358536928892,
0.02070423774421215,
0.000592484197113663,
-0.07463055849075317,
-0.05744839832186699,
-0.033792514353990555,
-0.06360026448965073,
0.03483836352825165,
0.04321693629026413,
-0.02496475540101528,
0.015923412516713142,
-0.039604999125003815,
0.015201996080577374,
-0.010038337670266628,
0.06490827351808548,
-0.021082790568470955,
0.09203744679689407,
-0.009170129895210266,
-0.031060153618454933,
-0.011166705749928951,
0.0012526254868134856,
0.09243297576904297,
0.05216610059142113,
0.03217445686459541,
-0.07086091488599777,
-0.0003227780107408762,
-0.037338707596063614,
0.018195364624261856,
-0.053139738738536835,
0.0158708319067955,
-0.020335668697953224,
-0.011880007572472095,
0.03170672804117203,
0.054274771362543106,
-0.010157479904592037,
-0.06327947229146957,
0.03366773948073387,
0.007784026209264994,
-0.005602205637842417,
0.005758196115493774,
0.04075826704502106,
0.005764595698565245,
0.01472869236022234,
-0.005177844315767288,
0.024715598672628403,
-0.012922282330691814,
-0.021973328664898872,
-0.04655103385448456,
-0.025702673941850662,
-0.0011161084985360503,
-0.04036303982138634,
-0.03732028231024742,
-0.021143365651369095,
0.013676885515451431,
-0.029943251982331276,
-0.006715558934956789,
0.032503075897693634,
0.024223370477557182,
-0.012964269146323204,
-0.016966985538601875,
0.06484483927488327,
-0.008759500458836555,
0.025751633569598198,
0.012567542493343353,
0.015259572304785252,
-0.06671655178070068,
0.005199817940592766,
-0.003437365172430873,
0.02969621866941452,
-0.02152192033827305,
0.03249645605683327,
0.02224631793797016,
0.029794316738843918,
0.011953078210353851,
-0.051200058311223984,
0.003798295743763447,
-0.013161452487111092,
0.013586004264652729,
0.014304423704743385,
-0.019420448690652847,
-0.028646282851696014,
0.009148649871349335,
0.008561228401958942,
0.029705477878451347,
-0.008533325977623463,
-0.011978940106928349,
0.01860162429511547,
-0.015864606946706772,
0.027963213622570038,
-0.0548761747777462,
0.0002867291041184217,
-0.005158775486052036,
0.012299044989049435,
-0.04765491187572479,
-0.001848173444159329,
0.024021459743380547,
0.029235856607556343,
-0.0040379478596150875,
0.020056936889886856,
0.012393227778375149,
-0.01578695885837078,
-0.07971862703561783,
0.023875650018453598,
-0.019077057018876076,
-0.04065987095236778,
-0.03551904112100601,
-0.011567098088562489,
0.02866232395172119,
0.020648283883929253,
-0.02390589378774166,
0.028372177854180336,
-0.02529425173997879,
0.031877633184194565,
0.008046972565352917,
-0.016880789771676064,
0.03190026804804802,
-0.00448570167645812,
-0.01109001599252224,
0.005647123325616121,
-0.013007808476686478,
0.038550980389118195,
0.056821320205926895,
0.011567886918783188,
0.026667000725865364,
0.006611193064600229,
-0.022511500865221024,
0.012449818663299084,
0.00923239067196846,
-0.03870589658617973,
0.00497061014175415,
0.01525670476257801,
0.026973962783813477,
-0.004963595885783434,
-0.03210316225886345,
-0.03624008968472481,
-0.03402908518910408,
-0.01813732646405697,
0.026600560173392296,
-0.023874567821621895,
0.034721627831459045,
-0.011339995078742504,
-0.012825755402445793,
-0.057246673852205276,
0.014436542987823486,
-0.020204614847898483,
0.02927052043378353,
0.015149700455367565,
-0.03949545696377754,
-0.006852432154119015,
0.01147611066699028,
-0.025286594405770302,
0.002214391017332673,
0.012587619945406914,
0.02948050945997238,
-0.006097144912928343,
0.01601862721145153,
0.03994611278176308,
-0.03491109609603882,
0.056643709540367126,
-0.008794157765805721,
-0.023455115035176277,
0.018663588911294937,
-0.03928574547171593,
-0.04547860845923424,
0.07395186275243759,
-0.009922964498400688,
0.047089699655771255,
0.02599455416202545,
-0.014063111506402493,
-0.022124672308564186,
0.07013953477144241,
-0.031172970309853554,
-0.0273779034614563,
0.013372247107326984,
0.0003949688107240945,
-0.02871578373014927,
0.009151876904070377,
0.04172215610742569,
-0.05603085085749626,
-0.003264680737629533,
0.019353069365024567,
-0.028384139761328697,
-0.022923540323972702,
0.03040974587202072,
0.005305050406605005,
0.003863988909870386,
0.008410044014453888,
0.001975119346752763,
0.005045745987445116,
0.04012008756399155,
0.05252500995993614,
0.002479827031493187,
0.0725570023059845,
0.0350174754858017,
0.017261074855923653,
-0.11970517039299011,
-0.0011505766306072474,
-0.007507713045924902,
0.05076522380113602,
0.051591791212558746,
-0.07931125164031982,
0.039761077612638474,
0.017974188551306725,
-0.0715244933962822,
0.02418331243097782,
-0.04980063810944557,
-0.006770417559891939,
-0.02846621163189411,
-0.007756033446639776,
0.016972867771983147,
0.049549248069524765,
0.05488530546426773,
0.03640393540263176,
0.01403452455997467,
-0.0031542442739009857,
-0.043864134699106216,
-0.02493220940232277,
-0.004045894835144281,
0.011949561536312103,
-0.009031441994011402,
-0.023584000766277313,
0.057576753199100494,
0.0017650896916165948,
-0.018994828686118126,
0.023846661671996117,
0.03427696228027344,
0.021461518481373787,
0.0077091241255402565,
0.009105559438467026,
0.029385140165686607,
0.004556446336209774,
0.03534414619207382,
-0.04021153971552849,
-0.03405328094959259,
0.015198939479887486,
-0.013579662889242172,
0.01934068277478218,
-0.03425610437989235,
-0.007120722439140081,
0.0024419929832220078,
-0.038189779967069626,
-0.015331383794546127,
0.007787022739648819,
-0.021350238472223282,
-0.03530208766460419,
0.0055427043698728085,
0.00514636468142271,
0.009845622815191746,
-0.048185672610998154,
0.01433655433356762,
-0.06008721515536308,
-0.011961114592850208,
0.024834705516695976,
0.002771425526589155,
0.000032344363717129454,
0.018597669899463654,
0.007943803444504738,
-0.014232419431209564,
-0.0075418404303491116,
-0.01564165949821472,
0.01784505508840084,
-0.03422514721751213,
0.008275519125163555,
-0.008599595166742802,
-0.016382630914449692,
0.022614574059844017,
-0.056858692318201065,
0.006819600239396095,
0.042013995349407196,
0.00251829344779253,
0.02191365882754326,
0.009628238156437874,
-0.01971535012125969,
-0.029837438836693764,
-0.04842482879757881,
-0.011877523735165596,
-0.014732127077877522,
0.025532811880111694,
-0.045734427869319916,
-0.022114135324954987,
0.027549000456929207,
-0.015440130606293678,
0.07279158383607864,
-0.008417004719376564,
-0.007853488437831402,
0.04198828339576721,
0.0035607055760920048,
0.0017269519157707691,
-0.06412453949451447,
0.0001942650560522452,
-0.011505544185638428,
-0.05965178459882736,
0.0011074045905843377,
0.012664757668972015,
0.012695698998868465,
0.040171366184949875,
0.016160061582922935,
-0.009788857772946358,
0.041110847145318985,
0.015913182869553566,
-0.009657270275056362,
0.04501480236649513,
0.02185559645295143,
0.007539856247603893,
0.07967062294483185,
0.016275444999337196,
0.01891014724969864,
0.05424252152442932,
-0.022008994594216347,
-0.015298914164304733,
0.0454464815557003,
0.02137279137969017,
-0.02327609993517399,
0.005738877225667238,
-0.021435344591736794,
-0.01368928886950016,
-0.0686110183596611,
-0.02644677460193634,
0.05924874544143677,
-0.021411186084151268,
-0.022001609206199646,
0.0492066815495491,
0.0245460607111454,
0.04778842628002167,
-0.02237299084663391,
0.020152870565652847,
0.00832835491746664,
-0.001762785017490387,
-0.01711520552635193,
0.030638016760349274,
0.026225341483950615,
-0.024938177317380905,
0.025838853791356087,
0.024103136733174324,
-0.000998894334770739,
0.022643113508820534,
0.015529015101492405,
0.05802842974662781,
-0.0459577850997448,
-0.028222378343343735,
-0.009581075049936771,
-0.013094646856188774,
0.03764237090945244,
0.014641226269304752,
-0.06841521710157394,
0.06510331481695175,
-0.014499396085739136,
0.00020243666949681938,
0.0022244916763156652,
-0.008991687558591366,
-0.027977313846349716,
0.03843769431114197,
0.008404913358390331,
0.045966070145368576,
0.012315908446907997,
-0.016537047922611237,
0.008360791951417923,
-0.009960525669157505,
0.0294814333319664,
-0.02831254154443741,
0.016930563375353813,
-0.002085380721837282,
-0.003024527570232749,
-0.010794821195304394,
-0.02922283485531807,
-0.023809311911463737,
-0.008540770038962364,
0.031965430825948715,
0.015522874891757965,
0.01453397050499916,
0.0017166618490591645,
-0.012065952643752098,
0.01296665333211422,
0.04953838512301445,
-0.07761550694704056,
-0.007583092898130417,
-0.03192371129989624,
0.026028767228126526,
-0.02569178305566311,
-0.017147965729236603
] |
<p>First, I would like to apology for my lousy English used here, as being a non-native english speaker, </p>
<p>I am currently using Classical Mechanics as a tool to learn how to construct a theory as an end. Therefore, I have a few questions, and a few reasonings behind them (I only consider reality, not imagined world), and I would like your suggestions or corrections :D </p>
<p>To make things simple, I first consider when mass is a constant, so F=dp/dt can be written as F=ma.</p>
<p>Why F=ma? Instead of, say, I define new constants or variables, and claim</p>
<p>1.) $I=N \frac{d^3x}{dt^3} $ ? </p>
<p>Or using the same F both literally and physically, and claim
2.) $F=N(x,\dot x,\ddot x,...x^{(n)};t) \frac{d^3x}{dt^3} $ or </p>
<p>3.) $F=Q \frac{dx}{dt} $?</p>
<p>I mean, force is not something that you can touch nor see, either is mass;
so, we pretty much define them via indirect observations, recording the data, and then comparing with other objects, in order to give operational definitions on mass and force (in case of "mass", we will have to define a unit mass first, and then use F= ma as operational definition for mass.). </p>
<p>Under this line of reasoning,
So why can't we work things in a simple way - $I=Q \dot x $? Yes, we can indeed. </p>
<p>for question 1.) given reality: A falling object a=g:</p>
<p>$I=Q \frac{dx}{dt}$</p>
<p>$\dot x=gt$ </p>
<p>$I=t$</p>
<p>$Q=1/g$</p>
<p>So if I define such way $I=Q \dot x $, it is just the law of falling.
So my answer to my 1st question is:
Yes, we can define things such way, but it has nothing to do with the subject we are dealing right now - inertia. Lesson learned: Know what you want to deal with.</p>
<p>For question 2.) $F=N(x,\dot x,\ddot x,...x^{(n)};t) \frac{d^3x}{dt^3} $</p>
<p>Since I only consider our reality, that means F=ma is truth.
So I will comparing F=Na' with F=ma with a few cases (constant a, and SHM)
And it turns out that F=Na' is far more complicated (often a variable) and N is going to be ill defined given constant a.</p>
<p>Reality: A falling object a=g:</p>
<p>$F=N\dot a=0
=>N\dot a=mg
=>N=mg/\dot a$.</p>
<p>as $\dot a=0$, N(x,t) is ill defined.</p>
<p>Reality: SHM:</p>
<p>$ m\ddot x=-Ax
=>\dddot x= -A\dot x/m
$.
Given
$ Na'=ma
=> N= ma/a'=-m^2\ddot x/\dot x A=(-m^2/A)(d\dot x/dx)
$</p>
<p>Too complicated. (comparing with the fact that m is just a constant.)</p>
<p>Lesson learned:
1.) best work for most of the cases. 2.)When a constant will do, don't use a function. 3.)Theory is about productivity.</p>
<p>For question 3.) $F=Q \frac{dx}{dt} $
or any other orders,
actually, I am just asking: </p>
<p>for $ F= \frac {d^nR(W,\dot W,...,W^{(n)},x,\dot x,...,x^{(n)};t)}{dt^n}= \frac {dP(m,\dot m,x,\dot x;t)}{dt}
$</p>
<p>4.) is there exist a n, such that there exist a R makes things simpler than $F=\dot P$ ? Define $R(W,x;t)=W(x,\dot x,\ddot x,...x^{(n)};t) x$, (R, W new variables, x is position function of time)</p>
<p>if there doesn't exist such an n, then
5.) why F= ma turns out to be the simplest way to work things out?</p>
<p>And thanks for your reading. Please give me some criticisms to my reasonings. </p>
<p>p.s.
I think I am making the reinvent wheel mistake.
I hope these fancy mathematical philosophy will end up some educational purpose on physics. </p>
| 8,496 |
[
-0.02548258751630783,
0.047317251563072205,
-0.005742543376982212,
-0.04943496361374855,
0.030418679118156433,
-0.007538578473031521,
-0.06199295446276665,
-0.02041732147336006,
-0.0016817585565149784,
0.0023351421114057302,
0.01276451162993908,
0.012093348428606987,
0.04906676709651947,
0.0055101970210671425,
-0.004081816412508488,
0.02774619683623314,
-0.03202531114220619,
-0.029531605541706085,
0.00684450613334775,
-0.05043153837323189,
0.01180316787213087,
0.035498663783073425,
0.009860350750386715,
-0.0024378662928938866,
0.021648168563842773,
0.006635930389165878,
0.019871963188052177,
-0.01512208767235279,
-0.00041906177648343146,
0.02617509849369526,
0.0261071790009737,
-0.00944528728723526,
0.003947840072214603,
0.012250653468072414,
0.01196969859302044,
0.05249575152993202,
-0.026255611330270767,
-0.0015863955486565828,
0.007402592804282904,
0.03829646855592728,
-0.020161166787147522,
0.009867125190794468,
-0.017235394567251205,
0.013332972303032875,
-0.003779197111725807,
0.0502728633582592,
0.03284596651792526,
-0.0399458073079586,
0.03447232022881508,
-0.049754563719034195,
0.07009940594434738,
0.01725752465426922,
0.03256181627511978,
0.0427846685051918,
-0.04533708468079567,
-0.03582200035452843,
0.07180655747652054,
0.057087864726781845,
-0.02250738814473152,
-0.07329203188419342,
-0.029330626130104065,
0.0012464444153010845,
0.010339119471609592,
-0.022867979481816292,
0.00963836070150137,
0.05152205750346184,
-0.017027471214532852,
0.005490883253514767,
0.0017425189726054668,
-0.0603293851017952,
0.029774697497487068,
0.006658975966274738,
0.007522454485297203,
0.01662701554596424,
-0.026158500462770462,
-0.01658327504992485,
0.0089358389377594,
-0.020088447257876396,
0.06784507632255554,
0.030673295259475708,
-0.009950595907866955,
0.0009669415885582566,
0.05029578134417534,
0.027436867356300354,
0.018787598237395287,
-0.01284123957157135,
0.07131199538707733,
0.014993501827120781,
0.015454488806426525,
0.029764866456389427,
-0.0421324260532856,
0.010437767021358013,
0.021774183958768845,
-0.025923535227775574,
0.009811772964894772,
0.010038251988589764,
0.00936066173017025,
0.020461753010749817,
-0.0015494613908231258,
-0.011529459618031979,
-0.03140263259410858,
-0.027019359171390533,
-0.009170621633529663,
0.060435906052589417,
0.013368863612413406,
-0.02081051468849182,
-0.023360956460237503,
0.008275726810097694,
-0.0013638777891173959,
-0.003911333158612251,
-0.025006746873259544,
0.009177513420581818,
-0.0027051838114857674,
0.014078657142817974,
0.000023800041162758134,
0.001357154338620603,
0.020716365426778793,
-0.025632502511143684,
0.06276924163103104,
0.05901258811354637,
0.016001924872398376,
-0.04314921051263809,
0.033145468682050705,
-0.02344435825943947,
-0.02609027922153473,
0.003081457456573844,
0.03877752274274826,
0.014683250337839127,
0.0014934474602341652,
-0.0017469206359237432,
0.005970826372504234,
-0.023834271356463432,
-0.003465689020231366,
0.016690462827682495,
0.01691916584968567,
-0.033676184713840485,
-0.11098842322826385,
-0.06122582033276558,
0.036402132362127304,
0.017210466787219048,
-0.028425900265574455,
-0.10306551307439804,
-0.01970226876437664,
0.04024511203169823,
0.04354612156748772,
0.026101533323526382,
-0.04072502255439758,
0.017718156799674034,
0.03792493790388107,
-0.0006882665329612792,
-0.004870730917900801,
-0.003211909905076027,
-0.00412672059610486,
-0.059770144522190094,
-0.004982016980648041,
-0.00963832437992096,
0.04754986986517906,
0.03078126162290573,
-0.007837140932679176,
-0.01592055708169937,
0.08827190846204758,
-0.034988485276699066,
0.002095842035487294,
0.05740688368678093,
-0.005133607424795628,
-0.0435788631439209,
0.034795794636011124,
0.013934185728430748,
0.0168518777936697,
0.030836312100291252,
0.028514692559838295,
0.046929363161325455,
-0.002441400894895196,
0.019683025777339935,
0.01739039458334446,
-0.07198494672775269,
-0.01999518647789955,
-0.044799841940402985,
-0.008663118816912174,
0.013730990700423717,
-0.03783315047621727,
-0.03233478590846062,
-0.019174497574567795,
-0.03426516056060791,
-0.011230415664613247,
0.03726743161678314,
-0.007892047986388206,
0.06495527923107147,
0.027255592867732048,
-0.020470134913921356,
-0.03269007429480553,
-0.055034711956977844,
0.044711049646139145,
-0.02430182695388794,
-0.001071814214810729,
-0.03199780732393265,
0.014790921472012997,
-0.0007513558957725763,
-0.004851801320910454,
-0.002644775900989771,
0.026229914277791977,
0.037100113928318024,
0.03607112169265747,
-0.017932601273059845,
0.029740165919065475,
0.05145816132426262,
0.011215988546609879,
0.012765880674123764,
-0.020013725385069847,
-0.0006751006585545838,
0.013369103893637657,
0.01277427189052105,
-0.02717057801783085,
0.025127673521637917,
-0.0099120968952775,
0.0014522820711135864,
0.0421295091509819,
-0.03617310896515846,
-0.038200292736291885,
0.04998968541622162,
-0.04313952103257179,
0.09153909236192703,
0.04651757702231407,
-0.01906418986618519,
0.008237754926085472,
0.04556486755609512,
-0.009688588790595531,
0.02446974813938141,
-0.013067995198071003,
-0.012923718430101871,
-0.05212967097759247,
-0.017950521782040596,
0.005220030900090933,
0.02482680417597294,
-0.01501783262938261,
0.030489813536405563,
0.0342228040099144,
-0.004354503937065601,
0.022514747455716133,
0.005437537562102079,
0.00332835060544312,
-0.049725454300642014,
0.01526105310767889,
0.017242297530174255,
0.0021180843468755484,
0.024546587839722633,
0.01023896224796772,
0.02026784047484398,
-0.004592711105942726,
-0.03748050332069397,
0.03752876818180084,
0.049126036465168,
-0.004501580726355314,
0.018415549769997597,
0.05255967006087303,
-0.01173605676740408,
0.04955427721142769,
-0.03777505084872246,
-0.004866643808782101,
0.03390577435493469,
-0.02870061621069908,
-0.020918577909469604,
-0.02222839556634426,
-0.005790051072835922,
0.015113911591470242,
0.01342888455837965,
-0.011546862311661243,
-0.033530399203300476,
0.021156542003154755,
-0.03019174560904503,
-0.014438574202358723,
-0.024041658267378807,
0.0008547879406251013,
-0.0007359987939707935,
-0.007700699381530285,
-0.011711891740560532,
0.03538462892174721,
0.056743960827589035,
-0.05801721662282944,
0.002221112372353673,
0.04187435284256935,
-0.0488373301923275,
0.004209537524729967,
0.019350552931427956,
-0.04102504253387451,
-0.008505423553287983,
-0.06139887869358063,
-0.05075474828481674,
0.04717263579368591,
-0.03293135017156601,
0.01617887057363987,
0.01695728302001953,
-0.012068737298250198,
-0.04587385803461075,
-0.011682355776429176,
-0.0440441332757473,
-0.01054868008941412,
-0.02366754412651062,
-0.011242981068789959,
0.04393494501709938,
0.001726732007227838,
-0.04475808143615723,
0.016044117510318756,
-0.024859022349119186,
-0.06133272126317024,
-0.035273753106594086,
0.003712241305038333,
0.008262567222118378,
-0.0029348176904022694,
0.0002925473090726882,
0.025968370959162712,
-0.03557145223021507,
0.019538642838597298,
-0.04914498329162598,
-0.04530688747763634,
0.016420312225818634,
0.00611915672197938,
0.06985960155725479,
0.040284208953380585,
-0.03152787685394287,
0.06420940160751343,
0.03542834892868996,
-0.03909081593155861,
-0.01181510929018259,
-0.015644898638129234,
0.004791158717125654,
-0.028176702558994293,
0.009956356137990952,
0.020029602572321892,
-0.03615809977054596,
-0.006211703643202782,
0.002078804187476635,
0.007927254773676395,
0.001387429772876203,
0.017914123833179474,
-0.011884848587214947,
0.023546326905488968,
0.015271330252289772,
-0.0094232689589262,
0.060884688049554825,
0.03609001636505127,
-0.020450981333851814,
0.012919587083160877,
-0.03944464027881622,
0.022465873509645462,
-0.014064725488424301,
-0.05331078916788101,
0.07201285660266876,
0.03437994047999382,
-0.0473526194691658,
0.0032207972835749388,
0.016540182754397392,
0.000593112432397902,
-0.02322969399392605,
0.01994718611240387,
0.04225492849946022,
0.0367233082652092,
-0.01592029072344303,
0.007709011435508728,
0.05231466144323349,
0.03913922980427742,
-0.030846402049064636,
-0.022685963660478592,
-0.01072951965034008,
-0.00915522500872612,
0.023768944665789604,
-0.0154896704480052,
0.005064613651484251,
0.015414482913911343,
0.02551991119980812,
0.07471512258052826,
0.017246201634407043,
0.007931371219456196,
-0.022714780643582344,
-0.041009776294231415,
-0.020442984998226166,
0.013870613649487495,
0.04159045219421387,
-0.004488753154873848,
0.06012129411101341,
0.049632180482149124,
0.027288783341646194,
-0.0023615979589521885,
0.01601429656147957,
-0.10236826539039612,
0.03319471701979637,
-0.029002295807003975,
-0.026481637731194496,
-0.008072922937572002,
0.005531568545848131,
-0.008444590494036674,
-0.043776679784059525,
-0.020473403856158257,
5.212505698182213e-7,
-0.016324039548635483,
-0.06107308715581894,
0.010285459458827972,
-0.03397383913397789,
-0.04159301519393921,
-0.007672949228435755,
0.015872707590460777,
0.041969623416662216,
-0.010743574239313602,
-0.023082055151462555,
0.03245579078793526,
-0.034579820930957794,
-0.04152742773294449,
0.007825619541108608,
-0.04643724486231804,
0.0342806875705719,
0.031189674511551857,
0.011055316776037216,
0.026739658787846565,
-0.007502174004912376,
0.015558457002043724,
0.023992886766791344,
0.03384179621934891,
0.01185684185475111,
-0.033605579286813736,
-0.02072242461144924,
-0.051733847707509995,
0.009242515079677105,
0.014081770554184914,
0.09181288629770279,
-0.023348797112703323,
-0.05036615580320358,
0.012625527568161488,
-0.0005029386375099421,
0.028607133775949478,
0.021828515455126762,
0.017277400940656662,
0.0036962570156902075,
-0.004102371633052826,
-0.05807946249842644,
0.025956327095627785,
-0.040027741342782974,
-0.008825486525893211,
0.033261969685554504,
-0.0010022803908213973,
0.004881354048848152,
0.008419481106102467,
0.016729258000850677,
0.008444397710263729,
-0.0291131641715765,
0.004813387058675289,
0.0010912559228017926,
0.021389199420809746,
0.00069308967795223,
-0.023630943149328232,
-0.0007494594901800156,
0.02096261829137802,
0.03833314776420593,
-0.01965508610010147,
0.003536833683028817,
-0.1138470247387886,
-0.02628527209162712,
0.015693772584199905,
0.026228932663798332,
-0.003426416777074337,
0.00714946398511529,
-0.022537024691700935,
-0.033790454268455505,
-0.0033675774466246367,
-0.017445433884859085,
0.0271434523165226,
-0.021999625489115715,
0.04064008593559265,
-0.04464782401919365,
-0.04758569970726967,
-0.012691591866314411,
0.020266957581043243,
-0.009916898794472218,
0.008608109317719936,
-0.012224046513438225,
0.029908642172813416,
0.014131354168057442,
0.0029101762920618057,
0.02905699610710144,
0.048655375838279724,
0.021345777437090874,
-0.0374019555747509,
0.005194644909352064,
-0.017335372045636177,
-0.04456597939133644,
-0.07352861762046814,
0.005277807358652353,
-0.018481533974409103,
0.018780462443828583,
0.02042970433831215,
-0.02607315592467785,
-0.07189503312110901,
0.00015755325148347765,
-0.01246757060289383,
-0.0077598546631634235,
0.0351189486682415,
-0.032807204872369766,
0.026733195409178734,
0.008994482457637787,
0.0007748779025860131,
0.016975896432995796,
0.03634810820221901,
-0.0056315152905881405,
-0.006320422515273094,
-0.016194913536310196,
-0.01091314572840929,
-0.02382134646177292,
-0.028433432802557945,
-0.053311921656131744,
-0.014501549303531647,
-0.039160847663879395,
0.025632934644818306,
0.03164974972605705,
0.010223736055195332,
-0.03265286609530449,
-0.05375463142991066,
0.027707556262612343,
0.00659546023234725,
-0.0038691689260303974,
0.022515302523970604,
-0.03436760976910591,
0.01201152615249157,
-0.008293566294014454,
-0.024183157831430435,
-0.005432406440377235,
0.04685203731060028,
-0.016585854813456535,
0.02086913026869297,
-0.01582663133740425,
0.0028165767434984446,
-0.010948196053504944,
-0.029045557603240013,
0.02484695240855217,
-0.05883307009935379,
0.0339626744389534,
-0.013324729166924953,
-0.005263845436275005,
0.02186271734535694,
-0.06278350204229355,
-0.07674658298492432,
-0.010967507027089596,
0.01901319995522499,
0.007834616117179394,
-0.013742423616349697,
-0.009805493988096714,
0.00667846342548728,
0.01200794242322445,
-0.03994711861014366,
-0.02169274352490902,
0.01967163197696209,
-0.017760926857590675,
-0.019223399460315704,
0.03445091471076012,
0.025624923408031464,
-0.03238208219408989,
-0.01155557669699192,
-0.001369781675748527,
0.07102888077497482,
-0.03251582011580467,
0.006250110920518637,
0.022355714812874794,
0.04471803084015846,
0.03834099322557449,
-0.04266813397407532,
-0.022346261888742447,
-0.03221143037080765,
0.0197078138589859,
0.009496890008449554,
0.004158835392445326,
0.051761794835329056,
-0.037568677216768265,
-0.0181850828230381,
-0.016839005053043365,
-0.022397013381123543,
0.028779927641153336,
-0.01764986477792263,
0.00029845317476429045,
0.0313253253698349,
0.02478385902941227,
-0.019344154745340347,
-0.04330200329422951,
0.037324417382478714,
0.018741611391305923,
0.027172572910785675,
0.0072656841948628426,
0.013272072188556194,
-0.01142114121466875,
-0.02317160740494728,
0.036206766963005066,
-0.04077960550785065,
-0.009968805126845837,
0.0058303214609622955,
0.023870669305324554,
-0.03834178298711777,
0.005362265277653933,
0.014275586232542992,
0.005196811631321907,
0.04521237686276436,
-0.006959243677556515,
-0.02180195413529873,
0.0008959721308201551,
-0.018069010227918625,
-0.023280566558241844,
-0.04495927318930626,
-0.06883002072572708,
0.046916790306568146,
0.048806507140398026,
0.016388406977057457,
0.06096513569355011,
-0.010322321206331253,
0.001786753535270691,
0.0021806848235428333,
0.003464684821665287,
-0.010631862096488476,
-0.02628556452691555,
0.021087758243083954,
0.030673881992697716,
-0.038860518485307693,
-0.03822861239314079,
0.0261041559278965,
0.03974594548344612,
-0.0337287113070488,
0.027589045464992523,
0.02259337157011032,
0.004469689913094044,
-0.024274414405226707,
-0.040736034512519836,
-0.02484063245356083,
0.01635923981666565,
-0.01551781129091978,
0.0355549193918705,
-0.01798403076827526,
-0.015376720577478409,
0.007881637662649155,
0.018385717645287514,
-0.008643271401524544,
-0.04294342175126076,
-0.022792760282754898,
-0.06937646865844727,
0.027955196797847748,
0.03929470479488373,
-0.0002225011558039114,
0.01880197785794735,
-0.0021563235204666853,
0.010744315572082996,
-0.03127099573612213,
0.05503404513001442,
0.020122341811656952,
-0.0417875275015831,
-0.02531355805695057,
-0.019512763246893883,
-0.06269089132547379,
0.0809783861041069,
-0.030754419043660164,
-0.04638906940817833,
-0.0008861127425916493,
-0.023694442585110664,
0.02444836124777794,
0.037008997052907944,
-0.0008696481236256659,
-0.04338444396853447,
0.09432948380708694,
-0.02701914682984352,
-0.0014010079903528094,
-0.005032036919146776,
0.034552861005067825,
0.13616006076335907,
0.027667546644806862,
0.006412711925804615,
-0.00958658941090107,
0.01984243653714657,
-0.012377766892313957,
0.01992054656147957,
-0.005393486004322767,
0.013819440267980099,
0.022895559668540955,
-0.0022173465695232153,
-0.004302380606532097,
0.037102848291397095,
-0.02582453563809395,
-0.011510547250509262,
0.06657072901725769,
-0.031658243387937546,
-0.04876283183693886,
-0.0001172344564110972,
0.02081100270152092,
0.00971931777894497,
0.03945160284638405,
-0.002530514495447278,
0.03683438524603844,
-0.008841087110340595,
0.039334736764431,
0.02649187669157982,
-0.022233041003346443,
0.04102090373635292,
0.010046553798019886,
-0.0925641730427742,
-0.0030299669597297907,
0.024056512862443924,
-0.04572617635130882,
-0.032529786229133606,
0.03358403593301773,
0.0024709103163331747,
-0.04430530592799187,
-0.01096101850271225,
0.020357314497232437,
-0.003164212917909026,
-0.0015913386596366763,
0.00732242688536644,
0.007863889448344707,
-0.03787646070122719,
-0.01156298816204071,
-0.029788531363010406,
0.020971760153770447,
-0.021338004618883133,
0.023692404851317406,
0.0027847259771078825,
-0.014746475033462048,
-0.039640720933675766,
-0.051792748272418976,
0.005419640336185694,
-0.008938460610806942,
0.043121881783008575,
-0.028255391865968704,
-0.022818630561232567,
-0.013296933844685555,
0.02022322081029415,
0.009939963929355145,
0.023617718368768692,
-0.021857263520359993,
0.007677389774471521,
0.006380958948284388,
0.006039206404238939,
0.046989355236291885,
-0.047746334224939346,
0.00813461747020483,
-0.0332774855196476,
-0.010295046493411064,
-0.03752501308917999,
-0.0562734492123127,
0.00976707972586155,
0.0718139111995697,
0.03943837061524391,
0.025393495336174965,
0.03385356068611145,
-0.04185691103339195,
-0.012816708534955978,
0.02061724290251732,
0.009795889258384705,
0.004505779128521681,
-0.046337928622961044,
-0.020512700080871582,
-0.006604873575270176,
0.036508992314338684,
-0.02346164546906948,
0.004744271282106638,
0.003352874657139182,
0.014117623679339886,
0.021722160279750824,
-0.015154572203755379,
-0.01879371702671051,
0.05543743446469307,
-0.02738226018846035,
0.028016962110996246,
-0.02519945614039898,
-0.00968877412378788,
0.04142000898718834,
-0.033605676144361496,
-0.029000848531723022,
0.058317918330430984,
0.023182271048426628,
0.010974577628076077,
0.018111001700162888,
-0.0074197594076395035,
0.03245258331298828,
0.0407627634704113,
0.014394006691873074,
-0.034479398280382156,
-0.038806259632110596,
-0.03631845489144325,
-0.0033153174445033073,
-0.04110052436590195,
0.04039836302399635,
-0.03685363754630089,
0.02415298856794834,
-0.029260333627462387,
0.012716668657958508,
-0.036523763090372086,
-0.012511318549513817,
-0.05126376450061798,
0.003736625425517559,
-0.029408928006887436,
-0.023955529555678368,
-0.048951826989650726,
0.03649722784757614,
-0.03375764191150665,
-0.0027755789924412966,
0.010438293218612671,
0.008311024866998196,
-0.01757577247917652,
-0.03816685080528259,
-0.001470915973186493,
-0.0024548876099288464,
0.047557033598423004,
0.013373428955674171,
-0.027953458949923515,
0.0312800258398056,
-0.01878482475876808,
-0.05115281790494919,
0.03510068729519844,
0.0004838541499339044,
0.03485310077667236,
0.030875293537974358,
-0.0008917352533899248,
-0.011178664863109589,
0.06213632598519325,
-0.01458677463233471,
0.0192219540476799,
-0.04552817717194557,
-0.0669742226600647,
-0.026884067803621292,
-0.03129328042268753,
0.02086362987756729,
-0.011067001149058342,
0.006477773655205965,
-0.008913303725421429,
0.029343031346797943,
0.004278612323105335,
-0.026990074664354324,
0.053028639405965805,
-0.011073681525886059,
-0.015374962240457535,
0.04216016083955765,
0.03008170798420906,
0.0147765027359128,
0.054281000047922134,
-0.03660633787512779,
0.025933457538485527,
0.0013880438636988401,
0.006661190651357174,
-0.0952819436788559,
-0.017331883311271667,
0.014268342405557632,
0.01755530573427677,
0.05111507326364517,
-0.0072695170529186726,
-0.02595149725675583,
0.025930751115083694,
-0.052960190922021866,
0.037612102925777435,
-0.04243270680308342,
-0.013449148274958134,
0.015938149765133858,
-0.02839890867471695,
0.0013123566750437021,
0.033796440809965134,
0.013935121707618237,
0.02105548046529293,
0.007516810204833746,
0.03145000338554382,
0.006261770613491535,
-0.018447818234562874,
-0.0034642776008695364,
0.06811657547950745,
-0.00795139092952013,
0.016523310914635658,
0.057602863758802414,
-0.02023337408900261,
0.003541490761563182,
0.06355492025613785,
0.014207535423338413,
0.04651076719164848,
0.0049290843307971954,
-0.018011612817645073,
0.013380836695432663,
0.008877278305590153,
0.034140683710575104,
0.010034054517745972,
-0.029812967404723167,
0.015358914621174335,
0.018439384177327156,
0.019056519493460655,
0.002068880945444107,
-0.009830506518483162,
0.03960607200860977,
-0.041606541723012924,
-0.03432127833366394,
-0.011440743692219257,
-0.025070445612072945,
0.0044480604119598866,
-0.004867414012551308,
0.008727628737688065,
-0.008649442344903946,
-0.010398783721029758,
0.009910228662192822,
-0.0244173351675272,
-0.003009525127708912,
0.025126859545707703,
-0.005156113300472498,
-0.0022628747392445803,
0.0381171815097332,
0.011335618793964386,
-0.007705083116889,
0.027340075001120567,
-0.0056268610060215,
0.015136842615902424,
-0.05109081417322159,
-0.003236374817788601,
0.02283870428800583,
0.013310118578374386,
-0.003903922624886036,
-0.048964325338602066,
-0.04934016987681389,
0.041690465062856674,
-0.0006052326643839478,
-0.019734304398298264,
-0.030267244204878807,
-0.024234049022197723,
-0.015763385221362114,
-0.09339755028486252,
0.03003714792430401,
0.02480793185532093,
-0.0187384020537138,
-0.024733582511544228,
-0.003123576520010829,
-0.012561678886413574,
-0.002252638339996338,
0.05742022767663002,
-0.01446541491895914,
-0.028152190148830414,
0.04858972877264023,
-0.003781131701543927,
0.01738685928285122,
-0.026325268670916557,
-0.02012893557548523,
0.003970474936068058,
0.003702657064422965,
0.021084168925881386,
0.023830682039260864,
-0.009599943645298481,
0.023463770747184753,
0.013078609481453896,
-0.010517657734453678,
0.04738316684961319,
0.0459008514881134,
-0.031965456902980804,
0.03225836902856827,
-0.008427269756793976,
-0.00012808246538043022,
0.02712281607091427,
-0.010092790238559246,
0.010671503841876984,
0.039228588342666626,
-0.03994528576731682,
-0.032925963401794434,
0.01883896254003048,
-0.019275937229394913,
0.0006270254962146282,
-0.03811163455247879,
-0.019574595615267754,
0.032759975641965866,
-0.036370713263750076,
-0.021684248000383377,
0.03327132388949394,
-0.020292403176426888,
0.007086586207151413,
0.033195171505212784,
0.02969965524971485,
0.04281540587544441,
-0.0024515341501682997,
0.02530222199857235,
0.008694707415997982,
-0.02688020095229149,
0.029552051797509193,
-0.014541403390467167,
0.039356086403131485,
-0.04083631932735443,
0.013767382130026817,
0.09681982547044754,
-0.019702421501278877,
-0.0009221581858582795,
0.014347491785883904,
0.0296613909304142,
-0.019858229905366898,
-0.031088748946785927,
0.008309539407491684,
-0.007550147827714682,
-0.014995567500591278,
0.03182314708828926,
0.022811582311987877,
0.0738128200173378,
0.012211892753839493,
0.030349569395184517,
0.0010809588711708784,
0.019374411553144455,
-0.02693989872932434,
0.000293116201646626,
-0.024704430252313614,
0.04014749825000763,
-0.01683724671602249,
0.0012765935389325023,
-0.0033568108920007944,
-0.019101228564977646,
0.001017316011711955,
0.002539396518841386,
0.002979051787406206,
0.01625000312924385,
0.005281375255435705,
-0.027751052752137184,
-0.017197012901306152,
-0.043110039085149765,
-0.02053295634686947,
0.1089201495051384,
0.02802952378988266,
0.03415391966700554,
0.010375874117016792,
0.00891551561653614,
-0.010331113822758198,
0.04857569932937622,
-0.06254734843969345,
-0.040442876517772675,
-0.026246966794133186,
0.02663683332502842,
0.03863257169723511,
-0.0064969598315656185
] |
<p>I always think that it is not possible to escape from within event horizon. However, some one recently told me with deep conviction that it <em>is</em> possible with sustained energy output. I countered with calculations in Schwarzschild metric showing that any objects below event horizon in the simplistic black hole will hit the singularity within a finite proper time, and was met with the response that Schwarzschild metric was a bad choice for coordinate system.</p>
<p>Now I understand that the singularity at $r=\frac{2GM}{c^2}$ in Schwarzschild metric is an artifact of the coordinate choice, and thus it seems that he could have a point. So my question is, can one prove that it is (or not) possible to escape from within the event horizon of a simple static black hole using a better metric?</p>
| 8,497 |
[
-0.03743574023246765,
-0.029721388593316078,
0.017593134194612503,
-0.043371353298425674,
0.020245477557182312,
0.0007771302480250597,
-0.06817283481359482,
-0.04970034211874008,
-0.02274223603308201,
-0.038786616176366806,
0.001304078847169876,
0.017529552802443504,
0.041712526232004166,
0.02830664813518524,
-0.006672068499028683,
-0.02375089004635811,
-0.024699652567505836,
-0.011310129426419735,
-0.004917262587696314,
-0.03431622311472893,
0.03175957873463631,
0.010729988105595112,
-0.007179511245340109,
-0.038257382810115814,
-0.007330660242587328,
-0.01434871181845665,
0.0003203225205652416,
0.015623225830495358,
0.001367018441669643,
0.07224119454622269,
-0.04177619889378548,
-0.012999662198126316,
0.004392832517623901,
0.03825749456882477,
0.021849220618605614,
-0.0003215545730199665,
-0.02504805102944374,
-0.04062836989760399,
-0.030974198132753372,
-0.010958483442664146,
-0.03183908388018608,
-0.02699633501470089,
0.018524181097745895,
0.06941424310207367,
-0.03414836898446083,
-0.013436002656817436,
-0.007848191075026989,
-0.01246437057852745,
0.023842211812734604,
-0.047370873391628265,
0.061220504343509674,
-0.00932967010885477,
0.03466856852173805,
0.009692712686955929,
0.0014571256469935179,
0.01657598838210106,
0.08981835842132568,
0.05211030691862106,
-0.03047032654285431,
-0.005251066293567419,
-0.03832367807626724,
-0.010255686938762665,
-0.0007943696691654623,
-0.028970278799533844,
-0.017335470765829086,
0.02904869243502617,
-0.0032977431546896696,
-0.010851318947970867,
0.027454597875475883,
-0.047640714794397354,
-0.024018341675400734,
-0.0017959546530619264,
-0.00875443872064352,
0.00013976928312331438,
0.03894587606191635,
-0.03613688424229622,
0.031542643904685974,
-0.025830622762441635,
0.019089384004473686,
0.0663822814822197,
0.014869029633700848,
0.01694444939494133,
0.08332201838493347,
0.04794406145811081,
-0.00000345728426509595,
0.023749956861138344,
0.06585399061441422,
-0.011836926452815533,
0.022469686344265938,
0.010093462653458118,
-0.00996596459299326,
-0.02208453230559826,
0.025029487907886505,
-0.022311044856905937,
-0.015166152268648148,
0.021822193637490273,
0.001985993469133973,
0.07584885507822037,
-0.015738653019070625,
-0.05173761397600174,
0.0032114533241838217,
0.0005102764698676765,
0.02210836298763752,
0.05689216032624245,
0.06523148715496063,
-0.026379665359854698,
-0.0549214668571949,
0.010052366182208061,
-0.0320349857211113,
-0.020809605717658997,
-0.03818600997328758,
0.016456367447972298,
0.0013630964094772935,
-0.016203459352254868,
0.027399085462093353,
-0.054168883711099625,
-0.030114952474832535,
-0.050348058342933655,
0.065842404961586,
0.05968323349952698,
0.02066984958946705,
-0.014440793544054031,
0.013095107860863209,
-0.03263029828667641,
-0.0434371754527092,
-0.012884268537163734,
0.054835498332977295,
-0.00957683939486742,
-0.06072013080120087,
-0.025478782132267952,
0.02172628603875637,
-0.007727507967501879,
0.006202063988894224,
0.021007072180509567,
0.04801041632890701,
-0.014264398254454136,
-0.12016109377145767,
-0.062122270464897156,
0.05178862810134888,
-0.014169465750455856,
-0.01855052448809147,
-0.05941399559378624,
0.010783814825117588,
0.049186207354068756,
0.07403606921434402,
-0.0023326308000832796,
-0.006506337318569422,
0.010751276277005672,
0.04013978689908981,
0.0008278255118057132,
-0.031532615423202515,
0.011280225589871407,
-0.013025114312767982,
-0.026934044435620308,
0.017233898863196373,
-0.07750218361616135,
0.015323293395340443,
0.018539581447839737,
0.025278523564338684,
-0.0285089910030365,
0.0940161794424057,
-0.018051354214549065,
0.00672363443300128,
0.013775297440588474,
-0.009118858724832535,
0.016374900937080383,
0.10306102782487869,
0.019931457936763763,
-0.00605915067717433,
0.010621034540235996,
0.024354113265872,
0.06356804072856903,
0.02449137158691883,
-0.01608298346400261,
0.022116422653198242,
-0.06865856796503067,
-0.0041336361318826675,
-0.017864609137177467,
0.016986951231956482,
0.027997758239507675,
-0.02853739634156227,
-0.040164537727832794,
-0.012850387021899223,
-0.027062810957431793,
0.01721838489174843,
0.04708504676818848,
-0.027358461171388626,
-0.005415381398051977,
-0.015413501299917698,
-0.03462425246834755,
-0.0005069788312539458,
-0.048807542771101,
0.04200759902596474,
0.040564846247434616,
0.023122582584619522,
0.04023469239473343,
0.010432110168039799,
0.019441349431872368,
-0.038755450397729874,
0.0028212680481374264,
-0.02338564395904541,
0.033908311277627945,
0.0005229088710620999,
-0.02420760504901409,
0.018425434827804565,
0.04761025682091713,
0.04057397320866585,
0.027585003525018692,
0.003948046825826168,
0.025417877361178398,
-0.01720193587243557,
0.007909012027084827,
0.007757259998470545,
0.018480893224477768,
0.017379481345415115,
-0.0032338888850063086,
0.009945731610059738,
0.006711585912853479,
-0.01563503034412861,
0.039200108498334885,
-0.01847642846405506,
0.09849604219198227,
0.017595389857888222,
0.019359629601240158,
-0.0274676326662302,
0.024845851585268974,
0.021547956392169,
-0.0031151643488556147,
0.012530974112451077,
-0.015638846904039383,
-0.02147850953042507,
0.01611323468387127,
0.01965957134962082,
0.017271341755986214,
-0.09353207796812057,
0.015010811388492584,
0.03891046345233917,
-0.011419638060033321,
0.03256188705563545,
0.06211024522781372,
-0.01530313678085804,
-0.010263798758387566,
0.029454704374074936,
0.02930259332060814,
0.03406849503517151,
0.0021788321901112795,
0.03338288143277168,
-0.0006172000430524349,
-0.050655242055654526,
-0.01948367990553379,
0.04255171865224838,
0.009689396247267723,
-0.023543627932667732,
-0.01721268706023693,
0.009095834568142891,
0.0057439920492470264,
0.02442847192287445,
-0.026392610743641853,
0.024804526939988136,
0.026554789394140244,
0.004567558877170086,
0.009021787904202938,
-0.04386806860566139,
-0.00345645472407341,
0.017001919448375702,
0.005092203617095947,
-0.0046964893117547035,
-0.022158175706863403,
0.028070436790585518,
-0.03627562150359154,
0.004612719174474478,
-0.039058439433574677,
-0.014694219455122948,
-0.023376649245619774,
-0.003995060455054045,
0.031060656532645226,
0.017302973195910454,
0.005310622043907642,
0.00039543831371702254,
-0.040603309869766235,
0.02264593169093132,
-0.00842827558517456,
-0.009139826521277428,
0.006825238931924105,
-0.03783867508172989,
0.015333184972405434,
-0.04380384087562561,
-0.030580325052142143,
0.06184520199894905,
0.006019233260303736,
0.03620215877890587,
0.027575165033340454,
-0.01921018585562706,
-0.04298306256532669,
0.03208715096116066,
-0.030736565589904785,
0.005537702236324549,
-0.03882135450839996,
-0.009182309731841087,
0.07909613847732544,
-0.0030122827738523483,
-0.03788816183805466,
0.035412680357694626,
-0.00929204560816288,
-0.03023676760494709,
0.001113837119191885,
0.009283429943025112,
0.0031560079660266638,
-0.028380710631608963,
0.04411459341645241,
0.009423349983990192,
-0.07021913677453995,
0.011877802200615406,
-0.0490669384598732,
-0.03599546477198601,
0.036165498197078705,
-0.002631318988278508,
-0.008442707359790802,
-0.01797662302851677,
-0.030380330979824066,
0.03868190944194794,
0.00190148432739079,
-0.043609607964754105,
-0.0093831866979599,
-0.013532562181353569,
-0.005730436183512211,
0.0013183166738599539,
-0.04244516044855118,
0.013091376051306725,
-0.0014610212529078126,
-0.0026421849615871906,
0.014392630197107792,
0.045035507529973984,
0.024278033524751663,
0.0016455079894512892,
-0.01731543056666851,
-0.017546573653817177,
0.016903607174754143,
0.01823795773088932,
0.03523213043808937,
0.013632751069962978,
-0.062371883541345596,
0.02651546522974968,
0.006374836899340153,
0.046812668442726135,
0.014247230254113674,
-0.055606137961149216,
0.02570413611829281,
-0.023086266592144966,
0.025053231045603752,
-0.009406010620296001,
0.010400170460343361,
-0.02011563815176487,
-0.01420679409056902,
0.012662798166275024,
-0.002439312171190977,
0.04606155678629875,
-0.00855939369648695,
0.006339345593005419,
0.03748458996415138,
0.027948474511504173,
-0.020830482244491577,
-0.03742010518908501,
0.005305207800120115,
-0.019116753712296486,
0.04993584007024765,
0.03951088339090347,
-0.02879023738205433,
0.037367574870586395,
0.02316824533045292,
-0.004802940413355827,
0.021293675526976585,
0.006599382497370243,
0.013780823908746243,
-0.10669844597578049,
-0.011804301291704178,
-0.001977459993213415,
0.04022517055273056,
-0.009769292548298836,
0.02040039747953415,
0.052446700632572174,
-0.00578621169552207,
0.00601839879527688,
-0.024203089997172356,
-0.10891143232584,
-0.00029512375476770103,
-0.028898324817419052,
-0.013624944724142551,
-0.0007048517582006752,
-0.02897917479276657,
-0.025948327034711838,
-0.035745564848184586,
-0.01984311267733574,
0.004515463020652533,
0.017939181998372078,
-0.044184740632772446,
0.026668531820178032,
-0.04275233671069145,
-0.027430355548858643,
-0.025449512526392937,
0.04919200763106346,
0.04956364259123802,
-0.006965603679418564,
-0.028356196358799934,
0.025041908025741577,
-0.0336231105029583,
-0.013799324631690979,
0.02300439216196537,
0.016519317403435707,
-0.018411127850413322,
0.03433844447135925,
0.014304419048130512,
0.013121901080012321,
0.015531628392636776,
-0.020696626976132393,
0.030816849321126938,
0.021006925031542778,
-0.020852457731962204,
-0.00619023060426116,
-0.04312555864453316,
-0.041105009615421295,
-0.022709401324391365,
0.003265675390139222,
0.06620918214321136,
-0.021747693419456482,
-0.0015075552510097623,
0.01105978712439537,
-0.008371691219508648,
-0.010319963097572327,
0.016049383208155632,
0.06887660920619965,
-0.021057521924376488,
-0.03479991480708122,
-0.06263253092765808,
-0.05901549383997917,
-0.021343423053622246,
-0.004660214763134718,
0.012408625334501266,
-0.024843668565154076,
-0.04744059219956398,
0.014441550709307194,
0.034971170127391815,
0.011582056060433388,
-0.014891048893332481,
-0.036045584827661514,
0.022093230858445168,
0.03688966855406761,
0.011533978395164013,
0.03043578751385212,
0.03326806053519249,
0.009239153005182743,
0.045606937259435654,
0.006007596850395203,
0.0015228827251121402,
-0.06730608642101288,
-0.02817271649837494,
0.03025832585990429,
0.01948334462940693,
0.038004763424396515,
0.008242610841989517,
-0.06853502988815308,
0.007618284318596125,
0.044997528195381165,
-0.015700872987508774,
0.04939064756035805,
0.004580722190439701,
0.014039769768714905,
-0.010233053006231785,
-0.018211159855127335,
0.00037134141894057393,
0.021089529618620872,
-0.021442444995045662,
-0.01092706061899662,
-0.028872111812233925,
0.023204708471894264,
-0.017939802259206772,
-0.009649548679590225,
0.024867087602615356,
0.06446614861488342,
0.043502096086740494,
-0.010353974997997284,
0.00047285654000006616,
0.008668106980621815,
-0.01840370148420334,
-0.06705942749977112,
-0.0015965657075867057,
0.014705538749694824,
-0.024020060896873474,
0.014644194394350052,
-0.02500155381858349,
-0.008041526190936565,
0.029848165810108185,
-0.01748470589518547,
0.0011405062396079302,
0.022264162078499794,
-0.04893109202384949,
-0.005575763527303934,
0.02398083172738552,
-0.013746771030128002,
0.028461996465921402,
0.013233824633061886,
0.016027923673391342,
0.007086195517331362,
-0.035520896315574646,
0.02112163044512272,
-0.04424126073718071,
-0.037213779985904694,
-0.02525380067527294,
0.022215068340301514,
-0.02475324273109436,
0.04532455652952194,
0.006588571239262819,
0.01968596689403057,
0.015642985701560974,
-0.006212740205228329,
-0.0019412649562582374,
0.03514019772410393,
0.014704343862831593,
0.017850887030363083,
-0.012554575689136982,
0.014439798891544342,
0.010292635299265385,
-0.0362817719578743,
-0.002601172309368849,
-0.015413310378789902,
-0.010305704548954964,
0.047207076102495193,
-0.025569967925548553,
0.017036138102412224,
0.009957567788660526,
-0.0178154855966568,
0.028363946825265884,
-0.057837486267089844,
0.05624346062541008,
-0.022594524547457695,
-0.00012926183990202844,
0.0025670554023236036,
-0.03880714625120163,
-0.021915607154369354,
-0.007772727403789759,
0.028075844049453735,
0.011402067728340626,
-0.06493283808231354,
0.03836147114634514,
0.04088485985994339,
0.0038714942056685686,
-0.11564570665359497,
-0.050522297620773315,
0.02719416841864586,
0.024695036932826042,
-0.0385831855237484,
-0.017696496099233627,
0.020888211205601692,
-0.036670584231615067,
-0.012084772810339928,
-0.04274289309978485,
0.026792233809828758,
-0.014312448911368847,
0.008400484919548035,
-0.012699172832071781,
0.01938595250248909,
0.029172096401453018,
-0.012089363299310207,
-0.02767684869468212,
0.02276185154914856,
0.027280200272798538,
0.014343409799039364,
-0.03767458721995354,
0.060296282172203064,
-0.007474548649042845,
-0.029030082747340202,
-0.033573780208826065,
-0.009320525452494621,
0.019758697599172592,
-0.0019952459260821342,
0.036524515599012375,
0.06492973864078522,
0.0024341631215065718,
0.013111609034240246,
-0.005252877715975046,
0.014770212583243847,
-0.03686697036027908,
0.01830323599278927,
-0.007658236660063267,
0.004247498232871294,
-0.006467408500611782,
-0.03806271404027939,
0.04225306212902069,
-0.006182938814163208,
-0.00673467293381691,
-0.027630100026726723,
0.070982925593853,
0.01186235062777996,
-0.03303821012377739,
-0.02516075409948826,
-0.040088996291160583,
0.00875302217900753,
0.005879136733710766,
0.008379136212170124,
0.01924801990389824,
0.032309986650943756,
-0.014523864723742008,
-0.03985683619976044,
-0.03442388400435448,
0.02695273421704769,
0.07151608914136887,
0.010434942319989204,
0.02766343392431736,
0.023639267310500145,
0.022287484258413315,
0.00512936245650053,
-0.022230878472328186,
-0.006900130305439234,
-0.013807251118123531,
0.003845881437882781,
0.026238538324832916,
-0.008808756247162819,
-0.002224698895588517,
0.03675646334886551,
0.04366419091820717,
-0.009748956188559532,
0.031676676124334335,
0.010638101026415825,
0.008930446580052376,
-0.025752469897270203,
0.014121335931122303,
-0.022976236417889595,
0.036838989704847336,
-0.036378975957632065,
0.02944166027009487,
-0.0005152732483111322,
0.006835748441517353,
0.013166488148272038,
-0.016193566843867302,
0.009883131831884384,
-0.013680252246558666,
-0.04672177881002426,
-0.037014562636613846,
0.019889559596776962,
-0.022746670991182327,
0.0027587946970015764,
0.001252459012903273,
0.011366905644536018,
-0.009031502529978752,
0.005739826709032059,
0.011468710377812386,
-0.0010492936708033085,
-0.05465681105852127,
-0.04747471585869789,
-0.049104806035757065,
-0.03735522925853729,
0.029834313318133354,
0.03341355919837952,
-0.018015943467617035,
-0.004821090493351221,
-0.03991145268082619,
-0.007451476063579321,
0.019315460696816444,
0.08812404423952103,
0.001990810502320528,
0.07316508144140244,
-0.023807350546121597,
-0.0012855124659836292,
-0.01882227137684822,
0.010753108188509941,
0.1068820059299469,
0.0696977749466896,
-0.002241957001388073,
-0.061005380004644394,
0.02037234418094158,
-0.018735190853476524,
0.014502976089715958,
-0.060315996408462524,
0.05656872317194939,
0.015565091744065285,
-0.02333478443324566,
0.029558109119534492,
0.05373234301805496,
0.005529606249183416,
-0.029307255521416664,
0.06395329535007477,
-0.019558006897568703,
-0.0185631662607193,
0.0050009447149932384,
0.03342253342270851,
-0.018590517342090607,
-0.009889521636068821,
0.03482086583971977,
0.009019420482218266,
-0.01455655973404646,
-0.014651985839009285,
-0.018728846684098244,
-0.014193474315106869,
0.01989465020596981,
-0.019002877175807953,
-0.036826834082603455,
-0.02684096060693264,
-0.0025378733407706022,
-0.023562144488096237,
-0.01105222012847662,
-0.004477759823203087,
-0.00307191489264369,
-0.01898087002336979,
-0.0037272556219249964,
0.04824086278676987,
0.028453344479203224,
0.012173139490187168,
-0.0018892936641350389,
-0.0022128215059638023,
-0.04632630944252014,
0.001596787478774786,
-0.016897687688469887,
0.036447715014219284,
-0.020761003717780113,
0.007001855876296759,
0.01640714332461357,
-0.00281604309566319,
0.0020718080922961235,
-0.03949363902211189,
-0.010282982140779495,
-0.027393845841288567,
-0.011201232671737671,
0.021294832229614258,
-0.023226378485560417,
-0.036066845059394836,
0.029965152963995934,
0.037893664091825485,
-0.002978930715471506,
-0.006666077766567469,
-0.0017369658453390002,
0.002619508421048522,
-0.017551053315401077,
0.023469021543860435,
-0.01454666443169117,
-0.03252461925148964,
-0.015674863010644913,
0.009499849751591682,
-0.051778193563222885,
-0.009821044281125069,
0.033409737050533295,
0.008923732675611973,
0.02223457396030426,
0.0593627393245697,
0.03251764178276062,
0.004448203835636377,
-0.05476316064596176,
0.01659781113266945,
-0.01704031601548195,
-0.02376384660601616,
-0.02762032486498356,
0.03743646293878555,
0.025459857657551765,
0.050475962460041046,
-0.029237711802124977,
-0.028943665325641632,
-0.020567918196320534,
0.00962747260928154,
-0.010718543082475662,
-0.00514901103451848,
-0.0261546578258276,
-0.018519217148423195,
-0.040665153414011,
0.023051250725984573,
-0.02667357586324215,
0.04622254893183708,
0.026564422994852066,
0.025083642452955246,
0.015460438095033169,
0.02875349670648575,
-0.014576646499335766,
0.0074021783657372,
0.01751810871064663,
-0.008136189542710781,
-0.01555285882204771,
-0.002436061156913638,
0.04213655740022659,
-0.009149111807346344,
-0.04826609417796135,
-0.011302025988698006,
-0.0010498963529244065,
-0.0204735416918993,
0.02094068005681038,
-0.0006663077510893345,
0.015655312687158585,
0.0028091385029256344,
-0.03169211372733116,
-0.07628373801708221,
0.0073824692517519,
-0.004247015342116356,
0.0008955287630669773,
-0.0012378711253404617,
-0.03422662243247032,
-0.0047185784205794334,
0.01872537098824978,
-0.007449289318174124,
-0.03466322273015976,
0.013189173303544521,
0.03780718892812729,
-0.047276969999074936,
0.0070970128290355206,
0.05267708748579025,
0.002011794364079833,
0.03757588192820549,
0.011816018261015415,
-0.017097745090723038,
0.014303348958492279,
-0.025100406259298325,
-0.042797304689884186,
0.02186131291091442,
-0.021979920566082,
0.037159185856580734,
-0.004748506937175989,
-0.019012954086065292,
-0.004632097203284502,
0.09518943727016449,
0.012837223708629608,
-0.010266975499689579,
0.033754102885723114,
-0.012348474934697151,
-0.046470072120428085,
0.011135095730423927,
0.05481603741645813,
-0.042225174605846405,
0.004129606299102306,
0.007581054233014584,
-0.010514776222407818,
0.02360258810222149,
-0.031447768211364746,
0.013143843971192837,
0.004581904970109463,
0.0322110690176487,
0.012523441575467587,
-0.02263481914997101,
0.06711282581090927,
0.07084321975708008,
-0.020087283104658127,
0.013699246570467949,
0.027545379474759102,
0.011323886923491955,
-0.09048503637313843,
-0.01035534217953682,
0.013394620269536972,
0.029990453273057938,
0.052510667592287064,
-0.05948919057846069,
0.03701455146074295,
0.04050886258482933,
-0.07433286309242249,
0.006040805950760841,
-0.03705810382962227,
-0.008271723054349422,
-0.02473577670753002,
-0.021278349682688713,
-0.04358253255486488,
0.0458928719162941,
0.07356742024421692,
0.05410834029316902,
-0.002051368122920394,
-0.009575046598911285,
-0.028039131313562393,
-0.031747523695230484,
-0.015127241611480713,
0.0467003658413887,
-0.007120270282030106,
-0.004339350387454033,
0.10036881268024445,
-0.0023226169869303703,
-0.042285121977329254,
-0.005881390068680048,
0.011779253371059895,
-0.01967347040772438,
0.036582525819540024,
0.029911508783698082,
0.026048436760902405,
0.030425382778048515,
0.04333970695734024,
-0.0011486008297652006,
-0.020051995292305946,
-0.008404873311519623,
-0.005434271413832903,
0.0053499904461205006,
-0.044466160237789154,
-0.012882707640528679,
0.009701590985059738,
-0.0443163700401783,
-0.03282538801431656,
0.01998770795762539,
-0.028931379318237305,
-0.04698294401168823,
0.017762627452611923,
0.008734211325645447,
0.030724825337529182,
-0.033829107880592346,
0.0020796048920601606,
-0.054558176547288895,
-0.011126215569674969,
0.03267287835478783,
0.02311740815639496,
0.03853264078497887,
0.007344510406255722,
-0.013713979162275791,
-0.04992994666099548,
0.050229400396347046,
-0.023098157718777657,
-0.0040192026644945145,
-0.04747900739312172,
0.011539558880031109,
-0.026298096403479576,
-0.006264973431825638,
0.0245109461247921,
-0.05364049971103668,
0.010724508203566074,
0.02488923817873001,
0.017298920080065727,
0.01861628331243992,
0.016492262482643127,
-0.010475100949406624,
-0.03349022939801216,
-0.07239829748868942,
0.020210562273859978,
-0.03179691359400749,
0.009564531967043877,
-0.03611369431018829,
-0.028699642047286034,
-0.007181957829743624,
-0.020315801724791527,
0.04701754078269005,
-0.06335930526256561,
-0.001010441454127431,
0.030767954885959625,
0.00024789184681139886,
-0.006349625997245312,
-0.02703055553138256,
-0.0014584205346181989,
0.022697683423757553,
-0.041173055768013,
-0.0169292613863945,
0.013285348191857338,
-0.016290565952658653,
0.04492809250950813,
0.03387825936079025,
-0.003474252065643668,
0.047142740339040756,
0.01939261145889759,
-0.026180939748883247,
0.03620612248778343,
0.02368236891925335,
0.011349008418619633,
0.05035035312175751,
0.005681798327714205,
0.023638049140572548,
0.020170699805021286,
-0.02958112210035324,
0.0006289434968493879,
0.024735521525144577,
-0.025403132662177086,
-0.0050786505453288555,
-0.018163040280342102,
-0.014039091765880585,
-0.003471462521702051,
-0.057729244232177734,
0.006215241272002459,
0.026146816089749336,
-0.03711027652025223,
-0.013857131823897362,
0.0366998165845871,
0.03193536400794983,
0.042241547256708145,
0.0031289744656533003,
0.004037182312458754,
0.013453525491058826,
0.02474331110715866,
0.003430018201470375,
0.04437992349267006,
0.032625630497932434,
-0.02080175094306469,
0.023411903530359268,
-0.004155834671109915,
-0.012422250583767891,
0.01908729039132595,
-0.00655617518350482,
0.06214658170938492,
-0.009061570279300213,
-0.02269577421247959,
0.001832208363339305,
0.0010577243519946933,
0.004142923280596733,
-0.004167479462921619,
-0.05665631964802742,
0.04247797653079033,
0.0006338020320981741,
0.01605658046901226,
-0.008154095150530338,
-0.013159483671188354,
-0.039740998297929764,
0.03790596127510071,
0.000648971414193511,
0.06563596427440643,
0.005899200215935707,
0.012128015048801899,
0.009913170710206032,
0.025310590863227844,
0.02708701230585575,
0.0049880752339959145,
0.025104142725467682,
-0.02628096006810665,
0.0016036361921578646,
-0.034981776028871536,
-0.01753384992480278,
-0.011394208297133446,
-0.02240549400448799,
-0.0038544312119483948,
0.014145592227578163,
0.030308425426483154,
0.01669403910636902,
-0.015027507208287716,
-0.03886137530207634,
0.05307600274682045,
-0.05098570138216019,
-0.007949503138661385,
-0.0015470420476049185,
0.006608780473470688,
-0.0319688618183136,
-0.011666282080113888
] |
<p>I'm a little unclear as to how <a href="http://en.wikipedia.org/wiki/Quantum_field_theory" rel="nofollow">QFT</a> differs from Elementary <a href="http://en.wikipedia.org/wiki/Particle_physics" rel="nofollow">particle physics</a>. They both use pictorials of Feynman graphs, is it that Elementary particle physics assumes the point particle perspective, while QFT treats them as fields?</p>
| 8,498 |
[
0.01193286757916212,
-0.019660042598843575,
-0.017247676849365234,
-0.014737448655068874,
0.018071403726935387,
0.01618298515677452,
-0.0009764406131580472,
-0.01734468713402748,
-0.0027129920199513435,
-0.042915910482406616,
0.020687270909547806,
0.020239612087607384,
0.032575540244579315,
0.010797262191772461,
-0.013976559974253178,
0.02810235321521759,
-0.005324572324752808,
-0.01547541469335556,
-0.0069794743321835995,
-0.025864331051707268,
-0.008018704131245613,
0.04491490498185158,
0.0014319694600999355,
0.04491313919425011,
-0.01613813266158104,
0.03961886465549469,
0.04236772656440735,
0.04962239786982536,
0.007067927625030279,
0.0571848601102829,
0.0033984866458922625,
-0.05467108637094498,
0.014934366568922997,
0.004615820478647947,
0.001317183836363256,
0.003100295551121235,
-0.024924660101532936,
-0.03429163247346878,
0.007078373339027166,
-0.012261616066098213,
-0.04564903303980827,
-0.021260179579257965,
-0.027978859841823578,
0.04380080848932266,
-0.03476779907941818,
0.027742179110646248,
0.003870135871693492,
-0.0024491294752806425,
0.07441676408052444,
-0.04548581317067146,
0.024549968540668488,
0.03187042102217674,
0.011910265311598778,
0.047557979822158813,
-0.015732932835817337,
-0.015892013907432556,
0.05897251516580582,
0.06337407231330872,
-0.015588287264108658,
-0.10097217559814453,
-0.031827010214328766,
-0.04102553799748421,
-0.0026462282985448837,
-0.02120228111743927,
-0.05553252622485161,
0.021985458210110664,
0.018892750144004822,
-0.02305338904261589,
-0.005739142186939716,
-0.0027781729586422443,
-0.0019760895520448685,
0.04467162489891052,
0.05083006992936134,
-0.01964815892279148,
0.0239623561501503,
-0.029702719300985336,
0.020748980343341827,
0.017645008862018585,
0.021231142804026604,
0.027748920023441315,
-0.021386396139860153,
0.020078375935554504,
0.02382662333548069,
0.019348125904798508,
0.025806685909628868,
-0.005261845421046019,
0.05575323849916458,
-0.00011202270979993045,
-0.039210911840200424,
0.049996983259916306,
-0.05431441590189934,
0.0033064999151974916,
0.06424916535615921,
-0.023282062262296677,
-0.026444388553500175,
0.03475748747587204,
0.031054498627781868,
0.002701100194826722,
0.03345675393939018,
-0.012522107921540737,
0.014678066596388817,
-0.012201829813420773,
0.030019979923963547,
0.053826022893190384,
0.005393217317759991,
-0.015797998756170273,
-0.05574868619441986,
0.020611761137843132,
-0.003300280310213566,
-0.009908453561365604,
-0.04055580496788025,
0.019059425219893456,
-0.02296885848045349,
0.04085545614361763,
-0.008636560291051865,
-0.03778583183884621,
-0.005812244955450296,
-0.01622941344976425,
0.10023155808448792,
0.06998202204704285,
0.03695016726851463,
-0.05555743724107742,
0.013732188381254673,
-0.019772380590438843,
-0.07206442207098007,
-0.007369368337094784,
0.0235985666513443,
-0.01615079864859581,
-0.03094431385397911,
0.018884878605604172,
-0.01125260442495346,
0.02400536835193634,
0.022585391998291016,
0.004329530056566,
0.072606161236763,
-0.015483074821531773,
-0.09544571489095688,
-0.03599125146865845,
0.033658601343631744,
-0.005608343053609133,
-0.003704177448526025,
-0.06462295353412628,
0.0184120312333107,
0.024094203487038612,
0.04952533170580864,
-0.02014746330678463,
-0.00236615352332592,
0.0044791363179683685,
0.04462340846657753,
0.013949699699878693,
-0.017509158700704575,
0.02577180229127407,
-0.021196959540247917,
-0.028477346524596214,
0.003935531247407198,
-0.04256153851747513,
0.023565901443362236,
0.01625633053481579,
0.000745279947295785,
-0.03257333114743233,
0.08289303630590439,
-0.003520828438922763,
0.01359844021499157,
0.013468286022543907,
-0.01603384129703045,
-0.014196138828992844,
0.06203677877783775,
0.003073706990107894,
0.02942119538784027,
0.061469536274671555,
-0.024354927241802216,
0.02489459700882435,
0.009306685999035835,
0.02973244898021221,
0.02836240455508232,
-0.02364901453256607,
-0.062014009803533554,
-0.021350856870412827,
0.008099690079689026,
-0.0009219949133694172,
-0.0742122009396553,
-0.020255764946341515,
-0.02583049051463604,
0.004985492676496506,
-0.0224282406270504,
0.039430852979421616,
-0.02655045874416828,
0.003217335557565093,
0.001889683655463159,
-0.04164349287748337,
-0.07420381158590317,
-0.06471842527389526,
0.02358919195830822,
-0.010668996721506119,
0.0066922856494784355,
0.022799154743552208,
0.008924524299800396,
-0.009703699499368668,
-0.05390927568078041,
-0.0514451265335083,
0.0006666425615549088,
0.045249149203300476,
-0.009520592167973518,
-0.01684596762061119,
0.012855288572609425,
0.06090550497174263,
0.035989321768283844,
0.005108303856104612,
0.022587230429053307,
-0.041067395359277725,
-0.026629187166690826,
0.018814224749803543,
-0.03168827295303345,
0.02546810172498226,
0.0028260727412998676,
0.0066169388592243195,
0.0032023105304688215,
0.022840028628706932,
-0.038667626678943634,
0.05038546770811081,
-0.011838835664093494,
0.08167561143636703,
0.012305469252169132,
-0.0014134483644738793,
-0.007398996502161026,
0.00508842384442687,
-0.0031424113549292088,
0.012912320904433727,
0.009838787838816643,
-0.019977057352662086,
-0.04120853915810585,
0.0011450010351836681,
0.04581141844391823,
0.004245568532496691,
-0.041088953614234924,
0.021274780854582787,
0.013521387241780758,
0.05792480334639549,
-0.003485183697193861,
0.0342741422355175,
-0.030670253559947014,
-0.037540193647146225,
0.0002990099892485887,
0.023450715467333794,
0.008751669898629189,
0.010889939963817596,
0.017076965421438217,
-0.0059283128939569,
0.019955411553382874,
-0.012573695741593838,
-0.07210171222686768,
0.04636746272444725,
-0.04745001718401909,
-0.006174578797072172,
0.029264062643051147,
-0.030817648395895958,
0.042240846902132034,
-0.02562788873910904,
0.004502327647060156,
-0.012536385096609592,
-0.0486169159412384,
-0.030097685754299164,
-0.00824024062603712,
-0.001219918834976852,
0.0027308755088597536,
0.03168192505836487,
-0.042603179812431335,
-0.006702855229377747,
0.010899635031819344,
-0.013679904863238335,
-0.011344938538968563,
-0.022194571793079376,
-0.014483646489679813,
-0.019650379195809364,
0.023055722936987877,
0.03739007189869881,
-0.005191368516534567,
0.039057664573192596,
-0.061066634953022,
-0.04266694560647011,
0.019698990508913994,
-0.055749163031578064,
0.016337677836418152,
0.04821078106760979,
-0.039641063660383224,
0.01124980766326189,
-0.08684275299310684,
-0.0270084235817194,
0.029329128563404083,
-0.03331105038523674,
0.02308698743581772,
-0.01264065783470869,
-0.030480630695819855,
-0.02766130119562149,
-0.012677766382694244,
-0.03235791623592377,
0.041565392166376114,
-0.011599352583289146,
-0.012254899367690086,
0.016290588304400444,
0.011934639886021614,
0.011146614328026772,
0.009165626019239426,
-0.023682499304413795,
-0.038019292056560516,
-0.007961006835103035,
0.03987199440598488,
0.019283052533864975,
-0.026982827112078667,
0.008166179992258549,
0.03092881664633751,
-0.062286704778671265,
-0.011348397471010685,
-0.04622013121843338,
-0.035295095294713974,
0.019542740657925606,
0.00974028930068016,
0.007139495108276606,
0.0026400533970445395,
-0.033599548041820526,
0.05186907574534416,
0.06406645476818085,
-0.04753530025482178,
-0.020826278254389763,
-0.016311442479491234,
-0.026623038575053215,
-0.00492735905572772,
0.017749270424246788,
0.019196767359972,
-0.02969702146947384,
0.03648671880364418,
-0.003409031545743346,
0.0280163511633873,
0.0017610326176509261,
0.0002155372640118003,
-0.0043677776120603085,
-0.020233118906617165,
0.001307605067268014,
0.007107485085725784,
0.053337130695581436,
-0.0038238135166466236,
-0.05858495086431503,
-0.006760618649423122,
-0.0037638922221958637,
-0.0009028115891851485,
-0.009118996560573578,
0.008052094839513302,
0.0767190232872963,
0.003923205658793449,
0.00577459204941988,
-0.04020625725388527,
0.03898525610566139,
0.0050327470526099205,
-0.018352070823311806,
0.009229868650436401,
0.011019877158105373,
0.01596388779580593,
-0.003155449405312538,
0.00515461852774024,
0.012643118388950825,
0.0641649141907692,
-0.06867282837629318,
-0.012240206822752953,
0.008164186030626297,
0.002212183317169547,
0.03336877375841141,
-0.021937845274806023,
-0.028953436762094498,
0.0560058057308197,
0.04952499270439148,
0.03424142673611641,
0.015571840107440948,
-0.02215624786913395,
-0.026450559496879578,
-0.058788035064935684,
0.0097806416451931,
0.008205588907003403,
0.0706440806388855,
0.016103539615869522,
0.06783188879489899,
-0.002088154200464487,
0.0005005054990760982,
-0.008943958207964897,
0.03354159742593765,
-0.07602225244045258,
-0.0004545561096165329,
-0.016693703830242157,
-0.02482827939093113,
-0.01786794513463974,
-0.027110958471894264,
0.011820145882666111,
-0.001867560320533812,
-0.037702254951000214,
-0.027991151437163353,
-0.0054596057161688805,
-0.0024100434966385365,
0.01532596442848444,
-0.06472300738096237,
-0.019443847239017487,
-0.01364806853234768,
0.03021787852048874,
0.010454929433763027,
-0.05572214722633362,
0.020989786833524704,
0.03820709511637688,
-0.057505618780851364,
-0.015030165202915668,
0.012054625898599625,
0.009611982852220535,
0.020944399759173393,
0.009824766777455807,
0.03317515179514885,
0.01944734901189804,
-0.04774865880608559,
0.0160093791782856,
0.011596346274018288,
0.07634047418832779,
0.01777399331331253,
-0.03417051210999489,
-0.010908262804150581,
-0.05565299466252327,
-0.007672301027923822,
-0.016918634995818138,
0.04567851126194,
-0.02684992551803589,
-0.023665759712457657,
0.05848965048789978,
0.01106042880564928,
-0.020381616428494453,
0.030224356800317764,
0.039087988436222076,
-0.0048327273689210415,
-0.019867386668920517,
-0.03661256656050682,
0.002060608472675085,
0.0011453059269115329,
-0.019807707518339157,
0.023927701637148857,
0.01714748702943325,
-0.03340472653508186,
-0.0024855267256498337,
0.02773955836892128,
-0.004219500347971916,
-0.0624355785548687,
0.01861555129289627,
0.00678046140819788,
-0.018173227086663246,
0.0007991098100319505,
-0.019372383132576942,
-0.0038686897605657578,
0.04460473358631134,
0.04885345324873924,
0.013818805105984211,
0.019394978880882263,
-0.06359555572271347,
-0.004818752408027649,
0.04978078603744507,
0.008382845669984818,
0.020036740228533745,
-0.025525230914354324,
-0.03348803520202637,
-0.012463000603020191,
0.03005080483853817,
-0.02089211903512478,
0.009153681807219982,
-0.019286343827843666,
0.012753067538142204,
-0.034437138587236404,
-0.04931474104523659,
-0.006832676474004984,
0.008198571391403675,
-0.014611332677304745,
0.030607961118221283,
-0.029707670211791992,
0.018917616456747055,
-0.02768838219344616,
0.01161236222833395,
0.0010196438524872065,
0.04311256855726242,
0.03128138929605484,
0.0176540594547987,
0.002532974351197481,
0.011051325127482414,
-0.017350705340504646,
-0.07763674855232239,
0.019559403881430626,
0.02648201398551464,
0.006575294304639101,
0.023130128160119057,
-0.019694030284881592,
-0.029095295816659927,
-0.024558695033192635,
-0.012477296404540539,
-0.007420837879180908,
0.002695115515962243,
-0.05734516680240631,
0.043723829090595245,
0.023613709956407547,
0.004593913909047842,
0.024758392944931984,
0.04933766648173332,
-0.049392495304346085,
-0.028175627812743187,
-0.007473444566130638,
0.03758140653371811,
-0.005107481963932514,
0.012001104652881622,
-0.023769279941916466,
-0.014667783863842487,
-0.029757162556052208,
0.03519830480217934,
-0.016515592113137245,
0.029340064153075218,
-0.029978789389133453,
-0.03811226040124893,
-0.03394217789173126,
-0.012446337379515171,
-0.014274142682552338,
0.011671477928757668,
-0.008010147139430046,
0.004711192566901445,
-0.00018584779172670096,
-0.0445137694478035,
-0.004966740030795336,
0.011448285542428493,
-0.011531938798725605,
0.0031725603621453047,
0.003687435295432806,
0.01829712465405464,
-0.03416156768798828,
-0.03821055591106415,
-0.022876789793372154,
-0.05972692742943764,
0.021696310490369797,
-0.013212705962359905,
0.00015730733866803348,
-0.0027318098582327366,
-0.06741036474704742,
-0.05524932220578194,
-0.004516534972935915,
-0.00883751455694437,
0.01925976388156414,
-0.028714073821902275,
0.031914662569761276,
0.013629991561174393,
0.015838606283068657,
-0.055072151124477386,
-0.07104630768299103,
-0.017624448984861374,
0.013075397349894047,
-0.027283182367682457,
0.006254941690713167,
0.01837530918419361,
-0.032044827938079834,
-0.009798333048820496,
0.01298513449728489,
0.04685629904270172,
-0.057670608162879944,
0.003114247927442193,
0.024483054876327515,
0.016821864992380142,
0.04038069769740105,
0.004895379766821861,
-0.0064865234307944775,
-0.0031108232215046883,
0.026659058406949043,
-0.0014021664392203093,
0.008656995370984077,
0.056591182947158813,
-0.0035639889538288116,
-0.03066100738942623,
-0.021755075082182884,
0.004418103024363518,
0.030536852777004242,
-0.029444901272654533,
0.024464072659611702,
0.035573143512010574,
0.035646531730890274,
-0.0022875473368912935,
-0.026633374392986298,
0.019525744020938873,
0.008031648583710194,
0.028628667816519737,
-0.03330378606915474,
-0.006694714073091745,
0.033033277839422226,
-0.0482354573905468,
0.03512915223836899,
-0.014853372238576412,
0.017801888287067413,
0.030819449573755264,
0.025466689839959145,
-0.03372242674231529,
-0.008240821771323681,
0.044834572821855545,
-0.03981969878077507,
0.012436561286449432,
-0.020016100257635117,
0.030990861356258392,
0.010881287045776844,
0.03354858234524727,
-0.0020049121230840683,
-0.004908910486847162,
-0.032297033816576004,
-0.03324146941304207,
0.026912005618214607,
0.015735361725091934,
0.05088488757610321,
0.03987215459346771,
-0.02069561555981636,
0.0011329568224027753,
-0.017247451469302177,
0.001560588600113988,
-0.010241622105240822,
0.008622552268207073,
0.0266262199729681,
-0.04518413171172142,
-0.01131104864180088,
0.03091955929994583,
0.055161252617836,
-0.03783952444791794,
0.024643966928124428,
0.03812554106116295,
0.038034986704587936,
0.016492394730448723,
0.007847043685615063,
-0.05196818709373474,
0.03156838193535805,
-0.03222539275884628,
0.040749114006757736,
0.007650287356227636,
-0.03472038358449936,
0.04113040491938591,
0.02626047283411026,
0.005221494939178228,
-0.004499360453337431,
-0.03131873905658722,
-0.059362683445215225,
0.0040374682284891605,
0.008285473100841045,
0.02793472446501255,
-0.052469853311777115,
-0.011481929570436478,
0.02234749309718609,
0.0045492216013371944,
0.0033208716195076704,
0.03347687050700188,
-0.04587879404425621,
-0.04964352399110794,
-0.02407688833773136,
-0.02933521382510662,
0.0301496684551239,
-0.0517062172293663,
-0.03409431502223015,
0.020332548767328262,
-0.02684985101222992,
0.034435030072927475,
-0.010829438455402851,
0.01826072484254837,
-0.044989194720983505,
0.03166844695806503,
0.020588263869285583,
0.011693245731294155,
-0.036776360124349594,
0.010710804723203182,
0.10594978928565979,
0.058276448398828506,
0.027378495782613754,
-0.05190800130367279,
0.026418538764119148,
-0.03244279325008392,
0.04323873296380043,
-0.01792018860578537,
0.033742766827344894,
0.009385330602526665,
0.013783800415694714,
-0.006763169076293707,
0.07598084956407547,
0.044733691960573196,
-0.020233185961842537,
0.058700766414403915,
-0.05428558215498924,
-0.06175536662340164,
-0.028944769874215126,
0.049392737448215485,
-0.00993126817047596,
0.042047951370477676,
-0.0640433058142662,
-0.003169075818732381,
-0.02232246659696102,
0.04850364103913307,
-0.0059148105792701244,
-0.04357285052537918,
0.024878820404410362,
0.026866046711802483,
-0.050174299627542496,
-0.009684747084975243,
0.01437608152627945,
-0.02956279180943966,
-0.025696441531181335,
0.006377519108355045,
0.004961176309734583,
-0.032696131616830826,
0.017092380672693253,
0.05608835071325302,
0.03740254044532776,
-0.013515247963368893,
-0.009805474430322647,
0.006563429720699787,
-0.03431685268878937,
0.0016845253994688392,
-0.04072045534849167,
0.029534397646784782,
-0.016275528818368912,
0.0172372218221426,
-0.01472469698637724,
-0.0014065576251596212,
0.009372914209961891,
-0.029630687087774277,
0.0023661525920033455,
0.00040482511394657195,
0.017418179661035538,
0.0002822751412168145,
0.009012049064040184,
-0.04242480918765068,
0.05893142148852348,
-0.02998277358710766,
0.023863336071372032,
0.014043409377336502,
-0.017422344535589218,
0.015870505943894386,
-0.0008335841121152043,
-0.0020552845671772957,
-0.01213663537055254,
-0.009357508271932602,
0.02567460387945175,
-0.025752635672688484,
-0.03574281930923462,
-0.018372301012277603,
0.026991428807377815,
0.04234373942017555,
0.07473994791507721,
0.015927400439977646,
0.005048469640314579,
0.004637690261006355,
-0.020480170845985413,
0.03033311851322651,
-0.009038574062287807,
-0.01806594245135784,
-0.008203132078051567,
0.022223105654120445,
0.030897758901119232,
0.0549638494849205,
-0.01981622911989689,
0.01771732233464718,
-0.003151203505694866,
-0.006887197960168123,
0.014619714580476284,
-0.030182160437107086,
-0.00786440260708332,
0.015108100138604641,
-0.02282399870455265,
-0.0014079378452152014,
-0.04027131199836731,
0.01547588873654604,
0.030419645830988884,
-0.0025028300005942583,
-0.0010141237871721387,
0.036953069269657135,
0.0135207399725914,
0.022321417927742004,
0.02319910190999508,
-0.0023255348205566406,
0.008501686155796051,
0.04550940543413162,
0.011288231238722801,
-0.05095261335372925,
-0.02998971752822399,
-0.009411690756678581,
0.018125684931874275,
-0.03941822797060013,
0.024381382390856743,
-0.032902877777814865,
-0.015156365931034088,
-0.03779073804616928,
0.022919850423932076,
-0.025204405188560486,
-0.01388209592550993,
-0.08982262760400772,
0.007106597535312176,
0.014996802434325218,
0.0007238591788336635,
-0.0444566048681736,
0.02739478275179863,
-0.016459312289953232,
-0.006235087756067514,
0.024094216525554657,
0.016988467425107956,
-0.0345291793346405,
0.01237811241298914,
0.012977322563529015,
0.02689397893846035,
0.01318077277392149,
-0.008813326247036457,
0.0031784886959940195,
0.047891389578580856,
-0.022369738668203354,
-0.05983191356062889,
0.03099721111357212,
0.011175093241035938,
0.010496757924556732,
0.05091118812561035,
-0.005697399843484163,
-0.0375525988638401,
0.05158461630344391,
-0.0030006589367985725,
-0.011425869539380074,
-0.0041252258233726025,
-0.039914682507514954,
-0.02247544750571251,
-0.0427883081138134,
0.011593811213970184,
0.015002009458839893,
-0.015047044493258,
0.02758597582578659,
0.0019828067161142826,
-0.010758912190794945,
-0.024420101195573807,
-0.005915799178183079,
-0.009179314598441124,
0.017523253336548805,
0.05549782142043114,
0.0027901700232177973,
0.012443233281373978,
0.029184475541114807,
-0.05087897181510925,
0.01337940152734518,
0.02664431929588318,
0.01165592111647129,
-0.10085694491863251,
-0.011126969009637833,
0.01935798116028309,
0.0031836279667913914,
0.0347263365983963,
-0.03606707230210304,
0.005322193261235952,
0.03926262632012367,
-0.06489133089780807,
0.027342166751623154,
0.018027689307928085,
-0.02738192304968834,
-0.016794582828879356,
-0.007902777753770351,
0.013070180080831051,
0.07141467183828354,
0.028472671285271645,
0.058354247361421585,
0.02410230040550232,
0.011676914989948273,
0.016868598759174347,
0.005889687687158585,
-0.04728161171078682,
0.029093638062477112,
-0.017988799139857292,
-0.03334661200642586,
0.06378861516714096,
-0.03225640952587128,
-0.02771109901368618,
0.030120786279439926,
0.023060837760567665,
0.0035490444861352444,
-0.0008218537550419569,
-0.017280424013733864,
0.03419589251279831,
0.012371991761028767,
0.01084127277135849,
-0.013759395107626915,
0.009015271440148354,
0.01107086706906557,
0.01764836348593235,
0.008735878393054008,
0.009634179063141346,
0.03433530032634735,
0.01468247827142477,
-0.016895456239581108,
-0.02653484418988228,
0.045231811702251434,
0.014255501329898834,
-0.02662527933716774,
-0.025424018502235413,
0.011469271965324879,
0.015628987923264503,
-0.010626059956848621,
0.018192147836089134,
-0.07238791137933731,
0.0022741106804460287,
0.020579390227794647,
-0.018931124359369278,
0.0019233535276725888,
0.014519290998578072,
0.012634397484362125,
-0.023165177553892136,
0.010873300023376942,
0.0332312136888504,
0.013885662890970707,
-0.07544437050819397,
0.01721704937517643,
0.03132794052362442,
0.011865715496242046,
0.044750817120075226,
-0.0758066400885582,
-0.01485099270939827,
-0.0025045813526958227,
-0.011044190265238285,
0.038146913051605225,
-0.00373803055845201,
0.005647860933095217,
-0.00476405443623662,
-0.07339715957641602,
0.029920442029833794,
0.013498049229383469,
-0.004691363777965307,
-0.040496181696653366,
0.004911215044558048,
-0.00917178113013506,
0.014137345366179943,
0.05860224366188049,
-0.0012905308976769447,
0.00724922027438879,
0.0011617258423939347,
-0.006581615190953016,
0.009914071299135685,
-0.04653557017445564,
-0.0317041277885437,
-0.02687053009867668,
-0.025971027091145515,
0.029529159888625145,
-0.011822761036455631,
-0.018043290823698044,
0.04781806468963623,
0.05670643597841263,
-0.023840727284550667,
0.006944649387151003,
-0.019592588767409325,
-0.056611012667417526,
0.027956007048487663,
-0.011243641376495361,
0.00925408024340868,
0.051157377660274506,
-0.011021271347999573,
0.011320375837385654,
0.06170212849974632,
-0.02948446199297905,
0.026300780475139618,
0.04109136015176773,
-0.04960742965340614,
-0.011951812542974949,
0.0062600187957286835,
-0.022278601303696632,
0.029771704226732254,
-0.07138904184103012,
-0.02489212155342102,
0.020640384405851364,
-0.02304461970925331,
-0.02858617715537548,
0.06478296965360641,
0.04671616479754448,
0.03357724845409393,
0.02040601149201393,
0.0015673459274694324,
0.03355410322546959,
-0.018451092764735222,
0.013287100940942764,
0.042468082159757614,
0.052856821566820145,
0.030410397797822952,
0.02739410102367401,
0.053750988095998764,
0.019695278257131577,
0.019228333607316017,
-0.005695831961929798,
0.045623160898685455,
0.0007843180792406201,
-0.0029287368524819613,
0.012350104749202728,
-0.010767810046672821,
0.040440063923597336,
0.013294370844960213,
-0.0258512981235981,
0.08128400892019272,
-0.044843729585409164,
-0.0032175041269510984,
0.003327583894133568,
0.03351282700896263,
-0.016567308455705643,
0.014994548633694649,
0.02290133200585842,
0.07587356865406036,
-0.002974907634779811,
-0.05297575518488884,
-0.0239262692630291,
0.011846756562590599,
0.0001849479303928092,
-0.030535129830241203,
0.005442103371024132,
0.0011523424182087183,
-0.032691869884729385,
-0.015383313409984112,
0.0010138108627870679,
0.00809793546795845,
-0.006400066427886486,
0.023082420229911804,
0.034788038581609726,
0.018992677330970764,
-0.017198752611875534,
-0.016763022169470787,
-0.029540561139583588,
0.03135170787572861,
-0.08866788446903229,
0.02509448491036892,
-0.010596799664199352,
0.015874164178967476,
0.010974598117172718,
0.00916468258947134
] |
<p>I'm afraid this question is a little too open-ended, but bear with me while I find a better formulation.</p>
<p>carbon allotropes (like fullerenes and graphene) are regular patterned. Conduction bands of electrons in graphene in particular, have energy-momentum relationships that make them behave as massless carriers (sticking to what is called a Dirac cone). More interestingly the propagation dynamics seem to be at first order, direction independent.</p>
<p>Given the above facts, is possible that the interactions of carriers on such 2D sheet is describable by the limit of some Conformal Field Theory. If that were to be the case, and I have a big closed surface of graphene material, what does the holographic principle will say about the fields in the volume bounded by the surface? What is the equivalent of the Gravitational Theory in that volume?</p>
| 8,499 |
[
0.012100019492208958,
-0.027810053899884224,
0.0277932807803154,
-0.043199557811021805,
0.010339036583900452,
-0.01988840661942959,
-0.039186395704746246,
-0.03239568695425987,
0.003285964485257864,
-0.05006416514515877,
0.013742183335125446,
0.005013145972043276,
0.044678159058094025,
0.05188794434070587,
0.02696133218705654,
-0.009693670086562634,
-0.04291407763957977,
-0.028281589969992638,
-0.015638230368494987,
-0.0652071163058281,
-0.0020626960322260857,
0.05868954211473465,
0.021463872864842415,
0.010405451990664005,
-0.03690757229924202,
0.008178437128663063,
-0.02844909206032753,
0.011057746596634388,
-0.004510102793574333,
0.050523970276117325,
-0.040980733931064606,
-0.01067427359521389,
0.010318318381905556,
0.0030327856075018644,
0.024411214515566826,
0.0050854249857366085,
-0.05526464432477951,
-0.042568132281303406,
0.013251041993498802,
-0.0070730336010456085,
-0.023511022329330444,
-0.021631821990013123,
-0.022125229239463806,
0.06808116286993027,
-0.0031688709277659655,
-0.009402113035321236,
0.008779343217611313,
-0.04438561201095581,
0.04578140005469322,
-0.09808193147182465,
0.058752648532390594,
-0.007782577537000179,
0.035051312297582626,
0.0022208213340491056,
0.028142061084508896,
-0.04847065359354019,
0.0522087961435318,
0.041881076991558075,
0.002287892857566476,
-0.015329334884881973,
-0.020174048840999603,
0.005580540280789137,
-0.0213190708309412,
-0.04488180950284004,
-0.02364368364214897,
0.04095464199781418,
-0.027437347918748856,
-0.038503438234329224,
0.029475102201104164,
-0.030272597447037697,
-0.00683172233402729,
0.013017989695072174,
0.03268812224268913,
0.03670196235179901,
0.027937714010477066,
0.00794919766485691,
0.02336316928267479,
0.03328084200620651,
-0.004658216144889593,
0.006556595675647259,
-0.020840954035520554,
0.01722537726163864,
0.014229221269488335,
0.056603819131851196,
0.017491986975073814,
-0.00877124909311533,
0.04559047147631645,
-0.019753970205783844,
0.0038598019164055586,
0.03388466313481331,
-0.01753506436944008,
-0.005107955541461706,
0.06115775182843208,
0.006168810650706291,
-0.033067669719457626,
0.0009684714023023844,
0.016142893582582474,
0.03824200853705406,
-0.005053018219769001,
-0.00390179012902081,
-0.04341071844100952,
-0.003482772968709469,
0.01927201636135578,
0.08118157833814621,
-0.010982753708958626,
-0.003308537881821394,
-0.03846963495016098,
0.00689594866707921,
-0.001707433839328587,
-0.014060898683965206,
-0.06006214767694473,
0.014271057210862637,
-0.013039066456258297,
-0.008438680320978165,
0.022339584305882454,
-0.014184101484715939,
-0.01831718161702156,
-0.021532580256462097,
0.01994883455336094,
0.06800686568021774,
0.04226335883140564,
-0.009907945990562439,
0.0389426089823246,
-0.031891047954559326,
-0.07244836539030075,
0.011433206498622894,
0.0346037857234478,
-0.008481936529278755,
-0.027442222461104393,
0.0038315807469189167,
0.014405040070414543,
-0.03089272417128086,
-0.04277428239583969,
-0.028933200985193253,
0.05361587554216385,
-0.022912222892045975,
-0.0862194150686264,
-0.047769904136657715,
0.03372716158628464,
-0.0009057229617610574,
0.014355012215673923,
-0.04892740026116371,
-0.013644867576658726,
0.03697223961353302,
0.08858384937047958,
-0.005937471520155668,
0.018818242475390434,
0.02236190065741539,
0.03405920788645744,
0.016970999538898468,
-0.03516039252281189,
-0.011969318613409996,
0.008294609375298023,
-0.04835426062345505,
-0.011166016571223736,
-0.05906377732753754,
0.026461469009518623,
0.026600005105137825,
0.03141046315431595,
-0.03815903142094612,
0.06297551840543747,
-0.01599983312189579,
-0.00002565346767369192,
0.002274651313200593,
-0.021100910380482674,
-0.027774116024374962,
0.07054463773965836,
0.013785157352685928,
0.010442688129842281,
0.026096366345882416,
0.014656552113592625,
0.012743989005684853,
0.04391041025519371,
0.036600008606910706,
0.027829710394144058,
-0.0071738469414412975,
-0.01174252014607191,
-0.0002458806266076863,
-0.024016112089157104,
-0.04181421920657158,
-0.013790074735879898,
-0.05512765794992447,
-0.017662372440099716,
0.019375739619135857,
0.014720051549375057,
0.02020271308720112,
0.003659362904727459,
-0.03910916671156883,
0.003666129894554615,
-0.021186795085668564,
0.04373877868056297,
-0.03356577455997467,
0.03639994561672211,
0.007022946607321501,
0.027421720325946808,
0.03252212703227997,
-0.017752811312675476,
-0.011816371232271194,
-0.03831542655825615,
-0.03865494951605797,
-0.007249870803207159,
0.050998348742723465,
-0.004366698209196329,
0.010147906839847565,
0.010607902891933918,
-0.0012442311272025108,
0.011419457383453846,
-0.021038809791207314,
0.023852838203310966,
-0.01125550176948309,
-0.0368875190615654,
0.010866664350032806,
-0.005046157166361809,
0.05908304825425148,
-0.04299625754356384,
0.02463901974260807,
-0.002284737303853035,
0.02104223147034645,
-0.03382033854722977,
0.06503313779830933,
-0.038745176047086716,
0.05723249912261963,
0.06734184920787811,
-0.01436682976782322,
-0.0073304129764437675,
0.026511697098612785,
-0.009158949367702007,
-0.05058595538139343,
-0.00539269158616662,
-0.053960103541612625,
-0.07968378812074661,
0.0002871821343433112,
0.049801234155893326,
0.041584767401218414,
-0.005997797939926386,
0.009930763393640518,
0.05292782187461853,
0.04654689505696297,
0.025733157992362976,
-0.013823936693370342,
-0.03210757300257683,
0.001420536544173956,
0.048872414976358414,
-0.029739713296294212,
-0.0022715386003255844,
-0.01630271226167679,
0.030498718842864037,
0.03269466385245323,
-0.006404258776456118,
-0.007346049882471561,
-0.030774232000112534,
0.016659030690789223,
-0.016436627134680748,
0.018203066661953926,
-0.00458898488432169,
-0.008424472063779831,
0.05373060330748558,
-0.02786705642938614,
-0.018450597301125526,
0.07797658443450928,
0.01064386684447527,
-0.015858380123972893,
-0.07268546521663666,
-0.013514846563339233,
0.04637191444635391,
0.025677211582660675,
-0.02410716935992241,
-0.04329311475157738,
0.013727299869060516,
-0.031624291092157364,
-0.001096477615647018,
0.008526521734893322,
-0.007659855764359236,
0.00725792208686471,
0.03561365231871605,
0.042371321469545364,
0.0020809366833418608,
0.06849061697721481,
-0.057772453874349594,
-0.053681012243032455,
0.008809035643935204,
-0.034662727266550064,
0.008618287742137909,
0.015773558989167213,
-0.0401085764169693,
-0.00006859066343167797,
-0.044492196291685104,
-0.027707455679774284,
0.04700517654418945,
0.01803288236260414,
0.0006489313673228025,
0.021255094558000565,
-0.031045788899064064,
-0.03453173115849495,
0.028372392058372498,
0.0003120474866591394,
0.03783561289310455,
-0.03779953345656395,
0.021308667957782745,
0.05289653688669205,
0.02102087065577507,
0.00646683294326067,
0.028688522055745125,
-0.015396695584058762,
-0.04781621694564819,
0.006641968619078398,
0.006131751928478479,
-0.02586878463625908,
-0.039269186556339264,
0.04611743241548538,
0.003865939797833562,
-0.02778327465057373,
-0.007779631298035383,
-0.056237976998090744,
-0.03071378357708454,
0.008654491044580936,
-0.03890763595700264,
0.004518798086792231,
-0.021323543041944504,
-0.017984723672270775,
0.05484054237604141,
0.02128206193447113,
-0.033780090510845184,
-0.00585825415328145,
-0.03218252956867218,
-0.016477299854159355,
0.012741333805024624,
0.05091356858611107,
0.024277325719594955,
0.0001968391879927367,
-0.01801901124417782,
0.007981876842677593,
0.010642725974321365,
0.030120808631181717,
-0.025475403293967247,
-0.006694249343127012,
0.017674444243311882,
0.01452118344604969,
0.019254527986049652,
0.0444985069334507,
-0.013976465910673141,
-0.010313916020095348,
0.015305887907743454,
0.0031301865819841623,
-0.013821801170706749,
0.055086102336645126,
-0.07128679752349854,
0.026978958398103714,
0.010653382167220116,
0.029882783070206642,
0.00538605684414506,
0.026323387399315834,
-0.023036420345306396,
-0.01956760697066784,
0.010958385653793812,
0.00737516675144434,
0.07088751345872879,
-0.013211235404014587,
0.006213994696736336,
0.0023688278160989285,
0.03560205549001694,
-0.02669535204768181,
-0.04587512090802193,
0.02390351891517639,
0.0187674630433321,
-0.005053464323282242,
-0.03966385871171951,
-0.02386103942990303,
0.0406612791121006,
0.051226966083049774,
0.04323118180036545,
0.02566862851381302,
-0.040294308215379715,
0.005857605952769518,
-0.0479789674282074,
-0.026293693110346794,
-0.02514648623764515,
0.06783544272184372,
0.0028874140698462725,
0.004054184537380934,
0.061811961233615875,
-0.01620584726333618,
0.022281402722001076,
0.01903236284852028,
-0.11302413791418076,
-0.047421056777238846,
-0.0021591598633676767,
0.008895644918084145,
-0.015153232030570507,
-0.04817260429263115,
0.0012163725914433599,
0.01380902249366045,
-0.018016712740063667,
-0.011387904174625874,
-0.016372134909033775,
-0.07493890821933746,
0.019276974722743034,
-0.04362434893846512,
-0.03128616884350777,
-0.018285105004906654,
0.034592561423778534,
-0.003101759124547243,
-0.005558541975915432,
-0.006226400379091501,
0.032198715955019,
-0.03422129899263382,
0.021755512803792953,
0.00608855253085494,
0.008763574995100498,
-0.003680586349219084,
0.04250256344676018,
0.00846005417406559,
-0.01272286381572485,
-0.004065813962370157,
0.00818624161183834,
0.020961590111255646,
0.07134594768285751,
-0.024089641869068146,
-0.008175780065357685,
-0.00584067590534687,
-0.058834612369537354,
-0.023933693766593933,
-0.004168529994785786,
0.06792058050632477,
0.0161578431725502,
-0.009888810105621815,
0.04293974116444588,
-0.005602302961051464,
-0.012834528461098671,
0.03126947581768036,
0.04474876821041107,
-0.023925522342324257,
-0.03270405903458595,
-0.049269042909145355,
-0.037323348224163055,
-0.013271324336528778,
-0.024354837834835052,
0.04552207514643669,
-0.03657284379005432,
-0.0465727336704731,
-0.0047422670759260654,
0.02048490382730961,
0.02367863431572914,
-0.021779481321573257,
-0.01865847222507,
-0.011520822532474995,
0.026874510571360588,
-0.03317299485206604,
0.004121558275073767,
-0.009090919978916645,
0.019489599391818047,
0.029289770871400833,
-0.005588074214756489,
-0.018914073705673218,
-0.050685103982686996,
0.013304370455443859,
0.013167552649974823,
0.02741558663547039,
0.024335922673344612,
0.00400640768930316,
-0.03847748413681984,
-0.0036879521794617176,
0.006524285767227411,
-0.020702751353383064,
-0.013284320943057537,
-0.012495288625359535,
0.008598591201007366,
-0.039629071950912476,
0.010917485691606998,
-0.012715981341898441,
-0.000584940193220973,
-0.0007601573597639799,
-0.025843564420938492,
-0.05205352604389191,
0.0347914844751358,
0.006572218146175146,
0.027532918378710747,
0.03996061161160469,
0.034304920583963394,
0.01002220157533884,
0.02317999303340912,
0.037985753268003464,
0.011816509068012238,
-0.051184747368097305,
-0.07758063822984695,
-0.013842642307281494,
0.032270368188619614,
-0.02788296341896057,
0.026082361117005348,
-0.018769700080156326,
-0.04041549563407898,
0.020256539806723595,
0.003832327201962471,
0.008513362146914005,
-0.0020869497675448656,
-0.02131420001387596,
0.04816465452313423,
0.02447638101875782,
-0.04031749814748764,
-0.001983985770493746,
0.034760672599077225,
-0.016504090279340744,
0.0184292271733284,
-0.008531714789569378,
0.07038790732622147,
-0.019151907414197922,
0.010845208540558815,
-0.02551387809216976,
-0.01733158342540264,
-0.027612857520580292,
0.02559046819806099,
0.0063124303705990314,
-0.0008162089507095516,
-0.03166443109512329,
-0.06633523851633072,
-0.04333734139800072,
-0.010665050707757473,
-0.0221572183072567,
0.00634772889316082,
-0.027091439813375473,
0.039257388561964035,
-0.002153840148821473,
-0.024028601124882698,
0.005363800562918186,
-0.034813396632671356,
-0.0015059640863910317,
0.06636788696050644,
0.031830210238695145,
-0.018490783870220184,
-0.04063612222671509,
0.04364705830812454,
-0.023992102593183517,
-0.06049460917711258,
0.07522017508745193,
0.006106084678322077,
0.016362980008125305,
-0.018764542415738106,
-0.03827618435025215,
-0.010199521668255329,
0.010504786856472492,
-0.02059871330857277,
0.031397439539432526,
-0.030046869069337845,
0.006549548823386431,
0.022763850167393684,
0.01408388651907444,
-0.07620012760162354,
-0.054460231214761734,
0.006116973701864481,
0.06172717735171318,
-0.019296349957585335,
-0.035756029188632965,
0.004324002657085657,
-0.041097648441791534,
-0.02301919087767601,
0.01458217017352581,
0.03187800571322441,
-0.04507661610841751,
-0.007951563224196434,
0.03976832702755928,
-0.009511780925095081,
0.07453065365552902,
0.00323339831084013,
-0.04665527120232582,
0.03615238890051842,
0.0021251661237329245,
-0.02144632861018181,
-0.018533380702137947,
0.020952312275767326,
-0.01712096482515335,
-0.01608514040708542,
-0.026645652949810028,
0.003529607318341732,
0.035834360867738724,
-0.013016392476856709,
0.01335122250020504,
0.04058028385043144,
0.03338990733027458,
-0.028943045064806938,
-0.03650619834661484,
0.006317283492535353,
-0.0026596328243613243,
0.018871083855628967,
-0.0026384994853287935,
-0.0030070028733462095,
-0.019192812964320183,
-0.04615190997719765,
0.009832719340920448,
0.010351262055337429,
0.002545592375099659,
0.0005491524934768677,
0.03589606657624245,
0.0033320493530482054,
-0.02173454686999321,
0.015599419362843037,
-0.009858828969299793,
0.03908628970384598,
-0.017855772748589516,
0.016371091827750206,
0.007553239818662405,
0.012519454583525658,
-0.02941179648041725,
-0.03750002756714821,
-0.0558004193007946,
0.00736638531088829,
0.05651885271072388,
-0.015769682824611664,
0.01756940595805645,
0.008682822808623314,
-0.01901320181787014,
-0.021327102556824684,
-0.005858548451215029,
-0.005224688444286585,
0.008505580946803093,
-0.027164293453097343,
0.006985828746110201,
-0.017356902360916138,
-0.013601305894553661,
0.035182226449251175,
0.03439993038773537,
-0.010405504144728184,
0.026166900992393494,
0.029540181159973145,
0.041390325874090195,
0.07689160108566284,
0.0049317074008286,
-0.010399783961474895,
0.05288565158843994,
-0.05024127662181854,
0.04055014252662659,
-0.01335836946964264,
-0.0015789318131282926,
0.04489728808403015,
0.020126523450016975,
0.009716883301734924,
-0.005681136157363653,
-0.04576968029141426,
-0.034439146518707275,
0.010037352330982685,
0.021099496632814407,
0.025655781850218773,
-0.025979509577155113,
0.01593642868101597,
0.027974294498562813,
0.0159382913261652,
-0.03368275612592697,
0.016448834910988808,
-0.07514838129281998,
0.009864723309874535,
-0.01619081012904644,
-0.01888074167072773,
0.04643561318516731,
0.0432426743209362,
-0.016630306839942932,
0.021560901775956154,
-0.022250395268201828,
0.005810756701976061,
0.01328077632933855,
0.04085918888449669,
-0.0003744936839211732,
0.050333671271800995,
-0.014368003234267235,
0.018685881048440933,
-0.04757700115442276,
-0.006445711012929678,
0.11497368663549423,
0.027954451739788055,
0.007410579826682806,
-0.04153880476951599,
0.03754877299070358,
-0.0088860047981143,
0.03303349390625954,
-0.0455363392829895,
0.03714778646826744,
0.005058130249381065,
-0.005919626913964748,
-0.007666385732591152,
0.06547363102436066,
-0.02809719741344452,
-0.00136914465110749,
0.04790652170777321,
-0.03824843093752861,
-0.012677730061113834,
0.015194765292108059,
-0.01018794160336256,
-0.02900432050228119,
0.03187820687890053,
-0.04926495999097824,
-0.005854818969964981,
-0.0041853017173707485,
0.0038661700673401356,
-0.029923131689429283,
-0.009380057454109192,
0.025157475844025612,
0.02402123063802719,
-0.055174123495817184,
0.010249710641801357,
-0.0208083875477314,
-0.022492170333862305,
-0.03783141076564789,
0.008237100206315517,
0.012426493689417839,
0.010762049816548824,
0.015817172825336456,
0.01607205718755722,
0.0021829656325280666,
0.017701532691717148,
0.022263579070568085,
0.008921344764530659,
-0.028277793899178505,
0.01735384203493595,
-0.025593729689717293,
0.0617867037653923,
-0.04340994358062744,
-0.013878467492759228,
0.03646616265177727,
-0.011601408943533897,
0.03370946645736694,
-0.03602609783411026,
0.006704162806272507,
-0.018939508125185966,
0.009843236766755581,
0.034499604254961014,
0.00550031429156661,
-0.0173256266862154,
0.06249214708805084,
0.01618773117661476,
0.011879905126988888,
0.008999166078865528,
0.010232127271592617,
0.017414791509509087,
-0.01829209364950657,
0.048223186284303665,
-0.006076576188206673,
-0.01183462142944336,
-0.030906684696674347,
-0.03987274318933487,
-0.05970555171370506,
-0.03179197385907173,
-0.0023531822953373194,
0.00577373756095767,
0.012381280772387981,
-0.0014127457980066538,
0.0001590337633388117,
-0.0044974456541240215,
-0.057921722531318665,
0.023312274366617203,
-0.016505451872944832,
0.0012755170464515686,
-0.013943511992692947,
-0.004077124409377575,
0.04452250525355339,
0.042582157999277115,
-0.02058044821023941,
0.007835986092686653,
-0.02407565712928772,
-0.00016103626694530249,
0.0016826530918478966,
-0.02072739414870739,
-0.033848829567432404,
-0.004957857541739941,
-0.05556665360927582,
0.022030843421816826,
-0.008634090423583984,
0.010596176609396935,
-0.011506253853440285,
-0.0015917617129161954,
0.003102879272773862,
0.040775928646326065,
-0.0444522425532341,
0.013178246095776558,
-0.0029112750198692083,
-0.007573729380965233,
0.008158564567565918,
0.009613648056983948,
0.010869462974369526,
-0.005309796426445246,
-0.06320897489786148,
-0.028185192495584488,
0.004347737412899733,
-0.004993777722120285,
0.027102548629045486,
-0.005807619541883469,
-0.007735653780400753,
-0.028397250920534134,
-0.011216992512345314,
-0.04923257604241371,
-0.014299210160970688,
-0.06545258313417435,
0.01417558267712593,
-0.0006594479782506824,
-0.0050818840973079205,
-0.005367397330701351,
0.03905452415347099,
-0.019493326544761658,
-0.02962660603225231,
0.012011404149234295,
0.002622671192511916,
-0.011959664523601532,
0.04923553392291069,
0.027524828910827637,
-0.021180439740419388,
0.042264197021722794,
-0.0012230277061462402,
-0.010836743749678135,
0.013098426163196564,
-0.01808270998299122,
-0.03664139285683632,
0.02631681226193905,
-0.021578634157776833,
0.038417380303144455,
0.005905841011554003,
0.00836965162307024,
-0.02783469669520855,
0.033142898231744766,
0.00013964236131869256,
0.011745525524020195,
-0.0019111082656309009,
-0.07469963282346725,
-0.01861434429883957,
0.005518403835594654,
0.052414365112781525,
-0.009208446368575096,
-0.001841451390646398,
0.007959251292049885,
-0.011340879835188389,
0.007027050014585257,
0.010349403135478497,
-0.0031199755612760782,
-0.00031046182266436517,
0.01232136134058237,
0.032877013087272644,
-0.029850531369447708,
0.030685709789395332,
0.06052996963262558,
-0.042025692760944366,
0.0008647312643006444,
0.029478514567017555,
0.044034697115421295,
-0.10307887941598892,
-0.014714621938765049,
0.03875484690070152,
0.023637082427740097,
0.017128681764006615,
-0.03783610835671425,
-0.004766988102346659,
-0.014545813202857971,
-0.05822538211941719,
0.06421972811222076,
-0.005303601734340191,
-0.03355657309293747,
-0.017260847613215446,
-0.009897880256175995,
-0.025167565792798996,
0.031759168952703476,
-0.0025715355295687914,
0.04616204649209976,
-0.014571347273886204,
0.009715110063552856,
0.01829427294433117,
-0.036725640296936035,
0.005196850746870041,
0.013926316052675247,
0.020449217408895493,
-0.009410527534782887,
0.06324901431798935,
-0.01328262872993946,
-0.04285673424601555,
0.014541162177920341,
0.0012416832614690065,
-0.03334639593958855,
-0.017869222909212112,
0.016107823699712753,
0.03560839965939522,
0.0323425717651844,
-0.002782296622171998,
-0.025586191564798355,
0.0026536830700933933,
-0.002808197634294629,
0.010228851810097694,
0.001140512409619987,
0.012418140657246113,
0.03308567777276039,
0.009184900671243668,
-0.03074752166867256,
0.01742161624133587,
0.04249396175146103,
-0.0022897531744092703,
-0.016242943704128265,
-0.02220161445438862,
0.017232641577720642,
0.015558267012238503,
0.005986385978758335,
0.006719376426190138,
-0.07471130043268204,
0.007369454018771648,
-0.002832494443282485,
0.023195752874016762,
0.006601221859455109,
0.03403456509113312,
-0.008606416173279285,
0.011039186269044876,
0.004447015002369881,
0.029835529625415802,
0.03707391768693924,
-0.055272117257118225,
-0.016675293445587158,
0.0030836272053420544,
-0.001864577759988606,
0.03173400089144707,
-0.06068781018257141,
0.012177253141999245,
0.03565241023898125,
0.014864318072795868,
0.06412618607282639,
-0.042086873203516006,
-0.041593942791223526,
0.04291307181119919,
-0.06952726095914841,
0.03973015770316124,
-0.022937757894396782,
0.007169180084019899,
-0.004253410268574953,
-0.01997138187289238,
0.017518384382128716,
0.05319061502814293,
0.05507741495966911,
-0.011259539984166622,
0.003172073746100068,
-0.008555211126804352,
-0.04490140825510025,
0.006958636920899153,
-0.02107052132487297,
-0.025272006168961525,
-0.016463400796055794,
-0.025041205808520317,
-0.00937457475811243,
0.009603578597307205,
-0.029111187905073166,
0.009317190386354923,
0.055504441261291504,
0.001920618349686265,
0.03232325240969658,
-0.027553042396903038,
-0.054153453558683395,
0.04186078906059265,
0.03715207055211067,
-0.0052507552318274975,
0.09250789135694504,
-0.004937044344842434,
0.03738130256533623,
0.04878172278404236,
-0.02885291911661625,
-0.04201725125312805,
0.04178021475672722,
-0.029827820137143135,
-0.024430440738797188,
-0.01816944219172001,
0.027374200522899628,
0.03016561083495617,
-0.04757075756788254,
0.00906853936612606,
0.04249479994177818,
-0.05037836730480194,
0.009177361615002155,
0.08461914211511612,
0.02857750654220581,
0.029586520045995712,
0.014439080841839314,
0.0007317446288652718,
0.0203255508095026,
-0.012656125240027905,
-0.02730168215930462,
-0.006502410396933556,
0.041646432131528854,
-0.004860106389969587,
0.002374084899201989,
0.0220413226634264,
-0.03337419405579567,
0.008493355475366116,
0.014161000959575176,
0.0058437371626496315,
-0.030753187835216522,
0.03514820337295532,
0.0422750823199749,
0.0053871190175414085,
0.0272798053920269,
0.011963614262640476,
-0.008939060382544994,
0.11179496347904205,
0.0049362387508153915,
0.014715169556438923,
-0.013426519930362701,
-0.012485924176871777,
-0.007134540472179651,
0.061357755213975906,
0.05593017116189003,
0.07024171203374863,
0.01539971400052309,
-0.007668347097933292,
-0.02920922264456749,
-0.013686751015484333,
-0.024002352729439735,
-0.027216095477342606,
0.02714463509619236,
-0.01540573500096798,
-0.025840330868959427,
0.031127117574214935,
-0.008194063790142536,
-0.015520050190389156,
0.009919230826199055,
0.018166176974773407,
0.01677590422332287,
-0.02013239823281765,
0.005684292875230312,
0.021593527868390083,
-0.0035319416783750057,
0.0461500883102417,
-0.0649208128452301,
0.020549239590764046,
-0.013600586913526058,
0.04960664361715317,
-0.00040770822670310736,
-0.020093467086553574
] |
<p>What are some good lecture notes to learn quantum field theory from, available online?</p>
| 282 |
[
0.01691322773694992,
-0.06522119045257568,
0.004482240416109562,
-0.019762123003602028,
0.022890841588377953,
0.001213012496009469,
0.014527489431202412,
-0.02102743461728096,
-0.004807292018085718,
-0.0507483072578907,
0.016834383830428123,
0.02074349671602249,
0.008232255466282368,
0.015152500942349434,
0.004318875726312399,
0.012291617691516876,
0.0069570778869092464,
-0.035950202494859695,
-0.015588734298944473,
0.01402147114276886,
-0.011661196127533913,
0.04155619442462921,
0.009339365176856518,
0.027163544669747353,
-0.00293488847091794,
0.02748679742217064,
0.023006347939372063,
0.05465320497751236,
0.005157525651156902,
0.08644324541091919,
-0.009266415610909462,
-0.03654112666845322,
-0.02115245908498764,
0.04424567520618439,
0.011542187072336674,
-0.015834752470254898,
0.0003137772437185049,
-0.020850684493780136,
-0.0004596320213750005,
-0.027752021327614784,
-0.03726629540324211,
-0.043140314519405365,
0.005507768597453833,
0.0571100153028965,
-0.008507313206791878,
0.020647482946515083,
-0.015974674373865128,
-0.02310185134410858,
0.06484176963567734,
-0.06336397677659988,
0.052991826087236404,
0.016104046255350113,
0.024947617202997208,
0.03827295079827309,
0.006096102297306061,
-0.0015822373097762465,
0.06822836399078369,
0.06722244620323181,
-0.008766666986048222,
-0.06456620991230011,
-0.04621630534529686,
-0.06321297585964203,
-0.006821766961365938,
-0.05317044258117676,
-0.03897273167967796,
0.05415785685181618,
0.014568725600838661,
-0.018346527591347694,
0.010817685164511204,
-0.009929683990776539,
-0.00953390821814537,
0.030406346544623375,
0.0719500407576561,
-0.004354433622211218,
-0.004560166969895363,
0.006723094265908003,
-0.0013964639510959387,
-0.003766670124605298,
0.021463986486196518,
0.034632764756679535,
-0.005402421113103628,
0.01943395473062992,
0.00823602918535471,
0.018702104687690735,
-0.011144068092107773,
-0.021743623539805412,
0.07823203504085541,
0.015071647241711617,
-0.04868173971772194,
0.04525135084986687,
-0.04954546317458153,
-0.02783738449215889,
0.03421946242451668,
-0.03549153357744217,
-0.03357388451695442,
0.038725823163986206,
0.019875114783644676,
0.03713268041610718,
0.032411713153123856,
-0.012000254355370998,
-0.012257358990609646,
-0.029828332364559174,
-0.008799047209322453,
0.0720532014966011,
0.013327036052942276,
-0.017287280410528183,
-0.0375872477889061,
0.034791868180036545,
-0.02058255858719349,
-0.011137282475829124,
-0.024842113256454468,
0.03174041584134102,
-0.01733098179101944,
-0.006566155701875687,
-0.01767883636057377,
-0.03372180461883545,
-0.00610340153798461,
-0.0350550040602684,
0.05307891219854355,
0.08535680174827576,
0.04474516585469246,
-0.05142742767930031,
0.026850538328289986,
-0.023282237350940704,
-0.06602299213409424,
-0.005107187665998936,
0.04401960223913193,
-0.02477962337434292,
-0.05859687924385071,
0.037757955491542816,
-0.01583605632185936,
-0.010811924934387207,
-0.0009825351880863309,
0.0024819914251565933,
0.028146129101514816,
-0.02028917334973812,
-0.10824988782405853,
-0.04194187372922897,
0.03083590418100357,
-0.03655340522527695,
-0.013964330777525902,
-0.02722109481692314,
0.02534109354019165,
0.022898603230714798,
0.062253471463918686,
0.019248098134994507,
0.01056322455406189,
-0.02747412584722042,
0.030922893434762955,
-0.028168749064207077,
-0.019145790487527847,
0.005784973967820406,
-0.025310978293418884,
0.009981674142181873,
0.006773484405130148,
-0.04309261962771416,
0.012953587807714939,
0.02251366339623928,
-0.0018569082021713257,
-0.035180334001779556,
0.08877167105674744,
-0.0270747859030962,
0.0282608550041914,
0.00972613412886858,
-0.0280737467110157,
-0.01630319096148014,
0.05184469744563103,
-0.014736589975655079,
0.020997175946831703,
0.041736770421266556,
0.0014694331912323833,
0.023440038785338402,
-0.02993512526154518,
0.025921212509274483,
0.009517966769635677,
-0.03028940223157406,
-0.014749784953892231,
0.008994990028440952,
0.006766024511307478,
-0.018441958352923393,
-0.03130932152271271,
-0.036377739161252975,
0.0041242497973144054,
0.03995339944958687,
-0.06371121108531952,
0.038042742758989334,
0.013472437858581543,
0.025129543617367744,
0.016535017639398575,
-0.04570388421416283,
-0.04738137871026993,
-0.0532100573182106,
0.04508241266012192,
0.008708983659744263,
0.03292660787701607,
0.05621740594506264,
0.03412090614438057,
0.014155065640807152,
-0.050422586500644684,
-0.07064637541770935,
-0.02248562127351761,
0.037014350295066833,
0.008223767392337322,
-0.011836359277367592,
0.023166343569755554,
0.04078809916973114,
0.029703643172979355,
-0.007844030857086182,
0.04554859921336174,
-0.037280235439538956,
-0.01255476288497448,
0.013041699305176735,
-0.012180489487946033,
0.05302207171916962,
-0.0478736087679863,
0.020889457315206528,
-0.01018843799829483,
-0.0018854959635064006,
-0.022960050031542778,
0.017469963058829308,
-0.025673475116491318,
0.037993740290403366,
0.0072110723704099655,
0.04577610641717911,
-0.021216321736574173,
0.019863801077008247,
0.0018722843378782272,
-0.010557611472904682,
-0.00530523806810379,
-0.03057585470378399,
-0.02437671460211277,
0.013060566037893295,
0.07360558956861496,
0.015670031309127808,
-0.017020324245095253,
0.045645058155059814,
0.01772993803024292,
0.02724386565387249,
0.017129618674516678,
0.021891752257943153,
-0.049002714455127716,
-0.0463826060295105,
0.00787034910172224,
-0.021208707243204117,
0.0035686842165887356,
0.015852175652980804,
0.035783641040325165,
0.023847632110118866,
0.020063146948814392,
0.02877049148082733,
-0.0732339471578598,
0.0033161912579089403,
-0.04120390862226486,
-0.010511497035622597,
0.009137910790741444,
-0.06126716732978821,
0.02962806262075901,
-0.035522498190402985,
0.037612903863191605,
-0.0283036045730114,
-0.05935477465391159,
0.010891769081354141,
-0.013261324726045132,
-0.03929619491100311,
0.04932079836726189,
-0.022471878677606583,
-0.025397974997758865,
0.021609174087643623,
0.03946608304977417,
-0.04723770543932915,
0.012470549903810024,
0.009442998096346855,
-0.028100989758968353,
-0.01916256919503212,
-0.010991403833031654,
0.028126096352934837,
0.00040175957838073373,
0.003958995919674635,
-0.005011518020182848,
-0.010825643315911293,
0.05109556391835213,
-0.043737951666116714,
0.03029526397585869,
0.020776143297553062,
-0.008341138251125813,
0.031957417726516724,
-0.06196453422307968,
-0.04759528860449791,
0.04348370432853699,
0.004919217433780432,
0.017478780820965767,
0.013357098214328289,
-0.005847690161317587,
-0.03146645426750183,
-0.015697773545980453,
-0.0001362139591947198,
0.010181523859500885,
-0.0007825259235687554,
0.015528182499110699,
0.007851672358810902,
-0.027908042073249817,
-0.024845298379659653,
0.008562573231756687,
-0.011431179940700531,
-0.03288956359028816,
-0.013246134854853153,
0.017443548887968063,
0.0162749532610178,
-0.04165247082710266,
0.000015954365153447725,
0.019729191437363625,
-0.054965946823358536,
-0.011622139252722263,
-0.02890845388174057,
-0.01601293310523033,
0.010814500041306019,
0.03059486299753189,
0.025494758039712906,
-0.005246555432677269,
-0.009846228174865246,
0.0684753805398941,
0.04185470566153526,
-0.025169197469949722,
-0.011814283207058907,
-0.01932806707918644,
-0.03124072402715683,
-0.01160411350429058,
0.04759376496076584,
-0.018648898229002953,
-0.0331258662045002,
0.01713898964226246,
0.00249232305213809,
0.00980935338884592,
0.03296596556901932,
0.01600036397576332,
-0.0017449097940698266,
0.020915668457746506,
-0.024565106257796288,
-0.01816132478415966,
0.0367501899600029,
0.005131813697516918,
-0.06010221317410469,
-0.006071504205465317,
0.020840153098106384,
0.009030768647789955,
0.004001783672720194,
-0.005611857865005732,
0.07722769677639008,
0.002591540338471532,
-0.001387994852848351,
-0.03863637149333954,
0.0339377224445343,
-0.025563642382621765,
-0.03253033012151718,
0.013453071005642414,
-0.005099666770547628,
-0.0017174611566588283,
0.002185857156291604,
0.01586133800446987,
0.023915402591228485,
0.04746103659272194,
-0.06274056434631348,
-0.024969523772597313,
-0.005849913228303194,
-0.013764706440269947,
0.023010320961475372,
-0.026961706578731537,
-0.01171525102108717,
0.04780003800988197,
0.05764460563659668,
0.013148369267582893,
-0.019244041293859482,
-0.034123744815588,
-0.010516492649912834,
-0.0690263882279396,
0.030025437474250793,
-0.006108215544372797,
0.042556218802928925,
0.017752937972545624,
0.05565237998962402,
0.003234302392229438,
0.01650342345237732,
0.019330762326717377,
0.02050807513296604,
-0.07145755738019943,
0.017483435571193695,
-0.050250012427568436,
-0.0026653725653886795,
0.0006502943579107523,
0.025202739983797073,
0.01929379440844059,
0.008879829198122025,
-0.06999221444129944,
-0.03893183171749115,
-0.010952468030154705,
-0.042258795350790024,
-0.008564714342355728,
-0.05402911826968193,
-0.02423122525215149,
-0.005375420209020376,
0.01601565256714821,
0.019752228632569313,
-0.044836074113845825,
-0.00024967288482002914,
0.0603274442255497,
-0.04493337124586105,
-0.011032299138605595,
0.02879030816257,
0.04331006482243538,
0.00025014474522322416,
0.012115322053432465,
0.03986617177724838,
0.02677103877067566,
-0.045654673129320145,
-0.005304696969687939,
-0.017037708312273026,
0.05608925595879555,
0.0029950644820928574,
-0.03885551542043686,
0.010064116679131985,
-0.041096389293670654,
-0.00856600608676672,
0.0028419606387615204,
0.05314040184020996,
0.017977934330701828,
0.004776495974510908,
0.05568400397896767,
-0.010769981890916824,
-0.030713791027665138,
0.02113465592265129,
0.053880658000707626,
-0.018291277810931206,
-0.0325259231030941,
-0.006280339322984219,
0.007295318879187107,
-0.019768113270401955,
-0.0002282313071191311,
-0.008914560079574585,
0.006316458340734243,
-0.022334793582558632,
-0.0037787032779306173,
0.02893356792628765,
0.017859287559986115,
-0.04540371522307396,
0.0001111946112359874,
0.01917036809027195,
0.012920853681862354,
-0.013300009071826935,
-0.026076115667819977,
0.0017658465076237917,
0.056793831288814545,
0.057820919901132584,
0.019315650686621666,
-0.008298886008560658,
-0.07517451047897339,
-0.009967309422791004,
0.05306650698184967,
0.026026930660009384,
0.011867621913552284,
0.01289444975554943,
-0.05071601644158363,
-0.043304573744535446,
0.0768205001950264,
-0.015018794685602188,
-0.00280574057251215,
-0.014435677789151669,
-0.036845527589321136,
-0.02014766074717045,
0.0003984019858762622,
-0.03233032673597336,
0.024486221373081207,
-0.004217904061079025,
0.027120370417833328,
-0.029273273423314095,
-0.005998249165713787,
-0.028972137719392776,
0.019630271941423416,
0.02741238661110401,
0.04415983334183693,
0.03865443170070648,
0.018955370411276817,
-0.004193703643977642,
0.04732978716492653,
-0.0536997988820076,
-0.06388325989246368,
-0.003177610458806157,
0.006117525044828653,
-0.023178404197096825,
0.02507833018898964,
-0.020371973514556885,
-0.05647856742143631,
-0.0015408007893711329,
-0.009033823385834694,
-0.028890585526823997,
0.006201303564012051,
-0.048768576234579086,
0.004210554528981447,
-0.02080865018069744,
0.017110969871282578,
0.041276223957538605,
0.043922942131757736,
-0.03066311776638031,
-0.025086713954806328,
-0.021663974970579147,
0.06867331266403198,
-0.007701193448156118,
0.034111715853214264,
-0.03191716969013214,
-0.027695003896951675,
-0.03564037010073662,
0.03238257020711899,
-0.052511297166347504,
0.010419410653412342,
-0.021595245227217674,
-0.0308227501809597,
-0.01849583350121975,
0.009055702947080135,
-0.005814639385789633,
-0.008964869193732738,
0.012852366082370281,
0.0026228823699057102,
0.006369979586452246,
-0.011471965350210667,
0.029983771964907646,
0.022312430664896965,
-0.01382360514253378,
-0.0025409096851944923,
-0.02273496426641941,
0.01557223405689001,
-0.040285564959049225,
-0.044365063309669495,
-0.01643545739352703,
-0.04571482911705971,
0.0676787793636322,
0.0047766040079295635,
-0.012835978530347347,
0.0032081541139632463,
-0.04359547048807144,
-0.0454859659075737,
-0.003061153693124652,
-0.007832626812160015,
0.014292094856500626,
-0.036694031208753586,
0.011295861564576626,
0.001550947199575603,
0.01188572309911251,
-0.03828490898013115,
-0.06619598716497421,
0.017497189342975616,
-0.0024096283596009016,
-0.010149192065000534,
-0.035792604088783264,
0.05252755433320999,
-0.02280496247112751,
-0.00431060092523694,
-0.025941772386431694,
0.0402836874127388,
-0.023293379694223404,
0.0027366785798221827,
0.004163416102528572,
0.02338823862373829,
0.026671774685382843,
0.02826623246073723,
-0.005368524231016636,
0.025768183171749115,
0.02272968739271164,
-0.022752629593014717,
0.006482558790594339,
0.046966854482889175,
-0.017517145723104477,
0.005493827164173126,
-0.018662458285689354,
0.015187280252575874,
-0.006892087869346142,
-0.051416750997304916,
0.030828645452857018,
0.0487251840531826,
0.017885638400912285,
-0.019477834925055504,
-0.052337292581796646,
0.012865718454122543,
-0.0009520581807009876,
0.02949102222919464,
-0.014830831438302994,
-0.011225061491131783,
0.02906704507768154,
-0.03350691497325897,
0.0199674591422081,
0.023402811959385872,
0.018644878640770912,
0.019161516800522804,
0.05804947391152382,
0.011150469072163105,
-0.029409000650048256,
0.046744704246520996,
-0.04729260131716728,
-0.006238855887204409,
0.007092522457242012,
0.052240099757909775,
0.00853358581662178,
0.015311512164771557,
-0.017984146252274513,
-0.03691666200757027,
-0.023704536259174347,
-0.00917131919413805,
0.04570538550615311,
0.04548778384923935,
0.047350864857435226,
0.04459232836961746,
-0.009130368009209633,
-0.005041216034442186,
0.009798051789402962,
-0.04348504915833473,
0.007565511856228113,
0.01750349998474121,
0.04244070127606392,
-0.05159446597099304,
0.027345899492502213,
0.004204168450087309,
0.04333793744444847,
-0.03540785238146782,
0.04355678707361221,
0.03654826804995537,
0.01599806360900402,
0.034158773720264435,
-0.013415299355983734,
-0.059962689876556396,
0.03157922253012657,
-0.05309796705842018,
0.03635578602552414,
-0.026046453043818474,
-0.008043454959988594,
0.0351613387465477,
0.0044401721097528934,
0.013846255838871002,
-0.006934355944395065,
-0.03384490683674812,
-0.05526028946042061,
0.01851373165845871,
0.0012602814240381122,
0.009251777082681656,
-0.008004185743629932,
0.033835746347904205,
0.03302532434463501,
0.012520705349743366,
0.017787812277674675,
0.016849081963300705,
-0.05837376043200493,
-0.061198294162750244,
-0.02896786853671074,
-0.053086988627910614,
0.030145466327667236,
0.02232416719198227,
-0.023569080978631973,
0.00328790838830173,
-0.029285898432135582,
0.03690977767109871,
0.006369637791067362,
0.03361808508634567,
-0.0360228605568409,
0.0432080514729023,
-0.02285761944949627,
-0.01916397549211979,
-0.007433402352035046,
-0.004217874258756638,
0.1147289127111435,
0.06582191586494446,
0.040347009897232056,
-0.09528017044067383,
0.044392988085746765,
-0.014683411456644535,
0.025723896920681,
-0.06143640726804733,
0.031403012573719025,
-0.015905005857348442,
0.025190474465489388,
0.027294080704450607,
0.04610775038599968,
0.026085438206791878,
0.01064075157046318,
0.052302997559309006,
-0.027216624468564987,
-0.05926449969410896,
-0.0314890518784523,
0.02418852597475052,
-0.0071938540786504745,
0.038965124636888504,
-0.050902772694826126,
0.013912689872086048,
-0.02694941870868206,
0.018305087462067604,
-0.017297500744462013,
-0.0388120636343956,
0.0534590445458889,
0.002009453484788537,
-0.004415474366396666,
0.00026390067068859935,
0.012035006657242775,
0.00865707453340292,
-0.02769896760582924,
0.021613834425807,
0.0468272902071476,
0.010551833547651768,
0.02809709869325161,
0.009171219542622566,
0.02777084894478321,
0.004996938165277243,
-0.0038160469848662615,
0.017115773633122444,
-0.037786275148391724,
-0.0009414314408786595,
-0.029654311016201973,
0.03955509513616562,
-0.024042237550020218,
0.0061739045195281506,
-0.005003522150218487,
0.010562902316451073,
0.01710139773786068,
-0.022609470412135124,
-0.013728192076086998,
0.02582053281366825,
0.03945920616388321,
-0.05787091702222824,
0.01812942512333393,
-0.032424286007881165,
0.039036110043525696,
-0.014569206163287163,
0.003381178481504321,
0.005701035726815462,
-0.015932707116007805,
0.011778149753808975,
0.004433217458426952,
0.005822329316288233,
-0.01940961182117462,
-0.027432706207036972,
0.031151315197348595,
-0.003714524442330003,
-0.018907316029071808,
-0.024019142612814903,
0.015655741095542908,
0.009454828687012196,
0.04503907635807991,
-0.00099570257589221,
0.008418258279561996,
0.004676135256886482,
-0.052308738231658936,
0.011244915425777435,
-0.0398397371172905,
-0.022063031792640686,
0.004416576121002436,
0.006972155999392271,
0.014021949842572212,
0.03594852238893509,
0.014279771596193314,
0.004926284309476614,
0.0014694469282403588,
-0.005425226408988237,
0.039831001311540604,
-0.020832689478993416,
0.02408997341990471,
-0.019118035212159157,
-0.0483626089990139,
-0.020107921212911606,
-0.03933170810341835,
0.014804903417825699,
0.05407138168811798,
-0.019533352926373482,
0.012873074039816856,
0.01674102246761322,
-0.02606767788529396,
0.007330758962780237,
0.014044929295778275,
-0.05380985140800476,
0.0034145803656429052,
0.045080091804265976,
0.03540906682610512,
-0.045884475111961365,
-0.08107489347457886,
0.00439309049397707,
0.0096714086830616,
-0.01246742345392704,
0.02707737311720848,
-0.03484310582280159,
0.025767207145690918,
0.004551293794065714,
0.03631177544593811,
-0.05641278252005577,
-0.00243130954913795,
-0.04875868186354637,
-0.012259241193532944,
0.030663583427667618,
-0.0257351603358984,
-0.01617279276251793,
0.019927214831113815,
0.004198206122964621,
-0.001081025809980929,
0.027840254828333855,
0.02295391447842121,
-0.0019919159822165966,
0.002273027552291751,
0.01960536651313305,
0.000613281677942723,
0.023164980113506317,
0.009815122000873089,
-0.0316007137298584,
0.006572541315108538,
-0.05382939428091049,
-0.055203501135110855,
0.03844505548477173,
-0.016057558357715607,
0.02905416116118431,
0.020778585225343704,
-0.027264421805739403,
-0.022251928225159645,
0.03946348652243614,
-0.012365134432911873,
-0.02872825413942337,
0.008820518851280212,
-0.01895763725042343,
0.009187784045934677,
-0.01262617390602827,
0.025878215208649635,
-0.007159985601902008,
-0.022373026236891747,
0.006221634801477194,
0.02323959767818451,
0.008309167809784412,
0.00044594870996661484,
0.0023557725362479687,
-0.0009109348757192492,
0.05587002635002136,
0.020685452967882156,
-0.012738103047013283,
0.0066495840437710285,
0.05168412998318672,
-0.030922310426831245,
0.025729568675160408,
0.010771566070616245,
0.031959645450115204,
-0.08384934067726135,
-0.01240647304803133,
0.00792374275624752,
0.0012867822078987956,
0.04239673539996147,
-0.06298457086086273,
0.004229113459587097,
0.06053333356976509,
-0.053479310125112534,
0.04388302192091942,
0.00005802032319479622,
-0.048344533890485764,
0.00321793369948864,
-0.011071830987930298,
-0.004631455522030592,
0.0783209428191185,
0.018573995679616928,
0.048504143953323364,
0.0054036350920796394,
0.011907437816262245,
0.007839553989470005,
-0.018498780205845833,
-0.015766343101859093,
0.011576659046113491,
0.009667309001088142,
-0.03751223534345627,
0.035631876438856125,
0.005410597659647465,
-0.02154279500246048,
0.02171928435564041,
-0.003355814376845956,
-0.002810486126691103,
-0.016852399334311485,
0.014003623276948929,
-0.005341861862689257,
0.05114806070923805,
0.00313263526186347,
-0.009375234134495258,
0.007982234470546246,
-0.00031447812216356397,
0.012987286783754826,
0.01295687910169363,
-0.004905368201434612,
0.038150060921907425,
-0.007811958435922861,
-0.04268061742186546,
-0.04509001597762108,
0.035649947822093964,
-0.008596683852374554,
-0.040689725428819656,
-0.019523175433278084,
-0.006977562792599201,
-0.026400238275527954,
-0.027182063087821007,
0.021728718653321266,
-0.0584859661757946,
-0.019641680642962456,
0.02495243214070797,
-0.005200705956667662,
0.016886426135897636,
0.03327605128288269,
-0.007340732496231794,
-0.01493827160447836,
0.039472807198762894,
0.016465257853269577,
0.021568382158875465,
-0.03827648609876633,
-0.004645610228180885,
0.017330357804894447,
-0.0006130945403128862,
0.01574588194489479,
-0.046924933791160583,
-0.01484494749456644,
-0.02069174125790596,
-0.017181716859340668,
0.014164194464683533,
-0.016902601346373558,
-0.01241594273597002,
0.009403994306921959,
-0.042033761739730835,
0.021532874554395676,
0.0032911014277487993,
0.017079290002584457,
-0.026452966034412384,
0.0134115656837821,
0.014360698871314526,
-0.016184238716959953,
0.02644267864525318,
-0.021588735282421112,
0.013696095906198025,
-0.006523848976939917,
-0.007930617779493332,
0.024581361562013626,
-0.018711421638727188,
0.019551506265997887,
-0.035001616925001144,
-0.028368450701236725,
-0.022473540157079697,
-0.0019639059901237488,
0.03648833930492401,
0.040683794766664505,
0.030338717624545097,
0.03796286880970001,
0.007631505839526653,
-0.01290399394929409,
-0.050893720239400864,
0.04562114551663399,
0.02702084556221962,
-0.0007247930625453591,
0.053481604903936386,
-0.036429330706596375,
0.026824939996004105,
0.022790713235735893,
-0.02531898394227028,
-0.011180252768099308,
0.044420428574085236,
-0.05047299712896347,
-0.01303766667842865,
-0.006962452549487352,
-0.010191100649535656,
-0.030893150717020035,
-0.04316628351807594,
0.02196764573454857,
0.051646918058395386,
-0.004870875738561153,
0.006023940164595842,
0.05517447739839554,
0.013461343944072723,
0.05374810844659805,
0.028835875913500786,
-0.0007613238994963467,
0.05824775993824005,
0.021999457851052284,
-0.007806851528584957,
0.008300714194774628,
0.05046107620000839,
0.004252464510500431,
0.04645863175392151,
0.02781243994832039,
-0.03764207661151886,
0.01370440423488617,
-0.01476974319666624,
0.021573128178715706,
-0.05697448551654816,
-0.04014643281698227,
0.017619414255023003,
-0.03202441707253456,
0.00948187243193388,
0.009201508946716785,
-0.03980636969208717,
0.07260904461145401,
-0.06032704561948776,
0.007096402812749147,
-0.0014457493089139462,
0.0011231311364099383,
-0.03428422287106514,
-0.001632547122426331,
0.010456092655658722,
0.08728370815515518,
-0.024677345529198647,
0.0004685967287514359,
-0.012924822978675365,
-0.009700204245746136,
0.010248756036162376,
-0.06340931355953217,
0.026941964402794838,
0.01738744229078293,
-0.013242039829492569,
-0.007098515518009663,
-0.008380956016480923,
-0.0005155295366421342,
0.004775603301823139,
0.014544851146638393,
0.05451943352818489,
0.013291051611304283,
-0.04244501516222954,
0.005737172905355692,
-0.05327700823545456,
0.047702159732580185,
-0.05421086400747299,
0.048483751714229584,
-0.0230849739164114,
0.004980983212590218,
-0.03564949706196785,
0.02345138043165207
] |
<p>I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 m.</p>
<p>Could somebody help me derive some equations to help with this? Or to get me in the right direction? I have been trying to derive some sort of equations from $E=\frac{I \cdot \omega ^{2}}{2}$ but I cant get anywhere without ending up at radius = radius or mass = mass.</p>
<p>I need the final angular velocity.</p>
| 894 |
[
-0.008430244401097298,
-0.021152669563889503,
-0.04435741901397705,
-0.0066589233465492725,
-0.010225350968539715,
0.006074018310755491,
-0.053427912294864655,
-0.006989808287471533,
0.02179817669093609,
-0.04358937591314316,
0.0029438366182148457,
0.06422852724790573,
0.04541463777422905,
0.02141110971570015,
-0.021902775391936302,
0.011028733104467392,
-0.038505952805280685,
0.006471717730164528,
0.000992880784906447,
-0.018996061757206917,
0.008923892863094807,
0.012598085217177868,
-0.009961100295186043,
-0.005073642823845148,
-0.014989659190177917,
0.007678542286157608,
0.06339524686336517,
-0.025275900959968567,
0.0054428111761808395,
0.052840832620859146,
0.024580171331763268,
-0.02215803973376751,
0.02037997357547283,
0.0633169412612915,
0.006600805092602968,
0.03852011635899544,
-0.04242323338985443,
-0.02172296866774559,
-0.0169984083622694,
0.05131206288933754,
0.0030347267165780067,
0.008708258159458637,
-0.024610834196209908,
0.028845909982919693,
0.004983111750334501,
0.02077155001461506,
-0.04330776631832123,
-0.000138722694828175,
0.06873562932014465,
-0.06023181974887848,
0.08032190054655075,
-0.0036926863249391317,
0.016457531601190567,
0.014371270313858986,
-0.012817585840821266,
-0.038620445877313614,
0.059033945202827454,
0.05451193451881409,
-0.0011253476841375232,
-0.06323806196451187,
-0.0074933175928890705,
-0.04666312783956528,
-0.0100493049249053,
-0.05008137226104736,
-0.026098880916833878,
0.00035968556767329574,
-0.022600997239351273,
0.015357404947280884,
0.02735186368227005,
0.0025939717888832092,
0.02588418498635292,
0.035238172858953476,
0.05804399028420448,
-0.02697393111884594,
0.0239116121083498,
-0.03167684003710747,
0.00886549986898899,
0.010192599147558212,
0.005708057899028063,
0.04306558147072792,
-0.0020304820500314236,
-0.013941938988864422,
0.03678132966160774,
0.031953249126672745,
-0.00003302740151411854,
-0.009700200520455837,
0.04580758139491081,
-0.0053296564146876335,
0.03272487595677376,
0.022870253771543503,
0.00905627477914095,
-0.0424700565636158,
0.01548297144472599,
-0.011071235872805119,
0.0021305985283106565,
0.03568050265312195,
0.0018180496990680695,
0.07434608787298203,
0.003790732240304351,
-0.0057885958813130856,
0.0006652504089288414,
-0.05118986964225769,
0.015422573313117027,
0.0894785225391388,
0.006500700023025274,
-0.009841548278927803,
-0.019416773691773415,
-0.0319584496319294,
-0.02669709175825119,
-0.02457522042095661,
-0.03393755108118057,
-0.0030530423391610384,
0.02039252780377865,
-0.03459819778800011,
-0.03704101964831352,
-0.04490281641483307,
-0.01734793558716774,
-0.035965193063020706,
0.057070840150117874,
0.02777998149394989,
0.02465517446398735,
-0.02197633683681488,
0.0012626497773453593,
-0.05147983878850937,
-0.024502871558070183,
0.009780197404325008,
0.050915323197841644,
-0.038125962018966675,
-0.060202669352293015,
0.003274851245805621,
-0.01368041429668665,
-0.04015905782580376,
0.012685841880738735,
0.0033238318283110857,
0.05067376047372818,
0.008363008499145508,
-0.10091811418533325,
-0.07057684659957886,
0.03347807750105858,
-0.01826905459165573,
-0.024513214826583862,
-0.08135618269443512,
-0.01125978771597147,
0.045141469687223434,
0.04069238901138306,
-0.0115934107452631,
0.02755187451839447,
-0.0034823487512767315,
0.022090116515755653,
0.009462318383157253,
-0.029231112450361252,
-0.024762701243162155,
-0.005214817356318235,
-0.018503768369555473,
-0.01101718284189701,
-0.04288545995950699,
0.0018286611884832382,
0.005791859235614538,
-0.017663318663835526,
-0.011151139624416828,
0.043958134949207306,
-0.002947992878034711,
0.0052921585738658905,
0.021741753444075584,
0.0340862050652504,
-0.05777280032634735,
0.08582247048616409,
0.04148588702082634,
-0.04218018054962158,
0.04160446673631668,
0.02409796603024006,
0.03223910927772522,
-0.014507931657135487,
-0.011381772346794605,
0.033084701746702194,
-0.041064485907554626,
0.018301870673894882,
-0.010828081518411636,
-0.01302291825413704,
0.010188775137066841,
-0.013943635858595371,
-0.07841155678033829,
-0.007997892796993256,
-0.036550406366586685,
0.0015508412616327405,
0.06289241462945938,
-0.021662110462784767,
-0.03543175756931305,
-0.0018228759290650487,
-0.02294088527560234,
0.011755704879760742,
-0.02673613838851452,
0.023732628673315048,
-0.013756869360804558,
-0.007207551971077919,
-0.007075812201946974,
0.035314030945301056,
0.036259427666664124,
-0.015532627701759338,
-0.012884538620710373,
-0.018528388813138008,
0.03894886374473572,
0.0009997356683015823,
0.01301407627761364,
0.0008496266673319042,
0.026517068967223167,
0.009879037737846375,
0.022361397743225098,
0.013268818147480488,
-0.014375810511410236,
-0.04964124411344528,
-0.017327362671494484,
-0.013383332639932632,
0.0069315568543970585,
0.035013094544410706,
0.001610895968042314,
0.01833314634859562,
-0.03256130591034889,
0.02615034207701683,
0.011042706668376923,
0.012066628783941269,
0.09785626828670502,
0.06385606527328491,
0.02780144102871418,
0.046848222613334656,
0.0004104857216589153,
-0.002337890211492777,
0.003553185146301985,
-0.04450764134526253,
-0.05085570365190506,
-0.0036304276436567307,
-0.0030176707077771425,
-0.002140701748430729,
0.04953776299953461,
-0.06372411549091339,
0.01996532268822193,
0.0336742140352726,
0.033482350409030914,
0.038517434149980545,
0.018678974360227585,
-0.028200581669807434,
-0.013637535274028778,
-0.000704534410033375,
0.008285559713840485,
-0.053631603717803955,
0.008525132201611996,
0.017902052029967308,
0.03786466643214226,
0.03709331899881363,
-0.002338629448786378,
0.004551582038402557,
0.012698449194431305,
0.028971165418624878,
-0.002436734503135085,
-0.00573554914444685,
-0.02355257421731949,
0.07683366537094116,
-0.00879030954092741,
0.02764761820435524,
0.06467440724372864,
0.009372786618769169,
0.023864025250077248,
-0.013550614938139915,
0.005479319952428341,
0.01878836378455162,
-0.015721190720796585,
0.011004920117557049,
-0.02135002799332142,
0.02980560064315796,
-0.009544448927044868,
0.019067516550421715,
0.0019425216596573591,
0.009999938309192657,
-0.01953190565109253,
-0.0107292290776968,
0.016520624980330467,
0.005627532955259085,
0.05590370297431946,
0.008069927804172039,
-0.030977701768279076,
0.015274030156433582,
-0.025704676285386086,
-0.013907858170568943,
0.02095486968755722,
-0.07015987485647202,
0.01858636923134327,
-0.05784038081765175,
-0.019961385056376457,
0.0579976886510849,
0.014459144324064255,
-0.017708290368318558,
0.01200083363801241,
0.0009075819398276508,
-0.03074217028915882,
-0.030755694955587387,
-0.008540172129869461,
-0.005583777092397213,
-0.03275178372859955,
-0.010201060213148594,
0.0619601272046566,
-0.015888715162873268,
0.01929348334670067,
0.058878909796476364,
-0.07948317378759384,
-0.0562378391623497,
-0.0072637274861335754,
0.03621283173561096,
0.045217934995889664,
-0.03510243445634842,
0.024113662540912628,
-0.0474957711994648,
0.034450121223926544,
0.01784444972872734,
-0.05110460892319679,
-0.04977616295218468,
-0.0034315786324441433,
0.00664362171664834,
0.03795212507247925,
0.037233866751194,
-0.0666893944144249,
0.08845586329698563,
0.014530682936310768,
-0.024652304127812386,
-0.026258280500769615,
0.004794800188392401,
-0.0029381210915744305,
-0.05644359439611435,
-0.017421429976820946,
-0.028288323432207108,
-0.0478324294090271,
0.0002671215042937547,
0.04051216319203377,
0.00873135682195425,
0.07653811573982239,
-0.006797475274652243,
-0.008112102746963501,
0.06571641564369202,
0.01227270346134901,
0.0006775311776436865,
0.05671083182096481,
-0.022340597584843636,
0.004165653605014086,
0.017275238409638405,
0.0008885940769687295,
0.019084803760051727,
-0.01615363359451294,
-0.07880669832229614,
0.03785182163119316,
-0.01633821427822113,
-0.026612432673573494,
0.031112022697925568,
0.04745704308152199,
-0.011081683449447155,
-0.0268561914563179,
0.019266551360487938,
0.031511105597019196,
0.03928021714091301,
0.010436518117785454,
0.01226096786558628,
0.0572747066617012,
0.028178829699754715,
0.02108721435070038,
-0.029442543163895607,
0.003654474625363946,
-0.01862320676445961,
0.02677924744784832,
-0.012759771198034286,
-0.029886357486248016,
-0.0009813817450776696,
0.03441299870610237,
0.026950232684612274,
-0.023151617497205734,
-0.05120496824383736,
-0.000601219420786947,
-0.059784870594739914,
-0.016542349010705948,
0.001948870369233191,
0.055892884731292725,
-0.015069657005369663,
0.03937721624970436,
0.007158784661442041,
0.03817905858159065,
0.05928344652056694,
0.04091450572013855,
-0.059648022055625916,
0.023297764360904694,
-0.05671679228544235,
-0.03590069338679314,
-0.001467486727051437,
0.013533699326217175,
0.020283346995711327,
-0.01208532229065895,
0.0055673508904874325,
-0.02891506999731064,
-0.003142721951007843,
-0.05531545355916023,
0.020464519038796425,
-0.035516031086444855,
0.005260403733700514,
0.03489368036389351,
0.037457175552845,
0.03641864284873009,
-0.022878019139170647,
0.01939072087407112,
0.05208048224449158,
-0.030228355899453163,
0.003356600645929575,
-0.03779800608754158,
-0.04161703214049339,
-0.026911554858088493,
-0.019291849806904793,
0.06738384813070297,
-0.0008325742091983557,
-0.022183319553732872,
0.017913131043314934,
-0.026505092158913612,
0.06792987138032913,
0.0004560856323223561,
0.004456001799553633,
-0.0232692901045084,
-0.03898991271853447,
-0.006391205824911594,
-0.008003330789506435,
0.04237624257802963,
-0.020674457773566246,
-0.010436047799885273,
0.03396061062812805,
-0.009177437983453274,
-0.014589166268706322,
0.02948659285902977,
0.025286173447966576,
0.030350565910339355,
-0.018803434446454048,
-0.0246582068502903,
-0.0014539225958287716,
-0.031856197863817215,
-0.0009917360730469227,
-0.024807916954159737,
0.021184567362070084,
-0.0357048436999321,
0.0012294274056330323,
0.044622667133808136,
0.018809204921126366,
0.004571637138724327,
0.03908996284008026,
-0.03256138414144516,
0.03376797214150429,
-0.03034353256225586,
-0.021548060700297356,
0.012185641564428806,
0.027377264574170113,
0.03991341590881348,
-0.003801509039476514,
0.028698425740003586,
-0.06672415137290955,
-0.041480932384729385,
0.015337600372731686,
0.04122474044561386,
-0.0007031881832517684,
-0.007529091089963913,
-0.07214979827404022,
-0.02746875397861004,
0.04195191338658333,
-0.01971733570098877,
0.07492922246456146,
0.0007060804055072367,
-0.014014971442520618,
0.021771280094981194,
-0.010754873976111412,
-0.026998333632946014,
0.009077482856810093,
-0.035072602331638336,
-0.0006562935304827988,
-0.028343118727207184,
0.0008180956356227398,
0.004138509277254343,
0.0038465431425720453,
0.04408848658204079,
0.006955905817449093,
0.011431255377829075,
-0.024554451927542686,
-0.001783463405445218,
0.029190151020884514,
-0.04701639339327812,
-0.019030550494790077,
-0.014529362320899963,
-0.018567323684692383,
-0.03463425114750862,
0.0319211408495903,
-0.04258565604686737,
-0.04175187274813652,
0.022046281024813652,
0.012908871285617352,
0.03132032975554466,
0.016223011538386345,
-0.016829583793878555,
-0.007044791243970394,
0.0294590312987566,
-0.0166443083435297,
0.019562896341085434,
0.057878829538822174,
-0.011861130595207214,
0.014654568396508694,
-0.027184082195162773,
0.04805958271026611,
0.01303657703101635,
-0.042426664382219315,
-0.017748311161994934,
0.015751060098409653,
-0.043795473873615265,
0.044410340487957,
0.010305391624569893,
0.030250156298279762,
-0.01973838172852993,
-0.05757927522063255,
0.009854198433458805,
0.05578796938061714,
0.024040263146162033,
-0.016265874728560448,
0.025733720511198044,
0.006002637557685375,
-0.005163189023733139,
-0.014299018308520317,
-0.008824639953672886,
0.022237133234739304,
0.022003965452313423,
-0.01455901563167572,
-0.04109754040837288,
0.010596358217298985,
-0.006585645955055952,
-0.01634061150252819,
0.01393907144665718,
-0.0777549296617508,
0.06417393684387207,
-0.05362163111567497,
-0.017194297164678574,
-0.004970379173755646,
-0.026325209066271782,
-0.04435639828443527,
0.008245197124779224,
-0.010065408423542976,
0.015563234686851501,
-0.03248826414346695,
0.0021269090939313173,
0.005984453950077295,
0.01673346571624279,
-0.014776073396205902,
-0.044705454260110855,
0.017543427646160126,
-0.020498663187026978,
-0.016477877274155617,
0.0028132665902376175,
-0.005666133016347885,
0.0023434201721102,
-0.06828872114419937,
-0.015425348654389381,
0.04783168435096741,
-0.04274831339716911,
0.02590731531381607,
0.016236351802945137,
0.005919223185628653,
0.06347385048866272,
0.017394550144672394,
-0.0019051970448344946,
0.01013869233429432,
-0.0106608085334301,
0.006387402303516865,
0.011288389563560486,
0.045583710074424744,
-0.020150162279605865,
-0.044650785624980927,
-0.0071881902404129505,
0.003744065761566162,
0.06645002216100693,
-0.003582246135920286,
0.03858848661184311,
0.03965064138174057,
0.06406866014003754,
0.014894264750182629,
0.001652317470870912,
0.024457145482301712,
-0.00852803885936737,
0.03339551016688347,
0.011809241026639938,
0.011436711065471172,
-0.017312435433268547,
-0.0307653546333313,
0.02607482299208641,
0.0014428884023800492,
0.007140861824154854,
-0.014245463535189629,
0.0758160725235939,
-0.012124327011406422,
-0.005057269241660833,
0.013278435915708542,
0.012905661948025227,
0.005525527987629175,
0.032069720327854156,
-0.027842802926898003,
0.03622924163937569,
0.03901396319270134,
-0.06267958134412766,
-0.05166155844926834,
-0.011759302578866482,
-0.004125609993934631,
0.060951005667448044,
-0.05858386307954788,
0.06245429068803787,
0.04068595543503761,
0.023686541244387627,
0.010371334850788116,
0.023963144049048424,
-0.005170466843992472,
-0.014303209260106087,
0.020416805520653725,
0.04805417358875275,
0.0037290845066308975,
0.021603144705295563,
0.028178323060274124,
0.03938228264451027,
-0.0302346833050251,
-0.0050119576044380665,
0.034617867320775986,
-0.0023773126304149628,
0.004486240446567535,
-0.007869158871471882,
-0.0330677330493927,
0.007941272109746933,
0.00738808698952198,
0.09284596145153046,
-0.021625777706503868,
-0.014494486153125763,
0.01478609163314104,
0.03949372097849846,
0.012608666904270649,
-0.014526735991239548,
0.023070354014635086,
-0.012855948880314827,
0.02328217774629593,
0.03353200480341911,
-0.030224237591028214,
-0.014917492866516113,
0.02617345005273819,
0.04717236012220383,
-0.021707838401198387,
0.051405131816864014,
-0.06205858662724495,
-0.020971156656742096,
-0.015165507793426514,
-0.019999077543616295,
-0.08479027450084686,
0.03808450326323509,
0.0005489191971719265,
-0.018593735992908478,
0.04378216341137886,
-0.006797613576054573,
0.011173733510077,
0.006141156889498234,
0.026559002697467804,
-0.03803779184818268,
0.12608206272125244,
-0.012679718434810638,
-0.03704925626516342,
-0.03400028124451637,
0.01758473739027977,
0.08997220546007156,
0.046518899500370026,
0.006995330099016428,
-0.03798781335353851,
0.013307657092809677,
-0.0010130854789167643,
0.016584521159529686,
-0.0270238034427166,
0.001985192531719804,
0.0109245041385293,
0.0028457900043576956,
0.012001077644526958,
0.01798814907670021,
-0.041560377925634384,
-0.013430332764983177,
0.0242011696100235,
-0.05270650237798691,
-0.0344051718711853,
-0.02093716710805893,
-0.02412157692015171,
0.004411234986037016,
-0.017734603956341743,
-0.04689729958772659,
0.04141799733042717,
-0.026148878037929535,
-0.0018025047611445189,
-0.03143317997455597,
-0.02049579843878746,
0.015755733475089073,
-0.01844753697514534,
-0.06382901221513748,
0.006016065366566181,
-0.0008316464372910559,
-0.04264596849679947,
-0.0031722676940262318,
0.041623689234256744,
-0.005720626562833786,
0.0034822963643819094,
0.020611058920621872,
0.029119309037923813,
0.004425377584993839,
-0.0006137751624919474,
0.05292537808418274,
0.015994105488061905,
-0.040826909244060516,
-0.008334350772202015,
-0.020801611244678497,
0.036145541816949844,
0.017623018473386765,
0.010544320568442345,
-0.00904343742877245,
0.0050049093551933765,
-0.0028560562059283257,
-0.041017163544893265,
0.00850294716656208,
-0.007141410373151302,
0.0374147854745388,
-0.03230635076761246,
-0.000524971226695925,
0.012480565346777439,
0.011975704692304134,
0.03417821601033211,
0.010007573291659355,
-0.006500115152448416,
-0.010947849601507187,
-0.01594056561589241,
0.01804840750992298,
0.030556393787264824,
0.004278416745364666,
-0.04635470360517502,
-0.021987931802868843,
-0.029640497639775276,
-0.0009147249511443079,
-0.005777842830866575,
0.004813624545931816,
0.016109198331832886,
0.014409364201128483,
-0.025290613994002342,
-0.03261364996433258,
-0.026713836938142776,
-0.027276813983917236,
0.027421735227108,
-0.023311369121074677,
-0.03271014988422394,
-0.0072050075978040695,
-0.02491927705705166,
0.005935022607445717,
0.02879532240331173,
-0.04316430911421776,
0.030181309208273888,
0.0049096448346972466,
0.0446653887629509,
0.013812301680445671,
-0.041025031358003616,
-0.035401925444602966,
0.026875395327806473,
0.008456398732960224,
0.01638619601726532,
-0.028704939410090446,
0.036336131393909454,
0.027395853772759438,
-0.015479461289942265,
-0.00016572244931012392,
0.034229621291160583,
-0.031196026131510735,
-0.008806870318949223,
0.004542463459074497,
-0.019674401730298996,
0.017154399305582047,
0.00904418621212244,
-0.009648818522691727,
-0.06185315176844597,
0.027286337688565254,
0.012509224936366081,
-0.03120638243854046,
0.001115072169341147,
0.0009492147364653647,
-0.026789944618940353,
0.04938933625817299,
-0.03887050971388817,
-0.009054933674633503,
-0.019826220348477364,
0.015122873708605766,
-0.050627607852220535,
-0.00800264161080122,
-0.007504762150347233,
0.011370544321835041,
-0.025165822356939316,
0.03612130507826805,
-0.011457330547273159,
-0.05432946979999542,
0.0019534165039658546,
0.01743432693183422,
-0.006984591018408537,
-0.007267338689416647,
-0.008004164323210716,
-0.020196618512272835,
0.04803686589002609,
-0.005494974087923765,
-0.02348731830716133,
0.014727731235325336,
-0.0021661522332578897,
-0.02056615985929966,
0.03307834640145302,
-0.0030581362079828978,
0.03283387050032616,
0.015721317380666733,
-0.028886334970593452,
-0.01958712749183178,
0.0423617959022522,
-0.024605659767985344,
-0.02661058120429516,
-0.020173465833067894,
-0.02027006819844246,
-0.006432523485273123,
-0.018736157566308975,
0.003100532339885831,
-0.01914576254785061,
0.008304108865559101,
-0.016905054450035095,
-0.0067244102247059345,
-0.008914973586797714,
0.0064431834034621716,
0.04279924929141998,
0.02189195714890957,
-0.002553989877924323,
0.036554839462041855,
0.013175617903470993,
0.025078199803829193,
0.05365090072154999,
-0.022634560242295265,
-0.0020646252669394016,
-0.02027484029531479,
0.019402870908379555,
-0.08249011635780334,
0.004370085429400206,
0.00745190167799592,
0.016009584069252014,
0.07504604011774063,
-0.025218540802598,
-0.005779740400612354,
0.03907850384712219,
-0.03798912838101387,
-0.00983442459255457,
-0.033535514026880264,
0.00031543144723400474,
-0.01672116480767727,
-0.026172101497650146,
0.0023045153357088566,
0.023855186998844147,
0.03259142488241196,
0.04963981360197067,
0.021329475566744804,
0.023900356143712997,
-0.05233994871377945,
-0.02017800882458687,
0.040214408189058304,
0.049795713275671005,
0.033270563930273056,
-0.018750181421637535,
0.04886849969625473,
-0.007772669196128845,
-0.03681110218167305,
0.06500667333602905,
-0.03523483872413635,
0.030691880732774734,
-0.026393968611955643,
0.01089412160217762,
-0.016259877011179924,
0.029980549588799477,
0.004219343885779381,
-0.005001662764698267,
0.008901744149625301,
0.029607564210891724,
0.00991626363247633,
0.0015252368757501245,
-0.058771900832653046,
0.0144603056833148,
0.009911620058119297,
-0.055572785437107086,
-0.016015775501728058,
0.03485048934817314,
-0.05729946121573448,
0.012188993394374847,
0.004810603801161051,
-0.01979966089129448,
-0.024841757491230965,
-0.07576025277376175,
0.0048881289549171925,
-0.015585174784064293,
0.033022716641426086,
0.00958888977766037,
-0.03795132413506508,
-0.004550233483314514,
-0.011729760095477104,
0.022753365337848663,
-0.0014429877046495676,
0.02910904958844185,
-0.012214794754981995,
0.0016588157741352916,
-0.07850828766822815,
0.012802916578948498,
-0.004228661768138409,
-0.007922046817839146,
0.0008900900720618665,
-0.04451480880379677,
-0.008497107774019241,
0.03205756098031998,
0.01408250629901886,
0.0166621170938015,
0.019841182976961136,
-0.024545943364501,
-0.023986846208572388,
-0.06028544157743454,
0.004070546478033066,
0.01899622566998005,
0.001808537170290947,
-0.01582152023911476,
-0.022331276908516884,
0.02076897770166397,
0.01613604836165905,
0.061628542840480804,
-0.012715400196611881,
-0.02228611707687378,
0.02671193704009056,
-0.041273653507232666,
-0.0203249491751194,
-0.008281970396637917,
0.026922037824988365,
-0.011888619512319565,
-0.021694375202059746,
0.006199539639055729,
-0.023108331486582756,
0.0003895717964041978,
0.014279356226325035,
0.0005040462710894644,
0.008625908754765987,
0.02349443919956684,
-0.01839773915708065,
-0.0392959788441658,
0.03334035724401474,
-0.011550289578735828,
-0.006144991144537926,
0.06702946126461029,
-0.022862771525979042,
0.026102688163518906,
0.026560883969068527,
-0.042842719703912735,
-0.015658246353268623,
0.04196532443165779,
-0.01812669076025486,
-0.006800908129662275,
-0.07429158687591553,
-0.014307515695691109,
0.014881501905620098,
-0.043092865496873856,
-0.054440777748823166,
0.04540015012025833,
-0.03775406256318092,
-0.03799654543399811,
0.02223721519112587,
0.0408424511551857,
0.021196557208895683,
-0.01348165888339281,
0.0007961647934280336,
0.0451928973197937,
-0.04541534185409546,
0.02329155057668686,
0.024670537561178207,
0.04999103769659996,
0.0011920236283913255,
-0.00991153996437788,
0.02331012859940529,
-0.00568685308098793,
0.04560980573296547,
-0.01927025243639946,
0.02790447697043419,
-0.03728793188929558,
-0.0373053252696991,
-0.01201613899320364,
-0.03081975132226944,
-0.018435833975672722,
0.03918620944023132,
-0.03353555127978325,
0.04372613877058029,
-0.011814807541668415,
0.016669491305947304,
-0.002063338877633214,
0.015503846108913422,
0.0036060046404600143,
0.011654971167445183,
-0.0057017384096980095,
0.020105956122279167,
0.001460377941839397,
-0.002847677795216441,
-0.020077381283044815,
0.005899736657738686,
0.02758697420358658,
-0.009779071435332298,
-0.014726388268172741,
0.010948044247925282,
0.018424952402710915,
-0.003468935377895832,
-0.08047109842300415,
-0.016081981360912323,
-0.03797075152397156,
0.0420895554125309,
0.005876314826309681,
0.017711583524942398,
0.006057391874492168,
-0.00017766832024790347,
0.01398688554763794,
0.07024861872196198,
-0.06414259225130081,
-0.0038529755547642708,
0.003594753798097372,
0.01733693853020668,
-0.0010248564649373293,
-0.00896112248301506
] |
<p>Where/what is emitting cosmic background radiation, and when did it come into existance, was immediately after the big bang?</p>
<p>I know that the universe isn't 3D in the traditional sense, and I don't pretend to understand it. However if the big bang originated from a single point, and the cosmic radiation was emitted from that point at the very start, then unless he explosion/expansion/inflation (whatever happened) wasn't faster the speed of light, then the CMB would have reached the edge of the universe and gotten out of it.</p>
| 8,500 |
[
-0.013630651868879795,
-0.01732698641717434,
0.03599659726023674,
-0.03777163103222847,
0.04757045954465866,
0.045878250151872635,
-0.013888079673051834,
-0.04379385709762573,
-0.008448285982012749,
-0.06613469123840332,
0.004658617079257965,
0.052047304809093475,
0.039912886917591095,
0.03769877552986145,
0.006855504587292671,
-0.005079312715679407,
-0.007862815633416176,
-0.030704673379659653,
-0.02651316486299038,
-0.03162095695734024,
0.03710278123617172,
0.029871055856347084,
-0.018164126202464104,
0.048141561448574066,
-0.06209450215101242,
-0.002302763517946005,
0.053462568670511246,
0.033363621681928635,
0.031095700338482857,
0.046655744314193726,
-0.03279319033026695,
-0.048862259835004807,
-0.012103375978767872,
0.0061531285755336285,
0.015016289427876472,
-0.009462282992899418,
-0.0156831257045269,
-0.048133812844753265,
-0.03672352805733681,
0.01675468310713768,
-0.039580270648002625,
0.014585665427148342,
-0.005596335045993328,
0.03461241349577904,
-0.048543114215135574,
0.005810897797346115,
0.005671004299074411,
0.006445226259529591,
0.08415226638317108,
-0.050955262035131454,
0.05271165817975998,
-0.044679753482341766,
0.034718550741672516,
0.004793843254446983,
-0.019620800390839577,
0.00833655521273613,
0.0969039797782898,
0.05941005423665047,
0.01775149255990982,
-0.013263129629194736,
-0.03195810317993164,
-0.0014816385228186846,
-0.003083129646256566,
-0.02032451145350933,
-0.02228548191487789,
0.054753322154283524,
-0.006217036861926317,
0.004522866103798151,
0.018351776525378227,
0.006621764041483402,
0.018446296453475952,
-0.011774777434766293,
0.03193434327840805,
0.0013337759301066399,
0.0404052734375,
-0.019874515011906624,
0.025502700358629227,
0.004780494142323732,
0.022332116961479187,
0.002385898493230343,
-0.0003820589336100966,
-0.02552824653685093,
0.021110499277710915,
0.019971277564764023,
-0.008994316682219505,
0.05076548829674721,
0.09380237013101578,
-0.02901291660964489,
-0.01109004020690918,
0.04501327872276306,
-0.01614273339509964,
-0.0044153365306556225,
0.04606527090072632,
-0.0069535868242383,
-0.02497096173465252,
0.04816469922661781,
-0.005971280392259359,
0.0609121210873127,
-0.0052628242410719395,
-0.02753833495080471,
0.04421812295913696,
-0.019464701414108276,
0.014204392209649086,
0.08196882903575897,
0.0227078665047884,
0.0003702971735037863,
-0.09627869725227356,
0.034701310098171234,
-0.0723499059677124,
-0.027778301388025284,
-0.05057234317064285,
0.006243621930480003,
-0.009407914243638515,
-0.006409692578017712,
-0.010182433761656284,
-0.018026206642389297,
0.03234293684363365,
-0.04230613633990288,
0.05715663731098175,
0.0527372881770134,
0.040432095527648926,
0.024300791323184967,
0.009151119738817215,
-0.018428677693009377,
-0.062386441975831985,
-0.01748032122850418,
0.01969185099005699,
-0.0326838381588459,
-0.05025656893849373,
0.045146308839321136,
-0.025879429653286934,
-0.014516014605760574,
0.044704873114824295,
-0.025744713842868805,
0.04221287742257118,
-0.00871578510850668,
-0.06374169141054153,
-0.07077783346176147,
0.026295281946659088,
0.005579102784395218,
0.003747651819139719,
-0.07500549405813217,
0.017451640218496323,
0.030132360756397247,
0.05461785942316055,
-0.03509937971830368,
-0.03453410416841507,
-0.027394955977797508,
0.051780715584754944,
-0.029034078121185303,
-0.02451234497129917,
-0.03390689566731453,
-0.008112689480185509,
-0.02043335884809494,
0.005587689578533173,
-0.08047185093164444,
0.024427464231848717,
0.028135176748037338,
-0.0068312957882881165,
-0.0441134087741375,
0.07393167912960052,
-0.02901717647910118,
0.004903055727481842,
-0.015066745691001415,
-0.039322007447481155,
-0.019959885627031326,
0.08712204545736313,
0.06314464658498764,
-0.030359534546732903,
0.030052784830331802,
0.025273198261857033,
0.014782287180423737,
0.015514167957007885,
0.0010207054438069463,
0.021856727078557014,
-0.05487436056137085,
-0.043141089379787445,
0.013378354720771313,
0.03581482917070389,
-0.001647313591092825,
-0.04776349291205406,
0.0012445589527487755,
0.021512623876333237,
0.007895453833043575,
0.03746512159705162,
0.047653499990701675,
0.0034772870130836964,
-0.034448087215423584,
0.009252222254872322,
-0.011795386672019958,
0.008609685115516186,
-0.023947767913341522,
-0.035827748477458954,
0.016971571370959282,
-0.024909213185310364,
-0.04692477732896805,
0.020419837906956673,
0.03335883095860481,
-0.03248634934425354,
-0.04681115224957466,
0.015580564737319946,
0.025880716741085052,
0.02018205262720585,
0.00015111044922377914,
-0.009779187850654125,
0.06953160464763641,
0.026828346773982048,
0.005056719295680523,
-0.030459092929959297,
0.022341618314385414,
-0.003315289970487356,
-0.01240796409547329,
-0.014135804958641529,
0.008033563382923603,
-0.0536828488111496,
0.023989390581846237,
0.005213756579905748,
-0.00507704820483923,
0.0014538986142724752,
-0.007311323191970587,
-0.018177485093474388,
0.07828844338655472,
0.02538386546075344,
-0.0032640681602060795,
-0.02180580608546734,
0.009039798751473427,
0.008451992645859718,
0.008568523451685905,
-0.021375445649027824,
-0.04550768807530403,
-0.07431070506572723,
-0.03385841101408005,
0.0341845378279686,
-0.0029024442192167044,
-0.0023633369710296392,
0.0033254295121878386,
-0.00481013860553503,
0.019571401178836823,
-0.005032029002904892,
0.03239830583333969,
-0.015439953655004501,
-0.03834036737680435,
-0.023139093071222305,
-0.003808182431384921,
0.005566150415688753,
0.010865048505365849,
0.04846224933862686,
0.006326856557279825,
-0.008185268379747868,
-0.021554498001933098,
-0.0051614027470350266,
0.02664230391383171,
0.01686980202794075,
0.006024929229170084,
-0.020252220332622528,
-0.038689542561769485,
0.027620954439044,
-0.02782633528113365,
0.015839336439967155,
-0.010144696570932865,
0.01855282299220562,
0.003763941116631031,
-0.046928297728300095,
0.011720001697540283,
-0.021746519953012466,
0.011680296622216702,
-0.029455116018652916,
-0.010983198881149292,
0.03247830644249916,
-0.03003738820552826,
0.02556803822517395,
-0.0027872666250914335,
-0.04164041951298714,
-0.006105692591518164,
-0.023569177836179733,
0.02004031278192997,
0.024644607678055763,
0.03187328204512596,
-0.05603625625371933,
-0.04450580105185509,
-0.0351126492023468,
-0.028866194188594818,
0.018152667209506035,
0.016723664477467537,
-0.016419269144535065,
0.06364718824625015,
-0.045010991394519806,
0.005082353483885527,
0.016574930399656296,
0.002334724413231015,
0.00019813321705441922,
0.052290596067905426,
0.000005264478204480838,
-0.03535693511366844,
-0.009229599498212337,
-0.026082267984747887,
0.0280824713408947,
-0.007477212231606245,
0.007903528399765491,
0.06404930353164673,
-0.02444307692348957,
-0.016405215486884117,
0.03328623250126839,
-0.04918477684259415,
-0.041091471910476685,
-0.04437801241874695,
0.023123549297451973,
-0.012595627456903458,
-0.024099290370941162,
0.03189070522785187,
0.005755562800914049,
-0.04765363410115242,
-0.0020658792927861214,
-0.027359921485185623,
-0.0686667189002037,
0.04427561163902283,
-0.0063447365537285805,
0.018137583509087563,
-0.044126853346824646,
-0.012822841294109821,
0.044477880001068115,
0.05154988542199135,
-0.01622464694082737,
-0.0003679322835523635,
0.0067824674770236015,
0.005281161051243544,
-0.02376641146838665,
0.008910172618925571,
-0.01902136020362377,
-0.009421096183359623,
-0.0151170389726758,
-0.0023451074957847595,
0.03642212972044945,
0.02673094905912876,
0.015656299889087677,
0.0021283545065671206,
0.008592694066464901,
-0.003630738938227296,
0.06225704401731491,
0.01921059936285019,
0.03118746541440487,
-0.028765717521309853,
0.021590597927570343,
-0.02314937673509121,
0.03252969682216644,
0.01753775030374527,
-0.018714649602770805,
0.026362190023064613,
0.009290860965847969,
0.0032623508013784885,
-0.039708562195301056,
0.04022698849439621,
0.0105189373716712,
0.004563829395920038,
0.010662524029612541,
-0.01674782484769821,
0.029843855649232864,
0.02307422272861004,
0.018656261265277863,
-0.010158909484744072,
0.007528088521212339,
-0.03036138229072094,
-0.0029757467564195395,
0.020670780912041664,
0.005312219262123108,
0.013357920572161674,
0.004721595905721188,
-0.013449261896312237,
0.0579802505671978,
0.06051504611968994,
-0.0012922282330691814,
0.003792004892602563,
-0.04357685148715973,
-0.024754425510764122,
-0.049647849053144455,
0.01717550866305828,
0.022905634716153145,
0.021923692896962166,
0.02432386204600334,
0.09696365147829056,
0.004502607975155115,
-0.006675280164927244,
-0.002396985422819853,
-0.005833894945681095,
-0.08026500046253204,
-0.041973426938056946,
-0.04580279812216759,
0.0010454923612996936,
-0.006280093919485807,
-0.009489407762885094,
-0.01735810749232769,
0.018029142171144485,
-0.044551245868206024,
-0.014895550906658173,
-0.0320989266037941,
-0.050470981746912,
0.04131979122757912,
-0.04394787177443504,
-0.038313474506139755,
-0.01975252665579319,
-0.0008749349508434534,
0.04349202662706375,
0.025980714708566666,
0.008874277584254742,
0.03143542259931564,
-0.032347891479730606,
0.0029690952505916357,
0.004501900169998407,
0.017057036980986595,
-0.013910493813455105,
0.0006881689187139273,
0.018472550436854362,
-0.00673025194555521,
-0.045381590723991394,
0.019507676362991333,
0.04017998278141022,
0.03266853839159012,
0.018756704404950142,
-0.027617285028100014,
-0.02255328930914402,
-0.03366154804825783,
-0.0014806530671194196,
0.002128817141056061,
0.03494994342327118,
-0.014435594901442528,
-0.005508176516741514,
0.029926847666502,
-0.0028066837694495916,
-0.010106025263667107,
0.043345652520656586,
0.07493644952774048,
-0.01039110403507948,
-0.020310230553150177,
-0.023819731548428535,
-0.025160234421491623,
-0.021079687401652336,
-0.028767220675945282,
0.024123728275299072,
-0.031032834202051163,
-0.031092261895537376,
0.009940986521542072,
-0.004201206844300032,
0.0029868127312511206,
0.005389572586864233,
0.005767003633081913,
0.016282502561807632,
0.021603988483548164,
-0.030378762632608414,
-0.01100592128932476,
0.017335990443825722,
0.0636695995926857,
0.07083621621131897,
0.014888854697346687,
-0.013058455660939217,
-0.05257316678762436,
-0.014505608938634396,
0.023859409615397453,
0.0414695106446743,
0.0122902300208807,
-0.014424420893192291,
-0.07996482402086258,
-0.02788861095905304,
0.04048268496990204,
-0.020837631076574326,
0.030638379976153374,
-0.03607314079999924,
-0.0070418547838926315,
0.0009901742450892925,
-0.05662181228399277,
0.003408323274925351,
0.015737848356366158,
-0.015962928533554077,
0.012111833319067955,
0.00047349618398584425,
-0.0074098799377679825,
-0.0477181151509285,
0.019361376762390137,
0.04113048315048218,
0.05198457092046738,
-0.002987935673445463,
0.02298182062804699,
0.005803375970572233,
0.029748130589723587,
-0.016208458691835403,
-0.04603073373436928,
-0.0005253979470580816,
-0.001405768794938922,
-0.031493138521909714,
0.05320959910750389,
-0.029361329972743988,
-0.016622917726635933,
-0.0038031190633773804,
0.04334116727113724,
-0.027767887338995934,
-0.015537682920694351,
-0.030980218201875687,
0.03868948668241501,
0.010197865776717663,
-0.006904857233166695,
0.05183914303779602,
0.01955719292163849,
-0.014626696705818176,
0.021379053592681885,
-0.04790901765227318,
0.02106950245797634,
-0.014160613529384136,
0.008574706502258778,
-0.03741537779569626,
-0.006087049376219511,
-0.02344570867717266,
0.04748334735631943,
-0.025471795350313187,
-0.028028806671500206,
0.003908942919224501,
-0.024855151772499084,
0.028915878385305405,
0.029578223824501038,
-0.013969916850328445,
0.02009541168808937,
-0.021193480119109154,
0.001432273187674582,
-0.008748544380068779,
-0.007794968783855438,
0.05433444678783417,
0.012205272912979126,
0.009333129972219467,
0.009131575003266335,
-0.00866928044706583,
0.021293427795171738,
-0.01341015100479126,
-0.010682793334126472,
0.004544558934867382,
-0.012443063780665398,
0.0442730113863945,
0.017427172511816025,
0.0014892343897372484,
0.016510451212525368,
-0.07123751193284988,
-0.022479014471173286,
0.007585643325001001,
-0.019154846668243408,
0.013938788324594498,
-0.04954192787408829,
0.02762106992304325,
-0.004731116350740194,
0.036807939410209656,
-0.0952080562710762,
-0.02792663499712944,
0.020665323361754417,
0.032748907804489136,
-0.04294290021061897,
-0.023751715198159218,
0.016535375267267227,
-0.04192054271697998,
-0.021845515817403793,
0.018580608069896698,
0.017061026766896248,
-0.02767476625740528,
-0.014771704562008381,
0.012979412451386452,
0.014362524263560772,
0.020241396501660347,
-0.00419602170586586,
-0.029555467888712883,
0.010630528442561626,
0.01834626868367195,
-0.018578028306365013,
0.013625018298625946,
0.07577625662088394,
0.007727440912276506,
0.0043284217827022076,
-0.027892690151929855,
0.026319149881601334,
0.013707160018384457,
-0.047971125692129135,
-0.04323508217930794,
0.06859330832958221,
0.008195390924811363,
-0.015509896911680698,
0.004095413256436586,
0.029116960242390633,
-0.021755818277597427,
0.023825760930776596,
-0.026391929015517235,
0.008254535496234894,
-0.010385840199887753,
-0.04393168166279793,
0.03741079568862915,
-0.02785434015095234,
0.050368424504995346,
-0.016829241067171097,
0.05022686719894409,
0.02782003954052925,
-0.030985256657004356,
-0.002171454718336463,
-0.013932500034570694,
0.004494496621191502,
-0.0036207560915499926,
-0.0012990165269002318,
0.02050355263054371,
0.011236853897571564,
-0.029617559164762497,
-0.008626068942248821,
-0.030385885387659073,
-0.0010814156848937273,
0.061191026121377945,
-0.002870643977075815,
0.05747222155332565,
0.0008009853772819042,
0.020126234740018845,
-0.0021019107662141323,
-0.05654604732990265,
-0.016902225092053413,
0.011136040091514587,
-0.004822400398552418,
0.011072645895183086,
-0.007163435220718384,
0.013293011114001274,
0.04354590177536011,
0.04405812919139862,
-0.04600192606449127,
0.046255145221948624,
0.04108313471078873,
0.0015827066963538527,
0.038043905049562454,
-0.007551990449428558,
-0.0350455678999424,
0.011455297470092773,
-0.024885190650820732,
0.02398030459880829,
0.03920279070734978,
-0.039403922855854034,
0.06543128937482834,
-0.0015301831299439073,
-0.02613523043692112,
-0.046847403049468994,
0.0019167601130902767,
-0.08057691901922226,
-0.01704315096139908,
0.01341584324836731,
0.05020107328891754,
-0.015888212248682976,
-0.0028379319701343775,
0.0065971785224974155,
-0.023371852934360504,
-0.01410764455795288,
0.01501745730638504,
-0.057808682322502136,
-0.05858216434717178,
-0.02566489204764366,
-0.025669777765870094,
0.0362098254263401,
-0.0064198607578873634,
-0.05206325650215149,
0.010513989254832268,
-0.03945145756006241,
-0.005071738269180059,
-0.005766606889665127,
0.035562917590141296,
-0.0059901936911046505,
0.05897701159119606,
-0.01617099717259407,
-0.011523936875164509,
-0.02626236341893673,
0.024260904639959335,
0.1042819395661354,
0.06125124543905258,
0.004650662187486887,
-0.09663330018520355,
0.03216894716024399,
-0.02105325274169445,
0.02545817568898201,
-0.02704961784183979,
0.01644916459918022,
-0.03845328837633133,
0.019034605473279953,
0.028141286224126816,
0.03848179057240486,
0.0004481787618715316,
0.02883807383477688,
0.01392426062375307,
-0.034666117280721664,
-0.041190255433321,
0.01246955618262291,
0.050571199506521225,
-0.0035666381008923054,
0.02804795652627945,
-0.05627632513642311,
0.005453161429613829,
-0.021165208891034126,
-0.017183925956487656,
-0.0327487476170063,
-0.03468023240566254,
0.003249496454373002,
-0.038322728127241135,
-0.05422281473875046,
0.018717719241976738,
-0.022684790194034576,
-0.02640802040696144,
-0.03514978289604187,
-0.0025335969403386116,
0.04581528156995773,
-0.0069104405120015144,
-0.0030611762776970863,
0.0064557380974292755,
0.027487823739647865,
0.004670311231166124,
-0.014149448834359646,
-0.0006035242113284767,
-0.00900622271001339,
-0.01882215403020382,
0.006664985790848732,
0.06847407668828964,
-0.019411027431488037,
0.00974916573613882,
-0.002056669443845749,
0.02481508068740368,
0.022500211372971535,
-0.01774483360350132,
0.02875266596674919,
0.01735621690750122,
0.020834974944591522,
-0.010919926688075066,
-0.006718638818711042,
-0.029290344566106796,
0.028553280979394913,
-0.0014447348657995462,
0.030355023220181465,
-0.0012258562492206693,
0.024782583117485046,
0.009381858631968498,
-0.012646018527448177,
0.03310044854879379,
-0.020920006558299065,
0.010770780965685844,
-0.009642336517572403,
0.004439027514308691,
-0.048200830817222595,
0.02021779492497444,
0.048670053482055664,
0.005294749513268471,
0.04955824092030525,
0.027534836903214455,
-0.01330200769007206,
-0.01080368459224701,
-0.02253039740025997,
0.024432485923171043,
-0.015679653733968735,
-0.011727162636816502,
-0.021342581138014793,
0.01707296259701252,
0.025179922580718994,
0.03825574368238449,
0.004769471473991871,
0.019676584750413895,
-0.016949186101555824,
0.02087719365954399,
0.03171275928616524,
-0.01101943850517273,
0.0002668449014890939,
0.024709349498152733,
-0.016050493344664574,
0.0005578060518018901,
-0.04318029806017876,
0.02566107176244259,
0.01430924516171217,
0.0029145153239369392,
0.012669267132878304,
0.02851145900785923,
-0.02062794752418995,
0.005099866539239883,
0.013496519066393375,
-0.049941521137952805,
0.01550125703215599,
0.009739745408296585,
0.013481199741363525,
-0.02169959805905819,
-0.01750876195728779,
-0.002549661323428154,
0.019637560471892357,
0.0031596252229064703,
0.03340825438499451,
-0.05731616169214249,
0.03804617375135422,
-0.005952248815447092,
0.010873665101826191,
-0.06278684735298157,
0.008093191310763359,
-0.04093874245882034,
-0.009983074851334095,
0.026068080216646194,
-0.016097960993647575,
-0.01525450311601162,
0.045749325305223465,
-0.052725546061992645,
-0.03189003840088844,
0.034634802490472794,
0.0037002561148256063,
-0.04160887375473976,
0.009610858745872974,
0.012661309912800789,
0.008555474691092968,
0.04074079543352127,
0.02797621488571167,
0.015437480062246323,
-0.007466902025043964,
-0.032971035689115524,
-0.07976986467838287,
-0.006261247210204601,
0.004546421114355326,
0.018183071166276932,
0.02221427671611309,
-0.007573217153549194,
-0.027492130175232887,
0.06124992296099663,
0.02560616284608841,
-0.011740594170987606,
0.011463787406682968,
-0.0005998204578645527,
0.024949688464403152,
0.01686752215027809,
0.040014345198869705,
-0.0020560144912451506,
0.027895905077457428,
0.023820925503969193,
-0.012247847393155098,
-0.009008405730128288,
-0.017441269010305405,
-0.03284083679318428,
-0.047119494527578354,
-0.0013292463263496757,
-0.009496231563389301,
0.009708037599921227,
0.038653191179037094,
0.05999398231506348,
-0.05567008629441261,
0.04939763620495796,
0.05076764523983002,
-0.010579503141343594,
-0.10763324052095413,
0.004880373366177082,
-0.004776493646204472,
-0.0030058978591114283,
0.012177466414868832,
-0.03186403959989548,
0.021256403997540474,
0.07228440046310425,
-0.08303506672382355,
0.0335037000477314,
0.01287862379103899,
-0.008084328845143318,
-0.020646575838327408,
-0.002198063302785158,
-0.011773605830967426,
0.04453914985060692,
0.06023455411195755,
0.07085660099983215,
0.023274710401892662,
0.020866286009550095,
-0.04418453201651573,
-0.05123135447502136,
-0.028147192671895027,
0.014081290923058987,
0.012816169299185276,
0.027111081406474113,
0.07169212400913239,
-0.012953181751072407,
0.018182478845119476,
0.05209347605705261,
-0.024361811578273773,
-0.0108914440497756,
-0.02130199410021305,
-0.00602650037035346,
0.013580470345914364,
0.029389312490820885,
0.013874462805688381,
0.0123579241335392,
0.011837223544716835,
0.0359206423163414,
0.017788909375667572,
0.01344303973019123,
0.01737949810922146,
0.01309211179614067,
-0.004116707947105169,
-0.027987221255898476,
-0.018717791885137558,
0.014652613550424576,
0.022305864840745926,
0.019582146778702736,
0.019734179601073265,
0.0012660700595006347,
0.014275024645030499,
-0.001299070892855525,
-0.008500511758029461,
-0.050521235913038254,
-0.029169680550694466,
0.023038392886519432,
0.027330977842211723,
-0.032362695783376694,
0.012047979049384594,
-0.0071947104297578335,
-0.015285751782357693,
0.0029738389421254396,
-0.021328449249267578,
-0.005604907870292664,
-0.04808826744556427,
0.0003403440350666642,
0.016158809885382652,
0.0035449357237666845,
0.023011276498436928,
-0.040448952466249466,
-0.06978471577167511,
0.03850260376930237,
0.023800604045391083,
0.014120747335255146,
0.010861526243388653,
-0.05753989890217781,
-0.024867208674550056,
-0.07751863449811935,
0.03867616131901741,
-0.004821494221687317,
0.016533102840185165,
-0.05223387852311134,
-0.02946433611214161,
-0.0161846112459898,
-0.012848819606006145,
0.04249183461070061,
0.005165003705769777,
-0.030602799728512764,
-0.008011486381292343,
0.003337117610499263,
0.024522310122847557,
-0.06246291846036911,
0.0338224433362484,
0.055166713893413544,
-0.027877556160092354,
-0.016578035429120064,
-0.025716569274663925,
-0.03676493465900421,
0.028690269216895103,
0.01847274787724018,
0.03219546750187874,
0.02058127522468567,
-0.02648283913731575,
0.003802370512858033,
0.03173743188381195,
0.015759002417325974,
-0.013333548791706562,
0.04965939745306969,
0.004409128800034523,
-0.009301816113293171,
0.06639692932367325,
0.025003284215927124,
-0.02830631472170353,
0.003274098737165332,
-0.01782575622200966,
0.015379680320620537,
-0.02086111158132553,
0.020767340436577797,
0.005566125735640526,
-0.03906066343188286,
-0.005990908015519381,
0.023042932152748108,
-0.01945546641945839,
0.013788638636469841,
0.0402914360165596,
-0.021761054173111916,
0.04523763060569763,
-0.029574858024716377,
-0.004488917998969555,
0.028807681053876877,
-0.020944658666849136,
-0.023822801187634468,
0.0321052260696888,
0.01590838097035885,
-0.0008347082766704261,
0.03018438257277012,
0.010481256060302258,
0.006882033310830593,
-0.0021256019826978445,
-0.0374055840075016,
0.04322778061032295,
-0.06548529863357544,
-0.024238595739006996,
0.005027259700000286,
-0.010751031339168549,
0.022911952808499336,
0.0358835905790329,
-0.02639465592801571,
0.0568155013024807,
-0.004106487613171339,
0.03444826602935791,
0.019747959449887276,
-0.011038102209568024,
-0.023215198889374733,
0.026281341910362244,
-0.010255296714603901,
0.032471925020217896,
-0.02364128641784191,
-0.017948312684893608,
-0.005636611022055149,
0.01520190853625536,
0.032160528004169464,
-0.0218999981880188,
0.021317383274435997,
-0.00556588638573885,
-0.01235034130513668,
-0.015959734097123146,
0.022442230954766273,
-0.007899604737758636,
-0.003375824075192213,
0.05458790063858032,
0.05291575938463211,
-0.009693676605820656,
-0.004288525320589542,
0.014883896335959435,
-0.04600704461336136,
0.017560429871082306,
-0.05566591024398804,
0.020234595984220505,
-0.027727389708161354,
0.04173947125673294,
-0.04295840859413147,
-0.03581925109028816
] |
<p>Recently I got the book "On the Shoulders of Giant" from Stephen Hawkings. It consists of more than 1000 pages of classical publications in physics. However 900 pages are given to the work of Copernicus, Galilei and Newton and 100 pages are given to the papers of Einstein. Therefore I think this books gives a wrong impression about what is really important for our knowledge in physics today. </p>
<p>If you could fill a book with the most important papers relevant for our knowledge in physics today, which ones would you select? </p>
| 8,501 |
[
-0.018340520560741425,
-0.018024064600467682,
0.01868598349392414,
-0.023335635662078857,
0.05038096383213997,
0.017969826236367226,
-0.005555305629968643,
-0.036791592836380005,
-0.0312203262001276,
-0.01694212295114994,
0.006275603547692299,
0.02064456418156624,
0.024272359907627106,
0.018836230039596558,
-0.003961887676268816,
0.023706858977675438,
-0.014401447027921677,
-0.008590439334511757,
-0.026665285229682922,
-0.01618318073451519,
0.0001868335239123553,
0.02598729357123375,
-0.006461367476731539,
0.022575972601771355,
-0.06927730143070221,
0.04388231039047241,
0.0010099972132593393,
0.016333725303411484,
-0.0013858677120879292,
0.048422493040561676,
-0.03415229916572571,
-0.011455227620899677,
0.00023283263726625592,
0.017495019361376762,
-0.01563091203570366,
-0.024309102445840836,
-0.01279326993972063,
-0.029373260214924812,
0.010443390347063541,
-0.013841859996318817,
-0.022683236747980118,
-0.048014890402555466,
0.010552852414548397,
0.03596450388431549,
-0.047074105590581894,
0.06339935213327408,
-0.008499630726873875,
-0.031663645058870316,
0.035106875002384186,
-0.07564839720726013,
0.031184891238808632,
0.028270985931158066,
0.03326118364930153,
0.016490481793880463,
0.019946828484535217,
-0.01256533432751894,
0.021169187501072884,
0.045457277446985245,
0.0010945552494376898,
-0.045987632125616074,
-0.013261518441140652,
-0.013549487106502056,
-0.03074171021580696,
-0.018930785357952118,
0.010490324348211288,
0.06629510968923569,
-0.020233938470482826,
-0.025327103212475777,
0.048165593296289444,
0.00033889731275849044,
-0.00023609951313119382,
-0.008565807715058327,
0.05811428651213646,
-0.011009164154529572,
0.01676565408706665,
-0.023984132334589958,
-0.019294463098049164,
-0.0023254230618476868,
0.02077893167734146,
0.0252997986972332,
-0.007058087736368179,
0.004642908927053213,
0.05808642506599426,
0.03444327786564827,
0.008083157241344452,
0.007438476663082838,
0.07840118557214737,
-0.00601314939558506,
-0.008095338009297848,
0.006207634229212999,
-0.045737385749816895,
-0.023212533444166183,
0.030678745359182358,
0.004862312693148851,
-0.014348692260682583,
-0.005733050871640444,
0.018260465934872627,
0.0487636923789978,
-0.02959137037396431,
-0.008398899808526039,
0.03342727944254875,
-0.032606661319732666,
0.027301177382469177,
0.06745956093072891,
0.03632393851876259,
-0.0319761261343956,
-0.04406560957431793,
-0.008306164294481277,
-0.026585500687360764,
0.0039075524546206,
-0.02192714810371399,
0.009704469703137875,
-0.007653376553207636,
0.015280593186616898,
0.017522282898426056,
-0.023677272722125053,
-0.0037983229849487543,
-0.01321947481483221,
0.07955886423587799,
0.06499183923006058,
0.06733988225460052,
-0.030774865299463272,
0.015802590176463127,
-0.019972369074821472,
-0.06916283071041107,
0.023163985460996628,
0.05562056601047516,
-0.023651795461773872,
-0.0006675653858110309,
0.039896655827760696,
-0.0056477501057088375,
0.016374796628952026,
-0.011363253928720951,
-0.003530586836859584,
0.038531556725502014,
0.004343763459473848,
-0.10372866690158844,
-0.04147372394800186,
0.06996171921491623,
-0.008446190506219864,
-0.02245820313692093,
-0.06322787702083588,
0.02146598882973194,
-0.0019559524953365326,
0.06458620727062225,
0.012659918516874313,
0.016635488718748093,
0.011381221003830433,
0.06590455025434494,
-0.028413908556103706,
-0.01872991770505905,
-0.0018345415592193604,
0.030622513964772224,
-0.014362482354044914,
0.01035392191261053,
-0.07991629093885422,
-0.0020065426360815763,
0.030017632991075516,
0.0028905468061566353,
-0.028707031160593033,
0.06100199744105339,
-0.03280927985906601,
-0.012593377381563187,
0.012762789614498615,
-0.008090521208941936,
0.006832514423877001,
0.060166001319885254,
0.012735395692288876,
0.017643196508288383,
0.02655208855867386,
0.043380286544561386,
0.04183761030435562,
0.029163481667637825,
-0.01733250916004181,
0.024533042684197426,
-0.034222494810819626,
0.012595852836966515,
0.022005068138241768,
-0.021306192502379417,
-0.014277161099016666,
-0.004403917118906975,
-0.06216591224074364,
-0.013875825330615044,
0.018084263429045677,
-0.001946823438629508,
0.09388798475265503,
-0.0005696542211808264,
0.0012637571198865771,
0.03559475392103195,
-0.0213493462651968,
-0.037116073071956635,
-0.03419027104973793,
0.018437163904309273,
-0.03883226960897446,
-0.012921812012791634,
0.05820661783218384,
-0.0012325290590524673,
0.009397609159350395,
0.004401456099003553,
-0.03410318121314049,
0.011417587287724018,
0.041727423667907715,
0.009713244624435902,
-0.0005778588238172233,
0.01441001333296299,
0.020205657929182053,
0.018364302814006805,
-0.010149230249226093,
-0.03416111692786217,
-0.008732396177947521,
-0.044393185526132584,
0.03197239339351654,
-0.0023646571207791567,
0.023012373596429825,
-0.009988903068006039,
-0.024423370137810707,
0.0249536894261837,
-0.013833248056471348,
-0.0228525809943676,
0.03425413742661476,
-0.03990260139107704,
0.05861806869506836,
-0.018007460981607437,
-0.013695057481527328,
-0.007890029810369015,
0.06044793128967285,
0.00804052408784628,
0.010650474578142166,
0.023785728961229324,
0.0007685400196351111,
-0.021509842947125435,
-0.0023187133483588696,
0.03351297602057457,
0.05039943382143974,
-0.022938765585422516,
0.013983748853206635,
0.00044219952542334795,
0.03489195182919502,
-0.001944917836226523,
0.018379412591457367,
-0.03608870878815651,
-0.07794784754514694,
0.03956758603453636,
-0.002811166225001216,
-0.02088683284819126,
0.02818915992975235,
0.03831559419631958,
0.018898537382483482,
-0.0015760461101308465,
-0.012872152961790562,
0.0010451639536768198,
0.03993704915046692,
-0.008382899686694145,
0.0029539549723267555,
-0.007136732805520296,
-0.04161553457379341,
0.018167302012443542,
-0.039892327040433884,
0.025842752307653427,
0.00443992717191577,
-0.018880948424339294,
0.014404469169676304,
-0.02872108481824398,
-0.006224457174539566,
0.01583165116608143,
-0.02230430580675602,
-0.016434265300631523,
-0.022922655567526817,
0.04692317172884941,
-0.08572397381067276,
0.009696451015770435,
0.03982485458254814,
-0.03937435522675514,
-0.0287350881844759,
0.00764769921079278,
0.027891794219613075,
-0.003911022562533617,
0.05378938093781471,
0.008737570606172085,
-0.030955875292420387,
-0.0008978829137049615,
-0.0643530935049057,
-0.006722525227814913,
0.012239563278853893,
-0.0579383410513401,
0.011860179714858532,
-0.038948461413383484,
-0.043583329766988754,
0.0605328306555748,
-0.058562714606523514,
0.015652669593691826,
0.023583967238664627,
-0.0010013780556619167,
-0.022314680740237236,
-0.026019373908638954,
-0.017872923985123634,
-0.022314945235848427,
-0.006558622699230909,
-0.010797419585287571,
0.020183458924293518,
-0.019925793632864952,
-0.051983557641506195,
-0.003032403066754341,
-0.022816916927695274,
-0.08167910575866699,
0.018738403916358948,
-0.006294319871813059,
0.00499389786273241,
-0.034278977662324905,
-0.01721561886370182,
0.01023330818861723,
-0.028073688969016075,
-0.016934821382164955,
-0.055969368666410446,
-0.04043152928352356,
-0.0017775853630155325,
0.015140904113650322,
0.014879909344017506,
-0.01205694954842329,
0.0132956113666296,
0.05816861242055893,
0.02547009103000164,
-0.06164615601301193,
-0.02288324385881424,
-0.013208647258579731,
0.0011011804454028606,
-0.008025194518268108,
-0.003153485944494605,
0.013874332420527935,
0.00239010713994503,
-0.005600059870630503,
0.017120445147156715,
0.005508980248123407,
0.0007857285672798753,
0.017449580132961273,
0.0022558290511369705,
-0.016882451251149178,
-0.02291514351963997,
0.022046944126486778,
0.019425123929977417,
0.03051804192364216,
-0.06981545686721802,
0.007574647665023804,
-0.002248059492558241,
0.016431888565421104,
0.03563939779996872,
-0.02992025390267372,
0.05132170766592026,
0.02436068281531334,
0.053617123514413834,
0.010556560009717941,
-0.02776530012488365,
-0.005450984928756952,
-0.026430251076817513,
0.028518717736005783,
0.03350251168012619,
0.005917420145124197,
-0.021177837625145912,
0.03248326852917671,
0.017321351915597916,
0.044868193566799164,
-0.01562982052564621,
-0.005029522348195314,
-0.03110557608306408,
0.010894321836531162,
0.0321703776717186,
-0.0015445343451574445,
-0.009462859481573105,
0.05448242276906967,
0.027339160442352295,
-0.006281144451349974,
-0.02617626078426838,
-0.02752843126654625,
-0.030073538422584534,
-0.037555813789367676,
-0.011566930450499058,
-0.012600732035934925,
0.04715123772621155,
0.01355336420238018,
0.02638849802315235,
-0.003525463165715337,
0.0007028182153590024,
0.011521528474986553,
0.0033325995318591595,
-0.0824948102235794,
0.00246452447026968,
-0.07268153876066208,
0.01644526794552803,
0.024057552218437195,
0.02731059305369854,
0.013470729812979698,
-0.024150799959897995,
-0.03249147906899452,
-0.018445057794451714,
0.0035046893171966076,
-0.05187593773007393,
0.0013468149118125439,
-0.05165461450815201,
-0.05655302479863167,
-0.0123737882822752,
0.005648318212479353,
0.03191130608320236,
0.020453594624996185,
0.021601632237434387,
0.03752606362104416,
-0.03851332515478134,
-0.040199313312768936,
0.0037573555018752813,
0.039853304624557495,
-0.023436760529875755,
0.016972247511148453,
0.010599484667181969,
0.014384061098098755,
-0.05657350271940231,
0.01886199787259102,
0.012531152926385403,
0.04670024663209915,
-0.029118988662958145,
0.0027928247582167387,
-0.0286337248980999,
-0.0526529960334301,
-0.022171281278133392,
-0.027339477092027664,
0.05112648010253906,
0.043617863208055496,
-0.032164961099624634,
0.058042705059051514,
-0.010078376159071922,
0.004813231527805328,
0.03791879490017891,
0.04115200415253639,
-0.015561814419925213,
-0.05327925086021423,
-0.006580694112926722,
-0.026094796136021614,
-0.024742763489484787,
-0.022268561646342278,
0.02982722409069538,
0.007375091314315796,
-0.019026119261980057,
-0.03601723536849022,
0.009938166476786137,
0.009859119541943073,
-0.061038341373205185,
-0.021568570286035538,
0.0006197823677212,
0.02869717963039875,
-0.02931438572704792,
-0.018271252512931824,
0.0064308964647352695,
0.050577156245708466,
0.06765647977590561,
0.002907601185142994,
-0.007633437402546406,
-0.03627529740333557,
-0.006212693639099598,
0.04184095561504364,
0.0681229755282402,
-0.032364606857299805,
0.018928060308098793,
-0.046229287981987,
-0.0281806793063879,
0.0640360489487648,
-0.03623481094837189,
0.014254915527999401,
-0.030346302315592766,
0.0008995311800390482,
-0.026606101542711258,
0.007282108999788761,
0.00043915954302065074,
0.007081330753862858,
0.03022429719567299,
0.03371598944067955,
-0.008974042721092701,
0.012194283306598663,
-0.002207245910540223,
0.0397074818611145,
0.021157702431082726,
0.030266795307397842,
0.04555817320942879,
0.01662898249924183,
0.02119063399732113,
0.04127077758312225,
-0.04746784642338753,
-0.058451950550079346,
-0.004749171435832977,
-0.027102330699563026,
-0.03313722088932991,
0.04088941216468811,
-0.023677192628383636,
-0.0889865830540657,
-0.005389323458075523,
-0.011081662960350513,
-0.03393087536096573,
-0.0059923576191067696,
-0.007652404718101025,
-0.0061650886200368404,
0.04268019646406174,
0.0011560105485841632,
0.01670168526470661,
0.05964287742972374,
-0.030496319755911827,
-0.0021298499777913094,
-0.021678077057003975,
0.020662963390350342,
-0.014922543428838253,
-0.0011580302380025387,
-0.04185062646865845,
0.008059673011302948,
-0.08133723586797714,
0.038897641003131866,
-0.052322160452604294,
0.0090970229357481,
0.006249333266168833,
-0.04699482023715973,
-0.03889550268650055,
0.002339745406061411,
-0.023933785036206245,
-0.011290921829640865,
0.005003785248845816,
0.05839592218399048,
0.03067377768456936,
-0.017877541482448578,
0.0005267398082651198,
0.03232268616557121,
-0.024869784712791443,
0.011554533615708351,
0.018706871196627617,
0.05122939497232437,
-0.03422475606203079,
0.0015054976101964712,
-0.00308829708956182,
-0.02067522518336773,
0.043372463434934616,
0.023829827085137367,
0.026659060269594193,
0.06914691627025604,
-0.055415403097867966,
-0.07739503681659698,
0.00812623929232359,
0.0022816071286797523,
0.03740657866001129,
-0.06238480657339096,
-0.018859244883060455,
-0.017468329519033432,
0.023928305134177208,
-0.03321744129061699,
-0.027382005006074905,
0.03137866035103798,
0.010611618869006634,
-0.008409596048295498,
-0.021527189761400223,
0.05914468318223953,
-0.046539418399333954,
0.021523479372262955,
-0.036951057612895966,
0.03301907703280449,
-0.02635597437620163,
-0.004596595652401447,
-0.00034034636337310076,
0.01880049705505371,
0.048084672540426254,
-0.021941568702459335,
0.017693854868412018,
0.0036892620846629143,
0.03572063893079758,
0.011787873692810535,
-0.017749285325407982,
0.05754672735929489,
-0.003762362524867058,
0.004110097419470549,
0.0225108340382576,
0.00020127053721807897,
-0.01230030320584774,
-0.044824305921792984,
0.01833420805633068,
0.06759700924158096,
0.005363297648727894,
-0.029776861891150475,
0.00478113628923893,
0.003382996656000614,
-0.020353784784674644,
0.025951864197850227,
0.028727268800139427,
0.010580422356724739,
0.022893773391842842,
-0.06947655975818634,
0.042353104799985886,
-0.00668043177574873,
-0.03012007847428322,
-0.0002685334475245327,
0.0222669318318367,
0.030664319172501564,
-0.010653877630829811,
0.04022803530097008,
-0.021768497303128242,
0.020062895491719246,
0.006670578382909298,
0.0411517359316349,
0.009012545458972454,
-0.01830301061272621,
-0.0007629756582900882,
-0.012066078372299671,
0.008942468091845512,
-0.009154561907052994,
0.060195449739694595,
0.01475699432194233,
0.030495667830109596,
0.04490688443183899,
0.004085090011358261,
-0.0020885076373815536,
-0.02880745194852352,
-0.020001200959086418,
-0.0008191111264750361,
0.051455698907375336,
-0.004485741723328829,
-0.051547080278396606,
0.029873697087168694,
0.05375360697507858,
0.016004906967282295,
-0.010333089157938957,
-0.022388461977243423,
0.032245587557554245,
0.05489933863282204,
0.0054610660299658775,
-0.05432656407356262,
-0.018534697592258453,
0.04998596012592316,
-0.03251739591360092,
0.01951412856578827,
-0.0007354877889156342,
0.02312649041414261,
-0.015046745538711548,
-0.006321461405605078,
0.027832236140966415,
0.0020012834575027227,
-0.007873144932091236,
-0.06269697844982147,
-0.0034331087954342365,
0.0015337985241785645,
-0.005584368947893381,
-0.02199145033955574,
0.026903914287686348,
0.021477065980434418,
0.02021755836904049,
0.025853753089904785,
-0.01820092834532261,
-0.07251763343811035,
-0.06897971034049988,
-0.02434934675693512,
-0.026844238862395287,
0.03193250298500061,
0.024740051478147507,
-0.022913971915841103,
0.0127756018191576,
-0.006094443611800671,
0.008865538984537125,
0.0015169609105214477,
0.015413765795528889,
-0.018574213609099388,
0.05045910179615021,
-0.009007539600133896,
0.002664439147338271,
0.02850157767534256,
0.007052730303257704,
0.12660451233386993,
0.03811931237578392,
0.026961449533700943,
-0.06691772490739822,
0.04339328035712242,
-0.019487224519252777,
0.025336196646094322,
-0.01884985715150833,
0.019699539989233017,
-0.0038537252694368362,
0.012655971571803093,
0.017237842082977295,
0.015633998438715935,
0.014873979613184929,
0.0009065782651305199,
0.04637928679585457,
-0.06511532515287399,
-0.035907089710235596,
-0.004204727243632078,
0.03139369562268257,
-0.0010512544540688396,
0.013974286615848541,
-0.053444355726242065,
0.006710350047796965,
-0.025819171220064163,
-0.02411011792719364,
-0.02789570763707161,
-0.03485540673136711,
0.014687451533973217,
-0.006232128012925386,
0.0030529729556292295,
-0.014130797237157822,
0.01805330440402031,
-0.005901122931391001,
-0.03893101215362549,
0.02811005339026451,
0.004926527850329876,
0.008359837345778942,
0.03364867717027664,
-0.002258946420624852,
0.0441306009888649,
0.0045073977671563625,
0.012431688606739044,
0.02273039147257805,
-0.05649765580892563,
-0.009487178176641464,
-0.035121530294418335,
0.05912414938211441,
-0.024512965232133865,
0.04404855892062187,
0.008460941724479198,
-0.019820313900709152,
0.01258141454309225,
-0.012731596827507019,
-0.014168694615364075,
0.022005021572113037,
0.014533285982906818,
-0.025906043127179146,
-0.010499296709895134,
-0.03627931326627731,
0.01633281633257866,
-0.015894347801804543,
0.06539157032966614,
0.00968236569315195,
0.010720837861299515,
-0.007569689769297838,
0.010714717209339142,
0.02586929313838482,
-0.024331649765372276,
-0.022449906915426254,
-0.06454280763864517,
0.009545141831040382,
-0.020408235490322113,
-0.03812504932284355,
-0.003472951939329505,
0.023104431107640266,
-0.01565973274409771,
-0.011972064152359962,
-0.008389481343328953,
-0.037921592593193054,
-0.013571120798587799,
0.030538205057382584,
-0.0005837963544763625,
0.012873285450041294,
-0.017370568588376045,
-0.023922644555568695,
0.016756299883127213,
-0.0057619190774858,
0.0050527555868029594,
-0.004724462516605854,
0.012700507417321205,
-0.006612875033169985,
0.04041767492890358,
-0.019226491451263428,
0.01970500685274601,
-0.0033330072183161974,
-0.02800830453634262,
0.007875456474721432,
-0.01353751216083765,
0.04899584874510765,
0.026475941762328148,
-0.02057921513915062,
0.0330519936978817,
0.03791474178433418,
0.004139775410294533,
0.003995773382484913,
0.0417100265622139,
-0.029431551694869995,
0.017626849934458733,
0.015963390469551086,
0.0369846373796463,
-0.04026157408952713,
-0.032347578555345535,
-0.0038069188594818115,
0.03307371214032173,
-0.006681832019239664,
0.0016014707507565618,
-0.02214069291949272,
0.06156349182128906,
0.01631949283182621,
0.07096235454082489,
-0.008731430396437645,
0.028688756749033928,
-0.09151804447174072,
0.0019792825914919376,
0.03637049347162247,
-0.012422794476151466,
-0.008078264072537422,
0.05038446933031082,
-0.0004832525737583637,
-0.042406272143125534,
0.0032588669564574957,
0.005344797857105732,
-0.04098540171980858,
-0.018880819901823997,
-0.01920606940984726,
-0.02214064821600914,
0.03424527868628502,
0.001119757886044681,
-0.023445134982466698,
0.02023501880466938,
-0.043175190687179565,
-0.07820086181163788,
0.0414593368768692,
-0.03691185265779495,
-0.016089389100670815,
0.012746392749249935,
-0.05070141702890396,
-0.043920744210481644,
0.048233553767204285,
-0.018229186534881592,
-0.015890121459960938,
0.02050136774778366,
-0.023401102051138878,
-0.0035249076317995787,
0.006601360160857439,
0.005354739259928465,
-0.007046171929687262,
-0.00940701924264431,
0.02402407117187977,
0.029910778626799583,
0.018374256789684296,
0.002571297809481621,
-0.026249287649989128,
0.01727312058210373,
-0.01567237637937069,
-0.0064735389314591885,
-0.02783055230975151,
0.046735044568777084,
0.07493236660957336,
-0.07422202825546265,
0.04187382385134697,
0.02569073811173439,
-0.00040015889680944383,
-0.07382909208536148,
0.005422933958470821,
-0.020904578268527985,
-0.003338644979521632,
0.015104013495147228,
-0.05121638625860214,
0.024702629074454308,
0.00693160854279995,
-0.04956468939781189,
0.03960190340876579,
-0.04209717735648155,
-0.0044729760847985744,
0.0016913460567593575,
-0.02116183191537857,
-0.01845518685877323,
0.07066473364830017,
0.02546875551342964,
-0.00010728724737418815,
0.017287326976656914,
-0.0007796473801136017,
0.013462485745549202,
-0.0385725237429142,
-0.01964770071208477,
0.03284730389714241,
-0.022770822048187256,
0.00032569002360105515,
0.05646256357431412,
0.002958763623610139,
-0.07294407486915588,
0.0344068743288517,
0.007235394790768623,
0.009725140407681465,
-0.02340533770620823,
-0.007817932404577732,
0.004511341452598572,
0.04976411536335945,
-0.009311280213296413,
-0.029459817335009575,
0.012785918079316616,
0.011209331452846527,
0.01769103854894638,
0.01546181458979845,
0.004516147542744875,
0.040721792727708817,
-0.01670391857624054,
-0.05353309586644173,
0.008317073807120323,
0.0021146892104297876,
-0.0005709559773094952,
0.005331647582352161,
-0.007227877154946327,
0.03646893426775932,
0.002973092719912529,
0.010568222962319851,
-0.006725176237523556,
-0.05443925783038139,
-0.013540990650653839,
0.012028465047478676,
-0.023028507828712463,
0.05526622384786606,
0.01502908207476139,
-0.03946900740265846,
-0.009062008932232857,
-0.005028802901506424,
0.005147204734385014,
0.012586893513798714,
-0.045236632227897644,
-0.016479890793561935,
0.031830523163080215,
0.012922041118144989,
-0.014196583069860935,
-0.05128111690282822,
-0.06302948296070099,
-0.010376300662755966,
-0.0023201145231723785,
0.03299741819500923,
-0.02786075323820114,
-0.01388026587665081,
0.035297781229019165,
-0.03937933221459389,
-0.0013200429966673255,
0.02376951090991497,
0.049343232065439224,
-0.024260688573122025,
0.0020866445265710354,
0.01771540194749832,
0.0037739817053079605,
0.03390657156705856,
-0.004849315620958805,
-0.03978262096643448,
-0.018224794417619705,
-0.03763832896947861,
0.012436475604772568,
-0.05640571191906929,
0.025765493512153625,
-0.02423938922584057,
-0.005193435121327639,
-0.019367197528481483,
-0.009914876893162727,
0.028966858983039856,
0.02475234866142273,
0.04581912234425545,
0.035072848200798035,
0.043529901653528214,
0.011075769551098347,
-0.009878851473331451,
0.04648113250732422,
0.025844864547252655,
-0.04044866934418678,
0.028025496751070023,
-0.002052301773801446,
0.005304484628140926,
0.03177591413259506,
-0.026124903932213783,
-0.024085478857159615,
0.06695818156003952,
-0.030670972540974617,
-0.033965688198804855,
0.01223867665976286,
0.01385344099253416,
0.01551907043904066,
-0.051455672830343246,
0.016764994710683823,
0.03838396072387695,
0.00623067282140255,
0.02048952691257,
0.060636166483163834,
0.020313439890742302,
0.02803235501050949,
0.003732808632776141,
0.004533000290393829,
0.04087182134389877,
-0.02136889100074768,
-0.04660503566265106,
0.015476690605282784,
0.030807161703705788,
0.04278938099741936,
0.016730157658457756,
0.029435737058520317,
-0.01297654677182436,
0.028847383335232735,
0.01375249307602644,
0.03139304742217064,
-0.05792932212352753,
-0.029246393591165543,
-0.012952798046171665,
-0.008919095620512962,
0.010849867016077042,
0.02532002329826355,
0.024093927815556526,
0.06084549427032471,
-0.05080137401819229,
-0.0071417768485844135,
-0.026027284562587738,
-0.00976525153964758,
-0.049632199108600616,
-0.007846442051231861,
-0.004088294692337513,
0.06816215813159943,
0.0034517908934503794,
-0.02337995357811451,
-0.02422984316945076,
0.0397491492331028,
0.0015230623539537191,
-0.06509113311767578,
0.04830677807331085,
-0.004189305938780308,
-0.0006081690080463886,
0.004243828821927309,
0.003125125076621771,
-0.026984788477420807,
0.011518226005136967,
0.04730580747127533,
0.04602614417672157,
-0.0020840687211602926,
-0.024290908128023148,
-0.007714003790169954,
-0.047056473791599274,
0.06093183904886246,
-0.028205040842294693,
0.022150257602334023,
-0.04534192383289337,
0.03081112541258335,
-0.048831332474946976,
0.0025966414250433445
] |
<p>So I know that conduction is transfer of thermal energy by direct contact via molecular collisions. </p>
<p>For conduction, $Q/t$ is the rate of heat flow and is heat current ($I$). My textbook says that the rate of heat flow is constant across any number of slabs between 2 heat reservoirs, and I understand why this is so because if I use electric current as an example, the current in constant through resistors of different ohms in a series circuit too.</p>
<p>But then, the textbook goes on to show how conservation of energy also explains why. It says that "If the rate of energy transfer were not steady across all slabs, the slab that conducted heat the fastest would become cold. A cold slab could not conduct heat to warmer slabs because heat moves from hot to cold."</p>
<p>I don't understand their explanation that they offered from a conservation of energy standpoint. Could you please clarify this for me?
Why would the slab that conducted heat the fastest become cold if the rate of energy transfer were not steady?</p>
<p>For your reference, the equation for conduction is:
$$\frac{Q}{t} = kA\frac{T[\text{hot}] – T[\text{cold}]}{L}$$</p>
| 8,502 |
[
-0.03113234043121338,
-0.03392333537340164,
-0.007911548018455505,
-0.01784009113907814,
0.015322239138185978,
-0.017049558460712433,
0.00956354383379221,
-0.011594505049288273,
-0.01344498060643673,
0.014220371842384338,
0.0411236546933651,
0.02001856453716755,
0.015167569741606712,
-0.010419802740216255,
0.015650928020477295,
0.01134294830262661,
-0.0009435021784156561,
-0.008829663507640362,
0.018348166719079018,
-0.008731282316148281,
-0.007449228782206774,
0.037648361176252365,
0.010969799011945724,
0.0016508441185578704,
-0.02771606482565403,
0.032300982624292374,
-0.04506031051278114,
0.00356570933945477,
0.025621574372053146,
0.029279159381985664,
-0.0011111510684713721,
-0.014228169806301594,
0.000366124848369509,
-0.021186763420701027,
0.013836510479450226,
0.01410653069615364,
-0.055221930146217346,
-0.03282840549945831,
0.003951748833060265,
0.020061206072568893,
-0.02091079205274582,
-0.0053211175836622715,
0.019427917897701263,
0.04004167765378952,
-0.012569752521812916,
-0.0027822295669466257,
0.05042113736271858,
-0.02329089120030403,
0.006349196657538414,
-0.06402669847011566,
0.03460703790187836,
-0.002846203511580825,
0.083297960460186,
0.03782793879508972,
-0.010156962089240551,
0.02359733171761036,
0.058605924248695374,
0.041657865047454834,
-0.04696303978562355,
-0.04906724765896797,
0.005439379718154669,
0.012208946980535984,
-0.012495757080614567,
-0.024138059467077255,
-0.010363389737904072,
0.009576858952641487,
-0.01905553601682186,
-0.004829558078199625,
-0.0177268348634243,
-0.008761301636695862,
0.014830000698566437,
0.012155360542237759,
0.010482958517968655,
-0.004068942274898291,
0.02119274251163006,
-0.0053062643855810165,
-0.0010785504709929228,
0.04731706529855728,
0.041385192424058914,
0.054505810141563416,
-0.002225073054432869,
0.005805047228932381,
0.04999154433608055,
0.03142429143190384,
-0.018773389980196953,
-0.026042984798550606,
0.050131846219301224,
0.0032252592500299215,
0.03512853384017944,
0.03237859532237053,
0.02457120642066002,
0.02780371531844139,
0.0033104042522609234,
0.029479647055268288,
0.01113728154450655,
0.004187111742794514,
-0.024385150521993637,
0.04952947050333023,
0.017781388014554977,
-0.037620704621076584,
0.015234443359076977,
-0.008427373133599758,
0.035897232592105865,
0.05190064758062363,
-0.02294974774122238,
-0.04730949178338051,
-0.029238611459732056,
-0.0023068326991051435,
-0.00056364486226812,
0.007118063047528267,
-0.05454689636826515,
0.02482793666422367,
0.0010516196489334106,
0.04070787876844406,
-0.007402665447443724,
-0.04365018755197525,
0.005004833918064833,
-0.030817389488220215,
0.01321496069431305,
0.04362178593873978,
0.020357204601168633,
-0.04190005734562874,
0.01131992507725954,
-0.012385230511426926,
-0.040092118084430695,
0.03918078914284706,
0.005240598693490028,
0.007616665214300156,
-0.01661011576652527,
0.02464413270354271,
-0.003449773881584406,
-0.01059051789343357,
-0.04363953694701195,
-0.006556272506713867,
0.017875414341688156,
-0.02187398262321949,
-0.07525931298732758,
-0.05531197786331177,
0.034529395401477814,
-0.027547957375645638,
-0.02046148106455803,
-0.08766411244869232,
-0.005724550224840641,
0.008434774354100227,
0.04581592231988907,
-0.042514435946941376,
-0.013120398856699467,
-0.011922233738005161,
-0.004603094886988401,
0.000569885887671262,
-0.008871449157595634,
-0.03370830416679382,
0.025040647014975548,
-0.006848371587693691,
0.025386735796928406,
-0.035204678773880005,
0.01783359795808792,
0.0426073893904686,
0.0045165871270000935,
-0.023611251264810562,
0.0005988642806187272,
-0.008391332812607288,
-0.02770128846168518,
0.017359929159283638,
-0.011531103402376175,
-0.015185096301138401,
0.06870302557945251,
0.0012857636902481318,
0.04100336506962776,
0.015134459361433983,
0.030450645834207535,
0.010782957077026367,
-0.015150693245232105,
0.001611594227142632,
0.016299601644277573,
-0.04095902666449547,
-0.006426059175282717,
-0.017117369920015335,
-0.02673116885125637,
0.020383238792419434,
-0.07006777822971344,
-0.0003340390685480088,
0.025182629004120827,
-0.026505356654524803,
-0.007116090971976519,
0.06391222774982452,
0.018516644835472107,
0.034550175070762634,
0.012110072188079357,
-0.022452998906373978,
-0.05477621778845787,
-0.060602400451898575,
0.030902935191988945,
0.01426090206950903,
0.003840131452307105,
0.01815582439303398,
0.012488859705626965,
0.03486894443631172,
-0.01391034945845604,
-0.029622571542859077,
0.01062997430562973,
0.012193364091217518,
-0.007084832061082125,
-0.02691160887479782,
0.025450846180319786,
0.034169524908065796,
0.015651708468794823,
0.024251790717244148,
0.013896793127059937,
-0.034114498645067215,
0.0007578785298392177,
0.009587339125573635,
-0.0655822828412056,
0.04900084435939789,
-0.0021980907768011093,
-0.025610212236642838,
-0.020775027573108673,
-0.014488414861261845,
-0.016636144369840622,
0.04106222093105316,
-0.023113036528229713,
0.06705883145332336,
0.03504209220409393,
0.017944246530532837,
-0.01303132064640522,
0.06337019056081772,
-0.04145175963640213,
-0.006236155517399311,
-0.059558406472206116,
-0.04707701504230499,
-0.06044258549809456,
0.003977171145379543,
0.030326973646879196,
0.01652970165014267,
-0.05933612212538719,
0.006825511809438467,
0.034629739820957184,
0.041594404727220535,
0.021268777549266815,
-0.0015424244338646531,
-0.00761027354747057,
-0.037636205554008484,
0.05723300948739052,
-0.019956450909376144,
-0.008048124611377716,
0.05109332874417305,
0.018528791144490242,
0.008631382137537003,
0.01147192157804966,
0.000739811104722321,
-0.0442219004034996,
0.05706002563238144,
0.02100740745663643,
0.01615024171769619,
0.013247426599264145,
-0.03103669174015522,
0.014071673154830933,
-0.03654637932777405,
0.04195020720362663,
0.014989485964179039,
0.02832859568297863,
0.01504164095968008,
-0.027515649795532227,
-0.037116289138793945,
-0.0018135389545932412,
0.006876343861222267,
0.0008765039383433759,
-0.02106110192835331,
0.01756788045167923,
-0.029130669310688972,
0.03549514338374138,
-0.03526902571320534,
0.0011010098969563842,
-0.016569169238209724,
-0.030959583818912506,
0.009928232058882713,
0.02843894064426422,
0.018646853044629097,
-0.10065789520740509,
-0.030150864273309708,
-0.02192259207367897,
-0.020737679675221443,
0.009847552515566349,
-0.027539093047380447,
-0.04008697718381882,
-0.0019672245252877474,
-0.02693130448460579,
-0.05827205628156662,
0.04175390675663948,
0.01572584919631481,
-0.004992450587451458,
0.028786027804017067,
-0.0223244559019804,
-0.06631161272525787,
0.012068372219800949,
-0.025124015286564827,
0.007698513101786375,
-0.028142379596829414,
0.03544934093952179,
0.08914289623498917,
-0.054780274629592896,
-0.010005361400544643,
0.010762975551187992,
-0.026937590911984444,
-0.028416339308023453,
0.011053577996790409,
-0.03352495655417442,
0.013708431273698807,
-0.0005009787273593247,
0.02884080819785595,
0.0037429719232022762,
-0.04518289491534233,
-0.02522139437496662,
-0.039070382714271545,
-0.020107708871364594,
0.03402554616332054,
-0.01180953811854124,
0.03253382444381714,
-0.021687254309654236,
-0.03482935577630997,
0.04607359692454338,
0.02907385490834713,
-0.02914532832801342,
0.02193872258067131,
-0.025460850447416306,
-0.00722827622666955,
-0.070221446454525,
0.027477262541651726,
0.010685530491173267,
-0.046311154961586,
0.0024303023237735033,
0.016275890171527863,
0.06702614575624466,
0.06108235567808151,
-0.0372430644929409,
-0.0029489565640687943,
-0.005343498662114143,
0.02266068011522293,
0.02246069349348545,
0.035507671535015106,
0.0016567105194553733,
-0.040841806679964066,
0.026472309604287148,
-0.02384946309030056,
0.03232897073030472,
0.03001287393271923,
-0.06230863928794861,
0.05600396916270256,
0.009871556423604488,
-0.004867390729486942,
-0.07685472816228867,
0.02953234314918518,
-0.027167191728949547,
0.014891097322106361,
0.024745116010308266,
0.07516782730817795,
0.0713646411895752,
-0.02107834443449974,
0.02593037858605385,
0.008499749936163425,
0.03763268515467644,
-0.02509651519358158,
-0.006304339040070772,
0.014857611618936062,
-0.027047932147979736,
-0.0005497517413459718,
0.0013546999543905258,
0.002935713157057762,
0.011961495503783226,
0.008560571819543839,
0.027561817318201065,
0.01731656678020954,
-0.045272886753082275,
-0.027386818081140518,
-0.06418123841285706,
-0.022188641130924225,
0.00843911524862051,
0.06376159936189651,
0.007274294272065163,
0.07363764196634293,
0.032829638570547104,
0.02459881827235222,
0.015400918200612068,
0.004716857802122831,
-0.06674928963184357,
0.038716867566108704,
-0.018257344141602516,
-0.019077157601714134,
-0.016582965850830078,
0.010448361746966839,
0.03296518325805664,
-0.025574924424290657,
-0.0070829554460942745,
0.0016177543438971043,
-0.002600722946226597,
-0.03912431001663208,
0.02408677712082863,
-0.03120197169482708,
-0.0706048533320427,
-0.04672953486442566,
0.011634075082838535,
0.02696962095797062,
-0.06691861152648926,
0.03627284988760948,
0.0428260937333107,
-0.013965992256999016,
-0.019261837005615234,
-0.02046477235853672,
0.0020105759613215923,
0.01088818721473217,
-0.01336132176220417,
0.0196674931794405,
-0.008595735765993595,
-0.01630326546728611,
0.03042910248041153,
0.04515600949525833,
0.030494743958115578,
-0.0035644578747451305,
-0.032028038054704666,
-0.051278263330459595,
-0.047269098460674286,
-0.005371858831495047,
0.01960884965956211,
0.03368110582232475,
0.029292557388544083,
-0.008236704394221306,
0.02667910046875477,
0.029613880440592766,
-0.0293745007365942,
0.023734794929623604,
0.040225833654403687,
-0.004148523323237896,
-0.005841192789375782,
-0.04612073674798012,
-0.018077917397022247,
-0.03873680904507637,
-0.0026569420006126165,
0.07159417867660522,
-0.007762836758047342,
-0.006119575817137957,
0.0077152736485004425,
0.007272425573319197,
0.006317943800240755,
0.004011127166450024,
-0.009363273158669472,
-0.0014037280343472958,
0.011041692458093166,
0.011833880096673965,
-0.005344793666154146,
0.03717481344938278,
0.017369650304317474,
0.011215056292712688,
-0.020795626565814018,
0.00006753338675480336,
-0.06874395906925201,
-0.027513813227415085,
-0.0045092361979186535,
0.057046424597501755,
-0.018640100955963135,
-0.00551183894276619,
-0.06337215006351471,
0.01234048418700695,
0.004144737496972084,
-0.022496547549962997,
0.05455140024423599,
-0.02679155021905899,
-0.02723059058189392,
-0.030120503157377243,
-0.021695207804441452,
0.0029219896532595158,
0.03003312274813652,
0.005279168952256441,
0.05380699038505554,
-0.03978484496474266,
-0.019780270755290985,
-0.00003994110011262819,
-0.07153915613889694,
0.009453636594116688,
0.056493278592824936,
-0.031150011345744133,
0.007731025107204914,
0.031038809567689896,
0.03780152276158333,
-0.03510743007063866,
-0.07176194339990616,
-0.013881627470254898,
-0.02204505167901516,
0.014879535883665085,
0.009703156538307667,
-0.02507202699780464,
-0.04327099770307541,
0.044803258031606674,
0.05629534646868706,
-0.008702768012881279,
-0.009726976044476032,
-0.050965454429388046,
0.05046480894088745,
0.03614258021116257,
-0.008705059066414833,
0.08009131252765656,
-0.0035183746367692947,
-0.02254604548215866,
0.005069836508482695,
-0.01974736712872982,
0.06230257451534271,
-0.018327763304114342,
0.006151852663606405,
-0.023932630196213722,
0.02465328946709633,
-0.018048420548439026,
0.04956701397895813,
-0.004516978748142719,
0.01005485188215971,
-0.031094864010810852,
-0.024070976302027702,
0.015122373588383198,
0.00856662355363369,
0.0007760751759633422,
0.0004494160821195692,
-0.022835278883576393,
0.05078967660665512,
-0.02148330584168434,
-0.02476709894835949,
0.03315601870417595,
-0.019553110003471375,
0.007882198318839073,
0.03526914864778519,
0.025356320664286613,
0.04476470127701759,
-0.041561052203178406,
-0.0029903696849942207,
-0.010337317362427711,
-0.01455402746796608,
0.028386404737830162,
0.017626427114009857,
0.014080129563808441,
0.0004465657111722976,
-0.03391018137335777,
-0.0436142161488533,
0.02253638580441475,
-0.006510304752737284,
-0.023445146158337593,
-0.04877287149429321,
0.025906819850206375,
0.04648645594716072,
0.03193996474146843,
-0.0928470715880394,
-0.05764198675751686,
0.012552587315440178,
0.0018803778802976012,
-0.015380854718387127,
-0.03568997606635094,
-0.020574646070599556,
0.004941024351865053,
-0.04983604699373245,
0.021568015217781067,
0.04810939356684685,
-0.019290918484330177,
-0.023734040558338165,
0.03940011188387871,
0.045743178576231,
0.04136013612151146,
0.020732775330543518,
-0.004502532072365284,
-0.01041156705468893,
-0.044875018298625946,
-0.06292761862277985,
-0.022829191759228706,
0.0736459270119667,
-0.022898737341165543,
-0.020804136991500854,
0.02577592059969902,
0.0017339196056127548,
0.07150444388389587,
0.005915175192058086,
-0.007974712178111076,
0.015796693041920662,
0.021667227149009705,
-0.04650865122675896,
-0.009732568636536598,
0.040854305028915405,
0.02760116569697857,
0.010627076029777527,
-0.02421675994992256,
-0.01576145365834236,
-0.039037201553583145,
-0.05353531986474991,
0.0061231679283082485,
0.009065491147339344,
0.006992153823375702,
0.028118278831243515,
0.07790789008140564,
-0.03163575753569603,
-0.001597125199623406,
0.020330160856246948,
-0.015071522444486618,
0.058643046766519547,
0.012857676483690739,
0.004005745518952608,
-0.011736814863979816,
-0.03189213573932648,
-0.011846106499433517,
-0.02089259959757328,
-0.04560269042849541,
0.019904257729649544,
0.05520382151007652,
-0.008169290609657764,
0.06554485857486725,
-0.009041819721460342,
0.008365483954548836,
0.047908056527376175,
0.0001326482160948217,
-0.007632771972566843,
0.008506766520440578,
-0.0043623801320791245,
0.014993879944086075,
0.006159937474876642,
-0.02245890349149704,
0.04293899983167648,
0.04064590483903885,
-0.03114357776939869,
-0.01887654885649681,
0.019974088296294212,
0.012829720042645931,
-0.012578869238495827,
0.016622573137283325,
-0.027240268886089325,
0.008587113581597805,
-0.020996449515223503,
0.04025045782327652,
-0.048136625438928604,
-0.021812960505485535,
0.05041564628481865,
0.004352901130914688,
-0.009799917228519917,
-0.045191001147031784,
-0.008055380545556545,
-0.04401534050703049,
0.05476874113082886,
-0.004870755597949028,
0.03738082945346832,
0.01502904575318098,
0.058928363025188446,
0.02208072505891323,
-0.027680668979883194,
0.001257647410966456,
0.0008174762479029596,
-0.01365321408957243,
-0.014917467720806599,
0.013338669203221798,
0.0013950447319075465,
0.01620779186487198,
-0.0027838414534926414,
-0.014591881074011326,
-0.02366732805967331,
-0.033193189650774,
0.018786367028951645,
0.020798228681087494,
0.04603613540530205,
-0.020081887021660805,
0.09769967943429947,
0.006652095355093479,
0.01654183305799961,
-0.02780723385512829,
0.010339613072574139,
0.09715703874826431,
0.07519705593585968,
-0.005925849080085754,
-0.06677397340536118,
-0.0037232590839266777,
-0.018419448286294937,
-0.023744918406009674,
-0.03201252967119217,
0.01132789347320795,
0.011662853881716728,
0.036428432911634445,
0.008451657369732857,
0.03987345099449158,
-0.006671566050499678,
0.006679998245090246,
0.03942699730396271,
-0.03898234665393829,
-0.009381883777678013,
0.0026090533938258886,
0.009946725331246853,
-0.022314826026558876,
0.04022456705570221,
-0.03943774104118347,
0.018937330693006516,
-0.0026979607064276934,
-0.0061664641834795475,
-0.017125258222222328,
-0.02842029184103012,
0.039464861154556274,
-0.0053904689848423,
-0.029127217829227448,
0.017500411719083786,
0.010066173039376736,
-0.017120417207479477,
-0.014298543334007263,
0.02803213894367218,
0.04836086556315422,
0.004138637334108353,
0.05250061675906181,
0.06405293196439743,
0.009179767221212387,
0.002824668074026704,
0.044947389513254166,
0.0389367938041687,
-0.024489393457770348,
-0.028418587520718575,
-0.0685298964381218,
0.006615420337766409,
-0.01593943126499653,
0.023636994883418083,
0.03911258652806282,
0.006305827293545008,
-0.0016894484870135784,
-0.005783683620393276,
0.02443358302116394,
0.03460310399532318,
0.017813609912991524,
-0.023247061297297478,
-0.020696962252259254,
-0.037423618137836456,
0.022461552172899246,
-0.0030629667453467846,
0.0008983745938166976,
0.04150165989995003,
-0.014987379312515259,
-0.010675888508558273,
-0.004842204973101616,
0.024896837770938873,
-0.029119646176695824,
0.012041392736136913,
-0.03813285380601883,
-0.02789316326379776,
-0.011971399188041687,
-0.04270371049642563,
0.005409928038716316,
0.036428630352020264,
0.011594690382480621,
-0.0009197951294481754,
-0.020981065928936005,
0.002778106601908803,
-0.06890542805194855,
0.05009276419878006,
0.032788485288619995,
-0.03174697980284691,
-0.020862281322479248,
-0.009317509829998016,
-0.005506420042365789,
0.03465428203344345,
-0.03749748691916466,
-0.005132943857461214,
0.022634580731391907,
0.011449362151324749,
0.03875661641359329,
-0.012794069945812225,
-0.05975816026329994,
-0.006826105527579784,
-0.06089439243078232,
0.0010473132133483887,
0.023181455209851265,
0.024594159796833992,
0.013940001837909222,
0.024723751470446587,
-0.012817214243113995,
-0.016193997114896774,
-0.02588709630072117,
0.028394369408488274,
0.015038705430924892,
0.00260740052908659,
0.011272565461695194,
0.008334598504006863,
-0.018415555357933044,
-0.01073491107672453,
-0.058761756867170334,
-0.013645999133586884,
0.0239228755235672,
0.019986629486083984,
0.020574424415826797,
-0.028255995362997055,
0.032676760107278824,
-0.025643231347203255,
0.008403264917433262,
-0.07120469212532043,
-0.02144421823322773,
-0.04929359257221222,
0.0023473971523344517,
0.02675284631550312,
0.033139150589704514,
0.01223946176469326,
0.05071752518415451,
-0.018786216154694557,
0.006057793740183115,
0.025184670463204384,
-0.007877025753259659,
-0.02795840986073017,
-0.040841568261384964,
0.02474946901202202,
-0.011850148439407349,
0.05120649188756943,
-0.04491627961397171,
-0.04254889115691185,
0.05971070006489754,
-0.038804516196250916,
-0.008104769513010979,
0.00010306420881533995,
0.014329950325191021,
0.01430610939860344,
0.022204771637916565,
0.022870035842061043,
-0.0008373237797059119,
0.04242197796702385,
-0.00358244008384645,
0.01346613373607397,
-0.0030442713759839535,
-0.030567772686481476,
-0.002656192984431982,
-0.022251881659030914,
0.0065080770291388035,
-0.014162070117890835,
0.030423909425735474,
0.038923464715480804,
0.049447886645793915,
-0.015730323269963264,
0.021707911044359207,
-0.015277889557182789,
-0.007886083796620369,
-0.005597810260951519,
0.043127596378326416,
0.040909718722105026,
0.0034599860664457083,
0.04864427074790001,
-0.009619293734431267,
0.027407629415392876,
-0.013607836328446865,
-0.014079705812036991,
-0.0825255960226059,
-0.011981124058365822,
-0.02737102471292019,
-0.010049774311482906,
0.0057380362413823605,
-0.04549705609679222,
-0.019402144476771355,
0.045096203684806824,
-0.06265194714069366,
0.0398847721517086,
-0.02017827332019806,
-0.012757389806210995,
-0.04898657277226448,
0.012646844610571861,
-0.014062023721635342,
0.014505567029118538,
0.06528984755277634,
0.03635413199663162,
-0.009706109762191772,
0.0011996504617854953,
0.029002925381064415,
0.028123244643211365,
0.00019593477190937847,
0.020162144675850868,
-0.018911510705947876,
0.008499263785779476,
0.05455924943089485,
-0.0038140485994517803,
-0.0032082214020192623,
0.02412046305835247,
-0.03853253647685051,
-0.015692131593823433,
0.016114508733153343,
0.004321450367569923,
-0.023218819871544838,
0.035550668835639954,
0.019544348120689392,
-0.0372026301920414,
-0.0024936406407505274,
0.015327850356698036,
0.044677190482616425,
0.033383212983608246,
-0.00538082979619503,
0.0038892237935215235,
0.03677905350923538,
-0.06807325780391693,
-0.04023095220327377,
0.029230505228042603,
-0.010349180549383163,
0.008917082101106644,
0.03944966197013855,
0.013727168552577496,
0.06832294166088104,
-0.019547946751117706,
-0.0004766654164995998,
-0.03155006468296051,
-0.03606649488210678,
0.02465767040848732,
0.01514423731714487,
0.04355696216225624,
-0.01259344071149826,
0.0004295145918149501,
-0.004857076797634363,
0.051298052072525024,
0.02322980761528015,
-0.01129706110805273,
-0.06817859411239624,
-0.018259521573781967,
0.03147590532898903,
0.00537478644400835,
-0.02889629453420639,
-0.04357221722602844,
-0.0390133373439312,
0.04112955182790756,
0.006473202258348465,
0.03683369234204292,
-0.004902021028101444,
-0.036993607878685,
-0.022104505449533463,
-0.027968045324087143,
0.016121868044137955,
-0.04021117463707924,
-0.019830187782645226,
-0.04285014048218727,
-0.024510221555829048,
-0.0498339869081974,
0.03922624886035919,
0.08761350065469742,
-0.009939800947904587,
-0.012483535334467888,
0.028187178075313568,
-0.007431173697113991,
0.02835681103169918,
-0.05784950405359268,
0.01222092006355524,
-0.0023294573184102774,
0.009066889993846416,
0.012886748649179935,
0.01630406081676483,
-0.03768837824463844,
0.03495416417717934,
0.013809910044074059,
-0.020465414971113205,
0.02121281623840332,
-0.0019201154354959726,
-0.03731801360845566,
-0.0023185573518276215,
0.010141914710402489,
-0.002177940681576729,
0.06028240919113159,
-0.050415635108947754,
-0.010844496078789234,
0.015208980068564415,
-0.03865879774093628,
-0.07249771058559418,
0.03595944494009018,
-0.032039765268564224,
0.019058536738157272,
-0.005842521321028471,
-0.029340537264943123,
0.04592756927013397,
-0.054080843925476074,
0.0016144572291523218,
0.02960207685828209,
-0.05348365753889084,
-0.038236103951931,
0.03971753269433975,
0.0069265710189938545,
0.027834000065922737,
-0.03392684459686279,
0.023801663890480995,
-0.058566149324178696,
0.013748673722147942,
-0.012259004637598991,
0.03858126699924469,
0.0036633911076933146,
-0.024997111409902573,
0.017951810732483864,
0.012207240797579288,
-0.01367639284580946,
0.04357582703232765,
0.013249639421701431,
-0.0007460889755748212,
-0.026616612449288368,
-0.03423461318016052,
0.03375246748328209,
0.001311543514020741,
-0.043249476701021194,
0.021188698709011078,
-0.009702343493700027,
0.0802479013800621,
-0.020599734038114548,
0.006098640151321888,
-0.020123859867453575,
-0.004997496493160725,
-0.02883068658411503,
0.01143690850585699,
0.0065915281884372234,
0.022292209789156914,
-0.013554902747273445,
0.009061704389750957,
-0.018031900748610497,
-0.020237546414136887,
0.016828861087560654,
-0.0334366150200367,
0.0193704254925251,
-0.005597439594566822,
-0.019315510988235474,
-0.02344641461968422,
-0.012504681944847107,
0.003867796156555414,
-0.0026513850316405296,
0.04099253565073013,
0.05577049031853676,
-0.027722567319869995,
0.020372409373521805,
0.005975100677460432,
-0.003330912906676531,
0.04933803156018257,
-0.058956537395715714,
-0.0035121480468660593,
-0.014003395102918148,
0.048058684915304184,
0.027887172996997833,
0.015634015202522278
] |
<p>Why sometimes we remember that "classical" lagrangians of fermions are constructed from grassmann numbers, while sometimes don't? </p>
<p>For example, for Majorana's field in terms of 2-component spinors (you can read about this representation <a href="http://www.mdpi.com/2073-8994/5/4/271" rel="nofollow">here</a> in details),
$$
L = \bar{\psi}(\alpha^{\mu}\partial_{\nu} - m)\psi , \quad \alpha^{\mu} = (\sigma_{2}K, \sigma_{1}, \sigma_{2}, \sigma_{3}), \quad K\psi = \psi^{*}, \quad \bar{\psi} = -\psi^{\dagger}\alpha_{0},
$$
and the mass term become
$$
\bar{\psi} \psi = -\psi^{\dagger}\sigma_{2}\psi^{*} = -\begin{pmatrix}\psi_{1}^{*} & \psi_{2}^{*}\end{pmatrix}\sigma_{2}\begin{pmatrix} \psi_{1}^{*} \\ \psi_{2}^{*}\end{pmatrix} = 0
$$
if the fields are "classical". So we must assume their grassmanian nature before making all calculations (there this expression won't be equal to zero).</p>
<p>But when we assume the mass matrix for see-saw type 1 model, we introduce the term
$$
-M_{ij}(\psi_{R}^{T})^{i}\hat{C}\psi_{R}^{j} + h.c., \quad M_{ij} = M_{ji}, \quad \hat{C} = i\gamma_{2}\gamma_{0}.
$$
If the fields are grassmann numbers, this expression is equal to zero (don't forget about symmetric mass matrix). So we forget about grassmannian nature of the fields even in "classical" level.</p>
<p>Here "classical" means that we set all of anticommutators to zero. If we set them not to zero, we will have new problems, but it's the other story.</p>
| 8,503 |
[
-0.008392593823373318,
-0.023539172485470772,
-0.013229968957602978,
-0.024535778909921646,
0.020906314253807068,
0.008773231878876686,
-0.03340793028473854,
-0.04215867072343826,
0.0023380080237984657,
-0.04313163831830025,
0.023796306923031807,
-0.049193646758794785,
0.06885509938001633,
0.021085618063807487,
0.030004793778061867,
0.034080132842063904,
0.005948446691036224,
0.0066907042637467384,
-0.02499116025865078,
0.015530837699770927,
0.023709736764431,
0.07263946533203125,
0.015613826923072338,
-0.01785283163189888,
-0.01101329643279314,
0.04293978959321976,
0.004217870533466339,
0.003469035727903247,
-0.014474584721028805,
0.051724623888731,
-0.03650079295039177,
-0.037226684391498566,
0.036659125238657,
-0.009030096232891083,
-0.027296053245663643,
0.005243871361017227,
-0.012437152676284313,
-0.04248707741498947,
-0.005829747766256332,
0.011210798285901546,
-0.030333319678902626,
-0.01262972503900528,
-0.06608394533395767,
0.025533288717269897,
-0.01347232423722744,
0.026057755574584007,
-0.024743719026446342,
-0.032865673303604126,
0.04920506477355957,
-0.0504218265414238,
0.042477305978536606,
0.03418230637907982,
0.0063689216040074825,
-0.004284835886210203,
-0.02430625818669796,
-0.02655145339667797,
0.03652143478393555,
0.03021753765642643,
0.03880517929792404,
-0.08941882103681564,
-0.025097673758864403,
-0.011481706984341145,
0.008910313248634338,
-0.04590447247028351,
0.013035750016570091,
0.017969580367207527,
0.06419103592634201,
0.0020298620220273733,
0.01650870591402054,
0.014146832749247551,
0.012462622486054897,
-0.04979037493467331,
0.03009113296866417,
-0.02022911049425602,
0.04267888516187668,
-0.011449347250163555,
-0.02394297905266285,
0.028858069330453873,
0.02952178567647934,
0.004803782794624567,
0.04062873125076294,
0.062332555651664734,
0.029665453359484673,
-0.01726202666759491,
0.004708395339548588,
-0.007152037229388952,
0.052666861563920975,
0.02310006506741047,
0.010629339143633842,
0.03042486123740673,
-0.019598644226789474,
-0.004575221333652735,
0.053483638912439346,
-0.02839851751923561,
-0.029282569885253906,
0.01032804511487484,
0.01316269300878048,
0.02267024852335453,
-0.007489346899092197,
-0.01620595157146454,
-0.042172886431217194,
-0.028703391551971436,
0.0021113462280482054,
0.058061014860868454,
0.013818112201988697,
-0.001440816675312817,
-0.03293905034661293,
0.020452767610549927,
-0.05017440393567085,
-0.05215981602668762,
-0.04218919575214386,
0.008263136260211468,
-0.025864534080028534,
-0.011699114926159382,
-0.03949831798672676,
-0.05912461504340172,
-0.018870364874601364,
-0.01187365036457777,
0.06125858426094055,
0.07048577815294266,
0.05882249027490616,
-0.01360640674829483,
0.0001273558009415865,
-0.030008157715201378,
-0.06255999207496643,
0.043756481260061264,
0.02408774010837078,
-0.010283789597451687,
-0.05779512599110603,
-0.001344202901236713,
0.05225696414709091,
0.020868564024567604,
0.021241163834929466,
0.03141924738883972,
-0.005183253437280655,
-0.029128240421414375,
-0.09006521105766296,
-0.02048651874065399,
0.013666021637618542,
-0.015051482245326042,
-0.006210269406437874,
-0.06816024333238602,
-0.016094395890831947,
0.02019321545958519,
0.10529384016990662,
-0.027884487062692642,
0.02942850813269615,
0.01264876313507557,
0.004060001112520695,
0.0013405324425548315,
0.007963856682181358,
-0.036803096532821655,
-0.004728174302726984,
-0.03097832389175892,
-0.03173956647515297,
-0.047911904752254486,
0.042665570974349976,
0.03399496525526047,
-0.009846163913607597,
-0.0020906536374241114,
0.04946831241250038,
0.004974551498889923,
0.02409418858587742,
0.03318558633327484,
-0.016688838601112366,
-0.020303869619965553,
0.035049889236688614,
-0.00971194263547659,
0.028518659994006157,
0.013452826999127865,
-0.02495507337152958,
0.026000522077083588,
0.027068965137004852,
0.07608906924724579,
0.04466912895441055,
-0.03101319819688797,
-0.04164685308933258,
-0.039581961929798126,
0.02864626981317997,
-0.015278207138180733,
-0.057876262813806534,
-0.020602460950613022,
-0.0505952350795269,
-0.0039395522326231,
-0.010574446059763432,
0.04730142652988434,
0.021674221381545067,
0.008407065644860268,
-0.011988244950771332,
-0.041481927037239075,
-0.03495413810014725,
-0.035587508231401443,
-0.007344997953623533,
0.01587500236928463,
-0.00587621470913291,
0.044604748487472534,
0.018780888989567757,
0.00036488589830696583,
0.0026419986970722675,
-0.039995837956666946,
0.02579568326473236,
0.048544611781835556,
0.01769878715276718,
-0.011240556836128235,
0.024034129455685616,
0.024715812876820564,
0.030236849561333656,
0.005757068283855915,
0.052647802978754044,
-0.03279094025492668,
-0.024778660386800766,
-0.011571686714887619,
0.008361775428056717,
0.037938445806503296,
0.015969492495059967,
0.009663661941885948,
0.0018438787665218115,
-0.01664893701672554,
-0.06386159360408783,
0.020540772005915642,
-0.04732755199074745,
0.025351760908961296,
0.0370401106774807,
-0.03106539137661457,
-0.005398713517934084,
0.038602735847234726,
-0.01829226128757,
0.022560589015483856,
-0.0020238514989614487,
-0.010765675455331802,
-0.03960816562175751,
-0.033780716359615326,
0.04718746989965439,
0.05513225123286247,
-0.043343108147382736,
0.03500688448548317,
0.011117714457213879,
0.045808736234903336,
0.018514765426516533,
0.0045171999372541904,
-0.019786188378930092,
-0.0444658100605011,
0.04778062924742699,
-0.0012628495460376143,
-0.03440346196293831,
0.0025795763358473778,
0.057113513350486755,
-0.004258802160620689,
0.002979828743264079,
0.0004192033957224339,
-0.0422377809882164,
0.03957971930503845,
-0.016820702701807022,
-0.005216595716774464,
0.001739670056849718,
-0.01551256887614727,
0.04835675656795502,
-0.004842860624194145,
0.059162355959415436,
0.03919800743460655,
-0.019620664417743683,
-0.03334024176001549,
-0.02962036430835724,
0.013724446296691895,
0.006677911151200533,
-0.00905890017747879,
-0.019437145441770554,
0.02144436351954937,
0.007551142014563084,
-0.03989270702004433,
0.016433309763669968,
-0.025715047493577003,
-0.02692815661430359,
-0.02173168770968914,
0.030413340777158737,
0.0230600293725729,
0.020361097529530525,
0.05088184401392937,
-0.03200811147689819,
-0.004959287587553263,
0.03862626850605011,
-0.010937890969216824,
0.04087730869650841,
0.04356992989778519,
-0.029416510835289955,
-0.012988600879907608,
-0.09003394097089767,
-0.01712588407099247,
0.03052980825304985,
-0.015899507328867912,
-0.009539895690977573,
-0.0037229815497994423,
-0.010012124665081501,
-0.048398204147815704,
-0.037686143070459366,
-0.028429176658391953,
-0.017804589122533798,
-0.0427730567753315,
0.012134416028857231,
0.010439204052090645,
0.027758168056607246,
-0.049816589802503586,
-0.011632275767624378,
0.01568850874900818,
-0.05811027064919472,
-0.031833305954933167,
-0.02400282584130764,
-0.0192889217287302,
-0.05006411299109459,
0.02318493090569973,
0.024911249056458473,
-0.019445205107331276,
0.018887603655457497,
-0.05383090674877167,
-0.0006467779166996479,
0.008775273337960243,
-0.012096256017684937,
0.018295416608452797,
0.01692991517484188,
-0.04985850676894188,
0.10568837821483612,
0.01150531880557537,
-0.016833482310175896,
-0.008763439022004604,
-0.01699955016374588,
-0.028290782123804092,
-0.008635184727609158,
-0.0035020282957702875,
0.01832963339984417,
0.009323098696768284,
0.039878711104393005,
0.014864147640764713,
-0.0017030210001394153,
0.029317261651158333,
0.00046464797924272716,
-0.005419849883764982,
-0.004120431374758482,
-0.013901926577091217,
-0.007830919697880745,
0.036801211535930634,
-0.03905379772186279,
-0.003316133515909314,
0.01533898152410984,
0.02671647258102894,
0.03805249556899071,
0.0004493031883612275,
-0.06002480536699295,
0.05070881545543671,
0.008112134411931038,
0.010365402325987816,
0.0006740413955412805,
0.012691224925220013,
0.004669608548283577,
-0.06407174468040466,
-0.014144686050713062,
0.025275178253650665,
0.023802701383829117,
-0.05153953656554222,
-0.006985201500356197,
0.008100258186459541,
0.04007616266608238,
-0.042071085423231125,
-0.020450474694371223,
0.00009347045852337033,
-0.019385894760489464,
0.027697281911969185,
-0.05424543842673302,
-0.035106465220451355,
0.013726365752518177,
0.049932826310396194,
-0.020400965586304665,
-0.00977774616330862,
-0.014806471765041351,
-0.022971604019403458,
-0.05535193160176277,
-0.005640385206788778,
-0.02135879173874855,
0.0339149571955204,
-0.0006082517211325467,
0.031037000939249992,
0.021654101088643074,
-0.0034588812850415707,
-0.010959108360111713,
-0.022557059302926064,
-0.041741468012332916,
-0.023265717551112175,
-0.03577384725213051,
-0.022355766966938972,
0.053451377898454666,
-0.0263324324041605,
0.017977116629481316,
-0.01234126091003418,
-0.03378935158252716,
-0.016730817034840584,
0.004291269928216934,
-0.010380575433373451,
0.0286369938403368,
-0.0311114601790905,
-0.043191857635974884,
-0.04323287680745125,
0.032922662794589996,
0.04233970120549202,
-0.0011560212587937713,
-0.013557425700128078,
0.02910413220524788,
-0.011798729188740253,
0.007116553373634815,
-0.024214910343289375,
0.03142834082245827,
0.03795754164457321,
0.01137455552816391,
0.06055663153529167,
-0.0217475313693285,
-0.017760343849658966,
-0.010392777621746063,
0.02085409313440323,
0.07847952842712402,
-0.010646585375070572,
-0.007284532301127911,
0.03256598860025406,
-0.013808849267661572,
-0.03682319074869156,
0.0074170250445604324,
0.07637029886245728,
-0.002932759001851082,
-0.01073511317372322,
0.019891513511538506,
0.00432736799120903,
0.002686078194528818,
0.03382112830877304,
0.04041871801018715,
0.016655903309583664,
-0.010191123001277447,
-0.062075722962617874,
0.02022670954465866,
-0.04938531294465065,
0.012130994349718094,
-0.026931609958410263,
0.0014951337361708283,
-0.011707624420523643,
-0.009939517825841904,
0.01936398819088936,
0.003489062888547778,
-0.027414729818701744,
0.01891147345304489,
0.020538881421089172,
0.019840428605675697,
0.024943919852375984,
-0.004231599625200033,
0.035931844264268875,
0.07723874598741531,
0.020556559786200523,
-0.03297879174351692,
0.004258099012076855,
-0.04643688723444939,
-0.015156344510614872,
0.010526287369430065,
0.047674424946308136,
-0.0011778466869145632,
-0.033069826662540436,
-0.06566660106182098,
-0.010229399427771568,
-0.009605560451745987,
0.012345388531684875,
0.024517858400940895,
0.000856716011185199,
-0.005177539773285389,
-0.032223306596279144,
-0.005972478073090315,
-0.03882618993520737,
0.0518573559820652,
-0.005071318708360195,
0.02963731437921524,
-0.046000782400369644,
-0.0035542829427868128,
-0.0323018953204155,
-0.006295164581388235,
-0.025749890133738518,
0.020368322730064392,
0.012841013260185719,
0.02440693974494934,
-0.0019316421821713448,
0.02977919392287731,
-0.009247426874935627,
-0.09850432723760605,
-0.007451264653354883,
-0.019221043214201927,
0.01361097302287817,
0.06404253095388412,
-0.034581296145915985,
-0.03372093290090561,
-0.010179545730352402,
0.02894943580031395,
0.0102259935811162,
0.030778678134083748,
-0.04107850790023804,
0.024919774383306503,
0.03155166283249855,
-0.037759169936180115,
0.02482450380921364,
0.012231639586389065,
-0.026359133422374725,
-0.008007778786122799,
-0.057588811963796616,
0.030028946697711945,
-0.019347529858350754,
0.022667232900857925,
-0.07230676710605621,
0.004190534818917513,
0.008102006278932095,
0.041177671402692795,
-0.041844479739665985,
0.05990758538246155,
-0.0026108967140316963,
-0.03952081501483917,
-0.03721017763018608,
-0.001359046553261578,
-0.012784566730260849,
-0.019041171297430992,
0.009295661002397537,
0.053860854357481,
0.02414132095873356,
-0.008482510223984718,
0.018760351464152336,
-0.03251410275697708,
0.011524153873324394,
0.044439297169446945,
-0.0072780693881213665,
0.04689747095108032,
-0.016605954617261887,
-0.013835517689585686,
0.00835589598864317,
-0.054049793630838394,
0.02179025299847126,
-0.004156051203608513,
0.001203327439725399,
0.0006645695539191365,
0.00930482055991888,
-0.02815781719982624,
-0.0074980915524065495,
-0.029248876497149467,
-0.02708243951201439,
-0.0276779867708683,
-0.029340527951717377,
0.05610133707523346,
-0.007500750944018364,
-0.05578894913196564,
-0.00881111342459917,
-0.022874318063259125,
0.013102265074849129,
-0.02701156958937645,
-0.010805847123265266,
0.0021240010391920805,
0.0016537494957447052,
-0.04496249184012413,
0.031312860548496246,
0.06223020702600479,
-0.018960565328598022,
-0.006944732740521431,
0.02887657843530178,
0.03831426054239273,
0.03892656788229942,
-0.02478896453976631,
-0.005589435342699289,
0.020632904022932053,
-0.026348194107413292,
0.013203286565840244,
0.027314141392707825,
0.06087927892804146,
0.013473032042384148,
-0.01669650338590145,
0.00034672749461606145,
-0.023054514080286026,
0.02598400227725506,
0.014687109738588333,
-0.0010263730073347688,
0.025963444262742996,
-0.017414681613445282,
0.04329323768615723,
-0.010157530196011066,
-0.030188219621777534,
0.020510314032435417,
0.04801963269710541,
-0.007364328484982252,
-0.025485290214419365,
-0.048000484704971313,
-0.016148073598742485,
0.017886701971292496,
-0.020851414650678635,
-0.014424963854253292,
-0.0015838075196370482,
0.055433183908462524,
0.00039465585723519325,
-0.007594686932861805,
0.04172724485397339,
-0.031110987067222595,
-0.020092187449336052,
0.015123697929084301,
0.049219291657209396,
0.012131079100072384,
0.017402751371264458,
0.012950516305863857,
-0.028103787451982498,
-0.031146202236413956,
0.041598863899707794,
0.05990118533372879,
0.02425820380449295,
-0.008124928921461105,
-0.003568128449842334,
-0.022184835746884346,
-0.027339335530996323,
-0.03395524621009827,
-0.04052465036511421,
0.021943267434835434,
-0.0134101128205657,
0.020994581282138824,
-0.046860210597515106,
0.003910214640200138,
0.048795830458402634,
0.026215270161628723,
-0.04746586084365845,
-0.00044375061406753957,
0.03519918769598007,
0.018760384991765022,
0.0032739641610533,
-0.03228645399212837,
-0.0065397885628044605,
0.06738736480474472,
-0.020541157573461533,
0.02110748365521431,
0.002640116959810257,
-0.012713370844721794,
0.0026359548792243004,
0.048536427319049835,
0.014883792959153652,
-0.03474189713597298,
-0.004588071722537279,
-0.04103030636906624,
0.040714994072914124,
0.03465177118778229,
0.004169141873717308,
0.017176564782857895,
-0.0034319893456995487,
0.032470010221004486,
-0.01784643530845642,
0.03023676946759224,
0.00847396720200777,
-0.021624449640512466,
-0.03258005529642105,
-0.05053424462676048,
-0.07335179299116135,
0.053750570863485336,
0.017874158918857574,
-0.026721691712737083,
-0.0023486511781811714,
-0.013244380243122578,
0.04661116003990173,
-0.0062011731788516045,
0.02441316843032837,
-0.02832850255072117,
0.04378603398799896,
0.00010784701589727774,
0.027640866115689278,
0.022509027272462845,
-0.008903200738132,
0.16182702779769897,
0.03138615936040878,
-0.0030203296337276697,
-0.06404531002044678,
0.019855478778481483,
-0.0010814451379701495,
0.008356332778930664,
-0.003386205993592739,
0.0308213047683239,
0.005094477441161871,
-0.00824621133506298,
-0.035720452666282654,
0.059356801211833954,
-0.012683803215622902,
0.0019457113230600953,
0.02329440228641033,
0.0019214415224269032,
-0.038514986634254456,
-0.0013787816278636456,
0.03647741302847862,
-0.03267116844654083,
0.032355159521102905,
-0.012167083099484444,
0.02640950307250023,
0.013421306386590004,
0.03511401265859604,
0.011571700684726238,
-0.018158283084630966,
0.02936124987900257,
0.004408521577715874,
-0.04138631001114845,
0.008708658628165722,
0.016487469896674156,
0.015181541442871094,
-0.03526050224900246,
0.008832158520817757,
0.03308987244963646,
-0.017734643071889877,
0.04125265032052994,
0.039284367114305496,
-0.021460698917508125,
0.0220045018941164,
0.02345343865454197,
-0.0020306797232478857,
-0.025499064475297928,
-0.012040051631629467,
-0.048761893063783646,
0.1008145734667778,
-0.025973474606871605,
-0.006654985249042511,
0.003336761612445116,
-0.0370626337826252,
0.033392954617738724,
-0.01899992860853672,
0.0016214309725910425,
-0.019093338400125504,
0.046966344118118286,
-0.040847185999155045,
0.005344302859157324,
-0.006775760557502508,
0.03344890847802162,
0.023341946303844452,
0.010657484643161297,
-0.013942179270088673,
-0.02977549470961094,
-0.04186159744858742,
0.0076749748550355434,
0.030077455565333366,
0.022904353216290474,
-0.007917042821645737,
-0.014940930530428886,
-0.03242998197674751,
-0.05031979829072952,
-0.009613380767405033,
-0.0034401314333081245,
0.007589268032461405,
0.03475939482450485,
-0.0293074082583189,
-0.03698280453681946,
-0.030313435941934586,
-0.05872907117009163,
-0.004238561727106571,
-0.02706468291580677,
-0.012880602851510048,
-0.0010038117179647088,
-0.024627190083265305,
0.002651225309818983,
0.033178336918354034,
-0.015428656712174416,
0.014390560798346996,
0.017434662207961082,
0.040312912315130234,
0.010370781645178795,
-0.032186947762966156,
-0.015779683366417885,
0.0004188415769021958,
-0.027828888967633247,
-0.0024279782082885504,
-0.03249302878975868,
-0.03331463783979416,
0.018899641931056976,
0.016690677031874657,
-0.01912001520395279,
0.023412970826029778,
0.018246326595544815,
-0.016006354242563248,
0.03039727918803692,
-0.0028719778638333082,
0.04918835684657097,
0.03258584812283516,
0.03165064752101898,
-0.025648176670074463,
-0.043636586517095566,
-0.007659715134650469,
-0.0012565759243443608,
-0.025999270379543304,
0.03119092807173729,
-0.06596576422452927,
-0.015270570293068886,
-0.03549732640385628,
0.01953411102294922,
-0.03475905954837799,
-0.011615347117185593,
-0.044727127999067307,
0.047086216509342194,
-0.012362992390990257,
0.011610288172960281,
-0.0288920346647501,
0.026449939236044884,
0.0114746680483222,
0.023772813379764557,
0.03820249065756798,
0.03893066942691803,
-0.0294045340269804,
-0.0037223759572952986,
0.03254309296607971,
-0.004027956631034613,
-0.001555348397232592,
0.04127572104334831,
-0.026805728673934937,
0.008023153990507126,
0.03363015875220299,
-0.03473546728491783,
0.047484684735536575,
0.01786283403635025,
0.057053107768297195,
0.05293525382876396,
-0.009348701685667038,
0.004337352234870195,
0.01372567005455494,
-0.034311845898628235,
-0.022694045677781105,
-0.021961240097880363,
-0.00563416350632906,
-0.029428904876112938,
-0.053221624344587326,
-0.002510650549083948,
0.0011895449133589864,
0.011104634031653404,
0.023888645693659782,
0.0030722497031092644,
-0.030111486092209816,
0.003285585204139352,
0.021525518968701363,
-0.01185391005128622,
0.03152741864323616,
0.04395097866654396,
-0.007276054006069899,
0.0039777858182787895,
0.03126497566699982,
-0.0017504107672721148,
0.017828159034252167,
0.014811594970524311,
0.019847983494400978,
-0.054880429059267044,
-0.023427024483680725,
0.00821753405034542,
0.034561533480882645,
0.08071962743997574,
-0.005030143540352583,
-0.008028088137507439,
0.025705605745315552,
-0.05002659186720848,
-0.009954036213457584,
-0.010576792061328888,
-0.03617002069950104,
0.0007144162664189935,
-0.026369793340563774,
-0.0031049971003085375,
0.060446955263614655,
0.010058212094008923,
0.015828963369131088,
0.02907850407063961,
0.0007082890369929373,
0.006681285798549652,
-0.03247557580471039,
-0.048970092087984085,
0.025620901957154274,
0.005585547536611557,
-0.016378892585635185,
0.07578963786363602,
-0.03126203268766403,
-0.03384365513920784,
0.008486920036375523,
0.0376034751534462,
-0.023996703326702118,
0.013203738257288933,
0.03649600222706795,
0.024988720193505287,
0.04152218997478485,
0.0061027891933918,
-0.0269789882004261,
-0.019554708153009415,
0.00756819685921073,
0.024350298568606377,
0.03506491333246231,
-0.017228104174137115,
0.014368021860718727,
-0.005201979540288448,
-0.056858621537685394,
-0.01481156051158905,
0.019710136577486992,
-0.041942451149225235,
-0.05102987959980965,
0.007980737835168839,
0.002019809326156974,
-0.031813424080610275,
-0.03231382742524147,
0.0538785457611084,
-0.03035844676196575,
0.020892105996608734,
0.025549031794071198,
0.03908338397741318,
0.0022894875146448612,
0.06368613988161087,
0.0024169585667550564,
-0.009664012119174004,
0.047540098428726196,
0.02454383671283722,
-0.014794710092246532,
-0.05893454700708389,
-0.017120815813541412,
-0.0007079344359226525,
0.005847053602337837,
-0.007616146467626095,
-0.035426877439022064,
-0.05762985348701477,
0.027707098051905632,
-0.012995239347219467,
-0.008278187364339828,
-0.05659250542521477,
-0.0233128871768713,
0.03131059184670448,
-0.03438275679945946,
0.020918777212500572,
0.014690798707306385,
0.013017748482525349,
-0.020517468452453613,
-0.0003981194749940187,
-0.026302307844161987,
0.028227562084794044,
0.0699506625533104,
0.014480850659310818,
-0.022838059812784195,
0.032039348036050797,
0.0049221389926970005,
-0.0017926845466718078,
-0.013315699994564056,
0.009213540703058243,
0.007973149418830872,
-0.014502528123557568,
-0.003984552808105946,
0.03617541491985321,
-0.0058761294931173325,
0.035734400153160095,
0.02666242979466915,
-0.0004647332534659654,
0.007000165991485119,
0.03216460347175598,
-0.037056758999824524,
0.04309775307774544,
-0.019470563158392906,
-0.02548527903854847,
0.06083716079592705,
-0.0035685638431459665,
-0.010490751825273037,
0.0342295803129673,
-0.0624920092523098,
-0.010485208593308926,
0.027986524626612663,
0.009021907113492489,
-0.00482789846137166,
-0.012843038886785507,
0.000929297530092299,
0.03860689699649811,
-0.02874915674328804,
0.044959764927625656,
0.04765019565820694,
0.010862179100513458,
-0.04072029888629913,
0.043064456433057785,
-0.004290036857128143,
0.020881429314613342,
0.01156292762607336,
0.04157960042357445,
0.01646720990538597,
0.021188240498304367,
0.04084303230047226,
0.04762880131602287,
0.010945911519229412,
0.009398329071700573,
0.01891227625310421,
0.020504646003246307,
-0.03667622059583664,
-0.00688336743041873,
-0.001231323811225593,
0.02153962478041649,
-0.03743000701069832,
0.012686855159699917,
0.046652331948280334,
-0.037484247237443924,
0.024999212473630905,
-0.004465984180569649,
-0.008666028268635273,
0.08451646566390991,
-0.004209099803119898,
-0.00792302843183279,
-0.04757259041070938,
0.018213359639048576,
0.02446870319545269,
-0.03230657801032066,
-0.016410131007432938,
0.05311262607574463,
0.007028356194496155,
-0.006221888121217489,
-0.04733024165034294,
-0.015313305892050266,
0.01549512892961502,
-0.09635622799396515,
-0.02255563624203205,
0.030395841225981712,
0.004523996729403734,
-0.02345261164009571,
-0.05045713111758232,
-0.005971794947981834,
-0.04276198148727417,
0.04263395071029663,
0.013734990730881691,
-0.002913309494033456,
-0.017638128250837326,
-0.061115242540836334,
-0.017263958230614662,
0.02902599796652794,
-0.023115556687116623,
-0.022523244842886925,
0.004333015531301498,
0.04434427618980408,
-0.02043822593986988,
0.0207719337195158
] |
<p>What is the modern mainstream way to deal with the <a href="http://en.wikipedia.org/wiki/Measurement_problem" rel="nofollow">measurement problem</a>? For this question, the measurement problem is the problem of formalizing wave function collapse when the observer is part of the model (say I want to simulate an observer+observee quantum system on a computer). I am aware of proposed solutions: Everett, Bohm, and decoherence (though decoherence apparently does not explain collapse). How does mainstream physics deal with this issue?</p>
<p>For example: Given two electrons initially isolated from each other and the universe which then interact , can each electron be considered an observer? With no-collapse theories each electron sees the other election's wave function collapse relatively. If the mainstream view holds that a single electron cannot be an observer what is the criterion for an observer?</p>
| 8,504 |
[
-0.01185568980872631,
0.004406599327921867,
-0.0031120560597628355,
-0.03587875887751579,
0.007918857969343662,
-0.018116559833288193,
-0.014591190032660961,
-0.019306501373648643,
0.01697925478219986,
0.004233804065734148,
0.02900112234055996,
0.03499186411499977,
0.02916337363421917,
0.0015713452594354749,
0.023960428312420845,
0.003925641532987356,
-0.011378545314073563,
-0.018225129693746567,
-0.0010783991310745478,
-0.014123732224106789,
-0.023221923038363457,
0.012487941421568394,
0.024078484624624252,
-0.01425217092037201,
0.003918075934052467,
0.022952208295464516,
0.01036496739834547,
0.023070788010954857,
0.04666958004236221,
0.05967291072010994,
-0.03345680236816406,
-0.05463920533657074,
-0.0068820081651210785,
0.02629993110895157,
0.0021538722794502974,
-0.019088994711637497,
0.0029107658192515373,
-0.02770267426967621,
-0.006964989472180605,
-0.008853413164615631,
-0.033481694757938385,
-0.01256684772670269,
0.00003010634463862516,
0.027139006182551384,
-0.04929792508482933,
-0.016253430396318436,
-0.0052916547283530235,
-0.03131882846355438,
0.054473962634801865,
-0.058130521327257156,
0.08008122444152832,
0.004176905378699303,
0.05194850265979767,
-0.0109658008441329,
-0.013349711894989014,
0.008786296471953392,
0.10262750089168549,
0.05762895569205284,
-0.021373825147747993,
-0.022796446457505226,
-0.05506237596273422,
-0.008731554262340069,
0.01163194328546524,
-0.017024489119648933,
-0.04089750722050667,
0.0629737451672554,
-0.005714528728276491,
-0.014921762980520725,
0.03660174459218979,
-0.010074010118842125,
-0.013554318808019161,
-0.01643362082540989,
0.040824830532073975,
-0.008774700574576855,
0.031610310077667236,
-0.015352106653153896,
0.03262298181653023,
0.010342150926589966,
0.038507938385009766,
0.029455343261361122,
-0.0031880694441497326,
-0.0022333674132823944,
0.024895349517464638,
0.028105074539780617,
-0.006154545582830906,
-0.03650384768843651,
0.08205253630876541,
-0.011557865887880325,
0.0004837196320295334,
0.02905844710767269,
-0.04369698837399483,
0.01183674018830061,
0.051136236637830734,
-0.017613960430026054,
-0.04509618133306503,
0.03772272169589996,
-0.004647409543395042,
0.10647643357515335,
0.009478294290602207,
-0.04166652634739876,
0.013562731444835663,
-0.010844852775335312,
0.036393631249666214,
0.0602961890399456,
-0.02944723144173622,
-0.002630106173455715,
-0.05263448879122734,
0.03334120288491249,
0.012050933204591274,
-0.05103772133588791,
-0.03169078007340431,
0.02844850718975067,
-0.007239603437483311,
0.049398165196180344,
0.03334955871105194,
-0.0007276907563209534,
-0.01455462072044611,
-0.02252592146396637,
0.06133607029914856,
0.052829157561063766,
0.0373125784099102,
-0.034719016402959824,
0.009776760824024677,
-0.026855316013097763,
-0.08712814003229141,
0.012556045316159725,
0.027353763580322266,
-0.004926376044750214,
-0.024564864113926888,
0.03289167210459709,
0.01524209976196289,
-0.019186487421393394,
0.028859376907348633,
0.002384504768997431,
0.034982651472091675,
-0.041838470846414566,
-0.11882822960615158,
-0.05451881140470505,
0.016821416094899178,
-0.0008965960005298257,
-0.017475327476859093,
-0.07148577272891998,
0.00034588357084430754,
0.05057801306247711,
0.08720998466014862,
-0.010473028756678104,
-0.023706458508968353,
0.00985017605125904,
0.018663732334971428,
-0.004280793480575085,
-0.0037517615128308535,
-0.03929658606648445,
0.018664823845028877,
-0.030650664120912552,
-0.012372034601867199,
-0.03529557213187218,
0.006738673895597458,
0.00400959886610508,
-0.021575873717665672,
-0.017617594450712204,
0.06416896730661392,
0.026422854512929916,
-0.018853498622775078,
0.005413944832980633,
0.019535327330231667,
-0.03961598128080368,
0.0681232437491417,
-0.010397511534392834,
0.008503265678882599,
0.05990492179989815,
0.03566426411271095,
0.022232702001929283,
-0.00494988402351737,
0.020698124542832375,
0.0023963041603565216,
-0.033448971807956696,
-0.046867940574884415,
-0.013833572156727314,
0.011982663534581661,
-0.007423449773341417,
-0.017635034397244453,
0.0006107392255216837,
0.005017481278628111,
0.011719366535544395,
0.02292458899319172,
0.007287079002708197,
-0.016242248937487602,
0.0033742208033800125,
-0.004192086402326822,
-0.04139605537056923,
-0.003674843581393361,
-0.07537473738193512,
-0.0016826536739245057,
0.02636764384806156,
0.014202599413692951,
0.037627074867486954,
-0.020450375974178314,
-0.005804584827274084,
-0.03527768701314926,
-0.04757138714194298,
-0.04205133765935898,
0.04458557441830635,
0.015879567712545395,
-0.016659926623106003,
0.02530188485980034,
0.042055968195199966,
0.07475000619888306,
-0.004698540084064007,
0.01184981968253851,
0.016462258994579315,
-0.039167944341897964,
-0.011878617107868195,
-0.021473273634910583,
0.007635653018951416,
0.02834724448621273,
0.01406120229512453,
0.011086516082286835,
-0.020760241895914078,
-0.015803152695298195,
0.03624209389090538,
-0.0397564172744751,
0.0758216381072998,
-0.013522391207516193,
-0.0038417845498770475,
-0.02429763600230217,
0.022644678130745888,
0.010613109916448593,
-0.002020100597292185,
-0.018508480861783028,
0.00048040563706308603,
-0.07023026049137115,
-0.0022974307648837566,
0.0048299748450517654,
0.0176633782684803,
-0.0372186005115509,
0.02544231154024601,
0.0041339099407196045,
0.03343075513839722,
0.02803264930844307,
-0.009034883230924606,
-0.0323629230260849,
-0.03250478580594063,
-0.006447094492614269,
0.0027649663388729095,
0.0068818251602351665,
0.034048862755298615,
0.02240217663347721,
0.037047501653432846,
-0.002659211866557598,
0.0009104855707846582,
-0.004805846139788628,
0.028671765699982643,
-0.023406021296977997,
0.013794811442494392,
0.0038264484610408545,
-0.04652385413646698,
0.024054596200585365,
-0.017849817872047424,
0.04065687954425812,
0.026414314284920692,
-0.0256408229470253,
-0.019689245149493217,
-0.03058144450187683,
-0.027617206797003746,
-0.004245275165885687,
-0.0012832926586270332,
-0.041166674345731735,
-0.014583837240934372,
0.013849135488271713,
-0.03007364086806774,
-0.012113159522414207,
-0.009953904896974564,
0.011466758325695992,
-0.027530362829566002,
-0.002777671441435814,
0.01589300110936165,
-0.02028464339673519,
0.02607940323650837,
-0.03723723068833351,
-0.057125646620988846,
-0.05546882748603821,
-0.04228072986006737,
0.014666520990431309,
0.030658721923828125,
-0.04811277985572815,
0.021932080388069153,
-0.022511962801218033,
-0.032165806740522385,
0.018401416018605232,
-0.002876258222386241,
0.04803480952978134,
0.002876899903640151,
-0.02340301126241684,
-0.030457383021712303,
-0.004538738168776035,
-0.0007791498210281134,
-0.016264352947473526,
-0.009370879270136356,
0.005762151442468166,
0.05233018845319748,
-0.0007068976410664618,
-0.016612008213996887,
-0.01303330808877945,
-0.05186086893081665,
-0.060461051762104034,
-0.017797688022255898,
-0.021296663209795952,
0.014217731542885303,
-0.0073797935619950294,
0.028753388673067093,
0.03672143071889877,
-0.050827525556087494,
0.006645070388913155,
-0.03769690915942192,
-0.07124608755111694,
0.011265010572969913,
-0.0013128715800121427,
0.03372151404619217,
0.022753946483135223,
-0.01535657700151205,
0.039781250059604645,
0.002596598817035556,
-0.0346636138856411,
-0.0132374232634902,
0.026580054312944412,
0.008421886712312698,
-0.010707329027354717,
-0.022354714572429657,
0.03825840726494789,
0.006149293854832649,
0.02665824070572853,
0.006724903825670481,
-0.0034943995997309685,
0.007532166317105293,
0.04426867514848709,
-0.01220763474702835,
-0.0014296056469902396,
0.021838566288352013,
0.005145774222910404,
0.056613799184560776,
0.006965049542486668,
-0.04643584415316582,
0.0068125431425869465,
-0.01575414463877678,
0.016621829941868782,
0.006338377017527819,
-0.0004598465166054666,
0.03817286342382431,
0.008145860396325588,
-0.003409645752981305,
0.0005151093937456608,
0.005941531155258417,
-0.012097806669771671,
0.011197997257113457,
0.011704962700605392,
0.03487768396735191,
0.034523144364356995,
0.005957941524684429,
-0.0027686497196555138,
0.04582767188549042,
-0.0016245084116235375,
-0.024560565128922462,
-0.04012985900044441,
0.015093845315277576,
-0.02295835129916668,
0.02020309865474701,
-0.007706066593527794,
-0.013979570008814335,
0.02646714262664318,
-0.004479385446757078,
0.049508754163980484,
-0.021803773939609528,
-0.01743343658745289,
-0.029781794175505638,
-0.058295078575611115,
0.020878318697214127,
0.01686307229101658,
0.056003183126449585,
0.02966589480638504,
0.026342090219259262,
0.0519985593855381,
-0.020769167691469193,
-0.01220699306577444,
-0.0007978687062859535,
-0.06689881533384323,
0.02836748957633972,
-0.0689917579293251,
-0.026283618062734604,
-0.00633205147460103,
0.01878243498504162,
0.040719881653785706,
-0.017450056970119476,
-0.010609176941215992,
-0.04682067036628723,
-0.008150174282491207,
-0.03278428316116333,
-0.01333730947226286,
-0.034568753093481064,
-0.027262695133686066,
-0.010860838927328587,
0.043734196573495865,
0.03428438678383827,
-0.017229989171028137,
0.007307738531380892,
0.05059202387928963,
-0.04380454868078232,
-0.008583439514040947,
-0.016490735113620758,
-0.002984176157042384,
0.008676188997924328,
0.02648358792066574,
0.06164612993597984,
0.03168270364403725,
-0.03993120416998863,
0.02670121006667614,
0.03741909936070442,
0.05710167437791824,
0.007635180372744799,
-0.026632729917764664,
-0.006071566604077816,
-0.021492982283234596,
-0.00589221203699708,
-0.028592441231012344,
0.045468296855688095,
-0.018679842352867126,
0.010243273340165615,
0.03216833993792534,
0.0002665181818883866,
0.0006597658502869308,
0.06416820734739304,
0.04541333019733429,
-0.009286054410040379,
-0.010369961149990559,
0.014522098936140537,
-0.010729463770985603,
-0.015114201232790947,
0.03411983698606491,
0.004439780954271555,
0.016283433884382248,
0.02044706605374813,
0.016598902642726898,
0.023226208984851837,
0.025601914152503014,
-0.01192973181605339,
0.009668161161243916,
0.002828118158504367,
0.02529911883175373,
-0.01032573264092207,
-0.009872165508568287,
-0.02770468406379223,
0.04688858985900879,
0.02771167829632759,
0.0020156074315309525,
-0.017347894608974457,
-0.05572750046849251,
0.014135448262095451,
0.016432981938123703,
0.021827997639775276,
0.009427225217223167,
-0.015617826022207737,
-0.054844919592142105,
-0.023216312751173973,
0.05017559230327606,
-0.03124447725713253,
0.013473550789058208,
-0.02749849483370781,
-0.0008314817678183317,
-0.021059878170490265,
-0.0031287288293242455,
0.023216567933559418,
0.020218275487422943,
0.01707405224442482,
0.0064472537487745285,
-0.012644677422940731,
-0.0018085880437865853,
-0.01739766076207161,
0.001414295518770814,
0.006479900795966387,
0.06541784852743149,
0.03288332372903824,
-0.01316620223224163,
0.019738735631108284,
0.035245902836322784,
-0.02723114937543869,
-0.07330898195505142,
0.009827137924730778,
-0.007039915304630995,
-0.04108186811208725,
0.017335282638669014,
-0.011913202702999115,
-0.05727323517203331,
0.0055289254523813725,
-0.015675483271479607,
-0.022638902068138123,
0.0278212521225214,
-0.03253509849309921,
0.04736699163913727,
0.014376049861311913,
0.02132287248969078,
0.048810165375471115,
0.01760892942547798,
0.009291400201618671,
0.003154582343995571,
-0.021518735215067863,
-0.01578816957771778,
-0.04010580852627754,
0.03904874622821808,
-0.036334775388240814,
0.032486166805028915,
-0.012352827936410904,
0.09137870371341705,
-0.018232570961117744,
0.023856554180383682,
-0.0028354148380458355,
-0.06006123498082161,
0.012899979948997498,
0.024763163179159164,
-0.03823418542742729,
-0.002409824635833502,
-0.03701009228825569,
0.0018948361976072192,
-0.014594501815736294,
-0.047767363488674164,
-0.0007027489482425153,
0.0010767817730084062,
0.0040329922921955585,
0.0038366406224668026,
-0.0514523908495903,
0.05939439684152603,
-0.04697961360216141,
-0.034025464206933975,
0.022674214094877243,
-0.05670821666717529,
0.04516734555363655,
-0.02071995846927166,
0.013320162892341614,
-0.004014823120087385,
-0.07259618490934372,
-0.06165075674653053,
0.011099903844296932,
0.005034733563661575,
0.04428479075431824,
-0.03730713576078415,
0.019748473539948463,
0.00812048651278019,
-0.0032135278452187777,
-0.09356595575809479,
-0.02604612708091736,
0.006392576731741428,
-0.01606070250272751,
-0.0049243890680372715,
-0.009245743975043297,
0.03848129138350487,
-0.02974584698677063,
-0.013235703110694885,
0.0015359862009063363,
0.020504901185631752,
-0.030013853684067726,
-0.02476583980023861,
0.00036952138179913163,
0.015280693769454956,
0.05472501367330551,
-0.005146856885403395,
-0.0009913352550938725,
-0.032071638852357864,
-0.02871415950357914,
-0.0013500968925654888,
0.019310899078845978,
0.02590157650411129,
-0.026338564231991768,
-0.04736434668302536,
-0.0325751006603241,
-0.015540207736194134,
0.0294171329587698,
-0.03134296461939812,
0.010272334329783916,
0.027894461527466774,
0.011121817864477634,
-0.019337963312864304,
-0.008245045319199562,
0.026629792526364326,
0.0006664852262474597,
0.021710773929953575,
0.006511286832392216,
0.023892231285572052,
0.01270726416260004,
-0.050097737461328506,
0.06774145364761353,
-0.006134954746812582,
0.016560111194849014,
-0.0015925521729514003,
0.007193090859800577,
0.035850025713443756,
-0.014753424562513828,
0.013615250587463379,
-0.013971421867609024,
0.017937151715159416,
-0.057031840085983276,
0.00888027623295784,
0.010531424544751644,
0.03077760897576809,
-0.03766871988773346,
-0.06063676252961159,
-0.0006491952808573842,
0.018567856401205063,
0.032756537199020386,
-0.020035699009895325,
0.05530480667948723,
0.029850376769900322,
0.008804606273770332,
-0.04106058180332184,
-0.023342594504356384,
0.02738921530544758,
0.023222876712679863,
0.009301269426941872,
0.022951742634177208,
-0.04709035903215408,
0.018950756639242172,
0.013579439371824265,
0.048866283148527145,
0.003696657484397292,
0.03316787630319595,
-0.0009009604691527784,
0.046742506325244904,
0.034993384033441544,
-0.026180140674114227,
-0.012336928397417068,
0.02197735570371151,
-0.022563178092241287,
-0.003488583955913782,
0.007188416551798582,
-0.03505035117268562,
0.022350920364260674,
0.006091013550758362,
0.020745323970913887,
0.012294030748307705,
-0.04179094359278679,
-0.052518442273139954,
0.0025816175621002913,
0.0007306357729248703,
0.019693616777658463,
0.004989554174244404,
0.009905338287353516,
-0.0194142684340477,
0.02293519861996174,
0.049005866050720215,
-0.02678416669368744,
-0.09782126545906067,
-0.0134984590113163,
-0.03663194179534912,
-0.0007947295671328902,
0.05430994927883148,
-0.004340798128396273,
-0.007028830237686634,
0.006216867361217737,
-0.02488662675023079,
0.004988237749785185,
0.01657917909324169,
0.02562393993139267,
-0.05007590726017952,
0.04034790024161339,
-0.03212638199329376,
0.01735512539744377,
-0.033090729266405106,
0.03462226688861847,
0.08568554371595383,
0.06472618877887726,
0.020061146467924118,
-0.08172646909952164,
0.003672149730846286,
-0.01902279630303383,
0.035680148750543594,
-0.03163112699985504,
0.05002842843532562,
0.011443004012107849,
0.023154547438025475,
-0.0120939826592803,
0.036555297672748566,
0.05953925475478172,
0.029695527628064156,
0.08226446807384491,
-0.029156995937228203,
-0.06510386615991592,
0.0032410083804279566,
0.004312258213758469,
-0.006735144183039665,
0.011598361656069756,
-0.029982998967170715,
0.0287847388535738,
-0.03327837586402893,
-0.021331794559955597,
0.0027930026408284903,
0.010984266176819801,
0.013361025601625443,
-0.004904736299067736,
-0.0344131663441658,
0.032123930752277374,
-0.018521623685956,
-0.0376485139131546,
-0.028043892234563828,
0.035335030406713486,
0.013625609688460827,
-0.0031215567141771317,
0.05345412343740463,
-0.003224017797037959,
-0.00064067542552948,
0.004558988381177187,
0.011143417097628117,
0.0018382759299129248,
-0.025024140253663063,
0.009266873821616173,
0.02041652239859104,
0.06734049320220947,
0.015142378397285938,
-0.025134362280368805,
0.004960678983479738,
-0.02685525082051754,
-0.008194717578589916,
-0.023674722760915756,
-0.030941786244511604,
0.005526069086045027,
0.024283194914460182,
-0.02165212668478489,
-0.03625413775444031,
-0.02317901700735092,
0.04785282909870148,
-0.021191926673054695,
0.049279116094112396,
-0.006378460675477982,
0.004227479919791222,
-0.03066360205411911,
-0.04477234184741974,
0.01612786203622818,
0.025117577984929085,
-0.015072884038090706,
-0.04531646519899368,
-0.019298644736409187,
-0.04505356401205063,
-0.048856377601623535,
0.03464527428150177,
0.041460007429122925,
0.04175568372011185,
-0.0014163483865559101,
0.06169048324227333,
-0.01777932606637478,
-0.058627691119909286,
0.01452675648033619,
-0.03647560626268387,
-0.016673700883984566,
-0.01944935880601406,
-0.0020405214745551348,
0.05105254426598549,
0.03699921816587448,
-0.05295360088348389,
-0.036820344626903534,
0.017200950533151627,
-0.011596706695854664,
0.025815801694989204,
-0.03892200067639351,
-0.0191948264837265,
0.029062483459711075,
-0.024867061525583267,
0.0015336283249780536,
-0.03267825022339821,
0.03159546107053757,
0.006086003966629505,
0.0007038628100417554,
0.014679051004350185,
0.01668829284608364,
-0.011049940250813961,
-0.007197714876383543,
0.00919185858219862,
-0.029383404180407524,
0.0052008857019245625,
-0.006025559734553099,
0.05653772130608559,
-0.010969128459692001,
-0.028028933331370354,
-0.0500958077609539,
0.020029215142130852,
-0.018032725900411606,
0.03755700960755348,
-0.05465737357735634,
0.027933407574892044,
-0.017472445964813232,
0.0318094864487648,
-0.029809409752488136,
0.0008191520464606583,
-0.04236533120274544,
-0.005028484854847193,
-0.0044378782622516155,
-0.028644470497965813,
-0.0259644016623497,
0.013414501212537289,
0.038947734981775284,
-0.042195260524749756,
0.010312258265912533,
0.058306556195020676,
-0.025121131911873817,
0.018025802448391914,
-0.01906544715166092,
0.023483717814087868,
0.06175929680466652,
-0.020716289058327675,
-0.012182229198515415,
0.04012783244252205,
-0.05639854073524475,
-0.035205498337745667,
0.039511311799287796,
-0.0018244353123009205,
0.05004360154271126,
0.02047683857381344,
-0.02666361629962921,
-0.037417419254779816,
0.00618535652756691,
-0.004483208991587162,
0.0043372465297579765,
0.01992068625986576,
-0.017833342775702477,
-0.03323580324649811,
0.019312962889671326,
0.03288373723626137,
-0.01262186374515295,
-0.01708608865737915,
0.04795006290078163,
0.05016196891665459,
0.030297504737973213,
0.017429187893867493,
0.017892230302095413,
0.01233254186809063,
0.04869978129863739,
0.02939550206065178,
0.011951482854783535,
0.01382522564381361,
0.07035704702138901,
-0.058242037892341614,
0.041360992938280106,
0.02756245620548725,
0.022777937352657318,
-0.0921529084444046,
0.007614967413246632,
0.0007880850462242961,
0.02872491255402565,
0.031744662672281265,
-0.014020576141774654,
0.015758760273456573,
0.07138102501630783,
-0.05170988291501999,
-0.008777603507041931,
-0.018944455310702324,
-0.03579264134168625,
-0.015675626695156097,
0.002761830808594823,
-0.037091463804244995,
0.052563801407814026,
0.00805825088173151,
0.03161674365401268,
-0.0006406719912774861,
0.011026798747479916,
0.009786290116608143,
-0.0376199372112751,
-0.038420990109443665,
-0.005543890409171581,
-0.006153183989226818,
-0.014297652058303356,
0.07003955543041229,
-0.047827042639255524,
-0.017617346718907356,
0.04957826808094978,
0.029306506738066673,
0.021186383441090584,
-0.017539747059345245,
-0.01794946938753128,
0.020192159339785576,
0.03725351765751839,
0.02757272683084011,
-0.03117789328098297,
0.004181507509201765,
0.03402688354253769,
0.024911100044846535,
0.03609992563724518,
0.017828499898314476,
-0.03618032857775688,
-0.017225753515958786,
-0.02949085459113121,
-0.05999843403697014,
0.0019163698889315128,
0.02262735366821289,
-0.0019306882750242949,
-0.0024767762515693903,
0.027968958020210266,
0.0020757776219397783,
-0.012543060816824436,
-0.008686753921210766,
-0.04314102232456207,
-0.014821800403296947,
0.04364785924553871,
0.004362483508884907,
-0.004584120586514473,
-0.007895434275269508,
-0.02737390622496605,
-0.022078633308410645,
0.030595730990171432,
-0.0033988123759627342,
0.011360129341483116,
-0.05625995248556137,
0.005042949691414833,
0.009362231940031052,
0.007267563138157129,
0.019812552258372307,
-0.050721175968647,
-0.04388018697500229,
0.038645509630441666,
-0.04136677086353302,
0.021294567734003067,
-0.01719668321311474,
-0.0335892029106617,
-0.026756200939416885,
-0.06044137105345726,
0.047797780483961105,
0.006421476136893034,
0.04840230569243431,
-0.01562227588146925,
-0.03515778109431267,
-0.019050784409046173,
0.007209524512290955,
0.055816859006881714,
-0.00927265640348196,
-0.01323763094842434,
0.022424990311264992,
-0.009058242663741112,
-0.013516652397811413,
-0.044530536979436874,
-0.0063560158014297485,
-0.01410998497158289,
-0.018789004534482956,
-0.03180238604545593,
-0.037985194474458694,
-0.003734758822247386,
0.008874459192156792,
0.0429360456764698,
0.0075050476007163525,
0.03860895335674286,
-0.00922421645373106,
-0.050204530358314514,
0.06206659600138664,
0.008970675058662891,
0.017759904265403748,
0.049448493868112564,
-0.034138258546590805,
0.05028211697936058,
0.04896321892738342,
0.001054079388268292,
-0.033153895288705826,
0.028192229568958282,
-0.051187772303819656,
-0.027750054374337196,
-0.010929679498076439,
0.019875966012477875,
-0.012802774086594582,
-0.030834870412945747,
-0.006844055838882923,
0.025105290114879608,
-0.024804815649986267,
-0.004467977210879326,
0.03622828796505928,
-0.006454726681113243,
0.05658751353621483,
-0.020467594265937805,
0.022929392755031586,
0.02014894224703312,
0.025593958795070648,
0.013649295084178448,
0.036327917128801346,
0.08290614187717438,
0.01614845171570778,
0.04527193680405617,
0.05183791369199753,
-0.005659210961312056,
0.04027268663048744,
0.0008914825157262385,
0.028140876442193985,
0.0018980246968567371,
0.006213570013642311,
0.01861821487545967,
-0.036630839109420776,
0.0026495938654989004,
0.001835474162362516,
-0.009525218978524208,
0.0639549270272255,
-0.028043409809470177,
0.016819650307297707,
0.0022719649132341146,
0.01768071949481964,
-0.03233182057738304,
0.007149566430598497,
0.0007417244487442076,
0.0440094955265522,
-0.05372454971075058,
0.006874028127640486,
-0.03447066619992256,
0.028523482382297516,
0.018174979835748672,
-0.05335891991853714,
0.03304143622517586,
-0.030157780274748802,
-0.02583087794482708,
-0.005230496637523174,
-0.00721376808360219,
-0.02351432479918003,
-0.021614540368318558,
0.03921639919281006,
0.04043352231383324,
0.017991339787840843,
-0.034992557018995285,
-0.0055284397676587105,
-0.0393390879034996,
0.05716655030846596,
-0.059138476848602295,
-0.00797287467867136,
-0.012577138841152191,
0.03583649545907974,
-0.05396599695086479,
-0.013649494387209415
] |
<p>This might be a stupid question, but nonetheless, it has been bothering me.</p>
<p>If you take a photon, make it go through some atoms in a solid, liquid or whatever, then you have the chance of this photon being absorbed by an electron, and thereby exciting the electron. This requires the photon to have enough energy to actually excite the electron to another energy level.</p>
<p>My question is then: How does the photon know if it has enough energy or not? Do they interact very quickly to determine if it's okay or not, or is it just something it "knows?"</p>
| 723 |
[
-0.0016257723327726126,
-0.04492313042283058,
0.02296270988881588,
-0.059153102338314056,
-0.002342334482818842,
0.023015540093183517,
-0.009169909171760082,
-0.016975706443190575,
0.014992970041930676,
-0.00867884885519743,
0.02645576186478138,
0.05908963456749916,
0.0186086967587471,
0.01620539277791977,
0.014468573033809662,
0.025182798504829407,
0.00026683154283091426,
-0.028373323380947113,
-0.016336923465132713,
-0.04307001456618309,
-0.016315821558237076,
0.01954277604818344,
-0.01815713942050934,
0.002637876197695732,
-0.0310515109449625,
0.03643864393234253,
0.0070926169864833355,
0.01701006479561329,
0.0359937846660614,
0.04403878375887871,
0.002049508737400174,
-0.02754782885313034,
0.006831848528236151,
0.025694290176033974,
0.022392727434635162,
0.004851740784943104,
-0.028052648529410362,
-0.05966833233833313,
-0.004222348798066378,
0.008544091135263443,
-0.022949770092964172,
-0.019907724112272263,
0.0042152306996285915,
0.02414490282535553,
-0.05168856680393219,
-0.006838435772806406,
-0.0008229155209846795,
-0.03348630294203758,
0.08157452195882797,
-0.06216668337583542,
0.04842669144272804,
-0.008695912547409534,
0.025514625012874603,
0.014506041072309017,
-0.010179628618061543,
-0.02524324506521225,
0.06595258414745331,
0.05413823202252388,
-0.022921456024050713,
-0.020881852135062218,
-0.015082054771482944,
0.001750774448737502,
-0.03709367662668228,
-0.0101707074791193,
-0.021740900352597237,
-0.0046282606199383736,
-0.01642216555774212,
-0.020839551463723183,
0.04218583554029465,
0.004872828256338835,
0.007939992472529411,
0.003172805532813072,
0.05792482569813728,
0.03333159163594246,
0.0007430541445501149,
-0.013747724704444408,
0.034314658492803574,
0.041032083332538605,
0.048412907868623734,
0.06514021754264832,
-0.0364905446767807,
-0.013019002042710781,
0.003887426806613803,
0.05416181683540344,
0.005492453929036856,
-0.007959382608532906,
0.05575241521000862,
-0.03822489082813263,
0.003931407351046801,
0.004741973709315062,
-0.027681611478328705,
0.028512483462691307,
-0.003410301636904478,
-0.012322000227868557,
-0.018262213096022606,
0.027131803333759308,
-0.00015534268459305167,
0.04516936093568802,
0.010904100723564625,
-0.02826710045337677,
0.05368032678961754,
-0.002982491161674261,
0.03295794129371643,
0.06385470181703568,
-0.021101808175444603,
-0.047346003353595734,
-0.05427085608243942,
0.026789285242557526,
0.0018102480098605156,
-0.006085120141506195,
-0.012409109622240067,
0.025442423298954964,
0.016905982047319412,
0.016035929322242737,
0.053937509655952454,
-0.014555183239281178,
-0.014333600178360939,
-0.0017734654247760773,
0.07360394299030304,
0.0468512699007988,
0.017990717664361,
-0.04377307742834091,
0.030102381482720375,
-0.00908564031124115,
-0.048437561839818954,
0.005466344300657511,
0.049604013562202454,
-0.001998238731175661,
-0.05372703820466995,
0.03701631724834442,
-0.03992992639541626,
-0.03567613661289215,
-0.001148918061517179,
0.003357797395437956,
0.036549750715494156,
-0.014439049176871777,
-0.08845342695713043,
-0.03986723721027374,
0.026088327169418335,
-0.0028286888264119625,
-0.044693127274513245,
-0.09171531349420547,
0.004729695618152618,
0.0327104851603508,
0.08425919711589813,
-0.008646314032375813,
-0.0007055433816276491,
-0.005537507124245167,
-0.0018114480189979076,
-0.003330220701172948,
-0.031453732401132584,
-0.039497166872024536,
0.016645019873976707,
0.011179219000041485,
0.03216087445616722,
-0.04201275482773781,
0.02356812171638012,
0.026454374194145203,
0.014395740814507008,
-0.015138259157538414,
0.04259068891406059,
-0.015001624822616577,
-0.020583726465702057,
0.014210127294063568,
0.012102080509066582,
-0.0572451688349247,
0.08709751069545746,
0.03130413219332695,
0.010482491925358772,
0.032053541392087936,
0.014290880411863327,
-0.004170777276158333,
-0.012100661173462868,
0.01804118975996971,
0.029901841655373573,
-0.009930997155606747,
-0.02869531325995922,
-0.041396614164114,
0.027590027078986168,
-0.03520630672574043,
-0.03482991084456444,
-0.04507340118288994,
-0.009471556171774864,
0.03226364031434059,
-0.011664848774671555,
0.006498778238892555,
0.003335406072437763,
-0.010559557937085629,
-0.048844385892152786,
-0.037369415163993835,
-0.015879152342677116,
-0.0460708811879158,
0.000997998402453959,
0.006838671397417784,
-0.033157702535390854,
0.03467388078570366,
0.009358488023281097,
-0.01863020844757557,
-0.0329379141330719,
-0.018635926768183708,
-0.026114290580153465,
0.023333268240094185,
-0.01929483190178871,
-0.043667662888765335,
0.05473201349377632,
0.0718783438205719,
0.04389207810163498,
0.015076273120939732,
0.02805837243795395,
-0.0318462960422039,
-0.03983896225690842,
0.01733996719121933,
-0.01541205495595932,
0.017747560515999794,
0.009219031780958176,
-0.009051023982465267,
-0.014073323458433151,
-0.03891223669052124,
-0.0023916633799672127,
0.010113603435456753,
0.0032893933821469545,
0.07804235070943832,
0.03844548389315605,
0.012338098138570786,
-0.001312152249738574,
0.05460458621382713,
-0.009561043232679367,
0.007893788628280163,
-0.014125165529549122,
-0.0715498998761177,
-0.03320103883743286,
-0.016748948022723198,
0.007257274352014065,
-0.01037241518497467,
-0.01615101471543312,
-0.014935273677110672,
0.008923390880227089,
0.05281047895550728,
0.03418142348527908,
0.05436530336737633,
-0.03758937865495682,
-0.010249536484479904,
0.0038070387672632933,
0.04516097530722618,
0.0021212073042988777,
0.02406703308224678,
0.03325367718935013,
0.04401526600122452,
0.0205793809145689,
-0.005852621514350176,
0.013726013712584972,
0.025161322206258774,
-0.02868211828172207,
0.013292858377099037,
-0.011765043251216412,
-0.04430362954735756,
0.035390179604291916,
-0.03357144072651863,
-0.016125285997986794,
-0.0038718716241419315,
-0.009418209083378315,
0.015288518741726875,
-0.020749663934111595,
-0.03988954424858093,
0.017268311232328415,
0.01293280441313982,
-0.012210927903652191,
-0.03252798691391945,
0.031029734760522842,
-0.02868693880736828,
0.025781873613595963,
0.013029019348323345,
0.004728259984403849,
-0.01652935892343521,
-0.03948667272925377,
0.030151644721627235,
0.007537746801972389,
0.03978542611002922,
-0.05514965206384659,
-0.06464703381061554,
-0.037803322076797485,
-0.044598545879125595,
0.013579746708273888,
0.015351567417383194,
-0.005109150893986225,
-0.0038496614433825016,
-0.011846938170492649,
-0.04027864709496498,
0.04019349813461304,
-0.030752431601285934,
0.041598130017519,
0.0049198889173567295,
-0.022277243435382843,
-0.03828578442335129,
-0.007656443398445845,
0.006747495848685503,
-0.04308483749628067,
-0.007278581149876118,
0.02554089017212391,
0.05652782693505287,
-0.0033173374831676483,
-0.05664283409714699,
0.015487341210246086,
0.004749951884150505,
-0.03533463180065155,
-0.012680014595389366,
-0.02120923064649105,
-0.0017192193772643805,
-0.059119243174791336,
0.028526514768600464,
0.022647999227046967,
-0.06252144277095795,
0.006436283700168133,
-0.06976747512817383,
-0.03894633799791336,
-0.011505733244121075,
0.017106905579566956,
-0.001570986583828926,
0.006078127305954695,
-0.030566038563847542,
0.049729980528354645,
-0.011293231509625912,
-0.04211520403623581,
-0.00967773050069809,
0.006113292183727026,
-0.0048670279793441296,
-0.029172170907258987,
0.03453003242611885,
0.02410311996936798,
0.018180634826421738,
0.009591621346771717,
0.014087429270148277,
0.05390900745987892,
0.004650156479328871,
0.02137633226811886,
0.007605762220919132,
0.001794610288925469,
0.00038060115184634924,
-0.03681880980730057,
0.008729210123419762,
0.01572752743959427,
-0.05128421261906624,
0.016882728785276413,
0.006052691023796797,
0.02743944339454174,
0.039076268672943115,
0.016226308420300484,
0.03378339856863022,
0.017809920012950897,
0.01784435845911503,
-0.06968867033720016,
0.035295527428388596,
-0.031750865280628204,
-0.0074041481129825115,
0.0021176787558943033,
0.02167687565088272,
0.06919067353010178,
-0.013627500273287296,
0.008895627222955227,
0.025230761617422104,
0.025066053494811058,
-0.05243530124425888,
-0.01013429556041956,
0.015339136123657227,
-0.004046202637255192,
-0.00232276925817132,
-0.009196676313877106,
-0.015287826769053936,
0.06922678649425507,
0.019674092531204224,
0.053770530968904495,
-0.025845665484666824,
-0.011315208859741688,
-0.055824536830186844,
-0.04063088819384575,
-0.011195275001227856,
0.014095824211835861,
0.0396888367831707,
0.012487960048019886,
0.09737861901521683,
0.05473511293530464,
0.03835676610469818,
0.034471217542886734,
-0.019190652295947075,
-0.07965778559446335,
0.014166377484798431,
-0.04911785200238228,
-0.03244267776608467,
-0.0249994695186615,
-0.014502597972750664,
0.00020606453472282737,
-0.04789555072784424,
-0.01780775748193264,
-0.011834495700895786,
-0.0151428934186697,
-0.03322693333029747,
-0.023757535964250565,
-0.0431072823703289,
-0.02684100903570652,
-0.03656119853258133,
0.026419075205922127,
0.016634153202176094,
-0.006616104394197464,
-0.022399019449949265,
0.056256748735904694,
-0.03243337199091911,
0.04457901790738106,
0.0027455701492726803,
-0.01029631681740284,
0.017793864011764526,
0.01970425620675087,
0.03714875131845474,
-0.013772254809737206,
-0.03608933091163635,
0.0044396608136594296,
0.001468739239498973,
0.06413417309522629,
0.04634033143520355,
-0.03893066942691803,
-0.03337496519088745,
-0.0260914396494627,
0.017887763679027557,
-0.011412223801016808,
0.033468097448349,
-0.01569993793964386,
0.03282720595598221,
-0.001147035975009203,
0.005219839513301849,
-0.0406811460852623,
0.05995316803455353,
0.06110566109418869,
-0.03533388301730156,
-0.03761545941233635,
-0.06770903617143631,
0.004127495922148228,
-0.043387848883867264,
0.0026708166114985943,
-0.005893989000469446,
0.0090393777936697,
-0.02627670206129551,
-0.025726623833179474,
-0.013681918382644653,
0.004215063992887735,
-0.01112097967416048,
-0.03152083605527878,
-0.010181630030274391,
-0.01436572801321745,
0.005391273647546768,
-0.010575762018561363,
0.002588303294032812,
0.003213269170373678,
0.01666557416319847,
-0.00041217729449272156,
0.027442628517746925,
-0.05139568820595741,
-0.005860265344381332,
0.06338991969823837,
0.047200292348861694,
-0.028593363240361214,
-0.028136854991316795,
-0.04992939159274101,
0.011463002301752567,
0.03768468275666237,
-0.03908117115497589,
0.029788972809910774,
-0.03133194521069527,
-0.021891139447689056,
-0.028254687786102295,
-0.005072175525128841,
0.00538825336843729,
0.02801351249217987,
0.007179688662290573,
0.015354265458881855,
-0.020674409344792366,
-0.02061031572520733,
-0.03335664048790932,
0.02812739461660385,
0.011650128290057182,
0.05186199024319649,
-0.03140375018119812,
-0.04266010969877243,
0.009318244643509388,
-0.007159281522035599,
-0.004138717893511057,
-0.1080675795674324,
-0.016246234998106956,
0.02157558500766754,
-0.005461697466671467,
0.07805383950471878,
-0.0028165201656520367,
-0.06669829785823822,
0.048371899873018265,
0.020275233313441277,
-0.008043956942856312,
-0.023870009928941727,
-0.03759513422846794,
0.032814349979162216,
0.007032914087176323,
0.03310154005885124,
0.04404978081583977,
0.04428344964981079,
-0.04383901134133339,
0.0233918409794569,
-0.00611748406663537,
0.02814166620373726,
-0.039705801755189896,
0.015526208095252514,
-0.02152649499475956,
0.012457908131182194,
-0.028865832835435867,
0.08051823824644089,
-0.0027668767143040895,
0.000956459145527333,
0.04405427351593971,
-0.061048153787851334,
-0.013715353794395924,
0.015912536531686783,
-0.02199622616171837,
-0.010966343805193901,
-0.019066547974944115,
0.033557236194610596,
-0.026205070316791534,
-0.0014958839165046811,
0.015816282480955124,
-0.004040989559143782,
0.004340029321610928,
0.047953199595212936,
0.007823307998478413,
0.014302754774689674,
-0.03822563216090202,
-0.010558332316577435,
0.032602861523628235,
-0.026311533525586128,
0.05679219588637352,
-0.003251064568758011,
0.010629664175212383,
-0.012076686136424541,
-0.05052764341235161,
-0.02380152978003025,
-0.013726621866226196,
-0.026569418609142303,
0.06754370778799057,
-0.009944845922291279,
0.04317998141050339,
-0.014356501400470734,
-0.010261871851980686,
-0.06895311921834946,
-0.03941784054040909,
0.017937015742063522,
0.023202793672680855,
-0.004103248938918114,
-0.01127792987972498,
0.04397397115826607,
-0.027957579120993614,
-0.010512747801840305,
0.013783209025859833,
-0.003354107728227973,
-0.0006568890530616045,
0.012391817755997181,
0.024640969932079315,
-0.0056333523243665695,
0.008499310351908207,
0.006794113665819168,
-0.009505003690719604,
0.007073953747749329,
-0.0089197913184762,
-0.059963054955005646,
-0.0031735035590827465,
0.049696292728185654,
-0.027158305048942566,
-0.07016384601593018,
0.007159389555454254,
-0.0013860727194696665,
0.038141798228025436,
-0.006024748552590609,
-0.01429474912583828,
0.04153776913881302,
0.018603937700390816,
0.010901138186454773,
-0.02033168449997902,
0.0443689338862896,
0.023907318711280823,
0.01747892051935196,
0.031593482941389084,
-0.023434484377503395,
-0.01903693936765194,
-0.03943336382508278,
0.026645317673683167,
0.024975435808300972,
0.0561867393553257,
0.04086526483297348,
0.030968623235821724,
-0.002811695681884885,
0.006117738783359528,
0.0020757124293595552,
0.01255310233682394,
0.004851669073104858,
-0.04855538159608841,
-0.008060098625719547,
0.012894109822809696,
-0.009563094936311245,
-0.018158702179789543,
-0.027165846899151802,
-0.033762428909540176,
-0.02853075973689556,
0.04872800037264824,
-0.04832841828465462,
0.037707455456256866,
-0.010102363303303719,
-0.012779169715940952,
-0.011105407029390335,
-0.006843731738626957,
-0.04610060900449753,
0.0036850604228675365,
0.007927192375063896,
0.009210317395627499,
0.003291744738817215,
0.02483987994492054,
0.031341303139925,
0.054495882242918015,
-0.010989349335432053,
0.03725989907979965,
0.025116506963968277,
0.06038591265678406,
0.050984498113393784,
-0.023685496300458908,
-0.0428025908768177,
0.046691905707120895,
-0.04175357520580292,
-0.00006109978858148679,
0.0028176738414913416,
-0.01252636220306158,
0.015369557775557041,
0.005317092407494783,
-0.007043500896543264,
-0.011394821107387543,
0.0010222139535471797,
-0.033021170645952225,
0.02844499796628952,
-0.00031575316097587347,
0.009159906767308712,
0.0029636635445058346,
0.02668786607682705,
0.0031000433955341578,
0.033493369817733765,
-0.00029549424652941525,
0.013344078324735165,
-0.059580110013484955,
-0.026625411584973335,
-0.04601805657148361,
-0.023709328845143318,
0.04319605603814125,
-0.010618440806865692,
-0.023217888548970222,
0.0016746019246056676,
-0.048377592116594315,
0.02651415951550007,
0.016748610883951187,
0.050109341740608215,
0.026939846575260162,
0.01740116998553276,
-0.04167855158448219,
0.021559283137321472,
-0.029021024703979492,
0.026793792843818665,
0.11077842116355896,
0.025988897308707237,
-0.003444225760176778,
-0.037574805319309235,
-0.01811017096042633,
-0.027068573981523514,
0.01566183939576149,
-0.013716444373130798,
0.018874002620577812,
-0.019255630671977997,
0.01590745709836483,
-0.01670655980706215,
0.03653084486722946,
0.030771156772971153,
0.02206486091017723,
0.042135175317525864,
-0.016152547672390938,
-0.048108868300914764,
0.03871939331293106,
0.026908788830041885,
-0.0017178123816847801,
0.011160283349454403,
0.0054689981043338776,
-0.010562518611550331,
-0.05844847112894058,
-0.00020353130821604282,
-0.0036195178981870413,
-0.013356899842619896,
0.006484899669885635,
-0.010159516707062721,
-0.015074094757437706,
-0.015214883722364902,
0.000057929351896746084,
-0.000014065682989894412,
-0.016076037660241127,
0.05741678178310394,
0.04648010432720184,
-0.013121172785758972,
0.005841555539518595,
0.003948862664401531,
0.022047214210033417,
0.010836712084710598,
-0.012461203150451183,
0.019291967153549194,
-0.028395820409059525,
-0.03494782745838165,
0.010297025553882122,
0.02863139472901821,
-0.006741949822753668,
-0.014664989896118641,
0.007696297951042652,
0.028515668585896492,
0.01368718035519123,
-0.02419726923108101,
-0.01736569218337536,
-0.028123730793595314,
-0.001298006041906774,
-0.02055414952337742,
0.01607518270611763,
-0.0029455036856234074,
0.024549517780542374,
0.016296789050102234,
0.016464995220303535,
-0.016588805243372917,
0.014788785018026829,
0.014498505741357803,
-0.021771226078271866,
0.004574053920805454,
-0.024573929607868195,
-0.02204056829214096,
-0.0014274829300120473,
-0.014702701941132545,
-0.05643398314714432,
-0.04269271716475487,
0.03311304748058319,
0.046368151903152466,
0.0020238058641552925,
0.005943817086517811,
-0.016729503870010376,
-0.04027796536684036,
-0.06966927647590637,
0.05487711727619171,
-0.026437699794769287,
-0.03923644870519638,
-0.012810979038476944,
-0.01895684190094471,
0.016710080206394196,
0.030651016160845757,
-0.02528464049100876,
0.024641811847686768,
0.012248794548213482,
-0.023635633289813995,
0.008041168563067913,
-0.027669981122016907,
-0.012979008257389069,
0.03207995742559433,
0.018085934221744537,
0.014436110854148865,
0.017777521163225174,
0.025505779311060905,
-0.02042090706527233,
0.025359760969877243,
0.01918342337012291,
0.006977411452680826,
-0.07052838802337646,
-0.02148822881281376,
0.008836360648274422,
-0.004301088396459818,
-0.02674182318150997,
-0.0065335966646671295,
0.0015158228343352675,
-0.00723855709657073,
-0.014957260340452194,
-0.04154081642627716,
0.010207665152847767,
-0.011391284875571728,
0.018001964315772057,
-0.019677910953760147,
0.01447426900267601,
-0.0008821202209219337,
0.04429882764816284,
-0.004369884263724089,
-0.013134441338479519,
-0.056755971163511276,
-0.016055012121796608,
0.016653666272759438,
-0.01881607063114643,
-0.022818462923169136,
0.012703285552561283,
-0.010700349695980549,
-0.040236495435237885,
0.012275994755327702,
0.029100783169269562,
0.012467112392187119,
-0.015052137896418571,
0.040640756487846375,
-0.035914402455091476,
0.05689498782157898,
-0.01953214779496193,
-0.010250653140246868,
0.038080066442489624,
-0.048112206161022186,
-0.007793526165187359,
0.03677966445684433,
0.005947093944996595,
0.04634130746126175,
0.03996673598885536,
-0.022206859663128853,
-0.011197438463568687,
0.0528145432472229,
-0.013823332265019417,
-0.004165663383901119,
-0.0033719628117978573,
-0.024708928540349007,
-0.002532986458390951,
0.06086346134543419,
0.03397820517420769,
-0.0338590070605278,
-0.00013213000784162432,
0.05979761481285095,
-0.014750225469470024,
0.009562995284795761,
-0.00015917830751277506,
-0.028877979144454002,
-0.02360047958791256,
0.03307473286986351,
0.00966381561011076,
-0.017456388100981712,
0.007234855554997921,
0.05040006712079048,
0.017083600163459778,
0.04999340698122978,
0.038516074419021606,
-0.0037326959427446127,
-0.11093300580978394,
-0.009991279803216457,
-0.023928416892886162,
0.0073611559346318245,
0.02428426221013069,
-0.026485495269298553,
0.038267772644758224,
0.045641254633665085,
-0.058736857026815414,
0.021904226392507553,
-0.02503240294754505,
-0.024765828624367714,
-0.029138365760445595,
0.08025272935628891,
-0.03592189773917198,
0.01642949879169464,
0.03361855819821358,
0.031331051141023636,
0.021070845425128937,
-0.00841281283646822,
-0.006347536575049162,
0.027181770652532578,
-0.02420739457011223,
0.059735897928476334,
0.0018826544983312488,
0.02437511458992958,
0.04537340626120567,
-0.04906377196311951,
0.01448011863976717,
0.005935093853622675,
-0.004487567115575075,
0.023359157145023346,
-0.006106267217546701,
0.02198638580739498,
0.00044491636799648404,
0.021922890096902847,
0.008906730450689793,
-0.03371889889240265,
0.043737418949604034,
0.0398542582988739,
0.04498094320297241,
0.03007449209690094,
-0.011084425263106823,
-0.014920738525688648,
0.011411234736442566,
-0.028132382780313492,
-0.05640093609690666,
0.03774867206811905,
0.007608810439705849,
0.010754835791885853,
0.016264544799923897,
0.01436936017125845,
-0.017075279727578163,
-0.028651002794504166,
-0.00672109005972743,
-0.06153954938054085,
-0.004819903522729874,
-0.007421156391501427,
0.03787398710846901,
-0.006353151984512806,
-0.014228574931621552,
-0.03429178521037102,
-0.021194279193878174,
0.013093553483486176,
0.019027983769774437,
0.011615372262895107,
-0.02122017927467823,
-0.0147106247022748,
0.006601552478969097,
0.013953318819403648,
0.011706233955919743,
-0.06448341906070709,
-0.07146966457366943,
0.027120057493448257,
0.004125335719436407,
0.027426766231656075,
0.043004196137189865,
-0.05618405342102051,
-0.04822413995862007,
-0.06322282552719116,
0.02127593569457531,
-0.02874043583869934,
0.03778304159641266,
-0.06153598427772522,
0.0009017938864417374,
-0.002501226030290127,
0.003331973683089018,
0.026403414085507393,
-0.014458972960710526,
-0.004874667152762413,
0.018359974026679993,
-0.025118131190538406,
0.0008111787028610706,
-0.017570598050951958,
-0.020499112084507942,
-0.05653268098831177,
-0.006466173566877842,
-0.061869051307439804,
-0.001887113437987864,
-0.009472481906414032,
0.017358597368001938,
0.023422878235578537,
-0.001458916929550469,
0.02657388709485531,
-0.05254632979631424,
-0.03374982997775078,
0.07306650280952454,
0.022341888397932053,
0.004899018909782171,
0.0432061105966568,
0.0006643908564001322,
0.04397254064679146,
0.035438720136880875,
0.011366097256541252,
-0.048085641115903854,
0.044106822460889816,
-0.014901150949299335,
-0.013257150538265705,
-0.0023442781530320644,
-0.01398596353828907,
0.019415149465203285,
-0.025183262303471565,
0.015183658339083195,
0.02437070570886135,
-0.03564154729247093,
0.0027198262978345156,
0.04534280300140381,
0.014874586835503578,
0.06111321225762367,
0.012097198516130447,
0.04823441058397293,
0.027276650071144104,
0.006053759716451168,
-0.014877392910420895,
0.06756856292486191,
0.030542882159352303,
0.011285856366157532,
0.030307214707136154,
-0.006258833222091198,
0.026799509301781654,
-0.021900363266468048,
0.009383508004248142,
0.04649253189563751,
-0.0074694519862532616,
-0.03266781195998192,
0.04872453957796097,
0.011017121374607086,
0.005609934683889151,
0.01055100280791521,
-0.0031960662454366684,
0.08506130427122116,
-0.05060116574168205,
0.01023133471608162,
-0.011325922794640064,
0.047458939254283905,
0.009589399211108685,
0.043121371418237686,
0.03105570748448372,
0.027248777449131012,
0.012569524347782135,
0.009230714291334152,
-0.04385925829410553,
0.017586635425686836,
0.027154086157679558,
-0.06758303940296173,
0.031265947967767715,
0.006842482835054398,
-0.0031369097996503115,
-0.018960339948534966,
0.008492855355143547,
-0.0033669969998300076,
-0.05394919961690903,
0.016216982156038284,
0.017785590142011642,
0.007576518226414919,
0.02545742876827717,
0.013597957789897919,
-0.006973711773753166,
0.03654272481799126,
-0.07407604902982712,
0.005647566635161638,
-0.05689435824751854,
0.02947567030787468,
-0.038155168294906616,
-0.005119750741869211
] |
<p>I started studying the BMS symmetry in connection with the paper:
<a href="http://arxiv.org/abs/1312.2229" rel="nofollow">http://arxiv.org/abs/1312.2229</a>
and there are a few strange things I noticed.</p>
<p>First of all, from reading the original papers by Bondi, Metzner and Sachs, I know that the "BMS symmetry" is just an allowed subset of coordinate diffeomorphisms which leaves the asymptotic flatness of the space-time intact. However, when I read the paper above, the BMS symmetry is stated in form of a vector field eq. (2.10) and (2.14). Therefore, my first question:</p>
<blockquote>
<p>How do I obtain from a given subset of coordinate diffeomorphisms (which is being considered a symmetry) a corresponding vector field a'la Killing vector?</p>
</blockquote>
<p>Furthermore, later in the paper they go from the BMS vector fields to generators of BMS symmetry in eq. (3.3). They do not mention how to do it, so I'd like to know:</p>
<blockquote>
<p>How do I go from vector fields characterizing a symmetry to an actual generator of the symmetry?</p>
</blockquote>
<p>I realize that this is some pretty advanced stuff. I am grateful for any help or suggestion!</p>
| 8,505 |
[
-0.018218958750367165,
0.0009866990149021149,
-0.013596788048744202,
-0.021828586235642433,
0.03004922717809677,
0.011361734941601753,
-0.04680849239230156,
-0.02810327149927616,
0.006385821383446455,
-0.07200035452842712,
-0.02392258122563362,
0.01340151485055685,
0.02034766785800457,
0.04690269008278847,
0.04383764788508415,
-0.010570202022790909,
-0.02119026891887188,
-0.0039917477406561375,
-0.010906867682933807,
-0.024439752101898193,
0.014911658130586147,
0.028925662860274315,
-0.015169824473559856,
-0.02991703525185585,
-0.005593122914433479,
0.024114079773426056,
-0.001192515715956688,
0.01645011268556118,
0.00648316228762269,
0.04869481548666954,
-0.02449272945523262,
-0.0490775965154171,
-0.004112022928893566,
-0.009634993970394135,
0.004587492905557156,
0.0006253197207115591,
-0.010353186167776585,
-0.03990371897816658,
0.007273971103131771,
0.006732312496751547,
-0.03744795173406601,
-0.013494984246790409,
-0.052422791719436646,
0.08161677420139313,
-0.05299505591392517,
0.0046442183665931225,
-0.022031478583812714,
0.028944887220859528,
0.028544507920742035,
-0.06627844274044037,
0.12210994958877563,
0.04878124222159386,
0.025838183239102364,
0.0013601931277662516,
-0.011700085364282131,
0.0034037090372294188,
0.0617675706744194,
0.05053647607564926,
-0.0003808049950748682,
-0.05452261120080948,
-0.014985202811658382,
-0.020405322313308716,
-0.011512653902173042,
-0.016765806823968887,
-0.014302408322691917,
0.03282700106501579,
0.011051340959966183,
-0.005234554409980774,
0.04318397864699364,
-0.02357831411063671,
-0.0029180385172367096,
0.001084233750589192,
0.01625765673816204,
-0.031054561957716942,
0.009985546581447124,
0.0019333141390234232,
0.018768630921840668,
-0.019990401342511177,
0.014777385629713535,
0.009412536397576332,
0.008952920325100422,
0.038867827504873276,
0.016181357204914093,
0.06660740077495575,
0.01765035279095173,
0.005497602745890617,
0.07212072610855103,
0.005207015201449394,
0.029762037098407745,
0.03740961477160454,
-0.0011054661590605974,
0.0172226894646883,
0.027533305808901787,
0.012786081992089748,
-0.0426272451877594,
0.028088277205824852,
-0.011308281682431698,
0.06131201237440109,
-0.00548400217667222,
-0.011196976527571678,
-0.014524093829095364,
-0.016958599910140038,
-0.009716177359223366,
0.023062169551849365,
0.02212793566286564,
-0.0048151384107768536,
-0.021522589027881622,
0.01787470281124115,
-0.05747193098068237,
0.01648465171456337,
-0.03276979550719261,
0.013745713979005814,
-0.020112821832299232,
-0.017899665981531143,
0.009437358006834984,
-0.006995427887886763,
-0.0008438599179498851,
-0.05303909629583359,
0.01225250493735075,
0.08126461505889893,
0.04788102209568024,
0.031935032457113266,
0.03407289832830429,
-0.02946721389889717,
-0.03896496817469597,
-0.01964450627565384,
0.05188511684536934,
0.00999660324305296,
-0.04103386029601097,
-0.014711512252688408,
0.011304331012070179,
-0.007844271138310432,
-0.001140036154538393,
-0.007479938678443432,
0.04300945624709129,
-0.003850374836474657,
-0.08413870632648468,
-0.041344303637742996,
0.0453605018556118,
0.025308191776275635,
0.0042093186639249325,
-0.06708091497421265,
0.027913209050893784,
0.02269255556166172,
0.061809152364730835,
-0.035197075456380844,
0.028090229257941246,
0.010546913370490074,
0.06883253157138824,
0.007795331533998251,
0.0010959676001220942,
-0.012673466466367245,
-0.020426439121365547,
-0.03745342046022415,
-0.024436935782432556,
-0.06431576609611511,
0.031169764697551727,
0.014175997115671635,
0.012095480225980282,
0.009942672215402126,
0.07879022508859634,
-0.009189371019601822,
-0.006127538159489632,
-0.007847334258258343,
0.0007672943756915629,
0.04968303442001343,
0.04962189123034477,
-0.011254419572651386,
0.0013103870442137122,
0.01881709322333336,
-0.010215990245342255,
0.02799326181411743,
-0.012331584468483925,
0.012678894214332104,
0.05100717768073082,
-0.05719403177499771,
-0.016957242041826248,
0.005430649966001511,
0.005762247834354639,
0.012831378728151321,
-0.028032569214701653,
-0.0353156179189682,
0.0028109769336879253,
0.03768913820385933,
-0.02677811123430729,
0.03448579087853432,
-0.012143825180828571,
0.009329577907919884,
0.008310911245644093,
-0.05761564522981644,
-0.029178503900766373,
-0.0976528599858284,
-0.015100979246199131,
-0.010348418727517128,
-0.046671945601701736,
0.04677443951368332,
0.019079772755503654,
0.004507546313107014,
-0.03867558762431145,
-0.02375393733382225,
-0.01365539338439703,
0.012968254275619984,
0.022268692031502724,
0.007621624507009983,
0.00952860713005066,
0.016862254589796066,
0.05497998371720314,
-0.012822875753045082,
0.0400887057185173,
0.012028520926833153,
-0.030367445200681686,
0.02777542546391487,
-0.008396555669605732,
-0.006784388329833746,
-0.006312182173132896,
-0.0036521307192742825,
0.039044976234436035,
0.03177417442202568,
-0.0061028217896819115,
0.01769307255744934,
-0.0473317913711071,
0.037651289254426956,
0.044271424412727356,
0.0010039384942501783,
0.02867382951080799,
0.07989811152219772,
0.041305217891931534,
0.01758033223450184,
0.015313579700887203,
-0.006395391188561916,
-0.04897535219788551,
-0.02175815962255001,
0.06368029862642288,
-0.006123595405369997,
-0.02491752617061138,
0.009144917130470276,
0.03464654088020325,
0.04215150699019432,
0.02994469366967678,
0.009227355942130089,
-0.023088930174708366,
-0.03132104128599167,
0.05162171646952629,
-0.017687827348709106,
0.010796300135552883,
-0.005744284950196743,
0.050730202347040176,
-0.03562379255890846,
0.004447553772479296,
0.012816781178116798,
-0.026667390018701553,
0.0322713665664196,
-0.0008100595441646874,
-0.0015732530737295747,
0.018211383372545242,
0.007743420545011759,
0.02669586054980755,
-0.0018313827458769083,
0.013928030617535114,
0.025095578283071518,
0.004326520022004843,
0.0041925935074687,
-0.015056478790938854,
-0.0011803163215517998,
0.037595100700855255,
0.009851176291704178,
-0.0032832392025738955,
-0.037001270800828934,
0.008203089237213135,
-0.04392486810684204,
-0.01904664933681488,
0.01374700665473938,
-0.04391896724700928,
-0.025576317682862282,
0.03417125716805458,
0.007388569880276918,
0.012897648848593235,
0.009594439528882504,
-0.02850111573934555,
-0.024092793464660645,
0.03092493675649166,
0.01485837996006012,
0.02173071913421154,
0.06228354200720787,
-0.03634994104504585,
0.02659393660724163,
-0.11251495033502579,
-0.034552618861198425,
0.04758203402161598,
-0.013172402046620846,
0.02873689867556095,
-0.0036031026393175125,
-0.007200263906270266,
0.001422247150912881,
-0.016152866184711456,
-0.03748208284378052,
0.011757557280361652,
-0.011819549836218357,
0.017626874148845673,
0.026725511997938156,
0.033571336418390274,
-0.03179033100605011,
0.011247831396758556,
-0.02586475946009159,
-0.016964592039585114,
-0.011956669390201569,
0.008472994901239872,
0.023344356566667557,
-0.04199911653995514,
0.07015374302864075,
0.02449616603553295,
-0.026150796562433243,
0.027245016768574715,
-0.06457488983869553,
-0.042626362293958664,
0.016076963394880295,
0.02621423825621605,
0.03755316510796547,
-0.004025045316666365,
-0.05433030426502228,
0.10394441336393356,
0.028764279559254646,
-0.03019927814602852,
0.0019149500876665115,
0.025013085454702377,
0.007856586948037148,
-0.022118883207440376,
0.0169658362865448,
0.029961708933115005,
-0.004764138720929623,
0.01734195277094841,
0.029145987704396248,
0.024764813482761383,
0.035104431211948395,
-0.017068607732653618,
-0.052088528871536255,
-0.016943298280239105,
0.005365054123103619,
0.04800686985254288,
0.011694964952766895,
-0.006910144351422787,
-0.023410271853208542,
0.02818336710333824,
0.025243867188692093,
0.012421400286257267,
0.0073080952279269695,
-0.078880675137043,
0.017024267464876175,
0.008825615979731083,
0.01566208340227604,
-0.03089790977537632,
0.00806980486959219,
0.0009752545738592744,
-0.029749881476163864,
0.00720391096547246,
0.014832247979938984,
0.030896207317709923,
-0.0056704021990299225,
-0.008474117144942284,
0.00016181118553504348,
0.014484178274869919,
-0.028071481734514236,
-0.00860272441059351,
-0.043321643024683,
-0.017192170023918152,
0.011682871729135513,
0.01750406250357628,
0.0020254135597497225,
0.0603792630136013,
0.04851071909070015,
0.013344871811568737,
0.008596677333116531,
-0.025560079142451286,
0.00038053380558267236,
-0.05482481047511101,
0.01711794175207615,
-0.027074657380580902,
0.006259300280362368,
-0.010343371890485287,
0.026581162586808205,
0.007307158317416906,
0.030810149386525154,
0.018203580752015114,
0.01008338201791048,
-0.08500758558511734,
0.0702548548579216,
-0.025570612400770187,
-0.018811559304594994,
0.022610947489738464,
-0.012746473774313927,
0.03577673062682152,
0.0032490056473761797,
-0.04639805108308792,
-0.026209756731987,
-0.002436600159853697,
-0.06885652244091034,
-0.003688774537295103,
-0.038699693977832794,
-0.04822918400168419,
0.002186187542974949,
0.021907053887844086,
0.06653182953596115,
-0.05806867405772209,
0.005204641260206699,
0.018061019480228424,
-0.03611965849995613,
0.01875634491443634,
0.005392249673604965,
0.03589818626642227,
0.0135364243760705,
0.015962189063429832,
-0.0032154694199562073,
0.01549848634749651,
-0.011013085022568703,
-0.025501208379864693,
0.03717508539557457,
0.06602098047733307,
0.012729807756841183,
0.004829881247133017,
-0.032913438975811005,
-0.0574372336268425,
-0.00033731921575963497,
0.001032810308970511,
0.0628160908818245,
0.020457886159420013,
-0.010560870170593262,
0.05530821904540062,
0.0529659204185009,
-0.024424254894256592,
0.023518940433859825,
0.05263759568333626,
-0.00932315830141306,
-0.002805150579661131,
-0.05744923651218414,
0.00216709659434855,
-0.02326212264597416,
-0.028876520693302155,
0.03183408081531525,
-0.008263847790658474,
-0.0337897464632988,
0.04198828712105751,
0.03458372876048088,
0.016940871253609657,
-0.04619951918721199,
-0.015338357537984848,
0.002781681716442108,
0.03872973099350929,
0.018045762553811073,
0.019620381295681,
0.004066273104399443,
0.07400501519441605,
0.05519472807645798,
0.006635676603764296,
-0.009804634377360344,
-0.07396513968706131,
0.0019817911088466644,
0.039039287716150284,
0.010484207421541214,
0.002618413418531418,
-0.021467234939336777,
-0.09349474310874939,
-0.010158679448068142,
0.03759529069066048,
-0.03639960289001465,
0.03505149111151695,
0.02407209761440754,
-0.0008205112535506487,
-0.032548632472753525,
0.023400282487273216,
-0.028372131288051605,
0.006156358402222395,
-0.015146775171160698,
0.031314313411712646,
-0.035537250339984894,
-0.0013133067404851317,
-0.055399853736162186,
0.00951290037482977,
0.0026110378094017506,
0.046691857278347015,
0.02778659015893936,
-0.0028553889133036137,
0.00502484105527401,
0.024483054876327515,
-0.056545864790678024,
-0.06306052207946777,
0.01143365167081356,
0.030270924791693687,
-0.0093913609161973,
0.0531747043132782,
-0.039240844547748566,
-0.03256706893444061,
0.03959192335605621,
-0.016407601535320282,
0.035663265734910965,
0.013391508720815182,
-0.05108308792114258,
0.03811964392662048,
0.03286616876721382,
0.0026280605234205723,
0.03471672162413597,
0.01630479469895363,
0.004475418943911791,
-0.029451126232743263,
-0.028997231274843216,
0.013394862413406372,
-0.05436040833592415,
-0.015544363297522068,
-0.05495724827051163,
0.01598762720823288,
-0.03838586062192917,
0.04496458172798157,
-0.011390114203095436,
-0.05426442250609398,
0.005116486921906471,
-0.04635954648256302,
0.0018830375047400594,
0.04627615213394165,
0.01407704409211874,
-0.03078749217092991,
-0.014979295432567596,
0.04797119274735451,
0.013630812056362629,
0.0056455740705132484,
0.039881136268377304,
-0.023465270176529884,
-0.018728269264101982,
0.022407809272408485,
0.012327450327575207,
0.008467523381114006,
-0.03466812148690224,
-0.02027931809425354,
0.020402250811457634,
-0.034856218844652176,
0.02755747362971306,
-0.013338233344256878,
-0.0354803204536438,
0.03296612948179245,
-0.04557238891720772,
-0.002658520359545946,
-0.012790026143193245,
-0.038643259555101395,
0.0027367323637008667,
-0.020694009959697723,
0.010408221744000912,
0.03954392671585083,
0.02046092227101326,
-0.08232634514570236,
-0.04298919439315796,
0.036539703607559204,
-0.0015255971811711788,
-0.04132743924856186,
-0.019149012863636017,
-0.012872328981757164,
-0.04094502702355385,
-0.03241885080933571,
0.04609673097729683,
0.05159839242696762,
-0.022947879508137703,
0.006888174451887608,
-0.009656776674091816,
0.045789945870637894,
0.012458190321922302,
-0.021778736263513565,
-0.007461116183549166,
0.024952363222837448,
-0.03770361840724945,
-0.009266075678169727,
0.015034951269626617,
0.06263384222984314,
-0.008835500106215477,
-0.00392596609890461,
-0.016091126948595047,
0.027695948258042336,
0.01828812062740326,
-0.01659172773361206,
0.0017851443262770772,
0.028073150664567947,
-0.0149597879499197,
0.002777150832116604,
-0.05625608190894127,
-0.01922178827226162,
-0.04496622458100319,
0.006791077088564634,
-0.05027901753783226,
0.0008552632643841207,
0.010480733588337898,
-0.054499488323926926,
0.061161257326602936,
-0.014397038146853447,
-0.007400086149573326,
-0.023931099101901054,
0.05678088217973709,
0.016475223004817963,
-0.002573787234723568,
0.015832001343369484,
-0.023293737322092056,
0.029361560940742493,
0.004721541423350573,
0.029950309544801712,
-0.001939830370247364,
0.0011931739281862974,
-0.0456591434776783,
-0.027335233986377716,
-0.029763413593173027,
0.015180271118879318,
0.07237634062767029,
0.009658641181886196,
0.05995337665081024,
0.030339445918798447,
0.010321315377950668,
0.0015651063295081258,
-0.03300643712282181,
0.002085525542497635,
-0.02476031519472599,
0.012714851647615433,
0.05433716997504234,
-0.06878872960805893,
-0.020160341635346413,
0.024489792063832283,
0.02257908508181572,
-0.008990167640149593,
0.03477564826607704,
0.03104281611740589,
0.011338873766362667,
0.03455683961510658,
0.021361401304602623,
-0.03450972959399223,
0.06674694269895554,
-0.018528668209910393,
0.03944575786590576,
0.01618415117263794,
-0.02532767504453659,
0.012913466431200504,
0.026005305349826813,
0.02748451568186283,
0.011942119337618351,
-0.03377518802881241,
-0.024449612945318222,
0.05855569988489151,
0.03369686007499695,
0.030639201402664185,
0.047623924911022186,
0.008930000476539135,
0.04443805664777756,
-0.023234160616993904,
-0.037195850163698196,
0.00004922086372971535,
-0.036866966634988785,
-0.008307100273668766,
-0.06070686876773834,
-0.05574136972427368,
0.04100353643298149,
-0.014795052818953991,
-0.016057923436164856,
-0.011307256296277046,
-0.01801476441323757,
0.016994260251522064,
-0.027514129877090454,
0.02846391499042511,
-0.014212777838110924,
0.03702909126877785,
-0.030973004177212715,
0.04372565448284149,
-0.00040002731839194894,
-0.0023327753879129887,
0.1136769950389862,
0.0390896312892437,
-0.003323393641039729,
-0.06173503398895264,
0.04502471536397934,
-0.00901889055967331,
0.019614236429333687,
-0.020633863285183907,
0.04146280139684677,
0.010220286436378956,
0.0037691378965973854,
-0.03637047857046127,
0.0501977875828743,
-0.031718168407678604,
-0.007733914069831371,
0.06928510218858719,
-0.02572237327694893,
-0.02735840156674385,
0.023026689887046814,
0.00520726665854454,
0.010378741659224033,
-0.009721426293253899,
-0.02705126814544201,
0.04293093830347061,
0.011074356734752655,
-0.01881924457848072,
-0.0627293735742569,
-0.06640318036079407,
-0.014827697537839413,
-0.00629073241725564,
-0.005195691715925932,
-0.009861108846962452,
0.0038175242953002453,
-0.02046125940978527,
-0.031420499086380005,
0.001969331642612815,
0.003254719078540802,
-0.022608982399106026,
0.07205548882484436,
0.051487069576978683,
0.009051579050719738,
0.0186699777841568,
0.0005122054717503488,
0.01889033056795597,
-0.03970423340797424,
-0.006039312109351158,
-0.030145393684506416,
0.05932768061757088,
-0.01685854233801365,
-0.02349902130663395,
-0.011682089418172836,
-0.001222752733156085,
0.00479900510981679,
-0.05887403339147568,
0.0019764481112360954,
-0.0067708780989050865,
-0.0037302894052118063,
-0.030423179268836975,
-0.01735999621450901,
-0.024248739704489708,
0.008571469224989414,
0.019452515989542007,
-0.0067011830396950245,
-0.00741830188781023,
-0.010543245822191238,
0.01595996506512165,
-0.007007410749793053,
0.047912996262311935,
-0.00935528427362442,
-0.021615147590637207,
-0.03481947258114815,
0.011338968761265278,
-0.045720767229795456,
-0.027902627363801003,
0.007074868772178888,
-0.014031603932380676,
0.03213457018136978,
-0.003555129049345851,
-0.021343672648072243,
0.003467925824224949,
-0.02150673046708107,
-0.006212051026523113,
0.016749026253819466,
-0.016130639240145683,
-0.010960705578327179,
0.014216102659702301,
0.011630776338279247,
0.06698952615261078,
-0.028680188581347466,
0.02014816924929619,
0.008343600668013096,
0.006627126131206751,
0.005407532677054405,
-0.006931164301931858,
0.00319173582829535,
0.0023194861132651567,
-0.012021694332361221,
0.0029792319983243942,
0.007407255005091429,
-0.01084948517382145,
0.019422361627221107,
0.03853800520300865,
0.01567927375435829,
0.021176347509026527,
-0.008233613334596157,
-0.014066165313124657,
0.011777789331972599,
-0.05090229585766792,
0.017616843804717064,
0.024967951700091362,
-0.012656738050282001,
-0.06565222144126892,
-0.048951923847198486,
-0.006266265641897917,
-0.006169423460960388,
0.012015372514724731,
-0.010380744934082031,
-0.057187769562006,
0.026903577148914337,
-0.03418741747736931,
0.009283558465540409,
-0.04054045304656029,
-0.012630924582481384,
-0.03399324789643288,
0.013730816543102264,
-0.028603598475456238,
0.010055040009319782,
0.019342081621289253,
0.045019395649433136,
-0.0049870312213897705,
-0.01806134544312954,
0.03057020716369152,
0.020594138652086258,
-0.04045751690864563,
0.016253605484962463,
0.038815371692180634,
0.02058056928217411,
0.027301866561174393,
0.012982898391783237,
-0.015167289413511753,
-0.007486605551093817,
-0.03389204293489456,
-0.04934489354491234,
0.02176298387348652,
0.010352617129683495,
-0.014317451044917107,
0.02898050844669342,
-0.045903924852609634,
-0.011595120653510094,
0.020996972918510437,
0.000025280927729909308,
0.001399151049554348,
-0.012160412967205048,
-0.031113415956497192,
-0.008187674917280674,
0.008558006025850773,
0.03348342701792717,
-0.03466235473752022,
-0.00998239777982235,
0.020276907831430435,
0.0008026587311178446,
-0.05024798959493637,
-0.017581071704626083,
-0.004496491979807615,
-0.003455681959167123,
0.016675183549523354,
-0.01906486228108406,
0.007200537249445915,
0.0346713624894619,
0.0766243115067482,
-0.0007684860611334443,
-0.00004648538742912933,
0.0036272562574595213,
0.005465962924063206,
-0.07487945258617401,
0.0014994891826063395,
-0.021964285522699356,
-0.006171101704239845,
0.05753137543797493,
-0.0677805170416832,
0.019419873133301735,
-0.007545981090515852,
-0.054035432636737823,
-0.024172065779566765,
-0.055824633687734604,
0.007662520743906498,
-0.060771409422159195,
-0.02825927920639515,
-0.029769204556941986,
0.06401368230581284,
0.05100543424487114,
0.027032604441046715,
0.0014243032783269882,
-0.0028746146708726883,
-0.016360722482204437,
0.016716454178094864,
-0.022618910297751427,
0.041048094630241394,
0.008299685083329678,
-0.015707699581980705,
0.07636290788650513,
-0.01901463232934475,
-0.055509958416223526,
0.019373496994376183,
-0.006516726221889257,
-0.025952110067009926,
0.01844376139342785,
0.00898702908307314,
0.037152454257011414,
0.0065978639759123325,
0.014037049375474453,
0.02203262224793434,
0.0016162828542292118,
0.010571212507784367,
0.011532504111528397,
0.01993103325366974,
-0.01675592176616192,
0.025947296991944313,
0.019650906324386597,
-0.048565905541181564,
-0.00203045760281384,
-0.0042457920499145985,
-0.05271737277507782,
-0.030998364090919495,
0.006032146513462067,
-0.031104862689971924,
0.034140437841415405,
-0.01660791225731373,
0.047771699726581573,
-0.019398827105760574,
-0.0007891746354289353,
0.02719615027308464,
-0.03759174793958664,
-0.014944387599825859,
0.048152241855859756,
-0.03964662924408913,
-0.02758546732366085,
0.019665755331516266,
0.007075906731188297,
0.00344221037812531,
-0.07076430320739746,
0.008795718662440777,
-0.0013398084556683898,
0.017324043437838554,
-0.029005590826272964,
-0.00873752310872078,
-0.015865487977862358,
0.02575291320681572,
0.04556526616215706,
0.03248424082994461,
-0.0480533167719841,
-0.030176782980561256,
-0.01505310833454132,
-0.03604081645607948,
0.027070902287960052,
0.020481254905462265,
-0.014045878313481808,
-0.04555050656199455,
-0.03368896618485451,
0.014216541312634945,
0.012764840386807919,
0.02705666795372963,
-0.03785228729248047,
0.007524985354393721,
0.036616966128349304,
0.0363013930618763,
0.018397625535726547,
-0.025951050221920013,
0.0018493199022486806,
0.006679580081254244,
-0.012851870618760586,
-0.00757638830691576,
-0.0007997379289008677,
-0.024813424795866013,
0.023357156664133072,
0.008066065609455109,
-0.012697547674179077,
0.03411847725510597,
0.008368401788175106,
-0.04722367972135544,
0.011694815009832382,
-0.00596793694421649,
-0.012958625331521034,
0.05590503662824631,
-0.013947314582765102,
-0.018815981224179268,
0.04903796315193176,
-0.024823078885674477,
-0.04784243926405907,
-0.016319191083312035,
-0.06498756259679794,
-0.035057369619607925,
-0.021176652982831,
-0.02479061484336853,
0.042706456035375595,
-0.007257396355271339,
0.013272401876747608,
0.03666854277253151,
-0.022461336106061935,
0.001442090724594891,
0.05661540478467941,
-0.020457793027162552,
0.008606914430856705,
-0.014815444126725197,
0.02040216512978077,
0.006441784091293812,
-0.013668272644281387,
0.015032672323286533,
0.05984882637858391,
0.020230770111083984,
0.011681239120662212,
-0.011988703161478043,
-0.0033308807760477066,
-0.033589258790016174,
0.022403942421078682,
0.0349554605782032,
0.03171014040708542,
-0.040016058832407,
-0.0046058231964707375,
0.02659868635237217,
0.009359866380691528,
0.01831568032503128,
0.009894407354295254,
-0.02993587590754032,
0.059331636875867844,
-0.003335969988256693,
0.002949302550405264,
-0.04256660118699074,
-0.0356312096118927,
-0.03670583665370941,
0.03825203329324722,
-0.012596414424479008,
0.05561386048793793,
-0.016221167519688606,
0.030469313263893127,
-0.010210374370217323,
0.0272313691675663,
0.012756344862282276,
-0.028068937361240387,
0.007875638082623482,
0.03329472243785858,
0.006399405188858509,
0.02259671315550804,
-0.010927898809313774,
-0.008878670632839203,
-0.01386350765824318,
0.018821435049176216,
0.03945168852806091,
-0.0012817904353141785,
-0.007622092496603727,
-0.01503270398825407,
-0.03758379444479942,
0.031049251556396484,
-0.052026279270648956,
-0.04407462850213051,
-0.018666066229343414,
-0.003330391366034746,
-0.02757730893790722,
0.021191416308283806
] |
<p>Consider the standard map (also known as <a href="http://www.scholarpedia.org/article/Chirikov_standard_map" rel="nofollow">Chirikov map</a>):
$$
p_{n+1} = p_n + K \sin(\theta_n) \\
\theta_{n+1} = \theta_n + p_{n+1}
$$</p>
<p>I know that the diffusion coefficient according to the Einstein relation is defined through the relation:</p>
<p>$$
\sigma^2 = 2Dt
$$</p>
<p>being $\sigma$ the variance of the position in the case of the $1$-D random walker. Can you figure out why the diffusion coefficient for the standard map is given by:</p>
<p>$$
D = \lim_{n \rightarrow \infty} \frac{<(p_n - p_0)^2>}{n} \quad ?
$$</p>
<p>I mean, the $n$ makes sense, but what about the variance, why this is given just in terms of $p$, what happens with the $x$.</p>
| 8,506 |
[
-0.021203462034463882,
-0.014159423299133778,
0.011701742187142372,
-0.026374084874987602,
0.0334182009100914,
0.004766868427395821,
-0.034558217972517014,
0.0117751844227314,
-0.038920238614082336,
-0.06184832751750946,
0.016931230202317238,
0.01411029789596796,
0.07550396025180817,
0.06020127609372139,
0.027582352980971336,
0.005336002446711063,
-0.001527127344161272,
-0.018802033737301826,
-0.03593997657299042,
-0.03780745714902878,
-0.0036509193014353514,
0.021191921085119247,
-0.013272889889776707,
-0.010066637769341469,
-0.03884865343570709,
0.008584967814385891,
0.02998178079724312,
0.00002696388037293218,
0.013197412714362144,
0.07291798293590546,
-0.051223110407590866,
0.0004255994863342494,
0.03277749568223953,
0.01857890374958515,
0.006880009081214666,
0.023341847583651543,
-0.04859958216547966,
-0.024254554882645607,
0.007625817786902189,
0.019821714609861374,
-0.044924214482307434,
-0.0185935627669096,
-0.02520512230694294,
0.030176358297467232,
-0.005617520771920681,
-0.0005777943879365921,
0.025714339688420296,
0.009493145160377026,
0.038985759019851685,
-0.0785517543554306,
0.08491083979606628,
0.022041773423552513,
0.047176867723464966,
0.006318756844848394,
0.0025577114429324865,
-0.013189037330448627,
0.05643020570278168,
0.0385718047618866,
-0.027260776609182358,
-0.05496210977435112,
-0.020913032814860344,
-0.02263590320944786,
-0.020859794691205025,
-0.026759224012494087,
0.025094367563724518,
-0.007632413879036903,
0.03680248558521271,
-0.04749744012951851,
0.046667132526636124,
-0.03223906457424164,
-0.008879385888576508,
-0.010286694392561913,
0.022998996078968048,
-0.023493722081184387,
0.014049741439521313,
0.00637449836358428,
0.003025596961379051,
0.023522965610027313,
0.01540257316082716,
0.02507992461323738,
0.005804009735584259,
0.005746141076087952,
0.010377847589552402,
0.017320305109024048,
0.003025719663128257,
0.005615894217044115,
0.04620467498898506,
-0.020703310146927834,
-0.007763691246509552,
0.050736647099256516,
0.017512446269392967,
0.010042107664048672,
0.025440750643610954,
-0.03956735506653786,
-0.03954153507947922,
0.0375826470553875,
-0.010255027562379837,
0.012129552662372589,
0.0032114004716277122,
-0.001975910970941186,
-0.04313620179891586,
-0.07207068055868149,
-0.006965084001421928,
0.02509353868663311,
-0.006261677481234074,
0.00867005530744791,
-0.000060184989706613123,
0.017005307599902153,
-0.030778830870985985,
-0.00618229852989316,
-0.04164479300379753,
-0.00872107408940792,
-0.011525178328156471,
0.0458751879632473,
-0.013404542580246925,
-0.01579390838742256,
-0.012905312702059746,
-0.026748565956950188,
0.026724709197878838,
0.09687884896993637,
0.01656263694167137,
-0.01586519367992878,
-0.0030507466290146112,
-0.016045987606048584,
-0.06716202944517136,
0.051522865891456604,
0.06212200969457626,
-0.0014800383942201734,
-0.0498148575425148,
0.018763460218906403,
0.0022815668489784002,
0.026961764320731163,
0.043194729834795,
0.04037598520517349,
0.010175131261348724,
0.0027488444466143847,
-0.10744559019804001,
-0.01579393818974495,
0.08444104343652725,
-0.020239531993865967,
0.04280102252960205,
-0.11372063308954239,
0.04462472349405289,
0.04060230404138565,
0.048371270298957825,
-0.01428199466317892,
0.039396148175001144,
-0.0009239539504051208,
0.03935568779706955,
0.014279734343290329,
-0.03816938027739525,
-0.05048617720603943,
0.02256965823471546,
-0.06415265053510666,
-0.01896461844444275,
-0.05617962405085564,
0.042777277529239655,
0.036160774528980255,
0.009074917063117027,
-0.025559760630130768,
0.05901731178164482,
-0.03334784880280495,
0.010639664717018604,
0.0023117787204682827,
-0.02362058125436306,
-0.05279967561364174,
0.06825672090053558,
0.03841085359454155,
0.031057201325893402,
0.007940799929201603,
0.0043412200175225735,
0.011577295139431953,
-0.00883790384978056,
0.019509175792336464,
0.060477837920188904,
-0.04352004826068878,
-0.0015768047887831926,
0.02626323141157627,
-0.05606209859251976,
0.004679287318140268,
-0.030229883268475533,
-0.01342883799225092,
-0.052255626767873764,
-0.007170615252107382,
-0.0033804643899202347,
0.025148257613182068,
-0.009500140324234962,
0.018980033695697784,
0.027194349095225334,
-0.09185140579938889,
0.01465637143701315,
-0.04904168099164963,
-0.004200262017548084,
-0.004745805636048317,
-0.021178999915719032,
0.015547486022114754,
-0.0037536651361733675,
0.008899431675672531,
0.02332283928990364,
-0.02973460778594017,
-0.02122260443866253,
0.008428637869656086,
-0.005615450907498598,
-0.056048471480607986,
0.006504990626126528,
0.06896502524614334,
0.04006364196538925,
-0.01636502705514431,
0.019218305125832558,
-0.010587881319224834,
0.0016238398384302855,
-0.00274069351144135,
-0.026397567242383957,
0.04593157395720482,
0.00800916738808155,
0.0006445369799621403,
0.0420977957546711,
-0.001463567023165524,
0.005961841903626919,
0.022047506645321846,
-0.03854219615459442,
0.08595192432403564,
0.1032462865114212,
0.006081099156290293,
-0.014079555869102478,
0.054939139634370804,
0.023443957790732384,
0.013039227575063705,
0.01057351939380169,
-0.0351501889526844,
-0.01794748567044735,
-0.01145294588059187,
-0.007355178706347942,
0.05672468990087509,
-0.045132510364055634,
0.007936054840683937,
0.042848408222198486,
0.017951563000679016,
-0.014218000695109367,
-0.008640089072287083,
0.004976572934538126,
-0.04363849014043808,
0.029190270230174065,
0.019954530522227287,
-0.00918257050216198,
0.00822191871702671,
-0.000990642816759646,
-0.0061243632808327675,
-0.006185625679790974,
0.0011301314225420356,
-0.038681089878082275,
0.0036892013158649206,
-0.026435453444719315,
0.0022092489525675774,
0.01101457979530096,
0.009493820369243622,
0.05947527289390564,
-0.004223288502544165,
0.016951121389865875,
0.04460735246539116,
-0.00859617069363594,
0.0006711230962537229,
-0.008215184323489666,
-0.016769608482718468,
0.007305984850972891,
0.047704946249723434,
-0.008421818725764751,
-0.04508034884929657,
0.00678642513230443,
-0.021925289183855057,
0.03977224975824356,
-0.018211212009191513,
-0.007956212386488914,
0.002397143980488181,
0.011292378418147564,
0.02743368409574032,
0.023681530728936195,
-0.030557792633771896,
-0.011111794039607048,
-0.012433764524757862,
0.010670936666429043,
0.01608836092054844,
0.008672812022268772,
0.014073638245463371,
-0.05290775001049042,
-0.00009794303332455456,
-0.03226621821522713,
0.006966342218220234,
0.03406475856900215,
0.020878678187727928,
0.03143741935491562,
-0.01898670569062233,
-0.018309246748685837,
-0.03230748325586319,
-0.03827279061079025,
-0.037353720515966415,
-0.008799007162451744,
-0.03904778137803078,
-0.018833188340067863,
0.06111646443605423,
-0.0427476167678833,
-0.013128113001585007,
0.027238253504037857,
-0.05036065727472305,
-0.05738033726811409,
-0.008912098594009876,
-0.001613094937056303,
0.01321340911090374,
-0.029639510437846184,
0.032734788954257965,
0.04456380009651184,
-0.017587250098586082,
0.0005735926679335535,
-0.06488972157239914,
-0.038028884679079056,
0.02201320230960846,
-0.03389687091112137,
-0.006110344082117081,
0.003714217571541667,
-0.03660890832543373,
0.07092408090829849,
0.051420908421278,
-0.007095548789948225,
-0.025516921654343605,
0.016460509970784187,
-0.03337150812149048,
-0.07458478212356567,
0.019130591303110123,
0.06257510930299759,
-0.036575641483068466,
0.031303051859140396,
0.009562283754348755,
0.03142556920647621,
0.044342316687107086,
-0.008294889703392982,
-0.01405795756727457,
0.019104018807411194,
-0.00834217295050621,
-0.02900000475347042,
0.04350213333964348,
0.01647934317588806,
-0.03689679875969887,
-0.02490493841469288,
-0.0030238640028983355,
-0.003966929391026497,
0.0012996646109968424,
-0.055291444063186646,
0.03427258878946304,
-0.01114838570356369,
-0.007782658562064171,
-0.024111034348607063,
0.03514307737350464,
0.016780314967036247,
-0.03220007196068764,
0.0043564061634242535,
0.0048906439915299416,
0.044864628463983536,
0.01629776693880558,
0.009928965009748936,
0.033889565616846085,
0.02490013651549816,
-0.02934289537370205,
-0.027202580124139786,
-0.013063902035355568,
0.030956078320741653,
0.005966215394437313,
-0.023603811860084534,
-0.030937407165765762,
0.019229913130402565,
0.02462966926395893,
0.0010928631527349353,
-0.015546306036412716,
-0.0021605994552373886,
-0.03456662967801094,
-0.061088431626558304,
-0.013402839191257954,
-0.01581144705414772,
0.05345102772116661,
-0.0005957132671028376,
0.047118064016103745,
-0.02965310774743557,
-0.022770781069993973,
0.022919954732060432,
-0.014796101488173008,
-0.08770564943552017,
0.004482680931687355,
-0.002624518470838666,
-0.05496935918927193,
-0.01374469231814146,
-0.027811558917164803,
0.05026876926422119,
-0.0034175857435911894,
0.010491483844816685,
0.030620891600847244,
-0.02891295962035656,
-0.05250629037618637,
0.0011719990288838744,
-0.032958995550870895,
-0.05807924643158913,
-0.025419052690267563,
0.035793472081422806,
0.05725395306944847,
-0.0373724065721035,
0.028471099212765694,
0.03194338455796242,
0.018302006646990776,
0.0035367149394005537,
-0.025610575452446938,
0.02771740034222603,
0.006506629753857851,
-0.03266831114888191,
-0.03738921135663986,
-0.04072828218340874,
-0.041594840586185455,
-0.005399757996201515,
0.00925485510379076,
0.03036537952721119,
0.05054142326116562,
0.019021468237042427,
0.009789275005459785,
-0.03989358991384506,
-0.012448583729565144,
0.01116103958338499,
0.014819475822150707,
0.020919237285852432,
0.021381791681051254,
0.061030250042676926,
0.017132310196757317,
-0.016389718279242516,
0.02757258713245392,
0.03591092675924301,
-0.018408115953207016,
-0.014498966746032238,
-0.02368783764541149,
-0.033112891018390656,
0.018742328509688377,
0.0022246004082262516,
0.011467156000435352,
-0.02965136431157589,
-0.02714998461306095,
0.04274069145321846,
0.011844299733638763,
0.04518995061516762,
-0.0022316519170999527,
-0.028377095237374306,
0.021742554381489754,
0.028698939830064774,
-0.009022768586874008,
0.015069092623889446,
0.008451228030025959,
0.00955132581293583,
0.036883387714624405,
0.05380617827177048,
-0.015062371268868446,
-0.053321462124586105,
-0.0029466592241078615,
0.00743179302662611,
0.03375309333205223,
-0.010586906224489212,
-0.005851584021002054,
-0.0525793731212616,
0.00011508254829095677,
0.0360727496445179,
-0.010897026397287846,
0.05584317445755005,
0.005664055701345205,
-0.031920142471790314,
-0.022824740037322044,
-0.032207734882831573,
-0.05818305164575577,
0.042528267949819565,
0.029421942308545113,
0.022695153951644897,
-0.031949032098054886,
0.027180692180991173,
-0.02071898803114891,
0.03976438567042351,
0.0018894477980211377,
0.060673486441373825,
0.0021051201038062572,
0.0025142051745206118,
-0.002874824684113264,
0.02232583425939083,
-0.026243317872285843,
-0.09291478991508484,
0.03436196595430374,
-0.027429524809122086,
-0.018364757299423218,
0.038950223475694656,
-0.015016851015388966,
-0.07073377072811127,
0.026621505618095398,
0.0051025268621742725,
0.0203936155885458,
0.007510306779295206,
-0.0004769808438140899,
0.05049823224544525,
0.05082172900438309,
-0.00912532303482294,
0.07392971962690353,
0.02973199635744095,
-0.004393040668219328,
0.025804869830608368,
-0.03379926085472107,
0.06438472121953964,
-0.031654782593250275,
0.02221105992794037,
-0.03479314595460892,
0.015393706038594246,
-0.061034005135297775,
0.05469775199890137,
0.008326244540512562,
0.024701222777366638,
-0.031636688858270645,
-0.014158396050333977,
0.023874009028077126,
0.027202991768717766,
0.028332216665148735,
0.0010591696482151747,
0.04910939559340477,
0.015859732404351234,
0.032838307321071625,
0.009332116693258286,
0.011503114365041256,
-0.0040889461524784565,
-0.006049999967217445,
0.018450049683451653,
0.014609185047447681,
0.01872226595878601,
-0.00346786854788661,
-0.0012244099052622914,
-0.014675060287117958,
-0.019559672102332115,
0.05580496788024902,
0.006869474425911903,
0.0025166489649564028,
0.015164832584559917,
-0.03082401305437088,
-0.022530565038323402,
-0.0122146587818861,
-0.00560089061036706,
0.0010271064238622785,
-0.03837766870856285,
-0.01795106939971447,
-0.005576173774898052,
0.04955943301320076,
-0.08547428995370865,
-0.02027285285294056,
0.01147376000881195,
-0.022908657789230347,
-0.01624230481684208,
-0.0302134919911623,
0.03988144174218178,
-0.04887272045016289,
-0.04928603023290634,
-0.012990621849894524,
0.03605225682258606,
-0.019912272691726685,
-0.0013829522067680955,
-0.023247288540005684,
0.05205290764570236,
0.07874830067157745,
0.000875915982760489,
-0.026075731962919235,
0.047924503684043884,
-0.02127152867615223,
-0.007941649295389652,
0.027573492377996445,
0.06224007532000542,
-0.033507559448480606,
-0.04230226203799248,
0.008219645358622074,
-0.006493903696537018,
0.017819596454501152,
-0.016151193529367447,
-0.013195726089179516,
-0.008694160729646683,
0.0175426434725523,
-0.012885300442576408,
-0.01811937242746353,
-0.01975332573056221,
-0.021598100662231445,
0.015286820940673351,
-0.01853194274008274,
0.03169010207056999,
-0.03053699992597103,
-0.022983325645327568,
0.01633661612868309,
0.03665750101208687,
0.009753691963851452,
-0.010056016966700554,
0.03345748782157898,
-0.0011801087530329823,
-0.04748727008700371,
0.015626298263669014,
-0.0002914986398536712,
0.05593778192996979,
-0.0015520444139838219,
0.010621258988976479,
0.035374339669942856,
-0.00593551667407155,
-0.030612504109740257,
-0.0243449155241251,
-0.024079209193587303,
0.021199312061071396,
0.05069402605295181,
-0.030796078965067863,
0.028044728562235832,
0.0070546939969062805,
-0.036668561398983,
0.0021986134815961123,
-0.008090418763458729,
-0.030338216572999954,
-0.012716139666736126,
-0.010151425376534462,
0.03715578839182854,
-0.01638994738459587,
-0.012525748461484909,
0.015948263928294182,
0.038234226405620575,
0.006932294461876154,
0.004933329299092293,
0.03495152294635773,
-0.0012401590356603265,
0.0020088013261556625,
-0.012920144014060497,
-0.027973294258117676,
0.05036632716655731,
-0.02024134248495102,
0.06114194169640541,
-0.003661414608359337,
-0.003759269369766116,
0.06395690888166428,
0.03803058713674545,
0.023090090602636337,
-0.02438376471400261,
-0.016938604414463043,
-0.05971097946166992,
-0.028040926903486252,
0.0379667729139328,
-0.016308240592479706,
0.016026590019464493,
-0.0306621715426445,
0.02928825281560421,
-0.006068187300115824,
0.01941671408712864,
-0.0009435208630748093,
-0.052300676703453064,
-0.009316601790487766,
-0.00358954886905849,
-0.06874904036521912,
0.04185157269239426,
-0.02585553005337715,
-0.034783102571964264,
0.011478614062070847,
-0.04349980130791664,
0.03545781597495079,
0.01493484154343605,
-0.011172055266797543,
-0.020698320120573044,
0.09574270248413086,
0.022452136501669884,
0.04872890189290047,
-0.03399889916181564,
0.01105382852256298,
0.12885549664497375,
0.039510585367679596,
0.013727429322898388,
-0.043575551360845566,
-0.04817504435777664,
-0.001781261758878827,
0.012783439829945564,
-0.0635547935962677,
0.028495734557509422,
0.037035856395959854,
0.00016736371617298573,
0.01685543917119503,
0.024374591186642647,
-0.008711103349924088,
-0.053062956780195236,
0.019938426092267036,
-0.0719107910990715,
-0.041316352784633636,
0.030103690922260284,
-0.012630827724933624,
-0.031454093754291534,
0.007803643587976694,
-0.045848168432712555,
0.013466604053974152,
-0.007997886277735233,
0.026663726195693016,
-0.042382270097732544,
-0.0058904667384922504,
-0.01620861329138279,
-0.0016549302963539958,
-0.011211119592189789,
-0.0048707700334489346,
0.012259768322110176,
-0.016641823574900627,
0.00856960192322731,
0.013643112033605576,
0.014859083108603954,
-0.015819640830159187,
0.02353566512465477,
0.04651869460940361,
0.012210558168590069,
0.012183421291410923,
0.04492197185754776,
0.0020546086598187685,
-0.02395017258822918,
-0.03308656066656113,
-0.015261905267834663,
0.07284006476402283,
-0.040396805852651596,
0.026786789298057556,
0.00812214519828558,
-0.020258216187357903,
-0.03129447251558304,
0.0039124153554439545,
0.021555786952376366,
0.011632089503109455,
0.006682020146399736,
-0.010521993041038513,
-0.009486297145485878,
-0.03222082555294037,
-0.0014089433243498206,
0.002676603617146611,
0.02685375325381756,
-0.028581270948052406,
-0.009817796759307384,
-0.02327463962137699,
-0.012701679021120071,
0.056117020547389984,
-0.006852088496088982,
0.009573021903634071,
-0.021822066977620125,
0.0029349876567721367,
-0.059926826506853104,
0.009086028672754765,
-0.008109145797789097,
-0.03912603482604027,
0.030420901253819466,
0.004533980041742325,
0.00032512901816517115,
0.02573009766638279,
-0.031348660588264465,
0.008353575132787228,
0.013535996899008751,
-0.011952994391322136,
-0.031092073768377304,
-0.011253973469138145,
-0.007905296050012112,
0.028049923479557037,
-0.010864890180528164,
0.007317608222365379,
0.00827609933912754,
0.05694672092795372,
0.0004797650035470724,
-0.013513765297830105,
0.0032462768722325563,
0.0036331680603325367,
-0.027440601959824562,
-0.016548778861761093,
0.02386569045484066,
0.03162648156285286,
0.02167278341948986,
0.016340257599949837,
-0.005655928514897823,
0.032677408307790756,
0.016662532463669777,
-0.0008381357183679938,
0.01842019148170948,
-0.026277819648385048,
0.011288906447589397,
0.04549526795744896,
0.010206655599176884,
-0.03016970306634903,
-0.04328392073512077,
-0.017300773411989212,
0.031578920781612396,
0.011232330463826656,
0.004930533934384584,
-0.05529103800654411,
-0.00407739682123065,
-0.056743524968624115,
0.03944220393896103,
-0.02618730068206787,
0.020908821374177933,
-0.0010513209272176027,
0.013895115815103054,
-0.011072748340666294,
0.03648693859577179,
0.027108941227197647,
0.01311544794589281,
-0.010097448714077473,
0.02024027332663536,
-0.0018923042807728052,
0.02119222655892372,
0.01246141642332077,
-0.039304833859205246,
-0.033167093992233276,
0.00015053969400469214,
0.04051412642002106,
-0.010571440681815147,
-0.09447033703327179,
0.04188656061887741,
-0.02744860202074051,
-0.0585637129843235,
0.008696962147951126,
0.01567877270281315,
0.033053457736968994,
0.0349021852016449,
-0.024620937183499336,
0.01460175309330225,
0.00777306966483593,
-0.012440210208296776,
-0.038173191249370575,
-0.013231762684881687,
-0.04727639630436897,
0.016000473871827126,
-0.021266408264636993,
0.02967790700495243,
-0.017222600057721138,
0.009852435439825058,
-0.0027746015693992376,
0.015017624013125896,
-0.009293561801314354,
-0.005108995363116264,
0.03097872994840145,
-0.020143641158938408,
-0.01883280836045742,
-0.020409710705280304,
-0.01766769215464592,
0.02518405020236969,
0.05676170438528061,
-0.016483651474118233,
-0.020628955215215683,
0.00377991097047925,
0.006720523349940777,
-0.04883497953414917,
-0.008075153455138206,
0.019855407997965813,
0.03002338297665119,
0.028475342318415642,
-0.05728381872177124,
0.02852085791528225,
0.07561343908309937,
-0.06094690039753914,
0.018118204548954964,
-0.005005521699786186,
0.0007921653450466692,
-0.05363062024116516,
0.002201441675424576,
-0.00028315174859017134,
0.07418221980333328,
0.06796037405729294,
0.04368361458182335,
0.012079372070729733,
0.010189726948738098,
0.0006980278994888067,
-0.03905993700027466,
0.0033198660239577293,
0.004607129376381636,
-0.014362781308591366,
-0.01019932609051466,
0.04117487743496895,
-0.027668237686157227,
-0.03720572963356972,
0.023448267951607704,
-0.0015841367421671748,
-0.024743370711803436,
-0.008133696392178535,
-0.010480768047273159,
-0.030114641413092613,
0.03003612905740738,
0.010679386556148529,
-0.009021874517202377,
0.04300307855010033,
0.013570370152592659,
0.025955552235245705,
-0.005392711143940687,
-0.015170861966907978,
-0.004621788393706083,
0.038154348731040955,
0.010902099311351776,
-0.03398953750729561,
0.05446330085396767,
0.005509047769010067,
-0.029768725857138634,
-0.0024592378176748753,
-0.0029431264847517014,
0.0391681045293808,
-0.011497877538204193,
0.017385903745889664,
-0.031191905960440636,
0.0021343075204640627,
-0.02656738832592964,
-0.01727822981774807,
-0.015057219192385674,
0.00793103501200676,
-0.025709660723805428,
-0.01720597967505455,
0.031104283407330513,
-0.0058970702812075615,
-0.013877873308956623,
-0.03961452841758728,
-0.033732715994119644,
-0.015118238516151905,
0.04219342768192291,
0.019204910844564438,
0.009138120338320732,
-0.02688383311033249,
0.008838470093905926,
-0.008094302378594875,
0.022188516333699226,
-0.004526181146502495,
-0.008558129891753197,
-0.03489091619849205,
-0.06933054327964783,
0.024499403312802315,
-0.00058093381812796,
-0.03355386108160019,
-0.024005210027098656,
0.002367652952671051,
-0.04419875890016556,
0.026022404432296753,
0.0543864369392395,
0.007039173971861601,
-0.007144071161746979,
0.013873746618628502,
0.033477783203125,
0.05278531461954117,
-0.06742750853300095,
0.011985409073531628,
-0.043083079159259796,
0.009591114707291126,
-0.012934325262904167,
0.025820204988121986,
-0.012297243811190128,
0.042634446173906326,
0.0016331657534465194,
0.025276267901062965,
0.008226679638028145,
-0.010647440329194069,
-0.015332006849348545,
0.01314498856663704,
0.05357784777879715,
-0.02533397264778614,
0.03980112448334694,
-0.013719866052269936,
-0.013625865802168846,
0.030165428295731544,
-0.0045953476801514626,
-0.039377424865961075,
0.007519020698964596,
-0.038158100098371506,
-0.04442715272307396,
0.014402614906430244,
0.001448630471713841,
0.0416935496032238,
-0.05331578850746155,
-0.016887914389371872,
0.03321744129061699,
-0.04543932154774666,
-0.027592359110713005,
0.031982388347387314,
0.020396431908011436,
0.02453373558819294,
-0.0015032854862511158,
0.00046788915642537177,
0.015145928598940372,
0.020970873534679413,
-0.036668431013822556,
0.045212481170892715,
0.020776456221938133,
-0.012993264943361282,
0.019885867834091187,
-0.025988895446062088,
-0.022390952333807945,
0.002865113317966461,
0.01779279112815857,
0.061336759477853775,
-0.023958005011081696,
0.0001549644221086055,
0.03817126899957657,
-0.010254550725221634,
0.030249478295445442,
-0.006204569712281227,
-0.03418370336294174,
0.047459397464990616,
0.014560441486537457,
-0.013492804020643234,
-0.038567978888750076,
0.032929178327322006,
-0.043031226843595505,
0.000894104887265712,
0.002130480483174324,
0.04949190095067024,
-0.00006628772098338231,
0.0004691239446401596,
-0.03765445575118065,
0.03391673415899277,
0.004222658462822437,
-0.04583533853292465,
0.009523440152406693,
0.011532739736139774,
-0.013669298030436039,
-0.006004070397466421,
0.008547188714146614,
-0.05391096696257591,
-0.017976833507418633,
0.019020134583115578,
0.03210645914077759,
0.008828056044876575,
0.0002488265745341778,
0.012636479921638966,
-0.018343709409236908,
0.05926724895834923,
-0.04190080612897873,
-0.0106026167050004,
-0.021551864221692085,
0.008711600676178932,
-0.011677034199237823,
0.009547797031700611
] |
<p>Imagine you have a sealed cylindrical vessel with a given radius with a compressed gas inside. Let's give some numbers, 5 cm radius and 100 atm pressure. You poke a hole in the vessel and the gas will flow out, propelling the vessel in the opposite direction with a given force. Intuition tells me that this force depends on the hole size. Suppose the pressure does not change as time goes by, what's the optimal hole size to deliver the best acceleration ? </p>
| 8,507 |
[
0.002083949279040098,
-0.01099390722811222,
-0.027508584782481194,
-0.023361412808299065,
0.03946353495121002,
-0.008584295399487019,
0.015843385830521584,
0.0036121848970651627,
0.014901116490364075,
0.03799140825867653,
0.02404196932911873,
0.03755222260951996,
0.03786205127835274,
-0.03636188805103302,
-0.008368163369596004,
0.027482494711875916,
0.0007106798584572971,
-0.033025819808244705,
-0.024271570146083832,
-0.039817530661821365,
-0.010967708192765713,
-0.02014831081032753,
-0.02407972328364849,
-0.03252972662448883,
-0.04333319142460823,
0.06695101410150528,
0.024347061291337013,
-0.0031247581355273724,
0.013303691521286964,
0.01055848691612482,
-0.0005189854418858886,
-0.010868643410503864,
-0.0016587802674621344,
0.03365039452910423,
0.020909704267978668,
-0.016532575711607933,
-0.041992176324129105,
-0.022627701982855797,
-0.0481647364795208,
0.013431631028652191,
-0.03740078583359718,
-0.013977153226733208,
0.019381485879421234,
0.037914201617240906,
0.0043938253074884415,
0.05429723113775253,
-0.007969154044985771,
-0.022683296352624893,
0.0574803464114666,
-0.0602860227227211,
0.0512569360435009,
-0.02154647558927536,
0.048973772674798965,
0.014607653953135014,
0.01263826247304678,
-0.03144403174519539,
0.04036334529519081,
0.04347454011440277,
-0.02488092891871929,
-0.010941945016384125,
0.006060038227587938,
-0.001515279640443623,
-0.015588963404297829,
-0.00931266974657774,
0.012732167728245258,
-0.009751087985932827,
-0.028477743268013,
-0.00031767573091201484,
-0.0029201069846749306,
-0.012361137196421623,
0.031990278512239456,
-0.020845996215939522,
0.06041572988033295,
0.013721821829676628,
0.009358488023281097,
-0.02080281637609005,
0.03743373230099678,
-0.0006615485181100667,
0.030297523364424706,
0.06359979510307312,
-0.029051030054688454,
-0.0047086202539503574,
0.0458652526140213,
0.039612554013729095,
0.0012246017577126622,
0.01326115895062685,
0.05131075158715248,
-0.010596863925457,
0.006684277206659317,
0.03685150295495987,
-0.014200927689671516,
0.0010045203380286694,
0.04215029254555702,
-0.019374016672372818,
0.011749021708965302,
0.027417229488492012,
-0.0020926701836287975,
0.047407541424036026,
0.004616051912307739,
0.005874670576304197,
-0.026806697249412537,
-0.02044927515089512,
-0.016553230583667755,
0.09522830694913864,
0.01537246908992529,
-0.034462980926036835,
-0.018131500110030174,
0.03601812943816185,
-0.06300722807645798,
0.024416424334049225,
-0.047698672860860825,
-0.029348669573664665,
-0.010470923036336899,
-0.009561676532030106,
0.02052079141139984,
-0.03300885483622551,
-0.008324178867042065,
-0.048990096896886826,
0.029257597401738167,
0.02005726657807827,
0.05333247408270836,
-0.023108188062906265,
0.04460348188877106,
-0.025456620380282402,
-0.04290037229657173,
-0.010903689078986645,
0.035874269902706146,
-0.024857711046934128,
-0.018820960074663162,
0.02161872386932373,
0.0029293640982359648,
-0.03821790590882301,
-0.0040853433310985565,
-0.0027032680809497833,
0.05897187069058418,
-0.0015008602058514953,
-0.08236683160066605,
-0.06719774752855301,
0.060379017144441605,
0.030145088210701942,
-0.024624016135931015,
-0.07127710431814194,
0.016870515421032906,
0.020404702052474022,
0.10169614851474762,
0.01308694202452898,
-0.0021098447032272816,
0.02153818868100643,
0.027432501316070557,
0.012309939600527287,
-0.018702127039432526,
0.007509018760174513,
-0.0315718911588192,
-0.03412407264113426,
0.003344452241435647,
-0.031171731650829315,
0.009236992336809635,
-0.007355956360697746,
0.040698133409023285,
-0.039881471544504166,
0.06282055377960205,
-0.06343699246644974,
-0.014706717804074287,
-0.03325367718935013,
-0.009535876102745533,
-0.025760246440768242,
0.06507913768291473,
0.010948062874376774,
-0.011051392182707787,
0.04915231093764305,
0.030358200892806053,
0.008707224391400814,
0.02806990034878254,
-0.029186531901359558,
0.030400050804018974,
-0.02509438432753086,
0.0349004752933979,
-0.028666531667113304,
0.014238877221941948,
0.014037864282727242,
0.0031205257400870323,
-0.037362635135650635,
-0.04028846323490143,
-0.010934432037174702,
0.01815776154398918,
0.012072062119841576,
0.01526786107569933,
0.019786179065704346,
-0.01127586793154478,
-0.03868458420038223,
-0.012827456928789616,
-0.07945402711629868,
0.07536476105451584,
0.0020697233267128468,
0.017126182094216347,
0.03855179250240326,
-0.03015376627445221,
-0.017183586955070496,
0.006831166800111532,
-0.00008597361738793552,
-0.01858438551425934,
-0.0054115429520606995,
0.012633753009140491,
-0.011480996385216713,
-0.0014696191065013409,
0.030387312173843384,
0.0022931902203708887,
-0.004056025296449661,
-0.005387215409427881,
0.003292707959190011,
-0.004432276822626591,
0.016206994652748108,
-0.044904399663209915,
0.0009558237507008016,
-0.006164676044136286,
-0.012979903258383274,
0.025121377781033516,
-0.0016270010964944959,
0.009839454665780067,
0.006013346835970879,
-0.04411350190639496,
0.0945342481136322,
0.04997876659035683,
0.02964412234723568,
0.005910176783800125,
-0.008433540351688862,
-0.013394219800829887,
-0.004257002845406532,
0.040732357650995255,
-0.02676786109805107,
-0.05351373553276062,
-0.02021784335374832,
0.008117795921862125,
0.034001924097537994,
-0.006841265596449375,
0.009283646941184998,
0.039557553827762604,
-0.013846916146576405,
0.009590488858520985,
0.04132216423749924,
-0.01137973926961422,
-0.01230242382735014,
0.029651574790477753,
0.06749144196510315,
-0.008195941336452961,
0.020786114037036896,
0.07103371620178223,
0.004880870692431927,
0.02107739821076393,
-0.002600124105811119,
0.015041285194456577,
0.0004399153694976121,
0.007961367256939411,
0.015812117606401443,
-0.03288472443819046,
-0.001875507296063006,
0.01264299638569355,
-0.015166031196713448,
-0.010062404908239841,
0.019878627732396126,
0.014419022016227245,
0.031226854771375656,
-0.0338110625743866,
0.034399814903736115,
0.0033456122037023306,
-0.023103145882487297,
0.004827527794986963,
-0.009819816797971725,
0.03049234300851822,
-0.028206463903188705,
0.003989344462752342,
-0.0523037388920784,
0.011804473586380482,
-0.052812136709690094,
-0.0332656055688858,
0.004031287040561438,
0.02271171100437641,
0.00005185756890568882,
-0.03522961586713791,
-0.02449955977499485,
-0.03034055046737194,
-0.011014037765562534,
0.020096736028790474,
0.037871941924095154,
-0.017956499010324478,
0.02396523207426071,
-0.013218279927968979,
-0.041729699820280075,
0.028156796470284462,
-0.005668176803737879,
-0.025952298194169998,
0.018381044268608093,
0.008461665362119675,
-0.023601658642292023,
0.013209540396928787,
-0.038773611187934875,
0.024414949119091034,
-0.01976185105741024,
0.003360204165801406,
0.0636896938085556,
-0.0015971866669133306,
-0.03271181136369705,
0.008484186604619026,
-0.04035390168428421,
-0.021863501518964767,
-0.038202956318855286,
-0.005217898637056351,
0.00408759992569685,
-0.01289341039955616,
0.0022782443556934595,
0.02375480905175209,
0.014738631434738636,
-0.024373997002840042,
-0.053614724427461624,
-0.006784333847463131,
-0.017727065831422806,
-0.010491333901882172,
0.07878582924604416,
-0.020559057593345642,
-0.011562981642782688,
0.06161115691065788,
-0.00632078293710947,
-0.044405750930309296,
-0.013264970853924751,
-0.02869022823870182,
-0.0071908640675246716,
-0.011114644818007946,
0.007443774491548538,
0.08296222984790802,
-0.0014836981426924467,
0.012076443061232567,
0.04671811684966087,
0.055972784757614136,
0.01808014139533043,
0.04767400026321411,
-0.004001028370112181,
0.004414463881403208,
0.06577006727457047,
-0.032212745398283005,
0.016062825918197632,
0.03899085149168968,
-0.014833558350801468,
0.06267311424016953,
-0.0011219201842322946,
0.0034648007713258266,
0.027843644842505455,
-0.07367119938135147,
0.041963521391153336,
-0.003778693964704871,
0.001021634554490447,
-0.009741909801959991,
-0.006866435054689646,
-0.04483304172754288,
0.0007745226612314582,
0.005239320453256369,
0.03056085668504238,
0.0067285499535501,
-0.0488559827208519,
-0.0009199381456710398,
0.008224526420235634,
0.07166738063097,
-0.018003789708018303,
-0.025619491934776306,
0.03314598277211189,
-0.009888381697237492,
0.054219577461481094,
-0.005577861797064543,
-0.012076533399522305,
0.0415019690990448,
0.018957974389195442,
0.0428052581846714,
0.009504662826657295,
-0.012819502502679825,
0.03387196734547615,
-0.09259314835071564,
0.00031486767693422735,
-0.036050520837306976,
0.05720129236578941,
0.0011497195810079575,
0.044297464191913605,
0.042570751160383224,
0.002388095948845148,
0.016987670212984085,
-0.01283315010368824,
-0.10141336172819138,
0.017752720043063164,
-0.010656610131263733,
-0.003679568413645029,
-0.015849430114030838,
0.0033971196971833706,
0.005038656760007143,
-0.04071745276451111,
0.009606488049030304,
0.03200935199856758,
0.003716472303494811,
-0.029876789078116417,
0.0174291729927063,
-0.05427001416683197,
-0.04238688200712204,
-0.0074689630419015884,
0.011553392745554447,
0.03293581306934357,
0.03803839907050133,
0.06547916680574417,
0.041746266186237335,
-0.0026925092097371817,
0.018019748851656914,
0.029091207310557365,
-0.00019058329053223133,
-0.011980223469436169,
0.06909006834030151,
0.013753785751760006,
0.0038676587864756584,
-0.017283402383327484,
-0.004864614922553301,
0.012128167785704136,
-0.022740133106708527,
-0.019991150125861168,
-0.00133567547891289,
-0.017929084599018097,
-0.03233630210161209,
-0.0014967877650633454,
0.0019835075363516808,
0.01277744211256504,
0.009719152934849262,
0.02596314437687397,
0.038359805941581726,
-0.041706472635269165,
-0.0013935021124780178,
0.01031607948243618,
0.06792569905519485,
0.014089163392782211,
-0.022744176909327507,
-0.05173252150416374,
-0.012082664296030998,
-0.01098864246159792,
-0.0003588579420465976,
0.005060780793428421,
0.022451380267739296,
-0.035405028611421585,
-0.011147042736411095,
0.024593187496066093,
0.03323012962937355,
0.006572833750396967,
0.02796700783073902,
-0.03129454702138901,
0.05453387647867203,
0.000045462737034540623,
0.029084043577313423,
0.038183484226465225,
-0.015733972191810608,
0.014766005799174309,
0.02409832924604416,
-0.04643850028514862,
-0.07593251764774323,
-0.0316040925681591,
0.02538829669356346,
0.022689107805490494,
-0.03714403882622719,
0.020352277904748917,
-0.051026601344347,
-0.05049679055809975,
0.042874716222286224,
-0.047373201698064804,
-0.0036098966374993324,
-0.019162524491548538,
0.005831263493746519,
-0.02306094951927662,
-0.018796171993017197,
-0.05811076611280441,
0.00645800493657589,
0.0035446560941636562,
-0.008604101836681366,
-0.024827808141708374,
-0.015928704291582108,
-0.0030689125414937735,
0.004381077364087105,
0.039400119334459305,
0.013628056272864342,
0.00833398848772049,
-0.01822720654308796,
-0.02726207859814167,
-0.008035426028072834,
-0.011827638372778893,
-0.06977646797895432,
-0.012284782715141773,
0.009893140755593777,
-0.028081266209483147,
-0.02148488350212574,
-0.03571706265211105,
-0.04323011264204979,
0.05276133865118027,
-0.016939831897616386,
-0.028981072828173637,
-0.01346385758370161,
-0.022522499784827232,
0.021489161998033524,
0.02982298657298088,
0.01699240319430828,
0.022977031767368317,
0.04734303057193756,
-0.022827323526144028,
0.006423657760024071,
-0.0032559195533394814,
0.004474705085158348,
-0.022275621071457863,
0.013086028397083282,
-0.026335274800658226,
0.016853386536240578,
-0.02643752470612526,
0.05887719988822937,
0.002552109071984887,
0.0364113487303257,
-0.0020499159581959248,
-0.03518048673868179,
0.005058402195572853,
0.04491211101412773,
0.004324834793806076,
-0.013173067942261696,
0.027998067438602448,
0.00842238962650299,
0.020566463470458984,
-0.044932976365089417,
-0.025514328852295876,
0.002096569864079356,
0.04032885283231735,
0.04605506733059883,
-0.031853996217250824,
-0.016400814056396484,
-0.010688584297895432,
-0.02818600833415985,
0.021150672808289528,
-0.03928869217634201,
0.09856557846069336,
0.0001779154408723116,
-0.014672653749585152,
0.034399643540382385,
0.002986454637721181,
-0.006898506544530392,
0.006895307917147875,
-0.01135176420211792,
0.008686286397278309,
-0.06449611485004425,
0.03456874564290047,
-0.024350494146347046,
0.01063363254070282,
-0.07890518754720688,
-0.02503015659749508,
0.03856721892952919,
0.0024820424150675535,
-0.02920045703649521,
-0.03911087289452553,
-0.017120951786637306,
-0.03754410147666931,
-0.02417997270822525,
-0.009075001813471317,
0.06454786658287048,
0.01932489313185215,
-0.004493186715990305,
0.03178003430366516,
0.007218294311314821,
0.03361063823103905,
-0.007864262908697128,
-0.009330264292657375,
-0.02002301625907421,
-0.004461338743567467,
-0.02529604360461235,
0.0022216509096324444,
0.02910584583878517,
-0.03553343936800957,
-0.02633952908217907,
-0.0013536987826228142,
-0.00016438777674920857,
0.0034477824810892344,
-0.04090360924601555,
0.03620043769478798,
0.03459709510207176,
-0.01769736036658287,
-0.020627152174711227,
0.0071227699518203735,
-0.023123957216739655,
0.004488229285925627,
0.04054005444049835,
0.03157402575016022,
-0.0015038796700537205,
-0.009259756654500961,
-0.03719715029001236,
-0.02355419471859932,
0.0016058458713814616,
-0.005810218397527933,
0.020013725385069847,
0.042424872517585754,
-0.028959479182958603,
0.01580493152141571,
-0.003288304666057229,
-0.011344443075358868,
0.048625268042087555,
-0.026753103360533714,
-0.03377382084727287,
0.019745292142033577,
-0.015881620347499847,
-0.015286407433450222,
-0.05754096060991287,
-0.03581377863883972,
0.003620874835178256,
0.058950453996658325,
-0.01525972317904234,
0.05177852883934975,
-0.003020936157554388,
-0.012492433190345764,
-0.01043085940182209,
-0.02413635142147541,
-0.002523448783904314,
-0.022875702008605003,
0.0017410351429134607,
0.018718888983130455,
-0.008940357714891434,
-0.011446064338088036,
0.036822281777858734,
0.013378903269767761,
-0.031071217730641365,
-0.020575612783432007,
0.02197800762951374,
0.01794518530368805,
0.028149181976914406,
-0.04838594049215317,
-0.010948153212666512,
0.02673017606139183,
-0.03788955882191658,
0.04610244557261467,
-0.022197166457772255,
0.029587414115667343,
0.016897933557629585,
0.01005767472088337,
-0.01982860267162323,
-0.041419584304094315,
0.01332943793386221,
-0.031224505975842476,
-0.011831489391624928,
0.025934476405382156,
-0.015808135271072388,
0.014999439008533955,
0.02554461546242237,
0.01772332191467285,
0.03211818262934685,
0.0017535226652398705,
-0.005076552275568247,
-0.025384142994880676,
-0.01941291242837906,
-0.019382813945412636,
-0.026553375646471977,
0.011200950480997562,
0.03651304543018341,
-0.04520523548126221,
0.025569887831807137,
-0.014037166722118855,
-0.0016494374722242355,
0.0016048902180045843,
0.02244604378938675,
0.028489703312516212,
0.09416316449642181,
0.005555583629757166,
0.0012189619010314345,
-0.0235139187425375,
0.043981920927762985,
0.12477432191371918,
0.05165945366024971,
0.01988230273127556,
-0.046242956072092056,
0.01492671761661768,
-0.024141686037182808,
-0.0062147267162799835,
0.0022677909582853317,
0.05917537212371826,
-0.013326802290976048,
0.00011416251072660089,
0.04011233150959015,
0.04234310984611511,
-0.0405905582010746,
0.006229930557310581,
0.034644268453121185,
-0.03153828904032707,
-0.008693470619618893,
-0.019842687994241714,
0.026688531041145325,
0.0247497595846653,
0.029825935140252113,
0.016594907268881798,
0.029402585700154305,
-0.042749833315610886,
-0.013660689815878868,
-0.016841908916831017,
-0.07330811768770218,
0.05290906876325607,
-0.034282270818948746,
-0.011971286498010159,
0.020661132410168648,
-0.022604774683713913,
-0.017992261797189713,
-0.04984179511666298,
0.04249802604317665,
-0.012146780267357826,
0.008301212452352047,
-0.012015441432595253,
0.011968370527029037,
0.022556837648153305,
0.014733103103935719,
-0.009846131317317486,
0.005900183226913214,
-0.03718157485127449,
0.004890028852969408,
-0.02933233231306076,
0.03362338989973068,
-0.019374791532754898,
0.011810424737632275,
-0.0020324354991316795,
0.009016062133014202,
0.02133609727025032,
-0.04828065633773804,
-0.04851173982024193,
0.0236200038343668,
0.05471111834049225,
0.008811620064079762,
-0.013727250508964062,
0.016325073316693306,
0.013823569752275944,
-0.003889670828357339,
0.03456984460353851,
-0.04091149568557739,
0.004421160090714693,
0.007230335846543312,
-0.004359768703579903,
0.09191763401031494,
-0.03639862313866615,
-0.03009975142776966,
-0.03191513195633888,
0.010560275986790657,
-0.06667206436395645,
0.008822490461170673,
-0.004548345692455769,
0.03479418903589249,
0.04546993598341942,
0.014967028982937336,
0.010849669575691223,
-0.0035638923291116953,
-0.07123502343893051,
0.026040831580758095,
0.009199039079248905,
-0.019340775907039642,
-0.029098300263285637,
-0.010931185446679592,
-0.020514732226729393,
0.049849554896354675,
-0.02177375927567482,
-0.028531435877084732,
-0.014427786692976952,
0.03232838958501816,
0.04708041250705719,
-0.04879213869571686,
-0.04180271551012993,
0.00991757120937109,
-0.04365421086549759,
0.002766906749457121,
0.014901883900165558,
0.05694250762462616,
-0.006202833727002144,
0.02185802161693573,
0.04297621175646782,
-0.0030947569757699966,
-0.03379325941205025,
0.02728593535721302,
0.007970273494720459,
-0.025457071140408516,
-0.02484770305454731,
0.01801183633506298,
0.015016884543001652,
-0.07142691314220428,
-0.044096413999795914,
-0.0204720851033926,
-0.014093341305851936,
-0.015090445056557655,
0.02624448575079441,
0.0277690626680851,
0.0639343112707138,
-0.03513326868414879,
0.0036868741735816,
-0.051030125468969345,
0.015651747584342957,
-0.06279867887496948,
-0.030599946156144142,
0.018810182809829712,
0.0015335222706198692,
-0.014772969298064709,
0.021239453926682472,
-0.046213917434215546,
0.013461138121783733,
-0.020469222217798233,
-0.003211618633940816,
0.007898670621216297,
-0.016081005334854126,
0.032675426453351974,
-0.005662280600517988,
0.017188314348459244,
-0.02824743464589119,
-0.019140949472784996,
-0.01990298554301262,
-0.043687280267477036,
-0.07347974926233292,
0.007823269814252853,
-0.0017456859350204468,
0.033657509833574295,
-0.003838155884295702,
-0.011114845052361488,
-0.015801310539245605,
0.08410538733005524,
-0.015925191342830658,
-0.042517248541116714,
0.00922423042356968,
0.013624675571918488,
0.03183953836560249,
-0.03574362397193909,
0.0226333886384964,
-0.03800401836633682,
0.0024269912391901016,
0.018130959942936897,
-0.0023762129712849855,
-0.00708455964922905,
0.02600722946226597,
0.012492784298956394,
0.004046172834932804,
0.03210262209177017,
-0.020455125719308853,
0.012274599634110928,
0.02440943568944931,
0.05007590353488922,
0.005053509958088398,
0.03355826064944267,
0.047749727964401245,
0.02780252695083618,
-0.09747696667909622,
0.006716194096952677,
0.014462892897427082,
-0.007786475587636232,
0.03259981796145439,
-0.028616085648536682,
0.043088801205158234,
0.01649758405983448,
-0.0633465126156807,
0.017374901100993156,
-0.05722358450293541,
0.009012410417199135,
-0.055589526891708374,
-0.03165150061249733,
0.005207639187574387,
0.02008005976676941,
0.03156287968158722,
-0.0037246530409902334,
0.013553572818636894,
-0.0066057913936674595,
0.006379616446793079,
-0.01390219945460558,
0.03698670491576195,
0.04580630734562874,
-0.020038628950715065,
0.025958962738513947,
0.05397048592567444,
-0.023546380922198296,
0.013661522418260574,
0.01130239199846983,
-0.02886585332453251,
0.005833195056766272,
-0.018847770988941193,
-0.0016984357498586178,
-0.0033937031403183937,
0.059095948934555054,
0.0284370519220829,
-0.007970998995006084,
-0.008093799464404583,
0.006547203753143549,
-0.013488628901541233,
-0.032735761255025864,
-0.021020425483584404,
0.04873362183570862,
-0.01682799495756626,
-0.011628249660134315,
-0.004575084429234266,
0.015493231825530529,
0.0018699237843975425,
-0.040692586451768875,
0.012851935811340809,
-0.004260064568370581,
-0.004557033535093069,
0.01108845230191946,
-0.015228210017085075,
-0.042972713708877563,
-0.001363816438242793,
0.047845497727394104,
-0.007371606770902872,
-0.02800307795405388,
0.009626021608710289,
-0.012017698027193546,
-0.014831757172942162,
-0.028109917417168617,
0.04786871001124382,
-0.008514286950230598,
-0.005054094363003969,
0.02411152422428131,
0.008148914203047752,
-0.016151007264852524,
-0.021014153957366943,
-0.07381407916545868,
0.024890681728720665,
0.0466810017824173,
0.04254154488444328,
0.04254889115691185,
0.030296625569462776,
-0.048982854932546616,
-0.01166414376348257,
-0.08014192432165146,
0.023632099851965904,
-0.04052006080746651,
-0.00999339111149311,
-0.0014298842288553715,
-0.08118265122175217,
0.01907120645046234,
0.015272088348865509,
0.04207334667444229,
-0.002637705532833934,
-0.04151614010334015,
0.013705497607588768,
0.002296309918165207,
-0.006570462137460709,
0.0054282499477267265,
0.0024728579446673393,
-0.014449892565608025,
-0.02268427610397339,
-0.007878157310187817,
0.033347614109516144,
0.010847078636288643,
-0.00016400431923102587,
0.002433485584333539,
0.0011437119683250785,
0.04517812281847,
-0.028489137068390846,
-0.04868507385253906,
0.03141075372695923,
0.05042903497815132,
-0.007106288336217403,
0.07013459503650665,
0.007709241006523371,
-0.016117440536618233,
-0.024865245446562767,
-0.020252645015716553,
-0.07956089824438095,
0.007523081265389919,
-0.028817439451813698,
-0.016680588945746422,
0.002419817028567195,
-0.012797622010111809,
0.019489048048853874,
-0.062458351254463196,
0.01825781539082527,
0.04785240441560745,
-0.0608704537153244,
-0.021648110821843147,
0.009271766990423203,
0.05047772824764252,
0.04274493083357811,
-0.04462392255663872,
0.020291434600949287,
0.01513041090220213,
0.010623295791447163,
-0.04613639414310455,
0.01689896173775196,
0.020132509991526604,
0.01869191974401474,
0.004286638461053371,
0.040707461535930634,
-0.016706202179193497,
0.02038753405213356,
-0.00611789571121335,
0.03914232924580574,
-0.023145029321312904,
-0.037397995591163635,
0.007639710791409016,
-0.02371947653591633,
-0.004873314406722784,
0.009366870857775211,
0.009360122494399548,
0.0600893534719944,
0.005289528518915176,
-0.00503560109063983,
-0.050176430493593216,
0.03330041840672493,
-0.01796266995370388,
0.04404515027999878,
-0.04528720676898956,
0.003126315074041486,
0.009401711635291576,
0.025730865076184273,
0.029276227578520775,
-0.007329063024371862,
0.0325770229101181,
-0.018929369747638702,
0.011678597889840603,
0.032548923045396805,
-0.029239164665341377,
-0.05832906439900398,
-0.02347087673842907,
-0.028232717886567116,
-0.031132442876696587,
0.02836710959672928,
0.05447501316666603,
0.01684884913265705,
0.05634626746177673,
-0.01778552308678627,
-0.01382907573133707,
0.06917431950569153,
-0.07073357701301575,
0.014207743108272552,
-0.03291773423552513,
0.016238149255514145,
0.0029389471746981144,
0.02807614766061306
] |
<p>Imagine there's a sphere of radius $R$ which has constant density $\rho$ and you can stand anywhere inside of the sphere. Wherever you stand within the sphere, you'll only feel gravity coming from the mass at smaller radii than the point at which you're standing. That is, you could be standing at some point with radius $r$ and if somebody come along and added more mass to the sphere so that the radius was extended to $R'>R$ you would feel no effect because you're insensitive to it.</p>
<p>Puzzle: What happens if somebody comes by and adds mass to the sphere until it extends out to infinity? Now the mass distribution is uniform everywhere in space so you'd expect no gravitational pull in any direction, by symmetry. What happens? Do you suddenly stop feeling a force? If you have an issue with extending the mass to infinity then imagine that we've added a point to $\mathbb R^4$ so that we're on $S^4$.</p>
<p>What's the intuitive way to understand what's happening in this limit? What's the technical explanation? Is it a boundary value issue?</p>
| 8,508 |
[
-0.0027872039936482906,
-0.00912938266992569,
0.005647628102451563,
-0.01326336432248354,
-0.01142739038914442,
0.01729045808315277,
0.003775441786274314,
-0.029667649418115616,
-0.015709977596998215,
-0.009652229025959969,
0.021434437483549118,
0.013676120899617672,
0.05722487345337868,
-0.015082009136676788,
0.022677237167954445,
-0.014523444697260857,
-0.02373560331761837,
-0.032971132546663284,
-0.013853789307177067,
-0.03891238942742348,
-0.009749212302267551,
0.030285406857728958,
0.02222425490617752,
-0.0022826020140200853,
-0.02064751833677292,
0.0021883142180740833,
0.026780812069773674,
-0.011342276819050312,
0.0008055600337684155,
0.05220668017864227,
-0.011859300546348095,
-0.004269993398338556,
-0.011475141160190105,
0.03067595325410366,
0.033546775579452515,
-0.0009164527291432023,
-0.02367829903960228,
0.005459064617753029,
-0.012750692665576935,
0.02050529234111309,
-0.07422985136508942,
-0.009089097380638123,
-0.006004296708852053,
0.050287894904613495,
-0.008279891684651375,
-0.016022667288780212,
0.04578349366784096,
0.0104796988889575,
0.06496874988079071,
-0.05404004454612732,
0.059343371540308,
0.034760214388370514,
0.05371365323662758,
0.023796433582901955,
0.03303426131606102,
-0.015314308926463127,
0.04960627108812332,
0.054471489042043686,
-0.011372426524758339,
-0.039083100855350494,
-0.03550831228494644,
-0.015099074691534042,
-0.030219096690416336,
-0.0553625114262104,
0.009489214047789574,
0.029600242152810097,
-0.005050718318670988,
0.011613466776907444,
0.004540341906249523,
-0.042960844933986664,
0.01898174174129963,
0.025341873988509178,
0.02693316340446472,
0.0074984547682106495,
0.025919044390320778,
0.02201150171458721,
0.02001938410103321,
0.001910570077598095,
0.03516525775194168,
-0.0009898358257487416,
0.002717781811952591,
-0.006707645021378994,
0.04948795586824417,
0.07453884184360504,
0.026597049087285995,
-0.008257928304374218,
0.031833890825510025,
0.013970871455967426,
0.0034281820990145206,
0.05723606422543526,
-0.00023688380315434188,
-0.005605366546660662,
0.03278158977627754,
-0.02699960581958294,
-0.017039725556969643,
0.04752270132303238,
-0.016658978536725044,
0.046445079147815704,
-0.018868546932935715,
-0.011337029747664928,
-0.00027251639403402805,
-0.013136615045368671,
-0.012277991510927677,
0.07034342736005783,
0.021913962438702583,
-0.03576930984854698,
-0.06859611719846725,
0.01260006707161665,
-0.00031525202211923897,
-0.007218805141746998,
-0.053602926433086395,
0.006676827557384968,
0.012502236291766167,
-0.0025945324450731277,
0.008424364030361176,
-0.02098577469587326,
-0.002881753956899047,
-0.043731238692998886,
0.008111655712127686,
0.0346970409154892,
0.05127193033695221,
-0.003909097984433174,
0.02263384312391281,
-0.05273715406656265,
-0.05784381553530693,
0.03845512121915817,
0.030186064541339874,
-0.07156277447938919,
-0.012567276135087013,
-0.002811882644891739,
0.03280132636427879,
0.018047824501991272,
-0.03149648383259773,
0.016399728134274483,
0.030805733054876328,
-0.006223141681402922,
-0.07517460733652115,
-0.045004092156887054,
0.05968761816620827,
0.023273052647709846,
-0.005544255021959543,
-0.05840674415230751,
-0.0059966230764985085,
0.01675311289727688,
0.08570262044668198,
0.0008682319312356412,
-0.009532207623124123,
0.014784359373152256,
0.05346433073282242,
0.0187976211309433,
-0.03404509276151657,
0.015802837908267975,
-0.05870223790407181,
-0.03536919131875038,
0.014681260101497173,
-0.057430945336818695,
0.012155275791883469,
0.014507622458040714,
0.034228939563035965,
-0.04129834473133087,
0.05904829502105713,
-0.014421009458601475,
0.019520582631230354,
0.006977389100939035,
-0.028363775461912155,
-0.006815330125391483,
0.08796947449445724,
0.03029101900756359,
-0.02774191088974476,
0.06018101051449776,
0.029227565973997116,
0.03956322371959686,
0.01565055549144745,
0.032893043011426926,
0.009019064716994762,
-0.036065153777599335,
0.005166749469935894,
-0.017561107873916626,
0.015165161341428757,
0.02654031664133072,
-0.04353225603699684,
-0.01524266880005598,
0.015963004902005196,
-0.030863460153341293,
-0.015228977426886559,
0.013051086105406284,
-0.012238421477377415,
-0.027386270463466644,
-0.029242832213640213,
-0.045819345861673355,
-0.0020719149615615606,
-0.08532293885946274,
0.02129906229674816,
0.017212631180882454,
-0.029181504622101784,
0.02411791868507862,
0.036370426416397095,
0.022066276520490646,
-0.05455829203128815,
-0.02757170982658863,
-0.02963506616652012,
0.03567228838801384,
0.012995822355151176,
-0.023456308990716934,
0.015416642650961876,
0.058640118688344955,
0.026630744338035583,
0.02691095508635044,
-0.004979773890227079,
-0.02358422242105007,
-0.02498513273894787,
0.009456691332161427,
-0.004236198961734772,
0.028329307213425636,
0.006210600957274437,
0.02222389169037342,
-0.022451506927609444,
0.0014619530411437154,
-0.023047341033816338,
0.05452725663781166,
-0.03585292771458626,
0.07613172382116318,
0.021854860708117485,
0.014142184518277645,
-0.012076438404619694,
0.048776522278785706,
0.026286663487553596,
-0.01713656820356846,
-0.04188757762312889,
-0.04968823119997978,
-0.024253973737359047,
-0.0013492436846718192,
0.022075321525335312,
0.025364186614751816,
-0.00702673988416791,
0.011176621541380882,
-0.00004982665632269345,
0.017520051449537277,
-0.019976815208792686,
-0.003677557921037078,
-0.0175482090562582,
-0.011974607594311237,
0.051233720034360886,
0.01749713346362114,
0.017198868095874786,
0.015441554598510265,
0.0258010383695364,
0.019344180822372437,
0.020420851185917854,
-0.006665387656539679,
0.000019732733562705107,
0.0006593558355234563,
-0.024703336879611015,
0.03473413363099098,
-0.00926226656883955,
0.00820393580943346,
0.021781759336590767,
0.0009652627632021904,
0.0068681794218719006,
0.0379766970872879,
0.005689620040357113,
-0.016414513811469078,
-0.0760628953576088,
-0.032894086092710495,
0.02703971229493618,
0.033223893493413925,
-0.020447127521038055,
-0.03360946848988533,
0.017121057957410812,
-0.05654565244913101,
0.009670780040323734,
-0.01534177828580141,
-0.02533537894487381,
-0.044249627739191055,
0.016970625147223473,
0.03969978168606758,
0.016919994726777077,
0.014926678501069546,
-0.04237009584903717,
-0.034177444875240326,
-0.012142734602093697,
-0.02056310325860977,
-0.01847253367304802,
0.029420871287584305,
-0.03323432803153992,
0.019345099106431007,
-0.04072785750031471,
-0.005436502397060394,
0.029732907190918922,
0.04350565746426582,
0.010742356069386005,
0.020704908296465874,
-0.005594226997345686,
0.009599900804460049,
-0.005780356004834175,
-0.0039667412638664246,
0.003681871807202697,
-0.024113565683364868,
0.020942943170666695,
0.061084043234586716,
-0.039125919342041016,
-0.015543394722044468,
0.039994221180677414,
-0.05779976397752762,
-0.047352422028779984,
-0.009326969273388386,
-0.0026959115639328957,
0.0341951958835125,
-0.02952054888010025,
0.006390677765011787,
0.0014434801414608955,
-0.03184274211525917,
-0.03275799751281738,
-0.042471084743738174,
-0.037201084196567535,
0.036729928106069565,
-0.018678005784749985,
0.046823009848594666,
0.04205232486128807,
-0.05515460669994354,
0.07986047863960266,
0.027685854583978653,
0.032924313098192215,
0.0011759945191442966,
0.005237297620624304,
0.005071415565907955,
-0.009758776985108852,
-0.00846452359110117,
0.026124363765120506,
-0.007416285574436188,
-0.012958270497620106,
0.08289068937301636,
0.04692566767334938,
-0.042571958154439926,
0.006405567284673452,
-0.013075930066406727,
0.008741446770727634,
0.016407813876867294,
-0.017807606607675552,
0.045378848910331726,
-0.0019138125935569406,
0.010829770937561989,
-0.03615088760852814,
-0.011516042985022068,
0.020083479583263397,
0.01758268103003502,
-0.042352791875600815,
0.03984271362423897,
-0.004445231519639492,
0.0028733201324939728,
-0.013853794895112514,
0.036342933773994446,
-0.008929410949349403,
-0.02709496207535267,
-0.00008350578718818724,
0.008955499157309532,
0.04532293602824211,
-0.026960160583257675,
-0.03237657621502876,
0.016563137993216515,
0.05620857700705528,
-0.025089921429753304,
-0.039480362087488174,
0.022661279886960983,
0.010334896855056286,
0.04550207033753395,
0.012590267695486546,
-0.007994266226887703,
0.020266814157366753,
0.042879391461610794,
0.002632396761327982,
-0.01651899144053459,
-0.06127918139100075,
-0.011082926765084267,
-0.06727463006973267,
0.008055668324232101,
-0.03604791313409805,
0.02441253885626793,
-0.010537968948483467,
0.01932559907436371,
0.049862250685691833,
0.02532283216714859,
0.014352180995047092,
0.004393646027892828,
-0.0888444259762764,
0.01248904224485159,
-0.0406562015414238,
-0.004254536237567663,
-0.0263417549431324,
0.00473477877676487,
-0.012413269840180874,
-0.023238033056259155,
0.007675355765968561,
-0.011561460793018341,
-0.01667448878288269,
-0.07919811457395554,
-0.001827453961595893,
-0.0356827937066555,
-0.04818080738186836,
-0.03125297650694847,
0.0249449722468853,
0.028695082291960716,
-0.0208705123513937,
0.03283112868666649,
0.03850344195961952,
-0.031461577862501144,
0.021034888923168182,
-0.028955558314919472,
-0.005617909133434296,
-0.014206238090991974,
0.006737090181559324,
0.01806829869747162,
0.04091409221291542,
-0.013648669235408306,
0.0024048895575106144,
-0.012909739278256893,
0.04101626202464104,
-0.013523020781576633,
0.008746125735342503,
-0.0076837134547531605,
-0.06942300498485565,
-0.024205463007092476,
-0.008222861215472221,
0.018785815685987473,
-0.012157220393419266,
0.004671997390687466,
0.033266447484493256,
-0.027347344905138016,
-0.01760745607316494,
0.033808860927820206,
0.038937970995903015,
0.009522912092506886,
-0.05395440757274628,
-0.041362497955560684,
-0.017891913652420044,
-0.028669998049736023,
0.013186879456043243,
0.033702410757541656,
-0.02017749473452568,
-0.05869079381227493,
0.020982535555958748,
0.011117552407085896,
0.010279110632836819,
-0.021557362750172615,
-0.03304855898022652,
-0.01915660873055458,
0.04198742285370827,
-0.027311084792017937,
0.009386667981743813,
0.02088051289319992,
-0.0045915814116597176,
0.06749818474054337,
-0.016181819140911102,
-0.008165275678038597,
-0.07970722764730453,
-0.013986803591251373,
0.045362334698438644,
-0.006062344182282686,
0.012584008276462555,
0.008789547719061375,
-0.051334086805582047,
-0.020635824650526047,
0.029283111914992332,
-0.030512947589159012,
0.000845210044644773,
-0.03379722312092781,
-0.0019517206819728017,
-0.022781187668442726,
-0.0529998317360878,
-0.058815229684114456,
0.001480634673498571,
-0.002924461616203189,
-0.011414525099098682,
-0.018745116889476776,
0.0224236398935318,
-0.0031507634557783604,
0.020043184980750084,
-0.006716595496982336,
0.024466317147016525,
0.005156382918357849,
-0.004006638191640377,
-0.011447185650467873,
0.013400605879724026,
-0.003936415538191795,
-0.06360990554094315,
-0.02063954807817936,
0.022405870258808136,
-0.0410287044942379,
0.045558538287878036,
-0.05983613431453705,
-0.04878194257616997,
0.03499968349933624,
-0.01712481863796711,
-0.0067577906884253025,
-0.00010361654130974784,
-0.032301630824804306,
0.02573833242058754,
0.04292326048016548,
-0.009057310409843922,
0.052849166095256805,
0.0056531550362706184,
0.005557097494602203,
-0.006002590525895357,
-0.014637615531682968,
0.05212259292602539,
-0.0330568365752697,
-0.02370796911418438,
-0.0045455810613930225,
-0.021442202851176262,
-0.04176662862300873,
0.040110014379024506,
0.02307528629899025,
0.004016328603029251,
-0.00922637153416872,
-0.04703632742166519,
0.03495346009731293,
0.04959039017558098,
0.0542445071041584,
0.038589708507061005,
0.01919271983206272,
0.01295105367898941,
0.04063134640455246,
-0.017537277191877365,
-0.019114719703793526,
0.011684928089380264,
0.005547352600842714,
0.0367557518184185,
-0.0010537734488025308,
0.022221198305487633,
0.0073549156077206135,
-0.007752314209938049,
0.01568334549665451,
-0.047379571944475174,
0.09652259945869446,
-0.013677584938704967,
-0.02369004115462303,
0.0188932903110981,
-0.0120429378002882,
-0.005212802905589342,
-0.045503564178943634,
-0.03701048716902733,
0.022998996078968048,
-0.029399538412690163,
0.02767515555024147,
0.03864535316824913,
0.03994935378432274,
-0.10809590667486191,
-0.03914470225572586,
0.03841231018304825,
0.014975612051784992,
0.0038474267348647118,
-0.05146175995469093,
0.0014995471574366093,
-0.07209520041942596,
-0.046507008373737335,
-0.019455114379525185,
0.026953577995300293,
-0.03453414514660835,
0.011390717700123787,
-0.0010289739584550261,
0.045079607516527176,
0.04402739554643631,
-0.06101004406809807,
0.007792294956743717,
0.034468211233615875,
0.040046680718660355,
-0.008589393459260464,
-0.011311804875731468,
0.06684119254350662,
-0.02453031577169895,
-0.04623546078801155,
-0.005807141773402691,
-0.048405278474092484,
0.006264401134103537,
-0.04454578086733818,
-0.017744582146406174,
0.01807280443608761,
0.011643829755485058,
0.008930133655667305,
-0.04617952182888985,
-0.020627042278647423,
-0.0015058298595249653,
0.026384476572275162,
0.01345490850508213,
0.00418851338326931,
0.0021139776799827814,
-0.03843744844198227,
0.02961692400276661,
0.013274189084768295,
0.02133817784488201,
-0.008882060647010803,
0.08816111087799072,
0.0157371424138546,
-0.011677991598844528,
0.0051658195443451405,
0.01382712833583355,
0.02127586491405964,
0.006312575191259384,
-0.03942417353391647,
0.02243207022547722,
-0.0029875345062464476,
-0.03815418854355812,
-0.010324549861252308,
-0.048142120242118835,
0.010662013664841652,
0.037426065653562546,
-0.016435550525784492,
0.04172925651073456,
0.03484693914651871,
-0.04345293715596199,
0.004367996007204056,
-0.013852622359991074,
-0.015885695815086365,
-0.002294636331498623,
-0.01553463377058506,
0.018846670165657997,
-0.016443371772766113,
0.02009023353457451,
0.030576804652810097,
0.04604597017168999,
-0.0427018441259861,
0.045811526477336884,
0.03981040045619011,
0.03699740394949913,
0.043082647025585175,
-0.01794632524251938,
-0.016118064522743225,
0.016524136066436768,
-0.028719965368509293,
0.024784423410892487,
0.0028155602049082518,
-0.011900736019015312,
0.02271091938018799,
0.02170499600470066,
0.01926281675696373,
-0.03403132036328316,
-0.02145976945757866,
-0.014779000543057919,
-0.014334009028971195,
0.04198360815644264,
-0.003918322268873453,
-0.0047407858073711395,
-0.01001916453242302,
-0.017497235909104347,
0.01696310192346573,
0.01769641786813736,
-0.01322042103856802,
-0.05315349996089935,
-0.011098397895693779,
-0.04076175019145012,
-0.038946159183979034,
0.04952574148774147,
0.004895760677754879,
-0.02645999938249588,
0.04147237911820412,
-0.05463685467839241,
0.029011161997914314,
0.032630205154418945,
0.032534159719944,
-0.033545807003974915,
0.045766718685626984,
0.00427155289798975,
0.018808459863066673,
-0.011002998799085617,
0.018180420622229576,
0.10491248220205307,
0.07085530459880829,
0.0019692350178956985,
-0.041889529675245285,
0.005254191346466541,
-0.009896001778542995,
-0.001237488933838904,
-0.05992686748504639,
0.013564386405050755,
-0.024118861183524132,
0.026885371655225754,
0.004483901895582676,
0.08659887313842773,
-0.028170444071292877,
0.010481977835297585,
0.051966797560453415,
-0.0343569815158844,
-0.02001952938735485,
-0.018382618203759193,
0.01357946451753378,
-0.005497296340763569,
0.023686397820711136,
-0.0444498136639595,
0.04352540522813797,
-0.02259806916117668,
0.019856490194797516,
-0.052998654544353485,
-0.012226046063005924,
-0.010493382811546326,
-0.008899047039449215,
-0.06358552724123001,
0.026310179382562637,
-0.0077001494355499744,
-0.07105357199907303,
-0.03472750633955002,
0.008727055974304676,
0.007354430854320526,
-0.0182502344250679,
0.008947070688009262,
0.04579544439911842,
-0.013282635249197483,
0.03067508153617382,
0.013607475906610489,
0.049505215138196945,
-0.015589426271617413,
0.012595284730196,
-0.01710977591574192,
0.07389786094427109,
-0.022981125861406326,
-0.0006478727445937693,
0.02634039893746376,
0.008326851762831211,
-0.005830184556543827,
-0.04663723334670067,
-0.022396745160222054,
-0.03443962335586548,
0.043736495077610016,
0.03898391127586365,
-0.01920233480632305,
0.03135741129517555,
0.031336843967437744,
0.0034770043566823006,
0.008533165790140629,
-0.0036979345604777336,
-0.007001234218478203,
0.002769767539575696,
0.01051322277635336,
0.03246806189417839,
-0.018680553883314133,
-0.016341248527169228,
-0.038787733763456345,
0.022426053881645203,
-0.041382014751434326,
0.0043404484167695045,
-0.003932177554816008,
0.024443339556455612,
0.04265500232577324,
-0.002692214911803603,
0.002043343847617507,
-0.037899527698755264,
-0.040285464376211166,
-0.003149587195366621,
-0.023140819743275642,
0.009537821635603905,
-0.028366222977638245,
-0.029002800583839417,
-0.024556422606110573,
0.025284714996814728,
-0.009807202965021133,
-0.02757124789059162,
0.006367256864905357,
0.05857187509536743,
-0.0034941346384584904,
0.007006353698670864,
-0.005658401176333427,
0.012561243958771229,
-0.03423353657126427,
0.0423320010304451,
-0.009507729671895504,
-0.0026470860466361046,
0.020936908200383186,
0.013111214153468609,
0.029223306104540825,
0.03030402585864067,
-0.03160044550895691,
0.018672367557883263,
0.03579119220376015,
-0.01980060525238514,
-0.008692668750882149,
0.00262834201566875,
-0.020605726167559624,
-0.04253729432821274,
-0.0371142253279686,
-0.011033657938241959,
-0.02919348143041134,
0.0007501175859943032,
0.028965795412659645,
-0.019905535504221916,
0.02306538261473179,
-0.017864888533949852,
-0.008920582942664623,
-0.018176881596446037,
-0.00572208734229207,
-0.0775105357170105,
-0.025040069594979286,
-0.003515949472784996,
-0.0035743440967053175,
0.022673718631267548,
0.03675004839897156,
-0.018388645723462105,
-0.02869509533047676,
-0.026847321540117264,
-0.0032882860396057367,
0.0003038605209439993,
0.006762524135410786,
0.01589185744524002,
-0.02666599489748478,
0.0007310585351660848,
0.01933104544878006,
-0.040131695568561554,
0.020791204646229744,
-0.030391303822398186,
-0.060173891484737396,
0.005126040894538164,
0.005289630498737097,
0.03891436383128166,
0.01752670481801033,
-0.01787460781633854,
-0.027397237718105316,
0.06037190183997154,
-0.008606765419244766,
-0.0004225573211442679,
-0.01519354060292244,
-0.003285774262621999,
-0.026599081233143806,
0.006720761302858591,
0.06731545180082321,
-0.03497171029448509,
-0.0018651161808520555,
-0.003747000591829419,
0.020894022658467293,
-0.04258376732468605,
0.005938382353633642,
0.020991133525967598,
-0.03888556361198425,
-0.01689111813902855,
-0.000508069118950516,
0.023504046723246574,
0.025484811514616013,
0.05233792960643768,
-0.03191807493567467,
0.023193426430225372,
-0.00732011254876852,
-0.007776095066219568,
-0.0812203586101532,
-0.01959315873682499,
0.002943099709227681,
-0.02977595292031765,
0.007781462278217077,
-0.050415586680173874,
0.017616141587495804,
0.013024588115513325,
-0.08753369748592377,
0.06366122514009476,
-0.03257222846150398,
0.015260090120136738,
-0.021293718367815018,
-0.030535228550434113,
0.015098788775503635,
0.035993289202451706,
0.053101636469364166,
0.05084532871842384,
-0.02297184430062771,
0.02425432577729225,
-0.01695850118994713,
-0.025895196944475174,
0.026935558766126633,
0.052539244294166565,
-0.011027101427316666,
-0.002039046958088875,
0.043563369661569595,
0.021494833752512932,
-0.0037721027620136738,
0.007495513651520014,
-0.0012731642927974463,
-0.003711622441187501,
0.019487174227833748,
0.018630193546414375,
-0.005149320233613253,
0.04712540656328201,
0.006386715918779373,
0.006041763350367546,
-0.029426274821162224,
0.0586310513317585,
0.013323367573320866,
-0.005740846507251263,
-0.062317002564668655,
-0.011545837856829166,
-0.0018927047494798899,
-0.03600773215293884,
-0.015637453645467758,
0.03930259495973587,
-0.03081142157316208,
0.0018071150407195091,
-0.005816433113068342,
-0.007345329970121384,
0.033137090504169464,
-0.021076248958706856,
0.013874596916139126,
-0.03551092371344566,
-0.009443467482924461,
0.03186817094683647,
0.00993407890200615,
-0.006480496842414141,
0.026783136650919914,
-0.02354864589869976,
-0.0005865515558980405,
-0.014100777916610241,
0.007683252915740013,
-0.010332153178751469,
-0.04984584078192711,
-0.010182992555201054,
-0.030541621148586273,
-0.008832055144011974,
0.029885679483413696,
-0.004515952430665493,
-0.03922906517982483,
0.05356128513813019,
0.0705871433019638,
0.015975695103406906,
-0.021143905818462372,
-0.06047776713967323,
-0.01142057217657566,
-0.10036849975585938,
0.03396282717585564,
0.015935687348246574,
-0.007250800728797913,
-0.03122604638338089,
0.0007139050867408514,
0.012287388555705547,
-0.012110993266105652,
0.05401962250471115,
0.036349959671497345,
-0.003492172108963132,
0.047343865036964417,
0.05005800351500511,
0.014679339714348316,
-0.05196327716112137,
-0.006578052882105112,
0.026934441179037094,
0.024057719856500626,
-0.023338479921221733,
0.008986827917397022,
0.014081371948122978,
-0.0003109684039372951,
-0.007513437885791063,
-0.016490865498781204,
0.026630951091647148,
0.026067163795232773,
-0.025612324476242065,
0.06652211397886276,
0.02371142990887165,
0.006197892129421234,
0.061017606407403946,
0.005725589580833912,
0.02037886343896389,
0.010654396377503872,
-0.03252329304814339,
0.004135181196033955,
0.05208827182650566,
-0.01192383375018835,
-0.021436776965856552,
-0.049275998026132584,
0.011597301810979843,
0.0011352610308676958,
-0.0048188092187047005,
-0.004011336714029312,
0.04354112222790718,
-0.06517080217599869,
-0.016552377492189407,
0.03859645128250122,
0.015550076961517334,
0.06619729846715927,
0.0058835032396018505,
-0.01441557053476572,
-0.0018770589958876371,
0.020182296633720398,
0.02459522895514965,
0.04188266769051552,
0.01967300847172737,
0.00495714507997036,
-0.04397744685411453,
0.05321522802114487,
-0.020080402493476868,
0.0003700069210026413,
0.004546886309981346,
0.03211437165737152,
-0.05230315774679184,
-0.027903685346245766,
-0.014742238447070122,
-0.033583831042051315,
0.02406303770840168,
0.044170718640089035,
0.002717746887356043,
0.0835845097899437,
0.04348824545741081,
0.010229997336864471,
0.0028512480203062296,
-0.019315199926495552,
0.028819143772125244,
0.024937059730291367,
0.002313540782779455,
0.03897323086857796,
-0.005830672569572926,
-0.018272701650857925,
-0.014407089911401272,
-0.019176719710230827,
0.02015112340450287,
0.005040672142058611,
0.017738303169608116,
0.017265554517507553,
0.010327419266104698,
-0.0011863282416015863,
-0.021236121654510498,
-0.008704272098839283,
0.0001567498838994652,
0.05338801071047783,
0.04444116726517677,
0.04863337427377701,
0.03010864183306694,
-0.010956116020679474,
-0.028438931331038475,
0.025373585522174835,
-0.06263154000043869,
-0.022798608988523483,
-0.007658340036869049,
0.015260548330843449,
-0.040247224271297455,
-0.01282686647027731
] |
<p>could exist 2 different Hamiltonians $ H1 $ and $ H2$ so</p>
<p>a) The SEMICLASSICAL eigenvalue staircase is equal i mean the expression $$ \oint _{C} p.dq = n+\alpha $$</p>
<p>but the real eigenvalues $ E_{n} (1,n) $ and $ E_{n}(2,n) $ are completely different</p>
| 8,509 |
[
-0.036234050989151,
-0.02629835158586502,
-0.015093107707798481,
-0.020703360438346863,
0.04298309236764908,
0.0016015622531995177,
-0.05258633568882942,
-0.036584094166755676,
0.03098413534462452,
-0.027264419943094254,
0.01787608489394188,
0.0016840602038428187,
0.017585108056664467,
0.04589375481009483,
0.026359939947724342,
0.02137072943150997,
0.01755107194185257,
-0.015587905421853065,
-0.01171331387013197,
0.031008685007691383,
-0.004515284672379494,
0.012255381792783737,
0.012902243062853813,
-0.01364415418356657,
-0.0038817450404167175,
0.014900974929332733,
0.03249374404549599,
0.03204534947872162,
0.019616400822997093,
0.060934752225875854,
0.0058362241834402084,
0.017778415232896805,
0.01453421451151371,
0.06017932668328285,
0.010053252801299095,
0.0077307759784162045,
-0.03125970438122749,
-0.03380850329995155,
-0.014155074954032898,
0.03047783672809601,
-0.024650124832987785,
-0.051544614136219025,
-0.004323471337556839,
0.051578499376773834,
-0.012819992378354073,
0.014867089688777924,
-0.0029613266233354807,
-0.02902699075639248,
0.024999815970659256,
-0.06252473592758179,
0.05800367146730423,
-0.006609866861253977,
0.017904983833432198,
0.017723161727190018,
-0.012790749780833721,
-0.0060099768452346325,
0.04484548047184944,
0.10851670801639557,
0.011622115969657898,
-0.05049937218427658,
-0.017443712800741196,
-0.029912032186985016,
0.0050630406476557255,
0.002329952083528042,
-0.051715187728405,
0.04003414511680603,
0.0227963849902153,
-0.05280785635113716,
-0.03153102472424507,
-0.01767883636057377,
0.004829964134842157,
-0.011094111949205399,
0.0025054370053112507,
-0.04533102363348007,
0.05808788165450096,
-0.031006572768092155,
-0.006658226251602173,
0.03273279592394829,
0.04628591239452362,
0.019988233223557472,
0.042708832770586014,
0.018607892096042633,
0.0508534274995327,
-0.006066886708140373,
-0.00936736911535263,
-0.0025853777769953012,
0.04606219381093979,
0.015224704518914223,
-0.004916326142847538,
0.009892746806144714,
0.020954467356204987,
0.054070550948381424,
0.02440168522298336,
-0.012265913188457489,
-0.021274622529745102,
-0.020440788939595222,
-0.00031694304198026657,
0.036895960569381714,
-0.017991669476032257,
-0.013009137474000454,
-0.004187802318483591,
-0.04277881607413292,
0.009600123390555382,
0.05754918232560158,
0.017869621515274048,
0.02079940028488636,
-0.007350364699959755,
0.015101277269423008,
0.009969523176550865,
-0.011033829301595688,
-0.0358278863132,
0.01496456190943718,
-0.007220003288239241,
0.013432408683001995,
0.0008003116818144917,
-0.021467547863721848,
-0.021956633776426315,
-0.02176874689757824,
0.06566821783781052,
0.09023793041706085,
0.007987689226865768,
-0.03140903636813164,
0.02260860987007618,
-0.024634452536702156,
-0.07133221626281738,
0.0028059203177690506,
0.016380922868847847,
0.0021542885806411505,
-0.052350178360939026,
-0.0014401478692889214,
0.01589028537273407,
0.0010174964554607868,
0.010268905200064182,
-0.004524072632193565,
0.02902890555560589,
0.020073218271136284,
-0.12713806331157684,
-0.06332072615623474,
0.009267706423997879,
-0.049933820962905884,
0.008165712468326092,
-0.06903669983148575,
0.027815109118819237,
0.04802205413579941,
0.047069478780031204,
0.012043461203575134,
-0.012342551723122597,
0.028927693143486977,
0.016586242243647575,
0.016662955284118652,
0.0180765800178051,
-0.005682164803147316,
0.005185250658541918,
-0.039597559720277786,
-0.034588295966386795,
-0.05889417603611946,
0.029371242970228195,
0.009142880327999592,
0.004997659008949995,
0.007598076947033405,
0.06311795115470886,
-0.026044512167572975,
0.0034659309312701225,
-0.0014252164401113987,
0.015516738407313824,
-0.014628210105001926,
0.06801152974367142,
0.020111793652176857,
0.02991984784603119,
0.011781730689108372,
-0.023952407762408257,
0.04339487478137016,
-0.026604043319821358,
0.011087199673056602,
0.017734810709953308,
-0.03652714937925339,
-0.05071719363331795,
-0.02125263772904873,
0.023166313767433167,
0.007259534206241369,
-0.030959472060203552,
-0.03661711513996124,
-0.03510923311114311,
0.05282556638121605,
0.005437458399683237,
0.048820506781339645,
0.014090880751609802,
0.026538390666246414,
-0.013903232291340828,
-0.03541352599859238,
-0.01869429647922516,
-0.05180099979043007,
0.02799031138420105,
0.028942789882421494,
-0.01989406906068325,
0.04006364569067955,
0.008606912568211555,
0.014035644009709358,
-0.0020873593166470528,
-0.017026260495185852,
-0.0043708160519599915,
0.013193923979997635,
0.009414490312337875,
-0.04551370069384575,
0.05743737891316414,
0.052584946155548096,
0.0654204711318016,
0.0028555113822221756,
0.06953541934490204,
-0.020039167255163193,
-0.025540636852383614,
0.019130311906337738,
-0.01751738041639328,
0.03809771686792374,
0.010929045267403126,
0.03929596021771431,
0.029303893446922302,
-0.01873784326016903,
-0.006136454176157713,
0.042405709624290466,
-0.06322326511144638,
0.04952899366617203,
0.061682023108005524,
0.027284393087029457,
0.048084914684295654,
0.01391928642988205,
-0.007750772405415773,
0.005725535564124584,
-0.009177764877676964,
-0.02605845406651497,
-0.025089377537369728,
0.01900656707584858,
0.029641402885317802,
0.026109321042895317,
-0.03913896903395653,
0.023639436811208725,
0.014156385324895382,
0.01921086758375168,
0.0196046382188797,
-0.008252149447798729,
-0.019319916144013405,
-0.02940225973725319,
0.018350236117839813,
0.03214985877275467,
0.004688131157308817,
0.026907622814178467,
-0.00246803998015821,
-0.0288864653557539,
0.03718063235282898,
-0.03951306641101837,
-0.018636805936694145,
0.0886821448802948,
-0.029236499220132828,
0.005253881216049194,
0.003328653983771801,
-0.016688985750079155,
0.05691247805953026,
-0.024798227474093437,
0.011670268140733242,
0.021075816825032234,
-0.03808651119470596,
-0.01126426737755537,
-0.007980626076459885,
-0.022917982190847397,
0.0203834380954504,
-0.009069806896150112,
-0.014018614776432514,
-0.024002281948924065,
0.0337284617125988,
-0.048032186925411224,
0.036407019942998886,
-0.06918599456548691,
-0.01757875084877014,
0.0021506689954549074,
-0.011235197074711323,
0.037503931671381,
-0.02278047800064087,
0.034077923744916916,
-0.059800222516059875,
-0.010402079671621323,
0.013238510116934776,
-0.05249665305018425,
0.01944141834974289,
0.0007974170730449259,
-0.05563332512974739,
0.027806801721453667,
-0.07463724166154861,
-0.02655387669801712,
0.04735174775123596,
-0.022749699652194977,
-0.007400356698781252,
0.03211820125579834,
-0.03521452844142914,
-0.024351634085178375,
-0.034867044538259506,
-0.03832295909523964,
-0.0043366397731006145,
-0.05268680304288864,
-0.025546682998538017,
0.015293464995920658,
0.008511923253536224,
0.00840156339108944,
0.021890321746468544,
0.001337026827968657,
-0.04110729694366455,
-0.007289839442819357,
-0.02511986345052719,
0.04227692633867264,
-0.006390480324625969,
-0.0007765298942103982,
0.04299076646566391,
-0.011843387968838215,
0.021879177540540695,
-0.04049870744347572,
-0.03681738302111626,
0.029752474278211594,
-0.022095998749136925,
0.026149431243538857,
-0.027838993817567825,
0.0021255083847790956,
0.055583033710718155,
0.042451538145542145,
-0.024160195142030716,
-0.00527793075889349,
0.009257232770323753,
-0.03068213164806366,
-0.00940709002315998,
0.008893469348549843,
0.039402443915605545,
-0.013259263709187508,
0.03355787694454193,
0.004962246399372816,
0.0013412367552518845,
0.03609853237867355,
-0.03156806528568268,
-0.023155290633440018,
0.05339117348194122,
0.04318755865097046,
0.01800510846078396,
0.07044234871864319,
-0.018627604469656944,
-0.04873981326818466,
0.02601650170981884,
0.015053622424602509,
0.0008447969448752701,
-0.002597416052594781,
-0.034855373203754425,
0.07763607054948807,
-0.013709950260818005,
0.05272567272186279,
-0.01924225501716137,
0.05653179809451103,
0.037100955843925476,
-0.022982744500041008,
-0.026053406298160553,
0.0722309872508049,
0.013648237101733685,
-0.04331790283322334,
0.008373329415917397,
0.05311844125390053,
0.0007031181012280285,
-0.023000694811344147,
-0.019498517736792564,
0.00016804404731374234,
0.006464439909905195,
0.023610003292560577,
-0.029857667163014412,
-0.07888022810220718,
-0.010170629248023033,
0.04034185782074928,
0.04359938204288483,
-0.014414051547646523,
-0.04843708500266075,
-0.032379645854234695,
-0.05561099201440811,
-0.013879849575459957,
-0.04655922204256058,
0.06970150768756866,
-0.004655532073229551,
0.04332546889781952,
0.022432610392570496,
0.009973271749913692,
0.011156775988638401,
0.011629242449998856,
-0.06593834608793259,
-0.0013318718411028385,
-0.03641143813729286,
-0.022729210555553436,
0.000840028515085578,
0.008742835372686386,
0.010844524949789047,
-0.00616062618792057,
-0.040982652455568314,
0.012285010889172554,
-0.01210214663296938,
-0.0347750298678875,
-0.009128502570092678,
-0.04386241361498833,
-0.009068567305803299,
-0.010252676904201508,
0.02853148989379406,
0.0031395384576171637,
-0.003138852771371603,
-0.0008776896283961833,
0.02763107232749462,
-0.042032111436128616,
-0.003302146214991808,
-0.014356796629726887,
0.02239876426756382,
0.015345962718129158,
0.018104471266269684,
0.04581662267446518,
0.01781572960317135,
0.020122479647397995,
-0.04335758462548256,
-0.016893303021788597,
0.01779695227742195,
0.02683844231069088,
-0.0006062559550628066,
0.02769416570663452,
-0.026070231571793556,
-0.005810708738863468,
-0.021188953891396523,
0.056489087641239166,
-0.024248862639069557,
0.029641099274158478,
0.008019430562853813,
0.015968644991517067,
-0.024257129058241844,
0.0359208881855011,
0.03146962448954582,
0.03707914426922798,
-0.015843261033296585,
-0.05332091823220253,
0.010011537000536919,
-0.04164744168519974,
-0.022508691996335983,
-0.0016435454599559307,
-0.0433647446334362,
-0.046791352331638336,
0.028944626450538635,
0.01925671473145485,
0.027280917391180992,
-0.008839613758027554,
-0.013863679021596909,
-0.007283891085535288,
0.028627322986721992,
-0.0032542948611080647,
-0.004152494017034769,
-0.005420319270342588,
0.006500218529254198,
0.0364292673766613,
-0.0259858425706625,
0.021642591804265976,
-0.0603945255279541,
-0.025580139830708504,
0.0077053275890648365,
0.051306385546922684,
-0.03962715342640877,
-0.006355831399559975,
-0.014832846820354462,
-0.011321929283440113,
0.016072086989879608,
-0.0302627831697464,
0.058470770716667175,
-0.009859949350357056,
-0.014431008137762547,
-0.02568908780813217,
-0.048075031489133835,
-0.02129543013870716,
0.035593993961811066,
0.019071631133556366,
0.01748642325401306,
-0.042998772114515305,
-0.011880066245794296,
-0.015405907295644283,
-0.023239118978381157,
0.03533059358596802,
0.07727134972810745,
-0.021270889788866043,
-0.011336015537381172,
0.0016445252113044262,
0.027668338268995285,
-0.024429718032479286,
-0.07493606954813004,
0.02375870756804943,
0.00514694070443511,
0.0024462570436298847,
0.005258772522211075,
-0.0506618358194828,
-0.06714916229248047,
0.02164020575582981,
-0.0024511520750820637,
0.005307587329298258,
0.014032583683729172,
0.03164742887020111,
0.03776847943663597,
0.056980203837156296,
-0.042114704847335815,
0.04061974212527275,
0.005500570870935917,
-0.010203106328845024,
-0.008365748450160027,
-0.010442291386425495,
-0.004715516697615385,
-0.049902528524398804,
-0.01520638819783926,
-0.04545574262738228,
0.002232218161225319,
-0.027933353558182716,
0.03055308572947979,
0.006973514333367348,
-0.002265619346871972,
-0.008827692829072475,
-0.004006185103207827,
0.003003655467182398,
0.04771957919001579,
-0.0029735236894339323,
0.012131941504776478,
-0.020691048353910446,
0.007720754947513342,
0.04123871028423309,
-0.01193044614046812,
0.021596157923340797,
-0.0015138142043724656,
-0.005934053100645542,
0.04365215077996254,
-0.006427498999983072,
0.03502415493130684,
-0.015869924798607826,
-0.005772559903562069,
0.0134074492380023,
-0.0918472409248352,
0.007992039434611797,
0.008350599557161331,
0.008271229453384876,
0.0224459208548069,
-0.035399530082941055,
-0.033392634242773056,
0.038737595081329346,
-0.0239625945687294,
0.005021506920456886,
-0.04574449732899666,
0.02861086279153824,
0.02219015173614025,
-0.02351953275501728,
-0.07796294242143631,
-0.01791049726307392,
0.001189004979096353,
0.03123834915459156,
0.002954112133011222,
-0.008068732917308807,
-0.017470117658376694,
-0.030067255720496178,
-0.017859704792499542,
0.003957872744649649,
0.03835737705230713,
-0.011212608776986599,
-0.01287212036550045,
0.0241408534348011,
0.04508288949728012,
0.03748375177383423,
0.024711288511753082,
-0.007951774634420872,
-0.03732118010520935,
-0.025990044698119164,
-0.005749416537582874,
-0.002888639457523823,
0.07365783303976059,
-0.03173224627971649,
-0.02025064267218113,
-0.00849828589707613,
-0.011147461831569672,
0.042187195271253586,
-0.0150214908644557,
-0.021243000403046608,
-0.012320899404585361,
-0.0021077680867165327,
0.00943777710199356,
-0.008594599552452564,
-0.0030052780639380217,
-0.0020053733605891466,
0.060769423842430115,
0.010570249520242214,
-0.009091177955269814,
-0.012937993742525578,
-0.04624047502875328,
-0.01137060672044754,
-0.0038123626727610826,
-0.037826646119356155,
0.020511891692876816,
0.10527361184358597,
-0.020462853834033012,
0.006845094263553619,
-0.0053816428408026695,
-0.028154708445072174,
0.0014355831081047654,
-0.009983615949749947,
0.022817697376012802,
0.015535528771579266,
-0.021114321425557137,
-0.02385317161679268,
-0.058873679488897324,
-0.051065195351839066,
0.05956112593412399,
0.049300484359264374,
-0.0004162890836596489,
0.04639194533228874,
0.005815652199089527,
0.00644946051761508,
-0.013985730707645416,
-0.018434058874845505,
-0.011659464798867702,
0.006308015901595354,
0.005382025148719549,
0.04638507589697838,
-0.038532767444849014,
-0.036024969071149826,
0.034746915102005005,
0.02706744521856308,
0.004376000724732876,
-0.010058932937681675,
0.02933407761156559,
0.036877166479825974,
-0.014711077325046062,
0.008246898651123047,
-0.033922579139471054,
0.04501483961939812,
-0.02171333134174347,
0.047871869057416916,
-0.016754241660237312,
-0.03552403301000595,
0.03808442875742912,
0.018976787105202675,
0.03145337104797363,
-0.04073023796081543,
-0.024122467264533043,
-0.03910568729043007,
0.037847213447093964,
0.009768528863787651,
0.04472949355840683,
0.019491000100970268,
0.01894799992442131,
0.025564808398485184,
0.039923522621393204,
0.04707181453704834,
0.0007351958774961531,
-0.042332813143730164,
-0.03452559933066368,
-0.03664248436689377,
-0.04879064857959747,
0.038091693073511124,
-0.023608839139342308,
-0.042938653379678726,
0.014664122834801674,
-0.01912044920027256,
0.013061901554465294,
0.022403204813599586,
0.030085450038313866,
-0.010197648778557777,
0.0501999631524086,
-0.009549668058753014,
0.047466665506362915,
-0.007585942279547453,
-0.00048619878361932933,
0.11295002698898315,
0.1016637533903122,
0.029470358043909073,
-0.04530680179595947,
0.005903949495404959,
0.009962939657270908,
0.030824266374111176,
-0.0019369394285604358,
-0.0072346837259829044,
0.01672387309372425,
-0.000017860826119431295,
-0.03276067599654198,
0.057935502380132675,
0.010633568279445171,
0.018164100125432014,
0.02788807824254036,
-0.038630932569503784,
-0.035262901335954666,
0.015785103663802147,
0.010499810799956322,
-0.0018333329353481531,
-0.0054214466363191605,
-0.008891765028238297,
0.015997176989912987,
-0.03314419090747833,
0.00909553375095129,
-0.036741774529218674,
-0.01991533488035202,
0.01867573708295822,
0.025809073820710182,
-0.030052615329623222,
0.01777217537164688,
0.038523897528648376,
-0.006871367804706097,
-0.009373435750603676,
0.055869363248348236,
-0.02420804090797901,
-0.023379459977149963,
0.027864394709467888,
0.08110427111387253,
0.011722463183104992,
-0.03191965073347092,
0.02155890502035618,
0.012600637041032314,
-0.06233929470181465,
0.0005848853033967316,
-0.030788592994213104,
0.016998490318655968,
-0.0060093700885772705,
-0.00417698547244072,
0.017952533438801765,
-0.028903258964419365,
-0.03605284169316292,
-0.04118194431066513,
-0.0006672900635749102,
-0.008939850144088268,
0.014302379451692104,
-0.042993802577257156,
0.01769481785595417,
-0.042854826897382736,
-0.03542620316147804,
0.014604582451283932,
-0.01875578984618187,
-0.004280150402337313,
-0.03305633366107941,
0.009773774072527885,
0.002477028174325824,
0.05102413520216942,
-0.004974242299795151,
-0.0008436257485300303,
-0.020754072815179825,
0.006339910440146923,
-0.06782007962465286,
-0.02091221511363983,
0.008947351016104221,
0.025029344484210014,
0.07927149534225464,
0.0271739661693573,
-0.02051176130771637,
-0.04923650994896889,
-0.07576680928468704,
0.023828817531466484,
0.032315436750650406,
0.008068935014307499,
-0.010262724943459034,
-0.05761857330799103,
0.03112533502280712,
0.015354666858911514,
-0.028099171817302704,
0.03005572035908699,
0.018196450546383858,
0.03748020529747009,
0.02541576698422432,
-0.02197963185608387,
-0.016679663211107254,
-0.002702011028304696,
-0.052450139075517654,
-0.012198526412248611,
-0.016728203743696213,
0.005854878108948469,
0.020327430218458176,
0.004541617818176746,
-0.010075953789055347,
0.018333720043301582,
-0.006538015324622393,
-0.01812487095594406,
-0.005673784762620926,
-0.028166450560092926,
0.023682059720158577,
0.035054080188274384,
0.035257961601018906,
-0.04850257188081741,
-0.05803937092423439,
-0.030858250334858894,
0.0013437005691230297,
0.03817743435502052,
0.01054017711430788,
-0.03440053015947342,
-0.009769342839717865,
-0.014908832497894764,
0.034443750977516174,
-0.03512706607580185,
0.009381772950291634,
-0.01574687846004963,
0.01887117698788643,
-0.009302289225161076,
0.008836483582854271,
-0.018395988270640373,
0.03142787516117096,
0.02119048871099949,
-0.03514242544770241,
0.041446853429079056,
0.052467331290245056,
0.0033394775819033384,
-0.024170726537704468,
-0.023082049563527107,
0.015259094536304474,
0.003824952058494091,
-0.010325273498892784,
-0.03753913193941116,
0.015752075240015984,
-0.047103866934776306,
-0.01944119669497013,
0.011314877308905125,
-0.016552245244383812,
0.01943182945251465,
0.046164389699697495,
-0.02327231504023075,
0.0149768041446805,
0.021787511184811592,
-0.028577568009495735,
-0.02508053369820118,
0.011167800985276699,
-0.030300989747047424,
-0.03550717979669571,
-0.0321895107626915,
0.0014882235554978251,
0.022413475438952446,
-0.004349326249212027,
0.011712086386978626,
0.019745608791708946,
0.007426275871694088,
0.013158980756998062,
-0.023950550705194473,
0.005745457019656897,
0.041503146290779114,
0.043894678354263306,
-0.007519266568124294,
0.01237042061984539,
0.022384973242878914,
-0.055097728967666626,
0.03256738930940628,
0.002495767781510949,
0.004815356340259314,
-0.05862586200237274,
-0.018062489107251167,
-0.013206340372562408,
-0.01589689962565899,
0.0363088957965374,
-0.04681581258773804,
0.04579578712582588,
0.0478455014526844,
-0.10064897686243057,
0.035247333347797394,
-0.007038781885057688,
0.024771269410848618,
-0.016847465187311172,
0.0007633684435859323,
-0.02549276128411293,
0.05088495835661888,
0.023114172741770744,
0.048618119210004807,
0.020890671759843826,
-0.00689063360914588,
-0.005860757082700729,
0.01295106578618288,
-0.01759190671145916,
0.03940216451883316,
0.001157906954176724,
-0.027678053826093674,
0.03697808459401131,
-0.026984097436070442,
-0.04792783781886101,
0.008001207374036312,
-0.029974276199936867,
0.026431361213326454,
0.004876972176134586,
0.00824641901999712,
0.017327262088656425,
0.0016996683552861214,
0.026066355407238007,
0.009477764368057251,
-0.04580390453338623,
-0.011288017965853214,
-0.017652882263064384,
0.029769083485007286,
-0.01166732981801033,
0.00497551541775465,
0.018416285514831543,
-0.01115031074732542,
-0.04134244844317436,
0.01916424185037613,
-0.011838910169899464,
-0.024688193574547768,
-0.002023109467700124,
-0.02486768178641796,
0.00633540702983737,
-0.007730311714112759,
0.010536693967878819,
-0.01165109220892191,
-0.021235691383481026,
-0.007393334060907364,
0.007554755546152592,
0.027696646749973297,
-0.02006339840590954,
-0.04074745997786522,
-0.0670674741268158,
0.048354215919971466,
0.012525255791842937,
-0.028673391789197922,
-0.06666306406259537,
-0.014412473887205124,
0.005034929141402245,
0.01471273135393858,
-0.0012096745194867253,
-0.03636094927787781,
-0.04328849911689758,
0.016621604561805725,
-0.012106494046747684,
0.0062401373870670795,
-0.02647354081273079,
-0.030865926295518875,
-0.027101879939436913,
-0.0320737324655056,
0.03806675970554352,
0.01684548705816269,
-0.04087440297007561,
0.014964203350245953,
0.0183874499052763,
-0.012082897126674652,
0.02184457890689373,
0.08555864542722702,
0.0025826767086982727,
0.00592284370213747,
0.0036153607070446014,
-0.043749142438173294,
0.04042726382613182,
-0.020276257768273354,
0.017322881147265434,
-0.00365985999815166,
0.008765233680605888,
-0.00402725487947464,
-0.0028968341648578644,
0.025187186896800995,
0.05396668240427971,
0.016866018995642662,
-0.024010222405195236,
0.030736086890101433,
0.005558991804718971,
-0.004682017490267754,
0.02021397463977337,
-0.04438329115509987,
-0.02128821425139904,
0.0619581863284111,
-0.01329899113625288,
0.030378585681319237,
0.0054676407016813755,
-0.025713197886943817,
-0.033922698348760605,
-0.0036992968525737524,
-0.00502185570076108,
-0.002774761291220784,
0.004785511177033186,
-0.0406099334359169,
-0.009281236678361893,
-0.029244467616081238,
0.003571586450561881,
0.023553431034088135,
-0.023182855919003487,
-0.018239760771393776,
0.0336533822119236,
0.02590228244662285,
0.030103443190455437,
-0.022161757573485374,
0.05367199331521988,
0.040859054774045944,
-0.0022068237885832787,
0.04270629212260246,
0.049836572259664536,
0.01734328269958496,
-0.03040473163127899,
0.04295341297984123,
0.04847012087702751,
0.009895194321870804,
0.014434704557061195,
0.034787390381097794,
0.017939025536179543,
-0.014573761261999607,
-0.026130275800824165,
0.04908249154686928,
-0.025785233825445175,
-0.00207694573327899,
-0.002163376659154892,
-0.0189996175467968,
0.0760972872376442,
-0.027337251231074333,
0.029192237183451653,
0.005439748056232929,
0.0014997059479355812,
-0.029341425746679306,
-0.03549904376268387,
0.016723698005080223,
0.020052753388881683,
0.007087992038577795,
-0.025638967752456665,
-0.0560210719704628,
0.0029039764776825905,
-0.00671673659235239,
-0.0566847138106823,
0.0018798577366396785,
-0.026797153055667877,
-0.023489192128181458,
-0.04495212435722351,
-0.0312354639172554,
-0.009296565316617489,
-0.040683548897504807,
0.03278433158993721,
0.039112191647291183,
0.034842636436223984,
0.0227322019636631,
-0.0365157388150692,
-0.004322815220803022,
0.057986821979284286,
-0.020120205357670784,
-0.053376276046037674,
-0.017016788944602013,
-0.004342118743807077,
0.014474179595708847,
0.00258520501665771
] |
<p>I am studying the transition from the second excited electronic state of molecular oxygen, $b^1\Sigma_g^+$ , to the ground state, $X^3\Sigma_g^-$. I know that the ground state has total angular momentum $J=1$, total spin $S=1$, and three spin sublevels $(m_s=-1,0,+1)$. The upper state has $J=0$, $S=0$, and one sublevel with $m_s=0$. I am specifically interested in the transition from the upper state to the ground state $m=\pm1$ level and I will refer to it as the $b-X,1$ transition. </p>
<p>I would like to understand the the selection rules that govern this transition and the language that is used to describe this transition. </p>
<p>Here is what I know so far about this transition.</p>
<ul>
<li><p><a href="http://campus.udayton.edu/~physics/rjb/MRSOxygenI.pdf" rel="nofollow">Brecha, Pedrotti, Krause, "Magnetic rotation spectroscopy of molecular oxygen with a diode laser" JOSA 1998</a>: They describe this transition as "doubly weak" and I quote, "First, it is a magnetic dipole transition and thus is roughly 5 orders of magnitude weaker than a normal electric dipole transition. Second, the transition is a singlet-triplet intercombination band, making it 3 orders of magnitude weaker still." </p></li>
<li><p><a href="http://pubs.rsc.org/en/content/articlelanding/1997/ft/a607263a" rel="nofollow">Minaev, Agren, 1997</a>: They describe this transition as "magnetic dipolar" and "spin-forbidden." They also say that it is spin-orbit coupling that accounts for this "doubly weak" transition being as large as it is. </p></li>
<li><p>Wikipedia-Selection Rules: Provides the rules for Magnetic Dipole (M1) transitions and discusses Spin-Obrit (LS) Coupling but I do not understand where this came from. </p></li>
<li><p>Sannigrahi, "Derivation of Selection Rules for Magnetic Dipole Transitions," 1982: This is pretty clear but just seems to say that $\Delta m_s=\pm1$. This is true for the $b-X,1$ transition but how do I tie in $L$ and $J$ into the selection rules?</p></li>
</ul>
<p>Most of what I have found on the internet and in textbooks relating to selection rules is directed to electric dipole transitions. Where I have found something discussing magnetic dipole transitions, it is either a summary of the rules or I do not have the required background to understand it. </p>
<ul>
<li><p>What does it mean for a transition to be spin-forbidden?</p></li>
<li><p>What is a singlet-triplet intercombination band? Does this change the selection rules? How is this related to being spin-forbidden?</p></li>
<li><p>What does spin-orbit coupling have with this?</p></li>
</ul>
<p>I look forward to any feedback on this topic. </p>
<h1>Follow up Questions</h1>
<h2>Meaning of Spin-Forbidden</h2>
<p>Does 'spin-forbidden' just mean that the transition from a $J=1$ to $J=0$ state is not allowed because the selection rules for magnetic dipole transitions say that $J$ cannot change? I expected 'spin-forbidden' to imply something about the change of the spin between the initial and final states. </p>
<p>For example, suppose I have a time-dependent perturbation like $V_{md}(t) = \frac{e}{m} \vec{S}\cdot \vec{B}(t)$ and I am interested in the transition rate between the initial state $\left| s m_s \right\rangle$ and the final state $\left| s' m_s' \right\rangle$ with the quantization axis in the z direction. As you pointed out, the transition rate will be proportional to $\left\langle s' m_s'\right| \vec{S} \cdot \vec{B}(t) \left| s m_s \right \rangle$. Now if $\vec{B}(t)$ is circularly polarized, the rules for an allowed transition will be $s'-s=0$ and $m_s'-m_s = \pm1$. For $\vec{B}(t)$ polarized in the z direction, $s'-s=0$ and $m_s'-m_s = 0$ so there is not a transition to other states. I would think that if $s'-s=0$ and $m_s'-m_s = \pm1$ are <strong>not</strong> true (like if $s'=1$ and $s=0$), then the magnetic dipole transition between $\left| s m_s \right\rangle$ and $\left| s' m_s' \right\rangle$ would be called 'spin-forbidden.' </p>
<p>The same arguments could be made for $\vec{L}$ or $\vec{J}$ as I did with $\vec{S}$. Would you also call a magnetic dipole transition between $\left| L=0 \right\rangle$ and $\left| L=1 \right\rangle$ 'spin-forbidden?'</p>
<h2>Spin-Orbit Coupling</h2>
<p>Now the difference in the energies of the singlet $(b)$ and triplet, ground state $(X)$ is $1.63\text{ eV}$. That seems too large to be due to spin-orbit coupling breaking a degeneracy. If I was pretending this was a hydrogen atom, I would say this was like a transition where the principle quantum number $n$ changed. I am not sure how to talk about this in a molecule.</p>
<p>This isn't key to the rest of your explanation but I did want to clarify to make sure we were on the page. </p>
<h2>Singlet-Triplet Intercombination Band</h2>
<p>Do you know what the expression 'singlet-triplet intercombination band' is referring to? After your explanation, it seems to refer to the mixing of the singlet and triplet states due to spin-orbit coupling (SOC). Is this true?</p>
<h2>Mixing of unperturbed states</h2>
<p>How did you know that the perturbed upper state could be written as a combination of the unperturbed upper state and the $M_s=0$ ground state? It makes sense that the states would get mixed up by SOC but I don't know how. If this is a messy explanation, don't worry about it. </p>
<p><strong>I would like to reiterate that your (George G's) explanation has been incredibly helpful. Thank you.</strong></p>
| 8,510 |
[
-0.019555991515517235,
-0.043368227779865265,
0.017084745690226555,
-0.03911997750401497,
0.04432535171508789,
0.04155191034078598,
-0.04206635057926178,
-0.03961791470646858,
0.03394724801182747,
-0.06909169256687164,
0.05745624750852585,
0.05570666491985321,
0.03352605551481247,
0.03824310004711151,
0.017131367698311806,
0.02779819816350937,
0.002122684149071574,
-0.008222068659961224,
-0.0268786009401083,
-0.012890075333416462,
0.005510931368917227,
-0.002294255420565605,
-0.031096430495381355,
0.027444249019026756,
-0.009223521687090397,
0.027187101542949677,
0.016439510509371758,
0.007624642923474312,
0.023107819259166718,
0.019966334104537964,
-0.015926752239465714,
-0.03667687997221947,
0.02117275260388851,
-0.020753325894474983,
0.03860512375831604,
0.0043785120360553265,
0.023880943655967712,
-0.028923090547323227,
0.022211337462067604,
0.03379342332482338,
-0.041918233036994934,
0.007586688734591007,
-0.05903476104140282,
0.016337253153324127,
-0.009493110701441765,
-0.01244165189564228,
-0.03738096356391907,
-0.0314759835600853,
0.03745077922940254,
-0.05335863679647446,
0.05534474179148674,
-0.03716805577278137,
0.03309501335024834,
0.02453698217868805,
-0.018739067018032074,
-0.01587310992181301,
0.07102543860673904,
0.08445468544960022,
0.013690879568457603,
-0.04143497347831726,
-0.016825145110487938,
-0.07004404813051224,
0.009706518612802029,
0.03736097365617752,
-0.04044009745121002,
-0.00363767403177917,
0.01001255214214325,
-0.015523764304816723,
0.05705563351511955,
0.035034481436014175,
0.03035668097436428,
-0.010025296360254288,
0.014814184047281742,
-0.028878405690193176,
0.01936153694987297,
-0.036497652530670166,
0.03953136131167412,
0.0119487838819623,
0.03819799795746803,
0.02104301005601883,
-0.003620229195803404,
0.00560063635930419,
0.00007450614793924615,
0.008844500407576561,
-0.006264889147132635,
0.027507996186614037,
0.09087485074996948,
-0.010984198190271854,
0.028280125930905342,
0.017083171755075455,
0.0024478661362081766,
0.03940870240330696,
0.026064475998282433,
-0.018240757286548615,
-0.027726219967007637,
0.0452650710940361,
0.014066767878830433,
0.044036783277988434,
-0.018650462850928307,
0.007498400751501322,
-0.023267704993486404,
-0.02508198842406273,
0.021322403103113174,
0.09280148893594742,
0.016019398346543312,
0.01628710888326168,
-0.0033949939534068108,
-0.0017520864494144917,
-0.020767437294125557,
-0.0491972416639328,
-0.004138277377933264,
0.02584196627140045,
-0.0521194189786911,
-0.016765618696808815,
-0.022355539724230766,
0.003134544938802719,
-0.02273302525281906,
-0.01820727065205574,
0.07100801914930344,
0.07202579826116562,
0.007826903834939003,
-0.01612064056098461,
-0.019797218963503838,
-0.020165331661701202,
-0.09407509863376617,
-0.0038504498079419136,
0.0546981580555439,
0.04858606308698654,
-0.04231102392077446,
0.007554599083960056,
-0.008095680736005306,
-0.005506161600351334,
0.02269173599779606,
-0.027782153338193893,
0.02019733563065529,
-0.022401737049221992,
-0.11230108886957169,
-0.025952579453587532,
0.029761280864477158,
-0.007415249943733215,
0.0026893916074186563,
-0.06207166612148285,
0.0023371337447315454,
0.009954346343874931,
0.0706363245844841,
-0.01639918051660061,
0.004476710222661495,
-0.023540185764431953,
0.0328981950879097,
0.017192544415593147,
0.0007939769420772791,
0.007891656830906868,
0.01887383870780468,
-0.029562242329120636,
-0.018845001235604286,
-0.04331865906715393,
0.04199722781777382,
0.024969352409243584,
0.01693190261721611,
-0.00729861855506897,
0.053410232067108154,
-0.059002626687288284,
0.0020359368063509464,
0.010608646087348461,
0.028955403715372086,
0.0072792451828718185,
0.06345131993293762,
0.008409201167523861,
0.020335650071501732,
0.05847684666514397,
-0.0042857457883656025,
-0.005493319593369961,
-0.022943951189517975,
0.06167509779334068,
0.051731497049331665,
-0.05641336739063263,
-0.009496118873357773,
-0.054919518530368805,
-0.019646625965833664,
-0.0028826098423451185,
-0.05797639116644859,
-0.026868028566241264,
-0.013228300958871841,
0.012532202526926994,
-0.002347966656088829,
0.017155947163701057,
-0.006460523698478937,
0.008539991453289986,
0.03770158439874649,
-0.09075864404439926,
-0.017758699133992195,
-0.04730236530303955,
-0.017958784475922585,
0.019245466217398643,
-0.03738849237561226,
0.03643970564007759,
-0.021486470475792885,
0.030535370111465454,
-0.015545443631708622,
-0.021810488775372505,
-0.01981201209127903,
0.03272191807627678,
0.04359878599643707,
0.015133807435631752,
0.060872774571180344,
0.04817899316549301,
0.008779121562838554,
-0.018583592027425766,
0.02509722299873829,
-0.05419421195983887,
-0.010110829025506973,
0.01067669689655304,
-0.016036387532949448,
0.027631061151623726,
0.0030302589293569326,
-0.0018481259467080235,
0.02598639205098152,
0.0016520214267075062,
0.020648134872317314,
0.0032083671540021896,
-0.0441453643143177,
0.04973278194665909,
0.07408996671438217,
0.010609670542180538,
0.02565431222319603,
0.03179975971579552,
0.017573406919836998,
0.008653152734041214,
-0.014345070347189903,
-0.026903502643108368,
-0.015369792468845844,
-0.015252864919602871,
0.04732953757047653,
0.025932947173714638,
-0.04002316668629646,
0.003910403233021498,
0.031485967338085175,
0.023243051022291183,
0.06689188629388809,
0.03817273676395416,
-0.04241352900862694,
-0.00891239382326603,
0.009335039183497429,
0.012586617842316628,
-0.006532142870128155,
0.06318001449108124,
0.018751364201307297,
-0.00697423005476594,
0.05404004827141762,
-0.0038170325569808483,
-0.015666481107473373,
0.02329041063785553,
0.010675784200429916,
-0.00998952891677618,
-0.0066169025376439095,
-0.04012583568692207,
0.07776159793138504,
-0.056147970259189606,
0.0454641729593277,
0.035249270498752594,
-0.014526302926242352,
0.044305622577667236,
-0.019746951758861542,
-0.037200186401605606,
0.007451297249644995,
-0.009827875532209873,
-0.021167973056435585,
-0.013874495401978493,
0.025933509692549706,
-0.02222423255443573,
0.026084054261446,
-0.012575516477227211,
0.0008081062114797533,
-0.008348049595952034,
-0.028005141764879227,
-0.00018255140457767993,
0.033935412764549255,
0.011747603304684162,
-0.050838734954595566,
-0.008643966168165207,
-0.054233450442552567,
-0.015249672345817089,
0.047913480550050735,
0.04096340760588646,
-0.015536414459347725,
-0.007293256465345621,
-0.05361750349402428,
-0.0027916645631194115,
0.01893780194222927,
-0.010181020945310593,
-0.045010603964328766,
-0.018329428508877754,
0.0166634488850832,
-0.058854423463344574,
-0.06023099273443222,
0.04031932353973389,
-0.013698242604732513,
-0.0019190632738173008,
-0.038522448390722275,
0.06747899204492569,
-0.0217251256108284,
-0.028300538659095764,
0.03526943922042847,
-0.04257361590862274,
-0.0412590391933918,
-0.008708149194717407,
0.004831348545849323,
-0.03688124939799309,
-0.025091970339417458,
0.028487004339694977,
0.028678586706519127,
0.004703353624790907,
-0.0006706229178234935,
-0.0332372821867466,
-0.04179573059082031,
0.01564728282392025,
-0.006105602253228426,
0.044818975031375885,
-0.036009542644023895,
-0.0329812727868557,
0.08409128338098526,
0.016326475888490677,
0.01024216040968895,
-0.05448982119560242,
0.018009239807724953,
-0.03015224076807499,
-0.031857747584581375,
0.02723647654056549,
0.03988756611943245,
0.010587677359580994,
0.01960788667201996,
0.021242549642920494,
0.05749284103512764,
0.004671551752835512,
0.0245740357786417,
-0.0006466030026786029,
0.04975219815969467,
-0.04064279422163963,
-0.008729270659387112,
0.044054772704839706,
-0.0032271919772028923,
0.020400753244757652,
0.002060483442619443,
-0.03306799754500389,
0.006326077040284872,
0.03877168148756027,
-0.06703877449035645,
0.05727143585681915,
-0.0006007750052958727,
0.0012473451206460595,
0.001017543487250805,
0.03418014943599701,
0.010095628909766674,
-0.03648465499281883,
0.015979710966348648,
0.02529105357825756,
0.022231828421354294,
-0.006028105039149523,
-0.041017286479473114,
0.0331924743950367,
-0.004132409580051899,
-0.012678372673690319,
0.003472293494269252,
0.019381240010261536,
-0.02642144449055195,
0.015018273144960403,
-0.05686748027801514,
-0.017020724713802338,
0.014020108617842197,
0.045963481068611145,
-0.007345055695623159,
-0.029949506744742393,
-0.018245859071612358,
0.025502236559987068,
-0.03043035976588726,
0.011705582961440086,
0.016731783747673035,
0.02961469255387783,
-0.0018046492477878928,
0.04741813987493515,
-0.030967779457569122,
0.0020535739604383707,
0.003398139961063862,
-0.006094524171203375,
-0.08458017557859421,
0.055751487612724304,
0.01836664043366909,
-0.003463361645117402,
0.01320362463593483,
0.007603846024721861,
0.01378703024238348,
-0.004742442164570093,
-0.00980957318097353,
-0.057236578315496445,
0.007615109905600548,
-0.038434796035289764,
0.030518487095832825,
-0.021812312304973602,
0.004349141847342253,
-0.02964179590344429,
0.05837465450167656,
0.04806923493742943,
-0.04599956050515175,
0.003526241285726428,
0.007755017839372158,
-0.023274531587958336,
0.023346727713942528,
-0.022242361679673195,
0.01464114524424076,
0.047442737966775894,
-0.01350373961031437,
0.023129718378186226,
0.00791590940207243,
-0.009160670451819897,
-0.07536584138870239,
0.02054368518292904,
0.04075273498892784,
0.05109944939613342,
0.00020605973259080201,
-0.002441108226776123,
0.004270716104656458,
0.012831727974116802,
0.027595844119787216,
0.0760878175497055,
-0.030159415677189827,
0.032732412219047546,
0.008886056020855904,
-0.004999948665499687,
-0.022264376282691956,
0.04004133492708206,
0.03431076928973198,
0.024102969095110893,
0.008989863097667694,
-0.01818803884088993,
-0.009189214557409286,
-0.05461862310767174,
0.031072469428181648,
-0.006423227488994598,
0.004810841288417578,
-0.03497300297021866,
-0.023761387914419174,
0.04912259802222252,
0.05053237825632095,
-0.028663940727710724,
-0.022270116955041885,
-0.010949262417852879,
0.013306000269949436,
0.004845196381211281,
0.01874317042529583,
-0.011321542784571648,
0.0012262316886335611,
0.05014939606189728,
-0.006049065385013819,
0.018085166811943054,
-0.04395891726016998,
-0.061221614480018616,
0.03442173823714256,
0.024493062868714333,
0.004201993346214294,
-0.0066979327239096165,
-0.05363095924258232,
-0.002935931319370866,
-0.01446903683245182,
-0.05201776698231697,
0.05194934830069542,
-0.001052300096489489,
-0.009423772804439068,
-0.02300584688782692,
-0.023085830733180046,
-0.022826874628663063,
0.019518982619047165,
-0.002217714674770832,
0.005388210993260145,
-0.014016298577189445,
-0.0048805600963532925,
0.014025966636836529,
0.019283946603536606,
0.0007690670317970216,
0.012625950388610363,
-0.0053324573673307896,
-0.010119976475834846,
0.027046971023082733,
0.022495362907648087,
-0.04440152272582054,
-0.07947168499231339,
0.0035442032385617495,
0.014961802400648594,
0.017248690128326416,
0.05785442516207695,
-0.042118608951568604,
-0.07198593020439148,
0.004419573117047548,
0.03911329433321953,
0.011434735730290413,
0.01592189632356167,
-0.014423161745071411,
0.054536428302526474,
0.016062727198004723,
-0.045894037932157516,
0.0482473187148571,
0.020234672352671623,
-0.018904929980635643,
0.030015720054507256,
-0.03520103543996811,
0.026122290641069412,
-0.025916781276464462,
-0.014487232081592083,
-0.03876885771751404,
0.04507322981953621,
-0.013923153281211853,
0.05365071818232536,
-0.012650900520384312,
-0.0055748517625033855,
0.0014128588372841477,
-0.052157212048769,
0.006074030417948961,
0.014234261587262154,
-0.02347014658153057,
-0.03803137317299843,
-0.011370012536644936,
0.03000774420797825,
-0.015528855845332146,
0.0010214745998382568,
0.03158661350607872,
-0.04549949988722801,
0.009819477796554565,
0.01964029110968113,
-0.038858309388160706,
-0.007832984440028667,
-0.07320345193147659,
-0.001994483172893524,
-0.020257778465747833,
-0.05529193952679634,
0.041758161038160324,
-0.025080803781747818,
-0.007881424389779568,
0.0027060694992542267,
-0.01990656368434429,
-0.000057156557886628434,
0.028520872816443443,
-0.004584892187267542,
0.006378136109560728,
-0.0045157382264733315,
0.005935571622103453,
-0.013207697309553623,
-0.0035337789449840784,
-0.03502477705478668,
-0.04253021255135536,
-0.018365537747740746,
0.027458343654870987,
-0.03173193335533142,
-0.0009139293106272817,
-0.009021059609949589,
-0.011761115863919258,
-0.010420087724924088,
0.013449604623019695,
0.018874993547797203,
-0.043642833828926086,
-0.003920315764844418,
0.027852538973093033,
0.0062166485004127026,
0.02512902393937111,
-0.029694747179746628,
-0.019981196150183678,
-0.013738005422055721,
-0.03617357462644577,
0.010638459585607052,
0.020882677286863327,
0.005881419405341148,
-0.007504473440349102,
-0.03697182983160019,
-0.02609797939658165,
0.027175823226571083,
0.0026542111299932003,
-0.030315913259983063,
-0.02284114621579647,
0.028301626443862915,
-0.03158889710903168,
-0.001335209235548973,
-0.034268639981746674,
0.003936287015676498,
-0.022722920402884483,
0.020350268110632896,
-0.003148104064166546,
0.0057328869588673115,
-0.024709150195121765,
-0.04641640558838844,
0.007374336011707783,
0.030319146811962128,
0.00858475361019373,
-0.000987703911960125,
0.06455017626285553,
0.029317378997802734,
0.014343904331326485,
0.04832231625914574,
-0.05028906092047691,
-0.006666556466370821,
0.013188609853386879,
0.0307698342949152,
0.02778402529656887,
0.048454590141773224,
-0.04910014942288399,
-0.03429799526929855,
-0.043251264840364456,
0.0034589434508234262,
0.03562219813466072,
-0.023760607466101646,
0.0286076832562685,
0.03215011954307556,
-0.037600550800561905,
-0.028401441872119904,
-0.05983215942978859,
-0.009113401174545288,
0.016657603904604912,
-0.009180310182273388,
0.054267384111881256,
-0.018637511879205704,
0.01558423787355423,
0.05465120077133179,
0.05278493091464043,
-0.010561288334429264,
0.050298649817705154,
0.06545194238424301,
-0.043192800134420395,
-0.0006250601727515459,
-0.015268071554601192,
-0.05437768995761871,
0.06225212290883064,
0.005440706852823496,
0.01712311990559101,
0.03404145687818527,
0.012856059707701206,
0.03845645859837532,
0.024284008890390396,
0.042295247316360474,
-0.043530602008104324,
-0.030169956386089325,
-0.07252403348684311,
0.035947322845458984,
-0.0012624040246009827,
-0.0502888448536396,
0.041931938380002975,
0.026017826050519943,
0.00835765153169632,
0.0043663023971021175,
-0.00044001772766932845,
-0.03146551921963692,
-0.027385875582695007,
0.006399510893970728,
0.017486024647951126,
-0.09348058700561523,
0.052488718181848526,
-0.03008701652288437,
-0.049152832478284836,
0.03134174644947052,
-0.02730853483080864,
0.037085238844156265,
0.008913409896194935,
0.04076836630702019,
-0.0037210641894489527,
0.03798538073897362,
-0.000937682983931154,
0.0074617513455450535,
0.048474811017513275,
-0.01917322725057602,
0.13204620778560638,
0.056125324219465256,
0.02304077334702015,
-0.0796651840209961,
-0.008406261913478374,
0.0038448700215667486,
0.02254645712673664,
-0.03022901341319084,
-0.02513311617076397,
-0.011361131444573402,
0.0018031118670478463,
-0.0053271399810910225,
0.024483073502779007,
-0.016733722761273384,
-0.012898365966975689,
0.015547423623502254,
-0.03602496534585953,
-0.04060716927051544,
0.022841565310955048,
0.027742739766836166,
-0.004918084014207125,
-0.024980200454592705,
-0.045589108020067215,
0.0009393580839969218,
-0.012566673569381237,
0.006062641739845276,
-0.029586097225546837,
-0.04093244671821594,
0.06499537080526352,
-0.0004909951821900904,
-0.03747263550758362,
-0.0014123707078397274,
-0.013420228846371174,
0.020607300102710724,
-0.04121290519833565,
0.01688501238822937,
0.03865635395050049,
-0.012881477363407612,
0.01833139732480049,
0.01335129514336586,
0.00166615704074502,
-0.0009349689353257418,
0.04517931863665581,
0.023459501564502716,
-0.02721397392451763,
0.006017074920237064,
-0.0023765212390571833,
0.036969274282455444,
-0.016228195279836655,
-0.002027178881689906,
-0.02660387195646763,
0.0035351503174751997,
0.0183024350553751,
-0.05025537684559822,
-0.00776444748044014,
0.015139835886657238,
0.05849621817469597,
-0.058174923062324524,
-0.03283236175775528,
-0.0016973515739664435,
-0.00575881265103817,
0.017825637012720108,
-0.005432982463389635,
-0.04001973569393158,
-0.02050585113465786,
0.02684233896434307,
0.0031646450515836477,
0.007049169857054949,
0.0055285003036260605,
0.0005839445511810482,
0.007743567228317261,
0.021657979115843773,
-0.005944484379142523,
-0.028917819261550903,
0.042425673454999924,
0.0008244628552347422,
0.04025566205382347,
0.02831612527370453,
-0.04065284878015518,
-0.03696519508957863,
-0.055448587983846664,
0.0006287808064371347,
-0.005850528832525015,
-0.024729905650019646,
0.005985518917441368,
-0.01185525767505169,
-0.0086725614964962,
0.020299088209867477,
-0.0072848983108997345,
0.0367562398314476,
0.03513292968273163,
0.04096713289618492,
0.007139450870454311,
-0.0401853546500206,
-0.05512117221951485,
0.027639273554086685,
-0.019735032692551613,
-0.039706941694021225,
-0.013762706890702248,
0.0345577672123909,
-0.012495496310293674,
-0.0032380600459873676,
-0.006301249377429485,
0.018414031714200974,
-0.04360818490386009,
-0.031106291338801384,
0.013872458599507809,
-0.011366812512278557,
0.01933794468641281,
-0.027051080018281937,
-0.0007495642639696598,
-0.008352012373507023,
-0.019969435408711433,
-0.00545303151011467,
-0.017512060701847076,
0.0026838623452931643,
0.009771808981895447,
-0.010081984102725983,
-0.0037053280975669622,
-0.04484719783067703,
-0.003936325665563345,
-0.00046295224456116557,
-0.039215754717588425,
-0.009276327677071095,
0.045032985508441925,
0.01651001162827015,
0.007080631330609322,
0.0016290502389892936,
0.0011338618351146579,
0.01731712371110916,
0.042410291731357574,
0.03810783103108406,
0.032560717314481735,
-0.000978879164904356,
-0.012736311182379723,
-0.006143038161098957,
-0.013380948454141617,
0.03868948668241501,
0.0026389167178422213,
-0.0220178235322237,
0.028109531849622726,
-0.02556104026734829,
-0.021226171404123306,
0.035718128085136414,
-0.002227242337539792,
0.016116579994559288,
0.001300640287809074,
-0.0044976696372032166,
-0.04545871168375015,
0.04019021987915039,
-0.023218819871544838,
-0.020120864734053612,
-0.0041751558892428875,
0.0016882757190614939,
0.03138013556599617,
-0.007390863262116909,
0.006429996807128191,
0.010922136716544628,
-0.02481396310031414,
0.004737896379083395,
-0.02593824826180935,
-0.028729237616062164,
-0.028847403824329376,
-0.04730672016739845,
-0.025879696011543274,
-0.006686534732580185,
0.010072669014334679,
0.01402987539768219,
0.02485881745815277,
0.06429499387741089,
-0.0014939518878236413,
0.05499058589339256,
0.012489630840718746,
-0.010295494459569454,
-0.06858713924884796,
-0.02321607619524002,
0.0033420391846448183,
0.01844533532857895,
0.034449245780706406,
-0.03810466080904007,
0.029902029782533646,
0.028697531670331955,
-0.04983146861195564,
-0.03723521903157234,
0.004369271453469992,
0.006988469045609236,
-0.026191476732492447,
-0.03429695963859558,
-0.03536774590611458,
0.013395383022725582,
-0.033612631261348724,
0.019537068903446198,
0.033517636358737946,
0.008552544750273228,
-0.048883967101573944,
-0.024140935391187668,
-0.0022246160078793764,
0.012544889934360981,
-0.02218582108616829,
-0.03113398887217045,
0.046165693551301956,
-0.031747717410326004,
-0.03425701707601547,
0.040102094411849976,
0.002418438671156764,
0.057024404406547546,
-0.010030768811702728,
-0.0013454011641442776,
0.0003268988511990756,
-0.005941854324191809,
0.01615099422633648,
-0.015371222048997879,
0.035931676626205444,
0.026291919872164726,
0.010126764886081219,
0.042882289737463,
0.011862454004585743,
-0.00683540478348732,
0.002645213855430484,
-0.05310237407684326,
-0.0348084419965744,
0.03844907507300377,
-0.03372526168823242,
-0.00223001791164279,
0.01069731917232275,
0.010937453247606754,
-0.004832372535020113,
-0.031599730253219604,
0.013896589167416096,
-0.03337283805012703,
0.011631119064986706,
0.01136083249002695,
-0.009476887062191963,
-0.007630542851984501,
0.02245342917740345,
-0.0018182144267484546,
-0.03599173575639725,
0.045414999127388,
-0.01516701839864254,
-0.0004909696872346103,
-0.044619638472795486,
-0.00880342535674572,
0.0034746236633509398,
-0.020160872489213943,
-0.033147409558296204,
-0.007213452830910683,
-0.024950306862592697,
0.028098898008465767,
-0.014711215160787106,
-0.004836398176848888,
-0.010776911862194538,
-0.0861281156539917,
-0.006672956980764866,
-0.09234612435102463,
0.028905846178531647,
0.014800391159951687,
-0.006533586885780096,
-0.04756281524896622,
-0.0395699180662632,
0.018134141340851784,
0.005854204297065735,
0.04033900797367096,
0.04424316808581352,
-0.011682843789458275,
-0.021973416209220886,
0.012534272857010365,
0.015944289043545723,
-0.012644928880035877,
0.039471711963415146,
0.0287619736045599,
0.0004977674689143896,
0.013125348836183548,
0.016887839883565903,
-0.04099102318286896,
0.0009597651078365743,
0.021007198840379715,
0.03508581966161728,
0.015013855881989002,
0.012412816286087036,
-0.014929920434951782,
0.05015309900045395,
-0.0060764397494494915,
-0.013298002071678638,
0.056339092552661896,
0.011547967791557312,
-0.012835152447223663,
0.04301290959119797,
-0.027298608794808388,
-0.04715566337108612,
-0.005864537786692381,
-0.014124331064522266,
-0.008548871614038944,
-0.01985846646130085,
-0.02687499299645424,
0.04118840768933296,
-0.0070581985637545586,
0.024034051224589348,
0.02819962427020073,
0.005465855356305838,
-0.01407028641551733,
0.06632635742425919,
0.005313107743859291,
0.024357879534363747,
-0.02887430414557457,
0.022927887737751007,
0.011076787486672401,
-0.02937072329223156,
0.008337530307471752,
0.01633565127849579,
0.0437135249376297,
0.039095040410757065,
0.017538446933031082,
-0.00011697917943820357,
0.002695320639759302,
-0.008920642547309399,
0.04335175082087517,
0.006666866596788168,
0.009230952709913254,
0.017852038145065308,
0.06012134253978729,
0.0022649001330137253,
-0.02200755476951599,
-0.0003895195259246975,
-0.00786915048956871,
0.073016457259655,
-0.04010651633143425,
-0.015715498477220535,
-0.03409930691123009,
0.024931371212005615,
0.007122725248336792,
0.040500640869140625,
0.012729119509458542,
0.025028375908732414,
-0.022138778120279312,
0.031553953886032104,
-0.005026611033827066,
-0.014168835245072842,
0.0444219745695591,
-0.034537382423877716,
0.043439265340566635,
0.019361786544322968,
0.03695634752511978,
0.008824501186609268,
-0.01674206554889679,
-0.032699596136808395,
-0.016792133450508118,
-0.009310847148299217,
-0.014097405597567558,
0.004861198365688324,
-0.022760631516575813,
0.02056407928466797,
-0.021906156092882156,
0.04474497213959694,
-0.05760553106665611,
-0.006397687364369631,
-0.02861340530216694,
0.018592456355690956,
-0.030403481796383858,
0.00021327032300177962
] |
<ol>
<li><p>All the linearly independent eigenfunctions of the parity operator $\mathcal{P}$ form an infinite set and all the linearly independent eigenfunctions of the unit operator $\bf 1$ also form an infinite set. Is the cardinality of these two sets same or different? </p></li>
<li><p>Every function is an eigenfunction of the unit operator $\bf 1$. Right? Can any arbitrary function be written as the linear combination of the eigenfunctions of $\mathcal{P}$? If not, doesn't this imply that the set linearly independent eigenfunctions of unit operator $\bf 1$ forms a much bigger set than that of $\mathcal{P}$?</p></li>
</ol>
<p><strong>EDIT:</strong> I just want to know since $[\mathcal{P},\bf{1}]=0$, whether the total number of linearly independent eigenvectors of $\mathcal{P}$ and $\bf{1}$, forms a basis i.e., do they have same number of linearly independent eigenvectors and and whether both spans the space? </p>
| 8,511 |
[
-0.020184319466352463,
0.034250058233737946,
-0.019594548270106316,
0.002592496806755662,
0.049956101924180984,
0.01714714802801609,
-0.005956076085567474,
-0.06000068038702011,
0.014994694851338863,
-0.026510069146752357,
0.05486520007252693,
-0.007883903570473194,
0.04428407549858093,
0.006484200246632099,
0.023872924968600273,
0.014741385355591774,
-0.033946096897125244,
0.02538485825061798,
-0.005394008010625839,
0.018399519845843315,
0.011249150149524212,
0.041278719902038574,
0.05748075619339943,
-0.03747215121984482,
-0.02858642116189003,
0.0407424122095108,
-0.029237795621156693,
0.021720534190535545,
0.03126281127333641,
0.07040654867887497,
-0.007096854504197836,
-0.021986858919262886,
0.04268037527799606,
0.024604076519608498,
0.013997411355376244,
-0.027691714465618134,
-0.029354369267821312,
-0.004596749786287546,
-0.004457714967429638,
-0.006721974816173315,
-0.034263256937265396,
-0.05959678068757057,
-0.0019290291238576174,
0.0407300740480423,
-0.00048713033902458847,
-0.009071732871234417,
0.020263388752937317,
-0.052073974162340164,
0.040901996195316315,
-0.044751569628715515,
0.05784539133310318,
-0.01570516638457775,
0.04177276790142059,
0.006002867128700018,
-0.003354252316057682,
-0.019991984590888023,
0.024702642112970352,
0.0805872455239296,
0.014751997776329517,
-0.07092642784118652,
-0.0018525320338085294,
0.0015513936523348093,
0.008409837260842323,
-0.002367550740018487,
-0.06102863699197769,
0.027427054941654205,
0.01595224067568779,
0.010057060047984123,
-0.007725120987743139,
-0.021279245615005493,
-0.015295254997909069,
0.05267677083611488,
0.03194188326597214,
-0.04057960957288742,
0.008321941830217838,
0.0051687671802937984,
0.036014147102832794,
0.02702387049794197,
0.05539573356509209,
0.006976236589252949,
0.01292426884174347,
0.045418545603752136,
-0.0016467248788103461,
-0.002650999929755926,
0.043193597346544266,
0.00815995316952467,
0.07566749304533005,
-0.023037303239107132,
0.00927804596722126,
0.005391767248511314,
0.02617757022380829,
0.0013542373199015856,
0.02150222286581993,
0.004947169218212366,
-0.021997395902872086,
0.0442085936665535,
0.02626142092049122,
0.006207834463566542,
0.009451939724385738,
-0.01720082014799118,
0.010276642628014088,
-0.04893740266561508,
-0.007964546792209148,
0.05205147713422775,
0.021970635280013084,
-0.013316352851688862,
-0.05174858495593071,
0.044227030128240585,
-0.042993493378162384,
-0.02113758958876133,
0.010107445530593395,
0.03833813592791557,
-0.021164072677493095,
0.0354345366358757,
0.002575088292360306,
-0.01755545847117901,
0.01514417678117752,
-0.006389569025486708,
0.035168975591659546,
0.08453517407178879,
0.046784281730651855,
-0.04409430921077728,
0.04105689749121666,
-0.03984467685222626,
-0.0336238294839859,
0.010610210709273815,
0.0048782480880618095,
-0.018093235790729523,
-0.06492341309785843,
0.03879215195775032,
0.01653575710952282,
0.0046401903964579105,
-0.0005023819394409657,
-0.0106525719165802,
0.0342823788523674,
-0.023052994161844254,
-0.09082597494125366,
-0.026722760871052742,
0.03923945501446724,
-0.05647465959191322,
-0.027424098923802376,
-0.039503734558820724,
0.0188333448022604,
0.025047000497579575,
0.04316257685422897,
-0.03710464760661125,
0.051661670207977295,
0.025253836065530777,
0.02285972610116005,
0.0064803375862538815,
-0.014030798338353634,
-0.0012625602539628744,
-0.015426892787218094,
-0.028671281412243843,
0.015174522064626217,
-0.04758361726999283,
0.03343411535024643,
0.03008921630680561,
0.025789247825741768,
-0.04854627698659897,
0.06384046375751495,
-0.015438474714756012,
0.0010527538834139705,
0.0030528604984283447,
0.019779300317168236,
-0.019231993705034256,
0.04058772698044777,
0.02918311022222042,
0.06731319427490234,
0.017147576436400414,
-0.01771002821624279,
-0.009794375859200954,
0.04683299735188484,
0.030295221135020256,
0.014623638242483139,
-0.009437763132154942,
-0.061254359781742096,
-0.044032081961631775,
0.01741480827331543,
0.028864629566669464,
-0.07491105794906616,
-0.007008547428995371,
-0.050310101360082626,
0.021227842196822166,
0.004424913786351681,
0.05710970237851143,
0.013154851272702217,
-0.03073599562048912,
-0.015385881066322327,
-0.04373367130756378,
-0.013245034962892532,
-0.06394355744123459,
0.03297480195760727,
0.027745693922042847,
-0.02497437223792076,
0.041631489992141724,
0.012174864299595356,
0.011341342702507973,
-0.0318785198032856,
0.00007004335930105299,
-0.04400009661912918,
0.030909668654203415,
0.007938490249216557,
-0.0266977958381176,
0.021391740068793297,
0.04736288636922836,
0.0757555440068245,
0.01594235561788082,
0.03288298845291138,
-0.02026468701660633,
-0.019543465226888657,
0.04853794351220131,
-0.003138215048238635,
0.022844946011900902,
-0.003534230636432767,
0.00042470660991966724,
-0.020490210503339767,
-0.007533574942499399,
-0.009043566882610321,
0.0470409020781517,
-0.05367676168680191,
0.009682686068117619,
0.010068217292428017,
0.020686820149421692,
-0.0018358842935413122,
0.03149840980768204,
0.02554609440267086,
0.0024091433733701706,
0.0019186618737876415,
0.012117060832679272,
-0.050321098417043686,
0.003742931177839637,
-0.0006164779770188034,
0.07074321806430817,
-0.0070007867179811,
0.03258705884218216,
0.025009213015437126,
0.03215654939413071,
0.020709654316306114,
0.006280425004661083,
-0.027678055688738823,
-0.02939174696803093,
0.01615690253674984,
0.02092740684747696,
0.05203959345817566,
-0.000029727108994848095,
-0.030072152614593506,
-0.0070220003835856915,
0.04067692160606384,
0.018533309921622276,
0.01390755083411932,
0.03680356964468956,
-0.016085492447018623,
0.002485287608578801,
-0.025752652436494827,
-0.03724236786365509,
0.02588360756635666,
0.005219044629484415,
-0.01584651693701744,
-0.008052402175962925,
-0.010412156581878662,
-0.0020474251359701157,
-0.03261949494481087,
-0.02044094353914261,
-0.007006379310041666,
-0.035799577832221985,
-0.07788880914449692,
-0.022970618680119514,
0.03968582674860954,
0.0007699079578742385,
0.00235187541693449,
-0.01723458245396614,
-0.029720159247517586,
-0.014614013954997063,
-0.035130612552165985,
0.06051123887300491,
-0.008793950080871582,
0.014359986409544945,
-0.048164982348680496,
-0.011164028197526932,
0.027491973713040352,
-0.03980077803134918,
0.04001685976982117,
-0.0021717511117458344,
-0.055316805839538574,
0.02429337427020073,
-0.06403740495443344,
-0.004433081950992346,
0.003830007975921035,
-0.016937537118792534,
0.024129820987582207,
0.03981010988354683,
-0.021613361313939095,
-0.049751996994018555,
-0.01876397803425789,
-0.027438567951321602,
0.040490198880434036,
-0.04423876106739044,
0.00966387428343296,
0.028016744181513786,
0.0010640661930665374,
-0.03489905595779419,
-0.034359827637672424,
-0.06078705936670303,
-0.017044033855199814,
-0.008803773671388626,
0.007106051780283451,
0.01990402117371559,
-0.027111873030662537,
-0.01585295982658863,
0.04294976219534874,
-0.029273275285959244,
0.00022380375594366342,
-0.0665351152420044,
-0.06585933268070221,
-0.013923106715083122,
-0.004993559326976538,
0.03754628449678421,
-0.012702898122370243,
-0.019278323277831078,
0.08751578629016876,
0.04319903999567032,
-0.03052285499870777,
-0.026004796847701073,
0.019184082746505737,
-0.012203914113342762,
-0.02170698717236519,
0.04499282315373421,
0.03860143572092056,
-0.007211808115243912,
0.009006842039525509,
0.04735616222023964,
0.026708465069532394,
0.014502746984362602,
0.0012965323403477669,
0.009407882578670979,
-0.002920469967648387,
0.00026696137501858175,
-0.03240635246038437,
0.026575878262519836,
-0.020926494151353836,
-0.015798453241586685,
0.011150792241096497,
0.0036623943597078323,
-0.00187139050103724,
-0.002064184285700321,
-0.012578029185533524,
0.05949215218424797,
0.02758610248565674,
0.044526357203722,
-0.07251088321208954,
0.05048082396388054,
0.0586576946079731,
0.009376090951263905,
-0.01852014660835266,
0.0071951840072870255,
0.03172387182712555,
-0.06519655883312225,
-0.006441878620535135,
0.029364150017499924,
0.007148463279008865,
-0.04100080579519272,
-0.0007934587774798274,
-0.023159420117735863,
0.023395847529172897,
0.022880449891090393,
-0.01623094454407692,
-0.030755827203392982,
0.02554108388721943,
0.011744794435799122,
0.03343721479177475,
0.009187080897390842,
-0.006109379231929779,
0.020513737574219704,
-0.053652916103601456,
0.011283942498266697,
-0.019589267671108246,
0.03999263420701027,
-0.010352923534810543,
0.05591081455349922,
-0.01070832833647728,
0.015031660906970501,
-0.008747120387852192,
0.0018228939734399319,
-0.09862013906240463,
-0.028553374111652374,
-0.01804742030799389,
-0.005039283074438572,
-0.009265098720788956,
-0.0021488263737410307,
0.00413910485804081,
-0.007138134445995092,
-0.0315123051404953,
0.008951220661401749,
-0.019821690395474434,
-0.04380929842591286,
0.036788832396268845,
-0.049595173448324203,
-0.01932532526552677,
-0.009980511851608753,
0.018940145149827003,
0.035536326467990875,
0.0048987967893481255,
0.023236965760588646,
0.031108379364013672,
-0.02543877437710762,
0.028861667960882187,
0.00423531886190176,
0.01039861049503088,
0.02360655926167965,
0.04339536279439926,
0.020891433581709862,
0.05479474738240242,
0.011158904992043972,
-0.008217916823923588,
-0.00695972703397274,
0.03762468695640564,
0.05417210981249809,
0.0026420368812978268,
0.018802549690008163,
-0.03670387342572212,
0.02186533622443676,
-0.018896030262112617,
0.04545070603489876,
-0.013612087815999985,
-0.0010970070725306869,
0.032631661742925644,
-0.0009308802546001971,
-0.018035851418972015,
0.02929988130927086,
0.05786404013633728,
-0.01085546612739563,
0.006094872485846281,
-0.025535931810736656,
0.0001227548928000033,
-0.03949287161231041,
-0.008053675293922424,
-0.03747255727648735,
-0.010893657803535461,
-0.006827466189861298,
0.002942116232588887,
0.013729222118854523,
0.002134311245754361,
0.007430055178701878,
-0.00001441778749722289,
0.01891518011689186,
-0.004075473640114069,
0.004095892887562513,
-0.03345797210931778,
-0.010348956100642681,
0.05500240996479988,
0.026676099747419357,
0.019995706155896187,
-0.006627599708735943,
-0.022203700616955757,
0.0011804651003330946,
0.04855175316333771,
0.014879767782986164,
-0.003280536737293005,
0.019302748143672943,
-0.027697576209902763,
-0.02005622908473015,
0.04606129229068756,
-0.021241111680865288,
0.04608520492911339,
-0.019323045387864113,
0.00741167739033699,
-0.010295595973730087,
-0.04663264751434326,
-0.02210831828415394,
-0.0015769777819514275,
0.006435946095734835,
0.0006782244308851659,
-0.04252643138170242,
0.02072875015437603,
-0.011817779392004013,
0.026630450040102005,
0.004964870400726795,
0.057762231677770615,
-0.008424793370068073,
0.03654373064637184,
0.0127711808308959,
0.02298773266375065,
0.014821705408394337,
-0.06393009424209595,
0.04259367659687996,
0.031083259731531143,
-0.00850242655724287,
0.003404036397114396,
-0.019742656499147415,
-0.047423433512449265,
0.03700728341937065,
-0.00032566679874435067,
-0.020566551014780998,
0.021690482273697853,
-0.046527501195669174,
0.07738181203603745,
0.03804647549986839,
0.011004194617271423,
0.07906003296375275,
0.035387106239795685,
0.0026885676197707653,
0.001122165471315384,
-0.02092956006526947,
0.00722088199108839,
-0.015066725201904774,
0.006760532036423683,
-0.038854703307151794,
-0.003537091426551342,
-0.03705029934644699,
0.04860195517539978,
0.0012126718647778034,
0.01616555266082287,
0.0027146816719323397,
-0.0015232888981699944,
-0.03486727923154831,
0.06176341325044632,
-0.009815467521548271,
-0.0033318151254206896,
-0.008722666651010513,
0.05129177123308182,
0.0018240782665088773,
-0.0162272397428751,
-0.004151082597672939,
-0.022859148681163788,
0.028414862230420113,
0.029466181993484497,
-0.00004256913598510437,
0.04386064410209656,
-0.027517668902873993,
-0.018616391345858574,
-0.00357775273732841,
-0.06137491390109062,
0.025065110996365547,
-0.008830268867313862,
0.025850623846054077,
0.048456016927957535,
-0.06705780327320099,
-0.052803270518779755,
0.03988983854651451,
0.0015379219548776746,
0.010048754513263702,
-0.04210304468870163,
0.03637988865375519,
-0.03297017887234688,
-0.02556920051574707,
-0.07369162142276764,
-0.044814907014369965,
0.032398778945207596,
0.03372662141919136,
-0.02086346037685871,
-0.019026385620236397,
0.012726559303700924,
-0.0024416944943368435,
0.002988760359585285,
-0.018510274589061737,
0.012378266081213951,
-0.05129854753613472,
-0.025888117030262947,
0.007930227555334568,
-0.018311815336346626,
0.045226629823446274,
-0.016081780195236206,
-0.006212351378053427,
-0.012672694399952888,
0.005527809262275696,
-0.02414075843989849,
-0.030516158789396286,
0.030617423355579376,
-0.001253877067938447,
-0.04308687895536423,
-0.025251731276512146,
-0.017088044434785843,
0.01543616782873869,
-0.03474970906972885,
-0.052068743854761124,
0.009094519540667534,
0.01170884445309639,
-0.024531938135623932,
0.031123680993914604,
-0.02201768569648266,
0.026928821578621864,
0.023155225440859795,
0.012794889509677887,
-0.025392159819602966,
-0.025346161797642708,
-0.08187887072563171,
-0.007112649269402027,
-0.023071888834238052,
-0.01946362853050232,
0.03574337437748909,
0.040980007499456406,
-0.02248501591384411,
0.015080815181136131,
0.012469864450395107,
-0.013076679781079292,
0.009264390915632248,
-0.019156506285071373,
0.01726355403661728,
-0.031703881919384,
0.00712973577901721,
-0.03295282647013664,
-0.006336018908768892,
-0.04099266603589058,
0.012599539011716843,
0.009208790957927704,
0.0277654230594635,
0.008065152913331985,
0.04810072109103203,
-0.009015316143631935,
0.007779145147651434,
0.006725693121552467,
-0.006152217276394367,
0.016934778541326523,
-0.012965556234121323,
0.03384881094098091,
-0.043786365538835526,
-0.020630238577723503,
0.04132414236664772,
0.061207354068756104,
-0.0039743478409945965,
-0.005150173790752888,
0.001162864500656724,
-0.03390176594257355,
0.05981413275003433,
-0.02586422860622406,
-0.05823085829615593,
0.011607945896685123,
-0.03780588507652283,
-0.009269101545214653,
-0.013332199305295944,
-0.04681684821844101,
0.04173961281776428,
0.04723485931754112,
0.028185907751321793,
-0.048825375735759735,
-0.03588288649916649,
-0.018168410286307335,
-0.0032900746446102858,
0.028149984776973724,
0.028990034013986588,
0.006461116950958967,
-0.0015765229472890496,
0.010876801796257496,
0.0012742473045364022,
-0.001800179248675704,
-0.01505263615399599,
-0.05389650911092758,
-0.027431229129433632,
-0.04734673351049423,
-0.06732993572950363,
0.008988895453512669,
-0.015011233277618885,
-0.017330309376120567,
0.015796704217791557,
-0.03984360024333,
0.044777221977710724,
0.023114867508411407,
0.033541034907102585,
-0.03311769291758537,
0.03016001731157303,
0.018491022288799286,
0.04877934604883194,
0.0072504072450101376,
0.009901249781250954,
0.11132882535457611,
0.05435289442539215,
0.027334414422512054,
-0.058196887373924255,
0.002475454704836011,
0.014267685823142529,
-0.016631267964839935,
-0.06612687557935715,
0.0190613754093647,
0.005067597609013319,
0.01960538886487484,
-0.009930773638188839,
0.041846685111522675,
-0.0244463998824358,
-0.02040213905274868,
0.006914461962878704,
-0.03593858703970909,
-0.05007516220211983,
0.00919654406607151,
0.015465322881937027,
0.012117189355194569,
0.03236230090260506,
-0.03665507212281227,
-0.029732154682278633,
-0.0007491238648071885,
-0.01931174099445343,
-0.032602280378341675,
-0.01837901398539543,
0.03270667418837547,
0.0008650350500829518,
-0.012807737104594707,
-0.03363518416881561,
0.002527265576645732,
0.00729020731523633,
-0.04754883795976639,
0.017201675102114677,
-0.011012307368218899,
-0.01381031982600689,
0.03763173148036003,
0.05394330993294716,
0.0020486204884946346,
-0.005135463085025549,
0.04243249446153641,
-0.016209645196795464,
-0.03239450603723526,
0.0012222047662362456,
-0.05677753686904907,
0.038931552320718765,
-0.039719708263874054,
-0.0029398328624665737,
-0.00841652974486351,
-0.007484251633286476,
-0.012151303701102734,
-0.0751018151640892,
-0.001999788684770465,
-0.0014239436713978648,
0.03285550698637962,
-0.0008568374323658645,
0.008137969300150871,
-0.014213747344911098,
-0.015108928084373474,
0.007307377178221941,
0.03377548232674599,
-0.02777278609573841,
-0.024014651775360107,
0.031920451670885086,
-0.0008376518380828202,
0.05762669816613197,
-0.015241188928484917,
0.0228083785623312,
0.018497494980692863,
-0.04480905830860138,
-0.0308229960501194,
-0.029217252507805824,
0.030068544670939445,
0.0362112782895565,
0.04811128228902817,
0.016004100441932678,
-0.02151207998394966,
-0.0342109352350235,
-0.06029330566525459,
-0.0060667903162539005,
-0.018743062391877174,
-0.01752641052007675,
0.0008333965088240802,
0.004154033958911896,
0.0042410255409777164,
0.028415221720933914,
-0.00017804172239266336,
-0.02074483223259449,
-0.0010082490043714643,
-0.013597008772194386,
0.019617384299635887,
-0.062589131295681,
-0.017152981832623482,
-0.006582311354577541,
-0.02282000705599785,
0.026159243658185005,
-0.027246957644820213,
0.02523929439485073,
0.0138898566365242,
0.01735490746796131,
-0.014091803692281246,
0.027836479246616364,
-0.01747698336839676,
0.01513981819152832,
-0.00385185400955379,
-0.02865850366652012,
0.020424839109182358,
0.05812850221991539,
0.0338248685002327,
-0.03649961203336716,
-0.05678597837686539,
-0.002195474226027727,
-0.0183334369212389,
0.011989926919341087,
0.024487817659974098,
-0.06724021583795547,
-0.03709659352898598,
0.021878208965063095,
0.026222938671708107,
-0.0026540241669863462,
-0.004024529829621315,
-0.028674932196736336,
0.01303014811128378,
0.015255606733262539,
-0.004769530147314072,
0.00954761728644371,
0.019756659865379333,
-0.03415792062878609,
-0.04701681435108185,
0.048276495188474655,
0.04091909900307655,
-0.026022376492619514,
-0.00860651582479477,
0.023332422599196434,
0.003394428174942732,
0.04911364987492561,
-0.026514293625950813,
0.018007300794124603,
0.023293782025575638,
-0.0638551414012909,
-0.035499803721904755,
0.03417111933231354,
-0.02311032824218273,
0.05790966749191284,
0.017701631411910057,
-0.01564646139740944,
-0.02753899246454239,
0.050087105482816696,
-0.017460040748119354,
0.026288997381925583,
-0.025217458605766296,
0.007736911065876484,
0.010104525834321976,
0.0097811846062541,
0.003477417165413499,
0.013486970216035843,
-0.017627989873290062,
0.013738276436924934,
0.04242158681154251,
-0.040079038590192795,
-0.0512005090713501,
0.0009787653107196093,
0.02805205248296261,
0.010408034548163414,
0.0039012543857097626,
-0.0036972861271351576,
-0.00383243546821177,
0.019340094178915024,
-0.027221478521823883,
0.06280150264501572,
0.03791681304574013,
-0.0066163064911961555,
-0.11335397511720657,
-0.02560308203101158,
-0.019459236413240433,
0.012593942694365978,
0.025974402204155922,
-0.049393098801374435,
-0.014679822139441967,
0.010223835706710815,
-0.08159123361110687,
0.06181308999657631,
0.000259367807302624,
-0.0021991345565766096,
-0.04262825846672058,
0.013491575606167316,
-0.05048704519867897,
0.013012868352234364,
0.040830347687006,
0.052453625947237015,
0.023557113483548164,
0.029081204906105995,
-0.008312721736729145,
-0.013976569287478924,
-0.03576960042119026,
0.005459131207317114,
-0.033987194299697876,
-0.030501194298267365,
0.06294107437133789,
-0.03387299180030823,
-0.025923695415258408,
0.023951034992933273,
-0.0019425605423748493,
-0.04618888348340988,
0.014658080413937569,
0.014350682497024536,
0.02217033877968788,
0.02257646434009075,
-0.013988626189529896,
0.001145708141848445,
-0.03767989203333855,
0.017935315147042274,
0.023209448903799057,
0.002428249455988407,
-0.011577412486076355,
0.003728459356352687,
0.028516916558146477,
0.005633838474750519,
-0.005990218836814165,
0.01702171191573143,
0.0003589258994907141,
-0.013236126862466335,
0.004677035845816135,
-0.013932020403444767,
-0.02564300410449505,
-0.008827905170619488,
0.014416137710213661,
-0.027471359819173813,
-0.013206793926656246,
0.012732383795082569,
0.0016328351339325309,
-0.015168284997344017,
0.021308355033397675,
0.011848226189613342,
-0.026036502793431282,
0.04158882424235344,
0.029912153258919716,
-0.01571054570376873,
-0.04955779016017914,
-0.0067580752074718475,
0.02368437871336937,
-0.00790044292807579,
0.015135201625525951,
-0.055116910487413406,
-0.07208504527807236,
-0.004421832039952278,
0.0004736976698040962,
0.014918231405317783,
-0.02345273271203041,
-0.02124563790857792,
-0.03564098849892616,
-0.052218612283468246,
0.03988850116729736,
0.014688562601804733,
0.002181398682296276,
-0.015565539710223675,
-0.0192903783172369,
0.014361985959112644,
0.016129741445183754,
0.042566929012537,
0.01632196642458439,
-0.018381435424089432,
-0.027378028258681297,
-0.0013552582822740078,
0.03793371841311455,
0.009711450897157192,
0.013995508663356304,
0.003708577249199152,
-0.034246500581502914,
-0.0012473396491259336,
-0.0030250928830355406,
0.02069476619362831,
0.010621215216815472,
-0.005262481048703194,
-0.008950382471084595,
-0.009403246454894543,
-0.022393114864826202,
-0.06306996196508408,
0.0823996439576149,
0.04715263471007347,
0.0037355278618633747,
0.06806132942438126,
0.012899099849164486,
0.03166944906115532,
0.009725434705615044,
-0.024712922051548958,
-0.008206194266676903,
-0.02124418318271637,
-0.0668407455086708,
-0.013132773339748383,
0.0011185205075889826,
0.03460810333490372,
0.037163764238357544,
-0.022494835779070854,
-0.03580782935023308,
0.05133820325136185,
-0.07137320190668106,
-0.04985832795500755,
0.03851086273789406,
0.02623768337070942,
0.0108161810785532,
0.002498890506103635,
0.02106093242764473,
0.02363794855773449,
-0.0023264079354703426,
0.0728706568479538,
0.02761716954410076,
-0.0014080229448154569,
-0.015215802006423473,
0.02669709175825119,
0.01936672069132328,
-0.00887650903314352,
0.012914715334773064,
0.031214388087391853,
0.03681477531790733,
-0.01364014483988285,
0.010845853947103024,
0.050473809242248535,
-0.01110310759395361,
-0.017842043191194534,
0.011621532961726189,
-0.03225244954228401,
0.09106986969709396,
-0.004053044132888317,
0.04065455496311188,
-0.02988201379776001,
0.010481608100235462,
0.0034295960795134306,
0.007431563455611467,
0.0383790098130703,
0.007722071371972561,
-0.021699747070670128,
-0.01757045090198517,
-0.05066812410950661,
0.024638790637254715,
0.04829373210668564,
-0.0843062698841095,
-0.015420103445649147,
-0.013946234248578548,
-0.006619569379836321,
0.004548374097794294,
-0.014518310315907001,
0.007280489429831505,
-0.024969633668661118,
0.00892071332782507,
0.0496947355568409,
0.056789904832839966,
-0.019355639815330505,
-0.0038774581626057625,
-0.0060996706597507,
0.04688302055001259,
-0.039194732904434204,
-0.009132260456681252,
-0.04717745631933212,
0.018777741119265556,
-0.019721155986189842,
0.03871464356780052
] |
<p>I am using <a href="http://chipmunk-physics.net/" rel="nofollow">Chipmunk</a>'s physics engine to simulate 2D classical mechanics of solid polygons (excellent by the way!). The only way you can alter the spontaneous behaviour of the the simulated objects is to apply <a href="http://chipmunk-physics.net/release/ChipmunkLatest-Docs/#cpBody-Forces" rel="nofollow">forces and impulses</a> to them.</p>
<p>I am given a certain amount $E$ of energy to spend (= to input into the system) over a certain period of time $\Delta T$, that I need to use to alter the motion of a given body. By the time I need to do so, it is rather difficult to access its mass, instantaneous speed, kinetic moment, energy, or other forces applied to it.. </p>
<p>(I can still track its shape, position and rotation.)</p>
<p>However, I feel like I don't need to access all these to actually spend this energy and alter its motion (with the only tools I am given) provided I decide I will do it by applying a single force $F$ to it over the period $\Delta T$, and provided I give myself an application point $P$ and a direction $d$ (both relative to the body's actual position and rotation).</p>
<hr>
<p>To be more precise about "my feeling": no matter the actual situation of the body, I will apply this force and spend this energy over $\Delta T$:</p>
<ul>
<li>if it turns out to be a very heavy object, then it won't move a lot</li>
<li>if it turns out to be in a super-fast race against $d$, then its speed won't change a lot</li>
<li>if it turns out to be blocked under a stone, then it won't move a lot</li>
<li>if it turns out to be free, light, resting.. then the change will be visible..</li>
</ul>
<p>(I am aware that the concept of <em>force</em> might be the wrong one to consider here, so I just want to make sure we'll agree about what I am talking about, whatever it might be. It is exactly like this body had a certain amount of energy to spend and used it to <em>move itself</em> without actually knowing anything about the world around.)</p>
<hr>
<p>If I was right about this feeling that I do have everything I need to perform this alteration without spending more than $E$, then how would I compute the actual intensity of $F$ to be applied?</p>
<p>If I was wrong, then what information am I missing?</p>
<hr>
<p>[EDIT]: It turns out from the discussion that I actually need to give myself a certain <em>cost of applying a force</em> $\beta\ (m.s^{-1})$, inspired from biophysics. Then the actual energy spent is simply $$E = \beta \int_{\Delta t} F(t) \mathrm{d}t,$$ and I just have to take care that it will never be lower than the actual work $W$ done by $F$ over $\Delta t$.</p>
<p>To achieve this, one solution seems to keep constantly track of the actual useful energy spent, which is difficult but.. not undoable.</p>
| 8,512 |
[
-0.008398817852139473,
-0.00831225048750639,
-0.004857296124100685,
-0.04376373067498207,
0.04076734557747841,
-0.022337831556797028,
-0.02223081700503826,
-0.04891779273748398,
-0.02949916385114193,
-0.032202333211898804,
0.02087145671248436,
0.06081610545516014,
0.0004339472798164934,
0.05831754207611084,
0.0071161407977342606,
-0.00041637520189397037,
-0.012624040246009827,
-0.015507739037275314,
-0.00800746027380228,
-0.03165598213672638,
0.03818189725279808,
-0.013448899611830711,
0.008462699130177498,
-0.012864361517131329,
-0.005026441533118486,
0.03142944723367691,
0.0007144922856241465,
-0.06905868649482727,
-0.03542270511388779,
0.049089789390563965,
-0.053409624844789505,
-0.03138124570250511,
0.00017602053412701935,
-0.014203060418367386,
0.005538041703402996,
0.03431867063045502,
-0.03424385190010071,
-0.0030310628935694695,
0.0426701158285141,
0.0005673557752743363,
-0.057607319205999374,
0.03297775238752365,
-0.004957182798534632,
0.07232940942049026,
0.008725178427994251,
0.04003137722611427,
0.011236007325351238,
-0.001345973345451057,
0.055074941366910934,
-0.03818003833293915,
0.05101337283849716,
0.004015878774225712,
0.029504278674721718,
0.02867554873228073,
-0.027177685871720314,
-0.049482762813568115,
0.053806956857442856,
0.05985531583428383,
-0.016404902562499046,
-0.03456678241491318,
0.010947403497993946,
-0.01350344903767109,
-0.014424607157707214,
-0.04197016358375549,
-0.0034648356959223747,
0.006101822014898062,
0.019983455538749695,
-0.02697710320353508,
0.0262108463793993,
-0.0251025203615427,
0.014239058829843998,
-0.007974876090884209,
0.032622065395116806,
-0.006973970681428909,
0.01695251651108265,
-0.030542124062776566,
-0.011979088187217712,
0.050038937479257584,
0.017589136958122253,
0.056498702615499496,
-0.037267476320266724,
-0.012409280985593796,
0.009299107827246189,
0.03946881368756294,
0.015417578630149364,
-0.03542524203658104,
0.04610401764512062,
0.02198786661028862,
-0.011900222860276699,
0.04439771920442581,
-0.022574439644813538,
-0.02483719028532505,
0.028836989775300026,
-0.03792628273367882,
0.019866690039634705,
0.0005372486775740981,
0.006453850772231817,
0.012995741330087185,
-0.01692274585366249,
-0.010147418826818466,
-0.03472111374139786,
-0.03614520654082298,
-0.0046890294179320335,
0.059306975454092026,
-0.007798006292432547,
0.016614286229014397,
-0.002184866461902857,
0.0159774087369442,
0.007744047790765762,
-0.0030796355567872524,
-0.012326818890869617,
0.0025241610128432512,
-0.027096150442957878,
0.025658318772912025,
0.027951063588261604,
-0.021610338240861893,
-0.04377582296729088,
-0.02964192070066929,
0.05506456270813942,
0.027063557878136635,
0.04078218340873718,
-0.04928277060389519,
-0.023598605766892433,
-0.05025995895266533,
-0.05473215878009796,
0.008454316295683384,
0.03678711876273155,
-0.00802753958851099,
-0.04003550112247467,
0.007974582724273205,
-0.00033189720124937594,
-0.021459955722093582,
0.01858699508011341,
-0.01939515583217144,
0.008042880333960056,
0.009622969664633274,
-0.10758265107870102,
-0.05949407443404198,
0.07760695368051529,
0.005876644514501095,
-0.009833133779466152,
-0.10046904534101486,
-0.032117411494255066,
0.03578820824623108,
0.05165841057896614,
-0.0017006340203806758,
-0.025809230282902718,
0.01808556355535984,
0.03544670715928078,
-0.021694829687476158,
-0.004708942491561174,
-0.0014185482868924737,
-0.005441566463559866,
-0.045767009258270264,
-0.01505509577691555,
-0.0427071712911129,
0.05206020921468735,
0.042068544775247574,
-0.026622096076607704,
0.04108618199825287,
0.039644092321395874,
-0.03762798011302948,
0.0055838036350905895,
0.012327576987445354,
-0.007020777557045221,
-0.028958840295672417,
0.06558092683553696,
0.009550880640745163,
0.023892244324088097,
0.002196826273575425,
0.0007184959831647575,
0.016021395102143288,
-0.01750473491847515,
-0.005402046721428633,
0.05248959735035896,
-0.011522702872753143,
-0.019197894260287285,
-0.014845214784145355,
-0.04629436880350113,
-0.015814360231161118,
-0.05715589597821236,
-0.056129757314920425,
0.01697031781077385,
-0.01886606588959694,
0.012601564638316631,
0.058907683938741684,
0.005854140501469374,
0.027259044349193573,
0.03267017379403114,
-0.03899642452597618,
-0.03518824279308319,
-0.058038994669914246,
0.0011996858520433307,
0.017669105902314186,
0.015027154237031937,
0.02387399412691593,
0.0007339548319578171,
-0.02613045647740364,
-0.01594805344939232,
-0.037049319595098495,
0.013384872116148472,
0.021872393786907196,
0.006432074122130871,
-0.03598102927207947,
0.009005029685795307,
0.03638966381549835,
0.019648300483822823,
0.0039116316474974155,
-0.02843134105205536,
-0.003297866554930806,
-0.014746224507689476,
-0.02605678141117096,
-0.06888820976018906,
0.022521819919347763,
0.027179086580872536,
0.01782376691699028,
0.04385387897491455,
0.01769915223121643,
0.00433043297380209,
0.0000017131935692304978,
-0.00945216417312622,
0.04989228397607803,
0.04867078363895416,
0.016770238056778908,
0.030195673927664757,
0.07022178173065186,
-0.016796208918094635,
0.04700598493218422,
-0.010718869976699352,
-0.033178139477968216,
-0.04622779041528702,
-0.010435677133500576,
0.002616757759824395,
0.04515928030014038,
-0.03464510291814804,
0.019507478922605515,
0.02508259192109108,
-0.0021088614594191313,
0.02431689202785492,
0.008222708478569984,
-0.0026277664583176374,
-0.014062793925404549,
0.04568826034665108,
0.01340754609555006,
-0.00551251508295536,
0.011018896475434303,
-0.017361678183078766,
0.018139837309718132,
-0.0013637071242555976,
0.043010979890823364,
0.005571306683123112,
0.014616463333368301,
0.01508583128452301,
-0.003076838329434395,
0.02066417969763279,
-0.0017547360621392727,
0.014517913572490215,
0.01656583696603775,
0.010762653313577175,
0.04964679479598999,
-0.03627213090658188,
-0.014840109273791313,
-0.045350734144449234,
-0.055287133902311325,
0.01614494062960148,
0.01942623220384121,
-0.020078297704458237,
-0.015221109613776207,
0.04593817517161369,
-0.005908009596168995,
0.02025064453482628,
0.007911210879683495,
-0.010481043718755245,
-0.031611837446689606,
-0.01473249215632677,
-0.015517453663051128,
0.04482855275273323,
0.025004146620631218,
-0.03999275714159012,
-0.003618568880483508,
0.01588178239762783,
-0.012580977752804756,
0.029018528759479523,
0.02977227047085762,
-0.05361529812216759,
-0.0006943456828594208,
-0.04794973134994507,
-0.05092720314860344,
0.03988449648022652,
0.002782112918794155,
-0.018821628764271736,
0.027917714789509773,
0.034472789615392685,
-0.04521971195936203,
-0.027489015832543373,
-0.016388561576604843,
0.012792701832950115,
-0.06197965517640114,
0.008585344068706036,
0.04249138385057449,
0.029222458600997925,
-0.06075671315193176,
0.002727781655266881,
-0.03592900186777115,
-0.0425073616206646,
-0.013590524904429913,
-0.018208550289273262,
-0.012609906494617462,
-0.011066297069191933,
-0.004154220223426819,
-0.0029469062574207783,
-0.03165287524461746,
0.009186250157654285,
-0.07337182760238647,
-0.06202486902475357,
-0.008262276649475098,
-0.011556027457118034,
0.0638168603181839,
0.003342048265039921,
-0.007521133869886398,
0.09749962389469147,
0.022128408774733543,
-0.0445890836417675,
-0.02877059578895569,
-0.020701711997389793,
-0.02555716782808304,
-0.07580675184726715,
-0.01154052559286356,
0.03848719969391823,
-0.05523260682821274,
-0.012135093100368977,
-0.01259603537619114,
0.0019292635843157768,
0.030769234523177147,
0.012842011637985706,
-0.02315189689397812,
-0.001830240129493177,
0.013578623533248901,
0.017461692914366722,
0.02077336795628071,
0.030988784506917,
-0.02329131029546261,
-0.003275423776358366,
-0.031279534101486206,
0.03015178255736828,
0.04110388830304146,
-0.0496087484061718,
0.06727277487516403,
0.003120540641248226,
0.0160461887717247,
0.01310459803789854,
0.045470841228961945,
-0.010313770733773708,
-0.05681374669075012,
-0.008595203049480915,
0.0017046777065843344,
0.021324338391423225,
0.0054563540033996105,
0.001824391190893948,
0.05073867365717888,
0.06566797196865082,
-0.015835462138056755,
-0.018923521041870117,
0.03950554504990578,
0.0062535470351576805,
0.03542663902044296,
-0.027005020529031754,
-0.0013205867726355791,
0.031726740300655365,
0.04038762301206589,
0.042434848845005035,
0.02091190032660961,
0.002292107092216611,
-0.0043804831802845,
-0.05859040468931198,
-0.016438627615571022,
-0.009233607910573483,
0.05981835350394249,
0.011221752502024174,
0.057152166962623596,
0.027579057961702347,
0.022515447810292244,
0.0021282555535435677,
-0.026356572285294533,
-0.08772995322942734,
0.05226736515760422,
-0.030167710036039352,
0.012440082617104053,
0.0004921214422211051,
-0.010700146667659283,
0.01893266662955284,
-0.014947404153645039,
0.006524750497192144,
-0.04642413556575775,
0.024535875767469406,
-0.017264019697904587,
0.013208601623773575,
-0.012295599095523357,
-0.04213621839880943,
-0.018545500934123993,
0.03492980822920799,
0.06983921676874161,
-0.044745977967977524,
0.0024156116414815187,
-0.009295228868722916,
-0.03910217434167862,
0.004480489995330572,
-0.009421967901289463,
-0.002691391622647643,
0.004643301013857126,
0.04987636208534241,
-0.025775345042347908,
0.02807120978832245,
-0.0027520114090293646,
0.014089821837842464,
-0.00680963508784771,
0.016379397362470627,
0.012549255043268204,
0.008597622625529766,
-0.0024248482659459114,
-0.05522770434617996,
-0.004029621835798025,
0.006844452116638422,
0.06895793974399567,
-0.0050889672711491585,
0.005922121461480856,
0.03086700476706028,
0.015327814035117626,
0.01030077412724495,
0.024446504190564156,
-0.0021609109826385975,
0.007358272559940815,
-0.02303699590265751,
-0.03892558068037033,
-0.001362572074867785,
0.000695765542332083,
0.019638923928141594,
0.017423687502741814,
0.04149048402905464,
0.016304373741149902,
0.015643255785107613,
-0.003709025913849473,
0.022699221968650818,
-0.018802566453814507,
0.019947566092014313,
-0.014236120507121086,
0.019553445279598236,
-0.012424495071172714,
0.03992052003741264,
0.026417270302772522,
0.03201791271567345,
0.011791173368692398,
-0.024720124900341034,
0.008736452087759972,
-0.05910777300596237,
-0.04332917556166649,
0.0297144316136837,
0.043578870594501495,
-0.01273679081350565,
0.011059450916945934,
-0.06415626406669617,
-0.03120477683842182,
0.02700694464147091,
-0.035162560641765594,
0.06440503895282745,
0.005608682986348867,
-0.006251466926187277,
-0.0480709932744503,
-0.03214914724230766,
-0.013347377069294453,
0.031291499733924866,
-0.04271753132343292,
0.013296330347657204,
-0.02377733215689659,
-0.03636259585618973,
0.01174972578883171,
0.022953249514102936,
0.003318036673590541,
0.0436863973736763,
-0.03937884047627449,
-0.005554606206715107,
0.00957808829843998,
-0.029777731746435165,
-0.00673131225630641,
-0.08068446069955826,
0.008797445334494114,
0.012473654933273792,
0.022674554958939552,
0.032294828444719315,
-0.013608555309474468,
-0.03812049329280853,
0.024708479642868042,
-0.04514975845813751,
-0.025666840374469757,
0.014149641618132591,
-0.04368889704346657,
0.057739321142435074,
0.033455200493335724,
-0.011067604646086693,
0.03556284308433533,
0.057494860142469406,
-0.04985201731324196,
-0.00028178392676636577,
0.012484150007367134,
-0.0219357181340456,
-0.008730322122573853,
0.001643344177864492,
-0.03241370618343353,
-0.0004441735509317368,
-0.03648274764418602,
-0.009444446302950382,
0.005128530319780111,
0.044996023178100586,
-0.015991773456335068,
-0.017752721905708313,
-0.04770518094301224,
0.030479885637760162,
-0.006576264277100563,
0.017784006893634796,
-0.021434396505355835,
-0.014920735731720924,
-0.01749126985669136,
0.00045637492439709604,
-0.0032146975863724947,
0.016303161159157753,
0.015559207648038864,
0.039455581456422806,
-0.029186615720391273,
0.0002645176718942821,
-0.0594940260052681,
-0.016410406678915024,
-0.0018184712389484048,
-0.053789883852005005,
0.06912431120872498,
-0.012878429144620895,
0.011993872933089733,
0.03202521428465843,
-0.08283530920743942,
-0.008610659278929234,
0.023100344464182854,
-0.008729088120162487,
-0.015356870368123055,
0.002445161109790206,
-0.00272906431928277,
-0.0009469217620790005,
0.01828412525355816,
-0.0022109125275164843,
-0.009456368163228035,
0.01015839446336031,
-0.012924947775900364,
-0.016389675438404083,
-0.007511479314416647,
0.0026712678372859955,
-0.017872566357254982,
-0.032934729009866714,
-0.0004825079522561282,
0.015317300334572792,
-0.026308219879865646,
0.04799240082502365,
0.008227682672441006,
0.007537639234215021,
0.0473615899682045,
0.005903621669858694,
0.012917029671370983,
0.028909048065543175,
0.0020468072034418583,
0.0009452728554606438,
0.005356659647077322,
0.023860856890678406,
-0.029063435271382332,
0.01994449645280838,
0.02205214649438858,
0.01275259256362915,
0.033073436468839645,
0.005835284944623709,
-0.013808175921440125,
0.048911791294813156,
0.0030556025449186563,
-0.014217013493180275,
-0.015778563916683197,
0.007715765852481127,
0.009825875982642174,
0.041818421334028244,
-0.008084377273917198,
0.018770389258861542,
0.0006681550876237452,
-0.0474439337849617,
-0.01087344903498888,
-0.006339929066598415,
-0.018044251948595047,
0.03016054630279541,
0.06464405357837677,
-0.047601692378520966,
-0.04484028369188309,
0.023006504401564598,
0.007204728201031685,
0.017102062702178955,
-0.005901600234210491,
0.005140652414411306,
0.0022633655462414026,
-0.029689015820622444,
0.0038838484324514866,
-0.056172993034124374,
-0.06238149106502533,
0.01451817899942398,
0.05417482554912567,
-0.008936561644077301,
0.08187897503376007,
0.031895287334918976,
0.020677980035543442,
0.028032176196575165,
-0.002771826460957527,
-0.01959521882236004,
-0.01752321608364582,
0.01875777170062065,
0.056490346789360046,
-0.015951726585626602,
-0.02031249925494194,
0.06110968068242073,
0.028581617400050163,
-0.019851410761475563,
0.04026123881340027,
0.03334793075919151,
0.008905497379601002,
0.03238628804683685,
-0.07897461205720901,
-0.037563711404800415,
0.018167128786444664,
-0.046732209622859955,
0.05042385309934616,
0.0030605020001530647,
-0.01080727856606245,
0.05473992973566055,
0.05544714257121086,
0.016931701451539993,
-0.04242163151502609,
0.03578662499785423,
-0.0644393041729927,
0.02103842794895172,
-0.0010168702574446797,
0.01993572525680065,
-0.01492052711546421,
-0.007726614363491535,
0.05350090563297272,
-0.01685202680528164,
-0.002733931876718998,
0.007978545501828194,
-0.03777565434575081,
-0.03460581973195076,
-0.014598770067095757,
-0.05931752547621727,
0.06207480654120445,
0.017766721546649933,
-0.014218081720173359,
0.06449155509471893,
-0.009593161754310131,
0.0321958065032959,
0.017267312854528427,
0.022913983091711998,
-0.01391345914453268,
0.043695855885744095,
-0.04238073527812958,
-0.012325380928814411,
-0.03926798328757286,
-0.008363846689462662,
0.1583641767501831,
0.0002589143405202776,
0.010391739197075367,
-0.02838326245546341,
0.0026238071732223034,
-0.010544231161475182,
0.02935456670820713,
-0.020705092698335648,
0.01010929699987173,
0.04892504960298538,
-0.03621218353509903,
-0.02962675876915455,
0.004674740135669708,
0.01166309230029583,
-0.039687540382146835,
0.027866311371326447,
-0.04877225309610367,
-0.007310273591428995,
0.001845500199124217,
-0.014015060849487782,
-0.032729826867580414,
-0.005968521349132061,
-0.010264748707413673,
-0.0013136271154507995,
-0.025110697373747826,
0.010499770753085613,
-0.012798521667718887,
-0.02130228467285633,
0.010167165659368038,
-0.0038688345812261105,
-0.053374964743852615,
0.003335168119519949,
-0.003440992906689644,
-0.030453551560640335,
-0.017122380435466766,
0.05819591507315636,
0.011210151948034763,
-0.020265867933630943,
-0.005659148097038269,
0.04534424841403961,
0.048084355890750885,
0.006271276623010635,
0.00027996065909974277,
-0.02632119134068489,
-0.014451633207499981,
-0.0298426765948534,
-0.08009587228298187,
0.059089500457048416,
-0.00952297355979681,
0.012998931109905243,
0.0016283749137073755,
0.029764650389552116,
-0.01845521293580532,
-0.06724724918603897,
0.019953878596425056,
-0.013886254280805588,
0.022673796862363815,
0.017025010660290718,
0.010731829330325127,
-0.0037874181289225817,
0.006576101761311293,
-0.002223898423835635,
-0.0005592782399617136,
0.012269198894500732,
-0.0178909320384264,
-0.007474907208234072,
0.0025273871142417192,
0.03660792112350464,
-0.007633942179381847,
0.0058596753515303135,
-0.018842827528715134,
-0.02335534803569317,
-0.04398947209119797,
0.020384741947054863,
0.01527041383087635,
0.03106687404215336,
0.007808397989720106,
-0.008981745690107346,
-0.001521877245977521,
-0.0852876529097557,
-0.04458640143275261,
0.018762368708848953,
0.012140398845076561,
-0.02740398235619068,
-0.0060222577303647995,
-0.019708452746272087,
0.04704893007874489,
0.017709869891405106,
0.028973497450351715,
-0.009778695181012154,
-0.004867169074714184,
0.023508118465542793,
0.017326653003692627,
0.012291484512388706,
-0.028106391429901123,
-0.01289408840239048,
-0.0033617073204368353,
0.04389498010277748,
-0.009503847919404507,
0.029980409890413284,
0.01010140310972929,
-0.06007979437708855,
0.018362615257501602,
0.05414619296789169,
-0.034861739724874496,
-0.005179856903851032,
0.062075793743133545,
-0.02578071877360344,
-0.02419484592974186,
-0.006644020788371563,
0.0029626968316733837,
-0.030070295557379723,
-0.017361775040626526,
-0.017540082335472107,
-0.02534395083785057,
-0.01235345471650362,
0.02209312468767166,
0.002985888859257102,
0.019741831347346306,
-0.06508699059486389,
0.025347063317894936,
-0.017696507275104523,
0.023903431370854378,
-0.03507167473435402,
0.002796836430206895,
0.015381339937448502,
-0.0009583815117366612,
0.008878692053258419,
-0.008451079949736595,
-0.021032894030213356,
-0.011560621671378613,
0.038122691214084625,
0.01443128939718008,
0.01041910145431757,
-0.03174179792404175,
0.030203985050320625,
-0.03033553436398506,
0.02364959754049778,
-0.0047797937877476215,
0.0038142374251037836,
0.049255240708589554,
-0.023373346775770187,
-0.03102732077240944,
0.010346325114369392,
0.007708876859396696,
0.06175582483410835,
0.02403073199093342,
-0.023540997877717018,
-0.004659315571188927,
0.07084255665540695,
-0.04507746919989586,
0.00022149999858811498,
0.03721870109438896,
-0.02227107249200344,
-0.032179925590753555,
-0.008572841994464397,
0.026721742004156113,
-0.03995548561215401,
0.0025534287560731173,
0.030983390286564827,
-0.0071751768700778484,
0.009977372363209724,
-0.020843112841248512,
0.003935347776859999,
-0.041872791945934296,
-0.020653385668992996,
0.008378642611205578,
0.004163552541285753,
0.05557895824313164,
0.019530469551682472,
-0.03578408062458038,
0.009339035488665104,
0.024037322029471397,
0.004804335534572601,
-0.11942529678344727,
0.01673421822488308,
-0.009291809052228928,
0.0016570637235417962,
0.04101282358169556,
-0.022719070315361023,
0.05126483365893364,
0.03126091510057449,
-0.06012965738773346,
0.04803985729813576,
-0.04956382140517235,
0.03585401922464371,
-0.0136494105681777,
-0.00788958091288805,
-0.03759685158729553,
0.00792850274592638,
0.028985852375626564,
-0.007766857743263245,
0.014902005903422832,
0.04199017956852913,
-0.021793801337480545,
-0.02692556567490101,
0.017516111955046654,
0.0525655671954155,
0.001097957487218082,
-0.002046608366072178,
0.03021465241909027,
-0.015559990890324116,
-0.009043743833899498,
-0.02635015919804573,
0.004746288992464542,
0.03160407394170761,
-0.04838023707270622,
0.005427055060863495,
0.0031768670305609703,
0.03510791435837746,
0.05806173384189606,
-0.022913334891200066,
0.014234540984034538,
-0.017908334732055664,
-0.031104564666748047,
0.014514272101223469,
-0.00275233993306756,
-0.0006128210225142539,
0.014756619930267334,
-0.025959627702832222,
-0.02240178734064102,
0.054100848734378815,
0.0035256545525044203,
0.0017138912808150053,
-0.003059531096369028,
-0.014335062354803085,
0.00931505486369133,
0.013026232831180096,
-0.0514267235994339,
-0.029512938112020493,
0.026389865204691887,
0.022987235337495804,
0.01591350883245468,
-0.002129920059815049,
0.012373230420053005,
-0.04119940474629402,
-0.009455525316298008,
0.00493583781644702,
-0.0003100474423263222,
-0.023595601320266724,
-0.056250300258398056,
-0.024519972503185272,
0.0008784350357018411,
0.016119252890348434,
-0.015443746000528336,
0.0033522469457238913,
-0.04834068566560745,
0.01811940222978592,
0.0626320093870163,
0.0008340846397913992,
-0.014502167701721191,
-0.00919144507497549,
-0.0026310672983527184,
-0.1078810840845108,
0.049103524535894394,
0.019940773025155067,
0.007476023398339748,
-0.045487407594919205,
-0.008386552333831787,
0.027385173365473747,
0.033471763134002686,
0.05740087851881981,
-0.03144475072622299,
-0.022672101855278015,
0.01801072433590889,
-0.002630437258630991,
0.028316954150795937,
-0.0076918406412005424,
0.0017093583010137081,
-0.022855978459119797,
0.0184917189180851,
0.029818914830684662,
0.01632138527929783,
-0.01022313628345728,
0.024828607216477394,
0.04220791906118393,
0.03686882182955742,
-0.011424306780099869,
-0.0010602521942928433,
-0.025261519476771355,
0.0288578849285841,
0.03850097954273224,
-0.008416987024247646,
0.028367606922984123,
0.03146837651729584,
0.03113299049437046,
-0.002557676285505295,
-0.06034949794411659,
-0.02506435103714466,
0.004741645883768797,
-0.057034920901060104,
0.0005328021361492574,
-0.019286062568426132,
-0.02731364592909813,
0.04121281951665878,
-0.05275600031018257,
0.003415303770452738,
0.053741734474897385,
-0.023026112467050552,
-0.011655942536890507,
0.027432356029748917,
0.04021506756544113,
0.013200832530856133,
0.017846202477812767,
0.10242810845375061,
-0.024827739223837852,
-0.030324961990118027,
-0.007815449498593807,
0.010248670354485512,
0.01794145442545414,
-0.0046148174442350864,
-0.0010089792776852846,
0.05698224529623985,
0.026588231325149536,
0.004151681438088417,
0.016649756580591202,
0.02946695126593113,
-0.0022673755884170532,
0.010620820336043835,
-0.0034894810523837805,
-0.005762553308159113,
-0.01825605146586895,
0.030242789536714554,
-0.017691146582365036,
0.06307562440633774,
-0.039459262043237686,
-0.01748872734606266,
-0.029928317293524742,
0.0005818099598400295,
0.031213149428367615,
0.018155939877033234,
-0.010673705488443375,
0.015669967979192734,
-0.006824314594268799,
-0.006164840888231993,
-0.019019026309251785,
0.011513235978782177,
0.008795395493507385,
-0.03697770833969116,
0.016923582181334496,
0.05570153892040253,
0.004927964881062508,
0.04985581710934639,
-0.015682823956012726,
-0.010252805426716805,
-0.04878632724285126,
0.02044297754764557,
0.05166201293468475,
-0.0018836467061191797,
-0.045558396726846695,
0.009686949662864208,
-0.007530840113759041,
0.037815432995557785,
-0.03849426656961441,
0.015025962144136429,
-0.03270374983549118,
0.03372766822576523,
0.007143588736653328,
0.010529120452702045
] |
<p>I am trying to find the energy of a wave travelling through a solid material in a 2D Finite Element Method (FEM) - Simulation. </p>
<p>As a general approach I would try to use $E_{kin}=\frac{1}{2}mv^2$ at the highest particle velocity $v$, as this would be the point, where all the energy in the wave is kinetic and potential energy should be zero. So I would know the energy of the wave</p>
<p>But what would I use for mass? Since it is a 2D simulation, I image that, as the third dimension is infinitely small, there is no mass. Now I remember seeing in a paper once (sorry, I don't know the source anymore), that people used density $\rho$ instead of mass in their 2D FEM simulations.</p>
<p>My questions have 2 parts:</p>
<ul>
<li>Is using density instead of mass justifiable? If not, what other approach could someone point me to?</li>
<li>The units would not match up anymore. So if it was ok to use density how would I use it.</li>
</ul>
| 8,513 |
[
-0.006251167971640825,
0.0019531401339918375,
-0.020797651261091232,
-0.0502057783305645,
0.02495654858648777,
0.014086001552641392,
-0.037865523248910904,
-0.0780533105134964,
0.014561709947884083,
-0.025305410847067833,
0.017156396061182022,
0.028524648398160934,
0.09156548976898193,
0.045310936868190765,
0.050079893320798874,
0.004225723911076784,
-0.007701267953962088,
-0.023433765396475792,
-0.017647774890065193,
-0.0640479028224945,
-0.013829894363880157,
0.003385836025699973,
0.004484187811613083,
-0.03171481192111969,
-0.025522299110889435,
0.07306978106498718,
0.019890479743480682,
-0.031055664643645287,
0.03537657484412193,
0.0014272405533120036,
-0.016501624137163162,
-0.03510153666138649,
0.019139312207698822,
0.0164936650544405,
0.023480653762817383,
0.006191235035657883,
-0.05525160953402519,
-0.037406861782073975,
0.028802540153265,
0.03856616094708443,
-0.023616719990968704,
0.005758198443800211,
-0.0010490448912605643,
0.027987031266093254,
-0.00003403546361369081,
0.031206106767058372,
0.05462987720966339,
-0.04292120039463043,
0.017635568976402283,
-0.06400830298662186,
0.06284318119287491,
0.02418316900730133,
0.041854094713926315,
0.01724238321185112,
-0.0016836393624544144,
-0.0370495468378067,
0.05548124387860298,
0.07736626267433167,
0.009938662871718407,
-0.03276587650179863,
-0.012595973908901215,
-0.017579952254891396,
-0.02814372070133686,
-0.06093809753656387,
0.01188753917813301,
0.03409877046942711,
-0.006811479106545448,
-0.008578019216656685,
0.028225358575582504,
-0.019851239398121834,
0.0022187193389981985,
-0.007082007359713316,
0.013833507895469666,
-0.03271050006151199,
0.034868352115154266,
-0.010237585753202438,
0.03772126883268356,
0.022454645484685898,
0.041856326162815094,
0.018576577305793762,
-0.01920449174940586,
0.003680599620565772,
0.04247335344552994,
0.042635660618543625,
0.009905827231705189,
-0.027028027921915054,
0.06386654078960419,
-0.0029159528203308582,
-0.024578481912612915,
0.02124093286693096,
-0.04274928942322731,
0.004951412323862314,
0.004505007062107325,
0.007899830117821693,
-0.002046730602160096,
0.01007236447185278,
0.009146606549620628,
0.050708189606666565,
0.027551796287298203,
-0.013886494562029839,
-0.01348680630326271,
-0.03516959026455879,
0.03588784486055374,
0.0723133310675621,
0.01818314753472805,
-0.015168821439146996,
-0.04602491855621338,
-0.019065730273723602,
-0.030056266114115715,
-0.015021959319710732,
-0.022687776014208794,
0.02197754569351673,
-0.019732138141989708,
0.013143826276063919,
-0.012683889828622341,
-0.02569671906530857,
0.01109400950372219,
-0.019466904923319817,
0.01398524921387434,
0.031239885836839676,
0.022041020914912224,
-0.0040866113267838955,
0.035493675619363785,
-0.03560338541865349,
-0.0620034895837307,
0.0094355009496212,
0.01808355748653412,
-0.02270050160586834,
-0.02205449342727661,
0.031338371336460114,
-0.005782218649983406,
-0.004357959143817425,
0.016263404861092567,
-0.044908445328474045,
0.03837110474705696,
-0.02003396302461624,
-0.06892993301153183,
-0.06073746830224991,
0.033523932099342346,
-0.002845445415005088,
-0.00996096059679985,
-0.07656852900981903,
-0.03382640331983566,
0.040219180285930634,
0.05807673558592796,
0.005617018789052963,
0.018454333767294884,
-0.025914417579770088,
0.05012332648038864,
-0.03585043549537659,
-0.016713576391339302,
-0.03368205577135086,
-0.013459276407957077,
-0.01679956540465355,
0.029669497162103653,
-0.03550020605325699,
0.032868288457393646,
-0.006099729798734188,
0.018947023898363113,
0.005591013468801975,
0.06239211931824684,
-0.004149158950895071,
-0.02197372168302536,
0.04526451230049133,
-0.03991539776325226,
-0.028103362768888474,
0.052273042500019073,
0.002002280903980136,
0.03927547484636307,
0.0034043218474835157,
0.006514990236610174,
-0.0009555347496643662,
0.006121381185948849,
-0.013134782202541828,
0.066304512321949,
-0.03020385280251503,
-0.006074755918234587,
-0.041333384811878204,
0.013691229745745659,
0.005260375794023275,
-0.03165045753121376,
-0.054449912160634995,
0.02769964188337326,
0.0037184504326432943,
0.009852968156337738,
0.016070883721113205,
-0.0021987278014421463,
-0.0209434125572443,
0.013341306708753109,
-0.011215745471417904,
-0.008637925609946251,
-0.03137754648923874,
0.06270033121109009,
-0.013051149435341358,
0.019244955852627754,
0.016866348683834076,
0.011979453265666962,
0.01572551019489765,
-0.048152320086956024,
-0.0012236805632710457,
-0.019561395049095154,
0.03380241245031357,
0.00007208974420791492,
-0.01603536680340767,
0.016062870621681213,
0.035988833755254745,
0.013577956706285477,
0.012664636597037315,
-0.00928326416760683,
0.01623634807765484,
-0.02874857559800148,
-0.0286191925406456,
-0.020548619329929352,
0.01763232797384262,
-0.006067495793104172,
-0.031206173822283745,
0.0077489158138632774,
-0.029991284012794495,
-0.03486239165067673,
-0.0004623106215149164,
-0.02224324271082878,
0.06635177880525589,
0.07157927751541138,
-0.0007070185383781791,
-0.003454832825809717,
0.01759384386241436,
-0.0015042569721117616,
0.0553898848593235,
0.02226962335407734,
-0.0181167833507061,
-0.046354107558727264,
-0.010629025287926197,
0.0578300766646862,
0.011496491730213165,
-0.044692687690258026,
0.00042176031274721026,
0.037987761199474335,
-0.01833232305943966,
0.045933205634355545,
0.010253623127937317,
-0.013057891279459,
-0.05391598865389824,
0.05243166536092758,
0.011279739439487457,
0.0032343408092856407,
0.02372032403945923,
0.054741110652685165,
0.025697119534015656,
-0.0038603523280471563,
-0.033308397978544235,
-0.0018743948312476277,
0.05119713768362999,
0.0008462850819341838,
0.013154655694961548,
0.021281510591506958,
-0.036116376519203186,
0.006459274794906378,
-0.027646638453006744,
0.011922912672162056,
0.021483419463038445,
-0.01854482851922512,
-0.016199413686990738,
-0.0321955643594265,
-0.03494862839579582,
0.013369902968406677,
0.057116471230983734,
0.020075837150216103,
-0.0031698544044047594,
0.023543570190668106,
-0.05618588253855705,
-0.023937001824378967,
-0.006840832531452179,
-0.03830995410680771,
0.0000719101371942088,
-0.013026239350438118,
0.05011032894253731,
-0.01339914370328188,
0.0176310483366251,
-0.03923872485756874,
-0.03995777666568756,
-0.01872199960052967,
-0.022574428468942642,
-0.016561582684516907,
0.018082551658153534,
-0.060081563889980316,
0.002978791017085314,
-0.04820312187075615,
-0.03709559142589569,
0.02499871701002121,
0.011121309362351894,
-0.010348355397582054,
0.04416011646389961,
-0.0042597153224051,
-0.06410226225852966,
0.007172970566898584,
-0.021550850942730904,
0.00798511691391468,
-0.00030758584034629166,
0.03646951913833618,
0.036992304027080536,
0.00001174097451439593,
-0.04074709117412567,
0.030128078535199165,
-0.027149852365255356,
-0.034460652619600296,
-0.04628174006938934,
-0.012202025391161442,
0.05164173245429993,
-0.03626568615436554,
0.026422370225191116,
0.036863528192043304,
-0.02459457889199257,
0.03296872228384018,
-0.07238102704286575,
-0.05031099170446396,
0.022046390920877457,
-0.02990652248263359,
0.07157699763774872,
-0.006534087471663952,
-0.04620370268821716,
0.1037592664361,
0.04519828036427498,
-0.034312982112169266,
0.012843743897974491,
-0.01690756529569626,
0.009395964443683624,
-0.0368155874311924,
0.018617048859596252,
0.0008454442722722888,
-0.01605352759361267,
-0.015727857127785683,
-0.006209886632859707,
0.014112802222371101,
0.047057200223207474,
0.0033666242379695177,
0.012230862863361835,
0.03862050175666809,
0.026303593069314957,
-0.006110906135290861,
0.0841899961233139,
0.011198279447853565,
-0.05315479636192322,
0.061047669500112534,
-0.017822904512286186,
0.011139287613332272,
0.029445072636008263,
-0.06724624335765839,
0.037807896733284,
0.0059885731898248196,
-0.02106378600001335,
-0.04223926365375519,
0.032676391303539276,
0.023836802691221237,
-0.02941824123263359,
0.03055882267653942,
0.04994053393602371,
0.04181182011961937,
0.013146385550498962,
-0.016341909766197205,
0.01765386201441288,
0.03872635215520859,
0.012623480521142483,
-0.033574022352695465,
0.005987235344946384,
0.02168995887041092,
0.017936240881681442,
-0.01769876480102539,
-0.02320949174463749,
0.04341408237814903,
0.0322706438601017,
0.05375239998102188,
0.0073089562356472015,
-0.029334470629692078,
-0.018052417784929276,
-0.04002252593636513,
-0.03213483840227127,
-0.037027470767498016,
0.05869900435209274,
-0.025074532255530357,
0.05973772704601288,
0.047362491488456726,
0.03346787393093109,
0.0529588982462883,
0.009830424562096596,
-0.08104714751243591,
-0.010718931443989277,
-0.014863970689475536,
0.0029356314335018396,
0.006213606335222721,
-0.028230324387550354,
-0.02295020781457424,
-0.0451321080327034,
-0.02883947640657425,
0.020162859931588173,
0.01821962371468544,
-0.046092890202999115,
0.019714485853910446,
-0.05638212710618973,
-0.0348527655005455,
-0.007406424731016159,
0.04471086338162422,
0.015599938109517097,
0.004536759108304977,
-0.01713542267680168,
0.06209367886185646,
-0.026662148535251617,
-0.00047141281538642943,
0.0016999280778691173,
-0.026549484580755234,
-0.01826479285955429,
0.04174460098147392,
0.009480179287493229,
0.025434652343392372,
-0.05242907628417015,
0.03517535701394081,
0.02677951566874981,
0.07358916103839874,
-0.017958812415599823,
-0.00960120651870966,
-0.046675242483615875,
-0.0050770193338394165,
0.0025948788970708847,
-0.023687098175287247,
0.06055682897567749,
-0.016407793387770653,
-0.013149738311767578,
-0.008732444606721401,
0.009745360352098942,
-0.01593647338449955,
0.0382239893078804,
0.03814801201224327,
-0.0004885660600848496,
0.0032523120753467083,
-0.0639408752322197,
0.01159103587269783,
-0.025983229279518127,
-0.015670817345380783,
-0.01886901818215847,
0.008765988051891327,
-0.009901155717670918,
0.029553376138210297,
0.0038743719924241304,
0.00027802473050542176,
-0.01036788523197174,
-0.00424599414691329,
0.01303062029182911,
0.009001950733363628,
-0.013210940174758434,
-0.023446395993232727,
-0.0034530237317085266,
0.01498018205165863,
0.0347801148891449,
0.005300494842231274,
0.01152249425649643,
-0.062457937747240067,
-0.03453530743718147,
0.025655530393123627,
0.023242594674229622,
-0.0071910712867975235,
-0.006214445922523737,
-0.05079861357808113,
-0.03886614367365837,
0.013055913150310516,
-0.014285145327448845,
0.005333447363227606,
-0.027058014646172523,
0.02134755067527294,
-0.0066714040003716946,
-0.013636543415486813,
-0.020199483260512352,
0.01528689544647932,
-0.0044444892555475235,
-0.014792966656386852,
-0.04365673288702965,
-0.005417091306298971,
-0.01356437522917986,
0.020909059792757034,
0.008129555732011795,
0.05933668464422226,
-0.032236892729997635,
-0.023342393338680267,
0.01106625609099865,
0.007673145271837711,
-0.03946073353290558,
-0.06138128414750099,
-0.010375319048762321,
-0.004616545978933573,
0.01049133576452732,
0.004884408321231604,
-0.023690178990364075,
-0.06086832284927368,
0.04231499880552292,
0.003713477635756135,
-0.006224082317203283,
0.005148804280906916,
-0.030943522229790688,
0.04927666857838631,
0.04765807092189789,
-0.01034359447658062,
0.022145071998238564,
0.012605013325810432,
-0.011403797194361687,
0.0000650881920591928,
-0.039295509457588196,
0.015307272784411907,
-0.05086914077401161,
0.014399003237485886,
-0.04160771891474724,
0.009791962802410126,
-0.04712357744574547,
0.0049507333897054195,
0.004080093931406736,
0.046263188123703,
-0.006411111447960138,
-0.02480139769613743,
0.001048582256771624,
0.02379727177321911,
0.007678890600800514,
-0.002166143385693431,
-0.027727888897061348,
0.004405823536217213,
-0.028678594157099724,
-0.016545632854104042,
-0.0018566637299954891,
0.013081301935017109,
0.0026048908475786448,
0.03866967931389809,
0.004175261594355106,
0.03904440999031067,
-0.034411851316690445,
0.011371506378054619,
0.01353496965020895,
-0.041119348257780075,
0.06388036906719208,
-0.0007272647926583886,
0.027259567752480507,
-0.011315446346998215,
-0.06008162349462509,
-0.03336789086461067,
0.0043654972687363625,
0.011230203323066235,
0.029083508998155594,
0.012492666952311993,
0.02262086048722267,
0.027468563988804817,
0.050430819392204285,
-0.030441343784332275,
-0.026422323659062386,
0.027418579906225204,
-0.0038365591317415237,
0.0019656128715723753,
-0.03392418101429939,
0.018737917765975,
-0.02967921271920204,
-0.01910429261624813,
0.02363342046737671,
0.05935325846076012,
-0.021829312667250633,
-0.02051858976483345,
0.025015467777848244,
0.04647570103406906,
0.06560710072517395,
-0.011521918699145317,
-0.029927948489785194,
0.029325665906071663,
-0.0052530402317643166,
-0.003795934608206153,
-0.019837863743305206,
0.03049490414559841,
-0.004048824310302734,
-0.015018059872090816,
0.007460061460733414,
-0.025911586359143257,
0.06063884124159813,
-0.02242388390004635,
-0.00487946905195713,
0.06803680956363678,
0.02249368652701378,
-0.01053949911147356,
-0.011190945282578468,
0.028908319771289825,
-0.04450037702918053,
0.027731381356716156,
-0.03565682843327522,
-0.020615549758076668,
-0.06381790339946747,
-0.012100419029593468,
0.03220970556139946,
-0.029056064784526825,
0.02110600844025612,
0.0005744821391999722,
0.059929344803094864,
-0.03444543853402138,
0.004949816502630711,
0.010641507804393768,
-0.026663124561309814,
0.002983050886541605,
-0.007331926841288805,
-0.0325654111802578,
0.035676050931215286,
0.04490657150745392,
-0.0026835864409804344,
-0.03580597788095474,
-0.043310414999723434,
-0.0008747294778004289,
0.05212421342730522,
-0.029934965074062347,
0.02559567801654339,
-0.009058787487447262,
-0.0007508823182433844,
0.020614411681890488,
0.041419658809900284,
-0.010193509981036186,
0.015092514455318451,
-0.0045818244107067585,
0.03260260447859764,
-0.01765451952815056,
-0.02048453874886036,
0.0342029333114624,
0.029882144182920456,
-0.028063500300049782,
0.023421283811330795,
0.0009871054207906127,
0.05154059827327728,
-0.005833029747009277,
-0.023597445338964462,
-0.01810336299240589,
0.036387406289577484,
-0.03156386688351631,
0.0204657930880785,
-0.03991524875164032,
-0.03732719644904137,
0.049804359674453735,
0.03473738208413124,
-0.015180086717009544,
-0.028033629059791565,
0.014260124415159225,
-0.0033698559273034334,
0.011671221815049648,
0.02988818660378456,
-0.009223810397088528,
0.00974972266703844,
0.03009049780666828,
0.0504368394613266,
0.007161826826632023,
0.006886153481900692,
0.0046590762212872505,
-0.0620420016348362,
-0.0025628297589719296,
-0.03929009288549423,
-0.07218559831380844,
0.02459571696817875,
0.014443399384617805,
-0.013147878460586071,
0.041608911007642746,
-0.04200524836778641,
0.029402397572994232,
0.022670365869998932,
0.002622758038341999,
-0.0209518913179636,
0.0489274226129055,
-0.004401282873004675,
0.018262680619955063,
-0.03921955078840256,
0.030377693474292755,
0.12445655465126038,
0.050871070474386215,
0.0681413933634758,
-0.024062851443886757,
0.003739861072972417,
-0.05334923043847084,
0.027272498235106468,
-0.02644888311624527,
0.02196863479912281,
-0.00214138044975698,
0.021125096827745438,
0.004291857127100229,
0.0781957358121872,
-0.016302207484841347,
0.012247259728610516,
0.040729548782110214,
-0.013241994194686413,
-0.006495573557913303,
0.01051774900406599,
0.012292438186705112,
-0.023679668083786964,
0.017958752810955048,
0.012523413635790348,
0.026786470785737038,
0.0027346264105290174,
-0.02918120287358761,
-0.03662364184856415,
-0.01291750930249691,
0.04053827375173569,
-0.009365036152303219,
-0.0506889671087265,
-0.012739158235490322,
0.004250330850481987,
-0.013029850088059902,
-0.024578940123319626,
-0.0020670422818511724,
0.009839339181780815,
-0.019134214147925377,
0.0049371602945029736,
0.009447465650737286,
-0.012674974277615547,
0.02253575809299946,
0.005627262871712446,
0.005113434977829456,
-0.01976567693054676,
-0.01030151080340147,
-0.016917627304792404,
0.059736836701631546,
0.006523899268358946,
-0.01894976943731308,
0.008716653101146221,
0.012981210835278034,
0.010088265873491764,
-0.03815877437591553,
0.01792202889919281,
-0.026211995631456375,
0.062091536819934845,
0.024205077439546585,
0.009581349790096283,
-0.03897704556584358,
0.004508673679083586,
0.022656872868537903,
-0.017633885145187378,
0.014591316692531109,
-0.03066534548997879,
-0.006918557453900576,
0.006286186631768942,
0.033680323511362076,
-0.02666100673377514,
-0.03379566967487335,
-0.02562451735138893,
-0.010709275491535664,
-0.06052844598889351,
-0.02824198640882969,
-0.015901412814855576,
0.015198443084955215,
0.05099009349942207,
-0.0009511981625109911,
-0.0032908888533711433,
-0.047446511685848236,
-0.09133648872375488,
0.033180151134729385,
-0.00224471976980567,
-0.0046369293704628944,
-0.02020467445254326,
0.012607075273990631,
0.0010325899347662926,
0.03462797775864601,
-0.01321395579725504,
0.010815711691975594,
-0.024301476776599884,
-0.029258087277412415,
-0.011862174607813358,
-0.03542700409889221,
-0.04046085104346275,
-0.006628107745200396,
-0.026001347228884697,
0.048914145678281784,
-0.022620776668190956,
-0.03415193781256676,
0.026364002376794815,
-0.005431892350316048,
0.02348491922020912,
0.048548195511102676,
-0.04226870834827423,
0.013396167196333408,
-0.028562478721141815,
-0.01050356961786747,
-0.00517155509442091,
0.02931370586156845,
0.03376118838787079,
-0.0069673736579716206,
-0.004670029506087303,
-0.04830588772892952,
-0.01964537426829338,
-0.03340756520628929,
0.025751633569598198,
-0.029814325273036957,
0.013433470390737057,
-0.0516473762691021,
-0.014017046429216862,
-0.010587234050035477,
0.0027201336342841387,
-0.02599858120083809,
0.00580303929746151,
-0.00017838319763541222,
-0.007033076602965593,
-0.0555303581058979,
0.04296620190143585,
-0.022331563755869865,
-0.011443634517490864,
-0.005933190695941448,
-0.0027710457798093557,
-0.013093225657939911,
0.005761623382568359,
0.036333177238702774,
0.019196942448616028,
0.024285074323415756,
-0.006915338337421417,
-0.01573672704398632,
0.03160516172647476,
-0.010092468932271004,
-0.04009910300374031,
0.004009773954749107,
0.016437716782093048,
0.016670841723680496,
0.04211125895380974,
0.01943538524210453,
-0.023077042773365974,
0.045953866094350815,
-0.004485365003347397,
0.01934327930212021,
-0.023819657042622566,
-0.05455372482538223,
-0.027663514018058777,
-0.004824415780603886,
0.022336240857839584,
0.00195735739544034,
0.009541450999677181,
0.04490537568926811,
-0.0006261127418838441,
-0.0004929485148750246,
-0.009044228121638298,
0.03285526484251022,
-0.030395420268177986,
-0.013818430714309216,
0.05950845777988434,
-0.0036404370330274105,
0.027926664799451828,
0.05769466981291771,
-0.010754166170954704,
-0.012616743333637714,
0.006757089402526617,
-0.027690960094332695,
-0.10955202579498291,
-0.03135199844837189,
0.015607590787112713,
0.025967344641685486,
0.05592513084411621,
-0.035467617213726044,
0.00148271513171494,
-0.019116198644042015,
-0.07767989486455917,
0.0534866601228714,
-0.013610951602458954,
-0.0064602321945130825,
-0.04350414499640465,
-0.03529179096221924,
-0.04298538342118263,
0.020897625014185905,
-0.01558960136026144,
0.046259671449661255,
0.02344990335404873,
0.029519734904170036,
-0.009211705066263676,
-0.022183649241924286,
0.025054005905985832,
0.058490898460149765,
0.00459818821400404,
0.010867908596992493,
0.06318685412406921,
-0.021088549867272377,
-0.019313741475343704,
-0.0027909541968256235,
-0.004134865012019873,
0.026954885572195053,
0.006343510001897812,
0.03619476035237312,
-0.02370566874742508,
0.03684840723872185,
0.07410343736410141,
0.004041059408336878,
-0.0038383998908102512,
0.014172062277793884,
-0.0033878309186547995,
-0.029105300083756447,
-0.03625273331999779,
0.00045510646305046976,
0.00982907135039568,
-0.028932292014360428,
-0.004915099591016769,
0.05141790211200714,
-0.04025854170322418,
-0.013076992705464363,
0.019355900585651398,
-0.015106553211808205,
0.01038142666220665,
-0.012284296564757824,
-0.004800456576049328,
-0.04787164926528931,
-0.02184470184147358,
0.03796452283859253,
-0.009291349910199642,
-0.015085643157362938,
0.012468183413147926,
0.0077323694713413715,
-0.02472214587032795,
0.0542483776807785,
-0.01487317867577076,
-0.04523305967450142,
-0.05049737170338631,
0.0005739848129451275,
-0.0014359004562720656,
0.04072202369570732,
-0.0010878352914005518,
-0.02879420667886734,
-0.035987723618745804,
0.05159365013241768,
0.02242116816341877,
0.011717146262526512,
-0.017616957426071167,
-0.028199784457683563,
-0.0032258378341794014,
-0.08220156282186508,
0.012595280073583126,
0.013446194119751453,
-0.030072849243879318,
-0.017160575836896896,
0.004271834623068571,
0.015188190154731274,
0.0387808158993721,
0.07528568804264069,
0.035924747586250305,
0.01032801903784275,
0.02568894624710083,
-0.018446678295731544,
0.034057263284921646,
-0.04212478548288345,
-0.03620615229010582,
-0.017785951495170593,
-0.03855418041348457,
-0.002958634402602911,
0.034767989069223404,
-0.0341995470225811,
0.013382506556808949,
0.05994128808379173,
-0.0021054178941994905,
0.015874935314059258,
-0.005560875404626131,
0.007580472622066736,
0.05481831356883049,
0.0019329303177073598,
0.005119435489177704,
0.07685147225856781,
-0.034298915416002274,
0.012431523762643337,
0.0057191080413758755,
-0.024665996432304382,
-0.04716753959655762,
0.010549573227763176,
-0.05186102166771889,
-0.02924824319779873,
0.004714599810540676,
0.0020930003374814987,
0.03526049107313156,
-0.05152236297726631,
-0.01868942566215992,
0.03206149861216545,
-0.05470491573214531,
-0.01037511508911848,
0.03138604015111923,
0.0598100908100605,
0.014504539780318737,
0.008517095819115639,
0.0518333725631237,
0.02592555433511734,
-0.03484058380126953,
-0.007400736678391695,
0.016933003440499306,
0.030756602063775063,
-0.008534264750778675,
-0.006359596271067858,
0.06741216778755188,
-0.019806450232863426,
-0.020746564492583275,
0.0215618833899498,
-0.01200341247022152,
-0.045853711664676666,
-0.015151029452681541,
0.035950563848018646,
-0.01536373607814312,
-0.0052670808508992195,
0.03260962665081024,
-0.03625185042619705,
0.09726154059171677,
0.020054563879966736,
0.033630549907684326,
0.000838394567836076,
-0.009110108017921448,
-0.017737437039613724,
0.013353035785257816,
-0.007790065836161375,
0.0403616800904274,
0.01621842011809349,
0.04522441700100899,
-0.029229314997792244,
-0.031505219638347626,
0.035174474120140076,
-0.05008405074477196,
-0.0037941397167742252,
0.018642691895365715,
-0.020124342292547226,
0.0003789733746089041,
-0.02339901216328144,
-0.02149975672364235,
-0.018045062199234962,
0.01908937655389309,
0.02384287118911743,
-0.000874169054441154,
-0.002403684426099062,
-0.013039478100836277,
0.016024064272642136,
0.03225572407245636,
-0.05052470415830612,
-0.002095109084621072,
-0.0007207110757008195,
0.026192087680101395,
-0.008148188702762127,
0.02979913353919983
] |
<p>If I stick a metal and insulator together, will the Fermi level of the metal align with the insulator?</p>
<p>When people draw a band diagram for a metal-oxide-semiconductor heterostructure, I never see them label the Fermi level of the oxide. What is the Fermi level of the oxide relative to the metal and insulator's?</p>
<p>I'm particularly interested in graphene/SiO2/Si field effect transistors. When we change the gate voltage between the graphene and Si, what happens to the SiO2 conduction band, valence band, and Fermi level? If the SiO2 Fermi level aligns with the graphene Fermi level, what is the mechanism that keeps graphene and SiO2 in thermal equilibrium so quickly?</p>
| 8,514 |
[
-0.025194404646754265,
-0.0020337074529379606,
0.01773684099316597,
0.002098727272823453,
0.00202089361846447,
0.0044807023368775845,
-0.004525177646428347,
-0.004943289794027805,
0.015735076740384102,
-0.04636543244123459,
0.03811659291386604,
0.02081368677318096,
0.03287050127983093,
0.0059591783210635185,
0.002700351644307375,
0.006164260674268007,
-0.0011354305315762758,
-0.050714872777462006,
-0.01548528578132391,
-0.012092053890228271,
-0.008648416958749294,
0.05058944225311279,
0.021617025136947632,
0.012444528751075268,
-0.0365469716489315,
0.012382077053189278,
-0.010043315589427948,
-0.048447929322719574,
0.011340389959514141,
-0.00005387273267842829,
-0.059551943093538284,
-0.00397474505007267,
0.025566499680280685,
0.00552105437964201,
0.013723758049309254,
-0.0019080323399975896,
-0.006572328507900238,
-0.07455185800790787,
-0.03633720427751541,
0.021024301648139954,
-0.029849829152226448,
0.005575752817094326,
-0.020772892981767654,
0.025478573516011238,
0.008462184108793736,
-0.026325402781367302,
-0.01210788358002901,
-0.014257554896175861,
0.026536673307418823,
-0.06796354055404663,
0.006176195107400417,
-0.010426556691527367,
0.04529213160276413,
0.08779893070459366,
-0.012694296427071095,
-0.029624877497553825,
0.09797126799821854,
0.07372777909040451,
-0.02386731095612049,
-0.023034662008285522,
-0.018151437863707542,
-0.053362730890512466,
-0.02563638985157013,
0.004688730463385582,
-0.015216222032904625,
0.04911397770047188,
-0.020850252360105515,
-0.03572184219956398,
-0.002489878097549081,
0.02208332158625126,
-0.0016185304848477244,
0.0010742726735770702,
0.009792367927730083,
0.0031934180296957493,
0.04923577979207039,
-0.04379000887274742,
0.024596096947789192,
0.03332557529211044,
0.016976406797766685,
0.054315440356731415,
-0.01868448592722416,
0.04613146930932999,
0.023279957473278046,
0.042121000587940216,
-0.022928092628717422,
0.0014786429237574339,
0.07128681242465973,
-0.0100058913230896,
-0.02362523227930069,
0.04639799892902374,
0.011812719516456127,
0.014966911636292934,
0.011789556592702866,
-0.004235557746142149,
-0.018313976004719734,
0.01916857622563839,
0.005423692986369133,
0.02486809343099594,
0.0004239409463480115,
0.0015933190006762743,
0.015112427994608879,
0.033497534692287445,
0.032690346240997314,
0.07243958115577698,
-0.00784518662840128,
-0.023071369156241417,
-0.026784688234329224,
0.0037492583505809307,
0.0040186671540141106,
0.002768679289147258,
-0.03448830544948578,
-0.012831281870603561,
-0.033205363899469376,
0.003295745002105832,
0.01589435338973999,
0.0058698831126093864,
-0.009888767264783382,
-0.044734690338373184,
0.05241021886467934,
0.03224988654255867,
0.008941175416111946,
0.015909535810351372,
0.015413000248372555,
-0.006286971736699343,
-0.09023731201887131,
0.0001970970188267529,
0.02186574600636959,
-0.049013979732990265,
-0.04266046732664108,
0.010075767524540424,
-0.0128951920196414,
0.007116901222616434,
-0.029721707105636597,
-0.038334015756845474,
0.05081390589475632,
0.0012386140879243612,
-0.09657535701990128,
-0.040094226598739624,
0.029912399128079414,
-0.025763308629393578,
-0.02423843927681446,
-0.07990355044603348,
0.010456091724336147,
0.022931184619665146,
0.0926632434129715,
-0.008141620084643364,
0.007871987298130989,
-0.02514134719967842,
-0.020165106281638145,
-0.010023481212556362,
0.007955225184559822,
-0.011254987679421902,
0.036918796598911285,
-0.021425258368253708,
0.014511319808661938,
-0.028598906472325325,
0.025347262620925903,
0.04520280659198761,
0.005444258917123079,
-0.017994320020079613,
0.06360716372728348,
-0.000499993038829416,
0.0029151428025215864,
0.001847241772338748,
-0.014693854376673698,
-0.013035869225859642,
0.07575716823339462,
-0.0096594775095582,
0.04666943848133087,
0.04791899397969246,
0.008756972849369049,
0.009271795861423016,
0.024626601487398148,
0.01330101490020752,
0.02127675712108612,
0.005802457686513662,
-0.004722520709037781,
-0.028398364782333374,
-0.012019285000860691,
-0.005988545250147581,
-0.06478425860404968,
-0.055227186530828476,
0.005094065796583891,
0.010993104428052902,
0.028241632506251335,
-0.0005344897508621216,
0.020175693556666374,
-0.01836879551410675,
-0.026378946378827095,
-0.040384016931056976,
-0.012485174462199211,
-0.06670941412448883,
0.006856968626379967,
-0.010337714105844498,
-0.0004731416411232203,
0.06062613055109978,
-0.0018647261895239353,
0.008570170029997826,
-0.0494513213634491,
-0.049153562635183334,
0.003250832436606288,
0.023446306586265564,
-0.008057605475187302,
0.010325117968022823,
0.04060756042599678,
0.06384362280368805,
0.029173634946346283,
-0.03574787825345993,
0.022804221138358116,
-0.04086679220199585,
-0.053381215780973434,
0.013335766270756721,
0.005179394502192736,
0.04942343756556511,
0.014858833514153957,
0.0022605881094932556,
-0.011288738809525967,
-0.01779930293560028,
-0.014196570962667465,
0.02017238736152649,
0.010355071164667606,
0.0815042182803154,
0.049021340906620026,
0.00773517694324255,
-0.0002889742609113455,
0.036622583866119385,
0.005063924007117748,
0.028539415448904037,
-0.0012527599465101957,
-0.011842272244393826,
-0.06317514926195145,
-0.05290045216679573,
0.03724038228392601,
0.030509600415825844,
-0.012921590358018875,
0.026650164276361465,
0.016302304342389107,
0.04570820927619934,
0.023463591933250427,
-0.009522255510091782,
-0.05334046110510826,
0.009958765469491482,
0.03897774592041969,
-0.030765853822231293,
0.0034875657875090837,
0.020209308713674545,
0.015144764445722103,
0.011847192421555519,
0.0048520611599087715,
-0.005926252342760563,
-0.013253442011773586,
0.02094358764588833,
0.06051614135503769,
-0.005366140510886908,
0.008938894607126713,
-0.06570211052894592,
-0.001535066869109869,
-0.028980616480112076,
0.021929511800408363,
0.032848067581653595,
0.0006906705093570054,
-0.008531110361218452,
-0.011459924280643463,
-0.024760045111179352,
-0.0028888967353850603,
0.006300447043031454,
-0.011929553002119064,
-0.017640667036175728,
0.01492100115865469,
-0.042837727814912796,
0.015379762277007103,
-0.02429860644042492,
0.0039649526588618755,
-0.006789537612348795,
0.01575787551701069,
0.02555859461426735,
-0.009782562963664532,
0.037213411182165146,
-0.042963411659002304,
-0.030833225697278976,
-0.0062904455699026585,
-0.020684050396084785,
0.013688711449503899,
0.014134249649941921,
-0.024972038343548775,
0.0363255999982357,
-0.015871217474341393,
-0.025713250041007996,
0.021136676892638206,
0.030985811725258827,
0.007668093778192997,
0.02334820292890072,
-0.008347642607986927,
-0.0770663172006607,
-0.020411133766174316,
0.018071815371513367,
0.0048903413116931915,
-0.027593223378062248,
-0.0067016808316111565,
0.0038103931583464146,
-0.03638949617743492,
-0.013661311939358711,
0.02797844260931015,
0.007796814665198326,
-0.032414086163043976,
0.0139438072219491,
-0.011595308780670166,
0.001663360744714737,
-0.0025088516995310783,
0.06602668017148972,
0.037948984652757645,
-0.04412750154733658,
-0.023074818775057793,
-0.05123526230454445,
-0.05460004881024361,
0.03579185530543327,
-0.02770090289413929,
0.018689963966608047,
-0.025905858725309372,
-0.03092966414988041,
0.08247311413288116,
0.0007015019073151052,
-0.009746113792061806,
-0.01689227484166622,
-0.05732247233390808,
0.0032975405920296907,
0.014959676191210747,
0.03917338326573372,
0.03762747347354889,
0.017796775326132774,
0.007205155212432146,
0.028344986960291862,
0.06620122492313385,
0.055051032453775406,
0.030621113255620003,
0.012216164730489254,
0.012922769412398338,
0.020740220323204994,
-0.01304619200527668,
0.057795699685811996,
-0.0022462815977633,
0.010140015743672848,
0.03313122317194939,
-0.002457022201269865,
0.02882327325642109,
0.06561186909675598,
-0.0369073748588562,
0.033576954156160355,
-0.0002173941902583465,
-0.018894294276833534,
-0.06337565183639526,
0.04637538269162178,
0.0222921185195446,
-0.031273722648620605,
-0.004677852150052786,
0.01836603321135044,
0.0740557610988617,
-0.022026266902685165,
0.025099460035562515,
0.025899238884449005,
0.025197939947247505,
-0.049324460327625275,
-0.03624827787280083,
0.007422422058880329,
0.01636679843068123,
0.031674545258283615,
-0.05965752527117729,
0.0076662045903503895,
0.03045441210269928,
0.026725932955741882,
0.026289405301213264,
-0.00038030382711440325,
-0.06183675304055214,
-0.028999701142311096,
-0.07612957805395126,
-0.0019230415346100926,
0.010603404603898525,
0.07152798771858215,
0.007131772115826607,
0.06165603548288345,
0.0350751057267189,
0.04134748503565788,
0.015939567238092422,
-0.016004404053092003,
-0.0746665969491005,
0.004363739397376776,
-0.021256884559988976,
-0.020134415477514267,
-0.016954515129327774,
-0.01237465813755989,
-0.014084432274103165,
0.0045381817035377026,
-0.041380129754543304,
-0.03806564211845398,
-0.0007323098834604025,
0.0005919269169680774,
0.04077371209859848,
-0.03906534984707832,
-0.04307318106293678,
0.01048626471310854,
0.03210337832570076,
0.00923649687319994,
-0.028566276654601097,
0.0006470608641393483,
0.027702711522579193,
-0.018266117200255394,
0.008243019692599773,
-0.022632813081145287,
-0.00014162310981191695,
0.020395906642079353,
0.04877123981714249,
0.02192152477800846,
-0.01080421730875969,
0.0018691022414714098,
-0.0091349296271801,
0.01810622401535511,
0.06586794555187225,
-0.008542305789887905,
-0.02431282214820385,
-0.02829454466700554,
-0.048571206629276276,
-0.05937415361404419,
-0.026845058426260948,
0.08199267089366913,
-0.0025059652980417013,
0.013148369267582893,
0.012070100754499435,
0.006648607086390257,
-0.03379559889435768,
0.03791248798370361,
0.05962497740983963,
-0.0033608537632972,
0.0023246402852237225,
-0.008825165219604969,
-0.05175626277923584,
-0.035332825034856796,
-0.00330869248136878,
0.021678520366549492,
0.0017774368170648813,
-0.04263075068593025,
0.005855945870280266,
0.013724906370043755,
0.028317872434854507,
-0.030758194625377655,
-0.007039198186248541,
-0.00250260136090219,
0.010333056561648846,
-0.0002753993321675807,
0.014812642708420753,
-0.04467349499464035,
0.03485256806015968,
0.04054209217429161,
-0.005268060602247715,
0.0047474815510213375,
-0.058479320257902145,
0.005781247746199369,
0.03160680830478668,
0.024340325966477394,
-0.007542298641055822,
0.0049927509389817715,
-0.03908749669790268,
-0.007782967761158943,
0.013619447126984596,
-0.010765389539301395,
0.02236228808760643,
-0.0167348925024271,
-0.03140854462981224,
-0.0550287663936615,
-0.03519989922642708,
0.006963226478546858,
-0.003236094955354929,
0.019669068977236748,
0.013404198922216892,
-0.04011969268321991,
-0.03658226504921913,
-0.039414357393980026,
0.0049216412007808685,
0.026267794892191887,
0.06583801656961441,
0.010269328020513058,
0.017483513802289963,
0.023950301110744476,
-0.02565169893205166,
-0.0435943603515625,
-0.1033916026353836,
-0.003840989200398326,
-0.010824277997016907,
0.018475370481610298,
0.04046523943543434,
-0.03498297929763794,
-0.038869813084602356,
0.013766907155513763,
-0.0031144702807068825,
-0.00510916393250227,
-0.001963972579687834,
0.0031817546114325523,
0.07711879909038544,
0.031225863844156265,
-0.007301163859665394,
0.038070857524871826,
-0.02090160734951496,
-0.012943907640874386,
0.015810860320925713,
-0.03861897438764572,
0.04346727207303047,
-0.04322785511612892,
0.01668936014175415,
0.011737782508134842,
-0.02046280726790428,
-0.022336188703775406,
0.0534912534058094,
-0.0006777113885618746,
0.04024822264909744,
0.0007807174697518349,
-0.029954051598906517,
-0.00450411532074213,
-0.008797732181847095,
0.005361831746995449,
-0.007249582093209028,
0.022143201902508736,
0.02689265087246895,
-0.011368630453944206,
-0.029897578060626984,
0.04475937411189079,
0.0020644813776016235,
0.013288641348481178,
0.01178015023469925,
-0.013391377404332161,
0.05063311383128166,
-0.06642670929431915,
0.01012581866234541,
-0.04336614906787872,
-0.007308532018214464,
0.01912253350019455,
0.01579934172332287,
0.04088783636689186,
0.010613992810249329,
-0.02926953136920929,
-0.015340941026806831,
0.050181396305561066,
0.02551385760307312,
0.008339614607393742,
-0.033586785197257996,
0.057048700749874115,
0.006359763443470001,
0.030554650351405144,
-0.04648280888795853,
-0.092915378510952,
0.008974717929959297,
0.018528256565332413,
-0.02493215911090374,
-0.01901095174252987,
0.04036295413970947,
-0.010593910701572895,
-0.028696425259113312,
0.0684502124786377,
0.023620715364813805,
-0.028034744784235954,
-0.03721904754638672,
-0.027544334530830383,
-0.01076794695109129,
0.10571867227554321,
-0.029147272929549217,
-0.029439164325594902,
0.0038130690809339285,
-0.040878839790821075,
0.009654270485043526,
-0.02261311188340187,
0.04449392110109329,
0.003109139855951071,
-0.011501689441502094,
-0.022127468138933182,
-0.005513083189725876,
0.039898581802845,
0.0078094941563904285,
-0.009271667338907719,
0.04221402853727341,
0.03250042349100113,
-0.009087653830647469,
-0.029671112075448036,
0.028039583936333656,
-0.008321193978190422,
0.034988198429346085,
0.026005232706665993,
0.018801948055624962,
-0.04541157931089401,
-0.033857159316539764,
0.03706777095794678,
0.0032962746918201447,
0.04031795263290405,
0.00497467489913106,
0.08808254450559616,
-0.01591246761381626,
0.03530433028936386,
0.06930322200059891,
-0.021945727989077568,
0.034759458154439926,
-0.035166360437870026,
-0.00712426844984293,
0.03795192763209343,
0.014210168272256851,
-0.04316236078739166,
-0.059264179319143295,
-0.024476340040564537,
-0.018693070858716965,
0.021990645676851273,
-0.04320739582180977,
0.05155795067548752,
0.01645425520837307,
-0.039513517171144485,
0.003981948364526033,
-0.026720043271780014,
-0.008586219511926174,
0.010858528316020966,
-0.0339176207780838,
-0.009897220879793167,
-0.017533868551254272,
-0.003717381041496992,
0.0347675085067749,
0.07030083239078522,
-0.02900192327797413,
0.023883307352662086,
0.05241372063755989,
-0.0011359965428709984,
0.049043696373701096,
-0.01694691926240921,
-0.0685470700263977,
0.051225658506155014,
-0.044972240924835205,
0.03271351754665375,
-0.01145237684249878,
-0.04184141755104065,
0.04981822520494461,
0.03520084172487259,
0.009508339688181877,
-0.01128354575484991,
-0.021290358155965805,
-0.016292793676257133,
0.011166751384735107,
-0.020410459488630295,
-0.016329197213053703,
-0.02335512265563011,
0.012046437710523605,
0.050218500196933746,
0.0019670724868774414,
-0.042576804757118225,
-0.03814063221216202,
-0.060886237770318985,
-0.038536038249731064,
0.0062219733372330666,
-0.0158062856644392,
0.021550200879573822,
0.00050748122157529,
-0.028127938508987427,
0.02211817353963852,
-0.024913407862186432,
0.02950366400182247,
0.003124901559203863,
0.03306013345718384,
-0.024758324027061462,
0.049806032329797745,
-0.03489518165588379,
0.018643785268068314,
-0.02890719100832939,
-0.012374237179756165,
0.11700683832168579,
0.05510479956865311,
0.018841862678527832,
-0.048247016966342926,
0.006835801061242819,
-0.005656090565025806,
0.0016456260345876217,
-0.01366802491247654,
-0.04105978086590767,
-0.012209323234856129,
0.03204326704144478,
0.0038451123982667923,
0.045355815440416336,
-0.00710712606087327,
0.026463065296411514,
0.019943807274103165,
-0.042712364345788956,
-0.0020048401784151793,
-0.008966879919171333,
0.020213089883327484,
-0.006627433933317661,
0.009203064255416393,
-0.0405157171189785,
-0.013603745959699154,
-0.03341122344136238,
0.013195080682635307,
-0.034395333379507065,
0.0017076341900974512,
0.07368063926696777,
0.011395085602998734,
-0.030209394171833992,
0.0011660618474707007,
0.011559117585420609,
-0.008461385034024715,
-0.01557073276489973,
0.02730168029665947,
-0.002673757029697299,
0.0019270583288744092,
0.02681822143495083,
0.014020404778420925,
0.019767606630921364,
0.007245728280395269,
0.0034044801723212004,
-0.0019389718072488904,
-0.008798121474683285,
-0.005672939587384462,
0.0016850099200382829,
0.022460324689745903,
-0.03487271070480347,
-0.049512915313243866,
-0.012464143335819244,
0.005056370049715042,
0.020189234986901283,
-0.014024602249264717,
-0.031557682901620865,
0.017123539000749588,
0.06873446702957153,
0.0032548662275075912,
-0.004068861249834299,
-0.022191612049937248,
0.050420381128787994,
0.007022346835583448,
-0.020893519744277,
-0.021582074463367462,
-0.009777093306183815,
0.008092598058283329,
-0.008759405463933945,
0.04468202218413353,
-0.036908168345689774,
-0.01800687424838543,
-0.0023106150329113007,
-0.004894453566521406,
-0.050721339881420135,
-0.038154132664203644,
0.021261122077703476,
0.04005419462919235,
0.02408069185912609,
-0.00504495482891798,
-0.02690359391272068,
0.002108370652422309,
-0.06218003109097481,
0.04181651398539543,
-0.015027452260255814,
-0.02504133991897106,
-0.03923744335770607,
-0.023817002773284912,
0.04720330983400345,
0.038732871413230896,
-0.033925559371709824,
0.03394463658332825,
0.0020684939809143543,
-0.014633777551352978,
0.01485659833997488,
-0.023877542465925217,
-0.03527575731277466,
0.011676238849759102,
-0.05019068345427513,
0.022334497421979904,
-0.032384052872657776,
0.04044763743877411,
0.011081722564995289,
-0.012380551546812057,
0.021185260266065598,
0.02640449069440365,
-0.02577221766114235,
-0.0006424359744414687,
0.011007842607796192,
0.02733452059328556,
-0.029453668743371964,
0.025990430265665054,
0.01980089582502842,
0.0024562354665249586,
-0.028011325746774673,
-0.021241459995508194,
-0.017447739839553833,
-0.018001491203904152,
0.0009501643944531679,
0.022406326606869698,
0.03277016803622246,
-0.04295163229107857,
0.030222833156585693,
-0.038169797509908676,
-0.017164969816803932,
-0.04494137316942215,
0.00005731308556278236,
-0.000606792513281107,
-0.01525894459336996,
0.009723600931465626,
0.025014782324433327,
-0.01901899464428425,
0.0065634483471512794,
0.006342735607177019,
0.02871107868850231,
-0.02212154120206833,
0.01625875197350979,
0.01987004652619362,
-0.021702993661165237,
0.019103534519672394,
-0.05845565348863602,
-0.03966117277741432,
0.0322866290807724,
-0.0059246402233839035,
-0.025876466184854507,
0.021001048386096954,
-0.006055252160876989,
0.040128450840711594,
0.002215675078332424,
-0.024999458342790604,
-0.008233251050114632,
0.027601411566138268,
-0.015559615567326546,
-0.019572895020246506,
-0.025712452828884125,
-0.03150022774934769,
0.0048636868596076965,
0.0022477349266409874,
0.020341096445918083,
-0.012933234684169292,
0.01701514422893524,
-0.0013224490685388446,
0.025603855028748512,
0.007069926243275404,
-0.004059482365846634,
0.029845597222447395,
-0.002297195140272379,
-0.007104538381099701,
0.029125429689884186,
-0.006493260618299246,
-0.0007946426630951464,
0.06623617559671402,
-0.019187970086932182,
0.03666957467794418,
0.041171956807374954,
-0.016277892515063286,
-0.06020199880003929,
-0.023708311840891838,
0.026426171883940697,
-0.00663387356325984,
-0.004078428260982037,
-0.022695966064929962,
-0.007878337986767292,
0.0281826239079237,
-0.0719052404165268,
0.010132348164916039,
-0.018919965252280235,
-0.048358384519815445,
-0.027918417006731033,
-0.0006942236213944852,
0.006181622855365276,
0.03311733901500702,
-0.013381612487137318,
0.05160229653120041,
-0.013519179075956345,
-0.011147120967507362,
-0.019649043679237366,
-0.0278449896723032,
0.0065210903994739056,
0.014012905769050121,
0.001073820167221129,
-0.004497568588703871,
0.056430425494909286,
-0.012339508160948753,
-0.01690480299293995,
0.011140788905322552,
-0.006338423117995262,
-0.04436784237623215,
-0.016210364177823067,
0.014593277126550674,
-0.029591886326670647,
0.03347500041127205,
-0.03248687833547592,
-0.012991506606340408,
-0.014334972016513348,
0.016464924439787865,
0.017464200034737587,
0.04625226929783821,
0.011381343938410282,
0.016209974884986877,
0.019131558015942574,
-0.016937661916017532,
0.02001645788550377,
0.053169503808021545,
-0.024307679384946823,
-0.038480471819639206,
0.029576530680060387,
0.040088310837745667,
0.024647705256938934,
-0.045525528490543365,
0.007900395430624485,
-0.04363199695944786,
-0.050290148705244064,
-0.005291937850415707,
0.022066807374358177,
0.03322818502783775,
-0.012472382746636868,
-0.008485368452966213,
0.028224511072039604,
0.05420626699924469,
0.006237419322133064,
-0.0026953110937029123,
-0.0477728471159935,
-0.039744406938552856,
0.015147367492318153,
-0.001555517315864563,
0.03686387836933136,
-0.05156777799129486,
-0.009905633516609669,
0.0446169488132,
0.0032923007383942604,
0.045917704701423645,
-0.03139514848589897,
-0.06346987187862396,
0.008762170560657978,
-0.010772526264190674,
0.015502420254051685,
-0.015974117442965508,
0.010555882006883621,
-0.021605348214507103,
-0.03926938399672508,
-0.004395445343106985,
0.011859088204801083,
0.07456062734127045,
0.020219815894961357,
-0.03625033050775528,
-0.022817576304078102,
-0.03691272437572479,
0.03080534189939499,
-0.016197137534618378,
0.00807466171681881,
0.006410502828657627,
-0.017527680844068527,
-0.023334600031375885,
0.02279461920261383,
-0.012618339620530605,
0.0034672142937779427,
0.03329421579837799,
-0.04427587613463402,
-0.019652292132377625,
-0.02222052589058876,
-0.0035933186300098896,
0.03968796879053116,
0.03704585134983063,
0.01422678492963314,
0.09942326694726944,
-0.006990704219788313,
0.02072463557124138,
0.034113187342882156,
0.022719016298651695,
-0.00865268986672163,
0.02972337044775486,
-0.02371806465089321,
-0.03461681678891182,
-0.004123154561966658,
0.017663026228547096,
0.0459190271794796,
-0.05053948611021042,
0.03434859961271286,
0.0107816057279706,
-0.03786931559443474,
-0.014466460794210434,
0.06728365272283554,
0.017453161999583244,
0.028669562190771103,
0.013095410540699959,
-0.01862468011677265,
0.0030293562449514866,
-0.014853127300739288,
-0.005501762963831425,
0.03820034861564636,
0.019624987617135048,
0.03642679750919342,
0.031066114082932472,
0.022207336500287056,
0.0018275371985509992,
-0.003569890046492219,
-0.0009928984800353646,
0.017474668100476265,
-0.007913989946246147,
0.0011456429492682219,
0.06174260377883911,
0.007951701991260052,
-0.005119003355503082,
0.010638447478413582,
-0.04176747798919678,
0.06259646266698837,
-0.03180927410721779,
0.01612347923219204,
-0.03651661425828934,
0.00668763043358922,
-0.01908804289996624,
-0.005376697052270174,
0.012512491084635258,
0.06051443889737129,
-0.029200684279203415,
-0.003117173444479704,
-0.0422310009598732,
0.043210793286561966,
0.0054831779561936855,
-0.042476311326026917,
0.03454344719648361,
-0.03657592087984085,
-0.017580661922693253,
-0.0007538782665506005,
-0.02436520904302597,
-0.06767748296260834,
-0.0014922036789357662,
0.037314288318157196,
0.03696199879050255,
-0.006390901282429695,
-0.009358929470181465,
0.0012392915086820722,
-0.024989154189825058,
0.03579779714345932,
-0.052294109016656876,
-0.01730550266802311,
-0.04050388187170029,
-0.012736506760120392,
-0.023752208799123764,
0.008271226659417152
] |
<p>The standard lore in relativistic QFT is that poles appearing on the real-axis in momentum-space Green's functions correspond to particles, with the position of the pole yielding the invariant mass of that particle. <em>(Here, I disregard complications tied to gauge-fixing and unphysical ghosts)</em></p>
<p>Schematically, I take this to mean:</p>
<p>$$\text{one particle state} \Leftrightarrow \text{pole on real axis}$$</p>
<p>It is easy to show the correspondence going $\text{particle} \Rightarrow \text{pole}
$. This is done in many textbooks, <em>e.g.</em> Peskin and Schroeder's text, where a complete set of states diagonalizing the field theoretic Hamiltonian is inserted into a $n$-point correlator, and a pole is shown to emerge.</p>
<p>However, how does one make the argument going the other way $\text{particle} \Leftarrow \text{pole}
$? That is, the appearance of a pole in a Green's function indicates an eigenstate of the Hamiltonian, with the eigenvalue corresponding to the particle energy?</p>
| 8,515 |
[
0.021702956408262253,
-0.011513627134263515,
0.005209204275161028,
-0.031705424189567566,
0.01966135948896408,
0.04226712882518768,
-0.01588902622461319,
-0.005456612911075354,
0.015266234055161476,
-0.030131317675113678,
0.006792895961552858,
0.01164521649479866,
0.06456024199724197,
0.002420096891000867,
-0.002834341488778591,
0.00628402316942811,
-0.0057906294241547585,
-0.02357732318341732,
-0.003255239687860012,
-0.05555402487516403,
0.0011301797349005938,
0.07605128735303879,
0.006133169401437044,
0.0005781808285973966,
-0.000146159203723073,
0.0428791344165802,
0.0025835486594587564,
0.035516347736120224,
0.00299642700701952,
0.05535878241062164,
-0.01428170781582594,
-0.033622924238443375,
-0.007025355007499456,
-0.006906246766448021,
0.02111283503472805,
0.008547586388885975,
-0.01650211028754711,
-0.03257608413696289,
0.029235810041427612,
-0.0013985643163323402,
-0.048774104565382004,
-0.031247656792402267,
-0.03459229692816734,
0.03509675711393356,
-0.01327162329107523,
-0.008106774650514126,
-0.0064132907427847385,
0.00032144220313057303,
0.05558571219444275,
-0.03836873173713684,
0.04435112327337265,
0.05272214114665985,
0.02318972535431385,
-0.011311029084026814,
-0.009973586536943913,
-0.014010000042617321,
0.05134459584951401,
0.05490116402506828,
-0.029903581365942955,
-0.05845656991004944,
-0.05382728949189186,
-0.02108447626233101,
-0.006149697583168745,
-0.021011896431446075,
0.003480911022052169,
-0.0038753272965550423,
0.03259511664509773,
0.010723557323217392,
0.011612102389335632,
-0.016473565250635147,
-0.020066512748599052,
0.03249593824148178,
0.03516339138150215,
-0.005497680511325598,
0.0017092926427721977,
-0.03266940265893936,
0.02261551283299923,
0.03714568167924881,
0.03901250660419464,
-0.00788210891187191,
-0.0017953530186787248,
0.003511983435600996,
-0.00037398425047285855,
0.0226860623806715,
0.00964284222573042,
0.008199549280107021,
0.041528571397066116,
-0.0066570108756423,
-0.008716976270079613,
0.05113998427987099,
-0.007938566617667675,
0.004702879581600428,
0.05467690899968147,
-0.025182846933603287,
-0.04220159724354744,
-0.005020773969590664,
0.016457222402095795,
0.022519411519169807,
-0.012579644098877907,
0.009525417350232601,
-0.03557918965816498,
-0.042101215571165085,
0.010758199729025364,
0.04707878828048706,
-0.028761528432369232,
-0.006537517998367548,
-0.04864484816789627,
0.008668813854455948,
-0.013875647448003292,
-0.03267437592148781,
-0.051886849105358124,
0.04131803289055824,
0.01235379371792078,
0.000020118819520575926,
-0.001066676457412541,
-0.01498484332114458,
0.009278680197894573,
-0.02953527309000492,
0.09016948938369751,
0.06396416574716568,
0.03391974791884422,
0.0001989331067306921,
0.008098242804408073,
-0.019110366702079773,
-0.06667745113372803,
-0.020972423255443573,
0.040515169501304626,
-0.0045156534761190414,
-0.025022080168128014,
-0.028084104880690575,
0.029114434495568275,
-0.009951378218829632,
0.025141406804323196,
-0.006815179716795683,
0.023107068613171577,
-0.023649508133530617,
-0.10995545238256454,
-0.03595947101712227,
0.0415300652384758,
-0.029800860211253166,
-0.018794424831867218,
-0.06650124490261078,
-0.01998942531645298,
0.028870150446891785,
0.07388610392808914,
-0.013058804906904697,
-0.022119013592600822,
-0.00974954292178154,
0.053345922380685806,
0.02727694809436798,
0.007447459734976292,
-0.030088258907198906,
-0.014191823080182076,
-0.038858622312545776,
-0.008953324519097805,
-0.024686401709914207,
0.016780391335487366,
0.026502158492803574,
0.0030616556759923697,
-0.003664693795144558,
0.05829954147338867,
-0.038443293422460556,
-0.02249467745423317,
0.0004961232771165669,
-0.013900944963097572,
-0.027590401470661163,
0.05532576143741608,
0.014582735486328602,
-0.004803062882274389,
0.043241795152425766,
0.01996382139623165,
0.02420436590909958,
0.013343535363674164,
0.028287755325436592,
0.03433581814169884,
-0.055496323853731155,
-0.05492422729730606,
-0.01909111812710762,
0.015292885713279247,
-0.02786148525774479,
-0.04546242579817772,
-0.04572589322924614,
-0.004311833530664444,
0.021929852664470673,
-0.022545624524354935,
0.013288362883031368,
-0.01796029694378376,
0.015476797707378864,
0.010240471921861172,
-0.029755279421806335,
-0.010607097297906876,
-0.08546023815870285,
0.02512282133102417,
0.013712028041481972,
-0.01841425709426403,
0.05635344237089157,
0.022803351283073425,
0.023629993200302124,
-0.026497041806578636,
-0.025827676057815552,
0.014664219692349434,
0.05838177353143692,
-0.008797279559075832,
-0.039568960666656494,
0.02022421732544899,
0.05296105518937111,
0.0424656942486763,
0.009028195403516293,
0.04193974658846855,
-0.023891910910606384,
-0.045188333839178085,
-0.0003335258224979043,
0.002978401957079768,
0.006005378440022469,
0.0069810776039958,
-0.006906474009156227,
0.006703268736600876,
-0.045126497745513916,
-0.022291818633675575,
0.046421390026807785,
-0.027556082233786583,
0.05099855735898018,
0.06292392313480377,
-0.019648047164082527,
-0.019482797011733055,
0.032456424087285995,
0.005439052823930979,
0.026495270431041718,
-0.03606167808175087,
-0.0540987066924572,
-0.03289399668574333,
-0.025017576292157173,
0.05775313451886177,
0.070419080555439,
-0.04328042268753052,
0.011458507739007473,
0.040640123188495636,
0.049045149236917496,
-0.008708177134394646,
0.016710178926587105,
-0.022373739629983902,
-0.023727815598249435,
0.01545444130897522,
0.009056719951331615,
0.004643409047275782,
-0.011808954179286957,
0.03532053157687187,
-0.014576329849660397,
-0.027820046991109848,
0.00857524573802948,
-0.0329723134636879,
0.023219337686896324,
-0.03731703385710716,
0.0380229689180851,
0.02875879406929016,
-0.05565807223320007,
0.002748130587860942,
-0.047538116574287415,
0.03430195152759552,
-0.016670798882842064,
-0.025633398443460464,
-0.042533133178949356,
-0.016769226640462875,
-0.011907723732292652,
0.015344769693911076,
-0.019842199981212616,
-0.0321488119661808,
-0.014896651729941368,
0.008023025467991829,
-0.03139740228652954,
0.01629309169948101,
-0.005433196201920509,
-0.03512457013130188,
0.05279695987701416,
0.013411403633654118,
0.02523821033537388,
-0.0009719603694975376,
0.024680590257048607,
-0.036231592297554016,
-0.04727788642048836,
0.01939566433429718,
-0.016021262854337692,
0.0054129138588905334,
0.06520407646894455,
-0.05975954979658127,
0.0011736609740182757,
-0.09067142009735107,
-0.04311913624405861,
-0.0009221269865520298,
0.002009027637541294,
0.00992345530539751,
-0.032852884382009506,
-0.012750097550451756,
-0.032213080674409866,
0.014678489416837692,
-0.007126278709620237,
0.0018228004919365048,
-0.029211122542619705,
-0.009733252227306366,
0.043712541460990906,
-0.026984017342329025,
-0.03570670261979103,
0.018196484073996544,
0.01902361586689949,
-0.023468052968382835,
0.014294736087322235,
-0.014547432772815228,
0.019709279760718346,
-0.023586837574839592,
0.04691245034337044,
0.01506532821804285,
-0.04260712116956711,
0.007477385923266411,
-0.04896259307861328,
-0.021189691498875618,
0.006294076330959797,
0.043358396738767624,
0.030706752091646194,
0.00610499270260334,
-0.027573946863412857,
0.09443673491477966,
0.007639565970748663,
-0.03943870961666107,
0.012878181412816048,
0.020819593220949173,
-0.0010647514136508107,
-0.009782552719116211,
0.0025507572572678328,
0.008116425946354866,
-0.00757469329982996,
0.04176131263375282,
0.02277754805982113,
-0.0021492941305041313,
0.0014523137360811234,
0.020977294072508812,
0.009374966844916344,
-0.002614877186715603,
0.005292825400829315,
0.02313859947025776,
0.03108975663781166,
-0.004942914936691523,
-0.01249741017818451,
0.031282685697078705,
-0.010226406157016754,
0.010174674913287163,
0.017859535291790962,
-0.023805884644389153,
0.052627284079790115,
-0.003811436705291271,
0.03895478695631027,
-0.026794832199811935,
0.044423408806324005,
0.013135517947375774,
-0.038793791085481644,
-0.004540483467280865,
0.016368098556995392,
0.032628271728754044,
0.009042167104780674,
-0.0036004858557134867,
0.008333329111337662,
0.02772248163819313,
-0.032240044325590134,
-0.01856118254363537,
0.00018865731544792652,
-0.015342343598604202,
0.008846791461110115,
-0.03831418231129646,
-0.04546578601002693,
0.06496217101812363,
0.03585318848490715,
0.013314769603312016,
-0.000504131312482059,
-0.039014097303152084,
-0.0015054126270115376,
-0.06122031807899475,
-0.007239972706884146,
0.006275229621678591,
0.02715441584587097,
0.007964761927723885,
0.06321030110120773,
0.01831868849694729,
0.013794593513011932,
-0.033912017941474915,
0.0007071377476677299,
-0.06703656166791916,
0.017876626923680305,
-0.018793821334838867,
0.028687121346592903,
-0.03090691938996315,
-0.028308194130659103,
0.0009734207997098565,
-0.007358403876423836,
-0.032474011182785034,
-0.015146591700613499,
-0.023233843967318535,
-0.02663339301943779,
0.018547603860497475,
-0.05319029837846756,
-0.0441124401986599,
0.005468500312417746,
0.02895641140639782,
0.04015050828456879,
-0.04741226136684418,
-0.009328028187155724,
0.05629004165530205,
-0.04909401014447212,
0.0058678025379776955,
-0.030996281653642654,
0.030980868265032768,
0.027701599523425102,
0.007542737759649754,
0.053304579108953476,
0.007118325214833021,
-0.015234068967401981,
0.006612077355384827,
0.0299701988697052,
0.061122581362724304,
-0.014302718453109264,
-0.03590431809425354,
0.04044850543141365,
-0.04776701331138611,
0.0386541523039341,
0.015373890288174152,
0.07466812431812286,
-0.01842878758907318,
0.0047373478300869465,
0.03141462430357933,
0.02533920668065548,
0.004225883632898331,
0.05084477737545967,
0.04926321282982826,
0.02705691009759903,
-0.018146000802516937,
-0.0470496341586113,
0.050020731985569,
0.020301900804042816,
-0.006600336637347937,
0.007752946112304926,
0.010209285654127598,
0.005686493590474129,
0.01887207105755806,
0.004752014763653278,
-0.002522030146792531,
-0.017508190125226974,
-0.01265090610831976,
-0.011812673881649971,
0.023784397169947624,
-0.033471785485744476,
0.014348408207297325,
-0.01040826365351677,
0.02920910343527794,
0.05536429584026337,
0.02027943916618824,
-0.01202097162604332,
-0.07369144260883331,
-0.005989399738609791,
0.028651507571339607,
0.032336484640836716,
0.02217220515012741,
0.0001730292715365067,
-0.023258259519934654,
-0.01180572621524334,
0.05962476134300232,
-0.01289151981472969,
-0.03048296831548214,
-0.02427729219198227,
-0.021707061678171158,
-0.0035340094473212957,
-0.010850219056010246,
-0.01466292329132557,
0.0350993350148201,
-0.003747964510694146,
0.005053229164332151,
-0.0536210760474205,
-0.028382007032632828,
-0.041542988270521164,
0.024594785645604134,
0.005078175570815802,
0.03713874891400337,
0.01615409553050995,
0.01814097724854946,
-0.01240326464176178,
0.02684180811047554,
-0.02903682179749012,
-0.09087850898504257,
-0.01477761846035719,
0.008225122466683388,
-0.01110893115401268,
0.051574911922216415,
-0.010810751467943192,
-0.0586409717798233,
-0.015605348162353039,
-0.014036169275641441,
-0.002397258300334215,
0.007973847910761833,
-0.051133111119270325,
0.06229323893785477,
0.0075088562443852425,
0.015303053893148899,
0.0725119486451149,
0.008704124018549919,
0.009214654564857483,
-0.017825644463300705,
0.017772376537322998,
0.025329340249300003,
-0.01506712380796671,
0.029052043333649635,
-0.05601857975125313,
0.0010661735432222486,
-0.03855246677994728,
0.03215290233492851,
-0.03020169585943222,
-0.011870983056724072,
-0.0061284517869353294,
-0.03331722691655159,
-0.04459796100854874,
0.02992325648665428,
-0.03341565281152725,
0.008697090670466423,
-0.006923388224095106,
0.03876512870192528,
0.03405015543103218,
-0.022857382893562317,
0.03376118466258049,
0.0039425319992005825,
-0.005266104359179735,
0.030083637684583664,
0.013139277696609497,
0.06874288618564606,
-0.0294293574988842,
-0.017039969563484192,
0.014649043790996075,
-0.03695603832602501,
0.02259274572134018,
-0.009423595853149891,
-0.009947195649147034,
-0.005548238754272461,
-0.04745369404554367,
-0.03287956118583679,
0.0073502277955412865,
-0.012277004308998585,
-0.007231813855469227,
-0.027519600465893745,
-0.023551903665065765,
0.0399734303355217,
0.02017161436378956,
-0.054555587470531464,
-0.036291033029556274,
-0.005344556178897619,
0.00932630430907011,
-0.015650801360607147,
-0.016174910590052605,
0.0036677387543022633,
-0.018086349591612816,
0.0020454558543860912,
-0.0028703827410936356,
0.04112180694937706,
-0.03406628221273422,
-0.012457524426281452,
0.025713389739394188,
0.0655415877699852,
0.05076063424348831,
-0.05565601587295532,
-0.03266410529613495,
0.022210488095879555,
-0.019505424425005913,
-0.007207862101495266,
-0.013530454598367214,
0.0346548892557621,
-0.017350569367408752,
-0.05325500667095184,
-0.015016392804682255,
-0.017164764925837517,
0.018840519711375237,
-0.002918447367846966,
-0.016640832647681236,
0.061136338859796524,
-0.0012826119782403111,
0.015011119656264782,
-0.006189324893057346,
-0.01238013431429863,
0.0061323936097323895,
0.04275554418563843,
-0.002900036983191967,
-0.010330605320632458,
-0.0021107536740601063,
-0.055182382464408875,
0.05659899115562439,
0.0057932292111217976,
0.010205565020442009,
0.0026052764151245356,
0.04668769612908363,
-0.05425731837749481,
0.020171741023659706,
0.01626495085656643,
-0.041771695017814636,
0.0036253081634640694,
0.01330523006618023,
0.03525786101818085,
-0.013788149692118168,
-0.004559757187962532,
-0.03975624591112137,
-0.03504062443971634,
-0.04388924688100815,
-0.0024737853091210127,
0.030405636876821518,
0.021533815190196037,
0.04615108296275139,
0.01701805554330349,
-0.007103438023477793,
0.0020409419666975737,
0.0018242349615320563,
-0.028194045647978783,
-0.01015404611825943,
-0.021424710750579834,
0.056519024074077606,
-0.07322866469621658,
-0.0009219032363034785,
0.041873499751091,
0.063866525888443,
-0.012930081225931644,
0.01793741062283516,
0.016289951279759407,
0.0589454211294651,
0.020026108250021935,
0.017201058566570282,
-0.05425403267145157,
0.0548458956182003,
-0.01836800016462803,
0.010348891839385033,
-0.0030948410276323557,
-0.0014829793944954872,
0.02568582072854042,
0.011636110953986645,
0.01829276606440544,
-0.01299693901091814,
-0.03638412430882454,
-0.052683137357234955,
0.04506294056773186,
0.008485125377774239,
0.007005600258708,
-0.004259010776877403,
-0.02692055143415928,
0.04410137981176376,
0.006970267742872238,
0.0022725947201251984,
0.022336553782224655,
-0.05106582120060921,
-0.057672109454870224,
-0.039232704788446426,
-0.04802278056740761,
0.013752583414316177,
-0.04304886981844902,
-0.025700222700834274,
-0.004371853545308113,
-0.012545508332550526,
0.00893176719546318,
0.007181292865425348,
0.04397350549697876,
-0.06266143918037415,
0.052224062383174896,
0.0007057738839648664,
0.0015244672540575266,
0.012825614772737026,
-0.0011715757427737117,
0.12432047724723816,
0.061777547001838684,
0.03610898554325104,
-0.07998018711805344,
0.017671022564172745,
0.0012337396619841456,
0.013939890079200268,
-0.003632679581642151,
0.027320554479956627,
-0.04555223882198334,
0.00215769256465137,
-0.024876045063138008,
0.05292866751551628,
0.010211861692368984,
-0.00020217460405547172,
0.05417238548398018,
-0.06514229625463486,
-0.041080329567193985,
-0.001496724202297628,
0.048407237976789474,
-0.02939027175307274,
-0.012171146459877491,
-0.024352286010980606,
0.008972139097750187,
-0.011046373285353184,
0.03012383170425892,
0.014672382734715939,
-0.014026344753801823,
0.030171873047947884,
-0.015491862781345844,
-0.04215496405959129,
0.005234725307673216,
0.017569752410054207,
0.003467945381999016,
-0.04141267389059067,
0.011561096645891666,
-0.002250851597636938,
0.01617256924510002,
0.042498234659433365,
0.014025069773197174,
-0.012883116491138935,
0.006670781411230564,
0.013149386271834373,
0.005542811471968889,
-0.029940318316221237,
-0.037241969257593155,
-0.02156555838882923,
0.05606292188167572,
-0.01913074590265751,
-0.028840981423854828,
-0.01210386399179697,
-0.028581490740180016,
0.024411702528595924,
-0.05817456543445587,
-0.003852148773148656,
-0.009155914187431335,
0.014624303206801414,
0.021535499021410942,
0.031110748648643494,
-0.030472205951809883,
0.035393211990594864,
-0.006461227312684059,
0.00044898700434714556,
0.010872862301766872,
-0.016736233606934547,
0.04177796468138695,
-0.016173474490642548,
0.044497329741716385,
0.0268747229129076,
0.021635491400957108,
-0.012220810167491436,
-0.01431669294834137,
-0.04275426268577576,
-0.05498112365603447,
0.020260360091924667,
0.0313139446079731,
0.05161084607243538,
0.025889020413160324,
0.03397756069898605,
-0.046868741512298584,
-0.058158207684755325,
0.021761776879429817,
0.007624706719070673,
-0.039638955146074295,
0.004548727534711361,
-0.005703178700059652,
0.045654602348804474,
0.07936781644821167,
-0.0481717549264431,
-0.0020074655767530203,
-0.004567143972963095,
0.03479228913784027,
0.0031146579422056675,
-0.025090042501688004,
0.0021407976746559143,
0.03829992190003395,
-0.03374116122722626,
-0.014195175841450691,
-0.021892331540584564,
-0.02025701105594635,
-0.0061518182046711445,
0.02413756027817726,
-0.010623954236507416,
0.045925624668598175,
-0.02080807276070118,
-0.017436135560274124,
0.026665901765227318,
-0.0152116809040308,
-0.0005644921329803765,
0.016867566853761673,
0.009777684696018696,
-0.08440952003002167,
-0.05473242700099945,
-0.011288494803011417,
-0.011796107515692711,
-0.012144211679697037,
0.03271352872252464,
-0.04120206832885742,
-0.023366602137684822,
-0.021356236189603806,
0.020497076213359833,
-0.04556497931480408,
-0.00017030398885253817,
-0.0679624155163765,
0.04067691043019295,
0.000018040782379102893,
-0.02288658916950226,
-0.02415219321846962,
0.03152976930141449,
-0.01962391659617424,
-0.010539469309151173,
0.013644209131598473,
0.030931591987609863,
-0.021462859585881233,
0.022159362211823463,
0.023521024733781815,
0.00018690311117097735,
0.009781936183571815,
0.00705404207110405,
-0.016474517062306404,
0.01915973611176014,
-0.04934460297226906,
-0.021239832043647766,
0.029983850196003914,
-0.0026264158077538013,
0.031164495274424553,
0.021854287013411522,
0.00017504984862171113,
-0.03015565499663353,
0.01208722684532404,
-0.026255501434206963,
-0.0164877250790596,
-0.010763143189251423,
-0.011467484757304192,
-0.034009017050266266,
-0.021524015814065933,
0.021361608058214188,
-0.00432042358443141,
0.005629268474876881,
0.03345937281847,
0.00949926394969225,
-0.03815016523003578,
0.012531683780252934,
-0.0013298322446644306,
-0.0036432319320738316,
0.03651491552591324,
0.026544975116848946,
0.028978802263736725,
0.009580996818840504,
0.04725152254104614,
-0.042692314833402634,
-0.006533678621053696,
0.0005794871831312776,
0.020670956000685692,
-0.10061374306678772,
-0.029524240642786026,
-0.001901264302432537,
-0.012447173707187176,
0.05053311586380005,
-0.035764534026384354,
0.010407855734229088,
0.018555326387286186,
-0.07441690564155579,
0.03211681544780731,
-0.00597697589546442,
-0.0353047139942646,
-0.032422006130218506,
0.0050071547739207745,
-0.035126857459545135,
0.06740927696228027,
0.03845055401325226,
0.039175812155008316,
-0.006154883187264204,
-0.01809086464345455,
0.016877707093954086,
-0.009381763637065887,
-0.015910787507891655,
0.03267575427889824,
-0.015047019347548485,
-0.03134787455201149,
0.09225703775882721,
-0.020222054794430733,
-0.03431347757577896,
0.033044230192899704,
0.01501232385635376,
-0.01329050026834011,
-0.00472849328070879,
0.03749097138643265,
-0.01008532289415598,
0.03526342287659645,
0.02863764762878418,
-0.0002683437487576157,
-0.03783848509192467,
-0.005412722006440163,
0.046875134110450745,
0.023587968200445175,
-0.0064308312721550465,
0.0009184982627630234,
0.009048914536833763,
-0.03534075990319252,
-0.014689584262669086,
0.023737413808703423,
-0.027892284095287323,
-0.01926013082265854,
-0.0040374211966991425,
0.004860414192080498,
0.003261938225477934,
-0.006042324937880039,
0.06440223008394241,
-0.02551603503525257,
-0.001081499271094799,
0.012217182666063309,
0.015962304547429085,
-0.002035281155258417,
0.018104586750268936,
-0.00012749740562867373,
-0.05003919079899788,
0.022942984476685524,
0.05876512825489044,
-0.016655227169394493,
-0.040262602269649506,
-0.004257777705788612,
0.05238671600818634,
0.006607489660382271,
0.02735033817589283,
-0.05056910961866379,
-0.009409968741238117,
0.01776900514960289,
0.02267761342227459,
0.018147192895412445,
-0.031740639358758926,
-0.01242552138864994,
0.007162807043641806,
-0.05412027984857559,
0.037520986050367355,
0.03524758294224739,
0.008670823648571968,
-0.013269463554024696,
-0.016852417960762978,
0.021465925499796867,
0.0015876076649874449,
0.061222124844789505,
-0.0068872664123773575,
-0.007600164040923119,
0.036308709532022476,
-0.01965080387890339,
0.007270751986652613,
-0.02970900759100914,
-0.007932715117931366,
-0.018850749358534813,
-0.021085036918520927,
0.025981836020946503,
-0.004698097240179777,
-0.006903232075273991,
0.05150787904858589,
0.04182383790612221,
0.01646079123020172,
0.013144725002348423,
0.0020260335877537727,
-0.04640226438641548,
0.07931650429964066,
0.011778056621551514,
0.010060658678412437,
0.04100006818771362,
-0.01370695699006319,
0.01570728048682213,
0.02433185838162899,
-0.05824043229222298,
-0.013290158472955227,
0.006457433104515076,
-0.043452244251966476,
-0.019727198407053947,
-0.0073974779807031155,
0.015262297354638577,
-0.002739529823884368,
-0.06342681497335434,
0.03516016900539398,
0.03407987579703331,
-0.024442598223686218,
-0.0413421206176281,
0.05170763283967972,
0.03407317027449608,
0.05495603755116463,
0.04113225266337395,
0.0024993373081088066,
0.03323468193411827,
0.00680537847802043,
0.02219114638864994,
0.04649161919951439,
0.046873789280653,
0.033375442028045654,
0.021001216024160385,
0.02606077864766121,
-0.006492548622190952,
0.011368060484528542,
0.01318153366446495,
0.04064110293984413,
-0.015899071469902992,
0.012715890072286129,
0.037018805742263794,
-0.022912131622433662,
0.034206364303827286,
0.002809361554682255,
-0.02375148795545101,
0.09819522500038147,
-0.02139022946357727,
-0.022522184997797012,
-0.0487440787255764,
0.009630023501813412,
0.006378477439284325,
0.010826087556779385,
0.01236843690276146,
0.06310565024614334,
-0.002823117421939969,
-0.013213608413934708,
-0.0417310856282711,
-0.020322328433394432,
-0.006297460291534662,
-0.054566532373428345,
-0.030995352193713188,
-0.003898120950907469,
-0.029617395251989365,
-0.002987942425534129,
-0.048345085233449936,
-0.009979660622775555,
0.0012765260180458426,
-0.005053512752056122,
0.03072238713502884,
0.024565255269408226,
-0.013552425429224968,
-0.009942274540662766,
-0.03443063050508499,
0.04289579391479492,
-0.05015741288661957,
0.010306857526302338,
-0.007104693446308374,
0.03211146965622902,
-0.0011439912486821413,
0.0301144327968359
] |
<p>Upon reading about the principal bundle picture of (quantum) field theory I encountered two different definitions of the gauge group:</p>
<ul>
<li><strong>Local gauge group $G$</strong>. Corresponds to the fibers of the $G$-bundle. Local gauge transformations correspond to the change of coordinates in which fields and form are written in trivializations. In other words, as far as I understand, local gauge transformations = transition functions for trivializations of the principal bundle and the associated bundles.</li>
<li><strong>Global gauge group $\mathfrak G=Aut(P)$</strong>. Is the group of principal bundle diffeomorphisms, and is claimed to be much bigger then $G$.</li>
</ul>
<p>I would like to understand which notions in physics correspond to these two, apparently very distinct, notions.</p>
<p>First, in physics, there is the notion of <em>global symmetry</em>, as far as I understand this has nothing to do with gauge/bundles. But on the other hand, the limit of a gauge symmetry where the parameter becomes constant is a global symmetry. Typical $U(1)$ example: $\exp(i\alpha(x))$ = $U(1)$ gauge transformation, but if $\alpha(x)=\alpha=const.$, then it is a global symmetry. Is there any deeper connection between global symmetry and gauge "symmetry"/bundles?</p>
<p>Second, I would appreciate some examples which clarify the distinction between local and global gauge groups mentioned above. If, for example we take a prototype $SU(2)$ gauge theory of the form
$$
\mathcal L = -\frac{1}{4}(F_{\mu\nu}^a)^2+|(D_\mu\phi)^a|^2-V(\phi)
$$
then we can put it in the bundle picture as a $SU(2)$ principal bundle, the fields $A_\mu^a$ living in the associated bundle $$(P\times\mathfrak su(2))/\{(p,A)\sim(pg,Ad_{g^{-1}}A)\}$$ and the doublet field $\phi$ in fundamental representation of $SU(2)$ living in the associated bundle $$(P\times\mathbb C^2)/\{(p,v)\sim(pg,\rho(g^{-1})\phi)\}.$$ So, the $SU(2)$ group which we are referring to here is what was the local gauge group $G$ above, is this correct? The gauge transformations apply to coordinate versions of the fields in the trivializations of the associated bundles to change between different coordinates.</p>
<p>Now if, this is the case, what is the global gauge group $\mathfrak G$ then? In particular I am seeking the answer for the following questions:</p>
<ul>
<li>Do global gauge transformations apply to the model $SU(2)$ theory above?</li>
<li>In what sense is the global gauge group much bigger then the local gauge group?</li>
<li>Is there a model example where one can clearly write down the local gauge group and the global gauge group?</li>
<li>Are there cases where the two groups are the same?</li>
<li>How does this discussion relate to quantization of classical fields (if it does at all)?</li>
</ul>
<hr>
<h1>Edit</h1>
<p>I'll post here answers to various questions in the comments/answers.</p>
<p>About the definitions I used in my text. I took them from my lecture notes from a course on mathematical gauge theories taught by a mathematician. Although there is no on-line version of this course, I can provide more detailed definitions if needed.</p>
<p>Specifically, concerning the distinction global/local gauge, I have found this piece of information on nLab, which seems to be agreement with my definition:
<a href="http://ncatlab.org/nlab/show/gauge+group" rel="nofollow">http://ncatlab.org/nlab/show/gauge+group</a>. Although this page provides some explanations, it uses some mathematical terminology which I am not entirely familiar with. The problem both with the nLab page and with the lecture I attended is to make the connection to physics (I am a physicist).</p>
<p>Ok, I'll just write down the definitions from my lecture notes.</p>
<h2>Local gauge</h2>
<p>Let $P\to M$ a principal $G$-bundle, $\omega$ a connection 1-form on $P$. $U_i, U_j\subset M$ such that $U_i\cap U_j\neq\emptyset$ over which P is trivial:
$$
\psi_i:\pi^{-1}(U_i)\to U_i\times G\\
\psi_j:\pi^{-1}(U_j)\to U_j\times G
$$
with transition functions
$$
\psi_i\circ\psi_j^{-1}:(U_i\cap U_j)\times G\to (U_i\cap U_j)\times G\\
\phantom{\psi_i\circ\psi_j^{-1}:XXX}(m,g)\mapsto (m,\psi_{ij}(m)g)
$$
where $\psi_{ij}:U_i\cap U_j\to G$.</p>
<p>Using these trivializations we can construct preferred sections as follows:
$$
\sigma_i:U_i\to\pi^{-1}(U_i)\\
\phantom{\sigma_i:x}m\mapsto \psi_i^{-1}(m,e)\,.
$$
Define
$$
\omega_i:=\sigma_i^*\omega\,,
$$
which is a $\mathfrak g$-valued 1-form on $U_i$. Changing between coordinates on $U_i$ and $U_j$ is what is called choice of local gauge. We would like to write down a transformation prescription for $\omega_{i/j}$.</p>
<p>On G we have the canonical 1-form $\theta$ with values in $\mathfrak g$ defined as follows:
$$
\theta_g(X_g)=A\in\mathfrak g\quad\text{if }(A^*)_g=X_g
$$
where by $A^*$ we mean the fundamental vector field on $G$ corresponding to $A$. One can show that the 1-forms transform in the following way:
$$
\omega_j=Ad_{\psi_{ij}}^{-1}\omega_i+\psi_{ij}^*\theta\,.
$$
This looks to me like a gauge transformation of guage fields $A=A_\mu dx^\mu$ in physics where we write
$$
A'=gAg^{-1}+gdg^{-1}
$$
and I even believe that the above transformation for $\omega_j$ can be rewritten as something like this
$$
\omega_j=Ad_{\psi_{ij}}^{-1}\omega_i+\psi_{ij}^{-1}d\psi_{ij}\,,
$$
Then it looks like the transformation for $A$ with $g=\psi_{ij}^{-1}$.</p>
<p>So much about the local gauge transformation.</p>
<h2>Global gauge group</h2>
<p>The group of global gauge transformation $\mathfrak G$ is the set of automorphisms of the principal bundle P:
$$
\mathfrak G = Aut(P)\,.
$$
This must not be confused with the structure group $G$, which is sometimes called gauge group in leterature, but is much smaller.</p>
<p>The (global) gauge group can be described in three ways:</p>
<ol>
<li>$\mathfrak G=\{\phi:P\to P|\phi\text{ is a diffeo., }\pi\circ\phi=\pi, \phi(pg)=\phi(p)g\,\forall g\in G\}$</li>
<li>$\mathfrak G=\{u:P\to G|u\text{ smooth s.t. }u(pg)=g^{-1}u(p)g\,\forall g\in G\}$. Note that $\phi(p)=p\cdot u(p)$.</li>
<li>$\mathfrak G=\{\text{sections }s:M\to F\}$, where $F=(P\times G)/\sim$ with $(p,h)\sim(pg,g^{-1}pg)\forall g\in G$.</li>
</ol>
<p>If $\omega$ is a connection 1-form which corresponds to a choice to the horizontal tangent space $H$ on $P$, then $\phi^*\omega$ is also a connection 1-form, defining the pull-back connection
$$
(\phi^*H)_p:=(D_p\phi)^{-1}H_{\phi(p)}\quad\Leftrightarrow\quad D_p\phi((\phi^*H)_p):=H_{\phi(p)}
$$
We conclude that $\mathfrak G$ acts on connections, but the explicit form of this action if fairly complicated. In contrast, the action of $\mathfrak G$ on the curvature is easy to understand.</p>
<p>From the last equation above we conclude that $\phi$ maps $\phi^*H$ to $H$, and so it maps $\tilde\Omega$, the curvature of $\phi^*H$, to $\Omega$, the curvature of $H$:
$$
\phi(\tilde\Omega(X,Y))=\Omega(X,Y)\quad\forall X,Y\in T_mM\,.
$$
One can show that the following transformation relation holds:
$$
\tilde\Omega=Ad_{u^{-1}}\Omega\,.
$$
where $u:P\to G$ is the map from the second definition of $\mathfrak G$ above corresponding to $\phi$.</p>
<p>Two connections $H_1$ and $H_2$ on P are called gauge equivalent if there is a $\phi\in\mathfrak G$ with $\phi^*H_2=H_1$.</p>
<hr>
<p>One of the things which I am curious about is that from the local gauge transformations the transformation law for the 1-form $\omega$ seems to be what we call the gauge transformation of gauge fields $A$ (see above), but from the global gauge group transformation, the transformation of the curvature is what we see in physics, namely if $F$ is the field strength corresponding to $A$, and $g$ an element of the gauge group then
$$
F\to F'=gFg^{-1}\,.
$$
Also, as I said at the very beginning, I would like to pin down what these mathematical definitions correspond to in what we learn in physics. In physics, when we discuss a certain gauge theory, there is THE gauge group, such as $U(1)$, $SU(2)$, etc. under which fields transform in certain representations, as well as the gauge fields themselves, which transform in the adjoint representation. Now in mathematics I see the distinction local/global gauge group. The essence of my question is do understand this distinction and to relate it to phyics.</p>
| 8,516 |
[
-0.017085591331124306,
0.03733224794268608,
0.003447545226663351,
-0.027730688452720642,
0.021907780319452286,
0.05723392218351364,
-0.07149598747491837,
-0.05486444756388664,
0.0013520224019885063,
-0.07598908990621567,
-0.0010390554089099169,
-0.010211152955889702,
0.035810574889183044,
0.02857695147395134,
0.0015071781817823648,
0.03659616410732269,
-0.011864532716572285,
-0.0204622820019722,
-0.0373278371989727,
-0.023897143080830574,
-0.020567238330841064,
0.02883021906018257,
0.012840372510254383,
0.004873956553637981,
0.013860185630619526,
0.033438295125961304,
0.0007237342069856822,
0.02150801196694374,
-0.032578274607658386,
0.0688706561923027,
0.0001459084451198578,
-0.01380243431776762,
-0.02398998662829399,
-0.011653832159936428,
-0.021604886278510094,
0.012204207479953766,
0.020958412438631058,
-0.027120070531964302,
0.0367668941617012,
0.02598278969526291,
-0.05995237082242966,
-0.02617611549794674,
-0.01802518218755722,
0.014229574240744114,
-0.013162548653781414,
0.03944425284862518,
0.0018677394837141037,
-0.01962261088192463,
0.041998375207185745,
-0.03827542066574097,
0.04582420364022255,
0.03320803865790367,
-0.023926468566060066,
0.026715172454714775,
-0.006406730506569147,
-0.0032645075116306543,
0.02884557470679283,
0.04443606361746788,
-0.00942043587565422,
-0.04441051185131073,
-0.01939532347023487,
-0.03866300359368324,
0.004442223813384771,
-0.03284229710698128,
-0.02500743605196476,
0.02885746769607067,
0.016895441338419914,
0.007916752249002457,
-0.014031887985765934,
0.017863431945443153,
-0.025387803092598915,
-0.007599448319524527,
0.03348343446850777,
-0.04545465111732483,
0.0219626035541296,
0.02564144879579544,
-0.027629127725958824,
0.009018192999064922,
0.03859978914260864,
0.03392884135246277,
-0.029108239337801933,
0.05190562829375267,
0.004332748707383871,
-0.008938551880419254,
0.014213313348591328,
-0.0036440868861973286,
0.08113083243370056,
-0.009484702721238136,
0.0006671285373158753,
0.027861058712005615,
-0.026574091985821724,
-0.0168947521597147,
0.017700884491205215,
-0.020399315282702446,
0.00673111155629158,
0.017789680510759354,
0.039731260389089584,
0.0021581912878900766,
-0.0012607858516275883,
0.014848864637315273,
0.006463907193392515,
-0.024943457916378975,
0.014581641182303429,
0.08259439468383789,
0.004488152917474508,
-0.0036182929761707783,
-0.04073642939329147,
-0.04677601531147957,
-0.0286664217710495,
0.005427362397313118,
-0.06086292117834091,
0.013358138501644135,
-0.02912208065390587,
-0.0017176513792946935,
-0.028656870126724243,
0.011814510449767113,
0.008872670121490955,
-0.006474468391388655,
0.05358229577541351,
0.05471154302358627,
0.06288433074951172,
-0.011432916857302189,
0.0374562107026577,
-0.009781189262866974,
-0.08616477251052856,
0.013836205936968327,
0.05135682225227356,
0.01305109541863203,
-0.03531668707728386,
0.003638354130089283,
0.013224857859313488,
-0.03223821520805359,
-0.01621926575899124,
-0.008172576315701008,
0.059658270329236984,
-0.009962204843759537,
-0.1023932695388794,
-0.0486077256500721,
0.05337592586874962,
0.023159757256507874,
-0.006254785228520632,
-0.0787123516201973,
0.020279712975025177,
0.008625905960798264,
0.05865072086453438,
-0.018924681469798088,
0.028790567070245743,
0.029397541657090187,
-0.0067850505001842976,
0.0011610366636887193,
0.009304498322308064,
0.006622749380767345,
0.001696328748948872,
-0.018347827717661858,
-0.022930430248379707,
-0.029270563274621964,
0.02470315247774124,
0.02150953747332096,
0.01821078546345234,
0.0036603822372853756,
0.087314672768116,
-0.03570052236318588,
0.012009655125439167,
0.024168195202946663,
0.001985208597034216,
0.01942342519760132,
0.06541262567043304,
0.011009187437593937,
0.027357714250683784,
0.02062210440635681,
-0.010441547259688377,
0.025501752272248268,
-0.009455196559429169,
0.028776150196790695,
0.05772439390420914,
-0.002413854468613863,
-0.010958857834339142,
-0.016621438786387444,
-0.05093199387192726,
0.02159794233739376,
-0.022003337740898132,
-0.01617058739066124,
-0.02005685493350029,
0.008074488490819931,
-0.0069060493260622025,
0.03339274600148201,
-0.0026717933360487223,
-0.017200184985995293,
0.008083036169409752,
-0.06014036387205124,
-0.03857288509607315,
-0.078922338783741,
0.013871992938220501,
0.009354475885629654,
-0.025081811472773552,
0.0468050017952919,
0.016203774139285088,
-0.04936927556991577,
-0.027418896555900574,
-0.057656846940517426,
-0.005287581589072943,
0.045108381658792496,
0.011682529002428055,
0.006746960803866386,
0.014111839234828949,
0.028254197910428047,
0.03594239801168442,
0.018804404884576797,
0.03364131972193718,
-0.01974933035671711,
-0.028598377481102943,
0.008103868924081326,
-0.015833133831620216,
0.041758228093385696,
-0.008382540196180344,
-0.0008132496732287109,
-0.016099872067570686,
0.03609700873494148,
-0.06818394362926483,
0.008716276846826077,
-0.04372423514723778,
0.013859136030077934,
0.034341197460889816,
-0.019892781972885132,
-0.0041275848634541035,
0.05181831121444702,
-0.0026538092643022537,
0.018963072448968887,
-0.028724050149321556,
-0.03655999153852463,
-0.03406354412436485,
-0.00094327621627599,
0.04752202332019806,
0.04807426780462265,
-0.012793509289622307,
0.0009048102656379342,
0.0014516558730974793,
0.05486670136451721,
0.022512061521410942,
-0.01839931681752205,
-0.0017376848263666034,
-0.04468502849340439,
-0.006415706127882004,
0.008784092962741852,
0.011803291738033295,
0.0025799493305385113,
0.02742571197450161,
-0.027893276885151863,
0.032205644994974136,
-0.012347105890512466,
-0.029437797144055367,
0.04294880852103233,
-0.02208310179412365,
0.004587167873978615,
-0.0026297993026673794,
0.00041211245115846395,
0.0482364185154438,
0.0018969516968354583,
0.046720270067453384,
0.03471537306904793,
0.00452254107221961,
0.002369013149291277,
-0.030019817873835564,
-0.0075668576173484325,
0.02908463031053543,
-0.014731665141880512,
0.0018487403867766261,
-0.029561087489128113,
0.010438783094286919,
-0.012143714353442192,
0.008968381211161613,
-0.003111269325017929,
-0.032021258026361465,
-0.020990239456295967,
0.019558176398277283,
0.030274083837866783,
-0.016571564599871635,
-0.009347793646156788,
-0.04210473597049713,
-0.019705094397068024,
0.05857305973768234,
-0.027594100683927536,
0.053715385496616364,
0.05352475494146347,
-0.005999690853059292,
0.03156917169690132,
-0.08446379750967026,
0.010635480284690857,
0.04651558771729469,
-0.013758459128439426,
0.03854851797223091,
0.000725089805200696,
0.0036667545791715384,
-0.05252715200185776,
-0.0033428610768169165,
-0.0343894399702549,
0.008104520849883556,
-0.018175063654780388,
0.007912110537290573,
0.0342000275850296,
0.0055974554270505905,
-0.023946963250637054,
-0.01390749029815197,
-0.0395679771900177,
-0.004351509734988213,
-0.018974298611283302,
-0.012851610779762268,
0.00012764721759594977,
-0.020618529990315437,
0.039377372711896896,
0.044350363314151764,
-0.03812488913536072,
-0.006370611488819122,
-0.03673076629638672,
-0.019988959655165672,
0.015604740008711815,
-0.0027142390608787537,
0.045162610709667206,
-0.004550407640635967,
-0.04838692769408226,
0.11354836076498032,
0.027170436456799507,
-0.033000439405441284,
-0.005115583539009094,
0.008586655370891094,
-0.020800882950425148,
-0.01691342145204544,
-0.007520691491663456,
0.015185023657977581,
0.030853329226374626,
0.026635097339749336,
0.03749573230743408,
0.014121278189122677,
0.0030820746906101704,
0.00824938528239727,
-0.017857342958450317,
0.018675092607736588,
0.006382330320775509,
0.031702667474746704,
0.043902281671762466,
0.007662681397050619,
-0.010479035787284374,
-0.022832678630948067,
0.010133696720004082,
0.004688684828579426,
0.010824384167790413,
-0.044562261551618576,
0.08177453279495239,
-0.001858995296061039,
0.023540103808045387,
-0.03822261095046997,
0.03187492862343788,
0.029546888545155525,
-0.0515168234705925,
0.0026872700545936823,
0.03161051124334335,
0.0009162815986201167,
-0.007000616751611233,
-0.016186228021979332,
-0.0011584507301449776,
0.03647838160395622,
-0.025136876851320267,
0.0025588013231754303,
-0.04977763071656227,
0.005859686061739922,
0.03589542210102081,
-0.004523988347500563,
-0.039936941117048264,
0.040684957057237625,
0.031594108790159225,
0.025690799579024315,
0.02431022748351097,
-0.04580980911850929,
-0.010294115170836449,
-0.035233911126852036,
0.01127405185252428,
-0.005600214470177889,
0.010059836320579052,
-0.008079332299530506,
0.04148763418197632,
0.010831618681550026,
0.05521824210882187,
-0.04205327853560448,
0.022098170593380928,
-0.08372259885072708,
0.00957294087857008,
-0.03635243698954582,
-0.024692287668585777,
-0.008030656725168228,
-0.006399412173777819,
0.013014226220548153,
0.01114087738096714,
-0.06125818192958832,
-0.012018323875963688,
0.001603830954991281,
-0.05914471298456192,
0.0005621256423182786,
-0.025473397225141525,
-0.04602605476975441,
0.008455703966319561,
0.04877839237451553,
0.06584298610687256,
-0.02420550398528576,
0.0019333636155351996,
0.008768615312874317,
-0.05842716246843338,
0.02868683449923992,
0.023847956210374832,
0.02537432499229908,
0.0485607348382473,
-0.010343288071453571,
0.015993675217032433,
0.014044981449842453,
-0.031390342861413956,
-0.01530440803617239,
0.04389338567852974,
0.05789819359779358,
-0.012337720952928066,
-0.020440606400370598,
0.00641500623896718,
-0.055855292826890945,
-0.01639755442738533,
-0.0030033192597329617,
0.05696982145309448,
0.02251317910850048,
-0.02205103076994419,
0.0065053412690758705,
-0.0064721121452748775,
-0.030429497361183167,
0.05072980001568794,
0.026760993525385857,
0.008258676156401634,
-0.04565224424004555,
-0.03794734179973602,
0.008976026438176632,
0.009137018583714962,
-0.024396993219852448,
0.01256010215729475,
-0.025070449337363243,
-0.029921408742666245,
0.016839228570461273,
0.027081765234470367,
0.007599370554089546,
-0.03439546748995781,
-0.04904264956712723,
0.020550502464175224,
0.00797200296074152,
0.07100243866443634,
-0.007368259131908417,
-0.004125028382986784,
0.04459633305668831,
0.05456291511654854,
0.009084515273571014,
0.002722106408327818,
-0.07295241951942444,
-0.026029538363218307,
0.05668354034423828,
0.00773833692073822,
-0.017147095873951912,
-0.029524344950914383,
-0.027661150321364403,
-0.006193503737449646,
0.044040482491254807,
-0.000014508796994050499,
0.025075212121009827,
0.018349016085267067,
0.02056783437728882,
-0.026635389775037766,
-0.04418883100152016,
0.0012265644036233425,
0.02719082124531269,
0.01619330421090126,
-0.010980105958878994,
-0.03163110837340355,
0.0024612757842987776,
-0.014422276988625526,
0.0072378371842205524,
-0.03490264713764191,
0.027750946581363678,
0.042837731540203094,
0.026637308299541473,
-0.0019900077022612095,
0.029203636571764946,
-0.025069981813430786,
-0.06460914015769958,
0.008461260236799717,
0.029198024421930313,
-0.002875174628570676,
0.03262126445770264,
-0.027699152007699013,
-0.040916088968515396,
0.026772821322083473,
0.010615257546305656,
0.018648412078619003,
0.023146873340010643,
-0.03657706081867218,
0.048271387815475464,
0.050036292523145676,
0.028006378561258316,
0.036138106137514114,
0.021173145622015,
-0.039958007633686066,
-0.03232428431510925,
-0.007350543048232794,
0.03281063586473465,
-0.03333541750907898,
0.0013070564018562436,
-0.026139911264181137,
-0.01260762382298708,
-0.04813399538397789,
0.06830013543367386,
-0.032937195152044296,
-0.00784078799188137,
0.010480109602212906,
-0.04210361838340759,
-0.006229646969586611,
0.0028498764149844646,
0.023492828011512756,
-0.047378264367580414,
-0.013584399595856667,
0.06811489164829254,
0.00710601732134819,
-0.012363567017018795,
0.03512674570083618,
-0.004829813726246357,
-0.012619821354746819,
0.004035264253616333,
-0.021403763443231583,
-0.01840559020638466,
-0.03325098007917404,
-0.0365026593208313,
-0.012195414863526821,
-0.06266631186008453,
0.028762243688106537,
-0.01382134947925806,
-0.03856368362903595,
0.029657993465662003,
-0.0567004531621933,
-0.049234528094530106,
0.03536726161837578,
-0.025626031681895256,
0.01269170455634594,
-0.007426450494676828,
-0.0031751510687172413,
0.04522205516695976,
-0.010012928396463394,
-0.07671400904655457,
-0.042365267872810364,
0.03362857550382614,
-0.012138818390667439,
-0.03862205892801285,
-0.030407246202230453,
-0.012101123109459877,
-0.03472909331321716,
-0.019059406593441963,
0.025426704436540604,
0.04953036829829216,
-0.03916080668568611,
0.03529356047511101,
0.004431822337210178,
0.06648137420415878,
0.03998508304357529,
-0.034317079931497574,
-0.002801521448418498,
-0.0011096058879047632,
-0.011118469759821892,
0.02052958309650421,
-0.012138452380895615,
0.04532596468925476,
-0.004963520914316177,
0.013996776193380356,
0.009163551963865757,
-0.05034172907471657,
-0.01637587696313858,
-0.0008274609572254121,
-0.01561849657446146,
0.05410410091280937,
0.0020405834075063467,
0.01709728129208088,
-0.014512112364172935,
-0.028918927535414696,
-0.0117770591750741,
0.03702009469270706,
-0.0477532297372818,
-0.006616752129048109,
0.014070224016904831,
-0.04983723163604736,
0.06501591950654984,
0.004252334125339985,
-0.016336895525455475,
0.038058988749980927,
-0.0018214879091829062,
-0.02897876501083374,
0.0069902618415653706,
0.018502583727240562,
-0.028452729806303978,
-0.009325934574007988,
-0.0250769704580307,
0.02993783913552761,
-0.0073454855009913445,
-0.04232129827141762,
-0.01642901636660099,
-0.019350886344909668,
-0.035211045295000076,
-0.019162053242325783,
0.044549573212862015,
0.02965717390179634,
0.051086779683828354,
0.01740868389606476,
-0.03806460276246071,
0.00213145324960351,
-0.03568316996097565,
-0.0011691341642290354,
-0.00039671239210292697,
0.016792675480246544,
0.025294175371527672,
-0.07585900276899338,
-0.02239397168159485,
0.027011757716536522,
0.02204163372516632,
-0.034987956285476685,
0.004163218196481466,
-0.0016482343198731542,
0.026044754311442375,
-0.004180098418146372,
-0.006190071348100901,
-0.061125677078962326,
0.060372237116098404,
-0.02978125773370266,
0.04608043655753136,
0.00808771699666977,
-0.005153890699148178,
0.015642430633306503,
0.024116558954119682,
0.01815079152584076,
-0.009204693138599396,
-0.025155331939458847,
-0.07382991164922714,
0.039828699082136154,
0.004859686363488436,
0.03069904074072838,
-0.003975190222263336,
-0.012422940693795681,
0.05380263924598694,
-0.04013415426015854,
0.020309550687670708,
0.005376229528337717,
-0.040739066898822784,
-0.01296492014080286,
-0.022261733189225197,
-0.032351262867450714,
0.06265129894018173,
-0.004550585523247719,
-0.02556021697819233,
-0.02176746167242527,
-0.010955256409943104,
0.0033905855379998684,
-0.010687572881579399,
0.04294246435165405,
-0.017995992675423622,
0.04457049444317818,
0.01045910269021988,
0.034435950219631195,
-0.02588157169520855,
-0.028719056397676468,
0.11737246066331863,
0.06516372412443161,
-0.00024281117657665163,
-0.06367398798465729,
0.01635761186480522,
-0.012199399061501026,
0.009505082853138447,
-0.017249753698706627,
-0.004159153904765844,
-0.0038974967319518328,
-0.033611495047807693,
0.01861632987856865,
0.06775043159723282,
0.006221235729753971,
-0.03265330567955971,
0.07904770970344543,
-0.06464719027280807,
-0.0420774444937706,
-0.02207309380173683,
0.016337137669324875,
-0.021451637148857117,
0.04586050286889076,
-0.018124623224139214,
0.04526236653327942,
-0.010887282900512218,
0.02037123031914234,
-0.01914507895708084,
-0.034193284809589386,
0.03725801408290863,
0.02171405218541622,
-0.02262762561440468,
-0.014369282871484756,
-0.016259435564279556,
-0.05273386463522911,
-0.033766407519578934,
-0.012211443856358528,
0.008421271108090878,
-0.024363236501812935,
0.05166463926434517,
0.036213330924510956,
-0.03770889714360237,
0.01068209484219551,
0.03054649941623211,
0.014127270318567753,
-0.06735293567180634,
-0.010181156918406487,
-0.015068820677697659,
0.013946088962256908,
-0.018540529534220695,
0.030551308766007423,
0.008180570788681507,
-0.0355767086148262,
0.0006571031408384442,
-0.014910027384757996,
-0.0029857431072741747,
-0.023894021287560463,
0.026650354266166687,
-0.026402056217193604,
0.0052918195724487305,
-0.03729460388422012,
0.03597552701830864,
0.008376224897801876,
0.02823808044195175,
-0.030511828139424324,
-0.010978691279888153,
0.011485081166028976,
-0.014931385405361652,
0.004229384940117598,
-0.0020505008287727833,
0.0012079359730705619,
0.005852351430803537,
0.035750627517700195,
-0.006501337513327599,
-0.046436160802841187,
0.021323222666978836,
0.031501274555921555,
0.054084260016679764,
0.022789161652326584,
-0.004577009938657284,
-0.02461922913789749,
-0.04078276827931404,
-0.0015084128826856613,
-0.018308602273464203,
-0.020024120807647705,
-0.01432727836072445,
0.007789957337081432,
0.03503013029694557,
0.052396852523088455,
-0.009717239066958427,
-0.006690903566777706,
-0.005293205846101046,
0.03537226468324661,
0.028361231088638306,
-0.014355200342833996,
-0.011493370868265629,
0.021327821537852287,
-0.029878046363592148,
-0.004658639896661043,
0.0018005568999797106,
0.02237842045724392,
0.03141717612743378,
-0.004541071131825447,
-0.0030301841907203197,
0.05291188135743141,
0.036826372146606445,
-0.012460087426006794,
0.043729666620492935,
-0.040355563163757324,
0.0468013659119606,
0.06543831527233124,
0.0005860632518306375,
-0.04491329938173294,
-0.005227983929216862,
0.028658969327807426,
-0.0058274841867387295,
-0.024888239800930023,
-0.011012229137122631,
-0.0040991525165736675,
-0.006343991495668888,
0.016605228185653687,
0.05502733215689659,
-0.022163257002830505,
-0.04110527038574219,
-0.04808006063103676,
0.030109750106930733,
-0.01086856797337532,
-0.016122961416840553,
0.005347222555428743,
0.04622102528810501,
-0.021461045369505882,
-0.03729045018553734,
0.023604201152920723,
0.0406234934926033,
-0.011016268283128738,
0.013802886940538883,
-0.0011920345714315772,
0.03742356598377228,
0.04007447510957718,
0.046547845005989075,
-0.03589081019163132,
-0.019804932177066803,
-0.019686440005898476,
-0.03636320307850838,
0.057404983788728714,
0.022487368434667587,
-0.009010598994791508,
0.047453612089157104,
-0.02503509446978569,
-0.010089702904224396,
0.008351207710802555,
-0.0029178159311413765,
-0.016698965802788734,
-0.03643215075135231,
-0.036505941301584244,
-0.030476508662104607,
-0.07026849687099457,
0.03514772653579712,
-0.01389045175164938,
-0.016614321619272232,
0.0090984171256423,
-0.00944574736058712,
-0.055664513260126114,
-0.029174787923693657,
-0.014658295549452305,
-0.04932471737265587,
0.019837496802210808,
0.0006162684294395149,
0.0405317097902298,
0.009920582175254822,
0.04014793783426285,
-0.04874921962618828,
0.007152738980948925,
-0.006755395792424679,
-0.013090074993669987,
-0.10442721098661423,
-0.026398584246635437,
0.044389985501766205,
0.027793705463409424,
0.049623847007751465,
-0.049788203090429306,
0.03200915455818176,
0.006308387499302626,
-0.05930245667695999,
0.009209060110151768,
-0.010591299273073673,
-0.008790111169219017,
-0.020713472738862038,
-0.030962137505412102,
0.0005466773291118443,
0.07722688466310501,
-0.0018611593404784799,
0.022882740944623947,
-0.0020637866109609604,
0.0235806442797184,
-0.010631326586008072,
-0.04174889251589775,
-0.05387985706329346,
-0.0014514562208205462,
0.007581283338367939,
-0.04203207045793533,
0.0853261798620224,
-0.0014537055976688862,
-0.009166749194264412,
0.02059830352663994,
-0.01873536966741085,
0.0029854506719857454,
0.0021097171120345592,
0.016896944493055344,
0.042489271610975266,
0.011268174275755882,
0.020757799968123436,
0.03094792552292347,
-0.03406890854239464,
-0.002167445607483387,
0.02197287231683731,
0.037290461361408234,
-0.01427342090755701,
0.015206700190901756,
0.0022289941553026438,
-0.027987783774733543,
0.02463531121611595,
0.03097577951848507,
-0.03651798516511917,
-0.04660988226532936,
0.012667346745729446,
-0.011391890235245228,
0.007247597444802523,
-0.0008098895777948201,
0.003022613935172558,
-0.019406242296099663,
0.007486691232770681,
0.006535934284329414,
-0.017667578533291817,
0.010554536245763302,
0.041862472891807556,
0.010850525461137295,
-0.0012385481968522072,
0.05922646075487137,
0.018895892426371574,
0.010914725251495838,
-0.057172954082489014,
-0.009330215863883495,
-0.022319000214338303,
-0.027846021577715874,
0.019395185634493828,
-0.032988179475069046,
0.01178721059113741,
0.013629886321723461,
0.013037005439400673,
0.018912527710199356,
-0.06411909312009811,
-0.006391860079020262,
0.00869673676788807,
-0.04297681897878647,
0.014422441832721233,
-0.0010135674383491278,
-0.0105888731777668,
0.001613752217963338,
-0.010295810177922249,
0.004575730301439762,
0.04450433701276779,
0.041220907121896744,
-0.002653597155585885,
0.001571760862134397,
0.052923399955034256,
0.02516196109354496,
0.050675567239522934,
-0.03167181462049484,
0.004675555974245071,
-0.0031446563079953194,
0.01537743303924799,
0.0024405394215136766,
-0.003850076114758849,
-0.022127637639641762,
0.025521621108055115,
0.0118779381737113,
-0.006801685318350792,
0.03725631907582283,
0.0297681987285614,
-0.03677782416343689,
0.05199664086103439,
0.007955582812428474,
0.005176416598260403,
0.0652971863746643,
-0.011989029124379158,
-0.004366208799183369,
0.04394000396132469,
-0.033846665173769,
-0.025728924199938774,
-0.0012453924864530563,
-0.021639307960867882,
-0.026104221120476723,
-0.0036833942867815495,
-0.02114330418407917,
0.02955637499690056,
-0.03997526317834854,
-0.023710308596491814,
0.026923641562461853,
-0.030192703008651733,
-0.030939197167754173,
0.08033032715320587,
0.01487643364816904,
-0.006825254298746586,
0.013298544101417065,
-0.007191885728389025,
0.027327263727784157,
0.011122792027890682,
0.019382376223802567,
0.015466823242604733,
0.049042440950870514,
0.00029534343047998846,
0.00643054349347949,
-0.000004026564056403004,
0.008639306761324406,
0.005854442249983549,
0.018481355160474777,
0.018914194777607918,
-0.04757317155599594,
-0.02260071225464344,
0.04167590290307999,
0.010316652245819569,
0.004775309003889561,
0.025367287918925285,
-0.04669453576207161,
0.08755619078874588,
-0.02774779126048088,
-0.01118375826627016,
-0.02022438682615757,
0.0331912636756897,
-0.022612063214182854,
0.024293916299939156,
0.019255533814430237,
0.059094756841659546,
-0.002553883707150817,
0.019257361069321632,
-0.04560260847210884,
-0.0012417263351380825,
-0.0004680276906583458,
-0.02937142364680767,
0.04191622510552406,
0.013425522483885288,
0.007545405998826027,
0.028290895745158195,
-0.03029073402285576,
-0.016991106793284416,
-0.03914651647210121,
-0.0032433737069368362,
0.0025689376052469015,
0.03406652808189392,
-0.0062140668742358685,
-0.05370716378092766,
-0.02597803995013237,
0.03198033571243286,
-0.044330302625894547,
-0.022762158885598183,
0.00015275186160579324,
-0.028321431949734688,
0.008926153182983398,
0.015770578756928444
] |
<p>What happens when the explosive energy of a grenade or a bomb is contained in a container, if you will, and no energy can be released through the container in the form of heat or sound etc...? Just theoretically asking?</p>
<p>I just want to know what happens when we take a huge explosion or any explosion and shrink it to a finite point. Theoretically, what happens?</p>
| 8,517 |
[
-0.04463021457195282,
-0.042392145842313766,
-0.00690913712605834,
-0.029745491221547127,
0.008426991291344166,
0.027264904230833054,
-0.02540326490998268,
-0.03229404613375664,
-0.004214852582663298,
-0.01970702037215233,
0.024632032960653305,
0.02273106575012207,
0.0290128942579031,
-0.042063307017087936,
-0.008732830174267292,
-0.03546753153204918,
-0.0018114583799615502,
-0.019077735021710396,
0.0069908942095935345,
-0.04799108952283859,
-0.01719067245721817,
-0.0019765463657677174,
0.004819170571863651,
-0.026878025382757187,
-0.02639184147119522,
0.04292646795511246,
0.04430590197443962,
0.023869765922427177,
0.027312446385622025,
0.0548899844288826,
-0.004951526876538992,
-0.03178195282816887,
-0.012662083841860294,
0.03585413470864296,
0.013218575157225132,
-0.009701940231025219,
-0.059499770402908325,
-0.016827698796987534,
-0.005480896681547165,
-0.014899896457791328,
-0.012539032846689224,
-0.025375710800290108,
0.007415748666971922,
0.054800454527139664,
-0.03625844419002533,
0.021441897377371788,
-0.02421717159450054,
-0.05218895152211189,
0.045216575264930725,
-0.03728602081537247,
0.03163778409361839,
0.01619345135986805,
0.031110698357224464,
0.04533858597278595,
0.02035117894411087,
0.032927531749010086,
0.07703563570976257,
0.08830366283655167,
-0.020815283060073853,
-0.03664238750934601,
-0.012087255716323853,
0.011383711360394955,
0.0027236854657530785,
-0.026831237599253654,
0.009917579591274261,
0.050867266952991486,
-0.02419755421578884,
-0.0060388860292732716,
0.0003281647223047912,
0.018800852820277214,
-0.0016539182979613543,
0.027595728635787964,
0.05825262516736984,
-0.019957423210144043,
0.01658499427139759,
-0.01166163757443428,
0.05702069774270058,
0.02062263898551464,
0.03258882090449333,
0.06512574851512909,
-0.017770910635590553,
-0.019299648702144623,
0.049143970012664795,
0.005841003730893135,
0.018885232508182526,
-0.028627151623368263,
0.04969817027449608,
-0.0007477485341951251,
-0.001097493339329958,
0.025235615670681,
-0.01566239818930626,
-0.0008508135797455907,
0.03274485468864441,
-0.007612706162035465,
-0.023809144273400307,
0.033842820674180984,
-0.01916033774614334,
0.09713637828826904,
0.004538998939096928,
-0.021005533635616302,
0.01784229464828968,
0.00769235473126173,
0.024035189300775528,
0.06678733974695206,
0.019142823293805122,
-0.036902278661727905,
-0.05140639841556549,
0.0095730135217309,
-0.006364891305565834,
0.016580045223236084,
-0.04132770746946335,
0.003429554169997573,
0.011808368377387524,
0.006706995889544487,
0.0242069773375988,
-0.027400722727179527,
0.012862629257142544,
-0.02657664567232132,
0.021283602342009544,
0.03795720264315605,
0.05070953071117401,
-0.016954191029071808,
0.022085020318627357,
-0.02247004583477974,
-0.06835749745368958,
0.0015567538794130087,
0.0134166544303298,
-0.012170487083494663,
-0.047338344156742096,
0.03169632703065872,
0.006263032555580139,
-0.02390221320092678,
0.006732493173331022,
0.007044113706797361,
0.03403759375214577,
-0.04439721256494522,
-0.08472339808940887,
-0.03937356173992157,
0.03611256927251816,
-0.009429643861949444,
-0.03594449535012245,
-0.05929247662425041,
0.000963193888310343,
0.026405449956655502,
0.05423877760767937,
-0.0006674915784969926,
-0.016785835847258568,
-0.012950731441378593,
0.06063860282301903,
0.0023646284826099873,
-0.039170585572719574,
0.005006906110793352,
0.0025275791995227337,
-0.02021859958767891,
0.01655360497534275,
-0.058563653379678726,
0.03579164668917656,
0.027974043041467667,
0.004002473782747984,
-0.023971982300281525,
0.021706771105527878,
-0.0609811469912529,
-0.007455239538103342,
-0.014722667634487152,
-0.03274175524711609,
-0.023073436692357063,
0.089905746281147,
0.02306233160197735,
-0.015654901042580605,
0.054196517914533615,
0.06372611969709396,
0.02910267934203148,
0.016474314033985138,
0.010982763022184372,
0.04678523913025856,
-0.02591516263782978,
-0.01628584787249565,
-0.032161030918359756,
0.048292022198438644,
0.03486812859773636,
-0.03211523965001106,
-0.022880185395479202,
0.0176484826952219,
-0.02660716138780117,
0.04389170557260513,
0.0298848245292902,
-0.00406334875151515,
-0.004866613075137138,
-0.036832261830568314,
-0.017128093168139458,
-0.013547386042773724,
-0.0712624117732048,
0.07760484516620636,
0.007239450700581074,
0.019727513194084167,
0.0252081211656332,
0.004714420530945063,
0.02107236348092556,
-0.06600668281316757,
-0.005551258567720652,
-0.021340906620025635,
0.029874294996261597,
-0.028179990127682686,
-0.034855540841817856,
0.011677701026201248,
0.04629361256957054,
0.05249028280377388,
0.004819678142666817,
0.02491035684943199,
-0.013517949730157852,
-0.034974176436662674,
-0.006865336559712887,
-0.001404569367878139,
-0.014577310532331467,
0.003930187784135342,
-0.03302696719765663,
0.015777425840497017,
0.010343757458031178,
0.006100970320403576,
-0.0033402172848582268,
-0.013435978442430496,
0.0822681114077568,
0.03278063237667084,
0.0011315799783915281,
-0.00987716019153595,
0.012850643135607243,
0.006338834762573242,
-0.008468065410852432,
0.009431794285774231,
-0.01546734943985939,
-0.060201872140169144,
0.015921471640467644,
-0.003984956070780754,
0.02580992318689823,
-0.030690548941493034,
-0.001200508326292038,
0.0179232619702816,
0.011413355357944965,
0.012426239438354969,
-0.003715552156791091,
-0.018686795607209206,
-0.0008196095004677773,
-0.002020427957177162,
0.005077560432255268,
0.019354037940502167,
-0.008327949792146683,
-0.027784563601017,
0.03513946756720543,
-0.018475841730833054,
-0.021230431273579597,
0.011475167237222195,
-0.0008126558386720717,
0.008789614774286747,
-0.02562040463089943,
-0.02752368152141571,
-0.022885238751769066,
0.011671267449855804,
-0.013161377981305122,
0.010345827788114548,
0.002345827640965581,
-0.001294538495130837,
0.007403610274195671,
-0.06767896562814713,
0.0010370007948949933,
0.013018879108130932,
0.021531453356146812,
-0.02690543420612812,
-0.006000376306474209,
0.03301194682717323,
-0.03042529709637165,
-0.027554607018828392,
0.009423152543604374,
0.014203845523297787,
-0.038415417075157166,
-0.0007852797862142324,
0.007167347241193056,
-0.020926764234900475,
0.017298636958003044,
-0.04797634109854698,
-0.030013134703040123,
-0.03163328021764755,
-0.032305121421813965,
-0.018171701580286026,
-0.01939624547958374,
-0.03738611191511154,
0.011053090915083885,
-0.011445038951933384,
-0.04000641033053398,
0.03495060279965401,
-0.02123383805155754,
0.02152397856116295,
0.06530957669019699,
-0.020644884556531906,
-0.05045361816883087,
0.021041639149188995,
0.01285682711750269,
-0.010767300613224506,
-0.03139154985547066,
-0.004798946436494589,
0.0913289487361908,
-0.019853312522172928,
-0.0292206984013319,
-0.005344220902770758,
-0.036275483667850494,
-0.04359053820371628,
-0.03539310768246651,
-0.011752118356525898,
0.05124913901090622,
-0.006382380146533251,
0.03684511408209801,
0.0012308903969824314,
-0.05795726552605629,
-0.0038304179906845093,
-0.03873147442936897,
-0.03313802555203438,
-0.0034990401472896338,
0.012560950592160225,
0.03145970404148102,
-0.021096304059028625,
-0.04161291942000389,
0.06567968428134918,
-0.013032625429332256,
-0.02347886748611927,
0.00440119206905365,
-0.02498624660074711,
0.042240455746650696,
-0.006357538979500532,
0.01421080157160759,
-0.002927527530118823,
0.016084570437669754,
0.013242354616522789,
0.012174961157143116,
0.022296644747257233,
0.0022328475024551153,
0.028248775750398636,
-0.009982200339436531,
0.005608850158751011,
0.038411810994148254,
0.018993055447936058,
0.0016964649548754096,
0.029890529811382294,
-0.04237337037920952,
0.04251300171017647,
0.006154635455459356,
0.024274207651615143,
0.018269840627908707,
-0.0550529882311821,
0.02638823911547661,
0.0354398675262928,
0.009532932192087173,
-0.025647787377238274,
0.0367787703871727,
-0.051012489944696426,
-0.0024322206154465675,
0.018704578280448914,
0.03926298767328262,
0.033398013561964035,
-0.004264495801180601,
0.011834636330604553,
-0.028923269361257553,
0.08214414119720459,
-0.05690921097993851,
-0.06747191399335861,
0.023707980290055275,
-0.004460344556719065,
0.010791008360683918,
0.044276610016822815,
-0.017345005646348,
0.05345709249377251,
0.01727127656340599,
0.0054706186056137085,
-0.008046453818678856,
0.017994007095694542,
0.002601878484711051,
-0.06260336935520172,
-0.021919025108218193,
-0.007075152359902859,
0.022150980308651924,
-0.0003248758730478585,
0.0516338124871254,
0.026367440819740295,
0.04177016764879227,
0.048335447907447815,
0.049715276807546616,
-0.09164731204509735,
0.0388217456638813,
-0.022866472601890564,
-0.012013294734060764,
-0.009803909808397293,
0.03343501314520836,
-0.01605919376015663,
-0.00032226453186012805,
-0.011587586253881454,
0.01243461761623621,
-0.007190558593720198,
-0.06867619603872299,
0.012981968931853771,
-0.007107376586645842,
-0.022601237520575523,
0.0047784908674657345,
0.02746635675430298,
0.04418618977069855,
0.009088144637644291,
0.020578311756253242,
0.03785562515258789,
-0.04111965000629425,
0.013410346582531929,
-0.005985727533698082,
-0.0039831106550991535,
0.02117476984858513,
0.045205142349004745,
0.02373899146914482,
0.03971756994724274,
-0.006615238264203072,
0.004362640902400017,
0.048011574894189835,
0.025787977501749992,
-0.0300839114934206,
0.0021049168426543474,
-0.027949918061494827,
-0.033341940492391586,
0.019807977601885796,
0.024820568040013313,
0.019177695736289024,
-0.022236386314034462,
0.03859466314315796,
0.016485827043652534,
0.02253316529095173,
0.022904612123966217,
0.014756877906620502,
0.05792783945798874,
0.017790982499718666,
-0.05606475844979286,
-0.012906443327665329,
-0.01069477666169405,
-0.03059283085167408,
-0.015006220899522305,
-0.0274195559322834,
-0.02053903415799141,
0.002787945093587041,
0.027407992631196976,
0.0036585568450391293,
0.03221962973475456,
-0.026117980480194092,
0.006301321554929018,
0.0041626146994531155,
-0.015414710156619549,
-0.02507728524506092,
-0.005797026678919792,
0.06456433236598969,
0.025518832728266716,
0.04101560264825821,
0.00024471551296301186,
0.001977843465283513,
-0.05104115977883339,
0.02755070850253105,
0.028398480266332626,
0.015746429562568665,
0.023780301213264465,
-0.0022672524210065603,
-0.041474465280771255,
-0.03761845827102661,
0.03601093217730522,
-0.03787030279636383,
0.02749570831656456,
-0.003370109712705016,
-0.0018335817148908973,
-0.0013308494817465544,
-0.02193249762058258,
-0.05463968589901924,
-0.01868630200624466,
0.0018073349492624402,
-0.02330922894179821,
0.008022944442927837,
0.015393050387501717,
-0.021734751760959625,
0.0013284473679959774,
0.056348808109760284,
0.0266350656747818,
0.010142921470105648,
-0.0012787393061444163,
-0.013138564303517342,
0.006849453318864107,
0.0019575818441808224,
-0.03822772577404976,
-0.027294503524899483,
0.006826233584433794,
-0.05210273712873459,
0.0482872873544693,
-0.018522942438721657,
-0.06389058381319046,
0.027668582275509834,
0.008060780353844166,
-0.017087120562791824,
0.010244115255773067,
-0.04389633610844612,
0.0661742091178894,
0.028301376849412918,
-0.008293597027659416,
0.006990574765950441,
0.04886079952120781,
-0.003255247138440609,
-0.0032380169723182917,
-0.03208696469664574,
0.01576073095202446,
-0.05723869800567627,
0.030317066237330437,
-0.04539048299193382,
0.06136184185743332,
-0.015359286218881607,
0.04770186170935631,
-0.02184714376926422,
-0.015476027503609657,
0.00955305527895689,
-0.042650915682315826,
0.019897276535630226,
0.050158675760030746,
0.019439611583948135,
0.023450326174497604,
-0.022245177999138832,
0.029757868498563766,
0.009473116137087345,
-0.024343451485037804,
-0.006680069025605917,
0.013233843259513378,
0.018492737784981728,
0.04175395891070366,
-0.07261040806770325,
0.03155434876680374,
-0.013659822754561901,
-0.0203463826328516,
0.05229717120528221,
-0.033285774290561676,
0.04464259743690491,
-0.019214801490306854,
-0.056351128965616226,
0.03973715752363205,
-0.06396368891000748,
0.004601842723786831,
-0.002940309001132846,
0.018898621201515198,
0.05035865679383278,
-0.06444143503904343,
0.04624730721116066,
0.0026492660399526358,
-0.012509995140135288,
-0.0787193700671196,
-0.035145245492458344,
0.04453609883785248,
0.0024404842406511307,
-0.010543899610638618,
-0.05919026583433151,
-0.010003436356782913,
-0.023923685774207115,
-0.045374974608421326,
-0.0022128152195364237,
0.04921269416809082,
-0.020490340888500214,
0.010885974392294884,
0.028483739122748375,
-0.0051110791973769665,
0.04293810948729515,
0.024824202060699463,
-0.037358514964580536,
0.02276201918721199,
0.005276763346046209,
-0.02300555258989334,
-0.009729474782943726,
0.030384313315153122,
-0.0289305467158556,
-0.008435405790805817,
-0.002924226922914386,
-0.027284078299999237,
0.010773149318993092,
-0.026345811784267426,
-0.0026832271832972765,
0.0019684082362800837,
0.035513631999492645,
-0.021604519337415695,
0.003694036975502968,
0.019160356372594833,
0.013950526714324951,
0.023488851264119148,
-0.0021411380730569363,
-0.013233063742518425,
-0.024326536804437637,
-0.04003956541419029,
-0.0018980243476107717,
0.0018876178655773401,
-0.008324691094458103,
-0.0045742131769657135,
0.04292752221226692,
0.0032246403861790895,
0.0004805007192771882,
-0.003102953778579831,
-0.03640647977590561,
0.022416329011321068,
-0.03706418722867966,
-0.025839688256382942,
0.016909534111618996,
0.0020203154999762774,
-0.047319196164608,
-0.043996021151542664,
-0.03639831393957138,
0.018026838079094887,
0.02595895156264305,
-0.05251668766140938,
0.01220722496509552,
0.01408227626234293,
0.01213215384632349,
0.021410683169960976,
-0.022872116416692734,
0.016575897112488747,
0.03148336336016655,
0.0027186807710677385,
0.04164543375372887,
-0.014137458987534046,
0.00158720335457474,
0.04333316907286644,
0.0352487787604332,
-0.04904184117913246,
0.029884643852710724,
0.017577074468135834,
0.028115762397646904,
0.012716824188828468,
-0.02611108496785164,
-0.037640877068042755,
0.017034215852618217,
-0.04965893179178238,
-0.001167261740192771,
0.023994021117687225,
-0.012437796220183372,
0.006949239410459995,
0.012774530798196793,
0.01585470139980316,
-0.022977856919169426,
-0.018135199323296547,
-0.03402674198150635,
0.014469929970800877,
0.004469092469662428,
0.02169509045779705,
0.007687384728342295,
0.012704581022262573,
0.01105848141014576,
0.007531024515628815,
-0.012742315419018269,
0.020251017063856125,
-0.03533044457435608,
-0.037127695977687836,
-0.023518282920122147,
-0.05033238232135773,
0.03194776177406311,
-0.008550467900931835,
-0.0084682023152709,
0.03666377812623978,
-0.030971813946962357,
0.009244567714631557,
0.016669971868395805,
0.03465044125914574,
0.009804661385715008,
0.06769924610853195,
0.02730894275009632,
0.0017222374444827437,
-0.03975469991564751,
0.035732902586460114,
0.08866826444864273,
0.02014319971203804,
-0.0037795566022396088,
-0.0566759929060936,
0.004308877047151327,
-0.027467280626296997,
0.0005236358847469091,
-0.015998538583517075,
-0.004377829376608133,
-0.021988339722156525,
0.015385170467197895,
0.03175798058509827,
0.0740625411272049,
-0.02434672974050045,
0.008544119074940681,
0.040474291890859604,
-0.04278630390763283,
-0.04412538558244705,
0.007399019319564104,
0.01720762997865677,
-0.01955624297261238,
-0.006931029260158539,
-0.04755110293626785,
0.01392420008778572,
0.00202532229013741,
-0.02883046679198742,
-0.03379332646727562,
-0.0393713116645813,
0.05459616333246231,
0.0011984497541561723,
-0.07372792065143585,
-0.005881721619516611,
0.017186103388667107,
-0.03671271726489067,
-0.041782841086387634,
0.026915589347481728,
0.05142093822360039,
0.011426870711147785,
-0.02605128288269043,
0.03209757059812546,
0.029318489134311676,
0.008879099041223526,
0.019606707617640495,
0.004228897392749786,
-0.01972086727619171,
-0.03609798103570938,
-0.02451257035136223,
0.03257649764418602,
-0.04317212104797363,
-0.006986785214394331,
-0.016107922419905663,
-0.021849170327186584,
0.014969752170145512,
-0.018901491537690163,
-0.03870738297700882,
0.006055363919585943,
0.019049186259508133,
0.021037941798567772,
-0.02874680608510971,
-0.025815071538090706,
0.002146968152374029,
-0.01635822281241417,
0.013328585773706436,
-0.033974211663007736,
0.0413566529750824,
0.03700098767876625,
-0.01985679380595684,
0.044243961572647095,
-0.006633194629102945,
-0.015190204605460167,
-0.0283698420971632,
0.0011648160871118307,
-0.03697143495082855,
-0.018712375313043594,
0.012028775177896023,
0.016852358356118202,
0.03880252689123154,
0.007167177740484476,
0.019333820790052414,
-0.02903364785015583,
-0.05661344528198242,
0.060303084552288055,
-0.022726107388734818,
-0.024234501644968987,
-0.030733969062566757,
0.008204803802073002,
-0.01913715898990631,
0.051862578839063644,
-0.03251172974705696,
-0.03363579511642456,
-0.020161259919404984,
0.030556853860616684,
0.024423660710453987,
-0.022230522707104683,
-0.010209359228610992,
0.02228471077978611,
-0.027839388698339462,
0.001825201790779829,
-0.0001722164306556806,
0.03761330246925354,
0.022610986605286598,
-0.021437369287014008,
0.026158446446061134,
-0.00765699427574873,
-0.017194069921970367,
-0.0023509711027145386,
0.01179744303226471,
-0.0002861532848328352,
-0.01601109467446804,
0.03936817869544029,
0.03731584548950195,
-0.014263766817748547,
-0.035594094544649124,
-0.015008690766990185,
-0.0013646897859871387,
-0.02291041985154152,
0.041047465056180954,
0.014468817971646786,
0.0004971432499587536,
-0.01377626322209835,
0.03522766754031181,
-0.015973947942256927,
0.01618514582514763,
-0.0377940908074379,
-0.007095697335898876,
0.048340074717998505,
-0.02318819984793663,
-0.014120510779321194,
0.010194973088800907,
-0.037563506513834,
-0.027274318039417267,
-0.0002518935361877084,
0.02191106230020523,
-0.015386510640382767,
-0.004449077881872654,
0.0003703216789290309,
0.0033507191110402346,
0.05124068632721901,
-0.00695876544341445,
-0.04593678191304207,
0.04794406518340111,
-0.045921579003334045,
-0.06567493826150894,
0.029776599258184433,
-0.02726968191564083,
0.04236885532736778,
0.03492773696780205,
0.03051588125526905,
-0.04461033269762993,
0.07620986551046371,
-0.006678776815533638,
-0.0019456347217783332,
0.03342748060822487,
-0.05008455365896225,
-0.022219831123948097,
0.019833697006106377,
0.005263112485408783,
-0.012133928015828133,
-0.07170575112104416,
0.010192384012043476,
0.010059076361358166,
0.014207709580659866,
0.010039296932518482,
0.06994759291410446,
0.00008559673733543605,
0.03565017133951187,
0.0031428171787410975,
0.013924839906394482,
0.013558351434767246,
0.09068556874990463,
-0.035093337297439575,
0.014521787874400616,
0.032314904034137726,
-0.008000754751265049,
-0.1409718096256256,
-0.0005093340878374875,
-0.0016372015234082937,
0.003557104617357254,
0.03339302912354469,
-0.01847289502620697,
0.0008929602336138487,
0.03328010439872742,
-0.08819098770618439,
-0.028175657615065575,
-0.06075078248977661,
-0.027420589700341225,
-0.025407910346984863,
-0.005352618172764778,
-0.021492818370461464,
0.07653623819351196,
0.04013598710298538,
0.0581289641559124,
0.010257408022880554,
0.01571924053132534,
-0.049724236130714417,
0.02266903780400753,
-0.005018079187721014,
0.02242760732769966,
0.00823875144124031,
0.0318901464343071,
0.07963617146015167,
-0.0403263196349144,
0.005480014719069004,
-0.0020386662799865007,
-0.04335770383477211,
-0.003182067768648267,
0.004522094968706369,
-0.008604200556874275,
-0.014314636588096619,
0.04500735178589821,
-0.001330984989181161,
0.02405424416065216,
0.03719474375247955,
0.031487490981817245,
0.016425181180238724,
0.00534467538818717,
-0.031728021800518036,
-0.006327485200017691,
0.011931190267205238,
-0.03409794345498085,
0.002067550318315625,
0.04017508029937744,
0.012733721174299717,
-0.01282940711826086,
0.004598990082740784,
0.01844147779047489,
0.0028238340746611357,
0.009056271985173225,
-0.00008923414134187624,
-0.04191805049777031,
-0.015461703762412071,
0.04684242606163025,
0.04367522895336151,
-0.015539553016424179,
0.015865834429860115,
-0.008706517517566681,
-0.0284320916980505,
-0.016410747542977333,
0.01645343005657196,
-0.043919529765844345,
-0.033838484436273575,
0.009325205348432064,
-0.006653647869825363,
0.011798158288002014,
0.011550253257155418,
-0.04579448327422142,
-0.04793432354927063,
0.03569738566875458,
0.040842507034540176,
0.04413345083594322,
0.016907235607504845,
-0.03115439973771572,
-0.024983162060379982,
-0.08077464997768402,
0.03844553977251053,
-0.04483756050467491,
-0.002965967869386077,
-0.04015801474452019,
-0.05373040959239006,
0.030086355283856392,
0.019769122824072838,
0.05916057899594307,
-0.0079379016533494,
-0.021740512922406197,
0.030109873041510582,
-0.02173137478530407,
0.017033137381076813,
-0.043159302324056625,
-0.015560565516352654,
-0.013447020202875137,
0.000016829722881084308,
-0.004470356740057468,
-0.01542715821415186,
-0.019229885190725327,
-0.02381531335413456,
0.0477948822081089,
-0.0028373568784445524,
-0.02089397981762886,
-0.05435866117477417,
-0.025264998897910118,
0.06868018209934235,
0.024200553074479103,
0.003939575515687466,
0.07217446714639664,
-0.019200073555111885,
0.01704283617436886,
-0.0019140227232128382,
-0.026462938636541367,
-0.02802383340895176,
0.011753019876778126,
-0.010155763477087021,
0.023883050307631493,
-0.015004129149019718,
-0.025688525289297104,
0.027755819261074066,
-0.018438223749399185,
0.0061373584903776646,
0.06374302506446838,
-0.019582925364375114,
-0.03123382478952408,
0.044643256813287735,
0.03317263349890709,
0.0593198798596859,
-0.027816390618681908,
0.0013163951225578785,
0.016567151993513107,
0.03918062895536423,
0.0006643200758844614,
0.05211121216416359,
0.04134684428572655,
-0.019045284017920494,
0.008354689925909042,
0.01781695894896984,
-0.04733346402645111,
0.0020242552272975445,
0.0033553868997842073,
0.02885057032108307,
-0.04827207699418068,
-0.06884817779064178,
0.004486864898353815,
-0.038821250200271606,
0.009048187173902988,
0.012534352019429207,
-0.019133703783154488,
0.06250511109828949,
0.020219113677740097,
0.0044790455140173435,
-0.0269453227519989,
-0.0012965705245733261,
-0.023864928632974625,
0.011898200958967209,
0.009742345660924911,
0.014391443692147732,
-0.006442669313400984,
0.027048831805586815,
-0.003269388573244214,
0.007297721225768328,
0.030278675258159637,
-0.012860567308962345,
0.009749652817845345,
-0.013554203324019909,
-0.025747517123818398,
-0.046995170414447784,
-0.021863283589482307,
-0.015417690388858318,
-0.012280876748263836,
0.046790771186351776,
0.04773201048374176,
0.010441968217492104,
0.04238729178905487,
-0.019065581262111664,
-0.019226064905524254,
0.0686989277601242,
-0.016617631539702415,
0.02461199462413788,
-0.015898650512099266,
0.046885620802640915,
-0.010636341758072376,
-0.000557290855795145
] |
<p>Usual central potentials produce quantum spectra with energy levels going as $n$, $n^2$, $n^3$ and so on, being $n$ the quantum number of the orbit. In the other extreme we have "dirac-delta" potentials which have only a single discrete eigenvalue. I was wondering, what kind of potential do we need for producing an exponential $e^n$ set of discrete eigenvalues?</p>
| 8,518 |
[
-0.015158358961343765,
-0.013719542883336544,
0.005135518033057451,
-0.01438420545309782,
0.03349332511425018,
-0.031228894367814064,
-0.04404710233211517,
-0.04964457452297211,
0.02314045839011669,
-0.046571191400289536,
0.015452447347342968,
0.00387777597643435,
0.0336461141705513,
-0.0008655862766318023,
0.021733276546001434,
0.03073386289179325,
-0.04573142156004906,
-0.005997506435960531,
-0.024500567466020584,
-0.06536301970481873,
0.022094344720244408,
0.012772778980433941,
0.02639910951256752,
0.0049133868888020515,
-0.02634045109152794,
0.03191269934177399,
0.02036285400390625,
0.023372218012809753,
0.012502938508987427,
0.06579932570457458,
-0.008808091282844543,
-0.022708579897880554,
0.01065756380558014,
0.04985633119940758,
-0.013445574790239334,
0.006739720236510038,
-0.05981948599219322,
-0.04787260293960571,
-0.008546882309019566,
0.008956321515142918,
-0.05109386146068573,
-0.07955782115459442,
-0.014943837188184261,
0.024410150945186615,
-0.01620752364397049,
0.008457648567855358,
-0.018137527629733086,
-0.036224521696567535,
0.0611090362071991,
-0.05174838751554489,
0.0667303130030632,
-0.004238450899720192,
0.028926119208335876,
0.00867808610200882,
-0.010890835896134377,
0.0112029192969203,
0.05835108831524849,
0.05734429508447647,
0.0035912843886762857,
-0.0032022518571466208,
-0.05946913734078407,
-0.016299637034535408,
-0.0004950260045006871,
-0.03889112547039986,
-0.029199765995144844,
0.01716868206858635,
0.014137793332338333,
-0.02548004500567913,
-0.018228089436888695,
-0.032773494720458984,
-0.010004677809774876,
0.04343690723180771,
0.030562063679099083,
-0.028976909816265106,
0.024285828694701195,
-0.017901264131069183,
0.019562939181923866,
0.017751440405845642,
0.044252827763557434,
0.002622404834255576,
-0.02547944337129593,
-0.0028069764375686646,
0.008772604167461395,
0.04056386649608612,
-0.033909644931554794,
0.02455233782529831,
0.052125222980976105,
-0.018851054832339287,
0.008660340681672096,
0.0472109392285347,
-0.016042325645685196,
0.016165969893336296,
0.037123192101716995,
-0.049777332693338394,
-0.03007669746875763,
-0.0034133309964090586,
0.008591938763856888,
0.03765072673559189,
-0.009817967191338539,
-0.044499754905700684,
-0.0013853085692971945,
-0.016835056245326996,
0.01672913134098053,
0.07612775266170502,
-0.007108212448656559,
0.027577755972743034,
-0.033824194222688675,
0.00809131283313036,
0.002704044571146369,
-0.008978661149740219,
-0.025188028812408447,
0.015409039333462715,
0.01483647245913744,
-0.0010071186115965247,
0.029743274673819542,
0.02438328228890896,
-0.03213566541671753,
-0.02379572205245495,
0.05025797709822655,
0.06962365657091141,
0.012448571622371674,
-0.04517345502972603,
0.03752705827355385,
-0.0327109657227993,
-0.05196116119623184,
-0.014798443764448166,
0.041669394820928574,
0.020057806745171547,
-0.035310909152030945,
-0.009662969969213009,
-0.012244734913110733,
-0.008909601718187332,
0.0071604023687541485,
0.004131201654672623,
0.03836488351225853,
-0.0229570921510458,
-0.11093452572822571,
-0.06334223598241806,
0.026863612234592438,
-0.041470933705568314,
-0.030509624630212784,
-0.038545217365026474,
-0.01342723798006773,
0.04827859625220299,
0.07280462980270386,
0.00003991097037214786,
0.0030463107395917177,
0.014402688480913639,
0.01844998076558113,
0.050101976841688156,
-0.0014025747077539563,
-0.033357854932546616,
-0.017509380355477333,
-0.040532246232032776,
-0.008201196789741516,
-0.011657764203846455,
0.040020380169153214,
0.026151400059461594,
0.03111688792705536,
-0.007987803779542446,
0.047892145812511444,
-0.05474957451224327,
-0.007928353734314442,
0.0026447696145623922,
0.04635269567370415,
-0.02423134632408619,
0.07074945420026779,
0.033346302807331085,
-0.009000686928629875,
0.03475717455148697,
-0.015619696117937565,
0.017183609306812286,
0.060274869203567505,
0.03288981318473816,
0.028040502220392227,
-0.024836109951138496,
-0.018959807232022285,
-0.061484988778829575,
0.03242059424519539,
0.005672906991094351,
-0.02046133577823639,
-0.022049957886338234,
0.008035024628043175,
-0.003934010397642851,
-0.02697412110865116,
0.07121552526950836,
-0.004197024740278721,
-0.009831649251282215,
-0.008153820410370827,
-0.0645977258682251,
0.02175254561007023,
-0.04742247238755226,
0.04232654720544815,
0.026053454726934433,
-0.009270844049751759,
0.06302264332771301,
-0.0016234680078923702,
0.0291293878108263,
0.004121003672480583,
-0.032803747802972794,
0.034594371914863586,
0.032836440950632095,
0.01431173924356699,
-0.02609655261039734,
0.05338364467024803,
0.06338068842887878,
0.026514777913689613,
-0.004083640407770872,
0.044829949736595154,
-0.029366470873355865,
-0.04143460467457771,
-0.01772366650402546,
-0.03158539533615112,
0.06143531575798988,
0.017908133566379547,
0.018847309052944183,
-0.025065604597330093,
0.005959455855190754,
-0.0008928252500481904,
0.02912556380033493,
-0.05259101837873459,
0.07585377246141434,
0.01639188639819622,
0.01732748933136463,
0.020765339955687523,
0.04967690631747246,
0.037044767290353775,
0.01891150511801243,
0.015360723249614239,
-0.0548182874917984,
-0.04166819900274277,
0.039170101284980774,
0.032202839851379395,
0.059582289308309555,
-0.08466637134552002,
0.029882708564400673,
0.010745353996753693,
0.05478601157665253,
0.047078248113393784,
0.01945403590798378,
-0.06608336418867111,
-0.016493242233991623,
0.01614227332174778,
0.0015177247114479542,
0.03495338186621666,
-0.0024068632628768682,
0.027077164500951767,
0.02866293117403984,
0.0063282945193350315,
-0.008060178719460964,
0.004342245403677225,
0.005852050147950649,
-0.04267637059092522,
0.0007922383374534547,
-0.016639841720461845,
-0.015016842633485794,
0.014219350181519985,
-0.04657291620969772,
0.009561452083289623,
0.022261684760451317,
-0.06614522635936737,
0.02195373922586441,
-0.008188240230083466,
-0.052554015070199966,
0.04073833301663399,
-0.003684901399537921,
-0.02394820749759674,
-0.008665713481605053,
0.02243136614561081,
-0.02138148993253708,
0.034171804785728455,
-0.019348956644535065,
-0.009240557439625263,
0.010625876486301422,
0.052720602601766586,
0.039168838411569595,
-0.006904329173266888,
0.02727963961660862,
-0.027970319613814354,
-0.03980344161391258,
0.005215488374233246,
-0.037354208528995514,
-0.011158798821270466,
0.026952994987368584,
-0.06012411788105965,
-0.0030390892643481493,
-0.03230758756399155,
-0.03958611935377121,
0.03811822831630707,
-0.006792375817894936,
0.026217171922326088,
-0.015827098861336708,
-0.0340573713183403,
-0.011846601963043213,
-0.01543678343296051,
-0.01142198871821165,
0.006339978892356157,
-0.024993620812892914,
-0.009461159817874432,
0.057150088250637054,
-0.02264128252863884,
-0.009450276382267475,
0.015702776610851288,
-0.013712259940803051,
-0.01991945691406727,
-0.03287728503346443,
0.005583392921835184,
0.021176885813474655,
-0.04025392606854439,
0.05406446009874344,
0.02350643277168274,
-0.010441615246236324,
0.013677912764251232,
-0.07697302103042603,
-0.023440305143594742,
-0.01295786164700985,
-0.040901068598032,
0.02527100220322609,
-0.01048754621297121,
-0.010820850729942322,
0.08793701976537704,
0.007226794958114624,
-0.039170216768980026,
-0.03476244956254959,
-0.01863884925842285,
0.006944876164197922,
-0.022484611719846725,
0.028358977288007736,
0.03755642846226692,
-0.03768295422196388,
0.014410304836928844,
0.04205457121133804,
-0.02163451910018921,
0.0103306258097291,
-0.007539086509495974,
-0.04324634000658989,
0.04014340415596962,
-0.008511874824762344,
0.03957294672727585,
0.04601600021123886,
0.0033968437928706408,
-0.022196318954229355,
-0.0009364723227918148,
-0.00830053724348545,
0.023956459015607834,
0.02896035462617874,
-0.05961213260889053,
0.030875610187649727,
0.014209426008164883,
0.028084849938750267,
0.01394631341099739,
0.026851307600736618,
0.015383187681436539,
-0.0133911008015275,
-0.03379019722342491,
0.05531977862119675,
0.040098194032907486,
-0.03930161893367767,
0.0032301624305546284,
0.03040672279894352,
0.02254972606897354,
0.002458381000906229,
0.011720940470695496,
0.002545269438996911,
0.005262929014861584,
0.01478520967066288,
-0.00842429231852293,
-0.013627656735479832,
0.01462265569716692,
0.016000887379050255,
0.029764845967292786,
-0.023304326459765434,
-0.024326611310243607,
-0.009653217159211636,
-0.0375836007297039,
0.00037326407618820667,
-0.04176050052046776,
0.06230478733778,
0.013318083249032497,
0.060054127126932144,
0.00006688776920782402,
0.015403169207274914,
0.03296836465597153,
-0.009936556220054626,
-0.08130238205194473,
-0.010501700453460217,
-0.030294880270957947,
0.005244518164545298,
0.00540219945833087,
0.00450926786288619,
0.008536170236766338,
-0.003431223565712571,
-0.05050696060061455,
-0.00019101507496088743,
-0.016056617721915245,
-0.035754576325416565,
-0.0005746331298723817,
-0.05644720792770386,
-0.018522579222917557,
-0.03072592057287693,
0.03245220333337784,
0.026638278737664223,
-0.00258808140642941,
-0.004498764406889677,
-0.008880159817636013,
-0.014508841559290886,
0.011548765003681183,
-0.01695946231484413,
0.021478356793522835,
-0.02673112042248249,
0.030406108126044273,
0.02238488756120205,
0.04429498314857483,
0.0018865283345803618,
-0.014730129390954971,
0.001435680314898491,
0.03609896078705788,
-0.0061953263357281685,
-0.023505832999944687,
0.025572394952178,
-0.050283804535865784,
0.014095374383032322,
-0.0045611136592924595,
0.07024842500686646,
-0.005445563700050116,
0.02669902890920639,
0.06968484818935394,
0.005722398404031992,
-0.035460975021123886,
0.00697379419580102,
0.043295204639434814,
-0.0062010386027395725,
-0.04448831453919411,
-0.022095441818237305,
-0.004042250104248524,
-0.03609583154320717,
-0.023616021499037743,
-0.02387934923171997,
-0.014750796370208263,
-0.014571696519851685,
0.03502896428108215,
0.021279150620102882,
-0.0009355053771287203,
0.006661409046500921,
-0.017390789464116096,
0.0016003911150619388,
0.035362258553504944,
-0.0659237951040268,
-0.01201499905437231,
-0.011129611171782017,
-0.006992488168179989,
0.05227358639240265,
-0.009507467970252037,
0.010980689898133278,
-0.08985348790884018,
-0.01985355094075203,
0.020548541098833084,
0.011959198862314224,
0.004610794130712748,
-0.03202429041266441,
-0.05045938491821289,
-0.007740462198853493,
0.04946977645158768,
-0.016408076509833336,
0.02078135870397091,
-0.018238551914691925,
-0.05755465477705002,
0.005860593635588884,
-0.0003958089801017195,
0.005150029435753822,
0.017213312909007072,
0.02736993134021759,
0.00982792116701603,
-0.03413739427924156,
0.006403557024896145,
-0.041512344032526016,
0.05644681304693222,
0.018310802057385445,
0.06352075934410095,
0.04738977923989296,
-0.01936243288218975,
0.005604013334959745,
0.016874944791197777,
0.018027739599347115,
-0.058663152158260345,
-0.007728099822998047,
0.028133783489465714,
0.00925805326551199,
-0.009370622225105762,
-0.05383787304162979,
-0.041461192071437836,
0.0012226165272295475,
-0.0017919171368703246,
0.01239432767033577,
0.03439538553357124,
0.011609328910708427,
0.04535564407706261,
0.04256980121135712,
-0.010143676772713661,
0.037065401673316956,
0.05915517359972,
-0.020412983372807503,
-0.04310528188943863,
-0.03506255894899368,
0.03485018387436867,
-0.022499335929751396,
-0.01300782524049282,
-0.004663265775889158,
0.02779349684715271,
-0.0418999120593071,
-0.000625256507191807,
-0.002611481351777911,
0.0061430479399859905,
0.03453940525650978,
-0.05295419320464134,
-0.01291078981012106,
0.040905777364969254,
0.00632663257420063,
0.016120487824082375,
0.01068693958222866,
0.04143647477030754,
0.013072669506072998,
-0.015021429397165775,
-0.005640442483127117,
-0.0005850394954904914,
0.01699271984398365,
0.019972652196884155,
-0.03517874330282211,
0.011097131296992302,
-0.02986619807779789,
0.00719580240547657,
0.04409641772508621,
-0.05940540134906769,
0.03059403784573078,
0.012850222177803516,
-0.002548946999013424,
0.03191929683089256,
-0.07124346494674683,
-0.005091069731861353,
-0.00014111146447248757,
-0.0019501461647450924,
0.006602520123124123,
-0.026845743879675865,
0.007944931276142597,
-0.017170989885926247,
-0.002975084586068988,
-0.08074890077114105,
-0.005805410910397768,
0.022506048902869225,
0.0007450939738191664,
-0.016574285924434662,
-0.03325851261615753,
0.00043210171861574054,
-0.04603677988052368,
0.02139410190284252,
-0.00478342454880476,
0.0237549040466547,
0.02293427288532257,
-0.005044948775321245,
0.022310251370072365,
0.054635629057884216,
0.018240083009004593,
0.023754389956593513,
-0.008824986405670643,
-0.002634467324241996,
0.012016724795103073,
0.011820114217698574,
-0.008616033010184765,
0.06034858524799347,
-0.042468637228012085,
-0.034731727093458176,
-0.02005583606660366,
-0.005287726875394583,
0.03668386489152908,
-0.04005754739046097,
-0.013981238007545471,
0.05383533984422684,
0.0238163061439991,
0.013722805306315422,
0.0010127236600965261,
-0.004271996673196554,
-0.02877218835055828,
0.014920073561370373,
0.008589502424001694,
-0.002150991465896368,
-0.012556854635477066,
-0.04728049784898758,
0.02192786894738674,
-0.005905161611735821,
-0.002848000731319189,
0.018717175349593163,
0.04630177468061447,
0.03394090011715889,
-0.022922104224562645,
0.0011108929757028818,
-0.02197534777224064,
0.020217398181557655,
-0.007271623704582453,
0.011282812803983688,
0.012921351008117199,
0.01180651132017374,
-0.018692519515752792,
-0.07949277758598328,
-0.016220707446336746,
0.0367581881582737,
0.01547983568161726,
-0.01249256543815136,
0.04294656589627266,
0.003956765402108431,
0.04735562205314636,
-0.026498092338442802,
-0.025820322334766388,
-0.027269180864095688,
0.017142536118626595,
0.003463722299784422,
0.02147280052304268,
-0.0402793325483799,
0.014562629163265228,
0.013812140561640263,
0.03374391421675682,
0.022980133071541786,
0.033532142639160156,
0.06470787525177002,
0.0004880540072917938,
-0.005061788950115442,
-0.034012604504823685,
-0.006751637440174818,
0.05267319828271866,
-0.01530152652412653,
0.04256555065512657,
0.05878104269504547,
0.003910881467163563,
0.037816230207681656,
0.026310529559850693,
0.035477738827466965,
-0.035140931606292725,
-0.015229256823658943,
-0.048154957592487335,
0.03369198366999626,
0.0097577553242445,
-0.004859147593379021,
0.012216228991746902,
0.0025029024109244347,
-0.002225810196250677,
0.026850556954741478,
0.001617460511624813,
-0.0077538867481052876,
-0.04309716075658798,
-0.0325855128467083,
-0.035248275846242905,
-0.09434068948030472,
0.05647660419344902,
0.034033577889204025,
-0.03785311058163643,
0.025755014270544052,
-0.0011195676634088159,
0.029847154393792152,
0.0009751190664246678,
0.014111588709056377,
-0.023399513214826584,
0.016753284260630608,
0.020346520468592644,
-0.02855871059000492,
0.0077388654462993145,
0.01616477593779564,
0.13153357803821564,
0.09529995918273926,
0.005417236126959324,
-0.06350632011890411,
0.008915964514017105,
0.0024185527581721544,
-0.018832404166460037,
-0.005949013866484165,
0.004475605674088001,
0.024790529161691666,
-0.02642417512834072,
-0.04744067043066025,
0.07554946839809418,
0.00392604386433959,
0.041077326983213425,
0.049807481467723846,
-0.02106150984764099,
-0.01906484179198742,
0.011602913960814476,
0.0019389101071283221,
0.01601306162774563,
0.0066071473993361,
-0.027358336374163628,
0.04054275527596474,
-0.0521622933447361,
0.012542149052023888,
-0.03495626524090767,
-0.01603502780199051,
0.03431534767150879,
0.006009986158460379,
-0.0016309114871546626,
-0.033185385167598724,
-0.0017700326861813664,
-0.00949113629758358,
-0.024864986538887024,
0.02153908461332321,
-0.020128706470131874,
-0.002077874494716525,
0.014271567575633526,
0.01760559342801571,
0.0031857278663665056,
0.0013288394547998905,
0.011124344542622566,
0.0033560493029654026,
-0.04823482781648636,
-0.041930437088012695,
-0.05233583599328995,
0.01599775440990925,
-0.026929406449198723,
-0.004023069981485605,
0.0015919995494186878,
-0.026410982012748718,
-0.03011983446776867,
-0.040407441556453705,
-0.03167851269245148,
-0.030823053792119026,
0.04110724851489067,
-0.019427308812737465,
-0.04131762310862541,
0.0014327423414215446,
0.029380930587649345,
0.005069993436336517,
0.02202524058520794,
-0.027300776913762093,
-0.044118139892816544,
0.027655579149723053,
-0.02123708836734295,
0.06182044744491577,
-0.003182366257533431,
-0.0384351871907711,
0.0034077391028404236,
-0.024157151579856873,
-0.046792853623628616,
0.0006900753360241652,
-0.016270088031888008,
-0.015346131287515163,
0.011020904406905174,
0.021481849253177643,
0.013215320184826851,
0.003128588665276766,
-0.04149528220295906,
-0.021443651989102364,
-0.015893839299678802,
-0.0023198470007628202,
-0.024767305701971054,
-0.0017297629965469241,
0.027632147073745728,
0.02187494747340679,
-0.0002265037182951346,
0.012604670599102974,
0.0028963179793208838,
-0.01790548488497734,
0.03814483806490898,
-0.026345333084464073,
0.023736469447612762,
-0.0016912942519411445,
-0.05441158264875412,
0.03765874728560448,
-0.03107110783457756,
0.006672759540379047,
-0.013703458942472935,
0.00220471085049212,
0.005687530618160963,
0.05346928536891937,
-0.0599544495344162,
-0.010991116054356098,
0.010027608834207058,
-0.06661151349544525,
-0.006974251475185156,
-0.0038814011495560408,
0.007363410200923681,
-0.03896940127015114,
-0.051354508846998215,
-0.04569704458117485,
0.00952379871159792,
0.008305741474032402,
0.05030880123376846,
-0.04109448939561844,
0.02515360899269581,
-0.033272113651037216,
0.03879090026021004,
-0.062488626688718796,
0.00858834944665432,
-0.03893176466226578,
0.0521259568631649,
0.013203798793256283,
0.002777884714305401,
-0.030060645192861557,
0.011529848910868168,
-0.013974800705909729,
-0.01394595019519329,
0.007883870974183083,
0.018195271492004395,
0.00018316236673854291,
-0.017717769369482994,
0.020108407363295555,
-0.0029780487529933453,
0.028342800214886665,
0.009511478245258331,
-0.025373294949531555,
0.04167748615145683,
-0.05399554967880249,
-0.058997102081775665,
0.00885800365358591,
-0.035084448754787445,
0.026263250038027763,
0.026850927621126175,
-0.030411554500460625,
0.007915601134300232,
0.03852040693163872,
-0.03618553653359413,
-0.015543096698820591,
0.0011531325289979577,
0.008042174391448498,
0.010006800293922424,
-0.009048323146998882,
0.023241698741912842,
-0.0038147943560034037,
0.01868189126253128,
-0.018845781683921814,
0.017572514712810516,
-0.011207305826246738,
-0.021886952221393585,
0.023103833198547363,
0.005378480069339275,
0.04208969697356224,
0.015167064033448696,
-0.0036674332804977894,
0.007871398702263832,
0.026515301316976547,
-0.04185003787279129,
0.009351450018584728,
0.04316210746765137,
-0.004140233621001244,
-0.05831972509622574,
0.006429971195757389,
-0.020567651838064194,
-0.022102560847997665,
0.01311485655605793,
-0.05476740375161171,
0.0004302070592530072,
0.06350608170032501,
-0.06279446929693222,
0.05732027441263199,
-0.01952478103339672,
0.015766093507409096,
-0.014655107632279396,
-0.0008565543685108423,
-0.03800150007009506,
0.022520292550325394,
0.03213329240679741,
0.044790320098400116,
0.005097361281514168,
-0.011489911936223507,
-0.014217174611985683,
-0.008360530249774456,
0.013212916441261768,
0.02033069171011448,
0.01814851723611355,
-0.03097357042133808,
0.05733164772391319,
-0.035409457981586456,
-0.03988362103700638,
0.027692941948771477,
0.025151189416646957,
0.0015307816211134195,
-0.032112330198287964,
0.006456101778894663,
0.011923950165510178,
0.04615878313779831,
0.057998962700366974,
-0.003024635836482048,
-0.027763182297348976,
0.0008206598577089608,
0.028991885483264923,
-0.0016965825343504548,
-0.005555992480367422,
-0.00009085244528250769,
0.06695646792650223,
-0.0024426549207419157,
-0.048072680830955505,
0.021918177604675293,
0.02131882682442665,
0.01865812949836254,
0.00023850529396440834,
0.008452908135950565,
0.010877670720219612,
-0.01825486123561859,
0.009851976297795773,
-0.03611289709806442,
-0.039353739470243454,
-0.023137373849749565,
0.013620657846331596,
0.022726433351635933,
0.030226700007915497,
-0.031161347404122353,
-0.058379191905260086,
0.026896081864833832,
0.02628566324710846,
-0.012993442825973034,
-0.04943236708641052,
-0.009121866896748543,
0.005634404718875885,
-0.019736945629119873,
-0.022502737119793892,
-0.008865962736308575,
-0.03831210359930992,
0.030825521796941757,
-0.025416331365704536,
0.031231511384248734,
-0.026539692655205727,
-0.05991499125957489,
-0.009239234030246735,
-0.0647202879190445,
0.033304281532764435,
0.014207223430275917,
0.033716198056936264,
0.006427444983273745,
-0.01222215499728918,
0.026703132316470146,
-0.018672043457627296,
0.06967762112617493,
0.00787730235606432,
-0.04605939984321594,
0.015248306095600128,
-0.00928095169365406,
0.03996577858924866,
0.00814031157642603,
-0.02022380940616131,
-0.011924903839826584,
-0.009150278754532337,
-0.020730776712298393,
0.004374456126242876,
-0.0009723239345476031,
0.038385115563869476,
0.033528733998537064,
0.0045168702490627766,
-0.05608963221311569,
-0.0015699031064286828,
-0.011645156890153885,
0.06797514855861664,
0.017635585740208626,
-0.043387699872255325,
0.05916929244995117,
-0.0033165235072374344,
0.004449674393981695,
-0.019017605111002922,
-0.01940738596022129,
-0.013466454111039639,
0.02573823556303978,
-0.023934155702590942,
-0.0074659246020019054,
-0.0189411211758852,
0.013295422308146954,
0.02820926159620285,
-0.02742058038711548,
0.0018079765141010284,
0.043343402445316315,
-0.0016429249662905931,
-0.028524452820420265,
0.026701288297772408,
-0.01366421114653349,
0.050654537975788116,
0.003097357228398323,
0.012981932610273361,
0.04117975011467934,
0.004478442016988993,
-0.00867398176342249,
0.052597206085920334,
0.025112692266702652,
-0.0035511392634361982,
0.02811538800597191,
0.003719341242685914,
-0.04148392379283905,
0.04829376935958862,
0.03093324601650238,
0.0145890973508358,
-0.020984835922718048,
-0.012393778190016747,
0.04510510712862015,
0.004137769341468811,
-0.011853246949613094,
-0.041684363037347794,
-0.02943287044763565,
0.10754267126321793,
-0.016678886488080025,
0.034916192293167114,
-0.049848370254039764,
-0.0017777604516595602,
0.012114075012505054,
-0.002834571059793234,
-0.014686167240142822,
0.02007117308676243,
-0.017245003953576088,
0.0014923533890396357,
0.009149477817118168,
0.03911815583705902,
-0.015942996367812157,
-0.06474120169878006,
0.010502377524971962,
0.0005232578841969371,
-0.0006890896474942565,
-0.009516778402030468,
0.005507550667971373,
-0.027360109612345695,
-0.024602852761745453,
0.0070387376472353935,
0.06220750883221626,
0.047980815172195435,
0.026510776951909065,
-0.019673049449920654,
0.009322975762188435,
0.0034273911733180285,
-0.05348404496908188,
-0.015656962990760803,
-0.030957257375121117,
0.025409966707229614,
0.014622742310166359,
-0.0027053882367908955
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.