question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>I found this related question: <a href="http://physics.stackexchange.com/questions/51511/what-happens-to-5-electrons-on-a-sphere">What happens to 5 electrons on a sphere?</a></p>
<p>But this question describes the case when there can only be 5 electrons on that sphere at all times. The answer linked to the <a href="http://en.wikipedia.org/wiki/Thomson_problem" rel="nofollow">Thomson Problem</a>, which gives a solution for the stable configuration of $N$ charges placed on a sphere. </p>
<blockquote>
<ul>
<li>So my question is that, will it not repel the extra electrons inside the metal to produce a state of non-uniformly distributed + and - charges?</li>
</ul>
</blockquote>
<p>If not, it would mean that there is a net non-zero field inside the <em>bulk</em> of the sphere, so that configuration cannot be a steady state, i.e. It will cause the sea of electrons to flow and achieve another steady state, which can be said from the <a href="http://en.wikipedia.org/wiki/Faraday_cage" rel="nofollow">Electrostatic Shielding Effect</a>.</p>
<blockquote>
<ul>
<li><p>So, what steady state will be achieved?</p></li>
<li><p>What if it is a solid sphere and not a hollow one? Will the extra electron still be on the surface of the sphere?</p></li>
</ul>
</blockquote>
<p>Any help is appreciated!</p>
<p>P.S. You can leave the last question for me to attempt, if its easily deducible from the answer for the first two!</p>
| 10,654 |
[
-0.06406649202108383,
-0.024612870067358017,
0.038942329585552216,
-0.011441588401794434,
0.00015687344421166927,
-0.048214346170425415,
-0.011037616059184074,
-0.02076565846800804,
0.00044908825657330453,
-0.01983395218849182,
0.05603865161538124,
0.019103839993476868,
0.0306550320237875,
0.032620225101709366,
-0.01594877801835537,
-0.01783742941915989,
0.010728154331445694,
-0.03799812123179436,
-0.0070052077062428,
-0.03604113683104515,
-0.016169602051377296,
0.04657629132270813,
-0.02815556526184082,
-0.007257308345288038,
-0.030910981819033623,
0.02301556058228016,
0.008323198184370995,
-0.011389831081032753,
0.015560355968773365,
0.044380199164152145,
-0.006411976646631956,
-0.005470911040902138,
0.020285973325371742,
-0.0005655708955600858,
0.00449065025895834,
0.000897511257790029,
-0.020766587927937508,
-0.04608036205172539,
0.025758899748325348,
0.011148624122142792,
-0.03150171786546707,
0.0049011423252522945,
-0.0031962841749191284,
0.01497459877282381,
0.013492797501385212,
-0.03098122775554657,
0.038369446992874146,
-0.012409110553562641,
0.056207891553640366,
-0.06830824911594391,
0.05437004193663597,
-0.010892430320382118,
0.042911358177661896,
-0.0023883136454969645,
0.016634896397590637,
-0.030557263642549515,
0.07158169895410538,
0.08514617383480072,
0.04764378443360329,
-0.042404573410749435,
-0.025404712185263634,
-0.027536366134881973,
-0.02264430746436119,
-0.021412856876850128,
-0.014198641292750835,
0.05264633148908615,
-0.005792466923594475,
-0.022219473496079445,
0.029131677001714706,
-0.002018872182816267,
0.011306826025247574,
0.016533561050891876,
0.008092096075415611,
-0.04438265413045883,
0.03688089922070503,
-0.008007864467799664,
0.03423984721302986,
-0.020555876195430756,
-0.00030063072335906327,
0.031554561108350754,
-0.021302605047822,
0.01985875517129898,
0.06596474349498749,
0.04552614316344261,
-0.01765785552561283,
-0.008580335415899754,
0.06372316926717758,
-0.028243273496627808,
0.02580271102488041,
0.02474777214229107,
-0.012150397524237633,
0.013194183818995953,
0.057885393500328064,
-0.0004356295394245535,
-0.03400573506951332,
0.001744279288686812,
-0.010717978700995445,
0.06305625289678574,
-0.0394505150616169,
-0.004729305859655142,
-0.008535739965736866,
-0.0030950764194130898,
0.025730526074767113,
0.07805315405130386,
0.014673336409032345,
-0.001568953157402575,
-0.03481786698102951,
-0.03157525509595871,
0.02438596449792385,
-0.013447239063680172,
-0.03456377238035202,
0.025538533926010132,
0.02018188126385212,
-0.015315059572458267,
-0.0034538619220256805,
-0.03998054936528206,
0.01490292139351368,
-0.005708437878638506,
0.04047584906220436,
0.05428697168827057,
0.00035376212326809764,
-0.00955658033490181,
0.04070083796977997,
-0.03676179423928261,
-0.05469454079866409,
-0.015994243323802948,
0.019403109326958656,
0.005293461959809065,
-0.005448704585433006,
0.01194804161787033,
0.0065345303155481815,
-0.006913268472999334,
0.008903410285711288,
0.021229440346360207,
0.03836100921034813,
-0.03155313432216644,
-0.07374220341444016,
-0.03199044615030289,
0.050858572125434875,
-0.014207419008016586,
-0.012127518653869629,
-0.045605044811964035,
0.004152157809585333,
0.021396055817604065,
0.09213674068450928,
0.002035341691225767,
-0.016379596665501595,
-0.03309706598520279,
0.06249752268195152,
0.026899881660938263,
-0.029001804068684578,
0.03178105875849724,
-0.0011615816038101912,
-0.012106935493648052,
0.004193339496850967,
-0.07137931138277054,
0.047550030052661896,
0.01292484812438488,
0.0285712331533432,
-0.025254150852560997,
0.05835146829485893,
-0.003965459298342466,
0.023527368903160095,
-0.009480820968747139,
-0.01873345673084259,
-0.002098134718835354,
0.05230671912431717,
-0.010269715450704098,
0.017735078930854797,
0.047139957547187805,
0.02157280035316944,
0.042370326817035675,
-0.008612305857241154,
0.01591005176305771,
0.03570817783474922,
-0.06267727166414261,
0.022731933742761612,
-0.08401477336883545,
0.0347137413918972,
0.0046347579918801785,
-0.02189573086798191,
-0.009020617231726646,
0.011514190584421158,
0.007559702731668949,
0.003415930550545454,
0.037720631808042526,
-0.01100330799818039,
-0.00921179261058569,
-0.04341153800487518,
-0.04478402063250542,
-0.02986832708120346,
-0.054799508303403854,
0.033163439482450485,
0.01629890874028206,
-0.04449648782610893,
0.03450225293636322,
-0.030773082748055458,
0.0293238814920187,
0.01941745914518833,
-0.025900129228830338,
0.009523077867925167,
0.03440038487315178,
-0.006502377800643444,
-0.011069435626268387,
0.024302365258336067,
0.0540802888572216,
0.03180274739861488,
0.043262820690870285,
0.04118023440241814,
-0.030284253880381584,
-0.015271554701030254,
-0.047935791313648224,
0.015454044565558434,
0.05903792008757591,
0.038648296147584915,
-0.010460076853632927,
0.008364491164684296,
-0.0028554170858114958,
-0.0037367616314440966,
0.01761077158153057,
-0.023255156353116035,
0.07722081243991852,
0.03445577248930931,
0.012335531413555145,
0.01316747721284628,
0.027770914137363434,
0.006375208962708712,
0.004619147628545761,
0.0006530191167257726,
-0.02628266252577305,
-0.05376489832997322,
0.03375302627682686,
0.018167691305279732,
0.02532706968486309,
-0.03588884696364403,
0.0448799803853035,
0.0035319775342941284,
0.042317669838666916,
0.023553408682346344,
0.009047300554811954,
-0.05671292170882225,
0.002322364831343293,
0.06077929213643074,
0.015926562249660492,
-0.017755767330527306,
0.011032245121896267,
0.03284052759408951,
-0.0034048398956656456,
-0.018625104799866676,
0.010539800859987736,
0.007211263757199049,
0.03972804918885231,
-0.023296352475881577,
0.007909148931503296,
-0.023781130090355873,
-0.03579932451248169,
0.02961602248251438,
-0.013750813901424408,
0.02621089667081833,
0.012891439720988274,
0.012306159362196922,
0.015073896385729313,
-0.026615425944328308,
-0.010658730752766132,
0.005117250140756369,
-0.014014420099556446,
-0.002134873066097498,
0.005039780866354704,
0.00143341941293329,
-0.06799863278865814,
0.003722929861396551,
-0.0075201615691185,
0.021218053996562958,
0.016413560137152672,
-0.026704728603363037,
0.01843148097395897,
0.008352166041731834,
0.036924827843904495,
-0.019356898963451385,
0.0030206828378140926,
-0.007330588065087795,
-0.033558495342731476,
0.011703740805387497,
0.02259262278676033,
-0.04783353954553604,
-0.013792503625154495,
-0.02445327118039131,
-0.02509070187807083,
0.06221483647823334,
0.0068616000935435295,
0.0019372551469132304,
0.03565853089094162,
-0.0166018046438694,
-0.03787364438176155,
0.030646180734038353,
-0.014976253733038902,
0.0032447290141135454,
-0.0422515943646431,
0.008045850321650505,
0.0671212449669838,
0.025077423080801964,
-0.026158148422837257,
-0.004443631507456303,
-0.04059721529483795,
-0.04190627485513687,
-0.012415757402777672,
-0.005615415051579475,
0.021474279463291168,
-0.021410562098026276,
0.04909522086381912,
0.03673682361841202,
-0.02310091257095337,
0.01006349828094244,
-0.03404565528035164,
-0.030406618490815163,
0.02594463713467121,
-0.030061913654208183,
0.010748464614152908,
-0.036622900515794754,
-0.05298755690455437,
0.05536720156669617,
0.013559858314692974,
-0.011455880478024483,
-0.008690801449120045,
-0.027464523911476135,
-0.015035822056233883,
-0.04445667937397957,
-0.02261926420032978,
0.06540929526090622,
0.020252985879778862,
-0.015290766954421997,
0.05841686949133873,
0.0429898202419281,
0.030093250796198845,
0.005208084359765053,
0.017845554277300835,
0.010352445766329765,
0.026487473398447037,
0.01601046696305275,
0.0319502130150795,
-0.0272037573158741,
-0.030135326087474823,
-0.024447869509458542,
-0.03635241463780403,
0.057991158217191696,
0.05483110621571541,
-0.02870168723165989,
0.002223279792815447,
-0.04068484902381897,
0.023248666897416115,
-0.03576578572392464,
0.02436068467795849,
-0.008831437677145004,
-0.04740925878286362,
-0.023324789479374886,
0.0453532338142395,
0.030409304425120354,
-0.020085718482732773,
-0.02869485318660736,
0.05483556166291237,
0.036176249384880066,
-0.021743083372712135,
-0.00960991159081459,
0.005019605625420809,
0.00544814532622695,
0.018796591088175774,
-0.04451388493180275,
-0.023283950984477997,
0.015286548994481564,
0.03801809251308441,
0.04225616157054901,
0.001891321036964655,
0.009685298427939415,
0.005347297061234713,
-0.07777178287506104,
-0.028276296332478523,
-0.008479620330035686,
0.05185025557875633,
-0.012904239818453789,
0.01976015232503414,
0.019280049949884415,
0.007689498830586672,
-0.009344719350337982,
0.014782239682972431,
-0.051787909120321274,
0.004582354798913002,
0.023762738332152367,
0.000343674881150946,
-0.008810389786958694,
0.025822259485721588,
-0.03151119872927666,
-0.016633208841085434,
-0.030366450548171997,
-0.003779360558837652,
0.03385934606194496,
-0.05890935659408569,
0.009566960856318474,
-0.03076586313545704,
-0.04025515541434288,
-0.01834114082157612,
0.03777613863348961,
0.03170105069875717,
-0.04773158207535744,
0.04385795444250107,
-0.037531837821006775,
-0.0426982156932354,
0.012731707654893398,
-0.02273007296025753,
0.01017810683697462,
0.028432572260499,
0.038248833268880844,
0.005637212190777063,
0.011943488381803036,
0.0011617536656558514,
-0.017787154763936996,
-0.005935207940638065,
0.0397857241332531,
0.0016964849783107638,
0.020215196534991264,
-0.03633643314242363,
-0.0411563366651535,
-0.02192586474120617,
-0.017483703792095184,
0.057583920657634735,
-0.024780331179499626,
0.06024688109755516,
0.03328308090567589,
-0.04693666845560074,
-0.0057987128384411335,
-0.006748147774487734,
0.05004660412669182,
0.004425788763910532,
-0.028574524447321892,
-0.03554476797580719,
-0.01865043304860592,
-0.04923895001411438,
0.022533250972628593,
0.02522294968366623,
-0.0005059441900812089,
-0.0019509007688611746,
0.008258167654275894,
0.02820042334496975,
0.01530432514846325,
0.0018224065424874425,
-0.029674077406525612,
-0.0038845434319227934,
0.042519841343164444,
-0.011193998157978058,
0.007059905212372541,
0.007140267174690962,
0.024922898039221764,
0.06382732093334198,
0.02198207378387451,
0.004612156189978123,
-0.08792303502559662,
-0.03674309700727463,
0.018976029008626938,
0.05900555104017258,
0.0111702224239707,
0.024311935529112816,
-0.07214228063821793,
0.011546030640602112,
0.03487031161785126,
-0.02318832091987133,
0.03043697588145733,
-0.03373529389500618,
-0.0010322751477360725,
-0.0008003364782780409,
-0.001356999739073217,
-0.04867181554436684,
-0.03555653616786003,
0.012388682924211025,
0.04502660036087036,
-0.03125949949026108,
0.011418282985687256,
0.015949279069900513,
0.009929732419550419,
0.02254374884068966,
0.05027627572417259,
-0.014391247183084488,
0.010389471426606178,
-0.005111877806484699,
0.0198882557451725,
-0.0009126228978857398,
-0.09678945690393448,
-0.00842785183340311,
-0.00183055829256773,
-0.02314552292227745,
0.039608076214790344,
-0.06840471923351288,
-0.019704047590494156,
0.0160337146371603,
-0.005656030029058456,
0.009342895820736885,
-0.016062764450907707,
-0.048255011439323425,
0.07448695600032806,
-0.011391003616154194,
0.003747700247913599,
0.044310204684734344,
0.032206881791353226,
-0.01696198061108589,
0.021975386887788773,
-0.022776635363698006,
0.038358233869075775,
-0.03568211942911148,
0.025921398773789406,
0.029321057721972466,
0.02211630530655384,
-0.0489162877202034,
0.04713285341858864,
-0.014850052073597908,
-0.003031764877960086,
-0.0019647039007395506,
-0.014899034984409809,
0.05792396143078804,
-0.006993803661316633,
-0.019325047731399536,
0.015691542997956276,
-0.01843934692442417,
0.044900622218847275,
0.02070487104356289,
-0.03540215641260147,
-0.020940620452165604,
-0.011032680980861187,
0.03173259273171425,
0.03052433207631111,
-0.017927037551999092,
0.007664482109248638,
-0.03870393708348274,
0.005110966507345438,
-0.004092423245310783,
-0.0766582116484642,
0.0803351178765297,
-0.00668435450643301,
0.0022160455118864775,
0.025493746623396873,
-0.0633043572306633,
-0.017140112817287445,
0.0353524275124073,
-0.016009889543056488,
0.02737577073276043,
-0.045079465955495834,
0.030066238716244698,
0.041097864508628845,
0.016682351008057594,
-0.07657168805599213,
-0.04143504053354263,
0.029199223965406418,
0.013402408920228481,
0.007788625080138445,
-0.030621446669101715,
-0.050260476768016815,
-0.02652093954384327,
-0.07860701531171799,
0.0025691790506243706,
0.032689228653907776,
-0.04145202785730362,
-0.03647932782769203,
0.0053102970123291016,
0.005463209934532642,
0.06243520602583885,
-0.026562415063381195,
-0.005030142143368721,
-0.022966185584664345,
-0.017838314175605774,
0.011798919178545475,
-0.008582917973399162,
-0.0028429406229406595,
-0.01974659040570259,
-0.05041847005486488,
-0.005361904390156269,
-0.001899282680824399,
0.023134076967835426,
-0.024646740406751633,
-0.02237311750650406,
0.03139960765838623,
-0.012486850842833519,
0.0014694574056193233,
-0.003770191688090563,
0.020456746220588684,
0.00591137632727623,
0.02907189540565014,
-0.0032490906305611134,
0.017997313290834427,
-0.03760455921292305,
-0.04232769459486008,
0.05257544293999672,
-0.016630806028842926,
-0.01998031511902809,
-0.018680401146411896,
0.07685196399688721,
0.011899927631020546,
-0.002668593544512987,
0.0019122445955872536,
0.004060542210936546,
0.0010707586770877242,
-0.01710374467074871,
-0.0020733738783746958,
-0.026707036420702934,
-0.013229056261479855,
-0.036453742533922195,
-0.053183142095804214,
-0.028176724910736084,
0.015551204793155193,
0.04111054912209511,
-0.018908658996224403,
0.009868908673524857,
0.011311866343021393,
0.003437821054831147,
-0.025868654251098633,
-0.014278803952038288,
-0.004939935635775328,
0.008097399957478046,
-0.003911655396223068,
0.04333734139800072,
-0.01563660241663456,
0.04458059370517731,
0.012396475300192833,
0.07141704857349396,
-0.004834957420825958,
0.005339819006621838,
0.051040809601545334,
-0.008852522820234299,
0.025039443746209145,
-0.014769838191568851,
-0.029584920033812523,
0.02820226363837719,
-0.04076265171170235,
0.03978370130062103,
0.009402083232998848,
-0.01382843405008316,
0.05823046714067459,
0.02554173208773136,
0.004294107668101788,
-0.034584760665893555,
-0.045325618237257004,
-0.008398010395467281,
0.036403439939022064,
0.003780004335567355,
-0.003950254525989294,
-0.02410585805773735,
0.009583682753145695,
0.009005365893244743,
-0.011027250438928604,
0.0027276617474853992,
-0.02603263594210148,
-0.04806957766413689,
-0.00756061403080821,
-0.04949400946497917,
-0.01906605251133442,
0.045207105576992035,
0.015775484964251518,
-0.04114402458071709,
-0.00002619191218400374,
-0.03087662160396576,
0.05655984207987785,
0.026620080694556236,
0.05832797288894653,
-0.014756438322365284,
0.0730164647102356,
-0.020958956331014633,
0.03502717986702919,
-0.009957145899534225,
-0.006896287202835083,
0.12642475962638855,
0.0348874032497406,
0.012955357320606709,
-0.06149417161941528,
-0.003567678155377507,
-0.015933845192193985,
0.027700873091816902,
0.004804604221135378,
-0.020281735807657242,
-0.06157834827899933,
0.016762390732765198,
0.00483373599126935,
0.04752979800105095,
0.015140780247747898,
0.02941913530230522,
0.01888052374124527,
-0.043932653963565826,
0.005362286698073149,
-0.0018136135768145323,
0.0288672037422657,
-0.0007174482452683151,
0.031725212931632996,
-0.06648371368646622,
0.06550245732069016,
-0.02301143668591976,
-0.0022080233320593834,
-0.05108267068862915,
0.00034638840588741004,
0.04076521843671799,
-0.0012643197551369667,
-0.042837388813495636,
0.024824604392051697,
-0.0254567451775074,
-0.03703855350613594,
-0.05262581631541252,
0.03218435123562813,
0.02996576577425003,
-0.001472468487918377,
0.011971326544880867,
0.038271643221378326,
-0.012398626655340195,
0.02836981788277626,
0.04311534762382507,
0.0377044752240181,
-0.03825773671269417,
0.025980336591601372,
-0.021744782105088234,
0.02293212339282036,
-0.01816597394645214,
-0.027876241132616997,
0.014835864305496216,
0.005475194659084082,
0.0069866059347987175,
-0.03644586354494095,
-0.02772798202931881,
-0.032861776649951935,
0.04222335293889046,
0.0006867091869935393,
-0.019953152164816856,
0.009127650409936905,
0.0422452874481678,
0.025036700069904327,
-0.03834697976708412,
0.012763848528265953,
-0.00033515063114464283,
-0.011992517858743668,
-0.009914753958582878,
0.054122135043144226,
-0.0007811671239323914,
-0.0009261182276532054,
-0.062355928122997284,
-0.017029613256454468,
-0.04144105315208435,
-0.016939828172326088,
0.0030725114047527313,
0.03288882598280907,
0.052112992852926254,
0.002213296014815569,
0.0007465219823643565,
0.03003990836441517,
-0.0779663696885109,
0.02677343040704727,
-0.0039823479019105434,
-0.02871275320649147,
-0.053002454340457916,
0.0021228352561593056,
-0.0366075336933136,
0.025983741506934166,
-0.02899709716439247,
0.02869604155421257,
0.033353280276060104,
0.03275751695036888,
-0.004274888429790735,
-0.013018188066780567,
-0.031025389209389687,
0.007343140430748463,
-0.004401287529617548,
0.011805475689470768,
-0.027787433937191963,
0.04045040160417557,
0.005647497717291117,
0.01956748403608799,
0.012543604709208012,
0.06706281751394272,
-0.01628570817410946,
-0.001986471703276038,
-0.010744269005954266,
-0.00810189452022314,
-0.0008033139747567475,
0.027713898569345474,
0.011979512870311737,
-0.019611964002251625,
-0.017575876787304878,
-0.01684270054101944,
-0.039327215403318405,
0.013681391254067421,
-0.0038115084171295166,
-0.03872150555253029,
0.0070441956631839275,
-0.005543670617043972,
0.013375764712691307,
-0.022621581330895424,
0.020257052034139633,
-0.04998301342129707,
0.003528149100020528,
0.02067885547876358,
-0.009659668430685997,
0.002408105880022049,
0.031418830156326294,
-0.030828578397631645,
0.016129828989505768,
0.0321091003715992,
-0.010565145872533321,
-0.004473453387618065,
-0.013104506768286228,
0.019158663228154182,
0.01113781239837408,
0.03136049583554268,
-0.012697603553533554,
-0.007908513769507408,
0.03256740793585777,
-0.008397890254855156,
-0.03597508370876312,
0.032548584043979645,
-0.01485821045935154,
0.03978043794631958,
0.024525528773665428,
0.0014710992109030485,
-0.03322954848408699,
0.06317439675331116,
-0.022311553359031677,
0.015773240476846695,
-0.006943241693079472,
-0.01982477679848671,
0.013713476248085499,
-0.018349725753068924,
-0.008220194838941097,
-0.009616062045097351,
0.0042319949716329575,
0.0392572283744812,
0.019238319247961044,
-0.02294856682419777,
-0.024306677281856537,
0.013347320258617401,
0.0016571443993598223,
-0.011329565197229385,
0.03062107414007187,
0.035554300993680954,
-0.006941989529877901,
0.05411025509238243,
-0.012024770490825176,
0.0058323838748037815,
0.01692795753479004,
-0.013950539752840996,
-0.09317361563444138,
-0.025140631943941116,
-0.00160754076205194,
-0.003744447370991111,
0.005792171694338322,
-0.044727668166160583,
0.008299189619719982,
0.018829431384801865,
-0.11860419809818268,
0.018890373408794403,
-0.011885615065693855,
-0.0433586984872818,
-0.049345795065164566,
0.016392594203352928,
-0.03652549907565117,
-0.025025950744748116,
0.03324791416525841,
0.03057694435119629,
0.015630869194865227,
0.04015999287366867,
-0.018095899373292923,
-0.04242153838276863,
-0.015467683784663677,
0.04728754237294197,
0.030216526240110397,
0.016333945095539093,
0.05833220109343529,
-0.003630958730354905,
-0.012964612804353237,
0.009519030340015888,
-0.01592089608311653,
-0.012439141981303692,
-0.021565139293670654,
0.020966222509741783,
0.0013982222881168127,
0.029005249962210655,
-0.02985774725675583,
0.01756635122001171,
0.0009189891861751676,
-0.015816863626241684,
0.06957675516605377,
-0.010303478688001633,
-0.021048137918114662,
-0.025611484423279762,
0.03077288717031479,
0.004332160111516714,
-0.0026103383861482143,
0.02079753763973713,
-0.03031289577484131,
-0.0034693428315222263,
0.01010054349899292,
0.03156566619873047,
0.0131972162052989,
-0.0038450423162430525,
0.001796497730538249,
-0.0632493793964386,
-0.014384372159838676,
-0.027389327064156532,
0.04142101854085922,
0.006281314883381128,
-0.0012503440957516432,
-0.010785943828523159,
-0.02369888499379158,
-0.002261832822114229,
-0.0018881558207795024,
-0.025332681834697723,
-0.040791627019643784,
-0.021471282467246056,
0.021936312317848206,
-0.012582872062921524,
0.01016519870609045,
-0.026011278852820396,
-0.025708576664328575,
0.03122026100754738,
0.02942805364727974,
-0.003558279247954488,
-0.006358805112540722,
-0.07955044507980347,
-0.003177228383719921,
-0.042441777884960175,
0.027135655283927917,
-0.0027895376551896334,
-0.049116846174001694,
0.016205711290240288,
-0.06987970322370529,
-0.018580548465251923,
0.040551863610744476,
0.059841930866241455,
0.002574112731963396,
0.01329350657761097,
0.02715900167822838,
-0.030238790437579155,
0.044082626700401306,
-0.06784210354089737,
0.017223762348294258,
0.01338237151503563,
-0.012284399941563606,
-0.008044799789786339,
0.009728273376822472,
-0.006727943196892738,
0.029583923518657684,
0.04769404977560043,
0.000726849480997771,
-0.017931818962097168,
-0.02803090214729309,
-0.03924892097711563,
0.04463118687272072,
0.043435391038656235,
-0.003441621083766222,
0.05703004449605942,
-0.01612839661538601,
0.0061627947725355625,
-0.012055644765496254,
0.021840136498212814,
-0.032656777650117874,
0.026565492153167725,
-0.028322726488113403,
-0.0023408751003444195,
-0.06260515004396439,
-0.019133659079670906,
0.02857571840286255,
-0.0442468598484993,
-0.02804914303123951,
0.04813176020979881,
-0.01482012216001749,
-0.03266241028904915,
0.06194223836064339,
-0.013642995618283749,
0.014343781396746635,
-0.0017521155532449484,
-0.01676841266453266,
-0.025311468169093132,
0.0007907921681180596,
-0.04026717320084572,
0.027243494987487793,
0.01555570773780346,
-0.00712790759280324,
0.017604393884539604,
0.05578036606311798,
-0.02945081889629364,
-0.007633484899997711,
-0.01482828427106142,
0.015555999241769314,
-0.04152333736419678,
-0.007135337218642235,
0.01783102937042713,
-0.010553610511124134,
-0.020161282271146774,
0.007234250660985708,
-0.028797080740332603,
0.09585662931203842,
-0.01199010107666254,
-0.010809315368533134,
0.011669696308672428,
0.00345271872356534,
0.040042225271463394,
0.004504379350692034,
-0.00806458666920662,
0.05689721181988716,
-0.014555537141859531,
-0.02291264757514,
-0.031242504715919495,
-0.017888497561216354,
0.02681109309196472,
-0.0579792745411396,
0.02190350741147995,
-0.010152077302336693,
0.01957341842353344,
-0.0064774006605148315,
-0.0028605281841009855,
0.008572750724852085,
-0.02893022820353508,
0.03712768852710724,
0.015303634107112885,
0.034122541546821594,
-0.033676255494356155,
-0.019006164744496346,
-0.023655835539102554,
0.06145023927092552,
-0.006779245566576719,
-0.05274861305952072,
-0.005829466041177511,
-0.007003777660429478,
-0.025740260258316994,
0.020574403926730156
] |
<p>In operator formalism, for example a 2-point time-ordered Green's function is defined as</p>
<p>$\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\theta(x_1-x_2)\phi(x_1)\phi(x_2)+\theta(x_2-x_1)\phi(x_2)\phi(x_1),$</p>
<p>where the subscript "op" refers to operator formalism. Now if one is to take a time derivative of it, the result will be $\frac{\partial}{\partial x_1^0}\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\langle\mathcal{T}{\frac{\partial \phi(x_1)}{\partial x_1^0}}\phi(x_2)\rangle_{op}+\delta(x_1^0-x_2^0)[\phi(x_1),\phi(x_2)]$, the delta function comes from differentiating the theta functions. This means time derivative does not commute with time ordering.</p>
<p>If we consider path integral formalism, the time-ordered Green's function is defined as </p>
<p>$\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{pi}=\int\mathcal{D}\phi\phi(x_1)\phi(x_2)e^{iS(\phi)}$. </p>
<p>Of course $\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{op}=\langle\mathcal{T}\phi(x_1)\phi(x_2)\rangle_{pi},$ as is proved in any QFT textbook. However in path integral case time derivative commutes with time ordering, because we don't have anything like a theta function thus $\frac{\partial}{\partial x_1^0}\int\mathcal{D}\phi\phi(x_1)\phi(x_2)e^{iS(\phi)}=\int\mathcal{D}\phi\frac{\partial}{\partial x_1^0}\phi(x_1)\phi(x_2)e^{iS(\phi)}$. I did a bit googling and found out that for the path integral case the time-ordered product is called "$\mathcal{T^*}$ product" and operator case just "$\mathcal{T}$ product".</p>
<p>I am not that interested in what is causing the difference(still explanations on this are welcomed), because I can already vaguely see it's due to some sort of ambiguity in defining the product of fields at equal time. The question that interests me is, which is the right one to use when calculating Feynman diagrams?</p>
<p>I did find a case where both give the same result, i.e. scalar QED(c.f. Itzykson & Zuber, section 6-1-4), but is it always the case? If these two formulations are not effectively equivalent, then it seems every time we write down something like $\langle\partial_0\phi\cdots\rangle$, we have to specify whether it's in the sense of the path integral definition or operator definition.</p>
<p><strong>EDIT:</strong> As much as I enjoy user1504's answer, after thinking and reading a bit more I don't think analytic continuation is all the mystery. In Peskin&Schroeder chap 9.6 they manage to use path integral to get a result equivalent to operator approach, without any reference to analytic continuation. It goes like this : Consider a T-product for free KG field $\langle T\{\phi(x)\phi(x_1)\}\rangle=\int\mathcal{D}\phi\phi(x)\phi(x_1)e^{iS(\phi)}$. Apply Dyson-Schwinger equation, we get $\int\mathcal{D}\phi(\partial^2+m^2)\phi(x)\phi(x_1)e^{iS}=-i\delta^4(x-x_1)$, then they just assume the $\partial^2$ commute with path integration(which is already weird according to our discussion) and they conclude </p>
<p>$(\partial^2+m^2)\int\mathcal{D}\phi\phi(x)\phi(x_1)e^{iS}=(\partial^2+m^2)\langle T\{\phi(x)\phi(x_1)\}\rangle=-i\delta^4(x-x_1)$. </p>
<p>This is just the right result given by operator approach, in which $\delta(x^0-x_1^0)$ comes from $\theta$ function. Given my limited knowledge on the issue, this consistency looks almost a miracle to me. What is so wicked behind these maths?</p>
<p><strong>Response to @drake</strong>:If $a$ is a positive infinitesimal, then $\int \dot A(t) B(t) \,e^{iS}\equiv\int D\phi\, {A(t+a)-A(t)\over a}B(t)\,e^{iS}=\frac{1}{a}\langle T\{A(t+a)B(t)\}\rangle-\frac{1}{a}\langle A(t)B(t)\rangle$, notice the second term has an ordering ambiguity from path integral(say $A=\dot{\phi},B=\phi$), and we can make it in any order we want by choosing an appropriate time discretization, c.f. Ron Maimon's post cited by drake. Keeping this in mind we proceed:</p>
<p>$\frac{1}{a}\langle T\{A(t+a)B(t)\}\rangle-\frac{1}{a}\langle A(t)B(t)\rangle\\=\frac{1}{a}\theta(a)\langle A(t+a)B(t)\rangle+\frac{1}{a}\theta(-a)\langle B(t)A(t+a)\rangle-\frac{1}{a}\langle A(t)B(t)\rangle\\=\frac{1}{a}\theta(a)\langle A(t+a)B(t)\rangle+\frac{1}{a}[1-\theta(a)]\langle B(t)A(t+a)\rangle-\frac{1}{a}\langle A(t)B(t)\rangle\\=\frac{\theta(a)}{a}\langle [A(t+a),B(t)]\rangle+\frac{1}{a}[\langle B(t)A(t+a)\rangle-\langle A(t)B(t)\rangle]$</p>
<p>Now taking advantage of ordering ambiguity of the last term to make it $\langle B(t)A(t)\rangle$(this amounts to defining A using backward discretization, say $A=\dot{\phi}(t)=\frac{\phi(t+\epsilon^-)-\phi(t)}{\epsilon^-}$), then the finally:</p>
<p>$\frac{\theta(a)}{a}\langle [A(t+a),B(t)]\rangle+\frac{1}{a}\langle B(t)[A(t+a)-A(t)\rangle]\to \frac{1}{2a}\langle [A(t),B(t)]\rangle+\langle B(t)\dot{A}(t)\rangle$.(Here again a very dubious step, to get $\frac{1}{2a}$ we need to assume $\theta(a\to 0^+)=\theta(0)=\frac{1}{2}$, but this is really not true because $\theta$ is discontinuous)</p>
<p>However on the other hand, since $a$ was defined to be a postive infinitesimal, at the very beginning we could've written $\frac{1}{a}\langle T\{A(t+a)B(t)\}\rangle-\frac{1}{a}\langle A(t)B(t)\rangle=\frac{1}{a}\langle A(t+a)B(t)\rangle-\frac{1}{a}\langle A(t)B(t)\rangle$, then all the above derivation doesn't work. I'm sure there are more paradoxes if we keep doing these manipulations.</p>
| 10,655 |
[
0.01882634125649929,
-0.00836163479834795,
0.02363157644867897,
-0.020062152296304703,
0.013777988962829113,
0.009200056083500385,
-0.030751066282391548,
-0.018028685823082924,
0.01713748089969158,
-0.022406011819839478,
-0.008075781166553497,
0.00688626803457737,
0.053487762808799744,
-0.004639238119125366,
0.037385907024145126,
0.017639724537730217,
0.01690080389380455,
-0.012351292185485363,
-0.006156308576464653,
0.0024368579033762217,
0.013523480854928493,
0.06513132154941559,
-0.005520239472389221,
-0.006479970645159483,
-0.0008624789770692587,
0.0363035649061203,
-0.005828899331390858,
0.03469846397638321,
-0.026441486552357674,
0.07564195990562439,
-0.026003846898674965,
-0.05014932155609131,
0.0007586359861306846,
0.0329386368393898,
0.005189661402255297,
0.009238452650606632,
-0.02751992829144001,
-0.04734715819358826,
-0.016000743955373764,
-0.006290461868047714,
-0.034578051418066025,
-0.02075001411139965,
-0.005350998602807522,
0.0524652898311615,
-0.01765364594757557,
0.007073040120303631,
0.015013577416539192,
0.007362424395978451,
0.06827781349420547,
-0.02103421464562416,
0.0548795647919178,
-0.010414736345410347,
0.03297295793890953,
0.006859577726572752,
-0.03787967190146446,
0.009823990054428577,
0.03422833979129791,
0.07321634143590927,
-0.011833706870675087,
-0.07191634923219681,
-0.03204669803380966,
-0.025076016783714294,
-0.000025343617380713113,
-0.02801596373319626,
0.018847601488232613,
0.00886868592351675,
0.05587500333786011,
0.008957514539361,
-0.022867785766720772,
-0.018786625936627388,
-0.00208318536169827,
-0.020298143848776817,
0.06646892428398132,
-0.0019024093635380268,
0.034860432147979736,
-0.026841312646865845,
0.015737691894173622,
-0.002795097418129444,
0.04623676836490631,
0.013813113793730736,
0.0017689496744424105,
0.02592620998620987,
0.0025748733896762133,
-0.005983859766274691,
-0.004112657159566879,
0.01779136434197426,
0.06671812385320663,
0.002500722650438547,
-0.02639031410217285,
0.06178371235728264,
-0.042728547006845474,
0.049539707601070404,
0.012248058803379536,
-0.04188356548547745,
0.009253744035959244,
0.02233867160975933,
0.02603534795343876,
0.005099500995129347,
-0.0469692125916481,
-0.0159889105707407,
-0.03975965827703476,
-0.05313890799880028,
0.018830470740795135,
0.036400098353624344,
0.011011370457708836,
-0.004719809629023075,
-0.02012113481760025,
0.0030803955160081387,
-0.05176218971610069,
-0.029034657403826714,
-0.045469269156455994,
0.007682358846068382,
-0.011357417330145836,
0.024420859292149544,
-0.05531090870499611,
-0.0211944617331028,
-0.015588102862238884,
0.006659911945462227,
0.03798713907599449,
0.07291433215141296,
0.05914480239152908,
-0.0437239408493042,
0.0011092936620116234,
-0.02734994702041149,
-0.06541744619607925,
0.019451487809419632,
0.03351509943604469,
-0.01380101591348648,
-0.03547589108347893,
-0.04138324782252312,
0.037543099373579025,
0.017390329390764236,
0.053850140422582626,
0.00945031177252531,
0.01437950786203146,
-0.027549197897315025,
-0.10448890179395676,
-0.03730123117566109,
0.009306772612035275,
0.00962937530130148,
0.007521592080593109,
-0.07635390013456345,
0.02524629235267639,
0.033133991062641144,
0.062030889093875885,
0.006040072999894619,
0.006603723391890526,
0.01381718646734953,
0.011662968434393406,
-0.008092470467090607,
-0.007161985617130995,
-0.036511387676000595,
0.03220335394144058,
-0.02739335596561432,
-0.027240345254540443,
-0.023373790085315704,
0.058288827538490295,
0.046965450048446655,
-0.015017086640000343,
0.003655780805274844,
0.06654302030801773,
-0.029693566262722015,
-0.011162596754729748,
-0.005242994055151939,
0.010036367923021317,
-0.042507849633693695,
0.055867597460746765,
0.04327317327260971,
0.020674530416727066,
0.02815237268805504,
0.004927268251776695,
0.0030209911055862904,
-0.01593289151787758,
0.03835678845643997,
0.010596408508718014,
-0.034076206386089325,
-0.02552185021340847,
-0.05141352117061615,
-0.01774677261710167,
-0.010671047493815422,
-0.04082098603248596,
-0.025301910936832428,
-0.04022558405995369,
0.010178809985518456,
-0.02774747461080551,
-0.0006283834227360785,
0.023469896987080574,
0.013694779016077518,
-0.0010142824612557888,
-0.04431210830807686,
-0.01956154778599739,
-0.0469401478767395,
0.023642312735319138,
0.02316957712173462,
-0.01564985327422619,
0.039628803730010986,
0.006518956273794174,
0.013931797817349434,
-0.02697732113301754,
-0.057572100311517715,
0.007853898219764233,
0.009581802412867546,
0.001961808418855071,
-0.02070385217666626,
0.025898413732647896,
0.04347340390086174,
0.06238473579287529,
0.012123159132897854,
0.00752773554995656,
-0.03945333883166313,
-0.010627850890159607,
0.026942992582917213,
-0.013505375012755394,
0.025523507967591286,
-0.004231434315443039,
0.010563626885414124,
0.019092217087745667,
0.009429976344108582,
-0.03143490478396416,
0.05693993344902992,
-0.02759646065533161,
0.035118598490953445,
0.08411804586648941,
-0.014104850590229034,
-0.01501550991088152,
0.057015497237443924,
-0.014571759849786758,
-0.004153640009462833,
-0.010154482908546925,
-0.03730979561805725,
-0.02643738128244877,
-0.022884923964738846,
0.03695346415042877,
0.04246286675333977,
-0.008860313333570957,
0.009071369655430317,
-0.004912109114229679,
0.04777239263057709,
0.03901083022356033,
0.037103746086359024,
-0.0042524137534201145,
-0.022403651848435402,
0.040668997913599014,
-0.006645279936492443,
0.018881024792790413,
0.005614333786070347,
0.05134327709674835,
-0.06497049331665039,
0.009846466593444347,
0.0038821331690996885,
-0.05186952278017998,
0.015145935118198395,
-0.013779022730886936,
0.004715732764452696,
0.012198084965348244,
-0.023554839193820953,
0.027159428223967552,
-0.004859298001974821,
0.04494677111506462,
0.018247729167342186,
-0.035031601786613464,
0.0006855548708699644,
-0.03665292635560036,
-0.029642196372151375,
0.03249140828847885,
-0.006780943367630243,
-0.03383196145296097,
-0.035381633788347244,
0.017352011054754257,
0.017194073647260666,
-0.053094930946826935,
-0.029630154371261597,
-0.03546609356999397,
-0.03619643300771713,
-0.030874034389853477,
0.03654470667243004,
0.01747559942305088,
0.04914557933807373,
0.004525559954345226,
-0.005772202275693417,
0.025574203580617905,
-0.018797850236296654,
0.029267994686961174,
0.01268626470118761,
-0.05220522731542587,
0.02490605041384697,
-0.016786683350801468,
-0.04393913224339485,
0.04687245935201645,
-0.0204507764428854,
0.03689806908369064,
-0.01965596340596676,
-0.025646721944212914,
-0.04609055072069168,
-0.024284768849611282,
-0.011389875784516335,
0.011074865236878395,
-0.001362991170026362,
-0.015513502061367035,
-0.006747499108314514,
-0.009225857444107533,
-0.057456500828266144,
0.038691598922014236,
-0.032280173152685165,
-0.00401192344725132,
0.011219244450330734,
0.0058191511780023575,
0.014742951840162277,
-0.03467867150902748,
0.030943816527724266,
0.017705954611301422,
-0.02684190683066845,
-0.02728506177663803,
-0.03995628282427788,
-0.021334301680326462,
0.01402564998716116,
0.01311681978404522,
-0.0058884103782474995,
-0.018669186159968376,
-0.04092185199260712,
0.08420071005821228,
0.04235421493649483,
-0.019232727587223053,
0.018249742686748505,
-0.0014179585268720984,
0.0038973167538642883,
-0.01675301045179367,
0.0527234710752964,
0.021398834884166718,
-0.009134048596024513,
0.05304044485092163,
0.012819196097552776,
0.013620763085782528,
0.04990014806389809,
-0.017063908278942108,
-0.0023617807310074568,
0.044733498245477676,
0.0251795444637537,
0.01147460751235485,
0.049532804638147354,
0.010103887878358364,
-0.012029662728309631,
0.022310582920908928,
0.013391097076237202,
0.003926177509129047,
0.013849983923137188,
-0.03234885632991791,
0.06444108486175537,
0.015878090634942055,
0.0052370913326740265,
-0.03472580760717392,
0.049931056797504425,
-0.0010458867764100432,
-0.07363056391477585,
-0.029288671910762787,
0.0009237046469934285,
0.023568756878376007,
-0.017315279692411423,
0.027464687824249268,
0.007199468091130257,
0.021950356662273407,
-0.037442486733198166,
-0.011736249551177025,
-0.019838891923427582,
-0.020325832068920135,
0.05612623319029808,
-0.06823353469371796,
-0.04634487256407738,
0.05499626323580742,
0.00977217499166727,
-0.004349208436906338,
-0.04439596086740494,
-0.017881564795970917,
-0.023822614923119545,
-0.0446540005505085,
0.02914240211248398,
-0.017978640273213387,
0.10110983997583389,
0.03295538201928139,
0.08716893941164017,
0.02036820352077484,
0.017708884552121162,
-0.003017257433384657,
-0.00984635017812252,
-0.07952474802732468,
0.024012912064790726,
0.008704937063157558,
-0.02687673084437847,
0.0028224082197993994,
-0.03867655247449875,
0.021099291741847992,
0.008757137693464756,
-0.006854740437120199,
-0.0041971211321651936,
-0.03402068093419075,
-0.04494256153702736,
0.03679897263646126,
-0.02684483863413334,
-0.04595508053898811,
-0.019113928079605103,
0.017018668353557587,
0.06565254181623459,
-0.026402559131383896,
0.00923181138932705,
0.05235031247138977,
-0.015034005045890808,
0.023822741582989693,
-0.029057743027806282,
0.005681001581251621,
0.0279327891767025,
0.00734192319214344,
0.01693829521536827,
-0.005115673411637545,
-0.016673240810632706,
0.03366730362176895,
-0.013061873614788055,
0.058607447892427444,
0.007810347247868776,
-0.034406617283821106,
-0.0005857431096956134,
-0.043912697583436966,
0.03029804863035679,
0.02264050580561161,
0.09163285046815872,
0.022284964099526405,
-0.01943020150065422,
0.016448169946670532,
0.01695331186056137,
0.007294560316950083,
0.017091305926442146,
-0.005330777261406183,
0.0037326377350836992,
-0.032327231019735336,
-0.023149151355028152,
0.012721429578959942,
-0.006716474425047636,
-0.020343927666544914,
-0.009739705361425877,
0.01932573691010475,
-0.010762840509414673,
0.036519184708595276,
-0.022226635366678238,
0.021607443690299988,
-0.016105394810438156,
-0.014593640342354774,
0.013859898783266544,
-0.02220936492085457,
0.0006611369317397475,
-0.009036119095981121,
0.005137743428349495,
0.04867713153362274,
0.03831902891397476,
0.01775524392724037,
0.02286238595843315,
-0.04576316103339195,
-0.008287888020277023,
0.029521053656935692,
0.020671097561717033,
0.00897179264575243,
-0.000791809638030827,
-0.03620332106947899,
-0.027309102937579155,
0.03004002571105957,
0.012781862169504166,
0.03640194609761238,
-0.03326481953263283,
-0.03432919830083847,
-0.05641159042716026,
-0.053714267909526825,
-0.028216172009706497,
0.043733131140470505,
-0.009092681109905243,
-0.0020956688094884157,
-0.034300629049539566,
0.013590351678431034,
-0.02522778883576393,
0.02642243169248104,
0.01070207916200161,
0.03658570721745491,
0.016540931537747383,
-0.0025860299356281757,
-0.004336916841566563,
0.017733944579958916,
-0.03234066441655159,
-0.06445750594139099,
0.004937329795211554,
0.014799999073147774,
0.009778975509107113,
0.02126283198595047,
-0.008960911072790623,
-0.02282227762043476,
0.03053559735417366,
0.01484960038214922,
0.00951115507632494,
0.04398409277200699,
-0.018467722460627556,
0.06657015532255173,
0.029208805412054062,
-0.008226209320127964,
0.07995890080928802,
0.04786353558301926,
-0.01032455638051033,
-0.010722154751420021,
-0.01889597252011299,
0.056983429938554764,
-0.007902966812252998,
0.05641947686672211,
-0.048606034368276596,
-0.031102150678634644,
-0.04805421829223633,
0.012459534220397472,
-0.048603370785713196,
0.013709945604205132,
0.010600724257528782,
-0.043799251317977905,
-0.017910409718751907,
0.026468798518180847,
-0.00926565658301115,
-0.0230768620967865,
-0.02389880083501339,
0.03203672543168068,
0.040521055459976196,
0.03482934832572937,
0.005759804043918848,
-0.010673707351088524,
-0.01181394699960947,
0.0407581701874733,
0.016986368224024773,
0.03530419245362282,
-0.02393108606338501,
-0.01215456798672676,
-0.003771585877984762,
-0.024623796343803406,
0.003706099698320031,
0.013155833818018436,
-0.022669054567813873,
0.005589642096310854,
-0.02880987338721752,
-0.048290692269802094,
0.01538887806236744,
-0.016325131058692932,
-0.011232145130634308,
-0.04154625162482262,
-0.008614614605903625,
0.05220978334546089,
-0.014119652099907398,
-0.07727064937353134,
-0.0323583260178566,
-0.011856471188366413,
-0.021167701110243797,
-0.028336863964796066,
-0.009439375251531601,
0.024248354136943817,
-0.018698174506425858,
-0.014475369825959206,
0.035764679312705994,
0.05397382006049156,
-0.007717978209257126,
0.011369953863322735,
-0.004010501317679882,
0.023789461702108383,
0.017053861171007156,
0.00803954154253006,
-0.023669902235269547,
-0.004313039127737284,
-0.03050604835152626,
-0.030290422961115837,
0.004070407710969448,
0.038129158318042755,
-0.028437072411179543,
0.014849160797894001,
-0.01188646350055933,
-0.009399164468050003,
0.007734444923698902,
0.029288051649928093,
-0.026361173018813133,
0.014008935540914536,
0.01397801749408245,
0.00628287997096777,
-0.017109472304582596,
0.004258112516254187,
-0.008777780458331108,
0.029596703127026558,
0.023582536727190018,
-0.018945610150694847,
-0.019946295768022537,
-0.056900233030319214,
0.007770658936351538,
-0.034115467220544815,
-0.03355928137898445,
0.035170961171388626,
0.03851044550538063,
-0.024027712643146515,
0.0011156172258779407,
0.049150850623846054,
-0.023210613057017326,
-0.007687588222324848,
-0.03151619806885719,
-0.009001174941658974,
-0.0022480632178485394,
0.00879655685275793,
-0.03192317485809326,
0.010731324553489685,
-0.019485967233777046,
-0.007398598361760378,
0.04038092494010925,
-0.015619599260389805,
0.021836211904883385,
0.017120197415351868,
-0.026719223707914352,
-0.050302017480134964,
-0.0028018150478601456,
-0.030059486627578735,
0.0156951155513525,
-0.028548644855618477,
0.061926405876874924,
-0.029810892418026924,
-0.04006269574165344,
0.0447801910340786,
0.039391450583934784,
-0.050595417618751526,
0.002113491063937545,
-0.014320733025670052,
-0.008424482308328152,
0.03703595697879791,
-0.02204669453203678,
-0.013926726765930653,
0.03509727492928505,
-0.02664731815457344,
0.027802051976323128,
-0.005874180234968662,
-0.019269270822405815,
0.013403218239545822,
0.003811811562627554,
-0.0012826176825910807,
0.011534305289387703,
0.0015165982767939568,
-0.03724890947341919,
-0.00847645103931427,
0.0017640477744862437,
0.0227942056953907,
0.014657094143331051,
0.023272700607776642,
0.04228018596768379,
0.015700189396739006,
0.0060746013186872005,
0.00788463931530714,
-0.040100693702697754,
-0.0033684815280139446,
-0.03547966852784157,
-0.04602554813027382,
0.061503294855356216,
-0.044709935784339905,
-0.034103743731975555,
-0.01698037050664425,
-0.024132611230015755,
0.050916291773319244,
0.017056217417120934,
0.01513591781258583,
-0.036834873259067535,
0.08069925755262375,
0.006963381078094244,
0.02303692325949669,
-0.015806207433342934,
-0.002941285027191043,
0.14964087307453156,
0.030851801857352257,
0.025946591049432755,
-0.06159205362200737,
-0.01690916158258915,
0.012707317247986794,
0.03423592075705528,
-0.03225427493453026,
0.04396362230181694,
-0.002334655961021781,
-0.018330737948417664,
-0.01007088739424944,
0.02861470729112625,
0.027880040928721428,
-0.048170868307352066,
0.03500152379274368,
-0.06117977574467659,
-0.04665203019976616,
-0.01737695187330246,
0.030429933220148087,
-0.030439112335443497,
0.016855888068675995,
-0.05156374350190163,
-0.01617264188826084,
-0.01802283711731434,
0.07257439196109772,
0.014229233376681805,
-0.051451750099658966,
0.034723322838544846,
-0.02028575912117958,
-0.019320162013173103,
-0.018742911517620087,
-0.005514264572411776,
0.0018329295562580228,
-0.03446635231375694,
0.02205091342329979,
-0.021043330430984497,
0.015366408042609692,
0.04667935520410538,
0.059312544763088226,
0.02077365480363369,
0.020251309499144554,
0.0033096065744757652,
0.012515490874648094,
-0.017213178798556328,
-0.001396876759827137,
-0.021554235368967056,
0.05896812304854393,
-0.02632727473974228,
-0.010642241686582565,
0.015955448150634766,
-0.050546351820230484,
0.00763677479699254,
-0.03567101061344147,
-0.01333997305482626,
-0.0013691466301679611,
0.03625453636050224,
0.023445354774594307,
0.045086026191711426,
-0.03510233759880066,
0.021129537373781204,
-0.00872021820396185,
0.04666711762547493,
-0.02049812488257885,
-0.037180982530117035,
0.010971787385642529,
-0.0026450289878994226,
0.028420988470315933,
-0.051071830093860626,
-0.007494906894862652,
0.009057074785232544,
-0.013315737247467041,
-0.030660659074783325,
-0.019396094605326653,
0.0226504597812891,
0.0036899878177791834,
0.045576781034469604,
-0.020684076473116875,
0.0022078424226492643,
-0.04357514530420303,
-0.04601806402206421,
-0.0013816029531881213,
0.00762922503054142,
-0.01639803685247898,
0.020803961902856827,
0.00828354898840189,
0.0021598164457827806,
0.04713762179017067,
0.023921551182866096,
-0.033210691064596176,
0.0023216658737510443,
-0.0013664124999195337,
0.04926253482699394,
-0.02696569263935089,
-0.031120527535676956,
0.016523294150829315,
0.02012975513935089,
-0.013541454449295998,
-0.0019332151859998703,
-0.02110808715224266,
-0.004856959916651249,
-0.01974387839436531,
-0.03924185037612915,
0.026706822216510773,
0.01778118871152401,
-0.008152701891958714,
0.021451378241181374,
0.02154930867254734,
-0.016679124906659126,
0.018112394958734512,
0.01946060173213482,
-0.02120685763657093,
-0.04938240721821785,
-0.017393186688423157,
0.02368040382862091,
-0.032242704182863235,
-0.0050896848551929,
-0.04702160507440567,
-0.05731175094842911,
-0.0250858087092638,
0.0432487428188324,
-0.0182740967720747,
0.034627486020326614,
-0.07142874598503113,
0.046082135289907455,
-0.03913572058081627,
-0.001639439375139773,
0.01446648221462965,
0.05386437103152275,
-0.02024400420486927,
-0.056875552982091904,
0.01008604560047388,
0.017644979059696198,
-0.02101079188287258,
0.02954832650721073,
0.02038944512605667,
-0.01448996365070343,
-0.009173932485282421,
0.03370795026421547,
-0.03781560808420181,
-0.0010526764672249556,
-0.04051322117447853,
-0.04868871346116066,
0.04294737055897713,
0.02621595934033394,
0.042731065303087234,
0.01903642527759075,
-0.0042815739288926125,
-0.021534336730837822,
0.025706984102725983,
-0.031776439398527145,
-0.030330989509820938,
0.010030919685959816,
-0.06866560876369476,
-0.013431972824037075,
-0.043139003217220306,
0.05637844651937485,
-0.019611209630966187,
0.013154611922800541,
0.013477700762450695,
-0.018764900043606758,
-0.008653996512293816,
-0.03392593935132027,
0.018951142206788063,
0.010515679605305195,
0.060353800654411316,
0.04213931784033775,
-0.030252547934651375,
0.02429218962788582,
0.028774986043572426,
0.015396068803966045,
0.021519286558032036,
0.012449410744011402,
0.021216223016381264,
-0.08197233080863953,
-0.01982971280813217,
0.021549640223383904,
0.016669999808073044,
0.0263680387288332,
-0.022658100351691246,
0.018275806680321693,
0.012516828253865242,
-0.043238651007413864,
0.08557047694921494,
-0.002975013805553317,
-0.011252925731241703,
-0.026549670845270157,
0.017940538004040718,
-0.026153910905122757,
0.06514443457126617,
0.059603188186883926,
0.0236576646566391,
-0.014597943983972073,
-0.013143588788807392,
0.015603714622557163,
0.004335151985287666,
-0.03509007766842842,
0.015028941445052624,
-0.00030551417148672044,
-0.03492489084601402,
0.04756561294198036,
-0.03506474569439888,
-0.006473935674875975,
0.023715630173683167,
0.03607780113816261,
-0.03889322280883789,
-0.023343682289123535,
0.04701726883649826,
0.03569028526544571,
-0.01454078033566475,
0.005156917031854391,
-0.06489212810993195,
-0.02793332189321518,
-0.013053002767264843,
0.022192662581801414,
0.022466829046607018,
-0.006660995539277792,
-0.013817623257637024,
-0.015364793129265308,
-0.010164245031774044,
-0.05345529690384865,
0.026983249932527542,
0.01553800143301487,
-0.047598954290151596,
-0.0010442702332511544,
-0.025434225797653198,
-0.0072811865247786045,
0.04942568764090538,
0.02247532457113266,
-0.02535627782344818,
-0.019041312858462334,
-0.0026123137213289738,
0.009469639509916306,
-0.03385771065950394,
0.015349169261753559,
-0.027782035991549492,
-0.02142167091369629,
0.04345373436808586,
0.027738776057958603,
0.00411013700067997,
-0.03350359946489334,
-0.02773325890302658,
0.012948395684361458,
-0.015972139313817024,
0.019929010421037674,
-0.009515122510492802,
-0.013759763911366463,
-0.007393303327262402,
-0.016612255945801735,
0.002713932655751705,
-0.026241926476359367,
-0.003713587298989296,
0.026448210701346397,
-0.07218854874372482,
0.04260509833693504,
0.019254453480243683,
0.0009900587610900402,
-0.05176762863993645,
-0.013215533457696438,
0.012186768464744091,
0.020450351759791374,
0.03592855855822563,
0.023480942472815514,
-0.060192253440618515,
0.02662815898656845,
-0.005540762096643448,
-0.006088267080485821,
-0.026053687557578087,
-0.04195878654718399,
-0.015637511387467384,
0.017442602664232254,
0.006088425870984793,
0.007517762947827578,
-0.006387101951986551,
0.058246929198503494,
-0.0022549647837877274,
-0.016773872077465057,
0.012783515267074108,
0.007427732460200787,
-0.04324996843934059,
0.034220896661281586,
-0.0056793238036334515,
0.01637033373117447,
0.06240750476717949,
-0.023072106763720512,
0.017908509820699692,
0.011499732732772827,
-0.028018789365887642,
-0.04579879343509674,
0.0096365911886096,
-0.022369733080267906,
-0.02952897734940052,
-0.0026122929994016886,
-0.03571239858865738,
0.029931658878922462,
-0.02870212309062481,
-0.024430666118860245,
0.022301387041807175,
-0.01248445175588131,
0.005298268049955368,
0.05815551057457924,
0.02652217075228691,
0.049614254385232925,
0.03485281392931938,
0.0027172849513590336,
0.016488775610923767,
0.020561108365654945,
0.012705318629741669,
-0.010781047865748405,
0.021851787343621254,
0.021540310233831406,
0.02080831490457058,
-0.010330723598599434,
-0.015385288745164871,
-0.006402469705790281,
-0.00783419981598854,
0.03733908012509346,
-0.009670540690422058,
0.018287215381860733,
0.0340055376291275,
-0.0011946805752813816,
-0.0008345351088792086,
0.030091889202594757,
-0.036289338022470474,
0.06843550503253937,
-0.009388032369315624,
0.039039693772792816,
-0.002262183465063572,
0.03158823773264885,
-0.008974315598607063,
-0.005842911079525948,
0.0577559769153595,
0.06612126529216766,
-0.05032423511147499,
-0.016434933990240097,
-0.013842236250638962,
-0.017956377938389778,
-0.01689968816936016,
-0.06069786101579666,
0.008792959153652191,
0.06487545371055603,
-0.02329128049314022,
0.029479438439011574,
-0.0633283331990242,
-0.0596744567155838,
-0.06536862254142761,
0.01911560632288456,
0.019139360636472702,
0.025666439905762672,
0.013561511412262917,
0.008861243724822998,
0.0007302220328710973,
0.061230000108480453,
-0.03731217980384827,
0.013591134920716286,
0.0016858800081536174,
0.026210201904177666,
-0.0038455945905297995,
0.000020563385987770744
] |
<p>My interest is purely in $\text{SO}(n)$ tensors and how one works out their irrep decomposition. For instance, for rank 2 tensors we simply split into an antisymmetric part, a traceless symmetric part and the trace. Is there a more general, recursive procedure for higher rank tensors? Even if not, what is the usual method when trying to do it for say rank 3 or 4? Any pointers to the literature would be more than helpful. </p>
| 10,656 |
[
-0.004191304557025433,
0.030341634526848793,
-0.03790471702814102,
-0.055561795830726624,
0.050243645906448364,
0.022045964375138283,
-0.013847867026925087,
-0.024415628984570503,
0.03089055046439171,
-0.05969517305493355,
0.009136272594332695,
0.011902294121682644,
0.04874834418296814,
-0.020556725561618805,
0.015287842601537704,
-0.008559580892324448,
-0.003858872689306736,
-0.0038481825031340122,
0.015021980740129948,
-0.007047872059047222,
0.030499128624796867,
0.037921514362096786,
-0.01880398392677307,
0.0042755757458508015,
-0.015825515612959862,
0.02814655192196369,
0.00788111798465252,
0.005165630020201206,
0.017387865111231804,
0.06107869744300842,
-0.03934098407626152,
-0.008159399963915348,
0.015751725062727928,
0.02678418904542923,
-0.02842545695602894,
-0.018068069592118263,
0.009260095655918121,
-0.03293774649500847,
-0.018640587106347084,
0.006290110293775797,
-0.025164803490042686,
-0.004673455376178026,
-0.058524686843156815,
0.03222610428929329,
0.010276108980178833,
0.030493471771478653,
-0.007474224083125591,
-0.013208022341132164,
0.014286190271377563,
-0.06150291487574577,
0.08940613269805908,
0.0037735842633992434,
-0.007447207346558571,
-0.01669401116669178,
-0.008374127559363842,
0.02252977155148983,
0.046561893075704575,
0.06832654029130936,
0.038139015436172485,
-0.01280579436570406,
-0.032710589468479156,
-0.029328539967536926,
0.028300169855356216,
-0.011377520859241486,
-0.05203484371304512,
-0.001506503322161734,
0.03859645128250122,
0.010735781863331795,
0.04052327945828438,
-0.008193780668079853,
0.01143315527588129,
0.016944073140621185,
0.014991295523941517,
-0.034513797610998154,
-0.014781028963625431,
0.010902177542448044,
0.022231394425034523,
-0.012864342890679836,
0.03231118619441986,
-0.003010520711541176,
-0.010177472606301308,
0.04149680212140083,
0.00803624838590622,
0.0012171955313533545,
-0.006107887253165245,
0.0022420291788876057,
0.06750231981277466,
0.010410552844405174,
0.009152594022452831,
0.028041312471032143,
0.004248218145221472,
-0.05303183197975159,
0.04797149822115898,
0.013709970749914646,
-0.04988275468349457,
-0.011528359726071358,
0.004369986243546009,
0.034560367465019226,
-0.012005489319562912,
-0.011573582887649536,
-0.034476764500141144,
-0.037276893854141235,
0.0018338089575991035,
0.06759237498044968,
-0.01306032482534647,
0.029644858092069626,
-0.025934504345059395,
-0.00448014447465539,
-0.027679890394210815,
-0.03668103367090225,
-0.030236562713980675,
0.0009502970497123897,
-0.025065358728170395,
-0.016225773841142654,
-0.005237257108092308,
0.0006111132097430527,
0.010451049543917179,
-0.03888385370373726,
0.02421051636338234,
0.09741150587797165,
0.034470539540052414,
0.011924205347895622,
0.0180598683655262,
-0.04189266636967659,
-0.08192531019449234,
0.02585754729807377,
0.03768209367990494,
0.0038398602046072483,
-0.040589649230241776,
-0.00016854378918651491,
0.042392779141664505,
-0.01747087948024273,
0.06217457354068756,
-0.01855805702507496,
0.03806164860725403,
-0.006902629975229502,
-0.07348886132240295,
-0.06631416827440262,
0.02038475312292576,
-0.02080339565873146,
0.010708644986152649,
-0.07420158386230469,
0.012556662783026695,
0.03581009805202484,
0.06010770797729492,
-0.01496308296918869,
0.05015560984611511,
0.04058222100138664,
0.03709455952048302,
0.028246747329831123,
-0.010650535114109516,
-0.04074137657880783,
-0.04951692745089531,
-0.0007408877718262374,
0.0005259615136310458,
-0.03816116228699684,
0.03385915234684944,
0.01868421584367752,
-0.018779709935188293,
-0.00875776819884777,
0.07177627831697464,
0.05473768338561058,
-0.00810224562883377,
0.02302508056163788,
0.028264153748750687,
0.01906909979879856,
0.04632258042693138,
-0.017966987565159798,
0.03856559842824936,
0.011319519951939583,
0.015582628548145294,
-0.010964209213852882,
0.027120530605316162,
0.06470801681280136,
0.05526889115571976,
-0.02827918902039528,
-0.013988745398819447,
-0.0020604196470230818,
0.027676420286297798,
0.002550008473917842,
-0.02529665268957615,
-0.04193863645195961,
0.026782969012856483,
0.020201802253723145,
0.013570082373917103,
0.02621627040207386,
-0.0019251385238021612,
-0.04334777221083641,
0.06296294182538986,
-0.04320259019732475,
-0.00965332891792059,
-0.02801394835114479,
0.0004163574194535613,
0.02386520244181156,
-0.05135783925652504,
0.036267366260290146,
0.02781449817121029,
0.009080224670469761,
-0.018003525212407112,
-0.055908456444740295,
-0.024956073611974716,
0.02003585733473301,
0.03409484773874283,
-0.049149613827466965,
0.0021715264301747084,
0.003974782768636942,
0.0252256840467453,
0.006117121782153845,
0.05699289217591286,
-0.05009148269891739,
-0.01454312726855278,
0.008341047912836075,
-0.0014819515636190772,
0.044198546558618546,
-0.021079285070300102,
-0.01528713945299387,
-0.006539100781083107,
-0.004189178813248873,
-0.018892979249358177,
0.005890411790460348,
-0.0364827923476696,
0.05471237376332283,
0.051267195492982864,
0.03791627287864685,
-0.016838420182466507,
-0.01215967908501625,
0.016407564282417297,
0.006070279981940985,
-0.010088935494422913,
0.01316047366708517,
-0.044418804347515106,
-0.028499554842710495,
0.04183889552950859,
0.03839852660894394,
-0.058550938963890076,
-0.016433987766504288,
0.04698951542377472,
0.015417631715536118,
0.025031188502907753,
0.03527921810746193,
-0.04328668862581253,
-0.03463618829846382,
0.013046054169535637,
0.022271137684583664,
0.004016624763607979,
0.03981807455420494,
-0.003245286177843809,
-0.01029931753873825,
0.03900844603776932,
-0.0052720485255122185,
-0.023263005539774895,
0.0350506491959095,
-0.004390666726976633,
0.025101952254772186,
0.021896978840231895,
-0.07829222828149796,
0.060000963509082794,
-0.016957812011241913,
0.005746906157582998,
0.03805842995643616,
0.00487278588116169,
0.014986701309680939,
-0.0027336596976965666,
0.004156617447733879,
0.05341517552733421,
-0.04668787494301796,
-0.047046344727277756,
0.01609203778207302,
0.015885042026638985,
-0.020928459241986275,
0.020944705232977867,
-0.039954472333192825,
-0.015168966725468636,
-0.037086121737957,
-0.0003104576899204403,
0.017075972631573677,
-0.04138314351439476,
0.04053403064608574,
-0.03481604531407356,
0.03180648386478424,
0.013853653334081173,
-0.01754647120833397,
0.03648752346634865,
0.048357851803302765,
-0.06979933381080627,
0.019757835194468498,
-0.03009258769452572,
-0.02998029626905918,
0.006899499800056219,
-0.006130345165729523,
-0.02037346176803112,
-0.010459642857313156,
0.00009477145067648962,
-0.06673111021518707,
-0.033109016716480255,
-0.0023025094997137785,
0.010854506865143776,
-0.051426321268081665,
0.0251619890332222,
0.06483354419469833,
-0.018232081085443497,
-0.03102436661720276,
-0.00521104084327817,
-0.01883128471672535,
-0.0020728835370391607,
-0.005209822673350573,
0.001677235821262002,
0.029630180448293686,
-0.01837269216775894,
0.009192186407744884,
0.03858307749032974,
-0.027777167037129402,
0.02616913430392742,
-0.04065713286399841,
-0.029830262064933777,
0.0052612535655498505,
0.015861209481954575,
0.04165381193161011,
0.03723433241248131,
-0.047140564769506454,
0.08588476479053497,
-0.004166063852608204,
-0.04896583408117294,
-0.024244138970971107,
0.02772779017686844,
0.0024489467032253742,
-0.0007837056764401495,
0.0073148030787706375,
-0.008932969532907009,
-0.01274077408015728,
0.023636098951101303,
0.02684265375137329,
0.03179708123207092,
0.0451948307454586,
0.012925084680318832,
-0.052162978798151016,
0.010275346226990223,
0.02147638238966465,
-0.004125929903239012,
0.012382833287119865,
0.01544645894318819,
-0.00787869282066822,
0.004608933348208666,
0.006432648748159409,
0.00901879370212555,
0.010813351720571518,
0.017752140760421753,
0.00979206245392561,
-0.02498096227645874,
0.0062561179511249065,
-0.022110989317297935,
0.04967591166496277,
0.031756747514009476,
-0.02093569003045559,
-0.018775494769215584,
0.037849828600883484,
-0.007176415994763374,
-0.025566861033439636,
0.015881314873695374,
0.02608279511332512,
0.01973377726972103,
-0.035531457513570786,
0.019077345728874207,
-0.03675440326333046,
-0.028499050065875053,
0.010438945144414902,
-0.011524384841322899,
-0.005344038363546133,
0.029815416783094406,
0.044558681547641754,
0.011716588400304317,
-0.01322278194129467,
-0.02521895244717598,
0.01205023005604744,
-0.018719661980867386,
-0.015430952422320843,
-0.020102838054299355,
0.055650439113378525,
-0.007088664453476667,
0.0432913675904274,
-0.0001733984099701047,
0.009460226632654667,
-0.009543593972921371,
0.027170328423380852,
-0.06855258345603943,
0.0040907422080636024,
-0.06561779230833054,
0.01858683116734028,
0.03131723031401634,
0.01973375864326954,
0.024906525388360023,
-0.030691800639033318,
-0.033691130578517914,
-0.010873203165829182,
0.01830809935927391,
-0.035356443375349045,
0.032738324254751205,
-0.04439366236329079,
-0.0065811690874397755,
-0.008322170004248619,
0.028444111347198486,
0.04651547968387604,
-0.03783288970589638,
-0.007641979958862066,
0.014127278700470924,
-0.0017450032755732536,
0.02683962509036064,
-0.013427934609353542,
0.05037863180041313,
-0.0006518799345940351,
-0.001137090497650206,
0.036438025534152985,
0.04158806428313255,
-0.024858422577381134,
0.002276516519486904,
-0.021464616060256958,
0.07319562137126923,
-0.0007403607596643269,
-0.03082408383488655,
0.01374122966080904,
-0.046509839594364166,
0.009077989496290684,
-0.0021871267817914486,
0.03596266359090805,
-0.014042823575437069,
-0.027993621304631233,
0.019887715578079224,
0.014646111987531185,
-0.0821404680609703,
0.03018626943230629,
0.06765703856945038,
-0.009676097892224789,
-0.030426226556301117,
-0.03472592309117317,
-0.020457573235034943,
0.005990839563310146,
0.01423692237585783,
0.03156217560172081,
-0.014241679571568966,
-0.017606962472200394,
0.010369539260864258,
0.02140931785106659,
-0.0209964606910944,
-0.020141059532761574,
0.021777577698230743,
0.04098884388804436,
0.030003860592842102,
-0.009570613503456116,
-0.01734931953251362,
0.0042732395231723785,
0.042264174669981,
0.049531031399965286,
0.027530618011951447,
0.004801805131137371,
-0.06696316599845886,
0.009213668294250965,
0.03236839920282364,
0.0418899729847908,
-0.016638044267892838,
-0.00801932904869318,
-0.051113393157720566,
-0.03417124226689339,
0.07083455473184586,
0.011766396462917328,
-0.001523310667835176,
0.01469634473323822,
-0.049307338893413544,
-0.018378449603915215,
0.009816555306315422,
-0.005645310506224632,
0.044330887496471405,
0.022210711613297462,
0.022214947268366814,
-0.02075500413775444,
0.004979411140084267,
-0.02787715010344982,
0.00823897123336792,
0.036258090287446976,
0.04998358339071274,
0.025164803490042686,
0.01497395895421505,
0.0028610879089683294,
0.07770074903964996,
-0.03845943883061409,
-0.06671997904777527,
-0.01364118605852127,
0.03369496762752533,
-0.028583034873008728,
0.019697625190019608,
-0.03885936737060547,
-0.06116027757525444,
0.0166315957903862,
0.03816501051187515,
0.010429928079247475,
0.028154898434877396,
-0.009248794056475163,
0.07550662010908127,
0.020668139681220055,
-0.013444078154861927,
0.048995863646268845,
0.031103307381272316,
0.014742951840162277,
-0.01449123676866293,
-0.007991218008100986,
0.02787887491285801,
-0.01518697664141655,
-0.008431664668023586,
-0.0341947041451931,
0.02238912507891655,
-0.023418225347995758,
0.06915714591741562,
-0.025415770709514618,
0.04103129357099533,
0.016264118254184723,
-0.006433858070522547,
0.007670211605727673,
0.05708520859479904,
-0.000846603827085346,
-0.008883371949195862,
0.05642934888601303,
0.061696913093328476,
-0.008771345019340515,
-0.03635920211672783,
0.010765044018626213,
0.0020366001408547163,
0.0004891877179034054,
0.02144811488687992,
-0.006744181737303734,
0.04620087519288063,
-0.06371985375881195,
-0.027626756578683853,
0.0379917174577713,
-0.023581989109516144,
0.05278932303190231,
0.00553616089746356,
-0.014789702370762825,
-0.00250403955578804,
-0.009941832162439823,
0.020858552306890488,
0.02890130877494812,
-0.01250447891652584,
0.007352166343480349,
-0.021668540313839912,
-0.007564732804894447,
0.04743713140487671,
-0.010228906758129597,
-0.09110791981220245,
-0.02923331968486309,
0.03686228021979332,
-0.019213031977415085,
-0.033767711371183395,
-0.04454197362065315,
-0.0069180382415652275,
-0.013323799706995487,
-0.0006791917840018868,
-0.004013559315353632,
0.09732426702976227,
-0.04238167032599449,
-0.009089677594602108,
-0.007063116878271103,
0.02949650026857853,
0.036071427166461945,
-0.028904715552926064,
0.010897506028413773,
0.012187010608613491,
0.005368297453969717,
0.012663290835916996,
0.012155796401202679,
0.04268501326441765,
-0.005070452578365803,
-0.005592785310000181,
-0.04391634464263916,
-0.0018007161561399698,
0.044008634984493256,
-0.01144407782703638,
0.0013023847714066505,
-0.003562054131180048,
0.026468629017472267,
0.01397361047565937,
-0.016324782744050026,
-0.013771053403615952,
0.008736775256693363,
0.019794458523392677,
-0.03526117652654648,
0.003990455996245146,
-0.02768019586801529,
-0.033995456993579865,
0.006815640721470118,
-0.027651894837617874,
0.05633096024394035,
-0.011203331872820854,
0.013856375589966774,
-0.020387036725878716,
0.000029252170861582272,
0.01721731387078762,
-0.014419416896998882,
0.009245166555047035,
0.017336616292595863,
0.023538142442703247,
0.034086648374795914,
-0.023607473820447922,
-0.023378819227218628,
-0.05393734201788902,
-0.03771916404366493,
0.014471824280917645,
0.08104094117879868,
-0.00201616995036602,
0.010131592862308025,
0.023955965414643288,
-0.019243238493800163,
-0.0003810044436249882,
-0.01445279736071825,
-0.03811933845281601,
0.008068961091339588,
-0.0006355736404657364,
0.06177746504545212,
-0.02652517892420292,
0.01060434803366661,
0.009157249704003334,
0.007238007616251707,
-0.029109209775924683,
0.029281429946422577,
0.014874737709760666,
0.0203557088971138,
0.01916222833096981,
-0.0404641330242157,
-0.03665441647171974,
0.014852462336421013,
-0.04691272974014282,
-0.001689664088189602,
0.012741952203214169,
-0.009712855331599712,
0.034662097692489624,
0.029156379401683807,
0.021764427423477173,
-0.024260101839900017,
-0.03858281299471855,
-0.06203946843743324,
0.03639190271496773,
0.025131596252322197,
0.03405560925602913,
-0.01719333603978157,
0.027945922687649727,
0.03886134922504425,
0.00959412194788456,
0.03234671428799629,
-0.012582310475409031,
-0.03402144834399223,
-0.025509454309940338,
-0.02708030305802822,
-0.048121944069862366,
0.019131693989038467,
0.0057813446037471294,
-0.02507583610713482,
0.009515482932329178,
-0.0166923888027668,
0.044853389263153076,
0.01118246465921402,
0.07153042405843735,
-0.022416191175580025,
0.032447487115859985,
-0.010714282281696796,
0.04506009817123413,
0.020054424181580544,
-0.018298374488949776,
0.08663178980350494,
0.10429918766021729,
0.02495066076517105,
-0.10103139281272888,
0.03591050207614899,
0.00879109650850296,
-0.042358603328466415,
-0.028051188215613365,
0.03584795817732811,
-0.013669457286596298,
-0.02274104580283165,
-0.007421649061143398,
0.062649205327034,
-0.012863538227975368,
-0.010979490354657173,
0.058575600385665894,
-0.022751839831471443,
-0.006127736531198025,
-0.0020400939974933863,
0.028384149074554443,
-0.03822644427418709,
0.018896333873271942,
-0.028793182224035263,
0.01908986084163189,
-0.01903880387544632,
-0.016269708052277565,
-0.0661797821521759,
-0.012148737907409668,
-0.023356562480330467,
-0.003665776224806905,
-0.020657118409872055,
0.00960496999323368,
-0.0074110738933086395,
0.007788911461830139,
-0.016188092529773712,
0.0241647157818079,
0.0070508685894310474,
-0.024072205647826195,
0.04808114841580391,
0.025453586131334305,
0.026117322966456413,
0.0010716106044128537,
0.003124076407402754,
-0.013755667954683304,
-0.02720140852034092,
-0.02247995138168335,
-0.002428437815979123,
0.0439278744161129,
-0.020936165004968643,
-0.006008864846080542,
-0.009848620742559433,
-0.03910248726606369,
0.027421897277235985,
-0.053272783756256104,
-0.01932534947991371,
0.020970022305846214,
0.04338603466749191,
-0.05110994726419449,
0.008243667893111706,
-0.026838649064302444,
0.03481370955705643,
-0.0008557503460906446,
0.02787521854043007,
0.014846645295619965,
-0.038630321621894836,
0.0023360266350209713,
-0.024307236075401306,
-0.004214384127408266,
0.0009712401661090553,
-0.027764931321144104,
-0.013254057615995407,
0.023159628733992577,
0.01473513524979353,
-0.038800545036792755,
0.024182476103305817,
0.023448532447218895,
0.022270986810326576,
-0.02036154828965664,
-0.037938058376312256,
-0.029933324083685875,
-0.04314542934298515,
-0.02362932823598385,
-0.03396666422486305,
-0.04486851766705513,
-0.004529835656285286,
0.0037356072571128607,
0.040177471935749054,
0.019353091716766357,
-0.019727535545825958,
0.014631006866693497,
-0.0012451924849301577,
0.025507381185889244,
0.046411290764808655,
-0.036626555025577545,
0.0030898824334144592,
0.0017996488604694605,
-0.008058457635343075,
0.010765288025140762,
-0.027261756360530853,
0.010126166976988316,
0.042230889201164246,
0.010586516931653023,
-0.02781584858894348,
0.042301252484321594,
0.009315422736108303,
0.023006532341241837,
0.033015865832567215,
-0.04747791215777397,
0.017209159210324287,
0.017516866326332092,
-0.002926293294876814,
-0.04395313933491707,
-0.024507002905011177,
-0.018565379083156586,
-0.010607118718326092,
-0.015058537013828754,
-0.024112237617373466,
-0.0404830276966095,
-0.030351104214787483,
-0.03513333946466446,
0.013891366310417652,
-0.01395164430141449,
-0.006103096529841423,
-0.0017233233666047454,
0.008389248512685299,
-0.004619170445948839,
0.008359161205589771,
-0.019311152398586273,
0.008432865142822266,
0.013088889420032501,
-0.022065624594688416,
0.027172286063432693,
-0.011585468426346779,
-0.012773475609719753,
-0.024820711463689804,
0.013252684846520424,
-0.009149149060249329,
0.05546830967068672,
0.006111435126513243,
-0.0337681919336319,
0.01725533790886402,
-0.03486735373735428,
-0.03648551180958748,
0.022558633238077164,
-0.013949685730040073,
0.018984807655215263,
0.025998299941420555,
-0.04337748885154724,
-0.05069068819284439,
0.006030273158103228,
-0.03600906580686569,
-0.008322905749082565,
-0.0007469786796718836,
-0.0019339059945195913,
-0.006343999411910772,
-0.025261981412768364,
0.042091332376003265,
-0.006599622778594494,
-0.025905122980475426,
-0.005489842500537634,
0.012641792185604572,
-0.017810141667723656,
0.0009086428908631206,
0.017959007993340492,
-0.023489447310566902,
0.019848903641104698,
-0.008426469750702381,
-0.0004000170447397977,
0.0032885705586522818,
0.06198551505804062,
-0.03887244686484337,
0.03486098721623421,
0.0027993449475616217,
0.02297726273536682,
-0.05503107234835625,
-0.015813009813427925,
-0.031013695523142815,
0.004470366984605789,
0.05654829740524292,
-0.10830257833003998,
-0.015627125278115273,
0.04544660076498985,
-0.024786902591586113,
0.05883416160941124,
-0.05185525864362717,
-0.0213776845484972,
-0.060004740953445435,
-0.008602938614785671,
-0.03468823432922363,
0.01920779049396515,
0.027807775884866714,
0.026477495208382607,
0.018345583230257034,
-0.0063217198476195335,
-0.01582784205675125,
-0.012808757834136486,
-0.03849252313375473,
0.002317868871614337,
-0.012673266232013702,
-0.08237318694591522,
0.04427993297576904,
-0.017517706379294395,
-0.03675319626927376,
0.03226879611611366,
-0.02718699537217617,
-0.02834773249924183,
0.005052951164543629,
0.00842634029686451,
-0.03284275159239769,
0.030200792476534843,
-0.001983363414183259,
-0.03077930025756359,
0.01835014298558235,
0.002895388752222061,
0.00713502848520875,
0.010219636373221874,
-0.02968321181833744,
0.03756233677268028,
0.008281082846224308,
-0.016124559566378593,
0.020159326493740082,
0.024745840579271317,
-0.03452268987894058,
-0.05206874758005142,
-0.03451080992817879,
-0.03582320362329483,
-0.01376876700669527,
-0.007837786339223385,
0.035248562693595886,
-0.03465311974287033,
0.009050305001437664,
-0.008806003257632256,
0.02075999416410923,
-0.0011652704561129212,
0.015041446313261986,
-0.00866792444139719,
-0.0406532846391201,
0.02673068456351757,
0.022005600854754448,
-0.013946687802672386,
-0.07191924750804901,
-0.012350525707006454,
0.006362282205373049,
-0.023414619266986847,
-0.00410075718536973,
-0.018317801877856255,
0.03794526681303978,
0.053689904510974884,
-0.014051638543605804,
0.022507203742861748,
0.0009623279911465943,
-0.03980735316872597,
0.014607264660298824,
-0.051915206015110016,
0.05000170320272446,
0.004943688865751028,
-0.01781350001692772,
-0.02396642230451107,
-0.023719923570752144,
-0.02093012072145939,
-0.014908643439412117,
0.041387490928173065,
-0.023633476346731186,
0.010273472405970097,
-0.0019132130546495318,
0.04176874831318855,
0.010951126925647259,
-0.012188063003122807,
0.004387435968965292,
-0.04289800301194191,
-0.002878379076719284,
-0.03512873873114586,
-0.05724124610424042,
0.014477016404271126,
0.020418033003807068,
-0.009138432331383228,
0.019324762746691704,
-0.027013307437300682,
-0.006002623122185469,
0.019566884264349937,
0.04157022386789322,
0.005102677270770073,
-0.018284913152456284,
0.03895578160881996,
-0.0020091047044843435,
-0.012766118161380291,
0.04558054357767105,
-0.028093945235013962,
-0.008400567807257175,
0.009761790744960308,
-0.015412699431180954,
-0.058483049273490906,
-0.027482079342007637,
0.00818193331360817,
0.034884899854660034,
-0.07132008671760559,
0.006448353640735149,
0.055280622094869614,
-0.03828447312116623,
0.01660267263650894,
0.07433519512414932,
0.00030931862420402467,
0.022783491760492325,
0.03601841256022453,
0.019377246499061584,
0.08099815994501114,
-0.03209400549530983,
0.05806950479745865,
0.04341921582818031,
0.0048230369575321674,
0.027411410585045815,
-0.018206598237156868,
-0.01753055863082409,
-0.029016908258199692,
0.028932100161910057,
-0.020680615678429604,
0.03734208643436432,
-0.03227038308978081,
-0.01738833077251911,
0.05862637981772423,
-0.0332617424428463,
0.007058128714561462,
-0.008607630617916584,
-0.05574365705251694,
0.066660575568676,
-0.005836892407387495,
0.022180180996656418,
-0.07246826589107513,
0.013609316200017929,
-0.011645535938441753,
-0.006964717525988817,
0.02449638396501541,
0.054793015122413635,
-0.03721640259027481,
-0.023659992963075638,
-0.023461338132619858,
-0.004014674574136734,
0.02178538590669632,
-0.02017391286790371,
0.04066288843750954,
0.01077062077820301,
0.008738365955650806,
-0.0075889695435762405,
-0.07195514440536499,
-0.03471594303846359,
-0.01597301848232746,
0.029975363984704018,
0.00966151524335146,
0.028700830414891243,
0.00035219325218349695,
-0.03639677166938782,
-0.045043062418699265,
0.05523080378770828,
-0.033209048211574554,
-0.010204410180449486,
-0.040514715015888214,
0.0008713639690540731,
-0.011590571142733097,
0.010938633233308792
] |
<p>Would different observers agree on the age? Or is this question nonsensical? e.g. what's north of the north pole?</p>
<p>There are ways of estimating the ages of stellar bodies using various methods but is there a method for black holes? </p>
<p>My main stumbling block is the slowing down and 'stoppage' of time of objects near the event horizon as far as faraway observers are concerned. Theoretically one should be able to 'see' everything that 'fell' into the black hole since the time it (the EH) was formed. Obviously the older stuff should be more red-shifted than newer stuff but the entire spectrum should be seen: from slightly shifted to slightly less than infinitely shifted.</p>
| 10,657 |
[
-0.020409710705280304,
-0.04873326048254967,
0.010267886333167553,
-0.050678178668022156,
0.035329319536685944,
-0.015010638162493706,
-0.05011642351746559,
-0.024157555773854256,
-0.044018425047397614,
-0.015404156409204006,
0.004363917745649815,
0.01490546204149723,
0.029372496530413628,
0.024409577250480652,
-0.0147472582757473,
0.012131071649491787,
-0.009415807202458382,
-0.03714488819241524,
-0.02834486961364746,
-0.017007337883114815,
0.037898655980825424,
0.014606701210141182,
0.007510054390877485,
-0.014543093740940094,
-0.06025715544819832,
0.010601185262203217,
0.02051572874188423,
0.00007873719005146995,
0.02061331458389759,
0.04927264526486397,
-0.020364947617053986,
-0.04552682116627693,
0.04625362902879715,
0.05324963107705116,
0.0317714624106884,
-0.023944256827235222,
0.0007956817862577736,
-0.03456336632370949,
-0.023657262325286865,
0.01566002517938614,
-0.06434239447116852,
-0.04444931074976921,
-0.005192957818508148,
0.04889087378978729,
-0.029342832043766975,
-0.019133614376187325,
-0.015967801213264465,
0.0007588423322886229,
0.05443006381392479,
-0.04299021512269974,
0.045372165739536285,
-0.009818699210882187,
0.0308262687176466,
0.028089430183172226,
-0.02804703451693058,
-0.013718736357986927,
0.07801146060228348,
0.08025144040584564,
-0.015022318810224533,
-0.02735898829996586,
-0.038860782980918884,
0.0014177093980833888,
0.010312879458069801,
-0.010367506183683872,
0.0029342828784137964,
0.011199336498975754,
-0.01647942326962948,
-0.007024561520665884,
0.02952422946691513,
-0.025456437841057777,
0.005425209645181894,
-0.006413960363715887,
0.008508999831974506,
0.014874766580760479,
0.000015069502296682913,
-0.0501730851829052,
0.014718540944159031,
-0.0001870686246547848,
0.012333651073276997,
0.048115167766809464,
-0.03330160677433014,
-0.020799938589334488,
0.06260687112808228,
-0.0016338992863893509,
0.01789158768951893,
0.030338697135448456,
0.10128779709339142,
0.0035289491061121225,
0.01533360593020916,
0.00232251500710845,
-0.0037383295129984617,
0.0003068166261073202,
0.002709067426621914,
-0.03592054545879364,
-0.0070503451861441135,
0.023745562881231308,
-0.016159752383828163,
0.06102469563484192,
-0.0379483625292778,
-0.00356032932177186,
0.018651986494660378,
-0.0075403437949717045,
0.01130388118326664,
0.04157164320349693,
0.0031722323037683964,
-0.0043550096452236176,
-0.08555684983730316,
0.008101259358227253,
-0.03330609202384949,
-0.03632134199142456,
0.006512553431093693,
0.029037754982709885,
-0.02293086238205433,
-0.018766263499855995,
-0.0006261136732064188,
-0.017092322930693626,
0.017637962475419044,
-0.03176126256585121,
0.08263015747070312,
0.05736897140741348,
0.00849735178053379,
-0.02873021736741066,
-0.007084775250405073,
-0.00810565147548914,
-0.04626030474901199,
0.04544882848858833,
0.06039268523454666,
-0.008005975745618343,
-0.015245605260133743,
0.025481047108769417,
-0.014525390230119228,
-0.022995414212346077,
0.04799153655767441,
-0.011358979158103466,
0.0341256707906723,
0.015711886808276176,
-0.10624167323112488,
-0.06668773293495178,
0.003410681849345565,
-0.03283020108938217,
0.0017675845883786678,
-0.04977010563015938,
0.018810631707310677,
0.005136743187904358,
0.08492380380630493,
-0.004164049867540598,
-0.0186396986246109,
0.00273064523935318,
0.018237249925732613,
0.002316430676728487,
-0.023812418803572655,
0.003646244527772069,
0.019009016454219818,
-0.012996291741728783,
-0.0049695223569869995,
-0.05527403950691223,
-0.009338634088635445,
0.031037168577313423,
0.01878540776669979,
-0.03142346069216728,
0.08941839635372162,
-0.0001097142812795937,
0.004710658919066191,
0.025726526975631714,
0.007498020771890879,
-0.038069143891334534,
0.1051931157708168,
0.03254540637135506,
0.0035162540152668953,
0.03664116933941841,
0.002801061375066638,
0.0375540591776371,
0.02639620564877987,
-0.014144347980618477,
0.039532434195280075,
-0.03376501053571701,
-0.03509188070893288,
-0.018067624419927597,
-0.01655472442507744,
-0.0047673871740698814,
-0.029769044369459152,
-0.025437751784920692,
-0.032412026077508926,
-0.003532341681420803,
0.023634931072592735,
0.015116008929908276,
-0.004191253799945116,
-0.03367530554533005,
0.00788344070315361,
-0.04733330011367798,
0.00572771392762661,
-0.05557342246174812,
0.021937457844614983,
0.027424054220318794,
0.02105112373828888,
0.021841060370206833,
-0.019672924652695656,
0.009298336692154408,
-0.04695328325033188,
-0.032075174152851105,
-0.004310669377446175,
0.05394291877746582,
-0.018673622980713844,
-0.039279595017433167,
-0.006298865657299757,
0.05242893472313881,
0.0205706674605608,
0.008351737633347511,
0.01982017606496811,
0.00515062315389514,
-0.040509987622499466,
0.0028456489089876413,
-0.004272774327546358,
0.007184508256614208,
-0.010887717828154564,
0.0157545767724514,
-0.006245460826903582,
0.0041342671029269695,
0.03602694720029831,
0.006381212268024683,
-0.02458706870675087,
0.09002994000911713,
0.022615697234869003,
0.008820327930152416,
-0.025401802733540535,
0.030363136902451515,
0.017055504024028778,
0.025082046166062355,
-0.013379784300923347,
-0.013226566836237907,
-0.08221212774515152,
0.004598530009388924,
0.023160353302955627,
0.024075813591480255,
-0.025543726980686188,
0.01768837869167328,
0.04011353850364685,
0.04514729231595993,
0.008210740983486176,
0.01960313506424427,
-0.021610673516988754,
-0.032215364277362823,
-0.020951945334672928,
-0.03257537633180618,
-0.00584662239998579,
0.027865219861268997,
0.0319318063557148,
-0.0000073907394835259765,
0.018650876358151436,
-0.01812656782567501,
0.010038969106972218,
0.026906006038188934,
-0.029884783551096916,
0.018971282988786697,
-0.006207863800227642,
-0.01786123588681221,
0.025040417909622192,
-0.030818093568086624,
0.0225254874676466,
-0.005104477051645517,
-0.003503468818962574,
0.0079056890681386,
-0.031216438859701157,
-0.005741074215620756,
0.014444791711866856,
0.00834665633738041,
-0.027387462556362152,
-0.012109767645597458,
0.0137120196595788,
-0.029282420873641968,
0.044824305921792984,
-0.04463930055499077,
-0.0364522784948349,
-0.024515453726053238,
0.013302016071975231,
0.039215654134750366,
0.0284054446965456,
0.025169435888528824,
-0.015149638056755066,
-0.03674262762069702,
0.019705425947904587,
-0.022425973787903786,
0.015355822630226612,
0.02601175755262375,
-0.04642554745078087,
-0.0008135523530654609,
-0.009270437061786652,
-0.029838746413588524,
0.028187043964862823,
0.0028455008286982775,
-0.006950031500309706,
0.017305709421634674,
0.00407698517665267,
-0.019420558586716652,
0.012081438675522804,
-0.03068573772907257,
-0.030574053525924683,
-0.03738180920481682,
-0.013101128861308098,
0.0333145409822464,
0.010943292640149593,
0.009788897819817066,
0.05084029957652092,
-0.019387420266866684,
-0.04640432074666023,
0.013653816655278206,
0.0014288113452494144,
-0.0061231390573084354,
-0.017636651173233986,
0.01701228879392147,
0.04665527865290642,
-0.0467057079076767,
-0.008548188023269176,
-0.02957211062312126,
-0.06378389894962311,
0.07820975035429001,
-0.024590346962213516,
-0.0037656540516763926,
-0.011551822535693645,
0.008103899657726288,
0.035582609474658966,
0.029691562056541443,
0.00840256828814745,
-0.03007243201136589,
0.021113606169819832,
0.00639951229095459,
0.008710457012057304,
-0.0017639955040067434,
-0.0033750373404473066,
0.0022339574061334133,
-0.02274310402572155,
0.02476099692285061,
0.026703497394919395,
0.010561530478298664,
0.005003862548619509,
0.009471125900745392,
-0.023006869480013847,
-0.013884306885302067,
0.02231178991496563,
0.05099599435925484,
0.010683920234441757,
-0.01468195952475071,
0.004040091764181852,
-0.01734626293182373,
0.05580078437924385,
0.025604695081710815,
-0.044505491852760315,
0.037239015102386475,
-0.02491564117372036,
-0.017590248957276344,
0.016623737290501595,
0.00582116236910224,
-0.01796307973563671,
0.027619674801826477,
0.0026057129725813866,
-0.03164677321910858,
0.041997406631708145,
0.025528427213430405,
0.009943663142621517,
0.025559384375810623,
0.03146789222955704,
-0.02646753191947937,
-0.012368864379823208,
-0.011712550185620785,
-0.0077415406703948975,
0.03391560912132263,
-0.024703586474061012,
-0.009140808135271072,
0.02507673390209675,
0.0089987488463521,
0.008096898905932903,
0.012232644483447075,
-0.007818466983735561,
0.005778690800070763,
-0.1197558268904686,
-0.017934128642082214,
0.01112772710621357,
0.01694776490330696,
-0.00023757600865792483,
0.05237423628568649,
0.02493666671216488,
-0.013229777105152607,
0.010717013850808144,
-0.01840687170624733,
-0.09708898514509201,
-0.011288912035524845,
-0.054416365921497345,
-0.023146552965044975,
-0.03088161163032055,
-0.011396469548344612,
-0.022279812023043633,
-0.021037695929408073,
-0.006803773809224367,
0.006376675330102444,
0.0012507762294262648,
-0.06594334542751312,
0.02402636781334877,
-0.03488362208008766,
-0.024514304473996162,
0.005052126944065094,
0.04366924241185188,
0.04664764180779457,
0.020134778693318367,
0.01110731903463602,
0.015622067265212536,
0.009968763217329979,
-0.0061439513228833675,
0.007926692254841328,
0.019856803119182587,
-0.009820261970162392,
0.059071000665426254,
0.02166193164885044,
-0.004759814590215683,
-0.05278807505965233,
0.006748644635081291,
0.027589287608861923,
0.003498989623039961,
0.007577170617878437,
-0.024356551468372345,
-0.02821870893239975,
-0.033629048615694046,
-0.02488958090543747,
-0.008860370144248009,
0.08281879127025604,
-0.025874098762869835,
0.005002634599804878,
0.030298013240098953,
-0.024687064811587334,
-0.024411754682660103,
0.00879256334155798,
0.06349189579486847,
-0.01853460632264614,
-0.020431047305464745,
-0.04292317479848862,
-0.040730543434619904,
-0.012967810966074467,
0.018418459221720695,
0.009948172606527805,
0.029090916737914085,
-0.03097507730126381,
0.004404866602271795,
0.021992510184645653,
-0.009511156007647514,
-0.034882232546806335,
-0.0018604604993015528,
0.001263908576220274,
0.021009622141718864,
-0.03491538017988205,
0.04122264310717583,
0.025001902133226395,
0.063296377658844,
0.05453314632177353,
0.011835276149213314,
0.0017227369826287031,
-0.07392527908086777,
-0.047380633652210236,
0.030202288180589676,
-0.00027518055867403746,
-0.01511598564684391,
-0.023696348071098328,
-0.07598745822906494,
-0.0077359238639473915,
0.07898978888988495,
-0.016526049003005028,
0.015802009031176567,
-0.0023907863069325686,
0.003922135569155216,
-0.034089699387550354,
-0.00897624809294939,
0.012499678879976273,
0.04148774594068527,
0.0019755649846047163,
0.023336132988333702,
-0.012989241629838943,
0.033608075231313705,
-0.01766657829284668,
0.023063145577907562,
0.04746976122260094,
0.05116191506385803,
0.045797109603881836,
0.022447800263762474,
-0.0012584582436829805,
-0.02006891369819641,
-0.024548811838030815,
-0.07044217735528946,
0.021285761147737503,
-0.007627800572663546,
-0.042072467505931854,
0.013095924630761147,
-0.038502659648656845,
-0.02909841202199459,
0.0474410280585289,
0.010294697247445583,
-0.03072766400873661,
0.03839952498674393,
-0.0434352308511734,
0.031257692724466324,
0.005533964838832617,
0.009886722080409527,
0.05869465693831444,
0.0017550310585647821,
0.028797734528779984,
0.0380617156624794,
-0.01896333508193493,
0.016032131388783455,
-0.05956370756030083,
-0.004091461654752493,
-0.007570072542876005,
-0.008861561305820942,
-0.06093640625476837,
0.05449387803673744,
-0.001390953897498548,
0.02580883353948593,
0.023847447708249092,
-0.017384158447384834,
-0.012693879194557667,
0.04947400838136673,
-0.015548179857432842,
0.03767289221286774,
0.02098429761826992,
0.00413169851526618,
0.0007048461120575666,
-0.012995055876672268,
0.0451156385242939,
0.011239611543715,
-0.01917055808007717,
0.01888335309922695,
-0.03126494958996773,
0.009177171625196934,
-0.00849643349647522,
-0.005794083699584007,
0.03775018826127052,
0.005418294575065374,
0.036455485969781876,
-0.01407614629715681,
0.026002025231719017,
0.03679945319890976,
-0.05231519415974617,
0.008374893106520176,
0.003925771918147802,
-0.00534896831959486,
0.041914574801921844,
-0.04644247144460678,
0.021451588720083237,
0.04052256420254707,
0.019638970494270325,
-0.0986737385392189,
-0.014058045111596584,
0.04879975691437721,
0.05284307524561882,
-0.014102490618824959,
-0.009984009899199009,
0.034210626035928726,
-0.05675025284290314,
0.006300174631178379,
-0.02480417862534523,
0.05145874246954918,
-0.013541835360229015,
-0.010216991417109966,
-0.011560068465769291,
0.021211549639701843,
0.04366607964038849,
-0.008839018642902374,
0.014104912057518959,
0.006465500686317682,
0.010178262367844582,
0.00782726425677538,
-0.003096755361184478,
0.028547680005431175,
-0.01232506800442934,
-0.014930198900401592,
-0.04197986423969269,
-0.004393039271235466,
0.01048645656555891,
-0.05254245921969414,
0.016874972730875015,
0.05606062710285187,
-0.034443892538547516,
0.010173304937779903,
-0.00560675049200654,
0.03475286439061165,
-0.0872674360871315,
-0.004530342761427164,
-0.0430254302918911,
-0.030065450817346573,
0.027427667751908302,
-0.037673283368349075,
0.03845459222793579,
0.015224630944430828,
-0.014736509881913662,
-0.0009300495148636401,
0.021555336192250252,
0.011975455097854137,
-0.03420991450548172,
-0.011748919263482094,
-0.03430786728858948,
0.021962352097034454,
0.008922305889427662,
0.01710926555097103,
0.04429167881608009,
-0.005246434826403856,
-0.007996932603418827,
-0.032934874296188354,
-0.016782451421022415,
-0.028004929423332214,
0.08725897967815399,
0.023066682741045952,
0.029363563284277916,
0.02221006527543068,
0.01988598145544529,
-0.01357354037463665,
-0.04349302127957344,
-0.004052963573485613,
0.009957827627658844,
-0.02429177053272724,
-0.005546069238334894,
-0.023634634912014008,
0.004790390841662884,
0.008013912476599216,
0.03887511417269707,
-0.01868681237101555,
0.04213147982954979,
0.016473496332764626,
0.015188129618763924,
0.029662149026989937,
0.007800121325999498,
-0.03356538340449333,
0.021131262183189392,
-0.016351915895938873,
0.026705216616392136,
-0.012078900821506977,
0.007478170096874237,
0.01959902234375477,
0.017765337601304054,
0.05189348757266998,
-0.026893630623817444,
-0.0366850309073925,
-0.06715872138738632,
-0.01704384945333004,
0.006368504837155342,
0.010021727532148361,
-0.0046042585745453835,
0.004179706331342459,
-0.008285678923130035,
0.0020753531716763973,
0.019334683194756508,
-0.002196269342675805,
-0.04842666909098625,
-0.03578191250562668,
-0.05944326892495155,
-0.06209259480237961,
0.05137009546160698,
0.041129130870103836,
-0.011726557277143002,
0.008885549381375313,
-0.012845475226640701,
-0.028839100152254105,
-0.0008585922769270837,
0.04913829267024994,
-0.01679679937660694,
0.06280398368835449,
-0.016193188726902008,
0.013247781433165073,
-0.00854668952524662,
0.020930146798491478,
0.10982859879732132,
0.07733795791864395,
0.028432149440050125,
-0.05243086814880371,
0.033096250146627426,
-0.00893879309296608,
-0.00797269307076931,
-0.039769552648067474,
0.025633538141846657,
-0.03390973433852196,
0.014526010490953922,
0.022163860499858856,
0.03316375985741615,
0.018165316432714462,
-0.03937641158699989,
0.0629749670624733,
-0.030180485919117928,
0.007993295788764954,
0.014870157465338707,
0.07628417015075684,
0.014014039188623428,
0.018562596291303635,
-0.022631878033280373,
0.02445799857378006,
0.015588000416755676,
-0.013768404722213745,
-0.023411622270941734,
-0.025857040658593178,
-0.005807939916849136,
-0.01498737744987011,
-0.059658683836460114,
0.012047450058162212,
0.00044736897689290345,
-0.04569625109434128,
-0.03306156024336815,
0.0130593441426754,
0.006554688327014446,
-0.012384630739688873,
0.03506948798894882,
0.03193502873182297,
0.004176917485892773,
0.009776746854186058,
-0.0022500744089484215,
0.016904860734939575,
-0.02881079912185669,
-0.01061447523534298,
-0.03483967483043671,
0.060344941914081573,
-0.03195970505475998,
-0.022460760548710823,
-0.012430381029844284,
-0.01072685793042183,
0.008815900422632694,
-0.06161975488066673,
0.012748096138238907,
0.0024345770943909883,
-0.00030299671925604343,
0.02218155562877655,
-0.04947100207209587,
-0.0014578262344002724,
0.01718716137111187,
-0.0011108200997114182,
0.03127208724617958,
0.007622961420565844,
-0.013137150555849075,
0.0035449492279440165,
-0.0480787418782711,
0.041873589158058167,
0.020424889400601387,
-0.02060113660991192,
-0.03521827980875969,
-0.0005721881752833724,
-0.05374322831630707,
0.025199096649885178,
0.007126012351363897,
0.040647052228450775,
0.02666347660124302,
0.01687338948249817,
-0.010415653698146343,
-0.012546236626803875,
-0.035645030438899994,
0.019578902050852776,
0.015947818756103516,
-0.0326036773622036,
-0.030179664492607117,
0.026885779574513435,
0.0283823162317276,
0.03169917315244675,
-0.03046548366546631,
0.018448667600750923,
0.006194126792252064,
0.03131159767508507,
0.01128638256341219,
-0.04045127332210541,
0.006997087504714727,
0.015819378197193146,
-0.04754498600959778,
-0.00987318903207779,
-0.0516323447227478,
0.03237345069646835,
0.007287335116416216,
-0.019299637526273727,
0.023780517280101776,
0.024716051295399666,
-0.02631627582013607,
-0.002708649495616555,
-0.00411364808678627,
-0.025062456727027893,
-0.002535297069698572,
-0.029097190126776695,
0.015619800426065922,
-0.04485960304737091,
-0.038589973002672195,
-0.042084284126758575,
0.0017034161137416959,
-0.010443314909934998,
0.00797656737267971,
-0.012579577974975109,
0.0653500035405159,
-0.010879098437726498,
-0.023043407127261162,
-0.038654737174510956,
0.014038005843758583,
-0.04367973655462265,
0.04314611107110977,
0.003684887196868658,
-0.020936474204063416,
0.02390880510210991,
0.013285687193274498,
0.001330769737251103,
-0.06554029136896133,
0.027216574177145958,
0.010754811577498913,
-0.030949177220463753,
0.011065395548939705,
0.003170552896335721,
-0.044506799429655075,
0.028240982443094254,
0.007998875342309475,
-0.037797071039676666,
0.003656473010778427,
-0.026487009599804878,
-0.036876194179058075,
0.06647013127803802,
0.02466963604092598,
0.01844010315835476,
0.005895472597330809,
-0.028281306847929955,
0.012192783877253532,
0.05706535279750824,
-0.033569060266017914,
-0.05962942913174629,
0.019338052719831467,
0.01120396051555872,
-0.005403699818998575,
0.023808695375919342,
0.04415507614612579,
0.00308787077665329,
0.002553461119532585,
0.053870007395744324,
-0.014755566604435444,
-0.007405977230519056,
-0.008349611423909664,
-0.004004331771284342,
-0.016266943886876106,
0.0165726188570261,
0.02579459175467491,
-0.013710835948586464,
0.0728207528591156,
0.07254587113857269,
-0.047528378665447235,
0.08015847206115723,
0.06766284257173538,
-0.020819714292883873,
-0.06939240545034409,
0.0028511693235486746,
0.011691255494952202,
0.038925155997276306,
0.068341925740242,
-0.057937126606702805,
0.019348839297890663,
0.03727230057120323,
-0.06471763551235199,
0.03567132726311684,
-0.025260692462325096,
-0.0020201413426548243,
-0.019478563219308853,
0.008814039640128613,
0.004163146484643221,
0.018526988103985786,
0.04379414767026901,
0.048272162675857544,
-0.0009220388019457459,
-0.016454389318823814,
-0.013293598778545856,
-0.053170740604400635,
-0.015503513626754284,
0.0014077139785513282,
0.03199818730354309,
-0.015915600582957268,
0.05690660700201988,
-0.028252113610506058,
-0.005342412274330854,
0.03043430671095848,
0.008247891440987587,
0.01758681796491146,
0.011717000976204872,
-0.0067757111974060535,
0.014826570637524128,
-0.01746043562889099,
0.022222191095352173,
-0.033361367881298065,
-0.0013449459802359343,
0.01465640775859356,
-0.0031452777329832315,
0.03733574599027634,
-0.018741045147180557,
-0.0055511449463665485,
-0.006766279228031635,
-0.05298552289605141,
-0.008433949202299118,
0.027299296110868454,
-0.011946899816393852,
-0.018842404708266258,
0.017836660146713257,
0.010753723792731762,
-0.010019727982580662,
-0.009381371550261974,
-0.011295892298221588,
-0.006399298552423716,
-0.015924492850899696,
0.021508503705263138,
0.021483296528458595,
0.0040618786588311195,
-0.00005267609594739042,
-0.038457877933979034,
-0.043082430958747864,
0.012148451991379261,
-0.03553619235754013,
0.033534176647663116,
-0.040094368159770966,
0.00043033933616243303,
0.0005382300005294383,
0.004172622226178646,
0.012974860146641731,
-0.051037099212408066,
-0.033835288137197495,
0.027411187067627907,
-0.003974693827331066,
0.0014586879406124353,
-0.02410198003053665,
-0.07608066499233246,
-0.025223471224308014,
-0.04791020601987839,
0.018973415717482567,
0.005759194493293762,
0.007447705138474703,
-0.04955248907208443,
-0.026416052132844925,
-0.004278964828699827,
0.0029871189035475254,
0.050236426293849945,
0.00020010562730021775,
-0.004644162952899933,
0.008844028227031231,
-0.01639946550130844,
0.021046752110123634,
-0.01395451184362173,
0.0111380061134696,
0.006046054419130087,
-0.039890825748443604,
-0.003093467094004154,
0.005090841557830572,
-0.02376047521829605,
0.021444149315357208,
0.03194485977292061,
-0.0041780052706599236,
0.05926985666155815,
0.037257060408592224,
-0.01710565574467182,
0.06362959742546082,
0.021602656692266464,
-0.007495734374970198,
0.0234477948397398,
-0.001819207682274282,
-0.0024614001158624887,
0.07349231094121933,
0.00046226195991039276,
-0.023781046271324158,
0.014110148884356022,
-0.023564158007502556,
-0.021016627550125122,
0.015926796942949295,
-0.005121064372360706,
0.013225984759628773,
-0.03705165535211563,
-0.016695963218808174,
0.03424427658319473,
-0.036943867802619934,
-0.011775901541113853,
0.04056186228990555,
-0.004454254638403654,
0.04062197357416153,
-0.004457439761608839,
0.005424506962299347,
0.029147645458579063,
-0.013411213643848896,
-0.01287671085447073,
0.04093240946531296,
0.03758995607495308,
-0.0097700459882617,
0.04750053212046623,
-0.012829672545194626,
0.023468652740120888,
-0.008636845275759697,
-0.034867387264966965,
0.07846242189407349,
-0.020084455609321594,
-0.01690315268933773,
0.009267808869481087,
0.018790213391184807,
0.02927907183766365,
0.05194009840488434,
-0.04613014683127403,
0.047087669372558594,
-0.013634824194014072,
0.013749281875789165,
-0.017298365011811256,
-0.016928043216466904,
-0.056020550429821014,
0.06880256533622742,
0.01634305901825428,
0.05363425984978676,
-0.007614383473992348,
-0.001196177676320076,
0.00007911889406386763,
0.02911991812288761,
0.03689635172486305,
-0.04491465538740158,
-0.018772143870592117,
-0.013319653458893299,
-0.0035578703973442316,
-0.010801265016198158,
-0.010181849822402,
-0.05200883746147156,
-0.017526524141430855,
0.029975082725286484,
0.03206212446093559,
0.05571505054831505,
-0.006653557997196913,
0.0030466739553958178,
-0.05793694779276848,
0.009692522697150707,
-0.07811575382947922,
-0.024606559425592422,
-0.018971240147948265,
0.03982115536928177,
-0.01571091264486313,
-0.03732357919216156
] |
<p>Sorry if this is a dumb question, but I'm only starting to get to grips with this quantum malarkey. Anyway...</p>
<p>Suppose I have two friends, Alice and Bob, both of whom have a random number generator. Alice's number generator will produce a number between 1 and 4, giving a probability density of:</p>
<p>A=[0.25 0.25 0.25 0.25] for each number possibility</p>
<p>Bob has the same generator, but his is faulty and will only give a number between 2 and 4, producing this probability density:</p>
<p>B=[0 0.33 0.33 0.33]</p>
<p>If Alice and Bob randomly select one of their generators and tell me what the number produced is, then it is a trivial matter using classical probability to calculate an odds/likelihood ratio as to which machine was used. But how does this situation work with quantum math?</p>
<p>Quantizing this problem (as far as I gather) produces two kets:</p>
<p>$|A\rangle = \left[\sqrt{\frac{1}{4}} \sqrt{\frac{1}{4}} \sqrt{\frac{1}{4}} \sqrt{\frac{1}{4}}\right]$ = [0.5 0.5 0.5 0.5]</p>
<p>$|B\rangle = \left[\sqrt{0} \sqrt{\frac{1}{3}} \sqrt{\frac{1}{3}} \sqrt{\frac{1}{3}}\right]$ = [0 0.58 0.58 0.58] </p>
<p>Presumably this can then be expressed as a superposition:</p>
<p>$$|\Psi\rangle = \frac{1}{\sqrt{2}} (|A\rangle \otimes |B\rangle)$$</p>
<p>But then, so what? Where does this get me in terms of producing a quantum version of the standard likelihood ratio?</p>
<p>Or am I barking up the wrong tree?</p>
<p>All help appreciated :) Thanks!</p>
| 10,658 |
[
0.028421174734830856,
-0.02175283059477806,
0.024032240733504295,
-0.06415490061044693,
0.03141633793711662,
0.015466212294995785,
-0.007406052201986313,
-0.015039622783660889,
0.013627239502966404,
0.008039512671530247,
0.05492796376347542,
0.03906835988163948,
0.057360269129276276,
0.016633475199341774,
0.003162082051858306,
0.019416294991970062,
0.0029271238017827272,
-0.012297073379158974,
-0.022727379575371742,
-0.04079066216945648,
0.02985278144478798,
0.04991384968161583,
0.011308330111205578,
-0.03233903646469116,
-0.04376356676220894,
0.03447018563747406,
-0.0114431856200099,
-0.0054685622453689575,
0.0007670085760764778,
0.08421339839696884,
-0.03390436992049217,
-0.06265730410814285,
0.04555825516581535,
0.024805257096886635,
0.017717860639095306,
0.014031458646059036,
0.0012797348899766803,
-0.020615573972463608,
-0.01792573370039463,
-0.010531952604651451,
-0.0546850748360157,
0.001103610498830676,
-0.011669514700770378,
0.01883826218545437,
0.006903846748173237,
0.015064424835145473,
-0.00025876722065731883,
-0.061064958572387695,
0.05019388720393181,
-0.056361470371484756,
0.06124017760157585,
0.05189869552850723,
-0.021798565983772278,
0.05183370038866997,
0.0004860787303186953,
-0.008640511892735958,
0.07526902854442596,
0.07474225759506226,
-0.00183278473559767,
-0.07024425268173218,
-0.020789144560694695,
-0.003306757193058729,
0.01310321781784296,
-0.033876337110996246,
-0.020976398140192032,
0.024702496826648712,
0.005973996594548225,
-0.026044391095638275,
0.026430310681462288,
-0.060645028948783875,
0.040502555668354034,
0.026051294058561325,
0.0437496043741703,
-0.04786745458841324,
0.0387202613055706,
-0.00199356977827847,
-0.013905786909162998,
-0.011924340389668941,
0.021227309480309486,
0.007061865646392107,
0.009303294122219086,
-0.003825539257377386,
0.021910857409238815,
0.00609904108569026,
0.030664633959531784,
-0.03367595374584198,
0.03574035316705704,
-0.03390925005078316,
0.015054895542562008,
0.042261552065610886,
-0.03400332108139992,
0.0015094357077032328,
0.059012167155742645,
-0.0458359569311142,
-0.041907038539648056,
0.057272471487522125,
-0.009432961232960224,
0.036674946546554565,
-0.011290824972093105,
-0.02373168244957924,
0.0022691672202199697,
-0.04675862565636635,
-0.008228913880884647,
0.06622156500816345,
-0.025028690695762634,
-0.022908831015229225,
0.002634722739458084,
0.03437073901295662,
-0.019552260637283325,
0.00619079265743494,
-0.005956191103905439,
0.0401327982544899,
-0.019894683733582497,
0.02968475967645645,
-0.020363619551062584,
-0.046754300594329834,
-0.0037581631913781166,
-0.035864025354385376,
0.07301011681556702,
0.023837052285671234,
0.021139949560165405,
-0.01782318390905857,
-0.03900771588087082,
-0.053213536739349365,
-0.023368755355477333,
0.02329765073955059,
0.0014595496468245983,
-0.008854488842189312,
-0.06038157641887665,
0.04160303622484207,
-0.011516719125211239,
0.024456636980175972,
0.02729671820998192,
-0.011584397405385971,
-0.00869061704725027,
-0.01967553235590458,
-0.10086631029844284,
-0.05990472063422203,
0.0627875104546547,
-0.020801743492484093,
-0.03252861648797989,
-0.06676716357469559,
0.03448031470179558,
0.053556691855192184,
0.07937844097614288,
-0.026341713964939117,
0.06836838275194168,
-0.015237219631671906,
0.00412713410332799,
0.04053417965769768,
-0.011425608769059181,
0.009610390290617943,
-0.0007736863335594535,
-0.014781632460653782,
0.02388908341526985,
-0.022837098687887192,
0.02312760055065155,
0.016061216592788696,
-0.021946724504232407,
-0.01688220165669918,
0.04412490129470825,
-0.006226855330169201,
-0.03755885362625122,
0.04676840826869011,
0.018430178984999657,
-0.015340247191488743,
0.06363499164581299,
0.03584994748234749,
-0.007875259034335613,
0.030409719794988632,
-0.025158366188406944,
0.022783834487199783,
0.013826239854097366,
-0.007165835238993168,
0.024224044755101204,
-0.044807009398937225,
0.0015265169786289334,
-0.020545994862914085,
0.017893938347697258,
-0.010125969536602497,
-0.02875957451760769,
-0.001033609383739531,
-0.025562569499015808,
0.011086809448897839,
0.006621056701987982,
-0.0006137572345323861,
0.015083247795701027,
0.0015455551911145449,
-0.02762783318758011,
-0.03069818578660488,
-0.00490568345412612,
-0.06474369764328003,
-0.026843499392271042,
0.007074595894664526,
-0.06053435802459717,
0.042513277381658554,
0.029823029413819313,
-0.009691792540252209,
0.009610886685550213,
-0.03435961902141571,
-0.018134869635105133,
0.024408232420682907,
-0.009887388907372952,
-0.013694451190531254,
0.04211296886205673,
0.07978186756372452,
0.03178903087973595,
0.006689533591270447,
0.00919073261320591,
-0.002688024425879121,
-0.03292330354452133,
-0.03615244850516319,
-0.00017571385251358151,
0.03480870649218559,
-0.004109252244234085,
-0.022760124877095222,
-0.0022536050528287888,
-0.028414323925971985,
-0.017229989171028137,
0.006415511481463909,
-0.05800819396972656,
0.023464759811758995,
0.007433657068759203,
-0.02235930971801281,
-0.03907155990600586,
0.03925059735774994,
0.006063240580260754,
0.020336583256721497,
-0.01791985332965851,
-0.010731500573456287,
-0.05320243537425995,
0.0061832088977098465,
0.011093045584857464,
0.04533984884619713,
-0.017840811982750893,
0.04789876565337181,
0.04967636242508888,
0.03174658119678497,
0.012519855052232742,
-0.003485045162960887,
-0.02157074399292469,
-0.01872825063765049,
-0.007510799448937178,
-0.005042812786996365,
0.019613485783338547,
0.01744251139461994,
0.016788220033049583,
-0.03804842382669449,
-0.019049303606152534,
-0.0192516278475523,
-0.042114660143852234,
0.004525101277977228,
-0.03157160431146622,
0.018904920667409897,
-0.011730111204087734,
-0.028229953721165657,
-0.01594950072467327,
-0.0035785497166216373,
-0.005648662336170673,
0.016512399539351463,
-0.014563002623617649,
-0.048311930149793625,
0.006787027698010206,
-0.06524921953678131,
-0.014412205666303635,
0.030652495101094246,
-0.03649720922112465,
-0.005007585976272821,
0.020759571343660355,
-0.011704469099640846,
0.0006493625114671886,
0.001738090068101883,
0.0006071030511520803,
-0.007352907210588455,
-0.017419910058379173,
0.010170863009989262,
0.004039029590785503,
0.04441427066922188,
-0.03844684362411499,
-0.030374614521861076,
0.040193118155002594,
0.035872071981430054,
0.0317622572183609,
-0.013047497719526291,
-0.04997957870364189,
0.0019602139946073294,
-0.03864363208413124,
-0.0232759490609169,
0.030302198603749275,
-0.01982215791940689,
0.0017180268187075853,
0.010007464326918125,
-0.02785397134721279,
-0.01487773098051548,
-0.0381968691945076,
-0.03639335557818413,
-0.012204347178339958,
-0.05241985246539116,
0.0003508758672978729,
0.04346148669719696,
-0.013486136682331562,
-0.043065592646598816,
-0.0014727571979165077,
-0.049595411866903305,
-0.03620496019721031,
-0.02233244478702545,
-0.00945083238184452,
0.008341454900801182,
-0.02753964439034462,
0.02548518218100071,
0.0028924462385475636,
-0.014011089690029621,
0.0035621875431388617,
-0.060162562876939774,
-0.0535120889544487,
0.008456896990537643,
0.006778066512197256,
0.03489599749445915,
0.02192043326795101,
-0.01343453023582697,
0.10585401207208633,
0.04465169459581375,
-0.02569933794438839,
-0.009679439477622509,
0.04588274285197258,
-0.005570734851062298,
-0.019602928310632706,
-0.004904055502265692,
0.03409044072031975,
-0.010485370643436909,
0.04543575644493103,
0.013062144629657269,
0.0531189888715744,
0.0661306232213974,
-0.039886925369501114,
-0.02049354836344719,
0.0471147745847702,
0.0077064502984285355,
-0.011457664892077446,
0.05279248207807541,
-0.017617078498005867,
-0.03073280118405819,
0.0032971822656691074,
-0.005180722568184137,
-0.0052666743285954,
-0.005003858357667923,
-0.020657656714320183,
0.03295507654547691,
0.013968665152788162,
0.018917856737971306,
-0.021702639758586884,
0.05626489967107773,
0.015608207322657108,
-0.062363434582948685,
0.010141071863472462,
0.025331076234579086,
0.034648459404706955,
-0.014083904214203358,
0.03606502711772919,
0.05402185395359993,
0.027408650144934654,
-0.028020016849040985,
-0.051960792392492294,
0.026036344468593597,
-0.015842130407691002,
-0.0012250677682459354,
-0.015391594730317593,
-0.05004914849996567,
0.020469825714826584,
0.013372175395488739,
0.011757687665522099,
-0.029291696846485138,
-0.006219975184649229,
-0.02348392643034458,
-0.02182088792324066,
-0.010433802381157875,
-0.019702119752764702,
0.055754344910383224,
0.036904238164424896,
0.04073629155755043,
-0.0009593426948413253,
-0.012521963566541672,
-0.027757853269577026,
-0.011262014508247375,
-0.06872320920228958,
0.0255495123565197,
-0.026335153728723526,
-0.0407395139336586,
-0.014679696410894394,
-0.027432389557361603,
0.010851901024580002,
-0.04837316274642944,
-0.05564219132065773,
0.004740730859339237,
0.0006081979372538626,
-0.016162509098649025,
0.03587641194462776,
-0.02082381211221218,
-0.04944709688425064,
-0.02429046668112278,
0.0217401385307312,
0.027724795043468475,
0.011619151569902897,
0.03545432537794113,
0.05452226847410202,
-0.01657579280436039,
0.004083459731191397,
-0.0035172319039702415,
0.00981799978762865,
0.009162466041743755,
0.06359656155109406,
0.043227192014455795,
0.01912214234471321,
-0.02501760795712471,
0.002747086575254798,
0.018629183992743492,
0.08331393450498581,
0.037474870681762695,
-0.035116542130708694,
0.007902048528194427,
-0.021132703870534897,
-0.02368752658367157,
-0.01987786404788494,
0.039955493062734604,
-0.012620922178030014,
-0.009493998251855373,
0.003311514388769865,
0.007067135069519281,
-0.01526036486029625,
-0.002570521319285035,
0.034401245415210724,
-0.036280691623687744,
-0.029173796996474266,
-0.03058510087430477,
-0.019974490627646446,
0.005141747649759054,
0.0011430527083575726,
-0.003815805073827505,
0.016095947474241257,
0.01911911740899086,
-0.008513562381267548,
0.037310101091861725,
0.034967124462127686,
-0.04624157398939133,
0.005097200628370047,
-0.010772807523608208,
-0.03907250612974167,
0.0003600005293264985,
0.0047840154729783535,
0.013238470070064068,
0.0097152478992939,
0.013120208866894245,
0.003768359078094363,
0.022046459838747978,
-0.07379180192947388,
0.005926942452788353,
0.037650927901268005,
0.04001588001847267,
-0.006654210854321718,
0.009485040791332722,
-0.04763654246926308,
-0.04029751196503639,
0.0407637283205986,
-0.009621869772672653,
0.054163895547389984,
0.0021418093238025904,
0.01627950556576252,
-0.012596264481544495,
-0.047175049781799316,
-0.006598613690584898,
0.017443513497710228,
0.01020764745771885,
0.03479735553264618,
0.0028770642820745707,
-0.0030790935270488262,
-0.05133592337369919,
-0.004748234990984201,
0.05866314843297005,
0.0809052437543869,
-0.03344077989459038,
-0.020065845921635628,
-0.020383404567837715,
-0.010092220269143581,
0.038616374135017395,
-0.06385088711977005,
0.03706694766879082,
-0.045319899916648865,
-0.01651330292224884,
0.05911586433649063,
-0.01839543879032135,
-0.052284467965364456,
0.025835799053311348,
-0.01414174772799015,
-0.02913818135857582,
0.02805650606751442,
-0.006565655115991831,
0.04847900569438934,
0.0014835322508588433,
0.02154066041111946,
0.032906703650951385,
0.022260308265686035,
-0.03844320401549339,
0.012408701702952385,
-0.07414335757493973,
0.016765151172876358,
-0.005183527246117592,
0.03210049495100975,
-0.020204799249768257,
0.007427483331412077,
-0.023630112409591675,
0.023953355848789215,
0.008629673160612583,
0.024680376052856445,
0.022381674498319626,
-0.018240489065647125,
-0.007697561755776405,
0.0028044700156897306,
-0.013204237446188927,
0.022334109991788864,
-0.016305293887853622,
-0.005212701391428709,
0.00547152291983366,
-0.011812600307166576,
0.01576961949467659,
-0.007375313900411129,
0.021131092682480812,
0.03574588894844055,
-0.03404330462217331,
0.03600262477993965,
-0.017551278695464134,
-0.014081773348152637,
0.011780014261603355,
-0.06549320369958878,
0.04718440771102905,
-0.0012768474407494068,
0.009428066201508045,
0.002239604014903307,
-0.04965311288833618,
-0.07400821894407272,
-0.014239863492548466,
-0.020144227892160416,
0.013474841602146626,
-0.030741319060325623,
-0.00864739902317524,
-0.0011227373033761978,
0.01259643118828535,
-0.05246896669268608,
0.02601235918700695,
-0.01630382612347603,
0.012502573430538177,
-0.032137852162122726,
-0.0020047237630933523,
0.005053803790360689,
0.006619797088205814,
-0.021634109318256378,
0.017115695402026176,
0.06526465713977814,
-0.02157290279865265,
-0.018016748130321503,
-0.010520675219595432,
0.01745563931763172,
0.04203559458255768,
-0.004629404284060001,
-0.014026271179318428,
0.004815979395061731,
0.021875396370887756,
0.0016491770511493087,
0.013087719678878784,
0.012157302349805832,
-0.04804098233580589,
-0.048373498022556305,
-0.003735113423317671,
0.010359839536249638,
0.03000049479305744,
-0.030086398124694824,
-0.02062070183455944,
-0.02634393982589245,
0.04889722913503647,
0.026505786925554276,
-0.0014515563379973173,
-0.03711100295186043,
0.0396265983581543,
0.027508175000548363,
-0.006755992770195007,
0.008013835176825523,
0.000039186466892715544,
-0.01229297835379839,
0.03132684901356697,
0.00612263148650527,
0.0029088740702718496,
0.022028863430023193,
0.0942305475473404,
-0.0007006661617197096,
-0.0004653495561797172,
0.009472447447478771,
-0.023258842527866364,
-0.001953377854079008,
-0.011542615480720997,
0.01433357410132885,
0.017319222912192345,
0.011617260985076427,
-0.013465122319757938,
-0.0037946475204080343,
-0.07581566274166107,
-0.013665265403687954,
0.04892011359333992,
0.03638693690299988,
0.05216898396611214,
0.05255184695124626,
-0.02362111210823059,
0.006776859518140554,
-0.035749927163124084,
-0.012807546183466911,
0.019129661843180656,
-0.01806545816361904,
0.019580090418457985,
-0.051685597747564316,
0.009489619173109531,
0.04723719507455826,
0.036891303956508636,
-0.008210860192775726,
0.022562064230442047,
0.034661635756492615,
0.04324133321642876,
0.05387813597917557,
-0.01689249835908413,
-0.05673709139227867,
0.06785380095243454,
-0.04502592235803604,
0.019584471359848976,
-0.009486047551035881,
-0.01577869988977909,
0.0282667838037014,
0.024033721536397934,
-0.03182939067482948,
-0.0365588553249836,
-0.01509033516049385,
-0.07150018960237503,
-0.01852942258119583,
0.004074523691087961,
0.002932720584794879,
0.018007412552833557,
0.01999492757022381,
-0.000312013435177505,
-0.008188100531697273,
-0.0014023669064044952,
-0.024487735703587532,
-0.03792409226298332,
-0.05548984557390213,
-0.027245281264185905,
-0.04344523698091507,
0.020863870158791542,
-0.04501434788107872,
-0.018842170014977455,
0.04049231484532356,
-0.04913564771413803,
0.07475023716688156,
0.005469287745654583,
0.014041056856513023,
-0.046040549874305725,
0.04492799565196037,
-0.001683334819972515,
0.028052231296896935,
-0.027912242338061333,
0.012335729785263538,
0.1409582495689392,
0.06273741275072098,
0.032905492931604385,
-0.05370163545012474,
-0.013256064616143703,
-0.027131402865052223,
0.02975921332836151,
-0.014533378183841705,
0.01298119779676199,
0.002759623108431697,
0.00007830261893104762,
0.029745491221547127,
0.02575421892106533,
0.0395691841840744,
-0.01984664797782898,
0.007897061295807362,
-0.006971081253141165,
-0.04229428619146347,
0.01723128743469715,
0.043061330914497375,
0.0004132885951548815,
0.02488662116229534,
-0.008850937709212303,
-0.03713729977607727,
-0.03992398455739021,
-0.0019869834650307894,
-0.031632330268621445,
0.0030959390569478273,
0.0070189605467021465,
-0.006148976739495993,
0.006977899465709925,
0.020791070535779,
0.01818552054464817,
0.010564634576439857,
0.007879507727921009,
0.020428532734513283,
0.009464974515140057,
-0.010680519044399261,
-0.019031206145882607,
0.04382586479187012,
-0.014052806422114372,
-0.008600681088864803,
-0.004759605508297682,
0.02938026189804077,
-0.031600918620824814,
-0.04617178440093994,
-0.04932720586657524,
0.06251249462366104,
-0.024496573954820633,
-0.007799653336405754,
-0.011104688979685307,
-0.022368857637047768,
0.02400958724319935,
-0.021832117810845375,
-0.004398786462843418,
0.008128655143082142,
0.007370776496827602,
-0.013077056966722012,
-0.012964015826582909,
0.015417768619954586,
0.0251711867749691,
0.004390334244817495,
0.024057308211922646,
0.0005831168964505196,
0.006564501207321882,
-0.029535336419939995,
0.006094836164265871,
-0.0003654342144727707,
-0.0011225147172808647,
0.01155725959688425,
-0.02420770190656185,
-0.01563609205186367,
-0.050286080688238144,
-0.05791000649333,
0.04048367962241173,
0.020081285387277603,
0.056610357016325,
-0.013532543554902077,
0.0014169820351526141,
0.016481060534715652,
-0.03434814512729645,
0.02500256523489952,
-0.026601165533065796,
-0.02811366692185402,
0.019792458042502403,
-0.017204726114869118,
0.0352986678481102,
0.046680748462677,
-0.023340240120887756,
-0.019996795803308487,
0.03434160351753235,
0.027680890634655952,
0.05054362863302231,
-0.046189866960048676,
0.02521056868135929,
0.03004230558872223,
-0.03770141676068306,
0.013005909509956837,
-0.02328796684741974,
0.009498145431280136,
0.002759775146842003,
0.02166627161204815,
0.0024888915941119194,
0.01664912886917591,
-0.017479516565799713,
-0.0023749058600515127,
0.017894500866532326,
-0.0261149313300848,
-0.04687416926026344,
0.030186809599399567,
0.037762708961963654,
-0.0020968185272067785,
-0.0311399158090353,
-0.017820604145526886,
-0.01525958813726902,
0.005698031280189753,
0.019871624186635017,
-0.05147838965058327,
-0.03567754104733467,
0.00689485901966691,
-0.00005218325895839371,
0.03877779096364975,
0.008457685820758343,
0.010617770254611969,
-0.0035965759307146072,
0.001455879770219326,
0.001523533253930509,
0.011696316301822662,
0.026009710505604744,
0.05352219566702843,
-0.022232532501220703,
0.006758640520274639,
0.048813529312610626,
0.002429852494969964,
-0.01375005766749382,
0.006802457384765148,
0.02529929205775261,
-0.010289812460541725,
-0.02311544120311737,
-0.021369775757193565,
0.02203853242099285,
-0.04064429551362991,
-0.032560065388679504,
0.05654300004243851,
0.014759817160665989,
0.021360257640480995,
0.06954700499773026,
0.0018722309032455087,
-0.008636570535600185,
0.04123406484723091,
-0.03473741561174393,
-0.02317776158452034,
-0.019824253395199776,
-0.0003609114501159638,
0.011475367471575737,
0.002325876150280237,
-0.0015308605507016182,
0.013180512934923172,
0.010928244329988956,
0.008420721627771854,
0.019026657566428185,
-0.00943644717335701,
0.017767541110515594,
0.03957688435912132,
0.006006202660501003,
0.016593782231211662,
0.02233685925602913,
0.013243052177131176,
-0.011835958808660507,
0.03224625810980797,
-0.03409804403781891,
0.0436515249311924,
0.02019086852669716,
0.021620463579893112,
-0.08312711119651794,
-0.03874728083610535,
0.03510775789618492,
0.00018957855354528874,
0.06414347887039185,
-0.03876686841249466,
-0.016439538449048996,
0.05201132968068123,
-0.08476385474205017,
0.008625227957963943,
-0.004092526622116566,
-0.034384261816740036,
-0.04168533533811569,
0.036642253398895264,
-0.029777077957987785,
0.0652209147810936,
-0.01301239337772131,
0.03300020098686218,
0.00021880264102946967,
0.001977562205865979,
0.01313040591776371,
-0.010705123655498028,
-0.018491245806217194,
0.0017218266148120165,
-0.02552802674472332,
-0.01859194040298462,
0.034044623374938965,
-0.04630871117115021,
0.008371441625058651,
0.04559660330414772,
0.026642223820090294,
-0.029673278331756592,
-0.013886705040931702,
0.027452345937490463,
0.034436143934726715,
0.03378649055957794,
-0.006837503984570503,
-0.016109086573123932,
0.00432883994653821,
-0.024748576804995537,
0.04546422138810158,
0.035952914506196976,
0.006669912487268448,
-0.01655500940978527,
0.021905234083533287,
-0.009602658450603485,
-0.04514415189623833,
0.02231379598379135,
0.0029567680321633816,
-0.03023727424442768,
0.018101071938872337,
0.03025926649570465,
0.004076686687767506,
-0.021946115419268608,
0.052805472165346146,
-0.03716341033577919,
0.017118118703365326,
0.03637276217341423,
-0.009098872542381287,
0.009549710899591446,
0.0120608601719141,
-0.07820463180541992,
-0.020946010947227478,
0.03913867101073265,
0.016609547659754753,
-0.010462488979101181,
-0.02849176712334156,
-0.01835852675139904,
-0.02305937558412552,
0.04412972554564476,
0.029584262520074844,
-0.04598018154501915,
-0.04376869276165962,
0.04369867965579033,
-0.027028562501072884,
0.02954425849020481,
-0.037766072899103165,
0.0059501174837350845,
-0.04653291031718254,
-0.07996613532304764,
0.04702966660261154,
0.022032713517546654,
0.0160876102745533,
-0.0922245979309082,
0.00886716227978468,
-0.0036397655494511127,
0.01416940800845623,
0.05300575867295265,
0.020355410873889923,
-0.012544318102300167,
0.0004837709420826286,
-0.014823319390416145,
0.0628323033452034,
-0.036825548857450485,
-0.005318864248692989,
-0.00523451017215848,
-0.0017710349056869745,
-0.040189120918512344,
0.0022845210041850805,
-0.029218178242444992,
0.03859368711709976,
-0.01570960134267807,
-0.008406602777540684,
0.0005680646281689405,
0.015915904194116592,
-0.0074400752782821655,
0.0608503483235836,
-0.018533919006586075,
-0.0018133125267922878,
0.04906240105628967,
0.0006363510037772357,
0.019417420029640198,
0.03906496614217758,
-0.019387714564800262,
-0.040466394275426865,
0.01629263535141945,
-0.003392506157979369,
-0.0158490352332592,
-0.017296968027949333,
0.004365435801446438,
0.03050643764436245,
-0.0492713488638401,
-0.033242832869291306,
0.030518637970089912,
-0.042915284633636475,
-0.009678276255726814,
0.03843411058187485,
-0.010596985928714275,
0.04576373100280762,
-0.008764847181737423,
0.038221076130867004,
-0.026187991723418236,
-0.015555432997643948,
0.006878688000142574,
0.003966799005866051,
0.01947147212922573,
0.02303973026573658,
0.0008585856412537396,
0.034482549875974655,
-0.029462609440088272,
0.028726214542984962,
0.014181978069245815,
0.013139170594513416,
-0.02527945302426815,
-0.006604571361094713,
0.04455817863345146,
-0.029747692868113518,
0.0022076559253036976,
0.030698005110025406,
-0.015577125363051891,
0.09730406850576401,
-0.022172825410962105,
0.002613372402265668,
-0.05211906135082245,
0.007034010719507933,
-0.002091189380735159,
-0.004138321615755558,
0.0014603041345253587,
0.030902165919542313,
0.0026204781606793404,
-0.02806508168578148,
-0.048395946621894836,
0.021628279238939285,
0.025060566142201424,
-0.06874535232782364,
-0.011862033046782017,
0.039784107357263565,
-0.02946167066693306,
0.005065754055976868,
-0.025764688849449158,
0.01223789807409048,
-0.01714141294360161,
0.02547445148229599,
0.0016367894131690264,
0.030244972556829453,
0.009518735110759735,
-0.029607266187667847,
0.03178180381655693,
0.04371342435479164,
-0.015204238705337048,
-0.004096006974577904,
-0.025727663189172745,
0.0379909947514534,
0.020933100953698158,
-0.03518803045153618
] |
<p>This is pressure in Newtonian mechanics: </p>
<p>$$P=\frac {dF}{dA}.$$
What does this mean?
(Doesn't it mean that force is a function of area?)
What type of function is force?</p>
| 10,659 |
[
-0.009647693485021591,
0.015266327187418938,
-0.02458346262574196,
-0.009541593492031097,
0.06682086735963821,
-0.005605751648545265,
0.0188907478004694,
-0.01164703257381916,
0.006196184083819389,
-0.029543504118919373,
0.04429018497467041,
0.016165737062692642,
0.04460964724421501,
-0.0233769528567791,
0.0024502950254827738,
0.01183069497346878,
-0.01805059053003788,
0.00994750764220953,
0.017715318128466606,
-0.028116783127188683,
0.018310002982616425,
0.030960669741034508,
0.0032058435026556253,
0.015200850553810596,
0.03694884479045868,
0.0498230941593647,
0.019876187667250633,
-0.0415528267621994,
0.03469422832131386,
0.06980285048484802,
-0.00730031356215477,
-0.023409785702824593,
0.014894237741827965,
0.020166918635368347,
0.023206403478980064,
-0.008266412653028965,
-0.020596329122781754,
-0.017771700397133827,
-0.04191536083817482,
0.05644441395998001,
-0.05308932438492775,
-0.010419277474284172,
0.03922821581363678,
-0.0012350458418950438,
-0.04421677812933922,
0.06096912547945976,
0.026538264006376266,
-0.038592588156461716,
0.034495849162340164,
-0.03862874209880829,
0.04528442397713661,
0.005546077154576778,
0.05499470233917236,
0.05093234032392502,
-0.0023621220607310534,
-0.019349001348018646,
0.06490125507116318,
0.05646529793739319,
-0.03204231709241867,
-0.05602337047457695,
-0.0066679734736680984,
0.014654587022960186,
0.013131900690495968,
-0.01815420761704445,
-0.04008841514587402,
0.021595025435090065,
-0.030125340446829796,
-0.04646376520395279,
0.00633478257805109,
0.02376016601920128,
0.011509186588227749,
0.012187320739030838,
0.033667899668216705,
-0.04460061341524124,
-0.01789705641567707,
-0.04220651835203171,
0.023605309426784515,
0.013514573685824871,
0.026263747364282608,
0.04775805398821831,
0.004276389256119728,
0.03928593173623085,
0.010021986439824104,
0.012669200077652931,
0.0109177865087986,
-0.017250098288059235,
0.08114691078662872,
0.010690353810787201,
-0.008274894207715988,
-0.0026836241595447063,
0.0038953935727477074,
0.014109011739492416,
0.023991378024220467,
-0.03342283144593239,
0.0016064520459622145,
-0.0014027768047526479,
-0.017409514635801315,
0.01022513397037983,
0.01261793915182352,
-0.017148394137620926,
0.003405231051146984,
-0.030564267188310623,
-0.010333497077226639,
0.04518189653754234,
0.02141585573554039,
-0.026608509942889214,
-0.03507271781563759,
0.018822604790329933,
-0.018849080428481102,
0.002482322044670582,
-0.034130748361349106,
0.011538549326360226,
-0.025324171409010887,
-0.010425004176795483,
0.007063572760671377,
-0.004089992493391037,
0.008216461166739464,
0.03223343938589096,
0.04622730612754822,
0.05907990410923958,
0.07707482576370239,
-0.045292582362890244,
0.03504279628396034,
-0.013270222581923008,
-0.06821826845407486,
0.021024756133556366,
0.0034854630939662457,
0.0019600335508584976,
-0.028678180649876595,
0.01250016875565052,
-0.011548145674169064,
-0.03337428718805313,
-0.02465204708278179,
0.019573936238884926,
0.02049676701426506,
-0.005426510702818632,
-0.061050206422805786,
-0.07201848924160004,
0.03852230682969093,
0.0005612828535959125,
-0.023059828206896782,
-0.050155267119407654,
0.03802291303873062,
0.006892146077007055,
0.02772841416299343,
0.006551575381308794,
-0.03671882301568985,
0.010746711865067482,
0.05509083718061447,
-0.02187628112733364,
-0.016538280993700027,
0.007942788302898407,
-0.015291767194867134,
-0.026840798556804657,
0.0036021042615175247,
-0.06068947911262512,
0.024176213890314102,
0.04135962948203087,
0.003497541416436434,
-0.05982855707406998,
0.06524457782506943,
-0.04821011424064636,
-0.0071241906844079494,
0.0006852130172774196,
-0.026725634932518005,
-0.024754062294960022,
0.04863046482205391,
0.00619471212849021,
0.011206191033124924,
0.0480697825551033,
0.03160317242145538,
0.01869874633848667,
0.02499530464410782,
0.022908298298716545,
0.04295046254992485,
0.021099042147397995,
-0.03887808695435524,
-0.03921101614832878,
0.013333526439964771,
-0.014526686631143093,
-0.036309320479631424,
-0.04109586402773857,
-0.026193983852863312,
0.02696571871638298,
0.005421599373221397,
0.057924479246139526,
0.01661739870905876,
0.0009801674168556929,
-0.019023334607481956,
-0.02263791300356388,
-0.05579241365194321,
-0.06835906207561493,
0.05357656255364418,
-0.034925542771816254,
0.019869500771164894,
0.005742612294852734,
0.007446835748851299,
0.035936396569013596,
-0.03463638201355934,
-0.013852545991539955,
0.0004964305553585291,
0.013097775168716908,
0.03990625590085983,
-0.008735769428312778,
0.026307404041290283,
0.037857357412576675,
0.043353691697120667,
-0.007895911112427711,
-0.0019751221407204866,
-0.0057187252677977085,
-0.018104199320077896,
0.018874412402510643,
-0.04551957920193672,
0.018761171028017998,
-0.04944729432463646,
0.012194355949759483,
0.013052345253527164,
-0.010628941468894482,
-0.014562356285750866,
0.031674958765506744,
-0.040958158671855927,
0.09098251909017563,
0.04504886269569397,
-0.0046080625616014,
0.024675065651535988,
0.018760325387120247,
-0.009974797256290913,
0.014296476729214191,
-0.038574159145355225,
-0.014766891486942768,
-0.04362881928682327,
-0.007020721677690744,
0.01862620934844017,
0.022841807454824448,
-0.018197644501924515,
0.002077544806525111,
0.042821113020181656,
0.007667066995054483,
0.04587563872337341,
0.023632420226931572,
-0.011873776093125343,
-0.032878514379262924,
0.020596276968717575,
0.023810379207134247,
0.012921572662889957,
0.025165438652038574,
0.002467059064656496,
0.06877995282411575,
0.04756411537528038,
-0.0018547711661085486,
0.02555588260293007,
0.04524509608745575,
-0.02416028454899788,
0.03833819180727005,
0.036559417843818665,
-0.00474562868475914,
0.039568204432725906,
-0.019587723538279533,
-0.0041814446449279785,
0.015971751883625984,
-0.005007905885577202,
-0.025223974138498306,
-0.05388863757252693,
-0.014039120636880398,
0.02863478660583496,
0.0060913595370948315,
-0.024902038276195526,
-0.03480914235115051,
0.036193039268255234,
-0.031899288296699524,
0.0074628619477152824,
0.004138454794883728,
-0.001404261915013194,
-0.026131300255656242,
-0.02276397868990898,
0.012848618440330029,
0.04132496938109398,
0.06640973687171936,
-0.02931896224617958,
-0.0019409630913287401,
0.009735282510519028,
-0.03730963543057442,
-0.005820252001285553,
-0.01972319930791855,
0.0012977654114365578,
0.010082362219691277,
-0.01855757273733616,
-0.02705041691660881,
0.043446801602840424,
-0.0065368241630494595,
0.007301460485905409,
0.03500424697995186,
-0.03420330584049225,
-0.042337093502283096,
0.012545007281005383,
-0.039526015520095825,
0.042564697563648224,
-0.029665280133485794,
-0.01364461611956358,
0.04559210687875748,
-0.044407691806554794,
0.005329817999154329,
-0.011761489324271679,
-0.04773705452680588,
-0.011653434485197067,
-0.06712044030427933,
-0.012566863559186459,
0.019953424111008644,
-0.024958070367574692,
0.0021248667035251856,
0.035751622170209885,
-0.05915020406246185,
0.014671271666884422,
-0.004140774253755808,
-0.01851583458483219,
-0.007561256643384695,
-0.005400423891842365,
0.020502036437392235,
-0.018584804609417915,
-0.05563503876328468,
0.06537044048309326,
0.0009554252028465271,
-0.027156490832567215,
0.0023244875483214855,
-0.02503705769777298,
-0.0345233678817749,
-0.07229090481996536,
0.023039843887090683,
0.05224711447954178,
-0.026013825088739395,
0.022164717316627502,
0.017081603407859802,
0.046302322298288345,
0.03244654834270477,
0.021753255277872086,
0.00011572254152270034,
-0.011726081371307373,
-0.004968148190528154,
-0.020152710378170013,
0.08468840271234512,
0.03403386101126671,
0.004201941657811403,
0.020064782351255417,
-0.021243900060653687,
0.022850152105093002,
0.014928820542991161,
-0.030354076996445656,
0.03657814860343933,
0.011316977441310883,
-0.017340371385216713,
-0.03219713270664215,
0.035095445811748505,
0.011832819320261478,
-0.018312346190214157,
0.04057265818119049,
0.013241469860076904,
0.03729025274515152,
-0.02838962711393833,
-0.032098438590765,
0.028434811159968376,
0.04032227769494057,
-0.035298239439725876,
-0.02900974079966545,
0.0031631658785045147,
0.013799757696688175,
0.03427259624004364,
0.00919502042233944,
-0.01930166222155094,
0.052039679139852524,
0.0052472916431725025,
0.0267424788326025,
0.023360084742307663,
-0.029507817700505257,
0.03173596411943436,
-0.0609821192920208,
-0.024815620854496956,
0.02856956049799919,
0.018701521679759026,
0.008473807014524937,
0.08591505885124207,
0.037219684571027756,
0.036293309181928635,
0.05069231241941452,
0.021708384156227112,
-0.07551664859056473,
0.03992394730448723,
-0.030801093205809593,
0.003133186837658286,
-0.022134743630886078,
-0.0071569159626960754,
-0.00961230043321848,
-0.03304046392440796,
-0.011959479190409184,
0.020358072593808174,
0.008193877525627613,
-0.05568396672606468,
-0.010153649374842644,
-0.011869240552186966,
-0.04742865636944771,
-0.029010627418756485,
0.02289075404405594,
0.04740538075566292,
-0.013126871548593044,
0.03268388658761978,
0.07107914984226227,
-0.0016281973803415895,
-0.021320970728993416,
0.0008313661091960967,
-0.027837907895445824,
0.0190745797008276,
0.03227755427360535,
-0.005215171724557877,
-0.01422059629112482,
0.03351638838648796,
0.019310077652335167,
0.024143876507878304,
0.05582459643483162,
0.032502181828022,
-0.023636823520064354,
-0.010122024454176426,
-0.07694163918495178,
-0.007424080744385719,
-0.008451740257441998,
0.028171511366963387,
-0.0035615924280136824,
0.011713847517967224,
0.0151958167552948,
0.0006027028430253267,
-0.004901690874248743,
0.05772734433412552,
0.022866062819957733,
0.018386512994766235,
-0.030806969851255417,
-0.07448708266019821,
-0.009854505769908428,
-0.06810170412063599,
-0.010341349989175797,
0.014636604115366936,
0.001443954766727984,
-0.0244539063423872,
0.016423864290118217,
-0.016426488757133484,
-0.03319071978330612,
-0.03969117999076843,
-0.031310055404901505,
-0.018803058192133904,
0.004114686045795679,
-0.03385418653488159,
-0.003953804727643728,
0.022274790331721306,
0.03893233835697174,
0.027250057086348534,
0.02198692411184311,
-0.023831725120544434,
-0.094605453312397,
-0.018917661160230637,
0.02824440784752369,
0.020240580663084984,
-0.011412739753723145,
-0.010959620587527752,
-0.026103394106030464,
-0.03140617161989212,
0.03856746107339859,
-0.04079417139291763,
0.01378225814551115,
-0.015015295706689358,
0.039710529148578644,
-0.02301095798611641,
-0.041474197059869766,
-0.05110694840550423,
0.0033148007933050394,
-0.02953232452273369,
0.010089017450809479,
-0.018196506425738335,
-0.009265942499041557,
-0.005415857303887606,
0.0030933774542063475,
0.014995194971561432,
0.03284051641821861,
0.013025042600929737,
-0.030100520700216293,
-0.01507631316781044,
0.0032651866786181927,
-0.03409009426832199,
-0.06744341552257538,
-0.011602705344557762,
0.0005183282773941755,
0.025994183495640755,
0.005112044978886843,
-0.02974390797317028,
-0.07003479450941086,
0.03832937031984329,
-0.041213858872652054,
-0.02471230737864971,
0.022176165133714676,
-0.04913889989256859,
0.04785892367362976,
0.030199971050024033,
0.019202208146452904,
0.03575187176465988,
0.019165033474564552,
-0.015940245240926743,
-0.03553245961666107,
-0.01831125281751156,
0.032303836196660995,
-0.01417385134845972,
-0.03118746168911457,
-0.06488070636987686,
0.00009133467392530292,
-0.03343340381979942,
0.014562572352588177,
0.0038225699681788683,
-0.0007493275916203856,
-0.022496376186609268,
-0.0340796634554863,
-0.011499827727675438,
0.04121781885623932,
0.01852051168680191,
0.01919509470462799,
0.01612875796854496,
0.01720362901687622,
0.0402209646999836,
-0.024892311543226242,
-0.0020646716002374887,
0.017672261223196983,
0.02739674225449562,
0.023687900975346565,
0.015412185341119766,
0.013562985695898533,
-0.0016383187612518668,
-0.05184083431959152,
0.02118898183107376,
-0.06410060077905655,
0.049296747893095016,
-0.006552663166075945,
0.006909549236297607,
0.027034591883420944,
-0.05394258722662926,
-0.04568222537636757,
-0.000530887977220118,
-0.001157875289209187,
0.03943992033600807,
-0.05811724066734314,
0.023557808250188828,
-0.03143931180238724,
0.013364977203309536,
-0.03479088097810745,
-0.025504034012556076,
0.02288631722331047,
0.00484808161854744,
-0.03019235096871853,
0.024382209405303,
-0.003463360946625471,
-0.03888867422938347,
-0.03093126229941845,
-0.002078642603009939,
0.05873776227235794,
-0.05364750698208809,
0.01107803825289011,
0.022548794746398926,
-0.03696218878030777,
0.05567988380789757,
0.01932458207011223,
-0.017051463946700096,
-0.03235040605068207,
-0.002091225702315569,
-0.011162448674440384,
-0.02787630259990692,
0.026541728526353836,
-0.03962533921003342,
0.01123465970158577,
-0.007549760863184929,
-0.006845963653177023,
0.03472238779067993,
-0.028605258092284203,
0.04389699548482895,
0.023478835821151733,
0.011067264713346958,
-0.0431586317718029,
0.015148104168474674,
0.030176518484950066,
-0.004619276616722345,
0.030030379071831703,
0.014807431027293205,
-0.0054261693730950356,
-0.054054178297519684,
-0.035977449268102646,
-0.01460249349474907,
-0.008645553141832352,
0.03135254606604576,
0.017851486802101135,
0.06886550784111023,
-0.040858589112758636,
0.015266170725226402,
-0.0011252687545493245,
-0.03133225813508034,
0.0649987980723381,
0.017552658915519714,
-0.016643904149532318,
0.002659361343830824,
0.01011991873383522,
-0.05254408344626427,
-0.017150724306702614,
-0.02723000757396221,
-0.029717562720179558,
0.0627293586730957,
-0.020947642624378204,
0.0751313641667366,
0.026872890070080757,
-0.014971805736422539,
0.027897555381059647,
-0.025331126525998116,
-0.02585228905081749,
-0.00928940437734127,
0.010160482488572598,
0.028887784108519554,
0.000809134857263416,
0.003082860028371215,
0.03661724925041199,
-0.00510363420471549,
-0.004139157012104988,
0.0013919638004153967,
0.02725135162472725,
0.029563484713435173,
0.003494575386866927,
-0.03724749758839607,
-0.036925654858350754,
0.031424593180418015,
-0.008068093098700047,
0.021130412817001343,
-0.01569734886288643,
-0.026992332190275192,
0.06499394029378891,
0.013753099367022514,
-0.015817252919077873,
-0.04336163029074669,
0.02280760556459427,
-0.044051725417375565,
0.008274580352008343,
0.04341096431016922,
-0.008061209693551064,
0.008212689310312271,
0.03160781040787697,
0.03065445087850094,
-0.0441342368721962,
0.01901376061141491,
0.011133182793855667,
-0.014893243089318275,
-0.02494247443974018,
-0.026590077206492424,
-0.048251811414957047,
0.005717472638934851,
-0.03664321079850197,
-0.041621215641498566,
0.010265312157571316,
-0.050838060677051544,
0.01644316501915455,
0.02283770777285099,
-0.00862501747906208,
-0.03109881281852722,
0.06545029580593109,
-0.006161811761558056,
0.00937102735042572,
-0.010404733009636402,
0.02575640007853508,
0.1107674166560173,
0.034143198281526566,
0.03931675851345062,
-0.0319705531001091,
0.009242547675967216,
-0.057908907532691956,
0.004478979390114546,
-0.04195744916796684,
0.011291546747088432,
0.011045015417039394,
0.0032917074859142303,
0.003630140796303749,
0.0396236814558506,
0.01697407104074955,
0.009244066663086414,
0.07470386475324631,
-0.0424274243414402,
-0.018291300162672997,
0.008191772736608982,
0.01085562352091074,
-0.05920180678367615,
0.04127701744437218,
-0.008592317812144756,
0.007350271567702293,
-0.013072671368718147,
0.011094746179878712,
-0.03518330305814743,
-0.027165133506059647,
0.022690830752253532,
-0.02620931901037693,
-0.045038964599370956,
0.002280763117596507,
-0.0022276178933680058,
-0.018631987273693085,
-0.046204663813114166,
0.03744100034236908,
0.015981467440724373,
-0.010479319840669632,
-0.04051133990287781,
0.03827357664704323,
-0.007070610299706459,
0.03454886004328728,
-0.015619240701198578,
-0.024441106244921684,
-0.03045990690588951,
0.004167941398918629,
-0.026619136333465576,
0.023562194779515266,
-0.003205427434295416,
0.045608025044202805,
0.022424878552556038,
0.026157112792134285,
-0.035069942474365234,
-0.05416332557797432,
-0.009997313842177391,
0.009019114077091217,
0.022769905626773834,
-0.0041222651489079,
-0.047521207481622696,
-0.025617552921175957,
0.012477441690862179,
-0.03948234021663666,
0.027574794366955757,
-0.002612945158034563,
0.01806890219449997,
0.03825468569993973,
0.011688903905451298,
0.07006214559078217,
-0.056458983570337296,
-0.007357034366577864,
0.01221184991300106,
0.010910910554230213,
-0.0784817710518837,
0.02195786125957966,
0.015144801698625088,
0.029765646904706955,
0.017408961430191994,
0.004796037916094065,
-0.0018472041701897979,
-0.029743921011686325,
-0.025895265862345695,
0.04893656075000763,
-0.033176567405462265,
0.025628525763750076,
-0.015025574713945389,
0.028816256672143936,
0.007478093728423119,
0.04617937281727791,
0.02472820319235325,
-0.015884367749094963,
-0.030177654698491096,
0.009055273607373238,
0.03925796225667,
-0.03151422366499901,
-0.024489764124155045,
0.02743907831609249,
-0.010748529806733131,
0.0027826044242829084,
0.030835295096039772,
0.04835706204175949,
0.03180696815252304,
-0.00804476160556078,
-0.02014240063726902,
0.00906710047274828,
-0.037656769156455994,
0.021080078557133675,
0.028628399595618248,
-0.02646743133664131,
0.009264240972697735,
0.006184056401252747,
0.0028025354258716106,
-0.051579978317022324,
-0.001023051212541759,
-0.0307809729129076,
-0.015253997407853603,
-0.014773829840123653,
0.042859166860580444,
-0.03436822071671486,
-0.0052107046358287334,
0.000494929205160588,
0.00866655446588993,
-0.043081410229206085,
-0.008150280453264713,
-0.0742359310388565,
-0.03640899062156677,
0.033386290073394775,
-0.011951983906328678,
-0.02238292247056961,
0.028335561975836754,
-0.0347125306725502,
-0.0020446544513106346,
-0.0017649353248998523,
0.010679817758500576,
-0.010625318624079227,
-0.00005992669684928842,
0.049809474498033524,
-0.02556256763637066,
0.051050346344709396,
-0.021228138357400894,
-0.016643645241856575,
0.03984811529517174,
-0.02436734549701214,
-0.056874342262744904,
0.026853028684854507,
-0.007500471081584692,
0.049954645335674286,
0.017769314348697662,
-0.011932162567973137,
-0.01679384708404541,
0.05117305740714073,
-0.031013386324048042,
0.016703614965081215,
-0.01630423031747341,
-0.02915913797914982,
-0.021560676395893097,
-0.010508363135159016,
0.024195367470383644,
0.004479195456951857,
0.025760753080248833,
0.026386884972453117,
-0.001133076730184257,
-0.009453879669308662,
-0.014220865443348885,
0.061349790543317795,
0.005720599554479122,
0.023275718092918396,
0.014601298607885838,
0.008966299705207348,
0.020016256719827652,
0.023666825145483017,
-0.008051915094256401,
0.02300839312374592,
0.007541261147707701,
0.011864184401929379,
-0.10259758681058884,
-0.012767437845468521,
-0.005439963657408953,
0.0017241800669580698,
0.057536765933036804,
-0.03947887569665909,
-0.02737484499812126,
-0.012945974245667458,
-0.05474742129445076,
-0.0015833922661840916,
-0.04409529268741608,
0.006228867452591658,
0.016755465418100357,
-0.00406284537166357,
-0.0009318581433035433,
0.09150658547878265,
0.009522151201963425,
0.035840634256601334,
0.009832541458308697,
0.009767185896635056,
0.015433525666594505,
-0.021090976893901825,
0.0020160372368991375,
0.05564836785197258,
-0.01436291541904211,
0.0040867929346859455,
0.06741805374622345,
0.01149254571646452,
-0.0393233448266983,
0.03809662163257599,
-0.014803899452090263,
0.02936002053320408,
-0.008944171480834484,
-0.013919282704591751,
0.010678612627089024,
0.024275775998830795,
0.0009395965607836843,
-0.01186769176274538,
-0.05210885778069496,
-0.00689307926222682,
-0.029517507180571556,
0.02384098991751671,
-0.0075187296606600285,
0.00204444513656199,
0.03961567208170891,
-0.040345415472984314,
0.01153753511607647,
0.004355591721832752,
-0.03445647284388542,
-0.01215327437967062,
0.00903104804456234,
0.0035736626014113426,
0.005538410507142544,
-0.038113877177238464,
0.02029385045170784,
-0.006042092572897673,
0.03572280704975128,
0.007248325739055872,
-0.00707488926127553,
-0.036681320518255234,
0.019735606387257576,
0.06581252813339233,
-0.01735043339431286,
0.0132975485175848,
0.005345435813069344,
-0.019305439665913582,
-0.057869065552949905,
0.014238571748137474,
-0.008344058878719807,
-0.024453988298773766,
-0.000016377684005419724,
-0.04015996679663658,
-0.02607620507478714,
0.021777505055069923,
0.03444070369005203,
0.003981837071478367,
-0.010901452042162418,
-0.04994577541947365,
0.006022481247782707,
-0.09201106429100037,
0.04864654690027237,
0.011717707850039005,
-0.03058568947017193,
-0.027213813737034798,
-0.005043357610702515,
-0.01254952047020197,
-0.021792437881231308,
0.03763751685619354,
0.009440205059945583,
-0.0055884611792862415,
-0.021592937409877777,
0.01599045842885971,
-0.008181482553482056,
-0.02481313981115818,
-0.010289696976542473,
0.000627867120783776,
-0.028335804119706154,
0.00601011049002409,
0.005778796039521694,
0.02700628526508808,
0.023630179464817047,
0.007900777272880077,
-0.0029038279317319393,
0.04060447961091995,
-0.02760256454348564,
-0.01873514987528324,
0.022691283375024796,
0.04649343341588974,
-0.0011654250556603074,
0.06602289527654648,
-0.011925270780920982,
0.038939595222473145,
-0.010958713479340076,
-0.00537553895264864,
-0.024147624149918556,
0.01576838456094265,
-0.04023044928908348,
-0.01898065395653248,
-0.011112287640571594,
0.014960508793592453,
0.04764164984226227,
-0.07411356270313263,
-0.011711187660694122,
0.04794660955667496,
-0.05536533519625664,
-0.004728584084659815,
0.06814401596784592,
0.04603235796093941,
0.0224226713180542,
-0.019263489171862602,
-0.011679095216095448,
0.021510133519768715,
-0.010162974707782269,
-0.03616832569241524,
-0.0020219183061271906,
0.050164949148893356,
-0.01142329815775156,
-0.03023884817957878,
0.08075018972158432,
-0.014295953325927258,
-0.013528543524444103,
-0.0018308184808120131,
0.030488885939121246,
-0.0209759883582592,
-0.03050745092332363,
-0.031520724296569824,
0.010382632724940777,
0.03668511286377907,
0.021058686077594757,
0.020838672295212746,
0.0829501748085022,
0.009410166181623936,
0.006708215922117233,
-0.03228821977972984,
0.0017328101675957441,
-0.03500066697597504,
-0.029221709817647934,
0.02466203086078167,
0.020246675238013268,
-0.017306072637438774,
-0.04164891690015793,
-0.018613433465361595,
-0.0030608363449573517,
0.028886064887046814,
-0.010642237029969692,
-0.01400474738329649,
0.012671584263443947,
0.015834743157029152,
-0.034965481609106064,
0.009742770344018936,
-0.03556433692574501,
-0.00439330842345953,
0.04727517068386078,
0.02571718767285347,
0.029463225975632668,
0.02348197065293789,
0.036095958203077316,
-0.000032338684832211584,
0.05147230997681618,
-0.07490140944719315,
-0.047721102833747864,
-0.009714174084365368,
0.04455586522817612,
0.030171791091561317,
-0.020665396004915237
] |
<p>Two separate suitably short but intense <a href="http://en.wikipedia.org/wiki/Charged_particle_beam#bunch_structure" rel="nofollow">bunches</a> of <a href="http://en.wikipedia.org/wiki/Muon" rel="nofollow">muons</a>, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration vectors $\bf a$ and $\bf b$ (as measured by any system of participants who are mutually at rest) in the same direction and co-linearly (let's say "A leading in front", and "B trailing behind"), but not necessarily equally accelerated (therefore acceleration vectors $\bf a$ and $\bf b$ don't necessarily have equal magnitudes).</p>
<p>Meanwhile the muons of both bunches decay, with equal and constant proper <a href="http://en.wikipedia.org/wiki/Mean_lifetime#Mean_lifetime" rel="nofollow">mean lifetime</a> $\tau_{\text muon}$, and correspondingly with equal proper "half-life duration Log[ 2 ] $\tau_{\text muon}$".</p>
<p>Also, the two bunches are separated such that they always "remain in sight" of each other; such that </p>
<ul>
<li><p>B (or some suitable accompanying instrumentation) always finds that it takes 1 half-life from "stating a ping" until "observing A's reflection", while </p></li>
<li><p>A always finds that it takes 2 half-lives from "stating a ping" until "observing B's reflection".</p></li>
</ul>
<p>Question:<br>
What's the magnitude $| \bf b | $ ?<br>
Can it be calculated at all, in terms of "mean lifetime $\tau_{\text muon}$" and "speed of light $c$", based on the described setup conditions?</p>
<p>(Surely the described setup conditions are consistent with bunches A and B being called "rigid to each other", or having been "ends of a rigid rod", in the sense of <a href="http://physics.stackexchange.com/questions/67037/is-it-possible-to-have-uniform-proper-acceleration-along-a-large-object-without">this question</a> and <a href="http://physics.stackexchange.com/questions/48392/extended-rigid-bodies-in-special-relativity">that question</a> and the various comments there.</p>
<p>My question is intended to obtain illustrations of different approaches to the "rigid rod" problem which were indicated in those comments; even if they obtain the same answer value.) </p>
| 10,660 |
[
-0.014886886812746525,
-0.022757312282919884,
0.0009085194324143231,
-0.05254809930920601,
0.046096522361040115,
0.012473296374082565,
-0.0028798996936529875,
-0.030943671241402626,
0.009896845556795597,
0.002549374708905816,
0.04981237277388573,
0.03763871267437935,
0.023796964436769485,
0.053649913519620895,
0.004868582356721163,
0.010067514143884182,
0.014781087636947632,
-0.014525769278407097,
-0.015865687280893326,
-0.028685521334409714,
0.033699359744787216,
0.011539293453097343,
-0.00047970839659683406,
0.012409801594913006,
-0.046198390424251556,
0.006854478735476732,
0.015199375338852406,
-0.03538869693875313,
-0.021695071831345558,
0.03522655367851257,
-0.026621738448739052,
-0.026347562670707703,
0.0116228386759758,
-0.014634593389928341,
0.01359725371003151,
-0.002614249475300312,
-0.006709541659802198,
-0.031912095844745636,
0.018703700974583626,
0.03177637979388237,
-0.04780377075076103,
0.008585232309997082,
-0.042444951832294464,
0.04184802249073982,
-0.03476274013519287,
0.005579050630331039,
-0.006321370135992765,
0.008702169172465801,
0.0667235255241394,
-0.03971533849835396,
0.032661404460668564,
-0.006655388046056032,
0.03158201649785042,
-0.025064021348953247,
0.000994973466731608,
-0.017629975453019142,
0.06369604170322418,
0.08872972428798676,
0.020307790488004684,
-0.06679827719926834,
-0.0034333080984652042,
-0.016865627840161324,
-0.006250521633774042,
0.021280843764543533,
0.004351235926151276,
0.011990278027951717,
-0.014760207384824753,
-0.012481809593737125,
0.0421936921775341,
-0.000884365988895297,
-0.00033176300348713994,
-0.01317411195486784,
0.018429365009069443,
-0.03254440054297447,
0.04033884406089783,
0.010387563146650791,
-0.0033819833770394325,
0.0014442142564803362,
0.011069098487496376,
0.062446415424346924,
-0.05912615358829498,
-0.006524143740534782,
0.0537693165242672,
0.014750821515917778,
0.04347817972302437,
-0.02240252122282982,
0.06965222954750061,
-0.03191051632165909,
-0.016971224918961525,
0.025493277236819267,
0.0015323760453611612,
0.02760113775730133,
0.004060625098645687,
0.02471841126680374,
-0.026327094063162804,
0.05346950516104698,
0.013474262319505215,
0.0547005832195282,
-0.006207282189279795,
-0.05077419430017471,
0.005187932401895523,
-0.018264539539813995,
0.008621747605502605,
0.06170571595430374,
-0.016610877588391304,
0.0019077608594670892,
-0.01829680986702442,
0.017919812351465225,
-0.049714233726263046,
-0.033668722957372665,
-0.06271632015705109,
0.0061207362450659275,
-0.029034409672021866,
0.018956413492560387,
-0.038236480206251144,
-0.03884159401059151,
0.019238311797380447,
0.012417634017765522,
0.08636973798274994,
0.036664459854364395,
0.04922553896903992,
-0.01558348536491394,
-0.004849467892199755,
-0.02193826250731945,
-0.07297162711620331,
-0.021253973245620728,
0.030960969626903534,
-0.011456383392214775,
-0.06797176599502563,
0.039740294218063354,
0.028315413743257523,
-0.015105222351849079,
0.012826750986278057,
-0.019885456189513206,
0.023768968880176544,
-0.017483964562416077,
-0.05534110590815544,
-0.04228290170431137,
0.05565362051129341,
-0.007156568579375744,
-0.015363471582531929,
-0.0931369885802269,
-0.021959513425827026,
0.01763799972832203,
0.10208497196435928,
0.0018720818916335702,
0.0015930734807625413,
0.010701680555939674,
0.028462521731853485,
0.022725418210029602,
0.004399723839014769,
0.006599767599254847,
0.006836595479398966,
0.002302028238773346,
0.00901732686907053,
-0.054698534309864044,
-0.0007458801846951246,
0.007736310828477144,
-0.01458520907908678,
0.022806134074926376,
0.05003993585705757,
0.023299360647797585,
0.0011212093522772193,
0.0009789677569642663,
0.02137843891978264,
-0.026083284988999367,
0.060667067766189575,
0.03221617266535759,
-0.027224324643611908,
0.031096821650862694,
-0.03274640440940857,
-0.0007320296717807651,
-0.010757885873317719,
-0.015334729105234146,
0.04793548956513405,
-0.0754462406039238,
-0.03587014600634575,
0.026834970340132713,
-0.022975513711571693,
-0.016546137630939484,
-0.02066066674888134,
-0.03697802126407623,
-0.044803544878959656,
0.019603202119469643,
0.009523491375148296,
-0.0032078581862151623,
0.012223429046571255,
0.029551925137639046,
0.013448517769575119,
-0.04397715628147125,
-0.014236600138247013,
-0.07922042161226273,
-0.042336493730545044,
0.021313058212399483,
-0.019656721502542496,
0.037331629544496536,
-0.03532963618636131,
-0.04671978950500488,
-0.021046839654445648,
-0.037754252552986145,
0.01986825466156006,
0.07803177088499069,
0.0025838445872068405,
-0.008228516206145287,
0.003355926601216197,
0.0447055846452713,
0.04410944879055023,
0.009854575619101524,
0.0003501553146634251,
0.0077515412122011185,
-0.01762036420404911,
-0.005998400039970875,
-0.05790463835000992,
0.03900580480694771,
-0.014759904704988003,
0.033929236233234406,
0.012609719298779964,
-0.02832207828760147,
0.013161774724721909,
0.008234581910073757,
-0.033445607870817184,
0.021768854930996895,
0.06325895339250565,
0.017759129405021667,
0.010283921845257282,
0.03034653514623642,
0.013163048774003983,
0.016408082097768784,
0.002269200747832656,
-0.044834766536951065,
-0.04670615494251251,
-0.020550450310111046,
0.012506664730608463,
0.00812504068017006,
0.0036279435735195875,
0.0449628047645092,
-0.01026557944715023,
0.038527168333530426,
0.006897378247231245,
0.070376917719841,
-0.031363021582365036,
-0.06651723384857178,
0.038169074803590775,
0.020186254754662514,
-0.0158805251121521,
0.032180238515138626,
0.010763703845441341,
-0.025420181453227997,
0.001642597489990294,
-0.030727365985512733,
0.0038715549744665623,
0.003592687426134944,
-0.015861907973885536,
-0.045058101415634155,
0.009954608045518398,
-0.04787861555814743,
0.034988194704055786,
0.003947022370994091,
0.04771837964653969,
0.017566382884979248,
-0.03328324854373932,
-0.002975485287606716,
-0.021645620465278625,
-0.04424913972616196,
-0.0036032467614859343,
0.0002677462762221694,
0.014652895741164684,
-0.04068943113088608,
0.020134136080741882,
-0.0070453668013215065,
0.03398820757865906,
-0.0027321611996740103,
-0.01700405403971672,
0.02191670425236225,
-0.045753251761198044,
0.016612473875284195,
0.0429590605199337,
0.010779625736176968,
-0.055118776857852936,
0.0027369707822799683,
0.015025249682366848,
-0.05126103013753891,
0.02048291452229023,
0.007881146855652332,
0.004827471449971199,
0.028517916798591614,
-0.006731303408741951,
-0.02744557335972786,
0.006743865553289652,
0.003986638505011797,
0.002464782912284136,
0.05097772926092148,
0.017784705385565758,
-0.06841064244508743,
-0.03457395359873772,
0.000698902877047658,
-0.029116934165358543,
-0.03853626549243927,
0.012587347067892551,
0.04484544321894646,
0.026793548837304115,
-0.09582656621932983,
0.020040448755025864,
-0.04641139134764671,
-0.024633899331092834,
0.013440893962979317,
-0.013606267049908638,
0.0028771476354449987,
-0.02564847283065319,
0.04529104381799698,
0.04175400733947754,
0.012426263652741909,
-0.026884686201810837,
-0.04663826897740364,
-0.05694706737995148,
0.031150681897997856,
-0.004976372234523296,
0.023416146636009216,
0.011221565306186676,
-0.04786098748445511,
0.04901643469929695,
0.021398115903139114,
-0.0026239166036248207,
-0.02700856514275074,
-0.0073420642875134945,
0.018347276374697685,
-0.02270757220685482,
-0.003383726580068469,
0.014377575367689133,
-0.01443600282073021,
-0.00519911153241992,
0.030843643471598625,
0.042602211236953735,
0.02692815661430359,
0.02587069943547249,
0.042204827070236206,
-0.019446514546871185,
-0.005545837339013815,
-0.01282001193612814,
0.025269970297813416,
-0.006132175680249929,
-0.0013516456820070744,
-0.0005897104274481535,
0.009405050426721573,
0.0241262074559927,
0.014160443097352982,
-0.06966527551412582,
0.05012893304228783,
0.013236929662525654,
0.006363188847899437,
-0.039345212280750275,
-0.009681505151093006,
0.006550755817443132,
-0.0289959404617548,
0.0011220085434615612,
0.0038441012147814035,
0.022719083353877068,
0.0026527782902121544,
0.036302778869867325,
0.0403544083237648,
0.0421566404402256,
-0.008692609146237373,
-0.06352666765451431,
-0.02390293776988983,
0.0015198771143332124,
0.019883455708622932,
-0.06927498430013657,
-0.0116913802921772,
0.04294903948903084,
0.031458303332328796,
0.00692284619435668,
0.012169559486210346,
-0.023987598717212677,
-0.027539527043700218,
-0.055555559694767,
0.0018210518173873425,
-0.03260991349816322,
0.03334742411971092,
0.030155254527926445,
0.043755266815423965,
0.02856634557247162,
-0.0010685145389288664,
-0.0208580419421196,
-0.018936172127723694,
-0.09653365612030029,
0.013726961798965931,
-0.047955263406038284,
-0.0332077331840992,
-0.009274831973016262,
-0.029137391597032547,
-0.020253349095582962,
-0.013164039701223373,
-0.017948433756828308,
-0.027785273268818855,
0.04587918519973755,
-0.053712148219347,
0.03286175802350044,
-0.06769706308841705,
-0.04505392536520958,
-0.03893614560365677,
0.022760462015867233,
0.05763673409819603,
-0.008880136534571648,
0.036931104958057404,
-0.018192196264863014,
-0.024732761085033417,
-0.005802994128316641,
-0.004362819716334343,
0.049028292298316956,
0.03843522071838379,
0.01624128222465515,
0.022651659324765205,
0.03821537271142006,
-0.02915465086698532,
-0.008205394260585308,
0.05609526112675667,
0.045921213924884796,
0.019558561965823174,
-0.034978222101926804,
-0.037350818514823914,
-0.012373611330986023,
-0.01951003633439541,
-0.007638191804289818,
0.05849713459610939,
-0.007808262947946787,
-0.0050596571527421474,
0.0060524484142661095,
0.016681112349033356,
0.01521988119930029,
0.04920639842748642,
0.026181645691394806,
0.006706842686980963,
-0.0008886268478818238,
-0.03521663695573807,
-0.03151598200201988,
0.021252786740660667,
0.014129327610135078,
0.021497629582881927,
0.01041658129543066,
0.003999252337962389,
-0.015211964026093483,
0.033327631652355194,
0.01863395981490612,
-0.02473059669137001,
0.02485513500869274,
0.0019696250092238188,
-0.009688667953014374,
-0.010701457969844341,
0.007977738045156002,
-0.006572590209543705,
0.050024501979351044,
0.02737952023744583,
0.06565336883068085,
0.01712661422789097,
-0.056218136101961136,
-0.04460063576698303,
0.021188318729400635,
0.04275311902165413,
0.01216663047671318,
-0.045917194336652756,
-0.039695050567388535,
-0.01980990543961525,
0.024983832612633705,
-0.027734501287341118,
0.05659390985965729,
0.006700280122458935,
0.04656323418021202,
-0.016097277402877808,
-0.04265826195478439,
-0.026249973103404045,
0.0429992638528347,
0.007257153280079365,
-0.011479661799967289,
-0.01467437669634819,
-0.016111379489302635,
0.024442126974463463,
0.020784445106983185,
0.056341394782066345,
0.04235745593905449,
0.0007883563521318138,
0.02955547720193863,
0.023840177804231644,
0.020728887990117073,
0.013625813648104668,
-0.08092287927865982,
0.035375092178583145,
-0.012820536270737648,
-0.009847063571214676,
0.03187309950590134,
-0.0367891862988472,
-0.03450111299753189,
0.03273351117968559,
0.01435320358723402,
0.0008568660705350339,
0.025224430486559868,
-0.06653213500976562,
0.03646796941757202,
0.01968446932733059,
-0.00842897966504097,
0.06410419940948486,
0.0241094920784235,
-0.03739100322127342,
-0.003390190191566944,
-0.03311995044350624,
0.003766713198274374,
-0.052676115185022354,
0.028492396697402,
-0.017374329268932343,
-0.002920223865658045,
-0.03087642975151539,
0.07106433808803558,
-0.031437087804079056,
-0.014514223672449589,
0.01374144945293665,
-0.03213723376393318,
0.0022506832610815763,
0.023774204775691032,
-0.05201566591858864,
-0.008034273982048035,
0.006139989942312241,
0.00001775653254298959,
0.003008357249200344,
-0.011153814382851124,
-0.007639924995601177,
-0.03330423682928085,
0.034848250448703766,
0.021292785182595253,
-0.020688166841864586,
0.013631457462906837,
-0.027229366824030876,
0.01763731800019741,
0.02267746813595295,
-0.016613580286502838,
0.07467375695705414,
0.016214439645409584,
0.014878694899380207,
0.038480278104543686,
-0.013571004383265972,
-0.029686667025089264,
0.03417721390724182,
-0.0009376564412377775,
0.022026613354682922,
-0.022014619782567024,
0.02023017220199108,
0.027547422796487808,
0.0070357429794967175,
-0.04195069521665573,
0.018853764981031418,
0.004639921709895134,
-0.010154063813388348,
0.002196177374571562,
-0.040118880569934845,
-0.02240176498889923,
-0.038568414747714996,
-0.02062443271279335,
-0.015410271473228931,
0.020224740728735924,
-0.036390211433172226,
-0.03249271214008331,
-0.017382251098752022,
0.007218542974442244,
0.018764764070510864,
0.02255386859178543,
-0.005639853421598673,
-0.04366128891706467,
-0.008912281133234501,
0.009639490395784378,
-0.005968338344246149,
0.05963096022605896,
-0.003776463447138667,
-0.02176288515329361,
-0.010709905996918678,
-0.007955996319651604,
0.06538564711809158,
-0.020668303593993187,
-0.03847573325037956,
0.037230752408504486,
0.021500403061509132,
0.00027531757950782776,
0.021148163825273514,
-0.002869849558919668,
0.039936818182468414,
0.03690682724118233,
-0.005145091563463211,
-0.03249794989824295,
-0.004378440789878368,
-0.02334349974989891,
0.020698362961411476,
0.0030086301267147064,
-0.0011530208867043257,
-0.00850987620651722,
0.02275916375219822,
0.0069036283530294895,
-0.014220698736608028,
0.01468780729919672,
0.015481939539313316,
0.012830253690481186,
-0.07619604468345642,
0.008654888719320297,
0.06280175596475601,
-0.016949303448200226,
-0.017207534983754158,
0.019027231261134148,
-0.05903744697570801,
-0.007503824308514595,
0.07365183532238007,
-0.001961407018825412,
0.017838118597865105,
0.00986018031835556,
-0.004496156238019466,
-0.01719805970788002,
-0.025070082396268845,
0.021726837381720543,
-0.025178272277116776,
0.02670437842607498,
0.020260414108633995,
-0.0689840242266655,
-0.023756330832839012,
0.046966660767793655,
0.02213378995656967,
-0.007237848360091448,
0.0061693815514445305,
0.0263819582760334,
0.03698473796248436,
-0.0055701592937111855,
-0.008711006492376328,
-0.04204419627785683,
0.03911140188574791,
-0.02281244844198227,
0.018760057166218758,
0.025165794417262077,
-0.018096935003995895,
0.045193254947662354,
0.028061149641871452,
0.011832931078970432,
-0.0523703396320343,
0.0009282820974476635,
-0.09098262339830399,
-0.00827204342931509,
0.021753128618001938,
-0.03248251974582672,
0.0032532059121876955,
-0.004166497848927975,
0.014519764110445976,
0.007961050607264042,
0.02237594686448574,
-0.015180791728198528,
-0.020242683589458466,
-0.003437529318034649,
-0.04523792490363121,
-0.03642699494957924,
0.05994827300310135,
-0.00861780159175396,
-0.013699114322662354,
0.03920479118824005,
-0.02722781151533127,
0.01554051786661148,
0.017177369445562363,
0.03302542865276337,
-0.02152177132666111,
0.02214072085916996,
-0.026809824630618095,
0.009649737738072872,
-0.04691510275006294,
-0.025146108120679855,
0.14772526919841766,
0.044691164046525955,
0.007751024328172207,
-0.022823648527264595,
0.04398799315094948,
-0.0035985149443149567,
0.0346364751458168,
-0.051706865429878235,
0.003409033175557852,
-0.0033702878281474113,
-0.025256777182221413,
0.011507711373269558,
0.05107410252094269,
0.012786926701664925,
-0.013216352090239525,
0.021494431421160698,
-0.004403930157423019,
-0.013695867732167244,
-0.008882889524102211,
0.060278698801994324,
0.00731970090419054,
0.004503966774791479,
-0.03461505472660065,
0.03809956833720207,
0.007124169729650021,
0.015610603615641594,
-0.03520874306559563,
0.0028373682871460915,
0.008156298659741879,
-0.03725103288888931,
-0.018811292946338654,
0.03510398790240288,
0.011898760683834553,
-0.012479985132813454,
-0.023039525374770164,
0.03478572890162468,
0.04525953158736229,
-0.028769049793481827,
0.027046404778957367,
-0.0010386117501184344,
0.04819473251700401,
-0.013075857423245907,
0.025976866483688354,
0.002342985477298498,
-0.03891073167324066,
0.00012099271407350898,
-0.01886218786239624,
0.05401497334241867,
-0.016054701060056686,
-0.007738935761153698,
-0.004746904596686363,
-0.026375891640782356,
0.040872521698474884,
-0.04616773501038551,
0.024607760831713676,
-0.005220968276262283,
0.013629955239593983,
-0.026543820276856422,
0.04083793982863426,
-0.0037032291293144226,
0.029662497341632843,
-0.01281560305505991,
0.0016648154705762863,
0.008691241964697838,
-0.004378341604024172,
-0.03543629124760628,
-0.008244025520980358,
0.02678505890071392,
-0.01696711778640747,
-0.01061992347240448,
-0.05388925224542618,
-0.0018059936119243503,
-0.02338113822042942,
-0.001619501505047083,
0.02885243110358715,
0.027215708047151566,
0.02376561611890793,
0.01615484058856964,
0.001955003710463643,
-0.027252694591879845,
-0.08030974864959717,
0.056211940944194794,
0.010278533212840557,
-0.05132395774126053,
0.011230811476707458,
-0.007969161495566368,
0.034048616886138916,
0.04674699902534485,
-0.0034825371112674475,
0.01718180626630783,
-0.013480573892593384,
0.0631493404507637,
0.019260769709944725,
-0.043534036725759506,
-0.0002903151325881481,
0.032909881323575974,
0.0005159580614417791,
-0.011178568936884403,
-0.017997536808252335,
0.027007728815078735,
0.012035627849400043,
0.05123407766222954,
-0.0065663945861160755,
0.02824277989566326,
-0.03390371426939964,
-0.01396132167428732,
0.04418131336569786,
-0.03799000382423401,
-0.005550054367631674,
0.03205676004290581,
0.04272153973579407,
-0.04493171349167824,
-0.001424906775355339,
0.0032104181591421366,
-0.002577015897259116,
0.016055477783083916,
-0.00683715520426631,
-0.02557644248008728,
-0.022845834493637085,
-0.009793387725949287,
-0.014319482259452343,
-0.017146766185760498,
0.0037346736062318087,
-0.012899757362902164,
-0.005280007142573595,
-0.03788084536790848,
-0.028784528374671936,
-0.04227067902684212,
0.04216766729950905,
-0.009579859673976898,
-0.008016563951969147,
0.014714057557284832,
-0.008427601307630539,
-0.01060581672936678,
-0.01884513348340988,
0.008266755379736423,
-0.007807510904967785,
0.005624780897051096,
0.02329442836344242,
-0.028134578838944435,
0.00799782294780016,
-0.01200328953564167,
-0.01893901824951172,
0.03966138884425163,
0.031801704317331314,
0.00751558318734169,
0.02152303047478199,
-0.04590258747339249,
-0.012368351221084595,
0.08378618210554123,
-0.032577063888311386,
-0.004949846304953098,
0.012700080871582031,
-0.037406761199235916,
0.01723247952759266,
-0.014520900323987007,
0.02634960599243641,
0.017644915729761124,
-0.0017133774235844612,
0.02905242145061493,
-0.0006278317887336016,
-0.03506844863295555,
0.025074485689401627,
-0.06504172831773758,
-0.02983781136572361,
0.009007919579744339,
-0.02091916836798191,
0.03203272819519043,
-0.00223880959674716,
0.05985818803310394,
0.005610370077192783,
0.01713126339018345,
-0.01557349506765604,
-0.012288161553442478,
-0.061205487698316574,
0.013933585956692696,
0.014422884210944176,
0.039356693625450134,
0.028634551912546158,
-0.023734882473945618,
0.0012297076173126698,
0.051567789167165756,
-0.07215453684329987,
0.020678598433732986,
-0.01905175670981407,
0.0023392713628709316,
-0.04694593697786331,
-0.01655815914273262,
-0.028596170246601105,
0.005798759404569864,
0.020257562398910522,
0.05364348739385605,
0.03157158941030502,
0.022841069847345352,
-0.013184142298996449,
-0.037788789719343185,
-0.005695131607353687,
0.00467882351949811,
0.023768465965986252,
0.011686827056109905,
0.08149366080760956,
-0.006822980474680662,
0.017512140795588493,
0.05213845521211624,
0.020120982080698013,
0.008331293240189552,
-0.038145847618579865,
0.04034392163157463,
0.027952391654253006,
0.013056362979114056,
-0.006166867911815643,
-0.016322627663612366,
0.006683733314275742,
-0.04919708892703056,
0.017036402598023415,
0.019869405776262283,
0.01899607479572296,
0.008105846121907234,
-0.0003502387262415141,
-0.039213526993989944,
-0.04006111994385719,
0.01579899899661541,
-0.012252341024577618,
-0.05291349068284035,
0.014935197308659554,
-0.02780970185995102,
0.03417452797293663,
-0.028037741780281067,
-0.015287821181118488,
-0.01865738444030285,
0.027613915503025055,
0.0162806436419487,
0.04419715330004692,
-0.027825936675071716,
0.010533147491514683,
-0.033892255276441574,
-0.012473903596401215,
0.02965148165822029,
-0.0012487622443586588,
-0.008094586431980133,
-0.05045656859874725,
-0.02978016808629036,
-0.03520545735955238,
0.02092440240085125,
-0.02338353730738163,
-0.04771307483315468,
-0.051416050642728806,
0.0296124629676342,
-0.0028420642483979464,
0.04760273918509483,
0.000014057211046747398,
0.009739995934069157,
-0.018646730110049248,
-0.0793369859457016,
0.018668167293071747,
-0.006091085262596607,
0.002239733934402466,
-0.08574157953262329,
-0.04392236843705177,
-0.018324516713619232,
0.03540423512458801,
0.048537589609622955,
0.02195848524570465,
-0.012262861244380474,
0.02856450527906418,
-0.024847503751516342,
0.024363627657294273,
-0.025685308501124382,
-0.005476414691656828,
-0.018364915624260902,
-0.02789001166820526,
-0.013468512333929539,
-0.026378003880381584,
-0.05016113817691803,
0.01708029955625534,
0.05149010196328163,
-0.003938117530196905,
-0.011451945640146732,
-0.0023972257040441036,
-0.0033484636805951595,
0.045918624848127365,
-0.001829994609579444,
-0.04539552703499794,
0.023955602198839188,
0.01638766936957836,
0.008686666376888752,
0.031796764582395554,
-0.046555351465940475,
-0.04797780513763428,
0.03823075070977211,
-0.022902067750692368,
-0.018482737243175507,
-0.03516450151801109,
-0.053719036281108856,
0.0279936995357275,
-0.06384553760290146,
-0.01258053258061409,
0.042701344937086105,
-0.033985208719968796,
-0.020843200385570526,
0.045437708497047424,
0.019893808290362358,
0.02240862138569355,
0.03241894021630287,
0.05323556810617447,
-0.007563508115708828,
-0.012788242660462856,
0.002071160124614835,
0.016904480755329132,
-0.018680796027183533,
-0.024268247187137604,
0.03184811770915985,
0.03434191271662712,
0.013207150623202324,
-0.0022684670984745026,
-0.012784037739038467,
0.021891307085752487,
0.016880590468645096,
-0.016332274302840233,
0.029776906594634056,
-0.025245405733585358,
0.013733777217566967,
0.05227327719330788,
0.00031985974055714905,
0.06687752902507782,
-0.04225717484951019,
0.044083643704652786,
0.024042770266532898,
0.023118458688259125,
-0.009324048645794392,
0.04379544034600258,
-0.010737438686192036,
0.02338939718902111,
0.013682817108929157,
0.01781168021261692,
-0.018336942419409752,
-0.0279063917696476,
0.03833996504545212,
-0.04094747453927994,
0.005311328452080488,
0.03999283164739609,
-0.015535295009613037,
0.028544919565320015,
-0.017873167991638184,
0.0021416835952550173,
-0.024581070989370346,
0.021060805767774582,
0.022255519405007362,
-0.013100262731313705,
-0.04840236157178879,
0.013033246621489525,
-0.024950768798589706,
0.05410577356815338,
-0.05815982446074486,
-0.010675834491848946,
-0.04156225174665451,
-0.004547338932752609,
-0.012736298143863678,
0.010324531234800816
] |
<p>What's the physical interpretation of constants in <a href="http://en.wikipedia.org/wiki/wave%27s_equation" rel="nofollow">wave equation</a> and <a href="http://en.wikipedia.org/wiki/Diffusion_equation" rel="nofollow">diffusion equation</a>?</p>
<p>$$u_{tt}=c^2u_{xx},$$</p>
<p>$$u_{t}=ku_{xx}.$$</p>
<p>Please introduce some reference about mathematical modeling of physical phenomenons such as wave, shocks and diffusion equation. </p>
| 10,661 |
[
-0.004298364277929068,
-0.01795646734535694,
-0.024291707202792168,
-0.036468494683504105,
0.01774122379720211,
-0.0016468929825350642,
-0.028063444420695305,
-0.04333820194005966,
0.00818604789674282,
-0.056175630539655685,
0.04069845378398895,
0.02600361593067646,
0.058949217200279236,
0.01643429882824421,
0.04484328627586365,
0.014164643362164497,
0.010939753614366055,
-0.011048532091081142,
-0.03171006962656975,
0.008215458132326603,
0.030779289081692696,
0.014304907992482185,
-0.00659983791410923,
0.015228554606437683,
-0.016835741698741913,
0.07167788594961166,
0.014332989230751991,
0.0379633754491806,
0.03998318314552307,
0.03249511122703552,
0.00400480767711997,
-0.04691864922642708,
0.005426953546702862,
0.029308678582310677,
-0.01375249121338129,
0.03205467760562897,
-0.03281404823064804,
-0.02108703926205635,
-0.01450798474252224,
0.0007408057572320104,
-0.02816055715084076,
-0.01694858819246292,
-0.010173830203711987,
0.025327662006020546,
0.01411511842161417,
0.00951484963297844,
0.05357978120446205,
-0.025419218465685844,
0.014047453179955482,
-0.04263429343700409,
0.07265658676624298,
-0.00035173690412193537,
0.03497330844402313,
0.029943391680717468,
-0.034307487308979034,
0.029649414122104645,
0.08001389354467392,
0.07905110716819763,
-0.0314258337020874,
-0.06075214594602585,
0.013102944940328598,
0.017409052699804306,
0.020092591643333435,
-0.0207199864089489,
0.0006830932688899338,
0.06643547117710114,
-0.003063545096665621,
-0.060738448053598404,
0.010074052028357983,
0.00616163806989789,
0.012033194303512573,
0.004272592719644308,
0.03235241025686264,
-0.028958581387996674,
0.03428143262863159,
-0.043929073959589005,
-0.018169129267334938,
0.008188829757273197,
0.011315871961414814,
0.054185111075639725,
-0.01103513315320015,
0.0017455348279327154,
0.01118954923003912,
0.007369561120867729,
-0.009334629401564598,
-0.001761781401000917,
0.07188230752944946,
0.013559550046920776,
0.03821813315153122,
0.0272868350148201,
-0.004277246072888374,
0.009484750218689442,
0.010764135047793388,
0.007429629098623991,
-0.01260437723249197,
0.0206611268222332,
0.03930221125483513,
0.031126951798796654,
0.01782769337296486,
-0.031219417229294777,
0.015923622995615005,
-0.013078376650810242,
0.026703661307692528,
0.05564417690038681,
-0.006840378511697054,
-0.023693665862083435,
-0.03181975707411766,
0.023518554866313934,
-0.005515603814274073,
-0.024311240762472153,
-0.0342777818441391,
0.002190761733800173,
-0.010675002820789814,
0.01049588993191719,
0.029439974576234818,
-0.003579776966944337,
-0.006097122561186552,
-0.04638001322746277,
0.06165769323706627,
0.05973665788769722,
0.05919910594820976,
-0.046419329941272736,
0.026821289211511612,
0.02578135021030903,
-0.0852368026971817,
0.002353064715862274,
0.02376198209822178,
0.006872189696878195,
-0.02095462754368782,
0.05253634601831436,
-0.028792744502425194,
-0.017550643533468246,
0.02031857520341873,
0.006523742340505123,
0.0623079314827919,
-0.0038782493211328983,
-0.09664719551801682,
-0.06325697153806686,
0.016979945823550224,
0.0025195865891873837,
-0.028447328135371208,
-0.06264133006334305,
0.01477364543825388,
0.033588919788599014,
0.0494050569832325,
-0.030848415568470955,
-0.03769318014383316,
-0.012714946642518044,
0.04423270747065544,
0.02401641383767128,
-0.024840783327817917,
-0.01356382668018341,
-0.0004016664170194417,
-0.015404706820845604,
-0.007624664809554815,
-0.06988842785358429,
-0.020773762837052345,
0.040088240057229996,
-0.008691909722983837,
-0.00914875976741314,
0.04133932292461395,
-0.033923592418432236,
-0.02619371935725212,
0.02334652468562126,
-0.03241078928112984,
-0.019474681466817856,
0.06309282779693604,
-0.009000662714242935,
0.030545812100172043,
0.049936097115278244,
0.014717783778905869,
0.03101237118244171,
-0.01225186511874199,
0.020146390423178673,
0.017621418461203575,
-0.014627130702137947,
-0.023281719535589218,
0.029990969225764275,
-0.03241702914237976,
0.029824718832969666,
-0.0425863191485405,
-0.04730205610394478,
-0.006640687584877014,
0.0032900162041187286,
-0.007348516024649143,
0.012706071138381958,
-0.004876040853559971,
0.010361484251916409,
-0.006886852439492941,
-0.05315117537975311,
0.008539708331227303,
-0.06705930083990097,
0.04375807195901871,
-0.023623274639248848,
0.012934643775224686,
0.022945242002606392,
0.00971951987594366,
-0.02517261728644371,
-0.049436356872320175,
-0.059183329343795776,
0.005359370727092028,
0.04683065786957741,
0.007219051476567984,
-0.01006260421127081,
0.009671277366578579,
0.06120165437459946,
0.02106909081339836,
-0.02778167836368084,
0.06012764945626259,
-0.026762988418340683,
0.009651655331254005,
0.03148069605231285,
-0.04459407553076744,
0.02819879539310932,
-0.031471867114305496,
-0.023065706714987755,
-0.00001619103022676427,
-0.039702001959085464,
-0.01121332123875618,
0.03135818988084793,
-0.04458324983716011,
0.051601894199848175,
0.05785676836967468,
0.04137992486357689,
0.02523200772702694,
0.0688551813364029,
-0.022337455302476883,
0.09368198364973068,
0.004192692693322897,
-0.03871968761086464,
-0.03193936496973038,
0.010078433901071548,
0.03703833371400833,
0.034076154232025146,
-0.026758108288049698,
0.016677608713507652,
0.025374211370944977,
0.04713062569499016,
0.06834191828966141,
-0.0014082837151363492,
-0.0009306588326580822,
-0.022243613377213478,
0.01655407063663006,
0.022983673959970474,
0.013110068626701832,
0.02375282160937786,
-0.006984675768762827,
0.010110790841281414,
0.020297512412071228,
-0.05985448509454727,
-0.04137092083692551,
0.04780687764286995,
-0.008405736647546291,
0.010361380875110626,
0.005171388387680054,
0.005482703913003206,
0.027406638488173485,
-0.009829084388911724,
0.016985133290290833,
0.044938281178474426,
-0.018098561093211174,
-0.004886375740170479,
0.000882948748767376,
-0.01464057620614767,
-0.026204243302345276,
0.027487952262163162,
-0.023480821400880814,
-0.022816700860857964,
0.012009984813630581,
-0.020897092297673225,
-0.04043808579444885,
-0.018215661868453026,
-0.04206632450222969,
-0.023783089593052864,
-0.019946029409766197,
0.041705552488565445,
0.023461490869522095,
0.027574559673666954,
-0.0474172979593277,
-0.042410675436258316,
-0.0016558162169530988,
-0.05535932630300522,
-0.0035675885155797005,
0.002490387065336108,
-0.04504571855068207,
0.05788193643093109,
-0.024961892515420914,
-0.03739401325583458,
0.043836917728185654,
-0.015597301535308361,
0.030555421486496925,
0.02623274177312851,
-0.057081520557403564,
-0.05688127502799034,
-0.014736046083271503,
-0.013505532406270504,
0.04098790884017944,
0.011432071216404438,
0.015418636612594128,
0.05255652591586113,
-0.016346188262104988,
-0.0009859073907136917,
0.006100818049162626,
-0.031342875212430954,
-0.05197695270180702,
-0.01345168799161911,
-0.016522573307156563,
0.0345272421836853,
-0.003450104035437107,
0.054759085178375244,
0.028595399111509323,
-0.068181112408638,
0.019483746960759163,
-0.052976470440626144,
-0.014316425658762455,
0.04463996738195419,
-0.03239765390753746,
0.06203891709446907,
0.002890887437388301,
-0.03539193794131279,
0.06643069535493851,
0.028288783505558968,
-0.024520693346858025,
-0.022705361247062683,
0.006409104447811842,
-0.018275709822773933,
-0.008323056623339653,
-0.012126104906201363,
0.044747646898031235,
-0.01040344126522541,
0.019248250871896744,
0.028779320418834686,
0.015751589089632034,
0.04732709005475044,
0.0006374565418809652,
0.0004284944152459502,
-0.014205391518771648,
-0.022591572254896164,
0.014467310160398483,
0.05438771843910217,
0.02830296941101551,
-0.020359737798571587,
0.019597230479121208,
-0.030167099088430405,
0.01944670081138611,
0.04775756597518921,
-0.03886757791042328,
0.014121703803539276,
0.03119763918220997,
-0.016037536785006523,
-0.04008728265762329,
0.02569739520549774,
-0.019910616800189018,
-0.035320065915584564,
-0.058716196566820145,
0.0254252627491951,
0.030844567343592644,
-0.015496804378926754,
-0.0019353998359292746,
-0.0038445808459073305,
0.027719847857952118,
-0.019168589264154434,
-0.012500379234552383,
-0.020982131361961365,
-0.012689036317169666,
0.0324212908744812,
-0.040286242961883545,
-0.007179863750934601,
0.07748700678348541,
0.021400725468993187,
0.028815696015954018,
-0.016496853902935982,
-0.047887030988931656,
-0.00724207516759634,
-0.06948304176330566,
-0.03856893256306648,
-0.005280531942844391,
0.06859255582094193,
-0.002430323511362076,
0.05589999631047249,
0.028899380937218666,
0.009536751545965672,
0.056786179542541504,
0.0064614941366016865,
-0.09467202425003052,
0.023311885073781013,
-0.01154255773872137,
-0.038323815912008286,
-0.01045201439410448,
-0.012366351671516895,
-0.004415011499077082,
-0.013184760697185993,
-0.032539185136556625,
0.00189548812340945,
-0.01071447879076004,
-0.07234140485525131,
0.034307338297367096,
-0.025787226855754852,
-0.03565229848027229,
-0.04032129794359207,
0.04001912847161293,
0.03319741412997246,
-0.009987042285501957,
0.003870574990287423,
0.04918608069419861,
-0.018113484606146812,
0.01118827611207962,
-0.01779693178832531,
-0.031080065295100212,
0.07528575509786606,
0.013405148871243,
0.018279626965522766,
-0.009434384293854237,
-0.01623750664293766,
0.02056656964123249,
0.002900258172303438,
0.07288610190153122,
0.007283046375960112,
-0.011529744602739811,
-0.04539762809872627,
-0.05370743200182915,
0.00529542425647378,
-0.009409300051629543,
0.04810004681348801,
0.004732570145279169,
-0.006168578285723925,
0.062163613736629486,
0.004140014760196209,
0.008473365567624569,
0.025223731994628906,
0.04170723631978035,
0.009349091909825802,
-0.022937005385756493,
-0.018888577818870544,
-0.015613235533237457,
-0.016758035868406296,
0.009430242702364922,
0.014776303432881832,
-0.008456631563603878,
-0.006884455215185881,
0.026738164946436882,
0.01447844598442316,
0.01065835077315569,
-0.02664767950773239,
-0.022687556222081184,
0.034324925392866135,
0.013822192326188087,
-0.014521103352308273,
-0.04025756195187569,
-0.006941177416592836,
0.06033947318792343,
-0.0015139076858758926,
-0.02774656005203724,
-0.00863393023610115,
-0.09503842890262604,
0.017679549753665924,
-0.004551967140287161,
0.02172832190990448,
-0.00012887234333902597,
-0.016970200464129448,
-0.05915645509958267,
0.00012417607649695128,
0.03748515248298645,
-0.013726264238357544,
0.035882700234651566,
0.01719159446656704,
-0.03828520327806473,
0.01908469945192337,
0.014101695269346237,
-0.0046869320794939995,
0.03649815917015076,
0.014575091190636158,
0.0005732711288146675,
-0.03097619116306305,
0.021079806610941887,
-0.011439246125519276,
0.03870771452784538,
0.010135039687156677,
0.048542656004428864,
-0.03995519503951073,
-0.016547664999961853,
0.02319904789328575,
0.022448988631367683,
-0.016878632828593254,
-0.05392714962363243,
-0.008187023922801018,
0.027159366756677628,
0.00958977174013853,
0.03147691860795021,
-0.01045695785433054,
-0.04776305332779884,
0.01543582882732153,
0.012012474238872528,
0.00470656668767333,
0.0165177620947361,
-0.012594807893037796,
0.05793981999158859,
0.027437275275588036,
-0.03508427366614342,
0.03792598098516464,
0.03806661069393158,
-0.022035134956240654,
-0.04274647310376167,
-0.050808150321245193,
0.022980453446507454,
-0.013410041108727455,
0.026552420109510422,
-0.041164226830005646,
0.00040643979446031153,
-0.020883331075310707,
0.015454436652362347,
-0.011492101475596428,
-0.005897512659430504,
-0.04135481268167496,
-0.010179349221289158,
-0.00877185259014368,
0.010879011824727058,
0.012773009017109871,
-0.003290757304057479,
0.03218603506684303,
0.02228095754981041,
-0.016828306019306183,
-0.056296784430742264,
-0.01573359966278076,
-0.01729303039610386,
0.015142181888222694,
0.03300381079316139,
0.016348622739315033,
0.001267871935851872,
0.0019034786382690072,
-0.0254402793943882,
0.04922032728791237,
-0.024712076410651207,
0.017161550000309944,
0.015762455761432648,
0.02018333040177822,
0.051305096596479416,
-0.028433138504624367,
-0.016369936987757683,
-0.008663780987262726,
-0.01868833415210247,
0.05953194200992584,
-0.033849019557237625,
0.09616411477327347,
0.037077419459819794,
0.04385038837790489,
-0.05362154170870781,
-0.05711503326892853,
0.055962126702070236,
-0.01135126780718565,
-0.0421915240585804,
-0.015166670083999634,
0.04052483290433884,
-0.036557845771312714,
-0.03696003183722496,
0.0018939495785161853,
0.04996618255972862,
0.0034649400040507317,
-0.04256796836853027,
0.0035546142607927322,
0.05481477826833725,
0.08196397870779037,
0.027325844392180443,
-0.0017547094030305743,
0.0024720425717532635,
-0.004367911722511053,
0.0008341369684785604,
0.026202557608485222,
0.0364103801548481,
-0.020146379247307777,
-0.043825842440128326,
-0.008068271912634373,
-0.010066209360957146,
0.0465664342045784,
-0.013797708787024021,
0.0016890710685402155,
-0.0022824080660939217,
0.0303117074072361,
-0.023839550092816353,
-0.04272172600030899,
0.026208220049738884,
-0.036861713975667953,
0.03555213287472725,
0.00033985034679062665,
0.004806585609912872,
-0.032404184341430664,
-0.0012568265665322542,
0.016322137787938118,
-0.00879085622727871,
-0.014763270504772663,
-0.02264583855867386,
0.035440269857645035,
-0.017768563702702522,
0.0023619725834578276,
-0.005470626521855593,
-0.007872669957578182,
0.02823181077837944,
-0.010286077857017517,
-0.013189153745770454,
0.03779953345656395,
0.0021874085068702698,
-0.022096965461969376,
-0.040514394640922546,
-0.05500587448477745,
0.0024073629174381495,
0.07530400902032852,
-0.05015493184328079,
0.06237342953681946,
0.030723564326763153,
-0.04061625525355339,
0.039351582527160645,
0.012819609604775906,
-0.026915330439805984,
0.005494004115462303,
0.00929118413478136,
0.01879996992647648,
-0.003246695501729846,
-0.032837096601724625,
0.021577775478363037,
0.034989964216947556,
0.0007169583113864064,
0.003036798443645239,
-0.0019836893770843744,
0.04057856276631355,
-0.06703566014766693,
-0.022830935195088387,
-0.029256019741296768,
0.056489814072847366,
-0.01315024308860302,
0.025276202708482742,
0.013502061367034912,
-0.005293563939630985,
0.038124896585941315,
-0.014401180669665337,
-0.008337278850376606,
-0.03591906651854515,
0.0028718612156808376,
-0.04711991548538208,
0.01158212311565876,
0.02667156048119068,
0.022180909290909767,
0.014272255823016167,
0.018042247742414474,
0.03335815295577049,
0.0020504824351519346,
0.02092655561864376,
0.021706078201532364,
-0.060937460511922836,
0.008057951927185059,
-0.028627118095755577,
-0.05739001929759979,
0.05618531256914139,
0.017429083585739136,
-0.0285260658711195,
-0.0004834143037442118,
-0.03730132430791855,
0.02065020240843296,
0.029586760327219963,
0.032677315175533295,
-0.029298193752765656,
0.08034830540418625,
-0.019650960341095924,
-0.007500391453504562,
-0.049820784479379654,
-0.010524614714086056,
0.09119409322738647,
0.049407679587602615,
-0.0010756191331893206,
-0.03645807504653931,
0.0031883614137768745,
-0.02140200510621071,
0.00434187101200223,
-0.02672380581498146,
0.02231741137802601,
0.013274910859763622,
0.03936679661273956,
0.03604225069284439,
0.030469799414277077,
-0.012013292871415615,
0.010327231138944626,
0.017029237002134323,
-0.03874459117650986,
-0.04688051715493202,
0.025721251964569092,
0.0037464594934135675,
-0.01320507563650608,
0.022559870034456253,
-0.016396282240748405,
0.039593975991010666,
-0.004412375390529633,
-0.005531306844204664,
-0.04908943176269531,
-0.034765053540468216,
0.04397093132138252,
0.0016748829511925578,
-0.047671712934970856,
0.01374130044132471,
-0.005486625712364912,
-0.01518157497048378,
-0.03773083910346031,
0.003114165272563696,
0.019604427739977837,
-0.04389554262161255,
-0.016315430402755737,
0.011365623213350773,
-0.003932713996618986,
-0.02582974173128605,
-0.027155617251992226,
0.0375383086502552,
-0.014345075935125351,
0.018614379689097404,
-0.021398793905973434,
0.03451554477214813,
-0.010387462563812733,
-0.00018201125203631818,
0.012408732436597347,
0.03322364762425423,
-0.011104516685009003,
-0.012218314222991467,
-0.03809983655810356,
-0.021187884733080864,
0.02788521908223629,
-0.030298739671707153,
0.004758619703352451,
-0.05281667783856392,
-0.011068101972341537,
0.01740243472158909,
0.036196138709783554,
-0.003839644603431225,
-0.03516971692442894,
-0.004150985274463892,
-0.026280712336301804,
0.05667318403720856,
-0.04647552967071533,
0.005541177466511726,
-0.015463693998754025,
-0.015446851029992104,
-0.06316282600164413,
-0.011094072833657265,
0.015404666773974895,
0.012038213200867176,
0.03580370545387268,
-0.008590646088123322,
-0.007317966781556606,
-0.010108808055520058,
-0.03765726834535599,
0.02395092323422432,
0.016474338248372078,
-0.012337830848991871,
-0.042288508266210556,
-0.0031769799534231424,
-0.010706545785069466,
0.02432609163224697,
-0.032641008496284485,
0.003100321162492037,
-0.009035766124725342,
-0.0004494354361668229,
0.0018441117135807872,
-0.03205842524766922,
-0.01586609147489071,
0.0019878072198480368,
-0.022355232387781143,
0.010256529785692692,
-0.0015863488661125302,
0.03492151200771332,
0.0372869148850441,
-0.030338382348418236,
-0.013399333693087101,
0.05227308347821236,
-0.03774487227201462,
-0.01966974139213562,
0.02057158760726452,
-0.04249213635921478,
0.02852293848991394,
0.031120512634515762,
0.023598214611411095,
0.00039623063639737666,
-0.01296547893434763,
-0.02938207983970642,
0.0109238401055336,
-0.01724575087428093,
0.0007431446574628353,
-0.028284553438425064,
0.02371356077492237,
-0.046596672385931015,
0.02189103700220585,
-0.05295918136835098,
-0.03551208972930908,
-0.042739760130643845,
0.0348624512553215,
0.018090462312102318,
-0.002673015696927905,
-0.0039893933571875095,
0.011104311794042587,
-0.014201005920767784,
0.0007884764927439392,
0.011312950402498245,
0.015622398816049099,
0.006857066880911589,
-0.008012475445866585,
0.025853518396615982,
0.020481230691075325,
0.04000932350754738,
-0.007642171811312437,
-0.04994284361600876,
0.017517467960715294,
-0.009959070943295956,
-0.04192744195461273,
0.02808740921318531,
-0.021023737266659737,
0.022038262337446213,
0.02026478201150894,
0.01128891296684742,
0.009763583540916443,
0.0509217195212841,
-0.02204994671046734,
0.022175827994942665,
-0.026175184175372124,
-0.06985101103782654,
-0.03439965471625328,
-0.03680470585823059,
0.030639057978987694,
0.027711018919944763,
-0.01957704685628414,
0.014453667216002941,
0.03110363706946373,
0.003099404973909259,
0.0067571536637842655,
0.03241002559661865,
-0.013876508921384811,
-0.018538089469075203,
0.01177277509123087,
-0.005422706250101328,
0.04660649970173836,
0.02841687947511673,
-0.02514597214758396,
0.0328044556081295,
0.008534081280231476,
0.009675828740000725,
-0.08523774892091751,
-0.006409027148038149,
0.0386417917907238,
0.01379319466650486,
0.023575270548462868,
-0.03604509308934212,
0.023778924718499184,
0.026004545390605927,
-0.02170737087726593,
-0.019481010735034943,
-0.05895646661520004,
-0.025428473949432373,
-0.008309468626976013,
-0.017002614215016365,
-0.013300147838890553,
0.06299781799316406,
0.023661797866225243,
0.01584908924996853,
-0.0007581889512948692,
0.010667288675904274,
0.028249001130461693,
-0.003283838275820017,
-0.029919065535068512,
0.006739957723766565,
0.00858275406062603,
-0.014529679901897907,
0.06445816904306412,
0.006900361273437738,
0.0007798693259246647,
0.004537075292319059,
-0.0039836931973695755,
0.0014931189361959696,
0.01366586983203888,
0.007688076235353947,
0.02251524105668068,
0.03944985941052437,
0.028237925842404366,
-0.02115035429596901,
-0.008873187936842442,
0.001722231856547296,
-0.0441611185669899,
-0.0009999246103689075,
0.02787344716489315,
-0.007630240637809038,
0.01358734630048275,
-0.03805728256702423,
-0.017217101529240608,
0.02442706935107708,
-0.015897441655397415,
-0.00891979318112135,
0.017851337790489197,
-0.029066994786262512,
-0.006857737433165312,
-0.03192167729139328,
0.018575748428702354,
-0.0348319374024868,
-0.019970839843153954,
0.0038974250201135874,
0.01088204886764288,
-0.020567188039422035,
0.03943410888314247,
-0.00041103060357272625,
-0.03921256959438324,
0.0208243690431118,
0.013752809725701809,
-0.01315978355705738,
-0.043151501566171646,
0.006850158330053091,
0.018810352310538292,
-0.02183268964290619,
-0.004754399415105581,
-0.03501058369874954,
-0.05291436240077019,
0.04124346002936363,
0.0023125680163502693,
-0.011312605813145638,
-0.02438890002667904,
-0.0165609922260046,
-0.05424816161394119,
-0.07258196920156479,
0.026175061240792274,
-0.0051645636558532715,
-0.023942435160279274,
-0.037461426109075546,
0.0071314433589577675,
-0.049444530159235,
0.05586579069495201,
0.07093895971775055,
-0.0009690093575045466,
-0.020516620948910713,
0.023533698171377182,
-0.025280646979808807,
0.028914345428347588,
-0.06582458317279816,
-0.018921008333563805,
0.004652468487620354,
-0.010151206515729427,
0.008814570493996143,
0.01865607127547264,
-0.009398029185831547,
0.04566109552979469,
0.04448283836245537,
-0.01641041599214077,
0.03596261516213417,
0.027626799419522285,
-0.02738923765718937,
-0.0015670753782615066,
0.03379984572529793,
-0.0240995641797781,
0.06509291380643845,
-0.026219863444566727,
0.01995435543358326,
0.01847778633236885,
-0.024723658338189125,
-0.03341367840766907,
0.04466035217046738,
-0.014135734178125858,
-0.012268263846635818,
0.021758539602160454,
-0.02355908416211605,
0.03644684702157974,
-0.06110252067446709,
-0.037029944360256195,
0.030137117952108383,
-0.05194404348731041,
-0.01555545162409544,
0.019422851502895355,
0.0219950582832098,
-0.010939684696495533,
0.002824468072503805,
0.02863381616771221,
0.014970011077821255,
-0.02745208702981472,
-0.012410517781972885,
0.025711193680763245,
0.03858906775712967,
-0.008382080122828484,
0.03324957191944122,
0.011783992871642113,
-0.021687084808945656,
0.016106901690363884,
0.005756754893809557,
-0.005335330497473478,
-0.04080354794859886,
-0.026915334165096283,
0.018106656149029732,
-0.0363459475338459,
-0.0204120185226202,
0.0034903138875961304,
-0.037644315510988235,
0.0897928848862648,
-0.04649902880191803,
0.005747369024902582,
-0.026087718084454536,
0.010491381399333477,
0.003967161290347576,
0.002584944013506174,
0.012364658527076244,
0.005067514255642891,
0.002109046559780836,
0.031377747654914856,
-0.011349162086844444,
-0.010710583999752998,
0.012691790238022804,
-0.06245703622698784,
0.01438503060489893,
0.0005671928520314395,
-0.02026437036693096,
-0.0006779757677577436,
-0.002938666148111224,
-0.031614769250154495,
0.0040847803466022015,
0.05016804486513138,
0.03575599193572998,
-0.027893373742699623,
0.004088860936462879,
-0.024191655218601227,
0.005266000051051378,
0.0704239085316658,
-0.07029718160629272,
-0.015044600702822208,
0.02567485347390175,
-0.005620263516902924,
0.019351642578840256,
-0.012796536087989807
] |
<p>My textbook gives the following explanation on how excess charges are spread over conductors:</p>
<blockquote>
<p>The excess charge on an isolated conductor moves entirely to the
conductor's surface. However, unless the conductor is spherical, the
charge does not distribute itself uniformly.</p>
</blockquote>
<p>I was studying for a test and there was the following question, regarding the thin-wall conducting cylindrical shell below (which is coaxial to the rod inside it):</p>
<p><img src="http://i.stack.imgur.com/jiLmD.png" alt="enter image description here"> $Q_1 > 0, Q_2 < 0$</p>
<blockquote>
<p>What is the charge on the interior and exterior surface of the
shell?</p>
</blockquote>
<p>At first I thought the excess charge on the interior surface would be zero, since all the excess charge would move to the outer surface of the shell. But according to my textbook, it is as follows:</p>
<blockquote>
<p>We consider a cylindrical Gaussian surface whose radius places it
within the shell itself. The electric field is zero at all points on
the surface since any field within a conducting material would lead to
current flow (and thus to a situation other than the electrostatic
ones being considered here), so the total electric flux through the
Gaussian surface is zero and the net charge within it is zero (by
Gauss's law). Since the central rod has charge $Q_1$, the inner
surface of the shell must have charge $Q_{in} = -Q_1 = -3.40 \times 10^{-12}\: \mathrm{C}$.</p>
<p>Since the shell is known to have total charge $Q_2 = -2.00\: Q_1$ it must
have charge $Q_{out} = Q_2 - Q_{in} = - Q_1 = -3.40 \times 10^{-12}\: \mathrm{C}$ on its
outer surface.</p>
</blockquote>
<p>So there is $-Q_1$ excess charge on the inner surface because said charges are being attracted by the rod? What if there was no rod, how would the excess charge be distributed over the shell's surface? Can I tell how the excess charge will be distributed over the surface of any non-spherical conductor, or only in special cases such as the above?</p>
| 10,662 |
[
-0.03269686922430992,
-0.010854380205273628,
0.006011696998029947,
-0.024880317971110344,
0.03043263964354992,
-0.039064954966306686,
-0.0193763580173254,
-0.022484369575977325,
0.005156523082405329,
-0.034670501947402954,
0.06069525331258774,
0.047767095267772675,
0.09501010924577713,
0.01862512156367302,
0.003428927157074213,
-0.001350704929791391,
-0.0014602143783122301,
-0.01974308490753174,
0.014393365010619164,
-0.05139673501253128,
-0.016705233603715897,
0.016606321558356285,
-0.0051793926395475864,
0.009119024500250816,
-0.03222927078604698,
0.027049478143453598,
-0.01799636520445347,
-0.026914475485682487,
0.016564324498176575,
0.05709940940141678,
-0.0017250224482268095,
-0.020151827484369278,
0.023443054407835007,
0.006895770784467459,
0.026177799329161644,
-0.008480376563966274,
-0.029348574578762054,
-0.044389788061380386,
-0.0037225133273750544,
0.019526535645127296,
-0.0019610614981502295,
-0.005757277365773916,
0.014507628977298737,
0.05260848253965378,
0.001037832349538803,
0.011605244129896164,
0.023634048178792,
-0.008160609751939774,
0.033112939447164536,
-0.0886264368891716,
-0.0018603471107780933,
0.0057393405586481094,
0.06590958684682846,
0.031684406101703644,
0.027089541777968407,
-0.007389735896140337,
0.07365093380212784,
0.05579301342368126,
0.033553242683410645,
-0.04380038008093834,
-0.02562984637916088,
-0.006208457518368959,
-0.041161056607961655,
-0.025926705449819565,
-0.021011976525187492,
0.02418314665555954,
-0.0175494197756052,
-0.003871155669912696,
0.002019953215494752,
-0.02793777547776699,
0.03547707945108414,
0.01849624142050743,
-0.016502179205417633,
-0.03258819505572319,
0.010882675647735596,
-0.02036760374903679,
0.008766858838498592,
0.01836550422012806,
-0.013042168691754341,
-0.010225344449281693,
-0.0067421137355268,
-0.0032108649611473083,
0.017665347084403038,
0.06991520524024963,
0.011873552575707436,
-0.0031615670304745436,
0.055911000818014145,
-0.028161637485027313,
0.04570322483778,
0.006017282139509916,
0.000252367666689679,
0.0230955071747303,
0.013443918898701668,
-0.021319830790162086,
0.0029182410798966885,
0.0372476689517498,
0.017865469679236412,
0.03537865728139877,
-0.03577720746397972,
-0.03693730756640434,
-0.008907194249331951,
-0.0006286517018452287,
0.03412841260433197,
0.10888609290122986,
0.014099031686782837,
-0.03599170222878456,
0.008181813172996044,
0.01718747615814209,
0.00090054637985304,
-0.005979134701192379,
-0.04775372892618179,
0.039802130311727524,
0.018818460404872894,
-0.012173191644251347,
-0.012450091540813446,
-0.03684178739786148,
0.021337082609534264,
-0.042409781366586685,
0.00439217546954751,
0.004152323585003614,
0.020535005256533623,
-0.022072212770581245,
0.010217326693236828,
-0.046992044895887375,
-0.044390540570020676,
0.04721594974398613,
0.01652030646800995,
0.004476542584598064,
-0.007736287545412779,
-0.0007448319811373949,
0.020041584968566895,
-0.013007066212594509,
0.006783742923289537,
0.027435414493083954,
-0.0019589071162045,
-0.013318756595253944,
-0.09759222716093063,
-0.05941779911518097,
0.04833531752228737,
0.020424190908670425,
0.017068419605493546,
-0.06690744310617447,
-0.032840076833963394,
0.04986170679330826,
0.04960688203573227,
-0.02010617032647133,
-0.010053997859358788,
-0.0007453372818417847,
0.05046921968460083,
-0.023368459194898605,
0.0058147115632891655,
0.018970239907503128,
-0.032778289169073105,
-0.025655988603830338,
-0.013419403694570065,
-0.022478055208921432,
0.00874324794858694,
0.03715648129582405,
0.008759980089962482,
-0.008600348606705666,
0.02754741720855236,
-0.012053261511027813,
0.02156015858054161,
-0.006551594007760286,
-0.012450272217392921,
-0.020560916513204575,
0.05248584598302841,
-0.0015972923720255494,
-0.03284980729222298,
0.04866442456841469,
0.021043188869953156,
-0.008957241661846638,
-0.0020471566822379827,
0.016842631623148918,
0.025041261687874794,
-0.0753716453909874,
0.01078601460903883,
-0.08817043155431747,
-0.008421970531344414,
0.015539667569100857,
-0.062184903770685196,
-0.042820364236831665,
0.00035716796992346644,
0.0076314182952046394,
0.034126803278923035,
0.05194436013698578,
-0.019282639026641846,
-0.03821437433362007,
0.004689950030297041,
-0.006845058407634497,
-0.036865293979644775,
-0.005822355393320322,
0.06913401931524277,
0.025571905076503754,
-0.0535944327712059,
-0.005028754938393831,
-0.016622617840766907,
0.03272412717342377,
-0.02497711032629013,
-0.014749228022992611,
-0.002647695131599903,
0.03587977960705757,
-0.014955777674913406,
-0.0023567669559270144,
0.02286781184375286,
0.016929689794778824,
0.026576921343803406,
0.02452513948082924,
0.009696723893284798,
-0.049612123519182205,
0.011761056259274483,
-0.00678621418774128,
-0.010635442100465298,
0.04490319639444351,
0.015115149319171906,
-0.04640820622444153,
0.026436876505613327,
0.00042977023986168206,
-0.011413604021072388,
0.05185229703783989,
-0.012487553060054779,
0.05541061609983444,
0.0359434112906456,
0.01750277541577816,
-0.038833070546388626,
0.022677980363368988,
-0.007839750498533249,
-0.00592995248734951,
-0.019937152042984962,
-0.05142663046717644,
-0.04655037820339203,
0.006452260073274374,
0.04865862801671028,
0.02075769379734993,
-0.01237242016941309,
-0.016352931037545204,
0.0007968404097482562,
0.02711358480155468,
0.017555728554725647,
-0.030360616743564606,
-0.04369726404547691,
-0.046409886330366135,
0.025918684899806976,
-0.006160453427582979,
-0.017743505537509918,
-0.024880802258849144,
0.02971256710588932,
0.00510767288506031,
0.023866210132837296,
0.017680220305919647,
0.02809467539191246,
0.04141843318939209,
-0.012867649085819721,
0.03916520997881889,
-0.02296445332467556,
-0.012315814383327961,
0.05606459453701973,
-0.02668076753616333,
0.032936982810497284,
0.027455121278762817,
0.018544454127550125,
0.03360266610980034,
-0.018460771068930626,
0.023618632927536964,
0.000877050741109997,
-0.0037452855613082647,
-0.013829676434397697,
0.0009584701037965715,
0.030778616666793823,
-0.07608029991388321,
0.004191992804408073,
-0.022917144000530243,
-0.013448827899992466,
-0.013629607856273651,
0.007690231781452894,
0.052300188690423965,
0.056518375873565674,
0.027851134538650513,
-0.054182883352041245,
-0.018198858946561813,
-0.017349595203995705,
0.00010509725689189509,
0.005915732588618994,
0.0317496582865715,
-0.06372439116239548,
0.0324304960668087,
-0.04521175101399422,
-0.01685805805027485,
0.04141755402088165,
0.016352137550711632,
0.00399045692756772,
0.025170788168907166,
-0.006770949810743332,
-0.0629948079586029,
0.011212323792278767,
-0.029225090518593788,
0.010245577432215214,
-0.040006570518016815,
-0.029350223019719124,
0.08099298924207687,
0.026146063581109047,
-0.030521873384714127,
0.01292271539568901,
-0.06018844246864319,
-0.030685363337397575,
0.008268301375210285,
-0.0005313337314873934,
0.03775651380419731,
-0.006406839936971664,
0.0379701666533947,
0.0055262004025280476,
-0.0001682931324467063,
-0.04611118882894516,
-0.0343359000980854,
-0.03841446712613106,
0.00346076930873096,
-0.009079411625862122,
0.02066023461520672,
-0.04485669732093811,
-0.030660122632980347,
0.06941895931959152,
0.009378287941217422,
0.0060141864232718945,
0.02076638676226139,
-0.013516156002879143,
-0.003855258459225297,
-0.04409154877066612,
-0.013408547267317772,
0.04356097802519798,
-0.016040248796343803,
0.015548755414783955,
-0.0005669734673574567,
0.038052093237638474,
-0.014966832473874092,
-0.008094286546111107,
0.020831767469644547,
0.020335273817181587,
-0.0013796415878459811,
0.010694647207856178,
0.06654428690671921,
0.015733858570456505,
0.0439922921359539,
0.015981702134013176,
0.0040830206125974655,
0.031404588371515274,
0.020218871533870697,
-0.0018867810722440481,
0.027844997122883797,
-0.023494379594922066,
0.03925706073641777,
-0.03856242075562477,
0.04231037572026253,
-0.014377938583493233,
-0.005579258315265179,
-0.01615726388990879,
-0.004878558684140444,
0.02445201575756073,
-0.0297224260866642,
0.025211019441485405,
0.0615861751139164,
0.03734603151679039,
-0.02379993349313736,
-0.024623766541481018,
0.0023728306405246258,
-0.009853193536400795,
0.02927551232278347,
0.00032896947232075036,
-0.050798043608665466,
0.010393064469099045,
0.08626765012741089,
-0.0012482970487326384,
-0.013309383764863014,
0.0026568991597741842,
0.011640188284218311,
-0.052514441311359406,
-0.021640580147504807,
-0.015891240909695625,
0.05703970789909363,
0.003788796253502369,
0.03565576300024986,
0.029320377856492996,
0.01959211193025112,
0.007395831402391195,
0.04875854775309563,
-0.04177436605095863,
-0.021053573116660118,
0.006868684198707342,
-0.013182621449232101,
-0.0007741510053165257,
-0.038739655166864395,
-0.0019648398738354445,
0.006660735700279474,
-0.03642554208636284,
-0.026621470227837563,
-0.008907933719456196,
-0.054995980113744736,
0.04340006783604622,
-0.025019844993948936,
-0.03597429394721985,
-0.02749646082520485,
0.05335003137588501,
0.03145003691315651,
-0.05898125469684601,
0.0017937137745320797,
0.01141368318349123,
-0.03894173353910446,
-0.013777010142803192,
0.007915484718978405,
0.022998269647359848,
0.028286468237638474,
0.0658724308013916,
-0.01201576553285122,
0.008054107427597046,
-0.022243164479732513,
0.005933241453021765,
-0.017881067469716072,
0.07485782355070114,
-0.010775185190141201,
-0.03319315239787102,
-0.01098207663744688,
-0.04323588311672211,
-0.006711799185723066,
-0.022912947461009026,
0.07919733971357346,
-0.021136056631803513,
0.02101237140595913,
0.04382430016994476,
-0.007329672574996948,
0.008281916379928589,
0.01063911709934473,
0.006465827114880085,
0.02210700325667858,
-0.013479122892022133,
-0.03983549028635025,
-0.024274112656712532,
-0.06823770701885223,
0.01104679424315691,
0.034473173320293427,
-0.03938407450914383,
0.0003057606518268585,
-0.004435930401086807,
0.04460366070270538,
-0.0007684103911742568,
0.015656301751732826,
0.008474954403936863,
-0.03104708343744278,
0.018335938453674316,
0.010940082371234894,
-0.041134584695100784,
0.033143483102321625,
-0.0254313163459301,
0.06664010882377625,
0.03397238627076149,
-0.014309518970549107,
-0.05832797288894653,
-0.02941240184009075,
0.0657757967710495,
0.032152190804481506,
0.007316228933632374,
0.003996752668172121,
-0.061591941863298416,
0.0012044304748997092,
0.03310685604810715,
0.004814865067601204,
0.036857523024082184,
-0.01251436211168766,
-0.005581879522651434,
-0.026751384139060974,
-0.022990239784121513,
-0.03523667901754379,
-0.018660161644220352,
-0.011729301884770393,
0.02819313295185566,
-0.03891618177294731,
0.029399314895272255,
0.032804857939481735,
0.03567483276128769,
0.022840511053800583,
0.029272377490997314,
-0.03315391764044762,
-0.007993640378117561,
0.0008391453302465379,
-0.003304585814476013,
0.0006344699650071561,
-0.047639161348342896,
-0.007298944052308798,
-0.0021645533852279186,
-0.005251691676676273,
0.02345144748687744,
-0.0196719691157341,
0.007154814433306456,
0.0064897374249994755,
0.014330655336380005,
0.05433996021747589,
0.007553049363195896,
-0.014226305298507214,
0.039666324853897095,
0.028435366228222847,
-0.012241922318935394,
0.06261920183897018,
0.0034158374182879925,
-0.01275879517197609,
-0.01900823973119259,
-0.012452973052859306,
0.0167106743901968,
-0.03354550898075104,
-0.016336165368556976,
-0.020139049738645554,
0.02198088727891445,
-0.005125730764120817,
0.051653847098350525,
-0.008194484747946262,
0.05171915516257286,
-0.023482665419578552,
-0.027702413499355316,
0.046935245394706726,
0.002773973625153303,
-0.01841292716562748,
0.010922590270638466,
-0.027041034772992134,
0.0065805041231215,
0.015138986520469189,
-0.034924350678920746,
-0.004947724286466837,
-0.022069642320275307,
0.008690818212926388,
0.01943812146782875,
0.008797409944236279,
0.005096249748021364,
-0.04713480919599533,
0.0047901831567287445,
-0.01666834205389023,
-0.05153871700167656,
0.05743419751524925,
-0.03041127510368824,
-0.017899800091981888,
0.021433314308524132,
-0.01865513063967228,
-0.030238309875130653,
0.030858471989631653,
0.02367791160941124,
0.0392363965511322,
-0.01777573674917221,
-0.010566571727395058,
0.03827178105711937,
0.0017689858796074986,
-0.07600708305835724,
-0.05110319331288338,
0.028309233486652374,
0.012179474346339703,
0.0022099055349826813,
-0.0106342863291502,
-0.042708687484264374,
0.009312322363257408,
-0.03004363738000393,
-0.004555231425911188,
0.03991241380572319,
-0.054158031940460205,
0.008576281368732452,
0.027235884219408035,
0.004226825665682554,
0.0934121236205101,
0.002952092094346881,
-0.007720111403614283,
0.008555463515222073,
-0.04481816291809082,
-0.059570375829935074,
-0.008894631639122963,
0.010521501302719116,
-0.016568567603826523,
-0.03406193107366562,
-0.014386571012437344,
-0.012842983938753605,
0.035165052860975266,
0.0005613289540633559,
-0.029778610914945602,
0.01876544952392578,
0.02858022414147854,
-0.03963455185294151,
0.014005138538777828,
0.030375530943274498,
0.01562106516212225,
0.034685295075178146,
-0.04278482124209404,
-0.006812707986682653,
-0.06436385959386826,
-0.07075304538011551,
0.01539843063801527,
-0.014202073216438293,
-0.021468928083777428,
-0.019699126482009888,
0.08701176196336746,
-0.032129451632499695,
-0.015361959114670753,
-0.004213894251734018,
0.015835553407669067,
0.006953099276870489,
0.009699788875877857,
0.010661018081009388,
0.0010500638745725155,
0.016667241230607033,
-0.00537166278809309,
-0.01858295314013958,
-0.043033305555582047,
0.03405904397368431,
0.05101066455245018,
-0.012443909421563148,
0.039721790701150894,
0.02530180662870407,
0.009927884675562382,
0.010663099586963654,
-0.01518561877310276,
-0.025441089645028114,
-0.019032470881938934,
-0.005451568868011236,
0.010733846575021744,
-0.03270871564745903,
-0.008486277423799038,
0.0140049047768116,
0.051532965153455734,
-0.036230139434337616,
0.0057350401766598225,
0.0056311399675905704,
0.016274383291602135,
-0.008030790835618973,
-0.003643648000434041,
-0.05483793839812279,
0.03235265985131264,
-0.03196268901228905,
0.026979221031069756,
0.000044680586142931134,
0.005740236025303602,
0.05881770700216293,
0.004177561495453119,
-0.02510431967675686,
-0.03461949899792671,
-0.00001797636468836572,
-0.02658124826848507,
0.01785329543054104,
-0.004576889332383871,
0.008646661415696144,
-0.06766976416110992,
0.001945065800100565,
0.03392111137509346,
-0.020761188119649887,
0.027249189093708992,
-0.012988226488232613,
-0.04883763939142227,
-0.014880326576530933,
-0.05220123007893562,
-0.026732662692666054,
0.04806455224752426,
-0.028529834002256393,
-0.03162933886051178,
0.009858357720077038,
-0.036101333796978,
0.05557815358042717,
0.05459635704755783,
0.029389292001724243,
-0.03187365084886551,
0.043219417333602905,
-0.0173741914331913,
0.03932737559080124,
-0.02575131319463253,
0.023744354024529457,
0.1407487839460373,
0.038059819489717484,
-0.010910208337008953,
-0.067440465092659,
-0.002404253464192152,
0.0012031800579279661,
0.012403440661728382,
0.00256558321416378,
-0.0031370678916573524,
-0.06643278151750565,
-0.018753984943032265,
0.01557900570333004,
0.04905879124999046,
0.00026215295656584203,
-0.013645479455590248,
0.029161138460040092,
-0.016275756061077118,
-0.0241633802652359,
0.00422942778095603,
0.037310291081666946,
-0.02783909998834133,
0.03441841900348663,
-0.056274428963661194,
0.022645343095064163,
-0.032538041472435,
0.020065926015377045,
-0.072377510368824,
-0.018063748255372047,
0.007100815884768963,
-0.0021753946784883738,
-0.06752590835094452,
-0.005861843004822731,
0.001918287482112646,
-0.030951138585805893,
-0.01566207967698574,
-0.0009800865082070231,
0.041065093129873276,
-0.009414833970367908,
-0.0029624029994010925,
0.056039195507764816,
0.007664480246603489,
0.029000813141465187,
0.060475364327430725,
0.047039300203323364,
-0.052914902567863464,
0.021365737542510033,
-0.035105232149362564,
0.040432047098875046,
-0.03839151933789253,
0.009019744582474232,
-0.021721575409173965,
-0.000629017420578748,
0.0034957248717546463,
-0.029945679008960724,
-0.009654125198721886,
-0.055047061294317245,
-0.012491206638514996,
0.011533580720424652,
0.02009514532983303,
-0.013304363936185837,
0.03749191015958786,
0.016593042761087418,
-0.012488546781241894,
0.015137875452637672,
0.017033837735652924,
0.0005705067305825651,
0.03655386343598366,
0.05425363779067993,
0.0014720341423526406,
-0.00918661616742611,
-0.03745774179697037,
-0.04225284233689308,
-0.023941945284605026,
-0.024299904704093933,
0.002862672321498394,
0.04535425454378128,
0.05018673464655876,
0.022745449095964432,
-0.002086734864860773,
-0.01394107099622488,
-0.06266772747039795,
0.020042521879076958,
0.03219810500741005,
0.02470976859331131,
-0.042378224432468414,
-0.01663113571703434,
-0.038009509444236755,
0.027363624423742294,
0.0006203966331668198,
-0.009758150205016136,
0.022503335028886795,
0.06096698343753815,
-0.025513097643852234,
0.04138072952628136,
-0.038818154484033585,
-0.03627091646194458,
-0.01670573651790619,
0.023392559960484505,
-0.020829467102885246,
0.00958633329719305,
0.02648639678955078,
0.02848788909614086,
-0.021182255819439888,
0.04805634915828705,
-0.007837776094675064,
-0.025321323424577713,
0.03226953372359276,
-0.02403140440583229,
0.039468154311180115,
0.00387475173920393,
0.001811266760341823,
-0.02670249529182911,
0.0006707505090162158,
0.00010189576278207824,
-0.015775054693222046,
-0.011254780925810337,
0.034274760633707047,
-0.020698314532637596,
-0.037379465997219086,
-0.02602243982255459,
0.0007551281596533954,
-0.03382399305701256,
-0.00945729948580265,
-0.043525636196136475,
0.0016724460292607546,
0.039360303431749344,
0.019209282472729683,
-0.03795513138175011,
0.021641932427883148,
-0.059091098606586456,
-0.024284187704324722,
0.022142194211483,
-0.04083539918065071,
-0.03339947387576103,
-0.012072262354195118,
0.014032412320375443,
0.022939005866646767,
0.02054564841091633,
-0.0030188406817615032,
-0.0037067329976707697,
0.03697660565376282,
-0.019909268245100975,
-0.032116588205099106,
0.008700735867023468,
0.03560202196240425,
0.031563762575387955,
0.01757856458425522,
-0.014129478484392166,
-0.03391319140791893,
0.05541297793388367,
0.003378370776772499,
0.0042783780954778194,
-0.031438197940588,
-0.034674592316150665,
0.023624489083886147,
-0.04539099335670471,
0.016826871782541275,
-0.012014771811664104,
-0.007148824166506529,
0.03125317767262459,
0.0021331822499632835,
-0.030914800241589546,
-0.03513214737176895,
-0.005933072417974472,
-0.009892522357404232,
-0.025266027078032494,
0.03890974447131157,
0.029019813984632492,
0.01898178830742836,
0.03826730698347092,
-0.01647740975022316,
0.017363620921969414,
-0.008899870328605175,
-0.010210668668150902,
-0.060240939259529114,
-0.035773422569036484,
0.011820033192634583,
0.015069952234625816,
-0.007207090500742197,
-0.0421774797141552,
-0.024228667840361595,
0.017267534509301186,
-0.06725211441516876,
0.04955966770648956,
-0.016685346141457558,
-0.011375111527740955,
-0.042000919580459595,
-0.024084381759166718,
-0.04892760515213013,
0.00626386096701026,
0.012213343754410744,
0.06043846905231476,
0.01826014555990696,
0.055209267884492874,
-0.017395496368408203,
-0.015391170047223568,
-0.04147743433713913,
0.041728608310222626,
0.0057973554357886314,
0.004403688013553619,
0.025901971384882927,
0.026941420510411263,
0.030522001907229424,
0.037519074976444244,
-0.007716405671089888,
0.005955562461167574,
-0.005180346313863993,
0.020826589316129684,
-0.014963767491281033,
0.06154073774814606,
-0.016288837417960167,
0.018328191712498665,
0.030324241146445274,
0.036489102989435196,
0.04808801785111427,
-0.015551406890153885,
-0.01688314601778984,
-0.015841098502278328,
0.03216119110584259,
-0.018918633460998535,
-0.02999507077038288,
0.02578422799706459,
-0.04449065402150154,
-0.008088991977274418,
0.007672046311199665,
0.026514114812016487,
0.034454263746738434,
-0.0031886249780654907,
-0.020639749243855476,
-0.022204022854566574,
-0.006123255472630262,
0.007326935883611441,
0.049178820103406906,
0.007437535095959902,
0.018954074010252953,
0.008470539003610611,
-0.007649525534361601,
0.022549128159880638,
0.01409490779042244,
0.027028175070881844,
-0.020125268027186394,
-0.027186503633856773,
0.009136837907135487,
0.011097689159214497,
0.03286158666014671,
-0.02159811183810234,
-0.07737400382757187,
0.004967553075402975,
0.018246959894895554,
0.02347618155181408,
-0.0012340834364295006,
-0.06864336133003235,
-0.010497670620679855,
-0.06681989133358002,
0.015500030480325222,
-0.022247198969125748,
-0.06762004643678665,
0.009871198795735836,
-0.036399636417627335,
0.0021695238538086414,
0.050382401794195175,
0.06498456001281738,
0.009265848435461521,
-0.02759280987083912,
0.03284537419676781,
-0.003618457820266485,
0.026770567521452904,
-0.06289095431566238,
-0.01252407394349575,
-0.003887544386088848,
0.021867193281650543,
0.027596531435847282,
-0.001970466924831271,
-0.04153336584568024,
0.034994639456272125,
0.001957921776920557,
0.016792798414826393,
-0.017829634249210358,
-0.00827556662261486,
-0.026883238926529884,
0.05440092831850052,
0.020543767139315605,
-0.016765262931585312,
0.09741804003715515,
-0.011833501979708672,
0.00011987408652203158,
-0.01536412350833416,
-0.03784208372235298,
-0.013431735336780548,
-0.007454690523445606,
-0.019617842510342598,
0.006663358770310879,
-0.027301017194986343,
0.00175870128441602,
0.04737439006567001,
0.004891091957688332,
-0.017419377341866493,
0.057635966688394547,
-0.014200825244188309,
-0.027576563879847527,
0.060482267290353775,
0.006933247670531273,
0.03003973886370659,
-0.02687767520546913,
0.006465375889092684,
-0.019669726490974426,
0.001212278031744063,
-0.015350970439612865,
0.035444702953100204,
0.018107764422893524,
-0.006458475720137358,
-0.03791333734989166,
0.08241496980190277,
-0.04044051468372345,
-0.007907900959253311,
-0.029141658917069435,
-0.010383972898125648,
-0.0480814203619957,
-0.014943460933864117,
0.04539618268609047,
-0.0403779000043869,
-0.029812267050147057,
0.0006559451576322317,
-0.026077114045619965,
0.044723991304636,
-0.011121710762381554,
-0.006686542648822069,
0.019397493451833725,
0.03559543564915657,
0.009674658067524433,
0.05538657307624817,
-0.008489597588777542,
0.032426103949546814,
-0.025943635031580925,
-0.04725203290581703,
-0.009471584111452103,
-0.01200902834534645,
0.02496541477739811,
-0.026491770520806313,
0.05791036784648895,
0.01471802033483982,
0.0434490405023098,
0.006268881261348724,
-0.027593515813350677,
0.023429861292243004,
0.001426969189196825,
0.05428832396864891,
0.021799929440021515,
0.007767745293676853,
-0.0030719053465873003,
0.023862212896347046,
-0.035773951560258865,
0.023512959480285645,
-0.023040253669023514,
0.01839626394212246,
0.015415024012327194,
0.030829794704914093,
0.019497018307447433,
-0.02139626070857048
] |
<p>The following was originally given to me as a homework question at
my physics 2 course:</p>
<blockquote>
<p>Consider the following circuit</p>
<p><img src="http://i.stack.imgur.com/KntDu.jpg" alt="enter image description here"></p>
<p>The difference of potentials between the point $V_{1}$and the point
$V_{2}$ is $4.4$ volts, the resistance of all the resistors is the
same $R=1\Omega$.</p>
<p>Find the current between point $A$ and point $B$.</p>
</blockquote>
<p>The answer given is simply $0$ and the argument was just the pair
of words ``using symmetry''.</p>
<p>I don't really understand the answer:</p>
<p>First, it is not completely symmetric: There is a difference of potentials
so the potential at the point $V_{1}$ is not the same as the potential
at the point $V_{2}$.</p>
<p>Secondly: How can I see that the symmetric structure will give me
that the current between $A$ and $B$ is $0$ ?</p>
<p>Also, I would appreciate to see a calculation of this current to get
a better feel for whats going on, I know the rule $V=IR$ (which seems
the most useful here, but I also know other rules that can be used),
but I don't understand how to use this rule to find the current.</p>
| 10,663 |
[
0.006804011296480894,
-0.025796029716730118,
-0.01667439565062523,
0.014912959188222885,
-0.0009432086953893304,
0.014856217429041862,
-0.005929690320044756,
0.024826984852552414,
0.008552948012948036,
-0.0025671387556940317,
0.021990438923239708,
0.016745243221521378,
0.044348880648612976,
-0.018468717113137245,
0.021857695654034615,
0.01938585750758648,
0.0022317194379866123,
-0.009166213683784008,
0.0005936965462751687,
-0.009313850663602352,
0.017567435279488564,
0.013215737417340279,
0.028968369588255882,
-0.011335322633385658,
-0.03693259507417679,
0.019001897424459457,
0.010400449857115746,
0.013647397048771381,
-0.030011557042598724,
0.04575687646865845,
-0.010393806733191013,
-0.02977983094751835,
-0.014551824890077114,
0.0026587522588670254,
0.00509952986612916,
0.03962196782231331,
-0.023365510627627373,
-0.04070739448070526,
0.0157333854585886,
0.03876590356230736,
-0.002725350670516491,
0.012262256816029549,
-0.003027313621714711,
0.07897302508354187,
-0.029461847618222237,
-0.031918805092573166,
-0.009593597613275051,
0.035522859543561935,
-0.00066283845808357,
-0.06135508790612221,
0.06798690557479858,
-0.003529294626787305,
0.07539200782775879,
0.015712035819888115,
0.00827674102038145,
-0.008562528528273106,
0.053396862000226974,
0.066701240837574,
-0.004059197846800089,
-0.02324201539158821,
-0.035192642360925674,
-0.022189702838659286,
0.008962638676166534,
-0.03819708153605461,
-0.05023770034313202,
0.03141481429338455,
0.006463329307734966,
0.00515616312623024,
0.01323099434375763,
-0.01850281096994877,
0.005725240800529718,
0.038445357233285904,
-0.011295828968286514,
-0.04989338293671608,
-0.0011186726624146104,
0.00037908501690253615,
0.014979489147663116,
0.02590804174542427,
0.025432804599404335,
0.0014204953331500292,
-0.010285231284797192,
0.015750212594866753,
0.0028340520802885294,
0.040874265134334564,
0.007317470386624336,
-0.04376019909977913,
0.05568987503647804,
0.013291209004819393,
0.007075803820043802,
0.0001229586632689461,
-0.021808821707963943,
0.02461148425936699,
0.021960293874144554,
-0.02875749208033085,
-0.029212672263383865,
0.03596723452210426,
-0.019676627591252327,
0.07151532173156738,
0.002787976060062647,
-0.037752918899059296,
0.020846055820584297,
-0.07161449640989304,
0.033683713525533676,
0.07704367488622665,
-0.012635963037610054,
-0.02037977986037731,
0.01639234833419323,
0.035040006041526794,
0.01928304135799408,
0.003808090928941965,
-0.05133659765124321,
0.061060961335897446,
0.011228684335947037,
0.04050399735569954,
0.011160717345774174,
-0.02139214612543583,
-0.023481335490942,
-0.010265552438795567,
0.023746786639094353,
-0.004235704895108938,
0.0424383319914341,
-0.004203283693641424,
0.026216227561235428,
-0.01972334459424019,
-0.06453309208154678,
0.015547560527920723,
-0.0056948112323880196,
0.007278784178197384,
-0.010360591113567352,
0.03291574865579605,
-0.000819264620076865,
-0.012990285642445087,
-0.0223865769803524,
0.014182900078594685,
0.04445204511284828,
-0.010167000815272331,
-0.06892231106758118,
-0.0680851861834526,
0.030053243041038513,
-0.003372834762558341,
-0.0302788894623518,
-0.07931765913963318,
-0.010204751044511795,
0.018641294911503792,
0.08636964857578278,
-0.04341580718755722,
-0.0032183360308408737,
0.0250451248139143,
0.05893375352025032,
0.05189160257577896,
0.0010529769351705909,
-0.035782426595687866,
-0.01260186918079853,
-0.008165878243744373,
0.015028778463602066,
-0.040512815117836,
0.01128294039517641,
0.006568943150341511,
-0.02152346633374691,
-0.01856113038957119,
0.07391614466905594,
-0.016882244497537613,
-0.017257830128073692,
0.017130305990576744,
-0.02548888698220253,
0.01150848064571619,
0.07547321915626526,
-0.008087500929832458,
-0.05717834457755089,
0.03671891987323761,
0.00634013069793582,
0.04578229784965515,
-0.031208747997879982,
-0.010111610405147076,
0.07476434856653214,
-0.0393952801823616,
0.006643812637776136,
-0.00914847757667303,
0.03291972726583481,
-0.002252470003440976,
-0.03432721644639969,
-0.043047260493040085,
0.011759951710700989,
0.016917582601308823,
-0.019689202308654785,
0.07031842321157455,
0.004687401466071606,
-0.0022688047029078007,
-0.01807992532849312,
-0.0003705582348629832,
-0.014997115358710289,
-0.06257987767457962,
-0.009265288710594177,
-0.0039339372888207436,
-0.05105014145374298,
0.01516182254999876,
0.021068379282951355,
0.011343165300786495,
-0.02396315522491932,
-0.017123473808169365,
0.021213367581367493,
0.023317374289035797,
-0.004259902983903885,
-0.010767262428998947,
0.0356953963637352,
0.03404330462217331,
0.02844409830868244,
0.025584004819393158,
0.05846991762518883,
-0.017431294545531273,
0.018046220764517784,
0.011752516031265259,
0.0033977588173002005,
0.026972223073244095,
0.023401832208037376,
-0.022177234292030334,
-0.008921295404434204,
0.004754857625812292,
0.023893987759947777,
0.04847927391529083,
-0.04095253348350525,
0.06430283188819885,
0.07563799619674683,
0.027171365916728973,
-0.015384603291749954,
0.04391012340784073,
0.03825068846344948,
0.02344399318099022,
-0.02289678528904915,
-0.0354706346988678,
-0.06251474469900131,
-0.014628111384809017,
0.06033440679311752,
-0.024923859164118767,
-0.045412011444568634,
0.0011275408323854208,
0.03021443635225296,
0.021304110065102577,
0.03634811192750931,
-0.012094531208276749,
-0.03556240722537041,
-0.016585348173975945,
0.030753912404179573,
0.019592279568314552,
-0.023083200678229332,
0.026384573429822922,
0.02207031659781933,
0.016161339357495308,
0.027555951848626137,
-0.008287625387310982,
-0.03473601117730141,
0.06139654293656349,
-0.004209870472550392,
0.020199161022901535,
-0.008925972506403923,
-0.011497252620756626,
0.03976091369986534,
-0.022468620911240578,
0.039982251822948456,
0.011464640498161316,
-0.0245075523853302,
-0.005556480493396521,
-0.01801750250160694,
0.006396022159606218,
0.005431578028947115,
-0.014187664724886417,
-0.019307725131511688,
-0.016419388353824615,
0.007312655448913574,
-0.022209135815501213,
-0.0028658313676714897,
-0.03260760009288788,
-0.005911310203373432,
-0.04488839581608772,
-0.037926092743873596,
0.018133558332920074,
0.002161337761208415,
0.024464646354317665,
-0.0662999153137207,
-0.007528854999691248,
-0.008755424059927464,
-0.012707407586276531,
-0.0005749653209932148,
0.025068489834666252,
-0.04496447369456291,
0.0034072711132466793,
-0.04652349278330803,
-0.013964257203042507,
0.04548376798629761,
0.05215930566191673,
0.011204641312360764,
-0.011082123033702374,
-0.00716209365054965,
-0.047420281916856766,
-0.026973698288202286,
-0.008099684491753578,
0.053460028022527695,
-0.056382667273283005,
-0.013104868121445179,
0.060134682804346085,
-0.016387002542614937,
-0.02109730988740921,
0.044851671904325485,
-0.02197161130607128,
-0.03407139331102371,
0.023903990164399147,
-0.007239027880132198,
0.005540961865335703,
-0.0217280313372612,
0.027988150715827942,
-0.008435642346739769,
-0.021070919930934906,
-0.028516430407762527,
-0.017588315531611443,
-0.02183414064347744,
0.00009680558287072927,
-0.018682388588786125,
0.03353392705321312,
0.017369965091347694,
-0.0709015280008316,
0.07701719552278519,
0.03434789180755615,
0.013410084880888462,
-0.0233480092138052,
-0.03964436054229736,
-0.03716300055384636,
-0.026757866144180298,
0.0011452510952949524,
0.06584614515304565,
-0.011326798237860203,
0.026349062100052834,
0.029622212052345276,
0.061912037432193756,
0.029955826699733734,
-0.01904221810400486,
-0.021641002967953682,
-0.010162637569010258,
-0.003254786366596818,
0.002773754531517625,
0.07023273408412933,
-0.01088783424347639,
0.009662020020186901,
0.0441938191652298,
0.025230448693037033,
0.010505978018045425,
0.04827616363763809,
-0.035396527498960495,
0.02658030577003956,
-0.02756420522928238,
0.016779230907559395,
-0.05193351209163666,
0.059137213975191116,
-0.009906254708766937,
0.03781500086188316,
-0.02564289979636669,
0.012007463723421097,
0.06535495817661285,
-0.029794543981552124,
-0.018445808440446854,
0.03212793171405792,
0.019028440117836,
-0.01589391380548477,
-0.04567009583115578,
0.019503135234117508,
-0.010660344734787941,
0.038596633821725845,
0.010511250235140324,
-0.05394764244556427,
0.04890025407075882,
0.029039602726697922,
0.0022049194667488337,
0.028412414714694023,
-0.06576734781265259,
-0.017337754368782043,
-0.03773783892393112,
0.001808986417017877,
-0.02206137217581272,
0.06360889226198196,
-0.022678356617689133,
0.04719577357172966,
0.03250487148761749,
0.013989428989589214,
-0.0033773002214729786,
-0.0029947904404252768,
-0.052955854684114456,
0.04243316873908043,
-0.014857381582260132,
-0.0024791357573121786,
-0.032129961997270584,
-0.0043454645201563835,
-0.001984331523999572,
-0.027926962822675705,
-0.01768413931131363,
-0.015214220620691776,
-0.004165292251855135,
-0.0351049080491066,
0.013590339571237564,
-0.033508989959955215,
-0.03193498030304909,
-0.04619210213422775,
0.02355361357331276,
0.042379364371299744,
-0.0624534897506237,
0.00851067341864109,
0.03143690153956413,
-0.005961831193417311,
0.009852380491793156,
-0.0472981333732605,
0.010460945777595043,
0.020989034324884415,
0.018629828467965126,
0.034075893461704254,
0.007616276852786541,
-0.004999419208616018,
-0.0030862479470670223,
0.0013573982287198305,
0.09033147990703583,
0.015089145861566067,
-0.022431034594774246,
-0.02339213341474533,
-0.03738433122634888,
-0.020225809887051582,
-0.041842810809612274,
0.05567953363060951,
-0.00944613479077816,
0.03801444172859192,
0.027657052502036095,
0.04519191384315491,
-0.022533591836690903,
0.008110569790005684,
0.051157157868146896,
0.029323438182473183,
-0.008608336560428143,
-0.057872820645570755,
-0.018019497394561768,
-0.07335483282804489,
-0.011396357789635658,
0.04518056660890579,
-0.03129786625504494,
-0.02561952732503414,
-0.017660437151789665,
0.056462351232767105,
0.027470404282212257,
-0.009770544245839119,
0.002017631893977523,
-0.0025460366159677505,
0.0003574931179173291,
0.013261531479656696,
-0.0005527596222236753,
0.018675612285733223,
0.026256311684846878,
0.054679591208696365,
0.0069596050307154655,
-0.007683086208999157,
-0.07833953946828842,
-0.031515929847955704,
0.012791184708476067,
0.015431149862706661,
0.007186034228652716,
-0.025344692170619965,
-0.04794984310865402,
-0.031595759093761444,
0.059960655868053436,
-0.017418373376131058,
0.06132405996322632,
-0.024664707481861115,
0.007539117243140936,
-0.03179822862148285,
-0.03189685940742493,
-0.009777791798114777,
0.013434283435344696,
-0.011293388903141022,
0.022264530882239342,
-0.012321812100708485,
-0.02617340348660946,
0.012871287763118744,
-0.03685702010989189,
0.013226114213466644,
0.04796839877963066,
-0.0210918840020895,
0.0031664855778217316,
0.012262864969670773,
0.05140776187181473,
-0.042446207255125046,
-0.059371866285800934,
-0.0077231149189174175,
-0.00483565591275692,
0.00862193200737238,
0.05838137865066528,
-0.05414388328790665,
-0.027927160263061523,
0.06581646203994751,
-0.023810112848877907,
0.052202749997377396,
-0.00907968357205391,
-0.0013382675824686885,
0.0442061722278595,
0.0424816757440567,
-0.005766141228377819,
0.04299557954072952,
0.02687418833374977,
-0.008805844932794571,
-0.03856561705470085,
0.0029133250936865807,
0.029722418636083603,
-0.00555857177823782,
-0.022307034581899643,
-0.017519064247608185,
0.028877917677164078,
-0.037671130150556564,
0.039309293031692505,
-0.009077480062842369,
0.023847967386245728,
-0.008678237907588482,
-0.02591981738805771,
0.035785336047410965,
0.006565514951944351,
-0.013990646228194237,
-0.011093325912952423,
0.02021798864006996,
0.03964950144290924,
0.029431231319904327,
-0.042869653552770615,
0.014559861272573471,
-0.06466285139322281,
-0.00882614217698574,
0.004715051501989365,
-0.0007250909693539143,
0.03596752509474754,
-0.045119624584913254,
-0.017998388037085533,
-0.00435596751049161,
-0.040961846709251404,
0.05867265164852142,
-0.03220808878540993,
-0.028326405212283134,
0.0030928333289921284,
-0.07017210125923157,
-0.04689408838748932,
0.016563814133405685,
-0.008240479044616222,
-0.008259668946266174,
-0.05456323176622391,
0.04013976454734802,
0.037357233464717865,
0.0009662398952059448,
-0.07560794800519943,
-0.05269748345017433,
0.0020030634477734566,
0.024209408089518547,
-0.009576790034770966,
-0.03232362121343613,
-0.02560918591916561,
0.023165298625826836,
-0.021459724754095078,
0.0387321375310421,
0.03495248034596443,
0.0063179475255310535,
-0.01779637113213539,
0.007710454985499382,
0.0175067987293005,
0.056568071246147156,
0.025701235979795456,
-0.002213470172137022,
-0.004177326802164316,
-0.06542052328586578,
-0.018807027488946915,
0.011213621124625206,
0.057880762964487076,
-0.04115419089794159,
-0.018982110545039177,
-0.014967498369514942,
-0.021788589656352997,
0.0561000257730484,
-0.012133073061704636,
-0.018445542082190514,
-0.001318607828579843,
0.017891714349389076,
-0.017604416236281395,
-0.048369403928518295,
0.0034810062497854233,
0.00585783738642931,
0.012711403891444206,
0.017698558047413826,
0.01235804334282875,
-0.04747648164629936,
-0.047588564455509186,
-0.0032224322203546762,
0.012177846394479275,
-0.004969700705260038,
-0.022041864693164825,
0.07491692900657654,
-0.036666903644800186,
-0.01169978454709053,
0.023820633068680763,
-0.017715198919177055,
0.006704988889396191,
-0.019975656643509865,
0.012809166684746742,
0.02231813594698906,
0.021883973851799965,
-0.04315875098109245,
-0.03254300728440285,
-0.03594038262963295,
0.03083915077149868,
0.0707828477025032,
-0.018706709146499634,
0.03748079389333725,
0.03511132672429085,
-0.01087980717420578,
0.014241238124668598,
0.011931162327528,
-0.009363360702991486,
0.001996454782783985,
0.007376580499112606,
0.04449429735541344,
-0.047855693846940994,
0.01667177677154541,
0.03188182786107063,
0.0424560122191906,
-0.014225073158740997,
-0.01268163975328207,
0.05283626541495323,
0.008438768796622753,
0.005955335218459368,
0.03096301481127739,
-0.007217534817755222,
0.017725929617881775,
0.004759092349559069,
0.03025214746594429,
0.004274139646440744,
-0.04369422420859337,
0.04410455375909805,
-0.0048397914506495,
0.011832929216325283,
-0.028142431750893593,
-0.01350681483745575,
-0.036741480231285095,
0.02760644070804119,
0.020853664726018906,
0.012813909910619259,
-0.01436914037913084,
0.0360034704208374,
0.016851285472512245,
0.0004756457929033786,
0.03870576247572899,
-0.009208014234900475,
-0.05095890909433365,
0.004448473919183016,
-0.027351627126336098,
-0.030566303059458733,
0.03489053249359131,
-0.010641139931976795,
-0.030672619119286537,
0.03823699802160263,
-0.022000158205628395,
0.0001676897081779316,
0.0274151973426342,
0.011285712942481041,
-0.034462232142686844,
0.06709279865026474,
0.002974834991618991,
0.05927367880940437,
0.005434283521026373,
-0.02622608281672001,
0.08596871793270111,
0.05489533022046089,
-0.004306239541620016,
-0.048407506197690964,
0.04695919156074524,
-0.03777892887592316,
0.00005006263745599426,
-0.025143584236502647,
0.03885626792907715,
0.002184313489124179,
0.012374303303658962,
-0.03387904167175293,
0.020592020824551582,
0.006537430454045534,
0.011039705015718937,
0.03453298285603523,
-0.026037488132715225,
-0.059063177555799484,
0.0005570731591433287,
0.020627062767744064,
-0.009468168951570988,
0.0074881999753415585,
-0.043154582381248474,
0.009915025904774666,
-0.046751927584409714,
-0.016059301793575287,
-0.035883400589227676,
-0.032001953572034836,
0.06258463859558105,
-0.006620567291975021,
0.0228011142462492,
0.04163883253931999,
0.03531929850578308,
-0.028053080663084984,
-0.04383023828268051,
0.02320794016122818,
0.021381327882409096,
-0.012880358844995499,
0.04934420436620712,
0.0471455380320549,
0.012347945012152195,
0.008684751577675343,
0.014958303421735764,
0.003889793297275901,
-0.04486267641186714,
-0.014661941677331924,
-0.03242826089262962,
0.030337641015648842,
-0.0017529134638607502,
0.02314867451786995,
0.005752998404204845,
0.01356026716530323,
0.015098837204277515,
-0.07268478721380234,
-0.04736623167991638,
-0.0026718212757259607,
0.01609605923295021,
-0.017103658989071846,
-0.01401214487850666,
-0.03631201758980751,
0.027326902374625206,
-0.022173982113599777,
-0.021960372105240822,
-0.0051953415386378765,
0.0025332048535346985,
0.00693849939852953,
0.0033386729191988707,
0.026631060987710953,
-0.003949332516640425,
-0.036820556968450546,
-0.03137928992509842,
-0.031870145350694656,
-0.019441504031419754,
-0.012944954447448254,
-0.015506182797253132,
0.029757317155599594,
0.024345500394701958,
-0.00855837482959032,
-0.032095931470394135,
0.02809813804924488,
-0.09440016001462936,
0.012532169930636883,
-0.007709542755037546,
0.0059255254454910755,
0.00825123954564333,
0.010690538212656975,
0.01840358041226864,
0.05007082596421242,
-0.03443251550197601,
-0.00796339102089405,
0.0898195207118988,
0.017600705847144127,
0.017447756603360176,
-0.031299274414777756,
-0.03928616642951965,
0.03708770498633385,
-0.039769381284713745,
0.025132762268185616,
0.010145832784473896,
0.011723407544195652,
0.0054120831191539764,
0.01757771335542202,
-0.00882999412715435,
0.021171852946281433,
-0.06496945768594742,
-0.017591407522559166,
0.01964361034333706,
-0.015370240435004234,
0.011947636492550373,
0.007987022399902344,
0.006079249549657106,
-0.021813971921801567,
-0.007644239347428083,
0.018833337351679802,
0.01599295064806938,
0.04557305574417114,
-0.012636449187994003,
-0.04497373104095459,
-0.023783177137374878,
-0.03532252088189125,
-0.009063590317964554,
-0.05921705812215805,
-0.013184125535190105,
-0.014104652218520641,
-0.022746140137314796,
0.022572318091988564,
0.023640543222427368,
-0.00619875593110919,
0.05057235434651375,
0.028902392834424973,
-0.0023529017344117165,
0.023121865466237068,
0.04329221323132515,
0.00956632662564516,
-0.029349159449338913,
0.026423459872603416,
0.0251560527831316,
0.05044470354914665,
-0.025897713378071785,
-0.03170608729124069,
0.048221442848443985,
-0.03135605901479721,
-0.009590472094714642,
0.03558235242962837,
0.042106710374355316,
0.007573213893920183,
-0.01658369041979313,
-0.026017215102910995,
-0.00018043466843664646,
0.028038689866662025,
-0.006949898321181536,
0.029180629178881645,
0.0017745891818776727,
-0.052637018263339996,
0.024508867412805557,
-0.025500338524580002,
-0.007194260135293007,
0.002862431574612856,
0.028084764257073402,
-0.007596502546221018,
0.017387589439749718,
-0.018610922619700432,
-0.023231741040945053,
-0.0008964734734036028,
0.014028666540980339,
0.020549699664115906,
0.040882427245378494,
0.022204160690307617,
0.0006679462385363877,
0.04933148995041847,
0.0010413193376734853,
0.0035159082617610693,
-0.020046142861247063,
-0.010783710516989231,
-0.057160329073667526,
-0.004313647281378508,
0.015775389969348907,
0.005938089918345213,
0.024513019248843193,
-0.058408599346876144,
-0.002701972844079137,
0.020011380314826965,
-0.051604971289634705,
-0.0062810820527374744,
-0.021451489999890327,
-0.018638504669070244,
-0.042295414954423904,
-0.030455080792307854,
-0.026561522856354713,
0.051595572382211685,
0.020656779408454895,
0.055738676339387894,
0.02770514041185379,
-0.004408417269587517,
0.009744852781295776,
-0.04541438817977905,
0.033024415373802185,
0.03407915309071541,
-0.0264559555798769,
-0.009894397109746933,
-0.013283143751323223,
0.007373661268502474,
-0.024168722331523895,
0.02798665314912796,
-0.06222308427095413,
-0.03042246587574482,
-0.0018403362482786179,
0.047049444168806076,
-0.009754221886396408,
0.05837436020374298,
-0.025585263967514038,
0.018919842317700386,
-0.04138604924082756,
-0.04695665463805199,
0.04128985479474068,
0.019199397414922714,
-0.015272578224539757,
-0.015349069610238075,
-0.002396938158199191,
-0.019886549562215805,
-0.031171349808573723,
0.025270434096455574,
-0.04504929482936859,
-0.013419329188764095,
-0.017365848645567894,
-0.016709333285689354,
0.019110118970274925,
-0.05206498131155968,
0.019208649173378944,
-0.020158013328909874,
0.005239811260253191,
0.050572723150253296,
0.011554763652384281,
0.01835457980632782,
-0.0046819280833005905,
-0.025228658691048622,
-0.020819077268242836,
0.02161874994635582,
0.03538307175040245,
-0.020927423611283302,
-0.08675417304039001,
-0.01326757576316595,
-0.005291736219078302,
-0.009957786649465561,
0.0018329344457015395,
-0.05649033933877945,
0.0004153421032242477,
0.022970713675022125,
0.027677807956933975,
-0.0178389735519886,
0.016473976895213127,
-0.030246524140238762,
-0.01725972257554531,
-0.05175577104091644,
0.03153378516435623,
0.02221515215933323,
-0.04219925031065941,
-0.044718749821186066,
-0.01969848945736885,
-0.041297443211078644,
0.009215829893946648,
0.0522741824388504,
0.02249342016875744,
-0.016881344839930534,
0.03261876478791237,
-0.009141898714005947,
0.04113110154867172,
-0.032776445150375366,
-0.018939437344670296,
0.002650390611961484,
0.019925765693187714,
0.020692458376288414,
0.0005635539419017732,
-0.021188434213399887,
0.03871872276067734,
-0.020953666418790817,
-0.0059678866527974606,
-0.009366347454488277,
0.0080002686008811,
-0.00878644548356533,
0.00733137596398592,
-0.027812663465738297,
0.0010943989036604762,
0.08069419860839844,
0.0008480308461003006,
0.0005980445421300828,
0.018837785348296165,
0.0005424470873549581,
-0.033000312745571136,
0.032230835407972336,
-0.033014554530382156,
-0.03128150478005409,
-0.019533488899469376,
-0.002970963716506958,
0.0511460117995739,
-0.05080249905586243,
-0.02416631020605564,
0.02710377238690853,
-0.009933093562722206,
-0.024452179670333862,
0.05949055030941963,
-0.02155560813844204,
0.02980751357972622,
-0.027656948193907738,
0.001566239632666111,
-0.002157641341909766,
-0.006724887061864138,
0.035913705825805664,
0.007385901175439358,
0.008636771701276302,
0.011846440844237804,
-0.00018880977586377412,
0.05572237819433212,
-0.005472337827086449,
0.01767830178141594,
0.02554897405207157,
-0.01299071591347456,
-0.008380754850804806,
-0.008446273393929005,
-0.010832460597157478,
-0.03357584401965141,
0.0066039846278727055,
-0.013998672366142273,
-0.012551402673125267,
0.10682488232851028,
-0.014504469931125641,
0.0011666144710034132,
-0.012266188859939575,
-0.003863867372274399,
-0.037444956600666046,
-0.004558287560939789,
0.020104514434933662,
-0.016884174197912216,
-0.04419581592082977,
-0.038708556443452835,
-0.017806200310587883,
0.004653852432966232,
0.017189713194966316,
-0.055085912346839905,
0.06268486380577087,
-0.0063956608064472675,
-0.012607984244823456,
-0.02605443075299263,
-0.0058185746893286705,
0.010437412187457085,
-0.022626757621765137,
0.02308908849954605,
0.04684385284781456,
0.029141001403331757,
0.00706225773319602,
0.011771994642913342,
-0.02903681993484497,
0.050915345549583435,
-0.04674660041928291,
-0.04688277468085289,
-0.01688380539417267,
0.002580305328592658,
0.022302953526377678,
-0.024578562006354332
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/31254/can-the-lightning-be-captured-and-used-as-power-source">Can the lightning be captured and used as power source?</a> </p>
</blockquote>
<p>Each lightning contains several kilo volts of electricity.<br>
Saving them could be a boon to soaring need of it.<br>
Is there a way?</p>
| 338 |
[
-0.05440794676542282,
-0.007455375045537949,
-0.005436607636511326,
-0.02436821535229683,
0.01959928311407566,
-0.0357469767332077,
-0.03342055529356003,
-0.0660998597741127,
0.0273920688778162,
-0.0074632735922932625,
0.0631721094250679,
0.05162212625145912,
0.015848899260163307,
0.030291521921753883,
-0.0015425292076542974,
0.003996461164206266,
-0.009976242668926716,
0.0009824021253734827,
0.030317602679133415,
-0.01492417324334383,
-0.03065960481762886,
0.03411586582660675,
0.0037678226362913847,
0.054164569824934006,
-0.031314313411712646,
0.0027748027350753546,
0.016531549394130707,
0.011179213412106037,
0.014183293096721172,
0.0670703575015068,
-0.0032317477744072676,
-0.0033466084860265255,
0.05724238604307175,
0.04869021847844124,
0.016107017174363136,
0.01957198604941368,
-0.042976830154657364,
-0.007451422046869993,
-0.006184939295053482,
-0.035506878048181534,
0.005156553350389004,
-0.0009265649714507163,
0.029498687013983727,
0.03862757980823517,
-0.016992652788758278,
0.023518666625022888,
-0.036544155329465866,
-0.044225968420505524,
-0.00004024687586934306,
-0.0771801769733429,
0.023966200649738312,
-0.0037126701790839434,
0.028211859986186028,
0.06630617380142212,
-0.009522845968604088,
-0.027590570971369743,
0.05736641585826874,
0.06652110815048218,
0.0009904903126880527,
-0.018145186826586723,
0.011238699778914452,
-0.008502860553562641,
0.012462676502764225,
-0.02477952092885971,
-0.0397295244038105,
0.03870660439133644,
0.012107964605093002,
0.01745900884270668,
0.01639379747211933,
-0.01685461774468422,
0.02255929820239544,
0.006098014768213034,
-0.02265385538339615,
0.002859897445887327,
0.0059242104180157185,
-0.010990739800035954,
-0.011501612141728401,
-0.0054915593937039375,
0.061347123235464096,
0.07206907868385315,
-0.01887873373925686,
0.03785894811153412,
0.019094213843345642,
-0.004845952149480581,
0.04282929375767708,
-0.023507224395871162,
0.09412404894828796,
-0.0023241708986461163,
0.042988721281290054,
-0.026555096730589867,
0.015442414209246635,
-0.00956777110695839,
0.003878913586959243,
0.034841928631067276,
0.007375719491392374,
0.014015470631420612,
-0.006907988339662552,
0.04307602345943451,
0.007001275196671486,
-0.02597697637975216,
0.0186744537204504,
0.0035844421945512295,
0.04481081664562225,
0.033791638910770416,
0.01354749035090208,
-0.051804520189762115,
-0.011755375191569328,
-0.0132161695510149,
-0.017471222206950188,
-0.027253063395619392,
-0.05302419513463974,
0.019206974655389786,
0.009606790728867054,
-0.05113775283098221,
0.007926084101200104,
-0.03261526674032211,
0.01819285750389099,
-0.013115973211824894,
0.04470942169427872,
0.04267568141222,
-0.005165968555957079,
-0.026775196194648743,
0.017509527504444122,
-0.025817090645432472,
-0.038263436406850815,
0.012212795205414295,
-0.0018924407195299864,
0.02908097580075264,
-0.020869145169854164,
0.03024180233478546,
-0.0019437664886936545,
-0.039783820509910583,
0.011831579729914665,
0.0002523961302358657,
0.0517314113676548,
-0.02277723327279091,
-0.09565383195877075,
-0.02648652344942093,
0.046017296612262726,
-0.018510280176997185,
-0.009801153093576431,
-0.08319184929132462,
0.040490202605724335,
-0.003641611197963357,
0.027694908902049065,
0.00480047008022666,
0.000926682841964066,
-0.012278381735086441,
0.029318520799279213,
0.02057976834475994,
-0.009520080871880054,
-0.005196812096983194,
0.02105891890823841,
-0.00557521590963006,
0.02897518314421177,
-0.08831501752138138,
0.0074006784707307816,
0.02473660558462143,
0.019438767805695534,
0.007148792501538992,
0.02400142140686512,
0.03180637210607529,
0.01861979067325592,
-0.014187738299369812,
0.006061135791242123,
0.010174447670578957,
0.06924236565828323,
0.008291387930512428,
-0.012385634705424309,
0.033510707318782806,
-0.007015791721642017,
0.025603050366044044,
-0.027684394270181656,
-0.0072771296836435795,
0.045617591589689255,
-0.03269680589437485,
-0.004133620299398899,
-0.05221448093652725,
0.04344774782657623,
-0.012066652998328209,
-0.05735021457076073,
-0.01677875407040119,
0.000051466795412125066,
-0.0006829769117757678,
0.027155114337801933,
0.08737844973802567,
0.007722055073827505,
-0.02796298824250698,
-0.03482245281338692,
-0.04027727618813515,
-0.008010456338524818,
-0.03145936131477356,
0.05161470174789429,
-0.009345753118395805,
-0.011176425963640213,
0.005231952760368586,
-0.027242165058851242,
0.04824970290064812,
-0.02860293723642826,
0.010681815445423126,
-0.004736384842544794,
0.04050188884139061,
-0.01369184348732233,
0.005910822190344334,
0.0016167224384844303,
0.034398987889289856,
0.03601543605327606,
-0.002812156453728676,
0.01951952651143074,
-0.0022896621376276016,
-0.0039881630800664425,
-0.02807191200554371,
-0.031512316316366196,
0.017556793987751007,
0.02467222698032856,
0.0019986594561487436,
0.01713709346950054,
0.0428338386118412,
0.004846077878028154,
0.021699585020542145,
-0.0037497931625694036,
0.0564921572804451,
0.034219108521938324,
-0.01991998590528965,
0.0009269405854865909,
0.03203442692756653,
0.0030096429400146008,
0.026399433612823486,
-0.008506319485604763,
0.011965714395046234,
-0.09159945696592331,
0.038875892758369446,
0.037274692207574844,
0.040492162108421326,
-0.06439352035522461,
0.05252127721905708,
0.028047097846865654,
0.03310514986515045,
0.025506628677248955,
-0.03740452602505684,
-0.009085120633244514,
-0.0304880291223526,
0.037315063178539276,
0.0017888479633256793,
-0.0029878439381718636,
0.01813829503953457,
-0.0017286436632275581,
0.003196107689291239,
0.01081144530326128,
-0.03742826357483864,
0.022765468806028366,
0.045800793915987015,
-0.022536635398864746,
-0.01579943113029003,
0.007514347322285175,
-0.04445233196020126,
0.05574760213494301,
-0.011880933307111263,
0.047845397144556046,
0.012997664511203766,
0.01485451404005289,
0.03133295103907585,
-0.014759602956473827,
-0.0312720462679863,
-0.018906593322753906,
0.000319383543683216,
-0.02315162681043148,
-0.022788168862462044,
0.03942815214395523,
-0.02824644185602665,
0.014366715215146542,
0.02307911403477192,
0.017052821815013885,
-0.006915715988725424,
-0.008399552665650845,
0.018928851932287216,
0.0036246159579604864,
0.04231264069676399,
-0.03684580698609352,
-0.03630463778972626,
-0.02001197822391987,
-0.005666196811944246,
-0.02855631522834301,
-0.009236054494976997,
-0.041265521198511124,
0.015834199264645576,
0.00982784852385521,
-0.029371637850999832,
0.04405961558222771,
-0.006697520148009062,
0.006439011078327894,
0.025483887642621994,
-0.007574902847409248,
-0.0388471893966198,
0.056094489991664886,
-0.024773191660642624,
0.013108788058161736,
-0.008061091415584087,
-0.0169685035943985,
0.05824041739106178,
-0.006641419138759375,
-0.04886026680469513,
-0.022702306509017944,
-0.0252920500934124,
-0.03750047832727432,
0.01602761261165142,
-0.020474079996347427,
0.02087787725031376,
-0.030286183580756187,
0.030078884214162827,
-0.006145537830889225,
-0.05676862224936485,
0.011628895066678524,
-0.05170142650604248,
-0.03145356476306915,
-0.017372312024235725,
-0.004172924440354109,
0.04568588733673096,
-0.01816204935312271,
-0.04860006645321846,
0.04308514669537544,
0.024780910462141037,
-0.0429689921438694,
0.0005500778206624091,
-0.04247574135661125,
-0.03996462747454643,
-0.0068491664715111256,
-0.027414986863732338,
0.032322075217962265,
-0.03894343227148056,
-0.01722179353237152,
0.021089155226945877,
0.023355571553111076,
0.03983534127473831,
0.002113587222993374,
-0.01716969721019268,
-0.02033812738955021,
-0.0027996499557048082,
0.022325865924358368,
0.049093034118413925,
-0.00234321691095829,
-0.044165581464767456,
0.0008511269697919488,
-0.023292750120162964,
0.020014584064483643,
-0.0003623822412919253,
-0.03205977752804756,
0.06328912079334259,
0.015248757787048817,
0.015105804428458214,
-0.05298697203397751,
0.040119677782058716,
0.015113519504666328,
-0.015277163125574589,
-0.001133487094193697,
0.023521047085523605,
0.04951310157775879,
0.0008971503702923656,
-0.003764426801353693,
0.02144021913409233,
0.08519835770130157,
-0.004574601072818041,
-0.04078081622719765,
0.003975388593971729,
-0.007797155063599348,
0.017081832513213158,
0.024851489812135696,
0.024549361318349838,
0.0015792539343237877,
0.013231866993010044,
0.029944822192192078,
0.008696354925632477,
0.013707992620766163,
-0.029688017442822456,
-0.0933108702301979,
0.003277459414675832,
-0.022368842735886574,
0.04338368400931358,
0.008288581855595112,
0.07649559527635574,
0.03067043051123619,
0.024719156324863434,
0.008656722493469715,
0.01461500022560358,
-0.08685643970966339,
0.01949974149465561,
-0.05426071584224701,
0.003635649336501956,
-0.01222346443682909,
-0.00030060874996706843,
-0.03644019737839699,
0.01274862326681614,
-0.0012545784702524543,
-0.03156323358416557,
-0.00381645979359746,
-0.030183177441358566,
-0.013300408609211445,
-0.00687137246131897,
-0.005148724652826786,
-0.0005247897352091968,
0.029280709102749825,
0.035264771431684494,
-0.03618422895669937,
0.03710539638996124,
0.025633027777075768,
-0.0312596894800663,
-0.012079929001629353,
0.010685518383979797,
-0.010261673480272293,
-0.0091727739199996,
0.03405420854687691,
0.0077503700740635395,
0.016989948228001595,
-0.009140302427113056,
-0.002468555700033903,
0.0055286758579313755,
0.0032886541448533535,
0.025936104357242584,
-0.006385463289916515,
-0.02606484480202198,
-0.030583718791604042,
-0.03137454390525818,
-0.011692077852785587,
0.05378846079111099,
-0.028411084786057472,
-0.018793970346450806,
0.006911967881023884,
-0.019831715151667595,
0.0029778596945106983,
0.019201204180717468,
0.03035622648894787,
-0.010910023003816605,
-0.012979000806808472,
-0.04237184673547745,
-0.022075258195400238,
-0.04700566828250885,
0.00876501016318798,
0.020558876916766167,
-0.025037838146090508,
-0.012832744978368282,
0.011007266119122505,
0.026500890031456947,
0.04267082363367081,
-0.025477057322859764,
0.05242729187011719,
0.012210501357913017,
0.007546095177531242,
-0.01498811598867178,
-0.02329893596470356,
0.0039641521871089935,
0.028346579521894455,
0.029554132372140884,
0.004715746268630028,
0.004881968256086111,
-0.0872877761721611,
-0.037752218544483185,
0.0106955012306571,
0.0607062429189682,
-0.04078618809580803,
-0.01392404641956091,
-0.04709726199507713,
-0.017235498875379562,
0.026878638193011284,
-0.03319718688726425,
0.05576697364449501,
-0.04016002267599106,
0.011906053870916367,
0.0018256859621033072,
-0.034557316452264786,
0.013117319904267788,
-0.019419586285948753,
0.001057751476764679,
0.007088881451636553,
-0.00698869489133358,
-0.0075835264287889,
0.04306427761912346,
0.04307963699102402,
0.03742559999227524,
0.09191524237394333,
0.002389811212196946,
0.014967484399676323,
-0.038346778601408005,
-0.02263316512107849,
-0.028088079765439034,
-0.07668926566839218,
-0.0030992645770311356,
0.012164848856627941,
-0.04043349623680115,
0.0006764648715034127,
-0.031225137412548065,
-0.092622309923172,
0.043038006871938705,
-0.0080111650750041,
-0.00044092079042457044,
-0.008289972320199013,
-0.057193417102098465,
0.0062714675441384315,
0.06068423017859459,
0.03295372426509857,
0.05729186534881592,
0.05324900895357132,
-0.04126674681901932,
0.005045811180025339,
0.01575109362602234,
0.014600785449147224,
-0.035729046911001205,
-0.03015575185418129,
0.015661925077438354,
0.04827307537198067,
-0.036588337272405624,
0.05376984924077988,
-0.015534436330199242,
0.021288175135850906,
-0.015025421045720577,
0.001609370345249772,
-0.0020066869910806417,
0.020067835226655006,
0.026461543515324593,
0.004233349114656448,
-0.032996274530887604,
0.041801679879426956,
-0.018839063122868538,
-0.021881762892007828,
-0.01431257277727127,
-0.009366328828036785,
0.013310982845723629,
0.03435450792312622,
-0.02066126838326454,
-0.01827586069703102,
-0.05088292434811592,
0.011168960481882095,
0.023082148283720016,
-0.04027903825044632,
0.05478878691792488,
0.0068303002044558525,
0.006836662534624338,
0.037575751543045044,
-0.09465646743774414,
-0.05158054083585739,
0.020183643326163292,
0.026645522564649582,
0.03089502640068531,
-0.03979659453034401,
0.06043359264731407,
0.02340603806078434,
-0.01518305391073227,
-0.045833658427000046,
-0.04884784296154976,
0.03831928223371506,
0.036972157657146454,
-0.0074038454331457615,
-0.01196490228176117,
-0.00015103971236385405,
-0.004863342270255089,
-0.010931476950645447,
-0.06547904759645462,
0.04327456280589104,
-0.03819325566291809,
-0.0027085058391094208,
0.018414698541164398,
-0.030187765136361122,
0.0631352886557579,
0.0076476833783090115,
-0.002953639719635248,
-0.0178369153290987,
-0.0528690405189991,
-0.031605981290340424,
-0.03614211454987526,
0.01761084608733654,
-0.03689431771636009,
-0.05067676678299904,
-0.01521357148885727,
-0.023313837125897408,
0.04401199519634247,
-0.018647154793143272,
0.013746732845902443,
0.04460623487830162,
0.010660743340849876,
-0.05123511701822281,
-0.0281162541359663,
0.04835948348045349,
0.019001467153429985,
0.02266160026192665,
-0.012872018851339817,
0.016401419416069984,
-0.02997797355055809,
-0.03513721749186516,
0.02340163104236126,
0.023053539916872978,
-0.02690311335027218,
-0.011495962738990784,
0.054804060608148575,
-0.050263021141290665,
-0.01837046630680561,
0.022128349170088768,
-0.012167628854513168,
0.06128339841961861,
-0.02275104820728302,
0.014852212741971016,
0.015193663537502289,
0.007503201719373465,
-0.012089614756405354,
-0.07034546881914139,
0.00543116545304656,
-0.0014190548099577427,
0.04221278801560402,
-0.000614694319665432,
0.045965440571308136,
0.03359273448586464,
-0.005112611223012209,
0.012913370504975319,
-0.003395023522898555,
0.040967799723148346,
0.0137410257011652,
0.0027877683751285076,
0.008611072786152363,
-0.017505550757050514,
0.026550328359007835,
0.007402169518172741,
0.007140233181416988,
0.015559626743197441,
-0.018104711547493935,
0.02354811504483223,
0.01679018698632717,
0.017917191609740257,
-0.014765682630240917,
-0.027186429128050804,
-0.00008252413681475446,
-0.04876910522580147,
0.019321871921420097,
0.036548223346471786,
-0.06300932168960571,
0.04275316372513771,
0.006965030450373888,
-0.003060487797483802,
-0.02808171883225441,
-0.014282181859016418,
-0.027157027274370193,
0.01667526178061962,
-0.00918128713965416,
0.012414645403623581,
0.0053718239068984985,
0.0482756607234478,
-0.02212514914572239,
0.003996606916189194,
0.020693741738796234,
-0.012026694603264332,
-0.06589708477258682,
-0.02630421705543995,
-0.027686849236488342,
-0.05970798060297966,
0.06472202390432358,
0.02349945902824402,
-0.013468164019286633,
0.040626902133226395,
-0.03921891748905182,
0.014591854996979237,
0.013120523653924465,
0.04932905733585358,
0.00800391472876072,
0.07725071907043457,
-0.022387633100152016,
0.02190915122628212,
-0.017691701650619507,
0.0019936044700443745,
0.09781382232904434,
0.04627569019794464,
-0.006457015872001648,
-0.05363871902227402,
-0.008076149970293045,
-0.002717572031542659,
-0.01699306070804596,
-0.054005227982997894,
-0.027635853737592697,
-0.03395873308181763,
0.024446746334433556,
0.025796018540859222,
0.019630858674645424,
-0.04220592975616455,
0.012623489834368229,
0.051548779010772705,
-0.0009817542741075158,
0.00022845172497909516,
0.020165493711829185,
0.030577074736356735,
-0.015742609277367592,
0.045056432485580444,
-0.04056178033351898,
0.019662242382764816,
-0.00874623004347086,
-0.022630561143159866,
-0.04054180532693863,
-0.012929114513099194,
0.03679705783724785,
-0.01827988401055336,
-0.015218379907310009,
-0.034683044999837875,
0.03681231290102005,
-0.01958242431282997,
-0.022651338949799538,
0.011357179842889309,
0.019164344295859337,
-0.00027631144621409476,
0.007851357571780682,
0.049867432564496994,
0.040402647107839584,
-0.002378662582486868,
0.004150986671447754,
0.021912015974521637,
-0.0625632256269455,
0.001457588979974389,
-0.03780657425522804,
-0.004803121089935303,
0.0032622891012579203,
0.04263381287455559,
0.010830908082425594,
0.015036897733807564,
0.03865455836057663,
-0.04773309826850891,
-0.038506947457790375,
-0.00697937048971653,
0.027895869687199593,
-0.011455608531832695,
-0.026803983375430107,
-0.06452076137065887,
-0.001071783946827054,
-0.016605110839009285,
-0.01124300342053175,
-0.031994812190532684,
-0.00042359292274340987,
0.013360978104174137,
0.0169833954423666,
-0.03168988227844238,
0.02272060140967369,
-0.005188495386391878,
-0.045792825520038605,
0.007840681821107864,
-0.034225944429636,
-0.022864175960421562,
0.015044580213725567,
0.047431107610464096,
0.03312467783689499,
0.044794779270887375,
0.012232850305736065,
-0.01921934261918068,
-0.05757245048880577,
0.03851516917347908,
0.02891482040286064,
-0.02192947082221508,
-0.03145090490579605,
0.017871364951133728,
0.017828479409217834,
0.03382878750562668,
0.019800757989287376,
-0.010501833632588387,
-0.02358788438141346,
0.06778891384601593,
0.009629253298044205,
-0.024758875370025635,
-0.03730481117963791,
0.0036404922138899565,
-0.05024394020438194,
0.013259628787636757,
0.020516132935881615,
0.0395190492272377,
-0.011529386974871159,
-0.00549293402582407,
0.004153619986027479,
0.01725865714251995,
-0.03816969320178032,
-0.0037964596413075924,
0.05361297354102135,
-0.015669750049710274,
-0.023698125034570694,
0.0021748163271695375,
-0.005511548835784197,
0.01873154751956463,
-0.013603012077510357,
-0.0046820323914289474,
-0.0018623984651640058,
0.030840082094073296,
0.0014987412141636014,
-0.04914787411689758,
0.014041367918252945,
-0.006267684977501631,
0.010821242816746235,
-0.03737833350896835,
-0.00885748490691185,
-0.0419580414891243,
-0.03947211056947708,
-0.011700139380991459,
-0.013760301284492016,
-0.011284451931715012,
0.03089326247572899,
-0.01260831207036972,
0.035203736275434494,
0.050291601568460464,
0.02338448539376259,
-0.01743248477578163,
-0.034777507185935974,
-0.010173030197620392,
0.01748345047235489,
0.06975846737623215,
-0.04696693271398544,
-0.02759701758623123,
0.09140488505363464,
-0.01567883975803852,
0.004168357700109482,
0.02540482021868229,
-0.02140195108950138,
0.044641900807619095,
0.047840192914009094,
-0.013366412371397018,
-0.008798672817647457,
0.07196886837482452,
-0.0042978799901902676,
0.01281355507671833,
0.005657890345901251,
-0.016676876693964005,
0.01638326793909073,
0.028818830847740173,
-0.01093230675905943,
-0.029315153136849403,
-0.0010228963801637292,
0.029698045924305916,
0.03271431475877762,
0.007867325097322464,
-0.01288085151463747,
0.025132346898317337,
0.024819253012537956,
0.02185792103409767,
0.02968561090528965,
0.008302812464535236,
0.004828253295272589,
0.007847758010029793,
-0.02395748719573021,
0.00910484604537487,
-0.02649892307817936,
-0.0073682512156665325,
-0.11897382885217667,
-0.016049442812800407,
0.016210224479436874,
0.007164022419601679,
0.010482177138328552,
-0.032799653708934784,
0.016193334013223648,
0.020077386870980263,
-0.0653117224574089,
-0.021364595741033554,
-0.002576233819127083,
-0.025197720155119896,
-0.02087387442588806,
0.05882633477449417,
-0.00959056243300438,
0.013230561278760433,
0.028040222823619843,
0.07896728068590164,
-0.004220591392368078,
0.068712517619133,
0.024792632088065147,
-0.0038870235439389944,
-0.01614386960864067,
0.021609755232930183,
0.006550830323249102,
-0.0036203707568347454,
0.07456839084625244,
-0.06477900594472885,
-0.004160498734563589,
0.022020747885107994,
-0.0037932435516268015,
-0.0027781252283602953,
-0.005663965363055468,
0.018562311306595802,
0.006031794007867575,
0.046060960739851,
-0.003670686623081565,
-0.009826083667576313,
-0.03685782104730606,
0.011302883736789227,
0.011634498834609985,
-0.011067060753703117,
-0.016789523884654045,
-0.01556161604821682,
0.03658556193113327,
-0.02620001509785652,
-0.02416306734085083,
0.058719150722026825,
-0.0335492342710495,
-0.030908983200788498,
-0.014738781377673149,
0.003580682445317507,
-0.0043751392513513565,
-0.001514459727331996,
-0.0597066730260849,
-0.04633035510778427,
-0.0169539675116539,
0.01876811496913433,
-0.048385296016931534,
0.009879376739263535,
0.004814326297491789,
-0.029669757932424545,
-0.023771191015839577,
0.019436726346611977,
-0.018230905756354332,
-0.03576953709125519,
-0.03927729278802872,
-0.006932537537068129,
0.06850022077560425,
0.004453952424228191,
0.005745194386690855,
-0.028013326227664948,
-0.02216905914247036,
0.026913855224847794,
0.002871951088309288,
0.03846459835767746,
0.039195869117975235,
-0.032493170350790024,
-0.02713909186422825,
-0.06419575214385986,
0.013225331902503967,
-0.014048222452402115,
-0.02282019704580307,
-0.04901689291000366,
-0.06735395640134811,
-0.002239934168756008,
0.0335070826113224,
0.02501172199845314,
-0.05492107570171356,
-0.00583528121933341,
0.044443320482969284,
-0.029069075360894203,
0.03204198181629181,
-0.030884208157658577,
-0.03791119158267975,
0.01476403046399355,
-0.013650334440171719,
0.01272337231785059,
-0.006524698343127966,
-0.016117071732878685,
0.014400338754057884,
0.06391990929841995,
0.007425553165376186,
-0.004609848838299513,
-0.013364237733185291,
-0.009024458937346935,
0.022793741896748543,
0.015601636841893196,
-0.006091415882110596,
0.0408686064183712,
-0.03399006649851799,
-0.01668618991971016,
-0.023079391568899155,
-0.03717535734176636,
-0.018772095441818237,
0.024222329258918762,
-0.0726243406534195,
0.024291792884469032,
0.0009006354957818985,
-0.01770140789449215,
0.02000567503273487,
-0.05870448052883148,
-0.002698509953916073,
0.024956470355391502,
0.0074233138002455235,
0.016386335715651512,
0.05363959074020386,
-0.020239148288965225,
0.014628492295742035,
-0.019795045256614685,
0.014894403517246246,
-0.00557750603184104,
-0.03058028221130371,
-0.02291146107017994,
0.012759567238390446,
0.04894644021987915,
-0.031235670670866966,
-0.014615397900342941,
0.01305358950048685,
0.05224316939711571,
0.011946744285523891,
0.01881924271583557,
0.009672398678958416,
-0.021692905575037003,
-0.050119128078222275,
0.05678100138902664,
0.011735627427697182,
0.00421671150252223,
0.01772632636129856,
0.0018232419388368726,
0.0828748270869255,
-0.006583572831004858,
0.003207098226994276,
-0.0011415211483836174,
0.011245789006352425,
-0.01834234967827797,
0.022454574704170227,
-0.01228468120098114,
0.021012907847762108,
-0.024719223380088806,
0.0009569547255523503,
-0.006456071510910988,
-0.011204356327652931,
0.02118365652859211,
-0.055399175733327866,
0.03979315981268883,
-0.033026453107595444,
0.008626580238342285,
-0.005629738327115774,
-0.008518216200172901,
-0.028080737218260765,
-0.01728828251361847,
0.02806486189365387,
0.001187615329399705,
0.026573611423373222,
-0.0022402156610041857,
0.003227983834221959,
-0.014709994196891785,
0.04159414768218994,
-0.02098514325916767,
0.0007262758444994688,
0.012372573837637901,
0.009773376397788525,
0.010737122036516666,
-0.016014816239476204
] |
<p><a href="http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence" rel="nofollow">$E=mc^2$</a> is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is speed of light in vacuum. </p>
<p>What I didn't understood is how we will introduce speed of light?</p>
<p>Atom bomb is made using this principle which converts mass into energy; in that the mass is provided by uranium but where did speed of light comes into play? How can speed of light can be introduced in atom bomb?</p>
| 1,029 |
[
-0.028991911560297012,
-0.04896533861756325,
-0.016207465901970863,
-0.03454185649752617,
0.014199567958712578,
-0.00043790810741484165,
-0.041277170181274414,
-0.050873082131147385,
0.0010924007510766387,
-0.018202699720859528,
0.027591196820139885,
0.031049242243170738,
0.07261978089809418,
0.01423105038702488,
0.0221879705786705,
0.010876283049583435,
0.009028463624417782,
-0.007271592505276203,
0.00010965866385959089,
-0.04324376583099365,
0.008560017682611942,
-0.024424800649285316,
0.000898373662494123,
0.009670139290392399,
-0.022137153893709183,
0.06427561491727829,
0.030223743990063667,
0.012682132422924042,
0.017921535298228264,
0.04897203668951988,
0.026626452803611755,
-0.03630736842751503,
0.026913655921816826,
0.01920313946902752,
-0.03269164264202118,
-0.0065983994863927364,
-0.043455470353364944,
-0.041637808084487915,
0.04701846092939377,
0.021579889580607414,
0.00684340251609683,
-0.03600308671593666,
0.00819004699587822,
0.020049909129738808,
-0.01272197812795639,
0.025004109367728233,
0.002287386218085885,
-0.02523908019065857,
0.03756236657500267,
-0.0493021234869957,
0.05783391371369362,
0.007823936641216278,
0.029938766732811928,
-0.003772786119952798,
-0.012538651935756207,
-0.013713727705180645,
0.07086789608001709,
0.050673339515924454,
-0.02351713553071022,
-0.029523305594921112,
0.006942993961274624,
0.01101379282772541,
0.0022959033958613873,
-0.02062733843922615,
-0.014043332077562809,
0.036335211247205734,
-0.03614301607012749,
0.023794755339622498,
0.015318361110985279,
0.012737267650663853,
0.020652957260608673,
0.016691816970705986,
0.03305206075310707,
-0.005612038541585207,
0.015376230701804161,
-0.05815017595887184,
0.008378715254366398,
0.01962965540587902,
0.004280576948076487,
0.05649605765938759,
-0.01567603275179863,
0.019439885392785072,
0.027094118297100067,
0.03393229842185974,
-0.006130876485258341,
-0.004833901766687632,
0.04087560996413231,
-0.0036612425465136766,
0.009229499846696854,
0.00187476328574121,
-0.01062069833278656,
0.020487746223807335,
0.02531301975250244,
-0.004897944629192352,
0.014027560129761696,
0.04558044299483299,
-0.001284619327634573,
0.05980747938156128,
0.013749365694820881,
-0.005415868014097214,
0.04948844015598297,
0.02932893857359886,
0.03724014014005661,
0.058605823665857315,
0.013387519866228104,
-0.028038227930665016,
-0.04673716798424721,
0.04046059772372246,
-0.023428838700056076,
0.010454224422574043,
-0.05827726423740387,
-0.005087410565465689,
0.033762041479349136,
-0.010921541601419449,
0.029457755386829376,
-0.05351143702864647,
0.013712351210415363,
-0.01587515138089657,
0.09379877150058746,
0.038117874413728714,
0.033931806683540344,
-0.027392446994781494,
0.03494875505566597,
-0.020161254331469536,
-0.07145531475543976,
-0.04128330945968628,
0.024843856692314148,
-0.009999316185712814,
-0.029116369783878326,
0.021535879001021385,
-0.011864987201988697,
-0.04843038320541382,
-0.022236233577132225,
0.016631416976451874,
0.019071383401751518,
-0.023426849395036697,
-0.14307178556919098,
-0.06678666919469833,
0.03269490972161293,
0.014866698533296585,
-0.025684058666229248,
-0.0952441468834877,
0.028780225664377213,
0.017176615074276924,
0.08356905728578568,
0.013822544366121292,
-0.02025800570845604,
-0.010294229723513126,
0.05122089385986328,
0.02742805890738964,
-0.010204343125224113,
-0.020427946001291275,
0.028508218005299568,
0.0025869461242109537,
0.024336284026503563,
-0.06648903340101242,
-0.015783336013555527,
0.03292377293109894,
-0.01946117728948593,
-0.024218900129199028,
0.05404168739914894,
-0.05142897367477417,
-0.005826161243021488,
0.015499277971684933,
-0.012500111944973469,
-0.025040989741683006,
0.06962507218122482,
0.05306150019168854,
-0.0055000330321490765,
0.04649388790130615,
0.02737090364098549,
0.05018627643585205,
0.012791001237928867,
0.009336598217487335,
0.000852355093229562,
-0.06379857659339905,
-0.02347780205309391,
0.0013067268300801516,
-0.01831524260342121,
0.01757770963013172,
-0.056531619280576706,
-0.050648365169763565,
0.005209117196500301,
0.006508195772767067,
0.01727505959570408,
0.053115688264369965,
-0.03248627856373787,
0.03241095691919327,
0.006052575074136257,
-0.056769609451293945,
-0.024177372455596924,
-0.07427512854337692,
0.032019127160310745,
0.005652261897921562,
0.009595463052392006,
-0.011259578168392181,
-0.005487542599439621,
0.014951792545616627,
-0.02069915644824505,
-0.014159757643938065,
-0.011860047467052937,
0.0673525258898735,
0.006911497563123703,
0.01943119801580906,
0.013242949731647968,
0.0363631509244442,
0.0029776941519230604,
-0.02259683609008789,
0.0012900250731036067,
-0.0018879444105550647,
-0.013368343934416771,
0.03539262339472771,
-0.011165083386003971,
-0.005978845991194248,
-0.013057402335107327,
-0.002309769857674837,
0.003015801077708602,
-0.01212998665869236,
0.009416354820132256,
0.042437706142663956,
0.0011058988748118281,
0.10176193714141846,
0.023438861593604088,
0.0011473295744508505,
0.016627974808216095,
0.05550966039299965,
0.020860886201262474,
0.047769512981176376,
-0.00767055619508028,
-0.054502636194229126,
-0.03933088481426239,
-0.03512946888804436,
0.0053611756302416325,
0.01374680083245039,
-0.06542904675006866,
0.02591823972761631,
0.003308249404653907,
0.030039526522159576,
0.02637847512960434,
0.029987338930368423,
-0.036611028015613556,
-0.037863168865442276,
0.009828174486756325,
0.02533590793609619,
-0.0021949303336441517,
-0.0010168288135901093,
0.009656987152993679,
0.021323662251234055,
-0.028401900082826614,
-0.0006877770647406578,
0.010126885958015919,
0.01873852126300335,
-0.0268089659512043,
0.0162334144115448,
0.000005037690698372899,
-0.024700229987502098,
0.014855653047561646,
-0.027089789509773254,
0.010796608403325081,
0.031369633972644806,
0.014196045696735382,
0.000492399965878576,
-0.032264161854982376,
-0.010629224590957165,
-0.0028896986041218042,
0.025769414380192757,
0.002994680544361472,
-0.0066068717278540134,
0.011210030876100063,
-0.013097353279590607,
0.015031707473099232,
0.0029461390804499388,
-0.01972542330622673,
-0.06414264440536499,
-0.003667763201519847,
0.00046042597386986017,
-0.012408262118697166,
0.023603463545441628,
-0.02916591428220272,
-0.06701075285673141,
0.003371017286553979,
-0.04980629310011864,
-0.02165941707789898,
-0.012215930037200451,
-0.025263847783207893,
0.041194185614585876,
-0.050637975335121155,
-0.010244186967611313,
0.06208527088165283,
-0.014994199387729168,
0.006898738443851471,
0.050993937999010086,
-0.009840771555900574,
-0.05557030439376831,
-0.006957337725907564,
-0.019004521891474724,
0.007773847319185734,
0.018358033150434494,
-0.008600110188126564,
0.05598893389105797,
-0.021575625985860825,
-0.031952232122421265,
0.0017421904485672712,
-0.04726110026240349,
-0.018927665427327156,
-0.03829234465956688,
-0.01991633139550686,
0.01576518639922142,
-0.04363957419991493,
0.0363682322204113,
0.022674506530165672,
-0.060745369642972946,
0.019865652546286583,
-0.020715180784463882,
-0.03045836091041565,
0.04305877909064293,
0.02443234622478485,
0.05943194404244423,
-0.0016788044013082981,
-0.03140236809849739,
0.04596031457185745,
0.05044643580913544,
-0.033895447850227356,
-0.02671702206134796,
0.003207354573532939,
0.03253571316599846,
-0.03396148234605789,
-0.002560578053817153,
0.0371939055621624,
-0.009901232086122036,
-0.004367932677268982,
0.01355763990432024,
0.04764479771256447,
0.02607155777513981,
0.0052032084204256535,
-0.00988034624606371,
-0.02158145233988762,
0.005131506826728582,
0.030719460919499397,
0.01888822577893734,
0.002737431786954403,
-0.03816508501768112,
0.00996552687138319,
0.0032234920654445887,
0.03897693380713463,
0.009507324546575546,
-0.023622194305062294,
0.03052547574043274,
0.017149675637483597,
-0.00569722056388855,
-0.030330659821629524,
0.017919868230819702,
-0.020560629665851593,
-0.011771631427109241,
0.051432255655527115,
0.006969118490815163,
0.027517538517713547,
-0.0002678468299563974,
-0.016901476308703423,
-0.0018474083626642823,
0.06041862815618515,
-0.03048277646303177,
-0.037850361317396164,
-0.0017843591049313545,
-0.01947615295648575,
0.03704576939344406,
-0.007682522293180227,
0.004690219648182392,
0.05120605230331421,
0.04839012771844864,
0.004055919591337442,
0.00102435692679137,
-0.013466253876686096,
0.002797540510073304,
-0.04870154336094856,
-0.019577838480472565,
-0.000656892079859972,
0.05422741174697876,
-0.015243401750922203,
0.08013718575239182,
0.03191167116165161,
0.010361990891397,
0.020228074863553047,
-0.03256964311003685,
-0.07293420284986496,
0.019993526861071587,
-0.07065892219543457,
-0.012612656690180302,
-0.022334637120366096,
-0.027595194056630135,
-0.04649840295314789,
-0.025107238441705704,
-0.04257115721702576,
-0.025819355621933937,
-0.0282889474183321,
-0.03768333047628403,
0.043298736214637756,
-0.06433522701263428,
-0.044211823493242264,
0.0007456114399246871,
0.04389013722538948,
0.013197104446589947,
0.00626329006627202,
-0.007721438072621822,
0.0451308935880661,
-0.06794844567775726,
-0.006040950305759907,
-0.001982886577025056,
-0.019789284095168114,
0.009277045726776123,
0.03414645045995712,
0.05895010009407997,
0.008328861556947231,
-0.03887508437037468,
0.009569083340466022,
0.022211000323295593,
0.026120034977793694,
-0.00032916307100094855,
-0.0297192744910717,
-0.05213870108127594,
-0.016338560730218887,
-0.018511494621634483,
-0.010926048271358013,
0.04182632267475128,
0.007528450805693865,
0.009964078664779663,
0.01440186146646738,
0.004446626640856266,
0.0012408330803737044,
0.05724494159221649,
0.08533448725938797,
-0.02260047011077404,
-0.0064099691808223724,
-0.06930229067802429,
-0.004822427872568369,
-0.01592038944363594,
-0.037531353533267975,
0.01895674504339695,
0.008610082790255547,
-0.0205097533762455,
0.02191871963441372,
0.033278729766607285,
0.025392672047019005,
-0.02817768231034279,
0.007894809357821941,
0.019214648753404617,
-0.01495725754648447,
0.034790582954883575,
-0.034033264964818954,
-0.013834713026881218,
0.007539378944784403,
0.03009128011763096,
-0.0333210788667202,
0.0036688530817627907,
-0.07061491161584854,
0.0029607475735247135,
0.002557227620854974,
0.047456566244363785,
-0.039820607751607895,
0.018707754090428352,
-0.07710031419992447,
-0.0014530379557982087,
0.0077429297380149364,
-0.031270142644643784,
0.04090559482574463,
-0.04020857810974121,
-0.018417926505208015,
0.012811282649636269,
-0.004151001572608948,
-0.009454034268856049,
0.040201179683208466,
0.0029245957266539335,
-0.029687505215406418,
-0.018274936825037003,
-0.0013093209126964211,
0.002289314055815339,
-0.012901011854410172,
0.04847608506679535,
0.02875976637005806,
-0.01089275348931551,
-0.012915775179862976,
0.00039019991527311504,
0.03702181205153465,
-0.020376650616526604,
-0.05738094449043274,
-0.004455904942005873,
0.0023047281429171562,
-0.025402003899216652,
0.01898004673421383,
-0.029534775763750076,
-0.04683615639805794,
0.02789212018251419,
0.049605052918195724,
-0.01399471890181303,
-0.03285576403141022,
-0.07193005830049515,
-0.004162909928709269,
0.04493827745318413,
-0.02345263957977295,
0.028866637498140335,
0.05147899314761162,
-0.041982971131801605,
0.00010163675324292853,
-0.022119253873825073,
0.04518578574061394,
-0.01287126261740923,
0.012049978598952293,
-0.0012444419553503394,
0.028924042358994484,
-0.047033894807100296,
0.03626366704702377,
-0.016696607694029808,
-0.004950270056724548,
-0.022071249783039093,
-0.04818975552916527,
0.007710551843047142,
0.024303480982780457,
0.003932012710720301,
0.009521703235805035,
-0.03847536817193031,
0.002949807560071349,
-0.014935560524463654,
-0.04204612597823143,
0.01613433100283146,
0.025914015248417854,
0.005013447254896164,
-0.012761212885379791,
0.0012938218424096704,
0.026560574769973755,
-0.0069871582090854645,
-0.036028921604156494,
0.031022973358631134,
-0.05145024508237839,
0.04429042339324951,
0.008130285888910294,
-0.021310366690158844,
-0.0010051294229924679,
-0.06926027685403824,
-0.05440105125308037,
0.013360001146793365,
0.015167384408414364,
0.0041258432902395725,
-0.04069002717733383,
0.03497842699289322,
0.009226934984326363,
0.02075977623462677,
-0.0516742467880249,
-0.05380511283874512,
0.005643393844366074,
-0.023437324911355972,
-0.0025171174202114344,
-0.03932499513030052,
0.020828602835536003,
-0.028923097997903824,
-0.033225491642951965,
-0.014454114250838757,
0.04026982933282852,
-0.014922871254384518,
-0.012332666665315628,
0.008435350842773914,
0.0070111434906721115,
0.0434279590845108,
-0.001809180830605328,
-0.036007098853588104,
0.011585329659283161,
0.0197185967117548,
0.007537861820310354,
0.012958534061908722,
0.07747294008731842,
-0.011027953587472439,
-0.05904466286301613,
-0.01047484390437603,
-0.0041927918791770935,
0.03306146711111069,
-0.024531498551368713,
0.015495266765356064,
0.019158435985445976,
0.056139398366212845,
-0.02690599113702774,
-0.024205734953284264,
0.010088087059557438,
0.013719405978918076,
0.05381173640489578,
-0.0029184625018388033,
-0.0037045322824269533,
-0.05708588659763336,
-0.054237186908721924,
0.046385787427425385,
-0.0044475579634308815,
0.04545570909976959,
-0.02139207161962986,
0.03826780989766121,
-0.01460715290158987,
0.01002220343798399,
-0.011344972997903824,
-0.04276558384299278,
0.006204500794410706,
0.019146358594298363,
-0.005067763384431601,
0.008255586959421635,
-0.033603403717279434,
0.008452416397631168,
-0.010755900293588638,
-0.03788422793149948,
-0.010083101689815521,
0.08249682933092117,
-0.023777702823281288,
0.06374993175268173,
0.012801784090697765,
-0.007131710648536682,
0.01603490486741066,
-0.04017966240644455,
-0.025218404829502106,
-0.0033788024447858334,
0.030195701867341995,
0.005614208057522774,
0.00032317161094397306,
-0.03180145472288132,
0.04977311193943024,
0.06586193293333054,
0.02754105068743229,
0.028004053980112076,
0.03697716444730759,
0.0316857174038887,
-0.019774507731199265,
-0.0068617756478488445,
-0.02869691513478756,
0.036763619631528854,
-0.0066629997454583645,
0.021571535617113113,
-0.007937967777252197,
0.020380774512887,
0.014423112384974957,
-0.007700973190367222,
-0.0035539313685148954,
-0.038568831980228424,
-0.029961775988340378,
-0.06206547096371651,
0.011138475500047207,
0.006037386134266853,
-0.010719028301537037,
-0.020550379529595375,
0.018476588651537895,
0.02191987819969654,
-0.017783012241125107,
0.031695105135440826,
0.005487936548888683,
-0.06652189791202545,
-0.04476815462112427,
-0.03126002475619316,
-0.02807345986366272,
0.02527972124516964,
-0.02199716493487358,
-0.027929257601499557,
-0.006227957550436258,
-0.015839748084545135,
0.013789394870400429,
0.006023730617016554,
0.03811565041542053,
-0.012055310420691967,
0.06768395006656647,
0.009136772714555264,
0.01353996992111206,
-0.0038004559464752674,
0.018938982859253883,
0.10750814527273178,
0.029471036046743393,
-0.012840747833251953,
-0.06930912286043167,
0.02575402334332466,
-0.03211653605103493,
0.015092444606125355,
-0.018246853724122047,
0.010477358475327492,
-0.03502587229013443,
0.03848310187458992,
0.006302318535745144,
0.05083629488945007,
0.022558508440852165,
0.028361685574054718,
0.03425610065460205,
-0.020484095439314842,
-0.04992254450917244,
-0.0051063126884400845,
0.009712206199765205,
-0.041405610740184784,
0.02786615863442421,
-0.01435992680490017,
0.01650429703295231,
-0.036414217203855515,
-0.005036721471697092,
-0.041261881589889526,
-0.036085549741983414,
0.03887873888015747,
0.011793017387390137,
-0.04621339216828346,
-0.015373710542917252,
-0.002514766063541174,
-0.04344480112195015,
-0.02044309861958027,
0.01613764837384224,
0.03927560895681381,
-0.0031553874723613262,
-0.004727864637970924,
0.0043540168553590775,
0.019717393442988396,
-0.00892011821269989,
0.01926015503704548,
-0.006001128349453211,
-0.05492064729332924,
0.009062978439033031,
-0.012510547414422035,
0.029407499358057976,
-0.02206556126475334,
-0.0019794395193457603,
-0.003454137360677123,
0.013677882961928844,
-0.015940390527248383,
-0.01484290137887001,
-0.023038847371935844,
0.012297076173126698,
0.008606507442891598,
-0.0050045764073729515,
0.012981254607439041,
-0.056315626949071884,
0.01491661835461855,
-0.0341222770512104,
0.046753376722335815,
-0.006003687158226967,
0.007694213185459375,
0.016601894050836563,
-0.011847438290715218,
0.007545283529907465,
-0.026174819096922874,
-0.017187613993883133,
-0.01397284958511591,
0.004069676622748375,
-0.054653968662023544,
-0.02653566375374794,
0.03486150503158569,
0.06140553578734398,
0.009462992660701275,
0.016030285507440567,
-0.00013539045176003128,
-0.01751738414168358,
-0.0762738287448883,
0.048157766461372375,
0.0020271495450288057,
-0.029061341658234596,
-0.041402384638786316,
-0.002125665545463562,
0.03875937685370445,
0.01651020161807537,
-0.025038614869117737,
-0.008053778670728207,
-0.03525782749056816,
-0.016338175162672997,
0.015085655264556408,
-0.015265793539583683,
0.008704612962901592,
0.015935994684696198,
-0.0013631780166178942,
0.011884544976055622,
-0.02855897881090641,
0.016455138102173805,
0.051802217960357666,
-0.002717070048674941,
-0.0075636873953044415,
0.011520635336637497,
-0.014346549287438393,
-0.004140958189964294,
0.010344317182898521,
-0.009135699830949306,
0.012780338525772095,
0.015971636399626732,
0.0305953212082386,
-0.008806318044662476,
-0.009085867553949356,
-0.029788948595523834,
-0.013851557858288288,
0.0011224399786442518,
0.000604416651185602,
-0.004884399473667145,
0.038688793778419495,
-0.04612142592668533,
0.030170680955052376,
-0.04982038959860802,
-0.00483680609613657,
-0.02520786039531231,
0.02657436951994896,
0.014173600822687149,
-0.015735605731606483,
-0.046652983874082565,
0.04761123284697533,
-0.02217348851263523,
0.018065618351101875,
-0.0048204101622104645,
0.04900795593857765,
-0.02133474498987198,
0.008974296972155571,
0.04163379967212677,
0.01771555468440056,
0.08300863951444626,
0.010485532693564892,
0.016264688223600388,
0.01579536311328411,
-0.03074636310338974,
-0.033513717353343964,
0.05700633302330971,
-0.0030450725462287664,
0.01627122424542904,
0.02297130413353443,
0.009281869977712631,
-0.0041755130514502525,
0.08712189644575119,
-0.03942074254155159,
0.01710836961865425,
0.007062216755002737,
-0.044960517436265945,
-0.00865555927157402,
0.030140230432152748,
-0.002441256772726774,
-0.03357240557670593,
-0.01588289812207222,
0.03985981270670891,
0.02874577045440674,
-0.01738034375011921,
0.0367821604013443,
-0.01703033223748207,
-0.006429199129343033,
0.017371438443660736,
0.026813294738531113,
0.01432496216148138,
0.039939627051353455,
0.07742235064506531,
-0.00849703699350357,
0.03515591099858284,
0.0007327029597945511,
-0.004683011677116156,
-0.10902813076972961,
0.011132060550153255,
0.010843195021152496,
0.003712212201207876,
0.04491919279098511,
-0.01059461385011673,
0.042638979852199554,
0.038583479821681976,
-0.0448969230055809,
0.011822967790067196,
-0.04340977966785431,
-0.03140581026673317,
-0.005954749882221222,
-0.013053837232291698,
-0.009565797634422779,
0.043760478496551514,
0.018981799483299255,
0.029027657583355904,
0.04755029082298279,
0.007750863675028086,
-0.023152010515332222,
-0.01740208826959133,
-0.01147681288421154,
0.02077329345047474,
0.0028365873731672764,
0.01640292815864086,
0.09127506613731384,
0.0017314075957983732,
-0.013604594394564629,
0.0393548309803009,
0.024966422468423843,
0.03481140732765198,
-0.006279326975345612,
-0.0019794015679508448,
0.004368247464299202,
0.029682043939828873,
0.007554950658231974,
0.006287646479904652,
-0.002894326578825712,
0.05213659629225731,
0.0036132780369371176,
0.004700337536633015,
0.001122192363254726,
0.007877962663769722,
0.016843745484948158,
-0.022096946835517883,
-0.03563482686877251,
0.023992888629436493,
0.0032166338060051203,
-0.049005549401044846,
0.03503923490643501,
0.006083866581320763,
0.01636776700615883,
-0.056850653141736984,
-0.006307095754891634,
-0.05572192743420601,
-0.03450547158718109,
0.047418806701898575,
-0.006197045091539621,
0.018238281831145287,
0.0066697984002530575,
-0.011265652254223824,
-0.003162909997627139,
0.00968899205327034,
0.0018179911421611905,
-0.025751762092113495,
-0.02641245909035206,
0.007397779263556004,
0.039688050746917725,
0.008997770957648754,
0.024342969059944153,
-0.028179993852972984,
-0.04368438944220543,
0.03245280683040619,
0.010609091259539127,
0.027514535933732986,
-0.018918046727776527,
-0.014234132133424282,
-0.01766924373805523,
-0.02188876084983349,
0.006419898476451635,
-0.013620293699204922,
0.010716001503169537,
-0.029061181470751762,
-0.011015430092811584,
-0.01224013976752758,
0.009156821295619011,
0.06577111035585403,
-0.009832430630922318,
-0.021795617416501045,
0.007969040423631668,
0.01580149680376053,
0.001646391930989921,
-0.043383147567510605,
0.0028068232350051403,
0.021906280890107155,
-0.04548453539609909,
-0.03281134366989136,
0.0003024745674338192,
-0.026567263528704643,
0.02385331690311432,
-0.00947633571922779,
-0.0017744677606970072,
0.0012388447066769004,
-0.02355472929775715,
-0.03738037496805191,
0.01870349608361721,
0.020695054903626442,
-0.012935321778059006,
0.0655665472149849,
-0.011162037029862404,
0.04065369814634323,
0.03897019103169441,
-0.0137697234749794,
-0.04198296740651131,
0.019718537107110023,
-0.02527550794184208,
0.017233174294233322,
-0.000209477060707286,
-0.020907685160636902,
0.024020614102482796,
-0.05523372441530228,
0.022110598161816597,
0.034891095012426376,
-0.03243863582611084,
-0.015410620719194412,
0.06131155416369438,
0.008077476173639297,
0.04283266142010689,
0.0304866936057806,
0.02124253287911415,
0.00437171570956707,
0.0009040649747475982,
0.01091600488871336,
0.04415331408381462,
0.02013472467660904,
-0.003196402220055461,
0.02874891273677349,
0.05554688721895218,
-0.0009006091277115047,
-0.02305205725133419,
0.020745905116200447,
0.011234773322939873,
-0.024354686960577965,
-0.04435773566365242,
0.002250032965093851,
-0.020977647975087166,
0.019636036828160286,
0.038744885474443436,
-0.033365100622177124,
0.07699384540319443,
-0.031083205714821815,
0.04098786786198616,
-0.003683751681819558,
0.003040504176169634,
-0.04816753789782524,
-0.01579960621893406,
-0.04897838085889816,
0.028559017926454544,
0.01252000406384468,
0.02773190848529339,
-0.012382376939058304,
-0.008945798501372337,
0.03308233991265297,
-0.013363643549382687,
0.028337033465504646,
-0.010968873277306557,
-0.05676387622952461,
-0.008149156346917152,
-0.031612642109394073,
0.022918906062841415,
-0.029629068449139595,
0.016740284860134125,
0.028883473947644234,
0.017002135515213013,
0.00452176108956337,
-0.024968577548861504,
-0.010728990659117699,
0.08681251108646393,
-0.05582161992788315,
-0.005283324979245663,
-0.028321072459220886,
-0.00023992032220121473,
-0.0414065420627594,
-0.024730883538722992
] |
<p>Here we have two magnets and they are sticking to each other. What I've learned that could possibly explain it is one magnet holds positive charge and the other one holds negative. But when the eletrons travel from the negative one to the positive one in order to be equilirium (just like static electricity won't stay long between a ballon and the wall), will they become both natural and are not sticky anymore? Maybe one day?</p>
| 10,664 |
[
-0.05151927471160889,
-0.022287441417574883,
-0.00878792256116867,
-0.007949789986014366,
0.01683557964861393,
0.016431191936135292,
-0.025492601096630096,
0.004110522102564573,
-0.018032977357506752,
-0.003125022863969207,
0.0057950615882873535,
0.05982242897152901,
0.03905646502971649,
0.04678826406598091,
0.02297448366880417,
-0.010834316723048687,
0.004902857355773449,
-0.01874486915767193,
0.02243751287460327,
-0.003500845981761813,
0.007054717745631933,
-0.020143387839198112,
0.03507537394762039,
0.01617676205933094,
-0.03715233877301216,
-0.006454915273934603,
0.009473034180700779,
-0.037026867270469666,
0.02261861227452755,
0.027225935831665993,
0.009903901256620884,
-0.024754192680120468,
0.00779417110607028,
-0.02826899103820324,
0.04325895011425018,
-0.00804103072732687,
-0.028492799028754234,
-0.0456039197742939,
-0.04306069016456604,
0.006586531642824411,
-0.018090710043907166,
-0.03132732957601547,
-0.02765309438109398,
0.027191435918211937,
-0.0439644418656826,
-0.04229942709207535,
0.0339798629283905,
0.012349260970950127,
0.07242847979068756,
-0.07946129888296127,
0.04141148552298546,
0.011499905958771706,
0.0392586924135685,
0.0018452281365171075,
-0.002455673413351178,
-0.04673762992024422,
0.06952329725027084,
0.045429524034261703,
0.0018137627048417926,
-0.04474956542253494,
-0.01886710710823536,
-0.012186596170067787,
-0.03480878472328186,
-0.01975974440574646,
-0.024573590606451035,
0.018756093457341194,
0.00854989979416132,
-0.03252696618437767,
0.04155834764242172,
-0.01248481310904026,
0.014089073054492474,
0.0408296175301075,
0.034630659967660904,
-0.009573913179337978,
0.00458186911419034,
-0.010774243623018265,
0.031271643936634064,
-0.006771020591259003,
0.013983548618853092,
0.040804386138916016,
-0.046429626643657684,
0.002085577929392457,
0.03897784277796745,
0.04913784936070442,
-0.007695946842432022,
-0.05654163658618927,
0.04781085625290871,
-0.024005502462387085,
0.021686509251594543,
0.026935070753097534,
0.026630066335201263,
0.012436317279934883,
0.039137013256549835,
-0.024075690656900406,
-0.054574400186538696,
0.02298917807638645,
0.008084626868367195,
0.03509046882390976,
-0.005659814458340406,
-0.008707081899046898,
0.02049407921731472,
0.021250762045383453,
0.016952715814113617,
0.06435221433639526,
0.018284309655427933,
-0.05234483629465103,
-0.05139413848519325,
0.009245472028851509,
-0.02426954172551632,
0.004502673167735338,
-0.02501516230404377,
-0.01814410835504532,
0.017902692779898643,
-0.02797461487352848,
0.04447238892316818,
-0.04765159264206886,
-0.0024835942313075066,
-0.027671363204717636,
0.03555561229586601,
0.10656289756298065,
0.03238165006041527,
-0.0032371035777032375,
0.027128545567393303,
0.0011423069518059492,
-0.07953939586877823,
0.00434077437967062,
0.023680971935391426,
-0.029895653948187828,
0.000782266550231725,
0.03086881712079048,
-0.011469018645584583,
0.0202418714761734,
-0.021255597472190857,
-0.021211234852671623,
0.02776748687028885,
0.016557786613702774,
-0.09618842601776123,
-0.01118533592671156,
0.04119433835148811,
-0.06761740893125534,
-0.0052265296690166,
-0.0852058082818985,
-0.03821822628378868,
-0.004462347831577063,
0.062106627970933914,
0.013914422132074833,
-0.01115124486386776,
-0.0010182177647948265,
0.02834223210811615,
0.00483935559168458,
-0.010858754627406597,
0.007333532441407442,
0.00400589918717742,
-0.055601105093955994,
-0.0014693366829305887,
-0.04919978976249695,
0.0500522181391716,
0.054221924394369125,
-0.003790889400988817,
-0.027231736108660698,
0.04422158747911453,
0.008680597878992558,
0.01115234661847353,
-0.006685859058052301,
-0.04699486866593361,
-0.052935317158699036,
0.0743812844157219,
0.026450522243976593,
-0.003024275181815028,
0.038464318960905075,
-0.006296925246715546,
0.036101844161748886,
0.012344233691692352,
0.03534339740872383,
-0.005369479767978191,
-0.02911187894642353,
-0.007407746277749538,
-0.052942097187042236,
0.010746306739747524,
-0.012881292961537838,
-0.0483318492770195,
-0.04762233793735504,
-0.005507121793925762,
0.022121481597423553,
-0.01869298331439495,
0.08296980708837509,
-0.013425427488982677,
-0.02512511797249317,
-0.0172551441937685,
-0.06347791850566864,
-0.040786903351545334,
-0.09920557588338852,
0.013787837699055672,
-0.014703599736094475,
-0.051998529583215714,
0.016175005584955215,
0.008305254392325878,
0.017356766387820244,
-0.056742824614048004,
-0.0527665801346302,
0.0012785911094397306,
0.0290546678006649,
0.020024580880999565,
-0.01403280533850193,
0.0014838011702522635,
0.037377841770648956,
0.017025819048285484,
0.013302003033459187,
0.03207923471927643,
-0.03265940025448799,
-0.02879832126200199,
-0.004632818978279829,
-0.006765952333807945,
0.04414762184023857,
0.056505925953388214,
-0.01868577115237713,
0.02556079626083374,
-0.019406402483582497,
0.011832015588879585,
0.012336436659097672,
-0.0008709378889761865,
0.060832083225250244,
0.013409201055765152,
-0.030114730820059776,
0.011722289957106113,
0.028246218338608742,
0.0061372797936201096,
0.014718693681061268,
-0.010849286802113056,
-0.02247978188097477,
-0.04699065163731575,
-0.0030495396349579096,
0.020538557320833206,
0.07310393452644348,
-0.02453671209514141,
0.030162591487169266,
-0.029773153364658356,
0.03332258388400078,
0.00006799625407438725,
0.04914598539471626,
-0.011781546287238598,
-0.01498643308877945,
0.018064429983496666,
0.010755342431366444,
0.022932013496756554,
0.008015520870685577,
0.06101997569203377,
0.01627170480787754,
-0.0035242640879005194,
0.00021821486006956547,
-0.01293653342872858,
0.009237142279744148,
0.020318716764450073,
0.011414643377065659,
0.026996491476893425,
-0.03372946009039879,
0.03795861825346947,
-0.022135602310299873,
0.01851276494562626,
-0.022263698279857635,
0.022578692063689232,
-0.006500124000012875,
0.0013423236086964607,
0.011109519749879837,
-0.009327552281320095,
-0.008398125879466534,
0.02122976817190647,
-0.016697272658348083,
0.03743162378668785,
-0.024892956018447876,
0.028844689950346947,
0.0022435823921114206,
-0.0027036438696086407,
0.012478969991207123,
0.01032832358032465,
0.023773884400725365,
0.0035329817328602076,
0.02143125608563423,
-0.027868380770087242,
-0.03883379325270653,
0.025378219783306122,
-0.050972163677215576,
0.01731530763208866,
0.04426954314112663,
-0.02196647599339485,
0.02613260969519615,
-0.004415032919496298,
0.0109233558177948,
0.0480712428689003,
0.009679405950009823,
0.03261890634894371,
0.010227233171463013,
-0.022287702187895775,
-0.05455097183585167,
-0.02158474735915661,
-0.0010685068555176258,
-0.006481525022536516,
-0.024255193769931793,
0.0028675987850874662,
0.03555595129728317,
-0.026539500802755356,
0.009711628779768944,
-0.012332851998507977,
-0.04757339879870415,
-0.026590559631586075,
-0.015694180503487587,
-0.04471509903669357,
0.03229163587093353,
-0.030822306871414185,
0.013446968980133533,
0.035350997000932693,
-0.04783033952116966,
-0.011696710251271725,
-0.051874447613954544,
-0.019484011456370354,
0.07032039761543274,
-0.026246320456266403,
0.024267086759209633,
-0.04537389054894447,
-0.019575247541069984,
0.07314858585596085,
0.016968507319688797,
-0.008615477941930294,
0.030214935541152954,
-0.05043008178472519,
-0.053080517798662186,
-0.025325998663902283,
0.012576819397509098,
0.06780444830656052,
-0.01236277911812067,
-0.004905637353658676,
0.049609918147325516,
0.01916470378637314,
-0.007836982607841492,
0.03369368240237236,
-0.0052624293603003025,
0.030962372198700905,
0.029470043256878853,
-0.005889665335416794,
0.06300568580627441,
0.01592794433236122,
-0.029270682483911514,
0.010642034932971,
0.042555972933769226,
0.03165031224489212,
0.051435764878988266,
-0.03658481314778328,
0.05980052798986435,
-0.0021698286291211843,
0.02322615683078766,
-0.01502168457955122,
0.040528275072574615,
0.030499672517180443,
-0.02551889419555664,
-0.03270845487713814,
0.00662210350856185,
0.05445447564125061,
-0.030098548159003258,
-0.007524438202381134,
0.05797223374247551,
0.039915576577186584,
-0.039311595261096954,
-0.04790269955992699,
-0.006095497403293848,
0.005132084246724844,
0.03733953833580017,
-0.027385547757148743,
-0.009645536541938782,
0.019820747897028923,
-0.007214776240289211,
0.01052182912826538,
0.011269004084169865,
-0.023771116510033607,
-0.025920117273926735,
-0.05997714400291443,
0.004029709845781326,
0.020022310316562653,
0.023951387032866478,
0.024352634325623512,
-0.00025417751749046147,
-0.01969238556921482,
0.059989217668771744,
-0.015511281788349152,
-0.0022715204395353794,
-0.09928085654973984,
-0.005665308330208063,
-0.023807449266314507,
-0.0012075761333107948,
0.02008107677102089,
0.007228217553347349,
0.0027966515626758337,
0.008634601719677448,
-0.03240002691745758,
-0.009825250133872032,
-0.0072484444826841354,
-0.04004055634140968,
-0.0015296140918508172,
-0.06515751034021378,
-0.03966277092695236,
-0.03400379791855812,
-0.00343147199600935,
0.014527371153235435,
-0.0221849475055933,
0.004407288506627083,
-0.02043474093079567,
-0.05874727666378021,
0.012111557647585869,
-0.03445473685860634,
-0.021917564794421196,
0.040132202208042145,
0.01627938263118267,
0.024059752002358437,
0.01776966080069542,
-0.006445936858654022,
0.0021295405458658934,
0.0501328743994236,
0.013050250709056854,
0.002388991415500641,
-0.012215926311910152,
-0.016727279871702194,
-0.04983406886458397,
-0.0560862235724926,
-0.0032270653173327446,
0.08971722424030304,
0.008400178514420986,
0.008164902217686176,
-0.0019066190579906106,
0.012629211880266666,
0.02149340696632862,
0.029500361531972885,
0.044842615723609924,
0.02457515336573124,
-0.01576361618936062,
-0.045271750539541245,
-0.006163406185805798,
-0.01141855027526617,
0.035822734236717224,
0.0039597381837666035,
-0.014010962098836899,
-0.03922297805547714,
-0.018178751692175865,
0.01618232950568199,
0.05200175940990448,
0.012007098644971848,
0.01601892150938511,
0.0026683099567890167,
0.036844830960035324,
-0.029080728068947792,
0.016538267955183983,
0.013488862663507462,
0.044411275535821915,
0.030286414548754692,
-0.002068999456241727,
-0.030845733359456062,
-0.09350146353244781,
0.01797380857169628,
0.04216495901346207,
0.027888761833310127,
0.012849879451096058,
-0.0039372132159769535,
-0.06437554210424423,
0.0014230532106012106,
0.07080768793821335,
-0.01565341278910637,
0.018925758078694344,
-0.004522935952991247,
-0.019816840067505836,
-0.040565166622400284,
-0.023222487419843674,
-0.0217516478151083,
-0.0032796196173876524,
0.008078635670244694,
0.03765494376420975,
-0.007503256667405367,
-0.034829407930374146,
-0.0038221143186092377,
0.03216670826077461,
0.03699205070734024,
0.07906243205070496,
0.005229551810771227,
0.036670949310064316,
-0.002694019814953208,
-0.008605396375060081,
-0.0029481537640094757,
-0.12101854383945465,
0.0236167274415493,
0.012351587414741516,
0.007915552705526352,
0.05476197227835655,
-0.0429927222430706,
-0.02157895639538765,
-0.015412445180118084,
0.00852030050009489,
-0.017681213095784187,
-0.002199810929596424,
0.002433306537568569,
0.021891266107559204,
0.02509499341249466,
-0.031769298017024994,
0.02463666908442974,
-0.029123766347765923,
-0.025524847209453583,
0.010798254981637001,
-0.0016473408322781324,
0.017135800793766975,
0.015239235945045948,
0.048232607543468475,
-0.0057897926308214664,
0.00009433825471205637,
-0.02367069385945797,
0.07671160995960236,
-0.04544106870889664,
-0.002728986321017146,
-0.0006240478833205998,
-0.006875230465084314,
-0.012509140186011791,
0.01609421893954277,
0.0002969646011479199,
-0.03635020554065704,
-0.01032419316470623,
0.0012935572303831577,
-0.030261553823947906,
-0.024967927485704422,
0.014970347285270691,
-0.03091452457010746,
-0.001346596167422831,
0.019700216129422188,
-0.02689025178551674,
-0.011600197292864323,
-0.03227932006120682,
0.00621295440942049,
0.010503972880542278,
-0.028859544545412064,
0.038023170083761215,
0.014404606074094772,
0.006065088324248791,
0.0009459495195187628,
-0.03661687672138214,
-0.03743557631969452,
0.033914316445589066,
-0.014794494956731796,
0.0010627011070027947,
-0.021184593439102173,
0.011259765364229679,
0.03275558352470398,
-0.014931079931557178,
-0.044019196182489395,
-0.045209310948848724,
0.013045242987573147,
-0.01477465033531189,
-0.02460603602230549,
-0.029826637357473373,
-0.017335781827569008,
-0.0002599290746729821,
-0.06421239674091339,
0.032803285866975784,
0.0565587654709816,
-0.044909343123435974,
0.005575981922447681,
0.03854084759950638,
-0.0014983132714405656,
0.08348451554775238,
0.010995491407811642,
-0.02597835473716259,
-0.003979740664362907,
-0.03641948103904724,
0.013585472479462624,
-0.013062458485364914,
0.06926676630973816,
-0.02766398712992668,
-0.031291134655475616,
0.013262603431940079,
-0.02028682641685009,
0.04854888841509819,
-0.03878583759069443,
-0.03241321071982384,
0.035849910229444504,
0.026715558022260666,
0.007320366334170103,
0.0009645204991102219,
0.032940976321697235,
0.01120095606893301,
0.022314930334687233,
0.0006853315862827003,
0.003372104838490486,
-0.045150477439165115,
-0.05113733559846878,
0.02622145414352417,
0.020043399184942245,
0.017761599272489548,
-0.009832922369241714,
0.07872720062732697,
0.0074181389063596725,
-0.046263936907052994,
0.05525480955839157,
-0.025661209598183632,
0.0436781644821167,
-0.030888311564922333,
-0.009692633524537086,
-0.040476102381944656,
-0.00008843968680594116,
-0.017721448093652725,
-0.03894100710749626,
-0.006312090437859297,
-0.011151512153446674,
0.027064526453614235,
-0.0063365125097334385,
0.04834599420428276,
0.007826977409422398,
0.002396486233919859,
-0.034051693975925446,
-0.02236427366733551,
-0.020305518060922623,
0.009843562729656696,
-0.012450315058231354,
0.01847456768155098,
-0.03547563776373863,
-0.00108630012255162,
0.015550299547612667,
0.044996634125709534,
0.018254349008202553,
-0.03246111795306206,
0.025153450667858124,
0.03102271258831024,
0.057440757751464844,
-0.0015069517539814115,
-0.06405303627252579,
0.03240273892879486,
-0.06142428144812584,
0.06667625904083252,
0.013134229928255081,
-0.03170504793524742,
0.04022657871246338,
0.004253030754625797,
0.012246237136423588,
-0.024602793157100677,
-0.05167584866285324,
-0.05388655140995979,
0.031304217875003815,
-0.01968139410018921,
0.014749059453606606,
-0.027918905019760132,
0.02635796181857586,
0.03480009362101555,
0.009930668398737907,
0.0038683395832777023,
0.007188819348812103,
-0.07520041614770889,
-0.03821473941206932,
-0.029056895524263382,
-0.0095831248909235,
0.05320582166314125,
0.016374988481402397,
-0.005031374283134937,
0.015604090876877308,
-0.013676663860678673,
0.03401440754532814,
0.029815606772899628,
0.02994907647371292,
-0.04441129043698311,
0.04727262631058693,
-0.014189410954713821,
0.04665954038500786,
-0.029981084167957306,
0.031144749373197556,
0.12602728605270386,
0.01912763901054859,
0.022865459322929382,
-0.05616871640086174,
0.04183359444141388,
-0.030086224898695946,
0.01856619119644165,
-0.0522150881588459,
-0.02335203066468239,
0.014941761270165443,
0.03430981561541557,
0.006741656921803951,
0.03563976287841797,
0.01591510698199272,
-0.02206118032336235,
0.05779644474387169,
-0.01709897816181183,
-0.03748888522386551,
-0.014194557443261147,
0.030414443463087082,
-0.02027931995689869,
-0.006877065170556307,
-0.035478558391332626,
0.036303963512182236,
-0.015167835168540478,
0.002642769133672118,
-0.009195503778755665,
-0.026491178199648857,
0.04286354035139084,
0.013614834286272526,
-0.03620416671037674,
0.010079776868224144,
0.020771034061908722,
-0.017269516363739967,
-0.01100345142185688,
-0.00429972168058157,
0.02713245153427124,
0.010670958086848259,
0.023512450978159904,
-0.019595755264163017,
0.04602262005209923,
-0.02310323901474476,
0.02921326272189617,
0.034454815089702606,
-0.023227816447615623,
0.021457388997077942,
-0.029238447546958923,
0.03972901031374931,
-0.028698481619358063,
-0.00515219010412693,
-0.0029829598497599363,
-0.006510930601507425,
0.03031073696911335,
-0.028098033741116524,
-0.03323693946003914,
0.0012442049337550998,
0.013244474306702614,
0.013500415720045567,
0.05704236403107643,
-0.043451666831970215,
-0.012479099445044994,
-0.011827915906906128,
-0.0188437607139349,
-0.010169975459575653,
0.03074854239821434,
0.029825668781995773,
0.009360463358461857,
0.04588526859879494,
0.018830569460988045,
-0.028486553579568863,
-0.028349004685878754,
-0.017717618495225906,
-0.05076318606734276,
-0.007706932723522186,
-0.010489296168088913,
0.02577863819897175,
-0.002329734619706869,
-0.027670742943882942,
-0.023632671684026718,
-0.02059800922870636,
-0.04273134469985962,
0.032541465014219284,
0.01911841332912445,
-0.01377097237855196,
-0.0059942929074168205,
-0.03001573123037815,
0.013595134019851685,
0.03235860913991928,
-0.050913646817207336,
0.010711845010519028,
0.009537299163639545,
0.00903200451284647,
0.01352425292134285,
0.009440324269235134,
-0.006304687354713678,
0.0003000538854394108,
-0.05420098453760147,
0.0024080208968371153,
-0.02216334268450737,
0.06334931403398514,
0.005134135019034147,
0.030372537672519684,
0.01116652600467205,
-0.005719045642763376,
-0.010803879238665104,
0.005862214136868715,
0.04812624678015709,
0.015382297337055206,
-0.002400927245616913,
0.022939374670386314,
-0.035216283053159714,
-0.02225746028125286,
-0.014308572746813297,
-0.04188881814479828,
-0.011319105513393879,
0.0032482463866472244,
0.044433265924453735,
-0.01951161026954651,
-0.00036720139905810356,
0.0019324879394844174,
0.06840142607688904,
-0.017695214599370956,
-0.018572822213172913,
-0.05719008669257164,
-0.0074895527213811874,
0.018310757353901863,
0.004725374281406403,
-0.02589823305606842,
0.010963878594338894,
-0.009061275981366634,
-0.014941266737878323,
0.004727090243250132,
0.028318822383880615,
0.00232164328917861,
-0.006521286908537149,
0.0297338105738163,
0.04455661401152611,
0.06324782222509384,
-0.014074955135583878,
-0.06494022905826569,
0.06336211413145065,
-0.0027117666322737932,
-0.05544993281364441,
0.006788711063563824,
0.0053932564333081245,
0.010993494652211666,
0.035537052899599075,
-0.03159036859869957,
0.02023162879049778,
0.05517435073852539,
-0.01397465169429779,
-0.0434148870408535,
0.0013441351475194097,
-0.034365929663181305,
-0.008533976972103119,
-0.036633264273405075,
0.018054144456982613,
-0.013820326887071133,
0.0018352953484281898,
0.014976335689425468,
0.026159795001149178,
0.004022757522761822,
-0.016465116292238235,
-0.01315215416252613,
-0.014282557182013988,
-0.004015943501144648,
0.008523393422365189,
0.011064247228205204,
-0.008318341337144375,
0.07308080792427063,
-0.023457273840904236,
-0.040406081825494766,
0.005246398039162159,
-0.017943600192666054,
-0.05360366776585579,
-0.005413184408098459,
0.02057637833058834,
-0.05966178700327873,
0.021714050322771072,
-0.009253625757992268,
0.02217632159590721,
0.029003534466028214,
-0.07484988868236542,
-0.01880001276731491,
-0.006503520533442497,
-0.02427433431148529,
-0.047525208443403244,
-0.005640598013997078,
-0.02085564285516739,
0.04500975087285042,
0.00949831958860159,
0.09707047790288925,
-0.010292726568877697,
0.02919650636613369,
-0.022321540862321854,
-0.029916025698184967,
-0.020597172901034355,
0.0038054438773542643,
-0.016320543363690376,
0.0005192417884245515,
0.06477786600589752,
-0.023811981081962585,
-0.00031287831370718777,
0.035891950130462646,
-0.03295020014047623,
-0.039833102375268936,
0.004039496183395386,
-0.0028319943230599165,
0.012279517948627472,
0.006242729723453522,
-0.007036636583507061,
0.009428092278540134,
0.005841117352247238,
0.032093361020088196,
0.016178498044610023,
0.041487518697977066,
0.029285311698913574,
0.014252226799726486,
0.01990131475031376,
-0.014815525151789188,
0.021959520876407623,
0.05767831578850746,
-0.04188946262001991,
0.02090698666870594,
0.01868060976266861,
0.03246794268488884,
0.001203235238790512,
-0.022325677797198296,
-0.03330974653363228,
-0.016449660062789917,
-0.0074942042119801044,
0.023271886631846428,
0.020874768495559692,
0.018419431522488594,
0.014918910339474678,
-0.015251786448061466,
-0.012611781246960163,
0.025566162541508675,
0.032209739089012146,
0.01403470803052187,
-0.02490040473639965,
-0.008968661539256573,
0.027193300426006317,
0.03940442577004433,
0.02155383490025997,
-0.028535805642604828,
-0.005044541321694851,
0.018273217603564262,
0.024942096322774887,
0.050159767270088196,
0.021868370473384857,
-0.07501735538244247,
0.0012536724098026752,
-0.006120334379374981,
0.014934399165213108,
-0.03158564865589142,
-0.001750459661707282,
-0.032118670642375946,
-0.04552479088306427,
-0.008593212813138962,
0.010233204811811447,
0.058690231293439865,
-0.030890872702002525,
0.014156686142086983,
0.010531662963330746,
-0.01821386069059372,
0.03620310127735138,
-0.0445353202521801,
-0.010986004956066608,
0.0016543276142328978,
-0.010812791995704174,
0.01810351200401783,
0.01692230813205242,
-0.015636228024959564,
-0.002956212731078267,
0.016589226201176643,
-0.011941039003431797,
-0.015826132148504257,
-0.03532544896006584,
-0.04960623383522034,
0.039192136377096176,
-0.016579926013946533,
-0.038670893758535385,
0.04630015045404434,
-0.03782590851187706,
0.015723295509815216,
-0.01630024053156376,
-0.05013719201087952,
-0.003623097902163863,
0.020671295002102852,
-0.024783674627542496,
0.045363325625658035,
-0.037290215492248535,
-0.024657174944877625,
0.03264057636260986,
-0.036770228296518326,
-0.0012182953068986535,
0.007764313369989395,
-0.01919981837272644,
0.0030972096137702465,
0.05350445583462715,
0.014304871670901775,
0.006514475215226412,
0.00279930024407804,
-0.007198750972747803,
0.015704380348324776,
0.014506357721984386,
-0.00021191829000599682,
0.048535481095314026,
-0.014442305080592632,
-0.007738328073173761,
-0.016257373616099358,
0.01754309982061386,
0.020197486504912376,
0.029218703508377075,
-0.014064431190490723,
0.0283699631690979,
-0.0028983871452510357,
-0.015305662527680397,
0.030415501445531845,
0.007450508419424295,
0.007554416544735432,
0.025291241705417633,
-0.02053908258676529,
0.07627298682928085,
-0.060122791677713394,
0.014305912889540195,
0.02313341200351715,
0.0003559916222002357,
0.033187706023454666,
-0.014458801597356796,
0.015728028491139412,
0.018781859427690506,
0.008204762823879719,
-0.03304705768823624,
-0.027457192540168762,
0.03004305623471737,
0.02246995083987713,
-0.04452979937195778,
0.013549292460083961,
-0.02524721249938011,
0.02034717984497547,
0.0027819883543998003,
-0.005233935080468655,
-0.0577642098069191,
-0.02494201809167862,
0.03354492038488388,
0.0010127810528501868,
0.004144505597651005,
-0.0009528860100544989,
-0.016250383108854294,
-0.010265285149216652,
0.05171635001897812,
-0.030707312747836113,
-0.019707150757312775,
-0.027913151308894157,
0.025202786549925804,
-0.006617766804993153,
0.03482338413596153
] |
<p>I have this relative simple-looking question that I haven't been able to solve for hours now, it's one of those questions that just drive you nuts if you don't know how to do it.
This is the scenario:</p>
<p>I have a <a href="http://2.bp.blogspot.com/_P4EHIyposmM/TImv2-brnOI/AAAAAAAAAMw/nK-NO8JUSEU/s1600/1781_PotApp_FlexibleMetal_Spring_Big.jpg" rel="nofollow">spring</a> that is on a flat surface, the springs details are like this:</p>
<p>spring constant = 100N/m</p>
<p>height = 0.1m</p>
<p>mass = 0.5kg</p>
<p>g = 10m/s^2</p>
<p>there is nothing attached to the spring.
The initial force exerted on the surface is 5N.
I compress the spring halfway until the force exerted on the surface is double, now 10N and then let it go.</p>
<p>The (simple) oscillation starts, and at one point the force exerted on the surface will be 0N (weightless).</p>
<p>I need to find out how much time has passed after letting it go, and reaching weightlessness.</p>
<p>as in:
10(N)---time--->0(N)</p>
<p>p.s. not homework, read comments.</p>
| 10,665 |
[
-0.006301356945186853,
-0.03233848139643669,
-0.029468748718500137,
-0.02050665393471718,
0.0049078334122896194,
-0.06294166296720505,
-0.02927512675523758,
-0.0374651737511158,
-0.004492506384849548,
-0.026656245812773705,
0.00007070879655657336,
0.06203779578208923,
0.02353094331920147,
0.03470845893025398,
0.00907768215984106,
-0.0156339630484581,
-0.03776819258928299,
-0.02254682406783104,
0.012874347157776356,
-0.03428249806165695,
0.012635238468647003,
-0.03557749092578888,
-0.0014850612496957183,
-0.014525397680699825,
-0.017096128314733505,
-0.012601997703313828,
0.05061282590031624,
-0.018904978409409523,
0.015927927568554878,
0.02962748147547245,
-0.022481944411993027,
-0.04912808910012245,
0.007322161458432674,
0.007543973624706268,
0.039093755185604095,
0.036133866757154465,
-0.03649616986513138,
-0.011173112317919731,
-0.046508289873600006,
0.018113544210791588,
0.0039057189133018255,
-0.005186721682548523,
-0.009799902327358723,
0.04327717423439026,
-0.009045640006661415,
-0.008742913603782654,
0.039053838700056076,
-0.009304665960371494,
0.08512692153453827,
-0.03505382686853409,
0.05909643694758415,
0.004087258595973253,
0.027699468657374382,
0.017086593434214592,
0.002744439523667097,
-0.03904218226671219,
0.06776008009910583,
0.038532696664333344,
-0.03181922808289528,
-0.06195608526468277,
-0.021279267966747284,
-0.015069919638335705,
-0.036094050854444504,
-0.014237457886338234,
-0.01685698702931404,
0.017270702868700027,
-0.036872465163469315,
0.012984706088900566,
0.04668831825256348,
-0.021604619920253754,
0.001722741755656898,
-0.003640279406681657,
0.062213774770498276,
-0.032038453966379166,
-0.025261785835027695,
-0.0514092892408371,
0.020549822598695755,
0.013908438384532928,
0.048889726400375366,
0.06435234844684601,
-0.025759829208254814,
0.01229031290858984,
0.021944690495729446,
0.06536738574504852,
0.01816459372639656,
-0.0254864152520895,
0.07286179065704346,
0.02535288967192173,
0.012813415378332138,
0.038749754428863525,
-0.0009424577583558857,
0.01170711126178503,
0.02534169703722,
0.001377401640638709,
-0.005243822932243347,
0.03874467685818672,
0.01753831095993519,
0.05609191209077835,
0.006534866522997618,
-0.03275241330265999,
-0.014327442273497581,
-0.0548454225063324,
0.003480562474578619,
0.07380782067775726,
0.0025189577136188745,
0.023093707859516144,
0.00762001471593976,
-0.021236209198832512,
-0.010789183899760246,
-0.009849314577877522,
-0.043947938829660416,
-0.025834377855062485,
0.004966062027961016,
-0.039599452167749405,
-0.02137737348675728,
-0.03730088099837303,
-0.0069085173308849335,
0.032207414507865906,
0.01517827995121479,
0.03686469420790672,
0.02641923725605011,
-0.026132551953196526,
0.039011161774396896,
0.004460152238607407,
-0.04784806817770004,
-0.01709747314453125,
0.04093444347381592,
-0.019820870831608772,
-0.024624431505799294,
0.02870296686887741,
-0.017894769087433815,
-0.035435743629932404,
0.0004898323677480221,
-0.020781293511390686,
0.05401499941945076,
0.03233203664422035,
-0.0829518586397171,
-0.04899904876947403,
0.046780187636613846,
-0.007769560441374779,
-0.012837391346693039,
-0.06359334290027618,
0.027822893112897873,
0.015338038094341755,
0.029187439009547234,
0.028132323175668716,
-0.003548024222254753,
-0.012583739124238491,
-0.007394474931061268,
-0.016470758244395256,
0.016955683007836342,
-0.01803463138639927,
-0.0004792263498529792,
-0.02931652031838894,
0.007034407928586006,
-0.016642605885863304,
0.04374726489186287,
0.06327647715806961,
0.0075494213961064816,
-0.05494057759642601,
0.04396149516105652,
0.00312853348441422,
0.02701902575790882,
-0.0009963028132915497,
-0.012242376804351807,
-0.0571446418762207,
0.08554577827453613,
0.008703741244971752,
-0.021130995824933052,
0.02885608747601509,
0.01843712292611599,
0.00716952932998538,
-0.030365698039531708,
0.003367165569216013,
0.0189870186150074,
-0.03588351234793663,
-0.007671327795833349,
-0.05135906860232353,
0.005502683576196432,
0.03096957691013813,
-0.039270367473363876,
-0.018393803387880325,
0.024560945108532906,
-0.010675557889044285,
-0.014472855255007744,
0.03904057294130325,
0.0048217978328466415,
-0.016837339848279953,
-0.044895071536302567,
-0.00477024307474494,
-0.015126754529774189,
-0.07575580477714539,
0.043841395527124405,
-0.0014266243670135736,
0.004201081115752459,
0.01236940361559391,
0.0013981249649077654,
0.05404053255915642,
-0.030314961448311806,
-0.03442861884832382,
-0.023743700236082077,
0.024400876834988594,
0.023388558998703957,
-0.026952575892210007,
0.014357254840433598,
0.050742458552122116,
0.03484995290637016,
0.0023402010556310415,
0.03577456623315811,
-0.022809172049164772,
0.006579112261533737,
-0.009262338280677795,
-0.014873772859573364,
0.02324439026415348,
0.026135269552469254,
-0.0035097277723252773,
0.03641829639673233,
-0.025707609951496124,
0.022579720243811607,
0.013933715410530567,
0.016813352704048157,
0.09713665395975113,
0.04620653763413429,
0.0021983091719448566,
0.01853976584970951,
-0.01886122301220894,
-0.006148841232061386,
-0.004165659658610821,
-0.0027092737145721912,
-0.0443606898188591,
-0.023140043020248413,
-0.02642105706036091,
0.009091496467590332,
0.042070016264915466,
0.0041928659193217754,
0.0021217342000454664,
0.030192259699106216,
0.010742348618805408,
0.03414252772927284,
0.03256697580218315,
0.0004231952771078795,
-0.021807311102747917,
0.025185249745845795,
0.02198915369808674,
-0.0279484074562788,
0.02115386538207531,
0.017448555678129196,
0.03078869730234146,
0.014777167700231075,
0.0013192547485232353,
-0.01044380757957697,
0.02923237904906273,
0.008508903905749321,
0.00933356024324894,
0.006964768748730421,
-0.04465516284108162,
0.03830237314105034,
-0.011115968227386475,
-0.01451028324663639,
0.02207326516509056,
0.031204290688037872,
0.027440279722213745,
-0.04300984740257263,
-0.002844150410965085,
0.028660252690315247,
-0.0322977639734745,
-0.006073204800486565,
-0.026831280440092087,
0.021626045927405357,
-0.02291969023644924,
-0.010826103389263153,
0.005165548529475927,
-0.0015128521481528878,
0.015274884179234505,
-0.010333236306905746,
0.039233483374118805,
0.028104834258556366,
0.03847067430615425,
-0.027081379666924477,
-0.021192369982600212,
0.0255449041724205,
-0.0652974471449852,
0.006971102673560381,
0.026721108704805374,
-0.05049974471330643,
0.017202945426106453,
0.01669769547879696,
-0.04063763469457626,
0.04454272240400314,
0.0013984562829136848,
-0.012341887690126896,
0.0345979742705822,
0.005684660281985998,
-0.01563456282019615,
-0.006558396387845278,
-0.04172990843653679,
-0.02015325427055359,
-0.05202477425336838,
-0.0026190578937530518,
0.0633690133690834,
-0.009018666110932827,
-0.017390161752700806,
0.05964053422212601,
-0.035274654626846313,
-0.04789645969867706,
-0.03048235923051834,
0.011959952302277088,
0.03850623592734337,
-0.03316763788461685,
-0.023529889062047005,
-0.01923743076622486,
-0.018659362569451332,
-0.008404585532844067,
-0.037711355835199356,
-0.06437520682811737,
-0.012179999612271786,
-0.035024892538785934,
0.05757267773151398,
0.015328727662563324,
-0.01903083547949791,
0.1102764904499054,
-0.0140651511028409,
-0.03695645183324814,
-0.020596224814653397,
-0.0259892288595438,
-0.0028171739540994167,
0.025844473391771317,
-0.012899039313197136,
0.02243008464574814,
-0.0392182283103466,
0.00945612695068121,
0.02067142352461815,
0.0198886189609766,
0.04424580559134483,
0.023456186056137085,
0.03298238664865494,
-0.022151168435811996,
0.022760551422834396,
0.0050047398544847965,
0.010074449703097343,
0.014419322833418846,
-0.002942705759778619,
0.025564126670360565,
-0.02339063584804535,
0.04447231814265251,
0.02809857949614525,
-0.05455543473362923,
0.052356574684381485,
-0.0052305241115391254,
-0.020405108109116554,
-0.0171730387955904,
0.030585307627916336,
-0.01390181202441454,
-0.03586084395647049,
-0.004760005511343479,
0.0534096360206604,
0.062221188098192215,
-0.031231176108121872,
-0.020521584898233414,
0.05652565136551857,
0.0414685383439064,
-0.00502624548971653,
-0.06240576133131981,
-0.02121604233980179,
-0.003317531431093812,
0.03562185913324356,
-0.03377135470509529,
-0.014540879055857658,
0.011206911876797676,
0.028488799929618835,
0.0787598118185997,
-0.0022298849653452635,
-0.03430876508355141,
-0.009495760314166546,
-0.07135084271430969,
-0.01721828617155552,
0.031025221571326256,
0.037242550402879715,
0.016794322058558464,
0.05735567584633827,
0.01666519232094288,
0.029851043596863747,
0.035845473408699036,
0.01676226779818535,
-0.07968796789646149,
0.05605437234044075,
-0.04414908215403557,
-0.025915931910276413,
0.02966226451098919,
0.003934825304895639,
0.01721981354057789,
-0.028403619304299355,
0.006697513163089752,
0.01891098916530609,
0.054299574345350266,
-0.06899654865264893,
0.006365587003529072,
-0.025689879432320595,
0.02286606840789318,
-0.00884851161390543,
0.017481030896306038,
0.020174751058220863,
0.012883522547781467,
0.008866405114531517,
0.06298170983791351,
0.010407880879938602,
0.0015932305250316858,
-0.010576735250651836,
-0.020752664655447006,
-0.038545411080121994,
0.039910949766635895,
0.020532088354229927,
0.043909501284360886,
0.006575420033186674,
-0.008082862012088299,
-0.0330582931637764,
0.03806092217564583,
0.006090760696679354,
0.040837232023477554,
-0.005673360079526901,
-0.07061535120010376,
0.0015504889888688922,
-0.005341848824173212,
0.048204440623521805,
-0.026419715955853462,
-0.011547182686626911,
0.003974893130362034,
-0.0238896943628788,
0.003443189663812518,
0.07160267978906631,
0.07202307879924774,
-0.009518317878246307,
0.018656469881534576,
-0.045267682522535324,
-0.012332592159509659,
-0.04171092435717583,
0.01991024799644947,
0.0041421870701014996,
-0.005808681715279818,
-0.015703067183494568,
0.002278989879414439,
0.024962682276964188,
-0.014290597289800644,
0.030489400029182434,
0.006708720698952675,
-0.014743028208613396,
0.054875556379556656,
-0.00399057986214757,
-0.021961422637104988,
0.015971554443240166,
0.036861129105091095,
0.06495598703622818,
-0.010443323291838169,
-0.006162300240248442,
-0.08443106710910797,
-0.05074891075491905,
0.037754546850919724,
0.02486591599881649,
-0.017202313989400864,
0.024498112499713898,
-0.041525982320308685,
-0.015387197025120258,
0.03987901285290718,
-0.06238117069005966,
0.024664442986249924,
-0.010518014430999756,
0.03917669132351875,
0.0011648462386801839,
-0.007887517102062702,
-0.03243660926818848,
-0.011450354941189289,
-0.01757744885981083,
0.030144521966576576,
-0.0018980101449415088,
-0.02110103890299797,
0.02930467389523983,
0.009147979319095612,
0.008374945260584354,
0.04945388808846474,
0.00416161585599184,
-0.010378115810453892,
-0.0023448229767382145,
-0.053144220262765884,
-0.06339400261640549,
-0.08729605376720428,
0.0036363594699651003,
-0.003985019866377115,
-0.016375156119465828,
0.021490005776286125,
-0.05619361624121666,
-0.05495772510766983,
0.035509079694747925,
0.015488867647945881,
-0.007735935505479574,
-0.025296282023191452,
-0.02909405343234539,
0.03855133801698685,
0.04500547796487808,
0.00725098792463541,
0.01197533868253231,
0.02894570119678974,
-0.003798675024881959,
0.012106032110750675,
0.03553612530231476,
0.020907383412122726,
-0.022669581696391106,
0.019605211913585663,
-0.021284541115164757,
0.006215513683855534,
-0.060251131653785706,
0.06736291199922562,
-0.021619755774736404,
0.007055926136672497,
-0.009502558037638664,
-0.012842180207371712,
-0.0041872174479067326,
0.017022477462887764,
0.020914632827043533,
0.01657574251294136,
0.03501962125301361,
-0.021941130980849266,
-0.009159749373793602,
-0.014353451319038868,
-0.02692287415266037,
0.014008714817464352,
0.0013653273927047849,
0.020250078290700912,
-0.012536552734673023,
0.0009374336805194616,
-0.009319464676082134,
-0.042044006288051605,
0.025965118780732155,
-0.0772867351770401,
0.053771089762449265,
-0.022495239973068237,
0.020247872918844223,
0.025932248681783676,
-0.031150590628385544,
-0.0008390389266423881,
-0.015204573050141335,
-0.0046972050331532955,
0.028098013252019882,
-0.07159602642059326,
-0.002304985886439681,
0.061147451400756836,
0.00932978093624115,
-0.0391848161816597,
-0.05637286230921745,
0.06613526493310928,
0.01663297228515148,
-0.0215535219758749,
-0.025809504091739655,
-0.02761952392756939,
-0.017312049865722656,
-0.005554697476327419,
0.0011906168656423688,
-0.0033141295425593853,
-0.017274992540478706,
0.0008624548790976405,
0.0468558631837368,
-0.009956365451216698,
0.06372341513633728,
0.02463676407933235,
-0.02827506884932518,
-0.018180515617132187,
0.015681665390729904,
-0.05158139392733574,
0.0034383779857307673,
0.05115501582622528,
-0.026812482625246048,
-0.0078073968179523945,
-0.003562039230018854,
-0.04107479378581047,
0.030013684183359146,
-0.01783083565533161,
0.015729602426290512,
0.04599202051758766,
0.01519028190523386,
0.004179694224148989,
-0.01817033626139164,
0.030481407418847084,
-0.012101134285330772,
0.056881990283727646,
0.01939687505364418,
-0.015334712341427803,
-0.02689657174050808,
-0.037802278995513916,
-0.022921696305274963,
-0.007252250798046589,
0.006072699092328548,
0.0026216385886073112,
0.047587741166353226,
-0.0025322730652987957,
-0.035878561437129974,
0.01573249138891697,
-0.01047392375767231,
0.010620737448334694,
-0.018329638987779617,
0.003245470579713583,
0.016629157587885857,
-0.012260372750461102,
-0.038645874708890915,
-0.04629229009151459,
-0.05156005546450615,
-0.006443817168474197,
0.0592561699450016,
-0.034517958760261536,
0.044844139367341995,
0.006196613889187574,
0.01756851188838482,
0.009951283223927021,
0.004134763032197952,
-0.01125278789550066,
-0.022065265104174614,
0.048815883696079254,
0.011891143396496773,
-0.0025330048520118,
0.007447788957506418,
0.010826642625033855,
0.03555436059832573,
0.005015411414206028,
0.03678739070892334,
0.010016378946602345,
-0.010915426537394524,
0.03583956137299538,
-0.04009557142853737,
-0.024831058457493782,
0.008474133908748627,
0.0069485995918512344,
0.05610882490873337,
0.009566724300384521,
-0.02538938634097576,
0.0074689039029181,
0.03515108674764633,
0.004320746753364801,
-0.030236002057790756,
-0.014528163708746433,
-0.036781419068574905,
-0.03096320666372776,
-0.008347110822796822,
0.007586417254060507,
-0.008587933145463467,
-0.0010538771748542786,
0.01991693116724491,
0.046439625322818756,
0.04541447386145592,
-0.022004006430506706,
-0.010421124286949635,
-0.01876330003142357,
-0.04332263022661209,
-0.038880787789821625,
0.044472865760326385,
0.020149197429418564,
-0.04555599018931389,
0.0574134960770607,
-0.030299311503767967,
0.05725303664803505,
-0.0052216085605323315,
0.02164815552532673,
-0.018508950248360634,
0.09444861114025116,
0.013097994029521942,
0.0063462164252996445,
-0.02703358605504036,
0.011230099946260452,
0.12738722562789917,
0.04749791696667671,
0.0023814882151782513,
-0.016186298802495003,
-0.012063202448189259,
0.0004132259055040777,
0.014499935321509838,
-0.01942806877195835,
-0.022338969632983208,
-0.009965363889932632,
-0.027489500120282173,
0.004927478730678558,
0.049322597682476044,
-0.045598529279232025,
-0.009117357432842255,
0.02448974922299385,
-0.015103093348443508,
-0.012941032648086548,
-0.019212190061807632,
-0.01413876935839653,
0.0029868423007428646,
-0.02293168567121029,
-0.027485420927405357,
0.036550432443618774,
-0.032790448516607285,
-0.015203770250082016,
-0.027407702058553696,
0.011748972348868847,
0.028746070340275764,
0.00043879845179617405,
-0.029919160529971123,
0.04102613404393196,
-0.014924552291631699,
-0.035736970603466034,
-0.03956714645028114,
0.036630358546972275,
0.025741616263985634,
0.021581709384918213,
0.025536783039569855,
0.08102685213088989,
0.019537273794412613,
0.017842940986156464,
0.026325222104787827,
0.007165230810642242,
-0.06303181499242783,
-0.006481664255261421,
-0.03293851763010025,
0.05164439231157303,
-0.01784634217619896,
0.003711968194693327,
0.023722974583506584,
-0.013494418933987617,
-0.001110722660087049,
-0.043432269245386124,
0.002914506010711193,
-0.0022780164144933224,
0.05060816928744316,
-0.01410516444593668,
-0.00380283803679049,
0.0008046975126489997,
0.003216040786355734,
0.035296760499477386,
0.008200683631002903,
-0.016467954963445663,
0.034394945949316025,
0.002265696180984378,
0.03104839101433754,
0.029960522428154945,
-0.013529051095247269,
-0.004750545602291822,
-0.00843694619834423,
-0.03320746868848801,
-0.023434046655893326,
0.0252608023583889,
0.018254723399877548,
0.03793332353234291,
0.014514791779220104,
0.0015323435654863715,
-0.022911176085472107,
-0.05573321878910065,
-0.01542783435434103,
0.02194490283727646,
0.0281891580671072,
-0.017501067370176315,
-0.03407542034983635,
-0.03508925437927246,
0.008454974740743637,
0.030758613720536232,
-0.013556125573813915,
0.04851550608873367,
-0.002916698344051838,
0.03485024347901344,
0.022931471467018127,
-0.034649558365345,
0.015973759815096855,
0.031608033925294876,
-0.01956086978316307,
0.04845274239778519,
-0.044262733310461044,
0.04606925696134567,
0.022721068933606148,
-0.002451050328090787,
0.025035478174686432,
0.026271838694810867,
-0.043708138167858124,
0.0020243728067725897,
-0.0006900624139234424,
-0.036879416555166245,
0.0021777257788926363,
-0.005125243216753006,
0.006460264325141907,
-0.04260515794157982,
-0.03209278732538223,
-0.03691842406988144,
-0.019335731863975525,
0.0021572744008153677,
0.04372723028063774,
-0.043896857649087906,
0.06157206743955612,
-0.006484895013272762,
-0.014646956697106361,
-0.04615200683474541,
0.022626938298344612,
-0.03743959590792656,
0.011149726808071136,
0.01743270456790924,
0.017103582620620728,
-0.03473268076777458,
0.030978519469499588,
-0.03712029382586479,
-0.0306545402854681,
0.005788050591945648,
0.022976592183113098,
0.026246294379234314,
-0.0239962637424469,
0.04409592226147652,
0.001444919966161251,
0.03192465007305145,
-0.02858773060142994,
-0.01234389003366232,
0.023615991696715355,
-0.05915223807096481,
-0.059188734740018845,
0.04088472202420235,
0.03302815929055214,
0.06953071802854538,
0.033118002116680145,
-0.053758833557367325,
0.004103713668882847,
0.03853689506649971,
-0.020913533866405487,
-0.0044085620902478695,
-0.015932051464915276,
-0.02492719329893589,
-0.038386840373277664,
0.017885858193039894,
-0.028391439467668533,
-0.02177487127482891,
0.020690951496362686,
-0.003983830567449331,
0.03618834540247917,
-0.0011026141000911593,
-0.020273549482226372,
0.006865270901471376,
-0.004646163433790207,
-0.03614814579486847,
0.019518477842211723,
0.0012516571441665292,
-0.019615041092038155,
0.07236937433481216,
-0.022596824914216995,
0.005754868965595961,
-0.033792003989219666,
0.022370124235749245,
-0.1181805208325386,
0.0076723648235201836,
-0.040494292974472046,
0.043108340352773666,
0.02947656437754631,
-0.03308750316500664,
0.006798118352890015,
0.01883433759212494,
-0.03651614487171173,
0.019863763824105263,
-0.03758111596107483,
0.000731172040104866,
0.007616720162332058,
0.0072152279317379,
-0.019513379782438278,
0.0314699187874794,
0.022841069847345352,
0.04849854111671448,
0.026268968358635902,
0.00700016412883997,
-0.025184905156493187,
-0.02528495155274868,
-0.002785996301099658,
0.029893362894654274,
0.024554690346121788,
-0.003314240602776408,
0.040985338389873505,
-0.0126816276460886,
-0.016810810193419456,
0.03469518572092056,
-0.04890306293964386,
0.011011550202965736,
-0.02913786470890045,
0.03758356720209122,
-0.009160703979432583,
0.01257400307804346,
0.004522108472883701,
-0.03373626992106438,
-0.018160203471779823,
0.04997643083333969,
-0.005329261068254709,
-0.026376448571681976,
-0.020505035296082497,
-0.009119805879890919,
0.02765599638223648,
-0.017527658492326736,
-0.04400148615241051,
0.0317242369055748,
-0.008766445331275463,
0.039511121809482574,
-0.0014591763028874993,
-0.008504430763423443,
-0.0011460290988907218,
-0.048815805464982986,
-0.03166498243808746,
-0.007795155048370361,
0.014290942810475826,
0.01606765389442444,
-0.011104929260909557,
-0.032532691955566406,
0.03772101178765297,
0.01212125550955534,
-0.011864503845572472,
-0.018267132341861725,
-0.029835768043994904,
-0.030457090586423874,
-0.07020212709903717,
-0.030751435086131096,
-0.00046500208554789424,
-0.00447550043463707,
-0.0005478634848259389,
-0.009725401178002357,
-0.030573315918445587,
0.027885504066944122,
0.04911059886217117,
0.022495588287711143,
0.00575628224760294,
-0.04447144642472267,
-0.011925522238016129,
-0.09976886212825775,
0.00864335149526596,
-0.005552344955503941,
0.00176130305044353,
-0.04035327956080437,
0.003919761162251234,
0.02818121574819088,
0.017787354066967964,
0.02927282825112343,
-0.015358645468950272,
-0.02638285420835018,
0.015512002632021904,
-0.029893100261688232,
-0.009167465381324291,
-0.040156710892915726,
0.005161497741937637,
-0.0036431674379855394,
-0.03977985680103302,
0.015221630223095417,
-0.00784275121986866,
0.011088871397078037,
-0.024033620953559875,
0.03595603257417679,
0.002702173078432679,
-0.02405261993408203,
-0.02210288867354393,
-0.022358722984790802,
0.012898686341941357,
0.002178443828597665,
0.027517542243003845,
0.07774195820093155,
-0.0018619701731950045,
0.01597357541322708,
0.024447310715913773,
-0.01820465549826622,
-0.05347192659974098,
0.025899747386574745,
-0.036584749817848206,
0.008535750210285187,
-0.05623066425323486,
-0.00399043969810009,
-0.0010725876782089472,
-0.07038065046072006,
-0.008560271002352238,
0.022396931424736977,
-0.0264399666339159,
-0.03740660473704338,
0.007306515239179134,
-0.0003672901075333357,
0.041050031781196594,
0.011717993766069412,
0.03737722709774971,
0.0080315126106143,
-0.002099120058119297,
0.03040982224047184,
0.0016427813097834587,
0.041248347610235214,
-0.02953597530722618,
0.004036216996610165,
0.007788027636706829,
0.0033310039434581995,
0.03747949004173279,
0.03411483019590378,
0.012744138017296791,
-0.026072043925523758,
-0.056290339678525925,
0.02371501363813877,
-0.00888630747795105,
-0.02180829457938671,
0.02536526508629322,
-0.02471381239593029,
0.052122294902801514,
0.005127552896738052,
-0.0010183320846408606,
-0.0003700344532262534,
0.017652524635195732,
-0.006347795948386192,
0.023728160187602043,
0.0037614230532199144,
0.029740795493125916,
-0.04155214875936508,
0.0023485543206334114,
-0.03751125931739807,
-0.004236248787492514,
0.022756177932024002,
-0.020617200061678886,
0.005706634372472763,
-0.01300142053514719,
0.015237214975059032,
0.005964915733784437,
-0.016797708347439766,
-0.050749536603689194,
-0.030810968950390816,
0.08290538191795349,
0.010546612553298473,
-0.01179227139800787,
-0.010503646917641163,
0.03603117913007736,
0.0031608089338988066,
0.05371105298399925,
-0.028360165655612946,
-0.014546094462275505,
-0.033306628465652466,
0.016987139359116554,
-0.00838800985366106,
-0.011088911443948746
] |
<p>all. I have tried Googling but have had no luck. My question is simple (although, I presume the answer is not): If one knows the chemical structure of, well, a chemical, could its optical properties (such as transparency) be mathematically derived from this information alone? Perhaps I'm naive for thinking so, but I would imagine it's possible, given the electron count and three-dimensional structure of the compound. </p>
<p>I ask this on the Physics Stack Exchange because I feel like it falls into the Optics/Physical-Side-of-Physical-Chemistry realm than into pure Chemistry territory.</p>
<p>If I need to elaborate some more, please feel free to comment and let me know. Likewise, if needed, please pardon any idiocy.</p>
| 10,666 |
[
-0.028944024816155434,
-0.02352912537753582,
0.015203716233372688,
-0.01658497005701065,
0.020154358819127083,
0.03130359575152397,
-0.028211701661348343,
-0.0017133051296696067,
0.023775611072778702,
-0.05075152590870857,
0.04973820969462395,
0.02964084781706333,
0.06474100798368454,
0.03137851879000664,
0.00487727764993906,
0.0008820139337331057,
-0.032072119414806366,
0.025925442576408386,
0.008133355528116226,
-0.011401079595088959,
0.023633532226085663,
0.03064165636897087,
-0.005459476727992296,
-0.0016834551934152842,
-0.024379774928092957,
0.05584240332245827,
0.01352135743945837,
0.021159712225198746,
0.03145788237452507,
0.024911707267165184,
0.014245429076254368,
-0.028374308720231056,
0.053686294704675674,
0.05539526790380478,
0.04768955335021019,
0.013621418736875057,
-0.03176695480942726,
-0.021399883553385735,
-0.02026032656431198,
0.010264418087899685,
-0.036449410021305084,
-0.02591688185930252,
0.01787632703781128,
0.03034212999045849,
0.000263882742729038,
-0.013230210170149803,
-0.0249935332685709,
-0.05567653104662895,
0.02817797288298607,
-0.0652015209197998,
0.0910922959446907,
-0.013795196078717709,
0.031652022153139114,
0.04500257968902588,
-0.01635308749973774,
0.00008223814802477136,
0.05641254410147667,
0.0830594003200531,
-0.019125357270240784,
-0.028064655140042305,
-0.017159229144454002,
0.002160724252462387,
0.013125385157763958,
-0.0046270452439785,
-0.06656727194786072,
-0.00048276473535224795,
-0.01196193415671587,
-0.04516630619764328,
0.050291482359170914,
-0.020987074822187424,
-0.026110906153917313,
-0.021603437140583992,
0.02436002343893051,
-0.003359263064339757,
-0.009972031228244305,
-0.03209293633699417,
0.008741356432437897,
0.028394419699907303,
0.026466194540262222,
0.01547330617904663,
-0.03778330609202385,
0.0010125947883352637,
-0.017579335719347,
0.026183664798736572,
-0.030062509700655937,
-0.003161161672323942,
0.05806781351566315,
-0.037737760692834854,
0.018593236804008484,
0.005830439738929272,
-0.03498604893684387,
0.0053589423187077045,
0.04153915122151375,
0.03386968746781349,
-0.013546275906264782,
-0.0011134821688756347,
-0.02340330369770527,
0.07669061422348022,
0.01366156805306673,
-0.018901748582720757,
0.022028854116797447,
-0.007714875973761082,
0.016784289851784706,
0.059220071882009506,
-0.020285679027438164,
-0.031290825456380844,
-0.003262421814724803,
0.017819011583924294,
0.034817323088645935,
0.011416063643991947,
0.0008236807188950479,
0.02017461694777012,
0.014425563625991344,
-0.016668526455760002,
0.030306782573461533,
-0.02406925894320011,
-0.002332462230697274,
-0.04360385239124298,
0.04222415015101433,
0.09135817736387253,
0.018348772078752518,
-0.0262280460447073,
0.0217897966504097,
0.009343174286186695,
-0.07380056381225586,
0.010257508605718613,
0.015516511164605618,
-0.003261011093854904,
-0.023186087608337402,
-0.0017532597994431853,
0.017493022605776787,
-0.051153793931007385,
0.04817400500178337,
-0.030668044462800026,
0.02683318592607975,
-0.00321372551843524,
-0.09018079191446304,
-0.057091377675533295,
-0.018586415797472,
0.017909538000822067,
-0.03486211970448494,
-0.08222232758998871,
0.008934050798416138,
0.037875790148973465,
0.07685106247663498,
0.008041661232709885,
0.02075202763080597,
-0.01732323318719864,
0.04504140838980675,
0.017064787447452545,
-0.011571859940886497,
-0.008604357950389385,
0.037298161536455154,
-0.0335376150906086,
0.015256866812705994,
-0.048992693424224854,
0.006568342912942171,
0.011747581884264946,
0.008466444909572601,
-0.04717705771327019,
0.08299480378627777,
-0.012335588224232197,
0.019065989181399345,
0.04041744023561478,
-0.005081938114017248,
-0.03515514358878136,
0.0672861859202385,
-0.01727408356964588,
0.04238810017704964,
0.0044661290012300014,
0.01488816924393177,
0.02128521539270878,
0.015405447222292423,
0.03009864315390587,
0.030237914994359016,
-0.02996424026787281,
-0.025205980986356735,
-0.012226712889969349,
0.010937968268990517,
0.012655151076614857,
-0.03867623955011368,
-0.03534500673413277,
0.005523224361240864,
0.024057159200310707,
0.018319901078939438,
0.003511761547997594,
0.013996518217027187,
-0.029102781787514687,
0.03389082849025726,
-0.06756092607975006,
0.01617605797946453,
-0.0405396930873394,
-0.005749208386987448,
0.014930886216461658,
-0.029542183503508568,
0.0391974151134491,
-0.005211960058659315,
-0.03274444863200188,
-0.012157167308032513,
-0.03040630742907524,
-0.004017941188067198,
0.013432684354484081,
0.03697360306978226,
-0.003101426176726818,
0.045537129044532776,
0.019937647506594658,
0.06844796985387802,
-0.010857382789254189,
0.008212334476411343,
-0.036718230694532394,
-0.04739639163017273,
-0.00892281997948885,
-0.010431047528982162,
0.0335998572409153,
-0.03522118553519249,
-0.025866318494081497,
-0.001050605089403689,
0.006467288359999657,
0.0037857536226511,
0.0468410961329937,
-0.040663979947566986,
0.07807032763957977,
0.05148525536060333,
0.03746039792895317,
0.004882216453552246,
0.024532554671168327,
-0.008326352573931217,
0.005011176224797964,
-0.00797174870967865,
-0.020777707919478416,
-0.02861190214753151,
-0.02764757350087166,
0.03695980831980705,
0.023608004674315453,
-0.04343770816922188,
-0.008163177408277988,
-0.0022918961476534605,
0.04637717828154564,
0.08377508819103241,
0.02844141609966755,
-0.05009088292717934,
0.0048823123797774315,
-0.012572607956826687,
-0.02425514906644821,
-0.005322373006492853,
0.018065935000777245,
0.004051467403769493,
0.04102637991309166,
0.03674818202853203,
-0.026386016979813576,
-0.017427362501621246,
0.04455246403813362,
-0.03070150874555111,
-0.012651899829506874,
0.008679455146193504,
-0.015055133029818535,
0.03279832378029823,
-0.03265915438532829,
0.0036042467691004276,
0.007948804646730423,
-0.01621429994702339,
0.0024190195836126804,
-0.01672954671084881,
0.015392155386507511,
0.03737633302807808,
0.005699844099581242,
-0.060803573578596115,
0.016616690903902054,
0.006535089109092951,
-0.024422965943813324,
0.012805581092834473,
-0.020221984013915062,
0.0303718913346529,
-0.004380462225526571,
0.0022894504945725203,
0.018947485834360123,
-0.0008020281093195081,
0.03382401540875435,
-0.025555957108736038,
-0.037881530821323395,
0.01138016115874052,
-0.009390497580170631,
0.0007448194082826376,
0.017385145649313927,
-0.03575650975108147,
-0.011326688341796398,
-0.006177792325615883,
-0.054814476519823074,
0.035155560821294785,
-0.03269870579242706,
-0.02942705526947975,
-0.004949026275426149,
-0.02663423679769039,
-0.044123414903879166,
0.0041138781234622,
0.012630735523998737,
0.019367288798093796,
-0.057418420910835266,
0.010551748797297478,
-0.03871351480484009,
-0.006633888464421034,
-0.0018921267474070191,
0.019755378365516663,
-0.025077693164348602,
-0.04674656689167023,
0.03420131281018257,
-0.005916158203035593,
-0.021087469533085823,
-0.03357933089137077,
0.016561023890972137,
0.0333840437233448,
-0.03876760974526405,
0.006999815348535776,
-0.0401151105761528,
-0.05294507369399071,
0.04935869202017784,
0.029037263244390488,
0.015497195534408092,
0.019007248803973198,
-0.010434748604893684,
0.055189065635204315,
0.012725287117064,
-0.05085592716932297,
-0.003742189845070243,
-0.02286069467663765,
0.01447280216962099,
-0.01709345541894436,
0.03788316622376442,
0.010231868363916874,
0.020053664222359657,
0.015027175657451153,
0.019029401242733,
0.008983699604868889,
0.038536470383405685,
0.017744971439242363,
-0.008365525864064693,
0.008929421193897724,
0.011762483976781368,
0.0010528471320867538,
0.011149232275784016,
0.046514738351106644,
-0.053667403757572174,
0.053881388157606125,
0.009973510168492794,
0.032618407160043716,
0.038919683545827866,
-0.06875357776880264,
0.03730609267950058,
0.014886816963553429,
0.029126811772584915,
0.003916147630661726,
0.04926005378365517,
-0.008152352645993233,
0.020603734999895096,
-0.005812427960336208,
0.04634002596139908,
0.014733579009771347,
0.00394815718755126,
-0.006043505389243364,
0.056148461997509,
0.04469973221421242,
-0.015166288241744041,
-0.02220781520009041,
0.004754857160151005,
-0.03862927854061127,
0.009338529780507088,
-0.027169154956936836,
-0.03551778197288513,
0.05455626919865608,
0.029266996309161186,
0.05323822796344757,
0.018624676391482353,
0.005084321368485689,
0.007527824491262436,
-0.0535089410841465,
-0.016273124143481255,
-0.026140056550502777,
0.03411690518260002,
-0.011378043331205845,
0.07578584551811218,
0.017820894718170166,
0.02077721618115902,
0.010680345818400383,
0.03343597427010536,
-0.061242636293172836,
0.010765500366687775,
0.00557916983962059,
-0.0025618281215429306,
-0.05695347487926483,
-0.006224578712135553,
0.011268447153270245,
-0.015310277231037617,
-0.045283202081918716,
0.002616501646116376,
-0.00015952737885527313,
-0.048698749393224716,
-0.010035621002316475,
-0.015875525772571564,
0.014422125183045864,
-0.023404976353049278,
0.06137105077505112,
-0.010786770842969418,
-0.014196052215993404,
-0.0034843329340219498,
0.010470344685018063,
-0.050343386828899384,
-0.01001498382538557,
-0.04775499179959297,
0.0375569723546505,
0.01997382566332817,
0.05857371538877487,
0.01365896500647068,
0.0029931231401860714,
-0.025441287085413933,
0.008461910299956799,
-0.041272830218076706,
0.07306993752717972,
-0.006448831874877214,
0.007275153882801533,
-0.0022503326181322336,
-0.04815056547522545,
0.012380659580230713,
0.0033184417989104986,
0.03815126419067383,
-0.03799697011709213,
0.020933998748660088,
0.03613881766796112,
-0.010948521085083485,
-0.038135167211294174,
0.008326398208737373,
0.026566490530967712,
0.02506004273891449,
-0.019209716469049454,
-0.03518384322524071,
0.002222787356004119,
-0.018423089757561684,
0.006189137697219849,
0.023717230185866356,
0.042049508541822433,
0.0181072149425745,
0.0011522817658260465,
-0.01349041797220707,
0.028433965519070625,
-0.028064947575330734,
-0.011678023263812065,
-0.02307400293648243,
0.013717015273869038,
-0.0031695375218987465,
0.0037012281827628613,
0.0017957192612811923,
0.06513617932796478,
0.04549702629446983,
-0.031061599031090736,
0.0021051340736448765,
-0.09074631333351135,
0.02860208973288536,
0.007562740705907345,
0.0393710657954216,
-0.02558056078851223,
0.015277129597961903,
-0.022813787683844566,
-0.003119930624961853,
0.034736257046461105,
0.010526413097977638,
0.04333614557981491,
-0.01750718429684639,
-0.0002821304078679532,
-0.02131941169500351,
0.011651973240077496,
-0.0000813860388007015,
0.010323110967874527,
0.04393399879336357,
-0.020693130791187286,
-0.011855118907988071,
0.028813686221837997,
-0.022158019244670868,
0.025199798867106438,
0.041982028633356094,
0.06793692708015442,
0.011178607121109962,
-0.00878702662885189,
0.03449122607707977,
0.014715016819536686,
-0.03622937574982643,
-0.06050221994519234,
0.00007642228592885658,
0.01565448008477688,
0.011001424863934517,
0.04801550880074501,
-0.041694752871990204,
-0.054245710372924805,
0.06071651354432106,
0.006990506779402494,
-0.0023492134641855955,
0.017860928550362587,
0.012174501083791256,
0.04345613345503807,
0.0424513965845108,
-0.011746932752430439,
0.049772754311561584,
0.06440795958042145,
0.02165091596543789,
0.014028839766979218,
-0.030382554978132248,
0.03907475993037224,
-0.014220885932445526,
-0.007728900760412216,
-0.015280189923942089,
0.012100107967853546,
-0.02823902666568756,
0.026323258876800537,
0.02597118727862835,
0.018685750663280487,
0.00045359908835962415,
-0.04798285663127899,
0.0005432605394162238,
0.0057549187913537025,
-0.03218556568026543,
0.006826537195593119,
-0.014173793606460094,
0.026006212458014488,
0.008456777781248093,
-0.05912462994456291,
0.015046585351228714,
-0.010692238807678223,
0.00552577106282115,
0.003000059863552451,
-0.008332433179020882,
0.004753401968628168,
-0.04976419359445572,
0.008696580305695534,
-0.005474334582686424,
-0.04346747696399689,
0.05520019307732582,
-0.03945426642894745,
0.015196789056062698,
0.037863533943891525,
-0.06941255927085876,
-0.015482453629374504,
0.04093363136053085,
-0.010156288743019104,
0.026803119108080864,
-0.017915457487106323,
0.015915710479021072,
-0.019250160083174706,
-0.007818137295544147,
-0.07562508434057236,
-0.024601604789495468,
-0.0006235571927390993,
0.0839872658252716,
-0.0465511828660965,
-0.014713107608258724,
0.026638945564627647,
-0.0010378716979175806,
-0.015253937803208828,
0.045017655938863754,
0.038364212960004807,
-0.010467187501490116,
-0.012027774006128311,
0.016251470893621445,
0.005885761696845293,
0.05486719310283661,
-0.03726654499769211,
-0.03346120938658714,
-0.002416549948975444,
-0.0524703711271286,
-0.00444974098354578,
0.021687114611268044,
0.01555046159774065,
-0.009757782332599163,
-0.002853952581062913,
-0.06707322597503662,
-0.007733476813882589,
0.03590046614408493,
-0.03175019472837448,
-0.022056303918361664,
0.029174111783504486,
0.02890917845070362,
0.017106756567955017,
-0.047558143734931946,
0.01580037921667099,
-0.019610300660133362,
0.020183701068162918,
0.00919237919151783,
-0.008249782025814056,
-0.011024245992302895,
-0.003800087608397007,
0.02419332042336464,
0.01762387715280056,
-0.021222379058599472,
-0.003476309822872281,
0.04228060320019722,
-0.007114643231034279,
0.0018095542909577489,
0.012970718555152416,
0.009299065917730331,
-0.0023807999677956104,
-0.017436165362596512,
0.010089214891195297,
0.022159624844789505,
0.036287665367126465,
-0.04974101111292839,
-0.07390967756509781,
-0.04486076533794403,
0.01654633693397045,
0.05363864451646805,
-0.03401859849691391,
0.01036673691123724,
0.011130372062325478,
0.004094098694622517,
-0.02508651092648506,
-0.010278292931616306,
-0.013437326066195965,
0.011590850539505482,
-0.025542454794049263,
0.06469018757343292,
-0.019425615668296814,
0.0006822627037763596,
0.004727390129119158,
0.05236636474728584,
-0.05000687763094902,
0.027600480243563652,
0.022067924961447716,
-0.008333173580467701,
0.024146724492311478,
-0.025436600670218468,
-0.030322108417749405,
0.02935040183365345,
-0.04902514070272446,
0.03167552873492241,
-0.008484606631100178,
-0.03741639107465744,
0.02813621796667576,
-0.01616128347814083,
0.026539908722043037,
-0.03173521161079407,
-0.033539727330207825,
-0.012830376625061035,
0.021492429077625275,
0.04103844612836838,
0.03872368484735489,
-0.0005698363529518247,
0.0018137912265956402,
0.02612839825451374,
0.002916072029620409,
0.02539059892296791,
0.004287109710276127,
-0.05091297999024391,
-0.046260446310043335,
-0.009163900278508663,
-0.017113003879785538,
0.009670179337263107,
0.017245568335056305,
-0.03937770426273346,
0.024846592918038368,
-0.023196082562208176,
0.029735073447227478,
-0.007562857586890459,
0.062131118029356,
-0.0001240011624759063,
0.009961136616766453,
-0.030999692156910896,
0.03532833606004715,
0.02287059649825096,
-0.0008578584529459476,
0.09959041327238083,
0.043504372239112854,
0.02917397767305374,
-0.06091412156820297,
0.0045690075494349,
-0.016122067347168922,
-0.01171893160790205,
-0.01804473251104355,
0.047615088522434235,
-0.01196694653481245,
0.020947208628058434,
-0.04066276550292969,
0.06565097719430923,
-0.009623819962143898,
0.017991628497838974,
0.04255955293774605,
-0.013348240405321121,
-0.024319378659129143,
0.026112420484423637,
0.018571149557828903,
-0.02747252583503723,
-0.0007237865938805044,
-0.06678304076194763,
0.008523114956915379,
-0.03454966843128204,
-0.007031043525785208,
-0.016473975032567978,
-0.023167965933680534,
0.05074484646320343,
-0.0006215085741132498,
-0.04879305884242058,
-0.008232652209699154,
0.014975671656429768,
0.010128775611519814,
-0.04576699435710907,
0.017858002334833145,
0.05497319623827934,
0.004041856154799461,
-0.003323314944282174,
0.029794519767165184,
0.04160197824239731,
0.009729723446071148,
0.004610373638570309,
0.012524290010333061,
-0.0072533609345555305,
-0.01324815209954977,
0.010364582762122154,
0.0074828630313277245,
-0.026727663353085518,
-0.013193881139159203,
-0.007882175967097282,
-0.03322787210345268,
-0.007650061976164579,
-0.05754023790359497,
0.002401682548224926,
0.009132138453423977,
0.0215605478733778,
-0.031982067972421646,
0.007607418578118086,
0.018682388588786125,
0.0277551356703043,
-0.03424319252371788,
-0.010242754593491554,
-0.014113719575107098,
-0.03537817671895027,
-0.004654195625334978,
-0.010930424556136131,
0.015964535996317863,
0.03183232620358467,
-0.06925422698259354,
-0.03854764252901077,
-0.04365608096122742,
-0.011110560037195683,
-0.05065811797976494,
0.02835213392972946,
0.021582024171948433,
0.02773944102227688,
-0.014670128002762794,
0.009066003374755383,
0.008714485913515091,
-0.06800612062215805,
0.013398389331996441,
-0.010154049843549728,
0.003499397309496999,
-0.03093154914677143,
-0.015501393005251884,
0.05811888352036476,
0.016626592725515366,
-0.03645088151097298,
0.0017093196511268616,
-0.0013110635336488485,
-0.00831419788300991,
0.011523189954459667,
-0.05764425918459892,
-0.022451603785157204,
0.0326605923473835,
-0.033841587603092194,
0.03389367461204529,
0.015610233880579472,
0.05166029557585716,
0.017830118536949158,
0.017762068659067154,
-0.004325088579207659,
0.025957860052585602,
-0.02789602428674698,
0.00814933143556118,
0.003713334212079644,
-0.020142102614045143,
0.004715228918939829,
-0.005938655696809292,
0.013087456114590168,
-0.011879757046699524,
-0.05533813312649727,
-0.06955499947071075,
-0.012220380827784538,
0.01280802022665739,
-0.00606679730117321,
0.01889520138502121,
-0.017606347799301147,
-0.0062406533397734165,
-0.017816822975873947,
-0.03153139725327492,
0.00009179402695735916,
-0.03635396808385849,
-0.0038822295609861612,
0.005008297972381115,
-0.014090345241129398,
0.011966635473072529,
0.011764856986701488,
0.0033748934511095285,
-0.030557183548808098,
0.0384027324616909,
0.04199734330177307,
0.010824041441082954,
-0.052170589566230774,
0.008185791783034801,
-0.005971265025436878,
0.06752181053161621,
-0.02584919147193432,
-0.015333328396081924,
0.0076947202906012535,
-0.033650629222393036,
-0.012923585250973701,
0.011615402065217495,
-0.057035356760025024,
0.04591015726327896,
0.006156438495963812,
0.01772933639585972,
-0.013343684375286102,
0.06323590129613876,
-0.03024214692413807,
0.002118147909641266,
0.019507938995957375,
-0.02844860590994358,
-0.005716999527066946,
-0.03171179071068764,
0.010988091118633747,
-0.03286284580826759,
-0.005295576527714729,
0.04251366853713989,
-0.011271823197603226,
0.0170674379914999,
0.0015388623578473926,
0.019658997654914856,
-0.002072041155770421,
-0.0350492000579834,
0.04861171543598175,
-0.0037208697758615017,
0.031009811908006668,
0.01621113158762455,
-0.009024055674672127,
0.0823541060090065,
0.07984041422605515,
0.028627801686525345,
-0.09502973407506943,
0.012356107123196125,
0.03611358255147934,
0.024738749489188194,
0.021459555253386497,
-0.06071176379919052,
0.03146475926041603,
-0.003584154648706317,
-0.08211018145084381,
-0.01192302443087101,
-0.04110907390713692,
-0.06384071707725525,
-0.02566090226173401,
0.02929079718887806,
-0.03479773923754692,
0.012413978576660156,
0.010835044085979462,
0.016305122524499893,
0.020582614466547966,
0.015925467014312744,
-0.019069600850343704,
0.024460023269057274,
0.023192603141069412,
0.028606070205569267,
0.005562484264373779,
-0.036095231771469116,
0.029153337702155113,
-0.002095242962241173,
-0.018382122740149498,
-0.0036143572069704533,
0.015024241991341114,
0.03619919717311859,
-0.010967221111059189,
-0.007519490551203489,
-0.004622889216989279,
0.009015943855047226,
0.00009890006185742095,
-0.016642218455672264,
-0.015530766919255257,
-0.013077364303171635,
0.036058519035577774,
0.035655613988637924,
0.005681899841874838,
-0.0038795939180999994,
0.004706979729235172,
-0.025739064440131187,
-0.04000400751829147,
-0.02056724764406681,
-0.008558056317269802,
0.0005802446976304054,
-0.020058363676071167,
0.002363119972869754,
0.0032631719950586557,
-0.036407072097063065,
0.023558061569929123,
-0.09085485339164734,
-0.020235037431120872,
0.011701284907758236,
0.04026103392243385,
0.011008921079337597,
0.023197820410132408,
-0.04445842653512955,
-0.07105301320552826,
0.015328362584114075,
0.011581440456211567,
0.001130439923144877,
-0.05476468428969383,
-0.010523952543735504,
0.036898672580718994,
-0.02307222969830036,
0.04073673486709595,
-0.03926326707005501,
-0.031664762645959854,
0.047994017601013184,
0.014077628031373024,
0.0022210394963622093,
0.03902999311685562,
-0.0606161393225193,
0.002275052247568965,
-0.05637262016534805,
0.038474906235933304,
0.0002143226593034342,
0.017436791211366653,
-0.02378855086863041,
-0.0016310415230691433,
-0.005222049076110125,
0.02199162356555462,
0.05834608152508736,
-0.046330526471138,
-0.012658671475946903,
-0.027937479317188263,
0.014869669452309608,
0.003111012512817979,
-0.03271831199526787,
-0.003984962124377489,
-0.0273562204092741,
-0.04901935160160065,
-0.026629874482750893,
-0.01905839331448078,
-0.04012091085314751,
0.014473347924649715,
0.022444039583206177,
0.01601240783929825,
-0.007603324484080076,
0.003475787816569209,
-0.03680306673049927,
0.05679881200194359,
-0.005998249165713787,
-0.025546083226799965,
0.053420696407556534,
0.012694784440100193,
-0.016113243997097015,
0.06527591496706009,
0.011950109153985977,
-0.06298644840717316,
0.03095468319952488,
-0.01929161138832569,
-0.03968651592731476,
-0.015824278816580772,
-0.02327599562704563,
0.006517017725855112,
-0.05481346324086189,
0.019203899428248405,
0.036171332001686096,
-0.03504722937941551,
0.007493294309824705,
0.049948304891586304,
-0.02826704829931259,
0.03827332332730293,
0.0008728947723284364,
0.01190167386084795,
0.026051513850688934,
-0.034369077533483505,
-0.01860186830163002,
0.031750887632369995,
0.04335770010948181,
0.021921439096331596,
0.03065446950495243,
0.00309551483951509,
-0.005825694650411606,
-0.019131990149617195,
-0.01322067342698574,
0.011922511272132397,
-0.030511055141687393,
0.011193552985787392,
0.017770180478692055,
-0.009723223745822906,
0.029203446581959724,
-0.011599150486290455,
-0.016901159659028053,
0.10420767217874527,
-0.015793122351169586,
0.03596349433064461,
-0.04093562811613083,
0.024277890101075172,
-0.04009595885872841,
0.02885664813220501,
0.03172939270734787,
0.006252272054553032,
-0.031892258673906326,
0.0013549088034778833,
-0.026432637125253677,
0.0032559484243392944,
0.02854308858513832,
-0.060271669179201126,
0.004275376442819834,
-0.007538327015936375,
-0.04547550901770592,
-0.00046985590597614646,
-0.018006790429353714,
-0.04140915721654892,
-0.01277739554643631,
0.010999915190041065,
0.02769537642598152,
-0.02111659198999405,
0.005466115195304155,
-0.012877145782113075,
-0.023199288174510002,
0.06446512788534164,
-0.0743597224354744,
-0.01915076933801174,
-0.01892165094614029,
0.00195405725389719,
-0.025500401854515076,
-0.03314833343029022
] |
<p>Is the fact that weak eigenstates are not mass eigenstates completely arbitrary? Or is there a deeper reason for the existence of the PMNS and CKM matrices?</p>
| 10,667 |
[
-0.0009238298516720533,
0.018332714214920998,
-0.045932624489068985,
-0.07070457935333252,
0.08264072984457016,
-0.00925477035343647,
-0.030738595873117447,
-0.05142974480986595,
0.006956724915653467,
-0.04544055461883545,
0.020350828766822815,
0.014397277496755123,
0.059950221329927444,
-0.0002862818946596235,
0.0241240244358778,
0.021456321701407433,
0.015820980072021484,
-0.03416616469621658,
-0.028429200872778893,
-0.035209354013204575,
0.005290220491588116,
0.04112929105758667,
0.01542256586253643,
0.03287135437130928,
-0.022733330726623535,
0.04170563444495201,
0.026127062737941742,
0.013691217638552189,
0.010040988214313984,
0.051474735140800476,
0.012968683615326881,
-0.034785572439432144,
0.014929022639989853,
0.018910421058535576,
0.033120349049568176,
-0.010832070372998714,
-0.009461596608161926,
-0.03915056213736534,
-0.0005130897043272853,
0.03306484967470169,
-0.042152874171733856,
-0.01545402966439724,
-0.028157951310276985,
-0.021037451922893524,
-0.035214900970458984,
0.030859794467687607,
0.024508420377969742,
-0.005673253443092108,
0.031022587791085243,
-0.06262417882680893,
0.07286225259304047,
0.011441659182310104,
0.014380572363734245,
0.0025896441657096148,
-0.051575567573308945,
-0.014308000914752483,
0.058677785098552704,
0.03967684134840965,
0.009169566445052624,
-0.059807561337947845,
-0.00574516924098134,
0.002664492931216955,
0.021287549287080765,
-0.02813965268433094,
-0.010423040017485619,
0.025337543338537216,
0.01389430183917284,
-0.017733754590153694,
0.025320053100585938,
0.012096617370843887,
-0.01580401323735714,
-0.0002193969557993114,
0.016309350728988647,
0.0010473949369043112,
0.025407815352082253,
-0.03965046629309654,
0.02358444221317768,
-0.0037421321030706167,
0.0306421909481287,
0.01180713064968586,
0.02239561825990677,
0.027118120342493057,
0.02643008902668953,
0.015047046355903149,
-0.03538978844881058,
0.0027372867334634066,
0.07037034630775452,
-0.006118340417742729,
0.01851165108382702,
0.06106442213058472,
-0.02405625768005848,
0.031272269785404205,
0.025760604068636894,
0.008347045630216599,
-0.0013469690456986427,
0.0020734183490276337,
0.034035809338092804,
0.033629074692726135,
-0.021912239491939545,
-0.005357144400477409,
-0.025362804532051086,
-0.014719489961862564,
0.016496069729328156,
0.06588765233755112,
-0.007231254130601883,
0.015014002099633217,
0.0032572592608630657,
0.03430943563580513,
-0.024036100134253502,
0.0007848467212170362,
-0.027246471494436264,
-0.0026778567116707563,
-0.015529020689427853,
-0.005912468768656254,
0.008175262250006199,
-0.019380824640393257,
-0.010931696742773056,
-0.055053289979696274,
0.034652404487133026,
0.07988864928483963,
0.04306463152170181,
-0.02653239108622074,
0.0092276306822896,
-0.06494555622339249,
-0.04952143132686615,
0.03847920894622803,
0.03892574459314346,
-0.010315044783055782,
-0.02213526889681816,
-0.004277088213711977,
-0.0006046377238817513,
-0.014574180357158184,
0.01018866803497076,
-0.005328856408596039,
0.037445131689310074,
-0.021888311952352524,
-0.12267798185348511,
-0.05834187939763069,
0.05634615570306778,
0.0049247825518250465,
-0.037405434995889664,
-0.05262888967990875,
-0.020708853378891945,
0.04803314059972763,
0.0659131184220314,
0.0003463073808234185,
0.012733065523207188,
0.01897522434592247,
0.03133381903171539,
0.012747338972985744,
-0.011776232160627842,
-0.0008319586049765348,
-0.009407405741512775,
-0.05693923309445381,
0.015749512240290642,
-0.06576214730739594,
0.02729209139943123,
0.03625338152050972,
-0.000621909333858639,
0.006725657731294632,
0.004796591587364674,
-0.03204943612217903,
0.03511418402194977,
0.009817594662308693,
0.007740034721791744,
-0.006898016668856144,
0.035080328583717346,
0.02535739541053772,
-0.002419671043753624,
0.04563385248184204,
-0.023024210706353188,
0.019830523058772087,
0.024505987763404846,
0.043602049350738525,
-0.003631141735240817,
-0.036414697766304016,
0.0011275013675913215,
-0.0072732772678136826,
0.011799869127571583,
-0.0010948269627988338,
-0.06258270144462585,
-0.016502568498253822,
-0.026927856728434563,
0.0029939247760921717,
0.014667092822492123,
0.040951550006866455,
-0.009795469231903553,
0.0185783039778471,
0.018910063430666924,
-0.03204846754670143,
-0.016146216541528702,
-0.04203162342309952,
0.02625162899494171,
0.00788144301623106,
-0.04305865243077278,
0.05380412936210632,
0.00032331826514564455,
-0.0034169272985309362,
-0.025523914024233818,
-0.02979312464594841,
-0.011993033811450005,
-0.00823381170630455,
-0.03956717252731323,
-0.008560078218579292,
0.0008640811429359019,
0.06116660684347153,
-0.013528004288673401,
0.006966105196624994,
0.03280077129602432,
-0.026387471705675125,
-0.06308507174253464,
-0.031703997403383255,
-0.001163153792731464,
0.02183377742767334,
-0.012061921879649162,
0.004905845038592815,
-0.00775747699663043,
-0.03539695963263512,
-0.013820958323776722,
0.02138172835111618,
-0.05827721953392029,
0.08742140978574753,
0.0218029897660017,
-0.0023410930298268795,
-0.03634550794959068,
0.04557160288095474,
0.03776708245277405,
0.02746398374438286,
0.007246692664921284,
-0.03949626535177231,
-0.06362772732973099,
0.0005935197114013135,
0.0161137618124485,
0.04567095264792442,
-0.060871969908475876,
0.02592535875737667,
0.013998710550367832,
0.058679789304733276,
0.005718023516237736,
-0.013719691894948483,
-0.041695717722177505,
-0.0339534766972065,
0.05136483907699585,
0.028866346925497055,
-0.019440170377492905,
0.015998339280486107,
0.019085442647337914,
0.01554841548204422,
0.016888350248336792,
-0.013947376981377602,
-0.03691941499710083,
0.027509044855833054,
-0.04673392325639725,
-0.030599065124988556,
-0.008099754340946674,
-0.042166851460933685,
0.03942351043224335,
0.01020242739468813,
0.045239247381687164,
0.02144179493188858,
0.01143315713852644,
0.012181799858808517,
-0.004385991021990776,
-0.04058418050408363,
0.012206397950649261,
-0.024498356506228447,
-0.02036355435848236,
-0.010555288754403591,
0.032255057245492935,
-0.01482364535331726,
0.015366296283900738,
-0.049880798906087875,
-0.01797335594892502,
0.010456142947077751,
-0.0035415845923125744,
0.06797204911708832,
0.003777300240471959,
0.008522757329046726,
-0.02925754152238369,
-0.01703941449522972,
-0.0019349156646057963,
-0.022858887910842896,
-0.011419054120779037,
0.04268092289566994,
-0.05090341717004776,
0.018729902803897858,
-0.049630869179964066,
-0.018155492842197418,
0.0051468368619680405,
-0.01067014317959547,
0.012890968471765518,
0.00018907884077634662,
-0.02256261371076107,
-0.025991497561335564,
-0.03083808906376362,
0.0026938454248011112,
-0.007817299105226994,
-0.03372454643249512,
0.010876741260290146,
0.037435319274663925,
0.019178641960024834,
-0.02631358616054058,
-0.011546800844371319,
-0.027456659823656082,
-0.038107238709926605,
-0.03480183705687523,
-0.020953647792339325,
0.001836220733821392,
-0.04155474156141281,
0.026996435597538948,
0.058746304363012314,
-0.016983505338430405,
0.010051575489342213,
-0.03253880888223648,
-0.02764260210096836,
0.0698745846748352,
-0.04533886909484863,
0.042940039187669754,
0.03373033180832863,
0.002404957776889205,
0.12780575454235077,
0.04516160488128662,
-0.012838250957429409,
-0.03572544828057289,
-0.013576201163232327,
-0.03634650260210037,
-0.028065068647265434,
0.002959647448733449,
0.011651930399239063,
-0.0024292452726513147,
0.030159324407577515,
0.04238912835717201,
0.02369864098727703,
0.020968187600374222,
-0.025538373738527298,
-0.03272124007344246,
0.01383228786289692,
-0.019925035536289215,
0.008719803765416145,
0.035023946315050125,
-0.01967691071331501,
-0.030900772660970688,
-0.01576710119843483,
0.015240813605487347,
0.0566282644867897,
-0.012842816300690174,
-0.06231316551566124,
0.054813284426927567,
-0.015753908082842827,
0.039653558284044266,
-0.035743795335292816,
0.055871058255434036,
-0.006678150966763496,
-0.011611602269113064,
-0.01698533073067665,
0.05286874622106552,
0.01443519163876772,
-0.05711236968636513,
0.010373723693192005,
0.029549626633524895,
-0.000539880886208266,
-0.009391114115715027,
0.0069629424251616,
0.03160744160413742,
-0.022558415308594704,
0.01349665131419897,
-0.03567676246166229,
-0.024982834234833717,
0.04643316939473152,
0.038995981216430664,
0.04197358340024948,
0.005866594146937132,
-0.03900684788823128,
0.0006173353176563978,
-0.03646994009613991,
0.009684124030172825,
0.007931212894618511,
0.030398061498999596,
-0.002906125970184803,
0.06357467919588089,
0.0149537343531847,
-0.021876035258173943,
-0.03608689084649086,
0.008988632820546627,
-0.05361684411764145,
-0.013237536884844303,
-0.03872890770435333,
-0.021341299638152122,
0.01980731263756752,
-0.02106436900794506,
-0.011841775849461555,
-0.01872423104941845,
-0.040070466697216034,
-0.022225867956876755,
-0.002344109583646059,
-0.0820707157254219,
-0.018460512161254883,
-0.05440061166882515,
-0.031860049813985825,
-0.003363028634339571,
0.0011271977564319968,
0.07594019919633865,
-0.009935270063579082,
0.03255532309412956,
0.014794575981795788,
-0.05227811634540558,
-0.009618662297725677,
-0.01128880400210619,
0.05501211807131767,
0.020633868873119354,
0.0057544829323887825,
0.04743821546435356,
0.06049578636884689,
-0.043222710490226746,
-0.008786777965724468,
0.02662643976509571,
0.06555802375078201,
0.03882975876331329,
-0.01933283917605877,
0.004134391900151968,
-0.059092339128255844,
-0.011224879883229733,
0.051540449261665344,
0.04072292894124985,
0.013251325115561485,
0.014126411639153957,
0.03318142518401146,
0.005149425473064184,
-0.04679812490940094,
0.036990031599998474,
0.038839828222990036,
0.03167077153921127,
-0.04877404496073723,
-0.044083040207624435,
0.006262608803808689,
-0.016099711880087852,
-0.0030922803562134504,
0.01643913984298706,
-0.02376250922679901,
-0.015053074806928635,
0.018192868679761887,
0.002072990173473954,
-0.02607601508498192,
-0.023076597601175308,
-0.04804248735308647,
-0.026649625971913338,
-0.00763079384341836,
-0.03365970402956009,
0.007283091079443693,
0.022326912730932236,
0.009914102032780647,
0.05093149095773697,
0.00841414276510477,
0.01464787870645523,
-0.03964056819677353,
0.0065352520905435085,
0.045340485870838165,
-0.0000561218912480399,
-0.012619443237781525,
-0.013116410002112389,
-0.03196089714765549,
-0.0492687001824379,
0.040369629859924316,
0.0006940001039765775,
0.057212796062231064,
0.033891621977090836,
-0.001431710785254836,
-0.027700286358594894,
-0.029740532860159874,
0.02011633664369583,
0.029754817485809326,
-0.0014994131634011865,
0.004555889405310154,
-0.016403894871473312,
-0.01797698438167572,
-0.030257700011134148,
-0.004500092007219791,
0.014433505944907665,
0.03842455521225929,
0.02161410264670849,
-0.022071516141295433,
0.0074471174739301205,
0.012309801764786243,
0.002996195573359728,
-0.11462467908859253,
0.0009091742103919387,
-0.0003238864883314818,
-0.006360399536788464,
0.024413341656327248,
-0.037281326949596405,
-0.06216750293970108,
0.00976763479411602,
-0.004241700284183025,
0.010358298197388649,
0.00548592209815979,
-0.031111950054764748,
0.016897452995181084,
0.020912252366542816,
-0.026263032108545303,
0.024272099137306213,
0.026009146124124527,
-0.015665452927350998,
0.010040054097771645,
-0.031043438240885735,
0.0345635786652565,
-0.06566144526004791,
0.028398223221302032,
-0.020176587626338005,
0.011546216905117035,
-0.008241120725870132,
0.034844499081373215,
0.03934745490550995,
0.026875168085098267,
0.02389405108988285,
-0.028845585882663727,
-0.018349552527070045,
0.04539689049124718,
0.027508016675710678,
-0.012471061199903488,
-0.0003290691238362342,
0.023472171276807785,
-0.027774479240179062,
-0.026968378573656082,
0.020968349650502205,
-0.02031658962368965,
0.022344930097460747,
0.02761288918554783,
0.010863004252314568,
-0.006246856413781643,
-0.030413782224059105,
-0.00048186627100221813,
0.01815631613135338,
-0.01903773471713066,
0.04845650494098663,
0.007003097794950008,
0.032936956733465195,
0.017503825947642326,
-0.04725683480501175,
-0.023817256093025208,
0.011081158183515072,
-0.026167219504714012,
0.02486170455813408,
0.00536498986184597,
0.027391383424401283,
0.014539928175508976,
0.013312223367393017,
-0.0787477195262909,
-0.022254152223467827,
-0.01223480049520731,
0.009197590872645378,
0.005388485733419657,
-0.027409566566348076,
0.022138385102152824,
-0.011752394959330559,
-0.017098018899559975,
0.02978532761335373,
0.06843552738428116,
-0.012732909992337227,
-0.02029208280146122,
0.04782698675990105,
0.019261354580521584,
0.060099225491285324,
0.021663492545485497,
0.007267151493579149,
0.036285463720560074,
-0.015418724156916142,
0.016418443992733955,
0.02578376606106758,
0.02360200509428978,
0.003798027988523245,
-0.038689326494932175,
-0.03891098126769066,
-0.006656121462583542,
0.020892946049571037,
-0.013081645593047142,
0.015011291019618511,
0.0567505769431591,
-0.022458510473370552,
0.01758967898786068,
-0.023544251918792725,
0.004526238422840834,
-0.02694886364042759,
0.023974020034074783,
-0.010356463491916656,
0.0004165418795309961,
0.02401749975979328,
-0.044245295226573944,
0.056082554161548615,
-0.012724103406071663,
-0.004479862749576569,
0.010135163553059101,
0.0192880742251873,
-0.016622325405478477,
-0.0074240341782569885,
0.007107206154614687,
0.014268792234361172,
0.025002656504511833,
0.004468920640647411,
-0.0010615030769258738,
0.0020793871954083443,
0.004188121762126684,
0.00852872896939516,
-0.05646636709570885,
-0.05715184286236763,
0.027167141437530518,
0.03951290249824524,
0.0014016699278727174,
0.004253467079252005,
0.018380029127001762,
-0.02295965515077114,
-0.012168830260634422,
-0.018548302352428436,
-0.0072244880720973015,
0.013263187371194363,
-0.03417162969708443,
0.0015670902794227004,
-0.07726944983005524,
0.01254248060286045,
0.02441326156258583,
0.06603463739156723,
-0.041641753166913986,
-0.04261991009116173,
0.049344927072525024,
0.01135679055005312,
0.021279053762555122,
0.015434352681040764,
0.004373196978121996,
0.05255930870771408,
-0.02521662227809429,
-0.0015374013455584645,
0.015451994724571705,
-0.034894511103630066,
0.012959467247128487,
0.006693595554679632,
0.004482146352529526,
-0.010011718608438969,
-0.025108449161052704,
-0.02076532505452633,
0.0382864847779274,
-0.000028748738259309903,
0.013146660290658474,
0.00779770826920867,
-0.00814273115247488,
0.02685312181711197,
0.049057502299547195,
0.02469722181558609,
0.02183733880519867,
-0.05082263424992561,
-0.0506218746304512,
0.018519366160035133,
-0.04254886507987976,
0.013928406871855259,
-0.029573405161499977,
-0.04379936307668686,
0.054064325988292694,
-0.02166326344013214,
0.010155785828828812,
0.02757113426923752,
0.027084993198513985,
-0.0221748948097229,
0.012646360322833061,
-0.002057810313999653,
-0.012092110700905323,
0.009340379387140274,
-0.006104489788413048,
0.13865375518798828,
0.02043917402625084,
0.023359574377536774,
-0.06803326308727264,
0.04828622564673424,
0.016909928992390633,
0.01794557459652424,
0.028699234127998352,
0.024657225236296654,
-0.007902930490672588,
0.018874719738960266,
-0.05314662307500839,
0.056709423661231995,
-0.010375870391726494,
0.020321443676948547,
0.028955936431884766,
-0.03660566359758377,
-0.04213707894086838,
0.02355177327990532,
0.04470635578036308,
0.012505562044680119,
-0.03294723853468895,
0.0009150936966761947,
0.04562786966562271,
0.016932792961597443,
-0.01461845077574253,
-0.008881477639079094,
-0.0026180660352110863,
0.01753106713294983,
0.0010034081060439348,
-0.036405980587005615,
0.001618952490389347,
0.034499820321798325,
-0.005809518042951822,
-0.03535487875342369,
0.05872786045074463,
-0.0015016032848507166,
-0.0045776511542499065,
0.04042034596204758,
0.01596938632428646,
0.002968944376334548,
-0.040428388863801956,
0.012856483459472656,
-0.0458548478782177,
-0.048385992646217346,
0.0035631204955279827,
-0.02110448107123375,
0.031077394261956215,
-0.008676422759890556,
0.03534196317195892,
0.016255969181656837,
-0.015539383515715599,
0.016068050637841225,
-0.04677540436387062,
0.003902133321389556,
-0.004778407979756594,
0.0403154231607914,
-0.04264948144555092,
-0.007290230598300695,
-0.013529734686017036,
0.006866977550089359,
0.02574392966926098,
0.03206685930490494,
-0.04184775799512863,
-0.027479227632284164,
-0.003308887593448162,
0.019496724009513855,
0.011984124779701233,
0.03330274298787117,
-0.0315668061375618,
0.013557218946516514,
-0.008864968083798885,
-0.04976994916796684,
-0.050077687948942184,
0.001489461399614811,
-0.0023001341614872217,
0.04883281886577606,
0.03317670524120331,
0.02666444517672062,
-0.03448602184653282,
-0.07321052253246307,
0.03723958134651184,
0.0034827219787985086,
-0.01904129981994629,
-0.00355814048089087,
-0.005052509251981974,
0.008382003754377365,
0.04877343773841858,
-0.017188601195812225,
0.005098921712487936,
-0.02631841041147709,
0.02907966449856758,
-0.016669033095240593,
-0.04475068673491478,
-0.017707541584968567,
0.0007953445892781019,
-0.024414563551545143,
0.02264421619474888,
-0.010779685340821743,
-0.02587161213159561,
0.028518784791231155,
0.005630593281239271,
-0.02081405743956566,
0.027271121740341187,
0.006872429512441158,
-0.04978454113006592,
0.02111489325761795,
-0.04815570265054703,
0.01741582714021206,
0.04620594531297684,
0.008295061998069286,
-0.05338834971189499,
-0.05727313086390495,
-0.06529660522937775,
-0.012735160999000072,
0.013749003410339355,
0.02782529778778553,
-0.038722261786460876,
-0.014893979765474796,
-0.030887894332408905,
0.027237700298428535,
-0.04616083204746246,
-0.019071297720074654,
-0.028360377997159958,
-0.0062372093088924885,
-0.01860848069190979,
-0.0154398363083601,
-0.04242584854364395,
-0.0009723989642225206,
-0.008477805182337761,
-0.00734437583014369,
0.0065599107183516026,
0.029265528544783592,
-0.009158593602478504,
-0.03943773731589317,
0.004934441763907671,
0.010432551614940166,
0.013332347385585308,
-0.008787388913333416,
-0.047588594257831573,
0.00695169810205698,
-0.05419133976101875,
-0.05190237984061241,
0.02473209984600544,
-0.024822132661938667,
0.032146889716386795,
0.028615403920412064,
-0.010467919521033764,
-0.023757318034768105,
0.030919166281819344,
-0.04029272496700287,
-0.01826498471200466,
0.032266803085803986,
0.034099970012903214,
-0.005328359082341194,
-0.027114257216453552,
-0.012692557647824287,
-0.004175949841737747,
0.0035894999746233225,
0.041543956845998764,
0.020043618977069855,
-0.015786295756697655,
-0.01435142196714878,
0.006660913582891226,
0.00916663184762001,
0.045260749757289886,
0.034843578934669495,
0.03038422390818596,
0.024021068587899208,
0.006183058489114046,
-0.016786811873316765,
-0.011163403280079365,
0.004670978058129549,
0.02452983893454075,
-0.08902193605899811,
-0.01786946877837181,
-0.0034292784985154867,
-0.03944920375943184,
0.03902735188603401,
-0.034867238253355026,
0.034695010632276535,
0.03163804113864899,
-0.0961238443851471,
0.011895916424691677,
-0.015023523010313511,
-0.005697900895029306,
-0.0019335643155500293,
-0.0074761598370969296,
-0.030434204265475273,
0.0721980407834053,
0.014611676335334778,
0.03302518278360367,
0.022219613194465637,
-0.009840551763772964,
0.018144706264138222,
-0.01432913076132536,
-0.02402123063802719,
-0.007407575845718384,
0.01847531460225582,
-0.03936745971441269,
0.05417467653751373,
-0.028048716485500336,
-0.013516916893422604,
0.023250706493854523,
0.007301106117665768,
-0.01314412523061037,
-0.00041882158257067204,
0.00722626643255353,
0.017790384590625763,
0.03398249298334122,
0.013322614133358002,
-0.017058568075299263,
0.004631443414837122,
0.024141261354088783,
-0.01530640758574009,
0.04656459391117096,
0.01972433179616928,
0.03946205601096153,
0.0006402586004696786,
-0.07565300166606903,
-0.05276847630739212,
-0.01745319552719593,
-0.025960158556699753,
-0.04601870849728584,
0.024829700589179993,
0.013467010110616684,
-0.030248451977968216,
-0.01577063277363777,
0.02979462593793869,
-0.03369811177253723,
-0.020729543641209602,
0.030011361464858055,
0.05667624995112419,
0.0235129501670599,
0.03013543412089348,
0.015016299672424793,
-0.04137265309691429,
0.00297302333638072,
0.04627294838428497,
-0.032957300543785095,
-0.04884050041437149,
0.008093039505183697,
0.043650370091199875,
0.013209396973252296,
-0.03718315064907074,
-0.019901739433407784,
-0.06859073042869568,
0.03987143188714981,
0.018219979479908943,
0.014791080728173256,
-0.05937674269080162,
-0.05471847951412201,
0.02071467414498329,
-0.03876986727118492,
0.02890740893781185,
0.01304589118808508,
0.026604527607560158,
-0.01305681373924017,
0.008785650134086609,
0.02036113850772381,
0.024541743099689484,
0.055398281663656235,
0.0015654952730983496,
-0.025836719200015068,
0.02367798238992691,
-0.0026772795245051384,
0.01790236495435238,
0.01151871308684349,
0.002794985892251134,
-0.032700128853321075,
0.0022058102767914534,
0.001205768552608788,
-0.017392566427588463,
0.00486387312412262,
0.0653107538819313,
0.02719626948237419,
-0.015926340594887733,
-0.0074884346686303616,
0.00781883206218481,
-0.016316557303071022,
0.09445584565401077,
-0.023783311247825623,
-0.027068516239523888,
0.05186526104807854,
-0.013843161053955555,
-0.0014110109768807888,
0.049342650920152664,
-0.03739059343934059,
-0.04838648438453674,
0.030297856777906418,
-0.028429755941033363,
-0.015330622904002666,
-0.00782984308898449,
0.0008352616569027305,
-0.007728299126029015,
-0.00951718632131815,
-0.02782396227121353,
0.02934263087809086,
-0.03382057324051857,
-0.0215445589274168,
0.015100630931556225,
0.017653953284025192,
0.04359805956482887,
0.052192654460668564,
0.05106750503182411,
0.029291028156876564,
0.015888497233390808,
0.03005855716764927,
0.039616722613573074,
0.07911168783903122,
0.014284712262451649,
-0.0071774753741919994,
-0.01200847141444683,
-0.03398595377802849,
0.014677712693810463,
0.0066384137608110905,
0.014603263698518276,
-0.004852370824664831,
-0.012671108357608318,
0.03947031870484352,
-0.0005559157580137253,
0.016054667532444,
-0.01586141251027584,
-0.0024303048849105835,
0.09073623269796371,
-0.012454204261302948,
0.0036535293329507113,
-0.004944172687828541,
-0.0003398479020688683,
0.01073236670345068,
0.031330689787864685,
-0.01607578620314598,
0.009106199257075787,
0.0024669920094311237,
0.0029978500679135323,
-0.033295053988695145,
-0.0008492469787597656,
0.009273692965507507,
-0.07674109190702438,
-0.02335955575108528,
0.033088356256484985,
0.010382919572293758,
-0.021105801686644554,
0.0028930851258337498,
0.0034903886262327433,
-0.012453830800950527,
0.023617703467607498,
0.022046206519007683,
0.02420405112206936,
-0.029536640271544456,
-0.03452908620238304,
-0.029044929891824722,
0.008940482512116432,
-0.03287121281027794,
0.0014785954263061285,
-0.02012637071311474,
0.004170543048530817,
-0.01365998387336731,
0.014076810330152512
] |
<p>I remember in the high school physics, my teacher told us that the design of the plane wing is because we want the air above the wing flowing faster than the air flowing below so the pressure above and below will be different so the net force is pointing upright. I am thinking if it is possible to explain this by bernoulli equation? But I soon stuck there because I don't know if bernoulli equation applicable to the case of the air flow in the open region? If so, what cross section we should choose?</p>
| 17 |
[
-0.03640684485435486,
0.019468296319246292,
-0.012971395626664162,
0.011275936849415302,
0.05659634992480278,
-0.005423849448561668,
0.0053197904489934444,
-0.017306726425886154,
0.0041572474874556065,
-0.03437960892915726,
0.01268189400434494,
0.031281810253858566,
0.048415862023830414,
-0.01374417170882225,
0.009522928856313229,
-0.0015875109238550067,
-0.036933690309524536,
-0.02298908680677414,
0.014216537587344646,
-0.03002878837287426,
-0.0007551446906290948,
0.007534844800829887,
-0.005317034665495157,
-0.011466950178146362,
-0.03269796818494797,
0.04316732659935951,
0.042148590087890625,
-0.0076926276087760925,
-0.013010953553020954,
0.001879284274764359,
-0.027178114280104637,
-0.004282635636627674,
0.009649827145040035,
0.03686381131410599,
0.03978656604886055,
-0.013121066614985466,
-0.030658798292279243,
-0.02128017507493496,
-0.036515239626169205,
0.018441013991832733,
-0.026006856933236122,
-0.026675846427679062,
0.023046454414725304,
0.0182570219039917,
-0.011687183752655983,
0.010491406545042992,
0.011400626040995121,
-0.026827942579984665,
0.05678530037403107,
-0.09421424567699432,
0.03738267347216606,
0.01421313639730215,
0.036932334303855896,
0.04628333821892738,
0.007647593505680561,
-0.01135313417762518,
0.049600232392549515,
0.04899447411298752,
-0.019100338220596313,
-0.03876964747905731,
0.0014203665778040886,
-0.009034630842506886,
-0.01135982759296894,
-0.061728592962026596,
-0.017131313681602478,
-0.012838445603847504,
-0.05301586911082268,
-0.014530041255056858,
0.01550313737243414,
0.030012978240847588,
-0.028560439124703407,
0.02556571736931801,
0.022444479167461395,
-0.017109563574194908,
0.055934786796569824,
-0.018561070784926414,
0.02559947781264782,
-0.007969857193529606,
0.03664843738079071,
0.021579178050160408,
-0.04434561729431152,
0.033722538501024246,
0.0426124669611454,
0.049970969557762146,
-0.011871712282299995,
-0.004510421771556139,
0.09791235625743866,
-0.007287495769560337,
0.0019341980805620551,
0.010594075545668602,
0.02676994726061821,
-0.009606601670384407,
0.04953280836343765,
0.03018920123577118,
0.036344338208436966,
0.015891125425696373,
-0.007293266709893942,
0.05195224657654762,
0.04396442696452141,
-0.030910762026906013,
0.01487034559249878,
-0.03483307734131813,
0.009767862968146801,
0.09137128293514252,
0.01212591677904129,
-0.022148791700601578,
-0.048054516315460205,
0.017275122925639153,
-0.028985148295760155,
-0.010491380468010902,
-0.06169905140995979,
0.04186073690652847,
-0.03051704354584217,
-0.00961274467408657,
-0.004277771804481745,
-0.015491795726120472,
0.02548198215663433,
-0.0004975041374564171,
0.04007691144943237,
0.0513877272605896,
0.055033762007951736,
-0.023935068398714066,
0.04126764461398125,
-0.010022364556789398,
-0.0689438134431839,
0.01861918345093727,
-0.002559000626206398,
-0.042667414993047714,
-0.022821327671408653,
0.01329898089170456,
-0.005720216315239668,
0.0019688571337610483,
0.009440412744879723,
-0.0030941693112254143,
0.036917027086019516,
-0.021744800731539726,
-0.06746606528759003,
-0.044183287769556046,
0.0532958023250103,
0.006441234145313501,
-0.01970456726849079,
-0.07033006101846695,
0.012178595177829266,
0.027649661526083946,
0.06784687936306,
-0.032783303409814835,
-0.006320899818092585,
-0.018694020807743073,
0.02507767081260681,
-0.00941447913646698,
-0.0047587016597390175,
0.013539950363337994,
0.01685534603893757,
0.0016898317262530327,
-0.010291972197592258,
-0.03621801733970642,
0.02453658916056156,
-0.007961622439324856,
-0.00008458274533040822,
-0.03886144608259201,
0.025250451639294624,
-0.022052088752388954,
-0.009376482106745243,
-0.026828616857528687,
0.01601068302989006,
-0.03605400398373604,
0.06571706384420395,
0.02013159729540348,
0.002719343639910221,
0.03281736373901367,
0.01174206379801035,
-0.01567484438419342,
-0.006976565346121788,
0.013635586015880108,
0.06639657914638519,
-0.021581538021564484,
0.0042121997103095055,
-0.04486759006977081,
0.027090784162282944,
0.01652098260819912,
-0.027051208540797234,
0.00003543294224073179,
-0.01667376421391964,
-0.001894283457659185,
-0.046950701624155045,
0.023624364286661148,
0.004322091117501259,
0.023956023156642914,
0.036909621208906174,
-0.024126430973410606,
-0.05161970108747482,
-0.089482881128788,
0.029097385704517365,
-0.047182295471429825,
-0.00022414860723074526,
0.010732305236160755,
0.010866452939808369,
0.02202335186302662,
-0.05660403147339821,
0.002628649352118373,
-0.02077341079711914,
0.010379616171121597,
0.01807521842420101,
0.013996731489896774,
0.033274468034505844,
0.009026682935655117,
0.0029371283017098904,
0.03255489468574524,
0.057235002517700195,
-0.010817480273544788,
0.0010044121881946921,
0.008060267195105553,
-0.07256609201431274,
0.018015174195170403,
0.01707899011671543,
-0.013315897434949875,
-0.010042060166597366,
0.013332911767065525,
0.03315122425556183,
0.04618425294756889,
-0.03297702968120575,
0.1010856032371521,
0.08486426621675491,
0.025580527260899544,
0.04433128610253334,
0.032991230487823486,
0.024462958797812462,
-0.012211954221129417,
0.0030760595109313726,
-0.03923213854432106,
-0.03797196224331856,
-0.026165839284658432,
0.022360719740390778,
0.0020873378962278366,
-0.03406285494565964,
0.006248215679079294,
0.007790876552462578,
-0.0010031707352027297,
0.011162295006215572,
0.023489996790885925,
0.015728430822491646,
-0.04300328716635704,
-0.015661749988794327,
0.031455375254154205,
0.00035968722659163177,
0.032996684312820435,
0.03268216922879219,
0.0137224942445755,
0.04776732623577118,
-0.04862667992711067,
-0.034891389310359955,
0.029715370386838913,
0.007690639700740576,
0.03355978801846504,
-0.004831187892705202,
0.0150815574452281,
0.03962552919983864,
-0.011226852424442768,
0.04730953648686409,
-0.0193648561835289,
-0.019233858212828636,
-0.014722678810358047,
0.0058348155580461025,
-0.003098157700151205,
0.03953753039240837,
0.014607653953135014,
-0.008667604997754097,
-0.005139980930835009,
0.039093177765607834,
-0.048951830714941025,
0.005907390732318163,
-0.010568213649094105,
-0.010421287268400192,
-0.01550758071243763,
-0.028953706845641136,
0.017933739349246025,
0.016382478177547455,
0.0010385646019130945,
0.011936659924685955,
-0.05959654971957207,
-0.006905077490955591,
0.014208718203008175,
0.0020859437063336372,
0.025963088497519493,
-0.03232778608798981,
0.035528287291526794,
-0.05343903228640556,
0.0054364693351089954,
0.05597924813628197,
-0.006158682517707348,
-0.010453860275447369,
0.0317886620759964,
-0.004085416905581951,
-0.02578575164079666,
0.004844527691602707,
-0.09679480642080307,
0.01743769645690918,
0.006530981045216322,
0.003177546663209796,
0.03673473745584488,
-0.03989802300930023,
0.0003276253992225975,
0.04205659404397011,
-0.054057519882917404,
-0.045081038028001785,
-0.038813043385744095,
0.012144450098276138,
-0.010956662707030773,
-0.017229953780770302,
0.02313818782567978,
0.03539002314209938,
-0.035026825964450836,
-0.004518249072134495,
-0.020901450887322426,
-0.0328301265835762,
-0.0010081998771056533,
-0.009789451025426388,
0.024479864165186882,
-0.012290146201848984,
-0.04129432514309883,
0.07902561128139496,
0.008943467400968075,
-0.052838269621133804,
0.0001817517913877964,
-0.0021373697090893984,
-0.034449681639671326,
-0.0022631848696619272,
0.055613383650779724,
0.0514601394534111,
-0.015957124531269073,
0.041685692965984344,
-0.00330555927939713,
0.0349915511906147,
0.014077804982662201,
0.008938141167163849,
-0.015936434268951416,
-0.013017062097787857,
0.01645134948194027,
0.020733559504151344,
0.04412512853741646,
-0.029419947415590286,
-0.014301568269729614,
0.0167949590831995,
0.023875882849097252,
0.03758685663342476,
0.06096397340297699,
-0.037797145545482635,
0.05699554458260536,
0.012009667232632637,
0.008185231126844883,
-0.04069286584854126,
0.0171528123319149,
0.0023976329248398542,
0.01255719643086195,
-0.003437753999605775,
0.04237273335456848,
0.032955437898635864,
0.007308394648134708,
0.020262088626623154,
0.06658801436424255,
0.04445020481944084,
-0.042523134499788284,
-0.02608456462621689,
0.0013209389289841056,
-0.003032124601304531,
0.04538523778319359,
0.006318625528365374,
-0.026301028206944466,
0.023509062826633453,
0.053264059126377106,
-0.023582035675644875,
0.03484147787094116,
-0.03087260201573372,
0.027560660615563393,
-0.05304599180817604,
-0.015574736520648003,
-0.0035141773987561464,
0.04876457899808884,
-0.006254684180021286,
0.05172833427786827,
-0.013729185797274113,
0.028211526572704315,
0.0366998016834259,
-0.021850645542144775,
-0.07130461931228638,
0.012356087565422058,
-0.021415283903479576,
-0.018044255673885345,
-0.02009664475917816,
-0.02887098491191864,
0.006294610910117626,
-0.026426194235682487,
-0.05142056569457054,
-0.001050537102855742,
0.002723485231399536,
-0.03980399668216705,
0.005831862334161997,
-0.03247526288032532,
-0.05128449201583862,
-0.01001956406980753,
0.03297807276248932,
0.014154968783259392,
-0.027461346238851547,
0.044032324105501175,
0.05173638463020325,
-0.005095489323139191,
-0.016797419637441635,
-0.041513293981552124,
0.0455661341547966,
-0.04096625745296478,
0.010551122948527336,
0.006336404476314783,
0.0010473023867234588,
-0.06062330678105354,
0.020612945780158043,
-0.0005000284290872514,
0.004011496435850859,
-0.02413567528128624,
0.032055530697107315,
-0.015444955788552761,
-0.06115969642996788,
-0.026131292805075645,
0.0053325314074754715,
0.0004745227633975446,
0.014927258715033531,
0.03550541400909424,
0.020784109830856323,
0.00971653126180172,
-0.02897677756845951,
0.0601920560002327,
0.029494108632206917,
0.0298537015914917,
0.0268107857555151,
-0.030361872166395187,
0.0057843332178890705,
-0.023533262312412262,
-0.009158671833574772,
0.018468843773007393,
0.0006035342230461538,
-0.02250540815293789,
-0.015280693769454956,
0.041766926646232605,
0.014745443128049374,
0.005617722403258085,
0.028261050581932068,
-0.025730429217219353,
-0.016130918636918068,
-0.0000829340351629071,
-0.04638265073299408,
0.003340197494253516,
0.03735017776489258,
0.015872342512011528,
0.02759602852165699,
-0.0017194525571539998,
-0.06765986233949661,
-0.03112059459090233,
0.0398099385201931,
-0.013806942850351334,
-0.01922653056681156,
0.02564547397196293,
-0.040652863681316376,
-0.012533680535852909,
0.028197336941957474,
0.015973176807165146,
-0.0014355999883264303,
-0.07549121975898743,
0.000951794849243015,
-0.00001961970338015817,
-0.009018250741064548,
-0.01838010363280773,
0.01637604646384716,
-0.013207395561039448,
-0.011874772608280182,
-0.01393034029752016,
0.007786364294588566,
-0.02097630314528942,
0.021603725850582123,
0.023558838292956352,
0.026134738698601723,
0.03300807997584343,
0.02851957082748413,
-0.027062952518463135,
0.004055888392031193,
-0.06709570437669754,
-0.059854812920093536,
0.0030197747983038425,
0.007755128666758537,
0.007340156938880682,
0.001897679758258164,
-0.010246994905173779,
-0.02524130418896675,
-0.0014200203586369753,
-0.015242639929056168,
-0.005289186257869005,
0.019212370738387108,
-0.008556192740797997,
0.034978196024894714,
0.05485677719116211,
-0.002794157713651657,
0.029931092634797096,
0.04458114504814148,
-0.0360933281481266,
-0.0126763004809618,
-0.009955190122127533,
0.025068623945116997,
0.005692056380212307,
-0.039661385118961334,
-0.04929918423295021,
0.0010821700561791658,
0.0067686960101127625,
0.04333573207259178,
-0.026470929384231567,
0.058337852358818054,
-0.03427845612168312,
-0.07236024737358093,
-0.012839785777032375,
0.033340223133563995,
-0.0031276571098715067,
-0.01802624575793743,
-0.008203204721212387,
0.006820772774517536,
0.03883473202586174,
-0.052685439586639404,
-0.004977023229002953,
0.016403241083025932,
0.031809139996767044,
0.032999198883771896,
0.005379650741815567,
-0.002966226078569889,
-0.031036226078867912,
-0.02964962273836136,
0.01675516553223133,
-0.06712807714939117,
0.048881638795137405,
0.00689738430082798,
-0.007867313921451569,
0.007925397716462612,
-0.06907787173986435,
-0.0612766332924366,
0.042186807841062546,
0.01985291950404644,
-0.0019675882067531347,
-0.01899767853319645,
0.024573659524321556,
0.011577421799302101,
-0.0013751606456935406,
-0.06960748881101608,
-0.056090906262397766,
0.020418893545866013,
0.005222651641815901,
0.023683756589889526,
-0.038963641971349716,
-0.016508808359503746,
-0.016875825822353363,
-0.06336409598588943,
0.05554095655679703,
-0.003171419259160757,
-0.027087727561593056,
-0.017546987161040306,
0.015779517590999603,
-0.015527392737567425,
0.054695408791303635,
-0.015414049848914146,
0.02151881717145443,
-0.013498324900865555,
-0.018100854009389877,
-0.0036524715833365917,
-0.0025228173471987247,
0.04376707598567009,
-0.0034153887536376715,
0.019551392644643784,
0.014793546870350838,
-0.0038323188200592995,
0.06483780592679977,
-0.051335014402866364,
0.043078891932964325,
0.045484766364097595,
0.02645011991262436,
-0.0013454090803861618,
-0.009594498202204704,
0.01553015410900116,
-0.0038104113191366196,
0.0009212333243340254,
-0.005136015824973583,
-0.010155406780540943,
-0.04128111153841019,
-0.05864576995372772,
0.02169099636375904,
0.002020733430981636,
-0.009629549458622932,
0.009291927330195904,
0.06439150124788284,
-0.017028285190463066,
-0.04637286439538002,
0.003609936684370041,
-0.019172048196196556,
0.035582251846790314,
0.029383445158600807,
0.013837030157446861,
0.014919028617441654,
0.030210383236408234,
-0.0019969071727246046,
-0.04344829171895981,
-0.01776699721813202,
0.027753710746765137,
0.05369948595762253,
-0.025344571098685265,
0.048955559730529785,
-0.013393688015639782,
0.018514065071940422,
0.00952962227165699,
0.0070235226303339005,
-0.017796285450458527,
-0.019248755648732185,
-0.02148272655904293,
0.032644711434841156,
-0.02945544570684433,
-0.007107332814484835,
0.028851481154561043,
0.005719013977795839,
0.0210387222468853,
-0.010314461775124073,
0.03224530816078186,
-0.002297224709764123,
0.01939449831843376,
0.01886577531695366,
-0.0023373544681817293,
0.04661506414413452,
-0.03331417962908745,
0.025614311918616295,
-0.03319692984223366,
-0.004625274799764156,
0.02092038467526436,
0.010829327628016472,
0.009137062355875969,
-0.04018114134669304,
0.01504504680633545,
-0.03438550606369972,
0.038561880588531494,
-0.0015337088843807578,
-0.0010523966047912836,
0.01192789152264595,
0.040696438401937485,
0.03574361652135849,
-0.0014759551268070936,
0.029075592756271362,
0.0023391444701701403,
-0.019095027819275856,
-0.04563302546739578,
-0.04766710475087166,
-0.0067205349914729595,
-0.017046473920345306,
-0.027794890105724335,
-0.04153279587626457,
0.012501604855060577,
-0.001485626446083188,
0.01516178622841835,
0.020397549495100975,
-0.025966458022594452,
0.005086742807179689,
0.054083701223134995,
-0.0029710358940064907,
-0.0031880298629403114,
-0.00911424309015274,
0.026911837980151176,
0.13640791177749634,
0.03360448405146599,
0.0047674765810370445,
-0.07037373632192612,
0.0021646274253726006,
-0.006378620862960815,
-0.014126121997833252,
-0.017802251502871513,
0.05221585929393768,
0.01943129114806652,
0.0293913371860981,
0.04998568072915077,
0.05217989161610603,
0.017562029883265495,
-0.012002432718873024,
0.04536444693803787,
-0.04830591008067131,
-0.030934184789657593,
0.008038513362407684,
0.019979149103164673,
-0.035760268568992615,
0.010006790049374104,
-0.019855327904224396,
0.018560262396931648,
-0.046942275017499924,
0.003951468039304018,
0.008732062764465809,
-0.046572476625442505,
0.0032733562402427197,
0.0043617370538413525,
-0.038742125034332275,
0.016957763582468033,
0.003283298807218671,
-0.01613524556159973,
-0.03324536979198456,
0.0021521097514778376,
-0.03058321215212345,
-0.01380741223692894,
0.04050033539533615,
0.03558269515633583,
0.011610331945121288,
-0.003405339550226927,
0.010707084089517593,
0.01449665892869234,
-0.022891707718372345,
-0.0392487496137619,
-0.02233400009572506,
0.02226049266755581,
-0.007459665648639202,
0.0029677352868020535,
0.008459675125777721,
0.021458368748426437,
0.0025518315378576517,
-0.03819408640265465,
-0.044550735503435135,
0.006529542151838541,
-0.00924704410135746,
-0.03896360844373703,
-0.06342552602291107,
0.0010749123757705092,
0.03825337812304497,
0.014162207953631878,
-0.0030493014492094517,
-0.033951908349990845,
0.005513085518032312,
-0.014699249528348446,
-0.0013711870415136218,
0.09485553205013275,
-0.028952956199645996,
-0.04048590734601021,
-0.025368690490722656,
-0.013003979809582233,
-0.05826215073466301,
-0.00804117787629366,
0.012008050456643105,
0.01960097625851631,
-0.013933458365499973,
0.03269677236676216,
-0.007629169151186943,
0.012355765327811241,
-0.02690613642334938,
0.007689434569329023,
0.020554400980472565,
0.023069432005286217,
0.03385034576058388,
-0.01817171461880207,
-0.004880707245320082,
0.05052283778786659,
-0.03169918805360794,
-0.030851194635033607,
0.017910683527588844,
0.031278882175683975,
-0.0013804897898808122,
-0.06481105834245682,
-0.038755279034376144,
0.002989456756040454,
-0.04066944122314453,
0.004591670352965593,
0.010657492093741894,
0.021451566368341446,
0.035362593829631805,
0.013408361934125423,
-0.026384549215435982,
0.048675332218408585,
-0.030361779034137726,
0.007177860010415316,
0.035318709909915924,
-0.04312952607870102,
0.004759208299219608,
0.010828668251633644,
0.015922095626592636,
-0.07267507165670395,
-0.024592755362391472,
-0.030000926926732063,
0.012980394065380096,
-0.05898065119981766,
-0.006257582921534777,
0.011975117959082127,
0.01723937876522541,
-0.016531920060515404,
-0.0011234311386942863,
-0.03327776864171028,
-0.006952970754355192,
-0.05600921809673309,
0.03233196958899498,
-0.015433433465659618,
0.01306363195180893,
-0.03494242951273918,
0.03802575543522835,
-0.02245897427201271,
-0.005431232042610645,
-0.016814282163977623,
0.0013639191165566444,
-0.007432411424815655,
-0.0020053803455084562,
0.03933433070778847,
0.007022863253951073,
0.04007566347718239,
-0.008307446725666523,
0.013473764061927795,
-0.0032185271847993135,
-0.014491226524114609,
-0.07441961020231247,
-0.008133385330438614,
0.019602784886956215,
-0.008872613310813904,
-0.0238982941955328,
0.014464851468801498,
-0.0053170835599303246,
0.07590512931346893,
0.009478340856730938,
0.001735531142912805,
-0.008850515820086002,
0.009824448265135288,
0.013012689538300037,
-0.02673785760998726,
0.021853789687156677,
-0.04104149714112282,
0.008195691742002964,
0.0045897457748651505,
0.019422302022576332,
0.0013941256329417229,
-0.03262240067124367,
-0.0019383886829018593,
-0.04874395579099655,
0.009415500797331333,
0.0012770058820024133,
0.012462636455893517,
0.010541286319494247,
0.06665179878473282,
-0.013212024234235287,
0.005341817624866962,
0.011244861409068108,
-0.007182594388723373,
-0.11472304165363312,
0.013685034587979317,
0.03584633022546768,
-0.024869143962860107,
0.04665748029947281,
-0.07202867418527603,
0.01916659250855446,
0.01849396526813507,
-0.04393188655376434,
-0.007829559966921806,
-0.03935570269823074,
-0.010395928286015987,
-0.049755312502384186,
0.002156446920707822,
-0.0019513191655278206,
0.09097398817539215,
0.01738266833126545,
0.014628350734710693,
0.005245892331004143,
0.010939477942883968,
-0.0008556013344787061,
0.0039436002261936665,
-0.00543122086673975,
0.010660121217370033,
0.0069555314257740974,
-0.04525177925825119,
0.06068931892514229,
-0.020835332572460175,
-0.029608968645334244,
0.026138508692383766,
-0.025167809799313545,
0.00021402905986178666,
-0.044273145496845245,
0.005363515578210354,
-0.022328006103634834,
0.017944486811757088,
0.012605801224708557,
0.03167314827442169,
0.024472977966070175,
0.04084126651287079,
0.005556313320994377,
-0.022544236853718758,
0.007033754605799913,
0.013065491802990437,
-0.014042777009308338,
-0.019914517179131508,
-0.06193235516548157,
0.030931798741221428,
-0.01895665004849434,
-0.0419711172580719,
-0.012048348784446716,
0.0036077171098440886,
0.0029363816138356924,
-0.033130329102277756,
0.0064024413004517555,
-0.04556044563651085,
-0.022173644974827766,
0.008661702275276184,
-0.012300843372941017,
-0.036887578666210175,
0.03475930541753769,
-0.004515540786087513,
-0.03708277642726898,
-0.015633322298526764,
-0.01148140151053667,
-0.01223142258822918,
-0.03895985335111618,
-0.022565260529518127,
-0.003121116664260626,
-0.025160156190395355,
-0.0051514757797122,
-0.05600395053625107,
0.001994911814108491,
-0.0193631574511528,
0.04586555063724518,
0.044757045805454254,
-0.007178625091910362,
-0.021139947697520256,
-0.02053976058959961,
-0.011136765591800213,
0.04292558878660202,
0.016497734934091568,
-0.0050230734050273895,
-0.028267227113246918,
-0.03544572740793228,
0.013501334935426712,
-0.005394486244767904,
0.04558712616562843,
0.00758168613538146,
-0.005233151838183403,
0.009594201110303402,
0.019814681261777878,
-0.007404245436191559,
0.010404122993350029,
0.010586980730295181,
0.0007776258862577379,
-0.047215670347213745,
-0.01994253508746624,
-0.010730392299592495,
0.01367189735174179,
0.04321679100394249,
0.004864376503974199,
0.0021990712266415358,
0.03454657644033432,
0.008018805645406246,
-0.054364629089832306,
0.00578592624515295,
0.04194082319736481,
0.0060721770860254765,
0.08322076499462128,
-0.021438224241137505,
-0.0077742659486830235,
-0.012313890270888805,
-0.01042572595179081,
-0.06276396661996841,
0.014826521277427673,
-0.054243285208940506,
0.015328502282500267,
-0.04416385293006897,
-0.030995605513453484,
0.029483657330274582,
-0.07062993943691254,
0.021384162828326225,
0.05499519035220146,
-0.03227827697992325,
0.022512268275022507,
0.019538771361112595,
0.026726732030510902,
0.040386490523815155,
-0.029170235618948936,
0.002389513421803713,
0.043458353728055954,
-0.014976506121456623,
0.011460033245384693,
0.023243028670549393,
0.021066635847091675,
0.02564164809882641,
0.017928622663021088,
0.037437811493873596,
0.01227400079369545,
0.03938010707497597,
0.03611692413687706,
0.03519314154982567,
0.005119896959513426,
-0.014740043319761753,
0.005577352363616228,
-0.0036807511933147907,
-0.014776618219912052,
0.015571272931993008,
-0.007864653132855892,
0.09540963172912598,
-0.014702145010232925,
0.04874743893742561,
-0.025688348338007927,
-0.00047803728375583887,
-0.04833564907312393,
-0.012431876733899117,
0.04174237698316574,
0.06209690496325493,
0.005732361692935228,
-0.029552090913057327,
0.012238498777151108,
-0.006391101982444525,
-0.005502127110958099,
-0.004275903105735779,
0.03903255984187126,
-0.01594773307442665,
0.012896315194666386,
-0.016712389886379242,
-0.03125562518835068,
-0.04820422828197479,
-0.0016826034989207983,
0.08581768721342087,
0.04043923318386078,
-0.0032054607290774584,
0.05543078854680061,
-0.016267167404294014,
0.006644547451287508,
0.08619996160268784,
-0.08742974698543549,
-0.011266457848250866,
-0.011543499305844307,
0.02950914576649666,
-0.020436281338334084,
0.013941768556833267
] |
<p>I have an idea of supersymmetry in quantum mechanics, can you suggest a book on "supersymmetry in quantum field theory", which has sufficient mathematical rigour like "Peskin and Schroeder" </p>
| 467 |
[
-0.01046004705131054,
-0.02812095731496811,
0.013720961287617683,
-0.02697424590587616,
0.016460033133625984,
0.005735591985285282,
0.005609496030956507,
-0.04535851255059242,
0.0001467074907850474,
-0.013658718205988407,
0.018690841272473335,
0.0008274252177216113,
0.05272332578897476,
0.006955779157578945,
0.00871532503515482,
0.0019353587413206697,
-0.0013353360118344426,
-0.03666996955871582,
-0.03920422121882439,
0.01540602371096611,
0.01216001808643341,
0.059717725962400436,
-0.0141054792329669,
-0.0018499871948733926,
-0.006705963984131813,
0.036646243184804916,
0.000744326738640666,
0.03189459070563316,
0.002837365260347724,
0.07386559247970581,
-0.021954461932182312,
-0.008926568552851677,
0.009407199919223785,
0.03132385015487671,
0.011927354149520397,
-0.007081317249685526,
0.002890694886445999,
-0.034685369580984116,
-0.002626012312248349,
-0.016106119379401207,
-0.03391117975115776,
-0.0348692312836647,
-0.02058420702815056,
0.03486676514148712,
-0.0018150861142203212,
0.01718786172568798,
-0.02572549693286419,
-0.027001215144991875,
0.05014360696077347,
-0.07295453548431396,
0.0867772176861763,
0.0389503575861454,
0.03540647029876709,
0.017802752554416656,
0.024392766878008842,
0.00446589570492506,
0.05071248859167099,
0.07701603323221207,
0.014275070279836655,
-0.05495675653219223,
-0.044527970254421234,
-0.060093801468610764,
0.015223111025989056,
-0.04310770705342293,
-0.053730640560388565,
0.023524176329374313,
0.007189313881099224,
-0.028092602267861366,
0.021554971113801003,
0.006970577407628298,
-0.02734392322599888,
0.012558190152049065,
0.041809458285570145,
-0.02859175018966198,
-0.0076315379701554775,
-0.019841913133859634,
-0.004804909694939852,
-0.006599087733775377,
0.033657632768154144,
0.009069468826055527,
-0.004552747588604689,
0.02117120660841465,
0.013654490001499653,
0.0406663604080677,
0.006908860988914967,
-0.019558487460017204,
0.08310936391353607,
0.0012336901854723692,
-0.02715497463941574,
0.019737940281629562,
-0.03632083162665367,
-0.010047291405498981,
0.027130283415317535,
-0.021478967741131783,
-0.04545065760612488,
0.031349338591098785,
0.007440987043082714,
0.07306666672229767,
0.013650772161781788,
-0.015885984525084496,
0.004653180483728647,
-0.028280114755034447,
-0.009716540575027466,
0.06698188185691833,
0.019688328728079796,
-0.02398376539349556,
-0.0258331336081028,
0.03542022407054901,
-0.024338407441973686,
-0.00406982284039259,
-0.01736965775489807,
0.0038353793788701296,
-0.01487202849239111,
0.00003562432175385766,
0.00018038401321973652,
-0.018541887402534485,
0.007816445082426071,
-0.026268362998962402,
0.0564778707921505,
0.09973734617233276,
0.05661748722195625,
-0.02830532006919384,
0.022731680423021317,
-0.03280102461576462,
-0.06387974321842194,
0.007431062404066324,
0.05140513554215431,
-0.005799491889774799,
-0.044812921434640884,
0.023313114419579506,
0.031070716679096222,
-0.010584418661892414,
0.013899845071136951,
-0.03418438881635666,
0.02514183335006237,
-0.026763150468468666,
-0.07231118530035019,
-0.06419762223958969,
0.044195834547281265,
-0.04532494768500328,
0.002850471530109644,
-0.015913065522909164,
-0.0012529962696135044,
0.03398871794342995,
0.08839041739702225,
0.00596935860812664,
0.005306310951709747,
-0.0038182451389729977,
0.05060805380344391,
-0.01365609373897314,
0.00256745726801455,
-0.026898110285401344,
0.0067782471887767315,
-0.021215809509158134,
0.003118059830740094,
-0.06755675375461578,
0.010229949839413166,
0.019740013405680656,
0.01623709499835968,
-0.011433458887040615,
0.07343243807554245,
-0.02806907519698143,
0.01571757160127163,
0.007910232990980148,
-0.010731210932135582,
-0.013525551185011864,
0.049632616341114044,
0.013302000239491463,
-0.002817782573401928,
0.021347839385271072,
-0.019282128661870956,
0.03485832363367081,
0.009403037838637829,
0.020411934703588486,
0.0004265103198122233,
-0.040033008903265,
-0.0186981949955225,
0.02751268446445465,
0.013184883631765842,
-0.0017667505890130997,
0.00029419586644507945,
-0.020550161600112915,
-0.0016165152192115784,
0.05579763278365135,
-0.019379649311304092,
0.01496758870780468,
-0.008485628291964531,
0.02155751921236515,
0.020199595019221306,
-0.05743290111422539,
-0.03551686555147171,
-0.03781574219465256,
0.01042641419917345,
0.008615910075604916,
0.0027935991529375315,
0.05695246532559395,
0.00020692392718046904,
0.01617901585996151,
-0.05269293114542961,
-0.051355842500925064,
0.005862409248948097,
0.03598807379603386,
0.014034968800842762,
0.010540441609919071,
0.023325232788920403,
0.028047112748026848,
0.02066628448665142,
-0.002126627368852496,
0.043050773441791534,
-0.026854699477553368,
-0.04710774123668671,
0.019874075427651405,
-0.0001453698641853407,
0.021700022742152214,
-0.02748485468327999,
0.008572176098823547,
0.025690525770187378,
-0.011254827491939068,
0.0019059807527810335,
0.033423494547605515,
-0.021723119542002678,
0.027155527845025063,
0.026998750865459442,
0.04209299385547638,
-0.005109529010951519,
0.015844902023673058,
-0.015360881574451923,
0.011254099197685719,
-0.021405711770057678,
-0.032986026257276535,
-0.022977758198976517,
0.01833133026957512,
0.030132686719298363,
0.04923604428768158,
-0.028169797733426094,
0.015580655075609684,
0.021492423489689827,
0.027841877192258835,
0.04766283929347992,
0.015112427063286304,
-0.036377839744091034,
-0.04680905491113663,
0.005215936806052923,
-0.010356131941080093,
0.00818549282848835,
0.012925933115184307,
0.0067663597874343395,
0.013619504868984222,
-0.0023643423337489367,
-0.005927294492721558,
-0.05965089052915573,
0.01804111897945404,
-0.022385861724615097,
0.011459610424935818,
0.04679177328944206,
-0.04538733512163162,
0.013670268468558788,
-0.04189108684659004,
0.03060752898454666,
0.008971176110208035,
-0.023985369130969048,
0.017426935955882072,
-0.027781343087553978,
-0.02403247356414795,
0.03234165906906128,
-0.007181857712566853,
-0.02719131112098694,
-0.024400874972343445,
0.017003800719976425,
-0.035425081849098206,
-0.014086373150348663,
0.0056546274572610855,
0.0023133570794016123,
-0.014815795235335827,
0.0005669947131536901,
0.017169419676065445,
-0.012013891711831093,
0.040531646460294724,
-0.012978504411876202,
-0.03901587799191475,
0.014656322076916695,
-0.02655429020524025,
0.05242704972624779,
0.018895216286182404,
-0.06022367253899574,
0.02192321978509426,
-0.06974766403436661,
-0.049818139523267746,
0.05401429161429405,
-0.020110391080379486,
0.02156950533390045,
-0.009802074171602726,
0.0021867863833904266,
-0.03774390369653702,
-0.020276732742786407,
-0.020017199218273163,
0.007738248445093632,
-0.02129063382744789,
-0.01067245751619339,
0.029270360246300697,
-0.017943568527698517,
-0.030796710401773453,
-0.0032097329385578632,
-0.012403224594891071,
-0.0644998848438263,
-0.025662174448370934,
0.03224031999707222,
0.007687085773795843,
-0.04650506749749184,
0.015248022973537445,
0.019187618046998978,
-0.05195922031998634,
0.013285741209983826,
-0.03212622553110123,
-0.039869941771030426,
0.02113325521349907,
0.0198106337338686,
0.03978852182626724,
-0.011070002801716328,
-0.0488501600921154,
0.10055220872163773,
0.022550469264388084,
-0.0365213081240654,
-0.007994845509529114,
0.006269191391766071,
-0.008154581300914288,
-0.010331999510526657,
0.0035945079289376736,
0.010296306572854519,
-0.012972941622138023,
0.03325381875038147,
0.020679960027337074,
0.010637839324772358,
0.033279914408922195,
0.018987921997904778,
-0.06187942996621132,
-0.016437938436865807,
-0.024169649928808212,
0.029464256018400192,
0.005340930540114641,
-0.010281204245984554,
-0.04756470024585724,
-0.011382002383470535,
-0.013451173901557922,
0.013915837742388248,
-0.0018641508650034666,
-0.02798543870449066,
0.04952213540673256,
0.009254684671759605,
0.004731074441224337,
-0.023066775873303413,
0.05893142521381378,
0.0019860342144966125,
-0.03498438373208046,
0.015453485772013664,
0.026658829301595688,
-0.00569356931373477,
-0.013862930238246918,
0.012496701441705227,
0.02420647256076336,
0.03733360767364502,
-0.039803653955459595,
-0.035076986998319626,
0.0007532667950727046,
-0.009249009191989899,
-0.005753174889832735,
-0.037982311099767685,
-0.05021815747022629,
0.05907168239355087,
0.045808516442775726,
-0.004219740629196167,
-0.015374199487268925,
-0.03971392661333084,
0.0007674831431359053,
-0.06206151470541954,
0.005144644994288683,
0.01563577726483345,
0.04824033007025719,
0.028198080137372017,
0.030795777216553688,
0.015599855221807957,
0.024079173803329468,
0.019955532625317574,
-0.0017236830899491906,
-0.08172812312841415,
0.013190526515245438,
-0.04262193664908409,
0.007188491057604551,
-0.0073671103455126286,
0.015437250956892967,
-0.012726003304123878,
-0.0074419304728507996,
-0.064426489174366,
-0.04840090870857239,
-0.006717754527926445,
-0.06292688101530075,
0.013838009908795357,
-0.04515020176768303,
-0.03448969125747681,
-0.020251434296369553,
0.019732192158699036,
0.015642628073692322,
-0.0479627288877964,
-0.023764528334140778,
0.03432943671941757,
-0.06591982394456863,
-0.01362350583076477,
-0.025236625224351883,
0.04726089909672737,
0.007294143084436655,
0.033863332122564316,
0.05265290290117264,
0.03506932035088539,
-0.058568403124809265,
0.013993533328175545,
0.0009128577657975256,
0.04061649739742279,
-0.0037623760290443897,
-0.007363175041973591,
0.012728295288980007,
-0.04798946902155876,
-0.012785350903868675,
0.005788399372249842,
0.06256606429815292,
0.024571871384978294,
-0.01906740479171276,
0.05472078546881676,
0.0005690464749932289,
-0.06132291257381439,
0.021689945831894875,
0.05508812144398689,
-0.008506844751536846,
-0.039335232228040695,
-0.011658204719424248,
-0.0029760932084172964,
-0.023140303790569305,
-0.005191247444599867,
-0.004122157581150532,
-0.026614444330334663,
-0.039268266409635544,
0.012220224365592003,
0.018419519066810608,
0.010371089912950993,
-0.05365808308124542,
-0.01369077991694212,
0.00866564642637968,
-0.007187188137322664,
0.009225429967045784,
-0.02287904918193817,
0.0019040126353502274,
0.021341266110539436,
0.04812026396393776,
0.010235248133540154,
-0.01264817826449871,
-0.037442442029714584,
-0.001722615910694003,
0.04537514969706535,
0.01761362887918949,
0.006599717307835817,
0.017309710383415222,
-0.025336923077702522,
-0.044074803590774536,
0.07893292605876923,
-0.015483551658689976,
0.008644547313451767,
-0.0046397605910897255,
-0.030848030000925064,
0.002568464959040284,
0.011480370536446571,
-0.007720977533608675,
0.0523955263197422,
0.026202058419585228,
0.010901710949838161,
-0.028392814099788666,
0.012241133488714695,
-0.03263726085424423,
0.03344234079122543,
0.03117607720196247,
0.0684485137462616,
0.04971686750650406,
0.014877069741487503,
-0.007960430346429348,
0.040408726781606674,
-0.04016221687197685,
-0.07884819805622101,
0.013577260076999664,
0.012170370668172836,
-0.03063405491411686,
0.0006732954643666744,
-0.03331853076815605,
-0.05067358911037445,
-0.011468841694295406,
-0.0008426656713709235,
-0.01117640733718872,
-0.01784844882786274,
-0.04911988601088524,
0.03389256075024605,
0.020233318209648132,
-0.0013570378068834543,
0.03505607321858406,
0.0417187325656414,
-0.02284899167716503,
-0.018069878220558167,
-0.010981431230902672,
0.032557226717472076,
0.0004711739020422101,
0.008948374539613724,
-0.06003827974200249,
-0.011252228170633316,
-0.07254216820001602,
0.06303104013204575,
-0.04382075369358063,
-0.0061548976227641106,
0.0008738109027035534,
-0.013887548819184303,
-0.015927914530038834,
0.008406436070799828,
-0.013144057244062424,
-0.014722336083650589,
0.012649161741137505,
0.01580275408923626,
0.03350447863340378,
-0.03181903809309006,
0.020662738010287285,
0.0022284258157014847,
-0.010410417802631855,
0.013855618424713612,
-0.017131516709923744,
0.027797652408480644,
-0.05795007944107056,
-0.05619093030691147,
0.0005258687306195498,
-0.05568820983171463,
0.051525384187698364,
-0.016904465854167938,
-0.023060772567987442,
0.026107825338840485,
-0.04028329998254776,
-0.04582368955016136,
0.03831913322210312,
-0.0039586215279996395,
-0.0015786545118317008,
-0.05229605361819267,
-0.012325586751103401,
0.02717125415802002,
0.0012021366273984313,
-0.06237095594406128,
-0.04317384213209152,
0.01801377162337303,
-0.030802834779024124,
-0.0053280130960047245,
-0.03244723007082939,
0.06119385361671448,
-0.04184577241539955,
-0.014351778663694859,
0.005532663781195879,
0.04865988716483116,
-0.032694362103939056,
0.004951652605086565,
0.007771559990942478,
-0.012030663900077343,
0.02408520318567753,
-0.004203553311526775,
-0.017542414367198944,
0.0013424224453046918,
0.016315264627337456,
-0.0011077868985012174,
0.0007920286152511835,
0.04665166139602661,
0.005838718730956316,
-0.02639652229845524,
-0.0176177266985178,
-0.01257340144366026,
0.029571861028671265,
-0.035201478749513626,
0.019726216793060303,
0.03786739334464073,
0.05211964249610901,
0.025252781808376312,
-0.03124437853693962,
-0.0016075102612376213,
-0.004822130780667067,
0.016933772712945938,
-0.010037744417786598,
0.016133040189743042,
-0.0025829924270510674,
-0.026858272030949593,
0.02738102339208126,
0.012789437547326088,
0.0017632129602134228,
0.0067430222406983376,
0.052956271916627884,
0.005309971049427986,
-0.004256239160895348,
0.028548821806907654,
-0.008528953418135643,
-0.04349841549992561,
0.00153048534411937,
0.020473793148994446,
0.019167447462677956,
0.016717683523893356,
0.001377645879983902,
-0.051093075424432755,
-0.004039071034640074,
0.0038400166667997837,
0.04280920699238777,
-0.012759190052747726,
0.03166038915514946,
0.03180602937936783,
0.0008669567760080099,
-0.006081488449126482,
-0.011257853358983994,
-0.019279638305306435,
0.021073488518595695,
0.007158754393458366,
0.024155734106898308,
-0.06104430556297302,
0.030934389680624008,
0.03788459300994873,
0.05284905061125755,
0.0010792077518999577,
0.061992451548576355,
0.016114352270960808,
0.04002023860812187,
0.059944573789834976,
-0.034445565193891525,
-0.056699033826589584,
0.047757163643836975,
-0.028271878138184547,
0.048493072390556335,
0.002869600895792246,
-0.009792591445147991,
0.010861290618777275,
0.006870920304208994,
0.033148862421512604,
0.017071252688765526,
-0.023523403331637383,
-0.056934233754873276,
0.0318266823887825,
0.011186094023287296,
0.02604062668979168,
0.011222545988857746,
0.0655437707901001,
0.017173459753394127,
-0.004320716951042414,
0.0008163932361640036,
0.018240299075841904,
-0.060105714946985245,
-0.036223094910383224,
-0.022886689752340317,
-0.06820911914110184,
0.027962688356637955,
-0.003380107693374157,
-0.01452984381467104,
0.01281691063195467,
-0.02677484042942524,
0.02648528665304184,
-0.0017859138315543532,
0.017480945214629173,
-0.011078345589339733,
0.04679631069302559,
-0.02189074084162712,
0.01894897222518921,
0.006417241878807545,
0.008506515994668007,
0.1095857247710228,
0.04445352777838707,
0.012850244529545307,
-0.0973430648446083,
0.060677289962768555,
0.0004892499418929219,
-0.010271667502820492,
-0.0504273921251297,
0.03414047881960869,
-0.012258177623152733,
-0.01157174352556467,
-0.02396172098815441,
0.09089112281799316,
-0.00944390706717968,
-0.01178742479532957,
0.06739906966686249,
-0.04070015251636505,
-0.059522468596696854,
-0.013579878024756908,
0.0018592863343656063,
-0.0006518044974654913,
-0.0022648179437965155,
-0.036098092794418335,
0.042115289717912674,
-0.03601207584142685,
0.011865326203405857,
-0.029536694288253784,
-0.03130311518907547,
0.02905932627618313,
0.008587310090661049,
-0.0015978377778083086,
-0.015410457737743855,
-0.0041062734089791775,
-0.009173289872705936,
-0.045501355081796646,
0.007853219285607338,
0.03798665106296539,
-0.006175572052598,
0.05944490060210228,
0.011653094552457333,
0.03304213657975197,
0.005917408503592014,
0.004483684431761503,
0.024380745366215706,
-0.016240764409303665,
-0.002439109841361642,
-0.0457456037402153,
0.08199595659971237,
-0.025994811207056046,
0.005007624626159668,
0.03522960841655731,
-0.003356872359290719,
0.026625117287039757,
-0.031713347882032394,
-0.025965670123696327,
0.0006627683760598302,
0.03325105458498001,
-0.054139990359544754,
0.01653238944709301,
-0.021019233390688896,
0.056374479085206985,
-0.020219480618834496,
0.009167240001261234,
-0.008542146533727646,
-0.041281767189502716,
0.005620045121759176,
0.005579625256359577,
0.0059778266586363316,
-0.01480218954384327,
0.002426896244287491,
-0.010869734920561314,
-0.006522814743220806,
-0.011720573529601097,
-0.01334890816360712,
0.03753478825092316,
-0.002302169566974044,
0.029755428433418274,
-0.017592983320355415,
-0.012436162680387497,
0.0010895458981394768,
-0.02056434191763401,
0.01430267933756113,
-0.006658997852355242,
0.01467010285705328,
0.00025428703520447016,
-0.029897555708885193,
0.08301959186792374,
0.04354751482605934,
-0.031286031007766724,
0.027575641870498657,
-0.01197680551558733,
0.00041679738205857575,
0.031043563038110733,
-0.040120866149663925,
0.008228495717048645,
-0.02862471342086792,
-0.02806372568011284,
0.014978541992604733,
-0.02092793397605419,
0.00709482142701745,
0.02436317689716816,
-0.02177317440509796,
0.008794650435447693,
0.0350283645093441,
0.012803864665329456,
-0.01461116038262844,
0.008818808943033218,
-0.048121921718120575,
0.012644927017390728,
0.03157059848308563,
0.04418076202273369,
-0.009137180633842945,
-0.04748502001166344,
-0.009602234698832035,
0.01770002767443657,
0.0008580854046158493,
0.041446857154369354,
-0.04172950237989426,
0.03231681138277054,
0.012477831915020943,
0.018687859177589417,
-0.02635354734957218,
-0.008426331914961338,
-0.03652834892272949,
0.016857029870152473,
0.014187455177307129,
-0.0019977944903075695,
-0.024180475622415543,
0.028608597815036774,
-0.012365676462650299,
-0.029097363352775574,
-0.01981835812330246,
0.002337415236979723,
-0.024482080712914467,
0.004471702501177788,
0.03006257861852646,
-0.01072773989289999,
0.03752274066209793,
-0.010101990774273872,
0.009149965830147266,
0.017985234037041664,
-0.07049071788787842,
-0.04521942511200905,
0.0451224260032177,
-0.020000359043478966,
0.02936813421547413,
0.02826191671192646,
-0.020924128592014313,
-0.055635981261730194,
0.013411072082817554,
-0.017751380801200867,
-0.028689676895737648,
0.015792757272720337,
-0.002617734018713236,
-0.01816934533417225,
-0.015298113226890564,
-0.02411939576268196,
0.009290880523622036,
-0.0371406190097332,
0.010237380862236023,
0.05490471050143242,
-0.0007424706709571183,
-0.0161944217979908,
0.012511718086898327,
0.02361212857067585,
0.013084561564028263,
-0.010916480794548988,
-0.013700935989618301,
0.015204044990241528,
0.029081691056489944,
-0.04769231006503105,
0.004694781731814146,
-0.0052605257369577885,
-0.0048937685787677765,
-0.08663003891706467,
0.009080487303435802,
-0.013430573046207428,
0.024735121056437492,
0.05505228415131569,
-0.08797390758991241,
0.020891284570097923,
0.009929003193974495,
-0.05635690689086914,
0.06242845207452774,
-0.02277355082333088,
-0.024976732209324837,
-0.0029816364403814077,
-0.016054373234510422,
-0.01847996935248375,
0.07650430500507355,
0.009857059456408024,
0.04063664376735687,
-0.014680218882858753,
0.015173094347119331,
0.021421782672405243,
0.003105789190158248,
-0.05335204303264618,
0.0170601774007082,
0.013257422484457493,
-0.032965876162052155,
0.04953019320964813,
-0.007478389423340559,
-0.04482923448085785,
0.024123728275299072,
-0.002445012331008911,
-0.025381533429026604,
-0.004573205020278692,
0.016993943601846695,
-0.01307316217571497,
0.04220006987452507,
0.03224174678325653,
-0.0036909019108861685,
0.02665184624493122,
0.001823694328777492,
0.03337942436337471,
0.012552364729344845,
-0.02200116589665413,
0.03531752899289131,
-0.004583229776471853,
-0.03004554472863674,
-0.0321911983191967,
0.045667655766010284,
0.0017528817988932133,
-0.04023261368274689,
-0.014545688405632973,
-0.0020975132938474417,
0.010852191597223282,
-0.017263762652873993,
0.03911927342414856,
-0.006507607642561197,
0.0022244625724852085,
-0.0025100596249103546,
0.0021130566019564867,
0.026863589882850647,
0.07217942178249359,
-0.013722993433475494,
-0.04045998677611351,
0.01901213824748993,
0.03373072296380997,
0.02854916639626026,
-0.06104828417301178,
-0.010538358241319656,
0.02217869646847248,
0.011664621531963348,
-0.02055000327527523,
-0.052697718143463135,
-0.03194335848093033,
0.02041902020573616,
0.006469523999840021,
0.028586914762854576,
-0.010684126056730747,
-0.020956920459866524,
0.022903047502040863,
-0.04243111610412598,
0.06228092685341835,
0.031994834542274475,
0.03408505395054817,
0.00123982026707381,
-0.0010188753949478269,
0.019659819081425667,
-0.02326434664428234,
0.025772305205464363,
-0.03443324938416481,
-0.05124502629041672,
0.02694910392165184,
-0.009252139367163181,
0.031073687598109245,
-0.011488201096653938,
-0.0038452562876045704,
-0.009169429540634155,
-0.040233924984931946,
-0.027051473036408424,
-0.02983449026942253,
0.0324379988014698,
0.012181257829070091,
0.019022537395358086,
0.02074333466589451,
-0.00034706329461187124,
-0.00827157311141491,
-0.04620392620563507,
0.06857392191886902,
0.024658536538481712,
0.01295367069542408,
0.060616765171289444,
-0.030809029936790466,
0.015941131860017776,
0.01667441427707672,
-0.03088335506618023,
0.0018837350653484464,
0.026569297537207603,
-0.043681468814611435,
-0.012289046309888363,
-0.005896410904824734,
-0.02528991736471653,
-0.001386243849992752,
-0.06135193258523941,
0.022319508716464043,
0.06015079468488693,
-0.04888997972011566,
-0.020120393484830856,
0.06533569097518921,
-0.000518093875143677,
0.035257745534181595,
0.03063870593905449,
-0.009604882448911667,
0.05967779457569122,
0.02687598019838333,
0.004839438013732433,
0.03428513556718826,
0.023732902482151985,
0.01665453426539898,
0.028286607936024666,
0.02333717793226242,
0.0016244843136519194,
0.03083363175392151,
0.022862685844302177,
0.022112788632512093,
-0.042942531406879425,
-0.006202949211001396,
0.02183668315410614,
-0.00574695598334074,
0.015202260576188564,
0.00669063301756978,
-0.04046115651726723,
0.07717279344797134,
-0.038333818316459656,
0.011949660256505013,
-0.011718971654772758,
0.040292877703905106,
-0.03266962990164757,
-0.010874389670789242,
0.019365178421139717,
0.07501513510942459,
-0.029503097757697105,
-0.003727081697434187,
-0.008793903514742851,
0.03138367459177971,
0.007902489975094795,
-0.07435236126184464,
0.016647247597575188,
-0.01240931823849678,
-0.02226852811872959,
-0.006076876539736986,
-0.008492388762533665,
-0.00487454142421484,
0.00864649098366499,
0.02387784980237484,
0.041163213551044464,
0.017757253721356392,
0.0037594253662973642,
0.0018814642680808902,
-0.03572932258248329,
0.03870293125510216,
-0.06680559366941452,
0.022466352209448814,
-0.0036758347414433956,
-0.03061726503074169,
-0.05271514132618904,
0.01804618164896965
] |
<p>I've been working my way through L. Baulieu's excellent paper [<em>Perturbative gauge theories</em>,
Physics Reports, Volume 129, Issue 1, December 1985, Pages 1-74]. Towards the end, he goes on to prove that renormalized Yang-Mills theories that are BRST invariant exhibit gauge independence and unitary. At the end of the proof he states: </p>
<blockquote>
<p><em>One should note that we have implicitly assumed in this demonstration the existence of the S-matrix, i.e., the applicability of LSZ reduction formula [...] the proof is only valid when all gauge bosons are massive. Whenever massless gauge bosons are present in theory, all our arguments become formal.</em></p>
</blockquote>
<p>In the case of QCD, the gluons are massless, so does the <a href="http://en.wikipedia.org/wiki/LSZ_reduction_formula" rel="nofollow">LSZ formula</a> not apply to QCD? Is there a formal argument that proves gauge-independence as he suggests? </p>
| 10,668 |
[
0.006164039019495249,
0.0167903583496809,
-0.003469756804406643,
-0.016871822997927666,
0.03189095854759216,
0.012993509881198406,
-0.034129753708839417,
0.003326897043734789,
0.02553667314350605,
-0.0757010355591774,
-0.0078020235523581505,
0.006733429152518511,
0.09082340449094772,
0.021381942555308342,
0.0029959504026919603,
0.006540227215737104,
-0.02547571435570717,
-0.007361624855548143,
0.01192247774451971,
-0.04600127413868904,
-0.0012968494556844234,
0.04343939200043678,
-0.01962410844862461,
-0.018705282360315323,
0.002571274060755968,
0.007536816410720348,
0.0032480775844305754,
0.03723502159118652,
-0.01214921846985817,
0.062375422567129135,
-0.02318532019853592,
-0.02231527864933014,
-0.007946456782519817,
-0.007138910703361034,
0.007059458177536726,
0.020594807341694832,
-0.013149254024028778,
-0.014859727583825588,
-0.007855583913624287,
-0.03063626028597355,
0.0040853628888726234,
-0.004829163663089275,
-0.014642033725976944,
0.06899852305650711,
-0.0169511828571558,
0.042852167040109634,
-0.014541020616889,
0.009176719933748245,
0.06711900234222412,
-0.06857594102621078,
0.04761497303843498,
0.03691903501749039,
0.0604311004281044,
0.036309365183115005,
-0.013363217003643513,
-0.029943613335490227,
0.042208220809698105,
0.04414346069097519,
-0.0009823322761803865,
-0.026097111403942108,
-0.013344930484890938,
-0.03292563930153847,
0.0027983461041003466,
-0.004237007349729538,
-0.034321606159210205,
-0.016950542107224464,
0.0024476342368870974,
0.019615354016423225,
0.038434483110904694,
-0.002817685017362237,
-0.03525938466191292,
-0.01709389127790928,
0.005045225843787193,
0.03239401429891586,
0.003783971769735217,
-0.0012780807446688414,
0.005036456976085901,
0.016727598384022713,
-0.0010222552809864283,
0.015892162919044495,
-0.05273453891277313,
0.041357818990945816,
0.01643415540456772,
0.016836347058415413,
0.03463120758533478,
-0.03822952136397362,
0.05015319958329201,
-0.020297938957810402,
-0.015873130410909653,
0.05641608685255051,
-0.014033126644790173,
0.003867530729621649,
0.0692748948931694,
-0.014248467050492764,
-0.038826752454042435,
0.014911124482750893,
0.022449156269431114,
0.04384807497262955,
-0.01951833814382553,
-0.02020944468677044,
-0.0111615601927042,
-0.011347856372594833,
0.013877931982278824,
0.03268798813223839,
-0.015376325696706772,
0.010233393870294094,
-0.021439647302031517,
-0.001055974862538278,
-0.007724902592599392,
-0.046240851283073425,
-0.03150565177202225,
-0.0003711064928211272,
0.00009638079791329801,
-0.039906974881887436,
-0.012949042022228241,
-0.04709285870194435,
-0.04591216519474983,
-0.0020450232550501823,
0.04837649315595627,
0.061550114303827286,
0.08362872898578644,
-0.00575170386582613,
-0.015103061683475971,
-0.04651397839188576,
-0.06838954985141754,
0.04326481744647026,
0.01503770425915718,
-0.012590443715453148,
-0.03746514394879341,
0.026578281074762344,
0.02460850030183792,
-0.023758482187986374,
-0.0014674147823825479,
-0.0027189801912754774,
0.0408284030854702,
-0.03037399612367153,
-0.08860596269369125,
-0.05781172960996628,
0.05040612816810608,
-0.006218587048351765,
-0.0002291807613801211,
-0.0583278127014637,
-0.019266191869974136,
0.01128394529223442,
0.08953023701906204,
-0.02193857915699482,
0.018077494576573372,
-0.027630027383565903,
0.027780262753367424,
-0.019490646198391914,
-0.005844305269420147,
-0.03066028654575348,
0.01009310968220234,
-0.04241376370191574,
-0.01713549718260765,
-0.04469965398311615,
0.005369641352444887,
0.009578279219567776,
0.0027034436352550983,
-0.0016538974596187472,
0.0735437348484993,
0.0013048258842900395,
-0.010231854394078255,
0.052246905863285065,
-0.012964188121259212,
-0.03800424560904503,
0.06465999782085419,
-0.023013245314359665,
0.017414521425962448,
0.04864641651511192,
-0.021062735468149185,
-0.004615987651050091,
0.025181636214256287,
0.04052214324474335,
0.04053649306297302,
-0.007099314127117395,
-0.07058417797088623,
0.015774013474583626,
-0.012903138063848019,
-0.012350651435554028,
-0.04853789135813713,
-0.0146568538621068,
-0.018878435716032982,
0.020732367411255836,
-0.01646847277879715,
0.04657957702875137,
-0.02260277047753334,
-0.007948230020701885,
0.046626754105091095,
-0.013229033909738064,
-0.03273824229836464,
-0.04344441741704941,
0.009697712026536465,
0.029696766287088394,
0.00015959743177518249,
0.01317919697612524,
-0.006261402275413275,
-0.00004680267011281103,
-0.0070007555186748505,
-0.014847079291939735,
-0.026252765208482742,
0.03485477343201637,
-0.012251563370227814,
-0.00449477368965745,
-0.009878421202301979,
-0.011452950537204742,
0.055542878806591034,
-0.0351981520652771,
0.048611655831336975,
-0.01029191818088293,
-0.03307860344648361,
0.01902226358652115,
0.0015200574416667223,
0.007586905732750893,
-0.035542018711566925,
0.005366092082113028,
0.014174379408359528,
-0.022854207083582878,
-0.026188300922513008,
0.07777169346809387,
-0.04723011329770088,
0.03443247452378273,
0.009529147297143936,
0.008302601985633373,
-0.00271969148889184,
0.045784901827573776,
0.02183600328862667,
0.03124205209314823,
0.017445677891373634,
-0.019883621484041214,
-0.07671796530485153,
-0.001216726377606392,
0.04714071750640869,
0.036056362092494965,
-0.02907588891685009,
0.017717208713293076,
0.04876488819718361,
0.026510749012231827,
0.00027635839069262147,
0.03986945003271103,
-0.014322588220238686,
-0.03570745885372162,
-0.0003583763900678605,
0.008127070032060146,
0.007679386995732784,
-0.012859300710260868,
-0.03633010759949684,
-0.02132945880293846,
0.03254334628582001,
0.008266241289675236,
-0.021210186183452606,
0.015652846544981003,
-0.019928887486457825,
-0.008549249731004238,
0.013786712661385536,
-0.025595085695385933,
0.054043449461460114,
0.00581973884254694,
0.057316023856401443,
0.04299837350845337,
-0.00905537512153387,
0.005491212476044893,
0.0019157642964273691,
0.006918907631188631,
0.004766794387251139,
-0.028257397934794426,
-0.051019299775362015,
-0.0240480974316597,
0.006555765867233276,
-0.05435941740870476,
-0.011392218992114067,
-0.005121887661516666,
-0.01668643392622471,
0.015888584777712822,
0.0029659238643944263,
0.03464963659644127,
0.0178635586053133,
0.03666704148054123,
-0.010351036675274372,
-0.032971955835819244,
0.04150673747062683,
-0.03288634866476059,
0.03760885074734688,
0.068136066198349,
0.007534913718700409,
-0.010132788680493832,
-0.0707845687866211,
0.007381519302725792,
0.01607525162398815,
-0.008657701313495636,
-0.003903650213032961,
0.007628140039741993,
0.0006443717866204679,
-0.048425618559122086,
-0.004028054885566235,
0.01638602279126644,
0.028406895697116852,
-0.004963830579072237,
0.0009242162341251969,
0.03186459839344025,
0.0704747885465622,
-0.04014582931995392,
-0.0127950981259346,
-0.04619026929140091,
-0.026767263188958168,
-0.004575343802571297,
0.034854721277952194,
-0.020841635763645172,
-0.029335152357816696,
0.04949308559298515,
0.02157340757548809,
-0.022850144654512405,
0.002292436081916094,
-0.04366586357355118,
-0.054064661264419556,
-0.00027576813590712845,
0.0378015898168087,
0.07653883099555969,
0.03083682432770729,
-0.05645375698804855,
0.10234195739030838,
0.01987059786915779,
-0.03559766337275505,
-0.01642533764243126,
-0.018593281507492065,
-0.002976328367367387,
-0.02656756527721882,
0.02116956003010273,
0.018720190972089767,
-0.02222278341650963,
0.03225313499569893,
0.024413082748651505,
0.019544396549463272,
0.007422657683491707,
0.002325386507436633,
0.02016267739236355,
-0.006840852089226246,
0.0038217983674257994,
-0.01689818687736988,
0.0454142801463604,
0.008027471601963043,
-0.007143741939216852,
0.0051245978102087975,
0.023266451433300972,
0.03220099210739136,
0.027811763808131218,
-0.038036048412323,
0.07747015357017517,
0.001762345782481134,
0.028223341330885887,
-0.03242942690849304,
0.032529525458812714,
0.014765411615371704,
-0.03798314556479454,
0.024145806208252907,
0.002779297297820449,
0.019847322255373,
-0.027538495138287544,
-0.013766116462647915,
0.03597158193588257,
0.05220886319875717,
-0.042997460812330246,
-0.00797608308494091,
-0.025423958897590637,
-0.04290962219238281,
0.021159395575523376,
-0.016564488410949707,
0.00018094158440362662,
0.02875717543065548,
0.025777293369174004,
0.015490579418838024,
-0.014831696636974812,
-0.03056049346923828,
0.0048849922604858875,
-0.06472881138324738,
0.04279595613479614,
0.011293381452560425,
0.028055956587195396,
0.03238417208194733,
0.026919489726424217,
-0.023326218128204346,
0.019879285246133804,
-0.004862774629145861,
-0.016295507550239563,
-0.058860521763563156,
0.017932012677192688,
-0.059672627598047256,
0.02222948521375656,
0.010823345743119717,
-0.0266558974981308,
-0.005766510032117367,
-0.008523109368979931,
-0.08151847124099731,
-0.06161179766058922,
0.012721125967800617,
-0.0626910999417305,
0.0347629114985466,
-0.057936299592256546,
-0.048770394176244736,
-0.01978136971592903,
0.010302174836397171,
0.02959955297410488,
-0.04874138534069061,
-0.005362941417843103,
0.01951451599597931,
-0.050369977951049805,
-0.0002387285785516724,
-0.0023052983451634645,
0.04748759791254997,
0.0047468324191868305,
0.023415615782141685,
0.06303795427083969,
0.0618249736726284,
-0.014747153967618942,
-0.022546891123056412,
0.04909409582614899,
0.0472106896340847,
0.009991989471018314,
-0.00009468908683629707,
-0.03083944320678711,
-0.031073611229658127,
-0.013602986931800842,
0.014363707974553108,
0.05387592315673828,
0.013700165785849094,
-0.003873484442010522,
0.03511437773704529,
0.02631610631942749,
-0.01584228314459324,
0.005033735651522875,
0.04650644585490227,
0.02253972925245762,
-0.005638824310153723,
-0.0495280846953392,
0.015342913568019867,
0.025863319635391235,
-0.01400307659059763,
0.007517163176089525,
0.01222774013876915,
-0.02842833288013935,
-0.030580293387174606,
0.04650500416755676,
0.0051918127574026585,
-0.036855656653642654,
0.02163373865187168,
-0.004673331510275602,
-0.024776186794042587,
-0.0031140653882175684,
0.014557218179106712,
-0.008825869299471378,
0.06608926504850388,
0.034793976694345474,
0.0037599443458020687,
-0.016106855124235153,
-0.00704636424779892,
0.013784452341496944,
0.02979801408946514,
0.05779895931482315,
0.0036024271976202726,
-0.007193038240075111,
-0.02953047677874565,
-0.00500973965972662,
0.04750379920005798,
-0.024885358288884163,
0.021984301507472992,
0.00903292279690504,
0.0029857985209673643,
-0.006500114221125841,
-0.025676192715764046,
0.03441164270043373,
-0.006761141121387482,
-0.018611295148730278,
-0.0005075714434497058,
-0.028704622760415077,
-0.024121204391121864,
-0.03225906938314438,
0.003308997955173254,
0.014922098256647587,
0.012644368223845959,
0.03148552030324936,
0.031505241990089417,
-0.03504137694835663,
0.044962212443351746,
0.0037236458156257868,
-0.0777253732085228,
0.01754721626639366,
0.004162456840276718,
0.006856841966509819,
0.053366392850875854,
-0.01825283095240593,
-0.0553666315972805,
0.007436433341354132,
0.0287970919162035,
-0.016010481864213943,
-0.008766057901084423,
-0.04957982525229454,
0.03777378425002098,
0.05785122141242027,
-0.018545232713222504,
-0.014288531616330147,
0.023813072592020035,
0.00032791399280540645,
-0.021350575610995293,
-0.013253189623355865,
-0.0018911265069618821,
-0.025995586067438126,
0.012112257070839405,
-0.01852438412606716,
0.008110332302749157,
-0.018739454448223114,
0.02131698653101921,
-0.03848307207226753,
0.02377382107079029,
0.008867538534104824,
-0.027591556310653687,
-0.013466183096170425,
-0.014863667078316212,
0.0000334044816554524,
0.004641926381736994,
0.003972381353378296,
0.041187409311532974,
-0.020708495751023293,
-0.03386286273598671,
0.031634293496608734,
-0.020347774028778076,
-0.0018252735026180744,
0.008156071417033672,
0.01687055081129074,
0.00900869071483612,
-0.030321769416332245,
-0.014366068877279758,
0.0017737504094839096,
-0.03244321793317795,
0.03047967702150345,
-0.00039391382597386837,
-0.015781445428729057,
0.017169427126646042,
-0.014946387149393559,
-0.03378376364707947,
0.021743133664131165,
0.004412482026964426,
0.016636386513710022,
-0.01578671857714653,
0.02845662645995617,
0.01401593443006277,
0.004806536715477705,
-0.09318694472312927,
-0.04314076155424118,
-0.0037955977022647858,
-0.009445065632462502,
-0.014319518581032753,
-0.025182340294122696,
-0.03678586706519127,
-0.01024640817195177,
-0.03808742016553879,
0.01267114095389843,
0.034387778490781784,
-0.02107415534555912,
-0.025837214663624763,
-0.006769260391592979,
0.04830223321914673,
0.05696471035480499,
-0.006237746682018042,
-0.03119707480072975,
0.013185523450374603,
-0.026659581810235977,
0.024445004761219025,
-0.01633758842945099,
0.07256448268890381,
-0.0008697193115949631,
-0.010609696619212627,
-0.0208137184381485,
0.009257666766643524,
0.00799469742923975,
-0.00568446796387434,
-0.02690817601978779,
0.044547270983457565,
-0.0021418347023427486,
0.012072473764419556,
-0.023343060165643692,
0.023990673944354057,
-0.0007931078434921801,
0.04957401379942894,
0.015931544825434685,
-0.016371991485357285,
0.016992436721920967,
-0.03292074054479599,
0.06236184388399124,
-0.006448606960475445,
0.01910221576690674,
-0.0012232717126607895,
0.022946380078792572,
0.0018029871862381697,
-0.016481539234519005,
0.034689415246248245,
-0.030883295461535454,
0.013918882235884666,
0.029220344498753548,
0.03428904712200165,
-0.03441888466477394,
-0.022056467831134796,
-0.037955835461616516,
-0.04103916883468628,
-0.02606305480003357,
0.047588612884283066,
0.0657762661576271,
0.032157741487026215,
0.021379228681325912,
-0.011015153490006924,
-0.06008118391036987,
0.02133440226316452,
-0.01540076732635498,
-0.008428900502622128,
-0.019292665645480156,
-0.0010835707653313875,
0.0439055934548378,
-0.0414864644408226,
-0.01944352686405182,
0.017720090225338936,
0.07897991687059402,
-0.020696057006716728,
0.001936300308443606,
0.04724406078457832,
-0.007008780725300312,
0.03448038548231125,
0.015093386173248291,
-0.027205154299736023,
0.05003245919942856,
-0.03245776891708374,
0.03066999651491642,
0.004383718129247427,
0.04947657510638237,
0.002192372689023614,
0.017641011625528336,
0.016307953745126724,
0.018137607723474503,
-0.038090769201517105,
-0.05067313835024834,
0.04075698181986809,
-0.0062348186038434505,
-0.001214280491694808,
0.0164505522698164,
-0.013397833332419395,
0.03393769636750221,
0.008008688688278198,
-0.012161104008555412,
-0.027230413630604744,
-0.03660864010453224,
0.014514945447444916,
-0.00559283047914505,
-0.03601624444127083,
0.059342388063669205,
0.0000632426017546095,
0.002471683779731393,
-0.020544100552797318,
-0.025101149454712868,
0.006553158164024353,
0.005700468551367521,
0.031243517994880676,
-0.0132218012586236,
0.0357062965631485,
-0.004037837032228708,
0.01406150870025158,
-0.016051556915044785,
-0.008453503251075745,
0.11221855133771896,
0.04570681229233742,
0.018117500469088554,
-0.06315849721431732,
0.003882103366777301,
-0.007380785420536995,
0.014316698536276817,
-0.02519410289824009,
0.044952746480703354,
-0.014522206038236618,
-0.02942921407520771,
-0.001182829262688756,
0.09138433635234833,
0.011947328224778175,
-0.0427592508494854,
0.03534671664237976,
-0.04581701010465622,
-0.07354771345853806,
-0.0021268357522785664,
0.03243254870176315,
-0.034654855728149414,
-0.005046876613050699,
-0.017703166231513023,
-0.000686843937728554,
-0.02622848190367222,
0.0009191262070089579,
-0.021746652200818062,
-0.005221386905759573,
0.004822149872779846,
0.029083462432026863,
-0.02487734705209732,
0.0012552151456475258,
0.006389860529452562,
0.0045425002463161945,
-0.04497341066598892,
0.008088955655694008,
0.001900936826132238,
0.017330950126051903,
0.050090957432985306,
0.02891547791659832,
-0.001370426849462092,
-0.021244561299681664,
-0.010196911171078682,
0.006602645386010408,
-0.026234161108732224,
0.002880066866055131,
-0.008570424281060696,
0.054884348064661026,
-0.018665648996829987,
-0.031909797340631485,
0.018309801816940308,
-0.019059527665376663,
0.04156536981463432,
-0.06398814916610718,
0.0061856834217906,
-0.018368039280176163,
0.008553804829716682,
-0.024279683828353882,
-0.0050923507660627365,
0.001651102676987648,
0.06334760040044785,
0.0022381749004125595,
-0.019481491297483444,
0.030333535745739937,
-0.00529231783002615,
0.007354478817433119,
0.011733457446098328,
0.023278163745999336,
0.008447043597698212,
0.007548901718109846,
-0.05311732366681099,
0.014142785221338272,
-0.015008924528956413,
-0.053600989282131195,
0.02763386256992817,
0.008611071854829788,
0.04910111427307129,
-0.01196312066167593,
0.013997707515954971,
-0.034557729959487915,
-0.06883443146944046,
0.03072090446949005,
-0.01745613105595112,
-0.027831872925162315,
0.010574904270470142,
0.016097651794552803,
0.01329528447240591,
0.06541360914707184,
-0.03250333294272423,
-0.01211996003985405,
-0.017702238634228706,
0.051287852227687836,
-0.01119750551879406,
-0.061812806874513626,
-0.025522800162434578,
-0.0003850082866847515,
-0.06187371537089348,
0.013421878218650818,
0.004396684933453798,
0.013676022179424763,
0.020447254180908203,
0.05671384558081627,
-0.01080018188804388,
0.02442038618028164,
0.01595192216336727,
-0.004579708445817232,
0.004031126853078604,
-0.028202945366501808,
0.03435364365577698,
0.041401397436857224,
0.019041698426008224,
0.006952797062695026,
-0.028696458786725998,
-0.010210680775344372,
0.037150513380765915,
0.012006030417978764,
0.024576207622885704,
-0.06453993171453476,
-0.006165008991956711,
-0.002363053848966956,
0.01714503765106201,
-0.03318110853433609,
-0.011342323385179043,
-0.0037547657266259193,
0.0033950968645513058,
-0.01859125681221485,
0.0070249419659376144,
-0.009934908710420132,
0.02693217620253563,
-0.009471755474805832,
0.0001014499066513963,
0.05030015856027603,
-0.011114622466266155,
-0.039728596806526184,
-0.02871411293745041,
-0.008513339795172215,
-0.0034759691916406155,
0.03368335962295532,
-0.01347310096025467,
0.010405468754470348,
0.005191640462726355,
-0.035324279218912125,
-0.05245563015341759,
-0.004168100655078888,
-0.019446812570095062,
0.014421735890209675,
0.010470913723111153,
-0.028097236528992653,
-0.04696328938007355,
0.04181838035583496,
0.008463465608656406,
-0.02823764644563198,
-0.03237577900290489,
-0.008636705577373505,
0.014666256494820118,
-0.04746584966778755,
-0.0065092346630990505,
0.03398546949028969,
-0.0002198515139752999,
0.011714047752320766,
0.02032531425356865,
-0.058954451233148575,
0.009420821443200111,
-0.006897789426147938,
0.005270043388009071,
0.014578231610357761,
0.009549472481012344,
0.0059760515578091145,
-0.015499824658036232,
0.060062769800424576,
-0.03476164489984512,
0.007261503487825394,
-0.036977071315050125,
-0.003193025477230549,
-0.09507175534963608,
-0.014196657575666904,
0.023991510272026062,
0.031164444983005524,
0.024787800386548042,
-0.059008896350860596,
0.010351331904530525,
0.021051324903964996,
-0.09819420427083969,
-0.0064264750108122826,
-0.02786254696547985,
-0.025651317089796066,
-0.050602491945028305,
-0.01950128749012947,
-0.014493994414806366,
0.02796298637986183,
0.0661153569817543,
0.023137105628848076,
-0.00800984539091587,
0.010020632296800613,
-0.0007488770643249154,
-0.0339554026722908,
-0.046686381101608276,
0.02770944871008396,
-0.0013363847974687815,
-0.05995183065533638,
0.06238425150513649,
-0.010381141677498817,
-0.0006655562901869416,
0.007119432557374239,
0.021631766110658646,
-0.03536887466907501,
-0.030534010380506516,
-0.010913346894085407,
0.019537504762411118,
0.01232762448489666,
0.026917580515146255,
-0.002746955258771777,
0.001792198047041893,
-0.009165911003947258,
-0.011093073524534702,
0.04250028356909752,
-0.041042257100343704,
0.022412382066249847,
-0.02960306592285633,
-0.030792204663157463,
-0.03544777259230614,
0.019869746640324593,
-0.02600911259651184,
-0.04693688079714775,
-0.026075683534145355,
-0.01025108341127634,
-0.023539895191788673,
0.011602635495364666,
0.017971927300095558,
-0.05772065371274948,
0.021645760163664818,
0.07975493371486664,
0.018186120316386223,
0.0010491496650502086,
0.030829351395368576,
0.01203611958771944,
-0.01849101111292839,
-0.005594351794570684,
0.002094832481816411,
-0.012606128118932247,
-0.035856906324625015,
-0.042032964527606964,
0.001847371575422585,
0.020210780203342438,
0.030334973707795143,
-0.06462346762418747,
-0.038377296179533005,
0.017042608931660652,
0.005251808557659388,
0.05012518912553787,
-0.0308415275067091,
-0.008474067784845829,
0.013306114822626114,
-0.07237933576107025,
0.05403172969818115,
0.02406613528728485,
0.018873728811740875,
-0.025648828595876694,
-0.03288213908672333,
0.046728357672691345,
0.019937776029109955,
0.052003562450408936,
0.021063316613435745,
-0.008657804690301418,
0.018737399950623512,
0.02742042951285839,
-0.010561259463429451,
0.006405896507203579,
-0.008922994136810303,
0.0031315316446125507,
0.012882888317108154,
-0.021961890161037445,
-0.01738736405968666,
-0.00791907962411642,
0.04352889209985733,
0.06190943345427513,
0.03321756422519684,
-0.026821671053767204,
-0.024755490943789482,
-0.08457770198583603,
0.0710780918598175,
-0.007904348894953728,
0.00521119125187397,
0.058823950588703156,
0.013042882084846497,
0.03339279443025589,
0.03561112657189369,
-0.011171352118253708,
-0.04089958965778351,
0.06348586082458496,
-0.05916247516870499,
0.0016712294891476631,
-0.013530246913433075,
-0.002953869756311178,
0.013027564622461796,
-0.004718340002000332,
0.029301514849066734,
0.05278092995285988,
-0.02659568190574646,
-0.038806162774562836,
0.030506430193781853,
0.008477481082081795,
0.026049450039863586,
0.024937059730291367,
-0.02053656429052353,
0.01942879892885685,
0.003665030701085925,
0.037576545029878616,
0.032271768897771835,
0.032784417271614075,
0.023752642795443535,
-0.010711513459682465,
0.05762559175491333,
-0.03120121918618679,
-0.003302529687061906,
0.015790080651640892,
0.018415888771414757,
-0.0073226820677518845,
-0.012987755239009857,
0.04811042174696922,
-0.021736809983849525,
0.007537337485700846,
0.02859296090900898,
-0.04016964137554169,
0.086493581533432,
-0.02624799683690071,
0.02299216389656067,
-0.018556486815214157,
-0.0014830294530838728,
-0.048805754631757736,
0.04796404018998146,
0.04196219891309738,
0.04198843985795975,
-0.050865430384874344,
-0.01759873330593109,
0.015581965446472168,
-0.02321457490324974,
0.014036842621862888,
-0.004399525001645088,
0.007616450544446707,
-0.011885247193276882,
-0.038018278777599335,
0.016812369227409363,
-0.035652052611112595,
0.015965083613991737,
0.02220548503100872,
-0.01777193322777748,
0.040368031710386276,
-0.0007135167252272367,
-0.04313742369413376,
-0.028747329488396645,
-0.04376387968659401,
0.024555422365665436,
-0.036960724741220474,
0.018468361347913742,
-0.018936583772301674,
0.00801818072795868,
-0.03274662047624588,
-0.012595295906066895
] |
<p>Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave function by observation. Here is my question. If we setup the camera to record like above but NEVER EVER EVER look at the result of what was recorded. Does the wave function still collapse. If so then perhaps its the camera causing it. If not then it is truly based upon the observer.</p>
| 10,669 |
[
-0.012693880125880241,
-0.03574345260858536,
-0.00003332164487801492,
-0.026218507438898087,
0.015534440986812115,
0.025057094171643257,
-0.03377468138933182,
-0.030614512041211128,
0.0026446033734828234,
-0.030655644834041595,
0.015353092923760414,
0.02390647679567337,
0.016942372545599937,
0.01871778629720211,
0.016590576618909836,
0.026339642703533173,
-0.03670236095786095,
0.0005355070461519063,
-0.013028920628130436,
-0.03680937737226486,
-0.028040606528520584,
0.04343700408935547,
0.03193707764148712,
0.01793971285223961,
-0.04274136573076248,
-0.007319703232496977,
-0.0019472213461995125,
-0.0010564937256276608,
0.04403692111372948,
0.05713481828570366,
-0.03940547630190849,
-0.03393885865807533,
0.0010552294552326202,
0.04367835447192192,
0.015543182380497456,
-0.020014360547065735,
-0.02422373928129673,
-0.017539525404572487,
0.0022200406529009342,
-0.01203244924545288,
0.039222557097673416,
0.013330357149243355,
-0.00819665752351284,
0.057342275977134705,
-0.0329555980861187,
-0.023780135437846184,
-0.011906134895980358,
-0.006818158086389303,
0.03584660589694977,
-0.06555578857660294,
0.07262216508388519,
-0.018967872485518456,
0.05003576725721359,
0.00879510398954153,
0.02171129360795021,
-0.0033394605852663517,
0.11128553748130798,
0.048141833394765854,
-0.02920653484761715,
-0.036758530884981155,
-0.017907917499542236,
-0.018822763115167618,
0.012745768763124943,
-0.018404046073555946,
-0.07253622263669968,
0.017419124022126198,
-0.0010901622008532286,
-0.03207729756832123,
0.03682024031877518,
-0.03783852607011795,
-0.016177745535969734,
0.016996415331959724,
0.03741218522191048,
0.004278065171092749,
-0.012751246802508831,
-0.008409198373556137,
0.024136535823345184,
0.009090200997889042,
0.04006953909993172,
0.03695767745375633,
0.03319283947348595,
-0.0011620770674198866,
0.023410644382238388,
0.03784741833806038,
0.01885456219315529,
-0.04232098534703255,
0.05484182387590408,
-0.014634046703577042,
0.0018353238701820374,
0.0018667656695470214,
-0.016284096986055374,
0.01575254648923874,
-0.0038275024853646755,
-0.01704103872179985,
-0.013697200454771519,
0.021332930773496628,
-0.0010530798463150859,
0.08554298430681229,
0.026076853275299072,
-0.030789174139499664,
0.020814795047044754,
-0.007714423350989819,
-0.0057535008527338505,
0.049244653433561325,
0.0005088456673547626,
-0.04194929450750351,
-0.043236080557107925,
0.09135205298662186,
0.0074350242502987385,
-0.006603096146136522,
-0.02693471685051918,
0.017749693244695663,
0.02862321212887764,
0.030911270529031754,
0.035414308309555054,
-0.040416646748781204,
0.005232366733253002,
-0.021176086738705635,
0.08792204409837723,
0.06117875128984451,
0.02202410064637661,
-0.05408424884080887,
0.0029488252475857735,
-0.019232437014579773,
-0.04802599176764488,
0.01898045465350151,
0.027179719880223274,
-0.03144676983356476,
0.0031230654567480087,
0.021722983568906784,
0.01355172973126173,
-0.03134249523282051,
0.033361829817295074,
-0.00123534572776407,
0.043999794870615005,
0.0021773413754999638,
-0.1286882758140564,
-0.0570966973900795,
0.01764199510216713,
-0.008340028114616871,
-0.012840238399803638,
-0.06256293505430222,
-0.014550994150340557,
0.05075825750827789,
0.08676043897867203,
-0.044462233781814575,
0.005981277674436569,
0.01811797358095646,
0.032016512006521225,
-0.008808786049485207,
-0.006456442642956972,
-0.034413669258356094,
0.0019456796580925584,
-0.029127074405550957,
-0.021053774282336235,
-0.05001141130924225,
0.004480769392102957,
0.019784195348620415,
0.0025008535012602806,
-0.056735921651124954,
0.0624062642455101,
-0.021791500970721245,
-0.0051336814649403095,
0.0055585624650120735,
-0.010055923834443092,
-0.04658897593617439,
0.07228481769561768,
0.02781108394265175,
-0.007398046087473631,
0.030560489743947983,
0.010982908308506012,
0.021089984104037285,
-0.028583599254488945,
0.00904945656657219,
0.017522303387522697,
-0.017792876809835434,
-0.035283125936985016,
0.0062879533506929874,
0.0440097451210022,
-0.0006654350436292589,
-0.01926828920841217,
0.005110566504299641,
0.00712762214243412,
0.012014084495604038,
0.03597622364759445,
0.05720805749297142,
-0.019216561689972878,
-0.010451903566718102,
-0.03931339085102081,
-0.04171235114336014,
-0.003424540162086487,
-0.04014192149043083,
-0.013515223748981953,
0.019343743100762367,
-0.005009434185922146,
0.006975690368562937,
-0.005197804421186447,
0.02662607841193676,
-0.016076697036623955,
-0.040507979691028595,
-0.024048861116170883,
0.03001158870756626,
-0.020985879004001617,
0.00014925404684618115,
0.027590615674853325,
0.04085538908839226,
0.05490899085998535,
0.00944528728723526,
0.03478371351957321,
0.002859703730791807,
-0.0068921963684260845,
0.031173771247267723,
-0.010219485498964787,
0.004466915503144264,
-0.010365772061049938,
-0.00390843627974391,
0.02430790290236473,
0.0011748047545552254,
-0.018810167908668518,
0.017929375171661377,
-0.04883046820759773,
0.062120597809553146,
0.018496546894311905,
-0.007085941731929779,
-0.020587190985679626,
0.019196564331650734,
0.015359275043010712,
0.01019610557705164,
-0.01921662874519825,
-0.01446725707501173,
-0.03666786476969719,
-0.018365060910582542,
0.020552173256874084,
0.00738676218315959,
-0.054876964539289474,
0.04242265596985817,
0.0064862193539738655,
0.016774719581007957,
0.02493763156235218,
0.014130011200904846,
0.0068254922516644,
-0.0360441617667675,
-0.02217799983918667,
0.02619868889451027,
0.012211160734295845,
0.003137527732178569,
0.01910547725856304,
0.034230396151542664,
-0.0023409537971019745,
0.00910651870071888,
-0.02477954886853695,
0.014757867902517319,
-0.024461351335048676,
0.022693967446684837,
-0.012477184645831585,
-0.04015946388244629,
0.013590889051556587,
-0.03008236549794674,
0.025177061557769775,
0.008204440586268902,
0.01831934042274952,
0.0021273670718073845,
-0.06786981225013733,
-0.03549269959330559,
0.027677496895194054,
0.004804456140846014,
-0.03688712790608406,
-0.020272770896553993,
0.03184306621551514,
-0.013015411794185638,
0.005223663058131933,
-0.014204015955328941,
0.01561063900589943,
-0.022943349555134773,
0.019298356026411057,
0.06024916097521782,
-0.002338054124265909,
0.024198448285460472,
-0.05933241918683052,
-0.06370317190885544,
-0.022814851254224777,
-0.042856086045503616,
0.02188427932560444,
0.032689161598682404,
-0.056669220328330994,
0.0025010965764522552,
0.020096302032470703,
-0.036480698734521866,
0.03539494052529335,
-0.011490970849990845,
0.03313612937927246,
0.02760668843984604,
0.00034619501093402505,
-0.030854791402816772,
0.001685449038632214,
-0.013478372246026993,
-0.0071288482286036015,
-0.014754208736121655,
-0.011951650492846966,
0.05289619415998459,
0.00749689806252718,
-0.006856734398752451,
-0.00519478740170598,
-0.03675977140665054,
-0.05476301163434982,
0.004979980643838644,
-0.02023560367524624,
0.031323764473199844,
-0.06451450288295746,
0.02681872248649597,
0.0361299030482769,
-0.05956641957163811,
0.0033041692804545164,
-0.038514021784067154,
-0.05069150775671005,
0.035897884517908096,
-0.0044974894262850285,
0.00807899609208107,
-0.026537474244832993,
-0.022456806153059006,
0.05120077729225159,
0.024323418736457825,
-0.03564036637544632,
-0.04407849907875061,
-0.009430784732103348,
0.023096386343240738,
-0.02911987341940403,
-0.0250388290733099,
-0.014876020140945911,
-0.0000633111412753351,
0.05754004418849945,
0.0101685281842947,
0.008283133618533611,
0.00815504975616932,
0.038905225694179535,
-0.00018434025696478784,
-0.006064465269446373,
0.02333666756749153,
-0.00039959533023647964,
0.04142669588327408,
0.02651677466928959,
-0.031426891684532166,
0.012339254841208458,
0.0006655000615864992,
0.03035205788910389,
0.007891577668488026,
0.01258469931781292,
0.058039866387844086,
0.017947178333997726,
0.03242101892828941,
0.002427750499919057,
0.024743927642703056,
-0.020420359447598457,
0.020657826215028763,
-0.02794480323791504,
0.010567797347903252,
0.030540520325303078,
0.002780025126412511,
0.007171989418566227,
0.019539466127753258,
0.00025948171969503164,
-0.0025770196225494146,
-0.043221328407526016,
0.011245477013289928,
-0.027585415169596672,
0.05504804104566574,
0.014594093896448612,
-0.02493251860141754,
0.06492720544338226,
0.030899904668331146,
0.0497746616601944,
0.00028151425067335367,
-0.04421263933181763,
-0.003076148685067892,
-0.016714660450816154,
-0.0036996505223214626,
0.031912244856357574,
0.020628392696380615,
0.0016304183518514037,
0.047682568430900574,
0.037654779851436615,
0.033625684678554535,
0.015093820169568062,
0.0071179973892867565,
-0.07781799882650375,
0.0015537380240857601,
-0.015897054225206375,
-0.02216162346303463,
-0.015574405901134014,
0.002244218485429883,
0.02789505012333393,
-0.010238495655357838,
-0.01464938372373581,
0.004203932359814644,
-0.021163005381822586,
-0.033911339938640594,
-0.022322140634059906,
-0.03470825031399727,
-0.029843391850590706,
-0.04976320266723633,
0.04281103238463402,
0.02229686640202999,
-0.009886356070637703,
0.0016330362996086478,
0.02352127991616726,
-0.0364140123128891,
0.008014287799596786,
0.01168346032500267,
-0.012575325556099415,
-0.007209085859358311,
0.013541734777390957,
0.08275465667247772,
0.016937676817178726,
-0.029227495193481445,
0.037090059369802475,
0.047752153128385544,
0.04498164355754852,
0.011272835545241833,
-0.009968440048396587,
-0.009435530751943588,
0.02872048132121563,
-0.030854258686304092,
-0.029865102842450142,
0.03973928466439247,
0.00827710796147585,
-0.024604296311736107,
0.005513472016900778,
-0.020785890519618988,
0.0005188832292333245,
0.045225054025650024,
0.0529828816652298,
0.01354709267616272,
0.0038957332726567984,
-0.05042962729930878,
-0.0072333128191530704,
-0.01753830909729004,
-0.02246650867164135,
0.003961117006838322,
0.03408209607005119,
-0.0063153342343866825,
0.01440100371837616,
0.019298192113637924,
0.006974772550165653,
-0.01727171428501606,
0.014888174831867218,
-0.018809949979186058,
0.019941119477152824,
0.028084050863981247,
0.012054032646119595,
0.02675730176270008,
0.04592142626643181,
0.031497929245233536,
0.0116273807361722,
-0.03368264436721802,
-0.06389839947223663,
-0.003545228624716401,
0.018306218087673187,
0.021823419257998466,
-0.01806342974305153,
0.01503534335643053,
-0.05943644419312477,
-0.04744114354252815,
0.03211190178990364,
-0.035835329443216324,
0.03003009408712387,
0.008054545149207115,
0.0037335518281906843,
-0.014286682941019535,
-0.0036971073132008314,
-0.00644503440707922,
0.015134750865399837,
-0.015453464351594448,
0.02082023024559021,
-0.0006030295044183731,
-0.005233023781329393,
-0.028243592008948326,
-0.023758448660373688,
0.020756227895617485,
0.053583692759275436,
0.0018137026345357299,
0.004415846895426512,
0.0034917627926915884,
0.027184994891285896,
-0.03550788015127182,
-0.07051733136177063,
0.040428388863801956,
0.005785880144685507,
-0.02059450000524521,
0.06041200831532478,
0.004730265121906996,
-0.005775031168013811,
0.00855205301195383,
-0.0064994171261787415,
-0.020107625052332878,
0.024919241666793823,
-0.03100246749818325,
0.01395330298691988,
-0.009681873954832554,
-0.01509119477123022,
0.024651719257235527,
0.03253645449876785,
0.028113627806305885,
0.02013007178902626,
-0.004358568694442511,
0.012836434878408909,
-0.036696381866931915,
0.03474327176809311,
-0.01843561977148056,
0.014348194934427738,
-0.038334254175424576,
0.05567128211259842,
-0.011709046550095081,
0.007791206240653992,
0.0005284379585646093,
-0.022158745676279068,
0.03333192318677902,
0.02591792680323124,
0.02235693298280239,
0.04046506807208061,
-0.0404239147901535,
0.008892719633877277,
-0.0082022650167346,
-0.028453446924686432,
-0.0362759530544281,
0.003700586035847664,
-0.0036066798493266106,
0.04591219127178192,
0.014107977040112019,
0.01979307271540165,
-0.02807091362774372,
-0.022230563685297966,
0.03227007016539574,
-0.05193537473678589,
0.004796826746314764,
-0.03213231638073921,
-0.0071199857629835606,
0.024390850216150284,
-0.0812375470995903,
-0.034557659178972244,
0.0036143881734460592,
-0.018399883061647415,
0.03492656722664833,
-0.06117170676589012,
0.020064836367964745,
0.02771018072962761,
0.0009594071889296174,
-0.0987313762307167,
-0.015742996707558632,
-0.005301406607031822,
-0.01025494746863842,
0.011801141314208508,
-0.0030709365382790565,
0.01917939819395542,
-0.03994305059313774,
-0.00787330698221922,
-0.027186319231987,
0.015235105529427528,
0.0016158673679456115,
0.0005655089626088738,
0.015317044220864773,
-0.007164445705711842,
0.04652216657996178,
-0.015975305810570717,
-0.0027403351850807667,
-0.008397075347602367,
-0.030963867902755737,
-0.0239034965634346,
0.023025445640087128,
0.024037396535277367,
-0.023763181641697884,
-0.011721181683242321,
-0.02512086182832718,
-0.028776763007044792,
0.0349053293466568,
-0.046651650220155716,
0.008100132457911968,
0.0026610547211021185,
0.037559185177087784,
0.011320234276354313,
-0.02046772837638855,
0.014400484040379524,
-0.004965993110090494,
0.001914581866003573,
0.025895467028021812,
-0.007847906090319157,
-0.018315976485610008,
-0.07873335480690002,
0.02263055369257927,
0.008251174353063107,
-0.01995369978249073,
0.005620042327791452,
0.039727531373500824,
0.008202919736504555,
-0.01908637024462223,
0.00003654816100606695,
-0.019185392186045647,
-0.015463069081306458,
-0.0017516984371468425,
0.024599390104413033,
0.03433571383357048,
0.005998344160616398,
-0.03142509609460831,
-0.014634438790380955,
-0.04959888756275177,
0.011348686181008816,
0.057689789682626724,
0.02114061452448368,
0.05088458210229874,
-0.006737913005053997,
0.0072495886124670506,
0.012328074313700199,
-0.029683327302336693,
0.025637349113821983,
0.00398918567225337,
0.032520782202482224,
0.019016245380043983,
-0.031984902918338776,
0.01934005692601204,
0.019504012539982796,
0.06280817091464996,
0.014758356846868992,
0.01221662200987339,
-0.004320802632719278,
0.025508657097816467,
0.05109803378582001,
-0.00036240866756998,
-0.03296831622719765,
0.011088202707469463,
-0.05242948606610298,
0.00658953795209527,
-0.02495546266436577,
-0.017711589112877846,
0.03527343273162842,
0.004667515866458416,
0.016986189410090446,
-0.03748631849884987,
-0.0464920848608017,
-0.05494464188814163,
0.013220342807471752,
-0.01985330879688263,
0.040597863495349884,
0.000924338644836098,
0.02274559997022152,
0.004060639534145594,
0.0333678275346756,
0.040122877806425095,
-0.01028500311076641,
-0.11033479124307632,
-0.04418659210205078,
-0.010675794444978237,
-0.008357529528439045,
0.062471091747283936,
-0.006186580751091242,
0.009649710729718208,
0.008894518949091434,
-0.03723909333348274,
0.014378481544554234,
0.022927913814783096,
0.05823538452386856,
-0.026701735332608223,
0.024853229522705078,
0.010400555096566677,
0.060388848185539246,
-0.008987067267298698,
0.01818399503827095,
0.07976050674915314,
0.0848350003361702,
-0.01421708706766367,
-0.05654650926589966,
0.004548042546957731,
-0.025815976783633232,
0.02157304249703884,
-0.01611453667283058,
0.053903624415397644,
0.020978940650820732,
0.003041438292711973,
0.002903963439166546,
0.0359356515109539,
0.030598381534218788,
0.001435628510080278,
0.03594069927930832,
-0.031806349754333496,
-0.052664805203676224,
-0.004095014650374651,
0.018205229192972183,
0.005751504097133875,
0.013936134986579418,
-0.028869565576314926,
0.015551579184830189,
-0.03819793835282326,
-0.03681812807917595,
0.027374396100640297,
-0.03697677329182625,
0.004123013466596603,
-0.0037917832378298044,
-0.04742360860109329,
0.00138870591763407,
-0.010660089552402496,
-0.02317841723561287,
-0.06882163882255554,
0.004328826442360878,
0.046576615422964096,
0.01032528467476368,
0.02947508543729782,
0.025557314977049828,
0.012761269696056843,
0.012109799310564995,
0.006861728150397539,
-0.00019479113689158112,
-0.034276969730854034,
0.010055012069642544,
-0.0030938463751226664,
0.06042115390300751,
0.006603475194424391,
0.01354976836591959,
-0.005792664363980293,
-0.0489494651556015,
0.009219815023243427,
-0.07660189270973206,
-0.025397462770342827,
0.007325534243136644,
0.009482545778155327,
-0.002920198952779174,
-0.04325499013066292,
-0.016702773049473763,
0.0010375076672062278,
-0.006804395467042923,
0.00829394068568945,
0.0068497126922011375,
0.03374220058321953,
-0.020541464909911156,
-0.0213585514575243,
0.03284680098295212,
0.008758125826716423,
-0.010573801584541798,
0.00965270958840847,
-0.040425896644592285,
-0.02607112005352974,
-0.045645684003829956,
0.05362536013126373,
0.03502776473760605,
0.03545064479112625,
0.006777568720281124,
0.03242235258221626,
-0.00964532420039177,
-0.06790222227573395,
0.010171175934374332,
-0.05141525715589523,
-0.04138575494289398,
-0.03477765992283821,
0.017199542373418808,
0.0624099038541317,
0.0709405168890953,
-0.049838870763778687,
-0.043404776602983475,
0.016424985602498055,
0.03252566605806351,
0.030600786209106445,
-0.035287242382764816,
-0.02028649114072323,
0.017299506813287735,
-0.03503900393843651,
-0.00886476319283247,
-0.04867235943675041,
0.015512213110923767,
0.004368339199572802,
0.010789689607918262,
0.01273660734295845,
0.03514956310391426,
-0.021782027557492256,
-0.00884631834924221,
-0.03878173604607582,
0.000965416431427002,
0.038501281291246414,
0.008848066441714764,
0.06657703220844269,
-0.02233133651316166,
-0.03638393431901932,
-0.030204514041543007,
0.02247443236410618,
-0.006445788312703371,
-0.022993529215455055,
-0.03715987503528595,
0.01911647617816925,
0.016914604231715202,
0.010159424506127834,
-0.00014202891907189041,
-0.027779417112469673,
-0.020823892205953598,
-0.0016550985164940357,
0.01471049152314663,
-0.024413468316197395,
-0.0215933695435524,
0.027944868430495262,
0.023080674931406975,
-0.0754733607172966,
0.00001926149161590729,
0.03263761103153229,
-0.045904695987701416,
-0.01283275242894888,
0.002565020928159356,
0.012373875826597214,
0.03154510632157326,
0.026715658605098724,
-0.01772608794271946,
0.0112359169870615,
-0.0670865923166275,
-0.0501299686729908,
0.06266466528177261,
0.008174332790076733,
0.027434322983026505,
0.04185152426362038,
0.000102547652204521,
0.020387038588523865,
0.02844175510108471,
0.0006323566194623709,
-0.008454330265522003,
0.04002979397773743,
-0.03704942390322685,
-0.04458564147353172,
-0.02760031260550022,
0.032635800540447235,
0.002533472143113613,
-0.021771248430013657,
0.034892406314611435,
0.03432048112154007,
0.021063705906271935,
0.03249850869178772,
0.02833566814661026,
-0.03917386755347252,
0.014422236941754818,
0.021906644105911255,
-0.013275502249598503,
-0.008619636297225952,
0.07007262855768204,
-0.08034173399209976,
0.02977331541478634,
0.010385540314018726,
0.0001507421548012644,
-0.13707146048545837,
0.00994658749550581,
0.018313072621822357,
0.010007448494434357,
0.006991770584136248,
-0.014339976012706757,
0.0052400194108486176,
0.04938597232103348,
-0.07358777523040771,
0.013856717385351658,
0.011915810406208038,
-0.004310477990657091,
-0.0225099828094244,
0.017710287123918533,
-0.04387703537940979,
0.0419795997440815,
0.028992753475904465,
0.04014528915286064,
0.026811713352799416,
-0.011809887364506721,
-0.01493285596370697,
-0.012863301672041416,
-0.04144887253642082,
0.014379520900547504,
-0.027997931465506554,
-0.023415690287947655,
0.07617757469415665,
-0.02827191725373268,
-0.013076146133244038,
-0.00480062747374177,
-0.014275820925831795,
0.008999536745250225,
-0.0036064041778445244,
0.016912346705794334,
0.02135297656059265,
-0.004039593506604433,
-0.006106759887188673,
-0.014056026004254818,
0.00016481206694152206,
0.017827920615673065,
0.029017439112067223,
0.004076784942299128,
0.011658095754683018,
0.012020070105791092,
0.0026919208467006683,
-0.028548216447234154,
-0.03498527780175209,
0.02578544244170189,
-0.003351835999637842,
0.009982435964047909,
0.01721031405031681,
0.040788907557725906,
-0.0001496771874371916,
-0.0168242696672678,
-0.022271938621997833,
-0.0674431324005127,
-0.015290466137230396,
0.023818131536245346,
0.02456970140337944,
0.00040150448330678046,
-0.0009169977274723351,
-0.018962612375617027,
-0.04507550597190857,
0.025720898061990738,
0.0013172439066693187,
-0.004013832192867994,
-0.046354737132787704,
-0.006902714725583792,
0.011520703323185444,
-0.00953330472111702,
0.06169528886675835,
-0.0431487150490284,
-0.01972224935889244,
0.04967363923788071,
-0.0058650728315114975,
0.022891519591212273,
0.014606371521949768,
-0.03748127818107605,
-0.04233381897211075,
-0.10568153113126755,
0.06936529278755188,
-0.01136815920472145,
-0.00030259659979492426,
-0.04205969348549843,
-0.004458889830857515,
0.0006404631421901286,
0.020715072751045227,
0.061209701001644135,
-0.013341075740754604,
-0.0008348014671355486,
0.045281652361154556,
-0.009394547902047634,
0.023978518322110176,
-0.060537442564964294,
0.002189087215811014,
-0.01306217722594738,
0.002821278292685747,
-0.027229323983192444,
-0.027174456045031548,
-0.020882871001958847,
0.022081440314650536,
0.032265979796648026,
-0.0031457424629479647,
0.012700160965323448,
-0.05848246067762375,
-0.0022696075029671192,
0.030699407681822777,
0.00048734742449596524,
0.01195687148720026,
0.06227530911564827,
-0.02156708762049675,
0.04445495456457138,
0.06467989087104797,
-0.029926763847470284,
-0.043443553149700165,
0.018350861966609955,
-0.034503597766160965,
0.004654670134186745,
0.00001978509135369677,
-0.00940149649977684,
0.017882702872157097,
-0.03359444439411163,
-0.030603284016251564,
0.005717892199754715,
-0.05381820723414421,
-0.01390334963798523,
0.05355605483055115,
-0.017814595252275467,
0.018873507156968117,
-0.019481366500258446,
0.028337545692920685,
0.03738043084740639,
0.02962370589375496,
0.00775492936372757,
0.0711606815457344,
0.017188042402267456,
-0.03238909691572189,
0.05292559042572975,
0.044192347675561905,
0.023736367002129555,
0.00996218528598547,
-0.026815522462129593,
0.059692081063985825,
-0.033856552094221115,
0.001995987957343459,
-0.007512220181524754,
-0.02075207233428955,
0.0016770523507148027,
0.015018919482827187,
-0.022461604326963425,
0.0723041519522667,
-0.036218900233507156,
0.01849566027522087,
0.0008829387370496988,
-0.009467032738029957,
-0.05322767049074173,
0.008772643283009529,
0.02121051773428917,
0.02875647321343422,
-0.00909850001335144,
-0.004439477808773518,
-0.04045472294092178,
0.017700251191854477,
0.01422815676778555,
-0.053789764642715454,
-0.017454659566283226,
-0.0268891341984272,
-0.03198523446917534,
-0.008881699293851852,
0.010096223093569279,
0.000022425971110351384,
-0.024911366403102875,
0.006455719005316496,
0.018040547147393227,
-0.017217764630913734,
-0.004750768654048443,
-0.006368924397975206,
-0.04465888813138008,
0.05929278954863548,
-0.0723765641450882,
-0.007053750101476908,
-0.00827962625771761,
0.047636065632104874,
0.015057134442031384,
0.011571084149181843
] |
<p>Just out of curiosity. In the game Mass Effect, devices called mass relays contain two rotating rings, one inside of the other. See <a href="http://www.youtube.com/watch?v=qPxw5QjxhIs" rel="nofollow">http://www.youtube.com/watch?v=qPxw5QjxhIs</a> for an example, best seen around 00:10. </p>
<p>I was wondering: is this a stable motion? Intuitively, I'd say it isn't. Obviously, the outer ring describes normal rotational motion, but when the inner ring is taken into consideration, it seems to me that an additional driving force is required to maintain the entire situation. Am I right? I've been trying to apply some mechanical principles to it, but had no luck so far... Could anyone give a decent mathematical description of this?</p>
<p>Richard Terrett pointed out that this is in fact called a 2-axis gimbal. I wasn't aware of this, thanks!</p>
| 10,670 |
[
-0.05228429287672043,
-0.03028162010014057,
-0.018542151898145676,
-0.0030292063020169735,
0.002689818385988474,
-0.012201308272778988,
-0.043019458651542664,
-0.008257548324763775,
-0.00950652826577425,
-0.031518302857875824,
-0.018037009984254837,
0.02131393924355507,
0.07785246521234512,
0.054943010210990906,
0.009609621949493885,
0.019464073702692986,
0.02476864866912365,
-0.00514557957649231,
-0.013383494690060616,
-0.08081432431936264,
-0.053504928946495056,
0.0035266687627881765,
0.00032836126047186553,
-0.019410843029618263,
-0.026961911469697952,
0.02327105402946472,
0.025822479277849197,
-0.05181393772363663,
0.007731564808636904,
0.05393369123339653,
-0.029521947726607323,
-0.022704197093844414,
0.005959615111351013,
0.005932141095399857,
0.05887895077466965,
-0.006337645463645458,
-0.0527011975646019,
-0.03791455924510956,
0.0037832758389413357,
0.06297731399536133,
-0.042117808014154434,
0.018634077161550522,
-0.025707043707370758,
0.05770932883024216,
0.0033278255723416805,
0.0008653289987705648,
-0.036729294806718826,
-0.003435276448726654,
0.08849913626909256,
-0.03746447339653969,
0.09788542240858078,
-0.023581739515066147,
0.030735544860363007,
0.02575341984629631,
-0.009906715713441372,
-0.016373708844184875,
0.06963197886943817,
0.025936132296919823,
-0.030894769355654716,
-0.04157201945781708,
-0.016003550961613655,
-0.02919233962893486,
-0.03771308436989784,
0.0003957055159844458,
0.033577192574739456,
0.0007475289748981595,
0.009148605167865753,
-0.0036578017752617598,
0.04096096381545067,
0.03987135738134384,
0.03352510556578636,
0.02470453828573227,
0.034344203770160675,
-0.034899208694696426,
-0.0016614937921985984,
-0.03370268642902374,
0.05126461759209633,
-0.007833662442862988,
0.006505525205284357,
0.04500650241971016,
0.0021378863602876663,
0.02117234654724598,
0.032460108399391174,
0.048019252717494965,
0.02641896903514862,
-0.000059047619288321584,
0.10499300062656403,
-0.026330910623073578,
0.041581735014915466,
0.014719008468091488,
-0.00003773058415390551,
0.011196755804121494,
0.022263316437602043,
-0.006683810148388147,
-0.05977515131235123,
0.03954725340008736,
0.028243478387594223,
0.053684052079916,
0.01357126235961914,
-0.006346597336232662,
-0.019548434764146805,
0.02250056155025959,
0.0042683277279138565,
0.07497980445623398,
0.01025976613163948,
-0.003603781573474407,
-0.003919508773833513,
0.028218485414981842,
-0.013972393237054348,
0.02683035284280777,
-0.05744538456201553,
-0.013575004413723946,
0.00867545884102583,
-0.003714312333613634,
-0.0031178011558949947,
-0.009857883676886559,
-0.01445290818810463,
0.03331868723034859,
0.03129301592707634,
0.05785840004682541,
0.07522746175527573,
-0.026527635753154755,
0.02090209163725376,
-0.029726389795541763,
-0.04722395911812782,
0.030892986804246902,
0.05336570367217064,
0.005945520009845495,
-0.06636285036802292,
0.03072419948875904,
0.032232075929641724,
0.015340092591941357,
0.012075922451913357,
-0.01864347979426384,
0.026786204427480698,
-0.023343371227383614,
-0.07390245050191879,
-0.07936546206474304,
0.03464733436703682,
0.013438000343739986,
-0.012125757522881031,
-0.07594083249568939,
-0.014432741329073906,
0.05298133194446564,
0.11520762741565704,
0.005459639709442854,
0.012607894837856293,
-0.010212667286396027,
0.04301449656486511,
-0.0141145596280694,
-0.013012247160077095,
-0.026439260691404343,
0.009025277569890022,
-0.05095516890287399,
-0.012377819046378136,
-0.08712136000394821,
0.0332171730697155,
0.015632733702659607,
0.006259738467633724,
-0.01916181482374668,
0.02544141188263893,
-0.02277928590774536,
0.020623447373509407,
0.02509172260761261,
0.006595320533961058,
0.0085020512342453,
0.04434220865368843,
-0.001688253483735025,
-0.034029122442007065,
0.034523580223321915,
0.017212258651852608,
0.04227583110332489,
0.0058801621198654175,
0.024664295837283134,
0.051858920603990555,
-0.03888064622879028,
0.02300335466861725,
-0.027144193649291992,
0.009759285487234592,
0.0025764834135770798,
-0.008421841077506542,
-0.04711854085326195,
-0.012520804069936275,
0.00015879400598350912,
0.004638375714421272,
0.025672057643532753,
0.009841286577284336,
0.020844969898462296,
0.008289714343845844,
-0.027581628412008286,
0.037241917103528976,
-0.036160796880722046,
0.006995937786996365,
-0.0008641460444778204,
-0.008670054376125336,
-0.006953292526304722,
0.035754673182964325,
0.03751131147146225,
-0.038122255355119705,
-0.019786110147833824,
-0.009075481444597244,
-0.019074806943535805,
0.010849151760339737,
-0.0026825792156159878,
0.018836025148630142,
0.03286721929907799,
-0.019664229825139046,
0.007149143144488335,
0.016126345843076706,
-0.02123422361910343,
-0.0060050226747989655,
-0.026858512312173843,
0.01437171921133995,
0.014167459681630135,
0.015303916297852993,
-0.01045004092156887,
0.010932867415249348,
-0.0026609711349010468,
-0.0073490263894200325,
0.014776610769331455,
-0.020740864798426628,
0.042681217193603516,
0.03944575414061546,
0.0020446262788027525,
0.01026247814297676,
0.027524434030056,
0.012361029163002968,
-0.01580294407904148,
0.0011421166127547622,
-0.05264994874596596,
-0.03942939639091492,
0.011571995913982391,
0.03281845897436142,
0.05068512260913849,
-0.039212923496961594,
0.04802621155977249,
0.052610334008932114,
0.04346677288413048,
0.029990334063768387,
0.003071662737056613,
-0.03940306231379509,
0.015233737416565418,
0.05026281997561455,
0.025832803919911385,
0.031647197902202606,
0.024122409522533417,
0.03141821175813675,
-0.0027512831147760153,
-0.0461142472922802,
0.02781085856258869,
-0.017555566504597664,
0.037576593458652496,
0.017855718731880188,
0.023579159751534462,
0.008308418095111847,
-0.01737777516245842,
0.050178125500679016,
-0.033550720661878586,
0.023633141070604324,
0.024522334337234497,
0.04690748453140259,
-0.02873823791742325,
-0.01555872056633234,
0.03102692775428295,
0.009682067669928074,
-0.011306594125926495,
0.01687472313642502,
-0.03753753751516342,
0.020209407433867455,
-0.033152785152196884,
-0.0014224022161215544,
-0.02515363320708275,
-0.002285111229866743,
0.008918213658034801,
-0.04557760804891586,
0.004275822080671787,
0.013917709700763226,
0.0297238789498806,
-0.007982692681252956,
-0.013635664246976376,
-0.020465975627303123,
-0.03717407211661339,
-0.01819111965596676,
0.00511103356257081,
-0.05942514166235924,
0.014543128199875355,
0.005337869748473167,
-0.001100101275369525,
0.06311226636171341,
-0.026593666523694992,
-0.026510683819651604,
0.00007587198342662305,
0.008335953578352928,
-0.05619457736611366,
-0.011713526211678982,
-0.016655435785651207,
-0.014248069375753403,
-0.04254015535116196,
-0.0033628835808485746,
0.0274687297642231,
-0.0028723017312586308,
-0.026638172566890717,
0.035546571016311646,
-0.041901495307683945,
-0.0026192485820502043,
-0.007025428581982851,
0.016952034085989,
0.021360617130994797,
-0.02019241824746132,
0.023274045437574387,
-0.002482728101313114,
0.009708832018077374,
0.026728233322501183,
-0.057304855436086655,
-0.02789323963224888,
-0.02493767999112606,
-0.01841316744685173,
0.06516996026039124,
-0.005989690311253071,
-0.021084755659103394,
0.1092708483338356,
0.015831081196665764,
-0.015931714326143265,
-0.0034261776600033045,
-0.02018636465072632,
0.01127085741609335,
-0.02190103568136692,
0.022829648107290268,
0.035625819116830826,
-0.0011077076196670532,
0.007871882058680058,
0.04661200940608978,
-0.019188283011317253,
0.02018093690276146,
-0.031229281798005104,
0.006962369196116924,
0.0361410416662693,
0.04589514434337616,
-0.027762774378061295,
0.036797475069761276,
0.04058381915092468,
-0.026794079691171646,
0.019893798977136612,
-0.0013610137393698096,
0.04772347956895828,
-0.0005730830016545951,
-0.059242282062768936,
0.029719511047005653,
-0.025703800842165947,
-0.01281714253127575,
0.05311010777950287,
0.03722609207034111,
0.02469753473997116,
-0.041625745594501495,
-0.00650453008711338,
0.03530367091298103,
0.05568929389119148,
-0.04297603666782379,
0.017078278586268425,
0.05355711281299591,
0.03612653166055679,
0.019673839211463928,
-0.016840152442455292,
0.0026571392081677914,
0.009242381900548935,
-0.0019963979721069336,
-0.04751680791378021,
-0.05813087895512581,
0.04269655421376228,
-0.014667592011392117,
0.00984528660774231,
0.010739332064986229,
-0.00451953150331974,
0.004633030854165554,
-0.07639339566230774,
-0.004200401715934277,
-0.029082540422677994,
0.035291921347379684,
-0.01097467914223671,
0.019575752317905426,
0.03684481978416443,
0.026292163878679276,
-0.008019412867724895,
-0.016665587201714516,
-0.07750429213047028,
0.007370552979409695,
-0.04284600913524628,
-0.03615421801805496,
0.02789054624736309,
-0.005598468706011772,
-0.02677125670015812,
-0.020755356177687645,
-0.03059801086783409,
-0.03439956158399582,
0.0012022238224744797,
-0.05192163586616516,
0.00484065106138587,
-0.03453569859266281,
-0.06344391405582428,
0.009493554942309856,
-0.02250385843217373,
0.044904883950948715,
-0.011934374459087849,
0.030498210340738297,
0.03929707780480385,
-0.03425491228699684,
-0.012480982579290867,
-0.016830410808324814,
0.004583503119647503,
-0.003966075833886862,
-0.0018875927198678255,
-0.008425860665738583,
0.009440786205232143,
-0.0042996094562113285,
-0.05252819508314133,
0.01389840617775917,
0.04564676061272621,
0.004608239512890577,
-0.01648603565990925,
-0.024721873924136162,
-0.015683429315686226,
-0.02524031512439251,
-0.006807828322052956,
0.060028910636901855,
0.008634736761450768,
0.025341017171740532,
0.033531270921230316,
-0.00751940393820405,
-0.014355110004544258,
0.021303841844201088,
0.06824623048305511,
0.028507038950920105,
-0.02932506799697876,
-0.07976967841386795,
-0.02892807312309742,
-0.03204933926463127,
-0.021787675097584724,
-0.018444117158651352,
-0.011388473212718964,
-0.03316169232130051,
0.042730432003736496,
0.04215685650706291,
0.010793760418891907,
-0.013524220325052738,
0.02328655496239662,
-0.00223722611553967,
0.042883098125457764,
-0.007191020995378494,
0.04448845610022545,
0.017210284247994423,
0.006773692090064287,
0.05337408930063248,
0.03205843269824982,
0.006572561338543892,
-0.07508549094200134,
-0.002601476851850748,
0.03078523650765419,
0.015888189896941185,
0.012339117005467415,
-0.01851724274456501,
-0.025604350492358208,
-0.04813661053776741,
0.017846673727035522,
-0.044448625296354294,
0.05735255777835846,
-0.0412849560379982,
0.018931731581687927,
0.0012013419764116406,
-0.017303194850683212,
-0.02827734500169754,
-0.03232221305370331,
-0.03230833262205124,
-0.006660725921392441,
-0.0104362266138196,
-0.006793663837015629,
-0.005569289438426495,
-0.007406896911561489,
0.042260121554136276,
0.028367601335048676,
0.018199363723397255,
-0.02602657675743103,
0.009740668348968029,
0.023743074387311935,
-0.04946346953511238,
-0.06859774142503738,
-0.002603353699669242,
-0.00643108319491148,
-0.0222151018679142,
0.005978075321763754,
-0.05264554172754288,
-0.002469220431521535,
-0.004783961921930313,
0.008873902261257172,
0.03122260980308056,
0.026207612827420235,
-0.014985878020524979,
-0.02427549846470356,
0.05680224299430847,
0.00583892036229372,
0.034824859350919724,
0.043981220573186874,
-0.033950768411159515,
-0.007125612813979387,
0.008865376934409142,
-0.01624646596610546,
-0.03120787814259529,
-0.009461520239710808,
0.010390952229499817,
0.029370687901973724,
-0.04155053570866585,
0.03826288878917694,
0.004463313613086939,
0.032025836408138275,
0.010921810753643513,
-0.007565172854810953,
-0.014672033488750458,
0.04375739023089409,
-0.02189449407160282,
-0.04431937634944916,
-0.022087462246418,
0.040521807968616486,
-0.002706122351810336,
-0.03733736276626587,
0.03151861950755119,
-0.006777830421924591,
-0.011708074249327183,
0.04038945585489273,
-0.006586917210370302,
0.013589235953986645,
-0.057394545525312424,
-0.02987064979970455,
-0.006829652935266495,
-0.02408781833946705,
0.061680763959884644,
-0.024586696177721024,
0.02219300903379917,
0.008118859492242336,
-0.038356389850378036,
-0.032260797917842865,
0.006746592465788126,
-0.006241113878786564,
-0.015609044581651688,
-0.03107520379126072,
0.017423301935195923,
-0.003541696583852172,
0.011522741988301277,
-0.05113917589187622,
-0.03810568153858185,
0.028264133259654045,
-0.014037641696631908,
0.029845545068383217,
0.005803752690553665,
0.020542824640870094,
-0.02486373484134674,
-0.07760544121265411,
0.01021405030041933,
0.018665987998247147,
-0.031992312520742416,
0.03399595618247986,
0.01452881470322609,
-0.013786288909614086,
0.05883736535906792,
0.012450914829969406,
-0.017527224496006966,
0.011938510462641716,
0.010046983137726784,
-0.005497729405760765,
-0.0071874577552080154,
0.055766716599464417,
-0.025187509134411812,
-0.02622520737349987,
-0.026176653802394867,
0.017535872757434845,
0.020633595064282417,
0.005921505857259035,
0.027585744857788086,
0.030605940148234367,
0.007050184532999992,
0.026745788753032684,
-0.01323386374861002,
0.013079605996608734,
-0.0009040202712640166,
0.03136264160275459,
-0.0038165913429111242,
-0.0009601014899089932,
-0.012930125929415226,
-0.04074709862470627,
0.05557737499475479,
0.025620833039283752,
-0.008447283878922462,
-0.012082010507583618,
0.06687569618225098,
-0.0122250746935606,
0.0058216978795826435,
0.029307084158062935,
0.0061372872442007065,
0.016534103080630302,
-0.04459228366613388,
-0.03343045338988304,
0.0033273797016590834,
-0.0024212447460740805,
-0.015431479550898075,
-0.04305260255932808,
-0.001031821477226913,
0.014642779715359211,
0.05707922577857971,
-0.028750423341989517,
0.044347576797008514,
0.02916046790778637,
-0.02562382072210312,
-0.02697785012423992,
0.016291426494717598,
-0.006870111916214228,
-0.016007928177714348,
-0.014631903730332851,
0.021297093480825424,
-0.0660923570394516,
0.006753511726856232,
0.007500496692955494,
0.057350222021341324,
-0.008546916767954826,
-0.019191211089491844,
0.008512857370078564,
0.018703604117035866,
-0.029606113210320473,
-0.0018053750973194838,
-0.05272449180483818,
0.0515209324657917,
-0.035016585141420364,
0.06533493101596832,
-0.007063666824251413,
0.009579156525433064,
0.017493408173322678,
-0.0058872029185295105,
0.005458963569253683,
-0.05351792648434639,
-0.026561716571450233,
-0.031069215387105942,
0.019867561757564545,
-0.010614393278956413,
-0.026947081089019775,
-0.00523742288351059,
-0.018513312563300133,
0.05434156581759453,
-0.0011426499113440514,
0.002308150054886937,
-0.03626113384962082,
-0.0306642334908247,
-0.031000973656773567,
-0.007310698740184307,
-0.04003458842635155,
0.05292675644159317,
-0.014200078323483467,
-0.02167382836341858,
0.02769002877175808,
-0.02113180235028267,
0.005341069307178259,
0.02862524427473545,
0.04640006273984909,
-0.05766987428069115,
0.07773703336715698,
-0.04239024221897125,
0.022580234333872795,
-0.037735648453235626,
0.0006650080322287977,
0.11265669018030167,
0.009086460806429386,
-0.0001573346380610019,
0.0025628062430769205,
0.010562802664935589,
-0.032832223922014236,
0.0378660224378109,
-0.02435372956097126,
-0.012874813750386238,
0.004138038493692875,
0.03638772293925285,
0.04220232367515564,
0.034184712916612625,
0.019579777494072914,
0.003645365359261632,
0.04236164689064026,
0.015509028919041157,
-0.012364761903882027,
-0.010831777937710285,
0.007650719024240971,
-0.025788089260458946,
0.00610728096216917,
-0.002336750039830804,
0.03848487138748169,
-0.04116141051054001,
-0.018666326999664307,
-0.01781974732875824,
-0.04189096391201019,
0.037632472813129425,
0.03023936040699482,
-0.02169727347791195,
-0.009520916268229485,
-0.00867867935448885,
-0.03235097602009773,
-0.026911262422800064,
0.022479958832263947,
-0.0031758160330355167,
-0.004939852748066187,
0.017165549099445343,
0.03427793085575104,
-0.0011418001959100366,
0.004978835117071867,
0.013510378077626228,
0.003526105545461178,
-0.051524918526411057,
0.0223022922873497,
-0.05301206558942795,
0.008031859993934631,
-0.009398868307471275,
0.020150357857346535,
0.03233874589204788,
-0.020083175972104073,
0.03084930218756199,
-0.014075915329158306,
-0.04078653082251549,
-0.002138229552656412,
-0.013757101260125637,
-0.01883477158844471,
-0.019847700372338295,
0.008179541677236557,
0.002129897940903902,
0.016301391646265984,
0.00853761937469244,
0.0060280924662947655,
-0.006277297157794237,
-0.0036151239182800055,
0.013987576588988304,
0.08834388852119446,
-0.033239323645830154,
-0.01782202161848545,
-0.0030310237780213356,
-0.00990004651248455,
-0.047625549137592316,
-0.003087397897616029,
-0.0006791557534597814,
0.01288508903235197,
-0.01785888522863388,
0.009760149754583836,
-0.017953692004084587,
0.016342492774128914,
-0.054021142423152924,
0.010302385315299034,
-0.02879495732486248,
-0.016878051683306694,
-0.0019542553927749395,
-0.03804045543074608,
0.026784544810652733,
0.0053864591754972935,
-0.05711829289793968,
0.010137312114238739,
-0.0034838267602026463,
-0.004423169884830713,
0.01771981082856655,
-0.04914111644029617,
-0.049285050481557846,
0.019443141296505928,
-0.03176870197057724,
-0.010319985449314117,
-0.05759713053703308,
0.052393630146980286,
-0.012997155077755451,
0.042637232691049576,
0.01645289547741413,
0.01680539920926094,
-0.032629407942295074,
0.011173318140208721,
0.02854304201900959,
-0.009926932863891125,
-0.02254292741417885,
-0.0121292844414711,
0.013660586439073086,
-0.0209796279668808,
-0.02934393472969532,
0.010420219041407108,
-0.06736618280410767,
-0.0041793533600866795,
0.03723933920264244,
-0.02712457813322544,
0.012014411389827728,
-0.029368607327342033,
-0.014945860020816326,
-0.023647885769605637,
0.03565610200166702,
-0.05100525543093681,
0.004180945921689272,
-0.0061361645348370075,
-0.013101098127663136,
-0.005003786645829678,
0.016168072819709778,
-0.0016265083104372025,
0.005706436932086945,
0.01087131816893816,
-0.010075964964926243,
-0.007892313413321972,
0.025460105389356613,
0.023627402260899544,
-0.0031909896060824394,
0.0035840189084410667,
-0.03458782657980919,
0.0021562092006206512,
0.050088297575712204,
-0.02567026950418949,
0.007561349775642157,
0.015297123230993748,
0.004604897927492857,
0.0021376945078372955,
-0.02310631051659584,
-0.03402542695403099,
0.025881653651595116,
0.025839505717158318,
-0.02025781385600567,
-0.05399569123983383,
-0.0037125067319720984,
-0.007442587520927191,
0.027972396463155746,
-0.007086943835020065,
0.008617301471531391,
-0.037726789712905884,
-0.03165785223245621,
0.016713164746761322,
0.05880521610379219,
-0.018965724855661392,
-0.02211482636630535,
0.008195387199521065,
0.025507085025310516,
0.018378103151917458,
-0.02456469088792801,
0.07816291600465775,
0.021594827994704247,
0.02706177346408367,
-0.03214314952492714,
-0.04191679134964943,
0.02239186316728592,
0.011181253008544445,
-0.061162807047367096,
-0.04625298082828522,
-0.015086740255355835,
0.0037082605995237827,
0.0177611093968153,
-0.05997910723090172,
-0.000366716121789068,
0.014553109183907509,
-0.06509801745414734,
0.010392087511718273,
-0.023724764585494995,
-0.05221940577030182,
-0.06408022344112396,
-0.030541537329554558,
0.016406914219260216,
0.03535129502415657,
-0.00938592478632927,
0.0012019631685689092,
0.014510799199342728,
0.010864095762372017,
-0.06256181001663208,
-0.01974220760166645,
0.006737483199685812,
0.018871279433369637,
-0.010400108993053436,
0.016951020807027817,
0.056909698992967606,
-0.01580321416258812,
-0.026941828429698944,
0.0486464686691761,
-0.01042186189442873,
0.041263747960329056,
-0.025495419278740883,
0.03097568079829216,
0.015146494843065739,
0.046645332127809525,
-0.04179822653532028,
-0.011124386452138424,
-0.020837660878896713,
0.034552186727523804,
0.02662435732781887,
0.04425531625747681,
0.001621645176783204,
0.010671908035874367,
0.04767119511961937,
-0.0364823155105114,
0.029232434928417206,
0.003965921700000763,
-0.035463228821754456,
-0.007936284877359867,
-0.005575406365096569,
0.016273194923996925,
0.012989997863769531,
-0.026466932147741318,
0.044206518679857254,
-0.03419322893023491,
0.026241691783070564,
-0.0008307946845889091,
-0.006740406155586243,
0.019197260960936546,
0.023281918838620186,
0.026514947414398193,
-0.013301332481205463,
0.02636478841304779,
0.0016247074818238616,
0.0074945962987840176,
-0.05377259477972984,
-0.0007692122599110007,
0.0035335151478648186,
-0.03659425675868988,
-0.02485675923526287,
-0.0034982161596417427,
-0.006697319447994232,
0.04519451782107353,
0.021647969260811806,
0.02801715023815632,
0.03017680160701275,
-0.03421798348426819,
-0.007369887549430132,
-0.05700511857867241,
-0.0045366231352090836,
0.028505047783255577,
0.008812792599201202,
-0.02818159945309162,
-0.06340596824884415,
0.013590550050139427,
-0.018242495134472847,
0.06953435391187668,
-0.007203445769846439,
0.005607211962342262,
0.03179807960987091,
-0.0048361849039793015,
-0.0256511140614748,
-0.025435345247387886,
-0.009704846888780594,
-0.0029837749898433685,
-0.06444316357374191,
-0.011601971462368965,
-0.010241331532597542,
-0.030737238004803658,
-0.026630761101841927,
0.02809789776802063,
0.007675718516111374,
0.05865209549665451,
-0.004282683599740267,
-0.02617175504565239,
0.018453888595104218,
0.009294047020375729,
-0.006532771047204733,
0.1114421859383583,
-0.008084769360721111,
-0.027825146913528442,
0.02175918221473694,
-0.025123264640569687,
-0.03889460861682892,
0.05403243377804756,
-0.03487072139978409,
-0.016579758375883102,
-0.04814223572611809,
-0.04220245033502579,
-0.002830226207152009,
-0.0516294464468956,
-0.026126908138394356,
0.03200926631689072,
-0.0007422303897328675,
-0.00792230200022459,
0.03728276118636131,
0.011061768978834152,
0.056803517043590546,
-0.025844968855381012,
0.02438117004930973,
0.0154610276222229,
0.0009407903417013586,
0.027593206614255905,
0.02043810859322548,
0.027430688962340355,
0.07268282771110535,
-0.02397686243057251,
0.023796897381544113,
-0.02336973138153553,
0.036223627626895905,
-0.02745789662003517,
0.007858356460928917,
0.00599684938788414,
-0.009256245568394661,
0.008748079650104046,
-0.03363434970378876,
-0.027121104300022125,
0.01903381384909153,
-0.040742527693510056,
0.08205972611904144,
-0.01074388436973095,
-0.012519861571490765,
0.04126980900764465,
0.024648701772093773,
0.011312119662761688,
-0.019186336547136307,
0.01796957105398178,
0.025540942326188087,
0.025139104574918747,
-0.030859077349305153,
-0.009105246514081955,
-0.007270182017236948,
0.021222444251179695,
0.014557337388396263,
0.05412377417087555,
0.020121660083532333,
0.01988915167748928,
-0.0016957891639322042,
-0.030727660283446312,
-0.04376378655433655,
-0.03837854042649269,
0.034155867993831635,
0.008242030628025532,
0.004454686772078276,
-0.004915283061563969,
-0.03375334292650223,
-0.001384792267344892,
0.07148024439811707,
-0.089937724173069,
-0.015319602563977242,
0.011315158568322659,
0.042089518159627914,
0.023314740508794785,
-0.0031312936916947365
] |
<p>Is there a minimal string length (maybe the <a href="http://en.wikipedia.org/wiki/Planck_lengthhttp://en.wikipedia.org/wiki/Planck_length" rel="nofollow">Planck length</a>), and is it quantized?</p>
<p>Do strings have a 0-dimensional (ie point) cross-section? </p>
| 10,671 |
[
-0.016209036111831665,
-0.009640206582844257,
0.008438502438366413,
-0.04772544652223587,
0.020109858363866806,
0.0410856232047081,
-0.027456464245915413,
-0.03228561207652092,
-0.0017218150896951556,
-0.04261412471532822,
0.036427367478609085,
0.02669072523713112,
0.032393720000982285,
0.034732162952423096,
0.011084618046879768,
0.011375508271157742,
-0.004931744188070297,
-0.008028058335185051,
-0.008154052309691906,
-0.01390814408659935,
-0.0027744967956095934,
0.023894356563687325,
0.04323139786720276,
0.004680966027081013,
-0.028674554079771042,
0.019551079720258713,
0.037594594061374664,
0.016571233049035072,
0.017782416194677353,
0.07384341210126877,
-0.01793546788394451,
-0.02118491753935814,
0.018666384741663933,
0.04680082947015762,
0.011730805039405823,
-0.007377923466265202,
-0.0481487400829792,
-0.0276472270488739,
-0.012464293278753757,
0.008847876451909542,
-0.029778707772493362,
-0.016458643600344658,
-0.005104203708469868,
0.031483497470617294,
-0.03191971778869629,
0.017157455906271935,
0.007472500670701265,
-0.03625696524977684,
0.054209738969802856,
-0.07317763566970825,
0.038842830806970596,
0.016027940437197685,
0.012627965770661831,
0.0016285463934764266,
0.004229201469570398,
-0.02607693150639534,
0.09762229025363922,
0.07035668939352036,
-0.03885902091860771,
-0.05049779266119003,
-0.02974095195531845,
-0.011246826499700546,
0.03116673044860363,
-0.03132336586713791,
-0.04560212418437004,
0.06438048183917999,
-0.031657103449106216,
-0.015049481764435768,
0.026215845718979836,
-0.0034253320191055536,
-0.010436990298330784,
0.042077284306287766,
0.0309967752546072,
0.01142958179116249,
0.04173595458269119,
-0.01826108992099762,
0.046867456287145615,
0.007826375775039196,
0.028057951480150223,
0.0928918644785881,
-0.01070091500878334,
0.0020093813072890043,
0.01833261176943779,
0.024247540161013603,
0.012667913921177387,
-0.012492909096181393,
0.07224269956350327,
-0.04001718759536743,
0.021378811448812485,
0.05929960310459137,
-0.004996798001229763,
-0.04531456530094147,
0.04972574859857559,
0.00211728666909039,
-0.02741878852248192,
0.042243633419275284,
0.032142769545316696,
0.04797316715121269,
-0.015911808237433434,
-0.03209296613931656,
0.002081482205539942,
-0.025796592235565186,
0.03608674556016922,
0.06499704718589783,
0.00047539902152493596,
0.006298599299043417,
-0.035922084003686905,
0.007891466841101646,
-0.04982469230890274,
-0.001075631589628756,
-0.042721718549728394,
0.009312610141932964,
-0.00032184107112698257,
-0.00011664522025967017,
0.023610832169651985,
-0.05981507524847984,
0.0006607207469642162,
-0.003434271551668644,
0.06526733934879303,
0.05769145488739014,
0.018102237954735756,
-0.03733648732304573,
0.02162572555243969,
-0.02463281713426113,
-0.042299263179302216,
-0.006912172306329012,
0.010943691246211529,
-0.003943213261663914,
-0.028074048459529877,
0.04907768592238426,
-0.05687801539897919,
0.02230396308004856,
0.05399979278445244,
-0.02136380411684513,
0.07590706646442413,
-0.023005172610282898,
-0.08919186145067215,
-0.04810800030827522,
0.06645701080560684,
-0.008719286881387234,
-0.04397159069776535,
-0.05576110631227493,
0.0066109453327953815,
0.002557756146416068,
0.07096750289201736,
-0.010050753131508827,
0.029027527198195457,
-0.005599552299827337,
0.013933914713561535,
0.026694953441619873,
-0.013474961742758751,
-0.012641790322959423,
0.013211768120527267,
-0.0004952861345373094,
0.025941597297787666,
-0.009070731699466705,
0.040376853197813034,
0.053797025233507156,
0.003771004732698202,
0.0032691126689314842,
0.04741061106324196,
-0.004174959845840931,
-0.0005471429321914911,
0.01565878465771675,
-0.02499471791088581,
-0.04496511071920395,
0.08749519288539886,
0.0262431800365448,
-0.013956467621028423,
0.011925858445465565,
-0.008499696850776672,
-0.012928631156682968,
0.013270161114633083,
0.013797922991216183,
0.016316035762429237,
-0.04210542142391205,
-0.040212154388427734,
0.014077901840209961,
0.025744633749127388,
0.02385353110730648,
-0.02258826605975628,
-0.016038665547966957,
-0.028320565819740295,
0.024175848811864853,
0.01799476332962513,
0.03258606791496277,
-0.021130187436938286,
-0.00900937058031559,
-0.03161422535777092,
-0.02505645342171192,
-0.0074568018317222595,
-0.039295922964811325,
0.01941731385886669,
0.0407869815826416,
-0.00944465771317482,
0.022461559623479843,
-0.0014396471669897437,
-0.03365064784884453,
-0.04951765760779381,
-0.05665060877799988,
-0.005249271634966135,
0.05239837244153023,
-0.020867034792900085,
-0.010621913708746433,
0.011522697284817696,
0.09160646051168442,
0.05092871934175491,
-0.016350043937563896,
0.025365538895130157,
-0.0006849744822829962,
-0.03800714761018753,
-0.007023673038929701,
-0.018839450553059578,
0.05000171810388565,
-0.01846493035554886,
0.02664797753095627,
0.03561464324593544,
-0.013524924404919147,
-0.0033502220176160336,
0.044012878090143204,
-0.03332488611340523,
0.0714261382818222,
0.024571768939495087,
-0.009902676567435265,
-0.008416368626058102,
0.002992169000208378,
0.007372270338237286,
0.0109440628439188,
0.015771370381116867,
-0.02006256766617298,
-0.06824000179767609,
0.0029074603226035833,
0.07253845781087875,
0.020345047116279602,
-0.028572823852300644,
-0.004520751070231199,
0.029478494077920914,
-0.00628619734197855,
0.017862442880868912,
0.017632892355322838,
-0.04169533774256706,
-0.024322668090462685,
-0.009515631943941116,
-0.0033843102864921093,
-0.01721816696226597,
0.0029245195910334587,
0.03190893307328224,
-0.007244932930916548,
0.03860267251729965,
-0.027051830664277077,
-0.004770056810230017,
0.027740376070141792,
0.011719309724867344,
0.00701215909793973,
-0.0172053724527359,
-0.03322739899158478,
0.03510310500860214,
-0.04952250048518181,
0.02592560648918152,
0.013834098353981972,
-0.009619742631912231,
-0.009418041445314884,
-0.030297886580228806,
-0.01810169406235218,
-0.004023903515189886,
-0.0031620762310922146,
-0.003587533487007022,
-0.005339749623090029,
0.011879554018378258,
-0.03515639528632164,
-0.00810256227850914,
-0.021795032545924187,
-0.001436573569662869,
-0.003009728854522109,
0.034365568310022354,
0.0652587041258812,
-0.008819494396448135,
0.033865440636873245,
-0.06883762031793594,
-0.020058348774909973,
0.008628517389297485,
-0.057358428835868835,
0.021632391959428787,
-0.00688420794904232,
-0.03288261219859123,
0.007699590176343918,
-0.02987915463745594,
-0.024126091971993446,
0.026933277025818825,
-0.02842230536043644,
0.0375375859439373,
0.00020602717995643616,
-0.05364570394158363,
-0.021388772875070572,
-0.013669813983142376,
-0.017037777230143547,
0.028591448441147804,
-0.05466511845588684,
0.01278775092214346,
0.03252516686916351,
-0.019892493262887,
-0.035830724984407425,
0.0277421772480011,
-0.028880275785923004,
-0.04592151194810867,
-0.040267281234264374,
-0.010631712153553963,
0.04426978528499603,
-0.02107291668653488,
0.017668813467025757,
0.04003491997718811,
-0.04972798749804497,
0.01681474968791008,
-0.06447405368089676,
-0.034571323543787,
0.04145021364092827,
-0.04009533300995827,
0.03275702893733978,
0.010583136230707169,
-0.07707274705171585,
0.05763116851449013,
0.026111384853720665,
-0.03159099072217941,
-0.02755061164498329,
-0.007971178740262985,
-0.011511780321598053,
-0.026702146977186203,
0.014252395369112492,
0.010657200589776039,
-0.0459907092154026,
0.011945663951337337,
0.0489044114947319,
0.052293866872787476,
0.016303475946187973,
-0.014761058613657951,
-0.013532284647226334,
-0.00007224243745440617,
-0.0017566934693604708,
-0.008249236270785332,
0.04418788477778435,
0.032969024032354355,
-0.02195807732641697,
0.018935570493340492,
0.0033674617297947407,
0.011704764328897,
0.017973873764276505,
-0.009969859384000301,
0.0514407642185688,
0.02602745220065117,
0.03912701830267906,
-0.007362183183431625,
0.03680615872144699,
-0.015087001025676727,
-0.020754778757691383,
-0.007585416082292795,
0.012286168523132801,
0.005466117057949305,
-0.017770973965525627,
0.019054481759667397,
0.009382477961480618,
0.04352857545018196,
-0.023925263434648514,
-0.010381953790783882,
0.008517748676240444,
0.029219722375273705,
0.024097483605146408,
-0.018725097179412842,
-0.03536562621593475,
0.016330687329173088,
0.06077868491411209,
0.0485524907708168,
-0.013869435526430607,
-0.03964710980653763,
-0.01238942053169012,
-0.0521015003323555,
-0.016582408919930458,
-0.0354769267141819,
0.05986184626817703,
0.005045624915510416,
0.020277442410588264,
0.0007355817360803485,
0.01858610473573208,
-0.020116927102208138,
0.02133377082645893,
-0.0891134962439537,
-0.004660718608647585,
-0.06625670939683914,
-0.03714607656002045,
-0.003629839513450861,
0.011839653365314007,
-0.022881029173731804,
-0.013730823062360287,
-0.03970528021454811,
0.015183629468083382,
0.00849899835884571,
-0.056107088923454285,
-0.013013177551329136,
-0.038847845047712326,
-0.01127875316888094,
0.012506487779319286,
0.011954580433666706,
0.02171923965215683,
-0.019748607650399208,
0.012650758028030396,
0.036951277405023575,
-0.04058879613876343,
0.00130845804233104,
0.009276922792196274,
0.0163193941116333,
-0.0032893067691475153,
0.02312035858631134,
0.03671039640903473,
0.0088083166629076,
-0.006153760477900505,
0.014588063582777977,
0.019041795283555984,
0.039228200912475586,
0.008167825639247894,
-0.021114272996783257,
-0.004443909041583538,
-0.0650831088423729,
-0.012743140570819378,
-0.03675760701298714,
0.04391873627901077,
-0.00895914901047945,
0.013605029322206974,
0.023832865059375763,
-0.014892776496708393,
-0.0458613783121109,
0.022074764594435692,
0.07301817834377289,
0.010126255452632904,
-0.014953326433897018,
-0.03156934306025505,
-0.027190834283828735,
-0.019418584182858467,
0.006257323082536459,
-0.01746174320578575,
0.0067207301035523415,
-0.002404992701485753,
0.014620744623243809,
0.03047173283994198,
0.015286433510482311,
-0.03159240633249283,
0.00836437288671732,
-0.010409855283796787,
0.015086687169969082,
-0.048877377063035965,
0.009949462488293648,
0.007700405549257994,
0.019416214898228645,
0.021505771204829216,
0.010649334639310837,
-0.023885924369096756,
-0.0726219192147255,
0.004465615376830101,
0.028139203786849976,
0.041324432939291,
0.02110399678349495,
-0.004340705461800098,
-0.036590661853551865,
-0.028747322037816048,
0.042300790548324585,
-0.010782844386994839,
0.016364019364118576,
-0.019972244277596474,
-0.019490007311105728,
-0.04423479363322258,
0.01597367227077484,
0.0004577248473651707,
0.02342032827436924,
0.001809267676435411,
0.03982619568705559,
0.004922917578369379,
0.011150575242936611,
-0.028699658811092377,
0.05485250800848007,
0.010473319329321384,
0.039652854204177856,
-0.009546692483127117,
0.001499594422057271,
0.021677982062101364,
0.0014381204964593053,
-0.04223254695534706,
-0.09660417586565018,
0.009008059278130531,
0.023448433727025986,
-0.0307343490421772,
0.01795422099530697,
-0.018068021163344383,
-0.012347042560577393,
0.006824924610555172,
0.0035113408230245113,
-0.016112934798002243,
0.054776158183813095,
-0.023912446573376656,
0.05393765866756439,
-0.009389316663146019,
-0.013331974856555462,
0.016848798841238022,
0.04550550878047943,
-0.02180788852274418,
-0.006746912840753794,
-0.0236524511128664,
0.03795401379466057,
-0.02388957515358925,
0.015099989250302315,
-0.04646047577261925,
0.00009448110358789563,
-0.048841919749975204,
0.029908588156104088,
-0.02233341708779335,
-0.014096815139055252,
-0.019588137045502663,
-0.05436325818300247,
-0.034242983907461166,
-0.0006926995702087879,
0.017590437084436417,
-0.011527005583047867,
-0.000026361969503341243,
0.02688281051814556,
-0.026416731998324394,
-0.02195555344223976,
0.009955698624253273,
0.04234490916132927,
0.003413628553971648,
0.016855115070939064,
-0.004801986273378134,
0.027604643255472183,
-0.0023265634663403034,
-0.02525068260729313,
0.04272633418440819,
-0.047857239842414856,
0.0562761090695858,
-0.00791727565228939,
-0.03679259121417999,
0.028239209204912186,
-0.04758445918560028,
-0.015011472627520561,
0.00542917987331748,
-0.017356684431433678,
0.03978386148810387,
-0.04562598466873169,
0.0711715891957283,
-0.02927146852016449,
0.010175433941185474,
-0.03550221025943756,
-0.020359765738248825,
0.03275077044963837,
0.02882739156484604,
-0.0012436432298272848,
-0.014651814475655556,
0.029924212023615837,
-0.0330706350505352,
-0.013342516496777534,
-0.004890551790595055,
0.023628422990441322,
-0.031847137957811356,
-0.007560092024505138,
-0.0036276355385780334,
0.019702887162566185,
0.04027538746595383,
0.03551220893859863,
-0.007875459268689156,
0.009069942869246006,
-0.005790530703961849,
0.012284449301660061,
-0.03767933323979378,
0.05294105410575867,
-0.01134947594255209,
-0.04821741208434105,
-0.008533012121915817,
-0.021206026896834373,
0.018424278125166893,
-0.021367954090237617,
-0.0027099039871245623,
0.020576845854520798,
0.016949014738202095,
0.005968994926661253,
-0.01399374008178711,
0.01620013266801834,
-0.015271874144673347,
0.029561171308159828,
-0.04570979252457619,
0.009504666551947594,
-0.030856875702738762,
-0.03082854673266411,
0.015307869762182236,
-0.0008521884446963668,
0.0018290497828274965,
0.009053668938577175,
0.041890792548656464,
-0.0009491576347500086,
-0.032150477170944214,
0.03593020141124725,
-0.030954958871006966,
0.012984043918550014,
-0.00003333225686219521,
-0.032188817858695984,
0.021477747708559036,
0.029789261519908905,
-0.02051953226327896,
-0.029377009719610214,
-0.018110524863004684,
0.0021067732013761997,
0.030889078974723816,
0.017009396106004715,
0.027729153633117676,
0.006068933289498091,
-0.027375852689146996,
0.0059165069833397865,
-0.019510598853230476,
-0.027694260701537132,
-0.008057079277932644,
0.013685919344425201,
0.02195732295513153,
-0.025351507589221,
0.00008265990618383512,
0.05151348561048508,
0.015701739117503166,
-0.03870069235563278,
0.018489999696612358,
0.03944320231676102,
-0.012940787710249424,
0.009029822424054146,
-0.03499437868595123,
-0.054849859327077866,
0.039545875042676926,
-0.03630056977272034,
0.03504497557878494,
0.021866267547011375,
-0.017876580357551575,
0.022868981584906578,
-0.008624856360256672,
0.02357446402311325,
-0.015731336548924446,
-0.0029044561088085175,
-0.031094998121261597,
0.030826546251773834,
0.008093195036053658,
0.0033939771819859743,
-0.021472012624144554,
-0.0327351838350296,
0.028039636090397835,
-0.00388227216899395,
0.03477150946855545,
-0.0054681384935975075,
-0.044346828013658524,
-0.007054127752780914,
-0.06276960670948029,
-0.06717995554208755,
0.05057292431592941,
0.02482660859823227,
-0.04173020273447037,
0.043669283390045166,
-0.034607142210006714,
0.08495394885540009,
0.018627261742949486,
0.03977586701512337,
-0.04993247240781784,
0.038432564586400986,
0.002473752945661545,
0.014755361713469028,
-0.03683175519108772,
0.0004257995751686394,
0.12694057822227478,
0.07643430680036545,
0.010868040844798088,
-0.0683729276061058,
0.030038367956876755,
-0.0011191999074071646,
0.021355999633669853,
-0.023566333577036858,
0.034701552242040634,
-0.009534903801977634,
0.0008907112060114741,
0.01472401525825262,
0.05090416595339775,
-0.029425131157040596,
-0.003317174268886447,
0.04624009132385254,
-0.04155135899782181,
-0.031686101108789444,
-0.012493090704083443,
0.015307010151445866,
0.011305401101708412,
0.017737485468387604,
-0.06479440629482269,
0.021944286301732063,
-0.0230655949562788,
-0.0078121391125023365,
-0.032549213618040085,
-0.04247787222266197,
0.028797660022974014,
-0.02459443174302578,
-0.01312242355197668,
-0.007601854857057333,
0.04019223153591156,
-0.019953999668359756,
-0.03739184886217117,
0.003948488738387823,
0.022449184209108353,
0.0031153454910963774,
-0.021700464189052582,
0.05870702490210533,
0.012819469906389713,
-0.005167769268155098,
0.01618150807917118,
0.015655286610126495,
-0.052205681800842285,
-0.0008788707200437784,
0.003890781197696924,
0.05559365078806877,
-0.018657781183719635,
-0.0011854458134621382,
-0.026671450585126877,
0.00079930922947824,
0.018528321757912636,
-0.061796821653842926,
-0.036661140620708466,
0.03158152475953102,
0.043342527002096176,
-0.010405811481177807,
-0.023735657334327698,
-0.015496509149670601,
0.04153436794877052,
-0.008486531674861908,
0.016195178031921387,
-0.006619499996304512,
-0.01286772359162569,
0.014741797931492329,
0.021185265854001045,
0.022486118599772453,
-0.02786337584257126,
-0.027925636619329453,
-0.004236490000039339,
-0.020541010424494743,
-0.01827431656420231,
-0.041350651532411575,
0.011898851953446865,
0.04623093828558922,
0.03572353348135948,
0.014713795855641365,
0.0197843499481678,
0.015830837190151215,
-0.009293250739574432,
0.025976046919822693,
-0.019152292981743813,
-0.010806112550199032,
-0.009949375875294209,
0.011399630457162857,
0.02435937710106373,
0.061312004923820496,
-0.03766117990016937,
0.03182615712285042,
-0.0022564269602298737,
0.02460796758532524,
0.020292479544878006,
-0.03215010464191437,
0.03087734431028366,
0.016134925186634064,
-0.012062134221196175,
0.019321875646710396,
-0.029383517801761627,
0.016441570594906807,
0.02874859608709812,
0.04336203262209892,
-0.0038890428841114044,
0.03026430681347847,
-0.051792778074741364,
0.00019810434605460614,
0.02572772093117237,
-0.04987950995564461,
-0.003813505405560136,
0.032310374081134796,
0.024304596707224846,
-0.061190634965896606,
-0.055945880711078644,
-0.016982385888695717,
-0.0010995583143085241,
0.004290882498025894,
0.012548602186143398,
-0.03164612874388695,
0.010443189181387424,
-0.05976920202374458,
-0.02222445420920849,
-0.07081934064626694,
0.00005942684583715163,
-0.0585804209113121,
0.003640491049736738,
-0.00815462227910757,
0.014382530935108662,
-0.003676277119666338,
-0.035700999200344086,
-0.0217219740152359,
-0.03102298453450203,
0.015825871378183365,
0.031008632853627205,
-0.009350936859846115,
0.0022972342558205128,
0.013769488781690598,
0.03883339464664459,
0.033751629292964935,
-0.0008667488000355661,
-0.045150645077228546,
0.043486934155225754,
-0.06361577659845352,
-0.034690313041210175,
0.044894445687532425,
-0.06386450678110123,
0.019414149224758148,
0.02725786156952381,
-0.031652435660362244,
-0.007197744678705931,
0.06258384138345718,
0.03305797651410103,
-0.010795005597174168,
0.015010441653430462,
-0.035108160227537155,
-0.0014842381933704019,
0.0015792549820616841,
-0.017251349985599518,
-0.012224690988659859,
-0.010899967513978481,
0.013319924473762512,
-0.012107307091355324,
0.009851254522800446,
-0.0036745506804436445,
0.016711687669157982,
-0.023470822721719742,
-0.00022629623708780855,
0.04505462571978569,
-0.0006450581131502986,
-0.02428998239338398,
0.043050602078437805,
-0.012008005753159523,
0.04262050241231918,
0.0036514378152787685,
0.01333461981266737,
-0.08075521886348724,
0.011799604631960392,
0.007066527381539345,
0.0229522455483675,
0.027278868481516838,
-0.036840252578258514,
0.00018549592641647905,
0.03729543462395668,
-0.0865926444530487,
0.05891142785549164,
-0.03055807761847973,
-0.0014247165527194738,
0.00048506580060347915,
-0.005744908470660448,
-0.042208556085824966,
0.044425465166568756,
0.0267468374222517,
0.07508576661348343,
0.013586774468421936,
0.035311803221702576,
-0.02545711025595665,
-0.0313589982688427,
-0.020018210634589195,
0.03176479414105415,
-0.04678455740213394,
-0.030212508514523506,
0.06267528980970383,
-0.020991593599319458,
0.0227366853505373,
0.021277733147144318,
-0.008253896608948708,
0.021618634462356567,
0.011077109724283218,
-0.0007809962844476104,
0.03421952575445175,
0.019297180697321892,
0.030938802286982536,
-0.01827150583267212,
0.030868643894791603,
0.015736181288957596,
-0.013630887493491173,
0.007203260436654091,
0.01732782833278179,
0.023440591990947723,
0.008039392530918121,
-0.053097762167453766,
-0.007003495469689369,
0.0235294122248888,
-0.03026295080780983,
0.00914091244339943,
-0.020429905503988266,
0.022043420001864433,
0.01189697440713644,
-0.01559753343462944,
0.006824388634413481,
-0.06401007622480392,
-0.03049634024500847,
0.029439395293593407,
-0.023978009819984436,
-0.02660064958035946,
0.04062776267528534,
0.013572349213063717,
-0.009811040945351124,
0.014044254086911678,
0.010277213528752327,
0.016335349529981613,
-0.057114750146865845,
-0.002724121557548642,
-0.0003598668845370412,
0.04167279973626137,
0.00993557833135128,
-0.034188978374004364,
0.004371412564069033,
0.02107275277376175,
-0.0013667301973327994,
0.009584150277078152,
-0.03368709236383438,
-0.025591082870960236,
-0.024896983057260513,
-0.09406999498605728,
0.04563821479678154,
0.015703922137618065,
0.02600282058119774,
-0.0414339154958725,
-0.02476584166288376,
-0.006456567440181971,
0.014011078514158726,
0.06702833622694016,
-0.016706742346286774,
-0.01940501108765602,
-0.002869649324566126,
0.004590092692524195,
0.025019077584147453,
-0.035950131714344025,
-0.014231817796826363,
-0.02715657278895378,
-0.042782366275787354,
-0.01249869167804718,
-0.026449747383594513,
-0.0012794840149581432,
0.009833593852818012,
0.026808971539139748,
-0.0062949503771960735,
-0.022868042811751366,
-0.05999080464243889,
-0.0300905704498291,
0.07689915597438812,
0.01311139203608036,
0.0074087087996304035,
0.03951151669025421,
0.010757680051028728,
0.05410200357437134,
0.02839731238782406,
-0.0034637677017599344,
-0.006471187341958284,
-0.0034689169842749834,
-0.024462467059493065,
-0.021300794556736946,
-0.02267894148826599,
0.03240380063652992,
0.027675312012434006,
-0.03115416318178177,
-0.006216746289283037,
0.05161513015627861,
0.007090914063155651,
-0.03210010379552841,
0.0471636988222599,
0.012040802277624607,
0.04976337403059006,
-0.012130403891205788,
0.012150012888014317,
0.050180815160274506,
-0.036479007452726364,
0.007600829936563969,
0.019214048981666565,
0.030645083636045456,
-0.025769542902708054,
0.008888980373740196,
0.0011470834724605083,
-0.04133898392319679,
0.0339987613260746,
0.006906469818204641,
0.03846530243754387,
-0.02738802321255207,
-0.018488619476556778,
0.038556259125471115,
-0.002183537697419524,
-0.00885105412453413,
0.007601547986268997,
-0.035367369651794434,
0.08043904602527618,
0.03009551391005516,
0.027217747643589973,
-0.020430471748113632,
0.005479471292346716,
-0.0077017382718622684,
0.014514598995447159,
-0.009287555702030659,
0.050721425563097,
-0.03553874045610428,
-0.03389136865735054,
-0.02282319776713848,
0.039566848427057266,
0.02264539524912834,
-0.062404815107584,
0.011618253774940968,
0.023042932152748108,
-0.005093884654343128,
-0.018945535644888878,
-0.014641382731497288,
-0.0035499436780810356,
0.0181647390127182,
0.05328265205025673,
0.004320116247981787,
-0.011804060079157352,
-0.03073870949447155,
0.0016367300413548946,
-0.006636172067373991,
0.03632614016532898,
-0.05643915757536888,
0.0467415526509285,
-0.0445132739841938,
0.034147102385759354,
-0.03793554753065109,
-0.008362109772861004
] |
<p>Just what the title states - </p>
<p>Does reversal of magnetic poles in a planet refer to the point in time when reversal is complete? </p>
<p>OR </p>
<p>Does it refer to the entire drawn out process (assuming the poles flip gradually from 0 through 180 degrees?</p>
| 10,672 |
[
-0.016152886673808098,
-0.02359299175441265,
-0.006719655357301235,
-0.0010555223561823368,
0.040089257061481476,
0.03616713732481003,
-0.03195526823401451,
0.02013731747865677,
-0.030292406678199768,
-0.017366677522659302,
0.018795348703861237,
0.030518345534801483,
0.03265111893415451,
0.022959716618061066,
-0.004538616631180048,
0.015552135184407234,
0.0014034765772521496,
0.013731026090681553,
0.01788376085460186,
-0.023160351440310478,
-0.0071000042371451855,
-0.013832742348313332,
-0.0063142539002001286,
0.018501421436667442,
-0.059045348316431046,
0.02992919459939003,
0.01337516587227583,
0.022488579154014587,
-0.027784384787082672,
0.033766839653253555,
-0.006839130539447069,
-0.028908411040902138,
0.02956352010369301,
-0.00020777946338057518,
0.025607191026210785,
-0.021712196990847588,
-0.007773039862513542,
-0.07041128724813461,
0.004276987165212631,
0.016672350466251373,
-0.0038609541952610016,
-0.00822173710912466,
-0.009344968944787979,
0.05080341547727585,
-0.0013786087511107326,
-0.017225872725248337,
-0.003303640754893422,
-0.001359822927042842,
0.0318140834569931,
-0.03540493920445442,
0.07145285606384277,
-0.020458750426769257,
0.03565746173262596,
-0.02127116732299328,
0.01670677959918976,
0.027907587587833405,
0.06080625206232071,
0.06721128523349762,
0.006239054258912802,
-0.044952575117349625,
-0.010538877919316292,
-0.000036885419831378385,
0.005172556731849909,
-0.018478667363524437,
-0.05543788895010948,
0.05865611881017685,
-0.034024450927972794,
-0.008646867237985134,
0.037695471197366714,
0.021234070882201195,
0.0024237320758402348,
-0.0005579927237704396,
0.02679808810353279,
-0.0012265540426597,
0.0322541669011116,
-0.0617845393717289,
0.010112293995916843,
0.010834512300789356,
-0.015424427576363087,
0.02965139038860798,
-0.000231527432333678,
0.00035837636096403003,
0.008829368278384209,
0.04150371253490448,
0.00976985041052103,
0.04030333086848259,
0.04762602224946022,
-0.014192921109497547,
0.035242848098278046,
0.03906870633363724,
0.03169344738125801,
0.015059852972626686,
0.009151891805231571,
-0.02362934872508049,
-0.0436469130218029,
-0.0021878378465771675,
-0.00046657727216370404,
0.04776155576109886,
0.009304062463343143,
0.029204871505498886,
-0.0016485685482621193,
-0.024893831461668015,
0.009117558598518372,
0.024631712585687637,
0.02958475425839424,
0.004782142583280802,
-0.05504406988620758,
0.005276158452033997,
-0.013352315872907639,
-0.01055204775184393,
-0.041267454624176025,
0.015121928416192532,
0.020212700590491295,
-0.0010159359080716968,
-0.0020748472306877375,
0.0064521413296461105,
0.004162400960922241,
-0.0047612376511096954,
0.04254335165023804,
0.0481811985373497,
0.01322729792445898,
-0.023472847416996956,
-0.007285404484719038,
-0.009913966991007328,
-0.05786870792508125,
-0.03780025243759155,
0.028761576861143112,
-0.010246207006275654,
-0.03474237769842148,
0.03960820287466049,
0.0184391550719738,
-0.024945715442299843,
0.006861446425318718,
-0.02661067433655262,
0.05840865895152092,
0.01734510064125061,
-0.09163050353527069,
-0.048803139477968216,
-0.00327250175178051,
-0.01525508426129818,
0.04372187331318855,
-0.027255399152636528,
-0.005352329462766647,
-0.0005555290263146162,
0.07078779488801956,
-0.0009322704863734543,
-0.0047652446664869785,
0.004673073533922434,
0.04555171728134155,
0.012352303601801395,
-0.031423721462488174,
0.026854902505874634,
-0.002656856318935752,
-0.053241971880197525,
-0.024129169061779976,
-0.05742540955543518,
0.038759347051382065,
0.026405803859233856,
-0.009077778086066246,
-0.017383335158228874,
0.06726163625717163,
-0.027505356818437576,
0.03448225185275078,
0.03990396857261658,
-0.045152317732572556,
-0.039393097162246704,
0.11545151472091675,
-0.00755793834105134,
0.02513844333589077,
0.006175010930746794,
0.05318629741668701,
0.015204813331365585,
0.013835135847330093,
0.04280180484056473,
0.0476660318672657,
-0.052861280739307404,
-0.012503922916948795,
0.025299035012722015,
-0.008490031585097313,
0.006649778224527836,
-0.05251472070813179,
-0.006055788137018681,
0.04002740606665611,
-0.003295525209978223,
0.012082431465387344,
0.07190120220184326,
-0.059201113879680634,
-0.01546954270452261,
-0.005903079640120268,
-0.03507149964570999,
0.0003828205808531493,
-0.03613903746008873,
0.023068958893418312,
-0.019228588789701462,
-0.012573011219501495,
0.015004421584308147,
-0.0010010282276198268,
0.051748596131801605,
-0.038273949176073074,
-0.05770197510719299,
0.0038992699701339006,
0.031090693548321724,
-0.012123094871640205,
-0.019415883347392082,
0.0029703977052122355,
0.06978091597557068,
0.015788229182362556,
0.019888978451490402,
0.0009662096854299307,
-0.03366472199559212,
-0.05783867463469505,
0.005136421415954828,
-0.0109182707965374,
0.04445425793528557,
0.035272229462862015,
-0.005532469134777784,
-0.0014354664599522948,
0.03970552980899811,
0.016751563176512718,
0.006196283269673586,
-0.008046291768550873,
0.04867292195558548,
0.045393552631139755,
0.002840476343408227,
0.02067282423377037,
0.02981625497341156,
0.01883895881474018,
0.024155357852578163,
-0.012751315720379353,
-0.037672314792871475,
-0.027556700631976128,
0.00770964752882719,
0.04402761161327362,
0.02039000578224659,
-0.020033150911331177,
0.016632912680506706,
0.02523360587656498,
0.03236726298928261,
0.019405070692300797,
0.021550841629505157,
0.009595775045454502,
-0.014483502134680748,
-0.019359983503818512,
-0.011537538841366768,
-0.0005147127085365355,
0.04079250618815422,
0.05316099151968956,
-0.027487104758620262,
-0.005353474989533424,
-0.00424916809424758,
-0.05317768454551697,
0.030965672805905342,
0.026009218767285347,
0.002017969498410821,
-0.011040174402296543,
-0.06851671636104584,
0.019579406827688217,
-0.04801850765943527,
0.030913393944501877,
0.005223721265792847,
0.04127870500087738,
0.03888378664851189,
-0.014871527440845966,
0.0312111247330904,
0.02091013267636299,
0.017289740964770317,
-0.015679344534873962,
-0.0006449822103604674,
0.04578402265906334,
-0.0342872180044651,
0.011407086625695229,
-0.032989393919706345,
-0.014937205240130424,
0.006363437976688147,
0.01015723217278719,
0.02491319738328457,
0.00574689032509923,
0.01793038845062256,
0.014218570664525032,
0.0035032853484153748,
-0.031556934118270874,
-0.03630191832780838,
0.014966760762035847,
0.007103660609573126,
-0.06950856000185013,
0.011636685580015182,
0.011633608490228653,
-0.03847634047269821,
0.015276883728802204,
0.0470738410949707,
0.0001394539576722309,
0.004919688683003187,
-0.00389953819103539,
-0.06301229447126389,
-0.017969416454434395,
-0.016083024442195892,
0.0022780694998800755,
0.00742157269269228,
-0.015816615894436836,
0.0839097797870636,
-0.03314162418246269,
0.023510562255978584,
0.025754453614354134,
-0.04587307199835777,
-0.010847995989024639,
-0.003937465138733387,
-0.0033460918348282576,
0.025890028104186058,
-0.02794535830616951,
0.01840810477733612,
0.03941764682531357,
-0.03137825056910515,
-0.006335526704788208,
-0.05203985422849655,
-0.07017084211111069,
-0.005249059293419123,
-0.03109598159790039,
0.023615261539816856,
0.002393024507910013,
-0.03404965624213219,
0.08405990898609161,
0.03718050941824913,
-0.001778201898559928,
-0.008823828771710396,
0.004720020107924938,
-0.0007557395147159696,
-0.00783710740506649,
-0.0004324588517192751,
-0.008081735111773014,
0.03212345018982887,
0.013085586950182915,
-0.04341914877295494,
0.030585642904043198,
0.0024061587173491716,
0.016907261684536934,
-0.027856366708874702,
0.028485095128417015,
0.020761702209711075,
0.02485467679798603,
0.022270886227488518,
0.021113695576786995,
0.009570708498358727,
0.0373835489153862,
-0.04222368821501732,
0.07619451731443405,
0.03006865084171295,
-0.038752663880586624,
0.020165888592600822,
-0.0541909858584404,
0.0063420990481972694,
0.01791008934378624,
0.05283340439200401,
-0.003766405861824751,
0.04139833524823189,
-0.02439148910343647,
-0.005871701519936323,
0.07320410758256912,
-0.0069019608199596405,
-0.03572354093194008,
-0.0029997501987963915,
0.017538653686642647,
-0.00754752941429615,
0.0022358607966452837,
-0.0005625212797895074,
-0.02416594699025154,
0.0494757816195488,
-0.06028280034661293,
-0.0009235857287421823,
0.03927206993103027,
0.03719313070178032,
0.004641355946660042,
0.034671954810619354,
-0.02043144777417183,
-0.014281600713729858,
-0.0714297816157341,
0.02053443156182766,
0.013288472779095173,
0.014599503017961979,
-0.007652228698134422,
0.05248291417956352,
-0.0091862129047513,
0.024583464488387108,
-0.021929670125246048,
0.034379325807094574,
-0.06317807734012604,
0.007096411194652319,
-0.019813990220427513,
0.00046616580220870674,
-0.017119867727160454,
-0.005159447435289621,
0.025322845205664635,
-0.005889261141419411,
-0.006909303367137909,
-0.012699354439973831,
-0.014924765564501286,
-0.07467136532068253,
0.025917094200849533,
-0.011140433140099049,
-0.012986645102500916,
0.010622578673064709,
0.027224889025092125,
0.03565014898777008,
-0.042616669088602066,
0.06860608607530594,
0.04992504417896271,
0.0049621546640992165,
0.009660855866968632,
-0.030845163390040398,
0.020176777616143227,
0.006473318208009005,
0.012655695900321007,
0.025848666206002235,
0.001220616279169917,
-0.06055904179811478,
0.01671191304922104,
0.013770153746008873,
0.023474903777241707,
-0.0008092925418168306,
-0.01503098662942648,
-0.022549761459231377,
-0.02933512069284916,
-0.004185822792351246,
0.0210832878947258,
0.02911885641515255,
-0.0009967637015506625,
-0.0009580802288837731,
0.008148686960339546,
-0.02070990763604641,
0.010803161188960075,
0.05926947668194771,
0.0681413784623146,
0.008187488652765751,
-0.02528977021574974,
-0.058081090450286865,
0.007987440563738346,
0.0024487306363880634,
0.0017636457923799753,
0.014610004611313343,
-0.02741440013051033,
-0.01517200656235218,
-0.05081194266676903,
0.002818312495946884,
0.020702732726931572,
0.0028171937447041273,
0.05593721568584442,
-0.00788889080286026,
0.04970424249768257,
0.01911383867263794,
0.01523317489773035,
0.052324097603559494,
0.030566399917006493,
0.03619362786412239,
0.02525184489786625,
-0.03435535356402397,
-0.05984151363372803,
-0.024519018828868866,
0.006766019854694605,
0.017051883041858673,
0.0015663114609196782,
-0.011248334310948849,
-0.0709383562207222,
0.0007028591935522854,
0.019963504746556282,
-0.038802359253168106,
0.016341369599103928,
-0.04544295370578766,
-0.02412785030901432,
-0.007435214705765247,
-0.026173533871769905,
-0.009144258685410023,
0.008441128768026829,
0.026373514905571938,
0.04621725529432297,
0.0216481015086174,
0.04653683304786682,
-0.0075921546667814255,
-0.030097218230366707,
0.005195099860429764,
0.022191554307937622,
0.012882677838206291,
0.0337093248963356,
-0.005391289014369249,
0.014153491705656052,
-0.03545719012618065,
-0.06475718319416046,
-0.014409519731998444,
0.013644671067595482,
-0.033606644719839096,
0.041774243116378784,
0.006437645293772221,
-0.04916398227214813,
0.03739701956510544,
-0.007238173857331276,
0.02085200510919094,
-0.015885980799794197,
-0.01407058909535408,
0.06041548773646355,
0.016107624396681786,
-0.014106049202382565,
0.07012872397899628,
0.04513992369174957,
-0.010872109793126583,
0.014246159233152866,
0.007806531619280577,
-0.013687537983059883,
-0.037457142025232315,
0.01572486385703087,
-0.020428746938705444,
-0.013068140484392643,
-0.048633456230163574,
0.049589190632104874,
-0.03513656184077263,
-0.004720768425613642,
-0.03901929035782814,
-0.007815719582140446,
-0.007641071919351816,
0.011741328053176403,
-0.007400158792734146,
0.0009082190226763487,
-0.011396625079214573,
0.015380298718810081,
0.0010100287618115544,
-0.006507875397801399,
0.02352801524102688,
-0.03770511969923973,
0.02219230867922306,
0.03522011637687683,
0.003314791014418006,
-0.016084136441349983,
-0.011840042658150196,
-0.0131300687789917,
-0.01778036542236805,
-0.035669535398483276,
0.03365923464298248,
-0.006628168281167746,
-0.021939527243375778,
0.01053217239677906,
-0.08086424320936203,
0.01377764530479908,
0.017407801002264023,
-0.0032416721805930138,
-0.03113417886197567,
-0.036580272018909454,
-0.0009885741164907813,
0.05918832868337631,
0.03231601044535637,
-0.03210481256246567,
-0.0795750692486763,
0.026848191395401955,
0.0033120482694357634,
-0.06636163592338562,
-0.023986538872122765,
-0.03007170371711254,
-0.000977790798060596,
-0.04045911133289337,
-0.0077781667932868,
0.07288672029972076,
-0.054390162229537964,
-0.004635834600776434,
-0.0052223727107048035,
0.021917587146162987,
0.07819443941116333,
-0.03239969164133072,
-0.022360222414135933,
0.030171062797307968,
-0.008566871285438538,
-0.03486461564898491,
-0.006489691324532032,
0.03372793644666672,
-0.007304787635803223,
-0.04958659037947655,
-0.006751916371285915,
-0.00002163446697522886,
0.03708261251449585,
0.021145490929484367,
-0.06380732357501984,
0.03880980610847473,
-0.006369177717715502,
-0.01002903189510107,
-0.048913925886154175,
-0.01557239517569542,
-0.009886888787150383,
0.021425297483801842,
-0.03543123975396156,
0.0010909884003922343,
0.022558437660336494,
-0.0502924770116806,
-0.0016885878285393119,
0.02091488242149353,
-0.0034233490005135536,
0.016620563343167305,
0.0693594217300415,
-0.04694565385580063,
0.005965942516922951,
0.009554318152368069,
-0.016924530267715454,
0.007236211560666561,
0.044602975249290466,
0.02520161122083664,
0.03015081025660038,
-0.027761265635490417,
-0.036987707018852234,
0.009349149651825428,
-0.005254644900560379,
0.01952933706343174,
0.04539307951927185,
0.006972293369472027,
0.03650449961423874,
0.01908629760146141,
0.02273772843182087,
0.03136168047785759,
-0.06168137863278389,
-0.024331852793693542,
-0.020728997886180878,
0.010325608775019646,
0.06695886701345444,
-0.022812016308307648,
0.006675578188151121,
0.04188331216573715,
0.03742370381951332,
-0.04139919951558113,
0.005854922812432051,
-0.008623636327683926,
0.02344569005072117,
0.011974096298217773,
0.03406664729118347,
-0.03950349986553192,
-0.010860810987651348,
-0.029745154082775116,
0.03254873678088188,
-0.01675557531416416,
-0.012081178836524487,
0.05485714599490166,
0.01853347010910511,
0.01814022660255432,
-0.04794192314147949,
-0.02471090853214264,
-0.020931301638484,
-0.022537101060152054,
0.015201592817902565,
0.019359098747372627,
-0.016102973371744156,
-0.029737476259469986,
0.01708167791366577,
-0.007928455248475075,
-0.008563266135752201,
-0.02233339287340641,
-0.03586530685424805,
-0.038786936551332474,
-0.014202884398400784,
-0.05940045043826103,
0.02286517433822155,
-0.04309587925672531,
0.0030441973358392715,
0.007287845481187105,
-0.00833916012197733,
0.021652845665812492,
0.03278709575533867,
0.04730038344860077,
-0.03617973253130913,
0.09118610620498657,
-0.001449656207114458,
0.0009234632016159594,
-0.015589330345392227,
-0.011937862262129784,
0.1403256207704544,
0.0715038925409317,
0.0017506820149719715,
-0.07963826507329941,
0.0276775062084198,
-0.0396684892475605,
-0.0024374844506382942,
0.0011139478301629424,
0.005878423806279898,
-0.050884637981653214,
-0.01073030848056078,
0.04646427184343338,
0.012555683963000774,
-0.009012664668262005,
-0.008474056608974934,
0.030611054971814156,
-0.011293499730527401,
-0.03047841042280197,
-0.017650648951530457,
0.022563595324754715,
-0.055547501891851425,
0.0012611483689397573,
-0.021776333451271057,
-0.004021358676254749,
-0.010486218146979809,
-0.017163950949907303,
0.0009760839166119695,
-0.015807826071977615,
0.005894915200769901,
0.022758403792977333,
-0.07092318683862686,
0.0335419625043869,
-0.000597921316511929,
-0.014195956289768219,
-0.03915076702833176,
0.02711540274322033,
0.011592005379498005,
0.02236754074692726,
0.011184463277459145,
0.046271778643131256,
0.005999721586704254,
0.01384068839251995,
-0.007965326309204102,
0.027709145098924637,
-0.04908764734864235,
0.018666807562112808,
-0.036163330078125,
0.03506108373403549,
0.010315457358956337,
0.005603850819170475,
-0.02776300720870495,
-0.011249884963035583,
0.04867805913090706,
-0.02574135735630989,
0.020418569445610046,
0.002390519715845585,
-0.025130528956651688,
-0.0021483104210346937,
-0.06201248988509178,
-0.005091079045087099,
0.020386405289173126,
0.01848105899989605,
0.002278842031955719,
-0.05451103299856186,
-0.037385787814855576,
0.027240300551056862,
0.015606916509568691,
0.03840197995305061,
-0.008027755655348301,
0.005685663782060146,
-0.05575672537088394,
0.030694209039211273,
-0.0414445586502552,
-0.002453145105391741,
0.04231206327676773,
0.010470886714756489,
0.0025968190748244524,
-0.003804645501077175,
-0.05698598548769951,
-0.04680902883410454,
-0.031459201127290726,
0.06349797546863556,
0.025417279452085495,
-0.05167807266116142,
0.0042676860466599464,
-0.020590338855981827,
0.04821142554283142,
0.038153026252985,
-0.053552065044641495,
0.021823685616254807,
0.027066301554441452,
0.03388824313879013,
-0.02080274187028408,
-0.008766312152147293,
-0.017111537978053093,
0.045683857053518295,
-0.06985867023468018,
-0.02679084613919258,
-0.030880847945809364,
0.027621502056717873,
0.044888053089380264,
0.01855381205677986,
-0.033171799033880234,
0.031982049345970154,
0.011419313959777355,
0.006890341639518738,
0.030843080952763557,
-0.03140843287110329,
-0.028241463005542755,
-0.015542613342404366,
-0.05781257525086403,
-0.043638259172439575,
-0.05186488851904869,
-0.03191729635000229,
0.00901221577078104,
-0.009389501996338367,
-0.016006432473659515,
-0.03305758163332939,
0.02934306673705578,
-0.02117316983640194,
0.009724268689751625,
-0.019802624359726906,
-0.02651214227080345,
-0.06763244420289993,
-0.008809655904769897,
0.014200175181031227,
-0.013151561841368675,
0.02851933240890503,
-0.008351322263479233,
-0.011433804407715797,
-0.024822866544127464,
0.016394540667533875,
-0.011016231961548328,
-0.023237530142068863,
0.02107338048517704,
-0.0015104231424629688,
0.003050206694751978,
0.03283526375889778,
-0.05076535418629646,
-0.036361344158649445,
0.028714999556541443,
-0.027985716238617897,
-0.022001059725880623,
0.04704266041517258,
0.04122362285852432,
0.034486085176467896,
0.020917298272252083,
0.04933809116482735,
0.004135651048272848,
0.03463027998805046,
0.0064744288101792336,
0.003557648742571473,
0.01100144162774086,
0.004453652072697878,
-0.03217661380767822,
-0.009255966171622276,
-0.015612680464982986,
0.004997410345822573,
0.014825480990111828,
-0.005525951273739338,
0.015113352797925472,
-0.020258288830518723,
0.0032758465968072414,
-0.019853554666042328,
-0.03124655969440937,
-0.013293026015162468,
0.0008194901747629046,
-0.010368919000029564,
-0.015065960586071014,
0.021417446434497833,
-0.011225503869354725,
0.033169738948345184,
0.027672724798321724,
-0.03300824388861656,
-0.09362822771072388,
0.0009660960640758276,
0.014727984555065632,
0.009234888479113579,
0.010908415541052818,
-0.02506593056023121,
0.0011538965627551079,
0.05872945860028267,
-0.07535725086927414,
0.01647491753101349,
-0.0051290118135511875,
-0.006355581805109978,
-0.01616160199046135,
-0.0003868477651849389,
0.020244374871253967,
0.02466851845383644,
0.027455100789666176,
-0.004737309645861387,
0.0022182620596140623,
0.0010954890167340636,
-0.022573746740818024,
-0.022774063050746918,
0.01010859478265047,
0.02320396527647972,
-0.0289077777415514,
-0.03558668866753578,
0.03798577934503555,
-0.026010973379015923,
-0.041862212121486664,
0.05876018851995468,
-0.028414025902748108,
0.017382679507136345,
0.029796361923217773,
0.031784914433956146,
-0.05067005008459091,
-0.028854411095380783,
0.007944270968437195,
-0.03564012795686722,
-0.035637516528367996,
0.03554913401603699,
0.022684641182422638,
0.016937674954533577,
-0.009321771562099457,
-0.0033223468344658613,
0.024288732558488846,
-0.030741717666387558,
-0.009156296961009502,
0.033087968826293945,
-0.051341231912374496,
0.009350457228720188,
-0.03062865324318409,
-0.001337281079031527,
0.01586928591132164,
0.015896452590823174,
0.016888698562979698,
-0.030833560973405838,
-0.04144679382443428,
0.03921773284673691,
-0.021717358380556107,
0.0039087943732738495,
0.015004866756498814,
-0.011498164385557175,
-0.054064445197582245,
0.023353686556220055,
-0.005589308682829142,
-0.013290000148117542,
-0.02590825781226158,
0.03766879066824913,
0.016402071341872215,
-0.011541048996150494,
-0.00006648107228102162,
-0.02436164766550064,
-0.03358229994773865,
0.026295732706785202,
0.014511935412883759,
0.01666199415922165,
0.02626933343708515,
-0.0651668906211853,
0.0040524182841181755,
-0.019170979037880898,
0.06098003312945366,
-0.03732685372233391,
-0.03834759443998337,
-0.02468978613615036,
-0.044803619384765625,
-0.010741416364908218,
-0.009510943666100502,
0.028829092159867287,
0.03278876468539238,
0.003616651054471731,
0.020163197070360184,
0.008192109875380993,
0.047255005687475204,
-0.09397447109222412,
-0.015389518812298775,
0.004162979312241077,
-0.023155324161052704,
0.0756654143333435,
-0.046893760561943054,
-0.026038916781544685,
0.024694012477993965,
-0.004426535218954086,
0.033793672919273376,
0.05216676741838455,
0.03077257052063942,
-0.02619123086333275,
0.04864503815770149,
0.023885250091552734,
-0.012106853537261486,
0.06538122147321701,
-0.05657069385051727,
-0.014340895228087902,
0.017103640362620354,
-0.03873555362224579,
-0.04832368716597557,
0.0047764708288013935,
-0.0152235496789217,
-0.011704675853252411,
-0.02574780397117138,
-0.01796821877360344,
0.0210502240806818,
-0.02536599151790142,
-0.02052137441933155,
0.015218286775052547,
-0.019559480249881744,
0.01481600757688284,
0.03351610526442528,
-0.015616748481988907,
0.011668200604617596,
-0.07456207275390625,
0.003344740718603134,
0.010162531398236752,
-0.006686768960207701,
0.01726517826318741,
0.0426473394036293,
-0.006027716677635908,
0.024037981405854225,
0.0035139776300638914,
-0.02771836519241333,
-0.007732813712209463,
0.064432293176651,
-0.00044625805458053946,
0.04164101183414459,
0.019552789628505707,
-0.01781645603477955,
0.050172410905361176,
-0.012431973591446877,
0.005881880410015583,
0.013836897909641266,
0.008834456093609333,
0.034649018198251724,
0.006597916129976511,
0.01867339387536049,
-0.015295013785362244,
-0.014296211302280426,
-0.043473608791828156,
-0.006185569800436497,
0.016047213226556778,
0.009866886772215366,
-0.019858265295624733,
-0.02596723660826683,
-0.018028706312179565,
0.02590944431722164,
0.06660211831331253,
-0.05500748008489609,
0.03894057869911194,
0.005234279669821262,
0.018522115424275398,
0.014640964567661285,
-0.012574316002428532,
-0.06380104273557663,
-0.0355946384370327,
0.004631294868886471,
0.013136989437043667,
0.025117196142673492,
-0.001579066039994359,
0.021941345185041428,
-0.013670489192008972,
0.015426595695316792,
-0.04937638342380524,
-0.009813064709305763,
-0.00723185483366251,
0.07326950132846832,
0.007099526468664408,
0.0006316096987575293
] |
<p>Continuing from my previous question <a href="http://physics.stackexchange.com/q/30355/5265">Is reversal of magnetic polarity in a planet an instantaneous occurence?</a></p>
<p>A change in magnetic flux is expected to generate an EMF. </p>
<p>In the case where the magnetic poles of a planet flip - What would be the magnitude of the induced voltage/current?</p>
| 10,673 |
[
-0.0005089706392027438,
-0.009823378175497055,
-0.04904700070619583,
-0.007019050884991884,
0.05567679554224014,
0.026145964860916138,
-0.03921066224575043,
-0.009743957780301571,
0.027463776990771294,
-0.039023011922836304,
0.021394040435552597,
0.06744905561208725,
0.047091759741306305,
0.039013441652059555,
0.02555137872695923,
-0.006274989806115627,
-0.015316207893192768,
0.001364468247629702,
0.012647293508052826,
-0.005700983572751284,
-0.0009669121936894953,
0.018277889117598534,
0.01654350943863392,
0.009938587434589863,
-0.029111402109265327,
0.029412927106022835,
0.030828185379505157,
0.022434914484620094,
-0.008870860561728477,
0.058192893862724304,
0.0224522203207016,
-0.03114800900220871,
0.022441035136580467,
0.007946314290165901,
0.01905561052262783,
0.004584701266139746,
-0.04393533244729042,
-0.06389221549034119,
0.0034996136091649532,
0.021902140229940414,
0.014403010718524456,
0.006334551610052586,
-0.013672806322574615,
0.07028426975011826,
-0.021209457889199257,
-0.022785630077123642,
0.006437227129936218,
0.007913962937891483,
0.03406240791082382,
-0.08586519956588745,
0.05477746203541756,
-0.03480549529194832,
0.047522757202386856,
-0.01139956247061491,
0.007601703051477671,
-0.0036611780524253845,
0.08196673542261124,
0.06792902946472168,
-0.006958885118365288,
-0.0397505909204483,
-0.016215911135077477,
-0.03170569986104965,
-0.024747710675001144,
-0.04887165129184723,
-0.06835702061653137,
0.05838889256119728,
-0.03355720639228821,
-0.01315566711127758,
0.015618443489074707,
0.045656196773052216,
0.02916051261126995,
0.004816392436623573,
0.0028390747029334307,
-0.015316236764192581,
-0.016851408407092094,
-0.042779915034770966,
0.017122920602560043,
0.011921786703169346,
0.015614987351000309,
0.025360876694321632,
0.006225546821951866,
0.0130525603890419,
-0.003667894983664155,
0.04858851060271263,
0.024490399286150932,
0.024479538202285767,
0.048824429512023926,
-0.017590055242180824,
0.03914138674736023,
0.0007774836267344654,
-0.012541796080768108,
0.01298838946968317,
0.017460700124502182,
-0.06077240779995918,
-0.016717497259378433,
0.005227110348641872,
-0.010663969442248344,
0.05000074952840805,
-0.010438382625579834,
0.00004643634019885212,
0.028268294408917427,
-0.008867845870554447,
0.02166016772389412,
0.05905291438102722,
0.018522176891565323,
-0.026172196492552757,
-0.03824344649910927,
-0.00499386340379715,
-0.008046990260481834,
-0.021414179354906082,
-0.039763376116752625,
0.043973684310913086,
0.015456237830221653,
-0.018045077100396156,
0.03722008317708969,
-0.03050505928695202,
-0.009256422519683838,
-0.023821013048291206,
0.031658463180065155,
0.04754050448536873,
0.035399820655584335,
-0.06588337570428848,
0.019386261701583862,
-0.036502406001091,
-0.038364995270967484,
-0.01176950428634882,
0.010481811128556728,
-0.0009848850313574076,
-0.016724377870559692,
0.02040424756705761,
-0.03184626251459122,
-0.06179480999708176,
-0.022197075188159943,
-0.03684934228658676,
0.04538820683956146,
0.0013224942376837134,
-0.083612360060215,
-0.05852387100458145,
-0.00498893391340971,
-0.02153637260198593,
-0.002018724801018834,
-0.0789591446518898,
-0.005441832356154919,
0.034120723605155945,
0.04190656170248985,
0.01833193749189377,
-0.003291449276730418,
0.007056483533233404,
0.058751918375492096,
0.022466659545898438,
-0.02898445911705494,
-0.009834982454776764,
-0.01074275653809309,
-0.05039782077074051,
-0.0038441643118858337,
-0.07651259750127792,
0.021576499566435814,
0.010736794210970402,
0.017052384093403816,
-0.006439201533794403,
0.05570126324892044,
-0.022160090506076813,
0.022460125386714935,
0.011509018018841743,
-0.0303987804800272,
-0.025026926770806313,
0.11866308748722076,
0.00922155287116766,
0.0010739476419985294,
0.026354119181632996,
0.016065239906311035,
0.017463644966483116,
-0.007428580895066261,
0.032226208597421646,
0.035222116857767105,
-0.04123503342270851,
-0.016934150829911232,
-0.029114946722984314,
0.03379153832793236,
-0.011375444941222668,
-0.04403061047196388,
-0.016696089878678322,
0.029981214553117752,
-0.000873990124091506,
0.02662772312760353,
0.05217408016324043,
-0.03484794497489929,
-0.01968015357851982,
0.011020083911716938,
-0.04096059128642082,
-0.01080448366701603,
-0.02732009068131447,
0.05019354447722435,
-0.011227491311728954,
-0.006777278613299131,
0.015231050550937653,
0.041818466037511826,
0.04114976152777672,
-0.04378221556544304,
-0.04440337419509888,
0.007986878044903278,
0.035048551857471466,
-0.02181996963918209,
-0.025113113224506378,
-0.003371089231222868,
0.047078270465135574,
-0.000018638786059455015,
-0.024568121880292892,
-0.0020691254176199436,
-0.03290436044335365,
-0.04152733460068703,
-0.004522345028817654,
-0.04131157323718071,
0.03290334343910217,
0.022692173719406128,
-0.0027797066140919924,
0.01642647758126259,
0.030284399166703224,
0.005053318105638027,
0.014480875805020332,
-0.02387377992272377,
0.05852506682276726,
0.05520950257778168,
0.021084580570459366,
0.024759357795119286,
0.039955753833055496,
0.030723681673407555,
-0.008314439095556736,
-0.016583073884248734,
-0.046119604259729385,
-0.08430881053209305,
0.017489368095993996,
0.03690255433320999,
0.0240982286632061,
-0.025230927392840385,
0.0452110655605793,
0.03298079967498779,
0.029596364125609398,
0.03505747392773628,
0.015323526225984097,
-0.0012585724471136928,
-0.0278469230979681,
0.010487902909517288,
-0.0005129225319251418,
-0.004017408937215805,
0.03835823014378548,
0.03896751254796982,
-0.0016246151644736528,
-0.006191788706928492,
-0.006358398590236902,
-0.05214932933449745,
0.04101663827896118,
-0.015691934153437614,
0.026833426207304,
0.0007432354032061994,
-0.05167510733008385,
0.04053464159369469,
-0.046306803822517395,
0.02805319055914879,
-0.01151724997907877,
0.012483312748372555,
0.02008044719696045,
-0.0036376966163516045,
0.0030261788051575422,
0.031405434012413025,
-0.0351925827562809,
-0.03296778351068497,
-0.025112804025411606,
0.03868722543120384,
-0.05949234962463379,
0.016412921249866486,
0.016248881816864014,
0.0012634445447474718,
-0.03038647770881653,
-0.02265298366546631,
0.008726910687983036,
0.01077426876872778,
0.0296571496874094,
-0.011298066936433315,
0.00515721132978797,
0.00031130315619520843,
-0.07237319648265839,
0.012949110008776188,
0.014697971753776073,
-0.051284823566675186,
0.02904842048883438,
-0.0062005543150007725,
-0.01597641035914421,
0.03158250078558922,
0.021469397470355034,
-0.007287116255611181,
0.013076922856271267,
0.012880804017186165,
-0.05414996296167374,
0.003647352335974574,
-0.03999705612659454,
0.034680791199207306,
-0.014135735109448433,
-0.019693369045853615,
0.05249691754579544,
-0.023922013118863106,
0.0029159400146454573,
0.012755734845995903,
-0.04961755871772766,
0.000010259175724058878,
0.0042181117460131645,
-0.009453753009438515,
0.005392297171056271,
-0.0449584499001503,
0.02280270680785179,
0.039462387561798096,
-0.039242688566446304,
-0.01753728836774826,
-0.03807474672794342,
-0.057119399309158325,
-0.004455864429473877,
-0.015145919285714626,
0.033865608274936676,
-0.01904483139514923,
-0.08085266500711441,
0.04195399582386017,
0.04580949991941452,
-0.021004725247621536,
-0.01700209267437458,
-0.021877141669392586,
-0.02502513863146305,
-0.04131508991122246,
0.014563540928065777,
0.012417186982929707,
-0.005659333895891905,
0.025223026052117348,
0.006318086292594671,
0.016848178580403328,
-0.009683139622211456,
0.043231043964624405,
-0.02838543988764286,
0.018457556143403053,
0.0003777407400775701,
0.01490364596247673,
0.06581844389438629,
0.026728816330432892,
-0.009826524183154106,
0.021119028329849243,
-0.018492812290787697,
0.021265897899866104,
0.028121111914515495,
-0.01144956611096859,
0.036852456629276276,
-0.040273115038871765,
0.02298075146973133,
-0.02990882657468319,
0.06443709880113602,
-0.0042382944375276566,
0.033599723130464554,
-0.004489447455853224,
0.021783631294965744,
0.05383247509598732,
-0.026802944019436836,
-0.030185412615537643,
0.05299937352538109,
0.006269747391343117,
0.0005327393300831318,
-0.034889835864305496,
-0.00902388896793127,
-0.00577787309885025,
0.028964420780539513,
-0.033198971301317215,
-0.0016399151645600796,
0.05053393170237541,
0.04608916491270065,
0.017824845388531685,
-0.0006759027601219714,
-0.028679706156253815,
-0.024039486423134804,
-0.0429527722299099,
0.005658881273120642,
-0.007258771453052759,
0.033331889659166336,
0.04383071884512901,
0.03363563120365143,
0.001066311146132648,
-0.001311571686528623,
-0.0028164484538137913,
0.010343233123421669,
-0.09764067828655243,
0.05051513388752937,
-0.04071708023548126,
0.0009739935048855841,
-0.02627471648156643,
0.009946467354893684,
0.009340779855847359,
-0.013178846798837185,
-0.010721912607550621,
-0.02970859594643116,
-0.02034071460366249,
-0.06495288014411926,
-0.01014692336320877,
-0.022861016914248466,
-0.02006618306040764,
-0.023583294823765755,
0.035218045115470886,
0.06043572351336479,
-0.039251893758773804,
0.025160904973745346,
0.03652683272957802,
-0.023169130086898804,
0.0041022952646017075,
-0.019225379452109337,
-0.019996032118797302,
-0.02635224163532257,
0.0299566350877285,
0.038978319615125656,
-0.01890895701944828,
-0.06151828542351723,
0.01270508673042059,
0.02180079184472561,
0.04645046964287758,
0.022326715290546417,
0.009608482010662556,
-0.021900007501244545,
-0.05555502697825432,
0.008903758600354195,
-0.012675036676228046,
0.04492231458425522,
-0.011714853346347809,
0.00544190127402544,
0.023621320724487305,
-0.009314226917922497,
0.0032681692391633987,
0.06491857767105103,
0.07629559189081192,
-0.009606481529772282,
-0.003786673303693533,
-0.06122264266014099,
-0.014054535888135433,
-0.023331215605139732,
-0.019380994141101837,
0.029405681416392326,
0.0017017654608935118,
-0.024860061705112457,
-0.028615713119506836,
0.016204239800572395,
-0.01250547356903553,
0.03451848402619362,
0.026985615491867065,
0.017310742288827896,
0.047188643366098404,
0.008133006282150745,
-0.007290838751941919,
-0.00033744017127901316,
0.03094988875091076,
0.058415137231349945,
-0.0015495632542297244,
-0.02927095629274845,
-0.08400072157382965,
-0.001215846510604024,
0.024828298017382622,
0.04985742270946503,
-0.01798423007130623,
-0.014095538295805454,
-0.08546317368745804,
0.008707677014172077,
0.04080810770392418,
-0.05442596599459648,
0.04445628821849823,
-0.001484366599470377,
-0.034405168145895004,
0.015865221619606018,
-0.017991548404097557,
-0.010561133734881878,
0.046337567269802094,
0.006835160311311483,
0.06820130348205566,
-0.024893952533602715,
0.007799578830599785,
-0.007213234435766935,
0.02462921477854252,
0.0392867848277092,
0.03368416428565979,
0.01098807342350483,
0.009560774080455303,
-0.01765764318406582,
-0.0018473134841769934,
-0.02594122849404812,
-0.05220112204551697,
-0.0013710017083212733,
-0.009463610127568245,
-0.03167032450437546,
0.019694359973073006,
-0.027465451508760452,
-0.03533976152539253,
0.00475542526692152,
0.025078924372792244,
0.013707236386835575,
-0.01042918860912323,
-0.014236037619411945,
0.048434652388095856,
0.012143820524215698,
0.0004560667439363897,
0.07044240832328796,
0.010421930812299252,
-0.02896750345826149,
-0.000189389698789455,
0.012654712423682213,
0.018991362303495407,
-0.04394122213125229,
-0.008462490513920784,
-0.001868248451501131,
0.0017893476178869605,
-0.03239756077528,
0.06252741068601608,
-0.04131124168634415,
0.0013156530912965536,
-0.013798955827951431,
0.008801640011370182,
-0.03085152432322502,
0.023182692006230354,
-0.012575832195580006,
-0.008654408156871796,
-0.005410882644355297,
0.01648177020251751,
-0.004477793350815773,
-0.03159536048769951,
0.006762073840945959,
-0.02371922880411148,
0.01318732462823391,
-0.009069357998669147,
0.001877175527624786,
0.011075916700065136,
-0.0037478352896869183,
-0.009112491272389889,
-0.027792740613222122,
-0.05049944669008255,
0.04960954189300537,
-0.010508844628930092,
0.0017931776819750667,
0.01101650670170784,
-0.09197265654802322,
0.005860013421624899,
0.0271161999553442,
-0.004394014831632376,
0.0023838665802031755,
-0.06680282950401306,
0.027988942340016365,
0.020467117428779602,
0.026529980823397636,
-0.042344722896814346,
-0.10235857963562012,
0.05226333811879158,
0.001039425958879292,
-0.022556982934474945,
-0.022481249645352364,
-0.03319475054740906,
-0.01249532401561737,
-0.022966569289565086,
-0.003902705851942301,
0.08451031893491745,
-0.0618470273911953,
0.006647566799074411,
0.006435547489672899,
0.01626654341816902,
0.055278386920690536,
-0.01954617351293564,
-0.016596898436546326,
0.041401006281375885,
-0.034507181495428085,
0.005041355267167091,
-0.04936715215444565,
0.04042598605155945,
-0.028439892455935478,
-0.039774831384420395,
-0.024422146379947662,
-0.04024317488074303,
0.012403039261698723,
-0.003122164634987712,
-0.020939070731401443,
0.046894773840904236,
-0.00012332655023783445,
-0.02991524711251259,
-0.03346769139170647,
0.005741895642131567,
0.009683734737336636,
0.021060535684227943,
-0.01885211654007435,
-0.009430844336748123,
-0.01371089555323124,
-0.03060976229608059,
0.007593151647597551,
0.020799994468688965,
0.0229834895581007,
-0.0036584981717169285,
0.08127212524414062,
-0.028249677270650864,
-0.009079858660697937,
0.017671043053269386,
-0.013421958312392235,
0.009430550038814545,
0.002327169291675091,
0.007822631858289242,
0.016430316492915154,
-0.012865683063864708,
-0.052176304161548615,
-0.011547302827239037,
-0.010162829421460629,
0.014493267051875591,
0.0641755536198616,
-0.019692793488502502,
0.04900233447551727,
0.025314662605524063,
0.042688414454460144,
-0.007469044532626867,
-0.01167006604373455,
-0.004313528072088957,
-0.009365050122141838,
0.00459579611197114,
-0.005775557365268469,
0.012530146166682243,
0.013882211409509182,
0.04590478539466858,
0.061598483473062515,
-0.01681024394929409,
0.03284906968474388,
0.030026797205209732,
0.0331343337893486,
0.04561888799071312,
0.016286013647913933,
-0.034861426800489426,
0.0031685112044215202,
-0.04317322000861168,
0.051710840314626694,
-0.008496526628732681,
-0.025411417707800865,
0.08627619594335556,
-0.01459599006921053,
0.02127409540116787,
-0.06003715470433235,
-0.019613267853856087,
-0.009245149791240692,
0.008665491826832294,
0.020307518541812897,
0.012730144895613194,
0.005114634521305561,
0.03627467900514603,
0.026843613013625145,
-0.002149730920791626,
-0.009805241599678993,
-0.0013962285593152046,
-0.13146309554576874,
-0.031016767024993896,
-0.0009218439226970077,
-0.0768124982714653,
0.040114156901836395,
-0.0066693625412881374,
-0.010679172351956367,
0.02223167195916176,
-0.01170451007783413,
0.03956621512770653,
0.01876170001924038,
0.04385226219892502,
-0.026738937944173813,
0.08745346963405609,
0.0010605118004605174,
0.0016446553636342287,
-0.022847281768918037,
0.002969970926642418,
0.09194392710924149,
0.03907483443617821,
-0.009595084004104137,
-0.056485164910554886,
0.03223882615566254,
-0.05433116853237152,
0.012837796472012997,
0.010455658659338951,
0.0017430996522307396,
-0.04170828312635422,
-0.004562425892800093,
0.038717158138751984,
0.017247263342142105,
0.02079152688384056,
-0.02333311177790165,
0.03953598812222481,
-0.013751990161836147,
-0.024790789932012558,
-0.04757414758205414,
0.03642357513308525,
-0.037310890853405,
0.017215648666024208,
-0.06025085225701332,
0.02335098199546337,
-0.05028371512889862,
-0.0005442157853394747,
-0.008879127912223339,
-0.00556434178724885,
0.025430604815483093,
0.011073780246078968,
-0.05189567059278488,
-0.006512338761240244,
0.010279950685799122,
-0.04054517671465874,
-0.04917534813284874,
0.05929582193493843,
0.016299260780215263,
0.03389718011021614,
0.01323265116661787,
0.020532095804810524,
-0.01963035576045513,
0.004369495436549187,
0.049950651824474335,
0.01727154105901718,
-0.04750003665685654,
0.018688397482037544,
-0.052117884159088135,
0.05225450173020363,
0.005365752149373293,
0.03070257604122162,
-0.0017096414230763912,
0.015610074624419212,
0.018318114802241325,
-0.04599855840206146,
-0.021755266934633255,
-0.015466851182281971,
-0.011051597073674202,
-0.031543560326099396,
-0.011738165281713009,
0.0007409077370539308,
0.057126905769109726,
0.002969800727441907,
0.03485022112727165,
-0.014762356877326965,
-0.01100708544254303,
-0.002834706800058484,
0.0029138843528926373,
0.04486694931983948,
0.012353419326245785,
-0.008411041460931301,
-0.03412982448935509,
-0.027387557551264763,
-0.03588427975773811,
-0.012502600438892841,
0.044214460998773575,
0.03405114635825157,
0.0025010707322508097,
0.005171658005565405,
-0.04948274418711662,
-0.014675416052341461,
-0.03279934078454971,
0.03125903382897377,
0.017855677753686905,
-0.03414588421583176,
-0.0047651613131165504,
0.019018344581127167,
0.040614061057567596,
0.00836615264415741,
-0.05074722319841385,
0.029239317402243614,
0.0037615769542753696,
0.016260359436273575,
0.007986186072230339,
-0.015856008976697922,
-0.020154684782028198,
0.02058234065771103,
-0.03503309190273285,
-0.007373250555247068,
-0.0111303785815835,
0.02348518557846546,
0.04394899681210518,
-0.00970081053674221,
-0.015293939970433712,
0.019664520397782326,
-0.021211279556155205,
-0.00927665177732706,
0.023221546784043312,
-0.00986594520509243,
-0.02321021445095539,
0.0029859619680792093,
-0.032158754765987396,
-0.010631910525262356,
-0.050967905670404434,
0.0021189532708376646,
0.0229859109967947,
-0.0038100555539131165,
-0.014972753822803497,
-0.041905004531145096,
0.016450757160782814,
-0.029238678514957428,
0.031431011855602264,
-0.01367948018014431,
-0.0281379371881485,
-0.0195187758654356,
-0.005227076821029186,
0.02485949732363224,
-0.007715373765677214,
0.024530692026019096,
0.013515104539692402,
-0.029285792261362076,
0.009701807983219624,
0.004573305137455463,
-0.00048437537043355405,
0.001886627054773271,
0.017177322879433632,
0.01663714461028576,
-0.026693494990468025,
0.04392469301819801,
-0.023619571700692177,
-0.051340244710445404,
0.053485650569200516,
-0.05778563767671585,
-0.046146687120199203,
0.04731173440814018,
0.015869533643126488,
0.04829464480280876,
0.03746478259563446,
0.007789946626871824,
-0.005930507089942694,
0.0654698833823204,
0.023154042661190033,
0.017733657732605934,
0.022784899920225143,
-0.003105459501966834,
-0.021330859512090683,
0.022440535947680473,
-0.011190277524292469,
-0.009167448617517948,
0.026333387941122055,
0.0005733297439292073,
0.01556365005671978,
-0.012860022485256195,
-0.011915761977434158,
-0.009698968380689621,
0.020317139104008675,
-0.00341060315258801,
0.018489940091967583,
-0.014661567285656929,
0.022555727511644363,
0.02574126422405243,
-0.03363755717873573,
0.024291696026921272,
0.002229298697784543,
-0.02499419078230858,
-0.08423890173435211,
0.013852306641638279,
0.029990345239639282,
-0.008665038272738457,
0.013494533486664295,
-0.05760817602276802,
0.0015688355779275298,
0.048848435282707214,
-0.07504485547542572,
-0.009263269603252411,
-0.007866686210036278,
0.003822782076895237,
-0.007402341812849045,
0.011117340065538883,
0.008934436365962029,
0.005900569725781679,
0.02337423339486122,
0.017219848930835724,
0.021233338862657547,
0.00516708055511117,
-0.019885826855897903,
-0.012354588136076927,
-0.012249408289790154,
0.04112355411052704,
0.014916811138391495,
-0.016483180224895477,
0.052154239267110825,
-0.01526735257357359,
-0.028936488553881645,
0.0323275551199913,
-0.02384437806904316,
0.025218119844794273,
0.0084299361333251,
0.028736930340528488,
-0.018762659281492233,
0.012149621732532978,
-0.0016231597401201725,
-0.0226450078189373,
-0.007947620004415512,
0.036231111735105515,
-0.00212711445055902,
0.037011273205280304,
-0.0027911909855902195,
-0.010462204925715923,
0.013027507811784744,
-0.006855550222098827,
0.021469760686159134,
0.018336590379476547,
-0.030709730461239815,
-0.0015289579750970006,
-0.021721340715885162,
0.016093332320451736,
0.007233277894556522,
-0.01609518565237522,
0.016592716798186302,
-0.07255010306835175,
-0.02902739681303501,
0.027352401986718178,
-0.03260474652051926,
0.03728891536593437,
0.027418149635195732,
-0.026287201792001724,
-0.03475023806095123,
0.05519460141658783,
-0.007254728116095066,
-0.017217887565493584,
-0.06463657319545746,
0.00837972667068243,
0.022684862837195396,
-0.01851876825094223,
0.007026349660009146,
-0.03612605854868889,
-0.04691512510180473,
0.02866276167333126,
0.004097944591194391,
0.02213548868894577,
-0.011183356866240501,
-0.05092015862464905,
0.018971318379044533,
-0.03733272850513458,
0.0682704895734787,
-0.024151038378477097,
-0.013496799394488335,
-0.011259711347520351,
-0.03197036683559418,
-0.01880345493555069,
-0.00964892003685236,
0.025207800790667534,
0.0015443674055859447,
-0.011646480299532413,
0.031409915536642075,
-0.016023769974708557,
0.022246064618229866,
-0.09050171822309494,
-0.00818841066211462,
0.009798974730074406,
-0.025052303448319435,
0.04767556115984917,
-0.034618787467479706,
0.019659990444779396,
0.02401328831911087,
-0.028224820271134377,
0.017201507464051247,
0.04543522000312805,
0.012120164930820465,
-0.0327395536005497,
0.023321589455008507,
0.011959892697632313,
-0.008319016546010971,
0.06296055018901825,
-0.01280735433101654,
0.013866902329027653,
-0.008897103369235992,
-0.004103108309209347,
-0.022716406732797623,
0.0010951763251796365,
-0.024209879338741302,
0.005986807402223349,
-0.02442641742527485,
0.011083180084824562,
0.017313910648226738,
-0.056253399699926376,
0.0006752389017492533,
0.020524783059954643,
-0.005798424128443003,
0.015006558038294315,
0.031256549060344696,
-0.011294993571937084,
0.018815580755472183,
-0.016218602657318115,
0.03818010538816452,
0.003018544986844063,
0.021721946075558662,
-0.02392484061419964,
0.01863018050789833,
0.0009599845507182181,
-0.010316145606338978,
0.02437608316540718,
0.012743846513330936,
0.010882525704801083,
0.041160356253385544,
0.019779501482844353,
0.0173896886408329,
-0.016867810860276222,
-0.02360074408352375,
0.03937781974673271,
0.02183627523481846,
0.005606916267424822,
0.013954649679362774,
-0.007820261642336845,
0.06184528395533562,
-0.01380328182131052,
0.00910656712949276,
-0.016219429671764374,
0.009755091741681099,
-0.0438968762755394,
0.0007590618915855885,
0.0007456520106643438,
0.01951023004949093,
-0.023465897887945175,
-0.027119368314743042,
-0.015080752782523632,
0.011891196481883526,
0.06457729637622833,
-0.052670300006866455,
0.041967809200286865,
-0.011658050119876862,
-0.01118479948490858,
0.0037332552019506693,
-0.00006246411794563755,
-0.04058941826224327,
-0.02213280461728573,
0.01289460901170969,
0.013550583273172379,
0.04411428049206734,
-0.004384265281260014,
-0.010480321012437344,
0.005841521546244621,
0.04371422156691551,
-0.05874677374958992,
-0.005871271714568138,
0.002356606302782893,
0.045759331434965134,
0.019475869834423065,
0.019239000976085663
] |
<p>Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum.</p>
<p>It is often said that an object that has been thrown up in the air and is rotating, is physically rotating about the center of mass. I don't think that is what is physically happening. We chose the center of mass as the point of rotation because it is convenient mathematically (it makes the separation of translation and rotational energy easier).
We could choose any other point (inside, outside the object, in motion or at rest relative to the object) and calculate the rotation about that arbitrary point.</p>
<p>It is not a physical fact that the free object rotates about the center of mass.</p>
<p>Even an object that is constrained to rotate about a fixed axis, we could describe the rotation about any point, not necessarily points on the fixed, constrained axis.</p>
<p>So when we see an object rotating, its state of rotation is totally relative, as it happens for many other physical quantities.
Is that correct?</p>
| 668 |
[
-0.06192110478878021,
-0.004968036897480488,
-0.019297463819384575,
-0.04445632919669151,
0.05390206351876259,
-0.019461125135421753,
-0.04290127754211426,
0.009259369224309921,
-0.0002148241037502885,
-0.03856903687119484,
0.015479001216590405,
0.06412385404109955,
0.018713507801294327,
0.03562389686703682,
-0.007092807907611132,
0.013191507197916508,
0.0037433872930705547,
-0.003881854470819235,
-0.012290997430682182,
-0.008705788291990757,
-0.009090992622077465,
0.011004018597304821,
-0.007310123182833195,
-0.007108590565621853,
-0.02441084198653698,
0.015585163608193398,
0.045374542474746704,
-0.01927366852760315,
0.04408036172389984,
0.06039982661604881,
-0.021507101133465767,
-0.011901002377271652,
0.0173028651624918,
0.024349527433514595,
0.03897227346897125,
0.021030796691775322,
-0.02862739935517311,
0.011122210882604122,
-0.009348353371024132,
0.02602340467274189,
-0.04192180559039116,
0.009938749484717846,
-0.04087404906749725,
0.060816120356321335,
-0.02736484259366989,
0.034430261701345444,
-0.030171088874340057,
0.016577064990997314,
0.059785425662994385,
-0.05744631960988045,
0.07463846355676651,
-0.03565132990479469,
0.014125406742095947,
0.025572622194886208,
0.0032819476909935474,
-0.007796559948474169,
0.08893584460020065,
0.05388320982456207,
-0.034731075167655945,
-0.059731025248765945,
-0.023344339802861214,
-0.027883168309926987,
0.013661605305969715,
-0.04045771062374115,
-0.006140118930488825,
0.015126798301935196,
0.01473277062177658,
-0.01637035235762596,
0.03284052386879921,
0.012542552314698696,
0.010524670593440533,
0.029843974858522415,
0.032444145530462265,
-0.014164856635034084,
0.005099740345031023,
-0.05198904871940613,
0.045599423348903656,
-0.019717596471309662,
0.0163316261023283,
0.02896834723651409,
-0.0014405545080080628,
-0.0036407439038157463,
0.04247947782278061,
0.002384765539318323,
0.016712741926312447,
-0.015862561762332916,
0.06335044652223587,
0.010234284214675426,
0.029108824208378792,
0.055956486612558365,
0.0237790048122406,
-0.0030848125461488962,
-0.009330380707979202,
-0.02981225773692131,
-0.03257391229271889,
0.026713460683822632,
-0.007530533708631992,
0.040292177349328995,
0.012461889535188675,
-0.005180213134735823,
0.014092539437115192,
-0.014843150973320007,
0.021061159670352936,
0.07825321704149246,
-0.022206338122487068,
-0.0008192784735001624,
-0.04853460192680359,
-0.0005554697127081454,
0.0004663429572246969,
-0.02131378836929798,
-0.04474059119820595,
0.0064812698401510715,
-0.03212704882025719,
-0.01518926303833723,
0.01639043353497982,
-0.026085879653692245,
-0.002632918069139123,
-0.0036262001376599073,
0.06390639394521713,
0.04358237609267235,
0.026648646220564842,
-0.03868884593248367,
-0.031056076288223267,
-0.02811810001730919,
-0.05850070342421532,
0.024646302685141563,
0.04063735902309418,
-0.018186606466770172,
-0.06333597004413605,
0.018483681604266167,
0.01728890836238861,
-0.0057224794290959835,
0.014097025617957115,
-0.004002853762358427,
0.021269982680678368,
-0.02783072367310524,
-0.12498853355646133,
-0.05170884355902672,
0.04640316218137741,
-0.0035146151203662157,
-0.025070827454328537,
-0.0664883628487587,
-0.004585836548358202,
0.031021639704704285,
0.07711271196603775,
-0.01586369425058365,
-0.004701268393546343,
-0.006179218180477619,
0.031214896589517593,
-0.021454738453030586,
0.005047087091952562,
-0.0112812714651227,
0.0010133598698303103,
-0.07636303454637527,
-0.024410448968410492,
-0.052836593240499496,
0.04245451092720032,
0.069078229367733,
-0.009922215715050697,
-0.0051966882310807705,
0.000560094544198364,
-0.04352336749434471,
0.011777152307331562,
0.039960332214832306,
-0.014197690412402153,
-0.051997337490320206,
0.05454166978597641,
0.03913365676999092,
-0.0013544075191020966,
0.05259346961975098,
0.029430318623781204,
0.04591284692287445,
-0.023963363841176033,
0.02088039182126522,
0.049235958606004715,
-0.03292923793196678,
-0.034681741148233414,
-0.0054725767113268375,
0.010451369918882847,
-0.02627708949148655,
-0.05886804684996605,
-0.029730122536420822,
0.019351698458194733,
0.015290209092199802,
0.017583152279257774,
0.07584074139595032,
-0.005862657446414232,
-0.011798098683357239,
-0.01393071562051773,
-0.03509581461548805,
0.008215971291065216,
-0.04919534921646118,
0.03217000514268875,
-0.027241354808211327,
-0.014149006456136703,
0.02234126813709736,
0.04530199244618416,
0.033371247351169586,
-0.04418390616774559,
-0.013377033174037933,
0.009550618939101696,
0.041287362575531006,
0.014290698803961277,
-0.02487746812403202,
-0.0084834024310112,
0.07823293656110764,
0.003850604873150587,
0.005369859281927347,
0.008702777326107025,
-0.012135442346334457,
-0.03633328899741173,
-0.010220487602055073,
0.0033348817378282547,
0.011684834025800228,
0.048329196870326996,
-0.002942293416708708,
0.008799073286354542,
0.04409169778227806,
-0.014744248241186142,
0.008826172910630703,
-0.010955014266073704,
0.0962432473897934,
0.05536500737071037,
-0.01219728123396635,
0.015836477279663086,
0.03809346631169319,
0.017004340887069702,
0.002603536006063223,
0.005861146375536919,
-0.00783495418727398,
-0.048228923231363297,
-0.023430269211530685,
0.0008075166842900217,
0.02603140100836754,
-0.04839387908577919,
0.009349943138659,
0.03900819644331932,
0.06124918907880783,
0.00903159286826849,
0.010945064015686512,
-0.020511632785201073,
-0.04114376753568649,
-0.020306605845689774,
-0.006222858093678951,
0.01268390566110611,
0.006716181989759207,
0.02214019000530243,
0.01103329099714756,
0.032127756625413895,
0.01557273417711258,
-0.031166983768343925,
0.07995688170194626,
0.01763433776795864,
-0.016061248257756233,
0.034100987017154694,
-0.05339507758617401,
0.026862597092986107,
-0.013166878372430801,
0.025491762906312943,
-0.009675826877355576,
-0.02528892643749714,
0.0023837918415665627,
-0.044500768184661865,
-0.009549549780786037,
-0.0058060926385223866,
0.020830487832427025,
-0.01632549986243248,
0.017644427716732025,
0.02508769929409027,
-0.027529867365956306,
-0.012983794324100018,
-0.03805141896009445,
-0.023926623165607452,
0.01183436531573534,
0.010345184244215488,
0.011410160921514034,
0.01270746998488903,
0.03650851920247078,
0.005156370811164379,
-0.01944793201982975,
-0.007930012419819832,
-0.026085512712597847,
-0.024552905932068825,
0.023265685886144638,
-0.07640998810529709,
0.002993509639054537,
-0.035933539271354675,
-0.01958155259490013,
0.014379498548805714,
-0.019623028114438057,
0.01313064806163311,
0.008720018900930882,
0.01127526257187128,
-0.06692271679639816,
-0.004616109188646078,
-0.018784208223223686,
-0.02859092876315117,
-0.0284647885710001,
-0.004378743469715118,
0.05093179643154144,
-0.010593944229185581,
-0.010312171652913094,
0.004080642480403185,
-0.030401067808270454,
-0.06057247146964073,
0.006626255810260773,
-0.00033126570633612573,
0.04659608379006386,
-0.032187700271606445,
-0.005856784991919994,
-0.00047392488340847194,
-0.018600324168801308,
0.008359524421393871,
-0.03506309911608696,
-0.05139201134443283,
0.02511606179177761,
-0.03950875997543335,
0.05050601065158844,
-0.0032271763775497675,
-0.016475273296236992,
0.12343230098485947,
0.008519177325069904,
-0.0586930587887764,
-0.02926901914179325,
0.0027593334671109915,
-0.017689963802695274,
-0.02700187638401985,
-0.0026993758510798216,
0.006753675639629364,
-0.04115143045783043,
0.029620232060551643,
0.009357875213027,
-0.016329996287822723,
-0.011042000725865364,
0.008510137908160686,
0.0018431560602039099,
0.007885511964559555,
-0.0036048288457095623,
-0.05975097417831421,
0.05218128114938736,
0.010684482753276825,
-0.02614501304924488,
0.013832244090735912,
0.007577383890748024,
0.0528426356613636,
-0.01586305722594261,
-0.07012706249952316,
0.05278961732983589,
-0.011617233045399189,
0.009500034153461456,
0.007610102649778128,
0.07762974500656128,
-0.00011624537000898272,
-0.01441271137446165,
-0.003268242347985506,
0.017402544617652893,
0.03569020330905914,
0.006431403569877148,
-0.01791071519255638,
0.052908990532159805,
0.0289226733148098,
-0.02429799921810627,
-0.019525397568941116,
0.00015767304284963757,
-0.001679004286415875,
0.03415868058800697,
-0.05560434237122536,
-0.03554747998714447,
0.018690528348088264,
0.03591770678758621,
0.03166167438030243,
0.015347190201282501,
-0.05081534385681152,
0.020859993994235992,
-0.0730285570025444,
0.0426577590405941,
0.013642290607094765,
0.04046916216611862,
-0.00952087715268135,
0.06881479918956757,
0.03380978852510452,
0.024894295260310173,
0.0005219804006628692,
0.007352596148848534,
-0.08566360175609589,
0.03217819333076477,
-0.03766555339097977,
-0.007698383182287216,
-0.012699568644165993,
-0.008977154269814491,
-0.011458616703748703,
-0.04013657569885254,
-0.013887069188058376,
-0.03734302893280983,
-0.02951386198401451,
-0.03428282216191292,
0.011305556632578373,
-0.02673608437180519,
0.006245940923690796,
0.006228325888514519,
0.03638185188174248,
0.04520130902528763,
-0.02602689526975155,
0.05230969190597534,
0.04673018306493759,
-0.045749254524707794,
0.021241014823317528,
-0.012988842092454433,
0.004141551908105612,
0.01148003526031971,
0.03835335373878479,
0.020748214796185493,
-0.012684609740972519,
-0.008482072502374649,
0.01654447615146637,
-0.016598636284470558,
0.03606633096933365,
0.003795736702159047,
-0.03962230682373047,
-0.041000835597515106,
-0.050785381346940994,
-0.01175822876393795,
-0.012747160159051418,
0.04345479607582092,
-0.018901022151112556,
-0.011684459634125233,
0.042630113661289215,
-0.0034240568056702614,
-0.012538808397948742,
0.02292400412261486,
0.05325523763895035,
0.029525749385356903,
-0.008003334514796734,
-0.06810807436704636,
-0.005465250462293625,
-0.007827695459127426,
0.000284776819171384,
0.014746307395398617,
-0.012543821707367897,
-0.008034786209464073,
-0.0038657363038510084,
-0.005037966184318066,
-0.003176066791638732,
-0.0011731995036825538,
0.023258788511157036,
-0.02794830873608589,
-0.00879630260169506,
-0.016368607059121132,
0.0060876780189573765,
0.04484708979725838,
0.03241617977619171,
0.027054842561483383,
-0.002664832165464759,
-0.020850829780101776,
-0.03475898504257202,
-0.02540469728410244,
0.04664791747927666,
0.0015385746955871582,
-0.005303069017827511,
0.0035057009663432837,
-0.008369970135390759,
-0.02377931959927082,
0.05663863942027092,
-0.06058017536997795,
0.06601494550704956,
-0.008304554037749767,
0.016684483736753464,
-0.010428434237837791,
-0.047649264335632324,
-0.02001480758190155,
-0.00793252233415842,
-0.03576111048460007,
0.01463303342461586,
-0.05253496393561363,
0.00602169381454587,
-0.03953976929187775,
0.016286594793200493,
0.023222265765070915,
0.022611793130636215,
0.031963761895895004,
-0.01977003552019596,
-0.022459402680397034,
0.02084936760365963,
-0.027178335934877396,
-0.07308931648731232,
-0.015468820929527283,
0.002267618430778384,
-0.002849562093615532,
0.029956230893731117,
-0.03324045613408089,
-0.04418710619211197,
0.008242280222475529,
-0.017709996551275253,
0.013321028091013432,
-0.005946377292275429,
-0.043105706572532654,
0.01769876852631569,
0.010698869824409485,
-0.007365957833826542,
0.012200319208204746,
0.019520830363035202,
-0.027399297803640366,
-0.021142054349184036,
-0.0316045843064785,
0.029223375022411346,
0.02688085101544857,
-0.0035893304739147425,
-0.03401937708258629,
0.032885752618312836,
-0.008550645783543587,
0.03385736048221588,
0.025527456775307655,
0.00868663378059864,
-0.01910696178674698,
-0.024469928815960884,
-0.05266343429684639,
0.017184125259518623,
0.01897476613521576,
-0.010554216802120209,
0.004637864883989096,
0.03212296590209007,
-0.012693296186625957,
-0.00040108291432261467,
0.01987411268055439,
0.03037264011800289,
-0.008551071397960186,
0.050200801342725754,
-0.015901772305369377,
0.0019292449578642845,
-0.03793235868215561,
-0.04185093566775322,
0.0027192349079996347,
-0.0629633292555809,
0.015715064480900764,
-0.030662501230835915,
0.0022385683842003345,
0.042240966111421585,
-0.08840522170066833,
-0.06400235742330551,
0.0014382892986759543,
0.008786376565694809,
0.02022339403629303,
-0.0456710159778595,
-0.00877255480736494,
0.01960359513759613,
0.01829921267926693,
-0.017371924594044685,
-0.03685881197452545,
0.025672441348433495,
0.02566639706492424,
-0.008299608714878559,
-0.012819204479455948,
0.031148020178079605,
-0.009268838912248611,
-0.048724740743637085,
-0.01285561453551054,
0.045467544347047806,
-0.024844765663146973,
-0.01643955148756504,
0.05023684352636337,
-0.00944590289145708,
0.07005510479211807,
-0.028869369998574257,
-0.05420556664466858,
-0.009190689772367477,
0.001311826636083424,
-0.0011527372989803553,
0.004040366038680077,
0.08678451180458069,
-0.012715859338641167,
-0.04985712096095085,
-0.0016006665537133813,
-0.003479732433333993,
0.014269418083131313,
0.028868310153484344,
-0.0034640636295080185,
0.021300261840224266,
0.010817009024322033,
0.010155991651117802,
-0.00005985659663565457,
0.0329529270529747,
0.030783088877797127,
0.040035467594861984,
0.016240881755948067,
0.004432764369994402,
-0.004409899935126305,
-0.038824450224637985,
0.016803590580821037,
0.004252234473824501,
0.016185497865080833,
0.002725862432271242,
0.04143623635172844,
-0.023534003645181656,
0.020576758310198784,
-0.009263093583285809,
-0.016949281096458435,
0.029660658910870552,
0.027372151613235474,
-0.008550358936190605,
-0.00872380193322897,
0.024855569005012512,
-0.0039674448780715466,
0.0032412896398454905,
0.00999598577618599,
-0.005784590262919664,
0.05920280143618584,
0.008008413016796112,
0.07939253747463226,
0.03588595241308212,
0.03528778254985809,
-0.01668388396501541,
0.007214365527033806,
-0.007983136922121048,
-0.01847948133945465,
0.01578463427722454,
0.03643050789833069,
-0.020637784153223038,
-0.00027136955759488046,
0.04598066583275795,
0.05401710048317909,
-0.04163093492388725,
0.0033053760416805744,
0.04608200863003731,
-0.013665711507201195,
0.016948146745562553,
0.011067204177379608,
-0.04084675759077072,
0.030783826485276222,
-0.03538447991013527,
0.0729341208934784,
-0.0005025534192100167,
-0.023015553131699562,
0.027122071012854576,
0.0004583743866533041,
0.021470103412866592,
-0.020623816177248955,
-0.005201288033276796,
-0.030410928651690483,
0.000733563385438174,
-0.029137510806322098,
-0.0021910304203629494,
-0.06411426514387131,
-0.02972004935145378,
0.03250351548194885,
-0.007145886775106192,
0.011272666975855827,
-0.023275764659047127,
-0.04990709573030472,
-0.042032044380903244,
-0.024303453043103218,
-0.04951979219913483,
0.047036249190568924,
-0.012511647306382656,
-0.003741876222193241,
0.0234737079590559,
0.005931199062615633,
0.022032320499420166,
0.0252049770206213,
0.047289833426475525,
-0.04780340939760208,
0.04786388948559761,
-0.010232786647975445,
-0.011365688405930996,
-0.01505015417933464,
0.0009604818187654018,
0.10703744739294052,
0.012589857913553715,
-0.014688725583255291,
-0.03304519131779671,
0.021288396790623665,
-0.020216871052980423,
0.0328906774520874,
-0.0005937629612162709,
0.015635069459676743,
-0.013391032814979553,
0.03794345259666443,
0.012948419898748398,
0.022282816469669342,
0.012425719760358334,
-0.0275637898594141,
0.046787966042757034,
-0.025698741897940636,
-0.03162534907460213,
-0.02399570308625698,
0.019813481718301773,
-0.036762386560440063,
0.0127228619530797,
-0.021033011376857758,
0.006441668141633272,
-0.027981577441096306,
-0.0370866023004055,
-0.013168171979486942,
-0.0602693110704422,
-0.025185780599713326,
-0.01897135004401207,
-0.061907894909381866,
0.024058010429143906,
0.011783706955611706,
-0.02704562619328499,
-0.057684484869241714,
0.054414305835962296,
0.011846735142171383,
-0.019587500020861626,
0.031649090349674225,
0.02310405671596527,
0.012326356954872608,
0.018528535962104797,
0.011747770942747593,
0.014827937819063663,
-0.05751078948378563,
0.004521691240370274,
-0.02400737628340721,
0.03339188173413277,
-0.020651578903198242,
0.029817264527082443,
-0.025452667847275734,
-0.016685517504811287,
0.013855376280844212,
-0.06325670331716537,
0.017323322594165802,
-0.011015255935490131,
0.021206242963671684,
0.0055359723046422005,
-0.011924341320991516,
-0.007047669962048531,
0.008143127895891666,
-0.0021192743442952633,
-0.004030774813145399,
-0.018400561064481735,
0.011616451665759087,
0.03152952343225479,
0.03814142197370529,
0.039146941155195236,
-0.0430978387594223,
0.015682727098464966,
-0.009528121910989285,
-0.01871880702674389,
-0.04450816288590431,
0.01757224090397358,
0.03196683153510094,
-0.010416297242045403,
0.053431786596775055,
-0.006272176746279001,
0.008915074169635773,
-0.030083132907748222,
-0.05470274016261101,
0.013306683860719204,
-0.03126906976103783,
-0.03143499791622162,
-0.029830124229192734,
0.024849532172083855,
0.03558884561061859,
0.0484798364341259,
-0.03004974126815796,
-0.01924772560596466,
0.0010895924642682076,
0.017680129036307335,
0.009882085956633091,
-0.014375144615769386,
-0.04081707075238228,
0.017983244732022285,
-0.009108268655836582,
0.01570112258195877,
-0.014183937571942806,
0.008977670222520828,
0.04156941920518875,
0.0168638676404953,
0.00026475792401470244,
0.03620697557926178,
-0.0004099504731129855,
0.020022224634885788,
0.03898787125945091,
-0.0016508415574207902,
-0.0299778301268816,
0.04385317116975784,
-0.02244405634701252,
-0.03868748992681503,
-0.0003895896370522678,
-0.023824423551559448,
-0.018975049257278442,
-0.013806677423417568,
0.04773884266614914,
-0.01850152760744095,
0.011374054476618767,
-0.03877772390842438,
0.0322067067027092,
-0.026467030867934227,
0.016143541783094406,
-0.051064323633909225,
0.010416301898658276,
0.028437139466404915,
-0.020531436428427696,
-0.026772575452923775,
0.01979553885757923,
0.018384158611297607,
0.007530951872467995,
0.028654051944613457,
-0.004352339077740908,
0.011169747449457645,
0.00528593547642231,
0.0591985285282135,
-0.0009426738834008574,
0.05352300405502319,
-0.008360641077160835,
-0.004578591790050268,
0.051351286470890045,
-0.006203200202435255,
-0.011021452024579048,
0.02669323980808258,
-0.04137216880917549,
0.023273395374417305,
0.03700660914182663,
-0.028251836076378822,
0.01338739413768053,
0.018154850229620934,
-0.014602141454815865,
-0.0015057830605655909,
-0.00624120095744729,
-0.018079355359077454,
-0.009017352014780045,
-0.0023839601781219244,
0.03826507180929184,
-0.03636942803859711,
-0.03875264525413513,
0.04576685652136803,
0.01528798695653677,
-0.01470372173935175,
0.001565549406222999,
0.012323333881795406,
0.007709250319749117,
-0.006431634537875652,
0.046894222497940063,
0.017192596569657326,
0.034970879554748535,
0.00711081875488162,
-0.047361671924591064,
0.03695803880691528,
0.026306068524718285,
-0.013112451881170273,
-0.08189301937818527,
-0.018291978165507317,
-0.002151471097022295,
-0.0020230470690876245,
0.02341541461646557,
0.0064688618294894695,
-0.0031396388076245785,
0.0490148700773716,
-0.10412409156560898,
-0.005183575674891472,
-0.04068606719374657,
-0.0005336313042789698,
0.0009972397238016129,
0.016346193850040436,
0.010519053786993027,
0.08330614864826202,
0.0002173286338802427,
0.028041036799550056,
0.01686868630349636,
-0.003919048234820366,
-0.011521956883370876,
-0.027564166113734245,
-0.01372828334569931,
0.028485126793384552,
-0.034518465399742126,
-0.023818880319595337,
0.06423378735780716,
-0.02258322574198246,
-0.029151123017072678,
0.03287892043590546,
-0.011921826750040054,
0.02198363095521927,
-0.009788833558559418,
0.0027333234902471304,
-0.0004957609344273806,
0.00843084417283535,
0.003362898947671056,
-0.00921423826366663,
-0.028734588995575905,
0.03358571603894234,
0.009400186128914356,
0.07259238511323929,
-0.02069409191608429,
-0.026657966896891594,
-0.012217819690704346,
-0.07374771684408188,
-0.020718161016702652,
-0.017944157123565674,
-0.033430811017751694,
0.010240726172924042,
-0.008921080268919468,
0.03576352447271347,
-0.04050843417644501,
-0.02328183688223362,
0.014591433107852936,
-0.05383821204304695,
0.00579935684800148,
0.012120798230171204,
0.00681715365499258,
-0.018699394538998604,
0.01412088330835104,
0.03442663699388504,
-0.021277988329529762,
0.0454663448035717,
-0.01728431135416031,
-0.010389729402959347,
-0.07376550883054733,
-0.01203102432191372,
0.03394642099738121,
-0.03389483690261841,
-0.0067418357357382774,
-0.02909773774445057,
-0.031654637306928635,
0.018370939418673515,
0.01986255683004856,
0.010801369324326515,
0.0063105919398367405,
-0.030174827203154564,
-0.032022736966609955,
-0.06541658937931061,
0.04689374938607216,
0.009221608750522137,
-0.0009126673103310168,
-0.037013985216617584,
-0.016808519139885902,
0.0057408506982028484,
0.0119656752794981,
0.04905132204294205,
0.02364513650536537,
0.0027857234235852957,
0.0188494473695755,
-0.01478385180234909,
0.028946498408913612,
-0.03383813425898552,
0.004847719334065914,
-0.012935330159962177,
-0.044816989451646805,
0.03832780197262764,
-0.044789869338274,
-0.057152848690748215,
0.00301109766587615,
0.03823252394795418,
-0.00258159963414073,
0.04019753262400627,
-0.007222010754048824,
-0.03627249598503113,
0.06242049112915993,
0.0274849534034729,
0.0064338864758610725,
0.053620681166648865,
0.0021616860758513212,
0.0062378994189202785,
0.07240085303783417,
-0.030545342713594437,
-0.026075169444084167,
0.02118002250790596,
-0.050987355411052704,
-0.007727860938757658,
-0.008755362592637539,
-0.021923858672380447,
0.052660100162029266,
-0.036955833435058594,
0.018831629306077957,
0.04890825226902962,
-0.0471898689866066,
-0.005433474667370319,
0.03764507919549942,
0.034046199172735214,
0.012700418941676617,
-0.0163282323628664,
0.032478343695402145,
0.015171668492257595,
-0.04565059393644333,
0.010899573564529419,
0.042709264904260635,
0.04494955763220787,
0.006466972175985575,
0.00154741236474365,
0.040277544409036636,
0.011066161096096039,
0.029950181022286415,
0.007253016345202923,
0.046117037534713745,
-0.017051352187991142,
-0.016734402626752853,
0.01294752862304449,
-0.006115742959082127,
0.0122156273573637,
0.03543820604681969,
-0.03234611824154854,
0.06619811803102493,
0.0030608063098043203,
-0.0019114138558506966,
-0.008212285116314888,
0.029230760410428047,
-0.011104538105428219,
-0.008460051380097866,
0.019877562299370766,
0.021524764597415924,
-0.011767697520554066,
-0.011928272433578968,
0.0011018321383744478,
-0.0065911272540688515,
0.02458486147224903,
0.00567867886275053,
0.00693557457998395,
0.009201128967106342,
0.02942216955125332,
-0.01623503491282463,
-0.017015380784869194,
-0.038449835032224655,
-0.0017400986980646849,
0.04546147212386131,
-0.0032181960996240377,
0.018302222713828087,
0.0134165333583951,
-0.01052577793598175,
-0.03922833129763603,
0.017952946946024895,
-0.07461940497159958,
-0.013481734320521355,
-0.021968746557831764,
0.06048627197742462,
-0.0004598199448082596,
-0.005560796242207289
] |
<p>Using a bit of classical reasoning I'm imagining black hole formation to be much like an ice skater pulling in her arms:</p>
<p><img src="http://i.stack.imgur.com/9fiOU.png" alt="skater pulls in her arms to increase angular velocity"></p>
<p>Now, the size difference between a star and its black hole can't even be effectively captured in an image. The black hole for our sun would be much less than a pixel in this image:</p>
<p><img src="http://i.stack.imgur.com/XoKDr.png" alt="size comparison of our sun and planets"></p>
<p>That suggests to me that even a very slowly rotating stars would have much more angular momentum than could be supported by their resulting black holes. I haven't done the calculation because I don't really understand the <a href="http://en.wikipedia.org/wiki/Kerr_metric">Kerr metric</a> but even with a bunch of classical hand-waving I'd think that just about every black hole formed in a stellar-collapse would be spinning maximally.</p>
<p>So my question is, do we expect nearly all black holes to be spinning maximally? If so, (roughly) how much angular momentum is lost because the star had much more than the black hole could support? And, how is all of this extra angular momentum shed during collapse? Is it just in the form of tons of matter being ejected until the the angular momentum is low enough to allow for the formation of a Kerr black hole?</p>
| 10,674 |
[
-0.05306529998779297,
-0.030112363398075104,
-0.031048649922013283,
-0.022128412500023842,
0.051081910729408264,
-0.007345134858042002,
-0.05336412414908409,
-0.034317728132009506,
-0.03936828672885895,
-0.03421842306852341,
0.0073716952465474606,
0.0144316665828228,
0.04189823567867279,
0.022730890661478043,
-0.01756368577480316,
0.00046449474757537246,
-0.026742523536086082,
-0.013649672269821167,
0.004097549710422754,
-0.01615021750330925,
-0.015308554284274578,
0.00886674877256155,
-0.016647333279252052,
0.008832773193717003,
-0.035145197063684464,
0.011707102879881859,
0.023612074553966522,
0.0015181833878159523,
0.04000748693943024,
0.06018573418259621,
-0.004688020329922438,
-0.007293532602488995,
-0.00005068456448498182,
0.04125845432281494,
0.04216580092906952,
0.005137019325047731,
-0.010461652651429176,
-0.01539313979446888,
-0.022506285458803177,
0.03909888491034508,
-0.05429791659116745,
-0.0020588552579283714,
-0.05174499377608299,
0.011833235621452332,
-0.022188380360603333,
0.010578187182545662,
-0.01697358302772045,
-0.00021938473219051957,
0.06003961339592934,
-0.058179330080747604,
0.053106773644685745,
0.011568308807909489,
0.03632184863090515,
0.002137505915015936,
0.006169130560010672,
-0.0077223218977451324,
0.12906134128570557,
0.04978181794285774,
-0.042376432567834854,
-0.03670346364378929,
-0.027079841122031212,
0.008279929868876934,
-0.03405355289578438,
-0.018052196130156517,
0.012151200324296951,
0.06498900055885315,
0.006173867266625166,
-0.012000312097370625,
0.057760804891586304,
0.013023901730775833,
0.010593526065349579,
-0.0035798661410808563,
0.016116684302687645,
0.015509352087974548,
-0.036060672253370285,
-0.015688050538301468,
0.015625320374965668,
0.0017949080793187022,
0.04760090634226799,
0.03398752957582474,
-0.03606582432985306,
0.02206183597445488,
0.06028393656015396,
0.04239174351096153,
0.04090988263487816,
0.03390809893608093,
0.08420663326978683,
-0.019259389489889145,
0.029879041016101837,
0.04290667176246643,
0.0019232023041695356,
-0.006131183356046677,
0.023815680295228958,
-0.05930715054273605,
-0.03456983342766762,
-0.0018674221355468035,
0.014954782091081142,
0.07436192780733109,
-0.00299318740144372,
-0.0009240967920050025,
-0.004200467374175787,
0.0041162739507853985,
-0.007941951043903828,
0.06173205375671387,
0.028763582929968834,
0.007070812396705151,
-0.06045077368617058,
0.03401535004377365,
-0.05216661095619202,
-0.03392689302563667,
-0.038141898810863495,
0.033843744546175,
-0.03143428638577461,
-0.02313256449997425,
-0.008457586169242859,
-0.050880853086709976,
0.0005420686211436987,
-0.002574808429926634,
0.0485340878367424,
0.0834360346198082,
0.03330359235405922,
-0.013895917683839798,
0.014921562746167183,
-0.03606811910867691,
-0.036741409450769424,
0.06017952039837837,
0.04482808709144592,
-0.007857860997319221,
-0.04399577155709267,
-0.00683479942381382,
-0.010223906487226486,
0.01628430187702179,
0.0224288497120142,
0.008130957372486591,
0.018030596897006035,
-0.08064138144254684,
-0.1026654988527298,
-0.014040857553482056,
0.02256617695093155,
-0.009134487248957157,
-0.02873779647052288,
-0.09431714564561844,
0.0003447432245593518,
0.008208369836211205,
0.0950947105884552,
-0.0010842185001820326,
0.012863458134233952,
0.010440289974212646,
0.04143228381872177,
-0.015124687924981117,
-0.04222247004508972,
0.0354875884950161,
0.015122816897928715,
-0.027673862874507904,
-0.022990411147475243,
-0.07802923768758774,
0.02004557102918625,
0.02850532904267311,
0.0321306511759758,
-0.006358051206916571,
0.005192049313336611,
-0.03301525115966797,
0.010812858119606972,
0.013133700005710125,
0.011773943901062012,
-0.038338180631399155,
0.08485700190067291,
0.020975209772586823,
-0.014163348823785782,
0.026833312585949898,
-0.008165252394974232,
0.031482040882110596,
0.049512267112731934,
0.0053838156163692474,
0.040083300322294235,
-0.025019124150276184,
-0.0014373940648511052,
-0.025030825287103653,
-0.021058503538370132,
0.007855406031012535,
-0.012591776438057423,
-0.04757332056760788,
-0.022541861981153488,
-0.025348154827952385,
0.006671392358839512,
0.07615084946155548,
0.006061551161110401,
-0.02522929199039936,
-0.033584460616111755,
-0.028228364884853363,
-0.0007175799109973013,
-0.036924079060554504,
0.009522960521280766,
0.013069135136902332,
-0.006847735494375229,
0.005452428478747606,
0.030289901420474052,
0.04515999183058739,
-0.010849539190530777,
-0.049796782433986664,
0.03422832489013672,
0.046097446233034134,
-0.016087152063846588,
0.0016370557714253664,
-0.0009286412969231606,
0.06302735209465027,
0.00980471819639206,
-0.02606888860464096,
0.0025960856582969427,
0.033782124519348145,
-0.020985517650842667,
-0.004525993950664997,
0.0040617831982672215,
0.003050723113119602,
0.014833147637546062,
0.030640732496976852,
0.0438200943171978,
0.015640245750546455,
0.01848139986395836,
0.02845887467265129,
-0.0042286524549126625,
0.10453219711780548,
0.02670690417289734,
0.004817112814635038,
0.0022144876420497894,
0.04708530753850937,
0.013065710663795471,
-0.018700487911701202,
-0.006774925626814365,
-0.006286515388637781,
-0.03710475564002991,
0.04005998745560646,
0.026181912049651146,
0.035625845193862915,
-0.06667958199977875,
0.013890277594327927,
0.05801256746053696,
0.037314534187316895,
0.01487149577587843,
0.021350909024477005,
-0.03225508704781532,
0.00675157317891717,
-0.009456327185034752,
-0.020061209797859192,
0.010842780582606792,
0.01647971011698246,
0.025790294632315636,
0.0030147102661430836,
-0.01322659570723772,
0.017625177279114723,
-0.048781152814626694,
0.009230594150722027,
0.010758655145764351,
0.029262743890285492,
-0.019775010645389557,
-0.03514842689037323,
0.060889631509780884,
0.0009672927553765476,
0.0014940077671781182,
0.0350022129714489,
-0.008315489627420902,
0.017341282218694687,
-0.06403089314699173,
0.0015581370098516345,
-0.0002749082341324538,
-0.007059403229504824,
0.0030589187517762184,
-0.02822554111480713,
0.017425233498215675,
-0.04685698449611664,
-0.0003892761596944183,
-0.04228750243782997,
-0.015636036172509193,
-0.0163828507065773,
0.0365225151181221,
0.02238386683166027,
0.027640800923109055,
0.01981731690466404,
-0.01990608312189579,
-0.034100595861673355,
-0.010328011587262154,
-0.02361449971795082,
0.004508690908551216,
0.03208032622933388,
-0.0876711905002594,
0.02766512893140316,
-0.06704775243997574,
-0.017873937264084816,
0.02206195332109928,
-0.03128703683614731,
0.010475819930434227,
-0.010973070748150349,
-0.006647284142673016,
-0.014667618088424206,
0.0009315593633800745,
0.03281991928815842,
-0.012992284260690212,
-0.028356172144412994,
0.007951898500323296,
0.0435960553586483,
-0.01312394067645073,
-0.01137338113039732,
0.007113959640264511,
-0.040466390550136566,
-0.07423847913742065,
-0.013322555460035801,
0.009941614232957363,
0.015477071516215801,
-0.0334496796131134,
0.011337474919855595,
0.027488600462675095,
-0.02090267650783062,
-0.007831868715584278,
-0.03956972807645798,
-0.0437115877866745,
0.035685207694768906,
-0.022809157148003578,
0.023903196677565575,
-0.0010046977549791336,
-0.02605445869266987,
0.06313331425189972,
0.00018726804410107434,
-0.03486764058470726,
-0.042107727378606796,
0.026581313461065292,
-0.002885090885683894,
0.009610242210328579,
-0.003653438063338399,
0.003204639069736004,
0.017507830634713173,
-0.003770059673115611,
0.04230283573269844,
-0.012157263234257698,
-0.016215957701206207,
-0.010898202657699585,
-0.011675683781504631,
0.0026496839709579945,
-0.013547836802899837,
-0.012785254046320915,
0.02906511351466179,
0.021972348913550377,
-0.009792499244213104,
0.03460877761244774,
-0.019416814669966698,
0.058519601821899414,
0.0009047143976204097,
-0.062403447926044464,
0.038036711513996124,
-0.024300791323184967,
0.021074656397104263,
0.015905335545539856,
0.01773207262158394,
-0.033926405012607574,
-0.0033186525106430054,
0.0561603344976902,
0.013460012152791023,
0.06243002042174339,
0.01745295710861683,
0.011790735647082329,
-0.005285393446683884,
0.030895646661520004,
-0.020246488973498344,
0.009940368123352528,
-0.039236824959516525,
-0.020794790238142014,
0.04407273605465889,
-0.031754665076732635,
0.010968271642923355,
0.027374539524316788,
0.0165164265781641,
0.011398459784686565,
-0.016462383791804314,
-0.010078530758619308,
0.026225879788398743,
-0.06403449177742004,
-0.0036911643110215664,
-0.007131863385438919,
0.01698390580713749,
0.0008650189847685397,
0.052284445613622665,
0.023964986205101013,
0.014290694147348404,
0.002760733710601926,
-0.028600171208381653,
-0.09267127513885498,
0.014830616302788258,
-0.024070685729384422,
-0.03421758487820625,
0.020106852054595947,
-0.015600795857608318,
0.010980142280459404,
-0.009374293498694897,
0.002467102138325572,
-0.024320034310221672,
0.0008064277935773134,
-0.049231067299842834,
0.01836586929857731,
-0.01537212636321783,
-0.02681964635848999,
-0.018610799685120583,
0.05367600917816162,
0.05151420459151268,
-0.004630835726857185,
0.03992724046111107,
0.02961043082177639,
-0.024490585550665855,
-0.0138936135917902,
-0.008306981064379215,
0.02799086458981037,
-0.023851385340094566,
0.022990548983216286,
0.044209662824869156,
0.00599087867885828,
-0.028404509648680687,
-0.030567578971385956,
0.04511368274688721,
0.03904162719845772,
-0.0008412914467044175,
-0.028431754559278488,
-0.01393458154052496,
-0.056734323501586914,
0.0013807460200041533,
-0.011825625784695148,
0.06857000291347504,
0.008909880183637142,
-0.011263265274465084,
-0.006893744692206383,
-0.014498285949230194,
0.019263898953795433,
0.008851568214595318,
0.06172334402799606,
0.023926444351673126,
-0.01922810822725296,
-0.05438220500946045,
-0.04760737717151642,
0.0036389450542628765,
0.00989103689789772,
0.021954845637083054,
0.0048295073211193085,
-0.009828126057982445,
0.013554624281823635,
0.02801695466041565,
-0.015714293345808983,
-0.031861405819654465,
0.03140063211321831,
-0.022246258333325386,
0.03916458040475845,
-0.051245059818029404,
0.03653840720653534,
0.014335568062961102,
0.05762583762407303,
0.052751630544662476,
-0.0033353259786963463,
-0.015177383087575436,
-0.06070490926504135,
-0.041557006537914276,
0.03839648887515068,
0.019535383209586143,
0.005557520780712366,
-0.02104952186346054,
-0.05781926214694977,
0.0185181125998497,
0.04109218716621399,
-0.0332469679415226,
0.03156989440321922,
-0.00043824309250339866,
0.005181320942938328,
0.005406724754720926,
-0.03280485048890114,
0.0064660729840397835,
0.011451708152890205,
-0.04515127092599869,
0.018333302810788155,
-0.03874983638525009,
0.022985098883509636,
-0.0031761692371219397,
0.021896541118621826,
0.011012233793735504,
0.02217535302042961,
0.02113346755504608,
-0.05175197497010231,
-0.004511337727308273,
0.0016260149423033,
-0.04098055511713028,
-0.07272268831729889,
-0.0027626315131783485,
-0.02299629896879196,
-0.046393316239118576,
0.04811025410890579,
-0.05045066401362419,
-0.04438145086169243,
0.006746819242835045,
0.013253716751933098,
-0.025578951463103294,
0.020996933802962303,
-0.06732173264026642,
-0.0031098034232854843,
-0.00615285150706768,
-0.0030349434819072485,
0.04071689769625664,
0.026500830426812172,
-0.004674393218010664,
-0.004790561739355326,
-0.010076512582600117,
0.04748348146677017,
-0.011261132545769215,
-0.022566266357898712,
-0.04599839821457863,
0.021375318989157677,
-0.013017403893172741,
0.06270705908536911,
-0.030646486207842827,
0.008009858429431915,
0.011172703467309475,
-0.03254721313714981,
0.002966321771964431,
0.027224285528063774,
0.030202757567167282,
-0.003264032071456313,
0.007267973851412535,
0.03338044136762619,
0.019183838739991188,
0.010287175886332989,
0.020604882389307022,
0.010562904179096222,
-0.00935592781752348,
0.06037186458706856,
-0.01680000312626362,
0.01521939318627119,
-0.015698684379458427,
-0.017650537192821503,
0.0031407370697706938,
-0.03248590603470802,
0.03667202964425087,
-0.03784257918596268,
0.016906797885894775,
0.029496245086193085,
-0.05763230845332146,
-0.009823158383369446,
-0.04074455052614212,
-0.021873442456126213,
0.022665567696094513,
-0.036793190985918045,
0.0026041255332529545,
0.014820008538663387,
-0.00692334957420826,
-0.052613649517297745,
0.0017977975076064467,
0.038818277418613434,
0.040054865181446075,
0.0008910088217817247,
-0.007469170726835728,
0.004981339909136295,
-0.034181736409664154,
-0.030182629823684692,
0.004788158927112818,
0.019764240831136703,
-0.028203275054693222,
0.005349957849830389,
0.02219657599925995,
0.02030317671597004,
0.04960154369473457,
-0.03340470790863037,
-0.050599247217178345,
0.022105390205979347,
-0.022061822935938835,
0.011602545157074928,
-0.010835417546331882,
0.04781841114163399,
-0.03303563967347145,
-0.03854244574904442,
-0.04054011031985283,
-0.0029114456847310066,
0.012129750102758408,
0.028037600219249725,
0.02463170327246189,
0.013600457459688187,
-0.00785780418664217,
0.024455279111862183,
-0.02461259625852108,
0.0015347286825999618,
-0.030572064220905304,
0.014817523770034313,
0.010488961823284626,
-0.023912910372018814,
0.0014425076078623533,
-0.061593249440193176,
0.04643263667821884,
-0.0009206572431139648,
-0.007148080039769411,
0.0071790493093431,
0.01668630726635456,
0.015633845701813698,
-0.030488304793834686,
-0.008535136468708515,
-0.03465074673295021,
0.030961694195866585,
0.023497529327869415,
0.019375059753656387,
0.01801472157239914,
0.019600164145231247,
0.0038723531179130077,
-0.04061860963702202,
-0.024764662608504295,
0.05122998356819153,
0.08165194094181061,
0.006860331166535616,
0.03537385165691376,
0.020256908610463142,
0.006895116064697504,
-0.027336232364177704,
-0.058438997715711594,
0.013817613013088703,
0.028604771941900253,
0.010887538082897663,
-0.0022544600069522858,
-0.01917693391442299,
0.002578199375420809,
0.05967842787504196,
0.0142554035410285,
-0.0017262531910091639,
0.022949038073420525,
0.020358620211482048,
0.00014431611634790897,
-0.007333193439990282,
0.0000662404127069749,
-0.01614299789071083,
0.030458873137831688,
-0.008927342481911182,
0.06343332678079605,
-0.006541549228131771,
0.002789499005302787,
0.0016596255591139197,
0.0025717115495353937,
0.04637012258172035,
-0.029024412855505943,
-0.03682813048362732,
-0.02440207079052925,
-0.004569887649267912,
0.0020172412041574717,
0.007087961304932833,
-0.00962691567838192,
-0.003581160446628928,
0.007137177046388388,
0.0024191613774746656,
0.015078917145729065,
-0.006058319006115198,
-0.07235325872898102,
-0.02276277355849743,
-0.046346891671419144,
-0.06395389139652252,
0.0456794835627079,
0.048852045089006424,
-0.01694096438586712,
0.03790803253650665,
-0.019647512584924698,
0.02675876021385193,
0.009512155316770077,
0.0489235520362854,
-0.0017576140817254782,
0.07462874054908752,
0.007254941388964653,
0.01297349389642477,
-0.03916744887828827,
0.010794045403599739,
0.10977531224489212,
0.040536947548389435,
0.02760349214076996,
-0.04229361563920975,
-0.02551877871155739,
-0.018311062827706337,
0.029580000787973404,
-0.02836565300822258,
0.028028737753629684,
-0.012504269368946552,
0.0007220334373414516,
-0.004035656806081533,
0.0471373088657856,
-0.005380454007536173,
-0.0407710000872612,
0.022019606083631516,
-0.018070774152874947,
0.012410474941134453,
-0.033124350011348724,
0.01305009052157402,
0.025410689413547516,
0.009975481778383255,
-0.0661267340183258,
0.025171570479869843,
0.017956392839550972,
-0.018550675362348557,
-0.007470501121133566,
-0.007637412752956152,
-0.018299924209713936,
-0.01138252578675747,
-0.058222491294145584,
0.003132864600047469,
0.01918514259159565,
-0.03648056462407112,
-0.027132397517561913,
0.02138717845082283,
0.019426578655838966,
-0.025919796898961067,
0.012943330220878124,
0.03972722962498665,
-0.014716111123561859,
0.04542951658368111,
0.024645725265145302,
0.024299196898937225,
-0.019920559599995613,
0.00913094449788332,
-0.04836944863200188,
0.07012931257486343,
-0.018210439011454582,
0.013782248832285404,
-0.009254436008632183,
-0.004778984934091568,
0.007644094992429018,
-0.04623794183135033,
0.01537311915308237,
-0.023167593404650688,
-0.006834034342318773,
-0.01622890867292881,
-0.05022391676902771,
-0.009426550008356571,
0.0007604752318002284,
0.03938165679574013,
0.03612032160162926,
-0.0191916786134243,
0.01180404331535101,
-0.007078035268932581,
-0.033334653824567795,
0.04089156538248062,
0.016032269224524498,
-0.01656142808496952,
-0.032191626727581024,
-0.013096773065626621,
-0.038440123200416565,
0.008036993443965912,
0.027287552133202553,
-0.010516547597944736,
0.027467167004942894,
0.022225549444556236,
0.011085898615419865,
-0.0015485796611756086,
-0.0389334075152874,
0.00997167732566595,
-0.02217605523765087,
-0.06086663901805878,
-0.006010669749230146,
0.026427576318383217,
0.031947094947099686,
0.01909697614610195,
-0.03529918193817139,
-0.0001866594684543088,
-0.010434329509735107,
0.03937852382659912,
0.027007505297660828,
-0.007734519895166159,
0.005259739235043526,
-0.018551072105765343,
-0.014680012129247189,
-0.01858857460319996,
-0.03335351496934891,
0.012926851399242878,
0.02821575477719307,
0.0005558355478569865,
0.04212130606174469,
0.030949626117944717,
0.008489685133099556,
0.012062889523804188,
0.006514397915452719,
-0.04507013037800789,
0.031013261526823044,
-0.014709734357893467,
-0.018660686910152435,
-0.05917336046695709,
-0.015501626767218113,
-0.021650979295372963,
-0.01135003287345171,
-0.03662261366844177,
0.0212173480540514,
-0.03186960890889168,
0.061633430421352386,
-0.028686903417110443,
0.034044135361909866,
-0.045633427798748016,
0.01203488651663065,
-0.03322510048747063,
0.048760540783405304,
0.020601650699973106,
-0.04372623562812805,
-0.000007793204531481024,
0.02069728448987007,
0.03570590913295746,
-0.044578667730093,
-0.0056970566511154175,
0.02146109752357006,
-0.02311219833791256,
0.007813324220478535,
0.03361614793539047,
-0.025211676955223083,
0.02021430991590023,
0.015372507274150848,
-0.009302658028900623,
0.03570680692791939,
-0.027980482205748558,
-0.03977324441075325,
0.014645266346633434,
-0.04804213345050812,
0.007744533009827137,
0.004098731093108654,
-0.03740714117884636,
-0.02365468442440033,
0.06881851702928543,
-0.0008343873196281493,
-0.050884947180747986,
0.022650862112641335,
0.0016262279823422432,
-0.018935751169919968,
0.0030660568736493587,
0.023508593440055847,
-0.03016314096748829,
-0.005995898973196745,
0.06618353724479675,
0.007493187207728624,
-0.04650600254535675,
-0.03709294646978378,
0.0039224098436534405,
0.005275850649923086,
0.02456291764974594,
0.026965949684381485,
-0.011316118761897087,
0.03827003017067909,
0.042746324092149734,
-0.051925864070653915,
0.07125908136367798,
0.024090087041258812,
0.020399590954184532,
-0.11130893975496292,
-0.00298604229465127,
-0.022206557914614677,
0.010698920115828514,
0.019562678411602974,
-0.035392433404922485,
-0.0018525971099734306,
0.03952161595225334,
-0.09350533038377762,
0.004376938566565514,
-0.024960551410913467,
0.012386837974190712,
-0.033667728304862976,
-0.023478850722312927,
-0.002144735539332032,
0.02321208268404007,
0.039121005684137344,
0.039722852408885956,
0.003953589592128992,
-0.0011140399146825075,
-0.031660374253988266,
-0.012009498663246632,
-0.02004431188106537,
0.01695173978805542,
-0.008011510595679283,
-0.012182229198515415,
0.09057075530290604,
-0.011298577301204205,
-0.050626955926418304,
0.045674510300159454,
0.006929508876055479,
0.006946175824850798,
0.005344458855688572,
-0.028278810903429985,
0.002550102537497878,
0.008616592735052109,
0.00803805235773325,
-0.032682888209819794,
0.02577500231564045,
0.01951165497303009,
0.005420860834419727,
0.03564959019422531,
-0.005024748854339123,
0.037264954298734665,
0.022731129080057144,
-0.06333881616592407,
-0.011345475912094116,
0.0020327528472989798,
-0.015020620077848434,
-0.006580465007573366,
-0.016577625647187233,
0.00751936249434948,
0.008562327362596989,
-0.008833382278680801,
0.020063601434230804,
-0.04435352236032486,
0.013288323767483234,
0.004915769211947918,
0.025459304451942444,
0.018082518130540848,
0.03138438239693642,
0.00972303282469511,
0.02263220027089119,
-0.035709187388420105,
-0.03805551305413246,
-0.0015811951598152518,
-0.028171155601739883,
0.011266838759183884,
-0.00341320619918406,
-0.03120834194123745,
-0.004766664933413267,
-0.05497194081544876,
-0.022014839574694633,
0.0445549339056015,
0.002759296679869294,
0.02054605260491371,
0.01801498793065548,
-0.05344273895025253,
-0.03179475665092468,
-0.09263009577989578,
0.0026019406504929066,
-0.027682282030582428,
0.023920482024550438,
-0.04875890910625458,
-0.03602280840277672,
0.019242439419031143,
0.006589863914996386,
0.030926112085580826,
0.016372764483094215,
0.0013790138764306903,
0.05925948917865753,
-0.030455084517598152,
0.011264024302363396,
-0.05946768447756767,
0.005664461757987738,
-0.011743748560547829,
-0.008599767461419106,
0.025336991995573044,
-0.004939816892147064,
0.002034588949754834,
-0.0036049254704266787,
0.06499367207288742,
0.00026212434750050306,
0.034291334450244904,
0.02599363960325718,
-0.008160172030329704,
0.059143420308828354,
0.011066184379160404,
0.015595597214996815,
0.07467884570360184,
0.038892216980457306,
-0.009412243030965328,
0.04064062982797623,
-0.01729235053062439,
-0.0020427389536052942,
0.02339375950396061,
-0.0015210479032248259,
0.015228573232889175,
-0.028404047712683678,
-0.030785830691456795,
0.0061447410844266415,
-0.039014726877212524,
0.004943592008203268,
0.022575220093131065,
-0.012331533245742321,
-0.029341286048293114,
0.01632543094456196,
-0.009937727823853493,
0.02168450877070427,
-0.022253675386309624,
-0.014402261935174465,
0.009135275147855282,
0.0044698165729641914,
-0.05028914287686348,
0.02822696603834629,
0.035224877297878265,
0.02616126649081707,
-0.004188284743577242,
0.004905762616544962,
-0.0020812752190977335,
0.013952440582215786,
-0.014305123127996922,
0.07155430316925049,
-0.04620467498898506,
-0.037072453647851944,
0.0014397634658962488,
0.0026369974948465824,
-0.004035660065710545,
0.028150631114840508,
-0.02704336680471897,
0.05419769138097763,
0.018241217359900475,
0.00827365554869175,
-0.013417499139904976,
-0.022437917068600655,
-0.003275369992479682,
0.03206486999988556,
-0.0017612639348953962,
0.04088149219751358,
-0.015338532626628876,
-0.012944865971803665,
-0.004059371072798967,
-0.005917247850447893,
0.0479373000562191,
0.0016226532170549035,
0.009116442874073982,
0.002166156889870763,
-0.011460789479315281,
0.025000251829624176,
-0.022001417353749275,
-0.03520911559462547,
-0.04005555063486099,
0.028945429250597954,
0.02122090756893158,
-0.004745858255773783,
0.007517662830650806,
-0.015350584872066975,
-0.02003674954175949,
0.01923513598740101,
-0.072316475212574,
-0.019477011635899544,
-0.004547753371298313,
0.04781930893659592,
-0.0025042977649718523,
-0.032029733061790466
] |
<p>What does exactly means "Small molecules may appear as solid, liquid, and gaseous phases without losing their molecular integrity"?, </p>
<p>I can't image how just a molecule can be a gas, liquid or solid. Or in fact the previous phrase refers to the state of aggregations of those small molecules?</p>
<p>My source is this article:</p>
<p><a href="http://www.sciencedirect.com/science/article/pii/S004060319900252X" rel="nofollow">B Wunderlich, A classification of molecules, phases, and transitions as recognized by thermal analysis, Thermochimica Acta, Volumes 340–341, 14 December 1999, Pages 37-52</a></p>
<p>If you could suggest me a reference that extend the previous one to more modern states of matter like Bose-Einstein condensates, i would really appreciate it.</p>
| 10,675 |
[
-0.025157438591122627,
-0.0102846659719944,
0.021397963166236877,
-0.0402284674346447,
0.04126165062189102,
0.0025635429192334414,
-0.03005285933613777,
-0.020786555483937263,
0.006828880403190851,
-0.035558462142944336,
0.051106538623571396,
0.02297816425561905,
0.042570747435092926,
0.006518977228552103,
-0.03254026174545288,
0.003743888111785054,
0.008248417638242245,
-0.02659899741411209,
-0.021018430590629578,
-0.016487648710608482,
0.033233821392059326,
0.0015654136659577489,
0.013982956297695637,
-0.005438521038740873,
-0.022772161290049553,
0.05739821866154671,
-0.030692221596837044,
0.006132226437330246,
0.0462174192070961,
0.013226592913269997,
-0.028068123385310173,
-0.011403891257941723,
0.015031315386295319,
-0.03374432399868965,
0.010125599801540375,
-0.0024313773028552532,
-0.024041369557380676,
-0.0205231960862875,
0.00380229321308434,
-0.006278378888964653,
-0.06678526103496552,
-0.02036847546696663,
-0.005935295484960079,
0.051127661019563675,
-0.043371040374040604,
-0.0072657461278140545,
0.024303380399942398,
-0.03933560848236084,
0.013015971519052982,
-0.053856752812862396,
0.05514201149344444,
0.017938069999217987,
0.029585596174001694,
-0.010331434197723866,
0.00850069709122181,
0.022246122360229492,
0.05776415020227432,
0.09184396266937256,
-0.030331403017044067,
-0.05541157349944115,
-0.02436477690935135,
-0.028469158336520195,
0.005362986586987972,
-0.000852252240292728,
-0.04055172950029373,
0.018336784094572067,
-0.0072827935218811035,
-0.05275479331612587,
0.02834034524857998,
0.015387656167149544,
0.00848018005490303,
-0.02803618088364601,
0.022956298664212227,
-0.0009695234475657344,
0.03584964573383331,
-0.0037654780317097902,
0.020425327122211456,
0.010862162336707115,
0.0051843393594026566,
0.04328593984246254,
0.011877227574586868,
0.025644250214099884,
0.014834878034889698,
-0.016165083274245262,
-0.029141739010810852,
-0.0024923356249928474,
0.10068874806165695,
-0.03705374151468277,
0.037630993872880936,
0.015873439610004425,
0.01625608466565609,
0.03350258991122246,
0.049234792590141296,
0.02268422581255436,
-0.005440338049083948,
-0.02370794117450714,
-0.009256104938685894,
0.04240084066987038,
-0.061421770602464676,
-0.010860058479011059,
-0.00013612324255518615,
0.018172843381762505,
0.05530958250164986,
0.05901043862104416,
-0.026192042976617813,
-0.02263777330517769,
-0.04602216184139252,
-0.0036164179909974337,
0.002101435326039791,
-0.014027247205376625,
-0.005093915853649378,
-0.006558608263731003,
0.004905183799564838,
0.0015437069814652205,
-0.02526226080954075,
0.004017357248812914,
-0.013255336321890354,
0.013103997334837914,
0.030512021854519844,
0.07833223789930344,
0.030272534117102623,
-0.025055192410945892,
0.015279052779078484,
0.010967902839183807,
-0.10769970715045929,
0.002077364129945636,
0.03585118427872658,
0.003033274784684181,
-0.055310193449258804,
0.03566047549247742,
0.001765175024047494,
0.021547865122556686,
0.04442296549677849,
-0.00008226049249060452,
0.028947142884135246,
-0.02892196550965309,
-0.08375203609466553,
-0.0316326841711998,
0.02897210419178009,
0.014851602725684643,
-0.010656611993908882,
-0.07625043392181396,
0.03656696155667305,
0.031138520687818527,
0.07938265055418015,
0.013013351708650589,
0.01153953094035387,
-0.008983077481389046,
0.013611678965389729,
0.02758587710559368,
-0.010357885621488094,
-0.013076822273433208,
-0.0013213438214734197,
-0.035041943192481995,
0.015499580651521683,
-0.04823357239365578,
0.048320524394512177,
0.08154602348804474,
0.009657029062509537,
-0.039550524204969406,
0.036039020866155624,
-0.01729326881468296,
0.004379414953291416,
0.004567362833768129,
0.006051427684724331,
-0.0025075541343539953,
0.04097311943769455,
0.0001329842780251056,
0.013194934464991093,
0.00037229288136586547,
0.03919772431254387,
0.014179019257426262,
-0.0320015549659729,
0.03794262930750847,
0.020523790270090103,
-0.01860162429511547,
-0.007051085587590933,
-0.004180291201919317,
0.006262377370148897,
0.024935446679592133,
-0.06256302446126938,
-0.008480856195092201,
0.0007625644793733954,
0.03561563789844513,
-0.036444537341594696,
0.004210342653095722,
-0.0012998894089832902,
0.0024724206887185574,
0.010087371803820133,
-0.0715889260172844,
-0.05374601110816002,
-0.07659684121608734,
-0.01316849049180746,
-0.03844568133354187,
-0.013082647696137428,
0.061843764036893845,
0.0341423898935318,
0.00034164838143624365,
0.0019194643246009946,
-0.012385744601488113,
-0.04962754249572754,
-0.005778591614216566,
0.016449881717562675,
-0.01209378894418478,
0.03897276148200035,
0.028743918985128403,
0.032833587378263474,
-0.02031208574771881,
-0.015189236961305141,
-0.011554431170225143,
-0.03558407723903656,
0.011009549722075462,
-0.018139256164431572,
0.03977527469396591,
-0.045817211270332336,
-0.04351802542805672,
0.0066041480749845505,
0.011078913696110249,
-0.01708126626908779,
0.04235193878412247,
-0.03896546736359596,
0.03209082409739494,
0.03853796049952507,
0.024267885833978653,
-0.024267666041851044,
0.048725444823503494,
0.033014144748449326,
0.0048554339446127415,
-0.020491980016231537,
-0.00516466936096549,
-0.06943552941083908,
-0.01884804293513298,
0.04354223981499672,
0.07733640819787979,
-0.057099778205156326,
-0.02418122999370098,
0.02672148309648037,
0.03291553631424904,
0.027420496568083763,
0.0220197644084692,
-0.019680699333548546,
-0.030590608716011047,
0.03072216920554638,
-0.01069228071719408,
0.05755305662751198,
0.01841740682721138,
-0.00756887998431921,
0.02977566421031952,
0.048044584691524506,
-0.000013860852050129324,
-0.025931166484951973,
0.04273606464266777,
-0.010388868860900402,
-0.00369685678742826,
0.006375649943947792,
-0.04304584488272667,
0.032322000712156296,
-0.002589983632788062,
0.01459230575710535,
-0.005255818832665682,
-0.002629000460729003,
-0.0015040492871776223,
-0.0677432045340538,
-0.013801103457808495,
0.013709837570786476,
0.021217847242951393,
-0.0585717149078846,
-0.029014762490987778,
-0.009209958836436272,
-0.06254622340202332,
-0.012337909080088139,
-0.018366528674960136,
0.008313610218465328,
-0.028144577518105507,
0.016917670145630836,
0.020514624193310738,
0.00175055384170264,
0.014275453984737396,
-0.03180215507745743,
-0.044612474739551544,
-0.027723681181669235,
-0.008041338995099068,
-0.0001496940094511956,
0.04334045201539993,
-0.05487634614109993,
0.01432135608047247,
-0.013756981119513512,
-0.039046723395586014,
0.0539584681391716,
-0.031512998044490814,
-0.01375314686447382,
-0.003580660093575716,
0.004585484974086285,
-0.066899374127388,
-0.014229497872292995,
0.018803615123033524,
-0.006138947792351246,
-0.02953610196709633,
-0.0036161853931844234,
0.031077558174729347,
-0.008195861242711544,
-0.01259683258831501,
0.02890009433031082,
-0.02333025448024273,
-0.04590088501572609,
-0.02013806812465191,
-0.0358818955719471,
0.0011359270429238677,
-0.010544216260313988,
0.0132392393425107,
0.027952339500188828,
-0.04524561017751694,
-0.03795953840017319,
-0.059765543788671494,
-0.0704384371638298,
0.017412692308425903,
-0.019948218017816544,
0.06227033957839012,
0.013107012026011944,
-0.002256385050714016,
0.07476769387722015,
-0.0036601207684725523,
-0.07645606249570847,
-0.0046082474291324615,
0.014997643418610096,
-0.019217723980545998,
-0.018123295158147812,
-0.014973371289670467,
0.026904979720711708,
0.022214651107788086,
0.0006031527882441878,
0.0361139215528965,
0.05158291384577751,
0.032293934375047684,
-0.04135584831237793,
-0.03430188074707985,
0.030086616054177284,
0.0024299435317516327,
-0.0015428736805915833,
-0.0037796690594404936,
0.022368067875504494,
-0.030129628255963326,
0.011936560273170471,
-0.03413577005267143,
0.03912991285324097,
0.051475800573825836,
-0.0866003930568695,
0.05684398114681244,
-0.010171182453632355,
-0.004733344539999962,
-0.027685703709721565,
0.03298744186758995,
0.012217013165354729,
-0.01801459677517414,
0.03521670773625374,
0.026373637840151787,
0.04561800882220268,
0.00953132938593626,
-0.02207014709711075,
0.039649005979299545,
0.02770436927676201,
0.001411777688190341,
0.012374119833111763,
0.0348128117620945,
-0.01377012673765421,
0.012554246932268143,
-0.026561548933386803,
-0.011324203573167324,
0.051587533205747604,
0.0005332163418643177,
0.032784461975097656,
-0.009666096419095993,
-0.020441077649593353,
-0.0006015881081111729,
-0.05014818534255028,
0.005394813138991594,
0.031285129487514496,
0.03368569165468216,
0.0007671100320294499,
0.038504187017679214,
0.013153865933418274,
0.0040206084959208965,
-0.011917855590581894,
-0.003947617951780558,
-0.06807804107666016,
0.0009479089640080929,
-0.004820114001631737,
0.02836131677031517,
-0.008282446302473545,
0.03007408417761326,
-0.011848775669932365,
-0.04271497204899788,
-0.046586040407419205,
-0.021280033513903618,
0.013867386616766453,
-0.06410396099090576,
-0.0008748613181523979,
-0.03337301313877106,
-0.001420282875187695,
0.006860658060759306,
0.03037167526781559,
0.04484567046165466,
-0.012652087025344372,
0.027661999687552452,
0.03548821434378624,
-0.004652326460927725,
-0.010601845569908619,
-0.013299588114023209,
0.016877638176083565,
0.022001836448907852,
0.05084936320781708,
0.01652037538588047,
0.026513969525694847,
-0.013817395083606243,
-0.0076088570058345795,
0.019516395404934883,
0.029978511855006218,
-0.016789212822914124,
-0.005852628033608198,
-0.023926058784127235,
-0.04185833781957626,
-0.00759700033813715,
0.020437853410840034,
0.0064056189730763435,
0.02067171409726143,
-0.001004180172458291,
-0.02350303903222084,
0.0032552059274166822,
-0.01723460480570793,
0.0690014585852623,
0.045673392713069916,
0.0228368379175663,
-0.024824121966958046,
-0.04037809744477272,
-0.03688477352261543,
-0.013381442055106163,
0.01941472291946411,
0.06686293333768845,
0.011453451588749886,
-0.021942751482129097,
0.0024280070792883635,
-0.03207698464393616,
0.017255302518606186,
-0.031097235158085823,
-0.056061167269945145,
-0.01275864988565445,
-0.006405954714864492,
-0.02743547037243843,
-0.014209062792360783,
0.0025084237568080425,
0.05078904703259468,
0.022485079243779182,
0.007915857248008251,
-0.018396100029349327,
-0.07957343757152557,
0.018455693498253822,
0.022777127102017403,
0.026591869071125984,
0.0015845006564632058,
-0.014118288643658161,
-0.06384669989347458,
-0.009997512213885784,
0.02494477853178978,
-0.015345009975135326,
0.04234418645501137,
-0.010789048857986927,
-0.01980847492814064,
-0.0026370270643383265,
-0.006484215147793293,
0.045649204403162,
-0.02931957319378853,
0.005698017776012421,
0.025321336463093758,
-0.03998040407896042,
-0.009620901197195053,
-0.018221648409962654,
-0.010342401452362537,
-0.015681017190217972,
0.045617446303367615,
-0.036107100546360016,
0.017451394349336624,
0.01202427688986063,
0.005050538573414087,
-0.05895444378256798,
-0.06877533346414566,
0.0017277576262131333,
0.00408032676205039,
0.010278614237904549,
0.029542243108153343,
-0.04257015883922577,
-0.06763629615306854,
0.001341917086392641,
0.02974911406636238,
-0.02895703911781311,
-0.018316112458705902,
-0.032832205295562744,
0.07199160754680634,
-0.0004634989018086344,
-0.01371894683688879,
0.048384517431259155,
0.008403063751757145,
0.0065515125170350075,
0.021126575767993927,
-0.05194368585944176,
0.04407601058483124,
-0.046809613704681396,
0.010145907290279865,
-0.0820690244436264,
0.004823735449463129,
-0.033675603568553925,
0.039960701018571854,
-0.019562534987926483,
-0.0005351424915716052,
0.02381081134080887,
-0.026499195024371147,
0.029355479404330254,
0.024804269894957542,
-0.00622777221724391,
-0.002146962331607938,
-0.02519928477704525,
0.03459380194544792,
0.00417135376483202,
0.015320954844355583,
0.02871810458600521,
-0.016255443915724754,
-0.02024206705391407,
0.03590831533074379,
-0.0004784995107911527,
0.031066905707120895,
-0.05547052249312401,
-0.01993146724998951,
0.010550351813435555,
-0.04410708323121071,
0.024497712031006813,
-0.0173804834485054,
0.029648834839463234,
0.0182331595569849,
-0.06809265166521072,
0.008468703366816044,
0.00039389519952237606,
-0.012923103757202625,
0.005108805373311043,
-0.036052312701940536,
0.023632284253835678,
0.016428835690021515,
0.005369506776332855,
-0.05940879136323929,
-0.07523646205663681,
0.02775486372411251,
0.025178750976920128,
-0.04537809267640114,
-0.023868100717663765,
0.04299972206354141,
-0.016548382118344307,
-0.022490549832582474,
0.015461305156350136,
0.029188107699155807,
-0.008173794485628605,
-0.027504006400704384,
0.047032978385686874,
0.05668888986110687,
0.03983767703175545,
0.012780183926224709,
-0.0005018798401579261,
-0.008449312299489975,
-0.009573671035468578,
-0.005336598958820105,
0.02833046205341816,
0.029245616868138313,
-0.025838514789938927,
-0.04154442250728607,
-0.009985036216676235,
-0.0059803929179906845,
0.029801253229379654,
-0.0006454194081015885,
-0.014306084252893925,
0.009419812820851803,
-0.03952686861157417,
-0.01374804973602295,
-0.010013042949140072,
0.009306897409260273,
0.011790907010436058,
0.0074598779901862144,
-0.000003949935944547178,
0.0000714836351107806,
0.030949091538786888,
-0.020180871710181236,
0.014372408390045166,
0.028315173462033272,
-0.0009133096900768578,
0.041425589472055435,
0.06879398971796036,
-0.0009160884656012058,
0.02131330408155918,
0.018723120912909508,
-0.05267658829689026,
0.05602598935365677,
0.0417686328291893,
0.008782037533819675,
0.012540812604129314,
0.017747854813933372,
-0.009669826366007328,
-0.03283316269516945,
-0.017670296132564545,
-0.009919734671711922,
0.013779394328594208,
-0.0009777583181858063,
0.011519967578351498,
0.011983181349933147,
0.00007742696470813826,
-0.001515218522399664,
-0.06358961760997772,
-0.01246483251452446,
0.06344559788703918,
-0.05945857614278793,
0.04141906648874283,
-0.025875823572278023,
-0.03062419407069683,
0.05254686623811722,
0.04602840170264244,
-0.03429587557911873,
0.02826450578868389,
0.0528135783970356,
-0.0025667420122772455,
-0.04282229021191597,
0.009461341425776482,
-0.03256506472826004,
0.06143210455775261,
-0.05314510688185692,
0.04951177164912224,
-0.005964711774140596,
0.012825972400605679,
-0.01418641023337841,
-0.009580091573297977,
0.016366450116038322,
-0.06869363784790039,
0.014485320076346397,
-0.031442634761333466,
0.05225350707769394,
-0.010422134771943092,
-0.02524295449256897,
0.008962878957390785,
0.0021247328259050846,
-0.0024240980856120586,
0.007765340153127909,
-0.014341110363602638,
0.04257694631814957,
-0.005718715023249388,
-0.016725318506360054,
0.006665188819169998,
-0.04683709144592285,
0.007124231196939945,
-0.022950083017349243,
-0.016235316172242165,
0.009316046722233295,
-0.01302269846200943,
-0.004920271225273609,
0.010081409476697445,
0.027977850288152695,
-0.012118960730731487,
0.04802056401968002,
0.011525062844157219,
0.05209355428814888,
0.012229470536112785,
0.03262990340590477,
0.1240924522280693,
0.03829541057348251,
0.013311401940882206,
-0.0383242666721344,
0.0356750451028347,
0.001713884063065052,
0.051249101758003235,
-0.016617635264992714,
-0.009296239353716373,
0.006010802928358316,
0.02995694987475872,
-0.013704922050237656,
0.052812423557043076,
0.001191117218695581,
0.04224823787808418,
0.03011281229555607,
-0.034314386546611786,
-0.024690400809049606,
-0.014355107210576534,
0.02786584384739399,
-0.05009589344263077,
0.020986728370189667,
-0.034307658672332764,
0.01561512891203165,
0.027848755940794945,
-0.025050152093172073,
-0.012599405832588673,
-0.03762776032090187,
0.047172240912914276,
0.03887321054935455,
-0.03133602812886238,
-0.016244271770119667,
0.012370423413813114,
0.025827564299106598,
-0.042548734694719315,
0.00958379078656435,
0.021779466420412064,
-0.031029310077428818,
0.02816983126103878,
0.053460776805877686,
0.02520364709198475,
0.0022063867654651403,
0.008641905151307583,
0.0372430644929409,
-0.05540011450648308,
-0.031177304685115814,
-0.024038102477788925,
0.022749096155166626,
-0.02647688053548336,
-0.01585840992629528,
-0.036928627640008926,
0.008002890273928642,
0.04588006064295769,
-0.04672777280211449,
0.005854991264641285,
0.008420564234256744,
0.01562841609120369,
-0.04019727557897568,
-0.026953639462590218,
-0.047965556383132935,
0.011642400175333023,
-0.010971692390739918,
-0.01486845500767231,
-0.003014707239344716,
0.0059286016039550304,
0.01586761511862278,
0.011914253234863281,
0.00795075111091137,
-0.027290260419249535,
0.03222930431365967,
-0.03531050682067871,
0.011365417391061783,
-0.04540294036269188,
-0.0048337276093661785,
0.03531664237380028,
0.0384073480963707,
0.055246587842702866,
0.000024697046683286317,
0.013448956422507763,
-0.01403783354908228,
-0.03350990638136864,
0.04542643204331398,
-0.023323439061641693,
-0.03893693536520004,
0.014107998460531235,
0.00460072560235858,
0.011577128432691097,
0.028135869652032852,
-0.06399549543857574,
0.01977662555873394,
0.008423754945397377,
0.023436715826392174,
0.011149224825203419,
0.00688792672008276,
-0.007624661549925804,
0.034378163516521454,
-0.021587202325463295,
-0.0062954481691122055,
0.029110638424754143,
0.04403780400753021,
0.05640949308872223,
-0.020183008164167404,
-0.014718087390065193,
0.01828274130821228,
0.0035988129675388336,
0.028250763192772865,
0.01960882544517517,
-0.00019885758229065686,
-0.0328771136701107,
0.018674837425351143,
-0.002345943357795477,
0.004510531201958656,
-0.06452957540750504,
-0.036215364933013916,
-0.005330149549990892,
-0.00043373554944992065,
0.03035307675600052,
0.0074815573170781136,
0.01032944954931736,
-0.022374633699655533,
-0.01760188117623329,
-0.045067258179187775,
0.005228993482887745,
-0.06494136899709702,
0.004887680057436228,
0.022840376943349838,
0.005074895918369293,
-0.04238341003656387,
0.022027915343642235,
-0.02811843529343605,
0.014037653803825378,
0.04592421278357506,
0.015540373511612415,
-0.02709771879017353,
-0.05060751363635063,
0.007380986120551825,
-0.01766473427414894,
0.06998057663440704,
-0.02428518608212471,
-0.01334596797823906,
0.029696812853217125,
-0.040984805673360825,
-0.044160664081573486,
0.02431890182197094,
-0.030515514314174652,
0.012674865312874317,
0.027913276106119156,
0.021169323474168777,
-0.022005567327141762,
0.06522594392299652,
-0.02740245684981346,
-0.005242880433797836,
-0.007411477621644735,
-0.009365607984364033,
-0.023093193769454956,
-0.014099215157330036,
0.01081690564751625,
-0.023852664977312088,
-0.010038439184427261,
0.043253932148218155,
0.013544848188757896,
0.023669207468628883,
-0.02569125033915043,
0.014809578657150269,
0.008060658350586891,
-0.014360262081027031,
0.011233693920075893,
0.04162752255797386,
0.00027885581948794425,
0.047464776784181595,
-0.022795382887125015,
0.04756467416882515,
0.0627901628613472,
0.013207836076617241,
-0.0836632177233696,
0.008663390763103962,
-0.012606029398739338,
-0.0011924735736101866,
0.016426527872681618,
-0.04901142045855522,
-0.005171697121113539,
0.017473362386226654,
-0.08518096059560776,
-0.02208138443529606,
-0.024773383513092995,
-0.0029576695524156094,
-0.00606667110696435,
-0.015168567188084126,
-0.06657547503709793,
0.04239435866475105,
0.03437671437859535,
0.041277382522821426,
0.025049734860658646,
-0.0006119308527559042,
-0.038951169699430466,
0.02200186625123024,
-0.011030925437808037,
0.05267375335097313,
-0.0016621731920167804,
-0.023557472974061966,
0.05543452128767967,
0.0003792845527641475,
-0.06727173179388046,
0.01943226531147957,
-0.014057249762117863,
0.01225961372256279,
0.014758354984223843,
-0.018616516143083572,
0.0020275155548006296,
0.00013321505684871227,
0.0016059590270742774,
0.01330056693404913,
0.017949923872947693,
0.024942951276898384,
0.025161096826195717,
0.028443479910492897,
0.04236209765076637,
-0.027035875245928764,
0.016183793544769287,
-0.045157402753829956,
-0.049398619681596756,
0.034273769706487656,
-0.00820930115878582,
0.008163279853761196,
-0.02689959481358528,
-0.0016365101328119636,
0.024858292192220688,
-0.0072358716279268265,
-0.007851144298911095,
-0.03851005434989929,
-0.02902698889374733,
0.02297944203019142,
0.04512518271803856,
0.006615194957703352,
0.027643652632832527,
0.003813610877841711,
-0.031716011464595795,
0.04983598738908768,
0.02825545147061348,
-0.04840904846787453,
-0.051822494715452194,
-0.014289455488324165,
-0.006891883909702301,
-0.013689965009689331,
-0.04447275027632713,
-0.002725100377574563,
0.000028682845368166454,
0.04885343089699745,
0.022010037675499916,
0.035683345049619675,
-0.012207470834255219,
-0.08237803727388382,
-0.02594277448952198,
-0.0341460257768631,
0.03650998696684837,
-0.00971430353820324,
0.01118726097047329,
-0.02880728244781494,
0.0025799281429499388,
0.00020248512737452984,
-0.008035445585846901,
0.04698754474520683,
-0.002680236240848899,
0.018705742433667183,
-0.03231719136238098,
-0.008452883921563625,
0.016358179971575737,
-0.026760851964354515,
0.01366304699331522,
-0.0018806485459208488,
-0.010645817033946514,
0.03025459125638008,
0.0019561199005693197,
-0.025813892483711243,
0.01850905641913414,
0.03575671836733818,
-0.04109308123588562,
0.011436212807893753,
0.006983115337789059,
-0.041133519262075424,
0.03543534129858017,
0.009433230385184288,
-0.026847049593925476,
0.06338399648666382,
-0.056340210139751434,
0.019793663173913956,
0.030892735347151756,
-0.005385265685617924,
-0.027287689968943596,
0.01986922137439251,
-0.020470041781663895,
-0.01789618283510208,
-0.017958106473088264,
0.00937255471944809,
0.023470060899853706,
-0.012801448814570904,
0.03370511531829834,
-0.001098254113458097,
-0.009543941356241703,
0.024951620027422905,
0.07033213973045349,
0.013216967694461346,
0.07322927564382553,
-0.012782539241015911,
-0.011833813041448593,
0.014111381024122238,
-0.008289359509944916,
-0.011751821264624596,
0.05941568687558174,
0.04431099444627762,
0.03303038701415062,
0.021735992282629013,
-0.00815154705196619,
-0.003928867634385824,
-0.002910926938056946,
0.02380320616066456,
0.008170723915100098,
-0.019907239824533463,
0.014087549410760403,
0.046504564583301544,
-0.0155792823061347,
0.021416615694761276,
0.0057747941464185715,
-0.013118432834744453,
0.08638313412666321,
-0.038949161767959595,
0.0038448150735348463,
-0.038335468620061874,
-0.014979489147663116,
-0.030753210186958313,
0.00706830807030201,
0.007416115142405033,
0.03372300788760185,
-0.009870845824480057,
0.015105938538908958,
-0.04081589728593826,
0.018004348501563072,
0.025111602619290352,
-0.029334712773561478,
0.003272492904216051,
-0.02863585203886032,
0.03891129419207573,
-0.026220789179205894,
-0.0011981321731582284,
-0.0014534927904605865,
0.012334494851529598,
0.009327122010290623,
0.004747624509036541,
-0.007692609913647175,
0.02225722372531891,
-0.004587641451507807,
-0.023704811930656433,
0.05262050777673721,
-0.03779883682727814,
0.01695285178720951,
-0.032302066683769226,
0.032578133046627045,
-0.017227374017238617,
-0.03485219553112984
] |
<p>What are the differences in the types of problems Ricci/Tensor Calculus and Matrix Calculus can solve? One formulation is generally used by the physics community and the other by statisticians and engineers, but what about each of them makes them desirable for each of their fields despite what at least superficially seems to be a great deal of overlap?</p>
| 10,676 |
[
-0.006820438429713249,
-0.0007679231348447502,
-0.011305704712867737,
-0.05598403885960579,
0.050661735236644745,
0.006368069443851709,
0.012599758803844452,
-0.0321846567094326,
0.023566951975226402,
0.005934158340096474,
0.008841028437018394,
0.02853170782327652,
0.05203095078468323,
-0.028865939006209373,
0.0412900373339653,
0.008945213630795479,
0.0024951279629021883,
-0.012813588604331017,
-0.028115540742874146,
-0.0076226177625358105,
0.01056393701583147,
0.01489696092903614,
0.02506149373948574,
0.015497731044888496,
-0.020035723224282265,
0.029889771714806557,
-0.02302148938179016,
-0.014471556060016155,
-0.0005953310173936188,
0.03889933228492737,
-0.01785845123231411,
0.0069206529296934605,
0.011805688962340355,
0.02455049380660057,
0.0195167176425457,
-0.02252369001507759,
-0.05258095636963844,
-0.043596602976322174,
-0.012370179407298565,
-0.0032697408460080624,
-0.05165591090917587,
-0.04634314775466919,
-0.003297232324257493,
0.014815788716077805,
-0.029874740168452263,
0.05734099820256233,
0.013007355853915215,
-0.04164838418364525,
0.037882398813962936,
-0.052175506949424744,
0.044447749853134155,
0.034041643142700195,
0.04713635891675949,
0.023122362792491913,
-0.011995281092822552,
0.024285949766635895,
0.06016805022954941,
0.07394092530012131,
0.020177999511361122,
-0.05054138973355293,
0.006602159701287746,
0.016824128106236458,
-0.006084968335926533,
-0.014953430742025375,
-0.026940491050481796,
0.062441274523735046,
-0.012518624775111675,
-0.02312975563108921,
-0.009857628494501114,
-0.03452512249350548,
-0.00006641281652264297,
0.014739631675183773,
0.03999463468790054,
0.009336907416582108,
-0.016856782138347626,
-0.008884210139513016,
-0.019364390522241592,
0.0006446292973123491,
0.04899822920560837,
-0.006551891565322876,
0.031100111082196236,
-0.001778660574927926,
0.03674158826470375,
0.03353332355618477,
-0.004570238292217255,
-0.00220835255458951,
0.07722650468349457,
-0.022184180095791817,
0.003671481739729643,
-0.01161789707839489,
-0.027864448726177216,
0.00657782144844532,
0.05554259568452835,
-0.0018454976379871368,
-0.04325884208083153,
0.029193168506026268,
0.011642948724329472,
0.023603904992341995,
0.03450562432408333,
-0.0236833393573761,
-0.02225595898926258,
-0.0251670703291893,
0.009526727721095085,
0.054815154522657394,
0.003802844090387225,
-0.017573002725839615,
-0.003345317207276821,
0.036237746477127075,
-0.02232717163860798,
-0.0002660476020537317,
-0.04813392832875252,
0.0284433551132679,
0.007385688833892345,
0.01090424694120884,
0.02800058387219906,
-0.004022767301648855,
0.028207028284668922,
-0.01595095545053482,
0.03228235989809036,
0.09348142892122269,
0.03983762487769127,
-0.026565933600068092,
0.034514013677835464,
-0.02376658283174038,
-0.06323830038309097,
0.0019481730414554477,
0.023747839033603668,
-0.022022800520062447,
-0.06492869555950165,
0.010348397307097912,
0.0027332198806107044,
-0.029117939993739128,
0.00016378694272134453,
-0.01203996129333973,
0.008516617119312286,
-0.028583917766809464,
-0.0782509297132492,
-0.04270157217979431,
0.03319786489009857,
0.00034446120844222605,
-0.022776467725634575,
-0.019708452746272087,
0.020658206194639206,
0.048102494329214096,
0.08218047022819519,
-0.00523691950365901,
0.0464542955160141,
0.037070684134960175,
0.045231737196445465,
-0.03774353489279747,
-0.031360771507024765,
-0.02561924420297146,
-0.03837877884507179,
0.003916374873369932,
0.022221021354198456,
-0.0649690330028534,
-0.020133180543780327,
0.030413316562771797,
-0.017263974994421005,
-0.00434913532808423,
0.05802381411194801,
0.02278801240026951,
-0.014353769831359386,
0.028869107365608215,
0.01854073256254196,
0.002702499972656369,
0.02834986336529255,
0.009357098489999771,
0.03857583552598953,
0.05285307392477989,
-0.0009337127557955682,
0.006444140337407589,
0.02404196746647358,
0.04984092712402344,
0.005255387630313635,
-0.027664922177791595,
0.007924946025013924,
0.06955070048570633,
-0.0019439073512330651,
0.019074279814958572,
-0.05951482802629471,
-0.010931764729321003,
0.0012535402784124017,
-0.012580067850649357,
-0.005324093624949455,
0.03647627308964729,
-0.009078212082386017,
0.01268286257982254,
0.016839852556586266,
-0.024445123970508575,
-0.018409520387649536,
-0.05166606232523918,
0.021638216450810432,
-0.02248895727097988,
-0.02100035548210144,
0.0673900842666626,
0.02529982291162014,
-0.011105703189969063,
-0.03261395916342735,
-0.05674080550670624,
0.002044605789706111,
0.026280738413333893,
-0.012105029076337814,
0.0149949686601758,
0.006605430040508509,
0.03676414117217064,
0.054401472210884094,
-0.0029582746792584658,
0.005033127032220364,
-0.028481630608439445,
-0.07494764775037766,
0.004308000206947327,
-0.03006161004304886,
0.0395805761218071,
0.008282925002276897,
-0.028927531093358994,
0.002818591659888625,
-0.05143987014889717,
-0.05443780869245529,
0.019101589918136597,
-0.04266994819045067,
0.04011988639831543,
0.03227474167943001,
0.022955745458602905,
0.002001908840611577,
0.06474008411169052,
-0.001930170226842165,
0.009831110015511513,
0.017940133810043335,
-0.030970264226198196,
-0.040347784757614136,
0.01531931385397911,
0.023957934230566025,
0.07928095012903214,
-0.0489891916513443,
-0.0031942962668836117,
0.05389404296875,
0.04408895596861839,
0.007294627837836742,
0.030880076810717583,
-0.05652214214205742,
-0.03154675289988518,
0.045900050550699234,
-0.018834520131349564,
-0.013005143031477928,
-0.01802261546254158,
-0.019622955471277237,
0.006777837872505188,
0.01988958939909935,
-0.00976811908185482,
-0.041091397404670715,
0.05371631681919098,
-0.003552644047886133,
0.005676191300153732,
0.020370598882436752,
-0.033078450709581375,
0.00788060761988163,
-0.021162012591958046,
-0.030575081706047058,
0.029642781242728233,
-0.0008036796352826059,
0.000013904890693083871,
0.013830309733748436,
-0.01851475052535534,
0.025706565007567406,
-0.02047124318778515,
-0.017199914902448654,
-0.03006560541689396,
0.023154908791184425,
-0.04246583580970764,
0.007886270992457867,
-0.009478512220084667,
-0.002047254703938961,
-0.042352739721536636,
-0.0019168363651260734,
0.0642203763127327,
-0.01684758812189102,
0.04650818556547165,
-0.005080739967525005,
-0.023302413523197174,
0.03553558886051178,
-0.053142230957746506,
0.009763543494045734,
0.02778802253305912,
-0.08176901191473007,
0.03952758014202118,
-0.0684162899851799,
-0.03486254811286926,
0.05262977257370949,
-0.017819887027144432,
0.005489105824381113,
0.004017641767859459,
-0.002646921668201685,
-0.05771913006901741,
-0.035249367356300354,
-0.007391577120870352,
0.025670181959867477,
-0.01068822294473648,
0.0003294053894933313,
0.04584847390651703,
-0.031083259731531143,
-0.01147786807268858,
-0.009833197109401226,
-0.009080100804567337,
-0.024640467017889023,
-0.013018978759646416,
0.0001134301710408181,
0.023545516654849052,
-0.024409614503383636,
-0.008966716006398201,
0.07449938356876373,
-0.06149416044354439,
-0.00898798555135727,
-0.07031818479299545,
-0.03746696934103966,
0.015810459852218628,
-0.005391118116676807,
0.0268393624573946,
0.053190551698207855,
-0.018685095012187958,
0.07351158559322357,
0.03326387703418732,
-0.030496029183268547,
-0.00014362439105752856,
0.0012243008241057396,
-0.04413598030805588,
-0.023722242563962936,
0.02266603894531727,
0.011465980671346188,
-0.013924112543463707,
0.03514140099287033,
0.01199578121304512,
0.0031783967278897762,
0.06094225496053696,
0.036412566900253296,
0.0011282525956630707,
-0.012496531940996647,
0.02012309804558754,
0.011244688183069229,
0.0324179083108902,
0.009873663075268269,
-0.03040519915521145,
0.02748887613415718,
0.009935591369867325,
-0.005386883392930031,
0.00989303644746542,
-0.036790598183870316,
0.031876321882009506,
-0.010188408195972443,
0.008960762992501259,
-0.018132733181118965,
0.028652064502239227,
0.008795985020697117,
0.0013428846141323447,
0.010991433635354042,
0.02630087547004223,
0.0008806367986835539,
-0.03249301761388779,
0.019973106682300568,
0.02308267541229725,
0.056877512484788895,
-0.03360552713274956,
0.014633211307227612,
-0.03350258991122246,
-0.011073716916143894,
0.029803749173879623,
-0.04391615837812424,
-0.005791615229099989,
0.07640687376260757,
-0.016011569648981094,
0.006623628083616495,
0.009086432866752148,
-0.03770546242594719,
-0.02464573085308075,
-0.07003477960824966,
0.014056571759283543,
-0.03915771096944809,
0.04953350871801376,
0.010958814062178135,
0.05015407130122185,
0.007373756263405085,
0.008118855766952038,
0.0451999232172966,
-0.013371246866881847,
-0.06429032236337662,
0.028659800067543983,
-0.024702975526452065,
0.003932498395442963,
0.0011690332321450114,
0.000918481033295393,
0.03758271411061287,
-0.013764923438429832,
-0.02468237653374672,
-0.027421751990914345,
0.03569784387946129,
-0.06764157116413116,
0.04532235860824585,
-0.04175637289881706,
-0.06218278035521507,
-0.000662822334561497,
-0.007274620234966278,
0.01182459481060505,
-0.012366355396807194,
0.026420144364237785,
0.06948524713516235,
-0.025330346077680588,
-0.013128070160746574,
0.007051683031022549,
0.021611372008919716,
0.03150361403822899,
0.019622614607214928,
0.03580879420042038,
0.02084224671125412,
-0.014532755129039288,
0.029634544625878334,
0.03266935050487518,
0.06159157305955887,
0.002714382717385888,
-0.020681556314229965,
-0.051371656358242035,
-0.0885368213057518,
-0.0010814996203407645,
-0.01324201188981533,
0.042513407766819,
0.010740210302174091,
-0.016955213621258736,
0.040566205978393555,
0.03000819683074951,
-0.011024003848433495,
0.01590476930141449,
0.0366850309073925,
0.018931018188595772,
-0.0181767288595438,
-0.03770169988274574,
-0.013557958416640759,
-0.0408095084130764,
-0.013709375634789467,
0.032743845134973526,
-0.008202968165278435,
-0.033175110816955566,
0.017999308183789253,
0.03237767890095711,
-0.04127207025885582,
-0.027215026319026947,
0.007913347333669662,
0.019242383539676666,
0.012897578068077564,
0.018345996737480164,
-0.03701113536953926,
-0.011031229980289936,
0.039797473698854446,
0.03689423203468323,
0.016026629135012627,
0.011620277538895607,
-0.07147804647684097,
0.0012649374548345804,
0.03807901591062546,
0.016549957916140556,
-0.01812775619328022,
-0.023166418075561523,
-0.045020125806331635,
-0.013584195636212826,
0.05490187183022499,
0.005632634740322828,
0.013266119174659252,
0.01335801463574171,
-0.014740710146725178,
-0.007727520074695349,
-0.021743636578321457,
0.009309750981628895,
0.011989912018179893,
0.004430113360285759,
0.01916520856320858,
0.003949255682528019,
0.0038067742716521025,
-0.01969754509627819,
0.017768001183867455,
0.03461866080760956,
0.04396894574165344,
0.010798662900924683,
0.004112711176276207,
0.017157649621367455,
0.040287893265485764,
0.018494609743356705,
-0.0962325856089592,
-0.026279455050826073,
0.04481024295091629,
-0.04488196223974228,
0.035605281591415405,
-0.016090892255306244,
-0.03791669383645058,
0.04158250242471695,
-0.023515280336141586,
-0.017077306285500526,
0.03584090247750282,
0.001934629981406033,
0.030114073306322098,
0.04694288969039917,
0.02005327306687832,
0.04487679526209831,
0.02086249738931656,
0.0018511704402044415,
-0.0005117587861604989,
-0.014869870617985725,
0.0280789602547884,
-0.01820904202759266,
-0.024886585772037506,
-0.03543869033455849,
0.000370498513802886,
-0.03918395936489105,
0.032259825617074966,
-0.003994987346231937,
0.016597529873251915,
-0.014707701280713081,
-0.012493913993239403,
-0.0025913789868354797,
0.040382616221904755,
-0.0368366576731205,
-0.0369231253862381,
0.02028598263859749,
0.015315868891775608,
0.007413426414132118,
-0.03734505921602249,
0.007575241383165121,
-0.0014527499442920089,
-0.0010379297891631722,
0.03081168420612812,
-0.006712974514812231,
0.005542304366827011,
-0.04660527780652046,
0.0010207424638792872,
0.043894946575164795,
-0.026462286710739136,
0.03948146104812622,
0.006295791827142239,
0.020226722583174706,
0.01313196960836649,
-0.02691003493964672,
-0.006431888788938522,
-0.009323272854089737,
-0.007232536096125841,
0.04662749916315079,
-0.02402174472808838,
0.018067939206957817,
-0.028709888458251953,
-0.02320304699242115,
-0.0718153789639473,
-0.04822281748056412,
0.0038486032281070948,
-0.0012157127493992448,
-0.051712099462747574,
-0.026683034375309944,
0.018330072984099388,
-0.04405497387051582,
-0.017576605081558228,
0.023476051166653633,
0.06573627144098282,
-0.05485520139336586,
-0.034050747752189636,
-0.00963437370955944,
0.007753218058496714,
0.04243994131684303,
-0.017478197813034058,
0.017763160169124603,
0.014671673066914082,
0.009314977563917637,
0.011050969362258911,
-0.021415160968899727,
0.04744429513812065,
-0.023144513368606567,
-0.0028413166292011738,
-0.04510890692472458,
-0.005914048291742802,
0.02387068420648575,
0.0015794106293469667,
0.018526136875152588,
0.06580063700675964,
0.04822653532028198,
-0.004167841747403145,
-0.004833370912820101,
0.014177829027175903,
-0.016585469245910645,
0.011199495755136013,
0.026086505502462387,
0.002360651036724448,
-0.007744469214230776,
0.0006479296716861427,
0.04050103574991226,
-0.004251694772392511,
0.003491822862997651,
0.006882923189550638,
0.0567898191511631,
-0.015458624809980392,
0.013128752820193768,
-0.010211280547082424,
0.011027025058865547,
0.03038868121802807,
-0.039360079914331436,
0.015057573094964027,
0.01916278712451458,
0.012774615548551083,
-0.023585081100463867,
-0.07192063331604004,
-0.03414808213710785,
0.028392566367983818,
0.06330567598342896,
-0.03220147266983986,
0.04109878093004227,
0.06593365222215652,
-0.031249290332198143,
0.004253610502928495,
-0.030017107725143433,
-0.02452872321009636,
0.012523476034402847,
-0.012392126023769379,
0.006031210068613291,
-0.0030600945465266705,
-0.030749300494790077,
0.032819878309965134,
0.030758455395698547,
-0.0389094278216362,
-0.01993030682206154,
-0.023091280832886696,
0.05850556492805481,
0.01581485942006111,
-0.02882063202559948,
-0.04198024049401283,
0.04013671725988388,
-0.04051356017589569,
0.03961428999900818,
-0.027781007811427116,
-0.043979059904813766,
0.055249545723199844,
0.014217382296919823,
-0.01588757522404194,
-0.013585424050688744,
0.0006640009814873338,
-0.07441603392362595,
0.015593642368912697,
0.025057947263121605,
0.02655794844031334,
-0.0054703401401638985,
0.021008552983403206,
0.03373441845178604,
-0.0057628159411251545,
0.01799963042140007,
-0.002043158747255802,
-0.0677647739648819,
-0.04158828407526016,
-0.04389173164963722,
-0.03350359946489334,
0.042372774332761765,
0.033772390335798264,
-0.03299115225672722,
0.018962590023875237,
-0.03606724366545677,
0.019153444096446037,
0.0037742238491773605,
0.033463504165410995,
-0.03555459901690483,
0.03967171907424927,
-0.02134574018418789,
-0.0005629653460346162,
-0.015344140119850636,
-0.004458343610167503,
0.08923741430044174,
0.04978179186582565,
0.02256743609905243,
-0.0561840794980526,
0.014084135182201862,
-0.015134358778595924,
0.0013698014663532376,
-0.04794805869460106,
0.04439985007047653,
0.016956260427832603,
0.03306471183896065,
0.0026709616649895906,
0.03336320072412491,
0.024013174697756767,
-0.01738481968641281,
0.03051699697971344,
-0.05858286842703819,
-0.020615823566913605,
-0.019007483497262,
0.0028390618972480297,
0.012866201810538769,
0.0408763624727726,
-0.02577783167362213,
-0.008706445805728436,
-0.04998207837343216,
0.011504268273711205,
-0.053968288004398346,
-0.016194259747862816,
-0.005431126803159714,
0.006335119716823101,
-0.034687966108322144,
0.004207807593047619,
0.006790398620069027,
0.006501260679215193,
-0.02617068588733673,
0.02569243311882019,
0.00748598063364625,
-0.0139060840010643,
0.014097452163696289,
0.02577085979282856,
0.025631610304117203,
-0.03975272923707962,
-0.01171251479536295,
-0.00937276054173708,
-0.07003822922706604,
0.01304287277162075,
-0.05647631734609604,
0.02864866703748703,
-0.01561284065246582,
0.007868954911828041,
0.012002270668745041,
-0.01955913007259369,
-0.027804572135210037,
-0.03365932032465935,
-0.03865595906972885,
0.005665349308401346,
0.03663522005081177,
-0.023757213726639748,
0.029979586601257324,
-0.0009942427277565002,
0.03982574865221977,
-0.003074806649237871,
0.04151847958564758,
0.011056688614189625,
-0.02341873198747635,
-0.023585688322782516,
-0.014140138402581215,
0.06665312498807907,
-0.055361825972795486,
0.013055398128926754,
-0.030261389911174774,
-0.0068068415857851505,
-0.018245762214064598,
-0.04860363528132439,
0.026315174996852875,
0.020358948037028313,
0.01845182105898857,
-0.008117537945508957,
0.014219680801033974,
0.004119900520890951,
-0.043859515339136124,
0.023193586617708206,
-0.0024713524617254734,
0.024291053414344788,
-0.05176157131791115,
-0.006871106568723917,
0.04525868222117424,
0.019109997898340225,
-0.024548491463065147,
-0.004887367133051157,
-0.017880599945783615,
0.0028085203375667334,
0.005784983746707439,
-0.026558151468634605,
-0.0022058591712266207,
0.015452519990503788,
-0.011706942692399025,
0.036314092576503754,
-0.027509236708283424,
0.028075747191905975,
0.04699378088116646,
0.006304931826889515,
-0.055688224732875824,
0.018629541620612144,
-0.010000715963542461,
-0.00826818123459816,
0.02440752275288105,
-0.049367740750312805,
-0.00480759097263217,
0.021028151735663414,
0.037065036594867706,
-0.05073331668972969,
-0.0044784522615373135,
-0.04897759482264519,
-0.014624211937189102,
-0.0036225973162800074,
0.031188497319817543,
-0.002844599075615406,
-0.015685852617025375,
0.006157205905765295,
0.06767038255929947,
-0.01677214354276657,
-0.0020206121262162924,
-0.042241260409355164,
0.05031167343258858,
-0.0015979609452188015,
-0.04687988758087158,
-0.007029663771390915,
0.0005986120668239892,
-0.0238418560475111,
-0.018486186861991882,
0.011061793193221092,
0.0053853439167141914,
-0.019944796338677406,
0.015517965890467167,
0.011869954876601696,
-0.02000170759856701,
0.049608293920755386,
-0.031376149505376816,
-0.017258407548069954,
0.03289173170924187,
-0.03357985243201256,
-0.07161200791597366,
0.03597193956375122,
-0.016432076692581177,
0.03292384743690491,
0.02849460393190384,
-0.022918451577425003,
-0.013225709088146687,
0.0387151762843132,
-0.04296179860830307,
-0.010868258774280548,
0.001833384158089757,
-0.040450043976306915,
-0.031716667115688324,
-0.026782991364598274,
0.05423327162861824,
0.0001470224087825045,
-0.014427589252591133,
0.004562042653560638,
0.05271069332957268,
-0.026861704885959625,
0.013926206156611443,
0.04625870659947395,
-0.026442989706993103,
0.054946109652519226,
0.02649272233247757,
0.01627325639128685,
0.032578326761722565,
0.054316550493240356,
-0.02477581612765789,
0.024243488907814026,
0.03615434840321541,
0.04291509836912155,
-0.1069951057434082,
0.01480202004313469,
0.027521004900336266,
-0.03475331515073776,
0.04510384052991867,
-0.03902873024344444,
0.006796547211706638,
0.047020748257637024,
-0.046634335070848465,
0.06069263815879822,
-0.04362528398633003,
-0.025941142812371254,
-0.0003048967628274113,
0.005959640722721815,
-0.014707371592521667,
0.046356603503227234,
0.03403075039386749,
-0.005279027856886387,
0.03574055805802345,
0.04354815557599068,
0.01311952993273735,
-0.0040616681799292564,
-0.024666087701916695,
0.001859484356828034,
-0.02058669924736023,
-0.014518159441649914,
0.033955588936805725,
-0.02826782874763012,
-0.040282607078552246,
0.028786934912204742,
0.0026867336127907038,
-0.01306450180709362,
-0.010739232413470745,
-0.004441050812602043,
-0.00708497129380703,
0.01409288588911295,
0.03666171059012413,
-0.03311637416481972,
0.013189352117478848,
0.006142581347376108,
-0.006339997984468937,
0.018366442993283272,
0.004680885002017021,
0.02881762757897377,
0.0189592856913805,
-0.013419854454696178,
-0.023199904710054398,
0.027959125116467476,
0.010894443839788437,
-0.05850518122315407,
-0.01348329707980156,
-0.016377724707126617,
0.021433275192975998,
-0.02029257081449032,
0.01126216072589159,
-0.04432399198412895,
-0.0017549507319927216,
0.007917328737676144,
0.049352776259183884,
-0.0032086835708469152,
-0.000788416073191911,
-0.013442335650324821,
-0.022717906162142754,
0.020239291712641716,
0.010085073299705982,
0.008533725515007973,
-0.05279900133609772,
0.0008587717893533409,
0.04187279939651489,
-0.009148414246737957,
-0.02056526392698288,
-0.04900949448347092,
-0.023917442187666893,
0.044175878167152405,
0.01645716466009617,
0.03192455321550369,
0.023459039628505707,
-0.030875785276293755,
-0.030451085418462753,
-0.08499706536531448,
0.02990938350558281,
-0.020855886861681938,
-0.012082083150744438,
-0.01677214913070202,
-0.012469427660107613,
-0.005316751543432474,
-0.0021511383820325136,
0.062149353325366974,
0.009146411903202534,
-0.009258275851607323,
0.015659786760807037,
-0.0049032727256417274,
-0.006605049129575491,
-0.014372291043400764,
0.003705310169607401,
-0.03474957495927811,
-0.022850720211863518,
-0.01026691310107708,
-0.026369279250502586,
0.00641564279794693,
0.004142396152019501,
-0.0065527004189789295,
0.0021382588893175125,
0.0328279510140419,
0.005221321247518063,
-0.006165480241179466,
0.05900275334715843,
0.03754608705639839,
-0.023498093709349632,
0.052646514028310776,
-0.03291761875152588,
0.015961145982146263,
0.0067661781795322895,
-0.03193342685699463,
-0.01704808697104454,
0.04406169429421425,
-0.016381701454520226,
-0.05305030569434166,
-0.017519306391477585,
-0.008613178506493568,
0.0012559526367112994,
-0.06146441027522087,
-0.02904888242483139,
0.04577602446079254,
-0.04624210670590401,
-0.008847248740494251,
0.024166302755475044,
0.034591659903526306,
0.030617354437708855,
-0.0011756425956264138,
0.007653281092643738,
0.06029413267970085,
-0.017777351662516594,
0.0007264583837240934,
0.028581149876117706,
0.050401512533426285,
-0.00900000799447298,
-0.0026284947525709867,
0.014106092043220997,
-0.044517405331134796,
0.025542117655277252,
0.008814815431833267,
0.03513667732477188,
-0.015168027020990849,
-0.04411040246486664,
0.011372319422662258,
-0.01751798950135708,
0.009783951565623283,
0.018300902098417282,
-0.026028340682387352,
0.08503111451864243,
-0.04091060906648636,
-0.031199093908071518,
-0.015212444588541985,
-0.014853899367153645,
-0.0004588342853821814,
-0.01219205278903246,
-0.00926198996603489,
0.04091368988156319,
-0.012105356901884079,
-0.009488207288086414,
-0.005069073289632797,
0.004839465022087097,
0.0369517058134079,
-0.037859957665205,
0.03377441689372063,
0.014220254495739937,
-0.0028165748808532953,
-0.03388882055878639,
-0.042738497257232666,
-0.028152955695986748,
-0.016337962821125984,
0.036940354853868484,
0.08093036711215973,
0.03539636358618736,
-0.011574840173125267,
-0.021485500037670135,
-0.026569945737719536,
0.028149889782071114,
-0.07099825143814087,
-0.01858392171561718,
-0.046483591198921204,
0.021919405087828636,
0.00988558679819107,
0.0049072192050516605
] |
<p>I'm making a table where columns are labelled with the property and the units it's measured in:</p>
<p>Length (m) |||| Force (N) |||| Safety Factor <strong>(unitless)</strong> ||| etc...</p>
<p>I'd like not to write "unitless" on several columns...and I'm quite surprised I can't seem to find a symbol for it. Any suggestions?</p>
| 10,677 |
[
-0.0447477288544178,
0.01834145188331604,
-0.013858486898243427,
0.006824881304055452,
-0.004878662060946226,
0.03148582577705383,
-0.011473850347101688,
0.005591797176748514,
-0.0010891883866861463,
-0.044789545238018036,
0.06341391801834106,
0.06544522196054459,
0.06125539541244507,
-0.0019965742249041796,
0.033757533878088,
0.012277086265385151,
0.0007721271831542253,
-0.01562989503145218,
-0.007333227898925543,
-0.05865974724292755,
0.009854708798229694,
-0.048758331686258316,
-0.015550415962934494,
0.021905269473791122,
0.03331421688199043,
0.09102576971054077,
-0.009048867039382458,
0.014580763876438141,
0.007251251954585314,
0.015265088528394699,
-0.007659576367586851,
-0.044421084225177765,
0.0016632649349048734,
-0.003154272446408868,
0.03378840535879135,
-0.004092364571988583,
-0.012193900533020496,
-0.005288701504468918,
-0.034459467977285385,
-0.006215410307049751,
0.006660399027168751,
-0.011899705976247787,
0.009828411042690277,
0.057481758296489716,
-0.03011533059179783,
0.036310214549303055,
-0.007822796702384949,
-0.0012595447478815913,
0.040028952062129974,
-0.02738022804260254,
0.05182192474603653,
0.005520340520888567,
0.0697300061583519,
0.028998209163546562,
-0.04101332649588585,
0.004180956166237593,
0.06552864611148834,
0.03417873755097389,
-0.03896167501807213,
-0.048547226935625076,
-0.001340119750238955,
-0.03954837843775749,
0.02448657713830471,
-0.03215824440121651,
-0.02434808574616909,
0.029604237526655197,
-0.04751099273562431,
-0.03164352476596832,
0.03989005461335182,
-0.023508088663220406,
-0.016595618799328804,
-0.0016083675436675549,
0.041504815220832825,
-0.04360334575176239,
-0.0003457584243733436,
-0.06317894905805588,
0.025972211733460426,
-0.0016334966057911515,
0.06678982079029083,
0.03485456109046936,
-0.006489339284598827,
0.011217065155506134,
0.028239687904715538,
0.008256858214735985,
-0.01426765788346529,
-0.02952365018427372,
0.015253054909408092,
-0.013775177299976349,
0.015567086637020111,
0.05851062014698982,
-0.012703422456979752,
-0.021099047735333443,
0.041291557252407074,
0.05004137009382248,
-0.018051523715257645,
0.028254304081201553,
0.000847727875225246,
0.0399932861328125,
0.0188799686729908,
0.036280933767557144,
-0.011138205416500568,
-0.017451448366045952,
0.022495664656162262,
0.04860717058181763,
-0.024319423362612724,
-0.007633541245013475,
-0.02028486132621765,
-0.03787289559841156,
-0.007698346860706806,
0.010313841514289379,
-0.009291385300457478,
-0.016173522919416428,
0.0050004529766738415,
-0.0009729749290272593,
0.036944903433322906,
-0.08212675154209137,
-0.015979181975126266,
0.013656902126967907,
0.044432513415813446,
0.06293527781963348,
0.07438518851995468,
-0.036741163581609726,
0.04745110869407654,
-0.03650689125061035,
-0.07814983278512955,
0.05855238810181618,
0.00014909730816725641,
-0.005556733347475529,
-0.014707659371197224,
0.012157443910837173,
-0.006898221559822559,
-0.006130774039775133,
0.015038123354315758,
-0.03930484503507614,
0.04690973088145256,
0.0031902361661195755,
-0.06136701628565788,
-0.05843077972531319,
0.014997968450188637,
-0.002377612516283989,
-0.032522182911634445,
-0.028799492865800858,
0.025911521166563034,
0.012039353139698505,
0.06841355562210083,
0.016610022634267807,
-0.0340116061270237,
-0.01727796345949173,
-0.022517522796988487,
0.030682848766446114,
0.015540913678705692,
-0.0008634434780105948,
-0.01693948358297348,
-0.06158299744129181,
0.025633927434682846,
-0.05567781627178192,
0.034366119652986526,
0.020612826570868492,
0.0014945091679692268,
-0.004592801909893751,
0.06191525608301163,
-0.030920835211873055,
0.031180020421743393,
-0.01643669232726097,
-0.027489909902215004,
-0.05189443752169609,
0.09037318825721741,
-0.016151677817106247,
0.018511353060603142,
0.019145427271723747,
0.02344662696123123,
0.004451673477888107,
0.013666912913322449,
0.028173226863145828,
0.05082123354077339,
-0.005006317049264908,
-0.006765568163245916,
-0.027479736134409904,
0.007445238064974546,
0.02317671850323677,
-0.060127582401037216,
-0.07854781299829483,
0.022467607632279396,
-0.014090904034674168,
-0.00876532681286335,
0.009213859215378761,
-0.023094933480024338,
-0.018271947279572487,
0.04574837535619736,
-0.018300676718354225,
0.0008121837745420635,
-0.06309844553470612,
0.042095720767974854,
0.012712135910987854,
-0.013759289868175983,
0.023185621947050095,
-0.02440822124481201,
-0.018451353535056114,
-0.03360765427350998,
-0.004900022409856319,
-0.015298085287213326,
0.0004060091159772128,
0.01413155347108841,
-0.05029355734586716,
-0.031063098460435867,
-0.007982048206031322,
0.058286264538764954,
0.012313887476921082,
0.04461437091231346,
-0.012968642637133598,
-0.007953299209475517,
0.01983877643942833,
-0.019844256341457367,
-0.005136918276548386,
0.004100899212062359,
-0.012313916347920895,
0.029264982789754868,
0.010518101043999195,
-0.014640448614954948,
0.01871820166707039,
-0.038942668586969376,
0.02911028079688549,
0.013364642858505249,
-0.011781217530369759,
0.012570085935294628,
-0.0160211231559515,
-0.018931545317173004,
0.031201716512441635,
-0.009115253575146198,
-0.010360202752053738,
-0.048643771559000015,
0.016838425770401955,
0.025660542771220207,
0.014149350114166737,
-0.01918964833021164,
0.00941668450832367,
0.030959542840719223,
0.025141414254903793,
0.03104504756629467,
-0.01059556845575571,
-0.033291250467300415,
-0.004859910812228918,
0.00978800281882286,
0.00729296263307333,
0.001076586078852415,
0.01570800691843033,
0.007777255028486252,
0.04035065323114395,
0.025642462074756622,
-0.023756345734000206,
0.002974224044010043,
-0.003885142505168915,
-0.01932605728507042,
0.01917886734008789,
-0.013828442431986332,
-0.04260120540857315,
0.01850813440978527,
-0.012232853099703789,
0.021054549142718315,
0.037467680871486664,
0.00552130164578557,
-0.0018646839307621121,
-0.001126660848967731,
-0.04416303336620331,
-0.017036037519574165,
0.017906440421938896,
-0.049913737922906876,
-0.02423916384577751,
0.031015917658805847,
-0.03158486634492874,
-0.013874158263206482,
-0.023626822978258133,
-0.002483291318640113,
-0.020653851330280304,
-0.0011473390040919185,
0.04346739128232002,
0.015486164018511772,
0.06250829994678497,
-0.004832400940358639,
-0.006648906972259283,
0.016614394262433052,
-0.057588305324316025,
0.02776150032877922,
-0.0245542973279953,
-0.00009047702769748867,
-0.012764902785420418,
-0.033822450786828995,
-0.05244426429271698,
0.04422818124294281,
-0.015590999275445938,
-0.025458218529820442,
0.02026555873453617,
-0.013844073750078678,
-0.059331297874450684,
-0.01855180598795414,
-0.012892449274659157,
0.038695938885211945,
0.010161652229726315,
0.003543180413544178,
0.031767211854457855,
-0.005579701624810696,
-0.058151062577962875,
-0.013794880360364914,
-0.08217544853687286,
-0.019131498411297798,
-0.04946894571185112,
0.00010372947144787759,
0.018060525879263878,
-0.006157841067761183,
-0.0131605863571167,
0.05018704757094383,
-0.03652958944439888,
-0.02228230983018875,
-0.06375747174024582,
-0.03976156562566757,
-0.025396162644028664,
0.03359782323241234,
0.06219573691487312,
-0.009533783420920372,
-0.03128940984606743,
0.05703511834144592,
-0.0030916298273950815,
-0.0354851670563221,
-0.036050744354724884,
-0.05624725669622421,
-0.037750452756881714,
-0.1001247838139534,
0.02265746146440506,
0.004965709522366524,
0.0073893312364816666,
0.03105808235704899,
0.015489326789975166,
-0.005289345979690552,
0.032484449446201324,
0.0081310560926795,
0.01775423251092434,
0.002148212632164359,
-0.025573821738362312,
-0.018376383930444717,
0.07668709009885788,
0.010065729729831219,
-0.032611697912216187,
0.027121692895889282,
-0.013801932334899902,
0.002824225462973118,
0.02246914431452751,
-0.01553258579224348,
0.032006219029426575,
-0.014394858852028847,
0.026078542694449425,
-0.00854681245982647,
-0.010682627558708191,
0.026581984013319016,
0.005445405375212431,
-0.016842380166053772,
0.039090584963560104,
0.020353570580482483,
-0.05904000625014305,
-0.010257592424750328,
0.02887984737753868,
0.024813847616314888,
-0.005305951926857233,
0.016658123582601547,
-0.004229311365634203,
0.04072597995400429,
-0.002811248181387782,
-0.02583768591284752,
-0.02164948359131813,
-0.00243832403793931,
0.005246378481388092,
0.04424702003598213,
0.07110899686813354,
-0.0053726499900221825,
0.024272292852401733,
-0.057295799255371094,
-0.023558417335152626,
0.017759248614311218,
0.04890352860093117,
0.01669989712536335,
0.023083101958036423,
0.033954035490751266,
0.027529403567314148,
-0.007100674323737621,
0.029502900317311287,
-0.04098029062151909,
0.04069977626204491,
-0.020835092291235924,
-0.03752950206398964,
0.03274647146463394,
-0.02155563235282898,
-0.0848056897521019,
-0.03429601714015007,
-0.030569840222597122,
0.06259122490882874,
0.014956125058233738,
-0.05176098272204399,
-0.003728605108335614,
-0.00151949399150908,
-0.00024567946093156934,
-0.005649856757372618,
0.016276517882943153,
0.03526013344526291,
-0.02730654925107956,
0.001259776297956705,
0.04477471113204956,
-0.001021092408336699,
-0.005587153602391481,
0.009973841719329357,
0.012692722491919994,
0.035381536930799484,
0.021680910140275955,
-0.0008211482781916857,
0.020858503878116608,
-0.0020608471240848303,
0.0069223567843437195,
0.026204071938991547,
0.015380500815808773,
0.015773454681038857,
0.009045075625181198,
-0.018740542232990265,
-0.04114283621311188,
-0.01600297912955284,
0.017527064308524132,
0.058946218341588974,
0.0054879202507436275,
0.01364079024642706,
-0.008884702809154987,
0.030295491218566895,
-0.03034532256424427,
-0.013656936585903168,
0.094788558781147,
0.048760708421468735,
-0.04848355054855347,
-0.002314844401553273,
-0.0036591733805835247,
0.04667240381240845,
-0.0407501719892025,
-0.0145224304869771,
0.04191794618964195,
0.01916332356631756,
-0.025736400857567787,
0.006261705886572599,
-0.007925763726234436,
-0.04542534053325653,
0.02120017446577549,
0.003527932334691286,
-0.01699923723936081,
-0.007650704123079777,
0.016206609085202217,
0.01112698670476675,
0.011566202156245708,
-0.017839280888438225,
0.051152270287275314,
0.0028629270382225513,
-0.08200819045305252,
0.01497274823486805,
0.049067623913288116,
0.02903619036078453,
0.009764987975358963,
-0.045336004346609116,
-0.027229029685258865,
-0.04916705563664436,
0.08579298853874207,
-0.03310484439134598,
0.012298747897148132,
-0.012691197916865349,
0.03819803521037102,
-0.013554136268794537,
0.0028967545367777348,
-0.052755288779735565,
-0.009436005726456642,
0.033073410391807556,
0.018608005717396736,
0.010655030608177185,
0.045368943363428116,
0.006055530626326799,
0.017268097028136253,
-0.020228343084454536,
0.02356262318789959,
-0.013661502860486507,
-0.02934584580361843,
0.005655329208821058,
0.012274283915758133,
-0.019966362044215202,
-0.06080421060323715,
0.03243856504559517,
0.009585562162101269,
0.036155104637145996,
0.025643061846494675,
-0.0367513969540596,
-0.019226744771003723,
0.007592617999762297,
-0.023950748145580292,
0.006937578320503235,
0.018060773611068726,
-0.01712917350232601,
0.02967783622443676,
0.016743164509534836,
-0.0018000041600316763,
0.027003992348909378,
0.06009790673851967,
0.008569320663809776,
0.03206436708569527,
-0.05044253170490265,
0.006278651300817728,
-0.01566724106669426,
-0.019177818670868874,
-0.048657629638910294,
0.007205406669527292,
-0.05447159335017204,
0.020041536539793015,
-0.020781440660357475,
0.04256119951605797,
-0.044788796454668045,
-0.031078390777111053,
-0.01203078217804432,
0.0382867231965065,
0.020978068932890892,
-0.0278529804199934,
0.0411137230694294,
-0.00025294884108006954,
-0.049599044024944305,
-0.016794396564364433,
-0.0060127126052975655,
-0.018097952008247375,
-0.03054945357143879,
0.0185862984508276,
-0.003975699655711651,
0.023006053641438484,
-0.0021545360796153545,
-0.01989925652742386,
0.020062772557139397,
-0.05832244083285332,
0.03853916749358177,
-0.01373021025210619,
0.0388638861477375,
0.00817054882645607,
-0.037744082510471344,
-0.0230418611317873,
0.054491445422172546,
0.01869603805243969,
0.02172226645052433,
-0.03436261788010597,
0.027476230636239052,
-0.02318265661597252,
0.02239934913814068,
-0.025563474744558334,
-0.03815937787294388,
0.019556725397706032,
0.01909032091498375,
-0.04019276425242424,
-0.011158937588334084,
-0.027448495849967003,
-0.029308076947927475,
-0.03237235173583031,
-0.017972340807318687,
0.02299763821065426,
-0.012561128474771976,
-0.020035212859511375,
0.025557976216077805,
0.014486407861113548,
0.04385746642947197,
0.0317380465567112,
-0.025746095925569534,
0.01558138057589531,
-0.011116217821836472,
-0.012247549369931221,
0.006299784407019615,
0.029599081724882126,
-0.024208951741456985,
-0.025678832083940506,
-0.02301870472729206,
-0.036036375910043716,
0.00045999008580110967,
-0.0022714142687618732,
0.06527079641819,
0.010220728814601898,
-0.015028455294668674,
-0.02744501270353794,
0.0034321125131100416,
0.047146499156951904,
-0.0032723555341362953,
0.01968906633555889,
0.014743625186383724,
0.012709817849099636,
-0.02996496856212616,
-0.011001072824001312,
0.0009237038320861757,
0.011800780892372131,
-0.0011883812258020043,
-0.0074547091498970985,
0.03611253574490547,
0.0008715091971680522,
-0.011302783153951168,
0.028600262477993965,
-0.012434353120625019,
0.042985592037439346,
0.039434634149074554,
-0.030730746686458588,
-0.02890854887664318,
0.02556922473013401,
-0.042286574840545654,
-0.014144529588520527,
0.009266569279134274,
-0.026050018146634102,
0.017046362161636353,
-0.016864899545907974,
0.04619189724326134,
0.027567684650421143,
-0.016924984753131866,
0.03168065845966339,
0.014119010418653488,
-0.05679910629987717,
0.015756934881210327,
0.014835425652563572,
0.058812737464904785,
-0.006709347944706678,
0.01805761642754078,
0.009725830517709255,
0.017985565587878227,
0.009539519436657429,
0.04308043792843819,
0.006872652098536491,
0.0072159538976848125,
0.027410216629505157,
-0.03157871961593628,
-0.017811715602874756,
0.051804643124341965,
-0.05259617790579796,
0.0315539576113224,
0.0026168536860495806,
-0.019362077116966248,
-0.014652139507234097,
0.03485744446516037,
-0.047416139394044876,
-0.007595501374453306,
-0.03934484347701073,
-0.055116549134254456,
-0.005450310651212931,
0.03156602755188942,
-0.052950069308280945,
-0.04351532459259033,
-0.0230802483856678,
0.02498050034046173,
-0.016284603625535965,
0.022219952195882797,
-0.03433840349316597,
-0.01323608960956335,
-0.011704886332154274,
-0.04398661106824875,
-0.002750071696937084,
0.056561898440122604,
-0.0015828380128368735,
-0.0035536610521376133,
0.012798385694622993,
0.023924317210912704,
0.043064817786216736,
0.0005712755373679101,
0.0014223206089809537,
0.006892697419971228,
0.02780315838754177,
-0.01227714866399765,
-0.001683014677837491,
-0.012798047624528408,
-0.04390900582075119,
0.11884118616580963,
0.06635086238384247,
0.046351946890354156,
-0.005294726695865393,
0.018033567816019058,
0.00535538187250495,
0.01579849049448967,
-0.021633798256516457,
-0.009852924384176731,
-0.013233937323093414,
0.011970517225563526,
0.026163676753640175,
0.06285358965396881,
-0.011281697079539299,
0.05065735802054405,
0.05820431932806969,
0.00030763400718569756,
0.004026480484753847,
-0.017073165625333786,
0.03219783306121826,
-0.014563092030584812,
-0.026554327458143234,
-0.03777318447828293,
0.0062569789588451385,
0.053882211446762085,
-0.009033204056322575,
-0.0346335843205452,
-0.006131329573690891,
0.04940880089998245,
0.027164574712514877,
-0.02537635713815689,
-0.008528528735041618,
0.0429028645157814,
0.033398598432540894,
-0.0007755872211419046,
-0.018962437286973,
0.03720683604478836,
0.03963692486286163,
0.004149872809648514,
0.020543335005640984,
0.0007386610377579927,
-0.024030236527323723,
0.014660398475825787,
-0.028482738882303238,
-0.05297842249274254,
-0.001468329457566142,
-0.02292129024863243,
0.006258124485611916,
0.017908116802573204,
-0.01201868150383234,
-0.004696370102465153,
0.03441288694739342,
0.025406967848539352,
-0.04140660539269447,
-0.0016991269076243043,
-0.017167432233691216,
0.018139876425266266,
-0.016718890517950058,
-0.001245708903297782,
0.00850000698119402,
0.020174413919448853,
-0.017701134085655212,
-0.02957022562623024,
-0.010191486217081547,
0.015643153339624405,
0.004897895734757185,
-0.02104448340833187,
0.004958690609782934,
0.000019078273908235133,
-0.004592869896441698,
0.03778894245624542,
-0.01802190952003002,
-0.057728782296180725,
-0.0009634586749598384,
0.001860514166764915,
0.04233744367957115,
0.05655469000339508,
0.002268704818561673,
0.04332853481173515,
-0.028293896466493607,
-0.03787414729595184,
0.08404004573822021,
-0.030131686478853226,
-0.04322906956076622,
0.0031475964933633804,
0.011856969445943832,
0.024415113031864166,
0.028260163962841034,
0.004885819740593433,
-0.012003527954220772,
-0.01727762632071972,
0.008756853640079498,
0.027018947526812553,
-0.0321708582341671,
-0.018770093098282814,
0.018936220556497574,
-0.03543886914849281,
-0.0006922143511474133,
-0.03749338164925575,
0.02475370652973652,
0.04435138404369354,
-0.0030429689213633537,
0.004498236812651157,
0.027236679568886757,
0.004243039526045322,
-0.03892152011394501,
0.035530924797058105,
-0.0639447271823883,
0.0034159875940531492,
0.01846792735159397,
-0.04829511418938637,
-0.0052042375318706036,
-0.03868720307946205,
-0.05013946443796158,
-0.007988310419023037,
-0.04745606333017349,
0.07532954216003418,
-0.03396792337298393,
-0.004235524218529463,
-0.03800501674413681,
-0.007518378552049398,
-0.027059800922870636,
0.011784224770963192,
-0.07428842782974243,
-0.060914672911167145,
0.019267557188868523,
-0.00025668280432000756,
-0.054299142211675644,
0.014318246394395828,
-0.030692292377352715,
0.006540827453136444,
0.0034552093129605055,
0.011412829160690308,
0.03301671892404556,
-0.03013908676803112,
-0.022404447197914124,
-0.0034764099400490522,
0.05024878308176994,
-0.03917064145207405,
0.01585312746465206,
0.005446356721222401,
-0.015550135634839535,
-0.01988118514418602,
0.023369163274765015,
-0.011413714848458767,
0.029364733025431633,
0.022959867492318153,
0.023550469428300858,
-0.03860052675008774,
0.05708332732319832,
-0.047775398939847946,
0.007323073223233223,
-0.012484178878366947,
-0.01758997142314911,
0.01554104033857584,
-0.012929641641676426,
-0.014147317968308926,
-0.029798096045851707,
-0.024122197180986404,
0.012421604245901108,
0.06813209503889084,
0.017543232068419456,
-0.032587550580501556,
-0.004694581031799316,
0.06266874819993973,
0.03352031111717224,
0.020418457686901093,
0.006344806868582964,
0.0062269652262330055,
0.007448243908584118,
-0.04272358864545822,
0.026604069396853447,
0.048993099480867386,
0.022047212347388268,
-0.07356537878513336,
-0.032898951321840286,
-0.033081505447626114,
0.033154457807540894,
0.062375884503126144,
-0.060033299028873444,
0.010940845124423504,
-0.009414318017661572,
-0.07361239194869995,
-0.0068710907362401485,
-0.025783462449908257,
-0.00584004819393158,
-0.017027834430336952,
-0.008214417845010757,
-0.005419677123427391,
0.06440167874097824,
0.01403016410768032,
0.042397383600473404,
0.05173054710030556,
0.03462447226047516,
-0.012541652657091618,
-0.039753906428813934,
-0.03425358608365059,
0.034170251339673996,
0.02055189572274685,
-0.05383734777569771,
0.026423608884215355,
-0.018530987203121185,
-0.028618479147553444,
0.02383243478834629,
-0.03755924850702286,
-0.003959807101637125,
0.012042853981256485,
0.0350494310259819,
0.027593424543738365,
0.06879936158657074,
0.025798862800002098,
-0.03964371606707573,
-0.05563582107424736,
-0.012829260900616646,
-0.008608420379459858,
0.017449209466576576,
-0.02024768479168415,
0.008959131315350533,
0.0014534068759530783,
-0.04039304703474045,
-0.04922296851873398,
0.023538881912827492,
-0.015617656521499157,
0.01710597239434719,
-0.05149402469396591,
-0.016181612387299538,
0.04792364686727524,
-0.028057904914021492,
-0.01013317983597517,
-0.06090924143791199,
0.017885638400912285,
0.0500914566218853,
-0.029523741453886032,
0.04062194377183914,
0.04008563235402107,
0.03543093428015709,
-0.024671480059623718,
-0.004413540940731764,
0.024609381332993507,
-0.032190512865781784,
-0.036514561623334885,
0.0004957342171110213,
0.0053210025653243065,
-0.025264229625463486,
-0.012083116918802261,
0.012221338227391243,
-0.0367547944188118,
-0.007289269473403692,
0.02246260829269886,
-0.012969933450222015,
0.0007242375868372619,
0.008839677087962627,
0.029146142303943634,
-0.07173368334770203,
0.026409167796373367,
0.043680112808942795,
0.007086419966071844,
0.012129400856792927,
-0.028290139511227608,
-0.0047944397665560246,
0.033189404755830765,
0.08031927049160004,
-0.022816020995378494,
-0.012665794230997562,
-0.041643090546131134,
0.010048188269138336,
-0.0003015445254277438,
-0.008214173838496208,
0.018307441845536232,
0.00030089367646723986,
-0.034637823700904846,
0.002618261147290468,
0.015879672020673752,
0.05224107950925827,
-0.02965460903942585,
0.03818678483366966,
-0.008051916025578976,
-0.0528443418443203,
-0.015131215564906597,
-0.07603225857019424,
0.0002257536252727732,
0.019971812143921852,
-0.03221183642745018,
0.05522342771291733,
0.002793495310470462,
0.018995484337210655,
0.039647478610277176,
-0.005439193919301033,
-0.018229486420750618,
0.04103626683354378,
-0.035674408078193665,
-0.04343413561582565,
-0.008528495207428932,
0.025775235146284103,
0.025795333087444305,
-0.05342983826994896,
0.030479878187179565,
0.010534480214118958,
-0.029622575268149376,
-0.018750177696347237,
0.030934611335396767,
0.0366956852376461,
0.034354839473962784,
0.031635794788599014,
-0.0004998529329895973,
0.0008048036834225059,
-0.030892523005604744,
0.03959072753787041,
0.015912776812911034,
0.010630246251821518,
-0.010428445413708687,
0.01331285573542118,
0.04120878875255585,
-0.04226742684841156,
0.022187452763319016,
0.02588796429336071,
0.017074350267648697,
-0.023939194157719612,
0.005688556469976902,
0.01134326308965683,
-0.01887650229036808,
0.039857350289821625,
0.024746039882302284,
-0.026004649698734283,
0.061280738562345505,
-0.01879878342151642,
-0.004567499738186598,
-0.05803057923913002,
0.03317372873425484,
-0.00648998050019145,
-0.03139915317296982,
0.021344369277358055,
0.021774761378765106,
-0.07691312581300735,
0.004035203717648983,
0.001574064022861421,
-0.028802549466490746,
-0.009939467534422874,
-0.02536737360060215,
0.015319893136620522,
-0.020084375515580177,
-0.003575562732294202,
-0.0033687741961330175,
0.014211672358214855,
-0.016146903857588768,
0.04530845582485199,
0.045399896800518036,
0.0162556990981102,
0.06389017403125763,
-0.02273220382630825,
-0.015967493876814842,
0.017603345215320587,
0.001360905822366476,
-0.014681012369692326,
0.005849436391144991,
0.0017895807977765799,
0.013580077327787876,
0.011716851033270359,
0.02313307113945484
] |
<p>Consider a solid spherical object of uniform density that is rotating on an axis A1. Perpendicular to that axis one can draw another line that passes through the sphere. On this axis, on both sides of the sphere one attaches mass-less springs with spring constants F, and then attaches point masses of mass M to both springs.</p>
<p>If the object is now rotated around the axis A1 and simultaneously both springs are pulled and then let go, what will be observed?</p>
<p>My intuition is as follows:</p>
<p>The rate of rotation of the system will undergo wave-like behavior. It will rotate faster as the point masses attached to springs come closer to the center and it will rotate slower as they move away from the center. </p>
<p>Is this correct?</p>
| 10,678 |
[
-0.05296150967478752,
0.015843993052840233,
0.004469736944884062,
-0.0037644878029823303,
0.0013969633728265762,
-0.016499673947691917,
-0.006177464034408331,
-0.023851701989769936,
0.005798642989248037,
-0.02497795969247818,
0.019349729642271996,
0.0375949889421463,
0.04667932167649269,
0.03453771397471428,
0.018320471048355103,
-0.034202344715595245,
-0.017789263278245926,
-0.01477205939590931,
-0.008740440011024475,
-0.05100277438759804,
-0.005021639633923769,
-0.010420825332403183,
0.03354722633957863,
-0.015966871753335,
-0.011773484759032726,
0.024890607222914696,
0.042268384248018265,
-0.015352469868957996,
0.028753140941262245,
0.021091986447572708,
0.0029117052908986807,
-0.021940803155303,
-0.012375683523714542,
0.034545041620731354,
0.040745850652456284,
-0.003249733941629529,
-0.02709307335317135,
-0.00784482341259718,
0.006082853302359581,
0.039874255657196045,
-0.031215613707900047,
-0.008396146818995476,
-0.04057317599654198,
0.05068755894899368,
0.011813173070549965,
-0.008129149675369263,
0.03623955696821213,
-0.02003609761595726,
0.0652669370174408,
-0.03833590820431709,
0.0839315801858902,
0.010474828071892262,
0.021143943071365356,
0.02412150427699089,
-0.009778110310435295,
-0.01865815557539463,
0.052814189344644547,
0.06942200660705566,
-0.03977135196328163,
-0.06298241764307022,
-0.003022477962076664,
-0.042859241366386414,
-0.016309233382344246,
-0.03149386867880821,
-0.028897417709231377,
0.030544737353920937,
-0.012832563370466232,
-0.020025355741381645,
0.05174938589334488,
0.0029250923544168472,
0.010212940163910389,
0.009322269819676876,
0.0773392915725708,
-0.053513988852500916,
-0.010562019422650337,
-0.022606557235121727,
0.007348988670855761,
0.015810763463377953,
0.019046112895011902,
0.04358041658997536,
-0.0033478504046797752,
-0.00807671993970871,
0.02817501500248909,
0.06099778786301613,
0.023528076708316803,
-0.018197791650891304,
0.05452016741037369,
-0.01312661450356245,
0.021007735282182693,
-0.006684117950499058,
0.035787634551525116,
0.004798709414899349,
0.012101767584681511,
-0.010233878158032894,
-0.04404422640800476,
0.052684079855680466,
0.016097070649266243,
0.05448122322559357,
0.021828671917319298,
-0.0571959912776947,
-0.03180466964840889,
-0.01582065410912037,
0.008464589715003967,
0.07212046533823013,
0.015437145717442036,
0.012671301141381264,
-0.03854097053408623,
-0.00372413732111454,
-0.034630049020051956,
-0.02675883285701275,
-0.058932650834321976,
-0.01668652519583702,
0.017170730978250504,
-0.0021516988053917885,
0.00951442215591669,
0.0047284867614507675,
-0.031191550195217133,
0.007057164795696735,
0.027997957542538643,
0.0458851233124733,
0.0463673435151577,
-0.004013990517705679,
-0.017313847318291664,
-0.028191113844513893,
-0.014008481986820698,
0.0009580525220371783,
0.03110220842063427,
-0.025031130760908127,
-0.04816320538520813,
0.03250662982463837,
0.030249938368797302,
-0.021144678816199303,
-0.016136089339852333,
-0.024153128266334534,
0.04297782480716705,
0.010008692741394043,
-0.11329532414674759,
-0.048062656074762344,
0.04795511066913605,
-0.031932707875967026,
0.016273293644189835,
-0.06032048910856247,
-0.0011240084422752261,
0.017267020419239998,
0.10215182602405548,
0.00808301754295826,
-0.015955815091729164,
-0.013651075772941113,
0.043316543102264404,
0.0019104847451671958,
-0.024532459676265717,
-0.005818553734570742,
0.01337987370789051,
-0.06547112762928009,
-0.014136135578155518,
-0.052300240844488144,
0.003640999086201191,
0.043257635086774826,
0.005976351443678141,
-0.011862250976264477,
0.011338216252624989,
-0.03469379246234894,
0.03216781094670296,
-0.00020455183403100818,
-0.01586989499628544,
-0.03936871513724327,
0.049097754061222076,
-0.0025757504627108574,
-0.010772127658128738,
0.04381094500422478,
0.012706629000604153,
0.04944197088479996,
-0.013647934421896935,
0.030542749911546707,
0.008759715594351292,
-0.050965625792741776,
-0.01276707649230957,
-0.00941279623657465,
-0.006435394752770662,
-0.011222398839890957,
-0.017181918025016785,
-0.04298076406121254,
0.016334829851984978,
0.027251312509179115,
-0.018056631088256836,
0.059501007199287415,
0.004100951831787825,
-0.023923641070723534,
-0.01983986422419548,
-0.06215588003396988,
0.04479266330599785,
-0.0677475556731224,
0.0383002907037735,
-0.031420137733221054,
-0.02266034297645092,
0.041148312389850616,
0.033323295414447784,
0.023983288556337357,
-0.00215149880386889,
-0.02610512264072895,
-0.03207666054368019,
0.0003583270008675754,
-0.008091079071164131,
-0.031986866146326065,
0.00007420353358611465,
0.09181837737560272,
0.009594338946044445,
-0.0021156882867217064,
0.029181502759456635,
-0.013059892691671848,
-0.020848426967859268,
0.005236546043306589,
-0.01373666524887085,
0.0012816759990528226,
0.029842089861631393,
0.02613210491836071,
0.015483690425753593,
-0.008984091691672802,
-0.01778716966509819,
0.0037968240212649107,
-0.010530752129852772,
0.0564398430287838,
0.047971002757549286,
-0.02804623916745186,
0.02423865720629692,
0.06098621338605881,
0.012290016748011112,
0.003052097512409091,
-0.029544413089752197,
-0.02647526189684868,
-0.02191084250807762,
0.028826676309108734,
0.01831202208995819,
0.054298579692840576,
-0.027631206437945366,
0.014943625777959824,
0.024348357692360878,
0.039058562368154526,
0.026063289493322372,
0.01211528666317463,
0.010872914455831051,
-0.038759320974349976,
0.014860883355140686,
0.007622709963470697,
-0.014900542795658112,
0.015759320929646492,
0.03499193862080574,
0.0076279835775494576,
0.021357165649533272,
0.00409606471657753,
-0.012986389920115471,
0.04324369132518768,
-0.0073227426037192345,
0.015310907736420631,
0.023973733186721802,
-0.012035137042403221,
-0.011774701066315174,
-0.003966037184000015,
0.004055083263665438,
0.014076132327318192,
0.001162777654826641,
0.005521344020962715,
-0.038641102612018585,
0.012257221154868603,
-0.00412298459559679,
0.015865808352828026,
-0.014824852347373962,
-0.03884148970246315,
0.0387086346745491,
-0.06567608565092087,
-0.026364080607891083,
0.008685051463544369,
0.005229511298239231,
0.010038013570010662,
0.007319796830415726,
0.014576783403754234,
0.0331428162753582,
0.03254993259906769,
-0.02946183644235134,
-0.05105578154325485,
-0.006551490630954504,
-0.04601798951625824,
0.013983418233692646,
0.014681224711239338,
-0.03758669272065163,
0.02558758296072483,
-0.028535671532154083,
-0.039077844470739365,
0.021683549508452415,
-0.016058415174484253,
-0.024270419031381607,
0.021361451596021652,
0.014573398977518082,
-0.06722019612789154,
-0.004118506796658039,
-0.00582175562158227,
0.009353118017315865,
-0.03213856741786003,
0.020209453999996185,
0.04469925910234451,
-0.02150244452059269,
0.003556641284376383,
0.0040474627166986465,
-0.03314375504851341,
-0.052505627274513245,
0.006530563347041607,
-0.00959373265504837,
0.06969557702541351,
-0.023044079542160034,
0.0123037314042449,
0.011937464587390423,
-0.032615311443805695,
-0.0012327875010669231,
-0.060691021382808685,
-0.030681170523166656,
0.015911046415567398,
-0.03932247310876846,
0.07890571653842926,
0.02230248413980007,
-0.025816660374403,
0.08768482506275177,
0.018133796751499176,
-0.031876664608716965,
-0.008420276455581188,
-0.001564798760227859,
-0.016865840181708336,
-0.021841824054718018,
0.01206396147608757,
0.040069978684186935,
-0.009787453338503838,
0.026726141571998596,
0.0353061705827713,
-0.008983690291643143,
0.0022353045642375946,
0.006652723532170057,
0.0035325682256370783,
0.01430112961679697,
0.021089738234877586,
-0.0076531614176929,
0.028068289160728455,
0.0016283552395179868,
-0.0320960134267807,
0.018969012424349785,
-0.030323723331093788,
0.03620469942688942,
0.017713701352477074,
-0.06861095130443573,
0.057903096079826355,
-0.0005199626903049648,
0.0008404467953369021,
0.010244916193187237,
0.03192225098609924,
0.028109870851039886,
0.01135988812893629,
-0.008473633788526058,
0.03521284461021423,
0.07717154175043106,
-0.0007366183563135564,
-0.0276174359023571,
0.03271198272705078,
0.024188624694943428,
0.002512355102226138,
-0.025257952511310577,
-0.018850984051823616,
-0.016939213499426842,
0.04379525035619736,
-0.034184832125902176,
-0.016769928857684135,
0.008174152113497257,
-0.015643607825040817,
0.018790341913700104,
-0.0014391840668395162,
-0.05713316798210144,
0.007656505797058344,
-0.08505980670452118,
-0.009717173874378204,
-0.007700915448367596,
0.023078076541423798,
0.0048120152205228806,
0.06771983951330185,
0.04652831330895424,
0.017808012664318085,
0.021391820162534714,
0.005631991196423769,
-0.08070547133684158,
0.050832659006118774,
-0.05957802012562752,
-0.023189248517155647,
0.0036049436312168837,
0.004095026757568121,
-0.0025289696641266346,
-0.014970644377171993,
-0.012340705841779709,
-0.03995140269398689,
0.0028097096364945173,
-0.0749613344669342,
0.015389981679618359,
-0.025657182559370995,
-0.009738723747432232,
-0.005983802955597639,
0.047263238579034805,
0.0206637941300869,
-0.004713199567049742,
0.054922815412282944,
0.03740591183304787,
-0.051432590931653976,
0.0387580543756485,
-0.004973801784217358,
-0.00971019733697176,
-0.0063796015456318855,
0.01192115806043148,
0.045425012707710266,
0.037540361285209656,
-0.021462585777044296,
0.009862910024821758,
0.001270113862119615,
0.044800665229558945,
0.010821838863193989,
-0.01275296974927187,
-0.024645179510116577,
-0.0627325102686882,
-0.021143104881048203,
-0.007930939085781574,
0.08250360935926437,
-0.004398779943585396,
-0.028190290555357933,
0.028214361518621445,
-0.023590760305523872,
0.017544487491250038,
0.053074438124895096,
0.0559985525906086,
0.05124104768037796,
-0.014553719200193882,
-0.06596382707357407,
-0.027017252519726753,
0.008926058188080788,
-0.019533904269337654,
0.016497541218996048,
-0.0170269925147295,
-0.023539861664175987,
0.019153788685798645,
-0.005587941966950893,
0.02164529077708721,
0.010026240721344948,
-0.007045052479952574,
-0.013121223077178001,
0.042356669902801514,
-0.01696544699370861,
-0.0032453981693834066,
0.038761939853429794,
0.038632165640592575,
0.04832497984170914,
0.024504998698830605,
-0.00029295444255694747,
-0.09316200762987137,
-0.029183754697442055,
0.022477421909570694,
-0.017702778801321983,
0.012821858748793602,
0.025208039209246635,
-0.02453470602631569,
-0.048564523458480835,
0.05063936486840248,
-0.03723521903157234,
0.042381349951028824,
0.019986240193247795,
0.003922899719327688,
-0.011278167366981506,
-0.014514612033963203,
-0.04150272533297539,
0.0041129933670163155,
-0.014760159887373447,
0.0055600362829864025,
-0.038974080234766006,
0.010855359025299549,
-0.0020186398178339005,
-0.018830478191375732,
-0.006680102087557316,
0.020495986565947533,
0.011268345639109612,
-0.007730342913419008,
-0.021674830466508865,
-0.0013057265896350145,
-0.034032516181468964,
-0.07530786842107773,
0.04110126569867134,
-0.0059343199245631695,
-0.044480640441179276,
0.056833550333976746,
-0.056890420615673065,
-0.01431446336209774,
-0.002083113184198737,
0.00048232608241960406,
0.03438637778162956,
0.017570775002241135,
-0.04384170472621918,
0.022451063618063927,
0.0038042012602090836,
0.012478130869567394,
0.002587848110124469,
0.015982579439878464,
0.010438972152769566,
-0.01343064196407795,
0.008171266876161098,
0.01597169041633606,
-0.04389718174934387,
0.028668606653809547,
-0.02402021922171116,
0.03038748912513256,
-0.04226271063089371,
0.030618498101830482,
0.0022847431246191263,
0.00963661540299654,
-0.026848800480365753,
-0.025928182527422905,
-0.030342020094394684,
0.028220077976584435,
-0.016766976565122604,
0.02617635764181614,
-0.00005025957216275856,
0.03526797518134117,
-0.015266398899257183,
0.007773663382977247,
-0.006685691885650158,
-0.001551576890051365,
-0.013030392117798328,
0.044404536485672,
-0.022948874160647392,
0.004476856905966997,
-0.028577707707881927,
-0.02871931530535221,
0.002328176749870181,
-0.07469488680362701,
0.07120658457279205,
-0.028532374650239944,
0.00753056351095438,
0.05565100908279419,
-0.033317964524030685,
-0.004483542870730162,
0.02117910608649254,
-0.020167376846075058,
0.028855452314019203,
-0.04715868830680847,
0.028048861771821976,
0.026156606152653694,
0.029947808012366295,
-0.04431353136897087,
-0.057021792978048325,
0.06496270000934601,
0.026522120460867882,
-0.01868247427046299,
-0.023100854828953743,
0.017481420189142227,
-0.03943183645606041,
-0.030780402943491936,
-0.03775646165013313,
0.021106671541929245,
-0.031128451228141785,
0.000798899563960731,
0.06311574578285217,
0.01986265368759632,
0.06264936178922653,
0.0028236019425094128,
-0.028297794982790947,
0.0026333017740398645,
-0.0029031289741396904,
-0.006579498294740915,
-0.015279681421816349,
0.08289513736963272,
-0.036382466554641724,
-0.03455197811126709,
-0.016674811020493507,
-0.031527888029813766,
0.01921869069337845,
-0.020060354843735695,
-0.0035435762256383896,
0.014336921274662018,
0.009531373158097267,
-0.01044138427823782,
-0.008324556052684784,
0.007841131649911404,
-0.004238947760313749,
-0.0013057295000180602,
0.025614401325583458,
0.004669088404625654,
-0.00976928323507309,
-0.055512864142656326,
0.025594795122742653,
0.04535117745399475,
-0.01867750845849514,
0.010595694184303284,
0.05399343743920326,
-0.01325848139822483,
0.012639450840651989,
-0.0058343419805169106,
0.01921280473470688,
0.023963414132595062,
0.011853060685098171,
0.015763619914650917,
-0.02863694727420807,
-0.009289572015404701,
-0.005676163360476494,
0.01075088232755661,
-0.01934240013360977,
-0.018818629905581474,
0.08206421136856079,
-0.04350227490067482,
0.04079097881913185,
0.027322446927428246,
0.014744366519153118,
-0.03285131976008415,
-0.01516144722700119,
0.018306991085410118,
-0.009311352856457233,
0.0029939778614789248,
0.028372377157211304,
-0.05581154674291611,
-0.004786275327205658,
0.03748778998851776,
0.03425542637705803,
-0.043202001601457596,
0.029799887910485268,
-0.00009445186151424423,
0.021377883851528168,
0.005362853407859802,
0.030220501124858856,
-0.024605417624115944,
0.010183589532971382,
-0.02238444983959198,
0.08561583608388901,
-0.024045199155807495,
0.012466635555028915,
0.024550655856728554,
0.02979491837322712,
0.010129264555871487,
-0.039528004825115204,
-0.015667423605918884,
-0.036030855029821396,
0.011232242919504642,
0.0055253575555980206,
0.012495194561779499,
0.00321998936124146,
-0.015457376837730408,
0.03449062630534172,
0.047806516289711,
0.023349128663539886,
-0.03764718398451805,
-0.026684513315558434,
-0.025155721232295036,
-0.03453895449638367,
-0.0672399029135704,
0.04448474198579788,
-0.014203418977558613,
-0.04093280807137489,
0.03487555310130119,
0.0032030921429395676,
0.027970410883426666,
0.02853570319712162,
0.019332658499479294,
-0.022791216149926186,
0.08935607224702835,
-0.013368016108870506,
0.01648525334894657,
-0.014904193580150604,
0.009223612025380135,
0.1157546415925026,
0.04383911192417145,
0.025329595431685448,
-0.024351514875888824,
0.014024888165295124,
-0.0162038654088974,
0.02270578406751156,
-0.020385434851050377,
-0.02314344234764576,
0.014701726846396923,
0.03281182050704956,
0.030646203085780144,
0.08664251863956451,
-0.030707532539963722,
-0.041246358305215836,
0.04702253267168999,
-0.016322335228323936,
0.005933823063969612,
-0.03979892656207085,
0.020595211535692215,
0.0006300538661889732,
0.004837339278310537,
-0.05236491933465004,
0.006200842093676329,
-0.02550329826772213,
-0.03844873607158661,
0.0013668403262272477,
-0.023105787113308907,
0.01641175150871277,
-0.01692885160446167,
-0.022385602816939354,
0.030128449201583862,
0.008974804542958736,
-0.05102115496993065,
-0.03958786651492119,
0.05409718304872513,
0.03587553650140762,
-0.021800335496664047,
0.013762252405285835,
0.06367851793766022,
-0.003026209305971861,
0.030091892927885056,
0.01895100623369217,
0.04152865707874298,
-0.02984696254134178,
0.025678444653749466,
-0.02542022243142128,
0.04193324223160744,
0.0016137920320034027,
0.009189586155116558,
0.006966509390622377,
-0.021375508978962898,
-0.0012269308790564537,
-0.06551285833120346,
0.012811379507184029,
-0.030122308060526848,
0.013745909556746483,
-0.004395550116896629,
-0.012249092571437359,
-0.007377695757895708,
-0.009700319729745388,
0.02458692528307438,
-0.003563059028238058,
-0.028739996254444122,
-0.01388726569712162,
-0.010059677995741367,
0.02507867105305195,
0.07016801834106445,
-0.03266896679997444,
0.007801036816090345,
-0.042061202228069305,
-0.010255194269120693,
-0.02881268598139286,
0.04915454611182213,
0.01458975113928318,
-0.013249839656054974,
0.032345496118068695,
-0.00616852892562747,
-0.008182598277926445,
-0.04059835895895958,
-0.04360506683588028,
0.03538250923156738,
0.010231725871562958,
-0.021706778556108475,
-0.014651542529463768,
0.009898325428366661,
0.05428849533200264,
0.023544196039438248,
-0.014548947103321552,
0.013080395758152008,
-0.017599761486053467,
0.028669040650129318,
0.022505085915327072,
-0.019910095259547234,
-0.003833735128864646,
0.011998008005321026,
-0.03335421159863472,
0.0010790347587317228,
-0.03893221914768219,
0.03466103971004486,
0.03188611567020416,
0.028662292286753654,
-0.003949297592043877,
0.031912945210933685,
0.0008491475600749254,
-0.0005023609846830368,
0.005814563017338514,
-0.01118803396821022,
-0.04628175124526024,
0.029147012159228325,
-0.040691208094358444,
-0.029408689588308334,
-0.03066505491733551,
-0.040598027408123016,
-0.0249994695186615,
-0.016217883676290512,
0.026654202491044998,
-0.03659137710928917,
0.02884582057595253,
-0.014403538778424263,
0.018260357901453972,
-0.022097736597061157,
0.018548842519521713,
-0.042079050093889236,
-0.03203599154949188,
0.014174734242260456,
0.00819762609899044,
0.020634623244404793,
0.0360909029841423,
-0.014298551715910435,
-0.02287236601114273,
0.019781887531280518,
0.02760489098727703,
0.009520993568003178,
0.020827023312449455,
0.027415402233600616,
-0.02397313341498375,
0.02177482284605503,
0.002537832595407963,
-0.05402986705303192,
0.04628843814134598,
-0.03420044854283333,
-0.02304955944418907,
0.019901501014828682,
-0.014781261794269085,
0.04724299535155296,
-0.009897327050566673,
-0.03414351865649223,
-0.004086580593138933,
0.054321371018886566,
-0.03552064672112465,
-0.005331519525498152,
0.007162899244576693,
-0.03127949684858322,
-0.05534250661730766,
-0.01500511635094881,
0.006824229843914509,
-0.024690410122275352,
-0.022710882127285004,
0.013788246549665928,
0.0361935980618,
-0.04900052398443222,
-0.02051425166428089,
-0.0026973222848027945,
-0.018706709146499634,
-0.0010050698183476925,
0.018917342647910118,
0.008555695414543152,
0.045153334736824036,
0.024751834571361542,
-0.0333251953125,
0.0203397274017334,
-0.0013970518484711647,
-0.006127194035798311,
-0.09338977932929993,
-0.0072148703038692474,
-0.024259209632873535,
0.0030761936213821173,
0.009394126944243908,
-0.02631094865500927,
-0.01995103992521763,
0.035316407680511475,
-0.06367326527833939,
0.033358801156282425,
-0.042764123529195786,
0.003961954731494188,
-0.039872344583272934,
-0.012842915952205658,
0.0050594983622431755,
0.038011278957128525,
0.01015517394989729,
0.036974985152482986,
-0.004481807816773653,
0.022290188819169998,
-0.032339371740818024,
0.00004803046249435283,
0.020448919385671616,
0.03276287764310837,
0.0017295376164838672,
-0.012750152498483658,
0.07529205828905106,
-0.04625815153121948,
-0.048150211572647095,
0.022035593166947365,
-0.0335061140358448,
0.03166765719652176,
0.021672213450074196,
-0.013461995869874954,
-0.006383528001606464,
0.020825954154133797,
0.013270902447402477,
-0.020091412588953972,
-0.03827163577079773,
0.06063542515039444,
0.0290986355394125,
0.010072818957269192,
-0.0890006572008133,
0.0021634423173964024,
-0.0005065923323854804,
-0.05622037872672081,
-0.004625558853149414,
0.003093402599915862,
-0.03212499991059303,
0.03921596705913544,
-0.017399273812770844,
0.005842122714966536,
0.0018217414617538452,
0.0015129370149224997,
0.012352630496025085,
-0.015657177194952965,
0.011016364209353924,
0.04352312907576561,
-0.003276765113696456,
-0.008407536894083023,
0.04460853338241577,
0.01370053831487894,
-0.003847123822197318,
-0.016773179173469543,
-0.04306640475988388,
0.002285369671881199,
-0.0663362368941307,
-0.016841193661093712,
0.0032681103330105543,
-0.01636630855500698,
-0.03843754529953003,
-0.03811874985694885,
0.005524619948118925,
0.0342102088034153,
0.037181224673986435,
0.04012318328022957,
0.00021317719074431807,
-0.026094088330864906,
-0.029730897396802902,
-0.10242380201816559,
0.0028564301319420338,
-0.007303028367459774,
-0.0137927932664752,
-0.029589278623461723,
0.0001429525000276044,
-0.002586643910035491,
0.005153424106538296,
0.04623735323548317,
0.023933809250593185,
0.01019864808768034,
0.039397891610860825,
-0.034924715757369995,
0.02920282818377018,
-0.06918955594301224,
0.001633291831240058,
-0.02848650887608528,
-0.021103721112012863,
0.027646003291010857,
-0.009597251191735268,
-0.018028821796178818,
-0.00553486030548811,
0.05319363996386528,
0.002272963523864746,
0.017425471916794777,
0.026407618075609207,
-0.02834116667509079,
0.025047654286026955,
0.02537996880710125,
0.029737094417214394,
0.0931984931230545,
-0.017987992614507675,
0.014913203194737434,
0.025980472564697266,
-0.050210945308208466,
-0.04586775600910187,
0.0606127493083477,
-0.019350046291947365,
-0.010013684630393982,
-0.025863416492938995,
-0.04085610434412956,
0.002032418502494693,
-0.009355827234685421,
-0.019030822440981865,
0.013122542761266232,
-0.06339655816555023,
-0.014984237030148506,
-0.020483048632740974,
0.0033586802892386913,
0.02471991814672947,
-0.027405548840761185,
0.04811590537428856,
0.0227114949375391,
-0.016274917870759964,
0.00493898568674922,
0.03750045970082283,
0.024008434265851974,
-0.004708492662757635,
-0.02819155342876911,
0.03545473888516426,
-0.002652671653777361,
0.027638500556349754,
-0.0026256984565407038,
0.017749890685081482,
-0.006412469781935215,
-0.036283306777477264,
0.013547808863222599,
-0.008672325871884823,
-0.007384155876934528,
0.0318099781870842,
0.004925572779029608,
0.048976652324199677,
-0.0392485037446022,
-0.01604941487312317,
-0.004818001762032509,
-0.0036020518746227026,
0.01683521457016468,
-0.000356060394551605,
0.02425054833292961,
-0.003295833244919777,
-0.004906498361378908,
0.01782061532139778,
-0.02032507210969925,
-0.03138104826211929,
0.032293710857629776,
-0.013352986425161362,
0.02109978348016739,
-0.017821703106164932,
-0.0013193635968491435,
0.03097539395093918,
-0.005721913184970617,
-0.040386002510786057,
-0.018792765215039253,
0.06093938648700714,
0.0006510756211355329,
-0.000590709678363055,
-0.015816688537597656,
-0.001887124148197472,
-0.005525603890419006,
0.055003561079502106,
-0.034419700503349304,
-0.017178671434521675,
-0.010424730367958546,
0.043565306812524796,
-0.0008923986461013556,
0.0060619753785431385
] |
<p>A continuous charge distribution flowing as a constant current in a closed loop doesn't radiate. Is it therefore true that as you increase the number of proton bunches in the LHC, while keeping the total charge constant, the synchrotron radiation decreases?</p>
| 10,679 |
[
-0.03324788063764572,
-0.0004731077642645687,
0.023593632504343987,
-0.024330679327249527,
0.01812569424510002,
0.044931091368198395,
-0.01928802579641342,
-0.03382027521729469,
-0.008652696385979652,
-0.04965737834572792,
-0.006510070990771055,
0.020122544839978218,
0.02028694748878479,
0.008739807642996311,
0.022222915664315224,
0.001570921391248703,
-0.0018234302988275886,
-0.005027465522289276,
0.02047371119260788,
-0.01562962867319584,
-0.021472018212080002,
0.06331337243318558,
0.007303095888346434,
0.011109735816717148,
-0.04066583141684532,
0.03425103425979614,
-0.021906601265072823,
0.020807117223739624,
0.004926769062876701,
0.03733154386281967,
-0.0003457019047345966,
-0.010572407394647598,
-0.011221866123378277,
0.02560793049633503,
0.04188767075538635,
-0.026094086468219757,
-0.0047936709597706795,
-0.03928004950284958,
-0.02711579017341137,
0.017983801662921906,
-0.006536152213811874,
-0.010760504752397537,
-0.013804762624204159,
0.04344555363059044,
-0.006986498367041349,
-0.018627479672431946,
-0.02864714525640011,
-0.007176383398473263,
0.08367623388767242,
-0.047161202877759933,
0.10314226895570755,
-0.00812157616019249,
0.05336491018533707,
0.022260287776589394,
-0.03336118534207344,
0.0026674638502299786,
0.08023213595151901,
0.05147886648774147,
-0.017245769500732422,
-0.014735618606209755,
-0.007856692187488079,
-0.05521120876073837,
-0.012201900593936443,
-0.007607289124280214,
0.005179004743695259,
-0.01468509528785944,
0.009127187542617321,
-0.03400532528758049,
0.01768253929913044,
0.02810937725007534,
0.017209772020578384,
0.021499205380678177,
0.013539574109017849,
-0.028717927634716034,
0.02437901683151722,
-0.002201881492510438,
0.035177286714315414,
0.016726398840546608,
0.01984916254878044,
0.018346698954701424,
-0.04902901500463486,
-0.018065106123685837,
0.027771208435297012,
0.06336713582277298,
0.010661394335329533,
-0.015423962846398354,
0.0648447573184967,
-0.039504051208496094,
0.0169571153819561,
0.03487420454621315,
-0.03386930376291275,
0.017132047563791275,
0.03886941075325012,
0.0342332161962986,
-0.021769415587186813,
0.07641348242759705,
-0.012614559382200241,
0.07853221893310547,
0.007333977613598108,
-0.04461333155632019,
0.035023462027311325,
0.029873844236135483,
0.004411714151501656,
0.03275468572974205,
0.0215380247682333,
-0.03497977927327156,
-0.01979990489780903,
0.0144762322306633,
-0.05492541939020157,
-0.00984067004173994,
-0.08266610652208328,
-0.031065069139003754,
0.011964844539761543,
-0.03544174134731293,
-0.0007041863282211125,
-0.047795046120882034,
-0.006596005521714687,
-0.010869785211980343,
0.038866933435201645,
0.07834206521511078,
0.040612004697322845,
-0.015946896746754646,
0.03023679554462433,
-0.012348289601504803,
-0.06318065524101257,
0.01892402023077011,
0.014862552285194397,
-0.020713815465569496,
-0.0662546306848526,
0.041874706745147705,
-0.01912742853164673,
-0.005544672254472971,
0.01264266949146986,
-0.02473917417228222,
0.03792000561952591,
0.004824008326977491,
-0.06222156435251236,
-0.05454258620738983,
0.0093325674533844,
-0.018736694008111954,
0.003915264271199703,
-0.061617378145456314,
-0.021777773275971413,
0.024962548166513443,
0.07856474071741104,
-0.022520221769809723,
-0.021998271346092224,
-0.019538605585694313,
0.02960701659321785,
0.019168701022863388,
-0.01571248099207878,
-0.0062452820129692554,
0.011137700639665127,
-0.02938300184905529,
-0.02580438181757927,
-0.08540651202201843,
0.024563360959291458,
0.05872933939099312,
0.02268950268626213,
-0.013213595375418663,
0.024235781282186508,
-0.0064856926910579205,
0.006319738458842039,
0.013123922049999237,
-0.020315876230597496,
-0.016282660886645317,
0.06815657764673233,
0.0075034815818071365,
0.016219783574342728,
0.008729572407901287,
0.01867711916565895,
-0.010479891672730446,
0.013879846781492233,
0.03945249691605568,
0.026987699791789055,
-0.05890767648816109,
-0.027773449197411537,
-0.019614743068814278,
0.04058371111750603,
0.002958887256681919,
-0.015245692804455757,
-0.01121453382074833,
-0.03135835379362106,
0.005608401261270046,
0.00525935273617506,
0.02509482018649578,
-0.011208978481590748,
-0.0016319041606038809,
0.0077645923011004925,
-0.02859731949865818,
-0.004959526937454939,
-0.07804800570011139,
-0.009199589490890503,
0.006715857889503241,
-0.0010537010384723544,
0.009217397309839725,
0.02384934015572071,
-0.023783670738339424,
-0.013397435657680035,
-0.033177267760038376,
0.018870582804083824,
0.03349427878856659,
-0.016712157055735588,
-0.009755848906934261,
-0.002916433848440647,
0.01518495287746191,
0.01943439431488514,
0.033211369067430496,
0.04073594510555267,
-0.011947857216000557,
-0.048254501074552536,
0.001084624556824565,
-0.0411105714738369,
0.03262807056307793,
-0.0016878879396244884,
0.014843156561255455,
0.0016685471637174487,
-0.03023158758878708,
-0.02437545359134674,
0.043270405381917953,
-0.0077117737382650375,
0.03670971468091011,
0.040927499532699585,
0.024775870144367218,
0.009943142533302307,
0.0010602384572848678,
-0.002587517024949193,
0.014198613353073597,
-0.007283242419362068,
-0.055250462144613266,
-0.047668445855379105,
0.015518305823206902,
0.013833551667630672,
0.005173401441425085,
-0.039261478930711746,
0.019359184429049492,
0.039845000952482224,
0.026933224871754646,
0.010358225554227829,
0.02305014617741108,
-0.03703675419092178,
-0.033346887677907944,
0.026614045724272728,
0.044166091829538345,
0.006373204756528139,
0.009134364314377308,
0.04130479320883751,
0.01091806124895811,
-0.006099062040448189,
-0.01801157370209694,
0.0004563862457871437,
-0.00016269763000309467,
0.00544159859418869,
-0.009683527052402496,
0.01810038462281227,
-0.05447661504149437,
0.031006628647446632,
-0.024317769333720207,
0.07451087981462479,
-0.00553164491429925,
-0.04129400476813316,
-0.008187299594283104,
-0.015209858305752277,
-0.01919379085302353,
0.0010280427522957325,
-0.0236348956823349,
-0.0461520217359066,
-0.009764578193426132,
0.037323564291000366,
-0.0709085613489151,
0.0004188018792774528,
-0.012523530051112175,
-0.01701628789305687,
-0.017473481595516205,
0.013498472981154919,
0.03797544538974762,
0.010369664058089256,
0.039031386375427246,
-0.06357526779174805,
-0.003721524029970169,
0.018574252724647522,
-0.021551137790083885,
0.03365173935890198,
0.02682836353778839,
-0.0037215480115264654,
-0.0016685607843101025,
-0.014884473755955696,
-0.042594701051712036,
0.004004357848316431,
-0.03331742808222771,
0.02637363225221634,
0.05871094390749931,
-0.02251293510198593,
-0.03057754784822464,
0.0035249057691544294,
-0.017305411398410797,
0.010074984282255173,
-0.0067426785826683044,
0.013593862764537334,
0.037514325231313705,
0.03614122048020363,
-0.029897943139076233,
0.006459452211856842,
-0.053904540836811066,
0.004099215380847454,
-0.012169933877885342,
-0.0034921530168503523,
0.016696596518158913,
-0.008752702735364437,
0.051577191799879074,
0.04057843238115311,
-0.030112730339169502,
0.004353080410510302,
-0.016247667372226715,
-0.025949150323867798,
0.03807331249117851,
-0.003946120385080576,
0.039620544761419296,
-0.0408182330429554,
-0.05572710186243057,
0.07834391295909882,
0.03854510188102722,
-0.027983808889985085,
0.003538597607985139,
-0.03984706103801727,
-0.003094022162258625,
-0.03247198835015297,
-0.003841663245111704,
0.017668388783931732,
0.023880058899521828,
-0.013801634311676025,
0.03137226402759552,
0.032214026898145676,
0.035427894443273544,
0.017102530226111412,
0.007688459940254688,
-0.019063623622059822,
0.019400516524910927,
0.019696487113833427,
0.0196826308965683,
0.022230152040719986,
-0.0429973378777504,
0.0014211449306458235,
0.015082857571542263,
0.027248041704297066,
-0.004908086732029915,
-0.05353384092450142,
0.06501402705907822,
0.04041227698326111,
0.07086912542581558,
-0.016243260353803635,
0.019149761646986008,
0.011854400858283043,
-0.00886853039264679,
-0.006207535974681377,
0.03428352251648903,
0.0033955120015889406,
-0.004358936566859484,
0.012307824566960335,
0.011447503231465816,
0.03666743263602257,
-0.01816180907189846,
-0.04559911787509918,
0.007556227967143059,
-0.034466538578271866,
0.039927784353494644,
-0.017608046531677246,
-0.02659127116203308,
0.007257299032062292,
0.021735545247793198,
0.03698422759771347,
0.006331881042569876,
-0.02841782197356224,
0.012349966913461685,
-0.07971193641424179,
-0.008520298637449741,
-0.027058200910687447,
0.04438527673482895,
0.04583455249667168,
0.04371154308319092,
0.005338600371032953,
0.01342723984271288,
0.03012184239923954,
-0.020202800631523132,
-0.09140025079250336,
-0.0021068535279482603,
-0.03850032389163971,
-0.012824400328099728,
-0.012401392683386803,
-0.02190815471112728,
-0.014034063555300236,
0.014342019334435463,
-0.016519002616405487,
-0.018817724660038948,
0.0006735502975061536,
-0.01983155496418476,
0.0031483140774071217,
-0.030798036605119705,
-0.04044637456536293,
-0.042899101972579956,
0.019731024280190468,
0.029913514852523804,
-0.018596159294247627,
0.040968820452690125,
-0.006929275579750538,
-0.0016499784542247653,
-0.005114229861646891,
-0.02534640021622181,
0.046552568674087524,
-0.0029174587689340115,
0.04548325017094612,
0.036383990198373795,
0.004322738852351904,
-0.07669179886579514,
0.014189359731972218,
0.019599149003624916,
0.031987227499485016,
0.013025431893765926,
-0.05256362631917,
-0.007224223110824823,
-0.057062383741140366,
-0.03915196657180786,
0.030070483684539795,
0.024213848635554314,
0.008323500864207745,
0.004545021336525679,
0.04900599271059036,
-0.03200560063123703,
-0.024031294509768486,
0.025038357824087143,
0.03840942308306694,
0.026035530492663383,
-0.03918660804629326,
-0.0038272636011242867,
0.019318589940667152,
0.02173651196062565,
-0.023457134142518044,
0.016771100461483,
-0.010184135288000107,
-0.021396920084953308,
0.012172305025160313,
0.011016393080353737,
0.03303350880742073,
-0.027067644521594048,
0.0036287365946918726,
0.027988111600279808,
0.03120858035981655,
0.011820570565760136,
0.039228349924087524,
0.02977456897497177,
0.04411279410123825,
0.0147298164665699,
0.022895455360412598,
-0.00108828186057508,
-0.1093621477484703,
-0.04214191809296608,
0.021359704434871674,
0.06861826032400131,
-0.005002071149647236,
-0.039517421275377274,
-0.017532721161842346,
0.0028318229597061872,
0.054014839231967926,
-0.015885021537542343,
0.028692804276943207,
-0.010605864226818085,
0.029432019218802452,
-0.038304559886455536,
-0.017509914934635162,
-0.052359212189912796,
0.03505473956465721,
-0.029162168502807617,
0.013885793276131153,
-0.02535005658864975,
-0.024319157004356384,
-0.004050923977047205,
0.032423995435237885,
0.05523071065545082,
0.05852532014250755,
0.029794858768582344,
0.018922148272395134,
-0.008749183267354965,
0.033206112682819366,
-0.0005784673267044127,
-0.08560111373662949,
0.022176383063197136,
-0.008455824106931686,
-0.016500746831297874,
0.05141527205705643,
0.0030277862679213285,
-0.0052710529416799545,
0.004977465607225895,
0.04393618553876877,
0.003016579430550337,
-0.020211029797792435,
-0.08057475090026855,
0.025146443396806717,
0.04991332069039345,
0.006228598766028881,
0.039213962852954865,
0.03341927006840706,
-0.026043148711323738,
0.011503222398459911,
-0.0037233002949506044,
0.05220704525709152,
-0.02296791598200798,
0.014273746870458126,
0.02012053318321705,
-0.015241344459354877,
-0.03280680626630783,
0.06180792301893234,
-0.0285844374448061,
0.027410471811890602,
0.011443980038166046,
-0.029471565037965775,
0.026692848652601242,
0.006853597704321146,
-0.036984629929065704,
-0.0061513278633356094,
0.0031850088853389025,
0.029852621257305145,
0.0000018958455711981514,
-0.03211045637726784,
-0.009972097352147102,
-0.03529678285121918,
-0.01016753725707531,
-0.0037723551504313946,
-0.011733101680874825,
0.022525904700160027,
-0.001228031818754971,
0.022745583206415176,
-0.0006306956056505442,
0.0016160247614607215,
0.036014046519994736,
0.011618943884968758,
-0.0321243554353714,
0.002552318386733532,
-0.027502553537487984,
-0.011406691744923592,
0.016070622950792313,
-0.02967471070587635,
0.025565266609191895,
-0.035285335034132004,
0.05470095947384834,
-0.002435317961499095,
0.0022894237190485,
-0.09016232937574387,
-0.03393171355128288,
0.03951672464609146,
0.020656540989875793,
0.02315189316868782,
-0.017660316079854965,
-0.007892235182225704,
-0.03728935495018959,
-0.050222381949424744,
-0.033794570714235306,
0.003116811625659466,
-0.043455611914396286,
0.007245090324431658,
0.0006285733543336391,
0.0027087919879704714,
0.04049535095691681,
0.0019711756613105536,
-0.028673803433775902,
-0.032088957726955414,
-0.014052879065275192,
-0.01714460738003254,
-0.016488170251250267,
0.050949692726135254,
-0.01667553000152111,
-0.017810609191656113,
0.004499971866607666,
-0.021318934857845306,
0.08065661787986755,
-0.050689697265625,
-0.039953913539648056,
0.04763602465391159,
0.03616056218743324,
0.042590152472257614,
0.020071612671017647,
-0.006197343580424786,
-0.03804997354745865,
0.02694777026772499,
-0.0031386043410748243,
-0.008684099651873112,
-0.029844608157873154,
-0.010401659645140171,
-0.010412490926682949,
0.0332249216735363,
0.0068026455119252205,
0.026024101302027702,
0.047914087772369385,
-0.014565163291990757,
-0.03841838985681534,
-0.0345604345202446,
-0.007434193044900894,
0.00296691688708961,
-0.02684212476015091,
0.04531756043434143,
0.00931956060230732,
0.010505208745598793,
0.011737246997654438,
-0.009440144523978233,
-0.022760514169931412,
-0.049101442098617554,
0.05120713636279106,
-0.028180431574583054,
0.04117801412940025,
-0.0064223762601614,
-0.01466542761772871,
-0.03744418919086456,
-0.01925298571586609,
0.005872196517884731,
-0.007922859862446785,
0.0332319512963295,
0.026280619204044342,
-0.04270755872130394,
-0.003286030376330018,
0.008463755249977112,
0.03577486053109169,
-0.013477184809744358,
0.010924277827143669,
0.013734747655689716,
0.003669844241812825,
0.006593788508325815,
-0.03432265669107437,
-0.05708828195929527,
0.030426912009716034,
-0.03462666645646095,
0.033551089465618134,
0.02153795398771763,
-0.024205965921282768,
0.03389096260070801,
-0.014425244182348251,
0.0015718875220045447,
-0.0003066226781811565,
-0.03367190435528755,
-0.06736148148775101,
0.012830466032028198,
0.0033520979341119528,
0.03145592287182808,
-0.024732455611228943,
0.023596150800585747,
0.016996359452605247,
0.029220813885331154,
0.046243760734796524,
0.02706778421998024,
-0.0450819656252861,
-0.031206758692860603,
-0.02751896157860756,
0.0045471396297216415,
0.06620465964078903,
0.0010258746333420277,
-0.016866309568285942,
0.01163412258028984,
-0.029849180951714516,
0.020315658301115036,
0.022172238677740097,
0.04218865931034088,
0.011666079983115196,
0.021661849692463875,
-0.01786031574010849,
0.020395345985889435,
-0.04676489159464836,
0.01258145458996296,
0.12500067055225372,
0.07453817874193192,
0.026726484298706055,
-0.04883507266640663,
0.012014252133667469,
-0.030227091163396835,
-0.013029741123318672,
-0.02509121410548687,
0.023628540337085724,
0.006517297122627497,
0.008680449798703194,
0.00744584621861577,
0.04984534904360771,
-0.021925777196884155,
0.013469160534441471,
0.07019776105880737,
-0.03501160070300102,
-0.005853582173585892,
0.040085624903440475,
0.029198436066508293,
0.036922529339790344,
0.04432004317641258,
-0.06155287101864815,
0.007820786908268929,
-0.003027921775355935,
0.0049780597910285,
-0.013496160507202148,
-0.04832588881254196,
0.00677343737334013,
-0.016651375219225883,
-0.045298367738723755,
0.003805347718298435,
0.019139936193823814,
-0.02179558016359806,
-0.04535975307226181,
-0.0030993232503533363,
0.024094687774777412,
0.0014018533984199166,
-0.007937359623610973,
0.027887798845767975,
0.04730847850441933,
-0.011959356255829334,
0.001618952606804669,
0.045048199594020844,
-0.004424508195370436,
0.04873686656355858,
-0.010004033334553242,
0.0060388497076928616,
0.0070535470731556416,
0.0011233632685616612,
0.022781625390052795,
0.015228407457470894,
-0.027381598949432373,
-0.023342525586485863,
-0.024050164967775345,
0.015709877014160156,
-0.014918441884219646,
-0.023663507774472237,
-0.010811029002070427,
-0.031008094549179077,
0.017346184700727463,
-0.032826006412506104,
-0.01660849153995514,
0.04986513406038284,
0.018372362479567528,
0.020996876060962677,
-0.001807997701689601,
0.05449637398123741,
0.00639147637411952,
-0.02212650142610073,
-0.006478848401457071,
-0.04239983856678009,
-0.06513377279043198,
-0.026303386315703392,
-0.00017185637261718512,
0.011364108882844448,
0.031092407181859016,
0.005565797910094261,
0.00902612041682005,
0.004096700809895992,
-0.08379232883453369,
0.025256728753447533,
0.044205185025930405,
-0.004248525481671095,
-0.04366747662425041,
0.0335359051823616,
-0.01761159859597683,
0.031080493703484535,
-0.031192416325211525,
-0.015404398553073406,
0.0027614999562501907,
0.06537527590990067,
-0.016291843727231026,
-0.05878166854381561,
-0.014425624161958694,
-0.007052963133901358,
-0.029314758256077766,
-0.011079634539783001,
-0.03191563859581947,
0.050821658223867416,
-0.01842573471367359,
0.017255909740924835,
0.006987224332988262,
0.018110672011971474,
-0.0056448811665177345,
0.02237512357532978,
0.03794064372777939,
-0.012087698094546795,
0.019565746188163757,
0.02157049998641014,
0.009636018425226212,
-0.02760082669556141,
-0.013596240431070328,
-0.0023924249690026045,
0.00993906520307064,
0.045447755604982376,
0.0346560999751091,
-0.016712740063667297,
-0.012177019380033016,
-0.0053644864819943905,
-0.01166568323969841,
-0.023508859798312187,
-0.024967104196548462,
-0.06420007348060608,
0.008891819976270199,
-0.0004866363015025854,
-0.0005806774715892971,
0.0036624979693442583,
0.023042595013976097,
-0.015085394494235516,
-0.019673772156238556,
0.017734507098793983,
-0.012401771731674671,
-0.025279391556978226,
-0.03417940065264702,
0.049997542053461075,
0.040276527404785156,
0.039794325828552246,
-0.02833544835448265,
-0.06135575473308563,
0.03738788142800331,
-0.03473671153187752,
-0.03899836912751198,
-0.005451872944831848,
-0.0051653687842190266,
-0.0001787803921615705,
0.022876650094985962,
-0.01821576990187168,
-0.03761649504303932,
0.04473768174648285,
-0.025090347975492477,
-0.029186120256781578,
-0.0143868587911129,
-0.0001239250268554315,
0.040256328880786896,
-0.019917013123631477,
0.03394068405032158,
0.007831576280295849,
0.01588747650384903,
0.04288618639111519,
0.02359810099005699,
-0.0261247418820858,
0.016094455495476723,
-0.056284207850694656,
0.0031626615673303604,
0.0013922210782766342,
0.01139196939766407,
0.03726629167795181,
-0.014010854065418243,
0.010253071784973145,
-0.04211293160915375,
-0.007564656436443329,
0.0028273866046220064,
-0.006670646835118532,
-0.11089730262756348,
-0.01849859021604061,
0.0008549947524443269,
0.0006200690404511988,
-0.009249845519661903,
-0.01592142879962921,
0.04116693139076233,
0.03489390388131142,
-0.09273362159729004,
0.0158982016146183,
-0.009377291426062584,
-0.02066560834646225,
-0.0630786344408989,
-0.02853112667798996,
-0.0037390422075986862,
0.037996966391801834,
0.06466125696897507,
0.07196733355522156,
-0.012533627450466156,
-0.005409230478107929,
0.012591575272381306,
-0.018736274912953377,
-0.052469298243522644,
0.011708740144968033,
0.02513936161994934,
-0.039973337203264236,
0.04271363839507103,
-0.003448129864409566,
-0.005786749999970198,
0.01704074628651142,
0.016106123104691505,
-0.029247649013996124,
-0.029732532799243927,
0.04521428048610687,
0.02220129407942295,
0.06108123064041138,
0.010510459542274475,
0.013219374231994152,
0.02491931803524494,
-0.015849431976675987,
0.018034346401691437,
-0.005739382468163967,
-0.01709553599357605,
0.04435339197516441,
0.02743041142821312,
-0.03312422335147858,
-0.01268789917230606,
0.02630489319562912,
0.0009405743330717087,
0.00040703557897359133,
0.013094951398670673,
0.014195996336638927,
0.045155975967645645,
-0.007135085761547089,
0.0070272767916321754,
-0.03780880570411682,
0.008592991158366203,
-0.00023368543770629913,
0.007632661610841751,
0.016521031036973,
0.01558050699532032,
0.008078815415501595,
-0.003357976907864213,
-0.00521284993737936,
0.03510662540793419,
0.002186449244618416,
-0.05331049859523773,
0.029199007898569107,
0.022883320227265358,
0.018720079213380814,
0.00898049771785736,
-0.0743703544139862,
-0.045161981135606766,
0.0305333212018013,
-0.007935251109302044,
0.014409229159355164,
0.02153123915195465,
-0.049195583909749985,
-0.03511304035782814,
-0.07048957794904709,
0.02883654087781906,
-0.0005801903898827732,
0.002570947166532278,
-0.03676367923617363,
-0.03367043286561966,
-0.05242854356765747,
0.0336139015853405,
0.054460130631923676,
0.0040625957772135735,
-0.011130271479487419,
0.011419734917581081,
-0.013376466929912567,
0.021360069513320923,
-0.04379257932305336,
-0.009567142464220524,
-0.010312417522072792,
-0.021449804306030273,
-0.024477457627654076,
-0.036396902054548264,
-0.05779213085770607,
0.00007913567969808355,
0.010805095545947552,
0.038535118103027344,
0.029633376747369766,
-0.033952586352825165,
-0.024383876472711563,
0.06290452182292938,
-0.0006062697502784431,
-0.030411573126912117,
0.06902526319026947,
-0.00758609501644969,
0.02308451011776924,
0.024115342646837234,
0.018435178324580193,
-0.04832164943218231,
0.007686909753829241,
-0.05063949152827263,
0.006983229890465736,
-0.004267377313226461,
-0.02329709194600582,
0.009981563314795494,
-0.04281240329146385,
0.013604646548628807,
0.03908204287290573,
-0.045784637331962585,
-0.03391057252883911,
0.016867099329829216,
0.0024374949280172586,
0.016468586400151253,
0.02285235933959484,
-0.010446524247527122,
-0.009169169701635838,
0.005677139386534691,
-0.0134450513869524,
0.059334930032491684,
0.02146761864423752,
-0.01772148348391056,
0.04534417390823364,
0.04061390087008476,
0.005487562622874975,
-0.006284678354859352,
-0.007783624809235334,
0.04256559535861015,
-0.015301122330129147,
-0.03529326990246773,
0.0038958964869379997,
-0.022617731243371964,
-0.008643525652587414,
-0.0032541195396333933,
-0.02267521433532238,
0.0456334613263607,
-0.02847452275454998,
0.013118239119648933,
-0.028107337653636932,
-0.029501495882868767,
0.014971538446843624,
0.010817931964993477,
0.014561383984982967,
0.09682778269052505,
-0.0005140121793374419,
-0.06315526366233826,
0.0002518027031328529,
-0.011904720216989517,
0.036558154970407486,
-0.056898728013038635,
0.005768926348537207,
0.0014455225318670273,
-0.01897415891289711,
-0.018715374171733856,
0.028065921738743782,
-0.0005165825714357197,
-0.020961925387382507,
0.036771878600120544,
0.0447390042245388,
0.016941577196121216,
0.0060120997950434685,
-0.04834028705954552,
-0.04374461993575096,
0.02451891079545021,
-0.010789135470986366,
0.026002371683716774,
0.005288644228130579,
0.0004991855821572244,
-0.027992913499474525,
-0.004282078705728054
] |
<p>What is the correct way to use the resistance and temperature correlation formula from <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html" rel="nofollow">http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html</a>?</p>
<p>In particular, does R have to be the higher resistance and R0 the lower or vice versa? The resulting calculated dT differs depending on this choice of R and R0.</p>
<p>Quick example of what I mean:</p>
<blockquote>
<p>Choose R = 7.97 and R0 = 7.28, copper a ~= .00393</p>
<p>dT = 24.1171</p>
<p>Choose R = 7.28 and R0 = 7.97, copper a ~= .00393</p>
<p>dT = -22.0292</p>
</blockquote>
<p>I believe the answer is to use the former (always choose R and R0 so R > R0) because this more closely correlates with my lab data.</p>
| 10,680 |
[
0.0008254114654846489,
-0.04009672626852989,
0.016130022704601288,
-0.0007889701519161463,
-0.018429091200232506,
0.03506208956241608,
-0.03181072697043419,
0.01136841531842947,
0.03266867995262146,
-0.005489636678248644,
0.046274855732917786,
0.04087254777550697,
0.02184390276670456,
0.005468333605676889,
0.04658909887075424,
0.04134279116988182,
0.018486108630895615,
0.0005480721592903137,
0.015562498942017555,
-0.037859540432691574,
0.010686403140425682,
0.014162195846438408,
-0.015167882665991783,
0.0036990593653172255,
-0.01291667576879263,
0.03484584763646126,
0.02483469620347023,
-0.035476185381412506,
0.0031756525859236717,
0.041845496743917465,
-0.006184314843267202,
-0.04133663699030876,
0.018521027639508247,
0.0310615673661232,
0.017726955935359,
0.014808841049671173,
-0.007736748084425926,
-0.04294714704155922,
-0.03127206116914749,
0.020096121355891228,
-0.019685765728354454,
0.0040983459912240505,
0.024232957512140274,
0.033778250217437744,
0.01380198448896408,
0.005325489677488804,
0.008220984600484371,
-0.017650946974754333,
0.02044028416275978,
-0.05727371945977211,
0.005843357648700476,
-0.004621267784386873,
0.04538833722472191,
0.0656418427824974,
-0.010395728051662445,
0.005858731921762228,
0.06827805191278458,
0.05216096714138985,
-0.030562838539481163,
-0.052194222807884216,
0.014417372643947601,
-0.05612614005804062,
-0.02238394506275654,
-0.006415039300918579,
-0.013470673933625221,
0.02151901088654995,
-0.004884589463472366,
-0.012859436683356762,
0.019764728844165802,
-0.015750611200928688,
0.056912608444690704,
-0.005665603093802929,
0.029284296557307243,
-0.018591884523630142,
0.02271275781095028,
-0.04040716588497162,
0.015926074236631393,
0.01342321652919054,
0.047933097928762436,
0.055340707302093506,
-0.026112066581845284,
0.014301801100373268,
0.03435844928026199,
0.0020831201691180468,
0.001828122534789145,
-0.03652030602097511,
0.02928541786968708,
-0.00038270087679848075,
0.020912891253829002,
0.029488377273082733,
0.005709276534616947,
0.016890164464712143,
0.02366853691637516,
0.026460202410817146,
-0.010906808078289032,
-0.010770042426884174,
0.015838416293263435,
0.047738149762153625,
-0.03306788206100464,
-0.019063662737607956,
-0.026638144627213478,
-0.00475664995610714,
-0.009067362174391747,
0.06883873045444489,
0.0012863122392445803,
-0.03213896602392197,
0.006910556927323341,
0.010959804989397526,
0.021124817430973053,
-0.033445507287979126,
-0.0461185984313488,
0.02273077890276909,
-0.03437525033950806,
0.001559153781272471,
-0.005576142575591803,
-0.04389581456780434,
0.014677098020911217,
-0.0041303476318717,
0.06753713637590408,
0.012648720294237137,
0.01263310108333826,
-0.02537284977734089,
0.015506576746702194,
0.0025695180520415306,
-0.0017291988478973508,
0.031827088445425034,
0.02381550520658493,
-0.0011245544301345944,
0.015775194391608238,
0.03510669618844986,
-0.025770509615540504,
-0.020622609183192253,
0.03197019174695015,
-0.0017011655727401376,
0.03354160860180855,
0.02685605175793171,
-0.07884389907121658,
-0.05128522962331772,
0.03842847794294357,
-0.0267733596265316,
-0.00845103058964014,
-0.05734725296497345,
-0.005362090189009905,
0.03786207363009453,
0.07711676508188248,
0.009437447413802147,
0.014957014471292496,
-0.04250425472855568,
0.02626921236515045,
0.023467080667614937,
0.018716467544436455,
-0.018099401146173477,
0.020852215588092804,
-0.03864645957946777,
-0.02168048545718193,
-0.040624987334012985,
0.012286795303225517,
0.017150601372122765,
-0.0007369456579908729,
0.005570072680711746,
0.040467992424964905,
-0.007731200661510229,
0.003100935835391283,
0.028186561539769173,
0.019717613235116005,
-0.011601603589951992,
0.08913731575012207,
-0.030106283724308014,
0.03567613661289215,
0.006790513638406992,
0.021842515096068382,
0.020915957167744637,
0.009097125381231308,
0.0012222492368891835,
0.04925158992409706,
0.008535459637641907,
0.025592127814888954,
-0.03613629564642906,
-0.0016873847926035523,
0.007896663621068,
-0.08706559240818024,
-0.038021158427000046,
0.004658309742808342,
-0.042144082486629486,
0.015335602685809135,
0.05865931510925293,
0.006868927273899317,
-0.0031031789258122444,
0.015086007304489613,
-0.006804504431784153,
-0.025326818227767944,
-0.03807482495903969,
0.008989732712507248,
-0.0317833311855793,
-0.03457063436508179,
-0.004116769414395094,
0.01879124343395233,
0.014273897744715214,
0.029216444119811058,
-0.010866067372262478,
0.011008919216692448,
0.0012419006088748574,
0.0036630043759942055,
-0.0206154752522707,
0.006719367578625679,
0.040516287088394165,
0.038956400007009506,
-0.03689151257276535,
0.011114641092717648,
-0.044823966920375824,
0.017874853685498238,
-0.0009572072885930538,
-0.010835832916200161,
0.029468849301338196,
0.03886522352695465,
-0.04167915880680084,
-0.006100834812968969,
0.05421285331249237,
-0.010461954399943352,
0.021138710901141167,
-0.02507469244301319,
0.04801362007856369,
0.06390228122472763,
0.06741507351398468,
-0.00814624223858118,
0.048825137317180634,
0.009889477863907814,
0.04477386176586151,
-0.025526423007249832,
0.0003396577958483249,
-0.03428138047456741,
0.011561250314116478,
0.05387667194008827,
0.016961321234703064,
-0.06213993579149246,
0.03679756820201874,
0.056043196469545364,
0.024630803614854813,
-0.0014667018549516797,
0.05056077614426613,
-0.0038665130268782377,
-0.04312313720583916,
-0.0065825642086565495,
-0.00023143761791288853,
-0.0047631701454520226,
-0.01310775987803936,
-0.020411796867847443,
0.0032346949446946383,
0.04513004049658775,
-0.02840469963848591,
-0.0328633189201355,
0.04884244501590729,
0.02682468295097351,
0.02579786442220211,
-0.0003817003162112087,
-0.03843037039041519,
0.03102816268801689,
-0.027201229706406593,
0.03354327008128166,
0.031029652804136276,
0.023839212954044342,
0.0158804040402174,
-0.019938908517360687,
-0.03634876385331154,
0.011187480762600899,
-0.004363102838397026,
-0.005832992028445005,
-0.002800249494612217,
0.0025169807486236095,
-0.02906167507171631,
-0.0222708061337471,
-0.05463368818163872,
0.024647213518619537,
-0.03984176740050316,
-0.014551065862178802,
0.0220169760286808,
0.029119960963726044,
0.050377242267131805,
-0.04597439989447594,
-0.02882208861410618,
-0.02624806948006153,
-0.011522205546498299,
-0.006079701241105795,
0.006987518165260553,
-0.03443765640258789,
-0.008377263322472572,
-0.009096645750105381,
-0.0398455373942852,
0.03725159913301468,
0.0039930748753249645,
-0.01941893808543682,
-0.011732039973139763,
0.0027613260317593813,
-0.08929633349180222,
-0.03623518347740173,
0.013078528456389904,
-0.008527371101081371,
-0.05154707282781601,
-0.02026413381099701,
0.051428359001874924,
-0.018597891554236412,
-0.038943856954574585,
0.017526870593428612,
-0.036273758858442307,
-0.03926331177353859,
0.03781775385141373,
-0.03237340599298477,
-0.010028514079749584,
0.003159583080559969,
0.01517691183835268,
0.026394978165626526,
-0.02072587050497532,
-0.03239503875374794,
-0.04466158524155617,
-0.08577144145965576,
0.024627095088362694,
-0.007516162935644388,
0.046401865780353546,
0.007166310679167509,
-0.01659146137535572,
0.08604820817708969,
0.014885437674820423,
-0.027457956224679947,
-0.017494648694992065,
-0.015180588699877262,
-0.03590599447488785,
-0.027376646175980568,
0.020947780460119247,
0.0723198726773262,
-0.03037494421005249,
0.013761285692453384,
0.023307258263230324,
0.06634858250617981,
0.032777100801467896,
0.002315441146492958,
0.03779295086860657,
0.02991700917482376,
0.0376761220395565,
-0.05575637146830559,
0.08765757083892822,
-0.004382906947284937,
-0.01099761575460434,
0.016214614734053612,
-0.04311269894242287,
0.04091395065188408,
0.023007944226264954,
-0.07786212861537933,
0.017288675531744957,
-0.026451725512742996,
0.030266819521784782,
-0.02161867544054985,
0.0033757691271603107,
0.000463667354779318,
-0.0176699161529541,
-0.027281904593110085,
0.060416966676712036,
0.061734750866889954,
-0.038720421493053436,
-0.014006170444190502,
0.04138840734958649,
0.03288377821445465,
-0.010092455893754959,
-0.028811899945139885,
0.02359437569975853,
-0.03495212271809578,
0.03208388760685921,
0.004116453230381012,
-0.023958340287208557,
0.038925934582948685,
0.012801850214600563,
0.03725212439894676,
0.03152962028980255,
-0.05564507842063904,
-0.00837530568242073,
-0.09256249666213989,
-0.028173226863145828,
-0.057130295783281326,
0.09172511845827103,
-0.005461975000798702,
0.0543600358068943,
0.03392714262008667,
-0.004325817339122295,
-0.0010221980046480894,
0.0035024385433644056,
-0.07825490087270737,
0.05620267614722252,
-0.02437581866979599,
-0.037736937403678894,
-0.001393284648656845,
-0.04047656059265137,
-0.010977301746606827,
-0.03838165104389191,
0.019306570291519165,
0.020287299528717995,
0.001986332470551133,
-0.0272197388112545,
0.0115891732275486,
0.03184407949447632,
-0.00328607065603137,
-0.039322689175605774,
0.01975058577954769,
-0.029187029227614403,
-0.036845117807388306,
0.011525087058544159,
0.04507441446185112,
-0.005849667824804783,
0.007641697768121958,
-0.013391447253525257,
0.03695104643702507,
0.04674682766199112,
0.06730432063341141,
0.001072061131708324,
-0.014988983981311321,
-0.008936746045947075,
0.004018472507596016,
-0.006702146492898464,
0.03459329903125763,
0.0002625544148031622,
-0.04183211177587509,
-0.03318798169493675,
-0.005898864008486271,
-0.02169266901910305,
-0.027533523738384247,
0.02244807593524456,
-0.0008973881485871971,
0.005822292063385248,
0.028246639296412468,
-0.008705899119377136,
-0.019222991541028023,
-0.004028035793453455,
0.04720701649785042,
0.012894936837255955,
0.0012533424887806177,
-0.0604981854557991,
-0.019647076725959778,
-0.029924480244517326,
0.00010697452671593055,
0.016175756230950356,
0.025510359555482864,
-0.010475482791662216,
-0.019698159769177437,
0.02700386755168438,
0.024618063122034073,
-0.009960418567061424,
0.028402341529726982,
0.004678879398852587,
0.06747297942638397,
-0.013025733642280102,
-0.02219049260020256,
0.02475626952946186,
0.027097295969724655,
0.03643476963043213,
-0.01462086196988821,
-0.0303056500852108,
-0.05964290723204613,
-0.026108935475349426,
0.02046966925263405,
0.057304710149765015,
-0.055178914219141006,
-0.03016609698534012,
-0.07228393107652664,
-0.014372364617884159,
0.06052830070257187,
-0.02197982184588909,
0.03185529261827469,
0.02303973026573658,
-0.008547901175916195,
-0.021875496953725815,
-0.03432050347328186,
-0.019420914351940155,
0.022848939523100853,
0.013617484830319881,
0.03589177131652832,
-0.026544617488980293,
-0.017633965238928795,
-0.006885791663080454,
0.0016720418352633715,
0.04445329308509827,
0.060182783752679825,
-0.030664615333080292,
0.032035768032073975,
-0.011822651140391827,
-0.0141144385561347,
0.0031281153205782175,
-0.0866357758641243,
0.016166137531399727,
0.0005071166669949889,
0.053906362503767014,
0.05062788352370262,
-0.01913292519748211,
-0.019023483619093895,
0.02618357539176941,
0.006073698867112398,
0.01282628532499075,
0.00007204591383924708,
-0.0007869932451285422,
0.05988168343901634,
0.025024138391017914,
-0.047814588993787766,
0.051509030163288116,
0.02239985577762127,
0.014514530077576637,
-0.019805245101451874,
-0.004179473966360092,
0.02493446320295334,
-0.02393784373998642,
0.005714501719921827,
-0.032482828944921494,
0.009875974617898464,
-0.04172676429152489,
0.011890899389982224,
-0.017831746488809586,
0.049845289438962936,
-0.045864470303058624,
-0.013495754450559616,
0.03396088257431984,
-0.0026620617136359215,
-0.014028128236532211,
0.0004166901344433427,
0.029326098039746284,
0.013384988531470299,
-0.020147643983364105,
-0.03575780242681503,
-0.021838653832674026,
-0.014563590288162231,
0.011852456256747246,
0.020938929170370102,
-0.0651351809501648,
0.019566545262932777,
-0.022609129548072815,
-0.007757424842566252,
-0.0026624174788594246,
-0.0791272222995758,
0.03926759958267212,
0.0005020715179853141,
-0.009261691942811012,
0.012225909158587456,
-0.02451908215880394,
0.018493860960006714,
0.026094648987054825,
0.02144431881606579,
0.011971312575042248,
-0.07857376337051392,
0.05800151824951172,
-0.002899388549849391,
-0.01698228344321251,
-0.06851336359977722,
-0.05865621566772461,
-0.009728451259434223,
0.006872247904539108,
-0.019645188003778458,
-0.01221641805022955,
-0.011677989736199379,
-0.010064014233648777,
-0.02545340545475483,
-0.0028170968871563673,
0.0560264065861702,
0.004024632275104523,
-0.043088532984256744,
-0.004542851820588112,
0.033882807940244675,
0.10868468135595322,
-0.0008762134821154177,
-0.0025642053224146366,
0.03267301991581917,
-0.024511057883501053,
-0.0170274805277586,
0.01575525291264057,
0.010283841751515865,
-0.02785188890993595,
-0.0055647059343755245,
-0.027175283059477806,
-0.00991662684828043,
0.0799754336476326,
0.0506766252219677,
-0.02408442832529545,
0.01061311736702919,
0.008565586060285568,
0.003595721675083041,
-0.04268747940659523,
0.029781363904476166,
0.017306724563241005,
-0.012970704585313797,
0.006982158403843641,
-0.007304697297513485,
-0.0474201999604702,
-0.0032071550376713276,
-0.019566109403967857,
-0.0027470537461340427,
-0.03257296234369278,
0.00860938336700201,
0.07418332993984222,
0.009816616773605347,
-0.02040257677435875,
0.011867859400808811,
-0.045421864837408066,
0.0027235569432377815,
0.011173771694302559,
-0.004748759791254997,
0.02044646441936493,
-0.029340749606490135,
-0.03416384011507034,
-0.056700199842453,
-0.055349577218294144,
0.015463610179722309,
0.05164671689271927,
-0.026259761303663254,
0.049940869212150574,
0.00591867184266448,
-0.021346120163798332,
0.013385257683694363,
-0.018091756850481033,
-0.004933520685881376,
-0.001843264908529818,
-0.0018188761314377189,
0.02434573508799076,
-0.003591779386624694,
-0.02614254504442215,
-0.013899940997362137,
0.01374594122171402,
0.00604992127045989,
-0.011406625621020794,
0.011490230448544025,
-0.0007695260574109852,
0.0010320729343220592,
0.007773879449814558,
-0.020911583676934242,
0.024458052590489388,
-0.05919693037867546,
0.035823676735162735,
-0.021126611158251762,
-0.022675208747386932,
0.04186064749956131,
0.006886328104883432,
0.003586710663512349,
-0.060458991676568985,
-0.0314977802336216,
-0.04364548996090889,
0.0010766027262434363,
0.015026263892650604,
-0.011922378093004227,
0.010432274080812931,
0.040736082941293716,
0.0545264333486557,
-0.003984828479588032,
0.02069082297384739,
-0.04933074489235878,
-0.04606819897890091,
-0.014881307259202003,
-0.005574481096118689,
-0.073748379945755,
0.07835323363542557,
-0.006084196735173464,
-0.01706850156188011,
0.02852777950465679,
-0.025606557726860046,
0.03347523882985115,
0.025705134496092796,
0.019430287182331085,
-0.02329280413687229,
0.08714813739061356,
-0.01935562863945961,
0.02752496488392353,
-0.005512838717550039,
-0.008236560970544815,
0.11312614381313324,
0.06146784871816635,
0.017081523314118385,
-0.05416156351566315,
0.015243155881762505,
-0.0009264801628887653,
0.007211504504084587,
-0.022018305957317352,
0.010118253529071808,
-0.024370724335312843,
0.02368890680372715,
0.05309756472706795,
0.01923457533121109,
-0.007036805152893066,
-0.0003663509851321578,
0.04947042465209961,
-0.019797319546341896,
-0.016465261578559875,
0.028654413297772408,
0.03174608573317528,
-0.006245413329452276,
-0.009246943518519402,
-0.018439745530486107,
0.010511285625398159,
-0.02615359239280224,
-0.03148849681019783,
-0.03296196088194847,
-0.01200099941343069,
0.004966808948665857,
0.010502873919904232,
-0.01009663287550211,
0.02760988473892212,
0.01603536866605282,
0.03905898705124855,
-0.019523829221725464,
0.007255693431943655,
0.029606444761157036,
-0.02666890062391758,
0.014974230900406837,
-0.003922720439732075,
-0.007853408344089985,
-0.013274767436087132,
0.023677363991737366,
0.016529014334082603,
-0.07483357936143875,
0.02303420566022396,
-0.011975589208304882,
-0.004046918824315071,
-0.02752847969532013,
-0.042520564049482346,
0.023341771215200424,
0.03605799004435539,
0.02627386897802353,
-0.05919414013624191,
-0.029678689315915108,
0.04058023542165756,
0.04266638681292534,
-0.009867439046502113,
-0.03349258005619049,
-0.05209127441048622,
0.02177674137055874,
-0.048580095171928406,
0.023323070257902145,
0.03672577068209648,
0.003339046612381935,
-0.007547392975538969,
-0.018336694687604904,
0.06279537081718445,
-0.027853289619088173,
0.003366763237863779,
-0.01428217627108097,
0.01024127472192049,
-0.024802139028906822,
-0.01336654182523489,
0.013663655146956444,
0.020851492881774902,
0.06580730527639389,
-0.017980938777327538,
0.005247680004686117,
-0.005276489071547985,
-0.0590280145406723,
0.03530862554907799,
0.00892767682671547,
0.0032588744070380926,
-0.019657742232084274,
-0.0038687342312186956,
-0.001425386406481266,
0.036704257130622864,
0.0003607521066442132,
0.0022171693854033947,
0.03811172395944595,
0.023107510060071945,
0.03505048155784607,
-0.04661785066127777,
-0.0076782056130468845,
0.008624793961644173,
-0.06817536056041718,
0.011967657133936882,
0.006410020869225264,
0.010208501480519772,
0.0012838118709623814,
-0.00013705785386264324,
-0.033531732857227325,
0.015919767320156097,
-0.015647633001208305,
-0.008898965083062649,
-0.00024370344181079417,
-0.0172207560390234,
-0.010234743356704712,
0.016840869560837746,
-0.02542858198285103,
-0.0038531413301825523,
-0.00863303430378437,
-0.029957901686429977,
-0.013332030735909939,
0.01652003824710846,
0.013482009060680866,
-0.04248017445206642,
-0.004856698215007782,
-0.02597806602716446,
-0.03779337555170059,
-0.0104156993329525,
0.006604147609323263,
-0.04500290006399155,
-0.0175979845225811,
-0.017021071165800095,
0.01028431300073862,
-0.0033247561659663916,
0.05563021078705788,
-0.012526157312095165,
0.0069572050124406815,
0.05292493849992752,
0.0015852948417887092,
0.02101537026464939,
-0.02357224002480507,
-0.020057057961821556,
-0.010051681660115719,
0.06642992049455643,
-0.05336902290582657,
-0.03949255123734474,
0.029670123010873795,
-0.02425742708146572,
0.0028948180843144655,
0.013435005210340023,
0.034668147563934326,
0.008908008225262165,
-0.014272719621658325,
0.004878870211541653,
0.04249650612473488,
0.08099076896905899,
-0.023801196366548538,
-0.019439689815044403,
0.006068903021514416,
-0.03943520411849022,
0.06179668754339218,
-0.032875239849090576,
-0.005831324495375156,
-0.010970461182296276,
0.022220583632588387,
0.030277270823717117,
0.039808887988328934,
-0.03134322538971901,
0.03309952840209007,
0.025142699480056763,
-0.0005836286582052708,
0.023128628730773926,
0.011221157386898994,
0.005591508932411671,
0.020589036867022514,
0.021830804646015167,
-0.025225989520549774,
0.031104786321520805,
0.0016231221379712224,
0.011213894933462143,
-0.04041752219200134,
-0.010153151117265224,
0.02258170396089554,
0.0009746131836436689,
-0.0070413933135569096,
-0.021838054060935974,
-0.03255002945661545,
-0.0069240378215909,
-0.02110607549548149,
-0.009675591252744198,
-0.015544547699391842,
-0.030673228204250336,
-0.029276976361870766,
0.0054565304890275,
0.0053244722075760365,
0.005990969482809305,
0.03845321387052536,
0.054284531623125076,
0.03800653666257858,
0.005102494265884161,
-0.003305211663246155,
-0.034092314541339874,
-0.01294209249317646,
0.03798095881938934,
0.01972600445151329,
-0.06215042993426323,
0.0309921707957983,
-0.009516872465610504,
-0.01925092563033104,
0.043487709015607834,
-0.030416585505008698,
0.0169359240680933,
-0.002029997296631336,
0.0132242850959301,
-0.014293702319264412,
0.04478942230343819,
0.009761755354702473,
-0.013997896574437618,
-0.035655226558446884,
-0.01354335155338049,
0.043335143476724625,
0.03414717689156532,
-0.00553342467173934,
0.006696166470646858,
0.009705823846161366,
-0.019174877554178238,
-0.04108727350831032,
0.048189520835876465,
-0.027434030547738075,
0.019525276497006416,
0.020063718780875206,
-0.011902323924005032,
0.02213623747229576,
-0.01472402922809124,
-0.021150415763258934,
-0.026832666248083115,
-0.020753879100084305,
0.05611767992377281,
0.006151682231575251,
0.015473388135433197,
0.010769888758659363,
-0.004890397656708956,
-0.01090843416750431,
-0.009051719680428505,
0.0029726549983024597,
-0.02571197785437107,
-0.05730902776122093,
-0.025742191821336746,
-0.013915122486650944,
-0.019003557041287422,
-0.03200826048851013,
-0.030200472101569176,
-0.025834275409579277,
0.0475950762629509,
0.011911029927432537,
0.020263152197003365,
0.0062337336130440235,
-0.057889971882104874,
-0.01176363229751587,
-0.050005730241537094,
0.031110653653740883,
-0.010471727699041367,
-0.038265589624643326,
-0.03876705840229988,
-0.06374409049749374,
-0.02236413024365902,
0.03510894626379013,
0.08650825172662735,
-0.0006606417591683567,
-0.006371899973601103,
-0.012531775049865246,
-0.01509696152061224,
0.028026893734931946,
-0.03859531879425049,
0.03255714476108551,
0.015607442706823349,
0.036089785397052765,
0.023947807028889656,
-0.026040615513920784,
-0.011172535829246044,
-0.0008119546691887081,
-0.0112301679328084,
-0.04048234969377518,
0.039620399475097656,
0.012092892080545425,
-0.0005237034638412297,
0.013503720052540302,
0.025743557140231133,
-0.02662753127515316,
0.07140430808067322,
-0.014405060559511185,
0.02294452302157879,
0.017749972641468048,
-0.0003696258063428104,
-0.056189700961112976,
0.039600670337677,
-0.03421679139137268,
-0.022953012958168983,
0.013872372917830944,
0.014153169468045235,
0.006334339734166861,
-0.06997261196374893,
0.006215783301740885,
0.027934977784752846,
-0.05487540364265442,
-0.02893093228340149,
0.014164038002490997,
0.014644804410636425,
0.021228443831205368,
-0.020830553025007248,
0.02928454801440239,
0.01331488136202097,
-0.0195855051279068,
0.02115350030362606,
0.029253734275698662,
0.030422978103160858,
-0.007727507501840591,
-0.011444605886936188,
0.04604543372988701,
0.012272953987121582,
0.004121979232877493,
-0.00289247022010386,
-0.008201909251511097,
-0.04843069612979889,
-0.010450847446918488,
0.046279244124889374,
-0.04834570735692978,
0.027025394141674042,
0.015431089326739311,
-0.012773900292813778,
0.06643382459878922,
-0.05754707008600235,
0.00006839398702140898,
-0.014185471460223198,
-0.009227477014064789,
-0.000813725870102644,
0.03434141352772713,
0.008477927185595036,
0.02413988672196865,
-0.024781540036201477,
-0.017406120896339417,
-0.015905408188700676,
-0.017912590876221657,
0.04573075473308563,
-0.04658155143260956,
-0.0055884202010929585,
-0.03920633718371391,
-0.007424554787576199,
-0.05127783492207527,
0.0065968879498541355,
-0.030817322432994843,
-0.004430105909705162,
0.04411746561527252,
0.012691276147961617,
0.001664355513639748,
-0.015948548913002014,
-0.004363043233752251,
0.009944579564034939,
0.023701485246419907,
-0.05823930352926254,
-0.04539325460791588,
-0.041493434458971024,
0.025476954877376556,
0.009657376445829868,
-0.003921761177480221
] |
<p>At time there are talks about <a href="http://en.wikipedia.org/wiki/Quantum_computers" rel="nofollow">quantum computers</a> and lot of talks and discussion on its exponential speed. But studying in some more details it makes reference to "Heisenberg uncertainty principle", which simply says that either position or momentum can be calculated for any electron. If we already know the limitation, then in which direction this research is going?</p>
| 10,681 |
[
-0.009276039898395538,
-0.04731973633170128,
0.02851981483399868,
-0.06352809816598892,
0.04069484770298004,
-0.02715866081416607,
-0.050940245389938354,
0.0023315066937357187,
-0.01890074834227562,
-0.0197479035705328,
0.021069083362817764,
0.06357209384441376,
0.027795474976301193,
0.03783433884382248,
-0.012376828119158745,
0.032459158450365067,
-0.006043257657438517,
-0.020266616716980934,
-0.03957327827811241,
-0.01485849916934967,
0.016134947538375854,
0.014304162003099918,
0.00363862793892622,
0.0131458705291152,
0.012846696190536022,
0.006768437568098307,
0.03623826056718826,
0.01796817034482956,
0.016595076769590378,
0.07985622435808182,
0.016906367614865303,
-0.0282460767775774,
0.040695615112781525,
-0.002300080843269825,
0.024648392572999,
-0.012052228674292564,
-0.0168979000300169,
-0.06923927366733551,
0.0009165090159513056,
-0.0005902660195715725,
-0.03185402229428291,
-0.011606779880821705,
-0.007881494238972664,
0.032308727502822876,
-0.021318217739462852,
0.04881418123841286,
-0.002622955944389105,
-0.04035338759422302,
0.052356019616127014,
-0.04760943725705147,
0.06728160381317139,
-0.00030085103935562074,
0.035382844507694244,
-0.03860801085829735,
0.013857790268957615,
0.011492098681628704,
0.07434389740228653,
0.0457884706556797,
-0.012367968447506428,
-0.06429260969161987,
-0.001332441926933825,
0.005505654960870743,
0.05403238534927368,
-0.026595044881105423,
-0.024311557412147522,
0.03126835450530052,
-0.020330309867858887,
-0.03616075590252876,
0.020773088559508324,
0.0049295793287456036,
0.0024058655835688114,
0.008368241600692272,
0.06325480341911316,
0.009217221289873123,
0.055090803653001785,
-0.05166592076420784,
0.023322341963648796,
0.009581214748322964,
-0.010588769800961018,
0.06018243730068207,
-0.011919032782316208,
0.004464314319193363,
0.042522918432950974,
0.014139336533844471,
-0.010622587986290455,
-0.016725288704037666,
0.011648188345134258,
-0.042115118354558945,
-0.014326198026537895,
0.04975023865699768,
-0.012496345676481724,
0.023174941539764404,
0.052159179002046585,
-0.021486325189471245,
-0.039650436490774155,
0.010980376973748207,
0.014804207719862461,
0.05674140900373459,
-0.005310822278261185,
-0.040095698088407516,
0.04259408637881279,
-0.003754905890673399,
0.02223017066717148,
0.06772148609161377,
-0.0052885632030665874,
0.025337710976600647,
-0.021247508004307747,
0.03854498639702797,
-0.012446043081581593,
-0.02467985451221466,
-0.005144410766661167,
0.008261917158961296,
-0.003944516181945801,
0.01402236707508564,
0.007529606111347675,
-0.023862944915890694,
0.0019290868658572435,
0.0018534153932705522,
0.07446938008069992,
0.03863482177257538,
-0.006702403537929058,
-0.020797936245799065,
-0.024923235177993774,
-0.027480946853756905,
-0.061555542051792145,
0.029723934829235077,
0.04706278070807457,
-0.01849500834941864,
-0.054209426045417786,
0.027261413633823395,
0.019196288660168648,
-0.010672057047486305,
0.025523174554109573,
0.021228499710559845,
0.030534764751791954,
-0.01814357377588749,
-0.13481293618679047,
-0.06925322115421295,
0.05423391982913017,
-0.013478406704962254,
0.006994433701038361,
-0.07113256305456161,
0.02629186026751995,
0.04043769836425781,
0.08850200474262238,
-0.008052119053900242,
0.023239176720380783,
-0.016944002360105515,
0.02589709870517254,
0.036778684705495834,
-0.010848881676793098,
-0.016201725229620934,
0.009834229946136475,
-0.024219946935772896,
0.02182682417333126,
-0.05335275083780289,
0.03827338665723801,
0.04320758208632469,
-0.017822174355387688,
-0.028208913281559944,
0.050629884004592896,
-0.008477172814309597,
0.008075064979493618,
-0.025345494970679283,
-0.007905947975814342,
-0.04874507337808609,
0.0876862034201622,
0.016133280470967293,
0.008725994266569614,
0.02707158587872982,
-0.03128935024142265,
0.006673831958323717,
0.0075454628095030785,
-0.002018637489527464,
0.05882707238197327,
-0.022047337144613266,
-0.0259544737637043,
-0.03982344642281532,
0.043208155781030655,
-0.012997034937143326,
-0.03070642426609993,
-0.03097512759268284,
0.027887441217899323,
0.027432706207036972,
0.01648430898785591,
0.026614071801304817,
-0.03680457919836044,
0.01994853839278221,
-0.0037745810113847256,
-0.034647367894649506,
-0.014351019635796547,
-0.07494030892848969,
0.02669292502105236,
0.01763695292174816,
-0.014845305122435093,
0.044919371604919434,
-0.017953157424926758,
0.009402737952768803,
-0.008635486476123333,
-0.03761664777994156,
-0.01865176297724247,
0.011884836480021477,
0.029243484139442444,
0.00878127384930849,
0.010176312178373337,
0.08168922364711761,
0.0006704193656332791,
-0.006171195302158594,
0.03781251609325409,
-0.0034585450775921345,
-0.08248970657587051,
0.026521941646933556,
0.008615725673735142,
0.031830571591854095,
0.08318698406219482,
0.00463089719414711,
-0.0007695143576711416,
0.0022720838896930218,
-0.04702093079686165,
0.00787600502371788,
0.004349845461547375,
0.09648581594228745,
0.009403510950505733,
0.0063287946395576,
0.02117418684065342,
0.01502737682312727,
0.026079891249537468,
0.0034354394301772118,
0.020681317895650864,
-0.021885080263018608,
-0.05222776159644127,
-0.008811571635305882,
-0.01711300201714039,
0.044848136603832245,
-0.03715559095144272,
-0.005850953981280327,
-0.0020714388228952885,
0.025399349629878998,
0.035343293100595474,
0.02207190915942192,
-0.04284696280956268,
-0.040592145174741745,
-0.005015251692384481,
0.011652907356619835,
-0.007002423983067274,
0.006918672006577253,
0.03436778485774994,
0.016268320381641388,
0.020814072340726852,
-0.011484558694064617,
-0.016669463366270065,
0.03102898597717285,
-0.02377859689295292,
-0.006493028253316879,
0.007170526776462793,
-0.061477627605199814,
-0.009438246488571167,
-0.027208229526877403,
-0.013730204664170742,
-0.01706496626138687,
-0.018696948885917664,
0.015508273616433144,
-0.03311343491077423,
-0.04823187738656998,
-0.015722572803497314,
0.005548456683754921,
-0.04800533130764961,
-0.008782302029430866,
0.024375151842832565,
-0.019663499668240547,
0.01922273263335228,
-0.03030920773744583,
0.011556409299373627,
-0.00939000491052866,
0.008146275766193867,
0.06291607767343521,
-0.023004751652479172,
0.043052565306425095,
-0.039360951632261276,
-0.0664067491889,
0.0037918940652161837,
-0.048191409558057785,
-0.005916895344853401,
-0.003849786939099431,
-0.030687609687447548,
-0.0018546285573393106,
-0.023442663252353668,
-0.051388103514909744,
0.0370686911046505,
-0.03712719306349754,
0.04051121696829796,
-0.01671319268643856,
-0.019173238426446915,
-0.039115894585847855,
-0.008136631920933723,
-0.029655152931809425,
-0.012185945175588131,
-0.021564101800322533,
-0.000048663790948921815,
0.02221957966685295,
-0.006497474852949381,
-0.009042677469551563,
-0.01020829752087593,
0.011446272023022175,
-0.033608328551054,
0.005644355900585651,
-0.0006177147733978927,
-0.0013707588659599423,
-0.04409237951040268,
-0.0025737101677805185,
0.03365931659936905,
-0.046823788434267044,
-0.035866715013980865,
-0.029497329145669937,
-0.0681062638759613,
0.05343533679842949,
-0.005646327044814825,
0.0553552471101284,
-0.041479576379060745,
-0.008547129109501839,
0.07464107871055603,
-0.014062426052987576,
-0.01736724004149437,
-0.03327631577849388,
-0.03660445287823677,
0.013130271807312965,
0.0012965253554284573,
-0.013534097000956535,
0.04179822653532028,
-0.00699579855427146,
0.03200423717498779,
0.0076247830875217915,
0.027228251099586487,
0.020603341981768608,
0.010683242231607437,
0.011172222904860973,
-0.005689821671694517,
-0.019835712388157845,
-0.023914247751235962,
0.06762893497943878,
0.026939233765006065,
-0.026234406977891922,
0.007708183955401182,
-0.00003964044663007371,
0.04089009761810303,
-0.02430853433907032,
-0.020405882969498634,
0.034806329756975174,
0.02342715673148632,
0.01883828267455101,
-0.010311386547982693,
0.041805971413850784,
-0.007044597994536161,
-0.0005120528512634337,
0.015575491823256016,
0.02809441275894642,
0.026344329118728638,
0.023565780371427536,
-0.012419172562658787,
0.02415338158607483,
0.027445418760180473,
-0.04424414038658142,
-0.006339728832244873,
0.0009914642432704568,
-0.021396176889538765,
0.027056412771344185,
-0.04996691271662712,
-0.07475204765796661,
0.04702885076403618,
0.013865393586456776,
0.01993749476969242,
-0.0035029686987400055,
0.0028561404906213284,
-0.015026743523776531,
-0.048639122396707535,
0.001957465196028352,
0.01625434309244156,
0.06974605470895767,
0.03162191063165665,
0.045322317630052567,
0.04369159787893295,
0.012143237516283989,
-0.018376952037215233,
-0.008831655606627464,
-0.07874926179647446,
-0.021857433021068573,
-0.036174993962049484,
-0.0037302770651876926,
0.0036814913619309664,
-0.025646891444921494,
0.00419554254040122,
-0.053521886467933655,
-0.03111889399588108,
-0.031015446409583092,
-0.008292041718959808,
-0.061769720166921616,
0.023733243346214294,
-0.03252052888274193,
-0.031710732728242874,
-0.0368477888405323,
0.021976958960294724,
-0.0061052897945046425,
-0.016648458316922188,
0.008793900720775127,
0.02501903846859932,
-0.07018257677555084,
-0.02347533404827118,
0.021744271740317345,
0.019934672862291336,
0.0015542260371148586,
0.04013105481863022,
0.03287115320563316,
0.029562903568148613,
-0.03724293410778046,
-0.0018774355994537473,
-0.00481838546693325,
0.06226995959877968,
-0.00102338008582592,
-0.02651945874094963,
-0.013785491697490215,
-0.026983922347426414,
0.003375626401975751,
-0.012399941682815552,
0.02828782983124256,
-0.00047269294736906886,
0.028291817754507065,
0.0424184687435627,
0.017712943255901337,
-0.024865085259079933,
0.01753626950085163,
0.06194673851132393,
0.023199105635285378,
0.011955655179917812,
-0.06849651783704758,
0.004253782331943512,
-0.019716190174221992,
-0.009600668214261532,
0.011576713062822819,
-0.023850977420806885,
0.0013340963050723076,
0.006474135909229517,
0.021796295419335365,
-0.0062134163454174995,
-0.04464871436357498,
0.0008091251947917044,
-0.0013525312533602118,
-0.010069325566291809,
-0.018425554037094116,
0.004066895227879286,
-0.00672554736956954,
-0.012159492820501328,
0.003041627584025264,
-0.0012296185595914721,
-0.0015987253282219172,
-0.06483680754899979,
0.012539912946522236,
0.04940694198012352,
0.04280632734298706,
0.012611576355993748,
0.016088899224996567,
-0.0479811392724514,
0.010225730948150158,
0.04255630448460579,
-0.0035004550591111183,
0.02497614547610283,
-0.03490454703569412,
-0.024620607495307922,
-0.02694823034107685,
-0.006364912260323763,
0.047509804368019104,
-0.0015042320592328906,
0.005175505764782429,
-0.02771739661693573,
-0.014345037750899792,
0.021738789975643158,
-0.010328855365514755,
-0.007076265290379524,
0.032493095844984055,
0.04782559722661972,
0.014277970418334007,
0.012004713527858257,
0.014013613574206829,
0.02005145139992237,
-0.045462656766176224,
-0.10395925492048264,
0.026791652664542198,
0.0000701827448210679,
-0.004980188328772783,
0.05876866728067398,
-0.06284037232398987,
-0.05496235564351082,
0.028687506914138794,
-0.004010410979390144,
-0.03187179937958717,
-0.0435628704726696,
-0.039829321205616,
0.04187088832259178,
0.023482413962483406,
-0.04495036229491234,
0.03320935368537903,
0.043272897601127625,
-0.02368437685072422,
0.006319436244666576,
0.01944013126194477,
0.01987772062420845,
-0.0063058119267225266,
0.04486191272735596,
-0.026586435735225677,
0.03289368376135826,
-0.03515900298953056,
0.03799368441104889,
0.012289751321077347,
0.03895910456776619,
-0.008171336725354195,
-0.04586132988333702,
-0.05684007704257965,
0.00011242056643823162,
0.0043035452254116535,
-0.005959894508123398,
-0.02749308943748474,
0.014621307142078876,
-0.028617331758141518,
-0.0147105623036623,
-0.017875298857688904,
0.015105233527719975,
0.06220915541052818,
0.03247896581888199,
0.015337098389863968,
0.0015184679068624973,
-0.03835245221853256,
0.0012284762924537063,
0.01871422491967678,
-0.041156694293022156,
0.04659075662493706,
-0.013167424127459526,
-0.015493140555918217,
0.022024931386113167,
-0.06005271524190903,
-0.022941531613469124,
0.008088596165180206,
-0.022172117605805397,
-0.009912542067468166,
-0.04300283268094063,
0.022155629470944405,
-0.015422782860696316,
0.021290579810738564,
-0.058391720056533813,
-0.025042764842510223,
-0.014985281974077225,
0.01373480074107647,
-0.017401481047272682,
-0.019251467660069466,
0.031981829553842545,
-0.03257354348897934,
-0.013068350963294506,
0.003031018190085888,
0.047810640186071396,
0.021794822067022324,
-0.01504513993859291,
0.04048756882548332,
-0.01954224333167076,
0.056460145860910416,
0.02043837681412697,
-0.003343709046021104,
0.005490458570420742,
0.013279289938509464,
0.041817065328359604,
-0.0036009615287184715,
0.015194580890238285,
-0.024181542918086052,
-0.023352675139904022,
-0.0067316689528524876,
-0.00638222973793745,
0.03916129469871521,
-0.021599726751446724,
0.013549461960792542,
0.01589471660554409,
0.04364527761936188,
0.0061152721755206585,
-0.024912040680646896,
0.010708787478506565,
-0.005483449436724186,
0.03814586624503136,
0.03147615119814873,
-0.013176591135561466,
-0.02178877778351307,
-0.010625718161463737,
0.0034854186233133078,
0.008679305203258991,
0.0004003985377494246,
0.0005435954080894589,
0.011792770586907864,
0.006891308352351189,
-0.02546081319451332,
0.018488053232431412,
-0.025462130084633827,
0.007978038862347603,
-0.01957012712955475,
-0.004025857429951429,
-0.03470876067876816,
0.015519371256232262,
-0.005364438518881798,
-0.02932889200747013,
-0.04481298103928566,
-0.0027545816265046597,
0.03602878004312515,
-0.004581062123179436,
0.03467218577861786,
0.026099825277924538,
0.012423817068338394,
-0.0630858838558197,
-0.026316408067941666,
-0.021974477916955948,
0.01633922941982746,
0.009665930643677711,
0.025621363893151283,
-0.013081423006951809,
-0.004899045918136835,
0.028513716533780098,
0.020890310406684875,
-0.012047864496707916,
-0.008985929191112518,
0.024457773193717003,
0.002085962798446417,
0.024911263957619667,
-0.029496319591999054,
-0.01152681652456522,
0.027948735281825066,
-0.036267686635255814,
0.03243304416537285,
0.009270817041397095,
-0.023917321115732193,
0.04287188500165939,
-0.012184885330498219,
-0.000011916838957404252,
0.008847304619848728,
0.0010144994594156742,
-0.037992529571056366,
0.011696580797433853,
0.002352309413254261,
-0.006552970036864281,
-0.041820280253887177,
-0.0018452558433637023,
0.021251779049634933,
0.024706747382879257,
-0.007733211386948824,
0.013712244108319283,
-0.0711115300655365,
-0.045428209006786346,
-0.04954509064555168,
-0.03401682898402214,
0.02970992587506771,
0.014266004785895348,
-0.027946151793003082,
-0.010737081058323383,
-0.0017663579201325774,
0.04694446921348572,
-0.016767501831054688,
0.05150160565972328,
-0.01817190833389759,
0.06973282992839813,
-0.0008557171677239239,
0.0327206589281559,
-0.02283661812543869,
0.039012398570775986,
0.10665599256753922,
0.05296395719051361,
0.009152434766292572,
-0.04534256085753441,
0.01295839436352253,
-0.01569756679236889,
0.04795076698064804,
-0.02482851967215538,
0.006975926458835602,
0.02963733673095703,
0.03753211721777916,
-0.028660228475928307,
0.02270115539431572,
0.013970404863357544,
0.025762610137462616,
0.037489328533411026,
-0.05695335939526558,
-0.04381662234663963,
0.02160954475402832,
0.04066094383597374,
0.03253820165991783,
0.0006068896036595106,
-0.0008375130710192025,
-0.019429408013820648,
-0.04359908029437065,
-0.006448532920330763,
-0.0010785782942548394,
-0.022309716790914536,
0.015874985605478287,
0.013048894703388214,
-0.04601043090224266,
-0.007320793811231852,
-0.010282224044203758,
-0.004478646907955408,
-0.05720442533493042,
0.027987008914351463,
0.01918036676943302,
-0.010374141857028008,
-0.031333085149526596,
0.05024288594722748,
-0.003607123391702771,
-0.026936953887343407,
0.0005809442955069244,
-0.00030167444492690265,
-0.0194301288574934,
-0.012347830459475517,
0.0005321201169863343,
0.011933720670640469,
-0.0389932282269001,
0.027361057698726654,
0.015594815835356712,
0.003721078624948859,
-0.00958926323801279,
-0.03191542625427246,
0.0017640760634094477,
0.009212711825966835,
0.0161975659430027,
0.023260632529854774,
-0.0074809277430176735,
-0.02624511532485485,
0.011429063975811005,
-0.025990692898631096,
0.0329524502158165,
-0.014428936876356602,
-0.015427237376570702,
-0.00019946748216170818,
0.007060634437948465,
-0.009418008849024773,
-0.032080136239528656,
-0.02578919008374214,
-0.011730575934052467,
0.006455658469349146,
-0.06625230610370636,
-0.017920875921845436,
0.03340253606438637,
0.016662953421473503,
-0.0019025836372748017,
0.004350132774561644,
-0.014563602395355701,
-0.004225056618452072,
-0.06014596298336983,
0.014274334535002708,
-0.03065411187708378,
-0.02237056940793991,
0.001961442641913891,
0.032011304050683975,
0.08053069561719894,
0.03117506206035614,
-0.06098577752709389,
0.03082573413848877,
0.004766751080751419,
-0.010012720711529255,
0.012447209097445011,
-0.01355928834527731,
0.00009906310879159719,
0.02628502808511257,
-0.0508732870221138,
0.04947606474161148,
-0.029393741860985756,
0.006556166801601648,
0.005712056066840887,
-0.010633353143930435,
0.0021975499112159014,
0.013650335371494293,
0.000151918749907054,
0.019920801743865013,
0.02772575058043003,
0.007875589653849602,
-0.01889093592762947,
0.011444766074419022,
0.05142636224627495,
-0.04525342956185341,
-0.006274627987295389,
-0.055094387382268906,
-0.027091776952147484,
-0.01787586137652397,
0.034840021282434464,
-0.01260304357856512,
-0.00952872820198536,
0.005792331416159868,
0.04418161138892174,
-0.016635917127132416,
0.026776917278766632,
-0.023793017491698265,
0.010680874809622765,
-0.022727539762854576,
0.00599663658067584,
-0.024543918669223785,
0.026166632771492004,
0.018631836399435997,
-0.006363653112202883,
-0.0016340368892997503,
0.040955767035484314,
-0.01923089474439621,
0.013703443109989166,
0.001020218594931066,
0.014574850909411907,
0.05890804901719093,
-0.022195803001523018,
-0.01304597593843937,
0.03929532319307327,
-0.045016877353191376,
-0.06803727149963379,
0.07108432054519653,
-0.04326480254530907,
0.0019688033498823643,
0.0757911428809166,
0.016959140077233315,
-0.006616953294724226,
0.031542908400297165,
-0.03451327607035637,
0.015554375015199184,
0.01984376832842827,
-0.034124188125133514,
-0.04520952329039574,
0.010920805856585503,
0.024204744026064873,
-0.02895396575331688,
-0.02791350521147251,
0.032085567712783813,
0.04101545363664627,
-0.008228465914726257,
0.023866601288318634,
0.005343241151422262,
0.01583082787692547,
0.052136924117803574,
0.03244396671652794,
-0.03915993124246597,
0.05614398792386055,
0.026459485292434692,
-0.020993798971176147,
0.03865465894341469,
0.006058332975953817,
0.016450246796011925,
-0.07305312156677246,
0.005596021190285683,
0.013286231085658073,
0.015833420678973198,
0.03699006512761116,
0.018540920689702034,
0.006471050437539816,
0.026315465569496155,
-0.09035629779100418,
0.028411230072379112,
-0.022952359169721603,
-0.01835411973297596,
-0.01664486899971962,
0.031646810472011566,
-0.019256893545389175,
0.053463760763406754,
0.010278533212840557,
0.04235256835818291,
0.025889884680509567,
0.025546766817569733,
-0.016653230413794518,
-0.05489128828048706,
-0.031147288158535957,
0.035967737436294556,
-0.03713429346680641,
-0.004643098916858435,
0.03756367415189743,
-0.044151678681373596,
-0.006439925171434879,
0.045504383742809296,
-0.00881450716406107,
0.030405180528759956,
-0.0252823643386364,
0.012276613153517246,
0.022448886185884476,
0.033670809119939804,
0.037055302411317825,
-0.02098795212805271,
0.0007311846711672843,
0.008759716525673866,
-0.014398670755326748,
0.05257650092244148,
0.04420371353626251,
0.028628606349229813,
-0.009084702469408512,
-0.03589104115962982,
-0.030201392248272896,
0.029704250395298004,
0.006703093182295561,
-0.005486260633915663,
-0.005335987079888582,
0.028942519798874855,
-0.04317629709839821,
-0.03807215765118599,
0.01686917431652546,
-0.06456448882818222,
-0.0235576331615448,
0.0020280226599425077,
0.009554061107337475,
0.0063590360805392265,
0.040652886033058167,
-0.0237586572766304,
-0.027080543339252472,
0.03669126331806183,
-0.011275052092969418,
-0.0016436557052657008,
-0.05794302374124527,
0.005835740361362696,
0.019560519605875015,
0.017513860017061234,
0.010882416740059853,
-0.05027751252055168,
-0.03630850091576576,
0.015501287765800953,
-0.007316460832953453,
0.018955757841467857,
-0.020750461146235466,
0.014134380035102367,
0.010840285569429398,
-0.05234687775373459,
0.05935800448060036,
0.019131619483232498,
0.03810920938849449,
-0.008480522781610489,
-0.042136888951063156,
0.0298936665058136,
0.004661366809159517,
0.058733902871608734,
-0.041478291153907776,
-0.017160771414637566,
0.017092376947402954,
-0.01766139082610607,
0.018200479447841644,
-0.01858479157090187,
-0.024758683517575264,
-0.01678389124572277,
-0.007934104651212692,
-0.034292712807655334,
-0.05397851765155792,
-0.02519230730831623,
0.017969772219657898,
0.031837210059165955,
0.03950963169336319,
-0.000008297157364722807,
-0.011125404387712479,
-0.05460822209715843,
0.04133390262722969,
0.04854752868413925,
0.0036360688973218203,
0.036729730665683746,
0.012839880771934986,
0.019492916762828827,
-0.0013169023441150784,
-0.006762403063476086,
-0.03833243250846863,
0.01929577812552452,
-0.014166148379445076,
-0.008345707319676876,
-0.00405390840023756,
-0.011421930976212025,
0.040230076760053635,
-0.0534675270318985,
-0.01728595420718193,
0.05569105222821236,
-0.040921904146671295,
-0.0004090611182618886,
0.07959876954555511,
-0.009503331035375595,
0.026175078004598618,
-0.012086433358490467,
0.024087712168693542,
0.022690294310450554,
-0.04898713901638985,
-0.021167371422052383,
0.033159881830215454,
0.014826398342847824,
-0.010808680206537247,
0.042312316596508026,
0.051815517246723175,
0.0145601537078619,
0.0272673349827528,
0.04108544811606407,
0.0202191099524498,
-0.022506773471832275,
-0.007646697107702494,
-0.010765152983367443,
-0.00805586390197277,
-0.0157991424202919,
0.029667122289538383,
-0.03907763585448265,
0.09218702465295792,
-0.011105912737548351,
-0.008080137893557549,
-0.011525485664606094,
0.01042825635522604,
-0.012307041324675083,
-0.03268413245677948,
-0.009662942960858345,
0.04658004269003868,
-0.02004002407193184,
-0.031975794583559036,
0.01767708733677864,
0.02219533361494541,
0.01184661965817213,
-0.06968327611684799,
0.03926914557814598,
-0.0010071999859064817,
-0.0015463121235370636,
-0.018888235092163086,
-0.017326096072793007,
-0.022837970405817032,
-0.006904477719217539,
0.043098557740449905,
0.00739396782591939,
0.011006142944097519,
0.017271187156438828,
-0.025312531739473343,
0.014929959550499916,
0.04992273822426796,
-0.026712441816926003,
0.014655177481472492,
-0.04905140772461891,
0.0240005012601614,
-0.04174429178237915,
-0.034724485129117966
] |
<p>I feel like the answer should be "no" since all superfluids are not strictly BEC since they can undergo a Kosterlitz–Thouless transition in 2D, for example. I believe the ideal gas isn't superfluid, but is there any experimental evidence of a BEC without superfluid properties? I've been searching with no luck.</p>
| 10,682 |
[
-0.06030990183353424,
-0.01714620180428028,
-0.028858456760644913,
-0.017028100788593292,
0.04096942022442818,
0.0030884824227541685,
-0.0314020998775959,
-0.021488185971975327,
-0.016526080667972565,
-0.05948426574468613,
0.03785824030637741,
0.026379533112049103,
0.04266531392931938,
-0.003962384536862373,
0.013805664144456387,
-0.0031978313345462084,
-0.018337704241275787,
0.037805620580911636,
0.015721458941698074,
-0.009716356173157692,
-0.019509200006723404,
0.03725329041481018,
0.03651287779211998,
0.019524356350302696,
-0.015775199979543686,
0.024325741454958916,
0.015848752111196518,
-0.016361258924007416,
0.03509262949228287,
0.022172121331095695,
-0.008322936482727528,
-0.02418329007923603,
0.026252709329128265,
0.02931247092783451,
0.033916160464286804,
0.027633287012577057,
-0.02634800598025322,
-0.012483438476920128,
-0.032105833292007446,
0.029118742793798447,
-0.029631737619638443,
-0.042434412986040115,
0.010392419062554836,
0.04120407998561859,
-0.015766896307468414,
-0.008363994769752026,
0.015143075957894325,
-0.04837192967534065,
0.036384712904691696,
-0.0909479409456253,
0.04536941275000572,
0.0046780891716480255,
0.044390760362148285,
0.021581171080470085,
-0.004469370003789663,
-0.022564047947525978,
0.040787260979413986,
0.09124784171581268,
-0.024881092831492424,
-0.05164923891425133,
0.03127548471093178,
-0.008231370709836483,
0.004041681531816721,
-0.006798144429922104,
-0.060351092368364334,
0.020175550132989883,
-0.0018752958858385682,
-0.02824060060083866,
0.022566579282283783,
-0.0004995597992092371,
-0.012082574889063835,
0.005316836293786764,
0.024052316322922707,
-0.01534522045403719,
0.015623454935848713,
-0.0029667948838323355,
0.015185425989329815,
0.03243304789066315,
0.015057523734867573,
0.05228174477815628,
-0.04848282039165497,
-0.021382542327046394,
0.030607594177126884,
0.01435929723083973,
-0.0016256782691925764,
0.01107766106724739,
0.05545369163155556,
-0.058341655880212784,
0.030803412199020386,
0.04412124678492546,
0.011943657882511616,
-0.018708836287260056,
0.06050387769937515,
-0.014265615493059158,
-0.023162320256233215,
-0.01587052084505558,
0.007182466797530651,
0.05421667546033859,
-0.029216453433036804,
-0.04918902367353439,
-0.005982690956443548,
0.015440674498677254,
0.03707859292626381,
0.09072074294090271,
0.011987220495939255,
-0.02827252633869648,
-0.04177457094192505,
0.020992154255509377,
-0.01275212038308382,
0.02305004931986332,
-0.05100052058696747,
-0.01073517370969057,
-0.006914363242685795,
-0.04819893836975098,
-0.005260528530925512,
-0.05310758948326111,
-0.02257082425057888,
-0.043802615255117416,
0.03861856088042259,
0.0934804379940033,
0.05382596701383591,
-0.03706887736916542,
0.004732390865683556,
-0.02633739449083805,
-0.038962848484516144,
0.009738671593368053,
-0.005355269648134708,
0.0040380144491791725,
-0.005366652272641659,
0.03299323841929436,
-0.006867869291454554,
0.0004917357582598925,
0.0285534355789423,
0.012617222033441067,
0.04046562686562538,
-0.049028005450963974,
-0.06252279877662659,
-0.05735098570585251,
0.016353776678442955,
-0.05359399691224098,
-0.02861897461116314,
-0.06267852336168289,
0.023601394146680832,
0.0452163927257061,
0.07242140918970108,
0.012979588471353054,
-0.0037982307840138674,
-0.025841886177659035,
0.060727935284376144,
0.018084701150655746,
-0.0017529467586427927,
0.003490799106657505,
0.0018813008209690452,
-0.05305950716137886,
0.010222586803138256,
-0.07876314967870712,
-0.0005497027887031436,
-0.0029826941899955273,
-0.010922519490122795,
-0.028766406700015068,
0.042622655630111694,
-0.01954171247780323,
0.005894377361983061,
-0.006792306434363127,
0.008846611715853214,
-0.026968583464622498,
0.07200109213590622,
0.010391900315880775,
0.009269259870052338,
-0.013337129727005959,
-0.015277359634637833,
0.009565586224198341,
0.010138495825231075,
0.015216031111776829,
0.04946235194802284,
-0.042474374175071716,
-0.021341850981116295,
-0.04487982392311096,
0.0779418796300888,
0.005132667720317841,
-0.048076994717121124,
-0.02519175037741661,
0.004073111806064844,
-0.024274155497550964,
-0.041048310697078705,
0.03224430978298187,
-0.007064180448651314,
-0.009500324726104736,
0.03574801981449127,
-0.07392346113920212,
-0.01396491564810276,
-0.03989308327436447,
-0.01734948717057705,
0.02658347226679325,
-0.007067300844937563,
0.026907306164503098,
0.03743468225002289,
0.046048711985349655,
-0.05478464066982269,
-0.021274549886584282,
-0.022460777312517166,
0.055888883769512177,
0.004826462361961603,
-0.011283227242529392,
0.02595278061926365,
-0.015720611438155174,
0.03304422274231911,
-0.027006473392248154,
0.014135130681097507,
0.0015416824026033282,
-0.025640906766057014,
-0.024045949801802635,
-0.02644416131079197,
0.022087886929512024,
-0.012578424997627735,
-0.0019059079932048917,
0.06623672693967819,
0.033349405974149704,
-0.03788113594055176,
0.03687126189470291,
-0.009634274989366531,
0.06025630235671997,
-0.004024870693683624,
-0.010900341905653477,
0.00789988785982132,
0.018794164061546326,
0.04131518676877022,
-0.012777394615113735,
-0.017221027985215187,
-0.005826622247695923,
-0.06403335183858871,
0.0028941109776496887,
0.035396043211221695,
0.0374143049120903,
-0.03800792619585991,
0.018869834020733833,
-0.011182446964085102,
0.020281903445720673,
0.033790960907936096,
0.020863322541117668,
-0.01832183636724949,
-0.029886186122894287,
0.03350147604942322,
-0.015946613624691963,
0.029872843995690346,
0.016872869804501534,
0.031074460595846176,
0.04228789359331131,
0.003934414591640234,
-0.017153022810816765,
-0.01018453761935234,
-0.004778931383043528,
0.014250161126255989,
-0.04292968288064003,
-0.022228995338082314,
-0.01739760860800743,
0.031113851815462112,
-0.036800846457481384,
0.03168662264943123,
0.03556274622678757,
0.021040864288806915,
0.0069025130942463875,
-0.012089166790246964,
-0.007656675297766924,
0.02081240527331829,
-0.008216139860451221,
-0.024102473631501198,
-0.005274702329188585,
0.029383966699242592,
0.00018641904171090573,
0.016447629779577255,
-0.00497188325971365,
0.0527830496430397,
-0.008296282961964607,
0.03613352030515671,
0.008486783131957054,
0.0078047215938568115,
0.043185241520404816,
-0.020002510398626328,
-0.04320763051509857,
-0.012562090530991554,
-0.045449741184711456,
0.03728015348315239,
0.036011356860399246,
-0.059267558157444,
0.0453529916703701,
-0.03127492964267731,
-0.018234461545944214,
0.012607814744114876,
-0.03487292304635048,
0.011735226958990097,
0.03603625297546387,
-0.03686080127954483,
-0.01888485997915268,
0.032523833215236664,
-0.03024120442569256,
-0.006866264622658491,
-0.022907165810465813,
0.03558211028575897,
0.04161495715379715,
-0.0016090109711512923,
-0.044776543974876404,
-0.00587297510355711,
-0.026982713490724564,
-0.07571612298488617,
-0.018500732257962227,
-0.030582258477807045,
0.03134427219629288,
-0.03435828909277916,
0.05677623674273491,
0.046130623668432236,
-0.05941985547542572,
-0.015886081382632256,
-0.028656834736466408,
-0.04974835738539696,
0.04120570793747902,
0.015534605830907822,
0.025112289935350418,
-0.015436586923897266,
-0.03130133077502251,
0.03843177109956741,
0.019568732008337975,
-0.0587124228477478,
0.028351295739412308,
-0.03209496662020683,
-0.03168041259050369,
-0.04873049631714821,
0.04156186804175377,
0.02230970188975334,
0.0078603969886899,
-0.010296597145497799,
0.015708616003394127,
0.05714006721973419,
0.010603134520351887,
-0.012805874459445477,
-0.03850686550140381,
0.02679128386080265,
0.03350408002734184,
0.025276247411966324,
0.05580775439739227,
0.004520910792052746,
-0.009328339248895645,
0.019419625401496887,
0.017057932913303375,
0.024157559499144554,
0.049744319170713425,
-0.03004511073231697,
0.07429969310760498,
-0.021059244871139526,
0.051936231553554535,
-0.02822721004486084,
-0.006537287496030331,
0.007386490702629089,
-0.005198364146053791,
0.023589592427015305,
0.04080754518508911,
0.033349256962537766,
0.004506056196987629,
0.007278439588844776,
0.05777788162231445,
0.01684110425412655,
0.010521252639591694,
0.0018135641003027558,
0.019970959052443504,
-0.03383827582001686,
0.021525833755731583,
-0.03147590532898903,
-0.03314969316124916,
0.03523782640695572,
0.031043661758303642,
0.03434719517827034,
-0.02380310371518135,
-0.02073409967124462,
0.024700209498405457,
-0.03378459811210632,
-0.02405969798564911,
-0.02065144293010235,
0.032147105783224106,
0.014220451936125755,
0.013043534941971302,
0.015334919095039368,
0.04123932123184204,
-0.017840690910816193,
-0.0017899960512295365,
-0.09484972804784775,
-0.036660972982645035,
-0.04173918068408966,
0.02237687259912491,
-0.0068352497182786465,
0.0004023298970423639,
-0.02448120340704918,
-0.04007456824183464,
-0.025309108197689056,
-0.03427993878722191,
0.015080630779266357,
-0.04543660208582878,
0.012226657941937447,
-0.002320342930033803,
-0.01929563842713833,
0.02115546353161335,
0.02589932270348072,
-0.008530721068382263,
-0.04625648632645607,
0.010680426843464375,
0.027963077649474144,
0.002167508704587817,
-0.010486963205039501,
-0.0031388455536216497,
0.023165149614214897,
-0.013074180111289024,
0.030337562784552574,
0.03020981326699257,
0.038250286132097244,
0.009072065353393555,
-0.018860798329114914,
0.02578071504831314,
0.003103780560195446,
-0.013923297636210918,
-0.007282100152224302,
0.012100601568818092,
-0.05022542551159859,
-0.032035671174526215,
-0.0022204378619790077,
0.08554448932409286,
0.016046730801463127,
0.0053875199519097805,
0.006163625046610832,
-0.0048776729963719845,
-0.008740444667637348,
0.031818728893995285,
0.040226615965366364,
0.02148006111383438,
-0.041554201394319534,
-0.047211650758981705,
-0.05344576761126518,
-0.012455033138394356,
-0.007287781219929457,
0.02828424982726574,
-0.003555766772478819,
-0.05283718183636665,
0.03532053157687187,
-0.0005816093180328608,
0.02966633066534996,
-0.018232708796858788,
-0.03645345941185951,
-0.0010196471121162176,
0.02584618702530861,
-0.027447737753391266,
0.0027311767917126417,
0.0006243247189559042,
0.023557469248771667,
0.0004887199029326439,
0.01875465176999569,
0.007171737961471081,
-0.09011578559875488,
0.00009051649976754561,
0.030904673039913177,
0.026371266692876816,
0.02578943781554699,
0.006551757920533419,
-0.04864520952105522,
0.013968008570373058,
0.05700486898422241,
-0.013988669961690903,
-0.014328381046652794,
-0.043086178600788116,
-0.012689459137618542,
0.029532883316278458,
-0.020300017669796944,
0.03038288652896881,
0.011472665704786777,
0.026585524901747704,
-0.01959804631769657,
-0.02760726399719715,
-0.01166892796754837,
0.01950695924460888,
0.014294520020484924,
0.02589288353919983,
0.07748480141162872,
-0.01548636145889759,
0.004053068812936544,
0.015050079673528671,
0.010067453607916832,
-0.054969657212495804,
-0.0674130842089653,
-0.004141178913414478,
0.02119002677500248,
-0.0064350333996117115,
0.017155233770608902,
-0.03698238730430603,
-0.09544648975133896,
-0.010180138982832432,
0.003985096234828234,
-0.024014145135879517,
0.026537690311670303,
-0.006889685522764921,
0.04804881662130356,
0.013544137589633465,
0.01846747286617756,
0.015150664374232292,
0.07278662174940109,
-0.02245258167386055,
-0.02504383958876133,
-0.023104581981897354,
0.05912962555885315,
-0.04630163684487343,
-0.01011497713625431,
-0.02247966267168522,
-0.010026507079601288,
-0.01616094820201397,
0.024743305519223213,
-0.03666467219591141,
0.0071266707964241505,
0.010134728625416756,
-0.034910980612039566,
0.022488079965114594,
0.02960997074842453,
0.020265374332666397,
-0.02657470479607582,
-0.039577074348926544,
-0.01668500155210495,
-0.03265618532896042,
-0.03063371032476425,
0.012970712035894394,
0.012586599215865135,
-0.001488949521444738,
0.01271363627165556,
-0.03265500068664551,
0.020632851868867874,
-0.013391914777457714,
-0.04260113462805748,
-0.034775637090206146,
-0.05127612128853798,
0.032788850367069244,
-0.020794173702597618,
-0.05348086729645729,
-0.007855599746108055,
-0.021377259865403175,
0.03593190014362335,
-0.014223925769329071,
0.020283488556742668,
-0.025806566700339317,
-0.01924976147711277,
0.023859426379203796,
0.007476092781871557,
0.01833794265985489,
-0.08459419012069702,
-0.054037462919950485,
-0.006848794873803854,
0.012508421204984188,
0.02323937602341175,
-0.021016256883740425,
-0.01158870104700327,
-0.038226913660764694,
0.0019279358675703406,
0.003659648820757866,
0.04116703197360039,
-0.03770091012120247,
-0.0036390090826898813,
0.01565716415643692,
0.024421337991952896,
0.029561540111899376,
0.03074006550014019,
-0.045740168541669846,
0.002180079696699977,
-0.012260891497135162,
0.01293425727635622,
0.0004736424016300589,
0.05781204625964165,
-0.014130051247775555,
-0.033333949744701385,
-0.010018385015428066,
-0.036929719150066376,
0.0536971352994442,
0.00675623957067728,
-0.009241413325071335,
0.030749129131436348,
-0.02681722119450569,
0.018005823716521263,
-0.033081021159887314,
-0.011770633980631828,
0.0026092645712196827,
0.03484116494655609,
-0.0008564311428926885,
-0.024800710380077362,
0.003491190727800131,
-0.04793408885598183,
0.04480520263314247,
-0.0052178301848471165,
-0.04432336241006851,
-0.0014106921153143048,
0.07624135911464691,
0.03299105539917946,
-0.005829900503158569,
0.0017787842079997063,
-0.054516326636075974,
-0.008709671907126904,
0.026185085996985435,
0.0009002951555885375,
-0.0016482111532241106,
0.02708962932229042,
-0.00954838003963232,
-0.05648837983608246,
-0.03353391960263252,
0.0014217746211215854,
0.05821417644619942,
-0.010818409733474255,
0.02506193518638611,
0.013280678540468216,
-0.01798359863460064,
0.009211146272718906,
-0.06721466779708862,
-0.00044561069807969034,
0.0648074746131897,
-0.027597147971391678,
0.019251585006713867,
0.007094896398484707,
-0.009156863205134869,
0.06493154168128967,
0.010305182076990604,
-0.020318929105997086,
0.04400133341550827,
0.042968396097421646,
0.035083573311567307,
0.031093111261725426,
0.01774747110903263,
-0.02720869891345501,
0.03644484654068947,
-0.031146423891186714,
0.046353209763765335,
-0.013362187892198563,
0.011040734127163887,
0.011017853394150734,
-0.03956593945622444,
0.007222963031381369,
-0.056119151413440704,
-0.01855306141078472,
-0.011284777894616127,
0.031187618151307106,
0.012376423925161362,
-0.014143183827400208,
0.022863097488880157,
-0.011146517470479012,
-0.005459032487124205,
0.0066071804612874985,
-0.0010943675879389048,
-0.0019677961245179176,
-0.05061306804418564,
-0.010759837925434113,
0.024823572486639023,
-0.010730610229074955,
0.011785151436924934,
0.014760900288820267,
-0.020415019243955612,
-0.001578153227455914,
-0.015876207500696182,
0.005893372464925051,
-0.010754224844276905,
0.040776755660772324,
0.009254920296370983,
0.028233379125595093,
-0.027136478573083878,
0.0529509037733078,
-0.027823420241475105,
0.011718363501131535,
0.11298411339521408,
0.02069787122309208,
0.03293292596936226,
-0.07779818028211594,
0.020368289202451706,
-0.007759297266602516,
-0.02582845836877823,
-0.03199576959013939,
-0.019663995131850243,
-0.03429201990365982,
-0.013218657113611698,
-0.0018993195844814181,
0.09279715269804001,
-0.012596938759088516,
0.0016342864837497473,
0.022626223042607307,
-0.016894420608878136,
-0.027746498584747314,
-0.01417727954685688,
0.05100277066230774,
0.0145275192335248,
-0.015129159204661846,
-0.015389980748295784,
0.005025927443057299,
-0.013731767423450947,
0.01899018883705139,
-0.01848493702709675,
0.017293250188231468,
0.02875114046037197,
0.027761010453104973,
-0.008109424263238907,
-0.0012451488291844726,
0.017479870468378067,
-0.0002863644913304597,
-0.03638365492224693,
-0.03971252217888832,
0.018821485340595245,
0.010224022902548313,
0.0052212984301149845,
0.025034625083208084,
0.01512882485985756,
-0.002450164407491684,
0.00792653951793909,
-0.009715721011161804,
-0.037361305207014084,
-0.0027733533643186092,
-0.016133001074194908,
0.016330640763044357,
-0.030113285407423973,
-0.013039723969995975,
-0.006461325101554394,
-0.004544097930192947,
0.019041188061237335,
-0.019555749371647835,
-0.026650547981262207,
-0.024249780923128128,
0.03691887483000755,
-0.008943203836679459,
-0.013156627304852009,
-0.018695276230573654,
0.02869773842394352,
0.00764343049377203,
0.020072706043720245,
-0.03722943365573883,
-0.014307704754173756,
0.032268352806568146,
0.024025933817029,
0.028345739468932152,
0.026256615296006203,
0.002538692206144333,
-0.012628717347979546,
0.004932216368615627,
-0.0334601067006588,
-0.0030319332145154476,
0.05053582414984703,
0.009771919809281826,
0.03027067333459854,
-0.011650819331407547,
-0.024703016504645348,
0.002975069684907794,
-0.04867149889469147,
0.010272246785461903,
-0.012279161252081394,
-0.03186134621500969,
0.016178732737898827,
0.000461087649455294,
0.02918846532702446,
0.057887256145477295,
-0.039942432194948196,
0.022062664851546288,
0.014428943395614624,
0.03719224035739899,
-0.015834588557481766,
-0.027075599879026413,
-0.013272984884679317,
0.01126786507666111,
-0.045926716178655624,
0.04329553619027138,
-0.016259822994470596,
0.00925054494291544,
0.03332267701625824,
0.016448458656668663,
-0.02469707280397415,
0.02224256470799446,
-0.018425265327095985,
0.016554931178689003,
0.027070559561252594,
-0.045342136174440384,
-0.01258712075650692,
0.01717272959649563,
0.013761069625616074,
-0.01565961353480816,
-0.08465085923671722,
-0.04705531522631645,
0.017680708318948746,
-0.02538161166012287,
0.02331937476992607,
-0.030142804607748985,
0.02452855370938778,
0.007263427134603262,
-0.005424667149782181,
-0.10732210427522659,
0.008622970432043076,
-0.03347017616033554,
-0.021874630823731422,
0.024791454896330833,
0.02243708074092865,
0.018311690539121628,
0.007169261109083891,
-0.03235552832484245,
0.022513791918754578,
0.05638132244348526,
0.025095082819461823,
-0.03685198724269867,
0.016517693176865578,
0.045085448771715164,
-0.006231892388314009,
0.021909376606345177,
-0.008439747616648674,
0.0016135643236339092,
0.04923107102513313,
-0.03168225288391113,
-0.052689310163259506,
-0.002951571950688958,
0.017029043287038803,
-0.02488620951771736,
0.03947960212826729,
0.024820292368531227,
-0.010173410177230835,
0.07563627511262894,
0.0015501410234719515,
0.01674290932714939,
0.018853705376386642,
-0.008647950366139412,
-0.018643464893102646,
0.009118652902543545,
0.011857454665005207,
-0.016606608405709267,
-0.006643109489232302,
0.060938771814107895,
0.028875907883048058,
0.003159994725137949,
-0.02467743307352066,
0.01194294448941946,
0.024553894996643066,
0.028614195063710213,
0.03413950651884079,
0.01366589218378067,
0.012256835587322712,
0.04984332248568535,
-0.019070126116275787,
0.06277824938297272,
0.023455604910850525,
0.001697068801149726,
-0.0896533653140068,
-0.0022682936396449804,
0.010926129296422005,
-0.01098191924393177,
-0.007764516398310661,
-0.030630066990852356,
0.027060681954026222,
0.03240838646888733,
-0.04883362352848053,
0.019702618941664696,
-0.04554956778883934,
-0.007963942363858223,
-0.03198082000017166,
-0.0028592869639396667,
-0.042201004922389984,
0.03863242268562317,
0.023476561531424522,
0.04746547341346741,
-0.010732629336416721,
0.022796638309955597,
-0.0035230049397796392,
0.02824951522052288,
-0.04461770877242088,
0.04147384315729141,
0.006349124480038881,
-0.023907026275992393,
0.032396916300058365,
-0.043195195496082306,
-0.007977831177413464,
0.002764330944046378,
0.050555843859910965,
-0.011930332519114017,
-0.024407008662819862,
-0.016563519835472107,
-0.00708604883402586,
0.023905528709292412,
0.012250261381268501,
-0.007864142768085003,
0.012339000590145588,
0.048300568014383316,
0.0002085262385662645,
0.046320486813783646,
-0.004253947641700506,
-0.009761861525475979,
0.013401568867266178,
-0.03130624443292618,
-0.018781574442982674,
0.0317247211933136,
-0.008901592344045639,
-0.02462499402463436,
-0.060775015503168106,
-0.030130373314023018,
0.0031699775718152523,
0.015749692916870117,
-0.011569763533771038,
-0.0679805651307106,
-0.03382617607712746,
0.03963058069348335,
0.02201111800968647,
-0.0008303657523356378,
0.030661918222904205,
0.008261730894446373,
-0.038756951689720154,
0.025798652321100235,
0.020086530596017838,
-0.00007614929199917242,
-0.0412941575050354,
-0.03619655966758728,
-0.028108377009630203,
-0.0048672775737941265,
0.016910752281546593,
-0.029707640409469604,
-0.04493255913257599,
0.03404248133301735,
0.018097469583153725,
0.0270717553794384,
-0.027424650266766548,
-0.04981984943151474,
0.0024136737920343876,
-0.049727585166692734,
0.04698551446199417,
-0.045827411115169525,
0.05050130560994148,
-0.012843813747167587,
0.004064976237714291,
-0.00458148866891861,
-0.008939248509705067,
0.04169468581676483,
-0.017062537372112274,
0.028558287769556046,
0.006050409749150276,
0.0021054663229733706,
-0.0031523031648248434,
-0.015982719138264656,
0.02020236663520336,
-0.02332734689116478,
-0.027089685201644897,
0.010607744567096233,
-0.0058485353365540504,
0.0037535750307142735,
0.011883371509611607,
0.03960500285029411,
-0.007711161393672228,
0.018830904737114906,
-0.016732539981603622,
-0.026108069345355034,
0.06307566910982132,
0.029812000691890717,
-0.04093022644519806,
0.05019363388419151,
-0.045029446482658386,
0.020857935771346092,
0.007033603265881538,
-0.017258314415812492,
-0.01926259882748127,
0.026407431811094284,
-0.008403419516980648,
-0.026325097307562828,
-0.04608812928199768,
-0.004839265253394842,
-0.02216567099094391,
-0.0032517623621970415,
0.0328877791762352,
0.03108833357691765,
-0.031175797805190086,
-0.015502615831792355,
0.037530478090047836,
-0.017290152609348297,
0.04481758549809456,
-0.032484691590070724,
-0.016432326287031174,
0.015960996970534325,
0.03174794465303421,
0.017533617094159126,
0.0803876668214798,
0.03153017908334732,
0.01648850552737713,
0.013564201071858406,
-0.02078726515173912,
-0.026959048584103584,
0.007057296112179756,
0.00620698370039463,
-0.008229992352426052,
-0.0021339431405067444,
-0.012723232619464397,
0.0800042375922203,
0.03944430500268936,
0.04863080382347107,
-0.0026723365299403667,
-0.006897637154906988,
0.06698396056890488,
-0.030090460553765297,
0.004001579247415066,
-0.04073471575975418,
0.004310901742428541,
-0.004837131593376398,
0.007705573923885822,
0.034738119691610336,
0.05809931084513664,
-0.001983317546546459,
-0.04477812722325325,
-0.023150287568569183,
0.00917078461498022,
0.048366229981184006,
-0.06352221220731735,
0.002292799297720194,
-0.031167805194854736,
0.011580012738704681,
-0.021216975525021553,
-0.0107155442237854,
-0.021823473274707794,
-0.016518456861376762,
-0.006526061799377203,
0.031317852437496185,
0.018194133415818214,
-0.01306234858930111,
0.0030400180257856846,
-0.028087252750992775,
0.0994110181927681,
-0.041166432201862335,
0.011315280571579933,
-0.007007990498095751,
0.02331422083079815,
-0.011766262352466583,
0.01142486184835434
] |
<p>I came across this question in an introductory physics course awhile back and I never got over it: "A hydrogen atom has an electron in the n=5 orbit, what is the maximum number of photons that might be emitted so that it decays to the ground state (n=1)?" The answer the professor was looking for was 4 since he was picturing the atom going $5 \rightarrow 4 \rightarrow 3 \rightarrow 2\rightarrow 1$. This sort of answer is how we are taught to think of atomic transitions in introductory physics courses, but I can't imagine its the complete picture. As far as I can tell the only constraints on the system are energy and angular momentum conservation and if you produce pairs of photons with opposite angular momentum you can produce infinitely many photon pairs, and thus infinitely many photons so there is no max number. There are obviously 'selection rules' on these sorts of transitions but they always seem to procede by some dominant process when as far as I can tell there can be higher-order processes that allow many more transitions to occur. </p>
<p>In short: given the full machinery of quantum mechanics, is the answer to the professor's question even finite? Is he right? Or is the number potentially infinite? </p>
<p>Note: I acknowledge this is a exam/HW problem, but from a loooonnnnngg time ago, and I'm looking for the 'real' answer, not the fake introductory answer, if there is a difference.</p>
<p>Thanks!</p>
| 10,683 |
[
-0.062381576746702194,
-0.03984887897968292,
0.0010275818640366197,
-0.020653538405895233,
0.021225983276963234,
0.020161405205726624,
-0.043561555445194244,
-0.04374789446592331,
0.036776695400476456,
-0.009036446921527386,
0.03154527395963669,
0.016516687348484993,
0.012534554116427898,
0.02459469623863697,
0.008417066186666489,
0.06808861345052719,
-0.007854413241147995,
-0.024004079401493073,
-0.011732491664588451,
0.019442535936832428,
-0.023481767624616623,
0.03808806836605072,
0.002404823899269104,
-0.04997873306274414,
-0.0379006452858448,
0.02049345336854458,
0.02466863952577114,
0.035572733730077744,
0.03870926797389984,
0.06125766783952713,
-0.0068081398494541645,
-0.0203030277043581,
0.020144321024417877,
0.06501850485801697,
0.04810091853141785,
0.024789419025182724,
-0.01900388114154339,
-0.04974320903420448,
0.00798874069005251,
0.031069207936525345,
-0.019236184656620026,
-0.024240324273705482,
-0.007286569103598595,
0.020695427432656288,
-0.010152152739465237,
-0.008041603490710258,
-0.021465342491865158,
-0.01954171247780323,
0.05968742072582245,
-0.04356217011809349,
0.0795603021979332,
-0.009381401352584362,
0.045904114842414856,
-0.022059647366404533,
0.014657771214842796,
-0.007749924901872873,
0.10554009675979614,
0.07221268117427826,
-0.00958161149173975,
-0.04698562249541283,
-0.05012594535946846,
-0.03965923562645912,
-0.021037083119153976,
0.02320966310799122,
-0.013495311141014099,
0.006276435684412718,
-0.0015450578648597002,
-0.020387519150972366,
0.010037921369075775,
0.017882224172353745,
0.0047900783829391,
-0.003164091845974326,
0.06471367925405502,
-0.007859848439693451,
0.019183726981282234,
0.005329360254108906,
0.061308182775974274,
0.0009104646160267293,
0.019978700205683708,
0.04711280018091202,
-0.03046979196369648,
0.009603113867342472,
0.008251970633864403,
0.03600134328007698,
-0.009549197740852833,
0.011066028848290443,
0.08019331097602844,
-0.013836558908224106,
0.006998821627348661,
0.05452173948287964,
-0.02991330623626709,
0.025235719978809357,
0.020911799743771553,
0.0017616626573726535,
-0.016502490267157555,
0.025822991505265236,
-0.0055871764197945595,
0.06993071734905243,
0.013373115099966526,
-0.0034071719273924828,
0.013596826232969761,
-0.05565290153026581,
-0.009244970977306366,
0.07059191912412643,
0.012963368557393551,
0.0049620396457612514,
-0.019092589616775513,
0.002905850298702717,
0.006873756181448698,
-0.0006276890053413808,
-0.012263583950698376,
0.03730570897459984,
0.01617356576025486,
0.035171158611774445,
-0.038759347051382065,
-0.011444773524999619,
0.004479856230318546,
-0.01945038139820099,
0.07798091322183609,
0.05316473916172981,
0.031534865498542786,
-0.04652636870741844,
0.01878235675394535,
-0.03228861838579178,
-0.03980758413672447,
-0.017560813575983047,
0.04822039604187012,
0.0426304005086422,
-0.060666121542453766,
0.026537476107478142,
0.014781725592911243,
0.00009334184869658202,
0.00025067178648896515,
-0.01636696793138981,
0.010615319944918156,
-0.06080162525177002,
-0.1047234833240509,
-0.05361722409725189,
0.004975049756467342,
-0.004580338019877672,
-0.045725636184215546,
-0.07730723172426224,
0.03293393924832344,
0.01410821732133627,
0.06560570746660233,
-0.02487100474536419,
-0.015522245317697525,
-0.003160531632602215,
0.010780003853142262,
0.0292667243629694,
-0.030889783054590225,
0.014946676790714264,
-0.02026953548192978,
-0.03977776691317558,
0.027355000376701355,
-0.056919876486063004,
0.025341441854834557,
0.02880621887743473,
0.04856110364198685,
-0.003687902120873332,
0.07317185401916504,
-0.01593467779457569,
0.024029260501265526,
0.02090291492640972,
0.03597154840826988,
-0.01777626760303974,
0.07878745347261429,
0.032564375549554825,
0.004708793479949236,
0.05381503701210022,
0.02152755856513977,
-0.014928756281733513,
-0.02365170605480671,
0.03321370109915733,
0.03326450288295746,
-0.04366191104054451,
-0.007642925251275301,
-0.07701971381902695,
0.021197594702243805,
0.01598220318555832,
-0.005672849249094725,
-0.0019129224820062518,
0.009385978803038597,
0.024282589554786682,
-0.041564151644706726,
0.014080099761486053,
-0.0243215449154377,
-0.004783694166690111,
-0.04826570302248001,
-0.041499391198158264,
-0.007859987206757069,
-0.04977235570549965,
0.017210884019732475,
0.02856374718248844,
0.010393878445029259,
0.020722264423966408,
-0.02464892528951168,
0.008749543689191341,
-0.03124849870800972,
-0.048747170716524124,
-0.02557847648859024,
0.02931807190179825,
0.008384010754525661,
-0.005496604833751917,
0.03965605050325394,
0.07676025480031967,
0.03307380899786949,
0.022660117596387863,
0.023073801770806313,
-0.05589849129319191,
-0.027257230132818222,
-0.005383612588047981,
0.015515923500061035,
0.04172525182366371,
0.041940901428461075,
0.021335506811738014,
-0.012162706814706326,
-0.035937175154685974,
-0.017002353444695473,
0.021879108622670174,
-0.05443672463297844,
0.04717399179935455,
0.037013065069913864,
0.011152215301990509,
0.018830135464668274,
0.0005318466573953629,
0.002482874318957329,
-0.009472178295254707,
-0.020106881856918335,
-0.04818657413125038,
-0.050351954996585846,
0.03781060129404068,
0.041164278984069824,
0.008822455070912838,
-0.048791512846946716,
0.024184953421354294,
-0.0008896799408830702,
0.050033703446388245,
0.034327659755945206,
0.042469944804906845,
-0.08611342310905457,
0.011153111234307289,
0.015822218731045723,
0.03549475222826004,
-0.005674093496054411,
0.040463149547576904,
0.03758680447936058,
0.025421498343348503,
0.02719392627477646,
0.03635384142398834,
-0.013956313952803612,
0.021817995235323906,
-0.013459261506795883,
0.0016635619103908539,
-0.024968501180410385,
-0.01869126968085766,
0.02165217138826847,
-0.05289185419678688,
0.012484009377658367,
0.04054279252886772,
-0.03510021045804024,
-0.0002076511736959219,
-0.011397385969758034,
-0.025328172370791435,
0.015679731965065002,
-0.01784180849790573,
-0.025673622265458107,
-0.004550066776573658,
0.011491774581372738,
-0.02704468183219433,
0.03732994571328163,
-0.036172423511743546,
0.008075128309428692,
-0.01955101639032364,
-0.013917450793087482,
0.030706636607646942,
-0.01032617874443531,
0.024366652593016624,
-0.03440891578793526,
-0.03559453412890434,
-0.000449484126875177,
-0.0433277003467083,
0.025959191843867302,
0.022890303283929825,
-0.054235611110925674,
-0.0045423186384141445,
-0.022547386586666107,
-0.04539242386817932,
0.0561862476170063,
-0.030755382031202316,
0.02875160425901413,
0.027613798156380653,
-0.01744275726377964,
-0.04249148443341255,
-0.01312400121241808,
-0.025376684963703156,
-0.009044007398188114,
-0.009554550983011723,
-0.002850659191608429,
0.07105103880167007,
-0.021744241937994957,
-0.06791086494922638,
0.00004906546018901281,
-0.026745276525616646,
-0.057521648705005646,
-0.03500265255570412,
-0.008524077013134956,
0.02824409492313862,
-0.03648420423269272,
0.011227118782699108,
0.010111027397215366,
-0.0013739016139879823,
0.0033701478969305754,
-0.06466904282569885,
-0.04727592691779137,
0.005698861088603735,
0.002102893777191639,
0.019788026809692383,
0.005681559443473816,
-0.00998828373849392,
0.08146624267101288,
0.04618719592690468,
-0.012922237627208233,
-0.020639177411794662,
0.008454778231680393,
0.02326594479382038,
-0.01990349218249321,
-0.015228296630084515,
0.039506979286670685,
0.014348264783620834,
0.013470623642206192,
0.024027951061725616,
0.049663200974464417,
-0.010296669788658619,
0.004540047142654657,
-0.008542359806597233,
0.034893691539764404,
0.020329663529992104,
0.008250369690358639,
0.051130201667547226,
0.025640733540058136,
-0.03198375552892685,
-0.007127751130610704,
-0.022999968379735947,
0.009351877495646477,
-0.01611199788749218,
-0.024729972705245018,
0.05715218931436539,
-0.0066885510459542274,
0.017164429649710655,
-0.01019207015633583,
0.015630993992090225,
-0.013179926201701164,
-0.02756328694522381,
-0.01610492169857025,
0.045558687299489975,
0.02337418682873249,
-0.031041467562317848,
0.0009351472835987806,
0.03955277055501938,
0.006546320393681526,
-0.001781797269359231,
-0.008491940796375275,
0.0014318616595119238,
0.0171680748462677,
-0.016176581382751465,
-0.00947547610849142,
-0.05587191507220268,
0.02980929985642433,
0.0017673083348199725,
0.025778304785490036,
-0.0010664776200428605,
-0.0480586513876915,
-0.026364188641309738,
-0.030910158529877663,
-0.004133877344429493,
-0.015154794789850712,
0.0751011073589325,
-0.010116956196725368,
0.02423025481402874,
0.010981420986354351,
0.01923644170165062,
0.025019574910402298,
-0.009169714525341988,
-0.089121513068676,
-0.004853606689721346,
-0.023506104946136475,
0.005419108085334301,
-0.03277638927102089,
0.0015501526650041342,
0.008973966352641582,
-0.013887560926377773,
-0.023388251662254333,
-0.027453798800706863,
-0.030386298894882202,
-0.031082477420568466,
-0.0020702374167740345,
-0.0627058818936348,
-0.01883137784898281,
-0.018576186150312424,
0.027712054550647736,
0.04373529180884361,
-0.029642269015312195,
0.011896328069269657,
-0.00782119482755661,
-0.04304151237010956,
0.008431725203990936,
-0.015111635439097881,
0.03798822686076164,
0.01170786190778017,
0.019735107198357582,
0.025834372267127037,
0.021508052945137024,
-0.014903523959219456,
-0.021373435854911804,
0.015095091424882412,
0.02516278252005577,
0.022047588601708412,
-0.016974538564682007,
-0.0073489113710820675,
-0.00263512902893126,
0.03930351138114929,
0.02457769773900509,
0.03833924978971481,
-0.006995755713433027,
0.05710480362176895,
0.04080794006586075,
-0.008875295519828796,
-0.021875083446502686,
0.04682908207178116,
0.0488852858543396,
-0.026624632999300957,
-0.04407303035259247,
-0.024685407057404518,
0.02499507926404476,
-0.01409014593809843,
0.021088024601340294,
-0.016661042347550392,
0.009914356283843517,
-0.025800777599215508,
0.0167219340801239,
0.0015202912036329508,
0.031431276351213455,
-0.014767360873520374,
-0.0038721191231161356,
-0.037136755883693695,
0.033526960760354996,
-0.0016372366808354855,
0.012173504568636417,
0.008734012022614479,
0.015776310116052628,
0.05709167197346687,
0.008893157355487347,
0.02200010046362877,
-0.060280654579401016,
-0.011211412958800793,
0.017278140410780907,
0.03935322165489197,
0.0023479375522583723,
-0.003526128362864256,
-0.022810494527220726,
0.0005687398952431977,
0.018596986308693886,
-0.05331765487790108,
0.038553375750780106,
-0.033304329961538315,
-0.012771781533956528,
0.02357863076031208,
-0.04482691362500191,
-0.030902519822120667,
0.0017444367986172438,
0.027398230507969856,
0.03132385388016701,
-0.02181030809879303,
0.023397525772452354,
-0.007519823033362627,
0.04557586461305618,
0.014190823771059513,
0.07384751737117767,
-0.012249993160367012,
-0.02758861891925335,
0.016994180157780647,
0.018078580498695374,
-0.011297961696982384,
-0.06082557141780853,
0.0008965994347818196,
0.013612739741802216,
-0.021783722564578056,
0.05368787795305252,
-0.06244810298085213,
-0.09100857377052307,
0.02301543764770031,
-0.0031348802149295807,
-0.012617805041372776,
0.005363728851079941,
-0.04656905680894852,
0.04969705641269684,
0.024235812947154045,
0.018257707357406616,
0.031071893870830536,
0.03698107972741127,
0.04238765686750412,
0.006998404860496521,
-0.00912101287394762,
0.02766180783510208,
-0.03799892216920853,
-0.020169204100966454,
-0.023693915456533432,
-0.008003110997378826,
-0.03593111038208008,
0.06872928887605667,
0.005968040786683559,
-0.0012751268222928047,
0.0024825362488627434,
-0.04350033402442932,
0.03581295162439346,
0.029155941680073738,
-0.003760747844353318,
0.007277791388332844,
-0.046323783695697784,
0.007738204672932625,
0.017220264300704002,
-0.03103519417345524,
-0.01768432930111885,
-0.01882757805287838,
0.01612594537436962,
0.02539071813225746,
-0.01878395676612854,
0.009435848332941532,
-0.036721792072057724,
-0.019982345402240753,
0.022991541773080826,
-0.040018171072006226,
0.03099828027188778,
0.005377579480409622,
0.015614436008036137,
0.015363332815468311,
-0.03126133233308792,
0.010059501975774765,
0.025246702134609222,
-0.010705798864364624,
-0.004374959506094456,
-0.02066284418106079,
0.005505173001438379,
-0.034699905663728714,
-0.011796113103628159,
-0.06473467499017715,
-0.03436741605401039,
0.012759720906615257,
0.031017445027828217,
-0.014327991753816605,
0.009557527489960194,
0.01157319825142622,
-0.035340066999197006,
-0.03132570907473564,
-0.013689842075109482,
0.01220316719263792,
-0.0373559407889843,
-0.020176881924271584,
-0.012468796223402023,
0.010332763195037842,
0.03086717240512371,
0.0012180004268884659,
-0.02477913163602352,
-0.02686350792646408,
0.037460219115018845,
-0.02523142844438553,
0.0018998548621311784,
0.03759071230888367,
-0.013289847411215305,
-0.05698884651064873,
-0.012756235897541046,
0.01365636195987463,
0.03494272753596306,
-0.047612011432647705,
-0.0004487066762521863,
0.06208493188023567,
-0.007003282196819782,
0.026000188663601875,
-0.017443440854549408,
0.01704651117324829,
-0.01687169075012207,
0.020799176767468452,
0.0353001207113266,
-0.012479511089622974,
0.016165442764759064,
-0.06591485440731049,
0.004806548357009888,
0.03464372828602791,
0.04293733462691307,
0.024846216663718224,
0.038138680160045624,
-0.0025522944051772356,
-0.00322205713018775,
0.011386046186089516,
-0.03060258738696575,
-0.0005140405264683068,
0.007047266233712435,
0.000898839149158448,
0.03549349680542946,
0.022259069606661797,
-0.037070661783218384,
-0.06866295635700226,
-0.03184988722205162,
0.034580908715724945,
0.030977077782154083,
-0.014606551267206669,
0.009177599102258682,
0.019302858039736748,
0.023210447281599045,
-0.01838151551783085,
-0.043504513800144196,
-0.02168729528784752,
0.014193612150847912,
0.010016214102506638,
0.03963576629757881,
-0.03715360909700394,
0.015439641661942005,
0.021651752293109894,
0.058980002999305725,
0.00730166444554925,
0.01599251851439476,
0.011081726290285587,
-0.0023873045574873686,
-0.008075587451457977,
-0.018022973090410233,
-0.03282153606414795,
0.01586742326617241,
-0.030437873676419258,
0.0475073978304863,
0.023369155824184418,
-0.012098620645701885,
0.02003488317131996,
0.008727394044399261,
0.03242114558815956,
-0.042716801166534424,
-0.021634191274642944,
-0.020027806982398033,
0.018056033179163933,
0.008358701132237911,
-0.0023076659999787807,
-0.0037602209486067295,
0.035460252314805984,
0.007394082844257355,
0.00999026745557785,
0.05382450670003891,
-0.0414021797478199,
-0.04697943851351738,
-0.037755902856588364,
-0.03285965695977211,
-0.05024883896112442,
0.05396058410406113,
-0.013885297812521458,
-0.01884680613875389,
-0.005279541946947575,
-0.03321332857012749,
-0.017824474722146988,
0.0038112534675747156,
0.08358212560415268,
0.024020511656999588,
0.047379180788993835,
0.009274907410144806,
0.019876999780535698,
0.003148123621940613,
0.05048329010605812,
0.080071359872818,
0.08586762845516205,
-0.0006005237228237092,
-0.023707052692770958,
0.006312992889434099,
-0.022441452369093895,
0.031093411147594452,
-0.010467121377587318,
0.015182317234575748,
0.0010286779142916203,
0.0017950007459148765,
0.0024444565642625093,
0.020422397181391716,
-0.005058526527136564,
0.006986871361732483,
0.042238250374794006,
-0.04141443595290184,
-0.03856124356389046,
0.00462727528065443,
0.042676445096731186,
0.032867368310689926,
0.01606839895248413,
-0.04371808096766472,
0.022109726443886757,
-0.03135969862341881,
0.017556246370077133,
0.004761462565511465,
0.016518792137503624,
0.024716468527913094,
-0.023629358038306236,
-0.036313496530056,
-0.025328567251563072,
-0.004854029510170221,
-0.022326232865452766,
-0.03780054301023483,
0.02108578011393547,
0.01501530222594738,
0.025922009721398354,
0.019015293568372726,
0.04212453216314316,
0.009623648598790169,
0.0173101294785738,
0.04735585302114487,
0.0021752102766186,
-0.017397116869688034,
0.003306216560304165,
-0.004256973043084145,
0.04250731319189072,
-0.009759237058460712,
0.014289863407611847,
0.0004792726249434054,
-0.012958291918039322,
-0.004509723745286465,
-0.04231938347220421,
-0.023878350853919983,
-0.00674840435385704,
0.03102610446512699,
-0.016197849065065384,
-0.014141151681542397,
0.0024634008295834064,
0.008553322404623032,
0.015278679318726063,
0.009811483323574066,
-0.008678226731717587,
-0.010820303112268448,
0.01220230758190155,
-0.003431362099945545,
0.02932700142264366,
0.00524057075381279,
0.0054365843534469604,
-0.008571984246373177,
0.016566310077905655,
-0.026093196123838425,
-0.04576873034238815,
0.06137227639555931,
0.008930763229727745,
0.06499587744474411,
0.020479487255215645,
-0.010960959829390049,
-0.01610414683818817,
-0.06977701187133789,
-0.004306082613766193,
0.02359064295887947,
-0.041111573576927185,
0.004770274739712477,
-0.02619275078177452,
-0.028024327009916306,
0.016701780259609222,
-0.0449054054915905,
0.014943630434572697,
0.04746992513537407,
0.020963624119758606,
0.02761927992105484,
-0.039344850927591324,
0.016379036009311676,
0.02816610597074032,
-0.027251483872532845,
-0.014371861703693867,
-0.01264388207346201,
0.046445369720458984,
0.014649411663413048,
0.043797966092824936,
0.03124137967824936,
0.0307482723146677,
-0.027791960164904594,
-0.0006177850882522762,
0.027524398639798164,
-0.056690312922000885,
0.037889815866947174,
0.017832279205322266,
-0.00269010616466403,
-0.04513359069824219,
-0.03956165909767151,
-0.010972083546221256,
0.004862659145146608,
0.023187991231679916,
-0.011740303598344326,
-0.007025266066193581,
0.030559062957763672,
-0.024461621418595314,
0.015065375715494156,
-0.020270897075533867,
-0.0012561845360323787,
-0.03971559926867485,
0.03724423050880432,
0.04789494723081589,
-0.031664248555898666,
-0.014721385203301907,
0.03319967910647392,
0.015179640613496304,
-0.0403125025331974,
0.013818263076245785,
0.03971579670906067,
-0.020867779850959778,
-0.045781053602695465,
-0.007475494407117367,
-0.009453702718019485,
0.03876121714711189,
-0.02029585652053356,
-0.031908199191093445,
0.05025076866149902,
-0.0392267182469368,
-0.03454223647713661,
0.021621961146593094,
-0.033459000289440155,
0.0072241234593093395,
0.04979116469621658,
-0.027838319540023804,
-0.036513276398181915,
0.07313859462738037,
-0.042552605271339417,
-0.015429568476974964,
0.01768820732831955,
0.039674337953329086,
-0.011457491666078568,
-0.0007297475240193307,
-0.006397821940481663,
0.007612565532326698,
-0.015645569190382957,
0.014633582904934883,
0.013433614745736122,
-0.01354833971709013,
0.010585525073111057,
-0.02871127240359783,
-0.025189723819494247,
0.03397301957011223,
0.0023267322685569525,
0.030583564192056656,
-0.005744263529777527,
0.026749003678560257,
-0.01287863589823246,
0.022229483351111412,
0.005497762467712164,
0.01093470398336649,
-0.0736461728811264,
-0.007310402579605579,
-0.01820758543908596,
0.002533282618969679,
0.00400686776265502,
-0.0599384568631649,
0.004823637660592794,
0.04455678537487984,
-0.09258852154016495,
0.027664223685860634,
-0.01656092144548893,
-0.0037521743215620518,
-0.05185101181268692,
0.0012470728252083063,
-0.03868522495031357,
0.0018124362686648965,
0.009870297275483608,
0.049158286303281784,
0.0072049652226269245,
0.005250248126685619,
-0.05282283201813698,
-0.05209389328956604,
-0.013955648057162762,
0.04009739309549332,
-0.02080824226140976,
0.0021557409781962633,
0.07245327532291412,
-0.008636999875307083,
-0.04832570627331734,
0.022288966923952103,
-0.0048870206810534,
0.023486176505684853,
-0.061578623950481415,
-0.00949172955006361,
-0.008094190619885921,
0.020587021484971046,
0.009419103153049946,
-0.019008206203579903,
0.0022245612926781178,
0.008042306639254093,
0.02474735677242279,
0.031401656568050385,
-0.019337156787514687,
-0.017473500221967697,
0.045030366629362106,
-0.06356064230203629,
-0.11334118992090225,
0.018925730139017105,
0.014917073771357536,
-0.002765276236459613,
0.006135697476565838,
-0.008636916987597942,
0.009576420299708843,
-0.036649689078330994,
-0.00181418820284307,
-0.05345112830400467,
-0.020830688998103142,
0.003706518094986677,
0.026878442615270615,
0.029832856729626656,
0.00028261393890716136,
-0.034955840557813644,
-0.002279821550473571,
0.04309125617146492,
0.0011015140917152166,
-0.020319050177931786,
-0.058738503605127335,
-0.005695778876543045,
0.030537821352481842,
-0.010255933739244938,
0.008385822176933289,
-0.022779464721679688,
-0.08061998337507248,
-0.009789311327040195,
-0.0014241394819691777,
0.001766976434737444,
0.012021435424685478,
-0.059555429965257645,
-0.043824464082717896,
-0.07615767419338226,
0.03669244050979614,
-0.013156574219465256,
0.05825807526707649,
-0.047786954790353775,
0.0014112535864114761,
0.004400222096592188,
-0.005906850565224886,
0.03395818546414375,
0.010589806362986565,
-0.035866592079401016,
0.00832277350127697,
-0.01870914176106453,
0.005677083507180214,
-0.03607611730694771,
0.009732739999890327,
-0.014153850264847279,
0.006188834551721811,
-0.04915766417980194,
0.0007643108838237822,
-0.01660364679992199,
0.018572747707366943,
0.0002904534339904785,
0.026243293657898903,
0.02594754286110401,
-0.009070281870663166,
-0.028676480054855347,
0.06436273455619812,
0.004016838036477566,
0.01840875670313835,
0.04564480111002922,
0.009804117493331432,
0.024806877598166466,
0.049034442752599716,
-0.008516366593539715,
-0.059533581137657166,
0.022091275081038475,
-0.01978841796517372,
-0.019234655424952507,
-0.04872673377394676,
-0.007677985820919275,
0.03099646046757698,
-0.012490439228713512,
0.008132178336381912,
0.0780889242887497,
-0.0042203012853860855,
-0.026808148249983788,
0.0071464283391833305,
0.014392709359526634,
0.0597614161670208,
-0.02289666421711445,
0.01731616072356701,
0.0044884528033435345,
-0.006184207275509834,
-0.0011902159312739968,
0.030052699148654938,
0.006857478525489569,
0.0048861633986234665,
0.08053700625896454,
0.0029599403496831656,
-0.006296610459685326,
0.0037512010894715786,
0.013642699457705021,
0.01941552199423313,
-0.035708293318748474,
0.026158461347222328,
0.010703370906412601,
-0.005446750205010176,
-0.026319241151213646,
-0.0013373387046158314,
-0.013457412831485271,
0.04886645823717117,
0.0043404242023825645,
0.006126019638031721,
-0.03249872848391533,
0.011035852134227753,
-0.01708473078906536,
0.023133059963583946,
0.0006455760449171066,
0.05239330232143402,
-0.012502878904342651,
-0.010792381130158901,
-0.04703405126929283,
0.025625236332416534,
0.0356701985001564,
-0.07163289934396744,
0.010046360082924366,
-0.016858374699950218,
-0.010306594893336296,
-0.01728169433772564,
0.00034990074345842004,
-0.03554071858525276,
-0.02150045894086361,
0.013317028060555458,
0.01236075721681118,
0.015762874856591225,
-0.012707795016467571,
-0.0316273458302021,
-0.0321282334625721,
0.047539979219436646,
-0.023029137402772903,
-0.01218124944716692,
-0.039333831518888474,
0.020637089386582375,
-0.022108139470219612,
-0.02363971434533596
] |
<p>The origin of linear birefringence in crystal can be easily explained by the symmetry of the crystal. However, it seems it is hard to be applied in circular birefringence (i.e. optical activity), since there is no macroscopic symmetry in sugar solutions. </p>
<p>So I wonder how we explain the levorotatory and the dextrorotatory in atom level POV?</p>
| 10,684 |
[
-0.03747813031077385,
0.021168261766433716,
-0.014011302031576633,
-0.02193824201822281,
0.046303391456604004,
0.04017391428351402,
-0.02835884690284729,
0.0013671834021806717,
-0.017151448875665665,
-0.007336232345551252,
0.03301696851849556,
-0.011354044079780579,
0.05844571441411972,
0.025319334119558334,
0.017758646979928017,
-0.048124175518751144,
0.020183801651000977,
0.0010691171046346426,
-0.04872167110443115,
-0.015095415525138378,
0.01700527034699917,
0.017696067690849304,
-0.02182425744831562,
0.011042794212698936,
-0.01865568570792675,
0.03511997312307358,
0.03212142735719681,
0.008145247586071491,
0.012484388425946236,
0.03865524381399155,
0.015583169646561146,
-0.01871258020401001,
-0.004455924965441227,
0.01537251751869917,
-0.007102328818291426,
-0.0014597713015973568,
-0.03240273892879486,
-0.03160436078906059,
-0.013415352441370487,
0.025542588904500008,
-0.03602070361375809,
0.027866076678037643,
-0.037523053586483,
0.05316925793886185,
0.009644823148846626,
0.05245891585946083,
-0.025474656373262405,
0.021050743758678436,
0.05159119889140129,
-0.06683441251516342,
0.025382516905665398,
0.0036067781038582325,
0.019476264715194702,
0.024078909307718277,
0.007193933706730604,
-0.007242498453706503,
0.04468756169080734,
0.04063928499817848,
-0.00837898813188076,
-0.07016162574291229,
-0.012393810786306858,
0.021151209250092506,
0.019726989790797234,
-0.03795155882835388,
-0.016286306083202362,
-0.009300172328948975,
0.05321265757083893,
-0.0435076579451561,
0.03501548990607262,
0.016456367447972298,
0.0006825591553933918,
-0.011965603567659855,
0.025179371237754822,
-0.006145399995148182,
-0.005714321043342352,
-0.006632291246205568,
-0.022207168862223625,
-0.001402177382260561,
0.002880754182115197,
0.011638185009360313,
0.01021365076303482,
0.03867555409669876,
0.004250873811542988,
0.026932422071695328,
-0.0470927357673645,
-0.03327954187989235,
0.04890895634889603,
-0.029633529484272003,
0.01046459749341011,
0.044063765555620193,
0.01696029119193554,
0.0028548454865813255,
0.05587742477655411,
0.009263473562896252,
-0.015995938330888748,
-0.005762840621173382,
-0.0076501923613250256,
0.017158284783363342,
0.020105751231312752,
0.03044547513127327,
0.0001611177431186661,
-0.038156282156705856,
-0.003287333995103836,
0.08966227620840073,
-0.017689794301986694,
-0.0569990798830986,
-0.03397443890571594,
0.032687410712242126,
-0.013125374913215637,
-0.005988192278891802,
-0.045842647552490234,
-0.0057870992459356785,
0.023012034595012665,
-0.012567556463181973,
-0.010505465790629387,
-0.02898184396326542,
-0.011754043400287628,
-0.03833314776420593,
0.0589757040143013,
0.09751493483781815,
0.032513249665498734,
-0.005510504357516766,
0.005795048084110022,
-0.008110147900879383,
-0.07756097614765167,
0.03970145061612129,
0.018202826380729675,
0.012263546697795391,
-0.01697748899459839,
0.013989162631332874,
0.008908352814614773,
-0.020649263635277748,
0.003612913191318512,
-0.011867373250424862,
-0.021190129220485687,
0.03642682358622551,
-0.12679846584796906,
-0.06041973456740379,
0.04211113601922989,
0.02147110551595688,
-0.017785727977752686,
-0.08744797110557556,
-0.032303906977176666,
0.04400559887290001,
0.06750234216451645,
-0.005029482301324606,
0.017652252689003944,
0.01492214109748602,
0.021111004054546356,
0.010920537635684013,
-0.011391948908567429,
0.01617567241191864,
0.004100940655916929,
0.00013096498150844127,
-0.016755513846874237,
-0.05678819492459297,
0.02617284469306469,
0.037370506674051285,
0.02479560859501362,
-0.011544822715222836,
0.038630411028862,
-0.05602208524942398,
-0.020162630826234818,
-0.0008867706637829542,
-0.03360844776034355,
-0.0466323122382164,
0.07989451289176941,
0.013167859055101871,
0.04812396690249443,
0.007846316322684288,
-0.01376950554549694,
0.049230266362428665,
-0.025403782725334167,
0.02516532875597477,
0.028346048668026924,
0.011760146357119083,
-0.020080557093024254,
0.011957990936934948,
0.030653370544314384,
0.00860750675201416,
-0.011167077347636223,
-0.027097733691334724,
-0.012284791097044945,
-0.00047517006169073284,
-0.038018595427274704,
0.05913525074720383,
-0.03490161523222923,
-0.003264238126575947,
0.006167231593281031,
-0.09014566987752914,
0.009706257842481136,
-0.05412575975060463,
-0.025502445176243782,
0.023517698049545288,
-0.052903011441230774,
0.03556200489401817,
0.05242057517170906,
-0.02739071659743786,
-0.02423190325498581,
-0.0071626813150942326,
-0.055668044835329056,
0.026482701301574707,
0.004434435628354549,
-0.0066377343609929085,
0.04319757595658302,
0.045077305287122726,
-0.00828548427671194,
-0.013190620578825474,
0.01133793219923973,
-0.012534240260720253,
-0.010282110422849655,
0.050735894590616226,
-0.020676273852586746,
0.042284052819013596,
-0.00481078727170825,
-0.010148217901587486,
-0.010282774455845356,
0.05260457471013069,
-0.0008072835044004023,
0.05207718908786774,
-0.032530367374420166,
0.048314858227968216,
0.059415996074676514,
0.011713266372680664,
0.01140707265585661,
0.033058762550354004,
0.014250167645514011,
0.017122937366366386,
-0.015740878880023956,
-0.0374516062438488,
-0.019561942666769028,
-0.01328000146895647,
0.060071855783462524,
0.03743230924010277,
-0.05593269690871239,
-0.009852569550275803,
0.015868740156292915,
0.062040288001298904,
0.017507730051875114,
0.008670584298670292,
-0.03309062123298645,
-0.0358428917825222,
0.011055169627070427,
-0.02228880114853382,
0.051750753074884415,
0.01177377812564373,
0.016836905851960182,
0.0030557492282241583,
0.013532161712646484,
0.00031728323665447533,
-0.041852839291095734,
0.019989091902971268,
0.02149258367717266,
0.00847153551876545,
0.03071996010839939,
-0.025952322408556938,
0.024998150765895844,
0.020817767828702927,
-0.0010431658010929823,
0.023522043600678444,
-0.017874807119369507,
-0.01373965758830309,
-0.02673063427209854,
0.004364375025033951,
-0.0020701484754681587,
0.0031379559077322483,
-0.03260321542620659,
-0.018178686499595642,
0.016432512551546097,
-0.04252668470144272,
0.013922161422669888,
0.008142111822962761,
0.018147243186831474,
0.050048813223838806,
-0.016739588230848312,
0.028701022267341614,
0.02159319445490837,
0.04404512792825699,
-0.02020706981420517,
-0.026340151205658913,
0.0016669378383085132,
-0.009444051422178745,
0.02939298376441002,
0.02800663746893406,
-0.01702573336660862,
0.027836930006742477,
-0.021641267463564873,
-0.00936631765216589,
0.05377471446990967,
0.02032330259680748,
0.008471590466797352,
-0.05691126361489296,
-0.021424079313874245,
-0.06091602146625519,
-0.026380745694041252,
0.019771497696638107,
0.014259765855967999,
-0.005539694335311651,
0.0036762161180377007,
-0.01269480586051941,
-0.043183524161577225,
-0.02846088632941246,
-0.021942945197224617,
-0.0532359778881073,
-0.008070527575910091,
0.04068896546959877,
0.005810546688735485,
-0.03061888925731182,
0.009644939564168453,
0.014199121855199337,
0.018328359350562096,
-0.02686350606381893,
0.013015098869800568,
-0.055219508707523346,
-0.013511495664715767,
0.010887376964092255,
-0.012097838334739208,
0.049349769949913025,
-0.011807833798229694,
0.009516226127743721,
0.05077332630753517,
0.024887466803193092,
-0.07656745612621307,
-0.020815188065171242,
-0.022730626165866852,
-0.02036721259355545,
-0.014974991790950298,
0.03077903762459755,
0.05408316105604172,
0.02274232730269432,
0.052596401423215866,
0.018602579832077026,
0.019665783271193504,
0.039973363280296326,
-0.005708460696041584,
-0.041381582617759705,
-0.007374746724963188,
0.016661640256643295,
0.01076829805970192,
-0.006390292663127184,
0.043169718235731125,
-0.00428927643224597,
0.005052491556853056,
0.015231641009449959,
-0.008756512776017189,
0.035643238574266434,
-0.07729709893465042,
0.027477199211716652,
-0.0006830192287452519,
0.025919757783412933,
0.016914265230298042,
0.02772705815732479,
-0.010287740267813206,
0.03120635822415352,
0.021335259079933167,
0.03205664083361626,
0.03412250056862831,
-0.009798740968108177,
-0.03835824131965637,
0.0009030997753143311,
0.03552914783358574,
0.01532705593854189,
-0.03887474164366722,
0.006578649859875441,
-0.013935068622231483,
0.057460375130176544,
-0.009587152861058712,
0.005887781735509634,
0.038774874061346054,
0.01870734989643097,
0.0029175092931836843,
0.024336185306310654,
-0.03322570398449898,
0.016869228333234787,
-0.052501436322927475,
0.0025620211381465197,
-0.019340982660651207,
0.019134286791086197,
0.007241704501211643,
0.03796376287937164,
0.0034385162871330976,
0.02287197858095169,
-0.019943727180361748,
0.02389461360871792,
-0.06664128601551056,
0.0036377646028995514,
-0.03361526131629944,
0.0010417131707072258,
-0.026552971452474594,
0.017023300752043724,
0.02807304449379444,
-0.016705242916941643,
-0.044425077736377716,
-0.062944695353508,
-0.022526584565639496,
-0.005760517902672291,
-0.012461059726774693,
0.005804407875984907,
-0.0411701537668705,
-0.04705313220620155,
0.01502907183021307,
0.01286279410123825,
-0.011630836874246597,
-0.010888859629631042,
0.0017128546023741364,
-0.04522078484296799,
0.03924040496349335,
-0.00876422319561243,
0.029570555314421654,
0.018696555867791176,
0.02061012014746666,
-0.002012460259720683,
-0.009097383357584476,
0.0031906827352941036,
0.009195680730044842,
0.027533218264579773,
0.02725830115377903,
0.024077409878373146,
0.011232133023440838,
-0.018698498606681824,
-0.04477856308221817,
-0.006319497246295214,
-0.01825331710278988,
0.01668442226946354,
-0.022064022719860077,
0.028758399188518524,
0.0070287552662193775,
0.021973462775349617,
-0.0323510617017746,
0.046260397881269455,
0.021376678720116615,
0.025478100404143333,
-0.04147690162062645,
-0.06304227560758591,
-0.03066284768283367,
-0.012234950438141823,
0.0026039748918265104,
0.07095541805028915,
-0.018757665529847145,
-0.019218910485506058,
0.014039630070328712,
-0.0039044846780598164,
-0.0021474105305969715,
-0.01227023545652628,
0.009616375900804996,
-0.02302888222038746,
0.029237668961286545,
-0.00364857935346663,
0.03903128206729889,
0.0029161840211600065,
0.03761821240186691,
0.04871980845928192,
0.029249848797917366,
0.017490364611148834,
-0.04199165850877762,
0.021077224984765053,
0.010041599161922932,
0.02257811464369297,
-0.046911656856536865,
0.015175139531493187,
-0.04316193610429764,
-0.033174123615026474,
0.026035714894533157,
-0.05414761230349541,
0.029388707131147385,
0.010329926386475563,
-0.044854190200567245,
-0.03711773455142975,
-0.0115272281691432,
-0.031491294503211975,
-0.008656475692987442,
-0.029608357697725296,
0.011896910145878792,
-0.039649464190006256,
-0.003589138388633728,
-0.012379955500364304,
0.00725460285320878,
0.0007773473626002669,
-0.006286257412284613,
0.0029291529208421707,
0.011045657098293304,
0.020139865577220917,
0.03199256211519241,
-0.0236598439514637,
-0.07017914205789566,
0.02926596626639366,
0.050128936767578125,
0.038518842309713364,
0.07097430527210236,
-0.03755785524845123,
-0.07087776064872742,
0.022457949817180634,
0.019459359347820282,
0.004972425289452076,
0.001866778708063066,
-0.00456768274307251,
0.01784057915210724,
0.018500743433833122,
-0.019832905381917953,
0.05952770635485649,
0.024527112022042274,
-0.05819110944867134,
-0.03401348739862442,
-0.028933055698871613,
0.023959778249263763,
-0.011412042193114758,
0.005669361911714077,
-0.029646284878253937,
0.04473297670483589,
-0.018258770927786827,
0.04895218461751938,
-0.019007356837391853,
0.02773277461528778,
0.0009971052641049027,
-0.027614079415798187,
0.020673299208283424,
0.022257858887314796,
0.026090728119015694,
-0.019874295219779015,
-0.008754823356866837,
0.028853032737970352,
0.034707773476839066,
-0.030439218506217003,
0.03100484609603882,
-0.032763171941041946,
0.008642060682177544,
0.040003661066293716,
0.008548975922167301,
-0.02852199412882328,
-0.040542542934417725,
-0.04158885404467583,
-0.02483595535159111,
-0.045564401894807816,
0.03416179493069649,
-0.007717747241258621,
0.005279551725834608,
0.03222279250621796,
-0.0682026818394661,
-0.03277001902461052,
0.0389973446726799,
-0.02553948014974594,
0.05547688528895378,
-0.03084724023938179,
0.02227974869310856,
0.01996667869389057,
-0.021404212340712547,
-0.04655938595533371,
-0.03715531527996063,
0.028756337240338326,
0.04997213929891586,
-0.03676362335681915,
-0.008381160907447338,
0.0025607431307435036,
-0.005780815612524748,
-0.015220941975712776,
0.023417335003614426,
0.04782038554549217,
-0.03327607735991478,
-0.020202558487653732,
-0.0007141183596104383,
0.011436283588409424,
0.05760405212640762,
-0.033450014889240265,
-0.02236098051071167,
0.019366858527064323,
0.0021680521313101053,
-0.015120452269911766,
0.031350262463092804,
0.04373897984623909,
-0.020028093829751015,
-0.020984016358852386,
-0.0023941409308463335,
-0.017564861103892326,
0.03592211380600929,
0.015590243972837925,
-0.004291300196200609,
-0.012581897899508476,
-0.01657320372760296,
-0.021459175273776054,
-0.05481402575969696,
-0.009589314460754395,
0.03715154156088829,
0.012451127171516418,
0.004317715764045715,
0.0020452605094760656,
-0.008035201579332352,
0.002812255173921585,
0.008489010855555534,
0.01915002427995205,
0.019021285697817802,
0.018819021061062813,
0.09675688296556473,
-0.019253943115472794,
0.023101743310689926,
0.03846994787454605,
0.012346256524324417,
-0.0036382030230015516,
0.008601225912570953,
0.024964410811662674,
0.03829365596175194,
0.024228524416685104,
-0.015132326632738113,
-0.07080596685409546,
-0.031073154881596565,
0.0456434041261673,
0.04813149571418762,
-0.03833760321140289,
0.03892887383699417,
0.025487590581178665,
-0.028028316795825958,
-0.043511901050806046,
-0.04929448291659355,
-0.009320206940174103,
0.020598702132701874,
-0.012961000204086304,
0.032119687646627426,
-0.02223745547235012,
-0.0313255712389946,
0.04974725842475891,
0.034858305007219315,
-0.07119914144277573,
-0.018157703801989555,
0.08222551643848419,
0.023443911224603653,
-0.0007198991952463984,
-0.023250920698046684,
-0.07227376848459244,
0.025447797030210495,
-0.05566992238163948,
0.07997177541255951,
0.007495936471968889,
-0.03904186934232712,
0.03891608864068985,
-0.007168537471443415,
0.015481590293347836,
-0.08754283934831619,
-0.024784209206700325,
-0.04059908911585808,
-0.0017196882981806993,
-0.025157414376735687,
0.03505093976855278,
-0.004679813515394926,
-0.02554747648537159,
0.02287864312529564,
0.023507380858063698,
-0.007420348469167948,
0.01620224304497242,
-0.07362381368875504,
-0.0038398420438170433,
0.010385029017925262,
-0.027211353182792664,
0.06225891783833504,
-0.01596355251967907,
-0.006988278590142727,
-0.01733618788421154,
0.0012045179028064013,
0.030668960884213448,
0.04612535610795021,
0.021425588056445122,
0.025610458105802536,
0.03185087442398071,
-0.01086281519383192,
0.03981567919254303,
0.004748532082885504,
-0.01566900499165058,
0.13737624883651733,
0.030473867431282997,
0.013940464705228806,
-0.08271483331918716,
0.04190296679735184,
-0.020251672714948654,
0.018383953720331192,
-0.0007298510754480958,
0.00283297011628747,
-0.021816732361912727,
0.03622053563594818,
-0.05459044128656387,
0.034390464425086975,
0.020755527541041374,
-0.016630779951810837,
0.03221602737903595,
-0.031822219491004944,
-0.022267289459705353,
0.04473751410841942,
-0.007871243171393871,
-0.02139139734208584,
-0.009826728142797947,
-0.050813641399145126,
0.008874129503965378,
-0.003648346522822976,
-0.02914677932858467,
-0.032595083117485046,
-0.042748693376779556,
0.00492716021835804,
0.03273407369852066,
-0.02849002555012703,
0.004372365307062864,
0.0031324904412031174,
0.022100575268268585,
-0.023478912189602852,
0.023523148149251938,
-0.008640803396701813,
0.0072683654725551605,
0.014547046273946762,
-0.00666114641353488,
-0.005623579025268555,
0.015183733776211739,
0.04814661294221878,
0.023520763963460922,
-0.04481106996536255,
0.01787867583334446,
-0.03888429328799248,
0.0177338607609272,
-0.025678616017103195,
-0.009005793370306492,
0.0007603796548210084,
-0.033523183315992355,
-0.017856961116194725,
-0.046675339341163635,
-0.03028005175292492,
0.016477253288030624,
0.012003179639577866,
-0.024896344169974327,
-0.02132047526538372,
0.010797649621963501,
0.014968262985348701,
0.019314566627144814,
0.019662514328956604,
-0.04153147712349892,
0.016200637444853783,
-0.012300784699618816,
0.00035929851583205163,
0.029314761981368065,
0.0023309511598199606,
-0.02474677748978138,
-0.03172333911061287,
0.02470588870346546,
-0.035526860505342484,
0.027095919474959373,
0.003928865771740675,
0.0023255562409758568,
0.041987352073192596,
-0.02900475636124611,
-0.03834829106926918,
-0.024506671354174614,
-0.056612372398376465,
0.01644130051136017,
-0.020760538056492805,
-0.015056664124131203,
-0.020905420184135437,
0.04218146950006485,
0.03586336225271225,
0.019766682758927345,
-0.05237710103392601,
0.007452243939042091,
-0.01709788292646408,
0.0028367755003273487,
0.00016961160872597247,
-0.007467150222510099,
-0.04568857699632645,
0.03708973899483681,
0.010006670840084553,
-0.03169264271855354,
0.002148926490917802,
0.04599572718143463,
0.01711571216583252,
-0.011302505619823933,
0.0024735131300985813,
0.019887663424015045,
0.012451714836061,
-0.008754768408834934,
-0.0012601296184584498,
-0.008196520619094372,
-0.006399036850780249,
0.04590018093585968,
-0.012312247417867184,
-0.045638564974069595,
-0.04679654538631439,
-0.04342519864439964,
-0.03514086455106735,
0.037720926105976105,
0.048816654831171036,
0.026682378724217415,
-0.04339337721467018,
-0.043933529406785965,
0.024174975231289864,
-0.008971934206783772,
-0.01987980306148529,
-0.023812515661120415,
0.003174351993948221,
-0.0166328065097332,
0.010834990069270134,
-0.02343636564910412,
0.03729422017931938,
0.009803163819015026,
-0.011830033734440804,
0.019491560757160187,
0.04475630074739456,
0.03222532942891121,
-0.015748752281069756,
0.04292217642068863,
-0.026547294110059738,
0.02247386798262596,
0.023177022114396095,
-0.053720586001873016,
0.006763040088117123,
0.009113623760640621,
-0.04926032945513725,
-0.013009927235543728,
-0.01267357636243105,
-0.028262795880436897,
0.00633151363581419,
0.028280936181545258,
0.0210095327347517,
0.028023473918437958,
-0.014693872071802616,
-0.008948891423642635,
-0.019223883748054504,
-0.0019924447406083345,
0.008917715400457382,
-0.04742195084691048,
-0.014172931201756,
-0.030897395685315132,
-0.009310027584433556,
0.07115380465984344,
0.004920460283756256,
0.010148484259843826,
-0.018496619537472725,
0.010804428718984127,
-0.013054246082901955,
-0.026300230994820595,
0.0008980570710264146,
0.029931606724858284,
0.020795628428459167,
0.039110250771045685,
-0.0245771873742342,
0.05719324201345444,
0.027385441586375237,
0.014042436145246029,
-0.07300344109535217,
0.004545867908746004,
0.05564029887318611,
0.002515986328944564,
0.03865329548716545,
-0.014630163088440895,
0.0032428649719804525,
0.017349746078252792,
-0.0970405787229538,
0.005828338675200939,
-0.041248925030231476,
-0.015013176947832108,
-0.026174865663051605,
-0.02696022391319275,
-0.041499946266412735,
0.037658412009477615,
0.00021052865486126393,
0.021545860916376114,
0.06542747467756271,
0.024791711941361427,
-0.012128517031669617,
-0.00618525268509984,
-0.022651180624961853,
0.018711933866143227,
0.0012582129565998912,
-0.04721751809120178,
0.06749307364225388,
-0.034494634717702866,
-0.05075264349579811,
-0.014240712858736515,
-0.04482294246554375,
0.00952422246336937,
0.045083437114953995,
-0.015294568613171577,
0.004352887626737356,
0.05110280215740204,
-0.02892434597015381,
-0.0018452317453920841,
-0.03997981175780296,
0.025187699124217033,
-0.03166632726788521,
0.047749437391757965,
-0.029147258028388023,
-0.013418890535831451,
-0.014855255372822285,
-0.0034832735545933247,
0.005752506200224161,
0.03496899455785751,
-0.020530663430690765,
-0.0320022813975811,
-0.016335615888237953,
0.034407779574394226,
0.012375476770102978,
-0.0035796333104372025,
0.019697796553373337,
-0.051703281700611115,
0.007736835163086653,
-0.00930757261812687,
0.003861540462821722,
-0.027047470211982727,
0.010212969034910202,
-0.030498012900352478,
-0.022121325135231018,
-0.010676855221390724,
0.005281304474920034,
-0.01773708313703537,
-0.018493730574846268,
0.029588043689727783,
0.01446986198425293,
-0.06745132058858871,
0.01922035403549671,
-0.029662054032087326,
-0.008752618916332722,
0.03951188921928406,
0.026275811716914177,
0.028249818831682205,
-0.00703632365912199,
-0.05077458173036575,
-0.0011897975346073508,
-0.06571832299232483,
0.06727823615074158,
0.021975716575980186,
0.027562523260712624,
0.014165123924612999,
-0.021902427077293396,
-0.017479103058576584,
0.046056464314460754,
0.05805166810750961,
0.012573504820466042,
-0.02286599949002266,
-0.023577440530061722,
-0.029610659927129745,
0.0028382432647049427,
0.001010459498502314,
-0.020181328058242798,
-0.019778424873948097,
-0.0013263339642435312,
0.0009513489785604179,
-0.015255700796842575,
-0.05023115128278732,
0.011230718344449997,
-0.0019473464926704764,
-0.01284037996083498,
-0.0010502078803256154,
-0.0019425204955041409,
-0.009348999708890915,
0.062065839767456055,
-0.03567841649055481,
-0.02332739159464836,
0.044650811702013016,
0.036512088030576706,
0.0050970097072422504,
0.013480575755238533,
-0.027165129780769348,
-0.04934154078364372,
-0.012319502420723438,
-0.042992040514945984,
-0.013636751100420952,
-0.036468636244535446,
-0.026424575597047806,
0.05682119354605675,
-0.013121395371854305,
0.010307009331882,
0.016796788200736046,
-0.03131593391299248,
0.057757750153541565,
0.023367127403616905,
-0.01683354750275612,
0.055528488010168076,
0.02694026380777359,
0.03865640610456467,
-0.004077934194356203,
0.010527247563004494,
-0.006079689133912325,
0.024243801832199097,
0.047181516885757446,
0.031134827062487602,
0.0023856002371758223,
0.01682440936565399,
-0.014717256650328636,
-0.010931591503322124,
0.029068151488900185,
0.018808364868164062,
-0.022072093561291695,
-0.006886675022542477,
0.028581388294696808,
-0.03164493665099144,
0.021335482597351074,
0.020716803148388863,
0.015112685039639473,
0.09020967781543732,
-0.01630101352930069,
-0.008407562971115112,
-0.045854225754737854,
0.01027367077767849,
-0.0278642438352108,
-0.014764368534088135,
0.02563054859638214,
0.035677485167980194,
0.01378814410418272,
0.0020855856128036976,
-0.014207681640982628,
-0.017662791535258293,
0.05263068154454231,
-0.01847161166369915,
0.02002020925283432,
0.012284363619983196,
-0.030460521578788757,
0.035824842751026154,
-0.026664260774850845,
-0.018801791593432426,
-0.008390041999518871,
0.02691015414893627,
-0.002323577646166086,
0.022923976182937622,
0.02555393986403942,
-0.019165070727467537,
0.007025927770882845,
0.07287316024303436,
-0.0625571683049202,
-0.012033598497509956,
-0.025808608159422874,
0.0009658253402449191,
0.007159319706261158,
-0.004979327321052551
] |
<p>If we thermally isolate a region in space, say using a hypothetical material of $0$ conductivity, and measure the region's temperature, will it be 2.7K?</p>
| 10,685 |
[
-0.0002395682968199253,
-0.02138127200305462,
-0.022302860394120216,
-0.005972747690975666,
0.0357503779232502,
0.0032092169858515263,
-0.06005439907312393,
-0.0005529469926841557,
-0.02117803506553173,
-0.06686727702617645,
0.03202153742313385,
0.007875165902078152,
0.02146586962044239,
0.01077194046229124,
-0.010911185294389725,
0.03034188225865364,
-0.019703460857272148,
0.021460186690092087,
0.0030509638600051403,
0.008119113743305206,
0.021594561636447906,
0.029533149674534798,
0.02034681849181652,
-0.0058935536071658134,
-0.04601272568106651,
0.0010697008110582829,
-0.02020532451570034,
-0.04703469201922417,
0.03470843657851219,
0.04639948159456253,
-0.006337567698210478,
-0.0066497134976089,
0.028432169929146767,
0.005391212180256844,
0.03792192414402962,
-0.02231115847826004,
-0.024390317499637604,
-0.04611482098698616,
-0.011942959390580654,
0.027025653049349785,
-0.03085528314113617,
-0.056158870458602905,
0.0254688560962677,
0.04490067437291145,
-0.024048272520303726,
-0.03481287136673927,
-0.005672778934240341,
-0.04133591055870056,
0.021418878808617592,
-0.034860242158174515,
0.023092079907655716,
-0.00855091493576765,
0.05972052365541458,
0.05027083680033684,
-0.018784618005156517,
-0.0076076677069067955,
0.08731996268033981,
0.04457336664199829,
0.007635279092937708,
0.004881825298070908,
-0.03663095086812973,
0.017430391162633896,
-0.014026430435478687,
-0.027576841413974762,
-0.01960783451795578,
0.01955757662653923,
-0.043118029832839966,
-0.015134508721530437,
0.007291013840585947,
0.02706627920269966,
-0.0059674629010260105,
0.020757056772708893,
0.010668298229575157,
0.0009510365198366344,
0.017769545316696167,
-0.013195653446018696,
0.022835953161120415,
0.017527908086776733,
0.058075737208127975,
0.017789671197533607,
-0.00946511048823595,
-0.014314382337033749,
0.022877760231494904,
-0.005674934480339289,
0.0071482122875750065,
0.00699613569304347,
0.06606579571962357,
-0.029349692165851593,
0.022180447354912758,
0.029197514057159424,
0.013715121895074844,
0.03475280851125717,
-0.0050692250952124596,
0.0027694394811987877,
-0.009725523181259632,
0.009070804342627525,
-0.005995729472488165,
0.07718846946954727,
-0.03729063272476196,
-0.044809598475694656,
0.0045884051360189915,
0.04444455727934837,
0.030858000740408897,
0.06107969582080841,
0.022056207060813904,
-0.025646710768342018,
-0.010053673759102821,
0.008185812272131443,
-0.00583639508113265,
-0.012632184661924839,
-0.036541759967803955,
0.007923640310764313,
0.003328922903165221,
-0.012166697531938553,
0.04824719578027725,
-0.02619783952832222,
-0.0017877010395750403,
-0.040942028164863586,
0.019882483407855034,
0.04807592183351517,
0.037418704479932785,
0.013570592738687992,
-0.012921979650855064,
-0.030390270054340363,
-0.05334804207086563,
0.02947348542511463,
0.005142952315509319,
-0.02191086672246456,
-0.028621576726436615,
-0.00024195737205445766,
-0.045320164412260056,
-0.017860980704426765,
0.02115340530872345,
-0.04504628852009773,
0.038763608783483505,
-0.004164410289376974,
-0.06400971114635468,
-0.06192926689982414,
0.010820616967976093,
-0.008984977379441261,
0.005660046357661486,
-0.023591097444295883,
-0.004867471754550934,
0.034921176731586456,
0.04809843748807907,
0.002341843442991376,
0.02239108271896839,
-0.034614093601703644,
0.010194380767643452,
0.008671129122376442,
-0.05479653924703598,
-0.04050939902663231,
0.006687473971396685,
-0.07878509908914566,
0.003021624404937029,
-0.056561827659606934,
0.02304850146174431,
0.05310393124818802,
-0.016506154090166092,
-0.02548960968852043,
0.020097341388463974,
-0.021592816337943077,
-0.003102343762293458,
0.008813922293484211,
-0.03117806278169155,
-0.011252881959080696,
0.09360821545124054,
0.019483497366309166,
-0.003295897040516138,
0.03756630793213844,
0.04333348199725151,
0.04947611317038536,
0.02459111623466015,
-0.008890779688954353,
0.06359671801328659,
-0.015341161750257015,
0.03398965671658516,
0.00154367636423558,
0.018302612006664276,
-0.0022653297055512667,
-0.08016567677259445,
-0.01223169919103384,
0.02221290022134781,
-0.023029889911413193,
-0.008048689924180508,
0.050135619938373566,
0.025014018639922142,
-0.022996971383690834,
0.015040367841720581,
-0.008333172649145126,
-0.006638414692133665,
-0.04334807023406029,
0.025135021656751633,
0.03999917581677437,
-0.008731639944016933,
0.007330615539103746,
0.028011858463287354,
0.05149334296584129,
-0.01158035360276699,
-0.07891198992729187,
0.021709615364670753,
0.03318063169717789,
-0.00305527588352561,
-0.01881982386112213,
0.0394856221973896,
0.045817483216524124,
0.05866466090083122,
0.022984519600868225,
0.016092482954263687,
-0.003372270381078124,
-0.04965965449810028,
-0.028020597994327545,
-0.025835830718278885,
0.02650279551744461,
0.009292582981288433,
0.0012034984538331628,
0.03811733424663544,
-0.0007752258097752929,
0.017857778817415237,
0.039819471538066864,
0.0016466762172058225,
0.09576954692602158,
0.023035408928990364,
0.04740149900317192,
-0.03810961917042732,
0.017215469852089882,
0.03686147928237915,
-0.011590681038796902,
-0.01805693842470646,
-0.05448644608259201,
-0.06446962803602219,
0.00410720519721508,
0.057625703513622284,
0.03435864299535751,
-0.0479736253619194,
0.029008207842707634,
0.020487120375037193,
0.018171897158026695,
0.003551164874807,
-0.005339562427252531,
-0.02050408534705639,
0.03641355410218239,
0.03869250789284706,
-0.004637453239411116,
0.015143265947699547,
-0.01452105212956667,
0.0273275263607502,
0.024090956896543503,
0.035654839128255844,
-0.012989908456802368,
0.030666345730423927,
0.029513955116271973,
0.02035527676343918,
0.00025128840934485197,
-0.008117018267512321,
-0.027407152578234673,
0.005726594477891922,
-0.0014323010109364986,
0.04730122536420822,
0.009674085304141045,
0.019359810277819633,
0.01071150228381157,
-0.03173062205314636,
-0.004282010719180107,
0.019167611375451088,
-0.03736385703086853,
-0.002644510706886649,
-0.013597977347671986,
0.0448460578918457,
-0.05366237461566925,
0.001521233469247818,
-0.04599007964134216,
0.03067600727081299,
-0.02333962172269821,
-0.04045364633202553,
0.0372864231467247,
0.0011397911002859473,
0.007291106507182121,
-0.045005913823843,
-0.043384019285440445,
-0.026665305718779564,
-0.0340719036757946,
0.0012266583507880569,
0.02914801612496376,
-0.05781642720103264,
0.0029730640817433596,
-0.003859163960441947,
-0.023564478382468224,
-0.007886845618486404,
-0.009147829376161098,
0.018173381686210632,
0.014302673749625683,
-0.012945493683218956,
-0.04937583953142166,
0.01027950644493103,
-0.009110198356211185,
-0.016330687329173088,
-0.0419435016810894,
-0.0030860838014632463,
0.07563869655132294,
-0.039892569184303284,
-0.02812071517109871,
0.003525212174281478,
-0.05303379148244858,
-0.03619999438524246,
-0.029087696224451065,
-0.04415562003850937,
0.02062591351568699,
-0.05174305662512779,
0.04997415840625763,
0.02493113838136196,
-0.035697661340236664,
-0.004548209719359875,
-0.037308644503355026,
-0.04351285099983215,
0.024840520694851875,
-0.028019849210977554,
0.006726177409291267,
-0.048344969749450684,
-0.041095949709415436,
0.08965087682008743,
0.025969363749027252,
0.01100493036210537,
-0.01383892260491848,
0.0006067310459911823,
-0.055385518819093704,
-0.03374757617712021,
-0.0329645499587059,
-0.026982005685567856,
-0.00024455611128360033,
-0.010537957772612572,
0.024900510907173157,
0.03189881891012192,
0.04952423274517059,
0.027779247611761093,
-0.023015156388282776,
0.010948315262794495,
-0.0182582288980484,
0.006356900557875633,
0.0841209664940834,
0.024487828835844994,
-0.022511029615998268,
0.05563877522945404,
-0.013127653859555721,
0.047482285648584366,
0.022458860650658607,
-0.05225492641329765,
0.051120419055223465,
0.006102600134909153,
0.03316535800695419,
-0.03255951404571533,
0.04468340426683426,
-0.026114461943507195,
0.028739413246512413,
0.012702959589660168,
0.0043793972581624985,
0.009904880076646805,
0.00862388126552105,
-0.019227284938097,
0.013763939961791039,
0.07547261565923691,
0.032321829348802567,
-0.01004695799201727,
0.020576922222971916,
-0.004371406510472298,
-0.0065118297934532166,
0.037599097937345505,
-0.025597088038921356,
0.03155050426721573,
0.04186897724866867,
0.03941104933619499,
0.02215665951371193,
0.010150968097150326,
-0.0032809891272336245,
-0.03276253491640091,
-0.021755946800112724,
-0.001988053321838379,
0.04579228162765503,
0.01970190368592739,
0.03569122031331062,
0.04046560823917389,
0.006221318151801825,
0.0111765805631876,
0.027321865782141685,
-0.0792926698923111,
0.010303273797035217,
-0.04936176910996437,
-0.012632264755666256,
-0.0002667945809662342,
0.012879214249551296,
-0.015559754334390163,
-0.021071964874863625,
0.027763962745666504,
-0.006338227540254593,
-0.010202690958976746,
-0.05851975083351135,
-0.005986933130770922,
0.004511790815740824,
-0.016356779262423515,
-0.030960699543356895,
0.053501833230257034,
0.08540809899568558,
-0.02748354710638523,
0.0048598176799714565,
0.001256983377970755,
0.023547349497675896,
0.011220368556678295,
0.007516281679272652,
0.018747294321656227,
-0.020233767107129097,
0.04049078747630119,
0.018942050635814667,
0.038379210978746414,
-0.04532187804579735,
-0.011648304760456085,
0.014705980196595192,
0.037799421697854996,
-0.02709338255226612,
-0.019667398184537888,
-0.0405745804309845,
-0.05317968502640724,
-0.03795255348086357,
-0.014872546307742596,
0.045894213020801544,
-0.023905593901872635,
0.004276062361896038,
0.04533083364367485,
0.0010371811222285032,
-0.01761055365204811,
-0.006592363119125366,
0.03467601165175438,
-0.01937885582447052,
-0.029986238107085228,
-0.004650235641747713,
-0.04554036632180214,
-0.042698781937360764,
-0.0021477164700627327,
0.02274785004556179,
-0.012757478281855583,
0.011807631701231003,
0.018042638897895813,
-0.008218428120017052,
0.00544418441131711,
-0.0006416038959287107,
-0.007894146256148815,
0.020835906267166138,
0.03847706317901611,
-0.01275066938251257,
-0.00784804206341505,
0.0024537278804928064,
0.04405488818883896,
0.017672916874289513,
-0.001998927677050233,
-0.031048091128468513,
-0.10328496247529984,
0.002060438971966505,
-0.008492439985275269,
0.007759575266391039,
0.03380286321043968,
-0.03457066789269447,
-0.0696159154176712,
-0.004372491035610437,
0.0637182965874672,
-0.008464341051876545,
0.03517239913344383,
-0.020502634346485138,
-0.011970206163823605,
-0.005319626536220312,
0.018720274791121483,
-0.003598364070057869,
0.04535159096121788,
0.02870543859899044,
-0.025669945403933525,
-0.022462869063019753,
0.004431496374309063,
0.036439865827560425,
0.0038719468284398317,
0.021061433479189873,
0.05845911055803299,
0.006807496305555105,
0.04112466424703598,
0.000290705676889047,
-0.043066829442977905,
-0.03744609281420708,
-0.05504511296749115,
-0.0064315227791666985,
0.009460890665650368,
-0.013925264589488506,
0.03215702250599861,
-0.0439668744802475,
-0.04276944324374199,
0.04823572188615799,
-0.0029340595938265324,
0.010250190272927284,
0.024657318368554115,
-0.026612216606736183,
0.05229289457201958,
0.01949881948530674,
0.005684640724211931,
0.06860766559839249,
0.006852541118860245,
0.020412374287843704,
0.006626269314438105,
-0.04803018644452095,
0.04629765823483467,
-0.04508185759186745,
-0.01404371578246355,
-0.002917980309575796,
-0.005781788844615221,
-0.028823453933000565,
0.06932306289672852,
-0.007373699452728033,
0.016288775950670242,
0.024050449952483177,
-0.05232860520482063,
0.016870802268385887,
0.004660957958549261,
-0.0036786196287721395,
0.016471518203616142,
-0.0004051430441904813,
0.0517817921936512,
-0.02939508855342865,
-0.03588547930121422,
0.0008605874609202147,
-0.009572896175086498,
0.022792797535657883,
0.031771715730428696,
-0.037095967680215836,
0.0444287545979023,
-0.02195236086845398,
-0.009468276984989643,
-0.015649572014808655,
-0.055268872529268265,
0.04627440869808197,
-0.05416896566748619,
-0.0029269952792674303,
0.01796245574951172,
-0.08340602368116379,
0.0208976361900568,
-0.017737900838255882,
0.017939649522304535,
0.04143476113677025,
-0.04671745002269745,
0.03523431345820427,
0.017111830413341522,
0.027077853679656982,
-0.09359908103942871,
-0.04680042341351509,
0.023233477026224136,
0.006654579192399979,
0.00474154157564044,
-0.02403981052339077,
-0.002323257038369775,
-0.028000567108392715,
-0.06345370411872864,
0.013295620679855347,
0.08317200839519501,
-0.002643922809511423,
-0.038704581558704376,
-0.037063825875520706,
0.050804901868104935,
0.0327061228454113,
0.01013057678937912,
-0.029748210683465004,
0.0336446650326252,
-0.010160927660763264,
-0.00959794595837593,
-0.010963615030050278,
0.029583722352981567,
-0.02737705036997795,
-0.009784203954041004,
-0.038180962204933167,
-0.028362050652503967,
0.00890763197094202,
0.025517666712403297,
-0.05654064565896988,
0.051400210708379745,
0.007541496306657791,
-0.023302175104618073,
-0.0032245838083326817,
0.03406456485390663,
0.023457657545804977,
-0.01351920422166586,
-0.025563102215528488,
-0.007408734876662493,
-0.03207292780280113,
-0.0009968706872314215,
0.01714324578642845,
0.0015954738482832909,
-0.003721807384863496,
-0.004458260722458363,
0.07323574274778366,
0.015535063110291958,
-0.01347948145121336,
0.010693843476474285,
0.03756226971745491,
0.005224042106419802,
-0.02383231185376644,
-0.02080368436872959,
0.015479386784136295,
0.018691793084144592,
-0.050801943987607956,
-0.013075088150799274,
-0.023591376841068268,
-0.00994823221117258,
0.06881796568632126,
-0.04845680668950081,
0.040341731160879135,
0.007217950187623501,
-0.007347962819039822,
0.015053176321089268,
-0.014324596151709557,
0.004304550122469664,
0.04751064255833626,
-0.024306461215019226,
0.014982438646256924,
-0.012732412666082382,
-0.00601007416844368,
0.01791505143046379,
0.043236833065748215,
-0.031068988144397736,
0.010861478745937347,
0.008947174996137619,
0.013601398095488548,
0.03236088156700134,
-0.03511930629611015,
-0.0374712198972702,
0.03729160502552986,
-0.038699500262737274,
0.02525012195110321,
0.030321748927235603,
-0.02628258988261223,
0.029284168034791946,
-0.03799936920404434,
0.00036756289773620665,
-0.054077062755823135,
-0.029162846505641937,
-0.06063087284564972,
0.026331298053264618,
0.011571385897696018,
0.026191968470811844,
0.01655643619596958,
-0.0011878939112648368,
0.017613694071769714,
-0.03428976237773895,
-0.014371860772371292,
0.031049059703946114,
-0.0467502698302269,
-0.03522254899144173,
-0.032118309289216995,
-0.05011730641126633,
0.05328313261270523,
0.02975546196103096,
-0.041145071387290955,
0.039127033203840256,
-0.0020767864771187305,
0.030970590189099312,
0.020331330597400665,
0.026995697990059853,
-0.04002232849597931,
0.040738362818956375,
-0.015717888250947,
-0.005822182632982731,
-0.04640955105423927,
0.03801640495657921,
0.11425676941871643,
0.049041736871004105,
0.002077653771266341,
-0.06327515095472336,
0.0066660004667937756,
-0.013047507964074612,
-0.007457217667251825,
-0.03951422870159149,
-0.005352157633751631,
0.006059746723622084,
0.0015927235363051295,
0.03713482618331909,
0.058888185769319534,
-0.036837730556726456,
-0.014464030973613262,
0.04326638951897621,
-0.02979830652475357,
0.017449840903282166,
-0.002322919899597764,
0.007420164067298174,
0.0006871382356621325,
0.011983836069703102,
-0.03421357274055481,
0.016258658841252327,
-0.02403832972049713,
0.01895878277719021,
-0.04005727171897888,
-0.025150321424007416,
0.016300013288855553,
-0.02324054390192032,
-0.03636188060045242,
-0.008687643334269524,
0.017160100862383842,
-0.016774412244558334,
-0.03184213861823082,
-0.01296111848205328,
0.017426224425435066,
-0.00540136406198144,
0.00825596135109663,
0.00860635656863451,
0.016137748956680298,
-0.006041886750608683,
0.020309627056121826,
-0.002601605374366045,
-0.039159175008535385,
-0.018522001802921295,
-0.01043532881885767,
0.05307919159531593,
-0.012318922206759453,
-0.011367961764335632,
-0.004467396065592766,
0.024287346750497818,
-0.012398685328662395,
-0.014140098355710506,
-0.009457975625991821,
0.01615579053759575,
0.01696745492517948,
0.00534436060115695,
-0.03172669932246208,
-0.03605003282427788,
0.025789128616452217,
-0.014030132442712784,
0.018734078854322433,
0.007268131244927645,
0.008102764375507832,
0.01579751819372177,
0.05146138370037079,
0.05928109213709831,
0.010157573968172073,
-0.022682739421725273,
-0.03595835343003273,
-0.055507879704236984,
-0.02729749120771885,
-0.01467165071517229,
-0.00212856731377542,
0.021797895431518555,
0.03397194668650627,
0.002568461699411273,
0.011662122793495655,
-0.009719704277813435,
-0.02610030770301819,
-0.015643684193491936,
-0.006522590294480324,
-0.0027933327946811914,
-0.013758481480181217,
0.014633143320679665,
0.016922708600759506,
0.04235668480396271,
-0.011784628964960575,
-0.0329216867685318,
0.02971460483968258,
0.03365395590662956,
0.034730464220047,
-0.034799620509147644,
0.014329473488032818,
-0.015079217031598091,
-0.03339933231472969,
0.038057975471019745,
-0.014223054051399231,
0.054380759596824646,
0.009777270257472992,
-0.003361418843269348,
0.03363821282982826,
0.011649657972157001,
-0.04658728465437889,
0.013207408599555492,
0.03904867172241211,
-0.024028517305850983,
-0.022493522614240646,
-0.015505615621805191,
-0.013030383735895157,
-0.023894673213362694,
-0.056765373796224594,
-0.013351858593523502,
-0.008721974678337574,
-0.0012164940126240253,
-0.0025787013582885265,
-0.016738243401050568,
0.028784804046154022,
0.000410532986279577,
-0.02952517382800579,
-0.06917175650596619,
-0.0324290469288826,
-0.028237415477633476,
-0.018159594386816025,
-0.008300784975290298,
-0.01622379943728447,
0.033806901425123215,
0.03678560256958008,
-0.03376052901148796,
-0.03521152213215828,
0.058202654123306274,
-0.00010634130012476817,
-0.0002875588834285736,
-0.01411774754524231,
0.007606510538607836,
0.014276059344410896,
0.04934311658143997,
-0.05716634914278984,
-0.008973059244453907,
0.012561742216348648,
-0.05281763896346092,
-0.07467974722385406,
0.03351350128650665,
0.010438591241836548,
0.06287705898284912,
0.027115309610962868,
-0.003525288077071309,
0.002390539739280939,
0.06239588186144829,
-0.0163602065294981,
-0.005356227979063988,
0.012498786672949791,
-0.02075454220175743,
0.0023370208218693733,
-0.0052570560947060585,
0.03536951169371605,
-0.012546990998089314,
0.0035575279034674168,
0.03980550169944763,
-0.02465927042067051,
0.0033650549594312906,
-0.031047973781824112,
0.0070654298178851604,
-0.008055539801716805,
0.011671776883304119,
0.03631853312253952,
-0.0026258944999426603,
0.02347756363451481,
0.03557376563549042,
-0.015772026032209396,
0.02330177091062069,
0.047586146742105484,
0.0017848260467872024,
-0.12607848644256592,
-0.012936977669596672,
0.0008094917866401374,
0.01487794704735279,
0.02063344232738018,
-0.03474815562367439,
0.01410802360624075,
0.027738181874155998,
-0.07389356940984726,
0.0077476161532104015,
-0.030819455161690712,
-0.02321222797036171,
-0.04099815711379051,
0.008443779312074184,
-0.02115440182387829,
0.02134236879646778,
0.06883058696985245,
0.05369866266846657,
-0.03396359086036682,
0.04249455779790878,
-0.04926665499806404,
-0.015295067802071571,
-0.004456896334886551,
-0.002253585262224078,
0.0010814950801432133,
0.0003495091514196247,
0.029661165550351143,
0.021104959771037102,
0.004334042780101299,
-0.010327530093491077,
-0.009821727871894836,
-0.008004537783563137,
0.007704632356762886,
0.030034823343157768,
0.0009981722105294466,
0.007359424605965614,
0.02920040301978588,
-0.03483167663216591,
0.001339064328931272,
0.01711408980190754,
0.008639396168291569,
0.01887102797627449,
-0.012115174904465675,
-0.018759984523057938,
0.03487405180931091,
-0.046515803784132004,
0.003241132479161024,
0.054953500628471375,
-0.013794656842947006,
0.009324879385530949,
0.03575607016682625,
0.019100317731499672,
0.008748733438551426,
-0.04070938006043434,
0.019185923039913177,
-0.0625787153840065,
-0.003970755729824305,
0.018930913880467415,
0.0253245010972023,
-0.04568780958652496,
-0.027845898643136024,
-0.011658597737550735,
0.0016456532757729292,
0.046778660267591476,
-0.013558769598603249,
-0.0012909433571621776,
-0.05028568580746651,
-0.018297119066119194,
-0.02070457488298416,
0.01599349081516266,
-0.007808048278093338,
-0.06414733827114105,
-0.024719685316085815,
0.04348362609744072,
0.015154332853853703,
0.03137435391545296,
-0.006312463898211718,
-0.03615475073456764,
-0.019875120371580124,
-0.05732404440641403,
0.033209383487701416,
-0.04291067272424698,
0.022452687844634056,
-0.03577432408928871,
-0.01746811904013157,
-0.017403367906808853,
0.004184096120297909,
0.060101576149463654,
0.020277516916394234,
-0.013616885989904404,
0.011469073593616486,
-0.00038145651342347264,
0.02650824561715126,
-0.04080788791179657,
0.026148341596126556,
0.009842931292951107,
-0.016643747687339783,
-0.01485040970146656,
-0.03357407823204994,
-0.021959062665700912,
0.018680589273571968,
0.027999263256788254,
0.01258847489953041,
0.010453175753355026,
-0.013812340795993805,
-0.011613202281296253,
0.04219349846243858,
0.0033947296906262636,
-0.0033348314464092255,
0.07681147009134293,
-0.01882307231426239,
0.04534424468874931,
-0.00009681803203420714,
0.0033212597481906414,
-0.03713580593466759,
0.005108267068862915,
-0.03137053921818733,
-0.01602266915142536,
-0.0027138253208249807,
0.008623173460364342,
-0.0007662569405511022,
-0.003017616458237171,
-0.0027646429371088743,
0.04561564326286316,
-0.036091238260269165,
-0.02151471935212612,
0.00417673634365201,
0.023756882175803185,
0.03329622745513916,
-0.02103736624121666,
0.02042432129383087,
0.023413950577378273,
0.020333509892225266,
-0.008506238460540771,
0.0504939928650856,
0.04181603342294693,
-0.007456368766725063,
0.00484270416200161,
0.014549645595252514,
-0.0072453999891877174,
0.007341042160987854,
0.020552020519971848,
0.032825734466314316,
-0.027899447828531265,
-0.02446836791932583,
0.0253814235329628,
0.0017779505578801036,
0.00034435157431289554,
0.004312887787818909,
-0.017285767942667007,
0.08979255706071854,
-0.008694024756550789,
0.011052791029214859,
-0.05336590111255646,
-0.0030796488281339407,
-0.0013018527533859015,
0.057224053889513016,
0.029609229415655136,
0.010815080255270004,
-0.026086149737238884,
-0.040023013949394226,
-0.01946333982050419,
0.01708841137588024,
-0.006057673133909702,
-0.05974958837032318,
0.03478250280022621,
-0.010414020158350468,
0.028472451493144035,
-0.010371374897658825,
-0.020363740622997284,
-0.02080114372074604,
-0.032027289271354675,
0.013861638493835926,
0.028417080640792847,
0.013323810882866383,
0.017265742644667625,
-0.014555742964148521,
0.01120079681277275,
0.05224892869591713,
-0.05526357889175415,
-0.01699685864150524,
0.013123279437422752,
0.04264877364039421,
-0.006758450530469418,
-0.02124548703432083
] |
<p>So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible?</p>
<p>I read this in Hawking's book and confused me because I assume when he says 99.9% speed of light, he means 99.9% speed of light in relation to someone outside observing?</p>
<p>I just cannot understand this notion of needing more and more energy to get closer to light as absolute velocity does not exist? (in that it is a purely relative concept). Surely the ability to accelerate further cannot possible be impeded because speed is all relative, there should be no limit to acceleration? If I 'accelerate' a further 50MPH, will I get to the destination exactly 50 miles early?</p>
<p>From what I can gather you 'can' accelerate FTL (sort off) but instead space bends towards you so you will get to your destination 'ftl' but only due to the curvature in space? So in effect, you can go light years in seconds (lets forget the practicals for a second), but from anyone observing, this will ALWAYS take light years.</p>
<p>Also, if for me I am going 'FTL', does outside observers see me as going light speed, or is it 99.999%.. is there a specific number?</p>
| 10,686 |
[
0.0004903440712951124,
-0.04388348013162613,
-0.004933618940412998,
-0.018478790298104286,
0.04957738146185875,
0.0012868806952610612,
-0.022424329072237015,
-0.026338467374444008,
-0.023610426113009453,
-0.008777170442044735,
-0.000815320760011673,
0.042347561568021774,
0.017370402812957764,
0.0030669530387967825,
0.0008976678946055472,
0.02479325607419014,
-0.020716335624456406,
0.0034029909875243902,
-0.02339569665491581,
-0.015370325185358524,
0.008814455009996891,
0.005178400781005621,
-0.00207778112962842,
0.007071805652230978,
-0.05407513678073883,
0.019485987722873688,
0.035545188933610916,
0.01382029615342617,
0.009540238417685032,
0.029966523870825768,
0.009609462693333626,
-0.037562619894742966,
0.020004767924547195,
0.028980394825339317,
0.04066463187336922,
0.01829088106751442,
-0.050632741302251816,
-0.016668209806084633,
-0.005392556078732014,
0.013692623935639858,
-0.03625749051570892,
-0.019070997834205627,
0.01742182858288288,
0.04594716802239418,
-0.014735139906406403,
0.015813231468200684,
0.02320517972111702,
-0.015435298904776573,
0.05704239383339882,
-0.03847123682498932,
0.07416629046201706,
0.012348211370408535,
0.05009573698043823,
0.006206226069480181,
0.052882324904203415,
0.006354331038892269,
0.07377343624830246,
0.07531610876321793,
-0.015801478177309036,
-0.03627699613571167,
-0.01252521201968193,
0.01600460894405842,
0.007159331347793341,
-0.03932885825634003,
0.01912340521812439,
0.02440386265516281,
-0.034181319177150726,
0.012333380989730358,
0.023624086752533913,
0.009509920142591,
0.016418080776929855,
0.024367447942495346,
0.04138200730085373,
-0.004552818369120359,
-0.01932424306869507,
-0.048234544694423676,
-0.009798289276659489,
-0.0005053746863268316,
0.060813356190919876,
0.06148158758878708,
-0.03396140784025192,
-0.02842908911406994,
0.047577694058418274,
0.04232846945524216,
0.010008865036070347,
0.011623457074165344,
0.04697079956531525,
0.013452828861773014,
0.03743218258023262,
0.026275470852851868,
0.01631409116089344,
0.02481638453900814,
0.027892008423805237,
-0.010585967451334,
-0.006548788398504257,
0.08665148913860321,
-0.008943036198616028,
0.012572181411087513,
-0.023778244853019714,
-0.00887482613325119,
-0.005919950548559427,
0.015980379655957222,
0.021396402269601822,
0.04756512492895126,
-0.0026374119333922863,
-0.04364793002605438,
-0.07184368371963501,
0.030232401564717293,
-0.02221909537911415,
-0.012696564197540283,
-0.00234988029114902,
0.02923552505671978,
0.0384121872484684,
0.027815554291009903,
-0.020111193880438805,
-0.05287778005003929,
0.016716666519641876,
-0.02894357405602932,
0.059426479041576385,
0.05108492448925972,
0.030299488455057144,
-0.034360531717538834,
0.03335979953408241,
0.018738413229584694,
-0.03474785014986992,
0.02028527297079563,
0.061693523079156876,
-0.02772027999162674,
-0.006579902954399586,
0.003176298225298524,
0.007767071947455406,
-0.037077195942401886,
0.003090193495154381,
0.029370006173849106,
0.03188857436180115,
0.002165290294215083,
-0.0954475924372673,
-0.053418781608343124,
0.05617319792509079,
0.0019499259069561958,
0.025343216955661774,
-0.07540176808834076,
0.030529726296663284,
0.0356999933719635,
0.10549673438072205,
-0.004594370722770691,
0.011095879599452019,
-0.0183268915861845,
0.00831510964781046,
-0.0022857559379190207,
-0.07296733558177948,
-0.007815100252628326,
-0.017711859196424484,
-0.021159349009394646,
0.03419880568981171,
-0.05768256261944771,
0.0083832498639822,
0.04792453721165657,
0.02435957081615925,
-0.05135924741625786,
0.04070992395281792,
-0.029238630086183548,
-0.0101862121373415,
0.021621564403176308,
-0.007685595192015171,
-0.008035505190491676,
0.12009479105472565,
0.01416819915175438,
0.003607045626267791,
0.05546843633055687,
0.024657322093844414,
0.020894184708595276,
-0.02506401762366295,
-0.0032719653099775314,
0.07215984910726547,
-0.05177299678325653,
0.0016704089939594269,
-0.04937940090894699,
-0.005981627851724625,
0.00593140535056591,
-0.07486800849437714,
-0.033816829323768616,
0.011540370061993599,
-0.01424262672662735,
0.02308984100818634,
0.023715345188975334,
-0.006751086562871933,
0.012481462210416794,
0.0020946040749549866,
-0.018725207075476646,
-0.012989676557481289,
-0.046940311789512634,
-0.00824663881212473,
0.01426408439874649,
0.04048996418714523,
0.03155269846320152,
-0.009383473545312881,
0.016306092962622643,
-0.04670635983347893,
-0.020165953785181046,
0.008233536966145039,
0.05997858941555023,
0.025257987901568413,
-0.044079482555389404,
0.046513140201568604,
0.06650333106517792,
0.019822783768177032,
0.01581922173500061,
-0.019603483378887177,
-0.012533326633274555,
-0.03153000399470329,
0.031312305480241776,
-0.010959235019981861,
0.03167393431067467,
0.019436081871390343,
0.022400137037038803,
-0.023240184411406517,
0.00125588895753026,
-0.014514056034386158,
0.016023891046643257,
-0.01287008821964264,
0.09784036874771118,
0.012496450915932655,
0.013956044800579548,
-0.03695552796125412,
0.029941825196146965,
-0.02065490186214447,
-0.008938690647482872,
-0.004212323576211929,
-0.005868750624358654,
-0.035724058747291565,
0.012928500771522522,
0.027537450194358826,
0.011863648891448975,
-0.034031596034765244,
-0.026416383683681488,
0.019191497936844826,
0.04896223172545433,
0.04004603251814842,
0.0363762341439724,
-0.04004788026213646,
-0.04072120040655136,
-0.014370767399668694,
0.004359587095677853,
0.008771371096372604,
0.040387533605098724,
0.04747391864657402,
0.007188976276665926,
-0.0007518706261180341,
-0.011422822251915932,
-0.013470896519720554,
0.02539152093231678,
-0.013087351806461811,
0.005394822917878628,
0.029787685722112656,
0.005465462803840637,
0.0497252456843853,
-0.044361215084791183,
0.026112576946616173,
0.029667960479855537,
-0.0006984800565987825,
-0.002233685227110982,
-0.044636908918619156,
0.014468000270426273,
0.003517396282404661,
0.024849766865372658,
-0.036533746868371964,
-0.010518766939640045,
0.023881467059254646,
-0.04108923673629761,
0.03222222253680229,
-0.03820319473743439,
-0.003209454007446766,
-0.04244902729988098,
-0.04289301112294197,
0.02471773885190487,
0.024977028369903564,
0.020596638321876526,
-0.01792953535914421,
-0.047812726348638535,
0.020748788490891457,
-0.027249686419963837,
0.01671365648508072,
0.0010010702535510063,
-0.029135001823306084,
0.04905015230178833,
0.00022667976736556739,
-0.0643623024225235,
0.04200482368469238,
-0.03316357359290123,
0.020159007981419563,
0.0352056547999382,
-0.015630006790161133,
-0.08302167057991028,
-0.0030750727746635675,
-0.032806579023599625,
-0.0045351190492510796,
0.027156071737408638,
0.004425037186592817,
0.04861263558268547,
-0.020777827128767967,
-0.03738633543252945,
0.030553394928574562,
-0.027177587151527405,
-0.0008969277841970325,
-0.03673775866627693,
0.014727089554071426,
-0.023493576794862747,
-0.039110515266656876,
0.02371498942375183,
-0.013406320475041866,
-0.03800438344478607,
0.020612426102161407,
-0.045111510902643204,
-0.05408743396401405,
0.015233145095407963,
0.05166252702474594,
0.016021694988012314,
-0.005831655114889145,
-0.013638666830956936,
0.06365030258893967,
0.045215874910354614,
-0.025131069123744965,
-0.04592039808630943,
-0.010179908014833927,
0.023152081295847893,
-0.004432796034961939,
-0.02939559891819954,
0.01587497442960739,
-0.027496064081788063,
0.0065881023183465,
0.017268652096390724,
0.05078892037272453,
0.008589099161326885,
0.004163388628512621,
0.0156813096255064,
-0.018612582236528397,
-0.001351537648588419,
0.03217848390340805,
0.027622036635875702,
0.035088349133729935,
-0.0711129680275917,
0.011616641655564308,
0.006823037285357714,
0.05862593278288841,
0.0518324077129364,
-0.029186269268393517,
0.051046714186668396,
0.021786043420433998,
0.009740556590259075,
-0.019897889345884323,
0.022190110757946968,
0.012198423035442829,
-0.01951076090335846,
0.032445523887872696,
0.0032245672773569822,
0.029903799295425415,
-0.016225336119532585,
0.0007003749487921596,
0.021840160712599754,
0.030028672888875008,
0.003389156423509121,
-0.025864936411380768,
0.007329162675887346,
0.008011797443032265,
-0.00005484729990712367,
-0.033736702054739,
-0.014346885494887829,
0.03709464147686958,
0.07514263689517975,
0.03333037346601486,
-0.013214586302638054,
-0.001914516557008028,
0.033043984323740005,
-0.08456788957118988,
-0.013025552034378052,
-0.021164467558264732,
0.039578113704919815,
-0.004269588738679886,
0.03998509794473648,
-0.004634421318769455,
0.004176557995378971,
0.02206616848707199,
0.006081613712012768,
-0.08452766388654709,
0.012877640314400196,
-0.040854230523109436,
-0.025614360347390175,
-0.011022701859474182,
-0.02823764458298683,
-0.027254490181803703,
-0.047219417989254,
-0.01138262264430523,
-0.015513083897531033,
-0.019821228459477425,
-0.030565040186047554,
0.02141648530960083,
-0.02982449159026146,
-0.02742687053978443,
-0.007027766201645136,
0.011273462325334549,
0.028763294219970703,
-0.002206944627687335,
0.002636023797094822,
0.0365564301609993,
-0.023875940591096878,
-0.028928633779287338,
-0.02678776904940605,
0.018019214272499084,
0.010273432359099388,
0.036942899227142334,
0.0312562994658947,
-0.0005840746453031898,
-0.03479573875665665,
0.014642322435975075,
0.023970993235707283,
0.004538587294518948,
0.0064813727512955666,
-0.018698859959840775,
-0.05976021662354469,
-0.023437749594449997,
-0.0057637873105704784,
0.017636409029364586,
0.022625520825386047,
0.01315101608633995,
0.017133591696619987,
0.034292805939912796,
0.015664972364902496,
0.00296545447781682,
0.024761218577623367,
0.03889745473861694,
-0.03504769504070282,
-0.05579981580376625,
-0.02895025722682476,
-0.028760969638824463,
-0.02550099976360798,
0.005417624022811651,
0.011625808663666248,
-0.004196216352283955,
-0.015522944740951061,
-0.007007075939327478,
0.007114221341907978,
-0.012112383730709553,
0.0061059012077748775,
0.024540426209568977,
-0.027638891711831093,
0.018887251615524292,
0.008053307421505451,
0.012278849259018898,
-0.002238718792796135,
0.008634733036160469,
0.05466677248477936,
-0.009853334166109562,
0.003724247682839632,
-0.05689740926027298,
-0.01174875721335411,
-0.001661885529756546,
0.062378011643886566,
-0.028689729049801826,
-0.013659881427884102,
-0.05708128586411476,
-0.012331686913967133,
-0.0006171281565912068,
-0.027593953534960747,
0.01514166034758091,
-0.018312403932213783,
-0.006589954253286123,
-0.010422629304230213,
-0.05455230921506882,
-0.041845206171274185,
0.013858187943696976,
-0.017660807818174362,
0.00006895435944898054,
-0.008512239903211594,
0.025693416595458984,
-0.0203595831990242,
0.010789905674755573,
0.0192533228546381,
0.04804677516222,
-0.009433471597731113,
-0.009661412797868252,
-0.0005151302902959287,
0.03841548413038254,
-0.017759431153535843,
-0.06556320935487747,
0.0158602986484766,
0.03754447028040886,
-0.019868262112140656,
0.030713599175214767,
-0.052397146821022034,
-0.03344530612230301,
0.059428632259368896,
0.04117293283343315,
-0.025437774136662483,
-0.009181760251522064,
-0.024310991168022156,
0.02722913771867752,
0.012061851099133492,
0.010806415230035782,
0.0640406459569931,
0.022141341120004654,
-0.03256390988826752,
0.0052621327340602875,
0.0056967828422784805,
0.0551193468272686,
-0.035104867070913315,
-0.002852401463314891,
-0.00963516253978014,
-0.009792495518922806,
-0.028440721333026886,
0.034310415387153625,
-0.04738549143075943,
0.003944001626223326,
-0.0010522077791392803,
-0.021666208282113075,
-0.0024139503948390484,
0.03717968612909317,
0.034845177084207535,
0.008514290675520897,
-0.061326418071985245,
0.014063241891562939,
-0.016091350466012955,
-0.015362928621470928,
-0.0038401619531214237,
0.005922646261751652,
-0.021826138719916344,
0.04200313612818718,
0.034370291978120804,
0.015329505316913128,
-0.005287843756377697,
-0.022420624271035194,
0.02940460294485092,
-0.030062390491366386,
0.03393278270959854,
-0.026742219924926758,
-0.012732120230793953,
-0.009831429459154606,
-0.025591282173991203,
-0.04034757241606712,
-0.014171268790960312,
-0.020692793652415276,
0.024276090785861015,
-0.03508543595671654,
0.018177319318056107,
0.014549286104738712,
0.03813711926341057,
-0.05963238701224327,
-0.04024891555309296,
0.017205797135829926,
-0.010052915662527084,
-0.032109539955854416,
-0.03195609524846077,
0.013643310405313969,
-0.049204304814338684,
-0.03995400294661522,
-0.0273574311286211,
0.03174767643213272,
-0.025921249762177467,
-0.006532410159707069,
-0.007266136817634106,
-0.00610235845670104,
0.02550758607685566,
-0.013125035911798477,
-0.03315434604883194,
0.0023891001474112272,
0.028828449547290802,
-0.009900686331093311,
-0.012814110144972801,
0.06256835162639618,
-0.02811216376721859,
-0.029686972498893738,
-0.017917992547154427,
-0.027432966977357864,
0.0012172645656391978,
-0.0035257020499557257,
0.013873271644115448,
0.05928787961602211,
0.0005997566040605307,
-0.008120734244585037,
0.01284431666135788,
0.020121758803725243,
-0.018279453739523888,
0.006317038554698229,
0.021102342754602432,
-0.026751557365059853,
-0.016843387857079506,
-0.055833958089351654,
0.07830654829740524,
0.018400387838482857,
0.03104911744594574,
-0.03934696689248085,
0.07759881764650345,
0.02303919568657875,
-0.010226293466985226,
-0.007942224852740765,
-0.028202807530760765,
0.008252596482634544,
-0.025846300646662712,
0.008050253614783287,
0.027345286682248116,
-0.031513214111328125,
-0.02139313332736492,
-0.02684618905186653,
0.0156300887465477,
-0.003657457185909152,
0.04365194961428642,
-0.011447872966527939,
0.03454960510134697,
-0.008505021221935749,
-0.012849326245486736,
0.004486865364015102,
-0.023070313036441803,
-0.030109860002994537,
-0.007970314472913742,
0.010135500691831112,
0.00974306371062994,
-0.008293954655528069,
-0.04266357421875,
0.055645037442445755,
0.05698510259389877,
0.01991976611316204,
0.017086980864405632,
0.0449795238673687,
0.011719943955540657,
0.02757248841226101,
-0.008525671437382698,
-0.012009707279503345,
0.030468089506030083,
-0.013646000996232033,
-0.0018385772127658129,
0.011440200731158257,
-0.015679465606808662,
0.0391373336315155,
-0.0013886699452996254,
0.005591446999460459,
-0.028948035091161728,
-0.024726254865527153,
-0.027088018134236336,
0.006433622445911169,
0.0016105235554277897,
0.008252554573118687,
0.019376711919903755,
-0.046175695955753326,
-0.018577340990304947,
0.02780226245522499,
0.06367475539445877,
0.004566110670566559,
-0.05530397221446037,
-0.0646098330616951,
-0.03416825085878372,
-0.03294778987765312,
0.05162791535258293,
0.022683214396238327,
-0.03124064765870571,
-0.01254271436482668,
-0.029808783903717995,
0.0018934552790597081,
0.007024729624390602,
0.03847260773181915,
0.017745301127433777,
0.05685562640428543,
-0.0003244574763812125,
0.04039356857538223,
-0.04876435920596123,
0.00229453481733799,
0.09580045938491821,
0.022540632635354996,
-0.018588557839393616,
-0.04046773910522461,
0.010861995629966259,
-0.05305707827210426,
0.00781602505594492,
-0.035937175154685974,
0.030521493405103683,
-0.039487145841121674,
0.011585885658860207,
0.057184647768735886,
0.04641086608171463,
-0.008860637433826923,
-0.009113471955060959,
0.0657816082239151,
-0.029802951961755753,
-0.0152721693739295,
0.047976016998291016,
0.020434852689504623,
-0.019535474479198456,
0.016184240579605103,
-0.002159243216738105,
0.01854669488966465,
-0.012177109718322754,
0.00465234974399209,
-0.0023696229327470064,
-0.0340535007417202,
0.012073223479092121,
0.0211359690874815,
-0.09589401632547379,
-0.016006454825401306,
0.019367113709449768,
-0.04220104217529297,
-0.05571168661117554,
0.009516631253063679,
0.04199904575943947,
-0.004631216172128916,
-0.004524938762187958,
0.034555722028017044,
0.024985574185848236,
0.05148943141102791,
0.012146089226007462,
0.006158599629998207,
-0.03541228547692299,
-0.01268390379846096,
-0.0015364993596449494,
0.022057849913835526,
-0.0022863850463181734,
-0.0006024639587849379,
0.013809538446366787,
0.014766449108719826,
0.0289066880941391,
-0.06292406469583511,
0.01856573298573494,
-0.006263287737965584,
0.03203323855996132,
0.017751246690750122,
-0.005579632241278887,
-0.030835624784231186,
0.004006084520369768,
0.025116074830293655,
0.005687193013727665,
-0.006123967934399843,
0.005011578090488911,
0.012217992916703224,
-0.01642422564327717,
0.02970219776034355,
-0.025341061875224113,
0.0005212990217842162,
0.0021419706754386425,
0.002081839134916663,
-0.042189888656139374,
-0.0076263719238340855,
-0.0021439327392727137,
-0.0061049009673297405,
0.025758100673556328,
-0.020442785695195198,
0.01946205645799637,
-0.03703102841973305,
-0.05855812504887581,
0.02351437509059906,
-0.0027748264838010073,
-0.023156117647886276,
-0.00021787815785501152,
0.015485569834709167,
0.0003673600731417537,
0.0331580676138401,
-0.05184386298060417,
0.01567518524825573,
-0.020445173606276512,
0.02576342411339283,
0.010235259309411049,
0.008991559967398643,
-0.02200586535036564,
0.011952027678489685,
-0.023986848071217537,
0.0030272353906184435,
0.003720414126291871,
0.024710984900593758,
0.0316547267138958,
-0.02584686689078808,
-0.01243687979876995,
0.0012832068605348468,
-0.02675269916653633,
0.004541441798210144,
-0.007513070944696665,
-0.02822568640112877,
0.0034715437795966864,
0.007435346022248268,
0.02441420964896679,
-0.023961005732417107,
-0.013724598102271557,
-0.05078848451375961,
0.006400858052074909,
-0.038592882454395294,
0.033552348613739014,
-0.005017246585339308,
0.046108588576316833,
0.019368434324860573,
-0.027681265026330948,
-0.05148373171687126,
-0.030808405950665474,
-0.02552233450114727,
0.06964895129203796,
0.006427003536373377,
-0.005250570364296436,
-0.021744612604379654,
0.005907301791012287,
-0.012050679884850979,
-0.022723834961652756,
0.02511795423924923,
-0.02288253977894783,
-0.014417719095945358,
-0.024144304916262627,
0.01575149968266487,
-0.024212712422013283,
0.034092288464307785,
-0.04775961488485336,
-0.021526416763663292,
0.008476944640278816,
-0.030946487560868263,
-0.04908780753612518,
0.041100312024354935,
-0.006806248798966408,
0.04001687094569206,
0.019204948097467422,
-0.031090890988707542,
-0.05086066573858261,
0.09168052673339844,
0.009478211402893066,
-0.027328504249453545,
0.01651412434875965,
0.011605312116444111,
-0.012657945044338703,
-0.00309049803763628,
0.016090136021375656,
-0.06658973544836044,
-0.004771368578076363,
0.03159605711698532,
0.02094695344567299,
-0.03108179196715355,
0.04926379397511482,
-0.02117033489048481,
-0.024502411484718323,
-0.012728484347462654,
-0.0016520512290298939,
0.008879335597157478,
0.000960357952862978,
0.059649497270584106,
-0.02473602257668972,
0.03444569930434227,
0.0340934656560421,
0.03389716520905495,
-0.09448188543319702,
0.019188007339835167,
-0.018825503066182137,
0.021024657413363457,
0.009491460397839546,
-0.042190711945295334,
0.03849675506353378,
0.046996090561151505,
-0.08792300522327423,
0.04583459720015526,
-0.01487439963966608,
0.009821315295994282,
-0.04343930259346962,
0.01904698647558689,
0.010783840902149677,
0.03919398784637451,
0.056489747017621994,
0.0058086770586669445,
0.005227063782513142,
0.0015988715458661318,
-0.014512634836137295,
-0.03267462179064751,
0.00044302758760750294,
0.010285296477377415,
-0.017387839034199715,
-0.006281228270381689,
0.04134165123105049,
-0.037537701427936554,
-0.03066360391676426,
0.0188826285302639,
-0.003628389211371541,
0.035743348300457,
0.022734811529517174,
0.04535779729485512,
0.02394743263721466,
0.023461004719138145,
0.023187201470136642,
0.007435289211571217,
-0.04622754082083702,
0.04210123047232628,
0.02606716752052307,
0.019139444455504417,
-0.03020423837006092,
-0.01786998100578785,
0.013479551300406456,
-0.05867893621325493,
-0.07343735545873642,
0.027597811073064804,
0.0018103946931660175,
0.002389162313193083,
0.03440392389893532,
0.0034872188698500395,
0.01810343749821186,
-0.0387820266187191,
0.00044300672016106546,
-0.057747628539800644,
-0.030719801783561707,
0.02182742953300476,
-0.048735957592725754,
0.010795543901622295,
-0.02705860510468483,
-0.018463268876075745,
-0.015928735956549644,
0.04466947913169861,
-0.024395260959863663,
0.001949392375536263,
-0.07294217497110367,
-0.005545434076339006,
0.015346730127930641,
-0.008122308179736137,
0.03578628599643707,
-0.06071958318352699,
-0.027882760390639305,
0.05205801874399185,
0.047352079302072525,
-0.012646946124732494,
0.014158666133880615,
-0.014566775411367416,
-0.046712908893823624,
-0.06572487205266953,
0.04121140390634537,
-0.047864027321338654,
0.020373322069644928,
-0.053222399204969406,
-0.04081929847598076,
-0.003920857794582844,
0.008524386212229729,
0.045721326023340225,
-0.010057003237307072,
-0.01919868215918541,
0.017098184674978256,
0.019851233810186386,
-0.01831153966486454,
-0.041526228189468384,
-0.00617569126188755,
-0.008162340149283409,
-0.07094785571098328,
-0.04810991883277893,
-0.009382244199514389,
-0.04527734965085983,
-0.006131515838205814,
0.027188727632164955,
0.0012101983884349465,
0.06293615698814392,
-0.015384171158075333,
-0.016344767063856125,
0.03402817249298096,
0.030698137357831,
-0.015714457258582115,
0.04435651749372482,
-0.004023824352771044,
0.012669920921325684,
0.05904533341526985,
-0.026755474507808685,
-0.04198170825839043,
0.016618357971310616,
-0.008479028008878231,
0.0009087063954211771,
-0.018682202324271202,
-0.01255134865641594,
0.03196360915899277,
-0.0508868433535099,
0.015776928514242172,
0.023320354521274567,
-0.02028232254087925,
0.016842413693666458,
0.057847749441862106,
0.024045059457421303,
0.04833553358912468,
-0.019215155392885208,
0.02512519247829914,
-0.03539377823472023,
-0.007664831820875406,
0.007935409434139729,
0.026784198358654976,
0.032803792506456375,
0.008571759797632694,
0.05262128263711929,
0.03242674842476845,
0.029931822791695595,
0.011933163739740849,
-0.02647998183965683,
0.05233411118388176,
-0.05256982147693634,
0.008762740530073643,
0.004370325710624456,
-0.01669551245868206,
0.005734148435294628,
0.04634503647685051,
-0.010732725262641907,
0.061509277671575546,
-0.0412752628326416,
0.0036636742297559977,
0.011169802397489548,
-0.008233542554080486,
-0.0018492391100153327,
0.005081178620457649,
-0.01904595084488392,
0.032109346240758896,
0.015499508008360863,
-0.010647114366292953,
-0.04500962793827057,
0.007216016296297312,
0.05193211883306503,
-0.024181058630347252,
0.0024674045853316784,
-0.011140200309455395,
-0.03183407336473465,
-0.01220067497342825,
-0.020303532481193542,
-0.004257253836840391,
-0.0025140107609331608,
0.020326072350144386,
0.00497400714084506,
0.015496705658733845,
0.02286088466644287,
-0.006804059259593487,
-0.002683221362531185,
0.04751276224851608,
-0.058697424829006195,
0.008013769052922726,
-0.015719329938292503,
0.0037356179673224688,
-0.017362499609589577,
-0.055913109332323074
] |
<p>In class when we talked about the harmonic oscillator in QM we noticed that the eigenfunctions to the annihilation operator are coherent states in the sense that they have minimum uncertainty in momentum and position. My question is: What is the physical meaning behind this? Why are coherent states eigenfunctions to the annihilation operator and: Was this only a lucky punch and a special property of the harmonic oscillator or is this true for more physical problems?</p>
| 339 |
[
-0.010945294052362442,
-0.016424555331468582,
0.012152024544775486,
-0.06639634072780609,
0.04239504784345627,
0.013127205893397331,
-0.018681688234210014,
-0.04822534695267677,
0.021610181778669357,
-0.003118813270702958,
-0.0032807262614369392,
0.035345640033483505,
0.04692259430885315,
-0.019502980634570122,
0.03477593883872032,
0.006992438808083534,
0.017868930473923683,
-0.019930431619286537,
-0.043754756450653076,
-0.03463719040155411,
0.0016682625282555819,
0.004393694922327995,
0.011058162897825241,
0.0013107301201671362,
-0.0015269801951944828,
0.025719983503222466,
0.018473517149686813,
0.038158126175403595,
0.02395281009376049,
0.05167650058865547,
0.011141364462673664,
-0.036112792789936066,
-0.017520975321531296,
0.021243030205368996,
-0.01645459234714508,
-0.026687119156122208,
0.002841185312718153,
-0.030394621193408966,
-0.013468124903738499,
0.03270918130874634,
-0.06514346599578857,
-0.03892981633543968,
-0.003025555517524481,
0.027772216126322746,
-0.01860368438065052,
0.027717474848031998,
-0.009714149869978428,
-0.010580046102404594,
0.032221145927906036,
-0.043837301433086395,
0.0632031038403511,
0.02479679137468338,
0.01802419126033783,
-0.008198024705052376,
0.007577627897262573,
0.030570000410079956,
0.06258930265903473,
0.09101905673742294,
-0.03177279978990555,
-0.061646901071071625,
-0.03275836631655693,
-0.06933052837848663,
-0.00861432310193777,
-0.02470279112458229,
-0.02330015040934086,
0.0013665305450558662,
0.01707742176949978,
-0.02004004269838333,
0.02614418976008892,
0.024136913940310478,
-0.04153210669755936,
-0.008546673692762852,
0.0433434322476387,
-0.014548642560839653,
0.012882350943982601,
-0.03403828293085098,
0.02460332028567791,
0.001479790429584682,
0.02587769366800785,
0.013233713805675507,
-0.011548792012035847,
-0.014733053743839264,
-0.0033815933857113123,
-0.0003974653664045036,
-0.03648488223552704,
0.012945991940796375,
0.07752601057291031,
-0.008899892680346966,
-0.007420070003718138,
0.0388953872025013,
-0.014672473073005676,
0.02947208099067211,
0.034329451620578766,
0.01183763425797224,
-0.008993254974484444,
0.03163709118962288,
0.03126265108585358,
0.03834447264671326,
0.003075339598581195,
-0.049564704298973083,
0.021599505096673965,
-0.02812669612467289,
0.0271608904004097,
0.06897497177124023,
-0.013000189326703548,
-0.01860128715634346,
-0.03356614336371422,
0.032932210713624954,
-0.028999563306570053,
-0.011101395823061466,
-0.012971442192792892,
0.026338214054703712,
-0.00681711919605732,
-0.0034489461686462164,
0.03832279145717621,
0.008972875773906708,
0.015222132205963135,
-0.002792340936139226,
0.08940335363149643,
0.08057066798210144,
0.00662819342687726,
-0.0035235141403973103,
0.03420140966773033,
-0.03903527557849884,
-0.04224750027060509,
0.0151978163048625,
0.03194194659590721,
0.017322132363915443,
-0.026459233835339546,
0.017332619056105614,
0.02911229245364666,
0.004089223686605692,
0.024728015065193176,
0.01450647134333849,
0.015443671494722366,
-0.07186319679021835,
-0.10699134320020676,
-0.045767027884721756,
0.05704886466264725,
-0.024367868900299072,
-0.05169547721743584,
-0.06527253240346909,
0.01683853752911091,
0.03252502530813217,
0.08510330319404602,
-0.031965114176273346,
-0.004591936711221933,
-0.007334195543080568,
0.023359518498182297,
0.02009083330631256,
-0.0005802622763440013,
-0.040144115686416626,
0.004562621470540762,
-0.04619141295552254,
0.007182245142757893,
-0.028418419882655144,
0.024487288668751717,
0.02430715039372444,
0.030228886753320694,
-0.028687182813882828,
0.058330707252025604,
-0.03578471019864082,
-0.000322312320349738,
0.025653352960944176,
0.016515936702489853,
-0.020762355998158455,
0.09321729093790054,
0.026151143014431,
-0.020464753732085228,
0.051325809210538864,
0.0359497144818306,
0.011217201128602028,
0.0272207148373127,
0.03188344091176987,
0.011266539804637432,
-0.05970083177089691,
-0.0004361300962045789,
-0.022491052746772766,
0.005250199697911739,
-0.021201591938734055,
-0.013109925203025341,
-0.03506042808294296,
0.001579863834194839,
0.025164669379591942,
0.006145374849438667,
0.045074064284563065,
-0.017737338319420815,
-0.009715107269585133,
0.008555109612643719,
-0.04916940629482269,
-0.00033407818409614265,
-0.04532832279801369,
0.03785192221403122,
0.030451146885752678,
-0.008636308833956718,
0.04432773217558861,
0.024945411831140518,
0.015003621578216553,
-0.029403775930404663,
-0.014192018657922745,
-0.024508608505129814,
0.011231813579797745,
-0.024492720142006874,
-0.03076578490436077,
0.04263671115040779,
0.05964326858520508,
0.015848442912101746,
-0.012109201401472092,
0.058281779289245605,
-0.029149256646633148,
-0.04318755120038986,
-0.015255020000040531,
-0.030517304316163063,
0.017111510038375854,
0.015599682927131653,
0.012028589844703674,
-0.007971183396875858,
-0.035754263401031494,
-0.012473147362470627,
0.013966094702482224,
-0.016520529985427856,
0.05266036093235016,
0.022292736917734146,
0.009924573823809624,
-0.005166287533938885,
0.03305607661604881,
0.01737472601234913,
0.007212791126221418,
0.002216024324297905,
-0.04842761531472206,
-0.038585785776376724,
0.019786948338150978,
-0.002168348291888833,
0.04608500748872757,
-0.037345387041568756,
-0.0000063458519434789196,
0.01078683603554964,
0.06481296569108963,
0.04567249119281769,
0.032465800642967224,
-0.035651013255119324,
-0.012613659724593163,
-0.00784835871309042,
-0.0074312384240329266,
0.006023031193763018,
0.011672517284750938,
0.017555661499500275,
0.046591829508543015,
0.02626349776983261,
0.012883634306490421,
-0.02434545010328293,
0.04364972934126854,
-0.04023413732647896,
-0.00438691396266222,
-0.0013389524538069963,
-0.0347764827311039,
-0.02114562876522541,
-0.035599544644355774,
0.017968982458114624,
0.014609208330512047,
-0.05036548525094986,
0.011790422722697258,
-0.029064364731311798,
-0.038487378507852554,
0.028593912720680237,
-0.009443940594792366,
-0.03415140137076378,
-0.025261135771870613,
0.02062644250690937,
-0.02913038060069084,
-0.024902742356061935,
-0.003858755575492978,
-0.012977609410881996,
-0.01856369525194168,
0.009946207515895367,
0.08224312961101532,
0.004630061332136393,
0.02361639402806759,
-0.017853081226348877,
-0.04539112001657486,
-0.030915942043066025,
-0.02048414759337902,
0.008238337002694607,
0.013005333952605724,
-0.0715278834104538,
0.005751746241003275,
-0.06593117862939835,
-0.026809845119714737,
0.02531467191874981,
0.0009561310289427638,
0.011941974051296711,
0.003192545846104622,
-0.02943025715649128,
-0.056308720260858536,
-0.00489653367549181,
0.00003554020804585889,
0.036884158849716187,
0.005492480471730232,
0.0013393639819696546,
0.03446309641003609,
-0.05525166541337967,
-0.02968909591436386,
-0.009208053350448608,
-0.02014705166220665,
-0.07268685847520828,
-0.03869304060935974,
-0.03976496681571007,
0.029289662837982178,
-0.008042959496378899,
0.028801675885915756,
0.04052264243364334,
-0.03408418223261833,
-0.019899882376194,
-0.036741599440574646,
-0.0432315357029438,
0.008824871852993965,
-0.014543582685291767,
0.0386483296751976,
-0.008163481950759888,
-0.015169292688369751,
0.08579591661691666,
0.02210553176701069,
-0.04203391075134277,
-0.011397454887628555,
0.01938159205019474,
-0.029795708134770393,
0.013323940336704254,
-0.0014818174531683326,
0.033315110951662064,
-0.0007570092566311359,
0.06594052165746689,
-0.005277565680444241,
-0.002497892128303647,
0.030759325250983238,
0.012064062058925629,
-0.006493690889328718,
0.0011961276177316904,
0.004806821700185537,
-0.006498790346086025,
0.01753017120063305,
-0.008120981976389885,
-0.054751742631196976,
0.026077819988131523,
-0.015569932758808136,
0.0037151745054870844,
-0.0016035427106544375,
-0.07046137750148773,
0.05642561987042427,
-0.008493869565427303,
0.023937026038765907,
-0.02523004077374935,
0.045050639659166336,
-0.01715691015124321,
0.015171946957707405,
0.006015644874423742,
0.015879811719059944,
0.03202437981963158,
-0.0200777817517519,
0.017279336228966713,
0.0245820339769125,
-0.020661290735006332,
-0.031611111015081406,
0.006422569043934345,
-0.0018948204815387726,
-0.011372800916433334,
0.040733128786087036,
-0.004180427640676498,
-0.0830061137676239,
0.044151630252599716,
0.008653240278363228,
0.016773175448179245,
-0.03038777969777584,
-0.05611949414014816,
-0.02843920700252056,
-0.055431801825761795,
0.004270649515092373,
0.02448415942490101,
0.01895729824900627,
0.017306387424468994,
0.060203757137060165,
0.03210556507110596,
0.01608428917825222,
-0.015055995434522629,
-0.0013902607606723905,
-0.07032439112663269,
0.010861371643841267,
-0.035981435328722,
0.01025552861392498,
-0.02717106230556965,
-0.025859510526061058,
0.039156943559646606,
-0.017482146620750427,
-0.050763897597789764,
-0.005842521321028471,
0.016865547746419907,
-0.07977017760276794,
-0.011345495469868183,
-0.02247985452413559,
-0.013238325715065002,
-0.04287656024098396,
0.002852352801710367,
0.019794845953583717,
0.005738393869251013,
0.03354356065392494,
0.0350252166390419,
-0.04410596564412117,
0.035028863698244095,
0.005846524145454168,
0.0045678941532969475,
0.02887239120900631,
0.0010488413972780108,
0.04353877529501915,
0.013195645064115524,
-0.01607116311788559,
0.014369294978678226,
-0.008891581557691097,
0.08679603785276413,
0.011282984167337418,
-0.023775409907102585,
0.03451629355549812,
-0.016684802249073982,
-0.003697281004860997,
0.024744093418121338,
0.036016061902046204,
-0.03244956582784653,
0.013065287843346596,
0.007498727645725012,
0.04736679047346115,
-0.015315051190555096,
0.028279706835746765,
0.06285717338323593,
0.01763804443180561,
0.009107694961130619,
-0.04584112763404846,
0.014887622557580471,
-0.02632160112261772,
-0.003960197791457176,
-0.00592486746609211,
-0.03641562908887863,
-0.0019416717113927007,
0.003422552952542901,
0.04336390644311905,
0.034306563436985016,
-0.031198447570204735,
-0.03224091976881027,
-0.020098431035876274,
0.0021386225707829,
0.004357617814093828,
0.012503789737820625,
-0.01234960276633501,
0.005208865273743868,
0.032920632511377335,
0.022860923781991005,
0.032408442348241806,
-0.044747017323970795,
-0.01886737532913685,
0.02054280787706375,
0.015076160430908203,
-0.021209126338362694,
-0.007827166467905045,
-0.028965333476662636,
-0.04848434031009674,
0.07114207744598389,
-0.016079965978860855,
0.0028140400536358356,
-0.009062289260327816,
-0.0575532540678978,
-0.020871035754680634,
-0.03976017236709595,
0.017287561669945717,
0.022540923207998276,
-0.006949255708605051,
0.00005980761125101708,
-0.03385937586426735,
-0.022774003446102142,
-0.03673582896590233,
-0.0015529176453128457,
-0.006234823726117611,
0.04690692201256752,
0.014900215901434422,
-0.017751922830939293,
0.024179957807064056,
0.040915802121162415,
-0.013868809677660465,
-0.08284512907266617,
-0.02099115401506424,
0.02022448182106018,
-0.0039007668383419514,
0.04378407448530197,
-0.031621672213077545,
-0.04636092483997345,
-0.01736120693385601,
0.009078985080122948,
-0.006699687801301479,
0.02698468416929245,
-0.00402649212628603,
0.033635884523391724,
0.03260411322116852,
-0.02167068049311638,
0.04536982998251915,
0.0474020279943943,
-0.021511167287826538,
-0.015837790444493294,
-0.03791485354304314,
0.04488656297326088,
-0.0530158206820488,
0.030080335214734077,
-0.041418008506298065,
0.019689317792654037,
-0.0225082878023386,
0.05205048248171806,
-0.016326243057847023,
0.008145005442202091,
0.003783812513574958,
-0.030550288036465645,
-0.011844780296087265,
0.028159650042653084,
0.018230712041258812,
-0.029039863497018814,
0.01889386959373951,
-0.012724321335554123,
0.015591178089380264,
-0.028012657538056374,
0.0017544426955282688,
0.015948990359902382,
0.020241443067789078,
0.023945709690451622,
0.007720135618001223,
0.026922285556793213,
-0.07421422004699707,
-0.013779550790786743,
0.05586524307727814,
-0.039856359362602234,
-0.002159583382308483,
-0.0014862617244943976,
-0.023939067497849464,
0.018505290150642395,
-0.05906616151332855,
-0.06709548085927963,
0.0027053821831941605,
-0.025454988703131676,
0.057533252984285355,
-0.015911197289824486,
0.030589062720537186,
0.0269018542021513,
-0.004929485730826855,
-0.062350206077098846,
-0.02571563981473446,
0.019428597763180733,
0.029114536941051483,
-0.012753548100590706,
-0.013863089494407177,
0.024838212877511978,
-0.007443671114742756,
0.012450739741325378,
0.004860129673033953,
0.003788469359278679,
-0.002131868852302432,
-0.02243594452738762,
0.042801350355148315,
0.0006244435789994895,
0.030232327058911324,
0.010573471896350384,
-0.017923403531312943,
0.009971360675990582,
0.00660548685118556,
-0.0033110426738858223,
0.022394653409719467,
0.05135994032025337,
-0.0220474973320961,
-0.06250394135713577,
-0.021740633994340897,
0.01526443287730217,
0.016334472224116325,
-0.019777020439505577,
-0.016360055655241013,
0.029150504618883133,
0.024161770939826965,
0.03318113088607788,
0.015234203077852726,
-0.008640781044960022,
-0.050685834139585495,
0.002652394352480769,
0.03947806358337402,
-0.0013565465342253447,
0.01202258002012968,
-0.058453384786844254,
0.00829373486340046,
0.003997257445007563,
0.0020441976375877857,
0.026103414595127106,
0.026903579011559486,
-0.01078512892127037,
0.026672374457120895,
0.014103171415627003,
-0.0037158019840717316,
0.017169160768389702,
-0.01404450461268425,
0.023095887154340744,
0.0137404790148139,
0.038504838943481445,
0.00013917651085648686,
-0.028060324490070343,
-0.06227967515587807,
0.010224198922514915,
0.025383595377206802,
-0.0425175242125988,
0.050116926431655884,
0.03514392301440239,
0.022016558796167374,
-0.0299982950091362,
-0.008445674553513527,
-0.02868083119392395,
0.01368750911206007,
0.004706706386059523,
0.025656050071120262,
-0.03082718327641487,
0.011082732118666172,
0.03554610535502434,
0.0361328162252903,
-0.021521402522921562,
0.010813750326633453,
0.021650154143571854,
0.038189712911844254,
0.016725270077586174,
0.026483822613954544,
-0.04016190767288208,
0.033617354929447174,
-0.02653670683503151,
0.007628799416124821,
0.0030488711781799793,
-0.05099146068096161,
-0.00696978997439146,
-0.010440622456371784,
-0.010772100649774075,
-0.016071300953626633,
-0.008949174545705318,
-0.04478898271918297,
0.02943463623523712,
-0.002552986843511462,
-0.014086809940636158,
0.018306588754057884,
0.03719569370150566,
0.03187171369791031,
0.015514875762164593,
0.02494620718061924,
0.006692403927445412,
-0.05612774193286896,
-0.037339769303798676,
-0.023667391389608383,
-0.032600514590740204,
-0.007239115424454212,
-0.014904736541211605,
-0.02453502267599106,
0.011867500841617584,
-0.03516750782728195,
0.017810214310884476,
0.016183212399482727,
-0.0073798419907689095,
-0.029453618451952934,
0.05721824988722801,
0.017489921301603317,
-0.011579567566514015,
0.011479039676487446,
0.025424273684620857,
0.12056883424520493,
0.048861511051654816,
0.03037596121430397,
-0.0700480118393898,
-0.012648036703467369,
0.04922126978635788,
0.023198407143354416,
-0.0315624438226223,
0.030631843954324722,
0.03081391379237175,
0.037608809769153595,
-0.02382098138332367,
0.03562939167022705,
0.03349224478006363,
0.011739959008991718,
0.018717389553785324,
-0.03764667361974716,
-0.06737630814313889,
-0.000176471789018251,
-0.016089919954538345,
0.015403478406369686,
-0.004966714885085821,
-0.041723448783159256,
0.013377420604228973,
-0.004969860892742872,
-0.0009020045981742442,
-0.010747438296675682,
-0.028106026351451874,
-0.011085033416748047,
0.004792319145053625,
-0.01588585041463375,
0.014323163777589798,
0.010233147069811821,
0.01587943732738495,
-0.009808781556785107,
0.053570639342069626,
0.023959223181009293,
0.004720370285212994,
0.002545112743973732,
0.005938871763646603,
0.021343115717172623,
-0.020936984568834305,
0.014223149046301842,
0.008339932188391685,
-0.02673809416592121,
-0.012775735929608345,
-0.011958373710513115,
0.041878752410411835,
-0.020017452538013458,
0.009097585454583168,
-0.0012664453824982047,
-0.010086691938340664,
-0.01143074780702591,
-0.042046189308166504,
-0.01351182535290718,
-0.006212535314261913,
0.04172268509864807,
-0.026996741071343422,
-0.011862939223647118,
-0.0360039621591568,
-0.022412624210119247,
-0.02054380252957344,
0.024649707600474358,
-0.01741514354944229,
-0.009075351059436798,
-0.0043283021077513695,
0.017870688810944557,
0.026860008016228676,
-0.020462099462747574,
-0.02632148563861847,
-0.0049390168860554695,
-0.002792549319565296,
-0.04563872143626213,
-0.056865252554416656,
0.05835345387458801,
-0.011684408411383629,
0.054627712815999985,
0.026578202843666077,
-0.008538429625332355,
0.011267445050179958,
-0.10877778381109238,
0.029629673808813095,
0.002352870302274823,
-0.036769717931747437,
-0.010171458125114441,
0.01748834364116192,
0.0031770276837050915,
0.02365766279399395,
-0.01517034787684679,
0.007844201289117336,
-0.03962291032075882,
-0.00006656000186922029,
-0.0028530119452625513,
-0.010150684975087643,
-0.008326680399477482,
0.02156798355281353,
-0.02863401547074318,
-0.016515206545591354,
-0.020867617800831795,
0.01779463328421116,
0.022448871284723282,
0.007554414216428995,
0.003364116884768009,
0.02297995239496231,
-0.010174966417253017,
-0.03737452253699303,
0.019113639369606972,
-0.04899489879608154,
0.00035041969385929406,
0.02997550182044506,
0.03741954639554024,
-0.05489830672740936,
-0.031903449445962906,
-0.029155034571886063,
-0.003967402968555689,
0.021205153316259384,
0.04031355306506157,
-0.020115436986088753,
-0.011491172015666962,
0.02394387312233448,
0.05450780317187309,
-0.022678479552268982,
-0.007837925106287003,
-0.05383438244462013,
0.03274257853627205,
0.00854199193418026,
-0.03675635904073715,
-0.005660501308739185,
-0.007578724063932896,
0.03265410661697388,
-0.042540520429611206,
0.0046813092194497585,
0.06300622224807739,
0.00168284319806844,
-0.0019666594453155994,
0.052003152668476105,
-0.024814192205667496,
0.06433766335248947,
-0.013210499659180641,
-0.014094555750489235,
0.047072604298591614,
-0.0412893146276474,
-0.04827744886279106,
0.021729061380028725,
-0.011504537425935268,
0.03418624401092529,
0.035492103546857834,
-0.021064547821879387,
-0.012888412922620773,
0.043654102832078934,
-0.036481697112321854,
0.002935933880507946,
0.004625669680535793,
-0.02170548401772976,
-0.02513772062957287,
0.002394425217062235,
-0.03208952769637108,
-0.0014090373879298568,
-0.004154833033680916,
0.03642989322543144,
0.036296527832746506,
0.013071847148239613,
0.029659835621714592,
-0.0011174151441082358,
-0.00044623215217143297,
0.05424129590392113,
0.02450292557477951,
0.011014912277460098,
0.012425700202584267,
0.05198388919234276,
-0.014094141311943531,
0.05126454681158066,
0.0464148074388504,
0.050798650830984116,
-0.06927304714918137,
-0.0030047025065869093,
0.020132645964622498,
-0.016883250325918198,
0.027709797024726868,
-0.022548019886016846,
0.023450395092368126,
0.06466982513666153,
-0.04017288610339165,
0.023496627807617188,
-0.021257732063531876,
-0.041907645761966705,
-0.03780892863869667,
0.02177615277469158,
-0.025637857615947723,
0.052633631974458694,
0.02933594211935997,
0.020911069586873055,
0.04372972995042801,
-0.004717412404716015,
-0.004417382180690765,
0.001927363919094205,
-0.031541548669338226,
0.03176730498671532,
-0.03743252530694008,
0.018762584775686264,
0.05520958453416824,
-0.008226719684898853,
-0.00014447922876570374,
0.04888075962662697,
-0.03954682871699333,
-0.05311831831932068,
-0.03127902373671532,
0.021139325574040413,
-0.0066468664444983006,
0.009391112253069878,
0.018309714272618294,
-0.00563805503770709,
0.0022967029362916946,
0.03797515854239464,
0.02179734967648983,
0.027735687792301178,
0.022776460275053978,
-0.005308975465595722,
0.023733166977763176,
-0.04576139152050018,
-0.050271980464458466,
0.024944836273789406,
0.03427690267562866,
-0.006353085394948721,
0.035579849034547806,
0.006000124383717775,
-0.015214646235108376,
-0.039790377020835876,
0.02866997756063938,
-0.03259764611721039,
-0.03954201936721802,
0.0004413012065924704,
0.0370413139462471,
0.0012561463518068194,
0.005135736428201199,
-0.02248464711010456,
-0.06500609219074249,
0.03335912898182869,
0.0003095182473771274,
-0.02272135019302368,
-0.04244016855955124,
-0.017378943040966988,
0.02645348571240902,
0.0073103634640574455,
-0.012124835513532162,
-0.05234583839774132,
-0.03752180561423302,
0.019614202901721,
-0.02751954458653927,
0.036666542291641235,
-0.015268130227923393,
-0.05508918687701225,
-0.0738883838057518,
-0.07262428104877472,
0.043395671993494034,
0.004481384996324778,
0.021214138716459274,
-0.03277278319001198,
0.012820904143154621,
0.01641634851694107,
0.016423065215349197,
0.009921622462570667,
0.0024308310821652412,
-0.021775027737021446,
0.03269787132740021,
-0.008021711371839046,
0.04010625183582306,
0.018955767154693604,
-0.009573346935212612,
-0.04391245171427727,
-0.010782814584672451,
-0.008623545058071613,
0.027721360325813293,
-0.0012834417866542935,
0.026384079828858376,
0.014852303080260754,
-0.01135830394923687,
0.020313706248998642,
-0.016174038872122765,
-0.02197093702852726,
0.0938371792435646,
-0.007474228274077177,
-0.013025660999119282,
0.08301141113042831,
-0.004817190580070019,
-0.008652144111692905,
0.012082798406481743,
-0.007540153805166483,
-0.038771580904722214,
0.02410029247403145,
-0.004618073347955942,
-0.0227716863155365,
0.0403200127184391,
0.017449771985411644,
0.021767958998680115,
-0.04309532791376114,
-0.020761871710419655,
0.029082417488098145,
-0.057992659509181976,
-0.020214242860674858,
0.0398075170814991,
0.019083211198449135,
0.04891066998243332,
0.025233225896954536,
-0.0033241913188248873,
0.03512002155184746,
0.022427812218666077,
-0.004727540537714958,
0.049692150205373764,
0.04798232391476631,
0.014686095528304577,
-0.0035734509583562613,
-0.0018254712922498584,
-0.027381552383303642,
0.02294941619038582,
0.0059131234884262085,
0.036885954439640045,
-0.06171908602118492,
-0.01796291582286358,
0.042118992656469345,
-0.040845997631549835,
-0.014427262358367443,
0.0007733984966762364,
-0.028977224603295326,
0.09941448271274567,
-0.04662066698074341,
0.00442381389439106,
-0.027472296729683876,
0.03742590919137001,
-0.015161464922130108,
-0.004876047372817993,
0.011714362539350986,
0.04287312924861908,
-0.019381117075681686,
0.018499387428164482,
-0.012981821782886982,
-0.007191456388682127,
0.04884127527475357,
-0.06867970526218414,
0.001500957878306508,
0.013889255002140999,
-0.03334604576230049,
-0.000013315070646058302,
0.0004697510157711804,
-0.01921338401734829,
-0.018737824633717537,
0.010210864245891571,
0.048211053013801575,
0.0312071293592453,
0.002044638153165579,
-0.039362967014312744,
-0.037619948387145996,
0.03331845998764038,
-0.041095707565546036,
-0.004833240527659655,
-0.038614917546510696,
0.003111243015155196,
-0.016933243721723557,
0.02459007501602173
] |
<p>For example, take a water bottle. Fill it with water and then turn it upside down.
Instead of flowing steadily downward, it gulps down in parts. Why?</p>
| 10,687 |
[
-0.04072714224457741,
-0.022735878825187683,
0.009173471480607986,
-0.006579880136996508,
0.00003930679667973891,
0.0005415233317762613,
0.0026894353795796633,
0.014668328687548637,
0.015446809120476246,
0.015192308463156223,
0.029488787055015564,
0.05189448222517967,
0.02704283967614174,
-0.019079910591244698,
-0.012066293507814407,
0.03290689364075661,
0.006868792697787285,
-0.031402405351400375,
0.003187465015798807,
0.017609572038054466,
-0.010913480073213577,
0.020503243431448936,
0.010467533022165298,
0.014247062616050243,
-0.006206535268574953,
-0.010581472888588905,
0.03830329328775406,
-0.013255327008664608,
0.04475124925374985,
0.03291188180446625,
-0.0006191470893099904,
0.011605965904891491,
-0.010277352295815945,
0.0276375450193882,
0.022120727226138115,
-0.022424211725592613,
-0.0154070183634758,
-0.022839827463030815,
-0.024068783968687057,
0.03228378668427467,
-0.025341453030705452,
0.01316543947905302,
-0.02994556538760662,
0.07606898248195648,
-0.019746392965316772,
0.02976013906300068,
-0.018725821748375893,
0.002265718299895525,
0.03895452991127968,
-0.06749047338962555,
0.0607067234814167,
0.005067098420113325,
0.0423416830599308,
0.0361105240881443,
0.025148069486021996,
0.02006596326828003,
0.08578439056873322,
0.06707318127155304,
-0.035312116146087646,
-0.0704910084605217,
-0.010879866778850555,
-0.010852501727640629,
-0.02954600378870964,
0.012555254623293877,
-0.015903575345873833,
0.022807259112596512,
-0.016802718862891197,
-0.009940489195287228,
0.039488837122917175,
-0.014446180313825607,
0.025163695216178894,
0.00479554058983922,
0.04597994312644005,
-0.020555682480335236,
0.008685177192091942,
-0.033115144819021225,
0.03694234415888786,
-0.0039393240585923195,
0.04503002390265465,
0.058222874999046326,
-0.010459449142217636,
-0.022953681647777557,
0.012837507762014866,
0.02201494388282299,
0.015055224299430847,
-0.049472611397504807,
0.06847824901342392,
-0.022653453052043915,
0.008334911428391933,
0.04913583770394325,
-0.010755800642073154,
-0.021209467202425003,
0.005780358333140612,
0.021275699138641357,
-0.005678229965269566,
0.014499333687126637,
-0.0037356195971369743,
0.056702252477407455,
0.04131618142127991,
-0.0319458432495594,
0.008598791435360909,
-0.009532718919217587,
0.009968363679945469,
0.09134064614772797,
-0.002782829338684678,
-0.017849061638116837,
-0.0210396908223629,
0.01075043436139822,
0.012470372952520847,
0.02548537403345108,
-0.003108374075964093,
-0.014755485579371452,
-0.010218178853392601,
-0.006505239754915237,
0.03983325883746147,
-0.015068874694406986,
-0.02563546411693096,
-0.022437825798988342,
0.015561684034764767,
0.06354579329490662,
0.02855944260954857,
-0.02215142361819744,
0.05394262820482254,
-0.027216751128435135,
-0.04720602557063103,
0.03296029567718506,
0.009604441933333874,
-0.027250828221440315,
-0.042452290654182434,
0.017483627423644066,
0.012766284868121147,
-0.00913043599575758,
0.04099937155842781,
-0.021437490358948708,
0.0560590885579586,
0.04029759392142296,
-0.10175902396440506,
-0.05203964188694954,
0.056010641157627106,
-0.015599624253809452,
-0.035482652485370636,
-0.05549583584070206,
0.01513220090419054,
0.023451318964362144,
0.0717010572552681,
-0.006768671330064535,
0.02489486150443554,
0.020563609898090363,
0.009263467974960804,
-0.0017179989954456687,
0.033300429582595825,
0.03832729160785675,
-0.0035200028214603662,
-0.030537160113453865,
0.010263587348163128,
-0.047906294465065,
0.03261168301105499,
0.03425336256623268,
0.0020789022091776133,
-0.04392506927251816,
0.015470823273062706,
-0.02263648435473442,
-0.004398697521537542,
-0.013528438284993172,
-0.025641048327088356,
-0.0135743273422122,
0.04474598541855812,
0.0298902727663517,
-0.014871611259877682,
0.05325707048177719,
-0.014116188511252403,
0.024499377235770226,
-0.005457890219986439,
0.0024554706178605556,
0.019693419337272644,
-0.01422661542892456,
-0.022076809778809547,
-0.004687567241489887,
0.017432818189263344,
0.020693499594926834,
0.0056752790696918964,
-0.008066321723163128,
0.0015557992737740278,
0.03781943395733833,
0.002160910051316023,
0.010474720038473606,
0.0070869652554392815,
-0.025765860453248024,
-0.0032508212607353926,
-0.07853276282548904,
-0.015846244990825653,
-0.04896446317434311,
0.017096122726798058,
-0.04811136797070503,
0.005168349947780371,
0.02121668867766857,
0.008071767166256905,
0.017782600596547127,
-0.0392417311668396,
0.004610192030668259,
-0.00294788577593863,
0.0021207446698099375,
-0.002925107255578041,
-0.0022202543914318085,
-0.00045971147483214736,
0.06517799198627472,
0.042197730392217636,
-0.007136418484151363,
0.01617794670164585,
-0.01020820438861847,
0.01270808931440115,
0.015392078086733818,
-0.006585321389138699,
-0.011213346384465694,
-0.04830766096711159,
-0.027712907642126083,
0.02462206780910492,
0.030105773359537125,
0.03695661202073097,
0.04381213337182999,
-0.026331599801778793,
0.07529612630605698,
0.05933431535959244,
-0.008127033710479736,
0.02624032087624073,
0.008910343050956726,
0.017460256814956665,
0.001656663604080677,
0.04189544916152954,
-0.04751625657081604,
-0.01955648511648178,
-0.027785638347268105,
-0.015770476311445236,
0.00934934988617897,
-0.01198884192854166,
0.011291037313640118,
0.007688543759286404,
0.025471430271863937,
-0.004023842513561249,
0.030800627544522285,
0.004586029332131147,
-0.014698033221065998,
-0.021045204252004623,
-0.015441077761352062,
0.038454655557870865,
0.046461738646030426,
0.020240304991602898,
0.0055319336242973804,
0.04446994513273239,
0.006174818612635136,
-0.025568634271621704,
0.01783807948231697,
0.005871457513421774,
0.008794390596449375,
-0.000613431038800627,
-0.0364469550549984,
0.026340143755078316,
-0.04549483582377434,
-0.04131964594125748,
0.031611718237400055,
-0.013789011165499687,
0.030258988961577415,
-0.054142553359270096,
-0.028634363785386086,
0.01233289111405611,
0.03347203508019447,
-0.0054086120799183846,
-0.02097404934465885,
0.044979918748140335,
-0.006548325996845961,
0.009604603983461857,
-0.03719616308808327,
0.025774778798222542,
-0.0509185753762722,
0.027541060000658035,
0.031952109187841415,
-0.007655145600438118,
0.012532445602118969,
-0.028611572459340096,
-0.008067278191447258,
-0.0040143015794456005,
-0.02364368923008442,
-0.007723623421043158,
-0.00360588519833982,
-0.03413517773151398,
0.0465967170894146,
0.009165766648948193,
-0.017722321674227715,
0.0386497788131237,
0.05723156780004501,
0.0032716223504394293,
-0.007643268443644047,
-0.003942466340959072,
-0.024533158168196678,
-0.020506521686911583,
-0.055590469390153885,
0.0330076590180397,
0.002307901158928871,
0.03506486862897873,
0.0550222247838974,
-0.010269089601933956,
-0.012506145052611828,
0.031093813478946686,
-0.03444332629442215,
-0.037674929946660995,
-0.02487260475754738,
-0.024741875007748604,
0.01818452961742878,
-0.042462341487407684,
-0.033643487840890884,
0.014991851523518562,
-0.05089540407061577,
0.005228972062468529,
-0.05110999196767807,
-0.07482843846082687,
-0.026045965030789375,
0.019443275406956673,
0.02925870195031166,
0.01680278405547142,
-0.00504072941839695,
0.04983682185411453,
-0.032494839280843735,
-0.07508798688650131,
-0.001023585326038301,
-0.04429163038730621,
-0.029091034084558487,
-0.06841351091861725,
0.03298480436205864,
0.04272214695811272,
-0.029089374467730522,
0.04573698341846466,
0.0512118823826313,
0.051921162754297256,
0.017124345526099205,
0.013196717016398907,
-0.04809068143367767,
0.009389938786625862,
0.03843240067362785,
-0.024579854682087898,
-0.006046288181096315,
-0.006457730196416378,
-0.04619612172245979,
0.04072433337569237,
-0.0027875860687345266,
0.019680047407746315,
0.026303855702280998,
-0.009641585871577263,
0.05012493580579758,
-0.011131123639643192,
-0.02494785748422146,
-0.01544272806495428,
0.05475892871618271,
-0.034921787679195404,
0.003600318683311343,
-0.010011199861764908,
0.03491972014307976,
0.07232744991779327,
-0.011170567013323307,
-0.0003830247151199728,
0.037603337317705154,
0.03477277234196663,
-0.05507476627826691,
-0.037902917712926865,
-0.025373058393597603,
0.01332402415573597,
0.044278014451265335,
-0.025066673755645752,
-0.015567963942885399,
0.0698433518409729,
0.031179195269942284,
0.042070213705301285,
0.0011882619000971317,
-0.038251083344221115,
0.009127942845225334,
-0.0612037219107151,
-0.003643001662567258,
-0.00873526744544506,
0.0000707078434061259,
-0.006530711892992258,
0.06630183011293411,
0.03919946774840355,
0.055078744888305664,
-0.011275077238678932,
0.012779912911355495,
-0.07254572212696075,
0.034652601927518845,
-0.017455456778407097,
0.017810557037591934,
-0.032986730337142944,
0.023659009486436844,
0.024105872958898544,
-0.05880538374185562,
-0.038868021219968796,
-0.01253485307097435,
0.0002423729602014646,
-0.05177757143974304,
0.0062714568339288235,
-0.011166494339704514,
0.0020599314011633396,
-0.02279331535100937,
0.017242485657334328,
0.05230854079127312,
-0.03024962730705738,
0.044408369809389114,
0.013494838960468769,
0.002388366963714361,
0.00629414664581418,
-0.017904840409755707,
0.008326863870024681,
0.03334346041083336,
0.025065017864108086,
0.023542847484350204,
0.01797211542725563,
-0.00971999578177929,
0.02068108320236206,
0.003577780444175005,
0.05350295826792717,
-0.020890867337584496,
0.007769076153635979,
-0.05158437043428421,
-0.03696956858038902,
-0.03023076057434082,
0.014122872613370419,
0.03499990329146385,
0.008918222971260548,
0.042578015476465225,
0.02561962977051735,
0.0035078374203294516,
-0.004487886559218168,
0.04095698148012161,
0.025254780426621437,
0.008317370899021626,
-0.02295135147869587,
-0.06788385659456253,
-0.008884100243449211,
-0.031358737498521805,
-0.015103123150765896,
0.01932932622730732,
0.015412924811244011,
-0.02771163545548916,
0.028102440759539604,
0.029321474954485893,
-0.02811877429485321,
-0.005130109842866659,
-0.005458453670144081,
-0.02197187952697277,
0.009612576104700565,
-0.02542818710207939,
0.0296618789434433,
0.028702983632683754,
0.0379667766392231,
0.04180904105305672,
0.005495269317179918,
-0.055283963680267334,
-0.09243232756853104,
0.0007020459743216634,
0.023457864299416542,
0.014104018919169903,
-0.05737437307834625,
0.03426569327712059,
-0.06056933104991913,
-0.012729959562420845,
0.05850837752223015,
-0.06064560264348984,
0.017722051590681076,
-0.03070078417658806,
-0.013758285902440548,
-0.030420076102018356,
0.003796301782131195,
-0.007235662080347538,
-0.007317590992897749,
-0.0472906231880188,
0.006300176959484816,
-0.021313540637493134,
0.010577808134257793,
-0.055223386734724045,
-0.0054047564044594765,
0.027842365205287933,
0.028960781171917915,
0.00010675286466721445,
0.0031232472974807024,
-0.023996105417609215,
0.02589070051908493,
-0.06202073022723198,
-0.06436431407928467,
0.017412882298231125,
-0.010224591940641403,
0.010836474597454071,
0.012471657246351242,
-0.013245665468275547,
-0.029222870245575905,
0.021764984354376793,
-0.03351999819278717,
-0.01816670596599579,
-0.018869709223508835,
-0.012594732455909252,
-0.023067502304911613,
0.03390910476446152,
0.00038868695264682174,
0.05236088111996651,
0.06069500744342804,
0.005580116529017687,
-0.037367481738328934,
-0.013022112660109997,
0.03678305819630623,
-0.053370073437690735,
0.009450279176235199,
-0.018803853541612625,
0.0003281019744463265,
-0.03071988746523857,
0.09461810439825058,
0.036779023706912994,
0.015594158321619034,
0.02156272530555725,
-0.025255030021071434,
-0.02027910389006138,
0.020492317155003548,
0.041273538023233414,
-0.03423597663640976,
0.025163941085338593,
0.004693301860243082,
-0.0064452472142875195,
-0.01020381785929203,
0.03000650182366371,
-0.012538696639239788,
-0.004907767754048109,
0.02368408814072609,
-0.02116064541041851,
-0.0018224583473056555,
-0.026469361037015915,
-0.021164754405617714,
0.017244437709450722,
-0.016969449818134308,
0.014192851260304451,
-0.032973844558000565,
-0.009582044556736946,
0.022645140066742897,
-0.04097384586930275,
-0.012269848957657814,
0.03533123806118965,
-0.02691647596657276,
0.014495234936475754,
-0.020165398716926575,
0.011795048601925373,
0.01828266866505146,
0.04106409475207329,
-0.05629594624042511,
-0.07190991193056107,
0.05289500951766968,
0.02755563333630562,
-0.0005738923791795969,
-0.0039404346607625484,
-0.0004122316895518452,
0.005363762378692627,
-0.03639349713921547,
-0.013165358453989029,
0.05039293318986893,
-0.01607842743396759,
0.004102584905922413,
-0.0012429277412593365,
-0.032364219427108765,
0.053365666419267654,
0.03032805398106575,
-0.012496337294578552,
0.0014634081162512302,
-0.020947441458702087,
-0.029413601383566856,
-0.009511122480034828,
0.05412759631872177,
-0.025875594466924667,
-0.022828979417681694,
0.02269713021814823,
-0.009022747166454792,
0.02214130014181137,
-0.046815045177936554,
-0.002822525566443801,
0.0034890351817011833,
0.010405109263956547,
0.0029291477985680103,
-0.026462426409125328,
0.025322571396827698,
0.020362980663776398,
-0.0007472227443940938,
0.016239305958151817,
0.005731097422540188,
-0.030299341306090355,
-0.08406431972980499,
0.014245739206671715,
-0.006874504499137402,
-0.023067088797688484,
0.01517733745276928,
0.08693096786737442,
-0.01870673894882202,
-0.007468387018889189,
0.0340038426220417,
-0.0173356793820858,
0.030544312670826912,
0.016657445579767227,
-0.004506004508584738,
-0.0030486066825687885,
-0.0005049986066296697,
-0.021252620965242386,
-0.02499103918671608,
0.016257336363196373,
0.008347922004759312,
0.044729575514793396,
-0.0029159248806536198,
0.025911128148436546,
0.019358690828084946,
-0.001985107781365514,
0.011723946779966354,
0.0067179882898926735,
-0.012072003446519375,
-0.006629077717661858,
0.014319652691483498,
0.04070572927594185,
-0.008389816619455814,
0.0035864966921508312,
0.016454055905342102,
0.03838634863495827,
-0.028577279299497604,
0.013582991436123848,
0.07054401189088821,
0.031992774456739426,
0.018527550622820854,
-0.016942782327532768,
-0.047628507018089294,
0.021872133016586304,
-0.022542959079146385,
0.009732997044920921,
-0.017768623307347298,
-0.02547682449221611,
0.03072820045053959,
-0.0111417006701231,
0.003196645760908723,
-0.054157767444849014,
0.003371064318343997,
-0.04860452935099602,
0.002396306488662958,
-0.00526880519464612,
0.05024678260087967,
-0.01656099036335945,
0.008712141774594784,
0.039028435945510864,
0.0018868678016588092,
0.011826377362012863,
-0.031175704672932625,
-0.0508587621152401,
-0.014905747957527637,
-0.02801898866891861,
-0.03412500023841858,
0.03161633014678955,
-0.016673868522047997,
-0.007355418521910906,
-0.012689654715359211,
-0.0007344675832428038,
0.013229570351541042,
0.022843297570943832,
0.02517736330628395,
-0.03647672012448311,
0.045682404190301895,
0.0007682659197598696,
0.012282665818929672,
-0.023821314796805382,
-0.0012816386297345161,
0.12589652836322784,
0.026990700513124466,
0.007642360869795084,
-0.05434706062078476,
0.013968158513307571,
-0.004709208384156227,
0.021630598232150078,
-0.00696371728554368,
-0.00035317116999067366,
0.007317594718188047,
0.04298906773328781,
-0.012960501946508884,
0.06269832700490952,
0.020278606563806534,
0.029546745121479034,
0.046665750443935394,
-0.08628867566585541,
-0.009945910423994064,
0.01616922952234745,
-0.021240849047899246,
-0.04919656738638878,
0.034619979560375214,
-0.07338511198759079,
0.039559174329042435,
-0.041555680334568024,
-0.011268790811300278,
0.0003903646138496697,
-0.033121101558208466,
-0.001463339664041996,
0.02236524596810341,
-0.050838906317949295,
0.008767087943851948,
0.000678827113006264,
-0.014354524202644825,
-0.031060172244906425,
0.06936652958393097,
0.014201502315700054,
-0.04329254478216171,
-0.0036906194873154163,
-0.0006061470485292375,
0.044853221625089645,
0.028389494866132736,
-0.006003426853567362,
0.016925884410738945,
-0.06481491029262543,
-0.010281234979629517,
-0.01832694001495838,
-0.030743610113859177,
-0.007793981581926346,
-0.004108803812414408,
-0.0249633826315403,
0.007499147206544876,
-0.020557817071676254,
-0.08981932699680328,
-0.02232416719198227,
0.023264462128281593,
-0.012916995212435722,
0.012680579908192158,
-0.042851440608501434,
-0.010009631514549255,
0.010850704275071621,
-0.025644509121775627,
0.012714548967778683,
-0.033176831901073456,
0.0013972712913528085,
-0.006861411035060883,
0.030957723036408424,
0.01387334056198597,
-0.0255271065980196,
-0.018234509974718094,
-0.030341483652591705,
0.017932740971446037,
-0.04732417315244675,
0.04487411677837372,
0.02554973028600216,
0.01636658050119877,
0.011123928241431713,
-0.020397817716002464,
-0.016005532816052437,
0.019195059314370155,
-0.027240220457315445,
0.06036293879151344,
-0.00006748392479494214,
-0.014203128404915333,
-0.028349660336971283,
-0.031203441321849823,
0.022343693301081657,
-0.0023684226907789707,
-0.038592252880334854,
0.016556154936552048,
-0.027585668489336967,
0.036606475710868835,
-0.003674045205116272,
-0.015102916397154331,
-0.06671424210071564,
0.03292662277817726,
-0.004506254103034735,
-0.021662896499037743,
-0.003777290228754282,
0.05530080199241638,
0.033502522855997086,
0.02486640028655529,
-0.03456100448966026,
-0.004619416315108538,
-0.04422864317893982,
0.018995391204953194,
0.046404626220464706,
-0.02218872494995594,
-0.04119909554719925,
0.015212733298540115,
-0.00108496961183846,
-0.05720115453004837,
-0.03588204085826874,
-0.0009800345869734883,
0.007097626104950905,
0.01070343516767025,
0.047499217092990875,
0.011426606215536594,
0.005367627367377281,
-0.05937432870268822,
0.03967909887433052,
-0.0273891631513834,
-0.0036855358630418777,
-0.11671802401542664,
-0.04123859852552414,
-0.008968168869614601,
-0.016291016712784767,
0.0061614359728991985,
0.0014895995846018195,
-0.03424643725156784,
-0.019891146570444107,
-0.012693388387560844,
0.021928496658802032,
0.0008065763395279646,
-0.011131910607218742,
0.039019811898469925,
-0.013927295804023743,
-0.022524965927004814,
-0.014861121773719788,
-0.07113217562437057,
0.026631705462932587,
-0.04665473476052284,
-0.035836249589920044,
-0.016719333827495575,
-0.015593644231557846,
0.0191680695861578,
0.009603671729564667,
-0.04498898237943649,
0.018893280997872353,
0.04147396236658096,
-0.019957542419433594,
0.01541572529822588,
0.0012725763954222202,
-0.002927950117737055,
0.00871528685092926,
0.0034483717754483223,
-0.00011147899203933775,
-0.02753482572734356,
-0.01811355911195278,
0.04730111360549927,
0.044654399156570435,
0.022075708955526352,
-0.02083900198340416,
0.010811027139425278,
-0.03325524926185608,
0.05052279680967331,
0.004711941350251436,
0.0015732856700196862,
0.010109250433743,
0.017176548019051552,
-0.04930221289396286,
0.026620356366038322,
0.013816073536872864,
-0.023760976269841194,
-0.08732153475284576,
0.017096465453505516,
-0.03926614671945572,
-0.02743006870150566,
0.012457584030926228,
-0.027722923085093498,
-0.014602761715650558,
0.02919669635593891,
-0.032281432300806046,
0.02418752759695053,
-0.04229016602039337,
-0.03655371814966202,
-0.03870747610926628,
0.0012856547255069017,
-0.006234120577573776,
0.07046084851026535,
0.03493581712245941,
0.020154401659965515,
0.009561735205352306,
-0.013837133534252644,
-0.03562534973025322,
0.013026165775954723,
0.010590105317533016,
0.046221744269132614,
-0.02613307535648346,
-0.016119614243507385,
0.03830033540725708,
-0.0160520039498806,
-0.023469656705856323,
0.018498258665204048,
-0.016009658575057983,
0.0341726653277874,
0.019098492339253426,
-0.01586749590933323,
-0.011234466917812824,
0.02122078649699688,
0.010417125187814236,
0.012877103872597218,
-0.014725051820278168,
0.05324370414018631,
0.040000416338443756,
0.03560818359255791,
-0.011013421230018139,
0.022846879437565804,
-0.014806638471782207,
-0.048506010323762894,
-0.0025247903540730476,
-0.014583555981516838,
-0.03286173567175865,
0.005920723546296358,
0.020429424941539764,
-0.008510325103998184,
0.03846301510930061,
-0.023625222966074944,
0.016435446217656136,
-0.042489200830459595,
0.012083890847861767,
0.014200049452483654,
-0.013215631246566772,
-0.002937055192887783,
0.03246714919805527,
-0.0018995775608345866,
0.02599647454917431,
-0.02347935549914837,
0.03800784423947334,
-0.016533341258764267,
-0.035741474479436874,
0.008257572539150715,
-0.006946749985218048,
0.002578265033662319,
0.00011407593410694972,
-0.04657715931534767,
-0.009282084181904793,
0.058806411921978,
0.04786795377731323,
0.03722672909498215,
0.04053856432437897,
0.0013024344807490706,
-0.010737599804997444,
-0.06405807286500931,
0.05637491121888161,
-0.02426709420979023,
-0.006810650695115328,
0.007144033443182707,
0.019653504714369774,
0.030192553997039795,
0.04323834553360939,
0.06566172093153,
-0.008547049015760422,
-0.021015994250774384,
0.0072120437398552895,
0.021038280799984932,
-0.006383872590959072,
-0.03253926336765289,
-0.00861398782581091,
-0.02391824685037136,
-0.034160494804382324,
0.02657080627977848,
-0.002561418805271387,
0.016540851444005966,
0.01977945864200592,
-0.00023468855943065137,
0.015043135732412338,
0.017137154936790466,
-0.03008558414876461,
-0.011394022032618523,
0.04722972214221954,
-0.0062594907358288765,
-0.015460526570677757,
0.07458905130624771,
-0.008990667760372162,
0.030836548656225204,
-0.01874380372464657,
-0.010883559472858906,
-0.028519030660390854,
0.032708022743463516,
0.0022119993809610605,
-0.0020826258696615696,
-0.03598687797784805,
-0.05038900673389435,
0.043562646955251694,
-0.02777058444917202,
-0.0026036081835627556,
0.009968405589461327,
-0.05910094827413559,
0.019500745460391045,
0.029774747788906097,
0.05952341854572296,
0.028529779985547066,
-0.03910938277840614,
-0.017886348068714142,
0.026810351759195328,
0.028913408517837524,
0.0101063447073102,
0.047365445643663406,
0.04002174362540245,
0.00620794203132391,
-0.01480456255376339,
0.021618597209453583,
0.0008867367287166417,
0.025001605972647667,
0.026716355234384537,
0.02420620433986187,
-0.003918998409062624,
-0.03078886866569519,
-0.0045729088596999645,
-0.05456091836094856,
0.00669746333733201,
-0.010827996768057346,
0.0125524727627635,
0.047822222113609314,
0.02049170807003975,
0.04075998440384865,
-0.034788068383932114,
0.012465781532227993,
0.004043670371174812,
-0.004235066007822752,
0.01907055266201496,
-0.00004837028245674446,
0.029160339385271072,
-0.05098028853535652,
-0.045013703405857086,
0.004742711316794157,
0.010420837439596653,
-0.011073840782046318,
0.026695704087615013,
-0.054566361010074615,
0.016502927988767624,
-0.009632180444896221,
-0.00829773023724556,
-0.04686256870627403,
-0.08308779448270798,
0.041228726506233215,
0.023151636123657227,
0.02526135928928852,
0.0021929917857050896,
-0.02349904738366604,
-0.03744133934378624,
0.06698208302259445,
-0.06230403855443001,
-0.0443434938788414,
-0.009570357389748096,
0.05146513506770134,
-0.023368006572127342,
-0.0009041134617291391
] |
<p>Does vacuum or outer space contain any gases? Recently i watched a video on youtube,in which NASA installs a camera on a spacecraft.The footage shows some dust particles or some matter floating over the space craft's surface and as well from the thrust.What exactly is that? If there is nothing in vacuum,how come newton third law works out to make it move in turn?
Here is the link</p>
<p><a href="http://www.youtube.com/watch?v=HSnOTaCeSuk" rel="nofollow">http://www.youtube.com/watch?v=HSnOTaCeSuk</a></p>
| 10,688 |
[
0.005104890093207359,
-0.02225053869187832,
0.005951490253210068,
-0.00850493274629116,
0.04240691289305687,
-0.008591167628765106,
-0.019246665760874748,
-0.020961234346032143,
-0.0025795032270252705,
-0.05948689952492714,
-0.016288962215185165,
0.04485186189413071,
0.02645949088037014,
-0.0034622722305357456,
-0.014806983061134815,
-0.0017603215528652072,
0.0019181459210813046,
-0.020816843956708908,
0.011351642198860645,
-0.026365112513303757,
-0.016787761822342873,
-0.002277675550431013,
0.020655490458011627,
0.019785281270742416,
-0.04141886159777641,
0.008833500556647778,
0.005636082962155342,
-0.034021735191345215,
0.04979518800973892,
0.025231484323740005,
-0.0073095811530947685,
0.02432265877723694,
-0.009233727119863033,
-0.019310729578137398,
0.019455840811133385,
0.0012757995864376426,
-0.021654827520251274,
-0.0017114175716415048,
0.02890779823064804,
0.024426139891147614,
-0.07043399661779404,
-0.033396363258361816,
0.008613981306552887,
0.018767960369586945,
-0.04314310476183891,
0.00007488565461244434,
0.018316948786377907,
0.034085020422935486,
0.06294079124927521,
-0.0885951817035675,
0.04299355298280716,
0.00622563436627388,
0.0815851017832756,
0.028349019587039948,
0.0007514987955801189,
-0.009136773645877838,
0.08824419230222702,
0.0957288071513176,
-0.009739522822201252,
-0.002688721753656864,
0.001997926039621234,
-0.0036402703262865543,
-0.021406609565019608,
-0.044520679861307144,
-0.02078968845307827,
0.03967002406716347,
-0.03030453622341156,
-0.014688140712678432,
0.008062801323831081,
0.07149359583854675,
0.025309821590781212,
0.0069645303301513195,
-0.0022677602246403694,
-0.0014474544441327453,
0.007847842760384083,
-0.006817092187702656,
0.07267720252275467,
0.007958984933793545,
0.040813419967889786,
0.03653706982731819,
0.021424686536192894,
-0.010662613436579704,
0.014314122498035431,
-0.008832575753331184,
0.02537408284842968,
0.009471443481743336,
0.09709037840366364,
-0.03470895066857338,
0.017337888479232788,
0.01307005900889635,
0.015393276698887348,
0.027859589084982872,
0.00278885243460536,
0.0032581572886556387,
-0.014458023011684418,
0.038710158318281174,
-0.009693733416497707,
0.0394759364426136,
0.009467140771448612,
-0.029692968353629112,
-0.016258012503385544,
0.03924955800175667,
0.043835725635290146,
0.07221424579620361,
0.006139518227428198,
-0.029064614325761795,
-0.059291571378707886,
0.048290252685546875,
-0.030869409441947937,
0.01631169021129608,
-0.05216312035918236,
0.033499643206596375,
0.006547832861542702,
0.0005471059703268111,
0.014659248292446136,
-0.012549561448395252,
0.019263651221990585,
-0.023948300629854202,
0.04791025444865227,
0.08548862487077713,
0.033592551946640015,
-0.015905434265732765,
0.03018181025981903,
-0.0010207842569798231,
-0.07381929457187653,
0.019510481506586075,
0.005609517451375723,
-0.027581239119172096,
-0.014398671686649323,
0.010323060676455498,
-0.02315855771303177,
-0.008207419887185097,
0.005452203098684549,
0.009956153109669685,
0.04496132209897041,
-0.005830520763993263,
-0.09660830348730087,
-0.02409537322819233,
0.04614798724651337,
0.004420026671141386,
-0.016085971146821976,
-0.05803493782877922,
-0.008759387768805027,
0.026803800836205482,
0.06526312977075577,
-0.007527628447860479,
-0.03952905535697937,
-0.016180546954274178,
0.05239566043019295,
-0.005767602939158678,
-0.03682591766119003,
0.008870719000697136,
-0.005699791945517063,
-0.05980098247528076,
0.017602646723389626,
-0.06847527623176575,
0.033736616373062134,
0.04434725642204285,
0.0458049438893795,
-0.052915990352630615,
0.05014674738049507,
-0.024738850072026253,
0.001880566356703639,
0.00041284141479991376,
0.0143674835562706,
-0.03979593142867088,
0.042574360966682434,
0.022193677723407745,
0.022330880165100098,
0.046338584274053574,
0.02219613641500473,
0.0290374755859375,
0.013120275922119617,
0.010823002085089684,
0.05466090887784958,
-0.006624473724514246,
-0.04499439150094986,
-0.012788341380655766,
0.044519856572151184,
-0.02755669690668583,
-0.06248796731233597,
-0.014625875279307365,
-0.008201404474675655,
0.0338861383497715,
0.005231794901192188,
0.027163565158843994,
0.02224043942987919,
-0.020271513611078262,
0.008779996074736118,
-0.03189290314912796,
-0.01031577680259943,
-0.06586849689483643,
-0.0052192322909832,
-0.023554066196084023,
-0.031392939388751984,
0.007028949446976185,
0.019798217341303825,
0.03458167240023613,
-0.06565169245004654,
-0.028392015025019646,
0.007629176136106253,
0.05407894402742386,
-0.01816517673432827,
-0.012526335194706917,
0.008523126132786274,
0.05127672478556633,
0.02222372591495514,
0.0020539171528071165,
-0.013011706061661243,
0.026634592562913895,
-0.03507031127810478,
-0.01366945169866085,
-0.022841887548565865,
-0.0026903604157269,
-0.0010674736695364118,
0.018801826983690262,
0.05777366831898689,
-0.006637526676058769,
0.0036005291622132063,
0.018480945378541946,
-0.009386210702359676,
0.08873400092124939,
0.014502286911010742,
0.016465505585074425,
0.0007440379122272134,
-0.0034014505799859762,
-0.004776737652719021,
-0.020833129063248634,
0.030108831822872162,
-0.01763332448899746,
-0.05509424954652786,
-0.04756254702806473,
0.030092913657426834,
0.015510167926549911,
-0.015046373009681702,
0.018091287463903427,
0.013795663602650166,
0.006623726803809404,
0.013108015060424805,
0.02308478020131588,
-0.03102254308760166,
-0.012813763692975044,
0.032162073999643326,
0.025109421461820602,
0.029608305543661118,
0.018658623099327087,
0.041676755994558334,
0.060740891844034195,
0.03736792877316475,
-0.022151945158839226,
-0.010096895508468151,
0.02712019346654415,
0.017165672034025192,
0.04922294244170189,
-0.007519044913351536,
-0.01279427856206894,
0.025581900030374527,
-0.002655783435329795,
0.0068216025829315186,
-0.01294221356511116,
0.006073195021599531,
0.02538401447236538,
-0.027055641636252403,
-0.012387454509735107,
0.003892719279974699,
0.0031744535081088543,
-0.02505563385784626,
0.029062870889902115,
0.02515457198023796,
-0.07937736064195633,
0.02906544879078865,
-0.03711782023310661,
0.017354359850287437,
-0.009762510657310486,
0.03178757429122925,
0.02345692180097103,
0.024564137682318687,
0.030197899788618088,
-0.03575601428747177,
-0.030246902257204056,
-0.01154902670532465,
-0.06956780701875687,
-0.017757918685674667,
0.051807716488838196,
-0.03385322540998459,
0.05820663645863533,
-0.041660621762275696,
-0.05699516460299492,
0.042966440320014954,
-0.0136654581874609,
0.005595257971435785,
0.03626655787229538,
-0.04627544805407524,
-0.026697281748056412,
0.03202258422970772,
-0.024535654112696648,
0.0011806689435616136,
0.00647930009290576,
0.017174430191516876,
0.02520088292658329,
-0.025253329426050186,
-0.05450885370373726,
0.031146084889769554,
-0.06204895302653313,
-0.05072499066591263,
-0.05146864056587219,
0.02015082724392414,
0.027462026104331017,
-0.06628508865833282,
0.03493887931108475,
0.038015272468328476,
-0.025316059589385986,
0.003134434809908271,
-0.004554427228868008,
0.002245113020762801,
0.014564518816769123,
-0.009657023474574089,
-0.014690355397760868,
-0.04581818729639053,
-0.05193652585148811,
0.045755598694086075,
0.03749537095427513,
-0.01484204363077879,
0.0016257755924016237,
-0.03683992847800255,
-0.05957507714629173,
-0.028161896392703056,
0.016096064820885658,
-0.008024207316339016,
0.01782405376434326,
-0.01190317701548338,
0.01630169339478016,
0.04024979844689369,
-0.020204830914735794,
0.020666390657424927,
-0.01849270612001419,
-0.011436570435762405,
0.015043324790894985,
-0.012730366550385952,
0.09382881969213486,
0.03236078843474388,
-0.002588392933830619,
0.007278528530150652,
0.012350753881037235,
0.059632398188114166,
0.027069782838225365,
-0.05695759132504463,
0.04256633296608925,
0.008990149013698101,
0.022919904440641403,
0.005311525892466307,
0.010942821390926838,
-0.006544511765241623,
0.042305849492549896,
0.014383209869265556,
-0.0116944070905447,
0.013422777876257896,
0.02754051424562931,
-0.012545449659228325,
-0.0019130862783640623,
0.07071546465158463,
-0.03843797370791435,
-0.0013795235427096486,
-0.004200582392513752,
-0.03974663466215134,
0.0008654710836708546,
0.008829435333609581,
-0.009791991673409939,
0.03125225007534027,
0.04518304765224457,
0.027948865666985512,
0.012616528198122978,
-0.0397113673388958,
0.030733199790120125,
-0.01686117798089981,
-0.015372328460216522,
-0.019327711313962936,
0.00740405498072505,
0.001704735797829926,
0.0734095498919487,
-0.022472577169537544,
0.034045420587062836,
0.03883501514792442,
-0.04314234107732773,
-0.07397417724132538,
0.02945566736161709,
0.00825750082731247,
-0.029129981994628906,
-0.008818313479423523,
-0.012065515853464603,
-0.03223619610071182,
-0.008314241655170918,
-0.013025942258536816,
0.015646949410438538,
0.014659523963928223,
-0.07200893759727478,
-0.02330658957362175,
-0.018608495593070984,
-0.011050937697291374,
-0.017667612060904503,
0.025908106938004494,
0.023369526490569115,
-0.018827589228749275,
0.01392151415348053,
0.051010485738515854,
-0.018664145842194557,
0.00511962128803134,
-0.0023176968097686768,
-0.009549876675009727,
0.02058469131588936,
0.020164761692285538,
0.020122293382883072,
0.0008707850356586277,
0.003105634357780218,
-0.002022776985540986,
-0.0059307343326509,
0.015531244687736034,
-0.04092268645763397,
0.014195707626640797,
-0.03741513937711716,
-0.01655520685017109,
-0.0091386204585433,
0.002174055902287364,
0.028097739443182945,
0.0074129183776676655,
0.060018036514520645,
0.01053939014673233,
-0.02687932923436165,
-0.0029045932460576296,
0.038831792771816254,
0.04983530193567276,
0.015719491988420486,
0.00021906809706706554,
-0.03749598190188408,
-0.004830469377338886,
-0.05197612941265106,
-0.00546971196308732,
0.04483768716454506,
0.016174552962183952,
-0.034556709229946136,
-0.009740497916936874,
-0.01763911172747612,
0.022006217390298843,
-0.022580664604902267,
0.005782570224255323,
0.0010663698194548488,
0.013976646587252617,
-0.06259644776582718,
-0.020686710253357887,
0.007243534084409475,
0.034079499542713165,
0.030382808297872543,
-0.002797984052449465,
-0.020452972501516342,
-0.0853549987077713,
-0.009902509860694408,
0.03815435245633125,
-0.005087428726255894,
-0.0063150073401629925,
-0.03159826993942261,
-0.05683671683073044,
-0.0023356021847575903,
0.013932224363088608,
-0.05894730985164642,
-0.007046641316264868,
-0.0615682452917099,
0.01732572540640831,
0.00338368839584291,
-0.03201388940215111,
0.02653653733432293,
-0.00688608642667532,
-0.008566955104470253,
0.009037507697939873,
-0.0055380952544510365,
-0.010616346262395382,
-0.008098017424345016,
0.03748456388711929,
0.008227348327636719,
0.021600285544991493,
0.017598679289221764,
0.015822267159819603,
-0.02314351685345173,
0.005359801463782787,
-0.04349731281399727,
-0.0657242015004158,
0.007611825130879879,
0.019109036773443222,
-0.03081287071108818,
0.034010790288448334,
-0.02569219470024109,
-0.028900714591145515,
-0.0006780488765798509,
-0.007825430482625961,
-0.013782430440187454,
-0.041594166308641434,
-0.02077130228281021,
-0.004879716783761978,
0.008086321875452995,
0.01198301650583744,
0.035924963653087616,
0.03256763517856598,
0.0037239519879221916,
0.021675018593668938,
-0.03465292602777481,
0.06249595433473587,
-0.034826312214136124,
-0.04555291309952736,
-0.03802159056067467,
-0.0007742484449408948,
-0.021505849435925484,
0.05766436085104942,
0.0066793086007237434,
-0.002859242260456085,
-0.010953593999147415,
-0.02987242490053177,
-0.003623503725975752,
0.009677262045443058,
0.008683552034199238,
0.013368402607738972,
-0.045317672193050385,
0.02259674109518528,
-0.01037366222590208,
-0.03872044384479523,
-0.0031654860358685255,
0.04022946208715439,
-0.02649901807308197,
0.021382268518209457,
0.010796320624649525,
0.021883249282836914,
0.0017705934587866068,
0.016498861834406853,
-0.006725511513650417,
-0.02932620234787464,
0.03156976029276848,
-0.006330529227852821,
0.01178903691470623,
0.02485705353319645,
-0.04735679179430008,
-0.03779618814587593,
-0.011074576526880264,
-0.0042853462509810925,
0.018274931237101555,
-0.07557832449674606,
0.0372944101691246,
0.00826072134077549,
0.04663478210568428,
-0.05963999405503273,
-0.06788495182991028,
-0.0044890353456139565,
0.017509881407022476,
0.0038081209640949965,
-0.051578912883996964,
0.003989557269960642,
-0.058073990046978,
-0.045296452939510345,
0.013470233418047428,
0.03636540099978447,
-0.03580227494239807,
-0.022803721949458122,
0.01880049891769886,
0.010232849977910519,
0.04806586354970932,
0.012930890545248985,
-0.020340217277407646,
0.010888966731727123,
0.03260495886206627,
0.0017646452179178596,
-0.0026446396950632334,
0.01643824763596058,
0.005871311295777559,
-0.02340928465127945,
-0.017111530527472496,
0.005214504897594452,
0.005787850823253393,
-0.07659313082695007,
-0.008418835699558258,
0.05489552766084671,
0.029797041788697243,
0.013737817294895649,
-0.04035190865397453,
0.024896886199712753,
-0.017705481499433517,
0.03775839880108833,
0.014372745528817177,
-0.008821996860206127,
-0.014715585857629776,
-0.033898986876010895,
0.01623455621302128,
-0.029182832688093185,
-0.000976495910435915,
-0.009367215447127819,
0.03619006648659706,
0.025059133768081665,
-0.0035983368288725615,
0.0007815169519744813,
0.005340553820133209,
0.010203463956713676,
-0.025405844673514366,
0.006144016049802303,
0.020228799432516098,
0.009410903789103031,
-0.037193600088357925,
-0.028356632217764854,
-0.06636722385883331,
-0.006543439347296953,
0.05119645968079567,
-0.043095313012599945,
0.0308113731443882,
0.0034140057396143675,
-0.0036505714524537325,
0.004663003142923117,
-0.050330642610788345,
-0.001875446643680334,
0.019534334540367126,
0.01784621924161911,
-0.030467316508293152,
-0.019316932186484337,
0.037407469004392624,
0.03273111209273338,
0.027196114882826805,
-0.013780966401100159,
-0.03403765708208084,
0.021908601745963097,
0.007424762938171625,
0.007683131378144026,
0.008731181733310223,
-0.04653868079185486,
0.03328327462077141,
-0.023242468014359474,
0.05429410561919212,
0.02603176422417164,
-0.01194292027503252,
0.04651716724038124,
-0.003802491817623377,
-0.021490179002285004,
-0.04854998365044594,
-0.022274712100625038,
-0.02583783119916916,
0.04703583940863609,
-0.000194949287106283,
-0.007540363818407059,
-0.009026404470205307,
0.00040806044125929475,
0.02041703462600708,
-0.011209110729396343,
-0.000031537230825051665,
0.03999388590455055,
-0.08631420135498047,
-0.021916614845395088,
-0.03271842002868652,
-0.01675986684858799,
0.03108767233788967,
-0.006604161113500595,
-0.046627406030893326,
-0.013729996047914028,
-0.03469530865550041,
0.03454844653606415,
0.00413927249610424,
0.052531205117702484,
-0.010701628401875496,
0.03450442850589752,
-0.01922900229692459,
0.036039598286151886,
-0.0188670065253973,
0.0658927634358406,
0.11867954581975937,
0.010128261521458626,
0.015556005761027336,
-0.03861638531088829,
-0.03497269004583359,
-0.040146853774785995,
0.012445222586393356,
-0.029347440227866173,
0.01712641678750515,
-0.0007095474284142256,
0.046347588300704956,
-0.009220977313816547,
0.04643845558166504,
-0.0069615901447832584,
0.020988136529922485,
0.03419535607099533,
-0.02598836086690426,
-0.024285025894641876,
-0.029096020385622978,
0.02133527770638466,
-0.02184741571545601,
0.06130442023277283,
-0.0498284250497818,
0.018542854115366936,
0.0012524009216576815,
-0.009178212843835354,
-0.014724651351571083,
-0.04458598792552948,
0.03170125558972359,
-0.00545083312317729,
-0.05249478667974472,
0.0007261628052219748,
-0.0013812484685331583,
-0.03290058672428131,
-0.03030306287109852,
-0.017618820071220398,
-0.006080377846956253,
-0.024870160967111588,
-0.009825279004871845,
-0.024807123467326164,
0.0018799221143126488,
0.02486887387931347,
0.005219333339482546,
0.026772290468215942,
-0.04172747954726219,
0.025565439835190773,
-0.0017055257922038436,
0.051109183579683304,
-0.002520626410841942,
0.016426466405391693,
-0.008769997395575047,
0.04811633750796318,
0.005457672290503979,
-0.06987520307302475,
-0.03775908425450325,
-0.017874950543045998,
0.04927690327167511,
-0.016054760664701462,
-0.03750927001237869,
-0.013126296922564507,
-0.0007194578065536916,
-0.00443858141079545,
0.007665340788662434,
-0.003951871767640114,
0.021837225183844566,
0.01674620434641838,
0.019943445920944214,
0.04539842903614044,
-0.05142158642411232,
-0.009069747291505337,
-0.015972493216395378,
-0.010625310242176056,
-0.021930014714598656,
-0.011085759848356247,
0.02906857430934906,
0.05170748010277748,
0.011843639425933361,
0.008857853710651398,
-0.004358284641057253,
0.01175472792237997,
-0.04434385523200035,
0.032234594225883484,
-0.02535230852663517,
0.005285046063363552,
-0.0347885824739933,
-0.012937547639012337,
0.02526349201798439,
0.0580865815281868,
-0.029359176754951477,
-0.005461622029542923,
0.008246432058513165,
0.019102709367871284,
0.02701851911842823,
-0.016171030700206757,
-0.030294543132185936,
0.038189079612493515,
-0.014584172517061234,
0.003658355213701725,
-0.027857478708028793,
0.03883012384176254,
0.032676976174116135,
0.03983293101191521,
-0.020865943282842636,
0.03681930527091026,
-0.03678471967577934,
0.014975380152463913,
0.026351438835263252,
-0.015566030517220497,
-0.0033311995211988688,
0.02995048090815544,
0.017296258360147476,
-0.0432470366358757,
-0.030025571584701538,
-0.024016205221414566,
-0.0005418101791292429,
-0.024431763216853142,
0.02607155032455921,
-0.031728826463222504,
0.03619649261236191,
0.0011428716825321317,
0.04882179945707321,
-0.06888236850500107,
-0.002513298997655511,
-0.06181403622031212,
0.03917289152741432,
0.03711441159248352,
-0.009501222521066666,
-0.03202584385871887,
0.002619122853502631,
-0.047407764941453934,
-0.023426728323101997,
-0.0030324645340442657,
-0.0031729754991829395,
-0.019685789942741394,
-0.009838433004915714,
0.04095281660556793,
-0.017583442851901054,
0.018859663978219032,
0.022023670375347137,
0.03087626025080681,
0.01438363641500473,
-0.0457938015460968,
-0.06851644068956375,
0.002462622243911028,
-0.024794993922114372,
0.03980249539017677,
0.015692485496401787,
-0.04033144563436508,
-0.019937951117753983,
0.05458757281303406,
-0.02887727878987789,
0.008180673234164715,
-0.017685813829302788,
-0.04933294281363487,
-0.01642814837396145,
-0.016603002324700356,
0.04612630978226662,
-0.02414538338780403,
-0.0181896910071373,
0.06333219259977341,
0.01617003232240677,
0.00564952939748764,
-0.012846934609115124,
0.0303471852093935,
-0.04110826551914215,
-0.011301747523248196,
0.030733903869986534,
0.027266237884759903,
0.007971216924488544,
0.05398867279291153,
-0.03205772489309311,
0.052751556038856506,
0.051427118480205536,
0.027141666039824486,
-0.12207038700580597,
0.006402682512998581,
-0.006465693470090628,
-0.017315197736024857,
0.016800325363874435,
-0.04265136271715164,
0.013053999282419682,
0.01981697790324688,
-0.08742105215787888,
0.027768151834607124,
-0.03688305988907814,
-0.004189292900264263,
-0.02575324848294258,
0.002967813052237034,
0.012481649406254292,
0.030431704595685005,
0.014277425594627857,
0.017375441268086433,
-0.010165398940443993,
0.03771881014108658,
-0.01437886618077755,
-0.004435173701494932,
-0.010375000536441803,
0.039705730974674225,
-0.017658689990639687,
0.018316097557544708,
0.04168837144970894,
-0.013749907724559307,
0.02125890925526619,
0.05671575665473938,
0.01966804638504982,
0.02223692648112774,
-0.02002808079123497,
-0.007292016409337521,
-0.01464894786477089,
0.0038111943285912275,
0.033616915345191956,
0.01723453775048256,
-0.003652757266536355,
0.02748783491551876,
0.026573561131954193,
0.0028240205720067024,
0.027945896610617638,
0.0006847355398349464,
0.04211058467626572,
-0.04480619356036186,
0.020937848836183548,
-0.00047457971959374845,
-0.0014974913792684674,
0.014708451926708221,
0.00016597210196778178,
0.019006939604878426,
-0.011179151013493538,
-0.02402319386601448,
-0.005462043918669224,
-0.053548626601696014,
0.013692496344447136,
0.007611617911607027,
0.0013283378211781383,
-0.023548657074570656,
-0.0068294391967356205,
0.027145158499479294,
-0.009957834146916866,
0.02316874824464321,
-0.023996936157345772,
0.011468213051557541,
-0.01584143564105034,
-0.028241926804184914,
0.019475197419524193,
-0.01945416070520878,
0.036839939653873444,
-0.029033059254288673,
-0.02437075413763523,
0.06634444743394852,
0.004590448923408985,
-0.0002896372170653194,
-0.03298089653253555,
-0.049590397626161575,
-0.03055950626730919,
-0.04378396272659302,
0.02328878454864025,
-0.004981586243957281,
-0.017122287303209305,
-0.07460018247365952,
-0.01430746540427208,
0.0149253373965621,
0.005841741804033518,
0.03104977123439312,
0.009252570569515228,
0.019826849922537804,
-0.01349748857319355,
0.00035266944905743003,
0.019312698394060135,
-0.04543992877006531,
0.030431559309363365,
0.021853944286704063,
-0.06194978952407837,
-0.005573544651269913,
-0.009660804644227028,
-0.02315353974699974,
0.007616403046995401,
0.06496332585811615,
-0.01815737970173359,
0.01217077299952507,
-0.030827660113573074,
-0.026814313605427742,
0.024211209267377853,
0.05089764669537544,
-0.01007931400090456,
0.06525609642267227,
-0.03362210467457771,
0.029931697994470596,
0.043041884899139404,
0.025287656113505363,
0.009438115172088146,
0.010462994687259197,
-0.005110574420541525,
-0.011763026006519794,
-0.026634665206074715,
-0.015269861556589603,
0.022334212437272072,
-0.0663522332906723,
-0.01608775556087494,
0.04474719241261482,
-0.04807164892554283,
-0.0018463648157194257,
0.07664363086223602,
0.004028798546642065,
0.0675261914730072,
-0.023396501317620277,
0.019492335617542267,
0.03942614421248436,
-0.011771595105528831,
-0.014852451160550117,
0.059863798320293427,
0.013995911926031113,
-0.0112529331818223,
-0.020921628922224045,
0.013074981980025768,
-0.022718045860528946,
0.010581042617559433,
0.013950870372354984,
0.06377959251403809,
-0.011475869454443455,
0.002745973877608776,
-0.006367973051965237,
0.013308766297996044,
0.018317904323339462,
0.02653336338698864,
-0.004709494765847921,
0.08871737122535706,
-0.04590761661529541,
0.020757406949996948,
-0.01565520092844963,
0.012527575716376305,
-0.02261122316122055,
0.00893297977745533,
-0.026403218507766724,
0.01643688604235649,
0.007585533428937197,
-0.018251411616802216,
-0.03477231413125992,
0.021759066730737686,
0.0004004425718449056,
-0.012495952658355236,
0.01575658842921257,
-0.017116490751504898,
0.01971977949142456,
-0.022540731355547905,
-0.0018208222463726997,
-0.0013811385724693537,
-0.01131703145802021,
0.023728154599666595,
0.04165448248386383,
0.00504023302346468,
-0.008220391348004341,
-0.001556501374579966,
-0.0454641729593277,
0.0322856679558754,
-0.04551171138882637,
0.002654406474903226,
-0.012996108271181583,
0.019748922437429428,
-0.02872389368712902,
-0.0014898631488904357
] |
<p>Related post <a href="http://physics.stackexchange.com/questions/55687/causality-and-quantum-field-theory">Causality and Quantum Field Theory</a></p>
<p>In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory.</p>
<p>Consider commutator
$$ [ \phi(x), \phi(y) ] = D(x-y) - D(y-x) \tag{2.53} $$
where $D(x-y)$ is the two-point correlation function,
$$D(x-y):= \langle 0 | \phi(x) \phi(y) | 0 \rangle = \int \frac{d^3 p}{ (2\pi)^3} \frac{1}{ 2E_{\mathbf{p}}} e^{-ip(x-y)}\tag{2.50}$$</p>
<p>P&S argued that each term in the right-hand-side of (2.53) is Lorentz invariant, since
$$\int \frac{d^3p }{ (2\pi)^3} \frac{1}{2E_{\mathbf{p}}} = \int \frac{ d^4 p }{ (2\pi)^4} (2\pi) \delta(p^2-m^2)|_{p^0>0} \tag{2.40}$$ is Lorentz invariant.</p>
<p>Since there exists a continuous Lorentz transformation in the spacelike interval $(x-y)^2<0 $ such that $(x-y) \rightarrow - (x-y) $ and $D(y-x)=D(x-y)$, (2.53) equals zero in the spacelike interval. In timelike interval, since such continuous Lorentz transformation does not exist, (2.53) is non-zero in general.</p>
<p>My question is, consider a non-continuous Lorentz transmation in the timelike interval, $PT$, namely time reversal times parity transformation. I can also let $(x-y) \rightarrow - (x-y) $. Why (2.53) in the timelike interval is non-zero?</p>
<p>I guess $PT$ will let (2.40) go to $p^0<0$ branch. But I am not sure if it breaks the Lorentz invariant of (2.40) and (2.50). </p>
| 10,689 |
[
-0.0033315434120595455,
0.005134319420903921,
0.01806952990591526,
-0.0058100479654967785,
0.03722577169537544,
-0.0033326423726975918,
-0.02560865506529808,
-0.06198867782950401,
-0.011433631181716919,
-0.017613084986805916,
0.015865303575992584,
0.014419404789805412,
0.03426429256796837,
0.03378329053521156,
-0.020721307024359703,
0.006886085495352745,
-0.010035764425992966,
-0.00857299193739891,
-0.009842613711953163,
-0.0587698258459568,
-0.015923216938972473,
0.06047789007425308,
-0.006599546410143375,
0.011025683954358101,
-0.0259354580193758,
0.006716836243867874,
-0.014087870717048645,
0.0005915951915085316,
-0.0436987578868866,
0.08618098497390747,
-0.036820195615291595,
-0.04284670203924179,
-0.003880617441609502,
0.05792802944779396,
0.02206033281981945,
0.037265464663505554,
-0.013267725706100464,
-0.036229249089956284,
0.034799039363861084,
-0.007567140739411116,
-0.05330229178071022,
-0.023064864799380302,
-0.00496088620275259,
0.0415085069835186,
-0.009360474534332752,
-0.0006334882345981896,
0.0339149534702301,
-0.007344571873545647,
0.10491909831762314,
-0.032103173434734344,
0.08686856925487518,
-0.003930515144020319,
-0.011996994726359844,
-0.003457312472164631,
-0.015323210507631302,
-0.025440001860260963,
0.08232029527425766,
0.057106196880340576,
0.004970339126884937,
-0.026779428124427795,
-0.04726994037628174,
-0.02365086041390896,
0.027367061004042625,
-0.037956174463033676,
-0.013246575370430946,
0.003798956982791424,
0.02718709222972393,
-0.006555777043104172,
-0.02065952867269516,
-0.028226327151060104,
0.009822177700698376,
0.019011763855814934,
0.05605417117476463,
-0.027444038540124893,
0.053790003061294556,
0.020902488380670547,
0.012899736873805523,
-0.0011948075843974948,
0.032354895025491714,
0.051064591854810715,
-0.0004194124194327742,
0.01036797184497118,
0.015526947565376759,
-0.007571415044367313,
0.013955839909613132,
-0.0007449903059750795,
0.06210089474916458,
-0.0015047374181449413,
-0.024790314957499504,
0.047460295259952545,
-0.030070509761571884,
-0.00132843351457268,
0.01499477494508028,
-0.024242395535111427,
0.001449387869797647,
0.06636732816696167,
0.01385077927261591,
0.028300153091549873,
-0.007082461379468441,
-0.02399389259517193,
-0.046429842710494995,
-0.04098469763994217,
0.01834607869386673,
0.0458647795021534,
0.020232398062944412,
0.009369388222694397,
-0.04521777853369713,
0.04107394441962242,
-0.02960561215877533,
-0.02811427414417267,
-0.043739307671785355,
0.0047378623858094215,
-0.03244385868310928,
0.0019194390624761581,
0.008822981268167496,
-0.018761325627565384,
-0.011126023717224598,
-0.013595734722912312,
0.02247157134115696,
0.07581043988466263,
0.011370381340384483,
-0.005996449384838343,
0.012069537304341793,
-0.02841995470225811,
-0.06061405688524246,
-0.00976425502449274,
0.04261580482125282,
0.016729487106204033,
-0.0278911292552948,
0.009138244204223156,
0.028422677889466286,
0.00004440829070517793,
0.007462143432348967,
-0.012078498490154743,
0.018959788605570793,
0.002862463239580393,
-0.08693422377109528,
-0.05120202526450157,
0.055766332894563675,
-0.017628444358706474,
-0.009843891486525536,
-0.06648984551429749,
-0.02905076928436756,
0.016816308721899986,
0.09477715939283371,
-0.009121043607592583,
-0.018285483121871948,
-0.01163407415151596,
0.048113927245140076,
0.010882243514060974,
-0.01966686174273491,
-0.02303309366106987,
0.00332575011998415,
-0.046304989606142044,
-0.05131138488650322,
-0.01311814971268177,
0.052699532359838486,
0.059595439583063126,
-0.0037314731162041426,
-0.010903698392212391,
0.06070280447602272,
-0.0192964319139719,
0.007023939862847328,
0.01147425640374422,
0.00040450136293657124,
-0.02426222525537014,
0.07301394641399384,
0.032234854996204376,
-0.0036760850343853235,
0.02847442217171192,
-0.004637471400201321,
0.029229918494820595,
-0.00613408675417304,
0.04791967570781708,
0.003369075246155262,
-0.0616205558180809,
-0.055876150727272034,
-0.020094221457839012,
-0.002313456265255809,
-0.02468036860227585,
-0.0388188511133194,
0.0004334056284278631,
-0.0493440143764019,
0.006661529187113047,
-0.002106369473040104,
0.04798907786607742,
0.019961822777986526,
0.026276543736457825,
0.030077828094363213,
-0.023687131702899933,
-0.010486164130270481,
-0.0508868545293808,
-0.0029653962701559067,
0.05448976904153824,
-0.05410729721188545,
0.03685963153839111,
-0.008214030414819717,
0.009987990371882915,
-0.011044587008655071,
-0.01661517471075058,
0.0016765722539275885,
0.019767364487051964,
0.028769049793481827,
0.010378291830420494,
0.04305805265903473,
0.02564914897084236,
0.05146067962050438,
-0.011447747237980366,
-0.020916039124131203,
-0.032938066869974136,
-0.042735449969768524,
0.0009415766107849777,
0.018118415027856827,
0.02951943501830101,
-0.00983620248734951,
0.0004717352567240596,
0.037152498960494995,
0.020164400339126587,
-0.03665224090218544,
0.018581371754407883,
-0.030220316722989082,
0.03487830609083176,
0.05299786105751991,
-0.017833640798926353,
-0.002143098274245858,
0.04480154439806938,
0.01341194473206997,
0.03134491294622421,
-0.04564175754785538,
-0.047359973192214966,
-0.03080052137374878,
0.002311520976945758,
0.015162740834057331,
0.059903793036937714,
-0.018216677010059357,
0.006248988676816225,
0.01576799899339676,
0.0376439094543457,
0.016743939369916916,
0.009875289164483547,
0.03293856233358383,
-0.04085446149110794,
0.001316022826358676,
-0.012916269712150097,
0.02468600869178772,
-0.01997552625834942,
0.007246260065585375,
-0.03943690285086632,
0.010446213185787201,
-0.0039354292675852776,
-0.029346724972128868,
-0.018764112144708633,
-0.012527263723313808,
-0.007480937987565994,
0.0019420789321884513,
-0.003165094181895256,
0.012410949915647507,
0.018839769065380096,
0.04139545187354088,
0.026452723890542984,
0.012107153423130512,
-0.025731286033988,
-0.02661813609302044,
-0.04419759660959244,
0.03923094645142555,
-0.0011651787208393216,
-0.029262853786349297,
-0.03704614192247391,
0.004134403541684151,
0.00664173997938633,
-0.01969875954091549,
0.013045537285506725,
-0.004116000607609749,
-0.006427217740565538,
-0.01642361283302307,
0.05133948102593422,
0.04761112108826637,
0.01539330743253231,
-0.05976386368274689,
-0.0043707494623959064,
0.003058345289900899,
0.03792420029640198,
0.020518245175480843,
0.025198716670274734,
-0.05252659693360329,
-0.008069543167948723,
-0.011169688776135445,
-0.010369587689638138,
0.02867552824318409,
-0.018144192174077034,
0.02697543241083622,
0.0002576810074970126,
-0.009651528671383858,
-0.0499999076128006,
-0.0030363674741238356,
-0.021453162655234337,
0.01278761588037014,
-0.03947482258081436,
-0.04277705028653145,
0.034891825169324875,
-0.009161645546555519,
-0.08246056735515594,
0.021067773923277855,
-0.012988697737455368,
-0.03972374275326729,
-0.003492229152470827,
-0.007902637124061584,
0.029600944370031357,
-0.03616747632622719,
0.022336149588227272,
-0.008136224001646042,
-0.020958006381988525,
-0.007055297493934631,
-0.048795316368341446,
-0.049504611641168594,
0.03183156996965408,
-0.013118122704327106,
0.011210094206035137,
-0.02991572767496109,
-0.013984058052301407,
0.043408434838056564,
0.02627546712756157,
-0.012926326133310795,
-0.006984735373407602,
0.0250064916908741,
0.004562815651297569,
-0.02575729601085186,
0.00761731993407011,
0.016114285215735435,
-0.0036387844011187553,
0.05744994059205055,
0.01361545454710722,
0.03061843477189541,
0.008850902318954468,
0.011437276378273964,
-0.006488322280347347,
0.050788212567567825,
-0.017479564994573593,
0.009070164524018764,
0.03773104026913643,
0.036384470760822296,
-0.011264470405876637,
-0.017335942015051842,
-0.019485315307974815,
0.010761858895421028,
0.020376386120915413,
-0.05904171243309975,
0.056982770562171936,
-0.0006605159142054617,
0.010655505582690239,
-0.0008528634207323194,
0.011587121523916721,
0.01071123220026493,
-0.04319215193390846,
-0.059078894555568695,
-0.032331664115190506,
0.02635951340198517,
0.019658077508211136,
0.044292036443948746,
0.05353420972824097,
0.023680906742811203,
0.0010113456519320607,
0.001177399535663426,
0.006851593032479286,
-0.028390731662511826,
0.04038465768098831,
-0.016005635261535645,
-0.019088663160800934,
0.031701479107141495,
0.023630306124687195,
-0.006510937120765448,
-0.020557310432195663,
-0.013028698042035103,
-0.03310731053352356,
-0.036228254437446594,
0.02270754612982273,
-0.0505509115755558,
0.033558785915374756,
0.04167628660798073,
0.045664023607969284,
0.029193773865699768,
0.0028424302581697702,
-0.014445753768086433,
-0.00974300503730774,
-0.056248269975185394,
0.028856171295046806,
-0.027560770511627197,
-0.007557903882116079,
-0.012898768298327923,
0.006821546237915754,
0.019164228811860085,
0.010792412795126438,
0.01808316260576248,
-0.026269961148500443,
-0.03231043368577957,
-0.046092741191387177,
0.008760148659348488,
-0.019142912700772285,
-0.02869035303592682,
-0.029252855107188225,
0.03003985993564129,
0.061174772679805756,
-0.010380170308053493,
0.005643860436975956,
0.026633361354470253,
-0.054182156920433044,
0.017377300187945366,
-0.005783966276794672,
0.002522279741242528,
0.019350631162524223,
0.014841875061392784,
0.011202160269021988,
-0.015774978324770927,
0.002343658823519945,
-0.008387458510696888,
-0.003955515567213297,
0.034586746245622635,
0.01656215824186802,
-0.04651310294866562,
-0.0029114261269569397,
-0.02815205417573452,
0.0011847487185150385,
0.01315330807119608,
0.10608648508787155,
0.012105670757591724,
0.018955552950501442,
0.044510241597890854,
-0.010624243877828121,
-0.012915135361254215,
0.0018383197020739317,
0.046189598739147186,
-0.016413193196058273,
-0.010824831202626228,
-0.03610531985759735,
0.002412406262010336,
0.005186789203435183,
-0.0048784115351736546,
-0.008767960593104362,
0.028547657653689384,
-0.0033852022606879473,
-0.022976357489824295,
0.016487967222929,
0.05607035011053085,
0.02016591653227806,
-0.004350221715867519,
0.012725661508738995,
0.008816753514111042,
-0.014560269191861153,
-0.004713683854788542,
-0.01459719892591238,
0.01773807778954506,
0.020235896110534668,
0.04589167982339859,
0.004491506610065699,
-0.024750325828790665,
-0.02665434405207634,
0.023566866293549538,
0.07281506806612015,
0.0180536936968565,
0.01998579502105713,
-0.058877069503068924,
-0.03051372431218624,
0.0425419956445694,
-0.03171069175004959,
0.015570585615932941,
-0.011469410732388496,
-0.017801208421587944,
-0.028503423556685448,
-0.07479314506053925,
-0.03040829673409462,
0.031887151300907135,
0.014753840863704681,
-0.011615228839218616,
-0.04731305316090584,
-0.016929272562265396,
-0.01964632049202919,
0.004430216271430254,
0.006088227964937687,
0.05494345352053642,
0.01306047011166811,
0.023175325244665146,
-0.0037811424117535353,
-0.005128634627908468,
-0.001477599493227899,
-0.10421983152627945,
0.012887299060821533,
0.03335287794470787,
-0.0062720514833927155,
0.03354068845510483,
-0.030091430991888046,
-0.03909732773900032,
-0.002710979664698243,
-0.012752433307468891,
-0.007730281446129084,
0.07843165844678879,
-0.055167555809020996,
0.07313107699155807,
0.019044410437345505,
0.004944230429828167,
0.04681318998336792,
0.035110969096422195,
-0.04483388736844063,
-0.03267107158899307,
-0.013540944084525108,
0.03776516020298004,
-0.009182778187096119,
0.028028246015310287,
-0.022294005379080772,
-0.028365347534418106,
-0.009115103632211685,
0.038865093141794205,
-0.035876668989658356,
0.0158548504114151,
-0.00019138527568429708,
0.014917544089257717,
-0.007107343524694443,
-0.00517401285469532,
-0.008185811340808868,
0.016083022579550743,
-0.030051127076148987,
0.004192552529275417,
0.056258346885442734,
-0.03419871628284454,
0.013055427931249142,
0.00961556937545538,
0.0049364278092980385,
0.0514829158782959,
0.0012441730359569192,
-0.006591719575226307,
-0.0026586619205772877,
-0.03201112523674965,
-0.03816964477300644,
-0.0294340830296278,
-0.007551196962594986,
-0.004358605481684208,
-0.014204715378582478,
0.006682615727186203,
-0.008092525415122509,
-0.03095541149377823,
0.02091144025325775,
-0.0015521469758823514,
0.006423568818718195,
-0.05768901854753494,
-0.02374763786792755,
-0.01358463242650032,
0.02584208734333515,
-0.08190200477838516,
-0.03424007073044777,
-0.00027422505081631243,
-0.02067495696246624,
-0.026567969471216202,
-0.027807746082544327,
-0.01908973604440689,
-0.041948892176151276,
-0.03788875415921211,
0.011490222997963428,
0.03395342081785202,
-0.039525602012872696,
-0.004016649443656206,
-0.010392675176262856,
0.011270994320511818,
0.032509852200746536,
-0.0489325113594532,
-0.006809424143284559,
0.029824819415807724,
-0.0023536423686891794,
-0.021580157801508904,
-0.019808709621429443,
0.028319599106907845,
-0.018294241279363632,
-0.03458588942885399,
-0.0086908470839262,
-0.013401943258941174,
-0.014792082831263542,
-0.00596905080601573,
-0.02074810490012169,
0.027979731559753418,
0.013816076330840588,
0.01980893313884735,
-0.0059486390091478825,
-0.005094235762953758,
0.014867233112454414,
-0.0024257085751742125,
-0.010929875075817108,
0.006697712000459433,
-0.04638693109154701,
-0.029031528159976006,
0.025381887331604958,
-0.03053360804915428,
-0.026967711746692657,
-0.010454188100993633,
0.04603967070579529,
0.03481975942850113,
0.009154570288956165,
0.01496325433254242,
-0.000782518764026463,
-0.006418213248252869,
-0.01934369094669819,
0.0121894720941782,
-0.02019898220896721,
-0.005195064935833216,
-0.03798547759652138,
-0.00707396911457181,
-0.043938323855400085,
0.0196852944791317,
0.05414333567023277,
0.017040837556123734,
0.04275213181972504,
0.014519264921545982,
-0.021985281258821487,
-0.028074445202946663,
-0.015058420598506927,
0.0023248237557709217,
0.030328214168548584,
-0.02084210142493248,
0.021594218909740448,
-0.048550527542829514,
-0.009387089870870113,
0.05180404707789421,
0.015368811786174774,
-0.030531687662005424,
0.014413236640393734,
0.012729921378195286,
0.007590712048113346,
0.04816597327589989,
-0.048393115401268005,
-0.06094058230519295,
0.035406243056058884,
-0.04123628884553909,
0.025057625025510788,
0.0031766302417963743,
-0.026695536449551582,
0.03436173126101494,
0.01110856607556343,
-0.008385147899389267,
0.016859330236911774,
-0.01693628914654255,
-0.04189775884151459,
-0.019329551607370377,
0.02035338059067726,
0.01561425905674696,
0.005940192844718695,
-0.006427084561437368,
0.01948118396103382,
0.01063393335789442,
0.01160094141960144,
0.0012770001776516438,
-0.025130456313490868,
0.0244749803096056,
-0.03672273829579353,
-0.02876604162156582,
0.056601691991090775,
-0.0006668759742751718,
-0.0388249009847641,
-0.005319549702107906,
-0.0211181640625,
0.030522070825099945,
0.024318814277648926,
0.013270003721117973,
-0.04707694426178932,
0.0350581519305706,
-0.005819291342049837,
-0.021368272602558136,
-0.03931508585810661,
0.013727483339607716,
0.12965260446071625,
0.052413322031497955,
0.027607131749391556,
-0.08123509585857391,
-0.010632419027388096,
0.009136035107076168,
0.036384280771017075,
-0.035006292164325714,
0.02564201131463051,
-0.04038361832499504,
-0.038413580507040024,
0.0063910349272191525,
0.0669780969619751,
0.03199682757258415,
-0.03664225712418556,
0.03604007512331009,
-0.05614732578396797,
-0.03278154134750366,
-0.012301161885261536,
0.03019358217716217,
-0.005898511968553066,
-0.018194308504462242,
-0.022211860865354538,
0.00361404987052083,
-0.05683262646198273,
0.04298214614391327,
-0.05175343528389931,
-0.015430256724357605,
0.016865519806742668,
-0.0016728885238990188,
-0.032581619918346405,
-0.021286988630890846,
0.0029537465889006853,
-0.014285965822637081,
-0.02723270282149315,
-0.03827669471502304,
0.02593936398625374,
-0.011373599991202354,
0.04319017380475998,
0.05913905054330826,
0.010831763967871666,
0.0021907968912273645,
0.006030756048858166,
0.009865475818514824,
-0.03758654743432999,
-0.03863532841205597,
-0.03266112878918648,
0.08140741288661957,
-0.003912554122507572,
-0.0293081346899271,
0.02145346999168396,
-0.025417720898985863,
0.012052509933710098,
-0.029286351054906845,
-0.021923858672380447,
-0.014631559140980244,
0.016519732773303986,
0.005901309661567211,
0.029315071180462837,
-0.01171984151005745,
0.04521254822611809,
-0.024586254730820656,
0.008856402710080147,
-0.043822284787893295,
-0.027654048055410385,
-0.03509776294231415,
0.028939979150891304,
0.05272236466407776,
0.015588986687362194,
0.018916621804237366,
0.020714804530143738,
-0.010572548024356365,
-0.025899434462189674,
-0.026091109961271286,
0.015099771320819855,
0.022686544805765152,
0.06653886288404465,
-0.004825563170015812,
0.0017444697441533208,
-0.048923902213573456,
-0.057493917644023895,
-0.004766557365655899,
-0.0060383910313248634,
-0.009836810640990734,
-0.011766609735786915,
-0.022271929308772087,
0.0403914712369442,
0.06356912106275558,
-0.0050831930711865425,
-0.019993022084236145,
-0.01583215780556202,
0.05136764049530029,
0.03688699007034302,
0.000440311647253111,
0.0010591782629489899,
-0.01070296298712492,
-0.018904775381088257,
0.02706357277929783,
-0.0374552346765995,
-0.0031376974657177925,
0.013822367414832115,
0.028907593339681625,
0.023761337623000145,
0.035912368446588516,
-0.014345160685479641,
-0.013729425147175789,
0.023828832432627678,
-0.013462581671774387,
-0.007195890415459871,
0.045850060880184174,
0.0517672523856163,
-0.03968999162316322,
-0.0326676219701767,
-0.012203569523990154,
0.015196631662547588,
-0.03600381687283516,
0.005093364976346493,
-0.02348732016980648,
-0.03359932079911232,
-0.012755299918353558,
0.007409736979752779,
-0.027988562360405922,
-0.01046984363347292,
-0.06336045265197754,
-0.0029591284692287445,
-0.03320253640413284,
0.010555935092270374,
0.027715962380170822,
0.04543990641832352,
-0.004773527383804321,
0.008425717242062092,
0.009250888600945473,
0.03374040871858597,
-0.04123297333717346,
-0.014064067043364048,
0.014757784083485603,
0.030290568247437477,
-0.00417697336524725,
0.02376021258533001,
-0.046088192611932755,
0.007432096637785435,
-0.038261305540800095,
-0.025921035557985306,
0.06297126412391663,
0.004120158962905407,
0.012753530405461788,
0.01513596624135971,
0.012716933153569698,
-0.04318806156516075,
0.06001865118741989,
0.012762774713337421,
-0.021708045154809952,
0.027675893157720566,
-0.057302556931972504,
0.012788782827556133,
0.030527204275131226,
0.02179737202823162,
0.0012822082499042153,
-0.026211997494101524,
0.029131583869457245,
0.01620727963745594,
-0.009728112258017063,
0.010516049340367317,
0.02157493121922016,
-0.027783971279859543,
0.018886862322688103,
-0.008440843783318996,
-0.0019469836261123419,
0.026026377454400063,
0.055451761931180954,
-0.013223986141383648,
0.022881658747792244,
0.018432138487696648,
-0.01857323758304119,
-0.11436419188976288,
-0.0009667387930676341,
-0.0021681273356080055,
0.09439395368099213,
0.02861621230840683,
-0.04891365393996239,
-0.003774805925786495,
0.011479676701128483,
-0.07009857892990112,
0.03555355593562126,
-0.012807464227080345,
0.01657072640955448,
-0.03725283965468407,
0.006684326101094484,
-0.050924479961395264,
0.05562453344464302,
0.039284270256757736,
0.05597592517733574,
-0.024392947554588318,
0.05559379607439041,
-0.015285991132259369,
0.005051413085311651,
-0.038113951683044434,
0.005773295182734728,
0.018068823963403702,
-0.008978599682450294,
0.05677742138504982,
-0.015084943734109402,
-0.0017015434568747878,
0.03371967747807503,
0.03452262282371521,
-0.01242114044725895,
-0.055460747331380844,
0.027433304116129875,
0.03513088449835777,
0.016696307808160782,
0.03739974647760391,
0.026590676978230476,
0.03688919171690941,
-0.026893718168139458,
0.046500857919454575,
0.03391740843653679,
-0.03953765705227852,
-0.036919668316841125,
-0.0049300724640488625,
-0.037834249436855316,
-0.05234226956963539,
0.046141885221004486,
-0.004540835041552782,
-0.013713325373828411,
0.01687183789908886,
0.011629573069512844,
-0.0026404387317597866,
0.01834087260067463,
0.03954251483082771,
-0.05184502527117729,
-0.027111483737826347,
0.0205868910998106,
0.005986236967146397,
-0.011840780265629292,
0.0039706784300506115,
-0.03939363732933998,
-0.03007451258599758,
0.06456392258405685,
0.005156983155757189,
0.024596886709332466,
-0.05173622816801071,
-0.02133954130113125,
-0.02343149110674858,
0.0022198481019586325,
0.027056479826569557,
-0.027896936982870102,
-0.0322137326002121,
0.004093731753528118,
-0.003302141558378935,
0.015607630833983421,
-0.008206695318222046,
0.0033790303859859705,
-0.004966372158378363,
-0.062059566378593445,
0.022624755278229713,
0.05926878750324249,
-0.0024472421500831842,
-0.042351286858320236,
-0.024562545120716095,
-0.01144479401409626,
0.02227281592786312,
0.05217456817626953,
-0.009730227291584015,
-0.04272713512182236,
0.04103092476725578,
-0.006399698089808226,
0.0325261615216732,
-0.03243166208267212,
0.0008508769096806645,
0.0030756168998777866,
0.023873774334788322,
0.023001573979854584,
0.0014807535335421562,
-0.012782834470272064,
0.02189893089234829,
-0.0009320404496975243,
0.01516105979681015,
0.02535088360309601,
0.021216455847024918,
-0.0710582584142685,
0.039896946400403976,
0.009884115308523178,
0.014572973363101482,
0.07264581322669983,
0.0013480259804055095,
0.007536063436418772,
0.02787957340478897,
-0.0572211816906929,
-0.04464046657085419,
0.01565140299499035,
-0.01778286136686802,
-0.023161152377724648,
0.007308256346732378,
-0.005544697865843773,
-0.006924557499587536,
-0.025052327662706375,
0.002917962148785591,
0.07725608348846436,
-0.011641965247690678,
-0.042468320578336716,
0.06673824787139893,
0.008955772034823895,
0.04740123450756073,
0.033294178545475006,
0.011956187896430492,
0.03387003391981125,
0.016724303364753723,
0.047533489763736725,
0.00398511067032814,
0.03522346168756485,
-0.015655258670449257,
-0.01844489388167858,
-0.008009005337953568,
-0.03098544478416443,
0.01956615224480629,
0.0068648699671030045,
0.016620904207229614,
-0.018878309056162834,
0.017854120582342148,
0.053954239934682846,
-0.002529613208025694,
0.01932119019329548,
0.0323583148419857,
-0.027867263182997704,
0.060710757970809937,
-0.014639425091445446,
0.03831203654408455,
-0.002715149661526084,
0.0038089666049927473,
-0.03943812474608421,
0.037752214819192886,
0.02926916815340519,
0.0552336759865284,
-0.03160235285758972,
-0.028031138703227043,
-0.05527074635028839,
-0.014991100877523422,
-0.010650413110852242,
-0.05341430753469467,
-0.01679912395775318,
0.010220861062407494,
0.0006179320625960827,
0.041201796382665634,
-0.044142283499240875,
-0.014391344040632248,
-0.023814158514142036,
0.008551286533474922,
0.03518478199839592,
0.0292064156383276,
-0.017093731090426445,
0.04622839018702507,
-0.022707022726535797,
0.05275999382138252,
-0.04790293425321579,
0.019830958917737007,
0.008055146783590317,
0.0369468554854393,
-0.011241591535508633,
0.005438181106001139
] |
<p>Is it possible to have a VEV (vacuum expectation value) for tensor field? I am mainly concerned about second rank tensors. It seems it can have a VEV which will be proportional to the metric tensor (in flat space-time). Does this make any sense at all? If it does, then what are it's implications?</p>
| 10,690 |
[
-0.040756452828645706,
0.0028633049223572016,
0.005385024007409811,
-0.04636706784367561,
0.06380700320005417,
0.04065284505486488,
-0.026708099991083145,
-0.012732473202049732,
-0.012639452703297138,
-0.07051006704568863,
-0.005903440061956644,
-0.0025658041704446077,
0.03956601768732071,
0.0126289501786232,
0.010953179560601711,
0.008358558639883995,
0.009194856509566307,
0.004595278296619654,
-0.029984157532453537,
-0.04144776239991188,
0.024577250704169273,
0.07064174115657806,
0.02028275467455387,
-0.00683623319491744,
-0.005400034599006176,
0.02333075925707817,
0.007377967704087496,
0.004064491484314203,
-0.0011650160886347294,
0.06969607621431351,
-0.01580313965678215,
-0.004237066023051739,
0.017661284655332565,
0.026896463707089424,
-0.0003405976458452642,
-0.006437396630644798,
-0.023742573335766792,
-0.022673454135656357,
-0.007596474140882492,
-0.011384045705199242,
0.003818647703155875,
0.002823529066517949,
-0.023340849205851555,
0.06298242509365082,
0.02307174913585186,
0.03138811141252518,
0.03241787850856781,
0.005565506871789694,
0.04101010784506798,
-0.039603207260370255,
0.07140803337097168,
0.0251438207924366,
0.02865094318985939,
0.03301895409822464,
-0.03492289409041405,
0.013867580331861973,
0.05203554034233093,
0.03903903439640999,
-0.004784716758877039,
-0.02612411044538021,
-0.021046539768576622,
-0.019438611343503,
0.006985792890191078,
-0.021256448701024055,
0.015474795363843441,
0.03654097765684128,
-0.022036327049136162,
0.0019003277411684394,
0.027878882363438606,
-0.001549675827845931,
0.025969071313738823,
0.0075157685205340385,
0.03228932246565819,
-0.02153663896024227,
0.0202511977404356,
0.009937174618244171,
0.037661027163267136,
-0.0016691443743184209,
0.025398733094334602,
0.010199223645031452,
0.006204472854733467,
-0.006902050692588091,
0.048884548246860504,
0.03733667731285095,
0.01296543050557375,
0.028744904324412346,
0.03074551373720169,
-0.03546338900923729,
0.026282142847776413,
0.06758079677820206,
0.005305547267198563,
-0.034575704485177994,
0.06395024061203003,
-0.00662874523550272,
-0.055783651769161224,
-0.004176491871476173,
0.010223773308098316,
0.05542673543095589,
0.017588527873158455,
-0.027160851284861565,
-0.008667431771755219,
-0.0020922671537846327,
-0.017725368961691856,
0.06722456216812134,
0.011732984334230423,
-0.03266783058643341,
-0.05202129855751991,
0.01480130199342966,
-0.038380395621061325,
-0.025669340044260025,
-0.05158465355634689,
-0.011179567314684391,
-0.019211310893297195,
0.014191905036568642,
0.020805122330784798,
-0.054629623889923096,
0.0328889861702919,
-0.03518356382846832,
0.044662054628133774,
0.0903620645403862,
0.045517709106206894,
-0.005094974767416716,
0.03611357510089874,
-0.018793238326907158,
-0.05127662792801857,
0.00703498674556613,
0.06253505498170853,
-0.0042129443027079105,
-0.025524480268359184,
-0.00989219918847084,
-0.0032409895211458206,
-0.03261711448431015,
0.017881907522678375,
0.006824915762990713,
0.04476763308048248,
-0.03251061961054802,
-0.0720338374376297,
-0.048267219215631485,
-0.012533777393400669,
-0.011957635171711445,
-0.00627991184592247,
-0.06710314005613327,
0.024748023599386215,
0.07000724971294403,
0.04884500056505203,
0.02099870704114437,
0.014411230571568012,
-0.016774024814367294,
0.06175299361348152,
0.01102139987051487,
-0.04182081297039986,
-0.0403623953461647,
-0.028843870386481285,
-0.03683249652385712,
0.008550337515771389,
-0.09287697076797485,
-0.011075797490775585,
0.013431264087557793,
0.008788974024355412,
-0.0157382320612669,
0.05152938887476921,
0.0008820020593702793,
0.013660469092428684,
0.008014146238565445,
0.003901002462953329,
-0.020354533568024635,
0.0280449315905571,
-0.016369273886084557,
0.030313722789287567,
-0.0034709773026406765,
0.018181173130869865,
-0.007224519271403551,
0.05349946767091751,
0.0592920295894146,
0.03060292638838291,
-0.04654912278056145,
-0.023751627653837204,
-0.03305043652653694,
0.07531621307134628,
-0.0039725215174257755,
-0.02823423221707344,
-0.03440144285559654,
-0.031305406242609024,
0.02660483308136463,
-0.033183012157678604,
0.006580657791346312,
-0.013327511958777905,
0.006777304224669933,
0.003910412080585957,
-0.043660786002874374,
0.014142176136374474,
-0.031114058569073677,
0.016778025776147842,
0.025487521663308144,
-0.017505858093500137,
-0.00022949965205043554,
0.028686853125691414,
0.026384083554148674,
-0.07692127674818039,
-0.02993374690413475,
0.00036040745908394456,
0.05686815083026886,
0.006371490657329559,
-0.020033933222293854,
0.0154050188139081,
-0.003888014703989029,
0.02420452982187271,
0.014547951519489288,
0.02424856834113598,
0.019585562869906425,
-0.040050797164440155,
0.030323563143610954,
-0.0005993408849462867,
0.02539542317390442,
-0.022712141275405884,
-0.00162873649969697,
-0.000055361586419167,
-0.00031316341483034194,
0.0055089071393013,
0.04534272477030754,
-0.0376744344830513,
0.05362632870674133,
0.04864925146102905,
0.0020186437759548426,
-0.004230831749737263,
0.05856145918369293,
0.001949152210727334,
-0.0037013511173427105,
-0.007301753386855125,
-0.03558376803994179,
-0.023332366719841957,
0.02462192066013813,
0.045032188296318054,
0.046539075672626495,
-0.036098796874284744,
0.008213342167437077,
0.05429396033287048,
-0.004698954988270998,
0.028623465448617935,
0.04776052385568619,
-0.024564146995544434,
-0.04044542461633682,
0.02172454446554184,
-0.0031218703370541334,
0.060766711831092834,
0.006663271691650152,
0.026770561933517456,
0.013077340088784695,
0.03160125017166138,
-0.021596208214759827,
0.005075529683381319,
0.02026963047683239,
0.007434619124978781,
0.003926161676645279,
0.011679011397063732,
-0.007956285029649734,
0.04095781221985817,
0.00013537175254896283,
0.04067312553524971,
0.04185633733868599,
-0.0021285738330334425,
-0.004014299716800451,
-0.05169159919023514,
-0.0017386702820658684,
0.04028663784265518,
-0.0005325773963704705,
-0.025343285873532295,
-0.030604485422372818,
0.004076636862009764,
-0.052686236798763275,
0.008315903134644032,
0.020191878080368042,
-0.005312707275152206,
-0.00919624324887991,
-0.005082081072032452,
0.047312043607234955,
-0.012789815664291382,
0.01883111707866192,
0.002797923982143402,
-0.030824098736047745,
0.013384073972702026,
-0.005561082623898983,
-0.01809595339000225,
0.017157910391688347,
-0.059424735605716705,
0.03781309723854065,
-0.046252842992544174,
-0.07223764806985855,
0.024974366649985313,
-0.03561699017882347,
0.0270218662917614,
0.05000405013561249,
-0.01469405647367239,
-0.013359345495700836,
-0.007161227986216545,
-0.04811830446124077,
0.016958048567175865,
0.001150717493146658,
0.027550462633371353,
0.013799996115267277,
-0.024526521563529968,
-0.06823766231536865,
-0.0015660964418202639,
0.007900267839431763,
-0.05442386120557785,
-0.03189845010638237,
-0.0013557795900851488,
0.010537059046328068,
-0.058420199900865555,
0.0682067722082138,
0.05291455611586571,
-0.029329821467399597,
0.01796155981719494,
-0.06159868463873863,
-0.031138965860009193,
0.0222933292388916,
-0.005698978900909424,
0.047913409769535065,
-0.006516729947179556,
-0.07453227788209915,
0.09351638704538345,
0.02972223423421383,
-0.03279311954975128,
-0.012506554834544659,
-0.005599175114184618,
-0.005939285736531019,
-0.027847876772284508,
-0.016820933669805527,
-0.010100532323122025,
0.007638711482286453,
0.02945525385439396,
0.03760388493537903,
0.03843788430094719,
0.025661863386631012,
0.014614960178732872,
-0.03921320289373398,
-0.001934556756168604,
0.029264628887176514,
-0.0006325400900095701,
0.037546027451753616,
0.025989675894379616,
-0.0001640196132939309,
-0.005265796557068825,
0.027426691725850105,
0.029577748849987984,
-0.025459541007876396,
0.00033324488322250545,
0.0591893196105957,
-0.0014598621055483818,
0.017612114548683167,
-0.03194144368171692,
0.023893723264336586,
0.009848308749496937,
0.027848253026604652,
-0.009658602066338062,
0.0195199865847826,
-0.008337332867085934,
-0.019793296232819557,
0.0394926518201828,
0.03506090119481087,
-0.0004632911295630038,
-0.023010630160570145,
-0.011406604200601578,
-0.022254465147852898,
-0.013532097451388836,
0.029274359345436096,
-0.020963342860341072,
-0.024227824062108994,
0.04303761199116707,
0.05245811119675636,
0.010587084107100964,
0.007729990873485804,
-0.024723492562770844,
0.003981071524322033,
-0.03173741698265076,
0.010084535926580429,
0.010146538726985455,
0.015900868922472,
0.04445059597492218,
0.010554628446698189,
0.014852656982839108,
0.022106880322098732,
0.002236731816083193,
-0.039484523236751556,
-0.07081297785043716,
-0.026541363447904587,
-0.0659416988492012,
0.00045612305984832346,
-0.02836553193628788,
-0.03130213916301727,
-0.019173163920640945,
-0.03234390169382095,
-0.028620606288313866,
-0.008723875507712364,
0.018691323697566986,
-0.06544974446296692,
0.01142487209290266,
-0.01828380674123764,
-0.02714412473142147,
-0.01067410409450531,
0.03021480329334736,
0.042255885899066925,
-0.020823609083890915,
-0.006423350423574448,
0.019221937283873558,
-0.023790519684553146,
-0.02180284447968006,
-0.0018136638682335615,
0.037875253707170486,
0.028661273419857025,
0.015290098264813423,
0.038888461887836456,
-0.0029368193354457617,
-0.03454156965017319,
0.008554982952773571,
0.029593389481306076,
0.08659972995519638,
0.026689166203141212,
-0.021383287385106087,
-0.008995226584374905,
-0.06178794428706169,
-0.03022383153438568,
-0.019972283393144608,
0.05864040181040764,
-0.01407704595476389,
-0.012547232210636139,
0.016110189259052277,
-0.008690317161381245,
-0.05093558877706528,
0.017714252695441246,
0.0748964250087738,
-0.025108397006988525,
-0.03153916820883751,
-0.06005188822746277,
0.004562537185847759,
0.002461202209815383,
-0.013739212416112423,
0.011164801195263863,
-0.007072885986417532,
-0.05031276494264603,
-0.0032911603339016438,
-0.003107698867097497,
0.005082474555820227,
-0.03786935657262802,
0.012542765587568283,
0.02625134401023388,
0.02728499099612236,
-0.009441344067454338,
0.0016741513973101974,
-0.0057103075087070465,
0.024799786508083344,
0.03678993880748749,
0.013468489982187748,
0.013420719653367996,
-0.0765027403831482,
-0.0029693725518882275,
0.0008172430680133402,
0.02370286174118519,
0.00675036758184433,
-0.021734580397605896,
-0.015821227803826332,
-0.018230142071843147,
0.041878413408994675,
-0.024820663034915924,
-0.001389920013025403,
0.02812432125210762,
-0.0340941920876503,
-0.008439647033810616,
0.016752587631344795,
-0.016474060714244843,
0.046677570790052414,
-0.028487877920269966,
-0.03378733620047569,
-0.032613225281238556,
0.025561202317476273,
-0.020717041566967964,
0.04141295701265335,
0.017733849585056305,
0.028318824246525764,
0.03590953350067139,
0.02599240466952324,
-0.006307458970695734,
0.048111263662576675,
-0.03543776646256447,
-0.0551273375749588,
0.020261462777853012,
0.04526915028691292,
-0.018273813650012016,
0.006339936517179012,
0.01872931979596615,
-0.01910327561199665,
0.05157181993126869,
0.004719829652458429,
0.002461746335029602,
0.03535044938325882,
-0.03249816223978996,
0.055904943495988846,
0.006925920955836773,
0.012447535991668701,
0.04512045532464981,
0.0134785957634449,
0.007423826958984137,
0.0002778892230708152,
-0.018695298582315445,
0.06357213109731674,
-0.04404454678297043,
0.02927745133638382,
-0.045859210193157196,
0.0013386440696194768,
-0.043478019535541534,
0.04740453138947487,
-0.02272561565041542,
0.018314814195036888,
-0.005540208891034126,
-0.010998748242855072,
0.0020226535852998495,
0.034295953810214996,
0.033717572689056396,
-0.043165773153305054,
-0.004951959475874901,
-0.0032337261363863945,
0.0039991168305277824,
-0.0466223880648613,
-0.02128213830292225,
0.00569049222394824,
-0.005915079265832901,
0.012675301171839237,
0.005143070127815008,
0.03243822976946831,
0.02622339501976967,
0.010492675006389618,
0.02867797575891018,
-0.03623194247484207,
0.03451358154416084,
0.008710564114153385,
-0.027723457664251328,
0.005121077410876751,
0.005881170276552439,
-0.0003574840084183961,
0.03236282616853714,
-0.018056683242321014,
0.02249845117330551,
-0.04507238790392876,
0.013724671676754951,
0.03452112525701523,
0.033402107656002045,
-0.08013445883989334,
0.00029241087031550705,
0.028391893953084946,
-0.016331437975168228,
-0.02045201137661934,
-0.01356756966561079,
-0.007871541194617748,
-0.05258969962596893,
0.0029089171439409256,
0.01257982850074768,
0.08102665841579437,
-0.0259082093834877,
0.00105879339389503,
-0.04037719592452049,
0.03405991941690445,
-0.00015639547200407833,
-0.013115322217345238,
-0.0048850104212760925,
0.019750148057937622,
0.004244941286742687,
-0.009768851101398468,
0.02019999362528324,
0.05263689160346985,
-0.0143557945266366,
-0.012041527777910233,
-0.03274476155638695,
-0.007524213753640652,
0.01255706138908863,
-0.007137330714613199,
0.0008463968406431377,
0.040286242961883545,
0.01025412417948246,
-0.010495956055819988,
-0.02645161934196949,
0.007299478631466627,
0.003500200342386961,
0.01885608583688736,
-0.01416508387774229,
-0.012923664413392544,
-0.02423097752034664,
-0.028901254758238792,
0.016429169103503227,
0.0004859347245655954,
0.03346402570605278,
-0.05384631082415581,
0.04734421893954277,
0.013152765110135078,
-0.014530614018440247,
-0.011582253500819206,
-0.041285932064056396,
-0.020610447973012924,
0.044090043753385544,
-0.009136412292718887,
0.04363798722624779,
0.004015222657471895,
-0.05829828232526779,
-0.035134732723236084,
-0.03353926166892052,
-0.0009034408139996231,
0.11133059859275818,
-0.03456475958228111,
0.05085247755050659,
0.02462693862617016,
-0.015113932080566883,
-0.020819034427404404,
-0.006520298775285482,
-0.038908835500478745,
0.016047505661845207,
-0.017420437186956406,
0.010231374762952328,
-0.016900712624192238,
-0.005885266698896885,
-0.010110468603670597,
0.023574482649564743,
-0.01781124621629715,
0.05325824394822121,
-0.0024030618369579315,
0.03824058547616005,
0.016610275954008102,
0.023321226239204407,
-0.049812640994787216,
0.02247336320579052,
-0.032063983380794525,
-0.004092210903763771,
-0.00975389126688242,
0.022495929151773453,
0.032887812703847885,
-0.0062690433114767075,
0.004836170934140682,
-0.03716161474585533,
-0.0633869394659996,
-0.04534762352705002,
0.009646602906286716,
0.03694410249590874,
0.02056552655994892,
-0.00665507186204195,
0.033429890871047974,
0.040165647864341736,
0.016226153820753098,
0.027170011773705482,
-0.0036540143191814423,
-0.051118433475494385,
-0.023761149495840073,
-0.06180482357740402,
-0.013834725134074688,
0.046750765293836594,
0.022664610296487808,
-0.05310807749629021,
-0.03468620032072067,
-0.05163850262761116,
0.033060137182474136,
-0.025430642068386078,
0.04293331503868103,
-0.0023800625931471586,
0.06362927705049515,
-0.0015878506237640977,
0.03734571859240532,
-0.03552169352769852,
0.02751925401389599,
0.118084616959095,
0.07114140689373016,
0.01617242395877838,
-0.06044476106762886,
0.009940032847225666,
-0.0028046725783497095,
-0.0034166458062827587,
-0.04726974666118622,
0.028531057760119438,
-0.027636859565973282,
-0.0002479522372595966,
0.014151880517601967,
0.04084642976522446,
-0.0017798696644604206,
-0.04496518522500992,
0.058398034423589706,
-0.02432560734450817,
-0.044289957731962204,
-0.006911398842930794,
0.032728295773267746,
-0.002305317670106888,
0.01081392914056778,
-0.007105681579560041,
0.03396786376833916,
0.002554794307798147,
0.05569092184305191,
-0.03566233441233635,
0.031852759420871735,
-0.015431617386639118,
-0.007105499971657991,
-0.03524574264883995,
0.002435605274513364,
0.002902889158576727,
0.01945384219288826,
-0.07633602619171143,
-0.02387923188507557,
0.01613292284309864,
0.006081796251237392,
0.02212601900100708,
-0.0014745916705578566,
0.0087219113484025,
0.022175880149006844,
0.01519055850803852,
0.022969970479607582,
-0.052540674805641174,
-0.004697641357779503,
-0.0076758237555623055,
0.07660835981369019,
0.0016657017404213548,
0.017896603792905807,
0.020657621324062347,
-0.024775810539722443,
0.007582342717796564,
-0.04174596071243286,
-0.03803971782326698,
-0.015639718621969223,
0.00844287034124136,
0.0054131560027599335,
0.010973523370921612,
-0.040306076407432556,
0.03487987443804741,
0.005695813801139593,
0.021633435040712357,
-0.005976295098662376,
-0.03118846006691456,
-0.023847706615924835,
-0.016179369762539864,
0.08195380121469498,
-0.03126778081059456,
-0.034982047975063324,
-0.014037204906344414,
-0.0273037850856781,
-0.034015074372291565,
-0.044448234140872955,
-0.006467743311077356,
-0.015621067024767399,
0.012161052785813808,
-0.019334688782691956,
-0.011252015829086304,
-0.000029401513529592194,
-0.0449337363243103,
0.004788473714143038,
-0.039284318685531616,
-0.028102396056056023,
-0.04671629145741463,
0.049969419836997986,
0.01951124146580696,
0.024118511006236076,
-0.075694739818573,
0.0019163156393915415,
0.006709246430546045,
0.015912305563688278,
0.020966684445738792,
-0.013160424306988716,
0.007512858137488365,
-0.0040651652961969376,
-0.02491762675344944,
0.002139490796253085,
-0.029327357187867165,
0.008768070489168167,
0.022787410765886307,
0.019367467612028122,
-0.0176012571901083,
0.0045197028666734695,
-0.02574763633310795,
0.021480590105056763,
0.008123783394694328,
-0.045604392886161804,
0.0324351005256176,
-0.0010265199234709144,
-0.011796127073466778,
-0.05480053275823593,
-0.038659583777189255,
-0.016260329633951187,
-0.031889695674180984,
-0.003485598135739565,
0.002211124636232853,
-0.030051568523049355,
-0.010480762459337711,
-0.0055549549870193005,
0.01812981627881527,
-0.03726295381784439,
-0.03853418305516243,
-0.014293204993009567,
0.031633902341127396,
-0.020987145602703094,
-0.012384964153170586,
-0.014686883427202702,
0.02870084159076214,
-0.04505440965294838,
-0.02019331604242325,
0.005653103813529015,
0.012330599129199982,
-0.032722294330596924,
0.010970561765134335,
0.03919101133942604,
-0.0008753358852118254,
0.0617731548845768,
0.01997908018529415,
-0.04526638984680176,
0.007203042507171631,
-0.025350842624902725,
-0.04706801846623421,
0.038176294416189194,
0.02119126170873642,
0.05113746225833893,
0.02443419210612774,
-0.01771765947341919,
-0.029838087037205696,
0.07140719145536423,
-0.013812261633574963,
0.00476180762052536,
0.013063200749456882,
-0.08600423485040665,
-0.03087177872657776,
-0.028128542006015778,
0.012930460274219513,
-0.0016234219074249268,
-0.005195766221731901,
0.005179389379918575,
0.009252401068806648,
-0.031301986426115036,
-0.034278322011232376,
0.023956820368766785,
-0.01136433519423008,
0.015495496802031994,
0.006221086252480745,
-0.007406482473015785,
0.008531233295798302,
0.03972854092717171,
-0.021865075454115868,
0.015575374476611614,
0.03791572526097298,
0.02358807809650898,
-0.08907310664653778,
0.016414524987339973,
0.009473688900470734,
0.027240652590990067,
0.04746721684932709,
-0.07205681502819061,
0.0033756776247173548,
0.009670604951679707,
-0.03196828067302704,
0.03853408992290497,
-0.020011864602565765,
-0.03384968265891075,
-0.05349041149020195,
-0.003041155869141221,
-0.015538630075752735,
0.01025522779673338,
0.0714680477976799,
0.04321824014186859,
0.02695203758776188,
-0.0001998971274588257,
0.024367474019527435,
-0.036211345344781876,
-0.040211331099271774,
0.04693719744682312,
-0.022525504231452942,
-0.04061712324619293,
0.07044237852096558,
-0.018519744277000427,
-0.027382666245102882,
0.015882667154073715,
-0.008240181021392345,
-0.038223858922719955,
0.0015157993184402585,
0.013938038609921932,
0.020573889836668968,
0.03434019908308983,
0.010918516665697098,
-0.01652625948190689,
-0.01321248710155487,
-0.003152876626700163,
0.0015188916586339474,
-0.015133813954889774,
-0.016165191307663918,
0.018603025004267693,
0.029433757066726685,
-0.026276884600520134,
0.01299319975078106,
0.031226029619574547,
-0.020774343982338905,
-0.058934278786182404,
-0.008852171711623669,
-0.020979713648557663,
0.008824658580124378,
-0.035065703094005585,
0.0272380243986845,
-0.04681335762143135,
-0.004089161287993193,
0.027481067925691605,
0.007587275002151728,
-0.020351560786366463,
0.025094572454690933,
-0.01916765421628952,
-0.019763855263590813,
0.03960365056991577,
0.023935727775096893,
0.008864962495863438,
-0.096393883228302,
0.0036335752811282873,
-0.026638971641659737,
-0.016991516575217247,
0.030951498076319695,
-0.060994260013103485,
-0.02089660055935383,
0.055675484240055084,
0.006106986664235592,
0.05027604103088379,
-0.0300789512693882,
0.00966176949441433,
-0.02670208550989628,
-0.06728166341781616,
0.02659330703318119,
-0.015208830125629902,
-0.01158860418945551,
0.006664965767413378,
0.006068702321499586,
-0.006121234968304634,
-0.006199090741574764,
0.023132987320423126,
-0.017753366380929947,
-0.025037655606865883,
0.011552060954272747,
0.007245281711220741,
0.006583614740520716,
-0.040096551179885864,
-0.032922327518463135,
-0.013682465068995953,
-0.01667756401002407,
0.0033601538743823767,
-0.023087045177817345,
0.011554536409676075,
0.023445511236786842,
0.010682704858481884,
-0.031117910519242287,
0.027212046086788177,
-0.0023530242033302784,
-0.017125217244029045,
0.036761973053216934,
0.01931948959827423,
-0.008954725228250027,
0.05091318488121033,
-0.007089408580213785,
-0.007209962699562311,
0.001117634354159236,
-0.005418348591774702,
-0.023442234843969345,
-0.0019495143787935376,
-0.030931811779737473,
-0.042996011674404144,
-0.003834506031125784,
0.02136382833123207,
-0.000891914707608521,
-0.03068465180695057,
-0.04255697503685951,
0.08137568831443787,
-0.06595408171415329,
0.01596079021692276,
0.04742416739463806,
-0.019033685326576233,
0.022590534761548042,
0.0036957019474357367,
0.045997511595487595,
0.033764179795980453,
0.0007643598946742713,
0.03278786689043045,
0.03271123766899109,
0.0367678701877594,
0.0005568861961364746,
0.0034202286042273045,
0.0048300581984221935,
-0.039402201771736145,
0.02584248222410679,
0.0176071934401989,
0.05122904106974602,
-0.05360979214310646,
-0.0384732224047184,
0.011705951765179634,
0.02011720836162567,
0.0326114147901535,
0.0031462940387427807,
-0.018432047218084335,
0.05863399803638458,
-0.007448220159858465,
-0.0010116066550835967,
-0.0555005706846714,
0.011626382358372211,
-0.02273530699312687,
0.04497138410806656,
0.024820862337946892,
0.034528378397226334,
0.02601320669054985,
-0.0027487599290907383,
0.002974577248096466,
-0.0022537957411259413,
-0.009091606363654137,
-0.035549990832805634,
0.016856234520673752,
0.014580884017050266,
-0.027084413915872574,
0.014291652478277683,
-0.009728516452014446,
-0.013434918597340584,
-0.009756152518093586,
0.01011559646576643,
0.0048675499856472015,
0.05468319356441498,
-0.012993574142456055,
-0.008750101551413536,
-0.011602245271205902,
0.055403631180524826,
-0.054744306951761246,
-0.005654867738485336,
-0.0171994436532259,
-0.0013486547395586967,
-0.0076330737210810184,
-0.004329462070018053
] |
<p>In the coordinate representation, in 1D, the wave function depends on space and time, $\Psi(x,t)$, accordingly the time dependent Schrodinger equation is </p>
<p>$$H\Psi(x,t) = i\hbar\frac{\partial}{\partial t}\Psi(x,t)$$</p>
<p>In a representation-free notations we deal instead with the ket $|\Psi\rangle = |\Psi(t)\rangle$. Now how to write Schrodinger equation in this case?
I find some books write</p>
<p>$$H|\Psi\rangle = i\hbar\frac{\partial}{\partial t}|\Psi\rangle$$</p>
<p>and others write</p>
<p>$$H|\Psi\rangle = i\hbar\frac{d}{dt}|\Psi\rangle$$</p>
<p>So which one of the last 2 equations is correct?</p>
| 10,691 |
[
0.030568337067961693,
-0.026011371985077858,
0.0024621537886559963,
-0.03350010886788368,
0.0131836561486125,
-0.02479301020503044,
-0.0442456416785717,
0.00032313287374563515,
0.01784951612353325,
-0.014428559690713882,
0.05401471629738808,
0.024744508787989616,
0.06100164353847504,
-0.005010959226638079,
0.04420233890414238,
0.04589954763650894,
0.011826029047369957,
-0.011019223369657993,
-0.04020709544420242,
-0.04467173293232918,
0.015402092598378658,
0.014552980661392212,
0.004343230742961168,
0.002317009726539254,
-0.012637186795473099,
0.049297500401735306,
0.0004880136111751199,
0.05590144917368889,
0.017006922513246536,
0.06736146658658981,
0.001425660797394812,
-0.039427611976861954,
-0.004694520030170679,
0.04684441164135933,
-0.02012461982667446,
-0.023987894877791405,
-0.03458865359425545,
-0.031062018126249313,
-0.0183668565005064,
-0.02439168468117714,
-0.029945313930511475,
-0.020108835771679878,
0.006506280042231083,
0.02627122774720192,
0.003368712030351162,
0.03582033887505531,
0.001246456173248589,
-0.01896941103041172,
0.041889045387506485,
-0.050851009786129,
0.07615458965301514,
-0.012886305339634418,
0.03146616369485855,
0.011565889231860638,
-0.039931271225214005,
0.018041323870420456,
0.07650968432426453,
0.07468396425247192,
-0.00785443838685751,
-0.06981112062931061,
-0.0015223445370793343,
-0.03513254225254059,
0.02638884074985981,
-0.008782385848462582,
-0.009960480034351349,
0.007975444197654724,
-0.010593256913125515,
-0.02970203384757042,
0.015233025886118412,
-0.011561192572116852,
0.020587008446455002,
-0.018697742372751236,
0.048837143927812576,
-0.054255109280347824,
0.018898114562034607,
-0.010050790384411812,
0.017785124480724335,
0.012845569290220737,
0.04480430856347084,
0.0293135903775692,
-0.01571502722799778,
0.013337302021682262,
0.039045821875333786,
0.0048828828148543835,
-0.01975741796195507,
-0.021911153569817543,
0.08762512356042862,
0.034603048115968704,
-0.00615934282541275,
0.0287486482411623,
-0.021928323432803154,
0.026664214208722115,
0.040989458560943604,
-0.013492567464709282,
0.00652681291103363,
0.04057672619819641,
-0.006518002599477768,
0.06862573325634003,
-0.016504675149917603,
-0.039073046296834946,
0.019047804176807404,
-0.0513358935713768,
0.007989327423274517,
0.05719656124711037,
-0.03359808772802353,
0.002668643370270729,
-0.045264650136232376,
0.026328014209866524,
-0.02212142013013363,
-0.018463751301169395,
-0.05637267604470253,
0.0478590726852417,
-0.027436839416623116,
0.027465859428048134,
-0.013055611401796341,
-0.044474709779024124,
0.028113307431340218,
0.004340951330959797,
0.05397943779826164,
0.07352648675441742,
0.019262727349996567,
-0.04080250859260559,
0.015408802777528763,
0.024230647832155228,
-0.07755211740732193,
0.02800600603222847,
0.035813841968774796,
-0.008471864275634289,
-0.05276479944586754,
0.03210531175136566,
-0.02065207064151764,
-0.01058240607380867,
0.032746877521276474,
0.0012153969146311283,
0.03723696619272232,
-0.03242343291640282,
-0.10096751153469086,
-0.06932465732097626,
-0.014319813810288906,
-0.04116388410329819,
-0.03275390341877937,
-0.0753529965877533,
0.022354785352945328,
0.021346043795347214,
0.07551190257072449,
-0.023168528452515602,
0.023595178499817848,
0.011773583479225636,
0.009140788577497005,
0.0005233286647126079,
-0.026000335812568665,
-0.0591006837785244,
0.01930425688624382,
-0.038316428661346436,
0.00952109694480896,
-0.011398707516491413,
0.015484820120036602,
0.03224359080195427,
0.015270937234163284,
0.0032887544948607683,
0.09663885831832886,
-0.0307660810649395,
-0.005042528733611107,
0.03371710330247879,
0.0017082778504118323,
-0.04427152872085571,
0.07926937192678452,
0.01274181343615055,
0.05638031288981438,
0.02985849790275097,
0.029713451862335205,
0.014665673486888409,
-0.03287699818611145,
0.01568068377673626,
0.004550635814666748,
-0.025804905220866203,
-0.011984767392277718,
-0.01918184384703636,
-0.017387300729751587,
0.003516834694892168,
-0.003529536072164774,
-0.018804484978318214,
-0.0024026220198720694,
0.006942248437553644,
0.01724601909518242,
0.03430665656924248,
-0.0052181691862642765,
0.009028075262904167,
-0.046718474477529526,
-0.022054098546504974,
-0.00035529991146177053,
-0.027643723413348198,
0.016001544892787933,
-0.002883582143113017,
0.0071813855320215225,
0.06248774379491806,
0.016683561727404594,
0.009474585764110088,
-0.014491794630885124,
-0.04636763408780098,
-0.027675068005919456,
0.014490021392703056,
-0.01804518513381481,
-0.05324121192097664,
0.023385118693113327,
0.06175117939710617,
0.0429510697722435,
0.021373029798269272,
0.009365474805235863,
-0.009264040738344193,
0.005678493995219469,
0.013164762407541275,
-0.013704212382435799,
0.01452186331152916,
0.022572439163923264,
-0.017618950456380844,
-0.00447212066501379,
0.01985347829759121,
-0.03379783034324646,
0.009556572884321213,
-0.049884360283613205,
0.04137978330254555,
0.049965750426054,
-0.010169053450226784,
-0.01308520883321762,
0.035067297518253326,
0.0018434837693348527,
0.04006792977452278,
0.01636718586087227,
-0.036035072058439255,
-0.030148537829518318,
0.02642819657921791,
0.03805952146649361,
-0.0004900720086880028,
-0.02332160621881485,
0.00457832170650363,
0.028197485953569412,
0.015624663792550564,
0.03162361681461334,
0.0127150509506464,
-0.022609518840909004,
-0.057022012770175934,
0.02764236368238926,
-0.005953918676823378,
-0.007176292594522238,
-0.0017866258276626468,
0.05972083657979965,
-0.02024165913462639,
0.021774301305413246,
-0.013561173342168331,
-0.03704985976219177,
0.0460004061460495,
-0.051547661423683167,
-0.009659436531364918,
0.026971444487571716,
-0.04370446875691414,
0.0383414551615715,
-0.04050981253385544,
-0.011149903759360313,
0.023828288540244102,
-0.0426018089056015,
-0.008669543080031872,
-0.007250972092151642,
-0.0017487347358837724,
-0.02651938982307911,
-0.0035934976767748594,
-0.05620669573545456,
-0.03338227793574333,
0.011576633900403976,
-0.028768084943294525,
-0.013098550960421562,
-0.01940135285258293,
-0.030982626602053642,
-0.0005324772791936994,
-0.01354994811117649,
0.07885033637285233,
0.001177829341031611,
0.03350529074668884,
-0.01948987878859043,
-0.017166506499052048,
0.0013292807852849364,
-0.026044394820928574,
0.023635240271687508,
-0.005059840157628059,
-0.037856634706258774,
0.02040761150419712,
-0.06609424203634262,
-0.034964460879564285,
0.05936887115240097,
-0.008032170124351978,
-0.004375520162284374,
-0.02303026244044304,
-0.003883741330355406,
-0.0697098895907402,
-0.044152259826660156,
-0.05312906950712204,
0.04266655072569847,
-0.029315130785107613,
0.015491622500121593,
0.05694621801376343,
-0.003402205416932702,
-0.004496555309742689,
0.012528924271464348,
-0.001970968907698989,
-0.0473160557448864,
-0.013896828517317772,
-0.0029409208800643682,
0.012524411082267761,
-0.026852592825889587,
0.00957731157541275,
0.03590411692857742,
-0.04965582489967346,
-0.03033430688083172,
-0.050599779933691025,
-0.03805898129940033,
0.052578285336494446,
0.006305580493062735,
0.03583133965730667,
0.0011592963710427284,
-0.02373436838388443,
0.09026675671339035,
0.020002933219075203,
-0.009666727855801582,
-0.0004641723935492337,
0.0006647262489423156,
-0.0034017746802419424,
-0.03271443396806717,
-0.0032571121118962765,
0.025643831118941307,
0.02788574807345867,
0.02803013101220131,
0.0021100568119436502,
0.03672419860959053,
0.027604704722762108,
-0.010905884206295013,
-0.00400168914347887,
0.01478405762463808,
0.01071547158062458,
-0.023433566093444824,
0.06986458599567413,
0.030201595276594162,
-0.012552865780889988,
0.018773406744003296,
-0.03205312788486481,
0.0012287241406738758,
0.008460631594061852,
-0.03979397192597389,
0.054091837257146835,
0.004657996818423271,
0.0023159876000136137,
-0.0038776262663304806,
0.03151947632431984,
-0.003303858684375882,
-0.005272470414638519,
-0.0036404230631887913,
0.03276542201638222,
0.02511131390929222,
-0.044441189616918564,
-0.0054049184545874596,
0.014459691941738129,
0.0010035291779786348,
-0.015504521317780018,
-0.021895913407206535,
0.033289242535829544,
0.02321944572031498,
0.04276614636182785,
-0.023373425006866455,
-0.06194356828927994,
0.02688625454902649,
0.005621407646685839,
0.011469081975519657,
0.0022742871660739183,
-0.051221974194049835,
0.0031209236476570368,
-0.07237910479307175,
0.021949512884020805,
0.018439283594489098,
0.0666980966925621,
-0.004678103607147932,
0.05831848084926605,
0.04635224491357803,
0.03327123820781708,
0.023802615702152252,
0.024969125166535378,
-0.02266468107700348,
0.028014160692691803,
-0.005926323588937521,
-0.012315770611166954,
-0.016042424365878105,
0.0057660541497170925,
-0.0146127725020051,
-0.0466417595744133,
-0.013903990387916565,
0.03662647306919098,
-0.05110625550150871,
-0.05327973514795303,
0.04590706154704094,
-0.03343132138252258,
-0.005498781800270081,
-0.0304303839802742,
0.0377630777657032,
0.02442551776766777,
0.004699991550296545,
-0.016538817435503006,
0.08693508803844452,
-0.006201654672622681,
-0.002644347958266735,
-0.008689568378031254,
-0.026472091674804688,
0.029866520315408707,
0.02403920888900757,
0.03922765702009201,
-0.00835828110575676,
0.006702329032123089,
0.025907231494784355,
0.02940068580210209,
0.06908933818340302,
-0.029895160347223282,
-0.035363826900720596,
0.017094923183321953,
-0.05137232691049576,
0.047745294868946075,
-0.01884535700082779,
0.06600022315979004,
-0.00558621296659112,
0.016270745545625687,
0.01780320703983307,
0.0020733384881168604,
-0.0069285230711102486,
0.02786421775817871,
0.026729607954621315,
-0.017608987167477608,
-0.02453497052192688,
-0.03034774214029312,
0.02192508988082409,
-0.003971559461206198,
-0.01667393371462822,
0.011569367721676826,
0.010819397866725922,
-0.003185597015544772,
0.017224309965968132,
0.004957791417837143,
0.03685704246163368,
-0.027648305520415306,
-0.021305549889802933,
0.01002528890967369,
-0.03526502102613449,
0.026773646473884583,
-0.005296357441693544,
0.034260913729667664,
0.019752340391278267,
0.021817369386553764,
-0.030508482828736305,
0.0001353794359602034,
-0.06033206731081009,
-0.00645518908277154,
0.015011699870228767,
0.019330035895109177,
-0.008187424391508102,
-0.027641339227557182,
-0.04898949712514877,
-0.031840402632951736,
0.03788234665989876,
-0.0328223817050457,
0.01635550893843174,
0.014659736305475235,
-0.027989031746983528,
0.00043972188723273575,
-0.03828682005405426,
-0.014420983381569386,
-0.00028058787574991584,
0.011259054765105247,
0.03980931267142296,
-0.01494879461824894,
0.017257506027817726,
0.014990687370300293,
0.005707798060029745,
0.010271083563566208,
0.057043518871068954,
0.005223314743489027,
-0.01774018444120884,
-0.005839923396706581,
0.04827508702874184,
-0.04480121284723282,
-0.03825903311371803,
0.008361652493476868,
0.013662232086062431,
0.04041581600904465,
0.035370390862226486,
-0.03461625427007675,
-0.06366617232561111,
0.042022593319416046,
-0.0037349085323512554,
-0.019321579486131668,
0.005250212736427784,
-0.01331666111946106,
0.04835837706923485,
0.006983997765928507,
-0.01705929823219776,
0.024931984022259712,
0.03615421801805496,
-0.011049286462366581,
0.002948860405012965,
-0.021935662254691124,
0.014950381591916084,
-0.022064540535211563,
0.03629026561975479,
-0.053734708577394485,
0.0088919997215271,
-0.03701631352305412,
0.03788311779499054,
-0.02104429341852665,
0.02040807157754898,
-0.019778015092015266,
-0.010843989439308643,
-0.003052463522180915,
0.04395631328225136,
-0.026129575446248055,
-0.006179490126669407,
-0.016802756115794182,
0.0069127934984862804,
-0.02024148777127266,
-0.025347435846924782,
-0.009734377264976501,
-0.02674996852874756,
-0.045807257294654846,
0.03431938961148262,
-0.016219541430473328,
0.06770732998847961,
-0.033591046929359436,
-0.030605655163526535,
0.037882041186094284,
-0.07594095170497894,
0.0018946962663903832,
-0.015462164767086506,
0.01557894703000784,
0.019608398899435997,
-0.04343074932694435,
-0.03421677276492119,
0.0029226872138679028,
-0.002695226576179266,
0.01899203285574913,
-0.02919553406536579,
0.017019249498844147,
0.03515966981649399,
0.030396614223718643,
-0.0957031175494194,
-0.04887179285287857,
0.0169859379529953,
0.012062960304319859,
-0.06253093481063843,
-0.02010938711464405,
0.027271056547760963,
-0.04281400889158249,
-0.008507553488016129,
-0.002266020979732275,
0.03394762799143791,
0.002950918162241578,
-0.05070001259446144,
-0.004464167170226574,
0.03401736170053482,
0.0275300070643425,
-0.0027547532226890326,
0.0018618303583934903,
-0.027546288445591927,
-0.02874191477894783,
-0.012162959203124046,
0.0043386369943618774,
0.07503240555524826,
0.006208572071045637,
-0.008945976383984089,
-0.029994290322065353,
0.007751764729619026,
0.01829684153199196,
-0.006482741795480251,
-0.001230999710969627,
0.03636106103658676,
-0.004657444078475237,
-0.01365438848733902,
-0.0627843588590622,
-0.0036466256715357304,
-0.025632120668888092,
0.02039611153304577,
0.022503193467855453,
0.006576077546924353,
-0.03686342388391495,
-0.0003906872880179435,
0.004756199195981026,
0.008166034705936909,
0.01114492304623127,
0.02045632340013981,
0.08068317174911499,
0.020502593368291855,
0.04279894381761551,
0.039702095091342926,
0.003711625235155225,
0.010930747725069523,
-0.020835811272263527,
-0.0072584315203130245,
0.020084824413061142,
0.0081223975867033,
-0.004275578074157238,
-0.011632581241428852,
-0.012300067581236362,
0.04435553774237633,
0.04654204845428467,
-0.01096686813980341,
0.056374143809080124,
-0.010155030526220798,
0.006908529903739691,
0.026820048689842224,
-0.0016911287093535066,
-0.01829114742577076,
0.015622363425791264,
-0.008280341513454914,
0.0539749413728714,
-0.022535448893904686,
-0.008566579781472683,
0.04534696787595749,
0.037796493619680405,
-0.04968668892979622,
0.021238738670945168,
0.01506087277084589,
-0.026889340952038765,
0.003927144687622786,
-0.0069817774929106236,
-0.03478219360113144,
0.046008117496967316,
-0.024544909596443176,
0.06848520785570145,
-0.0012421633582562208,
-0.02859005704522133,
0.013822617009282112,
0.004670314025133848,
-0.00827244482934475,
-0.03364795073866844,
-0.02638850547373295,
-0.04508989676833153,
-0.009824519045650959,
-0.009797068312764168,
0.026485322043299675,
-0.010538331232964993,
0.035378243774175644,
0.02604391984641552,
0.012770225293934345,
0.0096933264285326,
-0.00908806174993515,
-0.05200967565178871,
-0.009365168400108814,
-0.03505533188581467,
-0.031391389667987823,
0.027865516021847725,
0.010160318575799465,
-0.0026041714008897543,
0.004690485540777445,
-0.03119138441979885,
0.02803187444806099,
0.013926118612289429,
0.015493533574044704,
-0.020371710881590843,
0.07546791434288025,
0.0015238055493682623,
0.005386290606111288,
0.007271625567227602,
0.012858458794653416,
0.09312156587839127,
0.08198243379592896,
0.029194235801696777,
-0.05996614694595337,
0.028716275468468666,
-0.0076727792620658875,
0.005262028891593218,
-0.025940345600247383,
0.03516227751970291,
0.013041864149272442,
0.01413473766297102,
0.015592512674629688,
0.03855917602777481,
-0.0011457832297310233,
-0.003527312073856592,
0.006747014354914427,
-0.04279395937919617,
-0.05902402848005295,
0.01235031709074974,
0.001779037294909358,
0.01677837409079075,
0.021647009998559952,
-0.03321215137839317,
0.007944098673760891,
-0.01617448404431343,
0.020608143880963326,
-0.035577137023210526,
-0.06112239882349968,
0.05298161506652832,
0.025064462795853615,
-0.04620559886097908,
-0.021222105249762535,
-0.02645636722445488,
0.0003399976994842291,
-0.04671305790543556,
0.008610825054347515,
-0.007437423802912235,
-0.038477979600429535,
0.028352834284305573,
0.023072924464941025,
0.027220211923122406,
-0.02756737731397152,
0.01017402857542038,
-0.0042465245351195335,
-0.029152194038033485,
-0.0011058244854211807,
-0.0172153040766716,
0.05648966133594513,
-0.014717583544552326,
-0.004309659358114004,
-0.01419871486723423,
-0.001264856313355267,
0.007302583195269108,
-0.0715731829404831,
-0.019226890057325363,
0.015458731912076473,
0.06246291100978851,
-0.013459805399179459,
0.033549897372722626,
-0.036053553223609924,
-0.011099115945398808,
-0.03488224744796753,
0.0346531942486763,
-0.009842517785727978,
0.005095341708511114,
0.04052848368883133,
-0.011867745779454708,
0.0024965477641671896,
-0.03142337128520012,
0.013273988850414753,
-0.0018054669490084052,
-0.022539667785167694,
-0.049185238778591156,
-0.07509566098451614,
0.07386291027069092,
0.016454683616757393,
0.055952321738004684,
-0.012790702283382416,
-0.008478902280330658,
-0.05349482223391533,
-0.07464051991701126,
0.01866205967962742,
0.010279393754899502,
-0.027378931641578674,
0.0030670487321913242,
-0.005697830114513636,
0.010072620585560799,
0.0222213976085186,
-0.01907522790133953,
0.030956406146287918,
0.0066633643582463264,
-0.013384721241891384,
0.05149258300662041,
-0.0617227703332901,
-0.00597932655364275,
0.009322110563516617,
-0.028142469003796577,
0.009835873730480671,
-0.04612806811928749,
-0.001094891456887126,
0.023077649995684624,
0.021572932600975037,
-0.009244509972631931,
0.031049586832523346,
-0.003216707846149802,
0.00095207808772102,
-0.02523934096097946,
-0.023426266387104988,
0.019148973748087883,
0.02746167592704296,
0.027527740225195885,
-0.04211430624127388,
-0.013230090029537678,
-0.018383366987109184,
0.047960203140974045,
0.025090618059039116,
0.0055547552183270454,
-0.04101080447435379,
0.023518873378634453,
-0.021877091377973557,
0.0014049122110009193,
0.019533447921276093,
0.012154552154242992,
-0.04817946255207062,
0.016038881614804268,
0.029288338497281075,
-0.013773182407021523,
-0.007591354660689831,
0.026146238669753075,
-0.007240112870931625,
-0.008856912143528461,
0.015384795144200325,
0.013961916789412498,
-0.0007090017898008227,
0.016933435574173927,
-0.006835059728473425,
0.008749792352318764,
0.011264931410551071,
-0.008846363984048367,
-0.010238490998744965,
-0.005293191876262426,
-0.014156358316540718,
-0.004213140346109867,
0.012716038152575493,
0.0185080636292696,
0.02073591761291027,
0.0399085208773613,
0.005311436951160431,
-0.03200278803706169,
0.056320272386074066,
-0.05568080022931099,
0.015955615788698196,
0.03913986310362816,
-0.06797470152378082,
-0.009504360146820545,
-0.028534678742289543,
-0.008540275506675243,
0.02209622785449028,
-0.02045009844005108,
0.03287865221500397,
0.015350240282714367,
0.00028379462310113013,
0.004957097582519054,
0.019322508946061134,
0.020457496866583824,
0.03883978724479675,
0.05239362269639969,
-0.012679954059422016,
0.014878473244607449,
0.03980448842048645,
-0.04603622853755951,
0.02006380259990692,
0.04078814014792442,
0.04926443472504616,
-0.07593976706266403,
-0.02185744419693947,
0.023971201851963997,
-0.0005473963101394475,
0.05807876959443092,
-0.033914417028427124,
-0.017343347892165184,
0.01767922006547451,
-0.08034294098615646,
0.010354029946029186,
-0.04401759058237076,
0.0017286046640947461,
-0.015022003091871738,
0.01107812114059925,
0.011027519591152668,
0.06868640333414078,
0.047444459050893784,
0.031039191409945488,
0.013259323313832283,
0.010084870271384716,
0.0329408198595047,
-0.02539088949561119,
0.01731502264738083,
0.026101043447852135,
-0.008678345009684563,
-0.04561528563499451,
0.04076961800456047,
-0.02710346132516861,
-0.013590659946203232,
0.013556607998907566,
0.0032900425139814615,
-0.019463088363409042,
0.0027642566710710526,
0.011321795172989368,
-0.0007378733716905117,
0.025971390306949615,
-0.012669555842876434,
-0.06395886838436127,
-0.024630900472402573,
0.0018392499769106507,
0.007797782309353352,
-0.004637455567717552,
0.01110153179615736,
-0.011062578298151493,
-0.03618091717362404,
-0.07599875330924988,
-0.03561457619071007,
0.03933582827448845,
-0.004369659814983606,
-0.02397037111222744,
-0.026189962401986122,
-0.013854922726750374,
0.008362933062016964,
-0.01488663349300623,
0.008352485485374928,
-0.044368840754032135,
-0.00988718867301941,
0.013988910242915154,
-0.03487779572606087,
0.0015760061796754599,
0.014958580955862999,
-0.04967859759926796,
-0.05886780470609665,
0.009249020367860794,
0.007588305976241827,
-0.02130495011806488,
-0.06414173543453217,
-0.03281546011567116,
0.01905391924083233,
0.007776455022394657,
-0.006383280269801617,
-0.038693737238645554,
-0.016127828508615494,
0.04014869034290314,
0.008315000683069229,
-0.003099645720794797,
-0.023330576717853546,
-0.032094042748212814,
-0.023784484714269638,
-0.03539532050490379,
0.03291958197951317,
0.03812573105096817,
-0.04694657027721405,
-0.045855555683374405,
-0.011949695646762848,
-0.025608712807297707,
0.020097576081752777,
0.07617117464542389,
0.010521669872105122,
-0.046579472720623016,
0.007124494761228561,
-0.040066879242658615,
0.015528729185461998,
-0.05372818559408188,
-0.036325853317976,
-0.004769458435475826,
-0.02017918974161148,
-0.015618646517395973,
0.0019138072384521365,
-0.018105005845427513,
0.04555467143654823,
-0.0027310855221003294,
0.007089695427566767,
0.0498628169298172,
0.015782563015818596,
-0.03441837057471275,
0.010523124597966671,
0.032850995659828186,
-0.002908688737079501,
0.07282505929470062,
0.006456228904426098,
-0.0067917234264314175,
0.050833847373723984,
-0.020340966060757637,
-0.030039582401514053,
0.02176556922495365,
-0.03774916008114815,
0.0051721190102398396,
0.03916718065738678,
-0.0008268321398645639,
0.02090837061405182,
-0.040465276688337326,
-0.012202462181448936,
0.026760989800095558,
-0.016015633940696716,
-0.01024374645203352,
0.04113616794347763,
0.012492997571825981,
0.025318462401628494,
-0.0045153554528951645,
0.018104035407304764,
0.02027362585067749,
0.022666694596409798,
0.029834935441613197,
0.047123752534389496,
0.008811458945274353,
-0.0004587890289258212,
0.014317426830530167,
-0.005358363967388868,
-0.02745061181485653,
0.006897554732859135,
0.008591149933636189,
0.037336044013500214,
-0.05340627580881119,
-0.0010726385517045856,
0.03110123984515667,
0.010724248364567757,
-0.022899728268384933,
0.013436184264719486,
-0.04031457379460335,
0.056189801543951035,
-0.023485949262976646,
0.02680293284356594,
-0.020380156114697456,
-0.013548986054956913,
-0.011005324311554432,
0.012787106446921825,
0.047362320125103,
0.04034901410341263,
-0.04960838332772255,
-0.028170155361294746,
-0.012272663414478302,
0.0017511184560135007,
-0.0024475674144923687,
-0.06957878917455673,
-0.013465151190757751,
-0.007172906305640936,
-0.03955312818288803,
-0.026763135567307472,
-0.008212815038859844,
-0.004175902344286442,
0.011291490867733955,
0.03363592550158501,
0.01824142225086689,
0.011785320937633514,
-0.00997886247932911,
0.0007283848826773465,
-0.011936286464333534,
0.058939699083566666,
-0.0475928820669651,
0.0018772406037896872,
0.018021972849965096,
0.019367994740605354,
0.023882800713181496,
0.029533682391047478
] |
<p>Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the wave) in the limit that the frequency of the oscillation goes to infinity?</p>
<p>I don't see how any experiment could test such a claim, but can this be proved/disproved on theoretical grounds?</p>
| 10,692 |
[
0.00037159930798225105,
0.007904807105660439,
0.018123848363757133,
-0.04375581815838814,
0.06477750837802887,
0.0019307245966047049,
-0.03322809189558029,
-0.043536197394132614,
0.003264776896685362,
-0.027555035427212715,
0.0018788866000249982,
0.04583599045872688,
0.005560378544032574,
0.0058417776599526405,
0.035062167793512344,
0.005991688929498196,
-0.008535025641322136,
-0.011317213997244835,
-0.04161994159221649,
-0.02205813117325306,
-0.006059229373931885,
0.06840293109416962,
0.006447273772209883,
-0.02576613985002041,
-0.029246456921100616,
0.011065615341067314,
0.022791722789406776,
-0.0019767042249441147,
0.03499585762619972,
0.07624749839305878,
0.005831017158925533,
-0.03803355619311333,
0.006611916236579418,
0.06429076194763184,
0.07670006155967712,
-0.011673759669065475,
-0.0035019507631659508,
-0.031049828976392746,
-0.005925916135311127,
-0.0020247544161975384,
-0.015484682284295559,
-0.0122007941827178,
-0.016727404668927193,
0.035989854484796524,
-0.015208910219371319,
-0.011699968948960304,
0.013812197372317314,
-0.031015004962682724,
0.03714434802532196,
-0.04040836542844772,
0.07577642053365707,
0.0010457379976287484,
0.023771459236741066,
-0.002060431055724621,
0.025061361491680145,
-0.014065268449485302,
0.0769633874297142,
0.07357857376337051,
-0.013213910162448883,
-0.04786250740289688,
-0.02322363667190075,
-0.0002629646915011108,
-0.021686142310500145,
-0.011907118372619152,
-0.040265075862407684,
0.03957419469952583,
0.016141707077622414,
-0.01884329691529274,
-0.01656569354236126,
-0.021611714735627174,
0.0017429508734494448,
0.030975578352808952,
0.05432482063770294,
-0.007882911711931229,
0.013920999132096767,
-0.013744298368692398,
0.01446979958564043,
-0.014873398467898369,
0.03707307204604149,
0.028787367045879364,
-0.0033680913038551807,
0.027708876878023148,
0.024871384724974632,
0.013306902721524239,
0.031054681167006493,
-0.034246060997247696,
0.03708299249410629,
-0.011018884368240833,
0.005996460560709238,
0.059934791177511215,
-0.03456403687596321,
0.009576836600899696,
0.03547973558306694,
-0.03949780762195587,
-0.04669101536273956,
0.046737682074308395,
0.004108360968530178,
0.04926639795303345,
0.002266026334837079,
-0.053549278527498245,
0.03531424328684807,
-0.042125154286623,
-0.007268152665346861,
0.062069959938526154,
-0.010319521650671959,
-0.00664000166580081,
-0.017551014199852943,
0.04879102483391762,
0.010243792086839676,
-0.011797934770584106,
-0.03284570947289467,
0.014826902188360691,
0.03254709020256996,
0.040228500962257385,
0.0028027212247252464,
-0.010915553197264671,
0.0172707661986351,
-0.034143537282943726,
0.0483713373541832,
0.08501050621271133,
0.018482409417629242,
-0.058832988142967224,
0.0017991486238315701,
-0.02362900786101818,
-0.041543666273355484,
-0.0043159970082342625,
0.011876484379172325,
0.0070706079714000225,
-0.0436323806643486,
0.019167223945260048,
0.016567671671509743,
-0.011778721585869789,
0.016376923769712448,
-0.005656134337186813,
0.023159511387348175,
-0.019753724336624146,
-0.11800536513328552,
-0.06468559056520462,
-0.008035729639232159,
-0.030650228261947632,
-0.04323461651802063,
-0.05024400353431702,
0.008826185017824173,
0.058801986277103424,
0.06198602542281151,
-0.014083939604461193,
0.014169448055326939,
0.0007980274967849255,
0.030065856873989105,
-0.0005733896396122873,
0.01044020988047123,
-0.01616564579308033,
0.018690474331378937,
-0.026409659534692764,
-0.005184713285416365,
-0.041073981672525406,
0.011512259021401405,
0.023542042821645737,
0.014424060471355915,
-0.030188241973519325,
0.029292503371834755,
-0.01888483762741089,
-0.015090296976268291,
-0.0010205138241872191,
0.010976708494126797,
-0.021373340860009193,
0.09123273193836212,
0.022654930129647255,
-0.016519997268915176,
0.024012060835957527,
0.0013986460398882627,
0.032917629927396774,
0.007544224616140127,
0.011477360501885414,
-0.01160366926342249,
-0.029745807871222496,
-0.023965591564774513,
-0.05972234904766083,
0.041188694536685944,
-0.0018223213264718652,
0.0049240319058299065,
-0.010587464086711407,
-0.008950280025601387,
0.02987348474562168,
0.031189613044261932,
0.03202437609434128,
-0.018964026123285294,
0.010471235029399395,
0.0023447887506335974,
-0.07033584266901016,
0.013819162733852863,
-0.03487404063344002,
0.03546218201518059,
0.00799387227743864,
-0.010527885518968105,
0.035769689828157425,
0.01783759519457817,
0.008779175579547882,
-0.06245272979140282,
-0.07535498589277267,
-0.02264752984046936,
0.05532504990696907,
0.007907883264124393,
-0.018453730270266533,
0.0459313690662384,
0.07352721691131592,
0.03134927153587341,
0.017905468121170998,
0.0197624359279871,
-0.02795262075960636,
-0.04768326133489609,
0.021969353780150414,
-0.02869582176208496,
0.043447282165288925,
0.0097361383959651,
0.03364233672618866,
0.0062582362443208694,
-0.012772670015692711,
-0.004828692879527807,
0.017847977578639984,
-0.03961663320660591,
0.07830896973609924,
0.019258644431829453,
-0.0021882180590182543,
-0.020584531128406525,
0.049363162368535995,
0.04202407971024513,
-0.0077559687197208405,
-0.005318213254213333,
-0.025489021092653275,
-0.04764208942651749,
0.0035928317811340094,
0.024295784533023834,
0.06207852438092232,
-0.020034564658999443,
0.01826811023056507,
0.011735953390598297,
0.051776159554719925,
0.025682898238301277,
0.02877712808549404,
-0.029557237401604652,
-0.008193505927920341,
0.0030218386091291904,
0.00004101148806512356,
0.005721010267734528,
0.01692797802388668,
0.04011473059654236,
0.017991993576288223,
-0.00813572108745575,
-0.029760077595710754,
-0.006761358119547367,
0.012153245508670807,
-0.014565760269761086,
0.0330403596162796,
0.0021764652337878942,
-0.04838996008038521,
-0.008722318336367607,
-0.04005543142557144,
0.02921132929623127,
-0.02364731766283512,
-0.02274227887392044,
-0.016245458275079727,
-0.018193816766142845,
-0.025864630937576294,
0.008636733517050743,
-0.006940626539289951,
-0.04686703532934189,
-0.018911145627498627,
0.03982853889465332,
-0.03929094225168228,
-0.010696414858102798,
-0.03314976766705513,
-0.0125429080799222,
0.003096034750342369,
-0.04451162740588188,
0.06703251600265503,
0.008817169815301895,
0.05329422280192375,
-0.04522569477558136,
-0.050826430320739746,
0.0028714993968605995,
-0.0674515813589096,
0.010897907428443432,
-0.00805207621306181,
-0.021482424810528755,
-0.0007634514477103949,
-0.013483344577252865,
-0.0453726202249527,
0.038667526096105576,
-0.0036468731705099344,
0.04168213903903961,
0.0272405743598938,
-0.013830691576004028,
-0.036841295659542084,
-0.008618236519396305,
-0.04498681798577309,
-0.001032329979352653,
-0.026537563651800156,
0.028115181252360344,
0.05483861640095711,
-0.019009767100214958,
-0.034297965466976166,
0.010357304476201534,
-0.0028936685994267464,
-0.03978533297777176,
-0.017356470227241516,
0.0003841920115519315,
0.030117567628622055,
-0.028168892487883568,
0.021934788674116135,
0.005142386071383953,
-0.061383944004774094,
-0.005279203876852989,
-0.0321819968521595,
-0.08412337303161621,
0.0462636724114418,
-0.018843980506062508,
0.038023632019758224,
0.02294255420565605,
-0.010552039369940758,
0.09550002217292786,
0.014004498720169067,
-0.01715710759162903,
-0.0010281602153554559,
0.005207343026995659,
0.006995929405093193,
0.008679560385644436,
0.012400713749229908,
0.017094343900680542,
-0.0016297338297590613,
0.08045398443937302,
-0.0016139335930347443,
0.027981320396065712,
0.007036182098090649,
0.017052344977855682,
0.019129572436213493,
0.02998836152255535,
0.018082251772284508,
0.03188803046941757,
0.04168323427438736,
0.007450680714100599,
-0.02597188390791416,
0.010627713054418564,
0.004774883389472961,
0.024191878736019135,
0.024111920967698097,
-0.00411280058324337,
0.05860602483153343,
0.007341252639889717,
0.028683770447969437,
-0.029827620834112167,
0.04489189386367798,
0.01276732049882412,
0.02507101744413376,
-0.010369693860411644,
0.029150454327464104,
0.05873086676001549,
0.016256064176559448,
0.023163918405771255,
0.04977978393435478,
0.011848922818899155,
-0.016546906903386116,
-0.04361460730433464,
0.004197100177407265,
-0.0022895680740475655,
0.02505728229880333,
-0.024753520265221596,
-0.06390456855297089,
0.029800940304994583,
0.012687495909631252,
0.03612695634365082,
-0.035940252244472504,
-0.04336225241422653,
-0.0023879476357251406,
-0.02585294283926487,
-0.027596957981586456,
-0.02106519788503647,
0.013822201639413834,
0.014091920107603073,
0.06933993846178055,
0.045721326023340225,
0.03488393872976303,
0.00420139217749238,
0.027045954018831253,
-0.09545928984880447,
-0.013974413275718689,
-0.03765857219696045,
0.01652579940855503,
-0.022883910685777664,
-0.021528739482164383,
-0.013992219232022762,
-0.007634398061782122,
-0.026904506608843803,
-0.01520398911088705,
-0.01910972408950329,
-0.06577400863170624,
0.0028307915199548006,
-0.027011876925826073,
-0.031023750081658363,
-0.043742913752794266,
0.017510369420051575,
0.025703605264425278,
-0.0241955928504467,
0.01035795733332634,
0.032582491636276245,
-0.046270184218883514,
0.03557485342025757,
-0.012317492626607418,
0.009190966375172138,
-0.0008771265274845064,
0.05566027760505676,
0.01701006107032299,
0.055291347205638885,
-0.008849350735545158,
0.028554081916809082,
0.017445141449570656,
0.06118365004658699,
0.012011642567813396,
-0.04296360909938812,
-0.014236202463507652,
-0.03338576480746269,
-0.0001375199353788048,
0.0061651174910366535,
0.03967200964689255,
-0.008248562924563885,
-0.0005420061061158776,
0.015129958279430866,
-0.025253823027014732,
-0.020409470424056053,
0.0371062271296978,
0.01776079088449478,
0.026207933202385902,
-0.007033422123640776,
-0.02099584974348545,
-0.0026197421830147505,
-0.03342623636126518,
0.00017129350453615189,
-0.03467126935720444,
-0.03936751186847687,
-0.02075210027396679,
0.01544802077114582,
0.00942591205239296,
0.04278210550546646,
-0.024268800392746925,
-0.029351994395256042,
-0.03326564282178879,
0.008834529668092728,
-0.018706941977143288,
-0.006338085979223251,
0.02297847904264927,
0.01682214066386223,
0.04325231537222862,
0.024946967139840126,
-0.008546656928956509,
-0.08478313684463501,
-0.017011644318699837,
0.049167271703481674,
0.019779875874519348,
0.02783350646495819,
0.018867487087845802,
-0.04607127606868744,
-0.034369029104709625,
0.06221749633550644,
-0.02126389741897583,
0.037928491830825806,
-0.025900157168507576,
-0.018435318022966385,
-0.03086419403553009,
-0.030053677037358284,
0.004573306534439325,
0.012714340351521969,
-0.013152243569493294,
-0.02115902490913868,
-0.009680845774710178,
-0.00029828978586010635,
-0.0033986233174800873,
0.033954888582229614,
0.034908413887023926,
0.08189284801483154,
0.0148584870621562,
-0.020410681143403053,
-0.0013121501542627811,
-0.002234001876786351,
-0.031205151230096817,
-0.08362367749214172,
0.008111306466162205,
0.02250206284224987,
-0.004848293960094452,
0.03417585417628288,
-0.0285726897418499,
-0.07760889083147049,
0.03097347728908062,
-0.0012382203713059425,
-0.022951370105147362,
0.03439797833561897,
-0.00944114476442337,
0.0710463672876358,
0.02877066470682621,
0.017394838854670525,
0.04770689457654953,
0.04837620630860329,
0.003975969739258289,
0.0036477819085121155,
0.007347665727138519,
0.026462657377123833,
-0.04115261510014534,
0.007740377448499203,
-0.009312676265835762,
0.001851793029345572,
-0.03811509534716606,
0.008988339453935623,
0.02472723089158535,
0.004845299292355776,
0.0217035710811615,
-0.0007463200599886477,
-0.00910094566643238,
-0.0017184567404910922,
-0.013516739942133427,
-0.011944320984184742,
-0.005291765555739403,
0.02661237306892872,
0.040729425847530365,
-0.043994367122650146,
-0.027713723480701447,
-0.0013578736688941717,
0.025658072903752327,
0.04378996044397354,
-0.003747783601284027,
0.01791645959019661,
-0.05152395740151405,
0.011637475341558456,
0.02622581087052822,
-0.0430007129907608,
0.037610914558172226,
-0.05588587746024132,
-0.0142997270449996,
0.00771908788010478,
-0.02951834350824356,
-0.049611546099185944,
0.006776497699320316,
-0.007968992926180363,
0.03312673419713974,
-0.01483516301959753,
0.009269659407436848,
0.014004246331751347,
-0.0032705492340028286,
-0.09113378822803497,
-0.015326885506510735,
0.034433118999004364,
0.031633079051971436,
-0.012745116837322712,
-0.01117637287825346,
0.02251979149878025,
-0.03258363902568817,
0.003356326138600707,
0.01056256890296936,
-0.002222133567556739,
-0.014657567255198956,
-0.02519533596932888,
0.000797117652837187,
-0.0031970441341400146,
0.05774558335542679,
0.011876627802848816,
-0.02372114546597004,
0.013310843147337437,
-0.016006870195269585,
0.0036741946823894978,
0.014481485821306705,
0.02254004031419754,
-0.04594849422574043,
-0.04457149654626846,
-0.015020879916846752,
-0.008335736580193043,
0.01655382476747036,
-0.009833159856498241,
-0.034395232796669006,
0.040610600262880325,
-0.004855325445532799,
0.036426667124032974,
0.001472469768486917,
-0.005625155288726091,
-0.024480106309056282,
0.020643875002861023,
0.03628503903746605,
0.0012480474542826414,
-0.052984949201345444,
-0.06740585714578629,
0.02341720461845398,
0.0071237701922655106,
-0.013889579102396965,
0.00939573347568512,
0.051321208477020264,
0.01873547025024891,
-0.04592013359069824,
-0.034824494272470474,
-0.018055429682135582,
-0.038438938558101654,
-0.02202628366649151,
0.011462373659014702,
-0.007056713104248047,
0.051263462752103806,
-0.0400419682264328,
-0.04112870991230011,
-0.04025115817785263,
-0.023312510922551155,
0.026720978319644928,
0.014630129560828209,
0.014799035154283047,
0.026879893615841866,
0.003806270193308592,
-0.019627142697572708,
-0.012004074640572071,
-0.00567108578979969,
-0.004922421649098396,
0.002865377813577652,
0.028624415397644043,
-0.03818156570196152,
0.004164830781519413,
0.026516711339354515,
0.01573922298848629,
0.0008403536048717797,
0.010695996694266796,
0.024533523246645927,
0.028154898434877396,
0.060095321387052536,
-0.027116745710372925,
-0.029765190556645393,
0.02291093021631241,
-0.03698824346065521,
0.021312430500984192,
0.004995754454284906,
-0.025450440123677254,
0.011259626597166061,
0.017458848655223846,
-0.004606875125318766,
-0.012291981838643551,
-0.0173158161342144,
-0.03424057736992836,
0.01439681090414524,
0.0001246773754246533,
0.04196658730506897,
0.029198000207543373,
0.028155319392681122,
-0.02217843197286129,
0.04912130907177925,
-0.0025083988439291716,
-0.013444790616631508,
-0.047682903707027435,
-0.035535525530576706,
-0.01552306953817606,
-0.06768735498189926,
0.019017601385712624,
-0.01253473199903965,
-0.01829945668578148,
-0.0010654290672391653,
-0.03932227939367294,
0.027559518814086914,
0.027030522003769875,
0.03202579542994499,
-0.06308772414922714,
0.043376341462135315,
0.004309377633035183,
0.043246157467365265,
0.006765739060938358,
0.030238380655646324,
0.09965302050113678,
0.07300204783678055,
0.00979221984744072,
-0.04259483888745308,
0.031087225303053856,
-0.020848963409662247,
0.008020070381462574,
-0.029523322358727455,
0.006857018917798996,
0.004623207729309797,
-0.013934710994362831,
-0.0076683261431753635,
0.0377606526017189,
-0.002439296105876565,
0.015982139855623245,
0.03867647424340248,
-0.031376101076602936,
-0.021951893344521523,
0.008477790281176567,
0.014618773944675922,
0.020016567781567574,
0.005628067534416914,
-0.007827907800674438,
0.014342866837978363,
-0.03444568067789078,
-0.03826623782515526,
-0.007861684076488018,
-0.015376940369606018,
0.008122117258608341,
-0.0005847116699442267,
-0.06249457225203514,
0.000618266174569726,
0.007173430174589157,
-0.01637229695916176,
-0.04577435925602913,
0.022974317893385887,
0.029148496687412262,
0.015009974129498005,
0.019646314904093742,
0.051933273673057556,
0.0200191680341959,
0.010076378472149372,
-0.011580604128539562,
0.026204170659184456,
-0.020388489589095116,
-0.015776919201016426,
0.0018336514476686716,
0.04224546626210213,
-0.003924913704395294,
-0.021481763571500778,
-0.004143933299928904,
0.005235358141362667,
0.015705173835158348,
-0.07045614719390869,
-0.011844452470541,
0.003955124411731958,
0.03547428920865059,
0.0008158938144333661,
-0.022733550518751144,
0.006689358036965132,
0.0084413206204772,
0.0032638399861752987,
0.028019726276397705,
-0.01025539729744196,
-0.015708651393651962,
-0.032803770154714584,
0.004844141658395529,
0.014350024983286858,
0.011376234702765942,
-0.019025476649403572,
0.02282875031232834,
-0.015938978642225266,
-0.04973365738987923,
-0.05118738114833832,
0.03737533837556839,
0.030065566301345825,
0.03765656054019928,
0.00435188552364707,
0.005452269688248634,
-0.015642821788787842,
-0.059671204537153244,
0.0009247411508113146,
-0.025139469653367996,
-0.04191002622246742,
-0.013853299431502819,
-0.009161929599940777,
0.02111882157623768,
0.03913174942135811,
-0.04690086841583252,
0.015036185272037983,
-0.003423292888328433,
0.01837703213095665,
0.011403708718717098,
-0.03957941010594368,
-0.007787858135998249,
0.0015764428535476327,
-0.03726844862103462,
0.043838199228048325,
-0.005907505284994841,
0.040217865258455276,
0.02812764048576355,
0.029361579567193985,
-0.0089350501075387,
0.02741282992064953,
-0.04287568852305412,
-0.011104806326329708,
0.003176035126671195,
-0.010007090866565704,
0.00017711315013002604,
0.013941480778157711,
0.03465099260210991,
-0.014887341298162937,
-0.05117306858301163,
-0.052283838391304016,
0.016651824116706848,
0.0022751318756490946,
0.030929140746593475,
-0.02614200860261917,
-0.009144891984760761,
0.018214713782072067,
0.008456702344119549,
0.0009061773889698088,
-0.015397241339087486,
-0.02672606334090233,
-0.006861877162009478,
-0.02668026089668274,
-0.019732270389795303,
0.015136164613068104,
0.031413253396749496,
0.009846891276538372,
-0.06598169356584549,
0.02310214564204216,
0.03164208307862282,
-0.03370978683233261,
0.008796941488981247,
0.036001428961753845,
0.024513494223356247,
0.01620751991868019,
0.003620069706812501,
-0.021573232486844063,
0.024522818624973297,
-0.05824662744998932,
-0.0005064927972853184,
0.025196971371769905,
-0.028532812371850014,
0.025680750608444214,
0.04718106985092163,
-0.001734491321258247,
-0.0016966190887615085,
0.012700985185801983,
-0.003943585325032473,
0.007730566430836916,
-0.0033031273633241653,
-0.012692698277533054,
-0.0001553678303025663,
0.03602076321840286,
0.018051236867904663,
-0.005429968237876892,
-0.012413364835083485,
0.036748435348272324,
0.025859201326966286,
0.010972222313284874,
-0.006041399203240871,
0.009412586688995361,
-0.025159481912851334,
0.04631015658378601,
0.03139685094356537,
-0.02972770854830742,
0.012426307424902916,
0.04913914576172829,
-0.030498076230287552,
0.07504002004861832,
0.013275502249598503,
-0.004397774580866098,
-0.10359936952590942,
-0.014172225259244442,
0.01846069097518921,
0.009634212590754032,
0.04950514808297157,
-0.004524566233158112,
0.003536479314789176,
0.010433655232191086,
-0.09158164262771606,
0.029223879799246788,
-0.01955169439315796,
0.01581118069589138,
-0.03720025718212128,
0.003787940600886941,
-0.09346456080675125,
0.023492053151130676,
0.03397751599550247,
0.045557234436273575,
-0.0001703775196801871,
0.014203655533492565,
-0.00960330106317997,
-0.02743401750922203,
-0.027961626648902893,
0.041694726794958115,
-0.010160733945667744,
-0.01387372799217701,
0.07598232477903366,
-0.038879405707120895,
-0.009495634585618973,
0.029261011630296707,
-0.0016091560246422887,
0.03893120959401131,
-0.019816933199763298,
0.01689862832427025,
0.01570720225572586,
0.022980911657214165,
-0.0013768471544608474,
-0.01066769752651453,
-0.028445331379771233,
0.027417225763201714,
-0.0020393934100866318,
0.01943720132112503,
-0.015043645165860653,
0.007437404710799456,
-0.0001247056934516877,
-0.05737835913896561,
-0.06368180364370346,
0.05997509881854057,
0.020792124792933464,
0.014527451246976852,
-0.010838866233825684,
0.007395164575427771,
0.015280560590326786,
-0.007009298540651798,
0.026055697351694107,
-0.05232794210314751,
-0.03200802952051163,
0.023350518196821213,
0.03579217568039894,
-0.019879326224327087,
0.0071539245545864105,
-0.023696115240454674,
-0.05136711895465851,
0.03576822951436043,
0.011613287031650543,
-0.017511602491140366,
-0.06610068678855896,
-0.01298719085752964,
0.009593717753887177,
-0.006514620501548052,
0.036979954689741135,
-0.02397761680185795,
-0.03549300506711006,
0.015588227659463882,
-0.007943809032440186,
0.01798258163034916,
-0.009355940856039524,
-0.049155786633491516,
-0.060679975897073746,
-0.10334309935569763,
0.08679407835006714,
0.003653014777228236,
0.044434208422899246,
-0.048259567469358444,
-0.02328491024672985,
0.01017177477478981,
-0.000554802711121738,
0.029833614826202393,
-0.010979993268847466,
-0.023754097521305084,
0.011767223477363586,
-0.023381588980555534,
0.011623565107584,
-0.04076239839196205,
-0.017217261716723442,
-0.022270454093813896,
-0.009227612987160683,
-0.0439540296792984,
-0.00001111418259824859,
-0.015072078444063663,
-0.026483336463570595,
-0.013808466494083405,
-0.0015400524716824293,
0.028115736320614815,
-0.014762439765036106,
-0.03718562051653862,
0.069717638194561,
0.017115166410803795,
-0.013754804618656635,
0.04625554010272026,
-0.017186125740408897,
0.03798560053110123,
0.03282822296023369,
-0.06606891006231308,
-0.054904937744140625,
0.0036978241987526417,
-0.01302381232380867,
-0.004048538394272327,
-0.00403739046305418,
0.027128465473651886,
-0.005131481681019068,
-0.007803845684975386,
-0.010906841605901718,
0.048380251973867416,
-0.037593379616737366,
-0.018164044246077538,
0.04291313514113426,
-0.01503000408411026,
0.048812828958034515,
-0.01590152271091938,
-0.027119116857647896,
0.022692561149597168,
-0.007822335697710514,
0.01613626815378666,
0.03368113189935684,
0.031145432963967323,
0.004465118050575256,
0.033391304314136505,
0.02898654341697693,
-0.007559850811958313,
-0.02170543558895588,
0.027633434161543846,
0.03369676694273949,
-0.05223580822348595,
-0.009794088080525398,
0.036334723234176636,
-0.015690959990024567,
-0.025823846459388733,
0.015000754967331886,
-0.033843718469142914,
0.0631972923874855,
-0.004316959995776415,
0.007728791330009699,
-0.011729737743735313,
0.009594027884304523,
-0.017924461513757706,
0.0004684996965806931,
0.04146035388112068,
0.04783296212553978,
-0.04367272928357124,
0.007223470136523247,
-0.026497917249798775,
0.042627640068531036,
0.014031377620995045,
-0.07673677802085876,
-0.007836350239813328,
-0.018382498994469643,
0.0008028069860301912,
-0.01088886708021164,
0.01113874465227127,
-0.03854646906256676,
0.0014824727550148964,
0.03302875533699989,
0.027606042101979256,
0.012196085415780544,
0.011834876611828804,
0.03697607293725014,
-0.020296892151236534,
0.047757137566804886,
-0.03636850416660309,
0.01580587960779667,
-0.02988279052078724,
0.04164916276931763,
-0.025003613904118538,
-0.017495496198534966
] |
<p>Well I had this thought experiment in which a particle observes itself, and something like the following is observed.</p>
<p>Taking in mind the uncertainty principle all particles even stopped at 0K jiggle about, but nothing stops us from going into there frame and observing from there. We do just that, we go in the frame of a particle and keep it at the origin, since we are in the frame of the particle it does not move, its entire universe seems to jiggle as from outside frame we would say the particle is jiggling.</p>
<p>So how the principle seems to have failed here? We most definitely know that our particle is motionless at the origin when we see from its own frame, we do not care about the entire universe jiggling about and we notice that the uncertainty principle becomes invalid! Why is such a thing happening? Am I doing something wrong? Or is this a known loophole to the principle?</p>
| 10,693 |
[
0.023603511974215508,
-0.024343421682715416,
0.02829350158572197,
-0.024262629449367523,
0.034599073231220245,
0.003824538318440318,
-0.020117569714784622,
-0.015615648590028286,
-0.04448341205716133,
-0.014170946553349495,
0.005001325625926256,
0.020447148010134697,
0.02933448925614357,
-0.025225095450878143,
-0.013174416497349739,
0.0071611907333135605,
-0.029226772487163544,
-0.014062133617699146,
-0.03115488775074482,
-0.034985195845365524,
0.0017709898529574275,
0.046662382781505585,
0.02257419005036354,
-0.026799030601978302,
-0.026128137484192848,
-0.016024833545088768,
0.0043861414305865765,
-0.0035513322800397873,
0.03852113336324692,
0.08910030126571655,
-0.04448666423559189,
-0.009030589833855629,
-0.007163864094763994,
0.013634439557790756,
0.032828956842422485,
0.007809051312506199,
-0.014950564131140709,
-0.048861801624298096,
0.008178248070180416,
-0.005112178158015013,
-0.03185079246759415,
-0.006110840477049351,
-0.00774966087192297,
0.09443209320306778,
-0.028422866016626358,
0.000026300283934688196,
0.04914354905486107,
0.014707986265420914,
0.08261802047491074,
-0.047260090708732605,
0.04358643293380737,
0.0063781640492379665,
0.011749597266316414,
-0.010132314637303352,
0.03135021775960922,
0.0053515504114329815,
0.09589719027280807,
0.03107324056327343,
-0.027859678491950035,
-0.04244199022650719,
-0.03432447463274002,
-0.03258189558982849,
-0.01597738265991211,
-0.023535538464784622,
-0.012366768904030323,
0.0048197307623922825,
0.0059820557944476604,
-0.012736617587506771,
0.019277622923254967,
0.005956916604191065,
-0.006686353590339422,
-0.006382680032402277,
0.0393662229180336,
-0.016063136979937553,
0.022253012284636497,
-0.029896704480051994,
0.044059280306100845,
0.028220398351550102,
0.0200998242944479,
0.05015239492058754,
0.005850574001669884,
0.00787432212382555,
0.03483239933848381,
0.03404475748538971,
0.017241211608052254,
-0.03768373280763626,
0.045356635004282,
-0.02066156081855297,
0.03810771182179451,
0.04280995577573776,
-0.02992984838783741,
-0.013451569713652134,
0.044828616082668304,
0.02215937152504921,
-0.013987661339342594,
0.03657624125480652,
0.014037035405635834,
0.0715283751487732,
-0.012679241597652435,
-0.056721292436122894,
0.03991054743528366,
-0.004377416800707579,
0.034631188958883286,
0.058824971318244934,
-0.013287258334457874,
-0.015888884663581848,
-0.033320799469947815,
0.04353015124797821,
0.004187732469290495,
0.007806990761309862,
-0.02977617084980011,
0.03602667525410652,
0.021603727713227272,
0.011870292015373707,
0.025185076519846916,
-0.022628702223300934,
0.0003783750580623746,
-0.0050003970973193645,
0.05080140009522438,
0.031558867543935776,
0.02605440653860569,
-0.003597110044211149,
-0.0008201475720852613,
-0.022380972281098366,
-0.06307870894670486,
0.03778216987848282,
0.0030047567561268806,
0.005566108506172895,
-0.019932281225919724,
0.02834318019449711,
0.025548040866851807,
-0.005794079042971134,
0.013276565819978714,
0.03978315368294716,
0.043314360082149506,
-0.017202109098434448,
-0.13642482459545135,
-0.06299039721488953,
0.07759523391723633,
0.00450147083029151,
0.004529871512204409,
-0.075237937271595,
0.014063412323594093,
0.06177564710378647,
0.08660497516393661,
0.0014564332086592913,
-0.019409550353884697,
0.013466455973684788,
0.027075333520770073,
-0.002397974254563451,
-0.02718808874487877,
-0.017488962039351463,
0.0009464586619287729,
-0.04084893688559532,
0.010236049070954323,
-0.04420115053653717,
0.03193868696689606,
0.022821485996246338,
-0.01094529777765274,
-0.05242536589503288,
0.05648944899439812,
-0.007279570680111647,
0.0228379238396883,
-0.031728897243738174,
-0.003041326068341732,
-0.028463605791330338,
0.07312312722206116,
0.021523356437683105,
-0.03079754300415516,
0.0274277925491333,
0.021785594522953033,
0.04015857353806496,
-0.029745064675807953,
-0.005126750096678734,
0.00857855100184679,
-0.05129056051373482,
-0.031034694984555244,
-0.02542617730796337,
0.021715279668569565,
-0.013919074088335037,
-0.02808208391070366,
-0.009154237806797028,
0.011402305215597153,
0.017016641795635223,
-0.03217097744345665,
0.03691323101520538,
-0.0021746186539530754,
0.007942218333482742,
-0.0017267155926674604,
-0.03850937262177467,
-0.022896384820342064,
-0.04979820176959038,
0.0014303826028481126,
0.01437425147742033,
-0.011219359934329987,
-0.003978921566158533,
0.0007798031438142061,
0.018258165568113327,
-0.03791583701968193,
-0.03763561695814133,
0.008437078446149826,
0.027353262528777122,
0.0006996900192461908,
0.009268266148865223,
0.007630723528563976,
0.031087776646018028,
0.01356946025043726,
0.028425244614481926,
0.011964469216763973,
0.022123156115412712,
-0.029347583651542664,
0.0248514823615551,
0.00553583400323987,
-0.004522776231169701,
0.025036413222551346,
0.02432382106781006,
-0.02082039788365364,
-0.007135344203561544,
0.010488390922546387,
0.05497467517852783,
-0.011722149327397346,
0.10596489906311035,
0.00006014056270942092,
-0.00482302438467741,
-0.03694220632314682,
0.04829985648393631,
0.010524535551667213,
-0.023707315325737,
-0.004456971772015095,
-0.031021106988191605,
-0.025801515206694603,
-0.015042076818645,
0.02308848313987255,
0.018541984260082245,
-0.017186710610985756,
-0.020657628774642944,
0.008933601900935173,
0.024889681488275528,
0.003557942807674408,
0.01994267851114273,
-0.00514994328841567,
-0.06025760620832443,
0.007095882669091225,
0.007617572322487831,
0.03222426772117615,
0.021425262093544006,
0.024021826684474945,
0.010069274343550205,
0.03153268247842789,
0.020048120990395546,
-0.0132745411247015,
0.015341270714998245,
-0.050587210804224014,
0.025318333879113197,
0.008253058418631554,
-0.045051563531160355,
-0.014024036936461926,
-0.013783822767436504,
0.012030264362692833,
0.02084660902619362,
-0.016194535419344902,
-0.0092055294662714,
-0.06270964443683624,
-0.03511486575007439,
0.005995461717247963,
0.020207887515425682,
-0.06678734719753265,
-0.024823375046253204,
0.01756555587053299,
-0.02894418314099312,
-0.01735667698085308,
-0.024259580299258232,
-0.0032872066367417574,
-0.024452177807688713,
-0.00489773228764534,
0.013373111374676228,
0.033146314322948456,
0.03076724149286747,
-0.03617643937468529,
-0.043126557022333145,
-0.010007739998400211,
-0.036221180111169815,
0.0022511566057801247,
0.022982368245720863,
-0.05840471759438515,
0.015281425788998604,
-0.0205297339707613,
-0.019928816705942154,
0.049301791936159134,
-0.010765131562948227,
0.05177538841962814,
-0.004080947022885084,
-0.008183044381439686,
-0.03704293817281723,
0.015331258997321129,
-0.03409215062856674,
-0.003480450017377734,
-0.009514415636658669,
0.008372174575924873,
0.06680084019899368,
-0.010425517335534096,
-0.013224287889897823,
0.026024356484413147,
-0.013044917024672031,
-0.05853891745209694,
-0.009998817928135395,
0.005784063600003719,
0.01710994727909565,
-0.04867253080010414,
0.011644164100289345,
-0.0037569189444184303,
-0.043389346450567245,
0.00692069623619318,
-0.0303400456905365,
-0.07087056338787079,
0.004163790959864855,
0.02482411079108715,
-0.00015253723540809005,
-0.02870948053896427,
-0.009203590452671051,
0.06411561369895935,
0.02445082738995552,
-0.014952476136386395,
-0.011656577698886395,
-0.0024075040128082037,
-0.0070576719008386135,
-0.019101588055491447,
-0.01693752035498619,
0.001609591068699956,
-0.0041153207421302795,
0.029933905228972435,
0.02781900204718113,
0.03370817005634308,
0.02441636472940445,
0.02181769534945488,
-0.0026629017665982246,
-0.03591091185808182,
0.015047922730445862,
-0.0069904751144349575,
0.02655009739100933,
0.03747052699327469,
-0.00974827166646719,
-0.009055089205503464,
0.042280301451683044,
0.04478694871068001,
0.014065904542803764,
-0.04752519354224205,
0.04740440845489502,
0.007474358193576336,
0.024229517206549644,
-0.01531124021857977,
0.03856455907225609,
-0.0005608085775747895,
0.03568154573440552,
0.0014363927766680717,
-0.020409224554896355,
0.04579173028469086,
0.015377352014183998,
0.02276158705353737,
0.026651499792933464,
-0.00363174919039011,
0.00613159965723753,
-0.036124516278505325,
-0.009298255667090416,
-0.014655375853180885,
0.02679326944053173,
-0.0022925182711333036,
-0.05532154440879822,
0.04580938443541527,
0.013942291960120201,
0.025696884840726852,
-0.0034695405047386885,
-0.04131663590669632,
-0.0035455706529319286,
-0.04726085066795349,
-0.005329780746251345,
0.000421826058300212,
0.030959688127040863,
0.015888670459389687,
0.04878274351358414,
0.05108971521258354,
0.028741054236888885,
0.010887539014220238,
-0.008586440235376358,
-0.07641211152076721,
0.05049488693475723,
-0.05756177753210068,
-0.013463709503412247,
-0.012449465692043304,
-0.022114645689725876,
-0.0020686506759375334,
-0.02346176467835903,
0.011405081488192081,
-0.02934734895825386,
0.0004169462190475315,
-0.03521675243973732,
-0.02413564920425415,
-0.01709103211760521,
-0.03010028786957264,
-0.06279288232326508,
0.06286162883043289,
0.047236014157533646,
-0.02255336195230484,
0.017391091212630272,
0.03024917282164097,
-0.05931511148810387,
-0.008932571858167648,
-0.02780437096953392,
-0.01150725781917572,
0.03228713944554329,
0.02745354361832142,
0.05074336379766464,
0.03632159158587456,
-0.026575220748782158,
0.03347507491707802,
0.02951844222843647,
0.03484070673584938,
-0.000933873001486063,
-0.007357465103268623,
-0.009334598667919636,
-0.01612994633615017,
-0.028685256838798523,
0.0028676376678049564,
0.053871527314186096,
-0.006163995247334242,
-0.0008187100756913424,
0.039222098886966705,
0.003048976417630911,
0.00042531132930889726,
0.01982630044221878,
0.0625702515244484,
0.014998489059507847,
-0.021707314997911453,
-0.045732010155916214,
-0.007801284547895193,
-0.02056601643562317,
0.004771463107317686,
0.014125698246061802,
-0.020972752943634987,
-0.01815999299287796,
-0.01125103235244751,
-0.0015122252516448498,
0.004365169443190098,
-0.006041609216481447,
0.004793771542608738,
-0.042858801782131195,
0.01410001702606678,
0.008928952738642693,
0.020643802359700203,
0.0066267321817576885,
0.02175356075167656,
0.04153692349791527,
0.03568105399608612,
-0.03353278711438179,
-0.03347516804933548,
-0.008876689709722996,
0.025757230818271637,
0.010487898252904415,
-0.011943886987864971,
0.007339300587773323,
-0.07345866411924362,
-0.05062441527843475,
0.0437844879925251,
-0.057697415351867676,
0.04390930384397507,
-0.03659633547067642,
0.000006147169187897816,
-0.02015194483101368,
-0.0027225210797041655,
-0.01768827997148037,
-0.012923597358167171,
-0.04552494361996651,
0.010092167183756828,
-0.0621158592402935,
-0.026980454102158546,
-0.02448164112865925,
0.014002813026309013,
0.01948520727455616,
0.028650905936956406,
0.0030727589037269354,
0.017456991598010063,
-0.014481333084404469,
0.027022821828722954,
-0.03642415255308151,
-0.0655905082821846,
0.014384781941771507,
-0.012510314583778381,
0.004067208152264357,
0.04172510281205177,
-0.03978526219725609,
-0.06188129261136055,
0.0015547889051958919,
0.013286948204040527,
-0.018871985375881195,
-0.005963040515780449,
-0.06084947660565376,
-0.014258340001106262,
0.020027948543429375,
-0.01527662854641676,
0.04697781056165695,
0.019211694598197937,
-0.007536742370575666,
0.010091793723404408,
-0.0016199485398828983,
0.051387686282396317,
-0.04373255372047424,
-0.002616303274407983,
-0.03478074073791504,
0.005781042855232954,
-0.03836001083254814,
0.06624184548854828,
-0.030967336148023605,
0.019299248233437538,
-0.008068970404565334,
-0.032322246581315994,
0.0003380876441951841,
0.03174139931797981,
0.013255864381790161,
0.03356531262397766,
-0.029275981709361076,
0.026014888659119606,
-0.01573508232831955,
-0.010313568636775017,
-0.008972067385911942,
-0.004284228198230267,
-0.01352932583540678,
0.056291189044713974,
-0.007971342653036118,
0.047383274883031845,
-0.005106104537844658,
-0.03230610117316246,
0.013558585196733475,
-0.0453115813434124,
0.014253095723688602,
-0.047672972083091736,
0.0012551845284178853,
0.012074672617018223,
-0.05506741628050804,
-0.0600411482155323,
-0.005631289444863796,
-0.005694548133760691,
0.031527258455753326,
-0.06071196869015694,
0.0007829300011508167,
0.007891914807260036,
0.005032872781157494,
-0.10545573383569717,
-0.05744948238134384,
0.017942188307642937,
0.02162562683224678,
0.0017796237953007221,
-0.00018509424990043044,
-0.0001798524463083595,
-0.00862734206020832,
-0.017124980688095093,
-0.02559364214539528,
-0.008967196568846703,
-0.0131217697635293,
0.0028540745843201876,
0.025873875245451927,
-0.018139580264687538,
0.04457320645451546,
-0.0409708172082901,
0.021069299429655075,
0.008725548163056374,
-0.0047020986676216125,
-0.00943164061754942,
0.018208228051662445,
0.046388085931539536,
-0.037349116057157516,
-0.041436608880758286,
0.011964280158281326,
0.0025450298562645912,
0.004251385107636452,
-0.0026889857836067677,
-0.017829762771725655,
0.021445075049996376,
-0.0010040162596851587,
0.0026995143853127956,
-0.01615823246538639,
-0.002006066730245948,
0.012462295591831207,
-0.022220276296138763,
0.025578022003173828,
-0.006467890460044146,
-0.021230492740869522,
-0.08512617647647858,
0.018405739217996597,
-0.009466472081840038,
0.008779598399996758,
-0.000626932829618454,
0.05706307291984558,
0.012460808269679546,
-0.0022617673967033625,
0.013454599305987358,
-0.006697101518511772,
-0.01559868361800909,
-0.024722276255488396,
0.011664002202451229,
-0.0027043609879910946,
0.010090406984090805,
-0.04147961363196373,
-0.01125368569046259,
-0.03437916189432144,
0.0016205463325604796,
0.05862756446003914,
-0.017721883952617645,
0.0445551723241806,
0.005958071909844875,
0.010853368788957596,
-0.019199369475245476,
0.01308578159660101,
-0.0048479619435966015,
0.0027415079530328512,
0.017635224387049675,
0.0208131056278944,
-0.01883910968899727,
0.00824956689029932,
0.039276860654354095,
0.06835994124412537,
-0.0013920230558142066,
0.027460142970085144,
0.028448626399040222,
0.025377772748470306,
0.03623544052243233,
0.003383500035852194,
-0.03494923561811447,
0.01489062700420618,
-0.026119930669665337,
0.011288775131106377,
-0.003658860456198454,
-0.040590379387140274,
0.01527967769652605,
-0.011070593260228634,
0.04093265160918236,
0.02534322999417782,
-0.005605291575193405,
-0.05289448797702789,
0.022672684863209724,
0.016682259738445282,
0.04346461221575737,
-0.003411452518776059,
0.023568376898765564,
0.005508631933480501,
0.03727763146162033,
0.012661412358283997,
-0.0027091586962342262,
-0.0858464315533638,
-0.05843134596943855,
-0.05731121823191643,
-0.06510621309280396,
0.04107115790247917,
-0.0073240227065980434,
-0.011909092776477337,
0.017367783933877945,
-0.0005532220820896327,
0.025602146983146667,
0.011642640456557274,
0.04398154094815254,
-0.018292561173439026,
0.05789835378527641,
0.01336394902318716,
0.02275867760181427,
-0.020362338051199913,
0.05539611726999283,
0.09117191284894943,
0.0162632055580616,
-0.018387610092759132,
-0.06313634663820267,
0.012244281359016895,
-0.01840565912425518,
0.023278549313545227,
-0.04410100355744362,
0.05891311541199684,
0.018035834655165672,
0.027427004650235176,
-0.00033034602529369295,
0.030467024073004723,
0.018715903162956238,
-0.023650750517845154,
0.053105372935533524,
-0.040566109120845795,
-0.04302625358104706,
-0.01256472896784544,
0.02588546834886074,
-0.026944242417812347,
-0.035975150763988495,
-0.027033591642975807,
0.03520715609192848,
-0.03481467440724373,
-0.0036710682325065136,
0.006804205011576414,
-0.047968726605176926,
-0.03144645690917969,
0.009518989361822605,
-0.025748834013938904,
0.0029256970155984163,
-0.019694626331329346,
-0.03447217866778374,
-0.05762195587158203,
-0.01312936469912529,
0.025420188903808594,
-0.030942628160119057,
0.044773079454898834,
0.05439963936805725,
-0.0035160654224455357,
0.015124018304049969,
-0.018083328381180763,
-0.005897637456655502,
-0.011080114170908928,
-0.05819439888000488,
-0.0016327360644936562,
0.080405592918396,
-0.010062180459499359,
0.011184044182300568,
-0.007917399518191814,
0.011076576076447964,
0.006440400145947933,
-0.06601765751838684,
0.016819406300783157,
-0.007383923511952162,
0.01373240165412426,
0.023041512817144394,
-0.030796991661190987,
-0.013469463214278221,
0.008042431436479092,
-0.0039368607103824615,
0.009408797137439251,
-0.005203175358474255,
0.03560304269194603,
-0.042518045753240585,
0.01479959674179554,
0.029730699956417084,
-0.0205011535435915,
-0.01756608858704567,
0.00895069818943739,
-0.005942951422184706,
-0.031828053295612335,
-0.0045380303636193275,
0.056356560438871384,
0.03807443380355835,
0.01799597591161728,
-0.019971638917922974,
-0.0088102538138628,
-0.01700248196721077,
-0.03799176216125488,
0.02047928050160408,
-0.059059418737888336,
-0.004810103215277195,
-0.006055968813598156,
0.02666586823761463,
0.057011090219020844,
0.04852873086929321,
-0.03556809201836586,
-0.040419984608888626,
0.009757188148796558,
0.013018021360039711,
-0.0017954942304641008,
0.010377180762588978,
0.004200201481580734,
0.012803768739104271,
-0.020179154351353645,
-0.01519826054573059,
-0.006732822395861149,
0.03372643142938614,
0.043791044503450394,
-0.00483891274780035,
0.023480188101530075,
0.03377607464790344,
-0.035047244280576706,
0.007522140629589558,
0.0500948429107666,
-0.01972571201622486,
-0.014694077894091606,
0.020815668627619743,
0.04690961539745331,
-0.029360314831137657,
-0.04513215646147728,
-0.020404230803251266,
0.012537725269794464,
-0.028019487857818604,
0.038239508867263794,
-0.027311448007822037,
-0.015024165622889996,
0.0008258966845460236,
0.014526238664984703,
0.00019747983606066555,
0.00867608655244112,
-0.061120644211769104,
-0.006557102780789137,
-0.019612498581409454,
-0.015642914921045303,
-0.05739498510956764,
0.027071086689829826,
-0.001520943595096469,
-0.04438300430774689,
0.006029882002621889,
0.021898286417126656,
-0.043722331523895264,
0.0038108534645289183,
0.057028476148843765,
0.012640434317290783,
0.02127065323293209,
0.0029239936266094446,
0.0041632563807070255,
0.021783679723739624,
-0.039596930146217346,
-0.04689594358205795,
0.057912010699510574,
-0.018133368343114853,
0.014456149190664291,
0.017891770228743553,
-0.030012236908078194,
-0.013882390223443508,
0.049631789326667786,
0.017864586785435677,
0.021689683198928833,
0.021438846364617348,
-0.0389825813472271,
-0.02833007089793682,
0.008958556689321995,
0.011315030977129936,
-0.03417990729212761,
-0.007974807173013687,
0.06130652502179146,
0.054324325174093246,
0.020718827843666077,
0.03136403486132622,
-0.0014373117592185736,
-0.012728299014270306,
0.008076098747551441,
0.005196691956371069,
-0.01156837958842516,
0.0087386230006814,
0.06499075889587402,
-0.05670278146862984,
0.02647930383682251,
-0.0073878588154911995,
0.04290730133652687,
-0.09950101375579834,
0.01692270115017891,
-0.02775553986430168,
0.03183368965983391,
0.0250241681933403,
-0.005146108567714691,
0.014685344882309437,
0.05386355519294739,
-0.07183490693569183,
-0.008062124252319336,
-0.028199633583426476,
-0.02602037414908409,
-0.034561458975076675,
0.020537786185741425,
-0.028797615319490433,
0.06650736927986145,
0.035362400114536285,
0.03080921247601509,
0.014019768685102463,
0.030039705336093903,
-0.038461703807115555,
-0.04369566589593887,
-0.014851647429168224,
0.020502394065260887,
-0.020528193563222885,
0.027780404314398766,
0.07066993415355682,
-0.03541794791817665,
-0.04243585839867592,
0.030270468443632126,
-0.033520545810461044,
0.003975060302764177,
-0.014596780762076378,
0.01803591661155224,
0.022176092490553856,
0.025251120328903198,
0.025948354974389076,
0.015838513150811195,
0.01370412390679121,
0.025016412138938904,
0.036567166447639465,
0.00641576899215579,
0.027819909155368805,
-0.023783527314662933,
0.018581220880150795,
-0.051277004182338715,
-0.016081148758530617,
0.011150090023875237,
0.02607104554772377,
0.014230807311832905,
0.012722332961857319,
0.037151679396629333,
0.02436782419681549,
-0.05616304278373718,
-0.011476165615022182,
-0.05354659631848335,
0.00746416300535202,
0.02701149508357048,
0.01581479050219059,
-0.03787877410650253,
-0.0047364444471895695,
-0.012944592162966728,
-0.023198695853352547,
0.028972197324037552,
0.006251197308301926,
-0.015070159919559956,
-0.056580282747745514,
0.0019673213828355074,
0.013538409024477005,
0.011173629201948643,
0.05123583599925041,
-0.03665510192513466,
-0.027336545288562775,
0.019087480381131172,
-0.0013005525106564164,
0.032384827733039856,
0.012353377416729927,
-0.02637512981891632,
-0.029314281418919563,
-0.08347570151090622,
0.06336414068937302,
-0.017274918034672737,
0.01874006912112236,
-0.026189841330051422,
-0.028723398223519325,
-0.009186149574816227,
0.010595226660370827,
0.032777223736047745,
-0.001303579774685204,
-0.0017460561357438564,
0.021458350121974945,
0.013684644363820553,
0.008001982234418392,
-0.013469276949763298,
-0.00342963938601315,
-0.021636085584759712,
-0.036214571446180344,
-0.01113349199295044,
-0.03186691552400589,
-0.05449986457824707,
0.011346920393407345,
0.03361117094755173,
0.006593522150069475,
0.029540281742811203,
-0.00886960793286562,
-0.04063749313354492,
0.03723641484975815,
0.0043163662776350975,
0.004804270341992378,
0.07466894388198853,
-0.005405487958341837,
0.02892191708087921,
0.056404273957014084,
-0.046872496604919434,
-0.041525211185216904,
0.023453883826732635,
-0.03801942989230156,
0.001142128137871623,
-0.016749007627367973,
0.027756504714488983,
0.02615581825375557,
-0.028024647384881973,
-0.021741949021816254,
0.04736499488353729,
-0.0456695482134819,
0.005208949092775583,
0.028228389099240303,
0.01625703275203705,
0.04192527011036873,
-0.007136160042136908,
0.01097895298153162,
0.02412622980773449,
0.038206759840250015,
0.024362092837691307,
0.07633373141288757,
0.00601209094747901,
-0.016100574284791946,
0.04804277792572975,
0.054056316614151,
0.001809696084819734,
0.010118489153683186,
0.0024952406529337168,
0.042071882635354996,
-0.031579937785863876,
-0.0009785272413864732,
-0.028476085513830185,
-0.04848315194249153,
-0.0072447690181434155,
0.04425599426031113,
-0.013795396313071251,
0.09118879586458206,
-0.02296670898795128,
-0.00001708432682789862,
0.023739932104945183,
-0.015636565163731575,
-0.004452979192137718,
0.017559317871928215,
0.012143128551542759,
0.043178740888834,
-0.00705619715154171,
-0.012431878596544266,
-0.0191961582750082,
0.032313574105501175,
0.028755031526088715,
-0.02582353726029396,
-0.022659188136458397,
-0.05316256359219551,
0.014414808712899685,
-0.01564030908048153,
-0.014944869093596935,
-0.008392557501792908,
-0.008796390146017075,
0.023986682295799255,
0.016092481091618538,
0.017213033512234688,
-0.018024925142526627,
-0.007373427972197533,
-0.035408373922109604,
0.06838071346282959,
-0.051152825355529785,
-0.028410742059350014,
0.009259139187633991,
0.06609193980693817,
-0.03450709953904152,
-0.021280523389577866
] |
<p>I have two questions.</p>
<p><strong>First</strong>, I understand that in a nuclear reaction
$$Q:=K_{after}-K_{before}\equiv E_{0,before}-E_{0,after} \qquad (1)$$
where $K$ is the total kinetic energy, and $E_0$ is the total rest energy.
My question is, in the reaction $^{9}Be\left(\gamma,n\right)^{8}Be$, where should I put the energy of the $\gamma$-photon?
I mean, conservation of energy says
$$Mc^{2}+h\nu=mc^{2}+M'c^{2}+K_{n}+K' \qquad(2)$$
where $M$=mass of $^{9}Be$, $m$=mass of the neutron, $M'$=mass of $^{8}Be$, and $K_{n}$, $K'$ are the kinetic energies of the neutron and of the $^{8}Be$, respectively. </p>
<p>Then, using (1) (with the rest energies version) I wrote
$$Q=(M-m-M')c^2 \qquad (3)$$
but this is equivalent to: (using (2))</p>
<p>$$Q=K_{n}+K'-h\nu \qquad (4)$$
So, my <strong>1st question</strong> is: is (4) the correct expression for $Q$?</p>
<p><strong>Second</strong>, I want to calculate the kinetic energies $K_n$ and $K'$. In order to do this, I'm thinking to use (4) (if it's correct) with $K_{n}=\frac{1}{2}mv^{2}$ and $K'=\frac{1}{2}M'V^{2}$, and the conservation of linear momentum</p>
<p>$$\frac{h}{\lambda}=mv+M'V \qquad (5)$$</p>
<p>Assuming that the neutron and the $^{8}Be$ continue moving in the direction of the $\gamma$-photon.</p>
<p>So, my <strong>2nd question</strong> is: can I make this last assumption? Or in other words, is (5) a correct expression for the linear momentum conservation?</p>
| 10,694 |
[
-0.01270976010710001,
-0.03483184799551964,
-0.01279458962380886,
-0.012002117931842804,
0.008636333979666233,
0.02180032804608345,
-0.030097076669335365,
-0.059151776134967804,
0.005931772291660309,
-0.050818342715501785,
0.06728190928697586,
0.002940535545349121,
0.06876268237829208,
0.012976296246051788,
0.0372467041015625,
0.040420278906822205,
-0.03754531964659691,
-0.02020319737493992,
-0.004166989587247372,
-0.03144535794854164,
0.023469913750886917,
-0.031079599633812904,
-0.03625641390681267,
-0.005205176770687103,
-0.07570008933544159,
0.04036884382367134,
-0.0013260088162496686,
-0.007520832121372223,
0.018711350858211517,
0.06371787935495377,
-0.0030240861233323812,
-0.0490691214799881,
0.049172814935445786,
0.03974378481507301,
-0.05710776895284653,
0.016031313687562943,
-0.05591097101569176,
-0.04319049045443535,
-0.009029058739542961,
0.0500020831823349,
-0.00797642208635807,
-0.018787315115332603,
-0.006991067435592413,
0.028180569410324097,
-0.013338175602257252,
0.02886299602687359,
0.014213120564818382,
-0.031912196427583694,
0.04228037968277931,
-0.042860422283411026,
0.07521599531173706,
0.006386098451912403,
0.035300396382808685,
0.013135268352925777,
-0.015870917588472366,
-0.03241035342216492,
0.05545170232653618,
0.0485185906291008,
0.030697567388415337,
-0.05657158046960831,
0.008840490132570267,
-0.012368490919470787,
-0.0028687019366770983,
0.022652773186564445,
0.029852205887436867,
0.03164370730519295,
0.013115732930600643,
0.028712602332234383,
0.033090740442276,
-0.006845240481197834,
0.03528311848640442,
-0.004803481511771679,
0.023573201149702072,
-0.02916663885116577,
-0.006881149020045996,
-0.0012631581630557775,
0.008791735395789146,
0.020448904484510422,
0.03641471266746521,
0.016122912988066673,
-0.026624714955687523,
-0.002606199122965336,
0.03173397108912468,
0.057962723076343536,
-0.019496100023388863,
-0.025028526782989502,
0.0462929829955101,
0.009559158235788345,
0.022687150165438652,
0.03843538090586662,
-0.0017301414627581835,
0.0210663340985775,
0.0204906165599823,
-0.0070987120270729065,
0.010149125941097736,
0.022172050550580025,
0.004650133661925793,
0.04613889008760452,
0.009184369817376137,
-0.0017404903192073107,
-0.013985850848257542,
-0.017613114789128304,
0.0332203172147274,
0.07741431146860123,
0.007867909967899323,
-0.010138365440070629,
-0.027265578508377075,
0.037224769592285156,
-0.029108021408319473,
-0.015712298452854156,
-0.030371304601430893,
0.017114296555519104,
-0.0065499949268996716,
-0.014713726006448269,
-0.0011039795354008675,
-0.08375079929828644,
-0.014874445274472237,
-0.02037471905350685,
0.07161074131727219,
0.04228745400905609,
0.0357373021543026,
-0.03201647102832794,
0.003283966099843383,
0.01579377055168152,
-0.07164561003446579,
-0.022460630163550377,
0.06211323291063309,
0.009190186858177185,
-0.029458122327923775,
-0.0037003657780587673,
0.012820425443351269,
-0.006924256216734648,
0.016579361632466316,
0.01546409260481596,
-0.01632707379758358,
-0.003075266722589731,
-0.106257364153862,
-0.0697508230805397,
0.027105484157800674,
-0.030604397878050804,
-0.03040747344493866,
-0.10930954664945602,
0.00218197307549417,
0.05108119547367096,
0.047744665294885635,
-0.02081390470266342,
-0.03627585247159004,
0.007297771982848644,
0.028398610651493073,
-0.01598036289215088,
-0.030570149421691895,
-0.018669260665774345,
-0.029963284730911255,
-0.012380080297589302,
-0.011552494950592518,
-0.057067595422267914,
0.01656239852309227,
0.020598581060767174,
0.01891232468187809,
0.025859633460640907,
0.08488385379314423,
-0.028456103056669235,
0.032757677137851715,
0.0057409172877669334,
0.022114338353276253,
-0.032507024705410004,
0.044577665627002716,
0.05880675092339516,
0.004383948631584644,
0.0188581645488739,
0.01855495385825634,
-0.017436916008591652,
-0.059445179998874664,
0.011320383287966251,
0.01362776942551136,
-0.027021363377571106,
0.007475603837519884,
-0.03400284796953201,
-0.011208622716367245,
0.010886702686548233,
-0.043834563344717026,
-0.03435254469513893,
-0.03978332132101059,
0.030562693253159523,
-0.0056489272974431515,
0.051751017570495605,
0.01005055382847786,
0.025708820670843124,
-0.020880723372101784,
0.0037353448569774628,
-0.023584555834531784,
-0.023372063413262367,
0.02357233501970768,
0.011840244755148888,
-0.024324815720319748,
0.01368319895118475,
-0.02110549807548523,
0.009286434389650822,
-0.005645066499710083,
-0.0007079075439833105,
0.011753193102777004,
0.036039941012859344,
-0.0174589641392231,
0.012081723660230637,
-0.008021481335163116,
0.029791956767439842,
-0.0018189450493082404,
0.013370639644563198,
0.04139456897974014,
0.018925262615084648,
0.013754064217209816,
0.0050080013461411,
-0.0012749817688018084,
-0.008996506221592426,
0.000022903059289092198,
-0.033385347574949265,
-0.004736823029816151,
-0.01720397360622883,
0.022438397631049156,
0.007934900000691414,
-0.046728480607271194,
0.07989241927862167,
0.03967628628015518,
-0.004033066798001528,
0.019029827788472176,
0.026375945657491684,
-0.0115042207762599,
0.0549015998840332,
-0.023323237895965576,
-0.024190623313188553,
-0.018632059916853905,
0.012426811270415783,
0.00544332480058074,
0.030306121334433556,
-0.07534626871347427,
0.024949505925178528,
0.023579226806759834,
0.011673987843096256,
0.040927909314632416,
-0.02431081049144268,
-0.03263721615076065,
-0.034694865345954895,
0.02749326266348362,
0.02090090699493885,
-0.04784383997321129,
0.019867125898599625,
0.0009510904783383012,
0.02191242389380932,
0.028088267892599106,
-0.0011366785038262606,
-0.013558479957282543,
0.004619209095835686,
-0.020778821781277657,
-0.016520187258720398,
-0.029097657650709152,
-0.047785304486751556,
0.07661178708076477,
0.015185382217168808,
0.04894484207034111,
0.0005213510594330728,
-0.001254163682460785,
0.022150220349431038,
-0.02597721479833126,
-0.003938712179660797,
0.002450700383633375,
-0.003223883919417858,
-0.0035024862736463547,
-0.0017845388501882553,
0.004966544918715954,
-0.010103156790137291,
-0.006583052221685648,
-0.02853560633957386,
-0.02121634967625141,
0.002650671638548374,
0.000784927571658045,
0.03924955427646637,
-0.007912578992545605,
-0.02679779753088951,
-0.03944952040910721,
-0.03183600679039955,
-0.032744958996772766,
-0.02412368915975094,
-0.0002057055535260588,
0.0167929045855999,
-0.06258410960435867,
-0.025592289865016937,
-0.062281135469675064,
0.011062848381698132,
0.051019102334976196,
-0.006677343510091305,
-0.00788927637040615,
0.06402304768562317,
-0.006376907229423523,
-0.09745792299509048,
-0.038873620331287384,
-0.0007684932788833976,
-0.01978270150721073,
-0.017173685133457184,
0.006578108295798302,
0.07782772928476334,
0.020659156143665314,
-0.016490718349814415,
0.013118394650518894,
-0.028506292030215263,
-0.04837527126073837,
-0.023552732542157173,
0.009883479215204716,
0.02772507257759571,
0.010455271229147911,
0.02350727468729019,
0.034711312502622604,
-0.005857138894498348,
0.012396004050970078,
-0.07229537516832352,
-0.016556810587644577,
0.03249935060739517,
-0.01393031980842352,
0.06469753384590149,
0.013252407312393188,
-0.026119396090507507,
0.09073613584041595,
0.024474453181028366,
-0.013873711228370667,
-0.011455867439508438,
0.04624566435813904,
-0.00960562564432621,
-0.0021960982121527195,
-0.0202234648168087,
-0.013607287779450417,
0.0014113179640844464,
0.009110817685723305,
-0.02112741395831108,
0.03956859931349754,
0.030048202723264694,
-0.026554038748145103,
0.008731549605727196,
0.006875905673950911,
0.0006851725047454238,
0.02608100138604641,
0.05265195667743683,
0.0021703732199966908,
-0.01249281782656908,
0.024794410914182663,
0.00565842492505908,
0.024508964270353317,
0.0003496902354527265,
-0.046832408756017685,
0.06078135967254639,
0.030296534299850464,
-0.0053527625277638435,
-0.02970358170568943,
0.05828123912215233,
0.005258641671389341,
-0.04154486954212189,
0.005475079640746117,
0.03298163041472435,
0.03081800788640976,
-0.038826242089271545,
0.028630785644054413,
0.029526952654123306,
0.047299932688474655,
0.02788734994828701,
-0.031780216842889786,
-0.015576576814055443,
0.0004680259444285184,
0.02000918984413147,
-0.026318535208702087,
0.05845176428556442,
0.018140582367777824,
0.028506072238087654,
0.04640856385231018,
-0.01080899778753519,
-0.025880148634314537,
-0.017151784151792526,
-0.033568188548088074,
-0.02399909496307373,
-0.000678623968269676,
0.02696145698428154,
-0.039046503603458405,
0.07486654072999954,
0.02035299874842167,
-0.015946030616760254,
0.05228620767593384,
-0.0018208397086709738,
-0.040074028074741364,
0.030528098344802856,
0.003955018240958452,
-0.04589517414569855,
0.02450631372630596,
-0.006440252996981144,
-0.0454837828874588,
-0.021645478904247284,
-0.027382368221879005,
0.004048113711178303,
-0.02815202996134758,
-0.03490203246474266,
0.02815205045044422,
-0.07427472621202469,
-0.012945388443768024,
-0.0024389633908867836,
0.040207553654909134,
0.0486004538834095,
-0.024221433326601982,
-0.0009027088526636362,
0.03983499854803085,
-0.05952118709683418,
0.03283802792429924,
-0.023494966328144073,
0.008479176089167595,
-0.007416354026645422,
0.020077135413885117,
0.01401007454842329,
0.036039046943187714,
0.021633366122841835,
-0.02115846984088421,
0.02625633403658867,
0.03653446584939957,
0.027965830639004707,
-0.024014344438910484,
0.004049473907798529,
-0.0052308435551822186,
0.0050601535476744175,
-0.010922462679445744,
0.06606020033359528,
0.03570149466395378,
0.026454932987689972,
0.0067730862647295,
0.02411474846303463,
-0.014708987437188625,
0.054634105414152145,
0.06473003327846527,
-0.02547970972955227,
-0.017465248703956604,
-0.04103195667266846,
0.044845689088106155,
-0.010765746235847473,
-0.01664917543530464,
-0.028610048815608025,
-0.007456982508301735,
-0.04512255638837814,
-0.0016973885940387845,
0.022379877045750618,
0.027334943413734436,
-0.016320202499628067,
0.01704493537545204,
-0.005534049589186907,
-0.020280862227082253,
0.022086404263973236,
-0.02471107617020607,
0.011355471797287464,
0.018088599666953087,
0.025222763419151306,
-0.01495822798460722,
-0.0007635614601895213,
-0.033630337566137314,
-0.025708742439746857,
0.0379611998796463,
0.07114345580339432,
-0.011737399734556675,
0.00037858387804590166,
-0.06497281789779663,
-0.033117178827524185,
0.005749364849179983,
-0.005278523545712233,
0.04601180553436279,
0.012672311626374722,
0.013147718273103237,
0.02419266290962696,
-0.020913943648338318,
-0.025708351284265518,
0.05115111544728279,
0.011500024236738682,
0.009385672397911549,
-0.0626082718372345,
-0.005521710962057114,
0.019498789682984352,
0.006747327744960785,
0.043646764010190964,
0.037387315183877945,
-0.0478796549141407,
-0.052083540707826614,
-0.005216571036726236,
0.026639658957719803,
-0.03710620105266571,
-0.025110982358455658,
-0.0002389162837062031,
-0.013821202330291271,
-0.020664751529693604,
0.03426617383956909,
-0.03260384127497673,
-0.05093150958418846,
0.051500994712114334,
0.031347837299108505,
-0.009907097555696964,
0.0012140916660428047,
-0.03828220069408417,
0.053213391453027725,
0.03534405305981636,
-0.009470831602811813,
0.02416491135954857,
0.04934176802635193,
-0.05083392560482025,
-0.021881714463233948,
-0.04483678936958313,
-0.0075084129348397255,
-0.00705365277826786,
0.004926009103655815,
-0.023687120527029037,
-0.011640070006251335,
-0.01607183739542961,
0.02609860710799694,
-0.051117487251758575,
0.011639353819191456,
0.008219785057008266,
-0.0045676943846046925,
0.011589132249355316,
0.03876369073987007,
0.03163512051105499,
0.02347131259739399,
-0.02553066797554493,
-0.014767327345907688,
-0.020062023773789406,
-0.013203809037804604,
0.04927263781428337,
0.011208017356693745,
-0.028647439554333687,
0.042033273726701736,
-0.03883786126971245,
-0.020391076803207397,
-0.028687192127108574,
-0.005692676641047001,
0.02324991673231125,
-0.018589405342936516,
0.017860615625977516,
0.03861355781555176,
-0.013061237521469593,
-0.012478502467274666,
-0.036595556885004044,
-0.060982294380664825,
-0.00026969736791215837,
-0.04013816639780998,
0.005348914302885532,
-0.017164891585707664,
0.04143378883600235,
0.031116381287574768,
0.02870946377515793,
-0.05399134382605553,
0.01322721503674984,
0.0072050248272717,
-0.023134693503379822,
-0.038121599704027176,
-0.016375962644815445,
-0.026689717546105385,
-0.013046031817793846,
-0.022898443043231964,
0.006399759091436863,
0.06567659974098206,
-0.01973000541329384,
0.004794460255652666,
0.01722128875553608,
0.03914161026477814,
0.04523610696196556,
-0.015174311585724354,
-0.01810307800769806,
-0.005838897079229355,
-0.0010296473046764731,
-0.029772143810987473,
0.013675061985850334,
0.03323407471179962,
-0.0031443925108760595,
-0.02809281088411808,
0.0035091706085950136,
-0.0032505120616406202,
0.04335501044988632,
-0.0016328791389241815,
-0.003463431028649211,
0.03709845989942551,
0.004688496235758066,
-0.007447176147252321,
-0.008665300905704498,
-0.004079461097717285,
-0.014055149629712105,
0.05120587721467018,
-0.009091569110751152,
-0.03833196312189102,
-0.030774762853980064,
-0.021417399868369102,
0.019487440586090088,
-0.03902933746576309,
0.015254650264978409,
-0.011242525652050972,
0.06400223076343536,
-0.017101626843214035,
0.013855971395969391,
-0.005331551190465689,
-0.00702901603654027,
-0.0020036292262375355,
-0.01040619146078825,
-0.004987864755094051,
-0.003400996793061495,
-0.035298723727464676,
-0.016510868445038795,
-0.025537092238664627,
-0.06499707698822021,
0.02131873369216919,
0.07296877354383469,
-0.01826423592865467,
0.03229221701622009,
-0.045789625495672226,
0.05800475552678108,
0.02482598088681698,
-0.005399997346103191,
-0.021717660129070282,
-0.029396172612905502,
0.02118801698088646,
0.04900629073381424,
0.011612050235271454,
-0.005850458052009344,
0.015848036855459213,
0.039530884474515915,
-0.03503797575831413,
-0.007802925538271666,
-0.005440706852823496,
0.023616928607225418,
-0.030564306303858757,
-0.010709524154663086,
-0.053244370967149734,
0.020283116027712822,
-0.05381469428539276,
0.03611619770526886,
-0.01292829867452383,
-0.029088858515024185,
0.0015304903499782085,
0.02178943157196045,
0.018241604790091515,
-0.04464045539498329,
0.013589270412921906,
-0.01678655296564102,
0.014682168141007423,
0.023923523724079132,
-0.003707583760842681,
-0.016816765069961548,
0.01219633873552084,
0.04197198152542114,
0.0011795706814154983,
0.022984636947512627,
0.00002523112198105082,
-0.034485090523958206,
-0.020386993885040283,
-0.03386490046977997,
-0.039892226457595825,
0.03585588186979294,
-0.018180163577198982,
-0.03810111805796623,
0.009095420129597187,
-0.014931688085198402,
0.05521802976727486,
0.04046923667192459,
0.03062700293958187,
-0.004123378079384565,
0.06682349741458893,
-0.003989815711975098,
-0.025233518332242966,
-0.014813298359513283,
0.011675854213535786,
0.12530741095542908,
0.054021503776311874,
-0.041961438953876495,
-0.04309472441673279,
-0.016598274931311607,
0.0031763515435159206,
0.03867707774043083,
-0.023057708516716957,
0.028525039553642273,
0.002154406625777483,
0.015320726670324802,
-0.003042880678549409,
0.04117492213845253,
-0.015736237168312073,
0.022226572036743164,
0.02983296476304531,
-0.00041684479219838977,
-0.051913224160671234,
-0.019173549488186836,
0.022320173680782318,
-0.01853344589471817,
0.014495141804218292,
-0.012992441654205322,
0.030360925942659378,
0.003631339641287923,
0.0004170015745330602,
-0.0456254705786705,
-0.022552158683538437,
0.011045277118682861,
0.01103647705167532,
-0.03579016029834747,
0.00964226946234703,
-0.01926882378757,
-0.042477454990148544,
-0.0014911536127328873,
-0.020166166126728058,
0.03904236480593681,
-0.03511524572968483,
0.04769383743405342,
0.0003819650737568736,
-0.010045180097222328,
-0.014237371273338795,
0.04701133444905281,
0.007782537955790758,
-0.05359531566500664,
-0.016053706407546997,
-0.043007683008909225,
0.07326450943946838,
0.009167454205453396,
0.00907446350902319,
0.019950808957219124,
-0.010896237567067146,
0.0009849683847278357,
-0.024417784065008163,
0.008786270394921303,
0.000043783988076029345,
-0.011209112592041492,
-0.03261203318834305,
-0.010703442618250847,
-0.047224994748830795,
-0.0024788498412817717,
-0.00041359043098054826,
-0.03191876411437988,
-0.02328699454665184,
0.019699255004525185,
-0.013932015746831894,
-0.015384703874588013,
-0.028562335297465324,
-0.03426389396190643,
-0.006181377451866865,
-0.002478403737768531,
-0.008268781937658787,
-0.009761578403413296,
-0.03726249188184738,
0.016231132671236992,
0.011443267576396465,
0.03475765138864517,
0.021928997710347176,
-0.01690124161541462,
-0.03952347859740257,
-0.07939804345369339,
0.04878946393728256,
0.0020504083950072527,
-0.02481129579246044,
-0.007782129105180502,
-0.0008436337229795754,
-0.004608211573213339,
0.041642408818006516,
-0.025347910821437836,
0.008108247071504593,
-0.007776102051138878,
0.06486445665359497,
0.027566304430365562,
-0.033536653965711594,
-0.018767327070236206,
0.016337906941771507,
-0.0055028898641467094,
-0.012354784645140171,
-0.04887969419360161,
-0.0030308931600302458,
0.01935071125626564,
0.020365571603178978,
0.016232188791036606,
0.04734491556882858,
0.017124736681580544,
-0.007642799522727728,
-0.009076423943042755,
-0.02319234609603882,
0.0009435094543732703,
0.004672233946621418,
0.00731343450024724,
-0.022976450622081757,
0.012039531953632832,
0.0059080347418785095,
-0.009383725002408028,
0.022762028500437737,
-0.02035682275891304,
-0.012714629992842674,
0.011030620895326138,
-0.04367979243397713,
0.007866914384067059,
-0.004486500285565853,
-0.01638426072895527,
0.016360433772206306,
0.058000970631837845,
-0.00028899175231345,
0.004064641427248716,
-0.040787432342767715,
0.025848019868135452,
0.014180976897478104,
-0.012533451430499554,
0.028254063799977303,
0.026057232171297073,
-0.0035948040895164013,
-0.061616163700819016,
0.0031655498314648867,
0.03892429545521736,
0.027943387627601624,
0.023768678307533264,
0.030613748356699944,
0.01804126426577568,
-0.03467841073870659,
-0.06575652211904526,
0.022622721269726753,
0.019439831376075745,
0.016375165432691574,
0.04059154912829399,
-0.02359735034406185,
-0.0026342920027673244,
0.07452474534511566,
-0.027272196486592293,
-0.00006095105709391646,
-0.0005568286869674921,
-0.06639406085014343,
-0.03179281949996948,
-0.02270515263080597,
-0.00047685924801044166,
0.01203832682222128,
0.03314269706606865,
0.01729125715792179,
0.015521954745054245,
-0.0305644404143095,
-0.003969838377088308,
-0.040309637784957886,
0.001974252751097083,
-0.007182097528129816,
0.03417593240737915,
0.022734059020876884,
-0.005714357830584049,
0.021546877920627594,
0.003943244926631451,
0.025679955258965492,
-0.0013185031712055206,
-0.012742968276143074,
-0.09595976769924164,
-0.03018144518136978,
-0.02078474499285221,
0.029599253088235855,
0.036300528794527054,
-0.05322699621319771,
0.038698915392160416,
0.04060781002044678,
-0.04115026816725731,
-0.011361852288246155,
-0.012526600621640682,
-0.018195265904068947,
0.0016328120836988091,
0.025765545666217804,
-0.005718864966183901,
0.07744421809911728,
0.0018079017754644156,
0.06623806059360504,
0.04952526092529297,
0.036483924835920334,
-0.009440351277589798,
-0.019141796976327896,
0.004580267705023289,
0.005467007867991924,
0.03853628411889076,
-0.01267817709594965,
0.07986587285995483,
-0.01498890295624733,
-0.03935698792338371,
0.0387655608355999,
-0.034180425107479095,
0.03327944874763489,
-0.04305342212319374,
0.051936108618974686,
0.006866938900202513,
0.04235446825623512,
0.021869635209441185,
-0.0066254534758627415,
0.014925958588719368,
0.018500791862607002,
0.024530209600925446,
0.013351921923458576,
-0.010443412698805332,
0.020743699744343758,
0.044264454394578934,
-0.022183330729603767,
-0.05071054399013519,
0.0575098842382431,
0.00023300871544051915,
-0.035674914717674255,
-0.001214158139191568,
0.0034202877432107925,
0.006377048324793577,
-0.03659338876605034,
-0.002272876678034663,
-0.05673998221755028,
-0.004373735282570124,
0.02779674157500267,
-0.01207044254988432,
0.044921670109033585,
0.006851750425994396,
0.010844250209629536,
-0.032966550439596176,
-0.011938336305320263,
0.018660714849829674,
-0.00005468549716169946,
-0.08737239241600037,
-0.002632313407957554,
0.021166080608963966,
0.02687991037964821,
-0.019117828458547592,
-0.033610906451940536,
-0.060223426669836044,
0.016714872792363167,
0.02443835698068142,
0.015106136910617352,
-0.013352416455745697,
-0.029639866203069687,
-0.004000012297183275,
-0.05776716023683548,
-0.00040476673166267574,
0.024321937933564186,
-0.022765763103961945,
-0.018064282834529877,
-0.010034090839326382,
-0.004537341650575399,
0.010125738568603992,
0.04812609776854515,
0.014208979904651642,
-0.064609594643116,
0.013597134500741959,
-0.03636471554636955,
0.00424947589635849,
-0.055120207369327545,
-0.013809809461236,
-0.005827174987643957,
0.028806759044528008,
-0.0022390224039554596,
0.04266054555773735,
-0.04543931409716606,
0.023751256987452507,
0.01578543893992901,
-0.02404710464179516,
0.005288401152938604,
0.012203874066472054,
-0.00826909951865673,
0.020502015948295593,
-0.004845780320465565,
-0.04021448269486427,
0.047098901122808456,
-0.021752461791038513,
0.027282262220978737,
0.06764465570449829,
-0.04011024907231331,
-0.06644026935100555,
-0.021022139117121696,
-0.01241722796112299,
-0.0159777645021677,
0.014476761221885681,
-0.02706834301352501,
0.04048686847090721,
-0.049257099628448486,
-0.02953276038169861,
0.04972878098487854,
-0.07285614311695099,
-0.026272963732481003,
0.06350095570087433,
0.055013369768857956,
0.02511649578809738,
0.02619907446205616,
0.03372478112578392,
0.028321607038378716,
-0.03270450606942177,
0.06049230322241783,
0.01555079035460949,
0.02094474993646145,
0.015402176417410374,
0.019030386582016945,
0.00684796366840601,
-0.005738706327974796,
-0.0011885090498253703,
0.0036768733989447355,
0.033599112182855606,
-0.022044077515602112,
-0.008543905802071095,
0.03891579061746597,
0.004871433135122061,
-0.019406182691454887,
0.002424282254651189,
-0.021802658215165138,
0.043793655931949615,
-0.03881165012717247,
0.015424688346683979,
-0.015141714364290237,
-0.01849588192999363,
-0.027236640453338623,
0.029803412035107613,
-0.027234766632318497,
0.04219934344291687,
0.005416268017143011,
0.021894296631217003,
-0.010724751278758049,
0.008486514911055565,
0.0079629672691226,
-0.052735090255737305,
-0.00029489403823390603,
0.024360807612538338,
0.012324701063334942,
-0.010170599445700645,
-0.05416451022028923,
0.0027005940210074186,
-0.0487193763256073,
0.01237941812723875,
0.03444063663482666,
0.021906254813075066,
-0.025155821815133095,
-0.011006769724190235,
-0.02854905091226101,
0.04175545275211334,
0.00022757836268283427,
-0.014028915204107761,
-0.01087458897382021,
-0.03583388030529022,
0.014682849869132042,
0.00671056704595685
] |
<p>Why is light produced when an underwater bubble is collapsed with a sound wave?</p>
<p>I have come across this fact on a page (<a href="http://www.scientificamerican.com/article.cfm?id=tiny-bubbles-explain-puzz">similar to this</a>) but can't understand "Why". I'm just curious about this interesting fact. And, I want to know what's the currently accepted model for this phenomenon and how good it holds. Any kind of help regarding this topic will be highly appreciated.</p>
| 340 |
[
-0.03433004394173622,
-0.03684762865304947,
0.01739204302430153,
-0.057481709867715836,
-0.009167362935841084,
0.003407170530408621,
-0.03295726701617241,
-0.02544889971613884,
0.03769959509372711,
-0.03335593268275261,
0.030310016125440598,
0.06702527403831482,
0.03451245278120041,
0.0007532357703894377,
-0.008668499998748302,
0.003602293087169528,
0.011865670792758465,
-0.025297436863183975,
-0.007513163611292839,
-0.01707921177148819,
-0.020864952355623245,
0.01974490098655224,
-0.027536917477846146,
0.0019069657428190112,
-0.020406467840075493,
0.03043755516409874,
0.024743830785155296,
0.027316994965076447,
0.03653515502810478,
0.032030776143074036,
-0.0011568666668608785,
-0.026503324508666992,
-0.032147277146577835,
0.04075774922966957,
0.011065332219004631,
-0.011416899971663952,
-0.008122118189930916,
-0.008982096798717976,
0.02453307807445526,
0.007069448474794626,
0.006942487321794033,
-0.010120494291186333,
0.0011589005589485168,
0.024151355028152466,
-0.03386535868048668,
-0.01274910382926464,
-0.01587306521832943,
-0.03954211249947548,
0.002246847143396735,
-0.09144352376461029,
0.05027366057038307,
0.02431650087237358,
0.04695899039506912,
0.024832498282194138,
-0.005105934105813503,
0.030741402879357338,
0.07930207997560501,
0.11827030777931213,
-0.01449104119092226,
-0.03715479001402855,
0.01633835956454277,
0.015729956328868866,
-0.04412957653403282,
-0.02583349123597145,
-0.020464111119508743,
0.017048031091690063,
0.0025302863214164972,
-0.00929675716906786,
0.03551528975367546,
0.0036851929035037756,
0.024906931445002556,
-0.033178869634866714,
0.05404970794916153,
-0.02000248059630394,
0.01377905998378992,
-0.028722373768687248,
0.02557956799864769,
0.022262562066316605,
0.01848023571074009,
0.05364758148789406,
-0.0024153904523700476,
0.02059980109333992,
0.02289663255214691,
0.015508112497627735,
-0.0015448787016794086,
0.004462383687496185,
0.08364883065223694,
-0.024485718458890915,
-0.005510026589035988,
0.013836586847901344,
-0.01484114583581686,
0.006494367960840464,
-0.00009922738536261022,
0.016507191583514214,
-0.006596486084163189,
0.022372964769601822,
0.019793493673205376,
0.05953608825802803,
0.038113921880722046,
-0.05604923889040947,
-0.022392351180315018,
-0.007485049311071634,
0.04547477513551712,
0.06415361166000366,
-0.024259842932224274,
-0.01909252628684044,
-0.07251133769750595,
0.03764447197318077,
-0.03329285979270935,
-0.011218623258173466,
-0.038068633526563644,
0.0005789782735519111,
-0.0367940254509449,
-0.004480747971683741,
0.02615572325885296,
-0.040006957948207855,
0.015120946802198887,
-0.015627892687916756,
0.06302091479301453,
0.02988380379974842,
0.02123226225376129,
-0.027343202382326126,
0.017431434243917465,
-0.032620228826999664,
-0.056938741356134415,
0.03099910356104374,
-0.0015937950229272246,
-0.031267572194337845,
-0.03776354342699051,
0.07327410578727722,
-0.022319907322525978,
-0.030178969725966454,
0.009106057696044445,
0.0054095108062028885,
0.03359752893447876,
-0.044931937009096146,
-0.08712773025035858,
-0.04298873245716095,
0.04036989063024521,
0.001377762295305729,
-0.012805336154997349,
-0.04996500164270401,
0.015342909842729568,
0.04078703373670578,
0.06746461242437363,
-0.018868884071707726,
0.012773607857525349,
-0.028845658525824547,
0.06605017930269241,
-0.009432133287191391,
0.0010101033840328455,
-0.012675483711063862,
0.018706627190113068,
-0.015000533312559128,
0.02458549663424492,
-0.057626962661743164,
0.011973725631833076,
0.0268165972083807,
0.004043160006403923,
-0.03232185170054436,
0.057370059192180634,
-0.03356766328215599,
-0.007301948498934507,
0.002509862883016467,
0.004343171138316393,
-0.02706904336810112,
0.08419425785541534,
0.009669605642557144,
-0.03315258026123047,
0.03900320455431938,
-0.06864012032747269,
0.01273704506456852,
-0.010978772304952145,
0.0168472770601511,
0.004305114038288593,
-0.0286940298974514,
-0.007895724847912788,
-0.01138553861528635,
0.05085495114326477,
0.016982443630695343,
-0.006645222660154104,
-0.00303490343503654,
-0.05149689316749573,
-0.00153011130169034,
0.024478470906615257,
0.05293182656168938,
0.00605618953704834,
-0.03391457721590996,
-0.012285368517041206,
-0.05951905623078346,
-0.02668323554098606,
-0.05721990391612053,
0.026211775839328766,
-0.012489193119108677,
-0.0017700532916933298,
0.0019380509620532393,
-0.005974918138235807,
0.010314518585801125,
-0.004447245970368385,
-0.000465573335532099,
-0.014428450725972652,
0.015899650752544403,
-0.0003909562947228551,
0.00577510567381978,
0.035639651119709015,
0.01867557317018509,
-0.01695144735276699,
0.004206028766930103,
0.0012008115882053971,
-0.0020004233811050653,
-0.004268602933734655,
0.00789352785795927,
-0.00156047020573169,
0.00591896940022707,
-0.052076760679483414,
-0.025765007361769676,
0.05261803790926933,
0.001864628167822957,
-0.02115001529455185,
0.0029635850805789232,
-0.019955627620220184,
0.06523445248603821,
0.025929875671863556,
-0.029960544779896736,
0.00559631921350956,
0.03470104560256004,
0.017217813059687614,
0.03419475257396698,
0.009573433548212051,
-0.01925027184188366,
-0.054079506546258926,
0.016129106283187866,
0.03981829807162285,
0.011324059218168259,
-0.011922149918973446,
0.024103637784719467,
-0.011528324335813522,
0.00892002135515213,
0.03568084165453911,
0.024203279986977577,
-0.026024257764220238,
-0.03525175154209137,
-0.001152771757915616,
0.054624054580926895,
-0.0035702150780707598,
0.012643867172300816,
0.029430201277136803,
0.04087616130709648,
0.04259900748729706,
-0.04632473364472389,
-0.04542797431349754,
0.02358660101890564,
-0.0079423813149333,
0.01663702167570591,
-0.061245355755090714,
0.011177359148859978,
0.024339158087968826,
-0.04717568680644035,
0.023605775088071823,
-0.0006919125444255769,
-0.005153936799615622,
0.026025641709566116,
-0.026175716891884804,
-0.03622685372829437,
-0.0024200885090976954,
0.03541145846247673,
0.012754539027810097,
0.0021646665409207344,
0.014795927330851555,
-0.05647074058651924,
0.0017914698692038655,
-0.02908431366086006,
-0.01105207484215498,
-0.03051917441189289,
-0.0168202705681324,
0.014811228029429913,
0.0307234525680542,
0.04439869895577431,
-0.053853027522563934,
-0.04450926557183266,
-0.010766956955194473,
0.00023903218971099705,
0.008887785486876965,
0.01534431241452694,
-0.023765457794070244,
0.025379236787557602,
-0.02187229134142399,
-0.0054075829684734344,
0.020703069865703583,
-0.038230638951063156,
-0.01537325605750084,
0.005894029513001442,
-0.0041023301891982555,
-0.043335769325494766,
-0.018608568236231804,
-0.06266938894987106,
0.011732405982911587,
-0.023577464744448662,
0.0004889683332294226,
0.0527924969792366,
0.020863626152276993,
-0.061334963887929916,
0.015320557169616222,
-0.025215066969394684,
-0.06023772433400154,
-0.01960545778274536,
-0.005465320311486721,
0.025080353021621704,
-0.058359574526548386,
0.03145580738782883,
0.006279026623815298,
-0.052961576730012894,
-0.005258446093648672,
-0.024010390043258667,
-0.04468539357185364,
0.02450878731906414,
-0.010342353023588657,
0.05852225050330162,
-0.01911909505724907,
-0.049635518342256546,
0.08030521869659424,
-0.015232201665639877,
-0.02579306624829769,
-0.029955197125673294,
-0.006140704266726971,
0.01340256817638874,
-0.03306389972567558,
0.0064309644512832165,
0.06797695904970169,
-0.05189260467886925,
0.032155826687812805,
-0.0012116995640099049,
0.026009956374764442,
0.005932140164077282,
0.03671690821647644,
-0.013758807443082333,
-0.018554335460066795,
-0.011999831534922123,
-0.005587515886873007,
0.013056358322501183,
0.008530844934284687,
-0.03887948766350746,
-0.018977858126163483,
-0.02649081125855446,
-0.021228164434432983,
0.028414521366357803,
-0.04778677597641945,
0.04230615124106407,
0.02273845113813877,
-0.028422849252820015,
-0.045035574585199356,
-0.012343755923211575,
-0.024901483207941055,
-0.0057080574333667755,
0.03010849468410015,
0.01577584631741047,
0.045336056500673294,
-0.012092855758965015,
-0.026043327525258064,
0.03139908239245415,
0.04749476537108421,
-0.031201105564832687,
-0.05308885499835014,
-0.021402621641755104,
-0.01309827622026205,
0.04795730486512184,
0.0008259091409854591,
0.012928861193358898,
0.0740678682923317,
0.023278234526515007,
0.033158302307128906,
-0.03147687762975693,
-0.018954750150442123,
-0.014146387577056885,
-0.023397447541356087,
0.009393200278282166,
-0.006733547430485487,
0.049990955740213394,
0.015479560010135174,
0.05463317409157753,
0.030763689428567886,
0.007149063516408205,
0.031336646527051926,
-0.012889975681900978,
-0.07544375956058502,
-0.015115777030587196,
-0.021195467561483383,
0.006978274323046207,
-0.02408265694975853,
0.00022909815015736967,
-0.028109615668654442,
0.005217122379690409,
-0.047761015594005585,
-0.06217114254832268,
0.009628250263631344,
-0.07825812697410583,
0.013185729272663593,
0.02189650759100914,
-0.03148182854056358,
-0.03535832092165947,
0.017424272373318672,
0.00029748614178970456,
0.025813033804297447,
0.010437743738293648,
0.018825115635991096,
-0.04780037701129913,
0.03536966070532799,
0.0028754419181495905,
-0.018549563363194466,
0.011784587986767292,
0.016612714156508446,
0.03543184697628021,
0.029231106862425804,
-0.01680152118206024,
0.0019974473398178816,
0.023589663207530975,
0.026554202660918236,
-0.021579386666417122,
-0.00301373191177845,
-0.024552566930651665,
-0.020161369815468788,
0.009963693097233772,
0.009271625429391861,
0.04105980321764946,
-0.013064289465546608,
0.00023706324282102287,
-0.007695208769291639,
-0.001541630132123828,
-0.005072612315416336,
0.04052327200770378,
0.020104987546801567,
0.017698535695672035,
0.014509538188576698,
-0.026986727491021156,
-0.019739801064133644,
-0.03951837867498398,
-0.0006329029565677047,
-0.003902301425114274,
0.0489903949201107,
-0.031598664820194244,
-0.018292006105184555,
0.018247632309794426,
-0.007142713759094477,
0.03649907559156418,
-0.0345822311937809,
0.013906176201999187,
-0.008371174335479736,
-0.029973097145557404,
0.011392052285373211,
-0.0003183719527442008,
0.05874935910105705,
0.05484791100025177,
0.013757623732089996,
-0.00694266427308321,
-0.049342766404151917,
-0.037963416427373886,
0.01764708198606968,
0.01718972437083721,
0.023035351186990738,
0.013562550768256187,
-0.07159759104251862,
-0.03902445361018181,
0.005859583616256714,
-0.062266185879707336,
0.025632742792367935,
0.0013069738633930683,
0.010316348634660244,
0.016372324898838997,
0.0027114779222756624,
-0.00003033245593542233,
0.033189620822668076,
0.007598294410854578,
0.020078938454389572,
-0.013702267780900002,
-0.026682326570153236,
-0.014803786762058735,
-0.00011548015027074143,
-0.0031346273608505726,
0.04380951449275017,
-0.018644820898771286,
-0.005730488337576389,
-0.017377976328134537,
0.018663395196199417,
-0.039902545511722565,
-0.055039044469594955,
0.015323391184210777,
-0.02758549526333809,
-0.024483827874064445,
0.046418365091085434,
-0.005173310171812773,
-0.06739100068807602,
0.019329413771629333,
0.03874358907341957,
-0.01816922426223755,
-0.010993490926921368,
-0.018956445157527924,
0.013372604735195637,
0.024712463840842247,
0.015158692374825478,
0.05345754697918892,
0.0518474355340004,
-0.0362577885389328,
-0.02763165533542633,
-0.03483846038579941,
0.014157476834952831,
-0.038152359426021576,
-0.023905178532004356,
0.010321041569113731,
0.022398250177502632,
0.004998748656362295,
0.04456198215484619,
-0.02545437216758728,
0.011616758070886135,
0.01661195419728756,
-0.03706233203411102,
0.008369091898202896,
0.031005961820483208,
-0.002615194534882903,
0.00616806885227561,
-0.015001427382230759,
0.03197892755270004,
0.059199269860982895,
-0.01528226863592863,
0.02833639644086361,
-0.004279640968888998,
0.002678743563592434,
0.010545125231146812,
-0.005140423774719238,
0.028580864891409874,
-0.00761767802760005,
-0.0016759581631049514,
0.03843243047595024,
-0.05038030073046684,
0.038370974361896515,
-0.016500303521752357,
0.00012062156019965187,
0.051313791424036026,
-0.049569521099328995,
-0.0021246611140668392,
0.004617557395249605,
-0.0017596130492165685,
0.06097742170095444,
-0.06856217980384827,
0.041094787418842316,
0.031404297798871994,
0.0030366242863237858,
-0.05903632193803787,
-0.05623193457722664,
0.06075851246714592,
0.041715625673532486,
-0.01390492357313633,
-0.04721103236079216,
0.007994737476110458,
-0.006135991308838129,
-0.04332739859819412,
0.016115568578243256,
-0.02532253786921501,
-0.04129885882139206,
0.014938371255993843,
0.029053105041384697,
0.004089167341589928,
0.034672148525714874,
0.0019211327889934182,
-0.027480443939566612,
0.008082903921604156,
-0.015254325233399868,
-0.020448071882128716,
0.0029598178807646036,
0.04541013762354851,
-0.025231316685676575,
-0.048708681017160416,
-0.01758861169219017,
-0.0013082684017717838,
0.01021175179630518,
-0.028300996869802475,
0.007416774518787861,
0.005483788903802633,
0.05937247350811958,
0.02371792681515217,
-0.018858948722481728,
0.009729022160172462,
-0.003031100146472454,
0.0302113126963377,
0.0070666042156517506,
-0.019482942298054695,
-0.0378115139901638,
-0.020031839609146118,
0.009542711079120636,
0.0037411944940686226,
0.007686682976782322,
-0.0160387996584177,
0.06228654459118843,
-0.04054607078433037,
-0.013488000258803368,
0.006644746288657188,
-0.02252974733710289,
0.03450249880552292,
0.007355682086199522,
0.012812083587050438,
0.03801482170820236,
0.039691247045993805,
-0.014072775840759277,
-0.03252584859728813,
-0.018171437084674835,
0.0003561178455129266,
0.06675523519515991,
-0.03153810277581215,
0.03546418249607086,
0.020159685984253883,
-0.04685257002711296,
0.008189923129975796,
-0.05968810245394707,
-0.014693685807287693,
0.011775973252952099,
-0.014118878170847893,
0.029161877930164337,
-0.033556412905454636,
-0.001342550851404667,
0.03412393853068352,
0.033193349838256836,
0.03671093285083771,
0.06499127298593521,
0.07812543213367462,
0.043564777821302414,
-0.0004175498033873737,
-0.006195682566612959,
-0.055298205465078354,
0.0538051575422287,
-0.04223731905221939,
0.056317489594221115,
-0.0023417051415890455,
0.01710035838186741,
0.031303100287914276,
-0.0062210154719650745,
0.018797297030687332,
-0.058489128947257996,
0.011964083649218082,
-0.0016902114730328321,
0.027253320440649986,
0.013653779402375221,
-0.01307271234691143,
0.0038291418459266424,
-0.000211215898161754,
0.021062113344669342,
0.012714176438748837,
0.047952573746442795,
0.0012335911160334945,
-0.04966167360544205,
-0.005219743121415377,
-0.0036914197262376547,
-0.01671978086233139,
0.03892367705702782,
-0.010600716806948185,
-0.045434024184942245,
0.026416726410388947,
-0.039134152233600616,
-0.000016491731003043242,
-0.011867127381265163,
0.007142453920096159,
-0.03223799541592598,
0.03645063191652298,
0.018436679616570473,
0.028832362964749336,
0.003013784531503916,
-0.03144789859652519,
0.13157671689987183,
0.013576463796198368,
0.023216091096401215,
-0.03371929004788399,
-0.0010410597315058112,
-0.02776665799319744,
0.020237762480974197,
-0.014871286228299141,
-0.015040344558656216,
-0.008697294630110264,
0.03606688603758812,
0.022053062915802002,
0.07452509552240372,
0.006870619021356106,
-0.018092263489961624,
-0.011867748573422432,
-0.017746735364198685,
-0.057778842747211456,
0.03256435692310333,
0.023207159712910652,
-0.02473266050219536,
0.04494132474064827,
-0.0482385978102684,
0.009022855199873447,
-0.022227780893445015,
-0.03764018788933754,
-0.03415635600686073,
-0.02612435817718506,
0.023498933762311935,
-0.02121639996767044,
-0.052391789853572845,
-0.01344236545264721,
0.01879757083952427,
-0.04621448367834091,
-0.03881356120109558,
0.00928038265556097,
0.007058895658701658,
-0.02170812338590622,
-0.00713487109169364,
-0.018601268529891968,
0.010058770887553692,
0.0048179165460169315,
0.009652000851929188,
0.02328004501760006,
-0.029461650177836418,
0.00710040470585227,
-0.017617737874388695,
0.07443257421255112,
-0.011290155351161957,
0.02520597167313099,
-0.029086019843816757,
0.01885353773832321,
0.009171325713396072,
-0.028544563800096512,
-0.036635272204875946,
0.020642122253775597,
0.019977495074272156,
-0.007854757830500603,
-0.04796547815203667,
0.004702750127762556,
0.008886314928531647,
0.011105620302259922,
0.01923244632780552,
-0.02085878700017929,
0.008031520992517471,
-0.018886417150497437,
-0.025281144306063652,
0.028386997058987617,
-0.014689198695123196,
-0.009155112318694592,
-0.026892872527241707,
0.00475666718557477,
-0.060776449739933014,
-0.00974255334585905,
0.018029602244496346,
0.009938167408108711,
0.041926391422748566,
0.03261391445994377,
-0.02266504056751728,
-0.0343492217361927,
-0.07313906401395798,
0.06216518208384514,
-0.01721779815852642,
-0.026990389451384544,
-0.066951684653759,
0.013975529931485653,
0.00993830431252718,
0.04107912257313728,
-0.0372653491795063,
0.011912253685295582,
0.0002913046919275075,
0.010939263738691807,
0.01163520384579897,
-0.029818551614880562,
-0.05580028519034386,
0.023947356268763542,
0.019942032173275948,
-0.025125470012426376,
0.020087700337171555,
-0.00004291554068913683,
0.019993815571069717,
-0.004906866699457169,
0.032958656549453735,
0.01503088977187872,
-0.03281830623745918,
-0.037777502089738846,
0.002585506998002529,
0.011537320911884308,
-0.01556890457868576,
0.013139421120285988,
0.03685050830245018,
-0.017227202653884888,
0.020333966240286827,
0.0024012664798647165,
0.029867341741919518,
0.012290707789361477,
0.02831890434026718,
0.0031586987897753716,
0.010803812183439732,
-0.03525688499212265,
0.022097306326031685,
-0.009295550175011158,
-0.022485807538032532,
-0.05060306191444397,
0.00020261968893464655,
0.014375166967511177,
0.00013018364552408457,
-0.023991093039512634,
0.01564416103065014,
-0.01924111321568489,
0.004496066831052303,
0.017796913161873817,
0.02901286445558071,
-0.00713866762816906,
0.005859485827386379,
0.06403258442878723,
0.009745837189257145,
0.03378162160515785,
0.019330741837620735,
-0.06703441590070724,
0.03662128001451492,
-0.03901413083076477,
-0.0543137826025486,
0.03785016015172005,
-0.002682372694835067,
0.014184464700520039,
0.022010890766978264,
0.035041168332099915,
-0.04169661924242973,
0.05384194850921631,
-0.002749650739133358,
-0.025354795157909393,
-0.01867024041712284,
-0.0194865632802248,
0.044776637107133865,
0.023483000695705414,
0.03100777603685856,
-0.005546249449253082,
-0.0236040148884058,
0.03673649579286575,
0.018785156309604645,
-0.0007442111382260919,
0.027324045076966286,
0.006755142472684383,
-0.01880238950252533,
0.02823038212954998,
0.011035006493330002,
0.023091468960046768,
0.045857902616262436,
0.05967342108488083,
-0.006076400633901358,
0.06762515008449554,
0.028145456686615944,
-0.011483732610940933,
-0.13265791535377502,
-0.011386467143893242,
0.003480008337646723,
0.01797502487897873,
0.019922172650694847,
-0.03913511335849762,
0.05633952096104622,
0.011079758405685425,
-0.08519111573696136,
0.014543343335390091,
-0.03761682286858559,
-0.01523368526250124,
-0.010444835759699345,
-0.01776459999382496,
-0.028978101909160614,
0.08302608877420425,
-0.008671225979924202,
0.01584833301603794,
0.02102787233889103,
0.024660073220729828,
-0.008531399071216583,
0.012023400515317917,
-0.014998437836766243,
0.04401606321334839,
0.010770507156848907,
0.032483480870723724,
0.0790339857339859,
-0.017222905531525612,
-0.005926819518208504,
0.01459116954356432,
-0.005050533916801214,
0.01257230807095766,
0.001759548089466989,
0.01714513450860977,
0.007147499825805426,
-0.0028336700052022934,
0.015261615626513958,
-0.0047829644754529,
-0.00980387069284916,
0.04053833335638046,
0.06569907814264297,
0.003963872324675322,
0.0019645285792648792,
-0.0260503850877285,
-0.0014155620010569692,
-0.05253729969263077,
-0.034896641969680786,
0.00992544461041689,
0.004602161701768637,
0.010314230807125568,
0.018704691901803017,
-0.01450476236641407,
-0.00391603447496891,
-0.0010867173550650477,
-0.016345178708434105,
-0.0750575140118599,
0.0044433241710066795,
0.002874205354601145,
0.032398078590631485,
-0.03265627846121788,
0.03148645907640457,
-0.00022692234779242426,
-0.04533035680651665,
-0.00427847309038043,
-0.02465476281940937,
0.00328302220441401,
-0.02287139929831028,
-0.031029298901557922,
0.01501155924052,
0.020390497520565987,
0.005394744221121073,
0.002649367554113269,
-0.032136157155036926,
0.026462193578481674,
0.019936522468924522,
0.030723076313734055,
0.02086779847741127,
-0.06122446060180664,
-0.0645982027053833,
-0.08141855150461197,
0.031342051923274994,
-0.005691990256309509,
-0.021747728809714317,
-0.036856360733509064,
-0.005630275700241327,
0.009179174900054932,
0.04731062427163124,
0.05760445073246956,
0.002093674149364233,
-0.018017251044511795,
0.0462527759373188,
-0.0030849226750433445,
0.020799580961465836,
-0.025682158768177032,
0.013011008501052856,
0.008409278467297554,
-0.006072322838008404,
-0.021013911813497543,
0.042767249047756195,
-0.02500283718109131,
-0.007860744372010231,
0.03206685930490494,
-0.01950553059577942,
0.009595407173037529,
-0.03787988796830177,
-0.02180112525820732,
0.0652076005935669,
0.017051460221409798,
-0.01156519167125225,
0.09479157626628876,
-0.0016546190017834306,
0.004928485490381718,
0.016510076820850372,
-0.031576547771692276,
-0.046412304043769836,
0.04062647745013237,
-0.012293944135308266,
0.009547240100800991,
0.005834683775901794,
-0.027942420914769173,
0.03987445309758186,
-0.039282459765672684,
0.022436680272221565,
-0.005786977242678404,
-0.03442069888114929,
-0.0126613425090909,
0.04551410302519798,
-0.007422246970236301,
0.03529674932360649,
-0.03163272142410278,
0.03573630005121231,
0.0015731033636257052,
-0.01403049100190401,
-0.019284363836050034,
0.045212678611278534,
0.004878331907093525,
0.02874482050538063,
0.02369352988898754,
0.021307652816176414,
0.014464232139289379,
0.0376812219619751,
0.0040342723950743675,
-0.02495325356721878,
-0.02163798175752163,
-0.030467458069324493,
0.0198782030493021,
-0.014109431765973568,
-0.019803281873464584,
0.014094325713813305,
-0.015819715335965157,
0.09106513857841492,
-0.02782929688692093,
0.03754552826285362,
-0.02097993716597557,
-0.02861209027469158,
-0.017123660072684288,
0.004685217048972845,
0.02226388454437256,
0.04101972654461861,
-0.015531906858086586,
-0.004068685229867697,
-0.004205638077110052,
0.004325742833316326,
0.018677840009331703,
0.0007049747509881854,
-0.005281571298837662,
0.014772304333746433,
-0.003232982475310564,
0.009300190024077892,
0.0035053687170147896,
-0.014486315660178661,
-0.010465792380273342,
0.02740912325680256,
0.022717265412211418,
-0.029332447797060013,
0.026641845703125,
-0.02311566472053528,
-0.035198237746953964,
0.07650324702262878,
-0.0603875033557415,
-0.0026554083451628685,
-0.008758564479649067,
0.017730940133333206,
-0.0036417057272046804,
-0.017606373876333237
] |
<p>I recently found out about sending stuff into space and using the unique zero gravity and cosmic radiation riddled environment to investigate stuff like crystal growth. Since thin film science is a hot topic still, I am wondering what can be done in space?</p>
<p>Things that come to mind, which likely have been covered already, include radiation protection, energy conversion, perhaps even using cosmic radiation to stimulate some desirable chemical reactions that only need some high-energy source to get started.</p>
<p>As an aside, it would be preferable if said experiments could be done on an amateur hobbyist's budget, but it not, it's a fun thought experiment at least to see what could be done.</p>
| 10,695 |
[
0.03571155667304993,
-0.05572100356221199,
-0.013297843746840954,
-0.0043897610157728195,
0.02755005843937397,
0.0032882308587431908,
-0.014365911483764648,
-0.005173769313842058,
0.009217718616127968,
-0.07961182296276093,
-0.0005298054893501103,
0.03963298350572586,
0.02773379348218441,
0.05966861546039581,
-0.03321291506290436,
-0.007289730943739414,
-0.006442531943321228,
-0.05956592783331871,
-0.03157811239361763,
-0.02177545242011547,
0.008612675592303276,
-0.00750989792868495,
0.003448045114055276,
0.01190140563994646,
-0.03827458620071411,
0.01800156757235527,
-0.03673489764332771,
-0.017261603847146034,
-0.0030388992745429277,
0.025879450142383575,
-0.012469799257814884,
-0.005243286490440369,
0.007134789135307074,
-0.0013662866549566388,
0.025262104347348213,
0.004318550694733858,
-0.02670992538332939,
-0.01968006044626236,
0.0008483274141326547,
0.004797686357051134,
-0.02107248082756996,
0.010038468055427074,
0.003720158012583852,
0.0217776820063591,
0.008893782272934914,
-0.008851238526403904,
0.019631294533610344,
-0.038446858525276184,
0.06650195270776749,
-0.07202492654323578,
0.013654942624270916,
-0.00314929336309433,
0.016541186720132828,
0.033947475254535675,
0.026593901216983795,
0.01071973331272602,
0.06767844408750534,
0.05978923663496971,
0.013842355459928513,
0.009665099903941154,
0.0075952098704874516,
0.0029704789631068707,
-0.02458604983985424,
-0.02874613367021084,
-0.003178847022354603,
-0.009025674313306808,
-0.02005648799240589,
-0.02070321887731552,
0.028169389814138412,
0.003365550423040986,
0.02257685549557209,
0.032658763229846954,
-0.024122437462210655,
-0.001395810511894524,
-0.02049405872821808,
-0.004109769593924284,
0.0013793972320854664,
-0.003275560447946191,
0.03382042795419693,
0.05498119443655014,
-0.015983695164322853,
-0.00298762833699584,
-0.025410611182451248,
0.06067946180701256,
-0.03816153481602669,
0.014846268109977245,
0.0795685350894928,
-0.020475558936595917,
0.010446793399751186,
-0.004497520159929991,
0.008476478047668934,
0.017511216923594475,
0.03832888603210449,
0.0559995137155056,
-0.06839516758918762,
-0.02765767276287079,
0.02264361083507538,
0.05484693869948387,
-0.03912211209535599,
-0.012336699292063713,
0.03177354484796524,
0.025560768321156502,
0.016376934945583344,
0.07472625374794006,
0.025979671627283096,
-0.042200252413749695,
-0.0035298659931868315,
0.007563968189060688,
0.00778510607779026,
0.02259957417845726,
-0.03183819726109505,
0.01959173008799553,
0.011768287047743797,
-0.02259274572134018,
0.049533676356077194,
0.003005007281899452,
-0.007964826188981533,
-0.040525827556848526,
0.042830485850572586,
0.045518357306718826,
0.04360270872712135,
0.0033084037713706493,
0.055431757122278214,
0.013233613222837448,
-0.07776835560798645,
0.02285025082528591,
0.0013658347306773067,
-0.0346660241484642,
0.0029680407606065273,
0.02447732351720333,
-0.0015427562175318599,
-0.016342902556061745,
0.016867971047759056,
-0.04485476389527321,
0.02154882438480854,
0.02844262681901455,
-0.061514534056186676,
-0.07020078599452972,
0.023667579516768456,
0.024310752749443054,
-0.03222997114062309,
-0.054271336644887924,
-0.017622945830225945,
-0.0034689309541136026,
0.03783782944083214,
-0.00020927131117787212,
-0.014727460220456123,
-0.04196249693632126,
0.05076374486088753,
0.01832282915711403,
-0.047181978821754456,
0.016683228313922882,
-0.006734393071383238,
-0.05032673850655556,
0.008950806222856045,
-0.053347595036029816,
0.026606980711221695,
0.02564316801726818,
0.011839954182505608,
-0.05529690161347389,
0.07436138391494751,
-0.04861962050199509,
0.016604522243142128,
-0.01661980152130127,
-0.018680015578866005,
0.015801122412085533,
0.035328689962625504,
0.013760347850620747,
0.015268951654434204,
0.022348247468471527,
0.018801433965563774,
0.04465554654598236,
0.028875967487692833,
-0.008985313586890697,
0.06558893620967865,
-0.043075066059827805,
-0.007056838367134333,
-0.00857501570135355,
0.0037181563675403595,
-0.016618961468338966,
-0.008155553601682186,
-0.0075309136882424355,
0.009446895681321621,
0.0033521540462970734,
0.015442919917404652,
0.06447341293096542,
-0.012992938049137592,
-0.0351058691740036,
0.0013655985239893198,
-0.025730298832058907,
0.0141313336789608,
-0.061269693076610565,
0.008143313229084015,
-0.03133309260010719,
-0.018878797069191933,
-0.0026472434401512146,
0.036452505737543106,
0.026766113936901093,
-0.029394056648015976,
-0.07900235801935196,
0.01979193650186062,
0.012072285637259483,
-0.012755411677062511,
0.01812834106385708,
0.034187037497758865,
0.02948088012635708,
0.006176373455673456,
0.01525860745459795,
-0.023350177332758904,
-0.01736355759203434,
-0.037836961448192596,
-0.018836570903658867,
-0.059941042214632034,
0.03829372674226761,
0.02471843734383583,
-0.015842625871300697,
0.01986081153154373,
-0.0009203372173942626,
-0.01735154539346695,
0.03339330106973648,
0.034191906452178955,
0.09226667135953903,
0.05299020931124687,
-0.003969361539930105,
0.03346993401646614,
0.009544573724269867,
0.05652116611599922,
0.04329582303762436,
0.016818836331367493,
-0.044880710542201996,
-0.05780988931655884,
-0.031874965876340866,
0.056132007390260696,
-0.00936745572835207,
-0.018301457166671753,
0.06265028566122055,
0.009123279713094234,
-0.008166383020579815,
0.03963249921798706,
0.03367086127400398,
-0.015491769649088383,
0.01881963387131691,
0.04110331833362579,
0.02285420522093773,
-0.003536032047122717,
0.0035163802094757557,
0.01629282906651497,
0.025595510378479958,
-0.01833074726164341,
-0.012326089665293694,
0.01240484043955803,
0.003977653570473194,
0.01512113120406866,
0.05001642927527428,
0.009810702875256538,
-0.041058894246816635,
0.0037426427006721497,
-0.014015274122357368,
-0.035535626113414764,
0.029484372586011887,
0.032774925231933594,
0.004902637097984552,
0.002593399491161108,
-0.003501896746456623,
-0.022316958755254745,
0.012913577258586884,
-0.018853317946195602,
0.01384155172854662,
0.04253385215997696,
-0.07499389350414276,
0.019813712686300278,
0.02362990193068981,
0.009708222933113575,
-0.016665183007717133,
0.005424929317086935,
0.04450554773211479,
0.012805604375898838,
0.06069980934262276,
-0.0168675035238266,
-0.03054339811205864,
-0.0007030095439404249,
-0.054422903805971146,
0.005286050494760275,
0.007657782174646854,
-0.0474240817129612,
0.021759500727057457,
-0.017018454149365425,
-0.03810906037688255,
0.0059277210384607315,
-0.008044408634305,
-0.007633841596543789,
0.03594140708446503,
-0.0035168719477951527,
-0.020269349217414856,
0.016354408115148544,
0.010288597084581852,
-0.01778712123632431,
-0.004176074638962746,
0.020916281268000603,
0.009651962667703629,
-0.0013828042428940535,
-0.025899820029735565,
0.038575466722249985,
-0.011283928528428078,
-0.008223473094403744,
0.020872414112091064,
0.01519745122641325,
-0.0023047099821269512,
-0.029011627659201622,
0.02554433047771454,
0.03278462588787079,
-0.049791119992733,
0.03430201858282089,
-0.04288423806428909,
-0.010901971720159054,
0.019700543954968452,
-0.012761007063090801,
0.013135342858731747,
-0.03596283122897148,
-0.0027748660650104284,
0.09323962777853012,
0.01961435005068779,
0.004321439191699028,
-0.0264758188277483,
-0.052429523319005966,
-0.014329439029097557,
-0.015441974624991417,
0.028477447107434273,
0.025537312030792236,
0.010801047086715698,
-0.017053933814167976,
0.03114328719675541,
0.016646811738610268,
0.003845394589006901,
0.03652707114815712,
-0.0003373398503754288,
-0.031361036002635956,
0.035167962312698364,
0.023897821083664894,
0.0138203464448452,
0.03940025344491005,
-0.02255212515592575,
0.0008734004222787917,
0.014297405257821083,
0.026001183316111565,
0.03245756775140762,
-0.04593938589096069,
0.01438963320106268,
-0.0068829781375825405,
0.013723611831665039,
-0.017059985548257828,
0.008081337437033653,
0.012596914544701576,
-0.0023455703631043434,
0.015846382826566696,
0.031051617115736008,
0.06513763964176178,
0.005629872437566519,
-0.028132211416959763,
-0.006370036397129297,
0.08362513035535812,
0.041687458753585815,
-0.021135743707418442,
-0.005585071165114641,
-0.002414820482954383,
-0.003328238846734166,
0.01042808685451746,
0.02549028769135475,
0.05911097675561905,
0.018415266647934914,
0.03316089138388634,
0.02375199645757675,
-0.021733002737164497,
-0.0032191742211580276,
-0.05391453951597214,
-0.018017051741480827,
-0.05608832836151123,
0.05955880135297775,
0.018221549689769745,
0.043317582458257675,
0.02913753315806389,
-0.03114444948732853,
0.03689685836434364,
-0.009279984049499035,
-0.06636660546064377,
0.01848723366856575,
-0.02961716242134571,
0.010862083174288273,
-0.006715335417538881,
0.06528567522764206,
-0.03944981098175049,
-0.0242883563041687,
-0.03495816886425018,
-0.022280149161815643,
0.03554375097155571,
-0.0434579998254776,
0.011591275222599506,
-0.03903955966234207,
-0.0677420124411583,
-0.06794687360525131,
0.012598364613950253,
0.05289581045508385,
-0.011792147532105446,
-0.014249540865421295,
-0.037758950144052505,
-0.03349225968122482,
-0.02533179521560669,
0.011212693527340889,
-0.014367811381816864,
-0.013052516616880894,
0.0712273120880127,
0.010923093184828758,
-0.006163428537547588,
-0.030585426837205887,
0.000011787637049565092,
-0.0009681807132437825,
0.01728634536266327,
-0.02993137575685978,
0.0232440996915102,
-0.03654441609978676,
-0.03723335638642311,
-0.010942162945866585,
0.008048114366829395,
0.007712026592344046,
0.005441822111606598,
0.0020946688018739223,
-0.016446156427264214,
0.0001754255499690771,
-0.021535037085413933,
0.004911568481475115,
0.0664568841457367,
0.0034726986195892096,
-0.014292187057435513,
-0.002299648243933916,
-0.04775640368461609,
-0.02446204423904419,
-0.02823708951473236,
0.03473791480064392,
0.011292671784758568,
-0.02078585885465145,
0.014699614606797695,
-0.01948736049234867,
0.027516674250364304,
-0.03976109251379967,
-0.028368499130010605,
-0.0025534224696457386,
0.05433083698153496,
-0.0010021647904068232,
0.008560001850128174,
-0.030550606548786163,
0.02914317697286606,
0.061167921870946884,
-0.008066465146839619,
0.028767190873622894,
-0.0802587941288948,
0.03372097387909889,
0.040257323533296585,
0.030644221231341362,
-0.025604136288166046,
-0.006992844864726067,
-0.05098031833767891,
-0.009206505492329597,
0.008098163641989231,
-0.02190469019114971,
0.02176593989133835,
-0.028693124651908875,
0.0029388226103037596,
-0.024802248924970627,
0.007232071831822395,
0.003030763240531087,
0.0060330708511173725,
-0.007474473677575588,
0.0015869237249717116,
-0.0002775140746962279,
-0.016162363812327385,
0.020808875560760498,
0.02122834138572216,
0.02175944484770298,
0.031704310327768326,
0.02679213508963585,
0.011559112928807735,
0.004105635453015566,
0.017237992957234383,
-0.013277769088745117,
-0.06310463696718216,
-0.005754433106631041,
0.02584715560078621,
-0.006983411964029074,
0.05342201516032219,
-0.02424098551273346,
-0.05536457523703575,
0.043273620307445526,
-0.01629989594221115,
-0.02984585054218769,
-0.08073287457227707,
-0.007221073843538761,
-0.007360071875154972,
0.050679728388786316,
0.04119614511728287,
0.05477117747068405,
0.06677553802728653,
-0.005752232391387224,
0.009563746862113476,
0.007095962762832642,
0.04405830800533295,
-0.04113268107175827,
0.004766609985381365,
-0.026581404730677605,
0.014176116324961185,
-0.025276057422161102,
0.036010921001434326,
-0.007109209895133972,
0.0033980209846049547,
0.025402983650565147,
-0.01030810084193945,
0.029379284009337425,
0.046983752399683,
-0.003934691660106182,
-0.04694914445281029,
0.018049489706754684,
0.04081406816840172,
-0.0394144169986248,
-0.007226032670587301,
0.00003392730650375597,
0.022159337997436523,
-0.013314428739249706,
-0.01005991455167532,
-0.0292974803596735,
0.01406316738575697,
-0.049675360321998596,
0.03317340090870857,
0.010777329094707966,
-0.02715320885181427,
0.06907543540000916,
0.011121535673737526,
0.0030097647104412317,
0.04957311972975731,
-0.04280039295554161,
0.01481120940297842,
0.0170882735401392,
-0.02933388203382492,
0.026423132047057152,
-0.062138158828020096,
0.024442220106720924,
-0.011915713548660278,
0.02491449937224388,
-0.07425030320882797,
-0.055690962821245193,
0.023001329973340034,
0.01985948160290718,
0.0200575590133667,
-0.07725351303815842,
-0.02158421464264393,
-0.029765736311674118,
-0.007870014756917953,
-0.0021658032201230526,
0.0014288746751844883,
-0.054941777139902115,
-0.031179111450910568,
0.002094508381560445,
0.0346873439848423,
0.05141454190015793,
-0.008779285475611687,
-0.04507775232195854,
0.029628239572048187,
0.00438406877219677,
0.015635518357157707,
-0.00546631682664156,
-0.007149337325245142,
-0.0354112945497036,
-0.02769877202808857,
0.006047757808119059,
-0.009844266809523106,
-0.013495796360075474,
-0.047500718384981155,
-0.003419333603233099,
0.06802573800086975,
0.025162221863865852,
-0.007772298064082861,
-0.028666960075497627,
0.01643526554107666,
-0.05124320089817047,
0.006722042337059975,
0.0025607396382838488,
-0.004685772117227316,
-0.038148559629917145,
0.00705705164000392,
0.0013189646415412426,
0.016668368130922318,
-0.004280698951333761,
0.013859287835657597,
0.04905598983168602,
0.0011596691329032183,
-0.02686680294573307,
0.038016777485609055,
0.012029560282826424,
-0.014083764515817165,
-0.015256869606673717,
0.04192676395177841,
0.016850681975483894,
0.021858230233192444,
-0.052280034869909286,
-0.029773058369755745,
-0.02030728943645954,
-0.029290560632944107,
0.06823546439409256,
-0.01845448464155197,
0.03386932983994484,
-0.023817971348762512,
-0.022201165556907654,
-0.005314353387802839,
-0.011172778904438019,
-0.01291641779243946,
0.004418651107698679,
-0.036628201603889465,
0.0020151406060904264,
-0.012949611060321331,
-0.02670043334364891,
0.018337903544306755,
0.051707781851291656,
-0.018902834504842758,
0.03006911464035511,
0.031013334169983864,
0.012769152410328388,
0.02892715483903885,
-0.07283429056406021,
-0.049915701150894165,
0.04843779280781746,
-0.0521869994699955,
0.053675126284360886,
0.027893243357539177,
-0.016596220433712006,
0.028251992538571358,
0.02217637561261654,
0.016543922945857048,
-0.05149375647306442,
-0.03257989510893822,
-0.04803898185491562,
0.0400426872074604,
0.042751092463731766,
-0.02799195796251297,
-0.002473148051649332,
-0.009682276286184788,
0.021383287385106087,
-0.0008139401325024664,
-0.02229897305369377,
0.014412987045943737,
-0.07378364354372025,
-0.008583432994782925,
-0.01016227062791586,
-0.013743606396019459,
0.04501793906092644,
-0.021961279213428497,
-0.033545609563589096,
0.015293297357857227,
-0.011063417419791222,
0.055346645414829254,
0.010109425522387028,
0.04778515547513962,
-0.01715126819908619,
0.025893477723002434,
-0.04298008233308792,
0.025945249944925308,
0.007812462281435728,
0.035054534673690796,
0.13895516097545624,
0.027279958128929138,
0.015833256766200066,
-0.03651642054319382,
-0.027461614459753036,
-0.051419105380773544,
0.03027305006980896,
0.0205551665276289,
0.023955756798386574,
0.002084854058921337,
0.031853511929512024,
-0.014662880450487137,
0.05773008614778519,
-0.021356208249926567,
0.06848635524511337,
0.06118177995085716,
-0.053328245878219604,
-0.013408591970801353,
0.005329871084541082,
-0.022214502096176147,
0.018863685429096222,
0.011119058355689049,
-0.028307322412729263,
0.03821304067969322,
-0.05100873485207558,
-0.0195311326533556,
-0.02534255012869835,
-0.04212092608213425,
0.02343047223985195,
0.0034728525206446648,
-0.04961979389190674,
-0.015662886202335358,
-0.013762393034994602,
0.023330481722950935,
-0.018965696915984154,
0.005568762309849262,
-0.00319664110429585,
-0.02462710812687874,
-0.01056482084095478,
0.03349539637565613,
0.024191493168473244,
-0.0016807435313239694,
-0.01873490959405899,
-0.011345899663865566,
-0.030239257961511612,
0.021427694708108902,
-0.014574505388736725,
0.007309334818273783,
-0.0396239310503006,
-0.03170611709356308,
-0.02674230933189392,
0.0009445674368180335,
0.011677091009914875,
-0.0007946671103127301,
-0.022855618968605995,
0.012642079964280128,
0.015616226941347122,
0.012569960206747055,
-0.0033616777509450912,
0.011882605031132698,
0.023343179374933243,
0.009032366797327995,
0.0040058596059679985,
0.01877467706799507,
0.013603630475699902,
-0.011969201266765594,
-0.021159030497074127,
0.037526197731494904,
-0.0355212539434433,
-0.05655859783291817,
-0.08705516159534454,
0.02434459514915943,
-0.01591348461806774,
0.014633068814873695,
-0.02133749984204769,
0.0672495886683464,
0.010324062779545784,
-0.016191765666007996,
-0.025557978078722954,
-0.00840769987553358,
0.006195950321853161,
0.03654295951128006,
-0.020747417584061623,
-0.02037101425230503,
-0.015477550216019154,
0.01609659753739834,
0.020501552149653435,
0.03671296685934067,
-0.017541101202368736,
-0.011633314192295074,
0.009512050077319145,
0.015469048172235489,
0.03218657150864601,
-0.014216754585504532,
-0.0146647859364748,
0.015872236341238022,
-0.0010084459790959954,
0.03226720914244652,
-0.019615452736616135,
0.04556424170732498,
0.04035981744527817,
-0.002032874384894967,
0.022173792123794556,
0.01364405732601881,
-0.0637374073266983,
0.03620341420173645,
0.004236113280057907,
0.0005118356202729046,
0.005001659970730543,
-0.01474231667816639,
0.009683318436145782,
-0.009852112270891666,
-0.03044557198882103,
-0.018605735152959824,
-0.01807039976119995,
-0.012385637499392033,
0.01833302713930607,
0.03217944875359535,
0.04578682780265808,
-0.01801789365708828,
0.02799525484442711,
-0.028985366225242615,
-0.0031204763799905777,
-0.041939109563827515,
0.015354864299297333,
0.0013508135452866554,
0.017517371103167534,
0.006633751560002565,
0.019057223573327065,
-0.013837470673024654,
-0.013233426958322525,
-0.00917148683220148,
0.03589252755045891,
-0.01697860285639763,
-0.007318513002246618,
0.004085911903530359,
0.017207937315106392,
0.014061461202800274,
-0.05003788322210312,
-0.013642418198287487,
0.001057949266396463,
-0.019117524847388268,
-0.06249706447124481,
0.006084142252802849,
-0.04085291177034378,
-0.006788614671677351,
0.027399208396673203,
-0.03525066748261452,
-0.023803405463695526,
0.04563169181346893,
0.01807025447487831,
-0.008321999572217464,
-0.01942429132759571,
-0.021434564143419266,
-0.03481300175189972,
0.018465369939804077,
0.02906179428100586,
-0.06339200586080551,
-0.010765929706394672,
0.033357128500938416,
-0.0014677306171506643,
0.018068112432956696,
0.008217193186283112,
-0.03000340238213539,
-0.0032531546894460917,
-0.09230133891105652,
0.010537714697420597,
-0.022509584203362465,
0.027457013726234436,
0.04525356367230415,
-0.011366121470928192,
0.03432261571288109,
0.04176973178982735,
-0.017545828595757484,
-0.09020993113517761,
-0.006222912110388279,
-0.010443031787872314,
-0.006543298717588186,
0.011912260204553604,
-0.0484384223818779,
0.03728090226650238,
0.012718439102172852,
-0.09940166026353836,
0.06405355781316757,
-0.04830342158675194,
-0.04050843417644501,
-0.015359646640717983,
-0.004448633175343275,
-0.02366507239639759,
0.013057886622846127,
0.018052736297249794,
0.012657460756599903,
0.004162291996181011,
0.022869933396577835,
0.005776002537459135,
0.024227460846304893,
0.022667990997433662,
0.023081785067915916,
-0.0012759530218318105,
0.005758175626397133,
0.053316500037908554,
-0.0010713104857131839,
-0.027575083076953888,
-0.028792712837457657,
0.007317106239497662,
-0.013579251244664192,
0.015691490843892097,
0.014371378347277641,
-0.03525411710143089,
0.04291277751326561,
-0.013490298762917519,
-0.032086439430713654,
-0.045795418322086334,
-0.0142279751598835,
0.042246319353580475,
0.018522709608078003,
-0.0027107580099254847,
0.01753784716129303,
0.034256141632795334,
-0.006872300058603287,
0.015853669494390488,
0.01002124510705471,
-0.016343357041478157,
-0.01464949268847704,
0.023849651217460632,
0.0437442846596241,
0.04457210376858711,
0.0004010079428553581,
-0.00010182796540902928,
-0.05104079097509384,
0.0043906643986701965,
-0.009256108663976192,
-0.002375028096139431,
-0.0030530658550560474,
0.004014667123556137,
-0.029717866331338882,
-0.019046947360038757,
-0.024407347664237022,
0.0004552342288661748,
-0.05388280749320984,
-0.0043913512490689754,
-0.006385274231433868,
-0.004519835580140352,
0.01410941407084465,
-0.009130744263529778,
-0.04191150516271591,
-0.036061402410268784,
0.08330249786376953,
0.02455035224556923,
0.05617139860987663,
0.0008594034588895738,
-0.03182394057512283,
0.0017612671945244074,
-0.047020286321640015,
0.03552582114934921,
-0.033929724246263504,
0.01315814908593893,
0.0005052332999184728,
-0.0023267511278390884,
-0.03181677684187889,
0.009812775999307632,
0.04935343936085701,
0.013002514839172363,
0.011787218041718006,
-0.015212859958410263,
-0.018861716613173485,
0.022174108773469925,
-0.08992927521467209,
0.045560117810964584,
0.03174099326133728,
-0.04859638959169388,
-0.022500958293676376,
-0.015224485658109188,
-0.029099542647600174,
-0.009916643612086773,
0.05533185973763466,
-0.0035642501898109913,
0.014472347684204578,
0.019152868539094925,
-0.014800796285271645,
0.05984955653548241,
0.015788733959197998,
-0.015509328804910183,
0.05089058727025986,
-0.007033709902316332,
-0.012174969539046288,
0.0067708054557442665,
0.0029175980016589165,
-0.023744530975818634,
0.043222639709711075,
-0.06536293774843216,
0.01005038246512413,
-0.07290343940258026,
-0.022147225216031075,
0.0027627889066934586,
-0.028179803863167763,
0.027186589315533638,
0.020157180726528168,
-0.025075798854231834,
0.02378227189183235,
0.05032489076256752,
0.0026620503049343824,
0.0007689765770919621,
-0.03216952085494995,
0.033969417214393616,
0.021337036043405533,
0.017637375742197037,
-0.04890616983175278,
0.035710446536540985,
0.014387591741979122,
-0.022758077830076218,
0.03841441124677658,
0.02167929895222187,
0.03188116475939751,
-0.008140875026583672,
0.023714760318398476,
0.018796829506754875,
-0.00797964259982109,
-0.0036869945470243692,
0.020857224240899086,
-0.016578229144215584,
-0.028869980946183205,
0.008011667057871819,
-0.014308715239167213,
0.0797688215970993,
-0.016076965257525444,
-0.02443516254425049,
-0.020381972193717957,
-0.03428832069039345,
-0.005197152495384216,
0.009046114981174469,
-0.02151544950902462,
0.06648225337266922,
0.007001334335654974,
0.01082752924412489,
-0.03697206825017929,
0.024126732721924782,
0.015495287254452705,
-0.02836022712290287,
0.06443670392036438,
-0.03266272693872452,
0.006283493246883154,
0.01859874092042446,
-0.01346608530730009,
-0.044956475496292114,
-0.07439029961824417,
0.019117770716547966,
0.015725363045930862,
-0.026680180802941322,
0.022043950855731964,
-0.015333937481045723,
0.02390698343515396,
0.05300917103886604,
-0.0357796773314476,
-0.02920885942876339,
-0.00030006159795448184,
0.009561839513480663,
-0.026452956721186638,
0.014018644578754902
] |
<p>From my high school physics class I remember that there are some particles which exhibit pure alpha decay (i.e. alpha decay to there stable isotope), like Po-210, Po-211 and Bi-209.</p>
<p>What I also know is that alpha particles, due to their low speed, will be absorbed already within a few cell layers of skin ($\sim 40 \mu$m if I remember correctly). </p>
<p>My question comes from the combination of these two points: if you where able to isolate e.g. Bi-209 in a pure form, would it be harmful to swallow it or will all alpha particles be captured in upper tissue layers, thus leaving you fairly unharmed?!</p>
<p>Note: I am asking in particular about particles with pure alpha decay, because if the decay product is a gamma or beta emitter you will probably be harmed by the decay products anyway.</p>
| 10,696 |
[
0.03657166287302971,
-0.05778471753001213,
0.018900901079177856,
-0.03659217059612274,
-0.0073696100153028965,
0.0006115531432442367,
-0.024731747806072235,
-0.03341004624962807,
0.02681628242135048,
-0.05158434808254242,
0.025025447830557823,
0.039728812873363495,
0.03540675714612007,
0.006743187550455332,
-0.022640932351350784,
-0.00604556780308485,
-0.025753729045391083,
-0.058061182498931885,
-0.009672524407505989,
-0.055700741708278656,
0.018839485943317413,
0.012889306992292404,
-0.01551880780607462,
0.004522857256233692,
-0.0127212293446064,
0.015777818858623505,
-0.025946324691176414,
0.014629627577960491,
-0.01581953465938568,
0.0253303200006485,
0.004619766026735306,
-0.01105206273496151,
0.008093663491308689,
0.0026029597502201796,
-0.002299679908901453,
-0.02788349613547325,
-0.01912453956902027,
-0.04576190188527107,
-0.07315050810575485,
0.04134320467710495,
-0.06862913817167282,
-0.022879410535097122,
0.044621095061302185,
0.008616077713668346,
-0.019038185477256775,
-0.010096129961311817,
0.01417609490454197,
-0.023457704111933708,
0.005044294521212578,
-0.04546421393752098,
0.017684783786535263,
-0.015603099018335342,
0.0739891454577446,
0.02021898701786995,
0.05579601600766182,
-0.018303897231817245,
0.06351840496063232,
0.040278997272253036,
0.004819733556360006,
-0.05921733006834984,
-0.024359675124287605,
-0.0005803903331980109,
-0.002262376481667161,
0.00798858143389225,
-0.038834262639284134,
0.017652319744229317,
-0.017408329993486404,
-0.0451614074409008,
0.03607331961393356,
0.025644904002547264,
0.03205623850226402,
0.01819605752825737,
0.00838436372578144,
-0.011113451793789864,
0.008921506814658642,
0.0009543733904138207,
0.04020870849490166,
0.041422780603170395,
0.054386552423238754,
0.03819037973880768,
0.007208322640508413,
-0.020451247692108154,
0.03296760469675064,
0.049175236374139786,
-0.003298587165772915,
0.011549942195415497,
0.09542027860879898,
-0.0160395298153162,
0.02194623276591301,
0.03526482358574867,
0.011219833046197891,
0.023962782695889473,
0.035445477813482285,
0.048213716596364975,
-0.00965502206236124,
-0.0008023886475712061,
-0.00542365200817585,
0.08545417338609695,
-0.012582095339894295,
0.00046600220957770944,
0.022339748218655586,
0.03580975905060768,
0.005840239115059376,
0.05837250500917435,
0.010814743116497993,
-0.012974427081644535,
-0.009895008988678455,
-0.024825289845466614,
-0.03974862024188042,
-0.03797426074743271,
-0.027102097868919373,
-0.0007805823115631938,
-0.024832330644130707,
0.009597213007509708,
0.010158691555261612,
-0.02082064002752304,
-0.003757513128221035,
-0.02615482360124588,
0.06347234547138214,
0.06601477414369583,
0.029499078169465065,
-0.020647188648581505,
-0.0036967326886951923,
-0.010970907285809517,
-0.05341111123561859,
0.021203648298978806,
0.007213065400719643,
0.0016637870576232672,
-0.0852944627404213,
0.007851183414459229,
-0.006946749519556761,
-0.06114435940980911,
0.03303215280175209,
-0.03340665623545647,
0.04952563717961311,
-0.0211341455578804,
-0.08561719954013824,
-0.04911032319068909,
0.039944250136613846,
0.010347181931138039,
-0.010480135679244995,
-0.08561093360185623,
-0.012009753845632076,
0.0055336663499474525,
0.03965124860405922,
0.011625662446022034,
-0.0293863695114851,
0.01937730982899666,
0.009682373143732548,
-0.017094306647777557,
-0.03124135360121727,
-0.01691693253815174,
0.00888054445385933,
-0.021551286801695824,
0.00940509419888258,
-0.07085242867469788,
0.00745520181953907,
0.0284725371748209,
0.007858765311539173,
-0.02432982437312603,
0.045396991074085236,
-0.020102111622691154,
0.038464173674583435,
0.013272242620587349,
-0.02119814231991768,
-0.06080326437950134,
0.05595400929450989,
0.04973728954792023,
0.0029842702206224203,
0.03005068749189377,
0.02944130450487137,
0.053726956248283386,
-0.013870997354388237,
-0.001899589435197413,
0.02257007360458374,
-0.03430556505918503,
-0.013935298658907413,
-0.03664570301771164,
0.005198266822844744,
0.019475409761071205,
-0.045073818415403366,
0.021645547822117805,
-0.017551258206367493,
0.03276791423559189,
-0.001026669517159462,
0.008474926464259624,
0.015021481551229954,
-0.03867184743285179,
0.02204010635614395,
-0.011500132270157337,
-0.012603185139596462,
-0.02008872665464878,
0.02720235288143158,
0.005497080273926258,
-0.04238135740160942,
0.012293939478695393,
-0.027381528168916702,
0.001031107152812183,
-0.012369588948786259,
-0.008033135905861855,
-0.0018165175570175052,
-0.0066575282253324986,
0.039795130491256714,
-0.0031930392142385244,
0.01002550683915615,
0.078932985663414,
0.022297360002994537,
0.01700691692531109,
0.02639889530837536,
0.018193384632468224,
0.001839853241108358,
-0.043121956288814545,
-0.03300471603870392,
0.03478638455271721,
0.011418881826102734,
-0.012021999806165695,
0.005490279756486416,
-0.056445058435201645,
-0.0012632315047085285,
0.02598819136619568,
-0.035890258848667145,
0.11972465366125107,
0.04157944768667221,
0.002900242805480957,
-0.048317696899175644,
-0.00010510034917388111,
0.01934872381389141,
-0.00019075529417023063,
-0.016934141516685486,
-0.07718007266521454,
-0.05640847235918045,
-0.030193841084837914,
0.011822516098618507,
-0.01862831600010395,
-0.044103141874074936,
0.03787718713283539,
-0.03291667625308037,
0.01780826412141323,
0.04272022098302841,
0.019531456753611565,
-0.0079648457467556,
-0.039675790816545486,
-0.0039419690147042274,
0.0022518131881952286,
0.009016957134008408,
0.001713412581011653,
-0.018439244478940964,
-0.008626386523246765,
0.0546872541308403,
-0.015294517390429974,
0.0017723961500450969,
0.015561736188828945,
-0.017155375331640244,
0.044877078384160995,
-0.010232006199657917,
-0.06957849860191345,
0.03382628411054611,
-0.02513502724468708,
0.042085397988557816,
-0.03291533514857292,
0.001508220098912716,
-0.028284281492233276,
-0.016117770224809647,
0.004196330439299345,
0.030986525118350983,
0.06748274713754654,
-0.024240555241703987,
-0.022619500756263733,
0.00025975110474973917,
-0.038788873702287674,
0.0012604952789843082,
-0.010944103822112083,
-0.0020770991686731577,
-0.0020087668672204018,
0.02304420806467533,
0.050202202051877975,
0.007559892721474171,
0.03136969730257988,
-0.04833871126174927,
-0.04089314863085747,
-0.0009876826079562306,
-0.03058464080095291,
-0.017109191045165062,
0.032017532736063004,
-0.06400258094072342,
0.03877700865268707,
-0.053390584886074066,
-0.0324958860874176,
0.05623486265540123,
0.0022659979294985533,
-0.0022485218942165375,
0.02826804853975773,
-0.018448056653141975,
-0.04343634098768234,
-0.008027642965316772,
-0.00004666133099817671,
0.000514934363309294,
0.003405921859666705,
0.008943802677094936,
0.057645540684461594,
0.032077301293611526,
-0.039621442556381226,
0.01051101554185152,
-0.040011513978242874,
-0.01613047905266285,
0.0010335457045584917,
-0.02405940555036068,
0.011353076435625553,
-0.019206494092941284,
-0.0332673154771328,
0.026043402031064034,
-0.06167595088481903,
0.006714183371514082,
-0.04569241777062416,
-0.05826614424586296,
0.05424778163433075,
0.006902662571519613,
0.00866245198994875,
0.0123317651450634,
0.010848530568182468,
0.08962083607912064,
0.0634274110198021,
-0.0565708689391613,
0.03434649109840393,
-0.00951291248202324,
-0.03354649990797043,
-0.008194372057914734,
0.014631018042564392,
0.02478909306228161,
-0.003940613940358162,
0.019228730350732803,
0.017683839425444603,
0.048860132694244385,
0.010059316642582417,
0.006813257001340389,
-0.03467005118727684,
0.004944717977195978,
0.039889778941869736,
-0.004746874328702688,
0.016889257356524467,
0.028580818325281143,
-0.052342407405376434,
-0.008162325248122215,
-0.02375408634543419,
0.06337707489728928,
0.04998946934938431,
-0.03930266201496124,
0.047680262476205826,
0.002813405590131879,
-0.02002839185297489,
-0.02954111434519291,
0.010431892238557339,
-0.01625858061015606,
-0.010101608000695705,
-0.011989317834377289,
0.03364637494087219,
0.05343306064605713,
-0.025625480338931084,
0.011989069171249866,
0.02279703877866268,
0.08726167678833008,
-0.009764568880200386,
-0.014063247479498386,
0.008819672279059887,
0.021574802696704865,
0.0018211777787655592,
-0.004702257923781872,
-0.015566740185022354,
0.023792410269379616,
0.027262981981039047,
0.018763350322842598,
-0.001112678088247776,
-0.014205088838934898,
-0.01789955422282219,
-0.08963863551616669,
-0.022196665406227112,
0.020342249423265457,
0.03246665000915527,
-0.00399527745321393,
0.05539904907345772,
0.011049536056816578,
-0.018084898591041565,
-0.01793394610285759,
0.037649765610694885,
-0.058386802673339844,
0.014546792022883892,
-0.019337747246026993,
-0.015947489067912102,
0.005673296749591827,
-0.017907531931996346,
-0.025259893387556076,
-0.029990343376994133,
-0.0383060984313488,
-0.009486919268965721,
0.010721880942583084,
-0.047414690256118774,
0.0030266207177191973,
-0.03998052701354027,
-0.034663308411836624,
-0.030188459903001785,
0.04703604802489281,
0.0047763641923666,
0.008305010385811329,
-0.02657981775701046,
-0.05138133466243744,
-0.031062139198184013,
0.02913191355764866,
-0.014693648554384708,
0.01612231880426407,
-0.01943596452474594,
0.02635600045323372,
0.015045857056975365,
-0.024044372141361237,
-0.014885302633047104,
0.011179894208908081,
-0.001254966133274138,
0.02307741902768612,
-0.03600975498557091,
-0.009977802634239197,
-0.029388030990958214,
-0.07537898421287537,
0.0019113403977826238,
0.005798072554171085,
-0.011094380170106888,
-0.007820770144462585,
0.019749650731682777,
0.032270438969135284,
-0.04256753250956535,
-0.014652613550424576,
0.04241695627570152,
0.04465547204017639,
0.013221207074820995,
-0.003763191169127822,
-0.03725956752896309,
-0.032412756234407425,
0.0042350259609520435,
0.0009169104741886258,
0.02067429944872856,
0.03168044611811638,
-0.05157467722892761,
0.0000019426304334047018,
-0.01071135327219963,
0.03862069174647331,
-0.029290812090039253,
0.013697981834411621,
0.02082032710313797,
-0.007387213408946991,
-0.027029870077967644,
-0.03215641528367996,
0.041063036769628525,
0.053268563002347946,
0.05137838423252106,
0.03262694925069809,
0.0166221484541893,
-0.07714886963367462,
0.0010785714257508516,
0.01290828175842762,
0.05364108830690384,
-0.007224405184388161,
0.00038659104029648006,
-0.013698681257665157,
-0.015323692001402378,
0.05470500886440277,
0.009009508416056633,
0.017291592434048653,
-0.028073176741600037,
-0.029139114543795586,
0.020695963874459267,
-0.019870905205607414,
0.011465280316770077,
0.013131249696016312,
-0.012643320485949516,
-0.030745593830943108,
-0.006814112421125174,
-0.0169990211725235,
0.020127490162849426,
0.028691517189145088,
-0.025891268625855446,
0.06891422718763351,
-0.011051008477807045,
-0.01440692599862814,
0.041483521461486816,
0.0031828905921429396,
-0.013836056925356388,
-0.060042839497327805,
-0.014042692258954048,
0.024073360487818718,
-0.01948605477809906,
0.03721298277378082,
-0.034016598016023636,
-0.056555647403001785,
0.04827925190329552,
0.016951272264122963,
0.005178230348974466,
-0.026062525808811188,
-0.08661233633756638,
0.03269941359758377,
0.040224432945251465,
-0.019803838804364204,
0.02897518500685692,
0.02784610167145729,
-0.028191275894641876,
-0.008028320968151093,
-0.015222806483507156,
0.029416432604193687,
-0.03428715839982033,
-0.0013919526245445013,
-0.03183707594871521,
0.025908207520842552,
-0.006371220573782921,
0.06638533622026443,
-0.031288910657167435,
-0.020882437005639076,
0.06278304755687714,
-0.007313746027648449,
0.0223805233836174,
0.030724067240953445,
-0.025262823328375816,
-0.015920238569378853,
-0.013253116980195045,
0.06631040573120117,
0.006570837460458279,
-0.005319747142493725,
0.027708329260349274,
-0.00800398737192154,
0.030161472037434578,
0.019648293033242226,
-0.051255907863378525,
-0.005413033999502659,
-0.025399725884199142,
-0.02289908565580845,
0.018512293696403503,
-0.04402090609073639,
0.04909450188279152,
0.001208509667776525,
-0.004364526830613613,
-0.01622994802892208,
-0.06323795765638351,
-0.02222159318625927,
-0.0016442867927253246,
-0.008593916893005371,
0.08567997813224792,
-0.05044688284397125,
0.06229253485798836,
0.0009524433990009129,
0.01848360151052475,
-0.04806200787425041,
-0.047557536512613297,
0.029281361028552055,
0.05226854979991913,
0.010709244757890701,
-0.05171748995780945,
0.007962672039866447,
-0.053379762917757034,
-0.03666647896170616,
0.0003319436509627849,
0.021870937198400497,
-0.025246089324355125,
0.01270830538123846,
0.0008666401845403016,
0.018921205773949623,
0.048171430826187134,
0.031584419310092926,
-0.014412682503461838,
0.027780085802078247,
0.009683921001851559,
-0.010276534594595432,
-0.007823680527508259,
0.031095996499061584,
-0.027342531830072403,
-0.0014590470818802714,
0.0312133077532053,
-0.044947072863578796,
0.034993939101696014,
0.0016537493793293834,
-0.01783187873661518,
0.0193044263869524,
0.022204093635082245,
0.01942008174955845,
-0.010314214043319225,
0.04983336105942726,
0.001439316663891077,
0.017437011003494263,
-0.030608100816607475,
0.015566057525575161,
-0.027689676731824875,
-0.027677712962031364,
0.055853113532066345,
-0.003706829622387886,
0.004142616409808397,
0.006009028293192387,
0.04540354758501053,
0.011046258732676506,
-0.010439077392220497,
0.0186992846429348,
-0.020051155239343643,
0.04704584181308746,
0.0012026478070765734,
0.023155486211180687,
0.05583743378520012,
0.0034815920516848564,
-0.01664840802550316,
-0.04325566068291664,
-0.0645638108253479,
0.009197711013257504,
0.02821616642177105,
-0.01563808135688305,
0.01720106415450573,
0.02163190394639969,
-0.008062707260251045,
-0.0047584413550794125,
-0.0043562049977481365,
-0.02187761478126049,
0.017627472057938576,
-0.04447432979941368,
0.019047269597649574,
0.012522115372121334,
-0.017447419464588165,
-0.0058930255472660065,
0.021400922909379005,
-0.03479866683483124,
0.029788468033075333,
-0.010602124035358429,
0.03587033972144127,
-0.0064657884649932384,
-0.014450518414378166,
-0.002033008262515068,
0.00369599019177258,
-0.06441622972488403,
0.0044203512370586395,
0.0007353320834226906,
-0.044631317257881165,
0.03883766010403633,
-0.012389592826366425,
0.029421143233776093,
-0.06661035865545273,
-0.03643522039055824,
-0.029831165447831154,
0.028826666995882988,
-0.022371307015419006,
-0.005663157906383276,
-0.04427533224225044,
-0.014222829602658749,
0.033016182482242584,
-0.023468103259801865,
0.024728702381253242,
-0.010427168570458889,
-0.06852841377258301,
0.0031293309293687344,
-0.05256032571196556,
-0.03514667600393295,
0.05301749333739281,
-0.03186294063925743,
0.0012719648657366633,
-0.0456387884914875,
-0.045419495552778244,
0.041570086032152176,
0.010280376300215721,
0.016113290563225746,
0.0262188371270895,
0.01298842579126358,
-0.003672830993309617,
-0.0003814017109107226,
0.02546560950577259,
0.0408075712621212,
0.12234572321176529,
0.08122801780700684,
0.01743900589644909,
-0.04000597819685936,
-0.015798291191458702,
-0.029089728370308876,
0.029122211039066315,
0.00319614983163774,
-0.01085725985467434,
0.030003590509295464,
-0.00024816946825012565,
0.005727406125515699,
0.0697450041770935,
0.02287047728896141,
-0.0012485163751989603,
0.04585915803909302,
-0.029694069176912308,
-0.01368646789342165,
0.0164773128926754,
0.008262692019343376,
-0.06603847444057465,
0.028780335560441017,
-0.027025694027543068,
0.04671194404363632,
0.008397492580115795,
0.008640357293188572,
-0.019550584256649017,
0.015753109008073807,
0.023232171311974525,
0.01390238106250763,
0.011165617033839226,
-0.05170769244432449,
-0.002996353432536125,
0.008876875974237919,
-0.009541908279061317,
0.02102890983223915,
0.04136301577091217,
0.002708856714889407,
0.0015561925247311592,
0.010829768143594265,
0.022443339228630066,
0.001695938059128821,
0.004586331080645323,
0.025962958112359047,
-0.03865547105669975,
-0.01651548035442829,
-0.037891943007707596,
0.04134035483002663,
-0.040597885847091675,
0.004195331130176783,
-0.022400790825486183,
-0.026473479345440865,
0.003991486504673958,
-0.0528378039598465,
-0.0366303026676178,
0.0006514732376672328,
0.010145864449441433,
-0.014018788002431393,
0.005887595470994711,
-0.013036276213824749,
0.0343581959605217,
0.005050021223723888,
0.025235099717974663,
0.012692609801888466,
-0.02249852567911148,
-0.02803264744579792,
0.021372130140662193,
-0.0018410671036690474,
-0.03954063728451729,
0.007165252696722746,
-0.025910714641213417,
0.018008515238761902,
-0.07409631460905075,
0.01913408376276493,
0.02991701103746891,
0.020081181079149246,
0.03226977214217186,
0.02431047335267067,
-0.020340409129858017,
0.00456390343606472,
-0.01873796619474888,
0.08352479338645935,
-0.022110499441623688,
-0.019207773730158806,
-0.01776035502552986,
0.01864602230489254,
-0.008957316167652607,
0.05965112894773483,
-0.037609849125146866,
0.008440224453806877,
0.013853499665856361,
0.0336947925388813,
-0.012920320965349674,
-0.02667113021016121,
-0.021165480837225914,
0.020554348826408386,
-0.052611254155635834,
0.020978236570954323,
-0.02957770600914955,
0.03955759108066559,
0.016659025102853775,
0.0051765707321465015,
0.026370828971266747,
0.0008405176340602338,
-0.024115702137351036,
0.014248148538172245,
-0.020746462047100067,
-0.04247172176837921,
0.00027675513410940766,
0.025832433253526688,
0.015701407566666603,
-0.032418616116046906,
-0.01090103480964899,
-0.04975825920701027,
0.00979564618319273,
-0.004445452243089676,
0.0005260820616967976,
0.004136036150157452,
0.024513592943549156,
-0.001049645827151835,
-0.014712857082486153,
-0.007253728341311216,
0.02420063130557537,
-0.0405057817697525,
0.031078752130270004,
0.03291107341647148,
-0.0005191406235098839,
-0.026597250252962112,
0.012033337727189064,
-0.013382472097873688,
-0.0235665962100029,
0.043734822422266006,
0.020721282809972763,
-0.05955032259225845,
-0.005531530827283859,
0.01883501559495926,
0.02855566330254078,
0.04843815416097641,
0.012470032088458538,
0.039795469492673874,
0.006360993254929781,
-0.01404037419706583,
-0.023175526410341263,
0.025594523176550865,
-0.050763629376888275,
0.021636294201016426,
0.03606577590107918,
0.00909128226339817,
-0.008080991916358471,
0.10878461599349976,
0.009040389209985733,
-0.01338486559689045,
0.005509281996637583,
0.005208044312894344,
-0.015208165161311626,
0.04027099907398224,
-0.004319941624999046,
0.025005260482430458,
0.004771091975271702,
0.04261777922511101,
-0.02588018588721752,
0.005167855881154537,
0.003139595501124859,
-0.03294084593653679,
-0.03037692792713642,
-0.01980370655655861,
-0.030736787244677544,
-0.01645042560994625,
0.016134420409798622,
0.057039592415094376,
-0.025576762855052948,
0.02959980070590973,
0.020517485216259956,
-0.024722255766391754,
-0.06471006572246552,
-0.013791018165647984,
0.005409763660281897,
0.03184136375784874,
0.024730807170271873,
-0.05856889486312866,
0.04850899800658226,
0.0552181750535965,
-0.0596194788813591,
-0.031392984092235565,
-0.034192994236946106,
-0.009230563417077065,
-0.06201007962226868,
0.007844598032534122,
-0.04869982227683067,
0.05205792933702469,
0.020965494215488434,
0.06515537947416306,
0.021023249253630638,
-0.0064835618250072,
0.009520919993519783,
-0.01885746791958809,
-0.006136088166385889,
0.0130543764680624,
0.013699687086045742,
0.011685519479215145,
0.07349197566509247,
-0.019994240254163742,
-0.022313864901661873,
0.01914447732269764,
-0.006697784177958965,
0.008593358099460602,
0.02267821505665779,
0.003109891200438142,
0.009908358566462994,
0.02000189572572708,
-0.00814923644065857,
0.04881332069635391,
0.03624895215034485,
0.030369596555829048,
0.005803531035780907,
0.016768252477049828,
-0.05676388740539551,
0.028653912246227264,
-0.00261457241140306,
0.0042889853939414024,
-0.02668888121843338,
0.005019102245569229,
-0.0026373318396508694,
-0.029777448624372482,
-0.01693044602870941,
0.009432077407836914,
0.00010510676656849682,
-0.0013326972257345915,
-0.035133522003889084,
-0.05010916292667389,
0.007458651438355446,
-0.02528075873851776,
0.03783351555466652,
0.013695045374333858,
0.013382346369326115,
-0.04463258013129234,
-0.017125967890024185,
-0.011194044724106789,
0.02908319979906082,
-0.005176412872970104,
-0.01616756059229374,
0.011748005636036396,
0.0180533304810524,
0.040083833038806915,
0.005368565674871206,
-0.017305288463830948,
-0.022967416793107986,
0.027070553973317146,
0.0016598314978182316,
0.02374969981610775,
0.011358623392879963,
-0.0262902919203043,
0.0049074990674853325,
-0.029833044856786728,
0.03625321015715599,
-0.019549576565623283,
0.013090820983052254,
-0.011613648384809494,
-0.024257440119981766,
0.011497864499688148,
0.010774445720016956,
0.013722654432058334,
-0.014331266283988953,
0.027001826092600822,
0.010472726076841354,
0.0036476494278758764,
-0.012971580028533936,
-0.03144650161266327,
0.01820620708167553,
0.007466920185834169,
-0.016529100015759468,
-0.051514387130737305,
0.039157167077064514,
-0.012796226888895035,
0.038186147809028625,
0.030464932322502136,
-0.0035294401459395885,
-0.02827264554798603,
-0.021718578413128853,
0.0006607022951357067,
0.0428832545876503,
-0.016241736710071564,
0.013629799708724022,
0.05894150957465172,
-0.03059634566307068,
0.01496373675763607,
0.029594946652650833,
-0.03293696790933609,
-0.009333718568086624,
0.018656812608242035,
0.04966539517045021,
0.019726572558283806,
0.03705785423517227,
0.014701319858431816,
-0.007631492335349321,
-0.02034931443631649,
0.009173321537673473,
-0.015754459425807,
0.003523837309330702,
0.004991735797375441,
0.038159165531396866,
0.021837372332811356,
0.032084472477436066,
0.04063514992594719,
0.02984575554728508,
0.031152889132499695,
-0.01870899274945259,
-0.02631702646613121,
0.016018155962228775,
0.018894337117671967,
-0.025060592219233513,
0.01796676404774189,
-0.020744778215885162,
0.012333650141954422,
0.028076844289898872,
0.009750775061547756,
0.0304696224629879,
-0.02884592115879059,
-0.006231158971786499,
-0.0011634239926934242,
-0.022230662405490875,
0.023212479427456856,
-0.0183540228754282,
-0.0044840178452432156,
0.05900173261761665,
-0.03346911445260048,
0.022029217332601547,
0.00426289439201355,
-0.01677367091178894,
-0.010491141118109226,
0.014742360450327396,
0.057845503091812134,
0.040427066385746,
-0.014216658659279346,
-0.043165113776922226,
-0.0562942735850811,
0.0011623096652328968,
-0.0016536744078621268,
-0.04962778463959694,
0.018071647733449936,
-0.012479165568947792,
-0.004125460982322693,
-0.018853960558772087,
-0.03746730461716652,
-0.007844999432563782,
-0.033211734145879745,
-0.004924190230667591,
0.03891628608107567,
0.021873366087675095,
-0.0002441063552396372,
-0.021587422117590904,
-0.059610649943351746,
0.0739203616976738,
-0.04196246340870857,
-0.0034438425209373236,
-0.011824766173958778,
0.03192654624581337,
-0.02127072960138321,
0.014131546020507812
] |
<p><a href="http://food.thefuntimesguide.com/2010/07/bamboo_cutting_board.php" rel="nofollow">http://food.thefuntimesguide.com/2010/07/bamboo_cutting_board.php</a></p>
<blockquote>
<p>Some bamboo cutting boards are glued together with adhesives that have formaldehyde in them — <strong><em>which could eventually leak into and contaminate food.</em></strong></p>
</blockquote>
<p>I wanted to understand the logic behind the above claim in italics. </p>
<p>The glue is <strong>between</strong> the sheets of bamboo cutting board. So, if I use only one side of cutting board all the time, will the gravitational force not stop the glue from going upwards and mix in the food?</p>
| 10,697 |
[
-0.01771448738873005,
-0.05558258667588234,
0.012442621402442455,
0.005104003474116325,
0.0024379922542721033,
-0.003914986737072468,
-0.01745271123945713,
0.005630495958030224,
0.0056084878742694855,
-0.014664639718830585,
0.03241292014718056,
0.05668843910098076,
0.045217230916023254,
0.04949395731091499,
-0.020821252837777138,
0.010984841734170914,
0.014006553217768669,
-0.02404339797794819,
0.011843589134514332,
0.0014014911139383912,
-0.01988479122519493,
0.002223345683887601,
0.02273777313530445,
0.005599703174084425,
0.006360762752592564,
0.00637440849095583,
0.02057943306863308,
-0.031058261170983315,
0.028333930298686028,
0.016791686415672302,
-0.008990134112536907,
-0.02668813429772854,
-0.01098631415516138,
0.011194802820682526,
0.03777052462100983,
0.006572081707417965,
-0.03357326611876488,
-0.011560820043087006,
-0.05664042383432388,
-0.01829609088599682,
-0.01862403005361557,
0.006945549976080656,
-0.041085384786129,
0.05701175704598427,
-0.05919553339481354,
0.06291811168193817,
-0.014269925653934479,
-0.010097961872816086,
0.04874790087342262,
-0.07051005959510803,
0.026310833171010017,
0.004117138218134642,
0.047764841467142105,
0.03607383742928505,
-0.009959083050489426,
-0.02644222043454647,
0.05779291316866875,
0.031076624989509583,
-0.014842783100903034,
-0.05714823678135872,
-0.021951710805296898,
-0.005146573763340712,
-0.005285770632326603,
-0.01360776275396347,
-0.04166794195771217,
0.011356406845152378,
-0.01314221229404211,
-0.017474792897701263,
0.021983301267027855,
0.01654096506536007,
0.0073575209826231,
-0.028823677450418472,
0.019736530259251595,
0.024553321301937103,
-0.037737421691417694,
0.011602034792304039,
-0.006831649225205183,
0.06338774412870407,
0.039703648537397385,
0.04086961969733238,
-0.021442482247948647,
-0.01050604972988367,
0.03241610899567604,
0.04205802083015442,
0.051799025386571884,
-0.028459463268518448,
0.06697902083396912,
-0.005617905408143997,
-0.01948465406894684,
0.04138457402586937,
-0.026574065908789635,
0.029838964343070984,
0.025399744510650635,
0.016924193128943443,
0.02022687718272209,
0.008319949731230736,
-0.005722050555050373,
0.04737740382552147,
-0.03574938699603081,
0.015662554651498795,
-0.01474293228238821,
-0.022250069305300713,
0.007234299089759588,
0.08915060758590698,
-0.006854967679828405,
-0.027841469272971153,
0.009813564829528332,
0.039985597133636475,
0.015020841732621193,
0.020114252343773842,
-0.036191754043102264,
-0.017389822751283646,
0.00400566216558218,
-0.05085789039731026,
0.03168165311217308,
-0.001126148272305727,
0.03414240479469299,
0.008470841683447361,
0.01665361598134041,
0.036649350076913834,
0.04655253887176514,
-0.019965793937444687,
0.019338982179760933,
-0.036588624119758606,
-0.036868300288915634,
0.04609687626361847,
-0.0026420331560075283,
-0.0178108848631382,
-0.038072071969509125,
0.04618406668305397,
0.0382954403758049,
-0.03682943060994148,
-0.04360160976648331,
-0.0024540089070796967,
0.03977900370955467,
0.029080744832754135,
-0.04320719093084335,
-0.03404058888554573,
0.08129507303237915,
0.014493723399937153,
-0.016945457085967064,
-0.07918035238981247,
-0.00954132154583931,
0.006705956533551216,
0.022534405812621117,
-0.010493176989257336,
0.01116724219173193,
-0.010458247736096382,
-0.0014800024218857288,
-0.010737475007772446,
-0.03859638050198555,
-0.0015719047514721751,
0.01489442028105259,
-0.01398917380720377,
-0.028893811628222466,
-0.0719989761710167,
0.035030387341976166,
0.0506935752928257,
0.03222154080867767,
-0.03540848195552826,
0.0535864531993866,
-0.011835652403533459,
0.008583557792007923,
-0.017890119925141335,
-0.0009892235975712538,
-0.04092900827527046,
0.03803715482354164,
-0.004778931383043528,
-0.00034269611933268607,
0.06179211661219597,
-0.016804656013846397,
0.012441741302609444,
-0.011770207434892654,
0.0018271817825734615,
0.000923040381167084,
-0.03261881321668625,
0.022709030658006668,
0.025777384638786316,
0.042357031255960464,
-0.004412771202623844,
-0.03462681546807289,
0.013636509887874126,
-0.026769086718559265,
-0.0006615532329306006,
0.03939734399318695,
0.061555106192827225,
-0.010606999509036541,
-0.009844381362199783,
0.008178744465112686,
-0.05200470983982086,
-0.019377874210476875,
-0.07491834461688995,
0.02172725461423397,
-0.004963179584592581,
-0.026742655783891678,
-0.013168813660740852,
0.003513709641993046,
0.011442692950367928,
-0.07142142206430435,
0.03454131260514259,
-0.01828550174832344,
-0.01211659237742424,
0.024714268743991852,
0.01621163636445999,
-0.014734810218214989,
0.07836919277906418,
0.04521143063902855,
-0.019793149083852768,
0.022481661289930344,
-0.02181006409227848,
-0.0018439680570736527,
0.027128588408231735,
-0.052033089101314545,
0.017208684235811234,
-0.003285500453785062,
-0.005921868607401848,
0.014879351481795311,
-0.029991399496793747,
-0.0292500127106905,
0.06269081681966782,
-0.013771845027804375,
0.07609960436820984,
0.023308731615543365,
-0.03232774883508682,
0.0338318794965744,
-0.024335047230124474,
0.05524782836437225,
-0.008687462657690048,
0.012282798998057842,
-0.040552034974098206,
-0.1001349687576294,
-0.06079213321208954,
-0.021596230566501617,
0.015704050660133362,
0.0020223460160195827,
0.012790249660611153,
0.012644695118069649,
-0.011010766960680485,
0.020937277004122734,
0.03311998397111893,
0.02805730141699314,
0.006867395713925362,
0.07762669771909714,
0.02863791026175022,
0.025201089680194855,
0.02994198352098465,
-0.0019386261701583862,
0.03134782984852791,
0.023555543273687363,
-0.012323698960244656,
-0.007572235073894262,
0.03307246416807175,
0.04438517615199089,
0.04549147188663483,
0.01201388705521822,
0.0015531792305409908,
0.0404619462788105,
-0.024295827373862267,
0.02440851554274559,
0.03504370525479317,
0.007352919317781925,
-0.04451770707964897,
-0.035852279514074326,
-0.04458087682723999,
-0.030084606260061264,
0.02642766572535038,
-0.017355624586343765,
-0.029160156846046448,
0.025666087865829468,
-0.04533948004245758,
-0.005164740607142448,
-0.017571257427334785,
-0.027083219960331917,
0.05432585999369621,
-0.011020852252840996,
0.016525087878108025,
0.011320503428578377,
0.03421846404671669,
-0.05068667605519295,
0.00484500965103507,
-0.017233742401003838,
-0.029803888872265816,
-0.03211674839258194,
-0.024364048615098,
-0.040619995445013046,
0.010120191611349583,
-0.001870434731245041,
0.002401922130957246,
0.05881064757704735,
0.034796614199876785,
-0.0011203584726899862,
0.010479024611413479,
-0.00845774170011282,
-0.03548390045762062,
-0.0212244875729084,
0.009868836030364037,
-0.001359369489364326,
-0.026238858699798584,
-0.02992657572031021,
0.02654847502708435,
0.03284909203648567,
-0.01379051897674799,
0.013382413424551487,
-0.01584394834935665,
-0.05678585171699524,
0.04232887923717499,
0.012911459431052208,
-0.004040719475597143,
-0.031317222863435745,
-0.04129171743988991,
-0.01717003807425499,
-0.016365254297852516,
-0.03142722696065903,
-0.04437709599733353,
-0.06486037373542786,
-0.011422419920563698,
0.013866938650608063,
0.0340074859559536,
0.042000576853752136,
-0.05172475054860115,
0.06802424788475037,
0.0016504450468346477,
-0.043984998017549515,
-0.016561785712838173,
-0.028562363237142563,
-0.010199026204645634,
-0.06356054544448853,
0.014899585396051407,
0.015943914651870728,
0.011274173855781555,
0.05263463407754898,
0.03744722902774811,
0.013839644379913807,
0.040366727858781815,
0.04702012613415718,
-0.02468678541481495,
-0.024139154702425003,
0.024597758427262306,
-0.0582839660346508,
0.0264595840126276,
0.014549866318702698,
0.00007198999082902446,
-0.04885878413915634,
-0.03847567364573479,
0.02541213482618332,
0.021026376634836197,
-0.058646611869335175,
0.05858396738767624,
-0.007536211982369423,
-0.014980672858655453,
-0.005069400649517775,
0.04802064225077629,
-0.008433276787400246,
-0.006953416392207146,
0.006885109003633261,
-0.007195794954895973,
0.057943087071180344,
0.02016732096672058,
-0.0068995412439107895,
0.029496775940060616,
0.07230057567358017,
0.0036906800232827663,
-0.015273700468242168,
0.013080931268632412,
0.010038035921752453,
0.022003449499607086,
-0.015200715512037277,
0.014352740719914436,
0.0020904720295220613,
0.03504481166601181,
-0.00368898524902761,
0.053306594491004944,
-0.048361122608184814,
-0.01661517471075058,
-0.07622255384922028,
-0.005783424712717533,
0.00767114432528615,
0.0032902308739721775,
-0.009106962941586971,
0.03522896021604538,
0.0035115338396281004,
-0.007272691931575537,
0.025550179183483124,
-0.013215738348662853,
-0.09647756069898605,
0.01645084097981453,
-0.0003279919910710305,
0.0061026690527796745,
-0.02000241167843342,
-0.018407991155982018,
-0.009640635922551155,
-0.03180443495512009,
-0.024444419890642166,
0.010132942348718643,
0.01895326003432274,
-0.04213561490178108,
0.023420346900820732,
-0.06419364362955093,
-0.021972477436065674,
-0.0028245989233255386,
0.02439204603433609,
0.029891200363636017,
-0.0007099728682078421,
0.05238133668899536,
0.023666052147746086,
-0.009247061796486378,
0.0073343301191926,
-0.023951949551701546,
-0.04012277349829674,
-0.006675519980490208,
0.019607800990343094,
-0.037871114909648895,
0.029711028560996056,
0.020626267418265343,
0.013917441479861736,
0.044259533286094666,
-0.0023608156479895115,
-0.02918962761759758,
0.01970728300511837,
-0.05932771787047386,
-0.006736649200320244,
-0.01960611529648304,
0.03417384624481201,
0.03429129347205162,
-0.025266969576478004,
0.007757007610052824,
-0.0012340096291154623,
0.01851375587284565,
-0.020613430067896843,
0.033498648554086685,
0.034753598272800446,
0.023246625438332558,
0.012186547741293907,
-0.035712964832782745,
-0.047334056347608566,
-0.03053034096956253,
-0.02505457028746605,
0.011551158502697945,
0.004135747440159321,
-0.07421456277370453,
0.029049411416053772,
-0.0051580797880887985,
0.01826714538037777,
-0.010289652273058891,
0.015466366894543171,
-0.03346266224980354,
0.02069581300020218,
-0.021970393136143684,
0.02028960920870304,
0.014190088026225567,
0.06200350448489189,
0.06880121678113937,
-0.014851360581815243,
-0.023942159488797188,
-0.0494423545897007,
0.009166223928332329,
0.04907511919736862,
0.02941477671265602,
-0.027879951521754265,
0.05135458707809448,
-0.037516504526138306,
-0.05334725230932236,
0.017842203378677368,
-0.003935285843908787,
0.04036889225244522,
-0.0390726774930954,
0.05400276929140091,
0.009187158197164536,
-0.017143307253718376,
-0.008896180428564548,
-0.006089337170124054,
0.009687165729701519,
-0.01018789317458868,
0.01529823150485754,
0.0400916151702404,
0.04000420495867729,
0.0326787531375885,
0.05763400346040726,
0.0024303339887410402,
0.006932357791811228,
-0.0070093171671032906,
0.015687203034758568,
-0.0017107913736253977,
-0.028955819085240364,
-0.0429629310965538,
0.01604139618575573,
0.009535151533782482,
0.016555219888687134,
0.05584064498543739,
-0.017823388800024986,
-0.0637517049908638,
0.021914750337600708,
0.02814524807035923,
0.012430216185748577,
-0.005560419987887144,
-0.008220373652875423,
0.00911932997405529,
0.06594158709049225,
-0.02077178843319416,
0.02962978184223175,
0.03289143368601799,
-0.01581251248717308,
0.01996108517050743,
-0.02208024449646473,
0.03665553033351898,
-0.05158403143286705,
-0.0011890425812453032,
-0.04625827819108963,
0.00628986582159996,
-0.060627441853284836,
-0.0055677033960819244,
0.03134973347187042,
0.020124858245253563,
-0.0029178017284721136,
-0.019290415570139885,
0.013167300261557102,
0.00813386496156454,
0.035810437053442,
-0.006187719758599997,
0.007342843804508448,
0.043708473443984985,
-0.004356605466455221,
-0.004160740878432989,
0.0019050142727792263,
-0.019726766273379326,
0.04880421608686447,
-0.014730777591466904,
-0.002642438281327486,
-0.013464540243148804,
-0.056453973054885864,
-0.018383556976914406,
0.015211343765258789,
-0.03436068072915077,
0.054033178836107254,
-0.013359833508729935,
0.017344007268548012,
0.00694201048463583,
-0.030749622732400894,
-0.012816674076020718,
0.04781735688447952,
-0.03663450852036476,
-0.03711570054292679,
-0.02196955494582653,
0.026632994413375854,
0.009510397911071777,
0.010537165217101574,
0.011505845934152603,
-0.017275944352149963,
0.023854900151491165,
0.027295803651213646,
0.002806765725836158,
-0.0486600324511528,
-0.039692509919404984,
-0.03226197883486748,
-0.02684984914958477,
-0.06167326495051384,
0.03652410954236984,
-0.027328282594680786,
-0.00936378724873066,
0.05914965271949768,
-0.01942320540547371,
0.05692105367779732,
0.01752200908958912,
-0.006262930575758219,
-0.0032292373944073915,
-0.02563893422484398,
-0.005323904566466808,
-0.020989246666431427,
-0.020263897255063057,
-0.011554108001291752,
-0.03548048064112663,
0.007673845160752535,
-0.010675367899239063,
0.009269765578210354,
-0.03451942652463913,
0.0008048738818615675,
0.07318533211946487,
0.03433183208107948,
0.004118871409446001,
-0.021039381623268127,
0.05554930493235588,
0.001572886249050498,
0.04402703791856766,
0.00392170762643218,
0.037639956921339035,
-0.0009830305352807045,
-0.03654283657670021,
0.028113091364502907,
-0.01195068284869194,
-0.038780078291893005,
0.014756529591977596,
0.05900442227721214,
-0.007754471153020859,
-0.014316852204501629,
-0.020217714831233025,
-0.047709088772535324,
0.0473598912358284,
-0.0015512717654928565,
0.002117718802765012,
0.02550536021590233,
0.02108168601989746,
-0.045336052775382996,
-0.029220713302493095,
-0.024018559604883194,
0.026152320206165314,
0.039655279368162155,
-0.026400107890367508,
0.009136728011071682,
0.006494589149951935,
-0.03613157570362091,
-0.04109792783856392,
-0.009626479819417,
0.01164890918880701,
0.04236506298184395,
-0.006755044683814049,
-0.004919788800179958,
-0.040371060371398926,
-0.017502857372164726,
0.01172149833291769,
0.034190062433481216,
0.015498697757720947,
-0.0015922774327918887,
0.08605559915304184,
-0.0033954381942749023,
0.028571587055921555,
-0.05198623985052109,
-0.029253970831632614,
0.02382553182542324,
-0.07573377341032028,
0.047355275601148605,
-0.03450717404484749,
-0.005274180788546801,
0.05361360311508179,
0.01787496916949749,
-0.002018286380916834,
-0.07461339980363846,
-0.025966577231884003,
-0.011090892367064953,
0.026223374530673027,
0.01583956740796566,
0.011142116971313953,
0.003059324575588107,
-0.014827590435743332,
0.034404654055833817,
-0.0007303442689590156,
0.004602502565830946,
-0.046784013509750366,
-0.06026393175125122,
0.006479386705905199,
-0.004166357684880495,
0.011700989678502083,
0.0489816777408123,
-0.026801640167832375,
-0.05422583222389221,
0.026526907458901405,
-0.023418612778186798,
0.00886349193751812,
0.03096682019531727,
0.05471424013376236,
0.0034921178594231606,
0.03458287939429283,
-0.022406119853258133,
0.009670568630099297,
0.03550269082188606,
0.02333306521177292,
0.15665362775325775,
0.012682526372373104,
-0.004460649564862251,
-0.03536590561270714,
0.015083328820765018,
-0.004571668803691864,
-0.00859001837670803,
-0.044510386884212494,
-0.0059564122930169106,
-0.017345085740089417,
0.05763832852244377,
0.003148451214656234,
0.04642964154481888,
-0.044464271515607834,
0.002405104460194707,
0.018299799412488937,
-0.04672954976558685,
-0.01878213882446289,
0.0041086506098508835,
0.019954774528741837,
-0.027100814506411552,
-0.03262131288647652,
-0.03056151792407036,
0.015817580744624138,
-0.005284222308546305,
-0.002975430339574814,
-0.03175025433301926,
-0.003418013919144869,
0.007883005775511265,
0.005043574143201113,
-0.01650836318731308,
-0.0003672940074466169,
0.020841268822550774,
-0.03338579833507538,
0.0017534636426717043,
0.02102813497185707,
0.011352243833243847,
-0.02240472473204136,
0.011021260172128677,
0.02310049906373024,
0.014581825584173203,
0.030178319662809372,
0.05118303373456001,
0.016028769314289093,
-0.03904197737574577,
0.025022407993674278,
0.015407309867441654,
-0.0016583523247390985,
-0.03910112753510475,
-0.03315500169992447,
0.024212272837758064,
-0.01814146712422371,
0.004519016481935978,
-0.015370327979326248,
-0.040485866367816925,
0.02161642163991928,
0.016219664365053177,
-0.0066686030477285385,
-0.006786740384995937,
-0.001211810391396284,
0.017767243087291718,
-0.0006070223753340542,
-0.015963368117809296,
0.029376406222581863,
-0.012051069177687168,
0.01976536028087139,
0.016893072053790092,
0.04828161001205444,
0.013430665247142315,
-0.010602819733321667,
-0.023136846721172333,
-0.005181001033633947,
-0.034925974905490875,
-0.0034353553783148527,
-0.03236520290374756,
0.023983178660273552,
0.036036062985658646,
-0.005383306182920933,
0.003247647313401103,
-0.001171113341115415,
-0.04944165423512459,
0.08369389921426773,
-0.028751319274306297,
-0.031889088451862335,
-0.03962818160653114,
-0.03517429903149605,
-0.005780856590718031,
0.04186801239848137,
-0.01494419015944004,
0.0012616156600415707,
-0.014261971227824688,
0.03257913142442703,
0.00587707431986928,
-0.012423994019627571,
-0.040700457990169525,
0.008472653105854988,
-0.04704969376325607,
-0.052284449338912964,
-0.0216144360601902,
0.043986450880765915,
0.02624003030359745,
0.010793015360832214,
0.012694486416876316,
-0.02199378050863743,
-0.0256218109279871,
0.025357523933053017,
0.03226445987820625,
-0.020726297050714493,
-0.01165392529219389,
0.05922188609838486,
-0.006677479948848486,
-0.017870604991912842,
-0.031522590667009354,
-0.03754834085702896,
-0.003145889611914754,
0.007323701865971088,
0.04806138202548027,
-0.02358260564506054,
0.018189355731010437,
0.01425827294588089,
0.0009952131658792496,
-0.04775422066450119,
0.003314594505354762,
-0.06413838267326355,
-0.015967704355716705,
-0.007094110362231731,
-0.03885534405708313,
-0.017997147515416145,
0.03746577724814415,
-0.00319501431658864,
0.035153016448020935,
-0.010363991372287273,
-0.012576275505125523,
-0.0030417239759117365,
-0.004682138562202454,
0.018624337390065193,
-0.006245721131563187,
0.059481047093868256,
0.02245602384209633,
-0.04462297633290291,
0.028572173789143562,
-0.018078530207276344,
-0.06589192152023315,
-0.017164655029773712,
-0.045166030526161194,
0.022175561636686325,
0.023195724934339523,
-0.009345264174044132,
-0.026865938678383827,
0.033145416527986526,
-0.04951249808073044,
-0.00098913605324924,
-0.024363785982131958,
-0.028954867273569107,
0.023266861215233803,
-0.015254448167979717,
-0.029161373153328896,
-0.014828152023255825,
0.005078550428152084,
0.0250735841691494,
-0.02806573174893856,
0.03719715029001236,
-0.0022706440649926662,
0.016561828553676605,
-0.04146049916744232,
-0.0024532810784876347,
-0.03250806778669357,
-0.011532441712915897,
-0.022815562784671783,
0.08017893135547638,
-0.031102996319532394,
-0.03906894475221634,
-0.02138868160545826,
-0.022429190576076508,
-0.06474748253822327,
-0.006206250749528408,
0.027844231575727463,
-0.043082095682621,
0.02175658382475376,
-0.010769507847726345,
0.029099619016051292,
0.016533154994249344,
-0.07033313065767288,
0.0005671078688465059,
-0.031888771802186966,
-0.008484352380037308,
-0.0684710219502449,
-0.015843380242586136,
-0.007548968773335218,
0.08881799131631851,
-0.018176980316638947,
0.01040179654955864,
-0.011856340803205967,
0.004550055600702763,
-0.001761502819135785,
-0.05314682424068451,
0.05681091174483299,
0.05342709273099899,
-0.018686193972826004,
-0.0062632509507238865,
0.07161388546228409,
0.02454485185444355,
0.0069963522255420685,
0.0004455627058632672,
-0.02944754995405674,
0.004835208877921104,
0.002576527651399374,
-0.002493123523890972,
0.0009432348888367414,
0.010340970940887928,
0.0052187577821314335,
0.01138350460678339,
-0.05124229937791824,
0.026192717254161835,
-0.016589965671300888,
0.03152478113770485,
-0.05669016018509865,
0.021771680563688278,
-0.034310825169086456,
-0.03484294191002846,
-0.05422237887978554,
-0.025792023167014122,
-0.04867353290319443,
-0.017416296526789665,
0.006350389216095209,
0.002415622118860483,
0.020323358476161957,
-0.030211176723241806,
-0.05577016994357109,
-0.03519965708255768,
0.03329681232571602,
0.06142299622297287,
0.0468842089176178,
-0.030977744609117508,
0.04158159717917442,
0.025141112506389618,
0.031146690249443054,
-0.009776902385056019,
0.04011610522866249,
-0.010387076064944267,
-0.003390928730368614,
-0.007615399546921253,
-0.02069544792175293,
0.004010459873825312,
-0.012101992033421993,
-0.021413665264844894,
0.0011070470791310072,
0.042164888232946396,
-0.0010224358411505818,
0.0360998697578907,
-0.0032717655412852764,
0.000055657237680861726,
0.0012710716109722853,
-0.04612499102950096,
0.025899402797222137,
0.02422827109694481,
-0.01590755768120289,
-0.05159745737910271,
-0.03191060945391655,
-0.018617229536175728,
-0.01097883377224207,
0.05561301112174988,
0.01068131159991026,
0.012072925455868244,
0.022917071357369423,
0.02450176700949669,
-0.022632287815213203,
-0.01308919582515955,
0.04488512873649597,
0.012782443314790726,
-0.02391289547085762,
0.03241593390703201,
0.031610675156116486,
0.002588672796264291,
0.02747667208313942,
0.008790189400315285,
-0.01664109155535698,
0.02977762185037136,
0.04578397795557976,
0.011296653188765049,
0.040073927491903305,
0.01242722850292921,
0.010580731555819511,
0.06843230128288269,
-0.01740957237780094,
-0.001055752974934876,
-0.0006390639464370906,
-0.019240684807300568,
-0.028777651488780975,
0.05822942033410072,
-0.004516281187534332,
0.02923799864947796,
-0.0013289233902469277,
-0.0101543627679348,
0.027039572596549988,
-0.03873439133167267,
-0.022684834897518158,
0.004125805571675301,
-0.05600975081324577,
-0.006713096983730793,
-0.0009081073221750557,
0.022443506866693497,
0.06289695203304291,
0.015484169125556946,
-0.003339445684105158,
0.03151281923055649,
0.016245633363723755,
0.036899179220199585,
-0.0033382829278707504,
0.01464505773037672,
-0.01457642950117588,
-0.017862992361187935,
0.016036605462431908,
0.01062227413058281,
0.027614207938313484,
0.048998698592185974,
0.025129053741693497,
-0.006603108253329992,
-0.014258796349167824,
-0.013227201998233795,
0.007304721046239138,
-0.01988607458770275,
0.003915079869329929,
-0.008308129385113716,
0.0824812576174736,
0.021493835374712944,
-0.004591676872223616,
-0.009066304191946983,
0.020137524232268333,
-0.022202488034963608,
0.030615219846367836,
0.04608115181326866,
0.0020995656959712505,
0.014736072160303593,
0.004867732524871826,
-0.01813242956995964,
-0.016916317865252495,
-0.030641738325357437,
-0.010709801688790321,
0.022862209007143974,
-0.02501062862575054,
-0.006835727486759424,
-0.016573112457990646,
-0.014477042481303215,
-0.03440045192837715,
-0.02324141189455986,
0.05368586257100105,
0.02745123952627182,
-0.015618305653333664,
-0.01082267239689827,
-0.018446922302246094,
-0.0031860251910984516,
0.04465482756495476,
-0.06127334013581276,
-0.026681028306484222,
-0.033082522451877594,
0.014396542683243752,
-0.01143552828580141,
0.019182445481419563
] |
<p>I was going through a problem in which they had given mass and speed and asked its wavelength. Now its de Broglie wavelength $h/\lambda$ and I had to find out which of them had wave nature which could be observed. I thought objects whose wavelength is greater than wavelength of light would have observable wave nature, with calculations I found out that electrons had wavelength of $0.78Å$ in that case so with my reasoning it should not be observed which turned out to be the wrong answer. Please help me how should we know whether one has observable wave nature or not.</p>
| 10,698 |
[
-0.018230147659778595,
0.002413395792245865,
-0.001979280263185501,
-0.0450119748711586,
0.020572464913129807,
-0.006714931223541498,
-0.07219517230987549,
-0.018725011497735977,
-0.0065512522123754025,
0.0074168299324810505,
0.04708665981888771,
0.02847127988934517,
0.03432926535606384,
0.03715677931904793,
0.03069603443145752,
0.03781963139772415,
-0.03765559196472168,
-0.01454069558531046,
-0.017986983060836792,
0.0005717840977013111,
-0.00420344527810812,
0.018573381006717682,
0.01410641148686409,
-0.02242419496178627,
-0.022098848596215248,
0.02197079174220562,
0.0018844061996787786,
0.047008778899908066,
0.0025004874914884567,
0.04763144627213478,
0.02407045103609562,
-0.03170756250619888,
0.03329740837216377,
0.03031500056385994,
0.010894278064370155,
0.009241645224392414,
-0.005376359447836876,
-0.025587378069758415,
-0.013744338415563107,
0.020011262968182564,
-0.014223054051399231,
-0.037771113216876984,
0.04165621101856232,
0.050718627870082855,
-0.01167939230799675,
0.0111125148832798,
-0.0016800976591184735,
-0.0583140030503273,
0.08187054842710495,
-0.053021788597106934,
0.08066532760858536,
-0.0013661454431712627,
0.038366805762052536,
-0.0037975646555423737,
0.026247253641486168,
-0.04465452954173088,
0.08022982627153397,
0.06478513032197952,
-0.015576147474348545,
-0.0353977270424366,
-0.019905446097254753,
-0.011890978552401066,
-0.005368401296436787,
-0.03549514338374138,
-0.02645382471382618,
0.02392343245446682,
-0.03560202941298485,
-0.02599734254181385,
0.011718224734067917,
0.020145168527960777,
0.010227151215076447,
0.0035520584788173437,
0.03303137049078941,
0.010816166177392006,
0.04169687628746033,
-0.029600922018289566,
-0.010875614359974861,
0.03282032534480095,
0.02623983845114708,
0.04001231491565704,
-0.0022402487229555845,
0.006334331817924976,
0.027621150016784668,
0.02455887570977211,
-0.003202941035851836,
-0.03832533210515976,
0.057399675250053406,
0.010522759519517422,
-0.020153557881712914,
0.01126787718385458,
-0.025649312883615494,
-0.027373995631933212,
0.06220582500100136,
-0.007787964306771755,
-0.004040369763970375,
0.04071894660592079,
0.0074861678294837475,
0.024961967021226883,
0.008966411463916302,
-0.04339177533984184,
0.00878821313381195,
-0.03631732985377312,
0.03063422255218029,
0.10712968558073044,
0.009756281971931458,
-0.047936394810676575,
-0.04524677246809006,
0.018844855949282646,
-0.02424565516412258,
-0.023398729041218758,
0.049468185752630234,
0.05739334225654602,
0.015132191590964794,
0.026363039389252663,
-0.03246108442544937,
-0.004317695740610361,
0.022102944552898407,
-0.0345323383808136,
0.05980261042714119,
0.08736656606197357,
0.01784028671681881,
-0.020616495981812477,
-0.013849222101271152,
-0.0025073066353797913,
-0.058807794004678726,
-0.02365564927458763,
0.044439688324928284,
0.0009843199513852596,
-0.028194716200232506,
0.0188498105853796,
-0.005026377737522125,
-0.02659633196890354,
0.02559620514512062,
-0.040847402065992355,
0.015905562788248062,
-0.024694830179214478,
-0.0960092842578888,
-0.07000860571861267,
0.020089516416192055,
0.012946147471666336,
-0.0388607382774353,
-0.06348494440317154,
-0.01069346722215414,
0.05964488163590431,
0.06519776582717896,
0.01505166944116354,
0.0018707657000049949,
0.026814911514520645,
0.03522684425115585,
0.009184660390019417,
-0.012680377811193466,
-0.005722058936953545,
0.02262197621166706,
-0.0517604798078537,
0.001549749169498682,
-0.006339687388390303,
-0.0447295606136322,
-0.008933119475841522,
-0.002933372277766466,
-0.006987404078245163,
0.10215859115123749,
-0.029473038390278816,
0.008371000178158283,
0.006176920607686043,
0.010078596882522106,
-0.0564315989613533,
0.08097203075885773,
0.011187192983925343,
0.027561360970139503,
0.0165467020124197,
-0.02052605152130127,
0.011595426127314568,
0.002704047132283449,
0.02618541195988655,
0.008006268180906773,
-0.0092716533690691,
-0.060549646615982056,
-0.025812124833464622,
0.02707580104470253,
-0.031124290078878403,
-0.020257525146007538,
-0.03916855528950691,
-0.017519697546958923,
0.029153885319828987,
0.007378674577921629,
0.031135274097323418,
-0.003573057474568486,
0.00426698150113225,
0.020297061651945114,
-0.06895714998245239,
-0.002321789972484112,
-0.02189560979604721,
0.018135949969291687,
0.03242184966802597,
0.0019273794023320079,
0.022722065448760986,
0.0171124879270792,
-0.02076619118452072,
-0.04221806302666664,
-0.010660244151949883,
0.00003901447416865267,
0.0832572802901268,
-0.0010170427849516273,
0.03154992684721947,
0.029399488121271133,
0.032579150050878525,
0.024656198918819427,
-0.009821663610637188,
0.008519870229065418,
-0.003676630323752761,
0.0048738825134932995,
-0.0010048082331195474,
-0.03080359846353531,
-0.013480590656399727,
0.017600752413272858,
0.015529208816587925,
-0.006996378768235445,
-0.024033991619944572,
-0.052036069333553314,
0.08076958358287811,
-0.020352546125650406,
0.07234128564596176,
0.02860310859978199,
-0.012070782482624054,
0.006383378058671951,
0.04121838137507439,
-0.009536621160805225,
0.017244558781385422,
-0.02497151680290699,
-0.005069390404969454,
-0.06778549402952194,
-0.0007938332273624837,
0.032651450484991074,
0.0055846101604402065,
-0.03355588763952255,
0.0034092338755726814,
-0.016733597964048386,
0.02288978546857834,
0.08359408378601074,
0.038506846874952316,
-0.040934182703495026,
-0.05243817716836929,
0.016867516562342644,
0.024577949196100235,
-0.009526046924293041,
0.009000560268759727,
0.04766758531332016,
0.027717532590031624,
0.03646572306752205,
-0.03277529403567314,
0.00429758382961154,
0.04157267138361931,
-0.023721670731902122,
0.03318016231060028,
-0.0019159773364663124,
-0.023768754675984383,
0.03203399479389191,
-0.008012514561414719,
0.024675587192177773,
0.021488677710294724,
-0.020680028945207596,
0.005618381313979626,
-0.03506043180823326,
-0.00978011079132557,
0.035553544759750366,
0.0008060556137934327,
-0.059908557683229446,
-0.032591529190540314,
0.013112850487232208,
-0.020206725224852562,
0.007562705781310797,
-0.03453733026981354,
-0.024333901703357697,
-0.0053233252838253975,
-0.00299355061724782,
0.07362151890993118,
0.01664556935429573,
0.04401279240846634,
-0.05010564997792244,
-0.03635073080658913,
-0.003904302604496479,
-0.04525468125939369,
0.025976989418268204,
0.004986220970749855,
-0.01743386685848236,
0.012966065667569637,
-0.07004076987504959,
-0.06576346606016159,
0.041309814900159836,
-0.004616021178662777,
-0.0025666190776973963,
0.014226751402020454,
-0.009615321643650532,
-0.02378068119287491,
-0.01600375957787037,
-0.05010230466723442,
0.02334350161254406,
-0.0377207025885582,
-0.012838470749557018,
0.03964455798268318,
-0.013639768585562706,
-0.027214080095291138,
0.03085649013519287,
-0.013031547889113426,
-0.03834816813468933,
0.016167590394616127,
-0.028488602489233017,
-0.012083807960152626,
-0.04057266563177109,
0.05613753944635391,
0.036443471908569336,
-0.02125728316605091,
0.02567363902926445,
-0.05057993158698082,
-0.05711793154478073,
0.04376491531729698,
-0.01806526631116867,
-0.001547300722450018,
-0.009956931695342064,
-0.01308507937937975,
0.04432324692606926,
0.033589910715818405,
-0.026773551478981972,
-0.0003114040882792324,
0.022419441491365433,
0.01794186420738697,
-0.054558053612709045,
0.011874794960021973,
0.04365716502070427,
-0.003080274211242795,
0.005266247782856226,
-0.006843216717243195,
0.053592123091220856,
0.007458972744643688,
0.014393454417586327,
-0.0061619458720088005,
-0.0025206981226801872,
0.009040940552949905,
0.007218762766569853,
0.0660378485918045,
-0.006823001895099878,
-0.014216898009181023,
0.05176623910665512,
-0.018006110563874245,
0.02570534311234951,
0.04414209723472595,
-0.03785395622253418,
0.03730378672480583,
0.023891568183898926,
0.022162042558193207,
0.011309598572552204,
0.006937886588275433,
0.023580944165587425,
0.012605703435838223,
-0.014441773295402527,
-0.006831657607108355,
0.01948835700750351,
0.002990724751725793,
0.019228177145123482,
0.07485737651586533,
0.008735959418118,
0.003064041258767247,
-0.04177119582891464,
-0.00966116413474083,
-0.006961469072848558,
0.021345429122447968,
-0.022955486550927162,
-0.0288247000426054,
0.015585625544190407,
0.04771589860320091,
-0.0070926896296441555,
-0.025083309039473534,
-0.04474397748708725,
-0.005659620277583599,
-0.027772443369030952,
-0.013560340739786625,
0.011095166206359863,
0.046399228274822235,
-0.0007576041389256716,
0.04516424611210823,
0.04829210042953491,
0.007168404757976532,
0.025280337780714035,
0.02397417277097702,
-0.05144382640719414,
0.0099667152389884,
-0.018327517434954643,
-0.013019520789384842,
-0.027034729719161987,
-0.03796093538403511,
-0.017949283123016357,
-0.03068537823855877,
0.010567467659711838,
-0.015296239405870438,
-0.04075344279408455,
-0.05792248994112015,
0.008373560383915901,
-0.01531138550490141,
-0.023621540516614914,
-0.02686360850930214,
0.04153678938746452,
-0.002548937452957034,
0.005249658599495888,
0.02244619093835354,
0.034797780215740204,
-0.057400573045015335,
-0.017747733741998672,
-0.00866867695003748,
-0.016538744792342186,
-0.0010408740490674973,
0.04202267900109291,
0.0528254508972168,
0.010508131235837936,
-0.044084660708904266,
0.008889034390449524,
0.054647479206323624,
0.068375363945961,
-0.03743669390678406,
-0.003912861924618483,
-0.0354560986161232,
-0.019311269745230675,
0.0015814404468983412,
-0.02800530567765236,
0.05899769440293312,
-0.017750000581145287,
-0.011488590389490128,
0.028091048821806908,
-0.036463066935539246,
-0.01041759829968214,
0.04433465003967285,
0.06531845033168793,
0.014167298562824726,
-0.029157795011997223,
-0.01609257236123085,
0.011320595629513264,
-0.06476172059774399,
-0.009629287756979465,
0.0024677743203938007,
0.022326722741127014,
0.007111439947038889,
-0.003685265313833952,
0.009433826431632042,
0.04220568388700485,
-0.025066189467906952,
-0.03724100813269615,
-0.047996122390031815,
-0.004615768790245056,
-0.016239026561379433,
-0.03837474808096886,
0.0059242527931928635,
0.057454098016023636,
0.0235904548317194,
-0.012037858366966248,
0.009592309594154358,
-0.0786236971616745,
-0.03269989416003227,
0.01828724332153797,
0.00493435887619853,
-0.017152652144432068,
-0.011105804704129696,
-0.0594976469874382,
-0.02493160590529442,
0.04739312082529068,
-0.03650735691189766,
0.03492831438779831,
-0.04088049381971359,
0.019317617639899254,
-0.028720475733280182,
0.02038811892271042,
-0.03152260184288025,
0.013217143714427948,
-0.011212002485990524,
0.0037714208010584116,
-0.04209044575691223,
0.025601128116250038,
-0.008233762346208096,
-0.006112248171120882,
0.01642550528049469,
0.04842878133058548,
0.01053124200552702,
-0.0007133164908736944,
0.0026674848049879074,
-0.005713385995477438,
-0.051988065242767334,
-0.059771887958049774,
0.023094942793250084,
0.020320072770118713,
0.006611332762986422,
0.03159299120306969,
-0.021732371300458908,
-0.014407189562916756,
0.025849852710962296,
0.014339850284159184,
0.016147103160619736,
0.024159852415323257,
-0.037316277623176575,
0.04903653636574745,
-0.010335435159504414,
-0.025470316410064697,
0.02077704668045044,
0.04752884805202484,
0.0017283896449953318,
-0.0056208097375929356,
-0.022489015012979507,
0.018951084464788437,
-0.031198972836136818,
-0.02469642460346222,
-0.007278070785105228,
0.01530437357723713,
-0.027458555996418,
0.049193061888217926,
-0.00726590771228075,
0.02591792307794094,
-0.004343993961811066,
-0.05395444110035896,
-0.01284854207187891,
0.026622159406542778,
0.012971539981663227,
-0.0049910275265574455,
-0.02931482344865799,
-0.0064056627452373505,
-0.0069616870023310184,
0.012681443244218826,
-0.006734955590218306,
-0.020983008667826653,
0.004426291678100824,
0.038959797471761703,
-0.03795584663748741,
0.04960941523313522,
-0.009132754057645798,
-0.011432536877691746,
0.018347641453146935,
-0.054692342877388,
0.0059105465188622475,
-0.012811020947992802,
0.0037344670854508877,
0.005561083555221558,
-0.053944725543260574,
-0.051427341997623444,
0.03123909793794155,
0.008372624404728413,
0.036205366253852844,
-0.027966385707259178,
0.04433237016201019,
0.011073402129113674,
0.0027690480928868055,
-0.05118904635310173,
-0.004918983206152916,
-0.0035873944871127605,
0.053317923098802567,
-0.019517933949828148,
0.03802535682916641,
0.05798543617129326,
-0.03686264157295227,
0.020660649985074997,
0.00450212974101305,
0.03157440200448036,
-0.05417944863438606,
-0.015405725687742233,
-0.009507455863058567,
0.03186904266476631,
0.04188450053334236,
-0.015981342643499374,
-0.0030250668060034513,
-0.025104423984885216,
0.013464904390275478,
0.006098316982388496,
0.0362919382750988,
-0.014282780699431896,
-0.006013978738337755,
-0.05306233838200569,
-0.028555557131767273,
-0.003953646868467331,
0.055981557816267014,
-0.019339827820658684,
0.02519422397017479,
0.04123827815055847,
-0.0023424436803907156,
-0.031123021617531776,
0.0004010442062281072,
0.02903509885072708,
-0.04010313004255295,
0.02249588444828987,
0.01537334080785513,
0.004706184379756451,
-0.057778242975473404,
-0.05195331573486328,
0.027953773736953735,
-0.01799694076180458,
0.008159437216818333,
-0.010164124891161919,
0.04366465285420418,
-0.011322078295052052,
0.0225503072142601,
0.001321099349297583,
-0.019325880333781242,
-0.03973216563463211,
-0.025036092847585678,
0.0045089274644851685,
0.01920543611049652,
0.04517852142453194,
-0.03874986991286278,
-0.013104354031383991,
-0.04647210240364075,
0.017837466672062874,
0.06723764538764954,
-0.006606701295822859,
0.028199471533298492,
0.012793373316526413,
0.028356220573186874,
-0.016643023118376732,
-0.01623222790658474,
-0.010689638555049896,
0.016826681792736053,
0.0028375855181366205,
0.015990320593118668,
-0.035150397568941116,
-0.0015538630541414022,
0.040166884660720825,
0.015003148466348648,
-0.01044568233191967,
-0.006792821921408176,
0.0659019872546196,
-0.0004051261057611555,
-0.0028820359148085117,
-0.037614766508340836,
-0.008540469221770763,
0.0003730138996616006,
-0.0015028880443423986,
0.020355872809886932,
-0.026845315471291542,
-0.0009421583963558078,
0.009155991487205029,
-0.0025553277228027582,
0.0025671483017504215,
-0.015730032697319984,
0.01139743346720934,
-0.04558885097503662,
0.013735632412135601,
0.037740834057331085,
0.011088000610470772,
0.006717676296830177,
0.00027197072631679475,
0.03322990611195564,
0.003258442273363471,
0.03014632873237133,
0.026698529720306396,
-0.07166913151741028,
-0.047313109040260315,
-0.025432931259274483,
-0.05683762952685356,
0.06302165240049362,
0.00509805278852582,
-0.022953446954488754,
0.005006004590541124,
-0.03242529183626175,
0.02269556000828743,
0.026042623445391655,
0.03427210450172424,
-0.009627715684473515,
0.05130048468708992,
-0.022163836285471916,
0.014000896364450455,
0.01557650975883007,
0.06759439408779144,
0.10125017911195755,
0.06331049650907516,
0.0036931615322828293,
-0.02432193048298359,
0.035032935440540314,
-0.007899058051407337,
0.03219236806035042,
-0.022759361192584038,
0.03884522616863251,
-0.008832788094878197,
-0.02197149209678173,
-0.030150767415761948,
0.0004905722453258932,
0.008618632331490517,
0.014862079173326492,
0.023551596328616142,
-0.06600247323513031,
-0.038417257368564606,
-0.009436937049031258,
0.012544559314846992,
0.027954481542110443,
0.03067205660045147,
-0.027179164811968803,
0.02703375369310379,
-0.019394375383853912,
-0.001985156210139394,
0.00487522641196847,
-0.03778713941574097,
0.01028550323098898,
-0.04020006209611893,
-0.05163862556219101,
0.004065495450049639,
0.02580002322793007,
-0.031184900552034378,
-0.04880770295858383,
0.022586235776543617,
0.04058050364255905,
0.0007826538057997823,
0.028143465518951416,
0.03447280824184418,
-0.031725574284791946,
0.014293178915977478,
0.013552390038967133,
0.042364224791526794,
-0.0645505040884018,
0.016175683587789536,
-0.005679385736584663,
0.0660935565829277,
-0.007388410158455372,
0.01905214972794056,
0.009623604826629162,
-0.003425434697419405,
-0.042013395577669144,
-0.06156041845679283,
-0.015676524490118027,
-0.027700234204530716,
0.008516998030245304,
-0.017303649336099625,
-0.0346517451107502,
-0.0382222943007946,
0.003547498257830739,
-0.01159388106316328,
0.03890566900372505,
-0.0016620069509372115,
0.014905969612300396,
-0.022593379020690918,
0.014843156561255455,
0.019665388390421867,
0.01960543729364872,
-0.012977155856788158,
0.009204825386404991,
-0.04221707955002785,
-0.009616849943995476,
-0.016431214287877083,
0.03297150507569313,
0.019549064338207245,
0.012502286583185196,
0.016298700124025345,
-0.003494374454021454,
-0.060414522886276245,
-0.05606681481003761,
-0.0021483474411070347,
-0.013983359560370445,
-0.010571718215942383,
-0.01449299231171608,
-0.010413659736514091,
0.00468924455344677,
0.04138905927538872,
-0.04271650314331055,
0.0059133064933121204,
0.03073725476861,
0.009658454917371273,
0.0320776142179966,
-0.03141006454825401,
-0.007669247221201658,
0.026497824117541313,
-0.012766416184604168,
0.024669386446475983,
-0.008988086134195328,
0.016082212328910828,
0.030997762456536293,
0.0013428430538624525,
0.002624970395117998,
0.049774736166000366,
-0.01288579311221838,
-0.018294930458068848,
0.023526238277554512,
-0.002644666936248541,
0.025891505181789398,
0.006392536219209433,
0.04852425679564476,
-0.052793312817811966,
-0.057296253740787506,
-0.04389147460460663,
-0.005827079992741346,
-0.01300876960158348,
-0.01453839149326086,
-0.001489520538598299,
0.017538685351610184,
0.009907240979373455,
0.00571275083348155,
-0.04019961878657341,
-0.029008282348513603,
-0.03572000190615654,
-0.0014466303400695324,
-0.007083474658429623,
-0.029778609052300453,
-0.03393740579485893,
0.06865499913692474,
0.03442118316888809,
-0.030703047290444374,
0.004000415559858084,
0.02641364187002182,
-0.009872399270534515,
-0.030099598690867424,
0.012298500165343285,
-0.016767844557762146,
0.04240214079618454,
0.03900815546512604,
-0.03556246683001518,
0.0033008751925081015,
-0.030540887266397476,
0.01371821016073227,
0.06594918668270111,
-0.020652910694479942,
0.03440415859222412,
0.030515028163790703,
-0.024331439286470413,
0.03412030264735222,
0.03618331253528595,
-0.01781289465725422,
0.02371797151863575,
-0.022554395720362663,
-0.0260612852871418,
-0.0486297570168972,
0.002359689213335514,
0.009928938001394272,
0.006958663463592529,
0.008924582973122597,
0.05326474457979202,
0.008981682360172272,
0.02258010022342205,
-0.001850453787483275,
-0.008197744376957417,
0.017364924773573875,
0.011101745069026947,
0.026089290156960487,
-0.004552960395812988,
-0.006425287574529648,
0.03307371959090233,
-0.05320465564727783,
0.05800703912973404,
0.02112921141088009,
0.0071302312426269054,
-0.08064932376146317,
0.008805702440440655,
0.028265444561839104,
0.03283563256263733,
0.0700940415263176,
-0.03101026639342308,
-0.008648134768009186,
0.04473649710416794,
-0.041994594037532806,
0.008085165172815323,
-0.027493605390191078,
0.033724311739206314,
-0.01892402581870556,
-0.019686708226799965,
-0.04916752502322197,
0.07013653218746185,
-0.019391095265746117,
0.05293089896440506,
0.05161641165614128,
0.06182251125574112,
-0.004090234637260437,
-0.057755351066589355,
-0.008073244243860245,
0.024056510999798775,
0.016252359375357628,
-0.02056295983493328,
0.056386303156614304,
-0.03623952716588974,
-0.005506108049303293,
0.049182698130607605,
0.007347441744059324,
0.02435397543013096,
-0.01756387948989868,
-0.008314848877489567,
0.016497991979122162,
0.012222355231642723,
-0.005300246179103851,
-0.0204250980168581,
-0.010532311163842678,
0.046595923602581024,
-0.0004436408053152263,
0.018398215994238853,
0.021510465070605278,
-0.022760236635804176,
-0.00043086003279313445,
-0.062020912766456604,
-0.05698059871792793,
-0.010345099493861198,
-0.009185261093080044,
-0.016403917223215103,
0.004355032462626696,
-0.012716700322926044,
-0.003285324899479747,
-0.050216663628816605,
0.0002709987747948617,
-0.0250774547457695,
-0.0015285307308658957,
0.03150012716650963,
0.0015953145921230316,
-0.02812085673213005,
0.008332488127052784,
-0.031142981722950935,
-0.025666551664471626,
0.05342192202806473,
-0.020394133403897285,
0.011783781461417675,
-0.04306897148489952,
-0.012588619254529476,
-0.03270014002919197,
0.000022865777282277122,
0.008810214698314667,
-0.036688175052404404,
-0.0577530600130558,
0.013480166904628277,
-0.02030395157635212,
-0.011489113792777061,
-0.038861099630594254,
-0.01574678160250187,
-0.015603110194206238,
-0.0634714812040329,
0.014902045018970966,
0.04600187763571739,
-0.009399390779435635,
-0.015280873514711857,
-0.007675482891499996,
0.005254407413303852,
0.03522968664765358,
0.050374094396829605,
0.01901722140610218,
-0.034297339618206024,
0.004400016274303198,
-0.013081091456115246,
-0.0011529315961524844,
-0.015038689598441124,
-0.008883075788617134,
-0.0163519699126482,
-0.030185749754309654,
-0.047596655786037445,
-0.0033290046267211437,
-0.00408669700846076,
0.03310148045420647,
0.012956835329532623,
0.02908599190413952,
-0.0038213543593883514,
-0.01355772279202938,
-0.0741824060678482,
0.0482679046690464,
0.022989606484770775,
-0.018012473359704018,
0.0712733268737793,
0.009044249542057514,
0.010626639239490032,
0.04862195998430252,
-0.04783521592617035,
-0.05734483152627945,
0.01354257483035326,
-0.01740950532257557,
0.0029161919374018908,
0.011381488293409348,
0.023622334003448486,
-0.008634974248707294,
-0.056515779346227646,
-0.0471988245844841,
0.0723758265376091,
-0.008935737423598766,
-0.017642110586166382,
0.04829379543662071,
0.008093904703855515,
0.01327904686331749,
0.005579421762377024,
0.024774961173534393,
0.011850148439407349,
-0.015562000684440136,
-0.002492977771908045,
0.03389232978224754,
0.030508553609251976,
-0.006578125059604645,
0.02968541719019413,
0.05806533619761467,
0.007444172631949186,
-0.0036215081345289946,
-0.017386101186275482,
0.04273165762424469,
-0.045591164380311966,
0.014088058844208717,
0.012138104997575283,
0.010965675115585327,
-0.002465287921950221,
0.03603578358888626,
-0.025962654501199722,
0.07047439366579056,
-0.02495105005800724,
0.027244606986641884,
-0.013976143673062325,
-0.025050822645425797,
-0.011737159453332424,
0.011957288719713688,
0.011452284641563892,
0.01404096931219101,
-0.02516607753932476,
0.01317376084625721,
-0.04232446104288101,
-0.0058640060015022755,
0.01868905872106552,
-0.027951443567872047,
-0.020434420555830002,
0.014397602528333664,
-0.03741173446178436,
-0.012446167878806591,
-0.03133760765194893,
-0.014857499860227108,
0.0172751285135746,
0.02013804391026497,
0.024354517459869385,
-0.00269098742865026,
-0.04066235572099686,
-0.01928919181227684,
-0.019596531987190247,
0.03464161232113838,
-0.037347156554460526,
-0.006295110564678907,
-0.013630006462335587,
0.026565151289105415,
-0.029604369774460793,
-0.018228420987725258
] |
<p>Bohr said that only certain orbits of definite energy are allowed inside the atom. He said that the electrons in their ground state do not emit radiation and that they will emit radiation when they fall from higher energy levels to lower energy levels. My question is what does orbits with definite energy mean? and why do the electron in their ground state not emit radiation?</p>
| 341 |
[
-0.033090103417634964,
-0.022924691438674927,
0.035179153084754944,
-0.019954383373260498,
0.03295775502920151,
0.006293654907494783,
-0.029081571847200394,
-0.029443763196468353,
0.0035271181259304285,
-0.027422379702329636,
0.04491577669978142,
0.0006163526559248567,
0.013391423970460892,
0.022030465304851532,
-0.009539460763335228,
-0.015005008317530155,
-0.004500261507928371,
-0.012723581865429878,
-0.030781399458646774,
-0.025949394330382347,
0.008604444563388824,
0.017874758690595627,
0.003025486133992672,
0.019695742055773735,
0.00002541332105465699,
0.02941814996302128,
-0.004130448680371046,
0.011355542577803135,
0.04911613464355469,
0.047992900013923645,
-0.002741551725193858,
-0.018545635044574738,
-0.004131173249334097,
-0.02250640280544758,
0.02428465336561203,
-0.002542436122894287,
-0.01772467978298664,
-0.00788111612200737,
-0.02799440547823906,
-0.003498698817566037,
-0.03189624473452568,
-0.03620782122015953,
-0.02122597210109234,
0.06787373125553131,
-0.030874213203787804,
-0.03787983953952789,
0.01645367406308651,
-0.011782180517911911,
0.04739965498447418,
-0.03676275536417961,
0.06727028638124466,
-0.02066759765148163,
0.02685553766787052,
0.025566697120666504,
0.018359854817390442,
0.008031227625906467,
0.07760637998580933,
0.08364405483007431,
-0.02741425670683384,
-0.030167171731591225,
-0.02181083709001541,
-0.059731729328632355,
-0.006916245445609093,
0.014068908989429474,
-0.007144187111407518,
-0.004159483127295971,
0.006495010573416948,
-0.0417790450155735,
0.0084376847371459,
0.030732667073607445,
0.04329221695661545,
0.010947240516543388,
0.01862330734729767,
-0.028695348650217056,
-0.002476780442520976,
-0.03971073776483536,
0.043089814484119415,
0.00027605818468146026,
0.04089875519275665,
0.033490024507045746,
-0.021224990487098694,
0.006287684198468924,
0.009392410516738892,
0.05138251185417175,
-0.04409008100628853,
0.0037789386697113514,
0.03545036539435387,
-0.036833710968494415,
-0.022462567314505577,
0.03885514289140701,
0.013187634758651257,
0.029713286086916924,
0.04293558746576309,
-0.007597119081765413,
-0.018542619422078133,
0.017677534371614456,
-0.009441697038710117,
0.0634608343243599,
-0.01859750971198082,
-0.01659919135272503,
0.05349857732653618,
-0.00842229276895523,
0.0182118508964777,
0.0914461612701416,
0.006840286310762167,
-0.019519269466400146,
-0.03679928928613663,
0.034371357411146164,
-0.0055458941496908665,
0.0017933775670826435,
-0.009944307617843151,
-0.006073411554098129,
-0.0035391077399253845,
-0.01505354419350624,
-0.014108660630881786,
-0.0029058672953397036,
-0.004801865201443434,
-0.005172627978026867,
0.03409041464328766,
0.0599878765642643,
0.01945919170975685,
0.012261996977031231,
0.0360453762114048,
-0.02397759072482586,
-0.08127643913030624,
0.004977992735803127,
0.0530380941927433,
0.03498198837041855,
-0.06529893726110458,
-0.015457789413630962,
0.004692927002906799,
0.0010453332215547562,
0.000005013337158743525,
-0.0028141795191913843,
0.05531497299671173,
-0.04065680131316185,
-0.11422146111726761,
-0.061880920082330704,
0.012893706560134888,
0.0009021181613206863,
-0.0373811274766922,
-0.07863356918096542,
0.005422642920166254,
0.044568393379449844,
0.05666298419237137,
-0.006522647570818663,
-0.03204804286360741,
-0.017560705542564392,
0.02668415568768978,
0.0032937368378043175,
-0.008143882267177105,
-0.03489553928375244,
0.000264738715486601,
-0.0630251094698906,
0.004922396037727594,
-0.0580584816634655,
0.034698549658060074,
0.016052916646003723,
0.02106275036931038,
-0.027741026133298874,
0.0641622245311737,
-0.062039755284786224,
-0.0005295847076922655,
-0.0028332655783742666,
-0.02008374035358429,
-0.02807203307747841,
0.07312265783548355,
0.032933298498392105,
-0.013092718087136745,
0.07091224193572998,
0.04633554071187973,
0.056968171149492264,
-0.005331688094884157,
0.030877739191055298,
0.025831783190369606,
-0.03587070479989052,
-0.028599433600902557,
-0.06513319909572601,
0.06365899741649628,
-0.003934754524379969,
-0.06308687478303909,
-0.006461734417825937,
0.022699935361742973,
-0.0014861701056361198,
-0.015524892136454582,
0.04030608385801315,
0.007526784669607878,
-0.0037736212834715843,
-0.0028686784207820892,
-0.031107250601053238,
-0.013537880033254623,
-0.07708708196878433,
0.040847864001989365,
-0.019977640360593796,
-0.004470755811780691,
0.0033025629818439484,
0.023845596238970757,
0.019587211310863495,
-0.023624496534466743,
-0.00007826989167369902,
-0.028097009286284447,
0.02398308552801609,
-0.003466410329565406,
-0.010686984285712242,
0.04626241698861122,
0.04545768350362778,
0.037580229341983795,
0.015368546359241009,
0.009682407602667809,
-0.02000565268099308,
-0.018268845975399017,
-0.00497096823528409,
-0.0019460499752312899,
0.024109508842229843,
0.04088452458381653,
-0.006309885531663895,
-0.02124004252254963,
-0.046192824840545654,
-0.02408181130886078,
0.04071639105677605,
-0.017265016213059425,
0.07281631231307983,
-0.00011394975445000455,
0.03669266030192375,
-0.00967266783118248,
0.028313716873526573,
0.0036205234937369823,
0.0014636194100603461,
-0.005630705505609512,
-0.036544401198625565,
-0.040495723485946655,
-0.0006012450321577489,
0.039930425584316254,
-0.003367369994521141,
-0.06823313981294632,
0.002163755940273404,
0.009649982675909996,
0.03938843682408333,
0.025136621668934822,
0.051670148968696594,
-0.05254162475466728,
-0.04973719269037247,
0.02650132216513157,
0.003903426928445697,
0.04094218462705612,
0.02456405758857727,
0.07033184915781021,
0.033069901168346405,
0.0014863881515339017,
-0.009083513170480728,
-0.004309969954192638,
0.05549374595284462,
-0.00886908732354641,
-0.024691326543688774,
0.014183844439685345,
-0.03936672955751419,
-0.0009446338517591357,
-0.03832685202360153,
0.01098940335214138,
0.0016424984205514193,
-0.049901388585567474,
0.008013910613954067,
-0.03698520362377167,
-0.020396148785948753,
0.009497670456767082,
0.012186895124614239,
-0.047036703675985336,
-0.003613465465605259,
0.024115554988384247,
-0.03097076341509819,
0.030586734414100647,
-0.021192476153373718,
-0.016145728528499603,
-0.03437463194131851,
-0.003856543218716979,
0.0596432201564312,
0.006011059507727623,
0.03497615084052086,
-0.02732655592262745,
-0.04902929067611694,
-0.04612644761800766,
-0.018877046182751656,
0.005852707661688328,
0.056456200778484344,
-0.03851386904716492,
0.01521486509591341,
-0.02429395355284214,
-0.05513802915811539,
0.03647110238671303,
0.0054506706073880196,
-0.0008966208552010357,
0.04371246322989464,
-0.02551816590130329,
-0.01700090803205967,
-0.013200832530856133,
-0.03166680410504341,
0.003156652208417654,
-0.028419645503163338,
-0.0016936385072767735,
0.07860922813415527,
-0.03501074016094208,
-0.003519587218761444,
-0.004085162654519081,
-0.03875273838639259,
-0.04790186136960983,
0.005455169826745987,
-0.007417508866637945,
0.024985618889331818,
0.007301861420273781,
0.06698218733072281,
-0.003248418914154172,
-0.055655691772699356,
-0.012860182672739029,
-0.03783632814884186,
-0.044098932296037674,
0.01872296817600727,
-0.01270640455186367,
-0.016660749912261963,
-0.014119335450232029,
-0.020050358027219772,
0.09356854110956192,
0.0053855860605835915,
-0.014704732224345207,
-0.018078306689858437,
-0.04338259994983673,
-0.04692363739013672,
-0.04552048444747925,
0.0034431738313287497,
0.029445776715874672,
0.04189072921872139,
-0.005377356894314289,
0.031279079616069794,
0.05064404383301735,
0.009154281578958035,
0.01598970778286457,
-0.0020391109865158796,
0.012067765928804874,
0.0188737940043211,
-0.01128233689814806,
0.050372373312711716,
0.006654880475252867,
-0.028346940875053406,
0.017254820093512535,
0.00951476488262415,
0.02743912674486637,
0.02064780332148075,
-0.0639498308300972,
0.04010038450360298,
0.015091156587004662,
0.01314393337816,
0.011839824728667736,
0.021474992856383324,
-0.0001551460154587403,
-0.016621533781290054,
-0.024224750697612762,
0.012802867218852043,
0.03788412734866142,
-0.021959496662020683,
0.011964002624154091,
0.036893293261528015,
0.025508632883429527,
-0.032618023455142975,
-0.009971392340958118,
0.03975840285420418,
0.0011203879257664084,
0.024004830047488213,
0.004469828214496374,
-0.043720632791519165,
0.03334692120552063,
0.03299073874950409,
0.03014999069273472,
0.010177445597946644,
-0.03684628754854202,
-0.02980050817131996,
-0.037098176777362823,
0.004959976766258478,
-0.0035769972018897533,
0.05790902301669121,
0.020078927278518677,
0.06191534176468849,
0.023299915716052055,
0.03295496106147766,
0.01669127121567726,
-0.011792666278779507,
-0.051740892231464386,
0.012752203270792961,
-0.031464241445064545,
-0.011214977130293846,
-0.008748579770326614,
0.011242419481277466,
-0.03133001551032066,
-0.03245609626173973,
-0.03737841546535492,
-0.0029750766698271036,
-0.02838333323597908,
-0.038722679018974304,
-0.003975483123213053,
-0.005206122994422913,
-0.04464036226272583,
-0.034209154546260834,
0.04691164568066597,
0.013980699703097343,
0.002730682957917452,
0.04544427618384361,
0.020851286128163338,
-0.04048836976289749,
-0.013467582874000072,
-0.021517841145396233,
-0.008879304863512516,
0.008418968878686428,
0.03807955980300903,
0.04878607764840126,
-0.0059913997538387775,
-0.036799825727939606,
-0.03398546576499939,
0.030075185000896454,
0.060047391802072525,
0.0012126596411690116,
-0.01647230051457882,
-0.0030807629227638245,
-0.02356105111539364,
0.010377348400652409,
0.022618314251303673,
0.02524184063076973,
-0.04265007749199867,
0.03587965667247772,
0.02145751565694809,
-0.012018789537250996,
-0.01420501247048378,
0.03660886362195015,
0.019602417945861816,
0.015644066035747528,
0.001255771960131824,
-0.0002085999440168962,
-0.011230789124965668,
-0.03804651275277138,
-0.03171546757221222,
-0.006613768171519041,
-0.026478661224246025,
-0.02010527066886425,
0.008935670368373394,
0.014902831986546516,
0.005010196473449469,
-0.029236825183033943,
-0.03715087100863457,
-0.01837361603975296,
-0.002915075747296214,
-0.01067802868783474,
-0.010241078212857246,
0.024675803259015083,
-0.00022357419948093593,
0.04009831324219704,
0.011364358477294445,
0.0360700823366642,
-0.06803414970636368,
-0.008417297154664993,
0.06380294263362885,
0.046592745929956436,
0.011951129883527756,
-0.030818196013569832,
-0.041531845927238464,
-0.0004201637639198452,
0.03172621130943298,
-0.046183135360479355,
0.041949305683374405,
-0.04608931392431259,
0.0003377669781912118,
-0.0366780124604702,
-0.05623869597911835,
0.0015372612979263067,
0.01772824488580227,
-0.01051122136414051,
0.01615203358232975,
-0.026127351447939873,
-0.01938454993069172,
-0.04798469319939613,
0.024339942261576653,
0.017464444041252136,
0.04947345703840256,
0.012187358923256397,
0.013119974173605442,
0.018998682498931885,
0.015447717159986496,
-0.013068615458905697,
-0.07649317383766174,
-0.01009815651923418,
0.021710017696022987,
0.010001485235989094,
0.0841192826628685,
-0.04683169722557068,
-0.06433653086423874,
0.0047015659511089325,
-0.007863680832087994,
-0.009772145189344883,
-0.02402118593454361,
-0.04790037125349045,
0.029234465211629868,
0.020017242059111595,
0.013868045061826706,
0.026985937729477882,
0.013044596649706364,
-0.015458444133400917,
0.013612505048513412,
-0.05096732825040817,
0.04238935559988022,
-0.03104131855070591,
0.018925795331597328,
-0.040713731199502945,
0.013187598437070847,
-0.01092833187431097,
0.050496090203523636,
-0.015767011791467667,
0.010650698095560074,
0.01373572088778019,
-0.055229123681783676,
0.0017288937233388424,
0.023807596415281296,
-0.0012114725541323423,
-0.006534287240356207,
-0.04847415164113045,
-0.010271398350596428,
-0.02010870911180973,
-0.011267484165728092,
0.018648885190486908,
-0.02422102726995945,
0.008421766571700573,
0.013058314099907875,
-0.0021843891590833664,
0.05652357637882233,
-0.020041225478053093,
-0.018366927281022072,
0.014920912683010101,
-0.02956657111644745,
-0.008442412130534649,
0.004666335415095091,
-0.05008688569068909,
0.030122317373752594,
-0.0430169478058815,
-0.03275823965668678,
0.019664309918880463,
-0.0067114816047251225,
0.03132615610957146,
-0.03816055878996849,
0.033223289996385574,
0.001493272720836103,
-0.01163196749985218,
-0.09683769196271896,
-0.01073604729026556,
0.02665613777935505,
0.007337111514061689,
0.0013804759364575148,
-0.01325525064021349,
0.03175557404756546,
-0.036150090396404266,
-0.005905748810619116,
0.03691066429018974,
-0.008377180434763432,
-0.04796726629137993,
0.0006282116519287229,
0.014170749112963676,
-0.00822455994784832,
0.03877542167901993,
-0.006474642548710108,
-0.05148732289671898,
-0.015077655203640461,
0.011830948293209076,
-0.0011377678019925952,
0.0022262248676270247,
0.03968178108334541,
-0.006456906907260418,
-0.046158358454704285,
-0.005463264882564545,
0.02469383366405964,
0.03564879670739174,
-0.0030845096334815025,
-0.008407320827245712,
0.04397885128855705,
0.025986909866333008,
0.0062184720300138,
0.009328455664217472,
0.01558145321905613,
-0.024530228227376938,
0.023966018110513687,
0.006587992887943983,
0.003216296434402466,
-0.012645671144127846,
-0.04523884877562523,
0.017160361632704735,
-0.015153474174439907,
0.019795438274741173,
0.015716778114438057,
0.06091834977269173,
0.001635464490391314,
0.02918749861419201,
0.007023944519460201,
0.011114758439362049,
0.00013369289808906615,
-0.032585155218839645,
0.01763743720948696,
0.003362298244610429,
0.03111867979168892,
0.005700969137251377,
-0.05606855824589729,
-0.053853463381528854,
-0.005642041098326445,
0.05014452710747719,
-0.0067474739626049995,
0.04869146645069122,
0.0010643363930284977,
0.006908200681209564,
-0.009877583011984825,
-0.020942363888025284,
-0.01224435307085514,
-0.0065489779226481915,
0.0021537416614592075,
0.036390479654073715,
-0.023747406899929047,
0.009470243006944656,
0.02603122591972351,
0.05456414073705673,
-0.04358379915356636,
0.03832018002867699,
0.05745996534824371,
0.02263183332979679,
-0.004658227786421776,
0.021348724141716957,
-0.01778004877269268,
0.011978928931057453,
-0.01430092565715313,
0.03968843072652817,
0.045719850808382034,
0.0004050812276545912,
0.03851310536265373,
-0.002247358439490199,
0.005686205346137285,
-0.0019874197896569967,
-0.024603238329291344,
-0.04128410667181015,
0.05170530825853348,
0.019757770001888275,
-0.024332653731107712,
-0.03784139081835747,
0.012532691471278667,
0.0408337377011776,
0.01412847638130188,
0.010215748101472855,
0.024180807173252106,
-0.054066505283117294,
-0.03124326653778553,
-0.03352329134941101,
-0.03512972220778465,
0.014242228120565414,
-0.04139501228928566,
-0.015990596264600754,
-0.013125598430633545,
-0.019386984407901764,
-0.03219752758741379,
0.04061219468712807,
0.04169319197535515,
0.0070549375377595425,
0.022198157384991646,
-0.008784440346062183,
0.0003342132258694619,
0.027792273089289665,
0.04098590835928917,
0.11253616958856583,
0.042761944234371185,
-0.04930999502539635,
-0.059243809431791306,
-0.011177710257470608,
-0.020273473113775253,
-0.000880186096765101,
-0.008584931492805481,
0.03972344100475311,
-0.01701797917485237,
0.0032986945006996393,
-0.019443761557340622,
0.019322026520967484,
-0.0062844110652804375,
0.02083277329802513,
0.04860921949148178,
-0.03645575791597366,
-0.05029139667749405,
0.01827988401055336,
0.0454220175743103,
0.003865920938551426,
0.012365887872874737,
-0.04191267117857933,
-0.010476547293365002,
-0.03965117037296295,
0.034997981041669846,
-0.020987998694181442,
-0.029109662398695946,
0.06872740387916565,
0.019663097336888313,
-0.043517716228961945,
-0.006337324623018503,
0.014417534694075584,
-0.006689307279884815,
-0.01719183661043644,
0.001868095132522285,
0.027371790260076523,
-0.012705070897936821,
0.027830062434077263,
0.05588804930448532,
0.016069412231445312,
0.010079865343868732,
0.024462547153234482,
0.006289219483733177,
-0.03243985399603844,
0.002197168068960309,
0.008365052752196789,
0.03157593309879303,
-0.02991405315697193,
-0.03260719031095505,
-0.011595125310122967,
-0.0004643176798708737,
-0.03743642941117287,
-0.052966248244047165,
-0.004800768103450537,
-0.027220463380217552,
0.019172482192516327,
-0.013722028583288193,
-0.050522517412900925,
-0.03265766426920891,
-0.022386960685253143,
-0.013204510323703289,
0.020571939647197723,
0.01693478226661682,
0.023488333448767662,
0.05046176165342331,
-0.03213616833090782,
0.06175079569220543,
-0.020375018939375877,
0.0007457805913873017,
-0.027532463893294334,
-0.02955857291817665,
-0.05466180294752121,
-0.0006476904381997883,
0.02077888883650303,
0.022434821352362633,
0.08497203886508942,
0.0012322540860623121,
0.013907581567764282,
-0.0025494417641311884,
-0.03765607625246048,
0.03199019655585289,
0.0033373849000781775,
-0.03578247129917145,
-0.01744724065065384,
0.006283066235482693,
-0.010309695266187191,
0.03666682913899422,
-0.028680628165602684,
0.0134315500035882,
0.038778454065322876,
-0.005913851782679558,
0.027282197028398514,
-0.02236877754330635,
-0.015775805339217186,
0.018022725358605385,
0.007114680949598551,
-0.0009472710662521422,
-0.023196952417492867,
0.017609378322958946,
0.022975502535700798,
0.01326280552893877,
0.01015528105199337,
0.03299732133746147,
-0.042696449905633926,
-0.004947592969983816,
0.02026883326470852,
-0.04587796330451965,
0.02861836738884449,
0.03698977455496788,
0.010316615924239159,
-0.05047127977013588,
-0.028129607439041138,
-0.04163658991456032,
0.0048288870602846146,
0.02704692631959915,
0.06008261442184448,
-0.007716437801718712,
0.029117731377482414,
-0.0009892500238493085,
0.027120979502797127,
-0.013421961106359959,
0.008560151793062687,
-0.025546910241246223,
0.04282447695732117,
0.0172102190554142,
-0.006818771827965975,
-0.04226374998688698,
0.025928912684321404,
0.03276262432336807,
-0.006034953519701958,
0.056168749928474426,
0.01699364371597767,
-0.04040403291583061,
-0.005890533793717623,
0.03165728598833084,
-0.024210995063185692,
0.08131447434425354,
0.0010336138075217605,
-0.013861224986612797,
0.026611389592289925,
-0.009279925376176834,
-0.022693993523716927,
0.0019319325219839811,
-0.0020108665339648724,
0.01963241584599018,
0.05827665328979492,
-0.028201693668961525,
-0.022111766040325165,
0.06924173980951309,
-0.020499004051089287,
0.004403508268296719,
0.00523440632969141,
0.017608825117349625,
-0.00689761433750391,
-0.006225196644663811,
0.03864210844039917,
-0.004272588063031435,
-0.00896522868424654,
0.024220256134867668,
0.0028334229718893766,
0.021990682929754257,
-0.01646774262189865,
-0.022825561463832855,
0.009152859449386597,
0.0006726087885908782,
0.00478009507060051,
0.03945496678352356,
0.02179030515253544,
0.037728503346443176,
-0.051396798342466354,
0.04915451630949974,
0.03734524920582771,
0.014712718315422535,
-0.05939626321196556,
-0.004416045267134905,
-0.034401215612888336,
-0.010315965861082077,
0.0033948151394724846,
-0.014785834588110447,
0.0006721207755617797,
0.05230361968278885,
-0.08232423663139343,
0.0060109421610832214,
-0.014353013597428799,
0.003567691193893552,
-0.040381669998168945,
-0.01593663915991783,
-0.0516437329351902,
0.060466911643743515,
0.02069775201380253,
0.04570553079247475,
0.005567906890064478,
0.013684523291885853,
-0.029934179037809372,
-0.03980967029929161,
-0.03210464492440224,
0.04148662090301514,
-0.02677050419151783,
0.02181743085384369,
0.06571099907159805,
-0.007168422918766737,
-0.013528048992156982,
0.032368920743465424,
0.004604259040206671,
-0.004396743141114712,
-0.04129616171121597,
0.006446866784244776,
-0.00022092794824857265,
0.01964828372001648,
0.010156591422855854,
0.021680476143956184,
-0.029965993016958237,
0.019590511918067932,
0.024221021682024002,
-0.005241441540420055,
0.009924689307808876,
-0.02253657393157482,
0.04651312157511711,
-0.03734009712934494,
-0.0720294862985611,
0.042165715247392654,
0.032572947442531586,
-0.0013929279521107674,
0.014246447943150997,
0.042428456246852875,
0.008438162505626678,
-0.02709951624274254,
-0.01839725859463215,
-0.017476404085755348,
-0.030624661594629288,
-0.010998306795954704,
-0.006322416476905346,
0.03593859449028969,
0.006173817440867424,
-0.011811922304332256,
-0.04425641894340515,
0.048603519797325134,
0.013421443291008472,
-0.014470476657152176,
-0.05298926681280136,
0.009806415997445583,
0.0027232160791754723,
0.00606121588498354,
-0.005842536687850952,
-0.05258430540561676,
-0.04665173217654228,
0.009222082793712616,
0.03179233893752098,
-0.0039483425207436085,
-0.05082570016384125,
-0.04067276790738106,
-0.04746304079890251,
-0.04641092196106911,
0.05317114293575287,
-0.007168248295783997,
0.013382586650550365,
-0.0433933362364769,
0.0011236106511205435,
-0.03660256415605545,
0.02657344378530979,
0.021029110997915268,
0.02093922533094883,
-0.002881845459342003,
-0.007881930097937584,
-0.025578146800398827,
0.02167171984910965,
-0.030610300600528717,
0.0038175631780177355,
-0.013356674462556839,
-0.04075999557971954,
-0.010808011516928673,
-0.014849819242954254,
-0.08728975802659988,
0.05157337710261345,
0.015161093324422836,
0.0003637571062427014,
0.017320480197668076,
-0.03166535869240761,
-0.018300579860806465,
0.07256907969713211,
0.05281107872724533,
-0.004320024512708187,
0.04871461167931557,
-0.009676653891801834,
0.01650756224989891,
0.027459600940346718,
-0.022601313889026642,
-0.028769314289093018,
0.03851842135190964,
-0.035639069974422455,
0.03105371817946434,
-0.008708144538104534,
-0.03131485730409622,
0.03348918259143829,
-0.03083350881934166,
0.0072649153880774975,
0.05666153505444527,
-0.026898358017206192,
-0.002516861306503415,
0.035085856914520264,
0.04731205105781555,
0.035403136163949966,
0.015099127776920795,
-0.0035889127757400274,
0.006325526628643274,
-0.02381899580359459,
-0.009156393818557262,
0.07514449208974838,
0.028186937794089317,
0.015923604369163513,
0.03474580496549606,
0.03289457783102989,
-0.011617735028266907,
0.017333973199129105,
0.0007355130510404706,
0.04598698392510414,
-0.030074365437030792,
0.017378974705934525,
0.009786341339349747,
0.007480146829038858,
-0.026370836421847343,
0.01122394297271967,
-0.02355489879846573,
0.06507472693920135,
-0.035037919878959656,
-0.019045518711209297,
-0.008562484756112099,
-0.024667734280228615,
-0.018047913908958435,
0.011500841937959194,
0.013061570934951305,
0.03828369826078415,
-0.02182428166270256,
-0.004508063197135925,
-0.04152285307645798,
-0.012581395916640759,
0.05186598375439644,
-0.046250198036432266,
-0.011049721390008926,
0.012256914749741554,
-0.017260568216443062,
-0.017760345712304115,
0.027113018557429314,
-0.017162762582302094,
-0.025852560997009277,
0.02403256483376026,
0.04851103574037552,
0.021761512383818626,
-0.01647636853158474,
-0.011810817755758762,
-0.03733658418059349,
-0.0024954371619969606,
-0.010424290783703327,
-0.0037229491863399744,
-0.027191638946533203,
0.03461826592683792,
-0.053680699318647385,
-0.010229930281639099
] |
<p>Like all stars, large ones are stable as long as there is a sufficient amount of hydrogen (or helium) to fuse. This fusion process is what prevents them from collapsing in on themselves. However, once the main elements have been fused up to iron, the star becomes unstable. Eventually, it may supernova and leave a black hole; a singularity that sucks in light and matter that enters the event horizon.</p>
<p>The star prevents collapsing in on itself with fusion. When it goes supernova, it expels a large amount of its mass. If the remaining bit is enough to create a black hole that is so dense that fusion cannot balance the gravitational force, then how did the star exist in the first place and why wasn't it dense enough to form a black hole?</p>
| 10,699 |
[
-0.07399725914001465,
-0.04281742870807648,
0.017546461895108223,
-0.030478911474347115,
0.04277491942048073,
0.011083985678851604,
-0.04481074959039688,
-0.05418282374739647,
-0.01859957166016102,
-0.053728558123111725,
0.040905848145484924,
0.0020868221763521433,
0.04932001978158951,
0.04725688323378563,
0.014190925285220146,
-0.004876445047557354,
0.004831986501812935,
-0.04602113366127014,
-0.01874421536922455,
-0.01615428924560547,
-0.02486560493707657,
-0.003935775253921747,
0.010386534035205841,
-0.01670350693166256,
-0.0361160971224308,
0.010269268415868282,
0.029645798727869987,
0.002989894710481167,
0.05022041127085686,
0.050642918795347214,
0.022291773930191994,
-0.0018647258402779698,
0.038264453411102295,
0.06213861331343651,
0.030743209645152092,
0.012458599172532558,
0.006542554125189781,
-0.018419111147522926,
-0.04701754450798035,
0.027144640684127808,
-0.014967520721256733,
-0.03348356857895851,
0.01606348156929016,
0.009384329430758953,
-0.022350674495100975,
0.0038877232000231743,
-0.00005626843631034717,
-0.030140748247504234,
0.037301138043403625,
-0.04136202484369278,
0.008770250715315342,
0.007950547151267529,
0.054634928703308105,
0.03852652758359909,
-0.02124757692217827,
-0.0035130679607391357,
0.06460260599851608,
0.07658568024635315,
-0.031738974153995514,
-0.04871897026896477,
-0.012162219732999802,
-0.01056688278913498,
-0.048305436968803406,
-0.0015108332736417651,
-0.011136856861412525,
0.05081057921051979,
-0.03943273797631264,
-0.04753623530268669,
0.03289083391427994,
0.0011464018607512116,
0.006490359082818031,
0.010376552119851112,
-0.017036763951182365,
0.03195519745349884,
-0.011935383081436157,
-0.037362467497587204,
0.035585667937994,
-0.005483809392899275,
0.059445831924676895,
0.05474940314888954,
-0.003300093114376068,
0.04072883725166321,
0.03417818620800972,
0.017061075195670128,
0.03500480577349663,
0.010193435475230217,
0.09345217794179916,
0.03899300470948219,
0.02322014793753624,
0.025044981390237808,
0.013126780278980732,
0.001797258504666388,
0.026815805584192276,
-0.026776932179927826,
-0.01446494646370411,
0.026490308344364166,
-0.006297740153968334,
0.0499001182615757,
-0.011439559981226921,
0.007804445456713438,
0.025878502056002617,
-0.004926454741507769,
0.02604849822819233,
0.06279405206441879,
0.044261254370212555,
-0.05019265040755272,
-0.06397613137960434,
0.014687793329358101,
-0.022318409755825996,
-0.02233089692890644,
-0.03036511316895485,
-0.0056314957328140736,
0.0016774083487689495,
-0.04016482084989548,
0.013925057835876942,
-0.026347531005740166,
-0.018378978595137596,
-0.009838688187301159,
0.03936253488063812,
0.07253570109605789,
0.05023851990699768,
0.016377732157707214,
0.03661816939711571,
-0.025912977755069733,
-0.05532144755125046,
0.04230036586523056,
0.02065284550189972,
-0.018204983323812485,
-0.02985602617263794,
0.0518006905913353,
-0.028777025640010834,
-0.00920883845537901,
0.01013865601271391,
-0.024199161678552628,
0.05220550298690796,
-0.00579907838255167,
-0.11481419950723648,
-0.05357007682323456,
0.040213823318481445,
-0.00850985012948513,
-0.03649531304836273,
-0.060129377990961075,
0.009618185460567474,
0.026821589097380638,
0.10277922451496124,
0.004551070276647806,
-0.02413639985024929,
0.017444349825382233,
0.03135908022522926,
-0.015341788530349731,
-0.02070257067680359,
-0.03311306610703468,
0.00606545340269804,
-0.0017221367452293634,
-0.017526166513562202,
-0.06889449805021286,
0.009519357234239578,
-0.0041620549745857716,
0.015543586574494839,
-0.04289540275931358,
0.046133290976285934,
-0.04293276369571686,
0.014841397292912006,
0.015284542925655842,
-0.012292769737541676,
-0.024300387129187584,
0.09190396219491959,
0.04088268429040909,
-0.0160758625715971,
0.06654433906078339,
0.007744812872260809,
0.025212030857801437,
0.031587373465299606,
0.031152818351984024,
-0.0004318154533393681,
-0.024517403915524483,
-0.006327627692371607,
-0.049207307398319244,
0.027582751587033272,
0.016821805387735367,
-0.02455391176044941,
-0.04637666419148445,
-0.015535975806415081,
0.010450644418597221,
0.04025303199887276,
0.0538216233253479,
0.0017843481618911028,
-0.012482290156185627,
-0.016389761120080948,
-0.03868524357676506,
-0.014973541721701622,
-0.07804573327302933,
0.005969909951090813,
-0.015405448153614998,
-0.0038221250288188457,
-0.010854723863303661,
0.022723669186234474,
0.025924712419509888,
-0.04418877139687538,
0.007737946696579456,
0.011203113943338394,
0.03239024430513382,
0.020662548020482063,
0.014726420864462852,
0.016407383605837822,
0.0657028779387474,
0.03345490247011185,
-0.02698276750743389,
0.007580719422549009,
0.012757787480950356,
-0.04134174436330795,
0.005094095133244991,
0.018871549516916275,
-0.003746328642591834,
-0.0033950151409953833,
-0.0132532250136137,
0.022887496277689934,
-0.0145233403891325,
0.026923807337880135,
0.010586130432784557,
0.006189262960106134,
0.0661408007144928,
0.011414551176130772,
0.018451116979122162,
0.029976975172758102,
0.011239612475037575,
-0.004722339566797018,
0.002870278898626566,
-0.020561831071972847,
-0.00836904626339674,
-0.06217547506093979,
0.028259851038455963,
0.036988381296396255,
0.04021685943007469,
-0.03512910380959511,
0.0037953949067741632,
0.03688018023967743,
0.03614826872944832,
0.009838665835559368,
0.03311949968338013,
-0.04809209331870079,
-0.02456689439713955,
0.010575821623206139,
-0.03769101947546005,
0.024741679430007935,
0.00992860272526741,
0.03271534666419029,
0.05564866587519646,
-0.0010575170163065195,
-0.02069365791976452,
0.0049943141639232635,
0.03648439794778824,
0.022069884464144707,
-0.0018680236535146832,
0.007534186355769634,
-0.039056286215782166,
0.03823963180184364,
-0.010261232033371925,
-0.005378535483032465,
-0.011971831321716309,
-0.01761433482170105,
0.010169950313866138,
-0.05824524909257889,
-0.0016378337750211358,
0.016089782118797302,
0.056382402777671814,
0.02056426741182804,
-0.0038144418504089117,
0.008711953647434711,
-0.009494940750300884,
0.0015742572722956538,
-0.03734254091978073,
-0.014862896874547005,
-0.04545605182647705,
0.019847635179758072,
0.026574883610010147,
0.005420582368969917,
0.018087344244122505,
-0.028369424864649773,
-0.04434497281908989,
-0.01985304243862629,
-0.04828900471329689,
-0.016264041885733604,
0.019617730751633644,
-0.06617805361747742,
0.027716537937521935,
0.003272946458309889,
-0.020575663074851036,
0.03564564883708954,
0.018202276900410652,
0.0451168529689312,
0.0035623181611299515,
0.015986040234565735,
-0.015382063575088978,
0.007375472690910101,
-0.006174884736537933,
-0.04219844937324524,
-0.017045767977833748,
0.010611671954393387,
0.06359224766492844,
-0.029183048754930496,
-0.010189133696258068,
0.03327656909823418,
-0.048018794506788254,
-0.04634104669094086,
-0.02030426263809204,
-0.004649595823138952,
0.003357533598318696,
-0.015916690230369568,
0.03232279792428017,
0.02144593559205532,
-0.05724097415804863,
0.006840867456048727,
-0.04570801183581352,
-0.027820274233818054,
0.001123257214203477,
-0.037681303918361664,
0.0051285382360219955,
-0.010572122409939766,
-0.025330597534775734,
0.04609961062669754,
0.01293217483907938,
-0.02765478752553463,
-0.024911880493164062,
0.007671711500734091,
-0.01490019727498293,
-0.003361655166372657,
0.02882637083530426,
0.019909577444195747,
0.03272242844104767,
-0.011843047104775906,
0.043712910264730453,
0.005019062664359808,
0.0066708168014883995,
0.0004419968754518777,
-0.02684277482330799,
-0.03607161343097687,
-0.027075694873929024,
-0.009867478162050247,
0.011616219766438007,
0.01232500746846199,
-0.02181142568588257,
0.028531694784760475,
0.008567167446017265,
0.05631055310368538,
0.010806465521454811,
-0.025441095232963562,
0.0007846195949241519,
-0.004279596731066704,
0.0159161239862442,
-0.04566509276628494,
0.02408389374613762,
-0.021174971014261246,
-0.01822332665324211,
0.05032121390104294,
-0.015467030927538872,
0.09130986779928207,
-0.011358346790075302,
-0.022938275709748268,
-0.01759350299835205,
0.013263723812997341,
-0.04530408978462219,
-0.026790935546159744,
0.001822192221879959,
-0.012243427336215973,
-0.01402206625789404,
-0.02840355597436428,
0.01898844912648201,
0.06128482148051262,
0.029749952256679535,
0.019017422571778297,
-0.03389481082558632,
-0.014971763826906681,
-0.01805809885263443,
-0.08171304315328598,
-0.010173523798584938,
0.02879124879837036,
0.022365354001522064,
-0.022358326241374016,
0.041806675493717194,
0.043218351900577545,
0.02683190442621708,
0.01762745901942253,
-0.027590490877628326,
-0.09442415833473206,
0.010864467360079288,
-0.03515547886490822,
-0.01550336740911007,
-0.013409478589892387,
0.0009282457758672535,
-0.030808132141828537,
-0.0008887420990504324,
0.007356255315244198,
-0.013391999527812004,
-0.024291248992085457,
-0.03648173809051514,
0.03833511099219322,
-0.03697112947702408,
-0.05046491697430611,
0.006987525150179863,
0.03617693856358528,
0.07246574014425278,
0.0009302126127295196,
0.02007530815899372,
0.025036552920937538,
-0.033736422657966614,
-0.011286909691989422,
-0.010329006239771843,
-0.0017644334584474564,
-0.008569150231778622,
0.02395704574882984,
0.02004878781735897,
0.002849286887794733,
0.015948409214615822,
-0.01622428558766842,
0.07390226423740387,
0.022184379398822784,
0.02029479667544365,
0.0036336607299745083,
-0.014185648411512375,
-0.026733852922916412,
-0.027766508981585503,
0.01691850647330284,
0.05446507781744003,
-0.023811662569642067,
0.010904822498559952,
-0.008528498001396656,
-0.007385747507214546,
-0.018917229026556015,
0.04114728793501854,
0.05678495019674301,
0.03197389096021652,
-0.03396613895893097,
-0.03958478942513466,
-0.028851615265011787,
-0.033294327557086945,
-0.015129889361560345,
0.026915790513157845,
0.007565982174128294,
-0.051097363233566284,
-0.0031117252074182034,
0.009126353077590466,
-0.009490549564361572,
-0.07500562816858292,
-0.030114663764834404,
-0.008275106549263,
0.020680315792560577,
-0.021840229630470276,
0.0387302041053772,
0.026849322021007538,
0.01763218827545643,
0.05523635074496269,
-0.012360242195427418,
-0.020969226956367493,
-0.0874643623828888,
-0.01575520820915699,
0.030415035784244537,
0.04985872283577919,
0.01976650580763817,
-0.0073516177944839,
-0.08788850903511047,
0.003432396100834012,
0.04163014143705368,
-0.0480935163795948,
0.019688410684466362,
-0.020304134115576744,
0.0119185084477067,
0.015272311866283417,
-0.050975456833839417,
0.008953728713095188,
0.027428727596998215,
-0.06065277010202408,
0.02610022947192192,
-0.024986783042550087,
0.027753109112381935,
-0.006424965802580118,
0.010245120152831078,
0.01733536459505558,
0.03629935532808304,
-0.000423059071181342,
-0.0008002971881069243,
-0.00003168923285556957,
0.040812425315380096,
-0.04176666587591171,
-0.08351203799247742,
-0.028758209198713303,
-0.01016734167933464,
-0.06037784740328789,
0.03787119314074516,
-0.04478372260928154,
-0.06689821183681488,
0.020261652767658234,
0.01438738964498043,
-0.04231880232691765,
-0.012458184733986855,
-0.04672808572649956,
-0.006089824717491865,
0.02400205284357071,
-0.016735749319195747,
0.0406365729868412,
0.031605418771505356,
-0.018084116280078888,
-0.004075463395565748,
-0.04968908056616783,
0.0010892628924921155,
-0.0133511982858181,
0.025776900351047516,
-0.004520532675087452,
-0.006695657968521118,
-0.01826951839029789,
0.05598330497741699,
0.015926264226436615,
0.013425578363239765,
0.041964612901210785,
-0.011179422028362751,
0.021994853392243385,
0.02599669247865677,
0.013287555426359177,
-0.03838536515831947,
-0.012612844817340374,
0.03789703547954559,
0.017220554873347282,
-0.001651568803936243,
0.07502877712249756,
0.004038533195853233,
0.010755134746432304,
0.028949152678251266,
-0.01621728204190731,
0.018831081688404083,
0.004863452166318893,
-0.03925180435180664,
0.04468062147498131,
-0.04690110310912132,
0.054274532943964005,
-0.008941315114498138,
0.014569442719221115,
0.05803057178854942,
-0.03696832433342934,
-0.01150098443031311,
-0.05648430809378624,
-0.029381778091192245,
0.041909895837306976,
-0.023014167323708534,
0.03694112226366997,
0.020399538800120354,
0.019079264253377914,
-0.09686371684074402,
0.008687532506883144,
0.0409109853208065,
0.0020855204202234745,
-0.008724063634872437,
0.009869469329714775,
0.031911756843328476,
-0.024969633668661118,
-0.0300519447773695,
-0.005831023212522268,
-0.026128066703677177,
-0.0347357802093029,
-0.011201327666640282,
0.029158247634768486,
0.004547842778265476,
0.066363126039505,
-0.005923334043473005,
-0.009183979593217373,
0.015951424837112427,
-0.02701951190829277,
0.0010831378167495131,
-0.017952745780348778,
0.020415788516402245,
-0.02703428827226162,
-0.08201252669095993,
-0.010331510566174984,
0.014006982557475567,
0.0021977683063596487,
-0.0016696996754035354,
0.022950803861021996,
0.02972804754972458,
0.007037042174488306,
0.02283811941742897,
-0.008892059326171875,
0.02609461359679699,
-0.030055761337280273,
0.03337648883461952,
-0.002694646827876568,
0.019797703251242638,
0.010250883176922798,
-0.03902167081832886,
0.05263045057654381,
0.01731991209089756,
0.024493111297488213,
0.017622986808419228,
0.038363296538591385,
0.002672528848052025,
-0.0012180340709164739,
-0.0013922516955062747,
-0.03727751225233078,
0.040037333965301514,
0.025912972167134285,
0.015447022393345833,
0.019419291988015175,
0.006795117165893316,
-0.012019094079732895,
0.006466176826506853,
-0.021473996341228485,
0.018964426591992378,
0.051178429275751114,
-0.014224335551261902,
0.008450531400740147,
-0.015544096939265728,
0.0076302895322442055,
0.00800185464322567,
-0.04225553572177887,
-0.011078479699790478,
0.003081646980717778,
-0.001982587855309248,
0.003616365836933255,
0.0035542226396501064,
-0.001702222740277648,
0.049571700394153595,
0.01326721627265215,
-0.012698917649686337,
0.03701458498835564,
0.04338959977030754,
0.03605852648615837,
0.005026749800890684,
-0.010698724538087845,
-0.026453185826539993,
0.029274404048919678,
-0.025725431740283966,
0.04456230252981186,
-0.03133000433444977,
0.004213526379317045,
0.00992291048169136,
-0.03754599764943123,
0.05233495682477951,
-0.04336031526327133,
-0.05408265069127083,
-0.018847504630684853,
0.02764837071299553,
0.020936671644449234,
-0.0014398128259927034,
0.01401000190526247,
0.04682507365942001,
-0.012616995722055435,
0.0255596823990345,
0.008584823459386826,
-0.008030682802200317,
-0.06277883797883987,
-0.06482984125614166,
-0.021721070632338524,
-0.05404146388173103,
0.015297822654247284,
0.011544127948582172,
-0.048390842974185944,
0.02832924760878086,
-0.03292736038565636,
0.003600406227633357,
0.007695032749325037,
0.03326624631881714,
-0.017587844282388687,
0.03327907994389534,
-0.01624538004398346,
0.001275449525564909,
-0.0012515017297118902,
0.030708353966474533,
0.1160377487540245,
0.0577380396425724,
0.01561665814369917,
-0.046794407069683075,
-0.0046987999230623245,
0.0026246614288538694,
0.021748317405581474,
-0.02842031605541706,
0.046567294746637344,
-0.03927641361951828,
0.018801216036081314,
0.009174909442663193,
0.02628440037369728,
-0.004761300515383482,
0.008381580002605915,
0.042586490511894226,
-0.023034853860735893,
0.009974458254873753,
-0.0033477076794952154,
0.029192792251706123,
0.02439296804368496,
0.014311587437987328,
-0.04392550140619278,
0.027432052418589592,
0.0001904172677313909,
-0.026238124817609787,
-0.015412378124892712,
-0.025242051109671593,
0.012193659320473671,
0.0296183954924345,
-0.03286498039960861,
0.00636028777807951,
0.020263155922293663,
-0.024629538878798485,
0.023217737674713135,
0.01392673421651125,
0.02716103382408619,
-0.019806677475571632,
-0.002299550687894225,
0.026440726593136787,
0.003989900927990675,
0.009476181119680405,
-0.005955080036073923,
0.03858862817287445,
-0.03275073692202568,
-0.02031865157186985,
-0.03256940096616745,
0.03568398952484131,
-0.0008465285645797849,
0.0404340922832489,
-0.002213431289419532,
0.00792337954044342,
0.021605921909213066,
-0.015249167568981647,
-0.019823389127850533,
-0.0037865350022912025,
-0.046994831413030624,
-0.004741803742945194,
-0.057079214602708817,
-0.004271632991731167,
0.02378986030817032,
-0.021945899352431297,
0.031122995540499687,
-0.017762145027518272,
0.027457214891910553,
0.018459221348166466,
-0.04436185956001282,
0.02284395694732666,
-0.031224094331264496,
0.01877211406826973,
-0.036539528518915176,
-0.00607885280624032,
-0.051234230399131775,
-0.002250357298180461,
0.020506558939814568,
0.02748294547200203,
-0.0011265932116657495,
0.0477030910551548,
0.01666146144270897,
-0.027221983298659325,
-0.04893496260046959,
0.04196277633309364,
-0.01621238887310028,
-0.07620622962713242,
-0.03862173855304718,
-0.016551142558455467,
0.009639034979045391,
0.015470915473997593,
-0.018499238416552544,
0.007652306463569403,
-0.022402405738830566,
0.012096237391233444,
-0.016825906932353973,
-0.03518441319465637,
0.008787994273006916,
0.0035385433584451675,
-0.033393971621990204,
0.0048003732226789,
-0.029272353276610374,
0.029216598719358444,
0.050073426216840744,
-0.011376273818314075,
0.05443182215094566,
0.04206371679902077,
-0.026607148349285126,
0.017552955076098442,
0.017292380332946777,
-0.024130135774612427,
0.007503526750952005,
-0.008681666105985641,
0.03934112936258316,
-0.01857496052980423,
-0.02665076032280922,
-0.03188836947083473,
-0.03512114658951759,
-0.0062241205014288425,
0.0456610806286335,
-0.02772706374526024,
0.04574914276599884,
-0.01783077046275139,
0.02856961265206337,
-0.04031113535165787,
0.013227568008005619,
-0.05129755660891533,
0.009805035777390003,
0.025429509580135345,
-0.037057965993881226,
-0.012996331788599491,
0.004495556466281414,
-0.005362357944250107,
-0.006424987688660622,
-0.011723428964614868,
-0.003166432026773691,
-0.0132411178201437,
0.00833616778254509,
-0.0008427490247413516,
-0.016913479194045067,
0.04991136118769646,
0.00003605860547395423,
0.007261890918016434,
0.01598649099469185,
-0.03962463140487671,
-0.03477613627910614,
0.005700054578483105,
-0.008493738248944283,
0.013563143089413643,
0.01211266778409481,
-0.025987833738327026,
-0.008683504536747932,
0.0570947490632534,
-0.03079570271074772,
-0.03587362915277481,
0.034007053822278976,
-0.021680179983377457,
0.008900982327759266,
0.05955320596694946,
0.015818143263459206,
-0.009156819432973862,
-0.016681108623743057,
0.022858353331685066,
0.01998743787407875,
-0.02673700638115406,
0.0019590856973081827,
-0.012761468067765236,
0.004323870409280062,
0.017597630620002747,
-0.006839677691459656,
0.0053634862415492535,
0.04410717263817787,
0.03634393587708473,
-0.0390566810965538,
0.040407873690128326,
0.04444165527820587,
0.0017749284161254764,
-0.10918775945901871,
-0.005572297144681215,
-0.030386310070753098,
0.0036613314878195524,
0.005224226973950863,
-0.026122596114873886,
0.015611845068633556,
0.027335625141859055,
-0.05311461538076401,
0.015231526456773281,
-0.02674483135342598,
-0.03449590876698494,
-0.02089676633477211,
-0.020698387175798416,
-0.02145669050514698,
0.0700400248169899,
0.0322294607758522,
0.02967328391969204,
0.0008150929352268577,
-0.004888961557298899,
0.009143623523414135,
0.0124442670494318,
-0.028465814888477325,
0.0142650892958045,
-0.0341377928853035,
-0.004396232310682535,
0.059927452355623245,
-0.010415706783533096,
-0.013734778389334679,
0.03802096098661423,
-0.024153994396328926,
0.013356081210076809,
0.03209727630019188,
-0.009186520241200924,
-0.005861602257937193,
0.0009709214209578931,
0.005381150171160698,
0.028959034010767937,
-0.02212974987924099,
0.032321397215127945,
-0.004459076561033726,
0.01134972833096981,
0.027145588770508766,
0.010963109321892262,
0.01732759363949299,
-0.04345792531967163,
0.001190975192002952,
0.002265069866552949,
-0.01931069605052471,
0.01434037834405899,
-0.023111188784241676,
0.026122817769646645,
-0.018962332978844643,
-0.023376014083623886,
-0.032618433237075806,
-0.041227787733078,
-0.013508611358702183,
0.03642569109797478,
0.028946716338396072,
0.039857417345047,
0.051043469458818436,
-0.0012928415089845657,
-0.0005951103521510959,
-0.02584318071603775,
-0.011896908283233643,
-0.020928125828504562,
-0.015260094776749611,
0.04519079998135567,
0.007798987440764904,
-0.025194332003593445,
0.0002140528231393546,
-0.02561437524855137,
0.011082563549280167,
0.07248301059007645,
0.019356979057192802,
0.04674569144845009,
0.0016601223032921553,
-0.08942185342311859,
-0.007593381684273481,
-0.061485908925533295,
0.01063439529389143,
-0.0369122251868248,
0.005491466261446476,
-0.032342009246349335,
-0.04784389212727547,
0.01564665138721466,
-0.0024550713133066893,
0.010323574766516685,
0.006773338653147221,
0.008277038112282753,
0.03244484215974808,
-0.018793273717164993,
0.00045882066478952765,
-0.05469146743416786,
0.010141384787857533,
0.0008751816349104047,
-0.03792840987443924,
0.0030851990450173616,
0.011397219263017178,
0.03141920268535614,
0.0051324800588190556,
0.044499721378088,
-0.014196522533893585,
0.04468301311135292,
0.009759597480297089,
-0.015797900035977364,
0.025399694219231606,
0.0370316207408905,
-0.0010424333158880472,
0.08833888918161392,
-0.00936321821063757,
-0.012900479137897491,
0.03974035009741783,
-0.01574024371802807,
-0.01313023827970028,
-0.009509497322142124,
-0.014753272756934166,
0.011619094759225845,
-0.0033983271569013596,
-0.03819316253066063,
-0.010860252194106579,
-0.050691764801740646,
0.0015059002907946706,
0.03161074221134186,
-0.023581594228744507,
-0.0204234030097723,
0.043422456830739975,
0.012587550096213818,
0.05272771418094635,
-0.02125336229801178,
-0.04952959343791008,
0.0029251989908516407,
0.004202602431178093,
-0.031670089811086655,
0.04466700181365013,
0.020405886694788933,
-0.0016298495465889573,
-0.00006561534246429801,
0.012751518748700619,
0.0016065705567598343,
-0.020762912929058075,
-0.027476342394948006,
0.05402069911360741,
-0.06329359114170074,
-0.029585396870970726,
0.000714110501576215,
-0.010159618221223354,
0.04091080650687218,
0.004218893125653267,
-0.023479145020246506,
0.07104365527629852,
0.0223317202180624,
0.004354356322437525,
0.006465433165431023,
-0.009790114127099514,
0.004380380269140005,
0.053182221949100494,
-0.010497558861970901,
0.04710322245955467,
0.017938479781150818,
-0.022869864478707314,
-0.015546118840575218,
0.015869615599513054,
0.042102739214897156,
-0.02270020917057991,
-0.007490233052521944,
-0.00009968923404812813,
0.0050363680347800255,
-0.02854929119348526,
0.022076062858104706,
-0.010103076696395874,
-0.03841334953904152,
-0.005442306865006685,
0.03445107862353325,
-0.0042354450561106205,
0.0012922651367262006,
-0.0223276037722826,
-0.04425087571144104,
0.027345208451151848,
-0.060768116265535355,
-0.004391833208501339,
-0.03709600493311882,
0.037829965353012085,
-0.0556386336684227,
-0.023906094953417778
] |
<p>Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$.
How can one show or explain that $|B|/|A|$ gives the probability that a particle scattering off the potential is reflected?</p>
| 10,700 |
[
0.013570996932685375,
-0.03299254551529884,
0.007104852702468634,
-0.014004958793520927,
0.016658004373311996,
0.01334601454436779,
-0.0032780207693576813,
0.004149611108005047,
-0.007839555852115154,
-0.011906013824045658,
0.05804349482059479,
0.031174078583717346,
0.052482038736343384,
-0.002084197010844946,
0.009633451700210571,
0.04030700400471687,
-0.037977080792188644,
-0.007219829596579075,
0.0006401026621460915,
-0.03941782936453819,
0.00842004269361496,
0.010109419003129005,
0.02784896269440651,
-0.025569802150130272,
-0.02824060060083866,
0.010608200915157795,
-0.007865065708756447,
-0.0028991824947297573,
0.021450500935316086,
0.07430464029312134,
0.034535106271505356,
-0.011722736991941929,
0.025430811569094658,
0.05324496701359749,
-0.01083896029740572,
0.003061457071453333,
-0.020512962713837624,
-0.03303821384906769,
-0.014243473298847675,
0.014361806213855743,
-0.031077077612280846,
-0.042272623628377914,
0.005230288486927748,
0.06168908253312111,
-0.00026980365510098636,
-0.03224848210811615,
-0.012027674354612827,
-0.03430132567882538,
0.034556638449430466,
-0.05246568098664284,
0.04401230067014694,
0.015010186471045017,
0.02132357470691204,
0.01755695603787899,
0.028682854026556015,
-0.027156436815857887,
0.04019000753760338,
0.06676673889160156,
0.007842469029128551,
-0.029252447187900543,
-0.02227054536342621,
-0.02336902916431427,
-0.03134850785136223,
-0.0011664354242384434,
-0.018889449536800385,
-0.010819350369274616,
0.001620468799956143,
-0.05112878605723381,
0.02982195094227791,
-0.018056107684969902,
0.003859924152493477,
0.037886347621679306,
0.007869667373597622,
-0.027329664677381516,
-0.006674970965832472,
0.02554280310869217,
-0.0035850736312568188,
0.023084772750735283,
0.04368259012699127,
0.006138843949884176,
-0.04357946291565895,
0.0032444202806800604,
0.03684290871024132,
0.04610290750861168,
-0.00423557311296463,
-0.027443546801805496,
0.05013823136687279,
-0.02636677213013172,
0.0018062462331727147,
0.002766125136986375,
-0.020459860563278198,
0.018137414008378983,
0.021954648196697235,
-0.0023569921031594276,
-0.04400211572647095,
0.047328148037195206,
0.006390934810042381,
0.09001513570547104,
0.017052145674824715,
-0.05640670284628868,
-0.0040322113782167435,
-0.02145325392484665,
0.03902256116271019,
0.04868929833173752,
-0.06260733306407928,
0.00043664054828695953,
-0.041184116154909134,
0.04111344367265701,
-0.008543147705495358,
0.014819051139056683,
-0.018813416361808777,
0.0492815338075161,
0.0018875495297834277,
0.026861410588026047,
0.02673172578215599,
-0.0437009371817112,
-0.0009207346593029797,
-0.041810616850852966,
0.04082249477505684,
0.05725765600800514,
0.03787420690059662,
-0.016193224117159843,
0.016426363959908485,
-0.03372970223426819,
-0.04885644093155861,
-0.029198842123150826,
0.031248103827238083,
-0.01044005248695612,
-0.036713697016239166,
0.020068826153874397,
-0.007923584431409836,
-0.0042735072784125805,
0.013462010771036148,
-0.00031892009428702295,
0.016418403014540672,
-0.04152806103229523,
-0.07869427651166916,
-0.033735185861587524,
0.050163500010967255,
-0.023632057011127472,
-0.0339917428791523,
-0.06733477860689163,
-0.01677733100950718,
0.04069836810231209,
0.07171094417572021,
-0.014205307699739933,
0.02995128184556961,
0.005176362581551075,
0.006982547231018543,
0.020396001636981964,
-0.03347301855683327,
-0.011153722181916237,
-0.01005524955689907,
-0.02444114349782467,
0.027198562398552895,
-0.04907967150211334,
0.010402130894362926,
-0.008248040452599525,
-0.03186899423599243,
-0.04297247156500816,
0.06415113061666489,
-0.05247499421238899,
-0.01440335251390934,
-0.012289503589272499,
-0.01501833088696003,
-0.024781517684459686,
0.1037328764796257,
0.051655642688274384,
-0.015109747648239136,
-0.009893222711980343,
0.010687380097806454,
0.01836281642317772,
0.01180413831025362,
0.02429976500570774,
0.027736248448491096,
-0.047532934695482254,
0.02587904967367649,
-0.0020162181463092566,
0.04148918390274048,
-0.013703988865017891,
-0.002129850909113884,
-0.03004966676235199,
-0.0051574925892055035,
0.01575874164700508,
-0.013317298144102097,
0.011957217939198017,
-0.005053837783634663,
-0.02174074947834015,
0.013199182227253914,
-0.024374376982450485,
-0.009658604860305786,
-0.04778056591749191,
0.06271429359912872,
0.014521179720759392,
-0.013054778799414635,
0.036885082721710205,
0.027923839166760445,
-0.009129112586379051,
-0.020852742716670036,
-0.01595184952020645,
-0.0019213816849514842,
0.02306308224797249,
-0.042686548084020615,
-0.016908755525946617,
-0.020261578261852264,
0.055214472115039825,
0.0483003705739975,
0.014398069120943546,
0.019651956856250763,
0.008130822330713272,
-0.02753579616546631,
-0.05342446267604828,
-0.01913132518529892,
0.026571892201900482,
-0.01093094889074564,
-0.030344463884830475,
0.012265810742974281,
0.007525694090873003,
-0.006745069287717342,
0.012852031737565994,
-0.03994027525186539,
0.04665416106581688,
0.05136255919933319,
0.01706228032708168,
-0.04363910108804703,
0.04415697604417801,
0.023156724870204926,
0.03380312770605087,
0.03190341964364052,
-0.054986435920000076,
-0.019914783537387848,
0.01332811452448368,
0.03973495215177536,
0.0002353240124648437,
-0.04308977350592613,
0.02757667936384678,
-0.0022553778253495693,
-0.02185393124818802,
0.03158211335539818,
0.019977806136012077,
-0.0356423482298851,
-0.01053675264120102,
0.016480043530464172,
0.005803587380796671,
-0.017043886706233025,
-0.010047413408756256,
0.010873769409954548,
-0.018028639256954193,
0.012036886066198349,
-0.02081962116062641,
-0.040617041289806366,
-0.0019271756755188107,
-0.02527916058897972,
0.03529287502169609,
-0.013169638812541962,
-0.02613115683197975,
0.017916597425937653,
0.01434959564357996,
0.028089074417948723,
0.005826061591506004,
-0.044810984283685684,
-0.011077632196247578,
-0.010927310213446617,
-0.040685392916202545,
0.04369528964161873,
-0.016399739310145378,
-0.04045860469341278,
-0.002519887639209628,
0.04331915080547333,
-0.016337035223841667,
0.00969521701335907,
-0.018077122047543526,
-0.0013920791679993272,
-0.012422608211636543,
0.01687258668243885,
0.040393929928541183,
0.015373187139630318,
0.0050923326052725315,
-0.031359247863292694,
-0.06340426206588745,
0.015445665456354618,
-0.03161317855119705,
0.026109393686056137,
0.008763859048485756,
-0.021347271278500557,
0.038983460515737534,
-0.060463450849056244,
-0.01682118885219097,
0.05017389357089996,
-0.029535742476582527,
0.0018799032550305128,
-0.00015511618403252214,
0.004497670568525791,
-0.025070304051041603,
0.02759881503880024,
-0.024707600474357605,
-0.00629182206466794,
-0.04927143454551697,
-0.0053549716249108315,
0.02004672773182392,
0.006016504019498825,
-0.021038277074694633,
0.014331148006021976,
-0.028146540746092796,
-0.05782443657517433,
-0.028268055990338326,
-0.05532213672995567,
0.021476365625858307,
-0.045093756169080734,
0.06675243377685547,
0.017178328707814217,
-0.06665235012769699,
-0.022769661620259285,
-0.027681179344654083,
-0.03865842521190643,
0.007587687112390995,
0.02666591666638851,
-0.005822308827191591,
0.01043986901640892,
-0.025688331574201584,
0.08692941814661026,
0.03711593523621559,
-0.005604100879281759,
-0.002346908440813422,
-0.012708432041108608,
0.0016658720560371876,
-0.01747051440179348,
-0.037914250046014786,
0.0401000902056694,
0.007261800579726696,
0.0464276485145092,
-0.020629683509469032,
0.04557686299085617,
0.018874116241931915,
0.011411952786147594,
-0.0636666864156723,
-0.0063491216860711575,
-0.009449278935790062,
0.007040929980576038,
0.01992839388549328,
-0.007664862554520369,
-0.03326403349637985,
0.025541190057992935,
-0.005340725649148226,
0.0048338971100747585,
0.015928570181131363,
-0.04521145671606064,
0.053056105971336365,
0.0032173923682421446,
0.027095753699541092,
-0.02282896637916565,
0.03589339554309845,
-0.021448682993650436,
0.03124483861029148,
0.03584562987089157,
0.008622786030173302,
0.050966840237379074,
-0.02249142713844776,
0.011476259678602219,
0.016467895358800888,
0.033380571752786636,
-0.035732828080654144,
-0.038610149174928665,
-0.02886269986629486,
-0.0003171023854520172,
0.0268848966807127,
0.011123185977339745,
-0.04902813583612442,
0.036027777940034866,
0.016764216125011444,
0.033724404871463776,
-0.03854640945792198,
-0.0543157234787941,
-0.03560713678598404,
-0.014269020408391953,
-0.00803393591195345,
0.01121298037469387,
0.03267447650432587,
0.002779797650873661,
0.015029213391244411,
0.025951338931918144,
-0.0023057712242007256,
-0.008935082703828812,
0.011217539198696613,
-0.04983516037464142,
0.01167463418096304,
-0.009009440429508686,
0.015078360214829445,
-0.05068625509738922,
-0.0019815852865576744,
0.01102603878825903,
-0.04557952284812927,
-0.003068244084715843,
0.011532391421496868,
-0.017763148993253708,
-0.03043397143483162,
-0.00582374120131135,
-0.030034499242901802,
-0.04616729915142059,
-0.04853464290499687,
0.017507566139101982,
0.025402991101145744,
0.0024078157730400562,
0.028447536751627922,
0.02637297660112381,
-0.049690522253513336,
-0.04797506332397461,
-0.002976236864924431,
0.020758429542183876,
0.019669800996780396,
0.044683754444122314,
0.06158162280917168,
0.03400207310914993,
-0.02076849341392517,
0.0007556483615189791,
-0.009866402484476566,
0.05244991183280945,
0.007273998111486435,
-0.018695063889026642,
0.027608314529061317,
-0.06706234812736511,
-0.024222813546657562,
-0.03638207167387009,
0.03941962867975235,
-0.02161390148103237,
0.010393381118774414,
0.015603478066623211,
0.0025476061273366213,
-0.03002546727657318,
0.021297767758369446,
0.036295030266046524,
0.039751019328832626,
-0.011015084572136402,
-0.01358182355761528,
0.034266501665115356,
0.006218348629772663,
-0.012442578561604023,
-0.00994058232754469,
-0.022293318063020706,
-0.000148052436998114,
-0.0038971626199781895,
-0.0015142018673941493,
0.020358320325613022,
0.01036410965025425,
-0.018879719078540802,
-0.026034889742732048,
-0.01655646041035652,
-0.008470766246318817,
-0.010487101040780544,
0.018961796537041664,
0.02718195505440235,
0.026983067393302917,
0.023679684847593307,
0.02371871843934059,
-0.057878319174051285,
-0.028730977326631546,
0.0678233653306961,
0.02813059650361538,
-0.008769605308771133,
-0.015323759987950325,
-0.06942109018564224,
-0.04446329176425934,
0.06346306204795837,
-0.017637332901358604,
0.015006051398813725,
-0.014471176080405712,
0.0314120389521122,
-0.001262912293896079,
-0.04208145663142204,
-0.02780621498823166,
0.038060083985328674,
0.006519307382404804,
-0.0002682627527974546,
-0.006608877331018448,
-0.027497529983520508,
-0.029797421768307686,
0.01843915320932865,
0.00904538482427597,
0.09226696193218231,
0.00040712556801736355,
0.0014271639520302415,
-0.04509282857179642,
0.020811686292290688,
-0.02498975768685341,
-0.07969983667135239,
0.008785111829638481,
-0.01445215754210949,
0.014877020381391048,
0.04722679778933525,
-0.02270757034420967,
-0.06041890010237694,
0.021588018164038658,
0.0173195730894804,
-0.036513108760118484,
0.007127095479518175,
-0.0285225510597229,
0.04982999339699745,
0.008935347199440002,
0.01956282928586006,
0.0666859894990921,
0.009178931824862957,
0.013854104094207287,
-0.01186442095786333,
-0.02468746341764927,
0.05790964886546135,
-0.03073386661708355,
-0.010248121805489063,
-0.011354896239936352,
-0.011448138393461704,
-0.03441087156534195,
0.05924762040376663,
0.027520624920725822,
-0.01237563043832779,
0.004975526127964258,
-0.05433748662471771,
-0.054223060607910156,
0.022149253636598587,
-0.0296533964574337,
0.016289789229631424,
0.020434513688087463,
0.016134709119796753,
0.032109521329402924,
-0.02973143197596073,
0.017110951244831085,
0.01310739479959011,
-0.0015688518760725856,
-0.0010557187488302588,
-0.015826143324375153,
0.048874299973249435,
-0.023048391565680504,
-0.0004207106539979577,
0.023623822256922722,
-0.052510544657707214,
0.016897624358534813,
-0.022594694048166275,
0.0042035384103655815,
0.027716467157006264,
-0.04276615008711815,
-0.01683664135634899,
0.008547713048756123,
-0.01541011594235897,
0.023794757202267647,
-0.06001613289117813,
0.020685303956270218,
0.026696741580963135,
0.02449251152575016,
-0.08938942104578018,
-0.019893404096364975,
-0.009140274487435818,
0.014340667054057121,
-0.020678039640188217,
-0.04701004922389984,
-0.03915197402238846,
-0.029481662437319756,
-0.008964639157056808,
0.014127490110695362,
0.004912468139082193,
-0.008181392215192318,
-0.010250510647892952,
-0.0020677244756370783,
0.040262892842292786,
0.003302725963294506,
-0.023519305512309074,
-0.015914861112833023,
0.02855362743139267,
-0.016692249104380608,
-0.010694444179534912,
0.014027664437890053,
0.06935126334428787,
-0.031206822022795677,
-0.0035172931384295225,
0.009845782071352005,
0.005860040429979563,
0.028361594304442406,
-0.020289534702897072,
-0.028811490163207054,
0.008676583878695965,
0.004013949539512396,
0.04685119166970253,
0.005662687122821808,
-0.006733078975230455,
0.03698929026722908,
0.046189408749341965,
0.02128640003502369,
-0.005532031413167715,
-0.035564932972192764,
-0.019066473469138145,
0.04873327910900116,
-0.006528520956635475,
-0.007788302376866341,
0.0035262529272586107,
0.06919919699430466,
-0.011657903902232647,
0.003375282045453787,
0.002338295103982091,
0.004540476482361555,
0.006423399318009615,
-0.026288066059350967,
-0.012798609212040901,
0.036649420857429504,
-0.0025019366294145584,
-0.028409438207745552,
-0.03359276056289673,
-0.07094081491231918,
0.017528632655739784,
0.015272143296897411,
-0.0034614920150488615,
0.04394026845693588,
0.006480272859334946,
0.023078687489032745,
-0.02425612322986126,
-0.010263429954648018,
0.007387134246528149,
0.0003398196422494948,
-0.002624095883220434,
0.02731470577418804,
-0.05888330563902855,
0.018787240609526634,
0.009783591143786907,
0.019547704607248306,
0.003898882307112217,
0.0059572067111730576,
0.03555817902088165,
0.056185271590948105,
0.05336497724056244,
0.008219370618462563,
-0.020654363557696342,
0.041028693318367004,
-0.01377285085618496,
0.01892862096428871,
0.00500314449891448,
-0.05454227328300476,
0.04544118419289589,
0.0002839528606273234,
-0.009180261753499508,
-0.033744506537914276,
-0.016959255561232567,
-0.04132944345474243,
-0.009897681884467602,
0.01830083504319191,
0.009855570271611214,
0.05583307147026062,
0.000797133194282651,
-0.013439013622701168,
0.004777705762535334,
0.010414252057671547,
0.007051690015941858,
-0.0660797581076622,
-0.02439676970243454,
-0.05609465017914772,
-0.0661289319396019,
-0.014394436031579971,
-0.020512064918875694,
0.0022477803286165,
0.027469631284475327,
-0.06162598729133606,
0.020993826910853386,
0.0142402658239007,
0.00801893975585699,
0.005321059841662645,
0.06066502630710602,
0.03506859764456749,
0.037065207958221436,
-0.01298693846911192,
-0.0005917223752476275,
0.11002801358699799,
0.06914600729942322,
0.04433169960975647,
-0.061522215604782104,
0.016797944903373718,
0.010093798860907555,
0.01713891327381134,
-0.057770758867263794,
0.026123525574803352,
0.013735545799136162,
-0.006119898986071348,
-0.014090235345065594,
0.05173033848404884,
0.02238757722079754,
-0.0026979425456374884,
0.038808345794677734,
-0.052178338170051575,
-0.07119429111480713,
0.02524540014564991,
-0.01565771922469139,
-0.02535936050117016,
-0.00919797457754612,
-0.03214633837342262,
0.015495464205741882,
-0.01622532121837139,
0.0018584029749035835,
-0.02865622378885746,
-0.043640051037073135,
0.005795944947749376,
-0.009677239693701267,
0.01636524498462677,
0.014044740237295628,
0.048925384879112244,
-0.011327884159982204,
-0.012105989269912243,
0.017784282565116882,
0.054298464208841324,
0.006376140750944614,
0.02685476653277874,
-0.012214728631079197,
-0.0012406164314597845,
-0.01632193848490715,
-0.007411818020045757,
0.0247875414788723,
-0.04920922592282295,
-0.03064916469156742,
-0.0032063648104667664,
0.07505320757627487,
-0.00017843637033365667,
-0.02226334810256958,
-0.011869668029248714,
-0.0027076825499534607,
0.00042522710282355547,
-0.006998265162110329,
-0.022598862648010254,
0.007798639591783285,
0.014151116833090782,
-0.04912609979510307,
-0.019460000097751617,
0.02886827290058136,
0.015538481064140797,
-0.0148386899381876,
0.020547235384583473,
-0.009950671344995499,
-0.013944030739367008,
-0.0005654431879520416,
0.004691607318818569,
0.0050109922885894775,
0.020379673689603806,
-0.007156603969633579,
-0.04564283788204193,
0.00514014670625329,
-0.03224322944879532,
-0.06380531191825867,
0.026065150275826454,
0.002990957349538803,
0.04040108248591423,
0.002550187287852168,
-0.011862560175359249,
0.014714481309056282,
-0.0786595493555069,
0.029910707846283913,
-0.047529201954603195,
-0.028711000457406044,
-0.021532928571105003,
0.02223523147404194,
0.013259508647024632,
0.050717223435640335,
-0.019758466631174088,
-0.04014424607157707,
-0.0016300911083817482,
0.026159634813666344,
0.001956698950380087,
-0.03216448798775673,
-0.014852548949420452,
0.023402953520417213,
-0.03435799479484558,
0.03644575923681259,
0.008927580900490284,
0.002223231364041567,
0.002909019822254777,
0.03719714656472206,
0.01303531602025032,
0.044493239372968674,
-0.048090945929288864,
-0.010735605843365192,
-0.022510727867484093,
-0.03247928246855736,
-0.00435395585373044,
0.02490421198308468,
0.018458260223269463,
-0.02666204795241356,
-0.04364173486828804,
0.004070920869708061,
0.015744009986519814,
0.060251202434301376,
0.011354920454323292,
-0.017298651859164238,
0.0030358440708369017,
-0.012500312179327011,
0.026219679042696953,
-0.009744018316268921,
0.006187166087329388,
0.0006988700479269028,
0.002623257925733924,
0.01188737340271473,
-0.028487887233495712,
-0.0131306704133749,
0.0014297596644610167,
0.013275671750307083,
-0.03783257305622101,
0.02001865580677986,
0.042930617928504944,
0.022721316665410995,
-0.0010765604674816132,
0.052248381078243256,
-0.01100594736635685,
0.03784779831767082,
0.008220795542001724,
-0.03594500571489334,
0.05999654158949852,
-0.06518854200839996,
-0.03979538753628731,
0.02140510268509388,
0.007066730409860611,
0.030466340482234955,
0.046125952154397964,
0.012911788187921047,
0.001635617925785482,
0.05230984464287758,
0.008816294372081757,
-0.032255057245492935,
-0.007217128295451403,
-0.015415702946484089,
0.001221024664118886,
0.006616875529289246,
0.011454286053776741,
-0.001678206492215395,
0.006235373672097921,
0.027023840695619583,
-0.0016533243469893932,
-0.019046014174818993,
-0.009656134061515331,
0.034002337604761124,
0.016863035038113594,
0.04512001946568489,
0.02779899351298809,
-0.02010902389883995,
0.0026714454870671034,
0.054938528686761856,
-0.00023943903215695173,
0.062026940286159515,
0.023765213787555695,
-0.0014131179777905345,
-0.07001833617687225,
0.0015695096226409078,
-0.004124511498957872,
-0.002056391444057226,
0.08258433640003204,
-0.05975794792175293,
0.012760126031935215,
0.05672510713338852,
-0.05660693347454071,
0.013259614817798138,
0.006955577060580254,
0.0038092792965471745,
-0.03418770059943199,
0.018943173810839653,
-0.033432941883802414,
0.05388747900724411,
0.03769075870513916,
0.031297650188207626,
0.015090571716427803,
0.008127433247864246,
0.009351915679872036,
-0.03965749964118004,
-0.0023159917909651995,
0.039587244391441345,
-0.02566375769674778,
0.011282103136181831,
0.09172609448432922,
0.00019082419748883694,
-0.03265739232301712,
0.028885886073112488,
0.012438365258276463,
-0.04511575028300285,
-0.0008166647749021649,
0.01773892156779766,
0.030865492299199104,
0.04277271032333374,
0.015781119465827942,
-0.006421013735234737,
0.03836971893906593,
-0.0018360430840402842,
0.044075582176446915,
-0.0020367689430713654,
-0.0395931750535965,
0.0028363873716443777,
0.011774779297411442,
-0.04509320855140686,
-0.037761617451906204,
0.0382206067442894,
0.010417317971587181,
-0.029584772884845734,
-0.009837360121309757,
-0.019924404099583626,
0.034612055867910385,
-0.038400985300540924,
-0.007068639155477285,
-0.0724274143576622,
-0.007867425680160522,
0.023474205285310745,
-0.0007705252501182258,
0.0013541579246520996,
0.016118481755256653,
-0.04015631601214409,
-0.0599924772977829,
0.03442448750138283,
0.014276715926826,
-0.030786637216806412,
-0.03659094125032425,
-0.025506891310214996,
-0.038111574947834015,
0.02697681449353695,
-0.02073935605585575,
-0.03491051867604256,
-0.05060799419879913,
0.00590398907661438,
0.008866515010595322,
0.050679583102464676,
-0.027158500626683235,
-0.0076789590530097485,
-0.055775754153728485,
-0.05713880434632301,
0.04060988128185272,
0.04201667755842209,
-0.022220568731427193,
-0.04240892454981804,
-0.012389005161821842,
0.007822887971997261,
0.010423187166452408,
0.04475482553243637,
-0.023359280079603195,
-0.008776207454502583,
-0.0010761927114799619,
-0.031207282096147537,
0.015801167115569115,
-0.033033646643161774,
-0.005219294223934412,
-0.020529333502054214,
-0.008052261546254158,
-0.03410995751619339,
0.022144168615341187,
0.011616905219852924,
0.025889042764902115,
-0.01801016926765442,
0.006224048789590597,
-0.03679189085960388,
-0.021847855299711227,
-0.04973028972744942,
0.0876934602856636,
0.019623631611466408,
0.015517064370214939,
0.06659498810768127,
0.010794074274599552,
0.040786270052194595,
-0.012160301208496094,
-0.04734332114458084,
-0.000545308634173125,
0.052835624665021896,
-0.04775786027312279,
-0.028509167954325676,
0.013180043548345566,
0.025813966989517212,
0.029919100925326347,
-0.034614644944667816,
-0.022885411977767944,
0.03931219503283501,
-0.022168632596731186,
-0.03162888437509537,
0.034351661801338196,
0.024874979630112648,
0.059269387274980545,
0.06360332667827606,
-0.00961316004395485,
0.02664213627576828,
0.034705620259046555,
0.004673532210290432,
0.055101726204156876,
0.010299385525286198,
-0.02650449611246586,
0.03340132534503937,
0.008514486253261566,
0.015914972871541977,
0.03415451943874359,
-0.0038573509082198143,
0.02734936587512493,
-0.05176081135869026,
0.01765144243836403,
0.04542560502886772,
0.0012675697216764092,
-0.009305397048592567,
-0.01371309906244278,
-0.020548267289996147,
0.092051662504673,
-0.06043330579996109,
0.030912205576896667,
-0.022318558767437935,
0.010898957960307598,
0.0025190627202391624,
0.013866973109543324,
0.06454623490571976,
0.02311498485505581,
-0.030783619731664658,
-0.020395761355757713,
-0.020725088194012642,
0.037518374621868134,
0.0029406959656625986,
-0.0444180890917778,
-0.0020595300011336803,
0.0022307478357106447,
-0.049331918358802795,
-0.009110551327466965,
-0.01589461788535118,
0.024339625611901283,
0.0071931518614292145,
-0.020328892394900322,
0.06584172695875168,
0.0398438423871994,
0.02142362855374813,
-0.0016188706504181027,
-0.022361116483807564,
0.07913036644458771,
-0.03217840567231178,
0.0035791608970612288,
-0.03716530650854111,
0.018257910385727882,
-0.015441754832863808,
-0.007399820722639561
] |
<p>How can one prove that the number of images formed by two plane mirrors at right angles to each other is 3?</p>
<p>Is there a mathematical proof for the same ? </p>
| 10,701 |
[
-0.0600896030664444,
-0.04507838189601898,
-0.01120812352746725,
-0.01570028066635132,
0.02881125546991825,
-0.0003324350400362164,
-0.04595593363046646,
0.00018853928486350924,
-0.009155204519629478,
-0.013544891960918903,
0.016382599249482155,
0.03223661333322525,
0.008002725429832935,
0.03812679648399353,
0.02191714011132717,
0.011163176968693733,
-0.017383655533194542,
0.004742092918604612,
0.004020440857857466,
-0.024654770269989967,
-0.014264507219195366,
0.040909357368946075,
0.04224617779254913,
-0.019917141646146774,
-0.01263014879077673,
0.0039911214262247086,
0.03917193412780762,
-0.02220267616212368,
0.04930343106389046,
0.04221696779131889,
-0.0300187636166811,
0.0016896226443350315,
0.03339576721191406,
0.044333044439554214,
-0.011555573903024197,
-0.009892638772726059,
-0.01414373330771923,
0.01642906852066517,
-0.0007463570800609887,
-0.001370640704408288,
0.019649391993880272,
-0.0018322295509278774,
-0.03988178074359894,
0.04833776876330376,
-0.024111540988087654,
-0.011339657008647919,
-0.03908615931868553,
-0.04823678359389305,
-0.012478095479309559,
-0.07795210182666779,
0.13153472542762756,
-0.02896474488079548,
0.03375774621963501,
0.01405378058552742,
-0.01745431125164032,
0.007594815455377102,
0.04616830125451088,
0.0846482440829277,
-0.01799898035824299,
0.007510457653552294,
-0.029232414439320564,
-0.017489148303866386,
0.014650864526629448,
0.007151427678763866,
-0.03030933439731598,
0.015518082305788994,
0.0024257877375930548,
-0.015546373091638088,
0.01751980371773243,
-0.00888381153345108,
-0.033249180763959885,
0.02839045785367489,
0.0626303032040596,
-0.008547162637114525,
-0.022217145189642906,
-0.006951338145881891,
0.02555898204445839,
0.024638600647449493,
0.046625807881355286,
0.026688987389206886,
0.015824276953935623,
0.0252040047198534,
0.04863431677222252,
0.012062330730259418,
0.033608533442020416,
-0.012144414708018303,
0.07791592180728912,
0.01878330484032631,
0.0042040906846523285,
-0.013484413735568523,
0.012009416706860065,
-0.013410797342658043,
0.026397189125418663,
0.013587835244834423,
-0.030392825603485107,
0.03571096062660217,
-0.013323089107871056,
0.0626981183886528,
0.023001179099082947,
-0.03543595224618912,
-0.019433919340372086,
-0.04335601627826691,
-0.01703723520040512,
0.06654976308345795,
0.0010376772843301296,
0.001446557231247425,
-0.012734267860651016,
0.06575305014848709,
-0.006391088478267193,
0.026622673496603966,
-0.010610589757561684,
0.045285094529390335,
0.008030502125620842,
0.020972799509763718,
-0.003673812374472618,
0.011148005723953247,
0.028442945331335068,
-0.023217985406517982,
0.06190066784620285,
0.10465050488710403,
0.016553590074181557,
-0.04774928838014603,
-0.01150673720985651,
-0.042502447962760925,
-0.07821190357208252,
0.03756512701511383,
0.01604471541941166,
-0.012591879814863205,
-0.022330312058329582,
0.02795722708106041,
0.01350957527756691,
-0.003850539680570364,
-0.00508112832903862,
-0.0035218128468841314,
-0.009027569554746151,
-0.012076611630618572,
-0.10565576702356339,
-0.04840637743473053,
0.018179628998041153,
-0.002630166709423065,
-0.03736773505806923,
-0.07559379190206528,
0.03630385175347328,
0.09148207306861877,
0.07178346812725067,
-0.01294797845184803,
0.01915437914431095,
0.016625333577394485,
0.03515099734067917,
-0.01866978034377098,
-0.014223362319171429,
0.007145092822611332,
0.008697290904819965,
-0.011126963421702385,
-0.004007361363619566,
-0.062330882996320724,
0.03875013813376427,
0.03968678414821625,
-0.000519201741553843,
-0.03150773420929909,
0.048557329922914505,
-0.012813685461878777,
0.001875273766927421,
0.011061890982091427,
-0.014224265702068806,
-0.03811292722821236,
0.07725755870342255,
0.01666167937219143,
-0.009879950433969498,
0.032777540385723114,
-0.020533492788672447,
0.038655079901218414,
-0.0033975383266806602,
0.01020611822605133,
0.03853227570652962,
-0.03353603929281235,
-0.005323924124240875,
0.0141447139903903,
0.022693565115332603,
0.043221551924943924,
0.014045411720871925,
-0.012354531325399876,
0.013247146271169186,
0.038064878433942795,
0.025722797960042953,
0.020376361906528473,
-0.009464412927627563,
-0.012246697209775448,
-0.007725889794528484,
-0.02503812126815319,
0.00044847754179500043,
-0.04490816220641136,
0.013445242308080196,
-0.011597201228141785,
-0.014090966433286667,
-0.012457330711185932,
0.01114364992827177,
-0.01443366426974535,
-0.016112104058265686,
-0.052666932344436646,
-0.02577281929552555,
0.016422182321548462,
0.019904611632227898,
-0.018198179081082344,
0.02597413957118988,
0.06795252859592438,
0.07890055328607559,
-0.004695231560617685,
0.03163919970393181,
-0.03808591142296791,
0.021993285045027733,
0.001966274343430996,
-0.013515176251530647,
0.014101327396929264,
-0.000686108018271625,
-0.014692696742713451,
-0.013287613168358803,
0.021504083648324013,
-0.018410421907901764,
0.025884781032800674,
-0.037816159427165985,
0.052681535482406616,
0.034768201410770416,
0.03193697705864906,
0.035697951912879944,
-0.005081721115857363,
0.02119283936917782,
0.01951470784842968,
0.000951252703089267,
-0.03999956324696541,
-0.0508248433470726,
-0.024433963000774384,
0.029899002984166145,
0.04289389029145241,
-0.06229943409562111,
0.027472876012325287,
0.025059761479496956,
0.034509871155023575,
-0.005409068427979946,
0.01989815942943096,
-0.005345627665519714,
-0.01427908893674612,
-0.0022523982916027308,
0.015633638948202133,
0.0021167255472391844,
0.04540780186653137,
-0.015371639281511307,
-0.014518659561872482,
-0.010551758110523224,
-0.012650938704609871,
-0.06275080889463425,
0.028096728026866913,
-0.03385356441140175,
0.0018682933878153563,
0.00943936500698328,
-0.01931428164243698,
0.03788452595472336,
-0.015861302614212036,
-0.0029667122289538383,
0.004674652125686407,
0.01499198842793703,
0.014645502902567387,
-0.008023946546018124,
-0.005416921805590391,
0.0021195753943175077,
-0.000019381666788831353,
-0.013038678094744682,
-0.00395164405927062,
0.05681951344013214,
-0.015605544671416283,
0.026454119011759758,
-0.024700812995433807,
-0.025241844356060028,
-0.007678178139030933,
-0.011789844371378422,
-0.022040465846657753,
0.0020583895966410637,
0.02102603390812874,
-0.03672758862376213,
-0.03479261323809624,
0.016120124608278275,
-0.011659504845738411,
0.021663838997483253,
-0.028792841359972954,
-0.05354998633265495,
0.023563256487250328,
0.008538690395653248,
-0.0378061980009079,
0.010382036678493023,
-0.006293518003076315,
0.02550651691854,
-0.0028992504812777042,
-0.018974121659994125,
-0.022897616028785706,
-0.023899538442492485,
-0.046989988535642624,
0.02810893952846527,
-0.018701663240790367,
0.011698931455612183,
-0.001328598940744996,
0.008705792017281055,
-0.06125513091683388,
-0.0017069743480533361,
-0.029916709288954735,
-0.05005721375346184,
0.0005725859082303941,
0.009451765567064285,
0.02974240668118,
-0.0726357027888298,
0.01831286959350109,
0.02134062349796295,
-0.03253357484936714,
0.012761526741087437,
-0.05964507535099983,
-0.04876738041639328,
0.01125091128051281,
0.0036191074177622795,
0.027576817199587822,
-0.03517227992415428,
-0.07082811743021011,
0.04871667921543121,
0.012256420217454433,
-0.035422053188085556,
-0.021210981532931328,
0.0034379304852336645,
0.007218045182526112,
-0.018468555063009262,
0.03240601718425751,
0.016649795696139336,
-0.028830114752054214,
0.046756915748119354,
0.010722384788095951,
0.0003415838582441211,
0.028209103271365166,
0.009338236413896084,
-0.022844068706035614,
-0.014977313578128815,
0.007706416305154562,
0.009290090762078762,
0.013879138045012951,
0.03620651736855507,
-0.03150445967912674,
0.025543877854943275,
0.03712797164916992,
0.041354235261678696,
-0.012172585353255272,
-0.03808501735329628,
0.03128570690751076,
-0.022136371582746506,
0.0333205908536911,
-0.008461996912956238,
0.04423948749899864,
0.023012252524495125,
0.009883107617497444,
-0.0019838602747768164,
0.03144026920199394,
0.04643113166093826,
-0.03365716338157654,
-0.01741553097963333,
0.005750284064561129,
0.022399021312594414,
-0.015018360689282417,
-0.0393289253115654,
-0.02251662127673626,
-0.015474685467779636,
0.016864316537976265,
-0.014759291894733906,
-0.017667420208454132,
0.032229311764240265,
0.01907348819077015,
-0.004834328778088093,
0.041322920471429825,
-0.008159641176462173,
-0.01435256190598011,
-0.04851251468062401,
-0.017557596787810326,
-0.02662215568125248,
0.0018261369550600648,
0.0037276444490998983,
0.016319619491696358,
-0.00009161409980151802,
0.001903028809465468,
0.01955270953476429,
-0.029883187264204025,
-0.056612685322761536,
-0.009538821876049042,
0.006899223197251558,
0.023300250992178917,
-0.01571822166442871,
-0.007508033886551857,
0.01242158841341734,
-0.03788962960243225,
-0.01425427570939064,
-0.04818667098879814,
-0.015380613505840302,
-0.03617171198129654,
-0.010263596661388874,
-0.03039129078388214,
-0.03813154622912407,
-0.004646474029868841,
0.07285364717245102,
0.04003758355975151,
-0.057155437767505646,
0.015040124766528606,
0.04597504064440727,
-0.05861453339457512,
-0.018910834565758705,
-0.021338487043976784,
0.021454811096191406,
-0.023169025778770447,
0.023705512285232544,
0.02138592302799225,
0.03542513772845268,
0.03081202134490013,
0.0002749426057562232,
-0.031021788716316223,
0.011546273715794086,
-0.0006709899753332138,
-0.004886288195848465,
-0.016009757295250893,
-0.046460673213005066,
-0.016728047281503677,
-0.005348190665245056,
0.035420000553131104,
-0.056350771337747574,
0.0022480455227196217,
0.04062611609697342,
-0.0013734445674344897,
-0.009282244369387627,
0.026828361675143242,
0.027681471779942513,
0.0191902294754982,
-0.008945130743086338,
-0.04448048397898674,
-0.01075202040374279,
-0.015366878360509872,
-0.014786219224333763,
0.02649087831377983,
0.024191362783312798,
-0.03580097481608391,
-0.022077620029449463,
0.013224267400801182,
-0.011848298832774162,
0.0013214903883635998,
-0.0017629613867029548,
-0.012985752895474434,
-0.014237902127206326,
0.006431160494685173,
0.020815584808588028,
-0.017220543697476387,
0.049801282584667206,
0.03444763273000717,
0.009432896971702576,
-0.0413440465927124,
-0.04986848682165146,
0.038577523082494736,
0.04573777690529823,
0.029042614623904228,
-0.018570495769381523,
0.00010841331095434725,
-0.03211487829685211,
-0.005701710004359484,
-0.006828468758612871,
-0.0411536805331707,
0.009587899781763554,
-0.035464685410261154,
-0.01873144693672657,
-0.013782463036477566,
-0.022112036123871803,
-0.03520021587610245,
0.018741395324468613,
0.006952460389584303,
0.04242520034313202,
-0.016538387164473534,
0.0062711299397051334,
-0.004581226967275143,
0.018619393929839134,
0.04669249430298805,
0.047654785215854645,
0.020291227847337723,
0.01682664081454277,
0.010100452229380608,
0.051989857107400894,
-0.07000689208507538,
-0.03938431665301323,
0.04054481163620949,
-0.010891935788094997,
-0.015849998220801353,
0.04565844684839249,
-0.04220829904079437,
-0.021188633516430855,
0.01635782979428768,
-0.012782246805727482,
-0.015403295867145061,
0.03312525525689125,
-0.039362832903862,
-0.019834546372294426,
0.04454881697893143,
0.022036686539649963,
0.06698717921972275,
0.03241901099681854,
0.007901201024651527,
-0.009423392824828625,
-0.018578827381134033,
0.04731942340731621,
-0.023888012394309044,
-0.022723287343978882,
0.0035076888743788004,
0.0021371629554778337,
-0.042902685701847076,
0.032267000526189804,
-0.026839593425393105,
0.012825914658606052,
0.0042804693803191185,
-0.019569626078009605,
-0.04191310703754425,
0.016302675008773804,
0.025121888145804405,
0.025074699893593788,
0.001831211382523179,
0.02099127322435379,
0.03972362354397774,
-0.031033581122756004,
0.017836038023233414,
-0.038073744624853134,
0.00831428449600935,
-0.022457126528024673,
0.0258208978921175,
0.02313428930938244,
-0.030063072219491005,
-0.016246389597654343,
-0.006589614786207676,
-0.011186007410287857,
0.05506489798426628,
-0.03345362842082977,
0.014764959923923016,
0.02432103268802166,
-0.07012780010700226,
-0.007298439275473356,
-0.011977726593613625,
-0.03771213814616203,
0.051877573132514954,
-0.05573850870132446,
0.0002505406446289271,
0.010953628458082676,
0.006272103637456894,
-0.044183019548654556,
-0.037302661687135696,
0.01999637484550476,
0.027959851548075676,
0.0008999480050988495,
-0.018029818311333656,
-0.02156023494899273,
0.01393577829003334,
-0.051501866430044174,
-0.013924557715654373,
0.0460607074201107,
-0.02128530852496624,
-0.023494569584727287,
-0.021645646542310715,
0.011177288368344307,
0.053419776260852814,
-0.007981725968420506,
-0.03960246220231056,
-0.005101910326629877,
-0.048416391015052795,
-0.025063183158636093,
-0.00452415319159627,
0.030018527060747147,
-0.011904415674507618,
-0.056367337703704834,
0.0010063799563795328,
-0.002788444282487035,
0.028218941763043404,
-0.06988278776407242,
-0.005724442657083273,
-0.011521222069859505,
0.03026495687663555,
-0.02180514670908451,
-0.0330263152718544,
0.016575779765844345,
-0.002096661366522312,
0.019598571583628654,
-0.01909848302602768,
0.015839893370866776,
-0.010732891038060188,
-0.02914813533425331,
0.04695059359073639,
0.011268770322203636,
0.00721758184954524,
-0.0326727032661438,
0.07140078395605087,
0.006869613192975521,
-0.012059563770890236,
0.0020758500322699547,
-0.011561919935047626,
0.0010122267995029688,
-0.026790251955389977,
0.043514713644981384,
0.0020620496943593025,
0.03048662841320038,
-0.019460253417491913,
-0.04069133475422859,
-0.03913813829421997,
0.04403252154588699,
0.08028524369001389,
-0.035043831914663315,
0.06693864613771439,
0.028759216889739037,
-0.011158779263496399,
0.010938924737274647,
0.008046669885516167,
-0.011648131534457207,
0.000801648129709065,
0.03819167613983154,
0.05477941781282425,
-0.0769987404346466,
0.013844139873981476,
0.012115741148591042,
0.04516433924436569,
0.04045219346880913,
0.002032418269664049,
-0.008866862393915653,
0.01507541723549366,
0.006494590081274509,
-0.026610782369971275,
-0.04727567359805107,
0.03622724860906601,
-0.011437145993113518,
0.009967848658561707,
-0.00781097449362278,
-0.0006402023718692362,
0.042689815163612366,
-0.0103220846503973,
0.029035285115242004,
-0.03089095838367939,
-0.043527767062187195,
-0.0344550758600235,
-0.017246395349502563,
0.027187563478946686,
0.0438460111618042,
-0.019629839807748795,
-0.02203786000609398,
0.02976813353598118,
-0.005615473259240389,
0.03928365558385849,
-0.009404461830854416,
-0.039558183401823044,
-0.03256003186106682,
-0.02505582943558693,
-0.017288239672780037,
0.061023980379104614,
0.0144741740077734,
-0.0016254755901172757,
-0.01633778028190136,
-0.014464663341641426,
0.001615019398741424,
0.05674608796834946,
0.07628834247589111,
-0.047860171645879745,
0.02650681510567665,
-0.010872472077608109,
0.08488894253969193,
0.013022242113947868,
0.0043006474152207375,
0.10312402993440628,
0.05685918405652046,
0.029867155477404594,
-0.05878610536456108,
0.049272339791059494,
-0.03302787244319916,
-0.02185942977666855,
-0.0410873182117939,
0.04655812680721283,
0.0032078148797154427,
0.0354694202542305,
0.013557732105255127,
0.03274586424231529,
-0.041451968252658844,
-0.02515561319887638,
0.03767181932926178,
-0.02649211883544922,
-0.05333869159221649,
0.014021774753928185,
0.011482112109661102,
0.009126078337430954,
0.021734703332185745,
-0.02730425074696541,
0.015681074932217598,
-0.040529899299144745,
-0.021160610020160675,
0.0066337669268250465,
-0.034425877034664154,
0.03103776089847088,
0.002034901175647974,
-0.02480773814022541,
0.014719121158123016,
0.03015083260834217,
-0.04400588944554329,
-0.055423129349946976,
0.028879277408123016,
-0.0029048798605799675,
0.006305880378931761,
0.01847609505057335,
0.034620027989149094,
0.0024066197220236063,
0.0037659385707229376,
-0.004234442487359047,
0.004068153910338879,
-0.06294563412666321,
-0.02145017497241497,
-0.019169561564922333,
0.02822713367640972,
-0.011848931200802326,
0.0006144494982436299,
-0.03161683678627014,
-0.01131096575409174,
-0.010140441358089447,
-0.06470007449388504,
-0.01838904805481434,
0.005529702175408602,
-0.012656345963478088,
-0.051985081285238266,
-0.031898945569992065,
0.022219477221369743,
0.0472189337015152,
0.017952265217900276,
0.04555247351527214,
0.002324289409443736,
-0.016253849491477013,
0.01177301723510027,
-0.010773609392344952,
0.035929132252931595,
0.009757048450410366,
-0.024781716987490654,
-0.06397335231304169,
-0.0025448095984756947,
-0.0011542614083737135,
-0.03393925353884697,
0.015364370308816433,
0.020937561988830566,
0.041030630469322205,
0.03471517562866211,
-0.031380776315927505,
0.01586761325597763,
-0.03725224733352661,
-0.002384134568274021,
-0.02592282183468342,
-0.030604515224695206,
-0.02973460964858532,
0.012151085771620274,
0.05356163904070854,
0.031391631811857224,
-0.01897365041077137,
-0.004094413015991449,
0.02389153093099594,
0.011939981020987034,
0.014783794060349464,
-0.018189597874879837,
-0.02054331637918949,
0.0030025525484234095,
-0.02713780663907528,
-0.03333334997296333,
-0.00598069978877902,
0.013545854948461056,
0.05319826677441597,
0.025836443528532982,
0.0551426038146019,
0.03233320266008377,
-0.03480377420783043,
-0.0024153690319508314,
-0.016204828396439552,
-0.019881928339600563,
0.017488541081547737,
0.0029004027601331472,
0.019282499328255653,
-0.016391023993492126,
-0.013227126561105251,
0.021299436688423157,
0.007154181599617004,
0.04958491772413254,
0.014007181860506535,
-0.017181146889925003,
0.016623150557279587,
-0.038783084601163864,
0.049422215670347214,
-0.035492319613695145,
-0.0030327257700264454,
-0.02333441935479641,
0.028956681489944458,
-0.002046830952167511,
0.008414696902036667,
-0.043311502784490585,
0.024715488776564598,
0.025735095143318176,
-0.04433911293745041,
0.046132929623126984,
0.04038704186677933,
0.003788021393120289,
-0.011700453236699104,
0.01978149451315403,
0.0018658440094441175,
0.008737682364881039,
-0.029800694435834885,
-0.058642856776714325,
0.08348949998617172,
-0.037729889154434204,
-0.020788704976439476,
-0.00993573758751154,
-0.014580964110791683,
0.01941876858472824,
0.05584418773651123,
-0.027131877839565277,
-0.011874975636601448,
0.0166371688246727,
0.0025540143251419067,
-0.03589466214179993,
0.021958420053124428,
0.03400522470474243,
0.005943496711552143,
-0.024741560220718384,
0.02895241416990757,
-0.028410185128450394,
-0.020769819617271423,
0.016566971316933632,
0.04530703276395798,
-0.0032382020726799965,
0.004949687514454126,
0.01988966204226017,
0.003290685126557946,
-0.001384796923957765,
-0.011935103684663773,
0.025236397981643677,
0.013466292060911655,
0.003819627221673727,
-0.033711619675159454,
0.044905196875333786,
0.019868798553943634,
-0.00999521929770708,
-0.07970593124628067,
0.012475073337554932,
-0.018017886206507683,
-0.005837598815560341,
0.05576241388916969,
-0.07169031351804733,
0.044081639498472214,
0.06280047446489334,
-0.0768091157078743,
0.02468794956803322,
-0.021924888715147972,
-0.05508781597018242,
-0.06582740694284439,
0.011097406037151814,
0.01588211953639984,
0.05481671169400215,
0.001540705794468522,
0.03627482056617737,
0.03129483014345169,
0.009447051212191582,
-0.029148075729608536,
-0.03602290526032448,
-0.010116832330822945,
-0.006732484325766563,
-0.02683522179722786,
-0.0038299181032925844,
0.049406055361032486,
-0.003265977604314685,
-0.05446115881204605,
0.03422793373465538,
0.009293823502957821,
-0.011277063749730587,
0.004198912531137466,
0.01957010291516781,
0.021351603791117668,
0.03403663635253906,
0.004544960800558329,
-0.010176287963986397,
-0.019333694130182266,
-0.013421558775007725,
0.01204008236527443,
0.00924713909626007,
0.009557012468576431,
-0.022866137325763702,
0.03712639585137367,
-0.03585660457611084,
-0.05542365461587906,
0.025525657460093498,
0.01860610768198967,
-0.010467692278325558,
-0.0018303728429600596,
-0.021443376317620277,
0.022775620222091675,
-0.04597003012895584,
0.02299683913588524,
-0.03957980126142502,
0.01278174389153719,
0.028158271685242653,
-0.010863200761377811,
-0.001585847930982709,
0.03824741393327713,
0.009485621936619282,
-0.06331922858953476,
0.027907880023121834,
-0.019872939214110374,
-0.007560877129435539,
-0.048885174095630646,
0.005406680051237345,
0.04326990991830826,
0.008238062262535095,
0.008682011626660824,
-0.015380916185677052,
-0.034415390342473984,
0.015062559396028519,
-0.0033475400414317846,
-0.016101937741041183,
-0.0017703816993162036,
-0.03927750512957573,
-0.06135272979736328,
-0.045121777802705765,
0.035438619554042816,
0.00434811832383275,
0.02177361212670803,
-0.07132964581251144,
-0.01454218477010727,
-0.022406917065382004,
0.03457837179303169,
0.07295053452253342,
-0.01055697351694107,
0.004309378564357758,
-0.01414188276976347,
0.03241248428821564,
0.03280462697148323,
-0.07471884787082672,
0.002034505596384406,
-0.024541104212403297,
-0.008973426185548306,
-0.023134741932153702,
-0.015466065146028996,
0.029535604640841484,
-0.0008266994263976812,
-0.00778622692450881,
-0.018128711730241776,
0.02565028890967369,
0.012887530960142612,
-0.055367086082696915,
0.031159013509750366,
0.0009347103768959641,
-0.033441636711359024,
0.08216101676225662,
-0.006183133460581303,
0.02388806827366352,
0.02018105238676071,
-0.036175962537527084,
-0.05049701780080795,
-0.029014848172664642,
-0.05733272060751915,
0.010333229787647724,
-0.04358052462339401,
-0.009360107593238354,
0.05737864226102829,
-0.016039995476603508,
-0.0036041701678186655,
0.032452892512083054,
-0.025410328060388565,
-0.025569260120391846,
0.06639276444911957,
-0.0011321317870169878,
0.02506357803940773,
-0.022139394655823708,
0.049499399960041046,
0.031073063611984253,
-0.053202442824840546,
0.028409099206328392,
0.04775208607316017,
0.0037556153256446123,
-0.012860248796641827,
0.036055050790309906,
0.022500544786453247,
0.015991173684597015,
0.021184096112847328,
0.005728182848542929,
0.043092191219329834,
0.032495394349098206,
-0.010345117188990116,
-0.001425500842742622,
-0.02333897165954113,
-0.027212686836719513,
0.006510387174785137,
0.010849461890757084,
0.09672049432992935,
0.009381313808262348,
-0.01197036076337099,
-0.007547872141003609,
-0.0014425135450437665,
-0.03863789141178131,
-0.008730104193091393,
0.029394373297691345,
0.03514034301042557,
-0.020072318613529205,
-0.012488430365920067,
-0.0181721318513155,
0.00932244211435318,
0.005981437861919403,
-0.042858242988586426,
0.020831789821386337,
0.03526376932859421,
-0.01378174964338541,
-0.005043648649007082,
-0.0006215375033207238,
-0.0003943974443245679,
-0.0013485777890309691,
0.05243581533432007,
0.04448783025145531,
0.018694885075092316,
0.004399783443659544,
0.0023008256684988737,
-0.047755878418684006,
0.034322332590818405,
-0.06295336037874222,
-0.04304207116365433,
-0.02704457752406597,
0.03760014846920967,
0.021150488406419754,
-0.00783533975481987
] |
<p>Where would you say I can start learning about Hamiltonians, Lagrangians ... Jacobians? and the like?</p>
<p>I was trying to read Ibach and Luth - Solid State Physics, and <a href="http://imgur.com/a/5fc56" rel="nofollow" title="Picture from "Solid State Physics" by Ibach and Luth 1991. Published by Springer-Verlag">suddenly</a></p>
<p>(suddenly a Hamiltonian pops up. and then a wave equation and then $H_{aa}\ and\ H_{ab}$?</p>
| 10,702 |
[
0.006358704529702663,
-0.007291564252227545,
0.016029639169573784,
-0.028120970353484154,
0.04326905310153961,
-0.006887832190841436,
-0.034249287098646164,
-0.040107611566782,
0.0012958877487108111,
-0.04784480482339859,
0.03867192938923836,
0.014141746796667576,
0.04081358015537262,
0.02018033340573311,
0.03859598562121391,
0.023767324164509773,
0.0021155562717467546,
-0.06370145082473755,
-0.04811307042837143,
0.036421630531549454,
0.02147059328854084,
-0.03696219623088837,
0.004650447517633438,
0.013385557569563389,
0.002837969223037362,
0.02117471769452095,
0.025015199556946754,
0.02180319093167782,
0.012527301907539368,
0.06245933845639229,
0.00026278255973011255,
-0.007838627323508263,
-0.0012138099409639835,
0.015267323702573776,
0.0030061020515859127,
0.003181947860866785,
-0.007549287285655737,
-0.04309895634651184,
0.006255701649934053,
0.004551503341645002,
-0.059434182941913605,
-0.013119621202349663,
-0.023853769525885582,
0.03596526384353638,
-0.013586904853582382,
0.04701722785830498,
0.014433452859520912,
-0.015993578359484673,
0.03782743960618973,
-0.050485920161008835,
0.04810633510351181,
0.02592020481824875,
0.02649819664657116,
0.040348973125219345,
0.01767023280262947,
-0.011069386266171932,
0.0535912811756134,
0.05237722024321556,
-0.002516341395676136,
-0.0527566596865654,
-0.02026224695146084,
-0.023710792884230614,
-0.025340106338262558,
-0.07567346841096878,
-0.03161567449569702,
0.0203536543995142,
0.001725545502267778,
-0.056780796498060226,
0.022358477115631104,
0.001012497814372182,
-0.03297829627990723,
0.010076606646180153,
0.058632124215364456,
-0.04802364856004715,
0.02111586555838585,
-0.024530161172151566,
0.0063153584487736225,
0.023341955617070198,
0.009629261679947376,
-0.000669309520162642,
0.023743923753499985,
0.01617148518562317,
0.0063809677958488464,
0.017795180901885033,
-0.026624083518981934,
-0.02834722399711609,
0.08567517250776291,
0.004455877933651209,
-0.010286910459399223,
-0.0010335674742236733,
-0.023431329056620598,
-0.001663665403611958,
0.030666228383779526,
0.013885298743844032,
-0.017820902168750763,
-0.009450430981814861,
0.058312248438596725,
0.0442800298333168,
0.027862725779414177,
-0.03347353637218475,
0.01421983540058136,
-0.05143081396818161,
0.007422612514346838,
0.06468123942613602,
0.0025787921622395515,
-0.024810299277305603,
-0.026296094059944153,
0.01722077839076519,
-0.025331858545541763,
-0.005562979727983475,
-0.01002386212348938,
0.03334289789199829,
-0.0077359722927212715,
-0.0012633535079658031,
-0.020610155537724495,
0.00650180596858263,
0.020286109298467636,
-0.018683109432458878,
0.047291506081819534,
0.038976091891527176,
0.04598322510719299,
-0.026195470243692398,
0.052782513201236725,
-0.03786229342222214,
-0.05628589168190956,
-0.02036232501268387,
0.07304629683494568,
0.0016856882721185684,
-0.03374428302049637,
0.018643412739038467,
0.01373471412807703,
-0.016590362414717674,
-0.007812087889760733,
0.015930674970149994,
0.0033114817924797535,
0.0018992256373167038,
-0.10987348109483719,
-0.042910199612379074,
0.02516568824648857,
-0.008929682895541191,
-0.05017905309796333,
-0.050511546432971954,
0.00994681753218174,
0.034384001046419144,
0.05724503844976425,
-0.025310054421424866,
-0.008402099832892418,
0.005188227631151676,
0.025704070925712585,
0.0010435037547722459,
-0.012095498852431774,
-0.011224204674363136,
-0.021826861426234245,
-0.014246035367250443,
0.0065562487579882145,
-0.04166877269744873,
0.019948268309235573,
0.008375925943255424,
0.027966352179646492,
-0.01598551869392395,
0.07025822252035141,
-0.007006825879216194,
-0.011656914837658405,
0.008715945295989513,
-0.024222709238529205,
-0.022440386936068535,
0.08248613774776459,
-0.015691766515374184,
0.01575305312871933,
0.04065820947289467,
0.007270419504493475,
0.02190457656979561,
-0.017602581530809402,
0.02273465320467949,
0.041041430085897446,
-0.008374089375138283,
-0.0357707180082798,
0.018226873129606247,
-0.02468778006732464,
0.002414278918877244,
-0.0222978126257658,
-0.05523832514882088,
0.017457135021686554,
0.009240683168172836,
-0.02919916808605194,
0.02446730248630047,
0.014227338135242462,
0.02318873442709446,
-0.023256488144397736,
-0.03790544718503952,
0.015273451805114746,
-0.04735390096902847,
0.03159702941775322,
-0.03096718154847622,
-0.0020239234436303377,
0.06482074409723282,
0.03787796199321747,
0.0007811479736119509,
-0.015453106723725796,
-0.05212848260998726,
0.007570420857518911,
0.009829014539718628,
-0.00202027871273458,
-0.008241036906838417,
0.02469782903790474,
0.06757006049156189,
0.02758975140750408,
-0.000007707008080615196,
0.032956432551145554,
-0.031103814020752907,
-0.01400973554700613,
-0.0014153592055663466,
0.009277732111513615,
0.030571190640330315,
-0.013302023522555828,
0.039530109614133835,
-0.02132209576666355,
-0.02078823931515217,
-0.03495199978351593,
0.002377554774284363,
-0.028809186071157455,
0.04696100950241089,
0.04115575551986694,
0.0027780707459896803,
0.0023184726014733315,
0.0678558424115181,
0.017201030626893044,
0.029155367985367775,
-0.007877855561673641,
0.00016736806719563901,
-0.043404608964920044,
0.04508907347917557,
0.03193073347210884,
0.0383380651473999,
-0.053326718509197235,
0.00423350790515542,
0.03864014148712158,
0.04335605353116989,
0.04717477783560753,
0.02428274415433407,
-0.03561648353934288,
-0.048644859343767166,
0.03296757489442825,
0.018313299864530563,
-0.020480461418628693,
0.009253672324120998,
0.017169026657938957,
0.015117951668798923,
0.027266593649983406,
0.016941005364060402,
-0.06582126021385193,
0.05737747997045517,
-0.039362531155347824,
0.03219526261091232,
0.010723518207669258,
-0.03094324842095375,
0.048375487327575684,
-0.028668712824583054,
-0.00022025563521310687,
0.009557378478348255,
0.005026270169764757,
-0.024963628500699997,
-0.019120819866657257,
-0.015136702917516232,
-0.004288782831281424,
-0.013292539864778519,
-0.03950696066021919,
-0.012882230803370476,
0.03444715589284897,
-0.021599434316158295,
0.011738436296582222,
0.01662679761648178,
-0.00903096329420805,
-0.0318809375166893,
-0.003049135208129883,
0.0085600009188056,
0.04545387253165245,
0.03278568014502525,
-0.04060767590999603,
-0.019210733473300934,
0.004313834942877293,
-0.026802601292729378,
0.051353950053453445,
0.029632294550538063,
-0.01837170496582985,
0.05110355466604233,
-0.08970556408166885,
-0.03511609509587288,
0.05633319914340973,
0.006764567457139492,
-0.011887965723872185,
-0.017748337239027023,
-0.01527915894985199,
-0.046154290437698364,
-0.0280130784958601,
0.0018116722349077463,
0.03303719311952591,
-0.05389786884188652,
-0.005392264574766159,
-0.002149392617866397,
-0.036316774785518646,
-0.006190930027514696,
-0.02460036799311638,
-0.018655333667993546,
-0.010844764299690723,
-0.010281417518854141,
-0.0046436963602900505,
0.040000319480895996,
-0.012434151023626328,
-0.009123248979449272,
0.03260095790028572,
-0.010104362852871418,
0.0026888044085353613,
-0.0771554708480835,
-0.03051033243536949,
0.004180555697530508,
0.005416214466094971,
0.022848237305879593,
-0.0008580950670875609,
-0.013416152447462082,
0.08872482180595398,
0.019152728840708733,
-0.03540966659784317,
-0.009234785102307796,
-0.007872102782130241,
-0.04185512661933899,
-0.03179074823856354,
0.03331255167722702,
0.07840261608362198,
-0.03287695720791817,
0.027600349858403206,
0.025706324726343155,
0.014000928960740566,
0.038062527775764465,
0.014956814236938953,
0.002583171473816037,
0.01485421508550644,
-0.028005419299006462,
0.020749665796756744,
0.0562254898250103,
-0.005671282764524221,
-0.03332743048667908,
0.010687465779483318,
-0.025675078853964806,
0.007750405929982662,
0.019057072699069977,
-0.06402897834777832,
0.06284918636083603,
0.009516232647001743,
-0.03909742459654808,
-0.0300296638160944,
0.040063198655843735,
-0.005246712360531092,
-0.028963986784219742,
-0.00534906005486846,
0.017768625169992447,
0.020725857466459274,
0.014176245778799057,
0.01703110709786415,
0.02675412781536579,
-0.018496889621019363,
-0.0451476164162159,
-0.014476651325821877,
0.008465318940579891,
0.0016558334464207292,
0.018798507750034332,
-0.012839441187679768,
-0.03334825113415718,
0.029787907376885414,
0.024240393191576004,
-0.006037921644747257,
-0.021922294050455093,
-0.06565159559249878,
0.032572511583566666,
-0.06228848919272423,
-0.036205489188432693,
0.0005569335771724582,
0.04024115949869156,
0.0010908854892477393,
0.06881444156169891,
0.0047956728376448154,
0.02318202145397663,
0.0497300811111927,
0.010134766809642315,
-0.07991402596235275,
0.049686603248119354,
-0.02656594291329384,
-0.004414737224578857,
0.004076381679624319,
0.023610658943653107,
0.037892140448093414,
0.0047139497473835945,
-0.030478360131382942,
-0.013431086204946041,
0.009717793203890324,
-0.04170546680688858,
-0.007123495452105999,
-0.026318436488509178,
-0.03896686062216759,
-0.05056851729750633,
-0.0022698992397636175,
0.037980418652296066,
-0.019430024549365044,
0.020449217408895493,
0.04533078521490097,
-0.030247285962104797,
-0.010854859836399555,
-0.007856518030166626,
0.010597716085612774,
0.035326484590768814,
-0.017474442720413208,
0.0018932641251012683,
0.024795668199658394,
0.004553497768938541,
0.007600623648613691,
0.006282643415033817,
0.07612553238868713,
-0.02335183322429657,
-0.0019579133950173855,
0.03401327133178711,
-0.0412922203540802,
-0.009443674236536026,
-0.008777224458754063,
0.05771743506193161,
-0.011984108947217464,
0.016011271625757217,
0.0062855868600308895,
0.00040538611938245595,
-0.025116607546806335,
0.05185772851109505,
0.025508232414722443,
0.014485266990959644,
-0.02164335735142231,
-0.05383943021297455,
0.0026158378459513187,
-0.055199433118104935,
-0.00724635599181056,
0.0038627581670880318,
-0.011578209698200226,
-0.021575741469860077,
0.0016233286587521434,
0.03079151175916195,
0.023403452709317207,
-0.0253103319555521,
0.0006763340206816792,
-0.031778689473867416,
0.022211644798517227,
0.036863431334495544,
0.007503086235374212,
0.013723076321184635,
0.016289422288537025,
0.03159261867403984,
-0.02274836041033268,
0.03948722407221794,
-0.07003305107355118,
-0.01548790279775858,
0.015008628368377686,
0.016346657648682594,
-0.019565701484680176,
0.01748226024210453,
-0.0662970319390297,
-0.05192585662007332,
0.06222297623753548,
-0.025857267901301384,
0.03250833973288536,
-0.008256521075963974,
-0.043522924184799194,
-0.009963230229914188,
-0.022141218185424805,
-0.04757582023739815,
0.01901448890566826,
0.002174465684220195,
0.014193805865943432,
-0.03201736509799957,
0.009489331394433975,
-0.005678041372448206,
0.025566264986991882,
0.009961633011698723,
0.07114177942276001,
0.007709167432039976,
-0.02315010502934456,
-0.032911065965890884,
0.026965949684381485,
-0.03927241265773773,
-0.08766073733568192,
-0.020705824717879295,
0.01817387528717518,
-0.025817234069108963,
0.04964934289455414,
-0.042849037796258926,
-0.046825990080833435,
0.02251283824443817,
-0.0006337768863886595,
-0.002703401492908597,
-0.01030594389885664,
-0.01692931167781353,
0.03539525717496872,
0.03474840149283409,
-0.01723497547209263,
0.02706007845699787,
0.015123412013053894,
-0.02859475277364254,
-0.02332749031484127,
-0.017346195876598358,
0.05342259630560875,
-0.014904431067407131,
-0.00202766596339643,
-0.05614704266190529,
-0.023831048980355263,
-0.030909869819879532,
0.05748451501131058,
-0.04757215827703476,
-0.006749247666448355,
-0.043275002390146255,
-0.029375260695815086,
-0.013537751510739326,
0.03342412784695625,
-0.00460808863863349,
-0.013612627051770687,
-0.010244285687804222,
0.034236036241054535,
0.01334636565297842,
-0.01085636205971241,
0.018379386514425278,
-0.002438592491671443,
0.019998542964458466,
0.03242309391498566,
-0.009493031539022923,
0.03075438365340233,
-0.051597680896520615,
-0.037363819777965546,
-0.005422220565378666,
-0.07432949542999268,
0.07506732642650604,
0.011303937062621117,
-0.0034697921946644783,
0.03304038941860199,
-0.015155795030295849,
-0.043593570590019226,
0.014952100813388824,
-0.014371920377016068,
0.002062983810901642,
-0.05148680880665779,
0.01809651590883732,
-0.005400917027145624,
0.007474531885236502,
-0.02711566351354122,
-0.051309652626514435,
-0.002926838817074895,
-0.01482786051928997,
-0.048089057207107544,
-0.025840267539024353,
0.03358437865972519,
-0.004872207995504141,
-0.0010702927829697728,
0.026761872693896294,
0.005519587080925703,
-0.04903680086135864,
0.022214598953723907,
0.026565905660390854,
0.02981572598218918,
0.032888639718294144,
-0.02422916889190674,
-0.008994869887828827,
0.02621542103588581,
-0.01667843945324421,
0.026654310524463654,
-0.007945843040943146,
0.03618163615465164,
-0.021784141659736633,
-0.004301583394408226,
-0.027288388460874557,
0.0121552012860775,
0.06374232470989227,
-0.017497485503554344,
0.03155015408992767,
0.01724984496831894,
0.0176272951066494,
-0.023676708340644836,
-0.028420817106962204,
-0.03609617054462433,
-0.004382902290672064,
0.009321313351392746,
-0.020877230912446976,
0.0017447478603571653,
-0.01888936385512352,
-0.004709223750978708,
0.010798810049891472,
0.018373794853687286,
0.003635117784142494,
0.013497912324965,
0.07568395137786865,
-0.01875239610671997,
0.037347521632909775,
0.06313523650169373,
-0.017044352367520332,
0.014403716661036015,
-0.008599349297583103,
0.01860065758228302,
0.016419420018792152,
-0.006535639520734549,
-0.039030369371175766,
-0.04512304440140724,
-0.0598946139216423,
0.017588799819350243,
0.05846453085541725,
0.006681935861706734,
0.04905937612056732,
0.061099857091903687,
-0.01468702033162117,
0.006971209775656462,
0.008922595530748367,
-0.03620995953679085,
-0.01224240567535162,
0.019219353795051575,
0.013389479368925095,
-0.034482989460229874,
-0.0070876386016607285,
0.027360234409570694,
0.01317250169813633,
-0.03778906539082527,
0.005474195349961519,
0.007969647645950317,
0.015022695064544678,
-0.007772484328597784,
0.004356942139565945,
-0.01924883760511875,
0.037382256239652634,
-0.024502255022525787,
0.06763383001089096,
0.00687566539272666,
-0.04929828271269798,
0.05219298228621483,
0.04137161374092102,
0.0018986654467880726,
-0.02765313722193241,
-0.023845504969358444,
-0.04845530539751053,
0.04530319198966026,
0.0316476933658123,
0.011313805356621742,
0.00999937579035759,
0.0290687195956707,
0.0512196309864521,
-0.025196552276611328,
0.025175245478749275,
0.019020698964595795,
-0.03657480701804161,
-0.0006335016805678606,
-0.04257047176361084,
-0.0671147033572197,
0.03295470401644707,
0.009463283233344555,
-0.031223734840750694,
0.006551891099661589,
-0.0391433946788311,
0.027089854702353477,
-0.022923137992620468,
0.031206533312797546,
-0.049531009048223495,
0.07491612434387207,
-0.0035954785998910666,
-0.012079906649887562,
0.008104510605335236,
0.012240764684975147,
0.13358452916145325,
0.04530156031250954,
0.029031386598944664,
-0.07848066091537476,
0.017875786870718002,
0.014495255425572395,
0.018591715022921562,
-0.048970453441143036,
0.028670374304056168,
-0.006719676312059164,
0.03545298054814339,
-0.035974252969026566,
0.05602973699569702,
0.011546241119503975,
0.04073759540915489,
0.06848231703042984,
-0.043720461428165436,
-0.025759855285286903,
-0.026012027636170387,
-0.013122540898621082,
-0.017633551731705666,
0.027495063841342926,
-0.027813760563731194,
0.018898168578743935,
-0.029905004426836967,
-0.024221472442150116,
-0.05012716352939606,
-0.0477604866027832,
0.03222949802875519,
-0.01606113649904728,
-0.014606695622205734,
0.01732822321355343,
-0.004450004082173109,
-0.003642094088718295,
-0.006830756552517414,
0.01578550972044468,
0.0449100024998188,
0.0007839075988158584,
0.024179207161068916,
0.028882984071969986,
-0.030771546065807343,
-0.00850130058825016,
0.0019335841061547399,
0.00015500230074394494,
-0.004642427433282137,
-0.007874300703406334,
-0.054529305547475815,
0.05547049269080162,
-0.03961419686675072,
0.008090364746749401,
-0.0037386741023510695,
-0.00799885019659996,
-0.01911514811217785,
-0.02481873705983162,
-0.00606292812153697,
-0.004573409911245108,
0.008743012323975563,
-0.018925637006759644,
-0.002542169764637947,
-0.029251370579004288,
-0.018921466544270515,
-0.016936765983700752,
-0.010214339010417461,
-0.000014819082934991457,
0.0026185365859419107,
0.00021355980425141752,
-0.007932127453386784,
0.020015990361571312,
-0.039934251457452774,
0.01360080111771822,
-0.03769563138484955,
-0.015344096347689629,
-0.027314692735671997,
-0.03014778159558773,
0.021645929664373398,
0.0054275221191346645,
0.039207179099321365,
0.006140751764178276,
-0.033360496163368225,
-0.03688420355319977,
-0.06872553378343582,
0.022104032337665558,
-0.012242194265127182,
0.011616487056016922,
0.005315200891345739,
0.014887148514389992,
0.029309390112757683,
0.03300885483622551,
-0.0215653944760561,
0.027407532557845116,
0.013023816980421543,
-0.005862454418092966,
0.0323239229619503,
0.018155565485358238,
0.04027320072054863,
0.029314229264855385,
-0.026147248223423958,
0.019375497475266457,
0.0002348298003198579,
0.01229855976998806,
0.03404693305492401,
0.00904123019427061,
0.01577022112905979,
0.049146298319101334,
-0.009412333369255066,
-0.019207241013646126,
0.006483933422714472,
-0.011148962192237377,
0.02922666072845459,
0.035728491842746735,
0.04883810132741928,
-0.03858492895960808,
-0.04577988386154175,
0.027796395123004913,
0.004022534005343914,
-0.0019381714519113302,
0.044058870524168015,
-0.005846481770277023,
0.018231336027383804,
-0.004403993487358093,
0.03825533390045166,
-0.06679355353116989,
0.025960830971598625,
-0.05064982548356056,
0.05863238126039505,
0.011872484348714352,
0.023324251174926758,
-0.029509853571653366,
0.04831168055534363,
0.021586190909147263,
0.003569692373275757,
0.025705767795443535,
0.026759425178170204,
0.0013507730327546597,
-0.012697635218501091,
0.014493368566036224,
-0.050054945051670074,
0.03197260946035385,
0.03523974120616913,
-0.0376957468688488,
-0.00833373237401247,
-0.010349287651479244,
-0.03522580862045288,
-0.012587839737534523,
-0.0011208646465092897,
-0.003062083385884762,
0.034301191568374634,
-0.01749439723789692,
0.030880453065037727,
0.04425089433789253,
0.000707467959728092,
-0.007929251529276371,
0.02196803130209446,
-0.057829227298498154,
-0.05532300844788551,
-0.01159360259771347,
0.029456820338964462,
-0.00909559614956379,
0.0068917591124773026,
-0.005720612592995167,
0.056475862860679626,
-0.005060212686657906,
-0.005393038969486952,
0.007720191031694412,
-0.0043701655231416225,
0.02391314134001732,
-0.012350981123745441,
-0.033950164914131165,
0.04768998548388481,
0.030563930049538612,
-0.019901560619473457,
0.03448035940527916,
0.037222523242235184,
0.0370839424431324,
-0.07413598895072937,
0.007842048071324825,
-0.025477590039372444,
-0.0034621544182300568,
0.0725816860795021,
-0.06636939197778702,
-0.0002333550073672086,
0.03883514553308487,
-0.06651061773300171,
0.03285553678870201,
0.003979124594479799,
-0.003680923255160451,
0.020565802231431007,
0.007227188441902399,
-0.03187396377325058,
0.07835746556520462,
-0.023486241698265076,
0.04362455755472183,
0.03972825035452843,
0.014586091041564941,
-0.0016116308979690075,
-0.0006473350222222507,
0.019540710374712944,
0.04568257927894592,
-0.007945878431200981,
0.008452050387859344,
0.048548322170972824,
0.0013301960425451398,
-0.058073148131370544,
0.00834406353533268,
-0.0033515773247927427,
-0.02198156528174877,
-0.015848958864808083,
-0.01501504611223936,
-0.01663108915090561,
0.014965357258915901,
0.033037733286619186,
-0.023869192227721214,
-0.013276977464556694,
-0.007401132024824619,
0.0056183114647865295,
0.054834142327308655,
0.011031937785446644,
0.00674011604860425,
0.03038705512881279,
-0.03781967610120773,
-0.057471491396427155,
0.03345749154686928,
-0.02734791487455368,
0.01457806397229433,
0.023924212902784348,
-0.03775322809815407,
0.0027845303993672132,
-0.03258665278553963,
0.009347726590931416,
-0.019163060933351517,
-0.0025657792575657368,
-0.0018233837326988578,
-0.021471722051501274,
0.015224688686430454,
0.050380442291498184,
-0.04616960883140564,
-0.01336036715656519,
0.0473356731235981,
0.012403895147144794,
0.005227602552622557,
-0.07539074867963791,
0.006873644422739744,
0.011726419441401958,
-0.0372924879193306,
-0.03857049718499184,
-0.04009130224585533,
-0.026640241965651512,
0.04250991716980934,
-0.004383353516459465,
-0.007968844845890999,
-0.03023248165845871,
-0.030827773734927177,
0.0096720727160573,
-0.05137432739138603,
0.036790382117033005,
0.02063537761569023,
-0.03362853080034256,
-0.00016474111180286855,
0.012805942445993423,
0.0220622718334198,
-0.0016324905445799232,
0.03380388021469116,
-0.016368277370929718,
0.039609719067811966,
0.0016941085923463106,
-0.03806982561945915,
0.037544526159763336,
0.018653495237231255,
0.016180649399757385,
-0.031041111797094345,
0.004680677317082882,
0.00266326148994267,
0.0032410353887826204,
-0.007045523729175329,
0.03033050335943699,
0.022761782631278038,
-0.009399574249982834,
0.015322200022637844,
0.01011393778026104,
-0.06649690121412277,
0.01105575356632471,
0.01550872903317213,
-0.004725915379822254,
0.07391197979450226,
0.01580190472304821,
0.01958129182457924,
0.021398233249783516,
-0.0375467948615551,
0.004369586240500212,
0.02350269816815853,
-0.06938609480857849,
-0.0318094827234745,
-0.009867164306342602,
-0.02773851528763771,
0.008260895498096943,
-0.06387959420681,
-0.01462183054536581,
0.004247916396707296,
-0.019815783947706223,
0.0015207669930532575,
0.02027105912566185,
0.0146739911288023,
0.0036419888492673635,
0.03068305365741253,
0.0220992062240839,
0.040979962795972824,
-0.03463225066661835,
-0.003310520201921463,
0.013879329897463322,
0.033124640583992004,
-0.02899414487183094,
-0.0009216886828653514,
0.014815964736044407,
0.017842641100287437,
0.0202869214117527,
0.0021114766132086515,
0.03484029322862625,
-0.028394406661391258,
0.02473088912665844,
0.0017535848310217261,
-0.0015364807331934571,
-0.02915308251976967,
0.012164072133600712,
-0.016360394656658173,
0.07471615821123123,
-0.022565379738807678,
-0.026910141110420227,
-0.004650181625038385,
0.03339996933937073,
-0.014440654776990414,
-0.03847416862845421,
0.005912492983043194,
0.020186884328722954,
-0.027928590774536133,
-0.011295470409095287,
-0.06482896953821182,
-0.010690278373658657,
0.018484538421034813,
-0.01474527083337307,
0.01670220121741295,
0.0014638496795669198,
-0.009700006805360317,
0.03095538169145584,
-0.03993213549256325,
-0.042500413954257965,
-0.0006314760539680719,
0.028305720537900925,
0.02302597090601921,
-0.00640825554728508,
-0.03376467898488045,
-0.005988283548504114,
-0.022892460227012634,
0.056264478713274,
-0.061216436326503754,
-0.03412270545959473,
-0.03323681280016899,
0.010214452631771564,
-0.02772432565689087,
0.03135306388139725
] |
<p>I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and quadratic in others, but that's only trivially different. I am not referring to equally spaced as a limiting behavior either, I mean truly integer spaced.</p>
<p>Any ideas? If not, is there a proof for its uniqueness?</p>
| 10,703 |
[
-0.03219391778111458,
0.0014881205279380083,
0.02106807753443718,
-0.046055689454078674,
0.039778850972652435,
-0.01655791886150837,
-0.000770104001276195,
-0.04427378624677658,
0.0028898990713059902,
-0.046541761606931686,
0.018748655915260315,
0.01151202991604805,
0.05156302824616432,
0.02908998914062977,
0.03027912974357605,
-0.01658991351723671,
-0.006367414258420467,
-0.00972476415336132,
-0.014854500070214272,
-0.03813871741294861,
-0.009329239837825298,
0.010102400556206703,
0.030593881383538246,
0.0005144031601957977,
-0.011984801851212978,
0.016206959262490273,
0.031593743711709976,
0.01330419909209013,
0.0237228125333786,
0.09024115651845932,
0.003746808972209692,
-0.008029928430914879,
0.029203074052929878,
0.06219426915049553,
0.0388157032430172,
0.00404556468129158,
-0.015497193671762943,
-0.045503344386816025,
-0.016511114314198494,
0.03614238649606705,
-0.02335110306739807,
-0.04725427180528641,
-0.02087489701807499,
0.05832476168870926,
-0.004202869720757008,
0.011312237940728664,
-0.011073220521211624,
-0.03229578584432602,
0.056667957454919815,
-0.04862623289227486,
0.06415949761867523,
-0.006162081845104694,
0.02939298190176487,
0.033450063318014145,
0.0027110381051898003,
0.009670923464000225,
0.06883785873651505,
0.04977767914533615,
-0.01389333140105009,
-0.038814716041088104,
-0.01940886303782463,
-0.009828301146626472,
0.014007464051246643,
-0.0005531432689167559,
-0.05076700448989868,
0.006944512948393822,
0.0034795012325048447,
-0.050918158143758774,
-0.03160592168569565,
-0.04047970846295357,
-0.04303630068898201,
0.05265595391392708,
0.047522321343421936,
-0.029677454382181168,
0.012416161596775055,
-0.004748516716063023,
0.03951789066195488,
0.013995802029967308,
0.03897416964173317,
-0.005429619457572699,
-0.03649251535534859,
0.00015789212193340063,
0.029404882341623306,
0.01364225335419178,
-0.012665577232837677,
0.010038652457296848,
0.03772277012467384,
-0.04344161972403526,
0.03148840367794037,
0.0801166296005249,
-0.0037035669665783644,
0.027613500133156776,
0.039709918200969696,
-0.0027371395844966173,
-0.017799941822886467,
0.00996671337634325,
0.033650562167167664,
0.02422413043677807,
-0.0009050595690496266,
-0.02929113246500492,
0.019550053402781487,
-0.04260659217834473,
-0.026915712282061577,
0.07165683805942535,
-0.02144787833094597,
0.01000554021447897,
-0.023445459082722664,
0.03786565363407135,
0.012800916098058224,
0.016165034845471382,
-0.029205800965428352,
0.04414543882012367,
0.01097766775637865,
0.014463240280747414,
0.008431839756667614,
0.003191752126440406,
-0.027004176750779152,
0.002692518290132284,
0.058869801461696625,
0.07676119357347488,
0.026723559945821762,
-0.043859776109457016,
0.03252865746617317,
-0.05261368304491043,
-0.03749147802591324,
0.015497683547437191,
0.004228133708238602,
0.01878153346478939,
-0.04702523350715637,
0.04954734817147255,
0.0021715150214731693,
0.017135921865701675,
0.0068540978245437145,
-0.007179461885243654,
0.052284158766269684,
-0.0284863393753767,
-0.08061525225639343,
-0.026450486853718758,
0.035423118621110916,
-0.03119603730738163,
-0.04285215586423874,
-0.03871683031320572,
-0.0004810418759007007,
0.035782456398010254,
0.05984572693705559,
0.018406664952635765,
-0.004724125377833843,
-0.01061223167926073,
0.05220455303788185,
0.021463533863425255,
-0.019463805481791496,
-0.012822698801755905,
0.002900996943935752,
-0.037001755088567734,
0.028908224776387215,
-0.04117065668106079,
-0.008330981247127056,
0.012102287262678146,
0.018119312822818756,
-0.012546781450510025,
0.05444642901420593,
-0.041528232395648956,
-0.00025355329853482544,
0.013713671825826168,
0.013783122412860394,
-0.028212208300828934,
0.06477192789316177,
0.010878107510507107,
-0.025360383093357086,
0.01895122416317463,
-0.018147721886634827,
0.012230442836880684,
0.025007260963320732,
-0.000682768237311393,
0.03142205998301506,
-0.07040107250213623,
-0.027744656428694725,
-0.04622058570384979,
0.04019428789615631,
0.03976132348179817,
-0.04752786085009575,
0.001186220208182931,
-0.00036851686309091747,
0.0006366287125274539,
-0.03045814111828804,
0.06640055775642395,
-0.012821154668927193,
-0.011206120252609253,
0.01231253519654274,
-0.05193030461668968,
0.017639296129345894,
-0.021276023238897324,
0.047654349356889725,
0.034393664449453354,
-0.02218686230480671,
0.052585165947675705,
0.02450684830546379,
0.03409771993756294,
-0.04068199172616005,
-0.001765022985637188,
0.006579512730240822,
0.02066638134419918,
-0.012384249828755856,
-0.03766834735870361,
0.029351897537708282,
0.057785458862781525,
0.010923503898084164,
-0.007343785837292671,
0.0773019939661026,
-0.03477931767702103,
-0.01882251538336277,
-0.011479126289486885,
-0.02992134913802147,
0.056703273206949234,
0.001364031806588173,
0.04889965057373047,
-0.014802792109549046,
-0.011791322380304337,
-0.0007447724347002804,
0.06936490535736084,
-0.06342089921236038,
0.04318998008966446,
0.024164220318198204,
0.01929001696407795,
-0.04602852463722229,
0.03918660432100296,
0.0427653044462204,
0.021629922091960907,
0.00524555891752243,
-0.03417341411113739,
-0.030116701498627663,
0.0126082394272089,
0.025377413257956505,
0.05127990245819092,
-0.05004856362938881,
0.03826676681637764,
0.023293640464544296,
0.042142439633607864,
0.004323259461671114,
0.02961094304919243,
-0.05445864051580429,
-0.026577455922961235,
0.0196694303303957,
0.027406036853790283,
0.040109917521476746,
0.015444827266037464,
0.03012106753885746,
0.018511103466153145,
0.013072440400719643,
-0.022528158500790596,
-0.015949906781315804,
0.000029161328711779788,
-0.03263842687010765,
0.0012405837187543511,
0.014183185994625092,
-0.037750501185655594,
0.02940896898508072,
-0.0329594649374485,
0.022330239415168762,
0.018558776006102562,
-0.03276906907558441,
0.008490048348903656,
-0.012061390094459057,
-0.0018789266468957067,
0.007419923320412636,
-0.028523314744234085,
-0.022992810234427452,
0.0004291240475140512,
0.034147508442401886,
-0.018203169107437134,
0.004771486856043339,
-0.04641202464699745,
0.002088455716148019,
-0.006763167679309845,
-0.013307317160069942,
0.03387703746557236,
0.005285679362714291,
-0.0018435813253745437,
-0.045873310416936874,
0.008287953212857246,
0.027521247044205666,
-0.03413202241063118,
0.004762338008731604,
-0.006210279650986195,
-0.024528006091713905,
0.02715536579489708,
-0.03675365075469017,
-0.017020706087350845,
0.0319816954433918,
0.009930216707289219,
0.01867786981165409,
0.024431005120277405,
-0.016675302758812904,
-0.014603500254452229,
0.01826537773013115,
-0.023444492369890213,
0.013707793317735195,
-0.0374738872051239,
0.0015017969999462366,
0.06602150946855545,
0.024465439841151237,
-0.055079180747270584,
0.003412464866414666,
-0.01582520268857479,
-0.014196950942277908,
-0.04534674063324928,
-0.011628232896327972,
0.06287962198257446,
-0.01921244151890278,
0.022464986890554428,
0.04844934865832329,
-0.028032148256897926,
0.00772705115377903,
-0.061199530959129333,
-0.021664032712578773,
-0.001037031877785921,
-0.02699895389378071,
0.02959451638162136,
-0.013047569431364536,
-0.005531294271349907,
0.088907390832901,
0.03982144966721535,
-0.011996444314718246,
-0.053378377109766006,
-0.002168542006984353,
0.003675372339785099,
-0.012715192511677742,
0.0301097109913826,
0.0018404033035039902,
-0.04835042729973793,
0.013690929859876633,
0.015883304178714752,
0.04245371371507645,
0.003910315688699484,
-0.010927028954029083,
0.005853990558534861,
0.015692774206399918,
0.010878785513341427,
0.0035764987114816904,
0.03774334490299225,
0.01848599687218666,
-0.028341257944703102,
-0.02003602683544159,
0.035006675869226456,
0.030332131311297417,
0.037184394896030426,
-0.04670026898384094,
0.047089964151382446,
-0.010534447617828846,
0.03828204423189163,
-0.004693185444921255,
0.02173028513789177,
0.000023909888113848865,
-0.00021961801394354552,
-0.03671613708138466,
0.020719535648822784,
0.04247521981596947,
-0.01045655645430088,
0.01233708206564188,
0.019222112372517586,
-0.00963733159005642,
-0.017760230228304863,
0.01764019951224327,
0.009994015097618103,
0.005493117496371269,
0.01690475083887577,
0.002519577741622925,
-0.06275336444377899,
0.021950101479887962,
0.0027637488674372435,
0.04363188520073891,
-0.024336205795407295,
-0.02517879568040371,
0.00986266415566206,
-0.062031377106904984,
-0.0092957504093647,
-0.026203753426671028,
0.044306471943855286,
-0.004314215388149023,
0.01553958561271429,
-0.011216385290026665,
-0.019961493089795113,
0.029325243085622787,
0.010812169872224331,
-0.0666726604104042,
-0.027858028188347816,
-0.0407380685210228,
0.01780889742076397,
-0.008394882082939148,
-0.0031663794070482254,
-0.03842600807547569,
0.0007441065390594304,
-0.03525877371430397,
0.032493505626916885,
-0.015091060660779476,
-0.06453421711921692,
-0.00189468904864043,
-0.05267220735549927,
-0.014869020320475101,
-0.02675057202577591,
0.03011198528110981,
-0.006415881682187319,
-0.058198969811201096,
0.03966452181339264,
0.02701539173722267,
-0.030051862820982933,
0.021408267319202423,
-0.009318867698311806,
0.05446925386786461,
0.0036521372385323048,
0.04581853002309799,
-0.014510663226246834,
0.03392811492085457,
-0.018814662471413612,
-0.004446092527359724,
-0.04782579466700554,
0.048029374331235886,
0.014902341179549694,
-0.020711177960038185,
-0.00595075124874711,
-0.04185561090707779,
0.011617657728493214,
-0.0021184401120990515,
0.06383547931909561,
-0.0004541183006949723,
0.02233979105949402,
0.04721013084053993,
0.017983747646212578,
-0.026734674349427223,
0.040210261940956116,
0.06323888897895813,
0.01036845427006483,
-0.014875105582177639,
-0.03932470455765724,
-0.010158941149711609,
-0.020364131778478622,
0.013002823106944561,
-0.0231137927621603,
-0.03640159219503403,
-0.02315567433834076,
0.020660461857914925,
0.017398947849869728,
0.024876683950424194,
-0.002985832979902625,
-0.01564873568713665,
0.009920117445290089,
0.022883504629135132,
-0.07754478603601456,
0.0062699830159544945,
0.0069868480786681175,
-0.009274817071855068,
0.04088940471410751,
0.03925925865769386,
0.004695212934166193,
-0.060327984392642975,
0.015773359686136246,
0.0240566935390234,
-0.018215816468000412,
-0.007379025220870972,
0.004809491336345673,
-0.015948908403515816,
-0.01081428024917841,
0.056040603667497635,
-0.02493906393647194,
0.006513927597552538,
-0.014819255098700523,
-0.030964452773332596,
-0.005075003020465374,
-0.014531424269080162,
0.028137439861893654,
0.0016225596191361547,
0.0024716935586184263,
-0.0061822435818612576,
-0.010439128614962101,
-0.012579462490975857,
-0.026078443974256516,
0.05215379595756531,
0.015476723201572895,
0.06915590912103653,
0.04435962811112404,
0.013553095050156116,
0.034380458295345306,
0.006488461513072252,
-0.033381856977939606,
-0.06346601247787476,
0.011943171732127666,
-0.0016279096016660333,
0.026373105123639107,
-0.00047344109043478966,
-0.04628939554095268,
-0.02281961590051651,
0.01989380456507206,
0.006712971720844507,
-0.0014125836314633489,
0.03574690222740173,
0.016414979472756386,
0.015622777864336967,
0.03182996064424515,
0.01679360307753086,
0.03274745121598244,
0.08536621928215027,
0.011914940550923347,
-0.038824617862701416,
-0.03941715508699417,
0.042597170919179916,
-0.06643284112215042,
-0.03136174753308296,
-0.03806477412581444,
0.05145322158932686,
-0.044069189578294754,
0.01724758930504322,
-0.003897610120475292,
0.029638251289725304,
0.012382217682898045,
-0.02860151045024395,
-0.02863364666700363,
0.03865804895758629,
-0.0015232403529807925,
0.014672452583909035,
0.03601584956049919,
0.041519299149513245,
0.01200023666024208,
-0.0066698514856398106,
-0.005600339733064175,
-0.0131582822650671,
-0.0065409839153289795,
0.03445480763912201,
0.005595863331109285,
0.00009574093564879149,
-0.012629884295165539,
0.0029114498756825924,
-0.006457050330936909,
-0.036538366228342056,
0.043759364634752274,
-0.013167654164135456,
0.0008838172070682049,
0.02826569229364395,
-0.08407729119062424,
-0.03593673184514046,
0.04500722512602806,
0.00037375782267190516,
0.02598431706428528,
-0.05873286351561546,
0.04216916486620903,
-0.013001298531889915,
0.008896419778466225,
-0.10722505301237106,
-0.027264200150966644,
0.03493523225188255,
0.03083331137895584,
0.004054701887071133,
-0.015764305368065834,
-0.032423488795757294,
-0.010756546631455421,
0.01564587838947773,
0.010370071977376938,
0.02437557838857174,
0.02800004929304123,
-0.02331285923719406,
0.017724329605698586,
0.03835222125053406,
0.038938336074352264,
0.020338935777544975,
-0.0072733378037810326,
0.00005553907249122858,
-0.016226062551140785,
0.009195586666464806,
0.00037022342439740896,
0.06956412643194199,
-0.031820617616176605,
-0.017245832830667496,
-0.03150494769215584,
0.006883762311190367,
0.02202172763645649,
-0.049504831433296204,
0.01202222891151905,
0.022538302466273308,
-0.02204919420182705,
0.006758681032806635,
-0.011376486159861088,
-0.008876784704625607,
-0.012376743368804455,
-0.01459974143654108,
0.0035845893435180187,
-0.005178471561521292,
-0.014860086143016815,
-0.07109707593917847,
-0.0008469289750792086,
0.004801650531589985,
-0.018142350018024445,
-0.006978504825383425,
0.061735089868307114,
0.0212056003510952,
-0.06075924262404442,
0.006402310915291309,
-0.008965055458247662,
0.007536417804658413,
-0.028981491923332214,
0.01703881099820137,
-0.0167094599455595,
-0.015092583373188972,
-0.0473419651389122,
-0.06601520627737045,
-0.010656083934009075,
0.04605736956000328,
0.01703953929245472,
0.017177393659949303,
0.04280918464064598,
0.03039523772895336,
-0.004856863059103489,
-0.016175154596567154,
-0.030778707936406136,
-0.009184589609503746,
-0.003652540734037757,
0.0037349441554397345,
0.053495582193136215,
-0.035294901579618454,
0.02287052385509014,
0.034898847341537476,
0.04673565551638603,
0.026127997785806656,
0.007891419343650341,
0.032001789659261703,
0.026367513462901115,
0.04624688997864723,
0.02209721878170967,
-0.035632673650979996,
0.06969752907752991,
-0.04506630823016167,
0.03598354384303093,
0.014787407591938972,
-0.053861353546381,
0.03696488216519356,
0.016983844339847565,
0.010012275539338589,
-0.03010864555835724,
-0.035635292530059814,
-0.036248281598091125,
0.051931001245975494,
0.026719320565462112,
0.030185259878635406,
0.02534506842494011,
0.02885606698691845,
0.02445119246840477,
0.03701844811439514,
-0.023181473836302757,
-0.0035262182354927063,
-0.07358106225728989,
-0.05051731318235397,
-0.040271032601594925,
-0.06262952834367752,
-0.01438034325838089,
0.021048108115792274,
-0.050483569502830505,
-0.01439204066991806,
-0.021742161363363266,
-0.017129959538578987,
0.007209882140159607,
0.027836257591843605,
-0.009399740025401115,
0.0401315912604332,
-0.000901228457223624,
0.016171647235751152,
-0.020144397392868996,
-0.003362151561304927,
0.1309380680322647,
0.05731043964624405,
0.03739570453763008,
-0.06720716506242752,
-0.003765905974432826,
0.0006443411693908274,
-0.02853185124695301,
-0.009142114780843258,
0.005579906515777111,
-0.009853756055235863,
0.013908986933529377,
-0.023741140961647034,
0.07263164222240448,
0.005510346964001656,
0.0006016420666128397,
0.04175037890672684,
-0.005204946268349886,
-0.035086847841739655,
0.023071730509400368,
0.03765086084604263,
0.016607917845249176,
0.022363409399986267,
-0.03744255378842354,
0.03160936385393143,
-0.031692150980234146,
0.01493316050618887,
-0.029625263065099716,
-0.04598607122898102,
0.0027363495901226997,
0.03873606398701668,
0.01369756180793047,
-0.005667698569595814,
0.010245735757052898,
-0.0045644319616258144,
-0.05148607864975929,
-0.002799560781568289,
-0.004197743255645037,
0.02024388685822487,
0.00788953434675932,
0.06035400927066803,
0.017046811059117317,
-0.011642695404589176,
0.02753378637135029,
-0.021366020664572716,
-0.028218073770403862,
-0.036269411444664,
-0.04600962623953819,
0.0018927134806290269,
-0.036455366760492325,
-0.012102726846933365,
-0.0020258959848433733,
-0.0016516674077138305,
0.020367693156003952,
-0.058812644332647324,
-0.0494927354156971,
-0.018056470900774002,
0.02614663355052471,
-0.037545766681432724,
-0.01670060120522976,
0.0009867813205346465,
0.008602808229625225,
-0.011267947033047676,
-0.009029843844473362,
-0.03930012136697769,
-0.03191422298550606,
-0.004749279469251633,
-0.01637563295662403,
0.041802000254392624,
0.001773540978319943,
-0.03512386977672577,
0.01925474964082241,
-0.026548046618700027,
-0.06375151872634888,
-0.060847580432891846,
-0.019110914319753647,
0.04573819041252136,
0.03736463561654091,
0.02351289615035057,
-0.030841022729873657,
-0.029704170301556587,
-0.06028971076011658,
0.012164833024144173,
0.0005425105337053537,
0.009941632859408855,
0.000056990851589944214,
-0.02098764479160309,
0.021375037729740143,
0.05035813897848129,
-0.027669236063957214,
0.03257023170590401,
-0.02149469591677189,
0.018347272649407387,
-0.012094296514987946,
-0.02125818282365799,
-0.0299529992043972,
-0.017918912693858147,
-0.047207314521074295,
0.026693718507885933,
-0.02379162237048149,
0.007816464640200138,
0.02056127041578293,
0.019137267023324966,
-0.013772332109510899,
0.04910517856478691,
-0.05835050716996193,
0.0037421996239572763,
0.019741274416446686,
-0.04774905741214752,
0.013492578640580177,
0.025586480274796486,
0.030773872509598732,
-0.04754907265305519,
-0.059825122356414795,
-0.050734855234622955,
-0.009926757775247097,
-0.004894948564469814,
0.014174943789839745,
-0.060183387249708176,
-0.024410126730799675,
-0.02117777056992054,
-0.0018708077259361744,
-0.07129819691181183,
-0.012892171740531921,
-0.017755821347236633,
0.0021558967418968678,
0.01712743006646633,
0.0037048370577394962,
-0.014883930794894695,
-0.008006857708096504,
-0.03287390246987343,
-0.01708424650132656,
0.02322782576084137,
0.006777874659746885,
-0.040001802146434784,
-0.009210215881466866,
0.030510082840919495,
0.0017116707749664783,
0.04962622746825218,
-0.03156716749072075,
-0.027946095913648605,
-0.003199468832463026,
-0.040012989193201065,
-0.05357906222343445,
0.006206657737493515,
-0.031444232910871506,
0.009834318421781063,
0.03468814119696617,
-0.010115723125636578,
-0.007636365480720997,
0.058804117143154144,
-0.0013511269353330135,
-0.0019467928213998675,
0.006061454303562641,
-0.002428949810564518,
0.03801852464675903,
-0.003522085025906563,
0.0010991217568516731,
-0.004424029495567083,
-0.027349287644028664,
-0.0002521442074794322,
0.015254710800945759,
0.010760613717138767,
-0.03861505538225174,
0.01557787973433733,
-0.008467035368084908,
0.022218886762857437,
0.05162661150097847,
0.020581712946295738,
0.01338515616953373,
0.02964950166642666,
-0.03029189631342888,
0.038755208253860474,
0.055744633078575134,
0.03174441307783127,
-0.06660505384206772,
0.010702956467866898,
0.0027247220277786255,
0.019080273807048798,
0.00837851781398058,
-0.05972158536314964,
-0.00893437396734953,
0.028516333550214767,
-0.08940687030553818,
0.013955669477581978,
0.0070913927629590034,
0.010955828242003918,
-0.039462294429540634,
-0.013107383623719215,
-0.03075222484767437,
0.022568684071302414,
0.05896139144897461,
0.04774647206068039,
0.008530902676284313,
0.01389011088758707,
-0.017535191029310226,
0.015438762493431568,
-0.008211871609091759,
0.021702373400330544,
-0.022809820249676704,
0.017752980813384056,
0.02052745781838894,
-0.01553115900605917,
-0.0235111266374588,
0.014792578294873238,
-0.012815844267606735,
-0.018998991698026657,
-0.01412378903478384,
0.006898338440805674,
0.0015953467227518559,
0.05171041563153267,
0.0042707957327365875,
0.010717405937612057,
-0.0013170874444767833,
-0.01838497444987297,
-0.016087008640170097,
0.010518678463995457,
0.006396736484020948,
0.018657004460692406,
0.05000467598438263,
-0.02262553945183754,
-0.03073718212544918,
0.013793285936117172,
-0.0037747800815850496,
-0.0059308516792953014,
-0.007417722605168819,
-0.0030052263755351305,
0.018053382635116577,
-0.010763728991150856,
0.009800918400287628,
-0.026056068018078804,
-0.012677766382694244,
-0.0016326974146068096,
0.01646997407078743,
0.01007589790970087,
0.022009754553437233,
-0.019656434655189514,
-0.06370840966701508,
0.021384932100772858,
0.02706270106136799,
-0.02829444780945778,
-0.06391452252864838,
-0.022819753736257553,
0.008647946640849113,
0.0064241839572787285,
0.004150897264480591,
-0.028323890641331673,
-0.018874533474445343,
0.025175495073199272,
-0.006221003830432892,
0.01101586502045393,
-0.01397187914699316,
-0.015025843866169453,
-0.025580571964383125,
-0.06529385596513748,
0.04469073563814163,
-0.003659170586615801,
-0.012818978168070316,
-0.0006197034381330013,
-0.0025177092757076025,
0.029599981382489204,
0.0036225232761353254,
0.042913757264614105,
-0.024280637502670288,
0.004606050904840231,
0.017612215131521225,
-0.010740604251623154,
0.03178723528981209,
-0.02127513475716114,
0.0021458810660988092,
0.02695409208536148,
-0.03717450425028801,
0.010156206786632538,
0.010004259645938873,
0.0022850886452943087,
0.0007061545038595796,
0.0005392066668719053,
-0.013284425251185894,
-0.0312613919377327,
-0.020086735486984253,
-0.0679442435503006,
0.05288439989089966,
0.03437518700957298,
-0.03944559022784233,
0.076473169028759,
-0.008471568115055561,
-0.003252242226153612,
-0.040395237505435944,
-0.030100196599960327,
-0.019602090120315552,
0.025386370718479156,
-0.06868285685777664,
-0.03488725423812866,
-0.006552211008965969,
0.0344899520277977,
0.006882918067276478,
0.00037258106749504805,
-0.018943635746836662,
0.05543911084532738,
-0.032158657908439636,
-0.060024477541446686,
0.03388563543558121,
0.007885034196078777,
0.04601765796542168,
-0.01564236357808113,
0.0013746371259912848,
0.0308558139950037,
0.02952619269490242,
0.01714949496090412,
0.007128747180104256,
-0.002344683976843953,
-0.0005513541982509196,
-0.01402414869517088,
0.002935169730335474,
-0.019735941663384438,
0.01751163974404335,
0.05344638600945473,
0.01487767230719328,
-0.024828847497701645,
-0.0009354974026791751,
0.05436313897371292,
-0.0018884586170315742,
0.005068799015134573,
-0.0016885430086404085,
-0.038965608924627304,
0.08155320584774017,
-0.0217373576015234,
0.007131104823201895,
-0.03086789697408676,
0.014611908234655857,
0.017847727984189987,
-0.006571489851921797,
0.015051508322358131,
0.0076558771543204784,
-0.02479124255478382,
-0.02926037646830082,
-0.0047075869515538216,
0.03153499588370323,
0.03354845941066742,
-0.07122910767793655,
0.002028860617429018,
-0.0011032689362764359,
0.011337213218212128,
-0.03168901801109314,
0.003925713244825602,
-0.005017250310629606,
0.019701307639479637,
0.05725787580013275,
0.03193041309714317,
0.04902615025639534,
-0.032060783356428146,
-0.010564620606601238,
-0.025125013664364815,
0.05122355371713638,
-0.05956881120800972,
-0.020829301327466965,
-0.037386827170848846,
0.01569240726530552,
0.004174476023763418,
0.046785056591033936
] |
<p>So again I have two equations:</p>
<p>$$K= \frac{1}{2} m v^2 + \frac{1}{2} I \omega^2$$</p>
<p>And</p>
<p>$$K_w = \frac{1}{2} I \omega^2 $$</p>
<p>What's the difference between these two? Thanks.</p>
| 10,704 |
[
-0.013713099993765354,
-0.01747850887477398,
-0.009049327112734318,
-0.01653500273823738,
0.024417592212557793,
-0.013849436305463314,
-0.03500733524560928,
-0.031136581674218178,
0.028459904715418816,
-0.021169764921069145,
0.025202583521604538,
0.05184999853372574,
0.06655705720186234,
0.012750617228448391,
-0.002878532512113452,
-0.006992388982325792,
-0.005664841737598181,
-0.020358432084321976,
0.03112226165831089,
-0.010851084254682064,
-0.01310000754892826,
-0.018070079386234283,
0.0325050912797451,
-0.008115116506814957,
-0.03510832414031029,
0.03285064920783043,
0.04321566969156265,
-0.005139336921274662,
0.022972162812948227,
-0.02029559016227722,
0.001045439625158906,
-0.02187473513185978,
-0.008460750803351402,
0.030794396996498108,
-0.012569156475365162,
0.02881377376616001,
-0.048696137964725494,
-0.03402380645275116,
-0.010469064116477966,
0.015770329162478447,
-0.007998216897249222,
0.03137775883078575,
-0.004040096420794725,
0.034598078578710556,
-0.002450851257890463,
0.02874959446489811,
0.01933315396308899,
-0.045142773538827896,
0.016747260466217995,
-0.03640003129839897,
0.04188047721982002,
0.008615046739578247,
0.032125428318977356,
0.0473129004240036,
0.00863718707114458,
0.006779943127185106,
0.0667504295706749,
0.06877798587083817,
0.009187420830130577,
-0.04595554247498512,
0.011834969744086266,
0.027019565925002098,
-0.013312483206391335,
0.004026081878691912,
0.005861892830580473,
0.05529524385929108,
-0.002582297194749117,
-0.014537099748849869,
0.02125883288681507,
0.016689805313944817,
0.04169883579015732,
0.00038597724051214755,
0.04166773334145546,
-0.02649364434182644,
0.01376338116824627,
-0.01708417385816574,
0.01042489055544138,
0.026832494884729385,
0.01492636650800705,
0.012239101342856884,
0.03249913454055786,
-0.02312091924250126,
0.01776830665767193,
0.017656894400715828,
0.0013781423913314939,
-0.015724102035164833,
0.0672137513756752,
0.022546103224158287,
-0.001453827484510839,
0.03213917464017868,
-0.014190929010510445,
0.03541753813624382,
0.022273248061537743,
-0.002386135281994939,
0.028071580454707146,
0.020800430327653885,
0.0073113832622766495,
0.03946857899427414,
-0.005366765893995762,
0.0013161289971321821,
0.02621627412736416,
-0.0377751961350441,
-0.008866810239851475,
0.06693190336227417,
-0.020572224631905556,
-0.0013505556853488088,
-0.03706660866737366,
0.025051183998584747,
-0.04640475660562515,
-0.026298729702830315,
-0.03579626604914665,
0.013358771800994873,
0.006166073959320784,
0.021800074726343155,
0.0014958836836740375,
-0.03861020505428314,
-0.026901433244347572,
-0.031148115172982216,
0.04600510001182556,
0.06571647524833679,
0.0682619959115982,
-0.026885271072387695,
0.0072794645093381405,
-0.006033469457179308,
-0.06401806324720383,
-0.006796801462769508,
0.049847666174173355,
0.004896513652056456,
-0.020357714965939522,
0.020565196871757507,
-0.01065222267061472,
0.0221539493650198,
0.020055361092090607,
-0.005585052073001862,
0.035535890609025955,
-0.011290080845355988,
-0.07737229019403458,
-0.0636288970708847,
0.05149901658296585,
0.0041172015480697155,
0.011204998008906841,
-0.07337301224470139,
0.015032772906124592,
0.015390207059681416,
0.1000218465924263,
0.01624869555234909,
-0.02825402282178402,
-0.00006108447996666655,
0.03807758539915085,
0.025956816971302032,
-0.05370613560080528,
-0.013379846699535847,
-0.00709184817969799,
0.00781689491122961,
0.03963372856378555,
-0.044809721410274506,
0.00333069427870214,
0.027331745252013206,
-0.01849512942135334,
-0.0010388554073870182,
0.05282970517873764,
0.010822536423802376,
-0.01588297262787819,
0.01626000367105007,
-0.002560366177931428,
-0.01970045641064644,
0.061852745711803436,
0.034981466829776764,
0.037111546844244,
0.034853577613830566,
0.03265466168522835,
0.01737057790160179,
-0.03008917160332203,
-0.012832658365368843,
0.053210142999887466,
-0.0014774134615436196,
-0.0006438339478336275,
-0.00020121624402236193,
0.049787890166044235,
0.008309820666909218,
-0.03773247078061104,
-0.059736188501119614,
0.034711774438619614,
0.023873187601566315,
0.0040954346768558025,
0.05347781628370285,
-0.00538895558565855,
0.040660008788108826,
-0.024197036400437355,
-0.01360815018415451,
-0.013231773860752583,
-0.03188258036971092,
0.02977200411260128,
-0.019449343904852867,
-0.008387536741793156,
0.00792760495096445,
-0.0027371812611818314,
0.004201054107397795,
-0.02517937496304512,
-0.029628099873661995,
0.013017947785556316,
0.037513718008995056,
0.0001233790535479784,
-0.054084401577711105,
-0.009107998572289944,
0.06786775588989258,
0.021858835592865944,
0.009798385202884674,
0.05163947865366936,
-0.023233920335769653,
0.004584875423461199,
0.01843087188899517,
-0.02622002176940441,
0.018782319501042366,
-0.003626299789175391,
-0.009226367808878422,
0.03047659434378147,
0.008081444539129734,
0.005872394423931837,
0.01975972391664982,
-0.05009676143527031,
0.06184401363134384,
0.07517822086811066,
0.008306407369673252,
0.004413679242134094,
0.02258114702999592,
-0.02382725477218628,
0.05167791247367859,
-0.01510196179151535,
-0.01690050959587097,
-0.03846227005124092,
-0.007203813176602125,
0.03723491355776787,
-0.02572028711438179,
-0.06010326370596886,
0.02643403224647045,
0.041409336030483246,
0.028280066326260567,
0.026268618181347847,
-0.03015126660466194,
0.0207853764295578,
-0.038370952010154724,
0.018479058519005775,
0.029411422088742256,
0.0009248965652659535,
0.02422376535832882,
0.03703257068991661,
-0.0037787649780511856,
0.04496625438332558,
-0.06334348022937775,
-0.01955576241016388,
0.05689790099859238,
-0.02447408065199852,
-0.014944330789148808,
-0.0009200515924021602,
-0.021015547215938568,
0.023443765938282013,
-0.033625006675720215,
-0.011268408969044685,
0.05627710744738579,
0.002424853388220072,
-0.013129748404026031,
0.0018235980533063412,
0.020331144332885742,
0.021541282534599304,
0.0040122102946043015,
-0.010571740567684174,
-0.012216290459036827,
0.029415810480713844,
-0.005336159840226173,
-0.019842583686113358,
0.008145480416715145,
-0.03559889644384384,
-0.0066511076875030994,
0.012927783653140068,
0.021342206746339798,
-0.011941022239625454,
0.04864201322197914,
0.0019492678111419082,
-0.04337995871901512,
-0.006476271897554398,
-0.04526127874851227,
0.0006342375418171287,
-0.000011679238923534285,
-0.035237688571214676,
0.03508733585476875,
-0.03837232291698456,
-0.01620926894247532,
0.029404208064079285,
0.021274566650390625,
-0.012276665307581425,
0.010787153616547585,
-0.011331447400152683,
-0.05095232278108597,
-0.013095645233988762,
-0.029863841831684113,
0.0649789571762085,
-0.0016575218178331852,
-0.019846074283123016,
0.057937417179346085,
-0.0006411101785488427,
-0.02868529036641121,
-0.004677142016589642,
-0.042742129415273666,
-0.03403245657682419,
-0.04662415757775307,
-0.031269483268260956,
0.02881544642150402,
-0.029060302302241325,
-0.019888460636138916,
0.020477278158068657,
-0.04685816168785095,
0.0016845677746459842,
-0.0425923727452755,
-0.05474650859832764,
0.01343332976102829,
-0.028471287339925766,
0.048170462250709534,
-0.00599279860034585,
-0.030231153592467308,
0.07510438561439514,
0.04873545467853546,
-0.004636431112885475,
-0.02002791315317154,
0.023777373135089874,
-0.03513934463262558,
-0.0482684001326561,
-0.016418179497122765,
0.017539028078317642,
-0.031022990122437477,
0.03975651040673256,
-0.0023377109318971634,
0.01957346312701702,
0.044111017137765884,
-0.018220335245132446,
-0.017361648380756378,
0.032196756452322006,
0.003937315661460161,
0.002340370789170265,
0.06484345346689224,
0.00666740583255887,
-0.02242937497794628,
-0.009236572310328484,
0.006433817092329264,
0.010132454335689545,
0.027599722146987915,
-0.04622508957982063,
0.024304132908582687,
0.016605084761977196,
0.014979596249759197,
-0.05623161420226097,
0.036291539669036865,
0.013703077100217342,
-0.012099036946892738,
-0.028907498344779015,
-0.00872268620878458,
0.0546921081840992,
-0.04412896931171417,
0.008588511496782303,
0.011198067106306553,
0.01082741841673851,
-0.009652797132730484,
0.006308059673756361,
-0.023501280695199966,
0.00861795712262392,
0.021777978166937828,
-0.010824749246239662,
-0.004663390107452869,
0.06035204604268074,
0.013288125395774841,
0.023594887927174568,
0.008707289583981037,
-0.05689755454659462,
-0.017870156094431877,
-0.07049049437046051,
-0.028916196897625923,
-0.017056025564670563,
0.07693397998809814,
0.005987827200442553,
0.07869666069746017,
0.02631983906030655,
-0.0035483185201883316,
0.011572718620300293,
0.0069585335440933704,
-0.044276341795921326,
0.016497761011123657,
-0.037493348121643066,
-0.039696428924798965,
0.03028683364391327,
-0.03566892817616463,
-0.03637702390551567,
-0.05068005993962288,
-0.0471050851047039,
0.008729169145226479,
0.0003469745279289782,
-0.0681442990899086,
0.05169715732336044,
-0.04607003182172775,
-0.022467464208602905,
0.0024520824663341045,
0.006285248324275017,
0.0390457808971405,
-0.02672221139073372,
0.016144342720508575,
0.07454563677310944,
-0.037079181522130966,
0.018405644223093987,
-0.022988881915807724,
-0.0013477763859555125,
0.03592609986662865,
0.030587082728743553,
0.015376213937997818,
-0.0004440931952558458,
-0.018822260200977325,
0.002193269319832325,
0.02749636024236679,
0.029544612392783165,
0.013465873897075653,
0.018043244257569313,
-0.04314086586236954,
-0.03875189647078514,
-0.012493252754211426,
-0.03984495624899864,
0.061197493225336075,
-0.010072839446365833,
-0.012753005139529705,
0.009766761213541031,
-0.010878155939280987,
0.006183077115565538,
0.019271906465291977,
0.05154074728488922,
-0.015591628849506378,
-0.005624379031360149,
-0.014470398426055908,
0.00670625688508153,
-0.006704603787511587,
-0.04408017918467522,
0.006439873017370701,
-0.016461167484521866,
0.011329972185194492,
-0.024724891409277916,
0.02260308898985386,
-0.00017139366536866874,
-0.007334117311984301,
0.02707500569522381,
0.007255883887410164,
-0.018471313640475273,
-0.02301114983856678,
-0.04830172285437584,
-0.0036094109527766705,
0.04553868621587753,
0.04494311660528183,
-0.020390909165143967,
0.013253423385322094,
-0.06778618693351746,
-0.0077775511890649796,
0.030830958858132362,
-0.006332084536552429,
-0.013773557730019093,
-0.03139074891805649,
-0.07223126292228699,
-0.03807596489787102,
0.012475213967263699,
-0.04765269160270691,
0.05573011562228203,
0.037278007715940475,
0.024424923583865166,
0.0009322837577201426,
-0.009717884473502636,
-0.02241620421409607,
-0.01918826811015606,
0.0028742034919559956,
0.02310647815465927,
-0.01082611083984375,
0.01296947430819273,
0.005876720417290926,
0.0065522342920303345,
0.03898373618721962,
0.03694212809205055,
-0.002107083098962903,
-0.05421195924282074,
0.0016149827279150486,
0.018575424328446388,
-0.03683939203619957,
-0.05360780283808708,
-0.02274342253804207,
0.040743451565504074,
-0.006853953469544649,
0.01572095975279808,
-0.009030061773955822,
-0.05316369608044624,
0.04589167237281799,
-0.028150435537099838,
-0.017750073224306107,
-0.021078042685985565,
0.0105009526014328,
0.05164828151464462,
0.019455650821328163,
0.04508095607161522,
0.046696312725543976,
0.030496861785650253,
-0.039647091180086136,
-0.01947721838951111,
-0.0180450901389122,
0.020463235676288605,
-0.016574736684560776,
-0.021474197506904602,
-0.04230974242091179,
0.014609367586672306,
-0.019186627119779587,
0.01875637285411358,
0.002677438547834754,
0.020638860762119293,
-0.039431098848581314,
-0.057762086391448975,
0.005700962617993355,
0.03647477552294731,
0.03656003624200821,
-0.0011241494212299585,
0.016357073560357094,
0.01445873361080885,
-0.006344638764858246,
-0.05143774300813675,
0.04993173107504845,
-0.0021153478883206844,
-0.013067607767879963,
0.016278738155961037,
-0.011683942750096321,
0.004523042123764753,
-0.05765052139759064,
-0.022945772856473923,
0.04520686715841293,
-0.02509688027203083,
0.03156524896621704,
0.002026090631261468,
0.010668314062058926,
0.027663100510835648,
-0.04361860826611519,
-0.025132382288575172,
-0.0049908217042684555,
-0.022374648600816727,
0.022152148187160492,
-0.014634898863732815,
0.02882990799844265,
0.04390115663409233,
0.01929776556789875,
-0.05309790000319481,
-0.05406288057565689,
0.012938401661813259,
-0.008639034815132618,
-0.01166989654302597,
0.020445741713047028,
0.002363326493650675,
-0.027990657836198807,
-0.028715042397379875,
0.02725863829255104,
0.04712746664881706,
-0.03658812865614891,
-0.045025963336229324,
-0.0035377175081521273,
0.0627882331609726,
0.025268791243433952,
0.04350888356566429,
-0.03356548026204109,
-0.008492291904985905,
-0.052367404103279114,
0.001025195699185133,
0.03772428631782532,
0.07238281518220901,
-0.0100918123498559,
-0.021030789241194725,
-0.03280864655971527,
-0.024398477748036385,
0.048811353743076324,
0.01544979214668274,
0.003934001550078392,
0.03349980339407921,
0.02479364164173603,
-0.007012725807726383,
-0.05179525539278984,
0.0033507896587252617,
-0.00961840059608221,
0.06318623572587967,
-0.005656218156218529,
-0.0034037986770272255,
-0.020247390493750572,
-0.038507454097270966,
-0.00701040867716074,
0.010600519366562366,
-0.0005891870823688805,
-0.01520527247339487,
0.056055910885334015,
-0.06577567011117935,
0.04153482988476753,
0.0006543447379954159,
0.00004358592923381366,
0.024819087237119675,
-0.019168196246027946,
-0.00458997767418623,
0.031114086508750916,
0.03412053734064102,
-0.018813282251358032,
-0.03253438323736191,
-0.053473517298698425,
0.01686841808259487,
0.08301979303359985,
-0.011928899213671684,
0.054531652480363846,
-0.00471319118514657,
0.0075829210691154,
0.03939872980117798,
-0.039874523878097534,
-0.014980782754719257,
0.019770361483097076,
-0.028374923393130302,
0.05112524703145027,
-0.02584570273756981,
-0.027856068685650826,
0.010279523208737373,
0.062036722898483276,
-0.031035086140036583,
-0.03343171253800392,
0.014893447048962116,
0.03179948404431343,
-0.041414111852645874,
0.01870499737560749,
-0.0340929850935936,
0.03728310018777847,
-0.011143618263304234,
0.05471598356962204,
-0.0391102097928524,
-0.0028623712714761496,
0.05851270258426666,
0.03605193272233009,
-0.03917651250958443,
-0.03776884451508522,
0.005539700388908386,
-0.031667910516262054,
0.015558053739368916,
0.032182708382606506,
-0.03463955596089363,
-0.019001536071300507,
-0.0011854968033730984,
0.05402284860610962,
0.0005318067269399762,
-0.007111521903425455,
-0.011135071516036987,
-0.03496333211660385,
-0.0073499553836882114,
-0.04178299754858017,
-0.08509157598018646,
0.022898336872458458,
0.002162812277674675,
-0.03256175294518471,
0.02513098157942295,
-0.03766212239861488,
0.02760782465338707,
0.013784293085336685,
-0.007225061301141977,
-0.0017007228452712297,
0.04321112483739853,
-0.015731744468212128,
0.0017666792264208198,
0.006225538440048695,
-0.006462478078901768,
0.10320048779249191,
0.056065741926431656,
0.015185992233455181,
-0.03235422074794769,
0.02634548395872116,
-0.010190317407250404,
0.041715241968631744,
-0.0330522283911705,
0.022240161895751953,
-0.05892739072442055,
0.02899574674665928,
0.02228640578687191,
-0.004476431757211685,
-0.021352047100663185,
0.04529886692762375,
0.012120489031076431,
-0.02356993779540062,
-0.04570174217224121,
0.0006281820824369788,
-0.006872348487377167,
-0.018763437867164612,
0.03792395070195198,
-0.005991175305098295,
0.0739443376660347,
-0.02356097102165222,
-0.020545104518532753,
-0.03368702530860901,
-0.03265523537993431,
0.05540720745921135,
0.009455382823944092,
-0.05058106780052185,
0.03666894882917404,
0.018099643290042877,
0.005891152657568455,
-0.024376871064305305,
0.056842681020498276,
0.02920822612941265,
-0.05323205143213272,
0.03842617943882942,
0.035221174359321594,
0.007654356770217419,
-0.021374044939875603,
0.03070109710097313,
-0.023303352296352386,
-0.07588854432106018,
0.02047024480998516,
-0.04635997116565704,
0.035742029547691345,
0.02354765683412552,
0.005008721724152565,
-0.027614571154117584,
-0.0014693245757371187,
-0.007392450701445341,
-0.03826666250824928,
-0.007070343010127544,
0.008223073557019234,
0.00598547700792551,
-0.01917113922536373,
-0.0037024314515292645,
-0.03857433423399925,
0.024035809561610222,
0.005012511741369963,
0.022192224860191345,
-0.005935791879892349,
0.008946939371526241,
-0.005863404832780361,
0.05101793631911278,
0.05606650188565254,
-0.023246172815561295,
-0.024858970195055008,
-0.018964692950248718,
0.005989523138850927,
-0.027173100039362907,
-0.03206610679626465,
-0.0030489990022033453,
0.03203531727194786,
0.03799547255039215,
0.004472306929528713,
-0.04472693055868149,
-0.029341816902160645,
-0.08247967809438705,
0.0022840125020593405,
0.035240646451711655,
-0.01814720779657364,
-0.027872879058122635,
0.032464805990457535,
-0.004705323837697506,
0.013590257614850998,
-0.005981761030852795,
0.019318044185638428,
0.030068883672356606,
0.02972566895186901,
-0.0028282771818339825,
-0.03869559243321419,
-0.06737638264894485,
0.0453592911362648,
-0.01652158796787262,
-0.0035529080778360367,
-0.03635222464799881,
0.009618310257792473,
0.0282205231487751,
0.006769636180251837,
0.008442013524472713,
0.017857346683740616,
-0.02256184071302414,
0.022712424397468567,
0.021573415026068687,
-0.03300139307975769,
0.007452497724443674,
0.02600378915667534,
0.01187724806368351,
0.015711503103375435,
-0.005336265545338392,
-0.002795096719637513,
0.006777915172278881,
-0.0256778784096241,
-0.029644835740327835,
0.00006076943827793002,
0.011464942246675491,
-0.0572393424808979,
0.028981858864426613,
-0.02814387157559395,
-0.02411200851202011,
-0.02220502682030201,
0.03473886474967003,
0.024002723395824432,
0.02536955662071705,
-0.03501252084970474,
0.02138669230043888,
-0.024186164140701294,
0.03011668473482132,
0.018961289897561073,
0.05113209784030914,
-0.009822681546211243,
0.0004785069904755801,
-0.006442947778850794,
-0.01594708487391472,
0.06379526853561401,
-0.025361279025673866,
-0.0021842976566404104,
0.014186638407409191,
-0.011424262076616287,
-0.035803526639938354,
0.04252368584275246,
0.005352288484573364,
0.028422320261597633,
0.01820092275738716,
-0.01963416114449501,
-0.035734545439481735,
0.09521300345659256,
-0.03976191580295563,
0.028533488512039185,
-0.013282914645969868,
-0.07249684631824493,
-0.04889998584985733,
-0.015727132558822632,
-0.00044282409362494946,
0.005670998245477676,
0.003303447039797902,
0.028182286769151688,
0.03090829588472843,
-0.05790281295776367,
-0.028899259865283966,
-0.01080465130507946,
0.0054289810359478,
-0.021325573325157166,
0.05919838696718216,
0.013915793038904667,
0.04176040366292,
0.022646872326731682,
-0.020947767421603203,
-0.007471106946468353,
-0.011466607451438904,
-0.0017532354686409235,
-0.07609143853187561,
-0.02182401344180107,
-0.009812620468437672,
0.011678467504680157,
0.041359078139066696,
-0.03798169642686844,
0.0015750129241496325,
0.03845834732055664,
-0.08632166683673859,
-0.0022091353312134743,
0.01196580845862627,
-0.007997402921319008,
-0.06975383311510086,
0.007413347251713276,
0.016261287033557892,
0.0322621688246727,
0.014276341535151005,
0.01094474084675312,
0.04109042137861252,
0.038145359605550766,
0.013646787963807583,
-0.011575400829315186,
0.01231734175235033,
0.052008405327796936,
-0.03345133736729622,
-0.030786331743001938,
0.01912417635321617,
-0.04423212260007858,
-0.030133748427033424,
0.0219626035541296,
-0.0272081159055233,
0.02369230054318905,
-0.015382181853055954,
0.02674042247235775,
-0.00855319108814001,
0.046562906354665756,
0.020228011533617973,
-0.0003265677369199693,
-0.0024685021489858627,
-0.007189610973000526,
0.01431986689567566,
-0.004423650912940502,
0.0009066140628419816,
-0.002377670956775546,
0.03900642693042755,
-0.04555074870586395,
-0.020617935806512833,
0.04986103996634483,
-0.02165469340980053,
-0.010270558297634125,
-0.02080599218606949,
-0.011255759745836258,
0.024840058758854866,
-0.03886350989341736,
0.03131048008799553,
-0.06421217322349548,
0.0004459430929273367,
0.017926516011357307,
-0.05353833734989166,
0.014908603392541409,
0.0025174361653625965,
0.0032754435669630766,
-0.0172555074095726,
-0.0221882201731205,
0.009248427115380764,
-0.002600315725430846,
-0.07299226522445679,
-0.031061945483088493,
0.001522417413070798,
0.03032226674258709,
0.0037558269686996937,
-0.031486887484788895,
-0.023660413920879364,
0.05045148357748985,
0.031371962279081345,
-0.010286259464919567,
-0.0017303685890510678,
-0.015357947908341885,
-0.05090999975800514,
-0.05951434001326561,
0.03515978157520294,
0.010387442074716091,
-0.07177585363388062,
0.01811886765062809,
-0.03720955178141594,
-0.00173638213891536,
0.014149384573101997,
0.04355509206652641,
0.014788370579481125,
-0.012265740893781185,
0.0018505557673051953,
-0.024092264473438263,
0.026054751127958298,
-0.049086350947618484,
-0.006501726806163788,
-0.017472540959715843,
-0.0130101153627038,
0.006212950684130192,
-0.014262594282627106,
0.001288541592657566,
0.02325150929391384,
0.053258102387189865,
-0.041231680661439896,
0.01749255508184433,
-0.010957770980894566,
-0.02428068034350872,
-0.02389002963900566,
-0.006714846007525921,
0.005241180770099163,
0.0651233047246933,
-0.03115384466946125,
0.016038578003644943,
0.01591227948665619,
-0.018719766288995743,
-0.008023545145988464,
0.05129976570606232,
-0.006257872562855482,
0.023528611287474632,
-0.02935328334569931,
-0.0453961007297039,
0.03910060226917267,
-0.04705731198191643,
-0.022506415843963623,
0.020461006090044975,
-0.06252657622098923,
-0.008779792115092278,
0.02158335968852043,
0.03471757844090462,
0.0199758168309927,
-0.0005153983365744352,
0.03334437683224678,
0.014038285240530968,
-0.057500362396240234,
0.03527053818106651,
0.04299931228160858,
0.03984787315130234,
0.0302877314388752,
-0.005084744654595852,
0.04647164046764374,
-0.008253434672951698,
0.016330815851688385,
-0.02354954369366169,
-0.02662871778011322,
-0.00640426529571414,
-0.040319353342056274,
0.003464309498667717,
-0.019239652901887894,
0.017972322180867195,
0.006812867242842913,
0.0120560172945261,
0.028303835541009903,
-0.04796312004327774,
-0.004858717322349548,
-0.02637460082769394,
0.020282942801713943,
-0.030466439202427864,
-0.013662893325090408,
-0.001661236397922039,
0.005742763634771109,
0.0099240243434906,
-0.017026349902153015,
0.024602632969617844,
-0.027272513136267662,
0.013506146147847176,
-0.04362758994102478,
0.019713686779141426,
-0.009899109601974487,
-0.016246994957327843,
-0.01925267092883587,
-0.02276979386806488,
-0.004282151814550161,
0.012938393279910088,
0.0612449124455452,
0.0285098347812891,
0.027429163455963135,
-0.03009854443371296,
-0.04175029322504997,
-0.025168564170598984,
0.030982552096247673,
-0.050316572189331055,
0.005197390913963318,
-0.01867595873773098,
-0.008545756340026855,
0.04795550927519798,
-0.01972680538892746
] |
<p>In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as
$$
\tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu \nu} = 0,
$$
transformed as 4-vector under the Lorentz transformation (case "c"). The authors proposed the next explanation: in case "b" they proved that an integral
$$
\tag 2 p^{\mu} = \int T^{\mu \nu}\,\mathrm{d}S_{\nu}
$$
doesn't depend on choise of the hypersurface, so without loss of generality they choosed one with $t = const$ with $p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r$. After that they considered two integrals $(2)$ with hypersurfaces $t = const, t' = const$, but the first has constant $t$ in one Lorentz frame, while the second has constant $t'$ in another frame. Relate to the first frame the $t'$-line of the second surface only has slope in $t-x$ diagram compare to $t$-line. So they added timelike hypersurfaces on infinity and then they got closed surface
$$
\oint T^{\mu \nu} \,\mathrm{d}S_{\nu}.
$$
By the Stokes theorem it is equal to
$$
\int \partial_{\mu}T^{\mu \nu}\,\mathrm{d}\Omega = 0,
$$
and by another side (I wrote it in the first frame)
$$
\int_{t = const} T_{\mu 0}\,\mathrm{d}^{3}\mathbf r - \int_{t'} T_{\mu \nu}\,\mathrm{d}S^{\nu} = 0.
$$
So
$$
\tag 3 \int_{t = const} T_{\mu 0}\,\mathrm{d}^{3}\mathbf r = \int_{t'} T_{\mu \nu}\,\mathrm{d}S^{\nu}.
$$
I don't understand how exactly they made a consequence that this directly leads to the 4-vector nature of $p^{\mu}$ definition given in $(1)$.</p>
<p>I know that in the second frame I also can rewrite the right side of $(3)$ in a form
$$
\int T_{\mu 0}\,\mathrm{d}^{3}\mathbf r.
$$
So may I write
\begin{split}
\int_{t'} T_{\mu \nu}\,\mathrm{d}S^{\nu}
&= \int_{t' = const}{\Lambda_{\mu}}^{\alpha}T_{\alpha \beta}'{\Lambda^{\beta}}_{\nu}{\Lambda^{\nu}}_{\gamma}\,\mathrm{d}S^{\gamma}{'} \\
&= {\Lambda_{\mu}}^{\alpha} \int_{t' = const} T_{\alpha 0 }'\,\mathrm{d}^{3}\mathbf r{'}\\
&={\Lambda_{\mu}}^{\alpha}\int_{t = const}T_{\alpha 0}'\,\mathrm{d}^{3}\mathbf r{'} \\
\Longrightarrow\quad p^{\mu} &= {\Lambda^{\mu}}_{\alpha}p^{\prime\alpha},
\end{split}
which completes the proof? Or the completion is another?</p>
| 10,705 |
[
0.014288806356489658,
-0.012773962691426277,
-0.0020140905398875475,
-0.011440797708928585,
0.0614856593310833,
0.02889172174036503,
-0.027722986415028572,
-0.012142837978899479,
-0.01692616380751133,
-0.014818785712122917,
0.013961663469672203,
0.01574370265007019,
0.05345219001173973,
-0.004738180432468653,
0.02447950467467308,
-0.001589820021763444,
-0.018630512058734894,
-0.004844681825488806,
-0.004948372952640057,
-0.06508028507232666,
0.024985341355204582,
0.0036752682644873857,
-0.007180820684880018,
-0.010953185148537159,
0.024702714756131172,
-0.011926465667784214,
-0.002726722275838256,
-0.04228759929537773,
-0.020554987713694572,
0.07104316353797913,
-0.007117248140275478,
-0.008147525601089,
-0.019885029643774033,
0.005558965727686882,
-0.023340635001659393,
-0.01440441980957985,
-0.023907871916890144,
-0.015715720131993294,
-0.010413482785224915,
0.03635448217391968,
-0.02154695801436901,
-0.00663014454767108,
-0.03038807585835457,
0.058649688959121704,
-0.01874503865838051,
0.016133390367031097,
0.009827809408307076,
0.027639197185635567,
0.07617408037185669,
-0.06360748410224915,
0.08146817237138748,
0.002262222347781062,
0.04330288991332054,
-0.020750293508172035,
-0.0008081603446044028,
0.006539118941873312,
0.061597030609846115,
0.05827547609806061,
-0.03214583173394203,
-0.047429367899894714,
-0.05968916788697243,
0.004741285927593708,
-0.009098763577640057,
-0.032253362238407135,
0.0029938411898911,
0.014762542210519314,
0.012801749631762505,
0.008585457690060139,
-0.012478334829211235,
-0.016687773168087006,
0.003499614307656884,
-0.010698448866605759,
0.012320226989686489,
0.017149366438388824,
0.004708380904048681,
0.025634994730353355,
0.005800818093121052,
-0.0208430178463459,
0.01693914830684662,
0.018216297030448914,
0.008329019881784916,
0.012759529985487461,
0.024750690907239914,
0.03505910560488701,
-0.004319007508456707,
0.00834785494953394,
0.017716899514198303,
0.016063570976257324,
-0.00979196559637785,
0.03629258647561073,
0.013567304238677025,
0.007414306979626417,
0.0282906387001276,
-0.056913603097200394,
-0.012014399282634258,
0.03933059796690941,
0.015187125653028488,
0.002512040315195918,
-0.053312044590711594,
-0.0004385105276014656,
-0.013575214892625809,
-0.010694951750338078,
-0.01568988896906376,
0.05416899546980858,
0.06699459999799728,
-0.010541455820202827,
-0.0060843550600111485,
0.02478804625570774,
-0.029178394004702568,
-0.020883439108729362,
-0.06524036079645157,
0.02067718841135502,
-0.03325911611318588,
-0.01641221158206463,
0.0013042871141806245,
-0.0603947639465332,
0.024019824340939522,
-0.0037737786769866943,
0.04632925987243652,
0.06988046318292618,
0.043579284101724625,
-0.01701693795621395,
-0.010649383068084717,
-0.007849340327084064,
-0.09594035148620605,
-0.007936812937259674,
0.04036295413970947,
-0.016544794663786888,
0.010755353607237339,
-0.026744095608592033,
0.033154793083667755,
0.025132957845926285,
-0.004915568977594376,
0.05012347921729088,
0.0016763954190537333,
-0.02005881816148758,
-0.08819875121116638,
-0.04753011837601662,
0.06796308606863022,
-0.01946050114929676,
-0.010301795788109303,
-0.060589294880628586,
-0.017656881362199783,
0.043152548372745514,
0.07930640876293182,
-0.004484166856855154,
0.005512524396181107,
-0.005905242636799812,
0.06274021416902542,
0.00477521400898695,
-0.03229712322354317,
0.000137060196720995,
-0.02150925062596798,
-0.03348654881119728,
-0.032975777983665466,
-0.06908310204744339,
0.004321413580328226,
0.027091236785054207,
-0.030095849186182022,
-0.031140414997935295,
0.09572155773639679,
-0.04035946726799011,
0.027925170958042145,
0.02953745238482952,
-0.017482783645391464,
-0.00014621386071667075,
0.014814266934990883,
0.004576197359710932,
0.013995863497257233,
0.039807699620723724,
0.007551699411123991,
0.00446469709277153,
-0.00999387912452221,
0.03511878848075867,
-0.001996340462937951,
-0.0617612823843956,
-0.004973446950316429,
0.028813045471906662,
-0.03249449282884598,
-0.019617091864347458,
0.011430216953158379,
-0.03129681199789047,
-0.0012641443172469735,
-0.023702790960669518,
-0.005012220703065395,
0.04933890327811241,
-0.012853996828198433,
0.0063886274583637714,
-0.008884992450475693,
-0.008622393943369389,
-0.012302171438932419,
-0.03981957212090492,
-0.004128617700189352,
0.015492006205022335,
-0.003223633160814643,
0.015745434910058975,
-0.041267938911914825,
0.021361323073506355,
-0.049629077315330505,
-0.02179153449833393,
0.00470678461715579,
0.07939937710762024,
-0.005654104519635439,
0.009809416718780994,
0.039158426225185394,
-0.006580412853509188,
0.027858473360538483,
-0.004412650130689144,
-0.005467056762427092,
0.0030850698240101337,
-0.005107066128402948,
0.03349393978714943,
0.009860909543931484,
0.04006679728627205,
-0.021454663947224617,
-0.027764569967985153,
-0.011453662067651749,
0.024049285799264908,
0.009696215391159058,
0.042283982038497925,
-0.0267099030315876,
0.01154702715575695,
0.035064294934272766,
0.02022327296435833,
-0.022967571392655373,
0.03374021127820015,
-0.02385932207107544,
0.04037538170814514,
-0.007386552169919014,
-0.010231982916593552,
-0.02712659351527691,
-0.05443112924695015,
0.013544121757149696,
0.06581374257802963,
-0.020897453650832176,
0.019202472642064095,
0.03688088804483414,
0.01956917718052864,
0.016981644555926323,
0.014858872629702091,
0.027522800490260124,
-0.06825386732816696,
0.017340386286377907,
0.010850584134459496,
0.01851867139339447,
0.019007358700037003,
-0.0007168134907260537,
-0.0003236100892536342,
0.0092426473274827,
-0.019984140992164612,
-0.02013522945344448,
-0.0016489960253238678,
-0.03969999775290489,
0.0037101381458342075,
-0.03016626462340355,
-0.004788204096257687,
0.025902174413204193,
0.018026161938905716,
0.028983479365706444,
0.07260679453611374,
0.012072077952325344,
-0.008355027064681053,
-0.06644035875797272,
-0.0017798356711864471,
0.029077917337417603,
-0.029029959812760353,
0.007544279098510742,
-0.03658963739871979,
-0.0035834629088640213,
-0.0483725406229496,
-0.018318643793463707,
-0.008638057857751846,
-0.026526685804128647,
-0.011343128979206085,
0.006059818901121616,
0.04141306132078171,
-0.012578317895531654,
0.00771755538880825,
-0.034112852066755295,
0.0024391082115471363,
0.05753752216696739,
0.03779781609773636,
-0.01175976824015379,
0.003933636471629143,
-0.09685834497213364,
0.005124880000948906,
-0.06839701533317566,
-0.030660677701234818,
0.06135386973619461,
0.0059611499309539795,
0.04186221584677696,
0.03279278427362442,
-0.0012973240809515119,
-0.0468907430768013,
-0.057151149958372116,
-0.016165640205144882,
-0.04361578822135925,
-0.020172379910945892,
0.018928496167063713,
0.030512545257806778,
0.0065173255279660225,
-0.041982222348451614,
0.022228946909308434,
-0.00732357008382678,
-0.08568332344293594,
-0.002244086004793644,
-0.023548796772956848,
-0.032425206154584885,
-0.003765454050153494,
0.05146326497197151,
0.017839273437857628,
-0.007013091817498207,
0.006751672364771366,
-0.03887474536895752,
-0.03784630075097084,
0.04239451512694359,
-0.037363070994615555,
0.03318517282605171,
0.015578429214656353,
-0.06999552249908447,
0.05597780644893646,
0.024190355092287064,
-0.016775110736489296,
-0.032462526112794876,
0.018956586718559265,
0.01145345252007246,
-0.014134854078292847,
-0.00983961671590805,
0.026094025000929832,
0.009772447869181633,
-0.0006815286469645798,
-0.0029678374994546175,
0.04100145027041435,
0.04407942295074463,
0.010080946609377861,
0.004384794272482395,
0.02952607162296772,
0.0041420552879571915,
0.010353774763643742,
-0.001244147657416761,
-0.0030234120786190033,
0.02487371116876602,
0.005795850418508053,
-0.0051511251367628574,
0.018150174990296364,
0.0026444015093147755,
-0.051298920065164566,
0.061979275196790695,
0.007789240684360266,
0.011893857270479202,
-0.004932286683470011,
0.02237963303923607,
-0.004414328373968601,
-0.04913049563765526,
-0.021110743284225464,
0.045241229236125946,
0.027007117867469788,
-0.03866828233003616,
0.01329890824854374,
0.037773631513118744,
0.005113794468343258,
0.00927886925637722,
-0.021106690168380737,
-0.011951921507716179,
-0.016751796007156372,
0.02796907164156437,
-0.03023446537554264,
-0.00952135119587183,
0.022637806832790375,
0.05141441151499748,
-0.006314422469586134,
0.02497229352593422,
-0.0004904809175059199,
-0.0253607090562582,
-0.041602857410907745,
-0.006696636788547039,
0.007206859067082405,
0.034871943295001984,
0.0022383006289601326,
0.0237981416285038,
0.015173543244600296,
0.014382204972207546,
-0.026387814432382584,
-0.010760195553302765,
-0.03436698392033577,
0.01969609223306179,
-0.030031919479370117,
-0.0285039059817791,
-0.000037236546631902456,
-0.022729944437742233,
0.009245083667337894,
-0.013570357114076614,
-0.009815875440835953,
-0.02301008254289627,
-0.031101014465093613,
-0.0707387924194336,
0.03118281625211239,
0.01031777635216713,
-0.06432070583105087,
-0.053403280675411224,
0.07513080537319183,
0.07062464952468872,
-0.011881176382303238,
0.041471559554338455,
0.022388821467757225,
-0.041782304644584656,
-0.01822666823863983,
0.02964337356388569,
0.008807839825749397,
0.008913512341678143,
-0.008634701371192932,
0.042420417070388794,
-0.005101739428937435,
-0.0015272954478859901,
-0.021043241024017334,
0.019882965832948685,
0.05677710473537445,
0.027722934260964394,
-0.03648494929075241,
-0.0434945747256279,
-0.019209841266274452,
-0.00029500454547815025,
-0.010151233524084091,
0.10086340457201004,
0.03252492845058441,
-0.01295445580035448,
0.018341505900025368,
-0.006395384203642607,
0.024032725021243095,
0.029355498030781746,
0.039369016885757446,
-0.012726460583508015,
0.012483776547014713,
-0.06483520567417145,
-0.03786317631602287,
-0.034995436668395996,
0.023921530693769455,
0.03774765506386757,
0.003918086178600788,
-0.04583153501152992,
-0.014920289628207684,
0.017666654661297798,
0.004650054033845663,
-0.0031583954114466906,
-0.009284870699048042,
0.00410697516053915,
-0.01168318185955286,
0.04301832988858223,
0.0126875014975667,
-0.02141401171684265,
0.02656497247517109,
0.027095220983028412,
0.006303530186414719,
-0.019585615023970604,
-0.04168703034520149,
-0.052083659917116165,
0.022577468305826187,
0.05083721503615379,
0.002894771983847022,
-0.027751140296459198,
-0.04659641161561012,
0.006462017074227333,
-0.011072511784732342,
-0.018649525940418243,
0.00813864916563034,
0.003650850849226117,
0.012858588248491287,
-0.036558449268341064,
-0.03952149674296379,
-0.010770145803689957,
0.03310392051935196,
-0.0045065730810165405,
-0.0007667993777431548,
-0.061664968729019165,
-0.014279892668128014,
-0.0010340468725189567,
0.04229859635233879,
0.00009725883137434721,
0.010753218084573746,
0.004374712239950895,
0.0066170599311590195,
-0.03197581321001053,
0.0276224035769701,
-0.0645844042301178,
-0.0709640309214592,
0.006140943616628647,
-0.013305839151144028,
-0.003266142448410392,
0.04569418355822563,
-0.014215853065252304,
-0.01950957253575325,
0.031746406108140945,
0.018901627510786057,
0.007590663153678179,
0.050602611154317856,
-0.03768051788210869,
0.0234542153775692,
0.015274647623300552,
-0.03631936013698578,
0.04401080310344696,
0.0008107182802632451,
0.006299639120697975,
-0.04859842732548714,
-0.02846231684088707,
0.05453774333000183,
-0.04251350462436676,
-0.005374515429139137,
-0.010549493134021759,
-0.03406864404678345,
-0.019512992352247238,
0.04161539301276207,
-0.015774283558130264,
-0.022996751591563225,
-0.016540929675102234,
-0.009385883808135986,
0.007773151621222496,
-0.0011944207362830639,
0.0355646088719368,
0.011234323494136333,
0.01578683592379093,
-0.007311795838177204,
0.008318718522787094,
0.020156599581241608,
0.029678381979465485,
-0.0293976292014122,
0.011320683173835278,
0.052529916167259216,
0.03544839844107628,
0.0352199487388134,
0.01711513288319111,
0.0013695217203348875,
-0.007841259241104126,
-0.01736874133348465,
0.022861216217279434,
0.025146977975964546,
-0.006112485658377409,
0.023244289681315422,
0.002991148503497243,
-0.031020864844322205,
-0.00897684134542942,
0.004927555564790964,
0.014465604908764362,
-0.07992641627788544,
0.0016649754252284765,
0.06353557854890823,
0.04314275458455086,
-0.08044913411140442,
0.00014229006774257869,
0.0541909821331501,
0.011302506551146507,
-0.02221001498401165,
0.006182942073792219,
-0.014968176372349262,
-0.06021420657634735,
-0.04296265169978142,
-0.013585303910076618,
0.05044374614953995,
-0.04233241453766823,
-0.03179393708705902,
-0.02590656839311123,
0.04793674871325493,
0.01587238721549511,
-0.03822752833366394,
0.008782468736171722,
0.0068427035585045815,
0.00011526836169650778,
0.01263623870909214,
-0.011472952552139759,
0.003994576167315245,
0.003120004665106535,
0.0012029780773445964,
-0.010766015388071537,
-0.009091519750654697,
0.02274048887193203,
-0.016134995967149734,
-0.010323416441679,
0.00922535452991724,
-0.005168454255908728,
-0.034559216350317,
-0.03799467906355858,
-0.031217604875564575,
0.003514500567689538,
0.028320234268903732,
-0.017029184848070145,
0.008537827990949154,
0.0010025062365457416,
-0.046686723828315735,
0.027710791677236557,
-0.05375361442565918,
-0.009826154448091984,
-0.018447132781147957,
0.05920525640249252,
0.02041114866733551,
0.0011919829994440079,
-0.024818267673254013,
-0.012202139012515545,
0.0019302007276564837,
-0.01094074547290802,
0.027843380346894264,
0.010671294294297695,
0.009882744401693344,
-0.021486256271600723,
0.00939106848090887,
-0.05634317174553871,
0.054850995540618896,
0.08147072046995163,
-0.0331587977707386,
0.03397465869784355,
0.025990329682826996,
-0.01588616706430912,
-0.0225412305444479,
-0.0354081355035305,
0.009174266830086708,
0.04071609675884247,
-0.012389058247208595,
0.0035992448683828115,
-0.04260965436697006,
-0.03532194346189499,
0.029798954725265503,
0.03502625599503517,
-0.04395783320069313,
0.00989365391433239,
-0.0070829326286911964,
0.01157680619508028,
-0.007106867618858814,
-0.014246572740375996,
-0.03818122297525406,
0.055824436247348785,
-0.0026653818786144257,
0.031727518886327744,
0.021120069548487663,
-0.009880797937512398,
0.001919284462928772,
0.04795975610613823,
0.026800280436873436,
-0.02635628543794155,
0.01317890826612711,
-0.030147317796945572,
-0.004465827252715826,
0.03551217168569565,
0.017857948318123817,
0.014139167964458466,
-0.01034625619649887,
0.04017043858766556,
0.0008279199828393757,
0.026937441900372505,
-0.005680657457560301,
-0.03429717943072319,
-0.00489326985552907,
-0.04330815002322197,
-0.04554944485425949,
0.053050871938467026,
-0.03345116600394249,
-0.007852462120354176,
0.01136829610913992,
-0.03969024121761322,
0.049999646842479706,
0.030021626502275467,
0.03695923089981079,
-0.033390533179044724,
0.05933716893196106,
-0.03785622864961624,
0.032138969749212265,
-0.03869086131453514,
-0.02210627868771553,
0.14979027211666107,
0.06869476288557053,
-0.019681351259350777,
-0.04456834867596626,
-0.013645411469042301,
-0.009286974556744099,
0.04608609527349472,
-0.0638432651758194,
0.05701187252998352,
0.02084418572485447,
-0.046864982694387436,
-0.04089190438389778,
0.07571171224117279,
-0.021854743361473083,
-0.047836147248744965,
0.028349610045552254,
-0.03603971004486084,
-0.02495073527097702,
-0.006680928170681,
0.020869780331850052,
0.0022880355827510357,
-0.004899550229310989,
-0.05613354593515396,
-0.00001390905526932329,
0.004675759933888912,
0.05350092053413391,
-0.01947087235748768,
-0.006362414453178644,
0.011898979544639587,
-0.02737579122185707,
-0.059533990919589996,
0.02549854665994644,
-0.010632224380970001,
-0.03303273767232895,
-0.024362849071621895,
0.006004489492624998,
0.008330934680998325,
-0.030085500329732895,
0.0315328873693943,
0.035956449806690216,
-0.014169515110552311,
0.000753584667108953,
0.025826403871178627,
0.029100945219397545,
-0.04731288552284241,
-0.0052750143222510815,
-0.05234555900096893,
0.06881292164325714,
-0.018375303596258163,
-0.015135937370359898,
0.021484756842255592,
0.002457427093759179,
-0.0013155888300389051,
-0.04626331478357315,
-0.005282273516058922,
-0.005461346823722124,
0.018119052052497864,
0.026480063796043396,
-0.009274515323340893,
0.0042039211839437485,
0.030489981174468994,
0.025047246366739273,
0.009039470925927162,
-0.023280516266822815,
0.005148629657924175,
0.013152368366718292,
0.008778279647231102,
0.03678135201334953,
0.012254483997821808,
0.008710603229701519,
-0.015484491363167763,
-0.010776142589747906,
-0.019683847203850746,
0.0029133108910173178,
-0.004395406227558851,
0.021902598440647125,
0.015107373706996441,
0.020225994288921356,
-0.017056751996278763,
0.008064758032560349,
-0.039197832345962524,
0.02935648523271084,
-0.007039230316877365,
-0.014908782206475735,
-0.01664753630757332,
0.005141179542988539,
0.005764373578131199,
0.04978199303150177,
0.01746036671102047,
-0.0011852295137941837,
0.029905907809734344,
0.041330162435770035,
-0.018214251846075058,
-0.011049764230847359,
-0.043413519859313965,
-0.0031975479796528816,
0.04290849342942238,
-0.04620220884680748,
-0.032654549926519394,
-0.02440321259200573,
0.03528978303074837,
0.011948530562222004,
-0.0010640876134857535,
0.05125139281153679,
0.009272605180740356,
-0.017649834975600243,
0.015383487567305565,
-0.008223213255405426,
0.022487832233309746,
0.05010877177119255,
0.01680574007332325,
-0.04446260631084442,
-0.01947869546711445,
-0.014689132571220398,
0.011581026948988438,
0.026486685499548912,
-0.013519810512661934,
-0.039399437606334686,
0.0071218423545360565,
-0.021063724532723427,
0.011211956851184368,
-0.014753201976418495,
-0.0110695268958807,
0.003515658201649785,
0.040555164217948914,
-0.02200203761458397,
0.002957595745101571,
0.0012365250149741769,
0.0572814904153347,
-0.03196569159626961,
-0.052191946655511856,
-0.02807391993701458,
0.010544703342020512,
-0.05680045485496521,
-0.019797172397375107,
0.046557195484638214,
0.01206852775067091,
0.024374855682253838,
0.04294696822762489,
-0.02145005390048027,
-0.008890927769243717,
-0.026423197239637375,
-0.04730268940329552,
0.04679195210337639,
0.02179374359548092,
-0.0021840345580130816,
0.009092358872294426,
-0.04470323771238327,
-0.0057040113024413586,
0.062416527420282364,
-0.02953197807073593,
-0.010405694134533405,
-0.008650344796478748,
-0.04625978693366051,
-0.009303602389991283,
-0.040854670107364655,
0.03419879823923111,
0.021394357085227966,
0.02842644602060318,
0.018758339807391167,
0.004862687550485134,
-0.031572069972753525,
0.0042014773935079575,
-0.002290807431563735,
-0.036909159272909164,
0.020970389246940613,
0.015250906348228455,
-0.006932425778359175,
0.05512836202979088,
0.05232367664575577,
-0.032392144203186035,
0.010680434294044971,
0.01978922262787819,
-0.003722288878634572,
-0.09457920491695404,
-0.006521190982311964,
-0.002524912590160966,
0.05201060324907303,
0.05889749526977539,
-0.03450952097773552,
0.01348171103745699,
0.04887930676341057,
-0.0581388995051384,
0.022286269813776016,
-0.02623404935002327,
-0.0038014284800738096,
0.008738081902265549,
-0.023733604699373245,
-0.004744723439216614,
0.07045074552297592,
0.032060302793979645,
0.01625996083021164,
-0.008492987602949142,
0.015192324295639992,
-0.03753666952252388,
-0.02925199642777443,
-0.026428598910570145,
0.05282766371965408,
-0.015017607249319553,
-0.030249392613768578,
0.08265884220600128,
0.013925669714808464,
-0.01271410845220089,
0.027798501774668694,
0.02812267653644085,
0.006599558051675558,
-0.044513218104839325,
0.030602585524320602,
0.031510546803474426,
-0.013355286791920662,
0.024459073320031166,
-0.02096753567457199,
0.01630374975502491,
0.01367529109120369,
0.0010746087646111846,
0.010119483806192875,
0.026926115155220032,
-0.034646473824977875,
0.010508029721677303,
-0.03784314915537834,
-0.011427883990108967,
0.03905494138598442,
-0.028486130759119987,
-0.03119942918419838,
-0.00016699492698535323,
-0.024419056251645088,
0.006636304780840874,
-0.00875449925661087,
-0.008649101480841637,
-0.04846471920609474,
0.006100162863731384,
0.046090204268693924,
-0.035026125609874725,
0.028416525572538376,
0.03495180606842041,
-0.004692755173891783,
-0.0025360321160405874,
0.0242230836302042,
-0.0059522707015275955,
-0.012779940851032734,
-0.028735501691699028,
0.029639575630426407,
-0.010675829835236073,
0.00930714700371027,
0.014149358496069908,
-0.005392283201217651,
-0.046529948711395264,
-0.01914054900407791,
0.04148704186081886,
0.006932176649570465,
-0.01876893825829029,
-0.016161317005753517,
-0.032775696367025375,
-0.053291063755750656,
0.020882675424218178,
0.01962793618440628,
-0.01241373922675848,
-0.04015723615884781,
0.03160949423909187,
0.0019914961885660887,
0.04561300203204155,
0.02124185301363468,
-0.008663009852170944,
-0.02329750917851925,
0.021462753415107727,
0.027798401191830635,
0.02583685703575611,
-0.04882558062672615,
0.025296960026025772,
0.040032319724559784,
0.021209686994552612,
0.03019871562719345,
0.0188555046916008,
-0.002710932632908225,
0.013366359286010265,
-0.00572863407433033,
0.0018081602174788713,
0.0388660654425621,
0.023955263197422028,
-0.015657905489206314,
-0.005296357907354832,
0.02791832946240902,
-0.03469153493642807,
0.08459910750389099,
-0.007465822622179985,
0.004054944030940533,
0.02513793855905533,
-0.03864952176809311,
-0.024533970281481743,
-0.022532843053340912,
-0.0210738405585289,
-0.021014060825109482,
-0.004368248395621777,
-0.038232725113630295,
0.023631760850548744,
-0.0626516044139862,
0.0016325305914506316,
0.0302895437926054,
0.04199342429637909,
-0.051074299961328506,
0.06568537652492523,
0.003009578213095665,
0.01587405614554882,
0.031941287219524384,
0.02257198840379715,
-0.02488907426595688,
-0.018659936264157295,
0.012736838310956955,
0.01543953362852335,
0.06057499349117279,
-0.004365819972008467,
-0.005707308650016785,
0.03186711296439171,
-0.06874420493841171,
0.016355184838175774,
-0.0008543506846763194,
-0.0024246936663985252,
-0.006419150624424219,
0.003429485484957695,
0.04320286214351654,
-0.029591277241706848,
0.009874125011265278,
0.027391673997044563,
-0.005346565041691065,
0.07269119471311569,
-0.02531811222434044,
-0.009262255392968655,
0.011578935198485851,
-0.014429206028580666,
-0.031212549656629562,
0.07305695861577988,
0.020853282883763313,
0.057324208319187164,
-0.012789187021553516,
-0.03009512834250927,
-0.023927869275212288,
-0.005305416416376829,
-0.02231781557202339,
-0.026042496785521507,
0.008754168637096882,
0.021738020703196526,
0.02497919276356697,
0.009880702942609787,
-0.02598761022090912,
0.007278956938534975,
-0.01418942678719759,
0.004133567679673433,
-0.0016572348540648818,
0.04701921343803406,
-0.04904285445809364,
-0.005497609730809927,
-0.06308332085609436,
0.026616862043738365,
-0.051539286971092224,
-0.01219265442341566,
0.014054296538233757,
0.03484721481800079,
0.05193513259291649,
-0.012302299961447716
] |
<p>Michio Kaku's explanation of universes in hyperspace in <a href="https://www.youtube.com/watch?v=D6XAkVA7RmY" rel="nofollow">this youtube video</a> gives a metaphor of our universe being the surface of a hyperspace bubble that's currently becoming larger. He also says these bubbles colliding would produce the creation of new universes and the destruction of involved universes.</p>
<p>But this makes me think there's a lot of room in hyperspace for a universe to float for a very long time without encountering another universe.</p>
<ul>
<li><p>Is there anything significant to note about areas of hyperspace that don't currently have a universe? </p></li>
<li><p>Is it highly entropic? </p></li>
<li><p>Does hyperspace change in any way as a universe approaches? </p></li>
<li><p>Is it similar to how a galaxy will warp the space-time around it, in that hyperspace follows the same mechanics, but with more dimensions?</p></li>
</ul>
| 10,706 |
[
-0.016431715339422226,
-0.01121415477246046,
0.0019627979490906,
-0.014255914837121964,
0.05676329508423805,
0.023345833644270897,
-0.02413889393210411,
-0.021808473393321037,
0.01672637090086937,
-0.06135912612080574,
0.012512856163084507,
0.025407521054148674,
0.027293087914586067,
-0.02118680439889431,
0.007929254323244095,
0.02125857025384903,
-0.009190340526401997,
-0.0026728634256869555,
0.004548171069473028,
-0.015956802293658257,
0.01409255899488926,
0.020378511399030685,
0.036628130823373795,
-0.012067776173353195,
-0.0210136566311121,
0.026234595105051994,
0.030167581513524055,
-0.018426591530442238,
0.03144987300038338,
0.05049605667591095,
0.03472205996513367,
0.0035549586173146963,
0.021132739260792732,
0.014812910929322243,
-0.002901688916608691,
-0.05974356830120087,
-0.050839293748140335,
-0.0455235056579113,
-0.004451544489711523,
0.009709366597235203,
-0.059956297278404236,
-0.02614980936050415,
-0.024147646501660347,
0.06847235560417175,
-0.029771581292152405,
0.008293889462947845,
-0.06016485020518303,
-0.005411893129348755,
0.034966886043548584,
-0.03673107922077179,
0.032083235681056976,
0.015110391192138195,
0.043810561299324036,
0.040854111313819885,
0.006569144316017628,
-0.008462251164019108,
0.106403648853302,
0.07345332205295563,
-0.020515555515885353,
-0.01709030382335186,
-0.02726917900145054,
-0.009102297946810722,
-0.000979672884568572,
-0.03179841488599777,
-0.0011091994820162654,
0.06383828073740005,
-0.021493107080459595,
0.01805702969431877,
-0.015462825074791908,
0.0208236463367939,
-0.00489682424813509,
0.01824663020670414,
0.03203415870666504,
0.00962598156183958,
0.03365253657102585,
-0.018689854070544243,
0.015982236713171005,
0.0012053347891196609,
0.0735737681388855,
0.06513917446136475,
-0.0008234984125010669,
-0.008309883065521717,
-0.006319909356534481,
-0.011975761502981186,
0.050099000334739685,
0.019103823229670525,
0.08972825855016708,
-0.0030796288046985865,
-0.019412191584706306,
0.055044710636138916,
0.028167836368083954,
-0.00426122173666954,
0.04154367744922638,
-0.021266885101795197,
-0.03375273570418358,
0.04373755678534508,
-0.005251867696642876,
0.02683800645172596,
-0.0021943943575024605,
-0.0063948300667107105,
-0.015400035306811333,
-0.010112129151821136,
0.001464818837121129,
0.04435281828045845,
0.06910345703363419,
-0.06335469335317612,
-0.05963893607258797,
0.025678196921944618,
-0.007487847935408354,
0.0017839574720710516,
-0.010394970886409283,
-0.013335760682821274,
0.005770475137978792,
-0.016081249341368675,
0.0016433618729934096,
0.0024530307855457067,
0.02089991606771946,
-0.03804532438516617,
0.01589518040418625,
0.06073937192559242,
0.04871552065014839,
-0.009835422039031982,
0.03179365023970604,
0.019208425655961037,
-0.05938646197319031,
0.0011340376222506166,
0.04032652825117111,
-0.0036288376431912184,
-0.04843882843852043,
0.051554545760154724,
-0.0041330186650156975,
0.01125404890626669,
0.0019781740847975016,
0.004752852022647858,
0.06005053594708443,
-0.0021115990821272135,
-0.10200315713882446,
-0.05132095888257027,
0.08750801533460617,
0.01812809333205223,
-0.018131675198674202,
-0.026899266988039017,
0.010701226070523262,
0.028455765917897224,
0.09549261629581451,
-0.01085765939205885,
-0.03388851881027222,
-0.0226588174700737,
0.05552239716053009,
0.006864913273602724,
-0.03686251491308212,
0.004376025404781103,
-0.03103468008339405,
-0.03442967310547829,
0.001292729051783681,
-0.07805737853050232,
-0.0046950834803283215,
0.05092217028141022,
0.025414900854229927,
-0.039878375828266144,
0.08155858516693115,
0.0007668484468013048,
-0.007335288915783167,
-0.010907139629125595,
-0.02561565861105919,
-0.020840611308813095,
0.10964144766330719,
-0.0008885139250196517,
0.049174707382917404,
0.057049158960580826,
-0.05123770982027054,
0.009595119394361973,
0.02429518848657608,
0.020971879363059998,
0.06313817948102951,
0.0018558616284281015,
-0.013474089093506336,
-0.023728035390377045,
0.029620321467518806,
-0.022840360179543495,
-0.022929834201931953,
-0.0027591113466769457,
-0.02512207254767418,
-0.011384976096451283,
0.031146615743637085,
0.02623695693910122,
-0.05107634887099266,
-0.0013433486456051469,
-0.012774478644132614,
-0.05951919034123421,
-0.024777095764875412,
-0.07500674575567245,
0.0026548863388597965,
-0.006810181774199009,
0.04109537601470947,
0.0314023457467556,
0.015340890735387802,
0.04450121149420738,
-0.03959237039089203,
-0.015511566773056984,
0.0016405434580519795,
0.05844181776046753,
0.010647994466125965,
0.031660471111536026,
0.026984766125679016,
0.03862127289175987,
0.004217769950628281,
-0.004753048997372389,
0.004123386926949024,
-0.0022410722449421883,
-0.05353894084692001,
0.01739778369665146,
-0.01013173721730709,
0.004150073044002056,
-0.01859387755393982,
0.02537519484758377,
0.014419762417674065,
0.007386582437902689,
0.006847950164228678,
0.014168293215334415,
-0.04359379783272743,
0.04979177191853523,
0.017234500497579575,
-0.0025643273256719112,
0.017641570419073105,
0.03941957280039787,
0.0036459718830883503,
-0.0008174083195626736,
-0.013895982876420021,
-0.03525775298476219,
-0.10813472419977188,
-0.0048011476173996925,
0.03979058191180229,
0.04080967977643013,
-0.006117347627878189,
0.00026247071218676865,
0.0009608423570170999,
0.011955576948821545,
-0.0014925983268767595,
-0.013873212970793247,
-0.028847023844718933,
-0.033845704048871994,
0.00956163089722395,
0.003338560927659273,
0.030691638588905334,
0.003308212384581566,
0.029448557645082474,
0.006721172481775284,
-0.01188416313380003,
-0.041700154542922974,
-0.0034707908052951097,
-0.01309156697243452,
0.01972816325724125,
-0.015802502632141113,
-0.04293662682175636,
-0.038363851606845856,
0.016011012718081474,
0.009158894419670105,
0.024627074599266052,
0.00021523110626731068,
0.03508012369275093,
0.007940019480884075,
-0.0745362713932991,
-0.020785106346011162,
-0.019095590338110924,
0.005605537910014391,
-0.023938121274113655,
-0.00243232655338943,
0.02711966261267662,
-0.041425302624702454,
0.014854608103632927,
-0.0023828172124922276,
-0.0003227336856070906,
0.011618128046393394,
-0.01685681752860546,
0.010984353721141815,
-0.0029550082981586456,
0.008925757370889187,
-0.06319037824869156,
-0.027798552066087723,
-0.01050373911857605,
-0.0007387661025859416,
0.0007612403715029359,
0.0035287290811538696,
-0.040167417377233505,
0.04411785304546356,
-0.0049633122980594635,
-0.030198819935321808,
0.0015323541592806578,
-0.04026088863611221,
0.042758215218782425,
0.002548987977206707,
0.012204114347696304,
-0.05974331498146057,
-0.02121318131685257,
-0.002939380006864667,
-0.02419549599289894,
-0.030065905302762985,
0.023320863023400307,
0.08588990569114685,
-0.02162965200841427,
-0.06264082342386246,
0.016062196344137192,
-0.03204639256000519,
-0.04379166290163994,
-0.022125231102108955,
0.0022702065762132406,
0.01767471618950367,
-0.06257010251283646,
0.018787553533911705,
0.03157943859696388,
-0.003825032850727439,
-0.012693801894783974,
-0.05182424932718277,
-0.053794343024492264,
0.03820474445819855,
-0.030316926538944244,
0.0394168458878994,
-0.01597224548459053,
-0.04145054146647453,
0.06895993649959564,
0.023328252136707306,
-0.0004628851602319628,
-0.010378147475421429,
-0.0017276940634474158,
0.007406445685774088,
-0.027197228744626045,
-0.0036433434579521418,
0.016920991241931915,
-0.0065675340592861176,
-0.0033713066950440407,
0.04911172017455101,
0.058554790914058685,
0.015240811742842197,
-0.025397157296538353,
-0.010521936230361462,
-0.0033817754592746496,
-0.010825957171618938,
0.006340748630464077,
0.07135310769081116,
0.028207561001181602,
-0.010382803156971931,
-0.002387819578871131,
-0.0005584502359852195,
0.013478443957865238,
-0.010695417411625385,
-0.05434027686715126,
0.07762017846107483,
0.021143576130270958,
-0.015892354771494865,
0.0014627747004851699,
0.005355373024940491,
-0.022695763036608696,
-0.0007624608115293086,
0.0019649125169962645,
0.020169008523225784,
0.016835706308484077,
0.017075130715966225,
0.010844888165593147,
-0.002225259318947792,
0.04551706090569496,
-0.01899232342839241,
0.004675795789808035,
0.006549694109708071,
0.025203868746757507,
0.015221085399389267,
-0.004384004510939121,
-0.012533771805465221,
0.03302997723221779,
0.018932590261101723,
-0.020120520144701004,
0.0233044121414423,
-0.026777377352118492,
-0.019385749474167824,
-0.03190857172012329,
-0.018037820234894753,
0.03898711875081062,
0.0039102910086512566,
0.009361645206809044,
0.006230187136679888,
-0.012326503172516823,
0.001702056615613401,
0.0011368875857442617,
-0.036782156676054,
-0.07743091136217117,
-0.029107162728905678,
-0.034953124821186066,
-0.0006503488984890282,
-0.030360763892531395,
-0.0033443011343479156,
-0.025802938267588615,
-0.01742122508585453,
0.0004453466390259564,
-0.057237327098846436,
-0.021002909168601036,
-0.08825555443763733,
-0.008001331239938736,
-0.03686914220452309,
-0.030509017407894135,
-0.010999812744557858,
0.005852305795997381,
0.06989749521017075,
0.01775265857577324,
0.039201028645038605,
0.004788034595549107,
-0.022595154121518135,
-0.005729988683015108,
0.024969561025500298,
0.01922430284321308,
0.020300835371017456,
0.008799527771770954,
-0.011737542226910591,
0.030536524951457977,
-0.0072091007605195045,
-0.010232644155621529,
0.01250410359352827,
-0.012287098914384842,
-0.027582276612520218,
-0.018631571903824806,
-0.025373587384819984,
-0.029645591974258423,
-0.047870732843875885,
-0.03557291626930237,
0.05001082643866539,
0.013129503466188908,
0.0829826295375824,
0.04655393585562706,
0.02719057723879814,
-0.023320749402046204,
0.03319557011127472,
0.05935553088784218,
-0.019290121272206306,
-0.02415364980697632,
-0.03649520128965378,
-0.0364995114505291,
-0.040866654366254807,
-0.014408959075808525,
0.023634202778339386,
-0.028201816603541374,
-0.026452966034412384,
0.03377186506986618,
-0.008624663576483727,
0.0038637490943074226,
-0.02445577085018158,
-0.015229130163788795,
-0.025734756141901016,
0.0013552808668464422,
-0.011329304426908493,
0.0057896957732737064,
-0.007274386007338762,
0.0392669178545475,
0.028630679473280907,
0.0032690204679965973,
0.0071814111433923244,
-0.0537661649286747,
-0.019781555980443954,
0.02659686468541622,
0.010786652565002441,
0.013477254658937454,
-0.034185998141765594,
-0.09171298146247864,
-0.027401028200984,
0.0369180291891098,
-0.046127259731292725,
0.018507450819015503,
-0.012000796385109425,
0.04426714405417442,
-0.03808131068944931,
-0.03432055935263634,
-0.007141792681068182,
-0.013471719808876514,
-0.04731372371315956,
0.014270216226577759,
-0.014225145801901817,
0.02456575632095337,
-0.013439885340631008,
0.038476601243019104,
0.005453430116176605,
0.04061078280210495,
-0.004216364584863186,
0.020428894087672234,
-0.030465807765722275,
0.010787426494061947,
-0.014000797644257545,
-0.07199173420667648,
0.04936734214425087,
0.011533043347299099,
-0.04261869564652443,
0.026520393788814545,
0.0008128874469548464,
-0.0358344167470932,
-0.004151994362473488,
-0.020599674433469772,
-0.008673018775880337,
0.014406979084014893,
-0.018743189051747322,
0.026726892217993736,
0.025192933157086372,
-0.008313312195241451,
0.04057538881897926,
0.021303506568074226,
0.0011383151868358254,
-0.003951098769903183,
-0.02550637349486351,
0.038812343031167984,
-0.03762079402804375,
0.005804789252579212,
-0.03562593087553978,
-0.03156808018684387,
-0.023124631494283676,
0.030968517065048218,
-0.016604173928499222,
0.000494588864967227,
0.029813770204782486,
-0.009749763645231724,
-0.012959969229996204,
-0.009046878665685654,
0.030344899743795395,
0.0174386128783226,
-0.014632651582360268,
-0.0007735821418464184,
-0.014152883552014828,
-0.013095059432089329,
0.041306737810373306,
0.0184628963470459,
0.029134860262274742,
0.02340508997440338,
0.00467453571036458,
0.005566918291151524,
-0.03008180670440197,
-0.02070380188524723,
0.014529388397932053,
-0.029066354036331177,
0.05183771252632141,
-0.011148539371788502,
-0.007991808466613293,
0.0604013130068779,
-0.0067464495077729225,
0.0057164207100868225,
-0.004769814666360617,
-0.056025080382823944,
-0.04516058787703514,
-0.022395648062229156,
0.028904300183057785,
-0.021618133410811424,
0.008091721683740616,
-0.09432818740606308,
-0.02409244328737259,
0.031095994636416435,
-0.0008913498604670167,
0.010826284065842628,
-0.04968603700399399,
0.026969600468873978,
-0.07467402517795563,
-0.0019577075727283955,
-0.019468514248728752,
0.025898639112710953,
-0.013608360663056374,
-0.005141907837241888,
-0.008999012410640717,
-0.0017508696764707565,
0.026016350835561752,
-0.02128257043659687,
-0.016359589993953705,
0.0028811197262257338,
0.03176926076412201,
-0.0023222470190376043,
-0.02321130968630314,
0.04943368583917618,
-0.005737741943448782,
-0.03244330361485481,
-0.004948456306010485,
-0.010855920612812042,
0.024299900978803635,
-0.048340730369091034,
0.006048315204679966,
0.03156241402029991,
-0.013196336105465889,
0.01691971719264984,
0.0014318687608465552,
0.005579350050538778,
-0.00924811139702797,
0.031918954104185104,
-0.012054653838276863,
0.027944771572947502,
-0.0011970964260399342,
-0.058218784630298615,
0.055919796228408813,
-0.0007273918599821627,
0.02231108769774437,
0.0072376602329313755,
0.045527320355176926,
-0.0036696468014270067,
-0.027221033349633217,
0.022045571357011795,
-0.04651188850402832,
0.04234780743718147,
-0.009119357913732529,
-0.022297993302345276,
0.04443654790520668,
0.01813696324825287,
-0.057698849588632584,
-0.046570274978876114,
-0.035021137446165085,
0.005210862960666418,
0.033285439014434814,
-0.0846465677022934,
0.020783333107829094,
0.001794185722246766,
-0.045048270374536514,
0.010066639631986618,
-0.02782496064901352,
0.013223371468484402,
0.03501031920313835,
-0.007249854039400816,
0.02123229391872883,
-0.012569062411785126,
-0.00248778541572392,
0.03316564857959747,
0.053395047783851624,
-0.00035442429361864924,
0.005741363391280174,
0.03729599341750145,
0.03688189759850502,
0.051290396600961685,
-0.044244859367609024,
-0.038794487714767456,
0.03993237763643265,
-0.0478830486536026,
0.0004765807534568012,
0.015093401074409485,
0.009105606004595757,
0.011376476846635342,
0.025492366403341293,
0.037261638790369034,
-0.05371096730232239,
-0.035406116396188736,
-0.004060673527419567,
0.011662092991173267,
0.002641178434714675,
0.03872433304786682,
0.026860026642680168,
-0.001106318668462336,
0.027752632275223732,
-0.0008169196080416441,
0.004479765892028809,
0.0017135562375187874,
-0.037585340440273285,
-0.03726882487535477,
-0.01989484205842018,
-0.024235306307673454,
0.0569632388651371,
0.028111832216382027,
-0.034028735011816025,
-0.028273966163396835,
-0.009517372585833073,
0.025585608556866646,
0.012216133996844292,
0.03839526325464249,
0.006992429494857788,
0.08042524755001068,
-0.01425234880298376,
0.015153886750340462,
-0.05496123433113098,
0.0316174291074276,
0.1173102930188179,
0.09421425312757492,
-0.023339441046118736,
-0.012298551388084888,
-0.006103540305048227,
-0.025106308981776237,
-0.012439367361366749,
-0.06907574832439423,
0.0030837273225188255,
-0.014497554861009121,
0.03609796240925789,
0.018370352685451508,
0.04374319314956665,
-0.019692307338118553,
-0.05400938168168068,
0.010743526741862297,
-0.05797065794467926,
0.006933977361768484,
0.00854220800101757,
0.021634992212057114,
0.002946744207292795,
0.010662938468158245,
-0.07360072433948517,
0.014189311303198338,
0.003236845601350069,
0.006670296657830477,
-0.03619629517197609,
-0.01630377769470215,
0.02590499259531498,
0.027314838021993637,
-0.039181843400001526,
0.02515047788619995,
0.006984093692153692,
-0.05669980123639107,
-0.01935846172273159,
0.006858149077743292,
0.008892931044101715,
0.007625881116837263,
0.012350796721875668,
0.030245603993535042,
0.004860091023147106,
0.020097166299819946,
-0.004869092721492052,
0.0062696970999240875,
-0.05958348512649536,
0.024596497416496277,
-0.03112553246319294,
0.05034361034631729,
-0.037567202001810074,
0.03169681876897812,
0.001249495311640203,
0.010354612953960896,
-0.0062623778358101845,
-0.026715198531746864,
-0.01432405412197113,
0.028689352795481682,
0.003443449502810836,
0.030770592391490936,
-0.0017744002398103476,
-0.0013033736031502485,
-0.0007477032486349344,
-0.006408706773072481,
0.003199194557964802,
-0.044326551258563995,
0.01890541799366474,
0.01892940327525139,
-0.03759769722819328,
0.037921421229839325,
-0.05530437082052231,
0.01329734455794096,
-0.01604192703962326,
0.007895619608461857,
-0.04464937373995781,
0.001199181191623211,
0.0011134016094729304,
-0.005210944917052984,
0.024112220853567123,
0.06398690491914749,
-0.025906667113304138,
-0.029913125559687614,
-0.01701957918703556,
0.029270565137267113,
-0.024647565558552742,
-0.0020826261024922132,
-0.013504194095730782,
0.00007079318311298266,
0.01033515390008688,
0.028561148792505264,
0.002494784537702799,
0.001737420097924769,
0.00006351045885821804,
0.0020812733564525843,
0.0014586641918867826,
-0.0035191744100302458,
0.002538650296628475,
-0.01459628064185381,
-0.014894971624016762,
-0.0008846450946293771,
-0.027607539668679237,
0.02879316173493862,
0.02829749882221222,
0.0004277311381883919,
0.04454709589481354,
0.03650030866265297,
0.009551952593028545,
0.02452603168785572,
0.030121829360723495,
-0.052496593445539474,
-0.004835504572838545,
-0.008014143444597721,
0.04465124383568764,
-0.01785280741751194,
-0.01708761602640152,
0.022953087463974953,
-0.0016264275182038546,
-0.0022842746693640947,
-0.018010146915912628,
-0.01855303719639778,
0.02956022508442402,
0.004265970084816217,
0.026226582005620003,
-0.04177672788500786,
-0.017942463979125023,
-0.026460295543074608,
0.013989070430397987,
-0.007745715323835611,
0.019732803106307983,
0.03421544283628464,
0.022677544504404068,
-0.05815854296088219,
-0.014767023734748363,
0.008415617048740387,
0.011677391827106476,
-0.045555464923381805,
-0.01003195345401764,
0.024838050827383995,
0.010603564791381359,
0.017634643241763115,
-0.05267295986413956,
-0.049647845327854156,
0.04564352333545685,
-0.03109832853078842,
-0.059924714267253876,
0.02827112004160881,
-0.01690351590514183,
0.0278055090457201,
0.049900613725185394,
-0.03266594558954239,
-0.031035007908940315,
0.06085878610610962,
-0.02089889720082283,
0.01019842829555273,
0.01822371408343315,
-0.029146812856197357,
-0.006824857089668512,
-0.007549172267317772,
0.02739720419049263,
0.012105248868465424,
-0.012207986786961555,
0.029298333451151848,
0.038297928869724274,
0.0037531303241848946,
-0.008759753778576851,
-0.02792886458337307,
-0.015515655279159546,
0.02071976289153099,
0.007067337166517973,
0.019332682713866234,
0.015715548768639565,
0.022595979273319244,
-0.03880474343895912,
0.025054985657334328,
0.03791588917374611,
-0.01531973760575056,
-0.1203552708029747,
0.009563468396663666,
-0.002613246440887451,
0.0012657390907406807,
0.04890058562159538,
-0.044149789959192276,
0.031744442880153656,
0.0017442706739529967,
-0.06084390729665756,
0.03726990520954132,
-0.0158341396600008,
-0.007060805335640907,
-0.022708378732204437,
0.019619669765233994,
-0.03177894651889801,
0.06016245111823082,
0.05671263486146927,
0.05295443907380104,
-0.013058431446552277,
0.009715148247778416,
-0.027353206649422646,
-0.03649725764989853,
-0.0016425767680630088,
0.026229968294501305,
-0.0021176962181925774,
0.008702782914042473,
0.0916941836476326,
0.004789168015122414,
0.021647866815328598,
0.036581382155418396,
-0.02027735859155655,
0.01830861158668995,
-0.009915333241224289,
-0.02428501285612583,
0.03588556498289108,
-0.00440189940854907,
0.018293140456080437,
-0.02431114949285984,
-0.014250991865992546,
0.022863881662487984,
-0.0003841948928311467,
-0.002298849169164896,
0.022175101563334465,
-0.019919682294130325,
0.008600320667028427,
-0.024000536650419235,
0.005575987044721842,
0.040776725858449936,
-0.01961720734834671,
0.006969830486923456,
-0.05065435916185379,
-0.02978121116757393,
0.02533147670328617,
0.03228691220283508,
-0.00829471368342638,
-0.055156953632831573,
-0.005711800884455442,
0.03188137337565422,
-0.025669744238257408,
-0.022156842052936554,
0.026798628270626068,
0.027623172849416733,
-0.015536686405539513,
0.005186879076063633,
-0.00024224267690442502,
-0.0013456958113238215,
-0.0016112118028104305,
-0.042702991515398026,
-0.0029658556450158358,
-0.017142703756690025,
0.015250067226588726,
-0.026205144822597504,
-0.030991001054644585,
0.06331279873847961,
0.05673776939511299,
0.029236577451229095,
0.02903974987566471,
-0.026585042476654053,
-0.047610312700271606,
-0.07148154824972153,
0.022333204746246338,
-0.01659269817173481,
-0.028904840350151062,
-0.04437680169939995,
-0.016269313171505928,
0.014064067974686623,
-0.0032042446546256542,
0.06651145219802856,
-0.0010975667973980308,
-0.0015680617652833462,
-0.008654899895191193,
0.003657198278233409,
0.04305613413453102,
-0.048110462725162506,
-0.029445888474583626,
0.023422595113515854,
-0.04032327979803085,
0.01383225154131651,
0.003978825639933348,
-0.006516989320516586,
0.005439722910523415,
0.018998149782419205,
-0.002682364545762539,
0.029520602896809578,
0.012393137440085411,
0.007656527683138847,
0.013687686994671822,
0.03947308659553528,
-0.0005482701817527413,
0.04309890419244766,
0.013377781957387924,
0.024332420900464058,
0.03026074729859829,
0.009467474184930325,
-0.023943593725562096,
0.002358125289902091,
-0.02319217287003994,
-0.006960310973227024,
-0.014256929978728294,
-0.04605273902416229,
0.012890917249023914,
-0.024407872930169106,
0.0011810811702162027,
0.06123978644609451,
-0.04057885706424713,
-0.0035311589017510414,
0.06122484430670738,
-0.004177889320999384,
0.03025854378938675,
-0.0020429440774023533,
0.003342100651934743,
0.025034312158823013,
0.014337485656142235,
-0.025889866054058075,
0.06124749407172203,
0.049416907131671906,
-0.012226005084812641,
0.004228993784636259,
0.014519761316478252,
0.014414154924452305,
0.015941886231303215,
0.014862283132970333,
0.0422552190721035,
-0.056043241173028946,
-0.015722215175628662,
-0.02184530347585678,
0.024954907596111298,
0.0034778218250721693,
-0.004215110093355179,
0.0056306724436581135,
0.07758326083421707,
-0.018439490348100662,
0.027423612773418427,
0.009224583394825459,
-0.020488012582063675,
0.013930533081293106,
0.031051449477672577,
-0.019405800849199295,
0.04317966103553772,
-0.001733214478008449,
-0.008648181334137917,
-0.017292240634560585,
0.023257894441485405,
0.021452240645885468,
-0.029566336423158646,
0.019811011850833893,
-0.002466757083311677,
0.010741090402007103,
0.019821155816316605,
-0.022940007969737053,
-0.009257388301193714,
-0.033709026873111725,
0.03230152279138565,
0.002997642382979393,
0.0176798477768898,
0.012098485603928566,
0.0027336180210113525,
-0.030221210792660713,
0.02607642114162445,
-0.033209726214408875,
0.003076565219089389,
-0.037694528698921204,
0.025932032614946365,
0.004182160831987858,
0.01033639907836914
] |
<p>I know that displacement current is due to time-varying electric field and its not an electric current.</p>
<p>But then, is it charge that is actually being displaced?</p>
| 342 |
[
-0.014162683859467506,
0.011587012559175491,
0.03333904594182968,
-0.021496960893273354,
0.027442535385489464,
-0.013754741288721561,
-0.03308190405368805,
-0.0029137786477804184,
0.005546225234866142,
-0.010133098810911179,
0.046227771788835526,
0.02926173061132431,
0.056658197194337845,
0.011106264777481556,
-0.005182220600545406,
-0.014834847301244736,
0.012727728113532066,
-0.015177421271800995,
-0.005397666711360216,
-0.014355207793414593,
-0.0005938995163887739,
0.022380676120519638,
0.013946189545094967,
0.02253597229719162,
-0.009445448406040668,
0.03710057586431503,
0.057326897978782654,
0.02004593051970005,
0.013739140704274178,
0.0627794936299324,
-0.038249097764492035,
-0.04724869504570961,
-0.02143290266394615,
0.012378589250147343,
0.020389873534440994,
-0.014693704433739185,
-0.041297245770692825,
-0.06499744206666946,
-0.02041061595082283,
0.03932834416627884,
0.00895605143159628,
-0.029728904366493225,
0.00546637549996376,
0.05073673650622368,
-0.013831798918545246,
-0.001915415283292532,
-0.014433003962039948,
0.019944146275520325,
0.04532891511917114,
-0.073860764503479,
0.03567810729146004,
-0.030200840905308723,
0.050249677151441574,
0.009577537886798382,
-0.01865795999765396,
0.018856670707464218,
0.10582830756902695,
0.06674623489379883,
-0.049826402217149734,
-0.01854289509356022,
-0.005860330071300268,
-0.03157803416252136,
-0.003363128751516342,
-0.041565075516700745,
-0.010002964176237583,
0.012596217915415764,
-0.02384931780397892,
-0.05231044813990593,
0.01695883646607399,
0.012112011201679707,
0.009370346553623676,
-0.009480541571974754,
-0.02364373207092285,
-0.03227013722062111,
0.020030932500958443,
-0.035830773413181305,
0.022941049188375473,
0.012728193774819374,
0.026207413524389267,
0.06389662623405457,
-0.030923670157790184,
-0.0083907600492239,
0.030809488147497177,
0.03796948119997978,
0.0015883276937529445,
-0.048540811985731125,
0.053202737122774124,
-0.03293247148394585,
0.01000157929956913,
-0.009635351598262787,
-0.03547196090221405,
0.02260829694569111,
-0.012089655734598637,
0.015090779401361942,
0.003512987168505788,
0.0053410716354846954,
0.0016672116471454501,
0.041393622756004333,
0.02112548239529133,
-0.014615537598729134,
0.032954808324575424,
-0.0008612828678451478,
0.0403292179107666,
0.046259306371212006,
-0.04160738363862038,
-0.008626083843410015,
-0.009164688177406788,
0.030204348266124725,
-0.01756269671022892,
-0.020884456112980843,
-0.06995168328285217,
0.009721270762383938,
-0.00043066689977422357,
-0.012441092170774937,
0.04424889013171196,
-0.01744401641190052,
-0.0022800543811172247,
0.0023605090100318193,
0.02605055645108223,
0.06603928655385971,
0.007902780547738075,
-0.06582754850387573,
0.01847516931593418,
-0.005279161501675844,
-0.049702104181051254,
0.0037190003786236048,
0.04073696956038475,
-0.006432739086449146,
-0.01642606407403946,
0.06358177214860916,
-0.03313275799155235,
-0.014211243949830532,
0.03254687041044235,
0.0021008732728660107,
0.03619193285703659,
0.01480178628116846,
-0.08867809921503067,
-0.04407823830842972,
0.020597072318196297,
0.0008965616580098867,
-0.02306147664785385,
-0.07756083458662033,
-0.03244706615805626,
0.00827112514525652,
0.06234711408615112,
0.021973343566060066,
-0.032469529658555984,
-0.014460807666182518,
0.03512728214263916,
0.02188009023666382,
0.015853583812713623,
-0.01080020796507597,
0.042932990938425064,
-0.009362243115901947,
0.0024636222515255213,
-0.04097180813550949,
0.028000136837363243,
0.051547955721616745,
0.0007175321225076914,
0.0051459153182804585,
0.027668824419379234,
0.014137275516986847,
-0.021948503330349922,
0.04820001497864723,
0.004117502365261316,
-0.008918586187064648,
0.0634375512599945,
0.0037431453820317984,
-0.012395620346069336,
0.056383613497018814,
0.022569436579942703,
0.01454250793904066,
0.03046122007071972,
0.029777266085147858,
0.05456465482711792,
-0.04183501750230789,
-0.01986049674451351,
-0.048594068735837936,
0.006363693159073591,
-0.00248656515032053,
-0.013982480391860008,
-0.04019550234079361,
-0.008627473376691341,
-0.012507911771535873,
-0.005482511129230261,
0.024120938032865524,
-0.01848495565354824,
0.0012957847211509943,
-0.022798972204327583,
-0.048861175775527954,
-0.014866109937429428,
-0.03325861692428589,
0.04812835529446602,
0.0002230248210253194,
0.005470499396324158,
0.0057924226857721806,
0.008985781110823154,
0.01741456799209118,
-0.04472514986991882,
-0.048587579280138016,
0.018164390698075294,
0.0017857004422694445,
-0.052634142339229584,
-0.03115345910191536,
0.0227933581918478,
0.025065330788493156,
0.03545176610350609,
0.014284889213740826,
0.012481644749641418,
-0.021955685690045357,
-0.012140713632106781,
0.008771609514951706,
-0.02618013508617878,
0.040331702679395676,
-0.001583186211064458,
0.008068997412919998,
0.021399233490228653,
0.014931848272681236,
0.0012319955276325345,
0.03034253790974617,
0.00543510727584362,
0.065457783639431,
0.06758133322000504,
-0.011494705453515053,
-0.002004957292228937,
0.061569277197122574,
0.003488547634333372,
0.0009499485022388399,
0.0025090572889894247,
-0.03800958767533302,
-0.051805440336465836,
-0.014596359804272652,
0.022956931963562965,
0.03182496875524521,
-0.019497547298669815,
0.022882889956235886,
0.011844314634799957,
0.043470922857522964,
0.0397946871817112,
0.014140329323709011,
0.0035433920565992594,
-0.05516951158642769,
0.03348545730113983,
0.031340342015028,
0.006386792287230492,
-0.024500394240021706,
0.020456289872527122,
-0.0007069705752655864,
0.06520652770996094,
-0.02473452128469944,
0.0024363980628550053,
0.005158137530088425,
-0.0021132691763341427,
0.02847003936767578,
-0.005376940593123436,
-0.05256010219454765,
0.01805737242102623,
-0.017483601346611977,
0.025601902976632118,
-0.00886986032128334,
-0.03150942921638489,
0.036365311592817307,
-0.002561336848884821,
-0.0054193646647036076,
0.00954480841755867,
-0.016120238229632378,
0.013932124711573124,
-0.018549147993326187,
0.03597665950655937,
-0.06449972093105316,
0.03926501423120499,
-0.007329616695642471,
0.005830809939652681,
-0.009438621811568737,
0.0006828660261817276,
0.02702915668487549,
0.00022708909818902612,
0.046057529747486115,
-0.035718418657779694,
-0.0007011066772975028,
-0.009742027148604393,
-0.0294021163135767,
0.011625871993601322,
0.014158401638269424,
-0.054949983954429626,
0.03270546346902847,
-0.04173563793301582,
-0.03463241830468178,
0.05806991457939148,
0.004229228012263775,
0.0030529191717505455,
0.02027944289147854,
-0.015366352163255215,
-0.039935193955898285,
0.017932895570993423,
-0.03678872436285019,
0.03892948850989342,
-0.029777362942695618,
-0.010599643923342228,
0.04794515296816826,
-0.009999757632613182,
-0.012433717027306557,
-0.0031126351095736027,
-0.0338154099881649,
-0.0014430899173021317,
0.01221461035311222,
-0.0314929373562336,
0.01705646514892578,
-0.027864335104823112,
0.05220739170908928,
0.003277519717812538,
-0.0462520569562912,
-0.006053175311535597,
-0.017637401819229126,
-0.02519248053431511,
0.029935864731669426,
-0.013527327217161655,
0.04876457154750824,
-0.035473741590976715,
-0.05736623704433441,
0.054313790053129196,
0.014145632274448872,
-0.04085959121584892,
0.02870030701160431,
-0.043092742562294006,
-0.06079590320587158,
-0.02203155681490898,
0.004911771975457668,
0.06849857419729233,
0.0009061675518751144,
0.00322678848169744,
0.012469721958041191,
0.025946378707885742,
-0.004232245963066816,
0.03397607058286667,
0.0024624743964523077,
0.02728354185819626,
0.006642960011959076,
0.008995633572340012,
0.048807431012392044,
-0.004907787311822176,
-0.027973223477602005,
-0.022953622043132782,
0.0030208169482648373,
0.0356682725250721,
0.031417395919561386,
-0.01740313693881035,
0.030435744673013687,
-0.019065801054239273,
0.03008127585053444,
-0.030949214473366737,
0.04576057940721512,
-0.015897806733846664,
-0.026563426479697227,
-0.012410608120262623,
0.0055161332711577415,
0.018262039870023727,
0.009733119048178196,
-0.005472721066325903,
0.02547309175133705,
0.02165008895099163,
-0.017607904970645905,
-0.014696094207465649,
-6.957827025644292e-8,
-0.0356890968978405,
0.049415167421102524,
-0.04097551852464676,
-0.049554094672203064,
0.024336449801921844,
-0.006406104192137718,
0.03554655238986015,
0.023157313466072083,
-0.04606705531477928,
-0.006011139135807753,
-0.05331631004810333,
-0.018908780068159103,
0.046330686658620834,
0.028357796370983124,
0.025397298857569695,
0.03798096626996994,
0.033542025834321976,
0.021652214229106903,
0.00756104476749897,
0.010889038443565369,
-0.06911993771791458,
-0.026993954554200172,
-0.0398963987827301,
-0.015460381284356117,
-0.04262213781476021,
-0.02543444186449051,
-0.03416755422949791,
-0.027205396443605423,
-0.012523620389401913,
-0.02774059772491455,
-0.00031655290513299406,
-0.05512382090091705,
0.029025165364146233,
-0.004909634590148926,
-0.001316162757575512,
-0.05097458139061928,
0.018849525600671768,
0.03165673092007637,
-0.07085438817739487,
0.02105763740837574,
0.0540337897837162,
0.0032440735958516598,
0.0036526203621178865,
-0.00931860227137804,
0.025738371536135674,
0.031092258170247078,
0.024188341572880745,
0.045766886323690414,
0.00323776644654572,
-0.06332602351903915,
0.0006935137207619846,
0.002380728255957365,
0.02849818952381611,
0.014079539105296135,
-0.03598325327038765,
-0.03251410275697708,
-0.03665001317858696,
-0.01869431883096695,
-0.015638943761587143,
0.05058152228593826,
0.0339273102581501,
0.01632222905755043,
0.03479601442813873,
0.024829156696796417,
-0.015261545777320862,
0.03494223207235336,
0.04932659864425659,
0.04875946044921875,
-0.027322150766849518,
-0.06366058439016342,
0.021096862852573395,
-0.014313315972685814,
0.0014147922629490495,
0.0339873731136322,
0.012651251628994942,
-0.021632127463817596,
0.01638973131775856,
-0.00424955366179347,
0.012597432360053062,
0.0031062259804457426,
-0.015870532020926476,
0.009979729540646076,
-0.0009354109060950577,
-0.024584297090768814,
0.05913452431559563,
0.047996796667575836,
0.00497722253203392,
0.02897620014846325,
0.01675497740507126,
-0.013286983594298363,
-0.12700995802879333,
-0.0026914102490991354,
0.05970972776412964,
0.027474278584122658,
-0.033956073224544525,
-0.021087635308504105,
-0.0376066230237484,
0.005404932890087366,
0.05972505360841751,
-0.028064267709851265,
0.011561824940145016,
0.0031230063177645206,
-0.02647489495575428,
-0.00741579057648778,
-0.050849996507167816,
-0.02317449077963829,
0.026451140642166138,
-0.02095574140548706,
-0.0011486411094665527,
-0.03372944891452789,
-0.0077056665904819965,
0.011671195738017559,
0.003804785432294011,
0.04712697118520737,
0.08693376183509827,
0.012303845956921577,
0.02151196077466011,
-0.02772914431989193,
0.010588313452899456,
-0.04166756197810173,
-0.08026861399412155,
0.008333608508110046,
-0.019760943949222565,
0.009019635617733002,
0.016353579238057137,
-0.030199749395251274,
-0.007819104939699173,
0.0007982440292835236,
0.00004136062125326134,
0.029518362134695053,
-0.016120096668601036,
-0.05096857249736786,
0.04254481568932533,
0.03635396435856819,
-0.0059691304340958595,
0.065107561647892,
0.020868344232439995,
-0.02455073781311512,
0.02386726811528206,
0.003524451982229948,
0.05246923118829727,
-0.022834496572613716,
0.012357590720057487,
0.005669152829796076,
0.06741796433925629,
-0.023594949394464493,
0.07248897850513458,
-0.012094956822693348,
0.018353572115302086,
0.010372486896812916,
-0.0006820578710176051,
-0.0007674582302570343,
-0.004542401526123285,
-0.015298926271498203,
-0.0150653887540102,
-0.03744100406765938,
0.016495907679200172,
-0.007574304472655058,
-0.043494921177625656,
-0.011728374287486076,
0.0019975260365754366,
0.018819358199834824,
0.01289602555334568,
0.004041433334350586,
0.012720417231321335,
-0.03885495290160179,
-0.019436821341514587,
0.03588864952325821,
-0.02761530503630638,
0.04728206619620323,
-0.024547608569264412,
-0.01839206926524639,
-0.02969432808458805,
-0.09086640924215317,
-0.04131900891661644,
0.04455236345529556,
-0.01138146873563528,
0.05055835843086243,
-0.05292201042175293,
0.04594218730926514,
0.01860661990940571,
0.024039356037974358,
-0.07338330894708633,
-0.10120994597673416,
0.027736712247133255,
0.04630983620882034,
0.0069479928351938725,
-0.009221178479492664,
0.013262932188808918,
-0.027028461918234825,
-0.030315633863210678,
0.023382769897580147,
0.03720875084400177,
-0.024789368733763695,
-0.00029681134037673473,
0.038906894624233246,
-0.001446294947527349,
0.04523628577589989,
-0.003676476888358593,
0.006314515136182308,
0.0059670573100447655,
-0.03062622621655464,
-0.02238457463681698,
-0.017099427059292793,
0.04467166215181351,
-0.03050917573273182,
-0.029903074726462364,
-0.012744247913360596,
-0.013970290310680866,
0.05184047669172287,
-0.026482559740543365,
-0.03414691612124443,
0.04775302857160568,
0.006529144011437893,
-0.018772942945361137,
-0.02163117751479149,
0.03865489736199379,
0.0010283085284754634,
0.03417478874325752,
0.006060853600502014,
0.0014603226445615292,
-0.04547500982880592,
-0.03613629564642906,
-0.0007525645196437836,
0.04996229335665703,
-0.007763590198010206,
-0.003579638199880719,
0.014653588645160198,
-0.06680794060230255,
-0.012919995002448559,
0.054463572800159454,
-0.0012624304508790374,
0.025666549801826477,
-0.036518394947052,
0.012216819450259209,
0.0000928443914745003,
0.012489791959524155,
-0.010716735385358334,
0.02117130532860756,
-0.0073754689656198025,
-0.003446281189098954,
0.054696232080459595,
-0.018755663186311722,
0.03457726538181305,
-0.00814869999885559,
-0.01887725293636322,
-0.004892685916274786,
0.005283230450004339,
-0.0327514111995697,
0.0359952375292778,
-0.03809681162238121,
-0.014923677779734135,
-0.0346810482442379,
0.01562013290822506,
0.01254577748477459,
0.007492584642022848,
-0.0354546457529068,
0.0011088992469012737,
0.037078022956848145,
-0.0046751173213124275,
0.03501526638865471,
0.008004408329725266,
-0.058698806911706924,
0.028776424005627632,
-0.0403074249625206,
0.05992072448134422,
0.003515620017424226,
-0.010437767021358013,
0.06929372996091843,
0.0061974432319402695,
0.003536975709721446,
-0.030693640932440758,
0.009107721038162708,
-0.04285909980535507,
-0.011819922365248203,
-0.029548760503530502,
0.017157630994915962,
0.007724668364971876,
0.03084784932434559,
0.040797825902700424,
-0.0014713592827320099,
0.017609307542443275,
0.014025362208485603,
-0.0711083635687828,
-0.012025871314108372,
-0.024781500920653343,
-0.028620675206184387,
0.06072818115353584,
-0.02005448192358017,
-0.004838950000703335,
-0.015291096642613411,
-0.03135251998901367,
0.03565210849046707,
0.07178111374378204,
0.04512832313776016,
-0.04951095953583717,
0.0702693834900856,
-0.038562510162591934,
0.03822004422545433,
-0.058050889521837234,
0.0020529956091195345,
0.1259394735097885,
0.03948972001671791,
0.03474857658147812,
-0.05996600165963173,
-0.017603689804673195,
-0.052328139543533325,
-0.005846490152180195,
0.004262985195964575,
-0.009653454646468163,
-0.03222202509641647,
0.008978135883808136,
-0.015044360421597958,
0.05087694153189659,
0.022858796641230583,
0.03164200484752655,
0.010456137359142303,
-0.01590062491595745,
-0.03130815550684929,
0.04159536585211754,
0.011353401467204094,
0.0060601187869906425,
0.034353021532297134,
-0.06398046016693115,
0.009197641164064407,
-0.0358111634850502,
-0.012994104065001011,
-0.04426229000091553,
-0.04461280629038811,
0.005899024195969105,
0.005597166251391172,
-0.063339963555336,
-0.018814636394381523,
0.01019868440926075,
-0.04555949568748474,
-0.07590796798467636,
0.047182634472846985,
0.0008273647981695831,
0.010627763345837593,
0.01946854591369629,
0.035719938576221466,
0.019148653373122215,
-0.0050023021176457405,
-0.008805873803794384,
0.021633461117744446,
-0.055991869419813156,
0.019639072939753532,
-0.04219599813222885,
0.026828818023204803,
-0.01562067773193121,
0.006652468349784613,
0.035761456936597824,
-0.0027554528787732124,
-0.0019369205692782998,
-0.05493675172328949,
-0.059530820697546005,
-0.0010467503452673554,
-0.0007827092777006328,
-0.0003739888488780707,
-0.014983952976763248,
-0.03980612754821777,
0.022067051380872726,
0.014351572841405869,
-0.012393197976052761,
-0.008915442042052746,
0.010302197188138962,
0.02983430027961731,
0.05147440731525421,
0.029071003198623657,
0.013092843815684319,
-0.021933600306510925,
-0.014044800773262978,
0.0084944823756814,
-0.03214329853653908,
-0.001394580234773457,
-0.018645629286766052,
0.05134587734937668,
0.005963405594229698,
-0.03557262197136879,
-0.018843021243810654,
0.001432783086784184,
-0.09001028537750244,
0.05134420841932297,
0.017430512234568596,
-0.0014332118444144726,
-0.029567496851086617,
0.010668272152543068,
0.03250177204608917,
0.04341967776417732,
-0.011602749116718769,
0.01317717507481575,
-0.0018696254119277,
0.05560500547289848,
-0.0017096950905397534,
-0.03778311610221863,
0.007820605300366879,
0.00027054979000240564,
-0.009614755399525166,
0.017427809536457062,
0.0074524409137666225,
0.041585564613342285,
0.0078018344938755035,
0.0001383481576340273,
-0.028315773233771324,
-0.004925206769257784,
-0.039360858500003815,
-0.003267968073487282,
0.017001967877149582,
-0.013599197380244732,
-0.01835443079471588,
-0.005533568095415831,
-0.001129890326410532,
-0.016028089448809624,
-0.00014130388444755226,
-0.025460094213485718,
0.02883119136095047,
0.007266418542712927,
0.02703106962144375,
-0.04375210404396057,
-0.01426441129297018,
-0.0038727764040231705,
0.020147956907749176,
-0.038396645337343216,
-0.013987775892019272,
-0.05572887510061264,
-0.020721234381198883,
-0.01974710077047348,
0.01329964492470026,
-0.006729505490511656,
0.038048483431339264,
-0.04540132358670235,
0.039307355880737305,
0.005750524345785379,
-0.004191154148429632,
0.004460029769688845,
0.01063051912933588,
0.0111764594912529,
-0.034794848412275314,
0.06218262016773224,
-0.026716237887740135,
-0.017324943095445633,
0.04684543237090111,
0.013233648613095284,
-0.0147172249853611,
0.014263632707297802,
-0.014916930347681046,
0.003807414323091507,
0.003492071758955717,
0.02351261116564274,
0.02644408494234085,
0.032639529556035995,
-0.010883538983762264,
0.0014202096499502659,
-0.016907354816794395,
-0.02916303649544716,
-0.012244858779013157,
-0.03172525018453598,
-0.0030829960014671087,
-0.008181455545127392,
-0.00605356227606535,
0.0446736142039299,
0.009745072573423386,
0.026792209595441818,
-0.004106698092073202,
0.01548028364777565,
0.009097476489841938,
0.0012000547721982002,
0.08061351627111435,
-0.009586691856384277,
-0.020236870273947716,
0.019430011510849,
-0.0011084283469244838,
0.007428379263728857,
-0.0044058156199753284,
-0.02701558917760849,
-0.07229514420032501,
-0.03318623825907707,
0.008827676065266132,
0.005329868756234646,
0.022125085815787315,
-0.05083446204662323,
-0.01600559800863266,
0.03357506915926933,
-0.08014591783285141,
0.01517689973115921,
-0.031134694814682007,
-0.015541818924248219,
0.012408822774887085,
-0.01012439839541912,
0.01250544749200344,
0.022563379257917404,
0.05518009141087532,
0.04210688918828964,
-0.013942550867795944,
-0.0038992499466985464,
0.00822946336120367,
-0.014913570135831833,
-0.03369160369038582,
0.02917567454278469,
0.026441920548677444,
-0.02505282312631607,
0.03609386086463928,
-0.017121171578764915,
0.014120437204837799,
0.03518378362059593,
0.02479972504079342,
0.01679743267595768,
-0.020595427602529526,
0.030570894479751587,
0.0010548338759690523,
0.04070645943284035,
-0.02215971052646637,
-0.025905689224600792,
0.01778159849345684,
-0.0007364177145063877,
-0.020774222910404205,
0.0448702909052372,
0.014537355862557888,
-0.01957823522388935,
0.009238033555448055,
-0.04737545922398567,
0.00857128668576479,
0.02419333904981613,
-0.02238473854959011,
-0.006812296342104673,
-0.004319422412663698,
0.04956016317009926,
-0.0038498362991958857,
0.002611311385408044,
-0.00009480689186602831,
-0.04549775645136833,
-0.01804807037115097,
0.01759958267211914,
-0.017726458609104156,
-0.0011402377858757973,
0.010451320558786392,
0.0146874925121665,
-0.03498350828886032,
-0.006071881856769323,
0.0029409697744995356,
-0.017651591449975967,
-0.07157066464424133,
-0.0014058032538741827,
0.002641419880092144,
-0.003971008583903313,
0.005174967460334301,
-0.030068697407841682,
-0.030312275514006615,
0.0229628998786211,
0.01223573088645935,
-0.007397274021059275,
0.027112634852528572,
-0.062124863266944885,
-0.01718330755829811,
-0.07942362129688263,
0.05342983081936836,
0.02028971165418625,
-0.034318115562200546,
-0.02206861600279808,
-0.056692611426115036,
-0.01240917481482029,
0.019991490989923477,
0.08921300619840622,
-0.014576667919754982,
-0.02833230048418045,
0.050951797515153885,
-0.042504943907260895,
0.04944457858800888,
-0.06652368605136871,
-0.021751251071691513,
0.014651380479335785,
0.021247930824756622,
0.032785814255476,
0.0066944570280611515,
-0.03890851140022278,
0.02496335655450821,
0.021866675466299057,
-0.02072242833673954,
0.03152905032038689,
-0.03179210051894188,
-0.02646203525364399,
0.030406132340431213,
0.02242003194987774,
-0.0004856923478655517,
0.05169963091611862,
-0.009636344388127327,
0.00910374615341425,
-0.010460897348821163,
0.012437638826668262,
-0.03431985154747963,
0.0014631402445957065,
-0.04026477038860321,
-0.0003472829412203282,
0.006854761391878128,
0.0035385286901146173,
0.034359924495220184,
-0.041868411004543304,
-0.02058696188032627,
0.04825938865542412,
-0.01966823637485504,
-0.0005671458784490824,
0.03344402462244034,
-0.003986329771578312,
-0.00679057976230979,
0.012829871848225594,
0.006938780192285776,
0.0027970916125923395,
0.04229312762618065,
-0.01782197691500187,
0.03181832283735275,
0.014413009397685528,
-0.0315486378967762,
0.00264093279838562,
0.01381396222859621,
0.02212391421198845,
-0.01589510589838028,
0.01313686277717352,
0.016107361763715744,
-0.011756693944334984,
0.003035677131265402,
0.016494154930114746,
-0.002997260307893157,
0.006918579339981079,
0.031128406524658203,
-0.04007778689265251,
0.07882104814052582,
-0.015863629058003426,
0.03012269176542759,
-0.00392406340688467,
0.009531448595225811,
0.014060592278838158,
0.019012171775102615,
0.038297198712825775,
0.017514239996671677,
-0.025648359209299088,
-0.036982640624046326,
-0.00018512732640374452,
0.02952260710299015,
0.0185511764138937,
-0.07740450650453568,
0.013489173725247383,
-0.003602090757340193,
0.0016940408386290073,
-0.04149550944566727,
-0.004077097401022911,
-0.03299352526664734,
0.0059325192123651505,
0.026279229670763016,
0.0058133359998464584,
0.02427147887647152,
-0.0015970690874382854,
0.0068789999932050705,
-0.033106088638305664,
0.041732508689165115,
-0.031792230904102325,
0.022030601277947426,
-0.009246373549103737,
0.02827518619596958,
0.008309910073876381,
0.0016886689700186253
] |
<p>If negative mass is rotating around fixed positive mass, then what will be the nature of force and how?</p>
| 343 |
[
-0.041538454592227936,
-0.02668093889951706,
-0.031609077006578445,
-0.00575430179014802,
0.040617696940898895,
-0.0043224249966442585,
-0.027644773945212364,
-0.014963583089411259,
-0.009548530913889408,
-0.030665216967463493,
0.023685632273554802,
0.027196336537599564,
0.029103392735123634,
-0.006116901990026236,
0.021192079409956932,
0.005559281911700964,
-0.030146043747663498,
-0.005120915360748768,
-0.018445376306772232,
-0.013701656833291054,
0.007269734982401133,
0.016671331599354744,
0.030035102739930153,
0.04221363738179207,
-0.024371769279241562,
0.01878805086016655,
0.05776943266391754,
-0.026393413543701172,
0.025729363784193993,
0.07207317650318146,
0.013308003544807434,
-0.01684091053903103,
0.025065109133720398,
0.0413326695561409,
0.021237334236502647,
0.004462097771465778,
-0.031068876385688782,
-0.02141409181058407,
-0.029571132734417915,
0.03088892064988613,
-0.04450319707393646,
-0.015309905633330345,
-0.010765704326331615,
0.04989044368267059,
-0.03441190719604492,
0.01784265600144863,
-0.00481222802773118,
0.022407883778214455,
0.078421950340271,
-0.0685700997710228,
0.06242326274514198,
-0.004631086252629757,
0.04785851016640663,
0.0008546446333639324,
0.005578814540058374,
-0.02512148767709732,
0.0804014503955841,
0.046323057264089584,
-0.022423146292567253,
-0.0598447248339653,
-0.024683034047484398,
-0.013138636946678162,
0.0055281976237893105,
-0.05205395445227623,
-0.021435534581542015,
0.04082933068275452,
-0.035034339874982834,
-0.012789816595613956,
0.008577668108046055,
0.02029988169670105,
0.02417752705514431,
0.040908344089984894,
0.023428644984960556,
-0.00799722969532013,
0.0038409412372857332,
-0.05741296708583832,
0.016386808827519417,
0.008625452406704426,
0.0024554659612476826,
0.04315219447016716,
-0.01539930235594511,
0.010048872791230679,
0.03436453267931938,
0.027737965807318687,
0.008508197963237762,
-0.052855152636766434,
0.05941707268357277,
0.0028050828259438276,
0.011708537116646767,
0.032437801361083984,
0.009437637403607368,
-0.01627873070538044,
0.010034307837486267,
-0.04991675913333893,
-0.03770735487341881,
0.03213367238640785,
0.0050410013645887375,
0.022327223792672157,
0.005315124522894621,
-0.015906035900115967,
-0.0005506513989530504,
0.0051203235052526,
0.017322732135653496,
0.07553421705961227,
0.02440009079873562,
-0.018162932246923447,
-0.032697875052690506,
0.025817815214395523,
-0.012788360007107258,
-0.027384160086512566,
-0.013377761468291283,
0.0008785434765741229,
-0.015179998241364956,
-0.051536206156015396,
0.02876538783311844,
-0.05527742579579353,
0.023112375289201736,
-0.03735734894871712,
0.06393186748027802,
0.05309309437870979,
0.016523290425539017,
-0.021587984636425972,
0.013707336038351059,
-0.027760758996009827,
-0.014920552261173725,
0.0012299275258556008,
0.0438784584403038,
-0.00024402501003351063,
0.0018241044599562883,
0.025551920756697655,
0.013730162754654884,
-0.044258084148168564,
-0.031447555869817734,
0.01611248590052128,
0.049407582730054855,
-0.004133014008402824,
-0.11099240183830261,
-0.041245169937610626,
0.052571773529052734,
-0.033412009477615356,
-0.025842610746622086,
-0.048383183777332306,
0.013445727527141571,
0.01833478733897209,
0.0786469504237175,
0.029165226966142654,
-0.03405585139989853,
0.02534027211368084,
0.040946751832962036,
0.007326619233936071,
0.010646229609847069,
-0.017249321565032005,
-0.013901086524128914,
-0.034789249300956726,
-0.048504963517189026,
-0.05680374056100845,
0.013944791629910469,
0.017433522269129753,
0.001265967614017427,
-0.022869450971484184,
0.028959007933735847,
-0.027544014155864716,
0.03131666034460068,
0.03232871741056442,
-0.006786290556192398,
-0.03314962238073349,
0.054128654301166534,
0.028515707701444626,
-0.03135981410741806,
0.060153331607580185,
0.013173110783100128,
0.0500451922416687,
0.01494134683161974,
0.03137757256627083,
0.021678248420357704,
-0.04514288902282715,
-0.016441820189356804,
-0.02078559622168541,
0.03202512860298157,
-0.021819639950990677,
-0.03646200895309448,
-0.04032599925994873,
-0.03087841533124447,
0.0066472128964960575,
-0.0054033431224524975,
0.06093374639749527,
-0.013157102279365063,
0.028845231980085373,
0.012401171959936619,
-0.06334695965051651,
-0.00662436056882143,
-0.07297886162996292,
0.03513195365667343,
-0.01711089350283146,
-0.022005179896950722,
0.009808908216655254,
0.04673801735043526,
0.0371256060898304,
-0.04107707366347313,
0.006999381817877293,
0.0120958611369133,
0.050201114267110825,
-0.005618205294013023,
0.008076303638517857,
0.03201982378959656,
0.03767157718539238,
0.014764404855668545,
-0.014463852159678936,
0.036395423114299774,
0.016953280195593834,
-0.02831098437309265,
0.029553337022662163,
-0.004255102016031742,
0.0019404159393161535,
0.009591612033545971,
-0.011057634837925434,
0.03466884046792984,
0.009168810211122036,
-0.0003208841080777347,
0.03433334082365036,
-0.015282261185348034,
0.08104592561721802,
0.03112895041704178,
-0.010007700882852077,
0.030649075284600258,
0.06228211894631386,
0.023068178445100784,
0.0019936684984713793,
-0.03681768849492073,
-0.009420253336429596,
-0.04577025771141052,
-0.00973803736269474,
0.02444138564169407,
0.061081837862730026,
-0.03539295494556427,
0.03462054952979088,
0.025311971083283424,
0.02868151292204857,
0.031224772334098816,
0.017132923007011414,
-0.028194760903716087,
-0.034770842641592026,
0.024821100756525993,
0.0008180010481737554,
-0.0009556850418448448,
0.017628468573093414,
0.04336072504520416,
0.04350224509835243,
-0.0060931602492928505,
0.018940230831503868,
-0.04125995934009552,
0.04319152608513832,
-0.011234051547944546,
0.02383814938366413,
0.013943214900791645,
-0.03547206148505211,
0.03891424462199211,
0.00556739280000329,
-0.009033081121742725,
0.009179895743727684,
-0.017158333212137222,
-0.0006185175734572113,
-0.030789149925112724,
0.022701643407344818,
0.004646546207368374,
0.01967620849609375,
0.001889179926365614,
-0.040602076798677444,
0.029927212744951248,
-0.0404091402888298,
0.00291012623347342,
-0.008932220749557018,
0.003998358268290758,
-0.010241245850920677,
-0.0028026849031448364,
0.00653025833889842,
0.017537720501422882,
0.04192880168557167,
-0.012219641357660294,
-0.05275767296552658,
0.0064104050397872925,
-0.028701378032565117,
-0.01505114883184433,
0.02803802862763405,
-0.04608986899256706,
0.02641354314982891,
-0.04706751927733421,
-0.039745163172483444,
0.04988650977611542,
-0.00427979975938797,
0.014929033815860748,
-0.002045886591076851,
-0.005084459204226732,
-0.04125364497303963,
-0.008810809813439846,
-0.05526147037744522,
-0.00927494466304779,
-0.05253492295742035,
0.019980598241090775,
0.06200321018695831,
0.00448666512966156,
-0.02452133782207966,
0.00218026852235198,
-0.05911139398813248,
-0.08120302110910416,
-0.014138706028461456,
-0.00752666499465704,
0.06155594438314438,
-0.04030783101916313,
0.03443417698144913,
0.009239156730473042,
-0.03151704743504524,
0.027495315298438072,
-0.012126460671424866,
-0.02204003743827343,
0.027689754962921143,
-0.027927158400416374,
0.031427424401044846,
-0.001081571215763688,
-0.044821061193943024,
0.0686420202255249,
-0.0069799767807126045,
0.00002099615267070476,
-0.025953510776162148,
-0.020030098035931587,
-0.01598951406776905,
-0.031444210559129715,
0.031498320400714874,
0.03931890428066254,
-0.0005722695495933294,
-0.007998770102858543,
0.07585584372282028,
-0.0021651547867804766,
0.005912106484174728,
0.022798314690589905,
-0.03946913406252861,
0.002923313993960619,
0.0004089026479050517,
0.0028659203089773655,
0.04374593496322632,
-0.023441825062036514,
-0.008851555176079273,
0.027610233053565025,
0.03424927964806557,
0.016617845743894577,
0.0015680224169045687,
-0.04648583009839058,
0.06533291935920715,
0.012161321938037872,
0.0044534821063280106,
-0.00006019584907335229,
0.06125611439347267,
-0.016256658360362053,
-0.02541768178343773,
0.02895742654800415,
-0.018320877104997635,
0.058439213782548904,
-0.016290444880723953,
-0.012082686647772789,
0.038208119571208954,
0.05214053764939308,
-0.034817036241292953,
-0.06289106607437134,
-0.012832443229854107,
-0.023140445351600647,
0.03603264316916466,
-0.04229305312037468,
0.005069051403552294,
0.027682170271873474,
0.03187647461891174,
0.007843797095119953,
0.031599629670381546,
-0.014291753061115742,
0.006231263745576143,
-0.05789731442928314,
-0.008877254091203213,
0.010062224231660366,
0.03050893358886242,
-0.01343980897217989,
0.04464143142104149,
0.033591412007808685,
0.01972895860671997,
0.005849006585776806,
0.007382553070783615,
-0.09444473683834076,
0.04430881887674332,
-0.03923279047012329,
0.001877811155281961,
0.00020529130415525287,
0.01722249574959278,
-0.024739183485507965,
-0.018734196200966835,
0.0013078703777864575,
-0.04611523821949959,
-0.04916710406541824,
-0.0502593033015728,
0.006013778503984213,
-0.03581029921770096,
-0.031859271228313446,
-0.026826905086636543,
0.03503907471895218,
0.059682246297597885,
-0.023228269070386887,
0.020303484052419662,
0.028398839756846428,
-0.04508106783032417,
-0.011167860589921474,
-0.01346112322062254,
-0.01662631146609783,
0.013391832821071148,
0.035761214792728424,
0.030548935756087303,
0.025388961657881737,
-0.007127069402486086,
0.00868734996765852,
0.004495873115956783,
0.029577918350696564,
0.014723418280482292,
-0.02321094088256359,
-0.019030267372727394,
-0.0467827282845974,
-0.015878628939390182,
-0.02544480748474598,
0.05863972008228302,
-0.007791474461555481,
-0.012898111715912819,
0.04356834292411804,
-0.024731779471039772,
0.0014801942743360996,
0.037381865084171295,
0.06872955709695816,
0.05763852596282959,
-0.013873429037630558,
-0.06318385899066925,
-0.0008167336927726865,
-0.035278838127851486,
0.010563772171735764,
0.008516887202858925,
-0.017547912895679474,
-0.052724506705999374,
0.019819121807813644,
0.009824670851230621,
0.02359195612370968,
-0.010129427537322044,
0.00827412586659193,
-0.01993422955274582,
0.028646841645240784,
-0.0511690117418766,
-0.004910006187856197,
0.013378188945353031,
0.04724317044019699,
0.05283728986978531,
-0.014795387163758278,
-0.012843518517911434,
-0.09747814387083054,
-0.014177197590470314,
0.03238527849316597,
0.025795426219701767,
-0.006296128500252962,
-0.007790872827172279,
-0.03954657167196274,
-0.034441832453012466,
0.027138017117977142,
-0.04970347881317139,
0.025739118456840515,
-0.023565610870718956,
0.021946381777524948,
-0.014384052716195583,
-0.005182931199669838,
-0.03110705502331257,
0.02395259402692318,
-0.019556978717446327,
-0.028771480545401573,
-0.030165035277605057,
0.0278400257229805,
-0.009094199165701866,
0.016204826533794403,
0.028602469712495804,
0.028677230700850487,
0.02129710279405117,
-0.009078494273126125,
-0.014924571849405766,
0.016827309504151344,
-0.022882560268044472,
-0.1002996563911438,
0.018067263066768646,
0.0243731290102005,
-0.014311433769762516,
0.017192648723721504,
-0.02950538881123066,
-0.06546846777200699,
-0.031086314469575882,
-0.014561636373400688,
0.009137257002294064,
0.00600789999589324,
-0.06824858486652374,
-0.014866585843265057,
0.005876973737031221,
-0.01100328378379345,
0.02247782237827778,
0.017680710181593895,
-0.026563890278339386,
-0.03606485202908516,
-0.013847511261701584,
0.03686705604195595,
-0.012217889539897442,
-0.013308565132319927,
-0.033871348947286606,
0.018664376810193062,
-0.02092599868774414,
0.03922172263264656,
0.003932952415198088,
0.03520943596959114,
-0.024144873023033142,
-0.04206070676445961,
-0.029947929084300995,
0.055768389254808426,
0.018807198852300644,
-0.006850192788988352,
-0.0011751244310289621,
-0.005135149694979191,
0.0014761335914954543,
-0.03941160440444946,
-0.0028364304453134537,
0.023702843114733696,
0.0036138000432401896,
0.023505523800849915,
-0.006822798866778612,
0.004678362514823675,
0.0055749923922121525,
-0.04882898926734924,
0.0019829687662422657,
-0.05667285993695259,
0.04468245804309845,
0.0053765131160616875,
-0.01543592568486929,
0.04374530166387558,
-0.07180646061897278,
-0.04605158790946007,
0.029420364648103714,
-0.007094806060194969,
-0.002851952100172639,
-0.03570505976676941,
0.026130760088562965,
0.036545924842357635,
0.0004432878631632775,
-0.06173676252365112,
-0.04371817409992218,
0.008196594193577766,
-0.0018479381687939167,
0.01893698051571846,
-0.011346395127475262,
0.007248838897794485,
-0.026523517444729805,
-0.03417015075683594,
-0.02148163877427578,
0.06767503917217255,
-0.05955411121249199,
0.011908288113772869,
0.025446591898798943,
-0.018308740109205246,
0.06073124706745148,
-0.02764439955353737,
-0.01768774911761284,
-0.01549236848950386,
-0.0018734642071649432,
0.006250688806176186,
0.018859408795833588,
0.04816468432545662,
-0.023659439757466316,
-0.04095492139458656,
-0.019001178443431854,
-0.016950489953160286,
0.03652925044298172,
-0.02068360149860382,
0.041906844824552536,
0.023629656061530113,
0.03950909152626991,
-0.006348922848701477,
-0.023816488683223724,
0.04011528193950653,
0.004686386790126562,
0.04047631099820137,
0.0220834631472826,
-0.011390043422579765,
-0.05249989777803421,
-0.06441952288150787,
0.03251258283853531,
-0.0005118527333252132,
-0.029488133266568184,
-0.005612918641418219,
0.04788205027580261,
-0.00835680402815342,
0.0064614214934408665,
-0.001776388380676508,
-0.029204757884144783,
0.006453449837863445,
0.004533556755632162,
-0.0033214353024959564,
0.027646716684103012,
-0.003466905327513814,
-0.017488081008195877,
-0.02146979607641697,
-0.02295675314962864,
-0.03364534676074982,
0.05866217613220215,
0.0012858104892075062,
0.075275719165802,
-0.0012021200964227319,
-0.00524752214550972,
-0.018465276807546616,
-0.010600014589726925,
0.02631130814552307,
0.0024500449653714895,
-0.0034576687030494213,
0.023350698873400688,
-0.04057666286826134,
0.030169781297445297,
0.028601577505469322,
0.048332005739212036,
-0.0033131535165011883,
-0.0030188385862857103,
0.04096260666847229,
0.02793455868959427,
0.023282503709197044,
0.0034973458386957645,
-0.0261936467140913,
0.0216282419860363,
-0.024548247456550598,
0.045704517513513565,
-0.0035503176040947437,
-0.019863616675138474,
0.021323421970009804,
-0.020925087854266167,
0.032788749784231186,
-0.01874026656150818,
-0.012190270237624645,
-0.019012564793229103,
0.009079213254153728,
0.024652736261487007,
0.018263990059494972,
-0.028124090284109116,
0.03583713248372078,
0.022301021963357925,
0.006287445314228535,
0.02729635313153267,
0.01174220535904169,
-0.05964333936572075,
-0.02504703402519226,
-0.015907276421785355,
-0.046445172280073166,
0.04354424402117729,
-0.012881539762020111,
-0.03585928678512573,
0.02888568863272667,
-0.02333172596991062,
0.0178428515791893,
0.04110800102353096,
0.016355497762560844,
-0.043150246143341064,
0.0691383108496666,
-0.009966227225959301,
0.017344584688544273,
0.0011270398972555995,
0.01990438811480999,
0.11962094902992249,
0.03630171716213226,
0.010073010809719563,
-0.07134156674146652,
0.014162435196340084,
-0.015420208685100079,
0.024603920057415962,
-0.03236345201730728,
0.03232144936919212,
-0.00935172289609909,
0.023569107055664062,
0.0028011566027998924,
0.05264633893966675,
0.003227625275030732,
-0.007153692655265331,
0.06425582617521286,
-0.029217269271612167,
-0.03420374542474747,
-0.042939186096191406,
0.0026400270871818066,
-0.013366887345910072,
0.03089272230863571,
-0.0302423145622015,
0.030434412881731987,
-0.041022785007953644,
0.014118441380560398,
-0.04182467237114906,
-0.03929739445447922,
0.003630537772551179,
-0.011168216355144978,
-0.044705022126436234,
0.025900395587086678,
-0.0067782653495669365,
-0.036212824285030365,
-0.039394427090883255,
0.013845391571521759,
0.0034828209318220615,
-0.006351910065859556,
0.03581558167934418,
-0.0009448579512536526,
0.0022414540871977806,
0.010976140387356281,
-0.0071578738279640675,
0.00710039958357811,
-0.05319485813379288,
0.025668567046523094,
-0.019671818241477013,
0.053366564214229584,
-0.012412688694894314,
0.025476740673184395,
0.04053468629717827,
0.016670789569616318,
-0.028416454792022705,
-0.02465544454753399,
-0.00426600081846118,
-0.019840821623802185,
0.014263161458075047,
-0.013916482217609882,
-0.035791389644145966,
-0.011745516210794449,
0.026612844318151474,
-0.012424429878592491,
0.028160857036709785,
-0.023768005892634392,
0.021358966827392578,
0.029416784644126892,
0.03534075990319252,
0.036226607859134674,
-0.02741922438144684,
-0.02264614775776863,
-0.014946074225008488,
-0.02413424290716648,
-0.04042208939790726,
-0.0057802023366093636,
0.017242038622498512,
0.01706812158226967,
0.030153080821037292,
-0.013284911401569843,
0.024042489007115364,
-0.023697402328252792,
-0.03317082300782204,
0.03768497705459595,
-0.02750835008919239,
-0.010024160146713257,
0.009007151238620281,
0.013557178899645805,
0.018241791054606438,
0.03984447941184044,
-0.04410167038440704,
0.006337916944175959,
-0.006355467718094587,
-0.0011367819970473647,
0.021057046949863434,
-0.03339468687772751,
0.004939774051308632,
0.016212886199355125,
-0.03407839685678482,
-0.015464667230844498,
-0.025966238230466843,
-0.015150230377912521,
0.04549344629049301,
-0.012906907126307487,
-0.01673661358654499,
0.04308319091796875,
-0.022223234176635742,
0.008246703073382378,
0.03637159988284111,
-0.005087955854833126,
-0.01779634691774845,
0.025513986125588417,
-0.023477643728256226,
-0.04754505306482315,
-0.031737469136714935,
-0.007827366702258587,
-0.038857601583004,
0.004691908601671457,
0.0795280858874321,
-0.03847392648458481,
0.02279922179877758,
-0.021180840209126472,
0.010853341780602932,
-0.05012058466672897,
-0.013181935995817184,
-0.04432979226112366,
0.007964148186147213,
-0.006143290549516678,
-0.016432201489806175,
-0.023480843752622604,
0.03431149944663048,
0.0179994385689497,
-0.008260280825197697,
-0.01356465369462967,
0.0015487070195376873,
-0.003640295471996069,
0.01588822528719902,
0.059162598103284836,
-0.03454861789941788,
0.05310031771659851,
0.007827933877706528,
-0.01786947250366211,
0.03996897116303444,
-0.05013437941670418,
-0.04200640693306923,
0.02374141290783882,
-0.017361273989081383,
0.03629866614937782,
0.005308870691806078,
-0.029116854071617126,
0.017745407298207283,
0.049504686146974564,
-0.02492503821849823,
-0.01797817461192608,
-0.026345420628786087,
-0.03172001615166664,
-0.04011772572994232,
0.007099706679582596,
0.017351320013403893,
-0.0419653058052063,
-0.02289397455751896,
0.03685801476240158,
0.06745367497205734,
-0.04052219167351723,
-0.015449059195816517,
0.04450288042426109,
0.01512322947382927,
0.029347075149416924,
0.031573329120874405,
0.011099361814558506,
0.008291133679449558,
0.0379689522087574,
-0.029261557385325432,
0.01222015917301178,
-0.012220132164657116,
-0.006432076916098595,
-0.0906800851225853,
-0.03479364886879921,
0.03106079436838627,
-0.019691742956638336,
0.05119512230157852,
-0.044600531458854675,
-0.0162842757999897,
0.013848992064595222,
-0.0663689523935318,
0.01293521374464035,
-0.04516896232962608,
0.01407461054623127,
0.036079056560993195,
-0.032070841640233994,
0.005246184766292572,
0.06925453990697861,
-0.000013991598279972095,
0.0407431498169899,
-0.007615760900080204,
0.01700410805642605,
-0.005809123162180185,
-0.013454483821988106,
0.014490904286503792,
0.021694626659154892,
-0.006175430491566658,
0.009501910768449306,
0.07295267283916473,
-0.0014138828264549375,
-0.041184037923812866,
0.04864084720611572,
-0.005143086891621351,
-0.004510469734668732,
-0.005654321517795324,
0.015561185777187347,
0.00623399019241333,
0.026083698496222496,
-0.012608378194272518,
-0.009719286113977432,
-0.025783788412809372,
0.03652255982160568,
0.012184197083115578,
0.06541936099529266,
-0.0039016790688037872,
-0.0007080560899339616,
0.013703001663088799,
-0.04427572712302208,
0.003910730592906475,
0.0011839884100481868,
-0.02676188200712204,
0.0006957436562515795,
-0.010372504591941833,
0.020364347845315933,
-0.019405605271458626,
-0.014267230406403542,
0.010684389621019363,
-0.034298334270715714,
-0.0005199339939281344,
0.029096947982907295,
0.0010528468992561102,
-0.0039410763420164585,
0.03651091456413269,
0.025441523641347885,
0.0032790254335850477,
0.014423553831875324,
-0.016090162098407745,
0.029981156811118126,
-0.06495242565870285,
-0.008214765228331089,
0.009201047010719776,
0.011146477423608303,
0.009154458530247211,
-0.07011028379201889,
-0.012875624932348728,
0.035066552460193634,
0.034391701221466064,
0.0352436788380146,
-0.0230562761425972,
-0.0676138624548912,
0.004166510421782732,
-0.0670708566904068,
-0.011360298842191696,
-0.013285554014146328,
0.003307415172457695,
-0.038290366530418396,
-0.03558101877570152,
-0.028890592977404594,
-0.0055225747637450695,
0.04744642600417137,
0.01929977536201477,
-0.02992517501115799,
0.004444905091077089,
-0.01141918171197176,
0.01421540230512619,
-0.026116441935300827,
-0.009839868173003197,
-0.013946798630058765,
-0.05428983271121979,
0.03424736484885216,
-0.015824832022190094,
-0.024926060810685158,
0.029228175058960915,
0.0020803918596357107,
-0.010417402721941471,
0.03319982811808586,
-0.0006196973263286054,
-0.06738333404064178,
0.05675051733851433,
0.032267726957798004,
0.015531931072473526,
0.0622226744890213,
-0.004550363402813673,
0.028249111026525497,
0.022860802710056305,
-0.03220389783382416,
-0.03433581814169884,
0.0019442528719082475,
-0.0545121431350708,
0.011639591306447983,
-0.00912929605692625,
-0.01923862099647522,
0.03888241946697235,
-0.006271700374782085,
-0.026185346767306328,
0.059221867471933365,
-0.05140022933483124,
0.003897464368492365,
0.03148536756634712,
0.03653007745742798,
0.03827039897441864,
-0.01146102324128151,
0.016046008095145226,
0.004690220113843679,
0.0022451397962868214,
0.012821570038795471,
0.024119824171066284,
0.002894983859732747,
-0.004885244183242321,
-0.01813455857336521,
0.060562193393707275,
0.012208090163767338,
0.0357857309281826,
0.010201689787209034,
0.04145778715610504,
-0.021705089136958122,
-0.0029248627834022045,
-0.013584920205175877,
-0.008775577880442142,
0.03753934055566788,
0.025758398696780205,
0.007528549525886774,
0.08407069742679596,
-0.01889413222670555,
0.03345905616879463,
0.008856351487338543,
-0.014015396125614643,
-0.02401886135339737,
0.008600989356637001,
-0.001002462930046022,
0.03928424417972565,
0.0154465576633811,
-0.01914191246032715,
-0.0096511235460639,
-0.02289026789367199,
0.009978861548006535,
-0.0053087505511939526,
0.004709839820861816,
0.023689577355980873,
0.005043434910476208,
-0.009114598855376244,
-0.03116537444293499,
-0.043407078832387924,
-0.021039774641394615,
0.03931460529565811,
0.026484446600079536,
0.038160741329193115,
0.0017731280531734228,
0.022168271243572235,
-0.012419781647622585,
0.0210445374250412,
-0.053351111710071564,
-0.04138624668121338,
-0.01464939583092928,
0.017815569415688515,
-0.017434339970350266,
-0.016322772949934006
] |
<p>Usually when discussing Fermi liquid theory, it is stated that due to the quasiparticles effectively behaving like a free electron gas with effective mass, the specific heat is linear in $T$ at small temperatures.</p>
<p>However, it turns out the Helium-3 has also a dependence of type $T^3 \ln T$. I want to understand where this comes from. Apparently it has something to do with spin fluctuations. I found the relevant paper by Pethick et al ( Pethick, C. J., and G. M. Carneiro. “Specific Heat of a Normal Fermi Liquid. I. Landau-Theory Approach.” Physical Review A 7, no. 1 (January 1, 1973): 304–318. ) however a bit dense to read and not very elucidating. </p>
<p>Since at that time Pethick et al
didn't know about renormalization group and other nice modern techniques, is there today maybe a more accessible treatment of spin fluctuations?</p>
<p>For example, I think I have gleaned from their paper that the contribution somehow arises from a dressing of the two-particle vertex. But on the other hand, RG tells me that the Landau parameters $F$ don't renormalize, so I wouldn't expect such a dressing. </p>
<p>It also seems that their contribution to the specific heat gives a term that depends not only on the angle between two scattered momenta, but also their magnitude. However, in the usual RG approach all deviations from the Fermi surface give rise to irrelevant operators... (In the language of the review paper of Shankar, Shankar, R. “Renormalization-group Approach to Interacting Fermions.” Reviews of Modern Physics 66, no. 1 (1994): 129.)</p>
<p>I probably see this way more complicated than it really is... </p>
<p>Does anyone have a comment or a good source for this problem?</p>
| 10,707 |
[
0.021583236753940582,
-0.01018031407147646,
0.04273628443479538,
-0.038140930235385895,
0.03400705009698868,
0.01867234706878662,
-0.06117844209074974,
-0.024756964296102524,
0.018096748739480972,
-0.044821035116910934,
0.02579229697585106,
-0.003264561528339982,
0.05608362331986427,
0.03731365129351616,
0.03133423626422882,
-0.0006798552349209785,
0.005940774455666542,
-0.020587606355547905,
-0.014136063866317272,
-0.02234998531639576,
0.0012455731630325317,
0.052250031381845474,
-0.015439116396009922,
-0.04788675904273987,
0.0022481477353721857,
-0.003606748301535845,
-0.019812319427728653,
0.034801505506038666,
-0.008320876397192478,
0.041718319058418274,
-0.01445793267339468,
-0.028822053223848343,
0.010998895391821861,
-0.0555839017033577,
0.005032137501984835,
0.0042473431676626205,
-0.014465587213635445,
-0.04120335727930069,
0.011354540474712849,
0.039986394345760345,
-0.07067371904850006,
-0.022647300735116005,
-0.021751025691628456,
-0.002448772080242634,
-0.014585369266569614,
-0.00626177154481411,
-0.027846744284033775,
-0.02302013523876667,
0.0499153733253479,
-0.10552505403757095,
0.007915293797850609,
0.010091589763760567,
0.02836935594677925,
0.01297779195010662,
-0.014798512682318687,
0.017708776518702507,
0.05523979663848877,
0.0777025818824768,
0.03703143820166588,
-0.05556068196892738,
-0.004254681058228016,
-0.013805401511490345,
0.017305616289377213,
0.025058429688215256,
-0.021103015169501305,
0.0016138668870553374,
-0.012561588548123837,
-0.03283422440290451,
0.008941182866692543,
-0.008021149784326553,
0.0028056108858436346,
0.005542632658034563,
0.002505892189219594,
0.008692510426044464,
0.04482400417327881,
0.020141610875725746,
0.009460082277655602,
0.03339707478880882,
0.025333400815725327,
0.04980083182454109,
0.004464611876755953,
0.026446646079421043,
0.041331417858600616,
0.01896928809583187,
-0.05268293619155884,
0.02190241776406765,
0.04854892939329147,
-0.0379812978208065,
0.02643567882478237,
0.04544564336538315,
-0.013269943185150623,
0.0281062051653862,
0.044627826660871506,
-0.02175997756421566,
-0.03384250029921532,
0.012751852162182331,
0.00107661378569901,
0.02227798104286194,
-0.0022849654778838158,
0.00988723337650299,
-0.01816576160490513,
-0.03150174021720886,
-0.0031743852887302637,
0.07611903548240662,
-0.01361046265810728,
-0.032941196113824844,
-0.03752131387591362,
0.005058696027845144,
-0.035453200340270996,
-0.06568490713834763,
-0.02171132154762745,
-0.03318777307868004,
-0.013997421599924564,
-0.0053554074838757515,
-0.0054967100732028484,
-0.0147759560495615,
0.0037259540986269712,
-0.007334474008530378,
0.06294312328100204,
0.05520626902580261,
-0.016062773764133453,
-0.02201961539685726,
0.015474303625524044,
-0.03774057701230049,
-0.04501620680093765,
0.05751393735408783,
0.05944042280316353,
-0.011482986621558666,
-0.03599178045988083,
-0.003329915227368474,
-0.011856593191623688,
0.022969907149672508,
0.019219910725951195,
-0.008426809683442116,
-0.0005905005964450538,
-0.025549041107296944,
-0.0914837047457695,
-0.06637098640203476,
0.06595263630151749,
-0.031563449651002884,
-0.04035216197371483,
-0.07764206826686859,
0.002936380449682474,
0.04508853331208229,
0.07314877957105637,
-0.03377006575465202,
0.057978492230176926,
-0.014514168724417686,
0.03813530132174492,
-0.009350250475108624,
-0.03601318970322609,
-0.04081897810101509,
0.013888165354728699,
-0.04035859927535057,
-0.024906395003199577,
-0.0301023218780756,
0.03645972162485123,
0.028555456548929214,
-0.027377530932426453,
0.012362494133412838,
0.08357543498277664,
0.004621193278580904,
0.024303114041686058,
0.04146701470017433,
-0.03109695017337799,
-0.018365075811743736,
0.08634814620018005,
-0.010690046474337578,
0.006294318474829197,
0.013485509902238846,
-0.012919963337481022,
0.011776970699429512,
0.017018551006913185,
0.035934604704380035,
0.022466519847512245,
-0.017718082293868065,
-0.023964185267686844,
-0.04448382183909416,
-0.017369993031024933,
0.007831325754523277,
-0.026841746643185616,
-0.02091160975396633,
0.01217416487634182,
-0.028195522725582123,
-0.025406569242477417,
0.023543288931250572,
0.016321491450071335,
-0.0038144551217556,
0.04393512010574341,
-0.06967263668775558,
-0.023931454867124557,
-0.05986972525715828,
-0.023693036288022995,
-0.009222297929227352,
-0.001116598374210298,
0.058412857353687286,
-0.003291073488071561,
-0.012379897758364677,
0.017188193276524544,
-0.045962147414684296,
0.037238821387290955,
0.043911971151828766,
0.02987191453576088,
0.005390610545873642,
0.08412066102027893,
0.016030509024858475,
0.037400197237730026,
-0.015528146177530289,
0.01770608313381672,
-0.04455510154366493,
-0.024571681395173073,
0.0015656022587791085,
-0.024401523172855377,
0.05419287085533142,
0.0031976078171283007,
-0.030778495594859123,
-0.0005426853313110769,
0.011613587848842144,
-0.028979962691664696,
0.017517495900392532,
-0.030804544687271118,
0.06246151402592659,
0.018228039145469666,
-0.0011981899151578546,
-0.030324874445796013,
0.030863778665661812,
0.007898075506091118,
-0.0002949415356852114,
0.015081274323165417,
-0.021386610344052315,
-0.04433690756559372,
-0.013595079071819782,
0.05320791155099869,
0.02380415052175522,
-0.029922721907496452,
-0.013480144552886486,
0.0480317585170269,
0.02325485646724701,
0.010323370806872845,
0.01094904262572527,
-0.045229461044073105,
-0.02198985405266285,
0.02310183458030224,
-0.0006805768352933228,
-0.006260778289288282,
-0.014180345460772514,
0.001642788527533412,
0.03539004176855087,
0.007201665546745062,
-0.013256354257464409,
-0.019333887845277786,
-0.006357687991112471,
0.03561839833855629,
-0.019742798060178757,
-0.006004128139466047,
-0.03484642133116722,
0.04086100310087204,
-0.010163803584873676,
0.02755853720009327,
0.01936185732483864,
0.007313687354326248,
0.030695052817463875,
-0.01674262061715126,
-0.05802212655544281,
0.025733448565006256,
-0.012264530174434185,
-0.008000727742910385,
-0.017680682241916656,
0.0013645911822095513,
0.006952873896807432,
0.02134382352232933,
-0.055795058608055115,
0.03916265070438385,
0.0025683396961539984,
0.03858570009469986,
-0.007181988097727299,
0.010338583961129189,
0.0074721937999129295,
-0.03176151588559151,
-0.020667416974902153,
0.03684654459357262,
0.009012714959681034,
0.03376665711402893,
0.03462342172861099,
-0.049625322222709656,
0.013677512295544147,
-0.029883189126849174,
-0.037176717072725296,
-0.008448160253465176,
0.012760124169290066,
-0.00019538344349712133,
-0.020508339628577232,
-0.021787960082292557,
-0.022618934512138367,
-0.02272406779229641,
0.004726639948785305,
0.02603393979370594,
-0.033290669322013855,
0.017495356500148773,
0.029109962284564972,
-0.01991346664726734,
-0.03389729559421539,
0.012815684080123901,
-0.030541282147169113,
-0.04103270545601845,
-0.004093133378773928,
-0.007557653356343508,
0.006053118035197258,
-0.010954584926366806,
0.02507980354130268,
0.04360278323292732,
-0.06282761693000793,
-0.04984287545084953,
-0.060091324150562286,
-0.009702074341475964,
0.02003634162247181,
0.0013449674006551504,
-0.0018386043375357985,
-0.025737883523106575,
-0.07976426184177399,
0.03671503812074661,
0.018557531759142876,
-0.02829362079501152,
-0.010503721423447132,
0.02820757031440735,
-0.04767569899559021,
-0.017176104709506035,
0.05715640261769295,
0.03150953724980354,
0.031063279137015343,
0.03255125880241394,
-0.008793034590780735,
0.08051283657550812,
0.034727320075035095,
0.03246288001537323,
-0.009160474874079227,
0.05260356515645981,
0.020733283832669258,
0.0030168236698955297,
0.0375816635787487,
-0.0017967033199965954,
-0.0001365951175102964,
0.019519571214914322,
0.02290656976401806,
0.02158653922379017,
0.009130901657044888,
-0.073063924908638,
0.048925694078207016,
0.0024038131814450026,
0.02591254748404026,
-0.027093609794974327,
0.041864316910505295,
-0.011204692535102367,
-0.04215250164270401,
0.006582499947398901,
0.03603442758321762,
-0.009288904257118702,
-0.023372378200292587,
0.034633222967386246,
0.029813870787620544,
0.02800101786851883,
-0.019346004351973534,
-0.0687209740281105,
-0.011424707248806953,
-0.04326740279793739,
0.03481527417898178,
-0.03038226068019867,
-0.028606852516531944,
0.03385351225733757,
0.04884810373187065,
0.018730565905570984,
-0.024082323536276817,
-0.024444282054901123,
-0.023023540154099464,
-0.03914884477853775,
-0.027927856892347336,
-0.0345730185508728,
0.06611280888319016,
0.01454263273626566,
0.003808551235124469,
0.020323628559708595,
0.0011307861423119903,
0.02062673680484295,
-0.016645198687911034,
-0.08833860605955124,
0.014058695174753666,
0.0008093948708847165,
-0.01882532611489296,
0.014565357938408852,
0.016172172501683235,
0.04631614685058594,
-0.024137884378433228,
-0.025449072942137718,
-0.04862683266401291,
-0.010402028448879719,
-0.03646137937903404,
0.0058311885222792625,
0.014320914633572102,
-0.03687093406915665,
-0.020886989310383797,
0.02453547529876232,
0.030959075316786766,
-0.056391745805740356,
0.015444631688296795,
0.022117476910352707,
-0.02652653679251671,
-0.016483433544635773,
-0.023724667727947235,
0.04566444456577301,
0.0017505002906545997,
0.03258674219250679,
0.04828193783760071,
0.04866044223308563,
-0.010493993759155273,
0.006443124730139971,
0.001776507473550737,
0.03582257777452469,
0.03713764250278473,
-0.0038548156153410673,
-0.0042494856752455235,
-0.030466342344880104,
-0.012634538114070892,
0.0065720877610147,
0.07756856828927994,
0.015522179193794727,
-0.004029027186334133,
0.05115000903606415,
0.043114352971315384,
-0.00925695151090622,
-0.00044327552313916385,
0.0112210838124156,
0.0018521490273997188,
-0.0150389289483428,
-0.026651810854673386,
-0.010163889266550541,
0.012052194215357304,
-0.008802631869912148,
0.020327702164649963,
0.02432253770530224,
0.012168163433670998,
0.0024065093602985144,
0.04987772926688194,
0.006924353539943695,
-0.045380283147096634,
-0.02855275385081768,
0.018330469727516174,
-0.006277559325098991,
-0.027030086144804955,
0.022447746247053146,
0.00885094702243805,
0.02333173155784607,
0.008112667128443718,
-0.018128598108887672,
0.002828319324180484,
-0.025737639516592026,
0.0042118653655052185,
0.05515693500638008,
0.055070389062166214,
-0.04261017218232155,
-0.006244524382054806,
-0.026729445904493332,
0.026112694293260574,
0.03838840499520302,
0.024205923080444336,
0.029957639053463936,
-0.02185056358575821,
-0.04015184938907623,
-0.024317877367138863,
-0.008411181159317493,
-0.019096216186881065,
0.024949030950665474,
0.005535740405321121,
0.04247130826115608,
-0.055023614317178726,
-0.02071337215602398,
-0.02349483221769333,
0.021818356588482857,
-0.0058279745280742645,
0.013344096019864082,
0.005610946100205183,
0.02428523637354374,
0.041539717465639114,
0.0038774688728153706,
-0.018011748790740967,
-0.12214172631502151,
-0.028751293197274208,
0.0013929662527516484,
0.03314157575368881,
0.024809276685118675,
-0.01870821975171566,
-0.061010245233774185,
-0.02036932297050953,
0.00041355605935677886,
0.011373675428330898,
-0.00910195428878069,
-0.0036914129741489887,
0.07540684193372726,
0.04757824167609215,
-0.04533642530441284,
0.07738367468118668,
0.04732194170355797,
-0.030401425436139107,
-0.017061561346054077,
0.0016644230345264077,
0.043822407722473145,
0.0017479144735261798,
0.02296956069767475,
-0.041938845068216324,
0.005841710139065981,
-0.002401200355961919,
0.03938107192516327,
-0.03921970725059509,
0.023097854107618332,
-0.02459041029214859,
-0.029291750863194466,
-0.04967779666185379,
-0.021766655147075653,
0.01578490622341633,
-0.0384770892560482,
0.010481765493750572,
0.023809896782040596,
0.001327357953414321,
-0.016544857993721962,
0.03710717707872391,
-0.0359133817255497,
0.015449726954102516,
0.06024190038442612,
-0.009441757574677467,
0.004900003783404827,
-0.0032302422914654016,
-0.028655271977186203,
-0.012563825584948063,
-0.03319455310702324,
0.025676868855953217,
-0.012141966260969639,
0.00602332316339016,
-0.04475700110197067,
-0.011683513410389423,
-0.01577209308743477,
-0.005791280418634415,
0.02476191520690918,
0.014025493524968624,
-0.04091393202543259,
-0.007084645796567202,
-0.011564110405743122,
-0.026904430240392685,
-0.055669739842414856,
-0.0047849565744400024,
-0.021453911438584328,
0.004412274807691574,
-0.019786983728408813,
-0.028912577778100967,
-0.020038817077875137,
-0.022852106019854546,
-0.01562150102108717,
0.02543758973479271,
0.07012639194726944,
-0.02869711071252823,
-0.013134593144059181,
0.0018123957561329007,
0.029652461409568787,
0.04432116448879242,
0.00016767001943662763,
-0.03860779106616974,
0.018844010308384895,
-0.029017427936196327,
0.0039161029271781445,
0.013375917449593544,
0.01726370118558407,
-0.015121744945645332,
-0.023656101897358894,
0.017612610012292862,
0.013968966901302338,
0.03633379191160202,
-0.006329203024506569,
-0.009845297783613205,
0.008852826431393623,
0.015815602615475655,
-0.02478863298892975,
-0.0320291705429554,
0.031528327614068985,
0.012718452140688896,
0.04399982467293739,
-0.029528705403208733,
-0.006092130672186613,
0.01068901363760233,
0.015785351395606995,
0.03773021325469017,
-0.033106137067079544,
-0.023356974124908447,
0.024190247058868408,
0.07739841192960739,
0.030750367790460587,
-0.03530223295092583,
0.0321495458483696,
-0.04563811421394348,
0.014329205267131329,
-0.005614647641777992,
0.009212251752614975,
-0.00736605329439044,
0.023757126182317734,
-0.022499913349747658,
-0.04055795446038246,
-0.07412668317556381,
0.029806632548570633,
0.04394431784749031,
-0.01012196484953165,
0.02882304973900318,
0.013161678798496723,
-0.013247279450297356,
-0.011041309684515,
-0.026852313429117203,
-0.02014346420764923,
0.021750224754214287,
-0.03447716683149338,
0.03804604336619377,
-0.05701324716210365,
-0.007243317551910877,
0.042837973684072495,
0.04867852106690407,
-0.03943882882595062,
0.0349700041115284,
0.02985842153429985,
0.030807895585894585,
0.0334380567073822,
-0.012628408148884773,
-0.038006220012903214,
0.0723360925912857,
-0.015425817109644413,
0.013440179638564587,
-0.006354133132845163,
0.021753665059804916,
0.02709733322262764,
0.03560181334614754,
0.025695137679576874,
-0.04942426085472107,
-0.019001934677362442,
-0.04581082984805107,
-0.0007936324109323323,
0.05147071182727814,
-0.013230185955762863,
0.017873750999569893,
0.003304064739495516,
0.015369663946330547,
0.0054799458011984825,
-0.007770215626806021,
-0.001889086328446865,
-0.03536646068096161,
0.022793199867010117,
0.022873898968100548,
-0.024195197969675064,
0.025050541386008263,
-0.005422899033874273,
-0.03358576074242592,
0.04401687532663345,
-0.05493277311325073,
0.007086113560944796,
0.025851653888821602,
0.0286718737334013,
0.020369911566376686,
0.0651462972164154,
-0.0007926002144813538,
0.025177452713251114,
-0.002519344910979271,
-0.02679414115846157,
0.1407940834760666,
0.03839612379670143,
0.017406579107046127,
-0.0774335265159607,
0.018706360831856728,
0.018219759687781334,
0.008693339303135872,
-0.02235313691198826,
-0.0012177479220554233,
0.0004365648201201111,
0.028638647869229317,
0.012655846774578094,
0.08483799546957016,
-0.003318671602755785,
-0.008378839120268822,
-0.005220870021730661,
-0.05100635439157486,
-0.02988847903907299,
0.03860300034284592,
0.027821386232972145,
0.007906824350357056,
-0.01930585503578186,
-0.02612428367137909,
-0.027868211269378662,
-0.016050884500145912,
0.042119573801755905,
-0.037443097680807114,
-0.013012892566621304,
0.02389329858124256,
0.02118346467614174,
-0.05293814465403557,
-0.012128058820962906,
0.001507348264567554,
0.05934185907244682,
-0.022948218509554863,
0.022085674107074738,
0.010540475137531757,
-0.015705766156315804,
0.03925422579050064,
0.02581910975277424,
-0.016265831887722015,
-0.012262980453670025,
0.022727061063051224,
0.00947820208966732,
-0.06013248488306999,
-0.056768737733364105,
-0.009046563878655434,
0.021449865773320198,
-0.02085004933178425,
-0.016390766948461533,
0.0004445457016117871,
-0.015278955921530724,
0.0326317735016346,
-0.006393848452717066,
0.012083175592124462,
-0.0019100664649158716,
0.03877009451389313,
-0.05726459249854088,
0.027241960167884827,
-0.0043938341550529,
0.011126968078315258,
-0.014307072386145592,
-0.002288674470037222,
0.0010940395295619965,
-0.017605585977435112,
-0.010362234897911549,
-0.03869013860821724,
0.010573607869446278,
0.03201248124241829,
-0.04026596620678902,
-0.04480775073170662,
-0.017310699447989464,
-0.01238316297531128,
0.008660438470542431,
0.004263065289705992,
0.018184566870331764,
0.04538324475288391,
-0.00032773931161500514,
-0.018114838749170303,
-0.002205735770985484,
-0.0691232681274414,
0.008064409717917442,
-0.011102138087153435,
0.009909088723361492,
0.004521409515291452,
-0.018242323771119118,
0.020344750955700874,
0.03661442548036575,
-0.016412336379289627,
-0.05806277319788933,
0.03439828380942345,
0.03004910796880722,
0.017609290778636932,
0.004085900727659464,
-0.009804130531847477,
-0.017343129962682724,
-0.05140740051865578,
0.005880503449589014,
0.004296302795410156,
-0.009329346008598804,
0.02479013428092003,
-0.01628926768898964,
-0.022656280547380447,
-0.009448829106986523,
0.035516370087862015,
-0.020882869139313698,
0.02664307691156864,
-0.006924699526280165,
0.006785013247281313,
0.011030818335711956,
-0.02375965379178524,
-0.01180545799434185,
-0.06738243252038956,
-0.018572909757494926,
-0.01711854711174965,
-0.004370252601802349,
0.016107263043522835,
-0.0516849122941494,
0.009829293005168438,
0.0018351072212681174,
0.025889281183481216,
-0.033171407878398895,
0.01745898835361004,
-0.04018854349851608,
0.0024033074732869864,
0.015283671207726002,
0.04863706976175308,
-0.012983618304133415,
0.025724688544869423,
0.0033266968093812466,
-0.030914124101400375,
0.010836218483746052,
0.010367579758167267,
-0.002913614036515355,
-0.018846729770302773,
-0.0036828448064625263,
0.03439835458993912,
0.03491471707820892,
-0.03408823162317276,
-0.008602913469076157,
0.06432502716779709,
-0.04378553479909897,
-0.0759875625371933,
0.0469738245010376,
0.012574723921716213,
0.033095646649599075,
0.011821357533335686,
-0.009520290419459343,
-0.00397980771958828,
0.04728047922253609,
-0.022604256868362427,
-0.021987516433000565,
-0.028622522950172424,
-0.0027645514346659184,
0.030372338369488716,
-0.03703772649168968,
-0.004793776199221611,
0.0013311506481841207,
0.03149590268731117,
0.032911933958530426,
0.053100042045116425,
-0.04587380588054657,
-0.01481005921959877,
-0.020133955404162407,
-0.0373232364654541,
0.026911836117506027,
0.031361982226371765,
0.01368954312056303,
0.010897084139287472,
0.04039973020553589,
-0.02009355090558529,
0.01896420121192932,
0.008178426884114742,
0.01067465078085661,
-0.10986454039812088,
-0.025438247248530388,
-0.01324314996600151,
-0.0039103045128285885,
0.008559423498809338,
-0.08268740028142929,
0.043417755514383316,
0.004409397952258587,
-0.03526858240365982,
0.019400686025619507,
-0.016652598977088928,
-0.014024351723492146,
-0.03856154903769493,
-0.006657724734395742,
-0.04071522504091263,
0.026966392993927002,
0.010374002158641815,
0.01677791401743889,
0.013797429390251637,
0.013008847832679749,
-0.029873037710785866,
-0.021429743617773056,
-0.03709335997700691,
0.02378368377685547,
-0.0025883845519274473,
-0.008666301146149635,
0.048566531389951706,
-0.0017129225889220834,
-0.015809347853064537,
-0.008650265634059906,
-0.004087989684194326,
-0.02150915004312992,
-0.025958195328712463,
0.0015189909609034657,
-0.004050659015774727,
0.0023426255211234093,
0.036695145070552826,
-0.003096171421930194,
0.0481644831597805,
-0.0026218199636787176,
0.011629931628704071,
0.0356142520904541,
0.02193078026175499,
-0.023871714249253273,
0.009063639678061008,
-0.03636618331074715,
-0.00003700458546518348,
0.07290445268154144,
-0.036249250173568726,
-0.018049804493784904,
0.016773104667663574,
0.018519245088100433,
0.022885004058480263,
-0.023490862920880318,
0.024962231516838074,
-0.05819122865796089,
-0.03383548557758331,
0.01949174515902996,
0.028078913688659668,
0.027662768959999084,
0.015610603615641594,
-0.009297378361225128,
0.007566632702946663,
0.013072989881038666,
-0.010958223603665829,
-0.01765289343893528,
-0.024460213258862495,
-0.04362215846776962,
-0.024724913761019707,
0.031168518587946892,
-0.014440259896218777,
-0.024982009083032608,
-0.036290932446718216,
-0.0034889718517661095,
-0.032881077378988266,
0.0158870667219162,
-0.07174860686063766,
-0.02085394226014614,
-0.001122002606280148,
-0.045140013098716736,
0.006878896150738001,
0.031220095232129097,
0.01819673180580139,
0.00879622157663107,
-0.025752408429980278,
-0.025500306859612465,
0.04818406328558922,
0.05589113384485245,
0.005675434600561857,
-0.012157048098742962,
0.022510187700390816,
0.0005816335906274617,
0.040354255586862564,
-0.04150838777422905,
0.017966045066714287,
-0.01709641143679619,
0.03327423706650734,
0.0036273521836847067,
0.007815306074917316,
0.005279007367789745,
0.02250157669186592,
0.03141722083091736,
-0.013490765355527401,
-0.015378269366919994,
0.028490649536252022,
-0.04869448021054268,
0.05855149030685425,
0.035100389271974564,
-0.027331283316016197,
0.049354009330272675,
-0.0045775799080729485,
0.04086216911673546,
0.035559240728616714,
0.003820645622909069,
-0.03417930006980896,
0.010858799330890179,
-0.011090817861258984,
-0.006959009449928999,
-0.021957071498036385,
0.018623601645231247,
0.020802143961191177,
-0.009402969852089882,
0.009892654605209827,
0.03808197006583214,
-0.01816745474934578,
-0.015819810330867767,
0.03176949918270111,
0.012169389054179192,
0.037782300263643265,
0.019083093851804733,
-0.0031772202346473932,
-0.005592295899987221,
0.015077466145157814,
-0.007295145653188229,
0.054512474685907364,
0.03217298910021782,
0.05654579773545265,
0.014102794229984283,
-0.013043045997619629,
-0.032920658588409424,
0.02765100635588169,
0.0025419064331799746,
0.003799068508669734,
-0.016659757122397423,
-0.01676194742321968,
0.058493953198194504,
-0.030813459306955338,
-0.037913355976343155,
0.025039780884981155,
-0.025041766464710236,
0.09016397595405579,
0.011585263535380363,
0.03126026690006256,
-0.02885696105659008,
0.0061239623464643955,
-0.01338364090770483,
-0.025281289592385292,
0.018089255318045616,
0.0502748005092144,
-0.026730243116617203,
-0.019175583496689796,
-0.015947435051202774,
0.004927636124193668,
0.029981499537825584,
-0.06596717238426208,
-0.014087654650211334,
0.01958862505853176,
0.0313417874276638,
-0.0013172916369512677,
-0.026498207822442055,
-0.035932667553424835,
-0.02442295104265213,
0.01958867534995079,
0.041647687554359436,
0.027742672711610794,
0.011852793395519257,
-0.012222924269735813,
0.0004577303770929575,
0.058098867535591125,
-0.059041980654001236,
0.008789995685219765,
-0.009132035076618195,
0.021012913435697556,
-0.006862434558570385,
0.010970287956297398
] |
<p>This troubles me: We are talking about time and space being equivalent, but still only consider Spin in the $x$, $y$ or $z$-direction. What's Spin in time dimension? Is it distinction between particles and antiparticles?</p>
| 10,708 |
[
0.0008750651031732559,
-0.01046243216842413,
-0.008659944869577885,
-0.023625493049621582,
0.07520859688520432,
-0.005478993058204651,
-0.029123706743121147,
0.014140701852738857,
-0.009094178676605225,
-0.04446037486195564,
0.0342835858464241,
0.025463828817009926,
0.05448181927204132,
0.028017841279506683,
0.04867984727025032,
0.0438738688826561,
-0.028496308252215385,
-0.020056281238794327,
-0.004958875477313995,
-0.03097749873995781,
0.05685478076338768,
0.019886797294020653,
0.0006574754370376468,
0.034393709152936935,
-0.034872062504291534,
0.039775408804416656,
0.03732500970363617,
0.034297771751880646,
0.023858115077018738,
0.05805779621005058,
-0.016607731580734253,
-0.029202619567513466,
0.002112729474902153,
0.03604118525981903,
0.017271045595407486,
-0.052857790142297745,
-0.016176721081137657,
-0.06127804145216942,
-0.016920525580644608,
0.025903284549713135,
-0.02500113844871521,
-0.025432271882891655,
-0.013991807587444782,
0.04184902086853981,
-0.047972653061151505,
0.01910211332142353,
-0.005325074307620525,
-0.005365412216633558,
0.03879448398947716,
-0.045025307685136795,
0.08131365478038788,
-0.014816057868301868,
0.022907018661499023,
-0.03229868412017822,
-0.020374344661831856,
0.012567904777824879,
0.08949864655733109,
0.0463130921125412,
0.0037008593790233135,
-0.023376701399683952,
-0.02134242281317711,
-0.02454148791730404,
0.036049339920282364,
-0.034140605479478836,
-0.0472412146627903,
0.0070657129399478436,
0.009029249660670757,
-0.000016742573279771022,
0.015380310826003551,
0.00010315715189790353,
-0.00412461394444108,
0.01900452747941017,
0.02273528464138508,
0.0032741327304393053,
-0.013878623023629189,
-0.04016948491334915,
0.021286452189087868,
0.015514918603003025,
0.026385555043816566,
0.02024679258465767,
-0.007858521305024624,
0.029590705409646034,
0.014268052764236927,
0.014441040344536304,
-0.017046911641955376,
-0.022610660642385483,
0.07411522418260574,
-0.0014308297540992498,
0.006487714592367411,
0.02826872654259205,
0.006499228533357382,
-0.00022219850507099181,
0.04714084789156914,
0.005763889756053686,
-0.04295188933610916,
0.041854579001665115,
0.005532927345484495,
0.01575305312871933,
0.0004122715617995709,
-0.027513805776834488,
-0.00006565758667420596,
-0.001711887656711042,
0.03212762996554375,
0.03822685778141022,
0.00937422551214695,
0.008523082360625267,
-0.019151251763105392,
0.023009171709418297,
-0.00024536074488423765,
-0.01866409182548523,
-0.04676329344511032,
0.03192497417330742,
-0.021140912547707558,
0.0035838051699101925,
0.018500449135899544,
-0.009264685213565826,
0.022661447525024414,
-0.02672160044312477,
0.0483427420258522,
0.08320727199316025,
0.04000164940953255,
-0.03950988128781319,
0.020716160535812378,
-0.005088194739073515,
-0.10297739505767822,
-0.012171847745776176,
0.04549449309706688,
-0.015344180166721344,
-0.024751441553235054,
0.023145563900470734,
-0.004855060949921608,
-0.024977797642350197,
0.05391257628798485,
-0.02021918259561062,
0.06413041800260544,
-0.009185414761304855,
-0.0990690067410469,
-0.06950479745864868,
0.03133025020360947,
0.0037977450992912054,
-0.03261903300881386,
-0.052484266459941864,
-0.0032925368286669254,
-0.011972925625741482,
0.07541180402040482,
-0.019490312784910202,
0.031694162636995316,
0.030905062332749367,
0.02393164485692978,
0.013372081331908703,
-0.039116162806749344,
-0.006208142731338739,
0.014948800206184387,
-0.028412271291017532,
0.018025463446974754,
-0.02409948594868183,
0.011767948046326637,
0.028910871595144272,
-0.028269002214074135,
-0.020171985030174255,
0.03105253167450428,
-0.03609219565987587,
0.002220455789938569,
0.04215528443455696,
-0.006326130125671625,
-0.02250915765762329,
0.06802141666412354,
0.01648842543363571,
0.011540518142282963,
0.03656431660056114,
0.010672159492969513,
0.017144745215773582,
0.023670675233006477,
0.04803968593478203,
0.03092557191848755,
-0.0022772150114178658,
-0.0243525430560112,
0.012211629189550877,
0.0015551724936813116,
-0.01316472515463829,
-0.06678719818592072,
-0.03764401003718376,
-0.021669166162610054,
-0.0012265308760106564,
-0.029636137187480927,
0.06161417067050934,
-0.02199612557888031,
-0.01855199597775936,
-0.010617279447615147,
-0.056144751608371735,
-0.008505778387188911,
-0.07115290313959122,
0.011206123977899551,
0.004853835329413414,
-0.0056703537702560425,
0.055285681039094925,
0.03999039903283119,
0.03374508395791054,
-0.0698462426662445,
-0.060242898762226105,
-0.028462689369916916,
0.04080866649746895,
-0.011672050692141056,
-0.01635587401688099,
0.007613762281835079,
0.016505882143974304,
0.02017907053232193,
-0.011232942342758179,
0.017946217209100723,
0.03270455822348595,
-0.021054187789559364,
-0.008624451234936714,
-0.00888870470225811,
0.02601427398622036,
0.031607866287231445,
-0.022905340418219566,
0.00800270214676857,
-0.003679693676531315,
-0.02488618530333042,
0.04770267754793167,
-0.0048659006133675575,
0.05374167114496231,
0.04441229626536369,
-0.03176207095384598,
-0.014325563795864582,
0.02215159870684147,
0.021109025925397873,
0.022970587015151978,
0.010620249435305595,
-0.017021100968122482,
-0.005073497537523508,
-0.01800093799829483,
0.04527415335178375,
0.04100174456834793,
-0.03450588881969452,
0.0065987855195999146,
-0.0008298571337945759,
0.043137792497873306,
0.026600254699587822,
0.03722148761153221,
-0.029883040115237236,
-0.05961257964372635,
0.015490273013710976,
0.009380209259688854,
-0.004393329378217459,
-0.02150532230734825,
0.033479638397693634,
-0.0070149400271475315,
0.016515636816620827,
-0.003225700231269002,
-0.022583674639463425,
0.0320344902575016,
-0.050186797976493835,
0.0025457025039941072,
0.028514469042420387,
-0.07446113973855972,
0.016806710511446,
-0.009914766065776348,
0.023847362026572227,
0.007284519262611866,
-0.012779024429619312,
0.007489866577088833,
-0.02020258456468582,
-0.00842349138110876,
-0.004939625505357981,
-0.013890238478779793,
-0.03875286504626274,
-0.009159646928310394,
0.04524552822113037,
0.011616041883826256,
0.007959473878145218,
0.0016823671758174896,
-0.022048426792025566,
-0.002929199952632189,
0.005703947506844997,
0.049536943435668945,
0.00658596633002162,
0.026207568123936653,
0.015156950801610947,
-0.029356930404901505,
0.013266956433653831,
-0.014403237029910088,
0.019473129883408546,
0.04058598354458809,
-0.04751764237880707,
0.05277811735868454,
-0.06650059670209885,
-0.03099246695637703,
0.024149639531970024,
-0.011600797064602375,
0.022826064378023148,
0.015978978946805,
-0.0381610132753849,
-0.03510747477412224,
0.008525838144123554,
-0.020567508414387703,
0.03352508693933487,
-0.043573103845119476,
0.030258890241384506,
0.0516006276011467,
-0.020673831924796104,
-0.02005917578935623,
0.0030648568645119667,
-0.029734404757618904,
-0.060768287628889084,
-0.02799120359122753,
-0.014667433686554432,
0.03229186683893204,
-0.040721625089645386,
0.002403019228950143,
0.0674511268734932,
-0.0561576709151268,
-0.01822158880531788,
-0.032367363572120667,
-0.03592609614133835,
0.023611754179000854,
0.006497229915112257,
0.014045299030840397,
-0.006700605619698763,
-0.032788146287202835,
0.07204685360193253,
0.02499166876077652,
-0.01205055508762598,
-0.03174171224236488,
-0.013550259172916412,
-0.019884303212165833,
-0.03619280084967613,
-0.017413219437003136,
0.019942332059144974,
0.014565624296665192,
0.025915786623954773,
0.041690658777952194,
0.044667765498161316,
0.008032338693737984,
0.03096001222729683,
-0.012152397073805332,
-0.016410263255238533,
0.015975581482052803,
0.019129272550344467,
0.01311489101499319,
-0.004302639979869127,
-0.0335494726896286,
0.024876434355974197,
0.03378747031092644,
0.0499161072075367,
-0.007441920228302479,
-0.037801824510097504,
0.0607561357319355,
-0.003121188608929515,
0.05125093832612038,
-0.00015182801871560514,
0.04819313436746597,
-0.025637879967689514,
0.0028535311575978994,
0.02063761092722416,
0.01989392563700676,
0.009405932389199734,
-0.020918361842632294,
0.008026993833482265,
0.0432184562087059,
0.016126709058880806,
-0.03233499079942703,
-0.0028963424265384674,
0.005799672566354275,
-0.01549353078007698,
0.06728602945804596,
-0.025727765634655952,
-0.026906296610832214,
0.03474400192499161,
0.0347900316119194,
-0.006391942501068115,
-0.010056977160274982,
-0.05307786539196968,
0.005267242901027203,
-0.07033920288085938,
0.012140714563429356,
-0.0017949932953342795,
0.02887382172048092,
0.006795972585678101,
0.059973977506160736,
0.0197776909917593,
-0.01110732089728117,
0.008946842513978481,
-0.021757999435067177,
-0.06926954537630081,
-0.005740579217672348,
-0.05270376056432724,
0.019567176699638367,
-0.029238438233733177,
-0.007012376561760902,
0.005939173512160778,
-0.03849257528781891,
0.008865785785019398,
0.016524970531463623,
-0.043061088770627975,
-0.06830059736967087,
0.02450920082628727,
-0.047992292791604996,
-0.00801409874111414,
-0.03212980180978775,
0.03380562737584114,
0.025570152327418327,
0.0009413114166818559,
0.00790005549788475,
0.0420062430202961,
-0.014516427181661129,
0.024962717667222023,
0.015326021239161491,
0.014175892807543278,
0.030334291979670525,
-0.008639554493129253,
0.06285984814167023,
-0.006589929573237896,
-0.050984371453523636,
0.0030254488810896873,
0.009580741636455059,
0.034632399678230286,
-0.027345770969986916,
-0.04181381314992905,
-0.0263967402279377,
-0.06446003913879395,
0.0012670153519138694,
0.0033844870049506426,
0.07337425649166107,
0.03663157671689987,
0.0021038721315562725,
0.027411945164203644,
0.027191653847694397,
-0.02570558898150921,
0.04267825186252594,
0.06235916167497635,
-0.003119089175015688,
-0.03659655898809433,
-0.011238048784434795,
-0.00945720449090004,
-0.018026186153292656,
-0.0007472363649867475,
0.028262075036764145,
-0.025177201256155968,
-0.024992868304252625,
0.002865053480491042,
0.0021487176418304443,
-0.0021615338046103716,
-0.02413076162338257,
0.017307493835687637,
-0.009839102625846863,
0.018023360520601273,
0.027657920494675636,
-0.0035212284419685602,
-0.005530097056180239,
0.04011310636997223,
0.016760066151618958,
0.025896087288856506,
-0.020169222727417946,
-0.0753147229552269,
0.013750634156167507,
0.035305753350257874,
0.027045641094446182,
0.01462220586836338,
-0.04150531813502312,
-0.04766714572906494,
-0.01502223964780569,
0.06018204241991043,
-0.016401922330260277,
0.02633817307651043,
-0.010111390613019466,
-0.04222480580210686,
-0.006986161228269339,
0.015342878177762032,
-0.02380306087434292,
0.03391043469309807,
0.014953888021409512,
0.009799770079553127,
-0.006677019875496626,
-0.015097038820385933,
-0.0135484728962183,
-0.012108257040381432,
0.0028264583088457584,
-0.003692690748721361,
0.020641524344682693,
0.03316710889339447,
-0.0033394587226212025,
0.03933435678482056,
-0.02741035632789135,
-0.08626063913106918,
-0.00364534929394722,
0.03927631303668022,
-0.02391328662633896,
0.05645885691046715,
-0.031761039048433304,
-0.05047222599387169,
0.019753018394112587,
-0.02869168110191822,
0.012908827513456345,
0.015117350965738297,
-0.05370807647705078,
0.0147096561267972,
0.03683427721261978,
-0.013999390415847301,
0.034469690173864365,
-0.0020614403765648603,
-0.0008153770468197763,
-0.02268126606941223,
0.007950701750814915,
0.045841507613658905,
-0.04743258282542229,
0.022856947034597397,
-0.050121016800403595,
0.004368096590042114,
-0.002552647143602371,
0.048405054956674576,
-0.025594061240553856,
-0.021993614733219147,
0.004564950242638588,
-0.042537011206150055,
-0.05734000355005264,
0.015030181035399437,
0.021505309268832207,
-0.04793907329440117,
-0.018732309341430664,
-0.019103307276964188,
-0.029443269595503807,
-0.0067342366091907024,
-0.017833219841122627,
0.010586842894554138,
-0.016372565180063248,
0.05254631116986275,
0.01377910003066063,
0.033257849514484406,
-0.029684830456972122,
0.0016822210745885968,
0.014625180512666702,
-0.03224079683423042,
0.008275220170617104,
-0.019927671179175377,
-0.04744766280055046,
0.010464195162057877,
-0.06818991899490356,
-0.028762521222233772,
0.023576663807034492,
0.0007273315568454564,
0.010180762968957424,
-0.04885053634643555,
0.011072523891925812,
0.030658775940537453,
-0.0029249214567244053,
-0.10491719096899033,
-0.05707031488418579,
0.01180786732584238,
0.010550184175372124,
-0.020497266203165054,
-0.015698451548814774,
0.014189098961651325,
-0.01632094569504261,
-0.04896321892738342,
-0.003046368481591344,
0.07733222842216492,
-0.01965814083814621,
-0.0304812453687191,
-0.0019195141503587365,
0.03278946131467819,
0.03936655819416046,
-0.031122328713536263,
-0.0017278259620070457,
-0.0027294729370623827,
-0.00798704382032156,
0.04091721773147583,
0.001106157316826284,
0.05541330575942993,
-0.009161432273685932,
-0.003974062390625477,
-0.009610727429389954,
-0.0012999861501157284,
0.03219025954604149,
-0.03526029735803604,
-0.0027528556529432535,
0.018575547263026237,
-0.016372838988900185,
-0.03416885435581207,
-0.012922835536301136,
0.010864757932722569,
-0.010247349739074707,
0.012248425744473934,
-0.00850888155400753,
-0.0006405608728528023,
-0.03395532816648483,
-0.029161643236875534,
0.0464131124317646,
-0.008869742974638939,
0.000925771426409483,
0.01108360942453146,
0.04113825783133507,
-0.007695904932916164,
0.00033631999394856393,
0.0037473621778190136,
-0.01967806927859783,
0.02828877419233322,
-0.014758945442736149,
-0.01013820432126522,
0.023188618943095207,
0.00585237517952919,
-0.017348382622003555,
-0.003630189225077629,
-0.0055862064473330975,
0.025325199589133263,
0.05128001049160957,
-0.02316494844853878,
0.06703221052885056,
0.03239363059401512,
0.015431065112352371,
-0.010386861860752106,
-0.025646427646279335,
-0.00564176868647337,
0.026492051780223846,
0.004735632333904505,
0.03419739753007889,
0.005232975352555513,
-0.011820093728601933,
0.04938794672489166,
0.04079509153962135,
-0.01810886710882187,
0.0114807840436697,
0.03461083024740219,
-0.008501054719090462,
0.024439409375190735,
0.024452926591038704,
-0.04317020997405052,
0.031230716034770012,
-0.015110236592590809,
0.011669096536934376,
-0.004301825072616339,
-0.03174309432506561,
0.045308731496334076,
-0.010946630500257015,
0.04544321075081825,
-0.023130295798182487,
-0.00868613738566637,
-0.06580979377031326,
-0.025588462129235268,
0.005571251735091209,
0.042829785495996475,
-0.007171181496232748,
0.02787194959819317,
0.04644259810447693,
-0.006191183812916279,
0.0029423823580145836,
0.03499213978648186,
-0.05196871981024742,
-0.014927570708096027,
-0.037983350455760956,
-0.021850604563951492,
0.03678112477064133,
-0.0034388576168566942,
-0.02600126713514328,
-0.009999657981097698,
-0.03207540884613991,
-0.007864049635827541,
-0.007405393291264772,
0.03270569071173668,
-0.03876614570617676,
0.04423261433839798,
0.0015225372044369578,
0.030168646946549416,
-0.004029056988656521,
0.004246305208653212,
0.10049044340848923,
0.04071025922894478,
0.02079935558140278,
-0.06864333897829056,
0.01691637560725212,
-0.027038291096687317,
-0.002090238267555833,
-0.028165174648165703,
0.047549281269311905,
0.008094864897429943,
0.013029509223997593,
0.020396223291754723,
0.049346260726451874,
0.024328213185071945,
-0.04051288962364197,
0.04000589996576309,
-0.059096548706293106,
-0.04274363815784454,
-0.020871605724096298,
0.018791208043694496,
0.011259312741458416,
-0.012846074067056179,
-0.06476525217294693,
0.04164975881576538,
-0.031098898500204086,
0.029502548277378082,
-0.023265888914465904,
-0.043545085936784744,
0.009123137220740318,
-0.0073362537659704685,
-0.04604407399892807,
-0.006991125177592039,
-0.018480243161320686,
-0.016675151884555817,
-0.07165911793708801,
-0.001580002368427813,
0.01600104197859764,
-0.020062120631337166,
0.037978097796440125,
0.032662004232406616,
0.03672323748469353,
0.012921411544084549,
0.013595790602266788,
0.005051839631050825,
-0.049588967114686966,
0.008669117465615273,
-0.007374239154160023,
0.04518860578536987,
-0.00608843844383955,
0.03157010301947594,
0.00857743714004755,
-0.003461899934336543,
0.0034719668328762054,
-0.06164134666323662,
-0.015433069318532944,
-0.0120998565107584,
0.03942014276981354,
0.0024864133447408676,
0.04350763186812401,
-0.012438835576176643,
0.015728238970041275,
0.0030937716364860535,
0.04648097604513168,
-0.01105995662510395,
0.0001172177362604998,
0.05485982820391655,
0.004436646122485399,
0.028491508215665817,
-0.019856594502925873,
0.005597584415227175,
-0.021150831133127213,
-0.0037449169903993607,
-0.04312433302402496,
0.009339219890534878,
0.058766357600688934,
0.030897723510861397,
0.0023507147561758757,
-0.006946640554815531,
-0.022921044379472733,
-0.011486977338790894,
-0.039287861436605453,
0.024529842659831047,
-0.04628222435712814,
-0.0058970944955945015,
0.020848792046308517,
0.019778605550527573,
0.03780980780720711,
0.03746868669986725,
-0.03715261444449425,
0.01227955985814333,
-0.04306537285447121,
0.022736066952347755,
-0.0010150062153115869,
-0.02083301544189453,
0.027978288009762764,
0.010766168124973774,
-0.021655185148119926,
0.01694340817630291,
-0.011020373553037643,
0.011257431469857693,
0.04862220212817192,
-0.009568927809596062,
0.0062890551052987576,
0.0431252084672451,
0.009678632952272892,
-0.019386321306228638,
0.041410893201828,
-0.040719836950302124,
0.010540055111050606,
0.04160209372639656,
0.007438664324581623,
-0.057744212448596954,
-0.04260250926017761,
-0.032858096063137054,
0.006277381908148527,
0.020351935178041458,
0.00004507013727561571,
0.009020432829856873,
-0.029936959967017174,
-0.005135126877576113,
0.0043467311188578606,
-0.021089965477585793,
-0.013269939459860325,
-0.08450217545032501,
0.019047511741518974,
-0.0011055020149797201,
-0.01784966140985489,
0.0006906719645485282,
0.02553831972181797,
0.007395071443170309,
-0.020781980827450752,
0.003154848702251911,
0.02806040458381176,
-0.04391443356871605,
0.01038588397204876,
0.034225884824991226,
0.015265703201293945,
0.041857969015836716,
-0.020744357258081436,
-0.024790601804852486,
0.01923125796020031,
-0.03570333495736122,
-0.07227280735969543,
0.05198315158486366,
-0.027498919516801834,
0.02872738242149353,
0.029606249183416367,
0.01628880202770233,
-0.02417696639895439,
0.017136355862021446,
-0.035371601581573486,
-0.020643014460802078,
0.036400653421878815,
-0.032380953431129456,
-0.06902948766946793,
-0.0498194545507431,
0.03367851674556732,
0.02396664395928383,
-0.03583311662077904,
0.02676699496805668,
0.022664299234747887,
-0.012023556046187878,
0.011576589196920395,
0.0003024477628059685,
0.016882091760635376,
0.02370002679526806,
0.030611859634518623,
-0.02742120809853077,
0.012680565938353539,
0.05927357077598572,
-0.05422445759177208,
0.02936667576432228,
0.005081126932054758,
0.0028108737897127867,
-0.09924884140491486,
0.009962939657270908,
0.03285614028573036,
0.0008183221216313541,
0.026736153289675713,
-0.07317386567592621,
0.017559101805090904,
0.02466997131705284,
-0.09625313431024551,
0.05093734338879585,
-0.03340129926800728,
-0.01901262253522873,
-0.004798021167516708,
-0.024691523984074593,
-0.009181574918329716,
0.061453357338905334,
0.024893242865800858,
0.04711899533867836,
0.010279012843966484,
0.012710380367934704,
-0.05328812077641487,
-0.06347697973251343,
-0.025160029530525208,
0.04308256506919861,
-0.02187243103981018,
0.0016685042064636946,
0.06645325571298599,
-0.01098713744431734,
-0.02330523356795311,
0.03443634882569313,
0.01896236464381218,
0.0034718592651188374,
-0.011507109738886356,
0.029896093532443047,
-0.0049361553974449635,
0.008496475405991077,
0.009377114474773407,
-0.02940971963107586,
-0.014892726205289364,
0.024973172694444656,
-0.0026555906515568495,
0.014559396542608738,
0.015336050651967525,
0.01699868030846119,
-0.029171323403716087,
-0.035569921135902405,
0.01787388138473034,
0.01241561770439148,
-0.006528387311846018,
-0.04390125721693039,
-0.004982106387615204,
0.031116502359509468,
0.004388557747006416,
-0.024828391149640083,
0.011714868247509003,
-0.037575334310531616,
-0.00584029033780098,
0.03796776756644249,
-0.018367892131209373,
-0.015076038427650928,
0.0076150973327457905,
-0.025824306532740593,
-0.048412516713142395,
-0.0016195285134017467,
0.012912041507661343,
0.004082872066646814,
-0.015103387646377087,
0.014814491383731365,
0.023062480613589287,
-0.003221414051949978,
-0.009749497286975384,
-0.05452163890004158,
-0.036076150834560394,
0.016696056351065636,
0.007829904556274414,
0.02642403356730938,
0.0011989061022177339,
-0.05168085917830467,
-0.0019526502583175898,
-0.05484194681048393,
0.022220300510525703,
0.014981594868004322,
-0.004750991240143776,
-0.03894178941845894,
-0.003888408886268735,
-0.007282106671482325,
-0.0020608766935765743,
0.06417186558246613,
0.010503157041966915,
-0.01897081919014454,
0.032931022346019745,
0.02303386852145195,
-0.0006934881675988436,
-0.02362634614109993,
0.00661509670317173,
-0.040464404970407486,
-0.04925287514925003,
-0.0018597472226247191,
-0.014155566692352295,
-0.03305049240589142,
0.020659977570176125,
0.03138361871242523,
-0.005257652141153812,
-0.001991635886952281,
-0.0029544602148234844,
-0.023908093571662903,
0.05911866948008537,
0.010239101015031338,
0.01334923692047596,
0.041591521352529526,
0.036459989845752716,
0.019327348098158836,
0.0465790294110775,
-0.0013318092096596956,
-0.019662929698824883,
0.01146571896970272,
-0.016665762290358543,
-0.012644722126424313,
-0.008735615760087967,
0.003986602183431387,
0.02981080301105976,
-0.046723976731300354,
-0.012322556227445602,
0.05703803151845932,
-0.039490070194005966,
0.0028686081059277058,
0.034901008009910583,
0.037696775048971176,
0.0001361668255412951,
-0.03349313512444496,
0.01443452388048172,
0.021860063076019287,
0.056302305310964584,
0.004827285185456276,
0.04539307579398155,
0.02251322753727436,
0.0023162132129073143,
-0.001595320994965732,
0.003132560756057501,
-0.005171981640160084,
0.02298835851252079,
0.011172227561473846,
0.057583462446928024,
-0.00834754016250372,
0.004106085281819105,
-0.008526412770152092,
-0.03193962574005127,
0.0353938490152359,
-0.0021234722808003426,
-0.031111029908061028,
0.08963045477867126,
-0.03786412999033928,
0.03949560970067978,
-0.02642122097313404,
-0.02585047110915184,
-0.031577907502651215,
-0.01861894689500332,
0.04565531760454178,
0.025048846378922462,
-0.0351373627781868,
-0.053885385394096375,
0.0036436733789741993,
-0.006249685306102037,
0.021674178540706635,
-0.036200445145368576,
0.014154077507555485,
0.008295472711324692,
-0.011118779890239239,
-0.019537175074219704,
-0.0252776388078928,
-0.03324056416749954,
-0.01796482503414154,
0.031792037189006805,
0.024602185934782028,
0.036599837243556976,
-0.0019567408598959446,
-0.013232091441750526,
-0.03727253898978233,
0.03942985460162163,
-0.08977992087602615,
-0.03780273720622063,
0.0009114623535424471,
0.03352174907922745,
0.004153721034526825,
0.01561484020203352
] |
<ul>
<li>How Einstein's SR becomes GR?</li>
</ul>
<p>$$ds^2=dr^2-c^2dt^2,$$</p>
<p>$$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}.$$</p>
<ul>
<li><p>When the $s$ is constant $ds^2=0$, isn't it true?</p></li>
<li><p>How to connect Einstein's SR with GR?</p></li>
<li><p>What is the GR-differential $ds^2$?</p></li>
</ul>
| 10,709 |
[
-0.02652396634221077,
-0.008874434977769852,
0.01895444095134735,
-0.02742600627243519,
0.03812344744801521,
0.04612339660525322,
-0.049399036914110184,
-0.05650459602475166,
-0.022123675793409348,
-0.0610218308866024,
0.027752455323934555,
0.010045387782156467,
0.0680939331650734,
0.021280955523252487,
0.01956218108534813,
-0.008716776967048645,
0.003623778000473976,
-0.010746083222329617,
-0.006327080074697733,
-0.05205608904361725,
0.015247565694153309,
0.009855593554675579,
-0.012639421038329601,
-0.011591560207307339,
-0.01752214878797531,
0.018134847283363342,
0.009087820537388325,
-0.009614850394427776,
0.012640719301998615,
0.0713103860616684,
-0.010714629665017128,
0.009317588992416859,
-0.0319339781999588,
0.022568555548787117,
-0.0021371308248490095,
-0.015961408615112305,
-0.012572811916470528,
0.01051480695605278,
-0.009180818684399128,
0.008012616075575352,
-0.021125251427292824,
-0.013342699967324734,
-0.004055690485984087,
0.052387576550245285,
-0.0039167245849967,
-0.009202370420098305,
0.03305966779589653,
-0.004259670153260231,
0.05618026480078697,
-0.07082514464855194,
0.06301576644182205,
0.012043526396155357,
0.017147133126854897,
0.0023598086554557085,
-0.0274241603910923,
0.014507039450109005,
0.07891908288002014,
0.05485742539167404,
0.0031857534777373075,
-0.030458811670541763,
-0.007597834337502718,
-0.013768069446086884,
0.005116633605211973,
-0.015031020157039165,
0.009081847034394741,
0.07071882486343384,
-0.009678640402853489,
0.014183565974235535,
0.0036140265874564648,
-0.037936873733997345,
-0.010899044573307037,
0.003910729195922613,
-0.0008299018954858184,
-0.007566281594336033,
0.0075971027836203575,
-0.011962288990616798,
-0.006136446725577116,
-0.0010129958391189575,
0.022640693932771683,
0.018849125131964684,
0.0027217702008783817,
0.020495569333434105,
0.04507429152727127,
-0.005604979116469622,
0.0071088699623942375,
-0.0004491202416829765,
0.057591792196035385,
0.04828658699989319,
0.002545430324971676,
0.026174113154411316,
0.017831001430749893,
0.0127094192430377,
0.027994820848107338,
-0.04392357915639877,
-0.013622662983834743,
0.0245088841766119,
0.000139171868795529,
0.02872149646282196,
-0.022803984582424164,
-0.0304773710668087,
-0.0276118665933609,
-0.016663091257214546,
0.01146756112575531,
0.06517266482114792,
0.02086963690817356,
-0.02516654133796692,
-0.03867188096046448,
0.009868823923170567,
-0.03207521140575409,
0.0034318335819989443,
-0.03362810239195824,
0.007657804060727358,
0.0011786890681833029,
-0.03393865376710892,
0.012195462360978127,
-0.02769659459590912,
-0.003311749314889312,
-0.012906846590340137,
0.03625093027949333,
0.05732843652367592,
0.04936031624674797,
0.0007838375167921185,
-0.0010426375083625317,
-0.032002974301576614,
-0.06929293274879456,
0.01692340150475502,
0.06715153902769089,
-0.00820630881935358,
-0.010939680971205235,
-0.0100955069065094,
0.008925830945372581,
0.021530307829380035,
-0.04512226954102516,
0.019246287643909454,
-0.0014511924237012863,
-0.024945735931396484,
-0.0887734442949295,
-0.09284453094005585,
0.031326089054346085,
0.012607138603925705,
-0.011224402114748955,
-0.042370207607746124,
-0.0014188262866809964,
0.045048121362924576,
0.11034645140171051,
0.013426871038973331,
0.010872283950448036,
0.011410597711801529,
0.053455762565135956,
0.0011707519879564643,
-0.015300503000617027,
-0.018759073689579964,
0.0018754324410110712,
-0.03593424707651138,
-0.0038521760143339634,
-0.07839369773864746,
-0.014028089120984077,
0.039464764297008514,
0.023380201309919357,
-0.01933358609676361,
0.0880902037024498,
-0.0234823077917099,
0.0061935498379170895,
0.027240272611379623,
-0.01750621758401394,
-0.011850055307149887,
0.08914303034543991,
0.043647799640893936,
0.0034494695719331503,
0.03629693388938904,
0.015629125759005547,
0.07231759279966354,
0.01031887624412775,
0.02889062836766243,
0.011620396748185158,
-0.029836947098374367,
-0.0186352226883173,
0.03233899548649788,
-0.03279392048716545,
0.018415676429867744,
-0.008842123672366142,
-0.03933950513601303,
-0.012846468947827816,
-0.016685282811522484,
-0.01783536560833454,
0.022354360669851303,
-0.0017750869737938046,
0.03180548548698425,
-0.015975605696439743,
-0.06579827517271042,
0.021909363567829132,
-0.04903377220034599,
0.0029447225388139486,
-0.01132127270102501,
-0.014204279519617558,
0.001158003811724484,
0.03625298663973808,
0.032825667411088943,
-0.004309619776904583,
-0.04091348126530647,
-0.01577543281018734,
0.048754457384347916,
0.0037518772296607494,
-0.006090117152780294,
0.009983154945075512,
0.03054647706449032,
0.02968456782400608,
-0.007538445293903351,
-0.009072049520909786,
0.0030633385758847,
-0.021715698763728142,
0.010063935071229935,
0.01934121735394001,
0.040441058576107025,
-0.04671141505241394,
-0.007702370639890432,
0.0005576640251092613,
0.00919476430863142,
-0.030697906389832497,
0.033880919218063354,
-0.04620186239480972,
0.052338968962430954,
0.045640625059604645,
0.030382972210645676,
0.014252486638724804,
0.06800301373004913,
0.01742195524275303,
0.04202236980199814,
-0.014076744206249714,
-0.004542033653706312,
-0.026180732995271683,
-0.02382681332528591,
0.033626239746809006,
0.05787477269768715,
-0.03469252958893776,
0.01675412245094776,
0.030107125639915466,
0.05249262601137161,
-0.015970343723893166,
0.010426480323076248,
-0.009256799705326557,
-0.06853552162647247,
-0.005932831671088934,
-0.03330734372138977,
0.03083573840558529,
0.02127775363624096,
-0.00017842523811850697,
0.014566272497177124,
-0.005122595466673374,
-0.016904819756746292,
-0.009742993861436844,
0.03833978623151779,
-0.024891994893550873,
-0.010065142996609211,
0.03018563613295555,
-0.014866780489683151,
0.051509153097867966,
-0.00042944555752910674,
-0.010189010761678219,
0.057879071682691574,
0.00195616134442389,
-0.01460892241448164,
-0.035855554044246674,
-0.011695277877151966,
0.0020358555484563112,
0.0021499067079275846,
0.0038790437392890453,
-0.03261552378535271,
0.005124540533870459,
-0.03758299723267555,
-0.02394091710448265,
-0.008240099996328354,
-0.0077548581175506115,
-0.04641115292906761,
0.0031245192512869835,
0.0007613671477884054,
0.002794997999444604,
0.027238715440034866,
-0.025855710729956627,
-0.056362878531217575,
0.04459032043814659,
-0.00662415474653244,
0.0009313470800407231,
0.025247909128665924,
-0.03914704546332359,
0.04040396213531494,
-0.01232048962265253,
0.00787788163870573,
0.04085119068622589,
-0.0011568672489374876,
0.030845770612359047,
0.03358113020658493,
-0.00526192644611001,
-0.056069690734148026,
-0.03373339772224426,
-0.019909733906388283,
-0.0036890998017042875,
-0.060809336602687836,
0.010178405791521072,
0.05110142007470131,
0.0002865229034796357,
-0.040370021015405655,
0.01598580926656723,
-0.03330283612012863,
-0.06098706275224686,
-0.017987428233027458,
0.007449484895914793,
0.04966134577989578,
-0.04303738474845886,
0.022355062887072563,
0.012818335555493832,
-0.024164879694581032,
-0.0016322091687470675,
-0.06061108410358429,
-0.033719513565301895,
0.056394532322883606,
-0.0025460906326770782,
0.03856988251209259,
0.019765641540288925,
-0.031166113913059235,
0.08579980581998825,
0.02611369453370571,
0.0008296990999951959,
-0.029273342341184616,
0.02616817317903042,
0.0268305204808712,
-0.047517016530036926,
-0.027720125392079353,
0.03535803034901619,
-0.01572376675903797,
-0.008028849959373474,
0.004335399251431227,
0.03607827052474022,
0.030765855684876442,
0.0011502006091177464,
-0.020907212048768997,
-0.020738717168569565,
-0.008507330901920795,
0.0075964489951729774,
0.05170314386487007,
0.01814723201096058,
0.001808566739782691,
-0.012994547374546528,
0.003000809345394373,
0.05371076241135597,
-0.010785521939396858,
-0.04478108137845993,
0.04066486284136772,
-0.0006805766024626791,
0.009312160313129425,
-0.02927027828991413,
0.019444596022367477,
0.0008251074468716979,
-0.01958608627319336,
0.017573926597833633,
-0.010335609316825867,
0.03521616756916046,
0.0023372266441583633,
-0.015396470203995705,
0.016559479758143425,
0.016305280849337578,
-0.014742255210876465,
-0.05061579495668411,
-0.030263829976320267,
-0.014672496356070042,
0.03675747290253639,
-0.03255373612046242,
0.027477268129587173,
0.03277307003736496,
0.03346994146704674,
-0.00420090788975358,
-0.011676257476210594,
-0.028032442554831505,
-0.017719754949212074,
-0.0954224020242691,
-0.013893972150981426,
-0.022925861179828644,
0.036136895418167114,
0.0015688171843066812,
0.034997932612895966,
0.02131790481507778,
0.027826985344290733,
0.03311414271593094,
0.0005524525186046958,
-0.09760727733373642,
0.0213793832808733,
-0.07033446431159973,
-0.017514389008283615,
0.029369505122303963,
-0.001401194604113698,
-0.013238709419965744,
-0.042541760951280594,
-0.028672751039266586,
-0.048888448625802994,
-0.00070027238689363,
-0.03707227483391762,
0.023832669481635094,
-0.034662242978811264,
-0.06276857107877731,
-0.008975931443274021,
0.03207259997725487,
0.038089852780103683,
-0.000015558454833808355,
-0.024699199944734573,
0.032717619091272354,
-0.04272843897342682,
0.007074183318763971,
-0.008509241044521332,
-0.0104346489533782,
0.02260649763047695,
0.03180959075689316,
0.02588357776403427,
0.026227297261357307,
-0.029405944049358368,
-0.005277740769088268,
0.03150806203484535,
0.027659572660923004,
0.00831499695777893,
-0.02555975131690502,
-0.05812126025557518,
-0.05066882073879242,
-0.0436844564974308,
-0.03158900514245033,
0.06418758630752563,
-0.0014012735337018967,
-0.028858620673418045,
-0.0021080742590129375,
-0.003069146303460002,
0.011434243060648441,
0.01684807613492012,
0.03744341805577278,
0.008499858900904655,
-0.0391232855618,
-0.043549034744501114,
-0.05182294547557831,
-0.03240622952580452,
-0.006008510943502188,
0.04295160993933678,
-0.012721635401248932,
-0.036825645714998245,
0.005243545398116112,
-0.01855245791375637,
0.011041125282645226,
-0.021213090047240257,
-0.040961358696222305,
0.011284688487648964,
0.021250808611512184,
0.008816941641271114,
0.004689804743975401,
-0.007427701726555824,
0.04874003306031227,
0.05967113748192787,
-0.023165859282016754,
0.000600744504481554,
-0.06639230251312256,
0.0012272350722923875,
0.02977069839835167,
0.027416056022047997,
0.008258217014372349,
-0.02012353576719761,
-0.057822950184345245,
0.000261253269854933,
0.03525320440530777,
-0.014331110753118992,
0.03557925671339035,
0.029927322641015053,
-0.008069894276559353,
-0.008722733706235886,
-0.025835663080215454,
0.01632622629404068,
0.03783406317234039,
-0.00827100221067667,
0.0010401764884591103,
-0.027969758957624435,
0.022270655259490013,
-0.012191358022391796,
0.0012809975305572152,
0.01908421516418457,
0.0357840321958065,
0.026381859555840492,
0.0014134540688246489,
-0.0009921608725562692,
0.02266729064285755,
-0.05380825698375702,
-0.0935468003153801,
-0.01989705301821232,
0.02345842868089676,
-0.04525517299771309,
0.03087824583053589,
-0.028860339894890785,
-0.049549221992492676,
0.025855999439954758,
0.01958695985376835,
-0.004692281596362591,
0.04748312383890152,
-0.051845431327819824,
0.04234261065721512,
0.04819536581635475,
-0.004326504189521074,
0.008874841034412384,
0.0015732657629996538,
0.016892584040760994,
-0.024674521759152412,
-0.02049953117966652,
0.047226421535015106,
-0.05306042358279228,
-0.013178801164031029,
0.009153599850833416,
0.0015283578541129827,
-0.06312593817710876,
0.017974000424146652,
-0.0071194954216480255,
0.015293797478079796,
0.0055294400081038475,
-0.019396653398871422,
-0.007335609290748835,
0.024091804400086403,
0.03938448056578636,
0.006986637599766254,
0.037223439663648605,
0.00042821740498766303,
0.020332254469394684,
-0.017948172986507416,
0.04419592022895813,
0.010201601311564445,
-0.018273942172527313,
0.022709909826517105,
-0.0055768718011677265,
-0.0020298375748097897,
-0.00861840508878231,
-0.01118147000670433,
0.015476050786674023,
-0.048352181911468506,
0.052494436502456665,
-0.007371146231889725,
-0.03099643997848034,
0.05950184538960457,
-0.0005569374188780785,
-0.03833852708339691,
-0.007405320648103952,
-0.0071645621210336685,
-0.00794502254575491,
-0.05235918611288071,
0.005260003264993429,
0.049794118851423264,
-0.000453561166068539,
-0.09492997080087662,
-0.014316290616989136,
0.036947574466466904,
0.0001302506134379655,
-0.015376131050288677,
-0.014006735756993294,
0.024306826293468475,
-0.04975041374564171,
-0.010589992627501488,
-0.04053926095366478,
0.05434330180287361,
-0.00993932131677866,
-0.013999654911458492,
-0.02124500460922718,
0.04998253658413887,
0.05485248565673828,
-0.0493273101747036,
0.012256575748324394,
-0.004376539494842291,
0.006236907094717026,
0.018148265779018402,
0.0004714629321824759,
0.08982955664396286,
-0.01180021371692419,
-0.05328580364584923,
-0.025786319747567177,
-0.0234548207372427,
0.011995378881692886,
0.02061852626502514,
0.00028360047144815326,
0.017614293843507767,
0.01516424585133791,
-0.005653311498463154,
-0.011552239768207073,
0.007354914676398039,
-0.02007223665714264,
0.04678640514612198,
-0.009188701398670673,
0.0009349195170216262,
-0.014544523321092129,
-0.027386261150240898,
0.033929988741874695,
-0.014623001217842102,
0.024248488247394562,
-0.02378382533788681,
0.04502268508076668,
-0.020540446043014526,
-0.04304390773177147,
-0.021552350372076035,
-0.007963153533637524,
0.01674649305641651,
0.008219210430979729,
0.02664138935506344,
0.023080650717020035,
-0.006981161423027515,
-0.03930767625570297,
-0.023783715441823006,
-0.025591040030121803,
-0.013633006252348423,
0.10651253908872604,
-0.033901114016771317,
0.03907296434044838,
0.020236629992723465,
-0.04635818302631378,
0.030908221378922462,
-0.06299792975187302,
-0.018836483359336853,
-0.028450341895222664,
0.024747708812355995,
0.028234202414751053,
-0.0005118256667628884,
-0.018398504704236984,
0.013706786558032036,
0.02959269843995571,
-0.014197494834661484,
0.008326257579028606,
0.026350155472755432,
0.031080011278390884,
-0.0056666224263608456,
-0.02703920193016529,
-0.040000177919864655,
0.04458634555339813,
0.011233619414269924,
0.02332300692796707,
0.021342482417821884,
0.015620310790836811,
0.022151056677103043,
-0.011942273005843163,
0.04141594469547272,
-0.011495743878185749,
-0.020147476345300674,
-0.05778217315673828,
0.0035652280785143375,
0.0359809584915638,
-0.018243985250592232,
-0.0026405216194689274,
0.017172832041978836,
0.013724989257752895,
-0.014917794615030289,
0.03277353569865227,
-0.006148298736661673,
-0.06257537752389908,
0.02330876886844635,
-0.019064003601670265,
-0.04295569285750389,
0.05935043469071388,
-0.0016021369956433773,
-0.017443710938096046,
-0.021480241790413857,
-0.023459918797016144,
0.009665001183748245,
0.06073614954948425,
0.03005276620388031,
-0.014115296304225922,
0.03971799463033676,
-0.022905917838215828,
0.01805621013045311,
-0.01741211675107479,
-0.02259988524019718,
0.12657850980758667,
0.04209713265299797,
-0.014844221994280815,
-0.0352969728410244,
0.013328486122190952,
-0.02800225280225277,
0.018227271735668182,
-0.052501942962408066,
0.05525932088494301,
-0.032173626124858856,
-0.00023303323541767895,
-0.003682965412735939,
0.05093123018741608,
-0.010452325455844402,
-0.05149183049798012,
0.05363314971327782,
-0.042436204850673676,
-0.023315459489822388,
-0.006113559007644653,
0.031559765338897705,
-0.02958858758211136,
0.016240552067756653,
-0.008266331627964973,
0.034450653940439224,
-0.017130058258771896,
0.024078689515590668,
-0.07090561836957932,
-0.034591540694236755,
0.00919371098279953,
-0.0030507969204336405,
-0.07849188894033432,
0.0076933433301746845,
0.016706006601452827,
-0.02983635663986206,
-0.03953605517745018,
0.018682314082980156,
0.041440337896347046,
-0.027773667126893997,
-0.0015924463514238596,
0.04404984042048454,
-0.00909165944904089,
0.00854382012039423,
-0.013735918328166008,
0.027960453182458878,
-0.016013849526643753,
0.0050424267537891865,
-0.02725723572075367,
0.0766884982585907,
-0.02757376804947853,
0.003131919540464878,
0.021665293723344803,
-0.008970692753791809,
-0.007260037586092949,
-0.025529971346259117,
-0.005457636900246143,
0.007243562024086714,
0.01308632642030716,
0.0034412743989378214,
0.008944539353251457,
-0.021032515913248062,
0.039550721645355225,
0.0027711926959455013,
0.020195165649056435,
-0.010425985790789127,
-0.0026915334165096283,
0.0074104443192481995,
-0.04024992510676384,
0.018865663558244705,
-0.010447152890264988,
0.008931000716984272,
-0.041734810918569565,
0.006236210465431213,
-0.020363178104162216,
-0.006338645238429308,
0.006645309738814831,
0.016307028010487556,
0.03643818572163582,
0.009951419197022915,
-0.007673708256334066,
-0.011776620522141457,
-0.0520593635737896,
0.046737492084503174,
-0.03994427248835564,
0.004724295809864998,
-0.04836639016866684,
0.020498719066381454,
0.010966029949486256,
0.0359220989048481,
-0.015348457731306553,
-0.0055947620421648026,
-0.006210119929164648,
0.022040093317627907,
-0.005087848752737045,
0.013248510658740997,
0.00024749632575549185,
0.02738896943628788,
0.004339293576776981,
0.011791682802140713,
-0.0198268610984087,
0.0009359309915453196,
0.04954937845468521,
0.03531826660037041,
-0.026942690834403038,
0.03213738277554512,
-0.02353740483522415,
0.015467604622244835,
0.025948045775294304,
-0.0016605928540229797,
0.008755822665989399,
0.013626612722873688,
0.03699455410242081,
0.0006672953022643924,
0.0014588553458452225,
-0.00955418311059475,
0.0036153243854641914,
0.00980622973293066,
0.027916811406612396,
-0.0244697704911232,
0.03208736702799797,
-0.021802125498652458,
0.024478154256939888,
-0.05594529211521149,
-0.02423887699842453,
-0.04485371708869934,
0.021482571959495544,
-0.009476001374423504,
-0.022843852639198303,
0.013451214879751205,
0.02531488426029682,
0.003983088303357363,
-0.026694446802139282,
-0.002100764773786068,
0.019684482365846634,
-0.03579162806272507,
0.006577959284186363,
0.03434523940086365,
0.0035172903444617987,
0.04192804917693138,
0.03182679042220116,
-0.026746757328510284,
0.020121993497014046,
-0.03555519878864288,
-0.04101039841771126,
0.018079793080687523,
-0.010128363966941833,
0.008821569383144379,
-0.00016596312343608588,
-0.057095855474472046,
0.011018968187272549,
0.05057813972234726,
-0.015661779791116714,
-0.027450567111372948,
-0.016462698578834534,
-0.017851155251264572,
-0.0017414754256606102,
-0.007253922522068024,
0.021922575309872627,
0.006391433533281088,
-0.0070382882840931416,
0.012300843372941017,
-0.017865821719169617,
-0.022684918716549873,
0.02884490229189396,
0.009070249274373055,
-0.034208815544843674,
-0.02291046269237995,
-0.0058108665980398655,
0.010134768672287464,
0.03444647043943405,
0.03613331913948059,
-0.022010784596204758,
0.0419340655207634,
0.01625346578657627,
-0.0011473005870357156,
-0.11265809088945389,
0.005584255792200565,
0.010517335496842861,
0.011201749555766582,
0.06756151467561722,
-0.03540986403822899,
0.0357656255364418,
0.029030807316303253,
-0.06476214528083801,
0.03974002227187157,
-0.03913359344005585,
-0.00971912033855915,
0.005808449350297451,
-0.03141174837946892,
-0.020237376913428307,
0.07423824071884155,
0.04270736873149872,
0.043851908296346664,
-0.00020648552163038403,
0.002280690474435687,
-0.010309459641575813,
-0.010399851948022842,
-0.033968713134527206,
0.020254353061318398,
-0.02620636485517025,
-0.027313215658068657,
0.06923185288906097,
0.0011687787482514977,
0.010263213887810707,
0.008467989973723888,
0.008522242307662964,
-0.003993455320596695,
-0.010057525709271431,
-0.013325253501534462,
0.03418213874101639,
0.021825985983014107,
0.014098060317337513,
0.012934883125126362,
-0.020489195361733437,
0.01906527765095234,
-0.011539507657289505,
0.03101644665002823,
-0.030814090743660927,
-0.01223172340542078,
0.01910584419965744,
-0.06352779269218445,
-0.017996832728385925,
0.04128599911928177,
-0.04115739464759827,
-0.03906545788049698,
-0.0005988671910017729,
-0.01701817288994789,
0.013118201866745949,
-0.0020296932198107243,
0.010144430212676525,
-0.05091964080929756,
-0.009352492168545723,
0.02397361397743225,
-0.018293732777237892,
0.001556743518449366,
0.045951176434755325,
0.01158625166863203,
-0.023024575784802437,
0.009554428048431873,
-0.015344829298555851,
-0.013598315417766571,
-0.03864869475364685,
-0.004122460726648569,
-0.015114745125174522,
-0.004968198481947184,
0.02868848294019699,
-0.027886483818292618,
-0.0307985320687294,
0.06385402381420135,
0.031629037111997604,
0.018363436684012413,
0.002600515028461814,
-0.0627811923623085,
-0.020171474665403366,
-0.07744228094816208,
0.004692454356700182,
0.01793494075536728,
-0.0325680635869503,
-0.02564227394759655,
-0.0025154417380690575,
-0.007924528792500496,
-0.007779141888022423,
0.058823004364967346,
-0.02185927703976631,
0.010623629204928875,
0.01423653494566679,
0.01864485815167427,
0.04783903434872627,
-0.054843612015247345,
-0.0029284635093063116,
0.041916899383068085,
-0.008597243577241898,
-0.009638294577598572,
0.035589706152677536,
0.0010180508252233267,
0.02051432430744171,
0.025965917855501175,
-0.0002677199663594365,
0.06987309455871582,
0.013550718314945698,
-0.024348409846425056,
0.049405068159103394,
0.018912332132458687,
-0.01919788494706154,
0.07191545516252518,
-0.005260551813989878,
0.007460076827555895,
0.03985237330198288,
-0.023324154317378998,
-0.004047478083521128,
0.01957535184919834,
-0.012799111194908619,
-0.06011944264173508,
-0.010754077695310116,
-0.03064844012260437,
0.026030002161860466,
-0.01876281574368477,
-0.009637297131121159,
0.047616664320230484,
-0.016370601952075958,
-0.015257368795573711,
0.06295274198055267,
0.00042052980279549956,
0.004208904691040516,
0.04257248714566231,
-0.00008548393816454336,
0.013009718619287014,
0.012365280650556087,
0.017841121181845665,
0.017010215669870377,
0.022368449717760086,
0.0017400840297341347,
-0.02447604574263096,
0.06288855522871017,
-0.007711457554250956,
-0.029033293947577477,
-0.005913530010730028,
0.011776920408010483,
-0.05064323544502258,
-0.02089582569897175,
0.004514782223850489,
-0.012709161266684532,
0.049186933785676956,
-0.0008761524804867804,
-0.036680836230516434,
0.0871242806315422,
-0.053840093314647675,
-0.0001013781875371933,
-0.02108129858970642,
-0.0029904658440500498,
-0.04098214581608772,
0.027519123628735542,
0.018877539783716202,
0.055638156831264496,
0.02348358742892742,
-0.0028611035086214542,
-0.011958390474319458,
-0.011280986480414867,
0.026559174060821533,
-0.01977454125881195,
0.044013094156980515,
0.023665593937039375,
0.0003628365811891854,
0.00017239092267118394,
-0.02516080066561699,
0.006974681746214628,
-0.013409920036792755,
0.04578329622745514,
0.023309234529733658,
0.02063317410647869,
-0.023321794345974922,
-0.00015060146688483655,
-0.008101827464997768,
0.05502193421125412,
-0.08644548803567886,
-0.03431972116231918,
-0.02569224126636982,
-0.0027202442288398743,
-0.026441488415002823,
-0.048315003514289856
] |
<p>I am not a phycisist, so please forgive my ignorance. This is related to my <a href="http://physics.stackexchange.com/questions/30894/negative-and-positive-energy-and-hawking">posts</a> and <a href="http://physics.stackexchange.com/questions/30965/naive-question-on-quantum-mechanics-and-uncertainty-principle">this</a>.<br>
I am trying to undertand what is meant by the term <em>"Nothing"</em> in physics or Quantum Mechanics since it seems to me that this term is not used in the way we understand it in everyday language.<br>
So QM seems to suggest (in a nutshell) that "things pop out of <strong>nothing</strong>".<br>
But from <a href="http://en.wikipedia.org/wiki/Quantum_fluctuation" rel="nofollow">wiki</a> I see the following quote: </p>
<blockquote>
<p>"According to quantum theory, the vacuum contains neither matter nor
energy, but it does contain fluctuations, transitions between
something and nothing in which potential existence can be transformed
into real existence by the addition of energy.(Energy and matter are
equivalent, since all matter ultimately consists of packets of
energy.) Thus, the vacuum's totally empty space is actually a seething
turmoil of creation and annihilation, which to the ordinary world
appears calm because the scale of fluctuations in the vacuum is tiny
and the fluctuations tend to cancel each other out.</p>
</blockquote>
<p>So what is "Nothing" in QM? If this quote is correct, I can interpret it only as follows:<br>
The "Nothing" is not in the way used in everyday speech but is <em>composed</em> of "transitions" i.e. something that is "about to become"<br>
Is this correct? If yes, why is this defined as "Nothing"? Something that is "about to become" is not nothing but there is something prerequisite.<br>
In very lame terms: Einstein was born a non-physicist but became a physicist, so if this is a correct analogy, then there </p>
<ol>
<li><em><strong>there is something</strong> underlying</em> that was non-something that became
something</li>
<li>A non-something came into something because something else (not
nothing) <em>permitted it to become</em>. E.g. Einstein's talent (or
Mozart's) would have been lost had he been born in Africa or in a
country with no educational facilities. So he would not become a physicist (but the required talent would be present but not come into reality)</li>
</ol>
<p>Could someone please help me understand this (perhaps trivial to you) concept? </p>
| 10,710 |
[
-0.002309405477717519,
-0.02011808566749096,
0.024635355919599533,
-0.023163726553320885,
0.014022311195731163,
0.03131815418601036,
-0.032367631793022156,
-0.050519492477178574,
-0.008732963353395462,
-0.04242079332470894,
0.007942264899611473,
0.018422968685626984,
0.039447516202926636,
0.03400125727057457,
-0.009383372962474823,
0.025695258751511574,
0.03862543776631355,
-0.03292238712310791,
-0.024098951369524002,
-0.03502242639660835,
0.03977245092391968,
0.008543071337044239,
0.0001048297926899977,
0.020351823419332504,
-0.03806286305189133,
0.01814592257142067,
0.014562824741005898,
0.009228399023413658,
-0.012963158078491688,
0.06551308184862137,
-0.04321195185184479,
-0.030245639383792877,
-0.018322858959436417,
-0.020668506622314453,
0.02001541294157505,
0.006774633191525936,
-0.0036973159294575453,
-0.012489434331655502,
0.011012226343154907,
0.0042486912570893764,
-0.027657946571707726,
-0.005573088303208351,
0.007219540886580944,
0.07216192781925201,
-0.084163136780262,
-0.004912982229143381,
0.031363312155008316,
0.00232692644931376,
0.05102946609258652,
-0.054731789976358414,
0.024035103619098663,
-0.0060164714232087135,
0.028522618114948273,
0.012732550501823425,
-0.003011245746165514,
0.004065926652401686,
0.08993373066186905,
0.06748932600021362,
-0.04157978668808937,
-0.04901473969221115,
-0.02038443647325039,
-0.014197947457432747,
-0.01858087256550789,
-0.01696341671049595,
-0.009401357732713223,
0.07106219977140427,
0.0239398330450058,
-0.002951397793367505,
0.046197935938835144,
0.008713258430361748,
-0.0003759347600862384,
0.0202997587621212,
0.009481211192905903,
-0.020097117871046066,
0.05742010846734047,
-0.04391763359308243,
0.03677435591816902,
0.035480570048093796,
-0.0015313480980694294,
0.0873369574546814,
-0.006587497889995575,
0.004329432733356953,
0.04412901774048805,
-0.012555661611258984,
0.012120961211621761,
-0.014705001376569271,
0.10375116020441055,
-0.02291099540889263,
0.021298592910170555,
0.028114236891269684,
-0.0060975211672484875,
0.023009609431028366,
0.032203976064920425,
-0.01631978712975979,
-0.02052752487361431,
0.043341439217329025,
0.00863569788634777,
0.04984159395098686,
0.0005832062452100217,
-0.033171698451042175,
-0.005670930724591017,
0.019934941083192825,
0.07577937096357346,
0.05752098187804222,
-0.00223343214020133,
-0.025317512452602386,
-0.050399940460920334,
0.026343192905187607,
-0.022789470851421356,
-0.02427022159099579,
-0.01687672734260559,
0.0148099260404706,
0.019921887665987015,
0.01112503930926323,
-0.03524889796972275,
-0.05192439258098602,
-0.006202203221619129,
-0.020368846133351326,
0.03719719499349594,
0.04939770698547363,
0.026215141639113426,
-0.03831283748149872,
0.02235887572169304,
-0.024591373279690742,
-0.06322835385799408,
0.02104349434375763,
0.053858883678913116,
0.009763495996594429,
-0.03827040269970894,
0.003263794584199786,
0.020598866045475006,
-0.002769924933090806,
0.009783751331269741,
0.011372456327080727,
0.0458039864897728,
0.0024683268275111914,
-0.09202997386455536,
-0.05321362242102623,
0.0772169977426529,
0.018159780651330948,
-0.04297863692045212,
-0.04554058611392975,
-0.0017720464384183288,
0.022685164585709572,
0.05954670533537865,
-0.0010550983715802431,
-0.039568062871694565,
0.0082137705758214,
0.03850727155804634,
0.026435405015945435,
-0.04241278022527695,
0.0051011634059250355,
-0.001586519880220294,
-0.02788539044559002,
-0.005450456868857145,
-0.02588757313787937,
0.01897551864385605,
0.06247440353035927,
0.026730170473456383,
0.0083799809217453,
0.04014662280678749,
0.012138071469962597,
-0.0035859725903719664,
0.010421860963106155,
0.008470281027257442,
-0.006498895585536957,
0.07002551853656769,
0.03272898122668266,
-0.024470888078212738,
0.04842299595475197,
0.03815222159028053,
0.0015610127011314034,
-0.0031306168530136347,
-0.014411639422178268,
0.04546290263533592,
-0.045283637940883636,
-0.003185713430866599,
-0.05480906739830971,
0.02891489490866661,
-0.01442307885736227,
-0.05399015173316002,
-0.005666780285537243,
-0.044265393167734146,
0.014657246880233288,
0.02253738045692444,
0.05051431804895401,
-0.007041679695248604,
0.012631607241928577,
0.020018354058265686,
-0.04183536767959595,
-0.03871750459074974,
-0.040409963577985764,
-0.03398050367832184,
-0.007025123108178377,
-0.0006685922271572053,
0.015409762971103191,
0.0005477533559314907,
-0.010853566229343414,
-0.05208078399300575,
-0.013405251316726208,
0.013576055876910686,
0.031103067100048065,
-0.0044631133787333965,
-0.011504650115966797,
0.005923185031861067,
0.07177087664604187,
0.040705472230911255,
-0.007572697009891272,
-0.0037383425515145063,
0.008966370485723019,
-0.001980178989470005,
0.019164809957146645,
0.019602680578827858,
0.02674173004925251,
-0.009352577850222588,
-0.032135989516973495,
0.02955402433872223,
0.00870808120816946,
0.019941404461860657,
0.009094180539250374,
-0.031427398324012756,
0.035599708557128906,
0.011301877908408642,
-0.009076258167624474,
-0.023848291486501694,
0.04830330237746239,
-0.005554084200412035,
0.03602415323257446,
-0.00950008723884821,
-0.01794644445180893,
-0.04552925005555153,
0.012330811470746994,
0.03631552681326866,
0.015823639929294586,
-0.004239950329065323,
-0.01565006747841835,
0.018902471289038658,
0.015975575894117355,
0.019361890852451324,
0.02631419152021408,
-0.04796402528882027,
-0.021911878138780594,
0.01783125475049019,
0.005827632267028093,
0.022870153188705444,
0.0395641103386879,
0.003480530809611082,
0.0020750011317431927,
0.022070903331041336,
-0.014616464264690876,
0.005662295967340469,
0.038913022726774216,
-0.006832607090473175,
0.01634572260081768,
-0.015709247440099716,
-0.024586228653788567,
0.022527428343892097,
-0.020301716402173042,
0.0006234574248082936,
0.015775371342897415,
-0.01927231252193451,
-0.00020331166160758585,
-0.05070551112294197,
-0.011131683364510536,
0.0020578994881361723,
0.023782949894666672,
-0.03011447936296463,
0.006637771148234606,
0.021466383710503578,
-0.027570459991693497,
-0.025859272107481956,
0.03793640807271004,
-0.03017358109354973,
-0.008100451901555061,
-0.030976049602031708,
0.024742767214775085,
0.02863926999270916,
0.028810473158955574,
-0.07277783006429672,
-0.040631718933582306,
-0.0030368869192898273,
-0.013058208860456944,
-0.01431969739496708,
0.04386305436491966,
-0.005529958289116621,
0.03806421533226967,
-0.045833926647901535,
-0.07383935898542404,
0.05292049050331116,
-0.022166358307003975,
-0.003089070552960038,
0.012241875752806664,
-0.009773903526365757,
-0.05501823127269745,
0.009785962291061878,
-0.051590703427791595,
0.0028972027357667685,
-0.0278812013566494,
-0.015928957611322403,
0.07911290973424911,
-0.01633569411933422,
-0.08758162707090378,
0.020782550796866417,
-0.0361233726143837,
-0.06594602763652802,
-0.054009344428777695,
-0.011046498082578182,
0.03484919294714928,
-0.054467976093292236,
0.008052459917962551,
0.016713526099920273,
-0.030585719272494316,
0.01218810398131609,
-0.021083582192659378,
-0.0666617900133133,
0.016119739040732384,
-0.014983461238443851,
0.009289645589888096,
-0.015600789338350296,
-0.05404716730117798,
0.05497358366847038,
-0.004774237982928753,
-0.029467731714248657,
-0.019905494526028633,
0.007387225981801748,
-0.014498462900519371,
-0.003949867561459541,
0.0012599503388628364,
0.014976004138588905,
0.035788606852293015,
0.028087157756090164,
0.026352083310484886,
0.061940841376781464,
-0.024783587083220482,
-0.005231040064245462,
-0.03753075376152992,
0.005512417294085026,
-0.012613268569111824,
0.004320522770285606,
0.051764026284217834,
0.03287293761968613,
-0.005835944786667824,
0.007672947831451893,
-0.030702106654644012,
0.023109398782253265,
0.04398568347096443,
-0.03308403491973877,
0.06055554747581482,
0.004936549812555313,
0.017916198819875717,
-0.012568788602948189,
0.0268844161182642,
-0.03040921688079834,
-0.03119034133851528,
-0.003556792624294758,
-0.026993023231625557,
0.028858404606580734,
0.016736773774027824,
0.0030770867597311735,
0.010141012258827686,
0.057907894253730774,
-0.020960520952939987,
-0.030876843258738518,
0.0021693240851163864,
-0.002454745816066861,
0.04200916737318039,
-0.018694931641221046,
-0.01619228534400463,
0.04917530342936516,
0.04055047035217285,
0.02090003527700901,
-0.0073722731322050095,
-0.033348921686410904,
-0.010615975596010685,
-0.0480787567794323,
-0.02409397065639496,
0.013012814335525036,
0.04278033599257469,
-0.011734683066606522,
0.033583030104637146,
0.016675742343068123,
0.0132760526612401,
0.016851453110575676,
0.015040736645460129,
-0.05995756387710571,
0.00849349144846201,
-0.027358176186680794,
-0.02341267839074135,
0.01066543348133564,
-0.004083628300577402,
-0.0062422375194728374,
-0.01965063437819481,
-0.03944999724626541,
-0.0267948005348444,
0.01694543845951557,
-0.08382320404052734,
0.00712400209158659,
-0.020615294575691223,
-0.017404591664671898,
-0.00447453698143363,
0.0238313190639019,
0.07452350109815598,
0.010913011617958546,
0.010907042771577835,
0.02345757745206356,
-0.02634662762284279,
-0.00012093485565856099,
0.013603227213025093,
0.0003907652571797371,
0.038061048835515976,
-0.001140016713179648,
0.02682078443467617,
0.02197754755616188,
-0.044789329171180725,
0.03157918155193329,
0.04599735140800476,
0.02650722861289978,
-0.008670410141348839,
-0.027356259524822235,
-0.0077264499850571156,
-0.0065761106088757515,
-0.016038507223129272,
0.002992606721818447,
0.04336468130350113,
0.007830340415239334,
0.03963666036725044,
0.021225497126579285,
0.006730098742991686,
-0.005266026593744755,
0.05127808079123497,
0.08454425632953644,
-0.008775662630796432,
-0.013105498626828194,
-0.03858087584376335,
0.010677848942577839,
-0.022244151681661606,
-0.005657992325723171,
-0.020129118114709854,
0.013850321061909199,
-0.024953335523605347,
-0.01955263502895832,
-0.0008836919441819191,
0.015325034037232399,
-0.04091406613588333,
-0.014505167491734028,
-0.03786880150437355,
-0.0093768909573555,
-0.054296236485242844,
0.0027135091368108988,
-0.00478005688637495,
0.00827270932495594,
0.03459532931447029,
0.007232742849737406,
0.007951457053422928,
-0.09189267456531525,
-0.04394327476620674,
0.04701761528849602,
0.04173686355352402,
0.011565353721380234,
-0.03450101986527443,
-0.06586610525846481,
-0.020282065495848656,
0.03261701390147209,
-0.054563988000154495,
0.030188538134098053,
-0.02796759642660618,
0.0027326487470418215,
-0.01523575745522976,
-0.033489540219306946,
0.021581100299954414,
-0.0008588185301050544,
-0.023649057373404503,
0.012271469458937645,
0.00041777253500185907,
0.014022959396243095,
-0.009619423188269138,
0.0145956352353096,
-0.009396055713295937,
0.06415122747421265,
-0.02624894119799137,
-0.024297155439853668,
0.008196081966161728,
-0.009650452062487602,
-0.01991795003414154,
-0.07139457762241364,
0.05607815831899643,
0.027145227417349815,
-0.013160685077309608,
0.028030728921294212,
-0.014731618575751781,
-0.04038729518651962,
-0.03133885934948921,
0.005237916484475136,
-0.03289808705449104,
0.027850938960909843,
-0.05101832002401352,
0.03995857760310173,
0.02970018982887268,
0.008491904474794865,
0.021111076697707176,
0.0589614138007164,
-0.010124266147613525,
0.024336542934179306,
-0.028573546558618546,
0.03578329458832741,
-0.030168753117322922,
0.023659568279981613,
-0.05929119884967804,
0.007684694603085518,
-0.06441383808851242,
0.04085378721356392,
-0.045502692461013794,
-0.004472275264561176,
-0.008134533651173115,
-0.0520048625767231,
0.002877751598134637,
-0.01554680336266756,
0.012155807577073574,
0.006556512787938118,
-0.036324869841337204,
0.01795206405222416,
0.015254843980073929,
-0.02101614512503147,
-0.0091282082721591,
0.02542980946600437,
-0.019844384863972664,
0.053957000374794006,
-0.0007153481128625572,
0.02921803668141365,
-0.010874415747821331,
-0.03195146843791008,
0.029737381264567375,
-0.04805319756269455,
0.03266892582178116,
-0.00419682776555419,
-0.03346513956785202,
0.007639072835445404,
-0.06575410813093185,
-0.07782162725925446,
-0.029850274324417114,
-0.013046346604824066,
0.01445337850600481,
-0.039873283356428146,
0.03916066884994507,
0.017989743500947952,
0.012234427034854889,
-0.07673903554677963,
-0.023446962237358093,
0.02458096481859684,
-0.00010954487515846267,
-0.005303125362843275,
0.0038611870259046555,
0.011412636376917362,
-0.03314976766705513,
-0.025370463728904724,
-0.009266400709748268,
-0.0036457283422350883,
-0.03689485415816307,
0.011794009245932102,
0.029986273497343063,
0.009665627032518387,
0.018193544819951057,
0.02776271291077137,
0.02086101844906807,
0.004579761065542698,
0.025473637506365776,
-0.01132947113364935,
0.025520754978060722,
0.0347384512424469,
-0.01868441142141819,
-0.04889171943068504,
-0.021509390324354172,
0.0003649811551440507,
0.01352464035153389,
-0.036908943206071854,
-0.01052677258849144,
0.01636083424091339,
0.016582466661930084,
-0.014358485117554665,
-0.017816727980971336,
0.036649368703365326,
-0.014560390263795853,
0.010665955021977425,
0.021408872678875923,
0.0015227100811898708,
0.015062769874930382,
-0.053448326885700226,
0.015660395845770836,
-0.02773703634738922,
0.0073053669184446335,
-0.001412358251400292,
0.04989870265126228,
0.022623049095273018,
0.001231676316820085,
-0.004446049686521292,
-0.05681665986776352,
-0.0020542589481920004,
-0.00046674758777953684,
0.012963281944394112,
0.03313559666275978,
-0.026737330481410027,
-0.000654537056107074,
-0.047343771904706955,
-0.04677300900220871,
-0.020352333784103394,
0.019803859293460846,
-0.003067951649427414,
0.01036793552339077,
0.0042433044873178005,
-0.023070666939020157,
0.015171477571129799,
-0.034451019018888474,
0.019463812932372093,
0.00478657241910696,
0.020609570667147636,
0.014359721913933754,
-0.04764949157834053,
0.018885429948568344,
0.05157681554555893,
0.04399532079696655,
-0.025551721453666687,
0.02138315699994564,
0.03801426663994789,
0.07094809412956238,
-0.01850477047264576,
0.01151017565280199,
-0.06913238018751144,
0.027285845950245857,
-0.02220029942691326,
0.014502124860882759,
0.05216163024306297,
-0.018057022243738174,
-0.004849025513976812,
-0.019242482259869576,
0.002982544945552945,
-0.011347703635692596,
0.001467965543270111,
-0.05690091475844383,
0.02267516404390335,
-0.03665162995457649,
-0.0004114517942070961,
-0.03026723861694336,
0.022727245464920998,
0.00584155460819602,
-0.0012091693934053183,
0.012963338755071163,
0.02701738476753235,
-0.03821203485131264,
-0.0025534750893712044,
-0.06247013807296753,
-0.04053931683301926,
0.05606123059988022,
-0.03975393623113632,
-0.029915809631347656,
-0.004327693022787571,
-0.036461520940065384,
-0.008162196725606918,
0.005969875492155552,
0.038205452263355255,
-0.02849956974387169,
0.02092558704316616,
0.002179228002205491,
0.0353953056037426,
-0.04135556146502495,
0.019388975575566292,
0.12384984642267227,
0.05390162393450737,
0.004094600211828947,
-0.03901338949799538,
-0.0259502362459898,
-0.01739540696144104,
0.04371968284249306,
0.011564964428544044,
-0.006231315899640322,
-0.02492206171154976,
0.001771601033397019,
0.02424844540655613,
0.039817214012145996,
0.04552239924669266,
-0.010332519188523293,
0.04535689949989319,
-0.035620711743831635,
-0.018503854051232338,
-0.008676090277731419,
0.020777491852641106,
-0.023492300882935524,
0.006424092222005129,
-0.0279951561242342,
0.04599965363740921,
-0.003397688502445817,
0.002348263282328844,
-0.017403898760676384,
-0.017483476549386978,
0.01980343647301197,
0.004644221626222134,
-0.047185685485601425,
0.017420539632439613,
0.003871105145663023,
0.011948101222515106,
-0.008899230509996414,
-0.023817218840122223,
0.042430032044649124,
-0.012215616181492805,
0.015779122710227966,
0.04076716676354408,
0.025431623682379723,
-0.01987605355679989,
0.002309283707290888,
0.01794452965259552,
-0.06904985755681992,
-0.017427384853363037,
0.000400504213757813,
0.021594446152448654,
0.004482307471334934,
0.010869116522371769,
-0.015728699043393135,
-0.020757894963026047,
0.024693738669157028,
-0.016879238188266754,
0.014228614047169685,
-0.0010172029724344611,
0.004412495065480471,
-0.02844676561653614,
-0.014882835559546947,
-0.013233053497970104,
0.026260139420628548,
-0.010560451075434685,
0.031151991337537766,
-0.009941844269633293,
0.013191956095397472,
-0.006343746092170477,
0.01937929540872574,
0.010821545496582985,
-0.008073597215116024,
0.008319093845784664,
-0.020742099732160568,
-0.0008185646729543805,
-0.04412141442298889,
-0.024165721610188484,
0.012434598989784718,
0.035831108689308167,
0.06902431696653366,
-0.005864943843334913,
0.026946641504764557,
-0.029179180040955544,
-0.04970233514904976,
0.02824338525533676,
-0.027381565421819687,
-0.003151846816763282,
-0.003289035987108946,
0.02897023782134056,
-0.01492054108530283,
0.046193912625312805,
-0.03538202866911888,
-0.013477095402777195,
0.02246999368071556,
0.009646831080317497,
0.028901375830173492,
0.007962157018482685,
-0.01006227359175682,
0.043935712426900864,
-0.024874594062566757,
-0.011272147297859192,
-0.00632484070956707,
-0.0003640131908468902,
0.00012910683290101588,
0.0005357112386263907,
-0.014445696026086807,
0.04109092056751251,
-0.01674104854464531,
-0.021057385951280594,
0.013759646564722061,
-0.0029999325051903725,
-0.02108420804142952,
0.042317990213632584,
0.030498888343572617,
0.00786511693149805,
-0.013588177040219307,
0.0052134208381175995,
-0.005574058275669813,
-0.028412770479917526,
0.04999300092458725,
-0.030435049906373024,
0.035572778433561325,
0.01433405838906765,
0.01657908409833908,
-0.056342869997024536,
-0.02176295593380928,
-0.07575850933790207,
0.0319560281932354,
0.042582184076309204,
0.004251736681908369,
-0.004199953284114599,
0.008247602730989456,
-0.0053231315687298775,
-0.0676599070429802,
0.023188717663288116,
0.012582863681018353,
-0.04193533957004547,
0.009240527637302876,
0.021111035719513893,
-0.0028901491314172745,
0.04236624762415886,
0.02813289500772953,
-0.011474858969449997,
0.04668540507555008,
-0.04173613712191582,
-0.06578223407268524,
0.039062414318323135,
0.0018757819198071957,
-0.00147891731467098,
0.04476252570748329,
-0.02085771970450878,
-0.011042159982025623,
0.05379946157336235,
-0.002805267460644245,
0.009942809119820595,
0.0014675557613372803,
-0.06285114586353302,
-0.008480803109705448,
-0.013944261707365513,
0.005449219606816769,
0.014532368630170822,
0.015719527378678322,
0.019361941143870354,
0.03079325705766678,
-0.0003882817691192031,
-0.047658782452344894,
0.0227581188082695,
-0.039329644292593,
-0.008010631427168846,
-0.032594114542007446,
0.013036232441663742,
-0.00021788383310195059,
0.05549183487892151,
-0.0233487319201231,
0.03251735121011734,
-0.012788048945367336,
0.012306197546422482,
-0.10590289533138275,
-0.002004896756261587,
0.015345185995101929,
-0.003951776772737503,
0.018648983910679817,
-0.026153912767767906,
0.03819826990365982,
0.027283359318971634,
-0.05547351762652397,
0.012359059415757656,
0.0027258051559329033,
-0.001038959133438766,
-0.01967601105570793,
0.010797123424708843,
-0.04478522390127182,
0.0028584999963641167,
0.029284749180078506,
0.050948094576597214,
-0.014194495044648647,
0.05957707390189171,
-0.055900320410728455,
-0.025854574516415596,
-0.0195766594260931,
0.047198858112096786,
-0.020003922283649445,
0.02017184905707836,
0.07399871200323105,
-0.01775510609149933,
-0.006879548076540232,
0.05573122575879097,
0.001960195368155837,
0.028552420437335968,
-0.014289054088294506,
-0.010629723779857159,
0.0170998927205801,
0.01879316009581089,
0.030793050304055214,
0.015467076562345028,
0.008002372458577156,
0.018051857128739357,
0.016801506280899048,
0.029553163796663284,
0.03486258164048195,
-0.015305568464100361,
0.015789244323968887,
-0.06181548908352852,
-0.02615552395582199,
0.03740648180246353,
-0.028299711644649506,
0.02764252759516239,
0.003674033796414733,
0.023885732516646385,
0.0009069601073861122,
-0.008124335668981075,
-0.027369588613510132,
-0.019253194332122803,
-0.006921594962477684,
0.028880177065730095,
0.021544603630900383,
-0.024264145642518997,
0.008293500170111656,
-0.009358899667859077,
-0.04138324782252312,
0.028144992887973785,
-0.02109021134674549,
-0.022121530026197433,
-0.03910566493868828,
-0.027682511135935783,
-0.017820751294493675,
0.0350581593811512,
0.01952890120446682,
-0.020035114139318466,
-0.036201804876327515,
0.028446165844798088,
-0.00041223372681997716,
0.028097055852413177,
-0.053322046995162964,
-0.044109802693128586,
-0.027889519929885864,
-0.07931265980005264,
0.007334467489272356,
-0.0001880189956864342,
0.007688164245337248,
-0.0685926005244255,
-0.03492094948887825,
-0.0027303306851536036,
0.027827002108097076,
0.03632910177111626,
-0.020154206082224846,
-0.0455743633210659,
0.019725795835256577,
-0.02055203914642334,
0.04508581757545471,
-0.03651878610253334,
0.0022552309092134237,
0.01809859462082386,
-0.018175767734646797,
0.03731008991599083,
0.008875645697116852,
0.010065741837024689,
0.024197716265916824,
0.06868384033441544,
-0.023619117215275764,
0.025757228955626488,
-0.023769604042172432,
-0.0603024885058403,
0.06349625438451767,
0.019065316766500473,
-0.006515221204608679,
0.05224815756082535,
-0.037837497889995575,
0.05289529263973236,
0.04670273885130882,
0.007380318827927113,
-0.02169463038444519,
0.003397587453946471,
-0.022322649136185646,
-0.0342436283826828,
0.0229145847260952,
-0.0014840506482869387,
0.028246643021702766,
-0.027706952765583992,
-0.06481871753931046,
0.05467764660716057,
-0.0241437666118145,
-0.01849200390279293,
0.08716902881860733,
0.016559990122914314,
0.0798800140619278,
0.030602464452385902,
0.007694691885262728,
0.0006671262090094388,
0.021793099120259285,
0.007264872081577778,
0.06602412462234497,
0.015187831595540047,
0.02526385709643364,
0.01915263943374157,
0.01996360346674919,
-0.011465296149253845,
0.010813917964696884,
0.0020015928894281387,
0.028173476457595825,
-0.032878320664167404,
-0.007257048971951008,
-0.009662579745054245,
-0.0004164395504631102,
-0.028825193643569946,
0.04455876350402832,
0.003889471758157015,
0.07954727858304977,
-0.005241455044597387,
0.02484666369855404,
-0.007552844937890768,
0.04147540032863617,
-0.04718766361474991,
0.026214851066470146,
-0.01616402342915535,
0.02879473567008972,
-0.004132902715355158,
-0.004103146027773619,
-0.04128604754805565,
0.022840972989797592,
-0.0022968684788793325,
-0.059132881462574005,
-0.01437183003872633,
0.005497481673955917,
0.005044999998062849,
-0.009234346449375153,
0.004951144102960825,
0.028634516522288322,
-0.017647309228777885,
0.027350153774023056,
0.005434367340058088,
0.008328486233949661,
-0.029295729473233223,
0.0027602664195001125,
-0.03470094874501228,
0.03704594448208809,
-0.01001878920942545,
0.029487544670701027,
-0.009312981739640236,
0.02415018528699875,
-0.016871821135282516,
-0.05557337403297424
] |
<p>Recently I have been confused by the fact that: </p>
<p>Joseph Polchinski's name appear in FFP Physics Frontiers Prize 2013 here: <a href="https://fundamentalphysicsprize.org/laureates6" rel="nofollow">https://fundamentalphysicsprize.org/laureates6</a> </p>
<p>``<strong>Joseph Polchinski</strong> for his contributions in many areas of quantum field theory and string theory. His discovery of D-branes has given new insights into the nature of string theory and quantum gravity, with consequences including the AdS/CFT correspondence.''</p>
<p>However, the same award in the next year, FFP Physics Frontiers Prize in 2014 here: <a href="https://fundamentalphysicsprize.org/laureates3" rel="nofollow">https://fundamentalphysicsprize.org/laureates3</a>
which awarded Polchinski again. And for the exactly same news announcement. </p>
<p>I wonder <strong>whether Polchinski won the Physics Frontiers Prize twice, in 2013 and 2014? If so, is there a reason for that?</strong> (especially puzzling, since there are so many great candidates out there, why bother to award the same great person for the same acknowledgment?)</p>
<p>Excuse me this question may not be related to physical effect or phenomena, but it is about the puzzle caused by a physics prize. So, it is a puzzle of physics. I wish the physics puzzle is allowed to be asked here. (I am very puzzled!)</p>
| 10,711 |
[
-0.035936471074819565,
-0.020901497453451157,
-0.01724325679242611,
-0.07265444099903107,
0.02591411955654621,
0.02739103138446808,
-0.03184366226196289,
0.0029574763029813766,
-0.015311694703996181,
-0.024324733763933182,
0.023333119228482246,
-0.002708216430619359,
0.06378956139087677,
0.024384940043091774,
0.012338298372924328,
0.0042884452268481255,
0.02530497871339321,
0.010765987448394299,
-0.04508424177765846,
0.00557031249627471,
0.02323324792087078,
0.023968150839209557,
-0.030191658064723015,
0.022369660437107086,
-0.012319541536271572,
0.0039893863722682,
-0.027527734637260437,
0.024631548672914505,
-0.008668245747685432,
0.03889210894703865,
-0.015003872103989124,
-0.01739468239247799,
0.05159705877304077,
-0.02447936311364174,
0.00807914137840271,
-0.022689176723361015,
-0.01615726388990879,
-0.0018693357706069946,
0.035188935697078705,
0.009141220711171627,
-0.033096279948949814,
-0.0017620483413338661,
-0.0156338382512331,
0.0326039120554924,
-0.02695031650364399,
0.030908606946468353,
-0.02518290840089321,
-0.01844368502497673,
0.05269778519868851,
-0.051888156682252884,
0.048013169318437576,
0.011178887449204922,
0.03410422429442406,
-0.006721798330545425,
-0.04037325829267502,
0.00033012981293722987,
0.06744219362735748,
0.06737762689590454,
0.011312262155115604,
-0.05071656033396721,
-0.02770681120455265,
0.010880425572395325,
0.013518907129764557,
0.0488274060189724,
-0.01747695356607437,
0.05177932605147362,
-0.02496134489774704,
-0.0395011343061924,
0.04808059334754944,
0.0020654471591115,
-0.02880840189754963,
0.010065536014735699,
0.03903047367930412,
-0.011095255613327026,
0.04886040836572647,
-0.005145519971847534,
-0.009404313750565052,
0.008963274769484997,
0.0652930811047554,
0.019863320514559746,
-0.011751150712370872,
0.0023173645604401827,
0.014775935560464859,
0.004829117096960545,
0.02248482219874859,
-0.031028447672724724,
0.05939386785030365,
-0.033342987298965454,
-0.0063690743409097195,
0.06888984888792038,
-0.009955832734704018,
-0.020565949380397797,
0.05260686203837395,
-0.033337563276290894,
-0.03337892144918442,
0.019882353022694588,
0.015997279435396194,
0.013228604570031166,
-0.002917926525697112,
0.004871117416769266,
-0.011074614711105824,
-0.03493962064385414,
-0.01382205355912447,
0.08881328999996185,
0.03305979445576668,
-0.007059440016746521,
-0.032787028700113297,
0.019443707540631294,
-0.03370312228798866,
-0.027182841673493385,
-0.05540108308196068,
-0.00906621478497982,
-0.021303389221429825,
-0.01598244719207287,
-0.0168820358812809,
-0.011559195816516876,
-0.049704745411872864,
0.013687181286513805,
0.06811095774173737,
0.06852342933416367,
0.013610919006168842,
-0.00935825053602457,
0.011465299874544144,
-0.05364282429218292,
-0.05345702916383743,
0.017580833286046982,
0.10438709706068039,
0.009327983483672142,
-0.008077096194028854,
0.06405585259199142,
0.020564619451761246,
0.022871138527989388,
0.011263231746852398,
-0.0014701115433126688,
0.01897726207971573,
0.029706493020057678,
-0.08428018540143967,
-0.04638670012354851,
0.07333210110664368,
0.037868350744247437,
-0.024595635011792183,
-0.05916988104581833,
-0.023079412057995796,
-0.004206830635666847,
0.07186881452798843,
0.02400958351790905,
-0.024779129773378372,
0.0013221756089478731,
0.0408577136695385,
0.00829954631626606,
-0.01125576626509428,
0.02312633953988552,
0.035760555416345596,
-0.048432234674692154,
-0.023500122129917145,
-0.055802084505558014,
0.013778122141957283,
-0.00427963538095355,
0.0029493088368326426,
-0.006029773037880659,
0.1109793409705162,
0.018841758370399475,
0.01249322947114706,
-0.011864474974572659,
-0.01569799892604351,
-0.05004189535975456,
0.065733902156353,
0.020636802539229393,
0.02290847897529602,
0.016818184405565262,
-0.02548978663980961,
0.020893407985568047,
0.019013311713933945,
0.004951408598572016,
0.00881840381771326,
-0.04845188558101654,
-0.0034496590960770845,
0.008434821851551533,
-0.016053836792707443,
0.0041681877337396145,
-0.02854752168059349,
-0.02440796047449112,
-0.030963370576500893,
-0.023594211786985397,
0.009970090351998806,
0.03839247301220894,
-0.016013845801353455,
0.016155026853084564,
-0.004849338438361883,
-0.03182998299598694,
-0.03230874612927437,
-0.027446387335658073,
-0.011867446824908257,
0.0015048797940835357,
-0.015739941969513893,
0.033618420362472534,
-0.007621390279382467,
0.005992885213345289,
0.029273929074406624,
-0.02077748440206051,
0.020146775990724564,
0.049305833876132965,
0.009691551327705383,
0.009636811912059784,
0.008367090485990047,
0.05392895266413689,
0.0547129288315773,
-0.010372788645327091,
-0.002099329372867942,
-0.044921305030584335,
-0.011950056068599224,
0.03989681601524353,
0.01578286848962307,
0.014927740208804607,
0.0054657007567584515,
0.028383923694491386,
0.050598181784152985,
0.020785436034202576,
-0.035576287657022476,
0.0033450378105044365,
-0.025784656405448914,
0.06639912724494934,
0.026543647050857544,
0.025181498378515244,
-0.0044806525111198425,
0.016587408259510994,
0.002238580724224448,
0.028009885922074318,
0.01338236778974533,
-0.050740595906972885,
-0.0567915178835392,
-0.03218764811754227,
0.0030486704781651497,
0.047829918563365936,
0.014352836646139622,
0.023556524887681007,
0.009931694716215134,
0.017323676496744156,
0.003206463996320963,
0.01596674509346485,
-0.015125541016459465,
-0.019824739545583725,
0.006505647674202919,
0.04751043766736984,
-0.018339386209845543,
0.047706712037324905,
0.016220904886722565,
-0.05064850673079491,
-0.006619516294449568,
-0.0185716450214386,
-0.03152525797486305,
0.061783745884895325,
-0.0344097726047039,
0.03831357881426811,
0.03901589661836624,
-0.0021424961742013693,
0.023955706506967545,
-0.0021134987473487854,
0.015302755869925022,
0.056390054523944855,
0.020913459360599518,
-0.0021387776359915733,
-0.007007891777902842,
-0.017459476366639137,
0.01658756472170353,
-0.021722808480262756,
-0.05229409411549568,
-0.023411642760038376,
0.016926132142543793,
-0.02826772816479206,
0.04920216649770737,
-0.0050240615382790565,
-0.011593274772167206,
0.0391220822930336,
0.010221005417406559,
-0.03621194511651993,
0.009126771241426468,
0.06084990128874779,
-0.039395447820425034,
0.027751777321100235,
0.02114669233560562,
-0.045249223709106445,
-0.003892031963914633,
0.04791748896241188,
-0.027013109996914864,
0.011916114017367363,
-0.03845807537436485,
-0.010974721983075142,
0.0559840127825737,
-0.02606610395014286,
-0.0209131371229887,
0.0011271407129243016,
0.011497816070914268,
-0.026224320754408836,
-0.0242301058024168,
-0.05798593536019325,
0.0651729553937912,
-0.03440278396010399,
0.026439731940627098,
0.024404671043157578,
-0.012852197512984276,
-0.07869482785463333,
-0.0010345150949433446,
-0.012950303964316845,
0.00839143991470337,
0.025408517569303513,
-0.05301835387945175,
0.011253454722464085,
-0.03905823826789856,
0.00660627381876111,
0.008085987530648708,
-0.001835361821576953,
-0.03177037462592125,
-0.053354427218437195,
-0.05511436238884926,
0.028401359915733337,
-0.05083576962351799,
0.03285032883286476,
-0.03315119817852974,
-0.037494588643312454,
0.011643982492387295,
0.04672391712665558,
-0.020942460745573044,
-0.0012385781155899167,
0.028339194133877754,
-0.027878398075699806,
-0.01756637915968895,
-0.0003827984619420022,
0.05534305423498154,
-0.022701241075992584,
0.04723041132092476,
0.03262631222605705,
0.024122988805174828,
0.012979719787836075,
-0.02377142570912838,
-0.017085017636418343,
-0.028552690520882607,
0.02485191449522972,
0.009052569977939129,
0.013614179566502571,
-0.0037319704424589872,
-0.00942531879991293,
-0.012729511596262455,
-0.014083107933402061,
0.004891582764685154,
0.009038257412612438,
-0.008637696504592896,
0.023098066449165344,
-0.01279937382787466,
0.017955223098397255,
-0.024113081395626068,
0.004289783537387848,
-0.023985475301742554,
-0.05433184280991554,
-0.01967569626867771,
-0.010144131258130074,
0.03537818416953087,
-0.02020154893398285,
0.0031742898281663656,
0.03495597094297409,
0.03680941089987755,
-0.03962356597185135,
-0.04357346519827843,
-0.07826108485460281,
0.032938871532678604,
0.029540758579969406,
-0.005285814870148897,
-0.04173104837536812,
0.01700669713318348,
0.041989441961050034,
0.05437730997800827,
0.025180937722325325,
-0.023187654092907906,
0.01526386197656393,
-0.029931847006082535,
0.00016135133046191186,
-0.02479928731918335,
0.07436410337686539,
-0.002677161945030093,
0.04227759689092636,
0.02285652421414852,
0.02577238902449608,
-0.024706706404685974,
-0.016890959814190865,
-0.09736603498458862,
0.028255194425582886,
-0.01693299412727356,
0.02079344168305397,
-0.02477114647626877,
-0.046977974474430084,
-0.013939092867076397,
-0.03426786884665489,
-0.006022382527589798,
-0.0003702296526171267,
0.00680567929521203,
-0.07548742741346359,
0.016192743554711342,
-0.0281362347304821,
-0.017838023602962494,
-0.005352126434445381,
0.040740832686424255,
0.049550242722034454,
-0.03513694554567337,
0.03128717839717865,
-0.0173630528151989,
0.001960436813533306,
-0.01508362777531147,
-0.02289169281721115,
0.022396456450223923,
0.03348094969987869,
0.002722065197303891,
-0.016490347683429718,
0.03154086321592331,
-0.042301028966903687,
0.015878910198807716,
-0.019318224862217903,
0.024640053510665894,
-0.008331811055541039,
-0.009311124682426453,
-0.07560428977012634,
-0.05513005331158638,
-0.007026223000138998,
-0.003655590582638979,
0.052819471806287766,
0.0019053189316764474,
0.034399256110191345,
0.00330494437366724,
-0.00871797651052475,
-0.007577180862426758,
0.03368853032588959,
0.015464389696717262,
-0.04778732731938362,
-0.012875567190349102,
-0.010595584288239479,
-0.00453556003049016,
-0.02860427089035511,
-0.010800821706652641,
-0.010699060745537281,
0.03010452166199684,
-0.016934866085648537,
0.009567665867507458,
0.022456137463450432,
-0.009917881339788437,
-0.052748698741197586,
0.00791677925735712,
-0.02630416862666607,
0.0040496960282325745,
0.018777985125780106,
0.033912114799022675,
0.010698442347347736,
0.012351986020803452,
0.0718597024679184,
-0.03245300427079201,
-0.013812355697154999,
-0.05060723423957825,
-0.0194444227963686,
0.0009134015417657793,
0.017834611237049103,
-0.013196229934692383,
-0.01320137083530426,
-0.07031819224357605,
0.0068391128443181515,
0.021538248285651207,
-0.03673335909843445,
0.017291711643338203,
0.016963526606559753,
0.0020994581282138824,
-0.01703457720577717,
-0.01901441253721714,
-0.01412215270102024,
0.02941577509045601,
0.02959582582116127,
0.02074579894542694,
0.0040610600262880325,
-0.010973567143082619,
-0.018440930172801018,
0.017343299463391304,
-0.017505034804344177,
-0.0065206922590732574,
0.03760013356804848,
0.02616848237812519,
-0.01238467637449503,
0.013596792705357075,
-0.056778643280267715,
-0.07326643168926239,
0.011632365174591541,
-0.009133678860962391,
-0.040022287517786026,
0.034477151930332184,
-0.0515824593603611,
-0.05141213908791542,
-0.003062623552978039,
0.004957002587616444,
-0.04365452378988266,
-0.014265754260122776,
-0.042182695120573044,
0.05144251510500908,
0.05629173293709755,
-0.005249816458672285,
0.039787277579307556,
0.04432600364089012,
-0.015416721813380718,
-0.0018373833736404777,
-0.0049538626335561275,
0.05641663447022438,
-0.018343212082982063,
0.025987710803747177,
-0.006980902049690485,
0.015559706836938858,
-0.07469319552183151,
0.027942078188061714,
-0.003964284434914589,
-0.010923510417342186,
-0.0034556007012724876,
-0.04496029391884804,
-0.027567574754357338,
-0.010000480338931084,
-0.01844215579330921,
-0.009411276318132877,
0.003384919138625264,
0.017196722328662872,
0.023399854078888893,
-0.03573431447148323,
-0.008433560840785503,
0.007114515174180269,
0.007401413284242153,
0.03809740021824837,
0.03938192129135132,
0.03650759905576706,
-0.007071240339428186,
-0.0219370536506176,
0.02264525555074215,
-0.014020278118550777,
0.029828038066625595,
0.022678887471556664,
0.012599746696650982,
0.014894799329340458,
-0.06628475338220596,
-0.027999499812722206,
0.00007738402200629935,
0.0009203145746141672,
-0.03557030111551285,
-0.05491553992033005,
0.03846485912799835,
0.01938622072339058,
0.03156193345785141,
-0.04326016083359718,
0.013058462180197239,
0.007815312594175339,
0.07071339339017868,
-0.024887600913643837,
-0.004354698117822409,
0.02328811213374138,
-0.005402931943535805,
-0.02729823812842369,
-0.07611475884914398,
0.026150893419981003,
-0.046916812658309937,
-0.025119025260210037,
0.018782423809170723,
0.01722910813987255,
0.06021157652139664,
-0.025296369567513466,
0.025340311229228973,
0.02372869849205017,
0.0039722006767988205,
0.00976326409727335,
-0.03934792801737785,
0.020801527425646782,
-0.016590096056461334,
-0.05406111478805542,
-0.01593841426074505,
0.003993530757725239,
0.020090853795409203,
-0.003724601585417986,
0.0266767218708992,
0.055478062480688095,
-0.011558759957551956,
0.011576543562114239,
-0.012407680042088032,
0.030649205669760704,
-0.004985676147043705,
0.025137711316347122,
-0.001609183382242918,
0.021557433530688286,
-0.010182328522205353,
-0.0404147244989872,
-0.012397285550832748,
0.010136573575437069,
-0.03024262934923172,
0.01901162974536419,
0.03776257112622261,
-0.04344717040657997,
-0.03192896395921707,
0.01470766868442297,
-0.0215462576597929,
0.008630706928670406,
0.0032249765936285257,
0.016385426744818687,
0.004808087833225727,
-0.033271584659814835,
-0.040768228471279144,
-0.05196024104952812,
-0.020838798955082893,
0.00312346825376153,
0.011939194053411484,
-0.02336718887090683,
0.0332258939743042,
0.022417152300477028,
-0.041628140956163406,
0.02881714515388012,
-0.004204968921840191,
0.036233630031347275,
-0.007114957552403212,
-0.03213883936405182,
0.03578741103410721,
-0.03458493947982788,
0.002979578683152795,
0.041861943900585175,
0.052551548928022385,
0.02958006039261818,
0.01029307022690773,
0.016603218391537666,
0.030468368902802467,
-0.0014620092697441578,
-0.0371846929192543,
-0.017486462369561195,
0.04828433319926262,
-0.04729079455137253,
0.01565190777182579,
0.037653692066669464,
-0.02037155255675316,
0.008573419414460659,
0.030768146738409996,
-0.01220286637544632,
-0.033033061772584915,
-0.05087043344974518,
-0.025282876566052437,
0.025519641116261482,
0.03873853385448456,
0.010054338723421097,
0.0744125172495842,
-0.027976863086223602,
0.0182044580578804,
0.04958409070968628,
-0.03534257411956787,
-0.00985958706587553,
-0.07992245256900787,
-0.00934941042214632,
-0.024376552551984787,
-0.06301013380289078,
0.06002019718289375,
-0.014984851703047752,
-0.020096447318792343,
0.02728762850165367,
-0.014042049646377563,
0.030792441219091415,
0.01663152128458023,
0.021595720201730728,
-0.03244844079017639,
0.03198833763599396,
0.005683335475623608,
0.04754737764596939,
-0.015128147788345814,
-0.016977230086922646,
0.13099859654903412,
0.010169226676225662,
0.04807531088590622,
-0.0431334413588047,
0.021825633943080902,
0.02460232377052307,
0.014111372642219067,
-0.010142700746655464,
0.02080543339252472,
-0.0018443726003170013,
-0.015145980753004551,
-0.0037905892822891474,
0.041801661252975464,
0.03025565855205059,
-0.020760469138622284,
0.0334223248064518,
-0.026070378720760345,
-0.05226559191942215,
0.03801561892032623,
-0.0018264070386067033,
0.018797913566231728,
-0.027207396924495697,
-0.04264221340417862,
0.0078958785161376,
-0.01228339597582817,
0.05834900587797165,
-0.005035227630287409,
-0.03688977286219597,
0.01189988013356924,
0.025601310655474663,
-0.0019900258630514145,
0.02758430503308773,
0.010816190391778946,
0.020110683515667915,
-0.024589885026216507,
0.027951620519161224,
0.007900388911366463,
0.011532966047525406,
0.0543028861284256,
0.05042855069041252,
-0.0028977389447391033,
0.0014017707435414195,
0.015733543783426285,
0.011955291964113712,
-0.025340870022773743,
-0.015901977196335793,
0.0034866435453295708,
0.012944788672029972,
-0.030155982822179794,
0.006814596708863974,
-0.004998357966542244,
-0.010368600487709045,
-0.019749658182263374,
-0.015123525634407997,
-0.030572418123483658,
0.002994207665324211,
-0.011603173799812794,
-0.027461864054203033,
-0.0083086509257555,
0.016999302431941032,
0.03876573592424393,
0.008599263615906239,
0.03287527337670326,
-0.034146737307310104,
-0.031824514269828796,
-0.0015535689890384674,
-0.00397140346467495,
0.00649395352229476,
-0.007313495967537165,
0.017465554177761078,
-0.07252084463834763,
0.02019544132053852,
-0.048868630081415176,
-0.021347006782889366,
-0.025888998061418533,
-0.015065111219882965,
0.038286928087472916,
0.008841199800372124,
-0.0025856003630906343,
-0.06937383115291595,
-0.0018936364213004708,
0.012865042313933372,
0.019860312342643738,
0.03213537484407425,
-0.04582872986793518,
0.0026567205786705017,
0.007139736786484718,
-0.003950982354581356,
-0.018267886713147163,
0.02163395844399929,
0.01682063192129135,
0.0581778846681118,
-0.0025267773307859898,
0.007383532822132111,
-0.03843274340033531,
-0.03428170830011368,
-0.011193395592272282,
-0.006306846160441637,
-0.03162870556116104,
0.0332346186041832,
0.01199740543961525,
-0.009098892100155354,
0.011409841477870941,
0.018962420523166656,
-0.03759552910923958,
0.012870199978351593,
0.0427946001291275,
-0.0070671685971319675,
-0.01735757291316986,
-0.004520047456026077,
-0.01481628231704235,
-0.00861776527017355,
-0.025927074253559113,
0.014555811882019043,
0.005160100758075714,
0.030455492436885834,
0.024420401081442833,
-0.012921341694891453,
-0.01235145889222622,
-0.009628023952245712,
0.0073283277451992035,
-0.03688162937760353,
0.001343434676527977,
-0.062436386942863464,
0.030620504170656204,
-0.011155514046549797,
0.00715272594243288,
0.0025627275463193655,
0.06016389653086662,
-0.017286183312535286,
-0.00289456476457417,
0.006174140144139528,
0.02569820173084736,
-0.05158822983503342,
-0.01855451799929142,
0.026498226448893547,
-0.00829850323498249,
0.036445241421461105,
0.00873829796910286,
-0.03538260608911514,
0.036757707595825195,
-0.04118471220135689,
-0.05926387757062912,
0.033893126994371414,
0.008899053558707237,
0.036503542214632034,
0.0369206964969635,
0.00964526180177927,
-0.012529151514172554,
0.006918773520737886,
-0.03342895582318306,
0.015546205453574657,
-0.007803101558238268,
-0.006973909214138985,
0.0460534431040287,
-0.0021148258820176125,
-0.009872110560536385,
-0.00909462757408619,
-0.021937038749456406,
-0.005355037283152342,
0.028292912989854813,
0.002062336541712284,
-0.03973861783742905,
-0.010843399912118912,
-0.05964073911309242,
0.010693147778511047,
-0.029373478144407272,
0.020450249314308167,
0.014655484817922115,
0.043932829052209854,
-0.026494048535823822,
-0.022897178307175636,
0.014509356580674648,
0.015086975879967213,
-0.0330621711909771,
0.01977383904159069,
0.016116078943014145,
-0.0069640944711863995,
0.013943824917078018,
-0.025581570342183113,
0.04755217209458351,
-0.007899466902017593,
-0.044221241027116776,
0.05087989568710327,
-0.025829851627349854,
-0.008212954737246037,
-0.04939144849777222,
0.027361182495951653,
-0.03977400064468384,
0.04572971165180206,
0.046932123601436615,
0.026226002722978592,
0.019331052899360657,
0.01926572062075138,
0.0052429502829909325,
-0.05004176124930382,
-0.0689786970615387,
0.033909548074007034,
-0.014117629267275333,
0.0022543156519532204,
0.07187825441360474,
-0.02006586827337742,
-0.06522999703884125,
0.017225120216608047,
-0.002707473235204816,
-0.04461247846484184,
0.020242614671587944,
0.005100705195218325,
0.043510422110557556,
-0.009176049381494522,
0.016848158091306686,
-0.009986619465053082,
0.0446043536067009,
0.007074748165905476,
-0.01317442674189806,
0.03882623463869095,
0.021113626658916473,
-0.015483575873076916,
0.016950350254774094,
-0.01913154311478138,
-0.016549130901694298,
0.0011577029945328832,
0.005209621042013168,
0.020858239382505417,
0.0142816798761487,
-0.012042555958032608,
0.032496221363544464,
-0.011061731725931168,
-0.007047603372484446,
-0.05225372686982155,
-0.0017895587952807546,
0.031865205615758896,
0.04709766060113907,
-0.021539313718676567,
0.02719748578965664,
-0.018735216930508614,
-0.04796218499541283,
0.04578447341918945,
0.0018141943728551269,
-0.015254147350788116,
0.013595839962363243,
-0.004501596558839083,
0.05754954740405083,
0.049120981246232986,
0.022337675094604492,
-0.056591715663671494,
-0.014566076919436455,
0.03161492943763733,
-0.004706354811787605,
0.03774195536971092,
-0.045931752771139145,
-0.039226286113262177,
-0.01597139611840248,
-0.10175826400518417,
0.02291249670088291,
0.009061537683010101,
0.021058818325400352,
-0.014947121031582355,
0.007744581438601017,
-0.0008705271757207811,
0.05454059690237045,
0.012933793477714062,
-0.017842330038547516,
-0.05034232884645462,
0.025020664557814598,
-0.023894820362329483,
0.01876121573150158,
-0.013755188323557377,
0.018091514706611633,
0.008985201828181744,
0.029645105823874474,
-0.02886713296175003,
0.015865076333284378,
-0.018186334520578384,
-0.001319817965850234,
0.035111308097839355,
0.009425395168364048,
0.021764235571026802,
-0.030235672369599342,
-0.016766520217061043,
0.04110926762223244,
0.009986549615859985,
0.01783265918493271,
0.044809214770793915,
0.001606018515303731,
0.028603311628103256,
0.0028487311210483313,
-0.02530934475362301,
-0.024744372814893723,
0.050287798047065735,
-0.05477968603372574,
-0.04485103115439415,
-0.01975536346435547,
0.008747386746108532,
0.013248064555227757,
-0.03125370666384697,
-0.004747872240841389,
0.026599327102303505,
-0.05018586665391922,
-0.062048524618148804,
0.05631028488278389,
0.01319743413478136,
-0.013117947615683079,
-0.012762870639562607,
0.017284918576478958,
-0.0014065839350223541,
-0.019725115969777107,
-0.02380967326462269,
0.016932982951402664,
0.0476103350520134,
0.08432988822460175,
0.04454817250370979,
-0.004841956309974194,
0.029693637043237686,
0.017023898661136627,
0.021267753094434738,
0.031969137489795685,
-0.03128029406070709,
0.009223767556250095,
0.03602445870637894,
-0.024845127016305923,
-0.005182615946978331,
0.031632713973522186,
0.0019219628302380443,
0.07540465146303177,
0.004083765204995871,
0.03779883682727814,
0.004403280559927225,
0.014428618364036083,
-0.026752328500151634,
-0.005074504762887955,
-0.007199190557003021,
0.02554292045533657,
-0.017817974090576172,
-0.022045426070690155,
-0.057342279702425,
0.021856701001524925,
0.026326071470975876,
-0.05302441120147705,
0.02245069108903408,
-0.01848914474248886,
-0.017773499712347984,
-0.0023007758427411318,
-0.02897762507200241,
-0.035009417682886124,
-0.042004022747278214,
0.04273366183042526,
0.020453771576285362,
-0.009470105171203613,
-0.032427940517663956,
-0.025253698229789734,
-0.016166364774107933,
0.05689489096403122,
-0.041507698595523834,
-0.019938265904784203,
-0.040243905037641525,
0.036179523915052414,
-0.007001510355621576,
0.025320617482066154
] |
<p>A car is moving at a velocity of $10 \, \text{m}/\text{s}$. After point $A$ no acceleration is provided. By simple measurement, the acceleration is found to be $-1 \, \text{m}/\text{s}^2$.</p>
<p>Using standard equations: $$v = u + at, \; v=0, \; u = 10, $$ we arrive at $t = 10 \text{s}$.</p>
<p>$$S = ut + .5 at^2 = 50 \,\text{m}$$</p>
<p>ie- the car stops at $50\, \text{m}$ from point $A$.</p>
<p>However, by manual calculation, the car travels the following distance before coming to stop: $10 \, \text{m}$ at $t=0$, $9 \, \text{m}$ at $t =1$, etc since $a = -1$, the $v$ reduces by $1 \, \text{m}/\text{s}$, so on, so we get $S = 10 +9+..1 = 55 \, \text{m}$</p>
<p>Where am I going wrong here?</p>
| 10,712 |
[
0.0379435233771801,
-0.046389758586883545,
-0.03656003624200821,
0.01622774265706539,
0.03555355966091156,
-0.015149425715208054,
-0.0449841283261776,
0.0025512496940791607,
-0.016974447295069695,
0.014555335976183414,
0.04794684797525406,
0.029820477589964867,
0.0369393564760685,
0.026175571605563164,
0.02066073566675186,
0.016016626730561256,
-0.013670114800333977,
-0.04445435106754303,
-0.0009770011529326439,
-0.0026636281982064247,
0.01016000472009182,
-0.010523268021643162,
0.003698536893352866,
0.015113807283341885,
-0.015245179645717144,
-0.002265596529468894,
0.014451088383793831,
0.01722392812371254,
-0.02827494964003563,
0.045429687947034836,
0.019646193832159042,
-0.025239482522010803,
-0.0010996987111866474,
0.04206424206495285,
0.03727402538061142,
0.028698695823550224,
-0.012691427953541279,
-0.014843539334833622,
-0.021234408020973206,
-0.00613333098590374,
-0.018934190273284912,
-0.023305246606469154,
-0.015730328857898712,
0.04580206423997879,
-0.012091320939362049,
-0.019824596121907234,
0.04818948730826378,
0.001879187417216599,
0.0375659316778183,
-0.04174131527543068,
0.07479608058929443,
0.027756232768297195,
0.00513167679309845,
-0.008091396652162075,
0.008081554435193539,
-0.010254585184156895,
0.07029924541711807,
0.02557370811700821,
-0.030823105946183205,
-0.07007384300231934,
-0.0062138792127370834,
-0.03343604505062103,
-0.00950276106595993,
-0.015080180950462818,
-0.026276439428329468,
0.0007682435098104179,
-0.0373857207596302,
0.015567012131214142,
0.03226979449391365,
-0.04116596654057503,
0.015067051164805889,
0.02704581804573536,
0.0022662009578198195,
-0.01403424609452486,
0.017917992547154427,
-0.06636656075716019,
0.0350077822804451,
0.0032254077959805727,
0.051286280155181885,
0.04700528830289841,
0.01587444543838501,
0.01959404908120632,
0.05334021896123886,
0.03073372319340706,
0.02775968424975872,
-0.027398383244872093,
0.03779636323451996,
0.03661816194653511,
0.03437461331486702,
0.038093745708465576,
0.023564696311950684,
0.01960252784192562,
0.004176980350166559,
-0.007717612199485302,
0.04529813304543495,
0.07086839526891708,
-0.006328205578029156,
0.03367222845554352,
0.04023104906082153,
-0.02909030206501484,
-0.03710947930812836,
-0.04525236040353775,
0.05079418048262596,
0.05283336341381073,
-0.041168972849845886,
-0.004756817128509283,
-0.05220973119139671,
0.014066072180867195,
-0.008330761454999447,
-0.004652546718716621,
-0.03944762423634529,
0.023641126230359077,
0.027725836262106895,
0.05564095079898834,
0.004833942744880915,
-0.016577819362282753,
-0.004655434750020504,
-0.021618353202939034,
0.040382906794548035,
0.004454031120985746,
0.06015721336007118,
-0.04502058029174805,
0.023253824561834335,
0.005776046775281429,
-0.04679154232144356,
0.008578567765653133,
0.012301630340516567,
-0.006591979879885912,
-0.041538845747709274,
0.023291805759072304,
-0.0022693786304444075,
-0.03319378197193146,
0.017652610316872597,
0.0359371043741703,
0.03977607935667038,
0.014708004891872406,
-0.10226261615753174,
-0.09520970284938812,
0.025390909984707832,
0.02362794429063797,
0.010381778702139854,
-0.06255721300840378,
0.024514874443411827,
0.030934633687138557,
0.07081998884677887,
-0.02435302734375,
0.013015730306506157,
0.02793087624013424,
0.022628264501690865,
-0.01573975756764412,
0.04119596630334854,
-0.006059570237994194,
-0.020692545920610428,
-0.04150986671447754,
0.03321703523397446,
-0.04592081531882286,
0.04685397446155548,
0.04239563271403313,
0.00925852358341217,
-0.05135069414973259,
0.036599062383174896,
-0.008441632613539696,
0.0033790203742682934,
0.022233637049794197,
-0.0006563753704540431,
-0.005500687286257744,
0.07300131767988205,
0.030117422342300415,
-0.008297196589410305,
0.039352789521217346,
0.01955598033964634,
0.05242466181516647,
-0.001641461392864585,
0.006353849079459906,
0.04149922356009483,
-0.0562581792473793,
-0.03556598350405693,
-0.014147848822176456,
-0.012911740690469742,
0.03318055346608162,
-0.02807340770959854,
-0.05686322972178459,
0.00010607983858790249,
-0.0008394589531235397,
-0.028970791026949883,
0.023179423063993454,
-0.021130191162228584,
0.05615975335240364,
0.005481100175529718,
-0.007254381198436022,
-0.02638818509876728,
-0.07819800823926926,
0.016719289124011993,
0.012033326551318169,
0.04040174558758736,
0.03271724283695221,
-0.016752522438764572,
0.0030919404234737158,
-0.024083415046334267,
-0.006226919125765562,
0.013921351172029972,
0.04472002014517784,
0.00697445310652256,
-0.0334450788795948,
-0.0006124047795310616,
0.07151682674884796,
0.06145129352807999,
-0.01980624347925186,
0.008047202602028847,
-0.01774660125374794,
0.03150836378335953,
-0.0029660207219421864,
-0.015649160370230675,
0.008301607333123684,
0.0006353443022817373,
-0.03279649838805199,
-0.006485170219093561,
-0.013024385087192059,
-0.008741306141018867,
0.0631285086274147,
-0.044639952480793,
0.08258729428052902,
0.07620105892419815,
0.000963943952228874,
-0.019863806664943695,
0.04813309386372566,
-0.007785994093865156,
0.05004933848977089,
-0.00023743760539218783,
-0.03149370476603508,
-0.021309683099389076,
-0.013002431020140648,
0.03090582601726055,
0.008955666795372963,
-0.016509393230080605,
-0.012065897695720196,
0.06490049511194229,
0.02899754047393799,
0.03202753886580467,
0.03368936479091644,
-0.01398142147809267,
-0.0643855631351471,
0.020429085940122604,
-0.0013871985720470548,
0.013584655709564686,
0.015439214184880257,
0.004929365590214729,
0.037121523171663284,
-0.00911190640181303,
0.017990635707974434,
0.002832828089594841,
0.005881998222321272,
-0.00019544722454156727,
0.05041160061955452,
0.02816273458302021,
-0.006639397703111172,
0.054296355694532394,
-0.019271377474069595,
0.010715587064623833,
0.03707585856318474,
0.02088617905974388,
-0.016404559835791588,
-0.04326292499899864,
-0.0020247790962457657,
-0.0029375581070780754,
-0.0021197753958404064,
-0.041430313140153885,
-0.011740224435925484,
0.03304973617196083,
-0.004306152928620577,
-0.004851026460528374,
-0.0479605570435524,
0.01808696612715721,
-0.025521444156765938,
0.007008744869381189,
0.05138456076383591,
0.0053976853378117085,
0.006678494159132242,
-0.05520624667406082,
0.0024526286870241165,
0.026777349412441254,
-0.04135821759700775,
0.01813690736889839,
0.024637730792164803,
-0.04342195391654968,
0.03944616764783859,
-0.045431312173604965,
-0.04380247741937637,
0.05641583725810051,
0.04358590021729469,
-0.02609485201537609,
0.0076349047012627125,
-0.012992997653782368,
-0.026080206036567688,
-0.048322636634111404,
-0.00649780360981822,
0.0011189962970092893,
-0.03907092288136482,
-0.0035282333847135305,
0.06147915497422218,
0.01981036737561226,
-0.02112758904695511,
0.013320505619049072,
-0.05540064722299576,
-0.03465767949819565,
-0.03677218779921532,
0.01573064737021923,
0.018660152330994606,
-0.052735187113285065,
0.002118453849107027,
-0.01101007591933012,
-0.011812329292297363,
-0.0008445655694231391,
-0.037054430693387985,
-0.053606826812028885,
-0.016620025038719177,
0.01212784368544817,
0.06510992348194122,
0.01970769464969635,
-0.013487611897289753,
0.05685427784919739,
0.016480550169944763,
-0.016022631898522377,
-0.026875298470258713,
0.03464246168732643,
-0.006182379554957151,
-0.01755036786198616,
-0.06869916617870331,
0.026434248313307762,
-0.04569864645600319,
0.00999455712735653,
0.010793700814247131,
0.04873387888073921,
0.041241422295570374,
0.02256697416305542,
-0.02539421245455742,
-0.03174954652786255,
-0.0017906028078868985,
0.004169709514826536,
-0.0005187886999920011,
-0.01106060016900301,
-0.031511884182691574,
0.007147016003727913,
-0.006789724342525005,
0.056601159274578094,
0.02803208865225315,
-0.025961924344301224,
0.04098483920097351,
-0.023855652660131454,
0.016572197899222374,
-0.03696759417653084,
0.01564282551407814,
0.007523386739194393,
-0.0003331145562697202,
-0.028259236365556717,
0.03130557760596275,
0.04490939900279045,
-0.026290712878108025,
-0.04191107675433159,
0.00925389677286148,
0.023151883855462074,
-0.037263743579387665,
-0.04868661239743233,
0.007982628419995308,
-0.00934964045882225,
0.04025085270404816,
-0.03156726807355881,
0.0125376982614398,
0.03273657336831093,
0.068659707903862,
0.032237209379673004,
0.02117076888680458,
-0.06341296434402466,
0.016048364341259003,
-0.042627379298210144,
-0.038724616169929504,
0.004316137172281742,
0.043785810470581055,
0.0023986101150512695,
-0.0019412506371736526,
0.030830910429358482,
0.020890943706035614,
-0.00762277003377676,
0.008758633397519588,
-0.0976821631193161,
0.03546294569969177,
-0.015226687304675579,
-0.07760594040155411,
-0.01406176295131445,
-0.0006919782608747482,
0.0011168838245794177,
-0.043229296803474426,
0.032533321529626846,
-0.0006822054856456816,
-0.008121325634419918,
-0.043470751494169235,
0.014381223358213902,
-0.04112651199102402,
-0.06002916023135185,
-0.018101463094353676,
-0.029452914372086525,
0.05835900828242302,
-0.03495977446436882,
0.013384420424699783,
0.04291141405701637,
-0.021024368703365326,
-0.003911919891834259,
-0.040067557245492935,
-0.018991680815815926,
0.03659358620643616,
0.0364697240293026,
0.04084877297282219,
0.024107204750180244,
-0.002586067421361804,
0.039061661809682846,
-0.029679274186491966,
0.05248872935771942,
0.015805594623088837,
-0.008580522611737251,
-0.05512315034866333,
-0.01785147748887539,
-0.032443102449178696,
0.023743897676467896,
0.013767619617283344,
-0.011515509337186813,
0.021734096109867096,
0.02913852035999298,
0.0034051365219056606,
0.008154748938977718,
0.04637214168906212,
0.03242519497871399,
-0.017062222585082054,
-0.001789073459804058,
-0.023337388411164284,
-0.040065642446279526,
-0.02461078017950058,
0.012265786528587341,
0.040408726781606674,
0.02243553102016449,
0.014591464772820473,
-0.01265573687851429,
0.024886853992938995,
0.009366422891616821,
-0.017387699335813522,
0.0019367063650861382,
-0.009217215701937675,
0.009196443483233452,
0.027285359799861908,
-0.0280400812625885,
0.012405851855874062,
0.01600605621933937,
0.032398514449596405,
-0.02169218845665455,
-0.03528563678264618,
-0.09623308479785919,
0.0034628664143383503,
0.010850154794752598,
0.020472459495067596,
-0.01254726480692625,
-0.009465450420975685,
-0.0408487431704998,
-0.043378785252571106,
0.04242626950144768,
-0.03710481524467468,
0.03289349004626274,
-0.004723682533949614,
-0.009235215373337269,
0.01520304474979639,
-0.04396166279911995,
-0.04990968108177185,
0.012613415718078613,
-0.03401749208569527,
0.023345978930592537,
-0.006817854940891266,
-0.005748515948653221,
-0.054227083921432495,
-0.010108372196555138,
0.034543395042419434,
0.039535511285066605,
0.006195720285177231,
-0.006410274188965559,
-0.050844963639974594,
0.023410944268107414,
-0.03224966675043106,
-0.07371862977743149,
0.016444910317659378,
-0.012371636927127838,
-0.014618342742323875,
0.0007669607293792069,
-0.029333002865314484,
-0.01569901593029499,
0.0645655021071434,
-0.013323820196092129,
-0.01764138601720333,
0.00027124324697069824,
-0.002854382386431098,
0.014751800335943699,
0.007606751285493374,
0.017390774562954903,
0.0011760145425796509,
-0.0029977408703416586,
-0.025070317089557648,
0.007121591828763485,
-0.021785905584692955,
0.012766803614795208,
-0.015309952199459076,
-0.009028800763189793,
-0.029089873656630516,
0.023341648280620575,
-0.022671204060316086,
0.06493816524744034,
0.005121920723468065,
0.008584447205066681,
-0.05211959779262543,
-0.03532576560974121,
0.012310376390814781,
0.027603741735219955,
0.006141632329672575,
0.045875225216150284,
-0.025535203516483307,
-0.0018863185541704297,
-0.014713653363287449,
-0.026637179777026176,
0.011433607898652554,
0.005523833446204662,
-0.0008092204225249588,
0.014497831463813782,
0.00021339140948839486,
0.0005455035134218633,
-0.015317749232053757,
-0.016100022941827774,
0.0441296361386776,
-0.06673694401979446,
0.04515865817666054,
-0.031259845942258835,
-0.0187100600451231,
-0.0006443139864131808,
-0.0243359487503767,
-0.03897050768136978,
0.013122256845235825,
-0.007841016165912151,
0.027945956215262413,
-0.05096106603741646,
0.04464433714747429,
0.03534144163131714,
0.03551643341779709,
-0.0461789146065712,
-0.045434191823005676,
0.0332496240735054,
0.01650078222155571,
-0.0079496456310153,
-0.009009524248540401,
-0.009611480869352818,
-0.037247780710458755,
-0.038051970303058624,
-0.013830887153744698,
0.016244282945990562,
-0.02384059689939022,
-0.01572246663272381,
0.0066400510258972645,
0.012780062854290009,
0.06547632068395615,
-0.008040104061365128,
0.012659816071391106,
0.01998666301369667,
-0.014355890452861786,
-0.0009123572381213307,
0.010007865726947784,
0.07190627604722977,
-0.0493287593126297,
-0.0013858246384188533,
0.005963047966361046,
-0.045283228158950806,
0.025476990267634392,
0.011059151962399483,
0.0032199674751609564,
0.041412707418203354,
0.01566213369369507,
0.01291576400399208,
-0.01745465211570263,
0.044842712581157684,
-0.008642666041851044,
0.0014308419777080417,
0.0017872906755656004,
-0.0156587902456522,
0.011730886064469814,
0.010810276493430138,
0.02966960519552231,
0.005712755024433136,
-0.013327469117939472,
-0.013867887668311596,
0.0553978830575943,
-0.026811497285962105,
0.01611863449215889,
0.022284749895334244,
0.02989986352622509,
0.05845649912953377,
0.015258465893566608,
-0.02321220189332962,
0.004428524058312178,
-0.025817306712269783,
-0.018068181350827217,
-0.011815451085567474,
-0.024331938475370407,
0.025888657197356224,
0.06228858232498169,
0.004459126852452755,
0.04819152131676674,
0.01689986139535904,
0.011981436982750893,
0.023920385167002678,
-0.0235988050699234,
-0.04025821387767792,
-0.007118000648915768,
0.03513384982943535,
0.0261439997702837,
-0.030161233618855476,
-0.006514265667647123,
0.010867614299058914,
0.06061180680990219,
0.021579304710030556,
-0.01871057040989399,
0.003342259908095002,
-0.02622092328965664,
0.028642497956752777,
-0.021199971437454224,
-0.01419343426823616,
-0.0019220308167859912,
-0.0011757354950532317,
-0.00945239793509245,
-0.024602634832262993,
-0.006296449340879917,
0.066030353307724,
0.01235844288021326,
0.014618894085288048,
-0.016946762800216675,
0.009698805399239063,
-0.04574092850089073,
-0.005031627602875233,
-0.0033706845715641975,
0.021891171112656593,
0.004858013242483139,
-0.017210479825735092,
-0.0034112236462533474,
0.010458293370902538,
0.04325208440423012,
-0.031780730932950974,
-0.04162745922803879,
-0.01973520964384079,
-0.04378928989171982,
-0.019488895311951637,
0.044928744435310364,
0.013631070032715797,
-0.02713090367615223,
0.011851748451590538,
-0.03020765446126461,
0.0024773688055574894,
0.03380952402949333,
0.014723856933414936,
-0.001046237419359386,
0.08676563948392868,
-0.008539819158613682,
0.03817204385995865,
-0.025016363710165024,
-0.004855145234614611,
0.1202627569437027,
0.048890065401792526,
-0.014936610125005245,
0.0025227325968444347,
0.028771044686436653,
-0.03652903065085411,
-0.007315781898796558,
-0.013006762601435184,
0.03708232566714287,
0.0017271817196160555,
0.010816769674420357,
-0.005527046043425798,
0.04592432081699371,
-0.01990230567753315,
-0.014061380177736282,
0.04300843924283981,
-0.043714072555303574,
-0.03459375724196434,
-0.014368513599038124,
-0.014325268566608429,
-0.011948829516768456,
0.006585116032510996,
0.028264937922358513,
0.02092042937874794,
-0.03032745234668255,
-0.021063746884465218,
-0.0132152009755373,
-0.03134065121412277,
0.021083414554595947,
0.04192028567194939,
-0.05393742024898529,
0.045624662190675735,
0.04999847337603569,
-0.03146931901574135,
-0.08056779950857162,
0.038468137383461,
0.006429699249565601,
-0.031116247177124023,
0.00537926284596324,
0.048081256449222565,
0.003713658545166254,
0.02424875646829605,
0.0007934613386169076,
0.006339541170746088,
-0.060591500252485275,
0.010527925565838814,
-0.0527261458337307,
0.06647675484418869,
-0.01817057467997074,
0.0126238027587533,
-0.03555260971188545,
0.013925682753324509,
0.016998371109366417,
-0.06995182484388351,
-0.014298360794782639,
0.009984788484871387,
0.03562648966908455,
0.018057718873023987,
-0.0006489992374554276,
-0.036783814430236816,
0.0011066533625125885,
0.013998410664498806,
-0.02339899353682995,
0.05300802364945412,
0.0005802814266644418,
-0.010569705627858639,
0.01222954224795103,
0.0329604297876358,
-0.032556869089603424,
-0.01090304460376501,
-0.0164386797696352,
0.002113498281687498,
-0.030385054647922516,
-0.017416903749108315,
0.01860794983804226,
0.03639141470193863,
-0.00594270508736372,
0.01666867360472679,
0.02251051366329193,
-0.029725056141614914,
-0.053192563354969025,
0.016219470649957657,
0.006243208888918161,
-0.017605341970920563,
-0.028065714985132217,
-0.03355749323964119,
-0.040386639535427094,
0.03966616466641426,
-0.021929549053311348,
-0.017704656347632408,
0.011895367875695229,
0.0631585568189621,
0.01349707692861557,
-0.007808685768395662,
0.0016017780872061849,
-0.005161272827535868,
-0.041296206414699554,
0.0342710055410862,
0.016829615458846092,
0.04211676865816116,
0.01792365498840809,
0.007510068826377392,
-0.04209986701607704,
0.030109409242868423,
-0.022790728136897087,
-0.01218573097139597,
0.024061819538474083,
-0.03959192335605621,
-0.012980952858924866,
0.047315265983343124,
0.044133223593235016,
-0.02020355314016342,
-0.01275584939867258,
0.001082311850041151,
0.010014614090323448,
0.021634751930832863,
0.01658904179930687,
-0.003114494029432535,
0.049089834094047546,
-0.02802535891532898,
0.01911003515124321,
-0.044729966670274734,
0.0030732995364814997,
-0.03402463719248772,
-0.005602973513305187,
-0.0067703681997954845,
-0.040331486612558365,
-0.045708127319812775,
-0.022852838039398193,
0.020473172888159752,
0.056311074644327164,
0.003763905493542552,
0.0021901398431509733,
0.014592130668461323,
-0.02153492532670498,
-0.012788234278559685,
-0.010693726129829884,
0.05054362490773201,
-0.059533119201660156,
-0.021661629900336266,
0.015799477696418762,
-0.021977610886096954,
-0.012337172403931618,
0.03226318582892418,
-0.0023488118313252926,
0.042036544531583786,
-0.005850031040608883,
-0.017095711082220078,
-0.011133669875562191,
0.09105446189641953,
-0.016682026907801628,
-0.0048497808165848255,
0.027448706328868866,
-0.029464025050401688,
-0.019489727914333344,
-0.025386521592736244,
0.0035826843231916428,
-0.026021551340818405,
-0.01833588257431984,
-0.004931459669023752,
0.0487225279211998,
-0.017933448776602745,
0.033303339034318924,
0.02615906298160553,
-0.0052176713943481445,
0.004801562055945396,
0.030766429379582405,
0.0003959012683480978,
0.005070106592029333,
0.027746373787522316,
-0.017166441306471825,
0.02690190263092518,
-0.025104425847530365,
0.009133695624768734,
-0.06682393699884415,
-0.012035646475851536,
0.02082936465740204,
0.02278098277747631,
0.024655519053339958,
-0.025828076526522636,
0.0075387596152722836,
0.0454922579228878,
-0.053124815225601196,
-0.003805838292464614,
-0.06414565443992615,
-0.02962482161819935,
-0.03719302639365196,
-0.033583398908376694,
-0.013137290254235268,
0.03289308398962021,
0.020057503134012222,
0.010793247260153294,
0.01567772589623928,
-0.00863650068640709,
-0.005016350653022528,
-0.04112034663558006,
0.015633368864655495,
0.03306206688284874,
-0.022570420056581497,
-0.014508824795484543,
0.03684478998184204,
-0.02537308633327484,
-0.015569647774100304,
0.021587561815977097,
-0.02858097478747368,
0.03358469530940056,
0.013591746799647808,
0.010604683309793472,
-0.008821350522339344,
0.04918462038040161,
0.0158733818680048,
0.018177693709731102,
-0.005304369144141674,
0.006585682276636362,
0.0006185545353218913,
0.031223390251398087,
-0.012273615226149559,
0.000940641388297081,
0.0353722870349884,
-0.033827558159828186,
-0.07639503479003906,
-0.008787120692431927,
-0.011912038549780846,
-0.028819574043154716,
-0.024247922003269196,
0.015459968708455563,
-0.013906583189964294,
-0.07889924198389053,
-0.031198184937238693,
-0.019416457042098045,
-0.016029352322220802,
0.048542652279138565,
-0.03767424449324608,
-0.007158768363296986,
-0.0248968955129385,
-0.010308236815035343,
-0.013937181793153286,
0.0009076666319742799,
-0.020968595519661903,
-0.0187111534178257,
-0.058164577931165695,
-0.01463650818914175,
0.0023137705866247416,
-0.028429314494132996,
-0.008197720162570477,
-0.030204659327864647,
0.016535989940166473,
0.07532532513141632,
0.034453392028808594,
0.000860480300616473,
0.02505378983914852,
-0.004411561414599419,
-0.0073396083898842335,
-0.07305119931697845,
0.01911943219602108,
-0.00625908887013793,
-0.0492374449968338,
-0.012160315178334713,
-0.04253134876489639,
-0.0037909189704805613,
0.00008947895548772067,
0.08110535144805908,
-0.005369750317186117,
-0.016647322103381157,
0.04815121740102768,
-0.032845549285411835,
0.007665256038308144,
-0.004525762051343918,
0.00025447001098655164,
-0.0032830226700752974,
0.015413758344948292,
-0.013395661488175392,
0.005572212394326925,
-0.016307713463902473,
-0.005816387478262186,
-0.004003208130598068,
-0.01418076641857624,
0.01713121309876442,
-0.0004176409274805337,
-0.009499515406787395,
0.021372603252530098,
0.049066852778196335,
0.023184185847640038,
0.05350464582443237,
0.031266484409570694,
0.053144849836826324,
0.04434247687458992,
-0.044490452855825424,
-0.025964459404349327,
0.008901256136596203,
-0.04648863896727562,
-0.017300980165600777,
-0.044520843774080276,
-0.017980484291911125,
0.03246084228157997,
-0.055380888283252716,
-0.02596518211066723,
0.05244170129299164,
-0.05098213627934456,
-0.019731219857931137,
0.015047477558255196,
0.034182313829660416,
0.03177916631102562,
0.020823488011956215,
0.045554812997579575,
0.007756305858492851,
-0.034056153148412704,
0.0071960436180233955,
0.027759935706853867,
0.05308745056390762,
-0.010924886912107468,
-0.0381164588034153,
0.05587247386574745,
-0.022191347554326057,
0.0178188756108284,
-0.027289703488349915,
0.022994033992290497,
0.019466087222099304,
0.00006580728222616017,
-0.03555506467819214,
-0.02550259232521057,
0.011816870421171188,
0.017512302845716476,
-0.007591202389448881,
0.0402095653116703,
-0.04603457450866699,
0.015149223618209362,
-0.033444833010435104,
-0.006318847648799419,
-0.02649799920618534,
0.00122459651902318,
0.005642381496727467,
0.025119343772530556,
-0.005444762296974659,
-0.016606325283646584,
0.012426740489900112,
-0.00256097549572587,
0.055570945143699646,
0.04107670113444328,
-0.015393123030662537,
-0.030368225648999214,
-0.02567778155207634,
-0.018133988603949547,
-0.04504451900720596,
0.018327683210372925,
-0.007215782068669796,
0.03631128743290901,
0.04475807771086693,
0.010598164983093739,
-0.04141613841056824,
0.005235003307461739,
-0.0057729315012693405,
0.0667552575469017,
-0.07810235768556595,
-0.03212432563304901,
-0.01332030724734068,
-0.012574849650263786,
-0.025368526577949524,
-0.038855813443660736
] |
<p>It's not homework (I'm teacher). I would like to compute sum of forces on this study :</p>
<p><img src="http://i.stack.imgur.com/2bLUJ.png" alt="enter image description here"></p>
<p>The shape is symmetrical like that I'm sure the center of gravity is in the center of the shape. I compute forces on axis X only. No external gravity. Air container are fixed on big container. But air container has very low pressure, I don't want to compute it, consider it like vacuum. </p>
<p>I know force of pressure is like :</p>
<p>$\frac{1}{2}{\rho}h_{\epsilon}^2w^2R^2$ with R the distance to container from center of gravity of container, $h_{\epsilon}^2$ is a small area, true ? </p>
<p>I compute forces on water, depth is d, it's:</p>
<p>$$d\omega^2\rho*((\int_{0}^{h1}(r1^2+y^2)cos(atan(\frac{y}{r1}))dy)-(\int_{0}^{h1}(r2^2+y^2)cos(atan(\frac{y}{r2}))dy)+(\int_{0}^{h2}(r3^2+y^2)cos(atan(\frac{y}{r3}))dy))$$</p>
<p>so, it's:</p>
<p>$$d\omega^2\rho*((\int_{0}^{h1}\sqrt{(r1^2+y^2)}r1dy)-(\int_{0}^{h1}\sqrt{(r2^2+y^2)}r2dy)+(\int_{0}^{h2}\sqrt{(r3^2+y^2)}r3dy))$$</p>
<p>Is it ok ?</p>
<p>Now, if I want to compute forces on rectangle solid, I need to integrate 2 times ? Like that :</p>
<p>$$\frac{1}{2}d\rho\omega^2*(\int_{-h2}^{h2}\int_{0}^{r3}(x^2+y^2)^{0.5}cos(atan(\frac{y}{x}))dxdy-(\int_{-h1}^{h1}\int_{r1}^{r2}(x^2+y^2)^{0.5}cos(atan(\frac{y}{x}))dxdy)$$ </p>
<p>So it's:</p>
<p>$$\frac{1}{2}d\rho\omega^2*(\int_{-h2}^{h2}\int_{0}^{r3}(x^2+y^2)^{0.25}xdxdy-\int_{-h1}^{h1}\int_{r1}^{r2}(x^2+y^2)^{0.25}xdxdy)$$ </p>
<p>How to add mass inside integrales ?</p>
<p>I have a problem, I don't find 0 for the sum of forces.</p>
<hr>
<p>There are 2 additionnal forces Fa that decrease forces from liquid:</p>
<p><img src="http://i.stack.imgur.com/4grKT.png" alt="enter image description here"></p>
<p>But the shape can be like that:</p>
<p><img src="http://i.stack.imgur.com/WvBUj.png" alt="enter image description here"></p>
<p>So in this case forces Fa = 0. In last case, Fa are compensated by what forces ? </p>
<p>If I take a macroscopic model, with compressible balls for understand where F forces are compensated, consider the center of gravity like red point (balls have more density than solid, just enough for compensated):</p>
<p><img src="http://i.stack.imgur.com/gHjyW.png" alt="enter image description here"></p>
<hr>
<p>And there is another force to take in account it's the red force :</p>
<p><img src="http://i.stack.imgur.com/L77Pz.png" alt="enter image description here"></p>
<p>This red force is apply all along the surface of container ?</p>
| 10,713 |
[
-0.03311115875840187,
-0.009983489289879799,
-0.008118869736790657,
-0.023955048993229866,
0.04466196894645691,
-0.030082490295171738,
-0.023526733741164207,
-0.0264956783503294,
0.024550121277570724,
-0.015059973113238811,
0.04051559045910835,
0.03224705159664154,
0.07122208923101425,
-0.0003297837101854384,
0.009370448999106884,
-0.01260208711028099,
-0.0040894318372011185,
0.007669026032090187,
0.03571178391575813,
-0.02840222790837288,
-0.0007409104728139937,
0.00004951864684699103,
0.0009546997607685626,
-0.024264095351099968,
-0.022621555253863335,
0.0522947832942009,
0.06006084382534027,
-0.036448266357183456,
-0.010117650963366032,
0.03631419688463211,
-0.03586571663618088,
-0.003583592362701893,
-0.003491578623652458,
0.0013195613864809275,
0.029820051044225693,
0.03478570282459259,
-0.03936304524540901,
-0.0226290300488472,
-0.0073922304436564445,
0.04260823503136635,
-0.01783660426735878,
-0.01207529567182064,
0.014182193204760551,
0.04464521259069443,
-0.03401795029640198,
0.050474442541599274,
-0.0022315834648907185,
-0.00875290296971798,
0.04775424674153328,
-0.07190956175327301,
0.0621529296040535,
-0.0003125189687125385,
0.04783010110259056,
0.04203370213508606,
0.004325578920543194,
-0.01455602701753378,
0.006499674171209335,
0.01555938646197319,
0.0016259263502433896,
-0.032519131898880005,
-0.017503101378679276,
0.011203637346625328,
-0.03295554220676422,
-0.055474698543548584,
0.004710838198661804,
0.010888058692216873,
0.008014769293367863,
-0.009327652864158154,
-0.006381915416568518,
0.0019677174277603626,
0.040843065828084946,
0.014698856510221958,
0.03225676715373993,
-0.041911106556653976,
0.008275747299194336,
0.007212834898382425,
-0.0039732325822114944,
0.0250102486461401,
0.010343494825065136,
0.02068251185119152,
-0.0007115110056474805,
0.0011676459107547998,
0.030776357278227806,
0.011830674484372139,
0.03993869200348854,
-0.002364455722272396,
0.037648752331733704,
0.013624104671180248,
-0.050223108381032944,
0.021313441917300224,
-0.004676219541579485,
0.010876628570258617,
0.03864894062280655,
-0.013333403505384922,
0.006864650174975395,
0.018291782587766647,
-0.005921489093452692,
0.05821811035275459,
0.0017191371880471706,
-0.02915550209581852,
-0.02252807468175888,
-0.06816188991069794,
-0.0216301828622818,
0.12932009994983673,
0.025053156539797783,
-0.037057921290397644,
-0.004061392042785883,
-0.00436780508607626,
-0.02114805206656456,
-0.008004887029528618,
-0.019679373130202293,
-0.0053634303621947765,
-0.02294299006462097,
-0.04003620520234108,
-0.024960210546851158,
0.025681015104055405,
-0.003620552597567439,
0.002417225856333971,
0.04275825619697571,
0.022002294659614563,
0.056192442774772644,
0.005863601341843605,
0.015657570213079453,
-0.02959113009274006,
-0.05524127185344696,
0.043017949908971786,
0.02063588611781597,
-0.03806864097714424,
-0.00897055771201849,
0.03255011513829231,
0.047772325575351715,
0.002245452022179961,
-0.017092345282435417,
0.01272248849272728,
0.031129563227295876,
-0.026646437123417854,
-0.0628337487578392,
-0.05353932827711105,
0.023501679301261902,
0.009906580671668053,
-0.0051259915344417095,
-0.015853863209486008,
0.009259023703634739,
0.030429352074861526,
0.054361797869205475,
-0.010069433599710464,
-0.012104538269340992,
0.02479012869298458,
0.03096587024629116,
-0.007130508776754141,
-0.017185267060995102,
0.016132885590195656,
-0.01138383150100708,
-0.017273209989070892,
-0.025988193228840828,
-0.08051193505525589,
0.023816769942641258,
0.014703487046062946,
-0.006243385374546051,
-0.006281846668571234,
0.03998297080397606,
-0.008742562495172024,
0.007074921857565641,
0.005272059701383114,
-0.0172310471534729,
-0.050163377076387405,
0.04532899335026741,
0.004199558403342962,
0.0032612478826195,
0.030760642141103745,
-0.02749776467680931,
0.021081676706671715,
-0.03438550978899002,
-0.022627757862210274,
0.058308981359004974,
-0.034835346043109894,
0.004703563172370195,
-0.026259571313858032,
0.013664048165082932,
0.01559012196958065,
-0.04673454537987709,
-0.04500618577003479,
-0.031804390251636505,
-0.013803196139633656,
0.0060569243505597115,
0.06092577427625656,
0.01503424160182476,
-0.02856437861919403,
0.002358926460146904,
-0.02465170994400978,
-0.004279088694602251,
-0.05919865891337395,
0.015371031127870083,
-0.04434976354241371,
-0.031714435666799545,
-0.010665133595466614,
-0.007618850562721491,
-0.004130566492676735,
0.01988591067492962,
-0.0024634008295834064,
-0.02770519256591797,
0.021937847137451172,
0.049123961478471756,
0.021166164427995682,
0.06068026274442673,
-0.011952854692935944,
0.04278770834207535,
0.005545501597225666,
0.006638758350163698,
-0.019937502220273018,
0.00784570537507534,
-0.03746464475989342,
-0.042657699435949326,
-0.008673831820487976,
0.009118976071476936,
-0.006112575065344572,
0.03732100501656532,
0.0020168491173535585,
-0.006985026877373457,
0.0036406214348971844,
-0.0424632728099823,
0.06140291690826416,
0.05936315283179283,
0.026432273909449577,
0.027571644634008408,
0.002232407918199897,
0.02288896031677723,
0.03671715036034584,
0.015892790630459785,
0.018628496676683426,
-0.04644269496202469,
-0.032838862389326096,
0.023618008941411972,
0.030787304043769836,
-0.02534422278404236,
-0.01686745136976242,
0.06301748752593994,
0.0015501013258472085,
0.02653105929493904,
0.0019383830949664116,
0.005465805996209383,
-0.03850698843598366,
0.03539228439331055,
0.04530956596136093,
0.014328536577522755,
0.006077158264815807,
0.006287639029324055,
0.013034156523644924,
0.036604899913072586,
0.014306711032986641,
-0.0370602011680603,
0.032545335590839386,
0.008479433134198189,
0.011360579170286655,
-0.03286619111895561,
0.03272997587919235,
0.028629617765545845,
-0.029489589855074883,
0.022533945739269257,
0.021663950756192207,
0.01462813001126051,
-0.0030248411931097507,
-0.056114211678504944,
0.017436472699046135,
-0.00555386021733284,
0.010249072685837746,
0.00591098191216588,
-0.015465611591935158,
0.03499484807252884,
-0.05137714743614197,
0.0022005464415997267,
-0.03750308230519295,
-0.011959224939346313,
-0.03329082578420639,
-0.03307601436972618,
0.008632517419755459,
0.03366424888372421,
0.01736891083419323,
-0.007610545959323645,
0.0454992800951004,
-0.024392541497945786,
0.025066180154681206,
-0.02179381623864174,
0.014601008035242558,
-0.047692231833934784,
-0.025304362177848816,
-0.051245711743831635,
-0.006850984413176775,
0.04412851855158806,
0.016632895916700363,
-0.045235782861709595,
0.04383252561092377,
0.0336037278175354,
-0.04954591020941734,
-0.04741733521223068,
-0.022040478885173798,
0.04728091135621071,
-0.06362757831811905,
-0.010164969600737095,
0.012962321750819683,
0.010377634316682816,
-0.048026639968156815,
0.042655061930418015,
-0.002917187288403511,
-0.04359158128499985,
-0.03284914046525955,
0.0005085872253403068,
0.001607875106856227,
-0.026323648169636726,
-0.005181273445487022,
-0.01347392424941063,
-0.009626585058867931,
-0.009287510998547077,
-0.051624737679958344,
-0.03139425441622734,
0.010517779737710953,
0.005988755729049444,
0.0519692562520504,
-0.029543837532401085,
-0.04139804095029831,
0.06677328050136566,
-0.016757747158408165,
-0.030817752704024315,
-0.021701334044337273,
0.023587947711348534,
-0.012998096644878387,
-0.01726670190691948,
0.006020918022841215,
0.031444013118743896,
-0.017040515318512917,
0.0058195581659674644,
-0.0017832079902291298,
0.02038995362818241,
0.0089351125061512,
-0.017082318663597107,
-0.006303503178060055,
0.036023255437612534,
0.03924136981368065,
0.01116857584565878,
0.07794607430696487,
0.01343209482729435,
0.044350896030664444,
0.030674345791339874,
-0.003230827394872904,
0.00436775479465723,
0.026304423809051514,
-0.08703199028968811,
0.01090224739164114,
0.0014686455251649022,
-0.028233584016561508,
-0.017262350767850876,
0.03176353871822357,
-0.0071907988749444485,
-0.05815380439162254,
-0.0071356818079948425,
0.00971339363604784,
0.048099786043167114,
0.01713847741484642,
-0.01480564009398222,
0.068675197660923,
0.08589065819978714,
0.01190217025578022,
-0.03859930858016014,
0.008425946347415447,
0.010021503083407879,
0.035010144114494324,
-0.011082826182246208,
-0.015683826059103012,
0.014714262448251247,
0.027137303724884987,
0.004465238656848669,
0.012865487486124039,
0.004150427877902985,
0.01670791581273079,
-0.07823050767183304,
-0.04396665468811989,
-0.03314284235239029,
0.04935973882675171,
-0.03602574020624161,
0.03514156863093376,
0.010298202745616436,
-0.023427749052643776,
0.015858395025134087,
-0.010756720788776875,
-0.054024044424295425,
0.043578315526247025,
0.016157643869519234,
-0.0006965923821553588,
0.02520645409822464,
-0.007211756892502308,
0.011805050075054169,
-0.033726468682289124,
0.010510553605854511,
-0.027417166158556938,
0.0005964846932329237,
-0.0022313923109322786,
0.04581635445356369,
0.0077750422060489655,
-0.002999302465468645,
-0.0042747389525175095,
0.05825360491871834,
0.01711321622133255,
-0.003059880807995796,
0.03276727721095085,
0.05118410289287567,
-0.02219286747276783,
0.026334304362535477,
-0.024593079462647438,
0.004470816347748041,
0.03079024888575077,
0.037319645285606384,
0.010920682922005653,
0.045703090727329254,
0.02246076799929142,
-0.024494262412190437,
-0.004997925832867622,
0.026532679796218872,
-0.025731610134243965,
0.0207769013941288,
-0.03417513892054558,
-0.030045246705412865,
0.004610277712345123,
0.0171885434538126,
0.034030549228191376,
-0.0236318688839674,
0.0053646257147192955,
0.021249007433652878,
-0.020179463550448418,
0.030999258160591125,
0.023120803758502007,
0.0707676112651825,
-0.004072162788361311,
-0.030890287831425667,
-0.07239001244306564,
0.021426429972052574,
-0.033995386213064194,
-0.00731554813683033,
0.019343864172697067,
0.02950984053313732,
-0.05316246300935745,
0.007833775132894516,
0.04277623072266579,
0.025675255805253983,
-0.01357708964496851,
0.02214985340833664,
0.010173322632908821,
0.029084471985697746,
-0.018863629549741745,
-0.013192694634199142,
0.02219500206410885,
0.036136068403720856,
0.04608901962637901,
-0.011315868236124516,
-0.00460736034438014,
-0.030744224786758423,
-0.03729155287146568,
0.04810589179396629,
0.05446719378232956,
0.011639227159321308,
0.03323901444673538,
-0.05647019296884537,
-0.05612170696258545,
0.059868138283491135,
-0.02459612861275673,
0.027497244998812675,
-0.01984519138932228,
-0.004545592702925205,
0.025986837223172188,
-0.03577258810400963,
-0.09755086898803711,
-0.022847510874271393,
-0.03121711127460003,
0.0013563300017267466,
-0.07347096502780914,
0.0007289229542948306,
0.04134690761566162,
0.007251976523548365,
0.020165884867310524,
-0.016337674111127853,
-0.01859397441148758,
0.00437143724411726,
-0.02184114418923855,
0.019067876040935516,
-0.031895846128463745,
-0.054932527244091034,
-0.014938797801733017,
0.014079333283007145,
0.015846485272049904,
0.02292368747293949,
-0.0380299873650074,
-0.03666892275214195,
0.046507708728313446,
0.012941030785441399,
0.01873777061700821,
-0.006252781488001347,
-0.012404671870172024,
0.040227003395557404,
0.10851117223501205,
0.0034538041800260544,
0.02038063481450081,
0.04097719490528107,
-0.025632966309785843,
-0.05425653234124184,
0.0056677693501114845,
-0.03141503781080246,
-0.011077447794377804,
-0.04240569472312927,
-0.052075739949941635,
0.015912333503365517,
-0.02331952005624771,
-0.004042108077555895,
-0.02042574994266033,
0.014955652877688408,
-0.011344501748681068,
0.001794596086256206,
0.05104778707027435,
0.045910585671663284,
0.0036860888358205557,
-0.008799543604254723,
0.01979738101363182,
0.0049476101994514465,
0.049926236271858215,
-0.022544967010617256,
-0.005980623420327902,
-0.004945842549204826,
0.02900507301092148,
0.029593132436275482,
-0.016186095774173737,
0.00019475935550872236,
-0.04331694915890694,
-0.009924032725393772,
-0.007418564520776272,
-0.04244154319167137,
0.03974779695272446,
-0.04650486260652542,
0.030175618827342987,
0.05373988300561905,
-0.03401831537485123,
-0.021511701866984367,
0.01534873154014349,
-0.008194444701075554,
0.020437395200133324,
-0.011507496237754822,
0.013137058354914188,
0.02436409704387188,
0.008743345737457275,
-0.03614497184753418,
-0.006143514066934586,
0.018363913521170616,
-0.007479923311620951,
-0.006145323161035776,
-0.06064918264746666,
-0.007632849272340536,
-0.026768792420625687,
-0.025691857561469078,
-0.020435471087694168,
0.04340722784399986,
-0.038737207651138306,
0.023278210312128067,
0.030248936265707016,
-0.0029839922208338976,
0.032171402126550674,
-0.015754135325551033,
0.005337144248187542,
0.03577740490436554,
0.004778800532221794,
-0.015721259638667107,
-0.0005219990853220224,
0.02186887338757515,
-0.045764222741127014,
-0.02163263037800789,
-0.013807750307023525,
-0.029695458710193634,
0.01914975978434086,
-0.041028156876564026,
-0.015014746226370335,
-0.014719696715474129,
0.02545880153775215,
-0.01633378677070141,
-0.02100750245153904,
0.005003401543945074,
0.01875126361846924,
0.02058282308280468,
-0.0185297392308712,
0.016949288547039032,
-0.05613243952393532,
-0.021623749285936356,
-0.03234051540493965,
-0.04016544669866562,
-0.03453947976231575,
-0.023677457123994827,
0.06495270133018494,
0.0037339176051318645,
-0.009651473723351955,
-0.03204023838043213,
-0.02954847365617752,
0.021981820464134216,
-0.00022029285901226103,
-0.02819930389523506,
0.01140567660331726,
0.04182921722531319,
-0.026446795091032982,
-0.035241130739450455,
-0.07904943078756332,
0.04546581581234932,
0.10640555620193481,
-0.004586185794323683,
0.05046810582280159,
0.024048583582043648,
-0.021648237481713295,
-0.025619009509682655,
0.0007034830050542951,
-0.017400266602635384,
0.03513704240322113,
0.007379097398370504,
0.06392794102430344,
-0.017231907695531845,
-0.027722211554646492,
0.036151591688394547,
0.013926017098128796,
-0.024758705869317055,
0.0036118701100349426,
0.021567635238170624,
-0.0051756203174591064,
-0.016286198049783707,
-0.03430446609854698,
-0.021866369992494583,
0.03493548557162285,
0.012884685769677162,
0.05263402312994003,
-0.014897077344357967,
-0.03763587027788162,
0.03885677829384804,
0.05915273353457451,
0.0006234122556634247,
-0.06041939556598663,
-0.0063606142066419125,
-0.00978666078299284,
0.03194762021303177,
0.03782632574439049,
-0.026705028489232063,
-0.04719274491071701,
0.014117475599050522,
0.037863124161958694,
-0.011466138996183872,
0.015537778846919537,
-0.02823597379028797,
-0.018522368744015694,
0.01898183859884739,
0.003585864556953311,
-0.026783088222146034,
0.03224422037601471,
0.02000809833407402,
-0.012075457721948624,
0.033144135028123856,
-0.004051570314913988,
0.014290851540863514,
0.06452573835849762,
-0.0012628812110051513,
-0.008535338565707207,
0.0484757162630558,
-0.026357309892773628,
0.020537471398711205,
-0.04876044765114784,
0.02534915879368782,
0.14958292245864868,
0.0016096398467198014,
-0.0026574390940368176,
-0.023799845948815346,
-0.008327389135956764,
-0.009762968868017197,
-0.01588272675871849,
-0.026806101202964783,
-0.010864710435271263,
-0.0055902982130646706,
-0.013747386634349823,
0.027277715504169464,
0.06619074195623398,
-0.014938585460186005,
-0.008878378197550774,
0.005187247879803181,
-0.05466889962553978,
-0.03152663633227348,
-0.01432715356349945,
0.00973939523100853,
-0.01738584227859974,
0.021061545237898827,
-0.04952913150191307,
0.0390244796872139,
-0.05960303544998169,
-0.017781082540750504,
-0.04228983446955681,
-0.027330003678798676,
0.028529012575745583,
0.00966983288526535,
-0.07770279794931412,
0.023598384112119675,
-0.04419688880443573,
-0.024488020688295364,
-0.039387427270412445,
0.04146978631615639,
0.014028632082045078,
-0.03202557936310768,
0.012046505697071552,
0.05413312464952469,
0.023114411160349846,
0.01604427397251129,
-0.018169919028878212,
0.006365944165736437,
-0.030713818967342377,
0.010342475026845932,
-0.01628889888525009,
0.055008530616760254,
-0.0168174859136343,
-0.0061731114983558655,
-0.0029745756182819605,
-0.01601058803498745,
0.02148357778787613,
-0.05606735125184059,
-0.01087157242000103,
-0.008473600260913372,
0.030998986214399338,
0.0031033107079565525,
-0.0022026009391993284,
0.007391477003693581,
0.023940306156873703,
-0.012501750141382217,
0.023184187710285187,
-0.037835743278265,
0.009903914295136929,
-0.024496078491210938,
0.0034359151031821966,
0.07841482758522034,
-0.003621539333835244,
0.004683714359998703,
-0.011747521348297596,
0.004655911587178707,
-0.027348369359970093,
0.022587189450860023,
-0.01330866664648056,
-0.002704623155295849,
0.038508087396621704,
0.01920187473297119,
-0.004364745691418648,
-0.014743511565029621,
-0.050995804369449615,
0.007452997379004955,
-0.05932354927062988,
-0.02877485752105713,
-0.02995486930012703,
-0.058481477200984955,
0.006383473984897137,
0.07546796649694443,
0.037514638155698776,
-0.029984967783093452,
0.029664358124136925,
0.053985144942998886,
0.045354001224040985,
-0.01490215864032507,
-0.0718340054154396,
0.00600355863571167,
-0.017541950568556786,
-0.009147122502326965,
-0.019317174330353737,
-0.010371148586273193,
0.025288566946983337,
0.029704153537750244,
0.005142077337950468,
-0.0059518455527722836,
-0.04538688808679581,
0.007858279161155224,
0.014963882975280285,
0.003495321376249194,
-0.008825043216347694,
-0.014893988147377968,
0.006459435448050499,
-0.06822177022695541,
0.035773422569036484,
0.008236526511609554,
-0.03413282334804535,
-0.03836251422762871,
0.016538644209504128,
-0.0008974586962722242,
0.029500095173716545,
-0.03835409879684448,
0.009953141212463379,
-0.004851789679378271,
0.023060688748955727,
-0.0425523966550827,
-0.018023503944277763,
0.005212342832237482,
0.01879020407795906,
-0.06100647523999214,
0.04290979728102684,
-0.016882246360182762,
0.02942770905792713,
-0.024523545056581497,
0.01522738579660654,
0.00928235612809658,
-0.024520324543118477,
0.0415809229016304,
0.008353566750884056,
0.019388295710086823,
-0.009284726344048977,
-0.025945132598280907,
0.01910756155848503,
-0.01310407742857933,
-0.034490350633859634,
-0.002278117695823312,
0.0035214368253946304,
0.01741354912519455,
0.021333975717425346,
-0.01788836531341076,
-0.04031308367848396,
0.05230116471648216,
-0.019318288192152977,
-0.00896892324090004,
-0.0031280359253287315,
-0.021887019276618958,
-0.0018542727921158075,
-0.0017849201103672385,
0.043848805129528046,
-0.0075952704064548016,
0.0036900441627949476,
0.007506745867431164,
0.0007974531035870314,
-0.030680770054459572,
0.0024010224733501673,
0.01405973732471466,
-0.0022090738639235497,
0.00523532647639513,
-0.015115953050553799,
-0.0016096209874376655,
0.008672431111335754,
0.026840917766094208,
-0.05216089263558388,
0.025205111131072044,
0.008978930301964283,
-0.003994851838797331,
-0.10046392679214478,
-0.015243818052113056,
0.002769240876659751,
0.0012933692196384072,
0.051815979182720184,
-0.052493106573820114,
0.015435568988323212,
0.007829107344150543,
-0.08168382942676544,
-0.0010269839549437165,
-0.03207753598690033,
0.005763869732618332,
-0.0016746961046010256,
-0.00352104427292943,
0.028582291677594185,
0.03873612731695175,
-0.004146133083850145,
0.035964056849479675,
0.01306154578924179,
0.03248858079314232,
-0.021599987521767616,
-0.03597654774785042,
0.006529513746500015,
0.04666821286082268,
-0.006731605622917414,
0.0024779310915619135,
0.047450050711631775,
0.0012032637605443597,
0.025405071675777435,
-0.013122500851750374,
-0.02366086281836033,
0.02524334378540516,
-0.051521558314561844,
0.04318167641758919,
-0.00810522772371769,
0.04200538620352745,
-0.01779605634510517,
0.03855092078447342,
0.013850333169102669,
0.012697484344244003,
0.022259240970015526,
0.002262301743030548,
-0.017413584515452385,
-0.008100633509457111,
0.0012383871944621205,
-0.00411450257524848,
-0.012105608358979225,
0.06934083253145218,
-0.004973258823156357,
-0.009541541337966919,
0.026789521798491478,
-0.02662162110209465,
-0.009299681521952152,
-0.020605409517884254,
-0.009925163350999355,
-0.05648684874176979,
0.061339374631643295,
0.019352087751030922,
0.013342877849936485,
-0.04694213718175888,
0.004130073823034763,
-0.007659630849957466,
-0.032846931368112564,
0.01761629246175289,
-0.009602160193026066,
-0.031244320794939995,
-0.03894549235701561,
-0.006240888498723507,
-0.010295343585312366,
0.0017509042518213391,
0.020319581031799316,
-0.036514170467853546,
-0.023524882271885872,
0.004098659381270409,
0.03790729120373726,
-0.015986043959856033,
0.013921188190579414,
-0.0071985311806201935,
-0.011066246777772903,
-0.061366740614175797,
0.012921908870339394,
0.03400551900267601,
-0.048072073608636856,
-0.011312543414533138,
-0.010060878470540047,
0.006075926125049591,
0.021328946575522423,
0.04273122549057007,
0.01321024727076292,
0.008824221789836884,
-0.012794210575520992,
-0.012256128713488579,
-0.011212707497179508,
-0.029985889792442322,
0.033282820135354996,
0.009021898731589317,
0.012177586555480957,
0.03144737333059311,
0.016109511256217957,
0.06069524213671684,
-0.02233717031776905,
0.023897705599665642,
-0.013978629373013973,
0.052744071930646896,
0.01833519898355007,
-0.0338234081864357,
0.017102815210819244,
-0.03457621484994888,
0.00518310721963644,
0.08876118063926697,
-0.004419850651174784,
-0.01073670294135809,
0.007617239840328693,
-0.03948860615491867,
-0.016517972573637962,
-0.010186279192566872,
-0.011383505538105965,
0.00898684747517109,
0.0019148254068568349,
-0.025564279407262802,
0.05871870368719101,
-0.05895505100488663,
0.022833386436104774,
0.05440589413046837,
-0.018714645877480507,
-0.035051848739385605,
0.07437945902347565,
0.049524933099746704,
0.031074143946170807,
-0.027768587693572044,
0.03184362128376961,
0.02730286680161953,
-0.03647300973534584,
0.005479136481881142,
0.01866469532251358,
0.04889907315373421,
0.024096187204122543,
-0.011645900085568428,
0.06613675504922867,
-0.019254090264439583,
-0.0010011971462517977,
0.010871563106775284,
-0.03658591955900192,
-0.009432729333639145,
-0.039819154888391495,
-0.00036586218629963696,
-0.047793980687856674,
-0.0167764350771904,
0.007698180619627237,
0.028683049604296684,
0.08778688311576843,
-0.029934212565422058,
-0.0033390175085514784,
-0.007666794117540121,
-0.028925402089953423,
-0.0068919463083148,
0.041227295994758606,
-0.021534428000450134,
0.023941045626997948,
-0.01559914369136095,
0.014513893984258175,
-0.04957783594727516,
-0.0279229823499918,
0.007923102006316185,
0.010014032945036888,
0.00968093890696764,
0.019902868196368217,
0.027888944372534752,
-0.0018897148547694087,
-0.03688603639602661,
-0.019337253645062447,
-0.0293925479054451,
0.02905420772731304,
0.01808488927781582,
0.03556150197982788,
-0.005832944996654987,
0.009143938310444355,
-0.020533662289381027,
0.08553675562143326,
-0.06853397190570831,
-0.024375014007091522,
-0.004093430936336517,
0.041077639907598495,
0.0008951557101681828,
-0.029657457023859024
] |
<p>Is <a href="http://en.wikipedia.org/wiki/Loschmidt%27s_paradox" rel="nofollow">Loschmidt's paradox</a> a paradox even today? </p>
<p>In other words, is the paradox resolved or not?</p>
| 344 |
[
-0.0494687482714653,
-0.05709703639149666,
0.00648622028529644,
-0.06335946172475815,
0.04635656625032425,
0.00393333937972784,
-0.03405755013227463,
-0.03873969241976738,
-0.011435845866799355,
-0.001365029369480908,
0.05398322641849518,
0.04095809906721115,
0.04211992025375366,
0.03134351596236229,
0.010930377058684826,
0.01933242753148079,
0.021766647696495056,
0.0005348430131562054,
-0.0009670942090451717,
0.004676025360822678,
0.024501726031303406,
0.04654458537697792,
0.0012368682073429227,
-0.033143386244773865,
-0.04013216495513916,
0.004494444467127323,
0.018362050876021385,
-0.010400115512311459,
0.04482649266719818,
0.07804008573293686,
-0.022508664056658745,
-0.0032475367188453674,
0.037888187915086746,
0.006415115669369698,
0.024552524089813232,
-0.020548861473798752,
0.011702961288392544,
-0.050031691789627075,
-0.011870400980114937,
0.024922147393226624,
0.019913654774427414,
0.007137369830161333,
0.018772410228848457,
0.08376168459653854,
-0.03941714018583298,
-0.007692168466746807,
0.03904341906309128,
-0.03291837126016617,
0.037263721227645874,
-0.048695411533117294,
0.08778313547372818,
0.010894079692661762,
0.020593155175447464,
0.030092479661107063,
-0.020891765132546425,
0.00470238272100687,
0.07803574949502945,
0.04922556132078171,
-0.03543879836797714,
-0.022712459787726402,
-0.011324378661811352,
-0.022490907460451126,
0.009575378149747849,
0.02710624225437641,
-0.03910576552152634,
0.0425463430583477,
-0.02266828715801239,
-0.005911587737500668,
0.03196268528699875,
-0.011728390119969845,
0.007372139021754265,
0.05053629353642464,
0.06433194130659103,
-0.0024031156208366156,
0.05372275784611702,
-0.015152581967413425,
0.028176242485642433,
-0.021231504157185555,
0.03216593712568283,
0.01267433725297451,
0.018724795430898666,
0.014803939498960972,
0.0723712146282196,
0.020611926913261414,
0.030514521524310112,
-0.029371846467256546,
0.06084775924682617,
-0.05504756048321724,
0.026764776557683945,
0.016193734481930733,
-0.035722918808460236,
0.0019837687723338604,
0.0145973926410079,
-0.01828627660870552,
-0.02420179173350334,
0.03521360829472542,
-0.018689356744289398,
0.053618792444467545,
0.01633363589644432,
-0.017100879922509193,
0.023954996839165688,
0.005811825394630432,
0.014150777831673622,
0.03898138180375099,
0.010008465498685837,
-0.01685197837650776,
-0.03906133025884628,
0.031212808564305305,
0.027404023334383965,
-0.012628065422177315,
-0.026282571256160736,
0.028569959104061127,
0.017732735723257065,
0.027655964717268944,
0.01173766702413559,
-0.03496682643890381,
-0.008149274624884129,
-0.005932524800300598,
0.03447268530726433,
0.07989811897277832,
0.015441607683897018,
-0.03462611511349678,
0.01150144636631012,
-0.01880953088402748,
-0.06312909722328186,
0.012676315382122993,
0.019916359335184097,
0.0035882520023733377,
0.01563180983066559,
0.06733953207731247,
-0.008610947988927364,
-0.01415729895234108,
-0.004568877164274454,
0.009333807975053787,
0.040598899126052856,
-0.027119355276226997,
-0.10465136915445328,
-0.06710678339004517,
0.06587625294923782,
0.02117834985256195,
-0.013082833029329777,
-0.05664755776524544,
0.029970545321702957,
-0.012260744348168373,
0.06193939223885536,
0.013808798976242542,
-0.007484149187803268,
0.035563211888074875,
0.024335317313671112,
0.0053056082688272,
-0.01910759136080742,
0.01594989001750946,
0.02247783914208412,
-0.038872431963682175,
0.035117361694574356,
-0.09167148172855377,
-0.019598133862018585,
0.05298306792974472,
0.012070508673787117,
-0.04835895448923111,
0.032315824180841446,
0.030327685177326202,
-0.033816948533058167,
-0.0038046888075768948,
0.007691822946071625,
-0.013877468183636665,
0.08249177783727646,
0.024876581504940987,
-0.0031686818692833185,
0.026606081053614616,
0.007294097449630499,
0.023516006767749786,
0.026594914495944977,
0.01966359280049801,
-0.008060342632234097,
-0.022361602634191513,
0.017512613907456398,
-0.01954786293208599,
0.019068270921707153,
0.01071908324956894,
-0.0667496994137764,
-0.0271354541182518,
0.005024184472858906,
0.01191520132124424,
0.019744262099266052,
0.05485258251428604,
-0.012750156223773956,
0.0264699999243021,
0.01998898759484291,
-0.06803366541862488,
-0.050725389271974564,
-0.07481598109006882,
0.011196323670446873,
-0.0021242720540612936,
-0.024838855490088463,
0.020101716741919518,
0.020359013229608536,
0.03422277048230171,
-0.045647162944078445,
-0.0364193394780159,
-0.030526669695973396,
0.04050469025969505,
0.03555743023753166,
-0.0185028575360775,
0.01992158591747284,
0.054143454879522324,
0.052031487226486206,
-0.022183308377861977,
0.004714673850685358,
-0.008932611905038357,
-0.06243438273668289,
0.04985743761062622,
-0.03749789297580719,
0.0032058279030025005,
0.00866455864161253,
0.03144564852118492,
0.022462807595729828,
0.03185570612549782,
-0.03902028873562813,
0.01873224414885044,
-0.03468594700098038,
0.07009907811880112,
0.010380392894148827,
0.015953047201037407,
-0.0013331819791346788,
0.04633399471640587,
0.012745104730129242,
-0.0010534214088693261,
0.014177914708852768,
-0.02565162256360054,
-0.0383097380399704,
-0.009879483841359615,
-0.008061281405389309,
0.03046821430325508,
-0.03567267581820488,
0.024903664365410805,
0.023802870884537697,
0.018703049048781395,
-0.008602181449532509,
-0.003527557011693716,
-0.01499115489423275,
-0.010389224626123905,
0.013277572579681873,
-0.000816952669993043,
0.01873888075351715,
0.05964027717709541,
0.012445107102394104,
-0.017952654510736465,
-0.012159302830696106,
-0.0009592616697773337,
-0.0025325168389827013,
0.013315594755113125,
-0.00964195653796196,
-0.010649616830050945,
0.005120233632624149,
-0.008616507053375244,
0.012809723615646362,
-0.0012048290809616446,
0.0004950306611135602,
0.004027741961181164,
0.014604754745960236,
0.013983573764562607,
-0.019478488713502884,
-0.02186296321451664,
0.007993553765118122,
0.01104167103767395,
-0.026063915342092514,
-0.003003715304657817,
0.04502582550048828,
-0.00942779891192913,
-0.004844855982810259,
-0.06461972743272781,
-0.005052533932030201,
-0.027295546606183052,
-0.004532544407993555,
0.013474290259182453,
-0.0263292845338583,
0.0155611177906394,
-0.026667101308703423,
-0.030227595940232277,
-0.03479740768671036,
-0.003998471423983574,
-0.022697214037179947,
0.028514275327324867,
-0.0529414638876915,
-0.0008612779784016311,
-0.025373252108693123,
-0.02869843691587448,
0.03407751023769379,
-0.005086579360067844,
0.06382196396589279,
0.03749040514230728,
-0.01268179714679718,
-0.04666436091065407,
-0.03535064309835434,
-0.053987134248018265,
-0.023213829845190048,
-0.03752002865076065,
-0.028217801824212074,
0.03121439926326275,
-0.009149056859314442,
-0.025711309164762497,
0.0012181602651253343,
-0.04830298572778702,
-0.06207907199859619,
-0.05855719745159149,
-0.029486995190382004,
0.03845621272921562,
-0.024704717099666595,
-0.008584968745708466,
0.007380784954875708,
-0.0113010099157691,
0.0008496794034726918,
-0.06545872986316681,
-0.08425027132034302,
0.03783922269940376,
-0.03552977368235588,
0.05158495530486107,
-0.01173974759876728,
-0.02384207397699356,
0.05330663546919823,
0.033426132053136826,
-0.022121641784906387,
-0.011865313164889812,
-0.007065183017402887,
-0.010147564113140106,
0.019806012511253357,
-0.00022371039085555822,
0.03643384203314781,
0.0064163836650550365,
0.033207520842552185,
0.01511934120208025,
0.01592070423066616,
0.04003530368208885,
0.021640004590153694,
-0.009867005981504917,
0.0001799529418349266,
0.006539625581353903,
0.01398736983537674,
0.03357822448015213,
0.010570344515144825,
-0.05701985955238342,
-0.005554141476750374,
-0.014217006973922253,
0.024126950651407242,
0.0017802880611270666,
-0.046037737280130386,
0.03944375365972519,
0.013393913395702839,
0.03576678782701492,
-0.028913691639900208,
0.03957522287964821,
-0.00495542399585247,
0.009322657249867916,
0.01192559115588665,
0.008501709438860416,
0.050504233688116074,
0.003432211931794882,
-0.010979977436363697,
0.05123734846711159,
0.0040458072908222675,
-0.04075774550437927,
-0.02846037596464157,
0.012576403096318245,
-0.026740549132227898,
0.04887976869940758,
0.015688525512814522,
-0.026026247069239616,
0.021949229761958122,
0.04614420235157013,
0.025277549400925636,
-0.004067768808454275,
-0.04083212837576866,
-0.006688467226922512,
-0.08397546410560608,
0.01292297150939703,
-0.0032688535284250975,
0.012841015122830868,
0.005551502574235201,
0.029125254601240158,
0.0332191102206707,
0.053514063358306885,
-0.009356986731290817,
-0.010374349541962147,
-0.08116272836923599,
-0.0029086056165397167,
-0.05040121451020241,
-0.008974522352218628,
-0.004289657808840275,
-0.0208739060908556,
-0.006957031320780516,
-0.023548245429992676,
-0.04157457500696182,
-0.026696592569351196,
0.008459697477519512,
-0.044764842838048935,
0.01384651567786932,
-0.009375720284879208,
-0.037712834775447845,
0.004602362867444754,
-0.00273218285292387,
0.023186201229691505,
-0.02314731478691101,
0.003451067954301834,
0.04766059294342995,
-0.02235996164381504,
-0.0459916926920414,
-0.03202444687485695,
0.016225049272179604,
0.009230335243046284,
0.045842576771974564,
0.012674580328166485,
0.01403582189232111,
-0.03860895335674286,
0.04269573092460632,
0.01507601048797369,
0.027930159121751785,
0.005883439909666777,
-0.011747293174266815,
-0.0575481578707695,
-0.028608014807105064,
-0.033048227429389954,
-0.02833819016814232,
0.009408167563378811,
0.0017125388840213418,
0.024732060730457306,
0.048225659877061844,
-0.009936767630279064,
-0.022259844467043877,
0.013430499471724033,
-0.0022880970500409603,
-0.036377109587192535,
-0.02673589624464512,
-0.051346663385629654,
-0.01577679254114628,
-0.03193091228604317,
0.02135954424738884,
0.01630689762532711,
-0.015337405726313591,
-0.017360953614115715,
0.003575546434149146,
-0.010340019129216671,
0.03362176939845085,
0.015460925176739693,
-0.009461416862905025,
-0.011571422219276428,
0.010194944217801094,
0.013445749878883362,
-0.017359664663672447,
0.010687013156712055,
0.029002951458096504,
0.030344942584633827,
0.03931809589266777,
-0.033011358231306076,
-0.06483054161071777,
0.0015931640518829226,
0.03694695234298706,
0.030766945332288742,
-0.0463060662150383,
0.0034926377702504396,
-0.03359066694974899,
-0.0072484551928937435,
0.026128768920898438,
-0.02761862613260746,
0.026776134967803955,
-0.021832117810845375,
0.010568464174866676,
-0.04279173165559769,
-0.030760277062654495,
0.026384403929114342,
0.0071462527848780155,
-0.008353721350431442,
-0.016578184440732002,
-0.009099823422729969,
-0.012652669101953506,
-0.01799653097987175,
0.013831662945449352,
0.03521402180194855,
0.0600716769695282,
-0.006410879082977772,
0.0005486986483447254,
-0.017136631533503532,
0.028713295236229897,
-0.05242639780044556,
-0.09270481765270233,
0.0008710775873623788,
-0.0033261349890381098,
-0.019166240468621254,
0.03424302116036415,
-0.030103668570518494,
-0.04905589297413826,
0.0043808771297335625,
-0.0030503468587994576,
-0.03400043770670891,
0.014651927165687084,
-0.002846715971827507,
0.01036551408469677,
0.028742145746946335,
0.011828657239675522,
0.02676449529826641,
0.03557373210787773,
-0.0060230158269405365,
-0.004471456166356802,
-0.020447444170713425,
-0.0004617759259417653,
-0.030209412798285484,
0.0049852109514176846,
0.00007552695751655847,
-0.003088979749009013,
-0.03669967129826546,
0.04604165628552437,
0.014694866724312305,
0.023085756227374077,
0.008539342321455479,
0.0023192863445729017,
0.0023033390752971172,
0.0061365896835923195,
-0.0005575309623964131,
0.03915085271000862,
-0.026708923280239105,
0.02150542289018631,
0.012797948904335499,
-0.051508594304323196,
0.01705971360206604,
-0.013702329248189926,
0.01470455713570118,
0.028682874515652657,
-0.013075512833893299,
0.04071565717458725,
-0.004523256327956915,
0.008441900834441185,
0.007653400767594576,
-0.0252250786870718,
0.03986765444278717,
-0.0006077633588574827,
-0.003091955091804266,
-0.014650492928922176,
-0.06890176981687546,
-0.020411573350429535,
-0.009723766706883907,
-0.00727063650265336,
0.012944485060870647,
-0.03484297916293144,
0.0036113797686994076,
0.012530175037682056,
0.0022929226979613304,
-0.08959165215492249,
-0.050889380276203156,
0.017680035904049873,
0.003919255919754505,
0.013069641776382923,
-0.0029524315614253283,
-0.030659271404147148,
-0.015142842195928097,
-0.02650078944861889,
-0.01871723122894764,
0.06307719647884369,
0.001940292539075017,
-0.013598870486021042,
-0.013712339103221893,
0.0009403502917848527,
0.0735521912574768,
-0.025164149701595306,
-0.007275382522493601,
0.00003805461528827436,
-0.01252118218690157,
-0.01614813320338726,
-0.008004878647625446,
0.025060269981622696,
-0.020717354491353035,
-0.03400310501456261,
-0.0011711148545145988,
0.0023578533437103033,
0.043184831738471985,
-0.037690743803977966,
-0.03094804286956787,
0.015147116966545582,
-0.035490840673446655,
0.02509702742099762,
-0.023907382041215897,
-0.006292340811342001,
-0.01623472385108471,
0.005291188135743141,
0.011419574730098248,
-0.004335529170930386,
-0.015873560681939125,
-0.04522710666060448,
0.02589389495551586,
0.014924767427146435,
-0.003552792128175497,
0.0029791900888085365,
0.05397075414657593,
-0.02457326091825962,
-0.015495620667934418,
-0.0012200316414237022,
-0.024297554045915604,
0.03202115744352341,
0.01663993112742901,
0.004031626973301172,
-0.0059521496295928955,
0.01400254387408495,
-0.017458414658904076,
-0.016073690727353096,
-0.016010472550988197,
0.041901394724845886,
0.04459387809038162,
0.013684546574950218,
0.042290281504392624,
0.01448566559702158,
0.01982148550450802,
0.01812165230512619,
-0.015311692841351032,
0.014135748147964478,
0.024607272818684578,
-0.009228723123669624,
-0.004576975479722023,
-0.008467499166727066,
-0.0007687500910833478,
0.04769006744027138,
-0.009459484368562698,
0.019948190078139305,
0.003903899807482958,
-0.006222174037247896,
-0.019296593964099884,
0.01663820818066597,
-0.00417562760412693,
-0.051564380526542664,
0.06342502683401108,
-0.041775669902563095,
0.004602726083248854,
-0.014749760739505291,
-0.03809508681297302,
0.02475212700664997,
-0.012329638935625553,
0.008763769641518593,
-0.02027719095349312,
-0.011052178218960762,
-0.04004942625761032,
-0.024121100082993507,
-0.02224305085837841,
0.05496793985366821,
0.014156625606119633,
-0.04751654714345932,
0.024256229400634766,
0.005313192959874868,
0.03528643399477005,
-0.04375869408249855,
-0.09958335757255554,
-0.0387459434568882,
-0.0528099425137043,
-0.04688132554292679,
0.0492766909301281,
0.009523564949631691,
-0.005753671284765005,
0.0027143536135554314,
-0.03989649564027786,
-0.035930879414081573,
0.03592059388756752,
0.06868594139814377,
-0.0346042774617672,
0.06591292470693588,
-0.02219061739742756,
0.09099383652210236,
-0.043003637343645096,
0.023075537756085396,
0.12824107706546783,
0.0624118372797966,
0.03131526708602905,
-0.08307027816772461,
0.02832186222076416,
-0.01706327311694622,
0.017594097182154655,
-0.04605569317936897,
0.03476119041442871,
-0.015563431195914745,
0.002568424679338932,
-0.01157187670469284,
0.03866365924477577,
0.011592120863497257,
0.028915680944919586,
0.03010939061641693,
-0.04242036119103432,
-0.016277840360999107,
0.04873337969183922,
-0.008494973182678223,
0.0031933628488332033,
0.0023674790281802416,
-0.020459065213799477,
0.019435293972492218,
-0.023642035201191902,
0.0014639333821833134,
-0.0011783652007579803,
-0.004650371614843607,
-0.01959896832704544,
0.010998645797371864,
-0.0544707328081131,
-0.000982932047918439,
0.024878468364477158,
0.007296406198292971,
-0.030123217031359673,
-0.0005679992609657347,
0.0005597862764261663,
-0.004523694980889559,
0.015333732590079308,
0.06269829720258713,
0.02687525935471058,
-0.007406376302242279,
-0.015242164023220539,
0.0040569547563791275,
-0.044435225427150726,
0.016698652878403664,
-0.0040690409950912,
0.015071887522935867,
-0.021716078743338585,
0.02091047167778015,
-0.007779046893119812,
0.012310146354138851,
-0.02407046966254711,
-0.022387443110346794,
-0.022340405732393265,
0.00003539885437930934,
0.026186982169747353,
0.015846360474824905,
-0.06942804157733917,
-0.01915179193019867,
0.02008281648159027,
-0.014469021931290627,
0.04229877516627312,
-0.0076962606981396675,
-0.013704752549529076,
0.011273271404206753,
0.0007738009444437921,
0.024044709280133247,
0.0070320130325853825,
-0.005311818793416023,
-0.08171604573726654,
0.029699863865971565,
-0.04356691986322403,
-0.021210510283708572,
0.0022097916807979345,
0.04084330052137375,
0.027408862486481667,
-0.03231886401772499,
-0.01249122153967619,
-0.019864074885845184,
-0.02883146144449711,
0.033759016543626785,
-0.024373319000005722,
0.004198260605335236,
-0.024156883358955383,
-0.012404304929077625,
0.03222805634140968,
0.03847401589155197,
-0.06938744336366653,
0.0007529810536652803,
-0.01213388703763485,
0.026036620140075684,
-0.04040830209851265,
-0.050312962383031845,
-0.036156632006168365,
-0.012915031053125858,
-0.043079983443021774,
0.010891439393162727,
0.0059908851981163025,
0.053398650139570236,
0.01588890701532364,
0.034419406205415726,
-0.020824790000915527,
-0.001727307098917663,
-0.005452747922390699,
0.0436021089553833,
0.060503777116537094,
-0.012808102183043957,
-0.05967371165752411,
0.03675370663404465,
0.0268373005092144,
-0.02778133563697338,
-0.02975369244813919,
-0.051155127584934235,
-0.00012430046626832336,
0.05169760435819626,
0.008643710054457188,
-0.050552304834127426,
-0.02606259286403656,
-0.0003165995585732162,
0.04066058620810509,
-0.031097445636987686,
-0.01967722922563553,
-0.04102596268057823,
-0.013361687771975994,
-0.017832426354289055,
-0.02087702415883541,
0.012952882796525955,
0.03575859218835831,
-0.0017579281702637672,
0.002223264891654253,
0.008106296882033348,
0.023436781018972397,
-0.015351754613220692,
0.008507583290338516,
0.001528067048639059,
0.04559545964002609,
0.08072458207607269,
-0.02831614762544632,
-0.0361974760890007,
0.006380207370966673,
-0.03543901443481445,
-0.024385975673794746,
0.021853478625416756,
-0.00794287957251072,
0.03087892197072506,
0.03237411752343178,
0.012231997214257717,
-0.001786477048881352,
0.03700793534517288,
-0.02056192234158516,
0.02296898514032364,
0.0168461911380291,
0.0031855299603194,
0.007742629386484623,
0.03460126742720604,
0.00992879644036293,
-0.01234661415219307,
-0.03552721068263054,
0.03280177712440491,
0.07647397369146347,
0.024822993203997612,
0.006696597207337618,
0.030303234234452248,
-0.008333281613886356,
-0.0012743372935801744,
0.02451397106051445,
0.022211279720067978,
0.01436250563710928,
0.07837569713592529,
-0.012193918228149414,
0.0060597192496061325,
0.02864648960530758,
0.016024351119995117,
-0.10885072499513626,
0.00923075620085001,
0.011977470479905605,
0.007182924076914787,
0.027914127334952354,
-0.008356556296348572,
0.00035178681719116867,
0.014308060519397259,
-0.06087391451001167,
0.010998288169503212,
0.008544901385903358,
-0.03918997943401337,
-0.04763638228178024,
-0.00608555693179369,
-0.019055036827921867,
0.060395143926143646,
0.05793808400630951,
0.0291538517922163,
-0.001579214702360332,
0.04141589626669884,
-0.0064226058311760426,
-0.026572152972221375,
-0.003282786812633276,
-0.004412972833961248,
-0.05251600593328476,
0.0006887821946293116,
0.05438147485256195,
0.01045006513595581,
-0.027697447687387466,
0.06000611558556557,
0.019141577184200287,
0.05067985877394676,
-0.004314220044761896,
0.025266842916607857,
0.014789761044085026,
-0.024456370621919632,
-0.0165659561753273,
-0.014159850776195526,
-0.01154259406030178,
0.02596897818148136,
-0.004941197112202644,
0.040346384048461914,
0.00467426935210824,
-0.037528786808252335,
0.0072277607396245,
-0.05213559791445732,
-0.03595173358917236,
0.009675409644842148,
-0.0021825393196195364,
0.00437921704724431,
0.02633863501250744,
0.004139913711696863,
-0.01294110156595707,
-0.010041913017630577,
0.010690688155591488,
-0.02837936021387577,
-0.001581457443535328,
0.019763212651014328,
0.023445310071110725,
-0.025363827124238014,
0.012154923751950264,
-0.005152709316462278,
-0.016121897846460342,
0.03329568728804588,
0.006006044335663319,
0.006635522935539484,
-0.031227385625243187,
0.017764562740921974,
-0.016740385442972183,
0.010767236351966858,
0.03571305051445961,
-0.006435593124479055,
-0.025260454043745995,
0.03552282974123955,
0.012446656823158264,
0.031329717487096786,
-0.008227436803281307,
-0.07450135052204132,
-0.05126028507947922,
-0.058695483952760696,
0.04633554071187973,
-0.04337748885154724,
0.018833670765161514,
-0.0560472272336483,
-0.04209309071302414,
-0.025557199493050575,
-0.0019404774066060781,
0.0465652272105217,
-0.04299681633710861,
-0.0002065804583253339,
-0.01709975302219391,
-0.011464415118098259,
0.006641805171966553,
-0.0024692390579730272,
-0.005672086495906115,
-0.016279637813568115,
0.02169789746403694,
-0.024749798700213432,
-0.010707414709031582,
-0.008396562188863754,
0.014173949137330055,
0.02863941341638565,
-0.006704833824187517,
0.02281293086707592,
0.006307608913630247,
-0.020220186561346054,
0.023426488041877747,
0.036008670926094055,
-0.01554531417787075,
0.03973126783967018,
-0.02660614252090454,
0.021594563499093056,
0.012093477882444859,
-0.014002208597958088,
-0.0638480931520462,
0.032555125653743744,
-0.025516383349895477,
-0.04184015467762947,
0.0032066097483038902,
0.04111618176102638,
-0.02199186198413372,
-0.03068280778825283,
-0.006823033094406128,
0.07086857408285141,
-0.026942938566207886,
-0.010804873891174793,
0.011857297271490097,
-0.01414479035884142,
0.05155481770634651,
-0.025015557184815407,
-0.007771696895360947,
-0.005419169086962938,
-0.009847639128565788,
-0.0004185547004453838,
0.027645325288176537,
0.06042742356657982,
0.012940851971507072,
0.0025006020441651344,
0.0014251809334382415,
-0.009522831067442894,
0.038128115236759186,
0.01969345100224018,
0.02911592274904251,
-0.007444072514772415,
-0.0038428730331361294,
0.008697492070496082,
-0.01453312300145626,
0.027715804055333138,
0.04540472850203514,
-0.0008808783604763448,
0.07000778615474701,
-0.0038351169787347317,
0.05850253626704216,
0.009730784222483635,
-0.016111407428979874,
-0.05149773135781288,
-0.007251759059727192,
0.04322619363665581,
0.021259773522615433,
-0.029759328812360764,
-0.007328050676733255,
-0.006580522749572992,
0.020357497036457062,
0.03630365431308746,
-0.007065268233418465,
0.006271176040172577,
-0.029751157388091087,
0.028961386531591415,
-0.013845657929778099,
-0.019031649455428123,
-0.027540132403373718,
0.001710656681098044,
0.04680689051747322,
0.03542193025350571,
0.041153889149427414,
-0.04230790585279465,
-0.0016424554632976651,
0.0006485830526798964,
0.08629593253135681,
-0.06984969973564148,
-0.014269748702645302,
-0.01643659546971321,
0.01399245299398899,
-0.01896815374493599,
-0.018198546022176743
] |
<p>I have a question that's bugging me. Googling it only made me more confused so I really hope someone can help me clear this.</p>
<p>If a plane is flying up and down; or hovering (Like the x-wing scene from star wars for example, when yoda uses the force) does that result in constant acceleration or varied acceleration? </p>
<p>If the final velocity is 0, because it comes back to the same position, (please correct me if i'm wrong) and the time it takes to go up and come back down is 10 seconds, that would make a constant acceleration of (0/10) which is 0?! </p>
<p>EDIT: I know it sounds like such a weird question but the reason I'm asking this is that I'm doing a project on teaching academic subjects using pop culture (hence the yoda reference) and want to make sure the stated acceleration is theoretically correct.</p>
<p>EDIT: I drafted an image to help illustrate my question, I hope it helps.
<img src="http://i.stack.imgur.com/xWnw2.jpg" alt="are the acceleration values (figuratively) correct?"></p>
| 10,714 |
[
-0.022252069786190987,
-0.04401378706097603,
-0.03412590175867081,
0.020364681258797646,
0.07000824809074402,
0.010502870194613934,
-0.032997146248817444,
-0.004965560510754585,
0.0009634117013774812,
-0.03147129714488983,
0.015598186291754246,
0.047086913138628006,
0.0339171439409256,
0.005700515117496252,
0.025533203035593033,
0.032794564962387085,
-0.019744494929909706,
-0.010796829126775265,
0.006225514691323042,
-0.005492258816957474,
-0.03518897667527199,
0.006246376782655716,
-0.015255418606102467,
-0.012613204307854176,
-0.03444325551390648,
0.0003475994453765452,
0.021092476323246956,
0.00008617876301286742,
-0.0003596434253267944,
0.0550164170563221,
-0.013839569874107838,
0.015918562188744545,
0.012462325394153595,
0.05452572554349899,
0.03787695989012718,
0.01114082895219326,
-0.07201333343982697,
-0.02704906463623047,
-0.02375849522650242,
0.028688907623291016,
0.007113773375749588,
-0.007122540846467018,
-0.008319653570652008,
0.055951766669750214,
-0.026894783601164818,
0.005128415767103434,
0.0026362978387624025,
0.011889997869729996,
0.051783785223960876,
-0.05592401698231697,
0.07211601734161377,
-0.014877223409712315,
0.027372270822525024,
0.047037798911333084,
0.045873917639255524,
-0.019831497222185135,
0.07918273657560349,
0.0023352361749857664,
-0.011441417038440704,
-0.05555048957467079,
0.010791098698973656,
-0.03715796023607254,
-0.00968978926539421,
-0.005821176804602146,
-0.006969918496906757,
0.030952850356698036,
-0.028298920020461082,
0.0038057961501181126,
0.02540118433535099,
-0.028140895068645477,
0.01915665902197361,
0.01321557629853487,
0.011926157400012016,
-0.018202491104602814,
0.020079363137483597,
-0.06414538621902466,
0.055044420063495636,
0.030978919938206673,
0.049691278487443924,
0.0729876458644867,
-0.02997090108692646,
0.0119476318359375,
0.042368415743112564,
0.034645359963178635,
0.038478679955005646,
-0.009209182113409042,
0.07149451225996017,
0.011428751051425934,
0.018433649092912674,
0.047188982367515564,
0.017643360421061516,
0.009863622486591339,
0.006482145749032497,
0.020343974232673645,
-0.016047682613134384,
0.0554552860558033,
0.012128506787121296,
0.06739843636751175,
0.024369781836867332,
-0.04284168779850006,
0.0016967481933534145,
-0.039992354810237885,
0.022759363055229187,
0.06357652693986893,
-0.014336074702441692,
0.020611945539712906,
-0.03314958140254021,
0.004828243982046843,
-0.05585625767707825,
-0.012184195220470428,
-0.02799767255783081,
0.043958745896816254,
0.0008603582973591983,
-0.027673006057739258,
0.0177310798317194,
-0.011638084426522255,
0.03491725027561188,
0.011531699448823929,
0.0456598661839962,
0.006534773390740156,
0.05309760197997093,
-0.04986026510596275,
0.02273636683821678,
0.0355309434235096,
-0.034243613481521606,
-0.013887838460505009,
0.019553078338503838,
-0.006817482877522707,
-0.050778474658727646,
0.034818366169929504,
-0.032050032168626785,
-0.04239105060696602,
0.029746010899543762,
-0.016665494069457054,
0.035754915326833725,
0.016583099961280823,
-0.06379126757383347,
-0.07073104381561279,
0.0061002918519079685,
0.0013619804522022605,
-0.020832613110542297,
-0.06826113164424896,
0.010933923535048962,
-0.0036387944128364325,
0.05822401121258736,
-0.008566577918827534,
-0.006355328485369682,
-0.014124740846455097,
0.0028864166233688593,
0.002975084353238344,
0.021135011687874794,
-0.013110495172441006,
-0.02486993558704853,
-0.08310340344905853,
-0.018918929621577263,
-0.07856249809265137,
0.0010303857270628214,
0.029047925025224686,
0.010023052804172039,
-0.039956800639629364,
0.041772741824388504,
-0.027249528095126152,
0.03365856409072876,
0.004763288889080286,
-0.021480359137058258,
-0.03009278140962124,
0.07663367688655853,
0.019708219915628433,
-0.009276160039007664,
0.021610964089632034,
-0.015572507865726948,
0.021109407767653465,
-0.009726193733513355,
0.007041242439299822,
0.07007627189159393,
-0.02283516153693199,
-0.021193526685237885,
-0.04049978032708168,
0.014282922260463238,
0.0009740935056470335,
-0.02594909444451332,
-0.015726502984762192,
-0.02913662977516651,
0.0037963862996548414,
-0.004164454061537981,
0.030473537743091583,
0.007031020242720842,
0.038443341851234436,
-0.004028614144772291,
-0.029577376320958138,
-0.010763564147055149,
-0.10311119258403778,
0.036304324865341187,
-0.010067706927657127,
-0.013227809220552444,
0.02744372747838497,
-0.0033120031002908945,
0.02268148586153984,
-0.06547791510820389,
0.008265728130936623,
-0.02390667237341404,
0.013703910633921623,
0.01000977959483862,
-0.005301886238157749,
0.0039748759008944035,
0.020954931154847145,
0.003506510751321912,
0.021237868815660477,
-0.0010039129992946982,
-0.002278062514960766,
-0.024798622354865074,
-0.03583279997110367,
-0.029828287661075592,
0.013772619888186455,
-0.004410651978105307,
0.007130653131753206,
0.03734804317355156,
0.01619028113782406,
-0.008859368972480297,
0.02520887926220894,
-0.028042467311024666,
0.06852634996175766,
0.06763926893472672,
-0.006395505741238594,
0.013248924165964127,
0.01906629092991352,
-0.0006607822142541409,
0.009811495430767536,
-0.01710268296301365,
-0.048766765743494034,
-0.04036141559481621,
-0.0025257591623812914,
0.037487175315618515,
-0.005962078459560871,
-0.012953762896358967,
0.00883107353001833,
0.07272055745124817,
0.04745601490139961,
0.025469720363616943,
0.04433206468820572,
-0.004644495435059071,
-0.03490779921412468,
-0.00472838431596756,
-0.01562769152224064,
0.023698054254055023,
0.04927157983183861,
0.04803898558020592,
0.028330406174063683,
0.009014596231281757,
0.037818875163793564,
-0.016191814094781876,
0.028581105172634125,
0.024799806997179985,
0.01191800832748413,
0.007977514527738094,
-0.04005242511630058,
0.04801880195736885,
0.009392071515321732,
0.023593317717313766,
0.04107023775577545,
-0.02665465883910656,
-0.017372695729136467,
0.00330082094296813,
0.005629030987620354,
0.015776904299855232,
-0.016980411484837532,
-0.026368265971541405,
-0.03572532534599304,
0.015264822170138359,
-0.008363068103790283,
0.006852432154119015,
-0.055109307169914246,
0.016245726495981216,
-0.04476403445005417,
-0.021956967189908028,
0.03359128162264824,
0.01837618090212345,
0.04008815065026283,
-0.025940168648958206,
-0.009365019388496876,
-0.007921776734292507,
-0.05780547112226486,
0.003354809945449233,
-0.011574380099773407,
-0.06015746667981148,
0.04079810902476311,
-0.008757084608078003,
-0.04752691090106964,
0.05098600685596466,
0.01448989100754261,
0.000788888952229172,
0.04021851345896721,
-0.020559806376695633,
-0.06905864924192429,
0.004236537031829357,
-0.05167482793331146,
-0.025334369391202927,
-0.0294266939163208,
-0.00981779396533966,
0.038619719445705414,
0.008884770795702934,
-0.00037368739140219986,
0.07124784588813782,
-0.05887981504201889,
-0.03261790797114372,
-0.04600829258561134,
0.019047195091843605,
0.020353082567453384,
-0.04949115216732025,
0.0015381708508357406,
0.007471029181033373,
0.008360595442354679,
-0.016279732808470726,
-0.03602495789527893,
-0.05561979487538338,
0.008001161739230156,
-0.0032789111137390137,
0.05054472014307976,
0.012488325126469135,
-0.043294183909893036,
0.09073091298341751,
-0.00008910672477213666,
-0.024746116250753403,
-0.021606193855404854,
0.006428414024412632,
0.010772647336125374,
0.015371164306998253,
-0.027405211701989174,
0.023252343758940697,
0.006811076309531927,
-0.013061231933534145,
0.013791089877486229,
0.012529582716524601,
0.010595734231173992,
0.02210238389670849,
-0.006157193798571825,
-0.012879994697868824,
0.017581114545464516,
0.012995343655347824,
0.06016894802451134,
0.04316481947898865,
-0.04597491770982742,
0.013353953137993813,
-0.01875944621860981,
0.046645451337099075,
-0.014597353525459766,
-0.018155185505747795,
0.04953257739543915,
-0.009183903224766254,
-0.009590232744812965,
0.012113521806895733,
0.05475302413105965,
0.0022521489299833775,
-0.0014659937005490065,
-0.01892123930156231,
0.03367684409022331,
0.03929445520043373,
0.010888590477406979,
0.0023287346120923758,
0.035195354372262955,
0.0003113548445980996,
-0.028680123388767242,
-0.03622966259717941,
0.009958086535334587,
-0.004305827431380749,
0.02643267624080181,
-0.03785581514239311,
-0.024053240194916725,
0.057549938559532166,
0.021955005824565887,
0.04449586570262909,
0.02760201506316662,
-0.03930194303393364,
0.020549336448311806,
-0.05191716179251671,
-0.001058682450093329,
0.002822132548317313,
0.03648153692483902,
-0.006993850693106651,
0.07989945262670517,
-0.012086838483810425,
0.04023543372750282,
0.022705774754285812,
0.013719535432755947,
-0.08443085849285126,
0.04685511812567711,
-0.03594861924648285,
-0.0466071292757988,
0.004104777704924345,
0.02424919605255127,
-0.02469463273882866,
-0.03975272551178932,
-0.005388680379837751,
0.011384441517293453,
-0.030178461223840714,
-0.026679692789912224,
0.009167585521936417,
-0.054734040051698685,
-0.024387111887335777,
-0.0334322489798069,
0.005483769811689854,
0.0006731584435328841,
-0.0023438925854861736,
0.05880214273929596,
0.028203893452882767,
0.014426280744373798,
-0.005925488658249378,
-0.013846658170223236,
-0.029787305742502213,
0.01589074917137623,
0.01569019816815853,
0.021011430770158768,
0.022453121840953827,
-0.005933939944952726,
0.066130630671978,
-0.012155457399785519,
0.024957403540611267,
-0.016501540318131447,
-0.034104783087968826,
-0.06792319566011429,
-0.05929156765341759,
0.0008581376750953496,
-0.003106081858277321,
0.04445822536945343,
0.02695569209754467,
0.008342293091118336,
0.002525768242776394,
0.044808920472860336,
0.01086223404854536,
0.030492475256323814,
0.05609498545527458,
-0.012000533752143383,
0.03539685532450676,
-0.06033571809530258,
0.011241463012993336,
-0.028865771368145943,
-0.017227936536073685,
0.021145544946193695,
-0.00911456998437643,
-0.011554558761417866,
0.012576206587255001,
0.013549397699534893,
-0.029290324077010155,
0.01839425601065159,
0.021082289516925812,
-0.016624480485916138,
0.017127878963947296,
-0.014794478192925453,
-0.03407752513885498,
0.018991844728589058,
0.06052091345191002,
0.03043964132666588,
0.00931319035589695,
-0.04569022357463837,
-0.08296463638544083,
-0.01747911423444748,
0.026166237890720367,
0.04179094359278679,
-0.05109550058841705,
-0.012214486487209797,
-0.02678796462714672,
-0.04583723098039627,
-0.0028247872833162546,
-0.02470346726477146,
0.0238912682980299,
-0.011785397306084633,
0.02500714175403118,
0.02280246838927269,
0.01779380813241005,
0.01805686019361019,
0.0304692555218935,
-0.04846658185124397,
-0.015287901274859905,
-0.026843011379241943,
0.011611188761889935,
0.0019178955117240548,
0.0034470222890377045,
0.028827497735619545,
0.03675927594304085,
0.020921841263771057,
0.00926399789750576,
-0.01827041432261467,
-0.03077840805053711,
-0.054143019020557404,
-0.07696334272623062,
-0.01825767569243908,
0.012121153995394707,
0.0066698892042040825,
0.031482961028814316,
0.011403389275074005,
-0.04890400543808937,
0.022419417276978493,
-0.013126865029335022,
-0.009023534134030342,
-0.0006360067054629326,
-0.025526950135827065,
0.018079398199915886,
0.032758574932813644,
0.009359020739793777,
-0.002016801154240966,
0.06768804788589478,
-0.023740235716104507,
-0.024541568011045456,
0.014428887516260147,
0.014608173631131649,
-0.01681036502122879,
0.00031329013290815055,
-0.026185445487499237,
0.00837690569460392,
-0.048192866146564484,
0.05588196963071823,
-0.03165433555841446,
0.026895619928836823,
-0.035142116248607635,
-0.01368031557649374,
0.012636883184313774,
0.04190782457590103,
0.001575490110553801,
-0.0011983814183622599,
-0.02612483501434326,
0.008548534475266933,
-0.014789006672799587,
-0.02957865223288536,
0.0038018652703613043,
0.0272203516215086,
-0.009340428747236729,
0.026346378028392792,
0.00005795198740088381,
0.017628636211156845,
-0.03876909986138344,
-0.01916230097413063,
-0.002029245253652334,
-0.06280401349067688,
0.04206147789955139,
0.022816024720668793,
-0.003597137751057744,
-0.011251628398895264,
-0.02348821982741356,
-0.022478101775050163,
-0.017573511227965355,
-0.01004438754171133,
0.009252253919839859,
-0.05852566286921501,
0.03445204347372055,
-0.0027804335113614798,
0.00821380689740181,
-0.03766447305679321,
-0.055983081459999084,
0.04678431898355484,
0.05083794891834259,
0.007733501028269529,
0.0077675459906458855,
0.010964804328978062,
-0.05047880485653877,
-0.028072291985154152,
-0.035892777144908905,
0.02048095129430294,
-0.007032407913357019,
-0.02919202297925949,
0.02189883589744568,
-0.03641709312796593,
0.06102140620350838,
0.0016239691758528352,
-0.034479644149541855,
-0.015038714744150639,
-0.0006146673113107681,
-0.022298701107501984,
-0.017285944893956184,
0.06848995387554169,
-0.02513405866920948,
-0.009111313149333,
-0.006979954428970814,
0.004880313761532307,
0.03686129301786423,
-0.02669532597064972,
0.029114574193954468,
0.03155941143631935,
-0.013666766695678234,
0.020364878699183464,
-0.02515820972621441,
0.045087069272994995,
-0.029523583129048347,
-0.008848837576806545,
0.0037365276366472244,
-0.015515603125095367,
-0.02039613202214241,
-0.0491487942636013,
0.02854793146252632,
0.023005729541182518,
-0.005067838821560144,
0.02339814230799675,
0.057682547718286514,
-0.026286300271749496,
-0.05086227133870125,
-0.0015278906794264913,
-0.009281551465392113,
0.016372570767998695,
-0.00790385715663433,
-0.013598515652120113,
0.03225129470229149,
-0.008317112922668457,
-0.029988106340169907,
0.011915101669728756,
-0.0372532419860363,
0.01913296990096569,
0.07630173116922379,
-0.008841942995786667,
0.03794782608747482,
-0.01737649366259575,
0.023827726021409035,
0.016885418444871902,
-0.0015702153323218226,
-0.015681535005569458,
-0.023330964148044586,
0.028744911774992943,
0.009029822424054146,
0.00005659339512931183,
-0.016112802550196648,
0.01780155673623085,
0.023401381447911263,
0.02608196809887886,
0.021777991205453873,
0.02925008349120617,
-0.013465474359691143,
0.013585750944912434,
0.029582126066088676,
-0.029164321720600128,
0.014291723258793354,
-0.005768472794443369,
0.07398349046707153,
0.01546531543135643,
-0.05518657714128494,
0.026258815079927444,
0.020094819366931915,
0.015116631984710693,
-0.047093506902456284,
0.01994500868022442,
-0.03410937264561653,
0.013607456348836422,
-0.015285201370716095,
0.04978305846452713,
-0.026291007176041603,
0.0051007457077503204,
0.019169069826602936,
0.01516113243997097,
0.04308979585766792,
-0.008584778755903244,
-0.014012492261826992,
-0.02193828672170639,
-0.014226469211280346,
-0.009492499753832817,
0.01453731581568718,
0.020127784460783005,
-0.034408602863550186,
0.007634887006133795,
-0.039667341858148575,
0.03400299698114395,
0.025756997987627983,
0.046649906784296036,
0.009657301940023899,
0.06713791936635971,
-0.0017718460876494646,
-0.005689864046871662,
-0.031112775206565857,
0.01221865601837635,
0.10845279693603516,
0.03511723503470421,
-0.013476126827299595,
-0.01782204955816269,
-0.010680864565074444,
-0.03269682079553604,
0.026919284835457802,
-0.026720523834228516,
0.026454858481884003,
0.012884256429970264,
0.006898489315062761,
0.026928046718239784,
0.04158858209848404,
0.013232427649199963,
-0.025285080075263977,
0.03859403356909752,
-0.0033281429205089808,
-0.002360008656978607,
-0.038005441427230835,
0.012435084208846092,
-0.024531668052077293,
0.0010026170639321208,
-0.021435441449284554,
0.009591995738446712,
-0.0034780369605869055,
0.012915416620671749,
0.0007690917700529099,
-0.034722186625003815,
0.014984102919697762,
0.03240077942609787,
-0.09050650894641876,
0.0029738247394561768,
0.02200045995414257,
-0.016627198085188866,
-0.09574005007743835,
0.004572965204715729,
-0.009813680313527584,
-0.0020726111251860857,
0.018496844917535782,
0.06182662770152092,
0.031674716621637344,
-0.02015243098139763,
-0.0006956239230930805,
-0.018150819465517998,
-0.04828419163823128,
-0.011178628541529179,
-0.049381010234355927,
0.01934676058590412,
-0.01231158897280693,
0.0011440410744398832,
-0.011361462064087391,
0.0390160046517849,
0.00235772249288857,
-0.09243492037057877,
-0.026114434003829956,
0.006793722044676542,
-0.007512029260396957,
0.0017271515680477023,
-0.027507897466421127,
-0.022864386439323425,
0.010221609845757484,
-0.00501127727329731,
-0.00904430914670229,
-0.0038511815946549177,
0.026625990867614746,
0.0007576976204290986,
-0.0201842300593853,
0.05564705282449722,
-0.06343896687030792,
-0.004944666754454374,
-0.01360043603926897,
-0.024593733251094818,
-0.0563318207859993,
0.02943999506533146,
0.021093375980854034,
0.031572651118040085,
-0.008202039636671543,
0.010483852587640285,
-0.014577249996364117,
-0.029466446489095688,
-0.014012961648404598,
0.02793928049504757,
0.0438288152217865,
-0.02425382286310196,
0.009863331913948059,
-0.022972170263528824,
-0.00007568527507828549,
0.024166706949472427,
-0.024589525535702705,
0.024957949295639992,
-0.019155962392687798,
0.04818785563111305,
0.01745973527431488,
-0.05113053321838379,
-0.03149983659386635,
0.03443041816353798,
-0.01760457269847393,
0.004418728407472372,
-0.030153684318065643,
0.04868518188595772,
0.030164923518896103,
0.015107357874512672,
-0.022750496864318848,
-0.0008169474895112216,
-0.013292087242007256,
0.027533231303095818,
0.038670074194669724,
-0.06699759513139725,
0.0047370498068630695,
0.019790910184383392,
0.013778694905340672,
-0.05435088276863098,
-0.022742358967661858,
-0.0156246954575181,
-0.0005124384188093245,
-0.057075385004282,
0.04081529751420021,
0.038519807159900665,
0.04425284266471863,
-0.061062995344400406,
-0.010545416735112667,
-0.053578462451696396,
-0.0015366427833214402,
-0.05631767585873604,
0.027662398293614388,
0.01645103469491005,
-0.01295427605509758,
-0.009083038195967674,
0.008274133317172527,
-0.043976545333862305,
0.008440876379609108,
0.023172514513134956,
-0.0021527493372559547,
0.014404235407710075,
-0.028158292174339294,
0.0466618649661541,
-0.0006158477626740932,
0.01214208360761404,
-0.02107086591422558,
-0.02606264315545559,
0.013256331905722618,
-0.039425961673259735,
-0.03579636663198471,
0.055698294192552567,
0.040007494390010834,
0.03789130970835686,
0.0163941141217947,
-0.04685753211379051,
0.001484012114815414,
0.04211360216140747,
-0.010255273431539536,
-0.0037742466665804386,
0.00670568598434329,
-0.009460782632231712,
0.0025855237618088722,
0.023553287610411644,
-0.002265535295009613,
-0.0178813636302948,
0.004395902156829834,
0.030443359166383743,
0.021701758727431297,
-0.03309929743409157,
-0.016138026490807533,
-0.02490195818245411,
-0.01861974038183689,
-0.004050704184919596,
0.02100013941526413,
0.015912199392914772,
-0.012792747467756271,
0.04495816305279732,
-0.04662304371595383,
0.023521671071648598,
-0.003883987432345748,
-0.02848643995821476,
-0.1070363000035286,
-0.00807178020477295,
-0.005435162223875523,
0.013720516115427017,
0.022699575871229172,
-0.025238877162337303,
0.022658634930849075,
0.0376797616481781,
-0.06498920172452927,
0.00294886133633554,
-0.06477802991867065,
-0.0029396945610642433,
-0.018206164240837097,
-0.005576464347541332,
0.028205253183841705,
0.01528910268098116,
0.04114465042948723,
0.03660241514444351,
0.01539325900375843,
-0.03293408453464508,
0.004159704782068729,
0.017289234325289726,
-0.00016570609295740724,
0.030711252242326736,
0.008620258420705795,
-0.01850542612373829,
0.029441507533192635,
-0.007243980187922716,
-0.04046669602394104,
0.04695704206824303,
0.00024966750061139464,
0.05118236318230629,
-0.03138028830289841,
0.03277361020445824,
-0.004583746660500765,
0.025629183277487755,
0.01232829038053751,
0.00008486968727083877,
-0.05278923362493515,
0.03582937270402908,
0.016721077263355255,
0.04166953265666962,
-0.03354428708553314,
-0.009248173795640469,
0.024309514090418816,
-0.0437968447804451,
-0.021182704716920853,
0.03304347023367882,
-0.0047559491358697414,
-0.03353757783770561,
-0.028002135455608368,
-0.0000992941641015932,
0.007607953157275915,
-0.026119649410247803,
0.011867236346006393,
-0.05008499324321747,
-0.004618881735950708,
0.024612976238131523,
-0.03481500223278999,
-0.010990811511874199,
-0.00628121942281723,
-0.0021166347432881594,
0.00032618484692648053,
0.00893267523497343,
-0.0016203250270336866,
-0.018559344112873077,
-0.03601232171058655,
-0.007765083573758602,
-0.01652308739721775,
-0.05237862095236778,
0.018906673416495323,
-0.04833885282278061,
-0.014530640095472336,
0.037515319883823395,
0.043603893369436264,
0.007965531200170517,
0.012177923694252968,
-0.06566321104764938,
-0.03000810742378235,
-0.04972044751048088,
0.05777686834335327,
0.025412382557988167,
-0.030473435297608376,
-0.05934513360261917,
0.0043584504164755344,
-0.011669336818158627,
0.017236478626728058,
0.039666466414928436,
-0.019316453486680984,
-0.01256642397493124,
0.013669476844370365,
-0.013180049136281013,
0.007958561182022095,
-0.02281043864786625,
-0.007367326412349939,
-0.006797904148697853,
-0.07066965848207474,
-0.004622194450348616,
0.007310936227440834,
-0.037465717643499374,
0.007154724095016718,
0.022961728274822235,
0.0008662405307404697,
0.05983176827430725,
-0.010719855315983295,
-0.055610574781894684,
0.05476915463805199,
0.0630328506231308,
0.032767850905656815,
0.06687182933092117,
0.006742896977812052,
-0.010651646181941032,
0.018531665205955505,
0.003301868913695216,
-0.04154245927929878,
0.017847856506705284,
0.011429267935454845,
-0.01984129287302494,
-0.039083756506443024,
-0.015548603609204292,
0.02565009333193302,
-0.06978722661733627,
0.0033976801205426455,
0.059781961143016815,
0.012731587514281273,
-0.008911210112273693,
0.0373244546353817,
0.03486567735671997,
0.04193304479122162,
-0.003142479108646512,
0.025793325155973434,
0.027055608108639717,
-0.005093094427138567,
0.003833430353552103,
0.011743808165192604,
0.017666252329945564,
-0.003252003574743867,
0.015118556097149849,
0.0275078397244215,
0.003990512806922197,
0.03433660417795181,
0.008581331931054592,
0.042770612984895706,
-0.007310159504413605,
0.0034905250649899244,
-0.013123628683388233,
-0.012709914706647396,
-0.010433473624289036,
0.023896299302577972,
-0.02595469541847706,
0.027980536222457886,
-0.028707066550850868,
0.02510274015367031,
0.0005633386899717152,
-0.01184870395809412,
-0.03571593016386032,
0.0012355914805084467,
-0.008214235305786133,
0.04951779916882515,
0.03271489590406418,
-0.048355959355831146,
-0.007202713750302792,
-0.01739061251282692,
0.06391848623752594,
-0.010282795876264572,
0.028896089643239975,
-0.017337026074528694,
-0.026957005262374878,
-0.017920825630426407,
-0.0029984046705067158,
-0.050648339092731476,
-0.021596437320113182,
0.04021149501204491,
0.02041022852063179,
0.032617565244436264,
-0.013958463445305824,
0.003866754937916994,
-0.009611908346414566,
0.059375666081905365,
-0.06616350263357162,
-0.02597632445394993,
0.004882453940808773,
0.03466359153389931,
0.020743761211633682,
-0.00746771739795804
] |
<p>Given the Hamiltonian for the the harmonic oscillator (HO) as
$$
\hat H=\frac{\hat P^2}{2m}+\frac{m}{2}\omega^2\hat x^2\,,
$$
the Schroedinger equation can be reduced to:
$$
\left[
\frac{d^2}{dz^2}-\left(\frac{z^2}{4}+a\right)\right]\Psi=0~,
$$
where $a=-\frac{E}{\hbar\omega}$, $z=\sqrt{\frac{2m\omega}{\hbar}}$.
Now, the two independent solutions to this equation are the Wittaker's functions (Abramowitz section 19.3., or Gradshteyn at the beginning, where he defines the Wittaker's functions) $D_{-a-1/2}(z)$ and $D_{-a-1/2}(-z)$.
Apparently, there is no constraint on the values for $a$. In Abramowitz, especially, there is written "both variable $z$ and $a$ can take on general complex values".</p>
<p>Therefore my first question is:
Let us fix $a=i$ and let us therefore take the Wittaker's function $D_{-i-1/2}(z)$. This functions is solution of the time independent Schroedinger equation, and, therefore, is an eigenfunction of the ho hamiltonian. Since its value for the parameter $a$ is $i$, it follows that its eigenvalue $E$ must be $E=-i\hbar\omega$. However, this result is contradictory, since the hamiltonian must have only real eigenvalues, since it is hermitian. What do I do wrong?</p>
<p>My second question is:
Since the functions $D_n(z)$ form a complete set for $n$ positive integer with zero, I can expand my function $D_{-i-1/2}(z)$ onto the basis set $D_n(z)$.
$$
D_{-i-1/2}(z)=\sum_n C_n D_n(z)~.
$$
But, evidently, if $D_{-i-1/2}(z)$ is itself an eigenfunction with a different eigenvalue with respect to any of the $D_n(z)$, the expansion above does not make sense.
This question is somewhat correlated to the previous one. So, I believe I do something
wrong which is in common to both of them.</p>
| 10,715 |
[
0.017363613471388817,
-0.03975076600909233,
0.04251604154706001,
-0.03264128044247627,
0.06870153546333313,
-0.03987446427345276,
-0.08247531205415726,
-0.05022052675485611,
-0.012099464423954487,
-0.05812302604317665,
0.05714510381221771,
0.05260394886136055,
0.04369223862886429,
0.03448529168963432,
0.0025211856700479984,
0.00944458693265915,
-0.027501968666911125,
-0.0379374697804451,
-0.03133765608072281,
-0.011800589971244335,
-0.0017961529083549976,
0.05217757821083069,
0.02269861474633217,
-0.02607698179781437,
-0.003901336807757616,
-0.00523139676079154,
0.013750170357525349,
0.01736176386475563,
-0.000526345509570092,
0.07564682513475418,
-0.007735871709883213,
-0.02709542028605938,
0.017315005883574486,
0.06053044646978378,
0.03290675953030586,
-0.0017026019049808383,
-0.05519251897931099,
-0.05881021171808243,
0.0021838874090462923,
0.024234160780906677,
-0.045199718326330185,
-0.02991565130650997,
-0.025542547926306725,
0.021793382242321968,
-0.0016457110177725554,
0.020504416897892952,
0.016031600534915924,
-0.021509582176804543,
0.038984548300504684,
-0.07314243167638779,
0.0649440810084343,
-0.010925852693617344,
0.0350017286837101,
0.0022323401644825935,
-0.009554518386721611,
-0.048536501824855804,
0.04931391030550003,
0.07599937170743942,
0.032239969819784164,
-0.05273263528943062,
-0.018307890743017197,
0.016328919678926468,
0.0027724658139050007,
-0.026326816529035568,
-0.029261568561196327,
-0.01222922746092081,
0.03394588828086853,
-0.027603283524513245,
-0.003992158453911543,
0.0075743836350739,
0.04502620920538902,
0.0027931099757552147,
0.020767176523804665,
-0.07328527420759201,
0.030679209157824516,
-0.018761567771434784,
-0.00293243327178061,
0.016130656003952026,
0.01357088703662157,
-0.022712303325533867,
0.02603924088180065,
0.009053328074514866,
0.023844724521040916,
0.017009036615490913,
-0.006115894764661789,
-0.00885472446680069,
0.0391073152422905,
0.02656146138906479,
0.0013422738993540406,
0.016214273869991302,
0.018760427832603455,
0.040707945823669434,
0.0602165125310421,
-0.06091952696442604,
-0.003960005007684231,
0.030864203348755836,
-0.016037464141845703,
0.05836406350135803,
-0.02797078900039196,
-0.005249418318271637,
0.01951606385409832,
-0.05870894715189934,
0.0150498878210783,
0.06770402938127518,
-0.013338486663997173,
0.0308405589312315,
-0.020940091460943222,
0.019244208931922913,
-0.017795173451304436,
-0.018145503476262093,
-0.011898086406290531,
0.049088578671216965,
-0.017422981560230255,
-0.004785958677530289,
-0.013886230997741222,
0.0018589315004646778,
0.012794745154678822,
-0.013798264786601067,
0.056701213121414185,
0.05727522820234299,
0.009448354132473469,
-0.03041767328977585,
0.016688037663698196,
-0.0699702724814415,
-0.06403613090515137,
-0.0073169805109500885,
0.02868523821234703,
0.05250537022948265,
-0.022511417046189308,
0.004536759573966265,
0.034903980791568756,
-0.03845250606536865,
0.014224071986973286,
0.0414872020483017,
0.025638317689299583,
-0.03777901828289032,
-0.11051532626152039,
-0.037761181592941284,
0.018857808783650398,
-0.03828262910246849,
0.0001551619207020849,
-0.07857971638441086,
-0.0034663116093724966,
0.0538313202559948,
0.06341879069805145,
0.010867799632251263,
-0.0023654173128306866,
0.018255718052387238,
0.08424689620733261,
0.04576664790511131,
-0.021533293649554253,
-0.010519263334572315,
-0.042175475507974625,
-0.03690910339355469,
0.027404475957155228,
-0.013855135068297386,
0.04195944964885712,
0.024050232023000717,
0.012738232500851154,
0.005066420882940292,
0.07999779284000397,
-0.02531636320054531,
-0.008370177820324898,
0.012134186923503876,
0.002066485583782196,
-0.04118015244603157,
0.06717760860919952,
0.007815312594175339,
-0.006236836779862642,
0.040362127125263214,
-0.011545003391802311,
0.03778814524412155,
-0.027629271149635315,
-0.008635010570287704,
-0.004085313528776169,
-0.04762030020356178,
-0.0499553307890892,
-0.030711928382515907,
0.02193460799753666,
-0.003877086564898491,
0.009693874977529049,
-0.04110843315720558,
-0.008555355481803417,
0.034854955971241,
0.022402198985219002,
0.042232073843479156,
0.040844228118658066,
0.027872692793607712,
-0.016001712530851364,
-0.03229890018701553,
0.011916841380298138,
-0.03843754157423973,
0.03377951309084892,
0.016411757096648216,
-0.010479203425347805,
0.01980205811560154,
-0.005070003215223551,
-0.030518699437379837,
0.050290826708078384,
-0.02707618661224842,
0.030881362035870552,
-0.000998230534605682,
0.034147631376981735,
-0.01844184845685959,
0.06905069202184677,
0.0436398983001709,
0.011332670226693153,
0.015615659765899181,
0.06893591582775116,
-0.024809395894408226,
-0.010585092939436436,
-0.008337492123246193,
0.010575463995337486,
0.05099313333630562,
0.03480049967765808,
-0.003175149904564023,
0.008670635521411896,
-0.022077394649386406,
-0.008054863661527634,
0.023595348000526428,
-0.05219714343547821,
0.06562942266464233,
0.03377091512084007,
-0.01719905249774456,
0.024064509198069572,
0.052583932876586914,
0.03341623768210411,
0.036981359124183655,
-0.01802671328186989,
-0.01004478707909584,
-0.0282084159553051,
0.008596880361437798,
0.03646470978856087,
0.036380376666784286,
-0.0589020811021328,
0.0062682474963366985,
0.0352368988096714,
0.014602087438106537,
0.03677315264940262,
-0.009103325195610523,
-0.042147837579250336,
-0.04116516187787056,
0.009773540310561657,
0.007196143269538879,
0.024967283010482788,
0.024709753692150116,
0.030800946056842804,
0.011639588512480259,
-0.01564781740307808,
0.013912845402956009,
-0.008207934908568859,
0.0488106943666935,
-0.05658837780356407,
-0.0061689517460763454,
-0.008481313474476337,
-0.020558426156640053,
0.040735457092523575,
-0.04148763418197632,
0.008723435923457146,
0.031440816819667816,
-0.0060103656724095345,
-0.026208430528640747,
-0.029631922021508217,
-0.026392299681901932,
0.03677232563495636,
-0.012799426913261414,
-0.022107668220996857,
-0.008898423053324223,
0.010572666302323341,
-0.02705077826976776,
-0.019953828305006027,
-0.02159065753221512,
-0.02089729905128479,
0.003413411555811763,
-0.023061957210302353,
0.02689742110669613,
0.02761576510965824,
0.013730570673942566,
-0.01815175637602806,
0.0008000397938303649,
0.00676852697506547,
-0.01553458720445633,
0.022714320570230484,
0.013342686928808689,
-0.023042337968945503,
-0.012447541579604149,
-0.04738188907504082,
-0.011448122560977936,
0.04267902672290802,
0.01774546131491661,
0.004122311249375343,
-0.0054761916399002075,
-0.018040094524621964,
-0.022471899166703224,
-0.05184590816497803,
-0.04278842359781265,
0.007485563866794109,
-0.09140332043170929,
-0.0026846476830542088,
0.08836626261472702,
0.014974504709243774,
0.011888480745255947,
0.03542526811361313,
0.016116401180624962,
-0.027160460129380226,
-0.022855963557958603,
-0.02437126822769642,
0.03044380620121956,
-0.045039329677820206,
0.004231107886880636,
-0.007197975646704435,
0.006892726290971041,
0.023427940905094147,
-0.06282058358192444,
-0.03576752915978432,
0.011280178092420101,
0.015615487471222878,
0.01671910658478737,
0.0006105920765548944,
-0.011512226425111294,
0.06719604879617691,
0.0019519260386005044,
0.0069696493446826935,
-0.024765508249402046,
0.0455046184360981,
-0.01013993937522173,
-0.050678644329309464,
0.021714037284255028,
0.047955386340618134,
-0.028506692498922348,
0.05751394107937813,
-0.02551155537366867,
-0.008597081527113914,
0.04076188802719116,
-0.02263464219868183,
-0.0054892986081540585,
0.07846847176551819,
0.005095430184155703,
-0.006738544441759586,
0.07382633537054062,
-0.011988029815256596,
0.012140910141170025,
0.023982150480151176,
-0.01402261946350336,
-0.020898891612887383,
-0.002433870220556855,
-0.05353236570954323,
0.0314454585313797,
-0.026655344292521477,
0.044986169785261154,
-0.00019527312542777508,
0.04854655638337135,
-0.003926214762032032,
-0.0185872670263052,
-0.024474943056702614,
0.0132535919547081,
0.06477969139814377,
-0.025921979919075966,
0.02928919903934002,
0.03771235793828964,
-0.02191450260579586,
-0.03664826601743698,
0.009612302295863628,
-0.008357510901987553,
-0.005484904162585735,
0.014014067128300667,
-0.02336784265935421,
-0.044563956558704376,
0.02658098377287388,
0.04758409038186073,
0.009454202838242054,
-0.004475861322134733,
-0.03286834806203842,
-0.008830995298922062,
-0.04148947075009346,
-0.018160047009587288,
-0.04182712361216545,
0.06494107097387314,
0.010928336530923843,
0.05878284573554993,
0.014165741391479969,
0.015788152813911438,
-0.009777987375855446,
0.023016326129436493,
-0.0504329614341259,
-0.010001818649470806,
-0.008883662521839142,
0.003355754539370537,
-0.022203478962183,
-0.009347581304609776,
0.0018574027344584465,
-0.005751486402004957,
-0.04435606673359871,
-0.021579688414931297,
-0.029769817367196083,
-0.051522087305784225,
0.011827776208519936,
-0.052946530282497406,
-0.0263090617954731,
-0.023236840963363647,
0.06562277674674988,
0.008997410535812378,
0.005199582315981388,
-0.017604155465960503,
0.05601075664162636,
-0.04497631639242172,
0.019695106893777847,
-0.017628982663154602,
-0.023683108389377594,
0.011356967501342297,
0.044940073043107986,
0.0055941068567335606,
0.029034040868282318,
0.01821795105934143,
-0.0262815710157156,
-0.013223757967352867,
0.03908861055970192,
0.025209255516529083,
-0.022560901939868927,
0.015445329248905182,
-0.00016609842714387923,
0.03253946825861931,
0.0017721906770020723,
0.07607092708349228,
-0.007174105383455753,
-0.005091057159006596,
0.02092074416577816,
-0.019935794174671173,
0.006406345870345831,
0.03255157545208931,
0.013918260112404823,
-0.007441236637532711,
0.009532633237540722,
-0.05100027471780777,
-0.004105648025870323,
-0.053966421633958817,
-0.0022802127059549093,
-0.032285161316394806,
-0.026004141196608543,
-0.015301859937608242,
0.005250495858490467,
0.02775271050632,
0.03631403669714928,
0.029382582753896713,
-0.03410639241337776,
0.02563147433102131,
0.037727661430835724,
-0.0044651641510427,
0.0004507822741288692,
0.006172320805490017,
0.01012191828340292,
0.017183437943458557,
-0.012282256968319416,
0.004238736815750599,
-0.05187799036502838,
-0.028984444215893745,
0.03333405405282974,
0.05576431751251221,
0.006862059701234102,
-0.002928899135440588,
-0.048777781426906586,
-0.02858167514204979,
0.031408268958330154,
-0.014939766377210617,
0.03703279793262482,
0.01758374273777008,
0.013391826301813126,
-0.027305666357278824,
-0.05867026373744011,
-0.037204641848802567,
0.0023048329167068005,
-0.0037038512527942657,
0.017959801480174065,
-0.07384182512760162,
0.00025488357641734183,
-0.019223449751734734,
0.008587402291595936,
0.015930531546473503,
0.07391694188117981,
0.023710519075393677,
0.0016713396180421114,
-0.00839940644800663,
0.010234848596155643,
-0.025417622178792953,
-0.07772014290094376,
-0.02357557974755764,
-0.018559612333774567,
0.006450042128562927,
0.04302322119474411,
-0.04579178988933563,
-0.03560338541865349,
0.04114878550171852,
0.02333904430270195,
0.006557553540915251,
0.04710063710808754,
0.004316231701523066,
0.049165867269039154,
0.022695377469062805,
-0.011343097314238548,
0.03355595842003822,
0.028996169567108154,
-0.022820962592959404,
-0.01107934582978487,
-0.029339497908949852,
-0.017167631536722183,
-0.026363104581832886,
-0.0012182677164673805,
-0.05137822404503822,
0.004410403780639172,
-0.015944810584187508,
0.028158564120531082,
0.011963600292801857,
-0.00841093622148037,
-0.01870443858206272,
-0.015362069942057133,
0.026507774367928505,
0.019456209614872932,
-0.05729735270142555,
0.018677162006497383,
-0.020797934383153915,
0.036186184734106064,
0.020153332501649857,
-0.015205023810267448,
0.0261842031031847,
-0.02903944067656994,
0.01009346917271614,
0.04160156100988388,
-0.030571019276976585,
0.02745142951607704,
-0.06308171898126602,
-0.030931642279028893,
0.00531340204179287,
-0.047623950988054276,
0.03743167594075203,
0.0020775683224201202,
-0.01524632703512907,
0.010120095685124397,
-0.04465195909142494,
-0.024752482771873474,
0.02725236490368843,
0.0036687448155134916,
0.00009411761129740626,
-0.01670186221599579,
-0.014085152186453342,
0.037278756499290466,
-0.014290501363575459,
-0.07507046312093735,
-0.002749033272266388,
-0.020770518109202385,
-0.010412718169391155,
-0.006750345230102539,
-0.0169612318277359,
0.001356201828457415,
-0.0338568389415741,
-0.02718489058315754,
0.026162879541516304,
0.058458998799324036,
-0.02917037531733513,
0.021988296881318092,
0.024412406608462334,
0.04580147564411163,
0.02867077849805355,
-0.0035230631474405527,
-0.013908975757658482,
-0.010119566693902016,
-0.03634066879749298,
0.0024372555781155825,
0.02443896420300007,
0.029771629720926285,
-0.03236963972449303,
-0.036596450954675674,
0.007692511659115553,
-0.012453588657081127,
0.027011698111891747,
0.023203164339065552,
-0.047915417701005936,
0.020745843648910522,
-0.004855650942772627,
0.011087249033153057,
-0.01596897840499878,
-0.013141283765435219,
0.016201762482523918,
0.026886921375989914,
0.0024398111272603273,
-0.011423435062170029,
-0.04255319759249687,
-0.06020915508270264,
0.004135499708354473,
-0.007595243398100138,
-0.011502034962177277,
-0.00160274060908705,
0.06391908973455429,
0.013496981002390385,
0.0033976745326071978,
-0.0067013963125646114,
-0.03705922141671181,
-0.004621805157512426,
-0.040066443383693695,
0.013210125267505646,
-0.015185529366135597,
-0.027157606557011604,
-0.03155672177672386,
-0.07142146676778793,
-0.05582699179649353,
0.02939915843307972,
0.03263833373785019,
0.04826032370328903,
0.04753594473004341,
0.026149164885282516,
0.026254838332533836,
-0.019204530864953995,
-0.027377430349588394,
-0.012791244313120842,
0.02034316025674343,
0.004031394142657518,
0.03807675465941429,
-0.03062671609222889,
-0.024275783449411392,
0.06094825267791748,
-0.004872796591371298,
0.023554934188723564,
-0.009592209942638874,
0.037547990679740906,
0.023272903636097908,
0.013042806647717953,
-0.0010375092970207334,
-0.05115264654159546,
0.029336297884583473,
-0.01904718577861786,
0.05068590119481087,
-0.002138893585652113,
0.006817113142460585,
0.020234398543834686,
0.06590528786182404,
0.017177090048789978,
-0.020459085702896118,
-0.00577540835365653,
-0.03211420029401779,
0.03880500793457031,
0.026205945760011673,
-0.010634690523147583,
0.021434899419546127,
0.002261243062093854,
0.01392962783575058,
-0.0003797661338467151,
0.01942821405827999,
0.018701598048210144,
-0.017235692590475082,
0.0058710165321826935,
-0.041187990456819534,
-0.0920303538441658,
0.022968821227550507,
-0.021613186225295067,
-0.03921395167708397,
0.02505004219710827,
-0.014511879533529282,
0.0007348598446696997,
0.006733499467372894,
0.011420970782637596,
-0.009868140332400799,
0.05890665203332901,
-0.0040176683105528355,
-0.010569371283054352,
0.018606284633278847,
0.0035768814850598574,
0.15221258997917175,
0.05398835241794586,
0.02663380280137062,
-0.05596486106514931,
0.013094075955450535,
-0.003102234797552228,
0.027330337092280388,
-0.03534389287233353,
0.035660624504089355,
-0.015800705179572105,
-0.048127397894859314,
0.0008822710951790214,
0.04309603199362755,
0.003247031942009926,
-0.0025165684055536985,
0.029583489522337914,
-0.018788084387779236,
-0.055872075259685516,
0.01477264054119587,
-0.005779005121439695,
-0.0292982067912817,
0.003996465355157852,
0.01603884808719158,
0.004098866134881973,
-0.06005868315696716,
0.005237277131527662,
-0.03588708117604256,
-0.05391803756356239,
0.014374175108969212,
-0.02561115100979805,
-0.0664297565817833,
0.007739285938441753,
0.013323970139026642,
-0.038237977772951126,
-0.011443731375038624,
0.031802285462617874,
-0.011520171537995338,
-0.009057707153260708,
0.004763782024383545,
0.04339456930756569,
0.004968198947608471,
-0.013202049769461155,
0.01147001888602972,
-0.015127896331250668,
-0.054265525192022324,
-0.026063380762934685,
-0.01764497719705105,
0.05710955336689949,
-0.007326481398195028,
-0.03443746641278267,
0.03520572930574417,
-0.037146277725696564,
-0.012370008043944836,
-0.042798515409231186,
0.01115424558520317,
-0.00271613453514874,
0.006845827680081129,
-0.02467888966202736,
-0.007146921008825302,
-0.006859668996185064,
0.01862889900803566,
0.04080560430884361,
0.006859245710074902,
-0.015438912436366081,
-0.016787666827440262,
0.03450081869959831,
0.003502798033878207,
0.0012576138833537698,
-0.005385804921388626,
-0.018898209556937218,
-0.01242363452911377,
-0.006677855271846056,
-0.042667943984270096,
-0.05971481278538704,
0.015340897254645824,
0.00022205151617527008,
0.06298854947090149,
0.006360599305480719,
-0.0049730222672224045,
-0.041754208505153656,
-0.08289963006973267,
0.01302502490580082,
0.02983219176530838,
-0.048068609088659286,
-0.0017960030818358064,
-0.013299960643053055,
0.015863949432969093,
0.042057715356349945,
-0.025378523394465446,
0.017533091828227043,
0.014102142304182053,
0.03646349161863327,
0.007352565415203571,
-0.03161966800689697,
-0.013788067735731602,
0.03427013009786606,
-0.01935107447206974,
0.009062052704393864,
0.00984959676861763,
-0.0037823794409632683,
0.01114741712808609,
0.02523890510201454,
-0.009113593958318233,
0.04040408506989479,
-0.011400061659514904,
-0.02551632560789585,
0.03181837499141693,
-0.036053530871868134,
0.025769807398319244,
0.027094470337033272,
0.050461336970329285,
-0.05370471999049187,
-0.00908387079834938,
-0.038309648633003235,
-0.014742003753781319,
0.002775306813418865,
0.004566532094031572,
-0.016414636746048927,
0.01647465117275715,
-0.011320025660097599,
-0.008756444789469242,
-0.010288411751389503,
-0.007898695766925812,
-0.014998332597315311,
0.032598190009593964,
0.0030104073230177164,
0.029613392427563667,
-0.0024294767063111067,
-0.002503085881471634,
-0.006125362124294043,
-0.013975868932902813,
0.04082615301012993,
0.03588093817234039,
-0.0366140715777874,
-0.0008170884684659541,
-0.005065876990556717,
0.01494008582085371,
0.032628826797008514,
0.03895530477166176,
-0.008425724692642689,
-0.020217502489686012,
-0.04625343158841133,
-0.0030991339590400457,
0.00907963141798973,
-0.005883045960217714,
0.016881583258509636,
0.024265307933092117,
-0.02863502874970436,
-0.0225156731903553,
0.014325295574963093,
-0.015919018536806107,
-0.010507231578230858,
0.0027195028960704803,
-0.0361873060464859,
0.01600821129977703,
-0.005550281144678593,
0.014302881434559822,
0.007815051823854446,
0.012810874730348587,
0.03381211310625076,
0.017972292378544807,
-0.012012386694550514,
-0.006719736848026514,
-0.006958626676350832,
-0.02300647459924221,
0.004923938773572445,
0.022936832159757614,
0.032292455434799194,
0.04511115327477455,
0.05725236237049103,
-0.01941455900669098,
0.03832854703068733,
-0.0023381744977086782,
0.007884948514401913,
-0.1020890474319458,
-0.021428832784295082,
0.007178404368460178,
0.020671287551522255,
0.06992524117231369,
-0.011170226149260998,
-0.008861062116920948,
0.011516239494085312,
-0.07975634932518005,
0.039314910769462585,
-0.03276146203279495,
0.018790695816278458,
-0.007024036254733801,
-0.005985748488456011,
-0.05345935747027397,
0.026563383638858795,
0.024256151169538498,
0.045313239097595215,
0.038216765969991684,
0.017605852335691452,
-0.011154764331877232,
-0.02996290661394596,
0.01531263254582882,
0.0464460588991642,
-0.025345981121063232,
-0.013587536290287971,
0.05782928317785263,
-0.03727119043469429,
-0.010798928327858448,
0.00773493992164731,
-0.03490004315972328,
-0.0051797800697386265,
-0.05024542286992073,
0.023129144683480263,
0.002372733550146222,
0.044521868228912354,
0.02081029675900936,
0.00981801375746727,
-0.003004970960319042,
-0.019885459914803505,
0.04149463027715683,
-0.009098602458834648,
-0.02948729507625103,
-0.012653966434299946,
-0.008794623427093029,
-0.031037723645567894,
-0.051452621817588806,
0.03889485076069832,
0.012647353112697601,
0.01644672080874443,
0.0023175529204308987,
-0.015433046966791153,
0.0031442565377801657,
-0.027263356372714043,
0.0146045982837677,
-0.0014460518723353744,
-0.007301765959709883,
-0.019407445564866066,
0.011502740904688835,
0.022306518629193306,
-0.012906777672469616,
-0.03128235414624214,
-0.04308415576815605,
0.02947605587542057,
0.008066867478191853,
-0.007670987397432327,
-0.03817256540060043,
-0.012843645177781582,
0.0025339426938444376,
0.015019005164504051,
0.006164043676108122,
0.00379802193492651,
-0.018260115757584572,
0.0053149498999118805,
-0.041768282651901245,
0.002015745500102639,
-0.07381114363670349,
-0.030518248677253723,
0.0022837973665446043,
-0.05264674499630928,
0.015047751367092133,
0.024245239794254303,
-0.01287679560482502,
-0.024390626698732376,
-0.02383428066968918,
0.007001579739153385,
0.015178512781858444,
0.06099739298224449,
-0.009849398396909237,
-0.010040457360446453,
-0.015279036946594715,
-0.008404858410358429,
0.022989120334386826,
-0.005445331800729036,
0.014735832810401917,
-0.012543720193207264,
0.011839453130960464,
0.002574147656559944,
0.01436394639313221,
-0.02978099137544632,
0.03183767572045326,
0.012052527628839016,
-0.018079424276947975,
0.026602910831570625,
0.04412563890218735,
-0.05901302397251129,
0.07450854033231735,
-0.004973555915057659,
-0.03203437477350235,
0.07477102428674698,
-0.011542458087205887,
0.01325969584286213,
0.0441025011241436,
-0.03860577195882797,
-0.04836845025420189,
-0.010892331600189209,
-0.030666915699839592,
-0.009372743777930737,
-0.005184469744563103,
-0.006703040096908808,
0.03197420388460159,
-0.0083302091807127,
-0.020319154486060143,
0.019703054800629616,
-0.002570034470409155,
-0.04148612171411514,
0.0350644625723362,
0.026347482576966286,
0.04911743476986885,
0.0005246328073553741,
0.015167046338319778,
-0.002761813811957836,
0.005578217562288046,
0.035862281918525696,
0.019522372633218765,
0.02923508919775486,
-0.0002115212264470756,
0.015549401752650738,
0.040089141577482224,
-0.016447044909000397,
-0.001304176403209567,
0.04131457582116127,
0.018570158630609512,
-0.020037690177559853,
-0.04137907549738884,
0.03381634131073952,
-0.012592923827469349,
-0.016515249386429787,
0.020637474954128265,
-0.014592316932976246,
0.05972907319664955,
-0.003743207547813654,
0.0247619841247797,
-0.03205211088061333,
-0.005854317918419838,
-0.03409680351614952,
0.05095074698328972,
0.028444809839129448,
0.019313301891088486,
-0.01437115203589201,
-0.024898646399378777,
-0.01996534690260887,
0.007689932361245155,
0.002866708906367421,
-0.035039547830820084,
-0.013472254388034344,
0.03104187548160553,
-0.014422504231333733,
-0.022089563310146332,
-0.02379607781767845,
0.018943268805742264,
-0.0086596654728055,
0.02529747411608696,
0.050884127616882324,
0.028254810720682144,
-0.0011630493681877851,
0.018322428688406944,
-0.03952522575855255,
0.032326120883226395,
-0.06114352121949196,
-0.007474380545318127,
-0.015611274167895317,
0.0031115328893065453,
0.0016993110766634345,
-0.0034920661710202694
] |
<p>I have read multiple answers on StackExchange about this question, but I wasn't able to find a concrete answer. Like other questions, the reason I ask about the s-orbital is because it has a zero orbital angular momentum. But, the implication of having a zero angular momentum is unclear? Some answers discuss probability distributions, but the question is how can there be multiple places for an electron, if it can't move. I read another answer that says that the electron passes through the nucleus or curve around it as a wave. I would appreciate it if anyone could provide a resolution to this question.</p>
| 10,716 |
[
-0.04358290135860443,
0.002164809498935938,
0.025819405913352966,
-0.062306758016347885,
0.007264544256031513,
-0.020414603874087334,
-0.01165368128567934,
-0.006950791459530592,
-0.00449951970949769,
-0.05012216791510582,
0.04234563931822777,
0.017742587253451347,
0.04791945591568947,
-0.015229374170303345,
-0.009065954014658928,
-0.011179432272911072,
-0.006641293875873089,
-0.020565949380397797,
-0.017184307798743248,
-0.006732264533638954,
-0.009433065541088581,
0.007386078592389822,
-0.008176791481673717,
0.02023400366306305,
0.026276130229234695,
0.025640469044446945,
0.022559568285942078,
0.030118748545646667,
0.026766106486320496,
0.05062561482191086,
-0.008884810842573643,
-0.03525849059224129,
0.02042381465435028,
0.0560820996761322,
0.03491698578000069,
-0.0334884449839592,
-0.028891440480947495,
-0.028505034744739532,
-0.029649857431650162,
0.03538157790899277,
-0.021798739209771156,
-0.02210799977183342,
-0.05858142301440239,
0.047182146459817886,
-0.015400420874357224,
0.02014457993209362,
0.004640211816877127,
-0.004845805000513792,
0.05864501744508743,
-0.03222980722784996,
0.03409922868013382,
-0.018854258581995964,
0.0038188102189451456,
0.019105607643723488,
0.03447415679693222,
-0.009343387559056282,
0.10775866359472275,
0.049718186259269714,
-0.019855253398418427,
-0.02337235026061535,
-0.004988159518688917,
-0.017995012924075127,
0.0018320393282920122,
-0.01762022078037262,
-0.022407105192542076,
-0.0103370426222682,
0.04029159992933273,
-0.020476272329688072,
0.011895816773176193,
-0.005053853150457144,
0.032842788845300674,
0.020133310928940773,
-0.011139814741909504,
-0.027919184416532516,
0.021852461621165276,
-0.04178506135940552,
0.04817117750644684,
0.007957620546221733,
0.03197740763425827,
0.01520309504121542,
-0.024906491860747337,
-0.032794561237096786,
0.01974315568804741,
0.0025268623139709234,
-0.01713230460882187,
-0.02053050883114338,
0.05323341116309166,
-0.0086636608466506,
0.016049815341830254,
0.016777291893959045,
-0.001147638657130301,
0.03435322269797325,
0.03601783886551857,
0.0006453898386098444,
-0.0448334664106369,
0.024445869028568268,
-0.012992492876946926,
0.05746644735336304,
0.01142099965363741,
-0.028226573020219803,
0.02140682563185692,
-0.05477318540215492,
0.040377553552389145,
0.11312378197908401,
-0.020037971436977386,
0.02469932660460472,
-0.03407791629433632,
0.03302955627441406,
0.004631708841770887,
-0.005830224137753248,
-0.011717305518686771,
0.060052771121263504,
0.022676581516861916,
0.013411959633231163,
0.007863795384764671,
-0.006467621307820082,
-0.006902239751070738,
-0.004769426304847002,
0.021828653290867805,
0.07759961485862732,
0.016477495431900024,
-0.04472152516245842,
-0.0061693349853158,
-0.01854550838470459,
-0.05930894985795021,
-0.001483712811022997,
0.015271106734871864,
0.007927783764898777,
-0.013845046982169151,
0.017544399946928024,
0.02515885978937149,
0.01279375422745943,
0.03297910839319229,
-0.0008872126345522702,
0.041927170008420944,
-0.020252807065844536,
-0.11941290646791458,
-0.039471350610256195,
0.04887068271636963,
-0.009528825990855694,
-0.017956608906388283,
-0.05175754800438881,
-0.012930892407894135,
0.0013527671108022332,
0.07095121592283249,
-0.017147602513432503,
-0.0370744951069355,
-0.004483013413846493,
0.043426673859357834,
0.024897035211324692,
0.010800259187817574,
0.02626246213912964,
-0.02398473024368286,
-0.06317904591560364,
0.015254009515047073,
-0.03084973618388176,
0.058154698461294174,
0.020461764186620712,
0.044260066002607346,
-0.055684421211481094,
0.06108011305332184,
-0.01555874478071928,
0.019110236316919327,
0.00823352299630642,
0.022091956809163094,
-0.045593444257974625,
0.0789380744099617,
0.04090927168726921,
0.008903276175260544,
0.05573185905814171,
-0.009707653895020485,
0.02795383334159851,
-0.025806352496147156,
0.04279249161481857,
0.012019804678857327,
-0.07781994342803955,
-0.029075641185045242,
-0.03710594028234482,
0.004773210268467665,
-0.012419778853654861,
-0.046097949147224426,
-0.007710626814514399,
0.03228745609521866,
0.01354147493839264,
-0.0001314687542617321,
0.049810219556093216,
0.006864218972623348,
0.006366610527038574,
-0.035255808383226395,
-0.02762654237449169,
0.0005385809345170856,
-0.052570126950740814,
0.03898223116993904,
-0.011792624369263649,
-0.02750442549586296,
0.06330067664384842,
0.0368812270462513,
0.012811589986085892,
-0.023942558094859123,
-0.00677586579695344,
-0.022954728454351425,
0.033037520945072174,
-0.0034614824689924717,
-0.03179728612303734,
0.041110675781965256,
0.11415629088878632,
0.02319021336734295,
0.0010786476777866483,
0.01005413755774498,
-0.02362469770014286,
-0.018810776993632317,
-0.005098399706184864,
0.009407748468220234,
0.05718992277979851,
0.03349881246685982,
0.01010536402463913,
-0.026939189061522484,
-0.013832179829478264,
-0.027365321293473244,
0.02506706863641739,
-0.019457226619124413,
0.0867723673582077,
0.042659975588321686,
0.009513812139630318,
0.01708870194852352,
0.04869623854756355,
0.0016619382658973336,
-0.009569588117301464,
0.0258712749928236,
-0.027355816215276718,
-0.05311271920800209,
-0.012103534303605556,
0.05993147939443588,
0.014403074979782104,
-0.035842135548591614,
0.0016724532470107079,
-0.010978457517921925,
0.0394054614007473,
0.01862522028386593,
0.013439731672406197,
-0.056038010865449905,
-0.028830112889409065,
-0.006453048437833786,
-0.007634809240698814,
0.022061415016651154,
-0.002525944961234927,
0.04119992256164551,
0.00907389260828495,
0.030518028885126114,
0.021832238882780075,
-0.03423658385872841,
0.0641651600599289,
-0.023448005318641663,
-0.004015423823148012,
-0.008190912194550037,
-0.017571182921528816,
0.035985447466373444,
-0.01013199333101511,
-0.005989940371364355,
0.013472098857164383,
-0.02569071762263775,
0.023710696026682854,
-0.006453095469623804,
-0.008455824106931686,
0.026367750018835068,
0.023683099076151848,
-0.021308280527591705,
0.0031907244119793177,
0.004260952118784189,
-0.024832740426063538,
0.0004164224083069712,
-0.029246725142002106,
-0.001607936224900186,
0.010415012948215008,
0.0033817754592746496,
0.031668949872255325,
0.012968366034328938,
0.0019456491572782397,
-0.031208038330078125,
-0.03869975358247757,
-0.021829253062605858,
-0.029826637357473373,
0.005160225089639425,
0.03802039846777916,
-0.08189110457897186,
0.008018223568797112,
-0.04276428744196892,
-0.028017627075314522,
0.03975248709321022,
-0.008586286567151546,
-0.011564337648451328,
-0.014828871935606003,
-0.014640450477600098,
-0.06343735009431839,
0.0020004562102258205,
-0.011623580008745193,
-0.009255892597138882,
-0.05014989525079727,
-0.010512369684875011,
0.06126173958182335,
-0.021632859483361244,
-0.012025130912661552,
0.0269921962171793,
-0.016656290739774704,
-0.05505596473813057,
0.008966446854174137,
-0.015782548114657402,
0.0537843219935894,
-0.029904654249548912,
0.006012606434524059,
0.0314302034676075,
-0.03352124243974686,
-0.0011527369497343898,
-0.017308000475168228,
-0.020874153822660446,
0.007408942095935345,
-0.03906843438744545,
-0.0028405797202140093,
0.0026212576776742935,
-0.03269297257065773,
0.0869956761598587,
0.00013186954311095178,
-0.01926124095916748,
-0.005021767225116491,
-0.002097864868119359,
-0.03821641951799393,
-0.012825747951865196,
0.023333420976996422,
0.022481394931674004,
0.023697156459093094,
0.007925471290946007,
0.016497910022735596,
0.03136475011706352,
0.013695630244910717,
0.010360869579017162,
-0.01605544053018093,
0.019406378269195557,
-0.004389712121337652,
-0.021398399025201797,
0.0664810761809349,
0.0014605630422011018,
-0.01649797335267067,
0.010428071953356266,
-0.018397023901343346,
0.007548904977738857,
0.02157318964600563,
-0.05226699262857437,
0.039060913026332855,
0.005895145703107119,
0.005919125862419605,
-0.02568897046148777,
0.05053164064884186,
0.03137887641787529,
-0.0020903307013213634,
0.020038971677422523,
0.002636174438521266,
0.07542212307453156,
0.0020324918441474438,
0.008502531796693802,
0.015997467562556267,
-0.018222207203507423,
-0.01493940968066454,
0.009325210005044937,
-0.0005024182028137147,
-0.012762033380568027,
-0.024195311591029167,
-0.009000002406537533,
-0.0689459890127182,
0.005801186431199312,
0.026794740930199623,
0.03878575190901756,
-0.020714977756142616,
-0.040204789489507675,
-0.020365331321954727,
-0.03209216892719269,
0.023606901988387108,
0.02756866067647934,
0.03200036659836769,
0.018056323751807213,
0.04402855411171913,
0.019830433651804924,
0.018266141414642334,
-0.031233564019203186,
-0.0020904741249978542,
-0.06743721663951874,
0.016669198870658875,
-0.041090887039899826,
-0.012345810420811176,
-0.04002506658434868,
-0.016597384586930275,
-0.00717530120164156,
-0.01819879747927189,
-0.01707955077290535,
-0.039354708045721054,
-0.02333698235452175,
-0.014363381080329418,
0.008057559840381145,
-0.04207441955804825,
0.007351515349000692,
-0.05168194696307182,
0.06100338324904442,
-0.004230008460581303,
-0.005866030231118202,
0.025302017107605934,
0.029097644612193108,
-0.03985064849257469,
-0.019884591922163963,
-0.02198188006877899,
0.009421825408935547,
-0.030051153153181076,
0.007472032681107521,
0.043345917016267776,
0.0034499054308980703,
-0.03587396815419197,
-0.03069298155605793,
0.006711619906127453,
0.07747352868318558,
0.031143207103013992,
-0.04188905656337738,
-0.022175095975399017,
-0.02554437518119812,
0.013899654150009155,
-0.02921130694448948,
0.04078638181090355,
0.015425012446939945,
0.033326566219329834,
0.047175630927085876,
-0.002675337251275778,
-0.027013493701815605,
-0.006524099037051201,
0.017342986539006233,
0.037487514317035675,
-0.017649803310632706,
-0.05201001465320587,
-0.011918503791093826,
-0.04454328864812851,
0.03253140300512314,
0.009370625019073486,
-0.0295841284096241,
-0.0028191301971673965,
0.016070500016212463,
-0.012338283471763134,
0.024928715080022812,
-0.009456113912165165,
-0.007992719300091267,
-0.015446093864738941,
0.0038803627248853445,
-0.021993914619088173,
-0.0032609044574201107,
0.024359317496418953,
-0.0046631693840026855,
0.023940863087773323,
0.019640617072582245,
-0.001713584759272635,
-0.029345648363232613,
-0.008095833472907543,
0.036926064640283585,
0.03250608220696449,
-0.013194520957767963,
0.008042416535317898,
-0.057157810777425766,
-0.017086461186408997,
0.049867577850818634,
-0.03405323252081871,
0.026728544384241104,
-0.04153420776128769,
-0.024191396310925484,
-0.019544130191206932,
-0.06136784330010414,
-0.005538124591112137,
0.010003726929426193,
-0.017099451273679733,
-0.007933861576020718,
-0.03872086852788925,
-0.0005165192997083068,
-0.03717915341258049,
0.018809882923960686,
0.037974316626787186,
0.08342830091714859,
0.02104279026389122,
0.012955643236637115,
-0.004098598379641771,
0.0444662868976593,
0.02440355345606804,
-0.1065869927406311,
-0.01018612738698721,
-0.012839779257774353,
0.016392933204770088,
0.05696040391921997,
-0.0625825971364975,
-0.08489002287387848,
0.046789612621068954,
0.010773788206279278,
0.014219379052519798,
-0.0048766303807497025,
-0.015919050201773643,
0.04177894815802574,
0.043939195573329926,
0.0032591947820037603,
0.029898131266236305,
0.035166237503290176,
-0.015026082284748554,
0.004354606382548809,
-0.04291679337620735,
0.026233872398734093,
-0.03472211956977844,
-0.012356801889836788,
-0.0531216561794281,
0.042898841202259064,
-0.010765569284558296,
0.039585866034030914,
-0.01979457400739193,
0.02820255421102047,
0.0013877145247533917,
-0.05739549174904823,
-0.03453379124403,
0.018473736941814423,
0.003423715941607952,
-0.007154130842536688,
-0.023376643657684326,
0.005993000231683254,
-0.011312256567180157,
-0.017088215798139572,
0.002184856915846467,
-0.044534217566251755,
0.015102102421224117,
0.027535011991858482,
-0.03232584521174431,
0.03219490498304367,
-0.03554249182343483,
-0.02147337608039379,
-0.0027269385755062103,
-0.06035825237631798,
0.02918504737317562,
-0.03617439046502113,
-0.0167311392724514,
0.010233089327812195,
-0.06687040627002716,
-0.03495440259575844,
0.012230556458234787,
-0.007300182245671749,
0.030361155048012733,
-0.03655054047703743,
0.006670196540653706,
0.018259184435009956,
-0.004968949127942324,
-0.09730397909879684,
-0.034569837152957916,
0.0031900194007903337,
0.01546567864716053,
-0.022636543959379196,
-0.02379472739994526,
0.03240642324090004,
-0.016403188928961754,
-0.02102891355752945,
0.031442753970623016,
0.008618832565844059,
-0.04904031381011009,
-0.01403313409537077,
0.03509797528386116,
0.009482396766543388,
0.05587499961256981,
-0.012061703950166702,
-0.04600601643323898,
0.011826626025140285,
-0.023436009883880615,
0.02532217837870121,
0.005442468915134668,
0.03170682489871979,
-0.02436484396457672,
-0.046900369226932526,
-0.007265334017574787,
0.01879977062344551,
0.017828339710831642,
-0.006624304689466953,
-0.03044075332581997,
0.013596356846392155,
-0.0063474434427917,
0.03424714505672455,
-0.007707673124969006,
0.003929413389414549,
0.001425837050192058,
0.02440810203552246,
0.02750842459499836,
0.01353653147816658,
-0.02511722408235073,
-0.05048959702253342,
0.020092478021979332,
-0.00990830548107624,
0.0328342504799366,
0.01258932240307331,
0.05013219639658928,
0.007588219363242388,
0.02234727516770363,
0.006636191159486771,
-0.01821763813495636,
0.02215796336531639,
-0.017909185960888863,
-0.01348525658249855,
-0.01668640412390232,
0.010399334132671356,
-0.033356718719005585,
-0.026444658637046814,
-0.021047264337539673,
0.02894711308181286,
0.05162883177399635,
-0.022186478599905968,
0.02010035328567028,
0.007932196371257305,
0.0026841796934604645,
-0.04796482250094414,
-0.014499102719128132,
-0.012971301563084126,
0.009613025933504105,
0.00684197386726737,
0.032539840787649155,
-0.010923130437731743,
0.010316522791981697,
0.05871504917740822,
0.07744011282920837,
-0.021252650767564774,
0.03255317360162735,
0.05229400098323822,
-0.0045357574708759785,
0.05433650687336922,
0.023091880604624748,
-0.04692019894719124,
0.03915669023990631,
-0.022943619638681412,
0.058570899069309235,
0.018276236951351166,
-0.03161504492163658,
0.03836791217327118,
-0.006170688662678003,
0.0283459834754467,
-0.01727244071662426,
-0.023045390844345093,
-0.026782728731632233,
0.021790940314531326,
0.003806160297244787,
-0.011989579536020756,
-0.013115153647959232,
0.002856755629181862,
0.02788851223886013,
0.018904035910964012,
-0.03342684358358383,
0.004188036546111107,
-0.04411091282963753,
-0.006890240591019392,
-0.02867770567536354,
-0.04406861960887909,
0.03216584771871567,
-0.017765963450074196,
0.0036789157893508673,
0.00064089271472767,
-0.016249189153313637,
0.02071899175643921,
0.027496490627527237,
0.03756380453705788,
-0.01805185340344906,
0.06576508283615112,
0.0037487030494958162,
0.00534853944554925,
-0.020238684490323067,
0.012288942001760006,
0.10294754058122635,
0.033605869859457016,
0.017419172450900078,
-0.05308809503912926,
-0.04403434693813324,
0.004128936678171158,
0.04384844750165939,
-0.006081084720790386,
0.009550979360938072,
0.005077339243143797,
0.020364493131637573,
-0.011714767664670944,
0.05101243779063225,
0.011336405761539936,
0.03660472482442856,
0.018820548430085182,
-0.06991992890834808,
-0.006399555131793022,
-0.038192592561244965,
0.006035182159394026,
0.013125949539244175,
-0.009969564154744148,
-0.06340504437685013,
-0.014467969536781311,
-0.04596300423145294,
0.0014055939391255379,
-0.04400119185447693,
-0.05545057728886604,
0.018665630370378494,
-0.008239474147558212,
-0.049801699817180634,
-0.022664329037070274,
-0.010776400566101074,
-0.016717176884412766,
-0.03820057958364487,
0.03611571714282036,
0.02840553969144821,
-0.031017348170280457,
0.041465725749731064,
0.0362388901412487,
-0.016527416184544563,
-0.007031910587102175,
0.014928914606571198,
0.0028495558071881533,
-0.03401222079992294,
-0.018337752670049667,
0.008353865705430508,
0.023628484457731247,
-0.04244743660092354,
-0.04088263958692551,
-0.018020588904619217,
-0.003896061098203063,
0.026858359575271606,
-0.03189022094011307,
-0.010022943839430809,
-0.03469683974981308,
0.047798361629247665,
-0.012792625464498997,
-0.02897557057440281,
0.01138212624937296,
-0.007248457986861467,
-0.006851378828287125,
-0.0034253287594765425,
0.029854126274585724,
0.014347692020237446,
-0.017732495442032814,
0.012081816792488098,
-0.0024813306517899036,
0.016024360433220863,
-0.0017904769629240036,
-0.00716216629371047,
-0.017125990241765976,
-0.05833030492067337,
0.0003271551104262471,
0.06033174693584442,
0.016830679029226303,
0.03974590450525284,
0.016874831169843674,
-0.012073204852640629,
0.0013164476258680224,
-0.045755933970212936,
0.016466787084937096,
-0.012647002935409546,
-0.00837081391364336,
0.006513561587780714,
0.004116516560316086,
0.041113417595624924,
0.03957710042595863,
-0.036925699561834335,
0.05201748386025429,
0.014733637683093548,
0.01498718373477459,
-0.0023374303709715605,
-0.02985280193388462,
-0.030508434399962425,
0.02325691096484661,
-0.02604568563401699,
0.007842044346034527,
-0.021199101582169533,
-0.006404480896890163,
0.029608678072690964,
0.03359461948275566,
0.02183515392243862,
0.03604888170957565,
-0.0076970611698925495,
0.008585916832089424,
0.02041744999587536,
-0.04472508281469345,
0.014913970604538918,
0.03593586012721062,
0.006189196370542049,
-0.01506101805716753,
-0.008479032665491104,
-0.013293546624481678,
-0.007269709371030331,
0.034080181270837784,
0.03140066936612129,
-0.035369016230106354,
0.01736326329410076,
-0.010648207738995552,
0.005131394602358341,
-0.009672931395471096,
0.020043272525072098,
-0.01291578821837902,
0.04699116572737694,
0.026398401707410812,
-0.005669606849551201,
-0.027127498760819435,
0.018785761669278145,
0.04921899363398552,
-0.023028669878840446,
0.016956547275185585,
0.012372338213026524,
-0.010308959521353245,
0.01756466180086136,
0.049437083303928375,
-0.024552125483751297,
0.05427344888448715,
-0.0029327410738915205,
0.022113880142569542,
0.01893950253725052,
-0.03946555033326149,
-0.048284802585840225,
0.028709985315799713,
-0.026776334270834923,
0.020725293084979057,
0.04390028491616249,
-0.00897552166134119,
0.003970398101955652,
0.0581158846616745,
-0.018952831625938416,
-0.012306085787713528,
-0.018002424389123917,
-0.012460416182875633,
-0.024561021476984024,
-0.005461620166897774,
0.0027437445241957903,
-0.00874378066509962,
-0.02825040929019451,
0.038099225610494614,
0.014538240619003773,
-0.0218163151293993,
-0.014552553184330463,
-0.0004571643366944045,
-0.026543395593762398,
0.035521116107702255,
0.03612446412444115,
-0.0022421074099838734,
0.0009113733540289104,
0.02815873548388481,
-0.019717872142791748,
0.0924820825457573,
0.026405973359942436,
0.026434091851115227,
-0.07214367389678955,
-0.011629033833742142,
0.013272855430841446,
0.0033690149430185556,
0.025110498070716858,
-0.02647402323782444,
-0.03648362308740616,
0.04426582530140877,
-0.09113281220197678,
0.0034374413080513477,
-0.011075951159000397,
0.008142435923218727,
-0.053691353648900986,
-0.010916492901742458,
-0.06682686507701874,
0.04049217328429222,
0.00714093679562211,
0.07607731223106384,
0.01728396862745285,
0.027144625782966614,
-0.03998461738228798,
-0.03225955367088318,
-0.04064146801829338,
0.0701678991317749,
-0.00978968758136034,
0.0013180641690269113,
0.05554778501391411,
-0.018579401075839996,
-0.03268909081816673,
0.060750558972358704,
0.007639024406671524,
0.00793035700917244,
-0.04115758091211319,
-0.01040121354162693,
-0.012426343746483326,
0.04723970219492912,
0.015896616503596306,
0.02140427939593792,
0.005864870268851519,
0.019063496962189674,
0.038665324449539185,
0.027779920026659966,
-0.026909731328487396,
-0.004001439083367586,
0.017797406762838364,
-0.030301086604595184,
-0.06218159198760986,
0.017822764813899994,
0.023574933409690857,
0.006236518267542124,
0.0018141338368877769,
0.021524552255868912,
0.035801004618406296,
0.0019756327383220196,
-0.013623852282762527,
-0.05592026561498642,
-0.004567039664834738,
-0.007529230322688818,
0.007912331260740757,
0.025041380897164345,
0.009248598478734493,
-0.02273429185152054,
-0.049713943153619766,
0.030636755749583244,
-0.01370581891387701,
-0.01826905831694603,
-0.07051797211170197,
0.009732565842568874,
0.0026846514083445072,
0.017425861209630966,
0.02742362767457962,
-0.0209609717130661,
-0.029243487864732742,
0.016823872923851013,
-0.0004664678708650172,
0.030872587114572525,
0.012152137234807014,
-0.034125130623579025,
-0.013553803786635399,
-0.0663885548710823,
0.032710667699575424,
0.0033051481004804373,
0.0233796127140522,
-0.026186928153038025,
-0.02129029855132103,
-0.010109471157193184,
0.03311183303594589,
0.04017658159136772,
0.00906637404114008,
0.015833780169487,
0.005155824590474367,
-0.0009192269644699991,
0.043431028723716736,
-0.044306863099336624,
0.0024247977416962385,
-0.010520938783884048,
-0.05136922746896744,
-0.010578234679996967,
-0.011979873292148113,
-0.0548282116651535,
0.02667190693318844,
0.017483264207839966,
-0.024369817227125168,
0.019665122032165527,
-0.05201254040002823,
-0.02506353333592415,
0.051507655531167984,
0.04915599524974823,
-0.01076155249029398,
0.05292373150587082,
0.025543851777911186,
0.0017419954529032111,
0.01697719469666481,
-0.019498055800795555,
-0.020935112610459328,
0.030786365270614624,
-0.023198967799544334,
-0.03149699047207832,
-0.016217593103647232,
-0.01635279878973961,
0.05708407238125801,
-0.03336957469582558,
-0.013285741209983826,
0.04383253678679466,
-0.03268154338002205,
-0.038679953664541245,
0.03953529894351959,
-0.013247299008071423,
0.04836824908852577,
0.0218956395983696,
-0.0057563078589737415,
0.008201767690479755,
-0.00042043026769533753,
0.02080271765589714,
0.031509269028902054,
0.013760102912783623,
0.00024938536807894707,
0.014848530292510986,
0.01598837599158287,
0.007181405555456877,
0.020622603595256805,
-0.0014743393985554576,
0.012016954831779003,
-0.031751442700624466,
0.00828876718878746,
0.056273702532052994,
-0.011550240218639374,
-0.03100637160241604,
0.021562764421105385,
-0.06373421847820282,
0.08859341591596603,
-0.02244320884346962,
0.026637529954314232,
-0.029417669400572777,
0.03307164087891579,
0.0030360077507793903,
0.012154356576502323,
0.014902388677001,
0.025493957102298737,
-0.031323593109846115,
0.0006699274526908994,
0.02350110560655594,
-0.005694432649761438,
0.07727635651826859,
-0.03590165451169014,
0.01797771453857422,
-0.00031637822394259274,
-0.02456216886639595,
-0.05311241373419762,
0.000790449557825923,
-0.038863833993673325,
-0.02439497783780098,
-0.008769248612225056,
0.010735775344073772,
-0.002127984305843711,
0.00413694279268384,
0.001990539487451315,
-0.046812403947114944,
0.033349182456731796,
-0.020188607275485992,
-0.02745358645915985,
-0.02445356175303459,
0.03371002525091171,
-0.04629338160157204,
-0.00869688205420971
] |
<p>Suppose I have 2 fermions in a potential $V(x)$. Both particles are moving in one dimension: the $x$ axis.
Then, neglecting the interaction between the particles, the spatial wave function of the system would be of the form
$$\psi_{n_{1}}(x_{1})\psi_{n_{2}}(x_{2}) $$</p>
<p>Now, if I'm considering particles with spin 1/2, the notation $\alpha(1)$ indicates that the particle 1 has spin up, and $\beta(2)$ denotes the particle 2 having spin down.</p>
<p>Now, I want to write the complete wave function, a function of the form
$$\psi_{n_{1}n_{2}s_{1}s_{2}}(x_{1},x_{2},s_{1},s_{2})=\psi_{n_{1}}(x_{1})\psi_{n_{2}}(x_{2})F(\alpha,\beta)$$
where $F(\alpha,\beta)$ is a function of the spin of the system.</p>
<p>To this end, I have that the only physically possible functions $F(\alpha,\beta)$ are:</p>
<p>Symmetric: $\chi_{\alpha}:=\alpha(1)\alpha(2),\quad\chi_{\beta}:=\beta(1)\beta(2),\quad\chi_{+}:=\frac{1}{\sqrt{2}}\left[\alpha(1)\beta(2)+\alpha(2)\beta(1)\right]$</p>
<p>Antisymmetric: $\chi_{-}:=\frac{1}{\sqrt{2}}\left[\alpha(1)\beta(2)-\alpha(2)\beta(1)\right]$</p>
<p>In order to write down the complete wave function with spin, I understand I have to consider the energy levels. For example the ground state: $\psi_{1}(x_{1})\psi_{1}(x_{2})$.</p>
<p>If $\psi_{1}(x_{1})\psi_{1}(x_{2})$ is symmetric (<em>as I understand it is</em>), then I must multiply this function times the antisymmetric function $\chi_{-}$ (in order to get an antisymmetric wave function, for two fermions).</p>
<p>If $\psi_{1}(x_{1})\psi_{1}(x_{2})$ is antisymmetric (and I understand this is impossible, since the ground state is not degenerate), then I'd have 3 wave functions, obtained by multiplying $\psi_{1}(x_{1})\psi_{1}(x_{2})$ times $\chi_{\alpha}$, $\chi_{\beta}$ and $\chi_{+}$.</p>
<p>Now, for the 1st excited level, say $\psi_{2}(x_{1})\psi_{1}(x_{2})$, <strong>my question is</strong>, what happens when this function is not symmetric neither antisymmetric?</p>
<p>I mean, I could built a symmetric</p>
<p>$$f_S=\frac{1}{\sqrt{2}}\left[\psi_{2}(x_{1})\psi_{1}(x_{2})+\psi_{2}(x_{2})\psi_{1}(x_{1})\right]$$</p>
<p>or an antisymmetric</p>
<p>$$f_A=\frac{1}{\sqrt{2}}\left[\psi_{2}(x_{1})\psi_{1}(x_{2})-\psi_{2}(x_{2})\psi_{1}(x_{1})\right]$$
wave function. But which one of these must I choose?
Or, must I calculate the resultant complete wave functions with both? Then, when I count the states with the 1st excited energy, I'd have 4 instead of 1 or 3.</p>
| 10,717 |
[
0.00791917834430933,
0.004428602289408445,
0.009967368096113205,
0.0037084827199578285,
0.025562064722180367,
0.012332185171544552,
-0.007151218596845865,
-0.0103215416893363,
0.0058129047974944115,
-0.02176234871149063,
0.049754075706005096,
0.010816121473908424,
0.07360091060400009,
0.010757112875580788,
0.01750052534043789,
0.03131137043237686,
0.0022073539439588785,
-0.027513425797224045,
-0.03230776637792587,
-0.03925208002328873,
-0.0018672264413908124,
0.04821915179491043,
0.0019606449641287327,
-0.011028791777789593,
-0.0028415319975465536,
0.06111087277531624,
-0.007087129168212414,
-0.012557675130665302,
0.010758938267827034,
0.06006406247615814,
-0.013950507156550884,
-0.0405421257019043,
0.04188841953873634,
0.038614608347415924,
0.00953676924109459,
-0.013198529370129108,
-0.03852032124996185,
-0.05485393479466438,
0.009876764379441738,
0.04023842513561249,
-0.07313701510429382,
0.0030336822383105755,
-0.0418352410197258,
0.02212769165635109,
-0.009596670977771282,
-0.0011982028372585773,
0.0066047608852386475,
0.0075332242995500565,
-0.011348983272910118,
-0.06129761412739754,
0.06069694831967354,
0.007663231808692217,
0.07490184158086777,
-0.013069317676126957,
-0.02034888043999672,
-0.017466440796852112,
0.05526556447148323,
0.04560600221157074,
0.05249795690178871,
-0.050478629767894745,
-0.0343078188598156,
-0.00632484070956707,
-0.012093378230929375,
-0.019841864705085754,
-0.03388361260294914,
0.01657627895474434,
0.044988665729761124,
-0.0013803845504298806,
-0.009465780109167099,
-0.014917589724063873,
-0.00006548783858306706,
-0.022859014570713043,
0.027464760467410088,
-0.04864773526787758,
0.004167772363871336,
-0.010125997476279736,
0.02225181646645069,
0.033379197120666504,
0.011208980344235897,
-0.0016104893293231726,
-0.006844076327979565,
0.0561763271689415,
0.02820143662393093,
0.016453079879283905,
0.00735732214525342,
0.008340591564774513,
0.05189099162817001,
0.007628541439771652,
0.01057848148047924,
0.03697932884097099,
-0.015010513365268707,
0.0295577235519886,
0.07059576362371445,
-0.0300135500729084,
-0.046104077249765396,
0.004377284552901983,
0.024298924952745438,
0.014021669514477253,
-0.004933688323944807,
-0.047893282026052475,
-0.05515468120574951,
-0.04456716775894165,
0.014870514161884785,
0.060756098479032516,
-0.008794326335191727,
0.003379737725481391,
-0.010712845250964165,
-0.010740085504949093,
-0.009654371999204159,
-0.0017868953291326761,
-0.017329201102256775,
0.03091702237725258,
-0.014933176338672638,
0.026370670646429062,
-0.01233583316206932,
-0.013139480724930763,
0.006347267422825098,
-0.02522556483745575,
0.0365244597196579,
0.059185855090618134,
0.02791888453066349,
-0.010015476495027542,
-0.008997573517262936,
-0.02528349682688713,
-0.08655516058206558,
0.025933725759387016,
0.03781171143054962,
-0.022069672122597694,
-0.0662941038608551,
0.007079565431922674,
0.056357044726610184,
-0.015742124989628792,
0.006030927877873182,
-0.007138518616557121,
0.0004190268518868834,
-0.02189110592007637,
-0.08910781145095825,
-0.06152234226465225,
-0.0005852016038261354,
-0.008524193428456783,
-0.019869767129421234,
-0.05450528487563133,
-0.02353016287088394,
0.042003072798252106,
0.12181980162858963,
-0.04915085807442665,
0.015433570370078087,
0.0032910783775150776,
0.02648298256099224,
0.021124325692653656,
0.029132086783647537,
-0.03588894382119179,
-0.003257220610976219,
-0.0035550580359995365,
-0.03745162859559059,
-0.0214864332228899,
0.04210280627012253,
0.021175269037485123,
-0.04847745969891548,
0.02898855321109295,
0.07702035456895828,
-0.019169863313436508,
0.015016878955066204,
0.016554033383727074,
-0.0003577939060050994,
-0.03735097497701645,
0.059814196079969406,
0.01359520759433508,
-0.0063785770907998085,
0.048071809113025665,
-0.0606062225997448,
0.0018490221118554473,
-0.010220061987638474,
0.03387582302093506,
0.04177199304103851,
-0.0035353428684175014,
-0.03565481677651405,
-0.051119863986968994,
0.005830091889947653,
-0.017328709363937378,
0.007137599401175976,
-0.030996307730674744,
-0.030500467866659164,
0.05801354721188545,
0.028897736221551895,
0.050652094185352325,
0.03167721629142761,
-0.028386037796735764,
0.020969467237591743,
-0.046489134430885315,
-0.010159281082451344,
-0.047789014875888824,
0.0016427040100097656,
-0.01896359771490097,
-0.033156659454107285,
0.08406487852334976,
0.02228642627596855,
-0.009791174903512001,
0.02894691377878189,
-0.051533665508031845,
0.01985502801835537,
0.035195060074329376,
0.031891100108623505,
-0.012787295505404472,
0.02086564339697361,
0.0530536063015461,
0.03304741159081459,
0.031834159046411514,
0.035350553691387177,
-0.007203165907412767,
-0.010709199123084545,
-0.0045607080683112144,
-0.016873979941010475,
0.044080089777708054,
0.021362176164984703,
0.015334365889430046,
-0.028059130534529686,
-0.00005392494858824648,
-0.01770191639661789,
0.022225847467780113,
-0.04631216824054718,
0.04445381462574005,
0.07661732286214828,
-0.03299395740032196,
-0.019543742761015892,
0.04271647706627846,
0.028898155316710472,
0.040251776576042175,
0.004763753619045019,
-0.015982599928975105,
-0.034855641424655914,
0.000906724133528769,
0.03418651223182678,
0.013846593908965588,
-0.041811950504779816,
-0.00397972296923399,
0.01984705962240696,
0.02092653699219227,
0.039121199399232864,
-0.006776849273592234,
-0.029738575220108032,
-0.029157502576708794,
0.017417799681425095,
-0.025613438338041306,
0.0010550860315561295,
0.008861596696078777,
0.057951170951128006,
0.014773549512028694,
-0.006538657937198877,
0.013301130384206772,
-0.04676893725991249,
0.03618231415748596,
0.006105387583374977,
-0.0062012262642383575,
0.029645930975675583,
-0.04812171682715416,
0.04506608471274376,
-0.0008635682752355933,
0.03075089491903782,
0.03962871804833412,
-0.038565486669540405,
-0.020346971228718758,
-0.0011139893904328346,
0.00027402324485592544,
0.02440856769680977,
-0.0014040255919098854,
-0.01464281789958477,
-0.020321430638432503,
0.004069512244313955,
-0.02246098406612873,
-0.04139595851302147,
-0.022986311465501785,
-0.02187340334057808,
0.018156636506319046,
-0.023832812905311584,
0.03645598143339157,
0.015150838531553745,
0.034739233553409576,
-0.02167530171573162,
-0.010316403582692146,
0.030267156660556793,
-0.015334186144173145,
0.0708032175898552,
0.051013343036174774,
-0.05943721905350685,
0.02426306903362274,
-0.0866553857922554,
-0.012251454405486584,
0.016436858102679253,
-0.004045731388032436,
-0.002726644976064563,
-0.02805609628558159,
-0.04708552360534668,
-0.05791298300027847,
-0.023476416245102882,
-0.03398522734642029,
0.0008504826109856367,
-0.07377365231513977,
0.0235348641872406,
0.039009109139442444,
0.03144581988453865,
-0.047118935734033585,
0.008668102324008942,
0.01736254058778286,
-0.05617449805140495,
-0.01993141882121563,
-0.020633917301893234,
0.029508836567401886,
-0.03102235682308674,
0.01652996800839901,
0.03528469800949097,
-0.03929359093308449,
0.012145135551691055,
-0.06728693842887878,
-0.036399465054273605,
-0.01315718051046133,
0.022683843970298767,
-0.00028184877010062337,
0.006803753785789013,
-0.030725987628102303,
0.1063900887966156,
-0.007193205878138542,
0.010430552996695042,
0.0016944350209087133,
0.027931097894906998,
0.013423372991383076,
-0.008317717351019382,
0.015811597928404808,
0.028336351737380028,
-0.00849209725856781,
0.026334647089242935,
-0.030794980004429817,
0.05295079946517944,
0.04144635424017906,
0.003779898164793849,
-0.00014800656936131418,
0.03980877622961998,
-0.0031806547194719315,
-0.011302469298243523,
0.05742190033197403,
-0.0018177246674895287,
-0.005478051491081715,
0.05902428179979324,
-0.017461102455854416,
-0.005791004281491041,
0.03233427181839943,
-0.034838154911994934,
0.04374009743332863,
0.01006627269089222,
0.022958092391490936,
-0.01990792527794838,
0.07113352417945862,
0.00392088433727622,
-0.0453365184366703,
-0.018997754901647568,
0.005529080517590046,
0.05494709685444832,
-0.023780344054102898,
0.010494916699826717,
0.03856177255511284,
0.01221104059368372,
-0.04260668158531189,
-0.03709198534488678,
-0.01869162544608116,
0.014222853817045689,
0.010007180273532867,
-0.04346167668700218,
-0.045504845678806305,
0.011361127719283104,
0.05877165496349335,
0.0179901085793972,
-0.015222352929413319,
-0.024401430040597916,
-0.008032227866351604,
-0.05041508749127388,
-0.012537561357021332,
-0.03369084745645523,
0.04279691353440285,
-0.019053371623158455,
0.05771561339497566,
0.030223684385418892,
0.02042258344590664,
0.0072267064824700356,
0.007768436800688505,
-0.08411479741334915,
0.005496995523571968,
-0.00038762466283515096,
0.009881215170025826,
-0.01666371338069439,
0.003233398078009486,
0.015237522311508656,
-0.04809294641017914,
-0.040887318551540375,
-0.011088509112596512,
-0.041092123836278915,
-0.04559221863746643,
0.029685128480196,
-0.03191794082522392,
-0.03416372090578079,
-0.000054992258810671046,
0.07269330322742462,
0.021846888586878777,
-0.04849511384963989,
-0.0048293378204107285,
0.037693921476602554,
-0.03685455769300461,
0.04146454855799675,
-0.03055235743522644,
0.01692122034728527,
0.045281652361154556,
0.006988251581788063,
0.0377667099237442,
0.009836683049798012,
-0.01501323189586401,
0.0030215031001716852,
0.008431847207248211,
0.07579462975263596,
0.005912406835705042,
-0.022561725229024887,
0.017039883881807327,
-0.017426326870918274,
0.02529015578329563,
-0.02580011822283268,
0.060873955488204956,
0.019763201475143433,
0.03400937467813492,
0.017949510365724564,
0.015147816389799118,
-0.001880174153484404,
0.01773536205291748,
0.030594324693083763,
0.00016434017743449658,
0.010256480425596237,
-0.029431665316224098,
0.026205888018012047,
-0.0042643798515200615,
-0.0218088086694479,
-0.03350444883108139,
-0.042620569467544556,
-0.031868718564510345,
0.03315673768520355,
0.018926924094557762,
0.008996700868010521,
-0.05106398090720177,
0.0070824702270329,
-0.04373331740498543,
-0.0041189477778971195,
-0.012615866027772427,
-0.024280525743961334,
0.012320653535425663,
0.03298768773674965,
-0.006581879686564207,
-0.0003855492395814508,
0.006486705970019102,
-0.029554009437561035,
-0.015043176710605621,
0.04088279604911804,
0.02400684915482998,
0.028488554060459137,
-0.007250816095620394,
-0.01966092921793461,
-0.03676312044262886,
0.04604557156562805,
0.012616628780961037,
0.028376590460538864,
0.006596691440790892,
-0.008252285420894623,
-0.018946267664432526,
-0.03839299455285072,
-0.04150453582406044,
0.03284949064254761,
-0.03561410307884216,
0.042926572263240814,
-0.056512266397476196,
0.013537679798901081,
-0.025002839043736458,
-0.0005073847132734954,
-0.004620111081749201,
0.04244473949074745,
-0.007232411298900843,
-0.02583068422973156,
0.000026003795937867835,
0.021732691675424576,
-0.0381251685321331,
-0.1001216396689415,
-0.0013533160090446472,
-0.0012987435329705477,
0.00460289278998971,
0.020835233852267265,
-0.0252919290214777,
-0.04760054871439934,
0.035703759640455246,
-0.01345222257077694,
0.0156753771007061,
0.008934887126088142,
-0.02596184052526951,
0.08226015418767929,
0.040855035185813904,
0.0015570326941087842,
0.057007595896720886,
0.03479056805372238,
-0.016833828762173653,
0.011110794730484486,
-0.053347449749708176,
0.003248094115406275,
-0.019474709406495094,
0.01753518544137478,
-0.06711972504854202,
-0.02381616085767746,
-0.029583150520920753,
0.041862815618515015,
-0.03254517912864685,
0.02058207429945469,
0.009443916380405426,
-0.0056021492928266525,
-0.020466694608330727,
0.018993135541677475,
-0.02340034209191799,
-0.005495293531566858,
-0.017814865335822105,
0.03634139150381088,
0.04709441959857941,
-0.02127033658325672,
0.023769943043589592,
-0.02525123953819275,
-0.010383752174675465,
0.040868982672691345,
-0.029162753373384476,
0.021008672192692757,
-0.04586634039878845,
-0.02760498784482479,
-0.019654404371976852,
-0.04701188951730728,
0.021944312378764153,
-0.02964995615184307,
-0.002612854354083538,
0.0006140545592643321,
-0.03843085840344429,
-0.05789240822196007,
0.06095554679632187,
0.0069542741402983665,
-0.06218428164720535,
-0.03229435160756111,
-0.03456176444888115,
0.04499028995633125,
0.004275286570191383,
-0.06594172865152359,
-0.029999010264873505,
-0.012182949110865593,
-0.01610194519162178,
-0.00474039651453495,
-0.010039311833679676,
0.006734682712703943,
0.02442057430744171,
-0.01904849335551262,
0.027883686125278473,
0.00864280853420496,
-0.010922620072960854,
0.000037718858948210254,
0.022686023265123367,
0.010074385441839695,
0.033522624522447586,
-0.027770761400461197,
-0.012980062514543533,
-0.012029331177473068,
-0.006388925947248936,
0.018289269879460335,
0.02383670024573803,
0.02209950052201748,
-0.013504558242857456,
-0.04548455774784088,
-0.012234623543918133,
-0.0021741788368672132,
0.015272373333573341,
-0.009830792434513569,
0.0007726823096163571,
-0.018981019034981728,
0.00030897671240381896,
0.015294923447072506,
-0.013876170851290226,
-0.03200078010559082,
-0.005209166090935469,
0.014007778838276863,
0.005153406877070665,
0.02330765500664711,
-0.02798454277217388,
-0.03267133608460426,
0.017650095745921135,
-0.01886351779103279,
-0.021382706239819527,
0.009120342321693897,
0.06066706404089928,
-0.006198341958224773,
0.015805035829544067,
0.03284253552556038,
-0.00527438148856163,
0.007082833442837,
-0.0032763103954494,
0.016370480880141258,
-0.013755341060459614,
0.026424605399370193,
-0.024270890280604362,
-0.0015929907094687223,
-0.027905791997909546,
0.022678695619106293,
0.03751049563288689,
0.014361899346113205,
0.02103639766573906,
0.002596716396510601,
0.014171591028571129,
-0.030945533886551857,
-0.030017249286174774,
-0.010248212143778801,
0.0007157312356866896,
0.009580625221133232,
0.052192989736795425,
-0.03711359575390816,
-0.01133288349956274,
0.05679194629192352,
0.038368962705135345,
-0.0311847273260355,
0.004160089418292046,
-0.007667526602745056,
-0.009229308925569057,
0.03975781053304672,
-0.01747605763375759,
-0.039389822632074356,
0.03671470656991005,
-0.0031786875333637,
0.035544268786907196,
-0.013599160127341747,
-0.04778434708714485,
0.050275105983018875,
0.01778361201286316,
0.025866355746984482,
-0.04140924662351608,
-0.00662538968026638,
-0.03645777702331543,
0.008753238245844841,
0.03110959753394127,
-0.005104889627546072,
0.019100049510598183,
0.03204318881034851,
0.045335397124290466,
-0.01954410970211029,
0.004012652672827244,
-0.01624576561152935,
-0.036825526505708694,
-0.0011294815922155976,
-0.04615841060876846,
-0.05220787972211838,
0.033283039927482605,
-0.03307193145155907,
-0.014891894534230232,
0.012524895370006561,
0.010215220972895622,
0.036492109298706055,
-0.004447383806109428,
0.015556027181446552,
-0.03834914416074753,
0.05457814037799835,
-0.000018564998754300177,
0.04223056137561798,
0.008854779414832592,
0.005132703576236963,
0.14400222897529602,
0.012207495979964733,
0.031408507376909256,
-0.03967548906803131,
0.008284867741167545,
-0.020190855488181114,
-0.0024478361010551453,
0.003863056655973196,
0.03783969581127167,
0.00384651985950768,
-0.016914499923586845,
-0.004610750358551741,
0.06216476857662201,
0.013942300342023373,
-0.013996714726090431,
0.03434768319129944,
-0.043675731867551804,
-0.036479540169239044,
-0.005687500815838575,
0.029237471520900726,
-0.01852564886212349,
0.011831196956336498,
-0.03268641233444214,
0.003784121247008443,
-0.037247270345687866,
0.02755785919725895,
-0.031131820753216743,
-0.03466570004820824,
0.021309858188033104,
0.025838999077677727,
-0.04964460805058479,
0.00869675911962986,
0.021248335018754005,
0.012537546455860138,
0.006113962270319462,
0.04379163682460785,
0.03436457738280296,
-0.05263567715883255,
0.04303381219506264,
0.042969390749931335,
-0.02655346691608429,
0.03456059470772743,
0.002989939646795392,
-0.0025178599171340466,
-0.04005143791437149,
0.0039658923633396626,
-0.029325412586331367,
0.05906049534678459,
-0.020312920212745667,
-0.020289892330765724,
0.01348405983299017,
-0.011292746290564537,
0.041936829686164856,
-0.0347943939268589,
-0.004850628320127726,
0.02895989641547203,
0.02677167020738125,
-0.01623205840587616,
0.037570253014564514,
0.00862523540854454,
0.024117425084114075,
0.01789836399257183,
0.011068202555179596,
-0.022912658751010895,
-0.03783813491463661,
0.025722138583660126,
0.031918108463287354,
0.021888308227062225,
0.02072560228407383,
-0.02835390716791153,
-0.009530745446681976,
0.016656436026096344,
-0.038189128041267395,
-0.02476990409195423,
0.06747117638587952,
0.03438589721918106,
0.03758734464645386,
-0.012468166649341583,
0.011517067439854145,
-0.01876070909202099,
-0.07255107164382935,
0.011733869090676308,
-0.02533550001680851,
-0.021486489102244377,
0.01409563422203064,
-0.009087794460356236,
0.02194654941558838,
0.06110670045018196,
-0.04276169463992119,
-0.010923500172793865,
0.009376433677971363,
0.032969024032354355,
0.05454910174012184,
-0.05883585289120674,
-0.0341620072722435,
0.016787003725767136,
-0.028123758733272552,
0.02086956426501274,
-0.009750944562256336,
0.011139798909425735,
0.024047236889600754,
0.036062244325876236,
-0.029368268325924873,
0.06023331731557846,
0.019361117854714394,
-0.03370851278305054,
0.0019952780567109585,
0.015315936878323555,
-0.013185680843889713,
0.0233592689037323,
0.026450635865330696,
-0.03766200318932533,
-0.009972608648240566,
-0.005005275830626488,
-0.003057850291952491,
0.025414541363716125,
-0.004690815228968859,
-0.040121376514434814,
-0.040073566138744354,
0.0058574071153998375,
-0.004212507978081703,
-0.017630908638238907,
0.008449065499007702,
-0.012535184621810913,
0.039236653596162796,
-0.006946047302335501,
-0.016282126307487488,
0.0003595102170947939,
0.031053168699145317,
-0.018647832795977592,
-0.030065244063735008,
0.03227733075618744,
0.013547630980610847,
-0.016208741813898087,
-0.01982259936630726,
0.034312330186367035,
-0.026054413989186287,
0.038492005318403244,
0.023631872609257698,
-0.0070702508091926575,
-0.005303532350808382,
-0.013782940804958344,
-0.019508760422468185,
0.009248306043446064,
-0.001368073164485395,
0.05527224391698837,
0.025877006351947784,
-0.004893443547189236,
-0.04701610654592514,
-0.013816062361001968,
-0.04900306463241577,
-0.02050377056002617,
-0.02589663304388523,
-0.018136395141482353,
0.01053132489323616,
-0.03527483716607094,
0.0137507738545537,
-0.018543606624007225,
0.007409658282995224,
0.015609607100486755,
-0.0010050112614408135,
-0.0463319793343544,
-0.004112772643566132,
0.006245369557291269,
-0.009650349617004395,
0.03626571223139763,
0.03307218849658966,
-0.027846399694681168,
-0.007813146337866783,
0.045622967183589935,
-0.004781430587172508,
0.03952839970588684,
0.03381885215640068,
0.019147079437971115,
-0.09821333736181259,
-0.023043258115649223,
0.0027569523081183434,
-0.0012760094832628965,
0.022758664563298225,
-0.06019991636276245,
0.03495645150542259,
0.01871398463845253,
-0.059319715946912766,
0.04883439466357231,
-0.036269836127758026,
0.0028572995215654373,
-0.037162426859140396,
0.0037615534383803606,
-0.05870921164751053,
0.05363516882061958,
0.027094075456261635,
0.04317077249288559,
-0.04590737819671631,
-0.008003010414540768,
-0.016003696247935295,
-0.04019290208816528,
-0.03047100640833378,
-0.002465832745656371,
-0.025510257109999657,
-0.037612635642290115,
0.057742223143577576,
-0.02955658547580242,
-0.02723795920610428,
0.020735522732138634,
-0.02251366525888443,
-0.011081176809966564,
-0.015575596131384373,
0.040600765496492386,
-0.003478916361927986,
0.0467548668384552,
-0.00554825272411108,
-0.007379296701401472,
-0.01193935051560402,
-0.02094135992228985,
0.039296094328165054,
0.01733255386352539,
-0.013318168930709362,
0.015492989681661129,
-0.028964422643184662,
-0.024785440415143967,
-0.024151328951120377,
0.028531232848763466,
-0.017028043046593666,
-0.021564306691288948,
-0.005353962536901236,
0.014852484688162804,
0.023299066349864006,
-0.004874050617218018,
0.03924243152141571,
-0.03792119398713112,
0.002680320292711258,
0.005855582654476166,
0.003991578705608845,
-0.023080384358763695,
0.0026435002218931913,
-0.025970399379730225,
-0.04883033037185669,
0.026703501120209694,
0.01580096408724785,
0.003404135350137949,
-0.020899029448628426,
-0.04767891764640808,
0.013972115702927113,
0.03905097022652626,
0.029290713369846344,
-0.030635004863142967,
-0.007093233522027731,
0.01093977876007557,
-0.014204699546098709,
0.015342703089118004,
-0.02238684706389904,
-0.04467302933335304,
0.0009233836317434907,
-0.06418906897306442,
0.03362978622317314,
0.03876655176281929,
-0.01991884596645832,
0.002318226033821702,
-0.007597649469971657,
-0.020084816962480545,
0.002374473260715604,
0.05845968797802925,
0.006304910406470299,
-0.02339188940823078,
0.012847159057855606,
0.010527759790420532,
0.00981125794351101,
-0.029966378584504128,
-0.006583924405276775,
-0.017536433413624763,
0.005552549846470356,
0.015130926854908466,
0.01105035562068224,
-0.013594578020274639,
0.04309524968266487,
0.01202858705073595,
-0.024625631049275398,
-0.01179961021989584,
0.015405802056193352,
-0.06525658816099167,
0.04650483652949333,
-0.006927162408828735,
-0.012158961966633797,
0.0529240183532238,
0.0019578831270337105,
0.03609960526227951,
0.029130548238754272,
-0.015364560298621655,
-0.02786090038716793,
-0.010156385600566864,
-0.0011608792701736093,
-0.03901885449886322,
-0.010652023367583752,
-0.022322148084640503,
0.04536578059196472,
-0.05206356942653656,
0.004417662043124437,
0.03445090353488922,
-0.04393512010574341,
-0.03523433208465576,
0.03695306554436684,
0.009876655414700508,
0.01630881056189537,
-0.0046672821044921875,
0.006897849030792713,
0.019346781075000763,
0.0019807026255875826,
0.04363531619310379,
0.024860024452209473,
0.0041315290145576,
0.05146893858909607,
0.01378385815769434,
0.056382521986961365,
-0.031012382358312607,
0.013759617693722248,
-0.002328758127987385,
0.04492158815264702,
-0.021062839776277542,
0.023113613948225975,
0.04054618254303932,
-0.03242255747318268,
0.01567116752266884,
-0.01309897843748331,
-0.039427414536476135,
0.09197242558002472,
-0.013014474883675575,
0.040861837565898895,
-0.05256263539195061,
0.007604736369103193,
-0.00047991337487474084,
-0.0068941800855100155,
0.02027030847966671,
0.042202260345220566,
-0.04100817069411278,
-0.039376888424158096,
-0.04599226638674736,
-0.005949344485998154,
0.018017491325736046,
-0.04028846323490143,
0.004590857774019241,
-0.003132074838504195,
-0.0013141834642738104,
-0.0018004374578595161,
-0.023209862411022186,
-0.02554645948112011,
-0.017879923805594444,
0.03989935293793678,
0.027848295867443085,
-0.010153240524232388,
0.008137439377605915,
-0.007935374975204468,
-0.01777862198650837,
0.02433333545923233,
-0.02384861931204796,
-0.011012488044798374,
-0.009878280572593212,
0.02870688959956169,
0.01031420100480318,
0.011444123461842537
] |
<p>I found the problem described in the attached picture on the internet. In the comment sections there were two opposing solutions. So it made me wonder which of those would be the actual solution.</p>
<p>So basically the question would be the following. Assume we would have two identical beakers, filled with the same amount of the same liquid, lets say water. In the left beaker a ping pong ball would be attached to the bottom of the beaker with a string and above the right beaker a steel ball of the same size (volume) as the ping pong ball would be hung by a string, submerging the steel ball in the water as shown in the picture. If both beakers would be put on to a scale, what side would tip?</p>
<p>According to the internet either of the following answers was believed to be the solution.</p>
<ol>
<li>The left side would tip down, because the ping pong ball and the cord add mass to the left side, since they are actually connected to the system.</li>
<li>The right side would tip down, because of buoyancy of the water on the steel ball pushing the steel ball up and the scale down.</li>
</ol>
<p>Now what would the solution be according to physics?</p>
<p><img src="http://i.stack.imgur.com/Mj3Y0.jpg" alt="enter image description here"></p>
| 10,718 |
[
-0.050957296043634415,
-0.016315191984176636,
-0.02929498814046383,
0.006425612606108189,
0.006671106442809105,
-0.01310049369931221,
-0.02165629155933857,
0.038531139492988586,
0.016570409759879112,
0.00451870309188962,
0.046435363590717316,
0.05223723128437996,
0.04867670312523842,
0.022632595151662827,
0.041008830070495605,
0.05191586911678314,
0.0024272094015032053,
-0.008144097402691841,
-0.005725806578993797,
-0.015935664996504784,
-0.021038683131337166,
0.007186452392488718,
0.014348946511745453,
-0.014221744611859322,
-0.020493537187576294,
0.015473204664885998,
0.03294907882809639,
-0.023537199944257736,
-0.0020397319458425045,
0.0630662813782692,
0.006659126374870539,
-0.028366198763251305,
-0.004429755266755819,
-0.009322769939899445,
0.014621841721236706,
-0.021556640043854713,
0.016714002937078476,
-0.015276351943612099,
0.0018670757999643683,
0.007966248318552971,
-0.01432601548731327,
-0.00024011664208956063,
-0.007174852304160595,
0.015133052133023739,
-0.0234523955732584,
0.023076949641108513,
-0.017191190272569656,
-0.016921276226639748,
0.043500110507011414,
-0.07410722225904465,
0.05289563909173012,
0.020165331661701202,
0.04279486462473869,
0.03285832330584526,
-0.013888835906982422,
-0.00692242244258523,
0.05436798930168152,
0.05701049417257309,
0.006962749175727367,
-0.08888513594865799,
-0.026933884248137474,
0.014950329437851906,
-0.055241964757442474,
0.004809211473912001,
-0.02892206981778145,
0.03259570524096489,
-0.04188564792275429,
0.013070391491055489,
0.013416383415460587,
-0.018904320895671844,
-0.009835808537900448,
0.02600700780749321,
0.07154010236263275,
-0.020631881430745125,
0.02085176855325699,
-0.026950495317578316,
0.01613839901983738,
0.028142964467406273,
0.01569388620555401,
0.022633451968431473,
0.014124073088169098,
0.010800319723784924,
0.04316806420683861,
0.07232990115880966,
0.024647898972034454,
-0.0462704598903656,
0.036012955009937286,
-0.014992122538387775,
0.015186244621872902,
0.0589107945561409,
-0.014030123129487038,
0.03265604376792908,
0.019409487023949623,
-0.0064900959841907024,
0.025638926774263382,
0.014108630828559399,
0.00597535353153944,
0.056157685816287994,
-0.0086809191852808,
-0.005828511901199818,
0.020783960819244385,
-0.014745435677468777,
0.0011554077500477433,
0.10697052627801895,
0.015408391132950783,
-0.011602150276303291,
-0.020718980580568314,
0.035089392215013504,
-0.0012376452796161175,
0.0013967108679935336,
-0.032059792429208755,
0.0005954178050160408,
-0.007852395065128803,
0.012949186377227306,
0.019836967810988426,
-0.019149543717503548,
0.012378460727632046,
-0.009752384386956692,
0.05062625929713249,
-0.011067469604313374,
0.015890277922153473,
-0.020721742883324623,
0.039006877690553665,
-0.02089458331465721,
-0.039697304368019104,
0.020612575113773346,
0.0265376977622509,
-0.02544109709560871,
-0.036684196442365646,
0.034684158861637115,
0.011431822553277016,
-0.012112540192902088,
0.019113996997475624,
0.0027100928127765656,
0.046361085027456284,
-0.011789613403379917,
-0.10431752353906631,
-0.06016811728477478,
0.060660604387521744,
-0.004071479197591543,
-0.0436532236635685,
-0.07516030222177505,
-0.0049404907040297985,
0.047584109008312225,
0.07216641306877136,
-0.005305980797857046,
0.012532760389149189,
-0.012337734922766685,
0.046271149069070816,
-0.014299292117357254,
0.05014045536518097,
-0.020701948553323746,
-0.012803272344172001,
-0.018371127545833588,
0.022837407886981964,
-0.057313550263643265,
-0.004604944959282875,
0.03561956807971001,
0.0004821592301595956,
-0.031655240803956985,
0.019008837640285492,
0.0015358822420239449,
-0.0008523845463059843,
-0.018885215744376183,
0.0033240749035030603,
-0.05717288330197334,
0.0680023804306984,
-0.023845940828323364,
-0.020457662642002106,
0.054486069828271866,
-0.037260882556438446,
0.01217702031135559,
-0.004739892203360796,
-0.012810351327061653,
0.028734374791383743,
-0.00045994031825102866,
-0.029036972671747208,
-0.03278366103768349,
0.016919583082199097,
0.0223294235765934,
-0.03132445365190506,
0.004718429408967495,
0.0017691643442958593,
0.0019203642150387168,
0.036460671573877335,
0.04216979816555977,
0.007691137958317995,
-0.03316837176680565,
0.005034483969211578,
-0.02889666147530079,
-0.011876673437654972,
-0.049306463450193405,
-0.010260172188282013,
-0.02321684919297695,
-0.009034432470798492,
0.0412924624979496,
-0.004418292548507452,
0.017457103356719017,
-0.029381634667515755,
-0.0075856540352106094,
0.004441263619810343,
0.04336158186197281,
0.010891038924455643,
0.051132261753082275,
0.019131219014525414,
0.041937705129384995,
0.04165399819612503,
-0.02421582117676735,
-0.01062360405921936,
-0.025014672428369522,
-0.028926469385623932,
0.0030881520360708237,
-0.0018500522710382938,
0.0255744531750679,
-0.0028282899875193834,
0.009396250359714031,
0.003554107854142785,
-0.011299342848360538,
-0.02016514539718628,
0.020923569798469543,
-0.030591366812586784,
0.07646330446004868,
0.037071242928504944,
0.005301712546497583,
0.019619546830654144,
0.01404054369777441,
0.024388188496232033,
0.04673141613602638,
0.007506543770432472,
-0.02671937271952629,
-0.06276382505893707,
-0.007433275226503611,
-0.022096509113907814,
0.02710092067718506,
-0.02912883646786213,
0.013631198555231094,
0.011976622976362705,
0.027887480333447456,
0.0056681702844798565,
0.026278963312506676,
-0.013678290881216526,
-0.024332446977496147,
0.006161668337881565,
0.033067554235458374,
-0.013903521001338959,
0.02733408473432064,
0.01608792319893837,
0.007729345932602882,
0.020310256630182266,
-0.01929798349738121,
-0.010431990027427673,
-0.0008421129314228892,
0.011751261539757252,
0.01763118989765644,
-0.0027324880938977003,
-0.003946941811591387,
0.03160066902637482,
-0.027329450473189354,
0.010501713491976261,
0.008055553771555424,
-0.0032203698065131903,
-0.004626512993127108,
0.0009271251619793475,
0.014658146537840366,
-0.021282577887177467,
0.008078980259597301,
-0.014271104708313942,
-0.005838179960846901,
0.021368587389588356,
-0.039945926517248154,
0.0035796372685581446,
-0.01914934068918228,
0.048038188368082047,
-0.014129923656582832,
0.03221261128783226,
0.04048927128314972,
-0.0023836297914385796,
0.015337284654378891,
-0.03467663750052452,
-0.018086083233356476,
-0.030668659135699272,
-0.036388032138347626,
-0.027322063222527504,
0.019258305430412292,
-0.04796239733695984,
-0.002773107262328267,
-0.01154114305973053,
-0.018147841095924377,
0.03385593742132187,
0.011305139400064945,
0.017957711592316628,
0.026788270100951195,
0.025045795366168022,
-0.025580396875739098,
-0.04520740360021591,
-0.02895820513367653,
0.01050922367721796,
-0.020881904289126396,
-0.00500259455293417,
0.05989900976419449,
0.05403478816151619,
-0.024779818952083588,
0.03937990963459015,
-0.04211695119738579,
-0.0683283880352974,
0.013613785617053509,
0.01885230466723442,
0.009045260958373547,
-0.037095557898283005,
0.0005689057870768011,
0.017564766108989716,
-0.00838792696595192,
-0.059921350330114365,
-0.05462028831243515,
-0.05736005678772926,
0.016423678025603294,
0.008068494498729706,
0.046063512563705444,
0.014399264939129353,
-0.0023144131992012262,
0.0889996737241745,
-0.0021102968603372574,
-0.0032239712309092283,
-0.030295120552182198,
0.007087798323482275,
-0.01814460940659046,
-0.0365084633231163,
0.029577378183603287,
0.06407804042100906,
-0.011902336962521076,
0.0402233824133873,
0.03897447511553764,
0.01790504902601242,
0.016006333753466606,
0.056666962802410126,
0.034902576357126236,
-0.00351508054882288,
0.015747206285595894,
-0.019343486055731773,
0.07610031217336655,
-0.0035608091857284307,
0.0024969177320599556,
-0.028334923088550568,
-0.0037034510169178247,
0.053597159683704376,
0.0014940849505364895,
-0.024541540071368217,
0.06789633631706238,
-0.0017912192270159721,
0.0036650579422712326,
-0.024757020175457,
0.027527712285518646,
0.017025144770741463,
-0.003184086410328746,
0.02011343277990818,
0.027255194261670113,
0.03794857859611511,
-0.006460393313318491,
-0.016484089195728302,
0.05966612696647644,
0.04749045893549919,
-0.03023715317249298,
-0.052087124437093735,
-0.024095281958580017,
0.01944449357688427,
0.0193053986877203,
-0.024356231093406677,
-0.03520992025732994,
0.03142916038632393,
0.006088371854275465,
0.04968675225973129,
0.0023187485057860613,
-0.031540364027023315,
-0.032847240567207336,
-0.10044191032648087,
0.005669280420988798,
0.0016353614628314972,
0.03785884752869606,
0.017320511862635612,
0.018827693536877632,
0.0472596101462841,
0.044923149049282074,
0.011100451461970806,
0.005359362810850143,
-0.09449572116136551,
0.048407040536403656,
-0.04304076358675957,
0.0010292857186868787,
-0.015771031379699707,
-0.0020796540193259716,
-0.036750428378582,
-0.017501812428236008,
-0.009774950332939625,
0.012917990796267986,
0.030802709981799126,
-0.038207847625017166,
0.038393788039684296,
-0.026832234114408493,
0.00010823942284332588,
0.057086359709501266,
0.009122592397034168,
0.023400848731398582,
-0.020358333364129066,
0.018677307292819023,
0.0029071976896375418,
-0.017375290393829346,
-0.007746164686977863,
-0.007091475185006857,
0.015233933925628662,
0.025642458349466324,
0.010554177686572075,
-0.0029262250754982233,
0.04488148167729378,
-0.012190344743430614,
-0.004714283160865307,
0.03194807097315788,
0.024157600477337837,
-0.022767798975110054,
-0.0484750010073185,
-0.031493719667196274,
-0.03877909481525421,
-0.013936378061771393,
-0.01738191954791546,
0.061249665915966034,
-0.011009067296981812,
0.04646189138293266,
0.001753753749653697,
-0.006268290337175131,
-0.0012074410915374756,
0.04299969971179962,
0.03411344811320305,
0.042089011520147324,
-0.010700853541493416,
-0.039083585143089294,
-0.039189018309116364,
-0.03109949268400669,
0.002578407060354948,
0.034826260060071945,
0.015250901691615582,
-0.0043753148056566715,
0.004321499262005091,
0.046015601605176926,
0.0249368567019701,
-0.0029360498301684856,
0.015950985252857208,
0.001620616065338254,
0.047012344002723694,
-0.04745255410671234,
0.006134010385721922,
0.01920424960553646,
0.027094969525933266,
0.011730075813829899,
-0.008390658535063267,
-0.009861066937446594,
-0.07946363836526871,
-0.04252559691667557,
-0.004363843239843845,
0.037822552025318146,
-0.061348460614681244,
0.02061491273343563,
-0.03863122686743736,
-0.03781653195619583,
0.058368977159261703,
-0.03663640469312668,
0.05879850313067436,
0.0021604516077786684,
0.02383527345955372,
-0.010324414819478989,
-0.007946062833070755,
0.006810092367231846,
0.008047863841056824,
-0.03366946056485176,
0.008876255713403225,
-0.011201174929738045,
-0.011556112207472324,
0.0015614093281328678,
0.01306355744600296,
0.04004755988717079,
0.04006905481219292,
-0.000034838270948966965,
0.006636927369982004,
0.017355840653181076,
0.023689506575465202,
-0.028707945719361305,
-0.09640521556138992,
0.003355436259880662,
-0.01460903137922287,
-0.03801942616701126,
0.006796868983656168,
-0.05450340732932091,
-0.04194919392466545,
0.05138599872589111,
0.008699791505932808,
0.007457107771188021,
0.012363624759018421,
-0.0063178339041769505,
0.04257313907146454,
0.06725306063890457,
-0.001269431202672422,
0.019364764913916588,
0.03546815365552902,
-0.008816973306238651,
-0.036467473953962326,
-0.01933125965297222,
-0.0317591093480587,
-0.03346185386180878,
0.02782532200217247,
-0.009849104098975658,
0.017789602279663086,
-0.058545809239149094,
0.039202578365802765,
0.0015586382942274213,
0.023396050557494164,
-0.019446903839707375,
-0.00871350709348917,
-0.007054828107357025,
0.014018532820045948,
0.030518870800733566,
-0.019034938886761665,
0.025457371026277542,
0.028178276494145393,
0.02419915981590748,
-0.039122603833675385,
0.02317008189857006,
-0.015591687522828579,
-0.013737830333411694,
-0.009046250954270363,
-0.026489483192563057,
0.03257467970252037,
-0.020604869350790977,
-0.038794368505477905,
0.002083205385133624,
-0.05626337230205536,
0.05950245261192322,
-0.01737738959491253,
0.0020022420212626457,
0.04324669390916824,
-0.030722523108124733,
-0.03144034743309021,
0.0017385073006153107,
0.01622353121638298,
0.006725007202476263,
-0.05010715872049332,
0.01056884229183197,
0.01751595549285412,
0.00022816003183834255,
-0.03692285716533661,
-0.049601390957832336,
0.0404626801609993,
0.021749133244156837,
-0.002502402989193797,
-0.03263932839035988,
-0.0431903675198555,
-0.020149456337094307,
-0.009810471907258034,
-0.005303769372403622,
0.011209001764655113,
-0.008934586308896542,
-0.02294563688337803,
0.02680778130888939,
-0.011842718347907066,
0.040792230516672134,
-0.010416551493108273,
-0.007800720632076263,
-0.006835575215518475,
-0.025894446298480034,
0.008032050915062428,
-0.009350842796266079,
0.05958077311515808,
-0.03022407740354538,
-0.046302225440740585,
0.02402697131037712,
-0.0018156387377530336,
0.048723142594099045,
0.0003934570122510195,
-0.0014764294028282166,
0.013997365720570087,
0.04580240324139595,
-0.008010108955204487,
0.007686696480959654,
0.05181005597114563,
0.033971287310123444,
0.0390218049287796,
-0.01918708346784115,
-0.013143791817128658,
-0.024545898661017418,
-0.06509078294038773,
0.013871037401258945,
0.001064957119524479,
-0.020187826827168465,
-0.006913389079272747,
0.049051422625780106,
0.0033819349482655525,
-0.03517209738492966,
0.01481727883219719,
0.03037366457283497,
0.04377131909132004,
-0.010221075266599655,
0.02529238536953926,
-0.005807152949273586,
0.0029627475887537003,
-0.017064934596419334,
0.0009359114337712526,
-0.03505290299654007,
0.0378788523375988,
0.07259991019964218,
-0.022595239803195,
0.06561098247766495,
0.023677486926317215,
-0.011015166528522968,
0.010996201075613499,
-0.004171303007751703,
-0.004403697792440653,
-0.03397710621356964,
0.027979249134659767,
0.02378791570663452,
-0.07556069642305374,
-0.010404386557638645,
0.04150795191526413,
0.002335185185074806,
-0.005907224025577307,
0.049199990928173065,
0.0658574178814888,
0.010743456892669201,
0.020951909944415092,
-0.037671275436878204,
-0.014696256257593632,
0.026956826448440552,
-0.026036765426397324,
0.07132331281900406,
-0.006837388500571251,
-0.03336808457970619,
0.0536530427634716,
-0.00043294450733810663,
-0.028187597170472145,
-0.07618594914674759,
0.002205666620284319,
-0.04414629936218262,
-0.018999507650732994,
-0.017731061205267906,
0.028077224269509315,
-0.0020127000752836466,
0.00012757816875819117,
0.02977048046886921,
0.04241267219185829,
0.03640357777476311,
-0.07338765263557434,
-0.045841507613658905,
-0.018855782225728035,
-0.023251837119460106,
-0.0583505816757679,
0.04713580757379532,
0.005674683954566717,
-0.016617488116025925,
0.014120985753834248,
-0.038912542164325714,
-0.04691062867641449,
0.009907695464789867,
0.01890476979315281,
-0.07205222547054291,
0.05085378512740135,
-0.015158544294536114,
0.0319208949804306,
-0.004869585856795311,
0.004438057076185942,
0.12207615375518799,
0.03759220615029335,
-0.011823204346001148,
-0.0429903045296669,
0.04317815229296684,
-0.003643075469881296,
0.01499877031892538,
-0.027513163164258003,
-0.01728655770421028,
-0.012876383028924465,
0.019717911258339882,
0.008235881105065346,
0.0658901035785675,
0.007975060492753983,
0.009006036445498466,
0.02514571323990822,
-0.04460763931274414,
-0.03976302966475487,
-0.0010469264816492796,
0.015025894157588482,
0.011035481467843056,
-0.021310757845640182,
-0.020789016038179398,
0.059795115143060684,
-0.03735841438174248,
-0.0069899908266961575,
-0.007163702510297298,
-0.03932977467775345,
0.015954872593283653,
0.03576887771487236,
-0.06304225325584412,
0.008557050488889217,
0.021402616053819656,
-0.04841361567378044,
-0.04604510962963104,
0.03750322014093399,
0.004030798561871052,
-0.025160547345876694,
0.016807185485959053,
0.005890157073736191,
0.030408024787902832,
0.01687878742814064,
0.02488281950354576,
0.005134369246661663,
-0.042938292026519775,
0.017702298238873482,
-0.03902382403612137,
0.007609806023538113,
0.012603379786014557,
-0.02161874622106552,
-0.01844521425664425,
-0.04687696322798729,
0.01645001582801342,
-0.04644745960831642,
-0.03582029417157173,
0.031014634296298027,
0.03415975719690323,
-0.0019617844372987747,
-0.000028233918783371337,
0.0021668702829629183,
0.03275894373655319,
0.021524138748645782,
0.001972546335309744,
0.028412319719791412,
0.02576858177781105,
0.0019578447099775076,
0.026973048225045204,
0.08270150423049927,
0.014000997878611088,
0.014131679199635983,
-0.029019391164183617,
0.010663582012057304,
-0.03028230182826519,
0.0023698846343904734,
0.005390029400587082,
0.04910243675112724,
0.015640290454030037,
0.027197163552045822,
0.03888474032282829,
-0.016673831269145012,
-0.03826182708144188,
0.023347297683358192,
-0.004136663395911455,
-0.006101623177528381,
-0.06340718269348145,
-0.04316863417625427,
0.011727932840585709,
0.036308031529188156,
0.004199432209134102,
-0.010578345507383347,
0.0386364683508873,
0.019426697865128517,
0.0017138232942670584,
-0.035786863416433334,
-0.008493644185364246,
0.006239281035959721,
-0.038912348449230194,
0.004804125055670738,
-0.028038647025823593,
0.030689841136336327,
0.007204919587820768,
-0.0003897736023645848,
-0.007903612218797207,
0.002277625724673271,
-0.04990333691239357,
0.006892567966133356,
0.020707203075289726,
-0.028862586244940758,
-0.037582360208034515,
0.013598790392279625,
-0.017545143142342567,
-0.04819168522953987,
-0.02719375304877758,
-0.03781525418162346,
-0.006027688272297382,
-0.01434889156371355,
0.014438522048294544,
-0.015838228166103363,
-0.0017540267435833812,
-0.015919554978609085,
-0.0056502316147089005,
-0.004083237610757351,
0.01662379875779152,
-0.07612556964159012,
-0.030756380409002304,
0.011571751907467842,
-0.007383259944617748,
-0.026044627651572227,
0.060448382049798965,
-0.05598796531558037,
-0.013755898922681808,
-0.028418458998203278,
0.0009272413444705307,
-0.020153895020484924,
-0.06517454236745834,
-0.03423310071229935,
0.03271099552512169,
0.029736286029219627,
-0.026812249794602394,
-0.011723602190613747,
0.022189190611243248,
-0.022663433104753494,
-0.021718600764870644,
0.04491887986660004,
-0.004358742851763964,
0.010514645837247372,
0.017891040071845055,
-0.05254834517836571,
-0.006724218372255564,
0.07040313631296158,
-0.04520788788795471,
-0.011222629807889462,
0.0026816828176379204,
-0.023373613134026527,
0.014313783496618271,
-0.020579244941473007,
-0.01533142663538456,
-0.018396396189928055,
-0.020711751654744148,
0.03302517533302307,
0.014704616740345955,
-0.00426835473626852,
-0.0020783620420843363,
-0.041238028556108475,
-0.041923463344573975,
0.031306326389312744,
0.0017250773962587118,
-0.00548905972391367,
-0.010744343511760235,
0.049516499042510986,
-0.06501342356204987,
0.004268653690814972,
0.022530630230903625,
-0.004699666518718004,
-0.09995581209659576,
0.010724364779889584,
0.012156219221651554,
-0.04014376923441887,
0.0014326440868899226,
-0.04189412668347359,
0.0019357433775439858,
0.01576744019985199,
-0.10106295347213745,
0.01682010479271412,
-0.06290507316589355,
-0.030285364016890526,
-0.04240969568490982,
-0.03166015073657036,
-0.009985850192606449,
0.05739135667681694,
-0.007985438220202923,
0.000979037256911397,
0.017180461436510086,
0.0028877523727715015,
-0.03713151440024376,
-0.034954749047756195,
0.013251706957817078,
0.053416479378938675,
0.0009462407906539738,
0.0020896324422210455,
0.04077960178256035,
-0.035691067576408386,
-0.014513259753584862,
0.027781929820775986,
-0.02600250393152237,
0.03965585678815842,
-0.018590157851576805,
-0.00048598324065096676,
-0.023804888129234314,
0.016710296273231506,
-0.034352272748947144,
0.03319799154996872,
-0.006434077862650156,
0.03725970908999443,
0.07469267398118973,
0.0257585346698761,
-0.005951751954853535,
-0.02766038477420807,
-0.011978122405707836,
-0.014750041998922825,
-0.013763988390564919,
0.023701196536421776,
-0.052228137850761414,
0.02429857663810253,
0.005062567535787821,
-0.006132188718765974,
0.010847551748156548,
-0.034372154623270035,
-0.02625415101647377,
-0.0558309331536293,
-0.003068774938583374,
0.03136027976870537,
0.005886593833565712,
0.013526158407330513,
0.008618125692009926,
-0.008235392160713673,
0.019992481917142868,
-0.021123921498656273,
-0.010711210779845715,
-0.015994727611541748,
-0.03887750580906868,
-0.02483375370502472,
0.0018667880212888122,
0.014271422289311886,
-0.0022136010229587555,
-0.03778252750635147,
-0.019258521497249603,
0.07352787256240845,
0.04290128871798515,
0.03472480550408363,
0.04046129435300827,
-0.036779146641492844,
0.007075563073158264,
-0.08679578453302383,
0.024519026279449463,
0.003310356754809618,
-0.025096431374549866,
-0.011774883605539799,
-0.053398147225379944,
0.015969635918736458,
0.048147089779376984,
0.032732248306274414,
-0.00897513423115015,
-0.02621123380959034,
0.001921028713695705,
-0.033480335026979446,
0.0239210594445467,
-0.00915902853012085,
0.0006340229301713407,
-0.0035089466255158186,
-0.010940341278910637,
0.03483179956674576,
0.00816336926072836,
0.025522764772176743,
0.008479885756969452,
0.025557970628142357,
-0.0210031196475029,
0.012560212053358555,
-0.007083496078848839,
-0.02235993556678295,
0.0008734081056900322,
-0.004507782403379679,
-0.011152389459311962,
0.08815700560808182,
-0.024984797462821007,
0.0022395572159439325,
0.006187896244227886,
-0.013300162740051746,
-0.0016296127578243613,
0.052560240030288696,
-0.05045171454548836,
0.004011588171124458,
-0.039300329983234406,
-0.03689635545015335,
-0.018744422122836113,
-0.02668846771121025,
-0.006335719954222441,
0.0008929404430091381,
-0.029110746458172798,
-0.037690743803977966,
0.02296099066734314,
0.02855784259736538,
0.0024810282047837973,
0.013942324556410313,
0.019995229318737984,
-0.010656243190169334,
0.030877189710736275,
0.005633666645735502,
0.034817762672901154,
0.027354395017027855,
0.01720866560935974,
-0.03512250632047653,
0.047911692410707474,
-0.0060430774465203285,
0.031120557337999344,
0.019720232114195824,
-0.000929793925024569,
-0.0037930049002170563,
-0.006653073243796825,
0.0035539160016924143,
-0.02002977579832077,
0.025746144354343414,
0.019436398521065712,
-0.010453669354319572,
0.03665066882967949,
-0.007736146915704012,
-0.0097817312926054,
-0.02941979467868805,
0.021629514172673225,
0.047256626188755035,
0.027094021439552307,
-0.01129403430968523,
-0.004919329658150673,
-0.025642745196819305,
-0.03935346379876137,
-0.02894335612654686,
0.011357208713889122,
-0.01343499030917883,
-0.020951813086867332,
0.0030027327593415976,
-0.05055525526404381,
0.029771480709314346,
-0.008594715036451817,
-0.04362216964364052,
-0.02111133746802807,
-0.01014501042664051,
0.06366743892431259,
0.0112743666395545,
0.005436633247882128,
-0.03026576153934002,
0.002127573825418949,
-0.019044242799282074,
0.0857638567686081,
-0.0373755507171154,
-0.04731688275933266,
0.010645711794495583,
0.04129396378993988,
0.00559169752523303,
0.004522255156189203
] |
<p>Intuitively I would expect the thermal and electric conductivity to be positively related, and since electric conductivity increases with salinity, so should thermal. But according to <a href="http://web.mit.edu/seawater/Seawater_Property_Tables.pdf" rel="nofollow">this table</a> (p.10) it decreases. Why is this?</p>
<p>Related: is there such a thing as the Wiedemann-Franz law for liquids like water?</p>
<p>There's a paper that has theoretical derivations about it, but it's nowhere to be found:<br>
<code>Predvoditelev, A. S., "Some invariant Quantities in the Theories of Heat Conductance and the Viscosity of Liquids," Russian Journal of Physical Chemistry, Vol. 22, p. 339 (1948)</code></p>
| 10,719 |
[
-0.000006737809599144384,
-0.011544580571353436,
-0.0058996849693357944,
0.008604277856647968,
0.0015236764447763562,
-0.0004159182426519692,
-0.012650744989514351,
0.031244181096553802,
-0.0042077889665961266,
-0.03663978725671768,
0.0687674731016159,
0.02792794443666935,
0.06602394580841064,
0.007919851690530777,
0.017248688265681267,
-0.025468425825238228,
0.0012677720515057445,
0.0007593766204081476,
-0.002437471179291606,
-0.024021510034799576,
-0.007039682473987341,
0.048556189984083176,
-0.003470197319984436,
0.01207744237035513,
-0.01803572103381157,
0.03656847029924393,
-0.01817748136818409,
-0.01383022777736187,
0.027906470000743866,
0.0387500524520874,
0.011162681505084038,
-0.040756382048130035,
0.006098002195358276,
-0.008112682960927486,
0.021572602912783623,
0.015702318400144577,
-0.0602722205221653,
-0.014856724068522453,
-0.05874021351337433,
0.038651615381240845,
0.015568462200462818,
-0.010801482014358044,
-0.021451890468597412,
0.02579035423696041,
-0.004033150151371956,
0.00490792840719223,
0.03010953590273857,
-0.017344070598483086,
0.008130568079650402,
-0.06142299994826317,
0.04708884656429291,
0.0030284198001027107,
0.04863106831908226,
0.038799941539764404,
-0.014068822376430035,
0.027120593935251236,
0.07400614023208618,
0.05655188858509064,
0.008347486145794392,
-0.06819657236337662,
0.052329178899526596,
-0.040414027869701385,
0.00048438250087201595,
0.004978729411959648,
-0.016785359010100365,
0.023015221580863,
0.00971047393977642,
-0.07037948817014694,
0.037486352026462555,
-0.012281931936740875,
-0.0011252759722992778,
0.005428137257695198,
0.02534184791147709,
0.005778050050139427,
0.029583394527435303,
-0.0032808624673634768,
-0.01314378809183836,
0.05868653580546379,
-0.009236861951649189,
0.04587544873356819,
-0.018311478197574615,
0.016890689730644226,
0.036097344011068344,
0.009751659817993641,
-0.0058783795684576035,
0.007052418775856495,
0.031152013689279556,
-0.01746467873454094,
0.025098752230405807,
0.018601734191179276,
0.00022298586554825306,
0.008278883062303066,
-0.022993745282292366,
-0.018562236800789833,
0.002250266494229436,
-0.005409511271864176,
-0.013468137010931969,
0.011079548858106136,
0.013285592198371887,
-0.02656855806708336,
0.014888524077832699,
-0.0018434281228110194,
0.02014041133224964,
0.06660821288824081,
-0.023703470826148987,
-0.046180952340364456,
-0.07406854629516602,
-0.0047219241969287395,
-0.018942859023809433,
-0.02754371240735054,
-0.0030459060799330473,
0.013263039290904999,
0.004230868071317673,
0.007206502836197615,
-0.010101777501404285,
-0.060791876167058945,
0.04056224972009659,
-0.0063286772929131985,
0.01578458398580551,
0.03251580148935318,
0.02361796423792839,
-0.013796054758131504,
0.02546391822397709,
-0.012452839873731136,
-0.06408284604549408,
0.031203728169202805,
0.0035770318936556578,
-0.011122754774987698,
0.018518289551138878,
0.03636666759848595,
-0.033904604613780975,
0.003364941105246544,
0.024427548050880432,
-0.015682276338338852,
0.022815866395831108,
0.003499515587463975,
-0.06217847764492035,
-0.04417557641863823,
0.059359826147556305,
-0.015896465629339218,
-0.026993613690137863,
-0.08695314079523087,
0.01901564933359623,
0.026230545714497566,
0.07948960363864899,
0.0033839058596640825,
0.03465643525123596,
-0.03325076028704643,
0.020191237330436707,
0.012350008822977543,
-0.015497305430471897,
-0.04580013453960419,
0.016718899831175804,
-0.022072196006774902,
0.0037914335262030363,
-0.06466846913099289,
0.019796481356024742,
0.013206174597144127,
0.01714479923248291,
0.00006341356493066996,
0.04740503430366516,
-0.03639817237854004,
-0.021867183968424797,
-0.007264562416821718,
-0.0041718934662640095,
-0.04117278754711151,
0.07737263292074203,
0.010911178775131702,
0.01550286915153265,
0.0036849596071988344,
0.0007726445328444242,
0.006057447753846645,
-0.017363669350743294,
0.014805755577981472,
0.06515927612781525,
-0.004274317063391209,
0.005972772836685181,
-0.02682829648256302,
-0.004864330869168043,
0.025197172537446022,
-0.054594915360212326,
-0.024871449917554855,
-0.009205259382724762,
-0.026358693838119507,
-0.0015292840544134378,
0.011027815751731396,
0.012609337456524372,
-0.01834007166326046,
0.013178130611777306,
-0.03878738358616829,
-0.0039446549490094185,
-0.04814297705888748,
0.009152086451649666,
-0.0072339605540037155,
-0.006331185344606638,
0.05318545177578926,
0.010209765285253525,
0.026727033779025078,
-0.02613772079348564,
-0.0321982204914093,
0.0030529536306858063,
0.004892268218100071,
0.018036270514130592,
-0.04252180457115173,
0.029137644916772842,
0.03312651813030243,
0.024442564696073532,
0.005012688226997852,
-0.028543556109070778,
-0.04364136606454849,
-0.052905917167663574,
-0.00321865058504045,
-0.06253363937139511,
0.02275792881846428,
-0.0019409195519983768,
-0.044681366533041,
0.01155648659914732,
0.03529525175690651,
-0.001724150264635682,
0.012134735472500324,
-0.025293368846178055,
0.06010771542787552,
0.06739427894353867,
0.02231474220752716,
-0.01406234223395586,
0.03633217141032219,
0.004314982797950506,
0.004588056355714798,
-0.030653616413474083,
-0.015267354436218739,
-0.032937124371528625,
0.0007428913959302008,
0.020296212285757065,
0.024871092289686203,
-0.04339450225234032,
0.012905416078865528,
0.037914689630270004,
0.0351574569940567,
0.03217704966664314,
-0.012877698056399822,
0.006689074914902449,
-0.0511619858443737,
0.00750065827742219,
-0.027918066829442978,
-0.0011001357343047857,
-0.009894724935293198,
0.032941773533821106,
0.016148224472999573,
0.03821577504277229,
-0.034410879015922546,
-0.016320809721946716,
0.009267197921872139,
0.017951320856809616,
0.050092604011297226,
0.016479147598147392,
-0.005831740330904722,
0.009910969994962215,
-0.042077772319316864,
0.01624654419720173,
-0.0049820998683571815,
0.025491274893283844,
0.03223932906985283,
-0.030736302956938744,
-0.024774128571152687,
-0.01264821644872427,
-0.003218123223632574,
0.01369343139231205,
-0.025092707946896553,
0.010440816171467304,
-0.03882609307765961,
-0.003094329498708248,
-0.00830015167593956,
0.007350568193942308,
-0.036466967314481735,
-0.008352305740118027,
0.02862723544239998,
0.00720470305532217,
0.026628252118825912,
-0.028171278536319733,
0.0110773965716362,
-0.0020007633138448,
-0.019893357530236244,
0.01803572289645672,
0.0014991596108302474,
-0.01401999220252037,
-0.026310216635465622,
0.00017756805755198002,
-0.01550730038434267,
0.02070453390479088,
-0.0021402710117399693,
0.007309872657060623,
0.017117207869887352,
0.006423879414796829,
-0.036730535328388214,
-0.019110262393951416,
-0.010549291037023067,
0.019080420956015587,
-0.03919408470392227,
-0.005091554950922728,
0.055599309504032135,
0.0031702809501439333,
-0.04476168379187584,
0.02363995835185051,
-0.03598850220441818,
-0.065134696662426,
-0.01200098730623722,
-0.011755933985114098,
-0.009997295215725899,
-0.01554748322814703,
0.005723714362829924,
0.05584254860877991,
-0.062276605516672134,
-0.048877228051424026,
-0.034621283411979675,
-0.06010264903306961,
0.051507771015167236,
-0.0009718626970425248,
0.04064829647541046,
-0.01834225282073021,
-0.06816121190786362,
0.015092365443706512,
0.03225663676857948,
-0.02089715376496315,
0.01014794036746025,
0.007901123724877834,
-0.05223716422915459,
-0.045868225395679474,
-0.002906431909650564,
0.04389657452702522,
-0.008742970414459705,
0.01779426820576191,
0.011105109006166458,
0.04769720882177353,
0.022736303508281708,
-0.009776055812835693,
0.02882097288966179,
0.005499545019119978,
0.02642124332487583,
0.013560201972723007,
0.045863427221775055,
0.012718512676656246,
0.004401417914777994,
0.02030022256076336,
0.007865135557949543,
0.0412893183529377,
0.04238630086183548,
-0.01877306029200554,
0.040489595383405685,
-0.00747531745582819,
0.026827773079276085,
-0.07065322250127792,
0.029734434559941292,
-0.025525549426674843,
0.024891503155231476,
0.020264504477381706,
0.016568254679441452,
0.03510797396302223,
-0.011377310380339622,
0.004779065027832985,
0.034294307231903076,
0.06384622305631638,
0.004803876392543316,
-0.016847215592861176,
-0.031709302216768265,
0.011406583711504936,
0.018046893179416656,
0.000639739737380296,
0.008791623637080193,
0.03534672409296036,
-0.0013579680817201734,
0.018709788098931313,
0.004658689256757498,
-0.018816456198692322,
-0.027660077437758446,
-0.053395695984363556,
-0.02812758833169937,
-0.02923010103404522,
0.05843518301844597,
0.03645578399300575,
0.05493912845849991,
0.0036518163979053497,
0.024526113644242287,
0.017902856692671776,
0.03687984496355057,
-0.08249615132808685,
0.004832656122744083,
-0.010400994680821896,
0.001992476638406515,
-0.01972118765115738,
-0.001822657766751945,
-0.002212035469710827,
-0.007320854347199202,
-0.03427209332585335,
0.00713279889896512,
0.000045973138185217977,
-0.07245554029941559,
0.023732531815767288,
-0.018141960725188255,
-0.053726229816675186,
-0.0012149749090895057,
0.0038318075239658356,
0.011689083650708199,
-0.09358446300029755,
0.0038692981470376253,
0.02705051191151142,
-0.019198663532733917,
-0.011344077996909618,
-0.057864218950271606,
0.018360860645771027,
0.040002454072237015,
0.004527429584413767,
0.0011994329979643226,
0.010312625207006931,
-0.009555450640618801,
0.010474054142832756,
0.011506802402436733,
0.007156419102102518,
0.020633598789572716,
-0.015746844932436943,
-0.06528424471616745,
-0.03914465382695198,
0.006513161584734917,
0.028443345800042152,
0.06189971789717674,
0.04820767417550087,
0.022721832618117332,
0.0030339695513248444,
-0.0382942371070385,
-0.00557889137417078,
0.03002222254872322,
0.0023990694899111986,
0.011620874516665936,
-0.004272715654224157,
-0.023971769958734512,
-0.023177307099103928,
0.0011668051593005657,
-0.013372661545872688,
0.0412176139652729,
0.028696609660983086,
0.006373194511979818,
-0.020290307700634003,
0.004465012811124325,
-0.016493232920765877,
0.0024058569688349962,
-0.035934727638959885,
0.039999719709157944,
-0.0002530108322389424,
-0.03581377491354942,
-0.027997903525829315,
0.035040080547332764,
0.024894054979085922,
0.0433952696621418,
-0.01588466577231884,
-0.006446568761020899,
-0.0669465959072113,
0.011819246225059032,
0.02397848479449749,
0.022666113451123238,
-0.036096636205911636,
-0.0040657781064510345,
-0.0752408429980278,
0.003455142956227064,
0.04143907502293587,
-0.0043601784855127335,
0.016601914539933205,
0.00003878617280861363,
-0.027993643656373024,
-0.03471900150179863,
-0.04138513654470444,
-0.0017706739017739892,
0.010711834765970707,
0.0074748205952346325,
0.05223964899778366,
-0.027271203696727753,
-0.036979857832193375,
-0.00007649106555618346,
0.012804755941033363,
0.002530384575948119,
0.05736999586224556,
-0.018974576145410538,
0.004757741000503302,
-0.0004382806073408574,
-0.018783992156386375,
-0.002662296174094081,
-0.07049815356731415,
0.019198421388864517,
0.002086708787828684,
0.009451883845031261,
0.026679860427975655,
-0.041086480021476746,
-0.00867543090134859,
0.03358549252152443,
0.015272228978574276,
-0.04764607921242714,
-0.024879833683371544,
-0.03727773204445839,
0.06018561124801636,
0.008117370307445526,
0.005037378054112196,
0.07231368869543076,
0.026809347793459892,
-0.04865192249417305,
-0.04087083414196968,
-0.04636295512318611,
0.041162848472595215,
-0.02918689139187336,
-0.02110011875629425,
0.02066219411790371,
0.012683975510299206,
-0.026535511016845703,
0.05803437530994415,
-0.018942922353744507,
0.007166710216552019,
-0.013943706639111042,
-0.013468682765960693,
0.0026738408487290144,
-0.04393180087208748,
-0.004166383761912584,
-0.012736329808831215,
0.026189332827925682,
0.04806201532483101,
0.008247225545346737,
-0.06997605413198471,
0.04652412235736847,
0.00592397153377533,
0.002686551306396723,
0.007182457484304905,
-0.02449476532638073,
0.024431351572275162,
-0.005264829378575087,
0.0036250785924494267,
-0.0014866584679111838,
0.025365691632032394,
-0.018757015466690063,
-0.020742567256093025,
-0.015578510239720345,
0.04112960025668144,
-0.04508671909570694,
-0.004720012191683054,
0.03317618742585182,
0.0035793844144791365,
0.0055588847026228905,
-0.05681977793574333,
0.02477169595658779,
0.05060197785496712,
0.018413210287690163,
-0.06894370913505554,
-0.0809934213757515,
0.03452901542186737,
0.020809680223464966,
-0.02164553292095661,
-0.034245144575834274,
-0.024953993037343025,
-0.0402815118432045,
-0.0335012748837471,
0.009325566701591015,
0.06026835739612579,
-0.0037463579792529345,
-0.03173510730266571,
-0.002938969060778618,
0.04197416827082634,
0.07302455604076385,
-0.02947254106402397,
0.00785498321056366,
0.02459067478775978,
-0.052060358226299286,
-0.018545927479863167,
-0.013872094452381134,
0.03449663892388344,
-0.04202819988131523,
-0.016657143831253052,
0.02263781987130642,
-0.040382470935583115,
0.03187960013747215,
0.034711919724941254,
-0.04793807119131088,
-0.012415549717843533,
0.016130030155181885,
-0.024217242375016212,
-0.01103893481194973,
0.0238832738250494,
0.017288465052843094,
0.03595453128218651,
-0.021765155717730522,
-0.015640174970030785,
-0.026111582294106483,
-0.012234245426952839,
-0.004986284766346216,
-0.006077927071601152,
-0.01198988500982523,
-0.007812033407390118,
0.05254972353577614,
0.0012253865133970976,
-0.008864800445735455,
0.025804640725255013,
0.012775843031704426,
0.04192355275154114,
0.046165455132722855,
-0.021733861416578293,
-0.03403225541114807,
0.04689449816942215,
-0.05332489311695099,
-0.0504801943898201,
-0.03893769532442093,
0.001183561747893691,
0.06504072993993759,
-0.01209196262061596,
0.0319388248026371,
0.022349931299686432,
-0.026974311098456383,
0.04201547056436539,
-0.022671833634376526,
-0.019918499514460564,
0.04169382527470589,
-0.0056084939278662205,
0.028124477714300156,
-0.03532955422997475,
-0.006621698383241892,
0.009786678478121758,
0.047784190624952316,
-0.02474796772003174,
0.018553515896201134,
0.014945406466722488,
0.031032104045152664,
0.009591132402420044,
-0.05351798236370087,
-0.07327423244714737,
0.03272319212555885,
-0.028766406700015068,
0.06180354207754135,
0.013911381363868713,
-0.004640374798327684,
0.0418526791036129,
0.007829589769244194,
0.008820002898573875,
-0.06088390201330185,
0.003367906901985407,
0.0018566135549917817,
0.021853303536772728,
-0.0004144710546825081,
-0.010731331072747707,
0.012993058189749718,
0.023947274312376976,
0.019219353795051575,
0.006771744694560766,
0.009733478538691998,
0.003967063967138529,
-0.03181283921003342,
0.04464975744485855,
-0.0256911963224411,
-0.03890495002269745,
0.06302523612976074,
0.008630802854895592,
-0.026703236624598503,
-0.0026075250934809446,
-0.00427643209695816,
0.03451745584607124,
0.00860705878585577,
0.017697494477033615,
-0.015710778534412384,
0.03743725270032883,
-0.01723450981080532,
-0.00973963551223278,
-0.03533848002552986,
-0.008556799031794071,
0.12648187577724457,
0.04215405508875847,
0.037732068449258804,
-0.04485710710287094,
0.021943015977740288,
-0.032253578305244446,
-0.000978908035904169,
-0.0400957316160202,
-0.012971297837793827,
-0.02105831354856491,
0.042812492698431015,
0.03027166612446308,
0.06521181762218475,
7.982937404449331e-7,
0.0275214035063982,
0.011067301966249943,
-0.06168949604034424,
0.011739148758351803,
0.020563917234539986,
-0.0021495253313332796,
-0.055435992777347565,
0.041224703192710876,
-0.0382644459605217,
0.018422186374664307,
-0.011197448708117008,
-0.005776703357696533,
-0.029158804565668106,
-0.018075399100780487,
0.02891475521028042,
0.003609365550801158,
-0.05651140213012695,
-0.014272099360823631,
-0.0017741587944328785,
0.013062846846878529,
-0.038937535136938095,
0.028759853914380074,
0.014672653749585152,
-0.020978674292564392,
-0.009323514066636562,
0.01687084138393402,
0.036443524062633514,
0.008468342944979668,
0.02685047872364521,
0.04150375723838806,
-0.028215399011969566,
0.010090187191963196,
-0.008961841464042664,
0.033724285662174225,
0.025554122403264046,
-0.012847142294049263,
-0.01253865472972393,
0.029109379276633263,
0.032327089458703995,
-0.029192889109253883,
-0.02849538065493107,
-0.012530886568129063,
0.03263098746538162,
-0.035395342856645584,
0.00008514723594998941,
-0.020863031968474388,
0.003673277096822858,
-0.01848401501774788,
0.02194208651781082,
0.024403996765613556,
-0.010025554336607456,
-0.029325168579816818,
0.005003898870199919,
0.018896453082561493,
0.010922431945800781,
-0.027322929352521896,
-0.02587961032986641,
-0.020566076040267944,
-0.03399454057216644,
-0.032611578702926636,
-0.0034142318181693554,
0.023171015083789825,
0.05936821550130844,
0.000573460478335619,
-0.01429281197488308,
0.005099819973111153,
-0.09990321844816208,
0.08261356502771378,
-0.006028167437762022,
0.01214754581451416,
-0.0606713742017746,
0.006493763532489538,
0.00852352473884821,
0.058840248733758926,
-0.04206680878996849,
0.003542850958183408,
0.012194884940981865,
0.03561600670218468,
0.056972336024045944,
-0.02866131067276001,
-0.03190511837601662,
0.02715526893734932,
-0.038518574088811874,
-0.01563672348856926,
0.03234297037124634,
0.04136255383491516,
-0.0016637366497889161,
0.020561862736940384,
0.013938882388174534,
-0.020511146634817123,
-0.03507684916257858,
-0.02049391344189644,
0.015615791082382202,
-0.009275665506720543,
-0.017414186149835587,
0.012933453544974327,
-0.023383501917123795,
-0.03142083063721657,
-0.014914755709469318,
-0.04275956377387047,
0.03712261840701103,
-0.00041130135650746524,
0.010344896465539932,
-0.012054854072630405,
0.0028157641645520926,
-0.057313933968544006,
0.032828107476234436,
-0.0472775362432003,
-0.0495334230363369,
-0.07184252142906189,
-0.040060702711343765,
-0.03428950905799866,
0.02811749093234539,
-0.002885306952521205,
0.017413198947906494,
-0.06588634103536606,
0.014367189258337021,
0.031872235238552094,
0.005608472041785717,
0.00852138176560402,
-0.02781085856258869,
0.04612695425748825,
-0.02024630270898342,
0.051099665462970734,
-0.05351666733622551,
-0.07048715651035309,
0.0484880767762661,
-0.04356831684708595,
-0.023154621943831444,
0.02248138189315796,
-0.029065897688269615,
0.01881204918026924,
-0.011044354178011417,
0.045157290995121,
0.009047731757164001,
0.09945138543844223,
-0.01483064517378807,
0.01676732674241066,
-0.05447268486022949,
-0.05882028117775917,
0.03991395980119705,
-0.0018105957424268126,
0.01627005636692047,
0.013801784254610538,
0.0009886020561680198,
0.03977721557021141,
0.0612591952085495,
-0.02405291423201561,
-0.003936004359275103,
-0.013244577683508396,
-0.018341854214668274,
0.010339251719415188,
0.04394145309925079,
0.020172027871012688,
0.031919337809085846,
0.04192991182208061,
-0.014165055006742477,
0.019873840734362602,
0.023778852075338364,
0.005641248542815447,
-0.08666539937257767,
0.016329407691955566,
-0.019522953778505325,
0.039952170103788376,
0.020773768424987793,
-0.04833480343222618,
0.01696833223104477,
-0.013985369354486465,
-0.07714883983135223,
0.011139532551169395,
-0.028807779774069786,
-0.004084792919456959,
-0.0655330941081047,
-0.00279435608536005,
-0.01894603669643402,
0.05012645572423935,
0.02904028445482254,
0.035972319543361664,
0.008256844244897366,
0.03439842164516449,
-0.015009135939180851,
0.01348934043198824,
-0.051599010825157166,
0.04988498613238335,
0.016933543607592583,
-0.029253307729959488,
-0.002707079751417041,
-0.007198486011475325,
-0.015643954277038574,
0.014137008227407932,
-0.036129191517829895,
0.013242091052234173,
0.014588365331292152,
0.02782060205936432,
0.0003816917596850544,
0.024266870692372322,
0.012588965706527233,
-0.002710464410483837,
-0.022551633417606354,
-0.009858467616140842,
0.034575317054986954,
0.022769177332520485,
0.010016352869570255,
0.004668561741709709,
0.04982445761561394,
-0.02460503578186035,
-0.023899303749203682,
0.04635143652558327,
-0.01596764847636223,
0.014430655166506767,
0.008343083783984184,
-0.0034091908019036055,
0.019487077370285988,
0.006840623449534178,
0.012387716211378574,
-0.018514830619096756,
-0.027421602979302406,
0.04841925948858261,
-0.013545792549848557,
0.034337908029556274,
0.008355362340807915,
0.027221238240599632,
-0.027478737756609917,
-0.008616294711828232,
0.012885049916803837,
0.022490963339805603,
-0.043053485453128815,
-0.017245998606085777,
-0.004316878505051136,
0.01591084711253643,
-0.030591893941164017,
-0.060129620134830475,
-0.04373810812830925,
0.05067836493253708,
0.028723018243908882,
0.02851039357483387,
0.034655001014471054,
-0.0629928931593895,
-0.0160543043166399,
-0.045374367386102676,
0.03192414715886116,
-0.025510981678962708,
-0.012705542147159576,
-0.02461986616253853,
-0.006595928221940994,
0.003778337500989437,
0.043108195066452026,
0.0847431868314743,
-0.015176079235970974,
-0.008466318249702454,
-0.030254006385803223,
-0.004347290378063917,
0.023361193016171455,
-0.039649393409490585,
0.029081808403134346,
-0.004153492860496044,
-0.027982745319604874,
0.05663082376122475,
0.0007364358170889318,
-0.017135849222540855,
-0.006550331134349108,
0.022140981629490852,
-0.029157212004065514,
0.01418693084269762,
-0.007997360080480576,
-0.016077736392617226,
0.034203048795461655,
0.004876583348959684,
-0.0038126064464449883,
0.07009907811880112,
-0.026410212740302086,
-0.0037651199381798506,
0.019842326641082764,
0.007305518724024296,
-0.02668977528810501,
0.01852526143193245,
-0.001692863181233406,
-0.002815868007019162,
0.03655720874667168,
0.011570892296731472,
0.031422633677721024,
-0.04510759562253952,
0.0006529228412546217,
0.03670259565114975,
-0.019538069143891335,
-0.04706353694200516,
0.04816213622689247,
0.019321901723742485,
0.019207730889320374,
-0.007168032694607973,
-0.010787705890834332,
-0.028203614056110382,
0.0034392913803458214,
0.011923359706997871,
0.09365976601839066,
0.06488046050071716,
-0.0157186109572649,
0.008181839250028133,
-0.0003826512838713825,
-0.000610796210821718,
0.042830999940633774,
0.006279678083956242,
0.03445737436413765,
-0.016047080978751183,
-0.026171931996941566,
0.049429118633270264,
0.01267320942133665,
-0.01455647312104702,
0.007858962751924992,
0.003537585027515888,
0.053484901785850525,
-0.030658436939120293,
-0.02537623606622219,
-0.026435626670718193,
0.014799739234149456,
-0.03519406169652939,
0.01173946913331747,
0.03621222823858261,
0.01917916350066662,
-0.006373153999447823,
-0.017052922397851944,
-0.0005477790837176144,
-0.016340196132659912,
0.00624588830396533,
-0.039646439254283905,
-0.0111201461404562,
0.009017928503453732,
0.033370859920978546,
0.005124473012983799,
-0.011035412549972534,
-0.0037502769846469164,
0.009735831059515476,
0.054468847811222076,
0.030803058296442032,
0.0007020783377811313,
0.03676384314894676,
-0.0295051671564579,
0.0014655538834631443,
0.07937423884868622,
-0.07929788529872894,
-0.015550091862678528,
0.012185804545879364,
0.010504730977118015,
-0.0053023542277514935,
-0.024628181010484695
] |
<p>How many different types of (hypothetical) <a href="http://en.wikipedia.org/wiki/Multiverse" rel="nofollow">multiverse</a> theory exist? For example, the obvious Quantum MWI, eternal inflation, cyclic universe etc</p>
| 10,720 |
[
-0.030280303210020065,
-0.026716789230704308,
0.017823560163378716,
-0.038956284523010254,
0.0590616837143898,
-0.005168972071260214,
-0.01337512582540512,
-0.0720377266407013,
-0.0004382533661555499,
-0.041941192001104355,
0.008553472347557545,
0.02318611741065979,
0.0044504511170089245,
-0.008349287323653698,
0.009169170632958412,
0.026622159406542778,
0.0025856110733002424,
-0.008911996148526669,
-0.009651528671383858,
0.012368571013212204,
0.029282009229063988,
0.037790581583976746,
0.02014295943081379,
0.02265915274620056,
-0.014884326606988907,
0.011230711825191975,
0.033371083438396454,
0.018059078603982925,
0.05045296624302864,
0.054534267634153366,
-0.0009808177128434181,
-0.026268400251865387,
-0.0035747475922107697,
0.05560040846467018,
-0.0035816088784486055,
-0.011769081465899944,
-0.015003682114183903,
-0.015382847748696804,
-0.020193377509713173,
0.012805386446416378,
-0.04540227726101875,
-0.002207992598414421,
-0.028861243277788162,
0.04466916620731354,
-0.028539014980196953,
0.028927406296133995,
0.006266236305236816,
-0.029892291873693466,
0.03412015736103058,
-0.04445859417319298,
0.058092303574085236,
-0.02156759798526764,
0.02095666527748108,
0.040997155010700226,
-0.00025998061755672097,
0.006783905439078808,
0.10220074653625488,
0.05477352812886238,
-0.01700223609805107,
-0.04283147677779198,
-0.05279170349240303,
0.032689984887838364,
0.06407829374074936,
-0.03163153678178787,
-0.045219212770462036,
0.059961967170238495,
-0.0018381342524662614,
0.01823139563202858,
0.003148683812469244,
0.013379845768213272,
0.0005361905205063522,
0.017135031521320343,
0.04574522003531456,
-0.010051650926470757,
0.00030208067619241774,
-0.01083979383111,
0.014083552174270153,
0.0008982792496681213,
0.04413490369915962,
0.05455587059259415,
-0.0005120798014104366,
0.016643250361084938,
0.0016443748027086258,
-0.004726799204945564,
0.02144129015505314,
0.001899389666505158,
0.070768341422081,
0.004278052132576704,
-0.02849135734140873,
0.03143584355711937,
-0.04307832196354866,
-0.018488004803657532,
0.048217736184597015,
-0.014958827756345272,
-0.05509399622678757,
0.060418836772441864,
-0.002918975194916129,
0.0197539534419775,
-0.00714884465560317,
-0.03269583359360695,
0.024657491594552994,
0.022923976182937622,
0.004283797927200794,
0.06211816519498825,
-0.003953700419515371,
-0.015248688869178295,
-0.051578231155872345,
0.025530755519866943,
-0.030286436900496483,
0.004486831836402416,
-0.015909546986222267,
0.03642069920897484,
-0.01613316312432289,
0.008081894367933273,
-0.008926612325012684,
-0.016677336767315865,
0.00605176854878664,
-0.052249930799007416,
0.037567950785160065,
0.0843140259385109,
0.05456530675292015,
-0.04819316044449806,
0.04730387032032013,
-0.01596110314130783,
-0.08095543831586838,
-0.012432596646249294,
0.01296575553715229,
0.0272420234978199,
-0.01911521889269352,
0.018920473754405975,
0.010025463998317719,
-0.02874927967786789,
0.017645373940467834,
0.015066666528582573,
0.043757397681474686,
-0.015643879771232605,
-0.10340502858161926,
-0.09262720495462418,
0.04543601721525192,
-0.0310358889400959,
-0.03893144801259041,
-0.01629585400223732,
0.0477466806769371,
0.02378934621810913,
0.09383250772953033,
0.002877038437873125,
-0.0327557772397995,
0.03418007120490074,
0.061439137905836105,
0.02587800659239292,
-0.028744399547576904,
0.018741361796855927,
-0.005422846879810095,
-0.035636719316244125,
0.02067474275827408,
-0.08744393289089203,
-0.005382575560361147,
0.040617287158966064,
0.004254232160747051,
-0.013766254298388958,
0.07613292336463928,
0.012734781950712204,
-0.0070430622436106205,
-0.001893452717922628,
0.02396150678396225,
-0.01883690431714058,
0.07453557848930359,
0.0041755265556275845,
-0.010032893158495426,
0.02600082941353321,
-0.025463130325078964,
0.012499689124524593,
0.012057740241289139,
0.043981168419122696,
0.015063978731632233,
-0.015542255714535713,
0.008746321313083172,
-0.033658239990472794,
0.03041771613061428,
0.013550722040235996,
-0.04808918386697769,
-0.0030731623992323875,
-0.014753398485481739,
-0.028666503727436066,
0.006875097751617432,
0.04188153147697449,
-0.04821687936782837,
0.004664162639528513,
0.007723818067461252,
-0.04930170625448227,
0.011315681040287018,
-0.016836583614349365,
-0.001776058692485094,
0.011593076400458813,
-0.005917784292250872,
-0.007305264938622713,
0.020757265388965607,
0.028183424845337868,
-0.06421994417905807,
-0.0498959943652153,
-0.021779481321573257,
0.06331146508455276,
-0.0007972947787493467,
0.015126338228583336,
0.004172695800662041,
0.014972908422350883,
0.02648966945707798,
-0.02024652436375618,
0.002000462030991912,
-0.006528983358293772,
-0.022149229422211647,
-0.0041296472772955894,
-0.013654407113790512,
0.03933311253786087,
-0.03743928670883179,
-0.001455325516872108,
0.0029285233467817307,
0.021158559247851372,
-0.02188805863261223,
0.03562694042921066,
-0.04435354843735695,
0.024060964584350586,
0.031497109681367874,
0.011903999373316765,
-0.02187999337911606,
0.021764202043414116,
-0.006789227481931448,
-0.0011583681916818023,
-0.019687959924340248,
-0.04479489102959633,
-0.07429715991020203,
-0.019103366881608963,
0.023242134600877762,
0.034212928265333176,
-0.031501032412052155,
0.064115509390831,
-0.0003982132184319198,
0.07076722383499146,
0.003823274979367852,
0.019966628402471542,
-0.03474298119544983,
-0.05223372206091881,
0.011815512552857399,
0.015754345804452896,
0.03500435873866081,
0.03275527060031891,
0.03107243962585926,
-0.012614279985427856,
-0.013366879895329475,
-0.022666465491056442,
0.014911443926393986,
0.053452540189027786,
-0.018450099974870682,
-0.004888025112450123,
-0.0046232473105192184,
-0.018650595098733902,
-0.009293235838413239,
-0.008239262737333775,
0.02936643920838833,
0.029371164739131927,
0.017036231234669685,
-0.01765996590256691,
-0.017036376520991325,
-0.016053877770900726,
0.00890617910772562,
0.006905198097229004,
-0.03998764604330063,
-0.02395753003656864,
0.027794472873210907,
-0.01915215142071247,
-0.00124363845679909,
-0.030832458287477493,
0.05052361264824867,
-0.013662591576576233,
-0.013205882161855698,
0.0029463248793035746,
0.004661555867642164,
0.05032743886113167,
-0.0584307499229908,
-0.03601217269897461,
0.014007064513862133,
-0.036387596279382706,
0.0019211849430575967,
-0.040726155042648315,
-0.03772231563925743,
0.046244218945503235,
-0.032547727227211,
-0.03161389008164406,
0.0369378924369812,
-0.016249727457761765,
-0.008613660000264645,
0.014181967824697495,
0.010558423586189747,
-0.029387233778834343,
0.003077786648645997,
-0.028316820040345192,
0.021484874188899994,
-0.016566624864935875,
-0.028582215309143066,
0.03310570865869522,
-0.03009892627596855,
-0.07467319071292877,
-0.008821841329336166,
-0.02649719826877117,
-0.04704544320702553,
-0.023683445528149605,
0.0013651660410687327,
0.04929983243346214,
-0.050207920372486115,
0.018690375611186028,
0.007332930341362953,
-0.05950983986258507,
0.022456152364611626,
-0.03397147357463837,
-0.05714869126677513,
0.033613141626119614,
-0.029185166582465172,
0.020269891247153282,
-0.0014228604268282652,
-0.014744401909410954,
0.03723520413041115,
0.01566239446401596,
0.0014111160999163985,
-0.025115514174103737,
0.009492826648056507,
-0.002597367623820901,
-0.012980488128960133,
0.0023419794160872698,
0.025518862530589104,
-0.03833877295255661,
0.023027196526527405,
0.08799360692501068,
0.012602166272699833,
0.016761787235736847,
0.023643145337700844,
-0.015182175673544407,
0.016180697828531265,
0.0011717557208612561,
0.017628125846385956,
0.06216888502240181,
0.00729272048920393,
0.015286748297512531,
0.00806623138487339,
-0.022903138771653175,
-0.0025083301588892937,
0.019783902913331985,
-0.0011851565213873982,
0.06273068487644196,
0.011755607090890408,
0.0070606679655611515,
-0.043412480503320694,
-0.003079026937484741,
0.00854416936635971,
-0.014114351011812687,
-0.01227602269500494,
0.02571859396994114,
0.03305727243423462,
-0.022756900638341904,
0.026221146807074547,
0.012719149701297283,
0.007558961398899555,
-0.025702454149723053,
-0.00851478148251772,
-0.008770301006734371,
0.01713140681385994,
0.011140447109937668,
-0.031139519065618515,
-0.04677172005176544,
0.07562223076820374,
0.027418063953518867,
0.04331782087683678,
0.0151141919195652,
0.004088162910193205,
0.011127625592052937,
-0.04038657248020172,
-0.008177757263183594,
-0.06241034343838692,
0.041294507682323456,
0.024542763829231262,
0.006035828031599522,
0.0018358227098360658,
-0.017337903380393982,
-0.029394833371043205,
-0.009227858856320381,
-0.05265188589692116,
0.036453086882829666,
-0.05065397545695305,
0.03943768888711929,
-0.009180346503853798,
-0.007378530688583851,
0.01914709247648716,
-0.01682158373296261,
-0.007041584700345993,
-0.00879654474556446,
-0.017784716561436653,
-0.052892912179231644,
-0.01759951189160347,
-0.03405359014868736,
-0.057042255997657776,
0.00938059575855732,
0.03687569871544838,
0.04416520893573761,
0.008922342211008072,
0.016220735386013985,
0.005598792340606451,
-0.03896433115005493,
0.020213866606354713,
0.017323682084679604,
-0.011154348962008953,
-0.0018240191275253892,
0.015319650992751122,
0.02534380741417408,
0.029208026826381683,
-0.01952778920531273,
-0.007670114282518625,
0.054365672171115875,
0.03985784202814102,
0.021843506023287773,
-0.01969175413250923,
-0.01768525503575802,
-0.04991089552640915,
0.014779188670217991,
-0.004311173222959042,
0.041106730699539185,
0.02073078416287899,
0.00962776504456997,
0.028189092874526978,
0.027786074206233025,
-0.053185854107141495,
0.03731728345155716,
0.06534841656684875,
-0.05343801528215408,
-0.031413719058036804,
-0.002062371000647545,
-0.01319938339293003,
0.0052584074437618256,
0.014584301970899105,
0.009981595911085606,
0.015778526663780212,
-0.03198457509279251,
0.0311554204672575,
0.004267759621143341,
-0.0015640213387086987,
-0.024134434759616852,
0.017514163628220558,
-0.014689476229250431,
0.03878951445221901,
-0.031742047518491745,
-0.041629061102867126,
-0.020077064633369446,
0.037984706461429596,
0.06055761128664017,
0.02210223488509655,
-0.0305390153080225,
-0.07559407502412796,
0.01917390525341034,
0.03542467579245567,
0.038598980754613876,
0.024004751816391945,
-0.0017670287052169442,
-0.07261592894792557,
-0.038841672241687775,
0.047246646136045456,
-0.024839410558342934,
0.00979994423687458,
-0.002195964567363262,
0.00934569537639618,
-0.013862081803381443,
-0.013718572445213795,
0.018506431952118874,
0.014089693315327168,
-0.015417245216667652,
0.01235823892056942,
-0.007559350226074457,
0.05325678363442421,
0.009891165420413017,
0.02703622356057167,
0.02507786825299263,
0.02855422906577587,
0.0013649322791025043,
0.023417582735419273,
-0.014961065724492073,
0.02339796908199787,
-0.01773161254823208,
-0.05494072660803795,
-0.004307168535888195,
0.05302305892109871,
-0.04501582682132721,
0.04771406203508377,
-0.021573202684521675,
-0.04580165818333626,
-0.004216266795992851,
0.013788879849016666,
-0.010380598716437817,
0.028150297701358795,
-0.05601608380675316,
0.018549444153904915,
0.00692431116476655,
0.017583293840289116,
0.04420071840286255,
0.021134283393621445,
-0.007252033334225416,
-0.0031066357623785734,
-0.014625451527535915,
0.042353950440883636,
-0.02693266235291958,
-0.002144541824236512,
-0.023874511942267418,
-0.006521513219922781,
-0.03808605298399925,
0.028524087741971016,
-0.01880975440144539,
-0.030440669506788254,
0.008532947860658169,
-0.020719649270176888,
-0.04440254718065262,
0.0164805818349123,
0.004388648550957441,
0.009387458674609661,
0.0063871401362121105,
-0.006966209504753351,
0.020105035975575447,
-0.007412423845380545,
0.006393653806298971,
0.011971638537943363,
0.019601698964834213,
0.04248321056365967,
0.00409241346642375,
0.04449782520532608,
-0.012482166290283203,
-0.01302582211792469,
-0.003529955167323351,
-0.03093179315328598,
0.05611490085721016,
-0.004168306477367878,
0.003063508542254567,
0.03071228414773941,
-0.058934301137924194,
-0.011274286545813084,
0.019317833706736565,
-0.0306717399507761,
0.011355174705386162,
-0.02139657363295555,
0.009504415094852448,
0.005490091163665056,
0.002263177651911974,
-0.0827566385269165,
-0.016266480088233948,
0.02722468040883541,
0.004748689476400614,
0.014420493505895138,
-0.020746596157550812,
0.0062178922817111015,
-0.04167131334543228,
-0.006245683412998915,
-0.028400324285030365,
0.043972503393888474,
-0.021399669349193573,
-0.015250555239617825,
-0.02944714017212391,
0.021712595596909523,
0.02092813327908516,
0.016322938725352287,
-0.007130406331270933,
0.0032789395190775394,
0.012850052677094936,
-0.013463092036545277,
0.023627210408449173,
0.022083977237343788,
-0.027884818613529205,
-0.046848464757204056,
-0.028299396857619286,
-0.013513108715415001,
0.010624152608215809,
-0.05947457253932953,
0.0033184762578457594,
0.01483767107129097,
-0.007741050329059362,
-0.028609242290258408,
-0.01962565816938877,
0.026941480115056038,
0.0014358112821355462,
0.025025228038430214,
-0.011019615456461906,
-0.000889287272002548,
-0.021137135103344917,
-0.05967109650373459,
0.04780765622854233,
-0.015438941307365894,
-0.024341726675629616,
0.02738872915506363,
0.059912681579589844,
0.030787065625190735,
-0.02554148994386196,
0.0027267110999673605,
-0.05151314288377762,
-0.005861811339855194,
-0.049598488956689835,
-0.012160041369497776,
-0.0056190346367657185,
0.007157580927014351,
-0.023331718519330025,
-0.0549796000123024,
-0.0021945692133158445,
0.020045489072799683,
0.04008058086037636,
-0.01648900657892227,
0.027959058061242104,
0.0478847362101078,
-0.043560754507780075,
-0.028126712888479233,
-0.016691138967871666,
0.0059137544594705105,
0.03496142476797104,
0.008740351535379887,
0.03323699161410332,
-0.035261403769254684,
-0.003854980692267418,
0.03821861743927002,
0.040013641119003296,
0.007857858203351498,
0.05197044834494591,
0.024549834430217743,
0.04938480630517006,
0.029937226325273514,
-0.020719323307275772,
-0.055435847491025925,
0.05424095690250397,
-0.02212519384920597,
0.03384959325194359,
0.004787859972566366,
-0.028193378821015358,
0.034061498939991,
0.008384224027395248,
0.00144126545637846,
-0.002628745511174202,
-0.02006964385509491,
-0.04192258045077324,
0.02457142062485218,
-0.000903675623703748,
0.05626858025789261,
0.014581725001335144,
0.011349671520292759,
0.00779236713424325,
-0.027807047590613365,
0.004635866731405258,
0.014096426777541637,
-0.09272236377000809,
-0.04466801509261131,
-0.02213560976088047,
-0.03111754171550274,
0.04675785452127457,
0.02945663593709469,
-0.034524399787187576,
-0.0326106920838356,
-0.029131941497325897,
-0.0001616040535736829,
0.00026832037838175893,
0.03404148668050766,
-0.026169203221797943,
0.045748285949230194,
-0.026204191148281097,
0.027145080268383026,
-0.020418569445610046,
0.021413130685687065,
0.1008695736527443,
0.06784167140722275,
0.00863886158913374,
-0.09697666019201279,
0.018260439857840538,
-0.035699550062417984,
0.007971938699483871,
-0.035513974726200104,
0.036235760897397995,
-0.008283744566142559,
0.04003496840596199,
0.009630569256842136,
0.05379054322838783,
0.009615183807909489,
-0.025985728949308395,
0.04888971149921417,
-0.012673260644078255,
-0.031879156827926636,
-0.012548225931823254,
0.019156770780682564,
0.014101251028478146,
0.01071245688945055,
-0.04807117208838463,
0.0014172254595905542,
-0.022308234125375748,
0.0259709432721138,
-0.00934885535389185,
-0.02661100961267948,
0.04923497140407562,
0.02278929390013218,
-0.0065254936926066875,
-0.018835822120308876,
0.008589140139520168,
-0.0388961136341095,
-0.018600724637508392,
-0.0044813333079218864,
0.047421157360076904,
-0.006824368145316839,
0.022672101855278015,
0.041958101093769073,
0.03566392511129379,
0.0032356271985918283,
-0.021322455257177353,
-0.005873164162039757,
-0.06704994291067123,
0.01856229640543461,
-0.023429512977600098,
0.006627365946769714,
0.0007842346094548702,
0.0020661368034780025,
-0.027071064338088036,
-0.0026096978690475225,
-0.009247642941772938,
-0.0021002567373216152,
-0.026145806536078453,
0.007628945168107748,
0.05455154925584793,
-0.00882705394178629,
-0.031990617513656616,
-0.006836991291493177,
0.009362331591546535,
0.002873192075639963,
0.040095459669828415,
-0.05050094053149223,
-0.021980207413434982,
-0.014648405835032463,
-0.02587859518826008,
0.02181502804160118,
-0.0014724009670317173,
-0.007504674606025219,
-0.035363465547561646,
-0.00042683168430812657,
-0.019325081259012222,
0.007009301334619522,
-0.00570364436134696,
-0.0020372983999550343,
0.04320180043578148,
0.008434114046394825,
0.022632893174886703,
-0.018945816904306412,
0.0027647821698337793,
-0.004809853620827198,
-0.020130133256316185,
-0.0024036734830588102,
0.017357822507619858,
-0.003864108119159937,
0.03407860919833183,
0.048613231629133224,
-0.019214754924178123,
0.043637409806251526,
-0.03728857636451721,
-0.018003074452280998,
0.05116308107972145,
-0.022933034226298332,
0.021361108869314194,
-0.030392322689294815,
-0.026699019595980644,
-0.03273511677980423,
-0.06505249440670013,
0.04674656316637993,
0.014450408518314362,
-0.0034788846969604492,
0.02058539353311062,
0.032890111207962036,
0.01537246722728014,
0.012776557356119156,
0.016795068979263306,
-0.039602670818567276,
-0.00825653225183487,
0.01131676509976387,
0.041881754994392395,
-0.030474934726953506,
-0.03832811489701271,
0.004726620391011238,
-0.0026200665161013603,
0.0033964505419135094,
0.011670684441924095,
-0.05959035083651543,
0.012918440625071526,
0.003274559509009123,
0.007993999868631363,
-0.05701940879225731,
-0.005774813704192638,
-0.038740355521440506,
0.0032186282332986593,
0.00601512286812067,
-0.012327383272349834,
0.030621565878391266,
0.0016933907754719257,
-0.06149039790034294,
-0.021963512524962425,
0.021278060972690582,
0.02738017775118351,
-0.029310327023267746,
0.0323677733540535,
0.03475173935294151,
0.021861473098397255,
0.03202878311276436,
-0.03487074002623558,
-0.00021794911299366504,
0.0237604770809412,
-0.03578285500407219,
-0.042574457824230194,
0.029266107827425003,
-0.006559626664966345,
0.04640119522809982,
0.013587559573352337,
-0.010791303589940071,
-0.059564314782619476,
0.0519789382815361,
-0.03501402586698532,
0.0037856902927160263,
0.041062429547309875,
0.012486033141613007,
0.0033008947502821684,
-0.029285714030265808,
0.010897628031671047,
0.035050470381975174,
-0.03938424214720726,
0.032261915504932404,
0.041627366095781326,
0.009116753935813904,
-0.057092517614364624,
-0.011689617298543453,
-0.03837227821350098,
0.04753701016306877,
0.012670428492128849,
0.013172999955713749,
0.03464202582836151,
0.041343946009874344,
-0.03598705306649208,
0.05603506788611412,
0.041579969227313995,
-0.002069933107122779,
-0.07350799441337585,
-0.01875893957912922,
0.02511749230325222,
0.025951875373721123,
0.043178170919418335,
-0.017711518332362175,
0.000893662974704057,
0.03903617709875107,
-0.09094560891389847,
0.03066599927842617,
-0.013299770653247833,
0.004834893625229597,
-0.028352053835988045,
-0.014841059222817421,
-0.03750045597553253,
0.04781413823366165,
0.0670369490981102,
0.04841255396604538,
-0.00833675917237997,
0.003949697129428387,
-0.05140302702784538,
-0.05112863704562187,
-0.00982863362878561,
0.023599550127983093,
-0.025677083060145378,
-0.013108116574585438,
0.06692507863044739,
-0.025744332000613213,
-0.06592006981372833,
0.05177128314971924,
0.007805627305060625,
0.02459239587187767,
-0.0010127619607374072,
0.00794705469161272,
0.02083263173699379,
-0.018560661002993584,
0.027176493778824806,
-0.016712266951799393,
0.006836203392595053,
0.04870162904262543,
0.010845962911844254,
0.0354878306388855,
0.0120241055265069,
-0.026292230933904648,
-0.012472511269152164,
-0.03930598497390747,
0.0010396233992651105,
0.03029259853065014,
-0.0026662382297217846,
-0.009800812229514122,
-0.031629908829927444,
-0.018753917887806892,
0.01013655960559845,
-0.025953246280550957,
-0.012726917862892151,
-0.03803446888923645,
0.0012877664994448423,
0.050732534378767014,
0.00035456905607134104,
-0.006019068416208029,
-0.004453244153410196,
0.012076999060809612,
-0.03361443430185318,
0.01687294989824295,
-0.01910393126308918,
-0.008767522871494293,
-0.046626266092061996,
-0.011841975152492523,
0.015982110053300858,
-0.005484323482960463,
0.016064396128058434,
-0.05554473027586937,
-0.04451165720820427,
0.0293694157153368,
0.001659574219956994,
-0.007219992112368345,
0.006434174254536629,
-0.05889284238219261,
-0.01674775220453739,
-0.07613983750343323,
0.023134561255574226,
0.005600988864898682,
0.04410216212272644,
-0.05204286426305771,
-0.03277437761425972,
-0.004929384682327509,
-0.040383968502283096,
0.05773141607642174,
-0.011011997237801552,
-0.011480893939733505,
0.0117469048127532,
0.0230234507471323,
0.02709302119910717,
-0.058117032051086426,
-0.03151138871908188,
0.010010181926190853,
-0.04696383327245712,
-0.002314408775418997,
0.0022923096548765898,
0.014932298101484776,
-0.0497690811753273,
0.045336250215768814,
-0.03258980065584183,
0.02915790304541588,
0.02633565105497837,
-0.016456840559840202,
0.04312743991613388,
-0.016857171431183815,
-0.007221263833343983,
0.047844842076301575,
-0.01072414219379425,
0.016741761937737465,
0.0025912846904248,
0.006583204492926598,
-0.006689481902867556,
-0.0006172170978970826,
0.0072891623713076115,
-0.0013534099562093616,
-0.02931222878396511,
-0.010241870768368244,
0.01996263675391674,
-0.02282688207924366,
-0.014536373317241669,
0.03143090754747391,
-0.004962899722158909,
-0.023317284882068634,
0.0632435753941536,
0.014824260026216507,
0.05009757727384567,
0.02170697972178459,
-0.0031091750133782625,
0.012104479596018791,
-0.00634928559884429,
-0.0023542207200080156,
0.01748098060488701,
0.023861469700932503,
-0.006064185407012701,
0.005871855653822422,
0.007874147035181522,
0.0036459509283304214,
0.02213735692203045,
-0.014416311867535114,
0.05179957300424576,
-0.08472704887390137,
-0.00996475387364626,
0.020709684118628502,
-0.004460631869733334,
0.015800882130861282,
-0.0033515661489218473,
-0.018173823133111,
0.07129231840372086,
-0.010751177556812763,
0.044515226036310196,
-0.008734005503356457,
0.00014560826821252704,
-0.017714638262987137,
0.013741489499807358,
-0.013092038221657276,
0.05212032422423363,
-0.016762206330895424,
-0.01897432841360569,
-0.03580903261899948,
0.039196860045194626,
0.056417569518089294,
-0.0628449097275734,
0.007996169850230217,
-0.00916218664497137,
-0.012800424359738827,
0.0014827465638518333,
-0.011746465228497982,
-0.013685581274330616,
-0.011234474368393421,
0.03514586761593819,
0.04697186499834061,
0.04713398963212967,
-0.0470927432179451,
-0.004462686832994223,
-0.02105226367712021,
0.02091151848435402,
-0.04263272508978844,
0.027317140251398087,
-0.04117848351597786,
0.03459649905562401,
0.0038443785160779953,
-0.006198905408382416
] |
<p>I don't get a grip of what that exactly means. What IS an abstract singlet, doublet,... under $SU(N)$ or other groups?</p>
| 345 |
[
0.015309898182749748,
0.008707353845238686,
-0.005797259043902159,
-0.044812336564064026,
0.04062424972653389,
0.004558087792247534,
-0.029511092230677605,
-0.027714192867279053,
-0.005974030587822199,
-0.0715516209602356,
0.043081920593976974,
-0.016436126083135605,
0.06715009361505508,
0.029204702004790306,
-0.039716415107250214,
0.035489633679389954,
-0.023584384471178055,
0.006808689329773188,
-0.026610828936100006,
-0.011583240702748299,
0.03311050683259964,
0.032492876052856445,
-0.004963315092027187,
0.009309850633144379,
-0.004671950358897448,
0.034602172672748566,
0.022843269631266594,
0.029504697769880295,
0.054309312254190445,
0.04870200157165527,
-0.05899762734770775,
-0.034545984119176865,
0.03596140816807747,
0.01796489767730236,
-0.003163941204547882,
0.002986698178574443,
-0.0037144506350159645,
-0.032174091786146164,
-0.017668167129158974,
0.004629706963896751,
-0.01558204460889101,
-0.026387663558125496,
-0.047368552535772324,
0.02060825191438198,
-0.031488850712776184,
0.014621065929532051,
-0.04016678035259247,
-0.02014232985675335,
0.04830705374479294,
-0.04297798499464989,
0.08915602415800095,
0.025521306321024895,
0.029509780928492546,
0.007642345502972603,
0.005795637611299753,
0.037499476224184036,
0.04681578651070595,
0.051388438791036606,
0.031179551035165787,
-0.02268350124359131,
-0.007624667603522539,
0.02032940275967121,
0.03428579494357109,
-0.039374370127916336,
-0.045444589108228683,
-0.00519307516515255,
-0.013924365863204002,
-0.0314994677901268,
-0.004209039732813835,
0.013943002559244633,
0.004310824442654848,
0.03373599052429199,
0.010044137015938759,
-0.04340352490544319,
0.008936894126236439,
-0.04864197596907616,
-0.008400444872677326,
-0.016170958057045937,
0.05598381906747818,
-0.0062664407305419445,
-0.012318471446633339,
0.01980937458574772,
-0.01410010363906622,
0.026248738169670105,
-0.0039260368794202805,
-0.01446590293198824,
0.07804261893033981,
0.011892844922840595,
-0.013221553526818752,
0.00046321930130943656,
-0.014139791019260883,
-0.024052830412983894,
0.053387172520160675,
0.01432169508188963,
-0.05954791232943535,
0.028612365946173668,
-0.015159966424107552,
0.034186817705631256,
-0.007072477601468563,
-0.002690427005290985,
0.00961395911872387,
0.007742428220808506,
0.047596488147974014,
0.10964394360780716,
0.022477617487311363,
-0.004098368342965841,
-0.026662491261959076,
0.015586063265800476,
0.0006357210222631693,
0.015635335817933083,
0.00036882012500427663,
-0.0050602685660123825,
-0.05408012121915817,
-0.020838003605604172,
0.01978417858481407,
0.010421679355204105,
-0.007155176717787981,
0.0015421637799590826,
0.04504317790269852,
0.06450004875659943,
0.03402147814631462,
-0.02203921228647232,
0.015131824649870396,
-0.007070951163768768,
-0.0922059640288353,
0.03073444589972496,
0.04827844351530075,
0.020147481933236122,
-0.0418025441467762,
0.028193647041916847,
0.020775415003299713,
-0.015094734728336334,
0.02094319462776184,
0.008050544187426567,
0.02760487236082554,
-0.03486532345414162,
-0.11397621035575867,
-0.07853687554597855,
0.015956852585077286,
0.004432744812220335,
-0.018885336816310883,
-0.07315759360790253,
0.024787215515971184,
0.02669595181941986,
0.062176793813705444,
-0.029166921973228455,
-0.029236719012260437,
0.0065031638368964195,
0.015938814729452133,
0.049339886754751205,
0.015072564594447613,
-0.029648946598172188,
-0.0052024866454303265,
-0.057971928268671036,
0.004578819498419762,
-0.03393605723977089,
0.02851453609764576,
0.0013466420350596309,
-0.029099583625793457,
-0.020623058080673218,
0.1143353283405304,
-0.021990381181240082,
0.0011162461014464498,
0.0011309279361739755,
-0.0022658403031527996,
-0.025479109957814217,
0.07101764529943466,
0.001857974799349904,
0.015655430033802986,
0.04854792356491089,
0.01192945335060358,
0.020294517278671265,
0.0029719804879277945,
0.07461444288492203,
0.01326862070709467,
-0.015576375648379326,
-0.021529419347643852,
-0.05157991126179695,
0.009197580628097057,
-0.04138750955462456,
-0.06255685538053513,
-0.04411934316158295,
0.005352215841412544,
0.0069029987789690495,
-0.013099141418933868,
0.018922843039035797,
-0.002239908091723919,
-0.016601016744971275,
0.014118715189397335,
-0.049073923379182816,
-0.006925300695002079,
-0.04805077239871025,
-0.025962455198168755,
0.018069468438625336,
-0.02838796190917492,
0.008264537900686264,
0.05358197167515755,
0.036265913397073746,
-0.005532772745937109,
-0.013190780766308308,
-0.03185872361063957,
0.007491193246096373,
0.010919134132564068,
-0.034844085574150085,
0.02990768849849701,
0.006555101368576288,
0.02583182416856289,
0.019120482727885246,
0.04299478605389595,
-0.017119621858000755,
-0.0029395625460892916,
0.015513308346271515,
-0.015217078849673271,
0.014833919703960419,
0.024956652894616127,
-0.00648678420111537,
0.0047640204429626465,
-0.01647903583943844,
0.005426083691418171,
0.04322375729680061,
-0.024656815454363823,
0.06228196248412132,
0.0012167784152552485,
0.004578364081680775,
0.01682981476187706,
-0.018935207277536392,
-0.0023935113567858934,
-0.007616538088768721,
-0.018974054604768753,
-0.011982791125774384,
-0.026595525443553925,
0.005475975107401609,
0.036375414580106735,
0.026880688965320587,
-0.013130787760019302,
0.041738271713256836,
0.0051495046354830265,
0.037276677787303925,
0.03680102527141571,
0.016725661233067513,
-0.034792330116033554,
-0.008515617810189724,
0.010898061096668243,
0.006104121915996075,
0.013767789117991924,
-0.015811819583177567,
-0.001101633650250733,
0.024848951026797295,
0.005769134033471346,
0.010319435968995094,
-0.019235040992498398,
0.05427217856049538,
-0.015566116198897362,
-0.03765520453453064,
0.01869249902665615,
-0.025316668674349785,
0.0334688164293766,
-0.013495177030563354,
0.00027125654742121696,
0.003941521048545837,
-0.0007193933706730604,
-0.00048152529052458704,
-0.04000847414135933,
-0.02555478736758232,
0.040367286652326584,
0.001337928930297494,
-0.03288045898079872,
-0.015545079484581947,
0.024881111457943916,
-0.004572562873363495,
0.0317571684718132,
-0.029205461964011192,
0.02156429924070835,
0.015016145072877407,
0.019372055307030678,
0.03680378571152687,
-0.0025141665246337652,
0.013400272466242313,
-0.024327438324689865,
-0.009477673098444939,
-0.03034769929945469,
-0.0054093231447041035,
0.05169645696878433,
0.019957875832915306,
-0.03335810452699661,
0.02938520722091198,
-0.06378056854009628,
-0.0424271821975708,
0.030443567782640457,
-0.03114144690334797,
-0.0024857015814632177,
0.020140398293733597,
-0.020134566351771355,
-0.06787648051977158,
-0.020957957953214645,
-0.030723711475729942,
0.021442322060465813,
-0.02907479740679264,
-0.024414043873548508,
0.06285504251718521,
0.018470987677574158,
-0.03857035934925079,
0.029554439708590508,
-0.026575438678264618,
-0.018788008019328117,
-0.024829205125570297,
-0.04461810365319252,
0.04622410982847214,
-0.03798984736204147,
0.007349164225161076,
0.029680948704481125,
-0.0441841259598732,
-0.0013184406561776996,
-0.0590842179954052,
-0.038984958082437515,
0.0009191903518512845,
0.012266552075743675,
0.022322051227092743,
0.024746544659137726,
-0.008415226824581623,
0.10842707008123398,
0.026141952723264694,
-0.05091658979654312,
-0.011899452656507492,
-0.00008499182877130806,
-0.029215019196271896,
-0.0023686180356889963,
0.0444764718413353,
0.019878899678587914,
0.01778905652463436,
0.008477628231048584,
0.06735909730195999,
0.0289451964199543,
0.03680703043937683,
0.000008353021257789806,
-0.03874754533171654,
-0.0059627508744597435,
-0.005378877278417349,
0.00676132133230567,
0.02259698510169983,
0.002613615710288286,
-0.043982379138469696,
0.013992768712341785,
0.010212267749011517,
-0.00887337140738964,
-0.011542845517396927,
-0.013236280530691147,
0.06003114581108093,
0.007773552089929581,
0.01808982342481613,
0.0040903775952756405,
0.05285137891769409,
0.053462184965610504,
-0.01037469319999218,
-0.017999673262238503,
0.012068673968315125,
0.016505323350429535,
-0.05836522579193115,
0.0037041017785668373,
0.017318500205874443,
0.03173258155584335,
-0.03317373991012573,
-0.012118332087993622,
0.028701072558760643,
-0.008455868810415268,
0.01007054653018713,
-0.018128983676433563,
-0.02146333083510399,
0.04530792683362961,
0.037832360714673996,
0.01882149465382099,
0.03469972312450409,
-0.029466858133673668,
0.006259408313781023,
-0.0514848418533802,
0.009338896721601486,
0.02070182003080845,
0.05360059440135956,
-0.01176043413579464,
0.06471051275730133,
0.008842050097882748,
0.018459120765328407,
-0.006524526514112949,
0.01678605191409588,
-0.04894159734249115,
0.02564837411046028,
-0.02048725076019764,
0.007661422248929739,
0.007157778833061457,
-0.012144239619374275,
0.005901864729821682,
-0.010400458239018917,
-0.06228059530258179,
-0.014997079968452454,
-0.032529741525650024,
-0.007373161613941193,
0.021573012694716454,
-0.011131159029901028,
0.022063687443733215,
-0.010352140292525291,
0.04520440474152565,
0.05386596545577049,
-0.00204165349714458,
-0.010441374965012074,
0.021139618009328842,
-0.006390628404915333,
-0.012234068475663662,
-0.02263745665550232,
0.01639932580292225,
-0.014497097581624985,
0.003071663435548544,
0.06221160665154457,
0.02506035380065441,
-0.03355581685900688,
-0.005644334014505148,
-0.0011693367268890142,
0.04632898047566414,
-0.006131196394562721,
-0.023298876360058784,
0.026475518941879272,
-0.02995261922478676,
-0.02253814972937107,
0.03589032590389252,
0.015471931546926498,
-0.005596347618848085,
0.013795208185911179,
0.03498910740017891,
0.019905300810933113,
-0.03357335925102234,
0.03175458684563637,
0.0013506155228242278,
0.009246119298040867,
-0.04003164917230606,
-0.03188204765319824,
-0.0017678537406027317,
-0.0027895374223589897,
-0.013169456273317337,
0.029727395623922348,
-0.004765327088534832,
-0.04048629477620125,
0.0049955397844314575,
-0.004593287128955126,
0.008946816436946392,
-0.07603868097066879,
-0.03618669509887695,
-0.012423324398696423,
-0.01726439967751503,
-0.013779030181467533,
0.026071971282362938,
0.01867910474538803,
0.07236539572477341,
0.01880776695907116,
0.013042802922427654,
0.008785816840827465,
-0.0475277453660965,
0.008578176610171795,
0.050963208079338074,
0.020216085016727448,
0.008315978571772575,
-0.018187744542956352,
-0.028442589566111565,
0.013112163171172142,
0.048890046775341034,
-0.007251192349940538,
0.035703204572200775,
-0.0003885674523189664,
-0.026738671585917473,
-0.01081966795027256,
-0.003532530041411519,
0.008119161240756512,
0.016368936747312546,
-0.02108711749315262,
0.019052090123295784,
-0.024369508028030396,
-0.005169038660824299,
-0.06035556271672249,
0.031166864559054375,
0.009309937246143818,
0.03375890851020813,
0.038344819098711014,
0.02592870593070984,
0.017055809497833252,
0.03346281498670578,
0.004475064110010862,
-0.08332821726799011,
-0.004063328728079796,
0.042602475732564926,
-0.005532114300876856,
0.08356617391109467,
-0.04782651737332344,
-0.029819583520293236,
0.018559416756033897,
0.0024725724942982197,
0.021769985556602478,
-0.025668703019618988,
-0.05948982387781143,
0.014644555747509003,
0.03467836603522301,
0.018643653020262718,
0.024973265826702118,
0.00634678453207016,
-0.002367079257965088,
0.012067911215126514,
-0.04852552339434624,
0.022772427648305893,
0.009626435115933418,
0.03143428638577461,
-0.040260087698698044,
-0.015683617442846298,
-0.03642657399177551,
0.046474434435367584,
-0.021957596763968468,
0.005772664211690426,
0.054739825427532196,
-0.011287764646112919,
-0.013486872427165508,
-0.0006666280678473413,
-0.005743585992604494,
-0.011767176911234856,
-0.007592885755002499,
0.01384743768721819,
-0.007084906101226807,
-0.021423323079943657,
0.024670477956533432,
-0.0017102406127378345,
-0.002389713656157255,
-0.0003512265393510461,
-0.016119729727506638,
0.0015729853184893727,
-0.010680056177079678,
-0.04020875319838524,
0.04675175994634628,
-0.03784864768385887,
0.04653201624751091,
-0.04741223528981209,
0.0007881667115725577,
0.013091378845274448,
-0.05102132260799408,
-0.019040636718273163,
-0.010782754048705101,
-0.014778591692447662,
0.004989647306501865,
-0.037311654537916183,
0.03456658497452736,
0.015445252880454063,
-0.027931157499551773,
-0.06126866862177849,
-0.01913454383611679,
0.024462832137942314,
0.018289456143975258,
-0.048470206558704376,
-0.025281716138124466,
0.019244305789470673,
-0.03069489635527134,
-0.015443316660821438,
0.008698568679392338,
0.0793604776263237,
-0.025379711762070656,
-0.04891687259078026,
0.017179058864712715,
0.026174593716859818,
0.04448659345507622,
-0.018401743844151497,
-0.01739039272069931,
0.0131587665528059,
-0.0002889447787310928,
0.02670944854617119,
0.03220553323626518,
0.016258684918284416,
-0.01814282312989235,
-0.011054503731429577,
-0.019317829981446266,
-0.031882867217063904,
-0.01421866100281477,
-0.07057201117277145,
0.022919537499547005,
0.038796961307525635,
-0.012409611605107784,
0.020376037806272507,
-0.00485091982409358,
0.019673597067594528,
-0.019671766087412834,
0.03731973096728325,
-0.007740179542452097,
-0.016195090487599373,
0.005017102230340242,
-0.054830390959978104,
0.034221649169921875,
-0.0035131850745528936,
0.0008970407070592046,
0.04514981061220169,
0.050890155136585236,
0.001564221573062241,
0.003969105891883373,
0.023313939571380615,
-0.0511757917702198,
-0.0367942675948143,
-0.000018468377675162628,
0.023182673379778862,
-0.015794256702065468,
-0.004120377823710442,
-0.03316698595881462,
-0.010278302244842052,
-0.029371220618486404,
-0.003138020634651184,
0.025618553161621094,
-0.01657095178961754,
0.08130770921707153,
0.013289844617247581,
0.012291142717003822,
-0.004725711420178413,
-0.00656126718968153,
-0.018773337826132774,
-0.026626165956258774,
0.012545445002615452,
0.05195536091923714,
-0.02142251655459404,
-0.018909746780991554,
0.03549564257264137,
0.04123302176594734,
-0.013853807933628559,
0.07060272991657257,
0.04308793321251869,
0.0046070413663983345,
0.014495819807052612,
0.007366585545241833,
-0.04526835307478905,
0.030939636752009392,
-0.06984277814626694,
0.014355244114995003,
0.025368673726916313,
-0.00114636798389256,
-0.012445670552551746,
0.017258569598197937,
-0.00419557886198163,
-0.02233867347240448,
-0.03141958639025688,
-0.03686581179499626,
0.026855865493416786,
0.018183870241045952,
-0.024920843541622162,
-0.0003756984369829297,
0.0006227827980183065,
0.009658291935920715,
-0.014596167951822281,
-0.0004901622887700796,
0.0010944193927571177,
-0.04782865196466446,
-0.022120485082268715,
-0.025668738409876823,
-0.04800880700349808,
0.01454243715852499,
-0.017245080322027206,
-0.03383133187890053,
0.0018968050135299563,
-0.010250812396407127,
0.02331058867275715,
-0.0059224390424788,
0.03446142375469208,
-0.013886789791285992,
0.05494517460465431,
0.011097290553152561,
0.03383808583021164,
0.030021922662854195,
-0.035995688289403915,
0.14250485599040985,
0.018319128081202507,
0.013712992891669273,
-0.07586149871349335,
-0.008509100414812565,
-0.03750520199537277,
0.03625055029988289,
-0.028334377333521843,
0.03801858797669411,
0.0033741802908480167,
0.020989838987588882,
-0.023137293756008148,
0.07691692560911179,
0.040622953325510025,
-0.014334447681903839,
0.03274211660027504,
-0.018046854063868523,
-0.04477398842573166,
0.0027544626500457525,
0.03680041804909706,
-0.017369428649544716,
-0.009668847545981407,
-0.036921314895153046,
0.012784017249941826,
0.021764293313026428,
0.03250102326273918,
-0.017523210495710373,
-0.032035183161497116,
0.05991673469543457,
0.02341049164533615,
-0.008942227810621262,
0.0013732578372582793,
-0.03057253547012806,
-0.029138080775737762,
-0.054884910583496094,
0.028288662433624268,
0.01054541114717722,
-0.011966465972363949,
0.045397501438856125,
0.06201137602329254,
0.04486559331417084,
-0.008493520319461823,
0.021136412397027016,
-0.029864061623811722,
-0.05119752138853073,
-0.008875478990375996,
-0.021081099286675453,
0.027029674500226974,
-0.017303908243775368,
-0.01032625138759613,
-0.03466818854212761,
0.01617206633090973,
0.028456734493374825,
-0.02507537230849266,
-0.018613504245877266,
-0.009787417016923428,
0.02744535356760025,
-0.04090612754225731,
-0.00343718146905303,
-0.0005176045815460384,
0.0203207079321146,
-0.014173013158142567,
0.04099645838141441,
-0.00595554756000638,
-0.02060854062438011,
0.007817478850483894,
0.016125090420246124,
-0.00489562563598156,
0.017186719924211502,
-0.03352118656039238,
-0.024836337193846703,
0.00012882902228739113,
0.009482646360993385,
-0.0011889453744515777,
0.030629148706793785,
0.011353435926139355,
0.05393465980887413,
-0.01937837153673172,
0.03218650072813034,
-0.012136486358940601,
-0.036035630851984024,
0.00782201997935772,
-0.04198084771633148,
-0.01948179118335247,
0.015344115905463696,
-0.0007482408545911312,
0.04098604992032051,
0.056845523416996,
-0.06594141572713852,
-0.0034655218478292227,
-0.007356476504355669,
0.046412546187639236,
0.0417315736413002,
-0.03284556046128273,
-0.005248325876891613,
0.010802637785673141,
-0.03707641735672951,
0.019777506589889526,
-0.043733809143304825,
0.02602984569966793,
0.030212581157684326,
-0.004984789527952671,
0.00007633255154360086,
0.04074164479970932,
-0.007642274722456932,
-0.0014086755691096187,
0.011286281980574131,
-0.042119886726140976,
0.04438658431172371,
0.005140258930623531,
-0.013546673581004143,
-0.025537904351949692,
-0.05271804332733154,
-0.015686577185988426,
-0.03634350001811981,
0.00026488263392820954,
0.02721313014626503,
-0.05269870162010193,
-0.020942529663443565,
-0.015741169452667236,
0.02804848924279213,
-0.02877603843808174,
-0.014933332800865173,
-0.053781528025865555,
0.016437789425253868,
-0.00024319147632922977,
0.010335659608244896,
-0.024333832785487175,
0.013843030668795109,
-0.022772803902626038,
0.011170980520546436,
0.058349430561065674,
0.00013492096331901848,
-0.017762040719389915,
0.03946850821375847,
0.004597673658281565,
-0.016623960807919502,
0.023673366755247116,
0.031509220600128174,
-0.008608723059296608,
0.0443291999399662,
-0.01204529870301485,
-0.04180111736059189,
0.04033784940838814,
-0.018602212890982628,
0.03887446969747543,
0.006352500058710575,
-0.023450927808880806,
-0.03817647323012352,
0.03382822498679161,
-0.045849353075027466,
-0.034029521048069,
0.01150413416326046,
-0.00026097087538801134,
-0.01869298703968525,
-0.017360128462314606,
0.012498668394982815,
0.007180992979556322,
-0.003842513542622328,
-0.015314030461013317,
-0.008079866878688335,
-0.026557419449090958,
-0.023357944563031197,
-0.021491698920726776,
-0.01048558484762907,
0.03494451940059662,
0.0030160723254084587,
0.011579890735447407,
-0.01676267571747303,
0.048643048852682114,
-0.06157300993800163,
0.016695069149136543,
-0.00867199432104826,
0.05260630324482918,
-0.08729274570941925,
-0.008996514603495598,
0.01896195486187935,
-0.002263310132548213,
0.009712722152471542,
-0.059069812297821045,
0.015651335939764977,
0.024846987798810005,
-0.04234151169657707,
0.014042288064956665,
-0.04865896329283714,
-0.02350299060344696,
-0.02290632203221321,
0.007017286494374275,
-0.07400767505168915,
0.048233289271593094,
0.020509449765086174,
0.03438670188188553,
0.027718663215637207,
-0.0038305679336190224,
0.01518738642334938,
-0.0011695589637383819,
-0.04561670497059822,
0.0001610483304830268,
0.003700437257066369,
-0.011412115767598152,
0.06524472683668137,
0.0025068975519388914,
-0.05534595251083374,
-0.00021930639923084527,
-0.02581193298101425,
-0.02870783396065235,
-0.015441685914993286,
0.014113119803369045,
0.025263316929340363,
0.008588355034589767,
0.02011636644601822,
-0.04748256132006645,
-0.022297602146863937,
0.02039412595331669,
0.029931169003248215,
0.03239814192056656,
-0.02491459622979164,
0.0008047788869589567,
-0.017549952492117882,
-0.02671693079173565,
-0.010508657433092594,
0.025161411613225937,
-0.011954313144087791,
-0.049283090978860855,
-0.024676965549588203,
-0.04516175389289856,
-0.03290325775742531,
-0.021374668926000595,
0.002348091686144471,
-0.01039469800889492,
-0.06819316744804382,
0.011588203720748425,
0.023016048595309258,
0.021214591339230537,
0.03895706310868263,
-0.004400945268571377,
-0.053788311779499054,
0.013638889417052269,
0.011639456264674664,
0.002161468379199505,
-0.059525519609451294,
-0.00535997748374939,
0.03243095800280571,
-0.004438626114279032,
0.01400055643171072,
-0.053699471056461334,
-0.004602500237524509,
0.01086064986884594,
0.016337420791387558,
0.01033652015030384,
-0.011005187407135963,
-0.09278617054224014,
0.0020634362008422613,
-0.05099466070532799,
0.05358527973294258,
0.018161671236157417,
0.026158446446061134,
-0.001697065308690071,
0.018548211082816124,
-0.023233095183968544,
0.03785238415002823,
0.0526617206633091,
0.01858813315629959,
-0.029448796063661575,
0.04585559666156769,
-0.008799747563898563,
-0.008078289218246937,
-0.025231804698705673,
-0.0077384524047374725,
-0.04151457920670509,
0.0013893849682062864,
-0.01708224229514599,
-0.033111151307821274,
-0.03241829201579094,
0.013190016150474548,
0.048556849360466,
-0.027766594663262367,
-0.004717089235782623,
-0.03035208396613598,
-0.05507172271609306,
0.05725356936454773,
0.0292583666741848,
-0.003019877476617694,
0.06141794100403786,
0.0052891387604177,
-0.007380595430731773,
0.029413685202598572,
-0.005582176614552736,
-0.030580611899495125,
0.028807274997234344,
0.015935515984892845,
0.004269191063940525,
-0.031501512974500656,
-0.00043147397809661925,
0.027452116832137108,
-0.04423535615205765,
-0.01933220587670803,
0.03474043682217598,
-0.005140912719070911,
-0.012826671823859215,
0.0464947335422039,
-0.007028925698250532,
0.019602106884121895,
0.03073243983089924,
0.002621422754600644,
0.023394335061311722,
0.008163068443536758,
0.016058558598160744,
0.055353645235300064,
0.010289456695318222,
0.005530301947146654,
-0.015672985464334488,
0.004213904030621052,
0.020354678854346275,
0.04061579331755638,
0.01403183862566948,
0.05886660888791084,
-0.025187859311699867,
-0.00370441609993577,
0.0017018279759213328,
-0.04832840710878372,
0.04569670930504799,
-0.0035699941217899323,
-0.011613108217716217,
0.08630245923995972,
-0.03842847794294357,
-0.02858441323041916,
-0.03499286621809006,
0.01744692027568817,
-0.024443350732326508,
0.018770169466733932,
0.08604954183101654,
0.04575689509510994,
-0.05528156831860542,
-0.015273653902113438,
-0.02470964565873146,
-0.00900090578943491,
0.05888655409216881,
-0.04812135174870491,
0.04651305079460144,
-0.0020513408817350864,
0.001800201484002173,
-0.02014511451125145,
-0.019953392446041107,
-0.027552375569939613,
-0.006080707535147667,
0.02043035998940468,
0.027372540906071663,
0.008297650143504143,
0.03188026696443558,
0.005179227329790592,
-0.0017556428210809827,
0.04901811107993126,
-0.0624527707695961,
-0.0187949538230896,
-0.034741684794425964,
0.00455677742138505,
-0.002544058719649911,
-0.03367326036095619
] |
<p>I have three DC circuits in my solar array. I have a three lead + ground (bare copper) tec armoured cable (#6). Why not run one circuit using the bare ground as negative? In fact, why not run three circuits and use the the bare copper as the common negative? </p>
| 10,721 |
[
0.0038869264535605907,
-0.01234865840524435,
0.005221301224082708,
0.003143695183098316,
-0.02033456414937973,
0.0024535981938242912,
-0.00542464992031455,
-0.010811098851263523,
-0.008903875946998596,
-0.024028770625591278,
0.02720489911735058,
-0.0009409119957126677,
0.030255621299147606,
0.017768776044249535,
0.025636611506342888,
-0.03585190325975418,
0.044468119740486145,
-0.004932266194373369,
-0.010954361408948898,
-0.06959666311740875,
-0.002309083240106702,
0.01425881776958704,
-0.00057439279044047,
0.02328498847782612,
0.05364982411265373,
-0.007531719747930765,
0.011077170260250568,
-0.011321580968797207,
-0.0034073800779879093,
0.050198908895254135,
-0.02117104083299637,
-0.05214519426226616,
-0.013568146154284477,
0.00961987767368555,
0.036116812378168106,
-0.0029775213915854692,
0.014544463716447353,
-0.056897714734077454,
-0.009420512244105339,
0.03130873292684555,
-0.0294113140553236,
-0.016512185335159302,
0.003171865362673998,
0.020221669226884842,
0.002981862984597683,
0.0007139294175431132,
0.005523286759853363,
-0.03288554400205612,
0.02455587312579155,
-0.10317006707191467,
0.03530137613415718,
-0.05397802218794823,
0.025707069784402847,
0.04371003806591034,
0.009016128256917,
0.010825905948877335,
0.05106673762202263,
0.05025245621800423,
0.01621931977570057,
-0.0000899892402230762,
0.021790681406855583,
-0.009200835600495338,
-0.024936575442552567,
-0.008574716746807098,
-0.028646375983953476,
0.024898061528801918,
0.024692805483937263,
-0.02917575091123581,
-0.01847882568836212,
-0.010090108960866928,
0.026724915951490402,
-0.03882336989045143,
-0.0185630414634943,
-0.03285576403141022,
-0.0043229879811406136,
-0.01863834634423256,
0.020089512690901756,
0.044043902307748795,
0.01733928918838501,
0.035039279609918594,
-0.014690776355564594,
0.026351802051067352,
0.027074536308646202,
0.05411055311560631,
0.024499325081706047,
0.0004450850829016417,
0.03542237728834152,
-0.0429626926779747,
0.041544359177351,
-0.044697340577840805,
0.009433318860828876,
0.029991377145051956,
0.05885874480009079,
0.03341985121369362,
-0.01565004140138626,
0.009726639837026596,
0.03121621161699295,
0.010422784835100174,
-0.021577181294560432,
0.008958983235061169,
-0.0056983474642038345,
-0.01187191717326641,
0.036960676312446594,
0.07254970818758011,
0.01872311532497406,
-0.004509239457547665,
0.00011452852777438238,
0.004750173073261976,
0.043286293745040894,
-0.005002694204449654,
-0.019501276314258575,
-0.010275083594024181,
0.025149337947368622,
-0.007624816615134478,
-0.006789092905819416,
-0.019860142841935158,
0.061221249401569366,
-0.011446488089859486,
0.03909940645098686,
0.03257377818226814,
0.023248927667737007,
-0.018425336107611656,
0.05496232584118843,
-0.05568462610244751,
-0.04829069972038269,
0.00014045636635273695,
-0.026233071461319923,
-0.011411343701183796,
-0.012514878064393997,
0.003468085778877139,
0.011319703422486782,
-0.020377423614263535,
-0.006520972121506929,
-0.003631764790043235,
0.009236650541424751,
-0.009389279410243034,
-0.0907975360751152,
-0.07225850969552994,
0.0026961294934153557,
-0.042205166071653366,
0.012744569219648838,
-0.047369539737701416,
0.014157809317111969,
0.03734981641173363,
0.06577300280332565,
-0.028501084074378014,
-0.003646634519100189,
-0.0107080964371562,
0.0010175482602789998,
0.03456520661711693,
0.010598432272672653,
-0.03183584660291672,
0.008081413805484772,
-0.020708853378891945,
-0.02110915444791317,
-0.06153765693306923,
0.05467214435338974,
-0.0018446750473231077,
0.010507652536034584,
0.025213293731212616,
0.05475350841879845,
-0.009059317409992218,
0.024301253259181976,
0.019973382353782654,
-0.02710913121700287,
-0.00566885806620121,
0.0659494400024414,
-0.011773438192903996,
-0.01994132064282894,
0.03201719745993614,
0.03592598810791969,
0.01805214211344719,
0.038811419159173965,
0.03930893540382385,
0.011419367045164108,
-0.054873988032341,
0.037686899304389954,
-0.04451857507228851,
0.04278206452727318,
-0.02505965158343315,
-0.004999066703021526,
-0.022093994542956352,
0.030983194708824158,
0.020395739004015923,
-0.0003393885854166001,
0.04527921974658966,
-0.012109571136534214,
-0.044310636818408966,
0.018132012337446213,
-0.0029339767061173916,
-0.013475239276885986,
-0.02230137772858143,
-0.010095731355249882,
0.03754033148288727,
-0.020868364721536636,
-0.018060896545648575,
-0.01834511011838913,
0.01098597701638937,
-0.004178194794803858,
-0.010956062003970146,
0.013742909766733646,
0.0487448126077652,
0.02141985110938549,
-0.00774597330018878,
0.03860924392938614,
0.02699596807360649,
0.08246228843927383,
-0.011102749966084957,
0.0023056024219840765,
-0.033898185938596725,
-0.010973944328725338,
-0.00892594177275896,
-0.06232285499572754,
0.010579091496765614,
0.04934278875589371,
0.00004526213524513878,
-0.00825819093734026,
0.01784011349081993,
0.008974723517894745,
0.0597694106400013,
-0.020359627902507782,
0.07615025341510773,
0.04797430709004402,
-0.021948667243123055,
0.016855161637067795,
-0.013394029811024666,
-0.005948309786617756,
0.004649931099265814,
0.012948432005941868,
0.007387702353298664,
-0.0795857310295105,
0.03216545283794403,
0.04220570996403694,
-0.030291369184851646,
-0.04115847870707512,
0.0384841188788414,
0.027570536360144615,
-0.002741018543019891,
0.016727391630411148,
0.04926179721951485,
0.026462752372026443,
0.020947635173797607,
0.0007049411651678383,
0.02634757198393345,
-0.037843551486730576,
-0.031125115230679512,
0.004952471703290939,
-0.0060389987193048,
0.009166601113975048,
-0.04066433012485504,
-0.04583132639527321,
0.07961650937795639,
-0.007074190769344568,
0.03342896327376366,
0.02689109370112419,
-0.028497442603111267,
0.034564170986413956,
-0.06391815096139908,
0.011143635958433151,
0.012568648904561996,
0.020212464034557343,
0.01794162020087242,
-0.0017684645717963576,
-0.0227114986628294,
0.02590279094874859,
0.016372231766581535,
-0.02002805657684803,
-0.011075221933424473,
0.03099871054291725,
-0.030624285340309143,
0.007720049005001783,
-0.032962698489427567,
0.024968329817056656,
-0.02488679066300392,
0.0011051446199417114,
0.036253202706575394,
-0.007317936513572931,
0.06220333278179169,
-0.044355329126119614,
-0.04647495225071907,
-0.015616034157574177,
0.019543083384633064,
0.01883953996002674,
0.024939240887761116,
-0.03478018194437027,
0.012873291037976742,
-0.0016799350269138813,
-0.046516433358192444,
0.021805262193083763,
0.04116467759013176,
0.01804433949291706,
0.021325528621673584,
-0.010280978865921497,
-0.00440607126802206,
-0.03413175791501999,
-0.020039478316903114,
-0.01508480403572321,
-0.023832235485315323,
-0.05094398558139801,
0.0699935033917427,
0.01919829286634922,
-0.045940808951854706,
-0.0012618058826774359,
-0.08329849690198898,
-0.0334487147629261,
0.030503660440444946,
-0.016833314672112465,
-0.000411681248806417,
-0.057259779423475266,
0.04309719055891037,
0.01661357842385769,
-0.043138712644577026,
0.00978112407028675,
-0.027589719742536545,
-0.046773165464401245,
-0.023366309702396393,
0.00942922942340374,
0.012745952233672142,
-0.02504972741007805,
-0.0395406149327755,
0.0916287824511528,
0.05754989758133888,
-0.03330360725522041,
0.003293194342404604,
-0.047456711530685425,
-0.06090753152966499,
-0.036416321992874146,
0.03169853612780571,
0.03527168929576874,
-0.01136699877679348,
-0.018907545134425163,
0.01942255347967148,
0.04833691939711571,
0.04864094406366348,
0.024656688794493675,
0.0002947046305052936,
-0.01623213291168213,
0.018384773284196854,
-0.044227223843336105,
0.03878837823867798,
0.010376663878560066,
-0.05149281769990921,
-0.001366700162179768,
0.009057270362973213,
0.03493071720004082,
0.02434045635163784,
-0.016341185197234154,
0.007090444210916758,
-0.010406873188912868,
0.05747472122311592,
-0.024260804057121277,
0.0127867441624403,
0.06100118160247803,
-0.01862296089529991,
-0.03512788563966751,
0.020023252815008163,
0.007944820448756218,
-0.073868528008461,
-0.017992308363318443,
0.008890659548342228,
0.0602651871740818,
-0.02460872009396553,
-0.06459001451730728,
0.013475071638822556,
-0.003942658193409443,
0.004694594070315361,
0.008106420747935772,
-0.024854090064764023,
0.025625599548220634,
0.05406525358557701,
0.03137287124991417,
0.021905964240431786,
-0.03395109251141548,
-0.024110374972224236,
-0.0780603215098381,
-0.013980623334646225,
-0.026616085320711136,
0.03549685329198837,
-0.009459558874368668,
-0.012163638137280941,
0.03068360686302185,
-0.004643266089260578,
0.004743456374853849,
0.01708153448998928,
-0.08801817148923874,
0.005486000794917345,
-0.037631478160619736,
-0.009980536065995693,
-0.010062435641884804,
0.0009061616729013622,
-0.035063277930021286,
-0.02024584263563156,
-0.06290672719478607,
-0.017732612788677216,
0.006495595443993807,
-0.04879158362746239,
0.031135976314544678,
0.002885604975745082,
-0.015168273821473122,
-0.01885964721441269,
0.014717921614646912,
0.053015533834695816,
-0.028085796162486076,
0.013499034568667412,
-0.014765872620046139,
0.00010969289724016562,
-0.013908391818404198,
-0.002124810591340065,
0.004520388785749674,
-0.04085080325603485,
0.011975828558206558,
0.00794217735528946,
0.01807600073516369,
-0.01937757059931755,
-0.03294762969017029,
-0.00796550139784813,
0.0550273060798645,
0.014491674490272999,
-0.01956980675458908,
0.012513880617916584,
-0.06166971102356911,
-0.05644083395600319,
0.030258754268288612,
0.029149677604436874,
-0.017348552122712135,
0.004521923139691353,
0.02054140530526638,
-0.007382137235254049,
0.001855615759268403,
-0.003972940146923065,
0.02215985208749771,
0.010981546714901924,
-0.027212971821427345,
-0.047685474157333374,
-0.028683612123131752,
-0.022910920903086662,
-0.03839413821697235,
-0.0030000009573996067,
0.016857609152793884,
-0.024605702608823776,
-0.03857826068997383,
0.06742861121892929,
0.00929100438952446,
0.01658874750137329,
0.04490852728486061,
0.006187821738421917,
0.011243429034948349,
-0.001323115429840982,
0.00216938485391438,
0.01938481628894806,
0.03621206805109978,
0.03322466090321541,
-0.0056925369426608086,
-0.014777104370296001,
-0.08193165808916092,
-0.05530508980154991,
0.03902773931622505,
0.0650857612490654,
0.0016362897586077452,
-0.03452131897211075,
-0.03537626564502716,
-0.019175177440047264,
-0.012830686755478382,
-0.03484250605106354,
0.02601894922554493,
-0.04148120805621147,
0.0016537896590307355,
-0.052884314209222794,
-0.023876823484897614,
-0.05250651761889458,
0.03854195773601532,
-0.010503430850803852,
0.04468140751123428,
-0.0059224762953817844,
-0.016495348885655403,
0.019163481891155243,
0.06190212070941925,
0.035846129059791565,
0.04239978268742561,
-0.0009416518732905388,
0.010369696654379368,
0.0327257364988327,
0.028264425694942474,
0.0019764022435992956,
-0.05603542923927307,
-0.0009951929096132517,
-0.007323665544390678,
0.02696312963962555,
0.018390126526355743,
-0.05527981370687485,
-0.03779659792780876,
0.02070370689034462,
-0.004391172435134649,
-0.0037753258366137743,
-0.0285660270601511,
-0.06706482172012329,
0.0059876516461372375,
0.0500764362514019,
-0.04466935992240906,
0.052222512662410736,
-0.027280105277895927,
-0.00880627240985632,
-0.0005276203155517578,
0.0014625147450715303,
0.026441466063261032,
-0.06620921194553375,
0.02152528055012226,
0.019725821912288666,
0.010367397218942642,
-0.008884473703801632,
0.055808570235967636,
-0.03378782793879509,
0.04858766868710518,
-0.002833948703482747,
-0.03479482978582382,
0.02257840521633625,
-0.024045482277870178,
-0.0060852994211018085,
-0.02158154360949993,
-0.0019192470936104655,
0.02440859191119671,
-0.007128789555281401,
-0.024683726951479912,
-0.029704710468649864,
-0.0680684745311737,
0.010027021169662476,
0.011725828051567078,
-0.01308026909828186,
0.0036229684483259916,
-0.009266368113458157,
0.018088925629854202,
0.01485736109316349,
-0.038110703229904175,
0.03433389589190483,
0.014124628156423569,
0.015932966023683548,
0.011830857023596764,
-0.030410200357437134,
-0.006696801632642746,
0.011434373445808887,
-0.004247410222887993,
-0.0031265898142009974,
-0.06985766440629959,
0.058105118572711945,
0.015258658677339554,
-0.008256449364125729,
-0.06071380153298378,
-0.05007757991552353,
-0.014430689625442028,
0.025426985695958138,
0.0013126496924087405,
-0.015786845237016678,
-0.04695945978164673,
0.045687925070524216,
-0.045416831970214844,
-0.00028454570565372705,
0.0552237331867218,
-0.06025543808937073,
-0.015535138547420502,
0.031037162989377975,
0.02399859018623829,
0.023394400253891945,
-0.047126349061727524,
-0.00834878534078598,
0.00984433013945818,
-0.07368862628936768,
-0.030323244631290436,
-0.05026707053184509,
-0.021730029955506325,
-0.04542405158281326,
-0.037329789251089096,
0.023722775280475616,
-0.020046738907694817,
0.02255185879766941,
-0.011258082464337349,
0.0027400620747357607,
0.006359555758535862,
0.019457338377833366,
-0.021288324147462845,
-0.002064801286906004,
0.03649469465017319,
0.011902743950486183,
0.015303505584597588,
-0.010339953005313873,
0.029011953622102737,
-0.0576973482966423,
-0.03039327636361122,
0.03594229370355606,
0.005502049345523119,
-0.03299377113580704,
0.02553941123187542,
0.04800575599074364,
0.016446011140942574,
-0.029153110459446907,
0.016928276047110558,
0.018646785989403725,
0.025542402639985085,
-0.005705260671675205,
0.012824513018131256,
-0.0017648227512836456,
-0.026518719270825386,
-0.03042626939713955,
-0.012622068636119366,
0.02570490911602974,
0.016782723367214203,
0.037834249436855316,
-0.01838192529976368,
0.06845260411500931,
0.012043820694088936,
0.004947064444422722,
-0.013989875093102455,
0.008745723403990269,
-0.0056296102702617645,
0.014687977731227875,
-0.015919430181384087,
0.014464871026575565,
-0.04276224598288536,
0.019192244857549667,
0.03196791186928749,
0.04837992787361145,
0.011943347752094269,
0.01888510026037693,
0.03879983723163605,
0.006482055876404047,
0.02704498916864395,
0.018734678626060486,
-0.047457773238420486,
0.03437589481472969,
-0.02811593934893608,
-0.003246581880375743,
0.023813532665371895,
0.0030156064312905073,
0.045721787959337234,
-0.021629931405186653,
-0.04819002002477646,
-0.05182048678398132,
-0.04092726111412048,
-0.024884412065148354,
0.027654271572828293,
0.0376950167119503,
0.0041589997708797455,
0.015689222142100334,
-0.0056450823321938515,
0.046393051743507385,
-0.020453715696930885,
0.029451528564095497,
-0.018610524013638496,
-0.04642358422279358,
-0.04422709345817566,
-0.023048773407936096,
-0.0005147262127138674,
0.04183674231171608,
-0.01679382100701332,
-0.0021150936372578144,
-0.006589458789676428,
-0.01412999164313078,
0.04956841096282005,
0.01846017874777317,
0.015243539586663246,
0.003505455330014229,
0.04361439868807793,
0.013441034592688084,
0.069220170378685,
-0.014510869048535824,
-0.029628200456500053,
0.15607614815235138,
0.009453216567635536,
0.000800339737907052,
-0.04761756956577301,
0.02499198354780674,
-0.00042499916162341833,
0.024365318939089775,
0.002556603169068694,
0.030188309028744698,
0.004787884186953306,
0.041739076375961304,
0.014812902547419071,
0.006121151614934206,
-0.004026506096124649,
0.008401496335864067,
0.0456811897456646,
-0.02128460444509983,
-0.005994666367769241,
0.027215853333473206,
0.023568838834762573,
0.004151972942054272,
-0.027102768421173096,
-0.018543057143688202,
0.013059427961707115,
-0.01734641008079052,
-0.0183195061981678,
-0.01698286272585392,
-0.025848280638456345,
0.05305909365415573,
0.053963907063007355,
-0.005291524343192577,
0.017227161675691605,
-0.00005939889160799794,
-0.005924515426158905,
-0.042991798371076584,
0.02553189918398857,
0.022346796467900276,
0.0046844640746712685,
0.012562565505504608,
0.02827804535627365,
0.01270720362663269,
-0.035130515694618225,
0.012319391593337059,
0.03858065605163574,
-0.05605757609009743,
0.031680285930633545,
-0.0489780455827713,
0.003937265370041132,
-0.020536763593554497,
-0.022275874391198158,
-0.019175691530108452,
-0.006471209228038788,
0.030606089159846306,
-0.04636995494365692,
-0.05770597234368324,
-0.010865465737879276,
0.013398791663348675,
-0.025859493762254715,
-0.019565388560295105,
0.017858855426311493,
0.02353297919034958,
0.01555297989398241,
0.007102161645889282,
-0.009865854866802692,
0.029930660501122475,
-0.021597908809781075,
-0.020810442045331,
0.034223522990942,
0.00961463712155819,
-0.02818857505917549,
-0.034088436514139175,
-0.02511793002486229,
-0.005043128505349159,
0.008376458659768105,
0.0324782133102417,
0.04446800425648689,
0.010747448541224003,
-0.03266497701406479,
0.007948631420731544,
0.026711726561188698,
-0.032237112522125244,
0.04857717454433441,
0.006755509879440069,
0.03226156905293465,
-0.01307267602533102,
-0.028458377346396446,
0.004153367131948471,
-0.00020015980408061296,
0.028706084936857224,
0.03486190736293793,
0.007114158943295479,
0.09903248399496078,
0.005676836706697941,
-0.040086276829242706,
-0.008742393925786018,
0.005616872105747461,
-0.04757244512438774,
0.008883810602128506,
0.005644376389682293,
0.018560100346803665,
0.0071053034625947475,
0.010084595531225204,
-0.025564946234226227,
0.0165849681943655,
-0.03018135204911232,
-0.01338234543800354,
0.002177879214286804,
0.0023871292360126972,
0.02194894105195999,
0.016857005655765533,
0.012684187851846218,
-0.0115715516731143,
-0.044011589139699936,
0.02919243834912777,
-0.00799325667321682,
0.05654114484786987,
0.021948805078864098,
-0.04287038370966911,
-0.006228894926607609,
-0.03967522084712982,
0.041998960077762604,
-0.04285337030887604,
0.0064943693578243256,
-0.07963310182094574,
0.032565295696258545,
-0.011719887144863605,
0.005202449392527342,
-0.03404853865504265,
0.031186403706669807,
-0.011586856096982956,
-0.011924940161406994,
0.06827493757009506,
-0.011286808177828789,
-0.0017038661753758788,
-0.008523877710103989,
-0.010070272721350193,
-0.004867212381213903,
0.002723449608311057,
-0.015030227601528168,
-0.030019808560609818,
0.053443148732185364,
-0.01742474175989628,
0.0152642372995615,
0.0005843374528922141,
0.020720867440104485,
0.026616131886839867,
-0.010759190656244755,
-0.016101501882076263,
-0.015244219452142715,
0.029773173853754997,
-0.028619302436709404,
-0.021668091416358948,
0.008002758957445621,
0.019242241978645325,
0.009610829874873161,
0.03260980546474457,
-0.01942990906536579,
-0.04833964258432388,
0.03237028047442436,
0.004727953113615513,
-0.0038511238526552916,
0.004250849597156048,
-0.019958272576332092,
-0.018966469913721085,
0.0002970539790112525,
0.024110909551382065,
0.035992346704006195,
0.010311074554920197,
-0.0135756004601717,
0.011146681383252144,
-0.010566364042460918,
0.0340283066034317,
-0.0047593386843800545,
0.009894532151520252,
-0.017578868195414543,
0.0025945408269762993,
0.00007043027289910242,
-0.01845528371632099,
-0.009399417787790298,
-0.026364758610725403,
0.005004860460758209,
-0.002783791162073612,
-0.04863671213388443,
-0.001196213299408555,
-0.0006732223555445671,
-0.08526307344436646,
-0.03134841471910477,
-0.0025714081712067127,
-0.011720373295247555,
-0.0014596105320379138,
0.01092609390616417,
-0.00046424599713645875,
-0.030330149456858635,
-0.001974117709323764,
-0.02278057113289833,
-0.022098345682024956,
-0.028252432122826576,
0.02874770574271679,
0.006305214483290911,
0.018566057085990906,
0.010653069242835045,
-0.00420659314841032,
-0.01409361232072115,
0.02473069727420807,
-0.0119505375623703,
-0.034219589084386826,
-0.009551456198096275,
0.05459212139248848,
0.01501726359128952,
0.026949843391776085,
0.034051235765218735,
0.013418619520962238,
-0.00617699371650815,
-0.04356341436505318,
0.06072750687599182,
-0.011074752546846867,
0.02698259800672531,
0.03785179182887077,
0.04686632379889488,
-0.0045682284981012344,
-0.011164228431880474,
0.011615565046668053,
-0.06469755619764328,
-0.026493430137634277,
-0.010869857855141163,
0.013015187345445156,
0.05681878700852394,
0.008701053448021412,
-0.052957627922296524,
0.000889514631126076,
-0.04714911803603172,
0.016579339280724525,
0.012497925199568272,
0.0329638347029686,
-0.012722194194793701,
-0.00167043786495924,
-0.03715743124485016,
0.015687474980950356,
0.02629663050174713,
-0.000469488266389817,
-0.030084578320384026,
-0.002639014506712556,
0.046335164457559586,
0.01063850149512291,
0.008235110901296139,
-0.03120551072061062,
-0.021403498947620392,
0.028979463502764702,
-0.020011845976114273,
0.04386993497610092,
-0.011783037334680557,
-0.05093804746866226,
0.030732693150639534,
-0.02219344861805439,
0.07747437804937363,
-0.04104773327708244,
0.01914111338555813,
-0.008178123272955418,
-0.07504859566688538,
-0.03796183690428734,
0.035949524492025375,
0.04400808736681938,
0.0024911565706133842,
0.01392887718975544,
0.0060410103760659695,
-0.005405516363680363,
0.04268544167280197,
-0.07626748830080032,
0.05146593600511551,
0.03630959987640381,
-0.005844192113727331,
-0.00459705013781786,
-0.023803479969501495,
0.0012594121508300304,
0.017860479652881622,
0.03329229727387428,
-0.015778647735714912,
0.00006781987758586183,
-0.02360333502292633,
0.014203128404915333,
0.01114601455628872,
0.02427859418094158,
-0.023378226906061172,
0.09927752614021301,
-0.03175634145736694,
0.025425883010029793,
0.006256556138396263,
0.006713072769343853,
-0.008118631318211555,
0.02934650145471096,
-0.018287217244505882,
0.028720101341605186,
-0.00553384842351079,
0.010498566552996635,
0.07189814746379852,
-0.03649183735251427,
-0.023956429213285446,
0.0051740072667598724,
-0.05537210777401924,
-0.01374222431331873,
0.07319077849388123,
-0.031309910118579865,
0.009889144450426102,
-0.03367440029978752,
0.059151746332645416,
-0.011421358212828636,
-0.0038449238054454327,
-0.017775341868400574,
0.0004734656831715256,
0.003974138293415308,
-0.006453899201005697,
-0.006942077539861202,
0.025418100878596306,
-0.0025765071623027325,
0.027219850569963455,
-0.0344032384455204,
0.0354408361017704,
-0.01525078248232603,
-0.011679759249091148,
0.05065074563026428,
0.007915695197880268,
-0.016745412722229958,
-0.006989286281168461,
-0.0058095515705645084,
0.09374004602432251,
-0.011821902357041836,
0.0007494351593777537,
0.025956809520721436,
-0.007097803056240082,
0.03339254483580589,
-0.013245034962892532,
-0.008342926390469074,
0.05753835290670395,
-0.0038973574992269278,
-0.016108494251966476,
-0.00445599528029561,
-0.03449432924389839,
0.054642219096422195,
-0.05857384204864502,
0.023908616974949837,
-0.026549331843852997,
0.007715872023254633,
0.0013875891454517841,
-0.019522249698638916,
-0.04326467961072922,
-0.009003009647130966,
0.020362524315714836,
0.04201634228229523,
-0.002078841207548976,
-0.009872764348983765,
-0.04366438835859299,
0.018694279715418816,
0.017728878185153008,
-0.006103498861193657,
-0.05039658397436142,
-0.028224388137459755,
-0.00926253106445074,
0.06713824719190598,
0.0023736644070595503
] |
<p>The Big Bang looks like a lower bound to the "size" of the universe in the time dimension. Could it also have an upper bound, some furthest point in time from the Big Bang?</p>
| 10,722 |
[
-0.009606031700968742,
-0.044293031096458435,
0.02344333566725254,
-0.00917715486139059,
0.06061040237545967,
0.010891275480389595,
-0.036529790610075,
-0.01934448815882206,
-0.01994960568845272,
-0.03756802901625633,
0.011881615035235882,
0.04455950856208801,
0.023522917181253433,
0.028383968397974968,
0.019162345677614212,
0.008571089245378971,
-0.023311646655201912,
-0.011464453302323818,
-0.024142609909176826,
-0.027840981259942055,
0.0501951165497303,
0.0346219576895237,
0.013532865792512894,
0.02785220928490162,
-0.03726789355278015,
0.02279377356171608,
0.06043318286538124,
0.02705913782119751,
0.028789347037672997,
0.0728410929441452,
-0.01739533431828022,
-0.05036458000540733,
0.023538511246442795,
0.054378848522901535,
0.05108927935361862,
-0.04298248142004013,
-0.02792125567793846,
-0.03561469539999962,
-0.04522830620408058,
0.002857715357095003,
-0.024439089000225067,
-0.006896572653204203,
-0.009178581647574902,
0.0641726553440094,
-0.025639604777097702,
0.043244920670986176,
-0.015091647394001484,
-0.0204728152602911,
0.05130540207028389,
-0.022499466314911842,
0.05429597944021225,
-0.010747565887868404,
0.03659309074282646,
-0.010806390084326267,
-0.029240647330880165,
-0.006446155719459057,
0.10295411199331284,
0.06190019100904465,
0.009421180933713913,
-0.028363913297653198,
-0.030181650072336197,
-0.004288732539862394,
0.04009066894650459,
-0.004563660826534033,
-0.02176254615187645,
0.04081349074840546,
-0.048343759030103683,
-0.0036577843129634857,
-0.024493560194969177,
-0.02435634657740593,
-0.01841605454683304,
0.03997917100787163,
0.06278607249259949,
0.014478913508355618,
0.005919901188462973,
-0.013525690883398056,
0.01601237803697586,
0.0032005247194319963,
0.041992366313934326,
0.04963346943259239,
-0.013248550705611706,
0.022451715543866158,
0.05580713972449303,
0.03924764692783356,
-0.009562770836055279,
0.028748486191034317,
0.04771345108747482,
-0.035735320299863815,
-0.021840445697307587,
0.044182006269693375,
-0.022829491645097733,
-0.010606235824525356,
0.05069822445511818,
-0.025796689093112946,
-0.03265083581209183,
0.034372322261333466,
-0.009947801008820534,
0.030005570501089096,
-0.008929175324738026,
-0.021259015426039696,
0.026329217478632927,
-0.015983613207936287,
0.02092873677611351,
0.03610479086637497,
0.04584914818406105,
-0.02300424315035343,
-0.03865576907992363,
0.03134235367178917,
-0.02739068865776062,
-0.008058319799602032,
-0.036782778799533844,
-0.001926695927977562,
-0.01320653222501278,
0.0030634733848273754,
-0.0022338153794407845,
-0.037977978587150574,
0.011918595992028713,
-0.043691545724868774,
0.046358902007341385,
0.04378161206841469,
0.03328195586800575,
0.0025317552499473095,
0.015107523649930954,
-0.013318343088030815,
-0.07321081310510635,
0.02578071318566799,
0.010617619380354881,
-0.0219122301787138,
-0.05057474225759506,
0.060298383235931396,
-0.010563391260802746,
-0.0046653724275529385,
0.0387503057718277,
-0.02053038589656353,
0.08413811028003693,
0.001849121879786253,
-0.07480888813734055,
-0.04519820213317871,
0.06111521273851395,
0.011077988892793655,
-0.0363701693713665,
-0.06904394179582596,
0.014010169543325901,
-0.0020696702413260937,
0.05186400189995766,
0.018132079392671585,
0.000735101813916117,
0.0023649653885513544,
0.027125874534249306,
0.014536617323756218,
-0.017589595168828964,
0.001697193132713437,
0.02342226915061474,
-0.01727021299302578,
0.034783124923706055,
-0.0629420205950737,
0.005629281047731638,
0.020981792360544205,
-0.008290404453873634,
-0.020035024732351303,
0.05203987658023834,
-0.024174995720386505,
-0.01522474829107523,
-0.016523806378245354,
0.003779558464884758,
-0.02168833091855049,
0.07900669425725937,
0.030096951872110367,
-0.026070402935147285,
0.040138985961675644,
-0.011761559173464775,
0.010275362059473991,
0.040482353419065475,
0.02063964307308197,
0.022293558344244957,
-0.03532765060663223,
-0.016670851036906242,
0.008289498277008533,
0.01610107347369194,
0.005950762890279293,
-0.01183939166367054,
0.0003730845055542886,
-0.01482540462166071,
0.007327721919864416,
0.017708580940961838,
0.03538167476654053,
-0.03967546299099922,
-0.015223943628370762,
-0.02734268829226494,
-0.047099243849515915,
-0.004234389867633581,
-0.046872690320014954,
-0.01745021529495716,
0.03445596247911453,
0.0062084076926112175,
-0.0008460297249257565,
0.01011271495372057,
0.055588461458683014,
-0.08515948057174683,
-0.027078859508037567,
-0.01123848557472229,
0.02649618498980999,
0.006132558919489384,
-0.00876542367041111,
0.027755439281463623,
0.0750807672739029,
0.06867756694555283,
-0.03286123275756836,
0.002749969018623233,
0.013813752681016922,
-0.0610501766204834,
0.029552167281508446,
-0.01246226578950882,
0.02879025600850582,
-0.0011804744135588408,
0.00868027564138174,
0.015519356355071068,
-0.024382436648011208,
0.011222940869629383,
0.005201977211982012,
0.022034361958503723,
0.06486695259809494,
0.024632178246974945,
0.013583455234766006,
-0.02825903706252575,
0.014881358481943607,
0.010211012326180935,
-0.00021880347048863769,
-0.02173621766269207,
-0.026929639279842377,
-0.02336355671286583,
-0.00922719668596983,
0.029843006283044815,
0.07374387234449387,
-0.007794998586177826,
0.010171781294047832,
0.029900146648287773,
0.021094443276524544,
0.008652431890368462,
0.02714908868074417,
-0.018314095214009285,
-0.0426265187561512,
-0.038689952343702316,
-0.001240894547663629,
0.03145691379904747,
0.007025022059679031,
0.05158163979649544,
0.01993141509592533,
0.006808510981500149,
-0.05470704287290573,
-0.023619893938302994,
0.00716691417619586,
-0.008208012208342552,
0.007154280785471201,
0.03343658149242401,
-0.049918461591005325,
0.013503565452992916,
-0.03834583982825279,
0.015698911622166634,
0.015710527077317238,
-0.004200642928481102,
0.011671103537082672,
-0.03854674473404884,
0.007767785340547562,
-0.019354382529854774,
0.0356731154024601,
-0.017011797055602074,
-0.012120979838073254,
0.04617294296622276,
-0.046186160296201706,
-0.006791663821786642,
-0.025697652250528336,
-0.024294354021549225,
-0.025200778618454933,
-0.005774631164968014,
0.026898862794041634,
0.004746444057673216,
0.02103726752102375,
-0.02118629589676857,
-0.04715726524591446,
-0.013262885622680187,
-0.020549628883600235,
-0.011977600865066051,
0.016266444697976112,
-0.022846829146146774,
0.0368310809135437,
-0.013115440495312214,
-0.015688970685005188,
0.01396933663636446,
-0.006892485078424215,
0.04952692240476608,
0.05273178219795227,
-0.010566946119070053,
-0.01323726586997509,
-0.00008953407086664811,
0.001394295017234981,
0.03474069759249687,
-0.011425145901739597,
0.02006632462143898,
0.059428293257951736,
-0.00985480472445488,
-0.04825124889612198,
-0.006857611704617739,
-0.0035175334196537733,
-0.05699678510427475,
-0.05446575582027435,
0.03934629634022713,
0.0027425794396549463,
-0.025122225284576416,
0.03277420625090599,
0.03526756167411804,
-0.045553792268037796,
-0.001075154053978622,
-0.04556570202112198,
-0.053632739931344986,
0.05433548986911774,
-0.008331618271768093,
0.06911025196313858,
-0.024538293480873108,
-0.026426007971167564,
0.05053425580263138,
0.03174489736557007,
0.005680191330611706,
-0.04780610650777817,
-0.023433862254023552,
0.007951618172228336,
0.01692584529519081,
0.00865356344729662,
0.015090703032910824,
-0.004526300821453333,
0.00521030742675066,
0.03768245130777359,
0.029041437432169914,
0.02462771348655224,
-0.0023724788334220648,
-0.026533296331763268,
0.00033155205892398953,
-0.00506282364949584,
0.03263454511761665,
-0.0016644435236230493,
-0.01281448919326067,
-0.013617455959320068,
0.04346970096230507,
-0.019917001947760582,
0.06481967121362686,
-0.003394740866497159,
-0.03463344648480415,
0.04042951390147209,
0.007405052427202463,
0.004982792306691408,
-0.01534088421612978,
0.022163504734635353,
-0.0054731774143874645,
-0.0028443674091249704,
-0.008070440031588078,
0.02088557742536068,
0.041439782828092575,
0.020614616572856903,
0.015454618260264397,
0.00009535037679597735,
0.014329909346997738,
-0.021831590682268143,
-0.005079223308712244,
0.014005990698933601,
-0.006107375491410494,
0.041920118033885956,
-0.008471936918795109,
-0.009273379109799862,
0.04225228354334831,
0.03188776597380638,
0.018779391422867775,
0.006799139082431793,
-0.048613470047712326,
-0.007302438840270042,
-0.06968142837285995,
-0.017302675172686577,
0.01958966813981533,
0.025264140218496323,
0.01735811121761799,
0.043740253895521164,
0.006707147695124149,
-0.020962722599506378,
0.020080387592315674,
-0.028301896527409554,
-0.0766376480460167,
-0.029922721907496452,
-0.07436676323413849,
0.008998196572065353,
-0.020401572808623314,
0.0045449091121554375,
-0.021302971988916397,
-0.013561643660068512,
0.014281582087278366,
-0.0037389597855508327,
-0.03102566860616207,
-0.0561564639210701,
-0.004469384904950857,
-0.06816669553518295,
-0.012630623765289783,
0.020663142204284668,
-0.004392616916447878,
0.07721561938524246,
-0.0024642508942633867,
0.02948635444045067,
0.02568926475942135,
-0.01586666889488697,
-0.024948962032794952,
0.018477505072951317,
0.0019548479467630386,
0.00402298616245389,
0.05539015680551529,
0.012799957767128944,
0.011571639217436314,
-0.05599600449204445,
0.01709863916039467,
0.027185771614313126,
0.02304861508309841,
0.021040530875325203,
-0.03682805225253105,
-0.033934447914361954,
-0.019879326224327087,
-0.017087867483496666,
0.013904132880270481,
0.05165774002671242,
-0.016703829169273376,
0.02206956036388874,
0.05277546867728233,
0.0029502934776246548,
-0.03382689878344536,
0.020701449364423752,
0.08822929114103317,
-0.007383144460618496,
-0.020281430333852768,
-0.028991466388106346,
-0.03571729362010956,
-0.04598600044846535,
0.001923667616210878,
-0.002669836161658168,
-0.0481625460088253,
-0.03544382005929947,
0.02349182218313217,
0.0274861641228199,
0.0024772174656391144,
-0.05620277300477028,
-0.01186246145516634,
0.001241054036654532,
0.012397429905831814,
-0.004305066540837288,
0.010219691321253777,
0.012268532998859882,
0.01750340685248375,
0.05292574688792229,
0.015391632914543152,
0.0019947357941418886,
-0.08977816998958588,
-0.01092615444213152,
0.023020682856440544,
0.04326903074979782,
0.028831202536821365,
-0.007658756338059902,
-0.07953454554080963,
-0.024075031280517578,
0.0712277814745903,
-0.052010033279657364,
0.028465833514928818,
-0.02911190688610077,
0.008055207319557667,
-0.030732247978448868,
-0.04160206764936447,
0.014243734069168568,
0.015833571553230286,
0.0035929728765040636,
-0.007580593694001436,
0.008058849722146988,
0.033620934933423996,
-0.030042296275496483,
0.03631333261728287,
0.03437447175383568,
0.028782909736037254,
0.027727028355002403,
0.011729071848094463,
-0.004314852878451347,
0.013638325966894627,
-0.03558462858200073,
-0.06173402816057205,
-0.005991315934807062,
0.01987638883292675,
-0.04808812588453293,
0.02356623485684395,
-0.01564810797572136,
0.001504168612882495,
0.019066903740167618,
-0.00012156820594100282,
-0.04394545033574104,
-0.001357321278192103,
-0.040482617914676666,
0.017999757081270218,
0.012840544804930687,
-0.024032481014728546,
0.011698083020746708,
0.01703750155866146,
0.03153737634420395,
0.012386150658130646,
-0.02565036714076996,
0.04291924461722374,
-0.005317444913089275,
0.024050941690802574,
-0.015531137585639954,
-0.03717133030295372,
-0.028932543471455574,
0.028875257819890976,
-0.033422742038965225,
-0.026347285136580467,
0.018746422603726387,
-0.03319476544857025,
-0.01597648486495018,
0.02595692127943039,
0.03678259253501892,
0.009548400528728962,
-0.0026976563967764378,
0.0013929239939898252,
-0.011865496635437012,
-0.019451797008514404,
0.03060513362288475,
0.029006609693169594,
0.025470327585935593,
0.019337555393576622,
-0.005251365713775158,
0.03909355774521828,
-0.003345294389873743,
-0.01588408648967743,
0.020932430401444435,
-0.005902069620788097,
0.04400407895445824,
-0.028843453153967857,
-0.022330716252326965,
0.019747043028473854,
-0.0416436642408371,
-0.02468557469546795,
0.0037224404513835907,
-0.032762281596660614,
0.018265610560774803,
-0.04053695499897003,
0.02967507764697075,
0.01352377887815237,
0.020789848640561104,
-0.0942632183432579,
-0.028985697776079178,
0.04051528498530388,
0.027275236323475838,
-0.031584933400154114,
-0.024876585230231285,
-0.00577103067189455,
-0.06269930303096771,
0.00037265048013068736,
-0.025963451713323593,
0.05294421315193176,
0.03207375109195709,
-0.04015292227268219,
-0.026632798835635185,
0.003921975381672382,
0.024547681212425232,
-0.002768005942925811,
-0.007446972653269768,
0.0020734278950840235,
-0.007400729227811098,
0.0009050551452673972,
-0.012969408184289932,
0.038807086646556854,
-0.036955080926418304,
-0.021611256524920464,
-0.0075405919924378395,
0.005338485352694988,
0.003304624231532216,
-0.06705325096845627,
-0.010533999651670456,
0.04902764782309532,
-0.0037302724085748196,
0.009035675786435604,
-0.02642078325152397,
0.054127831012010574,
-0.00811249203979969,
-0.012312454171478748,
-0.025072013959288597,
0.009882689453661442,
0.03455910459160805,
-0.0625254213809967,
0.03459891304373741,
0.0113898990675807,
-0.010291210375726223,
-0.010962540283799171,
0.040537673979997635,
0.013288942165672779,
-0.043170150369405746,
0.006408369168639183,
-0.037291690707206726,
0.00806253682821989,
-0.007637427654117346,
-0.016453683376312256,
0.027715208008885384,
0.015334687195718288,
-0.0570596307516098,
-0.03747889772057533,
-0.02021460421383381,
-0.005644677672535181,
0.017905984073877335,
-0.027993647381663322,
0.05202452093362808,
0.008415194228291512,
-0.03923710063099861,
-0.016505640000104904,
-0.029244201257824898,
-0.012748395092785358,
0.036084748804569244,
-0.00009645374666433781,
0.05800430849194527,
-0.0024995978455990553,
0.0053804474882781506,
0.035745952278375626,
0.020773936063051224,
0.002964745508506894,
0.038137201219797134,
0.033756934106349945,
0.016260718926787376,
0.015024827793240547,
-0.028373023495078087,
-0.03098444640636444,
0.011016890406608582,
-0.04043107479810715,
0.009335454553365707,
-0.006869044154882431,
-0.016444873064756393,
0.02660289593040943,
-0.009247436188161373,
0.015674028545618057,
0.006968030706048012,
-0.009570405818521976,
-0.05090641975402832,
-0.016943495720624924,
0.022850049659609795,
0.0882684588432312,
0.014067664742469788,
-0.024908265098929405,
0.006863669026643038,
0.01241596881300211,
0.0024681268259882927,
0.01646624691784382,
-0.03523636981844902,
-0.035107698291540146,
-0.03570309281349182,
-0.041523564606904984,
0.03261555731296539,
-0.000317850528517738,
-0.03344722092151642,
0.005109818186610937,
-0.017568375915288925,
-0.022567210718989372,
0.001775878481566906,
0.042872216552495956,
0.0018520352896302938,
0.06318926811218262,
0.0247053112834692,
-0.008044245652854443,
-0.031105229631066322,
0.016997020691633224,
0.10554466396570206,
0.08897912502288818,
-0.004856435116380453,
-0.061117690056562424,
0.05435730516910553,
-0.039089929312467575,
-0.020042987540364265,
-0.042202699929475784,
0.013121173717081547,
-0.02575751394033432,
0.007584689650684595,
0.02407241240143776,
0.028914665803313255,
-0.002660287544131279,
-0.02763237990438938,
0.04490203410387039,
-0.055714014917612076,
-0.012596667744219303,
0.02248837798833847,
0.03146791085600853,
0.02133791148662567,
0.0205514095723629,
-0.047478027641773224,
0.017659876495599747,
-0.004195595625787973,
0.001595171052031219,
-0.025246568024158478,
-0.021642491221427917,
0.01458117738366127,
-0.04472352936863899,
-0.041697628796100616,
-0.0076512666419148445,
0.026531895622611046,
-0.0407724492251873,
-0.027375495061278343,
-0.015022136270999908,
-0.004405373241752386,
0.009249365888535976,
-0.00020861293887719512,
0.028746336698532104,
0.009842612780630589,
0.017897075042128563,
-0.027466997504234314,
-0.004902287852019072,
-0.009895921684801579,
-0.02457302063703537,
0.011536247096955776,
0.027053792029619217,
-0.026211364194750786,
0.024071911349892616,
-0.0038765210192650557,
0.03860494866967201,
0.0015897303819656372,
-0.03523300960659981,
-0.018187228590250015,
0.013531696051359177,
0.05024855211377144,
0.013222360983490944,
-0.028648551553487778,
-0.010761736892163754,
0.019488563761115074,
-0.0025529609993100166,
0.038424357771873474,
-0.02261599339544773,
0.027603713795542717,
0.04397272691130638,
-0.004960855469107628,
0.04119110852479935,
-0.02938159555196762,
-0.009132742881774902,
-0.021602388471364975,
0.010799930430948734,
-0.05127844959497452,
0.0006637275801040232,
0.0156988687813282,
0.029143890365958214,
0.010442377999424934,
0.029727468267083168,
-0.010039269924163818,
-0.024785948917269707,
-0.004834044259041548,
0.030955208465456963,
-0.04452209174633026,
-0.01785663329064846,
-0.024240389466285706,
0.02454407699406147,
0.02777041122317314,
0.05239814147353172,
-0.030366076156497,
0.033778175711631775,
-0.037076063454151154,
0.035152796655893326,
0.04500613734126091,
-0.01589110493659973,
0.034012626856565475,
0.004921514540910721,
-0.04278919845819473,
0.0004976935451850295,
-0.01721092313528061,
0.03332753852009773,
0.02365979738533497,
-0.030369168147444725,
0.045114096254110336,
0.017093699425458908,
-0.02392110601067543,
0.028871718794107437,
0.03451315686106682,
-0.05713766813278198,
-0.028421452268958092,
-0.010019495151937008,
0.014419324696063995,
-0.04454943537712097,
-0.040611740201711655,
-0.031334634870290756,
0.017141150310635567,
-0.006967554334551096,
0.028331879526376724,
-0.0278600063174963,
0.014664903283119202,
-0.018102960661053658,
-0.009438823908567429,
-0.04455743357539177,
-0.005210994742810726,
-0.05574212595820427,
-0.02497546561062336,
-0.006001431029289961,
-0.03660334274172783,
0.014324394054710865,
0.026391981169581413,
-0.027051851153373718,
-0.03147001564502716,
0.0018470212817192078,
0.01965598203241825,
-0.024649739265441895,
-0.000221898706513457,
0.02665000781416893,
0.006775394082069397,
0.039721786975860596,
-0.018736641854047775,
-0.024587638676166534,
0.008901204913854599,
-0.05804963782429695,
-0.06589247286319733,
0.05415206775069237,
-0.04790116101503372,
0.0023642582818865776,
0.05371082201600075,
0.00197444180957973,
-0.04894514009356499,
0.05499163642525673,
-0.024023398756980896,
-0.026022473350167274,
0.045467302203178406,
-0.004978744778782129,
0.00819483119994402,
-0.0008561855647712946,
0.032967571169137955,
-0.0037784893065690994,
-0.03177817538380623,
-0.0003240934165660292,
0.026920899748802185,
0.021765440702438354,
-0.029200514778494835,
-0.011228925548493862,
-0.02570698969066143,
0.03517954796552658,
0.001525305793620646,
-0.017426500096917152,
0.029624519869685173,
0.05682111531496048,
-0.06300964951515198,
0.03549480438232422,
0.05800393596291542,
-0.010657173581421375,
-0.09468923509120941,
0.008415556512773037,
-0.0012893758248537779,
0.012796623632311821,
0.0291102547198534,
-0.0399242527782917,
0.04931163415312767,
0.016874270513653755,
-0.06507788598537445,
0.026618126779794693,
-0.010037565603852272,
-0.005465709138661623,
-0.022439908236265182,
-0.0320182666182518,
0.0051032910123467445,
0.06180757284164429,
0.05099033936858177,
0.0830521360039711,
-0.001881190575659275,
0.019690968096256256,
-0.03474053367972374,
-0.06713510304689407,
-0.0006386469467543066,
0.05374918133020401,
-0.04512026533484459,
0.0020052387844771147,
0.051355503499507904,
-0.012447916902601719,
-0.01387657318264246,
0.020792223513126373,
-0.0017557831015437841,
0.02700629085302353,
0.003973942715674639,
0.0006139934994280338,
0.011314262636005878,
-0.0010728591587394476,
0.028662825003266335,
-0.005404219496995211,
0.013830193318426609,
0.05436606705188751,
-0.009952906519174576,
-0.0026683341711759567,
0.00567665183916688,
0.004069110378623009,
0.015834329649806023,
-0.022712336853146553,
0.0017108856700360775,
0.015257260762155056,
0.001081334426999092,
0.00020732858683913946,
-0.005446160677820444,
0.018735110759735107,
-0.013270242139697075,
-0.019245442003011703,
-0.03487303853034973,
0.0014134105294942856,
-0.015115691348910332,
0.05489489063620567,
-0.004074117634445429,
-0.04786890372633934,
-0.0047075385227799416,
0.004117003176361322,
-0.032122354954481125,
-0.001472556614317,
0.024213749915361404,
-0.0030323166865855455,
-0.057020436972379684,
0.0019120052456855774,
-0.005984113086014986,
0.010761938989162445,
0.02578119933605194,
-0.04412275180220604,
-0.03442810848355293,
0.039583999663591385,
0.006660659331828356,
0.019356338307261467,
0.03697946295142174,
-0.03400826081633568,
-0.015437961556017399,
-0.08717180788516998,
0.027761956676840782,
-0.025077803060412407,
0.021898090839385986,
-0.03691747412085533,
-0.041105806827545166,
-0.0010795716661959887,
-0.023240279406309128,
0.07319024205207825,
0.0007078118505887687,
-0.03517318516969681,
-0.01695559173822403,
0.024778032675385475,
0.021861059591174126,
-0.0059432112611830235,
-0.006219423376023769,
0.007597342133522034,
-0.03710098937153816,
-0.022212538868188858,
-0.044238608330488205,
-0.02026207745075226,
-0.005004644859582186,
0.013107174076139927,
0.01321537047624588,
0.023690974339842796,
0.0011520017869770527,
-0.00574506726115942,
0.05322913080453873,
-0.001174459233880043,
-0.009870779700577259,
0.05007532611489296,
0.012596352957189083,
0.001976280240342021,
0.014271455816924572,
-0.026418937370181084,
-0.03103196620941162,
-0.00002560480061220005,
-0.03303186967968941,
-0.007653422653675079,
0.000578662205953151,
0.026844823732972145,
0.00764960004016757,
-0.012419372797012329,
-0.030375661328434944,
0.06762371957302094,
-0.0248861126601696,
-0.001278446987271309,
0.026182299479842186,
0.001026946003548801,
0.046711862087249756,
-0.04849158972501755,
-0.01332454290241003,
0.02934233658015728,
0.00807375367730856,
-0.007350130006670952,
0.02407984435558319,
0.03880152106285095,
-0.006556216161698103,
0.029439406469464302,
0.01269594207406044,
0.016065215691924095,
0.00381678668782115,
0.00030134525150060654,
0.0503736287355423,
-0.044121935963630676,
-0.05418350175023079,
0.003201119601726532,
-0.026559606194496155,
0.036819037050008774,
0.009467830881476402,
-0.00812352355569601,
0.07057106494903564,
-0.01149793341755867,
0.025318101048469543,
-0.022365594282746315,
-0.032220397144556046,
-0.02725357934832573,
0.042800839990377426,
-0.013297079131007195,
0.017016708850860596,
-0.030359478667378426,
-0.0021903517190366983,
-0.00890868529677391,
0.04184332117438316,
0.022180216386914253,
-0.04408777132630348,
-0.004107809625566006,
0.015551098622381687,
0.0007962326053529978,
-0.035624343901872635,
0.011637884192168713,
-0.028841163963079453,
-0.02525297924876213,
0.04350341856479645,
0.04235663637518883,
0.02126501500606537,
0.019869526848196983,
0.010293449275195599,
0.002229259116575122,
0.0279984287917614,
-0.08014702051877975,
-0.00012041697482345626,
-0.06507904827594757,
0.0496535450220108,
-0.0456417016685009,
-0.013548657298088074
] |
<p>Why magnetic field generates around a wire when current flow through it ?</p>
| 346 |
[
-0.04465175047516823,
0.008584283292293549,
0.020671263337135315,
-0.05107883736491203,
0.01647186651825905,
0.007696067914366722,
-0.04116043448448181,
-0.01212328765541315,
0.014326936565339565,
-0.03202412277460098,
0.03132117912173271,
0.020473681390285492,
0.020552894100546837,
0.008180476725101471,
0.01767968200147152,
0.012570398859679699,
0.030787507072091103,
-0.002053310163319111,
0.00034170172875747085,
-0.012704347260296345,
-0.024263130500912666,
0.02057962864637375,
0.014202388934791088,
0.019636347889900208,
-0.038980476558208466,
0.009031358174979687,
0.04503294825553894,
0.030244583263993263,
0.03431374579668045,
0.037324294447898865,
-0.000403709476813674,
-0.023855527862906456,
0.002596442587673664,
0.00981905311346054,
0.02006213739514351,
-0.01756903901696205,
-0.02371211163699627,
-0.03086579591035843,
0.004402070306241512,
0.009578041732311249,
0.011404776945710182,
-0.01985897868871689,
0.010249143466353416,
0.04036970064043999,
-0.02333497628569603,
0.0030732587911188602,
-0.0032486652489751577,
-0.03079277276992798,
0.028094720095396042,
-0.07602150738239288,
0.028026128187775612,
-0.04951182007789612,
0.057481687515974045,
-0.022135544568300247,
0.006302858702838421,
-0.009004425257444382,
0.06525121629238129,
0.049546077847480774,
-0.0016979085048660636,
-0.03888785466551781,
-0.001187240006402135,
-0.014529307372868061,
-0.006702164188027382,
-0.048743732273578644,
-0.009498977102339268,
0.05772823840379715,
-0.00328673142939806,
-0.03405088186264038,
0.013750754296779633,
0.0015292421448975801,
0.0026020940858870745,
0.02692538872361183,
-0.008636966347694397,
-0.008562813512980938,
0.01300576888024807,
-0.01839333213865757,
0.023745175451040268,
-0.011636520735919476,
0.0517541766166687,
0.01475783996284008,
-0.0027196749579161406,
0.015511936508119106,
0.019577648490667343,
0.005177106708288193,
0.032986029982566833,
-0.017707232385873795,
0.07235188037157059,
-0.005042775068432093,
0.006408522371202707,
0.01816866174340248,
0.003779282560572028,
0.02149941772222519,
0.021721698343753815,
-0.036391276866197586,
-0.0005157084669917822,
0.022765176370739937,
-0.014742010273039341,
0.050025638192892075,
0.013545781373977661,
-0.021774297580122948,
0.018599530681967735,
-0.013021976687014103,
0.01310135331004858,
0.06909629702568054,
0.01353821624070406,
-0.02391957864165306,
0.007387470453977585,
-0.00595427630469203,
-0.01322480384260416,
0.006037227809429169,
-0.03320842608809471,
0.018937867134809494,
0.016355155035853386,
-0.01970641501247883,
-0.0037931983824819326,
-0.03059753216803074,
0.035929132252931595,
-0.017818041145801544,
0.025145024061203003,
0.060220956802368164,
-0.013753124512732029,
-0.050125665962696075,
0.014575461857020855,
-0.010579164139926434,
-0.042750146239995956,
0.00660698302090168,
0.013242633081972599,
-0.004496804438531399,
-0.006815639790147543,
0.040513403713703156,
-0.013183060102164745,
-0.04345246031880379,
-0.006483431439846754,
0.035455796867609024,
0.04165325313806534,
-0.006060237064957619,
-0.13990817964076996,
-0.07291574776172638,
0.050317950546741486,
-0.021719003096222878,
0.010378211736679077,
-0.058585476130247116,
0.0010354487458243966,
0.029161637648940086,
0.09618251770734787,
-0.015452432446181774,
-0.016584575176239014,
0.034529753029346466,
0.05024644359946251,
-0.006883423775434494,
-0.0014504427090287209,
-0.0322214737534523,
0.001505754073150456,
0.0015187208773568273,
-0.0013462285278365016,
-0.02283233217895031,
0.0218279380351305,
0.008819840848445892,
-0.014637100510299206,
-0.02249220944941044,
0.03039899282157421,
-0.023932786658406258,
0.0029911452438682318,
0.006615856662392616,
-0.038617268204689026,
-0.020319193601608276,
0.07928752154111862,
0.02185356803238392,
0.013555451296269894,
0.05346141755580902,
-0.002095024334266782,
0.028984438627958298,
0.011366778053343296,
0.02641497738659382,
0.009421294555068016,
-0.05081238970160484,
-0.0014785842504352331,
0.002466944744810462,
0.05794771388173103,
-0.00878445990383625,
-0.05141572654247284,
-0.015451387502253056,
0.007512667682021856,
0.006640120409429073,
0.004143757279962301,
0.060448504984378815,
0.0004176474758423865,
-0.008145746774971485,
-0.025849072262644768,
-0.039810776710510254,
-0.019713668152689934,
-0.042316947132349014,
0.03516771271824837,
-0.032569676637649536,
-0.05513809993863106,
-0.028124313801527023,
0.007723180111497641,
0.015030286274850368,
-0.0177660770714283,
-0.014993279241025448,
-0.011665833182632923,
0.04301806166768074,
-0.001472602947615087,
-0.01705353707075119,
0.016806742176413536,
0.05342908576130867,
0.0178043395280838,
0.03864573314785957,
0.06998336315155029,
-0.015902580693364143,
-0.019033988937735558,
0.00739578390493989,
-0.012093672528862953,
-0.0005976994289085269,
0.01311895065009594,
-0.02580142207443714,
0.04027630016207695,
-0.007354216184467077,
-0.013160166330635548,
0.05778829753398895,
-0.010396813973784447,
0.0865730494260788,
0.0457472987473011,
0.018349528312683105,
0.01948551833629608,
0.016630597412586212,
0.002018604427576065,
-0.028638960793614388,
-0.03103126585483551,
-0.025442779064178467,
-0.05908089503645897,
0.0012951690005138516,
0.05454177036881447,
0.012378294952213764,
-0.05086210370063782,
0.00158516108058393,
0.0021796643268316984,
0.024922721087932587,
0.023255672305822372,
0.040483258664608,
-0.03025706857442856,
-0.05018278956413269,
0.00913880206644535,
0.03823375701904297,
-0.019973507151007652,
0.008061038330197334,
0.02500738576054573,
0.03354679420590401,
0.024350741878151894,
-0.0021604031790047884,
-0.03426508232951164,
0.07918348163366318,
-0.018803337588906288,
-0.0007239385740831494,
0.029245557263493538,
-0.040796905755996704,
0.018177075311541557,
-0.035265710204839706,
0.012207341380417347,
-0.046019427478313446,
-0.01283634826540947,
0.02587404102087021,
-0.005180209409445524,
-0.009218517690896988,
0.02861686423420906,
-0.016795484349131584,
-0.01566748134791851,
-0.00970388576388359,
0.035266466438770294,
-0.0533762089908123,
-0.004404809791594744,
-0.009887241758406162,
-0.0032498142682015896,
-0.029963253065943718,
-0.002874265890568495,
0.01987604610621929,
0.004500042647123337,
0.04382125660777092,
-0.03236320987343788,
-0.030231667682528496,
-0.03139682859182358,
-0.028558215126395226,
0.0018464437453076243,
0.01237268652766943,
-0.012870347127318382,
0.04346906393766403,
-0.009266878478229046,
-0.02632913552224636,
0.04183057323098183,
0.035695333033800125,
0.038842614740133286,
0.013963600620627403,
0.005493256263434887,
-0.04142794758081436,
-0.007840871810913086,
-0.02707763761281967,
0.022473588585853577,
-0.01613437943160534,
0.00012610055273398757,
0.051848478615283966,
-0.014016814529895782,
-0.02632077783346176,
0.017032597213983536,
-0.05908055976033211,
-0.0366307832300663,
-0.004452806431800127,
-0.011479099281132221,
0.036857761442661285,
-0.02551306039094925,
0.0383676178753376,
-0.010989365167915821,
-0.06994978338479996,
-0.02369922399520874,
-0.024118533357977867,
-0.0027376271318644285,
0.006770770065486431,
-0.011260466650128365,
0.0219255480915308,
-0.011492555029690266,
-0.05001659691333771,
0.054832372814416885,
0.022419245913624763,
-0.0410374291241169,
-0.03960181400179863,
-0.056411564350128174,
-0.06590840220451355,
-0.0697154849767685,
0.04081907495856285,
0.07959951460361481,
-0.03535573184490204,
-0.01745385304093361,
0.0173186045140028,
0.01947711408138275,
0.012641238048672676,
-0.0038575860671699047,
-0.01097803469747305,
0.003570856526494026,
0.002477293834090233,
-0.004260061774402857,
0.056842394173145294,
-0.02279515378177166,
-0.02611471712589264,
0.00428436417132616,
0.010127873159945011,
0.04439485818147659,
0.010036488063633442,
-0.002808083314448595,
0.027848780155181885,
-0.020689908415079117,
0.0448748953640461,
-0.07930400222539902,
0.04270434007048607,
-0.014409496448934078,
-0.010035231709480286,
-0.028411932289600372,
-0.01335668284446001,
0.016143931075930595,
-0.013643658719956875,
-0.006960088852792978,
0.01831400953233242,
-0.005928158760070801,
-0.05527634546160698,
-0.054309796541929245,
-0.02112141251564026,
-0.00620269775390625,
0.024331988766789436,
-0.0302120391279459,
0.010141532868146896,
0.04311627149581909,
0.07396459579467773,
0.007973415777087212,
0.02880154922604561,
-0.03758124262094498,
-0.00884907878935337,
-0.06838059425354004,
0.009612983092665672,
-0.018889470025897026,
0.05364474654197693,
-0.003159655723720789,
0.07124022394418716,
0.007251909468322992,
0.03190583363175392,
0.01958162523806095,
-0.011078733950853348,
-0.09809263795614243,
0.014246014878153801,
-0.030864769592881203,
0.015813136473298073,
-0.035773277282714844,
-0.0180670116096735,
-0.027594314888119698,
-0.009395272471010685,
-0.00035476285847835243,
-0.0429842546582222,
-0.0524592287838459,
-0.03953135758638382,
-0.007252575363963842,
0.0024983633775264025,
-0.021579528227448463,
-0.04118362441658974,
0.03249862417578697,
0.04793402552604675,
-0.03474397584795952,
0.052502166479825974,
0.005567303858697414,
0.008495294488966465,
-0.020070558413863182,
-0.004388284869492054,
-0.017127491533756256,
0.013034763745963573,
0.020482800900936127,
0.01620762050151825,
-0.02200780063867569,
-0.041724275797605515,
-0.01003869716078043,
-0.0026864302344620228,
0.047376129776239395,
0.016670340672135353,
0.0033797253854572773,
-0.019308753311634064,
-0.038793761283159256,
-0.022997085005044937,
-0.025172362104058266,
0.03697130084037781,
-0.009452689439058304,
0.010213191621005535,
0.026462025940418243,
-0.008919194340705872,
-0.020045043900609016,
0.020596731454133987,
0.035409267991781235,
0.04029155150055885,
-0.009462523274123669,
-0.03658202290534973,
0.03181317076086998,
-0.05525320768356323,
-0.027375569567084312,
-0.010789584368467331,
-0.030220450833439827,
-0.018242930993437767,
-0.01117014791816473,
0.03817293047904968,
-0.002825781237334013,
0.01410724688321352,
0.010869286023080349,
0.04121876507997513,
0.036563411355018616,
0.003391857026144862,
-0.007030832581222057,
0.02669556997716427,
0.030579717829823494,
0.05527471750974655,
-0.0031006867066025734,
-0.0444532185792923,
-0.10585349798202515,
-0.0294054988771677,
0.03947339951992035,
0.04650323465466499,
-0.010642720386385918,
-0.02169395610690117,
-0.06919566541910172,
-0.006117532961070538,
0.033156298100948334,
-0.030028561130166054,
0.028188494965434074,
-0.039713725447654724,
-0.01229941938072443,
-0.03742203488945961,
-0.01672016642987728,
-0.045998819172382355,
0.04886271432042122,
-0.01226156298071146,
0.05529075115919113,
-0.02521466091275215,
-0.018175851553678513,
0.0038924284745007753,
0.011229800991714,
0.039687830954790115,
0.026072068139910698,
0.019006729125976562,
0.02097131498157978,
-0.02023695409297943,
0.046172432601451874,
-0.03466394916176796,
-0.07537944614887238,
0.006258679088205099,
0.012861436232924461,
-0.0013951105065643787,
0.04162317141890526,
0.002554861130192876,
-0.02993187867105007,
-0.00985655840486288,
-0.021866606548428535,
0.01946975849568844,
-0.01886564865708351,
-0.04080566391348839,
0.025936219841241837,
0.01664378121495247,
-0.023418789729475975,
0.05810973048210144,
0.018065515905618668,
-0.027783744037151337,
-0.030202064663171768,
0.005326755344867706,
0.06749927252531052,
-0.007197147235274315,
-0.02101643942296505,
-0.00734589621424675,
0.012866970151662827,
-0.03630286455154419,
0.06310637295246124,
-0.044799160212278366,
0.005523492116481066,
-0.03825405612587929,
-0.0024865102022886276,
0.0034690448082983494,
0.014680763706564903,
0.035303499549627304,
-0.01282525435090065,
-0.008428530767560005,
0.008143638260662556,
0.02253785915672779,
-0.03307824581861496,
0.02406061626970768,
-0.01099073514342308,
0.0245802104473114,
0.030066974461078644,
-0.019095469266176224,
-0.018790926784276962,
-0.03650161251425743,
-0.03523080423474312,
0.000434048124589026,
-0.057742949575185776,
0.056559376418590546,
-0.019655583426356316,
-0.02054288424551487,
0.022687343880534172,
-0.07434512674808502,
-0.02636159397661686,
0.0008158370037563145,
-0.0189327672123909,
0.04187773913145065,
-0.031298208981752396,
0.026319539174437523,
0.03952890262007713,
-0.015344147570431232,
-0.06688316911458969,
-0.08959950506687164,
0.007106017787009478,
-0.009136541746556759,
0.017940182238817215,
-0.012968716211616993,
0.013073100708425045,
-0.01676422543823719,
-0.06255221366882324,
-0.0021057825069874525,
0.012964747846126556,
-0.03872884064912796,
-0.0031705142464488745,
0.02725118026137352,
0.008312859572470188,
0.03791572153568268,
0.009505607187747955,
-0.0005601893644779921,
-0.006695760414004326,
-0.03823212534189224,
-0.010851796716451645,
-0.016451071947813034,
0.043613895773887634,
-0.022509433329105377,
-0.010163528844714165,
0.027957644313573837,
0.000028792590455850586,
0.04244108125567436,
0.0034523599315434694,
0.011754541657865047,
0.007343051489442587,
0.03918303921818733,
-0.01091305073350668,
-0.016638748347759247,
0.031594738364219666,
0.02370278909802437,
0.04946207255125046,
0.001680891145952046,
0.004221129231154919,
-0.06852282583713531,
-0.022244229912757874,
0.0054082321003079414,
0.024395784363150597,
0.012613498605787754,
-0.0019852821715176105,
0.05647587403655052,
-0.05496564880013466,
-0.026780173182487488,
-0.007579818833619356,
0.003509138710796833,
-0.010889827273786068,
-0.016758635640144348,
0.004565485753118992,
0.01705680787563324,
0.030565643683075905,
-0.021988026797771454,
0.005074717570096254,
0.014372878707945347,
0.0009939552983269095,
0.050685591995716095,
-0.03774493187665939,
0.06421615928411484,
-0.002975661540403962,
0.000492541235871613,
-0.009313889779150486,
-0.01308433897793293,
-0.016042206436395645,
-0.00846926961094141,
-0.012606816366314888,
0.039101433008909225,
-0.007097840774804354,
0.011709130369126797,
0.023615926504135132,
0.04686959087848663,
-0.02985859289765358,
0.0184414591640234,
0.05649503320455551,
0.03194917365908623,
0.02882957085967064,
0.036552794277668,
-0.02869502641260624,
0.012883642688393593,
-0.014329012483358383,
0.011310321278870106,
-0.006228768266737461,
-0.003672877559438348,
0.0454021617770195,
-0.025022534653544426,
-0.015012133866548538,
-0.011257581412792206,
-0.015218538232147694,
-0.01571972668170929,
0.008362256921827793,
0.007741622161120176,
-0.0051184589974582195,
-0.005010228604078293,
0.04941049963235855,
0.009380009956657887,
-0.015373684465885162,
0.0078135309740901,
0.014916333369910717,
-0.05596728250384331,
-0.006959330756217241,
-0.025470886379480362,
-0.018636317923665047,
0.07010971009731293,
0.016528679057955742,
-0.03894604742527008,
0.0014970846241340041,
-0.008905907161533833,
0.03682006523013115,
0.035350970923900604,
0.018412964418530464,
-0.025621652603149414,
0.0742664709687233,
0.005326136015355587,
0.021192986518144608,
-0.02143615111708641,
0.007338563911616802,
0.10774990171194077,
0.030916092917323112,
0.01227482222020626,
-0.07645253092050552,
0.012302417308092117,
-0.02551727369427681,
0.005516585428267717,
-0.010227550752460957,
0.05721570551395416,
-0.04263853281736374,
0.03225221857428551,
0.04173675552010536,
0.009324219077825546,
0.01820545271039009,
0.01751677691936493,
0.05264204740524292,
-0.04470892995595932,
-0.040379419922828674,
-0.02500607632100582,
0.0011416099732741714,
-0.013316935859620571,
0.04681515693664551,
-0.05874906852841377,
0.011862383224070072,
-0.06558824330568314,
-0.019912468269467354,
-0.02883339300751686,
-0.03344317525625229,
0.05217506363987923,
0.0010317184496670961,
-0.04626516252756119,
0.00004020445703645237,
0.022178281098604202,
-0.01990293338894844,
-0.07513431459665298,
-0.000799669127445668,
0.051320768892765045,
0.03087369166314602,
0.022831149399280548,
-0.006884247995913029,
0.024094142019748688,
0.006415363401174545,
-0.0002113851223839447,
0.049449726939201355,
-0.04052916541695595,
0.010302236303687096,
-0.039161309599876404,
0.033836688846349716,
0.006131055764853954,
0.03097444586455822,
0.01265482883900404,
0.05574243143200874,
-0.008047894574701786,
-0.014289691112935543,
-0.05442095547914505,
-0.014956986531615257,
-0.002686399267986417,
-0.02087377943098545,
-0.03567902371287346,
-0.03708476200699806,
0.008842537179589272,
-0.004433139227330685,
0.009421291761100292,
-0.007790360599756241,
0.005576867610216141,
0.031467195600271225,
0.007143222726881504,
0.0552653968334198,
-0.02362748049199581,
0.00022808558424003422,
-0.029892316088080406,
-0.028640976175665855,
-0.011167433112859726,
0.0024403973948210478,
0.024346385151147842,
-0.0017281898763030767,
0.012574556283652782,
0.0011093034408986568,
-0.012417461723089218,
0.022718794643878937,
-0.05462364852428436,
0.05597228556871414,
0.02406880259513855,
0.0005008640582673252,
-0.04017369821667671,
0.007863661274313927,
0.014549589715898037,
0.04579056054353714,
-0.014168893918395042,
0.017623523250222206,
-0.00026690628146752715,
0.01687508262693882,
0.0013892307179048657,
-0.018214518204331398,
-0.01423988863825798,
-0.00634613586589694,
-0.025278113782405853,
0.009885657578706741,
0.001683821901679039,
0.01629595458507538,
0.03836781531572342,
0.01682303100824356,
0.004607364069670439,
0.05082869157195091,
-0.02312442846596241,
0.010820897296071053,
0.027070825919508934,
-0.013118409551680088,
-0.005812631454318762,
0.015333874151110649,
0.006010663229972124,
-0.009188763797283173,
-0.02263506129384041,
0.009190858341753483,
0.001413444522768259,
0.038795311003923416,
0.03598206490278244,
-0.03978686407208443,
-0.003332495456561446,
-0.018822401762008667,
0.052056681364774704,
-0.056069910526275635,
-0.012600480578839779,
-0.07232631742954254,
0.01767679490149021,
0.005723257083445787,
-0.023562178015708923,
-0.003573049558326602,
0.036905743181705475,
-0.034822817891836166,
0.019954055547714233,
0.034718990325927734,
0.013040035031735897,
0.016065075993537903,
0.03854949399828911,
0.004045570269227028,
-0.013082477264106274,
0.025318073108792305,
-0.001037990557961166,
-0.03429049625992775,
0.07160944491624832,
-0.06093338876962662,
-0.030441872775554657,
0.004468316212296486,
0.0068721161223948,
0.025651397183537483,
0.021993106231093407,
-0.004323687870055437,
0.009955351240932941,
0.015031623654067516,
-0.009021923877298832,
-0.015150592662394047,
-0.007198810111731291,
-0.0019096138421446085,
0.035210981965065,
-0.011525159701704979,
0.0043918294832110405,
-0.007175978273153305,
-0.00836208090186119,
0.006322535686194897,
0.037002529948949814,
0.026565175503492355,
-0.025130227208137512,
0.02670438401401043,
0.01144192460924387,
0.0012433594092726707,
0.05807540565729141,
0.009143543429672718,
0.0024102781899273396,
0.031715843826532364,
-0.010890500620007515,
0.03242594376206398,
-0.027043694630265236,
-0.00849149003624916,
-0.10100549459457397,
-0.02642768807709217,
-0.007224513217806816,
-0.015558598563075066,
0.02085290662944317,
-0.031600482761859894,
-0.01299201138317585,
0.058084458112716675,
-0.08367861062288284,
0.005614497233182192,
0.015537397004663944,
-0.014580735936760902,
-0.009034226648509502,
-0.014934699982404709,
-0.002341324696317315,
0.07062754780054092,
0.053137991577386856,
0.04574115574359894,
0.0066328695975244045,
-0.004517138935625553,
-0.012307868339121342,
-0.0172804556787014,
-0.031070707365870476,
0.043753691017627716,
-0.019740737974643707,
0.0016035704175010324,
0.030582919716835022,
-0.004262024071067572,
0.011468855664134026,
0.020408961921930313,
-0.007702427450567484,
-0.009799920953810215,
0.005606359336525202,
0.013905948027968407,
0.017595695331692696,
0.03512748330831528,
0.011583891697227955,
-0.020122062414884567,
0.01727958209812641,
0.018397025763988495,
0.03035624511539936,
0.007742603775113821,
-0.005888957995921373,
-0.015429284423589706,
0.024308351799845695,
-0.0374484546482563,
-0.009474452584981918,
0.030538184568285942,
-0.031092233955860138,
-0.019035257399082184,
-0.020772000774741173,
0.04990598186850548,
0.020323770120739937,
-0.03674047440290451,
-0.0023943742271512747,
-0.01924200728535652,
-0.054419390857219696,
0.006403780542314053,
-0.000731252075638622,
-0.009049056097865105,
0.046113621443510056,
0.02103777416050434,
-0.02472110465168953,
0.023289348930120468,
0.01816200651228428,
0.005406117998063564,
-0.02193063125014305,
0.011608397588133812,
0.04342963546514511,
0.018897920846939087,
0.029425300657749176,
-0.04795199632644653,
-0.01872989721596241,
0.01846664398908615,
0.02021409198641777,
0.01297739241272211,
0.006752421613782644,
-0.07531313598155975,
-0.04437270388007164,
-0.033440664410591125,
0.05681275948882103,
-0.036817535758018494,
-0.04211461916565895,
-0.058608800172805786,
-0.054496631026268005,
-0.02146514318883419,
0.03982581943273544,
0.06473986059427261,
0.020850012078881264,
-0.016548052430152893,
0.024755526334047318,
0.006078272592276335,
0.058176856487989426,
-0.0535462312400341,
0.023231711238622665,
-0.0008720692130737007,
0.005909678991883993,
0.02693651057779789,
-0.010028879158198833,
0.000022685713702230714,
0.0408339686691761,
-0.01397648360580206,
0.010475202463567257,
0.02835366129875183,
-0.02472389116883278,
-0.01885381154716015,
0.0279525313526392,
0.03553850203752518,
-0.030002225190401077,
0.06427129358053207,
-0.04491385444998741,
-0.0038846791721880436,
-0.025290071964263916,
0.006227781996130943,
-0.03728749230504036,
0.0097833052277565,
-0.03391886502504349,
0.03362759202718735,
-0.038467682898044586,
-0.0021105154883116484,
0.060078129172325134,
-0.020157944411039352,
0.0024060718715190887,
0.03326350450515747,
-0.042418718338012695,
-0.021172836422920227,
0.06512462347745895,
-0.009935278445482254,
0.00763968750834465,
-0.034269142895936966,
0.02869979850947857,
0.015751289203763008,
-0.014946453273296356,
-0.035726968199014664,
0.039726462215185165,
-0.012755515985190868,
-0.012110666371881962,
-0.007401018403470516,
0.07040809839963913,
0.011264976114034653,
0.028239844366908073,
0.00994138978421688,
0.021265164017677307,
-0.037039924412965775,
-0.030016206204891205,
0.011417481116950512,
-0.01799662783741951,
0.029962627217173576,
0.014652566984295845,
-0.033294033259153366,
0.10128257423639297,
-0.03749430552124977,
0.010857414454221725,
0.008437525480985641,
0.009523928165435791,
0.0040768408216536045,
0.0065669831819832325,
0.004599593114107847,
0.057757120579481125,
0.01390488538891077,
-0.03232438862323761,
0.0034331008791923523,
-0.015479667112231255,
0.029895201325416565,
-0.02234133891761303,
0.03869922459125519,
-0.01247913297265768,
-0.0012449707137420774,
-0.057190436869859695,
-0.004942323546856642,
-0.025790801271796227,
-0.02255629561841488,
0.02620302326977253,
0.04510108008980751,
0.010169507935643196,
-0.00878777727484703,
-0.01715502329170704,
-0.027482781559228897,
0.025347817689180374,
-0.07313688844442368,
-0.0013559352373704314,
-0.041483424603939056,
0.011454290710389614,
-0.0011641219025477767,
0.007879970595240593
] |
<p>Can you help me to do this: </p>
<p>Two frames of references $S$ and $S'$ have a common origin $O$ and $S'$ rotates with constant angular velocity $\omega$ with respect to $S$.<br>
A square hoop $ABCD$ is made of fine smooth wire and has side length $2a$. The hoop is horizontal and rotating with constant angular speed $\omega$ about a vertical axis through $A$. A small bead which can slide on the wire is initially at rest at the midpoint of the side $BC$. Choose axes relative to the hoop and let $y$ be the distance of the bead from the vertex $B$ on the side $BC$. Write down the position vector of the bead in your rotating frame. Show that<br>
$\ddot y-\omega^2 y=0$ using the expression for the acceleration. Hence find the time which the bead takes to reach a vertex $C$. </p>
<p>I showed that $\frac{d^2\vec r}{dt^2}=(\frac{d^2\vec r}{dt^2})'+2\vec\omega\times(\frac{d\vec r}{dt})'+\vec\omega\times(\vec\omega\times\vec r)$ where $'$ indicates that it's done in rotating frame. $\vec r$ is position vector of a point $P$ measured from the origin. </p>
<p>I got that<br>
$\vec r=r\cos\theta\vec i+y\vec j$<br>
$\vec r'=(\dot rcos\theta-r\dot\theta \sin\theta)\vec i+\dot y\vec j$<br>
$\vec r''=(\ddot rcos\theta-\dot r\dot \theta sin\theta-\dot r\dot\theta\sin\theta-r\ddot\theta\sin\theta-r\dot\theta^2cos\theta)\vec i+\ddot y\vec j$<br>
$\omega\times\vec r'=-\omega\dot y\vec i+(\omega\dot r\cos\theta-\omega r\dot\theta\sin\theta)\vec j$<br>
$\vec\omega\times (\vec\omega\times\vec r)=-\omega^2 r\cos\theta\vec i-\omega^2 y\vec j$ </p>
<p>I suppose I have to write Newton's second law now, but I don't know which forces do I have in this motion.</p>
| 10,723 |
[
-0.024111207574605942,
-0.002992265159264207,
0.016365449875593185,
-0.015102080069482327,
0.03385608270764351,
-0.023569513112306595,
-0.036240898072719574,
-0.02532423660159111,
-0.011101213283836842,
-0.00501362606883049,
0.047963663935661316,
0.029554786160588264,
0.03952023759484291,
0.019675957038998604,
0.021832967177033424,
-0.015018836595118046,
-0.016574161127209663,
0.002295541577041149,
-0.0007376485737040639,
-0.03295878320932388,
0.06708481907844543,
-0.009333350695669651,
0.011241866275668144,
-0.0071055348962545395,
0.0019086534157395363,
-0.013063071295619011,
0.019661197438836098,
-0.0488421693444252,
-0.044529132544994354,
0.04260150343179703,
-0.03038042038679123,
-0.0017681968165561557,
0.009292804636061192,
-0.02700813300907612,
0.02791566587984562,
0.00739846657961607,
-0.05603773146867752,
-0.00853902380913496,
0.022179048508405685,
0.0264311321079731,
-0.034480612725019455,
0.03196587413549423,
-0.012026726268231869,
0.09705124795436859,
-0.0011852849274873734,
0.011431700550019741,
0.01006239838898182,
0.018476253375411034,
0.0645717978477478,
-0.03219902515411377,
0.056230951100587845,
-0.01872560940682888,
0.02436378225684166,
-0.015764223411679268,
-0.02499624714255333,
-0.024145863950252533,
0.05642760545015335,
0.010061063803732395,
-0.032221436500549316,
-0.05042964592576027,
0.027203889563679695,
-0.01347301434725523,
-0.02060498669743538,
-0.015700405463576317,
0.010110339149832726,
-0.005139569286257029,
-0.00977316964417696,
-0.018077069893479347,
0.0007680383278056979,
-0.02134406566619873,
0.02097606286406517,
-0.008413158357143402,
0.04899906367063522,
-0.009760281071066856,
0.005747641436755657,
0.0040243156254291534,
-0.011982740834355354,
0.018937503919005394,
0.003689602017402649,
0.027712738141417503,
-0.02264576591551304,
0.010713579133152962,
0.022412918508052826,
0.05698299780488014,
0.02475426346063614,
-0.03989074006676674,
0.039648037403821945,
0.004409279208630323,
-0.0033333110623061657,
0.02352859638631344,
0.02598692663013935,
-0.006707923952490091,
0.02696848474442959,
-0.015318050049245358,
0.002435119356960058,
0.03435685113072395,
0.01176020223647356,
0.037802666425704956,
0.014351041987538338,
-0.05224265158176422,
-0.01446735393255949,
-0.05255536735057831,
0.025996534153819084,
0.12242119759321213,
-0.009634491056203842,
-0.010831519961357117,
-0.005646257661283016,
0.0008770532440394163,
-0.03367011249065399,
-0.041175875812768936,
-0.05092088505625725,
0.050088562071323395,
-0.01856319047510624,
0.006788782309740782,
-0.04314320161938667,
-0.01301080733537674,
0.001141136628575623,
0.018260853365063667,
0.022727351635694504,
0.036715731024742126,
0.022389911115169525,
-0.03680961951613426,
-0.028849715366959572,
-0.013937077485024929,
-0.08000639081001282,
0.02417798340320587,
0.016628189012408257,
-0.014992588199675083,
-0.02052258886396885,
0.020726686343550682,
0.011559523642063141,
0.003957180771976709,
-0.010112094692885876,
0.0019914694130420685,
0.03261644020676613,
0.00307054934091866,
-0.1269131749868393,
-0.05155904218554497,
0.039472248405218124,
0.021308930590748787,
-0.012033623643219471,
-0.07347486168146133,
0.02896912582218647,
0.02439415454864502,
0.0792965441942215,
0.031280115246772766,
-0.014712291769683361,
0.011772718280553818,
0.01571548916399479,
-0.003225733293220401,
-0.009846040979027748,
-0.010479498654603958,
0.014957920648157597,
-0.02449798211455345,
-0.000513606471940875,
-0.017735367640852928,
0.019580092281103134,
0.01698148436844349,
0.014264660887420177,
-0.017181161791086197,
0.014383477158844471,
-0.01493294071406126,
0.024849725887179375,
0.03226739913225174,
-0.017176249995827675,
-0.018959159031510353,
0.06535622477531433,
-0.004494801629334688,
0.027434084564447403,
0.05490902438759804,
-0.020280146971344948,
0.019739516079425812,
-0.020243247970938683,
0.015149823389947414,
0.03344940394163132,
-0.0209053922444582,
-0.027066029608249664,
0.01757969707250595,
-0.03425724431872368,
0.004115857649594545,
-0.044268861413002014,
-0.05852251872420311,
-0.021264299750328064,
0.003344352822750807,
0.008179614320397377,
0.07413355261087418,
0.01800781488418579,
0.008971820585429668,
-0.06625598669052124,
-0.020163610577583313,
-0.0037352361250668764,
-0.08054164797067642,
0.026803189888596535,
-0.03222474828362465,
-0.04498700425028801,
0.022618448361754417,
-0.001629526843316853,
-0.023708371445536613,
-0.016199443489313126,
-0.007353165652602911,
-0.02331889234483242,
0.04762649908661842,
-0.005400264635682106,
-0.044720809906721115,
0.001956135733053088,
0.06289471685886383,
0.054059404879808426,
0.021263903006911278,
0.001981422770768404,
-0.009975496679544449,
0.027329450473189354,
-0.009574814699590206,
-0.0008019874803721905,
0.02661294862627983,
0.02477455325424671,
0.025583382695913315,
0.02073027193546295,
-0.012799921445548534,
-0.021023551002144814,
0.04201207309961319,
-0.013212165795266628,
0.059528548270463943,
0.052755579352378845,
-0.010301982052624226,
0.007976993918418884,
0.05717948079109192,
0.0022541112266480923,
0.04304882884025574,
0.013522729277610779,
-0.022707084193825722,
-0.025608878582715988,
0.014871210791170597,
0.014601053670048714,
0.029746251180768013,
-0.07398338615894318,
0.006378295831382275,
0.03349940851330757,
0.047459956258535385,
0.01774943433701992,
0.00988085102289915,
0.024997180327773094,
-0.028749050572514534,
0.019015341997146606,
-0.0063489098101854324,
-0.0188105721026659,
0.030256902799010277,
0.006192078348249197,
0.02458823472261429,
0.04085673391819,
0.007857411168515682,
-0.021263742819428444,
0.033560145646333694,
-0.0010362862376496196,
-0.016164612025022507,
0.033606044948101044,
0.00034958578180521727,
0.05132794380187988,
0.002711687935516238,
0.022495627403259277,
0.06478702276945114,
0.025514667853713036,
0.017890052869915962,
-0.035098541527986526,
0.0035503136459738016,
0.002238089218735695,
0.0014579262351617217,
0.0008437286596745253,
-0.024679727852344513,
0.01998458430171013,
-0.046156369149684906,
-0.032059960067272186,
-0.01160604041069746,
-0.01433130819350481,
-0.028671283274888992,
-0.017090190201997757,
0.0030433465726673603,
0.024577630683779716,
0.01601947844028473,
-0.024654660373926163,
-0.03173623979091644,
0.0007365597994066775,
0.01741201803088188,
-0.010805612429976463,
0.02824401669204235,
-0.02728128619492054,
0.027624886482954025,
-0.013147418387234211,
-0.03740175440907478,
0.042588088661432266,
0.005555892363190651,
-0.012537505477666855,
0.04345246031880379,
0.03159445896744728,
-0.057145047932863235,
-0.029757311567664146,
-0.0037145079113543034,
0.016927748918533325,
-0.08169889450073242,
0.005059143994003534,
0.025343917310237885,
0.0396760031580925,
-0.013986706733703613,
-0.011932088062167168,
-0.0232574213296175,
-0.04282117262482643,
0.009809855371713638,
0.00691264821216464,
0.024646636098623276,
-0.022685887292027473,
0.002669877838343382,
-0.02226359397172928,
0.03840004280209541,
0.010250844992697239,
-0.04690700024366379,
-0.03641137480735779,
0.01434594951570034,
0.013210039585828781,
0.05722653865814209,
-0.00712413527071476,
-0.025165000930428505,
0.08297649025917053,
0.018171723932027817,
-0.01702171005308628,
-0.009381333366036415,
0.03563360869884491,
-0.011823882348835468,
-0.05576084926724434,
0.01834472268819809,
0.05753609165549278,
-0.048303794115781784,
-0.03443339467048645,
0.00598859041929245,
0.013023712672293186,
0.036495503038167953,
0.007891057059168816,
0.026927564293146133,
-0.005784282460808754,
0.03808896243572235,
0.0011936702067032456,
0.04475482925772667,
0.010598274879157543,
-0.029310675337910652,
-0.0020199494902044535,
0.005765050649642944,
0.038103263825178146,
0.008077733218669891,
-0.07035860419273376,
-0.01058833859860897,
-0.0032746398355811834,
-0.01397647988051176,
0.028173884376883507,
0.032884493470191956,
0.008233864791691303,
-0.029993627220392227,
-0.025133725255727768,
0.022092614322900772,
0.05418623238801956,
0.022732188925147057,
0.00961444340646267,
0.04325871914625168,
0.01494544930756092,
-0.0014181986916810274,
0.015302794985473156,
-0.03223048895597458,
-0.009079198352992535,
0.04231347516179085,
-0.03930063545703888,
-0.023120952770113945,
0.02659793570637703,
0.03719230741262436,
0.006016443017870188,
-0.01174384169280529,
-0.033798184245824814,
0.029343103989958763,
-0.09526418894529343,
0.0038477296475321054,
-0.03365923464298248,
0.04103432968258858,
-0.012934654951095581,
0.07082540541887283,
0.02252502739429474,
0.016802480444312096,
0.005011539440602064,
-0.013085407204926014,
-0.0530460923910141,
0.049191951751708984,
-0.03726190701127052,
-0.036723967641592026,
0.007705958094447851,
0.013800803571939468,
0.011889182962477207,
-0.04807775467634201,
-0.016520828008651733,
-0.020852042362093925,
0.010426163673400879,
-0.034657079726457596,
0.012917191721498966,
0.001913327258080244,
-0.020414745435118675,
-0.034337595105171204,
0.029330797493457794,
0.06341381371021271,
-0.0469810776412487,
0.04815010726451874,
0.028751179575920105,
-0.043454401195049286,
0.012037670239806175,
-0.031615253537893295,
-0.03628713637590408,
0.018819907680153847,
0.0027116485871374607,
-0.005655280780047178,
0.016577227041125298,
0.02350320667028427,
-0.00196917075663805,
-0.0040984367951750755,
0.035005271434783936,
0.021810587495565414,
-0.035185057669878006,
-0.04136066511273384,
-0.039960455149412155,
-0.007048354484140873,
-0.03620001673698425,
0.09170716255903244,
-0.009523142129182816,
-0.01731794886291027,
0.04207067936658859,
-0.0007798755541443825,
0.042354971170425415,
-0.000027012512873625383,
0.02109368145465851,
-0.0017910805763676763,
-0.01122551690787077,
-0.05495388060808182,
-0.029923846945166588,
-0.026132214814424515,
-0.004138481803238392,
0.026186522096395493,
-0.018699267879128456,
-0.0008038227679207921,
-0.024410253390669823,
0.0370607003569603,
0.0012460571015253663,
0.011871040798723698,
0.03432222455739975,
-0.0450851246714592,
0.047367267310619354,
0.021415723487734795,
-0.010610328055918217,
-0.03288619592785835,
0.03700272738933563,
0.017021803185343742,
-0.023119475692510605,
-0.005886944942176342,
-0.05707405507564545,
-0.02473931759595871,
0.015383354388177395,
0.0656961128115654,
0.010493974201381207,
0.019438486546278,
-0.04343407601118088,
-0.03921947628259659,
0.04172592982649803,
-0.011982760392129421,
0.041214920580387115,
-0.009944970719516277,
-0.000229037061217241,
-0.042084965854883194,
-0.04563850909471512,
-0.0253131166100502,
-0.030752960592508316,
-0.042358458042144775,
0.020258460193872452,
-0.014744563028216362,
0.0015788465971127152,
0.015763653442263603,
-0.003960949834436178,
0.04726122319698334,
0.020020553842186928,
0.017949409782886505,
-0.014528256841003895,
0.005773648153990507,
0.031398724764585495,
-0.027753068134188652,
-0.06827381998300552,
0.028291471302509308,
0.025935204699635506,
-0.021087484434247017,
0.02734743058681488,
-0.0390004999935627,
-0.005913593806326389,
0.06930400431156158,
-0.011929384432733059,
-0.010930638760328293,
0.04173622280359268,
-0.06656833738088608,
0.0268230102956295,
0.027042748406529427,
-0.013749859295785427,
0.0037605215329676867,
0.022272542119026184,
-0.0142777469009161,
-0.04786306619644165,
0.0011901702964678407,
0.022247832268476486,
0.02850368618965149,
-0.017117636278271675,
-0.04008757695555687,
0.01733522117137909,
-0.017537888139486313,
0.033970680087804794,
-0.04039193317294121,
0.019008444622159004,
-0.03902404010295868,
-0.037900783121585846,
0.005960074719041586,
0.054771240800619125,
0.006519579794257879,
0.01246372889727354,
0.0009152226848527789,
0.004843516740947962,
0.04101339355111122,
-0.022166181355714798,
-0.00014596869004890323,
-0.02531561814248562,
0.018245551735162735,
0.049910321831703186,
-0.027468694373965263,
0.006124195177108049,
-0.047632548958063126,
0.005371609702706337,
-0.01121577713638544,
-0.11333785206079483,
0.05627574026584625,
-0.040942031890153885,
-0.016543172299861908,
0.03683353587985039,
-0.040459390729665756,
-0.043748948723077774,
-0.018164247274398804,
0.008557449094951153,
-0.01998790353536606,
-0.048969339579343796,
-0.02913425862789154,
0.0281649399548769,
0.03355803340673447,
-0.03272185102105141,
-0.07694899290800095,
0.004014209844172001,
-0.015449178405106068,
-0.003787645837292075,
0.008326455950737,
0.04164807125926018,
-0.017930282279849052,
-0.041128113865852356,
-0.0013548957649618387,
0.002648297231644392,
-0.027758659794926643,
0.017288068309426308,
0.021125616505742073,
0.018928537145256996,
0.026599096134305,
0.0031404341571033,
0.0018527486827224493,
-0.027175569906830788,
-0.01695368066430092,
0.0006194078014232218,
0.0002757964830379933,
0.04970931261777878,
-0.04714442789554596,
-0.025479763746261597,
-0.011713298037648201,
0.011848530732095242,
0.035246510058641434,
-0.03542809933423996,
-0.0016998486826196313,
0.01283774059265852,
-0.0030864374712109566,
-0.001939938054420054,
0.014303307980298996,
-0.010518156923353672,
0.039167627692222595,
0.006568240933120251,
0.0005255426513031125,
0.03139027953147888,
-0.03145316243171692,
-0.0197751484811306,
0.016407303512096405,
-0.007661094889044762,
0.009593678638339043,
-0.029824044555425644,
0.06565026193857193,
-0.053339771926403046,
-0.004516358021646738,
0.020000282675027847,
0.022633643820881844,
-0.00022133919992484152,
-0.012377308681607246,
-0.010465833358466625,
0.03963799402117729,
-0.0014213043032214046,
-0.03145706281065941,
-0.00959804467856884,
-0.051458172500133514,
0.014969040639698505,
0.11960937082767487,
0.010121284984052181,
0.059674326330423355,
0.00825000274926424,
-0.01804875209927559,
-0.022199595347046852,
0.00028942941571585834,
-0.016681544482707977,
0.001478060381487012,
0.028040289878845215,
0.030065709725022316,
-0.002602032385766506,
-0.03715527057647705,
0.014116237871348858,
0.052881691604852676,
-0.0282879788428545,
-0.013290239498019218,
0.01680406741797924,
0.0007324722828343511,
-0.016307007521390915,
-0.0074243624694645405,
-0.0008750510169193149,
0.018700754269957542,
0.011472636833786964,
0.04825704172253609,
-0.032731857150793076,
-0.029993444681167603,
0.04225108399987221,
0.03235870972275734,
0.031932283192873,
-0.019557621330022812,
-0.006669286172837019,
-0.04361739754676819,
0.018073352053761482,
0.010915394872426987,
0.023812953382730484,
-0.01129857823252678,
0.00012931307719554752,
0.0527733750641346,
-0.0028822575695812702,
0.0403774194419384,
-0.04826582968235016,
-0.015029714442789555,
0.006855949759483337,
-0.03200497105717659,
-0.01910862885415554,
0.06200367957353592,
0.014636087231338024,
0.006709742825478315,
0.02090880461037159,
-0.034712549299001694,
-0.0017396153416484594,
0.05757609382271767,
0.02180679701268673,
-0.02920159325003624,
0.08485474437475204,
-0.02577902190387249,
0.007910126820206642,
-0.004255965352058411,
-0.023402201011776924,
0.1385994255542755,
0.014192523434758186,
-0.030916033312678337,
-0.007470047101378441,
0.018620293587446213,
0.01571461744606495,
0.025398114696145058,
-0.05589693784713745,
-0.0038082492537796497,
-0.028986189514398575,
0.00215691770426929,
0.027007700875401497,
0.01670207642018795,
-0.007871201261878014,
-0.029776018112897873,
-0.01117186713963747,
-0.03774840012192726,
-0.014029138721525669,
-0.0493299774825573,
-0.013681501150131226,
0.005620360840111971,
0.02338995411992073,
0.009297973476350307,
0.029448112472891808,
-0.07312440127134323,
-0.03245549276471138,
-0.04723276570439339,
-0.013044252060353756,
0.0008967043831944466,
-0.052970368415117264,
-0.03912553936243057,
0.0445258691906929,
0.01974128559231758,
-0.03799692913889885,
-0.011845123022794724,
0.02718980237841606,
0.018045999109745026,
-0.007358244154602289,
0.02734188362956047,
0.016696328297257423,
-0.019177239388227463,
0.0005692220292985439,
0.030605625361204147,
0.04382622614502907,
-0.050521671772003174,
0.0035660809371620417,
-0.020814962685108185,
0.04077792167663574,
-0.04668261855840683,
-0.0043691350147128105,
0.012035476043820381,
-0.03311267867684364,
-0.0004394310526549816,
-0.06198820844292641,
0.00811231043189764,
-0.003845527768135071,
0.015112914144992828,
0.001735755824483931,
0.004763037897646427,
-0.019731976091861725,
0.02374066784977913,
0.03785361722111702,
-0.01052231714129448,
-0.023973066359758377,
-0.0030453959479928017,
-0.030055923387408257,
0.028473075479269028,
0.039143554866313934,
-0.04492656886577606,
0.016056731343269348,
-0.018958814442157745,
-0.012239093892276287,
0.022332990542054176,
0.029567906633019447,
-0.008281534537672997,
0.0002847553405445069,
-0.0039746942929923534,
0.0024309102445840836,
-0.038277119398117065,
-0.026379359886050224,
-0.060959383845329285,
-0.014093148522078991,
0.00023124889412429184,
-0.00013565566041506827,
-0.038558609783649445,
0.004237862303853035,
0.053509559482336044,
0.04546009749174118,
-0.0060161021538078785,
0.009540603496134281,
0.01684379018843174,
0.06727232784032822,
0.058555494993925095,
-0.016898974776268005,
-0.02446608990430832,
-0.022493286058306694,
0.04147574305534363,
0.020173408091068268,
-0.017945893108844757,
0.024995556101202965,
0.053069956600666046,
0.011353516019880772,
-0.006437463220208883,
0.04220718517899513,
-0.026805449277162552,
-0.00019533385057002306,
0.039736293256282806,
-0.028608907014131546,
0.00848249439150095,
0.02435317635536194,
0.011368353851139545,
-0.05046651139855385,
0.015219143591821194,
0.004057249519973993,
-0.012752302922308445,
-0.025759967043995857,
-0.014589773491024971,
-0.015687357634305954,
0.04019061475992203,
-0.040023770183324814,
0.018423786386847496,
-0.04274687543511391,
0.02843855693936348,
0.00023919000523164868,
0.006980783771723509,
-0.018480032682418823,
0.021170340478420258,
-0.01762198656797409,
0.03584181144833565,
0.01757829450070858,
-0.014603402465581894,
-0.0007308116182684898,
0.041894011199474335,
-0.002274405211210251,
-0.001086732605472207,
-0.0009712534374557436,
0.018734538927674294,
0.04156608134508133,
-0.017211636528372765,
-0.03395985811948776,
-0.007871925830841064,
-0.022449655458331108,
0.001275235554203391,
0.05764356255531311,
0.022586654871702194,
0.02357153408229351,
0.010537587106227875,
-0.060651492327451706,
0.002407462801784277,
0.05827820301055908,
-0.02708570659160614,
-0.01722797006368637,
-0.0031802973244339228,
-0.07028808444738388,
0.005650314036756754,
-0.03788180649280548,
0.012729511596262455,
-0.001118757063522935,
0.01944056712090969,
0.008543966338038445,
0.0017575770616531372,
-0.02024788223206997,
0.004257667809724808,
0.007856235839426517,
0.003422854468226433,
-0.01616801507771015,
0.01323212031275034,
0.01555540319532156,
0.03393041715025902,
0.005204118322581053,
-0.029311032965779305,
0.0002394987823208794,
0.020297821611166,
-0.019118789583444595,
-0.08896630257368088,
0.040403060615062714,
-0.0055777085945010185,
0.008236829191446304,
0.05026153847575188,
-0.04381252080202103,
-0.007271277252584696,
0.03677762299776077,
-0.07336527109146118,
0.013079865835607052,
-0.043695591390132904,
-0.015234698541462421,
-0.0154837341979146,
0.003746847854927182,
0.010837513953447342,
0.05224359408020973,
0.04427073895931244,
0.05504293739795685,
0.012565658427774906,
0.008068491704761982,
-0.025579866021871567,
-0.060994889587163925,
0.00013937025505583733,
0.05548432841897011,
-0.010942064225673676,
-0.016734246164560318,
0.02142307721078396,
-0.02415715903043747,
0.012109375558793545,
0.016196586191654205,
-0.016432423144578934,
0.010621020570397377,
-0.01935681328177452,
0.017369592562317848,
0.0043326267041265965,
0.030632924288511276,
-0.011547655798494816,
0.016676602885127068,
-0.02348385564982891,
-0.012371615506708622,
0.02240203507244587,
0.0037380557041615248,
-0.056805819272994995,
-0.019204743206501007,
0.030871029943227768,
-0.016163740307092667,
-0.07071685791015625,
0.03666166216135025,
-0.025951040908694267,
-0.0009741322719492018,
0.04429595172405243,
0.004776001907885075,
0.010834666900336742,
-0.03688003867864609,
-0.04247300326824188,
-0.019665589556097984,
0.009818137623369694,
0.020285509526729584,
-0.04363347217440605,
-0.04318265616893768,
0.03914029523730278,
-0.003693831618875265,
-0.01719575747847557,
0.0071073491126298904,
-0.012234832160174847,
-0.03918343409895897,
-0.053409118205308914,
-0.03090490773320198,
-0.006375950761139393,
-0.004205738194286823,
0.013104898855090141,
-0.0036488680634647608,
-0.0024179916363209486,
0.016528358682990074,
0.0321807786822319,
0.004419032484292984,
0.02389334887266159,
0.04856539145112038,
-0.03186199441552162,
-0.05474851652979851,
0.010637756437063217,
0.005165245849639177,
-0.06606125086545944,
-0.02429395541548729,
-0.04249311983585358,
0.018005119636654854,
0.061550892889499664,
0.06492862850427628,
-0.02071020007133484,
0.02534748800098896,
-0.006556403823196888,
0.0001747052010614425,
0.015475425869226456,
-0.04852297157049179,
0.02864241786301136,
-0.015541371889412403,
-0.014794275164604187,
0.020511358976364136,
-0.0016048438847064972,
-0.00454650167375803,
-0.002415895462036133,
0.02050437405705452,
0.01520898099988699,
0.052865322679281235,
-0.0007642812561243773,
-0.013386550359427929,
0.013613201677799225,
-0.004030819982290268,
-0.004438705742359161,
0.04509789124131203,
0.016088448464870453,
0.00854958314448595,
0.02694135345518589,
-0.043649423867464066,
-0.017206529155373573,
0.019622208550572395,
-0.03382793813943863,
-0.02493921108543873,
-0.02910643443465233,
-0.02943938784301281,
0.02596540004014969,
-0.06887047737836838,
0.007267578039318323,
0.010461816564202309,
-0.0012405760353431106,
-0.024568399414420128,
0.03633633628487587,
-0.021100057289004326,
0.01742730103433132,
-0.021598415449261665,
0.04010623320937157,
0.024831436574459076,
-0.041551049798727036,
0.028065882623195648,
0.016531523317098618,
0.01034477911889553,
-0.024615732952952385,
0.008546789176762104,
0.07606502622365952,
-0.008451852016150951,
0.03180855140089989,
-0.035877831280231476,
0.014877872541546822,
-0.009644771926105022,
0.022252388298511505,
0.001842420781031251,
-0.04795839264988899,
-0.02399592101573944,
0.0642782524228096,
-0.013735117390751839,
0.043223295360803604,
-0.008193928748369217,
0.008058100938796997,
0.026287782937288284,
0.009724009782075882,
-0.03457825258374214,
0.024959202855825424,
-0.008304678834974766,
0.03446986898779869,
0.00008111275383271277,
0.0014987665927037597,
-0.007973536849021912,
-0.05135896056890488,
0.015582084655761719,
0.030950188636779785,
0.030170051380991936,
0.06022673472762108,
-0.008119165897369385,
-0.00008145331230480224,
-0.0173354372382164,
0.0017316351877525449,
-0.017906781286001205,
0.04633518308401108,
0.00008351572614628822,
-0.03991211950778961,
-0.03442420810461044,
0.0361676849424839,
-0.00043966929661110044,
0.04245653375983238,
-0.07581483572721481,
-0.04515969753265381,
-0.0249466672539711,
0.01934465579688549,
0.01889212429523468,
0.008179794996976852
] |
<p>There is perfect parallelepipedal bar made of transparent crystal with cubic lattice floating in vacuum. Faces of parallelepiped are parallel to lattice axis. There is image, forming checkerboard pattern, each cell alternating between two distinct colors.</p>
<p>This image is projected in perpendicular on the one face of crystal bar, so projection has spatial resolution (e.g. density of outgoing photons) such high, so every single molecule in the first layer of crystal bar gets several photons of different wavelength.</p>
<p>Questions:</p>
<ol>
<li><p>How the output image at the opposite side of crystal bar compares to original image projected?</p></li>
<li><p>Will it correlate to thickness of bar?</p></li>
<li><p>How are multiple photons hitting same molecule handled?</p></li>
<li><p>What is the limit of resolution of incoming image, to perfectly match output image? Is it one-to-one correspondence of incoming photons to molecules in the first layer?</p></li>
<li><p>Will there be scattering of photons on the molecules of the last layer? If any, will interference between scattered photons cancel non-perpendicular directions?</p></li>
</ol>
| 10,724 |
[
-0.027413640171289444,
-0.019307689741253853,
0.026441873982548714,
-0.01899019628763199,
0.06248730421066284,
0.012769930064678192,
-0.012446505017578602,
0.0005424589617177844,
0.035200636833906174,
0.007947263307869434,
0.0781392902135849,
-0.0000219913235923741,
0.039341848343610764,
0.018660327419638634,
0.01264165434986353,
0.001123676192946732,
-0.014134664088487625,
-0.014974938705563545,
-0.01002456247806549,
-0.02344166859984398,
-0.0014515144284814596,
0.04908609762787819,
0.030576812103390694,
-0.0028371966909617186,
-0.050782863050699234,
0.034053198993206024,
-0.026197386905550957,
-0.007051768247038126,
0.0169812124222517,
0.05315639078617096,
-0.03804954141378403,
-0.0012043919414281845,
0.018973521888256073,
0.008537264540791512,
-0.012416817247867584,
0.02531241811811924,
-0.0030845189467072487,
-0.015176922082901001,
0.008271235972642899,
-0.003053812775760889,
0.018559293821454048,
0.025169329717755318,
-0.01476515643298626,
0.04693838208913803,
-0.010623031295835972,
0.021482054144144058,
-0.02566133812069893,
-0.020692694932222366,
0.055817537009716034,
-0.04655216634273529,
0.05511381849646568,
0.0009471374796703458,
0.03715035691857338,
0.0006012824014760554,
-0.0017654390539973974,
-0.06325358152389526,
0.044049832969903946,
0.1007322296500206,
0.0016021957853809,
-0.05231621861457825,
0.00899466685950756,
0.005820138845592737,
0.018794940784573555,
-0.0024815716315060854,
-0.051378604024648666,
0.017983492463827133,
0.0016802549362182617,
-0.02285187505185604,
0.033820800483226776,
0.005048070568591356,
-0.007356780115514994,
0.029830224812030792,
0.03221406042575836,
0.004914536606520414,
0.02169271931052208,
-0.003939715679734945,
-0.029770972207188606,
0.04457597807049751,
0.015264566987752914,
0.027632908895611763,
-0.010874730534851551,
-0.004917907994240522,
-0.008015235885977745,
0.04825379326939583,
-0.0010244360892102122,
0.009767778217792511,
0.0738125890493393,
-0.029865169897675514,
-0.01599058322608471,
-0.014219609089195728,
0.04253330081701279,
0.029004069045186043,
0.016641028225421906,
0.04746844246983528,
-0.023196429014205933,
0.00970488227903843,
-0.006946337874978781,
0.04031115397810936,
-0.008596411906182766,
-0.004996637348085642,
-0.026690825819969177,
-0.016504110768437386,
-0.016255531460046768,
0.06905872374773026,
0.009485971182584763,
-0.01565433107316494,
0.0028869733214378357,
0.028079865500330925,
-0.006644160952419043,
0.03216317668557167,
-0.03518186882138252,
0.024066558107733727,
-0.004051068797707558,
0.015429746359586716,
-0.002908688737079501,
-0.023974383249878883,
0.017571762204170227,
-0.035174861550331116,
0.05870001018047333,
0.07964961975812912,
0.00479968823492527,
-0.014910338446497917,
0.003882796736434102,
-0.003842234145849943,
-0.08654308319091797,
0.01566094346344471,
0.05061540752649307,
0.00964879710227251,
-0.04310021921992302,
0.010600907728075981,
0.05136973410844803,
-0.005648590624332428,
0.01319999061524868,
-0.012829557992517948,
0.011667880229651928,
-0.015481109730899334,
-0.13068430125713348,
-0.0345059297978878,
0.048788271844387054,
0.011836311779916286,
-0.02669265680015087,
-0.06580447405576706,
-0.004575315397232771,
0.03096337988972664,
0.06541708111763,
-0.018146593123674393,
0.01583440974354744,
0.021432705223560333,
0.0307431872934103,
-0.01565362513065338,
0.004515314474701881,
0.010004084557294846,
-0.004063194617629051,
-0.02820735238492489,
-0.018172942101955414,
-0.043775301426649094,
-0.004110407549887896,
0.03891756385564804,
0.007709817960858345,
-0.03475925326347351,
0.05704379081726074,
-0.008027537725865841,
0.027913330122828484,
0.01283449586480856,
-0.009644108824431896,
-0.045209020376205444,
0.039902787655591965,
0.022443043068051338,
0.0013512381119653583,
0.034907177090644836,
-0.011874149553477764,
0.010445617139339447,
-0.0009728058939799666,
-0.01569320261478424,
0.009108787402510643,
0.002813412109389901,
0.021147167310118675,
-0.004244865849614143,
0.01171924825757742,
0.004262219183146954,
-0.03779890015721321,
-0.04075755923986435,
-0.016168884932994843,
0.019574832171201706,
0.035636696964502335,
0.019762756302952766,
0.012326628901064396,
-0.053266704082489014,
-0.008467214182019234,
-0.0503389798104763,
-0.03532881289720535,
-0.03359818458557129,
0.020357610657811165,
-0.006622379180043936,
-0.01982652209699154,
0.04694429412484169,
0.009837021119892597,
-0.02854769118130207,
0.020628269761800766,
-0.03559843450784683,
-0.03174963220953941,
0.017917828634381294,
0.0037151218857616186,
0.02815091609954834,
0.018577879294753075,
0.07312541455030441,
0.06612241268157959,
-0.007054711692035198,
0.00041989790042862296,
-0.04417344555258751,
-0.02487720362842083,
-0.017569120973348618,
-0.007185682654380798,
0.03166916221380234,
-0.003181056585162878,
-0.006556633859872818,
0.0010483001824468374,
0.027966313064098358,
-0.000436786183854565,
0.009840911254286766,
0.006528737023472786,
0.05272672325372696,
0.07421515882015228,
0.00009329512977274135,
0.0007065567187964916,
-0.018625374883413315,
-0.015389814041554928,
0.00751594128087163,
-0.04166768491268158,
-0.051159463822841644,
-0.04069609194993973,
-0.011564786545932293,
0.012596216052770615,
0.025479773059487343,
-0.03814937546849251,
0.06310965120792389,
-0.010048513300716877,
0.03304203972220421,
0.017277726903557777,
0.014740344136953354,
-0.03736107796430588,
-0.010077644139528275,
0.028606127947568893,
-0.01069082785397768,
0.01140899769961834,
0.00830406416207552,
0.015633929520845413,
0.01953393593430519,
0.0012675485340878367,
-0.017439313232898712,
-0.010123083367943764,
0.013755008578300476,
-0.03245941177010536,
-0.009568440727889538,
-0.005994430277496576,
-0.01333665382117033,
0.018871352076530457,
0.02044360525906086,
0.006112600676715374,
0.041312966495752335,
-0.03927873075008392,
-0.013046813197433949,
-0.03063216432929039,
-0.012991483323276043,
-0.03666007146239281,
0.03421486169099808,
-0.028212295845150948,
-0.012255209498107433,
0.04964858666062355,
-0.03880355879664421,
0.03819733485579491,
-0.029230309650301933,
0.0001332301617367193,
-0.001933246268890798,
0.013005934655666351,
0.057434480637311935,
0.036128804087638855,
0.032603248953819275,
-0.07299089431762695,
-0.04458893463015556,
-0.014088374562561512,
-0.013581796549260616,
0.035822927951812744,
0.017765281721949577,
-0.05570767819881439,
0.00487377168610692,
-0.029459448531270027,
-0.020167887210845947,
0.0057695177383720875,
-0.0050586736761033535,
-0.026153497397899628,
-0.0018512789392843843,
-0.004363277927041054,
-0.04269053786993027,
-0.03390345349907875,
-0.025876283645629883,
0.0056754364632070065,
-0.016641374677419662,
-0.0024940778966993093,
0.0055959527380764484,
-0.03416629880666733,
-0.046137742698192596,
0.0026119626127183437,
-0.002600235166028142,
-0.01703142188489437,
0.025903262197971344,
-0.02386096864938736,
0.005213960073888302,
-0.01926296018064022,
0.012116693891584873,
0.029023610055446625,
-0.03682207316160202,
0.006499892100691795,
-0.06942625343799591,
-0.026549994945526123,
0.015127158723771572,
-0.014764209277927876,
0.04110252112150192,
-0.0015592885902151465,
0.023366179317235947,
0.05564946308732033,
-0.00038934062467888,
-0.027416681870818138,
-0.016039708629250526,
0.003506323555484414,
-0.013502744026482105,
-0.022053629159927368,
0.0539482906460762,
-0.010468000546097755,
0.004453611094504595,
0.04684051498770714,
-0.0166325643658638,
0.04497062414884567,
0.046934857964515686,
0.019000371918082237,
-0.023265650495886803,
-0.003820684039965272,
0.011860729195177555,
-0.024960100650787354,
0.005857984535396099,
0.04407747834920883,
-0.03269839286804199,
0.018907424062490463,
0.005339807365089655,
-0.022655844688415527,
0.010196642950177193,
-0.07738953828811646,
0.04383956640958786,
-0.009837175719439983,
-0.0009058054420165718,
-0.03556178882718086,
0.05609241500496864,
0.006958233658224344,
0.009688382036983967,
-0.029409436509013176,
0.03366946429014206,
0.03994657099246979,
0.0045483005233109,
-0.015941496938467026,
0.03520773723721504,
0.05412467196583748,
0.0008726698579266667,
-0.016220180317759514,
0.02520816959440708,
-0.0018410609336569905,
0.02307973988354206,
-0.03274761885404587,
-0.030081745237112045,
0.021752994507551193,
0.031039036810398102,
0.018390841782093048,
0.03224315121769905,
0.0038892917800694704,
-0.04294154793024063,
-0.04245228320360184,
0.0020654124673455954,
-0.0018469328060746193,
0.0519205778837204,
0.009038164280354977,
0.02619841694831848,
0.03533899411559105,
0.005526855122298002,
-0.0039130705408751965,
0.011963034979999065,
-0.07790526747703552,
-0.0311227235943079,
0.03607816621661186,
0.016885733231902122,
0.01058129407465458,
-0.03183114528656006,
0.0291525237262249,
-0.00878273043781519,
-0.03339383006095886,
-0.010251283645629883,
-0.005094552878290415,
-0.03992224112153053,
-0.029480868950486183,
-0.01275709830224514,
-0.010251758620142937,
-0.023564130067825317,
0.038366761058568954,
0.026777224615216255,
-0.006375001277774572,
0.008051528595387936,
0.022184154018759727,
-0.03350535035133362,
-0.0074496762827038765,
-0.0020459359511733055,
0.011374477297067642,
-0.0004948423011228442,
0.0579448938369751,
0.003056844463571906,
0.0077101076021790504,
-0.0017234317492693663,
-0.021760830655694008,
0.016725856810808182,
0.05309812352061272,
-0.008576455526053905,
0.021776167675852776,
0.032716866582632065,
-0.05325862020254135,
-0.027204209938645363,
-0.034967951476573944,
0.0499127097427845,
-0.018605707213282585,
-0.007436252664774656,
0.031948186457157135,
0.017514029517769814,
-0.039143722504377365,
0.0527753047645092,
0.03377382084727287,
0.007001917343586683,
0.01249768864363432,
-0.04862065985798836,
-0.0461762398481369,
0.005919762887060642,
0.020143190398812294,
0.01453159749507904,
0.0017891272436827421,
-0.024184733629226685,
0.018245387822389603,
-0.014664828777313232,
0.06845936924219131,
-0.02154785767197609,
0.003245055675506592,
-0.01720098778605461,
0.0060549089685082436,
-0.03784135729074478,
0.033386945724487305,
-0.06738415360450745,
0.030467137694358826,
0.07074880599975586,
-0.0038108150474727154,
-0.040781352669000626,
-0.0754021480679512,
-0.010369178839027882,
0.020803257822990417,
0.041816871613264084,
0.01666799932718277,
0.02579689957201481,
-0.05085304379463196,
-0.019974160939455032,
0.03052159957587719,
-0.036204446107149124,
0.03539155423641205,
-0.017834512516856194,
-0.021955981850624084,
-0.02713886834681034,
-0.01767261140048504,
-0.007666131015866995,
0.005947171710431576,
0.013074580579996109,
-0.006373019888997078,
-0.0035312625113874674,
-0.005313489586114883,
-0.015584602952003479,
0.035792913287878036,
0.03849154710769653,
0.02721995860338211,
-0.025613171979784966,
-0.01698702946305275,
-0.013792266137897968,
0.010341009125113487,
-0.04681716859340668,
-0.09131566435098648,
0.05086201801896095,
-0.004067368805408478,
-0.017134714871644974,
0.059244103729724884,
-0.021740717813372612,
-0.027605080977082253,
0.035012587904930115,
0.01678820326924324,
-0.006536166649311781,
-0.021210236474871635,
-0.03622708469629288,
0.02811514399945736,
0.03287016600370407,
-0.0019140209769830108,
0.04655873030424118,
0.03216952830553055,
-0.012854350730776787,
0.02150345779955387,
-0.0321221686899662,
0.04188011586666107,
-0.02101757936179638,
0.048935774713754654,
-0.027385232970118523,
-0.000936537457164377,
-0.026373203843832016,
0.03420623391866684,
-0.041141293942928314,
0.004332853015512228,
0.0032344397623091936,
-0.03513012081384659,
0.03621254861354828,
0.05275113135576248,
0.012992987409234047,
0.04664979502558708,
-0.014455266296863556,
0.03900766745209694,
0.02222844772040844,
-0.007756339851766825,
0.0017833472229540348,
-0.0009313109912909567,
0.002167020458728075,
-0.015522785484790802,
0.0056535168550908566,
0.027094190940260887,
-0.033620476722717285,
0.03465715050697327,
-0.021215274930000305,
-0.08065424114465714,
0.022970477119088173,
0.005037994589656591,
0.04751550406217575,
0.05860491842031479,
-0.06212268024682999,
-0.018199648708105087,
0.020402543246746063,
-0.04578343406319618,
0.004478193819522858,
-0.032680533826351166,
0.04439472779631615,
-0.03717973828315735,
0.019242430105805397,
-0.03189275041222572,
-0.02552870661020279,
-0.01184183731675148,
0.0360240638256073,
-0.010824638418853283,
-0.00784639548510313,
-0.010659197345376015,
0.031177952885627747,
-0.039710573852062225,
-0.018896741792559624,
0.013443178497254848,
0.026589786633849144,
-0.03417758643627167,
-0.00559657160192728,
-0.00576862134039402,
0.05132855474948883,
-0.010221065022051334,
-0.005325839389115572,
0.011467856355011463,
-0.021096257492899895,
-0.032229725271463394,
-0.0037097877357155085,
0.013375502079725266,
-0.04269425943493843,
-0.06775665283203125,
-0.04777974635362625,
0.027416085824370384,
0.060634054243564606,
-0.07175901532173157,
0.02020125836133957,
-0.012201933190226555,
0.020835179835557938,
-0.01900658756494522,
0.007303266786038876,
-0.019211390987038612,
0.004610348958522081,
0.02394310012459755,
0.020243855193257332,
-0.018076010048389435,
-0.04951371252536774,
-0.06695348769426346,
0.01611349917948246,
0.03234563395380974,
0.0071459198370575905,
0.022628340870141983,
0.0856042206287384,
-0.024292724207043648,
0.008158975280821323,
0.011297065764665604,
-0.05050259083509445,
0.024811070412397385,
-0.013306920416653156,
0.01576031744480133,
0.03503286838531494,
0.02599380351603031,
-0.04266418144106865,
-0.04838671535253525,
-0.03504554182291031,
0.0017774711595848203,
0.0463721863925457,
-0.0031295816879719496,
0.02714553475379944,
0.002926375949755311,
-0.01429115328937769,
-0.01755010336637497,
-0.019254151731729507,
-0.013896526768803596,
0.014801550656557083,
0.03538614884018898,
0.03536141663789749,
-0.03736116737127304,
-0.03814232721924782,
0.011117619462311268,
0.049113478511571884,
0.022201186046004295,
0.022617226466536522,
0.02664489857852459,
0.0014721007319167256,
0.04156789928674698,
-0.05435768514871597,
-0.03600434213876724,
0.053231801837682724,
-0.06428337097167969,
0.04568248987197876,
-0.013690427877008915,
0.00015716168854851276,
0.03865083307027817,
0.0512317530810833,
-0.013011917471885681,
-0.023717014119029045,
-0.022461557760834694,
-0.052863068878650665,
0.024602524936199188,
0.026981398463249207,
0.04983634501695633,
-0.01833409257233143,
-0.0061804973520338535,
0.047591257840394974,
-0.0026639241259545088,
0.015405047684907913,
-0.02222106233239174,
-0.09013508260250092,
-0.05789336562156677,
-0.0008290588739328086,
-0.024537328630685806,
0.04101398587226868,
-0.0034653497859835625,
0.008927734568715096,
-0.007734195329248905,
-0.0404575914144516,
0.04506677761673927,
0.002958259778097272,
0.027119504287838936,
-0.012155165895819664,
0.0035815490409731865,
-0.008534610271453857,
0.05610131472349167,
-0.005781721323728561,
-0.005803864449262619,
0.1257922351360321,
0.08775940537452698,
0.02732275240123272,
-0.029992690309882164,
0.008092140778899193,
-0.013025259599089622,
0.0010527813574299216,
0.001676917658187449,
0.021511893719434738,
-0.021849919110536575,
0.03750022128224373,
-0.017355581745505333,
0.025994019582867622,
-0.008649989031255245,
0.018155118450522423,
-0.0002931359922513366,
-0.06898178160190582,
-0.030162358656525612,
0.0311314444988966,
-0.017451221123337746,
0.012568322941660881,
-0.00044170633191242814,
-0.021060887724161148,
0.008013722486793995,
-0.018989818170666695,
-0.014936164952814579,
-0.044288117438554764,
-0.03188864514231682,
0.04105588048696518,
0.0008928891038522124,
-0.029391303658485413,
0.012595937587320805,
-0.03404165431857109,
0.009274126961827278,
-0.02522466331720352,
0.01289539597928524,
0.020042819902300835,
-0.0041800010949373245,
0.03991995006799698,
0.03876960277557373,
0.007955736480653286,
0.0012853966327384114,
0.015621582977473736,
-0.0029931431636214256,
-0.02039535716176033,
0.001690637436695397,
-0.00835177581757307,
0.036219898611307144,
-0.053601257503032684,
-0.03237813711166382,
-0.01076933927834034,
-0.016968118026852608,
0.010169584304094315,
-0.06212622672319412,
-0.005110978148877621,
0.05303197726607323,
0.0401688851416111,
-0.00822530034929514,
-0.008770436979830265,
0.00478913402184844,
0.044879574328660965,
0.0028903810307383537,
-0.017247868701815605,
-0.02064836397767067,
0.0024459727574139833,
-0.01607360690832138,
-0.011520185507833958,
0.07278307527303696,
0.023391081020236015,
-0.0016506968531757593,
-0.05313747376203537,
-0.027692435309290886,
-0.029273349791765213,
-0.04217904806137085,
0.005660885013639927,
0.04755627363920212,
0.02347678504884243,
-0.01387114729732275,
-0.02380826696753502,
0.0023292002733796835,
-0.019064459949731827,
0.0053232270292937756,
-0.044808801263570786,
-0.016492176800966263,
0.0012129544047638774,
0.008348311297595501,
0.0796995759010315,
0.017338979989290237,
-0.013742003589868546,
-0.0024360253009945154,
0.016358528286218643,
0.04030477628111839,
0.053971294313669205,
0.014100010506808758,
-0.05267374962568283,
0.007054442539811134,
-0.014702011831104755,
0.02863996848464012,
-0.009807403199374676,
0.0287186186760664,
0.0045186192728579044,
0.012109965085983276,
0.0059335785917937756,
0.033308908343315125,
-0.03716806322336197,
-0.029945408925414085,
-0.005733201280236244,
-0.01818191632628441,
0.005795892793685198,
-0.019876550883054733,
0.031436577439308167,
-0.04218026250600815,
-0.020207906141877174,
-0.02619914337992668,
-0.05488291755318642,
0.007815910503268242,
0.02212032862007618,
-0.008597489446401596,
0.010523824021220207,
-0.011474463157355785,
0.042848847806453705,
-0.025196973234415054,
-0.035077471286058426,
0.009219430387020111,
-0.002896009711548686,
0.02358982525765896,
-0.008465167135000229,
-0.01830729842185974,
0.011756033636629581,
-0.036176878958940506,
-0.040372010320425034,
-0.02060478925704956,
0.035120535641908646,
-0.0043340399861335754,
-0.003326974343508482,
-0.012063895352184772,
0.010720689781010151,
0.02620234340429306,
0.01211731880903244,
-0.033216528594493866,
0.06245039403438568,
-0.0022484995424747467,
-0.0505424402654171,
0.022180331870913506,
-0.044021785259246826,
0.022599952295422554,
0.042291656136512756,
0.0153607577085495,
-0.0066998181864619255,
0.006464193109422922,
-0.01774541474878788,
-0.03904550522565842,
0.005814659409224987,
-0.008866801857948303,
-0.006616753991693258,
-0.007547847926616669,
0.009597815573215485,
-0.03707384690642357,
-0.010768626816570759,
0.0227887611836195,
0.0005129638593643904,
-0.000024800961909932084,
0.006498322356492281,
-0.013780179433524609,
-0.05207245796918869,
-0.042386122047901154,
-0.0042536258697509766,
0.003878530114889145,
-0.023649515584111214,
0.03915119916200638,
-0.01383985299617052,
0.0468888133764267,
0.012237903662025928,
-0.036617085337638855,
-0.10749253630638123,
0.029983017593622208,
0.025876108556985855,
0.00000512335054736468,
0.02009083889424801,
-0.04240359738469124,
0.04837707057595253,
0.059870850294828415,
-0.08731772750616074,
0.030945636332035065,
-0.026831917464733124,
-0.03699459880590439,
-0.038646019995212555,
0.039845503866672516,
-0.03307970240712166,
0.000879660714417696,
0.004674251656979322,
0.036784473806619644,
0.003714370308443904,
0.037016380578279495,
-0.0024353761691600084,
-0.023218879476189613,
0.00013219100947026163,
0.02392643876373768,
-0.052163392305374146,
0.002557607600465417,
0.05085905268788338,
0.015764880925416946,
0.005183955188840628,
-0.03476378321647644,
-0.018306393176317215,
0.01699676923453808,
-0.002539260545745492,
-0.028309538960456848,
-0.006071957293897867,
0.02759312279522419,
0.006274282466620207,
0.0072167119942605495,
0.012689352966845036,
0.00874435156583786,
0.043586403131484985,
-0.004861957393586636,
0.00784052163362503,
0.027164170518517494,
0.009041286073625088,
-0.008340601809322834,
-0.027503937482833862,
0.024856284260749817,
0.034350939095020294,
-0.024833614006638527,
0.008497958071529865,
0.03668379411101341,
0.02340571954846382,
-0.05087076500058174,
0.00033513930975459516,
-0.05628950521349907,
0.020574675872921944,
0.007442864123731852,
0.0323779433965683,
-0.02872278168797493,
0.018095409497618675,
-0.021294288337230682,
-0.015165001153945923,
0.028730036690831184,
0.011350966058671474,
0.00770188681781292,
-0.014689424075186253,
-0.040794726461172104,
-0.0038716739509254694,
0.009634846821427345,
0.03793211281299591,
-0.03285285830497742,
-0.030671734362840652,
0.033773742616176605,
-0.01808321103453636,
0.038668036460876465,
0.008884303271770477,
-0.03152129054069519,
-0.06262454390525818,
-0.049178313463926315,
0.03425946831703186,
-0.0389152467250824,
-0.020129887387156487,
-0.016134461387991905,
-0.04358956962823868,
-0.012297194451093674,
0.06293783336877823,
0.04538458585739136,
0.011084532365202904,
-0.023430684581398964,
-0.024381369352340698,
-0.024203598499298096,
0.02873622067272663,
-0.036507271230220795,
-0.01617557369172573,
-0.016898466274142265,
-0.035176876932382584,
-0.02322482503950596,
0.024321092292666435,
0.008402211591601372,
0.003518798155710101,
0.040769774466753006,
-0.000692735833581537,
-0.01621866412460804,
-0.006286609917879105,
-0.039250899106264114,
0.06570432335138321,
-0.021810095757246017,
0.025140246376395226,
0.052977707237005234,
0.039353370666503906,
0.05603434145450592,
0.015331358648836613,
-0.028250399976968765,
-0.0655490979552269,
-0.03207070007920265,
-0.044596899300813675,
-0.038287922739982605,
-0.03603648394346237,
0.013288547284901142,
0.03415057063102722,
-0.036999911069869995,
0.03854037821292877,
0.030002599582076073,
-0.02509237267076969,
-0.010966611094772816,
0.060171760618686676,
-0.040686581283807755,
0.02394871413707733,
-0.012911606580018997,
0.03318353742361069,
0.01831120252609253,
-0.010910180397331715,
-0.027580009773373604,
0.038894761353731155,
-0.015564939938485622,
0.0004997895448468626,
0.041099414229393005,
0.040125828236341476,
-0.0014309077523648739,
0.006205390207469463,
0.029326455667614937,
0.049695923924446106,
-0.0244305320084095,
0.010709673166275024,
0.05323314294219017,
0.00751437759026885,
-0.013190501369535923,
0.03419683128595352,
0.006805150769650936,
0.06128908693790436,
-0.038005564361810684,
0.00041455068276263773,
-0.04146696999669075,
0.006584468297660351,
-0.044449009001255035,
0.0038305269554257393,
0.002739720745012164,
0.0636744573712349,
0.021775856614112854,
0.018286775797605515,
-0.05793246254324913,
0.017159478738904,
-0.01005084440112114,
-0.06756487488746643,
0.00992023479193449,
-0.015015289187431335,
-0.04332701489329338,
0.02127966471016407,
0.01923498883843422,
-0.01750260218977928,
-0.02899741567671299,
0.03345152363181114,
0.01753297448158264,
-0.04213309660553932,
0.015093406662344933,
0.03959864750504494,
0.0015326972352340817,
0.05680207163095474,
-0.058501362800598145,
-0.00839755218476057,
-0.016899922862648964,
0.009694754146039486,
-0.020829280838370323,
0.018049754202365875
] |
<p>I'm asking a question that has bothered me for years and years. First of all, let me give some context. I'm a layman in physics (college educated, math major). I've read Feynman's QED cover to cover, and watched his messenger lectures. My hope is to get an answer at the "Feynman level", ideally in the crystal clear terms that feynman himself uses :)</p>
<p>Okay, so with that out of the way, my question is about transparency. My understanding from Feynman and other materials is that when a photon hits an atom, the photon can either be absorbed, or absorbed and released. </p>
<p>What I don't understand is how transparency could arise from this. If the light were absorbed and then a new photon emitted, it seems incredible that the new photon would have the exact trajectory as the old one. Why wouldn't it go off randomly in a random direction? </p>
<p>Here's some of the homework I've done trying to find out the answer on my own:</p>
<p>1) <a href="http://physics.stackexchange.com/questions/11138/transparency-of-materials">Transparency of materials</a> (one commentor alludes to scattering not being explained here)</p>
<p>2) <a href="http://alemassociates.com/mambo/content/view/33/1/">http://alemassociates.com/mambo/content/view/33/1/</a> (this seems to address it, but I will admit it's mostly over my head)</p>
<p>3) <a href="http://www.av8n.com/physics/white.htm">http://www.av8n.com/physics/white.htm</a> (seems to talk about it, but doesn't explain <em>why</em> the photon would ever come out the same direction as it came in)</p>
<p>4) Discover magazine posted this: "when a packet of light energy, or photon, hits a solid object, three things can happen. Light can disappear: If the photon has the same vibrational frequency as the electrons in the material it strikes, those electrons absorb its energy, changing the photon from light into heat. Light can also be scattered: the surface electrons can grab the photon's energy and then eject a photon of the same wavelength which is how you see pretty much everything that doesn't emit light on its own. But if the photon doesn't have the right vibrational energy for absorption, and if the atoms in the material are arranged in patterns that discourage reflection (such as the random jumble of molecules in glass or air) <strong>then the photon's energy passes from atom to atom, emerging on the other side still bright and shiny.</strong> Then you have transparency."</p>
<p>I'm posting here for help. I realize that this forum is geared for graduate level and beyond physics, but I'm hoping that this transgression will be forgiven. I would really, truly, like to understand why anything is transparent at all. From my understanding, nothing should ever be transparent! At best we might get translucency (a bunch of photons coming out in random directions), but I cannot understand transparency. Why would a photon interacting with an atom come out the exact way it came from? In other words, as per that Discover magazine article, why would the photon be passed from atom to atom always at the exact same vector that it came from?</p>
<p>Thank you!</p>
<p>edit: If possible, I'd like to keep it in terms of photons. What's going on at the photon level, and avoid the wave framework. Let's talk about photons and probability amplitudes a-la Feynman.</p>
| 10,725 |
[
-0.03043859824538231,
-0.03467153385281563,
0.01788409799337387,
-0.07657080888748169,
0.0036349454894661903,
0.02196762152016163,
-0.009819652885198593,
0.006890332326292992,
0.022393129765987396,
-0.030402403324842453,
0.015194588340818882,
0.028736302629113197,
0.012650029733777046,
0.017731063067913055,
0.02779860608279705,
0.021365730091929436,
0.005190475378185511,
-0.043936844915151596,
0.002218129811808467,
-0.03458978608250618,
0.001736834878101945,
-0.019830645993351936,
-0.04390941187739372,
-0.013007042929530144,
-0.04641030728816986,
0.007368316408246756,
-0.011627137660980225,
0.026438098400831223,
0.030763721093535423,
0.03378710895776749,
-0.013645907863974571,
-0.00858556479215622,
0.022076299414038658,
0.01771780662238598,
-0.01677161641418934,
-0.007716311141848564,
-0.029629269614815712,
-0.034781817346811295,
-0.0031390085350722075,
0.008376737125217915,
-0.014647532254457474,
0.0286758653819561,
-0.043399080634117126,
0.047237578779459,
-0.02905408851802349,
-0.01752624288201332,
0.01410731766372919,
0.002996141789481044,
0.09376687556505203,
-0.055377714335918427,
0.07622844725847244,
-0.04133282229304314,
0.02746364288032055,
0.0067603751085698605,
-0.005006040446460247,
-0.03078528307378292,
0.06915277242660522,
0.08122963458299637,
-0.009024577215313911,
-0.017161749303340912,
0.003610785584896803,
0.004297470673918724,
-0.03084099479019642,
0.024695750325918198,
-0.018565025180578232,
0.04259062558412552,
-0.005179503466933966,
-0.056579943746328354,
0.016544753685593605,
-0.00029704568441957235,
0.01952911540865898,
-0.0040623489767313,
0.05870407819747925,
0.010259256698191166,
0.04010884836316109,
-0.02746778167784214,
0.03402451053261757,
0.05181552842259407,
0.03401869162917137,
0.02286171168088913,
-0.020215176045894623,
-0.0038204623851925135,
0.022972378879785538,
0.0390424020588398,
-0.008492072112858295,
-0.018509551882743835,
0.07331785559654236,
-0.02651551552116871,
-0.0005672305123880506,
0.03809172287583351,
0.017557960003614426,
0.025096720084547997,
0.036321092396974564,
0.05297040194272995,
-0.007524385582655668,
0.01097013894468546,
0.006872065365314484,
0.06278793513774872,
0.005069922190159559,
0.00951462984085083,
-0.00008666466601425782,
-0.026309441775083542,
0.026960384100675583,
0.06749172508716583,
-0.025421379134058952,
-0.015726681798696518,
-0.014256986789405346,
0.01576685532927513,
-0.008757229894399643,
0.006177822593599558,
-0.030703242868185043,
0.024261394515633583,
0.0031731922645121813,
0.008794848807156086,
0.0255684033036232,
-0.02861933223903179,
-0.0001480390055803582,
-0.022718757390975952,
0.07776177674531937,
0.08880746364593506,
-0.01738666370511055,
-0.03292606770992279,
0.02591552771627903,
-0.028630107641220093,
-0.03373301029205322,
-0.025887060910463333,
0.05168316140770912,
0.005908328108489513,
-0.03155294060707092,
0.011372760869562626,
0.008791904896497726,
-0.024883389472961426,
0.04233204200863838,
0.0023696355056017637,
0.014143501408398151,
-0.022532911971211433,
-0.13636678457260132,
-0.061612021178007126,
0.050264421850442886,
0.04441792517900467,
-0.020079035311937332,
-0.10697945207357407,
-0.006067751906812191,
-0.008064555004239082,
0.08962725102901459,
-0.013637286610901356,
-0.014571161940693855,
-0.009238743223249912,
0.06381569802761078,
-0.009352295659482479,
-0.015290667302906513,
0.012410220690071583,
0.004814448766410351,
-0.023907149210572243,
0.020407166332006454,
-0.05245767533779144,
0.03514290973544121,
0.031045010313391685,
0.015907255932688713,
-0.024475015699863434,
0.05507298931479454,
0.015050474554300308,
0.02076362818479538,
0.020225631073117256,
-0.01727261394262314,
-0.04541683942079544,
0.06676077842712402,
0.039992690086364746,
0.005182511173188686,
0.01756882295012474,
0.008632790297269821,
0.007891934365034103,
-0.03154032677412033,
0.01697980798780918,
-0.009415406733751297,
-0.03289194777607918,
-0.0031098490580916405,
-0.017111502587795258,
-0.005890930537134409,
-0.009400807321071625,
-0.052606478333473206,
-0.04212755337357521,
0.006893218494951725,
0.023949528113007545,
0.030875518918037415,
0.01999089866876602,
0.022423945367336273,
0.02712562307715416,
0.00407886179164052,
-0.034565940499305725,
-0.020035438239574432,
-0.01506485790014267,
-0.011975509114563465,
-0.018684890121221542,
-0.03234177082777023,
0.004996313247829676,
-0.006417026277631521,
-0.012630774639546871,
0.009899516589939594,
-0.016026802361011505,
-0.015033815987408161,
0.012600181624293327,
0.005672597326338291,
-0.00935443490743637,
-0.010590109042823315,
0.06560100615024567,
0.023075038567185402,
-0.017796240746974945,
0.01917346939444542,
-0.03658941015601158,
-0.016568247228860855,
-0.013925439678132534,
0.013489891774952412,
0.06013672426342964,
-0.04346969351172447,
-0.022010866552591324,
0.021212564781308174,
0.017039118334650993,
-0.0012859267881140113,
-0.003369151148945093,
0.00010875948646571487,
0.06619805097579956,
0.020790254697203636,
-0.001518165459856391,
-0.030542932450771332,
0.025903532281517982,
-0.022113602608442307,
0.018290027976036072,
-0.021766623482108116,
-0.050511687994003296,
-0.023502778261899948,
0.00010347198985982686,
0.016089865937829018,
-0.023690033704042435,
-0.013008080422878265,
0.03326619043946266,
-0.0026964081916958094,
0.0600513257086277,
0.022095361724495888,
0.021635985001921654,
-0.026605883613228798,
-0.027960188686847687,
0.0049219923093914986,
-0.03182041645050049,
0.004016099032014608,
0.016752272844314575,
0.0039234827272593975,
-0.005707383621484041,
0.031710319221019745,
-0.02326355315744877,
-0.02840956300497055,
0.0045826612040400505,
0.0011462834663689137,
0.02776605263352394,
0.001213782699778676,
-0.017785249277949333,
0.049975503236055374,
-0.011452071368694305,
-0.0064929332584142685,
0.008450797758996487,
-0.016847411170601845,
-0.006039751227945089,
-0.05077296867966652,
-0.007049243897199631,
-0.002978907898068428,
-0.005941278301179409,
0.0012189545668661594,
-0.0057139708660542965,
0.005261173937469721,
-0.02814341150224209,
0.011520138010382652,
-0.007489569950848818,
0.027670981362462044,
-0.04018167033791542,
-0.009434511885046959,
0.016789233312010765,
0.015868350863456726,
0.01960952952504158,
-0.05149495601654053,
-0.027956455945968628,
0.00968040432780981,
0.00924128107726574,
-0.011937330476939678,
0.02362324483692646,
-0.021490193903446198,
0.021980391815304756,
-0.06872063130140305,
-0.008643650449812412,
0.0308209415525198,
-0.005732174031436443,
-0.009149712510406971,
0.03240596130490303,
0.008873729966580868,
-0.08710292726755142,
-0.026224259287118912,
-0.0043626572005450726,
-0.01015515811741352,
-0.03791527822613716,
0.009096931666135788,
0.048438720405101776,
-0.0024303426034748554,
-0.0517989806830883,
0.0131072998046875,
-0.04795359820127487,
-0.053042538464069366,
-0.012492120265960693,
-0.023008177056908607,
0.002764028962701559,
-0.02160828188061714,
-0.014411353506147861,
0.016246214509010315,
-0.02434803918004036,
0.013934526592493057,
-0.055854104459285736,
-0.05641471967101097,
0.007166153751313686,
-0.0013053735019639134,
0.014582824893295765,
0.019594058394432068,
0.00963888131082058,
0.05249611288309097,
0.03483731672167778,
-0.025422776117920876,
-0.00802388321608305,
-0.0038650264032185078,
0.008856025524437428,
-0.06071753799915314,
0.03909938037395477,
0.04092247411608696,
-0.00020535006478894502,
0.01961013488471508,
-0.025058209896087646,
0.059718385338783264,
0.020881924778223038,
-0.018016306683421135,
-0.010810482315719128,
0.003497971221804619,
0.02079632878303528,
-0.03234636038541794,
-0.004068024456501007,
0.010140112601220608,
-0.026829728856682777,
-0.016531724482774734,
-0.003233653958886862,
0.025686852633953094,
0.021831728518009186,
-0.0192997045814991,
0.06678824871778488,
0.015722986310720444,
-0.0039457413367927074,
-0.04809252917766571,
0.03581612557172775,
-0.005802197847515345,
-0.01863490231335163,
-0.021672135218977928,
0.006975371856242418,
0.04756375774741173,
-0.005964506883174181,
0.02094847336411476,
0.044488582760095596,
0.054757267236709595,
-0.020034383982419968,
-0.023450395092368126,
-0.02720767632126808,
0.02949664369225502,
0.009098941460251808,
-0.021985726431012154,
0.015469773672521114,
0.0638473704457283,
0.036799464374780655,
0.05799464136362076,
-0.011814254336059093,
-0.020799044519662857,
-0.056761208921670914,
-0.01943143643438816,
0.0018855840899050236,
0.0034071817062795162,
0.0594012625515461,
0.016125038266181946,
0.06418668478727341,
0.039622049778699875,
0.03232917562127113,
-0.012303421273827553,
0.004501206800341606,
-0.07268761098384857,
0.017374273389577866,
-0.024750100448727608,
-0.025488227605819702,
-0.042481470853090286,
-0.01208136510103941,
-0.01762465201318264,
-0.01204746775329113,
-0.056793030351400375,
-0.009194632060825825,
-0.008633341640233994,
-0.058021239936351776,
-0.013385973870754242,
-0.0531279593706131,
-0.04022763669490814,
0.004947333596646786,
0.04839096963405609,
0.03558475524187088,
-0.011717020533978939,
0.017859814688563347,
0.006132067181169987,
-0.044197890907526016,
0.0010017009917646646,
-0.02383301965892315,
0.036519959568977356,
0.004837408661842346,
0.010528971441090107,
0.017349060624837875,
-0.0038294263649731874,
-0.024362921714782715,
0.011446901597082615,
0.027487127110362053,
0.0421687588095665,
0.016635354608297348,
0.0039049626793712378,
-0.010992025956511497,
-0.03567342832684517,
-0.0004638341488316655,
0.0032924071419984102,
0.04312235489487648,
-0.02593172900378704,
0.04115390032529831,
0.05271407216787338,
0.001905612414702773,
-0.019351482391357422,
0.056716013699769974,
-0.005404581781476736,
-0.027296822518110275,
0.038058944046497345,
-0.050205450505018234,
0.02326679788529873,
0.018058612942695618,
0.015244750306010246,
-0.023591160774230957,
0.012618369422852993,
0.0038746537175029516,
-0.007513060234487057,
0.003186799120157957,
0.020591789856553078,
-0.018433908000588417,
-0.027669141069054604,
-0.030390044674277306,
-0.028159277513623238,
-0.013425668701529503,
0.0021512636449187994,
-0.017385078594088554,
0.035455431789159775,
0.04630938917398453,
0.007117314729839563,
0.013577275909483433,
-0.06586766988039017,
-0.022907216101884842,
0.03146284073591232,
0.04476366564631462,
-0.03746585175395012,
0.029144112020730972,
-0.05481376126408577,
-0.03347169980406761,
0.00551264313980937,
-0.007428622338920832,
0.048574209213256836,
-0.020402099937200546,
0.0027665479574352503,
-0.014333206228911877,
-0.03721292316913605,
-0.014334295876324177,
0.004826359450817108,
0.012691971845924854,
0.02243199571967125,
-0.02126413956284523,
0.00472977664321661,
-0.027032634243369102,
0.02612248808145523,
0.03332401439547539,
0.07977823913097382,
-0.028630387037992477,
0.01106482557952404,
-0.006312903016805649,
-0.0009772148914635181,
-0.012964681722223759,
-0.10200721770524979,
-0.005413950886577368,
-0.016512729227542877,
-0.0032455441541969776,
0.03577832877635956,
-0.013529238291084766,
-0.04350569099187851,
0.056538667529821396,
0.03648046404123306,
-0.015329151414334774,
0.0038564419373869896,
-0.0497126467525959,
0.04163583740592003,
0.013819210231304169,
-0.00318100000731647,
0.0231003575026989,
0.06118271127343178,
-0.012269312515854836,
0.002879286650568247,
-0.013273745775222778,
0.05112011730670929,
-0.01587555557489395,
0.028934357687830925,
-0.038564492017030716,
0.008419019170105457,
-0.03759735822677612,
0.05598188936710358,
0.0022602116223424673,
-0.020891183987259865,
-0.006068529561161995,
-0.0633726716041565,
0.010217729955911636,
0.026891300454735756,
-0.02260005660355091,
0.02481129765510559,
-0.03070484660565853,
0.02644052729010582,
-0.04201271012425423,
-0.010986797511577606,
0.017630834132432938,
0.010192068293690681,
-0.0014593038940802217,
0.04035389795899391,
0.019865378737449646,
0.02675972320139408,
-0.042543333023786545,
0.011099965311586857,
-0.008562758564949036,
-0.06087706610560417,
0.050583548843860626,
0.04829099774360657,
0.03567234054207802,
0.052864838391542435,
-0.04799441993236542,
-0.008545387536287308,
0.014695117250084877,
-0.03887020796537399,
0.029799645766615868,
-0.04575078934431076,
0.028563018888235092,
-0.0011734887957572937,
-0.0008203909383155406,
-0.05452863126993179,
-0.06393732130527496,
-0.0027708641719073057,
0.012143655680119991,
-0.04581466689705849,
0.005270960740745068,
-0.01223746407777071,
-0.013621038757264614,
-0.01029503345489502,
0.020754262804985046,
0.005162813700735569,
-0.012059302069246769,
0.002095398958772421,
0.019514016807079315,
0.0234242994338274,
0.04094316437840462,
-0.017402876168489456,
-0.017206519842147827,
-0.02826436422765255,
-0.02239583060145378,
-0.054694242775440216,
0.029543008655309677,
0.03839400038123131,
-0.017330419272184372,
-0.043045930564403534,
-0.017366457730531693,
-0.01333835069090128,
0.061319608241319656,
-0.0136477742344141,
-0.020015619695186615,
0.024682896211743355,
0.027591660618782043,
0.002779396018013358,
-0.012025187723338604,
0.022731218487024307,
0.04588114842772484,
0.023874571546912193,
-0.005244335159659386,
-0.005154665093868971,
0.00032593097421340644,
-0.041771553456783295,
0.02501126378774643,
-0.002187206409871578,
0.00620820140466094,
0.029448376968503,
0.04153125733137131,
-0.039593275636434555,
-0.019451618194580078,
0.00573741877451539,
-0.001303336932323873,
0.03447071462869644,
-0.023021304979920387,
-0.009895123541355133,
0.018109267577528954,
-0.021735647693276405,
-0.034545112401247025,
-0.06494946032762527,
-0.043151602149009705,
0.01558807585388422,
0.03548714146018028,
-0.02272782288491726,
0.04134375974535942,
-0.008073120377957821,
-0.012549703009426594,
-0.009031165391206741,
-0.022251438349485397,
-0.015094812959432602,
-0.013180510140955448,
0.003210073569789529,
0.036830831319093704,
-0.017945293337106705,
-0.005917107220739126,
-0.013230021111667156,
0.07950308173894882,
-0.044179756194353104,
0.023860638961195946,
0.040851905941963196,
0.00545594934374094,
0.06342872977256775,
0.006295919418334961,
-0.015653591603040695,
0.03356754407286644,
-0.022247174754738808,
0.047334108501672745,
0.03329300507903099,
-0.04294689744710922,
0.057448118925094604,
0.01695885881781578,
0.004443176556378603,
-0.03773142397403717,
-0.0023642939049750566,
-0.05736913904547691,
0.009821152314543724,
0.00900522992014885,
0.04354698956012726,
0.005979728884994984,
0.0027529243379831314,
0.04509972035884857,
-0.009757221676409245,
0.014851713553071022,
-0.008664898574352264,
-0.05674365535378456,
-0.032284028828144073,
-0.04167138785123825,
-0.03776729479432106,
0.04130635783076286,
-0.03091178648173809,
-0.018397023901343346,
0.02157062105834484,
-0.07399442791938782,
0.034406643360853195,
0.006438516546040773,
0.036787424236536026,
-0.0022643706761300564,
0.018684282898902893,
-0.014409615658223629,
0.02432921901345253,
-0.03038966841995716,
0.008993010967969894,
0.1100117489695549,
0.03673161193728447,
-0.006071901880204678,
-0.030015751719474792,
-0.015545015223324299,
-0.01760563999414444,
0.011955724097788334,
-0.010000756941735744,
0.021982654929161072,
-0.02669588290154934,
0.039336688816547394,
0.016840355470776558,
0.06713942438364029,
0.028903182595968246,
0.007798144593834877,
0.03825678676366806,
-0.02359052747488022,
-0.02487729676067829,
0.02578040026128292,
0.0045976657420396805,
-0.026676665991544724,
0.03808573633432388,
-0.04860466346144676,
0.05079064518213272,
-0.033837057650089264,
-0.029301105067133904,
-0.015482556074857712,
-0.03938017413020134,
0.01885101944208145,
0.02660740539431572,
-0.03018312342464924,
-0.030697036534547806,
0.02355254627764225,
-0.00993428472429514,
0.010664382949471474,
0.033729568123817444,
0.034577708691358566,
-0.023656556382775307,
0.03315144404768944,
0.012020123191177845,
0.05898994207382202,
-0.02405604161322117,
0.030285971239209175,
0.020892959088087082,
-0.0395180806517601,
-0.035518962889909744,
-0.019127991050481796,
0.03602086380124092,
-0.025907445698976517,
-0.020136993378400803,
-0.003985603805631399,
-0.013325543142855167,
0.004344146698713303,
-0.04572339355945587,
0.025505485013127327,
0.028960904106497765,
0.006832975894212723,
-0.006951732560992241,
-0.0012852157233282924,
0.016539160162210464,
0.010602844879031181,
0.008699852973222733,
-0.014128779992461205,
0.011989104561507702,
0.0044844732619822025,
0.011699166148900986,
-0.008948632515966892,
0.007948973216116428,
0.030668433755636215,
-0.023608412593603134,
-0.042179469019174576,
-0.01652880385518074,
-0.056769195944070816,
-0.028309915214776993,
-0.005425823386758566,
0.021260930225253105,
0.03663163632154465,
-0.02796339988708496,
-0.006251009181141853,
-0.028476150706410408,
-0.06220462918281555,
0.03391500189900398,
-0.0024473394732922316,
-0.014747008681297302,
-0.031573548913002014,
0.008302338421344757,
0.004155423492193222,
0.013504424132406712,
-0.0011974009685218334,
-0.020982393994927406,
0.017420019954442978,
0.032432302832603455,
0.03023769147694111,
-0.02381446585059166,
-0.025927893817424774,
0.027846507728099823,
-0.02960139885544777,
0.017752014100551605,
0.00445452518761158,
0.03600228205323219,
-0.01870475336909294,
0.013999818824231625,
0.013064542785286903,
0.011301719583570957,
-0.029350055381655693,
-0.03343129903078079,
0.013475483283400536,
-0.01384604349732399,
-0.012369262054562569,
0.006867405958473682,
-0.01946873590350151,
-0.010517152026295662,
-0.024488475173711777,
-0.01488659717142582,
0.019216688349843025,
0.012355898506939411,
0.03044230490922928,
-0.025038909167051315,
0.030479421839118004,
-0.05595224350690842,
0.011591063812375069,
-0.02413545548915863,
-0.007395051419734955,
-0.02711615525186062,
-0.008463341742753983,
-0.008925863541662693,
0.007716599386185408,
-0.009645325131714344,
0.04866359010338783,
-0.006767717655748129,
-0.012986483983695507,
0.01505132857710123,
0.025665005668997765,
0.024038564413785934,
-0.02544601634144783,
0.03898506239056587,
0.0015185248339548707,
0.011361815966665745,
0.03096289560198784,
-0.03442194312810898,
0.0698075070977211,
-0.005900648422539234,
-0.07475671172142029,
0.01600150763988495,
-0.004876467399299145,
0.022799188271164894,
0.025394389405846596,
-0.01940976083278656,
0.008184360340237617,
0.07399817556142807,
-0.014504732564091682,
-0.029264720156788826,
-0.01606941968202591,
-0.0434776172041893,
0.018005812540650368,
0.008430445566773415,
-0.0017005266854539514,
-0.025973739102482796,
0.01618036814033985,
0.024785757064819336,
0.00041118881199508905,
0.0039861309342086315,
0.007497888058423996,
-0.012963554821908474,
-0.0350332111120224,
-0.02603982761502266,
0.01609613746404648,
0.010402537882328033,
-0.007993065752089024,
0.07074348628520966,
0.015394219197332859,
0.06842833757400513,
0.04327072575688362,
-0.02580684795975685,
-0.10188505798578262,
0.009133297018706799,
0.01376541331410408,
-0.0021958036813884974,
0.013802017085254192,
-0.03406937047839165,
0.025589359924197197,
0.04029283672571182,
-0.09679686278104782,
0.0144349941983819,
-0.021710800006985664,
-0.01936853863298893,
-0.04188813641667366,
0.06266254186630249,
-0.05491531267762184,
0.018322089686989784,
0.03682621568441391,
0.028234027326107025,
0.046114906668663025,
0.03883964568376541,
-0.016391696408391,
-0.015671227127313614,
-0.017881665378808975,
0.055052775889635086,
0.01708786003291607,
0.04555478319525719,
0.052194591611623764,
0.005490228068083525,
-0.0012816733215004206,
-0.005391090176999569,
-0.0031599043868482113,
0.014786644838750362,
-0.030288392677903175,
-0.028858477249741554,
0.014571089297533035,
-0.023090891540050507,
-0.008710275404155254,
0.02432270161807537,
-0.004499791655689478,
-0.021187782287597656,
0.04788138344883919,
0.016840502619743347,
0.03158823773264885,
-0.01935824751853943,
0.017178475856781006,
-0.04358803480863571,
-0.027729317545890808,
0.0005797792691737413,
-0.0030423481948673725,
0.012419396080076694,
0.00984450988471508,
0.024030471220612526,
-0.0069737215526402,
-0.017618387937545776,
-0.012988145463168621,
-0.06275234371423721,
-0.030942080542445183,
0.01712539792060852,
0.04603849723935127,
0.008864481933414936,
0.0262642540037632,
-0.0341922827064991,
-0.02133645862340927,
0.01997249573469162,
0.014365662820637226,
0.017445886507630348,
-0.05016358196735382,
-0.04564879089593887,
-0.007032702676951885,
0.005361395888030529,
0.024734962731599808,
-0.0013880393235012889,
-0.04931611567735672,
-0.004868379794061184,
-0.006085745990276337,
0.012016193941235542,
0.0025219472590833902,
-0.05268368870019913,
-0.03065069019794464,
-0.0593847893178463,
0.051200564950704575,
-0.010158155113458633,
-0.011599537916481495,
-0.05703642964363098,
0.007327795960009098,
0.011646373197436333,
0.07480809837579727,
0.053061116486787796,
-0.013471725396811962,
-0.018785852938890457,
-0.0014638422289863229,
-0.015033443458378315,
0.03335981443524361,
-0.03452349826693535,
0.000688734115101397,
0.002948098350316286,
0.004886094015091658,
-0.02817710116505623,
0.02682814560830593,
-0.020895501598715782,
0.04198911041021347,
0.009716170839965343,
-0.02978992648422718,
0.0017113866051658988,
-0.010682670399546623,
-0.050111934542655945,
0.044476062059402466,
-0.028233205899596214,
-0.018224339932203293,
0.024550756439566612,
0.006034164223819971,
0.02999359741806984,
0.04174661636352539,
-0.000785755692049861,
-0.05863438919186592,
0.011181254871189594,
-0.02987794764339924,
-0.0470421239733696,
-0.017354946583509445,
0.001582119264639914,
0.05116993933916092,
-0.05625077337026596,
-0.011308425106108189,
0.01417976152151823,
-0.02720583602786064,
-0.015504998154938221,
0.06637022644281387,
0.0018940233858302236,
0.03846783936023712,
0.028585709631443024,
0.034470103681087494,
0.01407534908503294,
-0.036625057458877563,
-0.019468506798148155,
0.029988707974553108,
0.022188259288668633,
0.02002939209342003,
0.04610839858651161,
0.005212163552641869,
0.03882972151041031,
-0.013001260347664356,
0.002887315582484007,
0.055339496582746506,
-0.029888620600104332,
0.020525861531496048,
0.03215289115905762,
0.009532551281154156,
-0.011865531094372272,
0.028936324641108513,
-0.004696792457252741,
0.05578463897109032,
-0.04543678089976311,
0.048485368490219116,
-0.01736386865377426,
0.014464957639575005,
-0.014046404510736465,
0.03330279886722565,
0.005145693197846413,
0.049765389412641525,
0.004763253498822451,
-0.029000964015722275,
-0.023124804720282555,
0.03830590099096298,
0.03121466562151909,
-0.0598493255674839,
0.00807645171880722,
-0.01571490988135338,
-0.049443673342466354,
-0.019435187801718712,
-0.0020126590970903635,
0.01234124880284071,
-0.0146060511469841,
0.002923066494986415,
0.031602952629327774,
-0.014381644316017628,
0.005169274285435677,
0.0023561890702694654,
-0.02643515169620514,
0.0841570645570755,
-0.05533825606107712,
0.009482061490416527,
-0.044637925922870636,
0.0342831015586853,
-0.06348546594381332,
0.003552284324541688
] |
<p>Why does a larger mass in a pendulum have the same period as a lighter mass? i know it has something to do with gravity and length but how can this be explained in depth? like for example the galileo's experiment where both masses were nearly the same but the lighter mass was slower (air resistance)</p>
| 347 |
[
-0.02169797383248806,
-0.015823516994714737,
-0.02275768853724003,
-0.013015108183026314,
0.025459252297878265,
0.002694510854780674,
-0.019253171980381012,
-0.04045731574296951,
0.010854944586753845,
0.011313578113913536,
0.017374416813254356,
0.034199975430965424,
0.06535331904888153,
-0.015758540481328964,
0.024496305733919144,
0.000053749703511130065,
-0.0037384903989732265,
0.0034860637970268726,
-0.0039944420568645,
-0.036486007273197174,
-0.016954220831394196,
0.00886960793286562,
0.04104161262512207,
-0.0022318637929856777,
-0.03521275520324707,
0.03274308890104294,
0.07732880115509033,
-0.0034415770787745714,
0.01790359988808632,
0.04433964937925339,
0.000054514039220521227,
0.015622654929757118,
-0.004493189975619316,
0.04113008454442024,
0.03477414697408676,
0.00745074637234211,
-0.0304481890052557,
-0.018834015354514122,
-0.012511109001934528,
0.04257555305957794,
-0.06800380349159241,
-0.013193142600357533,
-0.02458467148244381,
0.023667776957154274,
-0.012285809963941574,
0.036295272409915924,
0.024068357422947884,
-0.009377026930451393,
0.07161974906921387,
-0.06729312986135483,
0.07022400200366974,
0.018810903653502464,
0.030881119892001152,
0.04589005932211876,
0.0016566731501370668,
-0.005613625980913639,
0.06954293698072433,
0.06598935276269913,
-0.03595351800322533,
-0.0336458757519722,
-0.028406891971826553,
-0.0300159715116024,
-0.011688189581036568,
-0.04491964727640152,
-0.01567750982940197,
0.047619566321372986,
-0.026724789291620255,
-0.016156069934368134,
-0.004931915085762739,
0.011962587013840675,
0.03666524961590767,
0.012752247974276543,
0.04582302272319794,
-0.03219105675816536,
-0.009472676552832127,
-0.04233905300498009,
0.02885926514863968,
0.032140202820301056,
0.03318708389997482,
0.043280620127916336,
-0.032991550862789154,
-0.012145421467721462,
0.024001775309443474,
0.022650741040706635,
0.0029544425196945667,
-0.025090772658586502,
0.04042220115661621,
-0.008780562318861485,
-0.006437464151531458,
0.035080667585134506,
-0.011853479780256748,
0.01676671952009201,
0.01663989946246147,
0.004686295986175537,
-0.010897301137447357,
0.01973632536828518,
0.023914974182844162,
0.03145349398255348,
0.008853460662066936,
0.008235959336161613,
0.015349725261330605,
-0.03296278789639473,
0.020049970597028732,
0.09402105212211609,
0.034555695950984955,
-0.0002515680098440498,
-0.028300072997808456,
-0.004529654514044523,
-0.026672014966607094,
0.0008175340481102467,
-0.019882844761013985,
-0.02111591212451458,
-0.014056363143026829,
-0.01994932070374489,
0.027488192543387413,
0.0012533518020063639,
0.02607901208102703,
-0.025996387004852295,
0.06598850339651108,
0.04381692782044411,
0.02537534385919571,
-0.0336100272834301,
0.029584616422653198,
-0.04598415270447731,
-0.04285071790218353,
0.0201562512665987,
-0.010601235553622246,
-0.004175430629402399,
-0.012968521565198898,
0.03017512336373329,
0.019605595618486404,
-0.032986726611852646,
-0.0007925578975118697,
-0.013890971429646015,
0.030449388548731804,
-0.017017675563693047,
-0.11944640427827835,
-0.048703648149967194,
0.05575806647539139,
0.019276948645710945,
-0.05614776909351349,
-0.08702100813388824,
0.028892626985907555,
0.007538928184658289,
0.05633459985256195,
0.03299558907747269,
0.0014059843961149454,
-0.0029360014013946056,
0.025943387299776077,
0.03886289894580841,
0.030610812827944756,
-0.0067490823566913605,
0.05313502997159958,
-0.04770229011774063,
0.015458057634532452,
-0.06138657405972481,
-0.023187994956970215,
0.01691563054919243,
-0.019135257229208946,
-0.032399192452430725,
0.036685917526483536,
-0.04298161715269089,
0.011041018180549145,
0.018070882186293602,
0.03361069783568382,
-0.028162149712443352,
0.08522646129131317,
0.00710282102227211,
-0.04705182835459709,
0.05550571158528328,
0.018231453374028206,
0.040897417813539505,
0.02490248717367649,
0.04849647358059883,
0.02328936755657196,
-0.010388419963419437,
-0.04502711072564125,
0.009896885603666306,
0.02667064778506756,
0.017716920003294945,
-0.03552231937646866,
-0.058641403913497925,
0.001341436873190105,
0.02036905102431774,
-0.014292261563241482,
0.05433567613363266,
-0.00400964030995965,
-0.0029905366245657206,
0.008615080267190933,
-0.0557197704911232,
-0.02349032089114189,
-0.06508399546146393,
0.018382102251052856,
-0.008833565749228,
-0.035193536430597305,
0.017005858942866325,
0.01976357027888298,
0.020521361380815506,
-0.03755127638578415,
0.009942542761564255,
-0.04501774162054062,
0.040377430617809296,
-0.02537013404071331,
-0.018065543845295906,
0.021407263353466988,
0.022127656266093254,
0.021165214478969574,
0.012675420381128788,
0.03466982766985893,
0.003944232128560543,
-0.027085591107606888,
0.008833006024360657,
-0.01644587703049183,
-0.00546758808195591,
-0.034289248287677765,
-0.024789897724986076,
-0.0013092391891404986,
-0.015975074842572212,
0.000094752867880743,
0.06790339201688766,
0.001967016141861677,
0.09165449440479279,
0.04029681161046028,
-0.02177371457219124,
0.003149428404867649,
0.05052340030670166,
0.020925385877490044,
0.009019657969474792,
0.0061625102534890175,
-0.039631541818380356,
-0.01965203322470188,
-0.011214644648134708,
-0.0032764747738838196,
0.03339032828807831,
-0.01729079708456993,
0.023275939747691154,
0.021232083439826965,
0.049112677574157715,
0.0027545178309082985,
0.03708462417125702,
0.01813059113919735,
-0.027095140889286995,
-0.0072899735532701015,
0.015967262908816338,
-0.006879161577671766,
0.002858981490135193,
0.0829649493098259,
0.051274508237838745,
0.022684458643198013,
-0.027438605204224586,
-0.04089472442865372,
0.029363900423049927,
-0.0188923217356205,
0.02004941552877426,
0.017591645941138268,
-0.01715206168591976,
0.02218502387404442,
-0.037060245871543884,
0.020967282354831696,
0.011536596342921257,
-0.012557178735733032,
0.01559421606361866,
-0.04511105641722679,
-0.011430174112319946,
0.04247289523482323,
-0.003123620292171836,
-0.006470962893217802,
-0.004672493785619736,
0.026336723938584328,
-0.023455265909433365,
0.030037544667720795,
-0.042494505643844604,
-0.03305888921022415,
-0.04935365915298462,
-0.03664776310324669,
0.007262338884174824,
0.03200148046016693,
0.025262759998440742,
-0.008563367649912834,
-0.05807916447520256,
-0.01827605441212654,
-0.0357520617544651,
-0.02207038924098015,
-0.006521247327327728,
-0.04362872615456581,
0.03838910534977913,
0.003298096125945449,
-0.003980662673711777,
0.05964595079421997,
-0.013713136315345764,
0.029276708140969276,
0.01575404964387417,
-0.021084072068333626,
-0.02468007057905197,
-0.017215263098478317,
-0.03173072636127472,
-0.030866220593452454,
0.013123624958097935,
0.019431812688708305,
0.07215436547994614,
-0.02631981484591961,
-0.031948789954185486,
0.015713809058070183,
-0.0540461428463459,
-0.019504155963659286,
-0.01968942955136299,
0.005674084182828665,
0.007156745996326208,
-0.0076375436037778854,
-0.012355760671198368,
-0.0036832126788794994,
-0.06708010286092758,
-0.025975685566663742,
-0.018862422555685043,
-0.025992074981331825,
0.014589579775929451,
0.012400678358972073,
0.06996463984251022,
0.03287579119205475,
-0.024174151942133904,
0.09429800510406494,
0.02005794085562229,
-0.0017904499545693398,
-0.02873588353395462,
0.017311515286564827,
-0.0041894386522471905,
-0.007067112252116203,
0.03666938096284866,
0.048320915549993515,
-0.012485574930906296,
0.016699787229299545,
0.04082513228058815,
0.012657782062888145,
0.029357675462961197,
0.01052511390298605,
-0.0026824220549315214,
-0.0046448176726698875,
0.008904775604605675,
-0.00815601833164692,
0.01926005445420742,
0.009741762652993202,
-0.01414482295513153,
-0.00036167443613521755,
0.052225444465875626,
0.05855782330036163,
-0.01765291579067707,
-0.055602580308914185,
0.04033668711781502,
-0.02908211387693882,
-0.010605596005916595,
-0.006201854906976223,
0.02154392935335636,
-0.02664034068584442,
0.0036725085228681564,
0.012155682779848576,
0.048952359706163406,
0.050508640706539154,
-0.004344682674854994,
-0.01660878024995327,
0.04337058961391449,
0.043595291674137115,
-0.04166951775550842,
-0.015867168083786964,
0.011934627778828144,
-0.022872092202305794,
0.060224924236536026,
-0.03645896539092064,
-0.01822531782090664,
0.05480814725160599,
0.011264491826295853,
0.05487893894314766,
-0.02402893826365471,
-0.04505665972828865,
0.0034575392492115498,
-0.06795234233140945,
0.0003806785971391946,
0.021012816578149796,
0.029655572026968002,
-0.022389693185687065,
0.032377272844314575,
0.025089234113693237,
0.041517820209264755,
0.015312597155570984,
-0.020821208134293556,
-0.08713246881961823,
0.0593847781419754,
-0.07587208598852158,
-0.04077921435236931,
-0.004687729757279158,
0.007236186880618334,
-0.006739992182701826,
-0.026735560968518257,
-0.029220029711723328,
-0.02007843740284443,
-0.01764523983001709,
-0.043342314660549164,
0.005329911131411791,
-0.03994474932551384,
-0.013405686244368553,
-0.012011067941784859,
0.01636980101466179,
0.009778833948075771,
-0.010018371045589447,
0.024867190048098564,
0.04559588059782982,
-0.031380876898765564,
-0.004484936129301786,
-0.01734776236116886,
0.0006524858181364834,
0.015702800825238228,
0.00016510706336703151,
0.039068929851055145,
0.0162965040653944,
-0.017752697691321373,
-0.007114560343325138,
0.018760064616799355,
0.053022511303424835,
0.020079724490642548,
-0.03576188161969185,
-0.032536011189222336,
-0.04087764769792557,
-0.00665902066975832,
0.011172978207468987,
0.060065947473049164,
-0.003452189499512315,
-0.02178131975233555,
0.012191373854875565,
0.010041800327599049,
-0.006820250302553177,
0.05836512893438339,
0.016247635707259178,
0.023173876106739044,
-0.015113714151084423,
-0.043894171714782715,
-0.04098375141620636,
-0.049305129796266556,
0.011008781380951405,
0.01452853437513113,
-0.008543712086975574,
-0.04773645102977753,
-0.005686520598828793,
0.025220343843102455,
-0.005858733784407377,
0.016847282648086548,
-0.018156060948967934,
-0.013760660775005817,
0.04235197603702545,
-0.005810359492897987,
-0.01817477121949196,
-0.01187603734433651,
0.015070964582264423,
0.03577151149511337,
-0.019791649654507637,
-0.021376533433794975,
-0.08047745376825333,
-0.04039957746863365,
0.023418640717864037,
0.022548386827111244,
-0.05763869360089302,
0.011604933999478817,
-0.047991275787353516,
-0.04213706776499748,
0.05253690108656883,
-0.01645541563630104,
0.03365878388285637,
-0.01806216686964035,
0.004615976009517908,
-0.02326606959104538,
-0.004302781540900469,
0.015948273241519928,
0.04636332020163536,
0.009057092480361462,
0.0006416058749891818,
0.006107643712311983,
-0.006398598197847605,
-0.008244219236075878,
0.005072226747870445,
0.048287924379110336,
0.015026952140033245,
-0.00003110676334472373,
0.018286775797605515,
-0.0017915141070261598,
0.005245283246040344,
-0.02382699027657509,
-0.08256295323371887,
-0.018641337752342224,
-0.01902284286916256,
-0.005160974338650703,
-0.01768101379275322,
-0.037479549646377563,
-0.06732604652643204,
-0.008940012194216251,
0.011854936368763447,
0.01745579019188881,
0.013051366433501244,
-0.038949690759181976,
0.021320890635252,
0.015907414257526398,
-0.002875463804230094,
-0.0003759930550586432,
0.020088491961359978,
-0.010582339949905872,
-0.05436854064464569,
-0.014863583259284496,
0.026042858138680458,
-0.04899291694164276,
-0.03106875903904438,
-0.02715614065527916,
0.01100105419754982,
-0.02204914391040802,
0.08966150879859924,
0.012649394571781158,
0.027998948469758034,
-0.00402164226397872,
-0.052554432302713394,
-0.029380515217781067,
0.05268267169594765,
0.028065312653779984,
-0.006273538805544376,
0.002933705458417535,
0.013673086650669575,
0.031052637845277786,
-0.009321818128228188,
0.00918515957891941,
0.008097313344478607,
0.007084275130182505,
0.018622059375047684,
-0.02079407125711441,
0.020128576084971428,
-0.029527563601732254,
-0.0281980037689209,
0.023762479424476624,
-0.02797929011285305,
0.04022735357284546,
-0.019470829516649246,
-0.026395374909043312,
0.03078712895512581,
-0.03939318656921387,
-0.03366798162460327,
-0.004319438710808754,
-0.02748531848192215,
0.06297348439693451,
-0.07936815917491913,
0.033834196627140045,
0.027028318494558334,
-0.0014505434082821012,
-0.0853651687502861,
-0.034916531294584274,
0.02339830994606018,
0.0005698077147826552,
0.01725527085363865,
-0.01209670677781105,
0.012471930123865604,
-0.025021573528647423,
-0.025921059772372246,
0.0027411924675107002,
0.0339161641895771,
-0.01856163516640663,
-0.009756063111126423,
0.002741739619523287,
-0.02081277407705784,
0.038350820541381836,
0.0034278053790330887,
-0.018226075917482376,
-0.012821834534406662,
-0.0036363964900374413,
-0.009878148324787617,
-0.011311383917927742,
0.08021415770053864,
-0.014474750496447086,
-0.04337940365076065,
0.017072705551981926,
-0.007948050275444984,
0.02495737187564373,
-0.07042590528726578,
0.0014568299520760775,
0.03867877647280693,
0.015521286055445671,
0.028604576364159584,
-0.013257800601422787,
0.02334948629140854,
0.029838532209396362,
0.039579179137945175,
-0.0003582895442377776,
-0.0374806746840477,
-0.029080482199788094,
-0.06339570134878159,
-0.005154172424226999,
0.0033948752097785473,
-0.006734844297170639,
-0.03262021392583847,
0.0498516820371151,
-0.012672564014792442,
-0.024099308997392654,
0.016951272264122963,
0.0005713318823836744,
-0.0032098335213959217,
0.007503615692257881,
0.0021132295951247215,
0.019229957833886147,
-0.0073655168525874615,
-0.0011044986313208938,
-0.0280431117862463,
-0.010618766769766808,
-0.008558090776205063,
0.05072181671857834,
0.01958298496901989,
0.053292252123355865,
-0.0010115252807736397,
-0.021218514069914818,
0.02566394954919815,
-0.0008364120731130242,
-0.028902173042297363,
0.0037388193886727095,
-0.009950375184416771,
0.02483043074607849,
-0.013145302422344685,
0.009908624924719334,
0.03189424052834511,
0.06078682839870453,
-0.018558956682682037,
0.010480308905243874,
0.0650971531867981,
0.031283531337976456,
-0.0007654746295884252,
0.05539056658744812,
-0.04134434834122658,
0.05118364840745926,
0.012997820973396301,
0.045778147876262665,
-0.024139150977134705,
0.017010770738124847,
0.012338650412857533,
0.021783435717225075,
-0.004503352101892233,
-0.04311539977788925,
-0.01777116023004055,
-0.05354785919189453,
0.04948187246918678,
0.04648067429661751,
0.044096220284700394,
0.0048324172385036945,
0.02660401724278927,
0.0251055546104908,
0.03144129365682602,
0.01084599457681179,
-0.00554546806961298,
-0.0244558434933424,
-0.0486452654004097,
-0.012832929380238056,
-0.05703015998005867,
0.008836589753627777,
-0.037607867270708084,
-0.022714346647262573,
0.006765089929103851,
-0.017487743869423866,
-0.0019157822243869305,
-0.005974140018224716,
-0.00966874323785305,
-0.018867503851652145,
0.07132194936275482,
0.021138016134500504,
-0.012880325317382812,
0.010475032031536102,
0.01580834574997425,
0.09553565084934235,
-0.008858895860612392,
0.02123379334807396,
-0.06325564533472061,
0.047393519431352615,
0.020445354282855988,
0.01826346665620804,
-0.05167228356003761,
0.0013742864830419421,
0.009404235519468784,
0.025421883910894394,
-0.001055687083862722,
0.03021312691271305,
-0.008377805352210999,
0.0005730889388360083,
0.07261184602975845,
0.011676602065563202,
-0.0017293364508077502,
-0.002478586742654443,
0.027717605233192444,
-0.0037432489916682243,
0.03540501371026039,
-0.05065121874213219,
0.035630058497190475,
-0.03955221176147461,
-0.008681719191372395,
-0.013080584816634655,
-0.04211999848484993,
0.0001752876560203731,
-0.01449405774474144,
-0.056306272745132446,
0.022384772077202797,
0.018698809668421745,
-0.04149645194411278,
-0.07732067257165909,
0.04826124757528305,
0.005436390172690153,
0.00838608667254448,
0.009230437688529491,
0.006116898264735937,
-0.006465672980993986,
0.02359493263065815,
-0.012230019085109234,
0.0013623980339616537,
-0.0387183278799057,
0.00612275255843997,
-0.015263766050338745,
0.02955472469329834,
-0.015207414515316486,
0.007172422483563423,
0.030322246253490448,
-0.014924971386790276,
-0.025453750044107437,
-0.033701393753290176,
-0.005116358865052462,
-0.019179459661245346,
0.02715832181274891,
-0.029887711629271507,
-0.0406419076025486,
-0.0034444292541593313,
0.018726717680692673,
-0.034016989171504974,
0.02680005133152008,
-0.04180574789643288,
-0.003515420248731971,
0.027233606204390526,
0.004356625955551863,
-0.012453576549887657,
-0.024042576551437378,
-0.026076652109622955,
0.029690656810998917,
0.00016583327669650316,
-0.037614524364471436,
-0.03944051265716553,
0.051786862313747406,
0.06033961847424507,
0.005570352543145418,
0.023856598883867264,
-0.03317954018712044,
-0.016043515875935555,
-0.004173602908849716,
0.03856445476412773,
0.008830488659441471,
-0.015404721722006798,
0.010060396045446396,
-0.0238605048507452,
0.02689986675977707,
0.02789127640426159,
-0.034105341881513596,
0.018469825387001038,
-0.02955411560833454,
-0.010115302167832851,
0.015510128811001778,
-0.04224184900522232,
0.019448278471827507,
0.03698708862066269,
-0.01938357762992382,
-0.0093174297362566,
-0.016190452501177788,
0.014726337045431137,
0.023572655394673347,
0.017240529879927635,
-0.013404025696218014,
0.040752265602350235,
-0.022543447092175484,
-0.006824618671089411,
0.002594307530671358,
-0.041162822395563126,
0.004078553058207035,
0.02123807929456234,
-0.013641705736517906,
-0.07355048507452011,
-0.06744242459535599,
-0.0257254708558321,
0.008285981602966785,
-0.004215099383145571,
0.032134298235177994,
-0.024167247116565704,
0.03867458924651146,
-0.022578198462724686,
0.009579842910170555,
-0.04425817355513573,
0.003517954144626856,
-0.07169150561094284,
-0.016556428745388985,
0.013112860731780529,
-0.03549834340810776,
-0.018813004717230797,
0.023481396958231926,
-0.02014579065144062,
-0.025563614442944527,
0.0218045674264431,
0.04021036624908447,
0.0026517075020819902,
-0.008462723344564438,
0.0449259988963604,
-0.005644490011036396,
0.04886588454246521,
-0.007810824550688267,
-0.042950794100761414,
0.04260654374957085,
-0.049272872507572174,
-0.029059141874313354,
0.06409914046525955,
-0.03925521671772003,
-0.006091248709708452,
0.02036687731742859,
-0.027746805921196938,
0.012167112901806831,
0.0674334391951561,
-0.03688247129321098,
-0.0018095743143931031,
-0.01680191606283188,
0.011347169987857342,
-0.01178580243140459,
-0.011778488755226135,
-0.01854608580470085,
-0.050903160125017166,
-0.00647036312147975,
0.041282519698143005,
0.03031303733587265,
-0.015245592221617699,
-0.007968857884407043,
-0.004559246823191643,
-0.01481535378843546,
0.02364642359316349,
0.02064412087202072,
0.016211658716201782,
0.050193674862384796,
0.04607989266514778,
-0.04165255278348923,
0.05672057345509529,
-0.0027550815138965845,
0.018347665667533875,
-0.11029646545648575,
0.010104960761964321,
-0.01717694103717804,
-0.00014472527254838496,
0.014219935052096844,
-0.01741628535091877,
-0.014823962934315205,
-0.007605460938066244,
-0.053635865449905396,
-0.007878248579800129,
-0.05504127964377403,
-0.020289555191993713,
0.018253138288855553,
-0.043987102806568146,
0.009240713901817799,
0.030249254778027534,
0.029200822114944458,
0.018327530473470688,
0.011868171393871307,
-0.009300234727561474,
-0.0007978075882419944,
-0.030500883236527443,
-0.02432246319949627,
0.02634640783071518,
0.0022038379684090614,
-0.012934228405356407,
0.02443830482661724,
-0.0036235167644917965,
0.0012304481351748109,
0.039999473839998245,
-0.009562553837895393,
0.011263885535299778,
-0.024899788200855255,
-0.0033892979845404625,
-0.03365195170044899,
0.026062963530421257,
-0.02679230459034443,
-0.003028798382729292,
-0.01690475083887577,
0.036638494580984116,
0.008323312737047672,
0.04569366201758385,
-0.007261190097779036,
-0.021260851994156837,
0.014959312044084072,
-0.040918245911598206,
-0.015871206298470497,
-0.009671659208834171,
-0.016701528802514076,
0.03424394130706787,
0.015466224402189255,
0.012279077433049679,
0.010352974757552147,
-0.03839941322803497,
-0.016391778364777565,
-0.015918325632810593,
-0.008443980477750301,
0.003167571732774377,
0.017867062240839005,
-0.007637532893568277,
0.016589971259236336,
0.021921562030911446,
-0.018552063032984734,
-0.014385592192411423,
0.04095316678285599,
-0.0065214429050683975,
-0.04007568210363388,
-0.010806724429130554,
0.0038442006334662437,
-0.007165448274463415,
-0.0030757542699575424,
-0.04416347295045853,
-0.04218057170510292,
0.03172340244054794,
0.020503411069512367,
0.023200808092951775,
-0.05259109288454056,
-0.007716026622802019,
-0.01630488410592079,
-0.06088494881987572,
0.05244274064898491,
-0.018232742324471474,
-0.027519572526216507,
-0.04345912113785744,
0.01497318223118782,
-0.017983319237828255,
-0.012437202036380768,
0.04182310029864311,
0.00722108781337738,
-0.012618930079042912,
0.028470590710639954,
-0.0035365712828934193,
-0.00401622848585248,
-0.015457226894795895,
0.028518041595816612,
-0.009016414172947407,
-0.04210272431373596,
0.03356555104255676,
0.003732080804184079,
-0.022941868752241135,
-0.005497627425938845,
-0.005523091182112694,
-0.011045574210584164,
0.03734654188156128,
-0.006953530479222536,
-0.012978042475879192,
0.06234334409236908,
0.024219853803515434,
0.01787099614739418,
0.07701509445905685,
0.02457265369594097,
0.01552579551935196,
0.019663264974951744,
-0.03738068789243698,
-0.07579801976680756,
0.05343262106180191,
-0.039687108248472214,
0.02788751758635044,
-0.01890949159860611,
-0.003011577995494008,
0.02957530878484249,
-0.035196974873542786,
0.015458309091627598,
0.03492918610572815,
-0.007850231602787971,
-0.0007717497064732015,
0.03602759167551994,
0.021354133263230324,
0.02492021769285202,
-0.027421563863754272,
0.017957592383027077,
0.054015375673770905,
0.018951978534460068,
0.009296437725424767,
0.03162809833884239,
0.02742733247578144,
0.015372549183666706,
-0.017743784934282303,
0.04969030246138573,
0.00922453124076128,
0.03020397759974003,
0.0151506457477808,
0.03102809190750122,
-0.013958098366856575,
-0.05199701711535454,
-0.005957246292382479,
-0.0205933079123497,
-0.006597640458494425,
0.039805565029382706,
-0.0180888120085001,
0.06114776059985161,
-0.006816376466304064,
-0.002545970259234309,
-0.02342769131064415,
0.015540605410933495,
0.0018396651139482856,
-0.019982822239398956,
0.015541881322860718,
0.03710554540157318,
0.0022778890561312437,
0.024636393412947655,
-0.025323517620563507,
-0.029219770804047585,
0.014825720340013504,
0.0042028967291116714,
0.024959487840533257,
0.008560865186154842,
0.004188705235719681,
-0.0015231892466545105,
0.00923860166221857,
-0.04963437095284462,
-0.04652596265077591,
0.025411497801542282,
0.01973082683980465,
0.04556867107748985,
-0.0006759524694643915,
-0.012621373869478703,
-0.0007758112624287605,
0.05442655831575394,
-0.07893843948841095,
-0.06882548332214355,
-0.03878669813275337,
0.050533607602119446,
-0.00005811530718347058,
-0.0029740750323981047
] |
<p>I have watched Walter Lewin's lecture(<a href="http://www.youtube.com/watch?v=6QVbE_tU2sA" rel="nofollow">http://www.youtube.com/watch?v=6QVbE_tU2sA</a>) which was about the rainbows. But there is still a question bothering me. </p>
<p>I understood the first part of the lecture which he talked about axial symmetry that holds in the drop of water because the light beam is coming from a preferred direction. But I cannot understand that why he relates the semicircular shape of the rainbow to axial symmetry.<br>
To make my question clearer, I say an example. Considering the red part of the rainbow for instance, we found that this color of rainbow is seen if we look about 42 degrees above the reference line(from the sun). But I think that for looking at other red parts of the bow, one should rotate his head and other red parts have different angles than 42.I know that all red parts should be at 42 degrees but I am confused and cannot understand it. </p>
<p>I have another problem and that is why we emphasize on $\varphi_{max}$. For example,at the angle of 40 degrees, we have both blue and red color but they always use 40 degrees just for blue but we can have a mixture of red and blue.
I will be thankful if you can help me with these. </p>
| 10,726 |
[
-0.02630232833325863,
-0.026525428518652916,
0.010920250788331032,
0.009573416784405708,
0.04982513189315796,
0.003968721721321344,
-0.013693729415535927,
0.0013418212765827775,
-0.030705252662301064,
-0.008356024511158466,
-0.005487070884555578,
0.030543966218829155,
0.029032796621322632,
0.04468028247356415,
0.05400355905294418,
0.00456234160810709,
0.010366939939558506,
0.013332027941942215,
-0.013106826692819595,
-0.022258693352341652,
0.014741875231266022,
0.0011993866646662354,
-0.003753954079002142,
-0.011005296371877193,
-0.031089194118976593,
0.0059308819472789764,
0.04846268147230148,
0.010377490893006325,
0.012900300323963165,
0.03628892824053764,
-0.002688952023163438,
-0.015783485025167465,
0.012667573988437653,
0.010607581585645676,
0.046011507511138916,
-0.02016976661980152,
0.00045840724487788975,
-0.008854691870510578,
-0.027812711894512177,
-0.012860915623605251,
0.010348501615226269,
-0.003889309475198388,
-0.04474993050098419,
0.08009125292301178,
-0.03369154408574104,
0.005371979903429747,
-0.048383407294750214,
-0.01823490299284458,
0.03954445570707321,
-0.03088179975748062,
0.08802327513694763,
0.00895353127270937,
-0.011690767481923103,
0.007877517491579056,
0.0535353347659111,
0.008773691952228546,
0.026559900492429733,
0.078162282705307,
-0.011888681910932064,
-0.026097368448972702,
0.004560321103781462,
-0.024418747052550316,
-0.016115374863147736,
0.01416456326842308,
-0.012943071313202381,
-0.005134829320013523,
0.032206933945417404,
0.014234572649002075,
0.012881631031632423,
0.006328458432108164,
0.0025790471117943525,
-0.010627757757902145,
0.02499622106552124,
0.0017885493580251932,
0.0032812526915222406,
-0.02175191603600979,
0.021699683740735054,
-0.005148690193891525,
0.012284332886338234,
-0.0008395614568144083,
-0.0022144063841551542,
0.00681710010394454,
-0.020571133121848106,
0.026919931173324585,
0.01294645294547081,
-0.04909110814332962,
0.0669073686003685,
-0.004749725107103586,
0.005656207911670208,
0.006703230086714029,
0.029047492891550064,
-0.0015362421981990337,
0.017941489815711975,
0.0007083478267304599,
-0.04943064972758293,
0.036358289420604706,
-0.016831815242767334,
0.04024357721209526,
-0.017462018877267838,
-0.017143499106168747,
-0.006530181039124727,
-0.03378300741314888,
0.016267895698547363,
0.05353781580924988,
0.0035784950014203787,
-0.015320454724133015,
0.004238530062139034,
0.019411593675613403,
-0.0382390171289444,
-0.013092859648168087,
-0.01830197498202324,
0.012939093634486198,
0.011368442326784134,
-0.011348258703947067,
0.0017717519076541066,
0.014900797046720982,
0.027075033634901047,
-0.0006932094693183899,
0.05808522552251816,
0.05809670686721802,
0.038680560886859894,
-0.012580933049321175,
0.0339643731713295,
-0.02434404008090496,
-0.044898077845573425,
0.037420935928821564,
0.01475997269153595,
0.023052223026752472,
-0.03233969956636429,
0.024962902069091797,
0.014939582906663418,
0.015416018664836884,
0.0075837308540940285,
0.013553788885474205,
-0.003319195471704006,
0.002256081672385335,
-0.11133743822574615,
-0.04855864867568016,
0.04987442493438721,
0.04644913598895073,
0.003950829617679119,
-0.07631832361221313,
0.031644485890865326,
0.04813137277960777,
0.05558749660849571,
-0.04479159787297249,
0.0031016310676932335,
0.006819484289735556,
0.04094512760639191,
-0.0036766810808330774,
-0.04112986847758293,
-0.010596432723104954,
-0.02662190981209278,
-0.04023171216249466,
-0.021442998200654984,
-0.06727097928524017,
-0.002439522184431553,
0.030217744410037994,
0.04840730130672455,
-0.053405776619911194,
0.07252075523138046,
-0.03299914672970772,
-0.018896277993917465,
0.03734917193651199,
-0.0037621427327394485,
0.006148748565465212,
0.08524423092603683,
0.025524629279971123,
-0.0075813471339643,
0.02179972641170025,
0.004503575619310141,
0.04126134142279625,
-0.027433782815933228,
0.019302591681480408,
0.06367349624633789,
-0.04046314209699631,
-0.010303245857357979,
-0.015079043805599213,
0.00726274773478508,
0.004402427468448877,
-0.06371705234050751,
-0.05582801625132561,
-0.009437144733965397,
0.018332231789827347,
0.008164571598172188,
0.0677291601896286,
-0.0229926910251379,
-0.014562850818037987,
0.004952171351760626,
-0.06576373428106308,
0.005450218915939331,
-0.03215324133634567,
-0.003482805099338293,
-0.010241623967885971,
-0.03806966915726662,
0.03506278991699219,
0.02269306592643261,
-0.00030010976479388773,
-0.01209332887083292,
-0.0031642683316022158,
-0.029587918892502785,
0.04696161672472954,
0.04376119747757912,
0.0008076410740613937,
0.008020437322556973,
0.04998426139354706,
0.0019356167176738381,
0.03426419943571091,
0.0054534864611923695,
-0.03310822695493698,
-0.041405268013477325,
0.017508268356323242,
-0.032207366079092026,
0.017714668065309525,
0.03646720200777054,
0.011241961270570755,
-0.004084798041731119,
0.023484287783503532,
-0.013940205797553062,
0.015352579765021801,
-0.02156563103199005,
0.05709528923034668,
0.041412293910980225,
-0.023263605311512947,
0.02044224552810192,
0.027649428695440292,
0.02086060121655464,
0.00013356133422348648,
-0.008327174931764603,
0.014534595422446728,
-0.042559847235679626,
0.03977302461862564,
0.0386175811290741,
-0.015760408714413643,
-0.025356657803058624,
0.009505474008619785,
0.01039937138557434,
0.05695272982120514,
0.004456931259483099,
0.003450038842856884,
-0.01469816081225872,
-0.038935743272304535,
0.0013834916753694415,
0.008711329661309719,
0.020357303321361542,
-0.005220058374106884,
0.044266026467084885,
0.0007869963301345706,
0.029788462445139885,
-0.04266436770558357,
-0.05299118533730507,
0.03450104594230652,
-0.025897178798913956,
0.01736830174922943,
0.005819504614919424,
0.005038028117269278,
0.05672149360179901,
-0.06502319127321243,
0.002238467801362276,
0.023143500089645386,
-0.015171750448644161,
-0.01251797191798687,
-0.04733236879110336,
-0.0070820152759552,
-0.023774322122335434,
0.01879516988992691,
-0.006477922201156616,
-0.009641551412642002,
0.01645134575664997,
-0.04447389766573906,
0.005279547534883022,
-0.02616480179131031,
-0.023606551811099052,
-0.019069116562604904,
-0.018389517441391945,
0.04146984592080116,
0.030200885608792305,
0.013940883800387383,
-0.02666335739195347,
-0.031347934156656265,
-0.008698631078004837,
-0.0007447557873092592,
-0.025408778339624405,
0.0047544208355247974,
-0.059135738760232925,
0.026698322966694832,
-0.016537269577383995,
0.0060402872040867805,
0.004230227321386337,
-0.013052074238657951,
-0.004021053202450275,
-0.013936611823737621,
0.00790756568312645,
-0.03680049255490303,
-0.06766919046640396,
-0.027156710624694824,
0.03415752947330475,
-0.01839260198175907,
-0.059934861958026886,
0.03241850808262825,
-0.019711114466190338,
-0.005609352141618729,
0.026989126577973366,
-0.056768111884593964,
-0.033019062131643295,
0.010928677394986153,
0.036543067544698715,
-0.008377235382795334,
0.006792743690311909,
-0.002798347966745496,
-0.003336105262860656,
-0.009765150025486946,
-0.04851093143224716,
-0.03112543188035488,
-0.02140876278281212,
0.021389439702033997,
0.02875763550400734,
0.05129474774003029,
0.02620100975036621,
-0.007651748135685921,
0.06080898642539978,
0.018673567101359367,
-0.0479893684387207,
-0.0543607622385025,
0.03884328901767731,
-0.05997896194458008,
-0.022174151614308357,
-0.006973695009946823,
0.05485164374113083,
-0.02895386330783367,
0.03372088819742203,
-0.0011776196770370007,
0.02898924984037876,
0.03860461339354515,
0.00802790466696024,
-0.027084020897746086,
0.022731030359864235,
-0.014245480298995972,
0.020573528483510017,
0.04689374193549156,
0.022878147661685944,
-0.04355378821492195,
-0.03444511815905571,
0.003235758049413562,
0.049417488276958466,
0.044262100011110306,
-0.04970113933086395,
0.07565075159072876,
-0.026771651580929756,
-0.0005598572897724807,
-0.003807725617662072,
0.022053243592381477,
-0.00046944242785684764,
0.012617678381502628,
0.012281081639230251,
0.011189275421202183,
0.06800686568021774,
-0.02150985784828663,
-0.01341440249234438,
0.059581756591796875,
0.05016383156180382,
-0.016140960156917572,
-0.006555288098752499,
0.0008588540949858725,
0.002803394105285406,
0.08626681566238403,
-0.013951001688838005,
-0.02187933959066868,
0.04071993753314018,
0.054356954991817474,
0.001820166828110814,
0.008431999012827873,
-0.05345558375120163,
0.0057848053984344006,
-0.030749855563044548,
0.028876477852463722,
-0.02893579751253128,
0.027797816321253777,
0.007326261140406132,
0.05919531732797623,
0.02272389829158783,
0.03503769636154175,
-0.0016633538762107491,
-0.005540810059756041,
-0.0669616162776947,
0.005485864821821451,
-0.013213930651545525,
0.012755644507706165,
-0.007026776671409607,
-0.03552631661295891,
-0.000773733074311167,
-0.029361406341195107,
-0.03148797154426575,
-0.013920702040195465,
-0.008014323189854622,
-0.010143231600522995,
0.01824161969125271,
-0.041288457810878754,
-0.033048808574676514,
0.002806061413139105,
0.06034843251109123,
0.03061002306640148,
-0.06833881139755249,
0.05802195146679878,
0.05974666774272919,
-0.028996499255299568,
0.016705863177776337,
-0.029601188376545906,
0.0532849058508873,
-0.002419831929728389,
0.02647893689572811,
0.03209869563579559,
0.04646706581115723,
-0.0017481413669884205,
-0.008996518328785896,
0.024370422586798668,
0.0323859341442585,
-0.03091789223253727,
-0.026077305898070335,
-0.006879427004605532,
-0.019871411845088005,
-0.006212840788066387,
-0.04110109806060791,
0.040970124304294586,
0.004454429727047682,
-0.006880589760839939,
0.049955230206251144,
-0.004590206313878298,
-0.05907405912876129,
0.02181248366832733,
-0.002842864254489541,
0.0034817394334822893,
-0.014551432803273201,
-0.07108423858880997,
-0.010535500943660736,
-0.029348131269216537,
0.009125832468271255,
0.022068319842219353,
0.005842321552336216,
-0.032411281019449234,
-0.00018614187138155103,
0.05609821155667305,
-0.0024895668029785156,
0.010066214948892593,
0.0025480559561401606,
-0.039892878383398056,
-0.011323346756398678,
-0.02084735594689846,
0.011048585176467896,
-0.0063966722227633,
0.037356551736593246,
0.07453662902116776,
-0.019326483830809593,
0.014131561852991581,
-0.04511095583438873,
-0.028859050944447517,
0.012831121683120728,
0.01821143366396427,
-0.023714814335107803,
0.02820962853729725,
-0.08057375252246857,
-0.0403389111161232,
0.027153391391038895,
-0.006415918469429016,
0.028934961184859276,
-0.030284933745861053,
0.007779019419103861,
0.007617609109729528,
-0.012912877835333347,
-0.024356737732887268,
-0.013153876177966595,
0.002196471206843853,
0.015534844249486923,
-0.025970173999667168,
-0.003594106063246727,
0.01022884901612997,
0.001797755598090589,
0.046058520674705505,
0.014837008900940418,
0.01018218882381916,
0.011587100103497505,
0.02817494608461857,
0.027987273409962654,
0.007256628479808569,
-0.09071380645036697,
0.014348373748362064,
0.0559372715651989,
0.004496194422245026,
0.036334071308374405,
-0.016898885369300842,
-0.03385641798377037,
0.04958270117640495,
0.04169515147805214,
0.019299320876598358,
0.015188919380307198,
-0.033263515681028366,
0.02663605473935604,
0.034762896597385406,
-0.004271946847438812,
0.0319189615547657,
0.00444389320909977,
-0.021025028079748154,
-0.06153591722249985,
-0.011675279587507248,
0.043696943670511246,
0.01985105872154236,
-0.025330528616905212,
-0.031962037086486816,
0.0024625619407743216,
-0.019867870956659317,
0.03074214980006218,
-0.011703751981258392,
0.02606021799147129,
0.010889753699302673,
-0.03529615327715874,
0.017726825550198555,
-0.0037842767778784037,
0.027737930417060852,
-0.008971236646175385,
-0.02303781732916832,
0.04548167064785957,
0.016466790810227394,
-0.008951431140303612,
0.02638043463230133,
-0.03765957057476044,
-0.009265108965337276,
0.020833827555179596,
0.007402816787362099,
0.03505956009030342,
-0.02861137129366398,
-0.04289332032203674,
-0.004822182934731245,
-0.014438683167099953,
0.014698773622512817,
-0.0010554192122071981,
0.014677735045552254,
0.0720672532916069,
-0.04171709343791008,
-0.04741163179278374,
-0.008795523084700108,
-0.012271448038518429,
0.03552509844303131,
-0.036510974168777466,
0.001474094926379621,
0.02229706011712551,
0.007876342162489891,
-0.048679400235414505,
-0.028630543500185013,
-0.0005894339992664754,
0.028755178675055504,
-0.045805033296346664,
-0.017798492684960365,
0.015500420704483986,
-0.022926563397049904,
-0.016387540847063065,
0.0052032764069736,
0.016423789784312248,
-0.011390560306608677,
-0.03163078799843788,
-0.027382275089621544,
0.015087278559803963,
0.05505518615245819,
-0.033592578023672104,
-0.00466509722173214,
0.006577581167221069,
-0.022512294352054596,
-0.012181172147393227,
0.008806983008980751,
0.07210852950811386,
-0.0034142564982175827,
-0.025665592402219772,
-0.012745615094900131,
-0.016712479293346405,
0.023099301382899284,
-0.004103637766093016,
-0.0032682358287274837,
-0.00923706404864788,
0.017949623987078667,
-0.013214616104960442,
0.01814357005059719,
-0.00800974853336811,
-0.038443904370069504,
0.012568981386721134,
-0.026691047474741936,
0.0015200673369690776,
-0.0096915727481246,
-0.050786059349775314,
0.057103320956230164,
-0.024101736024022102,
0.015780432149767876,
0.0005357422633096576,
0.07318698614835739,
-0.05474444851279259,
-0.003485041670501232,
-0.002126936335116625,
0.004332860931754112,
-0.003459560452029109,
0.017610473558306694,
0.012877450324594975,
0.021425744518637657,
0.02373281680047512,
0.01545748021453619,
-0.036630623042583466,
0.0041630566120147705,
0.029097840189933777,
0.08227124065160751,
-0.022962184622883797,
0.08333130180835724,
0.004726187326014042,
0.016769247129559517,
-0.02140599861741066,
-0.0012076152488589287,
-0.02395860105752945,
-0.048400845378637314,
0.018344072625041008,
0.06325958669185638,
-0.07026591151952744,
-0.026811519637703896,
0.014790722168982029,
0.04136991873383522,
0.004958439152687788,
0.01913897693157196,
0.07548833638429642,
0.025815462693572044,
0.02071339823305607,
-0.015681670978665352,
-0.043448492884635925,
0.0027156532742083073,
-0.0244658924639225,
0.03221454843878746,
0.013618187047541142,
0.009462482295930386,
0.038395725190639496,
0.004014605190604925,
-0.01478018332272768,
-0.055452633649110794,
-0.01385582610964775,
-0.030151063576340675,
0.01235456857830286,
0.009588967077434063,
0.011528568342328072,
-0.03520061820745468,
-0.007149956654757261,
0.026597771793603897,
-0.0276090856641531,
0.02914871647953987,
-0.02542193792760372,
-0.057225313037633896,
-0.02708195522427559,
-0.05199117958545685,
-0.036295291036367416,
0.056969936937093735,
0.009854019619524479,
-0.006797280162572861,
-0.011236307211220264,
-0.029017917811870575,
-0.012040943838655949,
0.04385293647646904,
0.052921220660209656,
0.01475939154624939,
0.024937523528933525,
-0.012077059596776962,
0.04326913505792618,
0.011667282320559025,
0.003651623846963048,
0.12341668456792831,
0.038237228989601135,
-0.031851112842559814,
-0.03514760732650757,
0.015980813652276993,
-0.010181506164371967,
-0.0037414839025586843,
-0.04293128475546837,
0.04072932153940201,
-0.032752279192209244,
0.0473034493625164,
-0.02749641053378582,
0.03961177542805672,
0.030201556161046028,
-0.017362380400300026,
0.027920588850975037,
-0.056864168494939804,
-0.037814874202013016,
0.0012377414386719465,
0.004931904375553131,
-0.021255970001220703,
0.041591159999370575,
-0.07690967619419098,
0.012285551056265831,
-0.013007046654820442,
0.02576383762061596,
-0.023403078317642212,
-0.0483633428812027,
0.015209656208753586,
-0.014212122187018394,
-0.01196654886007309,
0.026665953919291496,
-0.0020941540133208036,
-0.036473847925662994,
-0.03521796315908432,
0.023721003904938698,
0.040712032467126846,
-0.04195602238178253,
0.025964651256799698,
0.005881637800484896,
0.0027569697704166174,
0.014669295400381088,
-0.010953742079436779,
0.052996598184108734,
-0.007479905616492033,
-0.017128344625234604,
-0.022934172302484512,
0.010707193985581398,
-0.017252685502171516,
-0.010945960879325867,
-0.044715479016304016,
-0.0006126298103481531,
-0.014669821597635746,
-0.09589777886867523,
-0.006041504442691803,
0.010687456466257572,
0.035223379731178284,
-0.009730272926390171,
-0.018041394650936127,
-0.007335243280977011,
0.005737374071031809,
0.029311981052160263,
0.01507666427642107,
-0.0037448948714882135,
0.02452271059155464,
-0.006241020746529102,
0.03969898447394371,
0.06030803546309471,
0.024425314739346504,
-0.031152592971920967,
-0.01792290061712265,
0.013717954978346825,
-0.030781090259552002,
0.0020759471226483583,
0.02800055406987667,
0.028719685971736908,
0.0033964768517762423,
0.01150423288345337,
-0.04358121380209923,
0.005500161554664373,
-0.026114465668797493,
-0.01564251072704792,
-0.018390392884612083,
-0.02836344577372074,
0.004586563445627689,
0.018529945984482765,
0.03765582665801048,
0.02680412493646145,
-0.03626351058483124,
-0.03199996054172516,
0.029473762959241867,
0.04620809480547905,
0.023337265476584435,
-0.0009593120194040239,
-0.0345289446413517,
0.03226197883486748,
-0.016056623309850693,
-0.003829894121736288,
0.008134556002914906,
0.03002741001546383,
0.03301166370511055,
0.02973164990544319,
-0.010673328302800655,
0.011684156022965908,
-0.007074542809277773,
-0.031432706862688065,
0.011864369735121727,
-0.06497745215892792,
0.0277890395373106,
0.010776815935969353,
-0.03444034233689308,
-0.0947084054350853,
0.022380998358130455,
-0.007842046208679676,
0.0043632639572024345,
0.021657411009073257,
-0.029837200418114662,
0.0011315849842503667,
0.010634960606694221,
0.0016591823659837246,
0.01648935116827488,
-0.025033915415406227,
-0.01743461564183235,
-0.009040539152920246,
0.023295480757951736,
-0.041288334876298904,
0.02132013626396656,
-0.056401919573545456,
0.0742647722363472,
-0.008223316632211208,
-0.02751106582581997,
0.04597735032439232,
0.004441284574568272,
0.003142317058518529,
0.0075565543957054615,
0.013184063136577606,
0.056884873658418655,
0.06022180616855621,
0.0162139143794775,
-0.05840140953660011,
0.03777190297842026,
-0.02887159213423729,
-0.01472704391926527,
0.030051659792661667,
-0.011641004122793674,
0.025584764778614044,
-0.0011666691862046719,
-0.02042512223124504,
0.009554021991789341,
0.03827289864420891,
-0.01739617995917797,
0.02509302832186222,
-0.02535962499678135,
-0.006834156345576048,
0.0423562154173851,
-0.016587866470217705,
0.04063817113637924,
-0.02340037189424038,
-0.02618139609694481,
0.035560138523578644,
0.025936424732208252,
-0.05126017704606056,
0.0013107439735904336,
-0.015271271578967571,
-0.023458007723093033,
0.01166379265487194,
0.005121325608342886,
0.011015104129910469,
0.0069604236632585526,
0.046173304319381714,
-0.05590642988681793,
0.08288037031888962,
-0.014432773925364017,
-0.0036419129464775324,
-0.07192929834127426,
0.0010151691967621446,
0.03597096726298332,
-0.007823043502867222,
0.008064009249210358,
-0.07866928726434708,
0.0023898500949144363,
0.030593613162636757,
-0.08144988119602203,
0.012388702481985092,
-0.01619245670735836,
-0.021134251728653908,
-0.01948961801826954,
-0.018485307693481445,
-0.055660758167505264,
0.06021353229880333,
0.014241266995668411,
0.04324733838438988,
0.034331414848566055,
-0.0007364295306615531,
-0.011326656676828861,
-0.025311438366770744,
-0.015550018288195133,
0.040546126663684845,
0.028105251491069794,
-0.004008325282484293,
0.04007319360971451,
0.002734622685238719,
-0.032978665083646774,
-0.004416837822645903,
-0.015124469064176083,
0.02881566993892193,
0.00851478986442089,
-0.002333484124392271,
0.0013119436334818602,
0.015253356657922268,
-0.00027132395189255476,
0.019823744893074036,
-0.03810470551252365,
0.009919706732034683,
0.006885430309921503,
-0.020778639242053032,
-0.009968656115233898,
-0.004675399977713823,
-0.004940205719321966,
-0.037776220589876175,
-0.08936452120542526,
0.027237607166171074,
-0.03751266375184059,
-0.021741833537817,
0.03887650743126869,
0.013738659210503101,
-0.03368759527802467,
-0.028006548061966896,
-0.0005076234810985625,
-0.016948403790593147,
0.013571033254265785,
-0.0031479529570788145,
0.0034122911747545004,
0.029420549049973488,
-0.011674558743834496,
-0.028131693601608276,
-0.05502692982554436,
0.017681855708360672,
-0.006070137955248356,
-0.03341169282793999,
-0.029862552881240845,
0.00948778074234724,
-0.010705459862947464,
-0.01364936213940382,
0.022731808945536613,
-0.008903564885258675,
-0.012888611294329166,
0.031024595722556114,
0.009447526186704636,
-0.005138464272022247,
-0.019969236105680466,
-0.015571638010442257,
-0.041156936436891556,
-0.06624902039766312,
0.052321646362543106,
-0.006306488532572985,
-0.014857434667646885,
-0.04282447695732117,
-0.02089955098927021,
-0.04402158036828041,
0.04557664319872856,
0.018094507977366447,
0.008227165788412094,
-0.012847778387367725,
0.01500813290476799,
0.004410298075526953,
0.011671408079564571,
-0.009505486115813255,
-0.012123288586735725,
-0.0018141067121177912,
-0.014825738966464996,
-0.017168084159493446,
-0.022147541865706444,
-0.004254440311342478,
0.011126313358545303,
-0.004488518461585045,
-0.0006141416961327195,
0.04940507188439369,
-0.012848436832427979,
-0.00838219840079546,
0.019830545410513878,
-0.015583706088364124,
-0.037429556250572205,
0.055933304131031036,
0.00028955613379366696,
-0.026606189087033272,
0.015190101228654385,
-0.03916965052485466,
-0.07887022942304611,
0.06351356208324432,
-0.021764416247606277,
-0.005734769161790609,
0.008320558816194534,
-0.024357574060559273,
0.04657763987779617,
-0.015039493329823017,
0.03541442006826401,
0.04375757649540901,
-0.03938594087958336,
-0.018104465678334236,
0.05482680723071098,
-0.007166814059019089,
0.020938022062182426,
-0.0021294995676726103,
0.0052420771680772305,
0.027354102581739426,
-0.038612525910139084,
0.03210167586803436,
-0.0033805668354034424,
0.04364682734012604,
0.04445040971040726,
0.0017259734449908137,
0.011946971528232098,
0.006626403424888849,
0.017695579677820206,
-0.0006601886125281453,
0.04044581577181816,
-0.018239229917526245,
-0.017544252797961235,
0.012600590474903584,
-0.008606442250311375,
-0.020325379446148872,
0.017310205847024918,
-0.024869192391633987,
0.07734141498804092,
-0.009861409664154053,
-0.006310973782092333,
-0.022201046347618103,
-0.02003253437578678,
-0.05943171679973602,
0.04142829775810242,
0.009215477854013443,
0.01681494526565075,
-0.038342975080013275,
-0.03640441223978996,
-0.018798954784870148,
-0.028694024309515953,
0.066841259598732,
0.009677707217633724,
0.018548764288425446,
0.014414554461836815,
-0.014387667179107666,
0.04223230481147766,
-0.0023251327220350504,
-0.006558566354215145,
-0.030699511989951134,
0.010164565406739712,
0.033213939517736435,
0.027181891724467278,
0.031508177518844604,
-0.013306036591529846,
-0.04328474774956703,
0.04883440211415291,
-0.08104979991912842,
-0.053258445113897324,
-0.015558384358882904,
-0.014961794018745422,
-0.021180476993322372,
-0.03895457088947296
] |
<p>What is meant by a local Lagrangian density? How will a
non-local Lagrangian look like and what is the problem that we do not
consider such Lagrangian densities?</p>
| 10,727 |
[
-0.03216221183538437,
0.015271932817995548,
0.027096886187791824,
-0.0023152038920670748,
0.028698531910777092,
0.03814651072025299,
-0.04264362156391144,
-0.026504600420594215,
0.021826239302754402,
-0.04317958280444145,
0.003050822066143155,
0.030612900853157043,
0.0436173751950264,
0.039110634475946426,
0.0033676503226161003,
0.010089511051774025,
-0.02879302203655243,
0.014557601884007454,
-0.020163027569651604,
-0.022566044703125954,
0.005772220902144909,
-0.0033415600191801786,
0.04007883369922638,
-0.03246306627988815,
-0.004963856656104326,
-0.003984164912253618,
-0.010352244600653648,
-0.02223137766122818,
0.014970251359045506,
0.07849068194627762,
-0.017171530053019524,
-0.017642101272940636,
0.0012836223468184471,
0.02243063412606716,
0.01014071237295866,
0.02307286113500595,
-0.049370042979717255,
-0.04500316083431244,
-0.0003328527382109314,
0.005529791582375765,
-0.07141712307929993,
-0.046229422092437744,
0.01570405252277851,
0.051348697394132614,
-0.04743741452693939,
0.008315829560160637,
0.04290178418159485,
-0.03296966478228569,
0.07214564830064774,
-0.06291622668504715,
0.03927360102534294,
0.028188465163111687,
0.002259894972667098,
0.052666183561086655,
-0.013449614867568016,
0.0016698860563337803,
0.07191933691501617,
0.06571971625089645,
0.0021930490620434284,
-0.040152743458747864,
-0.04934147372841835,
-0.03411782160401344,
0.01713535562157631,
-0.05312448740005493,
0.010117461904883385,
0.036653947085142136,
0.014304178766906261,
-0.020414244383573532,
-0.003932207357138395,
0.0069244662299752235,
-0.012715049088001251,
0.004891196731477976,
0.003140658838674426,
-0.048377614468336105,
0.03532802313566208,
0.009556958451867104,
0.014820697717368603,
-0.02228689007461071,
0.027921056374907494,
0.0438576266169548,
0.020693138241767883,
0.024067765101790428,
0.01444718986749649,
-0.02001735009253025,
-0.012813073582947254,
-0.014196250587701797,
0.09525137394666672,
0.013340254314243793,
-0.021750494837760925,
0.010987256653606892,
-0.0016052016289904714,
0.006250506266951561,
0.023755548521876335,
-0.033429671078920364,
-0.04486468434333801,
0.032274279743433,
0.029019033536314964,
0.03410918638110161,
-0.025750430300831795,
-0.005951018072664738,
0.005656132474541664,
-0.028863705694675446,
0.0033317357301712036,
0.0772283747792244,
-0.0027723212260752916,
-0.030408548191189766,
-0.0636272132396698,
-0.003985885065048933,
-0.019979819655418396,
0.0012972248950973153,
-0.04592829570174217,
0.026614468544721603,
0.0014814701862633228,
-0.023313529789447784,
0.02870788611471653,
-0.006530516315251589,
0.004748340230435133,
0.0023831899743527174,
0.011430945247411728,
0.0488390177488327,
0.0485699437558651,
0.02456320822238922,
0.026638126000761986,
-0.01429729349911213,
-0.02693992108106613,
0.039233941584825516,
0.045760463923215866,
-0.007446387782692909,
-0.006890640594065189,
-0.011366148479282856,
-0.002343125641345978,
-0.012738937512040138,
0.018508782610297203,
0.0184206273406744,
0.03954123705625534,
-0.043415166437625885,
-0.08895697444677353,
-0.010819162242114544,
0.04442548006772995,
0.026434574276208878,
-0.009802489541471004,
-0.026434045284986496,
-0.0060595860704779625,
0.010617154650390148,
0.05973999202251434,
0.00464248564094305,
0.005744061898440123,
0.012494835071265697,
0.009511720389127731,
-0.018203722313046455,
-0.016424356028437614,
-0.01374406274408102,
-0.004952305927872658,
-0.0533217154443264,
0.010873072780668736,
-0.07143605500459671,
0.0327196903526783,
0.007940411567687988,
-0.010543791577219963,
-0.045429736375808716,
0.059913501143455505,
-0.03356087952852249,
0.01661084219813347,
0.017091721296310425,
0.008586551994085312,
-0.004215162247419357,
0.08095774054527283,
0.011290020309388638,
0.027404000982642174,
0.04042266681790352,
0.0016504288651049137,
0.020343264564871788,
0.006556538864970207,
0.026504388079047203,
0.06629060208797455,
-0.02041250467300415,
-0.002028424059972167,
-0.006182265002280474,
0.022014427930116653,
0.014898761175572872,
-0.03458106145262718,
-0.005153639242053032,
-0.0056503089144825935,
0.004329117015004158,
-0.005634297151118517,
0.036359358578920364,
0.011958320625126362,
-0.0039688944816589355,
0.005162587855011225,
-0.03860853984951973,
-0.017064271494746208,
-0.08043422549962997,
0.029558438807725906,
0.0017118350369855762,
0.0008708752575330436,
0.0791594386100769,
0.039068322628736496,
0.0022240630351006985,
-0.038108162581920624,
-0.05873819813132286,
-0.01503533124923706,
0.02368137240409851,
-0.0005102713475935161,
-0.013034358620643616,
0.02931472286581993,
0.018389977514743805,
0.004720842465758324,
0.006276882719248533,
0.0073073860257864,
-0.03349815681576729,
-0.06490251421928406,
-0.005506826099008322,
-0.021631669253110886,
0.0395381823182106,
-0.03259515389800072,
0.006325203459709883,
-0.019094543531537056,
0.007897394709289074,
-0.026257455348968506,
0.012092973105609417,
-0.023941438645124435,
0.02607508935034275,
0.06706830114126205,
0.008441390469670296,
0.0013286331668496132,
0.036017078906297684,
-0.03667660802602768,
-0.01406710222363472,
0.010777274146676064,
-0.026966333389282227,
-0.0406174473464489,
0.011096546426415443,
0.06071169674396515,
0.07955139875411987,
-0.03339705988764763,
0.0016935485182330012,
0.029419731348752975,
0.021403804421424866,
0.039297398179769516,
0.0033641052432358265,
-0.05311572179198265,
-0.03411193937063217,
0.058313023298978806,
0.03401493653655052,
0.012831547297537327,
-0.014567600563168526,
0.030092187225818634,
0.011854643002152443,
0.011656041257083416,
-0.02908620983362198,
-0.045751314610242844,
0.0724046602845192,
-0.02834097109735012,
0.016345037147402763,
-0.039729971438646317,
-0.025392664596438408,
0.06777367740869522,
-0.028159208595752716,
0.029918290674686432,
0.010311701335012913,
-0.035058289766311646,
0.0004668839683290571,
-0.024484599009156227,
-0.013226952403783798,
0.036118730902671814,
0.02017894759774208,
-0.01918039284646511,
-0.018626157194375992,
0.02400503307580948,
-0.0408809632062912,
0.009822950698435307,
-0.019676413387060165,
-0.011045219376683235,
-0.04241572692990303,
0.02312290109694004,
0.029488295316696167,
-0.029626477509737015,
0.0085227582603693,
0.022300448268651962,
-0.0569084994494915,
0.014494894072413445,
-0.008170322515070438,
0.0024565609637647867,
0.033516280353069305,
-0.04488511383533478,
0.045122385025024414,
-0.043517597019672394,
-0.016418544575572014,
0.05251463130116463,
0.0061377170495688915,
-0.0030956356786191463,
0.026014819741249084,
-0.043874092400074005,
-0.033964335918426514,
0.004953421652317047,
-0.01695588044822216,
-0.012246203608810902,
-0.02958744950592518,
-0.003652917919680476,
0.025851182639598846,
-0.017508817836642265,
-0.02102012187242508,
-0.016024913638830185,
-0.0423109345138073,
-0.04903194308280945,
-0.03674183413386345,
0.007193068042397499,
0.020429689437150955,
-0.045204564929008484,
0.015382066369056702,
0.0680118054151535,
-0.032618578523397446,
0.05477694422006607,
-0.05294590815901756,
-0.010132595896720886,
0.007884482853114605,
-0.01212293840944767,
0.014637277461588383,
-0.01767801120877266,
-0.04556123539805412,
0.07464133948087692,
0.0005084051517769694,
-0.014103935100138187,
-0.0000463196229247842,
-0.03489385545253754,
-0.022846907377243042,
-0.005830962210893631,
0.008527819998562336,
-0.0058554913848638535,
0.005246586166322231,
0.014236961491405964,
0.029263630509376526,
0.013292711228132248,
0.03406790271401405,
0.020074672996997833,
-0.0008992679067887366,
0.007383445277810097,
0.015477367676794529,
-0.00392198795452714,
0.049446385353803635,
0.007746137212961912,
-0.028023460879921913,
0.016597457230091095,
-0.007604322861880064,
0.014908148907124996,
0.006554519757628441,
-0.04901644587516785,
0.06756848841905594,
0.0072274161502718925,
0.0048275901935994625,
-0.04181144759058952,
0.05871276557445526,
-0.008886530995368958,
-0.04003876447677612,
-0.004438858944922686,
0.019055260345339775,
0.022472985088825226,
0.01820426806807518,
-0.012375984340906143,
0.007486426737159491,
0.035728819668293,
-0.0536210872232914,
-0.04039309546351433,
-0.012833301909267902,
-0.007438822649419308,
0.007785596884787083,
-0.000572199234738946,
-0.016408773139119148,
0.021787524223327637,
0.011563589796423912,
-0.00843197200447321,
-0.029797319322824478,
-0.04062490910291672,
0.015268486924469471,
-0.07488720864057541,
0.0011634993134066463,
0.017443668097257614,
0.01933211460709572,
0.006801956333220005,
0.04229968413710594,
0.0065615796484053135,
0.009759800508618355,
0.0021811830811202526,
0.018410349264740944,
-0.05139704793691635,
0.00598037289455533,
-0.017351442947983742,
-0.027969082817435265,
0.0021878175903111696,
-0.009859738871455193,
0.030924838036298752,
-0.018574757501482964,
-0.014271206222474575,
0.0011003412073478103,
0.012446846812963486,
-0.04490787535905838,
-0.00876779854297638,
-0.02656693384051323,
-0.05544954910874367,
-0.05307932198047638,
0.004454953595995903,
0.04197186976671219,
0.0027788125444203615,
0.031206879764795303,
0.029847826808691025,
-0.016044525429606438,
-0.02628600224852562,
-0.024895867332816124,
0.0002901426050812006,
0.014926782809197903,
-0.02062206156551838,
0.006875201594084501,
0.02453438751399517,
-0.019866686314344406,
0.027907680720090866,
0.03900847211480141,
0.061977989971637726,
0.018009090796113014,
-0.0004648792673833668,
0.005014797206968069,
-0.047646574676036835,
-0.029946468770503998,
0.025162311270833015,
0.028044812381267548,
0.024568838998675346,
0.004455198533833027,
0.030893748626112938,
0.028091033920645714,
-0.007838789373636246,
0.018893634900450706,
0.023041773587465286,
0.03510364517569542,
-0.025810223072767258,
-0.0627455785870552,
-0.0002869737218134105,
0.002294133650138974,
-0.00825833436101675,
0.03830511495471001,
-0.039161887019872665,
0.006899058353155851,
0.047701336443424225,
0.003963543102145195,
0.012175953947007656,
-0.02000739984214306,
-0.02381686307489872,
0.011841279454529285,
0.008568039163947105,
-0.03904746472835541,
0.000870380608830601,
0.02932429313659668,
0.03750723972916603,
0.05079161003232002,
-0.004880242981016636,
0.0046431221999228,
-0.1015021950006485,
-0.023774780333042145,
0.036317527294158936,
0.016999300569295883,
-0.01347854919731617,
-0.007270056288689375,
-0.06794856488704681,
-0.03417746722698212,
0.04830223321914673,
-0.007632038556039333,
0.02520463988184929,
-0.005207815207540989,
0.02191399224102497,
0.0005345374811440706,
-0.03254309669137001,
-0.016338080167770386,
0.024117927998304367,
-0.005056883208453655,
0.0013844004133716226,
-0.04447041451931,
0.03312460705637932,
-0.031539611518383026,
0.012678107246756554,
0.007419861387461424,
0.07854649424552917,
0.016847576946020126,
-0.021143434569239616,
-0.06381099671125412,
0.043499790132045746,
0.01802232302725315,
-0.07317530363798141,
-0.01755816861987114,
0.011884455569088459,
0.0016795301344245672,
0.02752111852169037,
-0.020687377080321312,
-0.05675366520881653,
0.0010732196969911456,
-0.012762834317982197,
-0.002690687542781234,
0.017312925308942795,
-0.04644383117556572,
0.03715461120009422,
0.022872472181916237,
0.01978258043527603,
0.05276045948266983,
0.013456277549266815,
-0.024563176557421684,
-0.009920867159962654,
-0.029438134282827377,
0.05835787206888199,
-0.028670139610767365,
0.009173146449029446,
-0.07011895626783371,
-0.01224520243704319,
-0.0038156770169734955,
0.006443246267735958,
-0.039090972393751144,
-0.009124919772148132,
-0.0074094245210289955,
-0.05901200696825981,
-0.0251754280179739,
0.046261001378297806,
0.046796198934316635,
-0.01908859796822071,
0.007618481758981943,
0.03879416733980179,
0.02662316896021366,
-0.025064928457140923,
-0.0004128863220103085,
-0.013236586935818195,
0.003155328333377838,
0.041630249470472336,
-0.023566683754324913,
0.01000079046934843,
-0.017779862508177757,
-0.015481388196349144,
0.02850288897752762,
-0.03675302490592003,
0.05897751823067665,
0.05715890973806381,
0.003091919468715787,
0.013582823798060417,
-0.03287162259221077,
-0.02461872063577175,
0.00219869427382946,
-0.022987838834524155,
0.04898419976234436,
-0.06994670629501343,
0.03597882762551308,
0.003472519339993596,
0.014031498692929745,
-0.09493741393089294,
-0.028598453849554062,
0.011100496165454388,
0.020324811339378357,
-0.0240863636136055,
-0.05802780017256737,
-0.015482187271118164,
-0.037577006965875626,
0.007689191959798336,
0.01824856549501419,
0.0729394257068634,
0.004449936561286449,
0.000544720038305968,
0.0018226346001029015,
0.03456631302833557,
0.04899277538061142,
-0.02120545692741871,
-0.011025266721844673,
0.0010162407997995615,
-0.009822122752666473,
0.016705548390746117,
-0.033277727663517,
0.03771771490573883,
-0.03810807317495346,
0.03019065409898758,
-0.016775909811258316,
-0.037050358951091766,
0.016014374792575836,
-0.0181001927703619,
-0.005686518736183643,
0.016534119844436646,
0.015731632709503174,
-0.0005169009673409164,
0.017721565440297127,
-0.013652029447257519,
-0.027061406522989273,
0.0362374372780323,
-0.00365610234439373,
0.009297494776546955,
-0.021215174347162247,
-0.03179109841585159,
0.05247024446725845,
0.015653837472200394,
-0.012715078890323639,
0.04924442991614342,
0.038312893360853195,
-0.016700346022844315,
0.012970210053026676,
0.04050157219171524,
0.005739537999033928,
0.023161374032497406,
-0.012217821553349495,
0.01345413364470005,
0.038076456636190414,
0.01599389873445034,
-0.020373664796352386,
-0.01750364527106285,
-0.019755743443965912,
0.028017496690154076,
0.047514330595731735,
-0.0204465314745903,
0.023754488676786423,
-0.006965837441384792,
-0.032519347965717316,
0.024274803698062897,
-0.019671831279993057,
0.003812646958976984,
0.01153079979121685,
-0.03866508603096008,
0.05793985724449158,
-0.01740790344774723,
-0.025881009176373482,
0.02497866377234459,
0.03148822486400604,
-0.0348123237490654,
0.02129754237830639,
0.006936725229024887,
0.025821594521403313,
0.0038457417394965887,
0.0009528232621960342,
-0.07964181900024414,
0.07491720467805862,
-0.016494283452630043,
0.012155759148299694,
-0.0038396394811570644,
-0.050968874245882034,
0.05275319516658783,
-0.011061860248446465,
0.020287860184907913,
-0.01911398023366928,
-0.028081979602575302,
0.00839309487491846,
0.02101694978773594,
0.01754019781947136,
0.033576514571905136,
0.002583450870588422,
0.012555385939776897,
0.04281320422887802,
-0.011724693700671196,
-0.013630624860525131,
0.02979482337832451,
-0.05984737351536751,
-0.02700679935514927,
-0.0730133056640625,
-0.048565588891506195,
0.007517650723457336,
0.01656799018383026,
-0.011521287262439728,
0.0029644989408552647,
0.01069896761327982,
0.022410988807678223,
-0.006991223432123661,
0.015285748057067394,
-0.016778795048594475,
0.08706718683242798,
0.009005207568407059,
0.026530325412750244,
-0.025696158409118652,
-0.01440583635121584,
0.10365723073482513,
0.07106175273656845,
0.015858057886362076,
-0.06024610623717308,
-0.031678102910518646,
-0.041657280176877975,
0.006786915007978678,
-0.014987192116677761,
0.024899747222661972,
0.02004815824329853,
-0.011173109523952007,
-0.007604232989251614,
0.0370212197303772,
0.004848361015319824,
-0.010369736701250076,
0.07184625416994095,
-0.03411894291639328,
-0.04325096681714058,
0.010443382896482944,
-0.0029668163042515516,
-0.029440367594361305,
-0.013874301686882973,
-0.05044832453131676,
0.0017756797606125474,
0.012527826242148876,
-0.0011734646977856755,
-0.023383816704154015,
-0.0248495414853096,
0.02184227481484413,
-0.009723820723593235,
-0.04195565730333328,
-0.03387364372611046,
0.00046794002992101014,
-0.007401213515549898,
-0.042844489216804504,
-0.04170955717563629,
0.01448060479015112,
-0.03639351576566696,
0.05956796929240227,
0.029212573543190956,
-0.032174158841371536,
0.03426481410861015,
-0.00391912879422307,
0.0017489318270236254,
-0.05250168964266777,
-0.005138620734214783,
-0.01406404934823513,
0.04259642958641052,
-0.028943492099642754,
0.03664279356598854,
0.013481371104717255,
0.015884213149547577,
-0.006640224251896143,
-0.0055433353409171104,
-0.012156529352068901,
-0.02825772762298584,
0.04370666667819023,
0.007436825428158045,
-0.04385204613208771,
-0.04061545804142952,
-0.004568672738969326,
0.01916326768696308,
0.01969347707927227,
0.0030658298637717962,
0.007525146007537842,
-0.002622175496071577,
-0.021309951320290565,
0.05932615324854851,
-0.006807184778153896,
-0.00020480481907725334,
-0.06777442246675491,
0.007425446528941393,
-0.013581567443907261,
-0.010659533552825451,
-0.010881963185966015,
0.0078062936663627625,
0.016224846243858337,
0.004743586760014296,
0.008924707770347595,
0.014704708941280842,
-0.04596718028187752,
0.005496057216078043,
-0.047115664929151535,
-0.018136056140065193,
-0.006036818493157625,
0.03549934923648834,
0.03909929096698761,
0.04724690690636635,
0.0006471537635661662,
0.013253971934318542,
-0.036553848534822464,
0.047216132283210754,
0.008734059520065784,
-0.0168190598487854,
-0.0024728449061512947,
-0.0165272057056427,
-0.02050805650651455,
-0.027642931789159775,
0.0048033930361270905,
-0.008196922950446606,
0.01908288337290287,
0.033156055957078934,
0.01700945571064949,
0.04104159027338028,
0.007512211799621582,
-0.003156351624056697,
0.03354385122656822,
-0.01612776145339012,
-0.009818080812692642,
0.04444146528840065,
-0.006216815672814846,
-0.06065894290804863,
-0.023078469559550285,
-0.014890562742948532,
-0.023273933678865433,
0.013442178256809711,
0.033869486302137375,
-0.026406709104776382,
-0.06820732355117798,
0.006081169005483389,
0.06086859479546547,
-0.030529402196407318,
0.002652717987075448,
-0.05591666325926781,
0.049486253410577774,
-0.052462078630924225,
-0.005415167193859816,
-0.017872491851449013,
0.00813949853181839,
-0.03458179906010628,
-0.012718108482658863,
-0.00461931386962533,
0.022658756002783775,
0.005019391421228647,
0.020844992250204086,
-0.006699387915432453,
-0.0011460860259830952,
0.033025506883859634,
-0.0033044142182916403,
-0.06539294868707657,
0.03776916489005089,
-0.025126567110419273,
-0.07606212049722672,
0.033596478402614594,
-0.005787976551800966,
0.04986727610230446,
0.038089875131845474,
0.004407242871820927,
-0.01974630542099476,
0.023838087916374207,
-0.007980935275554657,
-0.002680834149941802,
-0.029671765863895416,
-0.006323838606476784,
-0.031238297000527382,
-0.029184240847826004,
0.004707701038569212,
-0.006914196535944939,
0.002190199913457036,
-0.007074718363583088,
0.033931490033864975,
-0.006433519069105387,
0.006735522300004959,
0.03616437315940857,
-0.015006841160356998,
0.014367631636559963,
-0.0134511673822999,
0.021483685821294785,
-0.006846592761576176,
0.03918168321251869,
-0.021212154999375343,
-0.012229839339852333,
0.0007249004556797445,
-0.012045457027852535,
-0.0994158387184143,
-0.023294217884540558,
-0.0006905216141603887,
-0.019785622134804726,
0.04955516383051872,
-0.02905595675110817,
0.012021050788462162,
0.019220730289816856,
-0.07386495172977448,
0.02629702351987362,
-0.01928183063864708,
-0.005537078250199556,
-0.004953120369464159,
0.01115475781261921,
0.0024322487879544497,
0.06748171150684357,
0.012526026926934719,
0.03392203524708748,
-0.0010587903670966625,
0.01811104081571102,
0.020416026934981346,
0.006040738895535469,
0.0192429032176733,
-0.000835957529488951,
0.015550725162029266,
-0.001463217893615365,
0.09440836310386658,
-0.009626599960029125,
-0.03805583715438843,
0.01990397460758686,
-0.01322123035788536,
-0.020790481939911842,
-0.007129273377358913,
0.025131195783615112,
-0.01910998858511448,
-0.002769722603261471,
0.03677168861031532,
0.000331182440277189,
-0.004447951912879944,
0.02798328548669815,
0.01360857579857111,
0.06043701991438866,
-0.08078209310770035,
-0.0010026901727542281,
0.023170333355665207,
-0.022002751007676125,
-0.0258583202958107,
0.04569101706147194,
-0.015654342249035835,
-0.032609011977910995,
0.03866121545433998,
0.027112597599625587,
0.015928160399198532,
-0.004218928050249815,
0.038221701979637146,
-0.01308325957506895,
-0.013967987149953842,
0.0392463393509388,
-0.01646696776151657,
-0.013724355027079582,
0.05125666409730911,
-0.014139378443360329,
-0.03720388188958168,
0.02242281287908554,
0.0036548543721437454,
-0.0021648334804922342,
-0.04360782727599144,
-0.006485081743448973,
-0.020647695288062096,
-0.04065671190619469,
-0.016933882609009743,
-0.021317629143595695,
-0.03035605512559414,
0.03454751521348953,
0.02599872276186943,
0.013264462351799011,
0.020719368010759354,
0.007286726497113705,
-0.0083566103130579,
-0.09095796197652817,
0.03035097010433674,
0.0004938521888107061,
-0.019672591239213943,
-0.004919214639812708,
-0.047831326723098755,
-0.004230496473610401,
0.01054498739540577,
0.024745728820562363,
0.04206838086247444,
-0.010492104105651379,
0.04151419922709465,
0.019329320639371872,
-0.0016105864197015762,
-0.0171631071716547,
-0.0008173887617886066,
-0.003764220280572772,
-0.015033325180411339,
-0.035421695560216904,
-0.0047620865516364574,
-0.013540605083107948,
-0.0047414423897862434,
0.04071026295423508,
0.005271772388368845,
0.002299065003171563,
0.008503075689077377,
-0.0040725404396653175,
0.09050201624631882,
0.026524977758526802,
-0.014408777467906475,
0.037818845361471176,
0.004591879900544882,
0.025370921939611435,
-0.007144558243453503,
-0.021078867837786674,
-0.046891048550605774,
-0.006524674594402313,
-0.02042432129383087,
-0.020284170284867287,
-0.014298643916845322,
0.012864899821579456,
0.013130863197147846,
-0.03855255991220474,
0.012438991107046604,
0.04690476506948471,
-0.028514036908745766,
-0.011777032166719437,
0.0382278673350811,
0.02842589095234871,
0.04517241567373276,
0.018246084451675415,
-0.001523401471786201,
0.046432334929704666,
0.011799506843090057,
-0.032662343233823776,
0.052888743579387665,
0.0305494237691164,
-0.024090802296996117,
0.023020312190055847,
0.025077201426029205,
-0.015558089129626751,
0.032985869795084,
0.006768431048840284,
0.06656255573034286,
-0.013036881573498249,
-0.03227151930332184,
0.009506206959486008,
-0.00745672732591629,
0.010692035779356956,
0.020847471430897713,
-0.036628346890211105,
0.08686427026987076,
-0.004667127970606089,
-0.006860784254968166,
-0.013238293118774891,
-0.013645751401782036,
-0.029905730858445168,
-0.011308864690363407,
0.014275890775024891,
0.0873803198337555,
0.028608577325940132,
-0.0035853104200214148,
-0.02530089020729065,
-0.003535988973453641,
0.047412119805812836,
-0.011160509660840034,
0.036636825650930405,
0.008852561935782433,
0.01057557575404644,
-0.01644422486424446,
-0.02700129896402359,
-0.034804292023181915,
-0.034088134765625,
-0.015617172233760357,
0.03739817067980766,
0.0649547278881073,
0.0017939674435183406,
-0.05323592200875282,
-0.03311898559331894,
0.0351954847574234,
-0.07841265201568604,
-0.0036405338905751705,
-0.025239072740077972,
0.015290766023099422,
-0.011082098819315434,
-0.019731910899281502
] |
<p>Is there any frequency at which cars can be charged with using wireless? Surely, wireless transmission can be safely assumed to be a form of energy transfer, and there can be charging of cars without physical electric outlets. Is there a frequency at which cars can be charged? One can see the problem of energy transmission as a form of optimization problem in which the parameter energy (E) is to the transmitted with maximal effect(I could be nebulous here!) Is there such a frequency for wireless car charging? </p>
| 10,728 |
[
-0.02281258814036846,
-0.036884959787130356,
0.02359604462981224,
-0.0007068432169035077,
0.040510158985853195,
0.010255329310894012,
-0.04288029670715332,
-0.021723994985222816,
0.028618359938263893,
-0.0356639102101326,
0.021865379065275192,
0.0675744116306305,
0.013729623518884182,
0.0009905375773087144,
0.03411572799086571,
0.004658151417970657,
0.008401964791119099,
-0.021758565679192543,
-0.011469269171357155,
0.024037914350628853,
0.014346440322697163,
0.013077273033559322,
-0.0074606891721487045,
0.015302249230444431,
-0.030906768515706062,
-0.014790121465921402,
0.02775423787534237,
-0.004735957831144333,
0.006451525259763002,
0.04785619676113129,
-0.02621980756521225,
-0.029503202065825462,
-0.007330776192247868,
0.044735562056303024,
0.019088055938482285,
0.0012501943856477737,
-0.04387035220861435,
-0.03567365184426308,
-0.01565273478627205,
-0.023077093064785004,
-0.019129542633891106,
-0.022789539769291878,
0.019037261605262756,
0.03794101998209953,
-0.019318368285894394,
0.0005100608104839921,
0.03509831801056862,
-0.06164167821407318,
0.022649969905614853,
-0.06992832571268082,
0.08761938661336899,
-0.0197403933852911,
0.023556970059871674,
-0.013915088959038258,
-0.01526185218244791,
0.01565934345126152,
0.0736939013004303,
0.06650254130363464,
0.0075851306319236755,
-0.023681333288550377,
-0.0505109541118145,
-0.008155744522809982,
0.0007087763515301049,
-0.03081020899116993,
-0.07507701963186264,
0.03335433080792427,
-0.016791528090834618,
-0.03043038211762905,
0.02799363061785698,
0.03238185867667198,
-0.02068197913467884,
0.0186479315161705,
0.05364302918314934,
0.011357365176081657,
-0.013238088227808475,
-0.026319557800889015,
0.023093421012163162,
0.0030238793697208166,
0.04944910109043121,
0.029156100004911423,
-0.039576686918735504,
-0.02052764967083931,
-0.009014698676764965,
0.05721459537744522,
0.00284326053224504,
-0.05154770612716675,
0.045912086963653564,
-0.03215053677558899,
0.03198555111885071,
0.004407443106174469,
0.0057407524436712265,
-0.0036054053343832493,
0.05301222577691078,
-0.029033508151769638,
0.007348327431827784,
0.07585051655769348,
0.015878016129136086,
0.02230593003332615,
0.00953774806112051,
-0.07583018392324448,
0.053294092416763306,
-0.018540015444159508,
0.010295893996953964,
0.05652149021625519,
-0.009077800437808037,
-0.04416956380009651,
-0.011676673777401447,
0.011160695925354958,
-0.00572602404281497,
0.012573163956403732,
-0.023124128580093384,
-0.007291569374501705,
0.01591476984322071,
0.01164312195032835,
0.017562273889780045,
-0.017208699136972427,
-0.007074072491377592,
-0.022628411650657654,
0.05375102162361145,
0.06815321743488312,
0.031736139208078384,
-0.061692096292972565,
0.03885965049266815,
-0.02230001986026764,
-0.045104410499334335,
0.018451932817697525,
-0.044453755021095276,
0.02344757504761219,
-0.017345136031508446,
-0.009422016330063343,
-0.002323381369933486,
-0.03729095682501793,
0.032236579805612564,
-0.025388561189174652,
0.016256552189588547,
-0.047852836549282074,
-0.07284561544656754,
-0.06014253571629524,
0.0018060447182506323,
-0.026480987668037415,
0.03650694712996483,
-0.05108627304434776,
0.029163749888539314,
0.05390829220414162,
0.04963691905140877,
0.012050584889948368,
0.0057386551052331924,
-0.02641686610877514,
0.04915999248623848,
0.010503828525543213,
0.0015010000206530094,
-0.03889384865760803,
0.010589669458568096,
-0.008570264093577862,
0.021285153925418854,
-0.007367962505668402,
0.032598838210105896,
0.031352922320365906,
0.03513757511973381,
-0.04257776215672493,
0.02287256345152855,
-0.018263351172208786,
-0.03806454688310623,
0.019476689398288727,
-0.003237796248868108,
0.011954274028539658,
0.02869400940835476,
0.03429160267114639,
0.020823394879698753,
0.013995377346873283,
0.002745544770732522,
0.04706038907170296,
0.04147150367498398,
0.04482778161764145,
0.03621106222271919,
-0.05821920558810234,
-0.017403118312358856,
-0.060642849653959274,
0.038952238857746124,
-0.003749933559447527,
-0.017798466607928276,
-0.011415470391511917,
0.004362108651548624,
0.025571607053279877,
-0.007409638725221157,
0.024218136444687843,
-0.040308207273483276,
0.03730085864663124,
0.010024460963904858,
-0.03144390508532524,
-0.00709887919947505,
-0.0011656720889732242,
0.044164154678583145,
0.010618900880217552,
-0.015813445672392845,
0.002718977862969041,
-0.027505800127983093,
0.01187654584646225,
-0.05641619861125946,
-0.04405907541513443,
0.007187685929238796,
0.03753945976495743,
0.021429335698485374,
-0.004390038084238768,
-0.0001601796830072999,
0.046051058918237686,
0.014675158075988293,
0.00377445830963552,
0.04514382407069206,
0.03692704439163208,
-0.07757777720689774,
-0.01952904649078846,
-0.015962593257427216,
0.028119048103690147,
0.014096170663833618,
0.009383033029735088,
0.01246725209057331,
-0.029872233048081398,
0.00012819322000723332,
0.05650503188371658,
-0.008491087704896927,
0.0464538112282753,
0.04469913989305496,
0.03341290354728699,
0.008410612121224403,
0.05047888308763504,
0.006072332616895437,
0.006051110103726387,
-0.05016374588012695,
-0.059338320046663284,
-0.052770886570215225,
0.042804617434740067,
0.03703297674655914,
0.05375039950013161,
-0.06652440130710602,
-0.0019118788186460733,
0.04979444295167923,
0.05123893544077873,
0.051133014261722565,
0.03849335014820099,
-0.019881214946508408,
-0.022364109754562378,
0.03204820677638054,
0.024235108867287636,
0.02400362677872181,
0.0016321006696671247,
-0.005293591879308224,
0.006759447976946831,
-0.0015997379086911678,
0.004234733991324902,
-0.023028112947940826,
0.01270627323538065,
-0.030043747276067734,
-0.031948965042829514,
-0.01555817574262619,
-0.030943606048822403,
0.026156850159168243,
-0.0821428969502449,
0.02504223957657814,
-0.001213276875205338,
-0.00320021016523242,
0.0037359269335865974,
0.03665692359209061,
0.0007379524176940322,
0.018711695447564125,
-0.019642528146505356,
-0.01849999465048313,
-0.014575263485312462,
0.028345691040158272,
-0.04116012528538704,
0.05684416741132736,
-0.005652339663356543,
0.034199975430965424,
0.019042085856199265,
0.0049271672032773495,
0.0306700412184,
-0.007615190930664539,
0.02441074326634407,
-0.015835436061024666,
-0.024442486464977264,
-0.015557575970888138,
-0.033082712441682816,
-0.013700855895876884,
0.0018677785992622375,
-0.01969556137919426,
-0.02211747318506241,
-0.0336400531232357,
-0.041111357510089874,
0.04952819645404816,
-0.015718592330813408,
0.004413307178765535,
0.030282894149422646,
0.007331944536417723,
-0.051564861088991165,
0.005529023241251707,
-0.03279457986354828,
0.03132361173629761,
-0.016081377863883972,
0.020888851955533028,
0.038700420409440994,
0.019175762310624123,
-0.034800320863723755,
0.003784728003665805,
-0.048372332006692886,
-0.03709351271390915,
-0.005380271002650261,
-0.01988048106431961,
0.028558196499943733,
-0.013841015286743641,
0.07002931088209152,
0.012849400751292706,
-0.07029584795236588,
-0.005587324500083923,
-0.0401562936604023,
-0.06586018949747086,
0.05620794743299484,
-0.03235824778676033,
0.04903855547308922,
0.0031915840227156878,
-0.04000493884086609,
0.05084897577762604,
0.01954065077006817,
-0.005037217866629362,
0.03072325699031353,
-0.04423973709344864,
-0.02848520129919052,
-0.03337329626083374,
-0.023329852148890495,
0.05446599796414375,
-0.009932866320014,
0.019198385998606682,
0.025320785120129585,
0.005075739696621895,
0.028278615325689316,
0.0134541355073452,
-0.018861209973692894,
0.01312603522092104,
-0.013451682403683662,
0.03740174323320389,
0.05586348846554756,
0.015983717516064644,
-0.049300748854875565,
0.016966192051768303,
0.019322330132126808,
0.019974594935774803,
0.006474957335740328,
-0.0030512872617691755,
0.034411124885082245,
0.03162623941898346,
0.023974180221557617,
-0.014717156998813152,
0.005560791585594416,
0.002597037237137556,
0.006741450633853674,
-0.024568811058998108,
0.05661472678184509,
0.04350702837109566,
-0.041008155792951584,
-0.011646025814116001,
0.0421639084815979,
0.030555425211787224,
-0.06477119773626328,
-0.05528082698583603,
0.004334955010563135,
-0.007331383414566517,
0.012293100357055664,
-0.0018505221232771873,
-0.04174484685063362,
0.01041953545063734,
-0.0014416822232306004,
0.07193268090486526,
0.028843248263001442,
0.023322489112615585,
0.03689359128475189,
-0.04379996284842491,
-0.041280899196863174,
0.0018435443053022027,
0.027353350073099136,
0.02051905356347561,
0.039480190724134445,
0.009359496645629406,
0.019146818667650223,
-0.017844360321760178,
-0.017191749066114426,
-0.056599296629428864,
0.019283059984445572,
-0.02287997677922249,
-0.014202275313436985,
0.0070656719617545605,
-0.01639600284397602,
-0.027324793860316277,
-0.03325418755412102,
-0.01601625792682171,
-0.016409287229180336,
-0.03015030175447464,
-0.047071658074855804,
0.012336481362581253,
-0.007245675660669804,
-0.04879208654165268,
-0.024198563769459724,
-0.006899145431816578,
0.02780095487833023,
-0.02217213623225689,
-0.014801005832850933,
0.037511665374040604,
-0.03212835267186165,
0.0071479557082057,
0.016022467985749245,
0.005940252915024757,
-0.020778130739927292,
0.02971828356385231,
0.0340864434838295,
0.015026227571070194,
-0.013702018186450005,
-0.004168611951172352,
0.006940725725144148,
0.04088936746120453,
0.02513781562447548,
-0.02933632582426071,
-0.028101326897740364,
-0.051310207694768906,
-0.027941297739744186,
0.009670209139585495,
0.04144738242030144,
-0.011361679062247276,
0.021348560228943825,
0.05119024217128754,
-0.03574173152446747,
-0.010272510349750519,
0.04625529795885086,
0.056186024099588394,
0.00828064326196909,
-0.01704850047826767,
-0.0278221033513546,
-0.006314065773040056,
0.023458659648895264,
0.04802439734339714,
0.029511358588933945,
0.0031783937010914087,
0.0011162742739543319,
-0.01224903017282486,
0.025967959314584732,
-0.004663011059165001,
-0.012986636720597744,
0.02365417405962944,
0.004949461668729782,
0.007639226969331503,
-0.01207416970282793,
-0.03073146380484104,
-0.032695163041353226,
-0.006423866376280785,
0.031604621559381485,
0.026805412024259567,
-0.033566609025001526,
-0.10548759251832962,
0.004998895805329084,
0.024217113852500916,
0.01264684647321701,
0.010081125423312187,
0.004141131415963173,
-0.03072265163064003,
0.040557559579610825,
0.028389237821102142,
-0.02663460187613964,
0.015069839544594288,
-0.006357322447001934,
-0.017059776932001114,
-0.007240665145218372,
-0.01064374390989542,
-0.007218518760055304,
0.003967592027038336,
0.029459329321980476,
0.003143349662423134,
-0.012794800102710724,
-0.041659172624349594,
0.0036538837011903524,
0.031391169875860214,
0.060982733964920044,
0.04630448669195175,
-0.0025569230783730745,
0.010090963914990425,
-0.02067882940173149,
0.028711838647723198,
-0.037096064537763596,
-0.06120409071445465,
0.004822013434022665,
0.01770625077188015,
-0.004381760489195585,
0.022353556007146835,
-0.014944992028176785,
-0.025741681456565857,
0.025703785941004753,
-0.0032063391990959644,
0.0015206632670015097,
0.021633556112647057,
-0.04045403003692627,
0.023335959762334824,
0.0032104963902384043,
0.03657243028283119,
0.05904321372509003,
0.04246431589126587,
-0.032288797199726105,
0.029594330117106438,
-0.010497990995645523,
0.060425590723752975,
-0.003894226858392358,
0.00013888470130041242,
0.013486254960298538,
0.020989101380109787,
-0.027705440297722816,
0.04995039850473404,
0.0012844596058130264,
0.001880537485703826,
-0.051182880997657776,
-0.028568211942911148,
-0.05230392888188362,
0.04358262941241264,
-0.031225962564349174,
-0.03118588775396347,
-0.022615468129515648,
0.0030776497442275286,
-0.020887890830636024,
-0.017655326053500175,
0.010202521458268166,
-0.018458310514688492,
0.003548216773197055,
0.033852141350507736,
-0.0157028641551733,
0.0015296974452212453,
-0.025619570165872574,
0.00803925096988678,
0.008022290654480457,
-0.027895743027329445,
0.05826020985841751,
-0.008422902785241604,
-0.021834250539541245,
-0.019168417900800705,
-0.07899761945009232,
-0.03228841722011566,
0.0416075624525547,
0.004059330560266972,
0.0594584085047245,
-0.016475215554237366,
0.0022550239227712154,
-0.007455531507730484,
-0.013439156115055084,
-0.053299158811569214,
-0.049398139119148254,
0.02157578058540821,
0.034419331699609756,
-0.0021028982009738684,
-0.011822844855487347,
0.01823996566236019,
-0.027631407603621483,
-0.03953670710325241,
0.007353524211794138,
0.03836854174733162,
-0.027288615703582764,
0.026563839986920357,
-0.03442208096385002,
-0.030279504135251045,
0.022646339610219002,
0.007280048914253712,
0.0020143436267971992,
0.05218178778886795,
-0.033552929759025574,
-0.01934206858277321,
-0.03658704087138176,
0.016012437641620636,
-0.025024401023983955,
-0.012182056903839111,
0.01072893850505352,
-0.02931075543165207,
0.049482811242341995,
-0.020540425553917885,
-0.04151720926165581,
0.05688184127211571,
-0.01934756152331829,
-0.03587309643626213,
0.018912969157099724,
0.04539281874895096,
0.023683158680796623,
-0.008554784581065178,
-0.032833248376846313,
-0.023645756766200066,
-0.046008169651031494,
-0.03342200443148613,
0.008667494170367718,
0.001960208173841238,
0.013924525119364262,
0.0004771222884301096,
0.07049203664064407,
-0.010121367871761322,
-0.03721172735095024,
0.0019275250378996134,
-0.004329055547714233,
0.0116321612149477,
-0.018333811312913895,
0.01051574107259512,
-0.0293339341878891,
0.002450366271659732,
-0.003921113908290863,
-0.05142584070563316,
-0.016988273710012436,
0.00637509161606431,
0.04800286889076233,
0.0009598226170055568,
0.033571094274520874,
0.014060016721487045,
-0.0237463116645813,
-0.015088338404893875,
-0.0051282960921525955,
-0.006683163810521364,
0.024269679561257362,
-0.015175134874880314,
0.00039893208304420114,
0.009084993973374367,
-0.025678865611553192,
0.0334891676902771,
0.02508121356368065,
0.0036262385547161102,
0.029992813244462013,
0.0433410108089447,
0.05684823542833328,
0.0072723133489489555,
-0.04236801713705063,
-0.06918569654226303,
0.01954944245517254,
-0.02207132801413536,
0.04180647432804108,
0.0008810438448563218,
-0.02480212226510048,
0.05509024113416672,
0.003198722144588828,
0.01279404852539301,
-0.010205904953181744,
-0.010606984607875347,
-0.04193807393312454,
0.049604207277297974,
-0.004584520123898983,
-0.010762439109385014,
-0.0007130626472644508,
-0.006013170816004276,
-0.012765551917254925,
-0.01989315263926983,
0.059910621494054794,
0.02746793068945408,
-0.03821196034550667,
-0.010510602034628391,
-0.019821608439087868,
-0.04234849661588669,
0.05148323252797127,
0.033951736986637115,
-0.02305876836180687,
0.03395073115825653,
-0.030750786885619164,
0.021287105977535248,
0.022260446101427078,
0.04264108091592789,
0.004380923230201006,
0.09347718209028244,
-0.01343490183353424,
0.0027233166620135307,
-0.014336857944726944,
-0.004339911974966526,
0.12857545912265778,
0.0527690164744854,
0.006870564538985491,
-0.02520114928483963,
0.007971318438649178,
-0.043880220502614975,
-0.02620876207947731,
-0.060282595455646515,
0.029825735837221146,
-0.01971638947725296,
0.008663500659167767,
0.026240739971399307,
0.031041255220770836,
-0.007242601364850998,
-0.004885031841695309,
0.07789110392332077,
-0.029528452083468437,
-0.021217675879597664,
0.02505730465054512,
0.04840553179383278,
0.018427502363920212,
0.00923292525112629,
-0.02941185049712658,
0.010354488156735897,
-0.05268927663564682,
-0.002097481396049261,
0.027246393263339996,
0.01098975632339716,
0.05740252137184143,
-0.024431142956018448,
-0.036463554948568344,
-0.016715489327907562,
0.0025110857095569372,
-0.015064217150211334,
-0.028106095269322395,
0.01015566661953926,
0.026738828048110008,
0.03985894098877907,
-0.05431235209107399,
0.025456510484218597,
0.03349415212869644,
-0.006695684976875782,
0.0033788150176405907,
0.042990878224372864,
-0.033203233033418655,
0.03373503312468529,
-0.03960496559739113,
0.0044248332269489765,
-0.01189755741506815,
0.0033519722055643797,
-0.005384625867009163,
0.03671330213546753,
-0.012202087789773941,
-0.017787015065550804,
-0.02803071029484272,
-0.011327965185046196,
0.022507784888148308,
-0.01425738725811243,
0.0033434799406677485,
-0.04661501944065094,
0.047736458480358124,
-0.0023804157972335815,
0.004124936647713184,
0.02494729310274124,
-0.018125811591744423,
0.019699066877365112,
-0.0006861906731501222,
0.040425289422273636,
-0.008317051455378532,
-0.04547351598739624,
-0.0029719711747020483,
-0.04352911189198494,
-0.03142483904957771,
-0.05175585672259331,
0.00622921995818615,
0.022881032899022102,
0.009946131147444248,
0.0011212542885914445,
-0.0016323886811733246,
-0.025934990495443344,
-0.0641295313835144,
-0.014836006797850132,
0.01970634236931801,
-0.012918290682137012,
-0.029381169006228447,
-0.017155693843960762,
0.012015575543045998,
0.04574586823582649,
-0.03933359682559967,
0.0008151103393174708,
-0.05056776478886604,
-0.008268197067081928,
0.018973099067807198,
-0.03566180542111397,
0.014670523814857006,
-0.0321960486471653,
-0.054154567420482635,
0.012286810204386711,
-0.026662005111575127,
0.031072447076439857,
-0.0011405092664062977,
-0.010981046594679356,
-0.019589068368077278,
-0.0037637895438820124,
-0.031170634552836418,
-0.011887507513165474,
0.02382705919444561,
-0.011648681946098804,
-0.007514415308833122,
-0.010450148023664951,
0.020550860092043877,
-0.03346998244524002,
-0.0390976183116436,
-0.018810929730534554,
0.02856660820543766,
-0.03708706051111221,
0.02218879573047161,
0.019865496084094048,
-0.005558212287724018,
-0.022163357585668564,
-0.01350101362913847,
-0.043233033269643784,
-0.03208579123020172,
-0.00966781098395586,
0.024529753252863884,
-0.014549133367836475,
0.00036694511072710156,
0.007510474417358637,
0.02405865490436554,
-0.04526597633957863,
0.018575256690382957,
0.028950773179531097,
0.011002518236637115,
-0.02125668339431286,
0.0004996040370315313,
0.015629960224032402,
0.01873699575662613,
0.052099816501140594,
-0.06033165380358696,
-0.04329558461904526,
0.07239795476198196,
-0.07017853856086731,
-0.022601572796702385,
0.008076392114162445,
-0.027740126475691795,
0.007111446000635624,
0.021972909569740295,
-0.004897927865386009,
-0.028735799714922905,
0.055171746760606766,
0.0046850997023284435,
0.02814601920545101,
0.0593942292034626,
0.03461907431483269,
-0.019117753952741623,
-0.022421598434448242,
0.022298458963632584,
-0.006673224736005068,
-0.0060954918153584,
0.03785739094018936,
0.025483904406428337,
-0.0015329117886722088,
-0.0019665055442601442,
0.03626510500907898,
-0.002430959139019251,
0.01023714430630207,
0.06303203105926514,
0.023426098749041557,
0.03692067041993141,
0.045119114220142365,
-0.012329642660915852,
0.02110869064927101,
0.002242638263851404,
-0.0036303920205682516,
-0.10383841395378113,
-0.030953673645853996,
0.022122260183095932,
-0.008146651089191437,
0.04563523828983307,
-0.03167176991701126,
0.01111203245818615,
0.00428572716191411,
-0.10283514857292175,
-0.021149776875972748,
0.014412304386496544,
-0.039081089198589325,
-0.026829009875655174,
0.004547567572444677,
-0.026133904233574867,
-0.022236870601773262,
0.04944342374801636,
0.047019291669130325,
0.019309071823954582,
0.0032788305543363094,
-0.023853810504078865,
-0.024221310392022133,
-0.0030757642816752195,
0.042168501764535904,
0.007614364381879568,
-0.012398377060890198,
0.07475228607654572,
-0.03691672533750534,
0.006169882602989674,
0.008009461686015129,
-0.007769332733005285,
0.007818957790732384,
0.0007868430693633854,
-0.000403703743359074,
0.026803279295563698,
0.07606573402881622,
0.035799216479063034,
-0.028943946585059166,
-0.020041026175022125,
0.021310972049832344,
0.010593191720545292,
0.025960372760891914,
-0.009448828175663948,
0.01657242327928543,
0.017627479508519173,
-0.013406790792942047,
-0.02606978639960289,
0.0261620432138443,
-0.030271198600530624,
-0.03153172507882118,
0.005404375493526459,
0.007948396727442741,
-0.014616167172789574,
-0.03471754863858223,
-0.02412809245288372,
-0.03838272765278816,
-0.052373893558979034,
0.0055016581900417805,
0.026827560737729073,
0.01374464388936758,
-0.023967890068888664,
-0.021775009110569954,
-0.00571683794260025,
0.03433553874492645,
0.010084658861160278,
-0.008844015188515186,
-0.06435614824295044,
0.010332666337490082,
0.0229660477489233,
0.013201558962464333,
0.004912948235869408,
-0.04223765805363655,
-0.01602332852780819,
0.048426248133182526,
0.014099634252488613,
0.021673012524843216,
0.019249536097049713,
-0.013635329902172089,
0.010631248354911804,
-0.057449277490377426,
0.028229117393493652,
-0.019651558250188828,
0.03398870304226875,
-0.022148368880152702,
-0.06250732392072678,
-0.005231092683970928,
-0.002050083829089999,
0.07419107854366302,
-0.03154072165489197,
-0.05204691365361214,
0.005571124609559774,
-0.012730839662253857,
0.016160588711500168,
-0.01103866845369339,
0.006773493718355894,
-0.02001279965043068,
-0.026565957814455032,
-0.03976641595363617,
-0.005995952989906073,
0.0005118254339322448,
-0.004295687191188335,
0.008723788894712925,
0.004899227060377598,
-0.013236639089882374,
0.005041867960244417,
-0.02896055392920971,
0.06151213124394417,
0.022425439208745956,
0.013182134367525578,
0.06308066099882126,
-0.02497195638716221,
0.032253652811050415,
-0.02418770082294941,
-0.0011432927567511797,
-0.0368620827794075,
0.011914141476154327,
-0.06107158586382866,
0.028704477474093437,
-0.009451182559132576,
0.025756075978279114,
0.02707860805094242,
-0.022004052996635437,
-0.015053444541990757,
0.0524577870965004,
-0.054444536566734314,
-0.0023818735498934984,
0.037030383944511414,
0.0167000163346529,
0.018180478364229202,
0.027842862531542778,
0.00624468456953764,
-0.030072281137108803,
0.013511491008102894,
-0.02914269082248211,
0.02929570898413658,
0.007449392694979906,
-0.04680044203996658,
0.018445953726768494,
0.026990452781319618,
0.0013860778417438269,
0.022233588621020317,
0.001108298427425325,
0.01610635221004486,
-0.0027298175264149904,
-0.06298268586397171,
0.022655822336673737,
0.023885566741228104,
0.022311381995677948,
0.0019448237726464868,
-0.016110539436340332,
0.04663849622011185,
-0.020607344806194305,
0.007442191243171692,
-0.0018992915283888578,
0.023583531379699707,
0.022485490888357162,
0.037963978946208954,
-0.006447792984545231,
0.02061469480395317,
-0.06382706016302109,
-0.008293936029076576,
0.014576366171240807,
-0.00876957830041647,
0.05621035769581795,
-0.0397789441049099,
0.023102719336748123,
-0.019961640238761902,
-0.00015090240049175918,
-0.07816404104232788,
-0.001191978924907744,
-0.019007667899131775,
0.0036645736545324326,
-0.01612217351794243,
0.03308557718992233,
0.007914843037724495,
-0.047955576330423355,
0.033030714839696884,
0.008522816002368927,
0.06584416329860687,
-0.05371905118227005,
0.02995442785322666,
0.0028264690190553665,
0.0028896417934447527,
-0.016630040481686592,
0.0012773096095770597
] |
<p>I am studying the global causality of the spacetime. Here, I come across a problem. </p>
<p>Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in spacetime. Then, it is claimed that $I^+(r)\subset I^+(p)$. But why? </p>
<p>Let me first try to prove this conclusion. I notice there is a theorem:</p>
<p>Let a subset $S\subset M$ ($M$ the spacetime manifold) and set $B=\partial I^+[S]$. Then, if $x\in B-\bar S$, there exists a null geodesic $\eta\subset B$ with future endpoint $x$ and which is either past-endless or has a past endpoint on $\bar S$.</p>
<p>So we can set $S=\{p\}=\bar S$. Since $r\in\partial I^+(p)$ and $r\ne p$, $r\in B-\{p\}$ with $B=\partial I^+(p)$. Therefore, there is a null geodesics $\eta$ lying on $B$ and passing through $p$. Is this correct? </p>
<p>Thank you! </p>
| 10,729 |
[
0.000819784530904144,
0.0038321809843182564,
0.0024541569873690605,
0.004737229086458683,
0.04086901992559433,
0.03361241891980171,
-0.020830705761909485,
-0.012044721283018589,
-0.007717642467468977,
-0.026397408917546272,
0.04198610782623291,
0.022094067186117172,
0.024591902270913124,
0.01364484429359436,
0.0061883823946118355,
0.012112235650420189,
-0.039354756474494934,
0.015554819256067276,
0.001362026552669704,
-0.014576022513210773,
0.023412542417645454,
0.0501810722053051,
0.013912498019635677,
-0.014139962382614613,
-0.02766467072069645,
-0.012700793333351612,
-0.0008652777760289609,
0.01047007367014885,
-0.03532976284623146,
0.06384052336215973,
-0.026902176439762115,
-0.04568345099687576,
-0.033631738275289536,
0.028707338497042656,
0.03345593065023422,
0.011408000253140926,
-0.053803201764822006,
-0.0362745001912117,
0.007458521984517574,
0.012124567292630672,
-0.030213918536901474,
-0.00045284017687663436,
-0.015229251235723495,
0.08050677180290222,
-0.02152973785996437,
0.02599472925066948,
0.004819797817617655,
0.02993353083729744,
0.03213472664356232,
-0.029752077534794807,
0.06305097788572311,
-0.02315167710185051,
0.03265243023633957,
-0.0019299433333799243,
-0.017478663474321365,
-0.043705206364393234,
0.06794525682926178,
0.06690790504217148,
0.0026464301627129316,
-0.032072409987449646,
-0.003390671918168664,
-0.009304452687501907,
0.00579129857942462,
-0.025525612756609917,
-0.04168775677680969,
0.007717869710177183,
-0.0005221825558692217,
0.0024815122596919537,
0.015406155958771706,
-0.06564144790172577,
-0.016512110829353333,
-0.012126653455197811,
-0.008283858187496662,
-0.005387443583458662,
-0.005301907192915678,
-0.018742099404335022,
0.01245028991252184,
0.0073542725294828415,
0.04481830447912216,
0.008290466852486134,
-0.027184095233678818,
0.008206825703382492,
0.033255256712436676,
0.02287505567073822,
0.031193872913718224,
-0.017105678096413612,
0.06455732136964798,
-0.005060282535851002,
0.0017569042975082994,
0.03949563205242157,
-0.02347307652235031,
-0.011630495078861713,
0.02764310874044895,
-0.028053581714630127,
-0.022419463843107224,
0.071025051176548,
-0.011593058705329895,
0.016048891469836235,
-0.01236705668270588,
0.010426889173686504,
-0.03220426291227341,
-0.06769276410341263,
-0.01608969457447529,
0.07979429513216019,
0.027510982006788254,
-0.01896487921476364,
-0.0386815182864666,
0.011484566144645214,
0.00445869704708457,
0.00269669434055686,
-0.06965998560190201,
0.025398045778274536,
0.006348755676299334,
0.014377657324075699,
0.0050189560279250145,
-0.04264959692955017,
-0.024092132225632668,
-0.033709753304719925,
-0.003228656481951475,
0.06665460765361786,
0.05462741106748581,
-0.0029776121955364943,
0.01989329420030117,
-0.024372631683945656,
-0.03806935250759125,
0.033097028732299805,
0.03632825240492821,
-0.010491041466593742,
0.0073127043433487415,
0.0010889465920627117,
0.043480440974235535,
-0.023195087909698486,
0.03965534642338753,
0.05564907193183899,
0.06291339546442032,
-0.012815442867577076,
-0.08008036762475967,
-0.03075059875845909,
0.02893039770424366,
-0.004894068464636803,
-0.0055426196195185184,
-0.0803181454539299,
0.006443812511861324,
0.010688688606023788,
0.10185877978801727,
0.011110498569905758,
0.017075728625059128,
0.025451665744185448,
0.053701069205999374,
0.035297710448503494,
-0.03338753804564476,
0.0032815737649798393,
-0.027002910152077675,
-0.01648048311471939,
0.009230509400367737,
-0.04743476212024689,
0.012318440712988377,
0.03236629441380501,
0.006484403274953365,
-0.04847085475921631,
0.09046483039855957,
-0.03160148486495018,
0.009029186330735683,
0.002734231296926737,
-0.012838774360716343,
-0.010576309636235237,
0.07254239916801453,
0.038493599742650986,
-0.00017454616317991167,
0.018831104040145874,
0.05318079888820648,
0.05718516185879707,
0.014586021192371845,
0.05283219367265701,
0.007975537329912186,
-0.0265783853828907,
-0.014329890720546246,
0.0064664785750210285,
-0.019968340173363686,
0.03043406829237938,
-0.02744259126484394,
-0.02371990866959095,
-0.03142973780632019,
-0.024656621739268303,
0.004917987156659365,
0.047692492604255676,
-0.001716517610475421,
0.007731516845524311,
0.003286323044449091,
-0.04884900897741318,
0.035849831998348236,
-0.059537556022405624,
0.01433483138680458,
0.040811024606227875,
-0.052742790430784225,
-0.014994042925536633,
-0.009466561488807201,
0.016687540337443352,
-0.030781155452132225,
-0.003419936867430806,
-0.005092445760965347,
0.020340995863080025,
0.004146324936300516,
-0.030267389491200447,
-0.010621453635394573,
0.03634151443839073,
0.031025540083646774,
0.018833691254258156,
0.022382458671927452,
-0.00664931396022439,
-0.002778143621981144,
0.04035628214478493,
0.007071474567055702,
0.017148332670331,
-0.03449665755033493,
-0.03877963498234749,
0.012298748828470707,
0.020992755889892578,
-0.011082847602665424,
0.030940979719161987,
-0.046989716589450836,
0.038582347333431244,
0.07248221337795258,
0.002224572468549013,
0.006820047274231911,
0.015726478770375252,
0.05385515093803406,
0.03268309682607651,
-0.012906861491501331,
-0.03307593613862991,
-0.025594143196940422,
-0.00815141573548317,
0.008235996589064598,
0.03937528654932976,
-0.02489214763045311,
0.03196099400520325,
0.0037210509181022644,
0.03261469304561615,
0.012004214338958263,
0.035357341170310974,
0.04022201523184776,
-0.0259085763245821,
0.03996500372886658,
-0.021765340119600296,
0.02496463991701603,
0.029611073434352875,
0.040669240057468414,
-0.03170838579535484,
0.015686839818954468,
-0.012214580550789833,
-0.018671002238988876,
0.04475284367799759,
-0.03468494117259979,
0.0040230113081634045,
0.039074089378118515,
-0.0017182505689561367,
0.015805799514055252,
-0.016034051775932312,
0.029319168999791145,
0.006520221941173077,
0.03821144253015518,
-0.02660035341978073,
-0.028998535126447678,
-0.005454321391880512,
0.012452970258891582,
-0.01326445396989584,
-0.015271466225385666,
-0.015414218418300152,
0.011909754015505314,
-0.021811796352267265,
0.005997462663799524,
0.011681427247822285,
0.0004685719613917172,
-0.03359334170818329,
-0.021979736164212227,
0.025836436077952385,
0.04554988443851471,
0.0056831915862858295,
-0.029650837182998657,
-0.012051020748913288,
0.020158154889941216,
-0.006718487944453955,
0.019305361434817314,
0.014840668998658657,
-0.03643907979130745,
0.033993445336818695,
-0.027534030377864838,
0.000557481893338263,
0.05038736015558243,
0.0016479759942740202,
-0.005425491835922003,
0.019580218940973282,
-0.023112701252102852,
-0.007031754124909639,
-0.029887180775403976,
-0.017584703862667084,
0.014014717191457748,
-0.030064759775996208,
-0.0019941716454923153,
0.05712061747908592,
0.06539887189865112,
-0.07671821117401123,
0.00321005005389452,
-0.032534632831811905,
-0.033200882375240326,
0.021274572238326073,
-0.050621211528778076,
-0.00903309229761362,
-0.061074402183294296,
-0.007538990583270788,
0.03363032266497612,
-0.023783108219504356,
0.0028706686571240425,
-0.03942769020795822,
-0.09527499228715897,
0.0309528149664402,
-0.007807218469679356,
-0.006918671540915966,
-0.013667155057191849,
-0.037593744695186615,
0.07185368984937668,
0.034198224544525146,
0.007778199389576912,
-0.027230575680732727,
0.014225579798221588,
0.03919684514403343,
0.0009014290990307927,
-0.006559074390679598,
-0.015005418099462986,
-0.016739243641495705,
0.011928834952414036,
0.04216094687581062,
0.07145936787128448,
0.030609140172600746,
0.022052837535738945,
0.004213196691125631,
-0.029182154685258865,
-0.0013954316964372993,
0.03140992298722267,
0.040443211793899536,
0.019010338932275772,
-0.0034020422026515007,
0.006157554220408201,
-0.027347823604941368,
0.037518519908189774,
0.010866962373256683,
-0.04042062163352966,
0.02531091310083866,
-0.02575269155204296,
0.03168376907706261,
0.033415406942367554,
0.03021164983510971,
-0.027127815410494804,
-0.023574208840727806,
-0.05430081486701965,
-0.021697521209716797,
0.05293279141187668,
-0.025012578815221786,
-0.0063039036467671394,
0.04501104727387428,
-0.0142052685841918,
-0.02980688400566578,
-0.006688552442938089,
-0.002481542294844985,
0.004746940452605486,
0.05082324147224426,
0.005140906665474176,
-0.033158160746097565,
0.05093342438340187,
0.060513343662023544,
-0.00917067751288414,
0.01795927621424198,
-0.025367429479956627,
-0.03211073949933052,
-0.05717635527253151,
0.014432145282626152,
-0.0013622026890516281,
0.03302394226193428,
-0.014098423533141613,
0.005826988723129034,
0.033105865120887756,
0.0068041556514799595,
-0.0002763683150988072,
0.016458487138152122,
-0.047368403524160385,
0.013113442808389664,
0.004008270800113678,
-0.01468079537153244,
-0.013551686890423298,
0.00011267967784078792,
0.010289555415511131,
-0.024461006745696068,
-0.02371101640164852,
0.012107913382351398,
-0.02474917843937874,
-0.08852683752775192,
0.009943615645170212,
-0.07456770539283752,
-0.014743959531188011,
-0.027144888415932655,
0.004845157265663147,
0.0559380017220974,
-0.021442782133817673,
0.021290792152285576,
0.03291556239128113,
-0.014271670021116734,
-0.02308153547346592,
-0.0065820785239338875,
0.0013938492629677057,
0.011539231054484844,
0.01751866564154625,
0.04848451539874077,
0.02556035667657852,
0.021900378167629242,
0.008134972304105759,
0.02506328374147415,
0.009787864983081818,
0.0005601522279903293,
-0.03075689636170864,
0.00959758274257183,
-0.043685849756002426,
-0.009635950438678265,
0.0029174601659178734,
0.0728256106376648,
0.02882903628051281,
-0.005020426586270332,
0.058105822652578354,
0.011112313717603683,
-0.00940428115427494,
0.047459255903959274,
0.03387497365474701,
0.026787469163537025,
-0.0008470059838145971,
-0.04616330936551094,
-0.018566101789474487,
-0.009116767905652523,
0.013075963594019413,
-0.00027354410849511623,
-0.006270125042647123,
-0.029544811695814133,
-0.019557349383831024,
-0.019973082467913628,
-0.0003197342739440501,
0.00036058545811101794,
0.016408516094088554,
0.0038188255857676268,
0.007234952412545681,
0.044254858046770096,
0.013355535455048084,
0.012425599619746208,
0.040346115827560425,
0.06152546405792236,
0.05966293811798096,
0.010429035872220993,
-0.06796585768461227,
-0.0017196808476001024,
-0.0012642483925446868,
0.0013926186366006732,
-0.03062819130718708,
-0.027573775500059128,
-0.075149767100811,
-0.01587068662047386,
0.036667656153440475,
-0.008880913257598877,
0.031331975013017654,
0.027430662885308266,
-0.00166810373775661,
-0.02414562553167343,
-0.05531968176364899,
0.0011827019043266773,
0.02215678058564663,
-0.011927214451134205,
0.04558679834008217,
-0.0077904341742396355,
0.00936021190136671,
-0.04171108081936836,
0.018023591488599777,
0.01641485095024109,
0.045553434640169144,
0.024418558925390244,
0.01927902363240719,
0.0011676909634843469,
0.04301724582910538,
-0.02894965186715126,
-0.05071025714278221,
0.06245936453342438,
0.028005732223391533,
-0.0551295205950737,
0.0336548313498497,
-0.04744939133524895,
-0.006963225547224283,
0.025099175050854683,
0.014532797038555145,
-0.013358447700738907,
0.028124306350946426,
-0.0502828024327755,
0.012604598887264729,
-0.0005426496500149369,
0.010000977665185928,
0.04371517524123192,
0.01417289674282074,
0.011245653964579105,
-0.008223279379308224,
-0.021135695278644562,
0.034976303577423096,
-0.033847175538539886,
-0.0023188372142612934,
-0.003950888756662607,
-0.013591237366199493,
-0.0119920764118433,
0.021023167297244072,
-0.01636515185236931,
-0.036621544510126114,
-0.0034597953781485558,
-0.027231339365243912,
0.01799057424068451,
0.056561198085546494,
0.016740038990974426,
0.009310265071690083,
-0.00022285323939286172,
0.011183763854205608,
0.02439155802130699,
-0.0017472509061917663,
0.01159959752112627,
-0.003511493792757392,
-0.011034373193979263,
0.025279127061367035,
0.004172145389020443,
0.014308207668364048,
-0.036878861486911774,
-0.01672349125146866,
-0.012676572427153587,
-0.040137216448783875,
-0.011048749089241028,
-0.00885305181145668,
-0.021846462041139603,
0.042075514793395996,
-0.027597475796937943,
-0.0133814737200737,
-0.02604561857879162,
-0.0410890094935894,
-0.04014987871050835,
-0.08703536540269852,
-0.00439556734636426,
0.0502406544983387,
0.02223493903875351,
-0.09225297719240189,
-0.042431894689798355,
0.0300917811691761,
0.005857297219336033,
-0.04523907229304314,
-0.008328983560204506,
0.028898635879158974,
-0.05764130875468254,
-0.007330626714974642,
-0.03102019615471363,
0.04657455533742905,
-0.04732048511505127,
-0.04535318911075592,
0.005403598304837942,
0.051552239805459976,
0.004665304906666279,
-0.03012467548251152,
0.018693923950195312,
0.035435546189546585,
-0.020737167447805405,
-0.0009723145631141961,
-0.04392358288168907,
0.03964846953749657,
-0.00930821243673563,
0.002316375495865941,
0.001244064187631011,
0.002028349321335554,
0.0020797564648091793,
-0.010333450511097908,
-0.04622369259595871,
0.0032536752987653017,
0.00961979664862156,
0.012005604803562164,
-0.016305478289723396,
-0.005412257742136717,
0.008921637199819088,
-0.028617771342396736,
-0.02156202308833599,
0.03224879503250122,
0.025425467640161514,
-0.08636277914047241,
0.03270556405186653,
-0.028318243101239204,
-0.03176676854491234,
0.0024297363124787807,
0.0489329993724823,
0.007698983885347843,
-0.002155974507331848,
0.0062675452791154385,
0.006489294581115246,
-0.005833338014781475,
0.020515255630016327,
-0.0028485958464443684,
0.0075980136170983315,
-0.012524602934718132,
-0.06192401051521301,
-0.006647941656410694,
-0.043950214982032776,
0.05809265002608299,
0.057003844529390335,
-0.021759193390607834,
0.019497308880090714,
0.0013473840663209558,
-0.005816672928631306,
-0.0029468336142599583,
-0.024683808907866478,
0.003296488896012306,
0.0064248451963067055,
0.005640826188027859,
0.02048187330365181,
-0.06337155401706696,
-0.0253312848508358,
0.05032984912395477,
0.05266755074262619,
-0.049493808299303055,
-0.008150334469974041,
0.0007229641196317971,
-0.0172258410602808,
0.04486588016152382,
-0.008714786730706692,
-0.012386750429868698,
0.037212666124105453,
-0.03238219395279884,
0.0012924550101161003,
-0.016953114420175552,
-0.023732449859380722,
0.020857052877545357,
0.016991261392831802,
0.03321930766105652,
-0.01599648781120777,
-0.0300266332924366,
-0.04397186264395714,
0.006022750400006771,
0.03874675929546356,
0.054731640964746475,
0.017867648974061012,
-0.018227210268378258,
0.03227357566356659,
0.006699326913803816,
0.019328497350215912,
-0.010863407514989376,
-0.013306446373462677,
-0.032021619379520416,
-0.06919193267822266,
-0.03197896108031273,
0.037121765315532684,
0.01580909825861454,
0.00233041075989604,
-0.018187621608376503,
-0.010450725443661213,
-0.002950004767626524,
0.008161470293998718,
0.05692711099982262,
-0.00791194848716259,
0.07472196221351624,
0.005563286133110523,
0.024133894592523575,
0.010531555861234665,
0.013386343605816364,
0.1105721965432167,
0.06736896932125092,
0.01612236723303795,
-0.06392205506563187,
0.01857283152639866,
0.01117686927318573,
-0.02489597350358963,
-0.06890039891004562,
0.04240870475769043,
-0.0031185117550194263,
-0.0358864963054657,
0.012042314745485783,
0.06391378492116928,
0.0087876683101058,
-0.035564955323934555,
0.04433348402380943,
-0.0413377471268177,
-0.05886262655258179,
-0.014932682737708092,
0.0018248350825160742,
-0.0001074769243132323,
-0.031570401042699814,
-0.02886214479804039,
0.03805778548121452,
-0.014827489852905273,
-0.012271430343389511,
-0.029626987874507904,
-0.016157057136297226,
-0.014849279075860977,
-0.0018178981263190508,
-0.024387814104557037,
-0.011331749148666859,
0.025476444512605667,
0.008959597907960415,
-0.023134632036089897,
-0.0014355158200487494,
0.011333636939525604,
0.006669983733445406,
0.06223071739077568,
0.049580059945583344,
-0.008654121309518814,
0.017725739628076553,
0.03690079599618912,
0.04870535060763359,
-0.03591867536306381,
-0.018455469980835915,
-0.020880606025457382,
0.06031571328639984,
-0.023943396285176277,
0.012484332546591759,
-0.017770232632756233,
-0.015561877749860287,
0.028627021238207817,
-0.05863092094659805,
-0.028349991887807846,
0.016164997592568398,
-0.0028261395636945963,
0.022386152297258377,
0.013065623119473457,
0.012905829586088657,
0.021307645365595818,
0.0159392561763525,
-0.00023179393610917032,
-0.021521979942917824,
-0.0012534799752756953,
0.029013268649578094,
-0.02652025781571865,
0.025371775031089783,
0.000847287243232131,
0.01449646707624197,
-0.009290501475334167,
-0.021073242649435997,
-0.05147908255457878,
-0.02905469387769699,
0.017115749418735504,
-0.004063136409968138,
0.0293030496686697,
-0.001104796421714127,
-0.028746996074914932,
-0.015856489539146423,
-0.03873845934867859,
0.004877571947872639,
-0.028599530458450317,
-0.03746125474572182,
-0.017484137788414955,
0.011940926313400269,
0.0017523779533803463,
0.04218870401382446,
-0.034919992089271545,
-0.0001657764514675364,
-0.017599357292056084,
0.05262499675154686,
-0.015960289165377617,
-0.008487234823405743,
-0.032209206372499466,
-0.009346839971840382,
-0.02519015595316887,
0.01937670074403286,
-0.024166561663150787,
-0.006761319003999233,
-0.00363137386739254,
0.02673187665641308,
0.03659076243638992,
0.0432240255177021,
-0.020989276468753815,
-0.013207506388425827,
0.03234213590621948,
-0.0323919877409935,
0.011295920237898827,
0.03339812532067299,
0.055857278406620026,
-0.0783010870218277,
-0.023266496136784554,
0.01302554365247488,
0.016023114323616028,
0.02548951655626297,
-0.048683010041713715,
-0.017101837322115898,
0.012147901579737663,
0.010584494099020958,
-0.024705668911337852,
-0.037633828818798065,
-0.01765602082014084,
-0.07034660875797272,
-0.006274734623730183,
0.0033119095023721457,
-0.035373080521821976,
-0.0016374451806768775,
0.004516703076660633,
-0.01961434632539749,
-0.03346753120422363,
-0.0014713570708408952,
0.016025220975279808,
-0.027912097051739693,
0.004498430527746677,
0.050565846264362335,
0.019414111971855164,
0.04718628153204918,
0.0034369120839983225,
-0.04692826420068741,
-0.001858103321865201,
-0.03480711951851845,
-0.06422803550958633,
0.019349899142980576,
0.03465288504958153,
0.0036350758746266365,
0.022902974858880043,
-0.021109191700816154,
-0.011687129735946655,
0.04156605899333954,
0.0012443355517461896,
-0.02701515518128872,
0.002589643467217684,
-0.030937308445572853,
-0.006703925784677267,
-0.0011819994542747736,
0.018450748175382614,
0.014332352206110954,
0.02733556553721428,
-0.0376620888710022,
0.026328152045607567,
0.0005231459508650005,
-0.02440243773162365,
0.023795805871486664,
-0.03244762495160103,
0.010839605703949928,
-0.004589130636304617,
-0.0202396921813488,
0.008339461870491505,
0.05514713004231453,
-0.03514069691300392,
-0.007313102018088102,
0.038590434938669205,
-0.014603500254452229,
-0.06403076648712158,
0.00017026669229380786,
0.013556525111198425,
0.01186180766671896,
0.03859814628958702,
-0.03049170970916748,
0.01767563633620739,
0.022941386327147484,
-0.04133991524577141,
0.012025298550724983,
-0.02374638430774212,
0.010545941069722176,
-0.05392530933022499,
0.0006624080124311149,
-0.06150366738438606,
0.053334176540374756,
0.08185965567827225,
0.06960882246494293,
-0.00003992797792307101,
-0.021046174690127373,
-0.00914610642939806,
-0.06170130521059036,
-0.03345185145735741,
-0.003285950981080532,
-0.02706187590956688,
-0.022456973791122437,
0.0722445547580719,
0.01443271990865469,
-0.03980349749326706,
0.01928282342851162,
0.010079750791192055,
-0.0030277306213974953,
0.0002709423715714365,
0.016074737533926964,
0.03523852303624153,
-0.01315065287053585,
0.04114314913749695,
-0.005174025893211365,
-0.001198143814690411,
0.02297477051615715,
0.008059391751885414,
0.033917490392923355,
-0.03568065166473389,
0.023583512753248215,
0.00546726118773222,
-0.037364814430475235,
0.006451260298490524,
-0.004898711573332548,
-0.03302307426929474,
-0.0465657040476799,
0.02864815667271614,
0.007821994833648205,
-0.011844193562865257,
-0.014399699866771698,
-0.0030225482769310474,
-0.009625907056033611,
-0.00314253824763,
0.07776328176259995,
0.0006833065417595208,
-0.011485211551189423,
0.010788136161863804,
-0.04068756476044655,
-0.07253073155879974,
0.02027801238000393,
0.015773363411426544,
0.016260340809822083,
-0.041953910142183304,
-0.018825478851795197,
-0.03954723849892616,
-0.024500276893377304,
-0.03351396322250366,
-0.010466224513947964,
-0.021278895437717438,
0.0386904813349247,
0.037649501115083694,
0.016665861010551453,
-0.02148975059390068,
-0.03755052760243416,
-0.004627288319170475,
-0.037083934992551804,
0.020238686352968216,
-0.005448035895824432,
-0.003222342114895582,
-0.0376056469976902,
-0.02746230736374855,
-0.00767091428861022,
0.015554273501038551,
0.06075235828757286,
-0.07358359545469284,
0.010377977974712849,
0.0794815719127655,
0.02609998732805252,
0.042720694094896317,
-0.01308863889425993,
0.008466288447380066,
0.008541597053408623,
-0.023994507268071175,
-0.005584872793406248,
-0.005958667024970055,
0.00046204341924749315,
0.021941697224974632,
0.009065556339919567,
0.00995276402682066,
0.039982449263334274,
0.036320675164461136,
-0.04241910204291344,
0.009355030953884125,
0.02304304949939251,
0.024721890687942505,
0.057022228837013245,
0.0385686457157135,
0.021324237808585167,
0.04306689649820328,
-0.03885165974497795,
-0.041649945080280304,
-0.006422310136258602,
-0.01771077699959278,
-0.020126745104789734,
-0.015551249496638775,
-0.04610171169042587,
-0.011340226978063583,
-0.023163801059126854,
-0.029457541182637215,
0.06001674756407738,
-0.03060324862599373,
-0.009599093347787857,
0.03913784399628639,
-0.029552139341831207,
0.0036665210500359535,
0.017325785011053085,
-0.0014741505729034543,
0.03621219843626022,
0.012444613501429558,
0.057551272213459015,
0.035985466092824936,
0.018332762643694878,
-0.027262171730399132,
0.006682512816041708,
0.028945326805114746,
0.005704598501324654,
-0.006093774922192097,
-0.01966685988008976,
0.07220225036144257,
-0.02530660480260849,
-0.0054367920383811,
0.01484477799385786,
0.008406816981732845,
0.021061010658740997,
0.021411485970020294,
-0.009687935002148151,
0.04974442347884178,
-0.052513767033815384,
0.01813383586704731,
-0.02526618354022503,
-0.002179725095629692,
-0.014742421917617321,
0.010526143945753574,
0.008376921527087688,
0.015387939289212227,
0.007422946393489838,
-0.03407995030283928,
0.011013689450919628,
-0.014540400356054306,
0.013637193478643894,
-0.04245628044009209,
-0.010379700921475887,
0.027198977768421173,
-0.02867809869349003,
-0.01565994694828987,
-0.03630996122956276,
-0.019491637125611305,
-0.03835318982601166,
0.011935618706047535,
0.01482329796999693,
0.020819421857595444,
-0.01607137732207775,
0.011431343853473663,
-0.06340348720550537,
0.06441735476255417,
-0.10293134301900864,
0.0035507366992533207,
-0.015890486538410187,
0.012279949150979519,
-0.033040329813957214,
0.0375068299472332
] |
<p>One often comes across news articles that claim that an earthquake shifted the earth's axis.</p>
<blockquote>
<p><a href="http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis">http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis</a></p>
</blockquote>
<p>If you ignore the influence of other celestial bodies, an internal event like an earthquake surely can't change the direction of the angular momentum of the Earth (unless stuff is ejected out of Earth), since angular momentum has to be conserved in the absence of an external torque. So the axis has to remain fixed.</p>
<p>Am I missing something? Or are geologists trying to say that the resulting movement of tectonic plates causes a change in the point of intersection of the axis (which remains the same) and the plates that include the poles, so that it <em>seems</em> as if the axis has shifted?</p>
<p><strong>EDIT</strong>
Some articles mention the value of the shift in the axis and also the change in the length of the day. If, as Ted Bunn's answer indicates below, the shift in the axis isn't actually real but is because of the movement of tectonic plates with respect to the axis, shouldn't the shift be different at the north and south poles? How are the shifts and the change in day-length calculated?</p>
| 10,730 |
[
-0.030622901394963264,
-0.028370678424835205,
-0.020925866439938545,
-0.0030648072715848684,
0.06975943595170975,
0.024885842576622963,
-0.02107548527419567,
-0.010100004263222218,
0.011939557269215584,
-0.03183365613222122,
-0.014804676175117493,
0.03446664661169052,
0.019281921908259392,
0.029985036700963974,
0.014205040410161018,
0.00891841109842062,
0.017657827585935593,
0.0025325980968773365,
-0.007877267897129059,
-0.036535847932100296,
-0.005155791994184256,
0.0024756179191172123,
-0.01873030699789524,
0.027074988931417465,
0.027661940082907677,
0.032237209379673004,
0.04340174421668053,
-0.00914679653942585,
0.03491709753870964,
0.059335269033908844,
0.013856825418770313,
-0.014499763026833534,
-0.014992992393672466,
0.01889968104660511,
0.0215739905834198,
-0.014040104113519192,
-0.012489721179008484,
-0.040747154504060745,
0.008453047834336758,
0.06924047321081161,
-0.04831010475754738,
-0.0009301924728788435,
-0.03404012694954872,
0.05666560307145119,
-0.04803500697016716,
0.06173696368932724,
-0.020607471466064453,
0.006767577957361937,
0.047781966626644135,
-0.031923238188028336,
0.056767359375953674,
-0.05105704069137573,
0.014506436884403229,
0.02474086731672287,
-0.02527228184044361,
0.003917334601283073,
0.07131761312484741,
0.02133786492049694,
-0.024525422602891922,
-0.06682789325714111,
-0.0499897301197052,
-0.01783539168536663,
0.018373269587755203,
-0.03282446414232254,
0.00446146447211504,
0.01607607863843441,
-0.013217608444392681,
-0.017544422298669815,
0.013282902538776398,
-0.003899569623172283,
-0.004283768590539694,
0.033731285482645035,
-0.00956741627305746,
-0.014003992080688477,
0.00220980541780591,
-0.07602269947528839,
0.031085314229130745,
0.04378214478492737,
0.03038218803703785,
0.014083127491176128,
0.01297059841454029,
0.006634766701608896,
0.06286714226007462,
0.007199033163487911,
0.03867001086473465,
0.0301629938185215,
0.04410651698708534,
-0.004994302522391081,
0.04508453607559204,
0.01634535752236843,
0.026469359174370766,
0.012562524527311325,
0.0027810886967927217,
-0.0696290135383606,
0.014820313081145287,
0.033848877996206284,
0.031514547765254974,
0.04479064792394638,
0.013322263024747372,
0.0002460354007780552,
0.017221007496118546,
-0.038356903940439224,
0.018510859459638596,
0.02839639224112034,
0.03848419338464737,
0.01706603169441223,
-0.032330941408872604,
-0.01845141313970089,
-0.02602674812078476,
-0.004237039014697075,
-0.03760630637407303,
0.004765868652611971,
-0.005438447929918766,
-0.012176180258393288,
0.028555767610669136,
-0.012426681816577911,
-0.002107786713168025,
-0.007125288713723421,
0.0346723236143589,
0.04827214777469635,
0.041121646761894226,
-0.034234605729579926,
-0.00032918015494942665,
-0.05209966376423836,
-0.0778178796172142,
-0.01719786785542965,
0.01779901795089245,
-0.009420945309102535,
-0.03852630779147148,
0.029241764917969704,
0.052668847143650055,
0.0013780309818685055,
-0.015660805627703667,
-0.04277796670794487,
0.029642652720212936,
0.0391983725130558,
-0.11615364253520966,
-0.06294731050729752,
0.07283810526132584,
0.04248944669961929,
-0.04637047275900841,
-0.06921159476041794,
-0.023013347759842873,
-0.0150893684476614,
0.08869441598653793,
0.005593009293079376,
0.04993871971964836,
0.002326294779777527,
0.031144900247454643,
-0.017844686284661293,
-0.016045410186052322,
0.001600379589945078,
0.0493653230369091,
-0.06443499028682709,
-0.006262714974582195,
-0.08140257000923157,
0.01899285800755024,
0.02963104471564293,
0.003967524506151676,
0.002871435135602951,
0.016650786623358727,
0.011730033904314041,
0.013525184243917465,
0.0006023754249326885,
-0.021739497780799866,
-0.03808603435754776,
0.0735764428973198,
0.0075384643860161304,
-0.04238288477063179,
0.048539116978645325,
0.012226281687617302,
0.02600076235830784,
0.015805743634700775,
0.03311638534069061,
0.004755369387567043,
-0.04784289374947548,
-0.013527208007872105,
0.007219734136015177,
-0.010113152675330639,
-0.006728649139404297,
-0.016720667481422424,
-0.00041599999531172216,
0.00027972020325250924,
0.006685799919068813,
-0.0017600830178707838,
0.0876818299293518,
-0.018476592376828194,
-0.010775850154459476,
0.017482073977589607,
-0.05626104027032852,
-0.026344813406467438,
-0.021869083866477013,
0.02994137816131115,
-0.02508673444390297,
0.02611042745411396,
0.0030221513006836176,
-0.0018158225575461984,
0.02507803775370121,
-0.03166835010051727,
0.0155381690710783,
0.024115052074193954,
0.057982027530670166,
0.010312593542039394,
-0.04212241247296333,
0.004233194515109062,
0.08350305259227753,
0.05508517101407051,
0.007955528795719147,
-0.0051713972352445126,
-0.013337510637938976,
-0.02733919769525528,
0.02785392664372921,
-0.034347835928201675,
-0.0007530192960985005,
0.015814289450645447,
-0.003238957840949297,
-0.04351828619837761,
0.037957802414894104,
-0.0018823816208168864,
0.007244795560836792,
-0.018157126381993294,
0.0821714773774147,
0.04092340171337128,
-0.03394537419080734,
0.02491498552262783,
0.048903170973062515,
0.053686074912548065,
0.012633522972464561,
0.006047246977686882,
-0.04546307027339935,
-0.060121092945337296,
-0.020677262917160988,
0.02967550791800022,
0.014698035083711147,
-0.016737518832087517,
0.03458588942885399,
0.02864711917936802,
0.07789973169565201,
-0.03354145213961601,
-0.007768759038299322,
0.0013595519121736288,
-0.046171803027391434,
-0.023196034133434296,
-0.01802651956677437,
0.015948379412293434,
0.03079848177731037,
0.019263790920376778,
-0.008402195759117603,
0.01778278313577175,
-0.02561228908598423,
-0.00987412128597498,
0.016111884266138077,
-0.008505665697157383,
0.047850631177425385,
0.012015299871563911,
-0.016187544912099838,
0.0418923944234848,
-0.023067444562911987,
0.013661909848451614,
0.004437126684933901,
-0.003433492500334978,
0.0015330980531871319,
-0.029894277453422546,
-0.004323896951973438,
-0.0032078418880701065,
-0.006479619536548853,
-0.016863346099853516,
-0.013743264600634575,
0.02493296004831791,
-0.04959540441632271,
-0.025365309789776802,
-0.01280030608177185,
-0.020595302805304527,
0.017565667629241943,
-0.0038739230949431658,
0.01522624772042036,
0.027626777067780495,
0.007836757227778435,
-0.004530110862106085,
-0.004407977685332298,
0.008536100387573242,
-0.013851180672645569,
-0.008942430838942528,
0.02861320599913597,
-0.054002463817596436,
0.059172432869672775,
-0.035538267344236374,
-0.004554283805191517,
0.039137616753578186,
-0.009188610129058361,
0.031839028000831604,
0.03352513909339905,
0.011341528035700321,
-0.034076135605573654,
-0.00047697467380203307,
-0.026457449421286583,
-0.008253401145339012,
-0.03461770340800285,
-0.014353081583976746,
0.062113940715789795,
-0.02669503167271614,
-0.0010834007989615202,
0.0009965309873223305,
-0.0540873184800148,
-0.0242986511439085,
-0.011207069270312786,
0.03395923972129822,
0.019305460155010223,
-0.028309393674135208,
-0.001436184742487967,
-0.01587480865418911,
-0.03628786653280258,
-0.021463138982653618,
-0.012354277074337006,
-0.0683014988899231,
0.007678327150642872,
-0.03623518347740173,
0.029232053086161613,
-0.007261826191097498,
-0.040501564741134644,
0.0773584395647049,
0.02012772299349308,
-0.056500598788261414,
-0.002596623729914427,
0.04957226663827896,
-0.00295994128100574,
-0.012561610899865627,
-0.004853865597397089,
0.017192862927913666,
0.028444278985261917,
0.03725498914718628,
0.029039816930890083,
0.034792713820934296,
0.001954552484676242,
0.06762296706438065,
-0.01801830716431141,
0.015465050004422665,
0.012504464946687222,
-0.005342595279216766,
-0.010455833747982979,
0.020235223695635796,
0.0038471072912216187,
-0.00522764353081584,
-0.025574717670679092,
0.021431872621178627,
0.012035404331982136,
-0.06408301740884781,
0.03693421557545662,
-0.008290663361549377,
-0.000900894170626998,
-0.03469133749604225,
0.03992290794849396,
0.002997618168592453,
0.05407710745930672,
-0.010660638101398945,
0.018067486584186554,
0.04617970809340477,
0.018467320129275322,
-0.010945480316877365,
0.027595829218626022,
0.04143507778644562,
-0.003997760824859142,
-0.011095202527940273,
-0.024517638608813286,
0.04147341102361679,
0.03568926453590393,
-0.04173901677131653,
-0.022615797817707062,
0.03626937419176102,
0.03386499732732773,
0.022071365267038345,
0.010039949789643288,
-0.03996869921684265,
0.012385164387524128,
-0.046634186059236526,
0.027651993557810783,
-0.002792299259454012,
0.012856245040893555,
0.0008166650077328086,
0.027392718940973282,
0.027943512424826622,
0.02041272073984146,
0.004861848428845406,
0.007533209398388863,
-0.07555488497018814,
0.029270052909851074,
-0.06784640997648239,
-0.03812886402010918,
-0.004606365226209164,
-0.021720631048083305,
-0.00007808375085005537,
0.005583202466368675,
0.007915700785815716,
-0.05969368666410446,
-0.004818831570446491,
-0.07517420500516891,
-0.011723961681127548,
0.02156917192041874,
-0.03328067064285278,
-0.017390916123986244,
0.03245997428894043,
0.06670543551445007,
-0.043064702302217484,
0.025020413100719452,
0.05386807397007942,
-0.00967859011143446,
-0.0046068644151091576,
-0.01892302930355072,
0.013485165312886238,
0.017501402646303177,
0.001643377123400569,
-0.0036595985293388367,
0.0024267795961350203,
-0.013513771817088127,
0.03825945407152176,
0.027699237689375877,
0.03012026473879814,
-0.0008081492851488292,
-0.004335637670010328,
-0.023027773946523666,
-0.039575763046741486,
0.005953515414148569,
0.01617133803665638,
0.04270413890480995,
-0.022651853039860725,
0.018140971660614014,
0.0500788576900959,
0.02415713295340538,
-0.010119704529643059,
0.026989156380295753,
0.04536380246281624,
0.01563955470919609,
0.010752263478934765,
-0.055415526032447815,
-0.045674990862607956,
-0.032475415617227554,
-0.02201210893690586,
0.008154826238751411,
-0.010031337849795818,
-0.010329537093639374,
0.0006829915218986571,
0.01332075148820877,
0.006899720523506403,
0.002614484168589115,
-0.005794363562017679,
0.011747586540877819,
0.013070180080831051,
0.004544929601252079,
0.02904506027698517,
0.02458197996020317,
0.0148394163697958,
0.03600520268082619,
-0.009535827673971653,
-0.021083271130919456,
-0.07758637517690659,
-0.01404532603919506,
0.01547960564494133,
0.04685702174901962,
-0.023811718448996544,
-0.02506949193775654,
-0.051637545228004456,
-0.018741434440016747,
0.03713062033057213,
-0.039873406291007996,
0.024996990337967873,
-0.03352119028568268,
0.025672610849142075,
0.006308852229267359,
-0.019461533054709435,
-0.012129193171858788,
-0.004275279585272074,
0.010414338670670986,
0.04381395876407623,
-0.014313715510070324,
-0.008039883337914944,
-0.013277284801006317,
-0.013606901280581951,
0.0535116009414196,
-0.0008967320318333805,
0.01944362185895443,
-0.023634281009435654,
-0.05048781633377075,
0.019657298922538757,
-0.018880361691117287,
-0.06722402572631836,
-0.02153516374528408,
0.022885488346219063,
-0.045793287456035614,
0.01810714788734913,
0.007793202064931393,
-0.050962306559085846,
0.024732399731874466,
-0.006746676750481129,
0.004959724843502045,
-0.0018648372497409582,
-0.051170676946640015,
0.02772587537765503,
0.011428040452301502,
-0.004173208028078079,
0.02615940570831299,
0.04797346517443657,
-0.015099282376468182,
0.012703885324299335,
-0.023936724290251732,
0.026026379317045212,
-0.032234396785497665,
0.01576613076031208,
0.026329604908823967,
0.0380605086684227,
-0.006271603982895613,
0.02616659365594387,
0.005931192543357611,
0.0023214903194457293,
-0.0312734991312027,
-0.03336719051003456,
-0.003803153755143285,
0.009063619188964367,
0.0031404101755470037,
0.017286159098148346,
-0.008224640041589737,
0.023775948211550713,
0.013724541291594505,
-0.01697925291955471,
0.015741297975182533,
-0.016463827341794968,
-0.014348650351166725,
0.021516865119338036,
0.01429890189319849,
0.004384963307529688,
-0.027224872261285782,
-0.045610200613737106,
0.01816861890256405,
-0.03616367280483246,
0.01632559671998024,
-0.01655310019850731,
-0.009379938244819641,
0.013289482332766056,
-0.055612970143556595,
-0.019083360210061073,
0.0022189635783433914,
0.022552654147148132,
0.024228092283010483,
-0.05517034977674484,
0.011311407200992107,
0.038931410759687424,
0.03557853773236275,
-0.07416647672653198,
-0.06194703280925751,
0.041196390986442566,
0.028689997270703316,
-0.011292921379208565,
0.0004635935474652797,
-0.014350091107189655,
-0.02654290571808815,
-0.02094724029302597,
-0.032018449157476425,
0.042237214744091034,
-0.0036227561067789793,
-0.012123849242925644,
0.027239985764026642,
-0.0037979211192578077,
0.06861451268196106,
-0.04096255823969841,
-0.007762214168906212,
-0.007908928208053112,
-0.03002599999308586,
-0.00009227484406437725,
-0.025810249149799347,
0.0773434117436409,
-0.04811619594693184,
-0.064366914331913,
0.007445049472153187,
-0.0061841364949941635,
-0.000986507162451744,
0.023173613473773003,
-0.008928207680583,
0.051217056810855865,
-0.012120201252400875,
-0.00681098410859704,
-0.02066100761294365,
0.04197118058800697,
0.005772889591753483,
0.0002748191182035953,
-0.015343936160206795,
0.010053128935396671,
-0.0002972442889586091,
-0.04939119145274162,
-0.030405402183532715,
0.014493273571133614,
0.007942751049995422,
0.010181104764342308,
0.023065244778990746,
-0.0029261112213134766,
-0.0017111380584537983,
0.011255034245550632,
-0.002963757375255227,
0.05184977874159813,
0.0077537898905575275,
0.008678240701556206,
0.0031245683785527945,
0.002891007112339139,
-0.009870626032352448,
-0.02680184319615364,
-0.013958396390080452,
0.04993204027414322,
0.0746244266629219,
-0.009066603146493435,
0.03037804737687111,
0.018605545163154602,
0.010149294510483742,
-0.00031057122396305203,
-0.04110397771000862,
0.02821333333849907,
-0.005947687663137913,
-0.03256453573703766,
0.03086313046514988,
-0.060366708785295486,
-0.004098557401448488,
0.027268197387456894,
0.0444759801030159,
-0.029692308977246284,
0.015928860753774643,
0.020394790917634964,
0.02157706208527088,
-0.005554190371185541,
-0.0007030878914520144,
-0.06331891566514969,
0.01191685814410448,
-0.01727181300520897,
0.0412478968501091,
0.02492605522274971,
0.001255291048437357,
0.03768990933895111,
-0.023437611758708954,
-0.01562846079468727,
-0.04765559360384941,
-0.002747568767517805,
-0.05968058854341507,
-0.0036016374360769987,
-0.022503715008497238,
0.017892254516482353,
-0.013342678546905518,
-0.029448093846440315,
0.05177079886198044,
-0.021586734801530838,
-0.013353188522160053,
-0.035576410591602325,
-0.0860767811536789,
-0.0287027508020401,
0.0011967686004936695,
-0.08404401689767838,
0.0533263273537159,
-0.0327632762491703,
-0.012565234676003456,
0.013510123826563358,
-0.03848890960216522,
-0.008972587063908577,
0.044364165514707565,
0.0437711738049984,
-0.05802469700574875,
0.10256171226501465,
-0.0405699759721756,
-0.004740126430988312,
-0.00974336639046669,
0.0008203177130781114,
0.11629437655210495,
0.06293191015720367,
-0.0007414211286231875,
-0.019783543422818184,
0.06453634798526764,
-0.03973865136504173,
-0.01797384023666382,
-0.01835794374346733,
-0.0315762460231781,
-0.0006739516975358129,
0.012471899390220642,
0.01829749532043934,
0.04834901541471481,
0.0138974878937006,
-0.06828222423791885,
0.03171028941869736,
-0.03165490925312042,
-0.03225746378302574,
-0.01068900991231203,
0.006400994025170803,
-0.024709023535251617,
-0.04212743788957596,
-0.04610027000308037,
0.0006883400492370129,
-0.030440254136919975,
-0.015607462264597416,
0.008350890129804611,
-0.05189170688390732,
-0.003780139610171318,
0.027074960991740227,
-0.06864765286445618,
0.03104991279542446,
0.0217867624014616,
-0.014629988931119442,
-0.05390152707695961,
0.02718040719628334,
0.02365146391093731,
-0.006191418506205082,
0.04072850942611694,
0.007790680509060621,
-0.03603377565741539,
-0.012129345908761024,
0.017239468172192574,
0.02678610570728779,
-0.046901993453502655,
-0.03203760087490082,
-0.04978274181485176,
-0.00007475734309991822,
0.03580380603671074,
-0.01558268629014492,
0.009628448635339737,
0.004898484330624342,
-0.006659900303930044,
-0.06295473873615265,
0.011093422770500183,
0.010960833169519901,
0.013503373600542545,
-0.0020029530860483646,
-0.014503992162644863,
0.03281129151582718,
0.016708752140402794,
0.015999270603060722,
0.038954004645347595,
0.014812570065259933,
0.01920546032488346,
-0.010326961055397987,
0.01684759557247162,
0.03809336945414543,
0.010554704815149307,
-0.006751616485416889,
-0.02649291791021824,
0.01442401111125946,
-0.039440326392650604,
0.00935114361345768,
0.03245863318443298,
0.0036502548027783632,
0.01792917028069496,
0.0181653443723917,
-0.00936096254736185,
-0.004781573079526424,
0.013237081468105316,
0.030570125207304955,
0.014642365276813507,
-0.03971867635846138,
-0.021021608263254166,
0.030417993664741516,
0.03883982077240944,
0.007060907781124115,
-0.0014469815650954843,
0.024226706475019455,
-0.042901042848825455,
0.009368074126541615,
0.026611633598804474,
-0.021694060415029526,
-0.028063109144568443,
0.03718041628599167,
-0.017678488045930862,
-0.032004714012145996,
-0.006530937273055315,
0.024809997528791428,
0.07233507931232452,
-0.018200213089585304,
0.00425930880010128,
0.028977565467357635,
-0.022238673642277718,
0.0233507938683033,
0.009920396842062473,
-0.023269450291991234,
-0.03667840734124184,
0.0430450402200222,
-0.03941963613033295,
-0.02991417422890663,
-0.030125392600893974,
0.003163854591548443,
0.008288315497338772,
0.02626003883779049,
0.028534213081002235,
-0.059310562908649445,
0.03182869032025337,
-0.05047469958662987,
0.030223803594708443,
-0.03759893774986267,
0.011015419848263264,
-0.06348869204521179,
-0.032608576118946075,
0.005681950133293867,
-0.03167148679494858,
-0.004986707586795092,
0.035102080553770065,
-0.01719450019299984,
-0.03058183565735817,
0.03293793275952339,
-0.003390728263184428,
-0.005357908550649881,
0.005228566005825996,
0.004153313115239143,
-0.0008836034103296697,
0.019148772582411766,
-0.0190329197794199,
-0.06256437301635742,
0.0403875857591629,
-0.021250100806355476,
-0.037330277264118195,
0.05814806744456291,
-0.056208088994026184,
0.013826201669871807,
-0.020364318042993546,
-0.015098609030246735,
-0.0001975946215679869,
0.07814368605613708,
-0.04464336484670639,
0.010836071334779263,
0.0002472184714861214,
0.02389872819185257,
-0.030476564541459084,
0.023395387455821037,
-0.0061422074213624,
-0.02106287144124508,
-0.018295977264642715,
0.05671607330441475,
0.02373122051358223,
-0.015069215558469296,
-0.005728046875447035,
-0.004535896237939596,
-0.0283703301101923,
-0.017219658941030502,
0.005715696141123772,
-0.00349640310741961,
0.020443020388484,
0.04025403410196304,
-0.043506916612386703,
0.005729828029870987,
-0.011361968703567982,
0.0004430672852322459,
-0.045655783265829086,
-0.005789145827293396,
0.000574975332710892,
-0.01571793481707573,
0.022188471630215645,
-0.05217153578996658,
0.018647439777851105,
0.013389982283115387,
-0.0740547627210617,
-0.00044161081314086914,
-0.02048788033425808,
-0.03174114599823952,
-0.0001881093776319176,
0.009502383880317211,
0.04118167608976364,
0.0467211939394474,
0.07274360954761505,
0.03556619584560394,
-0.01810522936284542,
-0.00113763811532408,
-0.015132610686123371,
-0.008169511333107948,
0.02491382509469986,
0.04777432233095169,
0.01811804063618183,
0.012991390191018581,
0.03367036581039429,
-0.04125814884901047,
-0.050330985337495804,
0.05531083792448044,
-0.018288196995854378,
0.027375271543860435,
0.0031196551863104105,
-0.02639058791100979,
-0.00745193287730217,
0.006981488782912493,
0.0035835911985486746,
-0.031156163662672043,
0.0030883830040693283,
0.04079912230372429,
-0.019092250615358353,
0.022959250956773758,
0.028844669461250305,
-0.02817385457456112,
-0.00563359959051013,
-0.0796814113855362,
0.010509338229894638,
-0.016170071437954903,
-0.01826416328549385,
0.0374416820704937,
0.007175364997237921,
0.005574443843215704,
0.011114301159977913,
0.00020326115190982819,
0.0026498062070459127,
-0.030174287036061287,
-0.0020525490399450064,
0.059414006769657135,
-0.017774546518921852,
-0.02565060742199421,
0.018830575048923492,
0.025746295228600502,
-0.019676368683576584,
0.01902494579553604,
-0.014893225394189358,
-0.041811637580394745,
-0.027262894436717033,
0.0005018336232751608,
-0.0076188393868505955,
-0.013967852108180523,
-0.010914741083979607,
0.003984768409281969,
-0.038698479533195496,
0.02898409590125084,
-0.003583347424864769,
0.02940930239856243,
0.004241949412971735,
-0.025729456916451454,
-0.011017517186701298,
-0.06929782778024673,
0.041499026119709015,
0.010305988602340221,
-0.0015264005633071065,
-0.04544556140899658,
-0.033771589398384094,
-0.008321189321577549,
-0.007913672365248203,
0.061200618743896484,
0.02309383638203144,
0.022418556734919548,
0.027247510850429535,
-0.010640018619596958,
0.013632740825414658,
-0.04510599374771118,
0.00655287504196167,
0.008226059377193451,
-0.01089462824165821,
0.048384834080934525,
-0.038559503853321075,
-0.03694026917219162,
0.0005361692747101188,
0.0003137171152047813,
-0.03911591321229935,
0.06883052736520767,
0.03779658302664757,
-0.01121077686548233,
0.03405434638261795,
-0.023306606337428093,
-0.014528856612741947,
0.07025205343961716,
0.02509491890668869,
-0.015748118981719017,
0.0309394970536232,
-0.021890021860599518,
-0.04712563008069992,
0.021061550825834274,
-0.05206317454576492,
-0.0011573778465390205,
0.016724184155464172,
-0.005620189476758242,
0.049721747636795044,
-0.001453237608075142,
0.022775311022996902,
0.0285484716296196,
0.027651332318782806,
-0.013587499037384987,
-0.00863195676356554,
0.022637391462922096,
-0.00741004990413785,
0.0027006983291357756,
0.028775863349437714,
0.005631573032587767,
-0.006787794176489115,
0.04165605828166008,
0.016104022040963173,
0.025080742314457893,
0.008721663616597652,
0.03270285949110985,
-0.00631526205688715,
0.010675757192075253,
0.06725163757801056,
-0.0037476136349141598,
0.043211936950683594,
0.020546460524201393,
-0.04280687868595123,
0.008650834672152996,
-0.02510925754904747,
-0.02596433274447918,
0.03912161663174629,
0.015398372896015644,
0.016364313662052155,
0.014482413418591022,
-0.0022982617374509573,
-0.022031530737876892,
-0.01910748891532421,
-0.022120604291558266,
-0.008030831813812256,
0.021239737048745155,
0.005661815404891968,
0.005934315267950296,
0.005335800815373659,
-0.0017089789034798741,
0.00694021862000227,
0.024637574329972267,
-0.01001120824366808,
0.010018710978329182,
-0.03386296331882477,
0.013424312695860863,
0.022502476349473,
0.007502949796617031,
-0.057230185717344284,
-0.004361492581665516,
0.04247109219431877,
0.012432442978024483,
0.03352877125144005,
-0.008965707384049892,
-0.034892868250608444,
-0.03340967744588852,
0.018767056986689568,
-0.08742616325616837,
-0.017635183408856392,
-0.017967401072382927,
0.06783632934093475,
-0.0016831917455419898,
-0.017636345699429512
] |
<p>I've read a few other posts, and none seem to give me an answer that satisfies my curiosity. Thus far I've only been studying time independent QM, so I'm not even sure how wave functions evolve over time for microscopic things, let alone macroscopic things. However, what mandates that events that expect to happen actually happen? Why does it make sense that when I put something in a box, that it should remain in the box, rather than tunneling elsewhere? Or why should a pot ever come to a boil? Certainly these questions are being caused from a tragic misunderstanding of quantum theory, can someone clarify for me? At the end of the day, there is a nonzero probability that macroscopic anomalies will occur, right?</p>
| 10,731 |
[
0.005835505668073893,
-0.04029606282711029,
0.006014875136315823,
-0.04732970893383026,
0.0309491828083992,
0.0022875096183270216,
0.011766750365495682,
0.005025928840041161,
-0.0016298402333632112,
-0.014948487281799316,
0.024808935821056366,
0.07317513972520828,
0.009315073490142822,
-0.03730098903179169,
0.016905026510357857,
0.008943629451096058,
0.000276021717581898,
-0.04844474792480469,
-0.011272178031504154,
-0.008028936572372913,
0.020158732309937477,
0.041502393782138824,
0.03847522288560867,
0.0012997012818232179,
-0.03309589996933937,
0.005193933378905058,
0.007229423616081476,
0.009604099206626415,
0.042152222245931625,
0.04911474511027336,
-0.0040530054830014706,
-0.03421185538172722,
-0.004108690191060305,
0.029146619141101837,
0.015220184810459614,
-0.030770936980843544,
-0.02404782921075821,
-0.04009603336453438,
-0.02624840848147869,
-0.0015574938151985407,
-0.041769471019506454,
-0.031467389315366745,
-0.019472556188702583,
0.04403245449066162,
-0.021906083449721336,
0.0064482614398002625,
0.022457659244537354,
-0.014484451152384281,
0.05828872323036194,
-0.0710749700665474,
0.0306845735758543,
0.011952616274356842,
0.03981969133019447,
0.032090626657009125,
-0.011969071812927723,
0.001541623380035162,
0.10143725574016571,
0.057531774044036865,
-0.04368516430258751,
-0.06015917658805847,
-0.01885073073208332,
-0.01158630196005106,
-0.01913544163107872,
-0.019184637814760208,
-0.03715137764811516,
0.05578100308775902,
-0.012796650640666485,
-0.0412273146212101,
0.032815176993608475,
-0.01951260305941105,
0.012861903756856918,
0.0019411983666941524,
0.053605757653713226,
0.010145745240151882,
-0.00825539045035839,
-0.01577005535364151,
0.01893538050353527,
-0.015911297872662544,
0.033815108239650726,
0.03659340366721153,
0.016640616580843925,
0.008917417377233505,
0.02940523624420166,
0.0030691614374518394,
-0.009298043325543404,
-0.005432291887700558,
0.09047339111566544,
-0.011699856258928776,
-0.0042456816881895065,
0.033950936049222946,
-0.021471578627824783,
0.013528979383409023,
0.04453953728079796,
0.0029825621750205755,
-0.017027756199240685,
-0.011004823260009289,
0.018947364762425423,
0.05500561371445656,
-0.0060381959192454815,
-0.02324781008064747,
0.027148712426424026,
-0.019702622666954994,
0.023870036005973816,
0.06522174179553986,
-0.04063504934310913,
-0.03136543184518814,
-0.03363809362053871,
0.0470903255045414,
0.010412776842713356,
-0.005935336463153362,
-0.02215651050209999,
0.027196483686566353,
-0.005295322742313147,
0.01029624231159687,
-0.014109666459262371,
-0.012348531745374203,
0.0018367612501606345,
-0.07047995179891586,
0.048117056488990784,
0.048391129821538925,
0.037497229874134064,
-0.05186356231570244,
0.0374269112944603,
-0.03671687841415405,
-0.05275878682732582,
0.006932345684617758,
0.017246829345822334,
-0.011965112760663033,
-0.01429569162428379,
0.01760329306125641,
0.015993531793355942,
-0.023922469466924667,
-0.005447656847536564,
0.005896384362131357,
0.03982583433389664,
-0.03563963994383812,
-0.13212856650352478,
-0.06693530082702637,
0.03486698493361473,
-0.02520928904414177,
-0.05572211369872093,
-0.08143234997987747,
-0.024852560833096504,
0.006252653896808624,
0.08110234886407852,
-0.03962593153119087,
-0.02603743225336075,
0.003087475197389722,
0.026664549484848976,
0.014963310211896896,
-0.05993613973259926,
0.018076322972774506,
0.013532749377191067,
-0.006287675816565752,
0.03382629528641701,
-0.05789867043495178,
0.025106262415647507,
0.025475123897194862,
0.016724806278944016,
-0.04387105628848076,
0.037177182734012604,
-0.032821375876665115,
-0.020557885989546776,
-0.007113600615411997,
-0.03236628323793411,
-0.032108839601278305,
0.10263848304748535,
0.023922866210341454,
0.010223207995295525,
0.06391505151987076,
0.037440039217472076,
0.01870674453675747,
-0.0011938568204641342,
0.04097418114542961,
-0.019872061908245087,
-0.024560417979955673,
0.0030912705697119236,
-0.01156833115965128,
0.018693529069423676,
-0.0005075478693470359,
-0.0191911943256855,
-0.005274996627122164,
0.0004285449394956231,
-0.010450482368469238,
-0.013425043784081936,
0.013126957230269909,
-0.032196108251810074,
-0.001409956137649715,
-0.01909114420413971,
-0.06412938982248306,
-0.0014922156697139144,
-0.09683088958263397,
0.018291613087058067,
-0.005921056494116783,
-0.007182098459452391,
0.04780151695013046,
-0.008170188404619694,
0.0256489384919405,
-0.06134212017059326,
-0.033722296357154846,
-0.03256986662745476,
0.02888939157128334,
-0.005094065330922604,
-0.04443441331386566,
0.027534864842891693,
0.0746716558933258,
0.016258208081126213,
0.021345119923353195,
0.03127729520201683,
-0.02786792255938053,
-0.02807634510099888,
0.021259678527712822,
-0.02341906726360321,
0.014366199262440205,
0.0029866669792681932,
-0.006078924518078566,
-0.00027347076684236526,
-0.04832926392555237,
-0.0025806459598243237,
0.011129993014037609,
-0.025353047996759415,
0.0679173395037651,
0.010570491664111614,
0.015578142367303371,
-0.05161735415458679,
0.06294286251068115,
0.0020752353593707085,
-0.003524508560076356,
-0.018238890916109085,
-0.04343301057815552,
-0.055944353342056274,
-0.00042178688454441726,
0.018445396795868874,
0.03836777061223984,
0.012832081876695156,
0.024511044844985008,
-0.027871616184711456,
0.03903277590870857,
-0.017027216032147408,
-0.0015199895715340972,
-0.017336376011371613,
-0.0010038426844403148,
0.027661198750138283,
-0.0031649800948798656,
0.012839477509260178,
0.016166584566235542,
0.01336990762501955,
0.019183168187737465,
-0.015425362624228,
-0.005433941259980202,
-0.030148163437843323,
0.02763320319354534,
-0.0230560302734375,
0.02136324532330036,
-0.01810111664235592,
-0.002536402316763997,
0.005993872880935669,
-0.0027291474398225546,
-0.018380867317318916,
-0.009810437448322773,
0.017145387828350067,
-0.005853204522281885,
-0.05708935856819153,
-0.04434884712100029,
0.008339561522006989,
0.0057490249164402485,
-0.043801724910736084,
-0.007692559622228146,
0.016556309536099434,
-0.007630246691405773,
0.0018065599724650383,
0.013377323746681213,
-0.0111312260851264,
0.005833270959556103,
-0.006190383806824684,
0.017849458381533623,
0.021773837506771088,
0.0462634302675724,
-0.024651141837239265,
-0.028355885297060013,
0.002793431980535388,
-0.032075103372335434,
0.011857766658067703,
0.030516022816300392,
-0.022701727226376534,
0.03840525448322296,
-0.03862886503338814,
-0.027630586177110672,
0.06634446233510971,
-0.012968739494681358,
0.040041472762823105,
0.009466971270740032,
-0.007505171466618776,
-0.03545836731791496,
-0.011246077716350555,
-0.028640063479542732,
-0.011842275969684124,
-0.027085108682513237,
0.017286578193306923,
0.06551963090896606,
-0.06165256351232529,
-0.01833953522145748,
0.018002888187766075,
-0.030757499858736992,
-0.0486508272588253,
-0.023932604119181633,
-0.026471517980098724,
0.020403355360031128,
-0.03646077960729599,
0.0027410751208662987,
0.01088592130690813,
-0.058292463421821594,
-0.02287430688738823,
-0.03376700356602669,
-0.05355845019221306,
0.0023093956988304853,
-0.010998834855854511,
0.05463578924536705,
-0.0009738749358803034,
-0.0005406870623119175,
0.0417083203792572,
0.03457481041550636,
-0.046818964183330536,
0.01860884018242359,
-0.019873086363077164,
-0.008590882644057274,
-0.019990399479866028,
0.013076025992631912,
0.03724950924515724,
-0.001752783078700304,
0.05982431396842003,
0.029357338324189186,
0.034467585384845734,
0.012774249538779259,
0.012089865282177925,
-0.025920165702700615,
0.007113145664334297,
0.03920474648475647,
0.006352900993078947,
0.0033566677011549473,
0.004189565312117338,
-0.00934426300227642,
0.008266464807093143,
-0.013164390809834003,
0.013902888633310795,
0.01842465251684189,
-0.03165179863572121,
0.0726134404540062,
-0.020050808787345886,
0.022934939712285995,
-0.035842977464199066,
0.07237617671489716,
-0.04966568574309349,
-0.002994644222781062,
0.01308522280305624,
-0.009903430938720703,
0.03954043239355087,
-0.014521615579724312,
0.03562022000551224,
0.03301799297332764,
0.018935369327664375,
-0.02429896593093872,
-0.008809885010123253,
-0.0008080900879576802,
0.007543395739048719,
0.02600833587348461,
-0.001258868956938386,
-0.034426912665367126,
0.041010886430740356,
0.03593003377318382,
0.01879214681684971,
-0.0073348646983504295,
-0.06504751741886139,
-0.023905804380774498,
-0.04738471284508705,
-0.030890149995684624,
0.021047700196504593,
0.025410540401935577,
-0.003217130433768034,
0.049261368811130524,
0.04947086423635483,
-0.0031870235688984394,
-0.01781153678894043,
-0.012245518155395985,
-0.05787266045808792,
0.04939265921711922,
-0.03311968967318535,
0.002085526240989566,
-0.040627025067806244,
-0.001410381868481636,
0.04593409225344658,
-0.019479498267173767,
-0.048684775829315186,
0.009572729468345642,
0.009143995121121407,
-0.05013953521847725,
0.005807844921946526,
-0.03768405690789223,
-0.01782785914838314,
-0.015848897397518158,
0.012245514430105686,
0.03254290670156479,
-0.007623462937772274,
0.01011055987328291,
0.035841092467308044,
-0.04263875260949135,
0.0042761932127177715,
-0.0012359913671389222,
0.01743532158434391,
0.02756493166089058,
0.009541424922645092,
0.06454331427812576,
0.007839393801987171,
-0.054852843284606934,
0.03206580504775047,
0.03925793617963791,
0.06416018307209015,
-0.023219620808959007,
-0.01156153529882431,
-0.025237029418349266,
-0.05567619204521179,
-0.008638745173811913,
0.0035308217629790306,
0.026282453909516335,
0.00973630603402853,
0.03147071972489357,
0.011414429172873497,
-0.00908899586647749,
-0.02635246515274048,
0.028593238443136215,
0.03504415601491928,
-0.02005125768482685,
-0.049372151494026184,
-0.03562544286251068,
-0.02908642403781414,
-0.04028204083442688,
-0.01730751432478428,
0.008721787482500076,
-0.01602385938167572,
-0.014249324798583984,
0.027525410056114197,
0.000041353850974701345,
0.020497819408774376,
-0.009364324621856213,
-0.023248085752129555,
0.010328797623515129,
0.04093800485134125,
0.005035674665123224,
0.016039427369832993,
0.004884038120508194,
0.0029690838418900967,
0.03576664626598358,
0.015758134424686432,
0.005640941206365824,
-0.04926721006631851,
0.02141975797712803,
0.04302127659320831,
0.027732152491807938,
-0.004514285828918219,
-0.003284487407654524,
-0.05507928133010864,
-0.055462609976530075,
0.0744333565235138,
-0.03362222760915756,
0.0032816368620842695,
0.005124492105096579,
-0.01733417436480522,
-0.025850659236311913,
-0.027349453419446945,
0.010557573288679123,
0.007340730167925358,
0.025071490556001663,
0.02211492508649826,
-0.014195387251675129,
-0.02394614927470684,
-0.02182680182158947,
0.012030159123241901,
0.02684018760919571,
0.06032051518559456,
-0.028581375256180763,
0.01650836691260338,
-0.008707910776138306,
0.0043981969356536865,
0.00807251874357462,
-0.06358867883682251,
0.003718530060723424,
-0.02483089454472065,
-0.010664274916052818,
0.031269561499357224,
-0.030826713889837265,
-0.047850172966718674,
-0.014366927556693554,
-0.0002391540474491194,
-0.01991797611117363,
0.009203756228089333,
-0.017474204301834106,
0.05471858009696007,
-0.006743329577147961,
0.011282014660537243,
0.003826608182862401,
0.03290447220206261,
-0.004723763559013605,
0.008702898398041725,
-0.03454573079943657,
0.039911944419145584,
-0.0036176182329654694,
0.04217333719134331,
-0.06048908084630966,
-0.026761233806610107,
-0.007764851674437523,
0.07411844283342361,
-0.0016804045299068093,
-0.017784276977181435,
0.0026191435754299164,
-0.03955980762839317,
0.00943538174033165,
0.04829200729727745,
0.022566858679056168,
0.0031525709200650454,
-0.009708153083920479,
0.014242618344724178,
-0.016947077587246895,
-0.04590880125761032,
-0.014238378964364529,
0.003042180323973298,
0.010367036797106266,
0.042602431029081345,
-0.020907044410705566,
0.054157841950654984,
-0.039904531091451645,
-0.017426855862140656,
0.024089863523840904,
-0.05101805552840233,
0.035187944769859314,
-0.002826269483193755,
-0.011907496489584446,
0.02708304114639759,
-0.07029738277196884,
-0.01734699122607708,
0.005921760108321905,
-0.0047311861999332905,
0.05356879532337189,
-0.03862057626247406,
0.005834731739014387,
-0.008886408060789108,
0.02223718725144863,
-0.0701080858707428,
-0.05545324459671974,
0.027847403660416603,
0.02354200929403305,
-0.01175721362233162,
-0.0285195242613554,
0.0150800421833992,
-0.026860453188419342,
-0.02975013107061386,
-0.0008516060770489275,
0.05276012420654297,
0.006593614816665649,
-0.012934352271258831,
0.0351087749004364,
0.042791493237018585,
0.05393481254577637,
-0.021986570209264755,
0.022987497970461845,
0.02023613080382347,
-0.030927471816539764,
-0.022342119365930557,
0.012768661603331566,
0.027002856135368347,
-0.031125769019126892,
-0.02186737023293972,
0.007966659963130951,
-0.01977001503109932,
0.037445731461048126,
-0.04226667433977127,
-0.02149350382387638,
0.01790180429816246,
-0.001090459292754531,
0.036284931004047394,
-0.017732534557580948,
0.013770640827715397,
0.021301519125699997,
0.012837300077080727,
0.024580085650086403,
-0.012270317412912846,
-0.011431348510086536,
-0.06330215185880661,
0.016597392037510872,
-0.008605415001511574,
0.022363971918821335,
0.04888363555073738,
0.017222052440047264,
-0.02929510362446308,
-0.009949170984327793,
0.009419145062565804,
-0.033983148634433746,
0.005953833926469088,
0.001466079498641193,
-0.011541128158569336,
0.002890049247071147,
-0.018438370898365974,
-0.01013693492859602,
-0.034049056470394135,
-0.04676203429698944,
0.043247830122709274,
0.05609923228621483,
-0.008787494152784348,
0.042428869754076004,
0.023910855874419212,
-0.023128900676965714,
-0.03165683522820473,
-0.03272572532296181,
-0.03347761929035187,
0.025126753374934196,
-0.0012908111093565822,
-0.0008180650183930993,
-0.03697814792394638,
0.04427530989050865,
0.018462475389242172,
0.03980075567960739,
-0.0214694831520319,
0.0043213642202317715,
0.0360499732196331,
0.0300589632242918,
0.04508204385638237,
0.010737454518675804,
-0.024655122309923172,
0.030927468091249466,
-0.04620573669672012,
0.038629598915576935,
-0.0053818728774785995,
-0.00223735929466784,
0.026130545884370804,
0.00011109461047453806,
-0.03457484394311905,
-0.028797274455428123,
-0.010658620856702328,
-0.026906758546829224,
-0.0020252978429198265,
-0.009011156857013702,
0.017860939726233482,
0.016067398712038994,
0.04745679348707199,
0.004696513060480356,
0.020913351327180862,
-0.019151626154780388,
0.006975678261369467,
-0.09365735948085785,
-0.03874334692955017,
-0.021192429587244987,
-0.05551296845078468,
0.024291522800922394,
-0.002897603902965784,
0.002170259365811944,
-0.01304314099252224,
-0.03723694384098053,
0.024361900985240936,
0.010084778070449829,
0.03475967422127724,
-0.03985963389277458,
0.06603140383958817,
0.02875848487019539,
0.027803724631667137,
-0.017674196511507034,
0.0396084189414978,
0.08990028500556946,
0.05172653868794441,
-0.0014560173731297255,
-0.07889421284198761,
0.014649054035544395,
-0.05366457253694534,
0.013123930431902409,
0.0028189171571284533,
0.02497556246817112,
0.00438935961574316,
0.017081115394830704,
0.01164993830025196,
0.05454855412244797,
0.039953261613845825,
0.03593555837869644,
0.06555907428264618,
-0.031753066927194595,
-0.06432776898145676,
-0.02635735273361206,
0.032820288091897964,
0.006820234470069408,
0.010728639550507069,
-0.06343265622854233,
0.0007784419576637447,
-0.039580751210451126,
0.011621266603469849,
0.025819946080446243,
-0.05640101805329323,
0.04160666465759277,
0.008270262740552425,
-0.018131276592612267,
0.011407047510147095,
0.018446611240506172,
-0.024020856246352196,
-0.0368555523455143,
0.04739544913172722,
0.06060968339443207,
-0.011274219490587711,
0.031422484666109085,
0.012934266589581966,
0.02968333102762699,
-0.014723775908350945,
-0.0036937561817467213,
-0.0056572300381958485,
-0.01709245704114437,
-0.023721199482679367,
-0.03601311519742012,
0.04479934647679329,
-0.03595799207687378,
0.001468706177547574,
-0.002240594010800123,
-0.04159892722964287,
0.0016915345331653953,
-0.04692815616726875,
-0.026722444221377373,
0.018498679623007774,
0.05509708821773529,
0.0024218568578362465,
-0.005720637738704681,
-0.004246382508426905,
0.019649358466267586,
-0.019470110535621643,
0.05417219549417496,
0.010343072935938835,
0.003541750367730856,
-0.028254110366106033,
-0.009969120845198631,
0.0155410785228014,
-0.014767879620194435,
0.002280101180076599,
-0.013818187639117241,
-0.013925804756581783,
-0.07449277490377426,
-0.023134268820285797,
0.0345330610871315,
0.03574472665786743,
0.055451638996601105,
-0.009883427061140537,
0.01607140526175499,
0.0013955928152427077,
-0.04108195751905441,
0.020710408687591553,
-0.03448515757918358,
-0.0056292773224413395,
-0.01386341918259859,
0.024783484637737274,
0.01990540511906147,
0.04635964334011078,
-0.027390338480472565,
-0.007136564236134291,
0.0045365565456449986,
0.001417432096786797,
0.013413585722446442,
-0.031171081587672234,
-0.0030165603384375572,
0.024087967351078987,
-0.03764250501990318,
-0.01898217387497425,
-0.026506297290325165,
0.019138971343636513,
0.0051367576234042645,
-0.012388081289827824,
0.013001015409827232,
0.019496053457260132,
-0.000694147078320384,
-0.0011061689583584666,
0.026973214000463486,
-0.03191467374563217,
-0.013876217417418957,
0.02661687135696411,
0.016561400145292282,
-0.0027855036314576864,
-0.08320316672325134,
-0.0186340119689703,
0.02473757229745388,
0.011218009516596794,
0.03691305220127106,
-0.026613770052790642,
0.001504213665612042,
0.00657804636284709,
0.04954852536320686,
0.003070784267038107,
-0.02252611704170704,
-0.0782579556107521,
0.002696792595088482,
0.006640568841248751,
-0.004561835899949074,
-0.007488140370696783,
0.03311005234718323,
-0.016051219776272774,
-0.0581866092979908,
0.012183558195829391,
0.07042473554611206,
-0.0048424433916807175,
0.009910296648740768,
-0.0066839479841291904,
-0.02300678938627243,
0.024663271382451057,
0.003753661410883069,
-0.04577125981450081,
0.03343101218342781,
-0.030671007931232452,
-0.040185097604990005,
0.039407290518283844,
-0.005530929658561945,
0.018227264285087585,
0.046120498329401016,
-0.006079190876334906,
-0.009183431044220924,
0.04769396409392357,
-0.027879098430275917,
0.02970765344798565,
0.016166631132364273,
-0.013155764900147915,
-0.025200506672263145,
0.0042388360016047955,
0.013531018048524857,
-0.005066342186182737,
-0.012151283212006092,
0.01092306524515152,
0.03087305836379528,
0.024372991174459457,
0.0046088253147900105,
0.007814272306859493,
-0.016505083069205284,
0.02095838636159897,
0.015518452040851116,
0.013867083005607128,
0.006871592719107866,
0.08808448165655136,
-0.0631999745965004,
0.042416058480739594,
0.01553554181009531,
0.004678933881223202,
-0.09864875674247742,
0.014182019978761673,
0.03218548372387886,
-0.006812774110585451,
0.019524462521076202,
-0.02552688680589199,
0.008523174561560154,
0.04141603410243988,
-0.047394007444381714,
0.033545129001140594,
-0.03138602152466774,
-0.002455304842442274,
0.013490822166204453,
-0.004805766511708498,
-0.015555969439446926,
0.054145652800798416,
0.03597172349691391,
0.017812883481383324,
0.02201096899807453,
-0.0056245108135044575,
-0.010116344317793846,
-0.005921579897403717,
0.00839193258434534,
0.05243949219584465,
-0.023098725825548172,
0.03381440043449402,
0.03040388599038124,
-0.024575399234890938,
-0.010273212566971779,
0.024079760536551476,
-0.008822287432849407,
-0.029800020158290863,
-0.007275063078850508,
-0.009803174063563347,
0.010496385395526886,
0.031017344444990158,
-0.004161574877798557,
-0.0031812379602342844,
0.03914698585867882,
0.0399918258190155,
0.03107617050409317,
0.018991295248270035,
0.00033190150861628354,
0.008723454549908638,
-0.025562498718500137,
-0.04987448826432228,
-0.008952106349170208,
0.008166464976966381,
-0.001060332404449582,
0.002930819056928158,
0.002568925032392144,
0.024837682023644447,
0.028424765914678574,
-0.016730323433876038,
0.024058807641267776,
-0.025459246709942818,
-0.01251192670315504,
0.05139823257923126,
0.05635156109929085,
0.018038026988506317,
0.011096539907157421,
-0.007113301195204258,
-0.019647134467959404,
-0.0012109522940590978,
0.002018475439399481,
-0.017796030268073082,
-0.06658105552196503,
-0.021163858473300934,
-0.01376932580024004,
0.01723768562078476,
0.04192342981696129,
-0.06153149530291557,
-0.035959575325250626,
0.003167907940223813,
0.007229182403534651,
0.026041287928819656,
-0.004450595937669277,
-0.0352356880903244,
-0.02991710975766182,
-0.058228448033332825,
0.06840091943740845,
-0.030695002526044846,
0.01730133406817913,
-0.054031096398830414,
-0.014312263578176498,
0.0012031346559524536,
0.027267396450042725,
0.053050097078084946,
-0.019054271280765533,
-0.011003509163856506,
0.004752093926072121,
-0.010282292030751705,
0.0485992468893528,
-0.01622171886265278,
0.023280367255210876,
-0.05223095417022705,
0.007370694074779749,
-0.013984132558107376,
-0.0017407297855243087,
0.02561187371611595,
0.03292013704776764,
0.021095816045999527,
-0.044371217489242554,
0.057608235627412796,
-0.014885581098496914,
-0.017322976142168045,
0.04071355611085892,
0.02554822526872158,
-0.017594506964087486,
0.04942440614104271,
-0.021204562857747078,
0.021335050463676453,
0.02055683173239231,
-0.03237304463982582,
-0.03346150368452072,
0.05719361826777458,
0.004349173977971077,
-0.015408270061016083,
-0.009830252267420292,
-0.0008859895169734955,
0.021698523312807083,
-0.03370460122823715,
-0.025668539106845856,
0.017172791063785553,
-0.01490981224924326,
0.0013052959693595767,
0.04456055909395218,
0.005055911373347044,
0.04702523723244667,
-0.008172334171831608,
-0.0012392994249239564,
0.01923566870391369,
0.049333199858665466,
0.005796382203698158,
0.05149943009018898,
0.029265981167554855,
-0.011349238455295563,
0.06273840367794037,
0.019414640963077545,
-0.030398696660995483,
0.005478709004819393,
-0.00505028385668993,
0.021837124601006508,
-0.025220170617103577,
-0.0008688921807333827,
0.01359462272375822,
-0.031320720911026,
0.003651631763204932,
0.006452013738453388,
-0.0187542624771595,
0.08011620491743088,
0.005026990547776222,
0.02145211026072502,
-0.023332694545388222,
0.013893126510083675,
0.0006537081208080053,
-0.010722002945840359,
0.00475542526692152,
0.042586036026477814,
-0.018266722559928894,
0.012106586247682571,
-0.026147035881876945,
0.045159660279750824,
0.045361340045928955,
-0.02911500819027424,
0.032902106642723083,
-0.01611478626728058,
-0.013807450421154499,
-0.03702402859926224,
-0.033422358334064484,
-0.01807861402630806,
-0.03682205080986023,
0.017646266147494316,
0.05098278075456619,
0.02018810249865055,
-0.004192611202597618,
-0.023660162463784218,
-0.017984632402658463,
0.059844423085451126,
-0.06200559809803963,
0.020468227565288544,
-0.05460633710026741,
0.02260541543364525,
-0.030201518908143044,
-0.003314563073217869
] |
<p>This may be a very simple question but somehow I can't seems to solve it. For the sake of completness, I will use the same original question I am working on.</p>
<p><strong>Question:</strong> The density of ice is $917 kg/m^3 $ and the density of seawater is $1020 kg/m^3$. If a piece of ice with dimensions $ 1m $ x $1m $ x $0.65m $ is left in seawater, what height of the ice will be above sea water?</p>
<p><img src="http://i.stack.imgur.com/rGScS.png" alt="enter image description here"></p>
<p>This is all it was given.</p>
<p><strong>My Attempt:</strong> This is how I understand this problem.</p>
<p>There will be two forces acting on this ice block</p>
<ul>
<li>The upthrust force ( which is equivalent to the weight of the seawater being displaced)</li>
<li>The weight of the ice block itself</li>
</ul>
<p>Since the ice block is floating, I assume that the upthrust is either equal or greater than the weight of the ice block.</p>
<p>This is the simple sketch I come up with </p>
<p><img src="http://i.stack.imgur.com/7bc8z.png" alt="enter image description here"></p>
<p>but now I am confused because according to my sketch:</p>
<p>$ upthrust = \rho_{seawater} vg $ (v being the volume of water being displaced by the ice block)</p>
<p>$ weight\,of\, ice\, block = mg = \rho_{ice} vg$ </p>
<p>If i subtract these two equations, the volumes will cancel out each other so there will be no height information left. I supposed I have to somehow retrieve the <code>height</code> inforation from <code>volume</code> using $v = Ah$ but I am not sure how. How do I find the height of ice block above sea water?</p>
| 10,732 |
[
-0.005985841620713472,
0.015717731788754463,
-0.01862538792192936,
-0.02849777229130268,
0.02741415426135063,
0.0013818570878356695,
-0.04678010195493698,
-0.033704232424497604,
0.02128271944820881,
-0.026767613366246223,
0.06897501647472382,
0.04074480012059212,
0.043148986995220184,
0.04250188171863556,
0.019602546468377113,
0.0359463170170784,
-0.012449567206203938,
-0.013509707525372505,
0.04492083564400673,
0.002272976329550147,
-0.011950122192502022,
0.011006772518157959,
0.009171739220619202,
0.007418401073664427,
0.008836870081722736,
0.01565319485962391,
0.06530667841434479,
-0.03776180371642113,
0.005868953187018633,
0.03990158066153526,
-0.012704705819487572,
-0.02129293791949749,
0.013248611241579056,
0.027601998299360275,
0.018459945917129517,
0.013205381110310555,
-0.026302939280867577,
0.009652427397668362,
-0.0017978637479245663,
0.047863367944955826,
0.019976915791630745,
0.0024081214796751738,
-0.020083729177713394,
0.04056920111179352,
-0.04133208841085434,
0.03454213589429855,
-0.000868100905790925,
-0.005435710307210684,
0.019634965807199478,
-0.05848498269915581,
0.05053389444947243,
0.04020954668521881,
0.036998964846134186,
0.07324069738388062,
0.007075796835124493,
-0.021386869251728058,
0.062049780040979385,
0.07116860151290894,
0.00690597714856267,
-0.03498060256242752,
-0.01803009770810604,
-0.006142249330878258,
-0.026040557771921158,
-0.017458448186516762,
-0.004880619700998068,
0.014663557521998882,
-0.0276966355741024,
0.0191582553088665,
0.007331298664212227,
-0.014734698459506035,
0.0008197277202270925,
-0.0030329700093716383,
-0.015081971883773804,
-0.04652341827750206,
0.047165654599666595,
0.0004921899526380002,
-0.04252540320158005,
0.0713297501206398,
-0.004546490032225847,
0.023345451802015305,
-0.017883239313960075,
0.052158478647470474,
0.039374470710754395,
0.039372075349092484,
0.03406806290149689,
-0.034055911004543304,
0.08001349866390228,
-0.00931831356137991,
0.011684916913509369,
0.014883726835250854,
-0.012850449420511723,
-0.015090660192072392,
-0.023345451802015305,
-0.02519221231341362,
0.015893908217549324,
0.01185001153498888,
0.005160152446478605,
0.0343993715941906,
-0.0022715625818818808,
0.007555353455245495,
0.006019397638738155,
-0.05739360675215721,
-0.0123910466209054,
0.08965327590703964,
-0.008933596312999725,
-0.007097371853888035,
-0.05196555331349373,
0.00964663177728653,
0.020839836448431015,
-0.030153721570968628,
0.028197389096021652,
0.032980069518089294,
0.003012990579009056,
-0.07263553142547607,
-0.022675922140479088,
-0.01049098465591669,
0.007671560626477003,
-0.007109778001904488,
0.041862498968839645,
-0.0043622637167572975,
0.05272556096315384,
-0.016431350260972977,
0.00151590327732265,
-0.04527892544865608,
-0.07074862718582153,
0.002288637449964881,
0.012422214262187481,
-0.020079735666513443,
-0.01850350946187973,
0.051125891506671906,
0.020460955798625946,
0.018366238102316856,
0.015301310457289219,
-0.013306641019880772,
0.04957534745335579,
-0.024909332394599915,
-0.07493215054273605,
-0.05652422830462456,
0.06923045217990875,
0.0018259483622387052,
-0.03415345400571823,
-0.04876280203461647,
0.021837064996361732,
0.029478609561920166,
0.06175094470381737,
-0.010337824933230877,
0.025104034692049026,
-0.016165809705853462,
0.004114707000553608,
-0.004594138357788324,
0.013904700055718422,
0.02313237451016903,
-0.012844135984778404,
-0.018856890499591827,
-0.0008146024192683399,
-0.0648614764213562,
0.0199787188321352,
0.014211365953087807,
-0.029425708577036858,
0.0016979359788820148,
0.04240460321307182,
0.01695963740348816,
-0.01278634648770094,
-0.02047344483435154,
-0.010419714264571667,
-0.04150218516588211,
0.06611232459545135,
-0.020605573430657387,
-0.006414532195776701,
0.025442996993660927,
0.001575131667777896,
0.003811334492638707,
0.022423477843403816,
-0.007723379414528608,
0.08215447515249252,
0.004416872747242451,
0.029897188767790794,
-0.03212183713912964,
-0.0011458797380328178,
0.010773124173283577,
-0.013136398047208786,
-0.03396225720643997,
-0.015305905602872372,
-0.01653512753546238,
0.031052246689796448,
0.027247438207268715,
0.009091074578464031,
-0.020977284759283066,
0.01647651381790638,
-0.050429798662662506,
-0.0269307978451252,
-0.05263649299740791,
0.01796821877360344,
-0.03439376875758171,
0.03603770583868027,
0.008777710609138012,
0.033043187111616135,
0.0037007005885243416,
-0.022309700027108192,
-0.010686083696782589,
0.025956260040402412,
0.061316851526498795,
0.009369038976728916,
0.00249898131005466,
0.04227891191840172,
0.023009372875094414,
0.0058013382367789745,
0.044514160603284836,
-0.012175089679658413,
-0.03094768337905407,
0.007075859699398279,
0.0003942375769838691,
-0.02285568229854107,
-0.01806403324007988,
-0.007036655209958553,
-0.006863102316856384,
0.013021523132920265,
0.02763022482395172,
-0.002564269583672285,
0.0019376896088942885,
-0.01515013538300991,
0.07824666798114777,
0.0474887415766716,
0.006474475841969252,
0.02066589705646038,
0.012412852607667446,
0.0162822175770998,
0.027854066342115402,
-0.0002814411709550768,
-0.009124442003667355,
-0.03832261636853218,
-0.016338232904672623,
0.0010514329187572002,
0.03185146301984787,
-0.019990477710962296,
0.034254416823387146,
0.019946785643696785,
0.02927558496594429,
0.02497321367263794,
0.009515907615423203,
-0.012187764048576355,
-0.01894834078848362,
0.013596635311841965,
0.027622662484645844,
-0.01705637015402317,
-0.002803694922477007,
0.00035695030237548053,
0.02751234918832779,
-0.00759150693193078,
-0.0262393020093441,
-0.03431985527276993,
-0.013713444583117962,
0.01183856651186943,
0.005670743528753519,
-0.04819418862462044,
-0.0010629022726789117,
0.03684007748961449,
-0.02169545739889145,
0.00797397829592228,
0.027979057282209396,
-0.02044511027634144,
0.004166606813669205,
-0.04531252011656761,
-0.01512727327644825,
0.035857222974300385,
0.0072128986939787865,
0.004279384855180979,
0.016690118238329887,
0.03176862373948097,
-0.02659246139228344,
0.02060162089765072,
-0.020981112495064735,
-0.003911112435162067,
-0.0017828415147960186,
0.04597414284944534,
0.02927098609507084,
0.014676275663077831,
0.04107261076569557,
-0.03327978402376175,
0.010646468959748745,
-0.004672375041991472,
0.005616809241473675,
-0.016866207122802734,
0.008212670683860779,
-0.06217442825436592,
-0.013796375133097172,
-0.05284779146313667,
-0.01732451841235161,
0.01329940278083086,
0.03229747712612152,
-0.041461825370788574,
0.03542124107480049,
0.012994589284062386,
-0.03135935962200165,
-0.035390209406614304,
-0.04819926992058754,
0.010913491249084473,
-0.047221750020980835,
-0.00660022534430027,
0.042868997901678085,
-0.005184526555240154,
-0.012989583425223827,
0.01451968215405941,
-0.061398498713970184,
-0.018961887806653976,
-0.00695901969447732,
0.026103787124156952,
-0.017083391547203064,
-0.03763342648744583,
-0.004979404620826244,
0.0015460132854059339,
-0.010225323960185051,
-0.012584258802235126,
-0.06495540589094162,
-0.06395706534385681,
0.0018209071131423116,
-0.007386006880551577,
0.04579460248351097,
-0.0003981590853072703,
-0.029226001352071762,
0.08183568716049194,
-0.0019121757941320539,
-0.004909937269985676,
0.002043384127318859,
-0.0010003414936363697,
-0.01235820259898901,
-0.020546462386846542,
-0.007916574366390705,
0.01922442764043808,
-0.01598091423511505,
-0.00601578364148736,
0.030924225226044655,
0.03127752244472504,
0.037968724966049194,
0.03651239722967148,
0.007243084721267223,
0.016239145770668983,
0.039754562079906464,
0.031277790665626526,
0.08166632056236267,
-0.025760414078831673,
0.006646167021244764,
0.0007021565106697381,
-0.02096988819539547,
0.05327023193240166,
0.04436446726322174,
-0.05283748358488083,
0.029947249218821526,
0.013622117228806019,
-0.02023248001933098,
-0.03946817293763161,
0.032933708280324936,
0.008642904460430145,
0.02074630931019783,
0.020934797823429108,
0.013876066543161869,
0.056678902357816696,
0.00958944670855999,
-0.03260679170489311,
0.0497065931558609,
0.049268804490566254,
-0.011768968775868416,
-0.05129692703485489,
-0.04428819939494133,
-0.008541581220924854,
0.05809580534696579,
-0.008897251449525356,
0.0067894975654780865,
-0.0005330653511919081,
-0.018633650615811348,
0.023681530728936195,
0.0032630530185997486,
-0.021781591698527336,
-0.017781274393200874,
-0.05226117745041847,
-0.012576580047607422,
0.02128189243376255,
0.03637544810771942,
-0.00963610503822565,
0.04684186726808548,
0.00657892320305109,
0.02435753308236599,
0.03205970302224159,
0.029155051335692406,
-0.061140283942222595,
-0.005061046220362186,
0.0029859719797968864,
-0.02657187171280384,
0.02376922406256199,
-0.022232472896575928,
0.02340056747198105,
-0.04757915809750557,
-0.02391793206334114,
-0.008387039415538311,
0.03089270554482937,
-0.05092443898320198,
0.016651198267936707,
-0.004962683189660311,
-0.011398126371204853,
-0.016233358532190323,
0.015627533197402954,
0.045901134610176086,
-0.04801255837082863,
0.017193686217069626,
0.04261244088411331,
-0.004458871204406023,
-0.004732060246169567,
-0.02166907675564289,
-0.010077394545078278,
0.02974056266248226,
-0.005167682189494371,
0.00446279626339674,
0.04352042078971863,
-0.0016285853926092386,
-0.027182430028915405,
-0.002723144832998514,
0.001307944068685174,
-0.02862543798983097,
0.013271271251142025,
-0.03134963661432266,
-0.03611059859395027,
-0.01731479912996292,
-0.0015341206453740597,
0.0303303524851799,
-0.004672631621360779,
-0.003550359047949314,
0.013931548222899437,
-0.01995822787284851,
-0.01913316361606121,
0.05945606902241707,
0.04954003915190697,
0.027530571445822716,
0.009114750660955906,
-0.049807287752628326,
-0.016560465097427368,
-0.045713379979133606,
-0.010942167602479458,
0.04474887624382973,
0.03403187915682793,
0.005944346077740192,
-0.013801886700093746,
0.0031709354370832443,
0.0013194942148402333,
-0.010897397063672543,
0.0035205241292715073,
0.009676272049546242,
0.0032576455269008875,
-0.03715391457080841,
0.010060827247798443,
0.013734453357756138,
0.014598038047552109,
0.014321666210889816,
-0.0306635033339262,
0.016831018030643463,
-0.07866822183132172,
-0.07364297658205032,
0.02530176192522049,
0.03586825355887413,
0.005933043081313372,
0.014506954699754715,
-0.08143151551485062,
-0.007999349385499954,
0.02494235523045063,
-0.04122758284211159,
0.03156101331114769,
0.01078228559345007,
0.026003753766417503,
0.008836138062179089,
-0.02959108166396618,
-0.019768575206398964,
-0.01603778265416622,
-0.025327127426862717,
0.010842305608093739,
-0.03352434188127518,
-0.004380907863378525,
0.03192690759897232,
0.0059035299345850945,
0.02963886223733425,
0.04914821684360504,
0.013080974109470844,
-0.014835527166724205,
-0.04644423723220825,
-0.010749916546046734,
-0.06735194474458694,
-0.0492217093706131,
-0.009491348639130592,
-0.022589363157749176,
0.02014494687318802,
0.036617085337638855,
-0.01612173207104206,
-0.07826758176088333,
0.04670020192861557,
-0.002636124612763524,
0.005236472003161907,
0.005924717523157597,
-0.02581818960607052,
0.039114587008953094,
0.059042803943157196,
-0.01769552007317543,
0.04870838671922684,
0.042784035205841064,
-0.04933711513876915,
-0.02602168172597885,
-0.03267486020922661,
0.005604145582765341,
-0.01413596048951149,
-0.04953752085566521,
-0.016695449128746986,
0.015100711956620216,
-0.05240989103913307,
0.029479004442691803,
-0.02360384352505207,
0.03786511719226837,
-0.00497617619112134,
-0.049076344817876816,
0.0277433879673481,
0.019294055178761482,
-0.006133894436061382,
-0.004436593968421221,
0.0003606525424402207,
-0.02559669129550457,
-0.006972262170165777,
-0.048928916454315186,
-0.0021844373550266027,
-0.003323331940919161,
0.01943635195493698,
-0.023418230935931206,
-0.03289595618844032,
0.0361751951277256,
0.0038306110072880983,
0.01866353489458561,
-0.0049993908032774925,
-0.017813367769122124,
0.047165460884571075,
-0.03160363808274269,
0.02947591431438923,
0.0050860438495874405,
-0.05104358121752739,
-0.03056231699883938,
0.03301925212144852,
-0.0005593623500317335,
-0.015071632340550423,
0.009027806110680103,
0.003789290552958846,
0.047845155000686646,
0.05101213976740837,
-0.03592844679951668,
0.0020330206025391817,
0.039752986282110214,
0.04414276033639908,
0.004000117536634207,
-0.015242249704897404,
0.0007292181835509837,
0.016017459332942963,
-0.03025140054523945,
-0.040311962366104126,
0.055596500635147095,
-0.013997752219438553,
-0.014275262132287025,
0.013312220573425293,
0.013325919397175312,
0.05216103047132492,
-0.05002754181623459,
-0.0022189789451658726,
0.005029609426856041,
-0.00904572382569313,
-0.0002780579379759729,
-0.0032358583994209766,
0.03088724985718727,
-0.02112698182463646,
-0.01928618736565113,
-0.00639012735337019,
-0.032528482377529144,
0.012683232314884663,
-0.043027978390455246,
-0.01621461845934391,
0.0024799578823149204,
0.05792471021413803,
-0.006944552529603243,
-0.04370180144906044,
-0.014401636086404324,
0.016763171181082726,
0.03263832628726959,
-0.031605154275894165,
-0.002645432483404875,
-0.03715472295880318,
-0.053664520382881165,
-0.025665167719125748,
-0.036301203072071075,
0.001756613957695663,
-0.0009695736225694418,
0.08713477104902267,
-0.03459945321083069,
0.01834120787680149,
0.003662331495434046,
0.0020919358357787132,
0.01921915076673031,
-0.007925573736429214,
-0.008713030256330967,
0.04914770647883415,
0.03179094195365906,
-0.03784644976258278,
-0.029201975092291832,
-0.07532893866300583,
0.030495094135403633,
0.07630612701177597,
-0.03253467008471489,
0.05466719716787338,
-0.024517113342881203,
-0.02728237397968769,
0.02846265211701393,
-0.00025545756216160953,
-0.020086856558918953,
0.030874356627464294,
0.00854087620973587,
0.03325458616018295,
-0.0229412242770195,
0.0007074919994920492,
0.05383693054318428,
0.006779598072171211,
-0.0202418714761734,
0.03263207897543907,
0.005845037288963795,
0.013726068660616875,
-0.015976550057530403,
-0.042714353650808334,
-0.06812760978937149,
0.05254427716135979,
-0.02282693050801754,
0.014700580388307571,
-0.0006455436232499778,
-0.017215024679899216,
0.06815281510353088,
0.04463784024119377,
0.011259772814810276,
-0.055331628769636154,
-0.008974898606538773,
-0.02551170624792576,
0.037855472415685654,
0.020636891946196556,
0.021547961980104446,
0.0039580101147294044,
0.023253826424479485,
0.002338868100196123,
-0.022413305938243866,
0.030673528090119362,
-0.04217848926782608,
-0.08637930452823639,
-0.0070182946510612965,
0.002186294412240386,
-0.033559735864400864,
0.017415912821888924,
0.060728639364242554,
-0.021682271733880043,
0.0415763333439827,
-0.04715603590011597,
0.03733057156205177,
0.048133186995983124,
0.018089057877659798,
-0.03351347893476486,
0.0697338730096817,
-0.019369222223758698,
0.05072439834475517,
-0.012119602411985397,
0.0014318025205284357,
0.12056659907102585,
0.09902387112379074,
0.042195942252874374,
-0.040074024349451065,
0.024328703060746193,
-0.013579999096691608,
-0.01981017179787159,
-0.04488886892795563,
0.008064936846494675,
0.0057889847084879875,
0.02456056885421276,
-0.031816285103559494,
0.034464918076992035,
-0.056672029197216034,
0.0001738863211357966,
-0.005855316296219826,
-0.051783833652734756,
-0.044842835515737534,
-0.025384949520230293,
0.007193578872829676,
-0.018026331439614296,
0.004038983024656773,
-0.006552811712026596,
0.028444156050682068,
-0.002165965735912323,
-0.0535309799015522,
-0.060326192528009415,
-0.0002968955086544156,
0.04628533497452736,
0.021253513172268867,
-0.07877673208713531,
0.022259235382080078,
-0.019927702844142914,
-0.0168076790869236,
-0.03272261470556259,
0.038628313690423965,
-0.026271136477589607,
-0.02157200500369072,
-0.022535601630806923,
0.022645236924290657,
0.0019532961305230856,
-0.018942464143037796,
0.023672280833125114,
0.019247878342866898,
-0.05354803055524826,
0.0191168375313282,
-0.05953309312462807,
0.03443795442581177,
-0.012352225370705128,
-0.01847238466143608,
-0.014399523846805096,
0.036518245935440063,
-0.006627253722399473,
-0.017940964549779892,
-0.005303582642227411,
0.009864512830972672,
0.05628581717610359,
-0.026426324620842934,
-0.018922604620456696,
0.026318607851862907,
0.025701485574245453,
-0.010398510843515396,
0.007291070185601711,
0.01763688027858734,
-0.021705908700823784,
-0.03172193840146065,
0.0016746602486819029,
0.05642376467585564,
0.012908069416880608,
-0.015326429158449173,
-0.0295204259455204,
-0.00006179654155857861,
-0.0020285830833017826,
-0.024495089426636696,
-0.023372448980808258,
0.07635448127985,
0.010256431996822357,
-0.00878554955124855,
-0.04613213241100311,
-0.03602452948689461,
-0.07636667788028717,
0.03099125437438488,
-0.056819744408130646,
-0.01728370413184166,
-0.03361263871192932,
-0.0023487070575356483,
-0.007948826998472214,
0.025299591943621635,
0.011995102278888226,
0.0032423639204353094,
0.0125484773889184,
0.0429919958114624,
0.030723826959729195,
-0.023323720321059227,
-0.050450824201107025,
0.01539330929517746,
-0.04476681724190712,
0.01863785646855831,
-0.0024695144966244698,
0.001202318468131125,
0.047779884189367294,
0.0024789345916360617,
0.02272268384695053,
0.023224007338285446,
-0.03525976464152336,
-0.015660161152482033,
0.012235037982463837,
-0.0043559749610722065,
0.010772811248898506,
0.03085331618785858,
0.0011466556461527944,
-0.021945850923657417,
0.02902212180197239,
0.03551444038748741,
-0.009876614436507225,
-0.009524859488010406,
0.01209306064993143,
-0.05243929475545883,
-0.006116658449172974,
-0.0067286137491464615,
0.010095682926476002,
-0.0012985073262825608,
-0.03934778645634651,
-0.0453256294131279,
-0.03458801656961441,
0.003404659917578101,
-0.013957391493022442,
-0.06606585532426834,
0.014269372448325157,
-0.025759506970643997,
0.008962362073361874,
0.006387039553374052,
-0.005208989605307579,
0.020792188122868538,
-0.04511810094118118,
0.028123747557401657,
0.01518426463007927,
0.0380629263818264,
-0.0017966560553759336,
-0.04294701665639877,
0.033766549080610275,
0.022598708048462868,
-0.021302564069628716,
0.01307680457830429,
0.016277946531772614,
0.03343876078724861,
0.009019097313284874,
0.0077047632075846195,
-0.030457904562354088,
0.0832524299621582,
-0.006690274458378553,
-0.006062251515686512,
-0.04710114002227783,
-0.041619595140218735,
-0.009322247467935085,
-0.011619854718446732,
-0.00007343239121837541,
-0.02347657084465027,
-0.0014048608718439937,
0.027147481217980385,
0.03417181223630905,
-0.005282032769173384,
-0.058270812034606934,
-0.022616304457187653,
-0.005288369953632355,
-0.023509858176112175,
0.0070013548247516155,
-0.0026544262655079365,
-0.006578976754099131,
0.029237423092126846,
-0.00133416592143476,
0.022222384810447693,
-0.003079585963860154,
-0.007631517015397549,
-0.09518016129732132,
-0.031496670097112656,
0.02865358255803585,
0.017584223300218582,
0.07465177029371262,
-0.07212293148040771,
0.04576462134718895,
0.05245846137404442,
-0.05419019237160683,
-0.001983336405828595,
-0.03518284112215042,
0.006429826375097036,
-0.01762072741985321,
-0.010299398563802242,
-0.017813876271247864,
0.002843224909156561,
-0.021720577031373978,
0.030446290969848633,
0.03062373399734497,
0.05281335115432739,
-0.004274431150406599,
-0.014308121055364609,
-0.002845701528713107,
0.06374375522136688,
0.04295998066663742,
0.008050579577684402,
0.034126248210668564,
-0.0033691395074129105,
-0.009045892395079136,
0.010781638324260712,
-0.03622554615139961,
0.023654013872146606,
-0.008566209115087986,
0.043908242136240005,
-0.0028498561587184668,
0.024472655728459358,
0.008809447288513184,
0.0185466930270195,
0.0027726104017347097,
-0.0027626221999526024,
0.014401343651115894,
0.014201769605278969,
-0.0035965198185294867,
-0.001487861736677587,
0.015438088215887547,
-0.04450681433081627,
0.010545293800532818,
0.0152512826025486,
-0.04504144936800003,
0.03711119666695595,
0.01859412156045437,
-0.01870787888765335,
0.00512799434363842,
-0.036005180329084396,
-0.022649623453617096,
-0.026942867785692215,
-0.012019701302051544,
0.04361075162887573,
-0.03728855773806572,
-0.03659111261367798,
0.009044178761541843,
-0.026982974261045456,
-0.008156610652804375,
-0.005769087467342615,
-0.004740471951663494,
-0.04596595838665962,
-0.03851553052663803,
-0.03521899878978729,
0.02562776207923889,
-0.033975981175899506,
0.00622157845646143,
0.00893328431993723,
-0.043978914618492126,
0.04783190041780472,
0.019758423790335655,
0.010081152431666851,
0.02145593985915184,
-0.025378243997693062,
-0.014917591586709023,
-0.0898219421505928,
0.016022365540266037,
0.033455800265073776,
-0.05368545278906822,
-0.021997200325131416,
-0.010128375142812729,
0.024632880464196205,
0.0031185911502689123,
0.06769847124814987,
-0.007299989461898804,
0.010931570082902908,
0.001276449766010046,
-0.020236456766724586,
0.005212300922721624,
0.0005591441877186298,
0.010727908462285995,
0.037448443472385406,
0.0306867528706789,
0.047565437853336334,
0.0001706037437543273,
0.03415752574801445,
-0.018224433064460754,
0.022275317460298538,
-0.023913230746984482,
0.02895764447748661,
0.04403839632868767,
0.0071118418127298355,
0.01554677914828062,
-0.03148004785180092,
-0.020153773948550224,
0.06209409236907959,
-0.016110463067889214,
-0.016258496791124344,
0.03643382713198662,
-0.024363398551940918,
-0.061795562505722046,
-0.003013785695657134,
-0.03242139890789986,
0.011639615520834923,
-0.027105851098895073,
-0.008284521289169788,
0.06814294308423996,
-0.08827188611030579,
-0.033015646040439606,
0.013728749938309193,
-0.04513774812221527,
-0.004263106267899275,
0.05526674538850784,
0.01592782512307167,
0.03345915675163269,
-0.02885841578245163,
0.046872176229953766,
-0.0011509861797094345,
-0.0428001843392849,
0.026631440967321396,
0.01676028221845627,
0.032530367374420166,
-0.0003137853345833719,
0.02178303524851799,
0.045393265783786774,
0.05335792154073715,
0.019548198208212852,
0.030657580122351646,
-0.005446074064821005,
-0.00965845212340355,
-0.03100394271314144,
0.01630641706287861,
-0.02826862968504429,
-0.01534538809210062,
0.02696375735104084,
-0.015776488929986954,
0.04397577792406082,
0.006286578718572855,
-0.013318232260644436,
-0.028310667723417282,
-0.018071910366415977,
-0.003993241116404533,
0.043428514152765274,
0.004308629315346479,
0.006434029433876276,
-0.005128127057105303,
0.0050858790054917336,
-0.007415299769490957,
-0.003608761355280876,
0.03193835914134979,
0.015125175938010216,
0.011470872908830643,
0.01690700836479664,
0.008443397469818592,
-0.009587900713086128,
-0.027458515018224716,
-0.01902908645570278,
-0.007626746315509081,
0.06413253396749496,
0.00960699375718832,
-0.009395343251526356,
0.014604303054511547,
-0.026637570932507515,
-0.03329388052225113,
0.04949967935681343,
-0.05760183930397034,
-0.02154684253036976,
-0.018104977905750275,
0.025461651384830475,
-0.013975609093904495,
-0.007123459130525589
] |
<p>The Japanese tsunami, moving at about 700 km/h, affected areas as distant as Chile's coast, 20 hours after the earthquake. How does the Coriolis force affect tsunami? Also, I saw an image of a boat caught within a large whirlpool. Is the whirlpool's rotation due to Coriolis force?</p>
| 10,733 |
[
-0.020316828042268753,
-0.02906583994626999,
-0.02186216413974762,
-0.011430419981479645,
0.054821405559778214,
0.0285695418715477,
-0.03644430264830589,
-0.0007527676643803716,
0.02276068553328514,
-0.0730697438120842,
0.003979336470365524,
0.07283346354961395,
0.04318474978208542,
-0.006137763615697622,
0.04175841808319092,
-0.010398877784609795,
-0.005608081351965666,
0.007517287041991949,
0.0024532752577215433,
-0.0037666831631213427,
-0.024161802604794502,
-0.002708044135943055,
-0.0034648755099624395,
0.007302890066057444,
-0.0063309683464467525,
-0.00008608175266999751,
0.056898556649684906,
0.008549638092517853,
0.04020654410123825,
0.038831207901239395,
0.0000496272296004463,
-0.016576863825321198,
-0.01418155338615179,
0.018381351605057716,
-0.0038742893375456333,
0.01397966593503952,
-0.04033999517560005,
-0.001515125622972846,
-0.04100976884365082,
0.04151657223701477,
-0.0125983702018857,
-0.01848531886935234,
-0.018018068745732307,
0.054103072732686996,
-0.05101020261645317,
0.05140722170472145,
-0.002958039054647088,
-0.014775104820728302,
0.04528062045574188,
-0.03965660184621811,
0.0759376585483551,
-0.0285365991294384,
0.03724474087357521,
-0.0020137520041316748,
0.04534154385328293,
0.005044430028647184,
0.04805019497871399,
0.03985312208533287,
-0.0342332161962986,
-0.05060448870062828,
-0.024177389219403267,
0.010830928571522236,
-0.009846878238022327,
-0.02414737083017826,
-0.008261069655418396,
0.04386121407151222,
0.023156771436333656,
-0.03600159287452698,
0.0011738957837224007,
-0.0004918904160149395,
0.004199799615889788,
0.020779013633728027,
0.0006948023219592869,
-0.040913064032793045,
-0.012493692338466644,
-0.05837465822696686,
-0.0050713191740214825,
0.027733245864510536,
-0.012882689014077187,
-0.0009771527256816626,
0.005062529351562262,
0.01821172796189785,
-0.0077043864876031876,
-0.008970876224339008,
0.03754894807934761,
-0.004973997361958027,
0.08710726350545883,
0.0017616432160139084,
0.01657356694340706,
0.04843585938215256,
-0.014482490718364716,
0.0022638633381575346,
-0.03626590222120285,
-0.03565574064850807,
-0.026374133303761482,
0.013880077749490738,
-0.014980179257690907,
0.05748993903398514,
0.051872335374355316,
0.020815281197428703,
0.006643982138484716,
-0.019365398213267326,
0.04744910076260567,
0.0608089342713356,
0.01890912652015686,
-0.00956458318978548,
-0.04485803097486496,
0.0036603729240596294,
-0.04875154420733452,
-0.01168233621865511,
-0.016215303912758827,
-0.027779636904597282,
-0.015243038535118103,
-0.04565741494297981,
0.01663590595126152,
-0.005617784336209297,
0.02555774711072445,
-0.004764093551784754,
0.03118758648633957,
0.08661634474992752,
0.06343633681535721,
-0.029610425233840942,
0.024197062477469444,
-0.009356312453746796,
-0.065308578312397,
0.011516756378114223,
0.021535616368055344,
-0.03444292023777962,
-0.030463458970189095,
0.02556859329342842,
0.027328921481966972,
-0.01707841455936432,
-0.006015694700181484,
-0.00678566750138998,
0.06842539459466934,
-0.014552242122590542,
-0.09982505440711975,
-0.07894532382488251,
0.05758770927786827,
0.03368229791522026,
-0.024398373439908028,
-0.06725417077541351,
-0.00024896717513911426,
0.015605372376739979,
0.08370719850063324,
0.0009447381016798317,
0.015752939507365227,
-0.00041557542863301933,
0.03237088397145271,
-0.003930149599909782,
-0.02512737363576889,
0.008306415751576424,
0.036837998777627945,
-0.03654676675796509,
-0.04321354255080223,
-0.10037370771169662,
-0.004445069003850222,
0.018070334568619728,
0.0009710610029287636,
-0.05669539421796799,
0.06113839149475098,
-0.005117962136864662,
0.010204149410128593,
0.02902345359325409,
-0.019942041486501694,
-0.031953513622283936,
0.08187288790941238,
-0.0014818672789260745,
-0.00528080714866519,
0.010579932481050491,
0.002619007835164666,
0.02455449290573597,
0.010339672677218914,
-0.002919927705079317,
0.04908157140016556,
-0.03560733422636986,
0.030477771535515785,
0.011481599882245064,
0.01533390674740076,
-0.03238457813858986,
-0.02235357090830803,
-0.04643189162015915,
-0.004368080757558346,
0.024130804464221,
-0.0151491928845644,
0.07863535732030869,
-0.008684598840773106,
-0.019769106060266495,
-0.008997747674584389,
-0.03635228052735329,
0.013517525047063828,
-0.007140114903450012,
0.045403968542814255,
-0.008610169403254986,
0.010808663442730904,
0.008763615973293781,
0.022743958979845047,
0.049710433930158615,
-0.0053234826773405075,
0.006661685649305582,
0.0011376719921827316,
0.045513175427913666,
0.00707844365388155,
-0.012269009836018085,
0.02763606794178486,
0.02850295417010784,
0.0032385236117988825,
-0.02368941716849804,
0.052788157016038895,
0.01970967836678028,
-0.02654253877699375,
0.003072181949391961,
-0.010725674219429493,
0.010515193454921246,
-0.003797962563112378,
-0.00910435151308775,
-0.022967029362916946,
0.005552937276661396,
-0.0031067482195794582,
0.02093057706952095,
0.0030522667802870274,
0.066762275993824,
0.03930368274450302,
0.0006617619073949754,
0.04205996170639992,
0.022053197026252747,
0.01982097513973713,
-0.029999317601323128,
-0.0016988428542390466,
-0.035429030656814575,
-0.05813734605908394,
0.0006177573231980205,
0.02779635787010193,
0.02126181870698929,
-0.036706823855638504,
0.021987877786159515,
0.030863629654049873,
0.043379463255405426,
0.03676695004105568,
0.0058090235106647015,
-0.015814345329999924,
-0.04796361178159714,
0.00794413685798645,
0.02364017255604267,
0.0007988941506482661,
-0.0031861013267189264,
0.03506685793399811,
0.015838144347071648,
-0.003633179934695363,
-0.01832173392176628,
-0.04464619979262352,
0.04936877265572548,
-0.011869724839925766,
0.03358246013522148,
-0.013035723939538002,
-0.012022366747260094,
0.05185744911432266,
-0.026788994669914246,
-0.008838167414069176,
-0.0011529478942975402,
0.019693180918693542,
-0.0005106538301333785,
-0.007096783258020878,
-0.014002565294504166,
0.026267724111676216,
-0.010879578068852425,
-0.0037872446700930595,
-0.0007225598092190921,
0.030492568388581276,
-0.06539555639028549,
0.002669957233592868,
-0.010064532980322838,
-0.00916085485368967,
-0.007138715125620365,
-0.007323910482227802,
0.047737520188093185,
-0.00001839622200350277,
0.07112029194831848,
-0.011627246625721455,
-0.026224536821246147,
-0.012859211303293705,
-0.023999009281396866,
-0.03381512686610222,
0.03625179082155228,
-0.03625044599175453,
0.0520239993929863,
-0.02589280530810356,
0.002820607041940093,
0.057666175067424774,
-0.028326427564024925,
0.021386202424764633,
0.004422444384545088,
-0.006118690595030785,
-0.02030559442937374,
-0.012772155925631523,
-0.041827041655778885,
0.03030473180115223,
-0.018994607031345367,
-0.007158823776990175,
0.04409058392047882,
0.0064500365406274796,
-0.029477911069989204,
0.04925176873803139,
-0.020137207582592964,
-0.03202822804450989,
-0.011867247521877289,
-0.006258442997932434,
0.02626780979335308,
-0.025924304500222206,
0.00961475633084774,
-0.01671467535197735,
-0.054152946919202805,
0.04971650242805481,
-0.0010761981830000877,
-0.06329832971096039,
0.02932092733681202,
-0.04209723323583603,
0.0542270727455616,
0.013566205278038979,
-0.03209478035569191,
0.042840369045734406,
-0.007048070430755615,
-0.03312361612915993,
0.005443106405436993,
-0.009775699116289616,
-0.03003603033721447,
-0.020413393154740334,
0.01782223954796791,
0.035371333360672,
-0.013882065191864967,
0.019413940608501434,
-0.008852535858750343,
0.009169889613986015,
0.04211673513054848,
-0.000880090577993542,
-0.04255026951432228,
0.024460848420858383,
0.02536812610924244,
0.022970935329794884,
0.002892392221838236,
0.030025245621800423,
0.004526079632341862,
0.020808346569538116,
0.014184348285198212,
0.016333146020770073,
0.02587839774787426,
-0.02593247778713703,
0.03038056567311287,
0.029496565461158752,
-0.026649611070752144,
-0.03857309743762016,
0.05576946213841438,
-0.02731645293533802,
0.04024059697985649,
0.005683153867721558,
0.029569489881396294,
0.06048407405614853,
-0.011264202184975147,
-0.02020479552447796,
0.017932524904608727,
0.0625542402267456,
-0.004543325398117304,
-0.016133824363350868,
-0.022227643057703972,
0.022944346070289612,
0.0364748053252697,
-0.023191271349787712,
-0.016469741240143776,
0.0026161756832152605,
0.004279113840311766,
0.006151263602077961,
-0.003642165567725897,
-0.01677780970931053,
-0.00060038804076612,
-0.08120360970497131,
0.007671781815588474,
-0.00767857301980257,
0.026520339772105217,
-0.009123728610575199,
0.04236016422510147,
0.021478774026036263,
0.02026010863482952,
0.03178315982222557,
0.024416077882051468,
-0.05909808352589607,
0.03206325322389603,
-0.06976785510778427,
-0.02032223343849182,
-0.022012120112776756,
-0.006419888231903315,
0.009029820561408997,
0.014580193907022476,
-0.04437776282429695,
-0.034983448684215546,
-0.047809798270463943,
-0.06444832682609558,
0.02790132723748684,
-0.018739446997642517,
-0.03786815330386162,
-0.011675551533699036,
0.021466968581080437,
0.023103978484869003,
-0.01990498974919319,
0.03963647037744522,
0.045765314251184464,
-0.029041247442364693,
-0.005464090965688229,
0.010281022638082504,
0.0029764617793262005,
-0.016921645030379295,
0.01719083823263645,
0.014583063311874866,
-0.01692940667271614,
-0.05405690148472786,
-0.020427854731678963,
-0.01224615890532732,
0.001451712567359209,
0.01615428365767002,
0.01674969121813774,
-0.006416794378310442,
-0.0500304214656353,
0.0012407597387209535,
-0.0003119641914963722,
0.02915615774691105,
-0.00436127744615078,
0.03845483809709549,
0.04208938404917717,
-0.009144512005150318,
-0.010006444528698921,
0.04508542641997337,
0.04949897155165672,
0.007589504588395357,
-0.0075405617244541645,
-0.06388723850250244,
-0.02778218314051628,
-0.009039924480021,
-0.0089939646422863,
0.01415130216628313,
-0.03831002861261368,
-0.029848089441657066,
0.016150787472724915,
0.02502925880253315,
-0.0014374678721651435,
-0.01207318902015686,
0.017722951248288155,
0.03691258281469345,
0.03677965700626373,
-0.026161056011915207,
0.015892930328845978,
0.008172279223799706,
0.034141018986701965,
0.0385035015642643,
-0.030688783153891563,
-0.014580613002181053,
-0.05701276659965515,
-0.01788625679910183,
0.025852689519524574,
0.07146076112985611,
-0.04006406292319298,
-0.019138021394610405,
-0.08351800590753555,
-0.01457352563738823,
0.07354626059532166,
-0.03147979453206062,
-0.007555845193564892,
-0.04356619715690613,
-0.006471958477050066,
-0.014002183452248573,
-0.0121469059959054,
-0.0057815019972622395,
0.017788222059607506,
-0.01718350686132908,
0.029699737206101418,
-0.014965728856623173,
-0.01477317325770855,
0.0021049233619123697,
0.003918903414160013,
0.0648566484451294,
0.00762532465159893,
0.03440968319773674,
0.008340765722095966,
-0.04139787703752518,
0.012317883782088757,
-0.037507906556129456,
-0.038945022970438004,
-0.001508836867287755,
0.011387809179723263,
-0.0275564007461071,
0.029187090694904327,
-0.018868504092097282,
-0.02225031889975071,
-0.011289478279650211,
0.016980931162834167,
-0.000575292797293514,
-0.014436347410082817,
-0.016158584505319595,
0.028216980397701263,
0.03189697116613388,
-0.0227044764906168,
0.03491167351603508,
0.005159297026693821,
-0.02899622917175293,
-0.02442735992372036,
0.004182327538728714,
0.03614732623100281,
-0.04776337370276451,
-0.03844127804040909,
-0.0073352595791220665,
0.026696059852838516,
-0.05440448969602585,
0.034457627683877945,
0.017861858010292053,
-0.016528675332665443,
-0.020455574616789818,
-0.007835527881979942,
-0.01606128364801407,
0.018925009295344353,
0.012093177996575832,
-0.04179738089442253,
0.0032213726080954075,
-0.009921090677380562,
-0.01928536221385002,
-0.02781272679567337,
0.040554292500019073,
-0.017692318186163902,
0.015618235804140568,
0.024148128926753998,
-0.018510641530156136,
-0.02193456143140793,
-0.04135013744235039,
0.0021506755147129297,
0.015382811427116394,
-0.042011357843875885,
0.006092054769396782,
0.00009970084647648036,
0.010073337703943253,
0.045923102647066116,
-0.07227937877178192,
-0.00402873707935214,
0.018886681646108627,
-0.014532502740621567,
0.03677970916032791,
-0.03120982088148594,
0.02779914252460003,
0.03703432157635689,
0.03729751333594322,
-0.06415748596191406,
-0.031597889959812164,
0.04804261028766632,
-0.024439489468932152,
-0.004115080926567316,
-0.018162472173571587,
0.006782070267945528,
-0.06160964071750641,
-0.02007344365119934,
-0.05736628174781799,
0.08631210029125214,
-0.02126018889248371,
-0.012345357798039913,
0.025353237986564636,
-0.01061963476240635,
0.08391380310058594,
-0.03300175815820694,
-0.029532263055443764,
0.04382048547267914,
-0.03001973405480385,
-0.0003805993474088609,
-0.029661519452929497,
0.07652680575847626,
-0.03299236670136452,
-0.03124590963125229,
0.027688078582286835,
-0.00450888043269515,
0.01558802928775549,
0.005511091556400061,
0.00911059882491827,
0.035342853516340256,
0.033974017947912216,
-0.01196134090423584,
-0.02501605823636055,
0.010135834105312824,
0.021538468077778816,
0.0364263579249382,
-0.028470449149608612,
0.01981600560247898,
-0.03283716365695,
-0.057310692965984344,
0.012926138937473297,
0.00032016384648159146,
0.001331054954789579,
0.00044856188469566405,
0.028086133301258087,
-0.015377471223473549,
-0.004609247203916311,
0.010769625194370747,
-0.0009465293260291219,
0.04006877541542053,
-0.006350999232381582,
-0.0009102313779294491,
0.00670313835144043,
0.044015686959028244,
-0.029211733490228653,
-0.04141559451818466,
-0.020583581179380417,
0.035571176558732986,
0.09016632288694382,
-0.034906480461359024,
0.049923866987228394,
0.0020666150376200676,
0.05034709349274635,
0.0076311067678034306,
0.00240763439796865,
-0.0008095359080471098,
0.021564284339547157,
-0.014962075278162956,
0.020762277767062187,
-0.015004883520305157,
0.015423271805047989,
0.0021306530106812716,
0.04593319818377495,
0.020242514088749886,
0.019172707572579384,
0.02739180438220501,
0.04248235374689102,
0.005813799798488617,
-0.027104953303933144,
-0.07298414409160614,
0.006041116081178188,
-0.0002833397884387523,
0.05190691351890564,
-0.02320910058915615,
-0.033510543406009674,
0.057216402143239975,
-0.000142964709084481,
0.00029088734299875796,
-0.038599949330091476,
-0.0037270167376846075,
-0.03924078866839409,
-0.003096387954428792,
-0.011584246531128883,
0.011186997406184673,
-0.04527590423822403,
0.004031146876513958,
0.0628235712647438,
0.027493920177221298,
-0.008406003937125206,
-0.029321379959583282,
-0.08558807522058487,
-0.017282962799072266,
-0.0018798911478370428,
-0.045429687947034836,
0.030004391446709633,
0.013710319064557552,
-0.029347002506256104,
0.0009090564562939107,
0.020751742646098137,
0.015806498005986214,
0.021457642316818237,
0.016974132508039474,
-0.004314707592129707,
0.08453778177499771,
-0.01936769112944603,
-0.014590485021471977,
-0.025336066260933876,
-0.002830986864864826,
0.0947820320725441,
0.03172288089990616,
0.00028991917497478426,
-0.06078376993536949,
-0.008796132169663906,
-0.040160540491342545,
0.00451708072796464,
-0.027212759479880333,
-0.011685504578053951,
0.04121020436286926,
0.023068854585289955,
0.030785461887717247,
0.057226911187171936,
-0.001473023323342204,
-0.013035429641604424,
0.04357676953077316,
-0.025183098390698433,
-0.03426486998796463,
-0.020083943381905556,
-0.009008336812257767,
-0.02726919949054718,
0.026220358908176422,
-0.07028765231370926,
0.007158457767218351,
-0.05873623490333557,
-0.006383315660059452,
-0.02660422958433628,
-0.03512350469827652,
0.008418291807174683,
0.0029085767455399036,
-0.05512232333421707,
0.001777459285221994,
0.014243142679333687,
0.018987515941262245,
-0.07481704652309418,
0.04543968662619591,
0.0056937807239592075,
-0.026625964790582657,
0.0290349293500185,
-0.03745219483971596,
0.003054153174161911,
0.03811052441596985,
0.009622875601053238,
0.036849312484264374,
-0.03167930245399475,
-0.0022673034109175205,
-0.014093542471528053,
0.020954513922333717,
0.0365368016064167,
0.034100595861673355,
-0.017672186717391014,
0.03623757138848305,
-0.006024887785315514,
-0.02115895040333271,
0.010302872397005558,
-0.00486108148470521,
0.01792903244495392,
-0.005336320027709007,
-0.021429527550935745,
-0.01178846973925829,
0.026834391057491302,
-0.013929847627878189,
0.032971594482660294,
-0.0010467635001987219,
-0.007097168359905481,
-0.005031705368310213,
-0.0013274401426315308,
0.03697764500975609,
-0.03853948041796684,
-0.016291800886392593,
-0.0030312787275761366,
0.0019694988150149584,
-0.04640563204884529,
-0.0010843027848750353,
0.02124132215976715,
0.035698022693395615,
0.012296375818550587,
0.03352753445506096,
-0.03345784917473793,
0.002380149206146598,
-0.05419854819774628,
0.026819152757525444,
-0.04359802231192589,
-0.024105016142129898,
-0.0012658415362238884,
-0.025586867704987526,
0.06747601926326752,
0.007507884409278631,
-0.01220332644879818,
0.024709440767765045,
-0.049338627606630325,
0.011024157516658306,
0.008589066565036774,
-0.03792472183704376,
-0.02934383787214756,
0.03190290555357933,
-0.014714113436639309,
-0.03263137862086296,
-0.04170643165707588,
0.027750255540013313,
0.05591536685824394,
-0.012570178136229515,
0.009428116492927074,
0.0002563935413490981,
-0.03127381578087807,
0.014629470184445381,
0.04022657498717308,
-0.039553746581077576,
-0.01987696997821331,
0.01598777435719967,
-0.0002548550837673247,
-0.02017105743288994,
-0.0023906740825623274,
-0.006738436874002218,
-0.0010517840273678303,
-0.0004664952284656465,
0.020587343722581863,
-0.05255884677171707,
0.031805265694856644,
-0.043406110256910324,
0.023306237533688545,
-0.03186418488621712,
-0.01770058088004589,
-0.09089646488428116,
0.010922013781964779,
-0.004468819592148066,
-0.016382424160838127,
-0.03945106640458107,
-0.0018088554497808218,
-0.03126426413655281,
-0.003495400305837393,
-0.017179206013679504,
-0.00016135838814079762,
0.011383989825844765,
0.011203857138752937,
0.021844852715730667,
-0.033511482179164886,
0.035646457225084305,
-0.005291860084980726,
-0.03776610270142555,
0.044954027980566025,
-0.037919990718364716,
-0.048143163323402405,
0.03562906011939049,
-0.04124632477760315,
0.029423149302601814,
0.034705765545368195,
0.012232481501996517,
0.005123775452375412,
0.08958037942647934,
-0.009070897474884987,
0.0032887072302401066,
-0.018625959753990173,
-0.0202728733420372,
-0.018723610788583755,
0.0026413879822939634,
0.007707981392741203,
-0.02909461222589016,
0.009180571883916855,
0.07387599349021912,
0.07159406691789627,
0.03348908945918083,
0.009173611178994179,
-0.008517737500369549,
0.0021883368026465178,
0.04088595137000084,
0.0007179338717833161,
-0.013916337862610817,
0.00858585350215435,
0.03266438469290733,
-0.051938243210315704,
0.011556815356016159,
-0.015477263368666172,
0.0046015228144824505,
-0.09621575474739075,
0.012530616484582424,
0.02189028635621071,
0.0005851865280419588,
0.05074295401573181,
-0.04537958279252052,
0.02240537479519844,
0.026705922558903694,
-0.034749533981084824,
0.000857601233292371,
-0.0369320884346962,
0.006945964880287647,
-0.01946958340704441,
0.0147625170648098,
0.05906529724597931,
0.069630928337574,
0.05485723167657852,
0.022126223891973495,
0.007713083643466234,
0.007689713966101408,
-0.034467119723558426,
-0.0030308805871754885,
0.05558782070875168,
0.05006789416074753,
0.008038115687668324,
0.0011157814878970385,
0.032888028770685196,
-0.02085055783390999,
-0.014074502512812614,
0.014485941268503666,
-0.041646406054496765,
0.04847410321235657,
-0.03598746284842491,
0.01100301742553711,
0.009680823422968388,
-0.00875869207084179,
-0.0030889404006302357,
-0.01604313962161541,
0.0007167072617448866,
0.045621663331985474,
-0.004703288432210684,
0.027580928057432175,
-0.0004350610252004117,
0.0034583641681820154,
-0.001502103521488607,
-0.04799965023994446,
0.01175741758197546,
0.01803494431078434,
-0.0023327211383730173,
-0.0056519582867622375,
-0.0035575355868786573,
-0.006618402898311615,
0.04986490309238434,
0.020425302907824516,
0.018023844808340073,
-0.03509708121418953,
-0.002565511269494891,
0.019649412482976913,
-0.04173106327652931,
-0.023760948330163956,
0.04580517113208771,
0.024835720658302307,
-0.01804596371948719,
-0.02394968830049038,
-0.018880940973758698,
-0.001147737493738532,
-0.042987652122974396,
0.011786477640271187,
0.004465836100280285,
-0.006651103962212801,
-0.04504363238811493,
-0.02468429133296013,
-0.016079509630799294,
0.04974006116390228,
0.006387511733919382,
0.00177671923302114,
0.04348175227642059,
-0.020027166232466698,
-0.04024839028716087,
-0.02759350650012493,
0.02902831882238388,
0.028341950848698616,
-0.028696002438664436,
-0.010703949257731438,
-0.016967957839369774,
-0.00909249484539032,
0.035367451608181,
0.03967839479446411,
-0.004721515811979771,
0.012715693563222885,
0.01198130939155817,
-0.019913578405976295,
0.013279506005346775,
-0.009397943504154682,
-0.0004913783632218838,
-0.00032845872920006514,
-0.07412735372781754,
0.009095940738916397,
-0.01027042604982853,
-0.006238986272364855,
-0.03510405123233795,
0.006303147878497839,
-0.004707627929747105,
0.056887008249759674,
-0.011148367077112198,
-0.002692106645554304,
0.05378791317343712,
0.03472051024436951,
-0.0024638099130243063,
0.072977714240551,
-0.003369684563949704,
0.010794157162308693,
0.007776984479278326,
-0.00981298740953207,
-0.03953470289707184,
0.01741950586438179,
-0.04328228533267975,
0.005307260900735855,
0.02058032900094986,
-0.02400735579431057,
0.02874680981040001,
-0.05679180100560188,
0.019538363441824913,
0.04317691922187805,
-0.016454990953207016,
-0.010388094931840897,
0.013978821225464344,
0.02044123224914074,
0.0057881055399775505,
-0.032425276935100555,
0.006547983735799789,
0.027052178978919983,
-0.008161237463355064,
0.014408405870199203,
0.041913919150829315,
0.03410952910780907,
0.007692634128034115,
-0.02708541601896286,
0.014099418185651302,
-0.013947470113635063,
0.027979841455817223,
0.001867559738457203,
0.018400445580482483,
-0.016122447326779366,
-0.0599394328892231,
-0.00579405389726162,
-0.02825886197388172,
-0.017690200358629227,
0.0012932148529216647,
-0.01899139955639839,
0.07645885646343231,
-0.008504275232553482,
0.04101791977882385,
-0.014026816934347153,
-0.04926515743136406,
-0.017902512103319168,
-0.022510869428515434,
-0.007624940015375614,
0.01732957549393177,
-0.02241848036646843,
-0.029614001512527466,
0.017293570563197136,
-0.010146587155759335,
0.025365034118294716,
-0.04900291562080383,
0.04566419869661331,
-0.007717055734246969,
0.025250129401683807,
-0.035298094153404236,
-0.005693489219993353,
-0.03826773166656494,
0.002457619644701481,
0.04965226352214813,
0.020648237317800522,
0.021143069490790367,
-0.013982514850795269,
-0.00979073066264391,
-0.0055551789700984955,
0.0387674979865551,
-0.10882595926523209,
-0.010917644016444683,
-0.011602739803493023,
0.021492483094334602,
-0.00553695997223258,
0.0010142510291188955
] |
<p>Does anyone know a reference or a paper which discusses string theory correction to Friedmann equations?</p>
| 10,734 |
[
0.006975507363677025,
-0.026188528165221214,
-0.002876752521842718,
-0.04154733568429947,
0.016695810481905937,
0.006604513619095087,
-0.023345820605754852,
-0.03502412512898445,
-0.02356843091547489,
-0.02895158715546131,
0.01894157938659191,
0.024750322103500366,
0.04845047742128372,
0.013670222833752632,
0.01353699155151844,
-0.012719976715743542,
0.0068093775771558285,
0.01674390397965908,
-0.01815594919025898,
-0.036708299070596695,
0.011215503327548504,
0.041578371077775955,
-0.0377458892762661,
-0.0000037205854823696427,
-0.00289167114533484,
0.018198484554886818,
0.031238622963428497,
0.03251179680228233,
0.014059781096875668,
0.05641183629631996,
-0.03073558583855629,
-0.00613985164090991,
-0.009127210825681686,
0.034119971096515656,
-0.028406888246536255,
-0.009846129454672337,
-0.016057530418038368,
-0.06560943275690079,
0.0013766316697001457,
0.005300698336213827,
-0.04842020198702812,
0.006319575011730194,
-0.010085420683026314,
0.0503457672894001,
-0.00596856651827693,
0.04341008514165878,
-0.013433154672384262,
0.0027298245113343,
0.0770808756351471,
-0.08231531083583832,
0.10500496625900269,
0.000689120905008167,
0.012578851543366909,
0.04233992099761963,
-0.01780623197555542,
-0.012077401392161846,
0.08281548321247101,
0.06542568653821945,
0.023511989042162895,
-0.07069375365972519,
-0.023470431566238403,
0.01132105477154255,
0.023838717490434647,
-0.04794272407889366,
-0.016810748726129532,
0.06178227812051773,
0.002931887051090598,
-0.02044776640832424,
0.007955017499625683,
0.007230452261865139,
-0.016528917476534843,
-0.017732474952936172,
0.04619992524385452,
0.006666250992566347,
0.0032964039128273726,
-0.027458807453513145,
0.007409302052110434,
-0.030046405270695686,
0.021358219906687737,
0.018641142174601555,
-0.028707757592201233,
-0.011463911272585392,
0.04582533985376358,
0.022662093862891197,
-0.007569660898298025,
0.02582605741918087,
0.04449331760406494,
-0.02882685326039791,
0.014375245198607445,
0.045471567660570145,
-0.02123102732002735,
-0.017097583040595055,
0.08857826888561249,
-0.04068371653556824,
-0.01605720818042755,
0.02624175138771534,
0.011077013798058033,
0.06316804885864258,
-0.007920065894722939,
-0.02438691444694996,
0.013002718798816204,
-0.026317201554775238,
-0.027326026931405067,
0.07466177642345428,
0.005899213254451752,
-0.0434148907661438,
-0.05804697051644325,
0.011577819474041462,
-0.030790532007813454,
-0.004184911493211985,
-0.05541081354022026,
0.0026210120413452387,
-0.036779433488845825,
-0.011976868845522404,
-0.01790066622197628,
-0.02006913535296917,
0.01033678837120533,
-0.03530155122280121,
0.04937489330768585,
0.056860409677028656,
0.04576573148369789,
-0.0008053170749917626,
0.022381873801350594,
-0.007930883206427097,
-0.058866940438747406,
-0.012122570537030697,
0.05223982781171799,
-0.02580811269581318,
-0.05965782701969147,
0.0019546085968613625,
0.018482936546206474,
-0.03520195931196213,
0.029046716168522835,
0.011782413348555565,
0.04163939133286476,
0.0039854650385677814,
-0.06430625170469284,
-0.04924583062529564,
0.03850708529353142,
0.0002930550544988364,
0.01724778302013874,
-0.055782511830329895,
0.003348910016939044,
0.0372079573571682,
0.09380506724119186,
0.024996737018227577,
0.021167181432247162,
0.0048456573858857155,
0.05849555507302284,
-0.023472607135772705,
-0.014499054290354252,
-0.021040553227066994,
0.010943789035081863,
-0.03538653254508972,
-0.011927181854844093,
-0.0656578540802002,
0.041171252727508545,
0.04984598979353905,
-0.009667378850281239,
0.0037901396863162518,
0.07280153036117554,
-0.0030522195156663656,
-0.008777628652751446,
0.014444991946220398,
-0.015232941135764122,
-0.00813934113830328,
0.0426214225590229,
0.0034614275209605694,
-0.02323148585855961,
-0.005342230666428804,
-0.02257232367992401,
0.03168921917676926,
0.02584439143538475,
0.004222515970468521,
-0.005089370533823967,
-0.06650650501251221,
-0.007509754970669746,
0.005134901963174343,
0.014101419597864151,
-0.007122936192899942,
-0.01688024401664734,
-0.00909106433391571,
0.013370038941502571,
0.00779868895187974,
-0.026020880788564682,
0.01697513461112976,
-0.041273072361946106,
-0.027045678347349167,
0.0075034634210169315,
-0.07713714987039566,
0.018395571038126945,
-0.02578853629529476,
0.0045874230563640594,
-0.03332098200917244,
0.020715633407235146,
0.021433379501104355,
0.027872124686837196,
0.015967676416039467,
-0.04296477884054184,
-0.029670244082808495,
0.027762992307543755,
0.04751507192850113,
-0.006232541520148516,
-0.011270755901932716,
-0.005857932381331921,
0.031569190323352814,
0.05798580124974251,
-0.01011369377374649,
0.027958620339632034,
-0.013433159328997135,
-0.01662941835820675,
0.006013693753629923,
-0.012386960908770561,
0.034090738743543625,
-0.05519169569015503,
0.012958395294845104,
0.02676265500485897,
-0.01428320724517107,
0.014070835895836353,
0.04095831513404846,
-0.055852796882390976,
0.04526263102889061,
0.044868577271699905,
0.03836621344089508,
-0.004070919938385487,
0.04292689636349678,
-0.0103322584182024,
0.010398301295936108,
0.01941935159265995,
-0.05107732117176056,
-0.05918208137154579,
-0.027442876249551773,
0.057913463562726974,
0.02355143614113331,
-0.016381122171878815,
-0.0005987375625409186,
0.07754919677972794,
0.031070159748196602,
0.01955273188650608,
0.032744862139225006,
-0.020514430478215218,
-0.0467701330780983,
0.035413287580013275,
-0.031598128378391266,
0.022578947246074677,
0.009450944140553474,
0.04183191806077957,
-0.008680000901222229,
-0.010934112593531609,
0.001988012343645096,
-0.05030492693185806,
0.004616368096321821,
-0.01136035192757845,
0.020478039979934692,
0.012946647591888905,
-0.030761949717998505,
0.012488435953855515,
-0.03050008974969387,
0.05298237130045891,
0.02980581670999527,
0.024682827293872833,
0.0009338983800262213,
-0.03388318791985512,
-0.0068750930950045586,
0.006403923965990543,
0.005482840351760387,
-0.017131121829152107,
-0.005689424462616444,
0.02446388639509678,
-0.044928133487701416,
-0.003256850643083453,
-0.0006739356904290617,
-0.010757321491837502,
-0.020846836268901825,
0.025356246158480644,
0.0021813642233610153,
0.019937802106142044,
0.02088828571140766,
-0.01791038177907467,
-0.027787622064352036,
0.018465347588062286,
0.010814709588885307,
0.004910109099000692,
0.014701512642204762,
-0.04803380370140076,
0.02675282210111618,
-0.026933619752526283,
-0.04652306064963341,
0.043749719858169556,
-0.015232071280479431,
0.019964510574936867,
0.001612277003005147,
-0.023212764412164688,
0.008298356086015701,
-0.020155295729637146,
-0.0118630426004529,
0.011215838603675365,
-0.016974275931715965,
0.006660137791186571,
0.03865101560950279,
0.020319776609539986,
-0.030395330861210823,
0.007814389653503895,
-0.046665262430906296,
-0.02575923129916191,
-0.02794862724840641,
0.01434234157204628,
0.0068969218991696835,
-0.034097686409950256,
0.04577026888728142,
0.010833995416760445,
-0.038074791431427,
0.005600651726126671,
-0.043867047876119614,
-0.034316591918468475,
0.04474771022796631,
-0.016836509108543396,
0.05924731492996216,
-0.01658136025071144,
-0.06364515423774719,
0.0370648056268692,
0.012950154952704906,
-0.011284925974905491,
0.011106864549219608,
0.01663828082382679,
0.005350573919713497,
-0.02162090688943863,
0.00029349306714721024,
0.018529830500483513,
-0.009886951185762882,
0.035520438104867935,
0.024910274893045425,
0.01407841220498085,
0.04125547036528587,
0.021585727110505104,
-0.033670537173748016,
0.013977296650409698,
-0.0015750558814033866,
0.027171673253178596,
0.03899013623595238,
-0.008339437656104565,
-0.028246494010090828,
0.020291823893785477,
-0.0015203029615804553,
0.009253243915736675,
0.005460906308144331,
-0.05832140892744064,
0.004955802112817764,
0.007309437729418278,
-0.010673041455447674,
-0.010580809786915779,
0.022861523553729057,
0.00023590816999785602,
-0.015601389110088348,
-0.003660093527287245,
0.036658745259046555,
0.04219185560941696,
0.026331506669521332,
0.029611723497509956,
0.0006149306427687407,
0.059022899717092514,
-0.041106026619672775,
-0.036892104893922806,
0.03283846005797386,
-0.011088117957115173,
0.03341758996248245,
-0.039228785783052444,
-0.03528399392962456,
0.04405747726559639,
0.030391426756978035,
0.01986905187368393,
-0.012981249950826168,
-0.03710736706852913,
0.015692370012402534,
-0.07299154251813889,
-0.0005677873850800097,
-0.06949333101511002,
0.04036752134561539,
0.0035142567940056324,
0.026493320241570473,
-0.01379374973475933,
0.019475635141134262,
0.034090038388967514,
0.03135300800204277,
-0.08696935325860977,
0.01002687867730856,
-0.06929587572813034,
-0.009968624450266361,
0.0072108069434762,
-0.0032075284980237484,
-0.002737682778388262,
-0.026464251801371574,
-0.016469672322273254,
-0.045524273067712784,
-0.0011222671018913388,
-0.059835970401763916,
-0.010947124101221561,
-0.031169848516583443,
-0.05146441608667374,
0.014529254287481308,
0.03616556525230408,
0.02365230955183506,
-0.023094462230801582,
-0.015178658068180084,
0.051093827933073044,
-0.011007444001734257,
-0.029992680996656418,
-0.032686758786439896,
0.043964724987745285,
0.001886051963083446,
0.052136171609163284,
0.03192661702632904,
0.021246565505862236,
-0.04762214794754982,
0.039627302438020706,
0.033718615770339966,
0.030134418979287148,
-0.015391050837934017,
-0.018430855125188828,
-0.02725403383374214,
-0.044190824031829834,
-0.03913487493991852,
-0.028045959770679474,
0.060661640018224716,
-0.002504541538655758,
-0.02242695726454258,
0.03539878875017166,
0.020287761464715004,
-0.011810227297246456,
0.016317671164870262,
0.04498028755187988,
-0.00527220917865634,
-0.03398429602384567,
-0.02696816250681877,
-0.027006756514310837,
-0.026717865839600563,
0.038810309022665024,
0.017086736857891083,
0.003151580924168229,
-0.05459132418036461,
0.03709908574819565,
0.02925560623407364,
0.006572190206497908,
-0.05115452781319618,
-0.04100435599684715,
0.033012304455041885,
0.017841266468167305,
0.014042967930436134,
0.014170329086482525,
0.026280177757143974,
0.03246599808335304,
0.020787283778190613,
0.008261782117187977,
-0.0047805048525333405,
-0.0801183208823204,
0.0035674325190484524,
0.011117242276668549,
0.001963266870006919,
-0.015068722888827324,
-0.01013452559709549,
-0.08662626147270203,
-0.023641444742679596,
0.051266662776470184,
0.0007337818969972432,
0.024187544360756874,
0.004632115829735994,
0.011358237825334072,
0.0369565449655056,
0.010068266652524471,
-0.006203267257660627,
0.01811608485877514,
-0.012277429923415184,
0.034574028104543686,
-0.003600182244554162,
0.03008227050304413,
-0.007016315590590239,
0.027317434549331665,
0.024570301175117493,
0.04789860546588898,
0.025786226615309715,
0.01830998621881008,
-0.004148309584707022,
0.01449329499155283,
-0.047830983996391296,
-0.06125779077410698,
-0.014341394416987896,
-0.006693567615002394,
-0.02121642790734768,
0.006041521206498146,
-0.013965316116809845,
0.0017957615200430155,
0.021818695589900017,
0.020195521414279938,
-0.01648314669728279,
-0.019025234505534172,
-0.037274815142154694,
0.014843850396573544,
0.015842868015170097,
-0.029331957921385765,
0.06170620396733284,
0.053656067699193954,
-0.029304558411240578,
-0.0005138148553669453,
-0.032770246267318726,
0.056997980922460556,
-0.03531843051314354,
0.01348103117197752,
-0.017901284620165825,
0.0004043338121846318,
-0.06701485067605972,
0.024558784440159798,
-0.03309901803731918,
0.015810202807188034,
-0.007302549667656422,
-0.013277741149067879,
-0.005152435041964054,
0.015422713942825794,
-0.0029983995482325554,
0.029921498149633408,
0.016653237864375114,
-0.0031149580609053373,
0.02259196527302265,
-0.012305238284170628,
0.04282334819436073,
0.027631882578134537,
-0.013338470831513405,
0.013446245342493057,
0.008331459015607834,
0.03980616107583046,
-0.023250561207532883,
-0.048637498170137405,
0.028094565495848656,
-0.021136105060577393,
0.05988077074289322,
-0.021719660609960556,
0.016853302717208862,
-0.012998003512620926,
-0.052437182515859604,
-0.020849939435720444,
0.0036539642605930567,
-0.03925030305981636,
0.0005999102140776813,
-0.0612192377448082,
-0.010960713028907776,
0.02883271314203739,
0.037139054387807846,
-0.05375908687710762,
-0.019330274313688278,
0.035255905240774155,
-0.023415790870785713,
-0.04268690571188927,
-0.039701905101537704,
0.03265319764614105,
-0.05701132118701935,
-0.013648522086441517,
0.007565345149487257,
0.04841043800115585,
-0.028927166014909744,
-0.03506889194250107,
-0.020004164427518845,
0.044054482132196426,
0.021107111126184464,
0.00653817830607295,
-0.023735739290714264,
-0.00587134575471282,
-0.02082451432943344,
-0.0046501061879098415,
0.004510757513344288,
0.04436200484633446,
-0.028645450249314308,
-0.018764225766062737,
-0.023881683126091957,
0.012718596495687962,
-0.008548111654818058,
-0.006870334967970848,
0.031176481395959854,
0.04607332497835159,
0.03050869330763817,
0.01146340649574995,
-0.03634970635175705,
0.03119742125272751,
-0.04346508905291557,
0.0024359873495996,
-0.03394993767142296,
-0.0033536264672875404,
0.0014845558907836676,
-0.020874537527561188,
0.014972814358770847,
-0.037927474826574326,
-0.02235312946140766,
0.0010137660428881645,
0.11710277199745178,
0.05151146277785301,
-0.036756716668605804,
0.032394811511039734,
-0.035531047731637955,
0.016866516321897507,
-0.0029429530259221792,
0.013268793933093548,
0.018942074850201607,
0.020604845136404037,
0.0017343834042549133,
-0.09722533822059631,
0.003556113224476576,
0.00773264467716217,
0.0621354915201664,
-0.0014879620866850019,
0.01574750989675522,
0.0322594940662384,
-0.0052617453038692474,
-0.004800877999514341,
-0.03574712574481964,
-0.013008113019168377,
0.03506825491786003,
-0.025001047179102898,
0.02478225715458393,
-0.030229555442929268,
0.012529835104942322,
0.013053521513938904,
0.03334071487188339,
-0.024320382624864578,
0.03526458144187927,
0.006058371625840664,
-0.001393664162606001,
0.04077310860157013,
-0.020461397245526314,
-0.02373356744647026,
0.05458422750234604,
-0.02825103886425495,
0.04084797203540802,
0.0006868827622383833,
0.006568789016455412,
0.02764436975121498,
0.03627241030335426,
-0.003280482953414321,
0.010552561841905117,
-0.016126198694109917,
-0.03491939976811409,
0.03932489454746246,
-0.010651977732777596,
0.023822085931897163,
0.02030133455991745,
-0.007865642197430134,
0.01626037247478962,
-0.009259991347789764,
0.0348610021173954,
0.016122518107295036,
-0.06102178245782852,
-0.012960616499185562,
-0.040198251605033875,
-0.05014848709106445,
0.04767203703522682,
0.03915299102663994,
-0.011340145021677017,
0.012835688889026642,
-0.03969850763678551,
0.02139558643102646,
0.02986821159720421,
0.0396268405020237,
-0.007187827490270138,
0.072969451546669,
-0.05495674908161163,
0.02439781278371811,
-0.0378781221807003,
0.016773628070950508,
0.1251075267791748,
0.06333989650011063,
0.01580173335969448,
-0.09074839949607849,
0.055158209055662155,
-0.02524934709072113,
0.02561708353459835,
-0.0779699832201004,
0.02669273130595684,
-0.02377030812203884,
-0.012209325097501278,
-0.016469290480017662,
0.052638355642557144,
-0.033964402973651886,
-0.05299865081906319,
0.05381445959210396,
-0.05358840525150299,
-0.03832746297121048,
0.03310127183794975,
0.016488518565893173,
0.016503047198057175,
0.0051954383961856365,
-0.03891811892390251,
-0.004570513032376766,
-0.029305873438715935,
-0.025361541658639908,
-0.06165000796318054,
-0.012124772183597088,
-0.004365675617009401,
0.006453089416027069,
-0.038079049438238144,
-0.0037553850561380386,
0.0002600833249744028,
-0.006207279395312071,
-0.025068532675504684,
0.009525409899652004,
0.007502332329750061,
-0.008468672633171082,
0.013008814305067062,
0.0533904954791069,
0.00926461722701788,
0.017597505822777748,
-0.008061377331614494,
0.020227430388331413,
-0.040869489312171936,
0.02976941131055355,
-0.028763683512806892,
0.039481934159994125,
-0.008532077074050903,
0.005828457418829203,
0.032691750675439835,
0.008940812200307846,
0.019508318975567818,
-0.026345618069171906,
-0.0014834189787507057,
0.012802368961274624,
0.006617655977606773,
-0.009159239940345287,
0.008756817318499088,
-0.0037810516078025103,
0.0228365920484066,
0.01691996119916439,
0.0316077321767807,
0.017923494800925255,
-0.020847536623477936,
0.009012418799102306,
-0.00655747763812542,
0.01569260098040104,
-0.057184141129255295,
-0.013367811217904091,
-0.03135187178850174,
0.02050395868718624,
-0.035895176231861115,
-0.0297393798828125,
0.010419528000056744,
0.037507131695747375,
0.028171664103865623,
0.0056398892775177956,
0.004295732825994492,
0.007026681676506996,
-0.05428609251976013,
0.018086804077029228,
-0.04568633809685707,
-0.007303806021809578,
-0.022228730842471123,
-0.026288699358701706,
0.05443549156188965,
0.015934044495224953,
-0.013992901891469955,
0.01043853908777237,
-0.02218272164463997,
0.016578909009695053,
0.03659190982580185,
-0.022735510021448135,
-0.009022553451359272,
-0.020866502076387405,
-0.04361024871468544,
-0.01377859991043806,
-0.015590043738484383,
0.010437593795359135,
0.028557995334267616,
0.004260437563061714,
0.01691698655486107,
0.052090562880039215,
-0.021251004189252853,
0.002758797723799944,
0.0016453799325972795,
-0.03354586660861969,
-0.013840137049555779,
0.02218831330537796,
0.04066144675016403,
-0.007440287619829178,
-0.014473126269876957,
0.008435279130935669,
0.000963554484769702,
0.015299513936042786,
0.023904552683234215,
-0.08424075692892075,
0.051144618541002274,
-0.0189674012362957,
-0.02677111327648163,
-0.06927716732025146,
-0.00006983584898989648,
-0.02299841307103634,
-0.006572982296347618,
-0.004923688713461161,
0.010089769959449768,
-0.021028876304626465,
0.018115844577550888,
-0.03930849954485893,
-0.024967167526483536,
0.05112325772643089,
-0.022148478776216507,
-0.014857865869998932,
0.01585135981440544,
0.029869217425584793,
0.025058582425117493,
0.024634581059217453,
-0.01563115604221821,
-0.043049510568380356,
0.015903975814580917,
-0.045761171728372574,
-0.0661403089761734,
0.03497788682579994,
-0.0011021032696589828,
0.013651314191520214,
-0.0016212203772738576,
-0.03764669969677925,
-0.033856362104415894,
0.0759667456150055,
-0.015491552650928497,
-0.013252543285489082,
0.009189310483634472,
-0.01805656962096691,
0.004075624048709869,
0.0018156662117689848,
0.022487424314022064,
-0.016440721228718758,
0.004465434700250626,
0.007443376816809177,
0.0449453704059124,
0.0067940629087388515,
-0.050198718905448914,
0.017499428242444992,
-0.05220354348421097,
-0.01775636337697506,
-0.02394568920135498,
0.008597717620432377,
-0.02406219206750393,
0.05604800581932068,
-0.015267066657543182,
0.01615213043987751,
0.05225341022014618,
0.00616145646199584,
-0.06509445607662201,
0.011880224570631981,
0.025576448068022728,
0.034267228096723557,
0.041534218937158585,
-0.03921566531062126,
0.05616147816181183,
0.004416486248373985,
-0.009214864112436771,
0.030878359451889992,
-0.015869932249188423,
-0.0036186676006764174,
-0.027729647234082222,
-0.005241689272224903,
-0.014551207423210144,
0.044486913830041885,
0.053776420652866364,
0.030554000288248062,
-0.025838080793619156,
-0.007187782321125269,
-0.005180053878575563,
-0.01211977656930685,
0.000034697455703280866,
0.024920128285884857,
0.007525780703872442,
0.004136398900300264,
0.036287274211645126,
-0.022653337568044662,
-0.05250829830765724,
0.03590040281414986,
0.047414980828762054,
-0.010729887522757053,
-0.034533239901065826,
0.01981535740196705,
0.022982489317655563,
0.006895566359162331,
0.022951973602175713,
-0.0013581818202510476,
0.02190704643726349,
0.014328112825751305,
-0.018641801550984383,
0.0016618273220956326,
-0.02824627421796322,
-0.0004088415880687535,
-0.0268770232796669,
-0.04456246271729469,
0.00166579510550946,
0.030806995928287506,
-0.0034908424131572247,
0.008713203482329845,
-0.02721426449716091,
-0.01109360158443451,
0.029485026374459267,
-0.004971932619810104,
0.009797671809792519,
-0.057695385068655014,
-0.0013239443069323897,
0.04844144359230995,
0.0027579586021602154,
-0.013478493317961693,
0.030434902757406235,
0.016811739653348923,
-0.015006139874458313,
0.03805459663271904,
-0.007332275155931711,
0.008139087818562984,
-0.03374125435948372,
-0.0012214996386319399,
-0.015906840562820435,
0.0014827682171016932,
-0.010104292072355747,
-0.06519387662410736,
-0.008273947052657604,
0.028072157874703407,
-0.008485817350447178,
-0.005741291679441929,
-0.015848727896809578,
-0.025147007778286934,
0.019380813464522362,
-0.03245018422603607,
0.027439594268798828,
0.0025384463369846344,
0.01640249788761139,
0.014486463740468025,
0.023598026484251022,
0.016329389065504074,
0.008895239792764187,
0.025457782670855522,
-0.044992245733737946,
-0.03537069261074066,
0.025146503001451492,
-0.03024647757411003,
0.0015159279573708773,
-0.03513045236468315,
0.014781867153942585,
0.021552402526140213,
-0.051894452422857285,
-0.013870981521904469,
-0.014530829153954983,
0.009888581931591034,
0.0280690249055624,
0.005488932132720947,
-0.014789543114602566,
0.03851509839296341,
-0.0044573103077709675,
-0.04015759006142616,
0.04629162698984146,
0.001178121310658753,
-0.019057098776102066,
0.06523846834897995,
-0.029806947335600853,
0.03060837648808956,
0.031162414699792862,
0.006332388147711754,
-0.047760508954524994,
0.001910082413814962,
-0.06423632055521011,
-0.0074934884905815125,
-0.01353768352419138,
-0.002118480857461691,
-0.005466921254992485,
-0.029570920392870903,
0.008311371318995953,
0.03827745094895363,
-0.018383508548140526,
0.000388805492548272,
0.049080103635787964,
0.007448538206517696,
0.043555695563554764,
-0.018647171556949615,
0.02357061207294464,
0.04000917077064514,
-0.0075210691429674625,
0.0026434806641191244,
0.03861687704920769,
0.05261685326695442,
0.03148271143436432,
0.03450359031558037,
0.009437862783670425,
-0.025046706199645996,
0.024680739268660545,
0.007475336082279682,
0.018403509631752968,
-0.06822502613067627,
-0.019348472356796265,
0.01278617512434721,
-0.03498482331633568,
0.04158704727888107,
0.03363844007253647,
-0.025621768087148666,
0.0642068013548851,
-0.009464290924370289,
-0.005200429819524288,
0.00788046419620514,
-0.01394171267747879,
-0.01928473263978958,
-0.003912465646862984,
-0.05063896253705025,
0.07394910603761673,
0.001496696611866355,
0.0054923431016504765,
-0.005711952690035105,
0.020483732223510742,
-0.010384720750153065,
-0.05353034660220146,
-0.006914912257343531,
-0.0016058951150625944,
0.009493996389210224,
0.02129458077251911,
-0.017703985795378685,
0.007776386570185423,
-0.013860978186130524,
0.043812524527311325,
0.023394139483571053,
-0.004334231838583946,
-0.04116667062044144,
0.008956010453402996,
-0.020483236759901047,
0.04573071748018265,
-0.05911067873239517,
-0.015490815043449402,
0.00553880026564002,
0.017679249867796898,
-0.030797801911830902,
-0.023267565295100212
] |
<p>In the Debye-Scherrer procedure a sample of crystalline powder is hit by a beam of monochromatic photons. The diffracted photons are measured with a detector. We have constructive interference of the photons if the Bragg conditions are met.
In my lecture notes it says that there are always crystalline planes oriented in a way that the Bragg conditions are fulfilled, thus leading to the typical rings observed with powder diffractometer.</p>
<p><img src="http://i.stack.imgur.com/f4Tes.png" alt="Graphic taken from Wikipedia">
(Graphic taken from Wikipedia)</p>
<p>I have a hard time seeing why there are discrete rings, because from the reason above I would expect that for every angle there is constructive interference and hence we would have a continuous intensity distribution for all angles. </p>
<p><strong>Question</strong>: Why are there discrete rings and not a continuous distribution?</p>
| 10,735 |
[
-0.0432453379034996,
-0.0031173909083008766,
0.023452576249837875,
-0.027863584458827972,
0.05066622793674469,
0.022852368652820587,
-0.006312742829322815,
-0.02277379110455513,
-0.014400000683963299,
-0.0066543822176754475,
0.08436499536037445,
0.0023255397100001574,
0.03700830787420273,
0.03261234611272812,
0.0006157358293421566,
-0.023465178906917572,
-0.01678805612027645,
-0.01924658939242363,
-0.004390728659927845,
-0.030071306973695755,
-0.02032465487718582,
0.048747144639492035,
-0.021803254261612892,
0.013717799447476864,
-0.032415494322776794,
0.03795653209090233,
0.0013492531143128872,
0.009707569144666195,
0.025951983407139778,
0.06457441300153732,
-0.03244488686323166,
-0.02255960740149021,
0.006621844135224819,
0.035133253782987595,
0.021032720804214478,
-0.018423615023493767,
0.011019790545105934,
-0.011409115046262741,
-0.024486977607011795,
0.028190067037940025,
-0.025882931426167488,
0.024305881932377815,
-0.03020009770989418,
0.025210916996002197,
0.003490716451779008,
0.024052634835243225,
-0.011393052525818348,
-0.038765352219343185,
0.04694031924009323,
-0.05169328674674034,
0.05359240621328354,
-0.029367933049798012,
0.011976516805589199,
0.03320333734154701,
-0.005669765640050173,
-0.04200020059943199,
0.03064306452870369,
0.05777282640337944,
-0.011850304901599884,
-0.03132656216621399,
-0.03930157795548439,
-0.021221423521637917,
-0.0001388819800922647,
0.0030589185189455748,
0.0106015894562006,
-0.0077718705870211124,
0.008873207494616508,
-0.011099470779299736,
0.013161472044885159,
-0.02701154351234436,
0.012512699700891972,
0.02707553841173649,
0.06378950923681259,
-0.044901832938194275,
-0.00239278725348413,
0.002816375344991684,
0.02976587601006031,
0.0038407333195209503,
0.015860218554735184,
0.009051444940268993,
-0.012964660301804543,
0.01891089789569378,
0.004366797395050526,
0.003406116971746087,
0.014251024462282658,
-0.01625642739236355,
0.06575467437505722,
-0.033210545778274536,
0.021255318075418472,
0.00437099440023303,
-0.013094690628349781,
0.01051048468798399,
0.060466621071100235,
0.002959678415209055,
-0.029951853677630424,
0.024160191416740417,
0.003160962602123618,
0.04207868501543999,
-0.027091411873698235,
-0.010738113895058632,
-0.0038303749170154333,
-0.019642306491732597,
0.03310145065188408,
0.09815061837434769,
-0.011375346221029758,
-0.024715915322303772,
-0.02629946917295456,
0.06857934594154358,
-0.016618365421891212,
0.00048645708011463284,
-0.053504571318626404,
0.034087736159563065,
0.00008835156040731817,
0.008971162140369415,
0.01637798734009266,
0.022610988467931747,
0.029477408155798912,
-0.009194006212055683,
0.06959802657365799,
0.06916272640228271,
0.032463788986206055,
-0.004522443749010563,
0.03200354427099228,
-0.047904111444950104,
-0.09777866303920746,
-0.006201926618814468,
0.05336703732609749,
0.009170678444206715,
-0.02504539303481579,
0.06169551983475685,
0.0340927354991436,
0.00615243474021554,
0.0380464568734169,
0.028650669381022453,
-0.008193298242986202,
-0.03052408993244171,
-0.09901518374681473,
-0.03805440291762352,
0.03384771570563316,
0.017752043902873993,
-0.01625085063278675,
-0.07564674317836761,
-0.01078314334154129,
0.022797981277108192,
0.0862531065940857,
0.01024310477077961,
0.028734780848026276,
0.02226238138973713,
0.07332665473222733,
0.0060025472193956375,
-0.011800143867731094,
0.011136852204799652,
0.005443920381367207,
-0.020344311371445656,
-0.0504397451877594,
-0.06291084736585617,
0.05362899601459503,
0.006414176896214485,
0.020813575014472008,
-0.04064696282148361,
0.03958480432629585,
-0.003810630412772298,
0.004186525940895081,
0.008106342516839504,
-0.015789397060871124,
-0.0246584415435791,
0.051520004868507385,
0.023411132395267487,
0.04459909349679947,
-0.0014502706471830606,
-0.00898241437971592,
0.019373001530766487,
-0.02219783328473568,
0.02990819327533245,
-0.022465549409389496,
-0.03188420832157135,
0.000562124652788043,
-0.052009083330631256,
0.03610781952738762,
0.006868190597742796,
-0.00341457175090909,
-0.036446571350097656,
0.0027877441607415676,
0.012144998647272587,
-0.011866952292621136,
0.037710875272750854,
0.03782707452774048,
-0.013705749064683914,
0.004296871367841959,
-0.03859592601656914,
-0.02423667162656784,
-0.06550059467554092,
0.01571364887058735,
0.009193098172545433,
-0.03472623601555824,
0.01283908449113369,
0.01994001306593418,
-0.015031130984425545,
0.02147500403225422,
-0.032609861344099045,
0.004209805745631456,
-0.009671960026025772,
-0.009592683054506779,
0.006990496069192886,
0.049826670438051224,
0.031142747029662132,
0.025507617741823196,
-0.016306821256875992,
0.026789236813783646,
0.008519238792359829,
0.0404125452041626,
0.0036496149841696024,
-0.04389286786317825,
0.03640218451619148,
-0.0041305506601929665,
0.01426529698073864,
0.02084915153682232,
0.05543968454003334,
-0.02262606844305992,
0.021027427166700363,
-0.037564221769571304,
0.049615178257226944,
0.06648359447717667,
-0.00796066876500845,
-0.00801101978868246,
0.012304351665079594,
-0.020510299131274223,
0.040261875838041306,
-0.007259696256369352,
-0.0579177588224411,
-0.042506780475378036,
-0.0070159537717700005,
0.06289661675691605,
0.04213091731071472,
-0.03525707870721817,
0.04009181261062622,
-0.00780501076951623,
0.021947519853711128,
0.0035804160870611668,
0.030707815662026405,
-0.0442391112446785,
-0.0073917945846915245,
0.030619610100984573,
0.03973250836133957,
0.018630724400281906,
0.007542889565229416,
0.003225428983569145,
-0.01127624325454235,
0.0007156766951084137,
-0.021539738401770592,
-0.010382023639976978,
0.0006658985512331128,
-0.012625563889741898,
0.02471092902123928,
-0.023519691079854965,
-0.032173801213502884,
0.01685289666056633,
0.011051692068576813,
0.03666641563177109,
0.006060078740119934,
-0.04394978657364845,
-0.019665999338030815,
-0.0447697676718235,
-0.03112943470478058,
0.02010277286171913,
0.022015418857336044,
-0.03411976248025894,
-0.05429939553141594,
0.0274259801954031,
-0.05357689782977104,
-0.022433480247855186,
-0.022209489718079567,
-0.016012052074074745,
0.007151171565055847,
-0.011380496434867382,
0.03265673667192459,
0.030175773426890373,
-0.003576083341613412,
-0.05457387492060661,
0.0004819982568733394,
0.01496556494385004,
-0.004259811248630285,
0.04241684079170227,
0.019442599266767502,
-0.03034730814397335,
-0.05439917370676994,
-0.009349239990115166,
0.012120173312723637,
0.03402328118681908,
0.011198853142559528,
-0.013550618663430214,
0.027470184490084648,
-0.016344167292118073,
-0.03479231894016266,
-0.0332021564245224,
0.008061280474066734,
0.0101738590747118,
-0.06211041659116745,
0.017793646082282066,
0.02913089655339718,
-0.02487504482269287,
-0.023933274671435356,
-0.00030716467881575227,
-0.029888266697525978,
-0.007498677354305983,
-0.02839014306664467,
-0.0399087518453598,
0.026140667498111725,
-0.023576047271490097,
-0.009291506372392178,
0.029438117519021034,
-0.0061140707693994045,
-0.003487643785774708,
-0.0751243308186531,
-0.05715388432145119,
-0.0188426710665226,
-0.034542523324489594,
0.042159803211688995,
-0.017326999455690384,
0.024591853842139244,
0.07101725041866302,
0.032683536410331726,
-0.05922667682170868,
-0.00931292399764061,
-0.010610313154757023,
-0.0008669369854032993,
-0.029687484726309776,
0.022016029804944992,
0.028717316687107086,
0.041935890913009644,
0.043616101145744324,
-0.02030027098953724,
0.03595901280641556,
0.061105262488126755,
0.015552789904177189,
-0.005654733628034592,
0.03163867071270943,
0.001523180864751339,
-0.028913943096995354,
-0.0045136925764381886,
0.030016912147402763,
-0.01893702894449234,
0.0054602413438260555,
-0.0368197076022625,
-0.0061118099838495255,
0.033918146044015884,
-0.09690845012664795,
0.0017174556851387024,
-0.009487793780863285,
0.027355588972568512,
-0.010160468518733978,
0.043445635586977005,
-0.0061757201328873634,
-0.03470168635249138,
-0.026377830654382706,
0.0024850466288626194,
0.0472579300403595,
-0.005532937124371529,
0.0032599573023617268,
0.037071343511343,
0.05693618580698967,
-0.017179472371935844,
0.013569864444434643,
0.018902156502008438,
0.005336359608918428,
0.02609160728752613,
-0.041771769523620605,
0.027716297656297684,
0.03132832795381546,
0.013440646231174469,
0.009332763962447643,
0.0016096922336146235,
-0.03365112841129303,
-0.026938486844301224,
-0.01884685456752777,
-0.0008251929539255798,
0.0005612863460555673,
0.06062649190425873,
0.017136378213763237,
0.05733229219913483,
0.032007310539484024,
-0.0030081935692578554,
-0.017935633659362793,
-0.026535583660006523,
-0.08730524033308029,
-0.0113654350861907,
0.023684943094849586,
-0.009637496434152126,
-0.00048342382069677114,
-0.009812780655920506,
-0.017340919002890587,
-0.02610643021762371,
-0.029290150851011276,
-0.006742084864526987,
-0.006801757495850325,
-0.06640371680259705,
0.006609516218304634,
-0.023781340569257736,
-0.03943254053592682,
-0.014224184677004814,
0.06687452644109726,
0.05988943949341774,
0.004415536765009165,
0.06442360579967499,
-0.01962975040078163,
-0.02570332959294319,
0.0336015485227108,
-0.020189665257930756,
0.029520444571971893,
0.03303872048854828,
0.04362262412905693,
-0.013719744980335236,
0.007417586166411638,
0.00812026858329773,
-0.04238178953528404,
-0.0009882926242426038,
0.06937801837921143,
0.04012484475970268,
-0.003145165042951703,
-0.004190852865576744,
-0.023321568965911865,
0.017292816191911697,
0.0062566217966377735,
-0.004264891613274813,
-0.036334164440631866,
-0.020642856135964394,
0.018688488751649857,
0.006238270550966263,
-0.007833553478121758,
0.019076835364103317,
0.03153723105788231,
0.011510948650538921,
0.0004965494736097753,
-0.03332309424877167,
-0.040143951773643494,
0.0022333867382258177,
0.013407588005065918,
0.029421022161841393,
-0.009273126721382141,
0.01322480570524931,
0.013980596326291561,
0.016336115077137947,
0.01851033791899681,
0.009141345508396626,
0.005823311861604452,
-0.07556971907615662,
0.0009505238849669695,
0.008621945977210999,
0.004505970515310764,
0.02985408715903759,
0.014478263445198536,
0.05645621195435524,
0.02440495602786541,
0.009522139094769955,
-0.07624168694019318,
0.01785706914961338,
0.02421334572136402,
0.04979045316576958,
-0.01758493110537529,
-0.017174558714032173,
-0.017837204039096832,
-0.018673554062843323,
0.04870069772005081,
-0.02290106751024723,
0.011042889207601547,
-0.05203314125537872,
0.02249755710363388,
-0.025866011157631874,
-0.026864612475037575,
-0.048460789024829865,
0.016387229785323143,
0.007275665644556284,
-0.0005714933504350483,
-0.02736036479473114,
-0.03322691097855568,
0.0028122728690505028,
0.0013612639158964157,
0.049660030752420425,
0.007286007981747389,
-0.0011962007265537977,
-0.020539427176117897,
-0.002820526948198676,
0.003367188386619091,
-0.005505537614226341,
-0.08756791055202484,
0.061091162264347076,
-0.0020434665493667126,
0.03419934958219528,
0.07415957748889923,
-0.0345863476395607,
-0.03149719908833504,
-0.007061334792524576,
0.009837152436375618,
-0.012197550386190414,
0.030006535351276398,
-0.050996892154216766,
0.04777493700385094,
0.05352184176445007,
0.0058106244541704655,
0.030895432457327843,
0.02471790835261345,
-0.0042040469124913216,
0.006853528320789337,
-0.0584905631840229,
0.044226229190826416,
-0.002376396907493472,
0.025141602382063866,
-0.05802221596240997,
0.011915523558855057,
0.013615035451948643,
0.017068183049559593,
0.005235497839748859,
0.014359831809997559,
0.015290833078324795,
-0.04526956006884575,
0.039672330021858215,
0.01270851120352745,
-0.01464669406414032,
0.03388241305947304,
-0.0012184524675831199,
0.04072247073054314,
0.04709818214178085,
-0.03936262056231499,
0.02090965025126934,
-0.010027358308434486,
0.006003250367939472,
0.01456371694803238,
0.0023677442222833633,
-0.008614828810095787,
-0.05546417459845543,
-0.007791262120008469,
-0.018136151134967804,
-0.017501993104815483,
0.05462218448519707,
0.010750745423138142,
0.03187544643878937,
0.013475736603140831,
-0.027895841747522354,
-0.009981730952858925,
0.010794419795274734,
-0.005250534042716026,
0.04523472860455513,
-0.04447046294808388,
0.004456262104213238,
-0.006696772295981646,
0.019771758466959,
-0.081551693379879,
-0.07554604858160019,
0.023237233981490135,
0.014466389082372189,
-0.043256841599941254,
-0.0316271036863327,
0.012647655792534351,
0.04527249187231064,
-0.03817976638674736,
0.014102224260568619,
0.01605309173464775,
-0.02509911172091961,
-0.015601903200149536,
0.0031205047853291035,
0.03186508268117905,
0.09184468537569046,
-0.012797302566468716,
-0.027373723685741425,
0.03239716216921806,
0.022189684212207794,
-0.0013644439168274403,
-0.01252684649080038,
0.011621486395597458,
-0.031713783740997314,
-0.05331612378358841,
-0.038366641849279404,
0.0027790814638137817,
0.04936334863305092,
-0.034981850534677505,
-0.05061209574341774,
0.017268376424908638,
-0.015077462419867516,
0.023137394338846207,
-0.019325340166687965,
-0.012374951504170895,
0.0009104745695367455,
0.009791233576834202,
-0.01562659814953804,
-0.018994849175214767,
-0.03085371106863022,
-0.033164333552122116,
0.01967068761587143,
0.02917720004916191,
0.008250226266682148,
0.00733037106692791,
0.035821422934532166,
-0.05465177074074745,
0.0021722132805734873,
0.0315697155892849,
-0.025228355079889297,
-0.0109677379950881,
-0.044194839894771576,
0.021058304235339165,
0.027747102081775665,
0.010083417408168316,
-0.013074829243123531,
-0.022171618416905403,
-0.06916947662830353,
0.026068126782774925,
0.08340942859649658,
0.005635243374854326,
0.046383894979953766,
0.05234856903553009,
-0.01992216520011425,
-0.027547162026166916,
-0.007161268964409828,
0.020940622314810753,
0.004069061949849129,
-0.006273237057030201,
0.02952958457171917,
-0.06230438873171806,
-0.0074442061595618725,
0.01642586477100849,
0.0367504358291626,
0.013399028219282627,
0.013269664719700813,
0.042037781327962875,
0.0023032701574265957,
0.0017904378473758698,
-0.013830907642841339,
-0.037485361099243164,
0.06517371535301208,
-0.037758104503154755,
0.047999635338783264,
0.03374720364809036,
-0.009239745326340199,
0.0653429925441742,
-0.014410647563636303,
-0.004876446910202503,
-0.03969463333487511,
0.0032323049381375313,
-0.020129509270191193,
-0.002468178514391184,
0.016810346394777298,
-0.00849408470094204,
-0.009827124886214733,
-0.00856715627014637,
0.025266898795962334,
0.0003188292612321675,
0.007255614269524813,
-0.004084967542439699,
-0.03508172929286957,
-0.0292928759008646,
-0.023396288976073265,
-0.05548768863081932,
0.04031571373343468,
-0.025013506412506104,
-0.031065812334418297,
0.007673610467463732,
-0.0749109610915184,
0.04102690517902374,
0.06868891417980194,
0.029042795300483704,
0.012990807183086872,
0.02904614433646202,
0.003218711819499731,
0.06824682652950287,
-0.0008062656270340085,
-0.029883334413170815,
0.13308575749397278,
0.008883693255484104,
0.004219463560730219,
-0.04679713025689125,
0.0074220034293830395,
-0.010645762085914612,
-0.00335216848179698,
-0.039796024560928345,
0.003701278939843178,
-0.03758414089679718,
0.004313693381845951,
0.02273515798151493,
0.04662788659334183,
0.014980434440076351,
-0.016568083316087723,
0.012813634239137173,
-0.009533701464533806,
-0.03699704259634018,
0.003168403869494796,
0.011150408536195755,
-0.017674224451184273,
0.03352469205856323,
-0.01727525144815445,
0.032031238079071045,
-0.03052009455859661,
-0.026811664924025536,
-0.023395614698529243,
-0.02803131565451622,
-0.0043021030724048615,
0.02915520779788494,
-0.00783460307866335,
0.010762540623545647,
-0.002991601824760437,
-0.06663545221090317,
-0.01224422175437212,
0.009308046661317348,
0.009789199568331242,
-0.023334786295890808,
0.04259061440825462,
0.005594892892986536,
0.011651590466499329,
-0.018916945904493332,
0.01375626865774393,
0.01959506794810295,
-0.009893860667943954,
-0.016267208382487297,
0.027485564351081848,
0.04241790249943733,
-0.04137643426656723,
-0.01376195065677166,
-0.019408201798796654,
-0.0063364687375724316,
0.021541446447372437,
-0.04663063958287239,
-0.02841823548078537,
0.017504388466477394,
0.0036723478697240353,
-0.020314717665314674,
-0.03484615311026573,
0.03184899315237999,
0.0014095130609348416,
0.014405995607376099,
-0.02668401598930359,
0.003560065058991313,
-0.0365842767059803,
0.0017220241716131568,
0.0013783976901322603,
0.019337693229317665,
0.041451841592788696,
-0.030746405944228172,
-0.015229098498821259,
-0.016260921955108643,
-0.023445088416337967,
-0.02091897651553154,
0.0054077343083918095,
0.0354696549475193,
0.048096563667058945,
-0.007414803374558687,
-0.027783887460827827,
0.03608584403991699,
-0.017445633187890053,
-0.022390244528651237,
-0.031541917473077774,
-0.04645312950015068,
-0.038009971380233765,
0.013960771262645721,
-0.004894845653325319,
-0.010329106822609901,
0.00844358466565609,
0.009982126764953136,
0.01939322240650654,
0.028548134490847588,
0.04200800880789757,
-0.004823844414204359,
-0.07955124974250793,
0.026288319379091263,
0.018685173243284225,
0.004061593674123287,
0.010257626883685589,
0.014284901320934296,
0.005431384313851595,
0.019320569932460785,
0.048914019018411636,
0.050782620906829834,
-0.013246810995042324,
0.0034306340385228395,
-0.0012507090577855706,
-0.022090163081884384,
0.013580522499978542,
0.05118716508150101,
-0.006886166520416737,
-0.06237345188856125,
0.00042014705832116306,
0.008325930684804916,
0.007603021338582039,
0.0007666044984944165,
-0.01104999054223299,
0.024166518822312355,
-0.040051206946372986,
-0.05462058633565903,
0.02913178689777851,
0.003807603381574154,
-0.03147391229867935,
-0.004666542634367943,
-0.009720000438392162,
-0.015481419861316681,
0.02304654009640217,
-0.03135541453957558,
0.041935279965400696,
0.03086346946656704,
-0.04472231864929199,
0.0025709131732583046,
0.008580842986702919,
0.01672520861029625,
-0.020537011325359344,
0.02785577066242695,
-0.003828971413895488,
0.029486093670129776,
-0.005221633240580559,
-0.05513425171375275,
0.030657945200800896,
-0.012809770181775093,
-0.024338670074939728,
-0.012140750885009766,
-0.006883986759930849,
-0.025405578315258026,
-0.00891875196248293,
-0.006252878345549107,
-0.020419210195541382,
0.048380233347415924,
-0.035167090594768524,
-0.02364252507686615,
-0.012567663565278053,
0.011015422642230988,
0.013675807043910027,
-0.027810081839561462,
0.003125787014141679,
0.014971769414842129,
-0.01944580487906933,
0.049007248133420944,
0.006703771650791168,
0.01599808782339096,
0.010684781707823277,
-0.014168278314173222,
-0.06597058475017548,
-0.019061269238591194,
0.004115264862775803,
0.045408062636852264,
0.0015613393625244498,
0.03948034718632698,
-0.011850649490952492,
0.028219178318977356,
0.01937285251915455,
-0.0056059835478663445,
-0.06324867904186249,
-0.04133365675806999,
0.024791652336716652,
0.01988264173269272,
0.017777353525161743,
-0.013848328962922096,
-0.027223724871873856,
0.04895956069231033,
-0.09951183944940567,
0.028040075674653053,
-0.02713257074356079,
-0.039304088801145554,
-0.08297120034694672,
-0.0211891271173954,
-0.05432552099227905,
-0.005461280699819326,
-0.00826597772538662,
0.04742347449064255,
0.05680273100733757,
0.023473339155316353,
-0.03990190848708153,
0.018453026190400124,
-0.024560976773500443,
-0.006775869522243738,
0.0201861672103405,
-0.007529810070991516,
0.0682339146733284,
-0.0015802712878212333,
-0.005187612026929855,
-0.0030673102010041475,
-0.024349987506866455,
-0.03513539955019951,
0.05148957297205925,
0.019909728318452835,
-0.021884523332118988,
0.04856874793767929,
-0.004543002229183912,
-0.013260461390018463,
-0.019918931648135185,
0.011715342290699482,
0.015100871212780476,
0.018213331699371338,
-0.004200116731226444,
0.013721947558224201,
0.003952688537538052,
-0.0497412383556366,
-0.026791848242282867,
0.02651340141892433,
0.016115376725792885,
0.015135623514652252,
0.01807749643921852,
0.022530650720000267,
0.02912360616028309,
-0.01887190341949463,
-0.0012549168895930052,
-0.06405548006296158,
0.002074731048196554,
0.004745748359709978,
0.04063943400979042,
-0.011458144523203373,
0.020691560581326485,
-0.03875656798481941,
-0.06465214490890503,
0.006968091707676649,
0.00544060068204999,
-0.018190424889326096,
-0.0115875955671072,
-0.013426718302071095,
0.0008078067330643535,
-0.022839050740003586,
0.03675645589828491,
0.011671007610857487,
-0.01865224726498127,
0.05025455355644226,
-0.046619899570941925,
-0.009366572834551334,
0.0019050793489441276,
-0.03793816268444061,
-0.03830553591251373,
-0.06058220937848091,
0.03034941479563713,
-0.024077147245407104,
-0.02315938100218773,
-0.030852526426315308,
-0.0154494009912014,
-0.036550868302583694,
0.029439182952046394,
0.004610253963619471,
0.0366070531308651,
0.0006853060913272202,
-0.01165266428142786,
-0.0035798950120806694,
0.023664092645049095,
-0.03344698250293732,
0.03639309108257294,
-0.023740332573652267,
-0.004881950560957193,
0.013527005910873413,
0.020836202427744865,
-0.06292487680912018,
0.0022788948845118284,
0.04516397789120674,
-0.03462724760174751,
-0.012791265733540058,
0.01063696388155222,
-0.023525862023234367,
0.06888972967863083,
-0.006659636739641428,
-0.03182695806026459,
0.07676085829734802,
0.017229178920388222,
-0.004416241310536861,
0.03127644583582878,
-0.016560109332203865,
-0.04546477273106575,
-0.010735754854977131,
-0.040915898978710175,
0.0019171031890437007,
-0.006856097839772701,
0.03527366369962692,
0.06232014670968056,
-0.0109228091314435,
0.035435937345027924,
0.02884175069630146,
-0.024293890222907066,
-0.014774548821151257,
0.02290915884077549,
0.0006404757150448859,
0.01151402946561575,
0.012466187588870525,
0.030219532549381256,
-0.020004762336611748,
-0.013204549439251423,
0.02789040468633175,
0.051633596420288086,
0.027126967906951904,
0.015999525785446167,
0.01099157240241766,
0.0321950763463974,
-0.02270413003861904,
-0.0017212872626259923,
-0.01586287096142769,
0.0308171845972538,
-0.026935352012515068,
0.018562650308012962,
0.031713563948869705,
-0.03430512920022011,
-0.02945920266211033,
0.005784239619970322,
0.015100688673555851,
0.06853672862052917,
-0.007646920159459114,
0.025279857218265533,
-0.005279286298900843,
-0.03491400182247162,
-0.02048802748322487,
-0.00018631912826094776,
0.06882774829864502,
0.034051235765218735,
0.02393602393567562,
-0.022853363305330276,
-0.04638800397515297,
0.0005263802013359964,
0.05615609139204025,
-0.022638458758592606,
0.013969111256301403,
0.012325634248554707,
-0.03827296197414398,
0.03143267706036568,
-0.02139601670205593,
-0.010339310392737389,
-0.02767125330865383,
0.013302427716553211,
0.008005178533494473,
-0.02149766869843006,
-0.004802086390554905,
-0.01548669021576643,
-0.04842411354184151,
-0.005248351022601128,
-0.03614490479230881,
0.0009442988666705787,
-0.05310944840312004,
0.006244230549782515,
-0.012295217253267765,
-0.0024403368588536978
] |
<p>Isn't this statement regarding projectile motion wrong?</p>
<blockquote>
<p><em>If a body is thrown at an angle to the horizontal with initial velocity $u$, then displacement of body as a function of time is $\vec{s}=\vec{u}t+\frac12\vec{g}t^2$. (Air drag is neglected)</em></p>
</blockquote>
<p>How can it be correct? Gravity acts in downward direction, so wouldn't the displacement be $\sqrt{x^2+y^2}$?</p>
| 10,736 |
[
-0.030836328864097595,
-0.03474026918411255,
-0.0029191970825195312,
0.016869552433490753,
0.007769586052745581,
-0.010699482634663582,
-0.011183190159499645,
-0.006129394751042128,
-0.0075891572050750256,
0.00784141756594181,
0.007906589657068253,
0.044440675526857376,
0.07148591428995132,
-0.001156723708845675,
0.03751123696565628,
0.001647652592509985,
-0.009359817951917648,
0.002441054442897439,
0.006304859183728695,
-0.018976133316755295,
-0.004662295803427696,
-0.00039018996176309884,
-0.010292012244462967,
-0.020088495686650276,
0.01606903411448002,
0.013860179111361504,
0.027213837951421738,
-0.004483927972614765,
0.025743644684553146,
0.051598649471998215,
0.013338029384613037,
-0.008337036706507206,
0.02191934362053871,
0.016616705805063248,
0.031554318964481354,
0.02145008184015751,
-0.031790561974048615,
-0.026895305141806602,
-0.010810131207108498,
0.027505530044436455,
-0.04889092966914177,
-0.02988186478614807,
-0.021923964843153954,
0.09605298191308975,
-0.02754325419664383,
0.038048312067985535,
0.026318881660699844,
-0.0012705454137176275,
0.0631014034152031,
-0.03770304471254349,
0.07239406555891037,
-0.01476548332720995,
0.05162055417895317,
0.03825967013835907,
-0.04294130578637123,
0.014606596902012825,
0.07778308540582657,
0.07247110456228256,
-0.030785271897912025,
-0.025832215324044228,
0.008500518277287483,
-0.04867955297231674,
-0.01909605786204338,
0.0026259191799908876,
0.035610876977443695,
0.018567392602562904,
-0.016234006732702255,
0.0036936430260539055,
0.0011373675661161542,
-0.035538218915462494,
0.00909645576030016,
-0.005503206513822079,
-0.00009199061605613679,
-0.028971809893846512,
-0.0037540660705417395,
-0.027685081586241722,
0.05470205098390579,
0.029574375599622726,
0.006270985119044781,
0.03184576332569122,
-0.014883243478834629,
0.0058915442787110806,
0.0849805623292923,
0.04645118862390518,
-0.013465243391692638,
0.001989996060729027,
0.03974049165844917,
0.003392826532945037,
0.050454143434762955,
0.03954477608203888,
0.009287267923355103,
0.01803409866988659,
0.004716877825558186,
-0.0025713962968438864,
-0.006786462850868702,
0.027471644803881645,
-0.0010339334839954972,
0.04502058029174805,
0.022097747772932053,
-0.0487118735909462,
0.009779124520719051,
-0.03287915885448456,
0.03194890916347504,
0.06083748862147331,
0.012610841542482376,
-0.004011794459074736,
-0.02369995042681694,
0.02948436699807644,
-0.027136581018567085,
-0.04865489900112152,
-0.035588644444942474,
0.0016591406892985106,
-0.05625041946768761,
-0.014801612123847008,
0.020306335762143135,
0.007650496903806925,
-0.004754391498863697,
0.04317577928304672,
0.03616706654429436,
0.030760079622268677,
0.023808708414435387,
-0.027371682226657867,
0.04071182757616043,
0.016064515337347984,
-0.06955694407224655,
0.03290141746401787,
0.0590268112719059,
-0.04772517457604408,
-0.052468448877334595,
-0.0007399422465823591,
0.011375290341675282,
0.002190368017181754,
0.015436447225511074,
-0.0028390150982886553,
0.04541289806365967,
0.028124511241912842,
-0.11615306884050369,
-0.06262970715761185,
0.004056509584188461,
0.03168758749961853,
-0.0003409264609217644,
-0.08034293353557587,
0.010393190197646618,
0.007399265188723803,
0.06424073874950409,
0.0027050566859543324,
0.024547839537262917,
-0.00995886605232954,
0.0202851053327322,
-0.022489916533231735,
0.0159054696559906,
-0.012504187412559986,
0.03868497908115387,
-0.059974294155836105,
0.008581218309700489,
-0.06691135466098785,
0.03186026215553284,
0.011566278524696827,
0.03867102414369583,
-0.02740655280649662,
0.03179707005620003,
-0.014129997231066227,
0.010284964926540852,
0.023928003385663033,
0.014332805760204792,
0.003724551759660244,
0.024488385766744614,
0.04543112590909004,
-0.018879644572734833,
0.037422798573970795,
0.018447991460561752,
0.02725839428603649,
0.010196484625339508,
0.02061803825199604,
0.07485392689704895,
-0.06593859195709229,
-0.01814895309507847,
-0.010597031563520432,
-0.017108581960201263,
-0.03597046434879303,
-0.03331461921334267,
-0.037559978663921356,
0.0048233093693852425,
0.026600483804941177,
-0.02329317107796669,
0.05084332823753357,
0.021972069516777992,
0.02242472395300865,
-0.021744633093476295,
-0.022133802995085716,
-0.023635581135749817,
-0.08695312589406967,
0.0489778146147728,
-0.005389997735619545,
0.010497232899069786,
-0.008815594017505646,
0.006374737713485956,
0.014257674105465412,
-0.029958637431263924,
-0.008149956353008747,
-0.00422692159190774,
0.0223764069378376,
-0.03428841382265091,
-0.012127552181482315,
0.019557848572731018,
0.06404881924390793,
0.04530256986618042,
0.02763999253511429,
-0.005130991339683533,
-0.0035685712937265635,
-0.010944193229079247,
0.012061403132975101,
-0.00823512114584446,
0.03145432844758034,
-0.008514218032360077,
-0.0009236393962055445,
0.03295426815748215,
-0.03704844415187836,
-0.018304724246263504,
0.04511182755231857,
-0.01898691989481449,
0.07255659252405167,
0.06818581372499466,
-0.011259172111749649,
0.002850935561582446,
0.05942422151565552,
0.036811795085668564,
0.016737395897507668,
0.026733575388789177,
-0.019475921988487244,
-0.044249527156353,
0.0034802695736289024,
0.005579354241490364,
0.022907234728336334,
-0.002667288528755307,
0.003014620626345277,
0.04958738386631012,
0.022639300674200058,
0.017102448269724846,
0.039690013974905014,
0.005976185202598572,
-0.08162064850330353,
0.030398311093449593,
-0.0008343598456121981,
0.02744945138692856,
0.0006775959045626223,
0.02324489876627922,
0.007578467484563589,
-0.004118895623832941,
0.009139031171798706,
0.009983019903302193,
-0.006683638785034418,
0.0061986567452549934,
0.01896592043340206,
0.02159261703491211,
-0.023068495094776154,
0.041412316262722015,
-0.0108652887865901,
0.038614604622125626,
0.032395925372838974,
0.0025351049844175577,
-0.008844551630318165,
-0.049703449010849,
0.006339233368635178,
0.01640830934047699,
-0.010639353655278683,
-0.014864634722471237,
-0.008416530676186085,
0.036771345883607864,
-0.060331080108881,
-0.009917743504047394,
-0.035300541669130325,
-0.03599513694643974,
-0.04860363155603409,
-0.011647593230009079,
0.019763579592108727,
0.05057421699166298,
0.018093669787049294,
0.0025730039924383163,
0.00729677639901638,
0.004406906198710203,
-0.021866245195269585,
-0.03674139827489853,
0.0006479168077930808,
-0.06024497002363205,
0.011347181163728237,
-0.028008567169308662,
-0.03419385477900505,
0.062065038830041885,
-0.005318945273756981,
0.006835289299488068,
0.030312569811940193,
-0.017093339934945107,
-0.008362638764083385,
-0.0012456717668101192,
-0.034670207649469376,
-0.027643729001283646,
-0.021395627409219742,
-0.04724239930510521,
0.02783660963177681,
-0.02250669337809086,
0.007944128476083279,
0.036217063665390015,
-0.03941148519515991,
-0.04332368075847626,
-0.027824141085147858,
0.02195693925023079,
0.040736086666584015,
0.0016528541455045342,
0.015744591131806374,
-0.004649948328733444,
-0.04517127573490143,
-0.010811860673129559,
-0.04547153040766716,
-0.035714004188776016,
-0.00288155279122293,
0.007131750695407391,
0.061306215822696686,
0.000840645981952548,
-0.01689993217587471,
0.08679771423339844,
-0.00010928340634563938,
-0.02339182421565056,
0.004044847097247839,
-0.01296763215214014,
0.022479459643363953,
-0.019046183675527573,
-0.029215097427368164,
0.0030012931674718857,
0.007874423637986183,
0.015286535955965519,
-0.007738930638879538,
0.012062542140483856,
0.027266114950180054,
0.04600002244114876,
-0.006725457031279802,
-0.040127068758010864,
0.006350296083837748,
0.00833072792738676,
-0.0017549728509038687,
0.016963031142950058,
-0.0015003611333668232,
0.01633644476532936,
0.002458051312714815,
0.057002611458301544,
0.010868333280086517,
-0.03889242187142372,
0.06538668274879456,
-0.020982667803764343,
-0.027105530723929405,
-0.003915244713425636,
0.05241769924759865,
-0.00018060891306959093,
-0.012514032423496246,
-0.008598088286817074,
0.014686740934848785,
0.031406205147504807,
0.015015223063528538,
0.02469528652727604,
0.0324365496635437,
0.028108982369303703,
-0.030592739582061768,
-0.04042086377739906,
0.0040718065574765205,
-0.01968868263065815,
0.08031866699457169,
-0.01393848191946745,
-0.02080337330698967,
0.008246329613029957,
0.024129757657647133,
0.010362514294683933,
-0.012210248969495296,
-0.04519813880324364,
0.013309852220118046,
-0.0665307343006134,
0.01886030286550522,
0.00841188058257103,
-0.0003122222260572016,
-0.0013212764170020819,
0.039037201553583145,
0.04964754730463028,
0.022135868668556213,
0.00792540330439806,
0.026492835953831673,
-0.08299331367015839,
0.00905747339129448,
-0.05542870983481407,
-0.029238726943731308,
-0.021612897515296936,
-0.02514973096549511,
-0.05248737707734108,
-0.0509612075984478,
-0.01160194631665945,
-0.003194050397723913,
-0.015526771545410156,
-0.022547297179698944,
0.0025684302672743797,
-0.028724296018481255,
-0.02626677043735981,
0.00936357956379652,
-0.0032633082009851933,
0.02971528097987175,
-0.059018440544605255,
0.04147525876760483,
0.08088432997465134,
-0.02929171547293663,
-0.03227321431040764,
-0.02932700514793396,
0.05020700767636299,
0.02449224703013897,
0.022083919495344162,
0.02995866723358631,
0.021480126306414604,
-0.010646479204297066,
0.012936940416693687,
-0.007783749606460333,
0.03994674235582352,
0.004346586298197508,
-0.023970920592546463,
-0.04135255143046379,
-0.05446016415953636,
-0.00875092577189207,
0.02420707792043686,
0.0537087619304657,
0.024959128350019455,
-0.0005188225186429918,
0.05505356937646866,
0.02395528368651867,
0.03242191672325134,
0.047181375324726105,
0.03271869197487831,
0.0037421113811433315,
-0.0031367577612400055,
-0.06079048663377762,
-0.007803847081959248,
-0.033183179795742035,
-0.041311971843242645,
0.02181650884449482,
-0.013512291014194489,
-0.016408193856477737,
-0.0072505781427025795,
0.013381903991103172,
0.006888158619403839,
0.007995761930942535,
0.026183199137449265,
-0.019627880305051804,
0.004313792567700148,
-0.014891153201460838,
0.008456080220639706,
0.025923611596226692,
0.035474639385938644,
0.01728200539946556,
0.007864624261856079,
-0.011310899630188942,
-0.06275227665901184,
0.01594357192516327,
0.02545611374080181,
0.03007589839398861,
-0.03346777334809303,
0.0024165883660316467,
-0.011102470569312572,
-0.034542106091976166,
0.057145580649375916,
0.006325340364128351,
0.053660161793231964,
-0.034609101712703705,
-0.00848662480711937,
0.0029731872491538525,
-0.06668253988027573,
-0.023225395008921623,
0.02001454122364521,
-0.018574349582195282,
0.004219548776745796,
-0.0072845835238695145,
0.00981113687157631,
-0.002196299144998193,
-0.0003372447390574962,
0.03484052047133446,
0.03458603471517563,
0.01917024701833725,
-0.00904696062207222,
-0.015314404852688313,
0.006711523048579693,
-0.05975008010864258,
-0.06014826521277428,
-0.015040040016174316,
-0.005726119969040155,
-0.014517536386847496,
-0.012366083450615406,
0.0028626774437725544,
-0.019551346078515053,
0.038632843643426895,
0.014059470035135746,
0.012209370732307434,
0.001500905491411686,
-0.0330585353076458,
0.006445310544222593,
0.06935584545135498,
0.004520986694842577,
0.03662634640932083,
0.02477268874645233,
-0.013296340592205524,
-0.009745792485773563,
-0.017912598326802254,
0.021428333595395088,
-0.04137907922267914,
-0.024600137025117874,
-0.013004996813833714,
0.01568729430437088,
-0.005138530395925045,
0.039174217730760574,
0.045359108597040176,
0.012774012982845306,
-0.008360655978322029,
-0.03665656968951225,
-0.02606555074453354,
0.015704791992902756,
0.04197950288653374,
0.008476789109408855,
0.006373755168169737,
0.004173517692834139,
-0.010935230180621147,
-0.006042389199137688,
-0.014520999044179916,
-0.02974165603518486,
-0.004510677419602871,
0.028796661645174026,
0.04468082636594772,
-0.0051549216732382774,
-0.03107037954032421,
-0.05819014832377434,
0.0026183202862739563,
-0.06064043194055557,
0.028100483119487762,
-0.029258448630571365,
-0.02621322125196457,
0.006363459397107363,
-0.06086185574531555,
-0.01596754416823387,
0.0063037509098649025,
0.04441540315747261,
0.02256547100841999,
-0.06975258141756058,
0.005112708546221256,
0.034432344138622284,
0.055933188647031784,
-0.08035452663898468,
-0.03278181329369545,
0.0019151077140122652,
0.0020915246568620205,
-0.0324086993932724,
-0.02373058907687664,
0.008325126022100449,
-0.07183350622653961,
-0.017589978873729706,
0.008491194806993008,
0.03535866364836693,
0.00927755143493414,
-0.015680858865380287,
0.013657087460160255,
0.015675241127610207,
0.06213342398405075,
-0.016403231769800186,
-0.001714669051580131,
0.0111767016351223,
-0.007153162267059088,
-0.003127564676105976,
-0.023016802966594696,
0.0826888456940651,
-0.03724927827715874,
0.02141674794256687,
0.0014384897658601403,
-0.03899841755628586,
0.0013783933827653527,
-0.005520807579159737,
-0.011145885102450848,
0.035092417150735855,
-0.007297910284250975,
0.006776472087949514,
-0.00356951542198658,
0.04528462886810303,
-0.03232307359576225,
-0.0002978439733851701,
0.009777441620826721,
0.009603484533727169,
-0.03349737823009491,
0.00989707000553608,
0.04163965582847595,
0.021425319835543633,
0.019592883065342903,
-0.0014982855645939708,
0.06165275722742081,
-0.039265140891075134,
-0.028024796396493912,
0.04161297529935837,
-0.015515903942286968,
0.027255794033408165,
0.00965522788465023,
-0.030894476920366287,
0.01863374188542366,
0.00961292628198862,
-0.010070058517158031,
-0.009382165037095547,
-0.013652974739670753,
0.03718491271138191,
0.10796761512756348,
-0.05265306308865547,
0.06665187329053879,
-0.012884276919066906,
0.012383836321532726,
-0.006380429025739431,
-0.03814791887998581,
-0.000499352696351707,
-0.01843434013426304,
-0.023959651589393616,
0.012475093826651573,
-0.006701229605823755,
-0.006408075336366892,
-0.0056498353369534016,
0.013514717109501362,
-0.001829872839152813,
-0.004620315507054329,
0.011100584641098976,
-0.004766556899994612,
0.016633624210953712,
0.018709786236286163,
-0.04479355365037918,
0.02206839993596077,
-0.02521943673491478,
0.05397617816925049,
-0.027396008372306824,
0.0007547585410065949,
0.03494869917631149,
0.0038209380581974983,
-0.0013292916119098663,
-0.05387087166309357,
0.017137499526143074,
-0.04021206498146057,
-0.02726864069700241,
-0.008541971445083618,
0.018111800774931908,
-0.013312207534909248,
0.016999077051877975,
0.059940360486507416,
0.0034145391546189785,
0.03504769504070282,
-0.04127580299973488,
-0.057836223393678665,
-0.014934509061276913,
-0.05636928230524063,
-0.0153210973367095,
0.015167967416346073,
-0.01931542530655861,
-0.016322661191225052,
0.0021859591361135244,
-0.009536805562675,
-0.01275756023824215,
0.008767995983362198,
0.05376022309064865,
-0.04455554112792015,
0.09428468346595764,
-0.027923237532377243,
-0.00511721009388566,
-0.006841386668384075,
-0.0035250831861048937,
0.117059126496315,
0.03915863856673241,
0.010415020398795605,
-0.004174835979938507,
0.013834537006914616,
-0.015178549103438854,
-0.02528577484190464,
-0.011171233840286732,
-0.01235005259513855,
0.014508296735584736,
-0.00015391955093946308,
0.006429301109164953,
0.04563942551612854,
0.021808844059705734,
-0.032217178493738174,
0.04083312302827835,
-0.05058359354734421,
-0.025241749361157417,
-0.022902805358171463,
0.011660321615636349,
-0.0012817097594961524,
0.02820822224020958,
-0.023456303402781487,
0.016256272792816162,
-0.03478800132870674,
-0.0014605813194066286,
-0.005938631948083639,
-0.03360607847571373,
-0.004333538003265858,
0.022209390997886658,
-0.060217857360839844,
0.0032531367614865303,
0.0450257733464241,
-0.0286604892462492,
-0.051306962966918945,
-0.0029181980062276125,
-0.018679490312933922,
-0.03308311104774475,
0.02309447154402733,
0.04668319597840309,
0.0028297575190663338,
0.03760959580540657,
0.02467728964984417,
0.0158642940223217,
-0.033614709973335266,
0.009411882609128952,
-0.046903375536203384,
0.03008330799639225,
-0.022105233743786812,
0.01168927364051342,
-0.0009022802114486694,
-0.002993813017383218,
-0.00526900589466095,
-0.09190019220113754,
-0.008248559199273586,
0.016556112095713615,
0.03867638111114502,
-0.017912447452545166,
0.025462498888373375,
-0.02094894088804722,
0.009045797400176525,
0.02530185878276825,
0.008559690788388252,
0.025548147037625313,
-0.0019149373983964324,
0.01605471409857273,
0.02093682996928692,
0.044193148612976074,
-0.018022585660219193,
-0.03433392569422722,
-0.008836926892399788,
0.01964297890663147,
-0.037137918174266815,
-0.008519490249454975,
0.022056423127651215,
0.04682428762316704,
-0.008211062289774418,
-0.007657997310161591,
0.01128623727709055,
-0.04284211993217468,
-0.02746453694999218,
0.056450553238391876,
-0.0024446905590593815,
-0.025451065972447395,
-0.052335597574710846,
-0.01843341812491417,
0.029279060661792755,
0.022418996319174767,
-0.005344560835510492,
0.008340077474713326,
-0.025942683219909668,
0.03957538679242134,
0.01655576564371586,
-0.04513581097126007,
-0.03155243396759033,
0.04125529155135155,
-0.008744669146835804,
0.03568066656589508,
0.009513297118246555,
0.03781605884432793,
0.03701511025428772,
0.03191598132252693,
-0.047133442014455795,
-0.014884294010698795,
-0.0030259538907557726,
0.011792571283876896,
0.04302286356687546,
-0.031361307948827744,
0.0029273296240717173,
0.04099259525537491,
-0.0015104415360838175,
0.002571364399045706,
-0.0058442698791623116,
-0.02032637409865856,
-0.024876685813069344,
-0.007899392396211624,
0.010402039624750614,
-0.003031103638932109,
0.03144019842147827,
-0.026344286277890205,
0.017561936751008034,
-0.024193469434976578,
-0.009538073092699051,
-0.07219047099351883,
-0.017354967072606087,
-0.008596647530794144,
-0.0429810956120491,
-0.01792699098587036,
0.028502080589532852,
-0.03429349511861801,
-0.008600028231739998,
0.02379121445119381,
0.026151813566684723,
-0.009230379946529865,
-0.02231215499341488,
0.02202875167131424,
-0.03221706673502922,
0.05516665801405907,
-0.010109280236065388,
-0.01802770420908928,
0.01581129990518093,
-0.00648122001439333,
-0.05750151351094246,
0.05086418613791466,
0.013446004129946232,
0.036106232553720474,
-0.008091935887932777,
-0.011444032192230225,
0.012360094115138054,
0.05267411842942238,
-0.03243234381079674,
0.028868578374385834,
0.007359519135206938,
-0.047695308923721313,
-0.015826724469661713,
-0.04488195478916168,
-0.003119883593171835,
-0.024071963503956795,
0.015797464177012444,
0.04002443701028824,
-0.007797830272465944,
-0.015079346485435963,
0.0019339307909831405,
0.0048024593852460384,
0.0101008927449584,
-0.0036508289631456137,
0.05140795186161995,
0.016935044899582863,
0.014085914008319378,
0.044929563999176025,
-0.018721159547567368,
0.030679909512400627,
0.015503838658332825,
0.00334236491471529,
-0.10813676565885544,
0.01873198337852955,
0.03180008754134178,
-0.00990137830376625,
0.0364195890724659,
-0.05888528749346733,
0.0014844724209979177,
0.00794090423732996,
-0.04611321538686752,
0.01750279776751995,
-0.06563849002122879,
-0.02067909948527813,
0.007648313418030739,
-0.042009055614471436,
0.03980272635817528,
0.008663922548294067,
0.03849201649427414,
0.029202111065387726,
-0.01988052763044834,
-0.006175277754664421,
0.004639448132365942,
-0.009892311878502369,
-0.004342317581176758,
0.04960846155881882,
0.010746537707746029,
-0.01448584720492363,
0.05826006457209587,
-0.014051811769604683,
0.008693677373230457,
0.035542458295822144,
-0.0034364606253802776,
0.029447659850120544,
-0.0016029401449486613,
0.015211607329547405,
0.009554078802466393,
0.010320857167243958,
0.005170544143766165,
-0.006048734299838543,
-0.004791405517607927,
0.015099838376045227,
-0.011335625313222408,
0.04128085449337959,
-0.020358018577098846,
-0.04918721318244934,
-0.04465112090110779,
-0.044946588575839996,
-0.0683615431189537,
-0.005562847014516592,
-0.042345765978097916,
-0.007880102843046188,
0.03553739935159683,
0.024362849071621895,
-0.0004390733956824988,
-0.027706293389201164,
0.006661745719611645,
-0.04949518293142319,
0.022293712943792343,
0.03271334618330002,
-0.021459680050611496,
-0.025427918881177902,
0.005391079466789961,
0.002911186311393976,
-0.014156859368085861,
-0.019227707758545876,
-0.019265007227659225,
0.0018902100855484605,
-0.05113781988620758,
-0.020467661321163177,
0.001787553890608251,
-0.04127204790711403,
-0.03853239864110947,
-0.028770720586180687,
-0.022247273474931717,
0.027803804725408554,
0.011789618991315365,
0.021239852532744408,
0.014808673411607742,
0.006810793653130531,
-0.025034163147211075,
-0.08159118890762329,
0.05692474916577339,
0.02165038138628006,
-0.017088597640395164,
-0.04492003098130226,
0.008542509749531746,
0.028211550787091255,
0.009379091672599316,
0.045298345386981964,
-0.05081448331475258,
-0.007960566319525242,
0.050637900829315186,
-0.022568846121430397,
0.0090872161090374,
-0.015346763655543327,
0.006057980936020613,
0.01054335292428732,
-0.04880758002400398,
0.015201925300061703,
-0.02057037316262722,
0.00008864677511155605,
-0.013277081772685051,
-0.014380557462573051,
-0.0334697850048542,
0.018266556784510612,
0.013228344731032848,
-0.022380493581295013,
0.016725366935133934,
0.027578966692090034,
-0.03128151223063469,
0.06467265635728836,
0.0018963780021294951,
-0.0015650707064196467,
0.029847484081983566,
-0.032115306705236435,
-0.03163576126098633,
0.045003410428762436,
-0.026830874383449554,
-0.01711335964500904,
-0.035974737256765366,
-0.024811677634716034,
0.012446840293705463,
-0.048014216125011444,
-0.037062034010887146,
0.045702818781137466,
-0.03457432985305786,
0.0016287959879264235,
0.028783656656742096,
0.008316140621900558,
0.03580022603273392,
-0.012182420119643211,
0.0026116902008652687,
0.05199798196554184,
-0.03861493244767189,
0.02101299725472927,
0.02038821019232273,
0.02913650870323181,
0.020189886912703514,
-0.026110149919986725,
0.04047669842839241,
-0.020285820588469505,
0.01621779426932335,
0.023447468876838684,
0.04591583088040352,
-0.030997665598988533,
-0.002042613457888365,
-0.049205973744392395,
0.002126023406162858,
-0.03994177654385567,
0.02245906926691532,
-0.03696843609213829,
0.02665894292294979,
-0.023060278967022896,
0.0013893553987145424,
-0.007516936399042606,
-0.01605874113738537,
-0.011555598117411137,
0.01870904117822647,
0.032343536615371704,
-0.002393953036516905,
0.006871841382235289,
-0.03532247990369797,
-0.007063396740704775,
0.016518039628863335,
0.023320259526371956,
0.006576147861778736,
0.009323883801698685,
-0.020149854943156242,
0.006493615917861462,
-0.02921207994222641,
-0.05020229518413544,
-0.028016846626996994,
-0.02726384624838829,
0.07353750616312027,
0.02169913612306118,
0.013264674693346024,
-0.04304533451795578,
0.015302642248570919,
-0.04986448958516121,
0.061520837247371674,
-0.09127943217754364,
-0.019577190279960632,
-0.03864390030503273,
0.034364257007837296,
0.02167169190943241,
-0.02975880168378353
] |
<p>Given a many body spin system, a collection of N spin-1/2 particles, under the interaction of the twisting Hamiltonian:
$$H_{int} = \sum_{i,j=1}^Na_{i,j}\sigma_{z,i}\sigma_{z,j}= A J_{z}^{2}$$
assume all $a_{i,j}$ are equal and define:
$$\mathbf{J} = \sum_{n=1}^{N} \mathbf{\sigma}_{n}$$
the collective spin operator, $\mathbf{\sigma}_{n}$ is the pauli spin operator for the $n$th spin, and $A$ characterizes the strength. </p>
<p>Which component of the spin system will display reduced variance/will be squeezed? What assumptions does this require regarding the initial state? </p>
<p>The context of the question is the notion of spin squeezed states, as originally put forward by (1) <a href="http://dx.doi.org/10.1103/PhysRevA.46.R6797" rel="nofollow">Wineland et al.</a> and (2) <a href="http://dx.doi.org/10.1103/PhysRevA.47.5138" rel="nofollow">Kitagawa & Ueda</a></p>
<p>EDIT</p>
<p>In particular in figure 2 of (2) the evolution of the coherent spin state $|\pi/2,0\rangle$ (pointing along $\hat{x}$) is described, they show that squeezing occurs along the y- and z-axes. As I see it these variances seem to oscillate out of phase.</p>
<p>What would be helpful is if someone could explain how to visualize this so-called twisting dynamics. So far i thought that, starting with an initial (Q-)distribution in phase space,
the distribution evolves with precession frequency proportional to $J_{z}$. But from there I do not see how the variance along $\hat{z}$ would change...</p>
<p>Also as a side note: to my knowledge these type of quadratic in angular momentum terms are not very common, but also appear in nuclear physics as the <a href="http://arxiv.org/abs/0805.4078" rel="nofollow">Lipkin model</a>.</p>
| 10,737 |
[
-0.015540004707872868,
-0.007921421900391579,
-0.00634298101067543,
-0.07428295165300369,
0.06126300245523453,
0.018640119582414627,
-0.029690386727452278,
-0.04858073964715004,
-0.005872697103768587,
-0.061024002730846405,
0.04570649936795235,
0.04601588845252991,
0.02924378775060177,
0.013818442821502686,
0.0009067641221918166,
0.02012619562447071,
-0.009547696448862553,
-0.03396962955594063,
-0.03986625373363495,
-0.014776615425944328,
0.011804750189185143,
0.025512976571917534,
-0.007940570823848248,
-0.0005478687817230821,
-0.012862436473369598,
0.03953954949975014,
0.008835324086248875,
0.007674830034375191,
0.018598217517137527,
0.07512809336185455,
-0.004269018769264221,
-0.041504278779029846,
0.01999974250793457,
0.0063391695730388165,
0.004726123064756393,
-0.014305847696959972,
-0.019778428599238396,
-0.06420789659023285,
0.0025924532674252987,
0.030408797785639763,
-0.08389449864625931,
0.021640805527567863,
-0.05885191634297371,
0.005117753054946661,
-0.037631820887327194,
0.015808600932359695,
-0.02608548291027546,
0.02460034191608429,
0.042652007192373276,
-0.03087480738759041,
0.08630017936229706,
0.03125520795583725,
-0.0001185481742140837,
-0.014445789158344269,
-0.01639602892100811,
0.0017692260444164276,
0.06299282610416412,
0.07091016322374344,
0.003260252298787236,
-0.06559761613607407,
-0.026039211079478264,
-0.0341142863035202,
-0.005513621494174004,
-0.03828415274620056,
-0.007716177497059107,
0.019216172397136688,
0.048696041107177734,
-0.03349057585000992,
0.014856726862490177,
-0.011621619574725628,
0.020541099831461906,
-0.03266196325421333,
0.06012282148003578,
-0.03935818001627922,
0.013915058225393295,
0.007355771958827972,
0.012740734033286572,
0.013913312926888466,
0.029800081625580788,
0.018924640491604805,
-0.0007730954675935209,
0.03454361483454704,
0.0168734360486269,
0.006858553737401962,
-0.011967910453677177,
-0.009740415029227734,
0.09199752658605576,
0.01657685823738575,
0.022976543754339218,
0.02921273186802864,
-0.024072246626019478,
0.02161385491490364,
0.04023994132876396,
-0.04054860770702362,
-0.05217842385172844,
0.02689965069293976,
0.011934522539377213,
0.04355134442448616,
-0.02333427034318447,
-0.04481574892997742,
-0.022966809570789337,
-0.04957123100757599,
0.004897197708487511,
0.052708547562360764,
0.0030377604998648167,
0.0027827853336930275,
-0.014887363649904728,
-0.005770595744252205,
-0.06443168222904205,
-0.027396185323596,
-0.022803908213973045,
-0.004935065750032663,
-0.027364660054445267,
-0.0279404167085886,
-0.01735677197575569,
-0.00031379179563373327,
0.011433189734816551,
0.0014605188043788075,
0.06957916170358658,
0.07471053302288055,
0.021762056276202202,
-0.030808907002210617,
0.009850196540355682,
-0.07145284861326218,
-0.05071233958005905,
0.002570252399891615,
0.0418732725083828,
0.028408480808138847,
-0.05901893973350525,
0.02327192947268486,
0.0051485993899405,
-0.020747492089867592,
0.025192029774188995,
-0.0124315544962883,
-0.00790878850966692,
-0.01726504974067211,
-0.13996927440166473,
-0.04553970322012901,
0.06487030535936356,
-0.07792697101831436,
0.008596118539571762,
-0.07521935552358627,
0.011310305446386337,
0.03181930631399155,
0.0784231424331665,
-0.01968136988580227,
0.0450572669506073,
0.015363185666501522,
0.052466925233602524,
0.052652448415756226,
-0.017315905541181564,
-0.020531712099909782,
-0.007987027987837791,
-0.002266830764710903,
-0.03691567853093147,
-0.032776691019535065,
0.04309820383787155,
0.06050531566143036,
-0.008516743779182434,
-0.03070511482656002,
0.025868874043226242,
0.0005697040469385684,
0.024812890216708183,
0.03330152481794357,
0.018063079565763474,
-0.009305198676884174,
0.08601819723844528,
0.014703817665576935,
0.002927868627011776,
0.0437830351293087,
-0.007357938215136528,
-0.0008272806298919022,
0.0006988327950239182,
0.03490809351205826,
0.019490204751491547,
-0.04883715137839317,
0.01475095096975565,
-0.02696147747337818,
-0.03376040235161781,
0.011301225051283836,
-0.028423532843589783,
-0.019587406888604164,
-0.04847314581274986,
0.019235432147979736,
-0.011935833841562271,
0.025725921615958214,
0.017210153862833977,
-0.004121930804103613,
-0.006532436702400446,
-0.08474144339561462,
0.00018006480240728706,
-0.04516664519906044,
-0.006469853222370148,
-0.0032756237778812647,
-0.049029089510440826,
0.062788225710392,
0.0236939936876297,
0.021969487890601158,
0.021166466176509857,
-0.05675961822271347,
-0.022918013855814934,
0.007495922036468983,
0.009259090758860111,
0.012715834192931652,
0.01447618380188942,
0.057291705161333084,
0.030823925510048866,
0.026185642927885056,
0.03872223198413849,
0.015851080417633057,
-0.0494777113199234,
-0.007337448187172413,
-0.014231451787054539,
0.016537001356482506,
0.0412331223487854,
0.011848846450448036,
0.005337393842637539,
0.0112325269728899,
-0.009674935601651669,
-0.04034813866019249,
-0.011192603036761284,
0.05461055040359497,
0.031901948153972626,
-0.027826206758618355,
0.0038331991527229548,
0.05535976216197014,
0.02311444841325283,
0.02606133744120598,
-0.018154213204979897,
-0.024107428267598152,
-0.03909864276647568,
0.002650276990607381,
0.030161941424012184,
0.08819431811571121,
-0.035500042140483856,
-0.018239280208945274,
0.03538098186254501,
0.05558888614177704,
0.008193356916308403,
0.00825541839003563,
-0.05249021574854851,
-0.04136611893773079,
0.013842429034411907,
0.007379748392850161,
-0.022185029461979866,
0.0019780686125159264,
-0.00011548360635060817,
-0.019003581255674362,
0.003762898501008749,
0.02126280404627323,
-0.04346032440662384,
-0.004037801641970873,
-0.059881679713726044,
0.0022293804213404655,
-0.00500713475048542,
-0.036316219717264175,
0.013625302352011204,
0.009785597212612629,
0.011421729810535908,
0.018121838569641113,
-0.026728753000497818,
0.0027261534705758095,
-0.04027552157640457,
-0.042624298483133316,
-0.01069403812289238,
-0.002220906550064683,
-0.011952475644648075,
-0.020810330286622047,
0.006175617687404156,
0.01643522083759308,
-0.018406713381409645,
0.012036670930683613,
0.013706677593290806,
0.0015391347697004676,
-0.008831653743982315,
0.05064721778035164,
0.013785299845039845,
0.003363588824868202,
-0.03645707666873932,
-0.02336917072534561,
-0.0045597124844789505,
0.027569135650992393,
0.043404072523117065,
0.05633879825472832,
-0.051031194627285004,
-0.011914640665054321,
-0.05609669163823128,
0.00025015731807798147,
0.040749482810497284,
-0.016454793512821198,
0.0038600286934524775,
-0.01040106825530529,
-0.02569562755525112,
-0.04219869524240494,
-0.01717483066022396,
0.032350387424230576,
0.015316840261220932,
-0.04097874090075493,
0.00254177488386631,
0.06044338643550873,
-0.007632195949554443,
-0.024808060377836227,
0.018717417493462563,
-0.019880998879671097,
-0.04225372150540352,
-0.020145807415246964,
-0.0021456710528582335,
0.019826486706733704,
-0.01615130342543125,
0.010682137683033943,
0.04703884944319725,
0.00414470536634326,
-0.02377929911017418,
-0.055483702570199966,
-0.050193510949611664,
0.012930755503475666,
-0.026117876172065735,
0.02903255634009838,
-0.003709295764565468,
-0.03766772150993347,
0.09929239749908447,
-0.013830291107296944,
-0.026081793010234833,
-0.04406663775444031,
0.0427280031144619,
0.005875930190086365,
-0.007200195454061031,
0.028482133522629738,
0.017398659139871597,
0.005942678544670343,
0.06480316072702408,
0.027592528611421585,
-0.006372775882482529,
0.05364363268017769,
0.010848327539861202,
-0.003056121990084648,
0.017308302223682404,
-0.030262550339102745,
-0.015529992990195751,
0.03818165510892868,
0.01629459485411644,
-0.007858569733798504,
-0.0057097868993878365,
0.006279484368860722,
0.013176234439015388,
0.0005529326153919101,
-0.07383141666650772,
0.059018734842538834,
-0.0054605393670499325,
-0.001484577194787562,
-0.00870362389832735,
0.08263394981622696,
-0.005059855990111828,
-0.0219068955630064,
0.021323751658201218,
0.024399003013968468,
0.02922636829316616,
0.010836346074938774,
0.013896173797547817,
0.04232388734817505,
-0.007155491039156914,
0.020639674738049507,
0.015312164090573788,
0.01110121700912714,
-0.0162902120500803,
0.05570892244577408,
-0.0717083290219307,
-0.019472012296319008,
-0.0092362891882658,
0.02452358603477478,
0.006470816675573587,
-0.05272587388753891,
-0.015083729289472103,
-0.008997977711260319,
-0.017215238884091377,
-0.00254772137850523,
-0.024535726755857468,
0.0184940155595541,
0.0030669893603771925,
0.09576313197612762,
0.0034921057522296906,
0.01293172873556614,
-0.004607019014656544,
-0.03432677686214447,
-0.045229021459817886,
0.03729022666811943,
-0.01197954174131155,
0.0035069307778030634,
0.0319056361913681,
-0.021538712084293365,
0.027896005660295486,
-0.012605218216776848,
0.006746780127286911,
-0.05095873773097992,
0.02269212156534195,
-0.029732713475823402,
0.0014057406224310398,
-0.016694776713848114,
-0.024078823626041412,
-0.002172325039282441,
0.047873638570308685,
0.05467711761593819,
-0.03608822077512741,
0.04948021471500397,
0.005649684928357601,
-0.012298250570893288,
0.04573121666908264,
-0.005293012131005526,
0.03842968866229057,
0.021532826125621796,
0.0017719699535518885,
0.031810175627470016,
0.011980702169239521,
-0.0021776969078928232,
-0.027124891057610512,
0.010190455242991447,
0.06928899139165878,
0.018481086939573288,
-0.01764415204524994,
0.044597327709198,
-0.038928646594285965,
-0.007717671804130077,
-0.004343201871961355,
0.03436664864420891,
0.009344547055661678,
0.013860603794455528,
0.0362459272146225,
0.021847177296876907,
-0.02185378037393093,
0.022828707471489906,
0.0322149395942688,
0.01158529706299305,
0.00971975177526474,
-0.02566405013203621,
-0.014776677824556828,
0.0033369807060807943,
-0.013887499459087849,
0.01085991133004427,
-0.01964184269309044,
-0.00998795684427023,
0.014111884869635105,
0.03616010397672653,
0.0335271917283535,
-0.03457363694906235,
-0.008264211006462574,
-0.013372708112001419,
0.0032425550743937492,
0.01714923232793808,
0.0229356549680233,
0.0024315526243299246,
0.011251253075897694,
0.003834282048046589,
0.02483757957816124,
-0.00017396092880517244,
-0.06258661299943924,
-0.058705564588308334,
0.020382482558488846,
-0.003181969979777932,
-0.014561169780790806,
-0.005222235340625048,
-0.018792400136590004,
-0.040261853486299515,
0.0394623801112175,
-0.020142648369073868,
0.06652507930994034,
0.000215299500268884,
-0.03851122409105301,
-0.02528136409819126,
-0.03483991697430611,
-0.03130317106842995,
0.016175761818885803,
-0.00787428580224514,
0.013465366326272488,
-0.03472156450152397,
-0.012169933877885342,
0.010267379693686962,
-0.010544807650148869,
-0.011449886485934258,
0.019419986754655838,
0.0021085813641548157,
-0.008037601597607136,
0.020902439951896667,
0.02940351702272892,
-0.013141931034624577,
-0.11082454770803452,
0.04145507514476776,
-0.01200658455491066,
-0.012806002050638199,
0.06719627231359482,
-0.048715196549892426,
-0.03375168889760971,
0.013430862687528133,
0.00005134401362738572,
0.03601014241576195,
0.04345439374446869,
-0.024955371394753456,
0.09550179541110992,
0.04532838985323906,
-0.014197833836078644,
0.042857129126787186,
0.03206982836127281,
-0.006726778578013182,
0.02224215865135193,
-0.0044643571600317955,
0.027770385146141052,
-0.018971476703882217,
0.00197353633120656,
-0.042660437524318695,
0.055731289088726044,
-0.008299075067043304,
0.05758034065365791,
-0.0202050618827343,
0.0066295405849814415,
0.01784329116344452,
-0.023838317021727562,
0.023452628403902054,
0.03089872933924198,
0.0025298085529357195,
-0.020458944141864777,
0.014041351154446602,
0.05289637669920921,
0.042445775121450424,
-0.009369508363306522,
-0.002485240576788783,
-0.023983359336853027,
0.004665868356823921,
0.04663524031639099,
-0.04131338745355606,
-0.002044948050752282,
-0.05309038981795311,
-0.015608644112944603,
-0.008531525731086731,
-0.05104409530758858,
0.0330195277929306,
0.003777138888835907,
0.008156604133546352,
0.019595395773649216,
-0.02079654484987259,
-0.014968992210924625,
0.00005699314715457149,
-0.02738841436803341,
0.02740657329559326,
0.006354974582791328,
-0.044627636671066284,
0.018041720613837242,
-0.01108765322715044,
-0.0659513771533966,
0.0037065576761960983,
0.009920399636030197,
0.0029164128936827183,
-0.030851785093545914,
-0.016918359324336052,
-0.004783058073371649,
0.017567964270710945,
-0.02641170099377632,
0.0003606611571740359,
0.019776657223701477,
-0.03357752785086632,
0.027891570702195168,
0.03459259495139122,
0.03821408003568649,
0.052611466497182846,
-0.020237822085618973,
-0.014709715731441975,
0.00019310464267618954,
-0.03004179149866104,
0.024378152564167976,
0.03879126161336899,
0.01406241487711668,
-0.02245614305138588,
-0.03449299558997154,
-0.024571765214204788,
0.00874753575772047,
0.02777751162648201,
-0.0025286234449595213,
0.002129740547388792,
-0.0008721511694602668,
-0.010031058453023434,
0.010587315075099468,
0.014408113434910774,
-0.04449554532766342,
-0.02072201855480671,
0.02603662759065628,
0.0057511539198458195,
0.01128302700817585,
-0.007300999481230974,
-0.015937702730298042,
0.017497749999165535,
0.0009473399841226637,
-0.024006959050893784,
0.015044881962239742,
0.05015810206532478,
0.002303436165675521,
-0.03552214428782463,
-0.011993925087153912,
-0.057512085884809494,
0.000025748260668478906,
-0.0019610081799328327,
0.01613396219909191,
0.014971956610679626,
0.004864892922341824,
-0.00996309146285057,
-0.014735907316207886,
-0.0390428863465786,
0.008941112086176872,
0.07315929234027863,
0.024420443922281265,
0.024937527254223824,
0.05063334479928017,
0.01855410262942314,
-0.03783801198005676,
-0.05156170576810837,
-0.004885873291641474,
0.024396102875471115,
-0.011400898918509483,
0.011205451563000679,
-0.033807944506406784,
-0.009968600235879421,
0.03789173439145088,
0.03613689914345741,
-0.009272998198866844,
0.01652476005256176,
0.04427289217710495,
-0.0027080571744590998,
0.03069338947534561,
-0.030213743448257446,
-0.04429299756884575,
0.06665189564228058,
-0.01996532641351223,
0.041818853467702866,
-0.013087472878396511,
-0.011521553620696068,
0.0036577628925442696,
0.04117117449641228,
0.037189945578575134,
-0.0076902336440980434,
-0.017850475385785103,
-0.055638961493968964,
0.004550353158265352,
0.011969766579568386,
-0.03535681217908859,
0.02145221270620823,
0.0199325792491436,
0.0309517290443182,
0.010409404523670673,
0.026425836607813835,
-0.027922125533223152,
-0.03724081814289093,
0.003128312760964036,
-0.0026372852735221386,
-0.054346710443496704,
0.003899830859154463,
-0.01985020376741886,
-0.025708993896842003,
0.015653928741812706,
-0.021946730092167854,
0.03270840272307396,
-0.013027353212237358,
-0.010966144502162933,
-0.02087944932281971,
0.0799233615398407,
-0.0007262704311870039,
0.04752793908119202,
0.0048359776847064495,
0.005582221318036318,
0.12216593325138092,
0.02591647580265999,
0.011807129718363285,
-0.034231770783662796,
0.01003409456461668,
0.037915442138910294,
0.01506593357771635,
0.005704609211534262,
0.0010153739713132381,
0.04851863533258438,
-0.005614083260297775,
-0.016972780227661133,
0.040583059191703796,
0.005403565242886543,
-0.03331119939684868,
0.02434602752327919,
-0.03199690580368042,
-0.008366037160158157,
-0.03731289878487587,
-0.007370676379650831,
-0.012758343480527401,
-0.020219149067997932,
-0.06661347299814224,
0.024591492488980293,
-0.023899680003523827,
0.007197109051048756,
-0.013834033161401749,
-0.017822900786995888,
-0.009791191667318344,
-0.0009658333146944642,
-0.03514104336500168,
0.028228994458913803,
-0.026996802538633347,
-0.022772260010242462,
-0.01595337875187397,
0.0018588112434372306,
0.03397483006119728,
-0.0063305506482720375,
0.05741899460554123,
0.034984007477760315,
-0.004110360983759165,
-0.026046214625239372,
0.020860258489847183,
0.018739672377705574,
-0.045331843197345734,
-0.037981513887643814,
-0.033428650349378586,
0.07816814631223679,
-0.020517045632004738,
-0.007386187091469765,
-0.005484041757881641,
-0.029915733262896538,
0.008163340389728546,
-0.022251037880778313,
0.011940456926822662,
-0.017524996772408485,
-0.011644377373158932,
-0.028990058228373528,
-0.007276967167854309,
-0.0020321363117545843,
-0.0026015329640358686,
0.016673071309924126,
0.02861759625375271,
-0.002964730840176344,
-0.03215227276086807,
-0.04207690805196762,
0.015982579439878464,
0.014618828892707825,
0.021680811420083046,
0.023432860150933266,
-0.03480030968785286,
-0.005226212553679943,
-0.031904738396406174,
-0.025984695181250572,
0.02062465250492096,
-0.013057900592684746,
0.05246519297361374,
0.017322011291980743,
-0.006201936863362789,
-0.002091243863105774,
-0.068559430539608,
0.010810129344463348,
-0.007954560220241547,
-0.028812136501073837,
-0.010520442388951778,
0.017086634412407875,
0.033513881266117096,
0.024549370631575584,
-0.03961358219385147,
0.030746575444936752,
-0.005152302328497171,
0.0490824393928051,
0.023067379370331764,
-0.0005008850712329149,
0.012003806419670582,
0.021259890869259834,
-0.016103172674775124,
-0.012567241676151752,
-0.007322446908801794,
0.016661545261740685,
0.02155134081840515,
-0.0012607020325958729,
0.017808115109801292,
0.03674646094441414,
0.024075161665678024,
-0.039464935660362244,
0.030805597081780434,
-0.0346074253320694,
-0.019242895767092705,
0.02972334250807762,
0.023780250921845436,
-0.05359756946563721,
0.012463364750146866,
0.010831456631422043,
-0.03699171543121338,
-0.005239528138190508,
0.00008937026723288,
-0.023381587117910385,
-0.03433067351579666,
-0.004272316116839647,
0.028984852135181427,
-0.02451370842754841,
-0.01109820231795311,
-0.03165464475750923,
0.007480511907488108,
-0.018326880410313606,
0.06348711997270584,
0.00275887968018651,
0.02806548774242401,
0.03673138469457626,
-0.0524764209985733,
0.007904067635536194,
0.03932497277855873,
-0.002259416040033102,
-0.010132157243788242,
0.04024122282862663,
0.0068494295701384544,
0.017560359090566635,
0.011138842441141605,
-0.04298778995871544,
0.02640792541205883,
-0.020841704681515694,
-0.03273209184408188,
0.033193208277225494,
-0.020696960389614105,
0.01946321502327919,
0.021301105618476868,
-0.028691481798887253,
-0.041566453874111176,
0.014102958142757416,
-0.013535470701754093,
-0.019595952704548836,
-0.01629960536956787,
0.004709846340119839,
-0.02841605246067047,
-0.018648741766810417,
0.0026730746030807495,
0.012775629758834839,
0.009704846888780594,
0.06119648367166519,
0.03667137026786804,
-0.04775715246796608,
0.00572018651291728,
0.0020260573364794254,
-0.0020752751734107733,
0.05169003829360008,
0.008881338872015476,
0.005960935726761818,
0.04452071711421013,
0.03560340404510498,
-0.0305204875767231,
0.032315608114004135,
-0.02289513871073723,
0.028008393943309784,
-0.07527647912502289,
-0.034556880593299866,
-0.006806607358157635,
0.015033095143735409,
0.05497174710035324,
-0.026085110381245613,
0.021711139008402824,
0.053260233253240585,
-0.07944341003894806,
0.03766823559999466,
-0.017513010650873184,
-0.008517211303114891,
-0.008800364099442959,
0.004377096891403198,
-0.051715414971113205,
0.029408017173409462,
-0.015097351744771004,
0.028210114687681198,
0.03436153754591942,
0.02850107103586197,
-0.053436122834682465,
-0.01086464710533619,
-0.01027010753750801,
0.012367653660476208,
0.023009901866316795,
-0.009261948056519032,
0.07081683725118637,
-0.005473086144775152,
-0.028593964874744415,
0.040007077157497406,
-0.006245543714612722,
0.007645332254469395,
-0.05001266300678253,
0.0006740922690369189,
0.009488373063504696,
0.015404497273266315,
-0.011985605582594872,
-0.001852473127655685,
0.04911316931247711,
-0.00723537290468812,
0.026273483410477638,
0.0020524233113974333,
-0.008634240366518497,
0.022760648280382156,
0.016976136714220047,
-0.03492221608757973,
-0.02819288708269596,
0.021830329671502113,
0.00718336459249258,
0.012739408761262894,
0.01364229153841734,
0.004357530269771814,
-0.0023686555214226246,
-0.03508847951889038,
0.037631094455718994,
-0.015088889747858047,
0.013718299567699432,
0.0021490349899977446,
0.03484908863902092,
-0.012620050460100174,
0.03262391313910484,
-0.01787979155778885,
-0.02943561226129532,
0.02581266313791275,
-0.011637960560619831,
-0.06446275860071182,
-0.05757177993655205,
-0.016401344910264015,
0.0006265356787480414,
0.014981436543166637,
0.01161910593509674,
-0.05678226798772812,
-0.045755282044410706,
0.011795878410339355,
-0.015026576817035675,
0.019820665940642357,
-0.016800053417682648,
-0.058226328343153,
-0.04633137583732605,
-0.096591517329216,
0.01433052122592926,
0.030100863426923752,
0.00001651425009185914,
-0.015659663826227188,
-0.0008966171299107373,
0.009147335775196552,
-0.0017162307631224394,
0.03347799554467201,
0.04218786582350731,
-0.026126645505428314,
0.008249464444816113,
0.0025592604652047157,
0.04355666786432266,
-0.026579871773719788,
0.027706142514944077,
-0.044768091291189194,
0.018711112439632416,
0.005435407627373934,
0.0050141275860369205,
-0.020952818915247917,
0.0051247538067400455,
0.02755870297551155,
0.0196858998388052,
-0.002819797955453396,
0.013125100173056126,
-0.0568283386528492,
0.056112244725227356,
-0.029665673151612282,
-0.02044777013361454,
0.0531216636300087,
-0.02975708805024624,
-0.011902025900781155,
0.02776661142706871,
0.004435272421687841,
-0.06554557383060455,
-0.010724903084337711,
-0.0046011717058718204,
-0.014887470752000809,
-0.01250840537250042,
-0.008517378009855747,
0.027886273339390755,
-0.03890637680888176,
-0.008686241693794727,
-0.0021203921642154455,
-0.034357815980911255,
-0.021378150209784508,
0.019621608778834343,
0.017514513805508614,
0.020823242142796516,
0.0160385612398386,
0.03065292164683342,
-0.002632267540320754,
0.013372792862355709,
0.027785249054431915,
0.042540498077869415,
0.03739525005221367,
0.02543715387582779,
-0.006028137169778347,
-0.013929111883044243,
-0.02930743247270584,
0.008823364973068237,
-0.00731296744197607,
0.018222298473119736,
-0.041500966995954514,
-0.012769094668328762,
0.058057382702827454,
-0.03372790291905403,
-0.007728366181254387,
-0.002911532297730446,
-0.019281607121229172,
0.08156626671552658,
-0.01693788915872574,
0.009242798201739788,
-0.02963581681251526,
-0.013760724104940891,
-0.004233804997056723,
-0.013238215819001198,
0.017080387100577354,
0.06420858949422836,
-0.039969172328710556,
-0.010711557231843472,
-0.027203787118196487,
-0.018426833674311638,
-0.0031225630082190037,
-0.041423700749874115,
0.018243582919239998,
0.02985461615025997,
0.019503876566886902,
0.0009721030364744365,
-0.023710234090685844,
-0.008287263102829456,
-0.033878251910209656,
-0.005851015914231539,
0.011240305379033089,
0.02779085747897625,
-0.02488309144973755,
-0.005100634880363941,
-0.018460310995578766,
0.039419036358594894,
-0.0381096750497818,
-0.040955543518066406,
-0.034159909933805466,
0.019132304936647415,
-0.008721675723791122,
-0.010786137543618679
] |
<p>Consider a point mass $A$ with mass $m$ in empty space. The point mass $A$ does not have a velocity and does not rotate.
Since gravity is symmetric for nonmoving objects, the spacetime curvature around $A$ is also symmetric.</p>
<p>So at a distance $d$ from the point mass $A$ how strong is the curvature $C$ ?</p>
<p>$$ C = f(d,m) $$ $$f = ???$$</p>
| 10,738 |
[
-0.03096502274274826,
-0.031341083347797394,
0.023844502866268158,
-0.03360694646835327,
0.030619779601693153,
0.009823095984756947,
-0.03710586950182915,
-0.04356999695301056,
0.001738199032843113,
-0.01569223217666149,
-0.0076944250613451,
0.023542962968349457,
0.06035256385803223,
0.014050472527742386,
0.022301627323031425,
0.021912245079874992,
-0.012378601357340813,
-0.006177753210067749,
-0.017251497134566307,
-0.0372922457754612,
0.004535100422799587,
0.06058361753821373,
0.0014019341906532645,
0.0008101864368654788,
-0.012370085343718529,
0.010193434543907642,
0.01476558018475771,
-0.006523030810058117,
-0.0022564034443348646,
0.057867757976055145,
-0.03334452956914902,
-0.01762372814118862,
-0.00017593210213817656,
0.04674478992819786,
0.01644524559378624,
0.015865348279476166,
-0.04054713621735573,
0.0008657860453240573,
-0.00011489923781482503,
0.030958250164985657,
-0.03041379526257515,
-0.04571051895618439,
-0.013993656262755394,
0.08542623370885849,
-0.04170292243361473,
0.019241375848650932,
0.02764030173420906,
0.009567784145474434,
0.07600033283233643,
-0.05247284471988678,
0.08482661098241806,
-0.006107774097472429,
0.054928068071603775,
0.003367671277374029,
-0.012180344201624393,
-0.02517116442322731,
0.047765664756298065,
0.048545509576797485,
-0.005537735298275948,
-0.03150054067373276,
-0.0556417852640152,
-0.019098330289125443,
-0.01826079562306404,
-0.03502415865659714,
-0.023122582584619522,
0.05548621714115143,
-0.02200576290488243,
-0.0019079666817560792,
0.021335935220122337,
-0.014973272569477558,
-0.011238617822527885,
0.012997971847653389,
0.05143071711063385,
-0.01612265035510063,
-0.010508773848414421,
-0.025729931890964508,
0.038578543812036514,
0.008940719068050385,
0.020770017057657242,
0.016917729750275612,
0.019550666213035583,
0.007277355063706636,
0.048225369304418564,
0.03347616642713547,
0.0013499300694093108,
0.012813987210392952,
0.05569928139448166,
0.03433222323656082,
0.02769576758146286,
0.0652519017457962,
0.014021694660186768,
-0.022139286622405052,
0.0012282651150599122,
-0.03761854022741318,
-0.02326877787709236,
0.013953027315437794,
-0.018324749544262886,
0.012474894523620605,
-0.026000740006566048,
0.010291222482919693,
-0.052952613681554794,
-0.02333628386259079,
0.01695619709789753,
0.09746582806110382,
0.029124019667506218,
-0.02032626047730446,
-0.026631828397512436,
0.016337942332029343,
-0.02367984689772129,
0.014215976931154728,
-0.031558066606521606,
-0.004291167017072439,
0.0012786767911165953,
-0.04156137630343437,
0.0439920648932457,
-0.010629555210471153,
-0.0006502245087176561,
-0.05180377885699272,
0.03088931366801262,
0.02696346305310726,
0.055915988981723785,
0.000452314066933468,
-0.0015889343339949846,
-0.048655860126018524,
-0.005188875366002321,
0.03224976360797882,
0.05641632527112961,
0.004269189666956663,
-0.03655943647027016,
0.0008941784617491066,
-0.00480708759278059,
-0.02875792793929577,
-0.006883136462420225,
0.01792380027472973,
0.044275764375925064,
-0.021322740241885185,
-0.07029542326927185,
-0.046361442655324936,
0.047149159014225006,
0.008952404372394085,
0.03519224748015404,
-0.040589842945337296,
0.009417553432285786,
0.03992744907736778,
0.08397582918405533,
0.006570377852767706,
0.018537886440753937,
0.030288804322481155,
0.07532565295696259,
-0.0019368212670087814,
-0.005488892085850239,
-0.0085912412032485,
0.02116287313401699,
-0.039863575249910355,
-0.03345279395580292,
-0.08565653860569,
0.013452021405100822,
-0.005934971384704113,
-0.010601073503494263,
-0.054334111511707306,
0.07766979932785034,
-0.015168070793151855,
0.03342864289879799,
-0.03357525169849396,
-0.005861752200871706,
-0.012279934249818325,
0.06184080243110657,
0.03662353754043579,
-0.015920566394925117,
0.05898062139749527,
0.0067584882490336895,
0.014293711632490158,
0.002405913081020117,
-0.001904654665850103,
0.05539882183074951,
-0.07666897028684616,
0.0016467117238789797,
-0.016187848523259163,
-0.005036762449890375,
0.01603618822991848,
-0.006234961096197367,
-0.019801532849669456,
-0.037717245519161224,
0.015217237174510956,
0.011904777958989143,
0.04518842324614525,
-0.006336316000670195,
0.02369067817926407,
-0.018901346251368523,
0.010536856949329376,
-0.016109777614474297,
-0.030314883217215538,
0.018484801054000854,
0.01028120145201683,
-0.026494478806853294,
-0.002894051605835557,
0.03460663557052612,
-0.002699734875932336,
-0.02777370810508728,
-0.019808411598205566,
0.0031971808057278395,
0.019499521702528,
-0.03680383414030075,
-0.0015625242376700044,
0.028738239780068398,
0.05851813778281212,
0.048852842301130295,
-0.004917274694889784,
0.018389390781521797,
-0.00297743477858603,
0.009548250585794449,
0.008697358891367912,
0.014739437960088253,
0.015870077535510063,
-0.006487492471933365,
0.03132619708776474,
0.011745366267859936,
-0.0086937565356493,
0.005752628203481436,
0.041590116918087006,
-0.04102811962366104,
0.0746232122182846,
0.051147282123565674,
-0.005141141824424267,
-0.0014414673205465078,
0.022586088627576828,
0.02550232969224453,
0.02859453856945038,
0.0020141247659921646,
-0.018150657415390015,
-0.05854678153991699,
-0.008226068690419197,
0.0016286963364109397,
0.0057830228470265865,
-0.054135411977767944,
0.00851267110556364,
0.03225284442305565,
0.009882044047117233,
0.001549293752759695,
-0.010225416161119938,
-0.04382162168622017,
-0.060119569301605225,
0.05258970707654953,
0.02255909889936447,
0.01636446639895439,
-0.0025776205584406853,
0.014440196566283703,
0.022214805707335472,
0.007140164729207754,
-0.001660275156609714,
-0.018015269190073013,
0.035792283713817596,
0.010948625393211842,
0.011584154330193996,
-0.0011511101620271802,
-0.001645961427129805,
0.04800204932689667,
0.009124262258410454,
-0.00035968454903922975,
0.05587680637836456,
-0.023961558938026428,
-0.000030439083275268786,
-0.05524575710296631,
-0.02586284652352333,
0.032190706580877304,
0.006084401626139879,
0.0016721709398552775,
-0.037902042269706726,
0.016556261107325554,
-0.03390739858150482,
-0.03346921131014824,
-0.028530379757285118,
-0.011139897629618645,
-0.015241476707160473,
-0.01989373005926609,
0.006428600754588842,
-0.003861166536808014,
0.03660909831523895,
-0.03052438236773014,
-0.00035868995473720133,
-0.004839049186557531,
-0.021145721897482872,
-0.015954207628965378,
0.01934899389743805,
-0.06450044363737106,
0.0308834258466959,
-0.029309028759598732,
-0.03564693033695221,
0.04625185579061508,
-0.0037901955656707287,
-0.00011785639071604237,
0.03884568810462952,
-0.00491298409178853,
-0.027720056474208832,
-0.002306652255356312,
-0.047341033816337585,
0.0012541277101263404,
-0.08638118952512741,
-0.00009148613753495738,
0.03689568489789963,
0.0065316674299538136,
-0.02982368879020214,
0.02788599394261837,
-0.009149991907179356,
-0.0436239093542099,
-0.019222639501094818,
0.03144288808107376,
0.02263590320944786,
-0.05208514630794525,
0.0003323543060105294,
0.011876299045979977,
-0.009541165083646774,
0.01732669398188591,
-0.07599768787622452,
-0.011407854966819286,
0.03923127427697182,
-0.005175173282623291,
0.036167070269584656,
0.016731619834899902,
-0.02927958033978939,
0.08236339688301086,
0.045671939849853516,
-0.011100750416517258,
-0.04302870109677315,
-0.007414371240884066,
0.012733065523207188,
-0.026764359325170517,
0.00445820577442646,
0.019503887742757797,
-0.012240249663591385,
-0.011204651556909084,
0.05499402806162834,
0.0030395828653126955,
0.00857474748045206,
-0.002452914835885167,
-0.036591049283742905,
-0.005396309774369001,
0.012458529323339462,
-0.008311868645250797,
0.03835297003388405,
0.03496605157852173,
-0.014974952675402164,
0.01618240214884281,
0.0012185993837192655,
0.012528132647275925,
-0.006619286723434925,
-0.057367440313100815,
0.03824619948863983,
-0.007018801756203175,
0.019914008677005768,
-0.032305192202329636,
0.022469954565167427,
-0.01617196388542652,
-0.017346763983368874,
0.028928352519869804,
-0.018262067809700966,
0.04875379428267479,
-0.028552405536174774,
-0.022511610761284828,
-0.001646122196689248,
0.05744778737425804,
-0.009850162081420422,
-0.03479661047458649,
-0.027979345992207527,
0.008095135912299156,
0.018246518447995186,
-0.008818075060844421,
-0.0058817872777581215,
0.04043465107679367,
0.0463382713496685,
0.018807590007781982,
0.009681843221187592,
-0.018045492470264435,
-0.005363787990063429,
-0.07865290343761444,
0.009129277430474758,
0.004093499854207039,
0.0396120660007,
0.00006634417513851076,
0.025573408231139183,
0.07341478019952774,
0.0024950248189270496,
-0.012130665592849255,
0.00869056861847639,
-0.07372544705867767,
0.03358788788318634,
-0.05620189756155014,
-0.006142091937363148,
-0.011019544675946236,
-0.015098698437213898,
-0.036496687680482864,
-0.021171091124415398,
0.006516759283840656,
-0.0029345855582505465,
0.01665867306292057,
-0.05656541883945465,
-0.018218014389276505,
-0.032049331814050674,
-0.06724807620048523,
-0.012140072882175446,
0.05923633649945259,
0.04178730025887489,
-0.03672760725021362,
0.03454195708036423,
0.027549518272280693,
-0.05413985997438431,
-0.013410115614533424,
0.0037520870100706816,
-0.00559792248532176,
-0.014786645770072937,
0.014035896398127079,
-0.012603170238435268,
0.007688634563237429,
-0.003289181971922517,
-0.009017704986035824,
-0.004624794237315655,
0.030958816409111023,
0.030666690319776535,
0.0013044413644820452,
-0.02553010731935501,
-0.06186780333518982,
-0.012244456447660923,
0.0032668740022927523,
0.04371638968586922,
-0.03721781075000763,
-0.008495095185935497,
0.03491775318980217,
0.013981685042381287,
-0.009257531724870205,
0.04488496854901314,
0.05849093198776245,
0.020349621772766113,
-0.026831483468413353,
-0.06475319713354111,
-0.038328222930431366,
-0.03218991309404373,
-0.01395834144204855,
0.025905417278409004,
-0.03980115056037903,
-0.04300570487976074,
0.023544933646917343,
0.005086527671664953,
0.030152510851621628,
-0.03860904648900032,
-0.02033989131450653,
-0.024261711165308952,
0.03690207377076149,
-0.045643340796232224,
0.00418081833049655,
-0.0040384624153375626,
0.0642908588051796,
0.06232425197958946,
0.0004729444917757064,
-0.000606299436185509,
-0.09653899818658829,
-0.009246043860912323,
0.04850678890943527,
0.025025103241205215,
0.007392477709800005,
-0.011739200912415981,
-0.06366176903247833,
0.002187359845265746,
0.03830290958285332,
-0.03407334163784981,
0.030166368931531906,
0.003067998681217432,
0.025734521448612213,
-0.030013540759682655,
-0.018708789721131325,
-0.0372956208884716,
0.01952257938683033,
-0.013669449836015701,
0.004616359248757362,
-0.022923195734620094,
0.029997413977980614,
-0.003544362261891365,
0.02289961837232113,
0.012471750378608704,
0.0378153994679451,
0.023781972005963326,
-0.03439648076891899,
0.008502994664013386,
0.011524167843163013,
-0.02090086042881012,
-0.08117382228374481,
0.009609059430658817,
0.003525600302964449,
-0.024881834164261818,
0.02770516835153103,
-0.05341899022459984,
-0.02637830190360546,
0.02559712342917919,
-0.011828448623418808,
0.02532556839287281,
0.02045171894133091,
-0.05018765851855278,
-0.008549883030354977,
0.009426875039935112,
0.009856383316218853,
0.027445290237665176,
0.03245580941438675,
-0.021526969969272614,
-0.026663504540920258,
-0.01789860427379608,
0.01311135571449995,
-0.04092120751738548,
-0.028919542208313942,
-0.03886229172348976,
-0.011453157290816307,
-0.08355671912431717,
0.009102827869355679,
-0.004457786679267883,
-0.0269343089312315,
0.012282990850508213,
-0.024915097281336784,
-0.010219787247478962,
0.05468009039759636,
0.026083681732416153,
0.03572008013725281,
0.01970161683857441,
0.008472000248730183,
0.021139945834875107,
-0.008083402179181576,
0.004397368989884853,
0.021431999281048775,
-0.028305737301707268,
0.014591425657272339,
-0.029957018792629242,
-0.015657827258110046,
0.004938533995300531,
-0.023258427157998085,
0.0031675035133957863,
-0.04358268901705742,
0.06254449486732483,
-0.02043193206191063,
-0.005178048741072416,
0.048706088215112686,
-0.05844666436314583,
-0.0135926129296422,
0.03936368227005005,
-0.013022650964558125,
0.008062914945185184,
-0.06607939302921295,
0.01103193499147892,
0.02872684970498085,
0.02882958948612213,
-0.0680587962269783,
-0.01868063397705555,
0.035563062876462936,
0.0008642919710837305,
0.0004713258531410247,
-0.0164159145206213,
0.000820295768789947,
-0.049461472779512405,
-0.02334490232169628,
-0.01055785734206438,
0.03145156055688858,
0.010964187793433666,
0.03563758358359337,
0.012897878885269165,
-0.0016625208081677556,
0.025642959401011467,
0.019494419917464256,
-0.01292808074504137,
-0.0018061286536976695,
0.005049689207226038,
-0.021800806745886803,
0.0010225387522950768,
0.05306876823306084,
-0.03895192965865135,
-0.029987022280693054,
-0.028275178745388985,
-0.01873897761106491,
0.014275167137384415,
-0.02257951907813549,
-0.013636565767228603,
0.0622083880007267,
0.01199658215045929,
-0.020445773378014565,
-0.036715537309646606,
0.005063585005700588,
-0.03607341647148132,
0.013551679439842701,
-0.013274678029119968,
0.008437540382146835,
-0.0009094261913560331,
-0.027005132287740707,
0.050006598234176636,
0.008910666219890118,
-0.021983234211802483,
-0.007492969278246164,
0.04429280012845993,
-0.0007353516994044185,
-0.026422712951898575,
-0.03427338972687721,
0.013526245951652527,
0.020352521911263466,
-0.010207843966782093,
-0.01073889434337616,
0.024976633489131927,
0.003006227780133486,
-0.04533947631716728,
-0.012567431665956974,
-0.0010663904249668121,
0.007325329817831516,
0.06547333300113678,
0.025698134675621986,
0.029201358556747437,
0.03250592574477196,
0.0012767512816935778,
-0.006958463694900274,
-0.040786050260066986,
-0.019068636000156403,
-0.0134210754185915,
0.02677985280752182,
0.04805554077029228,
-0.007974458858370781,
0.031004343181848526,
0.03439703956246376,
0.05002371966838837,
-0.034433551132678986,
0.0014879988739266992,
0.00044751152745448053,
0.015614287927746773,
0.009429539553821087,
-0.01315348781645298,
-0.027337757870554924,
0.015049419365823269,
0.02848806232213974,
0.04609910771250725,
-0.006676298566162586,
-0.008307822048664093,
0.0213918536901474,
-0.0007379920571111143,
0.07585979253053665,
0.0025712312199175358,
-0.03358080983161926,
-0.05036021023988724,
0.0018184371292591095,
0.03999364376068115,
0.008370771072804928,
-0.021850761026144028,
0.025103360414505005,
0.010753064416348934,
-0.004989088978618383,
0.021857017651200294,
-0.016168950125575066,
-0.06883789598941803,
-0.03801712766289711,
-0.037767890840768814,
-0.04354875534772873,
0.0275541041046381,
0.004948667250573635,
-0.05724192038178444,
0.0545651912689209,
-0.012812535278499126,
0.004037823528051376,
0.02728627622127533,
-0.0030861820559948683,
-0.01997021585702896,
0.05567620322108269,
-0.0219829510897398,
0.016631588339805603,
0.006032533943653107,
-0.03427550569176674,
0.10865098983049393,
0.03083759918808937,
-0.0025715597439557314,
-0.0357392318546772,
0.027729809284210205,
-0.019611353054642677,
0.014682992361485958,
-0.02141123265028,
0.02331417240202427,
-0.011516490951180458,
0.027552880346775055,
0.02069741114974022,
0.030398689210414886,
-0.021230332553386688,
-0.015009161084890366,
0.0650525912642479,
-0.03966078907251358,
-0.002742393407970667,
-0.004370727110654116,
0.0034305385779589415,
0.0026340666227042675,
0.02663680538535118,
0.009989658370614052,
0.04592283070087433,
-0.0456714890897274,
-0.0043341065756976604,
-0.0346287377178669,
-0.033916451036930084,
-0.021090516820549965,
-0.029806828126311302,
-0.04485626146197319,
0.01993079110980034,
0.01570741832256317,
-0.03478282690048218,
-0.04618387669324875,
0.03020313009619713,
0.01104884222149849,
-0.04528466984629631,
0.02113809622824192,
0.039736997336149216,
-0.03147173300385475,
0.041515808552503586,
0.010910069569945335,
-0.01193149946630001,
-0.03125843033194542,
-0.008544293232262135,
-0.052463456988334656,
0.058148205280303955,
-0.0072209700010716915,
0.0447053499519825,
0.043250951915979385,
-0.004611278884112835,
0.0021714037284255028,
-0.041989799588918686,
-0.0071183787658810616,
-0.012051082216203213,
0.023054402321577072,
0.0025444442871958017,
-0.031041596084833145,
-0.026649054139852524,
0.036966681480407715,
0.007092988584190607,
0.033196236938238144,
-0.018628105521202087,
-0.006130782421678305,
0.03276703134179115,
-0.009910425171256065,
0.07418494671583176,
-0.0276251919567585,
-0.02026420459151268,
-0.013407088816165924,
-0.04358731955289841,
-0.01957138441503048,
-0.0034052401315420866,
-0.0037953893188387156,
-0.01341885793954134,
0.04776129871606827,
-0.007211482152342796,
0.03611975908279419,
0.02240699715912342,
-0.0770156979560852,
0.002022061962634325,
-0.04028952121734619,
0.009473754093050957,
-0.029457995668053627,
0.006919718347489834,
0.014530697837471962,
0.034577470272779465,
-0.004681393504142761,
0.012476063333451748,
0.0034067267552018166,
0.0003509900998324156,
-0.009102683514356613,
-0.02645673230290413,
0.005063549615442753,
0.018927158787846565,
-0.04664592444896698,
-0.013920718804001808,
-0.015953147783875465,
0.0063391453586518764,
0.05054823309183121,
-0.0027659405022859573,
-0.002517081331461668,
-0.002417922019958496,
-0.05261282995343208,
-0.02757146768271923,
0.005728982854634523,
-0.014229138381779194,
-0.012436404824256897,
0.011432857252657413,
-0.0253852941095829,
-0.06603000313043594,
-0.005171819124370813,
-0.014920540153980255,
-0.00944011751562357,
0.007375750690698624,
0.01739552617073059,
-0.03880723565816879,
0.04147499054670334,
-0.028290612623095512,
0.018006259575486183,
-0.043275803327560425,
0.014449460431933403,
-0.02339688129723072,
0.0020765706431120634,
0.042151130735874176,
-0.006043090485036373,
0.000940513564273715,
0.02834041230380535,
-0.018059048801660538,
0.0016815559938549995,
-0.023510457947850227,
0.0004707600746769458,
0.01872587762773037,
-0.01894477754831314,
0.07869984954595566,
-0.019745122641324997,
0.052012864500284195,
0.012565040960907936,
-0.017046915367245674,
0.030582595616579056,
-0.04646322876214981,
-0.057068224996328354,
0.025747649371623993,
-0.010572537779808044,
0.02777179330587387,
0.015443524345755577,
-0.013690579682588577,
0.026225414127111435,
0.026935281231999397,
-0.009157414548099041,
-0.014531459659337997,
-0.0013324832543730736,
-0.035654276609420776,
0.03283146023750305,
-0.004514041356742382,
0.026608221232891083,
-0.027632232755422592,
-0.01592678762972355,
0.01132532861083746,
0.010145317763090134,
-0.04989370331168175,
-0.006800358649343252,
0.018872568383812904,
-0.0030595192220062017,
0.000302980188280344,
0.009828955866396427,
0.023726150393486023,
0.037454839795827866,
0.06296683102846146,
-0.011877931654453278,
0.009665489196777344,
0.046244677156209946,
0.030249493196606636,
-0.12079885601997375,
-0.014585512690246105,
-0.0014381688088178635,
-0.006137323100119829,
0.06951285153627396,
-0.05648725479841232,
0.02167080156505108,
0.03244020789861679,
-0.06143571436405182,
0.055889587849378586,
-0.06356284767389297,
0.026915403082966805,
-0.0295597855001688,
-0.015880480408668518,
0.0022656158544123173,
0.058431532233953476,
0.034607693552970886,
0.04835370182991028,
0.004272417165338993,
0.027507120743393898,
-0.012239290401339531,
-0.02360554412007332,
0.018920518457889557,
0.041349343955516815,
-0.0012831981293857098,
-0.015140273608267307,
0.07479406148195267,
0.010675955563783646,
-0.009252341464161873,
0.005377983208745718,
-0.04125528037548065,
-0.019134484231472015,
0.004714301787316799,
-0.012246143072843552,
0.01784067414700985,
0.012689790688455105,
0.00884443148970604,
0.009087638929486275,
-0.05947928875684738,
0.011837479658424854,
0.01984735019505024,
0.03624781221151352,
-0.03938087448477745,
-0.001354370848275721,
-0.010276319459080696,
-0.046872664242982864,
-0.025134628638625145,
0.005113068502396345,
-0.033229004591703415,
-0.011721091344952583,
0.004707233514636755,
-0.0205340925604105,
-0.014861772768199444,
-0.0179451871663332,
0.029431870207190514,
-0.03601070120930672,
0.022990407422184944,
0.04123925790190697,
-0.02536715753376484,
-0.02313663810491562,
0.037747375667095184,
0.013426550664007664,
-0.013937795534729958,
0.0069074854254722595,
-0.02298414334654808,
0.02651640959084034,
-0.06495334953069687,
0.03026605024933815,
0.008558413945138454,
0.0083034448325634,
0.002138772513717413,
-0.02784058079123497,
0.003779178485274315,
0.04592222720384598,
0.048697542399168015,
-0.008836177177727222,
-0.009405786171555519,
-0.034152060747146606,
-0.00433617178350687,
-0.10187198966741562,
0.009619292803108692,
0.012831263244152069,
-0.015483800321817398,
-0.0416797436773777,
-0.023550955578684807,
0.012506218627095222,
-0.034495312720537186,
0.035417791455984116,
-0.013369730673730373,
-0.036537837237119675,
0.046180278062820435,
0.030023928731679916,
-0.029474887996912003,
-0.031390417367219925,
0.005776587408035994,
-0.01195988617837429,
-0.03744443506002426,
0.00678299181163311,
0.035435810685157776,
-0.009627320803701878,
0.01126196701079607,
-0.008748422376811504,
-0.01717081107199192,
0.04961801692843437,
0.009571250528097153,
-0.031355418264865875,
0.05245276167988777,
0.032532934099435806,
-0.009074273519217968,
0.06701157242059708,
0.019245320931077003,
0.007059334311634302,
0.031963471323251724,
-0.007215812802314758,
-0.01642713136970997,
0.01216838788241148,
-0.011021284386515617,
-0.02783294953405857,
-0.009956168942153454,
-0.006086493376642466,
0.014710747636854649,
-0.009731779806315899,
-0.015114092268049717,
0.08145634829998016,
-0.03974401205778122,
-0.03329364210367203,
0.0486845038831234,
0.001004687394015491,
0.051892928779125214,
-0.012063076719641685,
0.0166559349745512,
0.023852264508605003,
-0.010145059786736965,
0.026622828096151352,
0.022894904017448425,
0.021514473482966423,
-0.0009185161907225847,
-0.015190573409199715,
0.03444022685289383,
-0.028747841715812683,
0.014089548960328102,
0.0005284722428768873,
0.05847350135445595,
-0.04253700003027916,
-0.02538498491048813,
0.013626882806420326,
0.006817362736910582,
0.021869659423828125,
0.01978614181280136,
-0.017759282141923904,
0.0791132003068924,
0.004445970989763737,
0.02505573071539402,
-0.01576966606080532,
-0.028923451900482178,
-0.008660940453410149,
0.03272945061326027,
0.003821706399321556,
0.040646571666002274,
0.018037674948573112,
0.012301987037062645,
0.02531120367348194,
-0.02521488256752491,
0.0005793177988380194,
-0.013013886287808418,
0.03705029934644699,
0.024279823526740074,
0.03202984854578972,
-0.027116959914565086,
-0.015091676265001297,
-0.004166459199041128,
-0.013526092283427715,
0.04504961147904396,
0.03682682290673256,
0.052243564277887344,
-0.0007163870614022017,
0.009350636973977089,
-0.009140443988144398,
0.04564609006047249,
-0.0783161148428917,
-0.01694580167531967,
-0.028099581599235535,
0.01313572097569704,
-0.028437819331884384,
-0.03387650102376938
] |
<p>How can we get the mass of an uncharged proton, i.e. how varies the mass of the charged proton if i remove the electric charge?</p>
<p>For the isotopic spin theory neutron and proton have the same mass and it is possible to distinguish that particles only for the different values of the third component of the isotopic spin.</p>
<p>This is an approximated symmetry because the masses are different and the charges too. In a ideal world we can remove the electric charge from the proton and we get a "uncharged" proton. The question is how the mass changes.</p>
<p>You can interpret that question as what it is the contribution to the mass due the charge, not only for proton but for all particles.</p>
| 10,739 |
[
0.0060441261157393456,
0.006166299805045128,
-0.01823161542415619,
-0.04026234894990921,
0.010933589190244675,
0.03239816799759865,
-0.061527401208877563,
-0.006227108184248209,
0.009475001133978367,
-0.044815532863140106,
0.03650670126080513,
-0.007171171251684427,
0.04534820467233658,
-0.005822297185659409,
0.03371525555849075,
0.020263945683836937,
0.01857619732618332,
-0.024011731147766113,
-0.0027543138712644577,
-0.029213057830929756,
0.0018471814692020416,
0.022840499877929688,
0.008505476638674736,
0.02224409021437168,
-0.03933457285165787,
0.04253268241882324,
0.04084876924753189,
0.0055566877126693726,
0.035084255039691925,
0.04190102964639664,
-0.013070560060441494,
-0.024456210434436798,
0.01672264002263546,
-0.0014780707424506545,
0.03751729428768158,
0.0038183024153113365,
0.007706922944635153,
-0.008661217987537384,
0.022396059706807137,
0.019200198352336884,
-0.035441454499959946,
-0.007659100461751223,
-0.02384844608604908,
0.00543632498010993,
-0.0189353059977293,
0.023983096703886986,
-0.007481969427317381,
0.018220139667391777,
0.05040932446718216,
-0.055181607604026794,
0.08440589904785156,
0.022637521848082542,
0.014832367189228535,
0.007183849811553955,
-0.026357272639870644,
-0.0021812475752085447,
0.07165930420160294,
0.023610901087522507,
0.00592935923486948,
-0.039151083678007126,
-0.02682631090283394,
0.00012318357767071575,
0.008577321656048298,
-0.001017714268527925,
0.005388128105551004,
0.04675690829753876,
0.00008682916813995689,
0.024306202307343483,
0.03772140294313431,
0.01583433523774147,
0.017235899344086647,
-0.005015267059206963,
0.019689302891492844,
0.01720237359404564,
0.02621380425989628,
-0.045145630836486816,
0.03957607224583626,
0.018131516873836517,
0.04239846393465996,
-0.0002950412454083562,
-0.01605081558227539,
0.021957959979772568,
0.007145533338189125,
0.036734189838171005,
0.02343926951289177,
-0.010450330562889576,
0.04438217729330063,
-0.010542082600295544,
0.007946065627038479,
0.08161318302154541,
0.003677322529256344,
-0.014852011576294899,
0.02509823627769947,
-0.015652894973754883,
0.007776404730975628,
0.04677031561732292,
0.018672121688723564,
0.03453142195940018,
-0.012537849135696888,
0.011062306351959705,
0.02217963896691799,
-0.005160455126315355,
0.023385129868984222,
0.05994672328233719,
0.0014433354372158647,
-0.007106794975697994,
-0.012097535654902458,
-0.00012589601101353765,
0.007391997613012791,
-0.016375986859202385,
-0.032881781458854675,
-0.002395645948126912,
-0.00023061170941218734,
-0.04659755900502205,
0.04514745995402336,
-0.006516491994261742,
0.027137136086821556,
-0.0542292520403862,
0.038368020206689835,
0.04209429770708084,
0.026621928438544273,
-0.013852126896381378,
0.020159026607871056,
-0.05551569163799286,
-0.09436791390180588,
-0.0213019922375679,
0.03591467812657356,
0.0156304482370615,
-0.019405897706747055,
0.02779504843056202,
-0.0034600659273564816,
-0.023992421105504036,
-0.013479731976985931,
-0.02055000327527523,
0.021605150774121284,
-0.02958720363676548,
-0.09667698293924332,
-0.044224683195352554,
0.005312362220138311,
-0.005054867826402187,
-0.021580684930086136,
-0.07312152534723282,
-0.025928501039743423,
0.026014138013124466,
0.0359150767326355,
-0.0010346445487812161,
0.0009906505001708865,
0.014046169817447662,
0.04704301059246063,
0.034244731068611145,
0.03292283043265343,
-0.01012130081653595,
-0.004391460679471493,
-0.01661039888858795,
0.001860345248132944,
-0.07071231305599213,
0.03674984350800514,
0.003297513583675027,
-0.042617496103048325,
0.007821436040103436,
0.06094104424118996,
-0.021274469792842865,
0.003567629726603627,
0.005065751262009144,
0.02157021127641201,
-0.0015083360485732555,
0.05339822545647621,
0.01135473046451807,
-0.017176654189825058,
0.02117687463760376,
-0.02042190171778202,
0.036904141306877136,
0.0028333787340670824,
0.0360429622232914,
0.06551900506019592,
-0.033580999821424484,
-0.04526267945766449,
-0.03850449249148369,
0.004175130743533373,
0.009661094285547733,
-0.0503963977098465,
-0.03360889479517937,
0.01087113469839096,
0.026771534234285355,
0.0036837293300777674,
0.013118850998580456,
-0.013588151894509792,
-0.00025922220083884895,
0.018753739073872566,
-0.03491174057126045,
-0.04794353246688843,
-0.07019262760877609,
0.0059159304946660995,
-0.01109229028224945,
-0.026353156194090843,
0.02272794209420681,
0.01684369519352913,
0.006442589219659567,
-0.05356498435139656,
-0.04354148730635643,
0.02209414727985859,
0.06592991948127747,
0.02426719479262829,
-0.004819588270038366,
0.013372780755162239,
0.004567986354231834,
0.005523372907191515,
-0.014276929199695587,
0.028418350964784622,
0.017009545117616653,
-0.030486248433589935,
0.01775216870009899,
-0.02243240736424923,
-0.015237618237733841,
0.021161839365959167,
0.017686545848846436,
0.001623249612748623,
-0.0029876225162297487,
0.00041974210762418807,
0.06381174176931381,
-0.004944173153489828,
0.08584915101528168,
0.042185068130493164,
-0.035691939294338226,
-0.0003868389467243105,
0.05429297685623169,
0.019556546583771706,
0.043037187308073044,
-0.01711270399391651,
-0.06221179664134979,
-0.038898810744285583,
-0.04591420665383339,
0.019505828619003296,
0.014681987464427948,
-0.0347016267478466,
0.03580855950713158,
0.02878875471651554,
0.022647030651569366,
0.01153284776955843,
0.00025777731207199395,
-0.020681079477071762,
-0.020831013098359108,
0.028178464621305466,
-0.006458626594394445,
-0.016968514770269394,
0.007494672667235136,
0.041772037744522095,
-0.02174355834722519,
0.0192934088408947,
-0.010858614929020405,
0.002846495248377323,
0.028082331642508507,
-0.011528502218425274,
0.00927440170198679,
0.006435816641896963,
-0.06549950689077377,
0.013991715386509895,
0.024186547845602036,
0.06300177425146103,
-0.0033212958369404078,
-0.030467664822936058,
-0.00862561073154211,
-0.005486139561980963,
0.009359545074403286,
-0.002617924241349101,
-0.0136917345225811,
0.012478121556341648,
-0.005678780842572451,
0.014377794228494167,
-0.01908583752810955,
0.029172806069254875,
-0.026859698817133904,
-0.03344469889998436,
-0.012895211577415466,
-0.011466610245406628,
0.04734392091631889,
-0.003218702971935272,
0.007211448159068823,
-0.044069934636354446,
-0.020436834543943405,
0.014255492947995663,
-0.020306775346398354,
-0.013171869330108166,
0.028503136709332466,
-0.04905962944030762,
0.02405543439090252,
-0.060977257788181305,
-0.01004843506962061,
-0.01132502406835556,
0.00320578389801085,
0.020413238555192947,
0.0009968907106667757,
-0.006887488998472691,
-0.03194092586636543,
0.009439497254788876,
-0.03829726576805115,
0.002394462935626507,
-0.019705072045326233,
0.024458641186356544,
0.03616102412343025,
0.03262029588222504,
-0.013687161728739738,
0.031089842319488525,
-0.059832923114299774,
-0.01950979232788086,
-0.020583132281899452,
-0.006988458801060915,
0.007891587913036346,
-0.034441810101270676,
0.02938549593091011,
0.0589638352394104,
-0.025633269920945168,
0.003179333172738552,
-0.05667925998568535,
-0.036298967897892,
0.034196436405181885,
0.015941748395562172,
0.05449838936328888,
0.035760559141635895,
-0.07314641773700714,
0.10011044889688492,
0.04007190093398094,
-0.06192183122038841,
0.018398504704236984,
0.011240935884416103,
-0.003854772774502635,
-0.02120763435959816,
-0.008880756795406342,
0.04211055114865303,
0.009391171857714653,
-0.025463489815592766,
0.059322092682123184,
0.045803140848875046,
-0.034329432994127274,
0.038860123604536057,
-0.017238928005099297,
-0.001495443400926888,
0.023521503433585167,
0.03063151426613331,
0.03910497948527336,
0.00495411129668355,
-0.022589758038520813,
0.00032755295978859067,
0.04681561142206192,
0.03962444141507149,
-0.009652207605540752,
-0.040204863995313644,
0.08256473392248154,
0.042627424001693726,
0.030532659962773323,
-0.014362186193466187,
0.0502651110291481,
0.0005360557697713375,
-0.037020616233348846,
0.03223090246319771,
-0.01178847998380661,
0.02358524315059185,
0.00018471607472747564,
-0.028513425961136818,
0.031384944915771484,
0.06709972769021988,
-0.04301976412534714,
-0.040733661502599716,
-0.006575542036443949,
-0.006525230593979359,
0.008902895264327526,
-0.01303688995540142,
-0.03207457438111305,
0.03900629281997681,
0.05199044942855835,
0.021820737048983574,
0.006481097545474768,
-0.04630235210061073,
-0.000928033608943224,
-0.06342405825853348,
0.015998773276805878,
0.009786556474864483,
0.0386928990483284,
0.004220111761242151,
0.07135795801877975,
0.016854794695973396,
-0.014080658555030823,
-0.013003508560359478,
0.0034395474940538406,
-0.08525887131690979,
0.030096227303147316,
-0.03536727651953697,
0.0021234643645584583,
-0.026938872411847115,
-0.021272040903568268,
-0.02343866415321827,
-0.016539210453629494,
-0.006225140765309334,
-0.02749216929078102,
-0.0178544782102108,
-0.039681728929281235,
0.008703065104782581,
-0.03733730688691139,
-0.029809296131134033,
-0.027619916945695877,
0.03965060040354729,
0.08781448751688004,
-0.030252719298005104,
-0.040200766175985336,
-0.0026088147424161434,
-0.03293280676007271,
-0.016874782741069794,
-0.03785228729248047,
0.028498709201812744,
0.0027227529790252447,
0.035548239946365356,
0.03576605021953583,
0.00935380719602108,
-0.00950836855918169,
-0.00008837510540615767,
0.02348492480814457,
0.07405467331409454,
-0.00914205051958561,
-0.02910849265754223,
-0.005816696211695671,
-0.05467456951737404,
-0.020621733739972115,
0.010235140100121498,
0.045154817402362823,
-0.028502995148301125,
0.03508012741804123,
0.02234724350273609,
0.002194686559960246,
-0.030678987503051758,
0.04857773333787918,
0.06732168048620224,
0.03474815934896469,
-0.03309487923979759,
-0.0625065267086029,
0.013181437738239765,
-0.00804994162172079,
-0.020490219816565514,
0.02930557355284691,
-0.003000607481226325,
-0.014375380240380764,
-0.0062281787395477295,
-0.021505894139409065,
-0.0038848191034048796,
-0.020093226805329323,
-0.009535269811749458,
0.0008401882951147854,
0.04116956517100334,
-0.008921921253204346,
-0.00915980339050293,
0.04203459620475769,
0.015193810686469078,
0.057143181562423706,
0.006201154552400112,
-0.024119963869452477,
-0.040883805602788925,
0.016738727688789368,
0.03982089087367058,
0.041169699281454086,
-0.026995962485671043,
-0.03449269384145737,
-0.04081327095627785,
0.03264078497886658,
0.05628887936472893,
-0.02781490981578827,
-0.0055562281049788,
-0.007180513348430395,
0.0026205615140497684,
0.014280961826443672,
-0.016272222623229027,
-0.00021282090165186673,
0.014611620455980301,
-0.026293989270925522,
-0.00512296287342906,
-0.037797052413225174,
-0.040652740746736526,
-0.0007182834669947624,
0.014824540354311466,
0.029697854071855545,
0.026328282430768013,
-0.01909196563065052,
0.033511072397232056,
0.009382462128996849,
0.03201105073094368,
-0.00828547589480877,
-0.10398497432470322,
0.0011502893175929785,
0.006369605660438538,
-0.03125029429793358,
-0.006344630382955074,
-0.02201087959110737,
-0.07354366779327393,
0.005955318920314312,
-0.005457038059830666,
-0.006939991377294064,
-0.03523789346218109,
-0.07662138342857361,
0.013683801516890526,
0.04082321375608444,
-0.011582582257688046,
0.027754774317145348,
0.024606825783848763,
-0.021821772679686546,
-0.040707286447286606,
-0.044116802513599396,
0.02624165266752243,
-0.013686338439583778,
0.002979993587359786,
-0.0408734492957592,
0.02491382509469986,
-0.00953648891299963,
0.03495633974671364,
0.008511518128216267,
0.019773056730628014,
-0.0052808308973908424,
-0.017810033634305,
-0.03644004836678505,
-0.001647390890866518,
-0.011241237632930279,
0.003042332362383604,
-0.012615603394806385,
0.010851415805518627,
0.03506974130868912,
-0.015572179108858109,
0.007941090501844883,
0.018753204494714737,
-0.0013539207866415381,
-0.011333147995173931,
-0.01388130895793438,
0.03317435085773468,
-0.025884797796607018,
-0.036462944000959396,
0.022158902138471603,
-0.03892117366194725,
0.017191700637340546,
-0.0464012436568737,
-0.011990627273917198,
-0.013948679901659489,
-0.05206260085105896,
-0.03340359404683113,
0.033549077808856964,
-0.03382262587547302,
-0.000080851350503508,
-0.04296726733446121,
0.022536417469382286,
0.02528085745871067,
0.007412421051412821,
-0.05523238703608513,
-0.044424500316381454,
0.0480097196996212,
0.0038902100641280413,
-0.01973670907318592,
-0.0051176645793020725,
-0.013616736978292465,
-0.00255455425940454,
-0.04370903596282005,
0.010240289382636547,
0.04561873897910118,
-0.02896365337073803,
-0.020142629742622375,
0.012545582838356495,
0.031256139278411865,
0.05395796149969101,
-0.03750142827630043,
-0.033168256282806396,
0.030949927866458893,
-0.013572189025580883,
0.005237755365669727,
0.010741730220615864,
0.053528204560279846,
0.0021295459009706974,
-0.0498056560754776,
-0.006225831340998411,
0.009913438931107521,
0.016230110079050064,
-0.051927242428064346,
-0.009289311245083809,
0.041135918349027634,
0.01694023236632347,
-0.009464757516980171,
-0.03960198536515236,
-0.003821553662419319,
0.015034935437142849,
0.06905242055654526,
-0.015047035180032253,
0.012831666506826878,
-0.022151069715619087,
-0.04369543120265007,
0.024893302470445633,
-0.0016618219669908285,
-0.005437192041426897,
0.008639209903776646,
0.012260916642844677,
0.009363104589283466,
-0.017036164179444313,
0.026335762813687325,
-0.04056112468242645,
0.01878037117421627,
0.005832640454173088,
0.012010968290269375,
0.0069798133336007595,
-0.0013525274116545916,
-0.018227696418762207,
0.007700406480580568,
-0.04427037760615349,
0.02524537406861782,
0.06471522152423859,
0.021986713632941246,
0.05488225072622299,
0.045154549181461334,
-0.0003198638733010739,
0.011239618062973022,
-0.009327005594968796,
-0.03550964593887329,
-0.017134882509708405,
0.011136146262288094,
0.04297482967376709,
-0.020990127697587013,
-0.02790461853146553,
0.05417671054601669,
0.05328039824962616,
-0.021779652684926987,
0.040559783577919006,
0.0714879110455513,
0.009785165078938007,
0.008805686607956886,
-0.032063744962215424,
-0.03116527386009693,
0.013188434764742851,
-0.01403554156422615,
0.024188896641135216,
0.0009958583395928144,
-0.004178067669272423,
0.030293090268969536,
-0.0014816154725849628,
0.05858223885297775,
0.0006059671868570149,
-0.02343730628490448,
-0.05419917032122612,
0.035398587584495544,
0.006179281044751406,
0.02216149866580963,
-0.012547568418085575,
0.03581037372350693,
0.026285385712981224,
-0.01988254114985466,
0.04197845235466957,
0.029659762978553772,
-0.05901405215263367,
-0.0413493774831295,
-0.026802245527505875,
-0.03306357190012932,
0.05574268475174904,
-0.0262527447193861,
-0.029441043734550476,
0.03900641202926636,
-0.0005932794883847237,
0.02914576418697834,
0.008953438140451908,
0.030404169112443924,
-0.05303173139691353,
0.04512981325387955,
0.002374363597482443,
0.03391742333769798,
-0.010636186227202415,
0.005127526819705963,
0.12543199956417084,
0.03880093991756439,
0.02356710657477379,
-0.07950735092163086,
0.01484728790819645,
-0.03309377655386925,
0.020349234342575073,
0.018039533868432045,
0.030439266934990883,
-0.025091135874390602,
0.053344838321208954,
-0.023326579481363297,
0.02644519694149494,
-0.030079171061515808,
-0.01459561288356781,
0.03951943665742874,
-0.035197388380765915,
-0.048274509608745575,
-0.0011170104844495654,
0.038185711950063705,
0.023792460560798645,
0.00424222694709897,
-0.06430678069591522,
0.07404164969921112,
-0.014570617116987705,
0.015334872528910637,
-0.05072171241044998,
-0.05902966484427452,
-0.027593426406383514,
0.017172986641526222,
-0.029986226931214333,
0.017759840935468674,
-0.003061742288991809,
-0.04530242457985878,
-0.05483260005712509,
0.02715730108320713,
0.007706199772655964,
-0.017224255949258804,
0.0006541438633576035,
0.018377557396888733,
0.009167189709842205,
-0.021371355280280113,
-0.006003826390951872,
0.02567369118332863,
-0.04125716909766197,
0.0074899327009916306,
-0.010842685587704182,
0.04736776649951935,
-0.009442934766411781,
-0.0135943703353405,
-0.0067102303728461266,
0.0328107625246048,
-0.0036970514338463545,
-0.05711936950683594,
-0.031048204749822617,
-0.0015221915673464537,
0.0016692571807652712,
-0.01929381676018238,
0.01013883575797081,
0.009480347856879234,
0.0056809596717357635,
-0.0028378935530781746,
0.01823643408715725,
-0.0036620330065488815,
0.004858228377997875,
0.007964299991726875,
0.007500785402953625,
0.01757756620645523,
-0.012146297842264175,
-0.028490521013736725,
0.003895325819030404,
-0.021742619574069977,
-0.03173481673002243,
-0.03544962406158447,
0.0025520457420498133,
0.04209192469716072,
0.06321007758378983,
0.0003345505683682859,
0.010355434380471706,
0.004648960195481777,
-0.052809301763772964,
0.034722700715065,
0.025025751441717148,
0.006521234288811684,
-0.03401494771242142,
-0.0034477796871215105,
0.0038900042418390512,
0.04998569190502167,
-0.042395081371068954,
-0.00992831215262413,
0.02747679129242897,
0.01668219082057476,
-0.011389082297682762,
-0.040269773453474045,
-0.0010045993840321898,
0.04007380083203316,
-0.01392339263111353,
0.017185615375638008,
0.004041314125061035,
-0.009136639535427094,
0.034081991761922836,
-0.009188850410282612,
-0.015787076205015182,
0.04767284542322159,
-0.004465077072381973,
0.012090650387108326,
-0.0023601921275258064,
-0.02846226841211319,
0.02375878021121025,
0.02730800397694111,
-0.02359527163207531,
-0.061108432710170746,
-0.011730730533599854,
0.0022112359292805195,
-0.004468522500246763,
-0.0027259052731096745,
0.008357514627277851,
-0.017364703118801117,
-0.0010806446662172675,
-0.04546434432268143,
0.048562150448560715,
-0.0003854609385598451,
-0.022551728412508965,
-0.026722390204668045,
-0.007081127725541592,
-0.023692462593317032,
0.008389398455619812,
-0.005111947190016508,
0.02291426993906498,
-0.013352182693779469,
-0.039234768599271774,
0.03543519973754883,
0.019147338345646858,
-0.03842004016041756,
-0.014894219115376472,
0.043039336800575256,
-0.0030957735143601894,
0.03757015988230705,
-0.007745811715722084,
-0.022039150819182396,
0.01994238793849945,
-0.05405420437455177,
-0.0387992262840271,
0.005473006516695023,
-0.03498200699687004,
-0.0007082014344632626,
0.028325241059064865,
-0.024613598361611366,
-0.008131983689963818,
0.01899881102144718,
-0.05403175950050354,
-0.0032791076228022575,
-0.009167945943772793,
-0.020397141575813293,
-0.0018579353345558047,
-0.023867381736636162,
-0.0050431061536073685,
0.0014453161275014281,
-0.035782404243946075,
0.06639324128627777,
0.010896839201450348,
-0.03658698871731758,
0.009066754020750523,
0.0020073538180440664,
0.022613437846302986,
0.0000937902950681746,
0.019517261534929276,
0.03940257802605629,
-0.02284056320786476,
0.058664511889219284,
-0.009054947644472122,
0.02750719152390957,
-0.000246789597440511,
-0.03162860497832298,
-0.08812306821346283,
-0.04053308069705963,
-0.008099891245365143,
-0.052637793123722076,
0.04808861017227173,
-0.023356297984719276,
0.016836773604154587,
-0.016415758058428764,
-0.08402819186449051,
0.02031685970723629,
-0.04163951054215431,
-0.020462840795516968,
0.008785978890955448,
-0.04791320115327835,
-0.03292934224009514,
0.048096898943185806,
0.024129018187522888,
0.0519576258957386,
-0.0015157620655372739,
0.02038758620619774,
-0.003702405607327819,
-0.030339248478412628,
-0.028527427464723587,
0.009087305516004562,
0.0304659865796566,
-0.024912258610129356,
0.04863720014691353,
-0.014383040368556976,
-0.007411457598209381,
0.05703507736325264,
-0.024807902052998543,
0.009805776178836823,
-0.03030567616224289,
0.009820790961384773,
0.003038999391719699,
0.03682481124997139,
-0.0072145308367908,
0.006337855476886034,
-0.0407429113984108,
0.01596006006002426,
0.017378097400069237,
0.04320328310132027,
0.012269365601241589,
0.012369045056402683,
-0.01591595821082592,
-0.008792215026915073,
-0.0013405715581029654,
0.0173261109739542,
-0.026882732287049294,
-0.004571513272821903,
-0.006401082966476679,
0.003455167170614004,
-0.014794519171118736,
-0.02702292799949646,
0.012296324595808983,
-0.03673547878861427,
0.043927907943725586,
0.046211887151002884,
0.02236211486160755,
0.030320992693305016,
0.034451600164175034,
-0.01751771755516529,
-0.007975997403264046,
0.015677936375141144,
0.012629603035748005,
-0.03880295902490616,
-0.05127602070569992,
0.025164930149912834,
0.055766016244888306,
0.06703684478998184,
0.010481332428753376,
-0.057673219591379166,
-0.06926292926073074,
0.024157732725143433,
0.015028725378215313,
0.001914575113914907,
-0.010954716242849827,
-0.06545057892799377,
-0.005933837033808231,
-0.06629759073257446,
0.03895735740661621,
0.011265198700129986,
0.0011573381489142776,
-0.05496226251125336,
-0.022165602073073387,
-0.02235099859535694,
0.026543328538537025,
0.07221329212188721,
0.034061454236507416,
-0.034012533724308014,
0.04229717701673508,
0.008854446932673454,
-0.003894325578585267,
-0.030911950394511223,
-0.005361820105463266,
-0.0072186049073934555,
-0.001839668257161975,
0.01045445166528225,
-0.022945046424865723,
-0.04797232523560524,
0.03608552739024162,
-0.0018901561852544546,
-0.024587294086813927,
0.004977185279130936,
0.03096013143658638,
-0.040383826941251755,
0.055798355489969254,
-0.02667625993490219,
0.004295127931982279,
0.04645001143217087,
0.014898572117090225,
0.018558040261268616,
0.020848501473665237,
-0.019740236923098564,
-0.022015366703271866,
0.012311503291130066,
-0.03386050462722778,
-0.01857891120016575,
-0.020580509677529335,
-0.023662369698286057,
0.04273310676217079,
-0.011508768424391747,
0.016386456787586212,
0.01904643513262272,
-0.032711539417505264,
-0.023905977606773376,
0.02387833036482334,
0.027248036116361618,
0.054732803255319595,
0.018224291503429413,
-0.004661488812416792,
0.012810726650059223,
-0.012834738940000534,
0.058442436158657074,
0.04132337123155594,
0.029899878427386284,
0.023743784055113792,
-0.022287825122475624,
0.007331621367484331,
-0.005697009619325399,
0.029261240735650063,
0.025972338393330574,
0.021923823282122612,
-0.025784220546483994,
-0.05894593894481659,
0.03789546713232994,
-0.011050126515328884,
0.04689515754580498,
0.008194176480174065,
-0.03369971737265587,
0.07450254261493683,
0.012225045822560787,
0.014713028445839882,
-0.01750960946083069,
0.02210661955177784,
-0.012997533194720745,
0.0065510994754731655,
-0.0030307562556117773,
0.029572419822216034,
-0.00595823535695672,
-0.01411523763090372,
-0.03150505572557449,
0.024492649361491203,
0.0010113846510648727,
-0.031779613345861435,
0.003212294541299343,
0.007268248125910759,
-0.009303993545472622,
-0.03268707916140556,
-0.023075345903635025,
-0.03330955281853676,
-0.011659927666187286,
0.03800228610634804,
0.03407909721136093,
0.05394085496664047,
0.022590268403291702,
-0.052525490522384644,
-0.058673981577157974,
0.03693991154432297,
-0.053778816014528275,
-0.03559575602412224,
-0.01837749034166336,
-0.013549783267080784,
-0.026080800220370293,
-0.02548416517674923
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.