question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>It's always nice to point out the structural similarieties between (semi-)Riemannian geometry and gauge field theories alla Classical yang Mills theories. Nevertheless, I feel the relation between the gauge group and the gauge bosons "$A_{\mu}\times T^i_{\ j}$" are much simpler than the relation betreen the diffeomorphisms/isometries and the Christoffel symbols $\Gamma_{\mu\nu}^\rho$. At the very least, at first glance, I don't see the $SO(3)$ matrix lingering in $\Gamma$. I don't really know the technicalities of the Erlangen program and I specifically don't know how that "generating a manifold from a single point using the isometry group" (as I understand it) really works. </p>
<p>I'd like to know if it is really directly possible to view both, that is general relativity and the classical gauge theories, just as special cases of the general Cartan connection framework, or if there is a fundamental difficulty to (I guess) general relativty which makes this not work. Especially if the answer is no, then what is it that makes the metric theory so different? (At first I'd guess it's the fact that the GR manifold looks different in each patch due to $g$, but $A$ can also be difficult and both are related to what else is <em>in</em> space. So I suppose it's the interplay between the isometry group and the bigger diffeomorphism group.)</p>
| 9,353 |
[
0.00642921170219779,
0.012820636853575706,
0.01383804902434349,
-0.03448796272277832,
0.038554731756448746,
0.04437915235757828,
-0.03389144688844681,
-0.03506849333643913,
0.004871714860200882,
-0.022936519235372543,
0.012486908584833145,
-0.009150279685854912,
0.05557100847363472,
0.02399507351219654,
0.04321993887424469,
-0.02100074477493763,
-0.02470030076801777,
-0.00995118822902441,
-0.00845856498926878,
-0.03937211260199547,
0.021748283877968788,
0.04459454119205475,
-0.012553281150758266,
-0.016159137710928917,
0.00348728708922863,
0.010846922174096107,
-0.006100750062614679,
0.011595578864216805,
-0.012891095131635666,
0.03842358663678169,
-0.014588271267712116,
-0.013982892967760563,
-0.01165401004254818,
-0.0060358536429703236,
-0.014809657819569111,
0.00570137333124876,
-0.05449077486991882,
0.006991841830313206,
0.01396213285624981,
-0.029698386788368225,
-0.08357500284910202,
-0.032161373645067215,
-0.043652504682540894,
0.04242469742894173,
-0.019415227696299553,
0.006129986606538296,
-0.023202212527394295,
-0.004101044964045286,
0.06599752604961395,
-0.025555960834026337,
0.05905565246939659,
0.026585843414068222,
-0.01865256205201149,
0.034494590014219284,
-0.021966682747006416,
0.011310875415802002,
0.06496076285839081,
0.046277258545160294,
-0.007312805391848087,
-0.061595018953084946,
0.00009686270641395822,
-0.0192597433924675,
0.02337428368628025,
-0.019527141004800797,
-0.0401134192943573,
0.021154653280973434,
-0.007027772255241871,
-0.0072136856615543365,
0.027917666360735893,
-0.03084024228155613,
-0.026160920038819313,
-0.0011267357040196657,
0.03396982699632645,
0.004976491443812847,
0.010840627364814281,
0.005430545192211866,
-0.010277021676301956,
-0.015529215335845947,
0.05115661770105362,
0.006196334958076477,
-0.03628659248352051,
0.04463964328169823,
0.03066621720790863,
0.03374982625246048,
-0.009081628173589706,
-0.00724372174590826,
0.06819470971822739,
-0.04171676188707352,
-0.027789337560534477,
0.04941929131746292,
-0.012602819129824638,
-0.018389040604233742,
0.04331593215465546,
0.005934189073741436,
-0.018764978274703026,
0.031232086941599846,
-0.0006421174039132893,
0.034458599984645844,
0.009783166460692883,
0.019095469266176224,
-0.014776280149817467,
-0.008545413613319397,
-0.002572782803326845,
0.06518064439296722,
0.011410764418542385,
0.02097371034324169,
-0.03154952451586723,
-0.006480530370026827,
-0.040509119629859924,
-0.0120127247646451,
-0.02454909309744835,
-0.01490273792296648,
-0.049110084772109985,
-0.016984710469841957,
-0.0022536602336913347,
-0.007833643816411495,
0.003449884010478854,
-0.03634689003229141,
0.06348523497581482,
0.07889615744352341,
0.05486884340643883,
-0.02578113041818142,
0.016328895464539528,
-0.04094729200005531,
-0.060026511549949646,
-0.0065964339300990105,
0.041212353855371475,
-0.011608240194618702,
-0.041391581296920776,
-0.03485754504799843,
-0.002368094865232706,
-0.007692168932408094,
0.012948693707585335,
0.03138761222362518,
0.02749025449156761,
-0.045442190021276474,
-0.1125158816576004,
-0.049971017986536026,
0.06571458280086517,
0.024961737915873528,
0.006477219983935356,
-0.05450676754117012,
0.014760354533791542,
0.0056703705340623856,
0.06570915877819061,
-0.010416523553431034,
0.02785418927669525,
0.02833648771047592,
0.04627251252532005,
0.016493044793605804,
-0.012906101532280445,
-0.004611351992934942,
-0.039431340992450714,
-0.056111350655555725,
-0.01245678961277008,
-0.0460100956261158,
0.020916176959872246,
0.01488589122891426,
0.023172613233327866,
-0.023239508271217346,
0.07238612323999405,
0.008886817842721939,
0.0317394994199276,
0.033387795090675354,
0.0006397474207915366,
-0.00033443866414017975,
0.022259261459112167,
-0.015179635025560856,
-0.013328192755579948,
0.022747498005628586,
-0.007310826797038317,
0.030948277562856674,
0.01702580600976944,
0.041953131556510925,
0.04380563646554947,
-0.05055447667837143,
-0.04554325342178345,
0.020654141902923584,
-0.017295029014348984,
0.00888154935091734,
-0.013918319717049599,
-0.03440514951944351,
-0.017292046919465065,
-0.028993122279644012,
0.011461966671049595,
0.03136492520570755,
0.00006709832814522088,
-0.003160113701596856,
0.024972066283226013,
-0.0537390261888504,
-0.01272527128458023,
-0.06839807331562042,
-0.0029155458323657513,
0.009044517762959003,
-0.014751063659787178,
0.042573608458042145,
0.012202795594930649,
-0.00033351645106449723,
-0.02216934971511364,
-0.05377200245857239,
0.007692717481404543,
0.050565339624881744,
-0.0013476033927872777,
0.012559928931295872,
0.03911014273762703,
0.021716728806495667,
0.02489793673157692,
-0.028707290068268776,
0.01732301153242588,
0.005971708334982395,
-0.03761396184563637,
0.008750729262828827,
-0.0009066825732588768,
0.01778845116496086,
-0.0034938196185976267,
0.01789407804608345,
-0.0006013113306835294,
0.016774019226431847,
-0.035787634551525116,
0.05415600538253784,
-0.06797483563423157,
0.06958816945552826,
0.01177321095019579,
-0.014897183515131474,
0.0003696215571835637,
0.0502079539000988,
0.009916968643665314,
0.02386896125972271,
0.0015863556182011962,
-0.005451651755720377,
0.0014237321447581053,
-0.019214320927858353,
0.041972171515226364,
0.05713416635990143,
-0.01647946611046791,
0.032059188932180405,
0.006879772990942001,
0.03779280558228493,
-0.04872499033808708,
0.018105225637555122,
-0.003022528951987624,
-0.0349329374730587,
0.012377009727060795,
-0.007113432977348566,
0.010126620531082153,
-0.012340392917394638,
0.008737503550946712,
-0.009288474917411804,
-0.0083652688190341,
-0.03272419795393944,
0.0008166699553839862,
0.02793901599943638,
-0.04058563709259033,
-0.02262590266764164,
0.005514366552233696,
0.016560997813940048,
0.06943627446889877,
-0.018193552270531654,
0.00983213447034359,
0.04128480330109596,
-0.0001587220176588744,
-0.017974620684981346,
-0.010506504215300083,
-0.03576222434639931,
0.01390796434134245,
0.005614524707198143,
-0.0016981892986223102,
-0.009011609479784966,
0.01731124520301819,
-0.054737746715545654,
0.000553897931240499,
-0.03582748770713806,
-0.016727857291698456,
-0.011327646672725677,
0.02538316696882248,
0.0016332847299054265,
-0.006527232006192207,
0.04343976080417633,
-0.04260343313217163,
-0.0393819734454155,
0.06423633545637131,
-0.01649205945432186,
0.02727866917848587,
0.035215746611356735,
-0.02944139763712883,
0.01707780361175537,
-0.05552854761481285,
0.017525266855955124,
-0.023354681208729744,
-0.0002881829859688878,
0.03363224118947983,
-0.02229355275630951,
0.0027135834097862244,
-0.02957025170326233,
-0.014508886262774467,
-0.0012774192728102207,
-0.008090599440038204,
-0.02008252777159214,
0.010087347589433193,
0.05545883625745773,
0.0012374335201457143,
-0.008200658485293388,
-0.04694799333810806,
-0.02583705075085163,
-0.03502452373504639,
-0.008355498313903809,
0.03483818098902702,
0.004136008210480213,
-0.03251812234520912,
0.034245334565639496,
0.03542202338576317,
-0.05339560657739639,
0.0029177844990044832,
-0.06373833864927292,
-0.01870267279446125,
0.013441074639558792,
0.01407298818230629,
0.012514051981270313,
0.01998230814933777,
-0.03614136949181557,
0.07891381531953812,
0.029663417488336563,
-0.0549449697136879,
-0.035979364067316055,
0.02178792655467987,
-0.01676110178232193,
-0.04918518662452698,
0.021585902199149132,
0.035979222506284714,
-0.007942640222609043,
0.029909953474998474,
0.04061145335435867,
0.042061131447553635,
0.008451228961348534,
0.01633034646511078,
-0.0032786002848297358,
0.010561431758105755,
0.035569414496421814,
0.005461652297526598,
0.043324682861566544,
-0.0002526042517274618,
-0.020914526656270027,
0.0021551912650465965,
0.015634233132004738,
0.020833615213632584,
0.00539360661059618,
-0.04811332747340202,
0.061263710260391235,
0.03491421788930893,
0.02869747206568718,
-0.01904214359819889,
0.012391306459903717,
0.014174059964716434,
-0.017353778705000877,
0.02591688372194767,
0.05908980593085289,
0.020116817206144333,
-0.02815871126949787,
-0.027118327096104622,
0.013367244973778725,
0.058395370841026306,
-0.04551217332482338,
-0.014830989763140678,
-0.021357597783207893,
-0.019295817241072655,
0.03600480034947395,
0.003553110873326659,
0.024724677205085754,
0.0543215274810791,
0.045746657997369766,
0.0055420114658772945,
0.0009517823928035796,
-0.04464924335479736,
-0.020986054092645645,
-0.08406074345111847,
-0.0014875559136271477,
-0.000643950595986098,
0.030787425115704536,
0.02267276495695114,
0.02842753753066063,
-0.011657309718430042,
0.019891249015927315,
-0.030215196311473846,
-0.009319760836660862,
-0.09152515977621078,
0.000565330614335835,
-0.04162515699863434,
-0.013294188305735588,
0.010880977846682072,
-0.033202044665813446,
0.024433108046650887,
0.0003051467065233737,
-0.05652979388833046,
-0.015148667618632317,
0.004597626160830259,
-0.07670653611421585,
0.0073448410257697105,
-0.07301299273967743,
-0.03912236914038658,
-0.012782023288309574,
0.043410781770944595,
0.03329741582274437,
-0.010291120037436485,
-0.004045423585921526,
0.0326550267636776,
-0.030304068699479103,
-0.006823054049164057,
0.014196651056408882,
0.05450718477368355,
0.006311014760285616,
0.019294004887342453,
0.04074039310216904,
0.046740345656871796,
0.01617898792028427,
-0.03140141814947128,
0.04240098223090172,
0.026183461770415306,
-0.019730694591999054,
-0.0023647251073271036,
-0.01548320334404707,
-0.046967875212430954,
-0.034350477159023285,
0.014595365151762962,
0.08775392919778824,
0.022230373695492744,
-0.024377910420298576,
0.016931457445025444,
0.040857382118701935,
-0.016155410557985306,
0.033434752374887466,
0.04157070815563202,
-0.025057420134544373,
-0.05948563665151596,
-0.04927358403801918,
-0.04071444645524025,
-0.0038119079545140266,
0.0049317022785544395,
0.012506444938480854,
-0.019714629277586937,
-0.00823222752660513,
0.021289924159646034,
0.013495373539626598,
-0.005451939534395933,
-0.009456227533519268,
-0.04545518010854721,
0.04835096374154091,
-0.002527601784095168,
0.018999982625246048,
0.004953630734235048,
-0.04070109501481056,
0.06641938537359238,
0.06979034841060638,
-0.005698059685528278,
-0.01580505631864071,
-0.09821759909391403,
0.011456727050244808,
0.04386769235134125,
-0.003463469445705414,
0.013743728399276733,
-0.038692545145750046,
-0.04073464870452881,
0.011672512628138065,
0.034737661480903625,
-0.006362596061080694,
0.024920903146266937,
0.014771872200071812,
-0.03993188962340355,
-0.03180386498570442,
-0.011016600765287876,
0.0014717436861246824,
0.039339467883110046,
-0.004087038338184357,
-0.01608734391629696,
-0.009321870282292366,
0.006891620811074972,
-0.019337208941578865,
0.0032687976490706205,
0.013279666192829609,
0.020373988896608353,
0.058990973979234695,
0.02010946162045002,
0.018507234752178192,
0.025088025256991386,
-0.015715230256319046,
-0.09705179184675217,
0.007945840246975422,
0.01325018797069788,
-0.024797214195132256,
0.01170664094388485,
-0.020446907728910446,
-0.039462655782699585,
0.015341619960963726,
0.0072888098657131195,
0.029702262952923775,
0.055416543036699295,
-0.038651928305625916,
0.033961329609155655,
0.022351950407028198,
-0.010713621973991394,
0.012464885599911213,
0.028224211186170578,
-0.011485675349831581,
0.0014837476192042232,
-0.028623482212424278,
0.043406590819358826,
-0.028470830991864204,
0.008798605762422085,
0.004012209363281727,
0.007256490644067526,
-0.03115183860063553,
0.055843647569417953,
0.008301584981381893,
0.009868552908301353,
-0.002491854364052415,
-0.04234099015593529,
-0.011487405747175217,
0.005328492261469364,
-0.013954713940620422,
-0.007945378310978413,
-0.005810463801026344,
0.03629349172115326,
-0.008630387485027313,
-0.01570270210504532,
0.03466596454381943,
0.0014997810358181596,
-0.023362355306744576,
0.016608238220214844,
-0.012658624909818172,
0.025533761829137802,
-0.01691633090376854,
-0.018793366849422455,
0.027162466198205948,
-0.02878819964826107,
0.020154621452093124,
-0.014135852456092834,
-0.018672684207558632,
0.024514732882380486,
-0.02541128173470497,
-0.02631811797618866,
-0.005548230372369289,
-0.008664303459227085,
0.03235773369669914,
-0.0414157509803772,
-0.007584301754832268,
0.03429143875837326,
-0.04752563685178757,
-0.08116291463375092,
-0.03340553492307663,
0.019571226090192795,
-0.00873384065926075,
-0.018056198954582214,
-0.01709151081740856,
0.01058527547866106,
-0.06064445152878761,
-0.011798294261097908,
0.001786246313713491,
0.06170715391635895,
-0.007163869217038155,
0.005581223405897617,
0.0011626295745372772,
0.07620397210121155,
0.048563096672296524,
-0.01988484337925911,
-0.009396449662744999,
0.014965064823627472,
0.006506327539682388,
0.014654670841991901,
0.016911638900637627,
0.05823897570371628,
-0.006988845765590668,
0.012810668908059597,
-0.0016820236342027783,
-0.016801295801997185,
-0.003917274996638298,
-0.01946365274488926,
0.0011459101224318147,
0.06269712001085281,
0.019550492987036705,
0.011901452206075191,
-0.04174774885177612,
-0.015841176733374596,
0.006561462767422199,
0.03896813839673996,
-0.04905617609620094,
-0.005554573610424995,
0.031974490731954575,
-0.03799132630228996,
0.08056123554706573,
-0.013144929893314838,
-0.010163681581616402,
-0.0069878799840807915,
0.0005222189356572926,
0.0023993540089577436,
-0.03303944692015648,
0.03459484875202179,
-0.007557312957942486,
0.023992128670215607,
-0.027846818789839745,
0.034534092992544174,
0.018011143431067467,
-0.013888920657336712,
-0.06486117839813232,
-0.041555970907211304,
-0.028264494612812996,
0.005020951386541128,
0.059789422899484634,
0.005879368167370558,
0.06330259889364243,
-0.0024904380552470684,
-0.03634827956557274,
0.014733268879354,
-0.017164096236228943,
-0.0366046205163002,
0.0035833667498081923,
0.02259744703769684,
0.06002375856041908,
-0.04710264876484871,
-0.03241903334856033,
0.02871127240359783,
0.03618684411048889,
-0.02851298451423645,
0.008515252731740475,
0.006759935058653355,
0.022688185796141624,
-0.006221425253897905,
-0.006786734331399202,
-0.037731658667325974,
0.033010877668857574,
-0.018848104402422905,
0.03371918201446533,
0.00653656292706728,
-0.004551583435386419,
0.024135321378707886,
0.07218001782894135,
0.0368821956217289,
0.014332368038594723,
-0.03069428727030754,
-0.07452543079853058,
0.023577773943543434,
0.024249009788036346,
0.02701476775109768,
0.01978069171309471,
0.018757972866296768,
0.012204342521727085,
-0.022440874949097633,
-0.01786579191684723,
-0.0082804374396801,
-0.06736332178115845,
-0.033172357827425,
-0.03809487819671631,
-0.04271898791193962,
0.06419843435287476,
-0.0015454250387847424,
-0.050978921353816986,
-0.02067815326154232,
-0.01803096942603588,
0.024857256561517715,
-0.004453187342733145,
0.03548804298043251,
-0.0446506030857563,
0.05093562602996826,
-0.015248864889144897,
0.01941664144396782,
-0.009906236082315445,
0.006724102422595024,
0.1111031323671341,
0.04849600791931152,
0.015298204496502876,
-0.066917285323143,
0.039809852838516235,
0.012114955112338066,
-0.002979092998430133,
-0.029385918751358986,
0.04018312320113182,
0.013854515738785267,
-0.014442319050431252,
-0.0015503109898418188,
0.06351268291473389,
0.01603015512228012,
-0.010468147695064545,
0.0703318789601326,
-0.03645637258887291,
-0.03515919670462608,
0.010917434468865395,
0.0042608147487044334,
0.006444838829338551,
-0.02056513912975788,
-0.00959343183785677,
0.012771396897733212,
-0.010722991079092026,
0.06244902312755585,
-0.01258422713726759,
-0.05810371786355972,
-0.0047779930755496025,
0.007909657433629036,
-0.03757064417004585,
0.01748734340071678,
0.008595351129770279,
0.0001582510449225083,
-0.04435492679476738,
0.01363085862249136,
0.006389498710632324,
-0.010681870393455029,
0.0578438863158226,
0.02307278849184513,
0.020021123811602592,
-0.0010047877440229058,
0.006436987780034542,
-0.010616949759423733,
-0.060568246990442276,
-0.024841178208589554,
0.016813665628433228,
0.06271137297153473,
-0.03663494065403938,
-0.00915276538580656,
-0.026654314249753952,
-0.02366000972688198,
0.04068020358681679,
-0.030102089047431946,
0.009070007130503654,
-0.041326478123664856,
0.011907769367098808,
-0.013575203716754913,
-0.03200002387166023,
-0.002613048069179058,
0.04553108662366867,
-0.006775485817342997,
0.035555873066186905,
-0.03258151933550835,
-0.03005196899175644,
0.02154208905994892,
-0.021692905575037003,
0.018392551690340042,
-0.00216250354424119,
-0.03396313637495041,
-0.031513113528490067,
-0.023417966440320015,
-0.02681179717183113,
-0.0561780110001564,
0.009109980426728725,
0.05285738781094551,
0.05870801582932472,
0.01512979343533516,
-0.000004441931196197402,
-0.01881451904773712,
-0.034359756857156754,
0.018906403332948685,
-0.010661585256457329,
-0.019283218309283257,
-0.007914355956017971,
0.005389931611716747,
0.04017748683691025,
0.047472286969423294,
0.012968206778168678,
-0.01734824664890766,
-0.022518280893564224,
0.01813231222331524,
0.0068227858282625675,
-0.0017288512317463756,
0.026526782661676407,
0.0033996556885540485,
-0.027879660949110985,
0.006630426738411188,
-0.02021285519003868,
-0.013015811331570148,
0.011937951669096947,
0.014974460005760193,
-0.009535273537039757,
0.03374088183045387,
0.02310306578874588,
-0.01347306091338396,
0.042408473789691925,
-0.04074500873684883,
0.019429868087172508,
0.03196233510971069,
0.0004389917594380677,
-0.04273097962141037,
-0.03244321793317795,
-0.020633885636925697,
0.00447606248781085,
-0.01750183291733265,
0.010385082103312016,
-0.02707054652273655,
0.005055970512330532,
-0.03624660149216652,
0.00030949042411521077,
-0.037025049328804016,
-0.008713825605809689,
-0.02465931512415409,
0.02269606478512287,
-0.02395501732826233,
-0.01117930468171835,
0.02699153684079647,
0.04581770673394203,
-0.00027106149354949594,
-0.018612202256917953,
0.0150760468095541,
0.03129870444536209,
-0.04423222690820694,
0.025509444996714592,
0.006728662643581629,
0.005708631593734026,
0.036316242069005966,
-0.008491698652505875,
-0.03693757951259613,
0.033297281712293625,
0.000027756748750107363,
-0.040472883731126785,
0.0338679663836956,
-0.040726810693740845,
0.011436684057116508,
0.04200665280222893,
-0.04145275801420212,
-0.00247210799716413,
0.0642644613981247,
-0.009656925685703754,
0.006027245428413153,
0.0005893001216463745,
-0.04693637415766716,
-0.0037709774915128946,
-0.0321480892598629,
0.0495062880218029,
0.0023952722549438477,
-0.009248151443898678,
0.011911961250007153,
0.011304589919745922,
-0.013906095176935196,
0.00413448316976428,
-0.0020198954734951258,
-0.02283775992691517,
-0.018342429772019386,
0.012701418250799179,
0.0014124091248959303,
0.032173994928598404,
0.05514880269765854,
-0.03432329371571541,
0.022556601092219353,
0.03645848482847214,
0.016791125759482384,
-0.08495939522981644,
0.00042224288336001337,
0.027126772329211235,
0.025039784610271454,
0.06489299237728119,
-0.03715837001800537,
0.03075031191110611,
0.020911037921905518,
-0.0696592777967453,
0.0034178150817751884,
-0.031112994998693466,
-0.021180033683776855,
-0.022629590705037117,
-0.0014001401141285896,
-0.009356408379971981,
0.05330083146691322,
0.034444209188222885,
0.03138941526412964,
-0.001544638187624514,
0.005132646299898624,
-0.02520829252898693,
-0.019617512822151184,
-0.05885729193687439,
0.03413478285074234,
0.02347712405025959,
-0.007239720318466425,
0.09468122571706772,
-0.014909647405147552,
-0.0559009425342083,
0.005362845025956631,
0.007740394677966833,
-0.018219145014882088,
-0.031236309558153152,
-0.011007805354893208,
0.026085590943694115,
0.021365148946642876,
0.041760437190532684,
-0.011075328104197979,
-0.018539484590291977,
0.014327061362564564,
0.019098179414868355,
0.01547567080706358,
-0.007224754896014929,
0.01949934847652912,
-0.006135455332696438,
-0.034903619438409805,
-0.02015562355518341,
-0.004063627682626247,
0.001863890211097896,
-0.053368132561445236,
-0.02387423627078533,
0.012089576572179794,
-0.015844425186514854,
-0.02550421468913555,
0.0030971409287303686,
-0.03951263055205345,
0.00969990249723196,
0.026072032749652863,
0.03209323808550835,
0.025687767192721367,
0.025653498247265816,
-0.01382926944643259,
-0.024803631007671356,
0.010452251881361008,
-0.021023962646722794,
0.0073267086409032345,
-0.059383027255535126,
-0.017953546717762947,
0.005068983882665634,
0.0024318608921021223,
0.021972553804516792,
-0.03289587423205376,
0.006203228607773781,
0.03659316897392273,
-0.00009453827806282789,
0.029060570523142815,
-0.018285958096385002,
-0.019188890233635902,
0.03078259713947773,
-0.06484623998403549,
0.03369522467255592,
0.008298533037304878,
0.010311505757272243,
-0.023095767945051193,
-0.008279005065560341,
-0.013832437805831432,
0.023010432720184326,
0.08596839010715485,
-0.016080226749181747,
0.015813730657100677,
0.037979476153850555,
0.01645790785551071,
0.02168319560587406,
-0.012009048834443092,
-0.025155391544103622,
-0.02185336872935295,
-0.006780277471989393,
0.02691764198243618,
-0.012366949580609798,
-0.029263878241181374,
0.023824166506528854,
0.020607635378837585,
-0.028102265670895576,
0.026635967195034027,
0.024274447932839394,
-0.05955230072140694,
0.020074794068932533,
0.007741307839751244,
-0.05705244466662407,
0.05622297152876854,
-0.005530834663659334,
-0.008248952217400074,
0.05484011769294739,
-0.04235396161675453,
-0.02129380777478218,
0.03201043978333473,
-0.015421115793287754,
-0.03835604712367058,
-0.015439110808074474,
-0.019303414970636368,
0.013251351192593575,
-0.028628477826714516,
0.030086904764175415,
0.04958779737353325,
-0.022717256098985672,
-0.0070072440430521965,
0.06814310699701309,
0.028368642553687096,
0.027255898341536522,
0.027942165732383728,
-0.013885189779102802,
0.03262626752257347,
0.01618005707859993,
0.024105362594127655,
0.020394552499055862,
0.03205223008990288,
0.017267752438783646,
-0.052322227507829666,
-0.0013097585178911686,
-0.02388559840619564,
-0.00568693783134222,
0.0018488455098122358,
0.05219428986310959,
0.010513640008866787,
-0.002959752455353737,
0.04393497109413147,
-0.007199855055660009,
0.03143696486949921,
0.01904728077352047,
-0.030014269053936005,
0.07520950585603714,
-0.04448699206113815,
-0.01296008750796318,
-0.025353029370307922,
0.00979972817003727,
-0.031974829733371735,
0.054208774119615555,
0.0025398051366209984,
0.041878435760736465,
0.004913245793431997,
0.007062529679387808,
-0.03794654831290245,
0.0012066650670021772,
-0.027919916436076164,
-0.028311992064118385,
0.027037154883146286,
0.0026524383574724197,
0.0015313486801460385,
0.0009341155528090894,
-0.04904874786734581,
-0.03576149418950081,
-0.048349082469940186,
0.022984087467193604,
0.012309948913753033,
0.023601973429322243,
-0.026953043416142464,
-0.036880817264318466,
-0.034428250044584274,
0.02951798588037491,
-0.0427648201584816,
-0.032770585268735886,
-0.03274212032556534,
0.022868694737553596,
0.003684321418404579,
0.005647365935146809
] |
<p>Now, humanity can <a href="http://www.engadget.com/2012/07/07/wireless-power-through-4-inch-concrete/" rel="nofollow">beam 50-60 watts power through 10 centimeter-thick concrete block</a>. Can such wireless power transfer harm us by anyways?</p>
| 9,354 |
[
-0.03165208175778389,
-0.038456548005342484,
0.011879961006343365,
-0.04360327869653702,
0.05551097169518471,
0.03526724874973297,
-0.017231086269021034,
-0.03297313675284386,
0.01994052156805992,
-0.03702499344944954,
0.03892751783132553,
0.056763652712106705,
0.01643189787864685,
0.00018191622802987695,
0.022631986066699028,
-0.002564207185059786,
0.005926260259002447,
-0.02097560465335846,
0.004307582974433899,
-0.04072282463312149,
0.00132923130877316,
0.017982805147767067,
-0.00645895441994071,
0.04545559361577034,
-0.015138690359890461,
0.011563308537006378,
0.020361823961138725,
-0.020768094807863235,
-0.027364900335669518,
0.044093601405620575,
0.02402733825147152,
-0.002382266102358699,
0.011454533785581589,
0.015336105599999428,
0.01658906415104866,
-0.024736901745200157,
-0.06030194088816643,
-0.03808169066905975,
0.006072774529457092,
-0.0037003755569458008,
0.027164284139871597,
-0.03905490040779114,
-0.007603141013532877,
0.04542654752731323,
-0.03351755440235138,
0.0036404673010110855,
-0.005778762977570295,
-0.01938467100262642,
0.0073572006076574326,
-0.04944678023457527,
0.041852351278066635,
0.0016405598726123571,
0.030131688341498375,
-0.008976069279015064,
-0.009766509756445885,
-0.0017735040746629238,
0.06268876791000366,
0.06529605388641357,
-0.014569893479347229,
-0.047184932976961136,
-0.01437418907880783,
0.0069085354916751385,
-0.022203339263796806,
-0.035750363022089005,
-0.03942590951919556,
0.050671301782131195,
-0.03041885793209076,
-0.017116395756602287,
0.010106246918439865,
-0.012363987974822521,
0.044177424162626266,
0.02766568958759308,
0.020896388217806816,
0.004490557126700878,
0.0036054032389074564,
-0.003937253728508949,
-0.032264064997434616,
0.026612212881445885,
0.042446739971637726,
0.04971396178007126,
-0.04630909487605095,
0.0009839159902185202,
0.0209184680134058,
0.053696226328611374,
0.00012977216101717204,
-0.032112568616867065,
0.04815100505948067,
-0.029557356610894203,
0.026084672659635544,
0.017502544447779655,
0.022895073518157005,
0.008241690695285797,
0.016747692599892616,
0.03932251036167145,
0.03278196230530739,
0.040003884583711624,
-0.0075949314050376415,
0.040128909051418304,
-0.01371160987764597,
-0.049144189804792404,
0.03278893604874611,
0.025373239070177078,
0.037032343447208405,
0.03088323026895523,
-0.013012167066335678,
-0.044915344566106796,
0.004385692533105612,
-0.00008579923451179639,
0.011587906628847122,
-0.002225908450782299,
-0.048133496195077896,
-0.01803644560277462,
0.020328687503933907,
-0.023600930348038673,
0.0420825369656086,
-0.0210647564381361,
0.012898427434265614,
-0.010569408535957336,
0.037759389728307724,
0.059098489582538605,
0.016959641128778458,
-0.00319270184263587,
0.0742759257555008,
-0.04151575639843941,
-0.044167086482048035,
0.004793953616172075,
-0.0000751334591768682,
-0.015282753854990005,
-0.05291635915637016,
0.01540615689009428,
0.033507298678159714,
-0.0017587802140042186,
0.0017493453342467546,
-0.03044077940285206,
0.027262547984719276,
-0.03076884150505066,
-0.1007118672132492,
-0.06382576376199722,
0.04212593659758568,
0.004865980241447687,
-0.012182692997157574,
-0.07122316211462021,
0.020807521417737007,
-0.007529331371188164,
0.06748145818710327,
-0.013391057029366493,
0.002706384751945734,
-0.010197287425398827,
0.053162965923547745,
0.002227143617346883,
0.002154397312551737,
0.007492582313716412,
0.011371877044439316,
-0.018168475478887558,
0.02439216710627079,
-0.06016857922077179,
0.021580563858151436,
0.04106379300355911,
0.001589880557730794,
-0.02968740090727806,
0.02825808711349964,
0.01238175854086876,
-0.028486626222729683,
0.003106113523244858,
-0.0687686949968338,
-0.0021645238157361746,
0.07371657341718674,
0.027550609782338142,
0.01843976229429245,
0.04310154542326927,
0.01413610577583313,
0.030403148382902145,
0.03107539936900139,
0.017927011474967003,
0.021865813061594963,
-0.05485915020108223,
0.020832287147641182,
-0.02519375830888748,
0.033402685075998306,
0.00022014307614881545,
-0.034945596009492874,
0.009332225657999516,
0.013319882564246655,
0.023118576034903526,
0.012680922634899616,
0.07446322590112686,
-0.03530411794781685,
0.0033557561691850424,
0.024756019935011864,
-0.032996952533721924,
-0.04546612501144409,
-0.06619804352521896,
0.04914920777082443,
0.0345027819275856,
-0.009007804095745087,
-0.02595265582203865,
-0.02210220694541931,
0.014518742449581623,
-0.035023223608732224,
-0.027775049209594727,
0.034489743411540985,
0.06740055978298187,
0.028086764737963676,
0.019527344033122063,
0.017871040850877762,
0.05033537372946739,
0.0210192259401083,
0.018286090344190598,
0.02283679135143757,
-0.008034554310142994,
-0.05979740619659424,
0.020450366660952568,
-0.02820134162902832,
0.020438969135284424,
0.05536970496177673,
-0.000853044621180743,
0.005496676545590162,
-0.03385154902935028,
-0.011942736804485321,
0.01138788927346468,
0.0031603730749338865,
0.04498886317014694,
0.03157965838909149,
0.04182355850934982,
-0.018580332398414612,
0.02121580019593239,
-0.013666728511452675,
-0.013771113939583302,
-0.031004486605525017,
-0.03188534826040268,
-0.07316912710666656,
0.019778747111558914,
0.005849004257470369,
0.048623356968164444,
-0.044491205364465714,
0.03052821196615696,
-0.015550472773611546,
0.052484575659036636,
0.02555788680911064,
0.015000922605395317,
0.004357836674898863,
-0.020223522558808327,
0.04101786017417908,
0.04103459417819977,
-0.011122533120214939,
0.005016995128244162,
-0.022567905485630035,
0.014670622535049915,
-0.011787786148488522,
-0.007994446903467178,
0.005023753270506859,
0.010219351388514042,
-0.024273734539747238,
0.00868962798267603,
0.0006570536061190069,
-0.03541302680969238,
0.036458343267440796,
-0.049572281539440155,
-0.01502955611795187,
0.01197232585400343,
-0.022251246497035027,
0.011859368532896042,
-0.014402301982045174,
-0.008908060379326344,
-0.004318954423069954,
0.010193629190325737,
-0.012425639666616917,
0.0014769998379051685,
0.02893519587814808,
-0.03953719511628151,
0.02166435308754444,
-0.014319774694740772,
0.016571352258324623,
-0.03739169239997864,
-0.006955158896744251,
0.003407760988920927,
0.004112341441214085,
0.05627748370170593,
-0.02982732281088829,
-0.02080351673066616,
-0.0036614888813346624,
-0.0005072919884696603,
-0.04623272269964218,
0.03206748887896538,
-0.021573539823293686,
-0.017858823761343956,
-0.028858881443738937,
-0.013661064207553864,
0.06015078350901604,
0.0107498150318861,
-0.0041887410916388035,
0.03896069899201393,
0.01909620501101017,
-0.056075431406497955,
0.010347430594265461,
-0.006930218543857336,
0.003271662164479494,
-0.018195107579231262,
-0.023635899648070335,
0.03551449626684189,
0.002111768815666437,
-0.052429813891649246,
-0.016721641644835472,
-0.021197117865085602,
-0.010137185454368591,
0.03793969750404358,
-0.04852494224905968,
0.01579405926167965,
-0.014044687151908875,
0.026240717619657516,
-0.013593098148703575,
-0.09142627567052841,
-0.009060751646757126,
-0.04720694199204445,
-0.07213751971721649,
0.032509539276361465,
-0.027343807741999626,
0.03428066149353981,
0.02412153221666813,
-0.03180734068155289,
0.05729276314377785,
0.027046453207731247,
0.006426672916859388,
-0.008268839679658413,
-0.06960471719503403,
-0.011837904341518879,
-0.03044402040541172,
-0.021736884489655495,
0.062212247401475906,
-0.011865148320794106,
-0.01588527299463749,
0.02177337557077408,
0.02271290495991707,
0.03422858938574791,
0.029804494231939316,
-0.025284387171268463,
-0.03241542726755142,
-0.01356151420623064,
-0.02820034697651863,
0.02778848074376583,
-0.009156364016234875,
-0.019388852640986443,
-0.005719113163650036,
-0.01377220917493105,
0.020912935957312584,
0.023354195058345795,
-0.0139766251668334,
0.011750977486371994,
0.006619505118578672,
0.040973443537950516,
-0.04769747704267502,
0.05097409710288048,
-0.011058525182306767,
0.01511493418365717,
-0.0006848818156868219,
0.01785092055797577,
0.049788594245910645,
-0.006155796814709902,
-0.0030839184764772654,
-0.010440194979310036,
0.07102649658918381,
0.0011766073293983936,
-0.03830108419060707,
0.015606846660375595,
0.019555289298295975,
0.0160613302141428,
0.05835903808474541,
-0.02685248851776123,
0.025700287893414497,
0.008775444701313972,
0.049646783620119095,
0.027174044400453568,
0.015538208186626434,
0.016672490164637566,
-0.01279998105019331,
-0.018389688804745674,
0.004811417777091265,
0.022344674915075302,
-0.006693656090646982,
0.023030061274766922,
0.020762355998158455,
0.0046142516657710075,
-0.0008931611082516611,
-0.025140812620520592,
-0.04426748678088188,
-0.009023907594382763,
-0.049821823835372925,
-0.010207102634012699,
-0.006305004470050335,
-0.04134127497673035,
-0.033219557255506516,
0.004948653280735016,
-0.02782447636127472,
-0.01846075989305973,
-0.010615842416882515,
-0.02693609520792961,
0.018926749005913734,
-0.0017083045095205307,
-0.0357796773314476,
-0.015253130346536636,
-0.022900104522705078,
0.022226471453905106,
-0.020377516746520996,
-0.005174355581402779,
0.015171212144196033,
-0.01718876138329506,
0.026845134794712067,
0.015024302527308464,
0.0023752504494041204,
-0.010955463163554668,
0.029581306502223015,
0.029195955023169518,
-0.012112888507544994,
-0.05373406782746315,
-0.007054460234940052,
-0.0037691735196858644,
0.026158275082707405,
-0.0033249000553041697,
-0.012312344275414944,
-0.03027699701488018,
-0.03427695110440254,
-0.031256452202796936,
-0.008318502455949783,
0.016909362748265266,
0.0028162766247987747,
0.03635343909263611,
0.035495780408382416,
-0.022561293095350266,
-0.031054068356752396,
0.002741747535765171,
0.0245649516582489,
-0.0024956734851002693,
-0.009277974255383015,
-0.06458406895399094,
-0.026226691901683807,
-0.00998448021709919,
-0.009657156653702259,
0.027881009504199028,
-0.008528849110007286,
-0.007795295678079128,
0.018546272069215775,
0.05567914992570877,
0.033930741250514984,
-0.012170527130365372,
0.07832371443510056,
0.00022570737928617746,
-0.016026340425014496,
-0.012571536004543304,
0.0027130600064992905,
-0.018867136910557747,
0.034371815621852875,
0.0233310554176569,
0.016963308677077293,
-0.03447467461228371,
-0.10436884313821793,
0.02565370313823223,
0.006059898529201746,
0.08516111969947815,
-0.004599986597895622,
-0.015099880285561085,
-0.03314962610602379,
-0.01127038337290287,
0.04907388985157013,
-0.018819132819771767,
0.04484912380576134,
-0.017668621614575386,
-0.0043776025995612144,
-0.05066365376114845,
-0.0033644642680883408,
-0.0172010138630867,
-0.0030484504532068968,
0.017915841192007065,
-0.009998739697039127,
0.0031043465714901686,
-0.014614914543926716,
0.04422029107809067,
0.023621832951903343,
0.05499305948615074,
0.06146650016307831,
0.009500276297330856,
0.007697786670178175,
-0.04599015414714813,
0.029238145798444748,
-0.02878960408270359,
-0.03630037605762482,
0.0154140405356884,
-0.00008505739970132709,
-0.046588100492954254,
0.07517300546169281,
-0.027126433327794075,
-0.022972289472818375,
0.052724938839673996,
0.02414507232606411,
-0.010775300674140453,
-0.01362842507660389,
-0.040424082428216934,
0.00908674020320177,
0.026232201606035233,
0.008584351278841496,
0.05342990905046463,
0.060465388000011444,
-0.04152262583374977,
0.02166936919093132,
-0.010877205990254879,
0.05987808108329773,
-0.03048323467373848,
0.014867142774164677,
0.04234233498573303,
0.02033509872853756,
-0.023317668586969376,
0.0501071996986866,
0.002726529259234667,
0.015775902196764946,
0.019649507477879524,
-0.01153428666293621,
0.006685733795166016,
0.030406171455979347,
-0.017424901947379112,
-0.019957851618528366,
-0.012879468500614166,
0.03715061396360397,
0.013494666665792465,
-0.04362243041396141,
-0.01001734845340252,
-0.0054865689016878605,
0.03640966862440109,
0.03656324744224548,
0.004504437558352947,
0.010288508608937263,
-0.04261967912316322,
0.00857209786772728,
0.02448577992618084,
-0.05303094536066055,
0.04917175695300102,
0.0008532200590707362,
-0.02082684263586998,
-0.00014205432671587914,
-0.07230770587921143,
-0.018309129402041435,
0.029940210282802582,
0.001797563279978931,
0.03736112639307976,
0.005676251836121082,
0.00848048459738493,
0.019630949944257736,
0.030969344079494476,
-0.021687235683202744,
-0.028085926547646523,
-0.011307687498629093,
0.03742728382349014,
0.012165038846433163,
-0.014100193046033382,
0.002306832931935787,
-0.008441086858510971,
-0.07348787784576416,
-0.05151599273085594,
0.040093015879392624,
-0.060965463519096375,
0.002217872068285942,
0.009722857736051083,
-0.04326055943965912,
0.07320618629455566,
0.007544401567429304,
-0.021003780886530876,
0.027540067210793495,
-0.03478345274925232,
0.004423568956553936,
-0.04347590357065201,
0.020334551110863686,
-0.018018566071987152,
-0.01603632979094982,
0.006830994505435228,
-0.02339646779000759,
0.03517782688140869,
0.005668897181749344,
-0.029752973467111588,
0.043962057679891586,
0.025071782991290092,
-0.02226368337869644,
0.01632748171687126,
0.033801086246967316,
0.02483343705534935,
0.05573312193155289,
0.008402922190725803,
0.0002247278462164104,
-0.06459145992994308,
-0.05459589511156082,
0.04358234256505966,
0.04498077556490898,
-0.006450776942074299,
-0.022865979000926018,
0.02525331825017929,
-0.02910083346068859,
-0.02808264084160328,
0.00228642369620502,
-0.026514675468206406,
0.02852960117161274,
-0.01590796373784542,
0.022561335936188698,
-0.005156788043677807,
0.012126006186008453,
-0.03303326293826103,
-0.01937706395983696,
-0.051062293350696564,
-0.005702302325516939,
0.05114985629916191,
-0.045305415987968445,
0.039800744503736496,
-0.003991284407675266,
-0.038662925362586975,
-0.008672217838466167,
-0.012233775109052658,
0.011799873784184456,
0.03737875074148178,
-0.022010093554854393,
-0.01714443229138851,
0.017167119309306145,
-0.025136170908808708,
0.027739515528082848,
0.04016350582242012,
-0.013301551342010498,
0.01535759773105383,
0.03523427993059158,
0.02865009382367134,
-0.0016841489123180509,
-0.024532465264201164,
-0.062128789722919464,
0.032055165618658066,
-0.10053650289773941,
-0.005043633282184601,
0.025938205420970917,
-0.017695672810077667,
0.0402190200984478,
-0.009141701273620129,
-0.021813658997416496,
-0.029640333727002144,
-0.007722135633230209,
-0.0338226854801178,
0.028763551265001297,
-0.006705618929117918,
-0.007084593176841736,
-0.008446439169347286,
-0.007370969746261835,
0.01877126470208168,
0.004333321936428547,
0.032260265201330185,
0.007879285141825676,
-0.06713514775037766,
-0.05866379663348198,
-0.02171163633465767,
-0.021461328491568565,
0.04616999998688698,
0.018915804103016853,
-0.019577637314796448,
0.05000454559922218,
-0.046228546649217606,
0.04855117201805115,
0.010059839114546776,
0.029464373365044594,
-0.0109843285754323,
0.029801364988088608,
-0.02880384773015976,
-0.0017146416939795017,
0.0027788865845650434,
-0.008374378085136414,
0.12282893061637878,
0.037840213626623154,
0.006421786732971668,
-0.024484727531671524,
0.022585175931453705,
-0.03300125151872635,
-0.004894215613603592,
-0.03360486030578613,
0.0017329244874417782,
-0.04193832352757454,
0.017175540328025818,
0.015163217671215534,
0.015088002197444439,
0.04139207676053047,
0.03934740647673607,
0.05488085001707077,
-0.021808186545968056,
-0.04449675604701042,
0.04068592190742493,
0.00735701946541667,
-0.01730685494840145,
-0.01781821995973587,
-0.03822797164320946,
0.022805100306868553,
-0.03630635887384415,
0.005211473908275366,
-0.015062415041029453,
0.0018202487844973803,
0.05953926220536232,
-0.0019177962094545364,
-0.04634975269436836,
-0.04054152965545654,
0.006081312894821167,
-0.030909553170204163,
-0.03686876595020294,
0.023922091349959373,
0.022379953414201736,
0.01582699827849865,
-0.02606404945254326,
0.02049408107995987,
0.024637969210743904,
-0.010637227445840836,
0.026108376681804657,
0.03838220238685608,
-0.05247947946190834,
0.03389918431639671,
-0.026506057009100914,
0.009672220796346664,
-0.010548258200287819,
0.005243506282567978,
0.014964984729886055,
0.01527775265276432,
0.016997475177049637,
-0.03924047574400902,
-0.031379617750644684,
0.01470242254436016,
0.03647187724709511,
0.01774258352816105,
0.0184648260474205,
-0.017185354605317116,
0.031816478818655014,
-0.022456470876932144,
0.005595932714641094,
0.016428817063570023,
0.013993875123560429,
-0.0017421059310436249,
0.007479954976588488,
0.02886262722313404,
-0.03218003362417221,
-0.02627168782055378,
-0.07893824577331543,
-0.019925137981772423,
-0.03247126564383507,
-0.024446766823530197,
-0.010092676617205143,
0.047469232231378555,
0.021531566977500916,
-0.0016124490648508072,
0.0043314420618116856,
-0.06081070005893707,
-0.05730202794075012,
0.032545700669288635,
-0.027142487466335297,
0.0036909510381519794,
-0.03395688906311989,
-0.018205678090453148,
0.04382667690515518,
0.07968529313802719,
-0.022573405876755714,
-0.023568416014313698,
-0.033505767583847046,
0.04549236223101616,
-0.002030947944149375,
-0.017986422404646873,
-0.010319606401026249,
-0.004475375637412071,
-0.022830292582511902,
0.03484990820288658,
-0.02762235887348652,
0.028658650815486908,
0.02677355520427227,
-0.02519466169178486,
-0.0020077258814126253,
0.0018525505438446999,
-0.019830137491226196,
-0.022174259647727013,
0.03580436110496521,
-0.010399844497442245,
-0.029127292335033417,
0.03011491522192955,
0.02282111532986164,
-0.01851016655564308,
-0.03178687021136284,
-0.060304101556539536,
-0.020345039665699005,
0.026688430458307266,
0.01729244366288185,
0.01209243107587099,
-0.04261830449104309,
-0.00984095223248005,
0.0023320794571191072,
-0.02405211143195629,
-0.016015170142054558,
-0.046514734625816345,
-0.006275413557887077,
-0.03185974061489105,
-0.020515911281108856,
0.030051525682210922,
0.048097457736730576,
-0.05113745853304863,
0.055439699441194534,
0.02491479180753231,
-0.00028585363179445267,
-0.04342886060476303,
-0.003535908879712224,
0.000005407459411799209,
0.00039701847708784044,
0.05766711011528969,
0.009293402545154095,
-0.02710219845175743,
0.03880668058991432,
-0.040846820920705795,
-0.037982333451509476,
0.02404963970184326,
-0.039078619331121445,
0.041046127676963806,
0.018207013607025146,
-0.029242413118481636,
0.015337199904024601,
0.04807135462760925,
-0.015326962806284428,
0.0009151896229013801,
0.02562057226896286,
0.01845141127705574,
-0.01417201291769743,
0.04014606773853302,
-0.0005655770073644817,
-0.05364670231938362,
-0.005315259099006653,
0.020342087373137474,
0.025470061227679253,
0.02215319313108921,
0.013968585059046745,
-0.00540578318759799,
-0.025752652436494827,
-0.0027721880469471216,
-0.007659320253878832,
0.02240508794784546,
0.002355427946895361,
0.05940109118819237,
-0.011863800697028637,
0.016789184883236885,
-0.0007073856540955603,
-0.004816208966076374,
-0.10084617882966995,
-0.005155304446816444,
-0.0060497489757835865,
-0.012780989520251751,
0.039341047406196594,
-0.04455958679318428,
0.06282373517751694,
0.013716758228838444,
-0.09627629071474075,
0.016574086621403694,
0.0005205671186558902,
-0.06401462107896805,
-0.020003685727715492,
0.052956387400627136,
-0.030997127294540405,
0.030574174597859383,
0.0356723926961422,
0.050097547471523285,
0.009737172164022923,
0.02610662207007408,
-0.020014751702547073,
-0.00809677504003048,
0.01688372902572155,
0.005073104053735733,
0.009882014244794846,
0.016497960314154625,
0.06629261374473572,
-0.003585193073377013,
0.004797765053808689,
0.014677874743938446,
-0.02773164212703705,
0.005476056598126888,
0.016995960846543312,
0.03491167351603508,
0.019730523228645325,
0.07614932954311371,
0.010997461155056953,
-0.03772634267807007,
-0.03318685293197632,
-0.0021482836455106735,
0.018255645409226418,
0.01890590786933899,
-0.004898927640169859,
0.0356818363070488,
0.024630241096019745,
-0.021847229450941086,
0.008975334465503693,
0.006390009541064501,
-0.04474315047264099,
-0.012655552476644516,
-0.0146713275462389,
0.015551270917057991,
0.025794029235839844,
-0.047468263655900955,
0.0017897215439006686,
-0.04244739189743996,
-0.03782021626830101,
0.030116058886051178,
-0.0027087426278740168,
0.019147317856550217,
-0.001451742835342884,
-0.02871806174516678,
0.004227966535836458,
0.017444925382733345,
0.03194655478000641,
-0.03546023368835449,
-0.041936419904232025,
0.0076982853934168816,
-0.012687058188021183,
0.021739309653639793,
-0.015022080391645432,
-0.04928671568632126,
-0.03601823374629021,
0.06332769244909286,
0.01276695728302002,
0.0565139539539814,
0.0798291563987732,
-0.009793035686016083,
-0.038165703415870667,
-0.061429720371961594,
0.022112863138318062,
-0.014905561693012714,
-0.0011128473561257124,
-0.05824270099401474,
-0.027263948693871498,
0.020725028589367867,
0.00039398661465384066,
0.07971853762865067,
-0.028360189869999886,
-0.00449970131739974,
0.013404225930571556,
0.01745678298175335,
-0.011731189675629139,
-0.026875540614128113,
-0.0083893071860075,
0.0318501777946949,
-0.01415169145911932,
0.0015945377526804805,
-0.0007927127298898995,
0.008014299906790257,
0.0028716418892145157,
-0.00852117594331503,
0.015152174979448318,
-0.01993323117494583,
-0.005460380110889673,
-0.004667510744184256,
0.041016560047864914,
-0.006383475381880999,
-0.0005374143365770578,
0.0727924108505249,
-0.04853116720914841,
0.03961297869682312,
-0.0020262757316231728,
-0.03877381607890129,
-0.0027365079149603844,
0.020417315885424614,
-0.03326672688126564,
0.04519026726484299,
-0.016302229836583138,
0.010601485148072243,
0.06206745281815529,
-0.03477584570646286,
-0.020832305774092674,
0.02251329831779003,
-0.06058141216635704,
0.009304755367338657,
0.03906155005097389,
-0.0014144752640277147,
-0.007339986506849527,
0.01383005641400814,
0.003878726391121745,
-0.018220193684101105,
0.008643323555588722,
-0.03292878717184067,
0.0022062112111598253,
-0.020012684166431427,
-0.028631655499339104,
0.004560637753456831,
0.03586210310459137,
0.01953970640897751,
0.009045841172337532,
0.040969155728816986,
0.03944140300154686,
-0.009991712868213654,
-0.052194252610206604,
-0.009809788316488266,
0.0033690407872200012,
-0.014774826355278492,
0.011807048693299294,
-0.007156668230891228,
0.06570427864789963,
0.017588764429092407,
-0.01108822412788868,
-0.0021566750947386026,
-0.05223077908158302,
0.021715853363275528,
0.03851361945271492,
0.020940715447068214,
0.03618444874882698,
-0.009675788693130016,
-0.038872070610523224,
-0.01501384936273098,
-0.02662225253880024,
0.026003224775195122,
-0.050427671521902084,
0.03921382129192352,
-0.04140044376254082,
0.03603952378034592,
-0.061121053993701935,
-0.021527571603655815,
-0.01326239388436079,
-0.009450724348425865,
0.018367990851402283,
0.03048471175134182,
-0.003534551477059722,
-0.017194651067256927,
-0.0053544556722044945,
-0.006407659500837326,
0.022885311394929886,
-0.05098111927509308,
0.023887373507022858,
-0.025995906442403793,
0.0191410630941391,
-0.0006142377969808877,
0.012422913685441017
] |
<p>I want to be expert to understand physics behind whirlpool, tornado, hurricane. Which topics are needed for this?</p>
| 9,355 |
[
-0.05798687785863876,
-0.05402172729372978,
-0.011669859290122986,
0.007394701708108187,
0.048908401280641556,
-0.01360951829701662,
-0.014121382497251034,
-0.03098229691386223,
-0.0024866072926670313,
-0.029346613213419914,
0.02305026538670063,
0.042013928294181824,
-0.004255910869687796,
0.0052253128960728645,
0.04509158432483673,
0.007526450324803591,
-0.00397435063496232,
-0.018005095422267914,
0.013554069213569164,
0.026977114379405975,
-0.04671473428606987,
-0.03252134472131729,
-0.011177494190633297,
0.039617713540792465,
-0.03487713634967804,
0.044470760971307755,
0.02260991744697094,
-0.00827122200280428,
0.01176599133759737,
0.02398739941418171,
0.02323920838534832,
-0.009736251085996628,
0.024849463254213333,
0.018270645290613174,
0.030601635575294495,
0.017692627385258675,
-0.03937062621116638,
0.0007425416260957718,
-0.04455428197979927,
0.013080508448183537,
-0.03335501253604889,
-0.009912591427564621,
-0.01923961378633976,
0.02081548422574997,
-0.06268584728240967,
0.06592702120542526,
0.013435709290206432,
-0.03048991970717907,
0.045725446194410324,
-0.0724588930606842,
0.0556066520512104,
-0.005175843834877014,
0.09219542890787125,
0.025941381230950356,
0.04065541550517082,
-0.0001250641798833385,
0.06958389282226562,
0.0623282790184021,
-0.039962414652109146,
-0.053727131336927414,
0.00995473749935627,
0.010091755539178848,
-0.01427848543971777,
-0.06321203708648682,
-0.038326945155858994,
0.040345869958400726,
0.017049437388777733,
-0.009555289521813393,
0.01576811447739601,
-0.011636069975793362,
0.0028428020887076855,
-0.002867617644369602,
0.03845701739192009,
0.028889190405607224,
0.03424324095249176,
-0.030734125524759293,
-0.019241292029619217,
-0.017673401162028313,
-0.0032787008676677942,
0.03558117896318436,
0.012440070509910583,
0.03194047138094902,
0.00825272873044014,
0.008871265687048435,
0.0013331298250705004,
-0.03420479595661163,
0.08870577812194824,
0.0010423162020742893,
-0.018555905669927597,
0.007072529289871454,
-0.010230973362922668,
-0.028311334550380707,
0.027455544099211693,
-0.00037569180130958557,
-0.024726511910557747,
0.017392082139849663,
-0.009155196137726307,
0.02000114694237709,
0.04355350509285927,
-0.017827756702899933,
-0.015059013850986958,
-0.020662270486354828,
0.03186974674463272,
0.09310879558324814,
0.01586601324379444,
0.0009885169565677643,
-0.03721671923995018,
-0.010266795754432678,
-0.04464654624462128,
-0.018767550587654114,
-0.003539239289239049,
0.024485180154442787,
-0.016680432483553886,
-0.009007344953715801,
-0.010860969312489033,
-0.0016760599100962281,
-0.004054192919284105,
-0.019480029121041298,
0.05506925657391548,
0.046824291348457336,
0.06850775331258774,
-0.027199089527130127,
0.029965544119477272,
-0.005667694844305515,
-0.1014491468667984,
-0.005155154038220644,
0.033737003803253174,
-0.027105705812573433,
-0.04718480259180069,
0.03610311076045036,
0.040917959064245224,
0.02812992036342621,
0.0009341411641798913,
0.0007393363630399108,
0.016283389180898666,
0.004611690994352102,
-0.11120166629552841,
-0.08260317146778107,
0.05594081059098244,
-0.04040590673685074,
-0.0389515645802021,
-0.05089252442121506,
0.021378250792622566,
0.035223543643951416,
0.08592089265584946,
-0.026685765013098717,
0.013004027307033539,
0.007370117120444775,
0.037522297352552414,
-0.0074460203759372234,
-0.03498435392975807,
0.006188519299030304,
-0.004756986629217863,
0.012374627403914928,
-0.006911297328770161,
-0.057368189096450806,
0.008594362996518612,
0.02599412202835083,
-0.03312543034553528,
-0.013437796384096146,
0.029216265305876732,
-0.03162240609526634,
0.010274889878928661,
0.017023833468556404,
-0.011189096607267857,
-0.01665203459560871,
0.0739443227648735,
-0.004735610447824001,
0.01305475179105997,
0.024500390514731407,
-0.018838267773389816,
0.015095841139554977,
-0.004190999548882246,
-0.0008473939960822463,
0.052332039922475815,
-0.03645706921815872,
0.01109708845615387,
-0.0051144990138709545,
0.00896395556628704,
0.000998235191218555,
-0.02520095370709896,
-0.025566335767507553,
0.015239352360367775,
0.027814753353595734,
-0.01917971484363079,
0.03821318596601486,
-0.018447961658239365,
-0.01750427484512329,
0.006940273102372885,
-0.03057357296347618,
-0.0069953324273228645,
-0.042764753103256226,
0.01949230022728443,
-0.04407975450158119,
0.01242388878017664,
0.024331793189048767,
-0.04193757846951485,
0.02999136596918106,
-0.051093779504299164,
0.011693920008838177,
0.008183950558304787,
0.03507782518863678,
0.02308141626417637,
0.010446522384881973,
-0.00218757800757885,
0.01610693521797657,
0.031208623200654984,
-0.04852425307035446,
0.017209580168128014,
-0.02988307736814022,
-0.04448028281331062,
-0.028779564425349236,
-0.0185245368629694,
0.006692973896861076,
0.0003001133445650339,
-0.012859041802585125,
0.029951507225632668,
0.04255598410964012,
0.010572475381195545,
0.0033864460419863462,
-0.0030369064770638943,
0.03917465731501579,
0.05569347366690636,
0.04728304594755173,
0.001898066489957273,
0.015032361261546612,
0.01738959737122059,
0.0030075686518102884,
-0.004190456587821245,
0.012557205744087696,
-0.06875735521316528,
0.01395348645746708,
0.013795493170619011,
0.0574193075299263,
-0.03255973383784294,
0.009321518242359161,
0.021261174231767654,
0.03679662197828293,
0.04519195854663849,
0.047028012573719025,
0.014070226810872555,
-0.032676491886377335,
0.024328110739588737,
0.008716450072824955,
0.016950152814388275,
0.02892351895570755,
0.06502345949411392,
0.04200846329331398,
-0.018949059769511223,
-0.008478730916976929,
-0.02915269508957863,
0.04088417440652847,
-0.009900769218802452,
0.002411561319604516,
0.008923671208322048,
0.002537160413339734,
0.024957535788416862,
-0.0354100726544857,
-0.01338172983378172,
0.010721275582909584,
0.022212602198123932,
0.020615501329302788,
0.005530192982405424,
-0.007110896985977888,
0.02724391408264637,
-0.003721759421750903,
0.0018563525518402457,
-0.007594792637974024,
0.06028091907501221,
-0.07768512517213821,
0.004154675640165806,
0.05950261279940605,
-0.011471303179860115,
-0.02332994155585766,
0.03212461620569229,
0.0405234731733799,
0.00039165327325463295,
0.04898717254400253,
-0.007415402214974165,
-0.019245604053139687,
0.003327723126858473,
-0.018710549920797348,
-0.04148593172430992,
-0.0038877108599990606,
-0.05292803421616554,
0.034604985266923904,
-0.02794334851205349,
-0.022092550992965698,
0.08345445990562439,
-0.022577602416276932,
-0.028513770550489426,
0.0012721562525257468,
0.010394029319286346,
-0.012005346827208996,
0.02016548439860344,
-0.017175449058413506,
0.03744957223534584,
-0.03987156227231026,
-0.013675530441105366,
0.04855151101946831,
-0.045806244015693665,
-0.02580736018717289,
-0.008758234791457653,
-0.04131709411740303,
-0.004933746065944433,
-0.00520144822075963,
-0.027862347662448883,
0.019612226635217667,
0.0031264140270650387,
-0.008600079454481602,
0.007770300842821598,
-0.05323801189661026,
0.02213830128312111,
0.0021085618063807487,
-0.06950926780700684,
0.004482200834900141,
-0.009563526138663292,
0.025083497166633606,
0.020057931542396545,
-0.02960076555609703,
0.05609988421201706,
-0.004299418069422245,
-0.03746916353702545,
-0.003983385395258665,
-0.027991823852062225,
-0.03459206223487854,
-0.027493663132190704,
0.03429765626788139,
0.04314492270350456,
0.006013707257807255,
0.019835537299513817,
0.019414035603404045,
-0.01111587230116129,
0.03973802179098129,
-0.0026903951074928045,
0.005045818630605936,
0.020227007567882538,
0.009401236660778522,
0.03852306678891182,
0.04087481647729874,
-0.02553580142557621,
-0.043432362377643585,
-0.004683168604969978,
0.000440495292423293,
-0.015833185985684395,
0.050462543964385986,
-0.052842866629362106,
0.03621990606188774,
-0.007831767201423645,
-0.022847242653369904,
-0.004249501973390579,
0.05596486106514931,
-0.022804856300354004,
-0.021904904395341873,
-0.0036141828168183565,
0.0024665738455951214,
0.06033717095851898,
0.019580475986003876,
0.020458107814192772,
0.0148424431681633,
0.03135599195957184,
-0.01767820678651333,
-0.028932694345712662,
-0.02237398736178875,
-0.02011103183031082,
0.010594863444566727,
-0.034183308482170105,
0.004195606801658869,
0.055072907358407974,
0.019405359402298927,
0.01411400269716978,
0.0133393295109272,
-0.005296861287206411,
0.016780592501163483,
-0.023626768961548805,
0.0008680678438395262,
-0.02557910606265068,
0.04616517946124077,
-0.025789419189095497,
0.03529709577560425,
0.005563109647482634,
0.02373422496020794,
0.014753359369933605,
-0.0038421181961894035,
-0.05778181180357933,
0.034172117710113525,
-0.028534336015582085,
-0.018384667113423347,
-0.023030061274766922,
0.03128775581717491,
0.02564172074198723,
0.00034046013024635613,
-0.04199405759572983,
-0.014591885730624199,
-0.011249380186200142,
-0.034515026956796646,
0.008878064341843128,
-0.019818639382719994,
-0.045328449457883835,
0.01220707781612873,
0.025666987523436546,
0.004601993132382631,
-0.023797249421477318,
0.031304821372032166,
0.048286695033311844,
0.005394084379076958,
-0.024141930043697357,
0.0036527824122458696,
-0.0006704692495986819,
-0.033940739929676056,
0.008578733541071415,
0.020226476714015007,
0.03383854031562805,
-0.03491315245628357,
0.01915617100894451,
0.0038485282566398382,
0.003262350568547845,
-0.02519400790333748,
0.00015815577353350818,
-0.030767733231186867,
-0.07487908750772476,
-0.0004965441185049713,
-0.0033835843205451965,
0.07152042537927628,
0.03156525269150734,
-0.01684766821563244,
0.021953243762254715,
-0.022958844900131226,
-0.06139296293258667,
0.046839989721775055,
0.02007584273815155,
-0.02012408711016178,
-0.00028953433502465487,
-0.019351007416844368,
-0.024499109014868736,
-0.02888968214392662,
-0.006732660345733166,
0.01176841463893652,
-0.005343740805983543,
-0.0238818246871233,
-0.004155523143708706,
0.03697960451245308,
-0.007560836151242256,
-0.02374272421002388,
0.033529482781887054,
0.04658903181552887,
0.02370527572929859,
-0.04025617241859436,
-0.013056712225079536,
0.00003790789196500555,
0.056364525109529495,
0.020302480086684227,
-0.04631543532013893,
-0.012112964875996113,
-0.049484528601169586,
-0.013070773333311081,
0.007732253056019545,
0.06707804650068283,
-0.03160814940929413,
-0.02473892644047737,
-0.05007249116897583,
-0.02825772576034069,
0.04659154638648033,
-0.025098556652665138,
0.024001512676477432,
-0.00985023844987154,
0.019805755466222763,
-0.010909374803304672,
-0.01692899689078331,
-0.017232947051525116,
0.02363657020032406,
-0.02509334124624729,
0.048908282071352005,
-0.032860223203897476,
-0.008084474131464958,
-0.016026362776756287,
0.015333423390984535,
0.05437086895108223,
0.01557995192706585,
0.05142451077699661,
0.04395249858498573,
-0.029890598729252815,
0.03957780450582504,
-0.05808708071708679,
-0.06634999066591263,
-0.011659549549221992,
-0.0017937744269147515,
-0.05343851074576378,
0.0286489799618721,
-0.003854991402477026,
-0.03172764927148819,
-0.02269446663558483,
0.02006663754582405,
-0.01161271333694458,
0.006872355937957764,
-0.013695132918655872,
0.017299387603998184,
0.03142431005835533,
0.03667033836245537,
0.029552515596151352,
0.04513998702168465,
-0.03547404706478119,
0.0014912831829860806,
-0.007684557233005762,
0.01653953082859516,
-0.03451826050877571,
-0.01962781511247158,
-0.01855444349348545,
0.0030714143067598343,
-0.047929584980010986,
0.06723794341087341,
-0.03917454555630684,
0.019377918913960457,
-0.02781369537115097,
-0.033739976584911346,
0.0023645684123039246,
0.027491772547364235,
0.01905079372227192,
-0.048071231693029404,
-0.005093597806990147,
0.008013379760086536,
0.007905285805463791,
-0.014365047216415405,
0.015442227013409138,
0.023061737418174744,
0.030491339042782784,
0.023707525804638863,
-0.0028491232078522444,
0.021159624680876732,
-0.07186517119407654,
-0.02678030915558338,
-0.0128848971799016,
-0.03608740493655205,
0.054567497223615646,
0.06420575082302094,
-0.006940982770174742,
0.06320451200008392,
-0.0638803020119667,
-0.022426733747124672,
0.033573295921087265,
0.020932985469698906,
0.02893705479800701,
-0.040045320987701416,
0.020292071625590324,
0.007675430737435818,
0.0036750405561178923,
-0.02324083261191845,
-0.03304576873779297,
0.010640461929142475,
0.03518865257501602,
-0.019263366237282753,
-0.0650414228439331,
0.060958381742239,
-0.06643328070640564,
-0.02581397444009781,
-0.04777001217007637,
0.030948322266340256,
-0.03208322450518608,
-0.003562722820788622,
0.028583502396941185,
-0.021704787388443947,
0.057085614651441574,
0.015605110675096512,
0.006584839895367622,
0.026274342089891434,
-0.014176142401993275,
0.018017765134572983,
-0.03581996262073517,
0.02795691043138504,
-0.025810791179537773,
-0.004880690015852451,
-0.0011081101838499308,
-0.022137479856610298,
0.04242604970932007,
-0.018629558384418488,
0.08921816200017929,
0.009776408784091473,
0.03226464241743088,
-0.044120319187641144,
-0.01106212381273508,
0.03802819550037384,
0.01241541001945734,
0.014416798949241638,
-0.023511812090873718,
0.00801557395607233,
-0.02111259661614895,
-0.03374507278203964,
0.007886270992457867,
-0.0017190267099067569,
-0.030279090628027916,
0.003910263068974018,
0.07444875687360764,
-0.008433165028691292,
0.00002717549432418309,
0.027821287512779236,
0.0021275163162499666,
0.016899239271879196,
-0.0036434736102819443,
0.0045143612660467625,
-0.005850575864315033,
0.030503135174512863,
-0.0011502895504236221,
-0.06539416313171387,
-0.03266014903783798,
0.02044392190873623,
0.059556931257247925,
-0.01635902374982834,
0.05228029564023018,
0.03254738450050354,
0.01972556672990322,
-0.010739758610725403,
-0.019230324774980545,
0.017698220908641815,
0.02125691808760166,
0.003378442721441388,
0.035043735057115555,
-0.014613582752645016,
0.004551952704787254,
-0.006109940353780985,
0.020588377490639687,
-0.027116216719150543,
0.007661351468414068,
0.008573479019105434,
0.017619816586375237,
0.001867579179815948,
-0.03137797862291336,
-0.03544013202190399,
0.020925866439938545,
-0.047530580312013626,
0.05703496187925339,
0.013864580541849136,
0.015310529619455338,
0.05410051718354225,
0.01391898188740015,
-0.02736746333539486,
-0.016282513737678528,
-0.00022218245430849493,
-0.05079001560807228,
0.007669421378523111,
-0.0016877424204722047,
-0.023049451410770416,
-0.045569099485874176,
0.04071001335978508,
0.03715077042579651,
0.004490278195589781,
0.0076451608911156654,
-0.014495190232992172,
-0.055619772523641586,
-0.0314091332256794,
-0.006731152534484863,
-0.04799449443817139,
0.04667419567704201,
0.002171962521970272,
-0.02243930660188198,
0.02437308244407177,
0.0018643628573045135,
0.03912629559636116,
-0.005442969035357237,
0.01761755533516407,
-0.008516601286828518,
0.032610174268484116,
-0.003324790857732296,
-0.01807582750916481,
-0.01590876281261444,
0.032652176916599274,
0.15863074362277985,
0.030904410406947136,
0.03471701592206955,
-0.06820891052484512,
-0.04462604597210884,
-0.025751620531082153,
-0.00890999287366867,
-0.044802505522966385,
0.008917633444070816,
0.0051904404535889626,
0.0256623737514019,
0.004767476115375757,
0.04236440360546112,
0.028355292975902557,
0.012301577255129814,
0.04566338658332825,
-0.03714413195848465,
-0.01868295855820179,
-0.04102502390742302,
0.002549024298787117,
-0.04327760636806488,
0.05518640577793121,
-0.08312491327524185,
0.012258799746632576,
-0.028174500912427902,
-0.0023064648266881704,
0.0016264710575342178,
-0.03595048934221268,
0.0639970526099205,
-0.040746163576841354,
-0.04159998893737793,
0.027474768459796906,
-0.0010020313784480095,
0.008087617345154285,
-0.043615713715553284,
0.03409302979707718,
0.012293832376599312,
-0.02166006900370121,
0.011151875369250774,
-0.0156499482691288,
0.030513597652316093,
-0.00482760276645422,
-0.013885953463613987,
0.015940837562084198,
-0.019267285242676735,
-0.0017622628947719932,
-0.030752265825867653,
0.01296804565936327,
0.021164657548069954,
0.023769013583660126,
-0.025467056781053543,
-0.018502172082662582,
-0.004778911825269461,
-0.03275507315993309,
-0.016896462067961693,
0.031189676374197006,
0.029496001079678535,
-0.0550825297832489,
-0.01065993495285511,
-0.059238873422145844,
0.019566882401704788,
-0.018515076488256454,
0.011677211150527,
-0.012784776277840137,
-0.007957578636705875,
-0.022084705531597137,
0.005438131280243397,
0.05353853851556778,
-0.04445328935980797,
-0.001160840387456119,
-0.039514102041721344,
-0.010211702436208725,
-0.03413572907447815,
-0.013470803387463093,
0.0173035915941,
0.0012287598801776767,
-0.00817820243537426,
0.049222592264413834,
-0.00438498193398118,
0.0013603874249383807,
-0.03399091586470604,
0.001601593685336411,
0.014218592084944248,
-0.009837932884693146,
-0.0029441809747368097,
-0.027649102732539177,
0.005582065787166357,
0.03940724581480026,
0.02265465073287487,
0.006908227689564228,
0.005449733696877956,
0.016365598887205124,
0.019132833927869797,
-0.020998675376176834,
-0.009208145551383495,
0.004609912168234587,
-0.0035794167779386044,
0.030730703845620155,
-0.003932514693588018,
0.0709599107503891,
0.027193227782845497,
-0.029594343155622482,
-0.002263573231175542,
0.018549881875514984,
-0.01787637174129486,
-0.0074654314666986465,
0.04447495564818382,
-0.06641203165054321,
-0.017086302861571312,
0.046233292669057846,
0.024687709286808968,
-0.01831582561135292,
-0.03576257824897766,
-0.013795372098684311,
-0.002577065024524927,
-0.020853936672210693,
0.034579627215862274,
-0.02386869490146637,
0.005233188159763813,
-0.014922530390322208,
0.05876554548740387,
-0.06573228538036346,
-0.01669677346944809,
-0.06076109781861305,
0.023382773622870445,
-0.003699210938066244,
-0.041714176535606384,
-0.023696819320321083,
0.009679410606622696,
-0.027945425361394882,
0.0017118800897151232,
0.01503688283264637,
-0.0010173636255785823,
-0.014588194899260998,
-0.017957530915737152,
-0.004094553645700216,
-0.04584651440382004,
0.052210234105587006,
-0.002793734660372138,
-0.027606861665844917,
0.05560673773288727,
-0.05057583376765251,
-0.022882070392370224,
0.03678807243704796,
0.019422559067606926,
0.006110831629484892,
0.05137178674340248,
-0.018261611461639404,
0.004086360801011324,
0.06840839982032776,
0.02404877170920372,
-0.005909925792366266,
-0.032758649438619614,
-0.013893265277147293,
-0.01813352480530739,
0.001191085553728044,
0.04425826296210289,
-0.04489503428339958,
-0.0046302746050059795,
0.01725406013429165,
0.045336902141571045,
0.028816118836402893,
-0.0182600449770689,
0.030153634026646614,
0.015321030281484127,
0.028464429080486298,
-0.021643750369548798,
0.007877732627093792,
0.036839559674263,
0.025425173342227936,
-0.04771062731742859,
0.024387415498495102,
-0.007077007554471493,
0.008306232281029224,
-0.09718918800354004,
0.027195731177926064,
0.04256267473101616,
-0.010711032897233963,
0.04871097207069397,
-0.038774143904447556,
0.017321879044175148,
0.05843810364603996,
-0.04173671081662178,
-0.028681140393018723,
-0.0008127943729050457,
-0.02701902575790882,
-0.001326521742157638,
0.00396780576556921,
0.016673525795340538,
0.025434982031583786,
-0.0005005414132028818,
0.021200554445385933,
0.009001844562590122,
0.00640556076541543,
-0.017148995772004128,
0.016858378425240517,
-0.0022828183136880398,
0.015224242582917213,
-0.01627553626894951,
-0.01671200431883335,
0.04679964482784271,
-0.039425499737262726,
-0.036347467452287674,
0.03636438399553299,
0.0005194233381189406,
0.0073618716560304165,
0.0053429692052304745,
0.008299763314425945,
-0.028706416487693787,
0.0540996789932251,
0.029085829854011536,
-0.034055598080158234,
0.03093366138637066,
0.011067928746342659,
-0.007037256378680468,
0.0370689332485199,
0.009652976877987385,
0.003301388816908002,
0.012019363231956959,
-0.04224170744419098,
-0.016239497810602188,
0.0021453178487718105,
-0.0017326630186289549,
-0.009760715067386627,
0.025534769520163536,
0.006089098751544952,
0.0028421971946954727,
0.019641347229480743,
-0.014817213639616966,
-0.03024480864405632,
0.014019003137946129,
0.02370966225862503,
-0.02078843116760254,
0.010275347158312798,
0.023769428953528404,
-0.0020655684638768435,
-0.05865020677447319,
0.0021690523717552423,
-0.015275760553777218,
-0.006415864452719688,
-0.04439116641879082,
0.0017303569475188851,
0.02441338635981083,
0.028694117441773415,
-0.02666020579636097,
-0.04353156313300133,
-0.0353533960878849,
0.04815658926963806,
-0.030492622405290604,
0.008969752117991447,
0.0301242433488369,
0.002490854589268565,
0.020429648458957672,
-0.06220763176679611,
0.041195016354322433,
0.01974709890782833,
0.01216940488666296,
-0.01930580474436283,
-0.002257764805108309,
0.026976102963089943,
0.016653627157211304,
0.015897363424301147,
-0.02716774120926857,
-0.007135300897061825,
0.008422059006989002,
-0.03839236870408058,
0.02942483313381672,
-0.014401775784790516,
-0.007736732251942158,
-0.03435267508029938,
-0.06518257409334183,
0.01935725472867489,
-0.016466472297906876,
0.027239304035902023,
-0.038383424282073975,
0.024188224226236343,
0.025163332000374794,
0.03667934238910675,
-0.015070379711687565,
-0.03317693993449211,
0.01346027571707964,
0.010817649774253368,
-0.01801297999918461,
0.04510482773184776,
-0.021876977756619453,
0.0046438430435955524,
-0.014901670627295971,
-0.03713928908109665,
-0.0108611099421978,
0.059720225632190704,
-0.039536796510219574,
0.010070370510220528,
0.0046314517967402935,
-0.07217047363519669,
0.016928913071751595,
-0.09132034331560135,
-0.011340712197124958,
0.01615462452173233,
-0.01669362001121044,
0.016213558614253998,
0.029067281633615494,
0.033809151500463486,
0.02745071053504944,
-0.04930367320775986,
0.005934485234320164,
0.006621379870921373,
-0.05418035387992859,
-0.040816351771354675,
0.02761719934642315,
0.05683344602584839,
-0.00033223952050320804,
0.013496169820427895,
0.01681823842227459,
-0.009455306455492973,
0.02618243731558323,
0.002743110293522477,
-0.008020976558327675,
-0.012248334474861622,
-0.040631409734487534,
-0.009893988259136677,
-0.010896765626966953,
0.011155808344483376,
0.0386866070330143,
-0.0037854432594031096,
0.04416891187429428,
-0.000541631830856204,
0.006567682605236769,
0.0019655865617096424,
-0.0021141727920621634,
-0.04765539616346359,
-0.02468213625252247,
-0.020939510315656662,
0.0683605894446373,
0.0018362466944381595,
-0.0014305865624919534,
-0.00018844717124011368,
0.002086822409182787,
0.03306705877184868,
-0.018631931394338608,
0.035871051251888275,
0.004659612197428942,
0.02649066038429737,
0.02392738126218319,
-0.001869011903181672,
-0.03977498412132263,
-0.027350878342986107,
0.014226548373699188,
0.043073687702417374,
-0.01302940584719181,
-0.021044153720140457,
-0.03231299668550491,
-0.03303278982639313,
0.022852053865790367,
-0.046612631529569626,
0.01000658143311739,
-0.047651369124650955,
0.02030937932431698,
-0.005353215616196394,
0.0037458089645951986
] |
<p>How would I normalize the wave function:
$ \psi (x)$ = $Ce^{i\rho_0x/\hbar}e^{-|x|/2\Delta x}$?
I squared it, which got rid of the imaginary part-Then I considered breaking up the absolute value-but this didn't seem to be integrable. I considered also using one of the exponential integrals from negative infinity to infinity, but I didn't seem to have one that fit the form, and I was uncomfortable using an integral I haven't shown to be true.</p>
| 9,356 |
[
0.0015796363586559892,
-0.031739793717861176,
0.002643064595758915,
-0.008846416138112545,
0.02394244819879532,
-0.020588116720318794,
-0.05356067791581154,
-0.04842468723654747,
0.020217834040522575,
-0.0186441782861948,
0.048320237547159195,
0.019951539114117622,
0.04997574910521507,
0.021113954484462738,
0.05651397630572319,
0.023529380559921265,
-0.017487971112132072,
-0.03366675600409508,
0.0017834235914051533,
-0.04990045726299286,
0.034473784267902374,
0.033275894820690155,
0.03379164636135101,
-0.012649741023778915,
-0.02260083146393299,
0.05627237260341644,
0.0029434135649353266,
0.004209157079458237,
0.009060260839760303,
0.0761764645576477,
-0.02444939687848091,
-0.05142092704772949,
0.015198783949017525,
0.053189896047115326,
-0.0118252569809556,
0.005885436665266752,
-0.0189964696764946,
-0.03616832569241524,
-0.0321405753493309,
0.04604222625494003,
-0.04860576614737511,
-0.009097717702388763,
0.0022648549638688564,
0.03580663725733757,
0.005351315718144178,
-0.0016402053879573941,
-0.002504387404769659,
-0.05195235088467598,
0.037879105657339096,
-0.054681260138750076,
0.07369094341993332,
-0.01485088374465704,
0.044573310762643814,
0.03072313591837883,
0.02340899035334587,
-0.04329383000731468,
0.046760424971580505,
0.03305143490433693,
0.003852308727800846,
-0.05849293991923332,
-0.011520924977958202,
-0.045108452439308167,
-0.01613624207675457,
-0.0052731954492628574,
-0.024123111739754677,
-0.0023990129120647907,
0.015670115128159523,
-0.0033329809084534645,
0.014576076529920101,
-0.030692126601934433,
0.03274133801460266,
0.036740321666002274,
0.025368450209498405,
-0.05966060608625412,
0.03579522296786308,
-0.012816892005503178,
0.012319783680140972,
0.02462647296488285,
0.012579726055264473,
0.0385347418487072,
0.02143983542919159,
0.015419824980199337,
0.012959123589098454,
0.01998235285282135,
-0.013003485277295113,
0.011798214167356491,
0.07221351563930511,
0.006265521049499512,
-0.025707317516207695,
0.04355812072753906,
0.005978832021355629,
0.008725732564926147,
0.06094016879796982,
-0.03536927327513695,
-0.034388236701488495,
0.05015764385461807,
0.019374411553144455,
0.05105389654636383,
0.0029080710373818874,
-0.043126363307237625,
-0.014027867466211319,
-0.02954823151230812,
0.0025487395469099283,
0.06122715771198273,
-0.00633186474442482,
0.004200182855129242,
-0.033519454300403595,
0.006800033152103424,
0.019702166318893433,
-0.03013618476688862,
-0.032677315175533295,
0.018656430765986443,
-0.0038560540415346622,
0.00197128439322114,
0.0007813646807335317,
-0.008779758587479591,
-0.020584601908922195,
-0.04040919244289398,
0.04673204571008682,
0.05521763116121292,
0.022978872060775757,
-0.009826052002608776,
0.04796537384390831,
-0.008809988386929035,
-0.072941854596138,
0.04072079434990883,
-0.001961930189281702,
0.01799330674111843,
-0.039615873247385025,
0.009044104255735874,
-0.006535835098475218,
0.00397536950185895,
0.02914336696267128,
-0.01816122978925705,
0.02823938988149166,
-0.025191936641931534,
-0.07746647298336029,
-0.06630638986825943,
-0.012773489579558372,
-0.008739297278225422,
-0.007198499981313944,
-0.08131202310323715,
0.0013859834289178252,
0.02869947999715805,
0.07428714632987976,
0.015607854351401329,
0.016159662976861,
-0.01591174118220806,
0.009627492167055607,
0.03116362914443016,
0.00907089188694954,
-0.06370646506547928,
-0.03336891904473305,
-0.057012032717466354,
-0.011014783754944801,
-0.04704797640442848,
-0.007821367122232914,
0.03221673518419266,
-0.0015865220921114087,
-0.0075175403617322445,
0.0881054699420929,
-0.004750356078147888,
-0.003486791392788291,
0.008078932762145996,
0.013030198402702808,
-0.04721866920590401,
0.09933061897754669,
0.02869894914329052,
-0.013031051494181156,
0.02736487425863743,
0.002875330625101924,
0.011018785648047924,
0.013349262997508049,
-0.0013172017643228173,
0.03820009157061577,
-0.035858362913131714,
-0.005927786231040955,
-0.07530804723501205,
0.032403286546468735,
0.008657370693981647,
-0.011534864082932472,
-0.007533034775406122,
-0.0457589365541935,
0.03986082226037979,
0.03335729241371155,
0.024216042831540108,
0.0019942475482821465,
-0.0515800341963768,
-0.010625290684401989,
-0.08048862218856812,
-0.004658685531467199,
-0.03587359935045242,
-0.005446227267384529,
0.015122424811124802,
-0.0004156293289270252,
0.039583176374435425,
-0.0017016587080433965,
0.053471148014068604,
-0.03880569338798523,
-0.06661181896924973,
-0.0004965915577486157,
0.023561010137200356,
0.03089655563235283,
-0.012015044689178467,
0.03171227127313614,
0.055587124079465866,
0.03440573066473007,
0.004847255535423756,
0.03731263428926468,
-0.01381849404424429,
-0.018054312095046043,
-0.026063283905386925,
-0.048547398298978806,
0.024067698046565056,
0.012516345828771591,
-0.003213742980733514,
-0.012624694965779781,
-0.0015288274735212326,
0.0004734376852866262,
-0.013520782813429832,
-0.03924098610877991,
0.0812443271279335,
0.02867312543094158,
0.011772220954298973,
-0.013659896329045296,
0.024730736389756203,
0.041839614510536194,
0.007336256094276905,
-0.0018428439507260919,
-0.058689262717962265,
-0.03219955787062645,
0.0017226217314600945,
0.03759285807609558,
0.01578826643526554,
-0.041025180369615555,
-0.004398778546601534,
0.00556538999080658,
0.02488418109714985,
0.05055145546793938,
0.029819319024682045,
-0.026169678196310997,
-0.010566030628979206,
-0.010210132226347923,
-0.013833901844918728,
0.005639142356812954,
0.006369799841195345,
0.01955375261604786,
-0.0036691518034785986,
0.008420052006840706,
0.0068982262164354324,
-0.00015704637917224318,
0.0383334681391716,
-0.023009702563285828,
0.017989058047533035,
-0.01767820678651333,
-0.029214445501565933,
0.015219793654978275,
-0.028852378949522972,
0.014924350194633007,
0.007260035257786512,
-0.0636097714304924,
-0.019287152215838432,
-0.013257568702101707,
-0.025021489709615707,
0.028573554009199142,
0.013555387035012245,
-0.02631966397166252,
0.01331024244427681,
0.02147751860320568,
-0.03352251648902893,
-0.007767896633595228,
-0.0560518279671669,
0.0028009566012769938,
-0.034700069576501846,
-0.01319883018732071,
0.0306459479033947,
0.040210362523794174,
0.027707040309906006,
-0.04904353246092796,
-0.05780048295855522,
0.007891040295362473,
-0.006676695309579372,
-0.0013204878196120262,
0.02418200485408306,
-0.03604719787836075,
0.00035021218354813755,
-0.03896489366889,
-0.012446138076484203,
0.040378350764513016,
-0.007460474967956543,
-0.002048010239377618,
-0.019235342741012573,
-0.013232570141553879,
-0.061388079077005386,
-0.030134590342640877,
-0.019057324156165123,
0.018293043598532677,
-0.03886629268527031,
-0.004165515303611755,
0.036820188164711,
-0.02056044153869152,
-0.014307809993624687,
0.05567469820380211,
-0.025299496948719025,
-0.05734342709183693,
-0.03742077946662903,
-0.006180365104228258,
0.0147185567766428,
-0.03324444219470024,
0.010730045847594738,
-0.007165632210671902,
-0.059966567903757095,
0.0026362300850450993,
-0.035768065601587296,
-0.03901674225926399,
0.023662904277443886,
0.026555916294455528,
0.023201752454042435,
0.02794003114104271,
-0.030901595950126648,
0.09277686476707458,
-0.0060296677984297276,
-0.03226752579212189,
-0.03570885956287384,
0.008470768108963966,
-0.012851879931986332,
0.007983582094311714,
-0.031337589025497437,
0.05496843159198761,
0.021561916917562485,
0.023455150425434113,
-0.009096676483750343,
0.0579361692070961,
0.02587316557765007,
0.016491761431097984,
-0.04766107350587845,
0.07749377936124802,
0.019196895882487297,
0.0025217828806489706,
0.0613766685128212,
-0.0003974720311816782,
0.004645538050681353,
-0.003828349756076932,
0.0017223755130544305,
-0.024273643270134926,
0.027361959218978882,
-0.027279512956738472,
0.059457775205373764,
-0.017602764070034027,
0.016618723049759865,
-0.010202726349234581,
0.034142956137657166,
-0.013763249851763248,
-0.024457063525915146,
-0.025988008826971054,
0.03336581215262413,
0.012490279041230679,
-0.022454477846622467,
0.04050687700510025,
0.026623396202921867,
0.039573706686496735,
-0.008839180693030357,
-0.027094315737485886,
0.019976695999503136,
0.008596000261604786,
0.03993143141269684,
-0.025880785658955574,
-0.06868081539869308,
0.04410576820373535,
0.030097270384430885,
0.03007800690829754,
-0.006381695158779621,
-0.03281983733177185,
-0.007929577492177486,
-0.032614853233098984,
-0.003852780442684889,
-0.020894231274724007,
0.03449331596493721,
0.01612330786883831,
0.012509106658399105,
0.04856831580400467,
0.014640598557889462,
0.024445971474051476,
0.00935365166515112,
-0.07109294831752777,
0.016392434015870094,
-0.047945842146873474,
-0.004594461061060429,
-0.01851245015859604,
0.016207566484808922,
0.010117080993950367,
-0.02380167692899704,
-0.007040804717689753,
-0.008431256748735905,
-0.030932260677218437,
-0.01596062071621418,
0.0017592330696061254,
-0.020427072420716286,
-0.023586465045809746,
-0.0323587991297245,
0.01643303781747818,
0.001197679783217609,
0.03175614774227142,
-0.029225988313555717,
0.03538094088435173,
-0.01382650900632143,
-0.007649559061974287,
0.014888584613800049,
-0.03332529962062836,
0.002450432162731886,
0.008487813174724579,
0.033984843641519547,
0.02534324862062931,
-0.004173811990767717,
0.005891884211450815,
0.01271785143762827,
0.06416589021682739,
0.0008943832363002002,
-0.008021421730518341,
0.033915624022483826,
-0.05180589109659195,
-0.006022600922733545,
-0.009439985267817974,
0.03718847781419754,
-0.01362176425755024,
0.021547041833400726,
0.01396945770829916,
0.010854504071176052,
-0.046119190752506256,
0.008576367050409317,
0.05030053108930588,
-0.012429900467395782,
-0.002353380434215069,
-0.05224264785647392,
0.01700085960328579,
-0.01435063499957323,
0.005205545108765364,
-0.010024474002420902,
-0.000697977258823812,
-0.042030420154333115,
-0.0076000806875526905,
0.04897509515285492,
0.0013821638422086835,
-0.001420535845682025,
-0.03733411431312561,
-0.016115864738821983,
-0.00716628460213542,
-0.005312933120876551,
-0.014264749363064766,
0.010415351018309593,
0.011141736060380936,
0.018264319747686386,
-0.0014760135672986507,
0.0011118407128378749,
-0.04719109460711479,
-0.017824826762080193,
0.032404884696006775,
0.04455612972378731,
0.05118801072239876,
0.001089894794858992,
-0.05708599090576172,
-0.06558874994516373,
0.0519852377474308,
0.00830558780580759,
0.03332708775997162,
-0.004491726402193308,
-0.02382984757423401,
-0.005954313091933727,
-0.022613191977143288,
-0.051384370774030685,
0.02420876733958721,
0.024885771796107292,
0.0009664326207712293,
-0.0439622700214386,
0.0022184117697179317,
-0.05664270371198654,
0.03636959567666054,
-0.019176285713911057,
0.08965649455785751,
0.005182316061109304,
-0.049131687730550766,
-0.008621198125183582,
0.05092586949467659,
-0.023159265518188477,
-0.08824224025011063,
-0.028950808569788933,
0.02188452146947384,
0.016791371628642082,
0.03954218700528145,
-0.0027017826214432716,
-0.048745568841695786,
0.03900415450334549,
0.02055351994931698,
-0.041181206703186035,
0.05819685384631157,
-0.019251832738518715,
0.06178833916783333,
0.028337620198726654,
0.030009714886546135,
0.06492383033037186,
0.06349565088748932,
-0.012906042858958244,
0.02328881435096264,
-0.041323546320199966,
0.013606589287519455,
-0.047896284610033035,
0.023350367322564125,
-0.03223210200667381,
0.007626290433108807,
-0.024402860552072525,
0.03128728270530701,
-0.024926157668232918,
0.05092358961701393,
0.0015717630740255117,
-0.010416227392852306,
0.00211571017280221,
0.015580510720610619,
-0.030180690810084343,
-0.03334667533636093,
0.04463895037770271,
0.020850982517004013,
0.008997836150228977,
-0.041462693363428116,
-0.006831833627074957,
-0.006978509481996298,
-0.0010216227965429425,
0.025536634027957916,
-0.03589605167508125,
0.04135599732398987,
-0.025820789858698845,
-0.032132528722286224,
-0.001976040191948414,
-0.06302959471940994,
0.018368402495980263,
-0.021594304591417313,
0.013378952629864216,
0.0003906299825757742,
-0.02473801001906395,
-0.007996906526386738,
-0.01910889521241188,
0.006717164535075426,
0.028623811900615692,
-0.06294097006320953,
0.021208258345723152,
-0.001966172596439719,
-0.002937951823696494,
-0.08963026106357574,
-0.025743281468749046,
0.0035741112660616636,
0.0025384367909282446,
-0.002456301124766469,
-0.056234605610370636,
0.018192369490861893,
-0.0004860032058786601,
0.00442454544827342,
-0.0006496331770904362,
0.039766259491443634,
-0.02634667232632637,
-0.0010574589250609279,
-0.004145936109125614,
0.013227978721261024,
0.03887736424803734,
-0.031725138425827026,
-0.00441248482093215,
0.01417591329663992,
0.008219539187848568,
-0.016446338966488838,
0.012247822247445583,
0.0528799407184124,
-0.0409848615527153,
-0.036603569984436035,
-0.024763386696577072,
-0.00980745255947113,
0.01507139764726162,
-0.0293978750705719,
-0.05242256075143814,
0.0031506966333836317,
0.026639332994818687,
0.022906774654984474,
0.000034144923120038584,
-0.03237612545490265,
0.001782233826816082,
0.010035787709057331,
0.023815438151359558,
-0.0007857452728785574,
-0.07704108208417892,
-0.04509563744068146,
0.02065877802670002,
-0.007243575993925333,
0.027369484305381775,
0.014978195540606976,
0.04691935330629349,
0.015412055887281895,
-0.006987948436290026,
0.045878905802965164,
-0.00828796997666359,
-0.013971332460641861,
0.0063187433406710625,
-0.02174251526594162,
0.014488033950328827,
0.01248000655323267,
-0.024650560691952705,
-0.05213484540581703,
-0.048852451145648956,
-0.03727063909173012,
0.03426918387413025,
0.011109850369393826,
0.03929061442613602,
0.021145503968000412,
0.007730202749371529,
-0.05066155269742012,
0.010047413408756256,
-0.02628467231988907,
0.017113065347075462,
-0.0005321548087522388,
0.01996058039367199,
-0.014603272080421448,
0.017150623723864555,
-0.02913491614162922,
0.04292827099561691,
0.00013791861420031637,
0.028862375766038895,
0.024494530633091927,
0.03099890425801277,
0.01723426952958107,
-0.013195516541600227,
0.005718299187719822,
0.06812325865030289,
-0.039921704679727554,
0.034290216863155365,
0.018399428576231003,
-0.004335799720138311,
0.04303092136979103,
0.004725458100438118,
0.004953609313815832,
-0.028129031881690025,
-0.009149344637989998,
-0.009542333893477917,
0.012843847274780273,
0.03601767495274544,
-0.021953126415610313,
0.03973178192973137,
0.015455668792128563,
0.005763013381510973,
0.017934340983629227,
0.024945465847849846,
-0.013248843140900135,
-0.03800470754504204,
0.005030894186347723,
-0.03497948497533798,
-0.015758398920297623,
0.032430365681648254,
-0.007398074958473444,
0.004123822785913944,
0.012380832806229591,
-0.04426771029829979,
0.018558038398623466,
0.0028616981580853462,
0.015668880194425583,
-0.006398961879312992,
0.030028831213712692,
0.02526484802365303,
-0.014569977298378944,
0.009961457923054695,
0.00007727308548055589,
0.11504041403532028,
0.0697922557592392,
0.023962901905179024,
-0.06145789474248886,
0.02944847196340561,
-0.015647506341338158,
0.028231024742126465,
-0.04206962510943413,
-0.014551546424627304,
-0.013381335884332657,
-0.0014998994302004576,
0.017986273393034935,
0.07760865241289139,
0.005340720061212778,
0.009605208411812782,
0.03690290451049805,
-0.011931589804589748,
-0.031205914914608,
0.030003346502780914,
0.0404195673763752,
-0.030096182599663734,
0.010164603590965271,
-0.029987070709466934,
0.01997416466474533,
-0.06705605983734131,
-0.004099095705896616,
-0.03401128202676773,
-0.01844322308897972,
0.051897190511226654,
-0.04275936633348465,
-0.03134958818554878,
-0.0023199862334877253,
-0.0028640367090702057,
-0.007151836063712835,
0.005716509651392698,
0.003485726658254862,
0.03440513461828232,
0.008699772879481316,
0.02503359504044056,
0.012489650398492813,
0.035057518631219864,
0.000933215138502419,
0.00024361176474485546,
-0.01613207720220089,
-0.027928413823246956,
-0.04429566115140915,
0.006123421713709831,
0.06741340458393097,
-0.0018096431158483028,
-0.003914061468094587,
0.007247842848300934,
-0.00016822820180095732,
-0.010727984830737114,
-0.03840811550617218,
-0.0028077946044504642,
-0.011638685129582882,
0.03368262201547623,
0.0011194777907803655,
0.005093326326459646,
0.012502487748861313,
0.025130946189165115,
0.02774086594581604,
0.016383564099669456,
-0.026865728199481964,
0.01270967721939087,
0.009089251980185509,
-0.020291313529014587,
0.026062125340104103,
-0.0016463212668895721,
-0.030397552996873856,
-0.025022273883223534,
-0.006510138977319002,
-0.019525323063135147,
-0.004526449367403984,
0.027152948081493378,
0.0002801604277919978,
0.08773212879896164,
-0.011940826661884785,
0.007159658707678318,
-0.07526233047246933,
-0.073166124522686,
0.01648413948714733,
-0.00824276264756918,
0.0028173711616545916,
0.009459110908210278,
-0.010532666929066181,
0.021523665636777878,
0.06118401885032654,
-0.006417910568416119,
-0.00930747389793396,
0.003535568481311202,
0.02300158143043518,
0.05695571377873421,
0.004422606434673071,
-0.029999202117323875,
-0.012247729115188122,
-0.04546190798282623,
0.044744882732629776,
-0.028836041688919067,
0.007148671895265579,
0.010355256497859955,
-0.0001600613322807476,
0.006394442170858383,
0.050519075244665146,
-0.03696989268064499,
0.0009991396218538284,
-0.02239033952355385,
-0.038906458765268326,
-0.008419196121394634,
0.006571807898581028,
0.015589809976518154,
-0.015782607719302177,
-0.04643262177705765,
-0.023256497457623482,
-0.0025241405237466097,
-0.010370099917054176,
0.03987905755639076,
-0.006351125426590443,
0.014263814315199852,
-0.01263098232448101,
0.016092438250780106,
-0.026675118133425713,
0.008438551798462868,
-0.03485767915844917,
0.004464374389499426,
-0.011888922192156315,
-0.013361619785428047,
-0.00839621014893055,
-0.0063638584688305855,
0.03892509639263153,
-0.032400984317064285,
0.04174588993191719,
0.03401888161897659,
-0.00589308375492692,
-0.023367999121546745,
-0.007580522447824478,
0.032272182404994965,
0.015811024233698845,
0.000717154995072633,
0.009869895875453949,
0.053140219300985336,
-0.036910392343997955,
-0.0207815021276474,
0.013242403976619244,
0.027314789593219757,
0.013713382184505463,
0.036760445684194565,
-0.015405084937810898,
-0.030817238613963127,
0.019342787563800812,
-0.00991150364279747,
-0.025369733572006226,
-0.008265365846455097,
-0.0350073017179966,
0.007694044150412083,
0.008177703246474266,
-0.008228122256696224,
-0.013126688078045845,
0.004827870521694422,
0.03496290743350983,
-0.00336610060185194,
-0.024341199547052383,
0.0203411765396595,
-0.007047104649245739,
0.02426236681640148,
0.028479624539613724,
0.010641384869813919,
-0.013308976776897907,
0.05338098108768463,
0.0205620639026165,
-0.04635227844119072,
0.04792003333568573,
0.0028301365673542023,
-0.015606045722961426,
-0.07581787556409836,
0.0061431461945176125,
-0.0073455930687487125,
-0.021229159086942673,
0.05079955235123634,
-0.043875351548194885,
-0.0023503799457103014,
0.030902473255991936,
-0.047258809208869934,
0.027606863528490067,
-0.059499938040971756,
-0.0074199503287673,
-0.010180938988924026,
-0.0045153298415243626,
-0.01912601664662361,
0.03343247249722481,
0.027718497440218925,
0.06257646530866623,
0.01435838732868433,
-0.011383689939975739,
0.015721308067440987,
-0.017557160928845406,
0.018380947411060333,
0.043712954968214035,
0.01560449879616499,
-0.01577027142047882,
0.02761296182870865,
-0.04050971195101738,
-0.041081298142671585,
0.019667277112603188,
0.00038558588130399585,
0.01680862344801426,
-0.013612516224384308,
0.022839698940515518,
0.007654761429876089,
0.03843306750059128,
0.0212425384670496,
-0.018711712211370468,
0.009871851652860641,
0.0132443243637681,
0.06037644296884537,
0.00443178741261363,
-0.0004506063414737582,
-0.025867128744721413,
0.009853867813944817,
-0.03660527616739273,
-0.05957775563001633,
0.08694397658109665,
0.007033086847513914,
0.009409433230757713,
-0.03139619529247284,
-0.02465227246284485,
0.02531454712152481,
-0.029605640098452568,
0.007665723562240601,
-0.0553387850522995,
0.0024705356918275356,
0.030461687594652176,
-0.00866659078747034,
-0.005313233472406864,
-0.0023310035467147827,
-0.0112754562869668,
-0.07927044481039047,
0.043349385261535645,
0.02902442216873169,
-0.00658376095816493,
-0.06009087711572647,
-0.015465044416487217,
0.004281902220100164,
0.004122617654502392,
0.015135427005589008,
0.009655825793743134,
-0.04468757286667824,
0.014703091233968735,
-0.010021382011473179,
0.019366327673196793,
-0.033065102994441986,
-0.044749412685632706,
-0.021003343164920807,
-0.051582708954811096,
0.03603197634220123,
0.0463767871260643,
0.011548591777682304,
-0.03580895811319351,
0.003643972100690007,
-0.01415474433451891,
0.006204038392752409,
0.0759933739900589,
0.0050109755247831345,
-0.024211302399635315,
-0.02366970293223858,
0.019656524062156677,
0.014326592907309532,
-0.0688411146402359,
-0.03186711668968201,
0.01022428646683693,
-0.000820542627479881,
-0.023555569350719452,
0.02099047414958477,
0.003800286678597331,
0.01314831618219614,
0.004437851719558239,
0.0010935160098597407,
-0.011512125842273235,
-0.010893620550632477,
-0.05249038338661194,
0.055670127272605896,
-0.00029030744917690754,
-0.043260082602500916,
0.05823107436299324,
-0.004179584328085184,
-0.004603345412760973,
0.02464590221643448,
-0.01750039868056774,
-0.03338079899549484,
0.022885259240865707,
-0.012904338538646698,
-0.03957965597510338,
0.007435845676809549,
0.0258457213640213,
0.042231760919094086,
-0.046480096876621246,
-0.007569558452814817,
0.04306449741125107,
-0.03925474360585213,
0.008663359098136425,
0.04077566787600517,
0.016995074227452278,
0.03486602380871773,
0.05076790973544121,
-0.0032876119948923588,
0.03947579115629196,
0.03690618276596069,
0.02577720396220684,
-0.0017231932142749429,
0.026785466820001602,
0.013195717707276344,
0.05047853663563728,
0.0198642760515213,
-0.048865146934986115,
0.014434220269322395,
0.019934553653001785,
0.0229163970798254,
-0.07458396255970001,
0.0012082384200766683,
0.0421019084751606,
-0.02711271308362484,
0.012046342715620995,
0.016288526356220245,
-0.016070611774921417,
0.08382941782474518,
-0.01909005269408226,
0.030354086309671402,
-0.013271686621010303,
-0.005641924683004618,
-0.026928508654236794,
0.044361066073179245,
0.0407281294465065,
0.06312338262796402,
-0.035984158515930176,
-0.01116061583161354,
-0.0567861944437027,
0.006017113570123911,
0.025529062375426292,
-0.0749153196811676,
0.0059901271015405655,
0.017788419499993324,
-0.03149192035198212,
-0.016411233693361282,
-0.022080501541495323,
-0.025633683428168297,
-0.019283002242445946,
-0.024168524891138077,
0.047402456402778625,
0.025261158123612404,
0.028226712718605995,
0.010318112559616566,
-0.0035778756719082594,
0.03596106171607971,
-0.05458196625113487,
-0.005962795577943325,
0.0032525290735065937,
0.01766335405409336,
-0.01828845590353012,
0.005022530443966389
] |
<p>I've searched for it but I only found contradicting answers from "scientists":</p>
<p>Dr. David Balson, Ph.D. states: "<a href="http://www.physlink.com/education/askexperts/ae380.cfm" rel="nofollow">entropy in a system can never be equal to zero</a>".</p>
<p>Sam Bowen does not refutes the following affirmation: "<a href="http://www.newton.dep.anl.gov/newton/askasci/1993/chem/CHEM001.HTM" rel="nofollow">It is know[n] that entropy is zero when a pure crystalline substance is at absolute zero</a>". He says there's residual motion in particles, but he doesn't say clearly that 0 entropy isn't possible.</p>
<p>I this <a href="http://www.physicsforums.com/showthread.php?t=474384" rel="nofollow">link</a> is a long discussion about that, it isn't really conclusive, but most people seem to agree that entropy can be zero.</p>
<p>I'm not very receptive to the idea of zero entropy.</p>
| 9,357 |
[
-0.001811093301512301,
-0.01897396333515644,
-0.007066670339554548,
-0.041366077959537506,
0.021321430802345276,
-0.005645953584462404,
-0.03421596810221672,
0.035786401480436325,
-0.05189919471740723,
-0.040802374482154846,
0.0050455378368496895,
0.031830575317144394,
0.0011269422248005867,
0.028188155964016914,
0.012373445555567741,
-0.02359030209481716,
-0.007965929806232452,
-0.01771683804690838,
0.002378694247454405,
-0.009134947322309017,
-0.0036181022878736258,
-0.0022927464451640844,
0.001862838165834546,
0.0019415989518165588,
-0.035144150257110596,
0.022054266184568405,
0.023294800892472267,
0.015375971794128418,
0.0014305200893431902,
0.0566442534327507,
0.013387162238359451,
-0.02845078706741333,
-0.007612581364810467,
0.020441671833395958,
0.04052773490548134,
-0.019025057554244995,
-0.015759535133838654,
-0.01839407905936241,
-0.009942391887307167,
0.018302109092473984,
-0.05427413061261177,
-0.029750173911452293,
0.0008880659588612616,
0.01431191060692072,
-0.0363813191652298,
0.00011519954568939283,
0.039501264691352844,
0.006722629070281982,
0.06791020184755325,
-0.06101421266794205,
0.04395595192909241,
-0.013123633340001106,
0.04655957221984863,
0.009792889468371868,
0.010653011500835419,
0.006695864722132683,
0.05564044788479805,
0.06358833611011505,
-0.04982592537999153,
-0.06534265726804733,
-0.017960190773010254,
0.0002948784385807812,
-0.003876463044434786,
-0.0022037005983293056,
-0.026018626987934113,
0.03978708013892174,
-0.009672287851572037,
-0.026766087859869003,
0.05754579231142998,
0.03408530354499817,
0.006019977852702141,
-0.0100658955052495,
0.032074328511953354,
-0.007338237017393112,
0.025564441457390785,
-0.03234320878982544,
0.019083663821220398,
-0.025830883532762527,
0.016963781788945198,
0.08749503642320633,
-0.030536875128746033,
-0.017851045355200768,
0.031222093850374222,
0.056332748383283615,
0.009698169305920601,
-0.027024472132325172,
0.07348575443029404,
-0.03410160541534424,
0.02139768749475479,
0.07266122847795486,
0.011811874806880951,
0.02042027935385704,
0.03163504600524902,
0.01612262614071369,
-0.04089571163058281,
0.04716365784406662,
0.0083612110465765,
0.08540377765893936,
-0.03085252270102501,
-0.04053649306297302,
0.02252194657921791,
0.006579063832759857,
0.03412550687789917,
0.05145127698779106,
-0.023940663784742355,
0.0066278837621212006,
-0.02821926213800907,
0.0241936594247818,
0.002164289355278015,
-0.004432051442563534,
-0.010990259237587452,
0.004709901288151741,
0.021899854764342308,
-0.011814147233963013,
-0.009249324910342693,
-0.025520017370581627,
0.01075785979628563,
-0.02067967876791954,
0.06904739886522293,
0.05709231644868851,
0.017434094101190567,
-0.014804213307797909,
-0.0056392597034573555,
-0.008155780844390392,
-0.08615917712450027,
-0.01015124935656786,
0.024913644418120384,
-0.006733772810548544,
-0.03012778051197529,
0.034889642149209976,
-0.006785466801375151,
0.00625703576952219,
0.018137453123927116,
-0.02101755701005459,
0.05170796439051628,
-0.02143131196498871,
-0.082792729139328,
-0.06406454741954803,
0.05416300892829895,
-0.0034432667307555676,
-0.04538983106613159,
-0.04913603514432907,
-0.0099358344450593,
-0.0020881660748273134,
0.058741625398397446,
-0.0028391708619892597,
0.026109952479600906,
-0.019661059603095055,
0.025049500167369843,
0.002625284483656287,
-0.0036486785393208265,
-0.006191158201545477,
0.02180420234799385,
-0.057797871530056,
-0.0075389062985777855,
-0.04842529073357582,
0.035056859254837036,
0.053667038679122925,
-0.01676878146827221,
-0.027814267203211784,
-0.011258469894528389,
-0.023296745494008064,
0.01124618761241436,
-0.003877395996823907,
-0.020128052681684494,
-0.019651705399155617,
0.09206419438123703,
-0.0026691770181059837,
0.006465546786785126,
0.010613330639898777,
0.03521982580423355,
0.02769852988421917,
0.014605886302888393,
0.0027330194134265184,
0.044382497668266296,
-0.03743685409426689,
-0.03981000930070877,
-0.0450100377202034,
-0.002200388116762042,
0.019015440717339516,
-0.04277995601296425,
0.005093955900520086,
0.03154381737112999,
-0.004932359792292118,
0.005085867363959551,
0.01574517972767353,
-0.011678059585392475,
0.008099903352558613,
-0.00007027963147265837,
-0.022739792242646217,
-0.02179730497300625,
-0.10300635546445847,
0.005131294019520283,
0.0028870797250419855,
-0.008868314325809479,
0.023863734677433968,
0.02722102403640747,
0.023438023403286934,
-0.046364206820726395,
-0.018269654363393784,
-0.02589986100792885,
0.019745871424674988,
-0.018910758197307587,
-0.02263312228024006,
0.004130840767174959,
0.046438682824373245,
0.06591788679361343,
-0.01457090862095356,
0.013567604124546051,
0.028970230370759964,
-0.054495807737112045,
-0.023089541122317314,
-0.005679626949131489,
0.003876808797940612,
-0.007332187611609697,
-0.005665501579642296,
0.03415728732943535,
0.0071037509478628635,
-0.0014465909916907549,
0.0005178852006793022,
0.0010893091093748808,
0.07399076968431473,
0.030446115881204605,
0.032766155898571014,
-0.0406738817691803,
0.018597356975078583,
0.016847891733050346,
-0.010275550186634064,
0.00024632486747577786,
-0.017953936010599136,
-0.05543571338057518,
-0.015757635235786438,
0.0361856073141098,
0.03544851019978523,
-0.036545880138874054,
0.01614527590572834,
0.02014326862990856,
0.025887252762913704,
-0.0025503523647785187,
-0.008405393920838833,
-0.008985939435660839,
-0.04118882492184639,
0.009352314285933971,
-0.021913107484579086,
0.02040530927479267,
0.045449964702129364,
0.05090522766113281,
-0.007413769140839577,
0.03315535560250282,
-0.005038153380155563,
-0.02003108151257038,
0.029269026592373848,
0.016631804406642914,
-0.01019512303173542,
0.015132022090256214,
-0.03388224169611931,
0.0021851263009011745,
-0.00007330075459321961,
0.028161972761154175,
-0.014108603820204735,
0.013969178311526775,
0.021874411031603813,
-0.029677851125597954,
0.0038342864718288183,
-0.02805708721280098,
0.0017683709738776088,
-0.019635554403066635,
-0.020327575504779816,
-0.0022221554536372423,
-0.025551479309797287,
-0.015933655202388763,
0.006601925007998943,
0.037641044706106186,
-0.028518658131361008,
-0.017718490213155746,
0.047655653208494186,
0.008603522554039955,
0.011850737035274506,
-0.0367475301027298,
-0.019874772056937218,
0.005412118975073099,
-0.031112296506762505,
-0.008356024511158466,
0.057364609092473984,
-0.04445333033800125,
0.025144241750240326,
-0.006896274164319038,
-0.03728792443871498,
0.03646502643823624,
-0.01752530224621296,
0.04267832636833191,
0.019626427441835403,
-0.04617727920413017,
-0.06761478632688522,
-0.00439134705811739,
-0.01699819229543209,
0.00006976502481848001,
-0.04825131967663765,
0.003640664042904973,
0.03509976714849472,
-0.03948751837015152,
-0.05033903196454048,
-0.0020674006082117558,
-0.05738505721092224,
-0.045427966862916946,
0.0016010875115171075,
0.008591987192630768,
0.009769348427653313,
-0.011898055672645569,
0.027187002822756767,
0.04232725128531456,
-0.03569444268941879,
-0.027015505358576775,
-0.02516983263194561,
-0.0825345441699028,
0.03711109608411789,
-0.024643823504447937,
0.0238883588463068,
-0.01671067625284195,
-0.03965608775615692,
0.06277401745319366,
0.027342496439814568,
-0.04132033884525299,
0.016522014513611794,
-0.00032071099849417806,
0.00011493585770949721,
-0.017214130610227585,
0.005493467673659325,
-0.007460932247340679,
0.006274541839957237,
0.017930226400494576,
-0.004072555806487799,
0.05894261598587036,
-0.00547234620898962,
-0.0032492908649146557,
-0.027172887697815895,
0.027104152366518974,
0.030178481712937355,
-0.00010312259837519377,
0.01941899210214615,
0.0276650283485651,
-0.024591274559497833,
0.022619854658842087,
0.013939427211880684,
0.04208901897072792,
0.01744217611849308,
-0.06855760514736176,
0.07384428381919861,
0.0144277885556221,
0.030856359750032425,
-0.047404464334249496,
0.028147414326667786,
-0.03062516078352928,
0.025415055453777313,
0.024928906932473183,
0.02757357433438301,
0.027520135045051575,
0.03411741927266121,
0.0018747705034911633,
0.010966992937028408,
0.033649493008852005,
-0.014672726392745972,
-0.0017904425039887428,
-0.010975317098200321,
0.012743513099849224,
0.009125666692852974,
0.0009422620641998947,
0.002931122900918126,
0.030786842107772827,
0.0022750128991901875,
0.048450857400894165,
-0.00769457221031189,
-0.028447819873690605,
0.004426684230566025,
-0.053125202655792236,
0.009403443895280361,
-0.025432195514440536,
0.03763503581285477,
-0.007648052182048559,
0.06368580460548401,
0.013296840712428093,
0.023213721811771393,
0.008230477571487427,
0.012732524424791336,
-0.10302331298589706,
0.05698065459728241,
-0.04477018117904663,
-0.030429832637310028,
-0.009542455896735191,
0.007458322215825319,
0.009495854377746582,
-0.018035266548395157,
-0.031134970486164093,
0.0019918051548302174,
0.03219801187515259,
-0.06547659635543823,
-0.023288177326321602,
-0.031872257590293884,
-0.000040336566598853096,
-0.007682086434215307,
0.03704381734132767,
0.023809585720300674,
-0.0194560419768095,
0.02477533370256424,
0.019245443865656853,
-0.02244877628982067,
0.009909807704389095,
-0.00198725494556129,
0.023083990439772606,
0.025621840730309486,
0.04463852196931839,
0.026456119492650032,
0.007208454888314009,
0.02235456369817257,
0.014065057039260864,
0.007927922531962395,
0.030064569786190987,
-0.002973051741719246,
-0.009023225866258144,
-0.028446316719055176,
-0.014791633002460003,
-0.009961789473891258,
-0.019622711464762688,
0.050989098846912384,
-0.002739071613177657,
0.032665420323610306,
0.0020477911457419395,
0.019053826108574867,
-0.02095974050462246,
0.030446207150816917,
0.05318731442093849,
-0.005151011515408754,
-0.023863229900598526,
-0.011537726037204266,
-0.03878399357199669,
0.0027400495018810034,
-0.0326545313000679,
0.02804972045123577,
0.017581095919013023,
-0.011001904495060444,
-0.03880320489406586,
-0.033054038882255554,
0.03306109830737114,
-0.0058773416094481945,
-0.008089922368526459,
-0.014732938259840012,
0.04978043958544731,
-0.010263769887387753,
0.010944795794785023,
-0.0029768976382911205,
0.015327143482863903,
0.0215385053306818,
0.0179801806807518,
-0.014814335852861404,
-0.060503456741571426,
0.004613450262695551,
0.030873235315084457,
0.07193993777036667,
-0.015602337196469307,
0.0352967344224453,
-0.03738681599497795,
-0.043169353157281876,
0.039278630167245865,
-0.02208097279071808,
0.01992005482316017,
-0.01835564896464348,
0.01768862083554268,
0.02514239028096199,
-0.030924897640943527,
0.01798933371901512,
-0.0068567413836717606,
0.015953481197357178,
0.02423420548439026,
0.010362819768488407,
-0.0066928984597325325,
-0.023083701729774475,
-0.005671179853379726,
0.010507871396839619,
0.05994858220219612,
-0.027389168739318848,
0.03465535119175911,
0.0325971320271492,
0.006018984131515026,
-0.012531026266515255,
-0.08832786232233047,
0.010372240096330643,
-0.0176682248711586,
-0.014094335027039051,
0.005461785942316055,
-0.04870432987809181,
-0.06255293637514114,
0.030087249353528023,
-0.011238586157560349,
-0.0068280864506959915,
0.00886286050081253,
-0.053381118923425674,
0.0373401865363121,
0.017826000228524208,
-0.011457495391368866,
0.034405771642923355,
0.05255618318915367,
-0.012820339761674404,
-0.00842673797160387,
-0.021975761279463768,
0.028786849230527878,
-0.036515459418296814,
0.009303958155214787,
-0.0600891076028347,
0.03462531790137291,
-0.03933754563331604,
0.03985917940735817,
0.013971216045320034,
0.02142975479364395,
0.015965575352311134,
-0.042089711874723434,
-0.015618525445461273,
0.008208876475691795,
0.023348664864897728,
0.03728716820478439,
-0.00037682903348468244,
0.020774535834789276,
-0.03153340891003609,
-0.032690998166799545,
0.0062832036055624485,
0.0006963383639231324,
-0.01964549720287323,
0.06646587699651718,
-0.017691655084490776,
0.018827004358172417,
-0.030723124742507935,
-0.016468284651637077,
-0.010950426571071148,
-0.052793655544519424,
0.05214953422546387,
-0.03635222837328911,
0.0007753551471978426,
0.016668429598212242,
-0.07014917582273483,
-0.01806020550429821,
0.004520497750490904,
-0.0015237554907798767,
0.04108107462525368,
-0.049981869757175446,
0.020086582750082016,
0.0064764260314404964,
0.007710948120802641,
-0.07264336943626404,
-0.05870983749628067,
0.014656782150268555,
0.01669585146009922,
-0.04451649636030197,
-0.04214004427194595,
-0.00984693318605423,
-0.02876189537346363,
-0.012136279605329037,
-0.007054963614791632,
0.04513349011540413,
0.009759253822267056,
-0.008521816693246365,
0.06280489265918732,
0.018331430852413177,
0.04254166781902313,
0.02227584831416607,
-0.036138810217380524,
0.014499844051897526,
-0.0012489998480305076,
0.004867079202085733,
0.026338724419474602,
0.04231884330511093,
-0.013828209601342678,
-0.015797048807144165,
0.026340508833527565,
-0.024673961102962494,
0.0609622448682785,
0.011881534941494465,
-0.015086788684129715,
0.0049083298072218895,
-0.009357251226902008,
-0.0165068618953228,
-0.006257341708987951,
0.030081816017627716,
-0.008788767270743847,
0.021862920373678207,
-0.023575501516461372,
-0.010746514424681664,
-0.010047085583209991,
-0.05720528960227966,
-0.012713946402072906,
-0.006139461882412434,
0.00281360000371933,
-0.007019923534244299,
0.06328324973583221,
0.04218391701579094,
-0.04529470577836037,
-0.00798275787383318,
-0.007538453675806522,
0.020714392885565758,
0.006989463232457638,
0.031383123248815536,
-0.030037933960556984,
-0.0004593299818225205,
-0.0169130377471447,
-0.03543056175112724,
-0.03102153353393078,
-0.0018703817622736096,
0.047027405351400375,
-0.021135015413165092,
0.044911958277225494,
0.018246598541736603,
0.014893769286572933,
-0.015186388976871967,
-0.01131526194512844,
0.024140961468219757,
0.04181767627596855,
0.020575666800141335,
0.02018926292657852,
-0.01819237880408764,
-0.029575694352388382,
0.012443804182112217,
0.04018428176641464,
-0.03455682098865509,
0.01946137100458145,
0.005300949327647686,
-0.0009713198523968458,
0.033638712018728256,
-0.00902832206338644,
-0.036918118596076965,
0.04018384963274002,
-0.023383431136608124,
0.07480398565530777,
0.041599374264478683,
-0.04098706319928169,
0.05857624486088753,
-0.025924669578671455,
0.023731067776679993,
-0.03611746430397034,
-0.043274860829114914,
-0.027527356520295143,
0.024049781262874603,
-0.025646349415183067,
0.0022660396061837673,
-0.009580081328749657,
-0.028778405860066414,
-0.004210565239191055,
0.04026399180293083,
0.013886270113289356,
0.01996617577970028,
-0.08025715500116348,
-0.0026550411712378263,
-0.02038753777742386,
-0.04446759819984436,
0.011102437973022461,
-0.000058088753576157615,
-0.02494777739048004,
0.00192157959099859,
-0.017034530639648438,
0.040857404470443726,
0.038569625467061996,
0.02352732978761196,
0.01015414111316204,
0.051749810576438904,
-0.00343554955907166,
0.05047645419836044,
-0.03317412734031677,
0.03920399025082588,
0.14918269217014313,
0.041268736124038696,
0.023771757259964943,
-0.0385599359869957,
-0.008027770556509495,
-0.010873634368181229,
0.015252427197992802,
-0.004712988156825304,
0.05653427913784981,
-0.007903470657765865,
0.02695896290242672,
0.02057023160159588,
0.06495924293994904,
-0.00015084611368365586,
-0.004815217107534409,
0.03477584198117256,
-0.04897921159863472,
-0.02693261206150055,
-0.02001737803220749,
0.05216047167778015,
-0.0018184719374403358,
-0.014969483949244022,
-0.040782660245895386,
0.004232638981193304,
0.003933056723326445,
0.0009096377762034535,
-0.01753244921565056,
-0.06677911430597305,
-0.011470995843410492,
0.007015630137175322,
-0.0527852363884449,
-0.010216751135885715,
0.0011465490097180009,
-0.0054543339647352695,
-0.05211273208260536,
0.0044655147939920425,
0.030120350420475006,
0.005461891181766987,
-0.026141803711652756,
0.048504527658224106,
0.03357873111963272,
0.02009066753089428,
0.03798079118132591,
-0.0015842994907870889,
-0.04154509678483009,
-0.02206510305404663,
-0.02128128707408905,
0.019004330039024353,
-0.04321572184562683,
-0.016779398545622826,
0.0016451908741146326,
-0.038839735090732574,
-0.013564353808760643,
-0.048913415521383286,
0.001489897957071662,
0.009638440795242786,
0.04744904115796089,
-0.0014124168083071709,
-0.056073226034641266,
0.0015278952196240425,
0.005617769900709391,
-0.02416079305112362,
0.02440625987946987,
-0.00381007743999362,
-0.008896224200725555,
-0.01964961737394333,
-0.012619120068848133,
0.0282388087362051,
-0.02683977596461773,
-0.0022117949556559324,
-0.013221733272075653,
-0.011488348245620728,
-0.07410471141338348,
0.006920482963323593,
-0.010819482617080212,
0.00965701974928379,
0.04555538669228554,
0.02036472223699093,
-0.0036625443026423454,
0.008157843723893166,
-0.02236105687916279,
0.02754940837621689,
-0.020199136808514595,
0.00399281270802021,
-0.00006117189332144335,
0.01589519903063774,
0.02967122197151184,
0.048009809106588364,
-0.03440185263752937,
-0.009628265164792538,
0.04392097145318985,
0.00948100071400404,
0.02350238524377346,
-0.006373567506670952,
-0.008574694395065308,
0.031392473727464676,
-0.06286590546369553,
0.0318288654088974,
0.028083158656954765,
0.02503702975809574,
0.03333144634962082,
0.021409502252936363,
-0.0026889301370829344,
0.036390870809555054,
-0.0037619685754179955,
0.0007883719517849386,
0.006628226954489946,
-0.009323233738541603,
-0.03680272027850151,
0.0486825555562973,
-0.0033182089682668447,
-0.01193428784608841,
-0.06343849003314972,
-0.05543297901749611,
0.030766742303967476,
-0.017153317108750343,
0.03480565547943115,
-0.027838632464408875,
-0.014479569159448147,
-0.03272588923573494,
0.012612025253474712,
-0.02958107925951481,
-0.036520931869745255,
-0.022895539179444313,
0.0015713493339717388,
0.021008089184761047,
0.046032585203647614,
-0.02416825480759144,
0.01179775781929493,
-0.012066224589943886,
-0.026255261152982712,
0.05377747118473053,
0.03377464786171913,
-0.028180699795484543,
-0.023235006257891655,
0.005450492724776268,
0.012506318278610706,
0.05024845525622368,
-0.0451437309384346,
-0.015795493498444557,
0.05709568038582802,
-0.04105570539832115,
-0.07618121057748795,
-0.005688411183655262,
-0.011451450176537037,
-0.01568002998828888,
0.014914787374436855,
-0.028073294088244438,
-0.024817803874611855,
0.059889473021030426,
-0.012145943008363247,
0.03575216233730316,
-0.01654481701552868,
-0.006901916582137346,
-0.04530829191207886,
-0.010100804269313812,
0.0002920906408689916,
-0.03971490636467934,
-0.029179640114307404,
0.03815879672765732,
0.006301208399236202,
-0.00035967264557257295,
-0.024324625730514526,
-0.004342411644756794,
-0.020929530262947083,
-0.019481291994452477,
0.04442410543560982,
-0.01466652937233448,
0.0022538062185049057,
0.05364435538649559,
-0.03670249506831169,
0.04916542023420334,
0.02415299415588379,
0.022370075806975365,
-0.1055033728480339,
0.029892699792981148,
0.0019967094995081425,
0.008438898250460625,
0.015184333547949791,
-0.03073354996740818,
0.02610616944730282,
0.0497964508831501,
-0.09670941531658173,
0.01835632137954235,
-0.030993402004241943,
-0.03906584531068802,
-0.012058734893798828,
0.019048824906349182,
-0.027106955647468567,
0.04588868096470833,
0.04386034235358238,
0.05811591073870659,
0.0029246313497424126,
0.016757329925894737,
-0.03840547055006027,
0.002463841810822487,
-0.004591349512338638,
0.037028804421424866,
-0.004492765758186579,
0.023894358426332474,
0.03352751582860947,
-0.04227128624916077,
-0.02194535918533802,
0.015459774062037468,
-0.048233360052108765,
-0.0036128514911979437,
0.005199027247726917,
0.020180081948637962,
-0.009043308906257153,
0.03430679813027382,
0.027519484981894493,
0.0015130876563489437,
-0.014682893641293049,
0.024533407762646675,
0.009676900692284107,
0.052380919456481934,
-0.0039489977061748505,
0.012843753211200237,
-0.00922410562634468,
-0.0144402040168643,
-0.036206234246492386,
0.022068370133638382,
-0.04056362807750702,
0.006172901019454002,
0.025845037773251534,
0.01873740740120411,
0.005739190615713596,
0.003088627941906452,
0.00779286865144968,
-0.05206996947526932,
0.0032150247134268284,
-0.00901838205754757,
0.034757182002067566,
-0.02136622741818428,
0.005176822189241648,
0.008020116947591305,
-0.014510520733892918,
0.03333282470703125,
-0.019235501065850258,
-0.021236056461930275,
-0.0628088191151619,
-0.0189292561262846,
0.005497368052601814,
0.01644289866089821,
-0.004184597637504339,
-0.0713830441236496,
-0.035118427127599716,
0.04462837427854538,
0.039135441184043884,
0.03869042173027992,
0.0009551149560138583,
-0.04463927075266838,
-0.04375996068120003,
-0.0599069818854332,
0.02592930756509304,
0.0038754926063120365,
0.046974699944257736,
-0.05031201243400574,
-0.022434603422880173,
-0.012213924899697304,
0.011731356382369995,
0.03601588308811188,
-0.03912695124745369,
0.01596422865986824,
0.016389762982726097,
-0.0048547349870204926,
0.04042802006006241,
-0.0029273792169988155,
-0.004032235126942396,
-0.02349693514406681,
-0.06460364162921906,
0.0031020769383758307,
0.0009755138889886439,
-0.04061809927225113,
-0.002897834638133645,
0.053741250187158585,
-0.05055873841047287,
0.024270134046673775,
-0.012170613743364811,
-0.022668160498142242,
0.07095322757959366,
0.018037039786577225,
-0.019990025088191032,
0.03599041327834129,
-0.058168500661849976,
0.031579580157995224,
0.042448222637176514,
0.02229924127459526,
-0.015159363858401775,
0.04694394767284393,
-0.0042333779856562614,
-0.0055935801938176155,
-0.009863041341304779,
-0.010123911313712597,
0.04885405674576759,
-0.028096269816160202,
-0.00841117650270462,
0.03278474137187004,
-0.0466594360768795,
0.01044904999434948,
0.019492685794830322,
0.009504511952400208,
0.05037536844611168,
0.0057754782028496265,
0.02703404612839222,
-0.01102445088326931,
0.010549514554440975,
0.0055913785472512245,
0.06306799501180649,
0.03363250568509102,
-0.019077442586421967,
0.035461027175188065,
0.029355313628911972,
-0.014350888319313526,
0.0126589210703969,
0.022011324763298035,
0.015844088047742844,
-0.0354025661945343,
-0.015217567794024944,
0.019583100453019142,
-0.03500007465481758,
-0.0017615797696635127,
0.0181210208684206,
-0.011939801275730133,
0.07013028860092163,
-0.007395000662654638,
0.013661149889230728,
-0.017633965238928795,
-0.004238575231283903,
-0.029389068484306335,
0.002092071110382676,
-0.01825813390314579,
0.04474657028913498,
-0.027939671650528908,
-0.01948850043118,
-0.006479558534920216,
0.012206804938614368,
0.024090513586997986,
-0.05639342591166496,
0.003449748968705535,
-0.033076848834753036,
0.003401733236387372,
-0.04509584233164787,
-0.0027463312726467848,
-0.018120834603905678,
-0.02485724352300167,
0.026620404794812202,
0.03035336174070835,
0.007863438688218594,
0.004110661800950766,
-0.04186224192380905,
-0.023898199200630188,
0.06082700937986374,
-0.0038539008237421513,
0.009881701320409775,
-0.03182648494839668,
0.04059837386012077,
-0.04882181063294411,
-0.010342287831008434
] |
<p>Gravitation force is always attractive.</p>
<p>Now assume(not a practical one): I took our Earth in my hand and started shaking up and down. This will create a disturbance in space-time warp and it moves like a wave outward direction. So when the crest part of this disturbance comes in touch with another mass, it should carry that mass with it and start moving away from Earth. It was visible because I used a very massive object like Earth. Though it is not visible it should be true with low mass objects too? So is gravitation field is always attractive?</p>
| 9,358 |
[
-0.0032968628220260143,
-0.016857698559761047,
-0.024337030947208405,
-0.004848912823945284,
0.03223521634936333,
-0.001522140228189528,
-0.034122858196496964,
-0.003536127507686615,
0.01166707742959261,
-0.04762555658817291,
0.017821719869971275,
0.005517805926501751,
0.06827317923307419,
0.0049880631268024445,
0.009858562611043453,
0.011595671996474266,
0.010226722806692123,
-0.00409512547776103,
-0.043317556381225586,
-0.019376860931515694,
-0.018940264359116554,
0.033537521958351135,
0.0021165646612644196,
-0.01974990777671337,
-0.01922839693725109,
0.02891589142382145,
0.029464827850461006,
0.018192287534475327,
0.014996951445937157,
0.04631743207573891,
-0.0014322265051305294,
0.006879235152155161,
-0.01693515107035637,
0.04212832450866699,
0.05573546513915062,
0.033717717975378036,
-0.04154051095247269,
0.007177029270678759,
0.0034338710829615593,
-0.017666276544332504,
-0.04092744365334511,
-0.030333342030644417,
0.009955184534192085,
0.07820567488670349,
0.008565474301576614,
0.02884570322930813,
0.024350665509700775,
0.011825019493699074,
0.07609289884567261,
-0.04349152743816376,
0.043772537261247635,
0.001737628597766161,
0.0446254201233387,
0.00017469654267188162,
0.030661629512906075,
-0.0797506645321846,
0.06691265106201172,
0.022502440959215164,
-0.028376730158925056,
-0.01984504610300064,
0.008232185617089272,
0.01504372525960207,
-0.030351221561431885,
-0.054270174354314804,
0.011750771664083004,
0.04716849327087402,
0.005540225189179182,
0.017204292118549347,
0.028965765610337257,
-0.0025722321588546038,
-0.00033178215380758047,
0.007303467020392418,
0.030585134401917458,
0.006582688540220261,
-0.02099931240081787,
-0.02148500084877014,
0.01770951971411705,
0.012008101679384708,
0.030599769204854965,
0.052014708518981934,
0.022943422198295593,
0.020567886531352997,
0.03248674049973488,
0.025097236037254333,
0.0389491468667984,
-0.011107162572443485,
0.06070815026760101,
-0.0088774673640728,
0.0075110746547579765,
0.06364848464727402,
-0.02454373426735401,
0.00879127811640501,
0.014120975509285927,
-0.007600757293403149,
-0.041668884456157684,
-0.022424262017011642,
0.013970034196972847,
0.033273156732320786,
0.03148193284869194,
-0.004104176070541143,
-0.03627381846308708,
-0.005792191717773676,
-0.0035230896901339293,
0.07328086346387863,
0.03324134647846222,
-0.009696000255644321,
-0.052060164511203766,
-0.0034343386068940163,
-0.02529301308095455,
-0.02710510976612568,
-0.02755962871015072,
-0.013928884640336037,
0.014494727365672588,
-0.05351538583636284,
0.019507134333252907,
-0.028758546337485313,
0.007853173650801182,
-0.020222298800945282,
0.023499242961406708,
0.06345687061548233,
0.04137700796127319,
-0.014343347400426865,
0.027524521574378014,
-0.035386957228183746,
-0.0445079430937767,
0.003064459189772606,
0.06549575924873352,
-0.0303079504519701,
-0.016109636053442955,
0.041217442601919174,
0.0009497481514699757,
-0.014705264940857887,
-0.030747907236218452,
-0.010867677628993988,
0.049036696553230286,
-0.010507427155971527,
-0.10930582880973816,
-0.037141744047403336,
0.06813235580921173,
-0.019909406080842018,
0.011747506447136402,
-0.03779483959078789,
-0.04156997427344322,
0.018658053129911423,
0.07996402680873871,
0.010849968530237675,
-0.01077654492110014,
0.0021623745560646057,
0.05366087704896927,
-0.010297657921910286,
-0.02525237388908863,
-0.03831712156534195,
-0.0047384765930473804,
-0.07477439939975739,
-0.022323347628116608,
-0.08083099871873856,
0.006904715672135353,
0.028201155364513397,
0.021630965173244476,
-0.015061885118484497,
0.04793187975883484,
-0.021421359851956367,
0.021928757429122925,
0.0011565271997824311,
-0.021751251071691513,
-0.01125003956258297,
0.07249388843774796,
-0.017613958567380905,
0.013946215622127056,
0.06145510450005531,
0.01714399643242359,
0.021309630945324898,
0.011627661064267159,
-0.0043852683156728745,
-0.027761539444327354,
-0.04198605567216873,
0.000526799529325217,
-0.002365320920944214,
-0.02005797252058983,
-0.015329624526202679,
-0.026409661397337914,
-0.03848071023821831,
-0.026817023754119873,
-0.004279038403183222,
-0.017238106578588486,
0.036776427179574966,
0.025221465155482292,
0.004347164183855057,
-0.011695226654410362,
-0.04553377255797386,
-0.030090032145380974,
-0.056941576302051544,
0.03295256569981575,
-0.023142093792557716,
0.0029156096279621124,
-0.00019677843374665827,
0.03097253479063511,
-0.00531406095251441,
-0.01991279236972332,
0.025287047028541565,
0.03101346455514431,
0.0020550470799207687,
-0.03410850092768669,
-0.01014779694378376,
0.004943531472235918,
0.05897294357419014,
-0.0033049245830625296,
0.011026471853256226,
0.01429027784615755,
-0.025487028062343597,
-0.018321098759770393,
0.028062885627150536,
0.006082735024392605,
0.02827330119907856,
-0.007806775625795126,
0.012412452138960361,
0.006130778696388006,
0.02276650071144104,
-0.010312621481716633,
0.025411147624254227,
-0.05663619190454483,
0.0755370706319809,
0.05754056200385094,
0.02003560960292816,
-0.003969341516494751,
0.04289832338690758,
0.030852017924189568,
0.02783944644033909,
-0.015047652646899223,
-0.007257460150867701,
-0.05098787322640419,
-0.015578375197947025,
0.025477809831500053,
0.060992222279310226,
-0.025497065857052803,
0.03778337314724922,
0.046376489102840424,
0.04029712453484535,
0.019363967701792717,
0.0022369585931301117,
0.00024430686607956886,
-0.031197385862469673,
0.046606842428445816,
-0.013382221572101116,
0.04780052974820137,
0.01501048170030117,
0.03800629451870918,
0.03738342598080635,
-0.038787391036748886,
0.03216928616166115,
-0.03286818414926529,
0.01073058508336544,
0.0035032460000365973,
0.03249260410666466,
0.009021914564073086,
-0.029004745185375214,
0.014837049879133701,
-0.023849744349718094,
0.00363540998660028,
0.011141253635287285,
-0.014467733912169933,
-0.027778835967183113,
-0.07365153729915619,
-0.011443357914686203,
-0.005776354111731052,
-0.011212966404855251,
-0.007233032025396824,
-0.03179798275232315,
0.026221638545393944,
-0.06584610044956207,
-0.020014232024550438,
-0.0011446712305769324,
0.019258994609117508,
-0.02482244186103344,
0.019880972802639008,
0.05242297425866127,
0.03528212383389473,
0.051935017108917236,
-0.05682344734668732,
-0.01726323924958706,
0.002390985144302249,
0.012539387680590153,
-0.019255852326750755,
0.01910974271595478,
-0.07512291520833969,
0.01759818010032177,
-0.055568743497133255,
-0.057893384248018265,
0.09335125982761383,
-0.024929141625761986,
-0.00914777535945177,
0.006331383716315031,
0.022335635498166084,
-0.05857254937291145,
-0.021604660898447037,
-0.04648783802986145,
-0.024344181641936302,
-0.045710910111665726,
0.001457572216168046,
0.043423205614089966,
0.04118838161230087,
-0.024221213534474373,
0.0020382562652230263,
-0.029695184901356697,
-0.03643110767006874,
0.016020897775888443,
0.012339979410171509,
-0.016490362584590912,
-0.031099958345294,
0.030604884028434753,
-0.03791719675064087,
-0.030727630481123924,
0.032690487802028656,
-0.056131891906261444,
-0.042010724544525146,
0.0007849041139706969,
-0.0014720492763444781,
0.06851905584335327,
-0.0017727692611515522,
-0.03843047842383385,
0.07488322257995605,
0.05090302228927612,
-0.02187458984553814,
-0.02832009084522724,
-0.03342554345726967,
0.019869044423103333,
0.006999064702540636,
0.02733561396598816,
0.034575674682855606,
0.02841527946293354,
-0.03134336695075035,
0.027614396065473557,
0.0024818654637783766,
-0.015019061043858528,
0.022246193140745163,
-0.02714809589087963,
0.017483731731772423,
-0.0037127132527530193,
-0.011388074606657028,
0.02521420270204544,
0.02290012501180172,
-0.06281478703022003,
0.030849875882267952,
0.008068581111729145,
0.03372704237699509,
-0.009609594941139221,
-0.036471541970968246,
0.044289566576480865,
0.012608973309397697,
0.012327303178608418,
0.004792241379618645,
0.049556806683540344,
0.0049822027795016766,
0.006531813181936741,
0.029728783294558525,
-0.04051399603486061,
0.052114952355623245,
0.0136032709851861,
0.0067961630411446095,
0.03439144045114517,
0.03209229186177254,
-0.016379687935113907,
-0.03718707337975502,
0.008806359022855759,
0.012294777669012547,
0.05119233950972557,
-0.026906022801995277,
0.004220243543386459,
0.0262661911547184,
0.032451316714286804,
0.0023545431904494762,
0.014109409414231777,
-0.028315963223576546,
-0.017304975539445877,
-0.08151818811893463,
0.0008640106534585357,
-0.010051649063825607,
0.05377698317170143,
-0.0002075379597954452,
0.04303336516022682,
0.050241075456142426,
0.006273310631513596,
0.0068501378409564495,
0.017965219914913177,
-0.08857911825180054,
0.03382188826799393,
-0.034867651760578156,
0.0168024729937315,
-0.017123112455010414,
-0.02131767012178898,
-0.04908930882811546,
-0.010450697503983974,
0.021469058468937874,
-0.04261970520019531,
0.014421690255403519,
-0.051383133977651596,
0.019327335059642792,
-0.013282026164233685,
-0.04877319559454918,
-0.027850518003106117,
0.010188902728259563,
0.03740045800805092,
-0.0020838454365730286,
0.024489227682352066,
0.023917535319924355,
-0.04521024972200394,
-0.030917296186089516,
0.005274810362607241,
-0.020397422835230827,
-0.00021152908448129892,
0.02373320981860161,
-0.004106989596039057,
0.012856701388955116,
-0.04777432605624199,
-0.0023019197396934032,
0.026727020740509033,
0.03156157582998276,
-0.00753935519605875,
0.004611988086253405,
-0.04748914763331413,
-0.020602988079190254,
-0.020968174561858177,
0.0022032938431948423,
0.033848706632852554,
0.0047918157652020454,
-0.019986765459179878,
0.027340440079569817,
-0.006894796155393124,
-0.0016152507159858942,
0.07259900867938995,
0.048933155834674835,
0.029085222631692886,
0.012464611791074276,
-0.060686975717544556,
0.00781206414103508,
-0.051067303866147995,
0.0046779378317296505,
0.02226622961461544,
-0.010747363790869713,
-0.03384476155042648,
0.0026097737718373537,
0.0034399249125272036,
0.047347813844680786,
-0.012120076455175877,
-0.023239396512508392,
0.012156038545072079,
0.024871721863746643,
-0.028911253437399864,
0.00511944992467761,
0.02935745380818844,
0.046494919806718826,
0.04024606570601463,
-0.0020331633277237415,
-0.030269555747509003,
-0.06548023968935013,
-0.015987837687134743,
0.04056897014379501,
0.00843828171491623,
-0.02008378691971302,
-0.01092051062732935,
-0.04874308034777641,
-0.010879824869334698,
0.011185863055288792,
-0.021616224199533463,
0.015267804265022278,
0.000040859456930775195,
0.02286715991795063,
-0.006866340059787035,
-0.04027252271771431,
-0.028910577297210693,
0.0020134386140853167,
-0.058655451983213425,
-0.026485322043299675,
-0.038560908287763596,
0.005281586199998856,
-0.0009623912046663463,
0.011246930807828903,
0.0374930165708065,
0.02141709253191948,
0.014333096332848072,
-0.009971695952117443,
-0.02541596069931984,
-0.011152774095535278,
-0.04766535758972168,
-0.091693215072155,
-0.012322910130023956,
0.00002437412149447482,
-0.029650773853063583,
0.04649561643600464,
-0.024912510067224503,
-0.02450638636946678,
0.01831517368555069,
0.0068293372169137,
-0.0009685404947958887,
-0.014456802047789097,
-0.03956313803792,
0.009920313954353333,
0.011931653134524822,
-0.008602804504334927,
0.05764276906847954,
0.04626532271504402,
-0.014599128626286983,
-0.0051850019954144955,
0.024912714958190918,
0.021020708605647087,
-0.033407360315322876,
-0.0010167694417759776,
0.017509406432509422,
0.007045364007353783,
-0.07742870599031448,
0.027417104691267014,
-0.019779600203037262,
0.005335657857358456,
-0.0032494596671313047,
-0.025189615786075592,
-0.014219592325389385,
0.0538409948348999,
0.02059772238135338,
0.005370524246245623,
-0.011763093993067741,
0.020069163292646408,
0.013133845292031765,
-0.005126798525452614,
0.01791704073548317,
0.009801910258829594,
-0.004984868224710226,
0.044968415051698685,
0.0007493115845136344,
0.02119138278067112,
-0.019040528684854507,
-0.016327649354934692,
-0.007231794763356447,
-0.05265606939792633,
0.04822441563010216,
-0.0012956256978213787,
0.009889722801744938,
0.05315602570772171,
-0.04283653199672699,
-0.017638664692640305,
0.0005114100640639663,
0.00525767682120204,
0.01388605311512947,
0.0036058772820979357,
-0.0036580145824700594,
0.02429920807480812,
0.03561730310320854,
-0.10087143629789352,
-0.04064497351646423,
0.0488528273999691,
0.033745307475328445,
0.003875900525599718,
0.03640247508883476,
-0.006426861509680748,
-0.0718635693192482,
-0.04337562993168831,
-0.008682852610945702,
0.04947208613157272,
-0.022410675883293152,
0.015615545213222504,
0.013410738669335842,
0.012339750304818153,
0.05544208362698555,
0.010703329928219318,
-0.009717799723148346,
0.004232260398566723,
-0.002451114123687148,
0.0064082881435751915,
-0.02942020446062088,
0.06853536516427994,
-0.034197255969047546,
-0.04754646122455597,
-0.02098103053867817,
-0.0549653023481369,
-0.012193458154797554,
0.013735346496105194,
-0.04038149490952492,
0.04140729457139969,
0.0008106378954835236,
-0.018531398847699165,
-0.03526689484715462,
0.03438630327582359,
-0.028911055997014046,
-0.012297045439481735,
-0.0045153419487178326,
-0.013504307717084885,
-0.02819335274398327,
-0.06243864819407463,
0.045787643641233444,
-0.010142188519239426,
-0.012707960791885853,
0.014067335054278374,
0.05906331539154053,
-0.022864660248160362,
-0.017082151025533676,
0.01355530135333538,
0.004641000181436539,
0.010604050941765308,
-0.020798033103346825,
0.008505959063768387,
0.012385752983391285,
0.014071590267121792,
-0.017656579613685608,
-0.008059411309659481,
-0.02386670745909214,
0.011446398682892323,
0.07682961225509644,
-0.030921373516321182,
0.04698440060019493,
0.031224312260746956,
-0.011909330263733864,
-0.036507800221443176,
-0.013421598821878433,
-0.0030480539426207542,
-0.009332678280770779,
0.011006523855030537,
0.014247249811887741,
-0.01634478010237217,
0.02987319976091385,
0.04851634055376053,
0.01590641587972641,
-0.015530329197645187,
0.039895784109830856,
0.02682286687195301,
0.03068273887038231,
0.009688246063888073,
-0.007002015132457018,
-0.016474958509206772,
-0.0032915810588747263,
-0.0440472811460495,
0.04147518426179886,
0.006246371194720268,
0.008048570714890957,
-0.0006398521945811808,
0.045855626463890076,
0.004659782163798809,
-0.04202601686120033,
-0.01664438284933567,
-0.003649716963991523,
0.014307410456240177,
0.01329865399748087,
0.02584855444729328,
0.036429181694984436,
0.021189823746681213,
0.047064345329999924,
0.022431407123804092,
-0.003832039888948202,
-0.009407909587025642,
-0.06355500966310501,
-0.04229951277375221,
-0.039403919130563736,
-0.02860702946782112,
0.03067365288734436,
0.013832099735736847,
-0.02653176337480545,
-0.008549547754228115,
-0.023897798731923103,
0.01326240599155426,
0.06453990191221237,
0.03173758089542389,
-0.030181966722011566,
0.05627169832587242,
-0.030638467520475388,
-0.0016307596815750003,
-0.023639880120754242,
0.048152659088373184,
0.13469834625720978,
0.030210597440600395,
0.028250163421034813,
-0.019237032160162926,
0.010441146790981293,
-0.019686967134475708,
-0.023233363404870033,
-0.027688806876540184,
0.00289210956543684,
-0.0271456241607666,
0.008848338387906551,
0.013485873118042946,
0.043264180421829224,
0.024310365319252014,
-0.04446595162153244,
0.021939143538475037,
-0.046812642365694046,
-0.01652257889509201,
0.000026350786356488243,
-0.0033677557948976755,
-0.0278079304844141,
0.01680755615234375,
-0.022759893909096718,
0.026398923248052597,
-0.01983242854475975,
0.00025090150302276015,
-0.01361057534813881,
-0.05890718847513199,
-0.012791464105248451,
0.010869549587368965,
-0.02635210193693638,
-0.009240783751010895,
-0.023098720237612724,
-0.06053270399570465,
-0.03967684134840965,
0.017695050686597824,
0.0034738262183964252,
-0.05619678273797035,
0.03277430683374405,
0.049775198101997375,
-0.025548266246914864,
0.0017686280189082026,
0.006466784980148077,
0.02857893891632557,
-0.035204604268074036,
0.0364893339574337,
-0.03803155571222305,
0.07937818020582199,
-0.029758548364043236,
-0.006551970262080431,
0.04532826319336891,
-0.019799446687102318,
-0.0003132825659122318,
-0.05587456375360489,
-0.0032237558625638485,
-0.01619391329586506,
0.02808562107384205,
0.01523276325315237,
-0.03167407959699631,
0.01131791528314352,
0.026782553642988205,
0.01818395033478737,
0.0038432639557868242,
0.02382492646574974,
0.02848254330456257,
-0.0037016200367361307,
0.003041936783120036,
0.07312269508838654,
0.014148822985589504,
0.00980968214571476,
-0.0454583615064621,
-0.027668042108416557,
-0.04798757657408714,
-0.010955620557069778,
-0.030307671055197716,
0.0394173227250576,
-0.014439954422414303,
0.0030209980905056,
-0.024726223200559616,
-0.039919089525938034,
-0.0212075337767601,
0.04143131524324417,
-0.03865782171487808,
-0.019819509238004684,
-0.010624151676893234,
-0.010397903621196747,
-0.03313310444355011,
0.044625964015722275,
-0.031786561012268066,
-0.010049117729067802,
0.008517058566212654,
0.03756342828273773,
-0.0011206655763089657,
-0.024425147101283073,
-0.006278636399656534,
-0.001401036512106657,
-0.01773086003959179,
0.014806866645812988,
0.018822118639945984,
0.018222587183117867,
0.037826623767614365,
-0.040849506855010986,
0.021711023524403572,
0.03741107136011124,
-0.024715660139918327,
0.02525969222187996,
0.027641022577881813,
0.021549973636865616,
-0.039291877299547195,
0.02457147091627121,
-0.03687717765569687,
-0.016307447105646133,
-0.016544921323657036,
0.0011935760267078876,
-0.015323354862630367,
0.0022625066339969635,
0.04402343928813934,
-0.038565125316381454,
0.035780169069767,
0.018306121230125427,
0.030529843643307686,
-0.04535282403230667,
-0.019062697887420654,
-0.0738011971116066,
-0.0002905596629716456,
-0.018411025404930115,
-0.02304011583328247,
-0.013233533129096031,
0.05113816261291504,
-0.026598922908306122,
-0.005697587039321661,
-0.01894928514957428,
-0.02462301030755043,
-0.012257850728929043,
0.01661050319671631,
0.05025335028767586,
-0.07178821414709091,
0.027188606560230255,
0.03404887020587921,
-0.02575690858066082,
0.03226754814386368,
-0.026500139385461807,
-0.03625550866127014,
0.025018952786922455,
-0.014261551201343536,
0.061542827636003494,
0.022512884810566902,
0.012326384894549847,
0.023254133760929108,
0.07298723608255386,
0.03653636574745178,
-0.011420131660997868,
0.0005870202439837158,
0.017138885334134102,
0.009467537514865398,
-0.02848351001739502,
-0.020512869581580162,
-0.0375320203602314,
-0.009266999550163746,
0.018704116344451904,
0.029480723664164543,
0.011797722429037094,
0.0019469703547656536,
-0.01223983708769083,
-0.009951812215149403,
-0.03967242315411568,
-0.02183546870946884,
-0.020336246117949486,
-0.0024595865979790688,
0.04398507624864578,
-0.030739905312657356,
-0.0279461108148098,
-0.0029039422515779734,
0.00017002159438561648,
-0.06544366478919983,
-0.050444819033145905,
-0.012469610199332237,
-0.0020087105222046375,
0.04661021754145622,
-0.045163024216890335,
0.023099863901734352,
0.020544255152344704,
-0.06102375313639641,
0.025755783542990685,
-0.03730691224336624,
0.019897110760211945,
0.0007200257387012243,
-0.0037589319981634617,
-0.01203598827123642,
0.045069798827171326,
0.01627250202000141,
0.040977850556373596,
-0.006739343050867319,
0.019040511921048164,
0.00032921278034336865,
-0.017368655651807785,
-0.010596458800137043,
0.022040680050849915,
-0.03527109697461128,
0.005402917042374611,
0.067813940346241,
0.019278261810541153,
-0.007840662263333797,
0.035044457763433456,
0.017298363149166107,
-0.003610814455896616,
-0.0238705575466156,
-0.013557539321482182,
0.028225131332874298,
0.02214517444372177,
0.009229660965502262,
-0.024647735059261322,
0.008563607931137085,
0.03804061561822891,
-0.03662840649485588,
0.014199366793036461,
-0.0014053258346393704,
0.002183500211685896,
0.004031097050756216,
-0.04471800476312637,
-0.015447607263922691,
-0.015497426502406597,
-0.030643023550510406,
-0.02292713150382042,
-0.017318343743681908,
0.007054814137518406,
-0.005200190935283899,
0.02497301623225212,
-0.004586968570947647,
-0.04825415089726448,
0.01678682118654251,
0.04761531949043274,
-0.011901780031621456,
-0.030890630558133125,
0.03233244642615318,
-0.02360311709344387,
-0.021571941673755646,
-0.01823352463543415,
-0.008633549325168133,
-0.006908796727657318,
-0.0033754506148397923,
0.0037691951729357243,
-0.019716791808605194,
0.019974559545516968,
0.021478038281202316,
-0.026686519384384155,
-0.0259493887424469,
0.04158284142613411,
0.00635768286883831,
0.03585856407880783,
0.039049796760082245,
-0.0417264960706234,
0.02015305869281292,
-0.054181985557079315,
0.02772657945752144,
0.008201836608350277,
-0.03864729404449463,
-0.04163762927055359,
-0.012731078080832958,
0.005659503396600485,
0.015760837122797966,
0.020326020196080208,
0.001098446431569755,
-0.007004647050052881,
0.07387248426675797,
-0.004585076589137316,
0.017008285969495773,
-0.024836402386426926,
-0.002089295070618391,
0.010610954836010933,
-0.025280386209487915,
0.015714894980192184,
0.04168660193681717,
0.007560719270259142,
0.02536788210272789,
-0.01396182831376791,
0.0010404278291389346,
0.08220594376325607,
0.021999990567564964,
-0.07700219005346298,
0.033021312206983566,
0.02156355232000351,
0.010714097879827023,
0.04893996939063072,
-0.011754409410059452,
0.0068924990482628345,
0.0013859692262485623,
-0.05970435217022896,
-0.02554788626730442,
0.01591126248240471,
-0.043404437601566315,
-0.00583956902846694,
0.007900292053818703,
-0.006999537814408541,
-0.0019453823333606124,
-0.02770252712070942,
-0.007438437081873417,
0.03205864876508713,
-0.018393369391560555,
-0.005175699945539236,
0.03976820409297943,
0.03803873434662819,
0.039597585797309875,
0.030330725014209747,
0.015744322910904884,
-0.029509155079722404,
-0.023571010679006577,
0.02085798978805542,
0.029992859810590744,
-0.020297270268201828,
0.004783653188496828,
0.01087475661188364,
0.04976574331521988,
0.041285187005996704,
0.006065196357667446,
0.06223882734775543,
-0.002990947337821126,
-0.031098034232854843,
0.012771693989634514,
0.02298576943576336,
0.032889146357774734,
0.008248962461948395,
0.018744036555290222,
-0.024475745856761932,
0.07152262330055237,
-0.04479058459401131,
-0.0059526292607188225,
-0.004436997231096029,
-0.03318173810839653,
-0.0048348442651331425,
0.04425288364291191,
-0.03281727433204651,
0.030857020989060402,
0.004277560394257307,
-0.026914671063423157,
0.02548491209745407,
-0.001323207514360547,
-0.016711626201868057,
-0.018274592235684395,
0.023238804191350937,
0.003181762294843793,
-0.013692452572286129,
0.017248038202524185,
-0.024542421102523804,
-0.031045449897646904,
-0.021174738183617592,
0.032230228185653687,
0.010077938437461853,
0.006242653820663691,
-0.035064972937107086,
-0.006945432163774967,
-0.018218424171209335,
0.05194905772805214,
-0.05924886837601662,
-0.018613720312714577,
-0.04273921251296997,
0.03031034581363201,
-0.0074755847454071045,
0.004499475471675396
] |
<p>I'm making a tea bag experiment (Make a hollow cylindrical tube from light paper e.g. from an empty tea bag. When the top end of the cylinder is lit, it takes off.) I need to know how hot air is moving so please help me if you have thermal imaging camera or with out it write your opinion</p>
| 9,359 |
[
-0.013435597531497478,
-0.04988706111907959,
0.004683963488787413,
-0.0033262495417147875,
0.022595789283514023,
-0.004394042771309614,
-0.030201587826013565,
-0.009941386990249157,
-0.02640380896627903,
-0.016242187470197678,
0.048399049788713455,
0.05298261716961861,
0.008076462894678116,
0.03259488195180893,
0.00012849728227593005,
-0.013782049529254436,
0.0044216676615178585,
-0.025684302672743797,
0.005700191482901573,
0.003480457002297044,
-0.03905588760972023,
0.026499943807721138,
0.01865481585264206,
-0.013632670976221561,
-0.03541642427444458,
0.030777551233768463,
-0.015069738030433655,
0.011076048947870731,
0.025149215012788773,
0.004874300677329302,
-0.03513750433921814,
-0.002689157845452428,
-0.006959038786590099,
0.020018965005874634,
0.015174373984336853,
0.004341834224760532,
-0.037546250969171524,
0.013003913685679436,
-0.00014649472723249346,
-0.0096062570810318,
-0.004132056143134832,
-0.01267825998365879,
0.0018106456845998764,
0.02801438979804516,
0.002640870399773121,
0.015904724597930908,
-0.018681470304727554,
-0.018011316657066345,
0.04978345334529877,
-0.08150417357683182,
0.04508915916085243,
-0.011723593808710575,
0.046995531767606735,
0.03835392743349075,
0.036498140543699265,
0.009784247726202011,
0.060439929366111755,
0.03789422661066055,
-0.0413060337305069,
-0.05720389634370804,
0.0219428688287735,
0.008189603686332703,
-0.042783867567777634,
-0.01879293844103813,
-0.046840228140354156,
-0.010551056824624538,
-0.007843066938221455,
-0.013217130675911903,
0.032244253903627396,
0.023882905021309853,
0.015987379476428032,
-0.022750362753868103,
0.0531000941991806,
0.0039197118021547794,
0.0012289532460272312,
-0.030869469046592712,
-0.028413357213139534,
0.0606493204832077,
0.03648765757679939,
0.07225296646356583,
0.016541415825486183,
-0.014703704044222832,
-0.00730632059276104,
0.016716256737709045,
0.01493158470839262,
-0.011934113688766956,
0.060664571821689606,
0.011842085979878902,
0.038534220308065414,
0.02485598437488079,
0.0007261823629960418,
-0.004459211602807045,
-0.007531292270869017,
0.009925324469804764,
0.03457372263073921,
0.045380499213933945,
0.01371016912162304,
0.06293334811925888,
0.01011626422405243,
-0.07182871550321579,
0.014247441664338112,
0.02929883636534214,
0.03858291357755661,
0.11459394544363022,
0.0035985116846859455,
-0.0017681530443951488,
-0.01724240370094776,
0.008779231458902359,
-0.005278656259179115,
0.01888221688568592,
-0.05758558586239815,
-0.015295036137104034,
0.013457675464451313,
-0.03071674332022667,
0.012439598329365253,
-0.02864101156592369,
0.03234676271677017,
-0.032270628958940506,
0.024594303220510483,
0.051530104130506516,
0.017309455201029778,
-0.017017899081110954,
0.009977459907531738,
0.004515498410910368,
-0.06401816755533218,
0.04899674654006958,
0.04309117794036865,
-0.030145011842250824,
-0.01095275953412056,
0.06351476162672043,
-0.011141381226480007,
-0.008189515210688114,
0.012006867676973343,
-0.01690131612122059,
0.04862670600414276,
-0.0180438794195652,
-0.08817537873983383,
-0.03922393172979355,
0.04596890136599541,
-0.014162187464535236,
-0.0025127679109573364,
-0.05709995701909065,
-0.009132561273872852,
0.05451078712940216,
0.07015267014503479,
-0.043030086904764175,
0.010095375590026379,
-0.03509063646197319,
0.028625695034861565,
-0.022875364869832993,
-0.034979838877916336,
0.01102898083627224,
0.015817340463399887,
-0.046715471893548965,
0.021542299538850784,
-0.039926256984472275,
-0.0021310949232429266,
0.07543082535266876,
-0.01947067491710186,
-0.023581326007843018,
0.006575056817382574,
-0.016304444521665573,
-0.03424398973584175,
0.024405213072896004,
-0.012797116301953793,
-0.05934671685099602,
0.048852019011974335,
-0.019658029079437256,
-0.0005837656790390611,
-0.020086927339434624,
0.0006560569745488465,
0.05504986643791199,
-0.007130967453122139,
-0.03327092155814171,
0.045325055718421936,
0.010239704512059689,
-0.01766369864344597,
-0.020368870347738266,
0.03103914111852646,
0.053211525082588196,
-0.04223651811480522,
-0.01879226043820381,
-0.01779157854616642,
0.0027949432842433453,
0.026585156098008156,
0.044372834265232086,
-0.012596553191542625,
-0.025526057928800583,
0.03437696769833565,
-0.04422096535563469,
-0.03740189969539642,
-0.0481564961373806,
0.0026498374063521624,
-0.03958601877093315,
0.00011386343976482749,
-0.016348931938409805,
0.01536526158452034,
0.01694929227232933,
0.007357318885624409,
-0.01839871145784855,
0.012942847795784473,
0.012995063327252865,
0.013587241061031818,
0.00459101889282465,
0.007179290521889925,
0.043984219431877136,
-0.0013092609588056803,
-0.007185996510088444,
0.04194200783967972,
-0.029118260368704796,
0.009525264613330364,
0.0015794634819030762,
-0.003240415593609214,
-0.02711266651749611,
-0.009403266943991184,
-0.0020098157692700624,
-0.0002768088015727699,
-0.011462938971817493,
-0.009361783042550087,
0.010667208582162857,
-0.013059164397418499,
0.09409448504447937,
0.022605866193771362,
0.010137385688722134,
-0.00545826181769371,
-0.023883787915110588,
-0.0021857048850506544,
-0.003875782247632742,
0.025619879364967346,
-0.001444346155039966,
-0.0429849736392498,
-0.026888122782111168,
0.026669897139072418,
0.006796678993850946,
-0.07545694708824158,
-0.002757206093519926,
0.02428022027015686,
0.030216529965400696,
0.023257365450263023,
-0.004328630398958921,
-0.006938203237950802,
-0.01092885248363018,
-0.022509850561618805,
0.02540181390941143,
-0.025186918675899506,
0.003727223491296172,
0.025511346757411957,
0.04789852350950241,
0.056928377598524094,
0.034418944269418716,
-0.02717708982527256,
0.04328715428709984,
-0.019505511969327927,
0.03359141945838928,
-0.01645437814295292,
0.012390395626425743,
0.004193954169750214,
0.0025856108404695988,
0.014821553602814674,
0.016204144805669785,
0.012951026670634747,
0.05029378458857536,
-0.018488364294171333,
-0.019177421927452087,
-0.021636778488755226,
0.020851129665970802,
0.002426465740427375,
-0.006804283708333969,
0.03460654616355896,
-0.025862161070108414,
0.03359101712703705,
-0.05099175497889519,
0.03524241968989372,
-0.034959569573402405,
0.03797651082277298,
0.039930615574121475,
0.05926177650690079,
0.004825900308787823,
-0.031788572669029236,
-0.06364624947309494,
-0.0026528541930019855,
0.009424739517271519,
0.009669234044849873,
0.031063005328178406,
-0.06270813196897507,
0.024943863973021507,
-0.024773918092250824,
-0.048213064670562744,
0.04185548797249794,
0.01985003426671028,
0.003322367323562503,
0.03792359307408333,
0.009044417180120945,
-0.05965377017855644,
0.012655538506805897,
-0.001226490712724626,
0.04423973336815834,
0.0013738754205405712,
0.01308160275220871,
0.03440080210566521,
-0.020072123035788536,
-0.0411188118159771,
0.03486022353172302,
-0.04927753657102585,
-0.05612027272582054,
-0.008052385412156582,
-0.017175650224089622,
0.03797784447669983,
-0.030385266989469528,
0.04307522252202034,
-0.002273312769830227,
0.006140858866274357,
-0.0009825790766626596,
-0.048710502684116364,
-0.0273443553596735,
0.011430026963353157,
0.04171396419405937,
0.021212182939052582,
-0.011238929815590382,
-0.03405165672302246,
0.029061105102300644,
-0.007965861819684505,
-0.07319827377796173,
-0.01654142141342163,
-0.009844235144555569,
-0.048448074609041214,
-0.03513959422707558,
0.013016714714467525,
0.006201562471687794,
-0.0005390573642216623,
0.02815524861216545,
0.03589629754424095,
0.03848518431186676,
0.07003974914550781,
0.04559020698070526,
-0.02503603883087635,
-0.008120305836200714,
0.0032091315370053053,
-0.012460868805646896,
0.07007095962762833,
-0.014395861886441708,
-0.017442923039197922,
0.021493641659617424,
-0.024379363283514977,
0.03572976589202881,
0.02432158961892128,
-0.03342636674642563,
0.06043088808655739,
-0.017666082829236984,
-0.02701214700937271,
-0.02151777595281601,
0.009130658581852913,
-0.025842459872364998,
0.01875177212059498,
-0.0033377695363014936,
0.031352050602436066,
0.04967804625630379,
0.02961660549044609,
-0.031287699937820435,
0.04021938145160675,
0.019617382436990738,
-0.0022416659630835056,
-0.021353093907237053,
0.01033977884799242,
-0.025487210601568222,
0.008733208291232586,
-0.00513475202023983,
-0.032000113278627396,
0.03989725559949875,
0.04292456433176994,
0.008904332295060158,
0.03558078780770302,
-0.029909474775195122,
0.012297993525862694,
-0.03781765699386597,
-0.003164886264130473,
0.006924370303750038,
0.06235778331756592,
0.014480232261121273,
0.055183954536914825,
0.0014703882625326514,
0.017869289964437485,
0.056848615407943726,
-0.01891797035932541,
-0.0825909823179245,
0.03114454448223114,
0.012634498998522758,
-0.0361061692237854,
-0.022611849009990692,
-0.012294969521462917,
0.012701564468443394,
-0.013251906260848045,
0.031233973801136017,
-0.010436398908495903,
-0.011429151520133018,
-0.02521132305264473,
0.03140784054994583,
-0.007988156750798225,
-0.0023454399779438972,
-0.00967900175601244,
0.07017896324396133,
0.05052501708269119,
-0.01898529939353466,
0.03829570859670639,
0.025551561266183853,
-0.022030768916010857,
0.01651223748922348,
-0.025802668184041977,
-0.002680977573618293,
0.015526201575994492,
0.03569221496582031,
0.005493924021720886,
-0.009397746063768864,
-0.03573185205459595,
0.003689174773171544,
0.05913548916578293,
0.015637964010238647,
-0.049886032938957214,
-0.030903011560440063,
-0.03841155394911766,
-0.013331281952559948,
-0.04636772722005844,
0.0035947738215327263,
0.04472390189766884,
-0.00438352907076478,
0.016021789982914925,
0.011419128626585007,
-0.019064880907535553,
-0.022457411512732506,
0.0003638300986494869,
0.05741490051150322,
-0.018970899283885956,
-0.004141294397413731,
-0.07334108650684357,
-0.013494174927473068,
-0.012001189403235912,
-0.006831122562289238,
0.058538176119327545,
0.03647090867161751,
0.00959622859954834,
-0.01489961426705122,
0.049007344990968704,
0.03070792369544506,
-0.017816243693232536,
0.018944336101412773,
-0.005835539661347866,
0.032093118876218796,
0.017064282670617104,
-0.029002167284488678,
0.007896747440099716,
0.08149805665016174,
0.00598163390532136,
0.007707537151873112,
-0.0531812347471714,
-0.10186345130205154,
-0.017535019665956497,
0.02310522086918354,
0.026720236986875534,
-0.04550451785326004,
0.000020811212380067445,
-0.05312473699450493,
0.0074031054973602295,
0.0691489577293396,
-0.035474393516778946,
0.03356048837304115,
-0.038514815270900726,
-0.033738769590854645,
0.02472909726202488,
0.013491655699908733,
-0.030817240476608276,
0.026289353147149086,
-0.01876739040017128,
-0.025411805137991905,
-0.03737426549196243,
-0.002033960772678256,
0.024434950202703476,
0.01518524531275034,
0.009361702017486095,
-0.013121632859110832,
0.01060054823756218,
0.04784035682678223,
0.00044073816388845444,
0.02385806106030941,
-0.04892219230532646,
-0.039673566818237305,
0.024235565215349197,
-0.00996323674917221,
-0.009487004950642586,
0.040651753544807434,
-0.014017417095601559,
-0.025392694398760796,
0.00597388157621026,
0.007052314933389425,
-0.017249982804059982,
-0.05869821459054947,
-0.08148959279060364,
0.013850336894392967,
0.00784633494913578,
-0.008541942574083805,
0.0340551882982254,
0.05918760970234871,
0.0005076357047073543,
0.015701336786150932,
0.01275706198066473,
0.03493060916662216,
-0.013437129557132721,
0.010331014171242714,
-0.039342258125543594,
0.01464297529309988,
-0.029113253578543663,
0.05934271588921547,
-0.000581176660489291,
0.032125767320394516,
-0.035233210772275925,
-0.03720540180802345,
0.015311366878449917,
0.03835892304778099,
0.006156308110803366,
0.02461363933980465,
0.0019365790067240596,
-0.01114110741764307,
-0.014631234109401703,
-0.03199080750346184,
-0.021880393847823143,
-0.006370579358190298,
-0.006422294769436121,
0.01580558530986309,
-0.04189635068178177,
-0.001180501887574792,
-0.03668757155537605,
-0.0036104097962379456,
-0.026845082640647888,
-0.033557865768671036,
0.025324026122689247,
-0.015032713301479816,
0.005086671561002731,
0.0217336006462574,
-0.045079030096530914,
-0.006700044497847557,
0.01259109377861023,
0.0054879928939044476,
0.03478849679231644,
-0.05763934552669525,
0.04103913903236389,
0.004280293360352516,
-0.007614579051733017,
-0.03940422832965851,
-0.06351961195468903,
-0.009996814653277397,
0.010536899790167809,
-0.007823167368769646,
-0.03552845120429993,
-0.0011470462195575237,
0.011046931147575378,
-0.0504833459854126,
0.011457025073468685,
-0.004084398504346609,
0.030766870826482773,
0.012908820062875748,
0.030447423458099365,
-0.04017738252878189,
0.04061009734869003,
0.026818858459591866,
-0.006968215573579073,
0.009753271006047726,
-0.00019829155644401908,
-0.08214469254016876,
-0.0070105683989822865,
0.001689223456196487,
-0.01649724692106247,
-0.02698017656803131,
-0.00470146955922246,
-0.005390075035393238,
0.02048385888338089,
0.006106207147240639,
-0.01358058676123619,
-0.008834004402160645,
0.03827344626188278,
-0.00777495838701725,
-0.04388615861535072,
0.02938973531126976,
0.030991118401288986,
-0.0013917344622313976,
-0.006354393437504768,
0.008049932308495045,
-0.020451728254556656,
-0.033298563212156296,
0.016719689592719078,
0.007957047782838345,
-0.015843069180846214,
0.01731429062783718,
0.018949346616864204,
0.002770013175904751,
0.01589532196521759,
0.013417170383036137,
-0.014327624812722206,
0.0033205619547516108,
-0.004233292769640684,
0.006808142643421888,
-0.0024950355291366577,
-0.009600380435585976,
-0.0019154108595103025,
0.004630564711987972,
-0.03452884033322334,
-0.003103334456682205,
0.060615431517362595,
0.017764940857887268,
0.06149296462535858,
0.008895916864275932,
-0.014662254601716995,
0.02130080759525299,
0.031943175941705704,
-0.008026552386581898,
0.03233809769153595,
-0.01906013675034046,
0.0022949432022869587,
-0.019446702674031258,
0.0066484552808105946,
0.017703484743833542,
0.03611674904823303,
0.005834926385432482,
0.023906314745545387,
0.024440165609121323,
0.010610484518110752,
0.034192703664302826,
-0.005064844619482756,
-0.05655791983008385,
0.03570311889052391,
-0.036284081637859344,
0.061451129615306854,
-0.013229705393314362,
0.01622876338660717,
0.04734372720122337,
0.0039006895385682583,
-0.03666793182492256,
-0.03470350429415703,
-0.017201237380504608,
-0.07663676887750626,
0.003920122981071472,
-0.015608900226652622,
-0.010740804485976696,
0.0059884656220674515,
0.015362562611699104,
0.013021638616919518,
-0.047840964049100876,
0.05088094249367714,
-0.030639803037047386,
-0.06360194832086563,
-0.02152693085372448,
0.0061729103326797485,
-0.014756075106561184,
0.08627527952194214,
-0.0037384505849331617,
0.0064081670716404915,
-0.007713796105235815,
-0.011838188394904137,
-0.014354219660162926,
0.024377256631851196,
0.06197494640946388,
-0.001433446304872632,
0.08783025294542313,
-0.043926458805799484,
0.035971350967884064,
0.012542280368506908,
0.06962475180625916,
0.1117882952094078,
0.0097974743694067,
-0.013647951185703278,
-0.04169415682554245,
-0.004538557026535273,
-0.015211062505841255,
-0.018456794321537018,
-0.01844768598675728,
0.046724576503038406,
-0.0007824666681699455,
0.019801512360572815,
0.034179188311100006,
0.07266488671302795,
-0.009120766073465347,
-0.004618947859853506,
0.01633130945265293,
-0.02409450151026249,
-0.04286043718457222,
0.005483272951096296,
-0.0035921090748161077,
-0.023457100614905357,
0.031537652015686035,
-0.050877805799245834,
0.012604291550815105,
-0.026077747344970703,
-0.024716470390558243,
0.0016901292838156223,
-0.07719045877456665,
0.03622594103217125,
-0.010445738211274147,
-0.08234236389398575,
-0.004416910000145435,
-0.03424596041440964,
-0.010350131429731846,
-0.02637668326497078,
-0.004895200952887535,
-0.0148600023239851,
-0.004062304738909006,
0.01456308364868164,
0.0016301239375025034,
0.04714391008019447,
-0.0006271037273108959,
0.03456375375390053,
0.029714401811361313,
-0.017176082357764244,
-0.020399704575538635,
-0.004891065880656242,
0.030339807271957397,
0.012518724426627159,
0.006302161142230034,
-0.023511067032814026,
0.03620167821645737,
0.01699647679924965,
-0.04598970338702202,
-0.044297728687524796,
0.03228282183408737,
0.044034749269485474,
-0.02561374194920063,
-0.07654218375682831,
-0.048882920295000076,
0.007451863028109074,
0.014004712924361229,
0.02236984297633171,
-0.0014868888538330793,
0.0170371625572443,
-0.04965543746948242,
-0.009356832131743431,
0.07537352293729782,
-0.006637073587626219,
-0.04367566108703613,
-0.01202486827969551,
-0.01935430057346821,
-0.010545503348112106,
0.025565536692738533,
0.013465885072946548,
0.041007205843925476,
0.020944632589817047,
0.003466657130047679,
-0.003970427438616753,
0.04115153104066849,
-0.04288388416171074,
-0.012016343884170055,
-0.01769731566309929,
-0.011709550395607948,
-0.014385346323251724,
-0.013081877492368221,
0.05249211937189102,
0.029535766690969467,
-0.005481223110109568,
-0.016130739822983742,
0.030149485915899277,
0.027445979416370392,
0.021182933822274208,
-0.04015696048736572,
-0.018865471705794334,
0.003039137227460742,
-0.06634704023599625,
-0.016013219952583313,
-0.023920822888612747,
0.040621813386678696,
0.043385934084653854,
-0.02921629138290882,
-0.026095066219568253,
-0.015806125476956367,
-0.032839711755514145,
0.013852505013346672,
0.008565980941057205,
-0.029744340106844902,
-0.016461722552776337,
-0.02158600091934204,
0.008280616253614426,
-0.0318966805934906,
-0.0200429018586874,
-0.01648639887571335,
0.012631136924028397,
-0.05996830016374588,
0.012845948338508606,
-0.011323724873363972,
0.03845168650150299,
-0.028265101835131645,
0.043559856712818146,
-0.037931885570287704,
-0.009493621066212654,
-0.057589344680309296,
0.001974275102838874,
0.05463029816746712,
0.01313137635588646,
-0.0405915230512619,
0.018699945881962776,
-0.029382511973381042,
-0.030676089227199554,
0.009659804403781891,
0.006658538710325956,
0.027172086760401726,
-0.042577046900987625,
-0.0032160335686057806,
-0.015653332695364952,
0.01788189262151718,
0.009843261912465096,
-0.009417576715350151,
0.022614633664488792,
-0.010329043492674828,
0.00510023720562458,
0.04696217551827431,
0.02638011798262596,
0.040791209787130356,
0.03546576574444771,
-0.04094598814845085,
0.027551710605621338,
0.06327800452709198,
-0.00717541528865695,
-0.03519453853368759,
0.01791834458708763,
-0.04505375772714615,
-0.0012415796518325806,
-0.01115688867866993,
0.005928159225732088,
-0.049797676503658295,
-0.025925366207957268,
0.029007216915488243,
0.025384580716490746,
0.04651181027293205,
-0.002321561798453331,
-0.017500393092632294,
-0.016820143908262253,
-0.00628721434623003,
0.009016450494527817,
-0.0033436689991503954,
0.06060294806957245,
0.03045031614601612,
-0.02873609960079193,
0.02075837180018425,
0.001809146604500711,
0.016743283718824387,
-0.125246062874794,
0.03391276299953461,
0.0005196816055104136,
-0.007814970798790455,
0.027296507731080055,
-0.07119979709386826,
0.014266695827245712,
0.0630795806646347,
-0.01411466859281063,
0.008932576514780521,
-0.03288695961236954,
-0.00016730916104279459,
-0.06195388361811638,
0.048913758248090744,
-0.00018695624021347612,
0.043403882533311844,
0.02207098715007305,
0.021454891189932823,
0.032118212431669235,
0.01662854291498661,
-0.005632815882563591,
-0.003466113470494747,
0.0061226882971823215,
0.004613329190760851,
0.03778375685214996,
-0.015952512621879578,
0.032067373394966125,
-0.007653187494724989,
0.008373801596462727,
-0.009285925887525082,
-0.04873403534293175,
0.04630056396126747,
0.011991322040557861,
-0.019162364304065704,
-0.0197865292429924,
0.044298816472291946,
0.030288103967905045,
0.02142726071178913,
0.004742719233036041,
0.02645098976790905,
0.050410300493240356,
0.03083615005016327,
-0.027035636827349663,
0.008656454272568226,
-0.0067820195108652115,
-0.03678969666361809,
-0.03587135300040245,
0.03439214453101158,
-0.013660979457199574,
-0.02706531248986721,
0.009795550256967545,
-0.04118501767516136,
0.008927451446652412,
-0.035931725054979324,
-0.010873406194150448,
-0.037585001438856125,
0.002752656815573573,
0.02145581878721714,
0.013053115457296371,
-0.024425530806183815,
-0.02923576720058918,
0.0006971222464926541,
-0.02492651157081127,
0.001300797681324184,
-0.028329383581876755,
-0.006775118876248598,
-0.02105501852929592,
-0.0018255783943459392,
0.0405629500746727,
-0.026213832199573517,
-0.0003722566762007773,
-0.03543445095419884,
-0.0033142368774861097,
0.030138108879327774,
-0.0133541664108634,
0.04747513309121132,
0.012578727677464485,
-0.011076857335865498,
-0.04967457801103592,
-0.04528322443366051,
0.0019989432767033577,
-0.039490845054388046,
0.020124636590480804,
-0.03142814338207245,
-0.008294511586427689,
-0.0026580558624118567,
0.017475511878728867,
0.03500629961490631,
-0.020452873781323433,
-0.042678918689489365,
0.008150262758135796,
-0.02973804995417595,
0.03693811595439911,
-0.033306583762168884,
0.010406247340142727,
-0.0477638877928257,
-0.022616365924477577,
0.006841788999736309,
-0.027092527598142624,
-0.019492454826831818,
0.02807432971894741,
0.06448189914226532,
-0.03414718806743622,
0.03992607817053795,
-0.023940937593579292,
-0.023474298417568207,
-0.009554905816912651,
0.04355236515402794,
-0.009483925998210907,
0.07228434085845947,
0.000887519505340606,
-0.02117561362683773,
0.018118076026439667,
-0.014890370890498161,
-0.00514730392023921,
0.02091374807059765,
0.010767960920929909,
-0.0151747465133667,
-0.004810065031051636,
-0.03489580377936363,
0.028239397332072258,
-0.05092497542500496,
-0.02438499964773655,
-0.010616208426654339,
-0.0500718392431736,
-0.02941059321165085,
0.022420842200517654,
-0.020352108404040337,
-0.0011773610021919012,
-0.0373053103685379,
0.06042741239070892,
0.011365733109414577,
0.03132056072354317,
0.0021220408380031586,
0.05534502491354942,
-0.021315816789865494,
-0.013589485548436642,
0.011634142138063908,
-0.027842318639159203,
0.008370416238904,
0.006297237239778042,
0.02250809781253338,
0.015133600682020187,
-0.0011655334383249283,
-0.003149745985865593,
-0.0019427096704021096,
-0.013177209533751011,
0.002807165728881955,
0.029806233942508698,
0.008632957004010677,
0.05552081763744354,
-0.037398021668195724,
-0.016278564929962158,
-0.03740151971578598,
-0.0004493391315918416,
-0.028018629178404808,
0.05482698604464531,
0.038491446524858475,
0.03656528517603874,
0.0008195736445486546,
0.04008437693119049,
-0.006099215243011713,
0.01546701043844223,
-0.016295786947011948,
-0.0354766920208931,
0.016743989661335945,
-0.0620967373251915,
-0.015828857198357582,
-0.03749769181013107,
0.0008582037407904863,
-0.017004122957587242,
-0.0009578776080161333,
0.015569784678518772,
0.03400344029068947,
-0.0031391982920467854,
0.03541894257068634,
-0.02408605068922043,
0.0011918984819203615,
0.05493751913309097,
-0.08087071031332016,
0.015483328141272068,
-0.020581966266036034,
0.008235751651227474,
0.03125235438346863,
0.00024622122873552144
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/296/is-energy-really-conserved">Is energy really conserved?</a><br>
<a href="http://physics.stackexchange.com/questions/19216/why-cant-energy-be-created-or-destroyed">Why can’t energy be created or destroyed?</a> </p>
</blockquote>
<p>One of the laws of the universe that dazzles me the most is the law of conservation of energy. I however have a couple of questions regarding this law. Since Einstein's equivalence tells us that matter and energy are different manifestations of the same thing:</p>
<ul>
<li>Does this mean that the amount of energy + matter has been the same since the beginning of the universe?</li>
</ul>
<p>If this is true, then another question pops up. Since the universe is expanding at an accelerating rate, and the law of conservation of energy tells us that the amount of energy can't increase:</p>
<ul>
<li>does this mean that the universe is getting emptier? </li>
</ul>
<p>Also, an intertwined question:</p>
<ul>
<li>Is there some sort of average 'energy density' in the universe? If so, can we notice the effects of the accelerating expansion of the universe by looking at this 'energy density'? (this might sound like/ be a stupid question).</li>
</ul>
| 307 |
[
-0.08168353140354156,
-0.02872549556195736,
0.00663214223459363,
-0.017285751178860664,
0.03673877194523811,
-0.004351523704826832,
-0.035542648285627365,
-0.06281871348619461,
0.013096855953335762,
-0.030638577416539192,
0.034891411662101746,
0.02402471750974655,
0.03501860797405243,
0.022193381562829018,
0.010470298118889332,
-0.010495907627046108,
0.003690213430672884,
-0.018025074154138565,
-0.015815161168575287,
-0.02412210963666439,
-0.0023254191037267447,
-0.0026073509361594915,
0.00408552773296833,
0.0034528167452663183,
-0.04828425869345665,
0.04506858438253403,
0.02854488231241703,
-0.0038695193361490965,
0.02685922011733055,
0.06885974854230881,
-0.006523563992232084,
0.00860747043043375,
0.0353914275765419,
0.018866609781980515,
0.025523096323013306,
0.005864358507096767,
-0.009878363460302353,
-0.016330597922205925,
-0.00019203350530005991,
0.037227291613817215,
-0.022375494241714478,
-0.014967038296163082,
-0.007340564392507076,
0.05824288725852966,
-0.04342498257756233,
0.017026124522089958,
-0.003701017936691642,
-0.0001255545357707888,
0.04015287011861801,
-0.035226039588451385,
0.06087039038538933,
0.0002013867488130927,
0.047173600643873215,
0.047051332890987396,
-0.022558432072401047,
-0.008444073610007763,
0.06512892991304398,
0.0573570542037487,
-0.004741193726658821,
-0.03508284315466881,
0.003995007369667292,
0.03454491123557091,
-0.022159850224852562,
0.00910140946507454,
-0.009595558047294617,
0.05018390342593193,
-0.009850687347352505,
0.003693230450153351,
0.035142626613378525,
0.011619916185736656,
0.009643582627177238,
0.04053310304880142,
-0.015516294166445732,
-0.001012362539768219,
0.022862069308757782,
-0.027755729854106903,
0.04044831916689873,
0.02185796946287155,
0.012199138291180134,
0.0898694172501564,
-0.012882948853075504,
-0.023927228525280952,
0.05269264057278633,
0.030027193948626518,
0.04409337416291237,
0.04519275948405266,
0.09026969224214554,
0.009398727677762508,
0.0027785440906882286,
0.05472510680556297,
0.03264523670077324,
-0.0031487508676946163,
0.02106604166328907,
-0.01856253109872341,
-0.019439993426203728,
0.04124663770198822,
-0.029891861602663994,
0.04197276756167412,
-0.0019235145300626755,
0.007081298157572746,
0.01661977544426918,
0.00404973654076457,
0.03120807558298111,
0.02768280915915966,
-0.0001059751957654953,
-0.06672415882349014,
-0.08215551823377609,
0.017992794513702393,
-0.03222556412220001,
-0.0003796694800257683,
-0.03921431675553322,
-0.0036418873351067305,
-0.0003705670533236116,
-0.017146741971373558,
0.04307611659169197,
-0.0530480332672596,
0.008805220946669579,
-0.009222031570971012,
0.04424254223704338,
0.06242363899946213,
0.04442685469985008,
-0.0014433721080422401,
0.02206156589090824,
-0.009979394264519215,
-0.06542813777923584,
-0.0021132484544068575,
0.012212804518640041,
0.0058849528431892395,
-0.05854712799191475,
0.05930078774690628,
-0.04056532680988312,
-0.01773017644882202,
-0.014003511518239975,
-0.014622899703681469,
0.04185881465673447,
0.02063148468732834,
-0.0768214762210846,
-0.0518001951277256,
0.06629478931427002,
0.00015902012819424272,
-0.038930363953113556,
-0.07926413416862488,
-0.005830323789268732,
0.0054084607400000095,
0.04095426946878433,
0.008105283603072166,
-0.029450563713908195,
0.0044473265297710896,
0.04834458604454994,
0.0039036558009684086,
-0.023440981283783913,
-0.03973551094532013,
0.0009886500192806125,
-0.04368937760591507,
0.027972949668765068,
-0.06472000479698181,
-0.023370472714304924,
0.03250059112906456,
0.005267252214252949,
-0.0035136830992996693,
0.06403150409460068,
0.00804917886853218,
-0.009311851114034653,
-0.02093666046857834,
-0.006808275822550058,
-0.01130692008882761,
0.08113749325275421,
0.0342537946999073,
0.004388730973005295,
0.04082522913813591,
-0.012472210451960564,
-0.0031865453347563744,
-0.037549521774053574,
-0.02384171634912491,
0.03604664281010628,
-0.02078367955982685,
-0.019252290949225426,
-0.04093579202890396,
0.006182232405990362,
0.020198695361614227,
-0.042229000478982925,
-0.017324334010481834,
-0.04204346239566803,
-0.042443081736564636,
0.04918060824275017,
0.041793446987867355,
0.001609962317161262,
-0.012743435800075531,
-0.010109122842550278,
-0.029842903837561607,
-0.025754300877451897,
-0.0949959084391594,
0.0028322527650743723,
-0.011178025975823402,
0.029858218505978584,
0.009025759063661098,
0.01886618323624134,
0.006353588774800301,
-0.04029470309615135,
0.0017047355649992824,
0.04561898112297058,
0.056285448372364044,
0.030625101178884506,
0.0029568865429610014,
-0.001029907027259469,
0.020997872576117516,
0.049828480929136276,
-0.025752665475010872,
-0.039913780987262726,
-0.012484694831073284,
-0.05257273092865944,
0.01571699231863022,
-0.028850531205534935,
-0.009704183787107468,
-0.01533462293446064,
0.01394709013402462,
0.014565983787178993,
0.04151534289121628,
0.01796492375433445,
0.004961562808603048,
-0.013923871330916882,
0.04733869060873985,
-0.000234410326811485,
-0.01387137919664383,
0.021474238485097885,
0.044720180332660675,
-0.01771015115082264,
0.028200650587677956,
-0.01864813081920147,
-0.015043291263282299,
-0.06355975568294525,
-0.005038645584136248,
0.03293894603848457,
0.007862042635679245,
-0.0342048741877079,
0.021457530558109283,
0.0265207402408123,
0.02409432642161846,
-0.0009669607970863581,
-0.01449634600430727,
-0.04452528804540634,
-0.06952394545078278,
-0.002721064491197467,
0.01408300269395113,
0.010906113311648369,
0.0423688068985939,
-0.02227117493748665,
0.023530548438429832,
-0.001436607912182808,
-0.006616890896111727,
0.030955858528614044,
0.01888643577694893,
0.007765559945255518,
-0.0064645870588719845,
0.005471055395901203,
-0.02942558377981186,
0.022951899096369743,
-0.009793882258236408,
0.004394897259771824,
0.04328923672437668,
-0.006994552910327911,
-0.0019542973022907972,
-0.057628631591796875,
-0.022277310490608215,
-0.020021049305796623,
0.0324530154466629,
-0.01884164847433567,
-0.01673586666584015,
0.026782309636473656,
-0.019556492567062378,
0.017047345638275146,
-0.0077520012855529785,
0.001234012539498508,
-0.033868636935949326,
-0.012545118108391762,
0.005031826440244913,
-0.0053400746546685696,
0.012855852954089642,
-0.08387743681669235,
-0.005288335494697094,
0.008586818352341652,
-0.03485236316919327,
-0.004130080807954073,
-0.02334171161055565,
-0.033008672297000885,
0.030305465683341026,
-0.0121790561825037,
-0.023139599710702896,
0.030391868203878403,
0.016711879521608353,
0.008087498135864735,
0.06798902153968811,
0.018958711996674538,
-0.07764176279306412,
0.004733455833047628,
-0.04740538448095322,
0.017612360417842865,
-0.011419846676290035,
-0.01628280058503151,
0.07715580612421036,
-0.05469382554292679,
-0.041371311992406845,
0.004937977995723486,
-0.04252122342586517,
-0.02140381559729576,
-0.027482103556394577,
-0.0008652721298858523,
0.00308243278414011,
-0.0017977739917114377,
0.01295556128025055,
0.02714608423411846,
-0.06343984603881836,
-0.006165270693600178,
-0.0779338851571083,
-0.022747214883565903,
0.012610658071935177,
-0.001949198660440743,
0.04649309441447258,
-0.00610343087464571,
-0.029915792867541313,
0.048285093158483505,
0.043582119047641754,
-0.0364873968064785,
-0.0270342119038105,
-0.028808897361159325,
0.029931962490081787,
-0.015043340623378754,
-0.009241566061973572,
0.010396088473498821,
-0.0000844288369989954,
-0.01167619600892067,
0.033878494054079056,
0.056186363101005554,
-0.006113428622484207,
0.025586893782019615,
-0.015789644792675972,
0.002108821179717779,
-0.005680962465703487,
0.02033359371125698,
0.061454854905605316,
0.035177238285541534,
-0.026813235133886337,
-0.01802860014140606,
0.009440089575946331,
0.04263085499405861,
0.006392764393240213,
-0.039057184010744095,
0.08958792686462402,
0.033400386571884155,
0.031809646636247635,
-0.06408341228961945,
0.03576819971203804,
0.020528774708509445,
-0.0021636541932821274,
-0.008960659615695477,
0.0049694194458425045,
0.04944799095392227,
0.025175074115395546,
0.003348789643496275,
0.0022858851589262486,
0.06024269387125969,
-0.030191412195563316,
-0.034264881163835526,
-0.014904443174600601,
0.007461797911673784,
-0.007137799635529518,
-0.01062029879540205,
-0.0259772427380085,
0.06154398247599602,
0.0275449026376009,
0.017289508134126663,
-0.010060990229249,
-0.054762810468673706,
-0.003968734759837389,
-0.0864894837141037,
-0.01733422838151455,
-0.04274478927254677,
0.026927903294563293,
0.03590438887476921,
0.048797041177749634,
0.013603008352220058,
0.006663192063570023,
0.038083650171756744,
-0.018392782658338547,
-0.09623466432094574,
0.021664373576641083,
-0.039770014584064484,
0.03196994215250015,
-0.009530192241072655,
0.003661861876025796,
-0.023810606449842453,
-0.037407830357551575,
0.010856651701033115,
-0.026179952546954155,
0.00040355202509090304,
-0.03837335482239723,
-0.0236782468855381,
-0.053909774869680405,
-0.04028923064470291,
-0.009672627784311771,
0.03458606079220772,
0.059468358755111694,
-0.0326479896903038,
0.027092410251498222,
0.02457921765744686,
-0.02969226986169815,
-0.05078164115548134,
-0.012168372981250286,
-0.0010959383798763156,
-0.021355334669351578,
0.014232343062758446,
-0.00917076412588358,
0.014561374671757221,
0.010289551690220833,
0.006229124963283539,
0.06187823787331581,
-0.010761750862002373,
0.004064643289893866,
-0.011335710063576698,
-0.03229638934135437,
-0.00927709974348545,
-0.015112876892089844,
0.010913821868598461,
0.0275358185172081,
0.00824881624430418,
0.022120527923107147,
-0.01182294636964798,
0.047008246183395386,
-0.01242218166589737,
0.06557711958885193,
0.06565714627504349,
-0.06429833918809891,
-0.011075478978455067,
-0.03888940438628197,
0.012233034707605839,
-0.034043703228235245,
0.006768737453967333,
-0.005602408200502396,
0.012649424374103546,
-0.029735630378127098,
0.026167402043938637,
-0.02890992909669876,
0.013216271996498108,
-0.009717483073472977,
-0.01171821914613247,
-0.011080116964876652,
-0.014917383901774883,
-0.021164804697036743,
-0.012463947758078575,
-0.006958829239010811,
0.03910486027598381,
0.06961552053689957,
0.00495600001886487,
-0.010917299427092075,
-0.0657387301325798,
0.0016250606859102845,
0.02750610187649727,
0.05148380249738693,
-0.011049065738916397,
0.01429138146340847,
-0.08289889991283417,
-0.004926043562591076,
0.05333822965621948,
-0.040004462003707886,
0.03843638673424721,
-0.020060107111930847,
-0.01029646210372448,
0.007214704528450966,
-0.037991177290678024,
-0.001309271203354001,
-0.01847044937312603,
-0.02161858230829239,
0.0071678683161735535,
0.0003146544913761318,
0.029280833899974823,
-0.04043201729655266,
0.045613981783390045,
0.011996675282716751,
0.044349636882543564,
-0.04730435088276863,
-0.00288485549390316,
-0.031654100865125656,
-0.008775999769568443,
-0.032528962939977646,
-0.0713716670870781,
-0.006743277423083782,
0.005114827770739794,
-0.03767675906419754,
0.03345463052392006,
-0.029621370136737823,
-0.060202356427907944,
0.03675481304526329,
0.015427024103701115,
-0.044265538454055786,
-0.00045642099576070905,
-0.05758671462535858,
0.058297205716371536,
0.038456808775663376,
0.013020540587604046,
0.034896671772003174,
0.06741093099117279,
-0.002155769383534789,
0.018566420301795006,
-0.017557481303811073,
0.02677476778626442,
-0.03398412838578224,
0.014877558685839176,
-0.029546616598963737,
-0.014372039586305618,
-0.04284358024597168,
0.04654211923480034,
-0.02547435462474823,
-0.008954892866313457,
-0.02044437825679779,
-0.009944475255906582,
0.03278598189353943,
0.018471065908670425,
0.031264279037714005,
0.00014126600581221282,
0.013120867311954498,
-0.0016232924535870552,
-0.0116103021427989,
-0.04127047583460808,
0.04672678932547569,
0.023537086322903633,
-0.007711363956332207,
0.003073566360399127,
-0.003573397407308221,
0.0595477819442749,
-0.010267101228237152,
-0.0010348957730457187,
0.01912609487771988,
-0.005221018102020025,
0.04458481818437576,
0.0037734131328761578,
0.03696440905332565,
0.026003846898674965,
-0.03051641769707203,
-0.03700708970427513,
0.013470982201397419,
-0.014406255446374416,
0.002132569206878543,
-0.00739133870229125,
0.054976776242256165,
0.002648561494424939,
0.0032652299851179123,
-0.07856550067663193,
-0.019710222259163857,
0.029017478227615356,
0.004289115779101849,
0.008642458356916904,
-0.039715010672807693,
0.00002068385038000997,
-0.046318814158439636,
-0.0001690733915893361,
-0.022458970546722412,
0.003729363204911351,
-0.014141620136797428,
-0.005688224453479052,
0.010262484662234783,
-0.019573191180825233,
0.03975215181708336,
-0.0073510766960680485,
-0.016436714679002762,
-0.013144285418093204,
0.006355272140353918,
-0.024125246331095695,
-0.015164355747401714,
0.040155667811632156,
-0.031906142830848694,
-0.055453985929489136,
0.003807690227404237,
-0.0338539220392704,
0.028253357857465744,
-0.039048369973897934,
-0.010138985700905323,
0.037718337029218674,
-0.007557861041277647,
-0.017810193821787834,
-0.02581755444407463,
0.0324077382683754,
-0.022702151909470558,
0.031199323013424873,
-0.0013367895735427737,
-0.020225591957569122,
0.0006827916949987411,
-0.04235775023698807,
0.010345875285565853,
0.0043023014441132545,
0.020988576114177704,
0.01431985106319189,
0.05509144812822342,
-0.01729775406420231,
-0.03209816664457321,
0.0005130178178660572,
-0.04720168560743332,
0.025409512221813202,
-0.014985700137913227,
-0.011643736623227596,
0.007129711098968983,
-0.028681302443146706,
-0.0483657531440258,
-0.05080104246735573,
-0.0007980174268595874,
-0.013505011796951294,
0.030131401494145393,
-0.012504073791205883,
0.014366311952471733,
0.017450183629989624,
-0.02648480050265789,
0.0220470167696476,
-0.03047526627779007,
0.0009452517260797322,
-0.0030855333898216486,
-0.0003473504912108183,
0.01119328010827303,
-0.0223283302038908,
-0.006877727806568146,
0.07671432197093964,
0.03848503157496452,
-0.009019890800118446,
0.014545016922056675,
0.02302619069814682,
0.05540776252746582,
0.01865769922733307,
-0.03811005502939224,
-0.05449466407299042,
0.026349138468503952,
-0.0199100561439991,
0.004719603806734085,
0.02812018245458603,
-0.025842811912298203,
0.045366719365119934,
0.014410165138542652,
-0.008409024216234684,
-0.006261451169848442,
-0.002537425374612212,
-0.05072571337223053,
-0.0014953500358387828,
-0.015560891479253769,
0.01794489473104477,
-0.028734903782606125,
0.02020903304219246,
-0.025252707302570343,
-0.002898246981203556,
-0.003020988078787923,
-0.010625212453305721,
-0.08272606879472733,
0.00610691774636507,
-0.015958772972226143,
-0.026274848729372025,
0.05276275798678398,
0.028183242306113243,
-0.05089929327368736,
0.013367856852710247,
-0.015581273473799229,
-0.000933418981730938,
0.013635269366204739,
0.02353817969560623,
-0.013104842975735664,
0.05838195979595184,
-0.032212719321250916,
0.021448804065585136,
-0.049268726259469986,
0.014223054982721806,
0.11264476180076599,
0.053137362003326416,
0.004138498101383448,
-0.015081016346812248,
0.014899804256856441,
-0.013027215376496315,
-0.013354670256376266,
-0.025386346504092216,
0.0011983753647655249,
-0.0286568496376276,
0.03332897275686264,
0.005194703582674265,
0.07332009822130203,
0.010809066705405712,
-0.01925201527774334,
0.03961104899644852,
-0.01691426895558834,
0.010033369064331055,
0.009687467478215694,
0.042623408138751984,
-0.0047172983177006245,
0.021980226039886475,
-0.022661009803414345,
0.006105590611696243,
-0.006438661366701126,
-0.0008846570854075253,
-0.026265030726790428,
-0.021975615993142128,
0.0015657132025808096,
-0.01815243624150753,
-0.052573394030332565,
0.03870803862810135,
0.018606705591082573,
-0.034293241798877716,
-0.030157338827848434,
-0.007046150043606758,
0.04579044505953789,
0.008863009512424469,
0.012791325338184834,
0.04672735556960106,
0.028659164905548096,
0.016148291528224945,
0.007184575777500868,
0.0239914171397686,
-0.033665731549263,
0.002780030481517315,
-0.0004119991499464959,
0.026301098987460136,
-0.01221465039998293,
-0.02045787125825882,
-0.01863882690668106,
0.0016344378236681223,
0.0017901720711961389,
-0.04322955384850502,
-0.009759469889104366,
0.012613114900887012,
0.019435057416558266,
0.019421186298131943,
-0.0033194010611623526,
-0.05435776710510254,
0.019581876695156097,
0.006634610705077648,
0.024102862924337387,
-0.008458893746137619,
0.01869633048772812,
0.017389213666319847,
-0.03491649776697159,
0.05554962530732155,
-0.00498379347845912,
0.0030809768941253424,
-0.027494437992572784,
-0.008111619390547276,
-0.03867540881037712,
-0.029414504766464233,
0.004505508579313755,
0.029288096353411674,
0.015326039865612984,
0.040860891342163086,
0.02302967570722103,
-0.035135723650455475,
-0.04355872422456741,
0.03692514821887016,
0.0015100807650014758,
-0.01377329882234335,
-0.030179351568222046,
0.012217550538480282,
-0.0032434710301458836,
0.0166214257478714,
-0.026046307757496834,
0.004407192580401897,
0.0009983968921005726,
0.04264548793435097,
-0.006151026114821434,
0.024913864210247993,
-0.03544757515192032,
-0.008286992087960243,
-0.003812322160229087,
-0.003417412517592311,
-0.00966048613190651,
0.026885153725743294,
0.005606879014521837,
0.009775468148291111,
0.017632849514484406,
0.004141537472605705,
-0.03265075758099556,
0.010832337662577629,
0.024613892659544945,
-0.035382580012083054,
-0.013979715295135975,
0.020869173109531403,
0.0355609692633152,
0.0035354115534573793,
-0.04069056361913681,
0.0026095076464116573,
0.005037588067352772,
-0.007644783705472946,
0.04316893219947815,
-0.024823002517223358,
0.019553612917661667,
-0.039106469601392746,
0.03679894655942917,
-0.09422119706869125,
-0.018006769940257072,
-0.04815998673439026,
-0.014047246426343918,
0.03134080395102501,
-0.017108313739299774,
0.00039620872121304274,
0.07152874767780304,
-0.011720992624759674,
-0.006851006764918566,
0.004807760007679462,
0.011328998021781445,
-0.025714397430419922,
0.0006876507541164756,
0.04469357430934906,
0.0003608702390920371,
0.046941936016082764,
-0.025984521955251694,
-0.054272301495075226,
0.06015370786190033,
-0.01373449619859457,
-0.029652416706085205,
0.017123892903327942,
-0.04570576921105385,
0.010564742609858513,
0.031876418739557266,
-0.005864867474883795,
-0.009112754836678505,
0.05371738225221634,
-0.015853870660066605,
0.0024662299547344446,
0.002699190517887473,
-0.036055825650691986,
0.03172123804688454,
0.007160136941820383,
0.01663496531546116,
0.011317890137434006,
-0.019188292324543,
0.046200793236494064,
0.009466326795518398,
-0.00958013441413641,
0.008705329149961472,
-0.018942812457680702,
-0.03208377957344055,
-0.021485019475221634,
-0.021836701780557632,
0.020433157682418823,
0.021211989223957062,
0.044987138360738754,
-0.024328241124749184,
0.0321311354637146,
0.012561403214931488,
0.0035020876675844193,
-0.09226993471384048,
0.025470515713095665,
-0.03027242422103882,
-0.005977430380880833,
0.011740957386791706,
-0.01977388933300972,
0.05120224133133888,
0.025377102196216583,
-0.0673522874712944,
0.05879658833146095,
-0.013604884035885334,
0.005931557156145573,
-0.046895209699869156,
0.03129655495285988,
0.0012370734475553036,
0.04851866140961647,
0.040366243571043015,
0.10857289284467697,
-0.018935440108180046,
0.0328882597386837,
-0.0015878068516030908,
-0.010729199275374413,
0.009049447253346443,
0.034507445991039276,
-0.01970725506544113,
0.019423529505729675,
0.06009787693619728,
0.001463721040636301,
-0.020023496821522713,
0.013343779370188713,
0.012003389187157154,
0.03626979514956474,
0.0018801063997671008,
-0.033512212336063385,
-0.009073938243091106,
0.03071211464703083,
0.032005853950977325,
-0.009344002231955528,
-0.027174754068255424,
0.04321587085723877,
0.007556638214737177,
0.030296292155981064,
0.025105439126491547,
-0.0165083147585392,
0.03282616287469864,
-0.0397970974445343,
-0.017664363607764244,
0.03482289984822273,
-0.00005143445741850883,
0.007436476182192564,
-0.001839716685935855,
0.011865331791341305,
-0.002274362603202462,
0.0008620943408459425,
-0.023136930540204048,
-0.03133824095129967,
-0.02007000707089901,
0.016858505085110664,
-0.03308490291237831,
-0.01388212013989687,
0.014618678018450737,
0.015433255583047867,
0.017559677362442017,
0.012299307622015476,
-0.013225520960986614,
0.006003655027598143,
-0.024504268541932106,
-0.00008299366891151294,
0.008109718561172485,
0.018656335771083832,
0.03550879657268524,
-0.04542957991361618,
-0.0715872049331665,
0.037023480981588364,
0.02791821025311947,
0.003069339320063591,
0.030977509915828705,
-0.05343607813119888,
-0.03559764102101326,
-0.07483909279108047,
-0.00499031413346529,
0.004151713568717241,
0.0103694973513484,
-0.06542285531759262,
-0.025040343403816223,
-0.008013778366148472,
0.002815765328705311,
0.041036657989025116,
0.01185923907905817,
-0.006793161854147911,
0.02658109739422798,
0.0013949843123555183,
0.022277668118476868,
-0.0741780698299408,
0.01014025416225195,
0.017416661605238914,
0.015177351422607899,
0.019396420568227768,
0.007718830369412899,
-0.02679678052663803,
-0.01572083868086338,
0.040604278445243835,
-0.02508564107120037,
0.011972544714808464,
-0.01675013080239296,
-0.009645792655646801,
0.03469199314713478,
0.0045581962913274765,
-0.010888215154409409,
0.05710478872060776,
-0.02256995625793934,
0.037472017109394073,
0.04506717622280121,
0.01586936227977276,
-0.011382601223886013,
0.032316409051418304,
-0.021666955202817917,
-0.019189534708857536,
-0.003369081299751997,
0.010956871323287487,
0.05305596813559532,
-0.04705389589071274,
0.012407597154378891,
0.06336382776498795,
-0.026136644184589386,
-0.03850599005818367,
0.041608285158872604,
0.00761736324056983,
0.06069232523441315,
0.005620112176984549,
0.002232792554423213,
-0.014171766117215157,
0.003830256871879101,
-0.02442147396504879,
0.03304438665509224,
0.044981732964515686,
-0.01622549258172512,
0.010117829777300358,
0.016998592764139175,
0.031014833599328995,
0.015206764452159405,
-0.0014995163073763251,
0.027638264000415802,
-0.03483721241354942,
-0.051051247864961624,
0.0024209036491811275,
-0.004157075192779303,
0.01681768335402012,
0.03628671169281006,
0.013464461080729961,
0.04839756712317467,
0.006460156291723251,
0.010838758200407028,
-0.009043470956385136,
-0.009147174656391144,
-0.037457916885614395,
0.022113095968961716,
0.004255424719303846,
0.006328184623271227,
0.01858397200703621,
0.0019893182907253504,
-0.03601787984371185,
0.02720201015472412,
0.013847893103957176,
-0.03345900774002075,
0.0019090883433818817,
0.010497062467038631,
-0.039068445563316345,
0.006718080956488848,
0.010043312795460224,
-0.032454460859298706,
-0.032736923545598984,
0.05683031305670738,
0.018217220902442932,
0.014214618131518364,
0.0066991206258535385,
-0.01817752607166767,
-0.03576699644327164,
0.06390604376792908,
-0.0162870641797781,
-0.0037957618478685617,
-0.03229505568742752,
-0.007967391982674599,
-0.0015118996379896998,
-0.06252951174974442
] |
<p>In David J. Griffiths' <em>Introduction to Electrodynamics</em>, he claims that the superposition principle is not obvious but has always been found to be consistent with the experiments. So I was wondering have we found some physics quantities which do not follow superposition principle? If we have not till now why can't we generalize and make it into a law?</p>
<p>More specifically: Griffiths was talking about electromagnetic force. My question is about the existence of something like mass or charge and which doesn't follow this superposition principle.</p>
| 9,360 |
[
-0.03566955775022507,
0.0336078442633152,
0.02014303207397461,
-0.0696520209312439,
0.044544074684381485,
-0.009001234546303749,
-0.0520850233733654,
0.0036715054884552956,
-0.021595671772956848,
-0.022667694836854935,
0.018790852278470993,
-0.017889291048049927,
0.07595179229974747,
0.004894095938652754,
-0.0026473766192793846,
0.009595079347491264,
0.012206196784973145,
-0.018345916643738747,
-0.020517099648714066,
-0.01825679838657379,
-0.013256636448204517,
0.034550175070762634,
0.006576801650226116,
0.009058554656803608,
0.008368860930204391,
0.0333193875849247,
-0.005082451738417149,
-0.029998062178492546,
0.033744942396879196,
0.052475959062576294,
0.00032256098347716033,
-0.014763936400413513,
0.002547282027080655,
0.011738196946680546,
0.032607391476631165,
0.02873891592025757,
0.008596024475991726,
-0.05497439205646515,
-0.01003491785377264,
0.005541795399039984,
-0.041382502764463425,
-0.010810701176524162,
0.015711938962340355,
0.03219207376241684,
-0.03792702034115791,
0.0326056033372879,
0.048232343047857285,
-0.007657360751181841,
0.05460390821099281,
-0.05820196866989136,
0.05123049020767212,
0.004213555250316858,
0.040969137102365494,
0.032323673367500305,
-0.010804339312016964,
-0.03162531554698944,
0.06785938888788223,
0.03681746497750282,
-0.012808549217879772,
-0.0657837837934494,
-0.04356051981449127,
-0.024241946637630463,
0.00926551129668951,
-0.04968913644552231,
-0.026182955130934715,
0.07137727737426758,
0.008134257048368454,
0.018515320494771004,
0.010761752724647522,
0.008755110204219818,
-0.0012973248958587646,
-0.002575348364189267,
0.04597875475883484,
0.020398247987031937,
0.00015441617870237678,
-0.03235544636845589,
0.027045784518122673,
-0.014448415488004684,
0.02873499132692814,
0.05823603644967079,
-0.04241538420319557,
0.026958871632814407,
0.02374373748898506,
0.034830790013074875,
0.00619277311488986,
-0.052317749708890915,
0.025773916393518448,
0.003444495378062129,
0.0009223585366271436,
0.07215817272663116,
-0.03544924780726433,
0.006438938435167074,
0.04237990826368332,
-0.0113863255828619,
-0.0024597730953246355,
0.04147528111934662,
0.01525792758911848,
0.030749382451176643,
-0.012530913576483727,
-0.041037991642951965,
0.03155520558357239,
-0.004052662756294012,
0.034970901906490326,
0.08556703478097916,
-0.006322737317532301,
-0.04740550369024277,
-0.015714209526777267,
0.015891410410404205,
-0.026300452649593353,
0.018840862438082695,
-0.0060772644355893135,
0.010111912153661251,
0.01728397235274315,
0.010471356101334095,
0.016233230009675026,
0.018404388800263405,
-0.0033838998060673475,
-0.004668056033551693,
0.0991683155298233,
0.07887626439332962,
0.014360944740474224,
-0.020311666652560234,
-0.012945389375090599,
-0.026358673349022865,
-0.07160712778568268,
-0.017476007342338562,
0.013742604292929173,
0.028069529682397842,
0.010262861847877502,
0.022478004917502403,
0.03401019424200058,
-0.013532048091292381,
-0.0014388535637408495,
0.03318861499428749,
0.025467664003372192,
-0.015121400356292725,
-0.10885222256183624,
-0.05520866438746452,
0.04305734112858772,
-0.028102736920118332,
-0.04383387044072151,
-0.030864398926496506,
-0.005420648027211428,
0.033488232642412186,
0.06905104964971542,
0.00824812613427639,
-0.025428688153624535,
-0.010504506528377533,
0.05066046863794327,
0.0011075043585151434,
0.010220513679087162,
-0.02836926467716694,
0.022865179926156998,
-0.024130195379257202,
-0.013433975167572498,
-0.0644880160689354,
0.022515105083584785,
0.022608639672398567,
0.007205754518508911,
0.004469108302146196,
0.03996560722589493,
-0.052669502794742584,
0.008496864698827267,
-0.0005165550392121077,
0.01525051984935999,
-0.05475025996565819,
0.0670231357216835,
0.010450736619532108,
0.014608738012611866,
0.03636099025607109,
0.004240988753736019,
0.013036402873694897,
-0.017413778230547905,
0.013881485909223557,
0.03719168156385422,
-0.02838481403887272,
-0.028237929567694664,
-0.028081169351935387,
0.054625675082206726,
-0.029523402452468872,
-0.01584515906870365,
-0.023449840024113655,
-0.006282361689954996,
0.023012423887848854,
-0.022525059059262276,
0.03569694980978966,
-0.011150628328323364,
-0.009724646806716919,
0.02716663107275963,
-0.05616774410009384,
-0.0011190277291461825,
-0.030151650309562683,
0.026548270136117935,
0.005422560032457113,
-0.02761104516685009,
0.04007278010249138,
0.009913479909300804,
-0.00919609609991312,
-0.053029317408800125,
-0.03963041678071022,
0.011700684204697609,
0.03601708263158798,
-0.011395481415092945,
-0.010078933089971542,
0.024437878280878067,
0.020183352753520012,
0.031421858817338943,
-0.0004156399518251419,
0.010421881452202797,
0.00785863772034645,
-0.0473657101392746,
0.022514088079333305,
-0.030245864763855934,
0.02292158454656601,
0.011650752276182175,
0.014494262635707855,
0.029352542012929916,
-0.013048501685261726,
-0.019471820443868637,
0.0430239662528038,
-0.033431291580200195,
0.0745721235871315,
0.0023373602889478207,
-0.010134820826351643,
0.019509313628077507,
0.05709514021873474,
0.02449082024395466,
-0.00461322208866477,
0.010573174804449081,
-0.025744883343577385,
-0.05635204538702965,
-0.011048677377402782,
0.012764012441039085,
0.03216908499598503,
-0.036548785865306854,
0.02346746064722538,
-0.007800176274031401,
0.05143854022026062,
0.020731890574097633,
0.020420167595148087,
-0.013217435218393803,
-0.05953151732683182,
0.002932862611487508,
0.02059367671608925,
0.01968136802315712,
0.03024335764348507,
0.03230723366141319,
0.00594209274277091,
0.012550042942166328,
-0.007377976085990667,
-0.008991106413304806,
0.014401953667402267,
-0.007696243468672037,
0.03528863936662674,
0.0014833267778158188,
-0.053808946162462234,
0.00984310731291771,
-0.036109957844018936,
0.04816541075706482,
0.027175724506378174,
-0.006943495012819767,
-0.014427677728235722,
-0.025710228830575943,
-0.02759869210422039,
-0.012100810185074806,
-0.020424341782927513,
-0.036234889179468155,
-0.02579684741795063,
0.022388529032468796,
-0.0496533028781414,
-0.008284930139780045,
-0.012175500392913818,
-0.012546762824058533,
-0.037890855222940445,
-0.014522174373269081,
0.04395570978522301,
-0.01011213194578886,
0.05730275809764862,
-0.038529399782419205,
-0.018389122560620308,
-0.011698161251842976,
-0.05367470160126686,
0.005804641172289848,
0.06526413559913635,
-0.043306734412908554,
0.0014025064883753657,
-0.06376739591360092,
-0.05447004735469818,
0.07871062308549881,
0.0012947721406817436,
0.03171719238162041,
0.03880951181054115,
-0.01964646950364113,
-0.028333066031336784,
-0.003312179585918784,
-0.01926923356950283,
-0.00747976778075099,
-0.06372766941785812,
0.017523687332868576,
0.047267716377973557,
-0.032034777104854584,
-0.04712396487593651,
0.00418111402541399,
-0.029722845181822777,
-0.06915710121393204,
0.004582148045301437,
-0.026661721989512444,
0.00024433148792013526,
-0.03750798478722572,
0.02435324713587761,
0.03335508331656456,
-0.06040625646710396,
-0.0010519198840484023,
-0.03175779804587364,
-0.059235863387584686,
0.029119446873664856,
-0.016167832538485527,
0.06696377694606781,
-0.0013464658986777067,
-0.032310329377651215,
0.0612199530005455,
0.01325884461402893,
-0.03421090543270111,
-0.007619050797075033,
-0.01883542910218239,
0.010114955715835094,
-0.0158598180860281,
-0.004208954982459545,
0.040745705366134644,
0.015500236302614212,
-0.021488165482878685,
0.015205051749944687,
0.024199992418289185,
-0.02866307459771633,
0.03163057193160057,
-0.005892133340239525,
-0.003811565227806568,
0.03242840617895126,
-0.004877452738583088,
0.05338666960597038,
0.017951292917132378,
-0.0145186148583889,
-0.01091532502323389,
0.0201138723641634,
0.04999008774757385,
0.02126440964639187,
-0.012933149002492428,
0.043779727071523666,
-0.00575542077422142,
0.007975466549396515,
-0.04006288945674896,
0.045271482318639755,
-0.031240494921803474,
-0.0018705918919295073,
-0.010041898116469383,
0.004296403843909502,
0.008232960477471352,
-0.026210056617856026,
0.009643393568694592,
0.05519263818860054,
0.004939163103699684,
-0.05591132864356041,
-0.018975449725985527,
-0.014750128611922264,
-0.011871745809912682,
0.011362802237272263,
-0.021180011332035065,
-0.0060583073645830154,
0.060247860848903656,
0.02355794981122017,
0.0034234514459967613,
0.0024834717623889446,
-0.02538413181900978,
0.0016629652818664908,
-0.010189393535256386,
-0.02606678567826748,
0.012959394603967667,
0.027846843004226685,
0.03541821241378784,
0.07278960943222046,
0.01633310690522194,
0.02196507155895233,
0.020458202809095383,
-0.015595040284097195,
-0.08865875005722046,
0.006808646954596043,
-0.025263911113142967,
-0.010899566113948822,
-0.010110423900187016,
-0.05184736102819443,
-0.02036946453154087,
-0.0031240428797900677,
-0.01584332436323166,
-0.030580131337046623,
0.017657114192843437,
-0.06670206785202026,
-0.007113968953490257,
-0.05556827411055565,
-0.08708422631025314,
-0.04295683652162552,
0.013087255880236626,
0.0012207601685076952,
-0.05211661383509636,
-0.014539425261318684,
0.00665066996589303,
-0.04436017945408821,
-0.0046872724778950214,
-0.01847558282315731,
0.025855382904410362,
0.006850176956504583,
0.03265940025448799,
0.02161918208003044,
0.006757347844541073,
-0.04103726148605347,
0.002789236605167389,
0.032799020409584045,
0.05609757825732231,
0.0073846373707056046,
-0.022332588210701942,
-0.018486911430954933,
-0.015775108709931374,
-0.021672839298844337,
0.0018418923718854785,
0.0822049006819725,
0.02184891887009144,
-0.0006129119428806007,
0.008098103106021881,
0.0014453785261139274,
0.012385372072458267,
0.042780183255672455,
0.034725941717624664,
0.027411676943302155,
-0.014434438198804855,
-0.031604405492544174,
0.03635099157691002,
-0.04145708307623863,
0.012842737138271332,
0.005148784723132849,
0.009438305161893368,
-0.009694524109363556,
-0.017796726897358894,
-0.010090801864862442,
0.026213737204670906,
-0.010298630222678185,
0.007826103828847408,
-0.025862041860818863,
-0.03008677251636982,
0.004502896685153246,
-0.011402091011404991,
0.034333113580942154,
-0.0008228740771301091,
0.04660438373684883,
0.027992725372314453,
-0.008681055158376694,
-0.06395862996578217,
0.043123193085193634,
0.03894851356744766,
0.04194911941885948,
-0.0218602754175663,
0.0004281457222532481,
-0.04348837211728096,
-0.01194828376173973,
0.005716896150261164,
-0.020912237465381622,
-0.0009215029422193766,
-0.04391119256615639,
0.008126934058964252,
-0.03695673868060112,
-0.05021117627620697,
-0.019409898668527603,
0.03233810514211655,
-0.010289440862834454,
0.02490697242319584,
0.003850530134513974,
-0.015595630742609501,
0.02657225914299488,
0.018252307549118996,
0.06704927980899811,
0.04858732968568802,
0.037306543439626694,
0.005941223353147507,
0.008789974264800549,
0.019802656024694443,
-0.04365259036421776,
-0.08993439376354218,
0.008673337288200855,
-0.0016093209851533175,
-0.015866238623857498,
0.016201077029109,
-0.03925621882081032,
-0.0869448110461235,
-0.005810737609863281,
-0.01857597939670086,
-0.021601885557174683,
0.00989388395100832,
-0.04714568331837654,
-0.013184170238673687,
0.046548739075660706,
0.02712215483188629,
0.014602676965296268,
0.023321492597460747,
-0.00042644425411708653,
-0.043619122356176376,
0.011258273385465145,
0.01601831242442131,
-0.028148366138339043,
0.021642476320266724,
-0.03783566504716873,
0.022466370835900307,
-0.05753065645694733,
0.032022587954998016,
0.033101730048656464,
-0.009021014906466007,
-0.011915876530110836,
-0.019996052607893944,
-0.023930493742227554,
-0.0006871520890854299,
0.019162513315677643,
-0.01960405334830284,
-0.02356080710887909,
0.05099702998995781,
-0.000042789735744008794,
0.014780784957110882,
0.034486353397369385,
0.02400599606335163,
-0.013103257864713669,
0.025968827307224274,
-0.009270206093788147,
-0.0009014145471155643,
-0.03606761619448662,
-0.024550404399633408,
0.014407345093786716,
-0.03782272711396217,
0.03333859145641327,
-0.019024517387151718,
-0.0053942217491567135,
0.020558178424835205,
-0.05179182067513466,
-0.07329346984624863,
0.026038262993097305,
0.006982941180467606,
0.0206314604729414,
-0.07420824468135834,
0.016840513795614243,
0.047209884971380234,
0.009656073525547981,
-0.05403420329093933,
-0.05579877272248268,
0.007442527916282415,
0.00002791462065943051,
0.038608066737651825,
0.011977125890552998,
0.005090532824397087,
-0.03207693248987198,
-0.019850831478834152,
0.018311748281121254,
0.040162887424230576,
-0.032388847321271896,
0.031279776245355606,
0.019573714584112167,
0.0038417561445385218,
0.04690663889050484,
-0.01674499921500683,
-0.03911439701914787,
0.03196056932210922,
0.027385400608181953,
0.04156267270445824,
0.004871127661317587,
0.04142988473176956,
-0.0056021432392299175,
-0.02632969617843628,
-0.021153569221496582,
0.008919432759284973,
0.029848970472812653,
-0.039536524564027786,
0.004240874201059341,
0.032732680439949036,
0.009256352670490742,
-0.0196395143866539,
-0.036362174898386,
0.019218364730477333,
0.015158802270889282,
-0.013803635723888874,
-0.0037373946979641914,
0.02966291457414627,
-0.012475808151066303,
-0.07214027643203735,
0.035590481013059616,
-0.018252475187182426,
0.03177744895219803,
-0.018660733476281166,
0.03780901059508324,
0.024185316637158394,
-0.03243956342339516,
0.03927907720208168,
-0.012717751786112785,
0.0032310006208717823,
0.006482056807726622,
0.02005176432430744,
-0.018791915848851204,
0.0016770604997873306,
-0.03466854616999626,
-0.016843920573592186,
-0.01604662463068962,
0.012582119554281235,
0.0783003717660904,
-0.03250913694500923,
0.07989241927862167,
0.04531138390302658,
-0.01593870110809803,
-0.019980888813734055,
-0.028837330639362335,
0.008546092547476292,
0.03378557041287422,
-0.01795223355293274,
0.020915579050779343,
-0.004689635243266821,
0.015194394625723362,
0.043472349643707275,
0.06898609548807144,
-0.02457577735185623,
-0.025027001276612282,
0.03392532467842102,
0.020851915702223778,
0.04688224196434021,
-0.024887584149837494,
-0.03804687410593033,
0.050507351756095886,
-0.010575084015727043,
-0.024591421708464622,
0.018650785088539124,
0.0006684526451863348,
0.0029923664405941963,
-0.006487175822257996,
0.01636967808008194,
-0.018279647454619408,
-0.02758113108575344,
-0.003967949189245701,
0.04341261088848114,
-0.01659410260617733,
0.019133929163217545,
0.00813576951622963,
0.02714230678975582,
0.017307713627815247,
0.027125654742121696,
-0.0008116945391520858,
0.024824194610118866,
-0.07072365283966064,
-0.030345214530825615,
-0.06108031049370766,
-0.018206851556897163,
0.028021614998579025,
-0.01878148503601551,
-0.023271720856428146,
-0.053658757358789444,
-0.017774246633052826,
0.02870185300707817,
0.017868991941213608,
-0.005203229375183582,
-0.012390801683068275,
0.03381939232349396,
-0.029723089188337326,
0.01490752212703228,
-0.040421366691589355,
0.0261119082570076,
0.11353062838315964,
-0.002721379976719618,
0.022205684334039688,
-0.03293429687619209,
0.008914881385862827,
-0.013732866384088993,
-0.031672749668359756,
-0.030330069363117218,
0.02847101353108883,
-0.012012781575322151,
0.030338531360030174,
0.004953072406351566,
0.028097789734601974,
0.030041389167308807,
-0.026859788224101067,
0.037373341619968414,
-0.035926297307014465,
-0.014033813960850239,
-0.0006871841032989323,
0.022942999377846718,
0.007709937635809183,
0.02026233822107315,
-0.026632608845829964,
0.023189816623926163,
-0.028985152021050453,
-0.014455277472734451,
0.04042525961995125,
-0.014614822342991829,
0.026853255927562714,
0.05796860530972481,
-0.03671939671039581,
-0.008875376544892788,
0.01362619362771511,
-0.038130924105644226,
-0.0596093125641346,
0.009440273977816105,
0.034318774938583374,
-0.010520747862756252,
0.004649423062801361,
-0.0022888726089149714,
0.05118526145815849,
-0.0030974838882684708,
0.008781777694821358,
0.03868952393531799,
-0.04926585033535957,
0.018959056586027145,
-0.015486571006476879,
0.05994260311126709,
-0.03320879861712456,
-0.0011004548287019134,
0.05172448232769966,
-0.019854726269841194,
-0.013484570197761059,
-0.05052705109119415,
-0.025167196989059448,
-0.011803905479609966,
0.01569475792348385,
0.01626262441277504,
-0.010103731416165829,
0.00936797447502613,
0.01519504003226757,
-0.027763156220316887,
0.008877445943653584,
-0.011878984048962593,
0.009372584521770477,
-0.019941702485084534,
0.02190239727497101,
0.023878658190369606,
0.019975226372480392,
-0.031583111733198166,
-0.024149781093001366,
-0.040436867624521255,
-0.01740148290991783,
0.012217119336128235,
0.01990448869764805,
0.039532773196697235,
-0.007860500365495682,
-0.01467242930084467,
0.010027631185948849,
-0.05678906664252281,
-0.007598564960062504,
0.03699870780110359,
-0.02161596715450287,
-0.021253203973174095,
-0.009613237343728542,
-0.020756442099809647,
0.024446411058306694,
0.052736539393663406,
-0.041459858417510986,
-0.004351846408098936,
0.023456569761037827,
0.029159173369407654,
0.018495971336960793,
-0.014634237624704838,
-0.029350504279136658,
0.007804453372955322,
-0.004401399753987789,
0.0053274258971214294,
-0.017362305894494057,
0.013179600238800049,
0.053708694875240326,
-0.01754256896674633,
0.0019976794719696045,
0.06458110362291336,
0.00933846179395914,
-0.0012740062084048986,
0.02404160238802433,
-0.015493884682655334,
0.026992229744791985,
0.024838687852025032,
0.027347365394234657,
-0.017850598320364952,
-0.025999194011092186,
-0.042178887873888016,
0.023532157763838768,
-0.009876765310764313,
0.030000872910022736,
0.008514095097780228,
-0.015933426097035408,
0.01638595387339592,
0.0003615480673033744,
-0.008276117965579033,
-0.006262470968067646,
-0.0319020040333271,
-0.01305095013231039,
-0.03689105436205864,
-0.03127602860331535,
-0.043024856597185135,
0.025010570883750916,
-0.015171052888035774,
-0.008470764383673668,
0.01427511963993311,
0.05686689540743828,
-0.04609474539756775,
0.002538053784519434,
0.033057622611522675,
-0.00375854829326272,
0.05094527080655098,
0.003574409754946828,
0.0012692861491814256,
-0.008814772590994835,
-0.04038166627287865,
-0.05091414600610733,
0.040657103061676025,
-0.025482462719082832,
-0.03572853282094002,
0.036385178565979004,
0.006516784429550171,
-0.00015707191778346896,
0.05270131677389145,
-0.028533846139907837,
0.02199389785528183,
-0.0017097046365961432,
-0.006210482679307461,
-0.01816295087337494,
-0.009647728875279427,
-0.0029153330251574516,
-0.019245494157075882,
-0.01870923489332199,
0.025738023221492767,
0.01784222386777401,
0.03343163803219795,
-0.02644835226237774,
0.018632730469107628,
-0.009724079631268978,
-0.0010988974245265126,
0.05865940451622009,
-0.004278843756765127,
-0.01036946102976799,
0.044544465839862823,
-0.04279237613081932,
0.0391695499420166,
-0.0068898871541023254,
0.019608573988080025,
-0.07317251712083817,
-0.03310946747660637,
0.027681579813361168,
0.03322533518075943,
0.04170091822743416,
-0.040692415088415146,
-0.0036332120653241873,
0.021331068128347397,
-0.0984823927283287,
0.027367612347006798,
-0.016532575711607933,
-0.035383012145757675,
0.0022427409421652555,
-0.008796483278274536,
-0.018860600888729095,
0.0715496763586998,
0.010584890842437744,
0.06887201219797134,
-0.017048122361302376,
0.024884747341275215,
0.000921220809686929,
-0.033540040254592896,
-0.057975396513938904,
0.001119612599723041,
-0.01211869902908802,
0.007711787708103657,
0.05942349135875702,
-0.016497783362865448,
-0.0212649405002594,
0.04596583917737007,
-0.0041419267654418945,
-0.0029160415288060904,
-0.0018093375256285071,
0.03378863260149956,
-0.007017467170953751,
0.03384518623352051,
0.016534041613340378,
-0.0047797514125704765,
-0.004813371226191521,
0.035876426845788956,
0.006589481141418219,
0.024248698726296425,
0.0008028229931369424,
0.005331310443580151,
0.016836019232869148,
-0.026285598054528236,
-0.028106581419706345,
-0.000025042672859854065,
-0.03537363559007645,
-0.025594109669327736,
0.0024193276185542345,
0.06550189107656479,
-0.015847118571400642,
0.016457630321383476,
-0.027737943455576897,
-0.048644207417964935,
-0.03123333491384983,
0.03843117132782936,
0.013860087841749191,
0.03147745877504349,
0.029287829995155334,
0.002004146110266447,
-0.016946639865636826,
0.03396104648709297,
0.03546147048473358,
0.013682517223060131,
-0.04886956512928009,
0.001369828823953867,
-0.002847671275958419,
0.004974051378667355,
0.013693724758923054,
-0.057843562215566635,
-0.059370044618844986,
0.025744765996932983,
0.006449482869356871,
0.008603175170719624,
-0.013197948224842548,
-0.028002623468637466,
0.022383831441402435,
-0.07728288322687149,
0.06290911138057709,
-0.009310017339885235,
0.028661206364631653,
-0.04421478137373924,
-0.013498148880898952,
0.005316056311130524,
-0.03677373379468918,
0.002954038791358471,
-0.026213329285383224,
0.02920275740325451,
0.022792764008045197,
-0.020870741456747055,
0.01839406043291092,
-0.014480500482022762,
-0.013482209295034409,
-0.0008391900337301195,
-0.02752254344522953,
-0.012720100581645966,
0.014785800129175186,
0.002280864864587784,
-0.024434680119156837,
-0.00722011411562562,
-0.0011608620407059789,
0.023394199088215828,
-0.01276662852615118,
-0.034599728882312775,
0.06108705699443817,
0.036288950592279434,
0.0013941358774900436,
0.03790196403861046,
-0.03792566433548927,
0.026969915255904198,
-0.011937268078327179,
-0.0313764289021492,
-0.043768011033535004,
0.01962284930050373,
-0.009546446613967419,
-0.009376060217618942,
0.0018073973478749394,
0.024036088958382607,
0.018505742773413658,
-0.006232315208762884,
-0.03807135671377182,
0.0615936741232872,
-0.006460694596171379,
-0.015758052468299866,
0.07172630727291107,
-0.02199094183743,
0.05781065672636032,
0.004180136136710644,
0.010376856662333012,
0.025256173685193062,
-0.012065605260431767,
0.00014015016495250165,
0.030299900099635124,
0.019230108708143234,
-0.016879715025424957,
-0.004383979365229607,
0.06974515318870544,
0.01003195345401764,
-0.007308425381779671,
0.02654917724430561,
0.036482252180576324,
-0.025529194623231888,
-0.010284586809575558,
-0.025201451033353806,
-0.016903378069400787,
0.04624847322702408,
0.008645202964544296,
-0.02798030897974968,
0.07484769821166992,
-0.049548421055078506,
0.012345151975750923,
-0.034503329545259476,
0.02382970042526722,
0.0026315064169466496,
-0.0022681986447423697,
-0.02359704114496708,
0.06848142296075821,
0.004788838792592287,
-0.03933529555797577,
-0.01618165336549282,
0.003364227944985032,
0.012346777133643627,
-0.030753426253795624,
0.0031279982067644596,
-0.00805783923715353,
0.018929703161120415,
-0.021467434242367744,
-0.004341043997555971,
-0.01126053649932146,
-0.024826517328619957,
0.0479641854763031,
0.00005652326581184752,
0.027661480009555817,
-0.025168173015117645,
0.022437775507569313,
-0.06911712139844894,
0.024341730400919914,
-0.03193727880716324,
-0.026103151962161064,
-0.032194435596466064,
0.05000804364681244,
-0.022681672126054764,
-0.01649290695786476
] |
<p>I want to build a geyser attached to a pump with copper tubing running into an oil tank. This is done because the oil solidifies at a temperature below 15 degrees Celsius. I have done a few calculations to determine the amount of time it would take to heat the oil, but i am not sure if they are correct.</p>
<p>Pumping velocity = $3m/s$</p>
<p>Water temperature = $60C$</p>
<p>oil temp =$ 5C$</p>
<p>Desired Temp $20C$</p>
<p>15000 liter oil tank</p>
<p>20mm diameter copper tubing was used</p>
<p>6m of tubing is submerged into the oil</p>
<p>Calculating the heat transfer coefficient:
$$Re=(C.d)/Vf$$
$$ =(3x0.02)/0.475x10^{-6}$$
$$=126 315$$ thus the flow would be turbulant</p>
<p>$$Nu=0.023Re^{0.8}xPr^{0.33} (0.33 for cooling)$$
$$Nu=397.98$$</p>
<p>$$Nu=(α.d)/λ$$
$$α=(Nu.λ)/d$$
$$=(397.98x654.3x10^{-6})/0.02$$
$$α=13.02kW/m^2.K$$</p>
<p>I then used the following equation for the heat transfer inside the tank:
$$Q^*=αA(deltaT)$$
$$Q^*=13020xπx0.02x6(60-40)$$
$$= 31.248kW$$</p>
<p>Energy required to heat the oil:
$$Q=mcpT$$
$$Q=15000x1800x(20-5)$$
$$Q=405000J$$</p>
<p>Heating time:
$$t=405000/31.248$$</p>
<p>$$t=3.6 Hours$$ </p>
<p>Can someone please tell me how you would do the calculations. Also please assume any information not provided.</p>
<p>Thank you.</p>
| 9,361 |
[
-0.004491592291742563,
-0.01687820814549923,
0.0034939381293952465,
0.018961923196911812,
0.01161479577422142,
-0.02431548573076725,
-0.033199671655893326,
-0.014827852137386799,
0.012480339966714382,
-0.01967012882232666,
0.06410397589206696,
0.020151395350694656,
0.04993933439254761,
0.028124764561653137,
0.010585220530629158,
0.006557205226272345,
0.015317206270992756,
-0.0064849103800952435,
0.023462830111384392,
-0.015416115522384644,
-0.0155088035389781,
0.0028509036637842655,
-0.03683267533779144,
-0.02907077595591545,
0.003118401626124978,
0.05005832388997078,
-0.0016589236911386251,
-0.02278142236173153,
-0.0389149934053421,
0.029110370203852654,
0.028722044080495834,
-0.04334273561835289,
-0.003914871718734503,
0.005676312372088432,
0.04052932560443878,
0.03823297843337059,
-0.027474405243992805,
0.0016158897196874022,
-0.02280922420322895,
0.020476913079619408,
-0.04888536036014557,
-0.006239540874958038,
0.03314803168177605,
0.00970466062426567,
0.01722005009651184,
-0.00873465184122324,
0.0219647865742445,
-0.029172347858548164,
0.028187736868858337,
-0.05568829923868179,
0.003041520481929183,
0.000592376512940973,
0.0011871110182255507,
0.021059906110167503,
-0.024423344060778618,
0.007233602460473776,
0.061199676245450974,
0.07002823799848557,
-0.00969590526074171,
-0.02210455946624279,
0.021065926179289818,
0.021309273317456245,
-0.04886116459965706,
-0.020208649337291718,
-0.008389914408326149,
-0.03129616379737854,
-0.009341784752905369,
0.03038012981414795,
-0.025178315117955208,
-0.011170892044901848,
0.05370216816663742,
-0.03556268289685249,
0.006149039603769779,
-0.024006998166441917,
-0.003993325401097536,
-0.026973308995366096,
-0.01629714109003544,
0.02683129534125328,
-0.0264242235571146,
0.05306462198495865,
-0.011086329817771912,
0.020698057487607002,
0.011302854865789413,
0.004139286000281572,
-0.005867986474186182,
0.01657775044441223,
0.03240913525223732,
0.002958862576633692,
0.046006232500076294,
0.004434455651789904,
0.01639881357550621,
0.02474459633231163,
0.009531001560389996,
0.018537526950240135,
0.006702563259750605,
0.017537258565425873,
0.019878003746271133,
0.030316784977912903,
-0.005794484633952379,
-0.026044342666864395,
0.017077365890145302,
-0.005645299796015024,
0.01874000020325184,
0.0925668254494667,
0.03817329555749893,
-0.020955760031938553,
0.000002586810296634212,
-0.02520325779914856,
0.008926505222916603,
-0.033050786703825,
0.0014816481852903962,
-0.038671188056468964,
-0.0012833514483645558,
-0.029640916734933853,
-0.03736621513962746,
-0.03151575103402138,
0.010923333466053009,
-0.040993236005306244,
0.02661188319325447,
0.00805079098790884,
0.04485606774687767,
-0.00706897908821702,
0.06305018067359924,
-0.02850867435336113,
-0.02772531844675541,
0.05087409168481827,
0.008945819921791553,
-0.02848733402788639,
-0.06859201937913895,
0.03866223990917206,
-0.005476139020174742,
0.010972611606121063,
0.0020873916801065207,
-0.015100025571882725,
0.024674836546182632,
-0.0015297544887289405,
-0.07986609637737274,
-0.08736419677734375,
0.03164747357368469,
-0.013880610466003418,
-0.026541491970419884,
-0.06728199124336243,
0.023062633350491524,
0.035976093262434006,
0.053363677114248276,
-0.008958029560744762,
-0.02846626192331314,
-0.024700762704014778,
0.02069857344031334,
-0.016696007922291756,
-0.023138156160712242,
0.0066617755219340324,
0.026529984548687935,
-0.012738279066979885,
-0.013510887511074543,
-0.0375792495906353,
-0.0077425697818398476,
0.022768573835492134,
0.0020506030414253473,
-0.030772408470511436,
0.013368448242545128,
-0.031575705856084824,
0.008842800743877888,
0.03091074712574482,
0.00498732877895236,
-0.03569328039884567,
0.07095429301261902,
0.033546727150678635,
0.036576446145772934,
-0.004205974750220776,
-0.009585537016391754,
0.011696185916662216,
-0.002355177653953433,
-0.021470993757247925,
0.04634609818458557,
-0.028073327615857124,
-0.007462053094059229,
-0.04002692550420761,
0.011839061044156551,
0.030935006216168404,
-0.05474076047539711,
-0.028177984058856964,
0.0011973661603406072,
-0.002392976311966777,
0.00893577840179205,
0.05105041712522507,
-0.0048928819596767426,
0.014607136137783527,
0.0137584637850523,
-0.011387977749109268,
-0.0213811956346035,
-0.02565813437104225,
0.010250316932797432,
0.014349522069096565,
-0.0012653693556785583,
-0.0028998875059187412,
0.0028877942822873592,
0.02968357503414154,
0.0032599943224340677,
-0.027494950219988823,
0.05970471352338791,
-0.015186307020485401,
0.04662838950753212,
-0.004742714110761881,
0.03068074956536293,
0.05580606311559677,
0.0639004036784172,
-0.03719177469611168,
0.020267246291041374,
-0.030826160684227943,
0.033087074756622314,
-0.03052421286702156,
-0.006860439665615559,
0.019755182787775993,
-0.05530589818954468,
-0.005850005894899368,
0.04610137641429901,
-0.004019895102828741,
0.04649169743061066,
0.033967044204473495,
-0.02185893803834915,
0.05218002200126648,
0.02349921315908432,
0.018412861973047256,
0.019789453595876694,
0.00954730436205864,
0.006459623575210571,
0.03552458807826042,
-0.0009073227411136031,
-0.04769789054989815,
-0.015298602171242237,
-0.04033909738063812,
0.00457477942109108,
0.007996926084160805,
-0.039483554661273956,
0.018182603642344475,
0.04007275402545929,
0.003453016048297286,
0.07368680089712143,
0.021169714629650116,
-0.024016790091991425,
-0.027181770652532578,
0.02022598497569561,
0.061211034655570984,
0.0014800840290263295,
0.010385452769696712,
-0.008059913292527199,
-0.0013143280521035194,
0.04122958332300186,
-0.03539702296257019,
-0.00025008671218529344,
0.04096367955207825,
0.05956389382481575,
-0.018325569108128548,
-0.017655909061431885,
-0.006754857487976551,
0.05464407801628113,
-0.028751950711011887,
0.011892490088939667,
0.0163417961448431,
-0.005470035132020712,
0.043116819113492966,
-0.0076989359222352505,
-0.017781632021069527,
-0.0045398143120110035,
0.041314173489809036,
-0.020608866587281227,
-0.02517341822385788,
0.015561020001769066,
-0.016693489626049995,
0.007405469659715891,
-0.018857071176171303,
0.013907305896282196,
-0.051780737936496735,
-0.00971743930131197,
0.02402309887111187,
0.011460325680673122,
0.006592409685254097,
-0.04091496765613556,
-0.011082899756729603,
-0.017467645928263664,
0.03291422873735428,
0.020041128620505333,
0.004917614161968231,
-0.060076650232076645,
-0.0006922594620846212,
0.030149154365062714,
-0.029627151787281036,
0.04091440141201019,
0.004161616787314415,
-0.01595599390566349,
-0.01898226886987686,
0.0060953847132623196,
-0.05916200950741768,
-0.01445254310965538,
-0.01782737486064434,
0.013410133309662342,
-0.06858095526695251,
-0.014691567048430443,
0.04543408006429672,
-0.013445014134049416,
-0.023493396118283272,
0.021050281822681427,
-0.06549087166786194,
-0.03657372295856476,
0.004820338450372219,
0.023266557604074478,
0.025884496048092842,
-0.05643445998430252,
0.04432811588048935,
-0.00020899134688079357,
-0.03154977411031723,
0.00917879305779934,
-0.022749926894903183,
-0.07326710969209671,
0.038473766297101974,
-0.02112751454114914,
0.030792534351348877,
-0.009876331314444542,
-0.0016270986525341868,
0.06997772306203842,
-0.00602592620998621,
-0.0687309131026268,
-0.00016460831102449447,
0.011478239670395851,
0.01696440950036049,
-0.06402377039194107,
0.01418998185545206,
0.055424392223358154,
-0.045160192996263504,
-0.009585758671164513,
-0.03470964357256889,
0.050920940935611725,
0.05893004685640335,
0.009123270399868488,
0.023818686604499817,
0.03595246374607086,
0.00753897987306118,
0.02380768582224846,
0.0639808252453804,
0.00009977918671211228,
-0.04262286797165871,
0.028821878135204315,
-0.044839683920145035,
0.03676317259669304,
0.02523818053305149,
-0.06441815197467804,
0.03544481098651886,
0.006945211905986071,
0.008054499514400959,
-0.057278111577034,
-0.012042665854096413,
0.010963615030050278,
-0.03239656612277031,
-0.01913175918161869,
0.02294478379189968,
0.05338818579912186,
-0.02607548050582409,
0.015051978640258312,
0.04380727559328079,
0.04556719958782196,
-0.0008779382333159447,
0.013259329833090305,
-0.04229491204023361,
-0.018434561789035797,
0.015769075602293015,
-0.0024240021593868732,
-0.013809802010655403,
0.04226487874984741,
0.009714394807815552,
0.03454943001270294,
0.006540969014167786,
0.012809254229068756,
-0.047396015375852585,
-0.061295539140701294,
-0.03801748901605606,
-0.02074328437447548,
0.09137950092554092,
0.015004750341176987,
0.0650840625166893,
0.04183460772037506,
0.0175308957695961,
-0.022127579897642136,
-0.0016607368597760797,
-0.08388470858335495,
0.03329789265990257,
-0.03542888164520264,
-0.033389218151569366,
0.01774553395807743,
-0.028910914435982704,
-0.03612690791487694,
-0.03583298623561859,
-0.031424619257450104,
0.04126543924212456,
0.010747553780674934,
-0.06197584792971611,
0.03687836602330208,
0.02770947478711605,
-0.02518821507692337,
-0.0018450268544256687,
0.022557105869054794,
0.05134781077504158,
-0.033676888793706894,
0.023377500474452972,
0.007890181615948677,
-0.028678975999355316,
0.020009856671094894,
0.012292120605707169,
-0.011097868904471397,
0.011858804151415825,
0.020165150985121727,
0.027235865592956543,
0.03371989727020264,
-0.04414331540465355,
0.021463444456458092,
0.05458475276827812,
0.019144047051668167,
-0.02471422404050827,
-0.014448268339037895,
-0.033954307436943054,
-0.017816929146647453,
-0.031129058450460434,
0.0761948749423027,
0.029845386743545532,
-0.016756651923060417,
0.03235568478703499,
-0.022197680547833443,
-0.059545762836933136,
-0.029850313439965248,
0.03146512061357498,
0.0549454502761364,
0.005198025144636631,
-0.007554147858172655,
-0.03777129575610161,
-0.03690784052014351,
0.004706512205302715,
-0.002314215060323477,
0.024131663143634796,
0.03199845552444458,
0.01925928331911564,
-0.03816407546401024,
0.012226772494614124,
0.00961962342262268,
-0.03217140585184097,
-0.013880551792681217,
0.007173316087573767,
0.02618701383471489,
-0.03155705705285072,
-0.015691475942730904,
-0.008665263652801514,
0.024947645142674446,
0.030698200687766075,
-0.0025772592052817345,
0.01796097680926323,
-0.04392394796013832,
-0.05872456356883049,
0.024297183379530907,
0.07298216968774796,
-0.009039314463734627,
0.01585162989795208,
-0.06305679678916931,
-0.030991079285740852,
0.07469500601291656,
-0.02577129192650318,
0.07080327719449997,
-0.018860429525375366,
0.016211003065109253,
-0.006700342521071434,
-0.03976018726825714,
-0.02451581507921219,
-0.010015630163252354,
-0.01520639006048441,
0.030373934656381607,
-0.046545181423425674,
-0.05220258608460426,
0.052917852997779846,
0.01276893075555563,
0.027334287762641907,
-0.0019203947158530354,
0.019741280004382133,
-0.016803931444883347,
-0.02597421407699585,
-0.0008453175541944802,
0.00831662304699421,
-0.0594707652926445,
0.004441686440259218,
-0.03698099032044411,
-0.013208114542067051,
0.016457639634609222,
-0.03619135543704033,
-0.006657308898866177,
0.053619399666786194,
0.05279947444796562,
-0.0041465843096375465,
-0.019266845658421516,
-0.06943149864673615,
0.055696602910757065,
-0.006716137286275625,
-0.0028049475513398647,
0.08690571039915085,
0.04080592468380928,
-0.017967019230127335,
-0.0036262627691030502,
-0.04741773381829262,
0.013181876391172409,
-0.017395788803696632,
-0.005540325306355953,
-0.018698064610362053,
0.02306065894663334,
-0.031186630949378014,
0.044037483632564545,
-0.03144382685422897,
0.035486333072185516,
-0.01755138300359249,
0.023882009088993073,
0.04652545601129532,
0.011465396732091904,
0.008037086576223373,
-0.021048620343208313,
-0.0066621797159314156,
0.010167742148041725,
0.004876336082816124,
-0.027450790628790855,
0.020646587014198303,
-0.005153168458491564,
-0.0014087382005527616,
-0.0054595861583948135,
-0.04889838397502899,
-0.004694113042205572,
0.005658283364027739,
0.01937810517847538,
0.031125172972679138,
-0.02689492329955101,
0.03366924822330475,
-0.01564987190067768,
0.04759955033659935,
0.045581281185150146,
-0.050711411982774734,
0.03567321598529816,
0.05122062936425209,
0.02581651136279106,
-0.00919280108064413,
-0.06578797101974487,
-0.010383957996964455,
-0.01921495981514454,
0.05706644430756569,
-0.060920678079128265,
-0.022871898487210274,
0.02176188863813877,
-0.011954576708376408,
-0.013933751732110977,
-0.015104408375918865,
-0.04286542907357216,
-0.014815145172178745,
-0.06852519512176514,
0.006191249471157789,
0.027587560936808586,
-0.014541318640112877,
-0.01493437122553587,
0.014891690574586391,
0.0358930304646492,
0.038250215351581573,
0.005108493380248547,
-0.006054086610674858,
-0.001843844074755907,
-0.014774074777960777,
-0.05402126535773277,
0.008155198767781258,
0.02350093051791191,
-0.02101055160164833,
-0.0113323163241148,
0.025205139070749283,
-0.011476153507828712,
0.01688278466463089,
0.032525163143873215,
-0.007338389288634062,
-0.016846630722284317,
0.016712987795472145,
-0.013921041041612625,
0.01186103094369173,
0.017818743363022804,
0.013975645415484905,
0.03530547767877579,
-0.02461668662726879,
-0.031838249415159225,
-0.027313055470585823,
-0.020923811942338943,
0.018178828060626984,
-0.02212749794125557,
-0.0006370933260768652,
0.022926002740859985,
0.0685972273349762,
-0.0370040088891983,
-0.02062959410250187,
-0.003855115035548806,
-0.001776615739800036,
0.017089050263166428,
0.005039510782808065,
0.005925820209085941,
-0.005131629761308432,
-0.03476464003324509,
0.01516314409673214,
-0.04868754744529724,
-0.047430507838726044,
-0.007182739675045013,
0.07818484306335449,
-0.013025292195379734,
0.03609044849872589,
0.010179153643548489,
-0.011856387369334698,
0.01694413088262081,
-0.006690382957458496,
-0.03822047635912895,
0.020952241495251656,
-0.0061762211844325066,
0.05276516452431679,
0.0021508208010345697,
-0.04654116928577423,
0.025287413969635963,
0.005991408601403236,
0.03279346972703934,
0.04521450027823448,
0.013997849076986313,
0.009723754599690437,
-0.035737138241529465,
-0.017718931660056114,
-0.04451954364776611,
-0.017447510734200478,
-0.01820080354809761,
0.07017076015472412,
-0.010023308917880058,
-0.031015146523714066,
0.016010187566280365,
0.03136689215898514,
-0.0233407411724329,
-0.02793075144290924,
0.009212336502969265,
-0.06141400709748268,
-0.007601018063724041,
0.006444714963436127,
0.012520079500973225,
-0.009241889230906963,
0.012724739499390125,
0.03358723595738411,
0.010900781489908695,
0.0299984123557806,
-0.02574137970805168,
-0.02005264163017273,
0.01104877982288599,
-0.017647601664066315,
-0.06792659312486649,
0.09013783186674118,
0.007467466872185469,
-0.0337492972612381,
-0.00981772132217884,
0.018633859232068062,
0.01287266705185175,
0.006222817115485668,
-0.01566256396472454,
-0.013587039895355701,
0.08771383762359619,
-0.0274676326662302,
0.0335264578461647,
-0.010649359785020351,
0.030249472707509995,
0.12545014917850494,
0.02002214454114437,
0.005806546192616224,
0.009610392153263092,
-0.006367416586726904,
-0.031236207112669945,
-0.01200330350548029,
-0.013958743773400784,
0.010195286944508553,
-0.03296218812465668,
-0.03894948586821556,
0.02157360501587391,
0.036837849766016006,
-0.010636931285262108,
-0.0065033626742661,
0.02619686722755432,
-0.05441436916589737,
-0.030462631955742836,
0.013791329227387905,
0.003782679094001651,
-0.005213742610067129,
-0.007456231862306595,
0.0010945271933451295,
0.010710250586271286,
-0.02697679214179516,
-0.020130308344960213,
-0.030378207564353943,
-0.006354203447699547,
0.06516668945550919,
0.005544525571167469,
-0.030153749510645866,
0.026861293241381645,
-0.021948635578155518,
-0.04582487791776657,
-0.0036009512841701508,
0.025163868442177773,
0.023720823228359222,
-0.05636410042643547,
0.03841693699359894,
0.05118517577648163,
0.02577352337539196,
0.00766903767362237,
0.010522277094423771,
0.06441833823919296,
-0.02862781099975109,
-0.011060348711907864,
-0.04270201921463013,
-0.00020477788348216563,
-0.0016966303810477257,
-0.034776471555233,
-0.013961102813482285,
-0.00002317142025276553,
0.02981479838490486,
-0.04405035078525543,
-0.01887170411646366,
0.0058160508051514626,
0.027681555598974228,
-0.018397729843854904,
-0.02991412580013275,
-0.018916714936494827,
-0.00039166733040474355,
0.010753249749541283,
0.0110135767608881,
0.029742497950792313,
-0.024937042966485023,
-0.015389946289360523,
-0.008848534896969795,
0.05916145443916321,
0.0022316593676805496,
-0.010217099450528622,
-0.034059684723615646,
-0.010638687759637833,
0.005799108184874058,
0.03877910599112511,
-0.009832063689827919,
0.023559492081403732,
0.04207116737961769,
0.011841275729238987,
-0.032344549894332886,
-0.013653495348989964,
-0.039402496069669724,
0.01925438642501831,
0.023888587951660156,
-0.0030578256119042635,
-0.03804420307278633,
-0.02566961944103241,
-0.023634742945432663,
0.04582030326128006,
0.030906621366739273,
-0.018555479124188423,
0.021087555214762688,
0.02363036572933197,
0.05878010764718056,
-0.026356618851423264,
-0.032266952097415924,
-0.002170346211642027,
-0.03094356693327427,
-0.051256924867630005,
-0.007236469071358442,
0.023707646876573563,
0.03029671497642994,
-0.0125642204657197,
-0.007241487503051758,
-0.0007141123642213643,
-0.03193815425038338,
0.02545386552810669,
0.02704078145325184,
0.012778951786458492,
-0.028594395145773888,
0.007874875329434872,
-0.002631343901157379,
-0.030501291155815125,
-0.012879765592515469,
-0.020587192848324776,
-0.01240517757833004,
0.013313988223671913,
-0.011982634663581848,
-0.02066739834845066,
0.028796996921300888,
-0.05945785343647003,
0.03454691916704178,
-0.031935032457113266,
-0.0016980321379378438,
-0.013357034884393215,
0.00999721884727478,
0.022983331233263016,
0.025154147297143936,
-0.06079684570431709,
0.03947697952389717,
-0.003455918049439788,
0.009169533848762512,
0.024359608069062233,
0.04373571276664734,
0.003946488723158836,
-0.02774067595601082,
0.009561687707901001,
-0.007389783393591642,
0.026215067133307457,
-0.03927767276763916,
-0.03761059790849686,
0.07654862850904465,
-0.019633429124951363,
0.0208780225366354,
0.0622616708278656,
0.03132355213165283,
-0.015515866689383984,
0.04388493672013283,
-0.012782160192728043,
0.0001918935013236478,
0.06294731050729752,
-0.025510497391223907,
-0.022522946819663048,
-0.006291614845395088,
-0.024818236008286476,
0.01926177181303501,
-0.007061443757265806,
0.020513560622930527,
-0.005324905272573233,
0.018188536167144775,
0.04354601725935936,
0.032904304563999176,
0.0040756706148386,
-0.02930235117673874,
-0.012618780136108398,
0.021445438265800476,
-0.01945524290204048,
0.038377054035663605,
-0.0026238667778670788,
0.009878185577690601,
0.0324881374835968,
-0.035291969776153564,
0.02129560522735119,
-0.008427761495113373,
-0.0053556328639388084,
-0.08567275106906891,
-0.0052210320718586445,
-0.03845896199345589,
-0.012539633549749851,
0.016960762441158295,
-0.04655790328979492,
0.018570587038993835,
0.022401362657546997,
-0.06484345346689224,
-0.005265093874186277,
-0.06086580455303192,
0.008713064715266228,
-0.055166780948638916,
-0.000011247089787502773,
-0.03966178372502327,
0.02981174737215042,
0.01798119768500328,
-0.012585032731294632,
-0.012018030509352684,
0.0199108999222517,
0.005039116833359003,
0.0017346293898299336,
0.027821656316518784,
0.044429950416088104,
0.008181708864867687,
-0.007086875382810831,
0.05242498591542244,
-0.029366541653871536,
-0.002101033227518201,
0.01681908406317234,
-0.05881563201546669,
0.0047410582192242146,
0.0008735901792533696,
0.015764374285936356,
-0.07148277014493942,
0.056359633803367615,
0.03317897394299507,
0.04824988543987274,
0.019603567197918892,
0.02752416767179966,
0.05590062215924263,
0.03488181531429291,
0.0018111233366653323,
-0.0034152274020016193,
0.0315483883023262,
0.010316879488527775,
-0.04317401349544525,
0.05750588700175285,
-0.015536193735897541,
0.009385509416460991,
0.05405021831393242,
-0.02306799590587616,
0.02067163959145546,
-0.00949940737336874,
0.022973516955971718,
-0.028949875384569168,
-0.013675895519554615,
0.032907892018556595,
-0.008964434266090393,
-0.01695534959435463,
-0.020665638148784637,
-0.006986535154283047,
-0.027853939682245255,
-0.029121164232492447,
-0.035365547984838486,
-0.029430873692035675,
-0.022157857194542885,
0.010488222353160381,
-0.01702379621565342,
-0.03289934620261192,
-0.05331191048026085,
-0.04312409833073616,
0.008947971276938915,
0.033290233463048935,
0.03684051334857941,
0.0339035727083683,
0.03404906019568443,
0.005960582289844751,
-0.015951834619045258,
-0.05505790188908577,
-0.002068007830530405,
-0.022225728258490562,
-0.025287674739956856,
-0.02835286781191826,
-0.030903270468115807,
0.018506968393921852,
0.036909956485033035,
0.01626371033489704,
-0.01633532904088497,
-0.03388870134949684,
0.013976533897221088,
-0.034114520996809006,
0.025913365185260773,
-0.038640689104795456,
0.03591872751712799,
-0.005405251402407885,
0.01474754698574543,
0.00020840243087150156,
-0.014622410759329796,
-0.009523462504148483,
0.009284237399697304,
0.05598064884543419,
-0.050056204199790955,
-0.00014343160728458315,
-0.004890971351414919,
-0.01940854638814926,
-0.021993376314640045,
0.0010263167787343264,
0.018147073686122894,
0.05041300877928734,
-0.014770524576306343,
0.015438883565366268,
0.035585418343544006,
0.007960362359881401,
-0.06740440428256989,
0.01645691692829132,
-0.01226082630455494,
0.040804557502269745,
0.010932307690382004,
-0.07882517576217651,
0.021232767030596733,
-0.029459718614816666,
0.025247501209378242,
0.02902643196284771,
-0.041562438011169434,
0.0093696853145957,
0.0055541605688631535,
0.01905069127678871,
-0.0062288218177855015,
-0.031503826379776,
0.046251799911260605,
-0.03902812674641609,
0.018917616456747055,
0.00045404795673675835,
0.007354918401688337,
0.03068927302956581,
0.03113064542412758,
-0.008647024631500244,
0.06200101599097252,
0.006993650458753109,
0.007838940247893333,
0.012888116762042046,
-0.011838397942483425,
0.006654095370322466,
-0.02455177903175354,
0.017158126458525658,
-0.006679297424852848,
-0.025536615401506424,
0.04780647158622742,
-0.019164571538567543,
0.04991644248366356,
-0.009841131046414375,
0.00211411458440125,
-0.04074551537632942,
-0.014138666912913322,
0.004655334632843733,
0.0163078922778368,
0.019530000165104866,
0.03208903595805168,
-0.04230121523141861,
0.007914849556982517,
-0.022198153659701347,
-0.010845250450074673,
0.032091520726680756,
-0.001232872367836535,
-0.02764793299138546,
0.008040842600166798,
0.012282510288059711,
-0.04206983000040054,
-0.04765654727816582,
0.000899521925020963,
-0.07591451704502106,
0.014950801618397236,
0.05768439918756485,
-0.022212130948901176,
0.016187816858291626,
-0.02799627184867859,
0.02900529094040394,
0.0746370330452919,
-0.05007554218173027,
-0.029732124879956245,
0.012847711332142353,
-0.0029414501041173935,
0.03527640923857689,
0.01652108132839203
] |
<p>Suppose I have two batteries one inside the laptop with 2.5 AH giving a backup for around 2 hours. The battery is external inside a UPS system with 7.5 AH. Since it has thrice the capacity of the previous one, can I conclude it will give backup for 6 hours?</p>
| 9,362 |
[
-0.036244362592697144,
-0.01110337395220995,
0.00875638797879219,
0.03707457333803177,
0.00579500338062644,
-0.023325234651565552,
-0.005220724269747734,
-0.003993423189967871,
0.017806144431233406,
-0.00784404668956995,
-0.0018231926951557398,
0.043339990079402924,
0.04570014774799347,
0.024037908762693405,
-0.010932216420769691,
-0.03619921952486038,
-0.008446622639894485,
-0.012284897267818451,
0.018966922536492348,
0.009608741849660873,
0.0060661365278065205,
0.0012174340663477778,
0.03199800103902817,
-0.021130207926034927,
0.007166371680796146,
-0.0036093536764383316,
0.04945754259824753,
-0.012315616942942142,
0.018431123346090317,
0.044442810118198395,
0.009843133389949799,
-0.026324566453695297,
0.040960051119327545,
0.059551697224378586,
0.031599778681993484,
-0.011498364619910717,
-0.012608145363628864,
-0.03078765608370304,
-0.029393965378403664,
0.05944487825036049,
0.008736676536500454,
-0.02151988074183464,
0.012951623648405075,
0.012652426958084106,
-0.013147584162652493,
0.029065100476145744,
-0.05393652617931366,
-0.03172514587640762,
0.0024181141052395105,
-0.07195106148719788,
0.06564485281705856,
-0.026189997792243958,
0.07161451131105423,
0.04379074648022652,
0.004931633360683918,
0.04322332888841629,
0.034839026629924774,
0.0803399309515953,
0.01352003775537014,
-0.004786434583365917,
-0.004408323671668768,
0.04313310980796814,
-0.022832373157143593,
-0.04187657684087753,
-0.04740084707736969,
0.0313103161752224,
-0.018195467069745064,
-0.029927657917141914,
0.03895587846636772,
0.009440826252102852,
0.042516738176345825,
0.029716897755861282,
0.05714261159300804,
-0.05021282657980919,
-0.005426804069429636,
-0.01564960926771164,
0.04050041362643242,
0.01176428236067295,
0.03507010638713837,
0.0496557280421257,
-0.005313883535563946,
0.009103219956159592,
0.0006990953697822988,
0.05662707984447479,
0.052949193865060806,
-0.019632328301668167,
0.03298422694206238,
-0.01988781802356243,
0.038831572979688644,
0.018053384497761726,
0.015079626813530922,
0.02193169668316841,
0.03035723976790905,
-0.012744419276714325,
-0.004308310803025961,
0.0239616297185421,
-0.028091857209801674,
0.07037506252527237,
-0.030883686617016792,
0.016483141109347343,
0.03234953060746193,
-0.0009534292039461434,
0.012226792052388191,
0.04507996141910553,
0.02668878436088562,
-0.04303843528032303,
0.0001356797874905169,
0.0061207981780171394,
0.010143859311938286,
0.025651048868894577,
-0.047389160841703415,
0.013482126407325268,
0.0345127247273922,
-0.03860568255186081,
0.021847760304808617,
-0.0011459595989435911,
-0.00568675110116601,
0.0034035546705126762,
0.0517970472574234,
0.09062781929969788,
0.031371109187603,
-0.030735066160559654,
0.024736644700169563,
-0.08014413714408875,
-0.025729943066835403,
0.013152947649359703,
-0.029163183644413948,
-0.010924657806754112,
-0.06175794079899788,
0.032360099256038666,
0.0032833022996783257,
-0.029405755922198296,
0.0211400855332613,
-0.019423317164182663,
0.0746091827750206,
0.007875201292335987,
-0.06218448653817177,
-0.04725932702422142,
-0.012295951135456562,
-0.026779400184750557,
0.028579723089933395,
-0.036192428320646286,
0.015113330446183681,
0.03069967031478882,
0.043634042143821716,
-0.005113495048135519,
0.017116697505116463,
0.01733921281993389,
-0.0023746853694319725,
0.010170052759349346,
-0.07394977658987045,
-0.01471577025949955,
0.03870653361082077,
-0.03458709642291069,
0.0832102969288826,
-0.06376263499259949,
0.031223246827721596,
0.02696504443883896,
0.028877312317490578,
-0.02979612722992897,
0.0072094532661139965,
-0.006709672976285219,
-0.01832909882068634,
-0.014798341318964958,
-0.022153345867991447,
-0.03266902640461922,
0.04036235436797142,
-0.017562922090291977,
-0.03561631962656975,
0.01232561282813549,
-0.0014383317902684212,
-0.009313637390732765,
-0.021340766921639442,
0.0069963824935257435,
0.04228625446557999,
-0.0057666730135679245,
-0.0330880768597126,
-0.053971726447343826,
0.01481157448142767,
0.019629187881946564,
-0.04163239523768425,
-0.03565332666039467,
0.03687579929828644,
0.03362855315208435,
0.02783016487956047,
0.024625256657600403,
0.004695078823715448,
-0.04401716962456703,
-0.00915494840592146,
-0.011262382380664349,
-0.05338553339242935,
-0.014914852567017078,
0.05088476836681366,
0.028407782316207886,
-0.01944606751203537,
0.021790945902466774,
-0.02521044760942459,
0.027769874781370163,
-0.05244902893900871,
0.0021316667553037405,
-0.01119158137589693,
-0.0011626288760453463,
-0.007005726918578148,
-0.024446256458759308,
0.042004719376564026,
0.06062893196940422,
0.024437077343463898,
0.0036391038447618484,
0.05037683621048927,
-0.045979999005794525,
-0.04237595200538635,
-0.023929771035909653,
-0.024334285408258438,
0.010724460706114769,
0.011430446989834309,
0.00047983715194277465,
0.016308026388287544,
0.006744485814124346,
0.030174072831869125,
0.03910196200013161,
0.006930171046406031,
0.054252371191978455,
0.06190655753016472,
0.019614767283201218,
-0.004384157247841358,
-0.02386208437383175,
0.014946642331779003,
-0.008583334274590015,
-0.03518685698509216,
0.0008971852366812527,
-0.043400444090366364,
0.027450859546661377,
0.030770733952522278,
0.029610224068164825,
-0.03892083093523979,
0.06033455207943916,
0.029739392921328545,
-0.012112299911677837,
0.007714452687650919,
0.030950987711548805,
-0.016618572175502777,
-0.031964078545570374,
-0.005167183931916952,
0.009272576309740543,
0.013858729042112827,
0.0070325033739209175,
-0.00033215401344932616,
0.004861074965447187,
0.005204690620303154,
-0.026498816907405853,
0.001925456221215427,
0.011812829412519932,
-0.017908964306116104,
0.06139053404331207,
-0.016263894736766815,
-0.040241874754428864,
0.009637292474508286,
0.003380782203748822,
0.028849614784121513,
0.018448401242494583,
0.014819555915892124,
0.049083955585956573,
-0.00229811854660511,
-0.02874586544930935,
-0.0056678494438529015,
-0.03209450840950012,
-0.024789897724986076,
-0.046302661299705505,
0.03577590361237526,
-0.033015523105859756,
0.023916419595479965,
-0.01630510576069355,
0.021761471405625343,
0.00014954911603126675,
-0.029870858415961266,
0.03646127134561539,
-0.02243858017027378,
0.0554964616894722,
0.012630335986614227,
-0.016921786591410637,
-0.00031555272289551795,
-0.010497977957129478,
-0.005414552055299282,
-0.06592770665884018,
-0.00542437843978405,
0.013881316408514977,
0.005631564650684595,
-0.023845413699746132,
0.05791740119457245,
0.021413903683423996,
0.014127964153885841,
0.02446695603430271,
0.0050273374654352665,
-0.060194000601768494,
0.04403700679540634,
-0.001079270034097135,
0.010697153396904469,
-0.04085557535290718,
-0.011107411235570908,
0.04841453209519386,
0.003965165466070175,
-0.06445842981338501,
0.02546517364680767,
-0.08847945928573608,
0.0013756569242104888,
0.0053405179642140865,
-0.023511815816164017,
0.015958424657583237,
-0.035693105310201645,
0.03252498432993889,
-0.0023216991685330868,
-0.039299167692661285,
-0.014406424015760422,
-0.06668666750192642,
-0.07335434854030609,
0.013233001343905926,
0.00002784581192827318,
0.0015844160225242376,
-0.0037305327132344246,
-0.06291177123785019,
0.06155356764793396,
0.015554822981357574,
-0.02665015496313572,
0.0020342888310551643,
-0.051253605633974075,
-0.004935726057738066,
-0.027821503579616547,
0.0365259051322937,
0.019034257158637047,
-0.017333952710032463,
-0.0012740176171064377,
0.022787895053625107,
0.03733517602086067,
0.06692396104335785,
-0.0011211567325517535,
-0.011035017669200897,
0.009457318112254143,
0.03507055342197418,
0.014602240175008774,
0.02902504801750183,
-0.035169169306755066,
0.00166704214643687,
-0.028262775391340256,
-0.03167903795838356,
0.04892782121896744,
-0.02719065733253956,
-0.015971971675753593,
0.03041415475308895,
-0.008180025033652782,
0.043882109224796295,
-0.030895160511136055,
0.03226508945226669,
0.03240934759378433,
0.005983495153486729,
-0.01572345197200775,
0.021714532747864723,
0.044887613505125046,
-0.0165239367634058,
0.02062843181192875,
0.04782312735915184,
0.07444366812705994,
-0.02483871951699257,
-0.07474730908870697,
0.008721431717276573,
0.007170670200139284,
-0.008641103282570839,
-0.0027749366126954556,
-0.08248182386159897,
0.010900702327489853,
0.009604999795556068,
0.0102678332477808,
0.0030292803421616554,
-0.0032037771306931973,
0.03338702395558357,
-0.10009410977363586,
-0.024472154676914215,
-0.000725477235391736,
0.04065713658928871,
-0.00040839659050107,
0.03316947817802429,
0.01392669789493084,
0.0032172417268157005,
-0.001750257215462625,
0.014181823469698429,
-0.0579155832529068,
0.012966676615178585,
0.010910672135651112,
-0.019401004537940025,
0.004960720892995596,
-0.01554248295724392,
0.010713692754507065,
-0.05713929608464241,
-0.016942664980888367,
0.0002933674259111285,
-0.02438562549650669,
-0.06149476394057274,
0.007335986010730267,
0.005961104296147823,
0.018241865560412407,
0.015103453770279884,
0.0024202971253544092,
0.014286198653280735,
-0.025739243254065514,
0.06593171507120132,
0.004670477006584406,
-0.04724748432636261,
0.004828901961445808,
-0.0030038151890039444,
0.0454280711710453,
-0.02552935667335987,
0.013063480146229267,
0.05105007439851761,
0.052750349044799805,
0.00765358516946435,
0.00006800433766329661,
-0.010012243874371052,
0.021267812699079514,
0.00932559184730053,
-0.036559633910655975,
-0.02773548662662506,
-0.036216747015714645,
-0.0612918958067894,
0.0008732703281566501,
0.007348709274083376,
-0.013210584409534931,
0.020984720438718796,
0.024735307320952415,
0.0008588104392401874,
0.011780730448663235,
0.013612790033221245,
0.06497357040643692,
-0.005245401058346033,
-0.022118670865893364,
-0.044549714773893356,
-0.031553834676742554,
-0.03247696906328201,
-0.01190182100981474,
0.02711743675172329,
-0.02642696723341942,
-0.04081350564956665,
-0.020681699737906456,
0.0028671182226389647,
0.025134310126304626,
-0.005184335634112358,
0.007432238664478064,
0.028132177889347076,
0.010662592947483063,
0.0038514595944434404,
-0.008047563023865223,
0.04990695044398308,
0.027851395308971405,
0.045405663549900055,
0.03226426988840103,
-0.012497050687670708,
-0.08913955837488174,
-0.01995651051402092,
0.030660411342978477,
0.04423291236162186,
0.007311492692679167,
0.01873343251645565,
-0.002702829660847783,
-0.006338374689221382,
0.060351669788360596,
-0.015217499807476997,
0.04508000984787941,
-0.04104923829436302,
-0.0049011483788490295,
0.014549894258379936,
0.00831688567996025,
0.002208332298323512,
-0.001962559763342142,
-0.013221860863268375,
0.014753430150449276,
-0.01793353632092476,
0.0029970065224915743,
0.011004212312400341,
0.025921164080500603,
0.055127084255218506,
0.05194410681724548,
0.014728778041899204,
-0.008533741347491741,
-0.016177820041775703,
0.018555181100964546,
-0.04288581758737564,
-0.023676704615354538,
0.013044251129031181,
-0.0305270217359066,
-0.017954794690012932,
0.03490571677684784,
-0.04599043354392052,
-0.03185509890317917,
0.007637273520231247,
0.02327784150838852,
0.0035762779880315065,
-0.00865983311086893,
-0.025631587952375412,
-0.0002758012560661882,
-0.007831587456166744,
0.010081496089696884,
0.051766712218523026,
0.0283069908618927,
0.0030722261872142553,
-0.033130090683698654,
0.003033242654055357,
0.0331488698720932,
-0.054053377360105515,
-0.021736163645982742,
0.010189920663833618,
-0.027520347386598587,
-0.03375892713665962,
0.04404962807893753,
0.007397666573524475,
0.027691982686519623,
-0.0021814985666424036,
-0.03550741448998451,
-0.000712621898856014,
0.007814531214535236,
-0.005828558467328548,
-0.0002123495942214504,
-0.02336651086807251,
0.020352143794298172,
0.02514730766415596,
0.0040930286049842834,
-0.016960881650447845,
-0.023386090993881226,
0.030212195590138435,
0.027900610119104385,
-0.01776515133678913,
0.011148635298013687,
-0.020477458834648132,
-0.009186064824461937,
0.019200634211301804,
0.022189203649759293,
0.03242100775241852,
0.015650635585188866,
-0.0022900677286088467,
0.024312792345881462,
-0.07904404401779175,
-0.0014173273229971528,
0.06602266430854797,
-0.008310501463711262,
0.0066567654721438885,
-0.0312355849891901,
0.04504740610718727,
0.04280446097254753,
-0.018721261993050575,
-0.06504187732934952,
-0.04118221253156662,
0.04465804621577263,
0.03290245309472084,
-0.014524878934025764,
-0.05448934808373451,
-0.006822922267019749,
0.014134698547422886,
-0.01851741410791874,
-0.028500104323029518,
-0.0034858430735766888,
-0.01154384482651949,
-0.012889853678643703,
0.02948174998164177,
0.016307765617966652,
0.039212994277477264,
0.04264237731695175,
0.004948719870299101,
-0.008095034398138523,
0.0008342439541593194,
-0.007599464617669582,
-0.033059023320674896,
-0.01639525033533573,
-0.026687130331993103,
-0.0030846702866256237,
-0.023485971614718437,
-0.04200248420238495,
0.04343114420771599,
-0.04826897382736206,
-0.03233672305941582,
0.047050587832927704,
-0.014451537281274796,
-0.003525870619341731,
-0.02839168719947338,
0.030538147315382957,
-0.009583758190274239,
0.025487355887889862,
0.01734922267496586,
-0.0392848402261734,
-0.02405119314789772,
-0.003407179843634367,
0.005767349619418383,
0.017191559076309204,
-0.010147074237465858,
0.002297303406521678,
0.045024652034044266,
0.008543306030333042,
-0.03796299174427986,
0.024999629706144333,
-0.005101678892970085,
-0.013903383165597916,
-0.03864610195159912,
-0.021506160497665405,
0.004746269900351763,
-0.02009359374642372,
-0.05586928874254227,
-0.036409009248018265,
-0.031862370669841766,
-0.014068657532334328,
0.013532513752579689,
-0.03285835310816765,
0.02360779233276844,
0.023002758622169495,
0.041549354791641235,
-0.02521952986717224,
-0.04301094263792038,
0.009212331846356392,
0.010311299934983253,
0.010561266914010048,
0.04790094494819641,
-0.0243839044123888,
0.0032801637426018715,
0.06564252078533173,
0.030851278454065323,
0.022811880335211754,
0.024618327617645264,
0.060696445405483246,
0.004447192884981632,
0.03121977299451828,
-0.014510056935250759,
-0.051573511213064194,
0.004525442607700825,
-0.0509692020714283,
-0.009755197912454605,
-0.02425633929669857,
-0.02251112274825573,
0.08077360689640045,
0.016739342361688614,
-0.015613129362463951,
-0.054887786507606506,
-0.06313402205705643,
-0.03494195267558098,
-0.026645831763744354,
0.008405695669353008,
0.048445362597703934,
0.02397206798195839,
-0.010778945870697498,
0.0383608415722847,
-0.0021528920624405146,
0.02006937935948372,
-0.037034500390291214,
-0.08155195415019989,
-0.02413189224898815,
0.012464240193367004,
-0.04247113689780235,
0.009353418834507465,
-0.0180288664996624,
-0.03499540686607361,
0.004848242271691561,
0.027516759932041168,
0.012085316702723503,
0.026125097647309303,
0.04456879198551178,
0.00006336090882541612,
0.08489929884672165,
-0.01799014024436474,
0.005809800233691931,
-0.011788904666900635,
0.0018711910815909505,
0.12211767584085464,
0.027028894051909447,
0.015125959180295467,
-0.061592455953359604,
-0.017473110929131508,
-0.01966671459376812,
0.022330569103360176,
-0.02520512044429779,
0.029636988416314125,
-0.04774647578597069,
-0.03196253255009651,
0.05083799734711647,
0.03146864473819733,
-0.03138883411884308,
-0.018407823517918587,
0.06977337598800659,
-0.03380228206515312,
-0.0076719047501683235,
-0.009428164921700954,
0.042423542588949203,
-0.0008329922566190362,
-0.017051318660378456,
-0.033032555133104324,
-0.020832763984799385,
-0.013615601696074009,
0.016231641173362732,
0.024694226682186127,
-0.009627623483538628,
0.01670870929956436,
-0.01051059365272522,
-0.03661778196692467,
0.022696036845445633,
0.014823033474385738,
0.03292600437998772,
-0.015872888267040253,
0.02211843430995941,
0.028138417750597,
0.02510642632842064,
-0.04139505326747894,
0.057453930377960205,
0.051897428929805756,
0.01844928413629532,
0.02537583000957966,
0.03708358854055405,
-0.06965948641300201,
0.008995173498988152,
-0.0037012724205851555,
-0.0004223194264341146,
0.010455834679305553,
0.015141863375902176,
-0.017310088500380516,
0.011207308620214462,
-0.00014595671382267028,
-0.0653628557920456,
-0.0391395203769207,
0.03456813842058182,
-0.007901707664132118,
-0.017910558730363846,
-0.019021444022655487,
-0.027349786832928658,
0.02467183768749237,
0.04185066744685173,
0.02894243597984314,
0.011956489644944668,
-0.01837366446852684,
0.05475471913814545,
-0.006882375106215477,
0.011459033004939556,
-0.009761551395058632,
0.012640431523323059,
-0.03586624190211296,
0.044607698917388916,
0.0014757788740098476,
-0.027032647281885147,
0.01452623400837183,
0.008037376217544079,
0.024977367371320724,
-0.005052849184721708,
-0.029869170859456062,
-0.011604858562350273,
-0.06355603039264679,
0.02708333730697632,
0.022879743948578835,
-0.017008336260914803,
-0.02622540481388569,
-0.00018980489403475076,
0.02779512107372284,
0.013178885914385319,
-0.004126379266381264,
0.0435091070830822,
-0.010914679616689682,
0.06244197115302086,
-0.029049595817923546,
-0.04819916933774948,
0.032561399042606354,
0.006611157674342394,
-0.07263471931219101,
-0.02099398337304592,
0.008302828297019005,
0.036611512303352356,
0.015227176249027252,
0.012873468920588493,
-0.028430506587028503,
-0.003508618799969554,
-0.022251136600971222,
0.017114585265517235,
-0.0136023024097085,
-0.022567328065633774,
-0.016107549890875816,
-0.002245417097583413,
0.052115488797426224,
-0.006557488813996315,
-0.010634588077664375,
-0.00746928621083498,
0.006170214153826237,
0.02294340170919895,
-0.018007688224315643,
-0.01933363638818264,
0.004646163433790207,
0.0006781948613934219,
0.031075049191713333,
-0.013673628680408001,
-0.00039650630787946284,
0.0013229078613221645,
-0.028097443282604218,
0.020542338490486145,
0.001750007621012628,
0.01867063343524933,
0.04457502067089081,
-0.009668818674981594,
-0.056551363319158554,
0.024674080312252045,
-0.028735602274537086,
-0.009725724346935749,
-0.03359373286366463,
-0.023878514766693115,
-0.01911300979554653,
0.04822834953665733,
-0.06396139413118362,
-0.06765086203813553,
0.04536992311477661,
-0.00984332337975502,
0.014039218425750732,
0.03611137717962265,
0.008982048369944096,
0.05762965977191925,
0.022921454161405563,
0.010322658345103264,
-0.005765101872384548,
0.04274369403719902,
-0.03032694384455681,
0.0004338858707342297,
0.0232639592140913,
0.005639455281198025,
-0.012996896170079708,
0.022413484752178192,
-0.02746092528104782,
-0.03841985762119293,
0.005445136222988367,
-0.019030271098017693,
0.016020553186535835,
0.006393305491656065,
-0.03285490721464157,
0.0019068119581788778,
0.03485054895281792,
0.05453905835747719,
-0.0026107369922101498,
-0.019964439794421196,
0.02817489206790924,
0.02401520311832428,
-0.011077750474214554,
0.019135186448693275,
0.024072369560599327,
0.004122874699532986,
-0.08648849278688431,
-0.009265457279980183,
0.007351906970143318,
-0.0053387898951768875,
0.010438496246933937,
-0.03161364421248436,
-0.014537147246301174,
0.00029332240228541195,
-0.09763120114803314,
0.0024710134603083134,
-0.014170346781611443,
-0.022686857730150223,
-0.048203449696302414,
0.019444534555077553,
0.005844305735081434,
0.012185411527752876,
0.052429746836423874,
0.030143894255161285,
0.03643440455198288,
-0.011327776126563549,
-0.03270060196518898,
-0.039734210819005966,
-0.02447148598730564,
0.025973312556743622,
0.028483491390943527,
-0.007605047896504402,
0.032155126333236694,
-0.030925069004297256,
-0.0018014019588008523,
-0.01755114272236824,
-0.03571692481637001,
0.026480555534362793,
-0.036135174334049225,
0.023750821128487587,
0.00349362101405859,
0.009891576133668423,
0.010596999898552895,
-0.02036776952445507,
-0.018078209832310677,
-0.03684180602431297,
0.007612430956214666,
0.028325088322162628,
-0.012636943720281124,
0.03003472462296486,
0.03586199879646301,
-0.019668880850076675,
-0.02547898143529892,
0.020059281960129738,
-0.013938468880951405,
0.008178667165338993,
0.030912868678569794,
-0.011546449735760689,
0.0006394642405211926,
-0.03297257050871849,
-0.00689554400742054,
-0.02489803172647953,
-0.03936672583222389,
0.05144127830862999,
-0.020008988678455353,
-0.009251696057617664,
-0.012022994458675385,
-0.02579270675778389,
-0.026523474603891373,
0.019703635945916176,
0.014735681936144829,
0.0028576066251844168,
-0.06594645231962204,
-0.020348772406578064,
0.007503157947212458,
0.011933605186641216,
0.005306597799062729,
-0.0343293733894825,
-0.03716997802257538,
0.04659975692629814,
0.0206246729940176,
0.04012918844819069,
0.05652186647057533,
-0.03624368831515312,
-0.013611340895295143,
-0.03917107731103897,
0.04187803715467453,
-0.03805828467011452,
-0.015928100794553757,
-0.054883331060409546,
-0.056331854313611984,
-0.01560270693153143,
0.024027127772569656,
0.09113068878650665,
0.004525029566138983,
-0.03574671968817711,
-0.010980385355651379,
-0.001524640596471727,
0.008747795596718788,
-0.061866845935583115,
0.012640932574868202,
0.02396264113485813,
-0.03624047338962555,
0.0018588898237794638,
-0.024253403767943382,
0.008830351755023003,
-0.025491800159215927,
0.011855553835630417,
-0.019245851784944534,
-0.008761929348111153,
0.0003360789851285517,
0.0010987793793901801,
0.030435798689723015,
0.012610584497451782,
0.001598008326254785,
0.08461697399616241,
-0.020226843655109406,
0.02204589731991291,
0.019100897014141083,
0.0036945240572094917,
-0.06302552670240402,
0.020755698904395103,
-0.025404682382941246,
0.03926621004939079,
-0.012129564769566059,
-0.01793157123029232,
0.01708173379302025,
-0.04742572084069252,
-0.028888680040836334,
0.024107350036501884,
-0.011877695098519325,
-0.010845591314136982,
0.03181880712509155,
0.03645091503858566,
0.04847139120101929,
-0.049432069063186646,
0.03980256989598274,
0.01656213030219078,
0.009443402290344238,
-0.005808711517602205,
0.004431005101650953,
0.005112240556627512,
-0.032848160713911057,
-0.007106753997504711,
0.005071632564067841,
0.03473601117730141,
0.037341564893722534,
0.0023511340841650963,
0.022281035780906677,
-0.042583856731653214,
-0.04193436726927757,
0.017053116112947464,
-0.011561645194888115,
-0.014028411358594894,
0.015785088762640953,
-0.0262860506772995,
0.04160972312092781,
-0.020710380747914314,
0.0345768965780735,
-0.02476130798459053,
0.03986428305506706,
-0.030796363949775696,
0.023902276530861855,
0.04619898647069931,
-0.010303792543709278,
-0.01991729997098446,
-0.013296151533722878,
-0.007128152996301651,
0.01012775581330061,
-0.016417160630226135,
-0.05497868359088898,
-0.0007247167523019016,
-0.018384527415037155,
0.012110806070268154,
-0.010071439668536186,
-0.01894286833703518,
-0.01728264056146145,
-0.019806576892733574,
0.0174483023583889,
0.048150695860385895,
0.028460435569286346,
-0.03842199593782425,
-0.05828084051609039,
-0.0021903440356254578,
0.07976758480072021,
-0.041290152817964554,
-0.014986410737037659,
-0.012552191503345966,
-0.010753401555120945,
0.02227042429149151,
-0.0314689464867115
] |
<p>In this video a single flick of a finger tips 116000 dominos. </p>
<p><a href="http://www.youtube.com/watch?v=3bxk-6GEK6w" rel="nofollow">Domino video</a></p>
<p>I understand the work that needs to be done to move 116000 pieces (at least 100 kilos) of plastic is greater then that expended by flick of a finger. How does the energy conservation law apply here?</p>
| 9,363 |
[
-0.016315605491399765,
-0.024445874616503716,
0.005515692755579948,
-0.04655653238296509,
0.034703269600868225,
-0.01936846598982811,
-0.05084696412086487,
-0.010603212751448154,
-0.02029186673462391,
-0.007533702068030834,
0.001958746463060379,
0.007506171707063913,
0.020233964547514915,
0.04494793340563774,
0.008333269506692886,
0.01141892559826374,
0.016210824251174927,
-0.01191510446369648,
0.0060654859989881516,
-0.05016859248280525,
-0.03163262456655502,
-0.02645418979227543,
0.011091134510934353,
-0.00284702074714005,
-0.053969431668519974,
0.013751138933002949,
0.02973431535065174,
0.019334053620696068,
0.02940051630139351,
0.0213764775544405,
-0.0025862567126750946,
-0.035663239657878876,
0.008961956948041916,
0.0019104807870462537,
0.005973722320050001,
0.009607112966477871,
-0.05328589305281639,
-0.03487471118569374,
-0.00659277243539691,
0.014993499964475632,
0.008932173252105713,
-0.013852731324732304,
0.022600237280130386,
0.0444258488714695,
-0.021022962406277657,
0.04931546375155449,
-0.01967221312224865,
0.014472001232206821,
0.055663324892520905,
-0.03946434706449509,
0.05003815516829491,
0.017973754554986954,
0.0276305191218853,
0.04141592979431152,
-0.0036733064334839582,
0.000252033380093053,
0.0691518634557724,
0.03988025709986687,
-0.03038446418941021,
-0.04709944128990173,
-0.006828697863966227,
0.008884880691766739,
-0.02730577439069748,
-0.0477365106344223,
0.017246559262275696,
0.00871395692229271,
-0.011194011196494102,
0.007128421682864428,
0.04356095939874649,
0.026406554505228996,
0.03233131766319275,
0.017443032935261726,
0.04559279605746269,
-0.019116433337330818,
0.01278464775532484,
0.0005950606428086758,
0.03314375877380371,
0.016307801008224487,
0.019348740577697754,
0.06748253852128983,
0.009978053160011768,
-0.017009984701871872,
0.029391827061772346,
0.05836601182818413,
0.036285217851400375,
-0.022267857566475868,
0.0686965137720108,
-0.020048262551426888,
0.04941146820783615,
-0.002665615174919367,
0.028890470042824745,
-0.024068279191851616,
0.016762295737862587,
0.03345616161823273,
0.002763979136943817,
0.02085680142045021,
-0.009647334925830364,
0.00989836361259222,
0.018012182787060738,
0.005562471225857735,
0.006049148738384247,
-0.0049956380389630795,
0.04256923869252205,
0.06341506540775299,
0.0048775263130664825,
-0.016195589676499367,
0.004837986081838608,
0.04028652235865593,
-0.020361561328172684,
0.026369228959083557,
-0.04233640059828758,
-0.03815639019012451,
0.0007922225049696863,
0.00559875275939703,
0.02786669321358204,
-0.015184587799012661,
-0.04525433108210564,
-0.0227329283952713,
0.033908579498529434,
0.044744011014699936,
0.021543631330132484,
-0.06990715861320496,
0.00006346156442305073,
-0.029499277472496033,
-0.04554980993270874,
0.04340177774429321,
0.019624769687652588,
-0.0023546062875539064,
-0.07673696428537369,
0.0201280415058136,
0.009945237077772617,
-0.034950729459524155,
-0.019278813153505325,
-0.011324846185743809,
0.03679962456226349,
0.0021880303975194693,
-0.09378088265657425,
-0.04039767384529114,
0.06932000815868378,
-0.005662616807967424,
-0.04102272912859917,
-0.05665823444724083,
-0.013045665808022022,
0.01820383593440056,
0.0472334548830986,
-0.023120427504181862,
0.003965804819017649,
0.004968784749507904,
0.012372787110507488,
0.007498010993003845,
0.010778914205729961,
-0.030848728492856026,
0.03704635053873062,
-0.05351107940077782,
-0.0058814906515181065,
-0.04610227048397064,
-0.00859590619802475,
0.020736951380968094,
0.0032852627336978912,
-0.02056674100458622,
0.0003815152158495039,
-0.012514082714915276,
-0.011769698932766914,
-0.03026616759598255,
-0.029450776055455208,
-0.0395333506166935,
0.06826242804527283,
-0.010060285218060017,
0.049216900020837784,
0.01603877916932106,
0.003472193842753768,
0.045709338039159775,
-0.038506023585796356,
0.042693816125392914,
0.014717413112521172,
-0.02749619632959366,
-0.006992954295128584,
-0.020471878349781036,
-0.027459358796477318,
0.018767401576042175,
-0.05311090499162674,
-0.05544917285442352,
-0.011075678281486034,
0.004038405138999224,
0.03796452283859253,
0.042858731001615524,
-0.04031694307923317,
-0.0315699502825737,
-0.014498966746032238,
-0.05841339752078056,
-0.0526362806558609,
-0.08081706613302231,
0.03884503245353699,
-0.010128703899681568,
-0.0037153412122279406,
-0.01699242927134037,
-0.005745049566030502,
0.008673779666423798,
-0.024476662278175354,
0.0017337818862870336,
-0.015710588544607162,
0.00573942344635725,
-0.012644333764910698,
-0.0007846005610190332,
0.007594283204525709,
0.08194080740213394,
0.04968271404504776,
0.015911493450403214,
0.006975093856453896,
0.008311768062412739,
-0.022321822121739388,
0.024921810254454613,
-0.04227369651198387,
0.01407612394541502,
0.0149697195738554,
-0.01009536162018776,
0.033359017223119736,
-0.006933859083801508,
0.0007863066275604069,
0.02091939002275467,
0.01646765135228634,
0.07676705718040466,
0.08264421671628952,
0.021921314299106598,
0.004227548837661743,
0.008639609441161156,
-0.04536917805671692,
0.01884670928120613,
0.010035225190222263,
-0.052704159170389175,
-0.02308160811662674,
0.0005560394492931664,
0.006868691649287939,
0.03229589760303497,
-0.023950930684804916,
-0.04155183210968971,
0.04047466814517975,
0.044582877308130264,
0.025210516527295113,
-0.010201468132436275,
0.022493088617920876,
-0.000392813264625147,
0.0236649252474308,
0.0195570420473814,
-0.0020804391242563725,
0.0005351709551177919,
0.00141232181340456,
0.008034481666982174,
0.022224927321076393,
0.017567163333296776,
-0.02819119766354561,
0.018395496532320976,
0.00894403550773859,
0.005055949091911316,
-0.00511105265468359,
-0.021592555567622185,
0.016349876299500465,
-0.030008774250745773,
0.013357898220419884,
0.051020607352256775,
0.008361002430319786,
0.047647107392549515,
-0.04444865509867668,
-0.057770367711782455,
0.021906528621912003,
-0.008328809402883053,
0.008453828282654285,
-0.03586352989077568,
0.03170398995280266,
-0.02116643451154232,
-0.00729675218462944,
0.03911450505256653,
-0.02605004422366619,
-0.0020985775627195835,
0.0035119690001010895,
0.022573411464691162,
-0.0130861084908247,
0.015179143287241459,
-0.05465495213866234,
0.004786404315382242,
-0.048713319003582,
0.0013548413990065455,
-0.015636926516890526,
0.002538543427363038,
-0.0759008601307869,
-0.004048395436257124,
-0.004582217428833246,
-0.006350376643240452,
0.06770774722099304,
-0.01826842501759529,
0.009282470680773258,
0.03605080395936966,
0.03717537969350815,
-0.05694720521569252,
0.046570245176553726,
-0.03653259575366974,
-0.00033836314105428755,
0.0003325888537801802,
-0.0023692254908382893,
0.018793750554323196,
-0.009436331689357758,
-0.07160362601280212,
0.041165031492710114,
-0.07317894697189331,
-0.04313195124268532,
-0.020958708599209785,
-0.010534423403441906,
-0.005705054383724928,
0.0038374844007194042,
-0.0007925315876491368,
-0.04617887735366821,
-0.007888012565672398,
-0.01505732536315918,
-0.05957138165831566,
-0.01654582843184471,
-0.01347383763641119,
0.010987682268023491,
0.06833347678184509,
-0.022538982331752777,
-0.05685451254248619,
0.0835728868842125,
0.03808046132326126,
-0.03969581425189972,
0.020239749923348427,
-0.046641331166028976,
0.019744204357266426,
-0.02689649537205696,
0.03701627999544144,
0.03356645628809929,
-0.008974380791187286,
0.003990115597844124,
-0.004055114462971687,
0.017073307186365128,
0.03158286213874817,
-0.03642342612147331,
-0.012493298389017582,
-0.026321159675717354,
-0.015481773763895035,
-0.00005516632882063277,
0.027888134121894836,
0.013780729845166206,
-0.04268202558159828,
0.015312832780182362,
0.004525389056652784,
0.03810722008347511,
0.0012966435169801116,
-0.04038269817829132,
0.06056108698248863,
0.01809263974428177,
0.027629466727375984,
-0.022422881796956062,
0.039044346660375595,
0.0019094102317467332,
-0.032659485936164856,
0.016616463661193848,
0.04388837143778801,
0.05666382983326912,
-0.009774920530617237,
0.013789067976176739,
0.011129958555102348,
0.07455386966466904,
0.02460801787674427,
-0.03490142896771431,
-0.013211879879236221,
-0.0010887645184993744,
0.02294209785759449,
0.013621780090034008,
-0.017141170799732208,
-0.0028614476323127747,
0.02171548455953598,
0.025275204330682755,
0.017504047602415085,
-0.0208940040320158,
-0.01942504569888115,
-0.06203395873308182,
-0.04639281705021858,
-0.0161741990596056,
0.021895291283726692,
0.009197150357067585,
0.06804602593183517,
0.007091601844877005,
0.015557891689240932,
0.007770578842610121,
0.0340382345020771,
-0.03235587850213051,
0.03998285159468651,
-0.007065776269882917,
-0.002455623121932149,
-0.019013019278645515,
-0.0018689461285248399,
0.001319634960964322,
-0.022108418866991997,
0.01652549020946026,
-0.010925134643912315,
0.023022595793008804,
-0.04266824200749397,
0.0011872549075633287,
-0.039234522730112076,
-0.048603300005197525,
-0.0012158924946561456,
0.0003399091074243188,
0.02631676383316517,
0.0012701699743047357,
0.0009305530111305416,
0.041319556534290314,
-0.032924406230449677,
-0.00468409014865756,
-0.0076797474175691605,
-0.05242697894573212,
-0.029050074517726898,
0.02288811467587948,
-0.03192634508013725,
0.01615789905190468,
-0.011681853793561459,
-0.0066716172732412815,
0.04113994166254997,
-0.014119481667876244,
-0.018371455371379852,
0.002248024567961693,
-0.049621567130088806,
-0.04805484041571617,
0.021979689598083496,
0.019985660910606384,
0.020027589052915573,
-0.02038024179637432,
0.032712969928979874,
0.009835912846028805,
0.03966729715466499,
0.000769506033975631,
0.06566014140844345,
0.06180979683995247,
0.009260165505111217,
-0.01821816712617874,
-0.07818187028169632,
0.003198744496330619,
-0.036180321127176285,
-0.015628190711140633,
0.04644758626818657,
-0.02375047653913498,
0.014461738988757133,
0.020970771089196205,
0.02131010964512825,
0.008683722466230392,
-0.022682875394821167,
0.019968148320913315,
-0.015049556270241737,
-0.013270947150886059,
-0.04523299261927605,
-0.0063050235621631145,
0.024763911962509155,
0.043896038085222244,
0.0451895110309124,
-0.014257446862757206,
-0.030072174966335297,
-0.08978094905614853,
-0.02163737826049328,
0.041488904505968094,
0.04631722718477249,
-0.02322409115731716,
0.030902335420250893,
-0.040968891233205795,
-0.009989782236516476,
0.03583543747663498,
-0.04360048472881317,
0.04904330521821976,
-0.040256984531879425,
0.02862251177430153,
-0.00921874213963747,
-0.024143686518073082,
-0.03193417936563492,
0.021495139226317406,
-0.04080422967672348,
0.011505326256155968,
0.018642690032720566,
-0.008078556507825851,
-0.0035814798902720213,
0.022341912612318993,
0.047352422028779984,
0.04163109511137009,
0.0015842270804569125,
0.014857468195259571,
-0.0017375327879562974,
-0.008026727475225925,
-0.04018833488225937,
-0.05659899860620499,
0.03698898106813431,
-0.0008974385564215481,
-0.010160158388316631,
0.05036795511841774,
-0.026655295863747597,
-0.054682813584804535,
0.028382236137986183,
0.01845555752515793,
0.0036465509328991175,
-0.03280038386583328,
-0.03258298709988594,
0.043831516057252884,
0.07368817180395126,
-0.00486751040443778,
0.0389685183763504,
0.04433336481451988,
-0.0465991385281086,
0.012503628619015217,
0.03136564791202545,
0.005453683901578188,
0.0011044454295188189,
0.01270125899463892,
-0.026332583278417587,
0.027596736326813698,
-0.034063585102558136,
0.016806568950414658,
-0.023820387199521065,
0.027231412008404732,
-0.027103275060653687,
-0.021724091842770576,
-0.03758968785405159,
0.04471847042441368,
0.03448091447353363,
-0.008299490436911583,
-0.03677302971482277,
0.0027424064464867115,
0.006560733076184988,
-0.032947685569524765,
0.005696696694940329,
0.009377838112413883,
0.021457085385918617,
-0.0063364095985889435,
0.013275159522891045,
0.01824481412768364,
-0.06555081158876419,
-0.011043271981179714,
0.020028527826070786,
-0.02867905981838703,
0.004439723212271929,
0.0016439614119008183,
0.026488374918699265,
0.018143508583307266,
-0.04003917798399925,
-0.014492587186396122,
-0.026309292763471603,
-0.03523804247379303,
0.007194212172180414,
-0.02238820679485798,
0.03660456836223602,
-0.005995289422571659,
0.012249299325048923,
-0.03363717347383499,
-0.08067835867404938,
0.047854915261268616,
0.003906387835741043,
0.009443569928407669,
-0.020446131005883217,
-0.004072003997862339,
0.0018229986308142543,
-0.033399779349565506,
0.0012976593570783734,
0.04298660531640053,
-0.010488826781511307,
0.03853274881839752,
0.001535065472126007,
-0.008709389716386795,
0.057473987340927124,
-0.016617728397250175,
-0.027713561430573463,
0.022661836817860603,
-0.007756087929010391,
-0.057706329971551895,
-0.006864858791232109,
0.0056457677856087685,
-0.03504941985011101,
-0.0015280089573934674,
0.05113601312041283,
-0.026051044464111328,
0.05220898240804672,
-0.04455478489398956,
0.019644664600491524,
0.02884349599480629,
0.014104323461651802,
-0.010218304581940174,
-0.012057989835739136,
0.02048370987176895,
-0.0075873578898608685,
0.031110350042581558,
0.023096954450011253,
-0.038495566695928574,
-0.023174401372671127,
-0.048890601843595505,
0.004865474533289671,
-0.002450329717248678,
-0.012447420507669449,
0.012670602649450302,
0.0477910041809082,
-0.04206579923629761,
0.013388680294156075,
0.013618124648928642,
-0.023781202733516693,
0.05100054293870926,
-0.036341343075037,
0.006330106407403946,
-0.027040567249059677,
-0.04139973595738411,
-0.041102245450019836,
0.0011479774257168174,
-0.013692041859030724,
0.02913743630051613,
0.0568801686167717,
-0.0029195076785981655,
0.040528759360313416,
-0.011849216185510159,
0.00613440852612257,
0.027823878452181816,
-0.00022124651877675205,
0.00029004598036408424,
-0.006458254065364599,
0.038478873670101166,
0.007570131216198206,
-0.007477279286831617,
-0.015057167038321495,
0.07163774967193604,
0.009456649422645569,
-0.018999647349119186,
0.004760217387229204,
0.024846982210874557,
0.027223091572523117,
-0.005118632689118385,
-0.08238441497087479,
-0.022857215255498886,
0.019222121685743332,
-0.0324004702270031,
0.03770676255226135,
0.02640053629875183,
-0.014347095042467117,
0.03955893591046333,
0.028058739379048347,
-0.0183930154889822,
-0.028602218255400658,
-0.02098163776099682,
-0.060054630041122437,
-0.016084089875221252,
0.005933266133069992,
0.018162565305829048,
0.025578871369361877,
-0.019210560247302055,
0.012396994978189468,
0.02253471128642559,
-0.013613835908472538,
-0.02933049574494362,
-0.04847372695803642,
-0.04186515510082245,
-0.003475987119600177,
-0.05229682847857475,
0.042453598231077194,
-0.011918521486222744,
0.009750626049935818,
0.028683943673968315,
-0.016860656440258026,
-0.0009577388991601765,
-0.0025811896193772554,
0.019960515201091766,
0.0005221384926699102,
0.07897459715604782,
0.013185679912567139,
0.06588448584079742,
-0.0598183311522007,
0.0322401188313961,
0.11953239142894745,
0.02130548655986786,
-0.017702428624033928,
-0.014131380245089531,
0.009826702065765858,
-0.025917470455169678,
-0.0161077119410038,
-0.034723296761512756,
-0.0023937849327921867,
0.0138931293040514,
0.02516692504286766,
-0.002273186342790723,
0.04789712280035019,
-0.016149256378412247,
-0.018584702163934708,
0.016589315608143806,
-0.0014362434158101678,
0.0012826821766793728,
0.03945652022957802,
0.010652986355125904,
-0.011556947603821754,
-0.04665016755461693,
-0.04668402671813965,
0.008923422545194626,
0.0026794723235070705,
-0.04216679185628891,
0.028174789622426033,
-0.04410868138074875,
0.02070569433271885,
0.013364249840378761,
-0.0193924717605114,
0.018608663231134415,
0.0013153263134881854,
-0.03862949460744858,
-0.02547411248087883,
0.05481359735131264,
0.030167805030941963,
-0.007381370756775141,
0.010817810893058777,
0.060983505100011826,
-0.006881206762045622,
-0.01765820011496544,
0.028594568371772766,
-0.0038458998315036297,
-0.04429301619529724,
0.00033120493753813207,
-0.028355775400996208,
0.01931600645184517,
-0.016340821981430054,
0.027370719239115715,
-0.001922150026075542,
-0.030606860294938087,
-0.02585216611623764,
-0.047462064772844315,
-0.006542616058140993,
0.03747741878032684,
-0.010997171513736248,
0.01968737691640854,
-0.019630316644906998,
-0.003830310422927141,
-0.024897797033190727,
-0.0030853331554681063,
0.02408088743686676,
0.02452453412115574,
-0.009168979711830616,
0.004587168805301189,
0.012969911098480225,
0.05954306572675705,
0.01639682427048683,
-0.005314660258591175,
-0.014890559017658234,
-0.03321806341409683,
-0.005217625293880701,
-0.007487396243959665,
-0.0055786436423659325,
0.03213312476873398,
-0.007970921695232391,
0.0031033619306981564,
-0.009054434485733509,
-0.029943009838461876,
-0.03701246902346611,
0.05605064332485199,
-0.009852692484855652,
-0.01605655997991562,
-0.007694993633776903,
-0.02046152763068676,
0.04299894720315933,
0.053819142282009125,
-0.020756905898451805,
0.01964680477976799,
0.011369213461875916,
0.023498784750699997,
0.021296076476573944,
-0.024112531915307045,
-0.045588765293359756,
-0.0013352272799238563,
-0.01668405905365944,
0.03510085865855217,
-0.020330257713794708,
0.046538472175598145,
0.025035008788108826,
-0.03177843987941742,
0.013339193537831306,
-0.019102955237030983,
-0.031540896743535995,
0.029823999851942062,
0.027819614857435226,
-0.01734316349029541,
-0.028474655002355576,
0.004927057307213545,
-0.015007448382675648,
-0.04168255999684334,
-0.006404300685971975,
-0.018767014145851135,
0.01833673194050789,
-0.02286737598478794,
0.03728935867547989,
-0.018647095188498497,
0.00957841519266367,
-0.05423085391521454,
0.03514280542731285,
-0.055206745862960815,
-0.01823362149298191,
-0.032273441553115845,
0.03412074223160744,
0.025482898578047752,
0.025049060583114624,
-0.03144660219550133,
0.026168718934059143,
-0.01764402538537979,
0.03239259123802185,
0.010051148012280464,
0.002946150954812765,
0.0246584415435791,
0.0024793001357465982,
0.03116358444094658,
-0.029728028923273087,
0.023023080080747604,
-0.02749256044626236,
-0.03400520607829094,
0.06682036072015762,
-0.03606154024600983,
-0.06098030135035515,
0.007291518151760101,
-0.04280726984143257,
-0.0047903661616146564,
0.034075818955898285,
-0.019330037757754326,
-0.000611030962318182,
0.06398015469312668,
-0.04969679191708565,
0.0037633522879332304,
0.012136206962168217,
-0.03598325699567795,
-0.011994453147053719,
-0.011184705421328545,
0.02321120724081993,
-0.005752886179834604,
-0.014066637493669987,
0.03261338174343109,
-0.009176104329526424,
0.006339090410619974,
-0.005296382587403059,
-0.009080933406949043,
-0.04107961431145668,
-0.029452109709382057,
0.005256985779851675,
0.03638937696814537,
-0.007186263799667358,
0.034894973039627075,
-0.05904733017086983,
-0.02002381533384323,
-0.002831807127222419,
-0.008629157207906246,
-0.08637162297964096,
-0.00713285943493247,
-0.030562538653612137,
0.005527066998183727,
0.06885126233100891,
-0.04958545044064522,
0.04412973299622536,
0.007191224489361048,
-0.06407128274440765,
0.013082550838589668,
-0.029235132038593292,
0.007789336144924164,
-0.018038198351860046,
0.01404663361608982,
0.0026966517325490713,
0.06398119777441025,
0.004788543563336134,
0.08091163635253906,
0.033616092056035995,
0.022005217149853706,
-0.0051857950165867805,
-0.00931391678750515,
0.04097413644194603,
0.04566090181469917,
-0.044520799070596695,
0.02839205041527748,
0.06616416573524475,
0.001722946995869279,
-0.021983066573739052,
-0.0063538397662341595,
-0.041647590696811676,
0.015990346670150757,
-0.01752905175089836,
0.02852884866297245,
-0.00452094292268157,
0.021320682018995285,
-0.0008723237551748753,
0.02091318555176258,
0.011597727425396442,
0.0009816782549023628,
-0.008088203147053719,
0.007364262826740742,
-0.006770489737391472,
-0.006364193744957447,
0.014783477410674095,
-0.004061709623783827,
-0.007332276087254286,
0.034021683037281036,
-0.005342770367860794,
-0.047340407967567444,
0.02945820614695549,
0.016035327687859535,
0.03260481357574463,
-0.01385657861828804,
-0.0038481149822473526,
-0.045119743794202805,
-0.03781843185424805,
0.015189330093562603,
-0.018883584067225456,
-0.02361489087343216,
-0.008946473710238934,
0.03425557166337967,
-0.014853519387543201,
-0.014743978157639503,
0.054693885147571564,
-0.002499301452189684,
-0.05901382863521576,
0.016087589785456657,
0.016455836594104767,
0.0014345988165587187,
-0.0013433202402666211,
-0.05136803165078163,
-0.07142577320337296,
0.022125476971268654,
0.03917670249938965,
0.052768755704164505,
0.020043935626745224,
-0.03632010146975517,
-0.010407816618680954,
-0.08029653877019882,
0.006700242403894663,
0.009318912401795387,
-0.02014821395277977,
-0.019720805808901787,
-0.015594844706356525,
-0.0004153005429543555,
0.016799071803689003,
0.05837254598736763,
-0.02949552610516548,
-0.034494224935770035,
0.014501900412142277,
-0.057235151529312134,
0.006219806149601936,
-0.04257413372397423,
0.024214407429099083,
-0.01848864182829857,
-0.017530402168631554,
0.014534003101289272,
0.009869765490293503,
-0.007151544559746981,
0.008297461085021496,
0.013317213393747807,
0.008721246384084225,
0.029237044975161552,
-0.030215580016374588,
-0.04550158604979515,
0.03731917589902878,
0.001781586790457368,
0.01150090154260397,
0.08557622879743576,
-0.004794002510607243,
0.07089098542928696,
-0.020849287509918213,
-0.030050160363316536,
-0.05139969661831856,
0.020864691585302353,
-0.024862919002771378,
0.04314495250582695,
-0.022370673716068268,
-0.009648818522691727,
0.06853550672531128,
-0.04378827288746834,
0.014763838611543179,
0.04424840584397316,
-0.024266960099339485,
-0.030466750264167786,
0.004001804627478123,
0.018681176006793976,
0.030393265187740326,
0.031159384176135063,
0.044278234243392944,
0.0018622985808178782,
-0.019521377980709076,
0.0207724217325449,
0.036652032285928726,
-0.008932680822908878,
-0.043366752564907074,
0.044008076190948486,
0.033046312630176544,
0.030514927580952644,
0.025626543909311295,
0.03388334438204765,
-0.0024886629544198513,
0.017109382897615433,
-0.049451544880867004,
-0.008952482603490353,
-0.003981109708547592,
-0.030578572303056717,
0.040095843374729156,
-0.010640152730047703,
0.07653554528951645,
-0.02560821734368801,
-0.005205297376960516,
-0.004158701281994581,
0.019664857536554337,
0.0083302091807127,
-0.03703665733337402,
0.021666638553142548,
0.004683625418692827,
-0.01758948527276516,
0.010355118662118912,
-0.03999229893088341,
0.03730642423033714,
0.007027542218565941,
-0.03304831311106682,
0.03029409795999527,
0.010260308161377907,
0.006587147247046232,
-0.015985336154699326,
-0.0023682191967964172,
-0.026700379326939583,
-0.04044163227081299,
0.05873582512140274,
0.05464351549744606,
-0.03907204046845436,
0.04164396971464157,
-0.006810708902776241,
0.02980225905776024,
0.07565101236104965,
-0.038487739861011505,
0.014469814486801624,
-0.025583649054169655,
0.01667446829378605,
-0.00026609477936290205,
0.03901804983615875
] |
<p>Say a red colour with 400nm mixes with blue colour with 700nm, but out of phase by a little. What would be the resultant colour?</p>
<p>I would know how to represent the resulting wave mathematically, but what colour is it? Is the colour only determined by the resulting wavelength?</p>
| 308 |
[
-0.005923582706600428,
-0.03799385949969292,
-0.0223993007093668,
-0.027561616152524948,
0.044811591506004333,
0.02008807100355625,
-0.022831028327345848,
-0.03389643877744675,
0.01854550465941429,
-0.009137197397649288,
0.02439057268202305,
0.0437939278781414,
0.05816524103283882,
0.036838751286268234,
0.005716090090572834,
0.044249195605516434,
0.039107777178287506,
-0.009728037752211094,
-0.03399578109383583,
-0.025452682748436928,
0.008103292435407639,
0.011762709356844425,
0.008142029866576195,
-0.013638162985444069,
-0.04138669744133949,
0.03809716925024986,
0.0634702742099762,
0.029322927817702293,
0.028020501136779785,
0.03256417065858841,
-0.005097479093819857,
-0.04900100827217102,
-0.005788762588053942,
0.06279292702674866,
0.011499674059450626,
0.0027968399226665497,
-0.03559434041380882,
-0.044186342507600784,
-0.033764179795980453,
-0.02477518655359745,
0.042936574667692184,
0.0036931969225406647,
0.029869111254811287,
0.0457097589969635,
0.009466256946325302,
-0.012645749375224113,
-0.019710229709744453,
-0.024051230400800705,
0.019143467769026756,
-0.03529154509305954,
0.07795355468988419,
-0.0256317388266325,
0.020102376118302345,
0.004452367313206196,
-0.008444816805422306,
0.02190965600311756,
0.061489351093769073,
0.06792350858449936,
-0.012253723107278347,
-0.003894232679158449,
0.008095168508589268,
0.013661437667906284,
-0.005611690226942301,
-0.007443252019584179,
-0.04391190782189369,
0.008547414094209671,
0.014549226500093937,
-0.03263946995139122,
0.04643366113305092,
0.015222369693219662,
-0.010275386273860931,
-0.009286248125135899,
0.036081161350011826,
-0.041280340403318405,
0.011948099359869957,
-0.08439714461565018,
0.0020009572617709637,
0.022002601996064186,
-0.004468643106520176,
0.01331760548055172,
-0.02834504097700119,
0.017737936228513718,
-0.07264753431081772,
-0.0043980940245091915,
0.004183520562946796,
-0.031982917338609695,
0.0963611900806427,
-0.016680225729942322,
-0.007389288395643234,
0.02205989882349968,
-0.018483754247426987,
0.0248869676142931,
0.024440018460154533,
0.011247770860791206,
-0.02409937046468258,
0.0026794199366122484,
-0.006065867375582457,
0.042281899601221085,
0.033852070569992065,
-0.025540988892316818,
0.02202695980668068,
-0.01600143499672413,
0.028460275381803513,
0.07858814299106598,
-0.020582880824804306,
-0.018667425960302353,
0.017200807109475136,
0.018357932567596436,
0.005092211067676544,
0.0020610434003174305,
0.0027590510435402393,
-0.025409679859876633,
0.0231942068785429,
0.012602558359503746,
0.0017230374505743384,
-0.023190537467598915,
0.0018057591514661908,
0.003658160800114274,
0.04985702782869339,
0.07407287508249283,
0.0041273958049714565,
-0.038701917976140976,
0.030645763501524925,
0.00392739474773407,
-0.0733306035399437,
0.002100304001942277,
0.009662234224379063,
-0.01653270795941353,
-0.03303612396121025,
0.019845567643642426,
-0.03372646123170853,
-0.023795651271939278,
0.0017151075880974531,
-0.026822775602340698,
-0.011632016859948635,
-0.02076019160449505,
-0.08691854029893875,
-0.07905495911836624,
0.008453675545752048,
-0.019222304224967957,
-0.02624697797000408,
-0.06166796758770943,
0.02740795910358429,
0.05163096636533737,
0.06920140236616135,
0.00042337141348980367,
0.011117898859083652,
-0.011600123718380928,
0.023466622456908226,
0.019785763695836067,
-0.01665003038942814,
-0.023289551958441734,
0.00910862348973751,
-0.029605312272906303,
0.01418765727430582,
-0.02783852070569992,
-0.005713001359254122,
0.06117141619324684,
0.022288037464022636,
-0.03432759270071983,
0.027712557464838028,
-0.0009542737388983369,
-0.004937672056257725,
0.07203912734985352,
0.011751915328204632,
-0.02541610784828663,
0.08253071457147598,
-0.005969420541077852,
0.01076086051762104,
0.016181744635105133,
0.000666258274577558,
0.012304188683629036,
0.009774114936590195,
-0.005044892895966768,
0.008758209645748138,
0.0007306208135560155,
0.021962281316518784,
-0.0032559544779360294,
0.02657151035964489,
-0.0239267535507679,
-0.01876043900847435,
-0.07225938886404037,
-0.03495008498430252,
0.033757295459508896,
0.03798459470272064,
0.023228975012898445,
-0.006295686587691307,
-0.010397345758974552,
0.044796060770750046,
-0.03808777034282684,
0.0053292992524802685,
-0.0008528965408913791,
0.05495574325323105,
0.006209221668541431,
-0.017541153356432915,
0.0003573000431060791,
0.03293905034661293,
0.011827381327748299,
-0.027542607858777046,
-0.038204632699489594,
-0.013686200603842735,
0.01975606195628643,
0.011273141950368881,
0.008128714747726917,
0.008268906734883785,
0.08492989093065262,
-0.014666060917079449,
-0.007493781857192516,
0.02748837135732174,
-0.03030734322965145,
-0.03952641785144806,
-0.007426748052239418,
0.00616723857820034,
0.03689316287636757,
-0.014466582797467709,
-0.014105948619544506,
0.0036918765399605036,
0.019380392506718636,
0.014530899003148079,
0.00705507630482316,
-0.007452106568962336,
0.0484791174530983,
0.051000140607357025,
-0.01943277195096016,
0.026107745245099068,
0.032100383192300797,
-0.010967334732413292,
0.029761770740151405,
0.023063449189066887,
-0.000031033581763040274,
-0.04053788259625435,
-0.004015118815004826,
0.03097596764564514,
0.0261989813297987,
-0.02710384503006935,
0.011419056914746761,
0.01091361977159977,
0.054012496024370193,
0.06464848667383194,
0.03734807297587395,
-0.01802915148437023,
-0.00538709107786417,
0.017538610845804214,
0.035585805773735046,
0.0030905853491276503,
-0.0019144120160490274,
-0.004986042622476816,
0.0034952880814671516,
0.004410045687109232,
-0.049116816371679306,
-0.04650186747312546,
0.031228629872202873,
-0.00497796293348074,
0.024297261610627174,
-0.030874289572238922,
-0.03833945840597153,
0.017138736322522163,
-0.0005022030090913177,
-0.010830883868038654,
0.02472866326570511,
-0.017609797418117523,
-0.02411549538373947,
-0.0039399899542331696,
-0.015236894600093365,
0.004830529447644949,
0.01410890743136406,
-0.05040564760565758,
-0.007648444268852472,
0.030823534354567528,
-0.013923882506787777,
0.016572382301092148,
0.008762025274336338,
0.015197031199932098,
-0.045114755630493164,
-0.007531260140240192,
0.0445718877017498,
-0.0029873771127313375,
0.05240480601787567,
-0.03637600317597389,
-0.06062043458223343,
0.01110189687460661,
-0.018059220165014267,
0.0018574269488453865,
-0.01211909856647253,
-0.05848971754312515,
0.025800161063671112,
-0.03249631077051163,
-0.03381289541721344,
0.015450634062290192,
0.003491366282105446,
-0.0154294827952981,
-0.009145835414528847,
-0.04003334417939186,
-0.06633584946393967,
-0.019296281039714813,
-0.035857561975717545,
0.008424094878137112,
-0.007500249892473221,
-0.01514792162925005,
0.018979867920279503,
-0.030417699366807938,
-0.06989362090826035,
0.001370691228657961,
-0.030124293640255928,
-0.025356359779834747,
-0.02293754182755947,
0.006697137374430895,
0.03533277288079262,
-0.05700360983610153,
0.023538144305348396,
0.026422476395964622,
-0.004860979504883289,
0.02608976513147354,
-0.02260301634669304,
-0.04699650779366493,
0.026423508301377296,
-0.03769085183739662,
0.02178324945271015,
-0.0006925293710082769,
-0.0018249850254505873,
0.065848708152771,
0.017176000401377678,
-0.019657518714666367,
-0.005887437146157026,
0.0020683000329881907,
0.005561257712543011,
-0.03688961640000343,
0.052208296954631805,
0.049677520990371704,
-0.010481449775397778,
0.03327977657318115,
-0.012702558189630508,
0.000996566261164844,
0.04685701057314873,
0.06460461020469666,
-0.017394529655575752,
0.036275606602430344,
-0.015355970710515976,
-0.00023655430413782597,
0.024488113820552826,
0.047773443162441254,
-0.057337384670972824,
0.048441335558891296,
-0.010196919552981853,
0.0273244958370924,
0.04820012301206589,
-0.021414069458842278,
-0.0009149916004389524,
0.00039374324842356145,
-0.008788416162133217,
-0.023278463631868362,
0.05310772359371185,
-0.0007143043330870569,
0.0024037426337599754,
-0.00562639907002449,
0.008835338987410069,
0.028913326561450958,
0.03908568248152733,
-0.029168739914894104,
0.057011306285858154,
0.025405753403902054,
0.01825476624071598,
-0.033519353717565536,
0.015408123843371868,
-0.012950095348060131,
0.03664437308907509,
-0.04358380660414696,
-0.025789668783545494,
0.06073582544922829,
0.012175020761787891,
-0.0005593597306869924,
0.010092678479850292,
-0.00613856827840209,
-0.02394077740609646,
-0.06630002707242966,
-0.03213196620345116,
-0.012186135165393353,
0.034144867211580276,
0.0030626782681792974,
0.11639730632305145,
0.018207183107733727,
0.03680950403213501,
0.03930160775780678,
0.04000049829483032,
-0.044074591249227524,
0.021649720147252083,
0.017198681831359863,
-0.026777680963277817,
-0.02139388397336006,
-0.03885101154446602,
-0.00993379857391119,
-0.055754758417606354,
-0.05522162467241287,
0.004085931461304426,
-0.01953766494989395,
-0.04626692458987236,
0.0029592816717922688,
-0.0015012630028650165,
-0.038015127182006836,
0.00948428176343441,
0.006816344801336527,
0.01621101424098015,
0.021472739055752754,
0.006324357818812132,
0.04656621813774109,
-0.01202264241874218,
-0.01297040842473507,
-0.0010070988209918141,
0.006689359433948994,
-0.02027801238000393,
0.04153506085276604,
0.03614642098546028,
0.04971496760845184,
-0.04488113895058632,
0.03161242604255676,
0.032740410417318344,
0.05953526124358177,
-0.017025567591190338,
-0.015408912673592567,
-0.008235587738454342,
-0.056365080177783966,
-0.001306206570006907,
-0.019846107810735703,
0.04206423461437225,
-0.013065772131085396,
-0.013901103287935257,
0.030363865196704865,
0.0017385558458045125,
-0.03916895017027855,
0.05237762629985809,
0.03305131942033768,
0.018476899713277817,
-0.028087995946407318,
-0.032225415110588074,
0.019069107249379158,
-0.0065311104990541935,
0.03533941134810448,
0.03456183150410652,
0.03527228906750679,
0.013160694390535355,
0.021181805059313774,
0.023333635181188583,
0.029842335730791092,
-0.042523209005594254,
-0.0006975441356189549,
-0.023305222392082214,
-0.021794017404317856,
-0.020995860919356346,
-0.016619931906461716,
0.005478858482092619,
0.04585498943924904,
0.013693680986762047,
0.000709044630639255,
-0.053625039756298065,
-0.14238804578781128,
-0.0020951852202415466,
0.030848927795886993,
-0.0025244455318897963,
-0.01152021810412407,
-0.04445858299732208,
-0.07216913998126984,
-0.045250553637742996,
-0.010862763039767742,
-0.01856636069715023,
0.03984832391142845,
-0.02778295986354351,
0.017544660717248917,
0.014479216188192368,
0.016081376001238823,
-0.01481170579791069,
0.06003967672586441,
0.027541546151041985,
0.012401469983160496,
-0.006816715467721224,
-0.015105361118912697,
-0.009315777570009232,
0.011434718035161495,
0.05746380612254143,
0.05053246393799782,
-0.01281228568404913,
-0.016854198649525642,
-0.008723331615328789,
0.002712549641728401,
-0.0011306655360385776,
-0.052088748663663864,
0.024515435099601746,
0.015676820650696754,
-0.005301351193338633,
0.057522427290678024,
-0.045251477509737015,
-0.026717020198702812,
0.04730251431465149,
0.0394805409014225,
0.022197803482413292,
0.014422626234591007,
-0.039699897170066833,
0.09064110368490219,
0.016831431537866592,
0.018320713192224503,
0.05400184169411659,
0.0036304770037531853,
-0.007890197448432446,
-0.009360210038721561,
-0.018001629039645195,
0.059662554413080215,
-0.024680471047759056,
0.01090085320174694,
0.016246335580945015,
-0.0017332973657175899,
-0.011629213578999043,
0.049161557108163834,
0.026637855917215347,
0.032490022480487823,
-0.007359789218753576,
-0.06264594942331314,
-0.03553721681237221,
-0.0059590269811451435,
-0.007486447691917419,
-0.001060178386978805,
-0.0012871971121057868,
-0.016731660813093185,
0.037464216351509094,
-0.007440969813615084,
0.007155993953347206,
-0.014825453981757164,
0.01130830217152834,
0.01397582609206438,
0.013389205560088158,
0.030432842671871185,
-0.02347497269511223,
0.01558256521821022,
-0.005091539584100246,
-0.0039389668963849545,
0.04157784581184387,
-0.005450819618999958,
0.05120524391531944,
0.03815266862511635,
-0.05438582971692085,
-0.023289985954761505,
-0.011683941818773746,
-0.020190902054309845,
0.009841391816735268,
-0.015165477991104126,
0.02022985927760601,
0.05750705674290657,
-0.014986654743552208,
-0.05393577367067337,
-0.06146300956606865,
0.031919896602630615,
0.03736717253923416,
-0.010988261550664902,
-0.008109824731945992,
0.03763541579246521,
-0.003502702107653022,
-0.010499108582735062,
0.014679335057735443,
0.024766776710748672,
-0.006366601213812828,
-0.025187382474541664,
-0.014817319810390472,
0.0004988344153389335,
0.049038007855415344,
-0.008593779057264328,
-0.0036476135719567537,
0.021673079580068588,
0.007675692439079285,
0.000583651359193027,
0.02503243274986744,
0.03593114763498306,
-0.014279300346970558,
-0.03054662048816681,
-0.008845520205795765,
-0.02321864850819111,
0.0457039400935173,
0.0029231628868728876,
0.013400987721979618,
0.00879889726638794,
0.04587015137076378,
-0.015354206785559654,
-0.027714723721146584,
-0.0043275929056108,
-0.03472866117954254,
0.027235182002186775,
0.0227341428399086,
-0.02041986770927906,
-0.02533767931163311,
-0.03557814657688141,
-0.007156180217862129,
0.021036824211478233,
-0.0030321956146508455,
0.009516682475805283,
0.05660621449351311,
-0.024207882583141327,
-0.003364421660080552,
-0.004417751915752888,
-0.008015676401555538,
-0.016117772087454796,
-0.029974769800901413,
0.006317934487015009,
0.006367247086018324,
0.04132005572319031,
-0.01361780520528555,
-0.03960314393043518,
-0.021861018612980843,
-0.016871841624379158,
0.06929308921098709,
-0.05394487455487251,
0.06165890395641327,
0.005694263149052858,
0.006313897669315338,
-0.028672587126493454,
-0.010135374031960964,
-0.005108976736664772,
0.010776173323392868,
-0.046341199427843094,
0.01544495951384306,
-0.024779576808214188,
-0.026825901120901108,
-0.02888188697397709,
0.03919209539890289,
-0.0053613875061273575,
0.00842805951833725,
0.05255437642335892,
0.0009665988618507981,
0.016976259648799896,
-0.02363058365881443,
-0.029874997213482857,
0.025744125247001648,
-0.029338443651795387,
0.014417540282011032,
0.007645268924534321,
-0.006719219498336315,
0.031146621331572533,
0.00866186898201704,
-0.012648820877075195,
-0.034023892134428024,
0.00022530881687998772,
-0.027724672108888626,
-0.01483678724616766,
0.014628445729613304,
0.002604489214718342,
0.0421103909611702,
-0.015356231480836868,
0.01369196642190218,
0.00205455394461751,
0.008171750232577324,
-0.03543999791145325,
-0.053955987095832825,
-0.05368362367153168,
-0.050600066781044006,
-0.05870882794260979,
0.02248457632958889,
-0.020495247095823288,
-0.0002953875227831304,
-0.0002708985994104296,
-0.05265315622091293,
0.028858499601483345,
-0.015141932293772697,
0.04071669280529022,
-0.031115390360355377,
0.03543372079730034,
0.007896513678133488,
0.07612498104572296,
0.01834186166524887,
0.022387726232409477,
0.10553494095802307,
0.0393650159239769,
0.029111934825778008,
-0.07995244860649109,
0.019027257338166237,
-0.03547145426273346,
-0.007548810448497534,
-0.03938935324549675,
0.03548195958137512,
-0.0031807448249310255,
0.025264479219913483,
-0.0133278276771307,
0.012061430141329765,
0.01196716446429491,
0.009272109717130661,
0.010829915292561054,
-0.025445230305194855,
-0.03418032079935074,
0.02481144480407238,
-0.03606198728084564,
0.0009028709027916193,
0.02551637589931488,
-0.04356776922941208,
-0.013777493499219418,
-0.0260505061596632,
-0.036046773195266724,
-0.024790611118078232,
-0.04412904009222984,
0.07872260361909866,
0.007882327772676945,
-0.016110870987176895,
0.021751241758465767,
0.006147462874650955,
-0.02614896558225155,
0.0035304564516991377,
0.012541045434772968,
0.06817527860403061,
-0.012246612459421158,
0.022495310753583908,
0.005149540491402149,
0.03136938810348511,
-0.02549247443675995,
-0.03724091500043869,
0.003171152900904417,
-0.04131314903497696,
0.007431135047227144,
-0.022153496742248535,
0.04028310626745224,
0.008475426584482193,
-0.011998545378446579,
-0.0037580158095806837,
0.011881166137754917,
-0.016767773777246475,
-0.05510516092181206,
0.003824354615062475,
0.03505752980709076,
0.029721656814217567,
-0.0022395628038793802,
-0.016056930646300316,
0.012652122415602207,
0.0028387876227498055,
-0.001785583095625043,
0.004658164922147989,
0.018099097535014153,
-0.02685455046594143,
-0.014877446927130222,
0.03219854459166527,
0.053773801773786545,
0.04843655601143837,
-0.05253559350967407,
-0.029378904029726982,
0.0038876424077898264,
-0.029062973335385323,
-0.03096724860370159,
0.020501434803009033,
0.053177885711193085,
-0.01997700147330761,
-0.018950853496789932,
-0.05408432334661484,
-0.01970350742340088,
-0.08622593432664871,
0.05085749924182892,
0.03636942431330681,
-0.01340989489108324,
0.0021605438087135553,
0.014020179398357868,
0.05896686390042305,
0.05552275851368904,
-0.043634142726659775,
0.0032343068160116673,
-0.006098233163356781,
0.01744130253791809,
0.049547914415597916,
-0.010215037502348423,
-0.001585264690220356,
0.03831201419234276,
-0.026254309341311455,
-0.017162686213850975,
0.004495089873671532,
0.03017561137676239,
0.0033950884826481342,
0.028816625475883484,
0.033581506460905075,
0.012161643244326115,
-0.025870872661471367,
-0.026713013648986816,
-0.018421996384859085,
-0.016909154132008553,
-0.01337931863963604,
-0.00765594094991684,
0.034284092485904694,
-0.02440505474805832,
0.0003228666028007865,
-0.0016218337696045637,
-0.013011305592954159,
0.0229245163500309,
0.006467691622674465,
-0.025418145582079887,
-0.02532927319407463,
0.017712144181132317,
-0.0138213150203228,
-0.03504190221428871,
-0.011154946871101856,
-0.015090744942426682,
0.016503430902957916,
-0.011325829662382603,
-0.030422521755099297,
0.00063544005388394,
0.0174400694668293,
-0.010546569712460041,
-0.029064811766147614,
0.015837280079722404,
0.055061448365449905,
0.032016344368457794,
0.0073195514269173145,
-0.004472583066672087,
0.007919901050627232,
0.03918225318193436,
-0.02962513267993927,
-0.05380146950483322,
0.041326574981212616,
-0.026904502883553505,
-0.0488828644156456,
0.045633308589458466,
-0.03257809579372406,
0.04631812870502472,
0.022095877677202225,
0.011245308443903923,
0.005068557802587748,
0.014069451950490475,
0.0013470640406012535,
-0.029962262138724327,
-0.022192850708961487,
-0.01566091552376747,
0.02014653943479061,
0.004043797496706247,
0.006808703299611807,
-0.03371841087937355,
0.00039043204742483795,
0.04714977741241455,
-0.0036586623173207045,
0.008806358091533184,
0.0002275069709867239,
-0.003161089727655053,
0.00828845240175724,
0.019525403156876564,
0.03347327560186386,
-0.03293638303875923,
0.002158648334443569,
-0.006420918274670839,
0.041217003017663956,
0.005802702158689499,
0.012481066398322582,
-0.054490622133016586,
-0.063166044652462,
-0.04453872889280319,
0.043412402272224426,
0.0026203251909464598,
0.06209307909011841,
-0.055340979248285294,
0.04083661362528801,
0.0021599712781608105,
-0.10962370038032532,
-0.0021525498013943434,
-0.002344381297007203,
-0.038191039115190506,
-0.02178434655070305,
0.059004705399274826,
-0.04898500442504883,
0.02686450444161892,
0.03519987314939499,
0.04834206774830818,
0.007899495773017406,
-0.013277960009872913,
-0.015349437482655048,
0.002987678162753582,
0.006848735734820366,
-0.013441150076687336,
0.01030964870005846,
-0.019414862617850304,
0.027825796976685524,
-0.023838452994823456,
-0.018579382449388504,
0.024286098778247833,
-0.04434590041637421,
0.0003404337039683014,
-0.021194951608777046,
0.02056199125945568,
-0.025998232886195183,
0.02126014418900013,
-0.02639593556523323,
-0.020761458203196526,
-0.045268554240465164,
0.02720082923769951,
0.03898884728550911,
0.0164894238114357,
0.003457607002928853,
-0.021351497620344162,
0.020639749243855476,
-0.03225373849272728,
-0.022344255819916725,
0.045902978628873825,
-0.046331726014614105,
-0.00290227634832263,
0.019993247464299202,
-0.004214400425553322,
0.026779212057590485,
-0.02218666858971119,
0.046781715005636215,
-0.034192945808172226,
0.009059969335794449,
-0.03157588094472885,
0.012238411232829094,
-0.011395123787224293,
-0.018156737089157104,
-0.018982259556651115,
-0.048485640436410904,
-0.00004547624848783016,
-0.01003908272832632,
-0.03518282622098923,
0.0035698285792022943,
-0.00602409802377224,
0.018533140420913696,
-0.0014250241219997406,
0.02962026372551918,
-0.01459358911961317,
-0.0239738617092371,
0.060858797281980515,
-0.011580883525311947,
0.021921886131167412,
-0.009723126888275146,
-0.07181469351053238,
-0.021228112280368805,
-0.035589683800935745,
0.021040569990873337,
0.020562706515192986,
-0.004349744413048029,
-0.059477586299180984,
0.00009252870950149372,
-0.03281376138329506,
0.05457513779401779,
0.047825660556554794,
-0.002196835121139884,
-0.05549333989620209,
-0.0005770738353021443,
-0.011273115873336792,
0.026481250301003456,
-0.04767872765660286,
-0.018890326842665672,
-0.0006877590785734355,
-0.02590368501842022,
-0.06914651393890381,
0.02141820453107357,
-0.038296688348054886,
0.02268228679895401,
0.02103026770055294,
0.0005630871746689081,
0.0166215430945158,
0.0037695164792239666,
-0.017352648079395294,
0.04621094837784767,
-0.011997545138001442,
-0.01128149963915348,
0.07967225462198257,
0.011985564604401588,
-0.016666488721966743,
0.009494606405496597,
-0.02088640071451664,
-0.08707894384860992,
-0.011245525442063808,
-0.017330782487988472,
-0.013770212419331074,
0.004799313843250275,
0.024128209799528122,
0.05157869681715965,
-0.06433947384357452,
0.019505612552165985,
0.03252534940838814,
-0.03594959154725075,
-0.040205907076597214,
0.058193329721689224,
-0.004542666487395763,
0.007109945174306631,
-0.015721889212727547,
0.010328116826713085,
0.01478024385869503,
0.014011326245963573,
0.016003165394067764,
0.008824581280350685,
0.004599106032401323,
0.014821569435298443,
0.052014559507369995,
-0.010519220493733883,
-0.013349270448088646,
-0.024604450911283493,
0.002323739230632782,
-0.004090053495019674,
0.005448541603982449,
-0.0057483757846057415,
0.032519545406103134,
0.013655191287398338,
0.0310815442353487,
0.06018940359354019,
-0.05337590351700783,
0.09285396337509155,
-0.024588964879512787,
0.022179579362273216,
-0.04967179894447327,
0.026734748855233192,
-0.030022509396076202,
0.005523969419300556,
0.023333905264735222,
0.0009587627137079835,
-0.004524257965385914,
-0.023589888587594032,
0.0037140571512281895,
-0.014535371214151382,
0.01389322616159916,
-0.07722461968660355,
0.012893392704427242,
-0.0026727865915745497,
-0.009924727492034435,
-0.01426495797932148,
-0.0019273010548204184,
-0.05567879229784012,
-0.0032561123371124268,
0.01598585955798626,
0.0012103667249903083,
-0.007459177635610104,
-0.0030417810194194317,
0.006917373277246952,
-0.02786441706120968,
0.019599003717303276,
-0.023657197132706642,
-0.0052407230250537395,
0.012354521080851555,
-0.012081723660230637,
-0.011511990800499916,
-0.01587526500225067
] |
<p><a href="http://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity" rel="nofollow">Gauss's law for Gravitation</a>:</p>
<p>$$\int g\cdot \mathrm{d}S=4\pi GM$$</p>
<p>where $g$ is the gravitational field and $S$ is the surface area.</p>
<p>Am I correct?</p>
| 9,364 |
[
-0.012948545627295971,
-0.0010927747935056686,
-0.006563008762896061,
0.007063298486173153,
0.04968886822462082,
0.01806744560599327,
-0.04207924008369446,
-0.046445608139038086,
-0.010530837811529636,
0.005658636800944805,
0.05544471740722656,
0.03811769187450409,
0.04821057245135307,
0.027382725849747658,
-0.004064988344907761,
0.01784173585474491,
-0.008140821009874344,
-0.021047545596957207,
-0.0060105412267148495,
-0.034166544675827026,
-0.022215252742171288,
0.04854389280080795,
-0.024493085220456123,
-0.001267509302124381,
-0.03997869789600372,
0.016710519790649414,
0.03145192936062813,
-0.02289428748190403,
0.022166242823004723,
0.11336342245340347,
-0.01817742921411991,
0.006716298870742321,
0.02275913767516613,
0.05744133144617081,
0.03064357303082943,
0.005087622907012701,
-0.0007722379523329437,
-0.003090938786044717,
-0.020010551437735558,
0.04320986196398735,
-0.01440365705639124,
-0.022711018100380898,
-0.0038144320715218782,
0.04905606433749199,
-0.004667084198445082,
0.02415384165942669,
0.004043231718242168,
-0.00021211507555563003,
0.055400192737579346,
-0.07096416503190994,
0.05289653688669205,
0.011148323304951191,
0.03471168130636215,
0.0334777906537056,
0.02134527452290058,
-0.01021942775696516,
0.08559995889663696,
0.034003619104623795,
-0.007475701626390219,
-0.0731673464179039,
-0.017805760726332664,
-0.010377000086009502,
0.00696524977684021,
-0.030162720009684563,
-0.028640266507864,
0.018208233639597893,
-0.020476218312978745,
-0.012240071780979633,
0.01588624157011509,
-0.01476056408137083,
0.01992207020521164,
0.024860745295882225,
0.0010117330821231008,
-0.010664074681699276,
-0.0015194228617474437,
-0.016239000484347343,
0.034951113164424896,
0.023345934227108955,
0.0007154271588660777,
0.046545904129743576,
0.01641964726150036,
0.018374640494585037,
0.030274566262960434,
0.031119951978325844,
0.046759579330682755,
0.012861533090472221,
0.06641259789466858,
-0.0035829744301736355,
0.019936228170990944,
0.018088720738887787,
0.0006753697525709867,
0.028548583388328552,
0.02417941391468048,
-0.03614189475774765,
0.02464810386300087,
0.02380000427365303,
-0.010986028239130974,
0.034982554614543915,
-0.025475865229964256,
-0.015451483428478241,
-0.018257027491927147,
-0.03275418281555176,
-0.029665334150195122,
0.0762881487607956,
-0.019845135509967804,
-0.034766003489494324,
-0.03550909459590912,
0.032269131392240524,
-0.028987685218453407,
-0.02916422113776207,
-0.04524359107017517,
0.02915862202644348,
-0.01255349162966013,
-0.0082358717918396,
0.04346561059355736,
-0.019010281190276146,
0.02277563139796257,
0.0018905067117884755,
0.012106819078326225,
0.027699552476406097,
0.04904526099562645,
-0.042214006185531616,
0.014484093524515629,
-0.021042387932538986,
-0.038874998688697815,
0.039232365787029266,
-0.006473334040492773,
0.004862341098487377,
-0.03108906000852585,
0.04418884217739105,
0.006617342121899128,
0.010669811628758907,
-0.015964780002832413,
0.03679601848125458,
0.005443707574158907,
0.005336197558790445,
-0.06677628308534622,
-0.05621334910392761,
0.05193459242582321,
-0.01919405162334442,
-0.00482879439368844,
-0.06943903118371964,
0.01767595112323761,
-0.003821578109636903,
0.027130743488669395,
-0.0021849346812814474,
0.015226366929709911,
0.011407680809497833,
0.018312403932213783,
-0.03746168687939644,
-0.013534843921661377,
-0.019067538902163506,
0.007930238731205463,
-0.05127106234431267,
-0.0074830730445683,
-0.07857900857925415,
0.005639968905597925,
0.042026687413454056,
-0.002160722389817238,
-0.03733709082007408,
0.062301408499479294,
0.007701832335442305,
0.026330089196562767,
0.011510546319186687,
0.008900848217308521,
-0.014262392185628414,
0.049829039722681046,
0.011448146775364876,
0.005825562868267298,
0.05658716708421707,
0.0025805935729295015,
-0.0164671391248703,
-0.04756387695670128,
0.009018141776323318,
0.052040230482816696,
-0.04140050709247589,
-0.046331167221069336,
-0.03692251443862915,
0.014704338274896145,
0.00758369779214263,
-0.026792213320732117,
-0.057079557329416275,
-0.025695836171507835,
0.006184089928865433,
-0.014521962031722069,
0.05008671432733536,
0.03706051781773567,
-0.011959463357925415,
-0.025829747319221497,
-0.0130429957062006,
-0.020798273384571075,
-0.07192103564739227,
0.05089174583554268,
0.027331765741109848,
-0.0025597955100238323,
-0.012285081669688225,
0.03370549902319908,
0.03813449293375015,
-0.042102694511413574,
-0.012328898534178734,
-0.0021398332901299,
0.0314667746424675,
-0.01662304997444153,
-0.03920983150601387,
0.022077729925513268,
0.07686655968427658,
0.030585844069719315,
-0.027484141290187836,
0.020645009353756905,
-0.008288513869047165,
0.012278929352760315,
0.004131999332457781,
-0.00142722949385643,
0.030704626813530922,
-0.039988696575164795,
-0.03169885277748108,
0.04802453890442848,
0.043663959950208664,
0.003982085734605789,
0.03505363315343857,
-0.058724693953990936,
0.08529951423406601,
0.05417738854885101,
0.0011381481308490038,
0.01602354273200035,
-0.015009324066340923,
-0.0032659280113875866,
0.03464897722005844,
-0.010009028017520905,
-0.027828399091959,
-0.0345173180103302,
-0.02697139047086239,
0.024577029049396515,
0.034855298697948456,
0.005407081451267004,
0.018320119008421898,
0.06693457067012787,
0.021398842334747314,
0.01080599520355463,
0.010651618242263794,
-0.004112087655812502,
-0.05123355612158775,
0.029638119041919708,
0.026516061276197433,
-0.008388648740947247,
0.029223276302218437,
-0.0034897460136562586,
0.04877569153904915,
0.026847222819924355,
0.007183648645877838,
-0.01730472594499588,
0.006414524279534817,
-0.015044565312564373,
0.036361195147037506,
0.0151418037712574,
-0.014654064550995827,
0.03590346872806549,
-0.011310391128063202,
0.005099003203213215,
0.04301154613494873,
-0.008220327086746693,
-0.0012249322608113289,
-0.06752268970012665,
-0.039636366069316864,
0.0022158976644277573,
0.011295393109321594,
-0.01679571531713009,
-0.04515113681554794,
0.01177660096436739,
-0.040694329887628555,
-0.001435984275303781,
-0.009647469967603683,
-0.03809308260679245,
-0.04205462709069252,
0.017075669020414352,
0.0027809604071080685,
0.009448723867535591,
0.015066412277519703,
-0.02650100365281105,
-0.010892340913414955,
0.02137112058699131,
0.01699923723936081,
0.0027393021155148745,
0.03137873858213425,
-0.0344853438436985,
0.004057163372635841,
-0.02159692347049713,
-0.00502652395516634,
0.057021819055080414,
-0.02042488195002079,
0.037207938730716705,
0.009249110706150532,
0.005380141083151102,
-0.028675399720668793,
0.003059815615415573,
-0.03374113887548447,
0.002295887563377619,
-0.048526328057050705,
-0.0052269925363361835,
0.014508385211229324,
-0.02990904450416565,
-0.050532758235931396,
0.03760023042559624,
-0.048545487225055695,
-0.06746517866849899,
-0.017237892374396324,
0.008881321176886559,
0.00908420979976654,
-0.005856739357113838,
0.018754636868834496,
-0.005391049664467573,
-0.02317545749247074,
-0.02380385249853134,
-0.0656791627407074,
-0.02748839557170868,
0.022015880793333054,
-0.026515750214457512,
0.028040310367941856,
-0.017305754125118256,
-0.04420830309391022,
0.09499122947454453,
0.04976741969585419,
0.008667311631143093,
0.012105886824429035,
-0.006781608331948519,
0.0001253164082299918,
-0.01680254377424717,
0.020437924191355705,
-0.0003509325906634331,
-0.029440298676490784,
-0.006416275165975094,
0.0008840339141897857,
0.046752434223890305,
0.017556585371494293,
0.03110734187066555,
0.03367418050765991,
-0.02050655335187912,
-0.020555440336465836,
0.0004643573483917862,
0.04946513473987579,
0.029683792963624,
0.020657476037740707,
-0.019307836890220642,
0.008219297043979168,
0.03864608332514763,
0.002502566436305642,
-0.036347273737192154,
0.060778286308050156,
-0.044982269406318665,
0.021355975419282913,
-0.04160883650183678,
0.030877016484737396,
0.0250694639980793,
-0.03084496781229973,
0.03415306285023689,
0.002736116526648402,
0.05083214491605759,
0.013173838146030903,
-0.013096518814563751,
0.021233944222331047,
0.024232467636466026,
-0.02584162726998329,
-0.00893435999751091,
0.00735012860968709,
-0.015168960206210613,
0.01165540050715208,
-0.00958315934985876,
-0.024122532457113266,
0.025418788194656372,
0.08238916844129562,
0.015376751311123371,
0.016050536185503006,
-0.05942549556493759,
-0.006596182473003864,
-0.10614441335201263,
-0.012888087891042233,
-0.003171420656144619,
0.043722864240407944,
0.01908484287559986,
0.025598343461751938,
0.05592827498912811,
0.01193047035485506,
0.02600489929318428,
0.016713790595531464,
-0.1023113951086998,
0.015308399684727192,
-0.05157788470387459,
0.001489925547502935,
-0.004587508272379637,
-0.034460995346307755,
-0.0177138801664114,
-0.029994042590260506,
-0.002802537987008691,
-0.0175277441740036,
-0.010575005784630775,
-0.044272299855947495,
-0.008833318017423153,
-0.004785171244293451,
-0.049498800188302994,
0.00450278352946043,
0.040485866367816925,
0.023009678348898888,
-0.03736748546361923,
0.016741523519158363,
0.05756188556551933,
0.0054764170199632645,
-0.017998704686760902,
0.0225224569439888,
-0.018856093287467957,
0.00268154707737267,
0.04407962039113045,
0.020334932953119278,
0.003627648577094078,
-0.0098801264539361,
-0.0025027371011674404,
-0.0023110457696020603,
0.04480500891804695,
0.009519173763692379,
-0.03643963113427162,
-0.0441250279545784,
-0.03822674602270126,
-0.0016278161201626062,
0.0028111902065575123,
0.029629863798618317,
-0.019069654867053032,
-0.02095130831003189,
0.00972177553921938,
-0.015114771202206612,
-0.013397449627518654,
0.051260314881801605,
0.06489390134811401,
-0.015165839344263077,
-0.0024565020576119423,
-0.04913729429244995,
-0.028949283063411713,
-0.07020117342472076,
-0.01902388222515583,
0.038359787315130234,
-0.016861479729413986,
-0.06765810400247574,
-0.01330666895955801,
-0.000058968260418623686,
0.010950358584523201,
-0.025553857907652855,
-0.0077630686573684216,
-0.015988366678357124,
0.004631777293980122,
0.014368919655680656,
0.0047228699550032616,
0.00616753613576293,
0.051733508706092834,
0.022341163828969002,
0.009985926561057568,
-0.03542380407452583,
-0.055841922760009766,
-0.014637992717325687,
0.047153592109680176,
0.03208116441965103,
-0.007645505480468273,
0.00987869780510664,
-0.04009507969021797,
-0.019774312153458595,
0.023889850825071335,
-0.017054840922355652,
0.023021141067147255,
-0.02747035212814808,
0.04129137471318245,
-0.013004991225898266,
-0.03503536805510521,
-0.015554836951196194,
0.013353194110095501,
-0.019187310710549355,
-0.004478771239519119,
-0.018392784520983696,
-0.005490344949066639,
0.014002774842083454,
0.03961360827088356,
0.011448250152170658,
0.03263650834560394,
0.010774748399853706,
0.0164739191532135,
0.0010749243665486574,
0.020159540697932243,
-0.06172570213675499,
-0.05696101486682892,
0.01311949361115694,
-0.009495486505329609,
-0.009557446464896202,
0.048496101051568985,
-0.018202733248472214,
-0.05725390091538429,
0.04287870228290558,
0.021688681095838547,
-0.001563600730150938,
0.0160855483263731,
-0.056032974272966385,
0.02141302078962326,
0.05006886646151543,
0.02035275474190712,
0.015673749148845673,
0.04669160023331642,
-0.014390966854989529,
-0.020334362983703613,
-0.06114763021469116,
0.03519809991121292,
-0.06602907925844193,
-0.03293875977396965,
-0.006653155665844679,
-0.019540885463356972,
-0.06205325573682785,
0.022017011418938637,
-0.01294651161879301,
0.020558997988700867,
-0.02983848750591278,
-0.017046604305505753,
0.0006809081532992423,
-0.011302916333079338,
0.04342128336429596,
0.03305577486753464,
0.028901105746626854,
0.0235737357288599,
0.02383541688323021,
-0.03136763349175453,
-0.002367922104895115,
-0.003084333147853613,
-0.024303685873746872,
0.012579606845974922,
0.02919096313416958,
-0.00957203283905983,
0.005131755489856005,
-0.04607856273651123,
0.0008096182136796415,
-0.03011370077729225,
0.05005064606666565,
-0.015063321217894554,
0.01646237261593342,
0.030106473714113235,
-0.022546205669641495,
-0.02952294610440731,
-0.007482651621103287,
0.048177361488342285,
0.022554678842425346,
-0.056711893528699875,
0.005736646708101034,
0.004912953358143568,
0.06328495591878891,
-0.06380370259284973,
-0.030055390670895576,
0.048533063381910324,
-0.008879984728991985,
-0.02009005844593048,
-0.02221463806927204,
0.001095233135856688,
-0.04554697126150131,
-0.03205382823944092,
-0.018665984272956848,
0.008495512418448925,
-0.0586269274353981,
0.022600900381803513,
0.013382408767938614,
-0.004150292836129665,
0.07078921794891357,
0.005129621364176273,
-0.023001279681921005,
0.013578866608440876,
-0.01281095203012228,
-0.016543494537472725,
-0.019770285114645958,
0.0297139510512352,
-0.010233416222035885,
-0.03514159098267555,
-0.021558260545134544,
-0.011538081802427769,
0.02640715055167675,
0.01415520440787077,
0.007107917219400406,
0.02531263791024685,
0.009443952701985836,
-0.03201908990740776,
-0.015366870909929276,
0.026385115459561348,
0.005707705859094858,
0.0006583019276149571,
-0.009387634694576263,
-0.000848432769998908,
0.011000535450875759,
0.012099334970116615,
0.013280789367854595,
-0.03550843894481659,
-0.0019194306805729866,
-0.007099024020135403,
0.0721377581357956,
-0.014753646217286587,
-0.01519103068858385,
0.008779576048254967,
-0.014460427686572075,
0.011997322551906109,
-0.007500217761844397,
-0.0014625113690271974,
0.003373292973265052,
-0.014625567942857742,
-0.04275861382484436,
-0.020286820828914642,
-0.029777757823467255,
-0.01970054768025875,
0.08438143879175186,
-0.0034031097311526537,
0.07090961188077927,
0.024213694036006927,
0.01670643873512745,
0.031119491904973984,
-0.0265179593116045,
-0.0008489103056490421,
-0.0028686504811048508,
-0.00910649448633194,
0.002803149400278926,
-0.004424992483109236,
-0.003889115760102868,
0.011953294277191162,
0.004519479349255562,
-0.006443329155445099,
0.008374316617846489,
0.039263490587472916,
0.0008647047798149288,
0.0006663432577624917,
-0.003977681510150433,
-0.07437571883201599,
0.06491884589195251,
-0.025516070425510406,
0.040070485323667526,
-0.03667715564370155,
0.0121513856574893,
0.022646937519311905,
0.01677820459008217,
0.016903575509786606,
-0.011890377849340439,
-0.00030125887133181095,
-0.029202386736869812,
-0.0027896182145923376,
0.026301613077521324,
-0.02909483015537262,
-0.044378187507390976,
0.006390159018337727,
0.01309901848435402,
0.011538466438651085,
0.0065022800117731094,
-0.0028118828777223825,
-0.05790027603507042,
-0.0082229133695364,
-0.04450666159391403,
-0.058827392756938934,
0.05093899369239807,
0.003537312150001526,
-0.02270810678601265,
0.00865235272794962,
-0.04328364133834839,
0.019341127946972847,
0.05240227282047272,
0.01932930387556553,
-0.02139916457235813,
0.06180964410305023,
-0.02710760198533535,
0.03464554622769356,
-0.03072184883058071,
-0.014140513725578785,
0.12949413061141968,
0.03848651796579361,
-0.004506864119321108,
-0.030760349705815315,
0.03012152574956417,
-0.042860738933086395,
0.004893122240900993,
-0.030864723026752472,
-0.006037452258169651,
-0.05836576223373413,
-0.023272249847650528,
0.01919466443359852,
0.03984423354268074,
-0.025831889361143112,
-0.04577277600765228,
0.048854731023311615,
-0.0063331155106425285,
-0.018419485539197922,
-0.0005136308027431369,
0.0507366918027401,
-0.030112972483038902,
0.058801040053367615,
-0.04160192236304283,
0.03300635144114494,
-0.06491922587156296,
0.01661485619843006,
-0.05855284258723259,
-0.008893237449228764,
0.0060920193791389465,
0.021965282037854195,
-0.06089949980378151,
0.018351411446928978,
-0.011061692610383034,
-0.04955291375517845,
-0.02887064963579178,
0.01226875837892294,
-0.011509288102388382,
-0.019378991797566414,
0.002903961343690753,
0.046807318925857544,
-0.04393152520060539,
0.03962647169828415,
0.011378067545592785,
-0.00021194221335463226,
-0.06312582641839981,
-0.007351851090788841,
-0.03112875111401081,
0.07604372501373291,
-0.0270649753510952,
0.02918786182999611,
0.00670568086206913,
0.014524010941386223,
0.025388946756720543,
-0.09019000828266144,
-0.030793072655797005,
-0.00949612446129322,
0.03008420392870903,
-0.011545587331056595,
-0.03124941885471344,
-0.0011026319116353989,
0.02331014908850193,
-0.005110607016831636,
0.013822648674249649,
0.015422411262989044,
0.0065368348732590675,
0.026409868150949478,
-0.013530667871236801,
0.04188726842403412,
-0.027318516746163368,
-0.0029214113019406796,
0.0034811757504940033,
-0.030978532508015633,
-0.044326044619083405,
-0.011587712913751602,
-0.008338233456015587,
0.03883155807852745,
0.006168339401483536,
0.018110979348421097,
-0.009512677788734436,
-0.025148307904601097,
-0.03184803947806358,
0.06641445308923721,
-0.015862813219428062,
0.012331933714449406,
-0.04689064994454384,
-0.023908575996756554,
0.02088533714413643,
0.04780399426817894,
0.006319398060441017,
0.02903992123901844,
0.0021352588664740324,
0.010102899745106697,
0.0020200686994940042,
-0.015564103610813618,
-0.004811587277799845,
0.0064151049591600895,
-0.026673492044210434,
-0.012561931274831295,
0.021645253524184227,
-0.0015193985309451818,
0.07243062555789948,
0.022007061168551445,
0.017623839899897575,
0.042499084025621414,
-0.014067449606955051,
0.01073522213846445,
-0.02655152790248394,
0.0033996785059571266,
-0.010062847286462784,
0.020581860095262527,
0.015781665220856667,
-0.04822345823049545,
0.008207960054278374,
-0.004346365109086037,
0.04087980091571808,
0.01728937029838562,
0.023572104051709175,
-0.034194450825452805,
0.04432614892721176,
-0.00912852305918932,
0.017183365300297737,
-0.04969169944524765,
-0.016934992745518684,
-0.05777379125356674,
-0.015310242772102356,
0.003997654654085636,
-0.00951337069272995,
-0.021013429388403893,
0.03207486867904663,
-0.000876092875842005,
0.010456560179591179,
0.055525440722703934,
-0.022156452760100365,
-0.00696544349193573,
-0.023630091920495033,
0.030568165704607964,
-0.027747541666030884,
0.04698018357157707,
0.013843541964888573,
-0.023253774270415306,
0.01059072744101286,
-0.025592420250177383,
-0.05443451181054115,
0.016355210915207863,
0.00856141559779644,
0.010563250631093979,
0.017641538754105568,
-0.015640605241060257,
-0.0166859719902277,
0.023647092282772064,
-0.0033591892570257187,
0.02855854667723179,
-0.02204318717122078,
-0.03279062733054161,
0.011293735355138779,
-0.0002810531004797667,
0.03371623158454895,
0.029427699744701385,
0.00025338452542200685,
0.012648234143853188,
-0.021160762757062912,
-0.008626874536275864,
0.005161799490451813,
0.02737148478627205,
-0.04223841801285744,
-0.019456615671515465,
0.02614300698041916,
-0.026829436421394348,
0.006273791193962097,
0.02421886846423149,
-0.0029546075966209173,
0.01615782640874386,
0.021690964698791504,
0.03265818580985069,
-0.07924532145261765,
-0.002730549080297351,
0.007235600147396326,
0.03927823156118393,
0.01464039832353592,
-0.05331652611494064,
-0.008182190358638763,
0.02662816271185875,
-0.07278946787118912,
0.03835446015000343,
-0.02764560654759407,
-0.0252708550542593,
-0.021431976929306984,
-0.016242660582065582,
0.000962487596552819,
0.06687726825475693,
-0.010002966970205307,
0.04074309021234512,
0.008491341024637222,
0.024002723395824432,
-0.004794514272361994,
-0.023906487971544266,
0.0024755727499723434,
0.03630582243204117,
-0.0149778937920928,
0.0013930099084973335,
0.04867814853787422,
-0.0004972801543772221,
-0.028301026672124863,
0.03311372548341751,
0.00470123952254653,
0.018840165808796883,
-0.013896270655095577,
0.004474431276321411,
0.01746722124516964,
0.03074018284678459,
0.016012756153941154,
0.010868164710700512,
-0.022757513448596,
0.01389442291110754,
0.0008775559836067259,
0.03611263260245323,
-0.015707148239016533,
-0.020076625049114227,
0.003833591239526868,
-0.051052920520305634,
-0.0433182567358017,
0.021086296066641808,
-0.03321061655879021,
0.006267877295613289,
-0.04045463353395462,
-0.01637350395321846,
-0.019996358081698418,
-0.04821251332759857,
-0.00721074640750885,
-0.04668495059013367,
0.02471710555255413,
0.0335620678961277,
-0.026071421802043915,
-0.0319099947810173,
0.024758318439126015,
0.06200191378593445,
0.008494514040648937,
0.02129380777478218,
0.005471247248351574,
-0.003983099013566971,
-0.013345131650567055,
0.011750243604183197,
-0.00886816717684269,
-0.012792091816663742,
0.04493069276213646,
-0.017779503017663956,
-0.03339117392897606,
0.02810634672641754,
0.02561412751674652,
-0.0005662433686666191,
-0.024830006062984467,
-0.03820416331291199,
-0.01824822649359703,
-0.0735313668847084,
0.021995477378368378,
0.006352289579808712,
-0.0626194030046463,
-0.042747870087623596,
0.009643830358982086,
0.002052509458735585,
-0.03672855347394943,
0.02438104897737503,
0.004121238831430674,
-0.006116783246397972,
0.027414429932832718,
-0.002720243763178587,
-0.019401390105485916,
-0.05330878123641014,
-0.004343784414231777,
0.01982652023434639,
-0.018768098205327988,
0.02312968112528324,
0.0018407301977276802,
-0.015108386054635048,
0.00013859821774531156,
-0.008654228411614895,
-0.023521265015006065,
0.03037511371076107,
-0.01629030331969261,
-0.039359163492918015,
0.03604811429977417,
0.0476335771381855,
-0.022886857390403748,
0.08378984779119492,
-0.02691013179719448,
0.012571494095027447,
0.033597756177186966,
-0.028111856430768967,
-0.009724147617816925,
0.0006868859054520726,
-0.03851674869656563,
-0.033430442214012146,
-0.01912493258714676,
0.009995671920478344,
0.03899231553077698,
-0.008068287745118141,
-0.008921584114432335,
0.08358736336231232,
-0.035197652876377106,
-0.013506235554814339,
0.07132641971111298,
0.007395334076136351,
0.054113805294036865,
-0.00866902805864811,
0.03299412876367569,
0.024297969415783882,
-0.04842366278171539,
0.017052188515663147,
0.014120812527835369,
0.019969787448644638,
-0.014536012895405293,
-0.02276829071342945,
0.08491979539394379,
0.026676353067159653,
-0.009124982170760632,
0.035702988505363464,
0.024055473506450653,
-0.03876488655805588,
-0.009761208668351173,
0.005953178741037846,
-0.022207824513316154,
0.026844941079616547,
0.04336080700159073,
-0.020719457417726517,
0.07395648956298828,
-0.014059250243008137,
-0.008677653037011623,
0.00773646030575037,
-0.00691301329061389,
-0.04106089100241661,
0.02070966176688671,
0.03754448518157005,
0.05657215416431427,
-0.010298281908035278,
-0.044275131076574326,
0.012089401483535767,
0.006049958057701588,
-0.0022050952538847923,
0.008662411943078041,
0.035299982875585556,
0.010276244021952152,
0.04492020979523659,
-0.003515315242111683,
0.009898684918880463,
-0.011873485520482063,
-0.002601309446617961,
0.023513546213507652,
0.013783407397568226,
0.009680764749646187,
-0.00932060182094574,
0.01279318705201149,
-0.028461413457989693,
0.058132220059633255,
-0.058743249624967575,
-0.03799412399530411,
-0.019677190110087395,
0.010523350909352303,
0.02580009214580059,
-0.04825703799724579
] |
<p>When and where on earth do we get the best view of the <a href="http://en.wikipedia.org/wiki/Milky_Way">Milky Way</a>?</p>
<p>I believe it helps</p>
<ul>
<li>if it is night</li>
<li>if it is winter</li>
<li>to look in the direction of the galaxy center</li>
</ul>
<p>I think that this information from wikipedia:</p>
<blockquote>
<p>The Galactic plane is inclined by about 60 degrees to the ecliptic (the plane of the Earth's orbit).</p>
</blockquote>
<p>is needed, but I can still not figure it out.</p>
<p>I am hoping to get a general sense of what to expect <em>when and where</em>, so that I can make sure to enjoy the view on future travels.</p>
<p><strong>Edit:</strong> From the answer of @Johannes and corresponding comment of @WetSavannaAnimal aka Rod Vance, I believe that a good time and place is December to February on the southern hemisphere. So what is the optimum? New years eve on the South pole?</p>
| 9,365 |
[
-0.0055378940887749195,
-0.0636206567287445,
0.016948608681559563,
-0.0018161979969590902,
0.036355189979076385,
0.051134590059518814,
-0.025937018916010857,
-0.012561763636767864,
0.0057246009819209576,
-0.054407332092523575,
0.02161196805536747,
0.08809696137905121,
0.02161290869116783,
0.05970137193799019,
-0.008331622928380966,
-0.012323485687375069,
-0.0026825752574950457,
-0.02586943469941616,
-0.04304010793566704,
0.006155809853225946,
-0.028353065252304077,
-0.000028446424039429985,
-0.023158816620707512,
0.02231866680085659,
-0.06129709258675575,
0.0276716947555542,
0.017371581867337227,
0.008542438969016075,
-0.03429052606225014,
0.054281238466501236,
-0.02589087188243866,
-0.035093121230602264,
0.01387446466833353,
0.027418846264481544,
0.05593579635024071,
0.0023309150710701942,
0.013792932033538818,
0.002264806069433689,
-0.0277901291847229,
-0.0036251347046345472,
-0.018265539780259132,
-0.001687358133494854,
-0.004996933043003082,
0.008001962676644325,
-0.061838164925575256,
0.014316247776150703,
-0.035868559032678604,
-0.018669581040740013,
0.05207248777151108,
-0.061542727053165436,
0.03197123855352402,
-0.006016260478645563,
-0.018698036670684814,
0.011229234747588634,
0.024571657180786133,
-0.02199947088956833,
0.04687000811100006,
0.05569502338767052,
0.024643395096063614,
-0.03235764801502228,
-0.020679205656051636,
-0.012731064110994339,
-0.012607129290699959,
0.011281898245215416,
-0.002085387473925948,
-0.002225001808255911,
-0.00841287150979042,
-0.008069243282079697,
0.03138574957847595,
0.026403076946735382,
-0.02922534942626953,
0.014173074625432491,
0.015188055112957954,
-0.026623133569955826,
0.00401066429913044,
-0.06809782981872559,
0.02610771171748638,
0.0209798701107502,
0.02772301807999611,
0.0018735608318820596,
-0.002302885986864567,
0.018444912508130074,
0.010977454483509064,
0.01475822925567627,
0.004602362401783466,
0.03529287874698639,
0.10796137154102325,
-0.016899259760975838,
-0.028431491926312447,
0.020152008160948753,
0.04509264975786209,
0.040462933480739594,
0.006217297166585922,
-0.020411614328622818,
-0.01642577536404133,
0.02493162639439106,
-0.003371055005118251,
0.03512100502848625,
-0.016113825142383575,
-0.03722026199102402,
-0.008084380067884922,
0.01588236726820469,
-0.027643000707030296,
0.06970459222793579,
0.011983600445091724,
-0.012486884370446205,
-0.049693427979946136,
-0.0003473627439234406,
0.006306122988462448,
-0.02140563726425171,
-0.05343220755457878,
0.028457144275307655,
-0.007756358943879604,
0.01576666533946991,
0.03059529885649681,
-0.01836441084742546,
-0.004618364851921797,
-0.0026692391838878393,
0.07254442572593689,
0.02907981164753437,
0.050904229283332825,
0.001712882542051375,
0.0231512151658535,
-0.057845424860715866,
-0.06097181513905525,
0.05777522921562195,
0.027523251250386238,
0.006654287688434124,
-0.0163041353225708,
0.010342215187847614,
0.02709539793431759,
-0.0010512873996049166,
0.004702789708971977,
-0.03198126330971718,
0.020309410989284515,
0.024889051914215088,
-0.06164252385497093,
-0.06013122946023941,
0.020445706322789192,
0.04087056219577789,
0.05025777593255043,
-0.039866819977760315,
0.002334943041205406,
-0.0013528778217732906,
0.057837069034576416,
-0.013945065438747406,
-0.01219569519162178,
-0.002729205647483468,
0.04061855375766754,
-0.03469959646463394,
-0.033943500369787216,
0.011939694173634052,
-0.024812743067741394,
-0.07967548072338104,
-0.0031346629839390516,
-0.05916830524802208,
0.057357072830200195,
0.0103726452216506,
0.04311414062976837,
-0.07145826518535614,
0.10666227340698242,
-0.010109003633260727,
-0.008166045881807804,
0.008747423067688942,
0.0072872270829975605,
-0.008146804757416248,
0.08900287747383118,
0.05577829107642174,
0.0019853736739605665,
0.03320911526679993,
-0.004758068826049566,
0.037166450172662735,
-0.0015067288186401129,
-0.0261140875518322,
0.04105720296502113,
-0.021298620849847794,
0.020550336688756943,
-0.03816445544362068,
-0.0076929861679673195,
0.018191475421190262,
-0.022699661552906036,
-0.01177990436553955,
-0.016350669786334038,
0.008404581807553768,
0.022113202139735222,
0.061825696378946304,
-0.002827750751748681,
0.01713995449244976,
0.022636499255895615,
-0.04296647757291794,
-0.013766401447355747,
-0.015967343002557755,
-0.015689969062805176,
-0.0011664243647828698,
-0.025479063391685486,
-0.004659757483750582,
0.005041161552071571,
0.00545445317402482,
-0.006180180702358484,
-0.039358049631118774,
0.025650478899478912,
0.059367723762989044,
0.05822824686765671,
-0.0023726087529212236,
0.009363151155412197,
0.07464864104986191,
0.002875802805647254,
-0.023033861070871353,
-0.016985449939966202,
-0.047110456973314285,
-0.026161955669522285,
-0.0038124050479382277,
-0.012852157466113567,
0.022941390052437782,
0.03534473851323128,
0.006640374660491943,
-0.012944629415869713,
0.05957118794322014,
0.02911883406341076,
0.016479434445500374,
-0.0072651207447052,
0.06732169538736343,
0.005894411820918322,
0.015618979930877686,
0.022303834557533264,
0.0517117977142334,
0.018039213493466377,
-0.0026000686921179295,
-0.008832959458231926,
-0.006837279070168734,
-0.048279423266649246,
0.0034637339413166046,
0.04046878591179848,
-0.0031401587184518576,
-0.01617305725812912,
0.018499989062547684,
0.029264476150274277,
0.0432208850979805,
0.033346932381391525,
0.02925695665180683,
-0.01957818865776062,
-0.009239861741662025,
-0.033491961658000946,
-0.0023904498666524887,
-0.0022024575155228376,
0.03465420380234718,
0.027849700301885605,
-0.011347640305757523,
0.005347003694623709,
-0.004012503195554018,
-0.06089723855257034,
0.042098551988601685,
0.03930282220244408,
0.010946093127131462,
0.01906256377696991,
-0.01563211902976036,
0.05249357968568802,
-0.04830624535679817,
-0.026133686304092407,
0.013030001893639565,
-0.010647633112967014,
0.006460642907768488,
-0.032411713153123856,
0.0018882696749642491,
-0.014894521795213223,
0.02445991337299347,
-0.03219056874513626,
0.016878709197044373,
0.047038447111845016,
-0.031073778867721558,
0.0526525154709816,
-0.03559490665793419,
-0.03015914186835289,
0.023826749995350838,
-0.02612052485346794,
0.0034043355844914913,
0.002828327938914299,
-0.029943102970719337,
-0.004424128215759993,
-0.04776179790496826,
-0.027239922434091568,
-0.000965242856182158,
0.009493405930697918,
0.02446131221950054,
-0.038191962987184525,
-0.01762215979397297,
-0.014759729616343975,
-0.04227064549922943,
0.031053651124238968,
0.04454810544848442,
-0.002499936381354928,
0.006651510018855333,
0.026869414374232292,
-0.06244346871972084,
-0.014104180037975311,
-0.0014751505805179477,
0.02515469118952751,
-0.05752404034137726,
0.0020599227864295244,
0.024584420025348663,
0.008219882845878601,
-0.0054809278808534145,
0.029923198744654655,
-0.05190490931272507,
-0.04900820553302765,
-0.010699188336730003,
0.027261696755886078,
-0.01825949363410473,
-0.030361942946910858,
-0.04741035774350166,
0.01416977122426033,
0.007077953312546015,
-0.011079054325819016,
-0.05329809710383415,
-0.025207918137311935,
0.020364394411444664,
0.0031148730777204037,
0.032296035438776016,
-0.02892852947115898,
0.010278687812387943,
0.029422037303447723,
0.041287753731012344,
-0.006311905104666948,
-0.03791702911257744,
0.007974022068083286,
-0.04242907837033272,
-0.014509974047541618,
0.009633440524339676,
0.022251436486840248,
0.014536571688950062,
0.0291458610445261,
-0.003950065933167934,
0.00489793810993433,
0.03052758425474167,
0.04509873688220978,
-0.005837764125317335,
-0.008220245130360126,
-0.00923484843224287,
-0.010544904507696629,
0.03809433802962303,
0.03400971367955208,
-0.04750382527709007,
-0.0011614600662142038,
-0.04465436562895775,
0.011154674924910069,
0.03277173638343811,
-0.026443546637892723,
0.029802298173308372,
-0.04946368560194969,
0.0072569348849356174,
-0.0034957751631736755,
0.033118411898612976,
0.02534155175089836,
0.008549648337066174,
-0.006299697794020176,
-0.04522884264588356,
0.03873291611671448,
-0.00003739578096428886,
-0.026028066873550415,
0.00946267694234848,
-0.0004724268219433725,
-0.02238704450428486,
-0.02572701685130596,
-0.0038763724733144045,
0.004759729839861393,
0.0033507992047816515,
-0.044458866119384766,
0.013433177955448627,
0.0011393174063414335,
0.019466018304228783,
0.018167655915021896,
0.017210133373737335,
-0.06074119359254837,
0.0011055470677092671,
-0.06762880086898804,
-0.010527600534260273,
-0.011984690092504025,
0.008202832192182541,
0.018230149522423744,
0.01301049254834652,
-0.0006446152692660689,
0.016293838620185852,
-0.001676142797805369,
0.017739301547408104,
-0.07874893397092819,
0.02626781165599823,
0.005027760285884142,
0.0037860756274312735,
0.011633551679551601,
-0.0035928445868194103,
0.009432069957256317,
-0.021632879972457886,
-0.007805039640516043,
-0.022754520177841187,
0.008429340086877346,
0.019524099305272102,
-0.0022892525885254145,
-0.009103900752961636,
-0.06753870844841003,
-0.034918349236249924,
0.037124648690223694,
0.03796316310763359,
-0.013848349452018738,
0.028141826391220093,
0.030215466395020485,
0.005208766087889671,
-0.022381050512194633,
0.028047027066349983,
0.039171259850263596,
-0.023568173870444298,
0.02693329006433487,
-0.0043236869387328625,
-0.013180640526115894,
-0.022237112745642662,
-0.006612762343138456,
-0.018497852608561516,
-0.005842182319611311,
-0.017698992043733597,
-0.012093921191990376,
0.02864760160446167,
-0.04723057895898819,
-0.0019096601754426956,
0.0170515775680542,
-0.0019489526748657227,
-0.017022795975208282,
0.04268576577305794,
0.056886881589889526,
-0.016572214663028717,
-0.014578117989003658,
0.002225779229775071,
0.05313747748732567,
-0.037193600088357925,
0.017892373725771904,
-0.027562307193875313,
-0.051332924515008926,
-0.01558790635317564,
0.03600094094872475,
0.04550550505518913,
0.018085680902004242,
0.00019472638086881489,
-0.04170192778110504,
-0.0019354209071025252,
-0.01177254505455494,
-0.006561818532645702,
0.038871102035045624,
-0.013333464041352272,
0.055836357176303864,
-0.021299267187714577,
0.0175702515989542,
-0.0028790661599487066,
0.01442002970725298,
0.05819441378116608,
-0.01274836901575327,
-0.019031353294849396,
-0.03973077982664108,
-0.02362845651805401,
0.03661007061600685,
0.06651394814252853,
-0.01602085307240486,
0.001542494399473071,
-0.08569690585136414,
-0.005607308819890022,
0.017366737127304077,
-0.009676298126578331,
-0.010369617491960526,
-0.024963749572634697,
-0.021419277414679527,
-0.0017656147247180343,
-0.02241670899093151,
-0.0206623412668705,
-0.008538370952010155,
0.010271089151501656,
0.02640298567712307,
-0.005103175062686205,
0.005464363377541304,
-0.01574094220995903,
0.01811976544559002,
0.052549321204423904,
0.019391804933547974,
0.05439969152212143,
-0.028893347829580307,
-0.015192223712801933,
0.008527198806405067,
-0.01642567478120327,
-0.05851167440414429,
-0.027426835149526596,
0.011263902299106121,
-0.03121519647538662,
0.03779607266187668,
0.000493579194881022,
-0.021384170278906822,
0.03441135957837105,
-0.007367783226072788,
-0.008201836608350277,
0.03819001093506813,
-0.0016956162871792912,
0.0026982538402080536,
0.0037868309300392866,
0.029637884348630905,
0.05889444053173065,
0.051189716905355453,
-0.028762254863977432,
-0.0021912120282649994,
0.00031891799881123006,
0.00364144379273057,
-0.022869151085615158,
-0.03667459264397621,
0.01697710156440735,
-0.04004201292991638,
-0.03218769654631615,
0.005309415515512228,
-0.028858311474323273,
0.008661475032567978,
-0.01982337236404419,
-0.014731242321431637,
-0.02732209675014019,
0.010026509873569012,
0.028775498270988464,
0.016346296295523643,
0.016884474083781242,
0.0180125180631876,
0.005032028537243605,
-0.015108030289411545,
0.012403229251503944,
-0.0016231968766078353,
0.015703393146395683,
0.04087967425584793,
-0.017212513834238052,
0.005526624619960785,
-0.02815662883222103,
-0.00748209934681654,
-0.003954371903091669,
-0.018664216622710228,
0.05953040346503258,
0.00985550694167614,
0.0031894829589873552,
0.04502963274717331,
-0.06835641711950302,
-0.0046450248919427395,
0.005089803598821163,
-0.028125204145908356,
0.023676447570323944,
-0.025370603427290916,
0.008230532519519329,
-0.012589739635586739,
0.03716960921883583,
-0.06531113386154175,
0.0016550166765227914,
0.02376539073884487,
-0.0027864559087902308,
-0.042779140174388885,
0.009080600924789906,
0.024623744189739227,
-0.050848398357629776,
-0.020093856379389763,
-0.019261807203292847,
0.07378403097391129,
-0.0006209289422258735,
-0.024931980296969414,
-0.03183092549443245,
0.04332846403121948,
0.07831348478794098,
-0.0012266143457964063,
-0.002532388549298048,
0.022752009332180023,
-0.007000076584517956,
0.0031970064155757427,
-0.007166474126279354,
0.02728940360248089,
-0.013904823921620846,
-0.03224572911858559,
-0.019338984042406082,
-0.005668823607265949,
0.012525469996035099,
-0.0034197536297142506,
0.009702491573989391,
0.0995897650718689,
0.0013330872170627117,
-0.03214998543262482,
-0.03465248644351959,
0.023136651143431664,
-0.03744657710194588,
-0.007064340636134148,
-0.050865523517131805,
0.012684236280620098,
0.02463546209037304,
-0.05030914768576622,
0.014685728587210178,
-0.01228770986199379,
0.04295770823955536,
0.0016153523465618491,
0.08678749948740005,
0.0035962669644504786,
-0.008110261522233486,
0.029964949935674667,
0.014269871637225151,
0.0130419647321105,
-0.00017675112758297473,
0.03068486973643303,
0.020634440705180168,
-0.0051757716573774815,
-0.033987294882535934,
-0.00834631733596325,
-0.013520674780011177,
0.01603507250547409,
0.058302026242017746,
-0.0026077181100845337,
0.0480554923415184,
-0.008738095872104168,
0.006648464128375053,
0.006338194012641907,
-0.07275588810443878,
-0.013802748173475266,
-0.039869535714387894,
-0.0020204365719109774,
0.029058435931801796,
-0.01605156995356083,
0.001457072445191443,
0.04004910960793495,
0.038310807198286057,
-0.009959076531231403,
0.06632471084594727,
0.03973066434264183,
-0.01465856097638607,
0.06170506402850151,
-0.04663242772221565,
-0.035625167191028595,
0.01631401665508747,
-0.05564824864268303,
0.051509495824575424,
0.0029603922739624977,
-0.03446551412343979,
0.027933040633797646,
-0.02356882579624653,
0.021259836852550507,
-0.055911291390657425,
-0.011409075930714607,
-0.06674908101558685,
-0.015686428174376488,
0.014854004606604576,
-0.02114095538854599,
-0.0507185123860836,
0.024997040629386902,
0.017863715067505836,
-0.01657775603234768,
-0.000030131164749036543,
-0.00008333771984325722,
-0.0714646577835083,
-0.03835870698094368,
0.007299702614545822,
-0.042792655527591705,
0.05231358855962753,
0.02879459597170353,
-0.02346087247133255,
-0.02125776931643486,
-0.005425004754215479,
-0.03821193426847458,
0.05088578537106514,
0.04140652343630791,
0.023198314011096954,
0.0653868243098259,
-0.021996911615133286,
-0.03210633620619774,
-0.007400656118988991,
0.015993235632777214,
0.13254937529563904,
0.06160515546798706,
0.011427121236920357,
-0.04826802387833595,
0.03519162908196449,
-0.01660018227994442,
0.0022920018527656794,
-0.0042955949902534485,
-0.03623006492853165,
-0.028307169675827026,
0.013303066603839397,
0.06412373483181,
0.047865912318229675,
0.020678656175732613,
0.005067524034529924,
0.012697120197117329,
-0.04055783897638321,
-0.0070833018980920315,
0.037227947264909744,
0.030075741931796074,
0.002334779826924205,
0.034328389912843704,
-0.029494144022464752,
0.02020607329905033,
-0.0392075851559639,
-0.0016364192124456167,
-0.0027484362944960594,
-0.0650346651673317,
0.0193027313798666,
-0.0012314103078097105,
-0.02831410989165306,
-0.006464267615228891,
-0.005112676415592432,
-0.010912406258285046,
-0.037547800689935684,
0.016026686877012253,
0.010983464308083057,
-0.050425734370946884,
0.04366912320256233,
0.011235358193516731,
-0.0019813249818980694,
0.016922898590564728,
0.009460697881877422,
0.016562923789024353,
-0.02240724116563797,
-0.0049862489104270935,
-0.009898032061755657,
0.029551716521382332,
-0.006968819070607424,
-0.03273574262857437,
-0.03316009044647217,
0.017130456864833832,
0.027845511212944984,
-0.012084472924470901,
0.017642637714743614,
0.005009994842112064,
0.06321261078119278,
-0.03251848369836807,
-0.04493321105837822,
-0.0076387980952858925,
-0.009250268340110779,
0.000026615884053171612,
0.005064090713858604,
0.024342618882656097,
0.0325147807598114,
-0.018547479063272476,
-0.014035011641681194,
0.05776294693350792,
0.0004885052912868559,
0.0024072553496807814,
-0.006980206351727247,
0.000620031263679266,
-0.028586141765117645,
-0.01360868476331234,
0.015006551519036293,
-0.007822762243449688,
-0.011268382892012596,
0.00261330627836287,
-0.02601633593440056,
-0.019911717623472214,
-0.02768843248486519,
-0.00816772598773241,
-0.024335430935025215,
-0.03904808312654495,
0.009486374445259571,
0.06943883001804352,
0.029827585443854332,
0.010235583409667015,
-0.02603389136493206,
0.010801517404615879,
0.014206485822796822,
0.06249701976776123,
0.039725471287965775,
-0.01788770593702793,
-0.009615857154130936,
0.007338649593293667,
-0.04105710983276367,
-0.015464279800653458,
-0.019224297255277634,
0.03426562622189522,
-0.006666937377303839,
0.010986996814608574,
0.015497084707021713,
-0.015415088273584843,
-0.0254631657153368,
-0.005793657619506121,
-0.004358166363090277,
-0.050372954457998276,
-0.022241491824388504,
-0.020461220294237137,
-0.013957610353827477,
-0.04071516916155815,
0.005030769854784012,
-0.0017953453352674842,
0.025127718225121498,
-0.019475847482681274,
0.0006448793574236333,
-0.014863099902868271,
0.08015017956495285,
-0.011307929642498493,
0.028488434851169586,
-0.03260647878050804,
0.010235399939119816,
-0.032544251531362534,
0.04182959347963333,
-0.03175867348909378,
0.006616673432290554,
-0.01851961761713028,
0.012934194877743721,
-0.0027781743556261063,
-0.06078674644231796,
0.012960524298250675,
-0.03636590391397476,
-0.0037993164733052254,
0.01884765364229679,
0.01104812603443861,
-0.021546242758631706,
0.029725557193160057,
-0.024220434948801994,
-0.048974860459566116,
-0.002158673945814371,
-0.04788029566407204,
-0.07171549648046494,
0.01527069229632616,
-0.02174217440187931,
0.03340999409556389,
0.0010372314136475325,
0.011428865604102612,
0.00665388535708189,
0.047995034605264664,
0.0014099229592829943,
-0.05857568606734276,
0.0033064603339880705,
0.031002655625343323,
0.07451474666595459,
0.01849307306110859,
-0.01703220047056675,
-0.033493004739284515,
-0.021094640716910362,
0.053054627031087875,
-0.0072793313302099705,
-0.05631675571203232,
0.02055705338716507,
-0.017497535794973373,
-0.031053908169269562,
0.0025078419130295515,
-0.012983936816453934,
-0.01491676364094019,
0.016091084107756615,
0.039790090173482895,
-0.0636044591665268,
0.07578200846910477,
0.03392146900296211,
-0.024017371237277985,
-0.043817825615406036,
-0.00900648720562458,
0.00490113440901041,
-0.01952708140015602,
0.03317813575267792,
-0.0439133420586586,
0.04308895394206047,
0.0682908222079277,
-0.03719707578420639,
0.03889450430870056,
0.029266614466905594,
-0.027815470471978188,
-0.020967913791537285,
-0.012048509903252125,
0.016534818336367607,
0.008652642369270325,
0.006934305652976036,
0.00962181854993105,
0.006480781827121973,
0.01708393543958664,
-0.01578214392066002,
-0.054781798273324966,
0.050324730575084686,
0.05028282850980759,
0.018874717876315117,
-0.012760616838932037,
0.0696813315153122,
-0.014456960372626781,
-0.03095315769314766,
0.0485277958214283,
0.0012089913943782449,
0.0355122946202755,
0.0003921130846720189,
-0.05107911676168442,
-0.053037360310554504,
-0.0028737615793943405,
0.013829684816300869,
0.010084649547934532,
-0.03416980803012848,
0.004000786226242781,
0.04941686987876892,
0.047238435596227646,
0.035985928028821945,
0.017463939264416695,
-0.04051567614078522,
-0.04075207561254501,
-0.026995917782187462,
0.00025637823273427784,
0.022521506994962692,
0.005158879328519106,
0.005500683560967445,
0.005440248642116785,
0.0077902283519506454,
-0.013830875977873802,
0.007067779079079628,
-0.03698829561471939,
-0.006775449030101299,
0.009423299692571163,
-0.025349946692585945,
0.04340533912181854,
-0.0075708189979195595,
0.0022526353131979704,
-0.0048864358104765415,
0.008936149999499321,
-0.013527058064937592,
-0.005733393598347902,
-0.016258856281638145,
-0.001981452340260148,
0.001180146005935967,
0.003998910076916218,
-0.004075364209711552,
-0.033646512776613235,
-0.04030562564730644,
0.06107250228524208,
0.0038423328660428524,
0.014835392124950886,
-0.01574690453708172,
-0.020944612100720406,
-0.017338568344712257,
-0.05363141745328903,
0.0423746295273304,
0.002551748650148511,
0.02580210007727146,
-0.038387589156627655,
-0.07145683467388153,
-0.02096923440694809,
-0.027614565566182137,
0.04915377497673035,
0.029324684292078018,
0.023772627115249634,
0.003357551759108901,
-0.016214502975344658,
0.017748354002833366,
-0.04835019260644913,
0.030890127643942833,
-0.02857140824198723,
-0.05552056431770325,
-0.019501104950904846,
-0.015676263719797134,
-0.03430958464741707,
-0.007511894218623638,
0.0008704346837475896,
-0.0009076637215912342,
0.0991063043475151,
0.01864193193614483,
0.043082572519779205,
0.04356355220079422,
0.027648495510220528,
-0.014809707179665565,
0.01963008940219879,
0.022644922137260437,
-0.028941430151462555,
0.03434799984097481,
0.012895177118480206,
-0.055221255868673325,
-0.00462512718513608,
-0.04306071624159813,
-0.06255818903446198,
-0.0015750278253108263,
0.015885386615991592,
0.0038076997734606266,
-0.07436297088861465,
0.03216388449072838,
0.04798126593232155,
-0.019482458010315895,
0.0018930239602923393,
0.005776910111308098,
-0.004770472180098295,
0.02904510870575905,
-0.006720938719809055,
0.00884633045643568,
-0.02309662476181984,
-0.014066088013350964,
0.005281813908368349,
0.02210191823542118,
0.007052164990454912,
0.003030977677553892,
0.04049929976463318,
0.010960501618683338,
0.06429244577884674,
0.08891678601503372,
-0.04547319933772087,
0.05145588144659996,
-0.02902371436357498,
-0.0036416961811482906,
0.030429711565375328,
0.00036152711254544556,
-0.00915058609098196,
0.021148601546883583,
-0.012807152234017849,
0.057677239179611206,
-0.03032006323337555,
-0.0031675896607339382,
-0.015699025243520737,
-0.021497344598174095,
-0.05029096081852913,
0.026129089295864105,
0.019795509055256844,
0.020213227719068527,
-0.030165590345859528,
-0.019505230709910393,
0.0024400511756539345,
0.008024049922823906,
0.03429216518998146,
-0.0389835387468338,
0.020084358751773834,
-0.009753537364304066,
0.005395388696342707,
-0.0177893228828907,
0.00002296293132530991,
-0.0241058561950922,
-0.024377623572945595,
0.017648056149482727,
0.045042239129543304,
0.02063744142651558,
0.013436487875878811,
-0.019296124577522278,
-0.012131994590163231,
0.029595395550131798,
-0.09035302698612213,
-0.004009434022009373,
-0.004429750144481659,
-0.005159913562238216,
-0.04220665618777275,
0.012351568788290024
] |
<p>let be the 2-loop integral...</p>
<p>$$ \int d^{d}l\int d^{d}k \frac{1}{k^{4}(k+p)^{2}(k+l)^{2}}=I(p)$$</p>
<p>dimensional regularization over the variable 'l0 to evaluate</p>
<p>$$ \int d^{d}l\frac{1}{(k+l)^{2}}=G(k,d)$$</p>
<p>this is the regularizñation of the subdivergence assumed to exist by dimensional rgularizaton</p>
<p>then the final step would be </p>
<p>$$ \int d^{d}k \frac{G(k,d)}{k^{4}(k+p)^{2}}$$</p>
<p>where $ G(k,d) $ must be taken in finte part to eliminate the pole when $ d=4-\epsilon $</p>
| 9,366 |
[
-0.015716133639216423,
0.025654977187514305,
0.029687317088246346,
0.0001925437245517969,
0.0333327017724514,
0.012483383528888226,
-0.021195773035287857,
-0.05249696597456932,
0.04051773622632027,
-0.05865447595715523,
0.0430288165807724,
-0.03404952213168144,
0.07464644312858582,
0.03144339099526405,
-0.007826653309166431,
-0.02409476600587368,
-0.009898907504975796,
-0.018536632880568504,
0.04490204527974129,
-0.022360317409038544,
-0.024576060473918915,
0.049994371831417084,
-0.02011112868785858,
-0.008951653726398945,
-0.04175494611263275,
0.009679107926785946,
0.019301638007164,
0.015576718375086784,
-0.012498125433921814,
0.07526557147502899,
-0.02519315294921398,
0.013652387075126171,
0.007989947684109211,
0.03325634077191353,
-0.0011057279771193862,
0.029841648414731026,
-0.047674331814050674,
-0.019712483510375023,
-0.028216946870088577,
0.04146623983979225,
0.006571429315954447,
-0.002296579536050558,
0.009283434599637985,
0.03861725330352783,
0.009320133365690708,
0.017320316284894943,
0.002681458368897438,
-0.00539800338447094,
0.06508263945579529,
-0.0636170357465744,
0.042210064828395844,
0.0034823203459382057,
0.027013536542654037,
-0.0323479063808918,
-0.03419548645615578,
-0.02026781626045704,
0.010548463091254234,
0.07170533388853073,
0.01315097976475954,
-0.062456164509058,
-0.0759207233786583,
0.010778599418699741,
0.007508742623031139,
-0.005163339897990227,
-0.012029850855469704,
0.009983956813812256,
0.007357684895396233,
0.002389631001278758,
0.00003392775761312805,
-0.013650044798851013,
-0.01064211968332529,
0.0027667360845953226,
0.046524904668331146,
-0.0039230273105204105,
0.04262103512883186,
0.023981278762221336,
-0.01908743940293789,
0.018290407955646515,
0.0236124899238348,
0.010968382470309734,
0.004364363849163055,
-0.001161673804745078,
-0.004730747547000647,
-0.014209987595677376,
0.01675875298678875,
0.02097415179014206,
0.05941419675946236,
0.006912545301020145,
-0.025054896250367165,
0.036148566752672195,
0.020938115194439888,
0.019437476992607117,
0.02315473183989525,
0.01603139005601406,
0.006927864626049995,
0.03424647077918053,
0.028836898505687714,
0.05445229262113571,
-0.022556891664862633,
-0.008861582726240158,
-0.03000301495194435,
-0.03329700604081154,
-0.04101972654461861,
0.0704263374209404,
0.004619342274963856,
0.03295431286096573,
0.012202906422317028,
-0.007668094243854284,
-0.03487078845500946,
-0.009798424318432808,
-0.04961027204990387,
0.02105303481221199,
-0.013241571374237537,
-0.038436032831668854,
-0.011800859123468399,
-0.040573351085186005,
-0.018698424100875854,
0.008836310356855392,
0.04450982064008713,
0.061612553894519806,
0.03391745314002037,
-0.013531280681490898,
-0.007669288665056229,
-0.013351064175367355,
-0.028677303344011307,
0.042678046971559525,
0.06403137743473053,
0.0006980536272749305,
-0.024807509034872055,
0.03714847192168236,
0.0278279148042202,
0.009276612661778927,
-0.001748686539940536,
0.015948576852679253,
0.026610350236296654,
-0.018760094419121742,
-0.07682593166828156,
-0.04582604393362999,
0.04397227242588997,
-0.0385277085006237,
0.04827335476875305,
-0.0888044461607933,
-0.04127174988389015,
0.02303954027593136,
0.1117660403251648,
-0.0019363000756129622,
0.02828061766922474,
0.03987521678209305,
-0.024220526218414307,
0.009421069175004959,
0.0012661815853789449,
-0.05138729512691498,
-0.012529983185231686,
-0.018946396186947823,
-0.02630305476486683,
-0.04028341919183731,
0.0085227582603693,
0.03556618094444275,
-0.04487128183245659,
0.03789692372083664,
0.03668602928519249,
0.00875765923410654,
0.011959834024310112,
0.038683779537677765,
-0.0017256042920053005,
0.0064398800022900105,
0.0531199648976326,
0.03969516605138779,
0.011220171116292477,
0.04336633160710335,
0.020330192521214485,
0.009167585521936417,
-0.01916365884244442,
0.025502290576696396,
0.0416349433362484,
-0.005174887366592884,
-0.025743970647454262,
0.0038263164460659027,
0.02754947915673256,
0.004568462260067463,
-0.03644314780831337,
-0.02972918376326561,
-0.02002650499343872,
0.011294957250356674,
0.013298865407705307,
0.032073624432086945,
0.03773437440395355,
0.010322886519134045,
0.017192166298627853,
-0.02847798727452755,
-0.03494170680642128,
-0.00572042353451252,
0.04139230400323868,
0.02299075573682785,
-0.03798086196184158,
0.03743286058306694,
-0.020511696115136147,
0.017785439267754555,
-0.00025904239737428725,
-0.05100012570619583,
-0.03428707644343376,
0.04072079434990883,
0.01794513128697872,
0.00014793674927204847,
-0.0070258984342217445,
0.02023741416633129,
0.055246490985155106,
0.0016650987090542912,
0.07598896324634552,
-0.005056706722825766,
-0.020654363557696342,
-0.010677278973162174,
0.00003171943535562605,
0.0035100376699119806,
-0.0060196490958333015,
-0.0351523756980896,
0.00855519250035286,
-0.006349606905132532,
0.0064483205787837505,
0.0017980592092499137,
-0.06213926523923874,
0.046667035669088364,
0.06917222589254379,
0.0361909382045269,
0.026098167523741722,
0.01513298787176609,
-0.028426874428987503,
0.056126922369003296,
-0.011688548140227795,
-0.06031143292784691,
-0.032549045979976654,
-0.03188923001289368,
0.03724277764558792,
0.06185581162571907,
-0.02659955993294716,
-0.0003026951744686812,
0.04455253854393959,
0.03293074294924736,
0.0034810130018740892,
-0.0007771022501401603,
0.001881927135400474,
-0.030923446640372276,
0.02945244312286377,
0.009494854137301445,
-0.03538668900728226,
-0.011797808110713959,
0.017471343278884888,
-0.026008108630776405,
0.013241984881460667,
-0.026459265500307083,
-0.03661594167351723,
0.02049371972680092,
-0.04743187874555588,
0.026123253628611565,
0.005939829628914595,
-0.03364158794283867,
0.06046949699521065,
0.017086412757635117,
0.047268837690353394,
0.02369799092411995,
-0.012002653442323208,
0.02711542323231697,
-0.001467009074985981,
-0.023044072091579437,
0.04261326044797897,
0.008624691516160965,
-0.025292150676250458,
-0.039173778146505356,
0.02584213763475418,
-0.010091103613376617,
-0.020326653495430946,
-0.0429023876786232,
-0.023064127191901207,
-0.06451355665922165,
0.027191493660211563,
0.04966460168361664,
0.008857094682753086,
0.02398565411567688,
0.0007616679067723453,
-0.005467717070132494,
0.022905463352799416,
0.0008372144657187164,
0.03140999749302864,
0.010900044813752174,
-0.0044694081880152225,
0.008579742163419724,
-0.04391837120056152,
0.03164239600300789,
0.02832026034593582,
0.02294876053929329,
0.027140678837895393,
0.004334551282227039,
0.0062148189172148705,
-0.029408102855086327,
-0.014216159470379353,
-0.02052241563796997,
0.08776400238275528,
-0.03400450199842453,
-0.019735179841518402,
0.03147220239043236,
0.01520135160535574,
-0.03018537349998951,
0.024372819811105728,
-0.01783124729990959,
-0.016189713031053543,
0.00010714854579418898,
-0.013139442540705204,
0.011767403222620487,
-0.011297518387436867,
0.040175631642341614,
-0.011587073095142841,
-0.038326118141412735,
-0.0061520361341536045,
-0.0711209774017334,
-0.058917462825775146,
0.022904440760612488,
0.0037492727860808372,
0.018347829580307007,
-0.038904570043087006,
-0.061894334852695465,
0.07157884538173676,
0.045501839369535446,
-0.029987070709466934,
0.004557180684059858,
0.00708756921812892,
-0.041529953479766846,
-0.011378227733075619,
0.007243900094181299,
-0.020250199362635612,
0.0007190287578850985,
0.03952167183160782,
0.018639883026480675,
0.07022751122713089,
0.0349850170314312,
0.000015075601368153002,
-0.045292675495147705,
0.03455556556582451,
0.028273848816752434,
0.003940344788134098,
0.03842766210436821,
-0.005459874868392944,
-0.010683128610253334,
-0.014761381782591343,
-0.007763016037642956,
-0.023983508348464966,
0.03644585236907005,
-0.0380854606628418,
0.032212622463703156,
-0.02210088260471821,
0.023118387907743454,
-0.020686252042651176,
0.03764330968260765,
0.01952996477484703,
-0.071928970515728,
-0.036398276686668396,
0.02301786281168461,
0.05643608793616295,
-0.002011452568694949,
-0.0034333027433604,
0.02253924310207367,
0.020315462723374367,
-0.01690228097140789,
-0.004516181070357561,
-0.025958126410841942,
-0.005316764581948519,
0.017400948330760002,
-0.041693899780511856,
-0.021282650530338287,
0.0032185036689043045,
0.0487990528345108,
-0.0051073189824819565,
-0.0072545395232737064,
-0.040707655251026154,
0.023262279108166695,
-0.10323451459407806,
-0.010571991093456745,
-0.03398080915212631,
0.07751107960939407,
0.018932612612843513,
0.0020866217091679573,
0.020091785117983818,
0.0009647028637118638,
0.025274837389588356,
0.019782718271017075,
-0.10889419168233871,
0.02437829226255417,
-0.02099413052201271,
0.016443608328700066,
0.014164332300424576,
-0.010777940973639488,
0.02692427672445774,
-0.013247774913907051,
0.0017919538076967,
0.004603410139679909,
-0.018700482323765755,
-0.021253524348139763,
0.015590834431350231,
0.004538008011877537,
-0.025905782356858253,
-0.022040164098143578,
0.013285825029015541,
0.05936889350414276,
-0.03088821843266487,
0.04194407910108566,
0.05334940180182457,
0.002984223421663046,
-0.007515849079936743,
-0.04782271757721901,
0.007218105252832174,
-0.00004131216701352969,
0.017545262351632118,
0.009162729606032372,
0.01347499992698431,
-0.02940697968006134,
-0.020480887964367867,
0.022739995270967484,
0.05722292140126228,
-0.015672199428081512,
0.04141346365213394,
-0.008489110507071018,
-0.06722763925790787,
0.004367478657513857,
-0.006982305087149143,
0.06985831260681152,
0.01626419648528099,
-0.0005293450667522848,
0.002518555847927928,
0.005964877083897591,
-0.025325600057840347,
0.034666143357753754,
0.050672806799411774,
-0.02091297134757042,
-0.03065800666809082,
-0.03777652606368065,
0.01218455284833908,
0.013951814733445644,
-0.026855506002902985,
0.01844305545091629,
-0.03720252215862274,
-0.030390137806534767,
-0.012701798230409622,
0.049521658569574356,
0.010299301706254482,
0.0030739433132112026,
0.01799912564456463,
0.023896344006061554,
0.01747136004269123,
-0.03128579631447792,
-0.009944812394678593,
0.02102396823465824,
0.020060628652572632,
0.06103005260229111,
0.020984698086977005,
-0.0363725870847702,
-0.06173954904079437,
-0.02393907494843006,
0.02667069621384144,
0.07691571861505508,
-0.011683259159326553,
-0.007344926707446575,
-0.04368821904063225,
-0.016191519796848297,
0.051253996789455414,
-0.01305355317890644,
0.02001110650599003,
-0.008191300556063652,
0.0026368165854364634,
-0.005645494442433119,
-0.03738091140985489,
-0.020349156111478806,
0.03290972858667374,
0.009782331064343452,
-0.021314725279808044,
-0.03806133195757866,
-0.012952971272170544,
-0.027554605156183243,
0.029594168066978455,
0.015554863959550858,
0.045496851205825806,
0.03523705527186394,
-0.020820507779717445,
-0.025481930002570152,
0.027996690943837166,
-0.05355871468782425,
-0.047802962362766266,
0.012497481890022755,
0.013617726974189281,
-0.0346677228808403,
0.03130393847823143,
-0.003056734334677458,
-0.06910206377506256,
0.012397976592183113,
0.04593526944518089,
0.01959318295121193,
-0.0037399972788989544,
-0.03720652684569359,
0.03401021659374237,
0.07306071370840073,
-0.010504468344151974,
0.06904596835374832,
0.03354031965136528,
-0.007444847375154495,
-0.024328449741005898,
-0.0016649020835757256,
0.025853678584098816,
0.005796568468213081,
0.010828979313373566,
-0.023731324821710587,
0.0169574823230505,
-0.017809053882956505,
0.03981562331318855,
-0.03722681105136871,
0.015695052221417427,
-0.0370325967669487,
-0.005328926723450422,
-0.025122107937932014,
0.028047364205121994,
0.023459067568182945,
-0.03907741978764534,
0.02926810458302498,
0.020517967641353607,
0.029494425281882286,
0.010143492370843887,
0.012120429426431656,
-0.01271872315555811,
0.011968401260674,
0.030022351071238518,
0.0027514982502907515,
0.010111178271472454,
-0.005691543687134981,
-0.02646498940885067,
0.006632607895880938,
-0.041984837502241135,
0.004012670833617449,
-0.0064816647209227085,
-0.012415685690939426,
-0.02204533852636814,
-0.028942760080099106,
-0.003968765493482351,
-0.029200943186879158,
-0.026040522381663322,
0.040732674300670624,
-0.06560210138559341,
0.020145608112215996,
0.025803519412875175,
0.014846766367554665,
-0.07784661650657654,
-0.012662596069276333,
0.03551652282476425,
-0.02413114719092846,
-0.0038784686475992203,
-0.03838955983519554,
-0.03310335427522659,
-0.027597978711128235,
-0.06702445447444916,
-0.024486104026436806,
0.05234876647591591,
-0.05125102400779724,
-0.021314824000000954,
-0.000636451703030616,
0.05831044167280197,
0.05454360693693161,
0.007366780657321215,
0.007890620268881321,
-0.005888550076633692,
-0.030299898236989975,
-0.010980752296745777,
-0.026967497542500496,
0.01669803261756897,
-0.024965927004814148,
-0.014361570589244366,
-0.03123410791158676,
0.019831130281090736,
0.02370089665055275,
-0.023700140416622162,
-0.032636914402246475,
0.010364160872995853,
0.01888309046626091,
0.015052512288093567,
-0.056603044271469116,
-0.04050280898809433,
-0.005142245441675186,
0.027324656024575233,
0.006515445187687874,
0.0013857620069757104,
-0.02249668724834919,
-0.00790212769061327,
0.016572754830121994,
-0.02629520185291767,
0.004861749242991209,
-0.05431671813130379,
0.06365480273962021,
-0.023602737113833427,
-0.01715058833360672,
0.005847159773111343,
-0.017180804163217545,
0.03529708832502365,
-0.04751855134963989,
0.0033526115585118532,
0.01924789696931839,
0.050729528069496155,
-0.051610998809337616,
-0.0019203260308131576,
-0.024093329906463623,
0.015830814838409424,
0.05864722654223442,
-0.03663081303238869,
0.0649198666214943,
0.0303213931620121,
-0.010011770762503147,
0.014935201965272427,
-0.021452689543366432,
-0.029386159032583237,
0.02070828154683113,
0.03688354045152664,
0.05395200103521347,
-0.020530249923467636,
-0.026884205639362335,
0.018256785348057747,
0.024285506457090378,
-0.05059696361422539,
-0.0037376137915998697,
-0.011462952010333538,
0.01429072581231594,
-0.01720164716243744,
-0.029942966997623444,
-0.03974124789237976,
0.042242757976055145,
-0.012226857244968414,
0.01777925342321396,
-0.014251009561121464,
-0.03041829913854599,
0.04535107687115669,
-0.007925882004201412,
0.007985031232237816,
0.00916773546487093,
-0.0052293455228209496,
-0.0026362219359725714,
0.010092041455209255,
0.010038771666586399,
0.005840070080012083,
0.0014987658942118287,
-0.012468901462852955,
0.0024877614341676235,
0.0130962785333395,
0.020440157502889633,
-0.01735541969537735,
-0.05861766263842583,
-0.04059496149420738,
-0.004944148939102888,
-0.03553231060504913,
0.06718745827674866,
0.015914730727672577,
-0.00916123017668724,
0.017856523394584656,
-0.013351780362427235,
0.01934150978922844,
0.03616530820727348,
0.007686789147555828,
-0.0035425431560724974,
0.02712658978998661,
0.014729226939380169,
0.0007054290035739541,
-0.01865299604833126,
0.010719065554440022,
0.11728519201278687,
0.07905242592096329,
-0.0006672773160971701,
-0.06969713419675827,
0.012120380066335201,
-0.016632484272122383,
0.008065082132816315,
-0.055186156183481216,
0.020780161023139954,
-0.0518399216234684,
-0.03268343210220337,
0.01613345928490162,
0.02944834530353546,
-0.030066654086112976,
0.009081769734621048,
0.027696125209331512,
-0.010176723822951317,
-0.02608208917081356,
0.004056249279528856,
0.001809626934118569,
-0.04970528930425644,
0.015320765785872936,
-0.040428489446640015,
0.02712525799870491,
0.006258387118577957,
0.027005650103092194,
-0.0628698319196701,
-0.010146033018827438,
0.013714918866753578,
-0.025150593370199203,
-0.061734795570373535,
-0.008604662492871284,
0.003849741769954562,
0.013438593596220016,
-0.001950827776454389,
0.019887609407305717,
-0.0010957155609503388,
-0.024869929999113083,
0.029887057840824127,
0.04507739469408989,
-0.018945561721920967,
-0.03191610053181648,
0.03890020772814751,
0.027166247367858887,
-0.024724146351218224,
-0.03921795263886452,
-0.024621712043881416,
0.040213629603385925,
-0.008631574921309948,
-0.015407796949148178,
0.012503367848694324,
-0.004157781135290861,
0.00809329841285944,
-0.040252335369586945,
-0.002295069396495819,
0.015924012288451195,
0.04753639176487923,
-0.02925139293074608,
0.0038565134163945913,
0.02427133545279503,
0.03265172243118286,
0.015803314745426178,
-0.002981268335133791,
-0.030951635912060738,
-0.03396255895495415,
-0.01621858961880207,
0.01882564090192318,
0.06447096914052963,
0.007589065469801426,
0.020568450912833214,
-0.02520047314465046,
0.013380174525082111,
0.010883758775889874,
0.014920549467206001,
0.012642597779631615,
0.02550378441810608,
0.04850983992218971,
0.0008587630582042038,
-0.052430931478738785,
-0.03706943243741989,
-0.042153436690568924,
0.00944837648421526,
0.0006339678657241166,
0.012148058041930199,
-0.021114304661750793,
0.004042831715196371,
0.012288641184568405,
0.03657810762524605,
0.01277802512049675,
0.00446696812286973,
-0.0008717684540897608,
0.056893445551395416,
0.0030466271564364433,
-0.042842186987400055,
-0.04050326719880104,
-0.0329119935631752,
0.0010938267223536968,
0.0019939453341066837,
-0.010133485309779644,
-0.0031123871449381113,
0.0030572533141821623,
-0.00575428269803524,
-0.018943065777420998,
0.0635683536529541,
-0.0371847078204155,
0.009957745671272278,
0.011646213941276073,
-0.021545294672250748,
0.0008082457934506238,
-0.027870332822203636,
-0.000945184612646699,
-0.05546196177601814,
0.005565207917243242,
-0.004597220569849014,
0.02146046794950962,
0.026833143085241318,
-0.0017897316720336676,
-0.04353959858417511,
-0.004068833310157061,
-0.028584424406290054,
0.007421878166496754,
-0.01837882772088051,
-0.0044854008592665195,
-0.01208391785621643,
0.024366725236177444,
-0.019895678386092186,
-0.011444619856774807,
-0.008059628307819366,
0.0007392573170363903,
-0.012084009125828743,
-0.02564067393541336,
0.011464608833193779,
0.03053506650030613,
-0.019655819982290268,
-0.0025885740760713816,
-0.017731696367263794,
0.004513218067586422,
0.01968153566122055,
0.001764149870723486,
-0.022305479273200035,
0.02178550884127617,
-0.07024239748716354,
-0.04308812692761421,
0.01683795638382435,
-3.7349349213400274e-7,
0.04237300902605057,
0.019725991412997246,
0.03171481564640999,
-0.051522452384233475,
0.01282413862645626,
0.012510295957326889,
-0.027795398607850075,
0.01604401133954525,
-0.018287163227796555,
0.012887712568044662,
-0.031012536957859993,
0.0007783047039993107,
0.023450622335076332,
-0.0012325238203629851,
-0.022989053279161453,
0.013912437483668327,
-0.02105098031461239,
-0.007348865270614624,
0.036484312266111374,
-0.024680472910404205,
0.019837232306599617,
-0.012123692780733109,
0.009124260395765305,
0.026703938841819763,
0.040776632726192474,
-0.0065701799467206,
-0.016894668340682983,
-0.03791888430714607,
-0.042661964893341064,
-0.10017219185829163,
-0.029488418251276016,
0.013689333572983742,
0.040846291929483414,
0.014087140560150146,
-0.06473369151353836,
0.03015763871371746,
0.015869298949837685,
-0.058585941791534424,
0.03083875961601734,
-0.02951778843998909,
0.012960631400346756,
-0.03091096319258213,
-0.023089149966835976,
-0.04518058896064758,
0.06697195768356323,
0.05474183335900307,
0.047259263694286346,
-0.002490247832611203,
-0.022018292918801308,
0.01703440397977829,
0.0011355458991602063,
-0.008779189549386501,
0.006289656274020672,
-0.008426043204963207,
-0.04801506549119949,
0.0711841955780983,
-0.026106297969818115,
-0.017206234857439995,
0.029779234901070595,
-0.012315821833908558,
0.015652814880013466,
-0.0365741066634655,
0.01090598851442337,
0.008942819200456142,
0.04099137336015701,
-0.0030525876209139824,
0.00837741605937481,
0.011067581363022327,
-0.0009014538954943419,
0.0031326725147664547,
0.022095253691077232,
-0.034019652754068375,
0.027958612889051437,
0.041210372000932693,
-0.012751107104122639,
-0.0467170812189579,
0.07333629578351974,
-0.030287347733974457,
-0.03902015462517738,
-0.0012942702742293477,
-0.003672894788905978,
0.020942552015185356,
-0.03998667374253273,
0.005816817749291658,
-0.034430719912052155,
-0.005429986398667097,
-0.014146930538117886,
0.009951640851795673,
-0.02164621651172638,
0.025848085060715675,
-0.002166218124330044,
-0.057474564760923386,
0.049605030566453934,
0.002919082762673497,
-0.04643631726503372,
-0.02070486731827259,
0.0056366645731031895,
-0.017647892236709595,
0.022650621831417084,
0.0055616265162825584,
-0.040432799607515335,
-0.04411157965660095,
0.002357184886932373,
0.012984385713934898,
0.03041120246052742,
-0.049038246273994446,
-0.023688696324825287,
-0.009415832348167896,
-0.06947449594736099,
0.0433722659945488,
0.026829248294234276,
-0.08199430257081985,
0.016376880928874016,
0.0005140607827343047,
-0.012784578837454319,
0.029387211427092552,
0.026976104825735092,
0.007288245018571615,
-0.03731802478432655,
0.007000237237662077,
0.01755378022789955,
0.04570678621530533,
-0.030094599351286888,
0.009997550398111343,
0.01690676622092724,
-0.014046288095414639,
0.00970570556819439,
0.0011933088535442948,
0.012599761597812176,
0.03898688778281212,
-0.010992038995027542,
0.030679067596793175,
0.03979387879371643,
0.00873734150081873,
-0.03952203691005707,
0.010506254620850086,
-0.04588695988059044,
-0.02798328548669815,
0.03954479470849037,
0.005860467441380024,
0.003066151635721326,
-0.018873680382966995,
-0.023926761001348495,
-0.007820378988981247,
0.015297078527510166,
-0.015212357975542545,
-0.0205601267516613,
-0.048864610493183136,
-0.013680724427103996,
0.0293213352560997,
-0.035504475235939026,
0.006896111648529768,
0.06863614916801453,
-0.005509162787348032,
-0.048566050827503204,
0.06416936963796616,
0.04282166436314583,
0.028515217825770378,
0.037643369287252426,
0.01109805703163147,
0.049525775015354156,
0.03139859065413475,
-0.004836204461753368,
0.035823382437229156,
-0.0033330514561384916,
-0.02078045904636383,
-0.008051129989326,
-0.016080191358923912,
0.01881450042128563,
0.02914585918188095,
-0.02888050302863121,
0.015313172712922096,
-0.048668261617422104,
-0.025840191170573235,
0.04517785459756851,
-0.034512653946876526,
0.056299950927495956,
0.04158826917409897,
-0.029418665915727615,
0.04230913892388344,
-0.019584666937589645,
0.018635481595993042,
-0.01823553815484047,
-0.01619599014520645,
-0.032348841428756714,
0.012785778380930424,
0.029081422835588455,
0.054995097219944,
-0.011590773239731789,
-0.018521541729569435,
-0.021560803055763245,
-0.028749780729413033,
0.007394701242446899,
-0.035750411450862885,
0.01236090436577797,
0.00880928710103035,
-0.04562041908502579,
-0.0230429507791996,
-0.027407975867390633,
-0.0010063470108434558,
-0.04635748267173767,
0.005257346201688051,
0.06351742148399353,
0.06326642632484436,
0.0011517434613779187,
-0.008796727284789085,
-0.0013649322791025043,
0.029219644144177437,
-0.057057179510593414,
-0.001660359208472073,
0.0014667122159153223,
0.0005748103139922023,
0.03465579077601433,
0.0044465577229857445
] |
<p>I'm studying for a test in electrostatics and I'm always failing on putting up the correct integrals.</p>
<p>In one problem I have the surface of a sphere with radius $a$ and an opening angle of $2\theta$. There is a total charge $Q$ evenly distributed on the surface. I want to calculate the potential.</p>
<p>In order to calculate the potential I first have to calculate the surface charge distribution, $\sigma(r)$, and this is where I always fail. I've done like this:</p>
<p>$Q=\sigma A=\sigma 4\pi r^2$</p>
<p>Then I tried to convert this into spherical coordinates by changing $r$ into $r=a \sin\theta \cos\phi +a \sin\theta \sin\phi +a \cos\theta$</p>
<p>The correct integral should be
$Q=\sigma a^2\int_0^\theta \sin \theta d\theta \int_0^{2\pi}\!d\phi$</p>
<p>Can someone explain how to put up integrals like these? </p>
| 9,367 |
[
-0.009470376186072826,
0.01309051364660263,
-0.0031828132923692465,
0.00794168934226036,
0.01573782041668892,
-0.003777500707656145,
-0.0012709405273199081,
-0.03949223831295967,
0.013478081673383713,
-0.00001976995190489106,
0.056974560022354126,
0.012291347607970238,
0.075234554708004,
0.0161296334117651,
0.03418973833322525,
-0.019943352788686752,
-0.026172958314418793,
-0.04610690847039223,
-0.01090923510491848,
0.005172116216272116,
-0.006974075920879841,
0.026166686788201332,
-0.014270646497607231,
-0.01961481012403965,
0.008210455998778343,
0.02574203535914421,
0.011815113946795464,
-0.040647827088832855,
0.02676008827984333,
0.08785506337881088,
-0.03156709671020508,
-0.03486495465040207,
0.051269810646772385,
0.03557464852929115,
0.01084586326032877,
0.010064464993774891,
0.0018420559354126453,
0.017004353925585747,
-0.04635155200958252,
0.030439510941505432,
-0.03459682688117027,
-0.014839287847280502,
-0.003887665458023548,
0.07560441642999649,
-0.0065073780715465546,
-0.000024114549887599424,
-0.027563462033867836,
-0.021707946434617043,
0.04900108650326729,
-0.08495848625898361,
0.05273422598838806,
0.040916960686445236,
0.041027508676052094,
0.08226161450147629,
0.040649473667144775,
0.008749468252062798,
0.05046877637505531,
0.053968194872140884,
-0.03512807935476303,
-0.04736844077706337,
-0.029130522161722183,
-0.05991257354617119,
-0.020045693963766098,
-0.048457950353622437,
-0.005170665681362152,
-0.0041608912870287895,
0.026651332154870033,
-0.0024448134936392307,
0.022080175578594208,
0.004485039971768856,
0.030979245901107788,
0.026463450863957405,
0.03661028668284416,
-0.041460927575826645,
-0.007276865653693676,
-0.020352423191070557,
0.036577221006155014,
-0.016397608444094658,
0.016959816217422485,
0.027795113623142242,
-0.022388024255633354,
0.03877367079257965,
0.05357225239276886,
0.03650457784533501,
0.011085385456681252,
0.0025561044458299875,
0.051976729184389114,
0.007196059450507164,
-0.00983386766165495,
0.006320717744529247,
-0.03746505081653595,
-0.0004970304435119033,
0.030604643747210503,
-0.021548818796873093,
-0.010714416392147541,
0.029670502990484238,
0.005181350279599428,
0.04722626134753227,
-0.0051484014838933945,
-0.03718823939561844,
-0.010378300212323666,
-0.02417626790702343,
0.007946362718939781,
0.08339883387088776,
-0.0030987432692199945,
-0.0194852352142334,
-0.0494140088558197,
0.007452087011188269,
-0.00418071448802948,
-0.03421223908662796,
-0.05094917491078377,
0.05901450663805008,
-0.02104850672185421,
0.014230203814804554,
-0.006742699071764946,
0.009807776659727097,
-0.034664418548345566,
0.00841992162168026,
-0.0005699300090782344,
0.031207751482725143,
0.040224235504865646,
-0.03094741329550743,
-0.0010993124451488256,
-0.02599232643842697,
-0.03960438445210457,
0.042374782264232635,
0.014212461188435555,
0.01097412034869194,
-0.03263948857784271,
0.012079563923180103,
0.029245996847748756,
-0.0022625778801739216,
-0.006597386673092842,
0.02814473770558834,
0.0024631069973111153,
-0.04386496543884277,
-0.07585486024618149,
-0.037085261195898056,
0.009433629922568798,
-0.017219385132193565,
-0.006865741219371557,
-0.07505250722169876,
0.0028465217910706997,
0.026229389011859894,
0.058329932391643524,
0.01811974309384823,
0.01093608420342207,
0.004288214258849621,
0.03976529464125633,
-0.01299810130149126,
-0.024294205009937286,
-0.004327475558966398,
-0.01427814643830061,
-0.012037401087582111,
-0.0017835884355008602,
-0.029840070754289627,
0.04059978574514389,
0.005968494340777397,
0.020813358947634697,
-0.027531586587429047,
0.06620454043149948,
-0.007394688669592142,
0.026578005403280258,
0.006530639715492725,
0.012590386904776096,
0.003519921563565731,
0.07969703525304794,
-0.0001444041554350406,
-0.006845271680504084,
0.05452343448996544,
-0.006615643855184317,
-0.00496952747926116,
-0.02661365084350109,
0.05235831066966057,
0.0639805793762207,
-0.04093163460493088,
0.007230215240269899,
-0.07665006071329117,
0.03368962183594704,
0.013184028677642345,
-0.02067739889025688,
-0.041311755776405334,
0.011203388683497906,
0.007376617752015591,
-0.017515553161501884,
0.05752317234873772,
0.02462078258395195,
-0.041963618248701096,
-0.049235887825489044,
-0.022860856726765633,
-0.03473285958170891,
-0.03942675143480301,
0.05493460223078728,
-0.019989531487226486,
-0.021838905289769173,
0.019282078370451927,
0.021590251475572586,
0.025319943204522133,
-0.009799499064683914,
-0.015615761280059814,
-0.026184502989053726,
0.041585102677345276,
-0.0217300858348608,
-0.012970617972314358,
0.04755247011780739,
0.039957426488399506,
0.053404610604047775,
0.007311664521694183,
0.024547500535845757,
-0.01860145479440689,
0.021718809381127357,
-0.023769158869981766,
-0.01775030791759491,
0.04748455062508583,
0.01707935519516468,
-0.02012631483376026,
0.003637564368546009,
0.04816291481256485,
-0.003984623122960329,
0.03177227824926376,
-0.03611907362937927,
0.06272905319929123,
0.028378382325172424,
0.00266244076192379,
-0.015928223729133606,
0.040702831000089645,
0.03006913885474205,
0.005348491948097944,
-0.004743124358355999,
-0.028872687369585037,
-0.010260013863444328,
0.026822617277503014,
0.057103972882032394,
-0.007210190407931805,
-0.060812532901763916,
-0.011857064440846443,
0.046825382858514786,
0.02786741778254509,
0.017342770472168922,
0.01895662397146225,
-0.03089483082294464,
-0.02053738944232464,
0.0021185753867030144,
0.008480013348162174,
-0.02507960796356201,
0.01057180855423212,
0.01400259230285883,
0.0121599230915308,
0.006273185834288597,
0.015589464455842972,
-0.025190776214003563,
0.02610800601541996,
-0.04455852136015892,
0.05181536450982094,
-0.0036269142292439938,
0.0023884139955043793,
0.03985978662967682,
-0.011158522218465805,
0.055061642080545425,
0.033279258757829666,
0.021075891330838203,
-0.018960673362016678,
-0.0422811284661293,
0.00378339271992445,
0.0465867780148983,
0.00294713256880641,
0.0025643028784543276,
0.0041992091573774815,
0.017185159027576447,
-0.027949869632720947,
-0.01683691330254078,
0.007461033761501312,
-0.017082959413528442,
-0.008646968752145767,
0.017958641052246094,
0.030264858156442642,
0.02264711633324623,
0.010949441231787205,
-0.010926466435194016,
-0.033290401101112366,
-0.002516640815883875,
0.008141403086483479,
0.024728601798415184,
0.051065318286418915,
-0.033157214522361755,
-0.009006716310977936,
-0.020509125664830208,
-0.016146579757332802,
0.06274092942476273,
0.0009796201484277844,
-0.00885009765625,
-0.006800101138651371,
0.00970427319407463,
-0.013717195950448513,
0.0053112865425646305,
0.00003405489042052068,
0.027170026674866676,
-0.027382636442780495,
-0.011640921235084534,
0.021543778479099274,
0.0006887604249641299,
-0.00798649713397026,
0.04228775575757027,
-0.04413192346692085,
-0.042944926768541336,
-0.00640850979834795,
-0.0012150643160566688,
0.0482175350189209,
-0.02162104658782482,
0.010903182439506054,
0.01422435324639082,
-0.03765391185879707,
-0.02740352600812912,
-0.048937130719423294,
-0.024826012551784515,
-0.030088966712355614,
-0.02938292920589447,
0.0038365644868463278,
-0.025544656440615654,
-0.051123131066560745,
0.07210420817136765,
-0.020849373191595078,
-0.03174004331231117,
0.024289680644869804,
0.0036414233036339283,
-0.015973344445228577,
-0.020111069083213806,
0.003616482485085726,
0.02392081543803215,
-0.04018617421388626,
0.020528804510831833,
-0.02114447019994259,
0.033952292054891586,
0.021863320842385292,
-0.0014717732556164265,
-0.008553694002330303,
0.03401779755949974,
0.007555999327450991,
0.0007949218270368874,
0.041445761919021606,
-0.024514544755220413,
-0.0014171268558129668,
-0.0012762713013216853,
0.020963303744792938,
0.03722381219267845,
0.053404636681079865,
-0.03624366968870163,
0.01927020028233528,
-0.0696842297911644,
0.016708919778466225,
-0.03595435991883278,
0.05430430918931961,
0.011105401441454887,
-0.0457247719168663,
0.0075112455524504185,
0.03102041967213154,
0.048323340713977814,
-0.029073933139443398,
-0.01125991903245449,
0.03747125715017319,
0.030600490048527718,
-0.024278275668621063,
-0.030631769448518753,
-0.010574612766504288,
0.004068142734467983,
0.0233700443059206,
-0.026008285582065582,
-0.012747429311275482,
0.04524870961904526,
0.048627354204654694,
0.0161295048892498,
-0.021027708426117897,
-0.038971759378910065,
0.01360912062227726,
-0.05387560650706291,
0.005501601845026016,
-0.01879098080098629,
0.0409696064889431,
0.016244513913989067,
0.053894370794296265,
0.052337948232889175,
-0.00006780402327422053,
0.011584877967834473,
0.024929797276854515,
-0.044333599507808685,
0.013724258169531822,
-0.010949678719043732,
-0.03968534991145134,
-0.049008581787347794,
-0.06306160241365433,
-0.006314964033663273,
-0.02970624342560768,
-0.02637934871017933,
-0.013838300481438637,
-0.02564610168337822,
-0.021461861208081245,
-0.003635608358308673,
-0.012444750405848026,
-0.011311108246445656,
-0.045726705342531204,
0.10109192132949829,
0.00868311244994402,
-0.029965965077280998,
0.01795332506299019,
0.07101016491651535,
-0.040668148547410965,
0.007948667742311954,
-0.031033789739012718,
0.012947337701916695,
-0.016078034415841103,
0.050618186593055725,
-0.0008119110716506839,
0.018931033089756966,
0.02247634157538414,
-0.0038845345843583345,
-0.02948729135096073,
0.0959344208240509,
-0.001978154992684722,
-0.0038950867019593716,
-0.049383778125047684,
-0.038741692900657654,
-0.0009274579351767898,
-0.05249819904565811,
0.0511477068066597,
-0.034666240215301514,
-0.0002534177911002189,
0.03938280791044235,
-0.024090681225061417,
-0.011319621466100216,
0.03290499374270439,
0.049479659646749496,
0.0040257154032588005,
-0.031647078692913055,
-0.0413186252117157,
-0.03343416005373001,
-0.023477397859096527,
-0.00680982181802392,
0.00320118828676641,
-0.02840232662856579,
-0.04080914333462715,
-0.009130391292273998,
0.045865677297115326,
-0.01825639232993126,
0.003319056238979101,
0.00023642655287403613,
-0.008897947147488594,
0.026836417615413666,
-0.005570320878177881,
-0.02711576223373413,
0.0016624054405838251,
0.003972561564296484,
0.035372935235500336,
-0.0020639928989112377,
-0.02499414049088955,
-0.04205900803208351,
-0.017987236380577087,
0.04913773387670517,
0.0189418513327837,
0.022428961470723152,
-0.021261924877762794,
-0.05749955400824547,
-0.003750282572582364,
0.07436396926641464,
-0.05301724374294281,
0.018967479467391968,
-0.017755839973688126,
0.022460276260972023,
-0.022855138406157494,
-0.027072373777627945,
-0.04699788615107536,
0.007904711179435253,
0.009327100589871407,
0.04832838103175163,
-0.02577679604291916,
-0.0055810208432376385,
-0.0014308120589703321,
-0.003890280844643712,
0.014274351298809052,
0.043800123035907745,
0.028022920712828636,
0.007590381428599358,
0.00002658310222614091,
-0.0019983057864010334,
-0.030230753123760223,
-0.07003402709960938,
0.016531188040971756,
-0.034506529569625854,
0.020194243639707565,
0.042418986558914185,
-0.026655053719878197,
-0.025397133082151413,
0.03053361549973488,
0.010015360079705715,
0.04202350229024887,
0.016459451988339424,
-0.04538929834961891,
0.032446302473545074,
0.050202496349811554,
0.04375423491001129,
0.05971395596861839,
0.02305981144309044,
-0.0062762112356722355,
-0.007331303786486387,
-0.06956754624843597,
0.03809398412704468,
0.002449223306030035,
-0.05173512548208237,
-0.024739153683185577,
0.005186941009014845,
-0.019198637455701828,
0.040411196649074554,
-0.02381584420800209,
0.053835369646549225,
-0.04740837216377258,
-0.029534297063946724,
-0.006534821353852749,
-0.017100568860769272,
-0.002909407950937748,
0.01391414925456047,
0.03923999145627022,
0.019682757556438446,
0.030090276151895523,
-0.0056631132028996944,
-0.002567100338637829,
-0.012700442224740982,
-0.030296770855784416,
-0.00661889836192131,
-0.0026061288081109524,
-0.0032987159211188555,
-0.001710080890916288,
-0.04755030572414398,
-0.010424227453768253,
-0.08357849717140198,
0.0701608881354332,
-0.039317987859249115,
-0.030477505177259445,
0.020270781591534615,
-0.07950382679700851,
-0.06803520768880844,
-0.00009342184785054997,
0.02718578651547432,
0.04605447128415108,
-0.07148785144090652,
0.012695079669356346,
0.02836725488305092,
0.036900050938129425,
-0.059896085411310196,
-0.035939231514930725,
-0.005057214293628931,
-0.00027035060338675976,
-0.013830256648361683,
-0.024928312748670578,
0.008058934472501278,
0.00063018110813573,
-0.028872797265648842,
0.011190012097358704,
-0.0019718054682016373,
-0.032392505556344986,
0.027565015479922295,
0.023332729935646057,
0.018532169982790947,
0.059815503656864166,
-0.015514461323618889,
0.018588179722428322,
0.01623658277094364,
-0.040850672870874405,
-0.01752712018787861,
0.02381911315023899,
0.03185620903968811,
-0.033610597252845764,
-0.030207471922039986,
-0.0034558684565126896,
-0.010759382508695126,
0.023016782477498055,
-0.013374282978475094,
-0.013328874483704567,
0.004287380259484053,
0.02302192710340023,
0.00781929213553667,
-0.005856767762452364,
-0.01277780719101429,
0.018365582451224327,
0.0073969196528196335,
-0.04860156774520874,
0.008188108913600445,
-0.06151299551129341,
-0.010589974001049995,
-0.003978865686804056,
-0.007537559140473604,
0.021856097504496574,
0.0015539294108748436,
0.08074317872524261,
-0.019886108115315437,
-0.012330704368650913,
0.018396712839603424,
0.01719428040087223,
0.008704474195837975,
-0.007941334508359432,
-0.008125333115458488,
0.011626260355114937,
-0.011279930360615253,
-0.026335222646594048,
-0.017061173915863037,
-0.021638570353388786,
0.011159481480717659,
0.07377848029136658,
-0.01638735644519329,
0.024675630033016205,
0.047145601361989975,
0.007382081355899572,
-0.036375194787979126,
-0.055886078625917435,
-0.02876610867679119,
-0.003810708876699209,
0.00694848969578743,
0.019081605598330498,
-0.022851116955280304,
0.01975763402879238,
-0.012079963460564613,
0.049605246633291245,
-0.03003333881497383,
0.0255966205149889,
-0.0071776132099330425,
0.024742888286709785,
0.01025272998958826,
0.007059882860630751,
-0.040520962327718735,
0.023043828085064888,
-0.030210787430405617,
0.027282027527689934,
-0.006576485466212034,
-0.012552834115922451,
0.05072943493723869,
0.007230605464428663,
-0.005553754046559334,
-0.010340609587728977,
0.006390704307705164,
-0.00012978627637494355,
0.00443324213847518,
0.02832348644733429,
-0.03222190961241722,
-0.013875827193260193,
0.007644674740731716,
0.04761135205626488,
-0.0074586886912584305,
-0.003680781926959753,
-0.048971615731716156,
-0.07761596143245697,
-0.024075040593743324,
-0.06759873032569885,
-0.05731279402971268,
0.04934832453727722,
-0.02857896313071251,
-0.024713052436709404,
0.012897486798465252,
-0.034567393362522125,
0.035632770508527756,
0.03515306115150452,
-0.009261290542781353,
-0.055019114166498184,
0.08842036128044128,
-0.019757581874728203,
0.019704680889844894,
-0.021523047238588333,
-0.014702429994940758,
0.12188157439231873,
0.050477106124162674,
-0.017291352152824402,
-0.07400870323181152,
-0.007106400094926357,
-0.02006666548550129,
0.019980981945991516,
-0.028580619022250175,
0.026814745739102364,
-0.03921710327267647,
-0.014201687648892403,
-0.004932684358209372,
0.04710987210273743,
-0.0020744565408676863,
0.007966943085193634,
0.04016216844320297,
-0.009311677888035774,
-0.059333961457014084,
-0.0024770074523985386,
0.02923237904906273,
-0.03225564584136009,
0.05604737997055054,
-0.06781764328479767,
0.020737627521157265,
-0.06600826233625412,
0.01316410955041647,
-0.04382670298218727,
0.006485326215624809,
-0.007642258424311876,
0.010247460566461086,
-0.050301093608140945,
0.0268858615309,
0.005310708656907082,
-0.022956417873501778,
-0.005280993413180113,
0.03421248868107796,
0.035525836050510406,
-0.013272317126393318,
0.018014373257756233,
0.023915786296129227,
0.00790478102862835,
0.016697794198989868,
0.024138392880558968,
0.03098178841173649,
-0.04191044345498085,
-0.022960472851991653,
-0.03477463126182556,
0.08419188112020493,
-0.038211897015571594,
-0.013379067182540894,
-0.015101538971066475,
0.0103946253657341,
-0.01123121939599514,
-0.0436214879155159,
-0.008577330969274044,
-0.02107173018157482,
0.02201804146170616,
-0.0034976715687662363,
-0.017891401425004005,
-0.0017804258968681097,
0.026619581505656242,
-0.015272418037056923,
0.04108796641230583,
-0.014344317838549614,
-0.005790111608803272,
-0.005373082123696804,
-0.013932587578892708,
0.018246283754706383,
-0.017954321578145027,
-0.02189391292631626,
0.006866369862109423,
-0.01142983976751566,
-0.04249270260334015,
-0.02773512527346611,
-0.013758724555373192,
0.023312166333198547,
0.041851092129945755,
-0.00868617370724678,
0.017071450129151344,
-0.006220013368874788,
-0.06732501834630966,
-0.0018090842058882117,
-0.013819372281432152,
-0.024754377081990242,
-0.02143239416182041,
-0.025945359840989113,
0.01665418967604637,
0.03058253601193428,
0.010953405871987343,
-0.0017878692597150803,
-0.004700652789324522,
0.03968707099556923,
0.02942660078406334,
-0.021257536485791206,
-0.033477287739515305,
0.00239716493524611,
-0.011455204337835312,
0.0017563144210726023,
-0.01926734670996666,
0.004349561873823404,
0.034821826964616776,
0.024162432178854942,
0.012285192497074604,
0.03217499330639839,
-0.0317121259868145,
0.014367559924721718,
-0.0005589292268268764,
0.00831578578799963,
-0.021250173449516296,
0.0007341435994021595,
0.001780814491212368,
-0.02510177530348301,
0.026982871815562248,
0.012954028323292732,
-0.010458356700837612,
-0.0039040688425302505,
-0.004609457682818174,
-0.04745132848620415,
0.008456667885184288,
-0.032511770725250244,
-0.013104821555316448,
-0.010096094571053982,
0.011046065017580986,
-0.02027427963912487,
0.006551343481987715,
-0.010425432585179806,
0.017940035089850426,
-0.04004085436463356,
0.04015734791755676,
-0.021903809159994125,
-0.012031706050038338,
0.021516555920243263,
-0.007925586774945259,
0.00007162676774896681,
-0.006568371318280697,
0.02147313393652439,
-0.01819012127816677,
0.048588480800390244,
-0.0077519710175693035,
-0.010516166687011719,
0.01002146303653717,
-0.016601117327809334,
-0.049281466752290726,
-0.012807168066501617,
0.015365168452262878,
0.0460345521569252,
0.03935137018561363,
-0.038475487381219864,
-0.013926059007644653,
0.045417338609695435,
-0.009651612490415573,
-0.01250164583325386,
-0.012883910909295082,
-0.014518789015710354,
0.016541369259357452,
-0.014982152730226517,
0.05277882143855095,
-0.0002464452409185469,
0.02326825074851513,
0.024024488404393196,
-0.020312005653977394,
-0.0271076001226902,
0.003878501011058688,
0.02997259423136711,
-0.02143384888768196,
0.0010144883999601007,
0.03849341347813606,
-0.0020081864204257727,
0.04056854173541069,
0.03756743296980858,
-0.001999997068196535,
0.03500603511929512,
0.005926143378019333,
0.00281472597271204,
-0.06532331556081772,
0.0013387902872636914,
0.02949352003633976,
0.011458712629973888,
0.0506395548582077,
-0.07350444793701172,
-0.02175239846110344,
0.04238707944750786,
-0.09392174333333969,
-0.013701641000807285,
-0.022325508296489716,
-0.002951023867353797,
-0.0015315497294068336,
-0.02027530036866665,
-0.006859402172267437,
0.04393747076392174,
0.002838460262864828,
0.040172282606363297,
0.04588720574975014,
-0.015627646818757057,
-0.02512001246213913,
-0.033353131264448166,
0.014935275539755821,
0.05375439301133156,
0.03154623508453369,
-0.028673507273197174,
0.07028015702962875,
0.00038983626291155815,
-0.035376813262701035,
0.001271832617931068,
-0.013804368674755096,
0.018210366368293762,
-0.003604199970141053,
0.024385126307606697,
0.015506826341152191,
0.03445996344089508,
-0.010025758296251297,
-0.000004645732587960083,
-0.00018427500617690384,
0.015869151800870895,
0.04989517107605934,
-0.009169121272861958,
-0.015851624310016632,
-0.02036409080028534,
0.012804816477000713,
-0.0009059486910700798,
-0.06197875365614891,
0.029320858418941498,
-0.02812161110341549,
0.007311609573662281,
-0.008705910295248032,
-0.018916793167591095,
0.060160472989082336,
-0.052949208766222,
0.002386520616710186,
-0.008778776973485947,
0.025814490392804146,
0.02680814452469349,
0.0015797907253727317,
0.04160675033926964,
0.028928767889738083,
0.018004829064011574,
-0.0173600222915411,
0.02029315009713173,
0.00033643326605670154,
-0.030268410220742226,
-0.0541393905878067,
0.013528881594538689,
-0.002574347658082843,
-0.029660766944289207,
0.014052099548280239,
0.012232291512191296,
-0.04427517205476761,
-0.010960837826132774,
0.038707662373781204,
0.010185612365603447,
0.010141095146536827,
-0.04223792254924774,
-0.009523996151983738,
-0.0801023468375206,
0.01656397432088852,
0.013378377072513103,
-0.04008570685982704,
-0.014666697941720486,
-0.014858446083962917,
-0.003896246198564768,
0.012448608875274658,
0.049842461943626404,
0.0268484428524971,
0.009168917313218117,
0.012935706414282322,
0.007533744443207979,
0.03823576122522354,
-0.07877159118652344,
-0.008710992522537708,
0.019912008196115494,
0.010063618421554565,
0.016446691006422043,
0.012381604872643948,
0.018319299444556236,
0.000087242282461375,
-0.02559778466820717,
-0.0068300566636025906,
0.03183082491159439,
0.007520657032728195,
-0.039206985384225845,
0.012552103027701378,
-0.009528164751827717,
-0.010771926492452621,
0.07359687238931656,
-0.007187607232481241,
0.023809166625142097,
0.01653144881129265,
-0.01794491708278656,
-0.004947441630065441,
0.03988172113895416,
-0.015479657799005508,
-0.028345167636871338,
-0.030123891308903694,
0.007406032644212246,
0.0323961079120636,
-0.05782480910420418,
-0.012992926873266697,
0.04427658021450043,
-0.01766403391957283,
-0.029868151992559433,
0.06402147561311722,
0.0020085270516574383,
0.03734052926301956,
0.02679072879254818,
0.018339965492486954,
0.01193978637456894,
0.007267794106155634,
0.021464522927999496,
0.004696127492934465,
0.0384412556886673,
0.0010709591442719102,
0.014918938279151917,
0.07608523219823837,
-0.008218747563660145,
-0.007907935418188572,
-0.031390104442834854,
0.023787233978509903,
-0.03684374317526817,
-0.004420116078108549,
-0.00013880571350455284,
-0.05164282023906708,
0.020500201731920242,
0.01802164316177368,
-0.024866804480552673,
0.07208588719367981,
-0.029361044988036156,
0.005839000456035137,
-0.006738579832017422,
-0.021779414266347885,
0.000010674753866624087,
0.018877141177654266,
0.036380331963300705,
0.04762975499033928,
-0.033648230135440826,
-0.04797416925430298,
-0.054097410291433334,
0.016773754730820656,
0.022300714626908302,
0.01620735041797161,
0.031354401260614395,
0.020023003220558167,
0.026899518445134163,
-0.026754504069685936,
-0.010095164179801941,
0.019995402544736862,
-0.021003788337111473,
0.043904390186071396,
0.021347736939787865,
0.021189622581005096,
-0.013143765740096569,
-0.015352279879152775,
-0.03975505754351616,
0.06050363555550575,
-0.058390822261571884,
-0.044221799820661545,
-0.002746414626017213,
0.023360447958111763,
-0.020335623994469643,
-0.01093230303376913
] |
<p>Consider an electric dipole and its electric field lines. </p>
<p>There will be many field lines that do not extend to or originate from infinity, but rather begin at the positive charge and loop back around to terminate at the negative charge. </p>
<p>However, the field lines exactly on the dipole axis will extend out to infinity (or originate from infinity). </p>
<p>But are these the only field lines that extend to infinity, or are there other off-axial lines that also go to infinity? How can one prove this? </p>
<p>I have tried writing out the differential equations for the field lines, but they seem impossible to solve. No heuristic argument has satisfied me either. One can assert that all off-axial electric field lines must curve away from the axis as one goes to infinity, but does this curvature ultimately cause them to curve all the way back or do they reach some sort of linear asymptote? </p>
| 9,368 |
[
-0.03289724513888359,
0.01900644600391388,
0.015520880930125713,
0.0015788200544193387,
0.03451839089393616,
0.009087433107197285,
-0.031266290694475174,
0.016620172187685966,
-0.009468031115829945,
-0.01935563050210476,
0.021688982844352722,
-0.020213564857840538,
0.028319722041487694,
0.03901650384068489,
0.019489765167236328,
-0.0005632988177239895,
-0.008896874263882637,
0.013525950722396374,
0.009854518808424473,
-0.06321203708648682,
0.007898413576185703,
0.028768017888069153,
-0.0037969083059579134,
0.01686808653175831,
-0.039883192628622055,
0.02788848616182804,
0.0672132819890976,
0.010722710750997066,
0.014668562449514866,
0.0633852630853653,
0.002264062175527215,
-0.029523413628339767,
0.011363958939909935,
0.0283054132014513,
0.057486649602651596,
-0.012670595198869705,
-0.002494476968422532,
-0.028703993186354637,
-0.014984714798629284,
-0.0010434871073812246,
-0.005689998157322407,
-0.020662637427449226,
-0.014224189333617687,
0.041285496205091476,
-0.02342488057911396,
-0.0122215636074543,
-0.021157972514629364,
-0.0020299137104302645,
0.06870825588703156,
-0.0528964027762413,
0.06932531297206879,
-0.005546926520764828,
0.06016506999731064,
0.007337864488363266,
0.04380255565047264,
-0.003039619652554393,
0.05526840686798096,
0.04775134474039078,
0.00012571689148899168,
-0.07755539566278458,
-0.022555509582161903,
-0.02519909292459488,
-0.03588501363992691,
-0.038024984300136566,
-0.040231503546237946,
0.07529230415821075,
0.0013968914281576872,
-0.008182580582797527,
0.004779406823217869,
-0.029119370505213737,
0.008135400712490082,
0.038396336138248444,
0.02027447335422039,
0.0007107894052751362,
0.01318608783185482,
-0.014951321296393871,
-0.0035535129718482494,
0.013718346133828163,
0.03392494097352028,
0.03512754663825035,
-0.011268092319369316,
0.029937416315078735,
0.03258372098207474,
0.02470184862613678,
0.016424350440502167,
-0.0031981314532458782,
0.048171188682317734,
0.006591574288904667,
0.04535443335771561,
0.05065258964896202,
0.02966701053082943,
0.0017658558208495378,
0.009926924481987953,
0.004785181954503059,
-0.021790817379951477,
0.03413840010762215,
-0.008432809263467789,
0.04730386659502983,
0.0005438118241727352,
-0.022843018174171448,
-0.01059635914862156,
-0.018785599619150162,
-0.016356423497200012,
0.04621010273694992,
0.0052001033909618855,
0.009071137756109238,
-0.0466492585837841,
0.018210120499134064,
-0.03305981308221817,
0.00368246017023921,
-0.030274514108896255,
0.0368836484849453,
0.026840442791581154,
0.009532111696898937,
-0.007714277133345604,
-0.03089206852018833,
0.008500680327415466,
-0.045394111424684525,
0.04503095895051956,
0.049878254532814026,
0.023059464991092682,
-0.038738932460546494,
0.015116440132260323,
-0.0451485738158226,
-0.07564982026815414,
-0.01861918903887272,
0.03949180990457535,
0.01957733742892742,
-0.050954341888427734,
-0.007094377651810646,
-0.003724428592249751,
0.014010760933160782,
-0.00693209283053875,
0.009913912042975426,
0.031887974590063095,
-0.009753713384270668,
-0.0929717943072319,
-0.06768734008073807,
-0.0027169324457645416,
0.018831446766853333,
0.00978429988026619,
-0.07316611707210541,
0.004475230351090431,
0.05935898423194885,
0.11088991165161133,
-0.011008095927536488,
-0.01836419105529785,
0.005671828053891659,
0.046840324997901917,
-0.0031211015302687883,
-0.007255055010318756,
0.0017065983265638351,
-0.016376826912164688,
-0.019342606887221336,
-0.010873877443373203,
-0.09304441511631012,
0.030770715326070786,
0.023519553244113922,
0.014412928372621536,
-0.0302372258156538,
0.06581589579582214,
-0.016791630536317825,
0.04280426353216171,
-0.02825871855020523,
-0.03590545803308487,
-0.007494285702705383,
0.10020916163921356,
0.016241174191236496,
-0.020779786631464958,
0.0686391294002533,
0.0007611264009028673,
0.04594119265675545,
-0.024964464828372,
0.027748458087444305,
0.04813341051340103,
-0.07567580789327621,
-0.006426619365811348,
-0.01560420636087656,
0.005774462595582008,
0.04359256476163864,
-0.03489205613732338,
-0.028102653101086617,
0.005632536020129919,
0.013651866465806961,
0.0115749416872859,
0.03643204644322395,
-0.015668315812945366,
-0.027613595128059387,
-0.001511117909103632,
-0.03501737117767334,
0.002013077260926366,
-0.047884829342365265,
0.05607108026742935,
-0.0031278966926038265,
-0.0454055480659008,
0.002423209836706519,
0.02047506533563137,
-0.018333956599235535,
-0.05534113571047783,
-0.049761101603507996,
-0.023063380271196365,
0.054174747318029404,
0.03601028770208359,
-0.032241541892290115,
0.017527351155877113,
0.0433928519487381,
0.024465592578053474,
0.009578428231179714,
0.022296693176031113,
-0.04730707034468651,
-0.01597878523170948,
-0.005412346683442593,
-0.027491440996527672,
0.04074494540691376,
0.014944545924663544,
0.04497115686535835,
-0.007039512507617474,
0.025182321667671204,
-0.016991866752505302,
0.043901897966861725,
-0.023818837478756905,
0.05814572796225548,
0.06469693779945374,
0.026151956990361214,
0.0026712219696491957,
0.02692936360836029,
-0.0031711612828075886,
0.016543110832571983,
-0.011106486432254314,
-0.01667061820626259,
-0.04780922085046768,
0.015470198355615139,
0.0431271493434906,
0.013522716239094734,
-0.03078174777328968,
0.011480875313282013,
0.01693497598171234,
0.04347812011837959,
-0.01262223906815052,
0.0011005377164110541,
-0.03939652815461159,
-0.02666492387652397,
-0.018072521314024925,
0.01145071443170309,
0.006782075390219688,
0.016811372712254524,
0.06690796464681625,
-0.027637934312224388,
-0.014306655153632164,
0.01974254474043846,
-0.008766507729887962,
-0.003433797275647521,
-0.022729981690645218,
0.013457036577165127,
0.028636010363698006,
-0.018978197127580643,
0.04405814781785011,
-0.03732524439692497,
0.03734307736158371,
0.013783575966954231,
-0.030774390324950218,
0.009367280639708042,
-0.020646825432777405,
0.03365454450249672,
0.029641542583703995,
-0.0015471657970920205,
-0.02705569565296173,
-0.04618985578417778,
0.027085023000836372,
-0.051924265921115875,
0.007383621297776699,
-0.03401803970336914,
-0.05770203098654747,
0.0007651931373402476,
0.011214240454137325,
0.05564672872424126,
0.015883048996329308,
0.03264313563704491,
-0.01448209397494793,
-0.029795734211802483,
0.027348404750227928,
-0.03332236781716347,
-0.0029028409626334906,
0.007255022879689932,
-0.03975919261574745,
0.021949032321572304,
-0.03798947110772133,
-0.006441803183406591,
0.05406511574983597,
0.013524578884243965,
0.01845618523657322,
0.019521502777934074,
-0.002287189709022641,
-0.022611377760767937,
-0.03658241778612137,
-0.02997549995779991,
0.02595001831650734,
-0.004177306778728962,
-0.00399123877286911,
0.04347631335258484,
-0.03985534608364105,
-0.025143619626760483,
0.05029572919011116,
-0.06216493993997574,
-0.039608992636203766,
-0.02249469980597496,
-0.00009230251453118399,
0.03031713142991066,
-0.017652466893196106,
0.03605546057224274,
-0.028156353160738945,
-0.06379421800374985,
-0.018849564716219902,
-0.052770085632801056,
-0.046938396990299225,
-0.0031529213301837444,
-0.0015079720178619027,
0.024828271940350533,
0.008125025779008865,
-0.02270044945180416,
0.07873702049255371,
0.04211178794503212,
-0.03627690300345421,
-0.02138444036245346,
0.00402273703366518,
-0.008242717944085598,
-0.0251604113727808,
0.011474999599158764,
0.024028906598687172,
-0.026880821213126183,
-0.02415086142718792,
0.002887007547542453,
0.03506899252533913,
-0.011006129905581474,
0.010416651144623756,
-0.021058449521660805,
0.012292793951928616,
-0.008592307567596436,
0.014397913590073586,
0.01982356794178486,
0.02798839844763279,
-0.0061760819517076015,
-0.02854372002184391,
0.02402346022427082,
0.03754652664065361,
-0.015235171653330326,
-0.05271325632929802,
0.036402877420186996,
-0.03607216477394104,
0.025653697550296783,
-0.021168166771531105,
0.01294715516269207,
-0.005967218894511461,
-0.002982931677252054,
-0.00251764222048223,
0.019838565960526466,
0.06476370245218277,
-0.03974880650639534,
0.01540463324636221,
0.0037687327712774277,
0.021114248782396317,
-0.05021092668175697,
-0.007717492990195751,
-0.004956560209393501,
-0.028071923181414604,
0.021823493763804436,
-0.019054289907217026,
-0.01900879107415676,
0.047664642333984375,
0.05894557014107704,
0.0019159564981237054,
0.009735285304486752,
-0.01691102236509323,
0.004507200326770544,
-0.06436198949813843,
0.012636175379157066,
-0.012785693630576134,
0.03733713924884796,
0.01669895276427269,
0.044314924627542496,
-0.01279553584754467,
0.02937806211411953,
0.020095394924283028,
0.029167303815484047,
-0.08313564956188202,
0.03224746510386467,
-0.04376411810517311,
-0.010804814286530018,
-0.03965109959244728,
-0.01530864741653204,
0.008043370209634304,
-0.010142079554498196,
-0.022332103922963142,
-0.02796832099556923,
-0.0213452260941267,
-0.04215643182396889,
0.010595552623271942,
-0.04046183079481125,
-0.05746924504637718,
-0.02305608242750168,
0.013462710194289684,
0.01065711211413145,
-0.07466532289981842,
0.02635057270526886,
0.009418210946023464,
-0.028057504445314407,
-0.028825420886278152,
0.0024261600337922573,
0.037496548146009445,
0.019082190468907356,
0.004748722538352013,
0.0011991369538009167,
0.0060513499192893505,
-0.003969127312302589,
-0.0002146190236089751,
-0.0019965677056461573,
0.03654324263334274,
0.031525153666734695,
-0.008372608572244644,
-0.012469788081943989,
-0.04693089425563812,
-0.00684088421985507,
-0.011786995455622673,
0.08338398486375809,
0.016094263643026352,
-0.004765425808727741,
0.04269016906619072,
-0.019772415980696678,
-0.014793943613767624,
0.016431136056780815,
0.017349401488900185,
0.02669159695506096,
-0.0161755308508873,
-0.050949424505233765,
-0.004106651991605759,
-0.023379959166049957,
0.03448421508073807,
-0.013083085417747498,
-0.04504997655749321,
-0.018567487597465515,
0.002913285279646516,
0.0390961579978466,
-0.0006785509176552296,
-0.008062341250479221,
-0.0037979939952492714,
0.016445115208625793,
0.00809441227465868,
-0.0177483931183815,
-0.0031567253172397614,
0.04656020924448967,
0.034865543246269226,
0.09106409549713135,
0.0262454766780138,
-0.018203791230916977,
-0.09403989464044571,
0.004732807166874409,
0.03522064536809921,
0.03907119855284691,
0.01623556576669216,
-0.008044661954045296,
-0.03977718576788902,
0.004050246439874172,
0.03310766816139221,
-0.02194545976817608,
0.02780967764556408,
-0.013999348506331444,
-0.006159971468150616,
0.004707000683993101,
-0.03175013139843941,
-0.07092009484767914,
0.00035590602783486247,
0.00020254100672900677,
0.006040420848876238,
-0.03130144998431206,
0.028640804812312126,
-0.005362325347959995,
0.03745265677571297,
0.034921806305646896,
0.06992225348949432,
0.02785533480346203,
0.01944621652364731,
0.014488457702100277,
-0.006035541649907827,
-0.012121996842324734,
-0.08456140011548996,
0.020820600911974907,
0.019926397129893303,
-0.005371559876948595,
0.07122179120779037,
-0.0476561114192009,
-0.05809002369642258,
0.023615526035428047,
0.012392397038638592,
0.016099199652671814,
-0.003126984927803278,
-0.02156023122370243,
0.02177133969962597,
0.03730958700180054,
0.04169125854969025,
0.04524843022227287,
0.04628059267997742,
-0.022593321278691292,
-0.018874498084187508,
-0.015448498539626598,
0.02549576573073864,
-0.0023289318196475506,
-0.011254774406552315,
-0.035384371876716614,
0.0295578520745039,
-0.031600210815668106,
0.05425800010561943,
-0.03167422488331795,
-0.022871702909469604,
-0.014776396565139294,
-0.052345044910907745,
0.0013396628201007843,
0.03032899834215641,
-0.013415060937404633,
0.004106992855668068,
-0.020324738696217537,
0.0177647415548563,
0.033147893846035004,
-0.008645173162221909,
0.025440365076065063,
0.0072274780832231045,
0.007836769334971905,
0.03402743861079216,
-0.020243460312485695,
-0.007230904418975115,
-0.0011704025091603398,
-0.027084119617938995,
-0.02516896091401577,
-0.04489339515566826,
0.04192258045077324,
-0.02250644564628601,
-0.047384507954120636,
0.06727778166532516,
-0.022470833733677864,
-0.00482163205742836,
0.007942462339997292,
-0.021387644112110138,
-0.009945157915353775,
-0.005113599356263876,
-0.0037416466511785984,
0.021419072523713112,
0.03477608412504196,
-0.05655508115887642,
-0.05786338821053505,
0.02505616843700409,
0.020551707595586777,
-0.031169485300779343,
-0.02627904899418354,
-0.015596090815961361,
-0.009884755127131939,
-0.035544782876968384,
-0.005019903648644686,
0.02032284438610077,
-0.0338374562561512,
0.005617187824100256,
0.0252632275223732,
0.027836140245199203,
0.049738526344299316,
-0.00945360492914915,
0.011921531520783901,
0.048967085778713226,
-0.04133249819278717,
-0.01819145493209362,
0.0016964812530204654,
0.07694001495838165,
-0.0012686182744801044,
-0.017351849004626274,
0.009348570369184017,
0.01607116311788559,
0.031664032489061356,
-0.042770035564899445,
-0.03873873129487038,
-0.006477730814367533,
-0.0033110361546278,
-0.022357650101184845,
-0.014972865581512451,
-0.00497891940176487,
0.0003677818167489022,
0.010998607613146305,
0.00505939731374383,
-0.000728075799997896,
-0.014542452059686184,
-0.045161060988903046,
0.017463358119130135,
0.029258091002702713,
0.017726628109812737,
-0.020373694598674774,
0.02429375797510147,
-0.010110137984156609,
-0.03841215372085571,
-0.004676828160881996,
-0.005811691749840975,
0.03133847191929817,
0.031998299062252045,
0.0015645110979676247,
-0.0007038163021206856,
0.018634643405675888,
-0.024894647300243378,
-0.01890198513865471,
0.009939395822584629,
0.034682292491197586,
0.05380911007523537,
0.04962281137704849,
0.03818414360284805,
0.030844606459140778,
0.01619715616106987,
-0.02993525005877018,
-0.04770800471305847,
-0.01113469060510397,
-0.008991059847176075,
0.011626346036791801,
0.038499873131513596,
-0.05340655893087387,
0.01867312751710415,
0.006835198495537043,
0.025211844593286514,
-0.033647794276475906,
-0.00818826723843813,
-0.00645995931699872,
0.03021520934998989,
0.03243923559784889,
0.008217083290219307,
-0.033610716462135315,
0.01836225762963295,
-0.019032210111618042,
0.01864394173026085,
0.031338028609752655,
0.00035791905247606337,
0.026500526815652847,
0.006685336586087942,
0.03184041008353233,
-0.007340581621974707,
-0.026969261467456818,
-0.03222737833857536,
0.014244480058550835,
-0.0021501919254660606,
0.0023336349986493587,
-0.020434465259313583,
0.025124847888946533,
0.02697627991437912,
0.011801517568528652,
0.0063316915184259415,
-0.009217040613293648,
-0.049209706485271454,
-0.033235494047403336,
-0.038988351821899414,
-0.04782456159591675,
0.04532940313220024,
0.007631327025592327,
-0.020881464704871178,
-0.004954738076776266,
-0.02967863902449608,
-0.006085841450840235,
0.012433165684342384,
0.03338533267378807,
0.0029690805822610855,
0.004329665098339319,
-0.022664712741971016,
0.052432749420404434,
-0.006857836153358221,
-0.025254026055336,
0.10290911048650742,
0.04735235869884491,
0.01251120213419199,
-0.07002688944339752,
0.024197742342948914,
-0.049553245306015015,
0.006891500670462847,
-0.03723844140768051,
0.029859254136681557,
-0.075931116938591,
-0.010342691093683243,
0.027692200616002083,
0.04815978929400444,
-0.03640816733241081,
0.006845721509307623,
0.07060287892818451,
-0.0418127067387104,
-0.005373647436499596,
0.0013890780974179506,
0.037059664726257324,
-0.020835408940911293,
0.031337521970272064,
-0.05403554439544678,
0.05315127968788147,
-0.023823272436857224,
-0.006003158632665873,
-0.03284750506281853,
-0.035334035754203796,
0.03835773840546608,
-0.0037742620334029198,
-0.05417730286717415,
-0.00007450874545611441,
-0.005132162477821112,
-0.03746223449707031,
-0.04189252480864525,
0.022051213309168816,
0.05088384449481964,
-0.02110593393445015,
0.017190927639603615,
0.04022801294922829,
0.025470249354839325,
-0.009605282917618752,
0.026854133233428,
0.03494298830628395,
-0.03908789902925491,
0.012358755804598331,
-0.03531917184591293,
0.05483883619308472,
-0.03573153540492058,
-0.012828877195715904,
-0.00043328775791451335,
0.006856733467429876,
0.04025566577911377,
-0.03670285642147064,
-0.033969447016716,
-0.03341666981577873,
0.00012022256851196289,
-0.00010499444033484906,
-0.005833389237523079,
0.0011986014433205128,
0.018341198563575745,
0.04898141697049141,
0.0036606204230338335,
0.007509513292461634,
-0.0033705662935972214,
0.02603488601744175,
0.007645843084901571,
0.05117889866232872,
0.03640899062156677,
-0.035861536860466,
-0.02160605415701866,
-0.006099780555814505,
-0.008702816441655159,
0.02767583355307579,
0.022938715294003487,
0.00745738809928298,
0.006422856356948614,
0.010322066023945808,
-0.030391108244657516,
0.0074416957795619965,
-0.05482367053627968,
0.02163054421544075,
-0.005714014172554016,
-0.026568718254566193,
-0.0318550281226635,
0.0019399162847548723,
0.032068002969026566,
0.043191418051719666,
-0.0023136360105127096,
0.021593835204839706,
0.0030051807407289743,
0.024964017793536186,
0.003866627812385559,
0.013373350724577904,
-0.00785046722739935,
-0.000208936064154841,
-0.04934024065732956,
0.0071761407889425755,
-0.009265491738915443,
0.022799057886004448,
0.02230711467564106,
0.03371401131153107,
0.011645983904600143,
0.03230291232466698,
-0.0341954231262207,
0.004579421132802963,
0.029582355171442032,
0.00008604763570474461,
0.021161040291190147,
-0.009196977131068707,
0.010254456661641598,
-0.08312960714101791,
-0.04268590360879898,
-0.029079461470246315,
0.014310351572930813,
0.003033802844583988,
0.03665590658783913,
-0.0057374355383217335,
0.021060442551970482,
-0.01080866064876318,
0.00021313481556717306,
-0.05713215842843056,
0.006270246580243111,
-0.05384141951799393,
-0.0057061524130403996,
0.013027841225266457,
0.01127480436116457,
0.012415059842169285,
0.02101043239235878,
-0.030936866998672485,
-0.03790218010544777,
0.024896591901779175,
0.044365253299474716,
-0.03728999197483063,
0.005159464664757252,
0.021948210895061493,
0.03329487517476082,
0.03817744553089142,
0.016965821385383606,
-0.02559593878686428,
0.013872084207832813,
-0.03982707858085632,
-0.03308913856744766,
-0.015551569871604443,
0.006372531410306692,
-0.007355223875492811,
-0.0005275133880786598,
0.0004383473424240947,
0.000366638763807714,
0.03840748965740204,
0.008428433910012245,
-0.03198012337088585,
-0.03940297290682793,
0.003629275131970644,
0.02246170863509178,
0.010674837976694107,
0.004325783345848322,
-0.0341486856341362,
-0.003840188728645444,
-0.005189886316657066,
0.01754760928452015,
-0.009915821254253387,
-0.03607621416449547,
0.007224715780466795,
0.008666564710438251,
-0.013226049020886421,
0.013986889272928238,
0.02584489807486534,
0.030178949236869812,
0.05088842660188675,
-0.026736915111541748,
0.03357360139489174,
0.030113866552710533,
0.026203054934740067,
-0.07967150211334229,
-0.025209104642271996,
-0.020848609507083893,
0.01118068303912878,
-0.013728423044085503,
-0.06225365027785301,
-0.015584750100970268,
0.05098097026348114,
-0.0921131819486618,
0.023335125297307968,
-0.023214735090732574,
-0.0011260912287980318,
-0.03490137308835983,
-0.03334983438253403,
0.0008063686545938253,
0.04852733388543129,
0.02828424610197544,
0.07250894606113434,
-0.009308231994509697,
-0.022045381367206573,
-0.03081463649868965,
-0.03172672912478447,
-0.03750792518258095,
0.04063957557082176,
-0.009143575094640255,
-0.04345603659749031,
0.04846538230776787,
-0.026671022176742554,
0.00957988016307354,
0.020319057628512383,
-0.015188589692115784,
0.00008322873327415437,
0.0201166570186615,
-0.013404140248894691,
0.031055670231580734,
0.02377641759812832,
0.011583460494875908,
0.00018295101472176611,
-0.015895182266831398,
0.0013721449067816138,
0.02070908434689045,
-0.010944927111268044,
-0.040268342941999435,
0.030172748491168022,
0.019052576273679733,
-0.029132073745131493,
-0.04324157536029816,
0.04335545748472214,
-0.02591041289269924,
-0.00953117199242115,
-0.006327240727841854,
0.031067682430148125,
-0.009446129202842712,
0.0064966981299221516,
0.028392687439918518,
-0.05005110800266266,
-0.014637530781328678,
0.00889327097684145,
0.009691525250673294,
-0.004452807363122702,
0.027055159211158752,
-0.020801285281777382,
-0.03253864496946335,
0.02645455300807953,
0.010952112264931202,
-0.00689751747995615,
-0.07273587584495544,
0.04218871891498566,
-0.013898107223212719,
-0.010405871085822582,
0.046209778636693954,
-0.028939109295606613,
-0.037793226540088654,
0.029515787959098816,
0.04710691422224045,
0.037638213485479355,
0.00922747515141964,
-0.05773703381419182,
-0.027977991849184036,
-0.07307684421539307,
0.03422049805521965,
-0.040754955261945724,
-0.03173919394612312,
-0.029741618782281876,
-0.044173501431941986,
-0.02361590415239334,
0.023443695157766342,
0.06455683708190918,
-0.03652627021074295,
0.007966198958456516,
0.017190955579280853,
0.02518472447991371,
0.009838243946433067,
-0.07984661310911179,
0.001953188795596361,
0.04427940398454666,
-0.02251344732940197,
0.017224663868546486,
0.006755388807505369,
-0.012560593895614147,
0.005555202253162861,
0.00850923266261816,
0.01489758025854826,
0.03106587752699852,
0.009906815364956856,
-0.07675420492887497,
0.022272927686572075,
0.01132279448211193,
-0.023978693410754204,
0.06473030149936676,
-0.019961755722761154,
-0.00160194409545511,
-0.00772544601932168,
-0.05624833703041077,
-0.02825278602540493,
0.023098578676581383,
-0.018065985292196274,
0.01093969400972128,
-0.08481239527463913,
0.018680410459637642,
0.029367657378315926,
-0.005029614083468914,
0.021786853671073914,
0.033000074326992035,
-0.028401335701346397,
-0.025621673092246056,
0.046972885727882385,
-0.056180551648139954,
0.027226697653532028,
-0.022598715499043465,
0.0007945336983539164,
0.014584831893444061,
-0.017063312232494354,
0.016991669312119484,
0.038997575640678406,
0.0393502414226532,
0.005030298605561256,
0.009340574033558369,
0.04489905759692192,
-0.00043400906724855304,
0.04091048240661621,
-0.024225525557994843,
0.009191998280584812,
-0.027350755408406258,
0.0072377342730760574,
0.054375022649765015,
0.0004276199615560472,
-0.0077754054218530655,
0.0045488011091947556,
-0.03805556893348694,
0.04613422229886055,
-0.03447297215461731,
0.024748701602220535,
0.011655808426439762,
-0.02509261481463909,
0.01904834620654583,
0.021921006962656975,
-0.0032917733769863844,
0.031338728964328766,
-0.0003499801969155669,
0.0055755251087248325,
-0.004188064485788345,
-0.004464165307581425,
0.03885948657989502,
-0.01310795359313488,
0.02420945279300213,
0.01847301982343197,
-0.0045593720860779285,
-0.0013142843963578343,
-0.0019910521805286407,
-0.0029891198500990868,
-0.006328070070594549,
0.021341796964406967,
0.0019770555663853884,
0.0010700924322009087,
-0.005952295381575823,
0.016542496159672737,
-0.048242826014757156,
0.04568580165505409,
-0.05944780260324478,
-0.02078578993678093,
0.0013488703407347202,
0.038613878190517426,
-0.002726530423387885,
-0.022341452538967133
] |
<p>Can thermal radiation from a cooler object (B, which emits longer wavelength radiation) ever ADD to the overall thermal energy level of a warmer object (A, which emits shorter wavelength radiation)? Subsidiary question: What exactly happens - at the molecular level - to the longer wavelength radiation from B as it arrives at A?</p>
| 9,369 |
[
-0.015800775960087776,
-0.02606016770005226,
-0.010725057683885098,
0.014041755348443985,
0.030332669615745544,
0.0576370432972908,
-0.02064877562224865,
-0.020513320341706276,
0.021295607089996338,
-0.06231481954455376,
0.03493449091911316,
0.037095677107572556,
0.022120976820588112,
-0.020462514832615852,
0.004926721099764109,
-0.0006273713079281151,
-0.01364086102694273,
-0.007380897644907236,
0.014744549058377743,
0.008365487679839134,
-0.0033242059871554375,
0.04705817252397537,
0.028399169445037842,
-0.002037295838817954,
-0.052476610988378525,
0.017242327332496643,
0.016108663752675056,
-0.010322264395654202,
0.04429108276963234,
0.017721466720104218,
0.011722886934876442,
-0.0025006914511322975,
-0.0069144354201853275,
0.04768718034029007,
0.023206431418657303,
-0.022480783984065056,
-0.03194670006632805,
-0.003852947847917676,
-0.026605168357491493,
0.020263565704226494,
-0.018697945401072502,
-0.026025013998150826,
-0.017050674185156822,
0.05535424128174782,
-0.007741963490843773,
-0.02637667953968048,
-0.015567781403660774,
-0.03925575688481331,
0.04835610091686249,
-0.048261359333992004,
0.058498017489910126,
-0.0017015732591971755,
0.0344504751265049,
0.03130214288830757,
-0.037959225475788116,
0.019955074414610863,
0.08317024260759354,
0.08025597780942917,
-0.035110823810100555,
0.00005877106013940647,
0.011547593399882317,
0.002083615632727742,
-0.01313862856477499,
0.029320860281586647,
-0.03772297129034996,
0.011377576738595963,
-0.028879893943667412,
-0.02946447767317295,
0.03007388487458229,
0.04738839715719223,
0.02124200202524662,
-0.012866852805018425,
0.05631300061941147,
-0.009589825756847858,
0.018665961921215057,
-0.006137083750218153,
0.010936171747744083,
0.03876100480556488,
0.0614643432199955,
0.03793228790163994,
-0.0075833359733223915,
-0.00917419046163559,
0.03614728897809982,
0.03528719022870064,
0.020605100318789482,
0.03125026077032089,
0.06024050712585449,
-0.028853895142674446,
0.008165299892425537,
0.02840198203921318,
-0.008864467032253742,
0.022767553105950356,
0.013091144151985645,
0.018852155655622482,
-0.006585610564798117,
0.021330146118998528,
-0.020291676744818687,
0.04506656527519226,
0.01900317892432213,
-0.034707069396972656,
0.03591548278927803,
0.01500951498746872,
0.023114550858736038,
0.05560869351029396,
0.0033073362428694963,
-0.04905357584357262,
-0.03898908942937851,
0.024278756231069565,
-0.013844117522239685,
0.0001013712608255446,
-0.04459422454237938,
-0.0111945616081357,
-0.030645063146948814,
-0.014794760383665562,
0.0012681708903983235,
-0.03476059436798096,
-0.007375463377684355,
-0.004448482766747475,
0.044238314032554626,
0.020532578229904175,
0.04177146777510643,
-0.009281736798584461,
0.019807660952210426,
0.027839012444019318,
-0.037192631512880325,
0.00476416852325201,
0.018180111423134804,
-0.013301254250109196,
-0.049517009407281876,
0.025116944685578346,
-0.017054375261068344,
-0.02058718353509903,
0.011494229547679424,
-0.06232002377510071,
0.002956539625301957,
-0.016904639080166817,
-0.05996040627360344,
-0.05435854196548462,
0.025450579822063446,
-0.009929140098392963,
-0.013972270302474499,
-0.07016715407371521,
-0.011346681974828243,
0.0214836485683918,
0.09066695719957352,
-0.011207176372408867,
-0.007579737342894077,
-0.03636340796947479,
0.04814750328660011,
-0.01230374164879322,
0.019025258719921112,
-0.03919165953993797,
0.012128572911024094,
-0.04990645498037338,
0.009481813758611679,
-0.05954711511731148,
0.014489715918898582,
0.05749528855085373,
0.005122071132063866,
0.0038403042126446962,
0.05042984336614609,
-0.04231385886669159,
0.015719735994935036,
0.03972022980451584,
0.041361093521118164,
-0.033710651099681854,
0.07672383636236191,
0.028067516162991524,
-0.016724953427910805,
0.02098117209970951,
0.03163135424256325,
0.011620870791375637,
-0.03386026620864868,
0.015053858980536461,
0.018029088154435158,
-0.03674038127064705,
-0.011766193434596062,
-0.014076449908316135,
0.016577014699578285,
0.014969797804951668,
-0.05161609873175621,
-0.020007528364658356,
-0.007029054686427116,
-0.021559786051511765,
0.013838130980730057,
0.03782551363110542,
0.003111371072009206,
-0.0019699260592460632,
0.006654089782387018,
-0.06164906919002533,
0.012397521175444126,
-0.04992743954062462,
0.011081023141741753,
-0.007041852921247482,
-0.016386626288294792,
0.023703357204794884,
0.024017609655857086,
0.04040636122226715,
-0.021043822169303894,
-0.049869559705257416,
0.021080080419778824,
0.0306340791285038,
-0.005166724789887667,
0.0015130332903936505,
0.02758270688354969,
0.07034581899642944,
0.06653868407011032,
0.017830681055784225,
0.021748874336481094,
-0.0410102903842926,
-0.07606743276119232,
0.0022939809132367373,
-0.03540496900677681,
0.02907988242805004,
-0.00703798932954669,
0.014938222244381905,
-0.011047251522541046,
-0.00836082361638546,
-0.005877479910850525,
0.02969011664390564,
-0.030388733372092247,
0.05293295159935951,
0.02965620346367359,
0.0243716798722744,
-0.03370741382241249,
0.06757700443267822,
0.049275729805231094,
-0.0045211114920675755,
-0.03539498150348663,
-0.049160394817590714,
-0.046157535165548325,
0.012871594168245792,
0.03433745726943016,
0.022667929530143738,
-0.07731470465660095,
-0.02466546557843685,
0.02708345092833042,
0.032642852514982224,
0.01583033800125122,
0.03286708891391754,
-0.00888596847653389,
-0.009714209474623203,
0.02870527096092701,
0.013677703216671944,
0.041562769562006,
0.026387866586446762,
0.041690435260534286,
0.01289636641740799,
0.013331041671335697,
0.020012974739074707,
-0.0233001746237278,
0.027914784848690033,
0.029239675030112267,
0.0265007596462965,
-0.0006307659787125885,
-0.005188762675970793,
0.017655301839113235,
-0.054354310035705566,
0.02692788653075695,
0.0002224924974143505,
-0.0013019643956795335,
-0.013670885935425758,
-0.009694544598460197,
-0.04016631096601486,
0.0013964810641482472,
0.0039067878387868404,
-0.015658920630812645,
0.01928693801164627,
0.02964910864830017,
-0.021803583949804306,
0.02343219518661499,
-0.0253108162432909,
0.017995215952396393,
-0.011747980490326881,
-0.01170813012868166,
-0.008024999871850014,
0.007822681218385696,
0.06345763802528381,
-0.071197509765625,
-0.06425242125988007,
-0.051977548748254776,
-0.05019725486636162,
-0.03381072357296944,
0.008385270833969116,
-0.027259986847639084,
0.03680577874183655,
-0.029494166374206543,
-0.020398344844579697,
0.02181096374988556,
-0.04302003234624863,
0.0009791970951482654,
0.0363132543861866,
-0.002795035019516945,
-0.056154754012823105,
-0.007077974267303944,
0.0076103596948087215,
0.008516980335116386,
-0.03144838660955429,
0.013162543065845966,
0.03418752923607826,
-0.049225322902202606,
-0.01464098785072565,
0.008736337535083294,
-0.04070490226149559,
-0.02035982720553875,
-0.006292805541306734,
-0.04852285236120224,
0.008189532905817032,
0.004963390063494444,
0.017931507900357246,
-0.0029769837856292725,
-0.05517533794045448,
-0.005292622372508049,
-0.02450069785118103,
-0.04814779385924339,
0.04880942776799202,
0.00580550916492939,
0.0241558775305748,
-0.03466982766985893,
0.005877864081412554,
0.02833372913300991,
0.014494339004158974,
-0.01877487078309059,
-0.011543141677975655,
0.0008850001613609493,
0.012153202667832375,
-0.006113456096500158,
0.020217623561620712,
0.0032738300506025553,
-0.0013219924876466393,
0.028878867626190186,
0.060758836567401886,
0.00945405475795269,
0.050257083028554916,
0.005473404191434383,
-0.04621952027082443,
0.02116570435464382,
0.028199657797813416,
0.04274902865290642,
0.03905580937862396,
-0.006650081370025873,
-0.033648572862148285,
0.030483689159154892,
-0.017900682985782623,
0.03467261418700218,
0.023252161219716072,
-0.03985815867781639,
0.04836444929242134,
0.020823806524276733,
0.009066116996109486,
-0.05720267444849014,
0.06888271868228912,
0.014353877864778042,
0.04658941179513931,
0.0035810270346701145,
0.05801789462566376,
0.06683400273323059,
-0.015306235291063786,
0.0009055688860826194,
0.029970260336995125,
0.05840703099966049,
-0.008621362037956715,
-0.022056130692362785,
0.024026017636060715,
0.002587985247373581,
-0.005799807142466307,
0.020892351865768433,
-0.019920917227864265,
0.021857203915715218,
0.018322374671697617,
0.016110511496663094,
0.039009734988212585,
-0.03792281448841095,
0.027810432016849518,
-0.05066492035984993,
-0.025221973657608032,
-0.023983946070075035,
0.03678343817591667,
-0.012462413869798183,
0.07405589520931244,
-0.003983671311289072,
0.03274807333946228,
0.05651401728391647,
-0.0037077823653817177,
-0.08082792907953262,
0.02902699075639248,
-0.040345679968595505,
-0.025382623076438904,
-0.02369024232029915,
-0.01640637405216694,
-0.027035556733608246,
-0.0533633716404438,
-0.01760253496468067,
-0.001208546687848866,
-0.008340433239936829,
-0.029465574771165848,
0.00002594685611256864,
-0.03451485559344292,
-0.07805465161800385,
0.004194652196019888,
0.022745203226804733,
0.019304845482110977,
-0.04818561300635338,
0.028623690828680992,
0.05376021936535835,
-0.015091078355908394,
-0.0037130420096218586,
-0.04728139564394951,
0.01673448644578457,
-0.026206977665424347,
0.03727473318576813,
0.018814759328961372,
0.04031693562865257,
-0.04177657887339592,
0.024523133412003517,
0.02490733005106449,
0.006704297848045826,
0.003284172620624304,
-0.04684356227517128,
-0.04363567382097244,
-0.054539117962121964,
-0.013541403226554394,
0.00040008730138652027,
0.049702297896146774,
-0.019646018743515015,
0.010850191116333008,
-0.0018052831292152405,
-0.003910185303539038,
-0.010698320344090462,
0.014295408502221107,
0.023869097232818604,
-0.007264742162078619,
-0.022908268496394157,
-0.023459602147340775,
-0.023825334385037422,
-0.013072957284748554,
0.008282848633825779,
0.04269980266690254,
-0.01718851365149021,
-0.005772127769887447,
0.009930509142577648,
-0.0011576502583920956,
0.010399512015283108,
-0.004195638932287693,
-0.022128935903310776,
0.014530844986438751,
0.012551405467092991,
-0.0035539334639906883,
-0.0022172117605805397,
-0.003631188999861479,
0.0334799624979496,
0.02682003378868103,
-0.018621381372213364,
0.006190205458551645,
-0.08466735482215881,
-0.016000255942344666,
0.04199352115392685,
0.018363839015364647,
-0.014865225180983543,
0.015271313488483429,
-0.02981785126030445,
-0.010652869008481503,
0.03805560991168022,
0.01593475416302681,
0.049086734652519226,
-0.024720611050724983,
-0.012325865216553211,
-0.01729840785264969,
-0.04281220585107803,
0.01552553940564394,
0.018964847549796104,
0.004867020528763533,
-0.003901519114151597,
-0.012810863554477692,
-0.03166567534208298,
0.030457105487585068,
0.02998974733054638,
0.058829620480537415,
0.009519338607788086,
-0.01873043179512024,
-0.025098981335759163,
-0.011262604966759682,
0.013122799806296825,
0.002877887338399887,
-0.0565594844520092,
-0.0308856088668108,
0.021148933097720146,
-0.042398594319820404,
0.06375285238027573,
-0.051730018109083176,
0.014904976822435856,
0.036980774253606796,
0.023402294144034386,
-0.02989034913480282,
-0.01850498653948307,
-0.029704928398132324,
0.07241445034742355,
0.026096539571881294,
-0.027728544548153877,
0.07438420504331589,
0.04119414463639259,
-0.009728373028337955,
0.003081517992541194,
-0.02044813707470894,
0.07046080380678177,
-0.03532852232456207,
-0.015981730073690414,
-0.014676028862595558,
-0.035265129059553146,
-0.014963232912123203,
0.05065371096134186,
-0.011565683409571648,
-0.02618465945124626,
-0.0010097139747813344,
-0.043635375797748566,
-0.0077324979938566685,
0.01821601577103138,
-0.0393708162009716,
0.002258123829960823,
-0.006341820117086172,
0.049707382917404175,
-0.02408693917095661,
-0.022134114056825638,
0.03716985136270523,
-0.00014908287266734987,
-0.032140713185071945,
0.00775120547041297,
-0.0483795590698719,
0.051697857677936554,
-0.030317522585392,
0.0032338679302483797,
0.0008183522149920464,
-0.01649034209549427,
0.00539811234921217,
-0.012517968192696571,
0.011063271202147007,
0.026329459622502327,
-0.07552134245634079,
0.015201522037386894,
-0.0024961766321212053,
-0.003493818687275052,
0.0062375497072935104,
-0.029510438442230225,
0.045962098985910416,
0.012981166131794453,
0.01376221515238285,
-0.05967935174703598,
0.014317231252789497,
-0.006417313124984503,
0.057212114334106445,
0.02454773336648941,
-0.05558950826525688,
-0.007336154114454985,
-0.06190117448568344,
-0.023085635155439377,
0.009952650405466557,
0.03497257083654404,
-0.007674032356590033,
-0.006308256648480892,
0.008287751115858555,
0.011163230054080486,
0.0015013589290902019,
-0.029438260942697525,
-0.017464198172092438,
0.015808051452040672,
-0.01182525884360075,
-0.03234086185693741,
-0.001207015011459589,
0.05953231826424599,
-0.011213020421564579,
-0.012924600392580032,
0.02989255264401436,
-0.0018393259961158037,
0.04157719388604164,
-0.01133816596120596,
-0.06215351074934006,
0.06267023831605911,
0.023929376155138016,
0.017778942361474037,
-0.022417303174734116,
0.01786229945719242,
-0.011496859602630138,
0.01586322858929634,
-0.004666708875447512,
-0.010919388383626938,
-0.0035066616255789995,
-0.05251319706439972,
-0.0073027703911066055,
0.017462942749261856,
0.01110090035945177,
0.01708347722887993,
0.08911111205816269,
-0.0367639884352684,
0.006612616125494242,
-0.0013326199259608984,
-0.011070845648646355,
0.008509716019034386,
-0.03929022699594498,
0.02550455369055271,
0.008702698163688183,
0.008312620222568512,
-0.0059240153059363365,
-0.03251156955957413,
-0.030170472338795662,
-0.033499300479888916,
0.05801837891340256,
-0.037236377596855164,
0.03984573855996132,
0.009846674278378487,
0.010182210244238377,
0.01770853064954281,
-0.06057451292872429,
-0.01172581221908331,
0.0014245336642488837,
-0.036345914006233215,
0.01658063940703869,
-0.02437550202012062,
0.004077437333762646,
0.03899956867098808,
0.05279531702399254,
-0.01558349933475256,
0.04190533980727196,
0.0004803257470484823,
0.019085252657532692,
-0.02409394271671772,
-0.013023242354393005,
-0.0598660446703434,
0.024758245795965195,
-0.04763093218207359,
0.017888527363538742,
-0.02034558355808258,
-0.00831623375415802,
0.010544277727603912,
0.020590251311659813,
0.03516537696123123,
-0.08170250803232193,
-0.024954617023468018,
-0.04229108244180679,
0.0308372862637043,
-0.008055469952523708,
0.05141881853342056,
0.035027533769607544,
-0.0020142628345638514,
0.01275565754622221,
0.00419339444488287,
-0.026671219617128372,
-0.021331552416086197,
-0.04888239875435829,
-0.0486551932990551,
-0.013357342220842838,
-0.046911559998989105,
0.03673354908823967,
-0.00917741283774376,
-0.025332288816571236,
0.020468443632125854,
-0.014484184794127941,
-0.0027429971378296614,
-0.004804241005331278,
0.04443792626261711,
0.04007839411497116,
0.05497080460190773,
0.0024178861640393734,
0.021354902535676956,
-0.010348338633775711,
0.03969607874751091,
0.1002202033996582,
0.03690226748585701,
0.01219660509377718,
-0.05219302698969841,
0.012470041401684284,
2.711833531066077e-7,
-0.022326495498418808,
-0.04054052010178566,
-0.004409737419337034,
-0.01898113265633583,
0.03134666010737419,
0.015866439789533615,
0.07667407393455505,
-0.019359350204467773,
-0.009538956917822361,
0.02986081875860691,
-0.020594097673892975,
0.008397145196795464,
0.03484698757529259,
-0.011761552654206753,
0.030039876699447632,
0.01919291354715824,
-0.04373219609260559,
-0.056758955121040344,
-0.03472088649868965,
0.008124977350234985,
-0.03326159715652466,
-0.01061897911131382,
0.039924729615449905,
-0.024914033710956573,
-0.05816800892353058,
0.02320963703095913,
0.014866438694298267,
0.021603772416710854,
-0.022846030071377754,
0.03031538799405098,
0.053599465638399124,
0.008161459118127823,
-0.012120057828724384,
0.025810841470956802,
0.05115751549601555,
0.015201399102807045,
0.01165379025042057,
0.020976999774575233,
0.0020146293099969625,
0.0036120994482189417,
0.00663772551342845,
0.009863064624369144,
-0.019766366109251976,
0.01661820523440838,
-0.022123869508504868,
-0.003803044790402055,
0.0020961202681064606,
-0.015150434337556362,
0.00543822068721056,
0.01532199326902628,
0.0250385869294405,
-0.02340422198176384,
-0.047285955399274826,
-0.009227663278579712,
0.060639407485723495,
0.0019453127169981599,
0.025634905323386192,
0.028856396675109863,
-0.0031731382478028536,
0.016623480245471,
0.0037197116762399673,
0.06162262707948685,
-0.017357373610138893,
-0.045799482613801956,
-0.03532401844859123,
-0.02484634704887867,
-0.008393103256821632,
-0.04891718924045563,
-0.010601279325783253,
0.0369914174079895,
0.03238407149910927,
0.007005533203482628,
-0.00666547566652298,
-0.052722640335559845,
-0.06275328993797302,
-0.031102502718567848,
0.005224384367465973,
-0.020893823355436325,
0.01923992857336998,
0.007137433160096407,
0.061187226325273514,
0.013753886334598064,
-0.023265721276402473,
0.01179983839392662,
-0.014004521071910858,
0.02411876805126667,
0.03372859209775925,
-0.02367442473769188,
-0.01895078644156456,
0.006505163386464119,
-0.024211887270212173,
-0.00559144327417016,
0.0027268030680716038,
0.026136407628655434,
0.011036507785320282,
-0.0035692784003913403,
0.0017939847894012928,
-0.0022917287424206734,
-0.05495626851916313,
0.02327672950923443,
0.02682427689433098,
-0.017775187268853188,
-0.012266693636775017,
-0.005381905473768711,
-0.025886494666337967,
-0.004811291117221117,
-0.035966016352176666,
-0.010252883657813072,
-0.0065839518792927265,
0.010095043107867241,
-0.000032686359190847725,
-0.025381626561284065,
0.034990131855010986,
-0.009108856320381165,
0.019564250484108925,
-0.03292078152298927,
-0.03147780895233154,
-0.04813472554087639,
-0.015249460935592651,
0.011183932423591614,
-0.028484368696808815,
0.005716007202863693,
0.02265835553407669,
-0.047972891479730606,
-0.031661637127399445,
0.026286428794264793,
0.061878502368927,
0.005846393760293722,
-0.0373709574341774,
0.00814676471054554,
-0.009019745513796806,
0.07417137920856476,
-0.00627494789659977,
-0.05040976405143738,
0.04748242348432541,
-0.05093136057257652,
-0.019411293789744377,
0.04239197075366974,
-0.004827647469937801,
0.03694061562418938,
0.014785981737077236,
0.002685573184862733,
-0.013799215666949749,
0.06473099440336227,
0.02229307033121586,
-0.01021629013121128,
0.01642804592847824,
-0.02059227228164673,
0.00352180702611804,
-0.004860286600887775,
0.021146604791283607,
-0.02823818288743496,
-0.012256556190550327,
0.06330004334449768,
0.014907865785062313,
-0.022065263241529465,
-0.015058262273669243,
-0.010861462913453579,
-0.03204476460814476,
0.0020461876410990953,
0.022141218185424805,
0.012486225925385952,
0.042883407324552536,
0.042767483741045,
-0.025484587997198105,
0.04590776190161705,
0.04713355749845505,
-0.014959845691919327,
-0.09925374388694763,
0.0177500881254673,
0.0028687044978141785,
-0.010221161879599094,
0.0031896396540105343,
-0.055809810757637024,
0.05222455412149429,
0.016610711812973022,
-0.07439428567886353,
0.01107309851795435,
-0.01864631660282612,
0.016248708590865135,
-0.024132458493113518,
0.015061945654451847,
-0.014270446263253689,
0.003377637593075633,
0.03304527327418327,
0.06283733993768692,
0.0040483660995960236,
0.0031376942060887814,
-0.018969321623444557,
-0.05560776963829994,
-0.008622180670499802,
0.012771333567798138,
0.005227277521044016,
-0.018144240602850914,
0.060406263917684555,
-0.0011835680343210697,
-0.006200650241225958,
-0.002760770032182336,
-0.0364975742995739,
0.0163105521351099,
-0.017275821417570114,
-0.021263228729367256,
0.0044927289709448814,
-0.014932971447706223,
-0.006559100467711687,
-0.011780600994825363,
-0.01028946042060852,
0.03620758280158043,
0.0318521149456501,
0.0148277273401618,
-0.007718733977526426,
-0.0006213656160980463,
0.02505599893629551,
-0.04806116595864296,
-0.027558306232094765,
0.04806893318891525,
0.006574742030352354,
-0.020806612446904182,
0.01629437506198883,
0.01759420707821846,
0.05857669189572334,
-0.010477952659130096,
-0.011862981133162975,
-0.07120400667190552,
-0.047018952667713165,
0.007228628732264042,
0.02086125686764717,
-0.012389900162816048,
-0.02281622402369976,
0.016514956951141357,
0.010028939694166183,
0.00733077060431242,
-0.006095763761550188,
0.024041390046477318,
-0.039702437818050385,
0.0040445649065077305,
-0.01985146850347519,
-0.016211776062846184,
-0.04317139461636543,
-0.05300070717930794,
-0.08320487290620804,
0.03375183790922165,
-0.03700760379433632,
0.03543024882674217,
-0.01979254186153412,
-0.05666840076446533,
-0.04736081883311272,
-0.06375226378440857,
0.02478453516960144,
-0.040441498160362244,
0.03217234089970589,
-0.053877294063568115,
-0.0006247917772270739,
-0.013049580156803131,
-0.0006414461531676352,
0.06263802200555801,
0.015014863573014736,
-0.02453600987792015,
0.03198980540037155,
0.008207058534026146,
0.03231092914938927,
-0.046057406812906265,
0.025959771126508713,
0.007012122310698032,
-0.016507133841514587,
-0.03225991502404213,
-0.026705730706453323,
-0.024542149156332016,
0.009943518787622452,
0.0013820481253787875,
0.004648922942578793,
0.04714461788535118,
-0.015701910480856895,
-0.0018372974591329694,
0.07268976420164108,
0.01594022661447525,
-0.02079782634973526,
0.032640647143125534,
0.01583287864923477,
0.02993837557733059,
0.04293620586395264,
-0.001830880530178547,
-0.04388773441314697,
0.009158778004348278,
-0.017893251031637192,
0.006705342326313257,
-0.021528948098421097,
-0.014001070521771908,
0.0017043474363163114,
-0.04220179468393326,
-0.007969432510435581,
0.029016463086009026,
-0.04183994233608246,
-0.006944444961845875,
0.033812448382377625,
0.0029921382665634155,
0.008004828356206417,
0.002312153810635209,
0.010449264198541641,
0.003278238233178854,
0.031073838472366333,
-0.04384647682309151,
0.04892366752028465,
0.012439371086657047,
0.007463815622031689,
0.018168693408370018,
0.006889805197715759,
-0.0017085790168493986,
-0.004028818570077419,
-0.00620916998013854,
-0.0024961447343230247,
-0.02244407683610916,
-0.041754309087991714,
0.033337756991386414,
0.044573668390512466,
0.00334722176194191,
0.040298011153936386,
-0.0028033447451889515,
0.038884662091732025,
-0.028806278482079506,
0.016822006553411484,
-0.04806901887059212,
0.008134535513818264,
0.015639696270227432,
0.02923573926091194,
0.009486800990998745,
0.024223696440458298,
0.009219028986990452,
-0.003755010198801756,
-0.018116310238838196,
-0.017304951325058937,
0.023151330649852753,
-0.0571121871471405,
0.021707966923713684,
-0.01856641285121441,
-0.0030049672350287437,
-0.03121141716837883,
0.009048081003129482,
-0.017575953155755997,
-0.018312744796276093,
0.026532139629125595,
0.08519283682107925,
-0.0007938979542814195,
0.046572502702474594,
-0.011088630184531212,
-0.010435439646244049,
0.0390072762966156,
-0.07096726447343826,
-0.01405434962362051,
-0.005888443905860186,
0.02901141345500946,
-0.02895001694560051,
-0.01672912947833538
] |
<p>I have found from <a href="http://en.wikipedia.org/wiki/Parity_%28physics%29" rel="nofollow">Wikipedia</a> that
"a parity transformation is the flip in the sign of spatial coordinates".</p>
<p>Now when we operate parity operator, does that mean we are taking any physical entity at ${\bf x}$ to $-{\bf x}$. Or we are just reverting axes of the co-ordinate system?</p>
<p>However if we take parity transformation as active transformation then what does it mean that parity of <a href="http://en.wikipedia.org/wiki/Proton" rel="nofollow">proton</a> is 1? Doesn't it anyway depend on the <strong>origin</strong> of the co-ordinate system? </p>
<p>Please elucidate the meaning of the parity. I get too much confused whenever I hear "parity"!</p>
| 9,370 |
[
0.006595082115381956,
0.012172134593129158,
-0.05270032584667206,
0.0013557968195527792,
0.04564394801855087,
0.06894278526306152,
-0.028996145352721214,
-0.015629617497324944,
0.0013129691360518336,
-0.043158408254384995,
0.05177655443549156,
0.010520143434405327,
0.053352583199739456,
0.01887846738100052,
0.017999155446887016,
0.033913321793079376,
0.02793445996940136,
0.007935551926493645,
-0.009749424643814564,
-0.01469773706048727,
0.03309517726302147,
-0.013393794186413288,
0.008474836125969887,
0.030513321980834007,
0.01017619576305151,
0.03508978709578514,
-0.0026935285422950983,
0.007522066123783588,
0.017790349200367928,
0.05344057455658913,
-0.0009238209458999336,
-0.021065734326839447,
0.018351126462221146,
-0.004950366448611021,
0.010228915140032768,
-0.020480643957853317,
0.0038503026589751244,
-0.04686576873064041,
0.017575012519955635,
0.03193270415067673,
-0.037865251302719116,
-0.04246068745851517,
-0.027355840429663658,
0.06492367386817932,
-0.01836196519434452,
-0.018564123660326004,
-0.013906036503612995,
-0.006776927039027214,
0.05182316526770592,
-0.045418672263622284,
0.09106246381998062,
0.0029260204173624516,
0.012779591605067253,
-0.001801552134566009,
-0.034571632742881775,
0.005303225480020046,
0.07809070497751236,
0.02413593977689743,
-0.014099576510488987,
-0.07362011075019836,
-0.0070839994587004185,
-0.033365607261657715,
0.009469752199947834,
-0.011158924549818039,
-0.01981763169169426,
0.013832722790539265,
0.008436707779765129,
-0.019000928848981857,
0.03459304943680763,
0.009905887767672539,
-0.005362784024327993,
0.014131124131381512,
0.007886922918260098,
-0.045195322483778,
0.007888625375926495,
-0.02591646835207939,
0.03505387529730797,
-0.0010369644733145833,
0.025632131844758987,
0.0429704524576664,
-0.016288533806800842,
0.010665570385754108,
0.0017779308836907148,
0.02836383320391178,
-0.011298240162432194,
-0.012543043121695518,
0.044443607330322266,
-0.028310175985097885,
0.023111572489142418,
0.026580646634101868,
-0.0013884089421480894,
0.0012727528810501099,
0.003948134370148182,
0.014375130645930767,
0.0017973295180127025,
0.047728344798088074,
0.013619685545563698,
0.04285379871726036,
0.002442675642669201,
-0.007461718749254942,
0.01205604150891304,
-0.014859970659017563,
0.0062507265247404575,
0.0565408393740654,
-0.0017269839299842715,
0.023746032267808914,
-0.04215450584888458,
0.00877942331135273,
-0.03958558291196823,
-0.007611927110701799,
-0.016980111598968506,
-0.012068691663444042,
-0.008809891529381275,
0.02435733564198017,
0.020973267033696175,
-0.05902871862053871,
-0.02054511196911335,
-0.004383270628750324,
0.0431012399494648,
0.057753100991249084,
0.05401012673974037,
-0.029583672061562538,
0.02623426541686058,
-0.006406932137906551,
-0.07381939142942429,
-0.018781138584017754,
0.040237538516521454,
0.009037121199071407,
-0.03475937992334366,
0.044646698981523514,
0.030064448714256287,
-0.01566193625330925,
0.004573797807097435,
-0.0312263872474432,
0.03034200891852379,
-0.006636379286646843,
-0.12486803531646729,
-0.059459079056978226,
0.03466233238577843,
0.005340522155165672,
-0.023820433765649796,
-0.07694932818412781,
0.022609243169426918,
0.0363459438085556,
0.060771383345127106,
-0.03446035459637642,
-0.006669602356851101,
0.027457498013973236,
0.010407663881778717,
0.021134741604328156,
-0.022726161405444145,
0.001965952105820179,
-0.022568441927433014,
-0.05035398155450821,
-0.022660309448838234,
-0.07720604538917542,
0.023725463077425957,
0.02992113307118416,
0.007545050233602524,
-0.03221646696329117,
0.07197068631649017,
-0.03447733819484711,
0.014570322819054127,
0.03945013880729675,
-0.03351084887981415,
-0.004896207712590694,
0.0891975685954094,
0.046185173094272614,
0.02088013105094433,
0.04916854575276375,
0.000031312869396060705,
0.02144831046462059,
-0.011881161481142044,
0.05156823620200157,
0.04485458880662918,
-0.028040094301104546,
-0.03336566686630249,
-0.019773636013269424,
-0.026509162038564682,
-0.0073090349324047565,
-0.07707115262746811,
-0.025176288560032845,
-0.025919372215867043,
0.006022458430379629,
-0.025176072493195534,
0.04147598519921303,
-0.03430871292948723,
-0.022055843845009804,
0.013826913200318813,
-0.05040457472205162,
-0.020895831286907196,
-0.09179868549108505,
0.013775947503745556,
0.008704974316060543,
0.0051397294737398624,
0.04141891375184059,
0.016750920563936234,
0.018510108813643456,
-0.020728159695863724,
-0.011088231578469276,
-0.03557955101132393,
0.03078112192451954,
-0.006119732744991779,
-0.02950288914144039,
0.008312682621181011,
0.05752398818731308,
0.014080079272389412,
-0.0035308862570673227,
-0.009372908622026443,
-0.011222973465919495,
-0.0015880262944847345,
0.02294318750500679,
-0.021365199238061905,
0.008573135361075401,
-0.002915428252890706,
-0.05117782950401306,
-0.011811114847660065,
-0.008990374393761158,
-0.010582443326711655,
0.016106165945529938,
-0.04794158786535263,
0.06511829048395157,
0.04699234291911125,
-0.008043269626796246,
0.024695856496691704,
0.03859638422727585,
0.016264256089925766,
0.00595461018383503,
-0.0007069152779877186,
-0.028490234166383743,
-0.016789790242910385,
0.014149198308587074,
0.008706066757440567,
0.01622089371085167,
-0.009766492992639542,
0.02557404525578022,
0.02409113384783268,
0.024179983884096146,
0.03264014050364494,
-0.005363669712096453,
0.0018286723643541336,
-0.05224552005529404,
-0.013657042756676674,
-0.001379277789965272,
0.019213112071156502,
0.037871889770030975,
-0.0037326074671000242,
0.008404918946325779,
0.04216437414288521,
0.01834067888557911,
-0.010260235518217087,
0.016816958785057068,
-0.005508022848516703,
0.014563817530870438,
0.018914906308054924,
-0.04095280170440674,
0.053672779351472855,
-0.0006145578227005899,
0.036389827728271484,
0.00788107980042696,
-0.006410699337720871,
0.011304986663162708,
-0.0257725827395916,
0.0022172231692820787,
-0.02989603392779827,
0.014650236815214157,
-0.05112531781196594,
-0.012721052393317223,
0.0030111719388514757,
-0.03821690008044243,
0.02299392782151699,
-0.015681564807891846,
0.004778414499014616,
-0.008835003711283207,
-0.04988835006952286,
0.030512772500514984,
0.012728022411465645,
0.013550842180848122,
-0.007399571593850851,
-0.008082483895123005,
0.009576470591127872,
-0.029999347403645515,
0.014661021530628204,
0.03860754892230034,
-0.052659571170806885,
0.01696047931909561,
-0.06504371017217636,
0.0024407273158431053,
0.017291905358433723,
-0.0299913939088583,
0.00034950379631482065,
0.001645480515435338,
0.005378624889999628,
-0.0751684308052063,
-0.05330432578921318,
-0.05516558140516281,
0.03410237655043602,
-0.030277622863650322,
-0.0006965231150388718,
0.085049569606781,
0.001103730988688767,
-0.024858850985765457,
-0.0077744596637785435,
-0.049374889582395554,
-0.025450455024838448,
-0.012323285453021526,
-0.006821490358561277,
0.003918505273759365,
-0.013681494630873203,
0.004490226041525602,
0.041717253625392914,
-0.04418707638978958,
-0.0015616222517564893,
-0.04921992868185043,
-0.03394510969519615,
0.020031576976180077,
-0.032499682158231735,
0.04061228781938553,
-0.0006086421199142933,
-0.0511605478823185,
0.08375395089387894,
0.026723159477114677,
-0.03812948986887932,
-0.01066027581691742,
0.02467108890414238,
-0.018485603854060173,
-0.054679080843925476,
-0.006411316338926554,
0.015721431002020836,
0.02234760671854019,
0.035063665360212326,
0.002710303757339716,
0.06471460312604904,
0.016034746542572975,
0.03127025067806244,
-0.03826672583818436,
-0.011910713277757168,
-0.0156296044588089,
-0.014464805833995342,
0.01726432330906391,
0.0019479045877233148,
-0.03182859718799591,
0.006086444947868586,
-0.011006581597030163,
0.0078570656478405,
-0.000027211550332140177,
-0.03640856593847275,
0.06930320709943771,
0.002530141966417432,
0.0029315748251974583,
-0.011009978130459785,
0.049440979957580566,
0.009162683971226215,
0.014184359461069107,
0.0041807848028838634,
0.0255905669182539,
0.019956564530730247,
-0.031369246542453766,
-0.029395312070846558,
0.009251192212104797,
0.0481119304895401,
-0.004713795613497496,
-0.006788325496017933,
0.016731083393096924,
0.014277184382081032,
0.027775458991527557,
0.006993914023041725,
-0.011844024993479252,
0.04458589106798172,
0.025424903258681297,
0.01809784211218357,
0.03395704925060272,
-0.014606148935854435,
0.03017626330256462,
-0.024692317470908165,
0.030719587579369545,
0.050243131816387177,
0.02712119184434414,
-0.019621480256319046,
0.05696004629135132,
0.02553090639412403,
0.006948254071176052,
-0.008991019800305367,
-0.01730678416788578,
-0.06952474266290665,
0.041818730533123016,
-0.033520981669425964,
0.010246221907436848,
-0.028292162343859673,
-0.00329939229413867,
0.01569891721010208,
-0.033325981348752975,
-0.038148876279592514,
-0.03295649215579033,
0.016996001824736595,
-0.053115252405405045,
0.028325526043772697,
-0.01981133036315441,
-0.001492252224124968,
0.0002107773325406015,
0.057287946343421936,
0.06560970842838287,
-0.03485307842493057,
0.05099606141448021,
0.025970080867409706,
-0.04174300283193588,
0.007616933900862932,
-0.010377143509685993,
0.025883128866553307,
0.04382999241352081,
0.013413768261671066,
0.03758532181382179,
0.018263358622789383,
-0.034808773547410965,
0.029861846938729286,
0.019571028649806976,
0.06344916671514511,
0.015796029940247536,
-0.02427506446838379,
0.010792804881930351,
-0.025447741150856018,
-0.007797148544341326,
-0.015580110251903534,
0.029652617871761322,
0.012625710107386112,
0.020136110484600067,
0.023778462782502174,
0.00870166253298521,
-0.03556326776742935,
0.058771248906850815,
0.07825293391942978,
0.0040023853071033955,
-0.007605423219501972,
-0.08166719228029251,
-0.009457036852836609,
-0.0004954955074936152,
-0.026777595281600952,
0.02181893400847912,
-0.018637217581272125,
-0.04007455334067345,
-0.014045504853129387,
0.02798951417207718,
0.042161859571933746,
-0.01836569607257843,
0.004426099825650454,
-0.009729482233524323,
-0.0031439349986612797,
0.027128037065267563,
0.007038892712444067,
0.00032474068575538695,
0.036621320992708206,
0.02813408337533474,
-0.010353663936257362,
0.02220422588288784,
-0.07115396857261658,
0.006340046413242817,
0.032249536365270615,
0.03466958925127983,
-0.0052617802284657955,
-0.007006341125816107,
-0.04694313928484917,
-0.005924122873693705,
0.04239260405302048,
-0.0476219542324543,
0.036460451781749725,
-0.0032323964405804873,
0.01171963196247816,
0.023447034880518913,
-0.019028540700674057,
-0.019347600638866425,
0.03454063832759857,
0.00020756723824888468,
0.02179555594921112,
-0.029752619564533234,
0.025719143450260162,
-0.004964986816048622,
-0.008211642503738403,
-0.029272953048348427,
0.011502916924655437,
-0.01083022728562355,
0.0279604010283947,
-0.0038887225091457367,
0.05913856253027916,
0.0040276735089719296,
-0.10802652686834335,
0.017443407326936722,
0.03988950699567795,
0.0071058934554457664,
0.05852292850613594,
-0.004964765161275864,
-0.03990193456411362,
0.02060112915933132,
-0.014030405320227146,
0.009431229904294014,
-0.006449464242905378,
-0.0649084523320198,
0.06414873898029327,
0.03473539277911186,
-0.026379089802503586,
0.04534972831606865,
-0.010994496755301952,
-0.043113697320222855,
-0.03172960877418518,
0.008155057206749916,
0.005541412625461817,
-0.03396742790937424,
0.031388331204652786,
-0.03248930722475052,
0.02615550346672535,
-0.017696496099233627,
0.07096189260482788,
-0.023891063407063484,
0.03042076714336872,
0.013332807458937168,
0.0068642194382846355,
-0.04514274001121521,
0.04884382709860802,
-0.02673787996172905,
0.0023315681610256433,
-0.0206966083496809,
0.013443440198898315,
-0.03265029937028885,
-0.044909801334142685,
-0.008011146448552608,
-0.013108744286000729,
-0.022795332595705986,
0.0019837203435599804,
0.004479205701500177,
0.0145819541066885,
0.009854196570813656,
-0.03620368242263794,
-0.020634964108467102,
-0.051893189549446106,
0.008032330311834812,
-0.0230382289737463,
0.0009019675781019032,
0.025900986045598984,
-0.0906553566455841,
-0.05668402835726738,
0.030471274629235268,
-0.012038321234285831,
-0.024521896615624428,
-0.038463570177555084,
0.009279155172407627,
-0.0029047641437500715,
0.04440824314951897,
-0.04327357932925224,
-0.07953334599733353,
0.04566354304552078,
-0.005360265728086233,
-0.05369558557868004,
0.035625506192445755,
-0.003927661571651697,
0.005963498260825872,
-0.05467189848423004,
-0.027919117361307144,
0.027910888195037842,
-0.07340952008962631,
-0.021380342543125153,
0.04333421215415001,
0.012560252100229263,
0.030745545402169228,
-0.06319743394851685,
-0.02750849723815918,
0.027351802214980125,
0.014529278501868248,
-0.0046994551084935665,
-0.009356548078358173,
0.05560654401779175,
0.007951215840876102,
-0.059265926480293274,
-0.035765960812568665,
-0.017085686326026917,
0.005500533618032932,
-0.010227736085653305,
-0.013428072445094585,
0.012147823348641396,
0.01693728007376194,
-0.0239044688642025,
-0.004169415216892958,
-0.005759698338806629,
0.0045758807100355625,
0.025200054049491882,
0.007034775335341692,
0.019893281161785126,
-0.024668924510478973,
-0.03903169929981232,
0.03147653862833977,
0.018064336851239204,
-0.0013319423887878656,
0.03121035359799862,
0.017054272815585136,
-0.02343774028122425,
0.042311035096645355,
0.029506947845220566,
-0.010156400501728058,
0.02816879376769066,
0.03112887404859066,
0.009969336912035942,
-0.01220804825425148,
-0.018635770305991173,
-0.04234708100557327,
0.00025910636759363115,
-0.027474263682961464,
0.02208736166357994,
0.03670630604028702,
-0.007903574965894222,
0.04706308990716934,
0.001802045851945877,
0.0127485990524292,
-0.004047533962875605,
0.02338876761496067,
-0.0016409892123192549,
0.0017503246199339628,
-0.021485475823283195,
0.028048353269696236,
-0.02416740544140339,
-0.00013838897575624287,
0.03646404296159744,
0.08632180094718933,
-0.02483278699219227,
0.0007146007847040892,
0.02862158790230751,
0.007718427572399378,
0.004423476289957762,
-0.0020377689506858587,
-0.05800068750977516,
0.041260216385126114,
-0.02164197526872158,
0.0469699464738369,
-0.0022230728063732386,
-0.010332729667425156,
0.061880599707365036,
0.009422446601092815,
0.01971951127052307,
-0.06209106370806694,
-0.02588239312171936,
-0.0445685088634491,
-0.012260488234460354,
0.0036413914058357477,
-0.0029957210645079613,
-0.019336171448230743,
-0.013502364978194237,
0.050888530910015106,
-0.019799310714006424,
-0.007821150124073029,
-0.019295411184430122,
-0.06813682615756989,
-0.022892383858561516,
-0.027152160182595253,
-0.04276565462350845,
0.03740251809358597,
-0.04305488243699074,
0.0008784422534517944,
0.004330332390964031,
-0.023022111505270004,
0.018980707973241806,
0.0394570492208004,
0.03644384816288948,
-0.027070418000221252,
0.08069854229688644,
-0.008787653408944607,
0.003922032658010721,
-0.0038375905714929104,
-0.018427258357405663,
0.11246725916862488,
0.059901658445596695,
-0.008076216094195843,
-0.08095996081829071,
0.007334544789046049,
-0.04556655511260033,
0.03278609365224838,
-0.023716909810900688,
0.021146701648831367,
-0.004870451055467129,
0.024997150525450706,
-0.003249836154282093,
0.05294553562998772,
0.01329542975872755,
-0.02667127549648285,
0.04027731716632843,
-0.05843253806233406,
-0.06057647615671158,
0.004130437504500151,
0.03266989812254906,
-0.010906165465712547,
-0.0057813613675534725,
-0.033744484186172485,
0.01830303855240345,
-0.011153372935950756,
0.008978186175227165,
-0.029992185533046722,
-0.029861370101571083,
0.02767733298242092,
0.013238947838544846,
-0.022315669804811478,
-0.010485001839697361,
-0.017506614327430725,
-0.026098651811480522,
-0.073763906955719,
0.017135566100478172,
-0.009462239220738411,
-0.025114042684435844,
0.02466539666056633,
0.026622792705893517,
-0.004186111502349377,
-0.0026766846422106028,
0.033806320279836655,
0.008647060953080654,
-0.04084641486406326,
-0.009017067961394787,
-0.037422940135002136,
0.027150534093379974,
0.004755661357194185,
0.005192660726606846,
-0.03950130194425583,
0.01720033772289753,
0.012309893034398556,
-0.06214934587478638,
0.009619178250432014,
0.010590838268399239,
0.018145989626646042,
-0.011359957978129387,
-0.017504921182990074,
-0.01574118807911873,
-0.006942451000213623,
-0.020915871486067772,
0.022266343235969543,
-0.039830535650253296,
-0.00023993055219762027,
0.020444974303245544,
-0.010635733604431152,
0.05053084343671799,
-0.012757944874465466,
0.014880005270242691,
-0.03874586895108223,
0.02423882484436035,
-0.030141981318593025,
0.006994027178734541,
0.044948138296604156,
0.013360164128243923,
0.0410257987678051,
0.0175776407122612,
-0.0006578763131983578,
-0.010572087951004505,
-0.03433779999613762,
0.023495826870203018,
-0.018681935966014862,
-0.016498276963829994,
0.016146628186106682,
0.01379481889307499,
0.020828677341341972,
0.04949086904525757,
-0.016100207343697548,
-0.024392496794462204,
-0.01762741431593895,
0.016027046367526054,
0.03213614225387573,
-0.024420836940407753,
-0.055729325860738754,
0.030956659466028214,
-0.016534706577658653,
-0.04985620453953743,
-0.016028372570872307,
0.011460297740995884,
0.023719992488622665,
-0.007542547769844532,
-0.006096354685723782,
0.012141679413616657,
-0.012826980091631413,
-0.01881321333348751,
0.010745876468718052,
-0.015968535095453262,
0.010878993198275566,
0.0032499521039426327,
-0.030691305175423622,
-0.05417484790086746,
-0.028572827577590942,
0.02111157961189747,
-0.019796598702669144,
0.022398896515369415,
0.04763069748878479,
-0.006112753413617611,
0.00009742887050379068,
-0.0062835016287863255,
0.014973931945860386,
0.0041059209033846855,
-0.02628905326128006,
-0.021604647859930992,
0.02704552374780178,
0.024197787046432495,
-0.0007653131615370512,
0.0021753692999482155,
0.0464300774037838,
0.00662578921765089,
-0.03447851538658142,
0.0507795549929142,
0.01647016406059265,
-0.03146418184041977,
-0.00027270414284430444,
0.00919432658702135,
-0.006592458579689264,
0.03388163447380066,
-0.03709297254681587,
-0.034276414662599564,
0.036435309797525406,
-0.055597249418497086,
-0.022579865530133247,
0.0619182251393795,
0.0059473589062690735,
0.03212977945804596,
0.03274640068411827,
0.009392933920025826,
-0.03209025040268898,
0.06740785390138626,
0.0018357965163886547,
0.033184975385665894,
0.005742877721786499,
-0.003162214532494545,
-0.03231531009078026,
-0.0056505147367715836,
-0.0002562482259236276,
-0.02103159762918949,
-0.022205308079719543,
0.025817835703492165,
0.0223909392952919,
-0.04185066372156143,
0.0028133071027696133,
-0.0271876472979784,
0.02614711970090866,
-0.012178773060441017,
-0.005635955836623907,
0.016201069578528404,
-0.015367900021374226,
0.028688553720712662,
-0.020403549075126648,
0.030370138585567474,
0.03629273176193237,
0.004070411901921034,
-0.0809992104768753,
0.008404106833040714,
0.03189906105399132,
0.0031713698990643024,
0.026001421734690666,
-0.0702248141169548,
0.05175989121198654,
0.022122686728835106,
-0.05990009009838104,
0.011340457014739513,
-0.005553159397095442,
-0.014031517319381237,
-0.00788998045027256,
-0.019531410187482834,
-0.007768884766846895,
0.0979083776473999,
0.02721324935555458,
-0.0059049250558018684,
0.005402192939072847,
0.02042088657617569,
-0.016063779592514038,
-0.05987463518977165,
-0.013616213575005531,
0.010377602651715279,
-0.004341647494584322,
-0.03345833346247673,
0.06581651419401169,
-0.03638920933008194,
-0.049713682383298874,
0.031451135873794556,
-0.023230286315083504,
-0.03147312253713608,
0.01799064129590988,
0.02707679010927677,
-0.007334566675126553,
0.024671021848917007,
-0.0022615594789385796,
-0.011996746063232422,
-0.0334065780043602,
0.03641630709171295,
0.018083442002534866,
0.028662899509072304,
-0.014632618054747581,
-0.0009612013236619532,
-0.003702143905684352,
-0.04095862805843353,
-0.021821139380335808,
-0.006024393253028393,
-0.03109108656644821,
0.0010986484121531248,
0.008116792887449265,
-0.0059186420403420925,
-0.002730988897383213,
-0.01235884428024292,
0.013678274117410183,
-0.016102315858006477,
-0.0026980354450643063,
0.049495864659547806,
-0.023487180471420288,
0.0005737141473218799,
0.019178606569767,
-0.019496405497193336,
-0.030998650938272476,
0.08015754073858261,
-0.00756949745118618,
-0.016147524118423462,
-0.05332733690738678,
0.00006641830259468406,
0.026291215792298317,
0.0010998517973348498,
-0.009621509350836277,
0.0017201475566253066,
-0.05478005111217499,
0.039556629955768585,
0.022799676284193993,
0.041268300265073776,
-0.008355417288839817,
-0.02466844953596592,
-0.019311342388391495,
-0.06329119950532913,
0.0014951002085581422,
0.03193321451544762,
-0.0057662115432322025,
-0.01790648326277733,
-0.00849904678761959,
-0.04175521433353424,
-0.0029944356065243483,
0.03670555725693703,
0.01726817898452282,
-0.026181690394878387,
0.012351837009191513,
0.026044726371765137,
-0.011458716355264187,
-0.023291027173399925,
-0.013837363570928574,
0.012354506179690361,
-0.02339487336575985,
0.039215777069330215,
-0.029481660574674606,
-0.026902398094534874,
0.0412033312022686,
-0.021546803414821625,
-0.0020623193122446537,
0.050161369144916534,
-0.011069628410041332,
-0.019952822476625443,
0.04578441381454468,
0.00014513920177705586,
0.027687758207321167,
0.08013022691011429,
0.010648412629961967,
0.0034930561669170856,
0.029223641380667686,
-0.01058580819517374,
-0.013834632933139801,
-0.006194277200847864,
-0.05485043674707413,
0.008720838464796543,
-0.004580231383442879,
-0.002864748239517212,
0.03005135804414749,
-0.030535928905010223,
0.0058855172246694565,
0.03486360237002373,
-0.06013788282871246,
-0.02578967809677124,
0.06479117274284363,
0.04206591099500656,
-0.006979607976973057,
0.01881098374724388,
0.011364493519067764,
-0.00523721007630229,
0.007421263959258795,
0.053674280643463135,
0.04503089189529419,
0.03856482356786728,
0.024102654308080673,
0.030250225216150284,
0.0012242787051945925,
0.019343558698892593,
0.012057728134095669,
0.030837543308734894,
0.055293161422014236,
-0.012168223038315773,
0.03417545184493065,
0.016277575865387917,
-0.021219899877905846,
0.031813688576221466,
-0.006998452823609114,
-0.0038386161904782057,
0.061716869473457336,
-0.02852337248623371,
-0.010974211618304253,
-0.009983303025364876,
-0.0004832108679693192,
-0.0028439706657081842,
0.00919407606124878,
0.021563095971941948,
0.04058602452278137,
-0.026443887501955032,
-0.007383621297776699,
-0.03818201646208763,
0.006084450054913759,
0.0078705083578825,
-0.04529589042067528,
0.007307601626962423,
-0.0038855557795614004,
-0.014395627193152905,
0.01355766411870718,
-0.00406491057947278,
-0.013477369211614132,
-0.031013894826173782,
-0.03292691707611084,
0.006752487737685442,
0.058017656207084656,
0.008378778584301472,
-0.008198106661438942,
0.001510494272224605,
0.03138517215847969,
-0.05577629432082176,
-0.033631086349487305,
-0.019086381420493126,
-0.0023873248137533665,
-0.03898469731211662,
0.012798406183719635
] |
<p>Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, $\omega=i\frac{d}{dt}$ to go back?</p>
<p>I came across one source which claimed that the original PDE could only be recovered to a certain extent. An example given was the Dirac and Klein Gordon equations which both satisfy the same dispersion relation. But I didn't quite follow. </p>
<p>Example: I have a polynomial dispersion relation of the form $\omega^2+c^2k^2=1$. Can I automatically say that the underlying PDE is $\frac{d^2u(x,t)}{dt^2}+c^2\nabla^2u(x,t)+u(x,t)=0$? Or is there a subtlety I'm missing?</p>
<p>Thanks</p>
| 9,371 |
[
0.01601845771074295,
0.011913733556866646,
0.05135529860854149,
-0.03223821520805359,
0.0031672471668571234,
-0.012785772792994976,
-0.050114162266254425,
-0.0252517256885767,
0.02068410813808441,
-0.044718701392412186,
-0.006370831746608019,
0.011736443266272545,
0.07299015671014786,
-0.010459008626639843,
0.006390408147126436,
0.017550336197018623,
-0.022182954475283623,
0.011982251890003681,
0.005452045705169439,
-0.037089236080646515,
-0.0081016905605793,
0.00159902882296592,
-0.030910542234778404,
-0.009205076843500137,
-0.0223567932844162,
-0.012062613852322102,
0.018856223672628403,
-0.002362611470744014,
-0.014530007727444172,
0.06258232146501541,
-0.0035027607809752226,
0.008007580414414406,
-0.0036691250279545784,
0.038180626928806305,
0.01719171553850174,
0.036836884915828705,
-0.06151057779788971,
-0.05012503266334534,
0.025181246921420097,
0.020123464986681938,
-0.015166044235229492,
-0.019542185589671135,
0.014909986406564713,
0.04327297583222389,
-0.000053600397222908214,
0.017426228150725365,
0.0411352701485157,
-0.03205474838614464,
0.02331390604376793,
-0.042645085602998734,
0.06058882921934128,
-0.007964028045535088,
0.041079990565776825,
0.03166458010673523,
-0.020050283521413803,
0.0044864811934530735,
0.06500924378633499,
0.0843956395983696,
0.02652071975171566,
-0.05187661573290825,
-0.002658455166965723,
0.030529262498021126,
-0.009467095136642456,
0.005129659548401833,
-0.057008352130651474,
0.017372626811265945,
0.007266787812113762,
-0.02501729130744934,
0.013923965394496918,
-0.031154759228229523,
-0.004601186141371727,
-0.009958014823496342,
0.03766118735074997,
0.01456369087100029,
0.016251035034656525,
-0.015022103674709797,
0.000050518727221060544,
0.02797374501824379,
0.031216757372021675,
0.01125077623873949,
-0.013868104666471481,
0.01690778136253357,
-0.011050913482904434,
0.02824145182967186,
-0.02295318804681301,
0.010542909614741802,
0.05749835446476936,
-0.0040898676961660385,
0.037380799651145935,
0.010195164941251278,
-0.009840651415288448,
0.002214169828221202,
0.005569788161665201,
-0.02896944060921669,
-0.008374910801649094,
-0.009869622066617012,
0.016316089779138565,
0.025921249762177467,
0.012284583412110806,
-0.04430484026670456,
-0.023515677079558372,
-0.056223995983600616,
-0.015596531331539154,
0.04947890341281891,
-0.00276905857026577,
-0.009046455845236778,
-0.03427056223154068,
0.027098799124360085,
-0.044523730874061584,
-0.006568382494151592,
-0.027616698294878006,
0.02121419459581375,
0.01912836730480194,
-0.008017866872251034,
-0.008348391391336918,
-0.006186038721352816,
-0.03347514942288399,
-0.02685428410768509,
0.05903075635433197,
0.06491369754076004,
0.03133787214756012,
0.00005943069845670834,
0.03280028700828552,
-0.015108532272279263,
-0.07035133987665176,
-0.009356976486742496,
0.05085970088839531,
0.007961675524711609,
-0.015620347112417221,
0.017213476821780205,
0.021226953715085983,
-0.0028799164574593306,
0.012324930168688297,
0.023468032479286194,
0.052184995263814926,
-0.017069488763809204,
-0.09742490947246552,
-0.045437589287757874,
-0.009983250871300697,
-0.005442728754132986,
0.015108863823115826,
-0.07288334518671036,
0.0065580918453633785,
0.04259277135133743,
0.053330790251493454,
0.023812968283891678,
-0.007306995801627636,
0.03053937666118145,
0.027516288682818413,
-0.009342005476355553,
0.025555213913321495,
-0.05153581127524376,
-0.0059897988103330135,
-0.028553307056427002,
-0.001029171166010201,
-0.05359495431184769,
-0.0015700942603871226,
0.04857521876692772,
0.0005969678750261664,
0.010260460898280144,
0.07903637737035751,
0.004176543094217777,
0.013962999917566776,
0.03088739886879921,
0.0037320281844586134,
-0.024413665756583214,
0.09021192044019699,
-0.0063257962465286255,
0.010127879679203033,
-0.03003709577023983,
-0.0012858507689088583,
-0.009671857580542564,
-0.019980791956186295,
0.0022157097700983286,
0.0411643423140049,
-0.03513423353433609,
-0.02997414954006672,
0.039779260754585266,
0.008854233659803867,
0.013998309150338173,
-0.00706851901486516,
-0.006939097307622433,
0.015271217562258244,
-0.003107792465016246,
-0.005600997246801853,
0.05338998883962631,
0.022605542093515396,
-0.01608102396130562,
0.02561894804239273,
-0.06660211831331253,
0.03370361402630806,
-0.011542802676558495,
0.016968753188848495,
-0.008035278879106045,
-0.003963538911193609,
0.015134642831981182,
-0.02384207956492901,
0.011971273459494114,
-0.008909068070352077,
-0.04486386105418205,
0.019561082124710083,
-0.0004413402930367738,
0.001986574614420533,
-0.031164024025201797,
0.011712480336427689,
0.03804606571793556,
0.044593535363674164,
-0.019713468849658966,
0.03979950770735741,
-0.01804562285542488,
-0.010536563582718372,
-0.0327473022043705,
-0.02840227633714676,
0.018552498891949654,
-0.008169389329850674,
-0.022344009950757027,
0.023884952068328857,
-0.0331716313958168,
0.00725204311311245,
-0.0018854415975511074,
-0.05106189846992493,
0.04064783826470375,
0.08735636621713638,
0.021889764815568924,
-0.00945404265075922,
0.06096600368618965,
0.031741224229335785,
0.050842031836509705,
0.0005109410267323256,
-0.04809652641415596,
-0.06979142874479294,
0.006883030757308006,
0.04091760516166687,
0.03437120094895363,
-0.06108492240309715,
0.03506346419453621,
0.00967496819794178,
0.022444458678364754,
0.04728497937321663,
-0.0064478605054318905,
-0.007443321403115988,
-0.0233172457665205,
0.07513254135847092,
0.0054272254928946495,
-0.00021208835823927075,
0.021476292982697487,
0.02777327597141266,
0.0010514503810554743,
0.013230645097792149,
-0.03015722706913948,
-0.007058028597384691,
0.015261796303093433,
-0.007272778078913689,
-0.035500235855579376,
0.005738480947911739,
0.0009803215507417917,
0.07031893730163574,
-0.03604445606470108,
0.029245799407362938,
0.014362012036144733,
-0.019923152402043343,
0.015958312898874283,
-0.0040361033752560616,
0.020952148362994194,
0.055823612958192825,
-0.02766856737434864,
-0.028092721477150917,
-0.02837521769106388,
0.030118051916360855,
-0.02552517130970955,
-0.02117309160530567,
-0.03181653842329979,
-0.024774644523859024,
-0.02176903374493122,
-0.011402971111238003,
0.010018499568104744,
0.02426833286881447,
0.004494061693549156,
-0.013704431243240833,
-0.016963673755526543,
-0.007523075677454472,
-0.01624487340450287,
0.00015982445620466024,
0.07656604796648026,
-0.04065493121743202,
0.05390096828341484,
-0.01709982007741928,
-0.018329275771975517,
0.028822440654039383,
-0.0033867964521050453,
0.022366276010870934,
-0.011202842928469181,
-0.023119715973734856,
-0.05056952312588692,
-0.032557107508182526,
-0.03689708560705185,
0.036581579595804214,
-0.04472925141453743,
0.0125845056027174,
0.03287201374769211,
-0.016128340736031532,
-0.02579420804977417,
0.021612852811813354,
-0.00620448449626565,
-0.03950450196862221,
-0.014276965521275997,
0.006558581255376339,
0.05487369745969772,
-0.018260963261127472,
0.018112139776349068,
0.03488130122423172,
-0.038901664316654205,
0.002443046774715185,
-0.04357251524925232,
-0.05869370698928833,
0.04117254912853241,
0.01147284172475338,
0.0060625881887972355,
0.01248952280730009,
-0.019357681274414062,
0.09736961126327515,
0.03678146004676819,
-0.008760690689086914,
-0.0005794602329842746,
-0.004889513831585646,
0.007736655417829752,
-0.0458008237183094,
-0.0126368822529912,
-0.015205851756036282,
-0.01668136566877365,
0.028960831463336945,
-0.029138248413801193,
0.04038938507437706,
0.03457879647612572,
0.020794767886400223,
-0.0270974300801754,
0.017969470471143723,
-0.015692954882979393,
0.01911800540983677,
0.05223844572901726,
-0.007093700114637613,
0.004852018319070339,
0.014275017194449902,
-0.004075375385582447,
0.05386466160416603,
0.039505451917648315,
-0.05505479499697685,
0.030389761552214622,
0.021119138225913048,
-0.02699364721775055,
0.0007320970180444419,
0.028689775615930557,
0.0012472597882151604,
-0.00955264177173376,
0.003495014738291502,
-0.00024980571470223367,
0.03543268144130707,
0.02555616945028305,
0.017455266788601875,
-0.0017533217323943973,
0.020533820614218712,
-0.019935868680477142,
0.011152262799441814,
-0.018718115985393524,
-0.0001645748852752149,
0.016166921705007553,
-0.0016577175119891763,
0.012694562785327435,
0.054552990943193436,
-0.005506623536348343,
-0.0017288203816860914,
-0.01988932304084301,
-0.03419089689850807,
0.0028215269558131695,
-0.06965818256139755,
-0.0052391053177416325,
-0.03399352729320526,
0.06730784475803375,
0.025611814111471176,
0.030484387651085854,
0.00017996809037867934,
0.019935350865125656,
-0.0022026801016181707,
0.01138139609247446,
-0.06739047914743423,
0.04326671361923218,
-0.03326064720749855,
-0.029012219980359077,
-0.031048698350787163,
-0.00414996687322855,
0.03382953628897667,
-0.009930147789418697,
-0.04550955817103386,
0.033434391021728516,
-0.004578118212521076,
-0.10539519041776657,
0.030710436403751373,
-0.024129902943968773,
-0.061053626239299774,
-0.014833339489996433,
0.018445352092385292,
0.030782833695411682,
-0.019528737291693687,
-0.006320159416645765,
0.03941308706998825,
0.00043433025712147355,
0.0017397524788975716,
-0.07006644457578659,
0.008462955243885517,
0.0420953705906868,
0.016385288909077644,
-0.004198347218334675,
0.012749938294291496,
-0.02680673822760582,
0.026949845254421234,
0.018845947459340096,
0.05282269045710564,
0.017474306747317314,
0.010428102687001228,
-0.02046387642621994,
-0.02275433950126171,
0.00275944615714252,
0.011750935576856136,
0.08374245464801788,
-0.02199779450893402,
0.011128724552690983,
-0.004023292101919651,
0.012798125855624676,
-0.009426362812519073,
0.04784264415502548,
0.03788517042994499,
-0.030274659395217896,
0.007177448831498623,
-0.03836578130722046,
-0.003647258970886469,
-0.02693583071231842,
-0.005738810170441866,
-0.016976479440927505,
0.014428798109292984,
0.01251564733684063,
0.010219971649348736,
0.038650400936603546,
0.06566894799470901,
0.004638316575437784,
0.011254355311393738,
0.023349285125732422,
0.016955140978097916,
-0.016550134867429733,
-0.007017765659838915,
0.04479582980275154,
0.05702685937285423,
0.05824562907218933,
0.013374925591051579,
0.024829458445310593,
-0.09178715199232101,
-0.03601950407028198,
0.005601857788860798,
0.019573133438825607,
0.027264414355158806,
-0.002307359129190445,
-0.07541178911924362,
-0.062240492552518845,
0.023955706506967545,
0.001894530956633389,
0.019377050921320915,
-0.0031929989345371723,
-0.013062353245913982,
0.014658402651548386,
-0.03537014126777649,
-0.003971422091126442,
0.01533224806189537,
-0.006588468793779612,
-0.00512700853869319,
-0.03706769645214081,
0.03184408321976662,
-0.01881132461130619,
0.05758652836084366,
-0.002713835332542658,
0.09017559140920639,
0.007304325699806213,
-0.05304659157991409,
-0.023872023448348045,
0.029553614556789398,
-0.06252684444189072,
-0.06896083056926727,
0.0015349779278039932,
-0.0020084651187062263,
0.007792680524289608,
0.02741340920329094,
-0.02252696081995964,
-0.05428316071629524,
0.03723161667585373,
0.021972108632326126,
-0.018238287419080734,
0.0322449617087841,
-0.0179486982524395,
0.011923943646252155,
0.018339773640036583,
0.014815261587500572,
0.065530925989151,
0.030745238065719604,
-0.005278900731354952,
-0.0352880023419857,
-0.01662687584757805,
0.035595960915088654,
-0.05266392230987549,
-0.009774504229426384,
-0.013222966343164444,
0.003479268169030547,
-0.005512524861842394,
0.057344187051057816,
-0.017727389931678772,
0.015938282012939453,
0.0015256208134815097,
-0.04081006348133087,
0.013903231360018253,
0.027845583856105804,
0.006115474738180637,
-0.014842677861452103,
-0.0041480762884020805,
0.017893142998218536,
0.007561356760561466,
-0.004153364337980747,
-0.001088252174668014,
0.010166238062083721,
-0.0029207009356468916,
0.0379292257130146,
-0.01607295498251915,
0.044701673090457916,
-0.0411493293941021,
-0.01395419705659151,
0.012451252900063992,
-0.022011149674654007,
0.01712336763739586,
0.011714582331478596,
0.008504134602844715,
0.04306287318468094,
-0.035072822123765945,
0.012612085789442062,
0.0007628595340065658,
0.00868507381528616,
-0.0045228805392980576,
-0.06242023780941963,
0.028152761980891228,
0.008208230137825012,
0.015378132462501526,
-0.06933748722076416,
-0.03135106712579727,
0.025146454572677612,
-0.016064979135990143,
-0.049517277628183365,
-0.020926034078001976,
0.0023997079115360975,
-0.00916361901909113,
-0.00012804185098502785,
-0.0030791875906288624,
0.05033166706562042,
0.0027162593323737383,
-0.014672336168587208,
0.007252593990415335,
0.04146161675453186,
0.025386113673448563,
-0.04673795402050018,
-0.02058814838528633,
0.01617923378944397,
-0.04757189378142357,
0.003967617638409138,
0.009463630616664886,
0.05131007730960846,
-0.010423458181321621,
0.03191687911748886,
-0.039705730974674225,
-0.006403936538845301,
0.039632514119148254,
-0.012148776091635227,
-0.0367385670542717,
0.06773025542497635,
-0.0017366494284942746,
0.02249513380229473,
-0.023830508813261986,
-0.033930178731679916,
-0.04557196423411369,
0.027083400636911392,
-0.0016210658941417933,
0.0007928777486085892,
-0.02000691369175911,
-0.009695895947515965,
0.01991526409983635,
-0.00882724393159151,
-0.03917397931218147,
-0.01706366427242756,
0.05509740486741066,
-0.017059767618775368,
-0.003565504215657711,
0.01904274895787239,
0.012769249267876148,
0.010378573089838028,
-0.008950849063694477,
0.01741107553243637,
0.012522373348474503,
0.0035368800163269043,
-0.05096138268709183,
-0.05358264967799187,
-0.05158613249659538,
0.025689104571938515,
0.07858720421791077,
-0.01360599510371685,
0.04020373523235321,
0.01326356828212738,
0.01876422017812729,
-0.009930445812642574,
-0.01063914317637682,
-0.005289556458592415,
-0.0049785347655415535,
-0.03203999251127243,
0.044015560299158096,
-0.042127128690481186,
-0.017680052667856216,
0.027677463367581367,
0.0370454415678978,
-0.019518110901117325,
-0.019773928448557854,
-0.043024126440286636,
0.014460141770541668,
0.011988719925284386,
-0.002239599823951721,
-0.06569560617208481,
0.0527765192091465,
-0.047244325280189514,
0.042852483689785004,
-0.003091774182394147,
-0.012935022823512554,
0.049445740878582,
0.0485416017472744,
0.025826120749115944,
-0.014788168482482433,
0.0016634601633995771,
-0.006570032332092524,
0.049457285553216934,
0.029223095625638962,
0.023820485919713974,
0.04545366019010544,
0.03655463829636574,
0.03857309743762016,
-0.0055369241163134575,
0.010839744471013546,
0.038373518735170364,
-0.0777401551604271,
0.0062924097292125225,
-0.06974084675312042,
-0.05333965644240379,
0.03421980142593384,
0.03893270343542099,
-0.002258843742311001,
0.012175100855529308,
-0.033434681594371796,
0.039948999881744385,
0.022561710327863693,
0.01770920120179653,
-0.01099308580160141,
0.06805261224508286,
-0.015142295509576797,
-0.015232398174703121,
-0.01126330066472292,
0.007702704984694719,
0.12097875773906708,
0.0493740551173687,
0.006717839743942022,
-0.04439558461308479,
-0.0062333582900464535,
-0.00616293353959918,
-0.026318155229091644,
-0.035512350499629974,
0.020484022796154022,
0.0020795916207134724,
-0.01649412140250206,
0.013622703030705452,
0.044310398399829865,
-0.01348702609539032,
0.014870144426822662,
0.042952314019203186,
-0.046486496925354004,
-0.03174906596541405,
0.012335846200585365,
-0.02327895537018776,
-0.010456972755491734,
0.0006909932126291096,
-0.019186271354556084,
0.014672387391328812,
-0.023083791136741638,
0.011978725902736187,
-0.03595290705561638,
-0.0412786565721035,
0.025075960904359818,
-0.013032018207013607,
-0.04706774652004242,
0.006963557563722134,
0.02955526113510132,
0.025962861254811287,
-0.03461508825421333,
0.02201809734106064,
0.011550278402864933,
-0.01708468608558178,
0.005728679709136486,
0.03598042204976082,
0.0007555047632195055,
0.0049597411416471004,
0.0065384008921682835,
-0.010890435427427292,
-0.011138652451336384,
-0.00771751906722784,
-0.030728163197636604,
0.029620423913002014,
-0.011151116341352463,
-0.010333748534321785,
0.01054599229246378,
-0.04623718187212944,
0.00579998642206192,
-0.05720888823270798,
-0.009054678492248058,
0.011129938066005707,
0.014945268630981445,
-0.04640429466962814,
0.0022487733513116837,
-0.01786019653081894,
0.015543525107204914,
0.02108917571604252,
0.04181915521621704,
-0.01328913401812315,
-0.01919865608215332,
-0.0075134336948394775,
0.017124660313129425,
0.025769738480448723,
0.010856215842068195,
-0.01132824644446373,
-0.026155805215239525,
-0.016570786014199257,
-0.0025146016851067543,
-0.04457331448793411,
0.008389207534492016,
0.02564517967402935,
0.05224073305726051,
-0.0031494516879320145,
-0.04104168713092804,
-0.030373312532901764,
-0.11056699603796005,
0.028989464044570923,
0.011213711462914944,
-0.00223171291872859,
-0.034649576991796494,
0.006099230609834194,
0.020280813798308372,
0.049735937267541885,
0.005570178851485252,
0.0049241106025874615,
0.0014220038428902626,
0.026921171694993973,
0.0620766319334507,
0.003718507243320346,
-0.030023718252778053,
0.006818033754825592,
-0.033967334777116776,
0.025001870468258858,
-0.005821609403938055,
-0.006102742161601782,
0.02703268826007843,
0.02870093286037445,
-0.034749485552310944,
0.06240019202232361,
-0.05480219051241875,
0.014804020524024963,
0.013649918138980865,
-0.045282330363988876,
0.03143160790205002,
-0.007584744598716497,
0.022769160568714142,
-0.0007136040949262679,
-0.022088736295700073,
-0.01432203408330679,
0.0008761819335632026,
0.005365792196244001,
-0.0055260867811739445,
-0.013016522862017155,
0.005459150765091181,
-0.053590111434459686,
-0.006675616838037968,
-0.02940879948437214,
-0.03584665805101395,
-0.05261850357055664,
0.0018386513693258166,
-0.005086053162813187,
-0.04278573393821716,
-0.017411764711141586,
0.0130173834040761,
-0.02608611062169075,
-0.014121681451797485,
0.028923172503709793,
0.05413113161921501,
-0.018347805365920067,
-0.017292600125074387,
0.01193956658244133,
0.034297242760658264,
0.049874886870384216,
-0.002398441080003977,
-0.032831259071826935,
0.01793612167239189,
-0.03358332812786102,
-0.012394423596560955,
0.01660231500864029,
0.021479787304997444,
0.031071513891220093,
0.04230795428156853,
-0.017547834664583206,
-0.012405235320329666,
0.030757984146475792,
-0.006003643851727247,
0.019190991297364235,
0.004812694154679775,
-0.046432096511125565,
-0.00046903989277780056,
-0.0027447459287941456,
0.028775718063116074,
-0.004430198576301336,
0.0029767826199531555,
-0.018653225153684616,
-0.0029641888104379177,
0.01930786482989788,
0.0026645073667168617,
0.052059926092624664,
-0.022321149706840515,
0.014449307695031166,
0.03190767765045166,
0.02685556188225746,
0.03627665340900421,
0.05629723146557808,
-0.023706676438450813,
-0.005167549010366201,
0.04356374591588974,
0.03221962973475456,
-0.1379116177558899,
-0.004251256585121155,
0.02829994447529316,
0.054793983697891235,
0.039288416504859924,
-0.032301414757966995,
0.022258827462792397,
-0.0020032236352562904,
-0.05435076728463173,
0.05024242401123047,
-0.02202669158577919,
0.00429181195795536,
-0.028214290738105774,
0.00755297439172864,
-0.046088702976703644,
0.05123535543680191,
0.08221395313739777,
0.018521031364798546,
0.001173857832327485,
0.005954733584076166,
0.00987804401665926,
0.029839426279067993,
-0.019395820796489716,
0.0016672719502821565,
-0.005222851876169443,
-0.039015769958496094,
-0.0022430233657360077,
-0.03942851722240448,
-0.03543449565768242,
-0.011172241531312466,
-0.005902912002056837,
-0.015165885910391808,
-0.031700827181339264,
-0.004681853111833334,
0.016430236399173737,
0.010388270951807499,
0.03984658047556877,
-0.013635913841426373,
-0.028756676241755486,
-0.018312295898795128,
0.004016724415123463,
0.004676434677094221,
-0.056202925741672516,
0.019753070548176765,
0.02963922545313835,
-0.039213526993989944,
-0.0171404667198658,
0.04459027200937271,
-0.05724750831723213,
-0.009978750720620155,
0.021280698478221893,
-0.03225267678499222,
-0.012251107022166252,
0.0011520290281623602,
0.028639361262321472,
-0.02047925442457199,
-0.016930608078837395,
-0.007778431288897991,
-0.006319447420537472,
-0.028966497629880905,
0.03773266077041626,
-0.059668850153684616,
-0.07249750941991806,
0.05402751266956329,
0.00027231863350607455,
-0.00465727923437953,
-0.04855373501777649,
-0.022274410352110863,
0.003978774882853031,
0.024197790771722794,
0.001470433664508164,
-0.04591676965355873,
-0.012508366256952286,
0.040875960141420364,
0.035075899213552475,
-0.004248742014169693,
-0.007935904897749424,
-0.020709529519081116,
-0.01966746151447296,
-0.038746900856494904,
-0.00044864913797937334,
0.001524485880509019,
-0.05654102936387062,
0.001081624417565763,
-0.005518821533769369,
0.01651386171579361,
0.002258192515000701,
0.007981505244970322,
-0.05517543852329254,
0.028817933052778244,
0.024189870804548264,
-0.013140029273927212,
0.032746706157922745,
-0.021695367991924286,
0.008052730932831764,
-0.014926674775779247,
-0.0147840715944767,
0.0012677686754614115,
0.017829198390245438,
-0.032317597419023514,
0.041355181485414505,
0.024143680930137634,
0.022837650030851364,
0.02367960661649704,
0.020155590027570724,
-0.017696307972073555,
0.036707643419504166,
0.01914781704545021,
-0.031545042991638184,
0.04810789227485657,
-0.001660459558479488,
0.02024168334901333,
0.025897309184074402,
-0.031216412782669067,
-0.03671443462371826,
0.025962742045521736,
-0.056235913187265396,
-0.008390276692807674,
-0.014594310894608498,
-0.03488762304186821,
0.0020095298532396555,
-0.03977567330002785,
-0.020199568942189217,
0.01953263022005558,
-0.053758371621370316,
-0.00037152189179323614,
0.04907107353210449,
-0.030652841553092003,
-0.010327217169106007,
0.006019459571689367,
-0.0024366285651922226,
0.04567299410700798,
-0.01343554724007845,
0.015377514064311981,
0.05259270220994949,
0.01843550242483616,
-0.0020975745283067226,
-0.013699638657271862,
0.012594090774655342,
-0.039405275136232376,
0.004978421609848738,
-0.0360921248793602,
0.046839743852615356,
-0.06950048357248306,
0.004609039518982172,
0.025849252939224243,
-0.03500804305076599,
-0.027332883328199387,
0.027364270761609077,
-0.03250521421432495,
0.06965478509664536,
-0.02868528664112091,
0.00925467535853386,
-0.031165413558483124,
-0.00479033961892128,
-0.026916731148958206,
0.014482492581009865,
-0.000197308836504817,
0.029755378141999245,
0.010346926748752594,
0.020958615466952324,
-0.05288359150290489,
-0.02065344527363777,
0.016694793477654457,
-0.0581539012491703,
-0.02019629068672657,
-0.002374099800363183,
-0.018574947491288185,
-0.0024477303959429264,
-0.012166379019618034,
-0.050635430961847305,
-0.029606075957417488,
0.016743745654821396,
0.026511546224355698,
0.018496647477149963,
-0.03395824879407883,
-0.015370307490229607,
-0.01994546502828598,
0.04598411172628403,
-0.055988240987062454,
0.0087022315710783,
0.016674159094691277,
0.02222527004778385,
0.0126268919557333,
-0.02681460790336132
] |
<p>In Polchinski's textbook String Theory, section 2.8, the author argues that the unit operator $1$ corresponds to the vacuum state, and $\partial X^\mu$ is holomorphic inside couture $Q$ in figure 2.6(b), so operators $\alpha_m^\mu$ with $m>=0$ vanishes.</p>
<p>I am a bit confused about why $\partial X^\mu$ has no pole inside the contour. Before this section $\partial X^\mu$ always has the singularity part ($1/z^m$). Therefore would it be possible for you to give a more mathematical argument what condition requires $\partial X^\mu$ having no poles in this case?</p>
<p>Thanks a lot for your time!</p>
| 9,372 |
[
0.04371369257569313,
-0.0062581379897892475,
0.015399918891489506,
-0.08054701238870621,
0.009582377038896084,
0.002994345035403967,
-0.049699366092681885,
-0.056665729731321335,
-0.017352676019072533,
-0.04690232500433922,
0.014573762193322182,
0.006099744699895382,
0.08886581659317017,
0.022775227203965187,
0.02112281508743763,
-0.017158085480332375,
-0.020836567506194115,
-0.043884266167879105,
-0.004178492818027735,
0.006661643739789724,
0.01107657328248024,
0.04675398766994476,
-0.007533994037657976,
0.012715363875031471,
0.0032266280613839626,
0.006087650544941425,
-0.024891534820199013,
0.0343778170645237,
0.030922086909413338,
0.044889554381370544,
-0.01317308284342289,
-0.02400258369743824,
-0.003437640145421028,
0.011734023690223694,
-0.020668014883995056,
0.011345092207193375,
-0.028397882357239723,
-0.022910937666893005,
-0.03564968332648277,
-0.009884207509458065,
0.014421485364437103,
-0.004707055166363716,
-0.0052582258358597755,
0.032835956662893295,
-0.01928863115608692,
0.027270494028925896,
0.0323624312877655,
-0.012739877216517925,
0.06718938797712326,
-0.059536874294281006,
0.03434377536177635,
0.021496618166565895,
0.01441227737814188,
0.018070010468363762,
0.030547307804226875,
0.004834591411054134,
0.08031337708234787,
0.09316994994878769,
-0.004596430342644453,
-0.05210835486650467,
-0.06020071357488632,
-0.008258027955889702,
-0.0402323454618454,
-0.012227323837578297,
-0.016043176874518394,
0.003458017250522971,
0.01620754972100258,
0.01814977638423443,
0.012961164116859436,
-0.02381812036037445,
-0.028296712785959244,
0.004945141728967428,
-0.0011935858055949211,
-0.007548315916210413,
-0.017175080254673958,
-0.004787839017808437,
-0.007706962060183287,
0.022465266287326813,
0.029355335980653763,
0.01876157708466053,
-0.012239689007401466,
-0.009490692056715488,
0.032332420349121094,
-0.014530560933053493,
-0.019929436966776848,
0.009971054270863533,
0.06290290504693985,
0.0019472632557153702,
-0.014737280085682869,
0.05881287902593613,
0.011582449078559875,
-0.015734491869807243,
0.027029894292354584,
-0.016405928879976273,
-0.05739082023501396,
0.011037128046154976,
0.0048215086571872234,
0.05550529435276985,
-0.0029842101503163576,
-0.01748335175216198,
-0.0380181260406971,
-0.021892214193940163,
0.019695322960615158,
0.03708651661872864,
0.013052836991846561,
0.02208307757973671,
-0.024326380342245102,
0.023568609729409218,
-0.053478967398405075,
-0.05215660482645035,
-0.0404999777674675,
0.040844012051820755,
-0.011136787012219429,
0.006687592715024948,
-0.005761397536844015,
-0.013103557750582695,
-0.006257425528019667,
-0.026337021961808205,
0.06637963652610779,
0.048357170075178146,
0.055706530809402466,
0.012546601705253124,
0.02134675905108452,
-0.04528333991765976,
-0.08264573663473129,
0.01706560142338276,
0.028882738202810287,
-0.007572802249342203,
-0.05943237617611885,
0.0018943140748888254,
0.05777539312839508,
0.010832229629158974,
0.024790575727820396,
0.005514778196811676,
0.03490856662392616,
-0.007389478851109743,
-0.044818177819252014,
-0.039685145020484924,
0.036145973950624466,
-0.013878881931304932,
0.020007334649562836,
-0.056713078171014786,
-0.026616083458065987,
0.05209134891629219,
0.10537397861480713,
-0.02568933553993702,
0.01252887025475502,
0.016747519373893738,
0.02274576760828495,
0.011437659151852131,
-0.0076541779562830925,
-0.03825467452406883,
-0.034432072192430496,
-0.0558411069214344,
0.014215084724128246,
-0.026467809453606606,
0.022140678018331528,
0.040893327444791794,
0.017679939046502113,
-0.021287504583597183,
0.06434573233127594,
-0.04933872073888779,
0.01697676070034504,
0.025722775608301163,
-0.004157994408160448,
-0.02650124579668045,
0.05273309350013733,
0.008569780737161636,
0.05122634395956993,
0.029146259650588036,
0.041991133242845535,
0.027482306584715843,
0.008368373848497868,
0.0242892075330019,
0.0018592061242088675,
-0.061135001480579376,
-0.03242472559213638,
0.005946727003902197,
0.018272319808602333,
-0.012549251317977905,
-0.04294750839471817,
-0.04923572763800621,
0.011890986934304237,
0.03678981959819794,
-0.015576028265058994,
0.03771718963980675,
-0.020817242562770844,
-0.014559893868863583,
0.003619606141000986,
-0.032460056245326996,
-0.01271893922239542,
0.011268368922173977,
0.021748049184679985,
0.04072833061218262,
-0.031004123389720917,
0.009828195907175541,
-0.01468660682439804,
-0.005465234629809856,
-0.019312208518385887,
-0.018834030255675316,
-0.003295108675956726,
0.016442766413092613,
-0.003008407773450017,
-0.03148014843463898,
-0.0017590156057849526,
0.020087674260139465,
0.05796325206756592,
-0.007831917144358158,
0.04691265523433685,
-0.02447698451578617,
-0.008183910511434078,
0.031074868515133858,
0.006221717223525047,
0.023105153813958168,
-0.0287238247692585,
0.007497577928006649,
0.03782106935977936,
-0.03092060424387455,
-0.022610150277614594,
0.049143802374601364,
-0.058930087834596634,
0.027085980400443077,
0.0365019291639328,
0.023954257369041443,
-0.005761029198765755,
0.004440533462911844,
-0.019317645579576492,
0.016523730009794235,
0.014760108664631844,
-0.037465665489435196,
-0.04097728803753853,
-0.027236662805080414,
0.037714045494794846,
0.010487241670489311,
-0.012311575934290886,
0.02101222798228264,
0.03505604341626167,
0.023670798167586327,
0.01560406107455492,
0.02175350859761238,
-0.006769789382815361,
-0.005490866489708424,
0.01575320027768612,
0.02413831278681755,
0.003365960204973817,
0.011882728897035122,
0.03391611576080322,
0.0032781583722680807,
0.02272585593163967,
-0.0029994850046932697,
-0.009096388705074787,
0.053626641631126404,
-0.0357474721968174,
0.027643440291285515,
0.00022647251898888499,
-0.0020445387344807386,
0.0032880359794944525,
-0.015148084610700607,
0.01885533519089222,
0.020350389182567596,
-0.004914889577776194,
0.020747682079672813,
-0.04488888010382652,
0.0053962827660143375,
0.019771603867411613,
0.004368423949927092,
-0.03717361018061638,
-0.03636271879076958,
0.017112307250499725,
-0.03658890351653099,
0.007375344168394804,
0.005524934735149145,
-0.04539530724287033,
0.031544920057058334,
0.015387071296572685,
0.07663650065660477,
-0.006885659880936146,
0.030156224966049194,
-0.03366309404373169,
0.0011258103186264634,
0.013324297964572906,
-0.010941465385258198,
-0.005050689447671175,
0.036345843225717545,
-0.0426265150308609,
-0.024341028183698654,
-0.0651145800948143,
-0.01499322522431612,
0.040508758276700974,
0.023008806630969048,
0.014015897177159786,
-0.025382453575730324,
-0.017690686509013176,
-0.013309597037732601,
-0.031030550599098206,
-0.0323515385389328,
0.0293735358864069,
-0.011906362138688564,
-0.012927240692079067,
0.04143056645989418,
0.029228506609797478,
-0.03396998345851898,
0.02321157418191433,
-0.027025364339351654,
-0.03483135625720024,
-0.02586548961699009,
-0.025552820414304733,
0.017510104924440384,
-0.049573495984077454,
0.022595318034291267,
-0.019198527559638023,
-0.03552953526377678,
0.013462896458804607,
-0.029988886788487434,
-0.03695439174771309,
-0.008901937864720821,
-0.004890160169452429,
-0.010362968780100346,
0.012235012836754322,
-0.08679475635290146,
0.08447055518627167,
0.023690490052103996,
-0.0407821424305439,
-0.021850720047950745,
0.02137359045445919,
-0.06129366159439087,
-0.054043255746364594,
-0.023509537801146507,
0.03348596766591072,
-0.018732452765107155,
0.01585940085351467,
0.03381240740418434,
0.03950585797429085,
0.0363847091794014,
0.009443284012377262,
-0.023368077352643013,
0.026666393503546715,
-0.002648057648912072,
-0.008606025017797947,
0.015972385182976723,
-0.010302949696779251,
0.0242264736443758,
0.027744553983211517,
-0.019101552665233612,
-0.005199227947741747,
0.02402297779917717,
-0.028703970834612846,
0.02249249629676342,
-0.030807694420218468,
0.013817565515637398,
0.002838848391547799,
0.058627430349588394,
-0.015335931442677975,
-0.04057013615965843,
-0.019932948052883148,
0.016828935593366623,
0.013907807879149914,
-0.029164139181375504,
-0.023248128592967987,
0.000678264070302248,
0.016751166433095932,
-0.046720415353775024,
-0.016999628394842148,
-0.024128718301653862,
-0.0230140071362257,
0.038108788430690765,
-0.02712015062570572,
-0.04735678434371948,
0.02569088712334633,
0.05387623608112335,
0.02501709945499897,
-0.02112247608602047,
-0.021601054817438126,
-0.014723552390933037,
-0.044843416661024094,
0.005308029241859913,
-0.02259439043700695,
0.04356953129172325,
-0.001789331785403192,
0.06766354292631149,
0.014401262626051903,
0.005877722054719925,
-0.010648982599377632,
0.025891074910759926,
-0.08505488187074661,
-0.006877627689391375,
-0.029619593173265457,
0.011008402332663536,
0.017441846430301666,
-0.038176484405994415,
-0.034619059413671494,
0.018581783398985863,
-0.04957060143351555,
-0.012890974059700966,
-0.015107538551092148,
-0.08101576566696167,
0.03689291700720787,
-0.054720375686883926,
-0.017827097326517105,
-0.012084946036338806,
0.04535241052508354,
0.03381242975592613,
-0.03970007970929146,
-0.009660447016358376,
0.0005718513275496662,
-0.03970120847225189,
0.012638951651751995,
0.0010700381826609373,
0.04938383772969246,
0.026407018303871155,
0.018753638491034508,
0.046939291059970856,
0.014546937309205532,
-0.011442883871495724,
0.01241857185959816,
0.05191543325781822,
0.07578621059656143,
-0.004736151546239853,
-0.001953992061316967,
-0.01097975391894579,
-0.01872894912958145,
-0.000709805462975055,
0.025495387613773346,
0.07761995494365692,
0.013742703013122082,
-0.01986018940806389,
0.01840156316757202,
-0.010731338523328304,
0.004023413173854351,
0.05459785461425781,
0.07129140943288803,
0.007626772858202457,
-0.036827486008405685,
-0.058405157178640366,
0.004488374572247267,
-0.03318551555275917,
-0.0007415282307192683,
-0.00484501151368022,
-0.019255520775914192,
-0.028422895818948746,
-0.03653700649738312,
0.006571147590875626,
0.010464085265994072,
-0.02631809189915657,
0.028384072706103325,
0.044858697801828384,
-0.03765620291233063,
-0.011427503079175949,
-0.0024283200036734343,
0.05091880261898041,
0.028277253732085228,
0.04194219782948494,
0.006909194402396679,
-0.02667948231101036,
-0.026689860969781876,
-0.02831769734621048,
0.013623969629406929,
0.006634676828980446,
0.023795543238520622,
-0.039581481367349625,
-0.06914907693862915,
0.01049408596009016,
0.02111603319644928,
-0.015607982873916626,
0.04760201275348663,
0.006221037823706865,
0.03267478942871094,
-0.00898757018148899,
-0.03984113037586212,
-0.007560761645436287,
0.022866113111376762,
-0.003707610536366701,
0.030802108347415924,
-0.03148902580142021,
-0.0265028178691864,
-0.051160767674446106,
0.009551971219480038,
-0.024274805560708046,
-0.003317154012620449,
0.05221955478191376,
0.010350325144827366,
-0.0146719329059124,
0.024657947942614555,
-0.016259323805570602,
-0.043177153915166855,
0.009693295694887638,
-0.03793325647711754,
-0.010842710733413696,
0.012884056195616722,
0.012682855129241943,
-0.02319175936281681,
0.03640562668442726,
0.03673240914940834,
0.0101231150329113,
-0.0054232594557106495,
-0.03357136994600296,
0.04822149872779846,
0.03830469399690628,
-0.006783643271774054,
0.03321535512804985,
-0.017947979271411896,
0.026411110535264015,
-0.006371720228344202,
-0.021956058219075203,
-0.005862963851541281,
-0.01717822439968586,
0.020293163135647774,
-0.04839777573943138,
-0.007605757098644972,
-0.047711119055747986,
0.03259760141372681,
-0.03356359153985977,
-0.013903805986046791,
0.010013949126005173,
-0.0303315632045269,
-0.01209401898086071,
0.02677583135664463,
-0.026774680241942406,
0.012719246558845043,
-0.0029663185123354197,
0.03564247116446495,
-0.02506694197654724,
-0.009047390893101692,
0.037104446440935135,
-0.025892581790685654,
0.01597471721470356,
0.03998512774705887,
0.0318804495036602,
0.04398851469159126,
0.018215971067547798,
0.0023383002262562513,
0.0216868594288826,
-0.040206510573625565,
0.04160579293966293,
-0.04016163945198059,
0.011052004061639309,
0.007944165728986263,
-0.022861482575535774,
-0.01702294684946537,
0.019159337505698204,
-0.026843033730983734,
0.040994878858327866,
-0.06999877095222473,
0.002008556155487895,
0.07805199176073074,
0.020046235993504524,
-0.04089222475886345,
-0.05644246190786362,
0.02313811145722866,
0.016528069972991943,
-0.0022041790653020144,
0.026789478957653046,
0.011789551004767418,
-0.04138437658548355,
-0.035478413105010986,
-0.02270261012017727,
0.027147041633725166,
-0.05468851700425148,
-0.007149216718971729,
0.012676957063376904,
0.09853366762399673,
0.03482845425605774,
0.013880034908652306,
-0.025516273453831673,
0.04058969020843506,
-0.00842108391225338,
-0.014408762566745281,
-0.01936746947467327,
0.05169210955500603,
-0.0005939657567068934,
-0.03810935840010643,
-0.011153141967952251,
-0.018220948055386543,
0.03786109760403633,
0.015102988108992577,
-0.03367804363369942,
0.023630749434232712,
0.06614961475133896,
0.030252376571297646,
0.001155732898041606,
0.015102756209671497,
0.006962702143937349,
0.01229124702513218,
-0.005683619529008865,
-0.028328724205493927,
-0.02313307300209999,
-0.03399801254272461,
0.025217831134796143,
-0.0012976134894415736,
0.0024077058769762516,
-0.024715712293982506,
0.1299663633108139,
0.004862615372985601,
-0.010463052429258823,
0.0007679574773646891,
-0.04424891620874405,
-0.00048692981363274157,
0.018176134675741196,
0.01209469698369503,
0.014949297532439232,
0.02410714142024517,
-0.007106258999556303,
-0.006361279170960188,
-0.027346719056367874,
0.026113612577319145,
0.022413484752178192,
0.004912906792014837,
0.012893741019070148,
-0.0017564184963703156,
0.010322426445782185,
0.021839963272213936,
-0.020963380113244057,
-0.04602828621864319,
-0.010585492476820946,
-0.034273285418748856,
0.04277310147881508,
-0.056780315935611725,
0.02459198608994484,
0.021170906722545624,
0.05286993458867073,
-0.057659853249788284,
-0.021972674876451492,
0.02305959165096283,
0.033632874488830566,
0.02121041715145111,
0.006945946719497442,
-0.03197586163878441,
0.033396098762750626,
-0.020267466083168983,
0.023741355165839195,
-0.006994336843490601,
0.021207435056567192,
-0.01624109223484993,
0.02373148873448372,
0.025293463841080666,
-0.01718006655573845,
-0.033996134996414185,
-0.03303489834070206,
0.05228021740913391,
0.0025513756554573774,
-0.006346925627440214,
-0.00545132253319025,
-0.001937694731168449,
0.027801094576716423,
-0.006666213274002075,
0.024880798533558846,
0.016528423875570297,
-0.04855455830693245,
-0.028032023459672928,
-0.053165484219789505,
-0.0724521055817604,
0.05160393938422203,
-0.009434599429368973,
-0.019509144127368927,
0.02514449506998062,
-0.04346645250916481,
0.03703552111983299,
-0.02178182452917099,
0.02331312745809555,
-0.013294754549860954,
0.044663816690444946,
-0.007902149111032486,
0.011769266799092293,
-0.026512306183576584,
0.025040511041879654,
0.11742912232875824,
0.07537997514009476,
0.007050441578030586,
-0.0656631737947464,
0.017925389111042023,
-0.0021096367854624987,
0.04355078935623169,
-0.06203911453485489,
0.038171976804733276,
0.005272177513688803,
-0.006326331757009029,
-0.02754152938723564,
0.04330022260546684,
-0.036049216985702515,
0.003136471612378955,
0.03343642130494118,
-0.036160532385110855,
-0.05876937136054039,
0.0068001579493284225,
0.010988936759531498,
-0.02082621306180954,
0.003928167745471001,
-0.05027102679014206,
-0.0012138780439272523,
0.021625738590955734,
-0.0037739495746791363,
-0.05647287517786026,
0.0049427528865635395,
0.02404629811644554,
-0.036902498453855515,
-0.025649748742580414,
-0.002136118710041046,
0.0020265558268874884,
0.009696836583316326,
-0.03682158514857292,
0.02328459918498993,
0.004595826845616102,
-0.003992978483438492,
0.04064022749662399,
0.062141746282577515,
0.020816517993807793,
-0.013867778703570366,
0.01730639487504959,
0.003379033412784338,
-0.0423663891851902,
0.008302084170281887,
-0.013497247360646725,
0.06332223862409592,
0.006895408965647221,
-0.02163628488779068,
0.002888457151129842,
0.0001552050089230761,
-0.019124608486890793,
-0.018806038424372673,
0.004985388368368149,
0.0021442847792059183,
-0.0017182223964482546,
-0.017132487148046494,
0.02032279595732689,
0.017199700698256493,
0.002851636614650488,
0.03632190078496933,
0.004565020091831684,
-0.013665462844073772,
-0.04748724400997162,
-0.004029277246445417,
0.020676342770457268,
0.03239278495311737,
-0.023142531514167786,
0.002207287587225437,
0.0017461661482229829,
0.007518697064369917,
-0.02223839797079563,
-0.026606833562254906,
0.009016795083880424,
0.01008626539260149,
0.05364859849214554,
0.013612201437354088,
0.004896840080618858,
-0.016398821026086807,
-0.045820482075214386,
0.02254129946231842,
-0.014058980159461498,
-0.02445186860859394,
-0.009542105719447136,
-0.0025099841877818108,
-0.0035705198533833027,
0.040397562086582184,
-0.020947813987731934,
-0.042284999042749405,
0.011301266960799694,
0.029368698596954346,
0.01059449091553688,
-0.004849687218666077,
-0.04384097829461098,
-0.0021491122897714376,
-0.04954960569739342,
0.01671670936048031,
0.0020454961340874434,
-0.0018732805037871003,
-0.013036428950726986,
0.028914205729961395,
-0.04175806790590286,
0.04372628033161163,
0.008636003360152245,
-0.024817297235131264,
0.010781673714518547,
-0.0553198903799057,
0.014807937666773796,
0.05357764661312103,
-0.003385541494935751,
-0.05441005527973175,
-0.03560711815953255,
-0.010913137346506119,
0.01204715482890606,
0.03179091587662697,
0.03041154332458973,
-0.0658869743347168,
0.009638718329370022,
0.011979821138083935,
0.010662529617547989,
-0.010430538095533848,
-0.022003183141350746,
-0.013087783940136433,
0.023825624957680702,
0.02923792600631714,
0.0007959461072459817,
0.0006280163070186973,
0.004874407313764095,
-0.02665489912033081,
-0.061657704412937164,
0.016331885010004044,
0.017188316211104393,
-0.0366210900247097,
0.025885045528411865,
0.00567066203802824,
0.004402622580528259,
0.04073702543973923,
0.02736840397119522,
-0.008584659546613693,
0.01685997284948826,
-0.041044820100069046,
-0.02439274825155735,
0.03492456674575806,
-0.018098672851920128,
0.03739440068602562,
-0.0026012505404651165,
0.0019342666491866112,
-0.02264857105910778,
0.03802059590816498,
-0.02125382423400879,
0.012823455035686493,
-0.018508967012166977,
-0.031080789864063263,
0.015162307769060135,
-0.023187126964330673,
-0.019578758627176285,
-0.003251110203564167,
0.03480122238397598,
0.001222892664372921,
0.050802670419216156,
-0.009350797161459923,
-0.040588200092315674,
-0.005439992994070053,
-0.0056221941486001015,
0.011757541447877884,
-0.00047954669571481645,
0.03170302137732506,
0.02227325364947319,
0.05937612056732178,
-0.04410022869706154,
0.012899198569357395,
-0.009025286883115768,
-0.024663424119353294,
-0.08666778355836868,
-0.03457442671060562,
0.004512648563832045,
0.07165168970823288,
0.04407462105154991,
-0.02149141952395439,
0.017957966774702072,
0.0529627688229084,
-0.07739201188087463,
0.01597379893064499,
-0.0003956128202844411,
-0.014634393155574799,
-0.03581692650914192,
-0.04196055978536606,
-0.03749372437596321,
0.03079124353826046,
0.0644093006849289,
-0.0069094314239919186,
-0.003088653087615967,
-0.008411409333348274,
-0.0007032809080556035,
-0.018704518675804138,
-0.0046860650181770325,
0.023235563188791275,
-0.04255783185362816,
0.004696385469287634,
0.07489103078842163,
0.004482836462557316,
-0.026456087827682495,
0.028678640723228455,
-0.03983474150300026,
-0.023073315620422363,
0.019808823242783546,
0.03526555001735687,
0.027482137084007263,
0.02351987548172474,
0.024601425975561142,
0.03758608177304268,
-0.01216939464211464,
-0.009912964887917042,
0.016214212402701378,
0.015340474434196949,
-0.026253676041960716,
0.006993842776864767,
0.012576542794704437,
-0.00899468269199133,
-0.030113404616713524,
0.016612762585282326,
-0.057148341089487076,
-0.029064804315567017,
0.020131563767790794,
0.02098417654633522,
-0.004360361956059933,
-0.017410606145858765,
0.027418863028287888,
-0.03939879313111305,
-0.003021345240995288,
0.023999974131584167,
0.038561515510082245,
-0.0037278521340340376,
0.00016033764404710382,
0.0049035861156880856,
-0.061622269451618195,
0.06979351490736008,
0.02477986551821232,
-0.03535917401313782,
-0.01054995134472847,
-0.002332516247406602,
-0.012846771627664566,
0.04441040754318237,
0.017477747052907944,
-0.04332320764660835,
-0.019062276929616928,
0.029656024649739265,
-0.009317092597484589,
0.026924310252070427,
-0.019091496244072914,
-0.007658409420400858,
-0.05180637910962105,
-0.05946608632802963,
0.058132946491241455,
-0.003546007676050067,
-0.008011351339519024,
0.01880807802081108,
-0.016487734392285347,
0.0007929716375656426,
0.03148533031344414,
0.012801084667444229,
-0.012436793185770512,
-0.024276047945022583,
0.03465808182954788,
0.023846959695219994,
0.01927735097706318,
-0.009869204834103584,
0.044635314494371414,
0.02099265344440937,
-0.007394330110400915,
0.0001691405923338607,
0.005562597885727882,
0.010162178426980972,
0.057220857590436935,
0.04513629898428917,
0.005476029589772224,
-0.004370958544313908,
-0.04069563001394272,
-0.028806013986468315,
0.029112083837389946,
0.015996892005205154,
-0.0005528191686607897,
0.07197371125221252,
-0.0053385039791464806,
0.02555854246020317,
0.026867112144827843,
-0.036997489631175995,
-0.06597503274679184,
0.023385848850011826,
-0.0480802059173584,
-0.022076832130551338,
-0.006811303552240133,
0.011456110514700413,
0.0115255331620574,
-0.017652053385972977,
-0.005434192251414061,
0.020902546122670174,
-0.041699349880218506,
-0.05833364278078079,
0.04612206667661667,
0.01939629204571247,
0.02012583054602146,
0.02123815380036831,
0.020433228462934494,
0.0126246502622962,
-0.012516291812062263,
0.03625866770744324,
0.06072111800312996,
0.038638073951005936,
0.03412077575922012,
-0.013799049891531467,
-0.0064645856618881226,
-0.021914469078183174,
0.02694721333682537,
-0.013556682504713535,
0.041762575507164,
-0.03903719410300255,
-0.02275095321238041,
0.0273123811930418,
-0.038369785994291306,
-0.012631970457732677,
-0.0192105770111084,
-0.011337310075759888,
0.07293207943439484,
-0.03469399735331535,
0.02097194828093052,
-0.036589641124010086,
-0.006114393938332796,
-0.03410039097070694,
0.006950777024030685,
0.06412354111671448,
0.043287742882966995,
-0.043784793466329575,
-0.027315817773342133,
-0.016556521877646446,
-0.004696983844041824,
0.033061448484659195,
-0.03460334241390228,
-0.04789120331406593,
-0.004800563212484121,
-0.034802086651325226,
0.0077892388217151165,
-0.06076327711343765,
-0.0019755500834435225,
-0.005894067697227001,
0.028390806168317795,
0.033171337097883224,
-0.0065688882023096085,
0.001157793216407299,
-0.008523376658558846,
-0.06531520187854767,
0.016804203391075134,
-0.03619537129998207,
0.00942628551274538,
0.014218159951269627,
0.04228222370147705,
0.02870124578475952,
0.022178636863827705
] |
<p>This problem is on Di Francesco's book I. It's exercise 7.1:
Calculate the norm of the following vector, where $\lvert h\rangle$ is the state of highest weight.</p>
<p>$$L_{-1}^n\lvert h\rangle$$ </p>
<p>I have just tried to use the commutation relations of the $L$ operators and the fact that $L_1$ acts on $\lvert h\rangle$ is $0$. But as the calculation goes on, things began to be troublesome. I just found them too complicated.</p>
<p>Commutation relations:
$$[L_n,L_m]=(n-m)L_{n+m}+\frac{c}{12}\delta_{n+m,0}n(n^2-1) $$<br>
It is in fact asking us to calculate:
$\langle h|L_1^nL_{-1}^n|h\rangle $.
And we have the following relations:
$$\langle h\rvert L_{-1}=0 \quad\mbox{and}\quad L_1\lvert h\rangle=0. $$ </p>
| 9,373 |
[
-0.002373832743614912,
-0.028575122356414795,
-0.028150297701358795,
-0.03719208016991615,
0.02972387708723545,
-0.0247809998691082,
-0.015669548884034157,
-0.02876981906592846,
0.03150363266468048,
-0.0542089119553566,
0.010137859731912613,
0.047434624284505844,
0.07639994472265244,
0.07656044512987137,
0.022411765530705452,
-0.03659125789999962,
-0.033516623079776764,
-0.026524165645241737,
-0.005341010633856058,
-0.004877218510955572,
0.03720260411500931,
0.044364623725414276,
0.01873290166258812,
-0.03486109897494316,
-0.054658133536577225,
0.03617018461227417,
0.013850213959813118,
-0.024162089452147484,
0.038872551172971725,
0.07124891132116318,
-0.04476260021328926,
-0.05326175317168236,
0.027428237721323967,
0.02486714906990528,
-0.018807174637913704,
0.030614225193858147,
-0.026465503498911858,
-0.0010098917409777641,
-0.00934320967644453,
0.008643441833555698,
-0.05339985340833664,
-0.014475492760539055,
0.0019378925208002329,
0.06480702012777328,
-0.03883117437362671,
0.020928559824824333,
0.00583280622959137,
-0.0012519180309027433,
0.05633726716041565,
-0.07200083136558533,
0.10228943824768066,
0.03241381049156189,
0.004211740102618933,
0.004350733943283558,
0.01574113592505455,
-0.022114356979727745,
0.027055256068706512,
0.07824327051639557,
0.04037875682115555,
-0.05662056431174278,
-0.014027939178049564,
-0.04911895468831062,
-0.03657664731144905,
-0.013986269012093544,
0.005217278841882944,
-0.012096492573618889,
0.06186973676085472,
0.029199538752436638,
0.03947153687477112,
0.00015052266826387495,
-0.039439424872398376,
0.019902996718883514,
0.055727966129779816,
-0.034077953547239304,
0.036953866481781006,
-0.014813968911767006,
0.021840739995241165,
0.02311975695192814,
-0.0020756155718117952,
0.021209334954619408,
-0.027477197349071503,
0.041301339864730835,
0.01137340534478426,
0.03836146742105484,
-0.028794704005122185,
-0.03935329616069794,
0.07272545993328094,
-0.0015746999997645617,
0.02101212367415428,
0.050996433943510056,
-0.01751893013715744,
0.00283266743645072,
0.007469789125025272,
0.002126242034137249,
-0.03559020534157753,
0.061475031077861786,
-0.017383696511387825,
0.028675982728600502,
0.002249583136290312,
-0.03076845034956932,
-0.0324459969997406,
-0.07239353656768799,
0.026452070102095604,
0.04274202883243561,
-0.0170320775359869,
0.0043610199354588985,
-0.021458301693201065,
0.02829226292669773,
-0.019346490502357483,
-0.010611935518682003,
-0.0470799058675766,
0.01721247285604477,
0.0022483542561531067,
-0.022633904591202736,
-0.04223182797431946,
-0.047943077981472015,
-0.02879103273153305,
-0.0013783687027171254,
0.008010155521333218,
0.033330317586660385,
-0.002263615606352687,
-0.014731988310813904,
0.009947563521564007,
-0.025640033185482025,
-0.0637904480099678,
0.03788384050130844,
0.029490876942873,
-0.010108034126460552,
-0.05294669419527054,
0.03604314103722572,
0.021248994395136833,
-0.00637059798464179,
0.015376940369606018,
0.018847189843654633,
0.011517309583723545,
0.026486609131097794,
-0.12560482323169708,
-0.07008102536201477,
0.042162805795669556,
-0.041501838713884354,
0.006544630043208599,
-0.07510457932949066,
0.021132811903953552,
0.035411957651376724,
0.07284967601299286,
0.04762808606028557,
0.04813002794981003,
0.019182639196515083,
-0.012232046574354172,
0.011169045232236385,
0.03995681181550026,
-0.01295743603259325,
-0.004031138028949499,
-0.05710035562515259,
-0.03137388452887535,
-0.03304971754550934,
0.007779408246278763,
0.027209484949707985,
0.0037358796689659357,
-0.03615517169237137,
0.08166657388210297,
0.009174196980893612,
-0.011304778978228569,
0.004249766003340483,
0.005916329566389322,
-0.05074435472488403,
0.05957715958356857,
0.030478350818157196,
0.01014797855168581,
0.027283011004328728,
0.012147667817771435,
-0.02492380701005459,
-0.006073111668229103,
0.02544993907213211,
0.0529082715511322,
-0.0033480802085250616,
-0.026861203834414482,
-0.059587735682725906,
0.01906818524003029,
-0.0007931869477033615,
-0.007480695843696594,
-0.015165853314101696,
-0.023406533524394035,
0.06698422878980637,
0.00011762302165152505,
0.028208641335368156,
-0.01896861381828785,
-0.00022859864111524075,
0.039918944239616394,
-0.021629782393574715,
0.02463221549987793,
-0.021370260044932365,
0.022195590659976006,
0.05311359465122223,
-0.03526458516716957,
0.031099891290068626,
-0.02145182341337204,
0.018896713852882385,
0.0010565347038209438,
-0.011125261895358562,
0.006303482223302126,
-0.012922057881951332,
-0.0198962539434433,
0.0037906637880951166,
0.026553349569439888,
0.047107912600040436,
0.03974425420165062,
0.00620232755318284,
0.047545235604047775,
-0.04371807724237442,
-0.01155613549053669,
0.034733545035123825,
0.026975512504577637,
0.03529030457139015,
0.027219530194997787,
0.015955409035086632,
0.01175357773900032,
-0.030576040968298912,
0.010821935720741749,
0.034584470093250275,
-0.03808342665433884,
0.05460631102323532,
0.0392025001347065,
0.015198674984276295,
0.011075431481003761,
0.022242102771997452,
0.007245606742799282,
-0.009186996147036552,
0.01150921918451786,
-0.01151281874626875,
-0.04548820108175278,
0.009154411032795906,
0.0004178073722869158,
0.02279505506157875,
-0.041120629757642746,
0.012131738476455212,
0.02445981837809086,
0.04596870765089989,
0.03447013720870018,
0.01513824611902237,
-0.03911649435758591,
-0.011478281579911709,
0.0202010590583086,
0.033971115946769714,
0.0037987064570188522,
0.021976668387651443,
0.011388842016458511,
0.036067526787519455,
0.04258640855550766,
0.035979170352220535,
-0.06171976029872894,
0.07345642894506454,
-0.017091425135731697,
0.010377236641943455,
0.011997527442872524,
-0.045570582151412964,
0.05472810938954353,
-0.024846650660037994,
0.006776265799999237,
0.04834543168544769,
-0.025124873965978622,
-0.0018213213188573718,
-0.005558074451982975,
-0.046390924602746964,
0.02009142003953457,
-0.0006276361527852714,
-0.023353934288024902,
-0.006387999746948481,
0.02377757430076599,
-0.04386250674724579,
-0.0007050677668303251,
0.003524600761011243,
-0.027284234762191772,
0.011325438506901264,
0.01712186634540558,
0.019530387595295906,
0.003144846996292472,
0.007645125035196543,
-0.021094365045428276,
0.0031818922143429518,
-0.01574411801993847,
-0.03559673950076103,
0.04313524812459946,
0.022851305082440376,
-0.04968181625008583,
-0.0364324115216732,
-0.011797524057328701,
-0.042005978524684906,
0.01939333975315094,
0.007604917045682669,
0.010323664173483849,
0.01305458601564169,
-0.008970087394118309,
-0.028341425582766533,
-0.04812631756067276,
-0.029501449316740036,
0.02679092437028885,
-0.0054272874258458614,
0.01411520317196846,
0.051446620374917984,
0.00621378980576992,
-0.047896239906549454,
0.009593416005373001,
0.007395172957330942,
-0.03152704983949661,
-0.05072103440761566,
-0.005955567117780447,
-0.0019769177306443453,
-0.02531859464943409,
0.0030662245117127895,
0.03597750887274742,
0.028555383905768394,
-0.02368965372443199,
-0.06632953882217407,
-0.04681156575679779,
0.008177297189831734,
-0.004392873961478472,
0.011875700205564499,
0.00880519114434719,
-0.01171183679252863,
0.10692044347524643,
0.03542780131101608,
-0.02653450146317482,
-0.027809813618659973,
-0.004344159737229347,
-0.01720726490020752,
-0.04999620467424393,
0.007117506582289934,
0.046673260629177094,
-0.036007110029459,
0.04985139146447182,
0.008541855029761791,
0.007468445226550102,
0.0391848124563694,
-0.011027862317860126,
-0.05162126570940018,
0.02581346035003662,
-0.02720711939036846,
-0.018125878646969795,
0.08637282252311707,
-0.02506142482161522,
0.015578294172883034,
0.013196296989917755,
0.034765008836984634,
0.028997858986258507,
-0.015202915295958519,
-0.05620386824011803,
0.022771084681153297,
-0.03270714730024338,
0.021276799961924553,
0.004482561256736517,
0.05105368047952652,
0.0024112246464937925,
-0.012292115949094296,
0.020672112703323364,
-0.0068299551494419575,
0.0291279423981905,
-0.059524815529584885,
-0.022012120112776756,
0.057120561599731445,
0.031318146735429764,
-0.004429670982062817,
-0.019429512321949005,
0.05395355448126793,
-0.0029444918036460876,
0.0366479717195034,
-0.034937627613544464,
0.007120764348655939,
0.013504037633538246,
0.027218669652938843,
0.016477307304739952,
-0.008231713436543941,
-0.058482155203819275,
0.004079736769199371,
-0.031822968274354935,
0.021610938012599945,
0.03692702203989029,
0.06757836788892746,
-0.014769922010600567,
0.034927912056446075,
0.039639513939619064,
0.016024066135287285,
0.03726552426815033,
0.015461700968444347,
-0.07961941510438919,
0.01388806477189064,
-0.010066388174891472,
-0.005096251145005226,
0.03693113476037979,
-0.01408546045422554,
0.048163190484046936,
0.0058553218841552734,
-0.049344152212142944,
-0.03259189426898956,
-0.009483559988439083,
-0.04259740188717842,
-0.0011847069254145026,
-0.048396043479442596,
-0.019263118505477905,
-0.008860629983246326,
-0.0027400122489780188,
0.03836124390363693,
-0.026559622958302498,
-0.009135501459240913,
0.05780116096138954,
-0.02447887323796749,
0.03269021958112717,
-0.001553263165988028,
0.025135299190878868,
0.030898598954081535,
0.0410672090947628,
-0.013442963361740112,
0.044038206338882446,
0.015014350414276123,
0.003750360105186701,
-0.050873249769210815,
0.03190769627690315,
0.0070187486708164215,
-0.0005486580776050687,
0.013131720013916492,
-0.0286905225366354,
-0.005172512959688902,
0.017488207668066025,
0.04770991951227188,
-0.017732858657836914,
0.028347838670015335,
0.06220969930291176,
-0.0021440531127154827,
-0.025590356439352036,
0.03453163430094719,
0.06099839136004448,
-0.016993260011076927,
-0.023213757202029228,
-0.02128935605287552,
-0.009921842254698277,
-0.02335517853498459,
-0.004675467032939196,
0.05027284845709801,
-0.018817376345396042,
-0.0038682788144797087,
-0.027418768033385277,
0.04861260578036308,
0.045166824012994766,
0.0060300445184111595,
0.023087387904524803,
0.020040618255734444,
0.03216572850942612,
-0.0027478127740323544,
0.0035834151785820723,
0.002520789857953787,
0.0005998868145979941,
0.030707035213708878,
0.008350488729774952,
0.018431825563311577,
-0.04438066855072975,
-0.012257660739123821,
0.010976515710353851,
0.0031672094482928514,
0.0013950758147984743,
0.030843673273921013,
-0.04043348878622055,
-0.05182446166872978,
0.037924110889434814,
-0.04926507547497749,
0.06036987155675888,
0.01961805671453476,
-0.007369953207671642,
-0.008412248454988003,
-0.02736547403037548,
-0.013325612992048264,
-0.0008938403334468603,
-0.01607370562851429,
0.05875737965106964,
-0.013802380301058292,
-0.02450101263821125,
-0.027245283126831055,
0.01350364089012146,
0.025163937360048294,
0.04539446160197258,
0.021242361515760422,
-0.028439942747354507,
-0.004948744084686041,
0.04548470303416252,
-0.05515039339661598,
-0.05743017420172691,
-0.007111331447958946,
0.027544984593987465,
-0.007469047326594591,
0.02977592684328556,
-0.037855103611946106,
-0.05261795222759247,
0.002867454430088401,
0.0017779301851987839,
-0.0074880970641970634,
-0.0035176221281290054,
-0.02401970513164997,
0.07066775113344193,
0.027963940054178238,
0.003836519317701459,
0.052991196513175964,
0.016947677358984947,
-0.015653379261493683,
0.0043345908634364605,
-0.0296210665255785,
-0.006780874449759722,
-0.001516546937637031,
0.023461543023586273,
-0.02151930332183838,
0.01774282567203045,
0.023455550894141197,
0.0444500558078289,
-0.01676681451499462,
0.04539371654391289,
0.025902876630425453,
-0.01510501280426979,
-0.030593425035476685,
0.025393160060048103,
-0.036314405500888824,
0.003694750601425767,
0.025717822834849358,
0.013243980705738068,
0.04261842742562294,
-0.022062141448259354,
0.005670433398336172,
-0.0030109649524092674,
0.006343952380120754,
0.0030027006287127733,
-0.023201461881399155,
0.030215993523597717,
-0.022277191281318665,
-0.00009985261567635462,
-0.024972043931484222,
-0.03204198181629181,
0.030859297141432762,
-0.00953717716038227,
-0.003489490831270814,
-0.011428301222622395,
0.0095401331782341,
-0.05174674838781357,
-0.010723811574280262,
-0.047428544610738754,
0.014695747755467892,
-0.02144952118396759,
-0.011961862444877625,
0.027006512507796288,
-0.0068542687222361565,
-0.046427126973867416,
-0.052352260798215866,
-0.0071421898901462555,
0.031837016344070435,
0.007355900947004557,
-0.018658528104424477,
-0.010789698921144009,
-0.008047626353800297,
0.006139283999800682,
-0.05616917461156845,
0.05282287672162056,
-0.0269350316375494,
-0.004356423392891884,
0.05625377222895622,
0.018387608230113983,
0.06325601041316986,
0.019817830994725227,
-0.039364490658044815,
0.02306496351957321,
-0.0008386080735363066,
-0.03751295432448387,
0.01419564988464117,
0.016917629167437553,
-0.029003549367189407,
-0.037340179085731506,
0.012330673635005951,
0.00966628361493349,
0.02612265944480896,
-0.00044306262861937284,
-0.010543600656092167,
0.030095165595412254,
0.019465535879135132,
0.024056755006313324,
-0.019829140976071358,
0.007016767282038927,
-0.0006167407264001667,
0.02382056601345539,
-0.02341213822364807,
-0.015789173543453217,
-0.031565386801958084,
-0.036790892481803894,
-0.012946282513439655,
0.028518086299300194,
0.013243669643998146,
-0.013559076003730297,
0.0905848890542984,
-0.008735207840800285,
-0.016668230295181274,
0.06444206088781357,
0.009328430518507957,
0.016743885353207588,
-0.0028302869759500027,
0.026307474821805954,
-0.005630218889564276,
0.006538716144859791,
-0.009179072454571724,
-0.019368179142475128,
-0.047928739339113235,
0.037977684289216995,
0.0425422377884388,
-0.0022963457740843296,
0.018838418647646904,
0.0028125448152422905,
0.022580737248063087,
0.014316914603114128,
-0.014765175059437752,
-0.04956018179655075,
0.00825163908302784,
-0.020985644310712814,
0.06296321749687195,
-0.025942765176296234,
0.023616433143615723,
0.04439288005232811,
0.006971647497266531,
-0.03965848311781883,
-0.02226031757891178,
-0.00363279040902853,
0.0014892247272655368,
0.03134609013795853,
-0.011345270089805126,
-0.015196233056485653,
0.02975749783217907,
-0.02039465494453907,
0.037638109177351,
-0.03736630454659462,
0.0004810993268620223,
0.0028212617617100477,
-0.005082765594124794,
-0.015070533379912376,
-0.028756452724337578,
-0.054619211703538895,
-0.007494579069316387,
0.00936516746878624,
0.013336634263396263,
-0.03815677762031555,
0.006492028944194317,
0.017427703365683556,
-0.0015253261663019657,
0.01854385994374752,
0.020395098254084587,
-0.02645164541900158,
-0.018300803378224373,
-0.006930030882358551,
-0.0261541735380888,
-0.046301569789648056,
0.016083385795354843,
0.0033347830176353455,
-0.002478141337633133,
0.04169651120901108,
-0.010694589465856552,
0.01956016942858696,
0.01486361213028431,
0.005165110342204571,
0.01451609842479229,
0.07101435959339142,
0.009926795959472656,
0.013140141032636166,
0.034316495060920715,
0.02742965705692768,
0.12438157200813293,
0.043526966124773026,
0.022999286651611328,
-0.09189264476299286,
0.013437414541840553,
0.05423441529273987,
-0.007422591559588909,
-0.03576427698135376,
0.03106338158249855,
-0.014843306504189968,
-0.001371803693473339,
-0.029016004875302315,
-0.022086981683969498,
-0.009893965907394886,
0.00415221881121397,
0.018543723970651627,
-0.03518570214509964,
-0.03565175458788872,
-0.02543768472969532,
0.03159200772643089,
-0.0059394496493041515,
-0.011590921320021152,
-0.026269536465406418,
0.04022166132926941,
-0.009985917247831821,
-0.013816098682582378,
-0.032876480370759964,
-0.03467150032520294,
0.010095971636474133,
-0.02059338614344597,
-0.013019975274801254,
0.01647540181875229,
0.01100448239594698,
-0.010087037459015846,
-0.05057742819190025,
0.014973332174122334,
0.02987990900874138,
0.025192469358444214,
0.032448142766952515,
0.006731336936354637,
0.014188598841428757,
0.0486878976225853,
0.006134269759058952,
-0.026061594486236572,
-0.0451885350048542,
-0.012806585058569908,
-0.04901804029941559,
0.06537964940071106,
0.006272314116358757,
0.00770884333178401,
0.05627601221203804,
-0.036346908658742905,
-0.004874211270362139,
-0.028691479936242104,
0.003994380589574575,
-0.007482148706912994,
0.044096264988183975,
-0.016941849142313004,
-0.012594594620168209,
0.015515806153416634,
0.011872967705130577,
0.010059275664389133,
-0.007158448453992605,
-0.0016542489174753428,
0.0022896151058375835,
0.02284061536192894,
-0.027973152697086334,
0.01906794309616089,
-0.003969607409089804,
-0.023796524852514267,
-0.028273994103074074,
0.006524324882775545,
0.0002171933010686189,
-0.017756681889295578,
0.006440482567995787,
0.011106831021606922,
0.05248032510280609,
0.010228926315903664,
-0.05269426852464676,
-0.012962006032466888,
-0.1104755774140358,
0.0009611136629246175,
-0.006930566858500242,
-0.0428733266890049,
0.014901108108460903,
-0.04650593176484108,
0.01392159890383482,
0.047820981591939926,
-0.01892753317952156,
-0.017170682549476624,
0.035300012677907944,
0.012202378362417221,
0.030092494562268257,
-0.05876006931066513,
-0.031211504712700844,
-0.010657303966581821,
-0.03507012128829956,
0.017144113779067993,
0.00014682243636343628,
0.0186139065772295,
-0.006234101951122284,
0.01927712745964527,
0.00450900150462985,
0.056184425950050354,
-0.0018977868603542447,
-0.00321016414090991,
-0.008962146006524563,
-0.03303612023591995,
0.02960999496281147,
0.0370311476290226,
-0.006258845329284668,
-0.046955399215221405,
-0.03315849229693413,
-0.02237078920006752,
-0.03799821063876152,
0.007875742390751839,
0.011838657781481743,
-0.057771310210227966,
-0.005057378672063351,
-0.014773303642868996,
0.010916545987129211,
-0.0007126510608941317,
0.01208796352148056,
-0.03166189417243004,
-0.006612361874431372,
-0.006288271397352219,
0.0003008688217960298,
-0.05895165354013443,
0.029529882594943047,
-0.006371509283781052,
-0.007732752710580826,
0.020097753033041954,
0.023514317348599434,
0.007089647464454174,
-0.06156798452138901,
-0.026351986452937126,
0.02365276962518692,
0.013539934530854225,
0.00376276602037251,
-0.03232941776514053,
0.039292942732572556,
-0.03180989250540733,
-0.010381176136434078,
0.025861458852887154,
-0.0026731095276772976,
0.02970079518854618,
0.02284160628914833,
-0.02735878713428974,
-0.023973241448402405,
0.048077844083309174,
-0.01159190945327282,
0.008675294928252697,
-0.006911046802997589,
-0.04470236599445343,
-0.0203391220420599,
0.017170824110507965,
-0.013817913830280304,
0.009830208495259285,
-0.0040816315449774265,
-0.0000739146998967044,
0.053708743304014206,
-0.018793068826198578,
-0.0024469541385769844,
-0.01761181838810444,
0.031792718917131424,
0.03786686062812805,
0.049369990825653076,
-0.018315579742193222,
0.012741830199956894,
-0.0005004505510441959,
-0.018942322582006454,
0.019959313794970512,
0.02141054905951023,
0.01721668243408203,
-0.07681961357593536,
-0.007362395990639925,
-0.012058946304023266,
0.0073687415570020676,
0.027957333251833916,
-0.05021407827734947,
0.006519121117889881,
0.03900381177663803,
-0.04262487590312958,
0.016511062160134315,
-0.00927232950925827,
0.0011336600873619318,
-0.03252456337213516,
-0.006252819672226906,
-0.03084024041891098,
0.011926157400012016,
-0.01564859040081501,
0.038789302110672,
0.026557940989732742,
0.00980303343385458,
-0.02726437710225582,
-0.04574766010046005,
-0.02091560699045658,
0.009512360207736492,
0.040989574044942856,
-0.00030282390071079135,
0.011166212148964405,
-0.019999902695417404,
-0.05132952332496643,
0.02795223891735077,
-0.03612791746854782,
-0.0022480436600744724,
-0.03508183732628822,
0.028148749843239784,
0.02354135736823082,
0.04543570801615715,
-0.003396356012672186,
-0.030593227595090866,
-0.010491304099559784,
-0.024589085951447487,
0.024397755041718483,
-0.004463821183890104,
-0.0200839564204216,
-0.003076659981161356,
0.0015640357742086053,
-0.04163369908928871,
-0.0460217222571373,
0.04200722649693489,
-0.012910249643027782,
-0.010381532832980156,
-0.0034341872669756413,
-0.03926573693752289,
0.025872426107525826,
-0.05441678687930107,
0.029510630294680595,
-0.013911368325352669,
-0.01690923050045967,
0.015320327132940292,
0.016843104735016823,
-0.03259792923927307,
-0.0008914534701034427,
-0.0450865775346756,
-0.04996105283498764,
0.023793302476406097,
0.01317578088492155,
-0.035425957292318344,
-0.040890827775001526,
-0.027708571404218674,
-0.0105558130890131,
0.030058860778808594,
-0.025664908811450005,
-0.02299724519252777,
-0.08390899002552032,
0.007199480198323727,
-0.009874545969069004,
0.021678445860743523,
-0.04303542152047157,
-0.02814519591629505,
0.00462945643812418,
-0.08386928588151932,
0.025371085852384567,
0.04326828196644783,
0.014924777671694756,
-0.02202363684773445,
-0.011616259813308716,
-0.008696867153048515,
0.013175898231565952,
0.035284776240587234,
0.0358230322599411,
-0.038927383720874786,
0.009166949428617954,
-0.05084231123328209,
-0.003132784506306052,
-0.001309896120801568,
0.015535852871835232,
-0.017050255089998245,
-0.023679502308368683,
-0.005431780591607094,
-0.009993358515202999,
-0.0030170681420713663,
-0.026491252705454826,
0.007251013070344925,
0.02782810665667057,
-0.042640626430511475,
-0.02643168717622757,
-0.020599713549017906,
0.021127009764313698,
-0.02394786663353443,
-0.010396554134786129,
0.07250487804412842,
0.01785171777009964,
0.0028205395210534334,
0.012396304868161678,
-0.04016613960266113,
-0.05833305045962334,
0.029138129204511642,
-0.041327524930238724,
-0.009533011354506016,
0.0016797902062535286,
0.012872958555817604,
0.06097402051091194,
-0.008351355791091919,
-0.014411959797143936,
0.07934516668319702,
-0.03134153410792351,
-0.0038703966420143843,
0.01585405506193638,
0.024827102199196815,
0.017897529527544975,
0.03409229964017868,
0.006889917887747288,
0.025249822065234184,
0.007373415865004063,
0.053941670805215836,
0.05776924267411232,
0.007320945616811514,
-0.0113053098320961,
-0.022448603063821793,
0.0319673977792263,
-0.030647989362478256,
0.010103554464876652,
0.017336314544081688,
-0.0008237190777435899,
-0.041742805391550064,
0.007060964126139879,
0.03258026763796806,
0.0073985750786960125,
-0.030774714425206184,
0.002508545760065317,
-0.017561038956046104,
0.03989575430750847,
-0.002752525033429265,
0.02316863276064396,
-0.034237660467624664,
0.018570877611637115,
0.007631558459252119,
0.004928928334265947,
0.014900476671755314,
0.05057588592171669,
-0.04671068862080574,
0.019178569316864014,
-0.04363599047064781,
-0.00883579347282648,
0.009329594671726227,
-0.05065513402223587,
-0.03237392008304596,
0.028149008750915527,
-0.017482103779911995,
-0.00892628077417612,
-0.05135876685380936,
-0.020447464659810066,
-0.05085664615035057,
0.0002881270193029195,
0.060516826808452606,
0.0023813555017113686,
-0.015241390094161034,
0.01662013679742813,
-0.016655446961522102,
0.019256580621004105,
-0.01200202014297247,
-0.011835996061563492,
-0.021311243996024132,
0.023405594751238823,
-0.010801348835229874,
-0.016420546919107437
] |
<p>My understanding of algebraic topology and Riemannian geometry come from Nakahara's <em>Geometry, Topology, and Physics,</em> which I do not think is sufficient. I am first year PhD student, and I want to do string theory at my university. Can you recommend me any other really nice books that I should read over the years. </p>
| 185 |
[
0.009585767984390259,
-0.04372845217585564,
0.05371774360537529,
-0.037236109375953674,
0.006989956833422184,
0.0445016510784626,
0.0065638343803584576,
-0.010979032143950462,
-0.026341771706938744,
-0.03695180267095566,
0.03654618561267853,
0.0076219760812819,
0.022898385301232338,
0.007926518097519875,
-0.0006574503495357931,
-0.03137538954615593,
-0.027458423748612404,
-0.03935980796813965,
-0.03899839147925377,
0.00089236133499071,
0.026083793491125107,
0.03392340615391731,
0.01699148863554001,
0.017875351011753082,
-0.008320294320583344,
0.04245223104953766,
0.010732066817581654,
0.009411964565515518,
0.006878978107124567,
0.05836286023259163,
-0.027285847812891006,
-0.010243738070130348,
0.0116445766761899,
0.006581814959645271,
-0.00011076480586780235,
-0.025691501796245575,
-0.013586989603936672,
-0.002647103276103735,
0.012023705057799816,
-0.013834569603204727,
-0.03648514673113823,
-0.041187211871147156,
-0.04286538437008858,
0.04153454303741455,
-0.017889345064759254,
0.04169420525431633,
-0.02503739297389984,
-0.02275041677057743,
0.0360649973154068,
-0.06601545959711075,
0.058974698185920715,
0.009773965924978256,
0.022060157731175423,
0.03560199588537216,
0.024255111813545227,
0.020039673894643784,
0.04272682964801788,
0.0860227644443512,
-0.015539939515292645,
-0.061028070747852325,
-0.03856705129146576,
-0.03154201805591583,
-0.011495820246636868,
-0.014858001843094826,
-0.046506911516189575,
0.0374862402677536,
-0.019838768988847733,
-0.014883945696055889,
0.029339779168367386,
-0.016451483592391014,
-0.0341460295021534,
0.015170895494520664,
0.022243604063987732,
-0.003637544345110655,
0.003575191367417574,
0.00871154572814703,
0.000535912171471864,
-0.03139996901154518,
0.04505300894379616,
0.02760196290910244,
-0.0056406911462545395,
-0.002824860392138362,
-0.003332125023007393,
0.03238119184970856,
0.014614998362958431,
-0.0028537269681692123,
0.07781725376844406,
-0.01820717379450798,
-0.04847326502203941,
0.02465902641415596,
-0.025877922773361206,
-0.034276895225048065,
0.028616376221179962,
-0.04679658263921738,
-0.021317139267921448,
0.019443083554506302,
-0.0204016100615263,
0.058596689254045486,
-0.0031382308807224035,
-0.0009077287395484746,
-0.019938291981816292,
-0.02860713005065918,
0.031191479414701462,
0.06621459126472473,
0.03659624233841896,
-0.031779687851667404,
-0.03212350234389305,
0.038015205413103104,
-0.025133009999990463,
-0.0259507205337286,
-0.02721245214343071,
0.02184353768825531,
-0.02108222246170044,
-0.014370501972734928,
-0.031985484063625336,
-0.01851452887058258,
0.033452555537223816,
-0.023231904953718185,
0.03314279392361641,
0.09837431460618973,
0.048440609127283096,
-0.04308813437819481,
0.05696913227438927,
-0.02597220242023468,
-0.08218701928853989,
-0.0037667143624275923,
0.08826159685850143,
-0.028630416840314865,
-0.03876963257789612,
0.01712675765156746,
-0.005013261456042528,
0.0055846525356173515,
0.0010241360869258642,
0.01984584517776966,
0.07791946828365326,
0.00735977990552783,
-0.09094217419624329,
-0.052729230374097824,
0.029976190999150276,
-0.003005153266713023,
-0.020806973800063133,
-0.054452791810035706,
0.013314420357346535,
0.03407471254467964,
0.0630183145403862,
-0.010408790782094002,
0.025066064670681953,
0.01562831923365593,
0.044057637453079224,
-0.023813141509890556,
-0.05832855775952339,
-0.03365110233426094,
0.006244780495762825,
-0.00794153194874525,
0.005928497761487961,
-0.0579008013010025,
-0.012354741804301739,
0.036272820085287094,
0.04347902536392212,
-0.007756636943668127,
0.08555635809898376,
0.005651589948683977,
-0.007136567495763302,
0.019178925082087517,
-0.036168184131383896,
-0.013098104856908321,
0.0719868615269661,
-0.00144028605427593,
0.026620343327522278,
0.0018749075243249536,
0.022938566282391548,
0.022269099950790405,
0.02082837000489235,
0.022631922736763954,
0.03942713141441345,
-0.0308314710855484,
0.02234937995672226,
0.047501593828201294,
-0.02171388454735279,
0.006913912482559681,
-0.001899055321700871,
-0.0419476144015789,
-0.009991015307605267,
0.024307915940880775,
-0.04037958383560181,
0.04665463790297508,
-0.006548164878040552,
-0.025996392592787743,
0.03466774895787239,
-0.022046230733394623,
-0.01228344440460205,
-0.030404604971408844,
0.00040240678936243057,
-0.0012787238229066133,
0.004914216231554747,
0.03468623012304306,
0.008029026910662651,
0.01141685526818037,
-0.05286669358611107,
-0.05212237685918808,
-0.023676583543419838,
0.01624445989727974,
0.020435109734535217,
0.004797243978828192,
-0.007622832432389259,
0.04335913807153702,
0.04036951810121536,
-0.02302851341664791,
0.02178775519132614,
-0.020739594474434853,
-0.02554294839501381,
0.017822129651904106,
-0.007485969923436642,
0.05023213103413582,
-0.02547319419682026,
0.008005942218005657,
-0.000025887598894769326,
-0.0034214428160339594,
-0.04992026463150978,
0.013751974329352379,
-0.03334911912679672,
0.033233486115932465,
0.02648678608238697,
0.024687385186553,
-0.010823196731507778,
0.03891308233141899,
0.00420242827385664,
0.016303814947605133,
-0.02723943069577217,
-0.0003066286153625697,
-0.016377674415707588,
0.02709648571908474,
0.04785836115479469,
0.043139323592185974,
-0.02765042893588543,
0.027819497510790825,
0.0304864551872015,
0.03303610160946846,
-0.007642132695764303,
0.011626169085502625,
-0.01675819791853428,
-0.03421006351709366,
0.024562513455748558,
-0.02118794247508049,
-0.01658504083752632,
0.0006581430207006633,
0.02650872990489006,
0.0023392566945403814,
-0.002639258746057749,
0.006898386403918266,
-0.022152021527290344,
0.0342116542160511,
-0.04279378801584244,
0.00005791070725535974,
0.05198254436254501,
-0.01772097498178482,
0.03928235173225403,
-0.034340888261795044,
0.009025678038597107,
0.0020918725058436394,
0.0000840974462334998,
-0.0027202912606298923,
-0.02610434964299202,
-0.02597871981561184,
-0.005577495321631432,
-0.009080416522920132,
0.014773976989090443,
-0.010422534309327602,
0.031425006687641144,
-0.06126983091235161,
-0.00583672383800149,
0.0295480377972126,
-0.025097036734223366,
-0.03554162383079529,
0.002754178596660495,
0.004738166928291321,
0.011326637119054794,
0.0329974964261055,
-0.024921314790844917,
-0.015134965069591999,
0.03208135440945625,
-0.028092751279473305,
0.0010019364999607205,
0.012675104662775993,
-0.0547412633895874,
0.027732208371162415,
-0.0406237356364727,
-0.023318050429224968,
0.06037994101643562,
0.003733647521585226,
0.00021913161617703736,
-0.02246187813580036,
0.00898863933980465,
-0.010569426231086254,
-0.026809565722942352,
0.010759178549051285,
0.009022228419780731,
-0.02326299622654915,
-0.005569188389927149,
0.04429347813129425,
-0.019930526614189148,
-0.001200652215629816,
-0.008810401894152164,
-0.020056065171957016,
-0.03382221609354019,
0.020998826250433922,
0.009631656110286713,
0.013884504325687885,
-0.03822813555598259,
-0.038821492344141006,
0.007939004339277744,
-0.04488696902990341,
-0.002702357480302453,
-0.040608882904052734,
-0.054363515228033066,
0.02362229861319065,
0.008265139535069466,
0.021981360390782356,
0.03024311549961567,
-0.04804139956831932,
0.06294267624616623,
0.03589741885662079,
-0.039692193269729614,
-0.018588900566101074,
0.0014637729618698359,
-0.03569842129945755,
-0.012450506910681725,
0.02775340899825096,
0.012825865298509598,
-0.018279733136296272,
0.0036938507109880447,
0.06141359731554985,
0.04359406232833862,
0.033197011798620224,
0.009227233938872814,
-0.024492710828781128,
-0.008323145098984241,
0.010874774307012558,
0.02931203879415989,
0.005632692947983742,
0.02473391592502594,
-0.009512844495475292,
0.006231892853975296,
0.01654672622680664,
-0.014230708591639996,
0.029020246118307114,
-0.03516118600964546,
0.04616857320070267,
-0.014283382333815098,
0.0164799727499485,
-0.010520691983401775,
0.043776851147413254,
-0.015698356553912163,
-0.045220620930194855,
0.012561504729092121,
0.004212754312902689,
0.002956126816570759,
0.01878625713288784,
0.016868602484464645,
0.018999597057700157,
0.04142984747886658,
-0.02762744389474392,
-0.020042477175593376,
-0.022607941180467606,
0.0071234446950256824,
0.04590032994747162,
-0.019457252696156502,
-0.0063580297864973545,
0.05395728349685669,
0.01836356334388256,
0.0082327239215374,
-0.002846432151272893,
-0.07416407018899918,
0.01468587014824152,
-0.06773058325052261,
0.009605091996490955,
-0.006369474343955517,
0.03656311705708504,
-0.03758979216217995,
0.015261922031641006,
0.008074922487139702,
0.011370592750608921,
0.030034279450774193,
-0.02972744032740593,
-0.09421912580728531,
-0.00040521053597331047,
-0.04238118603825569,
-0.02609005942940712,
0.0357535257935524,
0.02583412639796734,
0.0240761861205101,
0.019061220809817314,
-0.051348503679037094,
-0.031144803389906883,
0.005211612209677696,
-0.06427691131830215,
0.013194592669606209,
-0.08740787208080292,
-0.04766666516661644,
0.0029800906777381897,
0.03278231993317604,
0.04243515804409981,
-0.05301813408732414,
0.012330165132880211,
0.037627946585416794,
-0.024570416659116745,
-0.02214883826673031,
-0.001243055216036737,
0.02601585164666176,
-0.002195310080423951,
0.006279039662331343,
0.02584533952176571,
0.03796845301985741,
-0.02830401249229908,
0.03135966509580612,
0.0011669028317555785,
0.03448515385389328,
-0.04432838037610054,
-0.0403008870780468,
0.031443286687135696,
-0.05442037060856819,
-0.027027247473597527,
-0.04989278316497803,
0.053317904472351074,
0.018917301669716835,
-0.020627912133932114,
0.03940822184085846,
-0.0020987235475331545,
-0.044809892773628235,
0.030550125986337662,
0.015002477914094925,
-0.019010357558727264,
-0.02971781976521015,
-0.02980310656130314,
-0.019829394295811653,
-0.04889293387532234,
-0.0038081062957644463,
-0.010745439678430557,
-0.009225921705365181,
-0.05819685012102127,
0.0032372553832829,
0.019014054909348488,
0.003523984458297491,
-0.055178966373205185,
-0.05095089599490166,
0.012844112701714039,
0.013840897008776665,
-0.03901120647788048,
-0.020256010815501213,
0.03240063786506653,
0.02548629604279995,
0.06488338112831116,
-0.015984728932380676,
-0.001800019876100123,
-0.07876308262348175,
-0.002584588946774602,
0.020846039056777954,
0.00893006008118391,
-0.007790814619511366,
-0.014007573947310448,
-0.05663082003593445,
-0.048710037022829056,
0.06892616301774979,
-0.0023232779931277037,
0.028369858860969543,
-0.03174437955021858,
-0.04074568673968315,
-0.0289631187915802,
-0.007811287418007851,
-0.000056989785662153736,
0.01527120266109705,
0.0064409589394927025,
0.06294997036457062,
-0.004531725309789181,
0.013438597321510315,
-0.02662479504942894,
0.04299643263220787,
0.012996667996048927,
0.02549012191593647,
0.056972093880176544,
0.009978626854717731,
0.036213744431734085,
0.0510743148624897,
-0.028061097487807274,
-0.05117195472121239,
0.02673216722905636,
0.008000114932656288,
-0.050817061215639114,
-0.007048254832625389,
-0.027175694704055786,
-0.02267681248486042,
-0.005863924976438284,
-0.019914668053388596,
-0.00769822858273983,
-0.020350702106952667,
-0.024361053481698036,
0.005628855898976326,
-0.00029711253591813147,
0.019822558388113976,
-0.0024531970266252756,
-0.0031830540392547846,
-0.008238252252340317,
0.016943663358688354,
-0.027622967958450317,
0.056508444249629974,
-0.01101659145206213,
0.005508235190063715,
-0.01995641365647316,
-0.04459390789270401,
-0.08098866790533066,
0.03918198123574257,
-0.052732665091753006,
-0.013268325477838516,
-0.015336591750383377,
-0.019432956352829933,
0.0019210010068491101,
-0.0016374344704672694,
0.030408482998609543,
-0.00807332806289196,
0.044729672372341156,
0.024006430059671402,
0.011601131409406662,
-0.00924898311495781,
0.022517308592796326,
0.008512950502336025,
-0.00762128084897995,
-0.0006204569363035262,
0.027568919584155083,
0.04491622373461723,
-0.03456537798047066,
-0.0447266660630703,
0.006632488686591387,
-0.02494347281754017,
0.06608664244413376,
0.0029019208159297705,
0.0024761096574366093,
0.025871453806757927,
-0.03283875435590744,
-0.025255026295781136,
0.0038207818288356066,
-0.01896953396499157,
-0.0008450042805634439,
-0.045613281428813934,
0.008326309733092785,
0.013380485586822033,
-0.015139958821237087,
-0.024089230224490166,
-0.059576403349637985,
-0.0022578928619623184,
0.0023105742875486612,
-0.033077117055654526,
-0.04553065076470375,
0.07125392556190491,
-0.011132542043924332,
0.0025368924252688885,
-0.01679670251905918,
0.04650307446718216,
-0.022784199565649033,
-0.007696975022554398,
0.04667005315423012,
0.05055505782365799,
0.030309529975056648,
-0.00666411779820919,
-0.014193419367074966,
0.010958483442664146,
0.00029627783806063235,
-0.014931775629520416,
-0.023169711232185364,
0.040665701031684875,
0.01611381582915783,
-0.0030329490546137094,
-0.0280012134462595,
-0.01120961643755436,
0.034986864775419235,
-0.043053675442934036,
0.03572539985179901,
0.0647452101111412,
0.033080436289310455,
-0.00702334102243185,
-0.015111016109585762,
-0.005132903344929218,
-0.013415026478469372,
0.015271895565092564,
-0.038184136152267456,
0.01466958038508892,
0.02956511825323105,
-0.032222848385572433,
0.0056402781046926975,
0.011976170353591442,
0.016918234527111053,
0.009217577986419201,
0.024001671001315117,
0.019889691844582558,
-0.02370532788336277,
0.007342047523707151,
-0.024951858446002007,
-0.016447236761450768,
-0.01918463408946991,
0.00894128903746605,
0.007979180663824081,
0.01619625836610794,
-0.021935507655143738,
-0.08015327155590057,
0.002755645662546158,
-0.010378754697740078,
0.05141092464327812,
0.005601894110441208,
0.05126000940799713,
0.05669109895825386,
0.005892039276659489,
0.003215478966012597,
-0.003006473183631897,
-0.03537164255976677,
-0.02477712370455265,
0.02810380980372429,
0.0037263361737132072,
-0.04631495103240013,
0.025800475850701332,
0.002416245173662901,
0.05353749915957451,
-0.050807125866413116,
0.018472440540790558,
0.024297840893268585,
0.03909400850534439,
0.026995865628123283,
-0.014220074750483036,
-0.06628752499818802,
0.048096317797899246,
-0.028422914445400238,
0.053322263062000275,
-0.02052781730890274,
0.004593066871166229,
0.015530760399997234,
0.034822411835193634,
0.04294366016983986,
0.026791883632540703,
-0.011848384514451027,
-0.023762796074151993,
0.03192894905805588,
0.033355750143527985,
0.02593771554529667,
0.00253887171857059,
0.022121507674455643,
0.05254814773797989,
0.006398264784365892,
0.03376349061727524,
0.00017977265815716237,
-0.052416179329156876,
-0.04356089234352112,
-0.06504543870687485,
-0.03263314440846443,
0.033426810055971146,
0.014433088712394238,
-0.01688190922141075,
-0.00414387509226799,
-0.02633979357779026,
0.040276527404785156,
0.008388078771531582,
0.03339450806379318,
0.010638569481670856,
0.030361780896782875,
-0.0025334488600492477,
-0.00837156642228365,
-0.01888328231871128,
0.007577619981020689,
0.12740842998027802,
0.04828310012817383,
-0.00364667852409184,
-0.0850149467587471,
0.04576552286744118,
-0.03034651279449463,
0.006720215082168579,
-0.06915462762117386,
0.0423758439719677,
-0.008721884340047836,
0.02718411199748516,
0.01942601427435875,
0.03727686032652855,
-0.030187111347913742,
-0.016254741698503494,
0.0587819367647171,
-0.030208829790353775,
-0.07750564068555832,
-0.006966514978557825,
0.001252899644896388,
-0.010716620832681656,
0.022538689896464348,
-0.030770255252718925,
0.026344751939177513,
-0.029777899384498596,
0.020923389121890068,
-0.03691403940320015,
-0.05650974065065384,
0.03133149445056915,
0.007965597324073315,
0.0005014141206629574,
0.011718339286744595,
-0.001690883538685739,
-0.0008109080954454839,
-0.021897049620747566,
0.041752662509679794,
0.0287921242415905,
0.010732457041740417,
0.01623530127108097,
0.015805961564183235,
0.013303836807608604,
0.024478554725646973,
-0.015166081488132477,
0.05436376482248306,
-0.05239478126168251,
-0.012992095202207565,
-0.030115721747279167,
0.025490915402770042,
-0.009176012128591537,
0.052095912396907806,
-0.022904066368937492,
0.006895602680742741,
0.022061793133616447,
-0.028583968058228493,
-0.015436879359185696,
0.017940703779459,
0.03339916840195656,
-0.07330916076898575,
-0.0011525966692715883,
-0.017835361883044243,
0.0381348580121994,
0.0062599582597613335,
0.03234401345252991,
0.008995628915727139,
-0.039864473044872284,
0.01782948151230812,
-0.006952415686100721,
0.007920591160655022,
-0.033984020352363586,
-0.006938457023352385,
-0.05472820624709129,
0.04192159324884415,
-0.023949431255459785,
-0.016862777993083,
-0.008592294529080391,
0.04550549015402794,
0.06241883710026741,
-0.006445466540753841,
-0.01766072027385235,
0.024629192426800728,
-0.026763439178466797,
0.028353068977594376,
-0.00611301651224494,
0.005808794870972633,
-0.020044028759002686,
-0.00018141401233151555,
0.013414845801889896,
0.021611051633954048,
-0.007348297163844109,
0.013800270855426788,
0.01898256689310074,
-0.005993442609906197,
0.039825692772865295,
0.012583089992403984,
0.0086892768740654,
-0.03268466517329216,
-0.03479498252272606,
0.014682497829198837,
0.022395990788936615,
0.012077145278453827,
0.04549361765384674,
0.004076025914400816,
-0.0033541847951710224,
0.06473951786756516,
-0.013386085629463196,
-0.009260321967303753,
-0.015098169445991516,
-0.051484059542417526,
0.0007813132833689451,
0.02510973811149597,
0.04453324154019356,
-0.03885732591152191,
-0.04271029680967331,
0.024215565994381905,
0.010171984322369099,
0.00850251130759716,
-0.0039125834591686726,
-0.030222827568650246,
0.05495232343673706,
0.0065027447417378426,
0.03575136139988899,
-0.056997671723365784,
-0.0056188032031059265,
-0.06526732444763184,
0.039543937891721725,
-0.005114289931952953,
0.03659247234463692,
0.0014033929910510778,
0.015696747228503227,
-0.021102556958794594,
-0.01392136886715889,
0.03371087834239006,
-0.02332415245473385,
-0.021454600617289543,
-0.026649245992302895,
0.02975669875741005,
-0.03349410742521286,
0.048436813056468964,
-0.013017317280173302,
-0.0062279412522912025,
0.012246469967067242,
-0.045919269323349,
-0.05386022478342056,
0.01129965391010046,
0.001665051793679595,
-0.0010502771474421024,
0.02085898444056511,
-0.022355543449521065,
-0.05849840119481087,
0.01766311191022396,
0.00021232581639196724,
-0.03886575251817703,
-0.009207937866449356,
-0.008877875283360481,
-0.011488710530102253,
-0.011861028149724007,
0.038445260375738144,
-0.014231394045054913,
-0.0037543668877333403,
0.003020473290234804,
0.014829142950475216,
-0.0052861678414046764,
-0.009730096906423569,
-0.016754642128944397,
-0.006642026826739311,
0.007858481258153915,
-0.02918456308543682,
-0.008915811777114868,
0.0432606041431427,
0.015039864927530289,
-0.044444743543863297,
0.02105126529932022,
-0.002064954489469528,
-0.004683822393417358,
-0.03674831986427307,
0.0014364193193614483,
-0.00005160297587281093,
0.013799527660012245,
0.053648874163627625,
-0.05305635556578636,
-0.015360210090875626,
0.03920167312026024,
-0.04336656257510185,
0.08734043687582016,
-0.0065462118946015835,
-0.015268925577402115,
-0.04664478823542595,
-0.011543921194970608,
-0.006001249887049198,
0.04618111997842789,
0.026753054931759834,
0.04545404016971588,
-0.020062729716300964,
-0.006791396997869015,
0.01975931040942669,
0.0006890004733577371,
-0.029514897614717484,
0.02001366950571537,
-0.019871946424245834,
-0.03320711478590965,
0.021898195147514343,
-0.007983509451150894,
-0.03783746063709259,
0.022862542420625687,
-0.009994116611778736,
-0.015247494913637638,
0.02001541294157505,
-0.010903705842792988,
0.01801198720932007,
0.03527819737792015,
0.03194335103034973,
-0.013181820511817932,
0.0031800339929759502,
-0.002765809651464224,
0.007267016917467117,
0.02048151008784771,
-0.025169935077428818,
0.048973992466926575,
0.0008040970424190164,
-0.05248738452792168,
-0.011931175366044044,
0.011426277458667755,
-0.0029159709811210632,
0.00693941256031394,
0.021552152931690216,
0.01103418692946434,
-0.021017879247665405,
-0.014958159066736698,
-0.014375310391187668,
-0.015731174498796463,
0.009921392425894737,
0.021435100585222244,
-0.01487033348530531,
0.047906216233968735,
0.07406233996152878,
0.004379362799227238,
-0.018603002652525902,
0.020967580378055573,
0.061518337577581406,
0.03794501721858978,
-0.04370567202568054,
-0.006476013455539942,
0.033025406301021576,
0.022083599120378494,
-0.022589266300201416,
-0.06960944086313248,
0.04435163736343384,
0.02774123102426529,
-0.011514956131577492,
0.009042136371135712,
0.01755279116332531,
-0.04513455182313919,
0.002840431174263358,
-0.026105046272277832,
0.048437654972076416,
0.021336901932954788,
0.021022750064730644,
-0.008926504291594028,
0.02802279219031334,
0.012970116920769215,
0.0019650531467050314,
0.00789709109812975,
-0.013716809451580048,
0.02373412437736988,
0.0021538662258535624,
-0.024246564134955406,
0.024809477850794792,
-0.026646405458450317,
0.023481987416744232,
-0.017456037923693657,
-0.038037631660699844,
0.002421226352453232,
-0.0012539572780951858,
-0.011973807588219643,
0.026948511600494385,
0.020691225305199623,
-0.0023217026609927416,
0.02589653804898262,
-0.03302496299147606,
-0.012299733236432076,
0.06535624712705612,
0.024976102635264397,
-0.01974039524793625,
0.048464585095644,
-0.02294200286269188,
0.01754576340317726,
0.026494204998016357,
-0.03555520996451378,
0.012458150275051594,
0.03762290999293327,
-0.07365154474973679,
-0.010028917342424393,
-0.04763411730527878,
-0.015646737068891525,
-0.001566074090078473,
-0.02570299245417118,
0.0067434110678732395,
0.0481838621199131,
-0.03362855687737465,
-0.008725613355636597,
0.058879587799310684,
-0.006206377875059843,
0.014535746537148952,
0.0039946842007339,
-0.0015600944170728326,
0.05453385412693024,
-0.025815449655056,
0.006048846058547497,
0.025080054998397827,
0.06732600927352905,
0.018175948411226273,
-0.011934539303183556,
0.016380175948143005,
-0.011225691996514797,
-0.010578300803899765,
-0.001346840988844633,
0.07371563464403152,
-0.058766432106494904,
0.0011126748286187649,
-0.003400213550776243,
-0.009708309546113014,
-0.008538621477782726,
0.023322755470871925,
-0.02193279378116131,
0.09289839118719101,
-0.010614404454827309,
-0.011434447951614857,
0.003773642238229513,
0.0013272473588585854,
-0.049267128109931946,
0.002743341727182269,
-0.01084691658616066,
0.05273116007447243,
-0.007024736143648624,
0.03286313638091087,
-0.0374574288725853,
-0.012124154716730118,
0.041906289756298065,
-0.03163408860564232,
0.009927262552082539,
0.026308558881282806,
0.0054139140993356705,
-0.0022359048016369343,
-0.02025187388062477,
-0.010959523729979992,
-0.04290953278541565,
0.02000456489622593,
0.04320209100842476,
0.022384746000170708,
-0.02675638161599636,
-0.01380948070436716,
-0.052141688764095306,
0.03347558528184891,
-0.04173014685511589,
0.014277947135269642,
-0.03833679109811783,
-0.031359292566776276,
-0.04135085642337799,
0.03828165680170059
] |
<p>Can anyone tell me very basically how the <a href="http://www.google.com/search?as_epq=Euler+Poincare+equation" rel="nofollow">Euler-Poincare equation</a> generalises the <a href="http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation" rel="nofollow">Euler-Lagrange equation</a>? Further does anyone know if there is an "easy" relationship between the two, i.e. can anyone derive either equation from the other? Finally I would be jolly grateful if anyone had a good BASIC source of information at an introductory level to the subject.</p>
| 9,374 |
[
-0.022739969193935394,
-0.00015940841694828123,
0.0021368972957134247,
0.02416043169796467,
0.008609273470938206,
-0.0012899074936285615,
-0.019971907138824463,
-0.006866255309432745,
0.030135655775666237,
-0.03647429496049881,
-0.00795068871229887,
0.029702655971050262,
0.06469254940748215,
0.03561868518590927,
0.020273014903068542,
0.011039347387850285,
-0.01022814866155386,
0.01289885863661766,
0.034188661724328995,
-0.02835742197930813,
0.0035306375939399004,
-0.02338607795536518,
0.027582960203289986,
0.002126111416146159,
-0.03241816163063049,
0.02826050855219364,
0.055317915976047516,
-0.005719500593841076,
0.0022876702714711428,
0.05866023153066635,
0.007054859772324562,
-0.00448640575632453,
-0.013482896611094475,
0.039280474185943604,
0.010915487073361874,
0.02465379238128662,
-0.04160529002547264,
-0.011226643808186054,
-0.0012707399437204003,
0.0023015278857201338,
-0.046754591166973114,
-0.021388482302427292,
0.003091339021921158,
0.032539285719394684,
-0.02088276855647564,
0.041811686009168625,
-0.007236308418214321,
-0.026838764548301697,
0.06609675288200378,
-0.0712408497929573,
0.08332235366106033,
0.044532254338264465,
0.042793285101652145,
-0.005507815629243851,
0.00996482279151678,
-0.004139093682169914,
0.05335485562682152,
0.05536532774567604,
-0.03135421499609947,
-0.0746331512928009,
0.008151707239449024,
0.005726820323616266,
0.019435875117778778,
-0.05028584599494934,
-0.021157925948500633,
0.026419632136821747,
0.002460117917507887,
-0.03900047019124031,
0.05219237133860588,
0.0012227158294990659,
-0.004872873891144991,
0.03385554254055023,
0.05500657483935356,
-0.024728884920477867,
0.040931981056928635,
-0.02846209704875946,
0.002275410806760192,
-0.01642548106610775,
0.012642744928598404,
0.046328552067279816,
-0.01546537782996893,
0.031231656670570374,
0.030199594795703888,
0.055398717522621155,
0.006311899982392788,
-0.018004463985562325,
0.06705477833747864,
-0.00415044603869319,
0.012453274801373482,
-0.014283932745456696,
-0.00807966198772192,
0.0005733066936954856,
0.002364333951845765,
-0.033785078674554825,
0.0011879729572683573,
0.055888671427965164,
0.007853164337575436,
0.0345904715359211,
0.03995084390044212,
0.012751458212733269,
-0.0012772572226822376,
-0.034297216683626175,
-0.00472070649266243,
0.07298270612955093,
-0.005509385839104652,
-0.013715784065425396,
-0.04381927102804184,
0.021376214921474457,
-0.023530060425400734,
-0.014363313093781471,
-0.003823340404778719,
0.013472025282680988,
-0.007125956937670708,
-0.01453995518386364,
-0.021237259730696678,
0.0020411424338817596,
0.0045455037616193295,
-0.008507464081048965,
0.04606800153851509,
0.06193262338638306,
0.050467923283576965,
-0.0302425529807806,
0.03927040472626686,
-0.014181355945765972,
-0.08288434892892838,
-0.023736970499157906,
0.029864206910133362,
-0.015700440853834152,
-0.00591716542840004,
0.023483222350478172,
-0.018912794068455696,
-0.02474812977015972,
-0.021461142227053642,
0.052209846675395966,
0.04411255568265915,
-0.009416742250323296,
-0.09478819370269775,
-0.016311923041939735,
0.033861193805933,
0.01916453242301941,
0.00036058342084288597,
-0.0654744952917099,
0.016725309193134308,
0.014224696904420853,
0.06614294648170471,
-0.004989855457097292,
0.0024549816735088825,
-0.006820380687713623,
0.0006697361823171377,
-0.007513838354498148,
-0.027202347293496132,
0.0003593281435314566,
0.016861191019415855,
-0.058903250843286514,
0.02022743970155716,
-0.10344532132148743,
-0.024664325639605522,
0.008659093640744686,
-0.01416583452373743,
-0.038826070725917816,
0.07952021062374115,
-0.009050130844116211,
-0.001366512500680983,
0.004427852109074593,
0.02660263329744339,
0.000725229037925601,
0.09019768238067627,
0.002215295797213912,
-0.013708087615668774,
0.041650764644145966,
0.01881195604801178,
0.03090474382042885,
-0.008555027656257153,
0.02210058830678463,
0.05647357180714607,
-0.03678491711616516,
-0.036375973373651505,
-0.008774800226092339,
0.005646474193781614,
0.038091111928224564,
-0.043777599930763245,
-0.03816332295536995,
-0.008354919031262398,
-0.01454975362867117,
-0.011700062081217766,
0.0364370197057724,
0.004944950807839632,
-0.003227000357583165,
-0.023323459550738335,
-0.04479454085230827,
-0.023498177528381348,
-0.06312992423772812,
0.011249186471104622,
-0.033018212765455246,
-0.006136477459222078,
0.053412310779094696,
0.0071795228868722916,
0.002514404710382223,
-0.04187314212322235,
-0.03924921900033951,
-0.01165988389402628,
0.028003450483083725,
-0.022303257137537003,
-0.03217647597193718,
0.012036697007715702,
0.04609788581728935,
0.02880600467324257,
0.0024878676049411297,
0.037229862064123154,
-0.02686390094459057,
-0.01353932823985815,
0.015059392899274826,
-0.022983036935329437,
0.03530077263712883,
0.004154158756136894,
-0.012873537838459015,
0.01721121557056904,
-0.010653295554220676,
0.012548001483082771,
0.04576808959245682,
-0.03577077016234398,
0.0748240128159523,
0.07654332369565964,
0.05840998515486717,
0.013668454252183437,
0.04954985901713371,
0.022336943075060844,
0.0237156730145216,
-0.008227785117924213,
-0.0288669653236866,
-0.00789125356823206,
-0.02652963623404503,
0.036189332604408264,
0.043422240763902664,
-0.021753355860710144,
-0.003017786890268326,
0.04616935923695564,
0.01765328459441662,
0.02904529869556427,
0.05995948240160942,
-0.014459575526416302,
-0.030237440019845963,
0.0011190399527549744,
0.07622095942497253,
-0.016627877950668335,
0.023265685886144638,
0.03767329081892967,
0.008958767168223858,
0.01804632693529129,
-0.009814461693167686,
-0.06108291074633598,
0.05812527984380722,
0.003673053812235594,
-0.026963772252202034,
0.03863795846700668,
0.019241418689489365,
0.055887725204229355,
-0.024651695042848587,
0.044215042144060135,
0.013920105993747711,
-0.0173279270529747,
-0.028217988088726997,
-0.014281576499342918,
0.011470462195575237,
0.0023001881781965494,
-0.01967780850827694,
-0.018040476366877556,
-0.019348375499248505,
0.01189472060650587,
-0.03652728348970413,
-0.002305789617821574,
0.0004957853816449642,
-0.04210299253463745,
-0.04643988981842995,
0.010978481732308865,
-0.004973393864929676,
-0.0026258020661771297,
0.03616245836019516,
-0.00034029094967991114,
-0.04448428377509117,
-0.0071035888977348804,
-0.0328080840408802,
-0.0019168131984770298,
0.0028253982309252024,
-0.021703924983739853,
0.04946981370449066,
-0.019867638126015663,
-0.011048891581594944,
0.058697570115327835,
-0.007207415532320738,
0.031867679208517075,
0.010555071756243706,
-0.032266534864902496,
-0.03668256103992462,
-0.0021577649749815464,
-0.030902622267603874,
0.026924418285489082,
0.013977560214698315,
0.017423903569579124,
0.04051244258880615,
-0.014697988517582417,
0.0007180377142503858,
0.02355949766933918,
-0.056739553809165955,
-0.04035136103630066,
-0.06412983685731888,
0.05215767025947571,
0.004235571250319481,
-0.017332883551716805,
-0.015895208343863487,
0.018024325370788574,
-0.02901301346719265,
-0.004268610384315252,
-0.0683894082903862,
-0.03314613178372383,
0.030999597162008286,
0.0039746989496052265,
0.032409992069005966,
0.021101688966155052,
-0.05587254464626312,
0.07605841010808945,
0.005807867739349604,
-0.04158072546124458,
-0.03483958542346954,
0.002693941118195653,
0.012771526351571083,
0.015566467307507992,
0.014281295239925385,
0.0427006334066391,
-0.022650696337223053,
0.03192546218633652,
0.02517840266227722,
0.015245337970554829,
0.024938885122537613,
0.012178376317024231,
0.02103673480451107,
-0.033127833157777786,
0.009453504346311092,
0.0017352061113342643,
0.03483923524618149,
0.03200753033161163,
-0.028017722070217133,
0.002994016744196415,
0.006659518461674452,
0.04782520979642868,
0.00457334378734231,
-0.04760175198316574,
0.023623373359441757,
0.029798656702041626,
-0.016442464664578438,
-0.027680866420269012,
0.014074831269681454,
-0.0018781066173687577,
-0.011953220702707767,
0.024457693099975586,
0.04574572294950485,
0.026286210864782333,
-0.012800004333257675,
-0.006456790957599878,
0.044986285269260406,
0.07073426991701126,
-0.034506186842918396,
-0.034262750297784805,
-0.026510976254940033,
-0.012566070072352886,
0.04072263464331627,
-0.015351335518062115,
0.0003808760375250131,
0.05608600378036499,
0.007473432924598455,
0.011769418604671955,
0.013096567243337631,
-0.012656987644731998,
0.04279881343245506,
-0.09287919104099274,
0.011167053133249283,
0.0017095360672101378,
0.06151943653821945,
-0.0057883416302502155,
0.09112822264432907,
-0.01163997408002615,
0.014585522003471851,
0.0205231960862875,
0.04231514781713486,
-0.1083662137389183,
0.02711782418191433,
-0.03469780832529068,
-0.05571460723876953,
0.004622678738087416,
-0.009794029407203197,
0.04016941413283348,
-0.028882382437586784,
-0.0564783550798893,
-0.024204449728131294,
0.002928029978647828,
-0.05894964560866356,
0.014303930103778839,
-0.04777682200074196,
-0.038323186337947845,
-0.009625500068068504,
0.030405377969145775,
0.005298906937241554,
-0.007825622335076332,
0.016992997378110886,
0.08524508774280548,
-0.013313179835677147,
-0.031483497470617294,
0.0063429782167077065,
0.013688305392861366,
0.009271671995520592,
-0.01639035902917385,
-0.0022630842868238688,
0.025066593661904335,
-0.013642216101288795,
0.03427714481949806,
-0.027830656617879868,
0.04548729583621025,
0.018440861254930496,
-0.010896182619035244,
-0.028095100075006485,
-0.053365230560302734,
-0.007328283507376909,
-0.016715331003069878,
0.04990985617041588,
0.0016195947537198663,
0.012481878511607647,
0.010491080582141876,
0.021722083911299706,
0.0038824116345494986,
0.05449049547314644,
0.03651801869273186,
0.014061903581023216,
0.0010753327514976263,
-0.04229162260890007,
-0.002531725913286209,
-0.01866140216588974,
-0.007858537137508392,
0.03156980499625206,
0.0040482571348547935,
-0.016148662194609642,
-0.008216695860028267,
0.025672433897852898,
-0.00526169128715992,
-0.01593790575861931,
-0.008225149475038052,
0.012344206683337688,
0.016186483204364777,
0.00034551811404526234,
-0.022802118211984634,
-0.000005983766186545836,
0.010458712466061115,
0.04294874519109726,
-0.004528667777776718,
0.00856961403042078,
-0.10008994489908218,
-0.0009305126732215285,
0.0204818993806839,
0.0037170560099184513,
-0.03611103817820549,
0.006869551260024309,
-0.038434065878391266,
-0.0021273300517350435,
0.029879776760935783,
-0.033770643174648285,
0.01663491129875183,
0.002947903936728835,
0.015615362673997879,
-0.000585586647503078,
-0.032392337918281555,
-0.022357679903507233,
0.0040929364040493965,
-0.024151597172021866,
-0.006178854964673519,
-0.0061975400894880295,
0.0217274222522974,
-0.030676163733005524,
0.037770383059978485,
0.02981456369161606,
0.06117688864469528,
0.009468449279665947,
-0.009228663519024849,
-0.00905590783804655,
0.024292806163430214,
-0.022188037633895874,
-0.07709164172410965,
-0.02224026992917061,
0.02628435008227825,
-0.008263404481112957,
0.024212025105953217,
-0.031494058668613434,
-0.01983734592795372,
0.006600810214877129,
-0.0006965192151255906,
-0.016196437180042267,
0.030051253736019135,
-0.016597798094153404,
-0.014730663038790226,
0.033530283719301224,
-0.01756097748875618,
0.04093383252620697,
0.03684946149587631,
-0.03403071314096451,
-0.04391491785645485,
-0.02283407188951969,
0.025267187505960464,
-0.020218247547745705,
-0.029624324291944504,
-0.03557620570063591,
0.027656447142362595,
-0.031761087477207184,
0.03967566788196564,
-0.005110167432576418,
0.0017645915504544973,
-0.06037558987736702,
-0.03653348982334137,
-0.031156236305832863,
0.03922607749700546,
0.015219466760754585,
0.015425235964357853,
0.012277663685381413,
0.03398476168513298,
0.06280723214149475,
-0.037855278700590134,
0.028386127203702927,
0.01890995353460312,
-0.020142758265137672,
0.01537508238106966,
0.009372369386255741,
0.004342618398368359,
-0.0045202551409602165,
-0.023810043931007385,
0.03175767511129379,
-0.03775378316640854,
0.04950692132115364,
-0.010433491319417953,
0.014813369140028954,
0.0497911237180233,
-0.0335785374045372,
-0.04070112109184265,
-0.0017280778847634792,
-0.00827201921492815,
0.041114456951618195,
-0.015569432638585567,
0.017795508727431297,
0.019955074414610863,
-0.05279316380620003,
-0.0624568834900856,
-0.05909839645028114,
0.04885774105787277,
-0.026450403034687042,
-0.026855919510126114,
-0.04140639305114746,
-0.0260170865803957,
-0.04100501909852028,
-0.016373615711927414,
0.016982000321149826,
0.040607843548059464,
-0.029788464307785034,
-0.002910179551690817,
-0.004506383556872606,
-0.03140529245138168,
0.02683427557349205,
-0.010618495754897594,
-0.010679513216018677,
-0.021777940914034843,
-0.006078753154724836,
0.0017622882733121514,
0.0037778716068714857,
0.08501927554607391,
-0.011158151552081108,
0.007222472690045834,
-0.01108772773295641,
-0.02040194347500801,
0.03158247098326683,
-0.035322513431310654,
-0.007592091336846352,
0.04300491139292717,
0.02848368138074875,
0.012744304724037647,
-0.0370788499712944,
-0.003392319893464446,
0.0004915634635835886,
0.025031331926584244,
-0.0217746589332819,
0.009720218367874622,
0.0024115508422255516,
-0.018039239570498466,
0.040920622646808624,
0.0015326380962505937,
0.005356094799935818,
0.004535482730716467,
0.05723613500595093,
-0.02237408049404621,
-0.0007453058497048914,
0.026667732745409012,
0.013469853438436985,
0.03388733044266701,
-0.028720788657665253,
0.01196884922683239,
0.03367017209529877,
0.006745184771716595,
-0.024821534752845764,
-0.034225888550281525,
-0.023448504507541656,
0.017581136897206306,
0.07263975590467453,
-0.031080182641744614,
0.0688621997833252,
0.022834669798612595,
0.005175625905394554,
-0.010707295499742031,
0.014614824205636978,
-0.004292123019695282,
-0.01608659140765667,
-0.0019612167961895466,
0.05078030750155449,
-0.03215302154421806,
0.004492282867431641,
0.025593532249331474,
0.026196910068392754,
0.0031183790415525436,
-0.013500723987817764,
-0.017760245129466057,
0.018824497237801552,
0.01258524414151907,
-0.008015288971364498,
-0.05009225383400917,
0.05553627014160156,
0.012078567408025265,
0.06351175159215927,
0.0007626067381352186,
-0.043327827006578445,
0.03098633512854576,
0.0341898575425148,
-0.012662411667406559,
-0.03620719909667969,
-0.024779019877314568,
-0.023248134180903435,
0.031228765845298767,
0.021181559190154076,
-0.0026424864772707224,
0.00705723138526082,
0.011321166530251503,
0.007961184717714787,
0.015413440763950348,
0.0037261820398271084,
0.01804736629128456,
-0.0388057604432106,
-0.0036975047551095486,
-0.04363353177905083,
-0.055506907403469086,
0.013341134414076805,
0.016721703112125397,
-0.024658218026161194,
-0.01532870251685381,
-0.034300439059734344,
0.003471074625849724,
0.021259287372231483,
0.029271943494677544,
-0.02005770616233349,
0.07716890424489975,
-0.002645030152052641,
0.002154273446649313,
-0.04309432581067085,
0.0019109025597572327,
0.09160713851451874,
0.014981208369135857,
0.005596257746219635,
-0.10912340134382248,
0.022880088537931442,
-0.020475372672080994,
-0.004180373623967171,
-0.0510687455534935,
0.04412562772631645,
0.0008930198382586241,
-0.002374477917328477,
0.023368416354060173,
0.05093013122677803,
-0.007917608134448528,
-0.013984880410134792,
0.05382422357797623,
-0.019049642607569695,
-0.029476284980773926,
0.006425607018172741,
0.010580376721918583,
0.002626872854307294,
0.05267692357301712,
-0.012181391008198261,
0.01542353630065918,
-0.048200465738773346,
-0.0057504912838339806,
-0.033323485404253006,
-0.059169188141822815,
0.015515053644776344,
0.004650713875889778,
-0.0636044293642044,
0.01743931509554386,
0.029074693098664284,
-0.046090684831142426,
-0.04311652481555939,
0.016456108540296555,
-0.006859367713332176,
-0.0071757580153644085,
0.02712727151811123,
0.03390738368034363,
0.01611647941172123,
0.01226681750267744,
0.02846800722181797,
0.025766702368855476,
-0.03094515949487686,
0.0009906578343361616,
-0.03912181034684181,
0.019792847335338593,
-0.014137562364339828,
0.04297981783747673,
-0.012602626346051693,
0.0059734429232776165,
0.006779391784220934,
-0.04980017989873886,
-0.052519552409648895,
-0.028997888788580894,
0.026987779885530472,
-0.039630867540836334,
-0.007697155233472586,
-0.022747933864593506,
0.015054954215884209,
-0.029409155249595642,
0.05255356431007385,
-0.01623474434018135,
-0.011161155067384243,
0.005750031676143408,
-0.025303764268755913,
0.01930209808051586,
-0.034334734082221985,
-0.02805805578827858,
-0.03961677849292755,
-0.020276859402656555,
-0.01860077865421772,
-0.002888025948777795,
0.002926490269601345,
0.025283943861722946,
0.021232178434729576,
-0.007404179312288761,
-0.015531727112829685,
0.002619948470965028,
-0.0549401231110096,
0.03165445476770401,
-0.007659520488232374,
-0.011298240162432194,
-0.015807313844561577,
0.007045818027108908,
0.05395098403096199,
0.02936873398721218,
-0.017997324466705322,
0.03323991224169731,
-0.052853938192129135,
0.0049759987741708755,
0.005375322885811329,
-0.03211329132318497,
-0.010193961672484875,
0.03453585505485535,
-0.026744795963168144,
-0.009324431419372559,
0.0016929891426116228,
0.03503462299704552,
0.030916331335902214,
0.03610118851065636,
-0.01018048357218504,
0.03526348993182182,
0.006886178627610207,
0.006443234626203775,
0.016331054270267487,
-0.009448808617889881,
0.020400000736117363,
0.018667886033654213,
-0.010710658505558968,
-0.018148550763726234,
0.0017767723184078932,
-0.02628079615533352,
-0.006624334026128054,
-0.026939069852232933,
0.007908071391284466,
-0.026000358164310455,
0.004657842218875885,
-0.017737023532390594,
0.029804861173033714,
-0.0594881996512413,
-0.015726270154118538,
-0.07111314684152603,
0.043368879705667496,
0.0010409748647361994,
-0.007234490942209959,
-0.043699294328689575,
0.04350615292787552,
-0.030583998188376427,
-0.028280004858970642,
0.016172179952263832,
0.04702341556549072,
-0.029367543756961823,
-0.03783673048019409,
0.03797934949398041,
-0.018600381910800934,
0.05843299254775047,
0.001865064026787877,
-0.035001661628484726,
0.01699644699692726,
-0.04000231996178627,
-0.04295654222369194,
0.020582130178809166,
0.016791732981801033,
-0.019619170576334,
0.03584316372871399,
-0.026358583942055702,
-0.026312844827771187,
0.0911862701177597,
0.02460493892431259,
0.0026013089809566736,
-0.014948149211704731,
-0.036743756383657455,
-0.019031457602977753,
-0.025533635169267654,
-0.000809225020930171,
-0.032170336693525314,
-0.020896635949611664,
0.005428887438029051,
0.04820568114519119,
-0.03352988511323929,
-0.008843701332807541,
0.02349838614463806,
-0.02532886154949665,
-0.01164057943969965,
0.01521552074700594,
-0.015152647159993649,
0.03677811473608017,
0.047911763191223145,
-0.02083532325923443,
-0.0075839911587536335,
0.007374085020273924,
0.03232282027602196,
-0.08760003000497818,
0.012883482500910759,
-0.005736693274229765,
0.007095932494848967,
0.04535088315606117,
-0.047959573566913605,
0.003267657943069935,
0.011753317900002003,
-0.017629392445087433,
-0.008864108473062515,
-0.02804061770439148,
0.03010050766170025,
-0.007044866215437651,
-0.017055990174412727,
0.035680968314409256,
0.04159123823046684,
0.03219946101307869,
0.02203870378434658,
0.02887750416994095,
0.005685519892722368,
0.012983297929167747,
-0.0009369830368086696,
-0.008927755057811737,
0.010527177713811398,
-0.008134115487337112,
-0.04399406164884567,
0.03632405772805214,
-0.015275261364877224,
-0.019810883328318596,
0.02666872926056385,
-0.010546219535171986,
0.02801329642534256,
0.01353135984390974,
-0.002212223829701543,
0.0006655564066022635,
0.005088860169053078,
-0.017250198870897293,
0.012929149903357029,
-0.0051155099645257,
0.020191535353660583,
-0.0008918849052861333,
0.015827275812625885,
-0.043695371598005295,
-0.005691159050911665,
0.03180200979113579,
-0.024741554632782936,
-0.05584364011883736,
0.050395697355270386,
-0.0110090970993042,
-0.00812215730547905,
-0.02115405909717083,
0.004263729322701693,
0.0062031131237745285,
-0.00438610278069973,
0.017188264057040215,
-0.04210617020726204,
0.0015964837512001395,
0.028951270505785942,
-0.049287766218185425,
-0.012217005714774132,
0.02987588196992874,
0.013713383115828037,
0.017617331817746162,
0.010246505960822105,
0.004158960189670324,
0.040202777832746506,
-0.05539675056934357,
0.016361640766263008,
0.011258020997047424,
-0.03445161134004593,
-0.013270528987050056,
-0.05802810937166214,
0.0003703643742483109,
0.015317215584218502,
0.041135795414447784,
0.01751195453107357,
-0.0021272709127515554,
-0.004978962708264589,
0.012819178402423859,
-0.04899602755904198,
0.031632907688617706,
-0.004384196829050779,
-0.03204254060983658,
-0.06125752627849579,
0.0016221401747316122,
0.01686728186905384,
0.02819184586405754,
0.02250143140554428,
-0.04396238923072815,
-0.012304272502660751,
0.020780792459845543,
0.02398667111992836,
-0.0010075472528114915,
-0.0004354123375378549,
-0.01329454593360424,
-0.0183471217751503,
-0.038303401321172714,
-0.0019363213796168566,
-0.0068291472271084785,
-0.058831389993429184,
0.022590599954128265,
0.01354825310409069,
-0.009973574429750443,
0.03792519494891167,
-0.00726738665252924,
-0.06007134169340134,
0.027773652225732803,
0.03821472451090813,
0.003665245370939374,
0.05669829621911049,
-0.026951562613248825,
0.003820903832092881,
-0.0015761456452310085,
-0.028780974447727203,
-0.023555908352136612,
0.044516343623399734,
-0.07291131466627121,
0.006592488382011652,
-0.03862927854061127,
-0.03927714750170708,
0.04309842735528946,
-0.05871960520744324,
0.006112373899668455,
0.010329119861125946,
-0.03954809531569481,
-0.03156302869319916,
0.018170077353715897,
0.01972469873726368,
0.03232923150062561,
-0.043102048337459564,
-0.003330828854814172,
0.027481840923428535,
-0.04378320276737213,
0.007155134808272123,
0.03021770343184471,
0.0454440638422966,
-0.007933937944471836,
-0.02079285867512226,
0.012492659501731396,
0.019427470862865448,
0.01487547717988491,
-0.006717712618410587,
0.04536550119519234,
-0.004855734296143055,
-0.029248598963022232,
0.015575540252029896,
-0.036937206983566284,
0.021284984424710274,
0.024773677811026573,
-0.039246201515197754,
0.05855194851756096,
-0.04087067022919655,
0.009185424074530602,
0.01096078660339117,
0.024762380868196487,
-0.026147961616516113,
-0.035086095333099365,
-0.02987845614552498,
0.0402853898704052,
0.015047055669128895,
0.01937353052198887,
-0.014341715723276138,
-0.011133253574371338,
0.007544105406850576,
0.0042152004316449165,
0.006966021377593279,
0.01158912107348442,
-0.01849057339131832,
0.006562866736203432,
-0.017682461068034172,
-0.022091491147875786,
-0.012441296130418777,
0.05173914134502411,
0.053936272859573364,
0.005281358025968075,
-0.006509237922728062,
0.012988385744392872,
-0.02425851672887802,
0.07082882523536682,
-0.09142740815877914,
-0.03468912094831467,
-0.010729927569627762,
-0.013557703234255314,
-0.026163477450609207,
-0.012873418629169464
] |
<p>Since a polarization of the wave is described by complex numbers, we can try to give that mathematical formalism geometrical meaning. With having two different axes, one imaginary and other real, it is possible to represent the motion of the wave in three dimensions as the motion of 2 waves in two planes. These two planes are being observed in three-dimensional space from the point in the third plane which is perpendicular to the two other planes. This third plane is actually a complex plane, from whose perspective these two planes are viewed as lines. This also means that the notion of a complex plane just refers to the plane which is an auxiliary construction, on which coordinates of a point in two other planes are projected. The coordinates in each plane correspond to their motion in two dimensions, parametrically described, where one of two parameters is time. This can be mathematically interpreted as a function where y=y(x).</p>
<p>These two equations with two variables for each one, or the lines as viewed geometrically are real and imaginary part of a complex number. Each part is showing the two-dimensional projection of a curve in three dimensions. If we can observe these two projections as independent of each other, it is possible to describe this curve in three dimensions. This is done by introduction of mathematical abstraction, a complex number, where imaginary and real part are independent of each other.</p>
<p>If our attention is focused only on single point in this three-dimensional world, we can just determine its location from three spatial coordinates. In other words, there are two equations sharing the connection with same parameter. Uniqueness of that parameter arises from setting the same beginning of both planar coordinates system at the place where complex plane intersects two other planes. Therefore, the solution of the equation are the coordinates of the point in three-dimensional space (x, y, z). But if we bring in another dimension to an observed object, i.e. if we make that point a line (given algebraically as the function with two variables), we get a new, fourth variable or fourth dimension. That dimension is time, from the viewpoint of a physicist.</p>
<p>Is this geometrical interpretation of complex number description of polarization correct?</p>
| 9,375 |
[
-0.008847733028233051,
0.0020701554603874683,
-0.015288615599274635,
-0.034155331552028656,
0.06441713124513626,
0.013210929930210114,
-0.05147550627589226,
-0.008251514285802841,
0.006830568425357342,
-0.05222262069582939,
0.018390389159321785,
0.01629205420613289,
0.07005474716424942,
0.04956632852554321,
0.004427160602062941,
0.0246701929718256,
-0.0015340785030275583,
0.012609459459781647,
-0.04533294960856438,
-0.03874587640166283,
0.013820680789649487,
0.03624105826020241,
-0.002385624684393406,
-0.0023927425500005484,
-0.006166987586766481,
0.044779568910598755,
0.03448387607932091,
0.011599392630159855,
0.05186956003308296,
0.04298454895615578,
0.0006842939183115959,
-0.024997204542160034,
-0.008248282596468925,
0.041797470301389694,
0.03195933997631073,
-0.025235949084162712,
-0.04016667976975441,
-0.02385535091161728,
0.009739740751683712,
0.03699643909931183,
-0.0007222933345474303,
-0.004305860958993435,
-0.031102091073989868,
0.0380922332406044,
-0.04120524972677231,
0.006699355784803629,
-0.0010140230879187584,
-0.003355423454195261,
0.03842921927571297,
-0.06660699844360352,
0.06483043730258942,
-0.02028484083712101,
0.002446448430418968,
-0.0019348422065377235,
-0.02213827148079872,
-0.01257192064076662,
0.0826939269900322,
0.057121384888887405,
0.014046129770576954,
-0.05921761691570282,
-0.009976171888411045,
0.02248590812087059,
0.01826016791164875,
-0.021300261840224266,
-0.02364291064441204,
0.001001377939246595,
0.01592380553483963,
-0.03503085672855377,
-0.009979496710002422,
-0.012775016017258167,
-0.004991715308278799,
0.0065104360692203045,
0.037259627133607864,
-0.036469411104917526,
0.027529515326023102,
-0.021583667024970055,
-0.00042507582111284137,
-0.007250254508107901,
0.02455328404903412,
-0.018985897302627563,
-0.0008729565306566656,
0.0034934612922370434,
-0.011961414478719234,
0.008928191848099232,
0.011608917266130447,
-0.008682185783982277,
0.08158153295516968,
-0.0074946642853319645,
0.013443912379443645,
-0.02406168356537819,
0.013708185404539108,
0.018984412774443626,
0.020873595029115677,
0.017899205908179283,
-0.017665252089500427,
0.012322643771767616,
0.02530752494931221,
0.01680527999997139,
0.025315867736935616,
-0.02215568907558918,
0.03628252446651459,
-0.03889710083603859,
-0.012865033000707626,
0.04527021571993828,
0.021911608055233955,
0.0495799221098423,
-0.028367280960083008,
0.007192656863480806,
-0.016944216564297676,
-0.030431538820266724,
-0.024866973981261253,
0.029241155833005905,
0.010554836131632328,
0.03869478031992912,
-0.0007131962920539081,
-0.018019450828433037,
0.02715122140944004,
0.007350859232246876,
0.056959837675094604,
0.080415740609169,
0.007515360601246357,
-0.041195984929800034,
0.0034015937708318233,
-0.03212721273303032,
-0.09461993724107742,
-0.016621923074126244,
0.02265394665300846,
-0.0033921082504093647,
-0.036850705742836,
0.03538767248392105,
0.025594869628548622,
0.00643006619066,
0.03166370093822479,
-0.0023663844913244247,
0.04198717698454857,
0.003482755972072482,
-0.14347176253795624,
-0.04934405907988548,
0.009844070300459862,
0.013067922554910183,
-0.009955372661352158,
-0.058381665498018265,
0.003627690253779292,
0.0291520394384861,
0.05392897129058838,
-0.04402647912502289,
0.025091100484132767,
0.015513435006141663,
0.02270645834505558,
-0.0032563924323767424,
-0.008036071434617043,
0.01261451281607151,
-0.023098846897482872,
-0.05531088635325432,
-0.025919226929545403,
-0.02311905100941658,
0.017402639612555504,
0.025787657126784325,
-0.014341809786856174,
-0.02914164960384369,
0.039674315601587296,
-0.02407180704176426,
-0.008155478164553642,
0.0674145370721817,
-0.0499449260532856,
-0.013521452434360981,
0.06911125779151917,
0.011666173115372658,
0.01649065501987934,
0.0423903651535511,
-0.0018675285391509533,
0.060184232890605927,
-0.005221843253821135,
0.016595883294939995,
0.008944706059992313,
-0.045972563326358795,
-0.025229761376976967,
0.02986580692231655,
-0.029935333877801895,
0.01649455912411213,
-0.04003369063138962,
-0.06159243360161781,
0.013330488465726376,
0.022122269496321678,
-0.00511765293776989,
0.04678149148821831,
0.00044481357326731086,
-0.0016720767598599195,
0.02074563503265381,
-0.06813808530569077,
0.016236118972301483,
-0.048631325364112854,
0.05131294205784798,
0.022927554324269295,
-0.010897823609411716,
0.007682471536099911,
0.012225804850459099,
-0.0009847527835518122,
-0.01981053501367569,
-0.04952342435717583,
-0.030969351530075073,
0.06377387791872025,
0.05672120302915573,
-0.002078406047075987,
0.0315503291785717,
0.06277001649141312,
0.01403969619423151,
-0.015242081135511398,
0.010599053464829922,
0.008678266778588295,
0.020398108288645744,
0.015873832628130913,
-0.008991164155304432,
0.03809334710240364,
0.041097525507211685,
-0.011151807382702827,
-0.04149363562464714,
0.0008390481234528124,
-0.01884087547659874,
0.049355398863554,
-0.052618175745010376,
0.04552143067121506,
0.08554761111736298,
0.014317858964204788,
0.010847399942576885,
0.059761516749858856,
-0.013714847154915333,
0.019012929871678352,
0.026035841554403305,
-0.04823455587029457,
-0.02125142142176628,
-0.0016111081931740046,
0.03970969840884209,
0.062176115810871124,
-0.030633430927991867,
-0.02210007980465889,
0.01295715756714344,
0.04713909327983856,
0.01445222832262516,
0.030910944566130638,
0.0037543305661529303,
-0.02884691022336483,
0.011896184645593166,
-0.02318653278052807,
0.024172384291887283,
0.010224791243672371,
0.040472183376550674,
-0.018737271428108215,
0.004461204633116722,
-0.04319442808628082,
-0.01768587715923786,
0.036279261112213135,
-0.016119197010993958,
0.01333854254335165,
0.03145148232579231,
0.010491742752492428,
0.03164201229810715,
-0.01509150955826044,
0.013634531758725643,
0.02426888607442379,
0.005857855547219515,
-0.03628452122211456,
-0.0174374021589756,
0.008632071316242218,
0.0013606928987428546,
0.0036382435355335474,
-0.03692036122083664,
-0.029197636991739273,
0.04255322739481926,
-0.0012998000020161271,
-0.02076021395623684,
-0.010173296555876732,
-0.04844505339860916,
-0.006393279880285263,
-0.02497188188135624,
0.026226388290524483,
0.03163590654730797,
0.028477251529693604,
-0.007489361800253391,
-0.07904787361621857,
0.02781876176595688,
-0.010139787569642067,
0.00744233513250947,
0.013855010271072388,
-0.029372386634349823,
0.025586839765310287,
-0.054725151509046555,
-0.02194262482225895,
0.010476026684045792,
-0.005313322879374027,
0.0016617071814835072,
0.0014839381910860538,
-0.02424045279622078,
-0.07281585782766342,
-0.03684321790933609,
-0.04773419722914696,
0.031046701595187187,
-0.03013595938682556,
-0.013071480207145214,
0.05345779284834862,
-0.019027428701519966,
-0.0054060365073382854,
0.010461614467203617,
-0.008853577077388763,
-0.0461730994284153,
0.021369054913520813,
-0.02729400433599949,
-0.010081731714308262,
-0.03145182505249977,
0.04365210980176926,
0.03411861136555672,
-0.022019751369953156,
-0.013005892746150494,
-0.038148511201143265,
-0.06280586868524551,
0.01620698906481266,
-0.013880811631679535,
0.023779986426234245,
-0.020048566162586212,
-0.04178305342793465,
0.06921319663524628,
-0.004933162126690149,
-0.03802158311009407,
-0.01355664897710085,
0.0239806417375803,
-0.0073503185994923115,
0.008700930513441563,
-0.014937039464712143,
0.01531326025724411,
0.012523887678980827,
0.033453911542892456,
0.0028058732859790325,
-0.009173941798508167,
0.04646974056959152,
0.029807157814502716,
-0.006274389103055,
0.018254296854138374,
0.016631586477160454,
0.003991859499365091,
0.026030782610177994,
0.04148660600185394,
-0.04394369572401047,
0.03880543261766434,
0.005166835617274046,
-0.009350033476948738,
0.02417055331170559,
-0.031259458512067795,
0.020463882014155388,
0.019724206998944283,
0.051121704280376434,
0.002932619536295533,
0.03378124162554741,
0.014928807504475117,
-0.01942666620016098,
-0.0120853828266263,
0.01778768189251423,
0.04644734039902687,
-0.0013131496962159872,
0.008235152810811996,
0.000975168717559427,
0.015061706304550171,
-0.04172259569168091,
-0.013469642028212547,
-0.017211230471730232,
0.008716367185115814,
0.05161694437265396,
-0.015696462243795395,
-0.024267498403787613,
0.03546983748674393,
0.0050679477863013744,
-0.04462658613920212,
0.020943542942404747,
-0.02245025709271431,
-0.022038517519831657,
-0.04586128145456314,
0.006523607298731804,
0.019748449325561523,
0.032215751707553864,
0.011663084849715233,
0.05381378158926964,
-0.003721756860613823,
-0.002613689051941037,
0.020029397681355476,
0.0021590290125459433,
-0.08652139455080032,
-0.048729777336120605,
-0.006405532825738192,
-0.0008769113919697702,
-0.032191965728998184,
-0.021740173920989037,
0.004517534282058477,
-0.026121970266103745,
-0.018347546458244324,
-0.003707558149471879,
-0.05839037522673607,
-0.08423691987991333,
0.014905466698110104,
-0.021422164514660835,
-0.018349500373005867,
-0.041397854685783386,
0.056246474385261536,
0.06292470544576645,
0.0028890795074403286,
-0.02887001447379589,
0.0738874226808548,
-0.05425107479095459,
0.012040943838655949,
-0.005197415594011545,
-0.020451990887522697,
0.02212340012192726,
0.020801376551389694,
0.00580466166138649,
0.004287729039788246,
0.001719482708722353,
0.01562778279185295,
0.003804607316851616,
0.032079942524433136,
0.007876372896134853,
-0.010462678968906403,
-0.01237137708812952,
-0.019735362380743027,
0.011732221581041813,
-0.030821947380900383,
0.0733744278550148,
0.05707702785730362,
-0.012794199399650097,
0.007104253396391869,
0.021766673773527145,
0.016875887289643288,
0.009837220422923565,
0.017636943608522415,
-0.004524781368672848,
-0.01753624901175499,
-0.06729836016893387,
-0.008226013742387295,
-0.01924469694495201,
-0.018919890746474266,
0.02886085957288742,
-0.013487979769706726,
0.006857320666313171,
-0.0011147840414196253,
0.02621474675834179,
0.003822869388386607,
0.002877637045457959,
0.009606395848095417,
-0.0251407939940691,
-0.02642076462507248,
-0.017248548567295074,
0.009748322889208794,
0.01878240332007408,
0.058282963931560516,
0.02040226198732853,
-0.0007116087945178151,
-0.08105473965406418,
-0.07788868248462677,
-0.003947025164961815,
0.009527845308184624,
0.03419705107808113,
-0.0031405810732394457,
-0.012374456971883774,
-0.015861330553889275,
-0.00983696710318327,
0.04379348084330559,
0.0034209168516099453,
0.02288084663450718,
-0.02513173595070839,
-0.027890874072909355,
-0.0585298128426075,
-0.020723573863506317,
-0.016175976023077965,
0.028313681483268738,
-0.01154984999448061,
0.020555030554533005,
0.010975404642522335,
0.004171788226813078,
-0.011889764107763767,
0.02984795533120632,
-0.002346824388951063,
0.024217238649725914,
0.029878530651330948,
0.00988222099840641,
-0.02862931229174137,
0.022310784086585045,
-0.03621956333518028,
-0.07170930504798889,
0.018747400492429733,
0.004433515481650829,
-0.009253548458218575,
0.045105986297130585,
-0.02543240785598755,
-0.04456283152103424,
0.013335511088371277,
-0.007351648528128862,
0.022907886654138565,
0.016743125393986702,
-0.027221551164984703,
0.019598614424467087,
0.00953690055757761,
0.001997780054807663,
0.028692154213786125,
0.010653688572347164,
-0.007897931151092052,
-0.01970362849533558,
-0.017026230692863464,
0.007830698974430561,
0.010098621249198914,
0.01467408612370491,
-0.03362710401415825,
0.01629578322172165,
-0.008096553385257721,
0.0513613224029541,
0.011804623529314995,
-0.027566002681851387,
-0.06846682727336884,
-0.00013222740381024778,
-0.06685128062963486,
-0.003317218506708741,
-0.03718701750040054,
-0.01761195994913578,
-0.05816753953695297,
0.02822142094373703,
-0.002398679032921791,
-0.013801907189190388,
-0.03020748682320118,
-0.05002482235431671,
0.01492030918598175,
0.023396793752908707,
0.03657170385122299,
0.03161162883043289,
-0.021580921486020088,
-0.013322820886969566,
0.008720234036445618,
-0.05496262386441231,
0.006858589593321085,
-0.0427519716322422,
-0.0014528142055496573,
0.050146907567977905,
-0.06934789568185806,
-0.04500466212630272,
-0.015251499600708485,
-0.0006522915791720152,
0.011739922687411308,
-0.059658799320459366,
-0.012085400521755219,
0.013283182866871357,
0.007880019955337048,
-0.05763284116983414,
-0.04076122120022774,
0.03583279252052307,
0.01899951510131359,
-0.03557718172669411,
0.005133733153343201,
0.007809797301888466,
-0.01220676302909851,
-0.032320477068424225,
-0.01665513962507248,
0.04478619992733002,
-0.015181638300418854,
-0.031643081456422806,
0.007003061939030886,
0.03430208936333656,
0.047960881143808365,
-0.04714563116431236,
-0.03064100444316864,
0.00888179149478674,
-0.013843363150954247,
0.023257434368133545,
0.008677579462528229,
0.010485868901014328,
-0.00014469196321442723,
-0.04328019917011261,
-0.014013661071658134,
-0.014876171946525574,
-0.004991270136088133,
-0.0134354829788208,
0.016080264002084732,
-0.002516144420951605,
-0.0030395369976758957,
-0.033549703657627106,
-0.020783258602023125,
-0.013359813950955868,
0.009846747852861881,
0.01500135287642479,
-0.0047608851455152035,
0.0013877819292247295,
0.0075353519059717655,
-0.020509138703346252,
0.029436297714710236,
0.006780845578759909,
-0.050540320575237274,
-0.029209282249212265,
0.03397297114133835,
-0.013077651150524616,
0.004319839645177126,
-0.0074953981675207615,
0.0016065585659816861,
0.024784766137599945,
-0.005410145036876202,
-0.009520264342427254,
0.015621493570506573,
0.040395643562078476,
0.008994592353701591,
0.003513253526762128,
-0.04226135462522507,
0.03625808656215668,
0.05572853237390518,
-0.012610082514584064,
0.060767270624637604,
0.04463691636919975,
-0.007984367199242115,
-0.009711413644254208,
0.011249516159296036,
0.014433729462325573,
-0.0038866412360221148,
0.0027748027350753546,
0.04511508718132973,
-0.03429659083485603,
-0.03636867180466652,
0.01753232255578041,
0.04575207456946373,
-0.029589572921395302,
-0.007828149013221264,
-0.016305290162563324,
0.0113436384126544,
0.005724548827856779,
-0.009068265557289124,
-0.03991321474313736,
0.06542959064245224,
-0.005157900042831898,
0.025416413322091103,
0.027305658906698227,
-0.007684735115617514,
0.006969228386878967,
0.01172062661498785,
0.0011470874305814505,
-0.06731349229812622,
0.0006844869931228459,
-0.044063467532396317,
0.015297984704375267,
0.03843946382403374,
0.029132308438420296,
-0.011546052992343903,
-0.021204229444265366,
0.04764191061258316,
-0.0014952956698834896,
0.00878414697945118,
0.025266768410801888,
-0.025979815050959587,
-0.03038727305829525,
-0.028827091678977013,
-0.03615839406847954,
0.08334943652153015,
-0.018819648772478104,
-0.009580429643392563,
-0.013002270832657814,
-0.02263539656996727,
0.00013180600944906473,
0.0066374787129461765,
0.0466892309486866,
-0.02770305797457695,
0.053525641560554504,
0.0007593722548335791,
0.012188090942800045,
-0.02139907330274582,
-0.017177732661366463,
0.12084474414587021,
0.07803072035312653,
0.0020103314891457558,
-0.04372366890311241,
0.06020421162247658,
-0.014267406426370144,
0.024621451273560524,
-0.03259231522679329,
0.0317549966275692,
0.007019402459263802,
0.03337535634636879,
0.013731755316257477,
0.021089335903525352,
0.007510310970246792,
-0.005332211032509804,
0.014005436562001705,
-0.08575494587421417,
-0.043616779148578644,
-0.011102315969765186,
0.03797553852200508,
-0.021620403975248337,
0.03250053524971008,
-0.026013368740677834,
-0.00890729296952486,
-0.020967530086636543,
-0.013634251430630684,
0.003334824927151203,
-0.045897476375103,
0.05352386459708214,
-0.03001479245722294,
-0.053579457104206085,
-0.007417726330459118,
0.008827351033687592,
-0.04854494705796242,
-0.042096685618162155,
0.04284550994634628,
0.014457483775913715,
0.0006609179545193911,
0.024816356599330902,
0.019069813191890717,
0.02955634891986847,
-0.04030468687415123,
-0.007638141047209501,
0.02108687162399292,
-0.03906865417957306,
-0.025752810761332512,
0.01241257879883051,
0.04449472576379776,
-0.012624691240489483,
-0.01660349778831005,
-0.020160408690571785,
0.007001994177699089,
0.034692779183387756,
-0.06583215296268463,
0.012341313995420933,
-0.02318556234240532,
0.024088462814688683,
-0.024181777611374855,
0.012004637159407139,
0.018511749804019928,
-0.02992790937423706,
0.044575855135917664,
0.02681155689060688,
-0.0037964885123074055,
-0.021522685885429382,
0.020870473235845566,
0.0011306778760626912,
0.050033967941999435,
0.0058553582057356834,
-0.005299541167914867,
-0.05525070056319237,
-0.012970549054443836,
-0.04192555695772171,
-0.03274364396929741,
0.03850965201854706,
0.03245502710342407,
0.0022124077659100294,
-0.00974048487842083,
0.00029996581724844873,
0.0005403012619353831,
-0.018059268593788147,
0.006322155240923166,
0.023006068542599678,
-0.016510989516973495,
0.021798141300678253,
0.015556507743895054,
0.03263595700263977,
0.04529689624905586,
-0.013565994799137115,
0.016924865543842316,
-0.012006651610136032,
0.021651379764080048,
0.02942953258752823,
-0.05576138570904732,
-0.03128477558493614,
0.021812496706843376,
-0.00798244308680296,
-0.0025494839064776897,
0.004234684631228447,
-0.0027540873270481825,
0.0010653964709490538,
0.008679318241775036,
-0.006702502723783255,
0.07564215362071991,
-0.015741681680083275,
-0.008641758002340794,
0.020304888486862183,
-0.0292536411434412,
0.017846589908003807,
0.030706577003002167,
0.043697699904441833,
-0.053382255136966705,
0.0013536916812881827,
-0.02886607125401497,
-0.017234953120350838,
0.012054579332470894,
0.006690813694149256,
-0.028781866654753685,
0.01280802208930254,
-0.012345635332167149,
0.00019927509129047394,
-0.032968584448099136,
-0.015161503106355667,
-0.044633898884058,
0.042395494878292084,
-0.015496022067964077,
-0.0010033203288912773,
-0.009487679228186607,
0.013233943842351437,
-0.02338639833033085,
-0.06519696861505508,
0.011585577391088009,
0.024690451100468636,
-0.0442630909383297,
0.011840767227113247,
0.009118463844060898,
0.008213038556277752,
0.023770619183778763,
-0.012229952029883862,
-0.0435737706720829,
-0.017653383314609528,
-0.015132670290768147,
-0.03583984822034836,
0.0462619923055172,
-0.0029506077989935875,
0.031067190691828728,
0.04545663669705391,
0.015826016664505005,
0.008550407364964485,
0.01443319022655487,
0.010417661629617214,
-0.005387845449149609,
0.005406851414591074,
-0.013841095380485058,
-0.02184348739683628,
-0.01486141700297594,
0.04477328807115555,
0.0008439922239631414,
-0.04359131306409836,
0.029124824330210686,
0.01634884625673294,
0.0188300758600235,
0.0016874514985829592,
0.022776274010539055,
-0.021632717922329903,
-0.023170750588178635,
0.04607070982456207,
-0.014050804078578949,
0.05750340223312378,
0.02944568358361721,
-0.04480927437543869,
0.017310965806245804,
0.015631191432476044,
0.04032795876264572,
-0.09286824613809586,
-0.01327147614210844,
0.046477340161800385,
0.03101521171629429,
0.06477062404155731,
-0.03360966593027115,
0.014053123071789742,
-0.00012300597154535353,
-0.092710480093956,
0.013371002860367298,
-0.033917803317308426,
0.009229973889887333,
-0.0033359823282808065,
-0.03811294585466385,
-0.007363960146903992,
0.08301621675491333,
0.047391705214977264,
0.05670321732759476,
0.009281367994844913,
0.013952195644378662,
-0.00424179108813405,
-0.05571684241294861,
0.012881575152277946,
0.03574678301811218,
-0.006827544886618853,
-0.007134281564503908,
0.07774452865123749,
-0.018757306039333344,
0.00639769434928894,
0.020362304523587227,
-0.023367812857031822,
0.011439278721809387,
0.005927680991590023,
0.027774788439273834,
-0.005973436404019594,
0.011955115012824535,
0.009790501557290554,
-0.016391925513744354,
-0.04947550222277641,
-0.022537749260663986,
0.016796469688415527,
0.004992267116904259,
0.03192967548966408,
-0.032943516969680786,
0.003690081648528576,
-0.0218479186296463,
0.002447436796501279,
0.04028777778148651,
-0.0025065767113119364,
-0.008227135054767132,
-0.010310779325664043,
0.0074732317589223385,
-0.001658071530982852,
-0.0249964389950037,
0.018045976758003235,
-0.027300354093313217,
-0.0008644408662803471,
0.005158951040357351,
-0.025689607486128807,
-0.00843401812016964,
0.001610511913895607,
-0.009435177780687809,
-0.07361526787281036,
0.03683396801352501,
-0.03041555918753147,
0.011618423275649548,
-0.049897681921720505,
-0.0003691210877150297,
0.022123565897345543,
-0.02158665657043457,
0.006588227581232786,
-0.0437353141605854,
-0.026588326320052147,
0.008829453960061073,
0.00893488060683012,
-0.005853363312780857,
-0.016553735360503197,
-0.04875427484512329,
-0.035217706114053726,
-0.07274585217237473,
0.061479974538087845,
0.024426283314824104,
-0.013964502140879631,
-0.04836372286081314,
0.011159518733620644,
-0.036049578338861465,
0.07082277536392212,
0.0691431388258934,
-0.01880284957587719,
-0.020233022049069405,
-0.0011983379954472184,
0.012943713925778866,
0.02664080075919628,
-0.022891143336892128,
-0.0506688617169857,
0.038010407239198685,
-0.029366329312324524,
0.0019128686981275678,
-0.00584422517567873,
-0.02198360674083233,
-0.0007250600028783083,
0.024471428245306015,
0.004526262637227774,
0.08519447594881058,
0.02243885211646557,
-0.06532014906406403,
-0.011356016620993614,
0.013366231694817543,
-0.025274062529206276,
0.04801996052265167,
0.019740469753742218,
-0.011752248741686344,
0.035900797694921494,
-0.0430140495300293,
-0.028700798749923706,
0.007864266633987427,
-0.040885139256715775,
0.00996171310544014,
-0.010402176529169083,
-0.01879236288368702,
0.07054121047258377,
-0.05909401550889015,
-0.007406903430819511,
-0.00042831493192352355,
-0.027101757004857063,
-0.02623714692890644,
0.054550740867853165,
0.018702350556850433,
-0.001889831735752523,
0.003126503201201558,
0.01426459290087223,
0.0015526222996413708,
-0.010824009776115417,
0.023626670241355896,
0.011437877081334591,
0.024903185665607452,
0.018743213266134262,
0.013675256632268429,
0.005372651387006044,
0.0016417634906247258,
0.005570167675614357,
0.02763674035668373,
0.04966169223189354,
0.009618840180337429,
0.01376129500567913,
0.017623456194996834,
-0.0051449500024318695,
-0.018737342208623886,
0.03106866590678692,
0.023747369647026062,
0.08418487012386322,
0.0007668257458135486,
0.003895536996424198,
-0.011616590432822704,
0.013902743346989155,
-0.04171684384346008,
0.02083742804825306,
0.06101364269852638,
0.026804625988006592,
0.0023473806213587523,
-0.002133958274498582,
-0.03595108166337013,
-0.022637130692601204,
0.027872443199157715,
-0.004047804977744818,
-0.006786779034882784,
-0.008409096859395504,
-0.025305744260549545,
0.018163545057177544,
-0.012813357636332512,
-0.04532390087842941,
-0.01851673051714897,
0.02782822959125042,
0.01314912922680378,
0.04867210239171982,
0.020969387143850327,
0.013013961724936962,
-0.013744354248046875,
0.041421301662921906,
-0.07745376974344254,
0.009306015446782112,
0.024008963257074356,
0.06176023557782173,
0.03247496858239174,
-0.014217358082532883
] |
<p>Apparently the plane mirror makes virtual images, and virtual images cannot be projected onto a screen. If you look below, it is?</p>
<p><img src="http://i.stack.imgur.com/vg05N.png" alt="Virtual Image projection"></p>
<p>If the eye is basically a screen of rods and cones, then everything is a real image?</p>
<p>I'm guessing I'm wrong, but how?</p>
<p>Thanks</p>
| 9,376 |
[
-0.045969389379024506,
-0.050813935697078705,
-0.006564245093613863,
-0.036286596208810806,
0.023563826456665993,
-0.00404637586325407,
-0.04477345943450928,
0.00137000298127532,
-0.021145455539226532,
0.002128899795934558,
0.03754207491874695,
0.0414302684366703,
0.04252994433045387,
0.02943381294608116,
-0.013474239967763424,
0.011560032144188881,
-0.02527651935815811,
0.0061439815908670425,
-0.0013628785964101553,
-0.036748066544532776,
-0.0026481198146939278,
0.05295949801802635,
0.02892468124628067,
-0.01200883463025093,
-0.024597587063908577,
0.010798556730151176,
0.016240132972598076,
-0.005455917678773403,
0.04236380383372307,
0.05308157950639725,
-0.03020188957452774,
0.005324547179043293,
-0.00452004000544548,
-0.010185216553509235,
-0.006620506290346384,
-0.011358477175235748,
-0.04756158962845802,
0.009628395549952984,
0.00024125256459228694,
-0.0013195486972108483,
0.045883458107709885,
0.024785038083791733,
-0.01450661476701498,
0.09447479993104935,
-0.0014830762520432472,
-0.02444530464708805,
-0.045701317489147186,
-0.012379051186144352,
0.01770252175629139,
-0.07499954104423523,
0.08940056711435318,
-0.04295871779322624,
0.019491299986839294,
0.034886546432971954,
0.01117671001702547,
0.037250079214572906,
0.0796675756573677,
0.10175582021474838,
-0.026765279471874237,
-0.022652016952633858,
-0.0034447768703103065,
0.007243880536407232,
-0.009209198877215385,
-0.024666788056492805,
-0.025652602314949036,
-0.004997494630515575,
0.020988840609788895,
-0.012321272864937782,
0.024153009057044983,
0.006810012739151716,
-0.016767529770731926,
0.03927728533744812,
0.018546026200056076,
0.014241363853216171,
0.0086089838296175,
-0.028712354600429535,
0.05538784712553024,
0.01780736818909645,
0.05392216891050339,
0.023332970216870308,
0.013058215379714966,
0.015110998414456844,
0.00008095791417872533,
0.05064644291996956,
0.037575628608465195,
0.010428287088871002,
0.09114314615726471,
0.0031098644249141216,
0.016598578542470932,
0.03955036401748657,
0.015810536220669746,
-0.003682981478050351,
0.05725216493010521,
-0.00011933092173421755,
-0.045084625482559204,
0.0080449553206563,
-0.0023256109561771154,
0.06029343232512474,
0.02606685645878315,
-0.05365411564707756,
0.001210719463415444,
0.008601740002632141,
0.018710821866989136,
0.047028832137584686,
0.01235551293939352,
-0.027168994769454002,
-0.02989627793431282,
0.0440584160387516,
0.034585606306791306,
0.03383870795369148,
-0.015975765883922577,
0.040504083037376404,
-0.01232763472944498,
0.022525032982230186,
0.04132824391126633,
-0.028781043365597725,
0.0432884581387043,
-0.006897385697811842,
0.06506474316120148,
0.05202069133520126,
0.015199135057628155,
-0.021587565541267395,
0.0039687431417405605,
-0.02194293774664402,
-0.09732867777347565,
0.03973734751343727,
0.030302779749035835,
-0.024108504876494408,
-0.005185367073863745,
0.023521704599261284,
0.013045827858150005,
-0.002148289931938052,
0.041860345751047134,
-0.003702569054439664,
0.04117041081190109,
-0.013562040403485298,
-0.09470558166503906,
-0.022868560627102852,
0.027410617098212242,
-0.0022668112069368362,
-0.011128104291856289,
-0.057683978229761124,
0.0362735241651535,
0.06964465975761414,
0.055118054151535034,
-0.010476638562977314,
-0.0022396487183868885,
0.009119262918829918,
0.027165528386831284,
-0.011614306829869747,
-0.022712646052241325,
0.006789851933717728,
0.005403412971645594,
-0.018215464428067207,
-0.00037486740620806813,
-0.04861309006810188,
0.02494501695036888,
0.049990661442279816,
-0.01615038700401783,
-0.032712165266275406,
0.03495216742157936,
-0.016860276460647583,
0.012066428549587727,
-0.021574806421995163,
-0.0471964105963707,
-0.013139287009835243,
0.07508787512779236,
-0.01763751171529293,
0.002938824938610196,
0.03592608496546745,
-0.029435159638524055,
0.04955616965889931,
-0.0241460632532835,
0.026171835139393806,
0.019699571654200554,
-0.006856979336589575,
-0.01359947957098484,
-0.01560690626502037,
0.013787593692541122,
-0.0017083314014598727,
-0.027717269957065582,
-0.02806253358721733,
0.009489522315561771,
0.039460744708776474,
0.030744222924113274,
0.045725785195827484,
-0.023335624486207962,
-0.022014092653989792,
-0.007407627534121275,
-0.03217577934265137,
-0.031517837196588516,
-0.027872160077095032,
0.013863549567759037,
-0.010170903988182545,
0.025414543226361275,
-0.0363515242934227,
-0.013777630403637886,
0.01797596737742424,
-0.004745518323034048,
-0.030749624595046043,
-0.04957539215683937,
0.015772927552461624,
0.026089616119861603,
0.003143474692478776,
0.026864347979426384,
0.043117839843034744,
0.06961620599031448,
-0.034743621945381165,
-0.018097124993801117,
-0.006035697180777788,
0.009298271499574184,
-0.00315575348213315,
-0.008088134229183197,
0.025315437465906143,
-0.009552151896059513,
-0.033904001116752625,
0.01430803444236517,
0.07368889451026917,
-0.009388735517859459,
0.028606723994016647,
-0.00784264039248228,
0.048482876271009445,
0.03522258251905441,
0.014581306837499142,
0.007218703627586365,
0.022478731349110603,
0.005110434256494045,
-0.017869209870696068,
0.002059033140540123,
-0.01008369866758585,
-0.042733848094940186,
-0.024638868868350983,
0.04928138107061386,
0.011972194537520409,
-0.027119604870676994,
0.03737113997340202,
0.026711219921708107,
0.04987569525837898,
0.01965194381773472,
0.024508966132998466,
-0.03714689239859581,
-0.0036906821187585592,
-0.001768533606082201,
-0.002242450602352619,
0.022513048723340034,
0.04449810832738876,
0.02550981007516384,
-0.008441077545285225,
0.001136282691732049,
-0.044731445610523224,
-0.017224721610546112,
0.05251794680953026,
-0.024330444633960724,
0.007772872690111399,
-0.013477442786097527,
-0.024572327733039856,
0.02674231119453907,
-0.012204709462821484,
-0.0013893317664042115,
-0.0011186649790033698,
0.006552161183208227,
-0.02857130579650402,
-0.055426374077796936,
-0.01962307281792164,
0.0015625811647623777,
0.050442520529031754,
-0.05573375150561333,
-0.017764704301953316,
0.03797943517565727,
-0.028026631101965904,
0.03075515851378441,
-0.022366195917129517,
0.0011705338256433606,
-0.040445905178785324,
0.0005727067473344505,
-0.015695277601480484,
0.01615358702838421,
0.0258040651679039,
-0.02839871682226658,
-0.06144513934850693,
-0.02935739792883396,
-0.07226738333702087,
0.0008447459549643099,
-0.00491677550598979,
-0.06039828434586525,
0.015458319336175919,
-0.024626366794109344,
-0.029291121289134026,
0.03142813965678215,
0.004587810020893812,
0.005504062864929438,
-0.017022019252181053,
-0.034643691033124924,
-0.048835668712854385,
-0.0011298805475234985,
-0.0443895198404789,
0.012777828611433506,
-0.004542409908026457,
0.008814798668026924,
-0.004059515427798033,
0.020588155835866928,
-0.005323059856891632,
0.012115907855331898,
-0.03431550785899162,
-0.06004533916711807,
0.032795973122119904,
-0.0037276751827448606,
0.011949350126087666,
-0.05029842257499695,
0.015713846310973167,
0.011365758255124092,
-0.04026464372873306,
0.04331535845994949,
-0.022096918895840645,
-0.049021411687135696,
0.03616119548678398,
0.025938328355550766,
0.004948699846863747,
-0.03537081182003021,
-0.0418141707777977,
0.08244320005178452,
-0.012850860133767128,
-0.04979759454727173,
-0.006035530008375645,
0.011950082145631313,
-0.005322664976119995,
-0.039303261786699295,
0.0004816573637071997,
0.015700925141572952,
-0.018002251163125038,
0.04346295818686485,
0.005881292279809713,
0.0021148244850337505,
0.026559751480817795,
0.012511416338384151,
-0.03561067953705788,
-0.036902301013469696,
-0.012362714856863022,
-0.005719715729355812,
0.016947004944086075,
0.025616498664021492,
-0.04247353971004486,
-0.0001354423293378204,
-0.012575485743582249,
0.02517383173108101,
-0.006878703832626343,
-0.045606814324855804,
0.04395557567477226,
-0.0021062588784843683,
0.047628577798604965,
-0.01441644225269556,
0.054006852209568024,
0.017094746232032776,
0.025343021377921104,
-0.039540696889162064,
0.022314943373203278,
0.058804307132959366,
-0.012808781117200851,
-0.005563679616898298,
0.04728236794471741,
-0.0029223570600152016,
-0.014350815676152706,
-0.014578266069293022,
0.003324976423755288,
0.017755700275301933,
0.01383915077894926,
-0.021906496956944466,
-0.016218435019254684,
0.05523255467414856,
0.021036477759480476,
0.015581722371280193,
0.033243633806705475,
-0.010168883018195629,
-0.02739492990076542,
-0.037277963012456894,
0.024055374786257744,
-0.013075037859380245,
0.016194293275475502,
-0.002556410850957036,
0.019905799999833107,
0.03218918666243553,
0.025596844032406807,
0.004922829102724791,
-0.012618973851203918,
-0.060159262269735336,
0.005405216012150049,
-0.0009593783179298043,
-0.010392573662102222,
-0.03435885161161423,
-0.011574456468224525,
0.021848304197192192,
-0.029508111998438835,
-0.024806320667266846,
-0.02804318629205227,
-0.018582727760076523,
-0.03486651927232742,
-0.026494279503822327,
0.0013679403346031904,
-0.007625286933034658,
-0.020122181624174118,
0.02673685923218727,
0.009089997969567776,
-0.015832817181944847,
0.021382072940468788,
0.0480864979326725,
-0.04946022480726242,
0.00954714510589838,
-0.022795967757701874,
0.013863146305084229,
0.010839542374014854,
0.04380681738257408,
0.040638454258441925,
0.028729433193802834,
-0.017606453970074654,
0.00881956797093153,
-0.017311906442046165,
0.04178880155086517,
-0.0022907808888703585,
0.002406430197879672,
-0.014006146229803562,
-0.060490142554044724,
-0.03398091718554497,
-0.02773183025419712,
0.03832150623202324,
-0.024534624069929123,
-0.016259068623185158,
0.024013105779886246,
-0.0024769795127213,
-0.0019408835796639323,
0.017830070108175278,
-0.00043881245073862374,
-0.017901543527841568,
-0.0022689697798341513,
-0.05318634584546089,
-0.015947366133332253,
-0.03844912350177765,
0.005122603382915258,
0.05685972422361374,
0.006509528029710054,
-0.0053611318580806255,
-0.011696459725499153,
0.0078284852206707,
-0.0012286852579563856,
0.0034290419425815344,
0.0037075818981975317,
-0.004380601923912764,
-0.021557722240686417,
-0.006165362428873777,
0.022403104230761528,
0.019220883026719093,
0.04898332804441452,
0.025336863473057747,
-0.017760412767529488,
-0.04083869978785515,
-0.06672781705856323,
0.014806889928877354,
0.035537268966436386,
0.04835761338472366,
0.0007832993869669735,
-0.022539038211107254,
-0.0648665651679039,
-0.036669883877038956,
0.005743209272623062,
-0.028467949479818344,
0.03955715149641037,
-0.044932831078767776,
0.021260999143123627,
-0.005783192813396454,
0.004144842736423016,
-0.0013195185456424952,
-0.01252869050949812,
-0.032618891447782516,
0.033175691962242126,
-0.040652692317962646,
-0.00422405730932951,
0.0001984170376090333,
-0.00799105130136013,
0.004539710935205221,
0.04301345348358154,
-0.0003413038793951273,
0.022987518459558487,
0.017552748322486877,
0.03684121370315552,
-0.08004382997751236,
-0.021041126921772957,
0.028689544647932053,
0.030691023916006088,
-0.018712719902396202,
0.02840806171298027,
-0.030800137668848038,
-0.029962075874209404,
0.03125767782330513,
-0.00748105812817812,
0.010882867500185966,
-0.02231534570455551,
-0.0072782160714268684,
0.0028943857178092003,
0.0018352678744122386,
0.011227882467210293,
0.05809378623962402,
0.005645012017339468,
0.012799400836229324,
-0.010696389712393284,
-0.03310420364141464,
0.02054143138229847,
-0.042360495775938034,
-0.012748612090945244,
-0.02879275381565094,
0.004918712191283703,
-0.000536701234523207,
0.030545605346560478,
0.021766159683465958,
-0.00713583268225193,
-0.029010603204369545,
-0.03073086403310299,
-0.024136465042829514,
0.018552493304014206,
0.014994469471275806,
0.02153235301375389,
-0.008937183767557144,
-0.005219404585659504,
0.016047276556491852,
-0.018984677270054817,
0.00335949775762856,
-0.0031306734308600426,
-0.013528537936508656,
0.029962077736854553,
0.05526866018772125,
0.00930548831820488,
-0.014479692094027996,
-0.01302355621010065,
0.013134350068867207,
-0.04216714948415756,
0.03407476842403412,
-0.03565695509314537,
0.023380490019917488,
0.054643332958221436,
-0.10204087942838669,
0.000529433717019856,
-0.010620536282658577,
-0.060944948345422745,
0.030101057142019272,
-0.03638192266225815,
0.006676092278212309,
0.022631486877799034,
0.0098454924300313,
-0.024454578757286072,
-0.05516663193702698,
0.033712923526763916,
0.03211897239089012,
-0.030879836529493332,
-0.015279085375368595,
-0.004990404471755028,
-0.013112177141010761,
-0.03576172888278961,
-0.02849295362830162,
-0.028277724981307983,
-0.003581956261768937,
-0.01816185936331749,
0.017680739983916283,
-0.02234652079641819,
0.05135752260684967,
0.012397498823702335,
-0.04294464737176895,
-0.024978378787636757,
-0.03008108213543892,
-0.0060902368277311325,
-0.008453620597720146,
0.027531703934073448,
-0.01556636206805706,
-0.021654652431607246,
0.0032789562828838825,
-0.003843470476567745,
0.04612107574939728,
0.011499084532260895,
0.048572856932878494,
-0.022396255284547806,
0.00975164957344532,
-0.018397938460111618,
-0.033730655908584595,
0.027550525963306427,
-0.003656465094536543,
-0.003587767481803894,
-0.016887526959180832,
0.02500673569738865,
-0.03394411876797676,
-0.0053188856691122055,
0.05019509047269821,
-0.006558578461408615,
0.02993236854672432,
-0.02510753832757473,
0.06331128627061844,
-0.009533737786114216,
0.009373016655445099,
-0.004525843542069197,
-0.06634121388196945,
0.019847245886921883,
0.00576931843534112,
0.029912369325757027,
0.01662355847656727,
0.05203929543495178,
-0.033051278442144394,
-0.022497043013572693,
-0.03469857573509216,
0.004818287678062916,
0.051952049136161804,
-0.011121372692286968,
0.07056280970573425,
-0.0037456736899912357,
-0.024808306246995926,
-0.019228478893637657,
0.00044490586151368916,
-0.030024223029613495,
0.028815453872084618,
0.011025866493582726,
0.04493873938918114,
-0.0556216798722744,
0.0163271427154541,
-0.024633897468447685,
0.04594952613115311,
0.05710737407207489,
0.02274933084845543,
0.035417340695858,
0.02206827886402607,
0.02018168941140175,
-0.014326734468340874,
-0.03525557368993759,
0.028763437643647194,
-0.0228394977748394,
0.02478703297674656,
-0.008272328414022923,
-0.003533341223374009,
0.05854613706469536,
-0.021094195544719696,
0.03411814197897911,
-0.06368488073348999,
-0.030905751511454582,
-0.01629546843469143,
-0.021307343617081642,
-0.039780981838703156,
0.04379715025424957,
-0.03116973675787449,
-0.04280750826001167,
0.011523151770234108,
0.005301885772496462,
0.049779269844293594,
-0.0033055192325264215,
-0.07998961210250854,
-0.07532843202352524,
-0.03534058853983879,
-0.016607802361249924,
0.046614065766334534,
0.023944344371557236,
-0.017318902537226677,
-0.00045401311945170164,
-0.05123022943735123,
0.017111044377088547,
0.014194570481777191,
0.053475525230169296,
-0.01793806254863739,
0.025646941736340523,
-0.003457407234236598,
0.06641760468482971,
0.0167294442653656,
-0.00336830853484571,
0.09900832176208496,
0.005960383918136358,
-0.03664953634142876,
-0.0607866570353508,
0.013957113958895206,
-0.07574424892663956,
0.027535993605852127,
-0.055118486285209656,
0.044806189835071564,
-0.018526403233408928,
0.032054636627435684,
0.04766076058149338,
0.02682175487279892,
0.029992414638400078,
0.006936111953109503,
0.01637474074959755,
-0.04839848354458809,
-0.04029353708028793,
0.0020090651232749224,
-0.010945150628685951,
-0.04143613204360008,
0.03863421082496643,
-0.05547390878200531,
0.02219759114086628,
-0.0013953682500869036,
-0.02245260216295719,
-0.014844191260635853,
-0.03421773388981819,
0.02249843440949917,
0.023640889674425125,
-0.04089496284723282,
-0.005025467369705439,
0.002451864071190357,
-0.04471151530742645,
-0.05734475702047348,
-0.01829165406525135,
0.011618630960583687,
-0.007889658212661743,
0.04849473759531975,
0.047420039772987366,
-0.00308514223434031,
0.009726167656481266,
-0.022015346214175224,
-0.00652109831571579,
-0.03114418312907219,
-0.020502477884292603,
0.006646167021244764,
0.014901895076036453,
-0.024921145290136337,
0.005725146736949682,
-0.013291778974235058,
-0.021193034946918488,
0.004849092569202185,
-0.07766472548246384,
-0.006552882492542267,
0.01089284848421812,
-0.005915243644267321,
-0.006652947049587965,
-0.0392758771777153,
-0.02208242006599903,
0.04725658521056175,
0.0018891695654019713,
0.019287073984742165,
-0.0030524935573339462,
0.03300274536013603,
-0.00786702148616314,
-0.05403726547956467,
0.017309674993157387,
-0.0036567298229783773,
0.000522494432516396,
-0.010666013695299625,
0.0029112654738128185,
-0.02202380821108818,
-0.029005667194724083,
0.03370742127299309,
0.026075560599565506,
0.033549655228853226,
0.019609086215496063,
-0.0138226468116045,
-0.016606170684099197,
-0.010141868144273758,
0.019361138343811035,
-0.04549899324774742,
-0.05064459517598152,
-0.0466545969247818,
0.012835879810154438,
0.04059753939509392,
0.0498165637254715,
-0.013819525018334389,
0.005982489790767431,
-0.004957720171660185,
-0.005436428822577,
0.01563146896660328,
-0.04613981395959854,
-0.06380055099725723,
0.03570370003581047,
0.000011749988516385201,
-0.013771041296422482,
0.012907048687338829,
0.04750392213463783,
0.05983056500554085,
0.0031038084998726845,
0.016281044110655785,
0.029277345165610313,
-0.02768138237297535,
-0.011823620647192001,
0.003678672481328249,
-0.02954118885099888,
0.046139009296894073,
-0.02567128837108612,
0.014906341210007668,
-0.013081399723887444,
-0.014863021671772003,
-0.028040772303938866,
-0.03170349448919296,
-0.012061672285199165,
0.0228281170129776,
0.0384317971765995,
0.010285681113600731,
-0.028667883947491646,
0.02518484555184841,
-0.018141431733965874,
-0.027614060789346695,
-0.027708925306797028,
0.046166978776454926,
0.030088840052485466,
0.014452802017331123,
-0.054073598235845566,
0.02147395722568035,
-0.02819731831550598,
-0.02885345369577408,
0.03678736463189125,
0.027020150795578957,
-0.04149496182799339,
0.014104373753070831,
0.015076307579874992,
0.013790873810648918,
0.02037886530160904,
-0.01980794221162796,
-0.02283814176917076,
0.04643895477056503,
-0.02296523004770279,
-0.029697135090827942,
0.02709263563156128,
-0.022675400599837303,
0.024595316499471664,
0.06536891311407089,
0.002145728562027216,
-0.01994357258081436,
0.05175219476222992,
-0.0007484307279810309,
-0.004989642649888992,
0.0013301436556503177,
0.0026913501787930727,
-0.0026161351706832647,
0.012402653694152832,
0.00562963867560029,
-0.02488338202238083,
-0.014471922069787979,
0.024873625487089157,
0.005112132523208857,
0.024462146684527397,
0.017750157043337822,
-0.0011473230551928282,
0.0069852788001298904,
-0.007219709921628237,
0.013789144344627857,
0.009299593046307564,
0.021625397726893425,
0.012377358041703701,
-0.035381872206926346,
0.052669163793325424,
0.022567078471183777,
-0.030889999121427536,
-0.10164447128772736,
0.012287914752960205,
-0.034285299479961395,
-0.007506416644901037,
0.049604251980781555,
-0.05968515947461128,
0.02181568555533886,
0.02139815129339695,
-0.11377109587192535,
0.005901085212826729,
-0.0030310796573758125,
-0.0680484026670456,
-0.0514405183494091,
0.024557113647460938,
-0.0021350234746932983,
0.03000115416944027,
0.014703275635838509,
0.045610714703798294,
0.015214405953884125,
-0.02199016883969307,
-0.01351207960397005,
0.002158617600798607,
-0.011982563883066177,
0.016452429816126823,
-0.03728226572275162,
0.013539985753595829,
0.08379025757312775,
-0.04554196447134018,
-0.05041218176484108,
0.02127813920378685,
0.01612813025712967,
0.028793619945645332,
0.03235244005918503,
0.02472553588449955,
0.02178184874355793,
0.02978740632534027,
-0.002507719211280346,
-0.010193067602813244,
-0.03516557440161705,
0.030191335827112198,
-0.006946342531591654,
0.029167847707867622,
0.014141600579023361,
-0.002763911848887801,
0.0015057523269206285,
-0.017854908481240273,
-0.03824668005108833,
0.018270263448357582,
0.003702821210026741,
-0.012340167537331581,
-0.012603476643562317,
0.033995721489191055,
0.004457208327949047,
-0.020398156717419624,
-0.000311297393636778,
-0.04809963330626488,
0.02227206900715828,
0.012624071910977364,
-0.04500848427414894,
0.011389803141355515,
0.00813412293791771,
0.002365363761782646,
-0.0366353765130043,
0.042496029287576675,
-0.01472445297986269,
-0.025696100667119026,
-0.017372051253914833,
-0.029566895216703415,
0.04784686863422394,
-0.010326872579753399,
0.04311717674136162,
-0.01638096384704113,
-0.0007441246998496354,
0.011850173585116863,
0.03506695479154587,
-0.013789148069918156,
0.011662003584206104,
-0.05438593029975891,
-0.06489881873130798,
-0.029649430885910988,
0.03331482782959938,
-0.015675196424126625,
-0.02083410881459713,
-0.041331905871629715,
-0.018347613513469696,
0.0013954243622720242,
0.06585594266653061,
0.04818105697631836,
-0.031867120414972305,
0.011950423941016197,
0.0023567660246044397,
0.003350469982251525,
0.014179819263517857,
-0.05590719357132912,
0.0009174630977213383,
-0.006790866609662771,
-0.06191597133874893,
0.004629523493349552,
0.005217914469540119,
-0.012807990424335003,
0.02120658941566944,
0.032214682549238205,
-0.016391314566135406,
0.036802951246500015,
-0.011865125969052315,
-0.04685792326927185,
0.03100082464516163,
0.018836986273527145,
-0.007680942304432392,
0.06435885280370712,
-0.0031770714558660984,
-0.0043021636083722115,
0.019941743463277817,
0.0029991145711392164,
-0.000923335028346628,
-0.0043720281682908535,
-0.02765510417521,
0.0077125150710344315,
-0.05258778855204582,
-0.0040439702570438385,
0.04920019209384918,
-0.03651577606797218,
0.02857201173901558,
0.02093866467475891,
0.017237912863492966,
-0.01981440559029579,
0.08086284250020981,
-0.003092022379860282,
0.01585477963089943,
-0.006170874461531639,
0.04445956274867058,
-0.0003826292813755572,
-0.02419161982834339,
0.0343208909034729,
0.06378696113824844,
-0.002846641233190894,
-0.02877202071249485,
0.033454567193984985,
0.04053908586502075,
0.03112584538757801,
0.07579260319471359,
-0.031015625223517418,
0.06946250796318054,
-0.03595955669879913,
-0.010949268005788326,
-0.03611854463815689,
-0.022436153143644333,
-0.018951764330267906,
0.016984254121780396,
-0.00715121254324913,
0.08560483902692795,
-0.03293938562273979,
0.012369067408144474,
0.0007424512295983732,
0.016263265162706375,
-0.03951607644557953,
-0.001275641960091889,
0.029859373345971107,
0.016285762190818787,
-0.017907505854964256,
-0.03257904201745987,
-0.003955501597374678,
0.022755229845643044,
0.017208432778716087,
-0.020893104374408722,
0.025011779740452766,
-0.009015325456857681,
-0.02255435660481453,
0.025517556816339493,
-0.003348532598465681,
0.0014779992634430528,
0.022034846246242523,
0.042286135256290436,
0.0262753963470459,
0.006302698981016874,
-0.007392415311187506,
0.016769584268331528,
-0.005672345403581858,
0.02052835002541542,
-0.0808958187699318,
0.019060548394918442,
0.0288087110966444,
0.0369538851082325,
0.011790878139436245,
-0.02354608289897442
] |
<p>Does my question make any sense?</p>
<hr>
<p><strong>Context</strong>: The capacitor is charged with charge $Q_0$. There is a magnetic field $B=B_0 \hat{z}$ perpendicular to the monitor's screen. The length of the (AB) wire is $\ell$. There is no friction.</p>
<p><img src="http://i.stack.imgur.com/kfsS5.png" alt="enter image description here"></p>
<p><strong>Goal</strong>: I am trying to calculate the velocity of the (AB) wire. From the 2nd law of Newton, we have:</p>
<p>$$m \frac{du}{dt}=F_\text{Laplace} = B\ell I(t)$$</p>
<p>In my lecture notes I see that $I(t)$ is replaced by the current $I_c(t)$ which corresponds to the current due to the discharge of the capacitor, <strong>as if there was no magnetic field, i.e. as if $\mathcal{E}=0$</strong>. So it goes like:</p>
<p>\begin{align}
V_c(t)&=V_0 \exp(-t/RC) \Rightarrow\\dV_c/dt &= -V_0\left(\frac{1}{RC}\right) \exp(-t/RC)=-I_c(t)/C \Rightarrow\\I_c(t) &= -C dV_c/dt
\end{align}</p>
<p>And then substitutes $-C dV_c/dt$ in the place of $I(t)$ at the Newton's law:</p>
<p>\begin{align}
m \frac{du}{dt} &= B \ell \left( -C dV_c / dt \right) \Rightarrow\\
du &= -\frac{B C\ell}{m} dV_c \Rightarrow\\
u(t) - u(0) &= -\frac{BC\ell}{m} (V_c(t) - V_0)\Rightarrow\\
u(t) &= \frac{BC\ell}{m} \left(V_0 - V_c(t)\right)
\end{align}</p>
<p><strong>Questions</strong>: Why use $I_c(t)$ instead of $I(t)$? We do have an induced electromotive force so it should be: $$I(t) = \frac{V_c(t)-\mathcal{E}(t)}{R}$$</p>
<p>What am I missing here?</p>
<hr>
<p>After going through all the calculations he ends with the following differential equation:</p>
<p>$$
I(t) = \frac{V_c(t)-\mathcal{E}}{R} = \frac{V_c(t) - u(t)B\ell}{R} \Rightarrow\\
\frac{dV_c}{dt} + \underbrace{\left(\frac{\ell^2 B^2}{m R} + \frac{1}{RC}\right)}_
{k_1}V_c(t) = \underbrace{\frac{\ell^2 B^2}{m R}}_{k_2}V_0
$$</p>
<p>With the following solution:</p>
<p>$$
V_c(t) = V_0 \left(1 - \frac{k_2}{k_1}\right)e^{-k_1 t} + \frac{k_2}{k_1}V_0
$$</p>
<p>And after some calculations the velocity $u(t)$ is given by:
$$
u(t) = \frac{BC\ell}{m}V_0 \left(1 - \frac{k_2}{k_1}\right)(1-e^{-k_1 t})
$$</p>
<p>with $k_1,k_2$ being constants depending on $B,C,m,R$, etc.</p>
<p>This equation looks weird because there is a combination that leads to zero velocity ? ($k_1=k_2$)</p>
<p>I'm at a loss here! </p>
| 9,377 |
[
-0.049825455993413925,
-0.006946523208171129,
0.016346760094165802,
-0.01845148205757141,
0.04038824886083603,
-0.017175624147057533,
-0.04699505865573883,
0.00874843169003725,
0.005868158768862486,
0.020845314487814903,
0.032456476241350174,
0.06731840968132019,
0.0814967155456543,
0.010450792498886585,
0.02332567423582077,
0.011982114985585213,
-0.0034595115575939417,
0.015939529985189438,
0.01805478148162365,
-0.017586272209882736,
0.015713483095169067,
0.008745313622057438,
0.022261209785938263,
0.014126530848443508,
0.033203572034835815,
0.013291507959365845,
0.011317996308207512,
-0.013604357838630676,
-0.04900383576750755,
0.05253118276596069,
-0.022123999893665314,
0.012523557059466839,
0.0012937370920553803,
-0.017618900164961815,
-0.012848412618041039,
0.047819238156080246,
-0.03356945142149925,
-0.05757177993655205,
0.009804626926779747,
0.0615316703915596,
0.012392501346766949,
0.03501831740140915,
0.017097480595111847,
0.04313097894191742,
-0.02856847643852234,
0.03334810957312584,
-0.018607178702950478,
-0.011307498440146446,
0.02305017225444317,
-0.06134193018078804,
0.028783846646547318,
-0.02646360732614994,
0.06502743810415268,
0.0023218055721372366,
-0.03593580424785614,
-0.0021547977812588215,
0.07292892783880234,
0.0543614961206913,
0.026484815403819084,
-0.046617377549409866,
0.01961500570178032,
0.013743393123149872,
-0.007712983526289463,
-0.0381527878344059,
-0.02044861577451229,
0.03522718697786331,
-0.006702770013362169,
0.017405793070793152,
0.03609335795044899,
0.027029577642679214,
0.018331563100218773,
0.015161595307290554,
-0.005019033327698708,
-0.01152880024164915,
0.0327245332300663,
-0.008168977685272694,
-0.013835165649652481,
0.030722592025995255,
0.01266357023268938,
0.042997121810913086,
-0.03240961953997612,
-0.01642770878970623,
0.015346131287515163,
0.07452205568552017,
0.029434561729431152,
-0.008400162681937218,
0.06500358134508133,
-0.028619999065995216,
0.01759140007197857,
0.001999606378376484,
0.01200780551880598,
-0.008472668007016182,
0.007992709055542946,
-0.023540668189525604,
0.025661196559667587,
0.031836025416851044,
0.01864681951701641,
0.040741294622421265,
-0.012771621346473694,
-0.03532809391617775,
-0.045454517006874084,
0.010707438923418522,
0.026565514504909515,
0.05794313922524452,
-0.001045817043632269,
-0.052302006632089615,
0.014479434117674828,
-0.013051478192210197,
-0.020500019192695618,
-0.043368078768253326,
-0.057125337421894073,
0.03078559972345829,
0.014881998300552368,
0.025708049535751343,
-0.020306415855884552,
-0.02713140659034252,
0.006938714534044266,
-0.009430058300495148,
0.05738087370991707,
0.003872315399348736,
0.0359467975795269,
-0.022459253668785095,
0.01773349940776825,
-0.04267953708767891,
-0.04399644583463669,
0.01615726202726364,
0.007348348386585712,
0.006123023107647896,
0.01255742833018303,
0.02156575210392475,
-0.017198748886585236,
-0.005264163017272949,
0.002498552668839693,
0.014538987539708614,
0.022696008905768394,
-0.02014712244272232,
-0.042579445987939835,
-0.048964809626340866,
0.02394060418009758,
0.007187176961451769,
0.0052240630611777306,
-0.07768586277961731,
-0.03820544481277466,
0.029825877398252487,
0.04074469953775406,
0.0012729285517707467,
-0.013451976701617241,
-0.008205280639231205,
0.03263954073190689,
0.0049958135932683945,
0.016141878440976143,
0.010205353610217571,
-0.009422543458640575,
-0.016311705112457275,
0.014142847619950771,
-0.05826781317591667,
0.05380844697356224,
0.02046726644039154,
-0.0056863934732973576,
-0.01595948077738285,
0.06949746608734131,
0.011517108418047428,
0.002203518757596612,
-0.01871345192193985,
0.0008767573744989932,
0.005155917722731829,
0.058921635150909424,
0.004952962975949049,
0.004453365691006184,
0.022613754495978355,
0.014345841482281685,
0.006750244181603193,
-0.033331647515296936,
-0.012337235733866692,
0.028183117508888245,
-0.0548383928835392,
-0.008545788004994392,
-0.0335911363363266,
-0.025377782061696053,
-0.0018475772812962532,
-0.03556601703166962,
-0.06933065503835678,
-0.031091246753931046,
0.002870450960472226,
0.010064059868454933,
0.029642585664987564,
-0.0314992219209671,
0.0239971112459898,
-0.006431029178202152,
0.0035141680855304003,
-0.021815795451402664,
-0.05782794952392578,
0.03682473301887512,
0.0076009053736925125,
-0.04760221391916275,
0.015444229356944561,
-0.0412042997777462,
0.006423620972782373,
0.0007386932265944779,
0.006599907763302326,
0.03579622507095337,
0.028997933492064476,
0.00504651665687561,
-0.006962844170629978,
0.002581716515123844,
0.0412391796708107,
0.027367154136300087,
0.05143537372350693,
-0.007484822068363428,
-0.02349957451224327,
-0.006910055875778198,
-0.008212355896830559,
-0.02658882364630699,
0.022550905123353004,
0.05611417070031166,
-0.008606253191828728,
0.030932502821087837,
0.00019969980348832905,
0.00577373243868351,
-0.0020840622019022703,
0.032111432403326035,
0.05744488537311554,
0.06519664824008942,
0.008042730391025543,
0.00533653236925602,
0.04142013564705849,
-0.01214433740824461,
-0.007353310007601976,
-0.030341118574142456,
-0.04939759150147438,
-0.04240885004401207,
0.012139540165662766,
0.016687855124473572,
0.03022274188697338,
-0.051489416509866714,
-0.013282927684485912,
0.01802845299243927,
0.020681656897068024,
0.03980826586484909,
0.008204201236367226,
-0.021084439009428024,
-0.031095556914806366,
0.04413338750600815,
-0.00028748487238772213,
-0.020360510796308517,
-0.023504922166466713,
0.011790262535214424,
0.013801759108901024,
0.035617344081401825,
-0.01872103102505207,
0.0011727187084034085,
0.02299593947827816,
0.011740277521312237,
0.02835352160036564,
0.027005093172192574,
0.00001807398075470701,
0.046166058629751205,
-0.001074929372407496,
0.0057444279082119465,
0.06685464084148407,
0.005797684658318758,
0.038918714970350266,
0.0030973043758422136,
0.009546076878905296,
0.016365911811590195,
-0.006756514310836792,
0.02358577400445938,
-0.01499086432158947,
0.026595592498779297,
-0.027302563190460205,
0.022715996950864792,
0.008870295248925686,
-0.021087534725666046,
-0.006747848819941282,
-0.029565973207354546,
-0.007848487235605717,
0.042470116168260574,
0.018149010837078094,
-0.041344307363033295,
-0.01135248877108097,
-0.019175557419657707,
-0.016392670571804047,
-0.012356940656900406,
0.04373588413000107,
-0.013254973106086254,
0.024702100083231926,
-0.05762093886733055,
-0.050994277000427246,
0.04966597631573677,
0.03314553201198578,
-0.027379630133509636,
0.05274953693151474,
-0.0024891577195376158,
-0.06472153961658478,
-0.03409278020262718,
0.00824019219726324,
0.017302466556429863,
-0.06069507077336311,
0.004803145304322243,
0.07144108414649963,
0.006057103164494038,
-0.02759416773915291,
0.03403276577591896,
-0.06236680597066879,
-0.026549644768238068,
0.005516459234058857,
-0.014519957825541496,
0.019530227407813072,
-0.0374685563147068,
0.02258695848286152,
0.017931902781128883,
-0.02027156762778759,
-0.04534158483147621,
-0.054998405277729034,
-0.033899206668138504,
0.016170553863048553,
0.0421864353120327,
0.06684760749340057,
-0.0034068513195961714,
-0.04419364035129547,
0.06754492968320847,
0.04980270192027092,
0.016377849504351616,
-0.02717198058962822,
-0.04102712497115135,
-0.04029856622219086,
-0.08355807512998581,
-0.018277017399668694,
0.04323583468794823,
-0.06205771490931511,
-0.028505004942417145,
-0.003499113256111741,
0.026787055656313896,
0.02761606127023697,
0.025926826521754265,
0.0034232160542160273,
0.025496045127511024,
-0.003002192359417677,
0.021165138110518456,
0.07658795267343521,
0.0011637676507234573,
0.01661301776766777,
-0.00006236330227693543,
0.01705513894557953,
0.05753515288233757,
0.022012222558259964,
-0.03980843350291252,
0.03385680541396141,
-0.011399590410292149,
-0.010889274068176746,
-0.027167467400431633,
0.039777886122465134,
0.01921926997601986,
-0.02109694294631481,
-0.019061140716075897,
-0.01819842867553234,
0.02029285579919815,
-0.011930462904274464,
0.020204512402415276,
0.04827725887298584,
-0.004029001109302044,
-0.026889709755778313,
-0.06263675540685654,
-0.05303694307804108,
-0.04128573462367058,
0.006055723875761032,
-0.03835954889655113,
-0.01776852458715439,
0.01211272832006216,
0.05884518101811409,
0.000050802005716832355,
0.003667528508231044,
-0.027781561017036438,
0.0108784856274724,
-0.023364044725894928,
-0.021395258605480194,
-0.011737270280718803,
0.04492516815662384,
0.025942226871848106,
0.06346985697746277,
0.031646862626075745,
0.008266512304544449,
0.010548010468482971,
0.010340169072151184,
-0.06400024890899658,
0.029683049768209457,
0.0037312365602701902,
-0.049153074622154236,
-0.006931471172720194,
0.008729572407901287,
0.05022392421960831,
-0.03941502794623375,
-0.007403627969324589,
-0.0038672597147524357,
-0.019475098699331284,
-0.037715815007686615,
0.025533314794301987,
0.0029999378602951765,
0.0021886457689106464,
-0.04117630422115326,
0.010670850053429604,
0.02319337986409664,
-0.022757835686206818,
0.006803267169743776,
0.036813076585531235,
-0.014128378592431545,
-0.008486158214509487,
-0.027056563645601273,
-0.01834983192384243,
0.06507628411054611,
0.034255508333444595,
0.0005558456759899855,
0.0026264083571732044,
0.014533291570842266,
0.022939903661608696,
0.014505339786410332,
0.02906324341893196,
0.027089959010481834,
-0.043990474194288254,
-0.033426571637392044,
-0.07343228906393051,
-0.021932868286967278,
-0.023055950179696083,
0.08454714715480804,
0.0023238833528012037,
-0.011512970551848412,
0.052106574177742004,
0.011258053593337536,
0.041425205767154694,
0.025149904191493988,
0.0173433069139719,
0.004196455702185631,
0.004884777590632439,
-0.05257084593176842,
0.00808569323271513,
-0.02950873412191868,
-0.033988311886787415,
0.026277383789420128,
0.004853710066527128,
-0.04020994156599045,
-0.028452033177018166,
0.03644896298646927,
0.026112016290426254,
0.0039474680088460445,
0.031190473586320877,
-0.011296089738607407,
-0.0005182525492273271,
0.03066461905837059,
-0.007535156793892384,
0.03835418447852135,
0.02217043936252594,
0.013006022199988365,
-0.014349952340126038,
-0.015905357897281647,
-0.08964218944311142,
-0.04482517018914223,
0.01154895406216383,
0.04626158997416496,
0.005043461918830872,
-0.025591228157281876,
-0.07803516089916229,
-0.05097993090748787,
0.01961595006287098,
-0.03240693733096123,
0.045188646763563156,
0.01984204165637493,
0.017354171723127365,
-0.027731597423553467,
-0.06118970736861229,
-0.01954287476837635,
0.0064819022081792355,
-0.02496597170829773,
0.016596730798482895,
-0.04627445712685585,
0.02316661737859249,
0.01457486767321825,
-0.031565431505441666,
0.032132260501384735,
0.058828163892030716,
-0.022854233160614967,
-0.017707645893096924,
-0.005838945973664522,
0.022655189037322998,
-0.04066450148820877,
-0.06570380181074142,
0.013253412209451199,
-0.01711314544081688,
0.025629080832004547,
0.03426486998796463,
-0.017007717862725258,
-0.022837551310658455,
0.03901452198624611,
0.030754150822758675,
0.035664498805999756,
0.01631680503487587,
-0.028040487319231033,
0.06016359105706215,
0.012868426740169525,
-0.045340072363615036,
0.04031737893819809,
0.03870425000786781,
-0.03915580362081528,
0.0023682829923927784,
0.012418224476277828,
0.009080157615244389,
-0.005406520329415798,
-0.053874239325523376,
-0.05344511941075325,
0.017626434564590454,
-0.016368525102734566,
0.017718970775604248,
-0.014761047437787056,
-0.009344527497887611,
-0.05181633681058884,
-0.02820010297000408,
0.03469797596335411,
0.01456459704786539,
0.006662220228463411,
-0.037659306079149246,
-0.06043219193816185,
-0.005034525413066149,
-0.009664083831012249,
-0.032272353768348694,
-0.016993584111332893,
-0.012183253653347492,
0.023401979357004166,
0.04678511619567871,
-0.02189997211098671,
-0.03704411908984184,
-0.03217802196741104,
-0.015459469519555569,
0.00010325625044060871,
-0.054525651037693024,
0.0274640042334795,
-0.004194178618490696,
-0.007634232752025127,
0.009467018768191338,
-0.009227745234966278,
-0.062040336430072784,
0.016388120129704475,
-0.0061851064674556255,
-0.03769521787762642,
-0.043244972825050354,
-0.002945326967164874,
0.012906676158308983,
-0.021688707172870636,
-0.03576824441552162,
-0.04254034906625748,
-0.020945679396390915,
-0.004372990690171719,
-0.042287278920412064,
0.026447933167219162,
-0.03548526391386986,
0.02814558707177639,
-0.051042504608631134,
0.024969598278403282,
0.03829487785696983,
-0.016008291393518448,
0.00556974159553647,
0.05039852485060692,
0.003062065225094557,
0.04240928962826729,
-0.0005851368186995387,
-0.0030531897209584713,
0.006625055335462093,
-0.049142420291900635,
-0.02425096184015274,
-0.0038807170931249857,
0.0432107076048851,
-0.01753624528646469,
-0.0030904982704669237,
-0.014664511196315289,
0.0017700494499877095,
0.0159663837403059,
-0.010095758363604546,
-0.024477988481521606,
0.049966488033533096,
0.01887515000998974,
-0.015542522072792053,
-0.022738141939044,
0.002168056322261691,
0.029306737706065178,
0.028149979189038277,
0.018200313672423363,
-0.02589036338031292,
-0.04357670992612839,
-0.029710916802287102,
-0.01088110264390707,
0.000750820036046207,
0.012538069859147072,
-0.0015846035676077008,
0.042597416788339615,
-0.04154634103178978,
-0.000752711552195251,
-0.0012491681845858693,
-0.0122807202860713,
-0.0026109132450073957,
-0.0027942375745624304,
-0.02531851828098297,
0.015415249392390251,
0.0008130597998388112,
-0.03519826754927635,
0.010996592231094837,
-0.07285910099744797,
0.01434361096471548,
0.08385567367076874,
0.020015202462673187,
0.06934510916471481,
-0.034647684544324875,
-0.024124514311552048,
0.0044678752310574055,
-0.018802346661686897,
-0.0274348221719265,
0.01018438395112753,
0.014835279434919357,
0.012318643741309643,
-0.017870880663394928,
-0.013490758836269379,
0.04204170033335686,
0.005091404542326927,
-0.03770307078957558,
-0.026103831827640533,
0.044918324798345566,
-0.011589392088353634,
0.01967356540262699,
-0.000707878905814141,
-0.01741880737245083,
0.024040041491389275,
-0.02663569152355194,
0.057325128465890884,
-0.0012243695091456175,
-0.020389709621667862,
0.03803287446498871,
0.009866607375442982,
-0.016202205792069435,
-0.05715669319033623,
-0.002357651013880968,
-0.05322220176458359,
0.002739944029599428,
0.0032330146059393883,
0.009425563737750053,
-0.0013576119672507048,
0.0018569518579170108,
0.04507093131542206,
-0.02364966832101345,
0.06886785477399826,
-0.02207360230386257,
-0.047350890934467316,
-0.006453787442296743,
-0.022914931178092957,
-0.005558476317673922,
0.08400242775678635,
0.01212332583963871,
0.004005787428468466,
0.00701206736266613,
-0.03259153291583061,
0.07692350447177887,
0.035056229680776596,
0.04330110549926758,
0.0038753764238208532,
0.0914490818977356,
-0.027185309678316116,
-0.003678436391055584,
-0.061885155737400055,
-0.005779143888503313,
0.14336584508419037,
-0.004386756103485823,
0.02400250732898712,
-0.02612278237938881,
0.023970825597643852,
0.0027097302954643965,
0.03914370760321617,
-0.02137797698378563,
0.03906929865479469,
-0.0348983071744442,
0.0032922793179750443,
0.013661976903676987,
0.015618969686329365,
-0.014447619207203388,
0.023067548871040344,
0.03366179019212723,
-0.04348590597510338,
-0.024940742179751396,
-0.017641739919781685,
0.00666222395375371,
-0.005261674989014864,
0.05447961390018463,
-0.0103457635268569,
0.02051645889878273,
-0.035285141319036484,
-0.046996742486953735,
-0.052456822246313095,
-0.0011849444126710296,
0.014576676301658154,
-0.03929153084754944,
-0.08159761875867844,
0.016765927895903587,
0.013249821029603481,
-0.011411045677959919,
-0.023055998608469963,
-0.010982747189700603,
0.010669917799532413,
0.040110476315021515,
0.02482946589589119,
-0.0039322832599282265,
-0.027827803045511246,
-0.007385533768683672,
0.04024849086999893,
-0.009999517351388931,
-0.013475301675498486,
0.04700382798910141,
-0.04511735960841179,
0.03975725546479225,
-0.03619052469730377,
0.026754504069685936,
0.018804142251610756,
0.00941759068518877,
0.0017080192919820547,
-0.05749841034412384,
-0.005435002502053976,
-0.005889800377190113,
0.020977798849344254,
0.00012044596223859116,
0.021511990576982498,
-0.05020627751946449,
0.025836028158664703,
0.03449232131242752,
-0.0232233963906765,
-0.014893901534378529,
-0.027826691046357155,
0.004273013211786747,
0.018971797078847885,
0.055042579770088196,
-0.05153592303395271,
-0.00011583586456254125,
0.022628920152783394,
0.006682022474706173,
0.00538026774302125,
-0.020207302644848824,
-0.0030248663388192654,
0.029912948608398438,
0.030400292947888374,
-0.0054695578292012215,
-0.02822103723883629,
-0.033043794333934784,
-0.10544688999652863,
0.05353645235300064,
0.024793162941932678,
0.01142375823110342,
-0.04700913652777672,
-0.0064405822195112705,
0.021060016006231308,
0.05599698796868324,
-0.008637219667434692,
0.020192371681332588,
0.014260036870837212,
0.08011285215616226,
0.03428526595234871,
-0.0031597500201314688,
-0.04270077496767044,
0.02401038259267807,
-0.0035176377277821302,
0.02513951249420643,
-0.009957009926438332,
0.008399526588618755,
0.025441111996769905,
0.03124246746301651,
-0.04675838723778725,
0.015906600281596184,
0.006865210365504026,
0.028509465977549553,
-0.0005227981018833816,
-0.03317388892173767,
0.03555002436041832,
0.020065641030669212,
0.0045882645063102245,
-0.0417892225086689,
0.008929532952606678,
-0.028038788586854935,
-0.006459847558289766,
-0.007131742779165506,
0.025154374539852142,
-0.01915179193019867,
0.014206098392605782,
-0.05168133229017258,
0.030635705217719078,
-0.047247447073459625,
-0.02147061750292778,
-0.009907811880111694,
0.0017806957475841045,
0.002630718983709812,
0.01903732493519783,
-0.018791649490594864,
0.03606373071670532,
-0.043537456542253494,
0.016806019470095634,
0.02119159884750843,
0.011674108915030956,
-0.011917357333004475,
0.007664116565138102,
-0.0036598555743694305,
0.01474594697356224,
0.010740984231233597,
-0.030082309618592262,
0.0027279688511043787,
0.027785349637269974,
-0.02311740256845951,
-0.05394154414534569,
0.023920543491840363,
0.03858303651213646,
0.004996825475245714,
0.02012547105550766,
-0.01715569943189621,
-0.02141822688281536,
0.024354442954063416,
-0.025082379579544067,
-0.002656388795003295,
-0.027972640469670296,
-0.07678373903036118,
0.020625462755560875,
-0.03633074089884758,
0.019553888589143753,
-0.004715308081358671,
0.019632084295153618,
0.025034142658114433,
0.018631665036082268,
-0.01630999520421028,
0.008388272486627102,
0.0016272026114165783,
0.0027108886279165745,
-0.005004494450986385,
0.041352275758981705,
0.010761384852230549,
0.033970724791288376,
0.030250895768404007,
0.010804945603013039,
0.00282624876126647,
-0.010732988826930523,
-0.009738924913108349,
-0.0819764956831932,
-0.008411244489252567,
-0.007093595340847969,
0.004175148438662291,
0.06164514273405075,
-0.0405898317694664,
-0.013945686630904675,
0.023762008175253868,
-0.0444183275103569,
-0.032143283635377884,
-0.033486634492874146,
-0.020327342674136162,
-0.01875479891896248,
-0.03368063643574715,
-0.001439353683963418,
0.039668116718530655,
0.009962549433112144,
0.04290362447500229,
0.02635013498365879,
0.01802876405417919,
-0.018698614090681076,
-0.03203074634075165,
-0.00039930426282808185,
0.03494838625192642,
0.014689258299767971,
0.007918975315988064,
0.051799971610307693,
-0.01843228004872799,
0.00797498319298029,
0.04456768557429314,
-0.0036226585507392883,
0.011991577222943306,
-0.036752402782440186,
0.015101811848580837,
0.030563494190573692,
0.03085864894092083,
0.010021780617535114,
-0.01954890973865986,
-0.029099836945533752,
-0.000113134432467632,
0.016448233276605606,
0.03496894985437393,
0.013463162817060947,
-0.002728802151978016,
0.029644079506397247,
-0.05180579423904419,
-0.019362658262252808,
0.015648318454623222,
-0.031260643154382706,
-0.022839615121483803,
0.028523417189717293,
0.0018428636249154806,
0.0021945140324532986,
-0.026852929964661598,
-0.0036629806272685528,
-0.01245024148374796,
-0.00015858057304285467,
0.01513702142983675,
-0.024499492719769478,
0.009429498575627804,
-0.02884589321911335,
0.008855799213051796,
-0.02609405107796192,
0.021278085187077522,
0.03576355427503586,
-0.005938610527664423,
-0.04918043315410614,
-0.02165556699037552,
-0.017020223662257195,
0.008589837700128555,
0.02313634194433689,
-0.04491955041885376,
-0.03719402104616165,
0.018267611041665077,
0.007735341787338257,
0.012307493947446346,
-0.023605477064847946,
-0.04091056436300278,
-0.010273192077875137,
-0.04394128918647766,
0.03029046766459942,
-0.009592960588634014,
-0.06284584850072861,
-0.017494525760412216,
-0.07508508116006851,
-0.01571105606853962,
0.030331259593367577,
0.06849861890077591,
-0.028286218643188477,
-0.007484255358576775,
0.03028191812336445,
-0.027218593284487724,
-0.006637028884142637,
-0.05017658323049545,
0.028863057494163513,
0.01009882241487503,
0.01648969203233719,
0.037571053951978683,
0.05198753625154495,
-0.04205850884318352,
0.02201956696808338,
0.01780588924884796,
0.017272373661398888,
0.030422139912843704,
-0.0188485998660326,
-0.033228158950805664,
0.017074408009648323,
0.02966880053281784,
-0.061284586787223816,
0.07667098194360733,
-0.0028458035085350275,
0.010074272751808167,
-0.002580117667093873,
-0.008580001071095467,
-0.011639142408967018,
0.0008795242174528539,
-0.012769038788974285,
-0.007651926949620247,
-0.038318995386362076,
-0.005899687763303518,
0.05704733356833458,
-0.06484486162662506,
-0.04612194374203682,
0.0074404398910701275,
-0.03821570798754692,
0.004321499262005091,
0.05231097713112831,
-0.005980245303362608,
0.004433510825037956,
-0.026776602491736412,
0.02916623093187809,
0.018827104941010475,
-0.004574259743094444,
-0.0008944527362473309,
0.02125989831984043,
0.02218742109835148,
-0.03374208137392998,
-0.0021598569583147764,
0.08011852949857712,
0.007396209053695202,
0.02408626675605774,
-0.005182049702852964,
0.027408475056290627,
-0.003517140867188573,
-0.035792309790849686,
0.018820570781826973,
0.001425615861080587,
-0.01966005750000477,
0.034113314002752304,
-0.01185884140431881,
0.055507637560367584,
-0.008571851998567581,
0.012176460586488247,
0.025553299114108086,
0.037726979702711105,
-0.01576516404747963,
0.05053558573126793,
-0.01973370648920536,
0.00005041519762016833,
-0.03808819502592087,
-0.010622513480484486,
0.0019770499784499407,
-0.00390031305141747,
0.027300119400024414,
-0.05140697956085205,
-0.018872762098908424,
0.0672890767455101,
-0.015597076155245304,
0.000804675742983818,
-0.02161017432808876,
-0.018565112724900246,
-0.012446529231965542,
0.023089855909347534,
0.0058437068946659565,
-0.01761687733232975,
-0.02765384502708912,
-0.0076186503283679485,
0.002476498717442155,
0.061546690762043,
-0.04646187275648117,
-0.012538435868918896,
0.018486838787794113,
0.021998664364218712,
0.02614039182662964,
0.016672838479280472
] |
<p>I am just trying to wade through literature on classical mechanics and I really don't know where to start, everything is Fibre bundle this or manifold that, and doesn't really ease you in to the topic. I'm sure this is a common question but I would like help with a couple of specific points:</p>
<ul>
<li>What would be the main points to take away from the "symplectic structure of phase space". Specifically what does knowing its symplectic do for us? We quote it all the time when talking about Hamiltonian mechanics/Liouville equation/Poisson brackets... etc ... In other words what would I be saying in differential geometry terms when I say " a canonical transformation preserves the symplectic structure?"</li>
</ul>
<p>I understand this may have been answered before but so far having seen the previous question/answers I'm still struggling. I'm specifically after answers relating to classical mechanics linear/non-linear alike, but not relativity if it can be avoided.</p>
<p>So to summarise: what are the salient points of a geometrical understanding of classical mechanics and what does this do that a basic understanding doesn't! </p>
| 9,378 |
[
-0.03127984330058098,
-0.012952207587659359,
-0.010992441326379776,
-0.03526156768202782,
0.02235684171319008,
0.015087345615029335,
-0.013529393821954727,
-0.016575312241911888,
-0.007149623706936836,
-0.04536757990717888,
0.012981629930436611,
0.0044725327752530575,
0.018227871507406235,
-0.018913816660642624,
0.015551324002444744,
-0.021865354850888252,
-0.012756221927702427,
-0.05690409988164902,
-0.031713325530290604,
-0.021373877301812172,
0.0013881995109841228,
-0.0283098965883255,
0.012417111545801163,
0.003165449481457472,
-0.016914652660489082,
0.03965071216225624,
0.017973938956856728,
0.0047907112166285515,
0.036069516092538834,
0.047507062554359436,
-0.026382319629192352,
0.0029914495535194874,
-0.009004875086247921,
0.008944710716605186,
0.00040530861588194966,
0.013257063925266266,
-0.04093567654490471,
-0.023848246783018112,
0.027746515348553658,
0.002522515133023262,
-0.06508981436491013,
-0.028354203328490257,
-0.029019169509410858,
0.040012914687395096,
-0.015895674005150795,
0.05556713044643402,
0.01745971478521824,
0.003744565648958087,
0.03252427279949188,
-0.050130654126405716,
0.07528325170278549,
0.01733296923339367,
0.011695708148181438,
-0.002287536161020398,
0.0070944917388260365,
-0.0018041180446743965,
0.08057891577482224,
0.05508306995034218,
-0.029804637655615807,
-0.06180505454540253,
-0.02612302266061306,
-0.021100016310811043,
0.006424203980714083,
-0.046121638268232346,
-0.02924693562090397,
0.05620766058564186,
0.026218309998512268,
-0.03954952582716942,
0.06689464300870895,
0.0009137627203017473,
-0.022921226918697357,
0.003517111297696829,
0.03262914717197418,
-0.018503287807106972,
0.008433982729911804,
-0.026744166389107704,
0.024585269391536713,
0.004192555323243141,
0.04656129330396652,
-0.0009020372526720166,
-0.004617641679942608,
-0.01557230670005083,
-0.006843632087111473,
0.035032615065574646,
0.016275040805339813,
0.002027426613494754,
0.09588339179754257,
0.016602501273155212,
0.013470878824591637,
0.02618461847305298,
-0.022670935839414597,
0.002813452621921897,
0.004626045934855938,
0.0221463181078434,
-0.02082735113799572,
0.018765948712825775,
0.009427614510059357,
0.0419711135327816,
0.01257903128862381,
-0.010117316618561745,
0.002199245383962989,
-0.03851423040032387,
0.012345419265329838,
0.046399522572755814,
0.0019069809932261705,
0.02905954234302044,
-0.03503137826919556,
0.018606161698698997,
-0.0065290299244225025,
-0.021200768649578094,
-0.035910870879888535,
0.017030799761414528,
-0.015003827400505543,
-0.00047817305312491953,
0.007880525663495064,
-0.017938898876309395,
-0.018429193645715714,
-0.011542039923369884,
0.04174227640032768,
0.05659779906272888,
0.03924252465367317,
-0.021286318078637123,
0.016658581793308258,
-0.003766356036067009,
-0.0734325423836708,
-0.004271344747394323,
0.058007366955280304,
0.026805805042386055,
0.0189241673797369,
0.0014187910128384829,
0.004078179597854614,
-0.012907263822853565,
0.0062323384918272495,
0.02122080884873867,
0.028864378109574318,
-0.0379575751721859,
-0.11672156304121017,
-0.04140521213412285,
0.07501298934221268,
0.032894592732191086,
-0.01919492706656456,
-0.07919516414403915,
0.032976821064949036,
-0.00493753794580698,
0.057894010096788406,
-0.006044898182153702,
-0.013753632083535194,
0.023711223155260086,
0.01004023291170597,
0.009299985133111477,
-0.02291063219308853,
-0.006059858947992325,
0.012982603162527084,
-0.019456563517451286,
-0.002495730295777321,
-0.0659799724817276,
0.02352825552225113,
0.03678109124302864,
0.034363795071840286,
-0.03371679037809372,
0.0685628205537796,
-0.021403511986136436,
0.000612304313108325,
0.023352693766355515,
-0.023315660655498505,
0.009874112904071808,
0.058875031769275665,
-0.021048106253147125,
0.012658951804041862,
-0.003605132456868887,
0.03416939824819565,
0.03280334547162056,
-0.029804255813360214,
0.04015696421265602,
0.04257466271519661,
-0.03909868001937866,
-0.013836704194545746,
0.06299550831317902,
-0.014947191812098026,
-0.015253216028213501,
-0.029285835102200508,
-0.04983346909284592,
-0.013153278268873692,
0.017217967659235,
-0.0067695146426558495,
0.06403946876525879,
0.00027463503647595644,
0.02582673355937004,
-0.004348134156316519,
-0.03198467940092087,
-0.00681694969534874,
-0.058515407145023346,
0.04391486197710037,
-0.04570865258574486,
-0.029230104759335518,
0.0439876988530159,
0.030595287680625916,
0.011205518618226051,
-0.018991483375430107,
-0.036526404321193695,
-0.00024205401132348925,
0.017743222415447235,
-0.02384350635111332,
-0.018250199034810066,
0.024754537269473076,
0.033302418887615204,
0.03362346068024635,
-0.014845256693661213,
0.026406683027744293,
-0.0016765836626291275,
-0.01826910860836506,
0.0016640601679682732,
0.01937790960073471,
0.011326600797474384,
-0.004078725352883339,
0.01588604412972927,
0.010006435215473175,
-0.013696947135031223,
-0.01762831024825573,
0.020985275506973267,
-0.07084788382053375,
0.08736219257116318,
0.055153053253889084,
-0.018741751089692116,
-0.012245723977684975,
0.10120242089033127,
0.006977061275392771,
0.03770092874765396,
0.03135128691792488,
0.008379370905458927,
0.0012641160283237696,
-0.011654173023998737,
0.03699805587530136,
0.042785242199897766,
-0.04119062051177025,
-0.007488061208277941,
0.02094178833067417,
0.025701303035020828,
0.014054578728973866,
-0.0075681922025978565,
-0.014098024927079678,
-0.03574298694729805,
0.01581360027194023,
-0.010931473225355148,
-0.02239137887954712,
0.00861857458949089,
0.03180481493473053,
0.0056975167244672775,
0.014346291311085224,
0.0029760729521512985,
-0.057603996247053146,
0.08540014922618866,
-0.019233953207731247,
0.015935873612761497,
0.02724560536444187,
-0.018591925501823425,
0.04828379303216934,
0.010238888673484325,
0.04063044488430023,
0.003475042525678873,
-0.004917552229017019,
-0.0008652758551761508,
-0.0340212844312191,
-0.0022514048032462597,
0.0031871346291154623,
0.008472311310470104,
-0.008120073936879635,
-0.011309041641652584,
0.005690441001206636,
-0.06186988204717636,
-0.008129850029945374,
0.0012017834233120084,
-0.034544602036476135,
-0.024660343304276466,
-0.0072050499729812145,
-0.0011556567624211311,
0.007311491761356592,
0.03892289102077484,
-0.029962241649627686,
-0.04645445942878723,
0.008495950140058994,
-0.019829822704195976,
0.034585364162921906,
0.03641887381672859,
-0.046898309141397476,
0.01780763640999794,
-0.06377486884593964,
0.02962985262274742,
0.04631020873785019,
-0.045462220907211304,
0.0501871183514595,
-0.007106746546924114,
-0.018273331224918365,
-0.05711117014288902,
-0.021190641447901726,
-0.017444496974349022,
0.016491496935486794,
-0.03587422892451286,
-0.0055613210424780846,
0.060080405324697495,
-0.02341170608997345,
-0.011650346219539642,
-0.016919776797294617,
-0.03664293512701988,
-0.023619534447789192,
0.0031190929003059864,
-0.008112574927508831,
0.017656467854976654,
-0.015175910666584969,
-0.005912465509027243,
0.03748853877186775,
-0.07003577053546906,
0.011192284524440765,
-0.0351131372153759,
-0.043037284165620804,
0.028291428461670876,
0.006241966038942337,
0.03168473392724991,
0.016351960599422455,
-0.026017483323812485,
0.09830711036920547,
0.01183578372001648,
-0.06837882101535797,
-0.022365612909197807,
0.025766532868146896,
-0.00018175675359088928,
-0.021585039794445038,
0.038249582052230835,
0.02275273948907852,
-0.009405496530234814,
0.03666543960571289,
0.04782352223992348,
0.02750106155872345,
0.0016295433742925525,
0.00962751917541027,
-0.016413548961281776,
-0.010214598849415779,
-0.020852796733379364,
0.011129035614430904,
0.015832705423235893,
0.03938586637377739,
-0.059067241847515106,
0.007859540171921253,
-0.01911332830786705,
0.014827137812972069,
0.014377535320818424,
-0.058863282203674316,
0.05755268782377243,
0.02000938542187214,
-0.02598777785897255,
0.006532078608870506,
0.03454408049583435,
-0.03300291672348976,
-0.015170467086136341,
0.030369097366929054,
0.02902885712683201,
0.0316975861787796,
-0.00915607064962387,
-0.004443254787474871,
0.020701834931969643,
0.0335654690861702,
-0.016924234107136726,
0.022065749391913414,
0.0012369501637294888,
-0.03148173168301582,
0.023523971438407898,
-0.009397909976541996,
-0.020290395244956017,
0.032956089824438095,
0.015333820134401321,
0.03604365512728691,
0.0020274026319384575,
-0.04057011380791664,
0.0038053099997341633,
-0.051024895161390305,
0.025425922125577927,
0.016791369765996933,
0.034655988216400146,
0.0019067751709371805,
0.06402432173490524,
-0.006237732712179422,
-0.0050686378963291645,
0.007702430244535208,
0.01660626009106636,
-0.07277732342481613,
0.03446367755532265,
-0.03153795748949051,
-0.014573113061487675,
-0.001714208978228271,
0.015774747356772423,
0.04008321091532707,
-0.015787161886692047,
-0.04894958809018135,
-0.023347655311226845,
0.041899312287569046,
-0.06835128366947174,
-0.011022506281733513,
-0.0375034399330616,
-0.06535877287387848,
-0.026243500411510468,
0.012462000362575054,
0.06807340681552887,
0.005070589017122984,
0.02050461433827877,
0.046220239251852036,
-0.03207144886255264,
-0.017455581575632095,
-0.012789459899067879,
0.02956060692667961,
0.03545990586280823,
0.01593022607266903,
0.011874431744217873,
0.020489433780312538,
0.00548578379675746,
0.0249875970184803,
0.001290646381676197,
0.045284926891326904,
-0.003705473616719246,
0.005796831101179123,
0.011971348896622658,
-0.06430401653051376,
0.00320037710480392,
-0.020902037620544434,
0.04569362476468086,
0.018959978595376015,
-0.01562492921948433,
0.04528401046991348,
-0.0008604322792962193,
-0.0037963935174047947,
0.018412398174405098,
-0.007294658105820417,
0.014861814677715302,
-0.03054901212453842,
-0.045265305787324905,
-0.03469131514430046,
-0.027870023623108864,
0.01731671579182148,
0.009478040970861912,
-0.009193208068609238,
-0.016448907554149628,
0.031835172325372696,
0.012744634412229061,
-0.01928592659533024,
-0.0307450033724308,
-0.041644174605607986,
0.004918786231428385,
0.048993710428476334,
0.024871526286005974,
0.011360465548932552,
0.02381097339093685,
0.0160292387008667,
0.05528859421610832,
-0.01853778585791588,
0.007336284499615431,
-0.07828912138938904,
-0.01843218319118023,
0.026759600266814232,
0.01764131523668766,
-0.019191550090909004,
-0.007079415023326874,
-0.025899037718772888,
-0.03290623053908348,
0.055780306458473206,
-0.024022016674280167,
0.022936424240469933,
0.01194773893803358,
-0.009380011819303036,
-0.04684488847851753,
-0.04019380733370781,
-0.01917506568133831,
0.01943923346698284,
0.002923909341916442,
0.017224712297320366,
-0.012742842547595501,
0.0009792159544304013,
-0.023127898573875427,
0.02122833952307701,
-0.002439165022224188,
0.03506281599402428,
0.03712724149227142,
-0.01292495895177126,
-0.0018685422837734222,
0.05351277440786362,
-0.02649143524467945,
-0.09423702210187912,
-0.014216265641152859,
0.015388155356049538,
-0.020432328805327415,
0.029305122792720795,
-0.04727211594581604,
-0.05118877440690994,
-0.010448325425386429,
-0.010912776924669743,
-0.011675631627440453,
0.03502831235527992,
-0.03634956479072571,
0.025884097442030907,
0.007885890081524849,
0.021933281794190407,
0.0321987122297287,
0.01133693940937519,
-0.014369643293321133,
-0.03566935285925865,
-0.019587745890021324,
0.032006941735744476,
-0.03445374220609665,
-0.020011093467473984,
-0.05162271857261658,
0.016103670001029968,
-0.039183203130960464,
0.05768042802810669,
-0.007175086066126823,
0.0054012504406273365,
-0.010117440484464169,
-0.03994742035865784,
-0.020620981231331825,
0.046642597764730453,
0.02121446654200554,
0.005436391104012728,
0.013602233491837978,
0.04263458400964737,
0.024153605103492737,
-0.0360281839966774,
0.0042495583184063435,
-0.000030480363420792855,
-0.032739266753196716,
0.0342380590736866,
0.00009860954014584422,
0.018550775945186615,
-0.03509627655148506,
-0.03080437332391739,
0.013026096858084202,
-0.06691211462020874,
0.044403549283742905,
-0.01891724206507206,
-0.005478561390191317,
0.06316424906253815,
-0.057019710540771484,
-0.023145752027630806,
-0.0303984172642231,
-0.03393610939383507,
0.035344671458005905,
-0.03573235496878624,
-0.001511749578639865,
0.003303992561995983,
0.004341859836131334,
-0.06482401490211487,
-0.07463926076889038,
0.04304520785808563,
0.006801706738770008,
-0.054449643939733505,
-0.017262883484363556,
0.03130605071783066,
-0.04099700227379799,
-0.013083679601550102,
0.021351266652345657,
0.028680557385087013,
-0.03772490844130516,
0.0010806111386045814,
0.008767823688685894,
0.02532624453306198,
0.029064945876598358,
-0.03376743569970131,
-0.0001450111740268767,
0.0057678488083183765,
-0.01751035824418068,
0.0057803248055279255,
-0.019590487703680992,
0.06143094599246979,
-0.00483870692551136,
0.01284103374928236,
-0.028490329161286354,
0.005681307055056095,
0.012811090797185898,
-0.014045171439647675,
0.01256611105054617,
0.018497124314308167,
0.02086160145699978,
-0.012471277266740799,
-0.019811542704701424,
-0.021343683823943138,
-0.005185752175748348,
0.026398081332445145,
0.0027653316501528025,
0.02184937335550785,
0.0024302878882735968,
-0.05201048031449318,
0.0571405366063118,
-0.0008671795367263258,
-0.0071901134215295315,
-0.0009776086080819368,
0.026389343664050102,
-0.0014915538486093283,
0.01017273310571909,
0.005217410158365965,
-0.011335983872413635,
-0.0036510962527245283,
-0.00799529068171978,
0.017279034480452538,
0.011783690191805363,
-0.009083089418709278,
-0.009936708025634289,
-0.06457527726888657,
-0.01576213724911213,
0.03195340186357498,
0.08008234202861786,
-0.01334358286112547,
0.04954974353313446,
0.031146742403507233,
0.0202228594571352,
0.004258199594914913,
0.0073220739141106606,
0.010988912545144558,
-0.009869720786809921,
0.023182330653071404,
0.02676973305642605,
-0.05106252431869507,
-0.01078697107732296,
0.016811009496450424,
0.061542611569166183,
-0.03798807039856911,
0.01654704287648201,
0.026526261121034622,
0.0028609195724129677,
0.017606893554329872,
0.00855104811489582,
-0.040552061051130295,
0.04657397419214249,
-0.026441192254424095,
0.04590606689453125,
0.020509885624051094,
-0.010091615840792656,
0.03177831321954727,
0.03703044354915619,
0.0071770609356462955,
-0.0028264715801924467,
-0.022000985220074654,
-0.04734592139720917,
0.03128178045153618,
0.006704159080982208,
0.016513487324118614,
-0.0022883398924022913,
0.0072204237803816795,
0.0384722575545311,
0.00035223757731728256,
-0.010586188174784184,
0.006463504862040281,
-0.05419955030083656,
-0.04022704064846039,
-0.05128695070743561,
-0.0498897060751915,
0.05121826007962227,
0.029072873294353485,
-0.017060671001672745,
-0.00979906041175127,
-0.020525455474853516,
0.03672926500439644,
0.007582502439618111,
0.04149781912565231,
-0.03375078737735748,
0.0679829865694046,
0.018517211079597473,
0.0027739349752664566,
-0.023811718448996544,
0.011299455538392067,
0.09670094400644302,
0.05331707373261452,
-0.004760821349918842,
-0.0883624479174614,
-0.017190033569931984,
0.02758166939020157,
-0.008917874656617641,
-0.030490314587950706,
0.021478410810232162,
0.027787690982222557,
0.0289973933249712,
0.0025518424808979034,
0.05864384397864342,
0.008812076412141323,
0.010757244192063808,
0.07151230424642563,
-0.040709011256694794,
-0.026672905310988426,
-0.015312813222408295,
-0.0030381646938622,
-0.019535604864358902,
0.02011805959045887,
-0.042425304651260376,
0.022567585110664368,
-0.040072906762361526,
-0.01191638596355915,
-0.0285783838480711,
-0.040101416409015656,
0.016665641218423843,
-0.0007137531647458673,
-0.0055258069187402725,
0.01873076893389225,
0.011915411800146103,
-0.02810598537325859,
-0.06205078214406967,
0.023016737774014473,
0.01975964941084385,
0.0075619034469127655,
0.03558015450835228,
0.03528786823153496,
0.0025520813651382923,
0.029065614566206932,
0.026592133566737175,
0.019606338813900948,
-0.030272861942648888,
-0.040211036801338196,
-0.044639553874731064,
0.041424982249736786,
-0.03173156455159187,
0.02896413393318653,
-0.0073018004186451435,
-0.04435266926884651,
-0.003760828636586666,
-0.06177763640880585,
0.018553808331489563,
-0.014827496372163296,
0.022622959688305855,
-0.01671408861875534,
-0.02238593064248562,
-0.0592530220746994,
-0.01095894630998373,
-0.007745734881609678,
0.010477153584361076,
-0.007854752242565155,
-0.002158861607313156,
-0.02154139243066311,
-0.018439404666423798,
0.014633659273386002,
-0.011741811409592628,
-0.01959453895688057,
-0.040222346782684326,
-0.0014234971022233367,
-0.02748202532529831,
-0.017560703679919243,
0.03396562486886978,
0.021932316944003105,
0.04568219929933548,
-0.00312618026509881,
-0.013115732930600643,
0.00488228490576148,
-0.06610178202390671,
0.02935192361474037,
0.02330160327255726,
-0.014084876514971256,
-0.02424798347055912,
0.033632028847932816,
0.039951737970113754,
0.0403691902756691,
-0.012739087454974651,
0.023084226995706558,
-0.014834725297987461,
-0.018889890983700752,
0.030347425490617752,
-0.001232114969752729,
0.01960093155503273,
0.028645863756537437,
-0.009562669321894646,
-0.009427623823285103,
-0.003888835897669196,
0.042874254286289215,
0.04565667361021042,
-0.000082302802184131,
-0.012477738782763481,
0.048318199813365936,
0.01522066816687584,
-0.007017319556325674,
0.026553642004728317,
-0.029451517388224602,
0.0031846454367041588,
0.012085702270269394,
0.06492289900779724,
-0.041644271463155746,
-0.03938281536102295,
-0.006829041056334972,
-0.032763656228780746,
-0.02452622540295124,
0.008525146171450615,
-0.01648245006799698,
0.013913449831306934,
-0.008232034742832184,
0.02675676718354225,
-0.040506280958652496,
-0.0020267474465072155,
-0.0530230887234211,
0.045055091381073,
0.007730733137577772,
-0.03936361148953438,
-0.012242471799254417,
-0.0036173760890960693,
0.010079781524837017,
-0.0372537299990654,
0.0182623453438282,
0.0431768037378788,
0.0011981138959527016,
-0.028448767960071564,
0.002118549542501569,
0.006800216156989336,
0.06207280606031418,
-0.01320580579340458,
-0.025207029655575752,
0.03140411525964737,
-0.02781391516327858,
-0.04102398827672005,
0.0299224816262722,
-0.03065929003059864,
0.006466038525104523,
0.028324957937002182,
-0.0361664742231369,
-0.009950004518032074,
0.027737945318222046,
0.03195226937532425,
0.0028405128978192806,
-0.0063200402073562145,
-0.0631260797381401,
-0.042128536850214005,
-0.01089491881430149,
0.02614009566605091,
-0.03440023586153984,
0.004526837263256311,
0.03070930950343609,
0.056402288377285004,
-0.00920409057289362,
-0.007699163164943457,
-0.0060235983692109585,
0.009817072190344334,
0.00965716689825058,
0.011091244406998158,
-0.006533247884362936,
0.0297769233584404,
0.044078756123781204,
-0.02932645007967949,
-0.009336433373391628,
0.02251335233449936,
-0.002968231914564967,
-0.060177598148584366,
-0.004938367288559675,
0.005192411597818136,
0.004202034790068865,
0.061291493475437164,
-0.05360981449484825,
-0.016411159187555313,
0.035366494208574295,
-0.057092685252428055,
0.037778306752443314,
-0.04308799281716347,
-0.019675590097904205,
0.025939548388123512,
0.005644544027745724,
-0.016317293047904968,
0.06502024084329605,
0.03577664867043495,
0.008199675008654594,
0.015157232992351055,
-0.01282039936631918,
0.020511530339717865,
-0.015012897551059723,
-0.0038197978865355253,
0.028896456584334373,
-0.011960642412304878,
-0.016211654990911484,
0.07740029692649841,
-0.02291097678244114,
-0.06455022096633911,
0.0357084795832634,
-0.00871442724019289,
0.0029651590157300234,
-0.0031021079048514366,
-0.01778275892138481,
-0.006732352077960968,
0.026630522683262825,
0.04217001423239708,
-0.006232487969100475,
-0.03072236105799675,
-0.0023669155780225992,
0.029230687767267227,
0.00591927720233798,
-0.04227003827691078,
0.004205704666674137,
0.025629084557294846,
-0.033489782363176346,
-0.03798648342490196,
0.0061643533408641815,
-0.02446880005300045,
0.001219125115312636,
-0.00652026291936636,
0.007093821652233601,
0.01943209022283554,
-0.00918035488575697,
0.021733831614255905,
-0.04077460616827011,
0.0026895515620708466,
0.01856159418821335,
0.017091264948248863,
0.02303803339600563,
0.023386459797620773,
-0.0061979033052921295,
-0.008889805525541306,
0.024877408519387245,
0.013826126232743263,
-0.002109693828970194,
-0.07293560355901718,
-0.004045291803777218,
0.01543297991156578,
-0.021272674202919006,
-0.03916298225522041,
-0.0455869697034359,
-0.022850312292575836,
0.05479716882109642,
0.04936280846595764,
0.02972918190062046,
-0.03364017978310585,
-0.03486190363764763,
-0.002000036183744669,
-0.0620754212141037,
0.021928586065769196,
0.019922936335206032,
-0.04371827095746994,
-0.035542383790016174,
0.008729053661227226,
-0.0027826859150081873,
0.010497968643903732,
0.05655069649219513,
-0.029954692348837852,
-0.0016706708120182157,
0.028249673545360565,
0.006306647788733244,
0.03823419660329819,
-0.028110289946198463,
-0.009085583500564098,
-0.03945464268326759,
-0.024111932143568993,
-0.004580196924507618,
-0.03278890997171402,
-0.014868752099573612,
0.002314257202669978,
0.03397350758314133,
-0.018675997853279114,
0.04863232374191284,
-0.0125333983451128,
-0.03231995180249214,
0.05231539532542229,
0.025618620216846466,
-0.008028719574213028,
0.04459941387176514,
0.015599748119711876,
0.00562345189973712,
0.04386244714260101,
-0.0197747889906168,
-0.0057614464312791824,
0.013325664214789867,
-0.047341931611299515,
-0.014891420491039753,
-0.034450408071279526,
-0.03416852280497551,
0.02734721451997757,
-0.030734533444046974,
0.04404956102371216,
0.03783787786960602,
-0.029952535405755043,
-0.017234982922673225,
0.04642825201153755,
-0.013311158865690231,
0.024056777358055115,
0.0017954657087102532,
0.010946334339678288,
0.06775012612342834,
0.0032797434832900763,
0.007426339201629162,
0.04317199066281319,
0.04462430626153946,
-0.027273913845419884,
-0.020072810351848602,
0.016160398721694946,
-0.031193913891911507,
0.016088495030999184,
0.021880127489566803,
0.06712820380926132,
-0.06003996729850769,
-0.006132347043603659,
0.0004389229870866984,
-0.022081349045038223,
0.01890699937939644,
0.0303044356405735,
-0.0302965696901083,
0.05820833891630173,
-0.012155515141785145,
-0.01350120548158884,
-0.003106804331764579,
-0.004374342504888773,
-0.04601597785949707,
-0.018216466531157494,
0.01837482489645481,
0.08466244488954544,
-0.019237570464611053,
0.033152516931295395,
-0.03721410781145096,
-0.01139045786112547,
0.002962280297651887,
-0.011283284984529018,
0.035581644624471664,
-0.018550613895058632,
-0.02067173831164837,
0.010930707678198814,
-0.026458943262696266,
-0.02838193066418171,
-0.021124349907040596,
0.022019676864147186,
0.04310549423098564,
0.04303531348705292,
-0.029968127608299255,
0.0006793736247345805,
-0.045361727476119995,
0.059454236179590225,
-0.08129990845918655,
-0.0395684614777565,
-0.028914326801896095,
-0.005408160388469696,
-0.025327228009700775,
0.008975314907729626
] |
<p>If every body emits radiation at a given frequency and temperature exactly as well as it absorbs the same radiation, how do objects heat up?</p>
| 9,379 |
[
-0.0401923805475235,
-0.03161010891199112,
0.022699221968650818,
-0.038245707750320435,
0.028049057349562645,
0.0280136838555336,
-0.028914475813508034,
0.005671070422977209,
0.004156883805990219,
-0.04609118029475212,
0.05233689397573471,
0.035729601979255676,
0.036307621747255325,
-0.01674763299524784,
0.01795869506895542,
-0.015356178395450115,
-0.004731125198304653,
-0.007219887338578701,
-0.024088410660624504,
-0.010716396383941174,
0.00609106570482254,
0.0317806750535965,
0.004310705699026585,
-0.0038364615757018328,
-0.058643974363803864,
0.014352796599268913,
0.0005076328525319695,
0.006360751111060381,
0.0424543060362339,
0.03040340170264244,
0.0068222349509596825,
-0.009964323602616787,
0.01610906980931759,
0.00932453852146864,
0.021844318136572838,
-0.006672391667962074,
-0.024759288877248764,
0.017217079177498817,
-0.017672110348939896,
0.015802673995494843,
-0.023887699469923973,
-0.05059897154569626,
-0.02507135085761547,
0.035927459597587585,
-0.014437654055655003,
-0.022970400750637054,
-0.0011015996569767594,
-0.004096302203834057,
0.03759374842047691,
-0.07566231489181519,
0.06492060422897339,
-0.005622596479952335,
0.052509695291519165,
0.05035553127527237,
-0.03701082244515419,
0.031274519860744476,
0.07691449671983719,
0.057488251477479935,
0.001525897067040205,
-0.028133785352110863,
-0.01840110309422016,
-0.025416703894734383,
-0.03808840364217758,
-0.005789332091808319,
-0.029125994071364403,
0.036673109978437424,
0.003181553678587079,
-0.03699709102511406,
0.0034954892471432686,
0.050083987414836884,
0.026973716914653778,
0.0133291594684124,
0.05658984184265137,
-0.019259028136730194,
0.00911959633231163,
-0.030069919303059578,
-0.005838228389620781,
0.03803444653749466,
0.047812193632125854,
0.03039942868053913,
-0.03506699204444885,
-0.009497742168605328,
-0.009875237010419369,
0.0298629067838192,
0.006367978639900684,
-0.0025878935120999813,
0.08242957293987274,
-0.011512228287756443,
0.004809985868632793,
0.025938697159290314,
-0.01593388430774212,
0.027810389176011086,
0.02706020325422287,
0.013126246631145477,
-0.010224565863609314,
0.01149465050548315,
-0.001963351620361209,
0.031868867576122284,
-0.011506808921694756,
-0.057935681194067,
0.055198900401592255,
0.02546394057571888,
0.03367319703102112,
0.06123972684144974,
0.02369631640613079,
-0.04256929084658623,
-0.044771403074264526,
-0.0005194924888201058,
-0.005888537038117647,
-0.0016906557139009237,
-0.033567193895578384,
0.021643782034516335,
-0.01177689153701067,
-0.015767700970172882,
0.029909847304224968,
0.027573319151997566,
0.021235603839159012,
-0.04100903123617172,
0.04052678495645523,
0.0429273284971714,
-0.006069930735975504,
-0.007353896740823984,
0.01974639669060707,
0.0037140522617846727,
-0.03292715921998024,
0.026165982708334923,
0.004799691028892994,
-0.032540470361709595,
-0.05314952880144119,
0.010333970189094543,
-0.016161268576979637,
-0.03836856409907341,
0.005921631585806608,
-0.009995035827159882,
-0.01824934408068657,
-0.054059017449617386,
-0.09890826046466827,
-0.057708047330379486,
0.02706732228398323,
-0.017434248700737953,
-0.048924900591373444,
-0.07837133854627609,
-0.0009861510479822755,
0.027160007506608963,
0.053258489817380905,
-0.006081178318709135,
-0.015588710084557533,
-0.007418766617774963,
0.04318860173225403,
0.0007582743419334292,
0.012229095213115215,
-0.06074165552854538,
-0.000025453120542806573,
-0.037041693925857544,
-0.001304871286265552,
-0.07471557706594467,
0.03128710016608238,
0.041772399097681046,
-0.03419909626245499,
-0.0004924368695355952,
0.03163251280784607,
-0.036985523998737335,
-0.005743128247559071,
0.006875962484627962,
-0.00022392345999833196,
-0.02796931378543377,
0.06318430602550507,
0.01867903396487236,
0.0009057907736860216,
0.025297310203313828,
0.007845109328627586,
0.02693609893321991,
0.006172912195324898,
0.038737889379262924,
0.010602874681353569,
-0.05995853245258331,
0.013587241992354393,
-0.0012699776561930776,
0.009840443730354309,
0.028130393475294113,
-0.07302635163068771,
-0.023885173723101616,
0.06630917638540268,
-0.009582487866282463,
0.001709364471025765,
0.052631501108407974,
0.013446479104459286,
-0.004448855295777321,
0.016721220687031746,
-0.052685536444187164,
0.002207408891990781,
-0.08545273542404175,
0.024884264916181564,
-0.02408713847398758,
-0.01057837251573801,
-0.026444125920534134,
0.05630439147353172,
0.017813343554735184,
-0.028051458299160004,
-0.04416258633136749,
0.01349277887493372,
0.03134628385305405,
-0.010375246405601501,
-0.004233631771057844,
0.01875024475157261,
0.0978352278470993,
0.05596206337213516,
0.007611766457557678,
0.02419344335794449,
-0.03607277199625969,
-0.05017390474677086,
0.01714392937719822,
-0.055866699665784836,
0.008008605800569057,
0.010421168990433216,
-0.0023162581492215395,
0.005420946981757879,
-0.02109382674098015,
-0.004969792440533638,
0.03778330609202385,
-0.004019923973828554,
0.03800554946064949,
0.00028388501959852874,
-0.0013177370419725776,
-0.014277002774178982,
0.07814166694879532,
0.022244973108172417,
-0.012769140303134918,
-0.009954478591680527,
-0.05385411158204079,
-0.05529051646590233,
-0.004413226153701544,
0.03211696818470955,
0.026140008121728897,
-0.0499492809176445,
0.019681338220834732,
0.02118605561554432,
0.06226731091737747,
0.019375165924429893,
0.017651552334427834,
-0.00491375382989645,
0.010100368410348892,
0.031386058777570724,
-0.02066619321703911,
0.01813751459121704,
0.020984994247555733,
0.006846650969237089,
0.05218478664755821,
0.015633296221494675,
0.011884073726832867,
-0.0073843724094331264,
0.07449977099895477,
0.022213203832507133,
0.013422937132418156,
-0.004782401956617832,
-0.011781468987464905,
-0.004875673912465572,
-0.01141325943171978,
0.014218293130397797,
-0.02825947292149067,
-0.019738124683499336,
-0.00006738699448760599,
-0.020572802051901817,
-0.01925189048051834,
-0.0005019324598833919,
0.010892645455896854,
-0.007752480451017618,
0.0025120354257524014,
0.03393127769231796,
-0.025175312533974648,
-0.002151413122192025,
-0.0068748886696994305,
0.008242597803473473,
-0.01143586914986372,
0.0013108091661706567,
0.007662144023925066,
-0.007510913535952568,
0.035248227417469025,
-0.0724378153681755,
-0.048952117562294006,
-0.03256094828248024,
-0.06014331802725792,
0.007412369828671217,
0.0022506695240736008,
-0.05182959511876106,
-0.0011419735383242369,
-0.000984703772701323,
-0.05570439249277115,
0.024417102336883545,
-0.0095136146992445,
0.014101309701800346,
0.04986431822180748,
-0.018279293552041054,
-0.05983751639723778,
0.0057867043651640415,
-0.008479920215904713,
-0.0022632370237261057,
-0.020124465227127075,
0.04185508191585541,
0.052478283643722534,
-0.049906861037015915,
-0.03153330460190773,
0.002356074983254075,
-0.020471589639782906,
-0.04525034502148628,
0.009504093788564205,
-0.07192712277173996,
0.03779515251517296,
-0.010483887046575546,
0.04312503710389137,
0.02197842299938202,
-0.09163052588701248,
0.0021002115681767464,
-0.014949202537536621,
-0.04513954743742943,
0.009613369591534138,
0.0065545933321118355,
0.03991345316171646,
0.011766761541366577,
0.0003398199623916298,
0.033081624656915665,
0.0014254148118197918,
-0.0018371741753071547,
-0.02581845410168171,
0.009167298674583435,
-0.02667410485446453,
-0.0614938922226429,
0.027210552245378494,
0.03953104466199875,
-0.02563483640551567,
0.00316998059861362,
0.02726810798048973,
-0.01952844299376011,
0.07656138390302658,
0.005870602559298277,
-0.038497135043144226,
-0.015683380886912346,
0.008469265885651112,
0.008344621397554874,
0.008547843433916569,
0.0030629662796854973,
-0.024740204215049744,
0.052778493613004684,
0.01944573037326336,
0.05505643039941788,
0.022824103012681007,
-0.016648994758725166,
0.04697562754154205,
-0.002513871295377612,
0.008524801582098007,
-0.06645268201828003,
0.06073668971657753,
-0.007144836243242025,
0.012397637590765953,
-0.0040964693762362,
0.019533870741724968,
0.04561852663755417,
-0.008626802824437618,
0.01844688691198826,
0.03303777053952217,
0.048316314816474915,
-0.022643767297267914,
-0.04526256397366524,
-0.02021060697734356,
-0.00797124020755291,
0.0011938080424442887,
0.0035765809006989002,
-0.005343207158148289,
0.05396072566509247,
0.024697938933968544,
0.04528288543224335,
0.03399147465825081,
-0.02427692525088787,
-0.021536292508244514,
-0.05511299893260002,
-0.05252336710691452,
-0.0019682140555232763,
0.04179999977350235,
-0.0037326763849705458,
0.07115084677934647,
0.024821411818265915,
0.032621923834085464,
0.029624057933688164,
-0.01562880538403988,
-0.11054351925849915,
0.0300669576972723,
-0.04521220549941063,
-0.0050985137932002544,
-0.027400175109505653,
0.0074113295413553715,
-0.014968539588153362,
-0.006237639579921961,
-0.004479471128433943,
-0.0008422256796620786,
-0.03177211061120033,
-0.0329403430223465,
0.033917371183633804,
-0.029989242553710938,
-0.061293963342905045,
-0.013512847013771534,
0.0246072169393301,
0.04940192773938179,
-0.030385848134756088,
0.023412562906742096,
0.037746164947748184,
-0.026998715475201607,
0.0214138925075531,
-0.04188966378569603,
0.024432018399238586,
0.016181867569684982,
0.04276856407523155,
0.020222771912813187,
0.03273199871182442,
-0.03471808508038521,
0.014219185337424278,
-0.004237260203808546,
0.04651850834488869,
0.01339360699057579,
-0.06174373999238014,
-0.047687798738479614,
-0.05998217687010765,
-0.025432685390114784,
-0.00467305863276124,
0.050481781363487244,
-0.028128717094659805,
0.0071626282297074795,
0.03836414963006973,
0.006075901910662651,
0.0006428492488339543,
0.014686536975204945,
-0.0032582867424935102,
-0.003088122233748436,
-0.022388122975826263,
0.0062037380412220955,
-0.007678353227674961,
-0.02638985961675644,
-0.0005957447574473917,
0.007957526482641697,
-0.03180309385061264,
-0.0033355962950736284,
0.018453873693943024,
0.010488016530871391,
-0.003975495230406523,
0.01555988285690546,
-0.02442115731537342,
0.025668175891041756,
0.031977906823158264,
-0.01997443474829197,
-0.028950460255146027,
-0.012052684091031551,
0.04961271956562996,
0.03636474162340164,
-0.024673059582710266,
-0.03872672840952873,
-0.08316309750080109,
0.0063572535291314125,
0.01414661854505539,
0.024421337991952896,
0.006193059496581554,
0.0007284728344529867,
-0.033109400421381,
-0.001010552397929132,
0.03613307327032089,
-0.010364968329668045,
0.03765758499503136,
-0.0013099134666845202,
-0.031262997537851334,
-0.027799883857369423,
-0.010000530630350113,
0.006040090229362249,
0.04583582282066345,
0.005394696723669767,
0.024976348504424095,
-0.009916627779603004,
-0.030634228140115738,
0.012957972474396229,
0.040800441056489944,
0.02181095816195011,
-0.008312900550663471,
-0.009945309720933437,
0.01739998534321785,
-0.01366223581135273,
0.019109372049570084,
-0.01261322945356369,
-0.06740296632051468,
-0.010822579264640808,
0.009809556417167187,
-0.011684870347380638,
0.06362573057413101,
-0.0275545846670866,
-0.026127172634005547,
0.012269965372979641,
0.0014199628494679928,
-0.0023415805771946907,
-0.01945531740784645,
-0.03826702758669853,
0.062060680240392685,
0.0028437853325158358,
-0.0017227295320481062,
0.08700444549322128,
0.014187611639499664,
-0.021193137392401695,
-0.019100332632660866,
-0.02321045473217964,
0.03417659178376198,
-0.04136493057012558,
-0.010090023279190063,
-0.005694539751857519,
-0.004102268721908331,
-0.027552809566259384,
0.03940744325518608,
0.02688479609787464,
-0.004702378995716572,
0.020567789673805237,
-0.028441172093153,
-0.01435273326933384,
0.02826329879462719,
-0.026319371536374092,
0.013994075357913971,
0.02008078061044216,
0.04991217330098152,
-0.007503828965127468,
-0.011945105157792568,
0.025135288015007973,
-0.006300028413534164,
-0.0023853350430727005,
0.004909325856715441,
-0.012787070125341415,
0.0573132149875164,
-0.04257306456565857,
-0.00586537504568696,
-0.012732740491628647,
-0.022872600704431534,
0.027139313519001007,
-0.021975861862301826,
0.024461841210722923,
0.03005181811749935,
-0.0858716368675232,
-0.00820580217987299,
-0.012740976177155972,
0.032311514019966125,
0.03472825139760971,
-0.009503252804279327,
0.009973754175007343,
0.01405597198754549,
-0.021957967430353165,
-0.06718093156814575,
-0.017668718472123146,
0.021796615794301033,
0.042039453983306885,
0.0034890822134912014,
-0.04574206471443176,
0.023297134786844254,
-0.03724624589085579,
-0.03164501115679741,
0.010587155818939209,
0.023333346471190453,
-0.010003743693232536,
0.00984041765332222,
0.004035247955471277,
0.00936842244118452,
0.03238750621676445,
-0.005583432037383318,
-0.017296690493822098,
0.008403992280364037,
-0.012351639568805695,
-0.020552270114421844,
-0.0028305784799158573,
0.06562303751707077,
-0.009414215572178364,
-0.02499912679195404,
0.01215414796024561,
0.0028162996750324965,
0.04790220037102699,
0.01427703071385622,
-0.014483192004263401,
0.04344116523861885,
0.024503085762262344,
-0.010406053625047207,
-0.024810031056404114,
0.04993617907166481,
0.025281554087996483,
0.03412731736898422,
-0.004696947522461414,
0.004461708012968302,
-0.01757207326591015,
-0.03263573348522186,
0.022105978801846504,
-0.022113192826509476,
0.029636692255735397,
0.01659354567527771,
0.08703693002462387,
-0.018020933493971825,
0.017890527844429016,
-0.017038729041814804,
0.021760188043117523,
0.03439198434352875,
0.0027592929545789957,
0.007000567391514778,
-0.022522369399666786,
-0.00009435909305466339,
-0.00026722223265096545,
-0.011311335489153862,
-0.04180780053138733,
-0.035411372780799866,
0.0440693274140358,
-0.025921272113919258,
0.07020413130521774,
0.035928163677453995,
0.027025751769542694,
0.036288775503635406,
-0.004286543466150761,
-0.012512479908764362,
-0.00030592185794375837,
-0.026073582470417023,
0.010505196638405323,
-0.025231774896383286,
0.007911037653684616,
0.036121759563684464,
0.06297125667333603,
-0.01696406491100788,
0.016476452350616455,
0.014171582646667957,
0.04181049019098282,
-0.011950048618018627,
-0.0017138932598754764,
-0.018255038186907768,
0.03583526983857155,
-0.036705005913972855,
0.019038334488868713,
0.011923667043447495,
-0.011676615104079247,
0.02035924233496189,
-0.005993270315229893,
0.013603713363409042,
-0.05897405743598938,
-0.0028471392579376698,
-0.04913124442100525,
0.024109888821840286,
0.008272342383861542,
0.05817108228802681,
-0.007412769366055727,
0.01946016401052475,
0.02376369573175907,
-0.003212129697203636,
-0.0006535446154884994,
0.00910937413573265,
-0.0425441674888134,
-0.031750068068504333,
-0.0036295426543802023,
-0.025843415409326553,
0.036594830453395844,
0.0014202790334820747,
-0.011397553607821465,
0.047428760677576065,
-0.02293761633336544,
0.02229183353483677,
0.02034594491124153,
0.03803547844290733,
-0.0038803396746516228,
0.05262041464447975,
0.005673341453075409,
-0.0018438203260302544,
-0.006856787018477917,
0.027075709775090218,
0.11577311158180237,
0.026941047981381416,
0.006480202544480562,
-0.05449354276061058,
-0.007643554825335741,
-0.01826724037528038,
-0.022252224385738373,
-0.024424513801932335,
-0.0010062993969768286,
-0.0005784062668681145,
0.05504802241921425,
0.029618382453918457,
0.056255042552948,
0.03287743404507637,
-0.009281053207814693,
0.01544321421533823,
-0.04111695662140846,
0.0240143034607172,
0.00869059655815363,
0.001953819766640663,
0.016877833753824234,
0.036112651228904724,
-0.04075312241911888,
-0.02372966706752777,
-0.04635326936841011,
0.008110733702778816,
-0.0238373763859272,
-0.04222283139824867,
0.02889876440167427,
-0.0003438061976339668,
-0.050613537430763245,
0.015416279435157776,
0.0011596378171816468,
-0.0343819297850132,
-0.019888292998075485,
0.05293360352516174,
0.056932881474494934,
0.00451276870444417,
-0.011196600273251534,
-0.021259749308228493,
0.04227449744939804,
0.0031427384819835424,
-0.009844508953392506,
0.02799862064421177,
-0.009231756441295147,
-0.03269057720899582,
-0.03580625355243683,
0.028226418420672417,
-0.050322625786066055,
-0.006097231991589069,
0.0055491141974925995,
0.00031204387778416276,
-0.015055983327329159,
-0.027339864522218704,
0.024986563250422478,
0.006463461555540562,
0.017391715198755264,
-0.054151471704244614,
-0.05963756516575813,
-0.03362951800227165,
0.034024305641651154,
-0.027874276041984558,
0.02237493358552456,
0.019903279840946198,
0.0002513283398002386,
0.0033733644522726536,
-0.006761925294995308,
0.04602878540754318,
-0.00754297012463212,
-0.02328897826373577,
-0.026310717687010765,
-0.040851280093193054,
-0.018249699845910072,
-0.03438278287649155,
0.0004017296596430242,
0.016338728368282318,
0.01757197268307209,
0.021374130621552467,
0.007610711269080639,
-0.0316782146692276,
-0.06665491312742233,
-0.003979107365012169,
-0.0031733654905110598,
-0.041511669754981995,
-0.035401251167058945,
-0.031661804765462875,
0.04795190691947937,
0.019214142113924026,
-0.025919007137417793,
-0.0016449355753138661,
-0.0015152287669479847,
0.018913649022579193,
0.030484097078442574,
-0.02886902540922165,
-0.02396717108786106,
0.01295035146176815,
-0.019441233947873116,
-0.002286019269376993,
0.014643860049545765,
0.06557784974575043,
0.01500756200402975,
0.00004144111881032586,
0.022853203117847443,
0.04353530332446098,
-0.051555268466472626,
0.0031236244831234217,
0.018700728192925453,
-0.002739675808697939,
-0.011339453049004078,
0.029623668640851974,
-0.03425547853112221,
-0.02212396077811718,
-0.06874271482229233,
-0.018082039430737495,
-0.013928405940532684,
-0.002473298693075776,
0.034965015947818756,
-0.00619910703971982,
0.021052731201052666,
-0.008573870174586773,
0.035647302865982056,
-0.020674284547567368,
-0.005280767101794481,
-0.05794810131192207,
-0.013333315029740334,
0.008364317938685417,
-0.02427619695663452,
-0.01075910497456789,
0.018970511853694916,
-0.04632658138871193,
-0.016521606594324112,
0.05071089044213295,
0.0337594598531723,
0.00642028683796525,
-0.003622062038630247,
0.008431347087025642,
-0.04474387317895889,
0.05930054932832718,
-0.027279462665319443,
-0.04474633187055588,
0.057517826557159424,
-0.03823962062597275,
-0.02766229957342148,
0.03163759410381317,
-0.012479959055781364,
0.04120029881596565,
0.034274619072675705,
-0.02271439880132675,
0.01622054912149906,
0.06386654078960419,
-0.02981674298644066,
-0.010302931070327759,
0.022080209106206894,
-0.011562383733689785,
0.003571262350305915,
0.026175839826464653,
0.025136832147836685,
-0.022395582869648933,
-0.020002182573080063,
0.0577617846429348,
-0.000060143596783746034,
-0.005974548868834972,
0.002396566793322563,
0.023035861551761627,
-0.003002539509907365,
0.010458007454872131,
0.024439383298158646,
0.034460581839084625,
0.01952221244573593,
0.03098379634320736,
-0.020820001140236855,
0.042537443339824677,
0.007078056689351797,
-0.025055980309844017,
-0.10777327418327332,
0.003865540726110339,
-0.013593160547316074,
-0.02177182026207447,
0.00684453547000885,
-0.024905500933527946,
0.008152512833476067,
0.03721904754638672,
-0.07233841717243195,
0.01941702887415886,
-0.012081108056008816,
-0.018958238884806633,
-0.04437701031565666,
0.012013101018965244,
-0.028430981561541557,
-0.004885892383754253,
0.04679238796234131,
0.04169639199972153,
-0.021419629454612732,
0.027733925729990005,
-0.007749639917165041,
-0.026289384812116623,
-0.011260010302066803,
0.015480349771678448,
0.013360688462853432,
-0.00322875683195889,
0.050485361367464066,
0.02271352708339691,
0.012227306142449379,
-0.006285790354013443,
-0.017313595861196518,
-0.012855537235736847,
0.00046915162238292396,
-0.008064975962042809,
0.000987253850325942,
0.02861417457461357,
-0.01149778626859188,
-0.02409437485039234,
-0.01764320395886898,
0.03143831714987755,
0.05351736769080162,
0.035163912922143936,
-0.01193718146532774,
0.0034358040429651737,
0.039302900433540344,
-0.045248620212078094,
-0.02398575097322464,
0.01024804636836052,
0.023401206359267235,
-0.013851609081029892,
0.039499472826719284,
0.025684116408228874,
0.03649988770484924,
-0.011604993604123592,
-0.018373392522335052,
-0.06880258023738861,
-0.010903467424213886,
0.008994543924927711,
0.05135267972946167,
0.020420050248503685,
-0.02936660870909691,
-0.011709891259670258,
0.004792037419974804,
-0.0007569583831354976,
0.03700678423047066,
-0.007940485142171383,
-0.010009154677391052,
-0.005523448344320059,
0.03764423355460167,
0.014603971503674984,
-0.020919086411595345,
-0.07993004471063614,
-0.05483449250459671,
0.027285680174827576,
0.03778237849473953,
0.024089740589261055,
-0.02522536925971508,
-0.04682081937789917,
-0.07479222863912582,
-0.035147327929735184,
0.04699290171265602,
-0.015218749642372131,
0.008082706481218338,
-0.06174707040190697,
-0.004781660158187151,
-0.007924411445856094,
0.030917678028345108,
0.03609205409884453,
0.02096538431942463,
-0.043252650648355484,
0.010068517178297043,
-0.002297020982950926,
0.03817875683307648,
-0.0341157391667366,
0.029148636385798454,
-0.013215659186244011,
-0.033300403505563736,
-0.0032609968911856413,
-0.00035109135205857456,
-0.015075051225721836,
0.005042898003011942,
0.01581568829715252,
-0.017869435250759125,
0.012064686976373196,
-0.018842438235878944,
-0.0302601158618927,
0.05874600633978844,
0.028951607644557953,
-0.03533018007874489,
0.05149959772825241,
-0.026748862117528915,
0.00016973241872619838,
0.01095256395637989,
-0.0011321761412546039,
-0.036075253039598465,
0.020557157695293427,
-0.02172250673174858,
0.017332475632429123,
-0.007477177307009697,
-0.00219713244587183,
0.0216577909886837,
-0.05512144789099693,
0.014156274497509003,
0.025358226150274277,
-0.052828337997198105,
-0.020428132265806198,
0.025090519338846207,
0.02219528704881668,
-0.009070887230336666,
0.0016468039248138666,
0.006674314849078655,
0.014576662331819534,
-0.004607661627233028,
-0.03169441595673561,
0.07024385035037994,
-0.0053834468126297,
-0.013911309652030468,
0.027110733091831207,
0.04138776287436485,
-0.0018139604944735765,
0.018666114658117294,
-0.010850914753973484,
0.0408693291246891,
-0.03920486941933632,
-0.03703092038631439,
0.013477632775902748,
-0.022361664101481438,
-0.023036494851112366,
0.03758172690868378,
-0.006983347702771425,
0.08175547420978546,
-0.026234585791826248,
0.006984615698456764,
-0.03369719162583351,
0.023700473830103874,
0.0008658475708216429,
-0.004984939005225897,
0.02448303811252117,
0.04557538032531738,
-0.01668979600071907,
-0.014359659515321255,
-0.0317063182592392,
-0.012750056572258472,
0.05917653441429138,
-0.032016173005104065,
0.015662793070077896,
-0.014825157821178436,
-0.008997218683362007,
-0.0374707467854023,
0.003575321054086089,
-0.025457220152020454,
-0.032252103090286255,
0.006550152786076069,
0.04702385142445564,
-0.0014586288016289473,
0.023779071867465973,
-0.01266402192413807,
-0.03517213091254234,
0.031136075034737587,
-0.08398884534835815,
-0.0118962861597538,
-0.01609218120574951,
0.05232371762394905,
-0.007235192693769932,
-0.029307078570127487
] |
<p>The three Mandelstam-variables are defined as:
$$s=(p_A+p_B)^2=(p_C+p_D)^2,$$$$t=(p_A-p_C)^2=(p_B-p_D)^2$$$$u=(p_A-p_D)^2=(p_B-p_C)^2.$$ Where A and B are the incoming particles and C and D are the outgoing particles, and the second equation follows from the conservation of 4-momentum.</p>
<p>The Mandelstam-variable $s$ gives the center-of-mass energy and is thus always positive, now for the Mandelstam-variables $t$ and $u$ the demands can be found by looking at them in the laboratory-frame, after an easy calculation it can be shown that:$$s\geq \max[m_A^2+m_B^2,m_C^2+m_D^2],$$
$$t\leq \min[m_A^2+m_C^2,m_B^2+m_D^2],$$
$$u\leq \min[m_A^2+m_D^2,m_B^2+m_C^2].$$</p>
<p>This means that there should exist a situation in which the three Mandelstam-variables are positive. I was wondering is such a situation exists, or that I am simply overlooking some facts and that indeed only ONE Mandelstam-variable can be positive?</p>
<blockquote>
<p>To elaborate more on the calculation which lead me to this conclusion, I've calculated these variables in the frame in which particle A is at rest (since $s$, $t$ and $u$ are invariant I can do this). This yields for the momenta:
$$p_A=(m_A,0),$$$$p_B=(E_B,\vec{p}_B),$$$$p_C=(E_C,\vec{p}_C),$$$$p_D=(E_D,\vec{p}_D).$$
So for my Mandelstam variables I would get that:
$$s=(p_A+p_B)^2=p_A^2+p_B^2+2p_A\cdot p_B = m_A^2+m_B^2+2m_AE_B,$$
$$t=(p_A-p_C)^2=p_A^2+p_C^2-2p_A\cdot p_C = m_A^2+m_C^2-2m_AE_C,$$
$$t=(p_A-p_D)^2=p_A^2+p_D^2-2p_A\cdot p_D = m_A^2+m_D^2-2m_AE_D,$$
where I used the first equality in the definition of the Mandelstam variables. I could do the same calculation with the second equality, if I would then discard the terms of the form $2m_AE$ I would get the inequalities above.</p>
</blockquote>
<p>$\,$</p>
<blockquote>
<blockquote>
<p>Edit: I know that the second equality doesn't give simple terms $2mE$, but terms of the form $$E_CE_D-\vec{p_C}\cdot\vec{p_D}=E_CE_D-|\vec{p_C}||\vec{p_D}|\cos(\theta),$$ and since $E^2=m^2+|\vec{p}|^2$ we have that $E>|\vec{p}|$, so these terms are positive.</p>
</blockquote>
</blockquote>
<p>$\,$</p>
<blockquote>
<blockquote>
<p>Edit 2: I've calculated these for the non-elastic proces $e^-e^+\rightarrow\mu^-\mu^+$ (since inelastic problems are the source of the problem) and I found that:
$$s=2m(m+E_B),$$
$$t=m^2+M^2-2mE_C,$$
$$u=m^2+M^2-2mE_D,$$
where $m$ is the mass of the electron and $M$ is the mass of the muon, particle $A$ (either an electron or positron) is standing still and for particle $B$ (electron or positron) and $C$ and $D$ (the 2 muon particles) the energies are $E_B$, $E_C$ and $E_D$.
The variable $s$ is obviously positive, to check if $t$ of $u$ are positive I summed them and used the conservation of energy: $m+E_B=E_C+E_D$, which gives:
$$t+u=2(m^2+M^2)-2m(m+E_B)=2(m^2+M^2)-s,$$ now in order to be able to create 2 muons the energy should be high enough, hence $s=(2M)^2$, filling this in yields:
$$t+u=2(m^2-M^2).$$
Which brings me back to the question: ''Should only one of the three variables be positive (just as most books claim) or are there special cases''? In my derivation above I used the conservation laws, but as you can see in this example the possibility of $t$ and $u$ being positive (for small enough $E_B$) vanishes by demanding that de center of mass energy $\sqrt{s}$ is large enough, will this always be the case ?</p>
</blockquote>
</blockquote>
| 9,380 |
[
-0.013701889663934708,
-0.028219886124134064,
0.011680400930345058,
-0.03290953114628792,
0.0570608489215374,
0.00754061434417963,
-0.023907572031021118,
-0.04084103927016258,
-0.0285473745316267,
-0.013867074623703957,
0.03536110371351242,
-0.001967978198081255,
0.023015620186924934,
0.01430423092097044,
0.009570709429681301,
0.008335104212164879,
0.022044528275728226,
-0.0249178484082222,
-0.020983347669243813,
-0.03032166138291359,
-0.02255074307322502,
0.029504401609301567,
0.03459625318646431,
-0.0066622584126889706,
0.00481920363381505,
0.016308166086673737,
0.01038367860019207,
-0.0017575703095644712,
-0.038295723497867584,
0.0919673964381218,
-0.02811698615550995,
-0.022669514641165733,
-0.002186377765610814,
0.04251169040799141,
0.029852749779820442,
0.008910460397601128,
-0.03779347240924835,
-0.0187174491584301,
-0.0038252673111855984,
0.0339483767747879,
-0.0008336633909493685,
-0.017953338101506233,
-0.0003296459326520562,
0.018523655831813812,
-0.0055872295051813126,
-0.0043703000992536545,
0.01467612199485302,
-0.0005480305408127606,
0.07841441035270691,
-0.07014904916286469,
0.08876098692417145,
0.01558955479413271,
0.04832359775900841,
-0.005345062352716923,
-0.040704771876335144,
-0.06756702065467834,
0.04690565913915634,
0.06540779769420624,
0.03739658370614052,
-0.061920832842588425,
-0.00431249151006341,
0.026558710262179375,
0.03575603663921356,
0.004908835981041193,
-0.04014543816447258,
0.011518897488713264,
0.005780413281172514,
0.006172419525682926,
0.024647096171975136,
0.0015174462459981441,
0.011333231814205647,
-0.040940385311841965,
0.04744624346494675,
-0.02099609375,
0.025517985224723816,
0.010624108836054802,
0.011236791498959064,
0.02496580220758915,
0.01702137291431427,
0.034206002950668335,
-0.015829535201191902,
0.018539126962423325,
0.0127980662509799,
-0.0011664384510368109,
0.01462051086127758,
-0.0054811821319162846,
0.053748585283756256,
-0.012431539595127106,
0.02049686387181282,
0.020989341661334038,
0.0035253996029496193,
0.0011302746133878827,
0.039990827441215515,
-0.015432886779308319,
-0.0014848533319309354,
-0.008970456197857857,
-0.0019298492697998881,
0.040397364646196365,
-0.02597951702773571,
-0.013693230226635933,
-0.007059740833938122,
-0.0288607906550169,
-0.000173057327629067,
0.11239312589168549,
-0.005697283893823624,
0.01263524778187275,
-0.044872451573610306,
0.014988678507506847,
0.01765826717019081,
-0.011494513601064682,
-0.04604073613882065,
-0.020881686359643936,
0.011803962290287018,
0.018849091604351997,
0.023920342326164246,
-0.04459260776638985,
0.0055242967791855335,
0.0017739860340952873,
0.052417028695344925,
-0.0050848377868533134,
0.03917006030678749,
-0.025413958355784416,
0.019882215186953545,
-0.01684567891061306,
-0.06801903247833252,
-0.00260504730977118,
0.015148448757827282,
0.05526963621377945,
-0.027811601758003235,
0.012573794461786747,
0.04279356077313423,
0.0003887034545186907,
0.01872081123292446,
0.049283407628536224,
-0.008689493872225285,
-0.0255111176520586,
-0.09875988960266113,
-0.03191322833299637,
0.03875381126999855,
-0.043550483882427216,
-0.01961703971028328,
-0.08863623440265656,
-0.057257380336523056,
0.042425159364938736,
0.06601468473672867,
-0.04802512377500534,
-0.01623653806746006,
0.013315623626112938,
0.07609407603740692,
0.017664674669504166,
-0.00394717650488019,
0.03700849786400795,
-0.04601621255278587,
0.002051211893558502,
-0.0026198578998446465,
-0.0810575932264328,
0.007071393541991711,
0.011760779656469822,
-0.008637061342597008,
0.03995649516582489,
0.04521144926548004,
0.011207550764083862,
0.013478151522576809,
0.009906529448926449,
0.004953490104526281,
0.019760403782129288,
0.045354828238487244,
0.03226608783006668,
-0.03142022714018822,
0.0004641355772037059,
0.03562643751502037,
-0.002348272129893303,
-0.056969329714775085,
0.021520983427762985,
0.04164223372936249,
-0.04790051281452179,
-0.034367773681879044,
0.0031508482061326504,
-0.0066420044749975204,
0.027332928031682968,
-0.028610214591026306,
-0.001310023944824934,
-0.04060835391283035,
0.011385039426386356,
-0.0006598510080948472,
0.048873357474803925,
0.0007645359146408737,
0.05329558625817299,
-0.007700140587985516,
-0.028976861387491226,
-0.02872401475906372,
-0.03097577951848507,
0.007657044567167759,
0.00830897968262434,
-0.04131878912448883,
0.02897811494767666,
0.0027047579642385244,
-0.006419847719371319,
-0.00896384846419096,
-0.02749485708773136,
-0.005396583583205938,
0.06624803692102432,
0.020070362836122513,
-0.0048247817903757095,
0.02914408966898918,
0.028357239440083504,
0.04411808028817177,
0.03259620815515518,
0.0016001011244952679,
0.021072354167699814,
-0.024677105247974396,
0.027562938630580902,
-0.014821036718785763,
0.029169835150241852,
0.0225394107401371,
0.006479321047663689,
-0.007854528725147247,
-0.0035478202626109123,
0.003275298746302724,
0.012506925500929356,
0.00898039061576128,
0.04719076305627823,
0.010944862850010395,
-0.012120614759624004,
-0.006464505568146706,
0.035608675330877304,
-0.01297879870980978,
0.07367198169231415,
-0.020171547308564186,
-0.01740066334605217,
-0.01253171730786562,
-0.022307220846414566,
-0.03403456509113312,
0.05418096482753754,
-0.07838909327983856,
-0.0017128926701843739,
0.029917560517787933,
0.022468069568276405,
0.011566906236112118,
0.024928100407123566,
-0.005400529596954584,
-0.0657465010881424,
0.05820531025528908,
0.03590702265501022,
-0.02987954393029213,
0.020485177636146545,
-0.0081626633182168,
0.01067452784627676,
0.011155815795063972,
-0.018282735720276833,
-0.01635187864303589,
-0.022668275982141495,
-0.00840482022613287,
-0.017830276861786842,
-0.02737565152347088,
0.011754835955798626,
0.02913685142993927,
-0.0002714995061978698,
0.08438746631145477,
0.08319801092147827,
-0.002064936328679323,
0.0027555213309824467,
-0.0227777361869812,
-0.037856318056583405,
0.0035015048924833536,
0.0056451293639838696,
0.027911702170968056,
-0.02165004052221775,
0.007435998879373074,
-0.045232754200696945,
-0.01936715841293335,
-0.012038061395287514,
-0.047993700951337814,
-0.007504149805754423,
-0.01954273320734501,
0.05108977109193802,
0.03634105622768402,
-0.009028652682900429,
-0.004079177509993315,
0.007806865032762289,
-0.01161914598196745,
0.004026387818157673,
0.016939444467425346,
0.013402735814452171,
-0.056272394955158234,
-0.0045068711042404175,
-0.039024416357278824,
-0.02930394373834133,
0.06047936901450157,
-0.0028328518383204937,
0.01461884006857872,
0.040816500782966614,
-0.0022516874596476555,
-0.030075915157794952,
-0.024493608623743057,
-0.020717179402709007,
-0.03680280223488808,
-0.034725841134786606,
0.028632139787077904,
0.03259819373488426,
0.039748869836330414,
-0.08188160508871078,
-0.032640863209962845,
-0.03371983766555786,
-0.06483222544193268,
-0.036986369639635086,
-0.01220977958291769,
0.03576512262225151,
-0.013218577951192856,
0.04813331365585327,
0.024497784674167633,
0.016336992383003235,
-0.00011454627383500338,
-0.03379848971962929,
-0.027420587837696075,
0.012495694682002068,
-0.018246926367282867,
0.04330616816878319,
-0.0032588785979896784,
-0.018968569114804268,
0.0801640972495079,
0.017398664727807045,
-0.027238722890615463,
0.006940800696611404,
0.010724776424467564,
-0.0348498672246933,
-0.008437104523181915,
0.010814291425049305,
0.022405799478292465,
0.012427124194800854,
0.05336359143257141,
-0.013008708134293556,
0.02758052386343479,
0.01201383676379919,
0.0030963101889938116,
-0.013003615662455559,
0.040948670357465744,
-0.014601340517401695,
0.007745389360934496,
0.04547550901770592,
0.013815803453326225,
0.022101029753684998,
0.048713937401771545,
-0.004324164241552353,
0.02018256112933159,
-0.026506496593356133,
-0.019400063902139664,
0.05635548382997513,
-0.01566685549914837,
0.027000077068805695,
-0.013232716359198093,
-0.008064879104495049,
-0.003465828951448202,
-0.058178264647722244,
-0.015046939253807068,
-0.007205556612461805,
0.0334775485098362,
-0.009341043420135975,
0.01175031065940857,
0.026265637949109077,
0.011254836805164814,
0.012207342311739922,
-0.01823890581727028,
-0.008639147505164146,
-0.018925346434116364,
0.03119770623743534,
-0.010215004906058311,
-0.01227871235460043,
0.01320548728108406,
0.04849168658256531,
0.033643756061792374,
-0.0019009746611118317,
-0.041089970618486404,
-0.0012935684062540531,
-0.0612763985991478,
-0.011905345134437084,
0.004436378367245197,
0.01598758064210415,
0.003268317086622119,
0.026696691289544106,
0.027508467435836792,
0.0029179996345192194,
0.0056304894387722015,
0.0054278913885355,
-0.07365483045578003,
0.0067425938323140144,
-0.025199757888913155,
0.015765346586704254,
-0.010570292361080647,
-0.004762505181133747,
0.03340617194771767,
-0.052476342767477036,
-0.02036566659808159,
-0.022051148116588593,
0.010364874266088009,
-0.04924857243895531,
0.0014528777683153749,
-0.037506505846977234,
-0.0344831682741642,
-0.01991262659430504,
0.05152454972267151,
0.04677465185523033,
-0.04807199165225029,
0.0016944274539127946,
0.03798628970980644,
-0.07423388957977295,
-0.022286146879196167,
-0.014128084294497967,
-0.01024716254323721,
0.0017454266780987382,
0.019056489691138268,
0.03619425371289253,
0.017298411577939987,
-0.029392577707767487,
0.007845028303563595,
-0.015361359342932701,
0.037643518298864365,
-0.00945142563432455,
-0.060365889221429825,
-0.032287754118442535,
-0.018301978707313538,
0.003646430093795061,
0.010189351625740528,
0.03237413242459297,
0.015042261220514774,
0.02570127323269844,
0.03009525127708912,
-0.0018340093083679676,
0.005383098963648081,
0.04891287162899971,
0.052820343524217606,
-0.0022523507941514254,
-0.015425104647874832,
-0.06207262724637985,
0.0055293734185397625,
-0.016800101846456528,
0.003332374384626746,
0.028132712468504906,
-0.03065105527639389,
-0.04646393284201622,
0.0039239199832081795,
0.030470194295048714,
0.01991487480700016,
-0.028357794508337975,
0.012552816420793533,
-0.03165647014975548,
-0.007941334508359432,
0.03698566555976868,
-0.001972443889826536,
0.0005654662963934243,
0.011736332438886166,
0.018430335447192192,
-0.002770512830466032,
0.04071221128106117,
-0.02277819998562336,
-0.02900216542184353,
0.005883018486201763,
0.08300331234931946,
-0.0033758434001356363,
0.027600204572081566,
-0.028182189911603928,
-0.01306078676134348,
0.018577998504042625,
-0.02864769473671913,
0.05858111009001732,
0.04057368263602257,
0.008311565965414047,
-0.01874728873372078,
-0.07846322655677795,
-0.07197194546461105,
-0.02092805504798889,
-0.025880465283989906,
-0.028224801644682884,
-0.02322543039917946,
-0.006649314425885677,
-0.012243296951055527,
0.033586736768484116,
0.0023471489548683167,
0.050989292562007904,
-0.032471634447574615,
-0.013804905116558075,
-0.002068581525236368,
0.023663613945245743,
-0.011453386396169662,
-0.06395694613456726,
0.018448244780302048,
0.01332466397434473,
0.004988782107830048,
0.03461508825421333,
-0.046030160039663315,
-0.047620147466659546,
0.007712952326983213,
0.020332761108875275,
0.022056514397263527,
0.01717572659254074,
-0.0224347785115242,
0.00716005964204669,
0.013503783382475376,
-0.024749096482992172,
0.016882168129086494,
0.05044657737016678,
-0.006153610534965992,
-0.05069220811128616,
-0.02043605037033558,
0.035916395485401154,
-0.043715521693229675,
-0.024282801896333694,
-0.025631647557020187,
-0.004074419848620892,
-0.010907294228672981,
0.041758112609386444,
-0.05228748545050621,
0.010718069970607758,
0.00625183479860425,
-0.026917118579149246,
0.0027223359793424606,
0.01932573691010475,
0.03254646435379982,
-0.016670487821102142,
-0.02452111430466175,
-0.0193558931350708,
-0.01155098620802164,
-0.04991152137517929,
0.02106192708015442,
-0.03753146901726723,
0.018482623621821404,
0.03185334429144859,
-0.01568494364619255,
0.0007611979963257909,
-0.019956117495894432,
-0.022366374731063843,
-0.04648628085851669,
-0.01151223760098219,
0.026224926114082336,
0.0013484603259712458,
0.005525169428437948,
0.021653559058904648,
-0.021112116053700447,
-0.03903396800160408,
0.017187701538205147,
-0.022941485047340393,
0.019806697964668274,
-0.051965370774269104,
0.01951337791979313,
0.00242236303165555,
0.03636787086725235,
-0.07293759286403656,
0.00877649337053299,
-0.0037658289074897766,
0.02327783778309822,
-0.02100418135523796,
-0.04490940272808075,
-0.03800574317574501,
0.005583270452916622,
-0.031105922535061836,
-0.008658159524202347,
0.051752720028162,
-0.05130080133676529,
-0.0210683923214674,
-0.013666611164808273,
0.02934904396533966,
0.012700552120804787,
-0.02640273980796337,
-0.0023644736502319574,
0.02263903059065342,
-0.006567743606865406,
0.017763573676347733,
0.03652389720082283,
0.035618752241134644,
0.0012163430219516158,
-0.011288239620625973,
0.02291451208293438,
-0.020060522481799126,
0.01708722859621048,
-0.013311585411429405,
-0.0032439795322716236,
0.03600133955478668,
-0.008700774051249027,
-0.015439076349139214,
-0.0024928476195782423,
-0.0285342987626791,
0.000546323717571795,
0.01779470592737198,
0.020300811156630516,
0.006930212955921888,
0.014549244195222855,
-0.05543426424264908,
0.06399098038673401,
-0.04558846727013588,
-0.026580210775136948,
-0.000764091091696173,
0.03392123803496361,
0.03776086866855621,
0.015763066709041595,
-0.024339761584997177,
0.02000712975859642,
0.02707839384675026,
-0.015484998933970928,
0.025627590715885162,
-0.015465755946934223,
0.012318619526922703,
-0.005664931144565344,
-0.03326064348220825,
-0.058739807456731796,
0.03309616073966026,
0.06186092272400856,
0.01116623543202877,
0.07255477458238602,
0.009943177923560143,
-0.0008172440575435758,
-0.006852899212390184,
-0.023108728229999542,
0.036743197590112686,
0.038017552345991135,
-0.006584170740097761,
0.03632599487900734,
-0.04124991595745087,
-0.042437177151441574,
0.040660858154296875,
0.023221664130687714,
-0.03933398798108101,
0.009903347119688988,
-0.010071133263409138,
-0.002569835865870118,
0.0003446596674621105,
-0.022822506725788116,
-0.029075082391500473,
0.029533689841628075,
-0.01879911497235298,
0.019132670015096664,
0.031305477023124695,
-0.017484476789832115,
-0.012305115349590778,
0.006515562534332275,
0.015423404052853584,
-0.04751363396644592,
-0.007002618629485369,
-0.05324666202068329,
0.018097443506121635,
0.028452618047595024,
-0.05366320535540581,
-0.047865431755781174,
-0.01402629166841507,
0.03453169763088226,
0.0074855065904557705,
0.05078018456697464,
-0.014290641993284225,
-0.03171636164188385,
-0.047559309750795364,
-0.033293984830379486,
-0.01749502122402191,
0.050521112978458405,
-0.0033195943105965853,
0.012731647118926048,
-0.032016150653362274,
-0.022556930780410767,
0.0076201604679226875,
0.011941108852624893,
0.046229369938373566,
0.006957472767680883,
0.03650722652673721,
-0.0018805908039212227,
0.008468465879559517,
-0.024403279647231102,
0.004637969192117453,
0.1388072967529297,
0.05571167171001434,
0.0026018156204372644,
-0.0503639355301857,
0.03700590878725052,
-0.0079655097797513,
0.029157325625419617,
-0.02105265110731125,
0.010641628876328468,
-0.007097965106368065,
0.004385703708976507,
-0.02587004378437996,
0.004984890576452017,
-0.02004276029765606,
0.016037994995713234,
0.03211138769984245,
-0.05296511948108673,
-0.04519808292388916,
0.002978833392262459,
0.06275655329227448,
-0.010792732238769531,
0.0037230108864605427,
0.013605713844299316,
0.02673296444118023,
-0.04055517539381981,
0.023272641003131866,
-0.01350974477827549,
-0.002814826089888811,
-0.023917466402053833,
-0.0267992801964283,
-0.027049586176872253,
0.0065627433359622955,
-0.0007430558325722814,
-0.0398966521024704,
-0.04581013321876526,
0.01934296078979969,
0.00026080437237396836,
-0.040818195790052414,
0.0237806998193264,
0.03823985531926155,
-0.02184234745800495,
-0.0006470055086538196,
0.028134675696492195,
0.005167827010154724,
-0.05030880868434906,
-0.0012594755971804261,
-0.012962968088686466,
0.04529351741075516,
0.013474417850375175,
0.012118633836507797,
-0.0022669790778309107,
0.0019761088769882917,
0.010809452272951603,
-0.02725188620388508,
-0.015119253657758236,
-0.020892905071377754,
0.03571939095854759,
-0.018783889710903168,
0.03860689699649811,
0.004310658201575279,
0.013195555657148361,
0.015207496471703053,
-0.02512737549841404,
-0.029289722442626953,
0.014364037662744522,
-0.006917236372828484,
-0.026903610676527023,
0.05804264545440674,
0.02285173162817955,
0.011558416299521923,
-0.017799194902181625,
-0.043327562510967255,
-0.016195621341466904,
-0.0069347466342151165,
0.011173378676176071,
0.0028780088759958744,
0.0013650213368237019,
0.04771137982606888,
-0.02096375823020935,
-0.05413222312927246,
-0.06236984580755234,
0.018975283950567245,
-0.049226101487874985,
0.008487648330628872,
-0.018977846950292587,
0.00026293384144082665,
0.0057758851908147335,
0.08388395607471466,
-0.033150408416986465,
0.019941672682762146,
0.024601828306913376,
0.06730782985687256,
-0.0046056099236011505,
-0.012348894029855728,
-0.013071591965854168,
0.018547091633081436,
-0.025904640555381775,
0.0029496620409190655,
-0.008230087347328663,
0.009802864864468575,
0.012374773621559143,
0.0008406038978137076,
-0.011593918316066265,
0.015762576833367348,
-0.01644842140376568,
-0.009129230864346027,
0.0416724719107151,
-0.052285511046648026,
0.02566470578312874,
0.05166114866733551,
0.020757820457220078,
-0.02816806733608246,
0.008283829316496849,
0.003836324205622077,
0.004415954928845167,
0.0029067734722048044,
-0.0060323262587189674,
-0.00601035775616765,
-0.003780086524784565,
-0.015180394984781742,
0.008763846941292286,
-0.03390892967581749,
-0.002242160029709339,
-0.02635362185537815,
0.02987002395093441,
-0.0173836350440979,
-0.014237103052437305,
-0.03402714058756828,
0.016473280265927315,
-0.0024319160729646683,
-0.01742524839937687,
0.015042678453028202,
0.02880077436566353,
0.004757458809763193,
-0.055447980761528015,
0.00949172955006361,
0.04409711807966232,
0.0471859909594059,
0.03843342885375023,
-0.016181781888008118,
0.0291343592107296,
-0.06977187097072601,
-0.0010785809718072414,
0.04290192574262619,
0.014810839667916298,
0.0011239408049732447,
0.02371717058122158,
0.004311694297939539,
-0.013842475600540638,
0.05453750118613243,
-0.02466796524822712,
-0.005300858058035374,
0.006978857796639204,
-0.055399004369974136,
0.000439597963122651,
-0.026923393830657005,
0.029570752754807472,
-0.0053331078961491585,
-0.020019184798002243,
0.046165477484464645,
0.0262919869273901,
-0.04933663085103035,
-0.006127342581748962,
-0.013207501731812954,
-0.047911111265420914,
0.04292430728673935,
0.02952747233211994,
0.015036605298519135,
0.01655200868844986,
0.0709318220615387,
0.0036040160339325666,
0.00006306812429102138,
0.02225973643362522,
0.023470809683203697,
-0.12511222064495087,
-0.02311077155172825,
0.012599419802427292,
0.006437487434595823,
0.030021660029888153,
-0.037254974246025085,
0.06659915298223495,
0.07957839965820312,
-0.028888635337352753,
0.0023095915094017982,
-0.048807576298713684,
0.003393308725208044,
-0.02185778319835663,
-0.032645903527736664,
-0.012430787086486816,
0.06684383749961853,
0.005583734251558781,
0.04010186716914177,
0.02077656425535679,
0.052251435816287994,
-0.05841858685016632,
-0.031081074848771095,
-0.013480329886078835,
0.02896173857152462,
-0.0007745864568278193,
-0.023642925545573235,
0.06965739279985428,
-0.024393757805228233,
0.003646166529506445,
0.027881711721420288,
0.01712338998913765,
-0.011766851879656315,
-0.037512753158807755,
0.044103339314460754,
-0.011238428764045238,
0.0481174997985363,
0.048125896602869034,
0.023951848968863487,
0.01583315245807171,
-0.019746286794543266,
0.03448190167546272,
0.0033191374968737364,
-0.0040540192276239395,
-0.007856217212975025,
0.006262219976633787,
-0.05585670843720436,
-0.038702741265296936,
0.008472745306789875,
-0.024051085114479065,
-0.04533899202942848,
0.01716773398220539,
-0.011470349505543709,
0.0058948686346411705,
-0.05234377458691597,
-0.002499651163816452,
-0.040585704147815704,
0.010922492481768131,
0.03419746831059456,
0.01738642528653145,
0.017356742173433304,
0.00958127249032259,
0.009063550271093845,
-0.01735273376107216,
0.01782318204641342,
-0.006236732937395573,
-0.042530547827482224,
-0.050556283444166183,
-0.018122421577572823,
-0.02535545639693737,
0.00019317431724630296,
-0.02665119431912899,
-0.041287392377853394,
-0.05921917036175728,
-0.029154876247048378,
0.011709011159837246,
-0.009030490182340145,
-0.018487896770238876,
-0.011189064010977745,
-0.027385860681533813,
-0.08089128881692886,
-0.0022894595749676228,
0.0073594399727880955,
-0.0012816990492865443,
-0.030964255332946777,
0.004048983100801706,
-0.014682664535939693,
0.026057325303554535,
0.05057499557733536,
0.02265246957540512,
-0.018342124298214912,
0.05598817020654678,
-0.007268231827765703,
0.0006599555490538478,
-0.029966600239276886,
-0.0005524985608644783,
0.006192125380039215,
0.006784171797335148,
-0.0026880111545324326,
0.00817415863275528,
0.052917540073394775,
-0.008980036713182926,
-0.0005284008220769465,
0.0011376369511708617,
0.02624577097594738,
0.02595658041536808,
-0.0025100507773458958,
0.06905211508274078,
-0.029859308153390884,
-0.03197949007153511,
0.06277650594711304,
0.020354008302092552,
0.005235012620687485,
0.009110772050917149,
-0.026503589004278183,
-0.014549126848578453,
-0.000204749550903216,
0.006774236913770437,
-0.0016978161875158548,
-0.007348256651312113,
-0.01079142652451992,
0.02066516876220703,
-0.027874106541275978,
-0.001762883155606687,
0.062420543283224106,
-0.03493374213576317,
-0.0569748617708683,
0.013193454593420029,
0.040472012013196945,
0.06563788652420044,
0.03862982615828514,
0.03398485854268074,
0.015303380787372589,
-0.025034649297595024,
0.03287573531270027,
0.05732380971312523,
0.011553971096873283,
-0.004935622680932283,
-0.016602791845798492,
0.0368933379650116,
-0.03122754395008087,
0.012923257425427437,
0.012185080908238888,
-0.026159469038248062,
0.018961431458592415,
-0.06022493913769722,
-0.0068314289674162865,
-0.010319831781089306,
0.004621586762368679,
0.010682357475161552,
0.000928856257814914,
0.061570119112730026,
-0.00867754127830267,
-0.030289888381958008,
-0.009967977181077003,
0.047086115926504135,
0.014936301857233047,
0.0159660205245018,
0.024301595985889435,
0.03485003858804703,
-0.01893809251487255,
-0.018111394718289375,
-0.036462072283029556,
-0.032570283859968185,
-0.002886323956772685,
-0.0366361066699028,
0.03715258836746216,
0.05516184866428375,
0.033525265753269196,
-0.012896744534373283,
-0.016261469572782516,
-0.019471751525998116,
-0.043100036680698395,
-0.0007344355690293014,
0.05841884762048721,
0.04088534042239189,
-0.024046769365668297,
-0.007688086945563555,
-0.027135320007801056,
0.06497896462678909,
0.007689212914556265,
-0.052327655255794525,
-0.024403240531682968,
-0.016822462901473045,
-0.022019462659955025,
0.024747274816036224
] |
<p>What is preventing $Δ^{++}$ and $Δ^-$ baryons from going to a lower-energy state with spin 1/2 similar to that of protons and neutrons? I don't think the Pauli exclusion principle can prevent it because the quarks have different colors. The whole purpose of the quark color is to allow more than one quark to be in the same state. What's so special about protons and neutrons? What allows them to have lower energy compared to $Δ^+$ and $Δ^0$?</p>
| 9,381 |
[
-0.02301369234919548,
-0.0062568276189267635,
-0.0009455396793782711,
-0.028297586366534233,
0.04926082864403725,
0.02005929686129093,
-0.06051630154252052,
-0.01758488081395626,
-0.011557083576917648,
-0.08199070394039154,
0.05908559262752533,
-0.004695033188909292,
0.030531659722328186,
0.03045382723212242,
0.053744785487651825,
0.01211065985262394,
0.018599553033709526,
-0.03806475177407265,
-0.016655022278428078,
-0.022699497640132904,
0.02615746110677719,
0.0121114831417799,
0.01916615106165409,
0.043237678706645966,
-0.03979821130633354,
0.00857616774737835,
0.05314846709370613,
0.012676903046667576,
0.0249501820653677,
0.05296792462468147,
0.016511058434844017,
-0.03742217645049095,
0.03815874829888344,
0.012203984893858433,
-0.004042520187795162,
0.011419919319450855,
-0.02749590016901493,
-0.026165487244725227,
-0.03518640249967575,
0.02720918506383896,
-0.06062086671590805,
-0.01543448120355606,
-0.007376234512776136,
0.007468057330697775,
-0.0039603132754564285,
-0.01129362266510725,
0.03363647311925888,
-0.019609134644269943,
0.06742146611213684,
-0.03666370362043381,
0.03265661001205444,
0.017406687140464783,
0.01790117472410202,
0.020259277895092964,
0.005897164344787598,
-0.03086497262120247,
0.07757531106472015,
0.06035410985350609,
-0.003309396328404546,
-0.041244976222515106,
-0.026770135387778282,
-0.034274622797966,
0.020396985113620758,
0.03399860858917236,
-0.012062284164130688,
0.008748196996748447,
0.02811756543815136,
0.0029364507645368576,
-0.024528924375772476,
0.010156616568565369,
0.04318420961499214,
-0.017019324004650116,
0.03844989836215973,
-0.007617550902068615,
0.016540998592972755,
-0.01800486631691456,
0.033679332584142685,
-0.0010727206245064735,
0.027956778183579445,
0.05955822393298149,
-0.02271365560591221,
0.008508115075528622,
0.005448951385915279,
0.006584705784916878,
-0.0007940629730001092,
-0.004705736413598061,
0.05252207815647125,
0.00715298019349575,
0.010301352478563786,
0.06673692911863327,
0.007384225260466337,
-0.01639438606798649,
0.02073684334754944,
-0.006236519198864698,
-0.009775928221642971,
0.04622127115726471,
-0.001563992933370173,
0.01749482937157154,
0.0006406479515135288,
-0.021922461688518524,
-0.017488721758127213,
-0.01759600266814232,
0.047144122421741486,
0.09110722690820694,
-0.009320213459432125,
-0.00856601819396019,
-0.05383480712771416,
0.021205825731158257,
-0.014519289135932922,
0.02429148741066456,
-0.018520968034863472,
-0.030823929235339165,
-0.0041513461619615555,
-0.02252400480210781,
0.0037652435712516308,
-0.034396693110466,
-0.015650024637579918,
-0.040578678250312805,
0.03869648277759552,
0.07680501788854599,
0.03191130980849266,
0.001476943725720048,
-0.014494436793029308,
-0.04848697781562805,
-0.045634932816028595,
-0.022716419771313667,
0.043825119733810425,
0.0011749772820621729,
-0.0056789712980389595,
-0.02624952606856823,
0.0009254674077965319,
-0.03475519269704819,
0.011792450211942196,
0.008754304610192776,
0.044868867844343185,
-0.014728494919836521,
-0.11898303031921387,
-0.05298268049955368,
0.05515526980161667,
-0.00038518401561304927,
-0.04614124074578285,
-0.0785493329167366,
-0.015141717158257961,
0.03395329788327217,
0.07027294486761093,
-0.034764669835567474,
-0.018887175247073174,
0.004791580140590668,
0.022236021235585213,
0.00012888383935205638,
-0.01669147238135338,
-0.011200172826647758,
-0.021503448486328125,
-0.004748623818159103,
-0.00536998501047492,
-0.04472797363996506,
0.04804622754454613,
-0.006274987477809191,
-0.0357658788561821,
-0.025130929425358772,
0.04906419664621353,
-0.06919121742248535,
0.031960856169462204,
-0.005097509827464819,
0.015846945345401764,
-0.021924279630184174,
0.08942356705665588,
0.006373757962137461,
-0.0016584156546741724,
0.00933881662786007,
-0.020624034106731415,
0.021054444834589958,
-0.005378732457756996,
0.055374182760715485,
0.0493747740983963,
-0.021587206050753593,
-0.06763383001089096,
-0.05350995063781738,
-0.01665857993066311,
-0.022416748106479645,
-0.0477168969810009,
-0.02199379727244377,
-0.03849082440137863,
-0.00657920865342021,
-0.026234598830342293,
0.025019552558660507,
0.009864086285233498,
-0.012000675313174725,
0.0005460656830109656,
-0.04303106665611267,
0.009703824296593666,
-0.05106254667043686,
-0.004212940577417612,
-0.00909576378762722,
-0.00876782275736332,
0.03050939552485943,
0.03167947009205818,
0.020863329991698265,
-0.03985769674181938,
-0.019376210868358612,
-0.015900420024991035,
0.07280362397432327,
0.0029213225934654474,
0.005571845453232527,
0.00616378104314208,
0.05234728381037712,
0.035982802510261536,
-0.0035401552449911833,
0.004685669206082821,
-0.007746686227619648,
-0.02658694237470627,
-0.0026888514403253794,
-0.009071671403944492,
0.022745519876480103,
-0.0016027844976633787,
-0.007198522798717022,
0.008051595650613308,
-0.003331980435177684,
-0.0043389094062149525,
0.018834182992577553,
0.0037309187464416027,
0.09372790157794952,
-0.02726380154490471,
-0.010395499877631664,
0.010939435102045536,
0.049726035445928574,
0.027714859694242477,
0.017983192577958107,
-0.018309080973267555,
-0.023181648924946785,
-0.0005241525359451771,
-0.006583527196198702,
0.04753199592232704,
0.051441628485918045,
-0.0664907842874527,
0.024441825225949287,
-0.04255283623933792,
0.033469878137111664,
0.0033901820424944162,
0.008379658684134483,
-0.05120067670941353,
-0.0181589275598526,
-0.0025076509919017553,
0.010929280892014503,
-0.02302711270749569,
-0.0006503769545815885,
0.05099146068096161,
-0.01645987294614315,
0.020780332386493683,
-0.03920329734683037,
-0.012678682804107666,
0.03727078437805176,
-0.009904454462230206,
-0.010748820379376411,
0.0403268001973629,
-0.05900461599230766,
0.036327287554740906,
-0.0036162021569907665,
0.024376677349209785,
0.014947548508644104,
-0.005793403368443251,
0.015701163560152054,
0.0009314808994531631,
-0.016615498811006546,
0.0002641658065840602,
0.02978518232703209,
-0.03034144826233387,
-0.0248282290995121,
0.022075679153203964,
-0.011473911814391613,
0.00946500152349472,
-0.0018236683681607246,
-0.022470710799098015,
-0.008637987077236176,
-0.013090071268379688,
0.043653689324855804,
0.010594290681183338,
0.012473242357373238,
-0.05153925344347954,
-0.005983950570225716,
0.022320562973618507,
-0.017673971131443977,
0.003398182801902294,
0.04420127719640732,
-0.01171889528632164,
0.013159663416445255,
-0.06900236755609512,
0.02093668095767498,
0.0146627277135849,
-0.03391681984066963,
0.016423137858510017,
-0.004654372576624155,
-0.04269983619451523,
-0.041869960725307465,
-0.01515079103410244,
-0.023205293342471123,
0.004913133103400469,
-0.02151300758123398,
-0.009817787446081638,
0.05549450218677521,
0.01639685221016407,
-0.02460269257426262,
0.03932974860072136,
-0.07536385208368301,
-0.02975020930171013,
0.0053678108379244804,
0.024856191128492355,
0.029162432998418808,
-0.020899441093206406,
0.02455700747668743,
0.043876998126506805,
-0.03806447237730026,
0.017635388299822807,
-0.06067736819386482,
-0.024856986477971077,
0.004885307513177395,
-0.00020732349366880953,
0.029236137866973877,
0.0005408534780144691,
-0.00589967193081975,
0.06129569187760353,
0.0277942456305027,
-0.015474379993975163,
0.02040458843111992,
-0.028862345963716507,
-0.02267562225461006,
-0.030141819268465042,
0.025838518515229225,
0.041628845036029816,
-0.0018786592409014702,
0.02238648012280464,
-0.004614229779690504,
0.08369685709476471,
0.0015366538427770138,
0.012341580353677273,
-0.0331696942448616,
0.030149979516863823,
0.010376078076660633,
0.011591177433729172,
0.032715559005737305,
0.02718685381114483,
-0.04348321631550789,
0.004197041038423777,
0.028947699815034866,
0.038990750908851624,
-0.0015470574144273996,
-0.025784440338611603,
0.06716844439506531,
0.018199872225522995,
0.019763316959142685,
-0.005135703831911087,
0.04006855562329292,
-0.0028263763524591923,
-0.04266132041811943,
0.02361477166414261,
-0.017077220603823662,
0.03415888547897339,
0.010053223930299282,
0.01382377464324236,
0.002608965151011944,
0.04090067744255066,
-0.009790435433387756,
-0.00874475110322237,
0.003936321474611759,
-0.021176213398575783,
0.04736371710896492,
-0.028027446940541267,
0.0457315556704998,
0.051673635840415955,
0.026626767590641975,
0.008060229942202568,
-0.0354301854968071,
-0.030123278498649597,
-0.016602057963609695,
-0.06416600197553635,
0.007786101661622524,
-0.00698309438303113,
0.06383761763572693,
-0.009440844878554344,
0.05759147182106972,
0.022608036175370216,
0.010013510473072529,
0.004115245305001736,
-0.03495556116104126,
-0.06408091634511948,
0.020781435072422028,
-0.06455997377634048,
0.006802415940910578,
-0.01029783021658659,
-0.0015908132772892714,
-0.008057869970798492,
-0.02198278158903122,
-0.04920985549688339,
-0.0518425852060318,
0.019387196749448776,
-0.012044373899698257,
0.046834781765937805,
-0.060554780066013336,
-0.07035789638757706,
-0.011762148700654507,
0.03998412936925888,
0.04182128608226776,
-0.0286436565220356,
0.01137898676097393,
0.025714293122291565,
-0.06926172226667404,
0.027762502431869507,
-0.02575548179447651,
0.014308818615972996,
0.025030162185430527,
0.025034278631210327,
0.02511199750006199,
0.02446485310792923,
0.011602734215557575,
-0.057007428258657455,
0.055474042892456055,
0.04622959345579147,
0.0021345026325434446,
-0.023952782154083252,
0.0234011672437191,
-0.046701718121767044,
-0.02508615143597126,
-0.01249099150300026,
0.07123422622680664,
-0.046970196068286896,
0.025983724743127823,
0.0133011220023036,
-0.009028328582644463,
-0.03803963214159012,
0.052025772631168365,
0.04137056693434715,
0.0352531261742115,
-0.053392477333545685,
-0.03734428435564041,
-0.025971131399273872,
-0.04630735144019127,
-0.02881794236600399,
-0.04122082516551018,
-0.027591116726398468,
-0.027482151985168457,
0.016473352909088135,
0.00012340143439359963,
-0.016091523692011833,
-0.04595930501818657,
-0.02388760820031166,
-0.020923664793372154,
-0.006311042234301567,
-0.03060113452374935,
0.005905092228204012,
0.03403326869010925,
0.002615232951939106,
0.043694935739040375,
0.0006197548354975879,
0.015440546907484531,
-0.032944850623607635,
-0.028915058821439743,
0.04432753473520279,
0.064454585313797,
0.016813548281788826,
-0.01957024447619915,
-0.08946935087442398,
-0.025076070800423622,
0.03946533799171448,
-0.0277558546513319,
0.011168787255883217,
-0.0015179106267169118,
-0.0202354546636343,
-0.013156815432012081,
-0.06688737869262695,
-0.02936575561761856,
0.012921965681016445,
0.000016411046090070158,
-0.0016835820861160755,
-0.03830656781792641,
-0.031058257445693016,
-0.019865578040480614,
0.022882122546434402,
0.01664675585925579,
0.008893061429262161,
-0.02138025127351284,
0.03558376431465149,
0.017191946506500244,
-0.003069755621254444,
0.026220455765724182,
-0.10324851423501968,
0.01509930845350027,
0.0045593841932713985,
0.022681215777993202,
0.05231064558029175,
-0.05006120353937149,
-0.0631461888551712,
0.012660572305321693,
0.00357407471165061,
0.003788995323702693,
-0.03254344314336777,
-0.07407393306493759,
0.04608326405286789,
0.057718291878700256,
-0.026326600462198257,
0.02254112996160984,
0.041550807654857635,
-0.044103074818849564,
-0.021071452647447586,
-0.05585230514407158,
0.011256417259573936,
-0.026027919724583626,
0.02544076181948185,
-0.028250733390450478,
0.007271696347743273,
0.009285333566367626,
0.032250676304101944,
-0.009290835820138454,
0.008007840253412724,
0.030465416610240936,
-0.07175309211015701,
-0.02830490469932556,
0.022395635023713112,
0.02815324440598488,
-0.04142593964934349,
0.010917367413640022,
0.008197939954698086,
0.00843830592930317,
0.01607087440788746,
0.03709711134433746,
-0.004447079263627529,
-0.04379565641283989,
0.028284447267651558,
-0.036260683089494705,
-0.006326448172330856,
-0.011884619481861591,
-0.016073891893029213,
-0.011068949475884438,
-0.023479430004954338,
0.0324443057179451,
-0.011586007662117481,
-0.012994629330933094,
0.00492743868380785,
-0.01678946428000927,
-0.012625441886484623,
0.03842725232243538,
-0.056452903896570206,
0.0103424908593297,
-0.02021976187825203,
0.04719621315598488,
0.032200854271650314,
-0.0057118660770356655,
-0.07782665640115738,
-0.01804850995540619,
-0.012936095707118511,
-0.011080397292971611,
-0.009644156321883202,
-0.022141706198453903,
0.003800314385443926,
0.003425570437684655,
0.004749603103846312,
0.027000103145837784,
0.048487793654203415,
-0.03706449270248413,
-0.0025826410856097937,
0.03262351080775261,
0.04533220827579498,
0.02825620211660862,
-0.023252466693520546,
-0.029005561023950577,
0.013138008303940296,
-0.0019142164383083582,
-0.0007547839777544141,
-0.010574701242148876,
0.030391942709684372,
-0.023150406777858734,
-0.051045797765254974,
0.02994983270764351,
0.012003774754703045,
0.022110842168331146,
-0.025459399446845055,
-0.008951717987656593,
0.06516823172569275,
-0.0067763798870146275,
0.037972792983055115,
-0.0040758755058050156,
0.03841014951467514,
-0.0026520651299506426,
0.045035164803266525,
0.009042089805006981,
-0.014426693320274353,
-0.0583023875951767,
-0.054386332631111145,
0.03164604678750038,
-0.014429418370127678,
0.008711892180144787,
0.009469362907111645,
0.027751784771680832,
-0.001635893015190959,
-0.024678854271769524,
0.04543107748031616,
-0.03153165802359581,
0.016171133145689964,
0.0068026878871023655,
0.0013277146499603987,
-0.009338496252894402,
0.010594652965664864,
0.010300526395440102,
-0.029524309560656548,
-0.014807259663939476,
-0.006793164648115635,
0.0357804037630558,
0.007334547583013773,
0.036639727652072906,
-0.014063379727303982,
0.0076928515918552876,
-0.012937074527144432,
-0.033669665455818176,
-0.025345483794808388,
0.02202458307147026,
-0.03394779562950134,
0.030803415924310684,
-0.030549531802535057,
0.006144075654447079,
0.03101264126598835,
0.06136695668101311,
-0.023924127221107483,
0.012026889249682426,
0.04237622395157814,
-0.027864163741469383,
0.02900676429271698,
-0.036644261330366135,
-0.051952049136161804,
0.037877775728702545,
-0.032314714044332504,
0.0026587657630443573,
0.029157111421227455,
-0.039777133613824844,
0.05320798233151436,
-0.007578901015222073,
0.03922244906425476,
-0.04877330735325813,
-0.005504752974957228,
-0.04425240308046341,
0.024641498923301697,
0.010653010569512844,
0.0002865024725906551,
0.006758970208466053,
-0.020537277683615685,
-0.004867282230407,
0.015579096972942352,
0.011960148811340332,
0.024492843076586723,
-0.06113263592123985,
-0.04155372455716133,
-0.03197470307350159,
-0.05291956663131714,
0.05579480901360512,
-0.04459251090884209,
-0.051106762140989304,
-0.034047193825244904,
-0.018078312277793884,
0.00996276643127203,
-0.011054763570427895,
0.01766972430050373,
-0.008662601001560688,
0.024258075281977654,
-0.01381772942841053,
0.038436517119407654,
-0.007446505594998598,
-0.00034879663144238293,
0.11706306040287018,
0.04014049842953682,
0.001744264387525618,
-0.06497593224048615,
0.005836785305291414,
-0.015481457114219666,
0.04209556058049202,
-0.0036182249896228313,
0.03246627002954483,
0.033572521060705185,
0.03606176748871803,
-0.04051033407449722,
0.04327382519841194,
0.025837307795882225,
0.0011476423824205995,
0.04237395152449608,
-0.05213603377342224,
-0.023057499900460243,
0.0002747056423686445,
0.016799109056591988,
-0.015019410289824009,
0.03233875706791878,
-0.009591429494321346,
0.02876378409564495,
0.008825685828924179,
0.004253431223332882,
-0.011207855306565762,
-0.038708120584487915,
0.025659777224063873,
0.0023620000574737787,
-0.042996637523174286,
-0.007646053098142147,
-0.010095951147377491,
0.013602238148450851,
-0.01088972669094801,
0.02762470580637455,
0.02282620221376419,
-0.03579114004969597,
0.019877301529049873,
-0.009302699007093906,
0.02408383972942829,
-0.0015949599910527468,
-0.008090684190392494,
0.010674035176634789,
-0.010425924323499203,
-0.0051332334987819195,
-0.005892573390156031,
0.05957730859518051,
-0.04393595829606056,
-0.016124047338962555,
-0.0031894485000520945,
-0.0007765579503029585,
0.017052220180630684,
-0.04165791720151901,
-0.06301870942115784,
-0.009828103706240654,
-0.0014570396160706878,
0.015973052009940147,
0.02253846637904644,
-0.0124915586784482,
0.0443723239004612,
-0.0417497493326664,
0.050869349390268326,
-0.024429548531770706,
-0.018027234822511673,
-0.008437872864305973,
0.012404460459947586,
0.03009457141160965,
0.011475392617285252,
0.023924551904201508,
-0.00961322896182537,
0.030036628246307373,
-0.032346125692129135,
-0.014788296073675156,
0.010520730167627335,
0.041785307228565216,
0.051701370626688004,
0.029286764562129974,
-0.019832659512758255,
-0.02525109238922596,
-0.03458018973469734,
0.05510476231575012,
-0.013000477105379105,
0.004227953031659126,
0.0013800386805087328,
0.007048787549138069,
0.01476158294826746,
0.046565309166908264,
-0.015695776790380478,
-0.017086485400795937,
-0.008974311873316765,
0.03780164569616318,
0.023697758093476295,
0.0021628185641020536,
-0.021506454795598984,
0.03153195604681969,
-0.04092474281787872,
0.0038786218501627445,
-0.004969772882759571,
0.02122567407786846,
0.015725374221801758,
0.0005569817149080336,
0.024191102012991905,
-0.006865966599434614,
-0.026847217231988907,
-0.009412957355380058,
0.023484542965888977,
-0.01299714483320713,
0.002462696051225066,
-0.005749639123678207,
-0.0026693965774029493,
-0.008775642141699791,
-0.016771288588643074,
-0.00037718977546319366,
-0.025590995326638222,
0.014995009638369083,
0.020146485418081284,
0.009869423694908619,
-0.0024727468844503164,
-0.04578930884599686,
0.01189897395670414,
0.01785091497004032,
0.009531422518193722,
-0.04141984134912491,
0.0015636216849088669,
-0.02901451103389263,
0.007379868533462286,
-0.053530365228652954,
0.03213343024253845,
0.03387151658535004,
-0.009690610691905022,
0.009309632703661919,
0.06425118446350098,
-0.018772821873426437,
-0.007998768240213394,
0.046959467232227325,
0.015912119299173355,
0.010503803379833698,
0.019116103649139404,
-0.03259789198637009,
0.04724378138780594,
-0.015595022588968277,
-0.055909816175699234,
-0.017771486192941666,
-0.008809628896415234,
0.009264785796403885,
0.01013326644897461,
-0.014917777851223946,
-0.005585271865129471,
0.046149902045726776,
-0.033166758716106415,
-0.021512014791369438,
0.008730138652026653,
0.014860447496175766,
-0.002838793443515897,
-0.04423270747065544,
-0.0036697094328701496,
-0.01986101269721985,
-0.006803798023611307,
0.014011094346642494,
-0.012699217535555363,
-0.025253737345337868,
-0.01936347782611847,
-0.027148161083459854,
0.006470978260040283,
0.05634370818734169,
0.020179137587547302,
0.03668271005153656,
-0.018118567764759064,
0.013778459280729294,
-0.03959771990776062,
0.08502186834812164,
-0.0004218845861032605,
-0.01917416602373123,
-0.07359854876995087,
-0.006571930833160877,
0.008619981817901134,
-0.010664033703505993,
0.03182525560259819,
-0.022151926532387733,
0.04068097099661827,
0.04973422363400459,
-0.06887764483690262,
0.03373360633850098,
-0.044475238770246506,
-0.0035969761665910482,
-0.032461199909448624,
-0.023269180208444595,
-0.03820211812853813,
0.04478534311056137,
0.018773330375552177,
0.05884730443358421,
0.046770330518484116,
0.0027463515289127827,
-0.025365328416228294,
-0.026243790984153748,
-0.019319815561175346,
-0.012348207645118237,
-0.027196653187274933,
-0.00796170812100172,
0.060170985758304596,
-0.014757586643099785,
0.0004272178339306265,
0.016638116911053658,
0.024848060682415962,
-0.009981476701796055,
-0.027638861909508705,
-0.0032131648622453213,
0.0061966110952198505,
0.026389118283987045,
0.00025712489150464535,
0.01060666237026453,
-0.004659696947783232,
0.007117197848856449,
-0.008995046839118004,
0.022952474653720856,
0.0008080211118794978,
0.031561169773340225,
-0.02643817476928234,
-0.03292165324091911,
-0.024365153163671494,
0.03495941683650017,
-0.01708160527050495,
-0.012692494317889214,
0.004325192421674728,
0.01990687847137451,
0.013694475404918194,
-0.018473006784915924,
0.011542045511305332,
-0.03745871037244797,
-0.00560022983700037,
0.01748601347208023,
0.009417579509317875,
0.01781136356294155,
0.02529456838965416,
0.011742274276912212,
-0.008352164179086685,
-0.0014772348804399371,
0.03056446835398674,
-0.0227963849902153,
0.007759469095617533,
0.014179086312651634,
0.006592310965061188,
0.029479172080755234,
-0.025571104139089584,
-0.049484942108392715,
-0.05315724015235901,
0.04292899742722511,
0.010749573819339275,
0.04492499306797981,
-0.04416486620903015,
-0.04081420972943306,
-0.028851667419075966,
-0.07021445035934448,
0.02575366385281086,
0.005565778352320194,
0.0483362153172493,
-0.02480633370578289,
-0.02887832559645176,
-0.030872821807861328,
0.02442893385887146,
0.06277048587799072,
0.045788366347551346,
-0.046680301427841187,
0.023725679144263268,
0.004544646944850683,
0.013178329914808273,
0.009089594706892967,
0.008077604696154594,
-0.021781064569950104,
-0.004428819287568331,
-0.0030729088466614485,
-0.009286746382713318,
-0.03664575144648552,
0.016748331487178802,
0.024755049496889114,
0.0021723767276853323,
-0.02733093500137329,
0.03493843600153923,
-0.028795916587114334,
0.07438959926366806,
-0.01538500189781189,
0.016888750717043877,
0.07382884621620178,
0.02294159308075905,
0.01888415217399597,
0.01502256654202938,
-0.051877137273550034,
-0.038552943617105484,
0.024629520252346992,
0.0010229776380583644,
-0.034709155559539795,
-0.020584261044859886,
-0.01617228239774704,
0.042867615818977356,
-0.013212226331233978,
0.02279210276901722,
0.07390205562114716,
-0.004038997460156679,
-0.026152852922677994,
0.024943899363279343,
0.029892053455114365,
0.02648172341287136,
-0.02793942205607891,
0.009547468274831772,
0.025340832769870758,
0.039946142584085464,
0.027965925633907318,
0.04321940243244171,
0.023430494591593742,
0.02638172172009945,
0.017339477315545082,
0.004902939312160015,
0.0070776562206447124,
0.006326728966087103,
0.01578676514327526,
0.026013940572738647,
-0.021487193182110786,
-0.02623498998582363,
0.04407182335853577,
0.015033822506666183,
0.011633106507360935,
0.026177415624260902,
-0.034240249544382095,
0.08200401067733765,
-0.04309341683983803,
0.021858351305127144,
-0.030661823228001595,
-0.01363726332783699,
0.02171296253800392,
-0.01230985950678587,
0.011434496380388737,
0.03013961762189865,
-0.009997377172112465,
0.004684039857238531,
0.014482295140624046,
0.014160132966935635,
0.04436355084180832,
-0.024306070059537888,
0.01092652790248394,
0.02534305676817894,
0.017262160778045654,
-0.010887576267123222,
-0.003498421050608158,
-0.012269615195691586,
-0.03456095606088638,
0.03941195458173752,
0.034394215792417526,
0.02700730971992016,
0.01897895522415638,
-0.023295613005757332,
-0.015044708736240864,
0.033050958067178726,
-0.0372747927904129,
-0.013465936295688152,
-0.00785366166383028,
-0.00030889821937307715,
-0.0638902559876442,
0.0016287333564832807
] |
<p>i heard that a tear drop shap is the most aerodynamic shape possible or the best is this true? If this isn't true what is since i need to make a fast ROV? Also since i need to have a propeller to propel it should it be on the front or back to produce the most thrust and the best hydrodynamcics?</p>
| 9,382 |
[
-0.023065514862537384,
-0.05094826593995094,
-0.010307717137038708,
-0.00903354398906231,
0.0349077545106411,
-0.0006228476413525641,
0.001180615508928895,
0.006623209919780493,
0.03816166892647743,
-0.046815868467092514,
-0.013904571533203125,
0.0846073180437088,
0.01607854664325714,
0.011696895584464073,
0.023169901221990585,
-0.014340073801577091,
-0.001260847318917513,
-0.020661968737840652,
0.028410930186510086,
0.024094007909297943,
-0.009160356596112251,
-0.024336066097021103,
0.0239834226667881,
-0.02856961265206337,
0.012747041881084442,
0.001859932322986424,
0.0032819954212754965,
-0.02173544280230999,
0.03846346214413643,
0.026204008609056473,
-0.013739338144659996,
-0.06200749799609184,
0.029725799337029457,
0.019986089318990707,
0.023701904341578484,
0.013053303584456444,
-0.00412293104454875,
-0.008364587090909481,
-0.05584806576371193,
0.008001566864550114,
0.03540462255477905,
-0.0032760414760559797,
-0.027952522039413452,
0.041655536741018295,
-0.0016588608268648386,
0.04546884074807167,
-0.020968766883015633,
-0.06644506752490997,
0.04972260445356369,
-0.08500061184167862,
0.031223034486174583,
0.001553105772472918,
0.022846145555377007,
0.03839121386408806,
0.03720850497484207,
0.019617583602666855,
0.05338495969772339,
0.053139567375183105,
-0.04214518144726753,
-0.021372051909565926,
0.07378283143043518,
0.012221543118357658,
0.006386778317391872,
-0.022349132224917412,
-0.02285245805978775,
0.014428889378905296,
-0.012092738412320614,
-0.03892441838979721,
0.03676208108663559,
-0.012617222033441067,
0.015454608015716076,
-0.020397737622261047,
0.03816743195056915,
0.013492483645677567,
0.043702561408281326,
-0.020008986815810204,
-0.00034369787317700684,
0.03491358831524849,
0.008895106613636017,
0.0533621646463871,
-0.003886906895786524,
0.040732234716415405,
0.016453439369797707,
0.05118986964225769,
-0.02363976463675499,
0.0008401623927056789,
0.04036346822977066,
-0.016985267400741577,
0.024514533579349518,
0.01097346842288971,
-0.006163261830806732,
-0.025473473593592644,
0.055048778653144836,
-0.01372168306261301,
-0.013424166478216648,
0.006822685711085796,
0.01796169951558113,
0.014519093558192253,
-0.00018290645675733685,
-0.07631289958953857,
0.0019655742216855288,
0.006239940412342548,
-0.018032945692539215,
0.08515225350856781,
0.02750137448310852,
-0.004898130893707275,
-0.018086496740579605,
0.040740322321653366,
-0.04701387882232666,
-0.005978686735033989,
-0.015840422362089157,
0.005351503845304251,
-0.026257827877998352,
0.00003571134220692329,
-0.013553936034440994,
-0.03968282788991928,
0.029032088816165924,
-0.007304980885237455,
0.006579085253179073,
0.06539498269557953,
0.01177979726344347,
-0.012957562692463398,
0.018218185752630234,
-0.03153461962938309,
-0.05618177354335785,
0.06248743459582329,
0.05561462417244911,
-0.004552873317152262,
-0.023398984223604202,
-0.012724827043712139,
-0.007976466789841652,
0.03311464563012123,
0.01716545969247818,
-0.009114337153732777,
0.026575714349746704,
-0.016921738162636757,
-0.10068631917238235,
-0.06205982714891434,
0.03215404227375984,
0.003685998497530818,
0.005459915846586227,
-0.06454876065254211,
0.038924504071474075,
0.009197586216032505,
0.04930239915847778,
-0.029567351564764977,
0.02878103218972683,
-0.014492769725620747,
0.025529878214001656,
-0.024957772344350815,
-0.05715157091617584,
-0.0002724437217693776,
0.00021286298579070717,
-0.04730681702494621,
-0.01328582689166069,
-0.05208148434758186,
-0.008132323622703552,
-0.00033662814530543983,
0.03579047694802284,
-0.05301225557923317,
0.006867234129458666,
-0.05593736842274666,
0.01499306783080101,
-0.020845605060458183,
0.0015705396654084325,
-0.05352184548974037,
0.06441666185855865,
0.017397034913301468,
0.0030586521606892347,
0.014364566653966904,
-0.021339723840355873,
-0.03259468451142311,
0.024246837943792343,
-0.008407004177570343,
0.05440104752779007,
-0.0421842522919178,
0.034441228955984116,
-0.030926181003451347,
0.01251451950520277,
-0.004917673766613007,
-0.06659810990095139,
-0.023780908435583115,
-0.019586870446801186,
0.01201599184423685,
-0.0013306487817317247,
0.04842817038297653,
-0.002470435807481408,
-0.007996778935194016,
0.013472255319356918,
-0.02899240329861641,
-0.012854465283453465,
0.01571815460920334,
0.020983071997761726,
-0.024071360006928444,
-0.022119155153632164,
0.020495546981692314,
-0.006073924247175455,
0.027456367388367653,
-0.015103347599506378,
-0.023414067924022675,
-0.043929070234298706,
0.006261784117668867,
0.01511534396559,
-0.0022375660482794046,
0.031048523262143135,
0.041350580751895905,
-0.027033869177103043,
-0.030886458232998848,
0.005427430849522352,
0.004372679628431797,
-0.023383915424346924,
-0.021686241030693054,
-0.017988255247473717,
-0.015486154705286026,
-0.0027929458301514387,
-0.001551657565869391,
0.04821035638451576,
0.027731982991099358,
0.017235761508345604,
-0.006418696604669094,
-0.04459938779473305,
0.08220775425434113,
0.050073593854904175,
-0.0037432187236845493,
0.027896178886294365,
-0.015885004773736,
-0.009627350606024265,
0.008830059319734573,
0.03351415693759918,
0.02085144631564617,
-0.04092388600111008,
0.015277966856956482,
0.04434223845601082,
-0.0025312979705631733,
-0.02881607413291931,
-0.019942382350564003,
0.03427755460143089,
0.002944732317700982,
0.06374308466911316,
0.005712809041142464,
-0.03750920668244362,
-0.036793578416109085,
0.007891196757555008,
0.07892557233572006,
0.002030630363151431,
0.008077847771346569,
0.05414578318595886,
0.024920562282204628,
0.011804236099123955,
0.002734625246375799,
-0.03191538155078888,
0.043865155428647995,
0.0277646966278553,
-0.024736860767006874,
0.0013444467913359404,
-0.0010530868312343955,
0.04476580768823624,
-0.047450270503759384,
0.0017281585605815053,
0.024219658225774765,
0.031518157571554184,
-0.03514672815799713,
-0.03017747588455677,
0.006632496137171984,
-0.0016609851736575365,
0.033931292593479156,
0.0017385222017765045,
-0.009109359234571457,
0.05689056217670441,
-0.01591101661324501,
-0.015410460531711578,
-0.02028384618461132,
-0.004141669254750013,
-0.019489377737045288,
-0.019705960527062416,
0.0428726002573967,
-0.03466527536511421,
0.024939559400081635,
0.043501585721969604,
0.024340778589248657,
-0.009469380602240562,
0.007224446162581444,
0.023571547120809555,
-0.015232570469379425,
-0.07608864456415176,
0.00412732781842351,
-0.038439154624938965,
-0.013121787458658218,
0.0816720500588417,
-0.01924310438334942,
-0.030802210792899132,
0.03850484639406204,
-0.010405187495052814,
-0.012575231492519379,
0.00013075448805466294,
-0.006890606135129929,
0.04496099427342415,
-0.007346279453486204,
0.006388033274561167,
0.007116073742508888,
0.00981842540204525,
-0.04669574648141861,
0.007071211002767086,
-0.04561871290206909,
-0.007744545117020607,
-0.0040217614732682705,
-0.02474992908537388,
0.024703945964574814,
-0.011665319092571735,
0.003322852775454521,
0.006319075357168913,
0.008158056996762753,
0.022882582619786263,
-0.011779415421187878,
-0.030279098078608513,
0.02483036369085312,
-0.03272219002246857,
0.03749049827456474,
-0.03873419389128685,
-0.03427724912762642,
0.03825715556740761,
0.002490726998075843,
-0.0741015151143074,
-0.031877338886260986,
0.023577937856316566,
-0.001843905309215188,
-0.04211917519569397,
0.0287163183093071,
0.04935487359762192,
0.004150496795773506,
0.01051720418035984,
0.03282157704234123,
0.023287896066904068,
0.03219909593462944,
-0.003544226521626115,
0.022679708898067474,
-0.023568622767925262,
0.02870597317814827,
-0.02092871069908142,
0.026717534288764,
0.06722136586904526,
-0.026826247572898865,
0.026331264525651932,
-0.028124414384365082,
0.024280382320284843,
0.01891452632844448,
-0.04058150574564934,
0.03147416561841965,
-0.00720600038766861,
0.022119518369436264,
0.02772548422217369,
-0.01842411607503891,
-0.03382961452007294,
-0.0053708855994045734,
-0.03126109763979912,
0.033762767910957336,
0.009489678777754307,
-0.048374149948358536,
0.007196191232651472,
0.018715525045990944,
0.04361027106642723,
0.014378231950104237,
-0.020927956327795982,
-0.06787886470556259,
0.0007121317321434617,
0.016312865540385246,
0.0272805355489254,
-0.021216750144958496,
0.010851559229195118,
0.03925478458404541,
0.0493360310792923,
-0.005822132341563702,
0.0028287675231695175,
0.03817170113325119,
-0.07219326496124268,
-0.02435513772070408,
-0.010952934622764587,
0.051958777010440826,
0.008944611996412277,
0.06749171018600464,
0.005712323822081089,
0.03763994574546814,
-0.008845344185829163,
0.007389840204268694,
-0.08853194862604141,
0.012716288678348064,
-0.015081722289323807,
0.010373282246291637,
-0.02104038931429386,
-0.022124674171209335,
-0.008141142316162586,
-0.06458719819784164,
-0.031378328800201416,
0.050414420664310455,
-0.0009864794556051493,
-0.06065617874264717,
0.0568348653614521,
-0.019035600125789642,
-0.0035443296656012535,
0.014015509746968746,
0.0490800216794014,
0.023262450471520424,
-0.03213537856936455,
0.08255728334188461,
0.006013438105583191,
-0.03621719032526016,
0.00637794379144907,
-0.007862802594900131,
0.05037863552570343,
-0.02128487266600132,
0.06502751260995865,
0.030238788574934006,
0.018714478239417076,
0.010416277684271336,
0.005533585790544748,
0.01401586551219225,
0.023421762511134148,
-0.041485391557216644,
-0.0459943525493145,
-0.04348259046673775,
-0.0435154102742672,
0.018199989572167397,
0.010470089502632618,
0.020652510225772858,
0.04970209300518036,
-0.0016294207889586687,
-0.005766036920249462,
-0.018465865403413773,
-0.018640698865056038,
0.009534002281725407,
0.026515169069170952,
0.00924684014171362,
-0.016940321773290634,
-0.04487922415137291,
0.004613109398633242,
0.01554952934384346,
-0.01366177573800087,
0.02828993648290634,
0.0432317890226841,
-0.04726178199052811,
-0.017438897863030434,
0.023169375956058502,
-0.03181537240743637,
-0.023226071149110794,
0.00947808101773262,
0.000131372464238666,
0.018144724890589714,
-0.07348379492759705,
0.03364073857665062,
-0.04212644696235657,
0.019794706255197525,
0.021391861140727997,
0.010428708977997303,
-0.01652606949210167,
-0.06887639313936234,
0.011075284332036972,
0.031293485313653946,
0.0024640820920467377,
-0.06655508279800415,
0.0052237254567444324,
-0.03207410126924515,
-0.053825847804546356,
0.07138533145189285,
-0.014704536646604538,
0.011345172300934792,
-0.026791857555508614,
-0.035994842648506165,
-0.012747482396662235,
0.026726383715867996,
-0.005470416508615017,
0.014395145699381828,
-0.005448652897030115,
0.06915070861577988,
-0.02341955341398716,
0.004285546485334635,
0.0030482218135148287,
0.04985605180263519,
0.015921635553240776,
0.04419846832752228,
-0.0033779738005250692,
-0.03933073952794075,
-0.025562090799212456,
0.0501679889857769,
-0.04500789940357208,
-0.029378138482570648,
-0.0035890156868845224,
0.009684784337878227,
-0.04019397124648094,
0.020547404885292053,
0.003737501800060272,
-0.052450940012931824,
0.035483021289110184,
0.034286320209503174,
-0.039604827761650085,
0.03332015126943588,
-0.03050760179758072,
-0.01849365048110485,
0.0006694856565445662,
0.0190637968480587,
0.022805312648415565,
0.04991094768047333,
-0.013629209250211716,
-0.034508489072322845,
-0.0035912059247493744,
0.04903535172343254,
0.023942474275827408,
-0.055052388459444046,
-0.0020395463798195124,
-0.009935714304447174,
-0.05881261080503464,
0.01374176237732172,
-0.0369843989610672,
0.015379779040813446,
0.0016199513338506222,
-0.014829915016889572,
0.007853390648961067,
0.06007062643766403,
0.02673536352813244,
-0.053170543164014816,
0.012984632514417171,
0.03383467718958855,
0.02565930224955082,
-0.02332214079797268,
-0.01966516301035881,
-0.005656917113810778,
0.01983027160167694,
0.04343654587864876,
-0.03827371075749397,
-0.001870900159701705,
-0.025720389559864998,
-0.007733190897852182,
0.02239292487502098,
-0.0214881282299757,
0.06721595674753189,
-0.0034113379660993814,
0.007867417298257351,
0.032642662525177,
-0.08786225318908691,
0.023272156715393066,
-0.0028271235059946775,
0.009985079988837242,
0.011159959249198437,
-0.0683559700846672,
0.03544268012046814,
0.015065687708556652,
0.0008402913808822632,
-0.034162718802690506,
-0.005996025167405605,
0.03555586189031601,
0.02376702055335045,
-0.02804923988878727,
-0.024240871891379356,
0.027981290593743324,
-0.04780184477567673,
-0.03472251445055008,
-0.02491200715303421,
0.04318126291036606,
-0.034386515617370605,
-0.0061945016495883465,
0.03407543897628784,
-0.018209878355264664,
0.03976590186357498,
0.0446937270462513,
-0.0035902499221265316,
0.014715895056724548,
-0.04500862583518028,
0.02106264978647232,
-0.03808337077498436,
0.046257201582193375,
-0.014412051998078823,
-0.007692572195082903,
-0.012163392268121243,
-0.03649866208434105,
0.05116533488035202,
-0.007809200324118137,
0.06943977624177933,
0.02395438961684704,
-0.0012211395660415292,
-0.012814589776098728,
-0.03294098749756813,
-0.015527434647083282,
-0.010234363377094269,
0.009124868549406528,
0.0039519802667200565,
0.005976936314254999,
-0.017441576346755028,
-0.053862929344177246,
0.010185384191572666,
-0.011995727196335793,
0.025562750175595284,
0.007957960478961468,
0.050433360040187836,
-0.042955923825502396,
-0.025821799412369728,
0.0048685683868825436,
-0.042469631880521774,
0.013305649161338806,
0.03084436245262623,
0.02639700472354889,
-0.0023930645547807217,
0.05409379303455353,
0.004505741409957409,
-0.005722898058593273,
-0.03581366315484047,
0.03594032675027847,
0.07390286773443222,
-0.024380220100283623,
0.0211210735142231,
0.02460658922791481,
0.03580772504210472,
-0.001819771365262568,
-0.020429441705346107,
-0.049361761659383774,
-0.008484750054776669,
-0.013692344538867474,
0.10199569165706635,
-0.029952723532915115,
0.00739535316824913,
-0.007587834727019072,
0.03627520799636841,
0.00920545682311058,
0.04221493378281593,
0.005984378978610039,
0.006346812006086111,
0.004626892972737551,
-0.006775233428925276,
-0.004797846078872681,
0.01643243618309498,
-0.03543863072991371,
0.05660196766257286,
-0.028129959478974342,
0.01568666659295559,
0.011870062910020351,
0.00030376960057765245,
0.034081630408763885,
-0.0604202002286911,
-0.0048744515515863895,
-0.01088222861289978,
0.05265893042087555,
0.013816332444548607,
-0.0007581276004202664,
-0.02520778961479664,
0.0360533781349659,
0.03450533002614975,
-0.002729512518271804,
0.03461099788546562,
-0.05269167572259903,
-0.05582631751894951,
-0.0010908299591392279,
0.0030896218959242105,
-0.02576518803834915,
0.04768145829439163,
0.023676175624132156,
0.02106475830078125,
0.005884654354304075,
-0.009460953064262867,
-0.013157563284039497,
-0.0035864561796188354,
0.018200809136033058,
0.009842666797339916,
0.08465410768985748,
-0.016122562810778618,
0.022736167535185814,
-0.03937680274248123,
0.0011904522543773055,
0.13659816980361938,
0.007351520471274853,
0.04251487925648689,
-0.039002519100904465,
0.0014608372002840042,
-0.036006271839141846,
-0.022349536418914795,
-0.022210262715816498,
0.045401252806186676,
0.01245077047497034,
0.018069732934236526,
0.05258673056960106,
0.02279515005648136,
0.030546411871910095,
-0.006360306870192289,
-0.006531308870762587,
-0.03852522373199463,
-0.034540675580501556,
0.01314437948167324,
0.0019355284748598933,
-0.0174546018242836,
0.0360293909907341,
-0.014595813117921352,
0.024122867733240128,
-0.00050140026723966,
-0.01497451588511467,
0.010737255215644836,
-0.009845503605902195,
0.05272386595606804,
-0.011453165672719479,
-0.008138778619468212,
0.008198123425245285,
-0.011565947905182838,
0.007951254956424236,
-0.036443132907152176,
-0.018078971654176712,
-0.02625301294028759,
-0.030914075672626495,
-0.03258133679628372,
-0.03096611797809601,
0.04074278846383095,
0.026585733518004417,
-0.00486819026991725,
0.019320938736200333,
-0.035306256264448166,
-0.018442895263433456,
-0.03173962980508804,
-0.002145581878721714,
0.01240400318056345,
0.007898285984992981,
-0.05520423874258995,
0.048381902277469635,
0.05369022116065025,
-0.04489469155669212,
-0.05623145028948784,
-0.0007737062405794859,
0.061720412224531174,
0.0027702089864760637,
-0.0574711337685585,
0.04077151417732239,
0.01710026152431965,
0.010320517234504223,
0.007532333955168724,
-0.0183581355959177,
0.019094344228506088,
-0.019557107239961624,
-0.0200650617480278,
0.05877924710512161,
-0.0021828862372785807,
-0.03729997202754021,
-0.027102775871753693,
0.012355131097137928,
-0.05047115311026573,
-0.005336195696145296,
0.012136523611843586,
-0.0009305846760980785,
-0.012914186343550682,
-0.009856076911091805,
-0.0046194447204470634,
0.018584324046969414,
-0.014761277474462986,
0.05504433438181877,
-0.026627764105796814,
-0.009434515610337257,
-0.019182588905096054,
0.00821949727833271,
0.009501565247774124,
0.008464967831969261,
-0.01651836931705475,
-0.013141779229044914,
-0.01567412167787552,
0.05880123749375343,
-0.01210545189678669,
-0.027940241619944572,
-0.03720283880829811,
-0.013828938826918602,
-0.022050516679883003,
-0.006008523516356945,
0.0012923384783789515,
0.007078867871314287,
0.04328354820609093,
-0.013031153939664364,
-0.0021592245902866125,
0.01494440995156765,
-0.026356928050518036,
0.005664179567247629,
0.033860281109809875,
-0.04040248319506645,
0.006023678928613663,
-0.02618206851184368,
-0.020311210304498672,
-0.0798310711979866,
-0.03028547205030918,
-0.010205293074250221,
-0.01698508858680725,
-0.05512271821498871,
0.003765174886211753,
-0.010798852890729904,
0.02584606409072876,
-0.027492819353938103,
0.023474320769309998,
-0.031068162992596626,
0.0028665733989328146,
-0.03827495500445366,
0.01457639504224062,
-0.001611898303963244,
0.024683015421032906,
-0.014094870537519455,
0.00745311239734292,
-0.02739371731877327,
-0.0323592871427536,
-0.02454891987144947,
-0.024674253538250923,
0.008267265744507313,
-0.00028550231945700943,
0.026875128969550133,
0.018527409061789513,
0.050679903477430344,
-0.007908995263278484,
-0.008047341369092464,
-0.011515423655509949,
-0.05018625408411026,
-0.022246425971388817,
0.022922037169337273,
-0.035271476954221725,
0.0193845946341753,
-0.0188906230032444,
0.01497158594429493,
0.005449402146041393,
0.06275644898414612,
0.010180773213505745,
0.006730271503329277,
-0.022757599130272865,
-0.027585767209529877,
0.003299181815236807,
-0.02704419195652008,
0.029164576902985573,
-0.01459645014256239,
-0.007994809187948704,
0.037964388728141785,
-0.020734179764986038,
0.0054091173224151134,
0.013322427868843079,
0.015503513626754284,
0.010209535248577595,
0.01843082904815674,
-0.014874398708343506,
-0.027947355061769485,
0.0380876362323761,
0.012370309792459011,
-0.004018189385533333,
0.008569122292101383,
-0.018769431859254837,
-0.009635329246520996,
-0.05394900590181351,
0.008445053361356258,
-0.00939397606998682,
0.00044136462383903563,
0.01326770894229412,
-0.034131333231925964,
0.013831943273544312,
0.06508253514766693,
-0.05860915035009384,
-0.0032188002951443195,
-0.027488626539707184,
0.01342268567532301,
-0.06587579101324081,
0.0304582379758358,
0.006856138817965984,
0.01615309715270996,
-0.02901231124997139,
-0.011168713681399822,
0.042488329112529755,
0.024326300248503685,
-0.04322018101811409,
-0.03471263125538826,
-0.007423767354339361,
0.044890522956848145,
-0.02341333217918873,
-0.006271948106586933,
0.035531096160411835,
-0.03549668937921524,
-0.005601508542895317,
0.03141816705465317,
0.009260043501853943,
0.073273204267025,
-0.0008811121806502342,
0.003146905219182372,
-0.018313774839043617,
0.0022484762594103813,
0.022444255650043488,
0.027525098994374275,
-0.015857310965657234,
0.009208201430737972,
0.017913082614541054,
0.02264849655330181,
0.03488381206989288,
0.04254813864827156,
0.024773532524704933,
-0.024975862354040146,
-0.04614919796586037,
0.0034575064200907946,
-0.036329880356788635,
-0.007860475219786167,
0.01642168127000332,
-0.05007251724600792,
0.028450993821024895,
0.006405988708138466,
-0.015336655080318451,
-0.036228351294994354,
0.013058092445135117,
0.00506108021363616,
-0.02419533208012581,
0.03667463734745979,
0.030472036451101303,
-0.009026146493852139,
-0.04092798009514809,
-0.04953019320964813,
-0.016619322821497917,
-0.012684124521911144,
-0.013283406384289265,
0.016835782676935196,
-0.002023079665377736,
0.018846124410629272,
-0.020588679239153862,
-0.018369171768426895,
0.009860825724899769,
0.05291939526796341,
0.023358890786767006,
0.030619051307439804,
0.0404483936727047,
-0.0017952073831111193,
-0.029043862596154213,
-0.05586209148168564,
0.051184654235839844,
0.0015998880844563246,
-0.003291441360488534,
-0.020941216498613358,
-0.02883264422416687,
0.06001612916588783,
0.036014195531606674,
0.028510496020317078,
-0.04567499831318855,
0.02939523570239544,
-0.026436015963554382,
0.0324137918651104,
-0.014043658971786499,
0.03272462636232376,
0.00749929016456008,
-0.004974435083568096,
-0.04480209946632385,
-0.0059846495278179646,
-0.004805493168532848,
0.022694794461131096,
-0.00510491942986846,
0.03825375810265541,
0.00982196256518364,
0.0400184690952301,
-0.026098160073161125,
-0.03909948095679283,
-0.01651342213153839,
0.007022254168987274,
-0.032212480902671814,
0.06263776123523712,
-0.03422510251402855,
-0.028312476351857185,
-0.04757305979728699,
-0.03257152438163757,
-0.027020299807190895,
0.0055079953745007515,
-0.01734420843422413,
0.023190174251794815,
-0.03410402312874794,
-0.009013764560222626,
0.049795571714639664,
-0.01958637498319149,
0.004380051977932453,
-0.00022833122056908906,
-0.049564849585294724,
-0.01694955863058567,
0.0381251722574234,
0.011150943115353584,
0.005161594599485397,
-0.04759427160024643,
-0.0036659028846770525,
0.02256530337035656,
-0.03631484881043434,
0.007886165753006935,
0.050473254173994064,
0.048480600118637085,
0.05409475043416023,
-0.009285872802138329,
0.029393484815955162,
-0.00927846971899271,
0.05657943710684776,
-0.021129446104168892,
0.048441145569086075,
0.01777704246342182,
-0.020899547263979912,
0.017294667661190033,
-0.015340439975261688,
-0.05481918901205063,
-0.013557014986872673,
-0.025503966957330704,
0.05631928890943527,
-0.0017612878000363708,
-0.009280909784138203,
-0.024342715740203857,
-0.02186533249914646,
-0.029131677001714706,
0.014680888503789902,
-0.025550950318574905,
0.0060998015105724335,
0.0006389986956492066,
-0.035921361297369,
0.0063086519949138165,
0.026451943442225456,
0.04791027680039406,
0.024510487914085388,
0.023204747587442398,
-0.01626313291490078,
0.041655395179986954,
-0.04247944429516792,
-0.015868786722421646,
-0.02225581742823124,
-0.01443447545170784,
-0.010624377056956291,
0.0027441023848950863,
-0.013628671877086163,
0.04998313635587692,
-0.03555001690983772,
-0.030891424044966698,
0.04619228094816208,
-0.05182290077209473,
-0.027316605672240257,
0.004420374520123005,
0.034051768481731415,
0.001790524460375309,
0.02581632509827614
] |
<p>I'm a bit confused with some notation I encounter in physics calculus. Consider this:
<img src="http://i.stack.imgur.com/rAssQ.png" alt="enter image description here"></p>
<p>Taken from <a href="http://en.wikipedia.org/wiki/Impulse_(physics)" rel="nofollow">here</a>.
Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf p}}{dt} dt$? Could someone point me to some reading about the manipulation of Leibniz notation?</p>
| 9,383 |
[
0.024632731452584267,
-0.004733480978757143,
-0.04057442024350166,
-0.03988321125507355,
0.05405867472290993,
0.020874688401818275,
-0.006314590107649565,
-0.014265671372413635,
0.006818420719355345,
-0.02066400833427906,
0.02652093954384327,
0.019890282303094864,
0.051591333001852036,
0.004133037757128477,
0.026984790340065956,
0.01216261275112629,
-0.035494472831487656,
-0.01687971130013466,
0.012678176164627075,
-0.03768228366971016,
-0.006522764917463064,
0.00282386620528996,
0.025787867605686188,
-0.0028588916175067425,
-0.011426015757024288,
0.020134687423706055,
-0.004561072681099176,
-0.009328325279057026,
-0.0007940171635709703,
0.03435473516583443,
0.003124393755570054,
-0.019175535067915916,
0.029906628653407097,
-0.00006991792906774208,
-0.011396609246730804,
0.007874172180891037,
-0.018919609487056732,
-0.038361843675374985,
-0.0054460312239825726,
0.002529324032366276,
-0.013645459897816181,
-0.01333285216242075,
0.021198010072112083,
0.058562010526657104,
-0.015201586298644543,
0.01649397984147072,
0.02709256112575531,
-0.014186564832925797,
0.06665223091840744,
-0.06441369652748108,
0.05846257880330086,
0.02857590839266777,
0.05543887987732887,
0.03137583285570145,
-0.004582751542329788,
0.028276169672608376,
0.07471856474876404,
0.08277486264705658,
-0.050047822296619415,
-0.07446260005235672,
-0.03218476101756096,
-0.04880760237574577,
0.011483097448945045,
-0.017905252054333687,
-0.026079470291733742,
0.026630833745002747,
-0.0005527226603589952,
-0.06524866074323654,
0.0073298257775604725,
-0.00999023113399744,
0.013798311352729797,
0.020674273371696472,
0.03758382424712181,
-0.05515380948781967,
0.01702120713889599,
-0.014095833525061607,
0.05414063483476639,
-0.01739495061337948,
0.03472547233104706,
0.04767873138189316,
-0.005060440395027399,
-0.004607804119586945,
0.020427927374839783,
0.032712697982788086,
0.043756209313869476,
-0.02726314216852188,
0.06655624508857727,
-0.0025263396091759205,
0.048602256923913956,
-0.017025738954544067,
-0.054033614695072174,
0.035557907074689865,
-0.011727451346814632,
0.0032358611933887005,
-0.02159591019153595,
0.030427007004618645,
0.018148742616176605,
0.02431599050760269,
-0.010467665269970894,
-0.040305644273757935,
0.00021970990928821266,
-0.05487119033932686,
-0.0073574017733335495,
0.06043394282460213,
0.020851140841841698,
-0.010104449465870857,
-0.03932737931609154,
0.044882066547870636,
0.01006668247282505,
-0.010887814685702324,
-0.03695525974035263,
0.03450332581996918,
0.0044243307784199715,
0.01867341622710228,
-0.013572762720286846,
-0.007309134118258953,
-0.008181160315871239,
0.01954508014023304,
0.017446618527173996,
0.02472294308245182,
0.06623055785894394,
-0.03260241076350212,
0.05499204993247986,
0.008466195315122604,
-0.0741892084479332,
0.03159842640161514,
0.007557937875390053,
0.02518167532980442,
-0.016802001744508743,
0.022015582770109177,
0.004544621799141169,
-0.03513779491186142,
0.02299520932137966,
0.03778652846813202,
0.018527034670114517,
-0.04749879986047745,
-0.04530211165547371,
-0.04870779812335968,
0.02519097551703453,
0.0091690793633461,
-0.012215088121592999,
-0.07558199018239975,
0.016189640387892723,
0.004360346123576164,
0.06429800391197205,
0.016327213495969772,
-0.008057075552642345,
0.002943324623629451,
0.017627526074647903,
0.005687232129275799,
-0.01080259121954441,
-0.025879740715026855,
0.0070105139166116714,
-0.022533150389790535,
0.046077314764261246,
-0.0546623133122921,
0.03060978092253208,
0.04201476648449898,
0.0010867633391171694,
-0.030906690284609795,
0.079743891954422,
-0.028537912294268608,
-0.017740614712238312,
0.02710089460015297,
0.0005224630003795028,
0.005793668795377016,
0.09003175050020218,
0.029158515855669975,
0.016451150178909302,
0.030949536710977554,
0.04205719381570816,
0.023821983486413956,
-0.009834494441747665,
0.06501560658216476,
0.050140075385570526,
-0.018407095223665237,
-0.030649656429886818,
0.015054414980113506,
0.026974981650710106,
-0.010760192759335041,
-0.02771122381091118,
-0.045069269835948944,
-0.005004652310162783,
0.006411505863070488,
-0.01856507547199726,
0.04020656645298004,
0.025122210383415222,
0.01813417859375477,
-0.021424995735287666,
-0.03769384324550629,
-0.033189088106155396,
-0.07533291727304459,
0.04286189377307892,
-0.043126076459884644,
0.018244503065943718,
0.02504768595099449,
0.011939159594476223,
0.00027925841277465224,
-0.030932800844311714,
0.012598244473338127,
-0.0029085574205964804,
0.008698366582393646,
0.006531562190502882,
-0.025395270437002182,
0.003675064304843545,
0.040472809225320816,
0.039763692766427994,
0.009055192582309246,
-0.0011141010327264667,
-0.040230970829725266,
0.012456491589546204,
0.0162206944078207,
-0.05477168783545494,
0.014721830375492573,
-0.010430599562823772,
-0.011579122394323349,
0.015977809205651283,
-0.024191638454794884,
0.01634204387664795,
0.03307579085230827,
-0.04465460404753685,
0.05153368040919304,
0.03922457620501518,
0.03817913308739662,
-0.001840451150201261,
0.04719717800617218,
0.006155944894999266,
0.036148011684417725,
0.02498074434697628,
-0.049867838621139526,
-0.008740842342376709,
0.010725844651460648,
0.028590494766831398,
0.024033432826399803,
-0.02875717729330063,
-0.0003263665421400219,
0.03282133489847183,
-0.004716269206255674,
0.036441780626773834,
0.03024834394454956,
0.004919088911265135,
-0.024408908560872078,
0.0026004936080425978,
0.01022004708647728,
0.0318414643406868,
0.0007747843628749251,
0.002068851375952363,
0.018906962126493454,
0.04464258626103401,
0.01064024306833744,
-0.003906942438334227,
0.030834633857011795,
-0.01753278449177742,
0.048187006264925,
0.03363009914755821,
-0.00522248400375247,
0.035876624286174774,
-0.016942573711276054,
0.01666725054383278,
0.00743177579715848,
0.0027246293611824512,
-0.0066887387074530125,
-0.02566494233906269,
-0.01645042560994625,
0.0012872627703472972,
-0.009677514433860779,
-0.02833559364080429,
-0.06564877182245255,
0.02213200367987156,
-0.03684994950890541,
0.032389599829912186,
-0.01579175889492035,
-0.023859862238168716,
-0.04053924232721329,
-0.010080275125801563,
0.02171369455754757,
0.043625958263874054,
0.02064894512295723,
-0.03747531399130821,
-0.04640879109501839,
-0.004190140403807163,
-0.027926282957196236,
0.008075125515460968,
-0.013597514480352402,
-0.06773174554109573,
0.028436800464987755,
-0.032915569841861725,
-0.011601371690630913,
0.06615391373634338,
-0.02750273607671261,
0.011324288323521614,
0.011653455905616283,
-0.021559519693255424,
-0.06421677768230438,
-0.0323086678981781,
0.015455920249223709,
0.02517743967473507,
-0.014713822863996029,
-0.01854007877409458,
0.037403006106615067,
-0.017496932297945023,
-0.0026394929736852646,
0.031083475798368454,
-0.04845363274216652,
-0.047527946531772614,
-0.032495975494384766,
0.004050343297421932,
0.038851890712976456,
-0.013514227233827114,
0.006741534918546677,
0.0012189851840958,
-0.04474664106965065,
-0.0019117551855742931,
-0.06915773451328278,
-0.05561456084251404,
-0.01691562682390213,
0.004551524296402931,
0.031723782420158386,
0.00032764425850473344,
-0.05779401212930679,
0.05001821368932724,
0.01705251634120941,
-0.039072491228580475,
-0.022623758763074875,
0.004461328033357859,
0.0010846055811271071,
-0.03788496553897858,
-0.00410014484077692,
0.048047278076410294,
-0.035846367478370667,
0.03757379204034805,
0.011729015037417412,
0.030655814334750175,
0.034535832703113556,
-0.0031830209773033857,
0.02532680705189705,
-0.016509654000401497,
-0.004984395578503609,
-0.011410933919250965,
0.03120242804288864,
0.04742230847477913,
-0.023622116073966026,
0.032085616141557693,
-0.029758209362626076,
0.04473472386598587,
0.04058867692947388,
-0.019497253000736237,
0.06529796868562698,
0.021203501150012016,
-0.03677395358681679,
-0.013871479779481888,
0.013878696598112583,
-0.0016802821774035692,
-0.012378179468214512,
0.009159382432699203,
0.004029573407024145,
0.022132636979222298,
-0.047158949077129364,
0.023688610643148422,
0.017061153426766396,
0.003219352336600423,
-0.05460432171821594,
-0.029485557228326797,
0.02785598672926426,
0.01785753294825554,
0.04567284509539604,
0.01012108288705349,
0.00010471598943695426,
0.022877085953950882,
0.011972415260970592,
0.045030269771814346,
0.0030620256438851357,
-0.030631233006715775,
0.021778393536806107,
-0.03042859397828579,
0.01332671009004116,
0.02345641329884529,
0.04645245894789696,
-0.00036042480496689677,
0.08012937009334564,
0.039735063910484314,
0.0342283770442009,
0.05297263711690903,
0.0040566097013652325,
-0.08499672263860703,
0.04874188452959061,
-0.013600911945104599,
-0.035506706684827805,
-0.07332231849431992,
-0.0048718927428126335,
0.005812979303300381,
-0.027506953105330467,
-0.018129346892237663,
-0.0020827113185077906,
-0.020915962755680084,
-0.06931344419717789,
0.002157755196094513,
-0.0442240908741951,
-0.030191317200660706,
-0.02260735258460045,
0.015692759305238724,
0.031200416386127472,
-0.03060397319495678,
-0.017294056713581085,
0.0717177465558052,
0.002519028726965189,
-0.020030004903674126,
-0.021127529442310333,
-0.009199985302984715,
0.03462870419025421,
0.041983965784311295,
0.01576046645641327,
0.01890082284808159,
-0.013449130579829216,
0.04972277581691742,
0.0042734770104289055,
0.08379174023866653,
0.02855173870921135,
-0.04821449890732765,
-0.055540312081575394,
-0.04507051035761833,
0.029053853824734688,
-0.030696926638484,
0.04900170862674713,
0.017448604106903076,
-0.007013999857008457,
0.037792086601257324,
-0.011071911081671715,
0.022164037451148033,
0.01907356083393097,
0.022392844781279564,
-0.012389615178108215,
-0.01933649182319641,
-0.0651964321732521,
-0.008123328909277916,
-0.025276152417063713,
-0.014861180447041988,
-0.006707420572638512,
0.029276832938194275,
-0.00707141263410449,
0.030239755287766457,
0.01906185783445835,
-0.014242335222661495,
-0.014852548949420452,
-0.02481166087090969,
0.0027828391175717115,
0.001989819807931781,
0.008775822818279266,
-0.021375184878706932,
0.0087851257994771,
0.041506703943014145,
0.05035894736647606,
0.024954719468951225,
-0.01584349200129509,
-0.06457147747278214,
0.010228697210550308,
0.032687120139598846,
0.02935967594385147,
-0.02596091479063034,
-0.015363478101789951,
-0.04673287272453308,
-0.011708210222423077,
0.0691915899515152,
-0.024977466091513634,
-0.011357711628079414,
-0.04299871250987053,
0.01480952464044094,
-0.017200112342834473,
-0.0128563791513443,
0.0035301069729030132,
0.032114095985889435,
0.005733408499509096,
0.0024790908209979534,
-0.04859386384487152,
0.01781543530523777,
0.01022895984351635,
0.031332988291978836,
-0.0052161444909870625,
0.04281019791960716,
-0.006014897022396326,
0.00488007627427578,
-0.009157740511000156,
0.009237106889486313,
-0.05517071858048439,
-0.06121457368135452,
0.00431968504562974,
0.002381758065894246,
0.03350137919187546,
0.01968592405319214,
-0.05275676026940346,
-0.04399606212973595,
0.03640199080109596,
-0.035415031015872955,
0.008557209745049477,
0.039868686348199844,
-0.0310711320489645,
0.03800707310438156,
0.05271745100617409,
-0.002397569129243493,
0.04489313066005707,
0.0583387054502964,
-0.026842262595891953,
-0.010802905075252056,
-0.015332077629864216,
0.017897237092256546,
-0.028226390480995178,
-0.01954902708530426,
-0.03541422262787819,
-0.010687191970646381,
-0.06470619142055511,
0.02819032408297062,
-0.007746622432023287,
-0.01376334298402071,
-0.018381893634796143,
-0.02012074552476406,
-0.0092948442324996,
0.03151225671172142,
0.0006138207972981036,
0.01510290801525116,
-0.026713434606790543,
0.045567650347948074,
0.03109937161207199,
-0.02398930862545967,
-0.02289791963994503,
0.006002161186188459,
0.007334436755627394,
0.025810668244957924,
0.0029278649017214775,
0.03838888183236122,
-0.003225421765819192,
0.0023992974311113358,
0.06549637019634247,
-0.03814367204904556,
0.004732469562441111,
-0.002667065942659974,
-0.016717832535505295,
0.03424511477351189,
-0.052266545593738556,
-0.03995703533291817,
-0.015497605316340923,
-0.011280684731900692,
0.030323952436447144,
-0.11155319213867188,
0.038531020283699036,
-0.02449198067188263,
0.018846239894628525,
-0.03749283403158188,
-0.05394429713487625,
0.04989487677812576,
-0.01713537983596325,
-0.048813898116350174,
-0.02198784425854683,
0.00554075138643384,
0.00480730039998889,
-0.02272302471101284,
0.014712456613779068,
0.04126083478331566,
-0.01794867217540741,
-0.017344873398542404,
-0.0098402826115489,
-0.002361921826377511,
0.04795451462268829,
0.016927577555179596,
0.03563982993364334,
0.012979061342775822,
-0.011414874345064163,
-0.023028502240777016,
-0.0029025464318692684,
0.03574521839618683,
-0.00820932351052761,
0.021573444828391075,
-0.02952618896961212,
0.010413113981485367,
0.0043309577740728855,
-0.03124036081135273,
0.0026821282226592302,
0.018650133162736893,
0.025895630940794945,
-0.028199318796396255,
-0.002720029093325138,
0.004616513382643461,
0.002405645325779915,
-0.018019292503595352,
-0.011405057273805141,
0.020082829520106316,
-0.007570096291601658,
-0.038956090807914734,
0.005866379011422396,
-0.025720983743667603,
0.00881520938128233,
0.013250283896923065,
0.04915187507867813,
-0.014799490571022034,
0.02323101833462715,
0.03051084093749523,
0.00029952393379062414,
0.05694477632641792,
0.0056317332200706005,
-0.032893192023038864,
0.020381465554237366,
-0.025837667286396027,
-0.03614918142557144,
-0.010472978465259075,
-0.07330716401338577,
-0.007666707504540682,
0.040004655718803406,
-0.030661117285490036,
0.04170798882842064,
0.01875961385667324,
-0.004501470364630222,
0.027802439406514168,
-0.003388638375326991,
-0.02595372498035431,
0.023350197821855545,
-0.011388969607651234,
0.04103773087263107,
-0.03068690374493599,
-0.030236756429076195,
0.02116834744811058,
0.024256842210888863,
-0.03686295077204704,
0.0035339905880391598,
-0.01628296822309494,
0.017378684133291245,
-0.021240955218672752,
0.013876250013709068,
-0.04602626711130142,
0.04746520519256592,
-0.04378138855099678,
0.02404855750501156,
-0.032978106290102005,
-0.051908232271671295,
0.056142792105674744,
0.032594840973615646,
-0.015589929185807705,
-0.027708398178219795,
0.006336241029202938,
-0.03618178889155388,
-0.0019219297682866454,
0.048821594566106796,
0.023884668946266174,
0.02733680047094822,
-0.010289969854056835,
0.05293935909867287,
0.004712746478617191,
0.05065097659826279,
-0.002568773692473769,
-0.022912917658686638,
-0.038730185478925705,
-0.07816077768802643,
-0.039034225046634674,
0.05314524844288826,
-0.01310563925653696,
-0.0030403994023799896,
0.016471726819872856,
0.008273351937532425,
0.030726458877325058,
0.022962655872106552,
0.020567987114191055,
-0.01909962110221386,
0.09493167698383331,
-0.012514538131654263,
-0.007557621691375971,
-0.02606615237891674,
-0.030185099691152573,
0.10445783287286758,
0.03790697082877159,
-0.004797688219696283,
-0.040101367980241776,
-0.03196968510746956,
-0.030333664268255234,
0.01871546171605587,
-0.04453962668776512,
0.03112160414457321,
0.02549976110458374,
0.009525944478809834,
0.021682437509298325,
0.07501434534788132,
0.006316980812698603,
-0.007732005789875984,
0.04994109272956848,
-0.035930197685956955,
-0.02410048618912697,
0.009402553550899029,
0.03566201776266098,
0.010775499045848846,
0.015727486461400986,
-0.046178583055734634,
0.01368572935461998,
0.01046703476458788,
0.021148182451725006,
-0.02966945432126522,
-0.03828806430101395,
0.013500300236046314,
0.0017703635385259986,
-0.008365568704903126,
0.016494955867528915,
0.02278919890522957,
0.004821853246539831,
-0.02888202667236328,
0.01782660186290741,
0.022306619212031364,
-0.015007566660642624,
-0.006799773313105106,
0.04655395820736885,
0.044025175273418427,
-0.005430061370134354,
-0.002848981646820903,
0.024782218039035797,
-0.03544827178120613,
-0.028365259990096092,
-0.012891818769276142,
0.03560623899102211,
-0.015727823600172997,
0.02598542906343937,
-0.052782244980335236,
0.021896949037909508,
0.0033737430348992348,
-0.06383584439754486,
0.013732079416513443,
0.0066985199227929115,
0.0007039562333375216,
0.024742940440773964,
-0.038492601364851,
-0.039411019533872604,
-0.025447415187954903,
-0.04006161913275719,
0.0122366426512599,
-0.021829156205058098,
-0.005573097616434097,
0.039935845881700516,
0.0019070619018748403,
0.004893902689218521,
-0.05371728539466858,
-0.022423211485147476,
0.00035088660661131144,
-0.009205653332173824,
-0.034871138632297516,
-0.004530261270701885,
0.022016311064362526,
0.03692806512117386,
0.03222336620092392,
-0.012316139414906502,
0.010791881009936333,
-0.02504456602036953,
-0.024238744750618935,
0.04088660329580307,
-0.021817345172166824,
-0.0015292855678126216,
-0.005943631753325462,
-0.022065015509724617,
0.04101443290710449,
0.03203717991709709,
-0.02186901681125164,
-0.0031680772081017494,
-0.029063798487186432,
0.008774454705417156,
0.03162907063961029,
-0.004271768964827061,
-0.012160473503172398,
0.0070146494545042515,
-0.032402802258729935,
-0.01064768061041832,
0.008209762163460255,
0.028495067730545998,
0.019678547978401184,
-0.003978984896093607,
-0.022695885971188545,
0.021912831813097,
-0.03188594430685043,
0.008438056334853172,
-0.006420195568352938,
-0.03975958749651909,
-0.002138851210474968,
0.008561951108276844,
0.014894030056893826,
-0.0703035369515419,
0.004079313948750496,
-0.009902896359562874,
0.007437968160957098,
-0.03395620360970497,
0.05902276188135147,
-0.025931518524885178,
0.005075040739029646,
-0.03154802694916725,
0.010066600516438484,
-0.016250671818852425,
0.014865453355014324,
-0.08202759176492691,
0.0069864727556705475,
-0.0013272470096126199,
-0.027740279212594032,
-0.02909442037343979,
0.04421171545982361,
-0.025872545316815376,
-0.05010834336280823,
0.04064425081014633,
-0.0005186134367249906,
-0.016847100108861923,
-0.02502756007015705,
0.025134779512882233,
-0.02598724141716957,
0.011602729558944702,
-0.02259977161884308,
-0.03604045882821083,
0.017096219584345818,
-0.033749330788850784,
-0.07902726531028748,
0.051875222474336624,
0.04338490962982178,
0.021859990432858467,
0.03576963022351265,
-0.017110219225287437,
-0.04320133104920387,
0.06476019322872162,
-0.0007067011320032179,
-0.009469482116401196,
0.028779612854123116,
-0.08026497811079025,
-0.020691219717264175,
-0.04755566269159317,
0.01822984777390957,
0.009886413812637329,
0.00789296068251133,
-0.011676297523081303,
0.005538622848689556,
0.009819387458264828,
-0.02620772272348404,
0.020240426063537598,
-0.01662042737007141,
0.018039707094430923,
0.00033209475805051625,
-0.015324444510042667,
0.010108658112585545,
0.031690191477537155,
0.0003572239074856043,
-0.0036044504959136248,
0.017388610169291496,
0.009632046334445477,
-0.07383008301258087,
0.02569328248500824,
-0.0380767323076725,
-0.012555653229355812,
0.0345829613506794,
-0.04329059273004532,
0.014381524175405502,
-0.002939106896519661,
-0.025372931733727455,
0.026127681136131287,
-0.0739573985338211,
-0.03191206976771355,
0.004642925690859556,
-0.016628289595246315,
0.0044378372840583324,
0.06634308397769928,
0.03043842874467373,
0.002070603659376502,
0.048337217420339584,
-0.03310311585664749,
-0.0009002562146633863,
-0.013780757784843445,
-0.012310256250202656,
0.04706769436597824,
0.010898548178374767,
-0.017678309231996536,
0.05587434023618698,
0.004215000197291374,
-0.04218194633722305,
0.045090049505233765,
-0.007906891405582428,
0.015545576810836792,
-0.00018321123206987977,
0.014659561216831207,
0.010322047397494316,
-0.005357699003070593,
0.017273183912038803,
-0.0018637226894497871,
-0.03923938423395157,
0.0175238698720932,
0.041148360818624496,
-0.008103186264634132,
-0.0005573411472141743,
0.00869786273688078,
-0.0004176281508989632,
-0.016775183379650116,
-0.0517437644302845,
-0.00028437949367798865,
0.009969607926905155,
-0.03806501254439354,
-0.010843507014214993,
-0.0216752290725708,
0.022976182401180267,
-0.034635309129953384,
0.02370796725153923,
-0.02887777052819729,
0.018035488203167915,
0.0495588444173336,
-0.014251179993152618,
0.003216094570234418,
0.03096858598291874,
-0.002042118925601244,
-0.02656400389969349,
0.029216216877102852,
0.043145500123500824,
-0.0459529384970665,
-0.03998776897788048,
-0.0064495098777115345,
0.00037731634802185,
-0.028422890231013298,
-0.01516790222376585,
-0.0029130345210433006,
-0.03522662818431854,
0.009285989217460155,
0.023665593937039375,
0.019715813919901848,
0.024141859263181686,
-0.03873879462480545,
-0.023646026849746704,
-0.08974167704582214,
0.053221024572849274,
0.0015397397801280022,
-0.06570769101381302,
-0.028856903314590454,
0.01742611639201641,
0.0007573987822979689,
0.001107314950786531,
0.041049275547266006,
-0.009938717819750309,
-0.025323614478111267,
0.0056876009330153465,
0.028857262805104256,
0.03291398286819458,
-0.050230152904987335,
-0.028518764302134514,
-0.027121132239699364,
-0.004414205905050039,
0.017623433843255043,
0.012504681013524532,
-0.01904541254043579,
0.01766023226082325,
-0.0003963063645642251,
0.017723100259900093,
0.034647319465875626,
0.012364638037979603,
-0.07278065383434296,
0.006194184068590403,
0.01623249053955078,
-0.018664337694644928,
0.052887629717588425,
-0.01206221617758274,
0.017185740172863007,
-0.009832888841629028,
-0.025623029097914696,
-0.053390126675367355,
0.0008219642331823707,
-0.030132804065942764,
-0.03885583207011223,
-0.01243631262332201,
-0.007862301543354988,
0.022108206525444984,
-0.058352164924144745,
-0.0022811470553278923,
0.026534033939242363,
-0.040898289531469345,
0.0020947803277522326,
0.0717029720544815,
0.025768160820007324,
0.023824099451303482,
0.012418393045663834,
0.014029191806912422,
0.0202791690826416,
-0.03916045278310776,
-0.0064382171258330345,
0.006362938322126865,
0.020136352628469467,
-0.024227283895015717,
0.015104121528565884,
0.05751156061887741,
0.020078245550394058,
0.017024341970682144,
0.030552320182323456,
0.05555221438407898,
-0.011219902895390987,
-0.004037532955408096,
0.003953221719712019,
-0.01516545657068491,
0.01804262213408947,
0.04241536557674408,
0.005320376250892878,
0.07360614091157913,
-0.01747274212539196,
0.019498523324728012,
-0.0042222789488732815,
0.003615207504481077,
-0.027223462238907814,
0.021268967539072037,
0.03404451534152031,
0.016742417588829994,
-0.05346618965268135,
-0.00402558920904994,
-0.02649465948343277,
0.0044994293712079525,
0.001265592291019857,
-0.031262777745723724,
0.038203153759241104,
0.009792042896151543,
-0.034248385578393936,
-0.016363535076379776,
0.009060218930244446,
-0.04610442370176315,
-0.013803322799503803,
0.0324065238237381,
0.043277014046907425,
0.016992857679724693,
-0.002397165633738041,
0.016682276502251625,
-0.009177494794130325,
0.043954700231552124,
-0.07936657965183258,
0.0056695048697292805,
-0.01504033338278532,
0.025391114875674248,
0.025764601305127144,
0.003481985768303275
] |
<p>As I understand, photons are considered mass-less, which is a necessary condition for moving at the speed of light. However, does that mean their density is 0, as they will occupy some volume. If their density is zero, that means there is no matter inside a photon. Thus, shouldn't a photon be able to pass through matter instead of colliding with it? As $E = mc^2$, shouldn't a photon have zero energy, as it has zero mass?</p>
| 9,384 |
[
-0.018567131832242012,
-0.046212587505578995,
-0.016011325642466545,
-0.03237355500459671,
0.021930275484919548,
0.017319582402706146,
-0.05282118543982506,
-0.03632669895887375,
-0.023163439705967903,
-0.026022672653198242,
0.024005690589547157,
0.040085699409246445,
0.057482440024614334,
-0.00598790543153882,
0.04246224835515022,
-0.00030170215177349746,
-0.03088226355612278,
-0.008347643539309502,
-0.006240687798708677,
-0.04968695715069771,
-0.01640445552766323,
0.022385209798812866,
0.0314420610666275,
0.04210035502910614,
-0.025811729952692986,
0.025684021413326263,
-0.015592693351209164,
-0.005042393691837788,
0.011964818462729454,
0.029229413717985153,
0.008573396131396294,
-0.02261371538043022,
-0.014523887075483799,
0.05163620039820671,
-0.0024701650254428387,
-0.01939099282026291,
-0.04846613109111786,
-0.022266587242484093,
-0.02052663080394268,
0.015401415526866913,
-0.037089698016643524,
-0.0522608682513237,
0.02398589998483658,
0.02032059244811535,
-0.03397224843502045,
-0.014436759054660797,
0.05221165716648102,
-0.024537695571780205,
0.047648705542087555,
-0.0663132444024086,
0.07496827840805054,
0.008869332261383533,
0.06821398437023163,
0.017051709815859795,
0.015417159534990788,
-0.015218732878565788,
0.07493837922811508,
0.07521194964647293,
-0.03617936372756958,
-0.026918359100818634,
-0.02090000919997692,
-0.00089126022066921,
-0.006437520496547222,
-0.03237221762537956,
-0.02173941396176815,
0.03805049508810043,
-0.034653276205062866,
0.0023511755280196667,
0.032609209418296814,
0.004841300193220377,
0.01827467978000641,
0.009935438632965088,
0.01666513830423355,
0.002268797717988491,
0.0010499523486942053,
-0.021042468026280403,
0.04590313509106636,
0.012881569564342499,
0.04236098378896713,
0.047352276742458344,
-0.015499803237617016,
-0.0068075996823608875,
0.01877092942595482,
0.020223164930939674,
0.01117920596152544,
0.0034023134503513575,
0.06785476207733154,
-0.010692405514419079,
0.009678506292402744,
0.01479229424148798,
-0.008480358868837357,
-0.009662708267569542,
0.02682344987988472,
-0.003415693063288927,
-0.009109461680054665,
0.04062395170331001,
-0.012685557827353477,
0.0708729699254036,
-0.019063811749219894,
-0.03677420690655708,
0.02094096504151821,
0.0377945750951767,
0.05036590248346329,
0.07208351790904999,
0.011542044579982758,
-0.03686809167265892,
-0.047603826969861984,
0.04224291443824768,
-0.00934247113764286,
0.0001900169881992042,
-0.02986989915370941,
0.019531866535544395,
0.020413970574736595,
-0.016645122319459915,
0.053545791655778885,
-0.03831714391708374,
0.0030336491763591766,
-0.028988473117351532,
0.06351419538259506,
0.06154127046465874,
0.03594193980097771,
-0.04110734537243843,
0.035717010498046875,
-0.011616536416113377,
-0.07728946208953857,
0.005771841388195753,
0.026001039892435074,
0.01718614622950554,
-0.04800491780042648,
0.016464034095406532,
-0.023340441286563873,
-0.0112594123929739,
0.020031515508890152,
-0.010570130310952663,
0.05401057377457619,
-0.05058056861162186,
-0.08849736303091049,
-0.05519385635852814,
0.028340009972453117,
0.0010316858533769846,
-0.0358196459710598,
-0.07066144049167633,
-0.01078079268336296,
0.016064178198575974,
0.08695069700479507,
-0.016157574951648712,
-0.017228884622454643,
-0.013932810164988041,
0.051984675228595734,
-0.01735939271748066,
-0.02243061177432537,
-0.017384547740221024,
-0.020310169085860252,
-0.02696276269853115,
0.04338308796286583,
-0.06206871196627617,
-0.001824245206080377,
0.03640801087021828,
-0.003057103371247649,
-0.05787532776594162,
0.045069195330142975,
-0.06384532153606415,
0.006094646640121937,
0.023201804608106613,
-0.01077238004654646,
-0.042345866560935974,
0.04277399182319641,
0.05099901556968689,
0.022315358743071556,
0.039123792201280594,
0.06829998642206192,
0.03239624202251434,
0.0009662921074777842,
0.028294244781136513,
0.021284492686390877,
-0.050735484808683395,
-0.021292323246598244,
-0.02043239027261734,
0.04015176743268967,
0.004984072409570217,
-0.040997665375471115,
-0.028083287179470062,
0.0033475919626653194,
0.01453381683677435,
0.009135166183114052,
0.046513114124536514,
-0.014268475584685802,
-0.0267286729067564,
-0.03282187506556511,
-0.027771184220910072,
-0.019668331369757652,
-0.05284317210316658,
0.029674679040908813,
0.007533705793321133,
-0.0020116339437663555,
0.026858258992433548,
0.01282536331564188,
0.020668817684054375,
-0.0499529093503952,
-0.010654324665665627,
-0.031074367463588715,
0.04792885482311249,
-0.02821587398648262,
-0.04269569367170334,
0.03761231154203415,
0.03157200664281845,
0.03719734027981758,
0.007530373986810446,
0.0015575247816741467,
-0.007563385181128979,
-0.0307264793664217,
0.012703030370175838,
0.020689306780695915,
0.022794783115386963,
-0.011854970827698708,
-0.004405313637107611,
0.009691813960671425,
-0.009266526438295841,
-0.021639756858348846,
0.03652024641633034,
0.0020248196087777615,
0.08453705906867981,
0.033377524465322495,
-0.001090965699404478,
-0.010579136200249195,
0.015315999276936054,
0.006861713249236345,
0.003541139652952552,
-0.0167738888412714,
-0.027500493451952934,
-0.03082035295665264,
0.004914956167340279,
0.018751533702015877,
-0.011907747946679592,
-0.06624153256416321,
0.00873364694416523,
0.01733889803290367,
0.03264062479138374,
0.02828269451856613,
0.019318005070090294,
-0.0517604798078537,
-0.03940248116850853,
0.018424611538648605,
0.03538640961050987,
0.016659948974847794,
0.007455016486346722,
0.03383200615644455,
0.023945624008774757,
0.012210806831717491,
-0.006133743561804295,
0.006812587846070528,
0.027894752100110054,
-0.01994936540722847,
-0.0033675648737698793,
-0.010745318606495857,
-0.05081230401992798,
0.016196878626942635,
-0.025348307564854622,
0.007114472333341837,
0.03432672843337059,
-0.019071802496910095,
-0.004060454200953245,
-0.044564515352249146,
-0.014166613109409809,
0.014978166669607162,
0.018928341567516327,
-0.01771988905966282,
-0.011102651245892048,
0.015077450312674046,
-0.04829761013388634,
0.012867596000432968,
0.004289073869585991,
-0.002499418333172798,
-0.031734853982925415,
-0.005057786125689745,
0.055084869265556335,
0.006747238803654909,
0.02878524549305439,
-0.04768496751785278,
-0.0545472614467144,
-0.012116563506424427,
-0.03925606980919838,
-0.0467354990541935,
0.002864891430363059,
-0.046333640813827515,
0.019079012796282768,
-0.03442252054810524,
-0.037750810384750366,
0.047045279294252396,
-0.010758361779153347,
0.03397224470973015,
0.046405013650655746,
-0.04300926625728607,
-0.04378703981637955,
-0.008740583434700966,
0.001267425250262022,
-0.02936662547290325,
0.009770078584551811,
0.053499262779951096,
0.0452352799475193,
-0.021866297349333763,
-0.04936590790748596,
-0.010604241862893105,
-0.027339212596416473,
-0.05552388355135918,
-0.04229702055454254,
-0.044264648109674454,
0.02968406118452549,
-0.07525090873241425,
0.04436748847365379,
0.03606504946947098,
-0.08108874410390854,
0.04774342104792595,
-0.031187064945697784,
-0.01932568848133087,
0.03063114546239376,
-0.008100208826363087,
0.015878163278102875,
0.02111397311091423,
-0.04994576424360275,
0.04175683110952377,
0.03874295949935913,
-0.03158235177397728,
-0.0016499832272529602,
0.0024055768735706806,
-0.0010053026489913464,
-0.014115825295448303,
0.004790029488503933,
0.005682946182787418,
0.002664905274286866,
-0.012968008406460285,
0.007103927433490753,
0.03391522541642189,
0.01203926745802164,
-0.0005093429936096072,
-0.015101111494004726,
0.01610547862946987,
0.017921386286616325,
-0.008372316136956215,
0.021640190854668617,
0.024426838383078575,
-0.02417796291410923,
0.04711758717894554,
0.004222969990223646,
0.03582431748509407,
0.005797556135803461,
0.0031354164239019156,
0.07031580805778503,
0.02667374536395073,
0.03292566537857056,
-0.033356934785842896,
0.04216960817575455,
-0.01000254973769188,
-0.005470747128129005,
0.020139457657933235,
-0.002436443930491805,
0.0317990668118,
-0.01346217468380928,
-0.020443761721253395,
-0.005679853726178408,
0.022200722247362137,
-0.032829973846673965,
-0.016972504556179047,
0.014805256389081478,
-0.014226271770894527,
-0.002945054555311799,
0.013152886182069778,
0.004863587208092213,
0.056280527263879776,
0.038939062505960464,
0.04096447303891182,
-0.030162828043103218,
-0.00928895827382803,
-0.025810465216636658,
-0.027782833203673363,
0.0009928805520758033,
0.031169241294264793,
0.01471553836017847,
-0.012512638233602047,
0.06320760399103165,
0.034020207822322845,
0.03817968815565109,
0.019884442910552025,
0.0036413106136024,
-0.062058236449956894,
-0.008627583272755146,
-0.05492173507809639,
-0.0059564728289842606,
-0.015449943020939827,
-0.022847037762403488,
-0.03472623974084854,
-0.03615770861506462,
-0.017909158021211624,
-0.0029975888319313526,
-0.013482269831001759,
-0.05017326772212982,
-0.017584064975380898,
-0.0696476399898529,
-0.02092796564102173,
-0.0009311545290984213,
0.03444259613752365,
-0.007507224567234516,
0.00124075124040246,
-0.0007658185204491019,
0.043660979717969894,
-0.018708497285842896,
-0.008604245260357857,
0.012259024195373058,
-0.01076905895024538,
0.0015727661084383726,
0.02281906083226204,
0.06127237156033516,
-0.014937538653612137,
-0.03230348229408264,
0.02888665907084942,
0.024621887132525444,
0.05802110582590103,
0.0016313920496031642,
-0.0470113568007946,
-0.03184307739138603,
-0.017957091331481934,
-0.036272674798965454,
-0.02765262871980667,
0.04680398106575012,
0.014698785729706287,
-0.006841194350272417,
0.006569433957338333,
-0.00032842112705111504,
0.006658023223280907,
0.05832592025399208,
0.07780206948518753,
0.015500501729547977,
-0.019338373094797134,
-0.0628993958234787,
-0.00488186813890934,
-0.04468529298901558,
-0.007270290516316891,
0.011198139749467373,
-0.011392051354050636,
-0.016782762482762337,
0.011421799659729004,
-0.02640339732170105,
0.020515255630016327,
-0.03769427537918091,
-0.03702642396092415,
0.018884068354964256,
-0.00039264862425625324,
-0.016237851232290268,
-0.010201973840594292,
-0.005759671796113253,
0.003956264816224575,
0.0258027296513319,
-0.013555481098592281,
-0.002621554071083665,
-0.07690268754959106,
0.01250214222818613,
0.03630077838897705,
0.05935489013791084,
-0.0007861562771722674,
-0.005724436137825251,
-0.041145145893096924,
-0.013812943361699581,
0.015447420068085194,
-0.02175687626004219,
-0.0004676964017562568,
-0.03633842617273331,
-0.01605508103966713,
0.009642984718084335,
-0.008234207518398762,
0.006285123992711306,
0.01820206083357334,
-0.0009484550100751221,
-0.013831624761223793,
-0.014177770353853703,
-0.006150339730083942,
-0.008221478201448917,
0.02277233637869358,
-0.001054151332937181,
0.055907752364873886,
-0.00376907573081553,
-0.010107812471687794,
0.006551453843712807,
0.024579040706157684,
-0.0138995461165905,
-0.09314610809087753,
-0.020139368250966072,
0.0036940407007932663,
0.006524279713630676,
0.033424749970436096,
-0.0036513975355774164,
-0.07053965330123901,
0.0347687266767025,
0.018603505566716194,
-0.027128349989652634,
0.006624005269259214,
-0.048585932701826096,
0.02054131031036377,
-0.017030445858836174,
-0.012719068676233292,
0.03363056480884552,
0.03427540510892868,
-0.021951841190457344,
-0.01758037693798542,
-0.039657965302467346,
0.07113941758871078,
-0.023753488436341286,
0.006082447245717049,
-0.05594109371304512,
-0.001973799429833889,
-0.010252468287944794,
0.04331784322857857,
-0.023727014660835266,
0.008767201565206051,
0.026258883997797966,
-0.05346982926130295,
0.014123190194368362,
0.034473687410354614,
0.028293820098042488,
0.01045361440628767,
-0.05891846492886543,
0.010058687999844551,
-0.04802194982767105,
-0.016978997737169266,
0.02326696179807186,
0.009244460612535477,
-0.0072059836238622665,
0.03676207363605499,
0.009982885792851448,
0.024592187255620956,
-0.0230433139950037,
-0.015692060813307762,
0.006564430892467499,
-0.034961048513650894,
0.05280369147658348,
0.0025647408328950405,
-0.02609854005277157,
-0.006265973672270775,
-0.07543342560529709,
-0.03089805319905281,
-0.017412947490811348,
-0.014852480962872505,
0.05124180018901825,
-0.05876173824071884,
0.03724659979343414,
0.00822410173714161,
0.02092631720006466,
-0.0940924882888794,
-0.054633695632219315,
-0.02300417423248291,
0.010349372401833534,
0.010621889494359493,
-0.022436849772930145,
0.03905759006738663,
-0.04812382906675339,
-0.010049441829323769,
-0.028225844725966454,
0.05078023672103882,
-0.007993239909410477,
-0.0032803236972540617,
0.012555088847875595,
0.0010536442277953029,
0.011878341436386108,
0.01863943412899971,
-0.03985271230340004,
0.028652556240558624,
0.010774046182632446,
-0.011485861614346504,
-0.011213012970983982,
0.07237859070301056,
-0.011352368630468845,
-0.0520857535302639,
-0.02022339031100273,
-0.04045707359910011,
0.037013981491327286,
-0.008202658966183662,
0.01250919047743082,
0.03282567113637924,
0.009796885773539543,
-0.013504349626600742,
-0.008894884958863258,
0.032806020230054855,
0.0017272132681682706,
0.018192606046795845,
0.0063058133237063885,
-0.01655212789773941,
-0.02906200662255287,
-0.05237866938114166,
0.07997173070907593,
-0.020247019827365875,
0.04850012809038162,
0.003991236910223961,
0.06693755090236664,
0.011459695175290108,
0.02149667777121067,
-0.009719105437397957,
-0.0006025057518854737,
0.010805812664330006,
-0.007131457794457674,
-0.025497179478406906,
0.008657000958919525,
-0.018659306690096855,
-0.024849366396665573,
0.002701159566640854,
-0.035319581627845764,
-0.03186643496155739,
0.06562759727239609,
-0.025461718440055847,
0.038539815694093704,
-0.03317417576909065,
-0.030746249482035637,
0.02769232913851738,
-0.01653324067592621,
-0.016270235180854797,
0.032095637172460556,
0.013021244667470455,
0.023647146299481392,
0.011290222406387329,
0.008223219774663448,
0.05562008544802666,
0.053114596754312515,
-0.010888580232858658,
0.023861736059188843,
0.020112665370106697,
0.044300518929958344,
0.017654534429311752,
0.01833968423306942,
-0.02397729642689228,
0.02279711700975895,
-0.03393079340457916,
-0.008573477156460285,
0.0054587870836257935,
-0.03840232267975807,
0.02367602102458477,
0.003992171958088875,
0.019639313220977783,
0.005128102842718363,
-0.029541410505771637,
-0.03894764930009842,
0.046978965401649475,
-0.005532509181648493,
0.014904339797794819,
-0.023320870473980904,
0.013413929380476475,
-0.0072557651437819,
0.03582336753606796,
0.006792156957089901,
0.02807762287557125,
-0.054001640528440475,
-0.045376572757959366,
-0.033141981810331345,
-0.015131120570003986,
0.027612125501036644,
0.01397034339606762,
-0.00020526342268567532,
0.011280742473900318,
-0.02197159267961979,
0.02310219034552574,
0.033766262233257294,
0.017927955836057663,
-0.0014981124550104141,
0.037226300686597824,
0.009587752632796764,
0.005216762889176607,
-0.021175088360905647,
0.03980330750346184,
0.0826144590973854,
0.05096845328807831,
0.02440895326435566,
-0.05366106703877449,
-0.008057938888669014,
-0.018359756097197533,
0.021256696432828903,
-0.04656069353222847,
0.052022784948349,
-0.017415126785635948,
0.020674029365181923,
-0.007131895516067743,
0.05260072275996208,
-0.002081118058413267,
0.026913192123174667,
0.058251820504665375,
-0.00914589874446392,
-0.05499069765210152,
-0.003636937588453293,
0.03581000864505768,
-0.009579949080944061,
0.02747340314090252,
-0.01608407124876976,
-0.000030315486583276652,
-0.026528621092438698,
0.00865684449672699,
-0.01186180766671896,
-0.032848987728357315,
0.01802094280719757,
0.005456221289932728,
-0.04941241070628166,
-0.030505791306495667,
0.03279940038919449,
-0.021176258102059364,
-0.05270414426922798,
-0.0002879088278859854,
0.05218811333179474,
0.007097519002854824,
-0.005417348351329565,
-0.01072699949145317,
0.014676468446850777,
0.014554563909769058,
0.01920420117676258,
0.00961718987673521,
-0.05206700414419174,
-0.002027420327067375,
-0.0001215888187289238,
0.048594437539577484,
-0.02126462012529373,
0.023850662633776665,
0.009822286665439606,
0.016668427735567093,
-0.016357960179448128,
-0.033913590013980865,
-0.0035418870393186808,
-0.025119652971625328,
0.018172603100538254,
0.050400495529174805,
-0.00968128815293312,
-0.023974942043423653,
0.016712134703993797,
-0.0057500735856592655,
0.02604440413415432,
-0.019545691087841988,
0.014386991038918495,
0.02884063869714737,
-0.007085433695465326,
0.0037228309083729982,
-0.05762194097042084,
-0.006420806050300598,
0.020591970533132553,
0.0075538563542068005,
-0.05803479254245758,
-0.043897271156311035,
0.05206078290939331,
0.05022040009498596,
0.014891548082232475,
0.016520561650395393,
-0.007363345939666033,
-0.009988019242882729,
-0.08903910219669342,
0.03240233659744263,
-0.030843382701277733,
-0.0529247522354126,
-0.028745291754603386,
-0.00310216355137527,
0.015493763610720634,
0.0351283997297287,
-0.031365830451250076,
-0.015462451614439487,
-0.012379046529531479,
0.013593402691185474,
-0.009871355257928371,
-0.008086558431386948,
-0.0219784714281559,
0.0261620432138443,
0.0013956637121737003,
0.010362789034843445,
-0.01741619035601616,
0.0064997076988220215,
0.029646271839737892,
0.0334610641002655,
-0.003375964006409049,
0.020660800859332085,
-0.02670464478433132,
0.000567986280657351,
-0.0037221615202724934,
-0.02702607959508896,
-0.011206134222447872,
0.017280347645282745,
0.04062695428729057,
-0.01748785749077797,
-0.06384360790252686,
-0.042585745453834534,
0.008002514950931072,
-0.015885189175605774,
0.018971331417560577,
-0.0156979002058506,
-0.0018538929289206862,
-0.019390584900975227,
0.0023955253418534994,
-0.024287261068820953,
-0.012842326425015926,
-0.03404109925031662,
0.015873292461037636,
0.03315725177526474,
-0.02258335053920746,
-0.011689812876284122,
0.019712863489985466,
-0.01614905335009098,
-0.0009058354189619422,
0.026218406856060028,
0.03830811381340027,
-0.010729196481406689,
0.007839806377887726,
0.04311332851648331,
-0.00010689074406400323,
0.05357915163040161,
-0.011252382770180702,
0.005368324462324381,
0.05877106636762619,
-0.023248614743351936,
-0.05669296905398369,
0.023807087913155556,
-0.006731316912919283,
0.017677217721939087,
0.031971823424100876,
-0.0004183645942248404,
-0.027695700526237488,
0.08047778159379959,
-0.01315158698707819,
0.005930584855377674,
-0.014272749423980713,
-0.06012802943587303,
-0.03552277758717537,
0.020429391413927078,
0.018352601677179337,
-0.019333049654960632,
-0.019214700907468796,
0.04525003209710121,
0.025150468572974205,
0.009578636847436428,
0.0037873529363423586,
-0.00886237807571888,
-0.014704233966767788,
-0.008294031955301762,
0.03454805538058281,
0.00810966920107603,
-0.015423373319208622,
0.05354424938559532,
0.0012340496759861708,
0.03713183104991913,
0.04070618376135826,
0.0006811728235334158,
-0.13002486526966095,
-0.002088319743052125,
0.005433250684291124,
0.017704157158732414,
0.042756494134664536,
-0.044358380138874054,
0.019987577572464943,
0.0388600192964077,
-0.05476868525147438,
0.017804674804210663,
-0.034271642565727234,
-0.025472581386566162,
-0.023487519472837448,
0.018772590905427933,
-0.00946627277880907,
0.050138238817453384,
0.023041710257530212,
0.04239318147301674,
0.010312638245522976,
-0.0037774958182126284,
-0.029266400262713432,
0.0029530897736549377,
-0.015285923145711422,
0.057280153036117554,
-0.03653590753674507,
0.005912914406508207,
0.06873225420713425,
0.0034864540211856365,
-0.013676324859261513,
0.03180072829127312,
0.009563456289470196,
0.01240795012563467,
0.0031315400265157223,
0.010396373458206654,
-0.008707508444786072,
0.0034392443485558033,
0.02281714230775833,
0.011830179020762444,
-0.01518312655389309,
0.05420989915728569,
0.014356945641338825,
0.006894384976476431,
-0.0375911146402359,
-0.00045634389971382916,
0.018157612532377243,
-0.046884771436452866,
-0.043627697974443436,
0.02866337075829506,
-0.022231243550777435,
-0.007176602259278297,
0.0008095861994661391,
0.03050268068909645,
0.00846295990049839,
-0.03129434585571289,
0.012520448304712772,
-0.08110665529966354,
-0.02014678530395031,
0.007859297096729279,
0.0033641979098320007,
-0.006086460314691067,
-0.0004132235189899802,
0.03495406731963158,
-0.0348019115626812,
0.014455958269536495,
0.022478854283690453,
-0.007601514458656311,
-0.05551518499851227,
0.009166846983134747,
0.004203178454190493,
-0.019536377862095833,
0.029907168820500374,
-0.04156075790524483,
-0.03485650196671486,
0.04708830267190933,
0.01508793979883194,
0.018121225759387016,
0.021911976858973503,
-0.010428177192807198,
-0.058842942118644714,
-0.05857916176319122,
0.02317577786743641,
-0.029957156628370285,
0.032520510256290436,
-0.04508466646075249,
0.008329044096171856,
-0.03866491839289665,
0.01048118807375431,
0.03851459547877312,
-0.006997437682002783,
0.023993203416466713,
0.02065318450331688,
-0.004036690108478069,
0.0035968248266726732,
-0.04258669540286064,
-0.020082050934433937,
-0.02320355921983719,
-0.049927134066820145,
-0.024043960496783257,
0.017288004979491234,
-0.025623762980103493,
0.0113237164914608,
0.010419715195894241,
-0.004919774364680052,
0.021272709593176842,
-0.022980136796832085,
-0.03444577008485794,
0.06019573286175728,
0.030910709872841835,
0.009647268801927567,
0.05075298249721527,
-0.033749405294656754,
0.04533287510275841,
0.04905518889427185,
-0.012357862666249275,
-0.030163777992129326,
0.03343169763684273,
-0.016170941293239594,
-0.00961686298251152,
-0.0033775700721889734,
0.026984773576259613,
0.025252800434827805,
-0.012861646711826324,
0.03233754634857178,
0.0371871255338192,
-0.03516077995300293,
-0.004787840880453587,
0.05564763396978378,
0.013455132022500038,
0.05577060580253601,
0.01430488284677267,
0.020548420026898384,
0.036618672311306,
0.010069821029901505,
-0.006079480051994324,
0.06377941370010376,
0.02177121862769127,
0.013272921554744244,
0.021654609590768814,
0.027978669852018356,
0.00027915817918255925,
-0.012268987484276295,
0.0046793557703495026,
0.04270419850945473,
-0.02911081537604332,
-0.02943205088376999,
0.01224839873611927,
0.003957884386181831,
0.0048618558794260025,
-0.012581746093928814,
-0.011540252715349197,
0.07770026475191116,
-0.031378116458654404,
0.03655891865491867,
-0.006754609756171703,
-0.0050051249563694,
0.007985788397490978,
0.034939974546432495,
-0.0018506570486351848,
0.04672926291823387,
0.010408421978354454,
0.0018111392855644226,
-0.033938854932785034,
-0.022187089547514915,
0.04610085487365723,
-0.0505823940038681,
0.010266570374369621,
-0.0002991257351823151,
-0.03766760975122452,
-0.018766924738883972,
-0.009159576147794724,
0.03443474322557449,
-0.025575097650289536,
-0.010846785269677639,
0.038455940783023834,
0.0077041215263307095,
0.00024524563923478127,
0.015428030863404274,
-0.025567399337887764,
0.06894528865814209,
-0.033660512417554855,
0.02403244562447071,
-0.02861650288105011,
0.02011697180569172,
-0.009849334135651588,
0.0036796010099351406
] |
<p>I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting vector. I can't really understand how the momentum conservation laws apply to the situations in which there is a magnet(current through the loop) and in which this magnet is turned off. How should i write these laws?<br/>
I think I somehow understand the origin of hidden momentum, but I don't see how everything sums up in both situations. Could you please help me understand?</p>
| 9,385 |
[
-0.028830785304307938,
-0.017472777515649796,
-0.012996320612728596,
-0.050200093537569046,
0.0235651396214962,
0.007100539747625589,
-0.043165795505046844,
0.0057843648828566074,
-0.016958916559815407,
-0.009901435114443302,
-0.00801327545195818,
0.03387311473488808,
0.03386092558503151,
-0.005196388345211744,
0.020027106627821922,
0.006359597202390432,
0.022256985306739807,
-0.015388050116598606,
0.03131832927465439,
-0.04054765775799751,
-0.04036648944020271,
0.020127732306718826,
-0.012025119736790657,
-0.02677697129547596,
-0.03430899605154991,
0.03371299430727959,
0.02303340472280979,
0.04343102499842644,
-0.016550559550523758,
0.05948322266340256,
-0.00789764802902937,
-0.02141261100769043,
-0.01459492463618517,
-0.0018758911173790693,
-0.007094190455973148,
0.001052278559654951,
-0.009862888604402542,
-0.01032149139791727,
0.012885728850960732,
0.02224893495440483,
0.008917043916881084,
-0.0022745439782738686,
-0.02268022857606411,
0.06142554059624672,
-0.0017537231324240565,
0.006268996279686689,
-0.0481376014649868,
0.026752548292279243,
0.06567872315645218,
-0.06466452777385712,
0.07235106825828552,
-0.01013255026191473,
0.07155873626470566,
0.014666219241917133,
-0.0012215060414746404,
0.008070925250649452,
0.08206051588058472,
0.07139826565980911,
-0.007340540178120136,
-0.05843114107847214,
-0.018077215179800987,
0.00029808239196427166,
-0.027335822582244873,
-0.0356338806450367,
0.007706667296588421,
0.03989797830581665,
-0.014197694137692451,
0.010996539145708084,
0.04995880275964737,
0.029386132955551147,
0.0011701039038598537,
-0.006173976231366396,
0.03159922733902931,
-0.010588208213448524,
0.01184268668293953,
-0.0054972232319414616,
0.028782447800040245,
-0.0008576043765060604,
0.03150318190455437,
0.03521888330578804,
-0.03060058318078518,
0.005409049801528454,
0.028268050402402878,
0.05389443412423134,
0.026378747075796127,
-0.022138725966215134,
0.05327369645237923,
-0.017363285645842552,
0.02034483104944229,
0.037303365767002106,
0.002431353786960244,
0.02442622371017933,
0.00003341656702104956,
-0.01221864577382803,
-0.01618805341422558,
0.05356495454907417,
-0.03746379539370537,
0.07514681667089462,
0.006156302988529205,
-0.010819481685757637,
-0.013060183264315128,
-0.005294434726238251,
0.018282972276210785,
0.07242411375045776,
0.014298742637038231,
-0.0484151653945446,
-0.006343548186123371,
0.02103039249777794,
-0.04226812347769737,
-0.023585893213748932,
-0.06216906011104584,
0.02126835286617279,
0.013246772810816765,
-0.024029428139328957,
-0.009910100139677525,
-0.04784618690609932,
0.008048610761761665,
0.012025067582726479,
0.06984787434339523,
0.0658707320690155,
0.00891313049942255,
-0.010109457187354565,
0.016759376972913742,
-0.04746098443865776,
-0.09186510741710663,
-0.0035731750540435314,
0.011410013772547245,
-0.0012689430732280016,
-0.0483960285782814,
0.01950518973171711,
-0.014186334796249866,
-0.038856588304042816,
0.003768650349229574,
0.0015095147537067533,
0.027612457051873207,
-0.04103800654411316,
-0.09004586935043335,
-0.03646280616521835,
0.04128827899694443,
-0.04860889911651611,
0.00983204785734415,
-0.07173505425453186,
-0.02932639792561531,
0.01636248454451561,
0.057592906057834625,
-0.029261644929647446,
-0.023125726729631424,
-0.01907789148390293,
0.028745170682668686,
-0.013167832046747208,
-0.012422828003764153,
-0.01737220771610737,
-0.010061487555503845,
-0.019952936097979546,
-0.014532345347106457,
-0.06434803456068039,
0.04717455804347992,
0.04556090384721756,
0.007234449032694101,
0.010143847204744816,
0.03650882467627525,
-0.03292812779545784,
0.014632691629230976,
0.004234341438859701,
-0.0029324751812964678,
-0.03377477452158928,
0.06895335763692856,
0.002161032520234585,
-0.0006632449803873897,
0.04272273927927017,
0.03323616087436676,
-0.005760641302913427,
-0.0248271394520998,
0.011361266486346722,
0.06376423686742783,
-0.04199790954589844,
-0.028968971222639084,
-0.018635021522641182,
-0.005473840516060591,
0.004188472870737314,
-0.022629283368587494,
-0.06441336870193481,
-0.02107880264520645,
0.03068828582763672,
-0.009155293926596642,
0.02806526981294155,
0.003995152190327644,
0.013132912106812,
-0.01741827093064785,
-0.019219033420085907,
-0.02006758190691471,
-0.05896623805165291,
0.02113717421889305,
-0.05121861770749092,
0.0011688184458762407,
0.019750576466321945,
0.020745858550071716,
0.048977356404066086,
-0.018726926296949387,
-0.025848081335425377,
-0.0024773315526545048,
0.03984948620200157,
-0.019705303013324738,
0.007107546553015709,
-0.017998727038502693,
0.022943662479519844,
0.03280214965343475,
0.05145823210477829,
0.056212108582258224,
-0.012504098936915398,
-0.014732841402292252,
-0.019927483052015305,
-0.011856322176754475,
-0.02641919255256653,
0.04011787101626396,
-0.022257016971707344,
0.03088553436100483,
-0.0008955419179983437,
-0.003535335185006261,
0.014526564627885818,
0.005512413568794727,
0.07038242369890213,
0.03827274590730667,
0.0037343346048146486,
0.020277367904782295,
0.026815958321094513,
-0.020886937156319618,
-0.013138028793036938,
-0.02188309282064438,
-0.006282046437263489,
-0.010727503336966038,
0.01837017759680748,
0.0017733327113091946,
0.020413901656866074,
-0.03657660633325577,
0.015935685485601425,
0.017355263233184814,
0.024355566129088402,
0.015702595934271812,
0.05662663280963898,
-0.030165227130055428,
-0.030498579144477844,
-0.00711499759927392,
0.009658271446824074,
-0.010509354062378407,
0.010472802445292473,
0.03861673176288605,
0.011029524728655815,
0.00870013888925314,
0.008922016248106956,
-0.039687059819698334,
0.037964679300785065,
0.0006116315489634871,
-0.020509006455540657,
-0.0064232531003654,
-0.07983622699975967,
0.0576733760535717,
-0.006390030030161142,
0.034503769129514694,
0.006902470253407955,
0.0027381530962884426,
0.012085373513400555,
-0.02970827743411064,
-0.012184806168079376,
0.007391517516225576,
-0.04690476134419441,
-0.0018740762025117874,
-0.0068034399300813675,
0.0011816363548859954,
-0.004659336991608143,
0.010311839170753956,
-0.005287857260555029,
-0.021883662790060043,
-0.023795360699295998,
-0.01553540863096714,
0.01749754138290882,
-0.012823724187910557,
0.016331946477293968,
-0.04377374053001404,
-0.04982549697160721,
-0.039933402091264725,
-0.0010926357936114073,
0.027679916471242905,
0.020204249769449234,
-0.03824882209300995,
0.03149545192718506,
-0.07378912717103958,
-0.03946004435420036,
0.07243309915065765,
0.0019210133468732238,
-0.013738328590989113,
0.026784544810652733,
-0.01870153844356537,
-0.057568080723285675,
-0.021954011172056198,
-0.02528771199285984,
0.03178247809410095,
0.000505361589603126,
0.0014672521501779556,
0.08243338018655777,
-0.013403981924057007,
-0.0254470594227314,
0.0029930591117590666,
-0.04138796404004097,
-0.048515111207962036,
0.016006220132112503,
-0.017102204263210297,
-0.005021423101425171,
0.002472564810886979,
0.034539319574832916,
0.02686738595366478,
-0.07636900246143341,
0.01701749488711357,
-0.04195408150553703,
0.0002565091708675027,
0.005388702731579542,
-0.0008682167972438037,
0.023638498038053513,
-0.002132710302248597,
-0.01323190238326788,
0.11020548641681671,
0.04435489699244499,
-0.010268939658999443,
-0.004494623746722937,
-0.03911202400922775,
-0.024403275921940804,
-0.0380781851708889,
-0.003288918174803257,
0.04278815537691116,
-0.013385812751948833,
-0.019426196813583374,
0.01314915157854557,
0.04566322639584541,
-0.009144017472863197,
0.03180769830942154,
0.00035834687878377736,
0.03196287900209427,
0.011807633563876152,
0.015034030191600323,
0.055547527968883514,
0.00876410212367773,
-0.05033687502145767,
-0.0017492753686383367,
0.027019977569580078,
0.05050969496369362,
0.006737940013408661,
-0.04686439782381058,
0.056417204439640045,
0.02350616827607155,
0.03378322720527649,
-0.011940990574657917,
0.03164970502257347,
-0.009473211131989956,
-0.031238196417689323,
0.013676205649971962,
0.005106434691697359,
0.033562563359737396,
-0.03512037172913551,
-0.01977640949189663,
0.029507337138056755,
0.027064034715294838,
0.010802228935062885,
-0.05488789826631546,
-0.004811509512364864,
-0.014479704201221466,
-0.006110343150794506,
-0.03004494681954384,
-0.02147224359214306,
0.012864548712968826,
0.043043240904808044,
0.01669338345527649,
0.007717904634773731,
-0.021079251542687416,
0.0006055120029486716,
-0.0719531998038292,
0.02837623842060566,
0.005181027110666037,
0.05353733152151108,
0.02029585652053356,
0.04182618856430054,
0.00555243156850338,
0.0257793590426445,
0.005222276784479618,
-0.023474276065826416,
-0.08262711763381958,
0.047186464071273804,
-0.03370421752333641,
-0.034199487417936325,
-0.005960608832538128,
-0.00028858587029390037,
-0.01287789549678564,
-0.035048965364694595,
-0.013655098155140877,
-0.0250481516122818,
-0.021153513342142105,
-0.0537896603345871,
0.04095199704170227,
-0.015315770171582699,
-0.01343931257724762,
-0.027200762182474136,
0.03857420012354851,
0.06406641006469727,
-0.023195946589112282,
0.037698086351156235,
0.010604356415569782,
-0.04188885912299156,
-0.021677721291780472,
-0.04821145534515381,
-0.012048128992319107,
-0.008653383702039719,
0.011494964361190796,
0.058347176760435104,
0.004322954919189215,
-0.0295011717826128,
-0.0057188658975064754,
0.02147502824664116,
0.048774126917123795,
-0.00419613579288125,
-0.02768641524016857,
-0.019165081903338432,
-0.032527025789022446,
-0.020266255363821983,
-0.00973279308527708,
0.035199739038944244,
0.002831558231264353,
0.03867676481604576,
0.01987343095242977,
0.020055929198861122,
-0.00007781461317790672,
0.019255228340625763,
0.016494885087013245,
0.014343529008328915,
0.003594436217099428,
-0.0225274246186018,
0.061234306544065475,
-0.02463674731552601,
0.0038426388055086136,
-0.0014676861464977264,
-0.0002571176446508616,
-0.011306142434477806,
0.003232544520869851,
0.011238307692110538,
0.009475323371589184,
0.004960894118994474,
0.0002701185876503587,
0.004961221944540739,
0.014014695771038532,
0.010425003245472908,
0.011710749007761478,
0.02634221687912941,
0.04980168491601944,
0.024151863530278206,
0.0290365070104599,
0.000139491050504148,
-0.06280089169740677,
-0.04275640472769737,
0.05047906935214996,
0.016798969358205795,
0.015026845037937164,
-0.037793196737766266,
-0.037563569843769073,
0.006935565732419491,
0.03452606499195099,
-0.010073232464492321,
0.03568447381258011,
-0.025581935420632362,
-0.027895383536815643,
-0.029971085488796234,
-0.03981216996908188,
-0.027012472972273827,
0.03266105055809021,
-0.040450867265462875,
0.030495217069983482,
-0.014054580591619015,
0.0003049819788429886,
-0.014677133411169052,
0.016643254086375237,
0.019687214866280556,
0.034033212810754776,
-0.005181262735277414,
0.0009438884444534779,
0.011664297431707382,
0.04791230335831642,
-0.0425768718123436,
-0.09311505407094955,
0.017724348232150078,
-0.01172884926199913,
0.00782113615423441,
0.04311250522732735,
-0.03234515339136124,
-0.07226251810789108,
-0.006499346811324358,
0.02004331909120083,
-0.004868845455348492,
-0.007040339522063732,
-0.0515294149518013,
0.031781893223524094,
0.03084469772875309,
-0.045082930475473404,
0.036876481026411057,
0.03546295315027237,
-0.027491452172398567,
-0.00909361895173788,
0.013351980596780777,
0.03617173805832863,
0.0075454143807291985,
0.014929604716598988,
-0.05971657857298851,
0.015100596472620964,
-0.047413215041160583,
0.08481035381555557,
-0.03585077077150345,
0.02075263299047947,
0.0030291529837995768,
-0.003061265219002962,
-0.0037350975908339024,
0.020958242937922478,
0.033971719443798065,
-0.056700583547353745,
-0.03060603328049183,
-0.03907348960638046,
-0.023073391988873482,
-0.01913185976445675,
0.045947350561618805,
-0.020688654854893684,
-0.00024477936676703393,
0.019352000206708908,
-0.027236470952630043,
-0.00932827778160572,
-0.022500252351164818,
-0.02618282288312912,
0.02658911608159542,
0.002003602683544159,
0.02884136512875557,
-0.02593197673559189,
-0.019526956602931023,
-0.008071417920291424,
-0.03368254378437996,
-0.05435953661799431,
-0.009381989948451519,
-0.028949180617928505,
0.027349025011062622,
-0.059349462389945984,
0.017159972339868546,
0.036428507417440414,
-0.0036530508659780025,
-0.01546965166926384,
-0.013135177083313465,
0.03524855896830559,
-0.001981539884582162,
-0.015440203249454498,
-0.01703745685517788,
-0.007730941288173199,
-0.005114361178129911,
-0.06239365413784981,
0.010011065751314163,
0.028250476345419884,
-0.06449343264102936,
0.008656289428472519,
0.0032765467185527086,
-0.01202270295470953,
0.04600145295262337,
-0.012834666296839714,
-0.06134730577468872,
-0.023974180221557617,
-0.04269516468048096,
-0.012980055063962936,
-0.004455684218555689,
0.05051589384675026,
0.016337744891643524,
-0.02796074189245701,
0.013521279208362103,
-0.010976077988743782,
0.0694565623998642,
-0.05435493588447571,
0.017259981483221054,
0.03476475551724434,
0.027251040562987328,
-0.001453366712667048,
-0.024228224530816078,
-0.021612469106912613,
0.01198099460452795,
0.055092137306928635,
0.0010081869550049305,
-0.026106739416718483,
-0.03422807902097702,
-0.032287076115608215,
0.025804005563259125,
0.00752880796790123,
0.02296568639576435,
-0.006925641559064388,
0.03544352576136589,
-0.020914021879434586,
0.00037987378891557455,
-0.012626204639673233,
-0.0006235347245819867,
-0.006465025711804628,
-0.028131289407610893,
0.043904297053813934,
0.019665220752358437,
0.026431484147906303,
-0.015768786892294884,
-0.008006728254258633,
-0.04223090782761574,
0.009045017883181572,
0.05713983252644539,
-0.03378243371844292,
0.056072868406772614,
0.010828669182956219,
0.004498107824474573,
0.011596581898629665,
-0.011405888013541698,
-0.04298439621925354,
-0.016812974587082863,
0.022851379588246346,
0.016719285398721695,
-0.014358090236783028,
0.016069725155830383,
0.0707237645983696,
0.014994730241596699,
-0.04148104041814804,
-0.011539120227098465,
0.03870135545730591,
-0.002278134925290942,
-0.012651191093027592,
0.023965798318386078,
-0.03363048657774925,
0.03008958511054516,
-0.03157676383852959,
0.02602795884013176,
0.0036289338022470474,
0.019674530252814293,
0.04940728470683098,
0.04516618698835373,
-0.014152913354337215,
-0.015219404362142086,
-0.02847890928387642,
-0.027030227705836296,
0.0006730065797455609,
0.011769270524382591,
0.016474545001983643,
-0.02313661202788353,
0.028734704479575157,
0.04388599097728729,
-0.0028059775941073895,
0.030113855376839638,
-0.004819523077458143,
-0.015779562294483185,
-0.05857955664396286,
-0.04331493005156517,
-0.012391084805130959,
0.06415709108114243,
0.007736565545201302,
0.0012723075924441218,
0.0021659473422914743,
-0.026123106479644775,
0.01876460388302803,
0.036349888890981674,
0.005421902984380722,
-0.005960842594504356,
0.08159315586090088,
0.001852783258073032,
-0.0011292241979390383,
-0.05373605713248253,
0.028252234682440758,
0.12273822724819183,
0.023936115205287933,
-0.004064623732119799,
-0.07125690579414368,
-0.016588550060987473,
-0.026907678693532944,
0.018265487626194954,
-0.04190312325954437,
0.04374801367521286,
-0.00585665600374341,
-0.009541081264615059,
0.026899447664618492,
0.009945186786353588,
-0.004939533304423094,
0.013103383593261242,
0.055674415081739426,
-0.0326598696410656,
-0.015907226130366325,
-0.003528984496369958,
0.008417176082730293,
-0.03223084658384323,
0.003973833750933409,
-0.032936323434114456,
0.010374132543802261,
-0.021671803668141365,
-0.010691918432712555,
0.038233865052461624,
-0.03653937950730324,
-0.00090214324882254,
-0.027593670412898064,
-0.021607914939522743,
0.03587757796049118,
0.003043097909539938,
-0.034906089305877686,
-0.014044457115232944,
0.01699412241578102,
0.04358059540390968,
-0.006219130475074053,
0.0017999514238908887,
0.006138558033853769,
-0.00022370020451489836,
-0.015260188840329647,
0.021193912252783775,
0.04899493604898453,
-0.04303572699427605,
0.003825319465249777,
-0.017518458887934685,
0.054743848741054535,
-0.015321943908929825,
0.017808597534894943,
0.003121413988992572,
0.0027559699956327677,
0.025529123842716217,
-0.05239825323224068,
0.004812716506421566,
0.025493422523140907,
0.0314890593290329,
-0.046175263822078705,
0.014190723188221455,
-0.019370943307876587,
-0.004111533518880606,
0.023935843259096146,
0.00038632817449979484,
-0.0075304568745195866,
-0.0021415555384010077,
0.02115197479724884,
-0.005732348188757896,
0.012782050296664238,
-0.02209954522550106,
-0.003271212335675955,
-0.025172900408506393,
-0.052982281893491745,
-0.0033408894669264555,
0.012128894217312336,
0.02610836923122406,
0.0005738898762501776,
0.0000018548921616456937,
-0.00987687986344099,
-0.042065318673849106,
-0.006675017531961203,
-0.08178827911615372,
0.05343010649085045,
0.017495933920145035,
-0.029676401987671852,
-0.026758253574371338,
-0.018742695450782776,
-0.004098421428352594,
0.08239152282476425,
0.013675881549715996,
0.007375110872089863,
0.020279139280319214,
0.03740692883729935,
0.021812597289681435,
0.013696026057004929,
-0.012814318761229515,
0.015029121190309525,
-0.013381225988268852,
-0.02580306865274906,
-0.010693900287151337,
0.023189183324575424,
0.05775829404592514,
-0.00004515029286267236,
-0.03350245952606201,
0.04297083988785744,
-0.01084061898291111,
0.010792840272188187,
-0.0017382552614435554,
-0.01883450150489807,
-0.01274979766458273,
-0.0020838179625570774,
-0.0049251895397901535,
-0.04099322110414505,
-0.01655355840921402,
0.015438169240951538,
-0.011128395795822144,
0.015119101852178574,
0.021933050826191902,
-0.005700103472918272,
0.004908621311187744,
-0.01628434844315052,
0.040437690913677216,
-0.033124763518571854,
-0.018663814291357994,
-0.03938703238964081,
0.028753619641065598,
0.035242754966020584,
-0.02262631244957447,
-0.04793590307235718,
0.060089532285928726,
0.012536861002445221,
0.003425680799409747,
0.008445980027318,
0.004521733149886131,
-0.0030985609628260136,
-0.01019782479852438,
0.02654600888490677,
0.020444396883249283,
0.04039202257990837,
0.03159855678677559,
-0.006247426848858595,
0.06803452223539352,
-0.0035324112977832556,
-0.04305996000766754,
0.018217017874121666,
0.018961545079946518,
0.03439243882894516,
0.027622578665614128,
-0.05684945732355118,
-0.03327567130327225,
0.019267333671450615,
0.007383295800536871,
-0.028178110718727112,
0.009685369208455086,
-0.04833274707198143,
-0.02032676711678505,
-0.039406806230545044,
0.0225708968937397,
-0.019665993750095367,
-0.023616624996066093,
0.016471263021230698,
0.022621767595410347,
0.039273474365472794,
0.006168919615447521,
0.0019292471697553992,
0.0362863652408123,
-0.0007691287319175899,
0.031008636578917503,
-0.005297084338963032,
0.017943663522601128,
0.05106840282678604,
-0.006712258793413639,
0.010872118175029755,
-0.016876375302672386,
0.011906377039849758,
-0.08377578854560852,
0.001212450210005045,
-0.007973350584506989,
-0.0353255569934845,
0.04659885913133621,
-0.06557831168174744,
0.02515297196805477,
0.04402529075741768,
-0.0678277239203453,
-0.025302520021796227,
-0.03850783035159111,
-0.018020229414105415,
-0.025944389402866364,
0.01619686931371689,
0.0010192281333729625,
0.09849192947149277,
0.013903159648180008,
0.03117344342172146,
0.00385045213624835,
0.022740015760064125,
-0.015804341062903404,
-0.046422697603702545,
-0.058640602976083755,
0.003941780421882868,
-0.03112277388572693,
0.0019658897072076797,
0.05482758581638336,
0.008010088466107845,
0.0069907852448523045,
0.044345419853925705,
-0.0000335596087097656,
0.006985605228692293,
-0.047596774995326996,
0.07319630682468414,
0.029209772124886513,
0.02904430404305458,
-0.0069678183645009995,
0.017377352342009544,
0.0050243171863257885,
0.011534614488482475,
0.014822089113295078,
0.016758611425757408,
0.020349876955151558,
-0.006550673395395279,
0.018389083445072174,
-0.06046703830361366,
0.0017612973460927606,
0.02755546383559704,
-0.030699560418725014,
0.0039514400996267796,
0.007665226235985756,
0.014509366825222969,
0.01873539760708809,
-0.019474206492304802,
0.012228247709572315,
-0.06094358116388321,
-0.025304414331912994,
0.008807635866105556,
-0.043223850429058075,
0.02552689239382744,
0.035924702882766724,
-0.005839586723595858,
-0.0450345017015934,
0.02497541904449463,
0.005692940205335617,
-0.009262681007385254,
-0.03494755178689957,
0.0033463668078184128,
0.014353347942233086,
0.014170600101351738,
-0.004263560753315687,
-0.03237347677350044,
-0.037533972412347794,
0.03287442401051521,
0.04763998091220856,
0.0016455729492008686,
0.0039339205250144005,
-0.02843525819480419,
0.004335271194577217,
-0.035425182431936264,
0.03231756016612053,
0.0075861732475459576,
-0.013019156642258167,
-0.03395596891641617,
-0.02167903259396553,
0.022196916863322258,
0.019541794434189796,
0.06918185949325562,
-0.02332179620862007,
-0.015699241310358047,
0.04294988885521889,
-0.02935008332133293,
0.009256490506231785,
-0.07834078371524811,
0.011434787884354591,
0.002742519835010171,
0.004751937929540873,
0.000900405750144273,
-0.02346988394856453,
-0.02378232404589653,
0.008344964124262333,
0.0212933998554945,
0.019820787012577057,
0.008571572601795197,
-0.0022253263741731644,
-0.05118165165185928,
0.06160897761583328,
-0.0029531505424529314,
-0.029206186532974243,
0.017708800733089447,
-0.02517138421535492,
0.02590494230389595,
0.03191395848989487,
-0.012571992352604866,
-0.03728624805808067,
0.033644016832113266,
-0.03156346082687378,
-0.003154921345412731,
0.010031180456280708,
-0.0304847601801157,
0.06974725425243378,
-0.051571235060691833,
-0.015974469482898712,
0.031201213598251343,
-0.02517460472881794,
0.02634260803461075,
0.08870075643062592,
-0.007987603545188904,
0.027376748621463776,
0.006591986399143934,
0.04146203771233559,
0.0018709730356931686,
0.0017695162678137422,
0.012153579853475094,
0.0396898090839386,
-0.0007944194367155433,
0.008719732984900475,
-0.015684856101870537,
0.03920511528849602,
0.00587827991694212,
0.03379802405834198,
0.028406070545315742,
0.043615542352199554,
-0.05059349164366722,
-0.05202822387218475,
0.001244966173544526,
-0.041762370616197586,
-0.014395736157894135,
0.03609875589609146,
-0.0358259454369545,
0.07999498397111893,
-0.06671427935361862,
0.0042359489016234875,
0.0027016664389520884,
0.03678249567747116,
0.007182043511420488,
0.004293934907764196,
-0.017372624948620796,
0.04599636793136597,
-0.016153590753674507,
-0.01855737902224064,
-0.012877619825303555,
-0.024288464337587357,
0.02698308788239956,
-0.010369576513767242,
0.05269034206867218,
0.02932274155318737,
-0.014582855626940727,
-0.018980862572789192,
-0.025718579068779945,
-0.022613031789660454,
-0.01334399078041315,
0.010881244204938412,
0.018719037994742393,
-0.0035831488203257322,
-0.02681906521320343,
-0.010376852937042713,
-0.022317029535770416,
0.039189692586660385,
-0.056102119386196136,
0.0008129804627969861,
-0.02269759029150009,
0.03292375057935715,
0.006465924438089132,
0.011927982792258263
] |
<p>Is this correct? </p>
<p><a href="http://en.wikipedia.org/wiki/Tensor" rel="nofollow">Tensors</a> are linear mappings between two coordinate systems on a manifold. The elements of that mapping (which include the different changes of bases at each point of the manifold) are governed by the components of the <a href="http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant" rel="nofollow">Jacobian</a>. The Jacobian, the ratio of the volume elements of the two states – is itself a tensor.</p>
<p>(I expect this is elementary for those who know – I’d like to reach that state myself, so please feel free to expand).</p>
| 9,386 |
[
-0.029370736330747604,
-0.008999081328511238,
-0.018987635150551796,
-0.029639005661010742,
0.06248440593481064,
-0.0036989119835197926,
0.004207519814372063,
-0.016097651794552803,
0.012388458475470543,
-0.02594846487045288,
0.03070574812591076,
0.00666694575920701,
0.06692096590995789,
0.016241319477558136,
0.0011907799635082483,
0.008620795793831348,
-0.017811564728617668,
-0.001533334143459797,
-0.025159191340208054,
-0.02203477919101715,
0.050471868366003036,
0.02381271868944168,
-0.01760718785226345,
-0.003144690999761224,
-0.02082105167210102,
0.054950978606939316,
0.023814909160137177,
-0.009513870812952518,
0.02283194288611412,
0.07494831085205078,
-0.008199022151529789,
-0.04207596555352211,
0.04575470834970474,
0.04076338931918144,
-0.0005390179576352239,
-0.023756826296448708,
-0.04528025910258293,
-0.018655020743608475,
0.012455531395971775,
0.01387170609086752,
-0.012231918051838875,
-0.030930357053875923,
-0.05287574976682663,
0.055570002645254135,
0.0142276082187891,
0.03655722364783287,
0.03402995690703392,
-0.02200978249311447,
0.018628064543008804,
-0.053830768913030624,
0.10642454773187637,
0.02395809069275856,
0.03798693045973778,
0.03474504500627518,
-0.02250603586435318,
0.01677120476961136,
0.06254886090755463,
0.07479476928710938,
0.0024841544218361378,
-0.04917042702436447,
-0.013990102335810661,
-0.008859689347445965,
-0.007271343842148781,
-0.02507026121020317,
-0.03903868421912193,
0.021737826988101006,
-0.012294166721403599,
-0.022211449220776558,
0.03955944627523422,
-0.026380810886621475,
-0.005895678885281086,
0.019061168655753136,
0.039037857204675674,
-0.06916352361440659,
0.014706289395689964,
-0.03518201783299446,
0.05237334966659546,
0.03647797927260399,
0.001682491390965879,
0.04096461087465286,
-0.00044214673107489944,
-0.014818962663412094,
0.03036576509475708,
-0.006383403670042753,
0.013895322568714619,
-0.009250381961464882,
0.06459517031908035,
-0.028704693540930748,
0.006382952909916639,
0.03346431255340576,
0.0007400680333375931,
-0.010817458853125572,
0.021147824823856354,
-0.010265042074024677,
-0.03853066638112068,
-0.0046018813736736774,
-0.004129736218601465,
0.029712727293372154,
0.006667767651379108,
-0.03545913100242615,
-0.004131080117076635,
-0.028566423803567886,
0.006899157073348761,
0.028716836124658585,
-0.026435336098074913,
0.014742528088390827,
-0.046623796224594116,
0.013065865263342857,
-0.0011441740207374096,
-0.019791899248957634,
-0.04400961846113205,
0.01963234879076481,
-0.014045249670743942,
-0.022022966295480728,
-0.021801669150590897,
-0.04843517765402794,
0.01599828340113163,
0.00769182899966836,
0.0327693372964859,
0.07759804278612137,
0.037672046571969986,
-0.03774604946374893,
0.030003853142261505,
-0.010394809767603874,
-0.0481494702398777,
0.02283676154911518,
0.04721006378531456,
-0.006688835099339485,
-0.04016531631350517,
0.0083266356959939,
0.015675688162446022,
-0.03253614902496338,
0.014286624267697334,
0.03762511909008026,
0.015738660469651222,
-0.024160727858543396,
-0.1103685051202774,
-0.06973059475421906,
0.03287927061319351,
0.005231019109487534,
0.010899604298174381,
-0.08768071979284286,
0.023237792775034904,
0.05654960125684738,
0.045194853097200394,
-0.004894846118986607,
0.038804247975349426,
0.020330028608441353,
0.01620836742222309,
0.0025720701087266207,
-0.028330586850643158,
0.009040131233632565,
-0.0287442896515131,
-0.053501516580581665,
0.0027962317690253258,
-0.04246571660041809,
0.005372056271880865,
0.034636709839105606,
0.03371615335345268,
0.009763169102370739,
0.06259028613567352,
-0.018152648583054543,
0.0072652786038815975,
0.0495910719037056,
0.007144812028855085,
-0.05519448220729828,
0.05706818029284477,
-0.007563574239611626,
0.05669534206390381,
0.030912702903151512,
0.018730932846665382,
0.015360226854681969,
0.004072211217135191,
0.03491128236055374,
0.03344796597957611,
-0.04312119632959366,
-0.05552034452557564,
-0.03292029723525047,
0.0036863782443106174,
-0.011373896151781082,
-0.06788401305675507,
-0.03642541915178299,
-0.013969331048429012,
0.021200086921453476,
0.000599983730353415,
0.03586988151073456,
-0.0012492972891777754,
-0.002755639608949423,
-0.0005350071005523205,
-0.04772769659757614,
0.009120799601078033,
-0.02941759303212166,
0.02635016106069088,
-0.033618006855249405,
-0.024699335917830467,
0.04533819109201431,
0.02338380366563797,
0.0195684265345335,
-0.029108786955475807,
-0.020869892090559006,
-0.013045077212154865,
0.006709866225719452,
0.007635857909917831,
-0.02910209633409977,
0.008622674271464348,
0.0546441413462162,
0.04676787555217743,
-0.005584788043051958,
0.039748724550008774,
-0.00763680087402463,
-0.002004261128604412,
0.020227069035172462,
0.004029017873108387,
0.02492043748497963,
-0.022573385387659073,
-0.004826095886528492,
0.004102654755115509,
-0.006085990462452173,
-0.015404948964715004,
0.025833820924162865,
-0.05510387569665909,
0.06258853524923325,
0.03165540471673012,
0.012176589109003544,
-0.0013616940705105662,
0.02306879498064518,
0.008790270425379276,
0.050670262426137924,
-0.009314848110079765,
-0.012688453309237957,
-0.041873686015605927,
0.0309084914624691,
0.01029450073838234,
0.061396192759275436,
-0.04811246693134308,
0.013634380884468555,
0.040107596665620804,
0.046363163739442825,
-0.0027765717823058367,
0.00825791247189045,
0.0057448833249509335,
-0.026605647057294846,
0.011150392703711987,
-0.0004522394738160074,
0.028469590470194817,
0.02758791483938694,
0.010908210650086403,
-0.0017462957184761763,
0.04082834720611572,
0.009151797741651535,
0.005249406676739454,
0.050268400460481644,
-0.035236284136772156,
0.03840561956167221,
0.02431674674153328,
-0.008976791985332966,
0.047707635909318924,
-0.012416199781000614,
0.012383648194372654,
0.03765766695141792,
-0.007261591963469982,
-0.03770101070404053,
-0.019087720662355423,
-0.0021042285952717066,
0.010707259178161621,
0.01088803168386221,
-0.040397144854068756,
-0.004287187475711107,
0.015431647188961506,
-0.05341155827045441,
0.004384183324873447,
-0.005591200664639473,
0.00109625153709203,
-0.023249071091413498,
0.0210984218865633,
0.017441051080822945,
0.009267210029065609,
0.035658758133649826,
-0.023852145299315453,
-0.010197576135396957,
-0.007104447577148676,
-0.024087199941277504,
0.009188966825604439,
0.004100372549146414,
-0.05981237068772316,
0.019432825967669487,
-0.05822427570819855,
-0.015310671180486679,
0.022273428738117218,
-0.035091109573841095,
-0.0026186946779489517,
-0.01309683732688427,
-0.02982390858232975,
-0.03461746498942375,
-0.030049700289964676,
-0.02540779486298561,
0.04765751212835312,
-0.023976583033800125,
-0.008882040157914162,
0.029298938810825348,
-0.005348342005163431,
-0.023857073858380318,
-0.018115928396582603,
-0.02618914097547531,
-0.03254695609211922,
-0.0056509776040911674,
-0.010517316870391369,
0.03133310377597809,
-0.01744004711508751,
0.002245577285066247,
0.06349612027406693,
-0.022982679307460785,
-0.007230153772979975,
-0.08039794117212296,
-0.05977780371904373,
0.005705861374735832,
0.02178465574979782,
0.05677005276083946,
0.004629295319318771,
-0.052873801440000534,
0.07658246904611588,
0.02641642466187477,
-0.0413171648979187,
-0.020972492173314095,
0.009091143496334553,
-0.026755018159747124,
-0.053977545350790024,
0.018383920192718506,
0.02670164592564106,
-0.008637605234980583,
0.05188284069299698,
0.024570174515247345,
0.034790314733982086,
0.03842831403017044,
0.006954904645681381,
0.01145471353083849,
0.006584042217582464,
0.034459639340639114,
-0.036619048565626144,
0.05602245405316353,
0.010129038244485855,
0.012973189353942871,
0.008183936588466167,
-0.03180379047989845,
0.05116261541843414,
-0.03651825711131096,
-0.03707581385970116,
0.03777271881699562,
-0.01622852124273777,
0.03018464520573616,
-0.01170626375824213,
0.05351409316062927,
0.007106820587068796,
-0.014290006831288338,
-0.0002185433404520154,
0.05704423785209656,
0.01727033220231533,
-0.02122305892407894,
0.014437577687203884,
0.03556176275014877,
0.014996165409684181,
-0.045058488845825195,
0.0017855154583230615,
0.015423338860273361,
-0.014764181338250637,
-0.0010002199560403824,
-0.01901671290397644,
-0.038283154368400574,
0.06000037491321564,
0.0034739449620246887,
0.04278973489999771,
-0.0006014973623678088,
-0.028636526316404343,
0.030470291152596474,
-0.0945592075586319,
0.022259904071688652,
0.008785193786025047,
0.03755426034331322,
-0.00809451937675476,
0.058322686702013016,
-0.00011174095561727881,
0.012079480104148388,
0.020335685461759567,
-0.01806492544710636,
-0.08383062481880188,
0.015802063047885895,
-0.036917898803949356,
-0.004452970810234547,
0.026710543781518936,
-0.06087923049926758,
0.006739865522831678,
-0.041811443865299225,
-0.01597440429031849,
0.014830431900918484,
0.01086276862770319,
-0.057012300938367844,
0.007976196706295013,
-0.01717825047671795,
-0.022708095610141754,
0.01310904510319233,
0.029909778386354446,
0.04905225709080696,
-0.0030555869452655315,
0.015601127408444881,
0.049393560737371445,
-0.023554299026727676,
0.010067296214401722,
0.006060453597456217,
0.03456661477684975,
0.059023380279541016,
0.014719531871378422,
0.006154205184429884,
0.018065141513943672,
-0.011092756874859333,
0.012501178309321404,
-0.020815409719944,
0.044471513479948044,
0.0034244623966515064,
-0.05452512949705124,
-0.02190103381872177,
-0.03663028031587601,
-0.041263397783041,
-0.004807642661035061,
0.04085887596011162,
0.016816917806863785,
0.013424974866211414,
0.019480964168906212,
0.02989187091588974,
-0.005774626042693853,
0.043389108031988144,
0.0790417417883873,
-0.027526622638106346,
-0.026704732328653336,
-0.05728002265095711,
-0.00835290178656578,
-0.0217951238155365,
-0.013230289332568645,
0.02676462195813656,
-0.00897403247654438,
-0.045256372541189194,
-0.0012090635718777776,
-0.010544533841311932,
-0.008997292257845402,
-0.019484465941786766,
0.022423215210437775,
-0.020710788667201996,
0.02045239508152008,
-0.0014668338699266315,
0.026817528530955315,
0.014082283712923527,
0.013402050361037254,
0.021039200946688652,
0.012197569943964481,
-0.014996014535427094,
-0.07797253876924515,
-0.019141795113682747,
0.012050620280206203,
0.05010434240102768,
-0.0168263278901577,
0.010512039065361023,
-0.018840845674276352,
-0.03596172854304314,
0.04456666484475136,
-0.022805746644735336,
0.051132459193468094,
0.03189569711685181,
-0.03619163855910301,
0.0035836827009916306,
-0.02830919437110424,
-0.018963340669870377,
0.02665216475725174,
-0.018489360809326172,
0.018715759739279747,
0.013266346417367458,
0.02771042287349701,
-0.03276732191443443,
0.0071282777935266495,
0.022206153720617294,
0.050650082528591156,
0.012267877347767353,
-0.026085641235113144,
-0.01208257395774126,
0.028499450534582138,
-0.047479670494794846,
-0.09665285050868988,
0.00864430982619524,
0.042819056659936905,
-0.02651924453675747,
-0.0076962728053331375,
-0.01518374215811491,
-0.0698937252163887,
0.04046308994293213,
0.027397649362683296,
0.011896398849785328,
0.031182365491986275,
-0.038990799337625504,
0.058972276747226715,
0.03289361670613289,
-0.008273118175566196,
0.020567042753100395,
0.0044080112129449844,
-0.027976538985967636,
0.007300828117877245,
-0.025944501161575317,
0.05176384001970291,
-0.022952336817979813,
0.015156307257711887,
-0.02260037325322628,
0.0248623788356781,
-0.04778948053717613,
0.032209936529397964,
-0.02528476156294346,
0.021854951977729797,
-0.015442303381860256,
-0.016471538692712784,
-0.002446960425004363,
0.023168135434389114,
-0.013005928136408329,
-0.023919232189655304,
0.003157729050144553,
0.02435961365699768,
-0.019369086250662804,
-0.03851041570305824,
0.017252163961529732,
-0.02789420820772648,
-0.0008709458634257317,
0.04334532469511032,
0.0006480968440882862,
0.037350136786699295,
-0.011758881621062756,
-0.02654639445245266,
-0.0008197476854547858,
-0.08151658624410629,
0.04674253612756729,
-0.02162800170481205,
-0.02758953347802162,
0.012989556416869164,
-0.02789130061864853,
-0.012527377344667912,
0.013718613423407078,
-0.011693697422742844,
0.02526884898543358,
-0.027212513610720634,
0.008889509364962578,
0.008178784511983395,
0.019994046539068222,
-0.05370645225048065,
-0.05170576646924019,
0.01572316139936447,
0.00025732434005476534,
-0.0371074452996254,
-0.03936231508851051,
0.01371734868735075,
-0.05424671247601509,
-0.0017979013500735164,
-0.017715949565172195,
0.05924151837825775,
-0.06239388883113861,
0.00696200504899025,
0.04889178276062012,
0.015038607642054558,
0.037263598293066025,
-0.0021587719675153494,
0.01570110023021698,
-0.020057491958141327,
0.0099294139072299,
-0.0024047803599387407,
-0.0015551934484392405,
0.03584748134016991,
-0.01796434447169304,
-0.0014407755807042122,
-0.0320223830640316,
0.0035845907405018806,
0.047528598457574844,
-0.018599573522806168,
-0.007347726263105869,
0.0033357914071530104,
0.02072478085756302,
-0.01990347169339657,
-0.038663238286972046,
-0.001042535644955933,
-0.004010877572000027,
-0.007267866749316454,
-0.026965705677866936,
0.011662661097943783,
-0.01176285557448864,
-0.010608621872961521,
-0.007066520396620035,
-0.0017066494328901172,
0.04397236928343773,
-0.015932274982333183,
0.093633271753788,
-0.00654927222058177,
0.01578775979578495,
0.014747115783393383,
-0.03397861495614052,
0.01390157826244831,
0.028535597026348114,
-0.002469138242304325,
0.015574953518807888,
-0.029928192496299744,
-0.01989976316690445,
-0.01551455445587635,
-0.037993162870407104,
0.021973755210638046,
0.1093541756272316,
-0.004462044220417738,
0.034713178873062134,
0.039394959807395935,
-0.009689967148005962,
0.04486655816435814,
-0.008841048926115036,
-0.041656091809272766,
-0.013558164238929749,
0.0006817983230575919,
0.028902696445584297,
-0.010099639184772968,
-0.021342221647500992,
0.031566645950078964,
0.02809266187250614,
-0.05368693917989731,
0.016844293102622032,
0.010227932594716549,
0.003947580698877573,
-0.0036240508779883385,
0.014413024298846722,
-0.056253306567668915,
0.025717103853821754,
-0.026512565091252327,
0.041655007749795914,
-0.006728263106197119,
-0.017575882375240326,
0.05900832265615463,
0.00042981564183719456,
0.02765871398150921,
-0.04061523452401161,
-0.05028849467635155,
-0.04131796583533287,
0.02765319123864174,
0.001281973673030734,
0.037408847361803055,
-0.014968058094382286,
0.014721036888659,
0.08253578841686249,
0.01787295937538147,
0.03522795811295509,
-0.0072065736167132854,
-0.04433596879243851,
-0.008713536895811558,
-0.04154565557837486,
-0.03088567592203617,
0.042279936373233795,
-0.02225121669471264,
-0.042665932327508926,
0.002990808105096221,
-0.022141344845294952,
0.016484156250953674,
-0.013836836442351341,
0.04768199101090431,
-0.0035517511423677206,
0.06562688946723938,
0.008866798132658005,
0.02269040420651436,
-0.02849402464926243,
0.02202276512980461,
0.10594984889030457,
0.08406013250350952,
0.00418551079928875,
-0.059843260794878006,
0.02252558432519436,
-0.0028241793625056744,
-0.01993885636329651,
-0.013395923189818859,
0.036093756556510925,
-0.01729903183877468,
-0.006046593189239502,
-0.028805769979953766,
0.06090296059846878,
-0.025858350098133087,
-0.012925471179187298,
0.05327999219298363,
-0.023362642154097557,
-0.03925696760416031,
-0.010902730748057365,
0.007206565700471401,
-0.022311633452773094,
-0.01662190444767475,
-0.007599704898893833,
0.023975536227226257,
-0.023269416764378548,
0.0088029270991683,
-0.05300144851207733,
-0.0028625703416764736,
-0.004666104447096586,
0.02569233812391758,
-0.03865668550133705,
0.004253318998962641,
0.004143841564655304,
0.01580014079809189,
-0.06087062880396843,
0.02016960270702839,
0.010961862280964851,
-0.0008159711142070591,
0.0064872815273702145,
0.041862476617097855,
-0.011923550628125668,
0.00514819473028183,
0.015054888091981411,
-0.01886962726712227,
-0.06513049453496933,
0.0005593378446064889,
-0.05944100022315979,
0.03378598764538765,
-0.009350045584142208,
0.025836322456598282,
-0.019317718222737312,
-0.0059920381754636765,
-0.001274839392863214,
-0.07156583666801453,
-0.021296724677085876,
0.023699795827269554,
0.020056424662470818,
0.0007127136341296136,
-0.007303330581635237,
-0.04137389734387398,
0.0037517817690968513,
-0.0003628836420830339,
0.013736492954194546,
0.0037776301614940166,
0.022857418283820152,
0.011113355867564678,
-0.0178568996489048,
0.06484200805425644,
-0.01594661734998226,
0.00830577127635479,
-0.03801065683364868,
-0.03358793631196022,
-0.012625334784388542,
-0.0349762886762619,
0.012990826740860939,
0.016788871958851814,
0.025252560153603554,
0.004931693430989981,
-0.020354438573122025,
-0.0023881481029093266,
-0.06499744206666946,
0.021433668211102486,
0.003160941880196333,
-0.03709712252020836,
-0.018823567777872086,
0.02251020260155201,
0.026578906923532486,
0.01115818228572607,
-0.057859018445014954,
0.012079650536179543,
0.011499798856675625,
0.009552784264087677,
0.018388647586107254,
-0.03995835781097412,
0.01819859817624092,
0.01325979270040989,
-0.022884463891386986,
-0.008410591632127762,
-0.014802046120166779,
0.03735368326306343,
0.027838394045829773,
0.03421608358621597,
-0.024412501603364944,
0.02765154466032982,
-0.01998535357415676,
0.014217684045433998,
0.00040429597720503807,
-0.009118126705288887,
0.005471427924931049,
0.04380038008093834,
0.003453731769695878,
-0.05682455375790596,
-0.01285789255052805,
-0.015368511900305748,
-0.013996179215610027,
0.007130867801606655,
0.0013599480735138059,
-0.020583027973771095,
-0.014032816514372826,
-0.007529247552156448,
0.03543354570865631,
-0.023626968264579773,
-0.012212507426738739,
-0.047743119299411774,
0.0066629140637815,
0.039900895208120346,
0.020893217995762825,
-0.016165779903531075,
0.027633080258965492,
-0.012170734815299511,
-0.0015197232132777572,
0.0898120105266571,
0.019850311800837517,
0.009749040007591248,
-0.04459436610341072,
0.015088428743183613,
0.0238539669662714,
0.058162737637758255,
0.00013807274808641523,
-0.04103691503405571,
0.02363186702132225,
-0.030107971280813217,
-0.022606460377573967,
0.02331807278096676,
-0.00043305751751177013,
0.022176560014486313,
0.008137024007737637,
-0.002407986903563142,
-0.004786189645528793,
0.03701789677143097,
-0.017056582495570183,
0.013990992680191994,
0.009820627048611641,
-0.06000319868326187,
-0.008315667510032654,
-0.04691273719072342,
0.0021626127418130636,
0.03318190202116966,
0.005979301407933235,
0.016406390815973282,
0.028265314176678658,
0.013466717675328255,
-0.014453270472586155,
-0.018808729946613312,
0.010333642363548279,
0.014827671460807323,
-0.002240806818008423,
-0.000011204852853552438,
0.02316219173371792,
0.036595508456230164,
-0.038126032799482346,
0.0038695898838341236,
0.025030774995684624,
0.015683509409427643,
-0.09723786264657974,
0.009324786253273487,
-0.00014373002341017127,
-0.01811753213405609,
0.02983345091342926,
-0.08439436554908752,
0.014126419089734554,
-0.0012744698906317353,
-0.04807722568511963,
0.01603277027606964,
-0.00870308093726635,
-0.019298013299703598,
-0.01141717005521059,
0.012354460544884205,
-0.03395875543355942,
0.04457903653383255,
0.013331704773008823,
0.06134987995028496,
0.03480840101838112,
-0.008198417723178864,
0.01152666937559843,
-0.012360389344394207,
-0.027850374579429626,
0.0308693740516901,
-0.01668286882340908,
-0.04813435301184654,
0.052558839321136475,
-0.009017247706651688,
-0.04115403816103935,
0.023878930136561394,
-0.023248597979545593,
0.008415463380515575,
-0.0012400072300806642,
-0.007159715984016657,
0.023631626740098,
-0.007876447401940823,
0.03231215476989746,
0.005214465782046318,
0.009399792179465294,
-0.0026402748189866543,
-0.006523200776427984,
0.04276609793305397,
-0.0031503024511039257,
-0.01161586120724678,
0.04291485995054245,
-0.024330027401447296,
-0.029308058321475983,
0.033555157482624054,
-0.01740613766014576,
0.0038098169025033712,
-0.006489766761660576,
0.012203177437186241,
-0.01386923249810934,
-0.052747417241334915,
0.011856586672365665,
-0.03254864737391472,
-0.015866819769144058,
0.04737337678670883,
-0.0020740071777254343,
-0.022373031824827194,
0.029847607016563416,
-0.01971183717250824,
-0.021031510084867477,
0.014608057215809822,
0.007254056166857481,
-0.03330305963754654,
-0.06662265211343765,
0.00975358858704567,
0.007835258729755878,
-0.0036965354811400175,
-0.012240574695169926,
-0.05179522931575775,
-0.03181750699877739,
0.05568429455161095,
-0.0040987818501889706,
0.020434008911252022,
0.025112375617027283,
-0.026610707864165306,
-0.020890187472105026,
-0.07553240656852722,
0.04384699463844299,
0.024700334295630455,
-0.06394001096487045,
-0.030622057616710663,
0.017171399667859077,
0.010584852658212185,
0.025358490645885468,
0.05843720957636833,
0.01423609908670187,
0.020484745502471924,
-0.00592851871624589,
0.00897777359932661,
0.02756759710609913,
-0.03259044140577316,
0.0026220285799354315,
-0.025418946519494057,
-0.0124934958294034,
0.0275341235101223,
-0.0490914061665535,
-0.004055101424455643,
0.01496502198278904,
0.013830871321260929,
-0.03079824149608612,
0.021156443282961845,
-0.01304351445287466,
-0.030965683981776237,
0.01653836853802204,
0.009744944050908089,
-0.03006177954375744,
0.061253637075424194,
0.0046957265585660934,
-0.005505191162228584,
0.021917935460805893,
-0.018189426511526108,
-0.04644795134663582,
-0.0008741100318729877,
-0.03327776491641998,
-0.019463635981082916,
0.003086032345890999,
-0.027939464896917343,
0.03626082092523575,
-0.007182301487773657,
-0.02755449339747429,
0.05933859944343567,
-0.05640188604593277,
0.0047253770753741264,
0.03980303555727005,
0.011347522027790546,
0.012358350679278374,
0.003653336316347122,
0.060074783861637115,
0.029993386939167976,
-0.02251400798559189,
0.01055337768048048,
0.05370091274380684,
0.04496752843260765,
-0.023115143179893494,
-0.04777480661869049,
0.036729130893945694,
-0.029197070747613907,
0.0023443179670721292,
0.017324475571513176,
0.045189276337623596,
-0.03616765886545181,
-0.0007764422334730625,
-0.003227453213185072,
-0.010055662132799625,
-0.00793714914470911,
0.01068220566958189,
-0.010088043287396431,
0.0642281174659729,
-0.026521284133195877,
-0.018994765356183052,
-0.03043137490749359,
0.027746595442295074,
-0.02945031225681305,
0.02689903974533081,
0.03313220292329788,
0.02722293697297573,
-0.005791518837213516,
-0.037268150597810745,
-0.017581317573785782,
-0.02205783687531948,
0.012903447262942791,
-0.02702075056731701,
0.03915638104081154,
-0.012104128487408161,
-0.008204260841012001,
0.008065933361649513,
-0.002123559359461069,
-0.0106995590031147,
-0.024882176890969276,
0.025552697479724884,
-0.002340214094147086,
0.016871368512511253,
-0.027820970863103867,
-0.02184906415641308,
-0.02530110627412796,
0.06681642681360245,
-0.0657968670129776,
-0.032670240849256516,
-0.045397449284791946,
0.03312891721725464,
-0.0030043201986700296,
-0.0015982701443135738
] |
<p>I was reading this question: <a href="http://physics.stackexchange.com/questions/108470/was-titanics-captains-decision-correct">Was Titanic's captain's decision correct?</a> @oakad commented about a Russian vessel keeping itself afloat by going in reverse, using hydrodynamic pressure to keep its damaged bow high enough to prevent fatal flooding. This got me wondering...</p>
<p>My main question(s):</p>
<p>The Titanic stopped not long after it collided with the iceberg. Could she have stayed afloat a bit longer if she kept moving, either in forward or reverse? How much longer (or shorter, as the case may be?)</p>
<p>Would moving have had a net beneficial effect? For example, would the benefits of moving be outweighed by an increased rate of flooding due to the flowing water further widening the gash, or a reduced rate of pumping because less steam was available to be diverted to the pumps?</p>
<p>What are all of the phenomena that would have an effect on this scenario?</p>
| 9,387 |
[
-0.024474767968058586,
-0.043811045587062836,
-0.021257761865854263,
-0.007110251113772392,
0.03440555930137634,
-0.01229174342006445,
-0.02977086417376995,
0.004423866979777813,
0.023037897422909737,
-0.016825808212161064,
0.016871493309736252,
0.07396126538515091,
0.05385470390319824,
0.027754055336117744,
0.01113976538181305,
0.013005954213440418,
0.02930017001926899,
-0.03906544670462608,
-0.0005722341011278331,
-0.016443392261862755,
-0.008459561504423618,
-0.011128325946629047,
-0.015288826078176498,
0.0019451763946563005,
-0.03619967773556709,
0.0023559920955449343,
0.011435785330832005,
-0.02362002059817314,
0.017727404832839966,
-0.001204302883706987,
0.014733984135091305,
-0.035837262868881226,
0.005904028657823801,
0.026288695633411407,
-0.008545534685254097,
0.010111604817211628,
-0.04501500725746155,
-0.033510059118270874,
-0.048412516713142395,
0.041564520448446274,
0.03199802339076996,
-0.014383070170879364,
-0.0032321056351065636,
0.05690642446279526,
-0.0016565379919484258,
0.038896963000297546,
-0.030388368293642998,
-0.003754011355340481,
0.028668472543358803,
-0.043456707149744034,
0.017643015831708908,
-0.02975669503211975,
0.022189684212207794,
0.023270318284630775,
0.02849576435983181,
-0.0001786205975804478,
0.06030517816543579,
0.1061839684844017,
-0.005058612208813429,
-0.045243654400110245,
-0.0003862028243020177,
0.01923425681889057,
-0.010629665106534958,
-0.003500774037092924,
-0.012408612295985222,
0.03301403671503067,
0.01345544308423996,
-0.017559072002768517,
0.031227679923176765,
-0.033526889979839325,
0.009053817018866539,
-0.008901036344468594,
0.04178277403116226,
-0.0012934420956298709,
0.053937360644340515,
-0.05501572787761688,
0.03672332689166069,
0.04803050309419632,
0.007253265008330345,
0.02491641975939274,
0.003724482608959079,
-0.013696537353098392,
0.0437212772667408,
0.05278715118765831,
0.027928553521633148,
-0.012012260966002941,
0.07574833184480667,
0.005480599123984575,
0.02774447575211525,
0.008240173570811749,
-0.0032322751358151436,
0.000434096553362906,
-0.008895319886505604,
-0.01579391397535801,
-0.012635640799999237,
-0.01712282933294773,
0.016850944608449936,
0.04481418430805206,
0.029417334124445915,
0.016974886879324913,
-0.011581688188016415,
-0.03634865581989288,
-0.008404993452131748,
0.01645609363913536,
0.021976346150040627,
0.0034105568192899227,
-0.05275343731045723,
0.01580831967294216,
-0.012796326540410519,
-0.022947236895561218,
-0.026102907955646515,
0.02362029440701008,
0.011683358810842037,
-0.060273315757513046,
-0.021040109917521477,
-0.03734651207923889,
0.0018566470826044679,
-0.028418589383363724,
0.061058126389980316,
0.04273562133312225,
0.04572802409529686,
-0.005831150338053703,
0.02976798638701439,
-0.033694084733724594,
-0.03280177712440491,
0.01823929138481617,
0.03195458650588989,
-0.03725631907582283,
-0.06067550554871559,
0.045463453978300095,
0.021128496155142784,
0.026588717475533485,
0.020171860232949257,
0.020470069721341133,
0.063150554895401,
0.028592411428689957,
-0.0943189263343811,
-0.06743870675563812,
0.044926270842552185,
0.025476280599832535,
-0.022981997579336166,
-0.0760614424943924,
-0.04278678074479103,
0.0050573511980473995,
0.07305076718330383,
-0.007703699171543121,
0.013542902655899525,
-0.006647258065640926,
0.015119406394660473,
-0.0016676568193361163,
0.000775967026129365,
0.007819176651537418,
0.03618776425719261,
-0.005177298095077276,
-0.05431422218680382,
-0.0753825232386589,
-0.008000208996236324,
0.0246727354824543,
-0.0035821134224534035,
-0.02126757800579071,
0.05584079027175903,
-0.012477382086217403,
-0.008189365267753601,
-0.0012327751610428095,
-0.04714525118470192,
-0.03525121137499809,
0.0576072596013546,
0.0010506431572139263,
-0.03379208967089653,
-0.02083021216094494,
0.023401984944939613,
0.0352083221077919,
-0.03066912852227688,
-0.002746876096352935,
0.03704226016998291,
-0.03831188380718231,
0.043730005621910095,
0.030347980558872223,
0.012601831927895546,
-0.00867662113159895,
0.0034545036032795906,
-0.04391712322831154,
-0.028717197477817535,
-0.00969497300684452,
0.03552304953336716,
0.05745398625731468,
0.007593485061079264,
0.02089172601699829,
0.03184802085161209,
-0.040881942957639694,
-0.018164098262786865,
-0.043031442910432816,
0.03398161381483078,
-0.03139518201351166,
0.03822408989071846,
0.016753990203142166,
-0.01808342896401882,
0.029914671555161476,
-0.03805776312947273,
0.02285946160554886,
0.04881881922483444,
0.01629175804555416,
0.04316350817680359,
0.002385802334174514,
0.01837337575852871,
0.04682502523064613,
-0.0006674932083114982,
0.014722578227519989,
-0.006389921065419912,
-0.021769152954220772,
-0.03975554183125496,
0.025363007560372353,
-0.020820971578359604,
0.01587446965277195,
0.039931636303663254,
-0.00911492295563221,
0.030879218131303787,
-0.010309513658285141,
0.0015819320688024163,
-0.006524245720356703,
-0.014321047812700272,
0.09067777544260025,
0.03756272420287132,
-0.007186640053987503,
0.03090047463774681,
0.03828991949558258,
0.0009669811115600169,
-0.007398013491183519,
0.07230759412050247,
-0.04386059194803238,
-0.06066960468888283,
0.0018385067814961076,
0.001318083144724369,
0.02719276025891304,
-0.03570046275854111,
0.056170690804719925,
0.008715252391994,
0.0014665412018075585,
0.01676582172513008,
-0.0013054021401330829,
-0.02344430424273014,
-0.04217764735221863,
0.013912827707827091,
0.024412794038653374,
0.01082948874682188,
-0.009845545515418053,
0.022884950041770935,
-0.020071150735020638,
-0.005467605777084827,
-0.028293129056692123,
-0.015664726495742798,
0.017841359600424767,
0.04179513454437256,
0.03560476005077362,
-0.0315689742565155,
-0.01935213804244995,
0.029544927179813385,
-0.03551751375198364,
0.012748398818075657,
-0.012269942089915276,
0.017858272418379784,
0.02456595189869404,
-0.04576658830046654,
-0.003323568729683757,
0.011593473143875599,
0.01690289005637169,
-0.008497975766658783,
0.0020626431796699762,
0.04736015945672989,
-0.015933439135551453,
0.009449348784983158,
-0.04876174405217171,
-0.0034154870081692934,
-0.010857813991606236,
-0.013033022172749043,
0.026306593790650368,
0.019367074593901634,
0.06001187488436699,
-0.01692027784883976,
0.014557234942913055,
0.005077454727143049,
-0.05264116823673248,
-0.008371739648282528,
0.03662838414311409,
-0.042120277881622314,
0.0032518221996724606,
-0.04053403064608574,
-0.01515582948923111,
0.010307437740266323,
-0.008823899552226067,
0.021573424339294434,
0.04063378646969795,
0.005237769801169634,
-0.04031500965356827,
-0.009251800365746021,
-0.039121463894844055,
0.013261958956718445,
0.011327859945595264,
-0.019911635667085648,
0.07418614625930786,
-0.010021336376667023,
-0.007177575025707483,
0.018468130379915237,
-0.03218824416399002,
-0.0349227637052536,
0.016785385087132454,
0.025836344808340073,
0.008949106559157372,
0.015598349273204803,
0.009218276478350163,
0.0038951688911765814,
-0.04095468297600746,
-0.0137721486389637,
-0.0555262416601181,
-0.07142385840415955,
0.030952176079154015,
-0.026902487501502037,
0.016784774139523506,
-0.02556249313056469,
-0.016673730686306953,
0.027088792994618416,
-0.0027227874379605055,
-0.03817404434084892,
-0.027780143544077873,
-0.0065152752213180065,
-0.010859878733754158,
-0.007993563078343868,
0.012640545144677162,
0.04744453355669975,
0.010369202122092247,
0.06441357731819153,
0.015061529353260994,
0.04708481207489967,
0.03309224545955658,
0.01609712839126587,
-0.011494209058582783,
-0.003210096387192607,
0.02731558494269848,
0.020157745108008385,
-0.010272379033267498,
-0.019283756613731384,
0.02156182937324047,
0.04036858305335045,
-0.05668460577726364,
0.02341885305941105,
0.04663264378905296,
-0.029843231663107872,
0.06937608867883682,
0.017324475571513176,
-0.01627444475889206,
-0.012904146686196327,
0.01257553044706583,
-0.042946916073560715,
-0.012377617880702019,
-0.003986965864896774,
0.017394714057445526,
0.0432763397693634,
-0.025981156155467033,
0.0015422370051965117,
0.03396616131067276,
0.06545417010784149,
-0.011345408856868744,
-0.030624698847532272,
-0.018330305814743042,
0.01017480157315731,
0.053011294454336166,
-0.022301461547613144,
-0.011254382319748402,
0.025511546060442924,
0.029162157326936722,
0.0004102900275029242,
0.002614641794934869,
-0.031163444742560387,
-0.025146042928099632,
-0.07196535915136337,
-0.02197895757853985,
-0.042348913848400116,
0.04443541541695595,
0.001812926260754466,
-0.0002410222659818828,
0.04539376124739647,
0.014050829224288464,
0.013524086214601994,
0.021495403721928596,
-0.0772041603922844,
-0.011310877278447151,
-0.02815984934568405,
-0.006516008637845516,
-0.005471239797770977,
-0.02446269802749157,
0.01182985957711935,
-0.04844113439321518,
-0.02948341704905033,
-0.01183142326772213,
0.029534999281167984,
-0.04474872723221779,
-0.0018059929134324193,
-0.006029513198882341,
-0.05028402805328369,
0.02329912595450878,
0.011508959345519543,
0.01570737548172474,
-0.051806818693876266,
0.038767460733652115,
0.03584657609462738,
0.014184659346938133,
0.011936268769204617,
-0.013714154250919819,
0.022337675094604492,
-0.014464608393609524,
0.02807733416557312,
0.01574263721704483,
0.014544783160090446,
-0.035922594368457794,
0.018635304644703865,
0.02310974709689617,
-0.010464058257639408,
-0.014542454853653908,
0.003770951647311449,
-0.03613394498825073,
-0.00018590688705444336,
0.004706753417849541,
0.02081207185983658,
0.027076078578829765,
-0.01164854783564806,
0.002973562106490135,
0.02319350652396679,
-0.011848210357129574,
-0.0075812991708517075,
0.05174285173416138,
0.03962323069572449,
0.020834945142269135,
0.014439876191318035,
-0.03988724574446678,
-0.014181510545313358,
-0.005975506734102964,
-0.014381890185177326,
0.0296829454600811,
0.03863268718123436,
-0.02511567622423172,
-0.018253128975629807,
0.019835911691188812,
0.024587931111454964,
-0.04145859181880951,
0.014899238012731075,
-0.0018882325384765863,
0.03246794268488884,
0.022234590724110603,
0.04322212189435959,
0.030855201184749603,
0.009953314438462257,
0.06683793663978577,
0.011308697052299976,
0.015051218681037426,
-0.08573084324598312,
-0.06838370859622955,
0.005069687496870756,
0.029381942003965378,
-0.004190179519355297,
0.038739871233701706,
-0.06036682426929474,
-0.021706542000174522,
0.0202617347240448,
-0.013969847932457924,
0.0005999492132104933,
-0.06700899451971054,
-0.008290703408420086,
0.01343568041920662,
-0.05666791647672653,
-0.03454621508717537,
-0.0012050993973389268,
-0.0008684470667503774,
0.023048363626003265,
-0.005035566631704569,
0.013316899538040161,
-0.00407894141972065,
-0.015875626355409622,
0.038401730358600616,
0.030139537528157234,
-0.030233558267354965,
-0.003796333447098732,
-0.016395680606365204,
-0.005050180479884148,
-0.08455658704042435,
-0.07220548391342163,
-0.02454572729766369,
0.014642923139035702,
-0.02469627559185028,
0.01364949345588684,
-0.012822192162275314,
-0.048915110528469086,
0.052506182342767715,
0.015467885881662369,
-0.031167546287178993,
0.02250237762928009,
-0.024290382862091064,
0.01427987776696682,
0.045015737414360046,
0.011070093140006065,
0.03807234391570091,
0.07316011935472488,
-0.054398439824581146,
-0.014217794872820377,
-0.002966036554425955,
-0.003135428763926029,
-0.04673963040113449,
-0.02145669050514698,
0.0230119451880455,
0.0032233120873570442,
-0.02771650440990925,
0.0505872443318367,
0.025271840393543243,
0.03305196762084961,
0.0019448252860456705,
-0.016346298158168793,
0.0021147492807358503,
0.0018328812438994646,
0.011370990425348282,
-0.03462328761816025,
-0.03437928482890129,
0.02554311230778694,
-0.007229818496853113,
-0.00613737665116787,
0.007060838397592306,
-0.02088046446442604,
0.021298209205269814,
0.0160004161298275,
-0.02895384654402733,
0.02269698865711689,
0.011041168123483658,
-0.002467269776389003,
-0.01953018456697464,
-0.022992942482233047,
0.026667706668376923,
0.00027770159067586064,
-0.013326735235750675,
0.012603445909917355,
-0.04289518669247627,
0.02045673504471779,
0.01171032153069973,
-0.0012130449758842587,
-0.0354473739862442,
-0.01879691705107689,
0.07707002758979797,
0.050574056804180145,
0.0306538175791502,
-0.04354550689458847,
-0.03193403780460358,
0.06169091537594795,
-0.005872690584510565,
-0.03842523321509361,
-0.03979562968015671,
0.008512312546372414,
-0.015031424351036549,
-0.02522263675928116,
-0.015611144714057446,
0.05633579567074776,
-0.03001629188656807,
-0.00508146733045578,
0.038121018558740616,
-0.0168071947991848,
0.07963395118713379,
-0.030278528109192848,
-0.0374324806034565,
0.02675718627870083,
-0.01804584264755249,
0.005911072250455618,
-0.001242082566022873,
0.045084115117788315,
-0.029556281864643097,
-0.020510906353592873,
-0.0061612920835614204,
0.012568101286888123,
0.03477969393134117,
0.03377551585435867,
0.02686729095876217,
0.03409254923462868,
-0.018013881519436836,
0.0049918643198907375,
-0.020645547658205032,
0.012989246286451817,
-0.03839028254151344,
0.04110192880034447,
0.012051011435687542,
0.031592778861522675,
0.009474005550146103,
-0.05747341364622116,
-0.004455741960555315,
0.002852489473298192,
-0.023483868688344955,
0.015421392396092415,
0.04596409574151039,
-0.013836771249771118,
-0.007194571662694216,
0.016853420063853264,
-0.0007180976099334657,
0.05612592026591301,
0.006081145256757736,
-0.002866074675694108,
0.002421451499685645,
0.006613363977521658,
-0.027424583211541176,
-0.049813371151685715,
-0.02216310240328312,
-0.005880489945411682,
0.042817987501621246,
-0.01648174226284027,
0.03615273907780647,
-0.016866376623511314,
0.0026893746107816696,
0.012576973997056484,
0.00020742122433148324,
0.03070477396249771,
0.009589090943336487,
0.006094973534345627,
0.023363890126347542,
-0.05234827473759651,
0.0009212160366587341,
0.0253800917416811,
0.037133313715457916,
-0.00948652159422636,
-0.03634054958820343,
0.024129414930939674,
0.005563355516642332,
0.009257162921130657,
-0.007649966049939394,
-0.018548699095845222,
0.018107013776898384,
-0.04896249994635582,
0.010172256268560886,
-0.04463816434144974,
-0.018990591168403625,
0.04586467891931534,
-0.0010615946957841516,
0.014693859964609146,
-0.06021791696548462,
-0.0009455186082050204,
-0.024752309545874596,
-0.018129855394363403,
-0.020458361133933067,
-0.01246765535324812,
0.002533118473365903,
0.0028890848625451326,
0.026278207078576088,
-0.022268837317824364,
-0.007074621040374041,
-0.024853039532899857,
-0.08473193645477295,
0.008278832770884037,
-0.007633339148014784,
-0.024981195107102394,
0.011507479473948479,
0.02029213309288025,
-0.027171937748789787,
0.01858375035226345,
-0.014424663037061691,
-0.025608010590076447,
0.015625841915607452,
0.0601857528090477,
-0.023148881271481514,
0.08529559522867203,
-0.01691390946507454,
0.018775304779410362,
0.005643791053444147,
-0.018589429557323456,
0.1572055071592331,
0.04034624248743057,
0.05100273713469505,
-0.05164092779159546,
0.007241338025778532,
-0.028106676414608955,
-0.015258874744176865,
-0.016755621880292892,
0.003230354283004999,
0.006500157527625561,
0.010783740319311619,
0.006512641441076994,
0.06315530836582184,
-0.010690118186175823,
-0.024513641372323036,
0.02377813123166561,
-0.05765577405691147,
-0.0066944295540452,
0.004670091904699802,
-0.014388992451131344,
-0.02168932370841503,
0.010779592208564281,
0.0011072729248553514,
0.012557004578411579,
-0.010842882096767426,
-0.004260885063558817,
-0.023209448903799057,
-0.03442215174436569,
0.014413457363843918,
0.006923978216946125,
-0.04921358823776245,
0.00923934020102024,
0.001291027176193893,
0.0063469503074884415,
-0.036054227501153946,
0.03826848417520523,
-0.001279487507417798,
-0.005667847581207752,
-0.01892462931573391,
0.03471553325653076,
0.03390922024846077,
0.011043024249374866,
0.005845724605023861,
0.0034108213149011135,
-0.08739275485277176,
-0.0025890525430440903,
-0.04012765735387802,
0.01973985694348812,
0.04090917855501175,
-0.009998590685427189,
0.007254994008690119,
-0.022887911647558212,
0.00792786106467247,
-0.03526640683412552,
-0.03582112863659859,
-0.011841625906527042,
0.038175102323293686,
0.02012232132256031,
-0.05734055116772652,
-0.011113724671304226,
0.019175471737980843,
-0.016056856140494347,
-0.013651514425873756,
0.0014364905655384064,
0.00811116024851799,
-0.0598086453974247,
0.0017240369925275445,
0.03263535350561142,
0.01498781144618988,
-0.014628554694354534,
-0.035511065274477005,
0.023350339382886887,
-0.08284416049718857,
-0.0012998176971450448,
0.02022203803062439,
0.02017829194664955,
0.001735579571686685,
-0.0015520944725722075,
-0.01670367643237114,
-0.04500362649559975,
-0.08493325114250183,
0.09323055297136307,
-0.007460014894604683,
-0.02901066467165947,
-0.012717561796307564,
0.014598638750612736,
0.014931128360331059,
0.021246327087283134,
-0.026742806658148766,
0.013894164003431797,
0.02456805668771267,
0.03499079495668411,
-0.004802795592695475,
-0.004305453039705753,
-0.03538740798830986,
0.011059523560106754,
-0.031769078224897385,
-0.010216839611530304,
0.0031533294823020697,
0.039195235818624496,
0.022185472771525383,
-0.029942495748400688,
0.014970044605433941,
-0.004525645170360804,
-0.00580768845975399,
0.03579634055495262,
0.03188362717628479,
-0.019285162910819054,
-0.04836314544081688,
0.01949986442923546,
0.031967200338840485,
-0.021189330145716667,
-0.05176855996251106,
-0.000045519838749896735,
0.02077249065041542,
-0.012718233279883862,
0.01520675327628851,
-0.0206088125705719,
0.027830634266138077,
-0.04542556777596474,
0.0030109293293207884,
-0.03958072513341904,
0.00600286852568388,
-0.06949362903833389,
-0.037119630724191666,
-0.0009695268236100674,
-0.027059275656938553,
-0.04055700823664665,
0.0019990575965493917,
0.016684509813785553,
-0.012431561946868896,
-0.0010327380150556564,
0.011301054619252682,
-0.015581853687763214,
-0.009968551807105541,
0.016247481107711792,
0.014943128451704979,
0.05273234099149704,
-0.021472005173563957,
-0.04679114744067192,
0.0035332466941326857,
0.01103599090129137,
-0.019586212933063507,
0.038712576031684875,
-0.001378274755552411,
0.006450688000768423,
-0.02259061671793461,
0.0577913373708725,
-0.026820123195648193,
0.09487805515527725,
-0.027349229902029037,
0.016902847215533257,
-0.022660836577415466,
-0.03609856963157654,
-0.01363434549421072,
-0.010245376266539097,
0.028054557740688324,
-0.02647182159125805,
-0.02333039417862892,
0.020841913297772408,
0.05360545590519905,
-0.016484051942825317,
0.019189124926924706,
-0.02769387513399124,
-0.005968719255179167,
0.03180597350001335,
-0.0035470917355269194,
-0.010938437655568123,
0.022197993472218513,
0.04610654339194298,
-0.008362249471247196,
0.03815429285168648,
0.029946014285087585,
0.024672459810972214,
-0.10905981063842773,
0.009891682304441929,
0.007612778339534998,
0.00034492381382733583,
0.02592611499130726,
-0.01714017614722252,
-0.00026777025777846575,
-0.0007932949811220169,
-0.05709032341837883,
0.04779011011123657,
-0.02849450893700123,
-0.03322581574320793,
-0.050510015338659286,
0.016388721764087677,
-0.009969515725970268,
0.07463943213224411,
-0.009768227115273476,
-0.0014978591352701187,
0.040414050221443176,
0.007434949278831482,
0.030745768919587135,
0.005274404305964708,
0.02536928839981556,
0.07067696750164032,
0.025155331939458847,
0.04151897504925728,
0.04437817633152008,
-0.021551229059696198,
-0.05973175913095474,
0.01767510361969471,
-0.018885664641857147,
0.054593753069639206,
0.011940713971853256,
0.02164740301668644,
-0.03641915321350098,
0.002018797444179654,
0.012896554544568062,
0.008464756421744823,
-0.02917465567588806,
0.02912689559161663,
0.0016381809255108237,
0.009582940489053726,
0.022621294483542442,
0.03848186880350113,
-0.0030464367009699345,
-0.03999432176351547,
0.0037303618155419827,
0.0003060300077777356,
-0.02245940826833248,
0.012125148437917233,
0.023001397028565407,
-0.013502487912774086,
0.012674716301262379,
0.007709996309131384,
0.0064513059332966805,
-0.02943567931652069,
-0.022468306124210358,
0.026643015444278717,
-0.00001192885702039348,
0.007445987313985825,
0.00851143803447485,
-0.0038969640154391527,
-0.04557480663061142,
-0.047410499304533005,
-0.0243369247764349,
-0.03937903419137001,
-0.008275912143290043,
-0.020011814311146736,
-0.004826551768928766,
-0.02027079463005066,
-0.03624838963150978,
-0.0005181915475986898,
0.013563016429543495,
0.06101447343826294,
0.055974528193473816,
0.030465982854366302,
0.046983979642391205,
-0.06501377373933792,
-0.04018964618444443,
-0.05802470073103905,
0.02519867941737175,
-0.006677697412669659,
0.020818844437599182,
-0.001008418039418757,
-0.0025411085225641727,
0.004739850293844938,
-0.03795002028346062,
0.049721959978342056,
-0.051140882074832916,
0.019024405628442764,
-0.005925219971686602,
-0.011887762695550919,
-0.012704816646873951,
0.01386079378426075,
-0.005718642380088568,
-0.023186886683106422,
-0.03359709680080414,
0.020931540057063103,
-0.030438905581831932,
-0.023725509643554688,
-0.0252818763256073,
0.028181025758385658,
-0.026143042370676994,
0.031469810754060745,
0.013840687461197376,
-0.023428382351994514,
0.02697187289595604,
0.042746346443891525,
-0.031566303223371506,
0.06466031819581985,
-0.01265458483248949,
-0.01041816920042038,
0.000012113110642530955,
-0.03217938914895058,
-0.0698365643620491,
0.03667774796485901,
-0.0008914807694964111,
-0.03031458519399166,
0.011452319100499153,
-0.08990015089511871,
0.02241520769894123,
-0.04698828607797623,
0.011177899315953255,
-0.008014468476176262,
-0.012163630686700344,
0.005523849744349718,
0.017681743949651718,
0.03665542975068092,
0.021596165373921394,
-0.06259061396121979,
0.0009896977571770549,
0.01313374936580658,
-0.00194751366507262,
-0.01859510876238346,
0.011048284359276295,
0.028759662061929703,
-0.00354902446269989,
0.00144317711237818,
0.012003246694803238,
0.023576226085424423,
0.016142424196004868,
0.013052652589976788,
-0.01201589684933424,
0.01034876424819231,
-0.02222372591495514,
0.07844813913106918,
0.010393553413450718,
-0.028226181864738464,
0.025417065247893333,
0.011510882526636124,
0.060228072106838226,
0.021366780623793602,
0.032062266021966934,
-0.01640179753303528,
-0.029410654678940773,
-0.031058741733431816,
0.012488747015595436,
0.006292016711086035,
0.02043074741959572,
-0.012259934097528458,
-0.026055769994854927,
0.02803032658994198,
0.03458039462566376,
0.0006047806818969548,
0.013573882170021534,
0.043851789087057114,
-0.02346041426062584,
-0.0035981449764221907,
-0.011173434555530548,
-0.007256013806909323,
-0.04585978388786316,
-0.020349998027086258,
0.02298378199338913,
0.06711340695619583,
0.018949802964925766,
0.025872234255075455,
-0.04316503927111626,
-0.04392005503177643,
0.06070677563548088,
-0.0446120984852314,
-0.029298141598701477,
-0.031922340393066406,
0.025982730090618134,
-0.016151081770658493,
-0.0234022568911314
] |
<p>Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, \left|\uparrow\downarrow\right\rangle, \left|\downarrow\uparrow\right\rangle \} $, and then I apply a Hamiltonian that gives me the new basis, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, \cos(\gamma)\left|\uparrow\downarrow\right\rangle +\sin(\gamma)\left|\downarrow\uparrow\right\rangle, \sin(\gamma)\left|\uparrow\downarrow\right\rangle -\cos(\gamma)\left|\downarrow\uparrow\right\rangle \} $</p>
<p>Which gives us a transformation matrix linking the original basis kets to the new basis kets which corresponds to an inversion and rotation of the last two kets in the original basis. A few questions:</p>
<p>Is there any physical significance to the inversion, or is it just an "arbitrary phase"?</p>
<p>If not, what is the most convenient way to see a geometric interpretation of the state? What would be an arbitrary collective Bloch vector for this space?</p>
<p>I have heard of so-called Dicke states, in which a system of N spin-1/2 particles can be thought of as a single spin-N/2 particle, in state $\left|N/2,M\right\rangle $, where $M= -N/2,-N/2+1,...,N/2-1,N/2$. </p>
<p>Does this entail the use of a collective Bloch vector for all possible states solely excluding the singlet state $\left|0,0\right\rangle$ ?</p>
| 9,388 |
[
-0.004354780074208975,
0.0058929105289280415,
-0.005347637925297022,
-0.03026081621646881,
0.04121562838554382,
0.0014935412909835577,
-0.05944426730275154,
-0.039576850831508636,
0.01460759062319994,
-0.05588991940021515,
0.05470675975084305,
0.004384431056678295,
0.0571141317486763,
-0.0033746210392564535,
-0.0010045423405244946,
0.04452968388795853,
-0.006771300453692675,
-0.030673351138830185,
-0.04319700971245766,
-0.007575209718197584,
0.029834216460585594,
0.03286255523562431,
0.0013203262351453304,
0.0011563240550458431,
-0.028580956161022186,
0.06320765614509583,
0.015618356876075268,
-0.016276177018880844,
0.039512164890766144,
0.03830450400710106,
-0.010370819829404354,
-0.04414484277367592,
0.019616371020674706,
0.010649846866726875,
-0.00945221446454525,
-0.025070155039429665,
-0.007414888124912977,
-0.04927271604537964,
0.04529229551553726,
0.02111687883734703,
-0.08300787955522537,
-0.05745772272348404,
-0.03782153129577637,
-0.011513005010783672,
-0.004997135605663061,
-0.0301680825650692,
-0.004027020186185837,
-0.0018259555799886584,
0.04688851535320282,
-0.06823204457759857,
0.06918779760599136,
-0.0004431100969668478,
-0.024550607427954674,
-0.031387023627758026,
0.0036679760087281466,
0.007100298069417477,
0.06410577893257141,
0.04333701357245445,
0.03177832439541817,
-0.044339943677186966,
-0.007615330163389444,
-0.0010904851369559765,
-0.014860248193144798,
-0.014747940003871918,
-0.0030613671988248825,
-0.00595361553132534,
0.01541899610310793,
-0.014255296438932419,
0.01364984642714262,
-0.018311699852347374,
0.006720543373376131,
-0.005316584371030331,
0.030709175392985344,
-0.011304809711873531,
0.020525937899947166,
-0.026664741337299347,
0.02286224626004696,
-0.015731081366539,
0.008662745356559753,
-0.0012279056245461106,
-0.020565547049045563,
0.030282584950327873,
0.031840790063142776,
0.012414371594786644,
-0.017669929191470146,
-0.0167365912348032,
0.04870417341589928,
0.0034575245808809996,
0.05908641591668129,
0.029079465195536613,
-0.0009513826807960868,
0.002978923264890909,
0.05626257508993149,
-0.021243000403046608,
-0.04705715924501419,
0.0016203069826588035,
-0.0005885150749236345,
0.04751502349972725,
-0.020647773519158363,
-0.019146542996168137,
-0.015371437184512615,
-0.0031108104158192873,
0.0041295490227639675,
0.07468996196985245,
-0.008624476380646229,
0.03705413267016411,
-0.03508128598332405,
0.027294766157865524,
-0.023142406716942787,
-0.009918461553752422,
-0.03435114771127701,
0.018168723210692406,
-0.00820178259164095,
-0.017546726390719414,
0.008534761145710945,
-0.006485106889158487,
-0.0009713273611851037,
0.0013661420671269298,
0.060369573533535004,
0.09939195215702057,
0.05862561985850334,
-0.010904327034950256,
0.027921151369810104,
-0.05126021429896355,
-0.1073632761836052,
-0.004231225233525038,
0.038833845406770706,
-0.0017449056031182408,
-0.021646883338689804,
0.010348587296903133,
0.015780150890350342,
-0.019762348383665085,
0.02819308266043663,
0.02213490568101406,
0.032864637672901154,
-0.0442558228969574,
-0.14705489575862885,
-0.07260102778673172,
0.017784927040338516,
-0.021205658093094826,
0.00570237310603261,
-0.0599454790353775,
0.03419433906674385,
0.07410178333520889,
0.05723147094249725,
-0.02595684863626957,
0.03303162753582001,
0.002835811348631978,
0.01220313273370266,
0.01782294176518917,
0.009651688858866692,
-0.012438377365469933,
-0.009550271555781364,
-0.062233030796051025,
-0.011486444622278214,
-0.013931471854448318,
0.07022400200366974,
0.05854204297065735,
0.0007379726739600301,
0.0026872672606259584,
0.07195848971605301,
-0.008258434012532234,
0.004675145726650953,
0.025578366592526436,
-0.02456953190267086,
-0.01443634182214737,
0.08149277418851852,
0.008762259967625141,
0.010133207775652409,
0.01408302504569292,
-0.013419567607343197,
0.025318529456853867,
-0.0029737581498920918,
0.044429510831832886,
-0.006904060021042824,
-0.013012226670980453,
-0.03127053752541542,
0.005674663931131363,
0.011085477657616138,
-0.03594963252544403,
-0.007023347541689873,
-0.019191572442650795,
-0.012212321162223816,
0.033884018659591675,
0.018305543810129166,
-0.014428573660552502,
0.00410884665325284,
-0.0068107787519693375,
0.0008913652854971588,
-0.043822795152664185,
0.0060900854878127575,
-0.056498631834983826,
-0.01770133338868618,
0.002344126347452402,
-0.033332228660583496,
0.054842136800289154,
0.015945641323924065,
0.01061221957206726,
0.0202231053262949,
-0.04701175168156624,
-0.017426438629627228,
0.03528371825814247,
0.005946359597146511,
0.0036583428736776114,
0.01024425309151411,
0.04532696306705475,
0.010262810625135899,
-0.009156003594398499,
0.018245099112391472,
-0.024908199906349182,
-0.014436367899179459,
-0.02798004448413849,
0.00218211323954165,
0.027112696319818497,
0.0454462468624115,
0.01737895794212818,
0.014387271367013454,
-0.006436454132199287,
-0.00890623964369297,
0.003472263226285577,
-0.044791001826524734,
0.04669332504272461,
0.039491500705480576,
-0.021738849580287933,
0.016925297677516937,
0.08422906696796417,
0.024788837879896164,
0.005903968587517738,
0.0245834793895483,
-0.03544173017144203,
-0.024524373933672905,
0.0006174548179842532,
0.05639619007706642,
0.05399854853749275,
-0.02459055371582508,
0.012168602086603642,
0.004843615926802158,
0.03500162065029144,
0.015920579433441162,
-0.00746347289532423,
-0.027823586016893387,
-0.01754055917263031,
0.022760257124900818,
-0.0025806271005421877,
0.0012181950733065605,
0.013926450163125992,
0.003471923526376486,
-0.00866779126226902,
0.014737977646291256,
0.02902466617524624,
-0.050039079040288925,
0.030721275135874748,
-0.07071555405855179,
-0.007862060330808163,
-0.0012242181692272425,
-0.040545061230659485,
0.02048090472817421,
-0.01703302189707756,
0.03309517726302147,
0.022124653682112694,
-0.03554295003414154,
-0.021485570818185806,
-0.02443379908800125,
-0.01103545818477869,
-0.009158521890640259,
0.00837629847228527,
-0.005467190407216549,
-0.0406988225877285,
0.035032182931900024,
-0.07913367450237274,
0.007680142298340797,
-0.012121710926294327,
-0.03833022713661194,
0.015335416421294212,
-0.009344681166112423,
0.05196332186460495,
-0.0029371934942901134,
0.012037371285259724,
-0.04782480373978615,
-0.0010504095116630197,
0.012539534829556942,
0.0033900912385433912,
0.03730935975909233,
0.044764645397663116,
-0.06562750786542892,
0.0016309767961502075,
-0.06555318832397461,
0.025760270655155182,
0.014190621674060822,
-0.0093946922570467,
0.00024543082690797746,
-0.029212279245257378,
-0.012874189764261246,
-0.08530368655920029,
-0.03969914838671684,
-0.01790820248425007,
0.019564984366297722,
-0.03594117611646652,
-0.04241858422756195,
0.06326572597026825,
0.021664226427674294,
-0.027704937383532524,
-0.01933177374303341,
-0.037271648645401,
-0.02018570527434349,
-0.003062671748921275,
0.01637749932706356,
0.048692140728235245,
-0.016565853729844093,
-0.0027724651154130697,
0.037810903042554855,
-0.02254529297351837,
0.00007369071681750938,
-0.06834965944290161,
-0.037872299551963806,
0.014270861633121967,
0.0009736863430589437,
0.010219440795481205,
0.002011925680562854,
-0.031598471105098724,
0.10675979405641556,
0.009965004399418831,
-0.03913433477282524,
-0.012753108516335487,
0.018553420901298523,
-0.003066198667511344,
-0.0334090031683445,
0.005811192560940981,
0.019847845658659935,
0.008785493671894073,
0.04565241560339928,
0.011570514179766178,
0.04946604743599892,
0.03694792836904526,
0.007698144298046827,
-0.03463026136159897,
0.026961788535118103,
-0.0177259910851717,
-0.027026338502764702,
0.028463006019592285,
-0.02583897113800049,
-0.0054374076426029205,
0.006118644028902054,
-0.008131223730742931,
-0.022964470088481903,
0.03305715695023537,
-0.03011998161673546,
0.03919960558414459,
-0.002411309629678726,
-0.00927950069308281,
0.0029338484164327383,
0.03860045596957207,
-0.0007827809313312173,
-0.009026622399687767,
-0.01956462860107422,
0.0405907966196537,
0.012051112949848175,
-0.022420331835746765,
0.003261813661083579,
0.04433317109942436,
0.022502584382891655,
-0.017946848645806313,
-0.011852450668811798,
0.03930065780878067,
0.004064949695020914,
0.0002959068224299699,
-0.02818543277680874,
0.01639043167233467,
0.023521728813648224,
0.04613885283470154,
0.033343397080898285,
0.00019627493747975677,
-0.057683564722537994,
-0.01080514956265688,
-0.04790223017334938,
-0.000781417649704963,
-0.021392056718468666,
0.027315778657794,
0.0015786809381097555,
0.039461325854063034,
0.028565721586346626,
0.01962953619658947,
-0.0023208658676594496,
-0.004374938551336527,
-0.05100972205400467,
-0.0056387814693152905,
0.002662266604602337,
0.04225427284836769,
-0.002920904429629445,
-0.013892599381506443,
0.01633160002529621,
-0.0197044238448143,
-0.06230587884783745,
0.0140770198777318,
-0.034818973392248154,
-0.05253053829073906,
0.022784171625971794,
-0.03712882846593857,
-0.035406336188316345,
-0.012545520439743996,
0.0674772560596466,
0.043807584792375565,
-0.04379727691411972,
-0.014797341078519821,
0.026684356853365898,
-0.023378757759928703,
0.03737277165055275,
-0.03136809542775154,
0.03108804114162922,
0.0360572375357151,
0.022151196375489235,
0.05648256838321686,
0.03807530179619789,
0.03138215094804764,
-0.01315382868051529,
0.007215708959847689,
0.04556405916810036,
-0.03166148066520691,
0.010319644585251808,
0.024118619039654732,
-0.033110592514276505,
-0.007038112264126539,
-0.024998128414154053,
0.052959270775318146,
-0.005104232579469681,
0.005471698008477688,
0.02044864185154438,
0.013686793856322765,
-0.025214990600943565,
0.033059943467378616,
0.03312944993376732,
0.0032985317520797253,
-0.015315880067646503,
-0.05086516588926315,
-0.03445274382829666,
-0.003751793410629034,
-0.00013670354383066297,
0.01726083643734455,
-0.02642940543591976,
-0.022251633927226067,
0.021472131833434105,
0.022247981280088425,
0.03134826198220253,
0.013651720248162746,
-0.01682092994451523,
-0.015770021826028824,
0.028611641377210617,
0.041529033333063126,
0.014885329641401768,
-0.006228459533303976,
0.00150775583460927,
0.020842308178544044,
0.02857056073844433,
0.022955365478992462,
-0.08521319180727005,
-0.024688180536031723,
0.01546311192214489,
0.03715764358639717,
0.0023137470707297325,
-0.014992984011769295,
-0.021693922579288483,
-0.02641274780035019,
0.036183975636959076,
-0.013689407147467136,
0.05455242469906807,
0.009015634655952454,
-0.026828430593013763,
-0.002106276573613286,
-0.030970579013228416,
-0.007245772518217564,
0.03457513079047203,
-0.0015262567903846502,
0.047178301960229874,
0.0009129391401074827,
-0.01858428679406643,
0.003221022430807352,
0.00914051104336977,
-0.01599453203380108,
0.013549970462918282,
-0.012199782766401768,
-0.020209189504384995,
0.004707495216280222,
0.012838282622396946,
-0.04265741631388664,
-0.09469743072986603,
-0.007517918944358826,
0.03498200327157974,
-0.0032364358194172382,
0.044787559658288956,
-0.05152305215597153,
-0.06466248631477356,
-0.04907088726758957,
-0.007200350984930992,
0.0285643320530653,
0.00016030989354476333,
-0.019885951653122902,
0.07548967748880386,
0.029078172519803047,
-0.03783060237765312,
0.029171597212553024,
-0.00008608070493210107,
-0.009446436539292336,
-0.022798676043748856,
-0.009451224468648434,
0.03217894583940506,
-0.024304749444127083,
0.0273188054561615,
-0.02121357060968876,
-0.014649257995188236,
-0.024271899834275246,
0.06088079512119293,
-0.004974310286343098,
0.04221827909350395,
0.012672480195760727,
-0.024964898824691772,
-0.02802274189889431,
0.049592066556215286,
-0.017305269837379456,
0.0010053381556645036,
-0.03365345671772957,
0.021679816767573357,
0.016885148361325264,
-0.026072315871715546,
0.052855249494314194,
0.00324826966971159,
0.006835845299065113,
0.043015267699956894,
0.001242546713910997,
0.04691103473305702,
-0.016301123425364494,
-0.005766107700765133,
0.008755705319344997,
-0.06236285716295242,
0.05511195585131645,
-0.027378439903259277,
-0.01764623261988163,
-0.011044788174331188,
-0.05412806570529938,
-0.02480185404419899,
0.02248127944767475,
-0.013004087843000889,
-0.006868688389658928,
-0.010624074377119541,
-0.003348566824570298,
0.04675155133008957,
0.012795371934771538,
-0.08159307390451431,
-0.05628298595547676,
0.01725097745656967,
0.005134311970323324,
-0.023274913430213928,
-0.0073903086595237255,
0.02222830429673195,
0.015150872059166431,
0.001045043347403407,
0.019109468907117844,
0.04941094294190407,
-0.019950753077864647,
0.0032055415213108063,
0.037350863218307495,
0.054183218628168106,
0.03238024562597275,
-0.005150114186108112,
-0.02993682026863098,
0.03558747097849846,
-0.0038569720927625895,
0.01746544986963272,
0.010717139579355717,
0.01460081897675991,
-0.029728161171078682,
-0.03206406161189079,
-0.029167305678129196,
0.015034313313663006,
0.01114292349666357,
-0.021512402221560478,
0.008067534305155277,
0.045565154403448105,
0.017846282571554184,
0.02013433538377285,
-0.02021125890314579,
-0.034060195088386536,
-0.013436678797006607,
0.03900766372680664,
-0.01472284272313118,
0.0004350396920926869,
-0.02298997901380062,
-0.02779538743197918,
0.02654806151986122,
-0.009269352070987225,
0.005848425440490246,
0.009546085260808468,
0.06149591878056526,
0.004669948015362024,
-0.02937355265021324,
0.03546062484383583,
-0.00833140965551138,
0.009609270840883255,
0.012089957483112812,
0.006166013423353434,
0.019978391006588936,
-0.006854090373963118,
-0.04665854945778847,
-0.03035006858408451,
-0.03330248221755028,
0.008475846610963345,
0.04881737008690834,
-0.018808772787451744,
0.004879660904407501,
-0.0035420679487288,
0.0017090566689148545,
0.0016748085618019104,
-0.011637285351753235,
-0.011361604556441307,
0.018030131235718727,
-0.013556241057813168,
0.03285510838031769,
-0.04878544434905052,
-0.004107966087758541,
0.03346475958824158,
0.041983455419540405,
-0.010657240636646748,
0.0062630679458379745,
0.03404228761792183,
-0.005439916159957647,
0.017842253670096397,
-0.015916381031274796,
-0.0404965840280056,
0.057875100523233414,
-0.036945223808288574,
0.008008802309632301,
0.009381808340549469,
-0.020113928243517876,
0.042005348950624466,
0.021197378635406494,
0.0563240647315979,
-0.05858146771788597,
-0.0123166898265481,
-0.029746681451797485,
0.021519340574741364,
-0.004282766487449408,
-0.011323226615786552,
-0.03592854365706444,
-0.021458948031067848,
0.033539142459630966,
-0.007275794167071581,
0.02687998116016388,
0.03055049292743206,
-0.05315613001585007,
-0.0283441673964262,
-0.03114565834403038,
-0.053044285625219345,
0.005258201155811548,
-0.02787206694483757,
0.01940123923122883,
0.04124990478157997,
-0.016953812912106514,
-0.0009423161391168833,
-0.00009990915714297444,
0.018384752795100212,
-0.01884891279041767,
0.06038622185587883,
-0.0036326306872069836,
0.021975116804242134,
-0.006883605383336544,
-0.02437330037355423,
0.11715911328792572,
0.04080361872911453,
-0.005858255084604025,
-0.09239406883716583,
0.02298191376030445,
0.01569402776658535,
0.029120123013854027,
-0.008956394158303738,
0.00922077614814043,
0.015116430819034576,
-0.0021754587069153786,
-0.014426742680370808,
0.03127526491880417,
-0.012112596072256565,
0.006613823119550943,
0.010912301950156689,
-0.03233828768134117,
-0.0347590297460556,
0.0007592901820316911,
0.022134969010949135,
-0.0007825418142601848,
-0.0012057198910042644,
-0.0043217092752456665,
0.0049727861769497395,
-0.011206303723156452,
0.012920085340738297,
-0.04535207524895668,
-0.0242707971483469,
-0.00018453077063895762,
0.02196471020579338,
-0.01336374320089817,
0.04125294089317322,
-0.006720886565744877,
-0.0009990952676162124,
-0.017415765672922134,
0.008444317616522312,
0.0010138939833268523,
-0.0034131871070712805,
0.0330103263258934,
0.031589165329933167,
-0.0036131611559540033,
0.004033039789646864,
0.028552159667015076,
-0.011564064770936966,
-0.041753992438316345,
-0.011582644656300545,
-0.015725478529930115,
0.06479078531265259,
-0.030489474534988403,
0.005830525420606136,
-0.0378020741045475,
-0.03384140878915787,
0.03205609321594238,
-0.037496551871299744,
0.0016182165127247572,
-0.009600532241165638,
0.02367633394896984,
-0.025901539251208305,
-0.024404320865869522,
0.001558469608426094,
0.013264128938317299,
0.005737514700740576,
0.020472392439842224,
-0.031679920852184296,
-0.024268146604299545,
-0.004925127141177654,
0.02709551714360714,
0.06724097579717636,
0.02841736562550068,
-0.011904226616024971,
-0.02164897508919239,
-0.006463642697781324,
-0.04934696853160858,
-0.011253750883042812,
0.048579536378383636,
0.037846922874450684,
0.021431835368275642,
-0.0036813118495047092,
-0.026514140889048576,
0.013024190440773964,
-0.051973842084407806,
-0.00801838468760252,
-0.02361358515918255,
-0.01347497571259737,
0.03458292782306671,
0.00039615717832930386,
0.02279367670416832,
0.014835966750979424,
-0.05679355561733246,
0.0037060079630464315,
0.01972883939743042,
0.01810571923851967,
0.02649846114218235,
-0.047875985503196716,
-0.025290222838521004,
0.004928929265588522,
-0.02967238239943981,
-0.006197470705956221,
-0.04194771870970726,
0.0009723717230372131,
-0.004103496670722961,
-0.005347060970962048,
0.011339779011905193,
0.0727803185582161,
0.004072210285812616,
-0.023630032315850258,
0.012419155798852444,
-0.05976082757115364,
0.02858361043035984,
-0.0028454638086259365,
0.007213197182863951,
-0.05078660696744919,
-0.018618840724229813,
0.009281888604164124,
-0.012524085119366646,
-0.016759172081947327,
0.00454337103292346,
-0.024118924513459206,
-0.027343247085809708,
-0.020974116399884224,
0.003746488830074668,
0.02044631354510784,
-0.01462266594171524,
0.0000403045050916262,
0.018501531332731247,
-0.00207838648930192,
0.00011919719690922648,
-0.00404272461310029,
0.0182644110172987,
0.011005179025232792,
-0.015818491578102112,
0.04790779575705528,
0.08864441514015198,
-0.008901265449821949,
-0.024101898074150085,
0.01830459199845791,
0.021831993013620377,
0.015555210411548615,
0.0010537041816860437,
-0.056095950305461884,
0.014013194479048252,
-0.024756042286753654,
0.016416683793067932,
0.04354587197303772,
0.007697889115661383,
0.04131346568465233,
0.01414928212761879,
-0.015813840553164482,
-0.02693888172507286,
0.018462304025888443,
-0.045427508652210236,
0.002185117220506072,
-0.0027950736694037914,
0.014459650032222271,
-0.006580589804798365,
-0.06800056993961334,
-0.004941146355122328,
0.01026960276067257,
0.02126353606581688,
0.018881632015109062,
-0.008966376073658466,
0.007287235464900732,
0.005649331491440535,
-0.02442752942442894,
0.007382643409073353,
0.0484955757856369,
0.02377203293144703,
0.010022573173046112,
0.03149322792887688,
0.026211204007267952,
-0.03908438980579376,
0.035464610904455185,
0.02926335670053959,
-0.0069435457699000835,
-0.069992296397686,
-0.034571573138237,
0.061283282935619354,
-0.015108057297766209,
0.08613133430480957,
-0.025936942547559738,
0.03772115707397461,
0.017524195834994316,
-0.06560525298118591,
0.0567716546356678,
-0.005310491193085909,
-0.03308621793985367,
0.018607866019010544,
-0.009793493896722794,
-0.061205338686704636,
0.0709356814622879,
-0.021673284471035004,
0.016099320724606514,
0.01415091659873724,
-0.03997674211859703,
-0.03400171920657158,
-0.04583971947431564,
0.0003406743926461786,
-0.013969114981591702,
0.007967200130224228,
-0.020962124690413475,
0.07725528627634048,
0.005551575217396021,
-0.050310663878917694,
0.024139953777194023,
-0.05060499161481857,
0.01434378232806921,
-0.04017406702041626,
0.027971208095550537,
-0.011949009262025356,
0.03190842270851135,
0.018457505851984024,
-0.034574203193187714,
-0.0374867245554924,
-0.004536578431725502,
0.015675321221351624,
0.017678631469607353,
0.04718146100640297,
-0.0008609755896031857,
-0.0020150416530668736,
-0.04692160338163376,
0.013231206685304642,
0.015611929818987846,
-0.01855066791176796,
-0.006198463030159473,
0.017529841512441635,
-0.009596358053386211,
0.004515870474278927,
-0.029424000531435013,
0.04745351895689964,
-0.05065549910068512,
-0.012418004684150219,
-0.0003616073227021843,
0.02475612424314022,
0.03126724436879158,
0.03320837393403053,
-0.012388672679662704,
-0.042002953588962555,
0.06697840243577957,
-0.004491707310080528,
-0.05656097084283829,
-0.055068038403987885,
-0.03229765594005585,
0.04837070405483246,
0.011274050921201706,
0.007387114223092794,
-0.02618986926972866,
-0.029149305075407028,
0.03671583905816078,
0.0012189458357170224,
0.061211053282022476,
-0.028832916170358658,
-0.06508464366197586,
-0.01988724060356617,
-0.027981840074062347,
0.014783261343836784,
0.04216114059090614,
0.013388004153966904,
0.009295553900301456,
-0.02765168994665146,
0.012287592515349388,
0.0021907268092036247,
0.07321209460496902,
0.01786954514682293,
0.012101167812943459,
-0.007051666732877493,
-0.010398839600384235,
0.040942057967185974,
-0.008393173106014729,
0.025587860494852066,
-0.029852978885173798,
-0.009236302226781845,
0.029500091448426247,
-0.033275265246629715,
-0.031751956790685654,
0.029580678790807724,
0.007392470259219408,
-0.012900039553642273,
0.0012302560498937964,
-0.005740802269428968,
-0.03372979909181595,
0.03295699134469032,
-0.0000507393924635835,
-0.004365455824881792,
0.0449628122150898,
-0.005021607968956232,
-0.008787412196397781,
0.022803643718361855,
-0.04498686268925667,
-0.06251974403858185,
0.013679331168532372,
-0.020735908299684525,
-0.0456346832215786,
-0.014945357106626034,
0.011525195091962814,
0.03861703351140022,
-0.035195086151361465,
-0.01002581138163805,
0.019199514761567116,
-0.0290046539157629,
0.010076039470732212,
0.0364772230386734,
0.011827362701296806,
0.02338709495961666,
-0.0065179443918168545,
0.016820833086967468,
0.03119564987719059,
0.011166042648255825,
0.013598722405731678,
0.04765758290886879,
0.012012233957648277,
0.006123494356870651,
-0.010828598402440548,
0.030796624720096588,
0.0051661101169884205,
0.01118338480591774,
0.019187215715646744,
0.026885399594902992,
-0.02091304585337639,
0.02611943706870079,
0.04287160560488701,
-0.011462114751338959,
-0.00434578163549304,
0.004979967605322599,
-0.03601381555199623,
0.09554734081029892,
-0.001931190607137978,
0.009569279849529266,
-0.026217125356197357,
0.020583098754286766,
0.0025013405829668045,
-0.02732233703136444,
0.03274514898657799,
0.05948774889111519,
0.012498474679887295,
-0.02377340756356716,
-0.0463179387152195,
0.000222541275434196,
0.003377973334863782,
-0.03881657123565674,
-0.010274822823703289,
-0.021625058725476265,
0.03516063094139099,
0.0003745700523722917,
-0.046862583607435226,
-0.05481475219130516,
-0.0619342140853405,
0.004597402177751064,
0.006965904962271452,
0.04194020479917526,
-0.0003150525444652885,
-0.000948225730098784,
-0.04035378247499466,
0.06084407866001129,
-0.059498969465494156,
-0.01986764371395111,
-0.00136668945197016,
0.015524222515523434,
-0.01070396602153778,
0.015728482976555824
] |
<p>I know that the rotation period of the moon equals its revolution period. It's just so astonishing that these 2 values have such a small difference. I mean, what is the probability of these 2 values to be practically the same? I don't believe this to be a coincidence. It's just too much for a coincidence. What could have caused this?</p>
| 263 |
[
-0.033760394901037216,
-0.016135193407535553,
-0.029361020773649216,
-0.028110451996326447,
0.019826358184218407,
-0.0006744387210346758,
-0.007604068610817194,
-0.01106459740549326,
-0.0059781442396342754,
-0.03580022603273392,
0.00453905900940299,
0.03457385301589966,
0.03417307138442993,
0.0483226552605629,
0.021110689267516136,
0.0003292615874670446,
-0.005919220391660929,
0.014978194609284401,
-0.005170918069779873,
-0.020060177892446518,
0.037328802049160004,
0.02568039856851101,
0.002614076714962721,
-0.018708322197198868,
-0.02936919778585434,
0.022186562418937683,
0.04548228159546852,
-0.017239250242710114,
0.025967881083488464,
0.07718247175216675,
-0.0121351582929492,
0.0048751006834208965,
0.055680401623249054,
0.05463746190071106,
0.004286023322492838,
0.001627457095310092,
0.0016187098808586597,
0.0051056137308478355,
-0.021990172564983368,
0.04352279379963875,
-0.04601810872554779,
-0.00434823939576745,
-0.02534080483019352,
0.06036555767059326,
-0.015375593677163124,
0.01949106715619564,
0.0030797761864960194,
-0.042686183005571365,
0.08217214047908783,
-0.06889190524816513,
0.07474878430366516,
0.0024208403192460537,
0.029427066445350647,
0.00861124973744154,
-0.02279551327228546,
-0.00462478119879961,
0.061264995485544205,
0.06354117393493652,
-0.03908711299300194,
-0.04875657334923744,
-0.04667269438505173,
-0.02699751779437065,
0.001998616149649024,
0.011797054670751095,
-0.032560087740421295,
0.019353874027729034,
-0.014943614602088928,
-0.02562069334089756,
0.037032101303339005,
-0.009556792676448822,
0.044389426708221436,
0.03211987763643265,
0.05295851081609726,
-0.027635782957077026,
0.005080298520624638,
-0.054132867604494095,
0.017973586916923523,
-0.0020409496501088142,
0.004520697053521872,
0.02701783925294876,
-0.000020459887309698388,
0.01688755676150322,
0.05043318495154381,
0.015559324063360691,
0.037221163511276245,
0.004006938077509403,
0.043921247124671936,
-0.005115690641105175,
0.005785929970443249,
0.03353629633784294,
-0.020932452753186226,
0.010198195464909077,
0.016975028440356255,
-0.022110482677817345,
-0.049866847693920135,
0.041070833802223206,
0.008514254353940487,
0.042876239866018295,
0.013884610496461391,
0.0011268386151641607,
0.00027970928931608796,
-0.011527381837368011,
0.024787496775388718,
0.06802652776241302,
0.013904746621847153,
-0.006817797664552927,
-0.009415524080395699,
0.01168468501418829,
0.006893572397530079,
-0.002773229032754898,
-0.023484114557504654,
-0.020941898226737976,
0.01025380939245224,
0.002629672409966588,
-0.002919376129284501,
0.04018745198845863,
-0.014360692352056503,
-0.018453266471624374,
0.05815419182181358,
0.07152096927165985,
0.02121846191585064,
0.0034955961164087057,
-0.009953360073268414,
-0.05751233920454979,
-0.012303975410759449,
0.03906501829624176,
0.028154755011200905,
-0.03736977279186249,
-0.021980274468660355,
0.025752024725079536,
0.008745986968278885,
-0.03662934526801109,
-0.0052596707828342915,
-0.03065946139395237,
0.06422106176614761,
-0.0008828777936287224,
-0.08519849181175232,
-0.020678885281085968,
0.07017119228839874,
-0.0017383089289069176,
-0.04459095746278763,
-0.0809658020734787,
0.038261596113443375,
0.0009075879352167249,
0.05006137490272522,
0.02625584788620472,
0.023569246754050255,
-0.014704073779284954,
0.03369497135281563,
0.04194270074367523,
-0.030801303684711456,
0.0040004560723900795,
0.052130550146102905,
-0.06140175461769104,
-0.012152839452028275,
-0.07532664388418198,
-0.006103238090872765,
0.014773378148674965,
-0.009572045877575874,
-0.029050664976239204,
0.02554568462073803,
-0.027914205566048622,
-0.003605521284043789,
0.0220310240983963,
0.05177128314971924,
-0.06817791610956192,
0.0978456512093544,
0.003335774876177311,
-0.02099452167749405,
0.006017020903527737,
-0.00956795271486044,
0.07586908340454102,
0.07309591770172119,
0.04924242943525314,
0.02882453426718712,
-0.05375242233276367,
-0.0003939142625313252,
-0.003844575257971883,
0.013993676751852036,
-0.028483854606747627,
-0.04126233980059624,
-0.04142517223954201,
-0.000039924034354044124,
0.007265022490173578,
-0.011187608353793621,
0.06435253471136093,
-0.018469244241714478,
-0.04659568518400192,
0.011672084219753742,
-0.042262375354766846,
0.0065050977282226086,
-0.04210090637207031,
-0.007143132854253054,
-0.01883586309850216,
-0.03093254752457142,
0.018991658464074135,
0.05056488886475563,
0.005136906169354916,
-0.025994988158345222,
-0.013496235944330692,
-0.0325612910091877,
0.016267720609903336,
-0.008288273587822914,
-0.03575650602579117,
0.00911274366080761,
0.048211440443992615,
0.01243880856782198,
-0.0062349410727620125,
0.008629921823740005,
-0.0024570103269070387,
-0.021785613149404526,
-0.0020071305334568024,
-0.024308618158102036,
-0.0002351825387449935,
-0.019376106560230255,
-0.01633360981941223,
0.041898034512996674,
0.013395465910434723,
-0.004852724261581898,
0.049337197095155716,
-0.031032437458634377,
0.065716952085495,
0.011569456197321415,
-0.025405485183000565,
0.00428216764703393,
0.04763832688331604,
0.051407910883426666,
-0.013236389495432377,
0.010908341035246849,
-0.03814845159649849,
-0.024899115785956383,
-0.007655742112547159,
0.02611847035586834,
0.026275280863046646,
-0.007547291927039623,
0.00703417556360364,
0.05912712216377258,
0.06481319665908813,
0.0011396848130971193,
0.03575930744409561,
0.016749002039432526,
-0.010639950633049011,
-0.036722976714372635,
0.003428001655265689,
-0.005269855726510286,
0.007834404706954956,
0.034758009016513824,
-0.01812714710831642,
0.005639152135699987,
-0.012315145693719387,
-0.07411883771419525,
0.023858537897467613,
-0.011519347317516804,
0.04047476127743721,
0.011439565569162369,
0.0010101861553266644,
0.025981480255723,
-0.03615467995405197,
-0.017505593597888947,
0.01734558679163456,
0.003928524907678366,
0.011022024787962437,
-0.03322581946849823,
-0.031016819179058075,
0.008529577404260635,
-0.006496502552181482,
-0.03151537850499153,
-0.0013530615251511335,
0.04053463041782379,
-0.021331239491701126,
-0.01598799228668213,
-0.03229767084121704,
-0.03243233263492584,
-0.005330709740519524,
-0.01012194249778986,
0.012393519282341003,
0.02761130779981613,
0.017942193895578384,
0.017545877024531364,
-0.034736517816782,
0.0037916498258709908,
-0.0322992280125618,
-0.023902034386992455,
-0.006621255539357662,
-0.0355096310377121,
0.04099350795149803,
0.016836058348417282,
-0.0105876624584198,
0.045785486698150635,
-0.03169494867324829,
0.030333995819091797,
-0.01015985757112503,
-0.026227356866002083,
-0.028100939467549324,
0.0009710530866868794,
-0.027322735637426376,
0.007506452966481447,
-0.02325020171701908,
0.015269193798303604,
0.030987568199634552,
-0.03697676584124565,
-0.046127110719680786,
0.026110878214240074,
-0.021889207884669304,
-0.02334827184677124,
-0.014886785298585892,
-0.010480793192982674,
0.008271581493318081,
-0.04347824305295944,
-0.0211603045463562,
-0.01279131043702364,
-0.026672782376408577,
-0.021947011351585388,
-0.019102877005934715,
-0.06989741325378418,
0.005713565740734339,
-0.01826915331184864,
0.06900500506162643,
-0.015545797534286976,
-0.021552694961428642,
0.05702150613069534,
0.0320173017680645,
-0.019532902166247368,
-0.020531538873910904,
0.021006112918257713,
-0.011180318892002106,
-0.026296865195035934,
0.031618088483810425,
0.05471938103437424,
-0.009264255873858929,
0.06422585248947144,
0.02559952810406685,
0.02400962822139263,
0.018531568348407745,
0.015204771421849728,
-0.0031326934695243835,
0.002125730039551854,
0.011308583430945873,
0.007373897358775139,
0.021321196109056473,
-0.004281532950699329,
-0.04314518719911575,
0.007613416761159897,
0.024525655433535576,
0.027574682608246803,
0.009077893570065498,
-0.05593548342585564,
0.03454889357089996,
-0.003608215134590864,
0.02471151575446129,
0.005024609621614218,
0.02543085627257824,
0.0004160403914283961,
0.02897832915186882,
-0.013915177434682846,
0.014185575768351555,
0.047630809247493744,
-0.025067005306482315,
-0.020007189363241196,
0.04624372720718384,
0.020702935755252838,
-0.03319260850548744,
-0.012831782922148705,
-0.05179031193256378,
-0.007629995234310627,
0.06591691821813583,
-0.05101929232478142,
-0.021677352488040924,
0.052458591759204865,
0.015044301748275757,
0.03467853367328644,
-0.03541981428861618,
-0.052769821137189865,
-0.016173655167222023,
-0.06930122524499893,
-0.014786417596042156,
-0.022251851856708527,
0.02713821828365326,
-0.003890285501256585,
0.060725171118974686,
0.023506004363298416,
0.015980228781700134,
0.0032437052577733994,
-0.02941964380443096,
-0.09041780233383179,
0.03637287765741348,
-0.050385139882564545,
-0.0437745526432991,
-0.010991513729095459,
0.0014774886658415198,
-0.010156401433050632,
-0.012989613227546215,
-0.03962652385234833,
-0.03768264129757881,
-0.011357798241078854,
-0.047495849430561066,
0.006201921496540308,
0.0001552078902022913,
-0.017617499455809593,
-0.022066840901970863,
0.048452228307724,
0.018250808119773865,
0.009830331429839134,
0.03260619938373566,
0.01448702160269022,
-0.03672413155436516,
-0.005934151820838451,
0.0028029794339090586,
0.015128884464502335,
-0.004772649146616459,
0.026180557906627655,
0.0283332671970129,
-0.004102901555597782,
-0.009106832556426525,
-0.01230580173432827,
-0.011688746511936188,
0.039967507123947144,
0.041412353515625,
-0.011303686536848545,
-0.02383708395063877,
-0.033636365085840225,
0.01306142844259739,
0.005727828945964575,
0.04966973885893822,
-0.018474703654646873,
0.011199984699487686,
0.04695011302828789,
0.009890568442642689,
-0.00458672596141696,
0.019052354618906975,
0.05236818268895149,
0.002565160393714905,
-0.014455478638410568,
-0.04210017994046211,
-0.025079801678657532,
-0.02757604420185089,
-0.020435115322470665,
0.002629375783726573,
-0.021185271441936493,
-0.03534320741891861,
-0.04047713056206703,
0.019501440227031708,
-0.024934085085988045,
-0.024380793794989586,
-0.00956177432090044,
-0.03322148695588112,
0.06483247876167297,
-0.003960655070841312,
-0.002372405491769314,
0.02685678005218506,
0.027501465752720833,
0.04675795137882233,
0.01430695503950119,
-0.018744511529803276,
-0.03180456906557083,
-0.008865084499120712,
0.01978985033929348,
0.022866269573569298,
-0.04202941060066223,
-0.0056335171684622765,
-0.06674422323703766,
-0.024658014997839928,
0.039788320660591125,
-0.028207242488861084,
0.0468074232339859,
0.010180366225540638,
0.007722603157162666,
-0.012636442668735981,
-0.0046427370980381966,
0.020526355132460594,
0.04425199329853058,
0.03408330678939819,
0.08129774779081345,
-0.03481534868478775,
-0.0062727537006139755,
-0.04274376854300499,
0.035258516669273376,
0.0505419485270977,
0.032962772995233536,
0.027395013719797134,
0.004150690510869026,
-0.015730589628219604,
0.010657607577741146,
-0.011478479951620102,
-0.0936487689614296,
0.020633237436413765,
0.011239777319133282,
-0.00896814651787281,
0.017490467056632042,
-0.03648021072149277,
-0.0526629276573658,
0.004892108496278524,
0.00030640923068858683,
0.008336839266121387,
-0.02274112030863762,
-0.04140503332018852,
-0.0351073294878006,
0.04724835231900215,
0.007515905424952507,
0.028271708637475967,
0.015662817284464836,
0.002755445893853903,
-0.02614440768957138,
0.008831747807562351,
0.025157881900668144,
-0.042282238602638245,
-0.026220835745334625,
0.00023204844910651445,
0.010821719653904438,
-0.03993917256593704,
0.039737801998853683,
0.013183284550905228,
0.02749476209282875,
-0.001080337562598288,
0.006840664427727461,
-0.048021815717220306,
0.00018530750821810216,
0.006316885352134705,
0.003994011785835028,
0.01371770165860653,
0.011115211062133312,
0.007352045271545649,
-0.0011504526482895017,
0.016375143080949783,
0.013629565015435219,
-0.018369879573583603,
0.031231116503477097,
-0.005825679749250412,
-0.0005909673636779189,
-0.02183506265282631,
-0.001985244220122695,
0.021615833044052124,
-0.031171223148703575,
0.022951021790504456,
-0.041336484253406525,
-0.004511042032390833,
0.03621004894375801,
-0.05391886457800865,
-0.019076591357588768,
0.011334705166518688,
-0.014860792085528374,
0.06407850235700607,
-0.05149705335497856,
0.012983769178390503,
0.02536921575665474,
-0.007448399439454079,
-0.064205601811409,
-0.03128831088542938,
0.038763467222452164,
0.01859333924949169,
-0.05586925894021988,
-0.005988841410726309,
-0.014496131800115108,
-0.01860741898417473,
-0.026016347110271454,
0.0077966745011508465,
0.045315541326999664,
-0.015269278548657894,
-0.02466091513633728,
0.012320253998041153,
0.003237866796553135,
0.08772311359643936,
-0.03922143578529358,
-0.03304282948374748,
0.010933054611086845,
-0.012850931845605373,
-0.03274589776992798,
-0.008749262429773808,
0.07704674452543259,
-0.03795822337269783,
-0.03217180445790291,
-0.002175279427319765,
-0.02097192034125328,
0.020903049036860466,
-0.03517386317253113,
-0.013274925760924816,
0.05011528730392456,
0.01829804852604866,
0.024915868416428566,
-0.0022698494140058756,
0.02852868102490902,
0.008144921623170376,
0.028349557891488075,
-0.011715170927345753,
0.003810431342571974,
-0.004507945850491524,
-0.03912901505827904,
-0.006875128485262394,
-0.011495139449834824,
0.005246919579803944,
0.011241376399993896,
0.048235926777124405,
0.008855846710503101,
-0.05430971086025238,
0.006387969944626093,
0.0036599421873688698,
-0.022526463493704796,
0.005499976221472025,
0.002850115764886141,
0.004052860662341118,
-0.00009719803347252309,
-0.05012882128357887,
-0.04614890739321709,
0.00008496552618453279,
-0.008840242400765419,
0.06213280186057091,
-0.04463430494070053,
0.06017480418086052,
0.003510574344545603,
0.013431696221232414,
-0.017552679404616356,
-0.0025151914451271296,
-0.02163594216108322,
-0.004655161406844854,
-0.004742630757391453,
0.0032573624048382044,
-0.03565292805433273,
0.010472053661942482,
-0.008750651963055134,
0.05509451776742935,
-0.005940134171396494,
0.04960931837558746,
0.06326062977313995,
0.01533291582018137,
0.03620045259594917,
0.03557007759809494,
-0.03847762197256088,
0.03741630166769028,
0.0029830588027834892,
0.0713668093085289,
-0.012429949827492237,
0.020775167271494865,
0.03332258015871048,
-0.0023641709703952074,
-0.006886011455208063,
-0.028687389567494392,
-0.03311067074537277,
-0.032129332423210144,
-0.0028340707067400217,
0.03408867493271828,
0.023853596299886703,
-0.0026635867543518543,
-0.007078628055751324,
0.03330866992473602,
0.04069153964519501,
0.00018124605412594974,
-0.02614559233188629,
-0.041782084852457047,
-0.004084201529622078,
-0.023531118407845497,
-0.05869618430733681,
0.07450476288795471,
-0.024607805535197258,
-0.04435944929718971,
0.02113255485892296,
-0.016288025304675102,
0.0035210077185183764,
0.021660029888153076,
0.011310744099318981,
-0.02304469421505928,
0.10157094895839691,
0.012165918946266174,
0.004836291074752808,
-0.03929482772946358,
0.0041467878036201,
0.10486763715744019,
0.02390359155833721,
-0.005142475012689829,
-0.045019976794719696,
0.02510773576796055,
-0.00683045806363225,
0.02504933811724186,
-0.027300387620925903,
0.016868747770786285,
0.031145595014095306,
-0.0018679932691156864,
0.015168976970016956,
0.02814633585512638,
0.017425598576664925,
-0.012874792329967022,
0.03290987387299538,
0.010587815195322037,
-0.018236011266708374,
-0.027203058823943138,
0.02816932089626789,
0.0009496674174442887,
-0.013019257225096226,
-0.023685041815042496,
0.0032421948853880167,
-0.058115433901548386,
-0.01124627236276865,
-0.04624591022729874,
-0.05529365688562393,
-0.0016124906251206994,
-0.004870544653385878,
-0.051507577300071716,
0.03383103013038635,
0.040529925376176834,
-0.016854500398039818,
-0.01929134875535965,
0.01830633543431759,
0.020662659779191017,
0.007833922281861305,
0.006110608112066984,
0.01993418298661709,
-0.005767963360995054,
-0.00335878599435091,
-0.015360213816165924,
0.028015289455652237,
-0.06890257447957993,
-0.012309904210269451,
-0.05714554712176323,
0.015540310181677341,
-0.009185212664306164,
0.02473514899611473,
-0.020801326259970665,
-0.00911766104400158,
-0.026363853365182877,
-0.03601155802607536,
0.008640111424028873,
-0.0016842312179505825,
0.002749264007434249,
-0.04482307285070419,
-0.028945157304406166,
-0.01665247045457363,
0.00973682664334774,
-0.028208274394273758,
0.051974810659885406,
-0.013828028924763203,
-0.016361765563488007,
-0.015836557373404503,
-0.0037770040798932314,
0.03758930042386055,
-0.057216670364141464,
-0.03793589398264885,
-0.016228633001446724,
0.0057709552347660065,
-0.048178549855947495,
0.013503167778253555,
0.003952750004827976,
0.0015696028713136911,
0.05990508198738098,
0.02520940452814102,
-0.03727911412715912,
-0.0012413497315719724,
-0.021385138854384422,
0.03059636615216732,
0.026587659493088722,
-0.008280528709292412,
-0.03757335990667343,
-0.017739541828632355,
0.05776842311024666,
-0.01941068470478058,
-0.017207812517881393,
0.0018196356249973178,
-0.023998228833079338,
-0.0038015865720808506,
0.022371144965291023,
-0.04149725288152695,
-0.015927614644169807,
0.036893948912620544,
0.006446978077292442,
-0.0035797280725091696,
-0.040044162422418594,
0.0192102063447237,
0.03156348317861557,
0.0027766982093453407,
0.014546039514243603,
0.024861453101038933,
-0.02116900496184826,
0.010481493547558784,
0.0019706625025719404,
-0.024988356977701187,
-0.043243300169706345,
0.02349712699651718,
-0.040295425802469254,
-0.03228096291422844,
-0.02752668224275112,
-0.0197182334959507,
0.0114881731569767,
-0.01470255572348833,
0.0008926393929868937,
-0.054708082228899,
0.001058800844475627,
-0.021451154723763466,
0.020132027566432953,
-0.02174735814332962,
-0.00036996990093030035,
-0.0680035650730133,
-0.004893701523542404,
0.005744706839323044,
-0.012154766358435154,
-0.020609650760889053,
0.033569786697626114,
0.011961149983108044,
-0.04007718712091446,
0.058657560497522354,
0.012251843698322773,
0.00839311070740223,
0.005756185855716467,
0.05337446928024292,
-0.020362691953778267,
0.053045038133859634,
-0.06364419311285019,
-0.04527450352907181,
0.042046625167131424,
-0.048723720014095306,
-0.06603576242923737,
0.04644721746444702,
-0.038339417427778244,
0.0011807623086497188,
0.019515732303261757,
-0.008809606544673443,
-0.0007139149820432067,
0.07617110759019852,
-0.03476964309811592,
0.0030325553379952908,
-0.026940228417515755,
0.021598249673843384,
0.004878242965787649,
0.0022822259925305843,
0.01101879682391882,
-0.0368158183991909,
0.015276643447577953,
0.020621223375201225,
0.04765782132744789,
-0.039800193160772324,
0.0409151166677475,
-0.009409543126821518,
-0.004890592768788338,
0.024574872106313705,
0.0035383605863898993,
-0.009299885481595993,
0.047316774725914,
0.047678809612989426,
-0.023411687463521957,
0.08154454827308655,
0.01854984648525715,
0.0024918962735682726,
-0.03614374250173569,
0.008484488353133202,
-0.012140519917011261,
-0.02848859503865242,
0.053549788892269135,
-0.05352185294032097,
-0.010977216996252537,
0.042482875287532806,
-0.06667014956474304,
0.00532278697937727,
-0.03650150075554848,
-0.019470710307359695,
-0.017421647906303406,
-0.030188312754034996,
0.01457736361771822,
0.004938108846545219,
0.0472189299762249,
0.012937272898852825,
0.03564738854765892,
0.03184607997536659,
0.006207122001796961,
-0.03180248290300369,
-0.015265947207808495,
0.03127181902527809,
-0.0019542330410331488,
0.013002383522689342,
0.04130883142352104,
-0.027353230863809586,
-0.03631410747766495,
0.02812160924077034,
-0.010001190938055515,
0.022339578717947006,
-0.010700181126594543,
0.01343797892332077,
-0.009436319582164288,
0.029123282060027122,
0.013454153202474117,
-0.021274475380778313,
-0.061592236161231995,
0.0206286683678627,
0.016248879954218864,
0.07033505290746689,
0.0064048804342746735,
-0.009472827427089214,
-0.00012473922106437385,
-0.035275403410196304,
-0.0016216363292187452,
-0.007628375198692083,
-0.0034263734705746174,
0.02305714786052704,
0.04635303094983101,
0.015449203550815582,
0.008947895839810371,
-0.010744117200374603,
0.03107404336333275,
-0.027086002752184868,
-0.0011456185020506382,
0.007846937514841557,
0.010313629172742367,
0.0066394261084496975,
0.013451610691845417,
0.0026057225186377764,
-0.027577320113778114,
0.03076421096920967,
-0.007368200458586216,
-0.03550991788506508,
-0.05233708769083023,
0.016397817060351372,
0.015101502649486065,
0.0011947177117690444,
-0.004271257668733597,
-0.03840399533510208,
-0.012811463326215744,
0.013212495483458042,
0.013381961733102798,
0.02886074408888817,
-0.021637020632624626,
-0.023815374821424484,
-0.006763400975614786,
-0.052728887647390366,
0.04624563083052635,
-0.013680758886039257,
0.020069997757673264,
-0.048031751066446304,
-0.015148124657571316,
-0.03590751066803932,
-0.009248055517673492,
0.028864363208413124,
0.005763164255768061,
0.016092006117105484,
0.025475772097706795,
0.004969323985278606,
0.018541119992733,
-0.0328354611992836,
0.012650520540773869,
-0.016326989978551865,
-0.04223223775625229,
0.06668373197317123,
-0.050543855875730515,
-0.024912990629673004,
0.0007305230828933418,
0.017344405874609947,
-0.02067161537706852,
0.03627711907029152,
0.029605917632579803,
0.01754642277956009,
0.06757289171218872,
0.010506702587008476,
0.0007568565779365599,
0.04627855122089386,
0.018501853570342064,
-0.0037964668590575457,
-0.002328417496755719,
0.0041081951931118965,
-0.06664666533470154,
0.06684337556362152,
-0.02590051107108593,
-0.025353172793984413,
0.005646402481943369,
-0.010626712813973427,
0.029048409312963486,
-0.028183668851852417,
-0.00116277567576617,
0.028243184089660645,
-0.0235747043043375,
0.012568116188049316,
0.006555477157235146,
0.0016992014134302735,
0.029913613572716713,
-0.014785276725888252,
0.05364760383963585,
0.0301267858594656,
-0.01019254606217146,
0.01794852688908577,
0.036426495760679245,
0.02745630405843258,
0.005413775332272053,
-0.008904232643544674,
0.030297666788101196,
0.024782694876194,
0.0266096331179142,
0.015906190499663353,
0.0454266220331192,
-0.027176808565855026,
-0.06028797850012779,
0.0154876122251153,
-0.05301376059651375,
0.01852905936539173,
0.03496544808149338,
0.003706724615767598,
0.09138332307338715,
0.024589091539382935,
0.012702454812824726,
-0.016109716147184372,
-0.013708298094570637,
-0.02897671051323414,
-0.028170662000775337,
0.013398910872638226,
-0.005281790159642696,
0.008162293583154678,
-0.003444114699959755,
-0.006569241173565388,
0.01888979785144329,
0.0287358108907938,
-0.014991686679422855,
0.04013129696249962,
-0.024775318801403046,
0.016522357240319252,
-0.03710058331489563,
-0.019315499812364578,
-0.01723633147776127,
-0.043936438858509064,
0.037875283509492874,
0.023709584027528763,
0.03975948318839073,
0.010255293920636177,
-0.05601854994893074,
-0.014129288494586945,
0.05663372576236725,
-0.06610966473817825,
-0.04082917422056198,
-0.0446893535554409,
0.06143572926521301,
-0.00478025060147047,
-0.042286407202482224
] |
<p>As a homework assignment, we have to find $U_a(\omega)$, that is the voltage that drops over the right resistor in relation to the frequency $\omega$ of the input AC voltage $U_e$.</p>
<p><img src="http://wstaw.org/m/2012/07/01/blindleistung3.png" alt=""></p>
<p>For the two extreme cases, $\omega \to 0$ and $\omega \to \infty$ I expect $U_a = 0$ since in the $\omega \to 0$ case, the capacitors will block the whole current. In the $\omega \to \infty$ case, the left capacitor will short the whole thing so that the right resistor does not get any current through it.</p>
<p>To get the voltage $U_a(\omega)$ I tried these steps:</p>
<ul>
<li><p>Calculate the total impedance of the circuit $Z$:
$$ Z(\omega) = R + \left( \frac 1{Z_C(\omega)} + \frac 1{Z_C(\omega) + R} \right)^{-1}$$</p>
<p>The impedance of the capacitor with capacitance $C$ is:
$$ Z_C(\omega) = \frac{1}{i \omega C}$$</p></li>
<li><p>Calculate the total current:
$$ I(\omega) = \frac{U_e(\omega)}{Z(\omega)} $$</p></li>
<li><p>Use the current divider rule to get the current that flows through the right branch (with capacitor and resistor). The current should be just this:
$$ I_r(\omega) = I(\omega) \frac{Z_C(\omega)}{2 Z_C(\omega) + R} $$</p></li>
<li><p>Multiply that current with $R$ and get the result:
$$ U_a(\omega) = I_r(\omega) R $$</p></li>
</ul>
<p>When I plot real and imaginary parts of $U_a$ against $\omega$, I get the following: (The top line is the real part, the bottom line the imaginary part.)</p>
<p><img src="http://wstaw.org/m/2012/07/01/3.png" alt=""></p>
<p>When I plot the absolute value of $U_a$, I get the following plot:</p>
<p><img src="http://wstaw.org/m/2012/07/01/4.png" alt=""></p>
<p>Which one is the current that is really measured? The real part of the absolute value?</p>
<p>I have to find out the value of $\omega$ for which the output voltage is the highest. I tried $\frac{\mathrm d U_a(\omega)}{\mathrm d \omega} = 0$, but I only get $\omega = \pm \frac{i}{RC}$ as solutions, which do not really make sense to me. How can I find the actual maximum?</p>
| 9,389 |
[
-0.0010704577434808016,
-0.02465014159679413,
0.00047423873911611736,
-0.006566270254552364,
0.027271553874015808,
-0.01669139228761196,
-0.026787299662828445,
0.0028507800307124853,
0.023805420845746994,
0.006343069951981306,
0.024075284600257874,
0.04719000682234764,
0.04741819202899933,
0.019154727458953857,
0.002282738219946623,
-0.018006810918450356,
-0.03757116198539734,
0.019744420424103737,
-0.0017300721956416965,
0.0028718067333102226,
0.009875723160803318,
0.025304250419139862,
0.019305359572172165,
0.008196740411221981,
-0.009293938986957073,
0.020970644429326057,
0.03132728487253189,
-0.002379243029281497,
-0.016603311523795128,
0.013451511040329933,
-0.002763650845736265,
-0.03542330488562584,
0.0066156345419585705,
0.02888905256986618,
0.05011749267578125,
0.027587341144680977,
-0.023099124431610107,
-0.034585513174533844,
-0.022604309022426605,
0.032155733555555344,
0.01792386919260025,
0.01998002640902996,
-0.032545819878578186,
0.02500341646373272,
-0.043670084327459335,
-0.020795155316591263,
-0.010261055082082748,
0.000752097403164953,
0.02657848224043846,
-0.04752381518483162,
0.03577528893947601,
-0.032629989087581635,
0.051819611340761185,
0.0033529638312757015,
0.02431458607316017,
-0.0030660773627460003,
0.04863422363996506,
0.07876094430685043,
-0.019604718312621117,
-0.028424996882677078,
0.01058714184910059,
0.0037906195502728224,
-0.03808876872062683,
-0.017975643277168274,
-0.028493620455265045,
0.024449976161122322,
0.021808521822094917,
-0.0067887636832892895,
0.01937011070549488,
-0.021618491038680077,
0.02638271264731884,
-0.0008460606331937015,
-0.0005775480531156063,
-0.02658754400908947,
0.00003590093911043368,
-0.022009091451764107,
-0.024713782593607903,
0.05900189280509949,
0.0009782355045899749,
0.03271639347076416,
-0.02431868575513363,
0.0025037142913788557,
0.04705176502466202,
0.03247743844985962,
0.01914423145353794,
-0.05387755483388901,
0.0634380653500557,
0.01198669709265232,
-0.011720574460923672,
-0.004492065869271755,
0.034109070897102356,
-0.011529441922903061,
-0.01537125650793314,
-0.03043282963335514,
-0.0023138585966080427,
0.05190887302160263,
-0.023681368678808212,
0.01153514813631773,
-0.002382506849244237,
-0.05248275771737099,
0.020764945074915886,
-0.036027394235134125,
0.04178605601191521,
0.08713646978139877,
0.005099175497889519,
-0.017146984115242958,
-0.005754674784839153,
0.009742781519889832,
-0.0021738591603934765,
-0.024311048910021782,
-0.07455693185329437,
0.039216600358486176,
0.015411151573061943,
0.027380825951695442,
-0.018900154158473015,
-0.00809972919523716,
0.007870878092944622,
-0.036843929439783096,
0.02215849608182907,
0.00912897102534771,
0.043773867189884186,
-0.021915027871727943,
-0.01727217622101307,
-0.0347413495182991,
-0.04783923551440239,
0.03023780696094036,
-0.02307094633579254,
0.003242898266762495,
-0.011295963078737259,
0.04066943749785423,
-0.005223685875535011,
0.018424399197101593,
-0.006797092035412788,
0.020581752061843872,
0.019179249182343483,
-0.04343285784125328,
-0.07118313014507294,
-0.0433492474257946,
0.0103966249153018,
-0.02956063114106655,
-0.0010955476900562644,
-0.07401705533266068,
0.017122475430369377,
0.051312800496816635,
0.06858772784471512,
0.01396895945072174,
-0.00971828494220972,
-0.024514149874448776,
0.018505414947867393,
0.03382532671093941,
0.03150108456611633,
-0.000626749824732542,
-0.017566664144396782,
0.024459287524223328,
0.016634557396173477,
-0.019497334957122803,
0.027891846373677254,
0.019550083205103874,
-0.01449455227702856,
-0.017917895689606667,
0.057017095386981964,
0.012513944879174232,
-0.008402680978178978,
0.01839342899620533,
-0.053288087248802185,
-0.039699070155620575,
0.07469979673624039,
-0.0019377210410311818,
-0.010413233190774918,
0.01544731855392456,
-0.0002895060752052814,
0.007154557388275862,
-0.03401268273591995,
-0.019760018214583397,
0.06771795451641083,
-0.050835393369197845,
-0.025601759552955627,
-0.022880487143993378,
0.0008399301441386342,
0.006436892785131931,
-0.023986607789993286,
-0.038624707609415054,
-0.02651478722691536,
0.027381734922528267,
0.02729697711765766,
0.05214351788163185,
-0.008456556126475334,
-0.019025644287467003,
0.021314894780516624,
-0.02324012480676174,
-0.004446626175194979,
-0.026063816621899605,
0.02142512798309326,
-0.0006896643317304552,
-0.04573766142129898,
0.006088412832468748,
0.0045913164503872395,
0.020065825432538986,
-0.028571773320436478,
-0.011922160163521767,
0.004664282780140638,
-0.008935460820794106,
0.008905095979571342,
-0.009689141064882278,
0.0555514395236969,
0.03416626527905464,
0.0435420386493206,
0.016595125198364258,
0.04606066271662712,
-0.017334623262286186,
0.0009358312236145139,
-0.015321759507060051,
-0.01917637325823307,
0.05945531651377678,
0.016707392409443855,
0.006824629381299019,
0.045855335891246796,
-0.020504916086792946,
0.028350988402962685,
0.016888830810785294,
-0.014693017117679119,
0.05107911303639412,
0.08699480444192886,
-0.005233342759311199,
0.00863619614392519,
0.023977668955922127,
0.021314267069101334,
0.04493020102381706,
-0.043086081743240356,
-0.02021128311753273,
-0.058833226561546326,
-0.014888004399836063,
0.0633799284696579,
0.007208343129605055,
-0.04843161627650261,
-0.002349426271393895,
0.03642065078020096,
0.01095260214060545,
0.06437185406684875,
0.0022065015509724617,
-0.014365889132022858,
-0.03165357932448387,
0.017174869775772095,
0.004409372806549072,
-0.008793124929070473,
-0.010495967231690884,
0.00654368894174695,
0.0015030482318252325,
0.024747278541326523,
0.006186955608427525,
0.006839694455265999,
0.0477139912545681,
0.013207686133682728,
0.014466140419244766,
0.047564804553985596,
-0.021823540329933167,
0.02390342205762863,
-0.011600431986153126,
-0.012000414542853832,
0.02105645462870598,
-0.01763375848531723,
0.006115796975791454,
0.033460285514593124,
0.030231090262532234,
0.007614747155457735,
0.01003789622336626,
-0.02711639553308487,
-0.0029482548125088215,
0.0323401540517807,
-0.023463107645511627,
0.018217332661151886,
-0.01905168406665325,
-0.006967739202082157,
-0.037641413509845734,
-0.030738703906536102,
0.038034915924072266,
0.024703171104192734,
0.026711301878094673,
-0.05299767851829529,
-0.011954977177083492,
-0.008293893188238144,
0.01701090671122074,
0.02013843134045601,
0.033809226006269455,
-0.013624286279082298,
0.0009068012004718184,
-0.0212973952293396,
-0.03072606958448887,
0.04283040016889572,
0.05777418985962868,
-0.00871269404888153,
0.0059509617276489735,
0.018662329763174057,
-0.07016900181770325,
-0.06421773880720139,
-0.012630000710487366,
0.05945185571908951,
-0.07224734127521515,
-0.00875412579625845,
0.08820479363203049,
0.03331342339515686,
-0.02018234319984913,
0.02103259600698948,
-0.024030983448028564,
-0.0340145118534565,
0.014286220073699951,
-0.02136577107012272,
0.0010835343273356557,
-0.06354191154241562,
0.006624172907322645,
-0.03834833577275276,
-0.015642542392015457,
-0.0357932448387146,
-0.026341095566749573,
-0.0501200370490551,
0.015369081869721413,
0.014326103962957859,
0.05515784025192261,
0.05177736282348633,
-0.03896557167172432,
0.06833399832248688,
0.003277972573414445,
0.01718129776418209,
0.0017216380219906569,
-0.010535779409110546,
-0.008286732248961926,
-0.06463973224163055,
-0.009182626381516457,
0.06872346252202988,
-0.03368731588125229,
-0.022298140451312065,
0.02061789482831955,
0.034257061779499054,
0.058780305087566376,
0.024539584293961525,
0.038660578429698944,
0.03139803931117058,
-0.017994070425629616,
-0.038605548441410065,
0.0754830539226532,
-0.0005404321709647775,
0.01971856877207756,
0.01894884742796421,
0.016847653314471245,
0.040509603917598724,
0.024710819125175476,
-0.05307389423251152,
-0.0196159016340971,
-0.01354571245610714,
0.004659229423850775,
-0.03794880956411362,
0.052841298282146454,
0.014232802204787731,
0.037019032984972,
0.0025102647487074137,
-0.0036099283024668694,
0.08963341265916824,
-0.01767321303486824,
0.014909046702086926,
0.022787654772400856,
0.010318690910935402,
-0.02190946787595749,
-0.015017270110547543,
-0.02268208935856819,
-0.029875757172703743,
0.07490625232458115,
-0.020969990640878677,
-0.03684769943356514,
0.0679197609424591,
0.022718295454978943,
0.005040864460170269,
0.017472147941589355,
-0.05022881180047989,
-0.008256951346993446,
-0.026531178504228592,
-0.01729140244424343,
-0.05006708577275276,
0.05205840617418289,
0.0012176678283140063,
0.04603280499577522,
-0.020090190693736076,
0.0253917183727026,
-0.02256026305258274,
-0.004733583424240351,
-0.07288968563079834,
0.0073599196039140224,
0.009900842793285847,
-0.008542753756046295,
-0.015136511996388435,
0.027243124321103096,
0.0360555574297905,
-0.007818535901606083,
-0.029388876631855965,
-0.029852639883756638,
-0.014493909664452076,
-0.03698792681097984,
0.054596878588199615,
0.014062942937016487,
-0.030240995809435844,
-0.02773432433605194,
0.017448756843805313,
0.020248718559741974,
-0.03596935421228409,
0.008153881877660751,
0.004905921407043934,
0.009876305237412453,
0.019127078354358673,
-0.010560336522758007,
-0.02742265723645687,
0.04741901159286499,
0.010025286115705967,
0.0049914889968931675,
0.000717541144695133,
0.015469031408429146,
0.0007669381448067725,
-0.004352125804871321,
0.03676767274737358,
-0.00930382777005434,
-0.024637872353196144,
-0.0007250347407534719,
-0.05016053840517998,
-0.029375284910202026,
-0.01792389154434204,
0.05500936880707741,
-0.02599266730248928,
0.015969369560480118,
0.023106375709176064,
-0.0004497067420743406,
0.01194622740149498,
0.03189193084836006,
0.004912423901259899,
0.026454085484147072,
-0.015032641589641571,
-0.04599107801914215,
-0.014889568090438843,
-0.04017362371087074,
0.023824190720915794,
0.028656112030148506,
-0.007360379211604595,
-0.018461957573890686,
-0.014184371568262577,
0.05539222061634064,
0.0455651618540287,
0.009655577130615711,
0.017694029957056046,
0.008948268368840218,
0.009198377840220928,
0.01655540056526661,
-0.02833130769431591,
0.015667662024497986,
0.01211575511842966,
0.05873338133096695,
0.017711205407977104,
-0.01815260760486126,
-0.05358187109231949,
-0.048194315284490585,
0.02366304211318493,
0.035163722932338715,
0.013895704410970211,
0.002358259866014123,
-0.06369651108980179,
-0.042271990329027176,
-0.0064524393528699875,
-0.02767401747405529,
0.061497483402490616,
0.0005795969627797604,
0.029528625309467316,
-0.023647792637348175,
-0.08948367089033127,
-0.020313676446676254,
0.00450648320838809,
0.00588251231238246,
0.009389637038111687,
-0.024601813405752182,
-0.029851801693439484,
0.010124022141098976,
-0.001169229974038899,
0.04703488573431969,
0.0703955665230751,
-0.024831071496009827,
-0.0030107905622571707,
0.01748509891331196,
0.040294598788022995,
-0.03084014169871807,
-0.08749188482761383,
0.009678104892373085,
-0.033369217067956924,
0.0034502982161939144,
0.06860193610191345,
-0.041647858917713165,
-0.0324719063937664,
0.051022447645664215,
0.02083546109497547,
0.0030582963954657316,
0.014810966327786446,
-0.0003711934550665319,
0.03759758919477463,
0.031290203332901,
-0.025931818410754204,
0.04064122587442398,
0.021920474246144295,
-0.03022587113082409,
-0.0012794060166925192,
-0.0007310576038435102,
-0.0016812586691230536,
-0.015385854989290237,
-0.027196232229471207,
-0.011388883925974369,
0.006510772742331028,
-0.014996089972555637,
0.009905040264129639,
-0.011379721574485302,
0.03418479487299919,
-0.036316949874162674,
-0.026150153949856758,
0.02653437852859497,
-0.012930551543831825,
-0.05586095154285431,
0.01663653738796711,
-0.012231579050421715,
0.018978362902998924,
0.00782904401421547,
-0.02101241424679756,
0.0280039943754673,
-0.009406263008713722,
0.046515461057424545,
0.013202731497585773,
-0.027335653081536293,
0.01183938980102539,
-0.06422478705644608,
0.025033442303538322,
-0.0018510246882215142,
-0.04245855659246445,
0.06857582181692123,
-0.020050371065735817,
0.0025993590243160725,
0.0101222675293684,
-0.002957264194265008,
-0.06314924359321594,
0.024181747809052467,
0.015102420933544636,
-0.020192252472043037,
-0.02245568111538887,
0.003787402296438813,
0.025846609845757484,
0.0001596966467332095,
-0.022100023925304413,
-0.052476778626441956,
-0.003003015648573637,
0.046238064765930176,
0.017583416774868965,
0.017259536311030388,
-0.008597533218562603,
0.04990692809224129,
-0.038079146295785904,
0.022339189425110817,
0.010863983072340488,
-0.05064264312386513,
0.006274421699345112,
0.0012295879423618317,
0.015107164159417152,
0.030174465849995613,
0.027405276894569397,
-0.0003172417636960745,
0.007070302497595549,
-0.08835642039775848,
-0.032863665372133255,
0.013177255168557167,
0.0366196408867836,
-0.04256429150700569,
-0.03536568209528923,
0.010046317242085934,
0.0005478269886225462,
0.026482805609703064,
0.00015472051745746285,
-0.019931497052311897,
0.014605503529310226,
0.03327232971787453,
-0.0305594764649868,
-0.00032562363776378334,
-0.020336836576461792,
0.013851525261998177,
0.003989849705249071,
0.011643693782389164,
-0.025500185787677765,
-0.061973996460437775,
-0.03401866927742958,
-0.006127038970589638,
0.0036171316169202328,
-0.011069749481976032,
-0.02384968101978302,
0.0864027589559555,
-0.03702503442764282,
-0.034340497106313705,
0.0056874980218708515,
-0.01966003142297268,
0.02701190672814846,
-0.012442592531442642,
0.020339300855994225,
0.044325195252895355,
-0.002952991984784603,
-0.030984872952103615,
-0.010419095866382122,
-0.07656529545783997,
0.013489595614373684,
0.05763394385576248,
0.026635199785232544,
0.047197289764881134,
0.0103718601167202,
-0.016483459621667862,
-0.02906404435634613,
-0.00483988132327795,
-0.030776603147387505,
0.014796359464526176,
0.0020268657244741917,
0.0290182214230299,
-0.03794894739985466,
-0.018572261556982994,
0.03367464616894722,
0.016981713473796844,
-0.021557318046689034,
-0.0002696156152524054,
0.02927563153207302,
0.024983003735542297,
0.008204378187656403,
-0.014361281879246235,
0.0017822565278038383,
0.009791441261768341,
-0.04965095594525337,
0.03606190159916878,
-0.00430337805300951,
-0.04067341238260269,
0.03570210188627243,
0.05812228098511696,
-0.009461077861487865,
-0.04188479855656624,
0.018221311271190643,
-0.026607602834701538,
0.03467791900038719,
0.0038422923535108566,
0.011599505320191383,
0.014135819859802723,
-0.003602447919547558,
0.05521216243505478,
-0.027401655912399292,
0.06264597177505493,
-0.035877835005521774,
-0.02774818055331707,
0.01924261637032032,
-0.018213296309113503,
-0.04903372377157211,
0.029477965086698532,
0.0027685074601322412,
-0.01954600214958191,
0.035777073353528976,
-0.031181789934635162,
0.0274372398853302,
0.03578878566622734,
0.03153275325894356,
-0.022800443693995476,
0.06823205947875977,
-0.015757350251078606,
0.03327486291527748,
-0.015221609733998775,
-0.034796688705682755,
0.1422252506017685,
0.04012273624539375,
-0.024870485067367554,
-0.03740617260336876,
0.030400004237890244,
-0.00945874210447073,
0.04019051417708397,
-0.0464421883225441,
-0.0038269227370619774,
-0.014993585646152496,
0.007018986623734236,
0.019522182643413544,
0.025030849501490593,
0.005025621969252825,
-0.0032687890343368053,
0.027540532872080803,
-0.030206937342882156,
0.01615302637219429,
-0.034376151859760284,
0.024751875549554825,
-0.019962718710303307,
0.01845015212893486,
-0.009835137985646725,
0.03632412478327751,
-0.06369617581367493,
-0.02270667813718319,
-0.0833355262875557,
0.020008981227874756,
0.07110954076051712,
-0.03643681854009628,
-0.03431890532374382,
0.029730839654803276,
0.01224618311971426,
-0.042148228734731674,
0.000437968090409413,
0.051913902163505554,
0.037079107016325,
-0.0047849006950855255,
0.016396062448620796,
0.031656865030527115,
0.03653230145573616,
0.0020478435326367617,
0.018996132537722588,
-0.01649315655231476,
-0.03831090033054352,
-0.009299435652792454,
-0.05327976122498512,
0.018649671226739883,
-0.004427922889590263,
-0.022647220641374588,
-0.020774001255631447,
0.01757773570716381,
0.024598965421319008,
-0.021883655339479446,
-0.014339867047965527,
0.021667256951332092,
-0.023062802851200104,
-0.03850598633289337,
0.009084257297217846,
-0.007124533411115408,
0.013043814338743687,
0.03248067945241928,
-0.014038939028978348,
-0.020074274390935898,
-0.02816985547542572,
-0.027862660586833954,
-0.004751141183078289,
0.025278354063630104,
0.014261623844504356,
-0.03938087821006775,
-0.02284235693514347,
0.0027191289700567722,
0.01944158971309662,
-0.01607006974518299,
0.0038889453280717134,
0.009755206294357777,
0.03498252481222153,
-0.0020541155245155096,
-0.041602566838264465,
0.005661895498633385,
-0.08138415217399597,
0.02754116617143154,
0.04491199553012848,
0.007400777656584978,
-0.018381403759121895,
-0.018720023334026337,
-0.010875650681555271,
0.04834265261888504,
-0.01073521375656128,
0.0015022988663986325,
0.05836999788880348,
0.06659448146820068,
0.02833942323923111,
-0.021481230854988098,
-0.027317577973008156,
0.004697955213487148,
-0.046640172600746155,
0.0549875944852829,
0.03200756385922432,
0.04766574129462242,
0.04462410509586334,
0.02735065668821335,
-0.014629132114350796,
0.004045200068503618,
-0.059814829379320145,
-0.004893042612820864,
0.02559022605419159,
-0.040059905499219894,
0.015619173645973206,
0.0009355009533464909,
0.04407741129398346,
-0.024794334545731544,
0.012388129718601704,
0.010195543989539146,
0.007453452330082655,
-0.01193917728960514,
-0.018069837242364883,
-0.020624123513698578,
0.03921470791101456,
-0.0465618371963501,
0.01623314619064331,
-0.026089366525411606,
-0.01902778632938862,
0.011821465566754341,
-0.04635396972298622,
-0.003917271271348,
0.03213581442832947,
-0.013576670549809933,
0.03734980896115303,
-0.0018309226725250483,
0.027960574254393578,
0.007201465778052807,
0.05674181506037712,
-0.004768860526382923,
-0.011211718432605267,
0.030168840661644936,
0.022908462211489677,
-0.02930367738008499,
-0.023133058100938797,
-0.030545400455594063,
0.04371270164847374,
-0.02431103214621544,
-0.0014297966845333576,
0.009793014265596867,
0.02918737381696701,
0.03593842685222626,
-0.02276686392724514,
-0.038162607699632645,
-0.026372255757451057,
0.002725512720644474,
-0.01065346784889698,
-0.017021771520376205,
-0.027878666296601295,
-0.014462982304394245,
0.02432987280189991,
0.026260392740368843,
0.010077685117721558,
-0.0259377621114254,
0.02193273976445198,
-0.010136165656149387,
0.03476349636912346,
-0.04003334417939186,
-0.04078018665313721,
0.009244360961019993,
0.005139079410582781,
0.00892111100256443,
0.022816753014922142,
0.028563829138875008,
0.036803048104047775,
0.01285545527935028,
-0.0004885570961050689,
0.015505813993513584,
-0.006365558132529259,
-0.014252210967242718,
-0.08004948496818542,
-0.03384285792708397,
0.00045425823191180825,
0.026028208434581757,
0.04184632748365402,
-0.013422246091067791,
-0.02222217619419098,
0.01884128712117672,
-0.03821282461285591,
-0.02493218146264553,
-0.02289857715368271,
-0.001603253185749054,
-0.04198377951979637,
-0.042251452803611755,
-0.04160754382610321,
-0.013610266149044037,
-0.0022262479178607464,
0.00013206400035414845,
0.010189305990934372,
0.0043301573023200035,
-0.015456041321158409,
-0.04212215915322304,
0.025904834270477295,
0.03312656283378601,
-0.002136516384780407,
0.00916204135864973,
0.039627645164728165,
-0.02344825491309166,
0.027202945202589035,
0.018969422206282616,
-0.0045463009737432,
-0.007708309683948755,
-0.023915667086839676,
0.012933057732880116,
-0.008923712186515331,
0.05341169238090515,
-0.007172111421823502,
0.003164776135236025,
-0.02925819344818592,
-0.03573211655020714,
0.05752282589673996,
0.008496709167957306,
-0.010454152710735798,
-0.0034534779842942953,
0.027728062123060226,
-0.022888898849487305,
-0.04376357048749924,
-0.01780710183084011,
-0.036213237792253494,
-0.013609531335532665,
0.011879179626703262,
-0.012427889741957188,
-0.0013662133133038878,
-0.07741571962833405,
-0.014483527280390263,
-0.005258437246084213,
-0.022249454632401466,
0.0338960625231266,
0.0009130320395343006,
0.02838411182165146,
-0.05323568731546402,
-0.025348810479044914,
-0.0071008228696882725,
0.04840652644634247,
0.045240841805934906,
-0.03900284692645073,
-0.057777319103479385,
-0.028870118781924248,
-0.023790663108229637,
-0.0028272937051951885,
0.01973075605928898,
-0.06324334442615509,
0.02241043746471405,
0.005809384863823652,
0.017757534980773926,
-0.029269125312566757,
-0.027835821732878685,
-0.03517678752541542,
-0.008118151687085629,
-0.03352738916873932,
0.02909369207918644,
-0.00808947253972292,
-0.030728112906217575,
-0.03872527554631233,
-0.06842189282178879,
-0.02651343122124672,
0.013508415780961514,
0.06434650719165802,
-0.001513441326096654,
-0.011035257019102573,
-0.021916229277849197,
0.009965892881155014,
0.044047191739082336,
-0.0710502564907074,
0.03243586793541908,
0.0021091352682560682,
0.01933988928794861,
-0.010173318907618523,
-0.007271545473486185,
-0.009726290591061115,
0.005525520071387291,
0.011596095748245716,
0.009998397901654243,
-0.00916619785130024,
-0.016255760565400124,
-0.0018911404768005013,
0.009519029408693314,
0.005176875740289688,
0.00584819819778204,
0.06256816536188126,
-0.007546454202383757,
0.01264697965234518,
0.015005148015916348,
-0.02779320254921913,
-0.05202635005116463,
0.005795201286673546,
-0.0262695774435997,
0.02887994423508644,
-0.06271466612815857,
0.005794359836727381,
0.05311337113380432,
-0.050304166972637177,
-0.03791387751698494,
0.02713373489677906,
-0.03470883145928383,
-0.013855276629328728,
0.05117950588464737,
-0.05812789499759674,
-0.009961157105863094,
-0.031117472797632217,
-0.0036057953257113695,
0.00959972757846117,
-0.006567270960658789,
0.002387887565419078,
0.007380345836281776,
0.0021182263735681772,
-0.03054693713784218,
-0.016570668667554855,
0.0751778706908226,
0.01605345495045185,
-0.0004784139746334404,
-0.011224127374589443,
-0.019942250102758408,
-0.036510854959487915,
-0.02945856750011444,
0.014040441252291203,
-0.03869473189115524,
-0.021766813471913338,
0.05378365516662598,
0.003810036228969693,
0.04912332445383072,
0.0082998126745224,
0.031450945883989334,
0.0078025441616773605,
0.020772920921444893,
-0.024832366034388542,
0.04051718860864639,
0.02668299898505211,
0.018557636067271233,
-0.040083229541778564,
-0.027068037539720535,
-0.015344182029366493,
-0.017826713621616364,
0.05060466378927231,
-0.07409417629241943,
0.03495367616415024,
0.031152833253145218,
0.012222523801028728,
-0.0032314960844814777,
-0.038289450109004974,
-0.01932039111852646,
-0.07747392356395721,
0.04146362841129303,
0.02536025643348694,
0.004050998017191887,
0.0001340021553914994,
0.014735054224729538,
0.00093691615620628,
0.07517194002866745,
-0.012994110584259033,
-0.029260702431201935,
0.025361455976963043,
0.01122265961021185,
0.012621639296412468,
0.010706917382776737
] |
<p>In cartoons we can see, how vehicles brake by rotating wheels reverse.</p>
<p>Will this be helpful sometimes in real situations? I know that the main tactics of ABS is to maintain tractive contact. But may be it will be better sometimes, at some speeds, friction and so on -- to rotate back?</p>
<p>Does current ABS systems do something like that? Were any experiments on this performed?</p>
| 9,390 |
[
-0.01806226372718811,
-0.003572761081159115,
-0.001807503984309733,
0.023285062983632088,
0.0296529121696949,
0.0027275627944618464,
-0.0398675873875618,
0.0034109631087630987,
-0.009951832704246044,
0.007825515232980251,
-0.007286724168807268,
0.03383230045437813,
0.015823369845747948,
0.009699393063783646,
0.01096697524189949,
0.0016490687849000096,
-0.01184055581688881,
-0.03869309276342392,
-0.015687095001339912,
-0.005567088723182678,
0.014665643684566021,
-0.043310608714818954,
0.0006064643966965377,
0.009818587452173233,
-0.016096165403723717,
-0.007231004070490599,
0.007193279452621937,
-0.04601765051484108,
0.03004290536046028,
0.027029912918806076,
-0.02629348635673523,
0.01055801659822464,
-0.025698963552713394,
0.02627924084663391,
0.007487267255783081,
-0.014302261173725128,
0.00041517027420923114,
-0.044875357300043106,
-0.02008475735783577,
0.04608600214123726,
-0.031706877052783966,
-0.03308922052383423,
-0.03062819130718708,
0.06888152658939362,
-0.004298077430576086,
0.0272257961332798,
-0.026409197598695755,
-0.006880511995404959,
0.03231951966881752,
-0.08079902827739716,
0.06291172653436661,
-0.021722812205553055,
0.023433784022927284,
0.0013010627590119839,
0.04002737998962402,
0.023575954139232635,
0.09102773666381836,
0.0278988778591156,
-0.03358646109700203,
-0.03860476613044739,
0.03441326692700386,
-0.010276242159307003,
-0.030072953552007675,
0.01517503336071968,
-0.021583616733551025,
0.03230792284011841,
0.005340093281120062,
-0.015480433590710163,
0.025851095095276833,
0.0010404196800664067,
-0.00206537963822484,
0.008895370177924633,
0.024023132398724556,
-0.006526717450469732,
0.006140705663710833,
-0.07713226974010468,
0.03954135626554489,
0.012320209294557571,
0.030953658744692802,
0.049451541155576706,
-0.0117509625852108,
0.015045593492686749,
0.04006587341427803,
0.04447902366518974,
0.02924112044274807,
-0.027963021770119667,
0.0563945472240448,
-0.005693324841558933,
0.040565527975559235,
0.0307400394231081,
0.021162044256925583,
-0.008232317864894867,
0.009728049859404564,
-0.04929743707180023,
-0.02773064374923706,
0.025620542466640472,
0.01254915352910757,
0.05790483579039574,
0.025940552353858948,
0.004056646954268217,
-0.014345796778798103,
0.036555659025907516,
0.0007747049676254392,
0.025429528206586838,
0.0016024976503103971,
-0.02673906274139881,
-0.028565993532538414,
0.037870004773139954,
-0.012310893274843693,
-0.005939539987593889,
-0.04300714284181595,
-0.00798884965479374,
-0.02440084144473076,
-0.016515644267201424,
0.032023318111896515,
-0.021557265892624855,
-0.016447274014353752,
-0.01925124041736126,
0.000015773777704453096,
0.07650785893201828,
0.038631632924079895,
-0.028364630416035652,
-0.009615657851099968,
-0.03043586015701294,
0.021358391270041466,
-0.007275172043591738,
0.03817549720406532,
0.012516883201897144,
-0.025322645902633667,
-0.009045480750501156,
-0.007968517020344734,
-0.05028735101222992,
0.02090027928352356,
-0.014194326475262642,
0.027464821934700012,
-0.02027011848986149,
-0.0720004290342331,
-0.042588938027620316,
0.048121850937604904,
0.0014530535554513335,
0.00027331049204804003,
-0.06141556799411774,
0.02129768393933773,
0.016934774816036224,
0.065987728536129,
0.014483906328678131,
0.04025082290172577,
0.02100403606891632,
0.006065772846341133,
-0.012724440544843674,
0.014959242194890976,
-0.038447681814432144,
0.015057855285704136,
-0.03265346959233284,
-0.020326104015111923,
-0.06300915777683258,
0.02664804272353649,
0.035829585045576096,
0.01492172759026289,
-0.0305480994284153,
0.01592295989394188,
-0.0032186314929276705,
-0.027210356667637825,
0.042359549552202225,
-0.06492821127176285,
-0.02926073968410492,
0.04613790661096573,
-0.0004266425676178187,
-0.005623720586299896,
-0.0039945668540894985,
0.016916250810027122,
0.007229343988001347,
-0.004575731698423624,
0.023889685049653053,
0.033936336636543274,
-0.04416065290570259,
-0.005240385886281729,
0.001957877539098263,
-0.005637817084789276,
-0.04683281108736992,
-0.03842151165008545,
-0.021877065300941467,
-0.005392157938331366,
0.0060359518975019455,
-0.0035187399480491877,
0.05380074679851532,
-0.023413395509123802,
0.008204776793718338,
0.0516304187476635,
-0.054307855665683746,
0.019550388678908348,
-0.032700952142477036,
0.03696409612894058,
-0.003859549993649125,
-0.015595881268382072,
0.017109064385294914,
0.006397867575287819,
0.06334491819143295,
-0.014195040799677372,
0.025225790217518806,
0.03173143044114113,
0.025748252868652344,
0.01640171930193901,
-0.032224275171756744,
-0.020954644307494164,
0.060781124979257584,
-0.005751980468630791,
-0.033471472561359406,
0.00976658333092928,
-0.004944078624248505,
-0.04867669194936752,
-0.017936211079359055,
-0.02956167608499527,
0.007362767588347197,
0.002836640225723386,
-0.036103807389736176,
0.03227059170603752,
-0.022558601573109627,
-0.007200517226010561,
-0.01269253809005022,
-0.024725327268242836,
0.07055864483118057,
0.08152592927217484,
-0.013547404669225216,
0.02108904905617237,
0.04072096571326256,
-0.010626700706779957,
-0.008619867265224457,
0.02717929147183895,
0.010985353030264378,
-0.06961630284786224,
0.029217302799224854,
0.022522661834955215,
0.0440792515873909,
-0.05910228192806244,
0.03488853946328163,
0.03181075304746628,
0.02074192464351654,
0.024182038381695747,
0.0031341505236923695,
0.011722075752913952,
-0.04901717230677605,
0.030261432752013206,
0.0005185089539736509,
0.04663340002298355,
0.011659793555736542,
-0.010206310078501701,
0.010050421580672264,
0.007443557493388653,
0.027544831857085228,
-0.026554981246590614,
0.02003026381134987,
0.038501400500535965,
0.010783813893795013,
0.02314276061952114,
-0.05990830436348915,
0.009032271802425385,
-0.039837051182985306,
-0.0019148103892803192,
0.02457607537508011,
0.03998125344514847,
0.043052323162555695,
0.008793090470135212,
0.009379404596984386,
0.013978734612464905,
0.013610230758786201,
-0.01245263870805502,
-0.02002068981528282,
0.043456342071294785,
-0.03350931778550148,
0.013166548684239388,
-0.04335109144449234,
0.017115136608481407,
0.0032487253192812204,
0.007506243418902159,
0.039392225444316864,
-0.014672144316136837,
0.045165929943323135,
-0.0034248230513185263,
-0.007291428279131651,
0.0028778105042874813,
-0.00789270643144846,
0.019810635596513748,
0.03875146061182022,
-0.0373518243432045,
0.0396810807287693,
-0.05841832607984543,
-0.03696286678314209,
0.052401259541511536,
-0.021445265039801598,
-0.010115099139511585,
0.02396261878311634,
0.013429050333797932,
-0.07433605194091797,
-0.023389609530568123,
-0.016243359073996544,
-0.012809817679226398,
-0.0011377010960131884,
-0.0269234050065279,
0.06898584961891174,
0.0020824759267270565,
-0.02077239379286766,
0.005729034077376127,
-0.04890967160463333,
-0.02151641435921192,
-0.018695427104830742,
-0.021388236433267593,
0.03472692519426346,
-0.019420254975557327,
0.0032099734526127577,
0.018966859206557274,
-0.04192943871021271,
0.018005335703492165,
-0.044247061014175415,
-0.033604562282562256,
0.001819099299609661,
0.01001648884266615,
0.044645197689533234,
-0.030308693647384644,
0.03772497549653053,
0.09319356083869934,
0.0008600684814155102,
-0.035276155918836594,
0.000592416210565716,
-0.02367796190083027,
-0.005038699135184288,
-0.01884075067937374,
-0.01902400329709053,
0.029937544837594032,
-0.02468523196876049,
0.004955172538757324,
-0.00126551347784698,
0.027020106092095375,
0.04546060413122177,
0.01657176949083805,
-0.0338311605155468,
-0.033879175782203674,
0.0056597888469696045,
0.00801046472042799,
0.02033592201769352,
-0.0007927225669845939,
0.0008939251420088112,
0.0037562749348580837,
0.008033779449760914,
0.03373447060585022,
-0.002047620015218854,
-0.05715104937553406,
0.03578990697860718,
-0.0019046487286686897,
-0.024639874696731567,
0.04061875492334366,
0.019234316423535347,
0.022507205605506897,
0.01789703592658043,
-0.006684336345642805,
0.04769120365381241,
0.044195353984832764,
-0.016611622646450996,
-0.020230168476700783,
0.009131981059908867,
0.037778981029987335,
-0.028166769072413445,
-0.03277827799320221,
0.0036856038495898247,
-0.03129352629184723,
0.009572971612215042,
-0.04914507642388344,
0.013422303833067417,
0.025905214250087738,
0.03759855031967163,
0.012296367436647415,
0.04966786131262779,
-0.052788279950618744,
0.035823971033096313,
-0.07301365584135056,
-0.025096794590353966,
-0.011442923918366432,
0.026455901563167572,
-0.010565345175564289,
0.020344460383057594,
0.028409404680132866,
0.03901178017258644,
-0.004277776926755905,
-0.016433650627732277,
-0.0698346197605133,
0.03180105611681938,
-0.024542324244976044,
-0.015843695029616356,
0.008992095477879047,
-0.0021132645197212696,
0.04900243878364563,
-0.02466471679508686,
-0.008794594556093216,
-0.018085569143295288,
0.02371925860643387,
-0.05552486330270767,
-0.00364116532728076,
-0.02301998808979988,
-0.053309570997953415,
0.015485522337257862,
0.025343528017401695,
0.024070359766483307,
-0.012138310819864273,
0.03040740080177784,
0.027018070220947266,
-0.03553267940878868,
0.03145395591855049,
-0.015289978124201298,
0.007977224886417389,
-0.0075357467867434025,
-0.005259320139884949,
0.051196902990341187,
0.022146444767713547,
-0.017097849398851395,
0.015196308493614197,
0.016783295199275017,
0.016826089471578598,
-0.0025864019989967346,
0.009940189309418201,
-0.029665600508451462,
-0.030567649751901627,
-0.045427292585372925,
0.00939655490219593,
0.043119046837091446,
-0.04561880975961685,
0.001561306300573051,
0.032216232270002365,
-0.019797660410404205,
-0.018559930846095085,
0.010230484418570995,
0.011922042816877365,
0.04816928133368492,
-0.00902677420526743,
-0.10466916859149933,
-0.04841617867350578,
0.004343812819570303,
0.002408326603472233,
0.017805878072977066,
0.00846545398235321,
-0.04929881542921066,
0.012341372668743134,
0.05136462301015854,
0.012486869469285011,
0.016260484233498573,
0.07069552689790726,
-0.010043998248875141,
0.05334698408842087,
0.022027013823390007,
0.03233369067311287,
0.013838271610438824,
0.03669922053813934,
0.06421630829572678,
0.05287857726216316,
0.011594400741159916,
-0.0861656591296196,
-0.017879663035273552,
0.03800804540514946,
-0.000529544719029218,
-0.008058438077569008,
-0.04328694939613342,
-0.02175624668598175,
-0.03797255828976631,
0.05980448052287102,
-0.022834407165646553,
0.03444386646151543,
-0.05704766884446144,
0.006461988668888807,
-0.058879196643829346,
-0.001432921038940549,
0.01499406062066555,
0.020841103047132492,
-0.030509086325764656,
0.009498764760792255,
-0.004151647444814444,
0.004752486478537321,
-0.018349934369325638,
0.006762244738638401,
0.003716930514201522,
0.04717256501317024,
-0.008694161660969257,
-0.013840236701071262,
-0.018689651042222977,
0.02637023665010929,
-0.05003282427787781,
-0.05220013111829758,
-0.005768241360783577,
0.03721233084797859,
-0.006699183024466038,
0.01727222464978695,
-0.028969567269086838,
0.012500718235969543,
-0.0005116859683766961,
-0.0003956711443606764,
0.009690227918326855,
-0.003104311414062977,
-0.04886288568377495,
-0.02893398143351078,
0.01196956541389227,
-0.0049777524545788765,
0.0297735296189785,
0.001711750403046608,
0.019103318452835083,
0.00806918740272522,
0.02978721633553505,
0.011272935196757317,
-0.01708623208105564,
-0.03167709335684776,
0.011296207085251808,
0.013689044862985611,
-0.03178662434220314,
0.03856979310512543,
0.013628659769892693,
0.05817396193742752,
-0.014274858869612217,
-0.04204768314957619,
-0.04811866953969002,
0.01910456269979477,
0.001554149086587131,
-0.01690099760890007,
-0.015743950381875038,
0.021504467353224754,
-0.001196196535602212,
-0.012766283005475998,
0.016685521230101585,
0.027202952653169632,
-0.000395015231333673,
0.06769786775112152,
-0.029638156294822693,
-0.018998753279447556,
-0.030848149210214615,
-0.0059710000641644,
-0.006607533432543278,
-0.02280803956091404,
0.03817547857761383,
0.01907539553940296,
-0.022955823689699173,
0.04046548157930374,
-0.03963961824774742,
0.011755555868148804,
0.036217208951711655,
-0.030968423932790756,
-0.005011134315282106,
-0.09716551005840302,
0.03443820774555206,
0.013522325083613396,
0.019931666553020477,
-0.026721296831965446,
-0.11057471483945847,
0.04726728796958923,
-0.004113748203963041,
-0.0198848657310009,
-0.04110974818468094,
-0.004269653931260109,
-0.0113128162920475,
-0.05804206430912018,
0.0004742196178995073,
0.04675073176622391,
-0.06079566106200218,
0.04343520477414131,
0.04546472802758217,
-0.03750073164701462,
0.05800103768706322,
-0.04163051396608353,
-0.008381806313991547,
0.036192700266838074,
-0.02573011815547943,
-0.010982390493154526,
-0.020143665373325348,
0.01240204181522131,
-0.03578117489814758,
0.004308948293328285,
-0.03397499769926071,
0.021240081638097763,
0.023753944784402847,
0.043582141399383545,
-0.006037040613591671,
0.05519270896911621,
0.011960042640566826,
-0.008155981078743935,
-0.036479659378528595,
0.018273277208209038,
-0.002886888338252902,
-0.0032236299011856318,
-0.006347389426082373,
-0.018291516229510307,
-0.0054220594465732574,
-0.04294978082180023,
0.04323306307196617,
0.010279074311256409,
0.009792068973183632,
-0.020500298589468002,
0.035350069403648376,
-0.024652862921357155,
0.0006915075937286019,
0.007714023347944021,
-0.04249776527285576,
0.075392946600914,
-0.00507976021617651,
-0.014056487940251827,
0.002655626740306616,
-0.02215822972357273,
-0.01945597492158413,
-0.04928570240736008,
-0.0003300360112916678,
-0.027354514226317406,
0.03740876168012619,
0.009266589768230915,
0.07028224319219589,
0.05454208701848984,
0.0036849374882876873,
-0.01613103412091732,
-0.02460336685180664,
0.02804660052061081,
0.007139110472053289,
0.006889660842716694,
0.03960573673248291,
-0.025204816833138466,
0.032104577869176865,
0.033474117517471313,
0.02535577490925789,
0.005631776060909033,
-0.019401872530579567,
0.005899721756577492,
0.027633484452962875,
0.018866946920752525,
0.00050263328012079,
-0.05185649171471596,
-0.0043764556758105755,
-0.0660012736916542,
0.024821095168590546,
-0.02264275774359703,
-0.022839155048131943,
0.06434027850627899,
-0.01406159158796072,
0.04270920529961586,
-0.04043995216488838,
-0.009042513556778431,
-0.02115180343389511,
0.019889891147613525,
-0.010915896855294704,
-0.0065651824697852135,
-0.018288202583789825,
-0.008847368881106377,
0.0510498471558094,
-0.00024552817922085524,
0.01944328099489212,
-0.03611892834305763,
-0.06015385687351227,
-0.021714722737669945,
-0.0054497686214745045,
-0.057786859571933746,
0.020160414278507233,
0.03371455520391464,
0.015613836236298084,
0.02394162490963936,
-0.0250350683927536,
0.025793597102165222,
0.015061620622873306,
0.03448162227869034,
0.0033933352679014206,
0.07860767841339111,
-0.017310740426182747,
0.006802058778703213,
-0.009978395886719227,
-0.016141241416335106,
0.11808349937200546,
0.02197442762553692,
0.019208891317248344,
-0.019547531381249428,
0.02256345935165882,
-0.0011809199349954724,
0.023419713601469994,
-0.03912220522761345,
0.022153183817863464,
0.020276963710784912,
0.016419678926467896,
0.00920365285128355,
0.03519602492451668,
-0.0036916984245181084,
-0.07180643081665039,
0.01884148269891739,
-0.008578725159168243,
0.0060438234359025955,
-0.02460094727575779,
0.01772177778184414,
-0.02174360677599907,
0.012395508587360382,
-0.015974614769220352,
-0.016614818945527077,
-0.03449271619319916,
-0.036344803869724274,
-0.02568250149488449,
-0.018129602074623108,
-0.009651766158640385,
-0.0008055782527662814,
-0.03617556393146515,
0.027466973289847374,
0.03814229369163513,
-0.018370360136032104,
-0.04546438157558441,
0.02041229046881199,
-0.008353406563401222,
0.02636699192225933,
-0.006446478422731161,
0.007930182851850986,
-0.018369387835264206,
0.00010730118083301932,
-0.0049408492632210255,
0.03514360263943672,
-0.07155103981494904,
0.027246879413723946,
-0.06674731522798538,
0.025634773075580597,
-0.007792381104081869,
0.036377035081386566,
-0.023432249203324318,
-0.017073627561330795,
0.02962479367852211,
-0.04595649614930153,
-0.03749620541930199,
-0.007491427939385176,
0.00501221651211381,
-0.011194704100489616,
-0.042810287326574326,
-0.0016788869397714734,
0.020652566105127335,
0.0019968030974268913,
0.003660032991319895,
-0.016513099893927574,
-0.017530662938952446,
0.011143652722239494,
0.024318639189004898,
0.05606069043278694,
-0.03360970318317413,
-0.021583762019872665,
-0.018871858716011047,
0.014762714505195618,
-0.012110164389014244,
0.006687442306429148,
0.018561318516731262,
-0.00298991403542459,
-0.0002542983856983483,
-0.01525346003472805,
-0.02573605254292488,
-0.022640278562903404,
-0.05326959118247032,
0.04611993208527565,
-0.047498300671577454,
0.017799900844693184,
-0.031198933720588684,
0.0024577018339186907,
0.055246900767087936,
0.01193867065012455,
-0.05288512632250786,
-0.0010024214861914515,
-0.001058580819517374,
-0.0005425986018963158,
-0.00007672967331018299,
0.012279761023819447,
0.0008692960836924613,
0.01944195106625557,
-0.04960434138774872,
0.012779171578586102,
-0.02535334601998329,
0.04337981715798378,
0.03381993621587753,
0.006588535849004984,
-0.024109231308102608,
0.006609252654016018,
0.005995594896376133,
0.03605859354138374,
0.023237252607941628,
-0.03172625973820686,
-0.03479846939444542,
-0.019101787358522415,
0.030023176223039627,
-0.06303870677947998,
-0.0020537751261144876,
-0.03218524530529976,
-0.005522677209228277,
-0.027108442038297653,
0.03588145226240158,
-0.010108863934874535,
0.026015277951955795,
-0.03264016658067703,
0.042831987142562866,
-0.03289110213518143,
-0.008744889870285988,
-0.026381026953458786,
0.001702043111436069,
-0.02267416939139366,
-0.00923826452344656,
-0.019464464858174324,
0.011063066311180592,
0.015649260953068733,
0.03132958337664604,
0.020576640963554382,
0.03980479761958122,
0.00796462781727314,
0.024739818647503853,
0.02513079345226288,
-0.0007089815917424858,
0.022943900898098946,
-0.02235465683043003,
-0.017276372760534286,
0.03729674220085144,
-0.05020100623369217,
-0.02434774488210678,
-0.00995388813316822,
0.0029842681251466274,
0.011919299140572548,
-0.012185180559754372,
0.002115018432959914,
0.006861493922770023,
0.04650621488690376,
-0.020106276497244835,
-0.031234441325068474,
0.011205009184777737,
0.013566414825618267,
-0.005670465528964996,
0.0008541159331798553,
0.05355204641819,
-0.03624659404158592,
-0.0015221303328871727,
-0.0026555475778877735,
0.03504204750061035,
-0.02424655295908451,
0.025720298290252686,
0.03584342449903488,
-0.007698846515268087,
0.0019168411381542683,
0.0020826775580644608,
0.01128367893397808,
0.016056379303336143,
0.03861485794186592,
-0.04405488446354866,
0.006313246209174395,
0.01715187542140484,
0.020860295742750168,
-0.07227233797311783,
-0.013632135465741158,
0.05922664329409599,
-0.017220836132764816,
0.03921818733215332,
-0.024989053606987,
-0.008333706296980381,
0.03928913548588753,
-0.07926305383443832,
0.03807719051837921,
-0.028849132359027863,
-0.022281210869550705,
-0.04566193372011185,
0.0020709093660116196,
0.0005057434900663793,
0.05608275905251503,
0.011691492982208729,
-0.01325263362377882,
0.01988772116601467,
-0.00881035067141056,
-0.0453963577747345,
-0.023453708738088608,
0.042806051671504974,
0.02101544849574566,
0.002145538805052638,
0.0019170904997736216,
0.08315088599920273,
-0.03044283017516136,
-0.04730776697397232,
0.01800401136279106,
0.018032653257250786,
0.04589027538895607,
-0.03459581732749939,
0.025594979524612427,
0.00955568440258503,
-0.006975978147238493,
0.020634358748793602,
-0.030264897271990776,
-0.01583595760166645,
0.019828349351882935,
0.011065607890486717,
0.01523896399885416,
-0.002869897987693548,
0.060578614473342896,
0.03389061242341995,
-0.02693510241806507,
-0.008313349448144436,
0.0008354067686013877,
-0.01973799243569374,
-0.037632234394550323,
-0.016351766884326935,
0.010787343606352806,
-0.010165597312152386,
-0.005824903957545757,
-0.03321871533989906,
-0.01804237626492977,
-0.0422484427690506,
0.011649476364254951,
-0.03438955917954445,
0.02754688262939453,
0.05944625660777092,
-0.02722473256289959,
-0.014779592864215374,
-0.0037365274038165808,
-0.061181798577308655,
-0.0037431141827255487,
-0.0835789367556572,
0.03384135663509369,
0.021616129204630852,
-0.02506405860185623,
-0.05470869317650795,
-0.0433511808514595,
0.04584422707557678,
0.053303588181734085,
0.007124578580260277,
0.010138679295778275,
0.04728490859270096,
-0.04114225506782532,
-0.006160558667033911,
-0.04942947253584862,
-0.0012527898652479053,
-0.038640644401311874,
-0.04563430696725845,
-0.015227292664349079,
-0.03912203758955002,
-0.009785361588001251,
-0.030312513932585716,
0.06199616566300392,
-0.007832849398255348,
0.01389172300696373,
0.00661656865850091,
0.004171776585280895,
0.013450097292661667,
0.007505189161747694,
-0.0011047822190448642,
-0.005240295082330704,
-0.021360240876674652,
-0.011423845775425434,
-0.01843022182583809,
-0.02349688857793808,
-0.0023476576898247004,
0.032057031989097595,
-0.007927066646516323,
0.06969138979911804,
-0.014135995879769325,
-0.012071318924427032,
0.02462787926197052,
0.050971176475286484,
0.009105490520596504,
0.11258623003959656,
-0.028599118813872337,
0.037869371473789215,
-0.006220391020178795,
-0.03134287893772125,
-0.05094708874821663,
0.030563633888959885,
-0.012727438472211361,
-0.004130091052502394,
-0.0069322059862315655,
-0.007243821397423744,
0.037705399096012115,
-0.025658754631876945,
0.0021915885154157877,
0.009252742864191532,
-0.0537005215883255,
0.00684474129229784,
0.021810876205563545,
-0.002818191424012184,
0.013148387894034386,
-0.027367716655135155,
0.036753978580236435,
0.02641645446419716,
0.01915747858583927,
-0.006374077405780554,
0.03217410668730736,
0.017294548451900482,
-0.01982109621167183,
-0.017729979008436203,
0.04043435677886009,
-0.015435226261615753,
0.0795772448182106,
-0.018803777173161507,
0.06201104447245598,
0.008755117654800415,
0.006285143084824085,
0.02189948409795761,
-0.013500853441655636,
0.03480838984251022,
0.026923388242721558,
-0.035054951906204224,
0.06373867392539978,
-0.05620437487959862,
0.01867232844233513,
0.004996279254555702,
-0.016063695773482323,
-0.03486352413892746,
-0.026597367599606514,
0.019425438717007637,
0.028103332966566086,
0.021854959428310394,
-0.044973019510507584,
0.012652795761823654,
0.017189450562000275,
0.052789345383644104,
0.01618989184498787,
0.05456692725419998,
-0.013605323620140553,
0.03220158442854881,
0.0035678199492394924,
-0.04038640484213829,
-0.04444565623998642,
-0.058882467448711395,
-0.010703899897634983,
0.01676509529352188,
0.0410359688103199,
0.02162923291325569,
-0.07053425908088684,
-0.012052065692842007,
0.059537436813116074,
-0.0509459525346756,
-0.022515328601002693,
0.007569401524960995,
0.03103991225361824,
-0.004174642264842987,
0.012966119684278965
] |
<p>If we have a solenoid and a magnetic field passes through it, a DC voltage will be produced in the wire. If we want to calculate the power, we find out the current using Ohm's law.</p>
<p>I know there is power loss due to the resistance (joule effect). But what about the magnetic field due to current (lenz's law), does it contribute in the power loss?</p>
| 9,391 |
[
-0.04151293262839317,
-0.011277898214757442,
-0.0068060955964028835,
-0.03735784441232681,
0.053216733038425446,
0.034890078008174896,
-0.04239963740110397,
-0.005378496367484331,
0.009986267425119877,
-0.029264304786920547,
0.03547188267111778,
0.012975336983799934,
0.053295478224754333,
0.027253413572907448,
0.035496633499860764,
-0.002808263059705496,
0.005561001133173704,
0.015335017815232277,
0.005749245174229145,
-0.034595079720020294,
-0.021495576947927475,
0.023685144260525703,
0.013979155570268631,
-0.007778114639222622,
-0.03728366270661354,
0.02715972624719143,
0.05121564865112305,
0.02519541233778,
-0.00793506670743227,
0.04552101716399193,
0.03041926771402359,
-0.03698747605085373,
0.004637047648429871,
0.011078309267759323,
0.011760036461055279,
0.010664736852049828,
-0.04098450019955635,
-0.0692959576845169,
-0.0066602276638150215,
0.053996823728084564,
-0.015625575557351112,
-0.024704720824956894,
0.011185361072421074,
0.03419412672519684,
-0.013232903555035591,
0.009429189376533031,
0.007571947295218706,
-0.021083353087306023,
0.021196486428380013,
-0.04582849517464638,
0.042339906096458435,
-0.035644352436065674,
0.07735400646924973,
-0.02248593419790268,
-0.016877194866538048,
-0.03162754327058792,
0.07594506442546844,
0.0610959529876709,
0.005533508490771055,
-0.02609403245151043,
0.014283017255365849,
0.00625475961714983,
-0.008475231006741524,
-0.03846890479326248,
-0.018250318244099617,
0.02997245453298092,
-0.02608444169163704,
-0.013311415910720825,
0.02999892458319664,
0.010204708203673363,
0.035374369472265244,
0.023612186312675476,
-0.0010917630279436707,
-0.00010511883738217875,
0.005164790898561478,
-0.008044255897402763,
0.026834050193428993,
0.005734868347644806,
0.04429098963737488,
0.040067244321107864,
-0.030961399897933006,
0.002890443429350853,
0.03313214331865311,
0.04207586497068405,
-0.010723147541284561,
-0.009463723748922348,
0.01230501476675272,
-0.028002405539155006,
0.03271894529461861,
0.01868959330022335,
0.011087720282375813,
0.014082644134759903,
0.00419973349198699,
-0.03076491877436638,
-0.0026797628961503506,
0.01343742199242115,
-0.04402848333120346,
0.03576446697115898,
0.027786429971456528,
-0.024784166365861893,
0.02679581753909588,
0.022833753377199173,
0.025279618799686432,
0.04466287046670914,
0.025563454255461693,
-0.04048040881752968,
0.020526399835944176,
0.019461987540125847,
-0.017173442989587784,
-0.023287659510970116,
-0.038035571575164795,
0.007530608680099249,
0.019657917320728302,
-0.017331501469016075,
0.001732124830596149,
-0.04429514333605766,
0.02110338769853115,
-0.03718987852334976,
0.03274723142385483,
0.06831082701683044,
0.020692812278866768,
-0.03974439948797226,
0.009295566938817501,
-0.005866349209100008,
-0.048047054558992386,
-0.012115780264139175,
-0.007236546371132135,
-0.01778031513094902,
-0.02650226093828678,
0.020746637135744095,
-0.03453188017010689,
-0.040096741169691086,
-0.024492299184203148,
-0.01237837690860033,
0.026142815127968788,
-0.00028049704269506037,
-0.07803398370742798,
-0.039373140782117844,
0.03602518513798714,
-0.026007015258073807,
0.024119578301906586,
-0.07595109194517136,
-0.0005763392546214163,
0.007641029078513384,
0.06070892885327339,
0.0004057504120282829,
-0.011149679310619831,
-0.0024669161066412926,
0.05692293867468834,
-0.0011649178341031075,
-0.015530671924352646,
0.008397725410759449,
-0.01007060892879963,
-0.042267654091119766,
0.003024171106517315,
-0.03490060567855835,
0.04093731939792633,
0.03645915165543556,
-0.0036407867446541786,
-0.06036524102091789,
0.03702682629227638,
-0.006827257573604584,
0.007783196400851011,
0.012997124344110489,
-0.03459172695875168,
-0.05000536888837814,
0.06742630153894424,
0.007082965690642595,
0.0630478709936142,
0.02906230092048645,
0.017877643927931786,
0.012268181890249252,
0.018946347758173943,
-0.009467572905123234,
0.07258743792772293,
-0.026143314316868782,
-0.06640028208494186,
-0.041618093848228455,
0.04649696871638298,
0.01236150786280632,
-0.07746557891368866,
-0.06456834077835083,
-0.0012674509780481458,
0.020910274237394333,
-0.027847377583384514,
0.030023688450455666,
0.009649001993238926,
0.005955266300588846,
0.013418473303318024,
0.000001427097799933108,
-0.011996399611234665,
-0.061222825199365616,
0.0527966283261776,
-0.02963104471564293,
-0.03290117532014847,
0.034392040222883224,
0.030371302738785744,
0.019414713606238365,
-0.03112448938190937,
-0.03872814029455185,
-0.0037524206563830376,
0.016771936789155006,
0.004789982456713915,
-0.029711192473769188,
0.0060053300112485886,
0.010151645168662071,
0.03518877178430557,
0.002648043679073453,
0.05967617779970169,
-0.020356636494398117,
-0.05131568759679794,
-0.005825717002153397,
-0.04652874916791916,
-0.005320619326084852,
0.03449569642543793,
0.0011483245762065053,
0.058858443051576614,
-0.016156842932105064,
-0.010440804995596409,
0.03362613916397095,
0.015984592959284782,
0.08349990099668503,
0.06048016622662544,
0.010285922326147556,
0.012706938199698925,
0.02572239190340042,
-0.02674153260886669,
-0.02554430440068245,
-0.046175044029951096,
-0.020295454189181328,
-0.043741531670093536,
0.024646703153848648,
0.04795987159013748,
0.005938368383795023,
-0.04850417375564575,
0.003857998177409172,
0.0281850453466177,
0.00373065029270947,
0.009024351835250854,
0.030403459444642067,
-0.025448665022850037,
-0.02542342245578766,
0.00585308438166976,
0.03420739248394966,
-0.02165268547832966,
0.027431311085820198,
0.006761588156223297,
0.048362359404563904,
0.019394924864172935,
-0.015924938023090363,
-0.03739520162343979,
0.08862068504095078,
0.019091444090008736,
0.007567602675408125,
0.030545992776751518,
-0.05698058009147644,
0.023042509332299232,
-0.04541158303618431,
0.05207120627164841,
-0.033146195113658905,
-0.04377499595284462,
0.03526269644498825,
0.000699303112924099,
-0.027148347347974777,
0.0008564531453885138,
-0.01837151311337948,
-0.019939223304390907,
-0.001226047519594431,
0.02190237119793892,
-0.06940930336713791,
-0.0075465417467057705,
-0.011705768294632435,
0.004690014291554689,
-0.04467428848147392,
-0.015445836819708347,
-0.011709989979863167,
-0.010195821523666382,
0.040888115763664246,
-0.01482023298740387,
-0.03640611842274666,
-0.035068899393081665,
-0.04150779917836189,
-0.007289387285709381,
0.04913804307579994,
-0.02688448876142502,
0.002544884802773595,
-0.02524990402162075,
-0.03554471582174301,
0.028069449588656425,
0.0231560580432415,
0.011483877897262573,
0.04178661108016968,
-0.010393442586064339,
-0.08268342912197113,
-0.00012215692549943924,
-0.014700346626341343,
0.016923921182751656,
0.02100175991654396,
0.008778504095971584,
0.03816059231758118,
0.001468701520934701,
-0.014072458259761333,
0.014186866581439972,
-0.04634512960910797,
-0.04662357643246651,
-0.013308906927704811,
-0.020634455606341362,
0.028101475909352303,
-0.02044953964650631,
0.03138481453061104,
-0.00376982893794775,
-0.0774669498205185,
-0.030032996088266373,
-0.026709498837590218,
-0.014075687155127525,
0.028278743848204613,
-0.019953090697526932,
0.022827191278338432,
-0.023483170196413994,
-0.02391805499792099,
0.09327778220176697,
0.05786146968603134,
-0.029013535007834435,
-0.03000723011791706,
-0.05963011085987091,
-0.0012474547838792205,
-0.03812485188245773,
0.010021775960922241,
0.059468355029821396,
-0.029035180807113647,
-0.015805155038833618,
-0.009729561395943165,
0.015046059153974056,
0.007467442192137241,
0.01869170367717743,
0.007301142904907465,
0.014685207977890968,
0.02049669623374939,
0.0003493023104965687,
0.07197356224060059,
0.0030470341444015503,
-0.030201710760593414,
0.04215015470981598,
0.01025424338877201,
0.0622832365334034,
0.022977810353040695,
-0.010028094053268433,
0.04298374429345131,
-0.008556288667023182,
0.02936624363064766,
-0.04247643053531647,
0.04052985832095146,
0.006838772911578417,
0.02548416331410408,
0.03939194977283478,
0.049515094608068466,
0.013596606440842152,
-0.04240170866250992,
-0.004688897170126438,
0.009623219259083271,
0.04154793918132782,
-0.018900036811828613,
-0.05996660515666008,
-0.026676999405026436,
-0.0062069883570075035,
0.0046562389470636845,
0.002373727271333337,
-0.01936960406601429,
0.006028007250279188,
0.057131871581077576,
0.035985350608825684,
0.02830330654978752,
-0.00795215368270874,
-0.014427145011723042,
-0.06742359697818756,
-0.01286160945892334,
-0.00710047222673893,
0.05170285329222679,
0.02148052491247654,
0.05873731151223183,
0.005802676547318697,
0.021774649620056152,
0.03837774693965912,
-0.018946902826428413,
-0.09558159857988358,
0.03901141881942749,
-0.027541786432266235,
-0.016579069197177887,
-0.011747155338525772,
-0.006560663692653179,
-0.004273134749382734,
-0.006736341863870621,
-0.004258688073605299,
-0.02668064273893833,
-0.008110967464745045,
-0.04691111668944359,
0.008374064229428768,
-0.021265219897031784,
-0.03961385786533356,
-0.025439852848649025,
0.025641102343797684,
0.038485169410705566,
-0.06394767016172409,
0.01790718361735344,
-0.00345998746342957,
-0.01549364160746336,
-0.0024219625629484653,
-0.03563174605369568,
-0.01156535279005766,
-0.010550863109529018,
0.042247474193573,
0.021202480420470238,
-0.010586286894977093,
-0.033896926790475845,
0.0416010245680809,
0.027760932222008705,
0.03437015414237976,
0.0054575297981500626,
-0.01127095241099596,
-0.018373318016529083,
-0.04487864673137665,
-0.008719452656805515,
-0.012789064086973667,
0.03994906693696976,
0.008372945711016655,
0.019524214789271355,
0.029247956350445747,
-0.010584821924567223,
-0.02863556332886219,
0.0054084500297904015,
0.015408706851303577,
0.03042513318359852,
0.007111622951924801,
-0.04050562530755997,
0.02101311832666397,
-0.038634464144706726,
-0.02068512700498104,
-0.004271362908184528,
0.0013531030854210258,
-0.05503438413143158,
-0.02285761944949627,
0.03326413407921791,
0.027034658938646317,
-0.0011533718788996339,
0.03744213283061981,
0.041862018406391144,
0.027168553322553635,
0.004731946159154177,
-0.004933365620672703,
0.017775384709239006,
0.015894629061222076,
0.034541744738817215,
0.0038029851857572794,
-0.010246914811432362,
-0.11253032833337784,
-0.01214552391320467,
0.038001809269189835,
0.03582722693681717,
-0.004728436470031738,
0.005618672352284193,
-0.008118422701954842,
-0.017914600670337677,
0.02167825773358345,
-0.04247589409351349,
0.027853885665535927,
0.0060848514549434185,
-0.02218698151409626,
-0.06278187781572342,
-0.04546837881207466,
-0.03291572630405426,
0.04428122937679291,
-0.01581883244216442,
0.049818478524684906,
-0.0554916113615036,
-0.004716753959655762,
0.015104291960597038,
0.018350619822740555,
0.03526623174548149,
0.05435085669159889,
0.002254630671814084,
0.0023421517107635736,
-0.023138882592320442,
0.05027341842651367,
-0.019281506538391113,
-0.08206800371408463,
0.0012955631827935576,
-0.014730905182659626,
-0.013667763210833073,
0.04711389169096947,
-0.025405561551451683,
-0.03843578323721886,
0.0038406639359891415,
0.006456086412072182,
-0.030930886045098305,
-0.02649735100567341,
-0.0389704592525959,
0.029137834906578064,
0.031043963506817818,
-0.02429678477346897,
0.04224104434251785,
0.03418717905879021,
-0.02021721936762333,
-0.0015624024672433734,
0.0039072404615581036,
0.05813204124569893,
-0.005410697311162949,
-0.007751647382974625,
-0.002583663212135434,
-0.007283471524715424,
-0.013109791092574596,
0.05686559900641441,
-0.0068826330825686455,
0.008181879296898842,
-0.03761892020702362,
-0.003440406173467636,
0.01455900352448225,
-0.03379316255450249,
-0.00125901831779629,
-0.011326408013701439,
-0.025243544951081276,
0.041502829641103745,
0.015466948971152306,
-0.038731496781110764,
0.01761292852461338,
-0.002836503554135561,
0.005550766363739967,
0.020624026656150818,
-0.034100309014320374,
-0.00476862071081996,
-0.017213640734553337,
0.0005650899838656187,
0.0035227953922003508,
-0.019990213215351105,
0.04147609323263168,
-0.010810812003910542,
-0.017562123015522957,
-0.005116319749504328,
-0.048572756350040436,
-0.02886170707643032,
0.027033107355237007,
-0.03285766765475273,
0.0453871488571167,
-0.050912145525217056,
0.018607547506690025,
-0.0012456447584554553,
-0.019323185086250305,
-0.06360358744859695,
-0.06304004043340683,
0.003353336127474904,
-0.010827116668224335,
0.03244127333164215,
0.025134699419140816,
-0.01603001356124878,
-0.01935494691133499,
-0.06349948048591614,
0.015684574842453003,
0.021380562335252762,
-0.041119467467069626,
0.015377483330667019,
0.03340180218219757,
-0.007024614606052637,
0.07401398569345474,
-0.007352259010076523,
-0.03966693580150604,
0.017795739695429802,
-0.016291480511426926,
-0.011148585006594658,
-0.02244623750448227,
0.03363419696688652,
0.0024868142791092396,
-0.002105611376464367,
0.03084457851946354,
-0.01855410635471344,
0.03999042510986328,
-0.0017250098753720522,
-0.008505125530064106,
0.050608374178409576,
0.0192710030823946,
-0.017974166199564934,
0.008832127787172794,
0.01628265716135502,
0.054331108927726746,
0.05937329679727554,
0.003923268988728523,
-0.030552178621292114,
-0.045858073979616165,
0.0036959988065063953,
0.011000972241163254,
0.017040198668837547,
0.05812734737992287,
0.018487967550754547,
0.04200824722647667,
-0.031980954110622406,
-0.011457975953817368,
0.016821008175611496,
-0.007850779220461845,
0.0025571004953235388,
-0.003814361523836851,
0.027424151077866554,
-0.021876418963074684,
0.034965284168720245,
-0.03204202279448509,
-0.02783287689089775,
-0.03359057381749153,
-0.020662853494286537,
0.050059087574481964,
-0.020234882831573486,
0.043806292116642,
-0.008702373132109642,
0.014370501972734928,
-0.011633074842393398,
-0.009114567190408707,
-0.023324720561504364,
0.00021006976021453738,
-0.011820212937891483,
0.016401689499616623,
0.023485880345106125,
0.0031965840607881546,
0.05061812698841095,
0.011100363917648792,
-0.03504375368356705,
0.01833636499941349,
0.039366576820611954,
0.04801380634307861,
0.03011709824204445,
0.007622717414051294,
-0.04506112262606621,
-0.030796615406870842,
-0.035164639353752136,
0.01815992034971714,
-0.040037620812654495,
-0.0042524575255811214,
0.07786332070827484,
0.031023185700178146,
-0.007847174070775509,
-0.03271852433681488,
-0.03515636920928955,
-0.009616754949092865,
-0.013133824802935123,
-0.005708691664040089,
-0.003121891524642706,
0.02443433739244938,
0.061470579355955124,
0.04062263295054436,
-0.010767114348709583,
0.006664791144430637,
0.01599063351750374,
-0.0384775847196579,
-0.023422803729772568,
-0.0031409726943820715,
-0.031061189249157906,
0.05218684300780296,
-0.02508700266480446,
-0.028004586696624756,
-0.009940586052834988,
-0.01692904718220234,
0.005137475673109293,
0.007261252962052822,
0.015002506785094738,
-0.016722802072763443,
0.05137186869978905,
-0.005864811595529318,
0.01456713117659092,
-0.03196593001484871,
0.019936954602599144,
0.08412998914718628,
0.013111398555338383,
0.04540107399225235,
-0.06015900894999504,
0.02526765502989292,
-0.049129046499729156,
0.015438254922628403,
-0.02319529466331005,
0.01574588753283024,
-0.023575320839881897,
0.007554427720606327,
0.041593603789806366,
0.048497192561626434,
-0.0210469551384449,
-0.010794159024953842,
0.032659512013196945,
-0.015738248825073242,
-0.0023128357715904713,
0.021320773288607597,
0.03934507817029953,
-0.032095808535814285,
0.016287323087453842,
-0.040874019265174866,
0.025269456207752228,
-0.03377616032958031,
-0.035780441015958786,
0.0241567213088274,
-0.02871439792215824,
0.0032399301417171955,
-0.02252701297402382,
-0.04358961433172226,
0.044596537947654724,
0.0007322460296563804,
0.00975106842815876,
-0.057208817452192307,
-0.005600514821708202,
0.02884499356150627,
0.03514597937464714,
-0.011396512389183044,
-0.010467005893588066,
0.04606802016496658,
0.009872048161923885,
0.00031425824272446334,
0.037281714379787445,
-0.042306505143642426,
0.010982428677380085,
-0.03053923323750496,
-0.009192409925162792,
0.04069656878709793,
0.043667662888765335,
0.03729919344186783,
0.05040332302451134,
0.020458586513996124,
-0.04005146399140358,
-0.0181962288916111,
0.0003307053993921727,
0.01670108549296856,
-0.021647438406944275,
-0.03313436731696129,
-0.024832064285874367,
0.025647779926657677,
-0.026462983340024948,
-0.001273284200578928,
0.02660791575908661,
-0.020822161808609962,
0.032682716846466064,
0.043927717953920364,
0.05057834833860397,
-0.013678169809281826,
-0.029631085693836212,
-0.03678024187684059,
-0.014755447395145893,
0.012356714345514774,
0.02262645587325096,
0.021087875589728355,
0.012581012211740017,
-0.0007234779186546803,
-0.01796029321849346,
0.0012020175345242023,
0.004551513586193323,
-0.10634873807430267,
0.09540670365095139,
0.018739357590675354,
0.012061264365911484,
-0.03182273730635643,
0.014470339752733707,
0.03686909005045891,
0.04525964334607124,
-0.02550385519862175,
-0.019368203356862068,
0.0028302206192165613,
0.025543250143527985,
0.04382329061627388,
-0.03588646650314331,
-0.0025638528168201447,
0.012122726067900658,
-0.052941326051950455,
-0.021166998893022537,
0.0003615866298787296,
0.02014285698533058,
0.03213271498680115,
0.01646551862359047,
0.0020844126120209694,
0.022731425240635872,
-0.007712624501436949,
0.006677556782960892,
0.005998564884066582,
-0.032931242138147354,
-0.01884324662387371,
-0.014028606936335564,
0.005845268256962299,
-0.026074888184666634,
0.001603995100595057,
-0.03248429298400879,
0.0006941340980120003,
0.022716032341122627,
0.010078090243041515,
-0.005010109394788742,
-0.006127610802650452,
-0.01921030506491661,
0.02589249238371849,
-0.04529763013124466,
0.015190364792943,
-0.031235676258802414,
-0.01387939602136612,
0.02315940149128437,
0.009463135153055191,
0.016995448619127274,
0.03252919763326645,
-0.019194001331925392,
0.020407313480973244,
0.02090301737189293,
0.023867912590503693,
-0.0061546554788947105,
0.015931332483887672,
0.020996322855353355,
-0.00005922815398662351,
0.04081932082772255,
0.001018134760670364,
-0.009261412546038628,
0.07345045357942581,
-0.03783977031707764,
-0.04219439625740051,
0.013858637772500515,
-0.018333079293370247,
0.020275399088859558,
0.009372303262352943,
0.01676465943455696,
-0.04138379544019699,
0.008844302035868168,
0.003593156347051263,
0.02511880360543728,
-0.007635874208062887,
-0.021555611863732338,
0.016798673197627068,
-0.0011198173742741346,
-0.0024699417408555746,
0.012389886192977428,
0.023061402142047882,
0.03175356611609459,
0.04032834619283676,
-0.007544083520770073,
0.015412476845085621,
0.005542549304664135,
0.03940190374851227,
-0.030189992859959602,
0.050819262862205505,
0.001956678694114089,
0.026655806228518486,
0.03603925183415413,
-0.024883894249796867,
0.0068721710704267025,
0.0042826589196920395,
0.013845832087099552,
-0.09554935246706009,
0.005086270160973072,
-0.03401181474328041,
0.002971451263874769,
0.011215184815227985,
-0.05113058164715767,
-0.017530448734760284,
0.015584112145006657,
-0.07098083943128586,
-0.019948193803429604,
-0.022081902250647545,
-0.021343711763620377,
-0.03445815667510033,
0.000012963781955477316,
0.026373006403446198,
0.051423683762550354,
0.0011160083813592792,
0.03416110947728157,
-0.0013745208270847797,
0.007705401163548231,
-0.014218863099813461,
-0.024973822757601738,
-0.05707904323935509,
0.01999249868094921,
-0.033619869500398636,
0.01831936649978161,
0.05383121222257614,
-0.02198575623333454,
-0.010272972285747528,
0.03325812146067619,
-0.04252433031797409,
0.02714863233268261,
-0.006190237123519182,
0.0166495218873024,
0.00041652354411780834,
0.03281966969370842,
-0.01951747015118599,
-0.028144383803009987,
0.001814062474295497,
-0.0020759408362209797,
0.0022863850463181734,
0.016933051869273186,
-0.007815239951014519,
0.01773666962981224,
0.05099162459373474,
-0.02780953049659729,
-0.0073697445914149284,
0.02434290386736393,
-0.00966866035014391,
-0.010379971005022526,
-0.008062966167926788,
0.009477030485868454,
0.003326596226543188,
0.00025026584626175463,
0.01917295716702938,
-0.01555989496409893,
-0.04078735411167145,
0.06071159616112709,
-0.012570851482450962,
0.025027580559253693,
0.015392748638987541,
0.004634168930351734,
-0.029261061921715736,
0.042100246995687485,
0.004871140234172344,
-0.014661380089819431,
-0.02512996271252632,
0.03940623253583908,
0.03868934512138367,
-0.009610047563910484,
0.004378973972052336,
-0.07028710842132568,
-0.03802432492375374,
0.04503009840846062,
0.010824590921401978,
0.027529604732990265,
-0.005586064420640469,
-0.05381346866488457,
-0.016424287110567093,
-0.041269853711128235,
0.03683193773031235,
-0.03276048228144646,
-0.022768717259168625,
-0.040269359946250916,
-0.02517099119722843,
0.01824789121747017,
0.014762679114937782,
0.06056401878595352,
-0.038108453154563904,
-0.026918450370430946,
0.011326522566378117,
-0.02968643046915531,
0.022873960435390472,
-0.033604253083467484,
0.034035976976156235,
-0.036689870059490204,
0.00619948236271739,
-0.0023829133715480566,
-0.017295807600021362,
-0.03676804527640343,
0.006356676109135151,
0.002526751719415188,
0.019870609045028687,
-0.01391912903636694,
-0.046600013971328735,
-0.02201453410089016,
0.04123878851532936,
0.027795253321528435,
-0.01023055799305439,
0.060868021100759506,
-0.04464583098888397,
0.0026135286316275597,
-0.009994403459131718,
0.0029169556219130754,
-0.06952030956745148,
-0.010255830362439156,
-0.038257211446762085,
-0.006543661467730999,
-0.018713928759098053,
0.004180258139967918,
0.07389503717422485,
-0.00010635564103722572,
-0.023244641721248627,
0.05304981395602226,
-0.04566720873117447,
-0.0032449893187731504,
0.04285183921456337,
0.017405685037374496,
0.021747484803199768,
-0.04709574952721596,
0.0010834047570824623,
-0.007519610691815615,
0.021796902641654015,
-0.018693048506975174,
0.05149640887975693,
0.0007897134055383503,
-0.005761080887168646,
-0.03852299600839615,
0.06266581267118454,
-0.011593345552682877,
0.00957951694726944,
0.02594675123691559,
0.03061932511627674,
-0.05449729412794113,
-0.05592506751418114,
0.015044309198856354,
-0.0026563063729554415,
0.0197494737803936,
0.023444147780537605,
-0.0222804993391037,
0.0859343409538269,
-0.04772965610027313,
0.03579828143119812,
-0.02621186152100563,
-0.018201252445578575,
-0.018495066091418266,
0.006198279559612274,
0.009408111684024334,
0.06774057447910309,
0.006204940844327211,
-0.002590329386293888,
0.019268250092864037,
-0.016313854604959488,
0.04891027510166168,
-0.030402494594454765,
0.02919803187251091,
-0.02293301373720169,
-0.009318382479250431,
-0.03510646894574165,
-0.011062290519475937,
-0.029152436181902885,
-0.04185057803988457,
0.028976617380976677,
0.03003833442926407,
0.01619908958673477,
0.016251178458333015,
-0.017032425850629807,
0.003966061398386955,
0.044268809258937836,
-0.06878190487623215,
-0.024504482746124268,
-0.015046777203679085,
0.04116581380367279,
0.022897357121109962,
0.017250925302505493
] |
<p>Question goes as</p>
<blockquote>
<p>Show that the solutions to the <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations" rel="nofollow">Maxwell's equations</a>
$$ \nabla \times \vec H = \frac 1 c \frac{\partial \vec E}{\partial t}+\frac {4\pi} c \vec J, \hspace{ 2 mm} \nabla \times \vec E = -\frac 1 c \frac{\partial \vec H}{\partial t}, \hspace{ 2 mm} \nabla \cdot \vec H = 0, \hspace{ 2 mm} \nabla \cdot \vec E = 4 \pi \rho $$ are given by
$$ \vec E = -\nabla \phi - \frac 1 c \frac{\partial \vec A}{\partial t}, \hspace{2mm} \vec H = \nabla \times \vec A,$$
where $ \phi$ and $\vec A$ are scalar potential and vector potential respectively which satisfy the equations
<a href="http://en.wikipedia.org/wiki/Lorenz_gauge_condition" rel="nofollow">$$ 1) \nabla \cdot \vec A + \frac 1c \frac{\partial \phi}{\partial t} = 0 $$</a>
$$2) \nabla^2 \phi - \frac 1 {c^2} \frac{\partial ^2 \phi}{\partial t^2} = -4\pi \rho $$
$$3) \nabla^2 \vec A - \frac{1}{c^2}\frac{\partial ^2 \vec A}{\partial t^2}= -\frac {4\pi} c \vec J$$</p>
</blockquote>
<p>Hint requested thank you!!<br>
Also what kind of regions is described by
$$ \nabla \cdot \vec E = 4 \pi \rho?$$
It is uniformly charged region?</p>
| 9,392 |
[
-0.009327382780611515,
-0.002259318483993411,
0.008317888714373112,
-0.009789824485778809,
0.052489690482616425,
-0.01533475611358881,
-0.001553033129312098,
-0.0035797255113720894,
-0.012689708732068539,
-0.008706263266503811,
0.03927100449800491,
0.008017116226255894,
0.03804292529821396,
0.029795218259096146,
0.0054349154233932495,
-0.011198248714208603,
-0.02773178555071354,
0.00785675086081028,
-0.029237516224384308,
-0.04939261078834534,
0.00007148680742830038,
-0.026474229991436005,
-0.007517381105571985,
0.04789870232343674,
-0.033748023211956024,
0.01852601394057274,
0.031528692692518234,
-0.037722133100032806,
-0.019245697185397148,
0.04654435068368912,
-0.0041381921619176865,
-0.004904464818537235,
-0.001838106196373701,
0.003116780426353216,
0.008520911447703838,
-0.0017795851454138756,
-0.05255357548594475,
-0.009330364875495434,
-0.00014804395323153585,
0.0019161817617714405,
-0.04346655681729317,
-0.0007610648171976209,
-0.007466396316885948,
0.03342042863368988,
-0.040796369314193726,
0.007290715351700783,
0.013408318161964417,
0.005017745308578014,
0.05708726495504379,
-0.07600102573633194,
0.06684131920337677,
-0.00158188387285918,
0.04026287794113159,
0.01655065454542637,
0.013350664637982845,
-0.06880677491426468,
0.03201572224497795,
0.05535845458507538,
-0.0027163203340023756,
-0.03818602114915848,
-0.006550246383994818,
0.026844702661037445,
0.008862617425620556,
-0.038297608494758606,
-0.02919137291610241,
0.048120301216840744,
-0.003049510298296809,
-0.02919263020157814,
0.024335229769349098,
-0.017082536593079567,
0.009063507430255413,
-0.008805524557828903,
0.020114455372095108,
-0.0041114334017038345,
0.016158705577254295,
-0.025569060817360878,
-0.02440311759710312,
0.04088347777724266,
0.026924127712845802,
0.016027206555008888,
-0.012610414996743202,
0.03950517252087593,
0.01724797487258911,
0.026373112574219704,
-0.008968060836195946,
-0.011339463293552399,
0.08445948362350464,
0.006733638700097799,
-0.0002805320546030998,
0.010807333514094353,
0.026357270777225494,
0.004511840641498566,
0.014345625415444374,
-0.01790601573884487,
0.014819198288023472,
0.009666887111961842,
-0.011655894108116627,
0.038321759551763535,
0.03203431889414787,
-0.013614869676530361,
-0.02697012759745121,
-0.01850990206003189,
-0.01169862225651741,
0.06290774047374725,
-0.028645571321249008,
-0.004513447638601065,
-0.03248000144958496,
0.008306334726512432,
-0.023129340261220932,
-0.004791930317878723,
-0.05098854377865791,
0.04267497733235359,
-0.014911152422428131,
-0.010604441165924072,
-0.009563321247696877,
-0.052566856145858765,
-0.008602559566497803,
-0.02802935428917408,
0.040315527468919754,
0.028042303398251534,
0.0538422130048275,
-0.06844213604927063,
0.0073848566971719265,
0.0022779316641390324,
-0.10078918188810349,
-0.03628358989953995,
0.008245387114584446,
0.02228858321905136,
0.007099288050085306,
0.031360335648059845,
0.007473730016499758,
0.015025822445750237,
-0.027756331488490105,
0.01922685280442238,
0.011412044987082481,
-0.053447335958480835,
-0.08626151084899902,
-0.09014236181974411,
0.03355969488620758,
-0.020952505990862846,
0.01290564239025116,
-0.06367447227239609,
-0.014318504370748997,
0.011211534962058067,
0.0867249071598053,
-0.021883832290768623,
-0.006787230726331472,
0.011984740383923054,
0.052647337317466736,
0.006190159358084202,
-0.0036601705942302942,
0.01911958120763302,
-0.02767154760658741,
-0.020973989740014076,
0.025782719254493713,
-0.07617931813001633,
0.00014597635890822858,
-0.026324065402150154,
-0.016453299671411514,
-0.013958955183625221,
0.053946468979120255,
-0.004158379510045052,
0.016734793782234192,
0.0306838508695364,
-0.015205136500298977,
-0.0024551970418542624,
0.08783569931983948,
0.00007137615466490388,
0.02262556366622448,
0.04123388230800629,
-0.012048065662384033,
0.005651566665619612,
-0.05390945076942444,
0.0026004216633737087,
0.049528345465660095,
-0.02475213259458542,
-0.024666104465723038,
-0.016218794509768486,
0.04189017042517662,
0.0053566088899970055,
-0.03763049468398094,
-0.028814146295189857,
0.007962467148900032,
0.02307630144059658,
0.011211448349058628,
0.072703056037426,
0.00937740784138441,
-0.018450068309903145,
-0.011476058512926102,
-0.028131110593676567,
0.010302159003913403,
-0.03491302952170372,
0.02088014967739582,
0.023460034281015396,
-0.037724245339632034,
0.046884696930646896,
-0.007401044946163893,
0.007350984029471874,
-0.03538421913981438,
-0.017766421660780907,
0.0008039535023272038,
0.06383360177278519,
-0.022533217445015907,
-0.018017122521996498,
0.03628271818161011,
0.005958283320069313,
0.03343118354678154,
-0.011648951098322868,
0.040420517325401306,
-0.01309478934854269,
-0.005026184022426605,
0.007159180007874966,
-0.007350745610892773,
0.06326349079608917,
0.028427543118596077,
-0.0003766183217521757,
-0.023842930793762207,
0.04449627920985222,
-0.0375235453248024,
0.02969270385801792,
-0.048377010971307755,
0.058551687747240067,
0.044994253665208817,
0.022091418504714966,
-0.00633642403408885,
0.041861262172460556,
-0.011348670348525047,
0.04772050306200981,
-0.029116259887814522,
0.004931447096168995,
-0.022878266870975494,
0.004257050342857838,
0.05170991271734238,
0.02064228430390358,
-0.060173939913511276,
0.021940024569630623,
-0.0054535213857889175,
0.019496385008096695,
0.04008112847805023,
0.029466336593031883,
-0.025163454934954643,
-0.045952536165714264,
0.054856013506650925,
0.02793547883629799,
-0.030056070536375046,
0.044546011835336685,
0.027274591848254204,
0.014223956502974033,
0.017207682132720947,
-0.023442363366484642,
-0.01610727794468403,
0.05795934796333313,
-0.02811131253838539,
0.00039828396984376013,
0.03773476183414459,
0.02285485714673996,
0.07720748335123062,
0.00273944647051394,
0.05553726106882095,
0.0029656498227268457,
-0.03765004500746727,
-0.0006609813426621258,
-0.043834708631038666,
-0.0033873990178108215,
0.006869505159556866,
-0.03665364906191826,
0.016554955393075943,
-0.02818342298269272,
0.01301864255219698,
-0.06603290140628815,
-0.01853090338408947,
0.04876777157187462,
0.001093965140171349,
-0.03935029357671738,
-0.04006286710500717,
0.03316832706332207,
0.023012833669781685,
0.030502375215291977,
-0.016459984704852104,
-0.004115103278309107,
0.0016326488694176078,
-0.02372833527624607,
0.006544429808855057,
0.03632095828652382,
-0.00271520740352571,
0.0274253748357296,
-0.03541821241378784,
-0.022013165056705475,
0.05225854739546776,
0.008837166242301464,
0.0043248669244349,
0.014774112030863762,
0.007461750879883766,
-0.048929113894701004,
0.007851019501686096,
-0.04213366284966469,
0.023112595081329346,
-0.05700020119547844,
0.01884281262755394,
0.04597240313887596,
0.012760995887219906,
-0.037759553641080856,
-0.007744344882667065,
-0.04406582564115524,
-0.04885318875312805,
-0.015566152520477772,
-0.016567740589380264,
0.020768646150827408,
-0.00007532216841354966,
0.037703193724155426,
0.0177170280367136,
0.002268350450322032,
0.01125815324485302,
-0.04551973193883896,
-0.001620416296645999,
0.00517709506675601,
-0.016701851040124893,
0.033103879541158676,
-0.0026767172385007143,
-0.04911027103662491,
0.08154630661010742,
0.03923279419541359,
-0.025856608524918556,
-0.0018943030154332519,
0.01718825474381447,
-0.03826116770505905,
-0.025728024542331696,
0.017238881438970566,
0.056656450033187866,
-0.037432312965393066,
-0.005026631057262421,
0.011198950000107288,
0.0530383437871933,
0.02562125399708748,
0.024810761213302612,
-0.00041423190850764513,
0.041033193469047546,
-0.004094884730875492,
-0.009295793250203133,
0.07588797062635422,
0.00558222783729434,
0.02375655062496662,
-0.034043580293655396,
0.0012593375286087394,
0.03669606149196625,
0.04311682656407356,
-0.018114028498530388,
0.022905437275767326,
0.01281797606498003,
-0.00683167390525341,
-0.020281923934817314,
0.033808596432209015,
0.0030855457298457623,
-0.019473575055599213,
-0.0019289450719952583,
-0.02062791772186756,
0.030954288318753242,
-0.026710284873843193,
0.00028368091443553567,
0.05387398600578308,
0.028361370787024498,
-0.03517840802669525,
0.00763410609215498,
-0.010213043540716171,
0.0007615010254085064,
0.05947878584265709,
-0.03270149603486061,
-0.0027185394428670406,
0.056313205510377884,
0.04538862779736519,
0.01697481982409954,
-0.0038142718840390444,
-0.010566644370555878,
0.011346222832798958,
-0.05447665974497795,
0.0008098268299363554,
-0.00783347524702549,
0.05045546218752861,
-0.02594306506216526,
0.05110296234488487,
0.0088789789006114,
0.020713623613119125,
0.05017371103167534,
0.025301674380898476,
-0.06052081659436226,
0.02187599427998066,
-0.009974011220037937,
-0.006221357733011246,
-0.02039876952767372,
-0.011439898051321507,
-0.006317944265902042,
-0.023921264335513115,
-0.0009384638979099691,
-0.014066926203668118,
-0.020485807210206985,
-0.05862221121788025,
0.016232283785939217,
-0.018510151654481888,
-0.07299210876226425,
-0.035720095038414,
0.019214589148759842,
0.03723299875855446,
0.016781771555542946,
-0.00184929883107543,
0.058970965445041656,
-0.02487797848880291,
-0.00048667372902855277,
-0.006397412158548832,
-0.03057100996375084,
0.039518773555755615,
0.04412189871072769,
-0.003311830572783947,
-0.012438387610018253,
0.012349162250757217,
-0.004524623043835163,
-0.02133830077946186,
0.04056538641452789,
0.004015167709439993,
0.0075174965895712376,
-0.03514096140861511,
-0.009825743734836578,
-0.03472331166267395,
-0.024170424789190292,
0.07928494364023209,
-0.0017782485811039805,
0.008112622424960136,
-0.014878162182867527,
-0.0034322296269237995,
0.012398408725857735,
0.020372437313199043,
0.03266920521855354,
0.01119152083992958,
0.003132960293442011,
-0.04755880683660507,
-0.03619186207652092,
-0.04798390716314316,
-0.0022207286674529314,
0.032776184380054474,
-0.0307504590600729,
-0.010010558180510998,
-0.011215022765100002,
0.03207273408770561,
0.022192353382706642,
0.012156538665294647,
0.05083843320608139,
0.012085512280464172,
-0.004081843886524439,
0.014102868735790253,
-0.027005085721611977,
-0.007783538196235895,
0.02709662914276123,
0.03376477211713791,
-0.03143904730677605,
-0.015002232976257801,
-0.07835742831230164,
-0.040165822952985764,
0.023192284628748894,
0.030413731932640076,
0.018528487533330917,
-0.015946827828884125,
-0.05744996666908264,
-0.0008325990638695657,
0.009162599220871925,
-0.05461059510707855,
0.0326974019408226,
0.028564833104610443,
-0.0026364238001406193,
-0.03587479516863823,
-0.05487922579050064,
-0.025333525612950325,
0.02559012360870838,
0.011109407991170883,
-0.027529792860150337,
-0.040060631930828094,
0.010577613487839699,
0.024519911035895348,
0.01725754514336586,
0.03703394532203674,
0.0454401969909668,
0.00265036104246974,
-0.002744153141975403,
-0.027589337900280952,
0.010291319340467453,
-0.005154039245098829,
-0.041386764496564865,
0.012122208252549171,
0.010209482163190842,
-0.03277434781193733,
0.04141928628087044,
-0.042206812649965286,
-0.019695300608873367,
0.05672338604927063,
0.01776488684117794,
-0.03972418233752251,
0.03272330015897751,
-0.03849748149514198,
0.0031312156934291124,
0.009138179011642933,
-0.030285362154245377,
0.0193330105394125,
0.016924934461712837,
-0.008775751106441021,
-0.04769045487046242,
-0.04794803634285927,
0.0030163461342453957,
0.0006502280011773109,
-0.029022978618741035,
0.004031565971672535,
-0.004284066613763571,
-0.03998478874564171,
0.04866922274231911,
-0.031072845682501793,
-0.0019534605089575052,
-0.052268095314502716,
-0.018760064616799355,
0.017262233421206474,
0.00532635860145092,
-0.01333702728152275,
0.01063611451536417,
-0.00015798580716364086,
0.026136182248592377,
0.02236754074692726,
-0.0455784946680069,
0.032021183520555496,
-0.005008830688893795,
0.019458573311567307,
0.06930295377969742,
0.0015664325328543782,
0.020842673256993294,
-0.030335338786244392,
0.017254747450351715,
-0.023083189502358437,
-0.0804414451122284,
0.03829404339194298,
0.009610836394131184,
0.0043538399040699005,
0.036406997591257095,
-0.019453853368759155,
-0.0590924397110939,
-0.00289121619425714,
0.003065315540879965,
0.03348049148917198,
-0.03296113759279251,
0.010563957504928112,
0.05183195695281029,
-0.011039472185075283,
-0.04674718156456947,
-0.02233966812491417,
-0.014347955584526062,
0.014837434515357018,
-0.016188761219382286,
-0.007904702797532082,
-0.009177953004837036,
-0.03340545669198036,
-0.04311475530266762,
0.00831405259668827,
0.017929697409272194,
-0.031682100147008896,
-0.0039200736209750175,
0.021064424887299538,
0.03004901297390461,
0.05127134546637535,
0.03794306516647339,
-0.00008607599011156708,
0.05413442105054855,
-0.018374722450971603,
-0.020913338288664818,
-0.0002939100959338248,
0.05337188392877579,
-0.007889426313340664,
-0.038254283368587494,
0.005093103740364313,
0.003324114019051194,
0.026303676888346672,
0.004332855809479952,
-0.009479708969593048,
0.021497130393981934,
0.0035526466090232134,
-0.01909683458507061,
-0.04884529486298561,
-0.010129121132194996,
0.024234367534518242,
0.03190034255385399,
-0.024523472413420677,
-0.0015450494829565287,
-0.03279027342796326,
-0.044554453343153,
0.03871631249785423,
-0.04482191801071167,
0.013296284712851048,
-0.03713587671518326,
0.06718070060014725,
-0.0070920973084867,
0.008563551120460033,
0.031160984188318253,
0.022881411015987396,
0.025069691240787506,
-0.007323313970118761,
0.003041735617443919,
-0.001224909326992929,
0.008390008471906185,
-0.03032425418496132,
-0.03343309089541435,
-0.05418609455227852,
0.036465127021074295,
0.09444031864404678,
0.021423444151878357,
0.05953378975391388,
0.025021443143486977,
0.0027797312941402197,
-0.002173674525693059,
-0.008446386083960533,
-0.006106255110353231,
-0.0056226616725325584,
-0.006014136131852865,
0.03608877584338188,
-0.019419042393565178,
0.007837111130356789,
0.015907926484942436,
0.003811211558058858,
-0.05927778780460358,
-0.024679241701960564,
-0.006632277742028236,
0.01634914055466652,
0.0015320549719035625,
0.007408155128359795,
-0.02159062772989273,
0.04049711674451828,
0.007394872140139341,
0.02896152064204216,
0.014299975708127022,
-0.009005770087242126,
0.041344814002513885,
0.012334057129919529,
-0.005568735767155886,
-0.04724493622779846,
-0.0006704585393890738,
-0.01182088628411293,
0.035729967057704926,
0.008621248416602612,
-0.04236600548028946,
-0.01819797046482563,
0.04010730981826782,
0.011146867647767067,
-0.01375383697450161,
0.026546087116003036,
-0.008670955896377563,
-0.026931166648864746,
-0.027285903692245483,
-0.042362578213214874,
-0.038664162158966064,
0.04658756032586098,
0.037417370826005936,
-0.020662540569901466,
0.024939974769949913,
-0.051029182970523834,
0.02609558030962944,
0.04669186472892761,
0.0015391745837405324,
-0.008882894180715084,
0.028225798159837723,
-0.0028351210057735443,
0.01147423218935728,
-0.027037477120757103,
0.010372635908424854,
0.12565766274929047,
0.06153705343604088,
-0.01877497509121895,
-0.03862779214978218,
0.04911261796951294,
-0.01824580505490303,
0.023221926763653755,
-0.07524948567152023,
0.020749276503920555,
-0.06551821529865265,
0.030853265896439552,
0.026083478704094887,
0.02978658862411976,
0.005602451041340828,
0.04202042892575264,
0.024639906361699104,
-0.03230541944503784,
-0.05104800686240196,
-0.020288562402129173,
0.04481339454650879,
-0.01071873214095831,
0.03561224788427353,
-0.03830919787287712,
0.04577134922146797,
-0.07643086463212967,
0.029664261266589165,
-0.052905596792697906,
-0.017130393534898758,
0.017056161537766457,
-0.003531807567924261,
-0.03639809414744377,
0.026319384574890137,
-0.008419528603553772,
-0.0064039574936032295,
-0.04208511859178543,
0.027019010856747627,
0.022167980670928955,
-0.019715819507837296,
0.0161959957331419,
0.016839956864714622,
-0.017391838133335114,
-0.021038874983787537,
0.03680843859910965,
0.04378984495997429,
-0.042999595403671265,
0.032314732670784,
-0.04320831596851349,
0.05052223056554794,
-0.00973947811871767,
-0.00005763986337115057,
0.01019318401813507,
0.02637650817632675,
-0.03510373458266258,
-0.008517494425177574,
-0.050688982009887695,
-0.04986261948943138,
0.02354768104851246,
0.008249358274042606,
-0.014486006461083889,
-0.010760536417365074,
0.01413538958877325,
0.014009232632815838,
0.016259681433439255,
-0.03144967555999756,
0.0021150712855160236,
-0.0050386348739266396,
-0.009441210888326168,
0.04592180624604225,
-0.009417523629963398,
-0.0008904863498173654,
0.0017950765322893858,
-0.045594122260808945,
-0.013964950107038021,
-0.011700238101184368,
-0.015386772342026234,
0.02712090127170086,
0.022861653938889503,
0.02672605775296688,
-0.03734974563121796,
0.0071389926597476006,
-0.07105128467082977,
-0.04147712141275406,
-0.010926433838903904,
-0.010290372185409069,
-0.029334837570786476,
-0.011662156321108341,
0.0055754040367901325,
0.034659888595342636,
-0.008838982321321964,
-0.03462810814380646,
0.0273091122508049,
0.060052331537008286,
0.027046101167798042,
-0.0033045297022908926,
-0.02961294911801815,
-0.0049001905135810375,
-0.011550763621926308,
0.023624883964657784,
0.00926460511982441,
0.03508208319544792,
0.024401234462857246,
0.04304707050323486,
0.016241682693362236,
0.030238380655646324,
-0.03122718445956707,
-0.024369709193706512,
0.02615722268819809,
-0.02631324715912342,
0.01619856059551239,
0.02247670292854309,
0.03688047453761101,
-0.029243849217891693,
0.03191326931118965,
0.00730371568351984,
0.007402057759463787,
0.011804651468992233,
-0.010181019082665443,
-0.011223413981497288,
-0.014443688094615936,
-0.027139563113451004,
0.005507773719727993,
-0.06890447437763214,
-0.0011428374564275146,
-0.006685275584459305,
0.022597476840019226,
-0.008857516571879387,
0.0043778857216238976,
-0.01616840995848179,
0.02611539326608181,
-0.016025090590119362,
-0.0024110074155032635,
0.05556857958436012,
0.01503921952098608,
-0.02315644361078739,
-0.0047545055858790874,
0.031139278784394264,
0.03281950205564499,
0.017669524997472763,
0.03591940924525261,
-0.023879889398813248,
0.043835535645484924,
-0.012307458557188511,
-0.008590374141931534,
-0.00019620551029220223,
0.021751586347818375,
0.023180920630693436,
0.01761745661497116,
-0.0373084656894207,
0.009698506444692612,
0.09642313420772552,
0.006245299708098173,
0.028461303561925888,
-0.025653179734945297,
-0.06805621087551117,
0.02811456471681595,
-0.002585766604170203,
0.008170319721102715,
-0.00022112735314294696,
0.007573180831968784,
-0.01628299616277218,
0.01367789413779974,
-0.03079863078892231,
-0.05112016946077347,
0.01791999116539955,
0.01754686050117016,
0.02077360451221466,
-0.010417964309453964,
0.0023239708971232176,
0.01699049584567547,
0.03724612668156624,
-0.006826166063547134,
0.01836390793323517,
0.016576580703258514,
-0.011271047405898571,
-0.07528173923492432,
-0.007535293698310852,
0.015443939715623856,
0.027994738891720772,
0.03697625920176506,
-0.043206971138715744,
0.008210351690649986,
0.04218791425228119,
-0.04774780943989754,
-0.01367440540343523,
0.010674919001758099,
-0.007247016299515963,
-0.0013277600519359112,
-0.03416803479194641,
-0.005959774367511272,
0.047018133103847504,
0.018513446673750877,
0.019401466473937035,
-0.007210164796561003,
0.042719364166259766,
-0.04865144193172455,
-0.05266350880265236,
0.002796886255964637,
0.05913645774126053,
0.026062214747071266,
-0.02083371952176094,
0.05254679545760155,
-0.006855237763375044,
0.0017755571752786636,
0.020289991050958633,
-0.010626722127199173,
-0.02602721005678177,
-0.0004129610606469214,
0.005584407597780228,
0.008645007386803627,
0.02619035355746746,
0.004806541837751865,
0.02132042683660984,
-0.01259549055248499,
-0.017735622823238373,
-0.012910387478768826,
-0.028379172086715698,
-0.019615160301327705,
-0.023238662630319595,
0.028848575428128242,
-0.044878553599119186,
-0.0405854694545269,
0.033917754888534546,
-0.03265763819217682,
-0.026355262845754623,
0.0017941375263035297,
-0.016353189945220947,
0.024052688851952553,
-0.008959438651800156,
-0.0066602216102182865,
-0.022341078147292137,
-0.0039530228823423386,
0.009746388532221317,
0.02382359839975834,
-0.0325724259018898,
0.021101603284478188,
-0.004321396350860596,
-0.04381479695439339,
0.05541349947452545,
-0.00047793961130082607,
0.009424487128853798,
-0.06675169616937637,
0.009530310519039631,
-0.00762448413297534,
0.015866165980696678,
-0.019781792536377907,
-0.019488584250211716,
-0.05162821710109711,
0.03037261590361595,
0.04696245491504669,
0.01988968253135681,
-0.043364156037569046,
-0.0017200271831825376,
-0.003286120481789112,
-0.0661587342619896,
0.018229344859719276,
0.024901755154132843,
-0.05281790345907211,
-0.042267605662345886,
-0.030426835641264915,
-0.02519252710044384,
0.053146153688430786,
0.06330350786447525,
-0.015104607678949833,
0.0001422589411959052,
0.032128509134054184,
-0.020133521407842636,
-0.0036110905930399895,
-0.07548587769269943,
-0.011747032403945923,
0.040722474455833435,
-0.01793309673666954,
0.05692873150110245,
0.03113112598657608,
0.011546109803020954,
-0.013409524224698544,
-0.02172223851084709,
0.030415205284953117,
0.02930641919374466,
-0.007703001610934734,
-0.027905303984880447,
0.004582038149237633,
-0.017249101772904396,
-0.0031031693797558546,
0.0718287006020546,
-0.00872699823230505,
0.010398440062999725,
-0.015450557693839073,
-0.051447223871946335,
0.00978587195277214,
-0.002705593593418598,
-0.0823439359664917,
0.026566168293356895,
-0.018062619492411613,
-0.04037899523973465,
0.051592350006103516,
-0.027079425752162933,
-0.013545391149818897,
0.04535353556275368,
0.0021406353916972876,
-0.04327420890331268,
0.07860738039016724,
-0.00033668751711957157,
0.009908567182719707,
-0.041083890944719315,
0.006985326763242483,
-0.004563055466860533,
-0.05098768696188927,
0.005861660931259394,
0.040339790284633636,
-0.009240437299013138,
-0.01055126916617155,
-0.011819683946669102,
0.025380397215485573,
-0.035982828587293625,
-0.0006226754048839211,
0.001542737358249724,
-0.011471034027636051,
-0.021083973348140717,
-0.005840009544044733,
0.03596789017319679,
-0.013870579190552235,
-0.00402385089546442,
0.013983686454594135,
0.012273211032152176,
0.09014146775007248,
-0.03914260491728783,
0.03186461329460144,
-0.02587207965552807,
0.04723944142460823,
-0.022308755666017532,
0.06590192764997482,
-0.004478600341826677,
0.032909322530031204,
-0.016512209549546242,
-0.0060763186775147915,
-0.020933663472533226,
-0.05804300308227539,
0.004151677247136831,
-0.05699890851974487,
0.01854415237903595,
-0.001593547873198986,
0.0071532465517520905,
0.019451018422842026,
-0.0070022717118263245,
0.024352869018912315,
-0.013146697543561459,
-0.002316898899152875,
-0.0007291401852853596,
0.005529599264264107,
-0.02984055131673813,
0.032151855528354645,
-0.03559857979416847,
0.03130612522363663,
-0.05416116863489151,
-0.03076050616800785,
-0.011831407435238361,
-0.010357406921684742,
-0.03503210470080376,
-0.01988375559449196
] |
<p>I read somewhere that stress-energy tensor density is a symmetric tensor. But if I take the Dirac Field tensor:</p>
<p>$$T^{\mu \nu}=i \psi^\dagger \gamma^0 \gamma^\mu \partial^\nu \psi $$</p>
<p>How could I demonstrate this property?</p>
| 9,393 |
[
-0.02494022622704506,
-0.01810634508728981,
0.007645224221050739,
-0.048224616795778275,
0.02608163096010685,
0.025231147184967995,
-0.01866901107132435,
0.020460721105337143,
0.0011607251362875104,
-0.045560337603092194,
0.04261597618460655,
0.025096755474805832,
0.04207904636859894,
0.00733570009469986,
0.022148752585053444,
0.004250948317348957,
-0.03332691267132759,
0.01353844627737999,
-0.018924029543995857,
-0.05870994180440903,
0.0011150831123813987,
0.003265989478677511,
-0.03459951654076576,
0.025715414434671402,
-0.013921860605478287,
0.05340338125824928,
-0.02347661554813385,
-0.00413884362205863,
0.002827426651492715,
0.05744932219386101,
-0.036717962473630905,
-0.03895731642842293,
0.01251776423305273,
0.005385825410485268,
0.03650274500250816,
-0.009049957618117332,
-0.03981991857290268,
-0.019508233293890953,
-0.025180460885167122,
0.005313620436936617,
-0.008354895748198032,
-0.014283145777881145,
-0.018463250249624252,
0.04489315301179886,
-0.010798666626214981,
0.03679363802075386,
0.014460468664765358,
-0.031148944050073624,
0.06158052012324333,
-0.025355154648423195,
0.07470455020666122,
0.015745289623737335,
0.038878537714481354,
0.037400878965854645,
-0.011552699841558933,
-0.04064830765128136,
0.03151944652199745,
0.06230733543634415,
-0.012883170507848263,
-0.009824463166296482,
0.0004950645961798728,
-0.01223460491746664,
-0.02664046362042427,
-0.027342088520526886,
-0.011026978492736816,
0.04213561490178108,
0.008759459480643272,
-0.011223028413951397,
0.01772143878042698,
-0.027804823592305183,
-0.012479727156460285,
0.0027986096683889627,
0.03266631066799164,
-0.020859207957983017,
-0.03215392306447029,
-0.0168528500944376,
0.03136690706014633,
0.02048376202583313,
0.025802329182624817,
0.010600469075143337,
0.007695935666561127,
0.01831101067364216,
0.01050032489001751,
0.03673115745186806,
-0.024214252829551697,
0.0028578629717230797,
0.05585625395178795,
0.028903743252158165,
-0.022453375160694122,
0.04596855863928795,
0.018988074734807014,
-0.016597555950284004,
-0.0007454380975104868,
0.02208069898188114,
-0.021343447268009186,
0.013427291065454483,
-0.011972286738455296,
0.04294971749186516,
-0.009934361092746258,
-0.011432562954723835,
-0.02048485539853573,
-0.01416777539998293,
-0.0058220429345965385,
0.08105123788118362,
0.0036276397295296192,
-0.029148845002055168,
-0.04247841238975525,
0.044330842792987823,
-0.014536130242049694,
0.0010170394089072943,
-0.07537098973989487,
-0.023538464680314064,
-0.04836539551615715,
-0.0234534852206707,
0.020384933799505234,
-0.052464645355939865,
0.01659969799220562,
-0.0068559045903384686,
0.0501118041574955,
0.09496721625328064,
0.028143277391791344,
0.0061460440047085285,
0.03844243288040161,
-0.017689524218440056,
-0.08737235516309738,
0.047269366681575775,
0.06025225669145584,
-0.030170416459441185,
-0.0496562123298645,
0.0014871209859848022,
0.014457620680332184,
0.012500045821070671,
-0.022818971425294876,
0.003930536564439535,
0.03638162463903427,
-0.03824670985341072,
-0.1020406037569046,
-0.06409108638763428,
0.011859550140798092,
-0.0020058101508766413,
-0.03228015825152397,
-0.06196551024913788,
-0.006644885987043381,
0.041893262416124344,
0.0972362607717514,
0.0037724212743341923,
0.04000239446759224,
0.001706982497125864,
0.017943428829312325,
0.024028364568948746,
0.018021080642938614,
-0.04122844338417053,
-0.02452280931174755,
-0.04233953356742859,
-0.00035059594665654004,
-0.04951201751828194,
-0.004666874650865793,
-0.00768205476924777,
-0.014787903986871243,
-0.016619807109236717,
0.08039173483848572,
-0.01294719334691763,
0.011203263886272907,
0.007752142380923033,
-0.025592807680368423,
-0.04634469002485275,
0.07680404186248779,
0.018181996420025826,
-0.013197296299040318,
0.027609791606664658,
-0.021626660600304604,
-0.00017224384646397084,
0.0018097305437549949,
0.04376275837421417,
0.04086494818329811,
-0.0789220780134201,
-0.001455260906368494,
0.025726955384016037,
0.0001794385170796886,
0.018687603995203972,
0.004924943204969168,
-0.0038968694861978292,
-0.011836517602205276,
0.0071726166643202305,
0.016705118119716644,
0.021547669544816017,
-0.002718219067901373,
-0.018620997667312622,
-0.010039371438324451,
-0.05109478905797005,
-0.009235324338078499,
-0.018688375130295753,
-0.0007062052027322352,
-0.031025106087327003,
-0.02576032094657421,
0.027190621942281723,
0.006462646182626486,
0.010485727339982986,
-0.02432500198483467,
-0.04250543564558029,
0.006033098790794611,
0.02153518609702587,
0.02135493792593479,
-0.00021707768610212952,
0.021712549030780792,
-0.012334802187979221,
0.032579123973846436,
0.0055316477082669735,
0.026791267096996307,
-0.0057217758148908615,
0.01673455350100994,
0.04944944381713867,
-0.00897893961519003,
0.010852916166186333,
-0.008198271505534649,
-0.01067799236625433,
-0.012612911872565746,
-0.00544540211558342,
-0.01798228733241558,
0.03896181657910347,
-0.01851959340274334,
0.06485312432050705,
0.0348367914557457,
0.005498769227415323,
0.001773431315086782,
0.00845656730234623,
0.00887325033545494,
0.05399908125400543,
-0.0010085186222568154,
-0.009652804583311081,
-0.05500775948166847,
0.017049450427293777,
0.04491738602519035,
0.010546084493398666,
-0.07264278084039688,
0.035346273332834244,
0.01127605140209198,
0.021645141765475273,
0.0324343666434288,
0.015106427483260632,
-0.03689845651388168,
-0.06019139662384987,
0.03600796312093735,
0.0179415512830019,
0.009717906825244427,
0.005274335853755474,
0.017230579629540443,
-0.005526052787899971,
0.023289620876312256,
-0.027896536514163017,
0.0002922335988841951,
0.034991052001714706,
-0.052410420030355453,
0.011178153567016125,
0.019091784954071045,
-0.044157397001981735,
0.04934903234243393,
-0.02429562248289585,
0.05028042942285538,
0.06312747299671173,
-0.033619582653045654,
-0.004587785340845585,
-0.03375914692878723,
-0.005564887076616287,
0.02209557220339775,
-0.014704928733408451,
-0.01174340583384037,
-0.005115233827382326,
0.011101623065769672,
-0.02490471862256527,
-0.02116089127957821,
0.026888981461524963,
0.013854828663170338,
-0.03815368190407753,
-0.02652648463845253,
0.04045271500945091,
0.022489076480269432,
-0.00004525881740846671,
-0.00247731851413846,
-0.013044526800513268,
0.05203302949666977,
-0.00240711378864944,
0.00028725535958074033,
0.024441547691822052,
-0.05913982912898064,
0.008187773637473583,
-0.027216333895921707,
-0.03821243345737457,
0.024352164939045906,
0.01281948946416378,
0.028532741591334343,
0.007744822185486555,
-0.021716276183724403,
-0.04923955351114273,
-0.005312506575137377,
-0.024785323068499565,
0.010993887670338154,
-0.04179061949253082,
0.014823990873992443,
0.05146327614784241,
-0.010087980888783932,
-0.032994113862514496,
-0.011437976732850075,
0.025736544281244278,
-0.06017686426639557,
-0.015824604779481888,
-0.02886120043694973,
0.006014297250658274,
-0.03135006129741669,
0.054315827786922455,
0.044433850795030594,
-0.05312654376029968,
0.003983114846050739,
-0.05449580028653145,
0.006748491432517767,
-0.0018227502005174756,
0.015834350138902664,
0.019087737426161766,
0.010877969674766064,
-0.0824345275759697,
0.09675253927707672,
0.03810621425509453,
-0.052910760045051575,
-0.01420646347105503,
-0.023343011736869812,
-0.0042542279697954655,
-0.05170923098921776,
0.015164067037403584,
0.006984180770814419,
-0.007527880370616913,
0.040950167924165726,
0.03839854523539543,
0.05225468426942825,
0.02419198304414749,
0.023337215185165405,
-0.058175694197416306,
0.00009736521315062419,
0.001113222911953926,
-0.015696758404374123,
0.06710650771856308,
-0.0055392407812178135,
-0.009672981686890125,
-0.01793801039457321,
0.029972689226269722,
0.018486015498638153,
0.0014301285846158862,
-0.0369860902428627,
0.061838824301958084,
0.00942261889576912,
-0.0009542452171444893,
-0.07166146486997604,
0.026738695800304413,
0.004117906093597412,
-0.014769040048122406,
0.01867097057402134,
0.04251570254564285,
0.053975943475961685,
-0.037422459572553635,
-0.015322196297347546,
0.013471268117427826,
0.01981874369084835,
-0.03674810379743576,
-0.014272154308855534,
-0.015020863153040409,
-0.019199801608920097,
0.038728758692741394,
-0.038158971816301346,
-0.00359526788815856,
0.04809682071208954,
0.03031195141375065,
0.049382325261831284,
-0.014956342056393623,
-0.02400965988636017,
0.012340999208390713,
-0.042011044919490814,
0.035662226378917694,
0.015964392572641373,
0.04534420743584633,
0.026702966541051865,
0.03299177810549736,
0.05401623621582985,
0.004231269471347332,
0.04388534277677536,
-0.013808655552566051,
-0.05021790415048599,
0.03127327188849449,
-0.01835625246167183,
0.014550534076988697,
0.007717672735452652,
-0.053678959608078,
-0.03574840724468231,
-0.05477563664317131,
-0.014317167922854424,
-0.012085489928722382,
-0.003905026474967599,
-0.04998909309506416,
0.03655683249235153,
-0.05583049729466438,
-0.0378510020673275,
-0.016531769186258316,
0.05916063115000725,
0.025143105536699295,
-0.004414158407598734,
-0.020352311432361603,
0.04363840073347092,
0.0007263076258823276,
-0.005684290546923876,
-0.021906845271587372,
0.024064384400844574,
0.012019551359117031,
0.03374525159597397,
0.030655065551400185,
0.00034167279954999685,
-0.0012327784206718206,
-0.01249973475933075,
0.03905945271253586,
0.042060911655426025,
0.020079869776964188,
-0.011316427029669285,
-0.021654898300766945,
-0.03575322404503822,
-0.05732464790344238,
-0.003351619467139244,
0.07235916703939438,
0.02147487737238407,
-0.003674817271530628,
0.011755582876503468,
0.039223868399858475,
-0.03244584798812866,
0.04407675564289093,
0.055144939571619034,
-0.008380369283258915,
-0.02196543850004673,
-0.08111182600259781,
-0.010988176800310612,
-0.008822005242109299,
-0.03727828338742256,
-0.014942636713385582,
-0.009290657006204128,
-0.05463302507996559,
-0.004589239601045847,
0.00458518136292696,
0.018903790041804314,
-0.005701449234038591,
0.011403004638850689,
-0.015567350201308727,
-0.006331945303827524,
0.022222615778446198,
0.0031607646960765123,
0.0076482598669826984,
0.04172668606042862,
0.03475005552172661,
0.020515523850917816,
-0.008125538937747478,
-0.04318191856145859,
-0.0106983482837677,
0.023731417953968048,
-0.004560606088489294,
-0.01052823942154646,
-0.00792387593537569,
-0.03576778247952461,
-0.012818007729947567,
0.04477395862340927,
-0.011700846254825592,
0.04815070703625679,
0.007116193883121014,
0.008169114589691162,
0.016793133690953255,
-0.004855903331190348,
-0.01731869764626026,
0.07011233270168304,
-0.03252790495753288,
-0.005482412409037352,
-0.04757105931639671,
0.015424082987010479,
-0.032881319522857666,
-0.0152331767603755,
0.005235251039266586,
0.04965505003929138,
0.009232570417225361,
-0.020859483629465103,
0.0012252817396074533,
0.04734041541814804,
0.007404381409287453,
-0.08502962440252304,
-0.010513248853385448,
-0.012252156622707844,
-0.003270708257332444,
0.034593015909194946,
-0.0004486411053221673,
-0.020515430718660355,
0.040964942425489426,
0.02624605968594551,
-0.04076238349080086,
0.026854993775486946,
-0.04358796775341034,
0.04871443286538124,
0.027880195528268814,
-0.007620999123901129,
0.03726422041654587,
0.0307879950851202,
0.018683064728975296,
0.0060438900254666805,
-0.02544921636581421,
0.02656402997672558,
-0.04902048781514168,
0.027243999764323235,
-0.01016296911984682,
0.028483038768172264,
-0.060199301689863205,
0.018420547246932983,
-0.03708924353122711,
0.02745470032095909,
0.03846416249871254,
-0.022428147494792938,
0.016186019405722618,
0.05079417675733566,
-0.009246177971363068,
-0.010123762302100658,
0.03079785779118538,
0.00572639424353838,
-0.012555664405226707,
-0.025667862966656685,
-0.00694494741037488,
0.0024052090011537075,
-0.03821811079978943,
0.03719433769583702,
0.014538205228745937,
0.06824438273906708,
-0.004281924106180668,
-0.061399880796670914,
0.00770963542163372,
-0.026119910180568695,
0.0295152198523283,
-0.02196073718369007,
0.006366034038364887,
-0.007689430844038725,
-0.009508092887699604,
-0.002455967478454113,
0.025576910004019737,
-0.02233707904815674,
0.025824591517448425,
-0.05577049404382706,
0.015941010788083076,
0.027211418375372887,
0.007288588210940361,
-0.11347587406635284,
-0.03092252090573311,
0.018604636192321777,
-0.011715532280504704,
-0.008310928009450436,
-0.03273358568549156,
0.0009500632877461612,
-0.03137879818677902,
-0.024225426837801933,
0.0030447826720774174,
0.04760917276144028,
0.019229555502533913,
-0.028916725888848305,
-0.0310469139367342,
0.006852344144135714,
0.041739512234926224,
-0.002743474906310439,
-0.01569865643978119,
-0.0013016604352742434,
-0.03394933417439461,
0.012226726859807968,
-0.017484668642282486,
0.03446498513221741,
-0.027065357193350792,
-0.01350564043968916,
-0.012814640998840332,
-0.006339407060295343,
0.033600661903619766,
0.006432488560676575,
-0.022544102743268013,
0.017304295673966408,
0.021974045783281326,
-0.013366509228944778,
-0.05654750019311905,
0.0050048078410327435,
-0.02569749765098095,
0.02555527538061142,
-0.0008456825162284076,
0.005425619427114725,
-0.0782969519495964,
-0.045125797390937805,
0.015002013184130192,
-0.00655197910964489,
0.03856325522065163,
-0.014258356764912605,
0.08705185353755951,
0.01793520338833332,
0.0016808442305773497,
0.006362365558743477,
-0.023495448753237724,
-0.008843161165714264,
0.035116035491228104,
0.004437838681042194,
0.01635068468749523,
-0.00040941231418401003,
-0.04390932619571686,
0.012077814899384975,
-0.0008808656712062657,
0.0387917086482048,
0.06607763469219208,
-0.031100258231163025,
0.03844883665442467,
0.02074785716831684,
0.0014392937300726771,
0.017856406047940254,
0.029569653794169426,
-0.03725460544228554,
-0.013139582239091396,
-0.006032481323927641,
0.038572948426008224,
-0.00547260046005249,
0.0073602646589279175,
0.04331992566585541,
0.060908108949661255,
-0.03529614955186844,
0.03556039556860924,
0.0015135376015678048,
0.03367902338504791,
0.0006336188525892794,
0.007374056614935398,
-0.05817091464996338,
0.05381070449948311,
-0.015871886163949966,
0.057284001260995865,
0.00497819297015667,
0.021909529343247414,
0.006891368888318539,
0.004163884092122316,
0.029339933767914772,
0.02107764407992363,
-0.0378015860915184,
-0.0330686941742897,
0.015707682818174362,
0.03815107420086861,
-0.031175965443253517,
-0.008197424001991749,
0.05789390578866005,
0.0280955471098423,
0.009519550018012524,
0.026147471740841866,
-0.008798790164291859,
-0.03754853084683418,
-0.018100248649716377,
-0.03150549530982971,
-0.05045661702752113,
0.05370780825614929,
-0.04080121964216232,
-0.02902008220553398,
0.017104795202612877,
-0.003799925558269024,
0.03137626498937607,
0.01959564909338951,
0.02327827736735344,
0.0075410897843539715,
0.05083577334880829,
0.009853907860815525,
0.033519428223371506,
0.028604740276932716,
-0.022834083065390587,
0.11923839151859283,
0.03556251898407936,
0.04682152718305588,
-0.011722779832780361,
0.020178627222776413,
-0.009558049030601978,
0.0015297489007934928,
-0.011364432983100414,
0.05501353740692139,
0.008439581841230392,
-0.012096503749489784,
0.005600809119641781,
0.0686836913228035,
-0.01014640275388956,
-0.014432577416300774,
0.042050622403621674,
-0.02061060629785061,
-0.021034611389040947,
-0.003232573624700308,
0.05608917400240898,
-0.003465478541329503,
-0.028324950486421585,
-0.04464218392968178,
0.006886649876832962,
-0.032362036406993866,
0.03200498968362808,
-0.019180046394467354,
-0.05870995670557022,
-0.007977311499416828,
-0.014409413561224937,
-0.020722653716802597,
-0.01182912290096283,
-0.010330798104405403,
0.016636541113257408,
-0.04906326159834862,
-0.022624654695391655,
0.024277832359075546,
-0.002849381882697344,
0.04493071511387825,
0.010863293893635273,
-0.00032061347155831754,
0.02551291510462761,
0.013113963417708874,
0.03832753375172615,
-0.03872520476579666,
0.01705332100391388,
-0.017695453017950058,
0.056579433381557465,
-0.03239991143345833,
-0.002773663029074669,
0.02736787311732769,
-0.0077927918173372746,
0.02046169713139534,
-0.016160110011696815,
-0.03398854285478592,
-0.014748413115739822,
-0.006729371380060911,
-0.012042855843901634,
-0.017457004636526108,
-0.016219617798924446,
0.02616712637245655,
0.005474595353007317,
0.03161092847585678,
-0.028737682849168777,
0.0067028929479420185,
0.011482778005301952,
-0.029114356264472008,
0.02813030034303665,
-0.03377598896622658,
-0.019199347123503685,
-0.013834363780915737,
-0.05756868049502373,
-0.039758794009685516,
-0.03020038641989231,
0.014851243235170841,
-0.006172390189021826,
0.023310931399464607,
0.0008736178860999644,
-0.0037504241336137056,
0.00959416851401329,
-0.04311574622988701,
0.003643996547907591,
-0.04405801370739937,
-0.03165217861533165,
-0.007950536906719208,
0.019318250939249992,
-0.0003643914242275059,
0.06236240640282631,
-0.041562579572200775,
-0.011418495327234268,
0.03232526779174805,
-0.02885855734348297,
0.010450763627886772,
-0.03128068894147873,
-0.03958646580576897,
0.011375904083251953,
-0.0212522242218256,
0.015334764495491982,
-0.0017681728349998593,
-0.034745700657367706,
0.05501192808151245,
0.020870501175522804,
0.023012159392237663,
0.02194218523800373,
-0.034586865454912186,
-0.020562734454870224,
0.015233856625854969,
-0.014415732584893703,
-0.015393364243209362,
0.016918236389756203,
-0.0015273861354216933,
-0.014041822403669357,
-0.024815941229462624,
-0.013852251693606377,
-0.003680978436022997,
0.01312918122857809,
0.006081029307097197,
-0.015045265667140484,
-0.038089945912361145,
-0.019107380881905556,
0.020724941045045853,
-0.04398534446954727,
-0.024248626083135605,
-0.04883362352848053,
0.011167092248797417,
0.019429251551628113,
-0.011636895127594471,
-0.03861341252923012,
0.02959153614938259,
-0.0005007334402762353,
-0.01302940584719181,
0.03329804167151451,
0.015597918070852757,
-0.031628113240003586,
-0.0028768188785761595,
0.07578665018081665,
0.009877638891339302,
0.02467469312250614,
0.03448188304901123,
0.005627069156616926,
0.0439031720161438,
-0.013161235488951206,
-0.0207536481320858,
0.03420983627438545,
-0.005012643989175558,
0.009763075038790703,
0.000012003413758066017,
-0.021672029048204422,
0.010025525465607643,
0.046219270676374435,
-0.030446769669651985,
-0.014526581391692162,
-0.01897030510008335,
-0.03384047746658325,
0.00865765567868948,
-0.04918837547302246,
0.016284560784697533,
-0.012680286541581154,
-0.007467655930668116,
-0.0012372375931590796,
0.0027866829186677933,
0.0013890104601159692,
-0.01844210922718048,
0.016161169856786728,
0.01241598092019558,
0.01402368675917387,
0.0037641534581780434,
-0.012599732726812363,
-0.0009977801237255335,
0.075938880443573,
-0.04757872596383095,
0.02226898819208145,
0.03157810866832733,
0.026782872155308723,
-0.08936086297035217,
-0.0002762472431641072,
0.0046822065487504005,
-0.0324324369430542,
0.05180802568793297,
-0.03295760974287987,
0.045023273676633835,
0.010834289714694023,
-0.029175130650401115,
0.010293390601873398,
-0.009656781330704689,
-0.03218509256839752,
-0.006412597838789225,
-0.005683749448508024,
-0.012431059032678604,
0.08868497610092163,
0.009862653911113739,
0.07661084830760956,
0.022716453298926353,
0.01451006717979908,
0.0007679643458686769,
-0.008149317465722561,
-0.04382747784256935,
0.02628246881067753,
0.00168158661108464,
-0.01824471913278103,
0.07103275507688522,
-0.0008734884322620928,
-0.05668644607067108,
0.025737309828400612,
-0.01348789781332016,
-0.022268086671829224,
0.0005233705742284656,
0.013994632288813591,
-0.016416583210229874,
-0.0033781009260565042,
0.0010686255991458893,
-0.028566956520080566,
0.018788587301969528,
0.007704518269747496,
0.041881706565618515,
0.009643002413213253,
-0.029407642781734467,
-0.0012394370278343558,
0.023412218317389488,
-0.032951924949884415,
-0.011272348463535309,
0.08444464206695557,
-0.0328483022749424,
-0.03818035125732422,
-0.020073633641004562,
-0.029475606977939606,
0.03577084094285965,
-0.004562284331768751,
0.0244701337069273,
-0.04027591273188591,
-0.004095152486115694,
-0.016417762264609337,
0.045303020626306534,
-0.021978845819830894,
0.05569456145167351,
0.008317925035953522,
-0.05968405678868294,
0.030744878575205803,
0.022134412080049515,
-0.015322137624025345,
-0.059757377952337265,
0.004175290931016207,
-0.0014964452711865306,
0.012923137284815311,
0.007654496002942324,
-0.03609561547636986,
-0.051878802478313446,
0.037064846605062485,
0.04566105455160141,
0.016283772885799408,
-0.00939930509775877,
-0.023604542016983032,
0.002449121093377471,
-0.07934174686670303,
0.00387751217931509,
-0.005556243471801281,
0.006884560454636812,
0.004714422393590212,
-0.008960450068116188,
-0.01845596730709076,
0.014341202564537525,
0.056234490126371384,
-0.015583266504108906,
-0.013972634449601173,
0.025942327454686165,
0.013324950821697712,
0.009436086751520634,
-0.06369028985500336,
-0.023054292425513268,
-0.017707422375679016,
-0.03617475926876068,
0.013497496023774147,
0.017202267423272133,
-0.012608850374817848,
0.00897199660539627,
0.004691471811383963,
0.006703495047986507,
0.022926701232790947,
0.0049016294069588184,
-0.02766253612935543,
0.03475901484489441,
-0.03334398940205574,
-0.02723611705005169,
0.059476520866155624,
-0.029729535803198814,
0.009956182911992073,
0.018353916704654694,
-0.04618542268872261,
-0.01131040696054697,
0.04455123469233513,
-0.020291900262236595,
-0.01356720644980669,
-0.022228213027119637,
-0.0012745215790346265,
0.03965790569782257,
-0.0393945574760437,
0.0073502860032022,
0.03486541658639908,
-0.047556959092617035,
-0.027348456904292107,
0.035059310495853424,
0.012733724899590015,
0.020967131480574608,
0.013487512245774269,
0.004066568333655596,
0.008880258537828922,
0.0002460384857840836,
0.028569264337420464,
0.050604380667209625,
-0.015395315364003181,
0.012060479260981083,
-0.001987653085961938,
0.004603290464729071,
-0.05363418906927109,
0.016378596425056458,
-0.01066483836621046,
0.01102445274591446,
-0.03337995707988739,
-0.015749823302030563,
0.027586720883846283,
0.005210743751376867,
0.01599402353167534,
-0.00998921599239111,
-0.01446903683245182,
0.07874366641044617,
-0.032572854310274124,
0.02394530363380909,
-0.029638951644301414,
0.002668523695319891,
-0.04634464904665947,
0.020309563726186752,
0.033474285155534744,
0.057827237993478775,
-0.007030009292066097,
-0.008597418665885925,
-0.021199045702815056,
-0.010641975328326225,
-0.008427567780017853,
-0.05410686880350113,
-0.02558870241045952,
0.012175718322396278,
-0.022005250677466393,
-0.023346949368715286,
-0.0112546905875206,
-0.019955381751060486,
-0.01786421239376068,
0.041236910969018936,
0.02486901730298996,
-0.00813688337802887,
0.020668556913733482,
-0.01837845891714096,
-0.027130067348480225,
0.05383820831775665,
-0.0474102646112442,
-0.04248635470867157,
-0.05254881829023361,
0.020757440477609634,
-0.005645452067255974,
-0.006679757963865995
] |
<p>In particle physics, <a href="http://en.wikipedia.org/wiki/Supersymmetry" rel="nofollow">supersymmetry</a> (often abbreviated SUSY) is a symmetry that relates elementary particles...etc.</p>
<ul>
<li><p>what is <a href="http://en.wikipedia.org/wiki/Symmetry_breaking" rel="nofollow">symmetry breaking</a>?</p></li>
<li><p>What is supersymmetry (SUSY)?</p></li>
<li><p>What is <a href="http://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking" rel="nofollow">spontaneous symmetry breaking</a>?</p></li>
</ul>
| 9,394 |
[
-0.031667791306972504,
-0.03892301023006439,
0.015172770246863365,
-0.03834134340286255,
0.023875121027231216,
0.00483171921223402,
-0.02996259368956089,
-0.031573034822940826,
0.008011998608708382,
-0.03208431601524353,
0.04009805992245674,
0.024735206738114357,
0.017738232389092445,
0.03351454436779022,
0.011101569049060345,
0.030879464000463486,
0.01640423946082592,
-0.025609027594327927,
-0.0037972326390445232,
0.023818425834178925,
0.010414534248411655,
-0.001347301178611815,
-0.02876376174390316,
0.021153196692466736,
-0.01904248259961605,
0.04027435556054115,
0.05814158543944359,
0.02215128391981125,
0.04814770445227623,
0.07431869953870773,
-0.00908299908041954,
-0.013872812502086163,
0.00782473012804985,
0.020782772451639175,
0.026108039543032646,
-0.003389816265553236,
0.029807692393660545,
-0.03557276353240013,
0.01286926306784153,
0.011529432609677315,
-0.017160214483737946,
-0.0026284975465387106,
-0.025921229273080826,
0.0413513109087944,
-0.04973326995968819,
0.014207802712917328,
-0.013844085857272148,
-0.00574718602001667,
0.05136410519480705,
-0.06917072087526321,
0.052044130861759186,
-0.003909789025783539,
0.015177777037024498,
-0.0051825460977852345,
0.00802547950297594,
0.0345173217356205,
0.04862131550908089,
0.06246354430913925,
0.025888925418257713,
-0.0780843123793602,
-0.006629886105656624,
-0.04937875270843506,
0.0143671790137887,
-0.02033885382115841,
-0.059481196105480194,
0.0445987768471241,
-0.005469474475830793,
-0.007866373285651207,
0.014287267811596394,
0.02814416214823723,
-0.009435400366783142,
-0.00800887681543827,
0.02278062514960766,
-0.028413262218236923,
0.012204634957015514,
-0.038575429469347,
-0.001516719930805266,
-0.009045802988111973,
0.03186463564634323,
0.0637291669845581,
-0.0015260593499988317,
0.022484973073005676,
-0.021161265671253204,
0.01618567481637001,
0.015227668918669224,
-0.026029301807284355,
0.1048196479678154,
0.008860724978148937,
-0.017815271392464638,
0.013886247761547565,
0.0010848509846255183,
0.002579796127974987,
0.03526146709918976,
-0.0015349563909694552,
-0.022782886400818825,
0.035032402724027634,
0.0257597416639328,
0.042040206491947174,
-0.0006434593233279884,
-0.02475215122103691,
0.028116075322031975,
-0.008931594900786877,
0.01952492818236351,
0.07301533967256546,
-0.01393904909491539,
-0.019145959988236427,
-0.02187163382768631,
0.013198956847190857,
-0.0322972908616066,
0.009619910269975662,
-0.02720358595252037,
-0.01750067248940468,
-0.0057076346129179,
-0.0025748703628778458,
0.006952209863811731,
-0.018157878890633583,
0.017108719795942307,
-0.003785099135711789,
0.052686117589473724,
0.07976607978343964,
0.04651403799653053,
-0.022822972387075424,
-0.016640540212392807,
0.016180729493498802,
-0.09199191629886627,
0.022346142679452896,
0.02851206623017788,
0.02476481907069683,
-0.030986512079834938,
0.037510547786951065,
0.001716057420708239,
-0.016353726387023926,
0.00008937588427215815,
-0.04256700351834297,
0.028694380074739456,
-0.00973217561841011,
-0.09663525968790054,
-0.06525284796953201,
0.04950462281703949,
0.01720956712961197,
-0.04136247932910919,
-0.040844183415174484,
-0.00304802181199193,
0.014151097275316715,
0.0879245325922966,
-0.035207949578762054,
0.02739354409277439,
0.008253129199147224,
0.01830008625984192,
0.010656925849616528,
-0.004975911229848862,
0.006019293796271086,
0.025354739278554916,
0.0017859900835901499,
-0.004072691313922405,
-0.06781280040740967,
0.000836576393339783,
0.035555027425289154,
-0.000374892057152465,
0.0035126744769513607,
0.06789553910493851,
-0.021134482696652412,
0.03107105754315853,
0.009690100327134132,
-0.029404722154140472,
-0.001273523666895926,
0.07304556667804718,
-0.008810233324766159,
-0.014008969068527222,
0.05508994311094284,
-0.024416841566562653,
0.030061673372983932,
-0.010511974804103374,
0.023036839440464973,
0.016384052112698555,
-0.01580815762281418,
-0.034661710262298584,
-0.015094347298145294,
-0.005614782217890024,
0.01544205192476511,
-0.0711289569735527,
-0.043762631714344025,
0.013062842190265656,
0.04482176527380943,
-0.0052624051459133625,
0.04026969522237778,
-0.013497624546289444,
-0.009877512231469154,
0.019854459911584854,
-0.08637873828411102,
-0.06841389834880829,
-0.05513564869761467,
0.00390375847928226,
-0.045890677720308304,
-0.02991427294909954,
0.013879523612558842,
0.03436523675918579,
0.02166927047073841,
-0.06659802794456482,
-0.012598318979144096,
-0.0069591510109603405,
0.04155212268233299,
0.020624086260795593,
0.011427066288888454,
-0.0003615925379563123,
0.06667787581682205,
0.03634890541434288,
-0.0275769904255867,
0.02808236889541149,
0.0011089928448200226,
-0.004025506787002087,
0.0025105001404881477,
-0.012008671648800373,
0.0017393374582752585,
-0.007585407234728336,
0.0019957066979259253,
0.011866554617881775,
0.010722865350544453,
-0.026502534747123718,
0.05676386132836342,
-0.00890673790127039,
0.0568549707531929,
0.025854744017124176,
0.023160746321082115,
0.01139911264181137,
0.007658951450139284,
-0.004265592899173498,
0.019946862012147903,
-0.03812985494732857,
-0.008699432946741581,
-0.05754849687218666,
-0.021390143781900406,
0.03914819285273552,
0.01695682667195797,
-0.02212277427315712,
0.020352976396679878,
0.009087544865906239,
0.03083849512040615,
0.03496423736214638,
0.01964406855404377,
-0.06395696103572845,
-0.05033557116985321,
0.012098029255867004,
0.0103609599173069,
0.013052954338490963,
0.026593061164021492,
0.015253536403179169,
0.012080059386789799,
0.01853199675679207,
-0.006978570483624935,
-0.04986101761460304,
0.05865105614066124,
0.012352744117379189,
-0.021690355613827705,
0.038623664528131485,
-0.05012013763189316,
0.03255916386842728,
-0.01756145805120468,
0.05621413514018059,
0.010366540402173996,
-0.008319064043462276,
0.01083381287753582,
-0.03065803088247776,
0.006949214730411768,
-0.006956886034458876,
0.01813408173620701,
-0.02692404016852379,
-0.026227407157421112,
0.0032325503416359425,
-0.002883692504838109,
-0.027575820684432983,
-0.01406785286962986,
-0.029183419421315193,
-0.026789939031004906,
-0.022374505177140236,
0.01118240226060152,
-0.007476594299077988,
0.06710287183523178,
-0.03974103927612305,
-0.03155139088630676,
0.007524797227233648,
-0.03988402336835861,
0.04865797236561775,
0.01570017635822296,
-0.04050370678305626,
0.02418445236980915,
-0.043269652873277664,
-0.011013718321919441,
0.05189405009150505,
0.0038312801625579596,
0.009714155457913876,
0.006432345137000084,
-0.013355881907045841,
-0.04949689283967018,
-0.006580401677638292,
-0.019833259284496307,
0.04853716865181923,
-0.052711524069309235,
0.004155721515417099,
0.03181183338165283,
-0.009413616731762886,
-0.017337601631879807,
-0.00013613073679152876,
-0.04889795184135437,
-0.01860303431749344,
-0.023709362372756004,
0.016851484775543213,
0.01742246001958847,
-0.02163870818912983,
0.015764059498906136,
0.017338452860713005,
-0.06520954519510269,
0.02882372960448265,
-0.015728546306490898,
-0.06448052078485489,
0.003527064109221101,
-0.012794233858585358,
0.014341252855956554,
-0.016004709526896477,
-0.06539776176214218,
0.08589241653680801,
0.03300502523779869,
-0.03774753957986832,
-0.010128002613782883,
-0.020166849717497826,
-0.004251161124557257,
-0.05818954482674599,
0.01887630671262741,
0.014501679688692093,
-0.0028353636153042316,
0.016647960990667343,
0.03518389165401459,
0.07918021082878113,
-0.0015406226739287376,
0.011484182439744473,
-0.0640018954873085,
-0.06143259257078171,
-0.015048708766698837,
-0.029572948813438416,
0.015286126174032688,
0.004528469871729612,
-0.038532841950654984,
-0.021228408440947533,
-0.02689705789089203,
0.04010898619890213,
-0.012314384803175926,
-0.029694220051169395,
0.05284897983074188,
-0.00804505217820406,
0.028309069573879242,
-0.03779340907931328,
0.05645227059721947,
-0.013821573927998543,
-0.023504769429564476,
-0.006578896660357714,
0.0042190649546682835,
0.01627778634428978,
-0.021032467484474182,
-0.0021084093023091555,
-0.001503262552432716,
0.07066114991903305,
-0.05038202926516533,
-0.02001298777759075,
-0.024476267397403717,
0.0028212214820086956,
-0.0038816637825220823,
-0.020899666473269463,
-0.018718665465712547,
0.05325966328382492,
0.06548622995615005,
0.024021677672863007,
0.009845727123320103,
-0.032428327947854996,
-0.015391594730317593,
-0.0609024316072464,
0.024820813909173012,
-0.01691562682390213,
0.05572482943534851,
-0.004642018117010593,
0.07251738756895065,
0.02728152833878994,
0.022098498418927193,
0.013225804083049297,
-0.01728655770421028,
-0.09765015542507172,
0.03861920163035393,
-0.040540218353271484,
-0.0029733090195804834,
0.013646516017615795,
-0.0020105792209506035,
0.006632036995142698,
-0.02144295535981655,
-0.038134414702653885,
-0.030885299667716026,
0.010857910849153996,
-0.03797725960612297,
0.016596458852291107,
-0.024955160915851593,
-0.019898144528269768,
0.0178257804363966,
-0.005633282940834761,
0.06265329569578171,
-0.03714624419808388,
-0.0073092663660645485,
0.02780865505337715,
-0.025392454117536545,
-0.012977962382137775,
-0.02317536249756813,
0.039163075387477875,
0.01479017361998558,
0.0339265838265419,
0.024339376017451286,
0.034093376249074936,
-0.02867981791496277,
0.011649186722934246,
0.005848542787134647,
0.06226465851068497,
-0.0025890679098665714,
0.04145920276641846,
-0.004584222100675106,
-0.0515083409845829,
-0.005968686658889055,
-0.003809436224400997,
0.02145548164844513,
-0.00878044031560421,
0.0021438756957650185,
0.026698607951402664,
0.021527905017137527,
-0.0640811026096344,
0.0520438514649868,
0.033355262130498886,
-0.013735627755522728,
-0.02822529524564743,
-0.041157934814691544,
-0.03839057311415672,
-0.03070034272968769,
-0.016225069761276245,
0.01716100238263607,
0.007727358024567366,
-0.037325743585824966,
0.02735372632741928,
0.009655415080487728,
0.001608784543350339,
-0.05510894954204559,
0.00413271551951766,
-0.011996434070169926,
-0.0008172341622412205,
-0.015209374949336052,
-0.016163425520062447,
-0.01114562712609768,
0.02272975444793701,
0.04655064269900322,
-0.006696602329611778,
-0.015057042241096497,
-0.057089947164058685,
0.01065489649772644,
0.05152108147740364,
0.025289129465818405,
-0.015290594659745693,
-0.020372193306684494,
-0.04918143153190613,
-0.0000990062253549695,
0.0592668280005455,
-0.023189440369606018,
0.026422206312417984,
-0.022094694897532463,
0.007224211469292641,
-0.015382065437734127,
-0.007652989123016596,
-0.006176633760333061,
0.0429355688393116,
0.0065955608151853085,
0.02456710860133171,
-0.013998768292367458,
-0.009137227199971676,
-0.03548740968108177,
0.023918164893984795,
0.016882164403796196,
0.03837457671761513,
0.012244164943695068,
0.04316793009638786,
0.0007195278885774314,
0.03912321850657463,
-0.031071756035089493,
-0.08705656230449677,
0.017976222559809685,
0.024262655526399612,
-0.033201150596141815,
0.004337144084274769,
-0.019728653132915497,
-0.04345877468585968,
-0.0026911308523267508,
0.020386282354593277,
-0.01195566076785326,
-0.030842997133731842,
-0.027615105733275414,
0.04276837781071663,
0.07215540111064911,
0.014656364917755127,
0.004917579237371683,
0.03172779828310013,
-0.04225412383675575,
-0.031860560178756714,
-0.030088897794485092,
0.023371856659650803,
-0.012718592770397663,
0.02009478025138378,
-0.03398526459932327,
-0.01248039398342371,
-0.06236738711595535,
0.06883160769939423,
0.008260448463261127,
-0.016794241964817047,
0.012940088286995888,
-0.008025550283491611,
-0.014897581189870834,
0.027777407318353653,
0.014933397993445396,
-0.021715933457016945,
0.017575662583112717,
0.029983242973685265,
0.01427781768143177,
-0.017410824075341225,
0.029059048742055893,
0.0007997684879228473,
-0.03206083923578262,
0.005119923502206802,
0.001012197695672512,
0.006774518173187971,
-0.03277845308184624,
-0.05459201708436012,
0.04059907793998718,
-0.05361019819974899,
0.022166427224874496,
-0.02626257948577404,
0.003934620879590511,
0.014266491867601871,
-0.05804590880870819,
-0.02072025090456009,
0.026244280859827995,
-0.02331995964050293,
-0.014733179472386837,
-0.03423481807112694,
0.04804565757513046,
0.03180938959121704,
0.003375826869159937,
-0.052066512405872345,
-0.03394849970936775,
0.015367267653346062,
-0.031080521643161774,
-0.0007502200896851718,
-0.008140407502651215,
0.0057355742901563644,
-0.02928221970796585,
-0.04895074665546417,
0.018073108047246933,
0.022723659873008728,
-0.06199432536959648,
-0.002665481297299266,
0.006109840236604214,
-0.019386468455195427,
0.04739592969417572,
0.0069704907946288586,
-0.03624916821718216,
-0.0451999194920063,
0.002529577352106571,
0.04356831684708595,
0.005261921789497137,
0.05916909500956535,
0.004893401172012091,
-0.03212413936853409,
-0.004778414499014616,
-0.005916996393352747,
0.0353965163230896,
-0.008479639887809753,
0.023189419880509377,
0.019028829410672188,
0.027598338201642036,
0.022578392177820206,
-0.043224263936281204,
0.03934473544359207,
-0.0024591018445789814,
0.029814088717103004,
-0.021373918280005455,
0.013551897369325161,
-0.026448825374245644,
-0.023965347558259964,
0.026606382802128792,
-0.017493801191449165,
0.018982423469424248,
0.009305701591074467,
0.027863839641213417,
-0.03826151415705681,
-0.018840869888663292,
0.02355133555829525,
-0.03566544130444527,
-0.006642905995249748,
-0.013905218802392483,
0.002365135820582509,
-0.0007889863336458802,
0.012268096208572388,
0.009655374102294445,
-0.019084952771663666,
0.014273297972977161,
-0.02307693287730217,
0.04094725847244263,
-0.03898520767688751,
0.06513062864542007,
0.048748306930065155,
-0.03764577582478523,
0.015469580888748169,
-0.03657332435250282,
0.021882830187678337,
0.004499020520597696,
0.012757877819240093,
0.029446765780448914,
-0.03911744803190231,
-0.016318466514348984,
0.027148721739649773,
0.08487680554389954,
-0.00763727817684412,
0.007459689863026142,
0.056324273347854614,
0.013064371421933174,
0.02527553029358387,
-0.06614553928375244,
-0.04440086707472801,
0.06309815496206284,
-0.046583667397499084,
0.037792280316352844,
0.03399256244301796,
0.0007880636840127409,
0.0358843170106411,
-0.001144188572652638,
-0.004999237135052681,
-0.022620433941483498,
-0.0021356830839067698,
-0.043618492782115936,
0.03835979104042053,
0.0075442977249622345,
-0.0014820354990661144,
-0.006673271767795086,
0.032771799713373184,
0.02310289442539215,
-0.004976070486009121,
0.016344312578439713,
0.008560547605156898,
-0.08466792851686478,
-0.03666343167424202,
-0.007106955163180828,
-0.03395475074648857,
0.03043503686785698,
-0.026222582906484604,
-0.015683099627494812,
0.010325263254344463,
-0.011557748541235924,
0.013568731024861336,
0.017573555931448936,
0.041384506970644,
-0.042389318346977234,
0.03754568099975586,
-0.023498298600316048,
0.04049190878868103,
-0.012507849372923374,
-0.0025986141990870237,
0.11507774889469147,
0.05592216178774834,
-0.0002931566850747913,
-0.060435183346271515,
0.02593255043029785,
-0.009319976903498173,
-0.0006352477939799428,
-0.006495431996881962,
-0.005857465788722038,
-0.008686904795467854,
0.0005794381140731275,
0.008732158690690994,
0.04483436048030853,
0.023770062252879143,
-0.028669366613030434,
0.06741829216480255,
-0.04859722778201103,
-0.051149845123291016,
-0.021813558414578438,
0.012757585383951664,
-0.01914387010037899,
0.036797795444726944,
-0.057006221264600754,
0.04840080812573433,
-0.01307363249361515,
-0.015278239734470844,
-0.03658170998096466,
-0.05988186597824097,
0.031122079119086266,
0.03589189797639847,
0.004757043905556202,
0.009368667379021645,
0.01659383624792099,
0.01018595416098833,
-0.07682327926158905,
0.009324222803115845,
0.013460909016430378,
-0.01523010153323412,
0.025850379839539528,
0.03849301487207413,
0.01516903005540371,
-0.018683653324842453,
0.002803053241223097,
0.02550407685339451,
-0.03840982913970947,
-0.02188790962100029,
-0.012648448348045349,
0.060197021812200546,
-0.007734088692814112,
-0.01619621552526951,
-0.0021101634483784437,
0.02393883466720581,
0.008541177958250046,
-0.02983446791768074,
-0.041552700102329254,
0.02085173688828945,
-0.0016516461037099361,
-0.05872708559036255,
-0.02216457948088646,
-0.02351274900138378,
0.027369113638997078,
-0.049008775502443314,
0.020935630425810814,
-0.0021765504498034716,
0.0070794252678751945,
0.030704304575920105,
0.0016684631118550897,
-0.004248280543833971,
0.009498280473053455,
0.019915509968996048,
-0.018746905028820038,
-0.010969246737658978,
-0.014146341942250729,
0.011338640935719013,
0.03192192316055298,
0.005487690679728985,
0.04811001569032669,
0.01555316150188446,
-0.02257145568728447,
-0.020915696397423744,
-0.001439402112737298,
0.05589478090405464,
-0.0012878156267106533,
-0.006673519499599934,
0.006212778855115175,
-0.01094298530369997,
0.044258963316679,
0.03137417882680893,
-0.018611960113048553,
0.05197610706090927,
-0.02042221464216709,
0.012445271015167236,
0.008069060742855072,
-0.01900751329958439,
-0.017724085599184036,
0.009050053544342518,
-0.0218628142029047,
0.001996305538341403,
-0.012295934371650219,
0.027288231998682022,
0.02758672647178173,
-0.013927651569247246,
0.0028468759264796972,
0.06130126491189003,
-0.010700973682105541,
-0.02537047676742077,
0.04087354987859726,
-0.025523213669657707,
0.026762614026665688,
0.012715389020740986,
0.018906477838754654,
-0.0011957228416576982,
-0.019276704639196396,
0.010370069183409214,
0.010930562391877174,
0.017798304557800293,
0.01584618166089058,
-0.022402726113796234,
0.029338175430893898,
-0.018356919288635254,
0.029929226264357567,
-0.029849102720618248,
-0.020467694848775864,
-0.0327402763068676,
0.014949408359825611,
0.002742169424891472,
-0.010164134204387665,
-0.006314687430858612,
0.015771454200148582,
0.01616244576871395,
-0.006352171301841736,
0.012996886856853962,
0.016217702999711037,
0.006128550507128239,
-0.009581408463418484,
0.05841701477766037,
0.0077127995900809765,
0.04828320071101189,
0.0020758984610438347,
-0.01371810119599104,
0.04450858384370804,
-0.04988468065857887,
-0.03965257853269577,
0.017389975488185883,
-0.0320592038333416,
-0.0023682250175625086,
0.03421124443411827,
-0.03833721578121185,
-0.02245711162686348,
0.015716245397925377,
-0.029548078775405884,
0.007244768552482128,
-0.013129879720509052,
-0.013985813595354557,
-0.018409891054034233,
-0.017855770885944366,
-0.038494277745485306,
0.007805794943124056,
-0.04962434992194176,
0.036443546414375305,
0.015478003770112991,
-0.00775758596137166,
-0.014142838306725025,
0.003299471689388156,
-0.007843567989766598,
0.012355601415038109,
-0.0190318264067173,
0.020210808143019676,
0.01095470879226923,
0.025714507326483727,
-0.036652132868766785,
0.007469784468412399,
-0.023319117724895477,
-0.013248500414192677,
-0.07297421991825104,
0.014716015197336674,
-0.01729903370141983,
-0.013469437137246132,
0.024310750886797905,
-0.06511565297842026,
0.039973944425582886,
0.026448002085089684,
-0.020855456590652466,
0.04945029690861702,
-0.03204308822751045,
-0.014627390541136265,
-0.009447249583899975,
0.0074917832389473915,
-0.011176985688507557,
0.09374084323644638,
0.001130369259044528,
0.01576741226017475,
-0.007985186763107777,
0.012769403867423534,
0.006577622145414352,
-0.0174526646733284,
-0.05589214339852333,
0.015955859795212746,
0.00244341348297894,
-0.05231592804193497,
0.0554925873875618,
0.016860004514455795,
-0.025387559086084366,
0.011809414252638817,
-0.002723553217947483,
0.002553884871304035,
0.03532123938202858,
0.008678262121975422,
-0.02054455876350403,
0.022457825019955635,
-0.0008227310026995838,
0.015575041994452477,
0.0011875041527673602,
0.00814362708479166,
0.02254454419016838,
0.05793538689613342,
0.016918515786528587,
0.011778470128774643,
-0.009179849177598953,
-0.016036635264754295,
-0.0168489757925272,
0.024882333353161812,
-0.035662729293107986,
-0.0204392708837986,
0.02343689277768135,
-0.03509971871972084,
0.007926076650619507,
-0.015168369747698307,
-0.002644716762006283,
-0.008404897525906563,
0.017119335010647774,
0.03315659984946251,
0.010506995022296906,
-0.019961543381214142,
0.04026632383465767,
0.004503932781517506,
-0.010057922452688217,
0.03371627256274223,
0.004145562183111906,
-0.014335370622575283,
-0.028866607695817947,
0.0012862597359344363,
0.024122847244143486,
0.038789767771959305,
0.00857090950012207,
-0.015436956658959389,
-0.020162176340818405,
0.05307283625006676,
0.05012928694486618,
0.014381857588887215,
-0.021819669753313065,
-0.031386010348796844,
-0.006342409644275904,
-0.04293087124824524,
0.045085690915584564,
0.0179093386977911,
-0.0017175583634525537,
-0.04577917978167534,
0.007001982536166906,
0.002061220118775964,
-0.005290629342198372,
0.028353866189718246,
-0.011663895100355148,
-0.020045535638928413,
0.043561387807130814,
0.03631186857819557,
0.013242061249911785,
-0.029782734811306,
0.002331121824681759,
0.016938399523496628,
-0.04199599474668503,
-0.019072474911808968,
-0.049992773681879044,
-0.009023681282997131,
0.03716074675321579,
0.022049501538276672,
-0.014339528977870941,
0.04164811968803406,
0.000315237557515502,
-0.024123549461364746,
0.029519885778427124,
-0.0037691418547183275,
-0.03193230926990509,
0.05515770986676216,
-0.00446592690423131,
0.017056677490472794,
0.021572845056653023,
-0.004783086944371462,
0.018812905997037888,
0.0008128407644107938,
-0.04490906372666359,
-0.012265056371688843,
-0.011902857571840286,
-0.050021231174468994,
0.024907974526286125,
-0.06911274790763855,
0.006471832282841206,
0.03949534520506859,
-0.04860610514879227,
-0.03068017028272152,
0.061629943549633026,
0.019444923847913742,
0.02722504921257496,
-0.005576722323894501,
-0.020311202853918076,
0.012425481341779232,
-0.015917139127850533,
0.02616179920732975,
0.06944755464792252,
-0.00571459298953414,
-0.013534878380596638,
0.004430326633155346,
0.025830963626503944,
0.038549527525901794,
0.019718660041689873,
-0.004947826266288757,
0.03305807337164879,
-0.030226649716496468,
-0.006768104620277882,
0.008722146041691303,
-0.0017164599848911166,
0.04027343913912773,
0.033852528780698776,
-0.01778896152973175,
0.09510409086942673,
-0.05302443727850914,
0.01899685151875019,
-0.009496198035776615,
0.0288372915238142,
-0.011143112555146217,
-0.027725163847208023,
0.002661773469299078,
0.06093072518706322,
-0.001239948091097176,
-0.026911018416285515,
-0.021830212324857712,
0.023621512576937675,
0.04649491608142853,
-0.053341206163167953,
0.061350490897893906,
-0.012909851036965847,
-0.01568489521741867,
-0.014415640383958817,
0.008614622987806797,
-0.03186817094683647,
-0.036689694970846176,
0.02449411153793335,
0.003454797901213169,
-0.01797037199139595,
0.007132215425372124,
-0.03324051573872566,
-0.010927352122962475,
0.003576898016035557,
-0.07314390689134598,
-0.0222698375582695,
-0.0466141439974308,
0.003830024041235447,
-0.05641224607825279,
-0.010124057531356812
] |
<p>Is the number of states in the Universe countable? </p>
<p>What framework could be used to answer the question in the title?</p>
| 9,395 |
[
-0.036383964121341705,
-0.01840081624686718,
-0.006855471525341272,
-0.043639954179525375,
0.03428684547543526,
-0.011894427239894867,
-0.021533869206905365,
-0.035632070153951645,
-0.013016755692660809,
0.004517472814768553,
0.033178288489580154,
-0.00872619729489088,
-0.010036532767117023,
-0.015479224734008312,
-0.019716937094926834,
0.03565419092774391,
0.010578745044767857,
0.04096449539065361,
-0.021092325448989868,
-0.0008465559221804142,
0.03934378921985626,
0.04827062413096428,
0.037243593484163284,
-0.03583960980176926,
-0.024610096588730812,
0.04753737151622772,
0.01643425039947033,
-0.01607850007712841,
0.05654671788215637,
0.047842178493738174,
0.006114996038377285,
-0.04121394455432892,
0.05207091569900513,
0.02771763876080513,
0.030326684936881065,
-0.0326433926820755,
-0.025188924744725227,
-0.010896923951804638,
-0.013052907772362232,
0.006066653411835432,
-0.047773417085409164,
-0.03760656714439392,
-0.026105856522917747,
0.02186790481209755,
-0.005339530296623707,
0.0025118314661085606,
-0.009322849102318287,
-0.025614403188228607,
0.031573038548231125,
-0.014578386209905148,
0.06948132067918777,
-0.01816987246274948,
0.04297662526369095,
-0.0068613076582551,
-0.006519029848277569,
-0.0369969978928566,
0.09807923436164856,
0.06811196357011795,
0.005599128548055887,
-0.026144225150346756,
-0.049771688878536224,
-0.019847052171826363,
0.02497565932571888,
-0.03148277848958969,
-0.023220527917146683,
0.04135880246758461,
-0.019725900143384933,
0.010340499691665173,
-0.03280411288142204,
0.0178428515791893,
-0.015029202215373516,
-0.0019783524330705404,
0.02037554606795311,
-0.01370162796229124,
0.015224631875753403,
-0.03834540396928787,
0.05261171981692314,
-0.010839277878403664,
0.015088014304637909,
0.06141774356365204,
-0.010612222366034985,
-0.04052912816405296,
0.02170044369995594,
-0.004338452126830816,
0.0433046780526638,
0.009127470664680004,
0.050885144621133804,
-0.013087975792586803,
-0.0020530978217720985,
0.03368041664361954,
-0.0328516885638237,
-0.00808714423328638,
0.04418444633483887,
0.013384518213570118,
-0.06404437869787216,
0.031653158366680145,
-0.04590626433491707,
0.03140270337462425,
-0.008561615832149982,
-0.019314810633659363,
0.004334623925387859,
-0.062261100858449936,
0.04802542179822922,
0.05612190067768097,
0.010727903805673122,
0.013298475183546543,
-0.04550178721547127,
0.025807145982980728,
-0.021863974630832672,
0.01489452738314867,
-0.04984413459897041,
0.04215136170387268,
0.009097211994230747,
0.022473055869340897,
0.013215809129178524,
0.0262595247477293,
-0.013369911350309849,
-0.003528819652274251,
0.019597947597503662,
0.04987325519323349,
0.039684318006038666,
-0.02461683377623558,
0.0099925696849823,
-0.01856990158557892,
-0.0473618246614933,
0.015444040298461914,
0.004131500143557787,
-0.0077652959153056145,
-0.03283756971359253,
0.010884017683565617,
-0.0021232992876321077,
-0.000512171071022749,
-0.009735781699419022,
0.018783513456583023,
0.04006655514240265,
-0.007580772507935762,
-0.11781679838895798,
-0.07191959023475647,
0.039937421679496765,
-0.008460541255772114,
-0.042402442544698715,
-0.04266014322638512,
0.058714620769023895,
0.02233278751373291,
0.03259267657995224,
-0.017186198383569717,
0.006864763796329498,
0.03471289202570915,
0.04288696497678757,
-0.011712453328073025,
-0.04633547365665436,
-0.029501555487513542,
-0.0446111299097538,
-0.08175445348024368,
0.017505668103694916,
-0.048931822180747986,
0.027100246399641037,
0.02861594967544079,
0.019427208229899406,
-0.03550808131694794,
0.05210668593645096,
-0.013382669538259506,
0.003977821674197912,
0.026180235669016838,
0.014828566461801529,
-0.012051991187036037,
0.06729112565517426,
0.020795386284589767,
0.028848057612776756,
0.062255050987005234,
0.030510930344462395,
-0.0024729615543037653,
0.028316784650087357,
0.020645679906010628,
0.03153853490948677,
-0.021476374939084053,
-0.018075192347168922,
-0.03208399564027786,
0.003197945188730955,
-0.004287320654839277,
-0.02566804550588131,
0.021039942279458046,
-0.020458979532122612,
0.01739542931318283,
0.042377594858407974,
-0.003958648070693016,
0.01931513473391533,
-0.009655915200710297,
0.005370622966438532,
-0.04073011130094528,
-0.008143803104758263,
-0.05497826635837555,
0.003858205396682024,
0.007424784824252129,
-0.004951439332216978,
0.025667311623692513,
-0.0031775685492902994,
0.026865698397159576,
-0.04138984903693199,
0.0010322520975023508,
-0.039541635662317276,
0.018165063112974167,
0.014942244626581669,
-0.027799151837825775,
-0.03160326927900314,
0.046797335147857666,
0.0594242699444294,
0.0020886410493403673,
0.03581763431429863,
-0.020649608224630356,
-0.05787300318479538,
-0.03218531608581543,
-0.0070348624140024185,
0.04267052933573723,
-0.028947863727808,
0.020696720108389854,
-0.0059470077976584435,
-0.0067196376621723175,
-0.02620594948530197,
0.07192064821720123,
-0.05744323134422302,
0.054983094334602356,
0.022721530869603157,
-0.001545613631606102,
0.0017400085926055908,
0.021007513627409935,
-0.0019988713320344687,
-0.0296323224902153,
-0.021922964602708817,
-0.039154719561338425,
-0.08490383625030518,
-0.005587490275502205,
0.02538244239985943,
0.035419195890426636,
-0.010839272290468216,
0.027894748374819756,
0.023726999759674072,
0.06929703056812286,
-0.02128836326301098,
-0.007975596003234386,
-0.04770014062523842,
-0.010666369460523129,
0.013687556609511375,
-0.005385538563132286,
0.02955179288983345,
0.03287208452820778,
0.007469905074685812,
0.018716460093855858,
0.0026123221032321453,
0.01515593659132719,
-0.01745014823973179,
0.009860102087259293,
-0.00554598169401288,
0.019619574770331383,
-0.014930535107851028,
-0.07201365381479263,
0.019324911758303642,
-0.025845060124993324,
0.03827907517552376,
0.01180578675121069,
-0.0009181959903798997,
-0.025499511510133743,
-0.023349221795797348,
-0.02148742415010929,
-0.007564150728285313,
0.013534553349018097,
-0.04806806892156601,
-0.04412831366062164,
0.03533456102013588,
-0.03001476265490055,
0.03072994202375412,
-0.05585496500134468,
-0.009984203614294529,
-0.035009630024433136,
-0.0015694465255364776,
0.022985467687249184,
-0.007194287143647671,
0.0315258726477623,
-0.04649164155125618,
-0.007178412284702063,
0.011338010430335999,
-0.018402470275759697,
-0.03298327699303627,
0.024060126394033432,
-0.07517977803945541,
0.019004998728632927,
0.04298710823059082,
-0.025691308081150055,
-0.01964792050421238,
-0.0245987456291914,
-0.0014126497553661466,
0.005595494527369738,
0.0017891976749524474,
-0.033773232251405716,
-0.00384718319401145,
-0.048767853528261185,
-0.0006181102362461388,
-0.03304577246308327,
0.0012674168683588505,
0.0338653102517128,
0.0009839223930612206,
-0.04307103902101517,
-0.007878526113927364,
-0.06766673922538757,
-0.04362383857369423,
-0.00806757714599371,
-0.010213534347712994,
0.01623898185789585,
-0.016951294615864754,
-0.009259444661438465,
0.007288193795830011,
-0.06806632876396179,
0.0017951128538697958,
-0.05346778780221939,
-0.06799595057964325,
0.020155450329184532,
-0.024101413786411285,
0.055567625910043716,
0.020701654255390167,
-0.04467473924160004,
0.06168112903833389,
0.02616189792752266,
-0.028869682922959328,
-0.0027538833674043417,
-0.03615185245871544,
0.00917942263185978,
-0.01218410488218069,
-0.0025066204834729433,
0.011915036477148533,
0.011057890020310879,
0.004272677469998598,
0.028967658057808876,
0.02925713174045086,
0.015876004472374916,
-0.0011117600370198488,
0.013058137148618698,
0.014881023205816746,
0.015892598778009415,
0.03131288290023804,
0.05790243297815323,
0.03375280648469925,
-0.016200073063373566,
0.04196075350046158,
-0.026586269959807396,
0.00033298818743787706,
0.00838223472237587,
-0.04418502748012543,
0.027978822588920593,
-0.0026624584570527077,
0.005539008416235447,
-0.04725435748696327,
0.022456124424934387,
0.004949917085468769,
0.004559749271720648,
0.0038448881823569536,
0.025641027837991714,
0.03598644584417343,
-0.02490726299583912,
-0.022048931568861008,
0.020653629675507545,
0.02293781191110611,
-0.02460724487900734,
0.01616099290549755,
0.01352385152131319,
-0.0019516405882313848,
-0.0036103257443755865,
0.007419956382364035,
-0.020118730142712593,
0.02960137277841568,
-0.0022873212583363056,
0.04997318238019943,
0.0033364521805197,
-0.03329084813594818,
-0.02531537227332592,
-0.05575781688094139,
-0.015743695199489594,
-0.024026677012443542,
0.00806706678122282,
0.0027484979946166277,
-0.0025039161555469036,
-0.019382327795028687,
-0.014779578894376755,
-0.05296711623668671,
-0.007167118601500988,
-0.05082947388291359,
-0.0392417348921299,
-0.07795336097478867,
0.027816107496619225,
-0.01893433928489685,
-0.01626436971127987,
-0.016807274892926216,
-0.03872941806912422,
0.013605818152427673,
-0.049787070602178574,
-0.008924992755055428,
-0.05447349324822426,
-0.015682918950915337,
-0.035176195204257965,
-0.004002649337053299,
0.046429771929979324,
0.009573498740792274,
0.043654896318912506,
-0.033463165163993835,
0.026087215170264244,
0.021424230188131332,
-0.027437154203653336,
-0.014523572288453579,
-0.0011634738184511662,
0.012923204340040684,
-0.005638026166707277,
0.013293159194290638,
0.015276548452675343,
0.03895014524459839,
-0.004718353971838951,
0.0053511266596615314,
0.0054633039981126785,
0.035093724727630615,
0.01216723583638668,
-0.031845320016145706,
-0.044983163475990295,
-0.05101468786597252,
-0.007987619377672672,
0.010964685119688511,
0.038370925933122635,
-0.0017041307874023914,
0.036531683057546616,
0.048268504440784454,
0.022436924278736115,
-0.026071272790431976,
0.05649903789162636,
0.039709966629743576,
-0.007366970181465149,
-0.00750390999019146,
-0.010789650492370129,
0.01038974430412054,
-0.022673513740301132,
0.018748244270682335,
0.00869633536785841,
0.004880066495388746,
-0.022743916139006615,
0.03909829631447792,
-0.0370294451713562,
-0.019985850900411606,
-0.03951171040534973,
-0.03802366554737091,
-0.03406239300966263,
0.025665992870926857,
-0.002665353938937187,
-0.01316853053867817,
0.013026080094277859,
0.04693745821714401,
0.02487567812204361,
0.03256848827004433,
-0.013609840534627438,
-0.06607303768396378,
0.015077884308993816,
0.048760976642370224,
-0.028526239097118378,
0.0032727322541177273,
-0.01486078929156065,
-0.03427587449550629,
-0.04416288807988167,
0.050937991589307785,
-0.02084137126803398,
0.024194512516260147,
-0.03785167261958122,
0.020892616361379623,
0.005288111977279186,
-0.044755734503269196,
-0.008171726949512959,
0.01686594821512699,
0.00992116704583168,
0.029409395530819893,
-0.00850201677531004,
0.048401035368442535,
-0.03600399196147919,
0.02497905306518078,
0.0343981496989727,
0.03562786430120468,
-0.0007669336046092212,
0.010657746344804764,
-0.018522970378398895,
-0.005782986059784889,
-0.038574714213609695,
-0.03873321786522865,
0.024122394621372223,
0.02086375281214714,
-0.001146786380559206,
0.03397567197680473,
-0.010439259931445122,
-0.07047595083713531,
0.021314293146133423,
-0.026867179200053215,
-0.00427237106487155,
0.013177730143070221,
-0.02905510924756527,
0.08731512725353241,
0.03157544136047363,
0.026523539796471596,
0.027503740042448044,
0.004289822652935982,
0.016263891011476517,
0.03578152135014534,
-0.010656611993908882,
0.0163736492395401,
-0.04720265790820122,
-0.012164031155407429,
-0.032786887139081955,
0.0015301192179322243,
-0.0269105676561594,
0.05468423664569855,
-0.022755883634090424,
-0.004197786562144756,
0.000009426890756003559,
-0.016562670469284058,
-0.01692165806889534,
0.0070363255217671394,
0.0034461726900190115,
0.012620908208191395,
-0.02907402813434601,
0.04520007222890854,
0.016714241355657578,
-0.02493605762720108,
0.05856723710894585,
-0.004089525900781155,
0.005354456603527069,
-0.012318586930632591,
-0.02438812144100666,
0.0559861958026886,
-0.024652890861034393,
-0.008404056541621685,
0.011437470093369484,
-0.055727168917655945,
0.06694450974464417,
-0.024343790486454964,
-0.019688857719302177,
-0.004830814898014069,
-0.06072954833507538,
-0.03161897882819176,
0.011506413109600544,
-0.0011238233419135213,
0.015452323481440544,
-0.025896241888403893,
0.022304927930235863,
-0.025030871853232384,
0.012434149160981178,
-0.09469927847385406,
-0.03432886675000191,
0.04007972031831741,
0.015057679265737534,
0.009316043928265572,
-0.015385475009679794,
0.04855302348732948,
-0.029763324186205864,
0.013958703726530075,
-0.027912043035030365,
0.037766799330711365,
-0.028482137247920036,
0.0041873338632285595,
-0.002884061075747013,
0.015897609293460846,
0.053322236984968185,
-0.012159203179180622,
-0.023138660937547684,
-0.003223839681595564,
0.012577220797538757,
0.011258605867624283,
-0.028274456039071083,
0.04684436693787575,
-0.026449624449014664,
-0.04365115612745285,
0.007639841176569462,
-0.0007705619791522622,
-0.003658657893538475,
-0.04729434847831726,
-0.04058348387479782,
0.0005934252985753119,
-0.01869652234017849,
-0.016005324199795723,
-0.01963321678340435,
0.018112502992153168,
0.027168044820427895,
-0.007407741621136665,
0.0027968708891421556,
0.0026034810580313206,
-0.008006752468645573,
-0.028721336275339127,
0.03224708512425423,
0.011871482245624065,
0.014291332103312016,
0.060821712017059326,
0.05763435363769531,
-0.002520123263821006,
0.009995869360864162,
0.018687758594751358,
-0.01407656166702509,
0.02013181336224079,
-0.02532123774290085,
-0.01573842391371727,
0.022663278505206108,
-0.0052398634143173695,
-0.03893521800637245,
-0.0385088250041008,
-0.009994909167289734,
-0.018974924460053444,
0.015207663178443909,
-0.014483531937003136,
0.0075383917428553104,
0.02055228315293789,
-0.0026050335727632046,
0.03369065374135971,
-0.023510094732046127,
-0.017697835341095924,
0.020573634654283524,
0.03580658137798309,
0.03170717507600784,
-0.04068728908896446,
0.023217974230647087,
0.026872551068663597,
0.05109884589910507,
0.016677135601639748,
0.017705798149108887,
0.0323374979197979,
0.02700485847890377,
0.05306440219283104,
-0.05072843283414841,
-0.027251992374658585,
0.030338983982801437,
-0.032876625657081604,
0.004422504920512438,
0.0010666722664609551,
-0.030303383246064186,
0.011224059388041496,
0.0013015890726819634,
0.0164798591285944,
0.011314081028103828,
-0.04130951687693596,
-0.006983117666095495,
0.030993279069662094,
0.007833168841898441,
0.05203184112906456,
0.03321637585759163,
-0.02228478156030178,
0.007935893721878529,
-0.006277375854551792,
0.020837124437093735,
0.010752757079899311,
-0.05636732280254364,
-0.025157926604151726,
-0.03463200479745865,
-0.044374700635671616,
0.018634963780641556,
-0.0006961232866160572,
-0.0005271194968372583,
-0.03284915164113045,
-0.017606865614652634,
0.005718857049942017,
-0.010609930381178856,
0.053975362330675125,
-0.03729809448122978,
0.04209005832672119,
-0.012880503199994564,
-0.0009244070388376713,
-0.002744996687397361,
0.048192985355854034,
0.08563520014286041,
0.08456508815288544,
0.01419774442911148,
-0.05025230720639229,
0.012127760797739029,
0.003630084451287985,
-0.011617496609687805,
-0.04125216230750084,
0.02037202939391136,
0.0019379525911062956,
0.018298646435141563,
-0.003552303183823824,
0.02708076313138008,
-0.0353877879679203,
-0.01535992044955492,
0.07179056853055954,
-0.03976961225271225,
-0.01931154914200306,
-0.0024620837066322565,
0.045189227908849716,
-0.018741389736533165,
0.02484017238020897,
-0.030916396528482437,
0.007178882136940956,
-0.004261419177055359,
-0.01400404330343008,
-0.018417606130242348,
0.031187620013952255,
0.005129904020577669,
0.010825916193425655,
-0.03364342451095581,
-0.010812194086611271,
0.015872592106461525,
-0.013293426483869553,
-0.034039270132780075,
-0.0037670971360057592,
-0.008515552617609501,
-0.009210571646690369,
0.03740052878856659,
0.03255818784236908,
0.0035204237792640924,
-0.0003444985777605325,
0.0002332271251361817,
-0.014323189854621887,
-0.047106847167015076,
0.0010412514675408602,
-0.010753910057246685,
0.0003177190665155649,
-0.04383466765284538,
0.02903052791953087,
-0.027351371943950653,
-0.009217381477355957,
-0.022251157090067863,
-0.048522286117076874,
-0.03141491860151291,
0.001598284812644124,
0.03326826170086861,
-0.001371143851429224,
-0.056903302669525146,
0.0002472068590577692,
0.01986730843782425,
-0.032046690583229065,
0.03202321380376816,
-0.012600100599229336,
0.003938022069633007,
-0.002666551386937499,
0.008126494474709034,
0.025493890047073364,
-0.003438930958509445,
0.0026036500930786133,
-0.016405651345849037,
-0.006314431317150593,
-0.05270542576909065,
-0.009525489062070847,
0.03138035163283348,
0.03787984326481819,
0.03963187336921692,
0.03488638997077942,
0.02002907730638981,
-0.037323616445064545,
0.007031341083347797,
0.023158330470323563,
-0.03470691293478012,
-0.0325842946767807,
0.013073171488940716,
-0.005276358220726252,
-0.0015983914490789175,
0.05746353417634964,
-0.030723856762051582,
-0.013750799000263214,
0.0360371358692646,
0.014159378595650196,
0.024849608540534973,
-0.010695175267755985,
0.028028098866343498,
-0.005268443841487169,
-0.019530342891812325,
0.006060754880309105,
-0.03072134591639042,
0.023828642442822456,
0.0327632836997509,
0.02178097330033779,
0.03143930435180664,
0.05449874699115753,
-0.03281252086162567,
0.024303698912262917,
0.03120039403438568,
-0.043417058885097504,
-0.04328610748052597,
0.001034779124893248,
0.019594069570302963,
-0.021304063498973846,
-0.023968107998371124,
-0.014002389274537563,
0.004490124527364969,
0.04927444830536842,
0.0024673014413565397,
-0.05271310359239578,
-0.0016705954913049936,
0.009143236093223095,
0.01854061521589756,
-0.03522096946835518,
-0.00041948663420043886,
-0.046792857348918915,
-0.026681123301386833,
0.005085458979010582,
0.002306353999301791,
-0.01317118015140295,
0.02006833255290985,
-0.024845492094755173,
-0.01023172028362751,
0.032363153994083405,
0.002332377014681697,
-0.012304832227528095,
-0.033645253628492355,
0.03909669816493988,
0.016490446403622627,
0.03745751455426216,
-0.0330619141459465,
-0.01124621368944645,
0.031222514808177948,
-0.06053057312965393,
-0.02640170231461525,
0.05377405509352684,
-0.014095916412770748,
0.08374747633934021,
0.055504828691482544,
-0.036588914692401886,
-0.008560809306800365,
0.014750799164175987,
-0.02966422028839588,
0.01795121096074581,
0.001167421112768352,
0.03174373134970665,
0.020425260066986084,
-0.01593618467450142,
0.013922370038926601,
0.04090459272265434,
-0.007886519655585289,
0.002385707339271903,
0.03111407533288002,
0.013562151230871677,
-0.008570889942348003,
-0.03906640037894249,
-0.013650591485202312,
0.010678550228476524,
0.02472907118499279,
0.034053970128297806,
0.02189605124294758,
0.01974075473845005,
-0.006636344827711582,
0.015571768395602703,
0.06303637474775314,
0.00832400657236576,
-0.0839780941605568,
0.0007627704762853682,
-0.009530585259199142,
0.004198260605335236,
0.026953035965561867,
-0.018484918400645256,
0.028449269011616707,
0.03204326331615448,
-0.06912342458963394,
0.039184458553791046,
-0.01655905321240425,
-0.015401369892060757,
-0.04352942854166031,
0.004321540705859661,
-0.03670639172196388,
0.07737303525209427,
0.029035024344921112,
0.04666865989565849,
0.004390267189592123,
0.03670009598135948,
-0.007905048318207264,
-0.04708092659711838,
0.002432673005387187,
0.008885728195309639,
-0.050391338765621185,
-0.0450773760676384,
0.07693925499916077,
-0.02615388296544552,
-0.022423312067985535,
0.02750258333981037,
-0.003115028841421008,
0.058828726410865784,
0.008015425875782967,
0.037078857421875,
0.0635216012597084,
0.028474999591708183,
0.017880180850625038,
-0.03401796892285347,
-0.03579934686422348,
0.034049708396196365,
0.0005692849517799914,
0.01962847262620926,
0.0024157764855772257,
-0.05531391501426697,
0.04527944326400757,
-0.017947116866707802,
-0.03271444886922836,
-0.008680328726768494,
0.004813923966139555,
0.006508145481348038,
0.006708841770887375,
0.004080780316144228,
0.014641783200204372,
-0.011730390600860119,
-0.010469825938344002,
-0.06060217693448067,
0.029152246192097664,
0.057461079210042953,
-0.0020178777631372213,
-0.030809275805950165,
-0.02336149848997593,
0.01678336225450039,
-0.022440491244196892,
0.03198064863681793,
0.0073626404628157616,
0.021684328094124794,
-0.06834135949611664,
0.023711424320936203,
0.020522169768810272,
-0.009152550250291824,
0.0020971198100596666,
-0.03016587533056736,
-0.0512867271900177,
0.00597550580278039,
-0.0028080185875296593,
0.011452371254563332,
0.011223654262721539,
-0.06769149005413055,
-0.026892855763435364,
-0.06375256180763245,
0.04850528761744499,
0.026086559519171715,
0.04227043315768242,
-0.014195399358868599,
-0.001937790191732347,
0.00645580654963851,
-0.013541976921260357,
0.055949244648218155,
0.012709498405456543,
-0.021816976368427277,
-0.007727343589067459,
0.006181489676237106,
0.044638097286224365,
-0.037902623414993286,
-0.0027795361820608377,
-0.04555203393101692,
-0.031620923429727554,
-0.030209405347704887,
-0.01251266896724701,
0.00015297625213861465,
0.003180787432938814,
0.0030072068329900503,
0.019289502874016762,
0.002781132236123085,
0.012981043197214603,
-0.0390479750931263,
0.07814233005046844,
-0.008497391827404499,
0.006221548654139042,
0.046582214534282684,
-0.017895469442009926,
0.031446266919374466,
0.005543536506593227,
0.008229495957493782,
-0.04152245074510574,
0.021915540099143982,
-0.020706433802843094,
-0.029587430879473686,
-0.02326130121946335,
0.02342534065246582,
0.011191599071025848,
0.004378702957183123,
-0.012000148184597492,
0.07528038322925568,
-0.011728656478226185,
0.018887430429458618,
0.03243499994277954,
0.01077753584831953,
0.08043748140335083,
-0.0065171546302735806,
0.008019466884434223,
0.053749844431877136,
-0.0096220001578331,
0.014364218339323997,
0.045471690595149994,
0.07175610214471817,
0.021008023992180824,
0.018226124346256256,
0.04644893482327461,
-0.0034753039944916964,
0.023606957867741585,
0.04046453535556793,
0.03987428545951843,
-0.024295557290315628,
0.0026768301613628864,
-0.0036257444880902767,
0.012379243969917297,
0.03512277826666832,
0.0231698639690876,
-0.015789814293384552,
0.11653903871774673,
-0.01593058742582798,
-0.009800957515835762,
-0.029026838019490242,
-0.010267432779073715,
-0.010080264881253242,
0.012969576753675938,
-0.009641014970839024,
0.06106165423989296,
-0.022953178733587265,
0.0015131817199289799,
-0.04878849536180496,
0.02913288027048111,
0.053123340010643005,
-0.06476617604494095,
-0.0008476402144879103,
0.00142185902222991,
0.039869047701358795,
0.01620495319366455,
0.0027418530080467463,
-0.05083989351987839,
-0.001807962078601122,
0.07275891304016113,
0.031241100281476974,
0.06670445203781128,
-0.024137532338500023,
0.013196307234466076,
-0.03819713741540909,
0.01426232885569334,
-0.013231509365141392,
-0.02433561347424984,
-0.050172217190265656,
0.04963197931647301,
-0.03483736887574196,
-0.011275332421064377
] |
<p>If I draw a control volume around a single light wave traveling through empty space, is entropy increasing as it goes? How is the degradation of the quality of energy manifested?</p>
| 9,396 |
[
-0.03363547474145889,
-0.025585226714611053,
0.0005612646345980465,
0.0013111397856846452,
0.06010570377111435,
0.04875935614109039,
-0.04534468054771423,
-0.02822602167725563,
-0.03497156873345375,
-0.032912109047174454,
0.016502244397997856,
0.032344669103622437,
0.03844105079770088,
0.0224261786788702,
0.005815145559608936,
-0.020218970254063606,
0.008652507327497005,
0.03356266766786575,
-0.00633847713470459,
-0.07456893473863602,
-0.03383491933345795,
0.02951548621058464,
0.012596235610544682,
-0.017214227467775345,
-0.03682970255613327,
0.04590166360139847,
0.0144806494936347,
0.00332211097702384,
0.010719241574406624,
0.038137756288051605,
-0.007897299714386463,
-0.02267954684793949,
0.004947924055159092,
0.054270196706056595,
0.04471999406814575,
-0.04942355304956436,
-0.055057402700185776,
-0.02344881370663643,
-0.003548293374478817,
-0.007260137237608433,
-0.04322189465165138,
-0.014275848865509033,
-0.0305953249335289,
0.05018507316708565,
-0.023111512884497643,
-0.0016967910341918468,
0.02201675996184349,
0.0010713073424994946,
0.048775624483823776,
-0.04395652562379837,
0.06774510443210602,
-0.010237487964332104,
0.06663666665554047,
0.02414395473897457,
-0.004062752239406109,
0.02537454664707184,
0.07289419323205948,
0.06458140909671783,
-0.0009993610437959433,
-0.019287969917058945,
0.0080167967826128,
0.03798893094062805,
-0.007322326768189669,
-0.0330304391682148,
-0.027982162311673164,
0.01151169091463089,
-0.013669158332049847,
-0.013820047490298748,
0.0300123430788517,
0.011699153110384941,
-0.017556237056851387,
0.008314931765198708,
0.03126492723822594,
-0.009399308823049068,
0.024056270718574524,
0.00906086340546608,
0.019909903407096863,
0.003826082916930318,
0.03894224390387535,
0.04524095356464386,
-0.0024903907906264067,
-0.019015755504369736,
0.015432513318955898,
0.061739496886730194,
0.007579028140753508,
-0.001586640253663063,
0.06998727470636368,
-0.034771598875522614,
0.032949309796094894,
0.027995528653264046,
0.014614204876124859,
0.011067081242799759,
0.006187626160681248,
0.033232372254133224,
-0.030433278530836105,
0.02316691353917122,
-0.04574334993958473,
0.03766244277358055,
0.006835562642663717,
-0.05339813604950905,
0.02803952619433403,
0.01735129952430725,
0.06684622168540955,
0.034250471740961075,
-0.015799323096871376,
-0.03463232144713402,
-0.04048420861363411,
0.03554632142186165,
0.01113211177289486,
-0.0023845306131988764,
-0.051100656390190125,
-0.018385153263807297,
0.01712125726044178,
0.004739114549010992,
0.008418395183980465,
-0.043206218630075455,
-0.011656582355499268,
0.004737878683954477,
0.05520198494195938,
0.06028999388217926,
0.03341130539774895,
-0.015358351171016693,
0.046686965972185135,
-0.02313910610973835,
-0.047190792858600616,
0.02204396203160286,
0.04006855562329292,
-0.035344239324331284,
-0.07139088213443756,
0.021469075232744217,
-0.012267365120351315,
0.0012120617320761085,
0.0028128051199018955,
-0.028653426095843315,
0.040545109659433365,
-0.011667774990200996,
-0.08650542795658112,
-0.05402619019150734,
0.03308870270848274,
-0.00852556899189949,
-0.04670972004532814,
-0.056498005986213684,
-0.019999710842967033,
0.020859282463788986,
0.09631628543138504,
-0.02632943168282509,
-0.002779200440272689,
-0.0037498341407626867,
0.05870350822806358,
0.011260935105383396,
-0.023040249943733215,
0.005289027467370033,
0.010039908811450005,
-0.024405399337410927,
0.023030685260891914,
-0.0746307522058487,
0.0067233555018901825,
0.07728544622659683,
-0.013463769108057022,
-0.04404207691550255,
0.021812643855810165,
-0.03834811598062515,
0.008832789026200771,
0.01052433717995882,
-0.022356409579515457,
-0.03602317348122597,
0.0919366180896759,
0.023488258942961693,
0.0378936268389225,
0.017795467749238014,
0.042033445090055466,
0.03108072467148304,
0.0032423280645161867,
-0.04268821328878403,
0.03870953992009163,
-0.010927143506705761,
0.02379446104168892,
-0.023982776328921318,
0.01993587054312229,
-0.0023311907425522804,
-0.002977155614644289,
-0.053068336099386215,
-0.0161419827491045,
0.002086751163005829,
0.035442400723695755,
0.009705415926873684,
-0.011517924256622791,
0.00017240589659195393,
0.0010728179477155209,
-0.04524863883852959,
0.005453269463032484,
-0.0724944993853569,
0.035798363387584686,
0.017699528485536575,
0.0012703747488558292,
0.0029051147866994143,
0.02136009745299816,
0.04783231019973755,
-0.030560988932847977,
-0.04120328277349472,
-0.017091555520892143,
0.033528510481119156,
-0.002016395563259721,
-0.020146572962403297,
0.04277738556265831,
0.06349498778581619,
0.056650444865226746,
0.04885387793183327,
0.02648930810391903,
-0.028827760368585587,
-0.0564422644674778,
0.018354615196585655,
0.008197286166250706,
0.041847072541713715,
-0.0003273700422141701,
0.0034045218490064144,
0.007997223176062107,
0.018946092575788498,
0.003790472634136677,
0.0004923081723973155,
0.0017040626844391227,
0.04587283357977867,
0.06415427476167679,
0.017187917605042458,
-0.01482989639043808,
0.06122180074453354,
-0.0069916811771690845,
0.010585053823888302,
-0.011563394218683243,
-0.04872588440775871,
-0.016699235886335373,
0.022268980741500854,
0.03605605661869049,
0.005541539750993252,
-0.04574867710471153,
0.002050993498414755,
0.022197909653186798,
0.013885670341551304,
0.04117878898978233,
0.00538350734859705,
-0.011092409491539001,
-0.035365231335163116,
0.019120242446660995,
0.03333800286054611,
0.030598575249314308,
0.011573432013392448,
0.034287866204977036,
-0.001942574279382825,
-0.0013711313949897885,
0.0025667117442935705,
0.0018158062594011426,
0.015654852613806725,
-0.0146521320566535,
0.011628933250904083,
0.002357977908104658,
-0.012642059475183487,
0.0149717191234231,
-0.031401727348566055,
-0.036380693316459656,
0.02740607038140297,
-0.015102805569767952,
0.013582051731646061,
-0.03319787606596947,
-0.009508070535957813,
0.005413532722741365,
0.015098866075277328,
-0.0018510938389226794,
-0.020277725532650948,
0.03385571017861366,
-0.009816771373152733,
0.030590364709496498,
-0.0034794271923601627,
0.03129465878009796,
-0.039242204278707504,
-0.032928578555583954,
0.048098113387823105,
0.01177123375236988,
0.023255661129951477,
-0.05857209861278534,
-0.06010870635509491,
-0.009227970615029335,
0.01841655746102333,
-0.020951516926288605,
0.018072661012411118,
-0.03450598940253258,
0.038610007613897324,
-0.010552222840487957,
-0.03512324020266533,
0.021452611312270164,
-0.031035780906677246,
0.019658274948596954,
0.03445500507950783,
-0.02776058204472065,
-0.061066243797540665,
-0.020668746903538704,
-0.014773664064705372,
-0.014972632750868797,
0.013109827414155006,
0.015687763690948486,
0.06442325562238693,
-0.03734997659921646,
-0.06774263828992844,
-0.01250914391130209,
-0.023756518959999084,
-0.014087174087762833,
-0.00582530302926898,
-0.015856359153985977,
0.017202245071530342,
-0.05648576095700264,
0.03549310937523842,
0.008183298632502556,
-0.03967675939202309,
-0.005669720005244017,
-0.0400753878057003,
-0.05291776731610298,
0.03890957310795784,
-0.018421540036797523,
0.05818386375904083,
-0.021591728553175926,
-0.02379104495048523,
0.05722556263208389,
0.05048895254731178,
-0.04381484165787697,
-0.02898283861577511,
-0.04386720433831215,
0.013810520991683006,
-0.03192654997110367,
-0.013876174576580524,
0.029361341148614883,
-0.010584976524114609,
0.01646883599460125,
0.03369602560997009,
0.04190865531563759,
0.006425849627703428,
0.020493600517511368,
-0.02950875088572502,
0.06081199273467064,
0.004906793124973774,
-0.010095512494444847,
0.01733456179499626,
0.03421058878302574,
-0.036097317934036255,
0.0023995181545615196,
0.01904940977692604,
0.0202905535697937,
0.04472844675183296,
-0.02395065687596798,
0.054635461419820786,
0.026380449533462524,
0.06237635016441345,
-0.031022483482956886,
0.05893167853355408,
-0.01646677404642105,
0.01574280485510826,
-0.02655899152159691,
0.008451081812381744,
0.03438739478588104,
-0.0035903218667954206,
0.00018821180856321007,
-0.012213480658829212,
0.05380580946803093,
-0.005369151942431927,
-0.006289247423410416,
0.018766403198242188,
0.013525583781301975,
0.02782459929585457,
0.014813130721449852,
-0.02556881681084633,
0.02391093038022518,
0.028170745819807053,
-0.01248965598642826,
-0.019379636272788048,
-0.04749821126461029,
-0.01862216554582119,
-0.04872667044401169,
-0.02440447174012661,
-0.022332603111863136,
0.03881307691335678,
0.004717392381280661,
0.05007222667336464,
0.022331155836582184,
0.018880905583500862,
0.05949186533689499,
-0.024785831570625305,
-0.08323171734809875,
0.009073575027287006,
-0.03758666291832924,
-0.008793811313807964,
-0.005399871151894331,
0.02706865407526493,
-0.0069338176399469376,
-0.054542459547519684,
-0.03633761778473854,
-0.022453218698501587,
-0.0049232910387218,
-0.061845771968364716,
-0.01675819605588913,
-0.04375133663415909,
-0.01682034693658352,
-0.0032383673824369907,
0.035043634474277496,
0.03785746172070503,
-0.024231690913438797,
-0.005850066896528006,
0.01777823269367218,
-0.02658156305551529,
-0.017972003668546677,
0.014815605245530605,
-0.009299971163272858,
-0.0038028417620807886,
0.023594114929437637,
0.030275309458374977,
-0.017137249931693077,
-0.04041772335767746,
0.032004840672016144,
-0.00854385457932949,
0.030556824058294296,
-0.022335980087518692,
-0.015780242159962654,
-0.01928713731467724,
-0.005122021306306124,
-0.024588074535131454,
0.006254265550523996,
0.026307225227355957,
0.04031560942530632,
0.051378779113292694,
0.007240649312734604,
0.005482807755470276,
-0.03919137269258499,
0.019749678671360016,
0.020544085651636124,
-0.022640109062194824,
-0.020619696006178856,
-0.03910546749830246,
-0.0017835405888035893,
-0.011678609997034073,
-0.05143437534570694,
0.014970210380852222,
0.017843883484601974,
-0.0275300070643425,
0.006117457989603281,
-0.04797998443245888,
0.015841837972402573,
-0.012297021225094795,
-0.016893260180950165,
-0.007191795390099287,
0.004439209587872028,
0.02490910328924656,
0.014281223528087139,
0.02100997604429722,
0.007970121689140797,
0.012855300679802895,
0.010856292210519314,
-0.0169797632843256,
-0.07101628929376602,
-0.017174987122416496,
0.02886654995381832,
0.015583564527332783,
0.005821347702294588,
0.03930152207612991,
-0.05937103554606438,
-0.051571596413850784,
0.017860760912299156,
-0.008432185277342796,
0.03757929056882858,
0.001342050265520811,
-0.01938609778881073,
-0.011020081117749214,
-0.05030594393610954,
-0.016724612563848495,
0.025858107954263687,
-0.02334529720246792,
0.020842328667640686,
-0.019944950938224792,
0.019635343924164772,
-0.008687928318977356,
0.03224813938140869,
0.0016603338299319148,
0.07792968302965164,
-0.013048335909843445,
-0.017459811642766,
0.006307420786470175,
0.015118521638214588,
-0.03213192895054817,
-0.056219976395368576,
0.02979874424636364,
0.0002756822796072811,
-0.00781888235360384,
0.04596618935465813,
-0.0017031986499205232,
-0.02385939657688141,
0.01733609102666378,
0.013370306231081486,
-0.006523199379444122,
-0.0011180880246683955,
-0.0027769743464887142,
0.07336194813251495,
-0.005082160700112581,
-0.00033490537316538393,
0.05343722179532051,
0.06741144508123398,
-0.003089053789153695,
0.025224978104233742,
0.0009337535593658686,
0.07728424668312073,
-0.007519298233091831,
0.010335932485759258,
-0.027998536825180054,
-0.027321722358465195,
-0.0350395105779171,
0.08329560607671738,
-0.016915226355195045,
0.008909276686608791,
0.026887036859989166,
-0.027812516316771507,
0.02434377744793892,
0.021065985783934593,
0.020575331524014473,
-0.02286401204764843,
-0.026607505977153778,
0.030187321826815605,
0.0038741561584174633,
-0.02355976402759552,
0.008997687138617039,
-0.019563497975468636,
0.0277040284126997,
0.03915458917617798,
-0.020757269114255905,
0.03330860659480095,
-0.06573006510734558,
-0.006801644340157509,
-0.01376690436154604,
-0.013629589229822159,
0.06110583245754242,
-0.021449843421578407,
0.019862733781337738,
0.03749417886137962,
-0.04312339052557945,
-0.02271956577897072,
-0.011450258083641529,
-0.04879550635814667,
0.021551817655563354,
-0.03310263901948929,
0.04348825663328171,
-0.0009992033010348678,
-0.004295310005545616,
-0.09206978231668472,
-0.06095510721206665,
-0.0006826739409007132,
0.00673516234382987,
0.007184040267020464,
-0.023023616522550583,
0.01117778941988945,
-0.04843498021364212,
-0.024570925161242485,
-0.01684659905731678,
-0.007607558276504278,
-0.00916646420955658,
0.0034840276930481195,
-0.005391429644078016,
-0.0003412058867979795,
0.02548781968653202,
-0.005664571188390255,
-0.05264529958367348,
0.011297054588794708,
-0.029096942394971848,
-0.03636876866221428,
0.0012504459591582417,
0.02117489092051983,
-0.022080251947045326,
-0.04483699053525925,
0.006398933008313179,
-0.0035643817391246557,
0.024884263053536415,
-0.01881154254078865,
0.0011590276844799519,
0.0073862201534211636,
-0.009241168387234211,
-0.005690306890755892,
0.0007781057502143085,
0.016079243272542953,
-0.02000090293586254,
0.025673246011137962,
0.02505658008158207,
-0.020073870196938515,
-0.0005736055318266153,
-0.07668114453554153,
0.018348852172493935,
0.03474909067153931,
0.003674659878015518,
0.004462671931833029,
0.0813855305314064,
0.00977836549282074,
-0.024899177253246307,
-0.015714559704065323,
-0.012013895437121391,
-0.029922708868980408,
-0.01329097431153059,
0.025395467877388,
0.01664983667433262,
0.004687583539634943,
-0.015574070625007153,
-0.037471335381269455,
-0.04194315895438194,
-0.03079131618142128,
0.061204761266708374,
-0.014593558385968208,
0.040772393345832825,
0.03476100414991379,
-0.006496853660792112,
0.013619067147374153,
-0.019886547699570656,
0.0026814413722604513,
0.03348537161946297,
-0.004841715097427368,
0.027058862149715424,
-0.011817852035164833,
-0.04109184443950653,
-0.011048915795981884,
0.04618286341428757,
-0.0565054714679718,
-0.001873001572676003,
0.0025627505965530872,
0.030452413484454155,
0.022875603288412094,
-0.02255626581609249,
-0.040669020265340805,
0.030660158023238182,
-0.05615625157952309,
0.03815486654639244,
-0.01589011214673519,
0.014238097704946995,
0.012698488309979439,
-0.0018221264472231269,
-0.032543424516916275,
-0.02147763781249523,
-0.013488811440765858,
-0.06343279778957367,
-0.005872168578207493,
-0.03722310811281204,
0.012422640807926655,
0.0031663228292018175,
0.008356953039765358,
0.007501988671720028,
0.00617448752745986,
-0.02007010206580162,
0.0034506209194660187,
-0.045719608664512634,
-0.03603857383131981,
-0.02968067117035389,
-0.03867515176534653,
0.050946906208992004,
0.004550453275442123,
-0.017621299251914024,
-0.005227626767009497,
-0.021170848980545998,
0.017691483721137047,
0.01606878824532032,
0.003997002728283405,
0.025652043521404266,
0.02261543832719326,
0.0006213838933035731,
0.06233171373605728,
-0.023861879482865334,
0.0395735464990139,
0.10853226482868195,
0.042183369398117065,
0.013719704002141953,
-0.0652717724442482,
0.0128013975918293,
0.0003764720167964697,
0.03055199235677719,
-0.0202627070248127,
0.02347980998456478,
0.016922764480113983,
0.026530874893069267,
0.03966173902153969,
0.039863843470811844,
0.0020418232306838036,
-0.0013931771973147988,
0.046778470277786255,
-0.049735262989997864,
-0.018459174782037735,
0.032122962176799774,
0.021380992606282234,
-0.007625596597790718,
0.061558742076158524,
-0.04722224175930023,
0.006931522861123085,
-0.0203957948833704,
-0.010839438997209072,
-0.005576301831752062,
-0.07757337391376495,
0.034716419875621796,
-0.009063074365258217,
-0.020922981202602386,
0.0012443277519196272,
0.019980324432253838,
-0.020902089774608612,
-0.06112932041287422,
0.018792200833559036,
0.02775651216506958,
0.016865074634552002,
-0.021624529734253883,
0.05571664497256279,
0.03803277015686035,
0.007411525584757328,
-0.02115124836564064,
0.012804665602743626,
-0.029948173090815544,
-0.03026529960334301,
0.019621592015028,
0.004720056429505348,
-0.025415640324354172,
0.0056339106522500515,
-0.0068846289068460464,
0.016519151628017426,
-0.021537676453590393,
-0.08132556080818176,
-0.02360408566892147,
-0.014714375138282776,
0.048188138753175735,
0.017086086794734,
-0.014709191396832466,
0.009381928481161594,
-0.014092429541051388,
0.007599568460136652,
0.02942381240427494,
-0.023243892937898636,
0.0020030797459185123,
0.013545285910367966,
0.026942502707242966,
0.03558005392551422,
-0.031538523733615875,
-0.033975061029195786,
-0.05994756519794464,
-0.008415298536419868,
-0.051809899508953094,
-0.027130169793963432,
0.008201519027352333,
0.04833624139428139,
-0.014370318502187729,
0.022554807364940643,
0.0037131740245968103,
0.0009006622130982578,
-0.07992347329854965,
0.01270422711968422,
-0.01822918839752674,
-0.04118841141462326,
-0.010240837931632996,
0.008662564679980278,
0.02210219018161297,
0.04634420946240425,
-0.0018986266804859042,
-0.025258924812078476,
0.050710562616586685,
0.032288581132888794,
0.03605112433433533,
-0.004297175910323858,
-0.00885278545320034,
0.023039869964122772,
-0.0143998758867383,
0.007786684203892946,
0.0009269078145734966,
0.022670947015285492,
0.0008517112000845373,
-0.00010266834578942508,
0.008498105220496655,
0.0307339858263731,
-0.01356302760541439,
-0.0054328409023582935,
0.01264466904103756,
-0.036775022745132446,
-0.01139721181243658,
0.013508396223187447,
0.0050406851805746555,
-0.006542186718434095,
-0.04306548088788986,
-0.01549326628446579,
0.0035193050280213356,
-0.011521829292178154,
0.010768297128379345,
0.0013584836851805449,
0.0013427508529275656,
0.0037708815652877092,
0.020547974854707718,
-0.052903153002262115,
-0.04955632612109184,
-0.055072687566280365,
-0.006669412367045879,
0.00843433290719986,
0.027619492262601852,
0.0027142283506691456,
0.03435102105140686,
0.0033851454500108957,
-0.011447293683886528,
0.012245042249560356,
0.02394368313252926,
0.014192047528922558,
0.0015936661511659622,
0.029515622183680534,
0.0009571118280291557,
0.05290772020816803,
-0.013600688427686691,
-0.05170052871108055,
0.026250062510371208,
-0.030618466436862946,
-0.030229896306991577,
0.006807640660554171,
-0.006993507966399193,
0.023581044748425484,
0.017238711938261986,
-0.035642918199300766,
0.013773113489151001,
0.03225128352642059,
0.018387537449598312,
-0.01214937400072813,
0.0011723116040229797,
-0.04143506661057472,
-0.010925262235105038,
-0.019156470894813538,
0.0287934597581625,
-0.0491994246840477,
-0.006165242753922939,
0.043085016310214996,
0.04020102322101593,
-0.027179138734936714,
-0.019705357030034065,
-0.002211556537076831,
-0.03814743459224701,
0.005538849160075188,
-0.006980597972869873,
0.004951790906488895,
0.03033517301082611,
0.04478117823600769,
-0.006719004828482866,
0.027651706710457802,
0.035955388098955154,
-0.007574119605123997,
-0.1146916076540947,
-0.0074612139724195,
-0.015787560492753983,
0.00031560350907966495,
0.008867562748491764,
-0.027844281867146492,
0.0527285598218441,
-0.007034379988908768,
-0.054849520325660706,
0.01941562443971634,
-0.016573194414377213,
-0.011499542742967606,
-0.06516444683074951,
0.029545363038778305,
-0.021933170035481453,
0.028584439307451248,
0.059735726565122604,
0.05916537716984749,
0.006723723839968443,
0.012764542363584042,
-0.02241511642932892,
0.007593047805130482,
0.009088865481317043,
0.042087212204933167,
-0.006340858526527882,
0.01844768412411213,
-0.006060982588678598,
0.0074964361265301704,
0.00607532961294055,
-0.016168994829058647,
-0.025619905441999435,
0.013742534443736076,
-0.009122946299612522,
0.018053805455565453,
0.001715538208372891,
0.047242868691682816,
-0.0024252422153949738,
-0.016393575817346573,
-0.02785700000822544,
0.01876678504049778,
0.028186939656734467,
-0.0286276713013649,
-0.01925676129758358,
0.012992159463465214,
0.021039394661784172,
-0.042046044021844864,
-0.010303360410034657,
0.03387957438826561,
-0.020929677411913872,
0.006730653811246157,
0.027905255556106567,
-0.004012567922472954,
0.03308827057480812,
-0.006536718457937241,
0.033197060227394104,
-0.0504910871386528,
-0.021763740107417107,
0.005232279188930988,
-0.0032517993822693825,
-0.030887585133314133,
-0.029669269919395447,
0.020804865285754204,
-0.049383725970983505,
0.034390442073345184,
-0.001406669383868575,
0.008190199732780457,
-0.05805136263370514,
0.02580551989376545,
-0.026426617056131363,
-0.0013073666486889124,
0.03173675015568733,
-0.0509926974773407,
-0.017809826880693436,
0.03421467915177345,
0.03820981830358505,
0.001736595411784947,
-0.019529616460204124,
-0.042579565197229385,
-0.07660959661006927,
-0.057732049375772476,
0.02889981120824814,
-0.01787085086107254,
-0.002608852693811059,
-0.034119557589292526,
0.016274454072117805,
-0.023253077641129494,
0.034250423312187195,
0.055447984486818314,
0.008560788817703724,
-0.037407029420137405,
0.035792842507362366,
-0.003738837782293558,
0.05453015863895416,
-0.03512856736779213,
-0.0015614938456565142,
-0.02684926800429821,
-0.004116590600460768,
-0.03643341735005379,
0.0020094283390790224,
-0.013549614697694778,
0.016039971262216568,
0.03020918183028698,
-0.003350730985403061,
-0.00027325074188411236,
-0.033964090049266815,
-0.018023818731307983,
0.05395141616463661,
0.0005435061757452786,
-0.02399212308228016,
0.05574547126889229,
-0.04537614807486534,
0.03654206544160843,
0.05992495268583298,
0.008172855712473392,
-0.04206002876162529,
0.012285604141652584,
-0.011104440316557884,
0.0012813053326681256,
0.015511427074670792,
-0.01492592878639698,
0.04084518179297447,
-0.02533831261098385,
-0.041627198457717896,
0.0195140577852726,
-0.0747218057513237,
0.018788298591971397,
0.021451199427247047,
0.006064004264771938,
0.03179720789194107,
-0.021416151896119118,
0.022867051884531975,
-0.002965896390378475,
0.05579223483800888,
-0.020633816719055176,
0.06764353066682816,
0.03867347911000252,
0.022013138979673386,
0.0025590432342141867,
0.03409300372004509,
-0.025195101276040077,
0.004788719117641449,
0.023841582238674164,
0.017080500721931458,
-0.033316440880298615,
-0.04790659621357918,
0.015850240364670753,
-0.006858180742710829,
-0.02522713877260685,
0.025230826810002327,
0.00810808315873146,
0.06006405130028725,
-0.004060069099068642,
0.02673434279859066,
-0.03347272425889969,
-0.01218430045992136,
-0.010926984250545502,
0.0059850625693798065,
0.030634727329015732,
0.0731349065899849,
0.029569970443844795,
-0.015712076798081398,
-0.06136621907353401,
-0.026071935892105103,
0.000902122410479933,
-0.05018807575106621,
0.04139520972967148,
0.0005327224498614669,
-0.033689215779304504,
0.0026980736292898655,
-0.00393447931855917,
-0.01837565004825592,
-0.04214373230934143,
0.0071843466721475124,
0.03944000229239464,
0.014711222611367702,
0.041974008083343506,
-0.020157698541879654,
-0.022877927869558334,
0.07317637652158737,
-0.02559751458466053,
-0.005448661744594574,
-0.005563946440815926,
0.03818210959434509,
-0.014692661352455616,
0.020774999633431435
] |
<p>Let's have the Lagrangian
$$
L = L_{0} + \lambda V , \qquad (1)
$$
where $\lambda$ is constant which is small in the next senses: if $\lambda$ is dimensionless, it means that $\lambda < 1$; if it has dimension $[\lambda ] = l^{-n}$, it means that it is small in compare with characteristic energy of the free states: $\frac{\lambda}{ E^{n}} < 1$. </p>
<p>How to connect the dimension of $\lambda$ with renormalizability of theory which is given by $(1)$? Is a dimensionless of $\lambda$ the necessary condition for renormalizability of the theory? </p>
| 9,397 |
[
0.01581980288028717,
0.017696157097816467,
0.004907728638499975,
0.023052629083395004,
0.01436859741806984,
0.022013245150446892,
-0.022055186331272125,
-0.043726664036512375,
0.01943618804216385,
-0.05581105500459671,
0.035615306347608566,
-0.010947464033961296,
0.03609646111726761,
0.031762126833200455,
0.017431268468499184,
0.022753281518816948,
-0.008934034034609795,
-0.006938441190868616,
-0.0025940544437617064,
0.0016341587761417031,
0.015588427893817425,
0.03376830369234085,
0.007683631964027882,
0.011087408289313316,
-0.05179470404982567,
0.02160423994064331,
0.014106864109635353,
0.03918654844164848,
-0.0036860485561192036,
0.048665259033441544,
-0.005009573884308338,
-0.019113436341285706,
0.019487392157316208,
0.03276429325342178,
-0.02423451840877533,
0.013047381304204464,
-0.03037896938621998,
-0.03412947803735733,
0.03759731724858284,
-0.003212439129129052,
-0.03428864851593971,
-0.04502411186695099,
0.003952185157686472,
0.03388141095638275,
-0.029709959402680397,
0.045660827308893204,
0.027187563478946686,
-0.06034625321626663,
0.06066056713461876,
-0.03220631927251816,
0.04698847606778145,
0.02324143797159195,
0.05238175392150879,
-0.01660311408340931,
0.014962850138545036,
-0.03706159442663193,
0.04338608682155609,
0.07146873325109482,
-0.0005300180055201054,
-0.033036693930625916,
-0.03129676356911659,
-0.047197870910167694,
0.03357952460646629,
-0.013949098065495491,
-0.015497839078307152,
0.017052680253982544,
-0.016511553898453712,
0.009428439661860466,
0.028794247657060623,
-0.0050052376464009285,
-0.012739562429487705,
-0.02072652243077755,
0.012024307623505592,
0.009964751079678535,
0.009051519446074963,
0.020992431789636612,
-0.005953209009021521,
-0.009755556471645832,
0.029416078701615334,
0.034024469554424286,
0.012484840117394924,
0.04586547613143921,
0.027440601959824562,
0.03804294392466545,
-0.004715924616903067,
-0.019664118066430092,
0.040040578693151474,
0.015899496152997017,
0.008083865977823734,
0.04353053867816925,
-0.014996941201388836,
0.00696326419711113,
0.05204446241259575,
-0.03596729785203934,
-0.02617439441382885,
0.04973486065864563,
0.006080748047679663,
0.01835259422659874,
0.008422787301242352,
0.01284120138734579,
-0.028168434277176857,
-0.05020952597260475,
0.01509135402739048,
0.049528032541275024,
0.00218445947393775,
-0.024114936590194702,
-0.05272839218378067,
0.020175553858280182,
-0.02272031642496586,
-0.019817139953374863,
-0.036235708743333817,
-0.0021121921017766,
-0.009123594500124454,
0.014248616062104702,
0.01776881143450737,
-0.04300641268491745,
0.0007021451601758599,
-0.035545289516448975,
0.06857939809560776,
0.08520276099443436,
0.03131408989429474,
-0.019540993496775627,
0.03553042560815811,
0.008252870291471481,
-0.06729225814342499,
0.011976211331784725,
0.05865541473031044,
-0.024457363411784172,
-0.021497344598174095,
0.007473140023648739,
0.00966449361294508,
-0.024105079472064972,
0.011964097619056702,
0.028792433440685272,
0.06180604547262192,
0.01752985268831253,
-0.0939021185040474,
-0.02705705352127552,
0.04167480394244194,
-0.0051586925983428955,
-0.03554690629243851,
-0.06690620630979538,
0.0022535689640790224,
0.01844244822859764,
0.08408866822719574,
-0.01808556169271469,
0.05649417266249657,
0.01869838312268257,
-0.007801807019859552,
0.011570739559829235,
-0.02141767553985119,
-0.03054182231426239,
0.013013658113777637,
-0.04199451580643654,
-0.01579180546104908,
-0.05052963271737099,
0.009394997730851173,
0.024396395310759544,
-0.0033972510136663914,
-0.008493294008076191,
0.06409268081188202,
-0.049111802130937576,
0.005030129570513964,
0.004649733193218708,
-0.01885979250073433,
-0.0005531108472496271,
0.034145452082157135,
0.016211090609431267,
0.0338766947388649,
0.03749692440032959,
0.009107908234000206,
-0.01941515877842903,
0.010950642637908459,
0.047175418585538864,
0.025493644177913666,
0.03817082569003105,
-0.04963177070021629,
-0.037363048642873764,
0.026063788682222366,
0.009733211249113083,
-0.0739607959985733,
-0.06215720623731613,
-0.026187926530838013,
0.02622244507074356,
0.0099855437874794,
0.050508830696344376,
-0.007233012933284044,
0.03700514882802963,
0.015852011740207672,
-0.050021134316921234,
-0.0014956811210140586,
-0.05845211073756218,
0.015701385214924812,
0.023748178035020828,
-0.022255996242165565,
0.04872465506196022,
0.004486937075853348,
-0.000008577147127653006,
-0.0381903275847435,
0.001337356399744749,
-0.009427547454833984,
0.030144089832901955,
-0.009312671609222889,
-0.009646894410252571,
0.008336699567735195,
0.03324255719780922,
0.03299276530742645,
-0.003589967265725136,
0.05769265815615654,
0.00637068459764123,
-0.04167398810386658,
0.04216217249631882,
-0.00339056015945971,
0.032370831817388535,
-0.041940174996852875,
0.013462650589644909,
-0.008912784047424793,
-0.009981010109186172,
-0.019909679889678955,
0.057719938457012177,
-0.03319369629025459,
0.054243795573711395,
0.019383743405342102,
0.007994120009243488,
0.03885392099618912,
0.03072301112115383,
-0.002360064070671797,
0.0023011136800050735,
-0.010497326031327248,
-0.023779137060046196,
-0.058720897883176804,
-0.01865251734852791,
0.03286634013056755,
0.07102171331644058,
-0.02448047511279583,
-0.0021390507463365793,
0.03711014240980148,
0.031113987788558006,
0.044142138212919235,
0.013983123935759068,
-0.02162986621260643,
-0.03727935999631882,
0.028755122795701027,
0.04034270718693733,
0.009863736107945442,
-0.01608791947364807,
-0.010621776804327965,
0.03785393014550209,
0.05663175880908966,
-0.005703088827431202,
-0.015591822564601898,
0.04812363162636757,
-0.007527903188019991,
-0.018180247396230698,
-0.00440801540389657,
-0.0004330609808675945,
0.031940944492816925,
-0.035988517105579376,
0.019658248871564865,
0.007780537474900484,
-0.0032759597525000572,
0.02480217255651951,
-0.0420302152633667,
-0.020595883950591087,
0.022613877430558205,
0.02244008146226406,
-0.03203023225069046,
-0.02368202619254589,
0.010263561271131039,
-0.029733652248978615,
-0.0016639740206301212,
-0.011024853214621544,
-0.027547337114810944,
-0.03879806026816368,
0.02860044687986374,
0.058326009660959244,
-0.04984673112630844,
0.008143437094986439,
-0.000009540260180074256,
-0.04036770388484001,
0.03347132354974747,
-0.005195776931941509,
0.03138263151049614,
0.02209574170410633,
-0.0143082644790411,
0.026917757466435432,
-0.06557144969701767,
-0.020280921831727028,
0.006751521024852991,
-0.02055925503373146,
0.05745711922645569,
0.0010423635831102729,
-0.0371035598218441,
-0.038055870682001114,
-0.034336935728788376,
-0.0367191918194294,
0.035495053976774216,
-0.003888788865879178,
-0.03293333202600479,
0.07309457659721375,
0.0030462373979389668,
-0.0351373590528965,
-0.032944802194833755,
-0.0340275801718235,
-0.020048368722200394,
-0.021407678723335266,
0.0007870244444347918,
0.015176155604422092,
-0.028204241767525673,
0.041831109672784805,
0.03550892695784569,
-0.014581892639398575,
0.010779610835015774,
-0.06200315058231354,
-0.042110905051231384,
0.013277249410748482,
0.01785021647810936,
0.049661785364151,
-0.015394140034914017,
-0.022977028042078018,
0.059702515602111816,
0.03698134049773216,
-0.025565311312675476,
-0.006890685763210058,
-0.012596695683896542,
-0.03513012081384659,
-0.04884709417819977,
0.025408217683434486,
0.0019783368334174156,
0.023668162524700165,
0.03488796204328537,
0.03302902728319168,
0.03611447662115097,
0.0026240067090839148,
0.010296438820660114,
-0.0021700062789022923,
0.033778779208660126,
0.03838616609573364,
0.023522939532995224,
0.02985973097383976,
0.01748514547944069,
-0.031490426510572433,
0.007067137397825718,
0.004993516951799393,
0.038354143500328064,
-0.01034617330878973,
-0.046155896037817,
0.05759964883327484,
0.029190748929977417,
0.04523196071386337,
-0.009818597696721554,
0.01934809237718582,
0.021201908588409424,
0.0036256229504942894,
0.006320960819721222,
0.037326112389564514,
0.008533132262527943,
-0.03794369846582413,
-0.0039572748355567455,
0.018370019271969795,
0.03104354813694954,
-0.037985559552907944,
-0.02543766051530838,
-0.01913607306778431,
-0.01199641078710556,
0.02284322679042816,
-0.01761942356824875,
-0.022487608715891838,
0.03160502389073372,
0.04236823320388794,
0.04177527874708176,
-0.04871070757508278,
-0.045894160866737366,
-0.00736113591119647,
-0.058242037892341614,
-0.018355660140514374,
-0.005220917984843254,
0.06568706780672073,
-0.012058022432029247,
0.03969160467386246,
0.03703304007649422,
0.02474096044898033,
-0.02291868068277836,
-0.002033710014075041,
-0.08162631094455719,
-0.008719072677195072,
-0.05187774822115898,
0.004479691386222839,
0.026259563863277435,
0.006937510333955288,
0.020419137552380562,
-0.023789525032043457,
-0.040969762951135635,
0.01816888339817524,
-0.0062024882063269615,
-0.04347744211554527,
0.007840557023882866,
-0.03202947974205017,
-0.011622197926044464,
-0.015216275118291378,
0.02919764071702957,
0.020617913454771042,
-0.01042733434587717,
-0.0017714969580993056,
0.03895202651619911,
-0.026162298396229744,
-0.04398677498102188,
0.010202845558524132,
0.017464371398091316,
0.008156639523804188,
0.035434823483228683,
0.053653083741664886,
0.014737523160874844,
-0.012325266376137733,
0.01536155678331852,
0.05383610725402832,
0.0480356328189373,
0.018709536641836166,
0.034839339554309845,
0.011169771663844585,
-0.07367981225252151,
-0.016896618530154228,
-0.008416226133704185,
0.06492272764444351,
0.04232135787606239,
-0.02748292312026024,
0.04596523195505142,
0.03250887989997864,
-0.03069981560111046,
0.05532602220773697,
0.035346075892448425,
0.01316098589450121,
-0.04584759846329689,
-0.029881775379180908,
0.016512515023350716,
-0.008498769253492355,
0.0028314145747572184,
-0.0029611506033688784,
-0.01984231360256672,
-0.03878730162978172,
-0.0042118895798921585,
-0.0075709936209023,
-0.015128452330827713,
-0.05127769708633423,
-0.017424700781702995,
0.008191147819161415,
0.0455721952021122,
-0.03546692430973053,
0.008658532053232193,
-0.0022125656250864267,
0.0183380339294672,
-0.003903844626620412,
0.031177107244729996,
0.0006406058673746884,
-0.049643613398075104,
-0.00292190071195364,
0.022103777155280113,
0.06185918301343918,
-0.023506226018071175,
-0.0036118943244218826,
-0.08575437217950821,
-0.02374047040939331,
0.061134546995162964,
-0.023194096982479095,
0.03969305381178856,
0.004543410148471594,
-0.006807592231780291,
-0.012572296895086765,
-0.01857014186680317,
-0.02710915543138981,
0.01818578504025936,
0.010367284528911114,
0.03191521018743515,
-0.04404984787106514,
0.0067987386137247086,
-0.02974892593920231,
0.029316557571291924,
0.02077002078294754,
0.06355412304401398,
-0.010129567235708237,
0.009655649773776531,
-0.016643717885017395,
0.03233020007610321,
-0.013757527805864811,
-0.09963858872652054,
-0.024213027209043503,
0.039767589420080185,
-0.03139263764023781,
-0.00006537744047818705,
-0.016172289848327637,
-0.047954022884368896,
0.00785115547478199,
0.00780729902908206,
-0.01697819121181965,
0.007647186517715454,
-0.04941493272781372,
0.06558553129434586,
0.019784070551395416,
-0.03878550976514816,
0.04436581954360008,
0.04136257246136665,
0.026959571987390518,
0.02148309350013733,
-0.016780655831098557,
0.03291352838277817,
-0.007040599826723337,
0.022248677909374237,
-0.053867049515247345,
-0.010399972088634968,
0.004203129094094038,
0.035262178629636765,
-0.022016888484358788,
0.006942312698811293,
-0.011235488578677177,
-0.021266359835863113,
-0.04780542105436325,
0.019111337140202522,
0.04101424664258957,
-0.060468338429927826,
0.02807464823126793,
0.031363923102617264,
0.010433956980705261,
-0.019195154309272766,
-0.002752608386799693,
0.000011957206879742444,
0.012776510789990425,
0.033687204122543335,
0.005187964998185635,
0.009588444605469704,
-0.009923704899847507,
-0.01083826832473278,
0.007782227825373411,
-0.028154345229268074,
0.049688588827848434,
0.006972805596888065,
-0.00680534215644002,
-0.04436216503381729,
-0.03818095102906227,
-0.027480071410536766,
-0.025413241237401962,
0.010588135570287704,
0.019175583496689796,
-0.03447232022881508,
0.0034823990426957607,
-0.005677450448274612,
-0.01873188093304634,
-0.124855637550354,
-0.010915900580585003,
-0.029320748522877693,
0.00675407936796546,
-0.02348906919360161,
-0.008525153622031212,
-0.03138977661728859,
-0.04462762922048569,
-0.03668740764260292,
0.00034331053029745817,
0.051842913031578064,
-0.04148740693926811,
-0.01866273023188114,
0.017531171441078186,
0.0388917475938797,
0.032419245690107346,
-0.0018852794310078025,
-0.0035883167292922735,
0.006193382199853659,
-0.01459868811070919,
-0.030414411798119545,
-0.0034037018194794655,
0.06070355325937271,
-0.02010411210358143,
-0.03281771391630173,
0.008014317601919174,
-0.020457176491618156,
0.018208397552371025,
-0.030401157215237617,
-0.04268253594636917,
0.021153245121240616,
-0.000688812171574682,
0.008118735626339912,
-0.012443352490663528,
-0.020647255703806877,
0.019698316231369972,
0.04714495688676834,
0.008240753784775734,
-0.008403260260820389,
-0.014972919598221779,
-0.04684486612677574,
0.03533444553613663,
0.018377142027020454,
0.027942432090640068,
0.01913381554186344,
0.04642949625849724,
-0.031082578003406525,
-0.007782495114952326,
0.026797397062182426,
-0.013292291201651096,
-0.0035497795324772596,
0.028112133964896202,
0.028323005884885788,
0.018637923523783684,
0.011654980480670929,
-0.0208065714687109,
-0.038604553788900375,
-0.054386891424655914,
0.018787648528814316,
0.04087236151099205,
0.03762900456786156,
0.0218303594738245,
0.011607869528234005,
-0.04105507582426071,
0.02390372008085251,
-0.010617144405841827,
-0.0468834787607193,
-0.025615012273192406,
-0.00006690449663437903,
0.02438223548233509,
-0.015611800365149975,
-0.017725739628076553,
0.03669228404760361,
0.03001437336206436,
-0.01195595320314169,
0.03639528900384903,
0.05339035764336586,
0.011333290487527847,
0.016087710857391357,
-0.023349765688180923,
-0.04054494947195053,
0.0680696964263916,
-0.027044979855418205,
0.056713853031396866,
-0.005321289878338575,
-0.0039269276894629,
0.021118957549333572,
0.025473933666944504,
0.019773246720433235,
-0.05536632612347603,
-0.039674948900938034,
-0.06334995478391647,
0.032099973410367966,
0.06021203100681305,
0.028765510767698288,
0.0030713998712599277,
0.0032141145784407854,
0.0026741938199847937,
-0.0049999975599348545,
0.017635924741625786,
0.019949810579419136,
-0.02103719301521778,
-0.026864666491746902,
-0.027784932404756546,
-0.05418884754180908,
0.03881238400936127,
-0.01006279792636633,
-0.021456429734826088,
-0.0034197268541902304,
-0.046114444732666016,
0.011837438680231571,
0.012355185113847256,
0.02995261549949646,
0.005746631417423487,
0.060971736907958984,
0.005294961389154196,
0.04632411152124405,
0.0009530623792670667,
0.031103074550628662,
0.13206452131271362,
0.10139870643615723,
-0.045151595026254654,
-0.0657423883676529,
-0.0011909357272088528,
-0.012902460061013699,
0.008912383578717709,
-0.0345948226749897,
0.018014350906014442,
-0.030652955174446106,
-0.00580823328346014,
0.009089604020118713,
0.040798116475343704,
-0.00986032746732235,
0.011016221717000008,
0.039382223039865494,
-0.032148271799087524,
-0.04807918146252632,
0.009193843230605125,
0.010875467211008072,
-0.012334815226495266,
0.0004895675228908658,
-0.013265316374599934,
0.015410508960485458,
-0.0014722647611051798,
0.00452941469848156,
-0.011858378536999226,
-0.004303376190364361,
0.029671164229512215,
-0.018559366464614868,
-0.05361809581518173,
-0.0359673872590065,
0.007806575857102871,
0.0023178993724286556,
-0.020782457664608955,
-0.0020767918322235346,
0.004940101411193609,
-0.021463284268975258,
0.01991143263876438,
0.044607020914554596,
-0.015382901765406132,
0.013244415633380413,
-0.00685866316780448,
0.007686674129217863,
-0.025921033695340157,
-0.0325419120490551,
0.005895314272493124,
0.04141296073794365,
-0.011913040652871132,
0.04035991430282593,
0.00829225778579712,
0.02239805832505226,
-0.01479801069945097,
-0.033505819737911224,
-0.020289815962314606,
0.0035712732933461666,
0.043009188026189804,
-0.03543595224618912,
0.0011210136581212282,
-0.02814369834959507,
0.01650446653366089,
-0.01909799501299858,
0.002252653706818819,
-0.0020739666651934385,
-0.015138973481953144,
0.0041390834376215935,
-0.010696473531425,
0.007641445845365524,
0.013751490972936153,
-0.007647211197763681,
-0.04192480817437172,
-0.025868088006973267,
-0.03175834193825722,
-0.006566312164068222,
-0.009258069097995758,
0.029539600014686584,
0.012967041693627834,
0.00316384038887918,
-0.001747329835779965,
-0.021154113113880157,
-0.06639286130666733,
0.004878558684140444,
-0.026181522756814957,
-0.014487037435173988,
0.002496777568012476,
-0.01699981838464737,
-0.011299548670649529,
0.036849576979875565,
-0.00904726143926382,
-0.06143521890044212,
0.010784635320305824,
0.030230654403567314,
0.02898389846086502,
-0.030559638515114784,
0.005077573005110025,
-0.025926819071173668,
-0.03885028883814812,
0.01889592595398426,
-0.03341047838330269,
0.005805067718029022,
0.0019242896232753992,
0.003451352007687092,
-0.0030209855176508427,
0.03285256028175354,
-0.022888431325554848,
-0.01630072481930256,
0.008649581111967564,
-0.0026823473162949085,
0.02466568909585476,
0.04742179438471794,
0.012782826088368893,
-0.05842328444123268,
-0.08407226949930191,
-0.01907912828028202,
0.015553832985460758,
0.02522917650640011,
0.012201563455164433,
-0.05481239780783653,
-0.01742149144411087,
0.00859496183693409,
0.03468715399503708,
-0.04389384016394615,
-0.050400953739881516,
-0.043954141438007355,
0.008748532272875309,
0.0026656438130885363,
0.013540500774979591,
-0.0074820914305746555,
0.028727805241942406,
-0.00741812027990818,
-0.030468428507447243,
-0.04751453548669815,
0.04107050970196724,
-0.02496344782412052,
-0.01712118647992611,
-0.011788305826485157,
-0.0004496326728258282,
0.06833215802907944,
-0.01869756355881691,
-0.02951384335756302,
0.041893161833286285,
-0.05446820706129074,
-0.04254588857293129,
0.04112774878740311,
-0.01980854757130146,
0.04447392001748085,
0.016254937276244164,
-0.014581367373466492,
-0.013328621163964272,
0.019280865788459778,
-0.0036577801220119,
-0.012031598016619682,
-0.0020284377969801426,
-0.05227809026837349,
-0.034626126289367676,
-0.04028712958097458,
0.009320291690528393,
-0.019153643399477005,
0.030424129217863083,
0.021296318620443344,
0.042571764439344406,
-0.011818885803222656,
-0.02548394538462162,
0.015909885987639427,
0.01082745473831892,
0.019742203876376152,
0.016555218026041985,
-0.013624459505081177,
-0.023500921204686165,
0.05862656980752945,
-0.021359149366617203,
0.010990156792104244,
-0.004643421154469252,
-0.0007226756424643099,
-0.11712674796581268,
-0.029678497463464737,
0.006325975060462952,
0.022222913801670074,
0.02959226444363594,
-0.07325971126556396,
-0.0015918206190690398,
0.00821160152554512,
-0.030479902401566505,
0.00920762587338686,
-0.03217089921236038,
0.03844385966658592,
-0.039780545979738235,
-0.002179106930270791,
-0.004737864248454571,
0.04391657933592796,
0.059853583574295044,
0.041170548647642136,
0.024996452033519745,
0.001986668910831213,
-0.0039050811901688576,
-0.024931272491812706,
0.002716124290600419,
0.03832171857357025,
-0.023108763620257378,
-0.05030180886387825,
0.05365616828203201,
-0.016873611137270927,
-0.02817521058022976,
0.0048446375876665115,
-0.0021278078202158213,
-0.010664230212569237,
0.013365142047405243,
0.008371684700250626,
-0.011297124437987804,
0.04844469949603081,
0.026094259694218636,
0.0019143774406984448,
-0.010692667216062546,
0.006732536945492029,
0.011716103181242943,
0.010221012867987156,
0.027012815698981285,
-0.0074655162170529366,
0.012640216387808323,
-0.04491952806711197,
0.004374234937131405,
0.04596677049994469,
-0.015251594595611095,
-0.019920313730835915,
0.012575938366353512,
-0.014037193730473518,
-0.014793655835092068,
-0.024785058572888374,
0.011233067139983177,
-0.04607410356402397,
-0.042603909969329834,
0.016049107536673546,
0.010903690941631794,
0.006092349532991648,
0.011841675266623497,
0.011839061975479126,
-0.036015450954437256,
0.010282238945364952,
0.042956214398145676,
-0.021117018535733223,
-0.06801961362361908,
-0.015354537405073643,
-0.035181835293769836,
-0.02643757313489914,
-0.035103362053632736,
-0.02852414920926094,
-0.08011171221733093,
0.029508540406823158,
-0.006360769737511873,
0.04353056475520134,
-0.02621191181242466,
-0.04049881920218468,
-0.001539932214654982,
-0.06788131594657898,
0.022460389882326126,
0.037380438297986984,
0.023516016080975533,
-0.010504629462957382,
-0.0291318129748106,
-0.015084282495081425,
-0.0032416090834885836,
0.05659753456711769,
-0.0035699501167982817,
-0.04114425554871559,
0.004794279113411903,
0.01343282125890255,
0.015536265447735786,
0.011796106584370136,
-0.032180625945329666,
-0.03941596299409866,
-0.016157792881131172,
-0.019104281440377235,
-0.014636760577559471,
0.021537555381655693,
0.019296366721391678,
0.031149758026003838,
0.00365097401663661,
-0.0020945954602211714,
0.014497393742203712,
-0.043722350150346756,
0.058988817036151886,
0.00905747152864933,
0.0027819590177387,
0.04400421679019928,
0.0031964725349098444,
0.05679526552557945,
0.026698967441916466,
-0.013957042247056961,
-0.025015506893396378,
0.010094364173710346,
-0.04937588423490524,
-0.026452992111444473,
0.00717921694740653,
0.020526869222521782,
-0.006327271461486816,
-0.03795088455080986,
-0.00599698768928647,
0.05779402330517769,
-0.0010378824081271887,
-0.019703568890690804,
0.031313493847846985,
0.009851528331637383,
0.030168777331709862,
-0.029048968106508255,
-0.0056132967583835125,
0.06732277572154999,
0.048699524253606796,
0.0000650182701065205,
0.050564441829919815,
0.012031519785523415,
-0.028957201167941093,
0.020375005900859833,
0.029527705162763596,
-0.003705744631588459,
0.021675661206245422,
0.02034711092710495,
0.04386887699365616,
-0.027559597045183182,
-0.015271567739546299,
0.003995294217020273,
-0.006262471899390221,
0.0163969025015831,
-0.009633462876081467,
-0.018741924315690994,
0.07801105827093124,
-0.005186349153518677,
0.008457605727016926,
-0.016421524807810783,
0.003786028129979968,
-0.028861844912171364,
0.0001544230617582798,
0.0035129880998283625,
0.049248870462179184,
-0.002812429331243038,
-0.0023830775171518326,
-0.012622260488569736,
-0.0032686204649508,
0.01397437322884798,
-0.06532860547304153,
0.017393475398421288,
0.011434081010520458,
-0.01520758680999279,
0.0015352660557255149,
-0.007842696271836758,
0.0026256171986460686,
-0.025246532633900642,
0.005069297272711992,
0.041901253163814545,
0.0398685522377491,
0.028147771954536438,
-0.01705571636557579,
-0.007330979686230421,
0.05798671767115593,
-0.04886101931333542,
-0.026427699252963066,
-0.03618689998984337,
0.01681525632739067,
-0.00022401733440347016,
0.007589801214635372
] |
<p>My questions are based on this paper - <a href="http://arxiv.org/abs/0905.4013" rel="nofollow">http://arxiv.org/abs/0905.4013</a></p>
<ul>
<li><p>Firstly I want to know as to whether some assumptions are needed about the relationship between the systems $A$ and $B$ for the Hilbert space to factor as tensor products as ("assumed"?) on page 3? </p>
<p>I mean assume the more common reverse scenario - if you are given a system C and you decide to call some part of it as $A$ and the rest as $B$ then does it automatically mean that the Hilbert space of C factors between A and B? (...that doesn't intuitively feel to be true...then what exactly is the assumption being made here?..) </p></li>
<li><p>Secondly given the definition of $S_A$ and $S^{(n)}_A$ as in equations 2 and 3 how does this claimed equality follow that, $S_A = \lim _{n \rightarrow 1} S^{(n)}_A = - \lim_{n \rightarrow 1} \frac{\partial \rho^n_A }{\partial n }$</p></li>
</ul>
<p>I am unable to see the proof of the above 2 equalities.
It would be great if someone could help. </p>
| 9,398 |
[
-0.030856316909193993,
-0.008667237125337124,
-0.012564072385430336,
-0.03236178681254387,
0.021377230063080788,
-0.007012946531176567,
-0.028645634651184082,
-0.01664852164685726,
0.04126216843724251,
-0.02994021214544773,
0.029960984364151955,
-0.011760508641600609,
0.08460879325866699,
0.03183148801326752,
-0.017376355826854706,
-0.0033975213300436735,
-0.04914258047938347,
-0.008222348056733608,
-0.0062710936181247234,
-0.009768263436853886,
0.018094224855303764,
0.05541586875915527,
0.018403369933366776,
0.010474366135895252,
-0.003696695202961564,
0.02241862192749977,
-0.01283064391463995,
0.001295608701184392,
0.01306859590113163,
0.03858989104628563,
0.0025141655933111906,
-0.03502066433429718,
-0.018957804888486862,
0.04857699200510979,
0.0020653647370636463,
-0.01830817572772503,
-0.036361273378133774,
-0.010122084058821201,
0.02323332242667675,
0.0035891965962946415,
-0.047304779291152954,
-0.004710171837359667,
-0.04896935820579529,
0.03891390189528465,
0.005484134424477816,
0.021644003689289093,
0.0019929278641939163,
-0.009370879270136356,
0.010017423890531063,
-0.06062927097082138,
0.06943171471357346,
0.03774532303214073,
0.017348984256386757,
0.025236453860998154,
0.008871941827237606,
0.0016602607211098075,
0.059413980692625046,
0.060384780168533325,
0.025585610419511795,
-0.05513974651694298,
-0.012508106417953968,
-0.004916422534734011,
-0.03490866720676422,
-0.014504218474030495,
-0.01620124839246273,
0.00937379989773035,
0.02958889864385128,
-0.028627628460526466,
0.01664438098669052,
-0.0648530051112175,
0.0020724220667034388,
-0.023311631754040718,
0.038713257759809494,
-0.056642305105924606,
0.005537554156035185,
-0.0349494144320488,
-0.013487090356647968,
-0.011476823128759861,
0.03131505474448204,
0.027972660958766937,
-0.020159054547548294,
0.03987519070506096,
0.004213704261928797,
0.019482998177409172,
0.02067277953028679,
0.027291370555758476,
0.06766347587108612,
0.00774527108296752,
0.02900075539946556,
0.021487504243850708,
-0.0034710511099547148,
0.016753310337662697,
0.036851491779088974,
-0.04285041615366936,
-0.013971756212413311,
0.038654427975416183,
0.02305048145353794,
0.016489209607243538,
0.01249003130942583,
-0.036768052726984024,
-0.06256693601608276,
-0.054660823196172714,
0.0089197913184762,
0.028923921287059784,
0.00014923089474905282,
0.014086809009313583,
-0.039138298481702805,
0.052460744976997375,
-0.024546420201659203,
0.013104083016514778,
-0.06335200369358063,
0.008747066371142864,
0.00023724908533040434,
0.007723613176494837,
-0.04608640819787979,
-0.024066561833024025,
-0.0013256552629172802,
0.0162863340228796,
0.01722906343638897,
0.07394693046808243,
0.03595050796866417,
-0.01737462729215622,
0.02289922721683979,
-0.013897903263568878,
-0.07716234773397446,
0.0009160286281257868,
0.04290631413459778,
-0.029236674308776855,
-0.06386248767375946,
0.007144141010940075,
0.026958676055073738,
-0.007795895915478468,
0.012338574975728989,
0.03464078530669212,
0.026043230667710304,
-0.02240806818008423,
-0.1210990697145462,
-0.0695507749915123,
0.03580586984753609,
-0.019373750314116478,
0.030941134318709373,
-0.08289959281682968,
0.04190162941813469,
0.05445707216858864,
0.09570088237524033,
0.0007268458721227944,
0.02881692722439766,
0.006752410903573036,
0.013809921219944954,
0.034304484724998474,
-0.014918520115315914,
-0.018371056765317917,
-0.0034231676254421473,
-0.02523045800626278,
-0.02139815129339695,
-0.05857733637094498,
0.046370334923267365,
0.022282836958765984,
-0.006425236817449331,
-0.02499394491314888,
0.07959488034248352,
-0.0016372572863474488,
0.02459094114601612,
0.021136287599802017,
0.01587994396686554,
-0.024246077984571457,
0.07997032254934311,
-0.005672238767147064,
0.02514559030532837,
0.04664234444499016,
-0.007395170629024506,
0.010554179549217224,
-0.004919141065329313,
0.05031376704573631,
0.016138048842549324,
-0.021985124796628952,
-0.011572069488465786,
-0.011551907286047935,
-0.004835579078644514,
-0.006893382407724857,
-0.043646618723869324,
-0.01905004307627678,
-0.030126692727208138,
0.011583558283746243,
-0.016170769929885864,
0.03304683044552803,
-0.004084134940057993,
0.002319860737770796,
0.025217609480023384,
-0.04189160838723183,
-0.010390222072601318,
-0.0570870079100132,
0.026134788990020752,
-0.010366716422140598,
-0.023003021255135536,
0.0886010155081749,
0.005734006408601999,
0.021120529621839523,
-0.03299973905086517,
-0.00915931910276413,
0.0035388057585805655,
0.002255462808534503,
0.003620544681325555,
-0.0022972128354012966,
0.04103333130478859,
0.04882381483912468,
0.04644415155053139,
0.00791308656334877,
0.01618853583931923,
-0.010676205158233643,
-0.046592678874731064,
0.056073933839797974,
-0.020033620297908783,
0.055809419602155685,
0.010931083001196384,
0.005285260733217001,
-0.017059559002518654,
-0.0038844395894557238,
-0.037130650132894516,
0.019918743520975113,
-0.0784604623913765,
0.049908049404621124,
0.02569826878607273,
0.006189464591443539,
0.027087131515145302,
0.043323758989572525,
0.02113906852900982,
0.03611326962709427,
0.009785071946680546,
-0.028001481667160988,
-0.026485828682780266,
-0.020266205072402954,
0.01803414896130562,
0.046841636300086975,
-0.023945435881614685,
0.0038815129082649946,
0.014268260449171066,
-0.013990607112646103,
0.022387126460671425,
-0.017045749351382256,
-0.022813735529780388,
-0.007093675900250673,
0.02488945983350277,
0.023558536544442177,
-0.020762506872415543,
0.010914145037531853,
-0.01782633177936077,
-0.0464174710214138,
0.05111178755760193,
0.05607821047306061,
0.0012522513279691339,
0.05800126865506172,
-0.03901097550988197,
0.031746141612529755,
0.021917376667261124,
0.008868815377354622,
0.04896058514714241,
-0.003511097515001893,
-0.0023644089233130217,
0.043514881283044815,
-0.015510911121964455,
-0.001076969550922513,
-0.03244377300143242,
-0.018740331754088402,
0.02779616042971611,
-0.04419614002108574,
-0.04114222899079323,
-0.042222172021865845,
-0.004306882154196501,
-0.02417273260653019,
0.00924619473516941,
-0.038752876222133636,
-0.007388242520391941,
-0.0015645568491891026,
0.008852272294461727,
0.04774080216884613,
-0.013501001521945,
0.04033854231238365,
-0.05008196085691452,
-0.0019120033830404282,
0.018068142235279083,
-0.04181019589304924,
0.042563386261463165,
0.03234347701072693,
-0.08043693751096725,
0.008047357201576233,
-0.056420713663101196,
-0.004394376650452614,
0.04127248004078865,
-0.016683334484696388,
0.0059129539877176285,
0.02422924153506756,
0.004473259672522545,
-0.031073186546564102,
-0.04632900282740593,
-0.016227474436163902,
0.021456856280565262,
-0.012515384703874588,
-0.0041272807866334915,
0.05431223288178444,
0.005244630854576826,
-0.02736150287091732,
0.013997413218021393,
-0.01454515103250742,
-0.028723636642098427,
-0.0006715043564327061,
-0.006483221892267466,
0.023801462724804878,
-0.04271137714385986,
0.01307832170277834,
0.03902919590473175,
-0.022135118022561073,
-0.03035038337111473,
-0.05689563602209091,
-0.04805481806397438,
0.0076932115480303764,
0.03630140796303749,
0.04648492485284805,
0.033650919795036316,
-0.031707946211099625,
0.07475483417510986,
0.020914552733302116,
-0.03326164931058884,
-0.024957621470093727,
0.022186893969774246,
-0.04474692419171333,
-0.02499523013830185,
-0.00360589730553329,
0.023095499724149704,
-0.01580905355513096,
0.02978142350912094,
0.024660445749759674,
0.01886880211532116,
0.06406713277101517,
0.023087305948138237,
-0.026736589148640633,
0.001131540397182107,
0.006750131957232952,
0.008030657656490803,
0.042130857706069946,
-0.019922252744436264,
0.02323722653090954,
-0.012366453185677528,
-0.02815929800271988,
0.029015230014920235,
-0.007272594608366489,
-0.021942943334579468,
0.00907818228006363,
-0.010820943862199783,
-0.008028116077184677,
-0.04251289740204811,
0.01339637953788042,
0.003298372495919466,
0.007567213848233223,
0.04331596940755844,
0.029448825865983963,
0.03278527036309242,
-0.049859385937452316,
0.010168650187551975,
0.022636795416474342,
0.016648462042212486,
-0.020482297986745834,
-0.020819762721657753,
-0.008109906688332558,
-0.013057434931397438,
0.02069297432899475,
-0.03987172245979309,
-0.005564238876104355,
0.02277541160583496,
0.01707523502409458,
-0.00428937328979373,
-0.03775545209646225,
-0.03538157790899277,
0.007784374989569187,
-0.06853142380714417,
0.024516381323337555,
-0.012115931138396263,
0.043681561946868896,
-0.013429190963506699,
0.04870723932981491,
0.009104660712182522,
-0.0019258786924183369,
0.006184676196426153,
-0.014872068539261818,
-0.09707353264093399,
0.006741603370755911,
-0.026321740821003914,
-0.014539730735123158,
0.03976992145180702,
-0.014301423914730549,
0.011228960938751698,
-0.003303029341623187,
-0.024770619347691536,
-0.008067568764090538,
-0.012496326118707657,
-0.07323871552944183,
0.002591780386865139,
-0.055598415434360504,
-0.0689024031162262,
-0.0025311526842415333,
-0.0051039899699389935,
0.007018000353127718,
-0.015867140144109726,
0.009920634329319,
0.03323815390467644,
-0.038754966109991074,
-0.006573596969246864,
-0.007887127809226513,
0.03209412842988968,
0.027004970237612724,
0.01516985148191452,
0.03360928222537041,
0.030627869069576263,
-0.03422241657972336,
0.020901063457131386,
0.0036165760830044746,
0.05875520408153534,
0.00250440021045506,
-0.0039638252928853035,
-0.0365501269698143,
-0.055709898471832275,
-0.050051093101501465,
0.014102132059633732,
0.05137655511498451,
0.02893061935901642,
-0.027378251776099205,
0.035350676625967026,
-0.0009927077917382121,
-0.012577949091792107,
0.006766065489500761,
0.04253058135509491,
-0.022487090900540352,
-0.006664197891950607,
-0.03451763466000557,
-0.02785530686378479,
-0.02184309996664524,
-0.019267933443188667,
0.03667277470231056,
-0.04923538491129875,
-0.008693356066942215,
0.009135057218372822,
0.028820578008890152,
-0.006551466416567564,
-0.03378789499402046,
0.018817689269781113,
0.05832652375102043,
0.012509869411587715,
0.009425931610167027,
-0.01026327908039093,
0.010763132944703102,
0.03726533055305481,
0.05604054406285286,
-0.00981837511062622,
0.0020418562926352024,
-0.06422119587659836,
-0.0469578392803669,
0.02027672901749611,
0.004856121260672808,
0.03439002111554146,
-0.011113017797470093,
-0.037708185613155365,
-0.027620909735560417,
0.018235735595226288,
0.002125510945916176,
0.07481057196855545,
0.00956686306744814,
-0.010724872350692749,
-0.020125217735767365,
-0.0280263964086771,
-0.002456164686009288,
0.03252089396119118,
0.034518852829933167,
0.005094027612358332,
-0.00008129753405228257,
-0.006894152145832777,
-0.009763875976204872,
-0.0022506287787109613,
-0.002234839368611574,
0.07121903449296951,
-0.011044572107493877,
-0.03452782332897186,
0.010281914845108986,
0.05386056751012802,
-0.024281088262796402,
-0.07556481659412384,
0.050174444913864136,
0.009386220015585423,
-0.06215212121605873,
0.022264929488301277,
-0.0333048477768898,
-0.050256650894880295,
0.03879117965698242,
0.0013031736016273499,
-0.02751365303993225,
0.005144632421433926,
-0.016589492559432983,
0.07573706656694412,
0.010425343178212643,
-0.03691668063402176,
0.040476590394973755,
-0.004760083742439747,
0.007146216928958893,
0.009520807303488255,
-0.01005396619439125,
0.05527789518237114,
-0.046352870762348175,
0.02881372720003128,
-0.045194562524557114,
0.0187718253582716,
-0.012612977996468544,
0.050563424825668335,
-0.0059735835529863834,
0.008079343475401402,
-0.010850660502910614,
-0.02333783358335495,
0.020895984023809433,
0.006799807772040367,
-0.02612926810979843,
0.001132325385697186,
0.045676521956920624,
0.026384104043245316,
0.06766318529844284,
-0.03381919860839844,
0.014360897243022919,
-0.013269404880702496,
0.0012318509398028255,
0.023226141929626465,
-0.011258178390562534,
0.026597760617733,
-0.0046820202842354774,
-0.007922030054032803,
0.01744758151471615,
-0.025531640276312828,
0.012096232734620571,
-0.021024104207754135,
0.0306642334908247,
0.007875781506299973,
-0.013768303208053112,
-0.007193927187472582,
0.017946602776646614,
-0.03346983343362808,
-0.01772112399339676,
-0.04327377304434776,
-0.02304784208536148,
0.063639797270298,
-0.0008607571362517774,
-0.07048508524894714,
-0.027566934004426003,
-0.006241210736334324,
-0.025165600702166557,
0.0005459290696308017,
-0.06638934463262558,
-0.0011402369709685445,
-0.018387777730822563,
-0.022922633215785027,
-0.019866816699504852,
0.03616863489151001,
-0.07620115578174591,
-0.027959242463111877,
0.02840479090809822,
0.0444302037358284,
0.055128034204244614,
-0.006971203722059727,
0.0005539855919778347,
0.002592450240626931,
0.03995924070477486,
-0.009561910293996334,
0.0035878708586096764,
0.07318724691867828,
-0.00633158627897501,
-0.014531835913658142,
0.004706217907369137,
-0.002799816196784377,
0.01512434147298336,
-0.03379068523645401,
-0.016178634017705917,
0.008652438409626484,
0.03026352822780609,
0.013794715516269207,
-0.04003866761922836,
-0.03067965619266033,
0.012976276688277721,
0.031659841537475586,
-0.0032982220873236656,
-0.01789824292063713,
-0.003034964669495821,
-0.014393622055649757,
0.005952565465122461,
-0.009278974495828152,
0.0011196993291378021,
0.009378674440085888,
0.04589812830090523,
0.025443142279982567,
0.0021092721726745367,
0.03477860242128372,
-0.009891203604638577,
0.05381885543465614,
-0.017409110441803932,
0.02859453484416008,
0.025775281712412834,
-0.03376604989171028,
-0.03334707394242287,
-0.04327273741364479,
-0.09184244275093079,
0.03797474876046181,
0.05916578695178032,
0.0272133257240057,
0.029323428869247437,
0.03394656255841255,
-0.00404938030987978,
0.00012210449494887143,
-0.02548779547214508,
-0.008181850425899029,
-0.028482533991336823,
-0.010555115528404713,
0.03707675263285637,
-0.02947116084396839,
-0.007717927452176809,
0.032326020300388336,
0.03573998063802719,
-0.03321267291903496,
0.014124993234872818,
0.030915642157197,
0.016731806099414825,
0.012831928208470345,
0.014261726289987564,
-0.040253885090351105,
0.050238825380802155,
-0.0388282835483551,
0.014925511553883553,
0.0014069558819755912,
-0.012447222135961056,
0.03674784675240517,
0.02954418770968914,
-0.00040986144449561834,
-0.07449617981910706,
-0.03266251087188721,
-0.04448451101779938,
-0.019639942795038223,
0.017854701727628708,
0.0075874184258282185,
0.044553205370903015,
-0.006181370001286268,
0.034536879509687424,
0.027440523728728294,
0.040269989520311356,
-0.009097319096326828,
-0.02119927480816841,
-0.010800501331686974,
-0.05115257576107979,
-0.029260924085974693,
0.017080454155802727,
0.00030155282001942396,
-0.019177637994289398,
0.02231932058930397,
-0.03787629306316376,
0.016005171462893486,
0.022793352603912354,
0.013086517341434956,
0.025564532727003098,
0.05438932403922081,
0.03013322874903679,
0.03373407572507858,
-0.01838301308453083,
-0.008774282410740852,
0.0915638878941536,
0.06568248569965363,
-0.018550967797636986,
-0.05193282291293144,
0.02580048330128193,
0.00612933374941349,
0.03145349398255348,
-0.032181452959775925,
0.025298483669757843,
0.006885909475386143,
0.0005249487003311515,
0.006416323594748974,
0.035104457288980484,
0.009082669392228127,
0.0012764971470460296,
0.030617116019129753,
-0.040987528860569,
-0.03001619502902031,
0.0026170345954596996,
-0.018407469615340233,
-0.03592277690768242,
-0.03389860689640045,
-0.023141587153077126,
0.023417068645358086,
-0.0058791423216462135,
0.02575685642659664,
-0.031344763934612274,
0.0245309229940176,
-0.0017096117371693254,
0.006594039034098387,
-0.040567509829998016,
0.016058437526226044,
0.005710219033062458,
-0.007111383602023125,
-0.021139394491910934,
0.030880149453878403,
0.0030483491718769073,
0.017856288701295853,
0.018997937440872192,
0.0350075401365757,
0.026896899566054344,
-0.017352070659399033,
0.028144562616944313,
0.007528574671596289,
-0.03994327038526535,
0.013724049553275108,
-0.027172494679689407,
0.048025622963905334,
0.006096724886447191,
0.017664507031440735,
-0.005633250344544649,
-0.023406587541103363,
-0.0008138259290717542,
-0.020486995577812195,
-0.013702543452382088,
0.021157164126634598,
0.031207343563437462,
-0.02906038425862789,
-0.025602273643016815,
-0.006371762603521347,
-0.026879433542490005,
0.0023162795696407557,
0.024855423718690872,
-0.003060696879401803,
-0.025451894849538803,
0.03392157703638077,
0.00038568692980334163,
-0.011454138904809952,
-0.008922451175749302,
0.008473672904074192,
-0.03560648486018181,
0.020329274237155914,
-0.03718334063887596,
-0.03394157439470291,
0.03247890993952751,
0.007800451945513487,
0.06219672039151192,
0.01362643763422966,
0.02103305049240589,
0.018388325348496437,
-0.07752601057291031,
-0.006115328054875135,
-0.01737312041223049,
-0.04198635742068291,
-0.014537245035171509,
-0.037212442606687546,
0.030127502977848053,
0.04092675819993019,
-0.024992436170578003,
0.0040524969808757305,
0.020758161321282387,
0.04579835385084152,
0.048779018223285675,
-0.017108796164393425,
-0.013159941881895065,
0.01592838764190674,
-0.04668242484331131,
0.02296304702758789,
-0.0152061115950346,
0.01525129470974207,
0.04659673199057579,
0.028564028441905975,
-0.028221674263477325,
0.04019691422581673,
-0.01936451345682144,
0.0037118985783308744,
0.0024190640542656183,
-0.014088258147239685,
0.04218393936753273,
0.02757059410214424,
0.016837650910019875,
-0.03682861849665642,
-0.043510254472494125,
0.018940377980470657,
-0.006906903814524412,
0.02225547656416893,
-0.011462057940661907,
-0.034609030932188034,
-0.011339936405420303,
0.0018264023819938302,
0.026881026104092598,
-0.034119363874197006,
-0.005878455005586147,
-0.03699797764420509,
0.027287913486361504,
0.01178339309990406,
0.006530697923153639,
-0.01809246651828289,
0.03513442352414131,
0.009075804613530636,
-0.03456677496433258,
0.03618023917078972,
-0.02202370949089527,
-0.011003485880792141,
-0.029492303729057312,
-0.012760079465806484,
-0.0130325211212039,
0.03350565955042839,
0.01902899332344532,
-0.0429961197078228,
0.035140350461006165,
-0.04007032886147499,
-0.03680887073278427,
-0.00012155495642218739,
0.029132606461644173,
0.044198013842105865,
0.04842748865485191,
-0.021078268066048622,
0.005786755122244358,
0.04289223998785019,
-0.008750371634960175,
-0.009463148191571236,
-0.017719166353344917,
-0.06610312312841415,
-0.009455179795622826,
-0.029148254543542862,
0.013655434362590313,
-0.0001769958034856245,
0.017340505495667458,
0.002796074142679572,
0.03719107806682587,
-0.014056898653507233,
-0.03124260902404785,
-0.0012266263365745544,
-0.006626172922551632,
-0.0041711111553013325,
-0.004037047270685434,
0.013800280168652534,
0.02516927197575569,
0.02887917496263981,
-0.021378295496106148,
0.0017370028654113412,
-0.010884585790336132,
0.027323946356773376,
-0.0620654821395874,
-0.01857338473200798,
-0.015653295442461967,
-0.013471807353198528,
0.026764392852783203,
-0.05180695280432701,
0.00791088119149208,
0.0297375675290823,
-0.04716678336262703,
0.03569592535495758,
-0.015892866998910904,
-0.00029445026302710176,
-0.03832888975739479,
0.01730424165725708,
-0.03252169117331505,
0.021471871063113213,
0.031084906309843063,
0.024482939392328262,
0.019661879166960716,
0.01965508982539177,
-0.030782338231801987,
-0.033206116408109665,
-0.015605390071868896,
0.020643003284931183,
0.03235986456274986,
-0.048855263739824295,
0.0680212751030922,
0.01340561918914318,
-0.05925097316503525,
0.05207116901874542,
-0.01286645419895649,
-0.02047002874314785,
0.013875693082809448,
0.034231752157211304,
-0.004499369766563177,
0.040202654898166656,
0.035436343401670456,
-0.016016684472560883,
0.003490790957584977,
0.011208468116819859,
0.03350876271724701,
0.016613207757472992,
-0.027718646451830864,
-0.007550877518951893,
0.025633664801716805,
-0.03669047728180885,
-0.011960790492594242,
0.03492778539657593,
0.013478707522153854,
-0.008034356869757175,
-0.010152447037398815,
-0.03935348615050316,
-0.0005060196854174137,
-0.01809481717646122,
0.016185136511921883,
-0.024343213066458702,
-0.044818270951509476,
0.02995796874165535,
0.007581150159239769,
-0.033190373331308365,
0.019852520897984505,
-0.040364500135183334,
-0.036028798669576645,
0.02792854979634285,
0.01809738390147686,
0.001302542514167726,
-0.06348489969968796,
0.014694084413349628,
-0.0007273128721863031,
0.007119782269001007,
-0.05041467398405075,
-0.038429081439971924,
-0.07353606075048447,
0.04504682496190071,
0.0077613224275410175,
0.04576987773180008,
0.009232950396835804,
-0.05350489541888237,
-0.03206251189112663,
-0.08865867555141449,
0.014608345925807953,
0.04069005697965622,
-0.009861038066446781,
-0.038968876004219055,
0.010424692183732986,
-0.01604098454117775,
-0.00495786452665925,
0.05640227347612381,
0.006720251869410276,
-0.025182660669088364,
0.011331280693411827,
0.01240595243871212,
0.021625617519021034,
-0.03367201238870621,
0.03816216066479683,
0.0010352825047448277,
0.002816169522702694,
-0.01689770445227623,
-0.016459865495562553,
-0.006867375690490007,
0.011260178871452808,
-0.005899964831769466,
-0.01085128728300333,
0.0024050367064774036,
0.017725884914398193,
-0.04931427538394928,
0.05763497203588486,
0.00139132933691144,
-0.0028141229413449764,
0.09641075879335403,
-0.030221130698919296,
0.00042693287832662463,
0.010686014778912067,
-0.006902947556227446,
-0.015293764881789684,
0.019907811656594276,
-0.001957140862941742,
-0.008846699260175228,
0.001399675733409822,
0.011052824556827545,
0.048717547208070755,
-0.031516507267951965,
-0.033888936042785645,
0.04312431812286377,
-0.0318453311920166,
-0.00658179959282279,
0.03000260517001152,
0.014203725382685661,
-0.006820123177021742,
-0.000052715782658196986,
0.023213831707835197,
0.0403023362159729,
0.027528846636414528,
-0.0004481603973545134,
0.052343301475048065,
0.03127817064523697,
-0.01869852840900421,
-0.014776168391108513,
0.026651330292224884,
-0.05406060442328453,
0.02266719564795494,
-0.014163876883685589,
0.04391082748770714,
-0.0727277472615242,
-0.019569657742977142,
0.03343730419874191,
-0.03921346366405487,
-0.0025257349479943514,
0.0222481656819582,
-0.03849959000945091,
0.08420389890670776,
-0.014933204278349876,
0.030388344079256058,
-0.03541402146220207,
0.053260352462530136,
-0.017256565392017365,
-0.013232235796749592,
0.034097395837306976,
0.02660532109439373,
-0.009421540424227715,
0.01627814956009388,
-0.0016011190600693226,
-0.055097129195928574,
-0.030009837821125984,
-0.05231136456131935,
0.018093284219503403,
0.027364443987607956,
-0.002876423066481948,
-0.024377016350626945,
-0.04230453073978424,
0.013081884942948818,
-0.02283034846186638,
0.03924383968114853,
0.043424077332019806,
0.011101581156253815,
0.011236446909606457,
-0.01893758401274681,
-0.00858382973819971,
0.040997110307216644,
-0.03532789275050163,
-0.027086783200502396,
0.01768549345433712,
-0.004071058239787817,
-0.013662180863320827,
-0.019091423600912094
] |
<p>What will happen in young's double slit experiment, when instead of screen I put a black screen with a hole and a second screen behind the black one. Will it still form interference pattern albeit a faint one or no interference pattern will be observed?</p>
| 9,399 |
[
-0.05356156453490257,
-0.03632434457540512,
-0.012467426247894764,
-0.008971507661044598,
0.03011166863143444,
0.0005638320581056178,
-0.01110757328569889,
-0.06778598576784134,
-0.008007343858480453,
0.02026352658867836,
0.05038774013519287,
0.03802524134516716,
0.043421559035778046,
0.012221407145261765,
0.009280490688979626,
0.02826579660177231,
-0.011916662566363811,
-0.033435579389333725,
-0.03465038537979126,
-0.02196294255554676,
-0.038196153938770294,
0.005992121063172817,
0.02196628227829933,
0.0075267949141561985,
-0.021011291071772575,
0.028062937781214714,
0.03420514613389969,
-0.00960277859121561,
0.04005679488182068,
0.02332966960966587,
-0.031136365607380867,
-0.0010259391274303198,
-0.009178142063319683,
0.03285155072808266,
0.006585218943655491,
-0.027850138023495674,
-0.02544284053146839,
-0.04118889570236206,
-0.0005115552921779454,
-0.019659727811813354,
-0.0035715484991669655,
0.007281308528035879,
-0.025715190917253494,
0.07394596934318542,
-0.005603011231869459,
-0.009401272982358932,
0.006344560068100691,
-0.02974455989897251,
0.04935034364461899,
-0.045759957283735275,
0.046442851424217224,
-0.04138513281941414,
0.03359039127826691,
0.016997167840600014,
-0.0043447259813547134,
0.003260690253227949,
0.1048998311161995,
0.07706412672996521,
-0.012403708882629871,
-0.023261744529008865,
-0.013942508026957512,
0.006658934522420168,
0.006220223847776651,
-0.01392370369285345,
-0.03462255373597145,
0.0386686809360981,
-0.028965583071112633,
-0.05431284010410309,
0.0035590636543929577,
-0.004763716831803322,
0.00010060033673653379,
0.04364754259586334,
0.05415733903646469,
-0.017326291650533676,
0.019171565771102905,
-0.030679285526275635,
0.027723683044314384,
0.009926103986799717,
0.0008563086157664657,
0.043770499527454376,
-0.006377932149916887,
0.026336774230003357,
0.022182099521160126,
0.04038875922560692,
0.009692726656794548,
-0.025004681199789047,
0.09273917227983475,
-0.0300807673484087,
0.014743629842996597,
0.008338677696883678,
-0.021367844194173813,
0.019150417298078537,
0.03951771929860115,
0.013536759652197361,
-0.018571922555565834,
0.0034752588253468275,
-0.011637737043201923,
0.07425534725189209,
0.019404985010623932,
-0.004538065288215876,
0.005723406095057726,
0.024730492383241653,
0.02007744088768959,
0.08294850587844849,
0.035534605383872986,
-0.04686872661113739,
-0.03531590849161148,
0.052276384085416794,
-0.015780922025442123,
0.001483811647631228,
-0.001500582555308938,
0.026146870106458664,
-0.004340730141848326,
-0.002485402161255479,
0.04679657146334648,
-0.020003173500299454,
0.010344190523028374,
-0.01848602294921875,
0.04944251477718353,
0.07990702986717224,
0.038996510207653046,
-0.024274535477161407,
0.014601549133658409,
-0.01228814385831356,
-0.06804970651865005,
-0.00807199627161026,
0.05325023829936981,
-0.0283626988530159,
-0.027032680809497833,
0.026174599304795265,
-0.026216277852654457,
-0.015291568823158741,
0.012062023393809795,
0.008238101378083229,
0.03189530968666077,
-0.013035932555794716,
-0.11399735510349274,
-0.07551262527704239,
0.016663068905472755,
-0.033426009118556976,
-0.01572417840361595,
-0.04395147040486336,
0.012695521116256714,
0.02333451807498932,
0.07696769386529922,
-0.012645469047129154,
-0.017345312982797623,
-0.01798316091299057,
0.030933927744627,
0.0012018046109005809,
-0.012615269050002098,
0.025129036977887154,
0.008136880584061146,
-0.04445350915193558,
0.010211230255663395,
-0.04315889999270439,
0.022949928417801857,
0.03986392170190811,
-0.010055718012154102,
-0.06439848244190216,
0.06619586050510406,
-0.03414742276072502,
0.0030021672137081623,
-0.0020325344521552324,
-0.008112379349768162,
-0.03218121454119682,
0.06145380437374115,
-0.007317475508898497,
0.021746398881077766,
0.024662677198648453,
-0.02912185899913311,
0.050569698214530945,
-0.026297273114323616,
0.00373651715926826,
-0.0016380554297938943,
0.01978336274623871,
0.0012768054148182273,
-0.009242750704288483,
0.03263568505644798,
-0.024471649900078773,
-0.02610071562230587,
-0.02477797120809555,
-0.038925234228372574,
0.024595869705080986,
-0.009528054855763912,
0.013708149082958698,
-0.013358858413994312,
-0.01574307680130005,
-0.012305110692977905,
-0.04384952411055565,
-0.02691967785358429,
-0.03379512578248978,
0.01125277578830719,
0.034506656229496,
-0.005603157449513674,
0.01626582257449627,
0.018248671665787697,
0.0311701949685812,
-0.026676688343286514,
-0.013699580915272236,
-0.04042847454547882,
0.030552219599485397,
-0.011390522122383118,
-0.0008210060186684132,
0.03430527076125145,
0.02956836111843586,
0.020017018541693687,
-0.017055368050932884,
0.05416889116168022,
-0.04657521843910217,
-0.0074342843145132065,
0.02578762359917164,
0.00819525308907032,
0.025752844288945198,
-0.008699719794094563,
0.011504603549838066,
0.027637561783194542,
0.006413343362510204,
0.022183816879987717,
0.0015102132456377149,
-0.040358029305934906,
0.07971901446580887,
0.0498088002204895,
0.028285739943385124,
-0.0315888486802578,
0.021575942635536194,
0.017618346959352493,
-0.0007088846177794039,
0.0003009122156072408,
-0.018343759700655937,
-0.02968541532754898,
-0.004004784859716892,
0.016556674614548683,
0.009091240353882313,
-0.03263347968459129,
0.05365642532706261,
-0.007134789600968361,
-0.009566936641931534,
0.020215481519699097,
0.030059421434998512,
0.010437017306685448,
-0.01311765518039465,
0.009137828834354877,
0.006854560226202011,
-0.012870151549577713,
0.0021910560317337513,
0.016167394816875458,
0.0075435638427734375,
-0.019876746460795403,
-0.024147285148501396,
-0.03429888188838959,
0.008494029752910137,
-0.03359924256801605,
0.03851786255836487,
-0.015590192750096321,
-0.0382976271212101,
-0.014418029226362705,
-0.00827146228402853,
-0.005070558749139309,
0.015778325498104095,
0.0005323205841705203,
-0.009422168135643005,
-0.023698152974247932,
0.004951187875121832,
0.018380267545580864,
0.01147846132516861,
-0.01438682246953249,
-0.010698139667510986,
0.06056447699666023,
-0.03861621767282486,
0.04132604971528053,
-0.01659705676138401,
0.008149448782205582,
-0.042172931134700775,
-0.00490639777854085,
0.0036786929704248905,
0.0007459020125679672,
0.04517127946019173,
-0.047939617186784744,
-0.06819023936986923,
-0.01954568736255169,
-0.012388673610985279,
-0.009484084323048592,
0.007027403451502323,
-0.03818632662296295,
0.023389065638184547,
-0.03680984675884247,
-0.03147633373737335,
0.028032368049025536,
-0.029522214084863663,
-0.0014888579025864601,
-0.004011151846498251,
-0.03188696131110191,
-0.04038369655609131,
-0.038415227085351944,
-0.006008786149322987,
0.0122640086337924,
-0.007146418560296297,
-0.007512502372264862,
0.030821312218904495,
0.018619725480675697,
-0.028232373297214508,
0.016240861266851425,
-0.04155604541301727,
-0.02577664889395237,
0.002458785427734256,
-0.011210035532712936,
0.019931383430957794,
-0.031216111034154892,
-0.0015547090442851186,
0.017171254381537437,
-0.04550302401185036,
0.0191547442227602,
-0.03419818729162216,
-0.06426316499710083,
0.05914951115846634,
0.007808552123606205,
0.03211570158600807,
-0.058976009488105774,
-0.005513312295079231,
0.06293300539255142,
-0.001981783425435424,
0.010371221229434013,
-0.04025356471538544,
-0.017068615183234215,
-0.018953587859869003,
-0.03432711213827133,
0.046222299337387085,
0.019913438707590103,
0.02075956016778946,
0.04638725146651268,
0.05341999977827072,
0.014103508554399014,
0.04196176305413246,
0.04397023096680641,
-0.013981369324028492,
-0.018326392397284508,
0.0036020325496792793,
-0.005462215282022953,
0.023982416838407516,
-0.02287261374294758,
-0.02686529979109764,
-0.028670335188508034,
0.028010103851556778,
0.02985205501317978,
0.029667625203728676,
-0.014244291000068188,
0.05825200304389,
-0.027369963005185127,
0.01993362046778202,
-0.020904261618852615,
0.060283113270998,
0.012454263865947723,
0.016000574454665184,
-0.018420211970806122,
-0.024118777364492416,
0.051385704427957535,
-0.004365068394690752,
-0.02020297385752201,
0.04164556413888931,
0.01933257281780243,
-0.011038064956665039,
-0.02783413976430893,
0.02537764236330986,
-0.029642103239893913,
0.03678280487656593,
-0.017467651516199112,
-0.03933914750814438,
0.041016098111867905,
0.019151750952005386,
0.01960037089884281,
0.010129490867257118,
-0.004907894879579544,
-0.01754159852862358,
-0.05446743965148926,
-0.014872160740196705,
-0.02447814680635929,
0.023060504347085953,
0.006638034246861935,
0.012456117197871208,
0.04216793179512024,
0.014748641289770603,
0.006338665261864662,
-0.022971605882048607,
-0.04932110384106636,
0.018911859020590782,
-0.010669998824596405,
-0.015650557354092598,
-0.03316127508878708,
-0.003417394356802106,
-0.013355789706110954,
-0.054442405700683594,
-0.008190928027033806,
0.002035947982221842,
-0.005175191443413496,
-0.04888695850968361,
-0.014272953383624554,
-0.011529647745192051,
-0.021845443174242973,
-0.029065722599625587,
0.07952642440795898,
0.03553183749318123,
-0.0021776685025542974,
0.01838640682399273,
0.01685989648103714,
-0.029435982927680016,
-0.013238119892776012,
0.008917569182813168,
0.0019550127908587456,
-0.021483005955815315,
0.053634971380233765,
0.0577913299202919,
0.02394743822515011,
-0.05106297507882118,
-0.005939891096204519,
0.03578193858265877,
0.044971924275159836,
-0.004832569044083357,
-0.013239736668765545,
-0.003184019820764661,
-0.03027229756116867,
-0.029656734317541122,
-0.05144902691245079,
0.07180485874414444,
-0.04120732098817825,
-0.006495119538158178,
0.024049105122685432,
0.011820961721241474,
-0.03830401599407196,
0.04290502518415451,
0.06227673962712288,
0.02773653157055378,
-0.021263744682073593,
-0.028253627941012383,
-0.0030929220374673605,
-0.043701328337192535,
0.009076511487364769,
0.0036625026259571314,
0.01834862306714058,
-0.02759990282356739,
-0.01010118331760168,
0.020343458279967308,
0.03639654442667961,
-0.01615670695900917,
-0.007247000467032194,
-0.0630398690700531,
-0.013238238170742989,
-0.008257084526121616,
0.010774687863886356,
-0.0002533667429815978,
0.04509377479553223,
0.008408677764236927,
0.017724864184856415,
-0.015493019483983517,
-0.022029925137758255,
-0.022143103182315826,
0.04737278074026108,
0.05149615556001663,
-0.007347781211137772,
0.009283400140702724,
-0.059935107827186584,
-0.02668645977973938,
0.042629510164260864,
-0.021273160353302956,
0.0427897609770298,
-0.02743298001587391,
-0.007244783453643322,
-0.026975136250257492,
0.024128355085849762,
-0.04631827771663666,
0.030816862359642982,
-0.010250367224216461,
0.016528574749827385,
-0.007434039376676083,
-0.018564147874712944,
-0.004950894508510828,
-0.006478799972683191,
0.029542552307248116,
0.04500826075673103,
0.012094787321984768,
0.007054000627249479,
-0.04126828536391258,
0.00030304596293717623,
-0.029490794986486435,
-0.055961061269044876,
0.05304734781384468,
0.0031945451628416777,
-0.03015827015042305,
0.07520516216754913,
-0.045761846005916595,
0.014055200852453709,
-0.008520876988768578,
0.010847276076674461,
0.025054331868886948,
-0.0035335368011146784,
-0.033199820667505264,
0.03117343783378601,
0.010905991308391094,
0.015147375874221325,
0.027484335005283356,
0.0040278867818415165,
-0.0174662247300148,
0.04625016078352928,
-0.0126657634973526,
0.05886282026767731,
-0.04800549894571304,
0.013299660757184029,
-0.02550223283469677,
-0.02139008417725563,
-0.0409829281270504,
0.06445801258087158,
-0.01820225827395916,
0.039813149720430374,
-0.026665018871426582,
-0.038016628473997116,
-0.025131529197096825,
0.030692435801029205,
-0.007385119330137968,
0.013201512396335602,
-0.03183798864483833,
0.0014718935126438737,
0.014273668639361858,
-0.049476608633995056,
-0.03400105983018875,
-0.001988334348425269,
0.03255448117852211,
0.03273326903581619,
0.007125414442270994,
0.03796980530023575,
-0.0402044877409935,
-0.026883281767368317,
0.015947988256812096,
-0.05823156610131264,
0.019542807713150978,
-0.026496026664972305,
0.012767847627401352,
0.0290729571133852,
-0.07908279448747635,
-0.009541604667901993,
0.026914488524198532,
-0.032837338745594025,
0.014983420260250568,
-0.047139499336481094,
0.08422071486711502,
0.010354590602219105,
-0.022087208926677704,
-0.09461455047130585,
-0.05643509700894356,
-0.0006489437655545771,
0.00544752785935998,
0.010378174483776093,
-0.011872873641550541,
0.0024579884484410286,
-0.01259452011436224,
-0.037943482398986816,
-0.03289767727255821,
0.014568448998034,
-0.023337911814451218,
0.007516401819884777,
0.023613641038537025,
-0.022751009091734886,
0.06477632373571396,
0.02971366047859192,
-0.010705064982175827,
-0.0046326760202646255,
-0.053256452083587646,
-0.014160404913127422,
-0.02107565850019455,
0.009875867515802383,
-0.02726791799068451,
-0.01690427027642727,
-0.02201530523598194,
-0.026125676929950714,
0.023611636832356453,
-0.043426766991615295,
-0.007075128145515919,
0.021777402609586716,
0.043891508132219315,
-0.021383874118328094,
-0.011445339769124985,
-0.006106261163949966,
-0.02357710711658001,
-0.002562386216595769,
0.010192494839429855,
-0.017990553751587868,
-0.039829328656196594,
-0.05743984133005142,
-0.0028908499516546726,
0.01554633118212223,
-0.017788104712963104,
-0.022182585671544075,
0.06848660856485367,
0.017193211242556572,
-0.025311723351478577,
0.004040654748678207,
-0.05002191290259361,
-0.005780231207609177,
-0.026217544451355934,
-0.000943825114518404,
0.02868952788412571,
0.048950955271720886,
-0.025869276374578476,
-0.04773997887969017,
-0.016599703580141068,
-0.023151053115725517,
0.0653153508901596,
-0.019687842577695847,
0.04645492509007454,
-0.006707705091685057,
-0.035530317574739456,
-0.03465770184993744,
-0.010570051148533821,
0.010477306321263313,
0.01735047623515129,
-0.028430497273802757,
0.012185575440526009,
-0.018750755116343498,
0.026917126029729843,
0.025632482022047043,
0.03530120849609375,
0.034321170300245285,
0.05713487043976784,
0.06082538887858391,
0.015533670783042908,
0.04812248423695564,
-0.0007435044972226024,
-0.029151393100619316,
0.029309837147593498,
-0.06480531394481659,
0.02790643274784088,
-0.011357933282852173,
0.0212805587798357,
0.03837517276406288,
0.007246204651892185,
0.014869081787765026,
-0.02564801648259163,
-0.03610968217253685,
-0.049389034509658813,
-0.012479975819587708,
0.0017304851207882166,
0.03522759675979614,
0.0034808658529073,
0.0028774701058864594,
0.007809834089130163,
0.027907496318221092,
0.0005707250093109906,
-0.009467276744544506,
-0.07914260029792786,
-0.07942792773246765,
-0.033506039530038834,
-0.011397376656532288,
0.07487688958644867,
0.025819629430770874,
-0.010521036572754383,
0.02970724366605282,
0.00789193157106638,
0.023494554683566093,
0.014610395766794682,
0.043050430715084076,
-0.02060016244649887,
-0.002389095723628998,
0.01719091273844242,
0.06660240888595581,
0.0006645233952440321,
0.0044594439677894115,
0.10820355266332626,
0.019400233402848244,
0.03989410400390625,
-0.05790865048766136,
0.016399793326854706,
-0.04070061072707176,
0.023348277434706688,
-0.005980862770229578,
0.04081041365861893,
-0.004499099217355251,
0.025786999613046646,
0.03739527612924576,
0.046457186341285706,
0.012785680592060089,
0.01662447303533554,
0.03843452036380768,
-0.03673591837286949,
-0.03639085590839386,
-0.008519494906067848,
0.021563226357102394,
0.01235077902674675,
0.040614064782857895,
-0.0424395389854908,
0.01395121868699789,
-0.018843339756131172,
-0.011645746417343616,
-0.03608108311891556,
-0.02305026538670063,
0.04992877319455147,
0.008414754644036293,
-0.033646389842033386,
-0.007021382916718721,
-0.014649794436991215,
-0.010866815224289894,
-0.055328354239463806,
-0.002798141445964575,
0.03245893120765686,
-0.011063692159950733,
0.035191863775253296,
0.06871594488620758,
0.012964805588126183,
-0.007271604612469673,
0.020260794088244438,
0.007047956809401512,
-0.02965438924729824,
0.007111182902008295,
0.02751917578279972,
0.046883147209882736,
-0.006494553759694099,
-0.01683672145009041,
-0.03169424459338188,
-0.014930875040590763,
0.029030414298176765,
-0.04491133987903595,
-0.01761549711227417,
-0.0022709674667567015,
0.021296696737408638,
-0.021462755277752876,
-0.03246733918786049,
-0.007076262962073088,
0.011648224666714668,
0.004610663279891014,
0.013453276827931404,
0.006044571287930012,
0.012038771994411945,
-0.011841720901429653,
-0.001202765153720975,
0.04888303577899933,
0.019356418401002884,
-0.05318612977862358,
-0.03769773244857788,
-0.0026537065859884024,
-0.0035893279127776623,
-0.03274758160114288,
-0.003613047068938613,
0.057280804961919785,
0.03970344364643097,
-0.019023891538381577,
0.0038964597042649984,
-0.009838854894042015,
-0.07503664493560791,
0.016532929614186287,
-0.03522844240069389,
-0.00016001457697711885,
0.008439426310360432,
0.009659313596785069,
0.04564613476395607,
0.04786905273795128,
-0.023483624681830406,
-0.01976792700588703,
0.020115824416279793,
0.04213637858629227,
0.04404754564166069,
-0.051047325134277344,
-0.03558986261487007,
-0.002155903959646821,
-0.021197021007537842,
0.0005142045556567609,
-0.033240970224142075,
0.017581241205334663,
0.008107076399028301,
0.014597675763070583,
0.028523709625005722,
0.02249753847718239,
-0.034770142287015915,
-0.009700218215584755,
-0.03923387452960014,
-0.029361844062805176,
0.004885953851044178,
0.021766843274235725,
0.047328487038612366,
0.006325997412204742,
-0.026305118575692177,
-0.013544177636504173,
-0.009410395286977291,
0.017793500795960426,
0.023983657360076904,
-0.012650447897613049,
0.0018790584290400147,
0.022407077252864838,
0.0016584981931373477,
-0.00015591490955557674,
-0.029617367312312126,
-0.031847547739744186,
0.030312132090330124,
0.03080170415341854,
-0.025963163003325462,
-0.01993446983397007,
0.0392148494720459,
-0.001956561114639044,
-0.05554033815860748,
-0.02111322246491909,
0.019833125174045563,
-0.00960889458656311,
0.006864321883767843,
0.049458373337984085,
-0.03539809584617615,
0.03983622044324875,
0.03933364897966385,
-0.02947891317307949,
0.03839724883437157,
-0.0712466910481453,
-0.04248757287859917,
0.05081088840961456,
-0.006448716856539249,
0.0640697330236435,
0.012777197174727917,
0.0013680147239938378,
0.0036281482316553593,
0.0727163627743721,
-0.01826624572277069,
-0.02957257069647312,
0.019646693021059036,
-0.024927517399191856,
0.004213246516883373,
-0.022320078685879707,
0.0019963260274380445,
-0.02259247377514839,
-0.026062531396746635,
0.04530663043260574,
0.012828316539525986,
0.011759226210415363,
-0.017933469265699387,
-0.006079394370317459,
0.004474219866096973,
0.04131314530968666,
-0.020091751590371132,
-0.028844526037573814,
0.01607716828584671,
0.06090546026825905,
-0.017740538343787193,
0.04937339946627617,
0.019266277551651,
-0.029980788007378578,
-0.1183549016714096,
-0.011218990199267864,
0.041487108916044235,
0.006094071548432112,
0.040678296238183975,
-0.025102749466896057,
0.0011110249906778336,
0.038327377289533615,
-0.06360168009996414,
-0.009153115563094616,
0.030784880742430687,
-0.022802114486694336,
-0.046210989356040955,
-0.0274845901876688,
-0.01396737527102232,
0.009122527204453945,
0.013230712153017521,
0.05549563840031624,
0.0007371339597739279,
-0.001218564691953361,
-0.02748195268213749,
-0.036353085190057755,
-0.014244631864130497,
0.0021484948229044676,
0.011757772415876389,
0.00566718028858304,
0.061611492186784744,
-0.025013864040374756,
-0.011297597549855709,
0.015475056134164333,
-0.012584340758621693,
0.020898308604955673,
-0.01811368577182293,
-0.005526907742023468,
0.0054653058759868145,
0.004648212809115648,
-0.005596046335995197,
-0.023017464205622673,
0.03235694393515587,
0.02268255688250065,
-0.0003470175142865628,
-0.01136735174804926,
0.02111133188009262,
-0.005033733788877726,
-0.0023187892511487007,
-0.021733570843935013,
-0.019214646890759468,
-0.0020399217028170824,
0.021938487887382507,
-0.004632268100976944,
-0.0010078372433781624,
0.02845081314444542,
0.0367908701300621,
-0.018322380259633064,
-0.03516409173607826,
-0.0312843956053257,
-0.021268611773848534,
0.01981428638100624,
0.02950444631278515,
-0.010590675286948681,
0.020944736897945404,
-0.0060733589343726635,
-0.03260856494307518,
0.04230419918894768,
0.006078564561903477,
0.01353445090353489,
-0.04328528419137001,
-0.03165857121348381,
-0.006659317761659622,
0.012336664833128452,
0.044004157185554504,
-0.029667656868696213,
-0.010319664143025875,
0.010422985069453716,
-0.006228905636817217,
0.003566470229998231,
-0.024411875754594803,
-0.07014922052621841,
-0.020881759002804756,
-0.009692314080893993,
0.03745746240019798,
-0.01576870307326317,
-0.015612736344337463,
-0.06192278861999512,
0.009855306707322598,
-0.01982220448553562,
0.039643049240112305,
0.05005103349685669,
0.00934021919965744,
0.0011298678582534194,
-0.002942376071587205,
0.011908816173672676,
0.04024754464626312,
-0.05901272967457771,
0.01062367856502533,
-0.011209214106202126,
-0.036247484385967255,
-0.011991930194199085,
0.0028556850738823414,
-0.010142548941075802,
0.024728119373321533,
0.011178233660757542,
-0.006803981494158506,
0.017364373430609703,
-0.009432223625481129,
-0.029933638870716095,
0.021901581436395645,
0.044336579740047455,
0.022257164120674133,
0.08778566867113113,
-0.01395515725016594,
0.022640690207481384,
0.02041466347873211,
-0.0013886158121749759,
-0.05564291775226593,
-0.00135035568382591,
-0.06051183491945267,
-0.0009208451956510544,
-0.002879248233512044,
0.011774999089539051,
0.0013252099743112922,
-0.04868580400943756,
-0.049079108983278275,
0.04065859317779541,
-0.010580788366496563,
-0.044873178005218506,
0.06667813658714294,
0.013574120588600636,
0.017203764989972115,
-0.0027983440086245537,
0.026355454698204994,
0.0070261964574456215,
0.040428221225738525,
-0.015220528468489647,
0.05571805313229561,
-0.0035535418428480625,
-0.013383619487285614,
0.04242348670959473,
0.03374375402927399,
0.034694597125053406,
-0.0019480602350085974,
0.005091872066259384,
0.06894215941429138,
0.0033706093672662973,
0.004094501957297325,
-0.0020474118646234274,
0.011458429507911205,
0.0058460235595703125,
0.04429970309138298,
-0.009154715575277805,
0.042612411081790924,
-0.04345905780792236,
0.03847479820251465,
0.0018532199319452047,
-0.015420757234096527,
-0.044205714017152786,
0.013145201839506626,
0.06567491590976715,
0.053932078182697296,
0.009218307211995125,
-0.018955407664179802,
-0.009115795604884624,
0.024038875475525856,
0.012986544519662857,
-0.07927147299051285,
0.0021309014409780502,
-0.01947724260389805,
-0.015071057714521885,
-0.011791006661951542,
0.0248300451785326,
-0.01775294356048107,
-0.0024811604525893927,
0.048132456839084625,
-0.006273095030337572,
-0.01386040449142456,
-0.008234716951847076,
0.008868898265063763,
0.005949987564235926,
0.05514077842235565,
-0.05303456261754036,
-0.014712082222104073,
-0.01541233528405428,
0.02373340353369713,
-0.015548315830528736,
0.0037277042865753174
] |
<p>A wavefunction is inherently a multi-particle function. If you have a container that is perfectly isolated from the external universe (not possible, but just imagine it) and filled with $n$ particles, then the information necessary to perfectly describe everything there is to know about that system would be contained in $\Psi(\vec{r_1}, \vec{r_2}, ..., \vec{r_n}, t)$.</p>
<p>The probabilities of all obtainable measurements could be derived from that function.</p>
<p>However, I frequently read about wavefunctions of individual particles within a system such that the assumption</p>
<p>$$\Psi(\vec{r_1}, \vec{r_2}, ..., \vec{r_n}, t) = \Psi_1(\vec{r_1}, t) \Psi_2(\vec{r_2}, t) ... \Psi_n(\vec{r_n}, t)$$</p>
<p>is made. One of my professors has said that individual particle wavefunctions are a more fundamental description of reality; however, I did not think this was correct because it would completely exclude the effects of quantum entanglement (then again, this was a graduate chemical engineering course).</p>
<p>Where I'm going with this is: in what situations is it okay to separate the <em>complete</em> wavefunction like that? How do you know that an isolated electron in an experiment isn't influenced by the rest of the particles in the universe?</p>
<p>It's frequently said that when a measurement of a system is made, the wavefunction collapses into one of its eigenstates. But how is this possible if there is no such thing as a single-particle (or few-particle) wavefunction? Wouldn't it instead be the case that the overall</p>
<p>$$\Psi\left(\text{particle in experiment} + \text{measurement apparatus} + \text{all other particles}, t\right)$$</p>
<p>has evolved in time?</p>
<p>I realize my question is somewhat vague, but any kind of clarification on this issue would be appreciated.</p>
| 9,400 |
[
0.0007491278229281306,
0.016263017430901527,
0.008065233938395977,
-0.05002199858427048,
0.036244701594114304,
-0.012985093519091606,
-0.02665781043469906,
-0.009788847528398037,
0.004648082423955202,
-0.02457141876220703,
0.029646487906575203,
0.05042567476630211,
0.004049328155815601,
0.009804492816329002,
0.0035731878597289324,
0.01930111087858677,
-0.014731686562299728,
-0.01174975372850895,
-0.00996303092688322,
-0.023507915437221527,
0.017060264945030212,
0.056735824793577194,
0.003473049495369196,
-0.037388138473033905,
-0.005644046235829592,
0.053861554712057114,
-0.002793123247101903,
-0.010693357326090336,
0.03179251030087471,
0.07301056385040283,
-0.003000329714268446,
-0.03616676852107048,
-0.021510478109121323,
0.031016206368803978,
0.00036362139508128166,
-0.021938351914286613,
-0.044470176100730896,
-0.02666766196489334,
0.023588472977280617,
0.000006187950930325314,
-0.054734718054533005,
-0.01068509928882122,
-0.010219649411737919,
0.02018689177930355,
-0.015356998890638351,
0.025617143139243126,
0.0169368963688612,
-0.008597191423177719,
0.052396681159734726,
-0.04536060243844986,
0.016679584980010986,
0.0061667077243328094,
0.050288837403059006,
-0.005000332370400429,
0.01725146733224392,
0.02090279757976532,
0.082278773188591,
0.04832863062620163,
0.008036485873162746,
-0.0705898329615593,
-0.01345564890652895,
0.011467156931757927,
-0.0012327932054176927,
-0.021168867126107216,
-0.04179544746875763,
-0.011864649131894112,
0.04611813277006149,
0.019808350130915642,
0.0005894186906516552,
-0.01004872191697359,
0.021341998130083084,
-0.015090515837073326,
0.029981272295117378,
0.0008813170134089887,
0.017616864293813705,
0.009290162473917007,
0.04226839914917946,
0.005320324096828699,
0.008908290416002274,
0.010137823410332203,
0.006865425501018763,
0.0004830037651117891,
0.03876327723264694,
0.01864086277782917,
0.013650626875460148,
-0.014331633225083351,
0.07002958655357361,
-0.027422962710261345,
0.004012906923890114,
0.037231918424367905,
-0.034350257366895676,
0.014044579118490219,
0.05526486411690712,
0.00523543544113636,
-0.03933423385024071,
-0.0012607770040631294,
-0.0025585577823221684,
0.0280208270996809,
-0.005347926169633865,
-0.055446557700634,
-0.037633903324604034,
-0.0326390340924263,
0.01118504535406828,
0.07130905985832214,
-0.013755920343101025,
-0.01682707481086254,
-0.01599455624818802,
0.005836760625243187,
-0.0010936451144516468,
-0.006927328184247017,
-0.024273307994008064,
0.03790031373500824,
0.018901798874139786,
0.03346966207027435,
-0.005710569676011801,
0.019685426726937294,
0.016544362530112267,
-0.019384488463401794,
0.10373526811599731,
0.07827743142843246,
0.029416093602776527,
-0.040334250777959824,
-0.022395191714167595,
-0.04120225831866264,
-0.0737864226102829,
0.017467565834522247,
-0.0010078457416966558,
0.021275317296385765,
-0.039742909371852875,
0.003776934929192066,
0.041872262954711914,
-0.0005060575203970075,
0.038993142545223236,
0.014129003509879112,
0.02399718016386032,
-0.04125179722905159,
-0.15962255001068115,
-0.058610934764146805,
0.040145013481378555,
-0.02021576277911663,
-0.03345179930329323,
-0.040145616978406906,
-0.011431274935603142,
0.03117920085787773,
0.06956348568201065,
-0.03708174452185631,
-0.01798301748931408,
-0.0038333756383508444,
0.05324786528944969,
0.030275097116827965,
-0.012666992843151093,
-0.0028445518109947443,
-0.003949057310819626,
-0.01574752852320671,
-0.02809648960828781,
-0.03962527588009834,
0.05163184553384781,
0.05367286875844002,
-0.023572353646159172,
0.027519620954990387,
0.05936475470662117,
-0.011466248892247677,
-0.016097458079457283,
0.010919108986854553,
-0.004898835904896259,
-0.04409874603152275,
0.06641780585050583,
-0.003822912694886327,
0.013515371829271317,
0.024967767298221588,
-0.004325488582253456,
-0.0022716170642524958,
-0.009809386916458607,
0.019417650997638702,
-0.02930561825633049,
-0.020203182473778725,
-0.036485422402620316,
-0.021977394819259644,
0.016162950545549393,
-0.014842365868389606,
-0.03856419399380684,
-0.015236282721161842,
-0.010753441601991653,
0.015224610455334187,
0.014549139887094498,
0.027061935514211655,
0.02205055020749569,
-0.04452087730169296,
-0.02947344072163105,
-0.027051808312535286,
0.00046498357551172376,
-0.050835397094488144,
0.008390906266868114,
0.016256269067525864,
-0.018064351752400398,
0.028786055743694305,
-0.005208986345678568,
-0.006537667475640774,
0.0026278949808329344,
-0.048703767359256744,
-0.02929689921438694,
0.04390048608183861,
0.004279911983758211,
-0.025720002129673958,
0.024445567280054092,
0.036135945469141006,
0.059001754969358444,
0.03319472074508667,
0.004341399297118187,
0.0004958133213222027,
-0.03409843146800995,
-0.007112845778465271,
-0.03014805167913437,
0.0211003627628088,
-0.0034156842157244682,
-0.019706981256604195,
0.015234620310366154,
-0.01325899362564087,
-0.021320078521966934,
0.026631584390997887,
-0.05972438305616379,
0.04590819403529167,
0.016036611050367355,
-0.009060818701982498,
-0.022476738318800926,
0.020885175094008446,
0.010193243622779846,
0.012881145812571049,
-0.0057762302458286285,
-0.012799246236681938,
-0.06167728453874588,
-0.02403370290994644,
0.010343755595386028,
0.06255312263965607,
-0.0195561945438385,
0.028124429285526276,
-0.0016639111563563347,
0.033670321106910706,
-0.014510858803987503,
-0.013252473436295986,
-0.04508224129676819,
-0.009771045297384262,
0.020315127447247505,
0.02557932212948799,
0.004631613846868277,
0.009082332253456116,
0.002632319927215576,
-0.014883732423186302,
0.01274617575109005,
-0.01851973682641983,
-0.0017586018657311797,
0.03831515833735466,
-0.010284826159477234,
-0.00925804115831852,
-0.013296176679432392,
-0.020452290773391724,
-0.009405676275491714,
-0.024293122813105583,
0.0062630632892251015,
0.004503581672906876,
0.004464892204850912,
-0.021038146689534187,
-0.04638848453760147,
-0.03758345916867256,
-0.010715176351368427,
-0.005735276732593775,
-0.054090067744255066,
-0.01841680333018303,
0.022299332544207573,
-0.04907609149813652,
-0.03943340480327606,
-0.025382352992892265,
0.0004775208653882146,
0.025705479085445404,
0.004502173978835344,
0.036023806780576706,
-0.0020339335314929485,
0.02303130179643631,
-0.06339661777019501,
-0.02926534414291382,
-0.005347208585590124,
-0.021548854187130928,
0.02511284314095974,
-0.0033247405663132668,
-0.053131576627492905,
0.03204430639743805,
-0.051221512258052826,
-0.034035824239254,
0.037091031670570374,
-0.013898484408855438,
0.012376992963254452,
0.01281439047306776,
-0.007422036491334438,
-0.05844440311193466,
-0.02167312428355217,
-0.001360347494482994,
-0.019525893032550812,
-0.07972361147403717,
-0.022479426115751266,
0.048927728086709976,
-0.002700340934097767,
-0.042659301310777664,
-0.026739785447716713,
-0.030065899714827538,
-0.04429977759718895,
-0.005729429889470339,
-0.019401853904128075,
0.008243127726018429,
-0.022790273651480675,
-0.00897341500967741,
0.039176344871520996,
-0.025210924446582794,
-0.029702430590987206,
-0.03859708085656166,
-0.09031258523464203,
0.014348555356264114,
0.011317639611661434,
0.05629179999232292,
-0.013721369206905365,
-0.001551518333144486,
0.07745441794395447,
-0.0032311384566128254,
-0.02841928042471409,
0.015898913145065308,
0.01886928081512451,
-0.010835794731974602,
-0.0012593171559274197,
0.013260210864245892,
0.034088656306266785,
-0.005406780634075403,
0.06786780059337616,
-0.0036876739468425512,
0.015554293990135193,
0.00020784130902029574,
-0.0010801175376400352,
0.014547728933393955,
0.04880765825510025,
0.02214636094868183,
-0.009912313893437386,
0.05120418965816498,
0.028490986675024033,
-0.027773790061473846,
0.02278706431388855,
-0.015054002404212952,
0.005076674744486809,
0.025845395401120186,
-0.060933440923690796,
0.08239129185676575,
0.002043036976829171,
0.013979479670524597,
-0.044488195329904556,
0.029248738661408424,
-0.007258888334035873,
-0.005622671917080879,
0.009436139836907387,
-0.006538722664117813,
0.03682525455951691,
-0.013060634024441242,
0.01060667634010315,
0.04757481813430786,
0.025366423651576042,
-0.0311631727963686,
-0.0213612150400877,
-0.008972146548330784,
0.027910253033041954,
0.020125562325119972,
-0.007214127108454704,
-0.05612531676888466,
0.025720743462443352,
0.037985917180776596,
0.015074947848916054,
-0.016221914440393448,
-0.010854425840079784,
-0.013137726113200188,
-0.02126067318022251,
0.0010129133006557822,
0.007519821170717478,
0.038846246898174286,
0.0018118807347491384,
0.06569863110780716,
0.00926714763045311,
-0.010189628228545189,
-0.02214113250374794,
0.00767254875972867,
-0.060122475028038025,
-0.015049471519887447,
-0.009423737414181232,
-0.0031129401177167892,
0.01042972318828106,
-0.005539675243198872,
0.01625748910009861,
-0.047538500279188156,
-0.0637018159031868,
-0.018086032941937447,
0.00023608692572452128,
-0.049735262989997864,
-0.012185501866042614,
-0.01261906698346138,
-0.034534454345703125,
-0.029155150055885315,
0.06910883635282516,
0.023207254707813263,
-0.0022450322285294533,
-0.008110404014587402,
0.02632652223110199,
-0.03440294787287712,
0.01593141071498394,
0.0148838572204113,
-0.013228753581643105,
0.042998094111680984,
0.024788009002804756,
0.040455542504787445,
0.05109060928225517,
0.005308554042130709,
0.006246231030672789,
0.013281112536787987,
0.05438271164894104,
0.0019183257827535272,
-0.01652447134256363,
0.029402587562799454,
0.004389322828501463,
0.008905761875212193,
0.0036690998822450638,
0.048112787306308746,
0.002610057359561324,
0.01503006462007761,
0.01657784730195999,
0.012928776443004608,
0.0023929814342409372,
-0.009420478716492653,
0.024331538006663322,
-0.016576429829001427,
-0.009640096686780453,
-0.0012646233662962914,
0.007517954334616661,
-0.012904501520097256,
0.004358711652457714,
-0.05093010142445564,
0.007035085465759039,
-0.0118997348472476,
0.03774863854050636,
-0.0036528606433421373,
0.01711992174386978,
-0.019514409825205803,
-0.02074066735804081,
-0.0416129007935524,
0.00576076190918684,
-0.01914500817656517,
0.016630548983812332,
0.011164252646267414,
0.06216368079185486,
0.00997250061482191,
0.014531778171658516,
0.0014845281839370728,
-0.0343356654047966,
-0.032584547996520996,
0.033738624304533005,
0.038599587976932526,
0.013260455802083015,
-0.012153624556958675,
-0.024948449805378914,
-0.04645546153187752,
0.04933709651231766,
-0.013692235574126244,
0.033688195049762726,
0.001383360242471099,
0.0051511493511497974,
-0.019547345116734505,
-0.041668206453323364,
-0.019763460382819176,
-0.02467021904885769,
-0.041142355650663376,
0.007035212591290474,
-0.052214622497558594,
-0.006117146462202072,
-0.007681878283619881,
0.002885151654481888,
0.03246413171291351,
0.0485324002802372,
-0.0010140672093257308,
0.0038328811060637236,
-0.008591396734118462,
-0.00023863835667725652,
0.006381895858794451,
-0.07602802664041519,
0.030616767704486847,
-0.013573545962572098,
0.0011184487957507372,
0.025027699768543243,
-0.025811972096562386,
-0.055834390223026276,
0.013262015767395496,
-0.006648136302828789,
0.0014544939622282982,
0.0394873209297657,
-0.05006449297070503,
0.07996216416358948,
0.012751223519444466,
-0.0006064088083803654,
0.020353808999061584,
0.026400219649076462,
0.00791945867240429,
0.021758543327450752,
-0.026881590485572815,
0.011096509173512459,
-0.06131256744265556,
0.033183470368385315,
-0.05824599042534828,
0.004751953762024641,
-0.0183484498411417,
0.029140161350369453,
-0.010685710236430168,
-0.012841135263442993,
0.026392770931124687,
-0.04156799241900444,
0.03538566082715988,
0.01129479892551899,
-0.008709186688065529,
0.008638730272650719,
-0.03241429477930069,
0.008470931090414524,
0.006229930091649294,
-0.03318388760089874,
-0.009119902737438679,
0.02771267294883728,
0.021992776542901993,
0.03511783853173256,
-0.0038198947440832853,
0.03543974086642265,
-0.051736753433942795,
-0.05479481443762779,
0.017258211970329285,
-0.03741919621825218,
0.03676173835992813,
-0.03270455822348595,
0.04318774864077568,
0.00596557417884469,
-0.019188620150089264,
-0.04770760238170624,
0.0237114354968071,
-0.016755608841776848,
0.0003296672075521201,
-0.01799553446471691,
-0.007636930327862501,
-0.03031470626592636,
0.005847559776157141,
-0.0670589953660965,
-0.00047935047768987715,
-0.002842055633664131,
-0.02140124700963497,
-0.0025805397890508175,
-0.026260677725076675,
0.005469731520861387,
-0.022287419065833092,
-0.007514801807701588,
-0.01623779721558094,
0.03804164379835129,
-0.03233702480792999,
-0.017524326220154762,
-0.00018106015340890735,
0.025350218638777733,
0.03856580704450607,
-0.018622277304530144,
-0.019340308383107185,
0.0001806493237381801,
-0.016465848311781883,
0.03194718435406685,
0.03281034529209137,
-0.014794782735407352,
-0.019776929169893265,
-0.03098621591925621,
-0.014712097123265266,
0.006308236625045538,
0.013904280960559845,
-0.04617014899849892,
-0.018408700823783875,
0.02271456830203533,
0.014899480156600475,
-0.023546993732452393,
0.02185017429292202,
0.021842140704393387,
-0.009235796518623829,
0.016835693269968033,
0.04358794540166855,
0.008657457306981087,
-0.013483420945703983,
-0.07618153840303421,
0.0018225883832201362,
-0.042644158005714417,
-0.006504069548100233,
0.010177595540881157,
0.019878840073943138,
0.016006754711270332,
-0.0022123027592897415,
0.001834954833611846,
-0.024461818858981133,
0.005548529792577028,
-0.02831990085542202,
0.014726651832461357,
-0.02840351313352585,
0.008002091199159622,
-0.047252532094717026,
-0.017772968858480453,
-0.06944352388381958,
-0.02232678048312664,
0.019921859726309776,
0.0115437600761652,
0.015123275108635426,
0.01209824439138174,
0.014077004045248032,
-0.049136336892843246,
-0.037003811448812485,
0.016988251358270645,
0.033606816083192825,
-0.0006079772720113397,
0.04593919962644577,
-0.0424504317343235,
-0.02825535461306572,
0.0016944605158641934,
0.04293307662010193,
-0.05000339448451996,
-0.010627442970871925,
0.012432956136763096,
0.013667275197803974,
0.022587064653635025,
-0.048066146671772,
-0.028094517067074776,
0.017756255343556404,
-0.03569567948579788,
-0.0030644875951111317,
0.015531009994447231,
0.020128121599555016,
0.009988481178879738,
0.01789213716983795,
0.012837650254368782,
-0.057489559054374695,
-0.013952582143247128,
-0.0320134274661541,
0.004246515221893787,
0.020519673824310303,
-0.007808876223862171,
0.0002736671012826264,
0.00219131400808692,
0.03782926872372627,
-0.007702534552663565,
-0.000744373188354075,
0.01782626286149025,
-0.04747992381453514,
-0.011334618553519249,
-0.040814559906721115,
-0.043677978217601776,
0.030459553003311157,
-0.009513995610177517,
-0.019637761637568474,
0.016114043071866035,
-0.018969254568219185,
0.06345926225185394,
0.017638331279158592,
0.038930460810661316,
-0.049014195799827576,
0.028078433126211166,
0.013382643461227417,
0.025961969047784805,
-0.01883303001523018,
0.03500828891992569,
0.1413140445947647,
0.06152578070759773,
0.013079353608191013,
-0.020970208570361137,
-0.020177921280264854,
-0.008807852864265442,
0.042246636003255844,
-0.012271656654775143,
-0.0002435794594930485,
-0.004241436254233122,
-0.007138016168028116,
-0.01700131595134735,
0.06244542822241783,
0.009675220586359501,
-0.006265935953706503,
0.02641899324953556,
-0.07533777505159378,
-0.04585232958197594,
-0.018694037571549416,
0.03867418318986893,
-0.017260756343603134,
-0.0012088194489479065,
-0.036873869597911835,
-0.0015616248128935695,
-0.009315988048911095,
0.011812020093202591,
-0.02472851052880287,
-0.010763788595795631,
0.03238144516944885,
-0.007507801987230778,
-0.042132601141929626,
-0.014909551478922367,
-0.020255524665117264,
-0.005236542783677578,
-0.028752774000167847,
0.02880452759563923,
0.06497664749622345,
-0.03667944669723511,
0.022037003189325333,
0.03155599907040596,
0.005665131378918886,
0.01477131713181734,
0.019510909914970398,
-0.01332986168563366,
-0.03938610106706619,
-0.01631353422999382,
-0.002783128060400486,
0.08570234477519989,
-0.02846485562622547,
-0.04119207337498665,
-0.012418625876307487,
-0.012710624374449253,
-0.007632207125425339,
-0.05855191498994827,
-0.037768132984638214,
0.0022276153322309256,
0.029673226177692413,
-0.001313226530328393,
0.011633246205747128,
0.006878730840981007,
0.029430225491523743,
0.0017015476478263736,
0.020144544541835785,
-0.02752872370183468,
0.007671487517654896,
0.007195184472948313,
0.009069867432117462,
0.02988545037806034,
0.02941155806183815,
0.023656735196709633,
-0.03435109928250313,
0.0055581023916602135,
-0.03825392574071884,
-0.021825481206178665,
0.08537902683019638,
0.0234379880130291,
0.06851218640804291,
0.006033315323293209,
0.03401227295398712,
-0.01300081331282854,
-0.044412847608327866,
0.03578650951385498,
-0.014966090209782124,
-0.023107118904590607,
-0.0011965811718255281,
0.02683427929878235,
0.0010862434282898903,
0.08544772863388062,
0.006942328065633774,
-0.017346257343888283,
0.029137801378965378,
0.011119399219751358,
0.047162171453237534,
-0.010790645144879818,
-0.019832031801342964,
0.02807297557592392,
-0.038406841456890106,
0.01830693706870079,
-0.0349922813475132,
0.007798987906426191,
0.0027500216383486986,
0.02887476235628128,
-0.02144470624625683,
0.032728277146816254,
0.001684542396105826,
-0.007189930882304907,
0.012052325531840324,
-0.02551650069653988,
-0.00749838026240468,
0.035777829587459564,
0.06969668716192245,
-0.028051165863871574,
-0.036133427172899246,
-0.016730593517422676,
0.012300517410039902,
-0.008500702679157257,
-0.0011463428381830454,
-0.017172828316688538,
-0.019580062478780746,
0.02787725441157818,
0.024900145828723907,
-0.01212612446397543,
0.011962177231907845,
-0.04302803426980972,
0.022550523281097412,
0.005051311571151018,
0.0009056195267476141,
-0.013458575122058392,
0.030264420434832573,
-0.015231986530125141,
-0.028826750814914703,
0.038468651473522186,
0.02560584619641304,
-0.037706516683101654,
-0.032295241951942444,
0.02804703637957573,
0.01165827177464962,
0.016545457765460014,
0.011027351953089237,
-0.00190332334022969,
0.004427304957062006,
-0.040900975465774536,
-0.04504239186644554,
-0.0035714188124984503,
-0.01888204924762249,
0.036203235387802124,
0.03338593989610672,
0.00031919017783366144,
-0.04615001007914543,
0.029431264847517014,
-0.020247116684913635,
0.005260346457362175,
-0.010652067139744759,
-0.013226556591689587,
-0.0000326831141137518,
-0.0034384990576654673,
0.01822027750313282,
0.008753912523388863,
0.01219126395881176,
0.05838806927204132,
0.0054964227601885796,
0.024794578552246094,
0.0035478500649333,
0.017365306615829468,
-0.005388932768255472,
0.0348367914557457,
0.026352237910032272,
-0.030181631445884705,
0.0007608819869346917,
0.050707001239061356,
-0.03186407312750816,
0.06960117071866989,
0.04737021401524544,
0.01171592716127634,
-0.10384121537208557,
-0.01829914003610611,
0.009800251573324203,
0.018347587436437607,
0.018928347155451775,
-0.0013553877361118793,
0.015957171097397804,
0.022629862651228905,
-0.1012149378657341,
0.03360230103135109,
-0.014929836615920067,
0.016189267858862877,
-0.020839255303144455,
0.03269355371594429,
-0.08618175983428955,
0.04666754975914955,
0.01573997735977173,
0.06356268376111984,
-0.019766252487897873,
0.028745122253894806,
-0.007803735323250294,
-0.037826597690582275,
-0.05033334717154503,
0.03813447430729866,
-0.005199591629207134,
0.027380922809243202,
0.08472611010074615,
-0.0341680683195591,
-0.01376516092568636,
0.007006226107478142,
0.01621972769498825,
0.008186079561710358,
-0.05629768595099449,
0.0016564681427553296,
0.03385431692004204,
0.025945520028471947,
0.01052884105592966,
-0.017255274578928947,
0.027547314763069153,
0.02641621045768261,
0.014539164490997791,
0.0037153016310185194,
0.02444419078528881,
-0.025273555889725685,
0.011947746388614178,
-0.03066954016685486,
-0.025463808327913284,
0.019290383905172348,
0.03992985188961029,
0.009919735603034496,
0.03265216201543808,
0.014810522086918354,
-0.020007381215691566,
-0.00604617316275835,
-0.0008545513264834881,
-0.054025232791900635,
-0.006169503554701805,
0.031454894691705704,
0.0505557507276535,
-0.04243553802371025,
0.0034925639629364014,
-0.021899806335568428,
-0.03828451782464981,
0.027392756193876266,
0.010046835988759995,
-0.00929517112672329,
-0.06265358626842499,
-0.025589359924197197,
0.005509482230991125,
0.016352955251932144,
0.025902701541781425,
-0.0364932082593441,
-0.034913595765829086,
-0.009531652554869652,
0.010089108720421791,
0.020770996809005737,
-0.026603400707244873,
-0.03568195924162865,
-0.022725142538547516,
-0.08136593550443649,
0.06014256924390793,
0.03399369493126869,
0.03703313693404198,
-0.03440774232149124,
-0.030551858246326447,
0.025818105787038803,
0.03675893321633339,
0.06122347339987755,
0.019945288076996803,
-0.020675309002399445,
0.01005745679140091,
0.001397876301780343,
0.04299534857273102,
-0.03184134513139725,
0.02010417729616165,
-0.004803314805030823,
0.0065546599216759205,
0.0002670465037226677,
-0.005831501446664333,
-0.012621993198990822,
0.023168038576841354,
0.04322466999292374,
-0.014459827914834023,
0.015214292332530022,
-0.0021757313515990973,
-0.02965737134218216,
0.10664767026901245,
-0.013673298060894012,
-0.011423228308558464,
0.06846641004085541,
-0.004000467713922262,
0.04337005317211151,
0.033657122403383255,
-0.012569538317620754,
-0.032459333539009094,
0.0003493133408483118,
0.0019468346145004034,
-0.027854815125465393,
0.01179080456495285,
0.0190235935151577,
0.013872791081666946,
-0.013954143039882183,
-0.009393909014761448,
0.04215845465660095,
-0.04355946183204651,
-0.02062593773007393,
0.051303792744874954,
0.017007775604724884,
0.04926322400569916,
0.011042878963053226,
0.00175339390989393,
0.005658785346895456,
-0.004467243794351816,
0.0010761900339275599,
0.059238776564598083,
0.05317448824644089,
-0.0095379538834095,
0.055177655071020126,
0.06413961201906204,
-0.027443183586001396,
0.0044542779214680195,
0.02183382213115692,
0.00958994310349226,
-0.04626372456550598,
0.003616282483562827,
0.020249437540769577,
-0.02642611414194107,
-0.0027254039887338877,
0.020434854552149773,
-0.03354301303625107,
0.1273757666349411,
-0.010298224166035652,
0.01212330162525177,
-0.024529675021767616,
0.027732636779546738,
-0.026756903156638145,
0.01163733471184969,
0.01728716306388378,
0.06396079063415527,
-0.03721512481570244,
-0.019863680005073547,
-0.0579930879175663,
0.015392874367535114,
0.020066063851118088,
-0.05808695778250694,
0.025338470935821533,
0.01852918416261673,
0.01024770550429821,
0.008556557819247246,
-0.003731998847797513,
-0.02670523338019848,
-0.04537522792816162,
0.022073164582252502,
0.01982872374355793,
0.0008200739393942058,
-0.010125708766281605,
0.015545694157481194,
-0.0074365707114338875,
0.06277306377887726,
-0.03003552556037903,
0.0071183727122843266,
-0.005192175041884184,
0.05803613364696503,
-0.030676238238811493,
-0.018647363409399986
] |
<p>The no-cloning theorem implies that we cannot use entanglement to send signals faster-than-light. Has anyone proved the contrapositive? That is, if we are given a system for superluminal signalling can we use it to violate the no-cloning theorem?</p>
| 9,401 |
[
0.006904806941747665,
-0.002899064449593425,
0.007149340584874153,
-0.03643781691789627,
0.04560653865337372,
-0.009770684875547886,
-0.027224447578191757,
-0.01095674093812704,
0.013225647620856762,
-0.02452019229531288,
0.009540059603750706,
0.038523901253938675,
0.030591821298003197,
0.005163731053471565,
-0.013489081524312496,
0.012176216579973698,
0.00018897993140853941,
0.01295014563947916,
-0.007781782653182745,
-0.03133576735854149,
0.012919526547193527,
0.038636963814496994,
0.009159265086054802,
-0.020459327846765518,
-0.027930334210395813,
0.00345997023396194,
-0.00131780665833503,
-0.006428882479667664,
0.02379521355032921,
0.05550927296280861,
-0.010603073984384537,
-0.0025401036255061626,
-0.02021438628435135,
0.07417940348386765,
0.007593264803290367,
0.01966257207095623,
-0.05880637839436531,
-0.04232948645949364,
0.028630003333091736,
-0.02755128964781761,
0.002562187612056732,
-0.00903234537690878,
0.020873012021183968,
0.05562794208526611,
-0.010600483976304531,
-0.003754841396585107,
0.007862972095608711,
-0.02728521265089512,
0.04112332686781883,
-0.06455887109041214,
0.07050234824419022,
-0.01082066260278225,
0.0055300346575677395,
0.007822329178452492,
-0.019749313592910767,
0.02918729931116104,
0.08735234290361404,
0.05810164287686348,
-0.0029868585988879204,
-0.02773076295852661,
-0.03005264140665531,
0.002996409311890602,
0.007779437582939863,
-0.03488735109567642,
-0.05658527463674545,
-0.01130224671214819,
0.013510865159332752,
-0.00888662226498127,
0.02622358873486519,
-0.03587689250707626,
-0.010547517798841,
-0.0011334898881614208,
0.05316615849733353,
0.023980403319001198,
-0.036254461854696274,
-0.016525179147720337,
0.005383920390158892,
-0.020443061366677284,
0.033599063754081726,
0.0639728382229805,
-0.01833927258849144,
-0.002142110839486122,
0.016406234353780746,
0.0433536022901535,
0.01871577836573124,
-0.04046567901968956,
0.038774557411670685,
-0.015833737328648567,
0.010810707695782185,
0.0666809007525444,
-0.024955326691269875,
-0.010566183365881443,
0.033332791179418564,
0.007847040891647339,
-0.021228430792689323,
0.004332921002060175,
-0.018415037542581558,
0.04710374400019646,
0.011989409103989601,
-0.054225437343120575,
0.0013409339589998126,
-0.02582394704222679,
0.009866426698863506,
0.05126677826046944,
0.005205267574638128,
-0.023208556696772575,
0.006540545262396336,
0.035440653562545776,
-0.007943944074213505,
0.0032163704745471478,
-0.06137687712907791,
-0.012311810627579689,
0.02647566795349121,
0.0009707373101264238,
0.008406969718635082,
-0.021424617618322372,
-0.027883030474185944,
-0.007489055395126343,
0.06011152267456055,
0.0771673321723938,
0.033849071711301804,
-0.019221574068069458,
0.012375935912132263,
-0.04573171213269234,
-0.016166536137461662,
0.023967750370502472,
-0.010082775726914406,
0.009244203567504883,
-0.0046322098933160305,
0.015470510348677635,
0.038397416472435,
-0.01902635395526886,
-0.021074939519166946,
-0.008535107597708702,
0.06057826057076454,
-0.042864542454481125,
-0.12187454849481583,
-0.09180968254804611,
0.06679926067590714,
-0.005153589881956577,
0.005193330813199282,
-0.06213805451989174,
0.036006007343530655,
0.04346926882863045,
0.1023995503783226,
0.0037929199170321226,
0.012992636300623417,
-0.004083125852048397,
0.040011487901210785,
0.04023488610982895,
-0.00008442826947430149,
-0.00659135589376092,
0.02085263468325138,
-0.014032186008989811,
0.002464649500325322,
-0.08031392842531204,
0.008092572912573814,
0.0399150624871254,
-0.02937142923474312,
-0.05705026164650917,
0.06003537401556969,
-0.01729360967874527,
0.031501490622758865,
0.009159437380731106,
-0.03373824805021286,
-0.06484381854534149,
0.09202122688293457,
0.021956223994493484,
-0.00596641656011343,
0.015775704756379128,
-0.014790620654821396,
0.040324851870536804,
0.0016171749448403716,
0.016660451889038086,
0.013634027913212776,
-0.055216800421476364,
0.005164853762835264,
-0.014395056292414665,
0.012742566876113415,
-0.017590085044503212,
-0.00023460709780920297,
-0.007545921485871077,
0.01918930374085903,
0.0033463677391409874,
0.0008976381504908204,
0.01817968301475048,
-0.046511467546224594,
-0.01362537406384945,
0.03203383833169937,
-0.05870542302727699,
0.022093305364251137,
-0.03387918695807457,
0.04446952044963837,
0.06356391310691833,
-0.027250977233052254,
0.027804505079984665,
-0.0062515223398804665,
0.027271101251244545,
-0.01901630125939846,
-0.03434004262089729,
0.0048684896901249886,
0.043317925184965134,
0.0326024554669857,
-0.003317425027489662,
0.004095893818885088,
0.04849898815155029,
0.030085856094956398,
0.01771203801035881,
0.03512655198574066,
0.011646312661468983,
-0.04314468801021576,
0.025942988693714142,
0.034265682101249695,
0.046693406999111176,
-0.018933651968836784,
0.029719585552811623,
0.002927812049165368,
0.005618171766400337,
-0.00961039587855339,
0.05348200350999832,
-0.040915895253419876,
0.05338933691382408,
-0.0053769443184137344,
0.040468957275152206,
-0.012163919396698475,
0.0076384637504816055,
0.05187179893255234,
-0.0008840499795041978,
0.01481575332581997,
-0.05870264023542404,
-0.039993926882743835,
-0.026452695950865746,
-0.014292989857494831,
0.035057343542575836,
-0.045561086386442184,
0.00011952183558605611,
0.01915479637682438,
0.01693904772400856,
0.03313470631837845,
0.018784312531352043,
-0.04051514342427254,
-0.019615905359387398,
0.0042760176584124565,
0.007448230870068073,
0.02195580117404461,
0.015761736780405045,
0.0064159175381064415,
0.008038603700697422,
-0.013650358654558659,
0.008643461391329765,
-0.04107849672436714,
-0.029854239895939827,
-0.034067586064338684,
-0.0017271749675273895,
0.026705456897616386,
-0.052154313772916794,
-0.0018454979872331023,
-0.028399063274264336,
0.023274093866348267,
0.02600814402103424,
0.021490532904863358,
-0.017080524936318398,
-0.03066437691450119,
-0.013576868921518326,
-0.012712577357888222,
-0.02331819199025631,
-0.050274334847927094,
0.015688590705394745,
0.051997289061546326,
-0.03201478719711304,
0.03672957792878151,
-0.010598464868962765,
0.00792826060205698,
-0.006127913016825914,
-0.001852668123319745,
0.019245848059654236,
-0.045507535338401794,
0.0280769020318985,
-0.03500004857778549,
-0.022501865401864052,
-0.0028085752855986357,
-0.0301070474088192,
-0.003810917492955923,
0.025459060445427895,
-0.04835313931107521,
0.0317821241915226,
-0.03835119679570198,
-0.03313367813825607,
0.04451783373951912,
-0.03426451236009598,
0.04325668886303902,
0.0076111480593681335,
-0.020215295255184174,
-0.042170487344264984,
-0.012768624350428581,
-0.04833222180604935,
-0.009641422890126705,
-0.0003550172259565443,
0.03404610976576805,
0.0488978736102581,
0.020483389496803284,
-0.05853058397769928,
0.0225029569119215,
-0.03017285466194153,
-0.03676937520503998,
0.008845861069858074,
-0.014847946353256702,
0.017558874562382698,
-0.05405521020293236,
0.03761277720332146,
-0.006063987500965595,
-0.061632975935935974,
0.01685607247054577,
-0.030456872656941414,
-0.08443740010261536,
0.059410858899354935,
0.019062895327806473,
0.0510360524058342,
0.006681197322905064,
-0.0331248939037323,
0.060723695904016495,
0.038328103721141815,
-0.01605789177119732,
-0.011880861595273018,
-0.01702936366200447,
0.022952336817979813,
-0.0536198727786541,
-0.000705364509485662,
0.016360940411686897,
0.006644833367317915,
0.03696972131729126,
0.036913417279720306,
-0.007257757242769003,
0.028093857690691948,
-0.013597993180155754,
-0.026038363575935364,
-0.0238261129707098,
0.035191576927900314,
-0.002630616072565317,
0.045460641384124756,
0.009707244113087654,
-0.04426537826657295,
0.00032704678596928716,
0.015288730151951313,
0.04454764351248741,
-0.03061901405453682,
-0.01975514553487301,
0.04163547605276108,
0.03439349681138992,
0.03920941799879074,
0.0009570682886987925,
0.04545007646083832,
-0.029990356415510178,
0.019002823159098625,
-0.004995914176106453,
0.04595985263586044,
0.02581741474568844,
-0.03473275527358055,
0.020940527319908142,
0.058950163424015045,
0.014446433633565903,
-0.02774403616786003,
-0.015237368643283844,
-0.003096196101978421,
-0.004695633891969919,
0.015391617082059383,
-0.010420962236821651,
-0.036798231303691864,
0.043038222938776016,
0.002896650694310665,
-0.0046421536244452,
0.024253053590655327,
-0.0026057306677103043,
-0.013652895577251911,
-0.029157714918255806,
0.006588345393538475,
-0.02352401241660118,
0.03611498698592186,
0.0031804365571588278,
0.04976429045200348,
0.017182737588882446,
0.033666566014289856,
-0.03363620862364769,
-0.0081267599016428,
-0.06081894040107727,
0.005448545794934034,
-0.04185037314891815,
-0.028255147859454155,
0.006362202111631632,
-0.01269471738487482,
-0.01946081593632698,
-0.0450902059674263,
-0.05894504860043526,
-0.022316226735711098,
0.004282511305063963,
-0.08877931535243988,
0.006429015193134546,
-0.043166469782590866,
-0.05461397022008896,
-0.025098972022533417,
0.025077486410737038,
0.03238135576248169,
0.004426286090165377,
-0.02539236657321453,
0.015749812126159668,
-0.06918200105428696,
0.016826452687382698,
0.019129090011119843,
0.014931666664779186,
-0.019188515841960907,
0.010614126920700073,
0.04072340205311775,
0.01627178303897381,
-0.04221401363611221,
-0.0048645189963281155,
0.02396647445857525,
0.026943517848849297,
-0.008949177339673042,
-0.001875141984783113,
-0.02971232309937477,
-0.03990253061056137,
-0.04351828247308731,
0.02620702050626278,
0.06288230419158936,
-0.02700245939195156,
0.016596471890807152,
0.007963490672409534,
0.012050432153046131,
0.0024946187622845173,
0.011798813007771969,
0.06925404816865921,
0.007685924880206585,
-0.01689223386347294,
-0.014385177753865719,
-0.03418484702706337,
0.022006288170814514,
-0.005246336571872234,
0.01779797300696373,
0.01706661470234394,
-0.007215358316898346,
0.011129097081720829,
-0.015154246240854263,
0.036819860339164734,
-0.01712731644511223,
0.018871640786528587,
0.002969830995425582,
-0.012328892946243286,
-0.004794253036379814,
0.03661554306745529,
-0.017335427924990654,
0.016808757558465004,
-0.023817235603928566,
0.044151678681373596,
-0.017017917707562447,
-0.0733131542801857,
0.0018816463416442275,
0.026585709303617477,
0.031433332711458206,
0.027408640831708908,
-0.0018038980197161436,
-0.06426036357879639,
-0.0489070750772953,
0.016490258276462555,
-0.015239613130688667,
0.02877429686486721,
0.008316917344927788,
-0.005350304767489433,
-0.0077947280369699,
0.024423960596323013,
0.0345161110162735,
0.03079507127404213,
-0.023321595042943954,
0.00022878183517605066,
0.01737993210554123,
-0.01892954856157303,
-0.0009214907186105847,
0.011857322417199612,
0.03414171561598778,
0.09678807109594345,
0.007092101965099573,
-0.0038779026363044977,
0.0019952936563640833,
0.02648887038230896,
-0.04119150713086128,
-0.04585723206400871,
0.013267911039292812,
0.0031655936036258936,
-0.0636204183101654,
0.06416574865579605,
-0.015467137098312378,
-0.03229609131813049,
0.01843426190316677,
-0.007778092287480831,
-0.017607994377613068,
0.054974671453237534,
-0.03062690608203411,
0.022942017763853073,
0.00709280651062727,
0.016602931544184685,
0.02859986387193203,
0.0618426576256752,
-0.001009802334010601,
0.02077169343829155,
0.021808750927448273,
0.05579479783773422,
-0.05342858284711838,
0.03857642412185669,
0.008783872239291668,
0.012752474285662174,
-0.050179820507764816,
0.022907964885234833,
-0.02396669238805771,
-0.01701449044048786,
0.02206425927579403,
-0.007352184504270554,
-0.019722914323210716,
0.03898562863469124,
-0.010464858263731003,
0.01100634690374136,
-0.026745816692709923,
0.03397371619939804,
-0.0060555036179721355,
-0.017835566774010658,
0.022026052698493004,
0.013197667896747589,
0.006375831551849842,
0.0015937935095280409,
-0.010561860166490078,
0.024805692955851555,
-0.02601097710430622,
-0.016309931874275208,
0.019230661913752556,
-0.026813402771949768,
0.04521124064922333,
0.001812730566598475,
-0.014882144518196583,
0.00012416727258823812,
-0.05711717903614044,
-0.01888653077185154,
0.022654548287391663,
-0.04154421389102936,
0.011627093888819218,
-0.06100476533174515,
0.007858498021960258,
0.014804616570472717,
-0.021122734993696213,
-0.041374046355485916,
-0.04744105786085129,
0.011058725416660309,
0.022256802767515182,
0.012850929982960224,
-0.014153094962239265,
0.014236724004149437,
-0.02032071352005005,
-0.008096370846033096,
-0.06980452686548233,
0.04022374004125595,
-0.006033169571310282,
-0.00026301853358745575,
-0.02037557028234005,
0.004556587431579828,
0.006351890508085489,
-0.04232029244303703,
-0.010709894821047783,
-0.0005468230228871107,
-0.0005124840536154807,
0.015407569706439972,
0.003168649971485138,
0.03656775504350662,
-0.010233256965875626,
-0.028551088646054268,
0.009289140813052654,
0.0011342597426846623,
0.009607763960957527,
-0.0058728852309286594,
-0.031136268749833107,
0.032340992242097855,
0.002346110064536333,
0.0030863892752677202,
0.01054816972464323,
-0.01658201590180397,
0.0010551722953096032,
-0.006056223995983601,
-0.0002993781818076968,
0.018044238910079002,
0.0011904436396434903,
-0.054850880056619644,
0.04013993218541145,
0.02732921577990055,
0.021509287878870964,
-0.01925824023783207,
0.03582320734858513,
0.04135003685951233,
-0.019456736743450165,
-0.007892352528870106,
-0.026779284700751305,
0.014069424010813236,
-0.019835976883769035,
0.04475438967347145,
0.02262493222951889,
0.0006246853154152632,
-0.019225548952817917,
-0.056799501180648804,
-0.009221072308719158,
0.006126797758042812,
0.09251167625188828,
-0.009637078270316124,
0.016151858493685722,
0.000709915126208216,
-0.006854731123894453,
-0.017517060041427612,
-0.0319790244102478,
-0.011531953699886799,
0.021081844344735146,
0.002468165708705783,
0.023309141397476196,
0.030559251084923744,
-0.012433633208274841,
0.01860465481877327,
0.0630367174744606,
0.019498702138662338,
0.0070325396955013275,
0.05096067488193512,
0.02353404276072979,
0.04929628223180771,
-0.024840975180268288,
-0.022440457716584206,
0.026470690965652466,
-0.06371510028839111,
0.014895834028720856,
-0.022194677963852882,
0.008068939670920372,
0.0014272299595177174,
-0.0134670315310359,
0.01943250000476837,
-0.04443972557783127,
-0.046711515635252,
-0.05393547564744949,
-0.026330512017011642,
-0.005136232823133469,
0.014073656871914864,
0.03370225802063942,
-0.002218496985733509,
0.005016322247684002,
0.015167576260864735,
0.01690286584198475,
-0.04483785107731819,
-0.08138488978147507,
-0.04501896724104881,
-0.027019059285521507,
-0.0339420884847641,
0.05035366117954254,
0.012715567834675312,
-0.03776147961616516,
0.027558133006095886,
-0.02767755836248398,
0.03368394076824188,
-0.0184576865285635,
0.03787260875105858,
-0.03013005666434765,
0.058987073600292206,
-0.009843423962593079,
0.04449212923645973,
-0.014632364735007286,
0.019812926650047302,
0.08009161055088043,
0.04371035471558571,
-0.01304607279598713,
-0.08565584570169449,
0.05583731085062027,
-0.017512155696749687,
0.002538020024076104,
-0.06683363020420074,
0.021220631897449493,
-0.0007149021257646382,
0.009477310813963413,
0.03104882873594761,
0.031135879456996918,
-0.003980325069278479,
-0.04389021173119545,
0.04025626182556152,
-0.027218438684940338,
-0.0253343116492033,
0.023246612399816513,
0.022850871086120605,
0.009126634337008,
-0.013115172274410725,
-0.006586878560483456,
-0.0009213899611495435,
-0.03215744346380234,
-0.006494265981018543,
-0.009991648606956005,
0.013416633009910583,
0.04559434577822685,
0.03758549690246582,
-0.011918590404093266,
-0.031935758888721466,
0.02321549504995346,
-0.0073698111809790134,
-0.06198623403906822,
0.0165862999856472,
-0.013738168403506279,
-0.0030681330244988203,
0.009204690344631672,
0.05364250764250755,
0.06381041556596756,
0.0054502300918102264,
-0.013040989637374878,
-0.024525722488760948,
-0.06967921555042267,
0.004857116378843784,
0.0013793623074889183,
0.017638420686125755,
-0.021355072036385536,
-0.01215386763215065,
0.032271821051836014,
0.004654298070818186,
-0.00033145624911412597,
-0.021287987008690834,
-0.0376497283577919,
0.005559129640460014,
0.014437787234783173,
0.029699135571718216,
-0.016954470425844193,
-0.009669048711657524,
0.042439717799425125,
-0.010807943530380726,
0.022153489291667938,
-0.02111072465777397,
0.011456083506345749,
-0.00013586952991317958,
-0.01774502731859684,
-0.00809668842703104,
-0.006486785598099232,
-0.020773889496922493,
-0.04268771782517433,
-0.00470728101208806,
-0.02915327437222004,
-0.01119435764849186,
0.029978718608617783,
0.006099197082221508,
0.04915622994303703,
0.05284137278795242,
-0.011445302516222,
-0.018829958513379097,
-0.05407179147005081,
0.02560247853398323,
-0.037222784012556076,
-0.03449983894824982,
0.0023758707102388144,
0.006342452019453049,
0.04756100848317146,
0.05010208487510681,
-0.009124772623181343,
0.003914799075573683,
0.005953739397227764,
0.016464874148368835,
0.011482952162623405,
-0.03902392461895943,
-0.007253031712025404,
-0.027132295072078705,
-0.03861205279827118,
-0.025754673406481743,
-0.04656658321619034,
-0.001841002725996077,
0.04998542740941048,
0.04193679243326187,
0.01500382274389267,
0.003110685385763645,
-0.026066528633236885,
0.017292000353336334,
0.019447214901447296,
-0.011402851901948452,
-0.01840026304125786,
0.011157132685184479,
0.06910263001918793,
-0.0028891905676573515,
-0.028198713436722755,
-0.03338059410452843,
-0.011298228986561298,
-0.004857425112277269,
-0.007314810063689947,
-0.005118763539940119,
-0.007443527691066265,
0.013836671598255634,
0.009122106246650219,
-0.028442583978176117,
-0.00372781278565526,
0.004400116391479969,
0.019249331206083298,
-0.009447072632610798,
-0.015172386541962624,
-0.014052427373826504,
0.02512437105178833,
-0.01140258926898241,
0.0025548054836690426,
0.030280757695436478,
0.019076332449913025,
-0.02278328873217106,
0.004162621684372425,
0.017383292317390442,
0.023942360654473305,
0.02460368722677231,
-0.0273663979023695,
-0.023802246898412704,
0.05454989895224571,
-0.02895715832710266,
-0.033157456666231155,
0.0506635420024395,
-0.018874604254961014,
-0.014195051044225693,
0.046869996935129166,
-0.011192054487764835,
-0.017298178747296333,
0.029388904571533203,
0.018782323226332664,
0.02164807729423046,
0.018007811158895493,
0.005894883070141077,
-0.015532701276242733,
0.021316008642315865,
-0.030801240354776382,
-0.009092682972550392,
0.010678648017346859,
0.035520702600479126,
0.05323202535510063,
0.023507090285420418,
0.04318273067474365,
-0.009693097323179245,
-0.019790979102253914,
0.02016538381576538,
0.03698193281888962,
-0.012053316459059715,
0.016793832182884216,
0.07089106738567352,
0.008563568815588951,
0.03407233953475952,
0.041756145656108856,
-0.019490668550133705,
-0.11494193971157074,
-0.0022571473382413387,
0.0005592962843365967,
0.012870518490672112,
0.03492056950926781,
-0.04739906266331673,
0.04468633234500885,
0.02687988243997097,
-0.09132173657417297,
0.024699034169316292,
-0.026788709685206413,
-0.04470423609018326,
-0.03963404521346092,
0.036471132189035416,
-0.056101951748132706,
0.049561675637960434,
0.05299920588731766,
0.029668211936950684,
-0.007122637238353491,
-0.004520012065768242,
-0.017251765355467796,
-0.02854211814701557,
-0.03859985992312431,
-0.010380418039858341,
-0.00041743856854736805,
0.010249548591673374,
0.06107105687260628,
-0.027563726529479027,
-0.018951037898659706,
0.021969718858599663,
-0.0071936799213290215,
-0.007366592064499855,
-0.016167590394616127,
0.015799440443515778,
0.05746513232588768,
0.01962687261402607,
0.0020033062901347876,
-0.014262174256145954,
-0.012320934794843197,
0.027624808251857758,
-0.03157338500022888,
-0.0021345927380025387,
-0.015176121145486832,
-0.010185104794800282,
-0.01555817574262619,
-0.01767576113343239,
-0.0012691570445895195,
0.03273754566907883,
-0.025391731411218643,
-0.027808917686343193,
-0.017038699239492416,
0.032403960824012756,
-0.002314220881089568,
-0.01782434992492199,
0.012715853750705719,
-0.05671214312314987,
0.002031153766438365,
0.03289017826318741,
0.03806394338607788,
-0.03421787545084953,
-0.004600662272423506,
-0.02623867616057396,
-0.037518978118896484,
0.031076302751898766,
-0.0027329600416123867,
0.01801672950387001,
-0.05649128556251526,
-0.02712235040962696,
-0.005311086308211088,
0.03200377896428108,
0.0185213852673769,
-0.06446082890033722,
-0.016874369233846664,
0.05242891609668732,
-0.0005776167381554842,
0.0568174347281456,
-0.014098957180976868,
-0.03226704150438309,
-0.005991228390485048,
-0.039605699479579926,
0.05408967286348343,
0.019879823550581932,
0.047041069716215134,
-0.05284922942519188,
-0.017282187938690186,
-0.011151092126965523,
0.0014804670354351401,
0.045307453721761703,
-0.03048287145793438,
-0.007097434718161821,
0.04775829613208771,
0.03856535628437996,
-0.01803937554359436,
-0.010648047551512718,
-0.012872690334916115,
-0.01678377017378807,
-0.03115173988044262,
-0.0389053076505661,
-0.006354851182550192,
-0.023314932361245155,
-0.003329204861074686,
-0.004746099468320608,
0.032881733030080795,
-0.00996482279151678,
0.016578249633312225,
-0.04050525650382042,
0.06155458092689514,
0.007565268315374851,
0.011753786355257034,
0.06054713577032089,
-0.014705853536725044,
0.019489886239171028,
0.020731868222355843,
-0.04142092913389206,
-0.05556425452232361,
0.03248397260904312,
-0.02747604437172413,
0.017581263557076454,
-0.007460493128746748,
0.016366947442293167,
0.0020246354397386312,
-0.0032202068250626326,
0.021013909950852394,
0.03242971748113632,
-0.05691075325012207,
0.0029103655833750963,
0.049278005957603455,
0.012269913218915462,
0.008938664570450783,
-0.03566369414329529,
0.01811210811138153,
0.005271370522677898,
0.04006924107670784,
-0.008506117388606071,
0.032770052552223206,
-0.004531570244580507,
-0.017740577459335327,
0.04461125656962395,
0.019828004762530327,
-0.06127118319272995,
0.058545902371406555,
-0.033756617456674576,
0.025745492428541183,
-0.008275237865746021,
-0.0103734927251935,
0.007774346508085728,
-0.01822967827320099,
0.0017864796100184321,
0.026442691683769226,
-0.026143789291381836,
0.08671609312295914,
-0.026115812361240387,
0.018741264939308167,
-0.004243716597557068,
-0.005539354868233204,
-0.0037824574392288923,
0.0008004869450815022,
-0.01243137288838625,
0.04855777323246002,
-0.02621115744113922,
-0.01583656296133995,
-0.01779044046998024,
-0.018950894474983215,
0.004756355192512274,
-0.0909242033958435,
0.0006281138048507273,
-0.029344726353883743,
-0.03297668695449829,
-0.0276928897947073,
-0.028949502855539322,
-0.013673827052116394,
0.003772882279008627,
0.0008228635997511446,
0.009554117918014526,
-0.018141938373446465,
-0.02387218549847603,
0.00851593166589737,
0.005075296852737665,
0.03586011007428169,
-0.005253864452242851,
0.028155017644166946,
-0.03561662137508392,
0.0398096889257431,
-0.03271808847784996,
-0.0001467679103370756
] |
<p>The <a href="http://www.eenews.net/stories/1060004813" rel="nofollow">internet is ablaze</a> with the new nano particle based extraction method of converting water to hydrogen. In 2002/2003 when I was 16 there was a similar craze about a lawn mower motor which supposedly ran on water. Indeed there were even conversion kits on the internet for vehicles. They didn't work because of a fundamental inefficiency of the conversion. Will this new nanotechnology improve the process so that cars can run on converted water or does there still exist a limit?</p>
| 9,402 |
[
-0.003945527598261833,
-0.06141066551208496,
0.016924209892749786,
-0.027067527174949646,
0.03235596790909767,
-0.017818309366703033,
-0.06543123722076416,
-0.007490606512874365,
0.028768151998519897,
-0.04692331328988075,
0.03773340582847595,
0.07165610790252686,
-0.008024603128433228,
0.030338548123836517,
-0.00991796050220728,
0.0231693796813488,
0.023727137595415115,
-0.02116692066192627,
0.027846962213516235,
-0.026234468445181847,
-0.006921898107975721,
-0.029437612742185593,
-0.015061975456774235,
-0.006248959805816412,
-0.01211704220622778,
-0.018167516216635704,
-0.012162582948803902,
-0.005635294131934643,
-0.025113675743341446,
0.03506620228290558,
0.0006795156514272094,
-0.024627504870295525,
0.01501460000872612,
0.022565895691514015,
-0.0028152570594102144,
0.00439924793317914,
0.006383677013218403,
-0.046755559742450714,
0.00005029558087699115,
-0.015007871203124523,
-0.019885286688804626,
0.005902620032429695,
0.019551437348127365,
0.07483857125043869,
-0.01718856208026409,
0.0434422567486763,
-0.04567475989460945,
-0.049453821033239365,
0.006604729685932398,
-0.06097911298274994,
0.04792730510234833,
0.02714298851788044,
0.013349421322345734,
-0.018012937158346176,
0.033179860562086105,
0.025603508576750755,
0.06509286165237427,
0.037232905626297,
-0.032239846885204315,
-0.044417623430490494,
-0.0056319269351661205,
0.004904989618808031,
0.004251868464052677,
0.015676463022828102,
-0.07233817875385284,
0.0344276987016201,
-0.0246291346848011,
-0.019007107242941856,
0.031621646136045456,
-0.016365334391593933,
0.014840664342045784,
-0.01959281414747238,
0.04009232670068741,
0.049374546855688095,
0.03331521898508072,
-0.05242954567074776,
0.01697404496371746,
-0.005247954279184341,
0.022029638290405273,
0.0588659942150116,
-0.016111819073557854,
0.021757002919912338,
0.0029463358223438263,
0.04845471680164337,
0.036950867623090744,
-0.009309743531048298,
0.07133530080318451,
-0.026413602754473686,
0.05784814432263374,
0.015196634456515312,
0.010630995035171509,
0.018546443432569504,
0.06991385668516159,
-0.0003565822553355247,
0.015520461834967136,
0.049880724400281906,
0.01720406673848629,
0.04987166449427605,
0.03028237447142601,
-0.023613564670085907,
0.02000167779624462,
0.0033646810334175825,
0.026722168549895287,
0.05008349195122719,
-0.003544627921655774,
-0.056006744503974915,
-0.01610065996646881,
0.004682573955506086,
-0.04518862068653107,
-0.0036521360743790865,
-0.05376920476555824,
-0.0021783162374049425,
0.02758900076150894,
-0.007966041564941406,
0.023214738816022873,
-0.020092634484171867,
0.015152636915445328,
0.0064391340129077435,
0.069569893181324,
0.021720606833696365,
-0.01594558171927929,
-0.025162318721413612,
0.01752207987010479,
-0.01108583714812994,
-0.039788104593753815,
0.03395635262131691,
0.014274677261710167,
0.008793233893811703,
-0.01456981897354126,
0.005317195318639278,
-0.01649203710258007,
0.010709330439567566,
-0.005941718351095915,
-0.03060649149119854,
0.04165774583816528,
0.00829134602099657,
-0.08897554129362106,
-0.07639454305171967,
0.05020301789045334,
-0.008616293780505657,
-0.0030454271472990513,
-0.057808954268693924,
0.021701740100979805,
0.028803972527384758,
0.07582765817642212,
0.01681859791278839,
0.029644304886460304,
-0.011250634677708149,
0.06027303263545036,
0.005575359798967838,
-0.016673417761921883,
-0.02599203772842884,
0.03904090076684952,
-0.012947265058755875,
0.008566000498831272,
-0.05313084274530411,
0.018928932026028633,
0.06373288482427597,
0.037757739424705505,
-0.017157407477498055,
0.05015477165579796,
0.021298443898558617,
-0.018763186410069466,
-0.01543835923075676,
-0.023908909410238266,
-0.03469415009021759,
0.06145507097244263,
0.01594400405883789,
0.006753629073500633,
0.016412481665611267,
0.017824044451117516,
0.0454377606511116,
0.031864941120147705,
-0.004955232609063387,
0.013729788362979889,
-0.01651899144053459,
0.011358499526977539,
-0.05487282946705818,
0.054835621267557144,
0.028581807389855385,
0.0015412864740937948,
0.005052803084254265,
-0.024151792749762535,
0.0673767477273941,
0.03980862349271774,
0.022586341947317123,
-0.002925017848610878,
-0.04305431991815567,
-0.005464082583785057,
-0.031571030616760254,
-0.01801207847893238,
-0.038761258125305176,
0.011451291851699352,
0.013959284871816635,
0.014078699983656406,
0.0011017525102943182,
-0.022920576855540276,
0.030418692156672478,
-0.032882992178201675,
-0.009003616869449615,
-0.0011647072387859225,
0.04030827432870865,
0.0359170064330101,
0.023260243237018585,
-0.002126967301592231,
0.07527614384889603,
0.0015514101833105087,
0.006592846475541592,
0.0014950954355299473,
0.01248850580304861,
-0.0570550300180912,
-0.02107875794172287,
-0.02484687604010105,
-0.007093095686286688,
0.030738700181245804,
-0.009099305607378483,
0.027386588975787163,
-0.0604761578142643,
-0.02262677252292633,
0.029916934669017792,
-0.029425613582134247,
0.076728455722332,
0.021812213584780693,
0.03262661397457123,
-0.027718765661120415,
0.0026872202288359404,
0.011305428110063076,
0.025754446163773537,
-0.013591391034424305,
0.009783973917365074,
-0.06053008884191513,
-0.00284409336745739,
0.05148836225271225,
0.03178403526544571,
-0.030494987964630127,
0.008503700606524944,
0.02388656884431839,
0.006481631193310022,
0.024061961099505424,
0.007345930207520723,
-0.04305656999349594,
0.014378433115780354,
0.04335106536746025,
0.056565649807453156,
0.007389552891254425,
0.01676873117685318,
0.0040538557805120945,
-0.007832000032067299,
0.012251611799001694,
-0.02729291468858719,
0.013077417388558388,
0.03670550882816315,
0.0308335293084383,
-0.017385337501764297,
-0.005869543645530939,
-0.028930429369211197,
0.024814581498503685,
-0.06355282664299011,
-0.029491636902093887,
-0.0050917500630021095,
0.012958431616425514,
0.00933376420289278,
-0.030039655044674873,
-0.011669340543448925,
-0.020953768864274025,
-0.0027578435838222504,
-0.012928325682878494,
-0.015074950642883778,
0.035747360438108444,
-0.07838506251573563,
0.020779024809598923,
-0.034278880804777145,
0.01588951237499714,
-0.023859931156039238,
0.025816749781370163,
-0.03543609753251076,
0.005517631769180298,
0.02388223074376583,
-0.036616839468479156,
-0.045514561235904694,
0.008638941682875156,
-0.010744070634245872,
-0.03041006624698639,
0.01138568576425314,
-0.023632541298866272,
-0.0021273798774927855,
-0.01684953272342682,
-0.034026388078927994,
0.06108739972114563,
0.023001903668045998,
-0.01725533977150917,
-0.038624368607997894,
0.02124333567917347,
-0.05144483223557472,
-0.014296221546828747,
-0.006170041859149933,
-0.035337209701538086,
-0.033357810229063034,
-0.028052857145667076,
-0.006841793656349182,
-0.05137815698981285,
-0.047469738870859146,
-0.004365385975688696,
-0.007935569621622562,
-0.03682977333664894,
-0.0396951287984848,
0.03444897383451462,
0.0015231765573844314,
-0.017457686364650726,
0.030390523374080658,
0.013104000128805637,
-0.036893729120492935,
0.018169626593589783,
-0.04925420507788658,
-0.09565892815589905,
0.01969173736870289,
-0.03716731444001198,
0.07848163694143295,
-0.04355306178331375,
-0.03188444674015045,
0.043396372348070145,
0.01645171456038952,
-0.055630601942539215,
-0.021627526730298996,
-0.006711186841130257,
0.013668138533830643,
-0.0010313383536413312,
-0.02255239523947239,
0.08594387769699097,
-0.03770585358142853,
0.017895400524139404,
0.004225697834044695,
0.06868986785411835,
0.0076785036362707615,
0.004208642523735762,
-0.032026682049036026,
-0.013915620744228363,
-0.0003607612452469766,
0.028034377843141556,
-0.0036802582908421755,
0.0283140130341053,
-0.04949618875980377,
0.028201600536704063,
-0.03309496119618416,
0.04652940481901169,
0.03216506913304329,
-0.03611617535352707,
0.07479607313871384,
0.04225388914346695,
-0.017671966925263405,
-0.026573065668344498,
0.03180614858865738,
0.00801524706184864,
-0.00825915951281786,
0.016534268856048584,
-0.005971797276288271,
0.03732653707265854,
0.04703009873628616,
-0.032499417662620544,
0.026287304237484932,
0.05635593831539154,
-0.016296900808811188,
-0.03816010802984238,
0.0036648898385465145,
0.02673264592885971,
-0.003678517648950219,
-0.018418459221720695,
0.0031377195846289396,
0.02734680287539959,
-0.01267348974943161,
0.009436204098165035,
0.011963211931288242,
0.023115724325180054,
0.015046590939164162,
-0.060836225748062134,
0.011689994484186172,
-0.01978784240782261,
0.03691543638706207,
0.0007322257151827216,
0.036876026540994644,
-0.0072786263190209866,
0.01639690063893795,
-0.008503538556396961,
-0.031387582421302795,
-0.04822026565670967,
-0.0039925905875861645,
-0.055245354771614075,
-0.0011101181153208017,
-0.026359066367149353,
-0.01908848248422146,
-0.02727429009974003,
-0.014645655639469624,
-0.03772382438182831,
-0.019852010533213615,
-0.0052399709820747375,
-0.04819298908114433,
0.05156811326742172,
-0.045032016932964325,
-0.03386928141117096,
0.016326582059264183,
-0.02482352778315544,
0.04037199169397354,
0.02533474937081337,
-0.014692895114421844,
-0.005708598997443914,
-0.06510859727859497,
0.04666443169116974,
0.007053576409816742,
0.021783163771033287,
0.001044586068019271,
0.026142077520489693,
0.0002661831385921687,
0.021390780806541443,
0.004590936936438084,
0.01815955713391304,
-0.006358127109706402,
-0.027850981801748276,
-0.017140867188572884,
0.03677840903401375,
-0.06282879412174225,
-0.024735936895012856,
-0.021535273641347885,
0.027430547401309013,
0.017882846295833588,
-0.007130535785108805,
0.039228785783052444,
-0.009539428167045116,
-0.024611787870526314,
-0.02961496077477932,
0.0438910610973835,
0.04855605214834213,
0.0020836356561630964,
0.04728982597589493,
-0.046801455318927765,
-0.03663408383727074,
-0.009118017740547657,
0.007618273142725229,
0.02368001639842987,
0.024607308208942413,
-0.01909356191754341,
-0.049886442720890045,
0.04401344433426857,
0.025368714705109596,
-0.0280255489051342,
0.03127257898449898,
-0.045695334672927856,
0.007709232624620199,
-0.028526917099952698,
0.027147719636559486,
-0.03118528053164482,
0.0293426513671875,
0.04969104379415512,
0.014630402438342571,
-0.024913491681218147,
-0.1237722635269165,
0.005916927941143513,
0.023318083956837654,
0.011220097541809082,
-0.004190794192254543,
0.011180649511516094,
-0.03903403505682945,
-0.01165845151990652,
0.018737152218818665,
-0.03482707962393761,
0.0075860521756112576,
-0.033148232847452164,
-0.00282765063457191,
-0.011641355231404305,
0.012602203525602818,
0.03131331503391266,
-0.012655416503548622,
0.0009286060812883079,
0.02585478127002716,
-0.05375579372048378,
-0.010685116983950138,
-0.021151088178157806,
0.017793413251638412,
0.002006328897550702,
0.05504894629120827,
0.011143322102725506,
-0.01460484229028225,
-0.02256028912961483,
0.016438500955700874,
-0.07181084156036377,
-0.08734947443008423,
0.04302283003926277,
0.010240989737212658,
-0.008169176056981087,
0.031807199120521545,
-0.06232234090566635,
-0.028774524107575417,
0.022387072443962097,
-0.013243063353002071,
-0.01789061911404133,
-0.03107726201415062,
-0.07806189358234406,
0.016588250175118446,
0.010564897209405899,
0.018720371648669243,
-0.01803893968462944,
0.041432105004787445,
-0.006745049264281988,
0.013142690062522888,
-0.01898200437426567,
-0.013422536663711071,
-0.018766803666949272,
0.016212547197937965,
-0.0036181912291795015,
0.029789702966809273,
-0.023115402087569237,
0.02989976853132248,
-0.0010773787507787347,
0.015330045484006405,
-0.0358976386487484,
-0.034010011702775955,
-0.005565228872001171,
-0.014178602956235409,
-0.028796004131436348,
-0.05347584933042526,
-0.019361525774002075,
0.01995929330587387,
0.029367873445153236,
-0.010149182751774788,
-0.008891752921044827,
0.00008425558189628646,
0.011702464893460274,
0.019695479422807693,
0.0157950296998024,
0.005532037001103163,
0.0016142515232786536,
0.015185045078396797,
0.060845810920000076,
-0.0515170581638813,
0.033915553241968155,
-0.022923272103071213,
0.009786967188119888,
0.02350524812936783,
-0.043940458446741104,
0.0045081693679094315,
0.012428684160113335,
-0.009448004886507988,
0.009597093798220158,
-0.011640511453151703,
0.01375632081180811,
0.010366600938141346,
0.01791396550834179,
0.0018667466938495636,
-0.0639079138636589,
0.04404838755726814,
-0.0015622813953086734,
0.0051729511469602585,
-0.017199357971549034,
-0.03631926327943802,
-0.023125184699892998,
-0.044493019580841064,
-0.023432623594999313,
0.04266463965177536,
-0.004699609708040953,
0.006083350162953138,
0.04086437448859215,
0.025700241327285767,
0.09480232745409012,
-0.03676734119653702,
-0.010785743594169617,
0.02685953490436077,
-0.011153782717883587,
-0.007045646198093891,
-0.004930881317704916,
0.013115044683218002,
-0.03001478686928749,
0.013362127356231213,
0.0045968168415129185,
-0.03916586935520172,
0.024106357246637344,
-0.012639515101909637,
0.01778307557106018,
0.04648507013916969,
0.04061542823910713,
-0.051387302577495575,
-0.024148762226104736,
0.024615706875920296,
-0.014013893902301788,
0.052597787231206894,
-0.00227497355081141,
0.015985436737537384,
-0.03760867193341255,
-0.0023872959427535534,
0.023375680670142174,
0.026722876355051994,
-0.01705333963036537,
-0.014212890528142452,
0.03843425214290619,
-0.008775277994573116,
-0.03960953280329704,
0.021988144144415855,
-0.05053802952170372,
0.016593441367149353,
0.014353309758007526,
0.01240772195160389,
-0.023400593549013138,
-0.0044098724611103535,
-0.02586529590189457,
-0.04921021685004234,
-0.028984447941184044,
0.03213648498058319,
-0.006488968152552843,
-0.01700866036117077,
0.012901868671178818,
-0.005279470235109329,
-0.02047954499721527,
-0.014055886305868626,
-0.07204719632863998,
-0.006603865418583155,
0.01951565407216549,
-0.03331099823117256,
0.006414454896003008,
0.014621562324464321,
-0.01011471077799797,
0.02711286023259163,
0.015049696899950504,
0.000927773246075958,
0.006623668130487204,
0.048819467425346375,
-0.014710372313857079,
-0.008631053380668163,
-0.02306802198290825,
-0.04676597937941551,
0.003508170833811164,
-0.041594766080379486,
0.031786203384399414,
-0.008560200221836567,
0.012149407528340816,
0.06896671652793884,
-0.04393652454018593,
-0.0074041071347892284,
-0.03356413170695305,
0.005915197543799877,
-0.042277947068214417,
0.01450714748352766,
-0.048071712255477905,
-0.030988967046141624,
0.0003844684106297791,
0.028989573940634727,
-0.01802578568458557,
0.040920108556747437,
0.03483128547668457,
-0.030905546620488167,
-0.06742516905069351,
0.007578641176223755,
-0.027477653697133064,
-0.05241696536540985,
0.04281944781541824,
0.022646309807896614,
-0.047189775854349136,
0.04018379747867584,
0.004362028557807207,
0.03147296607494354,
0.011940473690629005,
0.01919383741915226,
-0.01251763105392456,
0.01652165874838829,
0.0051100533455610275,
0.05066230520606041,
0.02322155050933361,
0.01816472038626671,
0.13569840788841248,
0.04072902351617813,
-0.007645606528967619,
-0.04129016771912575,
-0.0032131157349795103,
-0.04203474149107933,
0.01807950809597969,
-0.011133747175335884,
-0.025408953428268433,
-0.02509358525276184,
0.024915367364883423,
0.015011195093393326,
0.03047557733952999,
0.0018806178122758865,
0.029704254120588303,
0.024415144696831703,
-0.0009943114127963781,
-0.028871968388557434,
0.0020196069963276386,
0.03712838143110275,
-0.024571869522333145,
0.013430511578917503,
-0.06329924613237381,
0.037879832088947296,
-0.024935606867074966,
-0.018173035234212875,
0.02847694605588913,
-0.025864575058221817,
0.029446111992001534,
0.0030674035660922527,
-0.0638682097196579,
-0.006047161761671305,
0.00857840571552515,
0.003930816426873207,
0.003455515019595623,
0.017826419323682785,
0.0004653331998270005,
0.03211240470409393,
-0.025058330968022346,
0.01594812050461769,
0.0593397431075573,
-0.0014098002575337887,
-0.0016409807140007615,
0.046356625854969025,
-0.02840396948158741,
0.04461883381009102,
-0.022037379443645477,
0.00015569795505143702,
0.000001140261360887962,
0.011496691964566708,
-0.028993699699640274,
-0.00960856955498457,
0.015838880091905594,
-0.05956338718533516,
-0.02109266072511673,
0.0027184358332306147,
0.028055209666490555,
0.03346852958202362,
-0.033891793340444565,
-0.009730186313390732,
0.00910922884941101,
-0.017413455992937088,
0.010701972991228104,
0.027371831238269806,
0.030060604214668274,
-0.017024226486682892,
0.030629752203822136,
0.036243144422769547,
-0.036069467663764954,
-0.04936767369508743,
-0.05735594034194946,
0.01727825216948986,
-0.051694732159376144,
-0.00011718761379597709,
-0.02023751474916935,
0.023787807673215866,
0.0411171093583107,
-0.003926633857190609,
0.012408435344696045,
0.004484403412789106,
-0.04296232759952545,
0.003160843625664711,
0.01455435436218977,
-0.0022879261523485184,
0.0015855423407629132,
-0.001722243963740766,
-0.012324650771915913,
0.03215838223695755,
-0.04943256452679634,
0.05133774131536484,
-0.022203311324119568,
0.013136987574398518,
0.018834808841347694,
-0.025394778698682785,
-0.0341147780418396,
-0.002655827207490802,
-0.042256638407707214,
-0.02760741300880909,
-0.022499332204461098,
0.028559008613228798,
-0.006511278450489044,
-0.016558833420276642,
-0.0021652241703122854,
-0.005953929387032986,
-0.004190877545624971,
0.015293139964342117,
0.029053527861833572,
0.02955583482980728,
-0.05115645006299019,
-0.014590549282729626,
0.028218921273946762,
-0.014520362950861454,
0.01165079977363348,
-0.03872198611497879,
-0.01238938421010971,
0.015937594696879387,
0.03192668408155441,
-0.007010543718934059,
0.005834217648953199,
-0.03572056069970131,
0.043035537004470825,
-0.002772020176053047,
0.008071514777839184,
-0.058248914778232574,
0.018501318991184235,
-0.03161364048719406,
0.028715789318084717,
-0.0004687621258199215,
0.049123965203762054,
-0.012513692490756512,
0.040571894496679306,
0.03733549267053604,
0.03843199834227562,
-0.03571483492851257,
-0.03222115337848663,
-0.0019622603431344032,
0.004881980828940868,
0.037796564400196075,
-0.06499096751213074,
-0.03603518381714821,
0.04016309604048729,
-0.03559925779700279,
-0.013684691861271858,
-0.00026044886908493936,
-0.03457668796181679,
0.004273221828043461,
0.06119148060679436,
-0.014129042625427246,
0.008584080263972282,
0.05230429768562317,
-0.01617322489619255,
0.021622367203235626,
0.03423939645290375,
-0.015216554515063763,
-0.006337095983326435,
-0.00237711938098073,
-0.003177405335009098,
0.009962506592273712,
-0.019644806161522865,
0.038721341639757156,
0.021250508725643158,
0.020969437435269356,
0.040992721915245056,
-0.020300736650824547,
-0.0008821744122542441,
0.03900112584233284,
0.03611714392900467,
0.011384240351617336,
0.02836967632174492,
0.07263398915529251,
-0.04206100478768349,
-0.004929154645651579,
-0.0007919579511508346,
-0.00009321638208348304,
-0.04064905270934105,
0.004709594417363405,
-0.0024029945489019156,
-0.033458273857831955,
-0.0008261665352620184,
-0.01947900466620922,
0.01420136634260416,
0.024129364639520645,
-0.11547596752643585,
0.03082181327044964,
-0.014494203962385654,
-0.005115647334605455,
-0.06931322067975998,
-0.002545991213992238,
0.002446978585794568,
0.021792111918330193,
0.00002414387017779518,
0.03627709671854973,
0.018095828592777252,
0.039998676627874374,
-0.05295341834425926,
-0.003449180629104376,
0.024218786507844925,
0.010561986826360226,
-0.02349616214632988,
-0.0035064115654677153,
0.02239343710243702,
-0.02530098333954811,
-0.044245000928640366,
-0.005084042903035879,
-0.03734173998236656,
0.05474450811743736,
-0.02153109200298786,
0.0015914738178253174,
0.031075362116098404,
0.03888090327382088,
0.0265163816511631,
-0.014588371850550175,
-0.011083547957241535,
0.05287269502878189,
0.028312450274825096,
0.033231593668460846,
-0.006961681414395571,
0.020819570869207382,
-0.00005597247582045384,
-0.0015795185463503003,
-0.014183401130139828,
0.012785438448190689,
-0.021805673837661743,
0.02602037601172924,
0.02980744279921055,
0.002217748435214162,
0.000675185292493552,
-0.0191942285746336,
0.0010971837909892201,
-0.0280301496386528,
-0.009963329881429672,
0.046097151935100555,
0.006039966829121113,
0.006632091011852026,
0.0361056923866272,
-0.04179324582219124,
-0.008203336969017982,
-0.00003992531856056303,
-0.029218314215540886,
-0.010951352305710316,
-0.026346005499362946,
0.028704728931188583,
0.04794316366314888,
0.04476919025182724,
-0.004451047163456678,
-0.01571354642510414,
-0.002383264945819974,
0.05122607573866844,
0.02136172726750374,
-0.008346152491867542,
0.03843558579683304,
-0.01603439450263977,
-0.0016930133569985628,
-0.06281590461730957,
0.014575428329408169,
0.04154932126402855,
0.031347036361694336,
-0.0024063228629529476,
-0.05139196291565895,
0.02902633138000965,
-0.012410960160195827,
0.07332311570644379,
-0.007167845033109188,
-0.013013697229325771,
-0.0026724841445684433,
0.008628366515040398,
0.012133019976317883,
-0.021660199388861656,
-0.007830475457012653,
0.011808052659034729,
0.0008931590709835291,
0.006931429263204336,
0.011974933557212353,
-0.03359740972518921,
-0.0011424862314015627,
0.03763001784682274,
0.0004823831841349602,
-0.02272692881524563,
0.013781003654003143,
-0.014130186289548874,
0.019443165510892868,
0.0035162167623639107,
0.03019258938729763,
0.058595847338438034,
-0.01857391744852066,
0.046515412628650665,
-0.02249213680624962,
0.01870974898338318,
-0.03781101107597351,
0.0024419324472546577,
-0.019196877256035805,
0.00427307840436697,
-0.01593664102256298,
-0.013362736441195011,
0.03807373344898224,
-0.01640341989696026,
0.0212217066437006,
0.0165170356631279,
0.007333093322813511,
0.006435954477638006,
0.04866069182753563,
0.027742372825741768,
-0.017220959067344666,
-0.007409893441945314,
0.021319760009646416,
-0.015827497467398643,
-0.012975453399121761,
-0.025638239458203316,
0.07591390609741211,
0.049511734396219254,
-0.0014851794112473726,
0.015567158348858356,
0.04162726178765297,
-0.004694628529250622,
0.017759138718247414,
0.052760425955057144,
0.017993295565247536,
-0.0007845747750252485,
-0.008993744850158691,
-0.001442109583877027,
-0.031918711960315704,
0.020993871614336967,
0.04079160839319229,
0.004332307726144791,
0.07170172780752182,
0.023148631677031517,
0.024363379925489426,
-0.02726045809686184,
-0.010735995136201382,
0.0009250647271983325,
0.008023119531571865,
-0.06743969768285751,
0.054743919521570206,
0.013266186229884624,
-0.05690823122859001,
-0.046895965933799744,
0.040111713111400604,
0.011999235488474369,
-0.004566971678286791,
0.06723389029502869,
-0.03666168078780174,
0.0009262232342734933,
-0.024151919409632683,
-0.03989430516958237,
-0.001796278520487249,
-0.02401931770145893,
-0.006075826473534107,
0.01472696103155613,
-0.030124962329864502,
0.004510711878538132,
-0.03498012572526932,
-0.013428906910121441,
0.04691418260335922,
-0.039943352341651917,
0.010208332911133766,
-0.0015998996095731854,
-0.026149336248636246,
-0.03521375730633736,
-0.05278819426894188
] |
<p>15th group elements like As, Sb, P can be used for doping whereas N and Bi cannot be used for doping even though they too belong belong to 15th group. Why ?</p>
| 9,403 |
[
-0.004042331129312515,
0.007085992954671383,
0.014758722856640816,
-0.026041556149721146,
0.0646716058254242,
0.002207774668931961,
-0.04718058556318283,
-0.0534018874168396,
0.0026685260236263275,
-0.02331969514489174,
0.10880275815725327,
-0.026488682255148888,
0.023659497499465942,
0.03320809081196785,
-0.0391559973359108,
0.011714167892932892,
0.015173525549471378,
-0.009152891114354134,
-0.018134018406271935,
0.024907616898417473,
0.01621997356414795,
0.008774559944868088,
-0.0163421668112278,
0.040899455547332764,
-0.003932065796107054,
-0.007051887921988964,
0.01824146881699562,
0.006771347485482693,
0.024262307211756706,
0.03659049794077873,
0.012581469491124153,
-0.03435149043798447,
0.032891642302274704,
-0.014983226545155048,
0.02582247368991375,
-0.0016100499778985977,
-0.006510994862765074,
-0.033403269946575165,
-0.03038967214524746,
0.0022830362431705,
-0.08113917708396912,
0.0028032055124640465,
0.020485034212470055,
0.036856405436992645,
0.029547376558184624,
0.054397884756326675,
0.04049668088555336,
0.015092399902641773,
-0.01195142138749361,
-0.07133707404136658,
0.03668529912829399,
-0.014002910815179348,
0.04150407761335373,
0.002427030587568879,
-0.019764328375458717,
0.006695087067782879,
0.048203155398368835,
0.06787415593862534,
-0.010724389925599098,
-0.05435408651828766,
0.019333695992827415,
-0.021967021748423576,
0.030968939885497093,
0.008654606528580189,
-0.02332310751080513,
0.00040988437831401825,
0.00020116381347179413,
-0.031848955899477005,
0.009229891933500767,
0.02464323677122593,
0.02111903205513954,
0.014778723008930683,
-0.02706177905201912,
-0.0412447527050972,
0.02290281280875206,
-0.022804662585258484,
0.024125302210450172,
0.004826012067496777,
0.06979533284902573,
0.037044983357191086,
-0.006229836028069258,
0.024650102481245995,
0.029795940965414047,
-0.000024709448553039692,
-0.0011598122073337436,
-0.006276674568653107,
0.03320082649588585,
-0.020200036466121674,
0.038094356656074524,
0.0016642151167616248,
-0.030833538621664047,
-0.01239407155662775,
0.06738600134849548,
0.05524057894945145,
-0.023178057745099068,
-0.0077784061431884766,
-0.021526498720049858,
0.016572799533605576,
-0.022894999012351036,
0.012866917997598648,
0.01427112054079771,
-0.014727567322552204,
0.054927825927734375,
0.08777784556150436,
0.011842788197100163,
-0.028560098260641098,
-0.025118378922343254,
-0.005576019175350666,
-0.00035721302265301347,
0.022645413875579834,
-0.0055963583290576935,
-0.008979116566479206,
-0.030653448775410652,
0.004851390141993761,
-0.0018328198930248618,
-0.007220304571092129,
-0.006741899531334639,
-0.001255222363397479,
0.02951148897409439,
0.047897692769765854,
-0.003959239460527897,
0.01700068637728691,
0.021223250776529312,
0.02360771968960762,
-0.046912580728530884,
0.021108604967594147,
0.030152002349495888,
0.001971977762877941,
-0.022448120638728142,
-0.008010019548237324,
0.013509517535567284,
-0.033161286264657974,
0.035139862447977066,
0.011789001524448395,
0.04572505131363869,
0.027500737458467484,
-0.12025436758995056,
-0.08918669819831848,
0.03282961621880531,
0.0013498683692887425,
-0.0315760001540184,
-0.06976274400949478,
0.031758300960063934,
0.005224559921771288,
0.08805139362812042,
-0.023704316467046738,
-0.0012685488909482956,
0.011225822381675243,
0.02559560537338257,
0.04915785789489746,
0.039476655423641205,
-0.04040169715881348,
0.010845029726624489,
-0.03445574641227722,
0.01580854132771492,
-0.07073694467544556,
0.020095594227313995,
0.015513208694756031,
0.0035422067157924175,
-0.055251531302928925,
-0.016921529546380043,
-0.025638699531555176,
0.018253842368721962,
-0.04775124043226242,
0.005122233647853136,
-0.01595834083855152,
0.03939454257488251,
0.04791693016886711,
0.033095620572566986,
0.015765594318509102,
-0.01647704280912876,
0.05247439444065094,
0.026088902726769447,
0.06155221536755562,
0.014233495108783245,
-0.03119784966111183,
-0.02056606113910675,
-0.044201161712408066,
0.03978210687637329,
0.024532955139875412,
-0.08924704045057297,
0.0029530294705182314,
-0.002303410554304719,
0.03372456505894661,
0.018153037875890732,
-0.003524706233292818,
0.008374457247555256,
0.01900125853717327,
0.02744521200656891,
-0.07182677090167999,
-0.01084484625607729,
-0.10631105303764343,
0.002551774960011244,
0.01607039012014866,
-0.05144418030977249,
-0.0018602366326376796,
-0.005970870144665241,
-0.012767663225531578,
-0.03147785738110542,
-0.0036137253046035767,
-0.04983028769493103,
0.013655686751008034,
0.007999655790627003,
-0.006903702858835459,
-0.009625117294490337,
0.06031259894371033,
0.036096204072237015,
0.00876215286552906,
0.06161504611372948,
-0.010538575239479542,
-0.026375191286206245,
0.028765972703695297,
-0.0010767250787466764,
0.021298857405781746,
-0.005183301866054535,
-0.029612146317958832,
-0.0221236739307642,
-0.013288290239870548,
-0.027292022481560707,
0.06676962226629257,
-0.03804206848144531,
0.12394537776708603,
0.038992058485746384,
0.01073470339179039,
0.01906905323266983,
0.004420766606926918,
0.028900332748889923,
0.010936498641967773,
-0.003802967257797718,
-0.046098556369543076,
-0.0702565535902977,
-0.02108394168317318,
0.001840837299823761,
0.03509357571601868,
-0.06668349355459213,
-0.0064819795079529285,
0.01447665598243475,
-0.003371510189026594,
0.031250618398189545,
0.05314747989177704,
0.005206683184951544,
-0.04029146209359169,
0.045042265206575394,
0.05220829322934151,
0.0332551971077919,
0.03638762608170509,
0.009732823818922043,
-0.028497040271759033,
0.04202759265899658,
-0.01159829180687666,
-0.02914385125041008,
0.03467482328414917,
-0.013805793598294258,
-0.035834409296512604,
0.013818727806210518,
-0.044226277619600296,
0.036068934947252274,
-0.03304946422576904,
0.02968749590218067,
0.007399527356028557,
0.00757788447663188,
0.002877283375710249,
-0.008262294344604015,
-0.0033594416454434395,
0.03287947550415993,
0.03317277505993843,
-0.04141847789287567,
-0.02518395707011223,
0.024998823180794716,
-0.018312441185116768,
-0.013121157884597778,
-0.03761259466409683,
0.03406858071684837,
-0.021136490628123283,
0.011116594076156616,
0.03229738399386406,
0.002000788226723671,
0.032325439155101776,
-0.04327120631933212,
0.008503184653818607,
-0.02907293289899826,
0.00845556240528822,
0.009798094630241394,
0.01745670475065708,
-0.05750647932291031,
0.004587162286043167,
-0.015482944436371326,
-0.025090854614973068,
0.039048463106155396,
-0.019496092572808266,
-0.020116012543439865,
0.01154094748198986,
0.008910306729376316,
-0.010747252963483334,
-0.018535198643803596,
0.008349606767296791,
-0.011431415565311909,
-0.01934577338397503,
-0.025983506813645363,
0.03188595175743103,
0.026886122301220894,
-0.021950889378786087,
-0.0017552089411765337,
-0.012512673623859882,
-0.01725398376584053,
0.001238496508449316,
0.0014411431038752198,
-0.024356575682759285,
-0.03315706551074982,
0.01811384968459606,
0.04756654053926468,
-0.013824439607560635,
-0.03763028606772423,
-0.013787765055894852,
-0.06600110977888107,
0.021768229082226753,
0.0021902634762227535,
0.003063160926103592,
-0.03512008488178253,
0.020588064566254616,
0.06670013070106506,
0.041359178721904755,
-0.017290543764829636,
-0.019399181008338928,
-0.044114649295806885,
-0.048635587096214294,
-0.026284415274858475,
0.0253373384475708,
0.05549019202589989,
0.0037026710342615843,
0.0008459683158434927,
0.007506265304982662,
0.040186136960983276,
0.04192323237657547,
-0.021433623507618904,
-0.04741906374692917,
-0.00447746692225337,
0.022744540125131607,
0.0018665579846128821,
0.03159854933619499,
-0.003873269772157073,
-0.030766937881708145,
-0.013819228857755661,
-0.004494016058743,
0.05706728249788284,
0.0006588614778593183,
-0.04393088072538376,
0.02931530587375164,
-0.008384610526263714,
0.03173096477985382,
-0.019110843539237976,
0.034498848021030426,
0.022200055420398712,
0.007012998219579458,
0.004015919752418995,
0.006404276937246323,
0.03500483185052872,
-0.044142916798591614,
-0.014234636910259724,
0.013697320595383644,
0.025008346885442734,
-0.04043631628155708,
-0.025458643212914467,
0.04074273258447647,
-0.010043502785265446,
0.02107745036482811,
-0.012029436416924,
0.0064012142829597,
0.0004102980892639607,
0.04166378825902939,
0.03417511656880379,
0.019633999094367027,
-0.012616939842700958,
-0.0065893870778381824,
-0.08209234476089478,
0.011575691401958466,
-0.03196282684803009,
0.031046373769640923,
-0.0018089284421876073,
0.06920876353979111,
0.013469183817505836,
0.013322129845619202,
-0.024143174290657043,
-0.048959098756313324,
-0.07361585646867752,
0.007728602271527052,
-0.00869908556342125,
0.015244171023368835,
0.007527417037636042,
-0.03758518397808075,
-0.02018289640545845,
-0.04453399404883385,
-0.05510178953409195,
-0.024835726246237755,
-0.016319360584020615,
-0.03810854256153107,
0.010067223571240902,
-0.023447586223483086,
-0.05354025214910507,
0.00009495281119598076,
0.0056336410343647,
0.018738359212875366,
-0.03205059841275215,
0.03895732760429382,
-0.01733284816145897,
-0.0042290412820875645,
-0.021344805136322975,
-0.021719958633184433,
0.010472874157130718,
0.033687517046928406,
0.027285996824502945,
0.03441443666815758,
0.032223135232925415,
-0.02211141400039196,
-0.0587364062666893,
-0.01418243907392025,
0.05638698488473892,
0.022991763427853584,
0.012871123850345612,
-0.02527710795402527,
-0.05647582560777664,
-0.020452314987778664,
0.012890106998383999,
-0.0012314011109992862,
-0.008659567683935165,
0.0017709676176309586,
0.0038471203297376633,
-0.03914137929677963,
-0.04502038657665253,
0.022788217291235924,
0.00027378121740184724,
0.050881821662187576,
0.0012729655718430877,
-0.03955189511179924,
-0.019137579947710037,
-0.0023952035699039698,
-0.025242645293474197,
0.03872204199433327,
0.03318236395716667,
-0.00742100877687335,
-0.0008628353825770319,
0.04479913413524628,
-0.0010787260252982378,
-0.037218596786260605,
0.059691593050956726,
0.03605499118566513,
0.03669402375817299,
0.01066583301872015,
-0.002624134998768568,
-0.00039657126762904227,
0.012338812462985516,
0.028035523369908333,
0.006335572339594364,
-0.00010208748426521197,
-0.0592242069542408,
0.014620582573115826,
0.04864325374364853,
0.058686140924692154,
-0.04694513976573944,
-0.024663543328642845,
-0.03568289801478386,
-0.003025075886398554,
0.019598282873630524,
-0.034893255680799484,
0.04170263558626175,
-0.044156819581985474,
0.011590617708861828,
-0.05800183117389679,
-0.0020621316507458687,
-0.01782906986773014,
-0.004045630339533091,
0.022397415712475777,
0.024384237825870514,
0.0015749931335449219,
-0.03658516705036163,
0.01723802648484707,
0.019947713240981102,
0.023034486919641495,
0.039526551961898804,
0.013488702476024628,
0.03669368848204613,
0.02270370163023472,
0.03331340104341507,
-0.019481515511870384,
-0.05251703038811684,
0.007532776333391666,
0.008521747775375843,
0.03144718334078789,
0.024995464831590652,
-0.03015328012406826,
-0.09548188745975494,
0.03393695503473282,
-0.016535842791199684,
-0.015851613134145737,
-0.03829508647322655,
-0.05925649404525757,
0.03573257103562355,
0.055359289050102234,
-0.03448294848203659,
0.020372850820422173,
0.014389676973223686,
-0.023438777774572372,
0.0072626229375600815,
-0.05981878191232681,
0.0038026967085897923,
-0.032096635550260544,
0.010676681995391846,
-0.021628418937325478,
0.01173813734203577,
-0.02607063017785549,
0.04216106981039047,
0.04659755527973175,
0.022642692551016808,
0.014744102954864502,
-0.07505232095718384,
-0.016132032498717308,
0.017941974103450775,
-0.003530825488269329,
-0.01815163716673851,
-0.03813309594988823,
-0.006518697366118431,
0.01338915340602398,
0.003992438316345215,
0.03827302157878876,
-0.014645485207438469,
0.0034510688856244087,
-0.011991151608526707,
0.016509616747498512,
-0.0030906950123608112,
-0.03513781726360321,
0.015890659764409065,
0.006545533426105976,
-0.009861205704510212,
0.08131009340286255,
0.021007979288697243,
-0.009842072613537312,
-0.00504024513065815,
-0.040746916085481644,
-0.009768163785338402,
0.030439935624599457,
-0.024384086951613426,
-0.006596901919692755,
-0.03607749938964844,
0.04633432626724243,
0.02161131612956524,
0.019481826573610306,
-0.085004523396492,
-0.033929336816072464,
0.011269724927842617,
-0.017317863181233406,
-0.010931629687547684,
-0.007228277623653412,
0.0003828021290246397,
0.027296248823404312,
-0.026856493204832077,
0.026851706206798553,
0.05975150689482689,
-0.032085202634334564,
-0.047663841396570206,
0.023110203444957733,
0.00784654077142477,
0.05091669037938118,
0.004438759293407202,
-0.032051365822553635,
0.007969795726239681,
-0.02524629794061184,
0.005163248162716627,
-0.03393014147877693,
0.03401963785290718,
-0.0028991939034312963,
-0.016598189249634743,
-0.006371563766151667,
-0.005380202550441027,
0.04432746767997742,
0.010493450798094273,
-0.017138715833425522,
0.0032791043631732464,
-0.01730094850063324,
-0.01772584579885006,
-0.009194905869662762,
0.005067459307610989,
0.014291109517216682,
0.04357078671455383,
0.009069867432117462,
0.006741887424141169,
-0.02482004091143608,
-0.006577709224075079,
0.046639714390039444,
0.015731405466794968,
-0.022546155378222466,
0.008295071311295033,
0.06832221150398254,
-0.010492399334907532,
0.005284910090267658,
0.04324474558234215,
-0.012091785669326782,
0.053056951612234116,
0.011032524518668652,
0.015134885907173157,
0.01723932847380638,
-0.0009993516141548753,
-0.026537636294960976,
-0.049959681928157806,
-0.051415711641311646,
0.02298055961728096,
-0.0019250153563916683,
-0.011858992278575897,
0.028656277805566788,
0.010247466154396534,
0.004572343546897173,
0.017751095816493034,
-0.016203319653868675,
0.0135648213326931,
-0.016464490443468094,
-0.04020598530769348,
0.02299731969833374,
0.01891646534204483,
-0.011807919479906559,
0.040017034858465195,
0.047196418046951294,
0.009060394950211048,
0.009421438910067081,
0.04248295724391937,
-0.006864479742944241,
0.003247353481128812,
-0.0020406199619174004,
-0.03631807863712311,
0.03912781924009323,
-0.036846552044153214,
0.012215620838105679,
0.00938459299504757,
-0.007484679576009512,
0.04138926789164543,
-0.06837629526853561,
-0.0209644827991724,
-0.048078134655952454,
-0.030349748209118843,
-0.041119981557130814,
-0.011990063823759556,
0.05242319032549858,
-0.008008615113794804,
0.006710161920636892,
-0.004812759347259998,
0.036028165370225906,
-0.0029269945807754993,
-0.009525811299681664,
-0.012018542736768723,
-0.07446764409542084,
-0.03179400786757469,
-0.013824339024722576,
-0.04065004736185074,
0.00925262551754713,
-0.029336337000131607,
0.0010670569026842713,
0.004147435072809458,
0.022681381553411484,
0.011973735876381397,
-0.04269373416900635,
0.03298095613718033,
-0.012387694790959358,
0.02908925525844097,
0.0015174468280747533,
0.051949888467788696,
0.04996012523770332,
0.013523809611797333,
0.1458956003189087,
0.04701034724712372,
0.03313766419887543,
-0.03426481410861015,
0.003750459523871541,
0.008679796941578388,
-0.019685709848999977,
-0.022905977442860603,
0.03520120307803154,
0.0158699918538332,
0.03001600317656994,
-0.02444526180624962,
0.00435034791007638,
0.013912932015955448,
0.003507352201268077,
0.010869340039789677,
-0.053795330226421356,
-0.02174164541065693,
0.014406152069568634,
0.047995422035455704,
-0.03203017637133598,
-0.0028097841423004866,
-0.018033726140856743,
0.0019673239439725876,
-0.01352773793041706,
-0.01285273116081953,
-0.0037252737674862146,
-0.023472312837839127,
0.04621003940701485,
0.03463304415345192,
-0.010804051533341408,
-0.013375273905694485,
-0.005117868073284626,
0.00665466021746397,
-0.047334443777799606,
0.01779390498995781,
0.01924918219447136,
-0.03342752158641815,
0.040944501757621765,
0.01985672488808632,
0.03547528386116028,
-0.010568189434707165,
-0.03707285597920418,
0.04965974763035774,
-0.04870319366455078,
0.011902129277586937,
0.006857088301330805,
-0.020622115582227707,
-0.06240136921405792,
-0.009855496697127819,
0.018451295793056488,
0.0019510291749611497,
-0.022690381854772568,
-0.04254603385925293,
-0.044309377670288086,
-0.013293646275997162,
0.0038582065608352423,
-0.015197502449154854,
-0.017707236111164093,
-0.010747574269771576,
0.0022903233766555786,
-0.000443594268290326,
0.0242932066321373,
-0.013657030649483204,
0.006386590655893087,
0.03877947852015495,
-0.0125827481970191,
-0.00413460424169898,
0.006822274997830391,
-0.01677790842950344,
-0.04699860140681267,
0.025404727086424828,
-0.051621779799461365,
0.009505809284746647,
0.021833093836903572,
0.04197400435805321,
0.032714780420064926,
0.012319457717239857,
0.012073436751961708,
0.0014523385325446725,
-0.019903220236301422,
0.037808239459991455,
-0.031790945678949356,
-0.0015947178471833467,
-0.015105717815458775,
-0.01873522810637951,
0.013790544122457504,
0.020938940346240997,
-0.045480839908123016,
0.012482648715376854,
-0.01906641758978367,
0.0009963870979845524,
0.026456018909811974,
-0.037271562963724136,
-0.01846420206129551,
0.003003921126946807,
-0.04410215839743614,
0.032658662647008896,
-0.0037449246738106012,
0.011904239654541016,
0.02525174245238304,
-0.021282687783241272,
0.002037398749962449,
0.005310164764523506,
-0.012014723382890224,
-0.022836338728666306,
0.037273965775966644,
-0.028575973585247993,
0.010159888304769993,
0.021532757207751274,
0.011369198560714722,
-0.05157146602869034,
-0.03803757205605507,
-0.03929543122649193,
-0.0035292331594973803,
0.07251852005720139,
-0.011594855226576328,
0.010689124464988708,
-0.027245046570897102,
-0.0247902013361454,
-0.01972835697233677,
-0.025565898045897484,
0.03259319067001343,
-0.06845110654830933,
0.01121226605027914,
-0.015436382964253426,
0.0012357831001281738,
0.0018059203866869211,
0.007125867996364832,
-0.011237300001084805,
0.05504200607538223,
0.06119658425450325,
-0.00033534984686411917,
-0.007228434085845947,
-0.014387352392077446,
-0.002301927190274,
-0.03126300871372223,
0.05741690471768379,
-0.0021374619100242853,
0.0297548770904541,
0.034394990652799606,
-0.024821966886520386,
-0.03649965301156044,
0.03070015273988247,
-0.008931605145335197,
0.03204112872481346,
0.019894694909453392,
0.006108763162046671,
-0.008540055714547634,
0.06030726060271263,
-0.045414362102746964,
-0.02414725534617901,
0.026703253388404846,
0.033392421901226044,
-0.004141937475651503,
0.03250058367848396,
-0.016260318458080292,
0.017209282144904137,
-0.0008156475960277021,
0.02853274904191494,
0.013527346774935722,
0.04018634185194969,
-0.03512156009674072,
0.02916371449828148,
0.006963071413338184,
-0.007388020865619183,
0.045058611780405045,
-0.009685450233519077,
-0.004236027132719755,
0.002145220059901476,
-0.00791018083691597,
0.03586740046739578,
-0.014813443645834923,
0.014017153531312943,
-0.05732111260294914,
-0.0408303439617157,
-0.0008060316322371364,
-0.015683498233556747,
0.011033868417143822,
-0.009964737109839916,
0.01895097643136978,
-0.004073691554367542,
-0.10565435886383057,
0.016421429812908173,
-0.01679510809481144,
-0.05030634626746178,
-0.06784400343894958,
0.008636299520730972,
-0.023986782878637314,
0.04639013111591339,
0.03879959136247635,
0.02486194670200348,
0.029141170904040337,
-0.02949383109807968,
0.015153585933148861,
-0.021323690190911293,
-0.03885362669825554,
-0.0010760407894849777,
0.004823090508580208,
-0.05312167853116989,
0.02411135844886303,
-0.015338562428951263,
-0.010161093436181545,
0.02084234543144703,
0.01486942172050476,
0.0024290275759994984,
0.006029190495610237,
0.017703605815768242,
-0.017081525176763535,
0.025921504944562912,
0.024485349655151367,
-0.030301811173558235,
-0.012790471315383911,
-0.0018647178076207638,
0.0034169177524745464,
0.029460150748491287,
-0.004608903545886278,
0.028150398284196854,
-0.013227242976427078,
-0.0183646809309721,
0.007100420538336039,
-0.015662403777241707,
0.006568712182343006,
-0.062219683080911636,
0.0236292015761137,
0.038787275552749634,
-0.004966214764863253,
-0.012996313162147999,
-0.04335155338048935,
0.025996778160333633,
-0.04170345887541771,
-0.003217108082026243,
-0.0011891665635630488,
0.021402420476078987,
0.011013017036020756,
-0.015035022981464863,
-0.029037490487098694,
-0.030978219583630562,
0.050633057951927185,
-0.03910859674215317,
-0.0015958737349137664,
0.04214811697602272,
0.04761865735054016,
-0.006755269132554531,
-0.000970856286585331,
-0.017061244696378708,
-0.006822621915489435,
0.054815229028463364,
0.010090724565088749,
0.05246729031205177,
-0.05478648841381073,
-0.03739623352885246,
0.006480169016867876,
-0.0595107227563858,
0.026025617495179176,
-0.0359020009636879,
-0.025005947798490524,
-0.04564867168664932,
-0.017107250168919563,
0.0005281895282678306,
0.01815074123442173,
0.016301002353429794,
0.0030346724670380354,
-0.04248441755771637,
-0.022366857156157494,
-0.012342110276222229,
0.008683609776198864,
0.0026825692038983107,
0.0545249842107296,
0.053473275154829025,
-0.03846466913819313,
-0.0011163563467562199,
-0.0024379596579819918,
-0.030889449641108513,
0.056282900273799896,
0.012318391352891922,
-0.01585778221487999,
-0.015550440177321434,
0.028583358973264694,
-0.0032503183465451,
0.0343659482896328,
0.005161208566278219,
0.004192395601421595,
0.06950998306274414,
0.006909919902682304,
-0.004685648251324892,
-0.00028005626518279314,
-0.02673863060772419,
-0.06071250140666962,
0.045375071465969086,
-0.004935416392982006,
-0.026608260348439217,
-0.003454561810940504,
-0.014351852238178253,
0.01835138350725174,
-0.050030190497636795,
0.023972533643245697,
0.03090837225317955,
-0.03550279140472412,
0.017245115712285042,
0.022854439914226532,
0.03385169431567192,
-0.0019075014861300588,
0.017918413504958153,
0.046810001134872437,
0.004615810699760914,
-0.016568275168538094,
0.016996104270219803,
0.033188994973897934,
0.006219752598553896,
0.006397442892193794,
0.016627155244350433,
0.01529222447425127,
0.03133336827158928,
0.01883062534034252,
0.06007041782140732,
0.05162836238741875,
-0.038408830761909485,
0.007243355270475149,
0.0315348356962204,
-0.011903087608516216,
0.07379233092069626,
0.034664105623960495,
-0.006899524480104446,
0.07150959223508835,
-0.03589280694723129,
0.012179559096693993,
-0.0027255197055637836,
-0.003993797115981579,
-0.013406339101493359,
-0.003966975025832653,
-0.001450177631340921,
0.01871507056057453,
0.004556907340884209,
-0.047257691621780396,
-0.011554830707609653,
-0.004097125492990017,
0.016033127903938293,
-0.04295899718999863,
0.012335889972746372,
0.026754077523946762,
-0.025661230087280273,
-0.052989959716796875,
-0.007218665909022093,
-0.01607811264693737,
0.0012038523564115167,
-0.016438012942671776,
0.07305607199668884,
0.011292900890111923,
0.006482960656285286,
-0.023447634652256966,
-0.02673841454088688,
0.004640376195311546,
-0.02449340932071209,
-0.024982202798128128,
-0.008095589466392994,
-0.00019403676560614258,
-0.048949696123600006,
-0.004768803250044584
] |
<p>I am taking for granted that when we say that something is conserved it is understood '<em>in its full integrity'.</em> <strong>Energy</strong> is represented by a number (of J, or other) and is usually conserved. </p>
<p>But <strong>momentum</strong> is the product of a number (of Kg) by velocity which is a <em>vector</em>, and therefore has a direction: p = m * v. In circular motion we say that speed is constant but velocity is constantly changing.</p>
<p>If an <strong>elastic ball</strong> is thrown against a wall energy is conserved, the value of the speed is unchanged, but the direction of the vector is not conserved.</p>
<p>In an <strong>elastic collision</strong> if a ball A (m =1) with v = +8 in the x axis hits a ball B at rest (M =3) , B will proceed ( v = 4 *3 = +12) and A will bounce in the opposite direction (p = v = -4). We conclude that: +12 -4 = +8, momentum is conserved.</p>
<p>I am asking: the momentum of what is conserved? if it is the momentum of the system this is not true in the first case, if it is the momentum of the single balls this is not true in the second case.</p>
<p>Language of science is and must be precise, I hope you will not consider this as hair-splitting, but I ask is there a general definition of 'conserved' valid for all instances? why do you apply such a broad/permissive interpretation of the principle in the case of momentum? Or, most likely, where did I go wrong?</p>
<p>EDIT: What puzzles me is that in an elastic collision with the wall the ball takes all energy when it rebounds and there is 0 energy available for the wall and therefore the wall <strong>must have momentum = 0</strong>, ball A will have p = <strong>-8</strong> and W = <strong>0</strong> , and not +16</p>
| 9,404 |
[
-0.0727757140994072,
-0.03806992620229721,
-0.03769843280315399,
-0.05762844532728195,
0.004815408959984779,
-0.01830686442553997,
-0.02451254054903984,
0.033074162900447845,
-0.0171416737139225,
-0.01020018570125103,
-0.012042212300002575,
0.012986649759113789,
0.02706300839781761,
0.01286616176366806,
0.04936549440026283,
0.003929502796381712,
0.016225049272179604,
-0.01460286881774664,
0.013709916733205318,
-0.030913107097148895,
-0.02250831387937069,
-0.038306694477796555,
-0.017209697514772415,
0.01818089373409748,
-0.017768656834959984,
0.025411533191800117,
0.030368488281965256,
-0.038106519728899,
0.020631618797779083,
0.04517499729990959,
0.011137395165860653,
-0.00555016566067934,
0.00006807668978581205,
0.008611682802438736,
0.00910843163728714,
0.008385597728192806,
-0.030702397227287292,
-0.021875441074371338,
0.012690341100096703,
0.03419337794184685,
-0.05497462674975395,
0.008712193928658962,
-0.006848365068435669,
0.052510470151901245,
-0.051550306379795074,
0.04617476090788841,
0.025865882635116577,
0.0021923286840319633,
0.05689401179552078,
-0.07937581092119217,
0.05339746177196503,
-0.0011442099930718541,
0.0688333585858345,
0.0038554740604013205,
-0.03645987808704376,
-0.026536937803030014,
0.04145833104848862,
0.051864612847566605,
-0.012226744554936886,
-0.04911282658576965,
-0.02142125554382801,
-0.008624791167676449,
-0.011633992195129395,
0.02856498397886753,
0.018946193158626556,
0.04081179201602936,
-0.004435814917087555,
-0.03657309710979462,
0.07539227604866028,
-0.003996043000370264,
0.006170245353132486,
0.012959643267095089,
0.05477476492524147,
-0.04356096684932709,
0.04169049113988876,
-0.00631751399487257,
0.028168151155114174,
0.03205501288175583,
0.01138373464345932,
0.05228741094470024,
0.00326520879752934,
-0.015532166697084904,
0.05821722373366356,
0.0629323199391365,
0.013825278729200363,
0.002108986722305417,
0.032220497727394104,
-0.010755813680589199,
0.040103137493133545,
0.03291712701320648,
0.039776258170604706,
-0.023490438237786293,
0.01682497374713421,
-0.005470311734825373,
-0.028188057243824005,
0.04979284107685089,
-0.011418899521231651,
0.06811197847127914,
-0.02167023904621601,
-0.013962368480861187,
0.007987824268639088,
-0.021733134984970093,
0.06299833953380585,
0.04586963355541229,
-0.012043515220284462,
-0.0005315273883752525,
-0.04184423014521599,
0.007706503849476576,
-0.013364455662667751,
0.009939901530742645,
-0.03239878639578819,
0.0029270362574607134,
-0.00039005474536679685,
-0.02676844783127308,
0.016230158507823944,
-0.053242482244968414,
-0.02878490462899208,
0.019676202908158302,
0.05965568497776985,
0.02458236552774906,
0.04139439016580582,
-0.028300147503614426,
-0.005498230457305908,
-0.008325302973389626,
-0.08159139007329941,
0.005880253855139017,
0.0014713823329657316,
0.0029657406266778708,
-0.017231913283467293,
0.026901956647634506,
0.033870138227939606,
-0.010040421970188618,
0.023875216022133827,
0.022095633670687675,
0.048947084695100784,
-0.041064709424972534,
-0.08147730678319931,
-0.05570594593882561,
0.08367670327425003,
-0.05109407380223274,
-0.05730593204498291,
-0.0889284536242485,
-0.03643243387341499,
-0.003703862428665161,
0.0737045407295227,
-0.027532439678907394,
0.004527165554463863,
0.01444871537387371,
0.03583582863211632,
0.009401069954037666,
0.011738689616322517,
-0.0013588694855570793,
0.0046898857690393925,
-0.03201878070831299,
-0.014346310868859291,
-0.045984625816345215,
0.022210238501429558,
0.01691446080803871,
-0.014553168788552284,
-0.016008779406547546,
0.06289897114038467,
-0.045816820114851,
0.013388409279286861,
0.007814105600118637,
-0.0023974396754056215,
0.005148735363036394,
0.05914922431111336,
0.023771239444613457,
-0.001464471104554832,
0.011035994626581669,
0.049161575734615326,
0.0017426832346245646,
-0.05484798178076744,
0.00924350693821907,
0.022229516878724098,
-0.019069422036409378,
-0.004195844288915396,
-0.019515283405780792,
0.002753190230578184,
-0.055553048849105835,
-0.036979250609874725,
-0.029505539685487747,
-0.01311542559415102,
0.006179723422974348,
-0.012868523597717285,
0.028290435671806335,
0.03439457714557648,
0.016397826373577118,
-0.014924900606274605,
0.0027592515107244253,
-0.03427325189113617,
-0.09156247228384018,
0.04619641974568367,
-0.012655169703066349,
-0.0037541345227509737,
0.002265345072373748,
0.013539713807404041,
0.0402483232319355,
-0.024035099893808365,
-0.002935308963060379,
0.016970457509160042,
0.05133423954248428,
-0.024623563513159752,
-0.020441781729459763,
-0.03604625537991524,
0.04382394999265671,
0.014702132903039455,
0.012035843916237354,
0.015831802040338516,
0.016521010547876358,
-0.01363958977162838,
0.017668819054961205,
-0.00199835654348135,
0.014864018186926842,
0.038815416395664215,
-0.017427394166588783,
0.0069222478196024895,
-0.03480035439133644,
0.01728038489818573,
0.024537263438105583,
-0.04403272643685341,
0.09658823162317276,
0.05074289068579674,
-0.008865109644830227,
-0.00872066617012024,
0.033479854464530945,
-0.014986919239163399,
0.011742392554879189,
-0.0017469036392867565,
-0.039701495319604874,
-0.019140340387821198,
-0.010964428074657917,
0.002619713544845581,
0.045354973524808884,
-0.013923040591180325,
0.016088277101516724,
0.011712264269590378,
0.005125176161527634,
0.023541880771517754,
0.003846570150926709,
-0.006349222734570503,
-0.0513245090842247,
0.03773096203804016,
0.03045983985066414,
-0.017095470800995827,
0.024087758734822273,
-0.027539964765310287,
0.0011162633309140801,
0.006525206845253706,
0.00931736920028925,
-0.01242030318826437,
0.0023101952392607927,
-0.002846884774044156,
0.018080616369843483,
0.006175316870212555,
-0.04441243037581444,
0.016186634078621864,
0.014627599157392979,
0.0315384641289711,
0.046777330338954926,
0.01847115159034729,
-0.0032971100881695747,
-0.04726794734597206,
-0.008769266307353973,
0.011538402177393436,
-0.001785682630725205,
-0.015737131237983704,
-0.01325150579214096,
0.008455274626612663,
-0.018772922456264496,
-0.0008179270662367344,
-0.007670561783015728,
-0.00445163156837225,
0.032059382647275925,
-0.005810596514493227,
-0.000424392957938835,
-0.008975903503596783,
0.0246152151376009,
-0.05821909010410309,
-0.000551191158592701,
-0.025026725605130196,
-0.058118149638175964,
-0.024995384737849236,
0.014068261720240116,
-0.026267770677804947,
-0.01674085296690464,
-0.06044755131006241,
-0.00003360387563589029,
0.04886717349290848,
-0.03063567355275154,
0.013746610842645168,
0.03927727788686752,
0.019665805622935295,
-0.05393502116203308,
-0.003674502717331052,
-0.04494239762425423,
0.004339864477515221,
-0.003790496150031686,
0.005615893751382828,
0.04608593136072159,
-0.010932300239801407,
-0.024581274017691612,
0.010688741691410542,
-0.025424204766750336,
-0.06726852059364319,
-0.03591667860746384,
-0.007198844570666552,
0.0442669540643692,
0.0233860295265913,
-0.022680697962641716,
0.039307691156864166,
-0.03534219413995743,
-0.053463760763406754,
-0.020335841923952103,
-0.053981415927410126,
0.007008303422480822,
-0.009732037782669067,
0.02811584435403347,
-0.01137940026819706,
-0.03317970037460327,
0.07302097231149673,
0.038140442222356796,
-0.012670866213738918,
-0.02072000689804554,
-0.013149643316864967,
-0.010538270696997643,
-0.03178691864013672,
-0.0244541447609663,
0.02067459188401699,
0.013258898630738258,
0.030309278517961502,
-0.013157244771718979,
0.026253432035446167,
0.010914182290434837,
0.0082461629062891,
-0.021108806133270264,
-0.01833338476717472,
0.014415443874895573,
-0.032944608479738235,
0.021978940814733505,
0.027819979935884476,
0.00362290907651186,
-0.011541556566953659,
-0.02130243368446827,
0.04869360104203224,
0.01675598695874214,
-0.06853259354829788,
0.060798097401857376,
0.0014762799255549908,
0.02854594588279724,
-0.012913845479488373,
0.027664830908179283,
-0.019083337858319283,
-0.012053112499415874,
0.00873976293951273,
-0.0005738478503189981,
0.018586207181215286,
-0.0029011541046202183,
0.03068634681403637,
0.03137164190411568,
0.0035049808211624622,
-0.03521052002906799,
-0.00937261339277029,
-0.00323863560333848,
0.021188972517848015,
0.06475113332271576,
-0.015156030654907227,
0.019608421251177788,
0.049095965921878815,
0.018396208062767982,
0.027860235422849655,
0.022817732766270638,
-0.056937314569950104,
-0.007010829634964466,
-0.06898786872625351,
0.027789777144789696,
0.013150114566087723,
0.019595278427004814,
-0.00926830992102623,
0.06682341545820236,
0.029065582901239395,
0.01929451897740364,
0.032883767038583755,
-0.008238130249083042,
-0.07879225164651871,
0.024286240339279175,
-0.043230459094047546,
0.018414728343486786,
-0.004056612029671669,
-0.021465353667736053,
-0.036727435886859894,
-0.022979561239480972,
-0.015790440142154694,
0.029021255671977997,
-0.014667697250843048,
-0.07433447986841202,
0.004692752845585346,
-0.06393671780824661,
-0.04540950059890747,
-0.004249487072229385,
0.03597070276737213,
0.057117585092782974,
-0.03986078128218651,
0.023174215108156204,
0.07371603697538376,
-0.017698699608445168,
-0.0019475673325359821,
-0.015127027407288551,
0.0015079950680956244,
0.03657921031117439,
0.030786417424678802,
0.019698606804013252,
0.019815858453512192,
0.011346315033733845,
-0.01004575565457344,
0.018295586109161377,
0.04205892235040665,
-0.0268291924148798,
0.010747457854449749,
-0.02386840060353279,
-0.033459413796663284,
-0.009257732890546322,
-0.023658253252506256,
0.042565539479255676,
0.019819511100649834,
-0.009291091933846474,
0.02201714739203453,
0.056588444858789444,
-0.016441738232970238,
0.029380518943071365,
0.07258199900388718,
0.02140878513455391,
0.002103763399645686,
-0.05811167508363724,
0.03654199466109276,
-0.03188859671354294,
-0.03819146752357483,
0.01490198727697134,
-0.023979393765330315,
-0.0015060424339026213,
0.004266216419637203,
0.03395560756325722,
0.024745209142565727,
-0.02173144742846489,
0.04729478433728218,
-0.04558506980538368,
-0.0031581835355609655,
-0.024790233001112938,
-0.009601984173059464,
0.007916245609521866,
0.04814941808581352,
-0.007490639574825764,
0.04288887977600098,
-0.02615770883858204,
-0.00902043841779232,
0.017309503629803658,
0.030937138944864273,
0.08706261217594147,
0.0024873181246221066,
0.006561211310327053,
-0.02533690631389618,
-0.034956298768520355,
0.05457914620637894,
-0.03382490575313568,
0.02393716759979725,
-0.03747766092419624,
0.02985173650085926,
-0.014022894203662872,
-0.04198478162288666,
-0.009590533562004566,
0.012053907848894596,
-0.03322463855147362,
0.02228999137878418,
0.007765249814838171,
-0.002155105583369732,
-0.0033522392623126507,
0.02703748643398285,
0.0029000923968851566,
-0.0030920510180294514,
-0.0012335798237472773,
-0.015599614009261131,
-0.03188939020037651,
0.010622292757034302,
-0.03685818240046501,
-0.08056525141000748,
-0.02147812396287918,
-0.009165247902274132,
-0.004564050585031509,
0.029438171535730362,
-0.028347894549369812,
-0.037908636033535004,
0.010005634278059006,
-0.014907097443938255,
0.024263998493552208,
0.043050121515989304,
-0.03161747753620148,
0.03047627955675125,
0.00033736624754965305,
-0.034251172095537186,
0.023895222693681717,
0.024272596463561058,
-0.004236471839249134,
-0.037040457129478455,
-0.007983706891536713,
0.030063603073358536,
-0.018044600263237953,
-0.025512853637337685,
-0.05316612496972084,
0.008913541212677956,
-0.0360211543738842,
0.03291623294353485,
0.011005735956132412,
0.024626009166240692,
-0.0104133989661932,
-0.052457548677921295,
-0.004171187989413738,
0.01246653962880373,
0.04104938358068466,
-0.004530956503003836,
0.005581602454185486,
0.03584469109773636,
-0.03480377048254013,
-0.015329104848206043,
0.008476684801280499,
0.0008873040205799043,
-0.02788267284631729,
0.037485312670469284,
0.0006565405637957156,
0.013068254105746746,
-0.014434011653065681,
-0.02386406622827053,
0.004771914798766375,
-0.0604543574154377,
0.0272613987326622,
-0.01808347925543785,
0.022716941311955452,
0.022868305444717407,
-0.056882839649915695,
-0.012411531992256641,
-0.015055305324494839,
0.015588540583848953,
-0.0010197776136919856,
-0.07707665860652924,
0.028007036074995995,
0.008558211848139763,
0.025754336267709732,
-0.06265734136104584,
-0.030405770987272263,
-0.028555359691381454,
0.03027067333459854,
-0.021938301622867584,
-0.003605157369747758,
-0.03522304445505142,
-0.00719215115532279,
-0.04061448574066162,
-0.003494104603305459,
0.055488891899585724,
-0.020782796666026115,
-0.0026598593685775995,
0.055092547088861465,
0.02933686599135399,
0.03362160548567772,
0.025541577488183975,
0.0055271293967962265,
-0.012443182989954948,
0.0031592724844813347,
0.004525191616266966,
-0.032109908759593964,
0.06799903512001038,
-0.022546498104929924,
-0.012747560627758503,
0.025212394073605537,
-0.02129322849214077,
0.04193417355418205,
-0.016233716160058975,
0.03744588419795036,
0.011457277461886406,
-0.009970472194254398,
-0.01987021416425705,
0.010796567425131798,
0.02320004068315029,
-0.03259800374507904,
0.025983622297644615,
0.034193988889455795,
-0.0060202679596841335,
-0.04907172545790672,
-0.032472919672727585,
0.008996500633656979,
-0.00011290182737866417,
0.024011580273509026,
0.0011179839493706822,
0.040230631828308105,
-0.009240411221981049,
-0.028074519708752632,
0.0009854877134785056,
-0.01711716502904892,
0.010578094981610775,
-0.045290615409612656,
-0.018969545140862465,
-0.040909647941589355,
0.008356993086636066,
-0.01240571215748787,
-0.03558408468961716,
-0.03000331111252308,
0.023101946339011192,
0.04291665554046631,
-0.047830209136009216,
0.04486265033483505,
0.0220237597823143,
0.011541061103343964,
-0.0014582292642444372,
-0.019842036068439484,
0.007321448531001806,
0.0048825060948729515,
0.0062765502370893955,
0.05752239376306534,
-0.010219011455774307,
0.01976964809000492,
0.032609544694423676,
0.010643236339092255,
-0.00019803058239631355,
-0.008877784013748169,
0.04639593884348869,
-0.005214400123804808,
0.017250891774892807,
-0.016442203894257545,
-0.020638849586248398,
0.039401378482580185,
-0.03553200513124466,
0.05881209298968315,
0.0030942417215555906,
-0.022994287312030792,
0.06033053994178772,
-0.0020387612748891115,
0.006963074207305908,
-0.04831347614526749,
0.018352394923567772,
-0.026228636503219604,
0.00968877226114273,
0.000565070251468569,
-0.014379391446709633,
-0.029628824442625046,
0.026101641356945038,
0.030136838555336,
0.0023615057580173016,
0.014216789044439793,
-0.0435449592769146,
-0.06382840871810913,
-0.015739191323518753,
-0.05449940264225006,
-0.024158714339137077,
0.0484124980866909,
0.016223259270191193,
-0.004571698140352964,
0.02382313460111618,
-0.03248552605509758,
0.027578534558415413,
-0.018243825063109398,
0.025971870869398117,
-0.016875699162483215,
0.05286019667983055,
0.02373674511909485,
0.003677577245980501,
-0.02559899352490902,
0.01897008717060089,
0.14769777655601501,
0.07091915607452393,
-0.009450221434235573,
-0.02264321781694889,
-0.007570739835500717,
-0.0032187432516366243,
-0.007199502550065517,
-0.027082571759819984,
0.019961630925536156,
0.012441878207027912,
0.010567608289420605,
0.02010028436779976,
0.07098045200109482,
0.016439583152532578,
-0.019967732951045036,
0.04898180812597275,
-0.0379260778427124,
-0.0233426783233881,
-0.04265155270695686,
0.0449051633477211,
-0.023047497496008873,
-0.007729777134954929,
-0.014435233548283577,
0.00396337453275919,
0.008491307497024536,
-0.020576536655426025,
0.021144038066267967,
-0.05783237889409065,
0.015045939944684505,
0.012871820479631424,
-0.0028696483932435513,
0.04685378074645996,
0.02018934115767479,
-0.022773349657654762,
-0.04730910807847977,
-0.009734230116009712,
0.04151371493935585,
-0.010822279378771782,
0.03240817040205002,
0.02905280701816082,
0.019740505144000053,
-0.02303689531981945,
0.01632298156619072,
0.03714081272482872,
-0.03462914377450943,
-0.0026665409095585346,
-0.03390010818839073,
0.06863690912723541,
-0.006594880484044552,
0.024463016539812088,
0.009594184346497059,
-0.042074620723724365,
0.005962659604847431,
-0.0670437291264534,
-0.021128840744495392,
-0.023061301559209824,
0.034771066159009933,
-0.01684255711734295,
-0.016429277136921883,
-0.017570488154888153,
0.004222284536808729,
0.0020844831597059965,
-0.00996071845293045,
-0.01799236238002777,
-0.01877051219344139,
-0.0005052199121564627,
-0.004650885239243507,
0.023988481611013412,
-0.00558349909260869,
-0.014999612234532833,
-0.034632377326488495,
-0.02825162746012211,
-0.060032665729522705,
0.014544285833835602,
-0.012738696299493313,
0.034776851534843445,
0.019839443266391754,
-0.0008484495338052511,
0.004896039143204689,
-0.01458707731217146,
-0.0553913339972496,
0.05355369672179222,
-0.028550289571285248,
-0.037444211542606354,
-0.012403412722051144,
-0.006782244425266981,
0.02374807558953762,
0.040641311556100845,
-0.04073932021856308,
-0.005060314200818539,
-0.007216797210276127,
0.02419278211891651,
0.009521341882646084,
-0.008523639291524887,
-0.05950532108545303,
0.03600895404815674,
-0.0289105623960495,
0.012953278608620167,
-0.03336372971534729,
0.032138656824827194,
0.01030429545789957,
-0.00950552523136139,
-0.012101352214813232,
0.028226487338542938,
-0.010776527225971222,
0.004519205074757338,
0.026813901960849762,
-0.04749695584177971,
-0.02691187895834446,
0.04160637781023979,
-0.017341872677206993,
-0.0024255455937236547,
-0.010164589621126652,
-0.03675566241145134,
-0.00391446752473712,
-0.025612611323595047,
0.028280815109610558,
-0.028788603842258453,
-0.013914680108428001,
-0.05794430896639824,
0.027852948755025864,
-0.047264214605093,
-0.013191602192819118,
-0.050304144620895386,
-0.01525022741407156,
0.039582058787345886,
-0.03342817723751068,
-0.026524784043431282,
0.04517163336277008,
-0.011234838515520096,
-0.030880488455295563,
0.023663539439439774,
0.007815110497176647,
-0.004982200916856527,
-0.0038993647322058678,
0.017991553992033005,
0.0009310253080911934,
0.056714918464422226,
0.016087321564555168,
-0.03357657045125961,
0.05301192030310631,
-0.02870391495525837,
-0.07997330278158188,
0.04008151590824127,
-0.011108988896012306,
-0.012921064160764217,
0.03935350850224495,
-0.009753693826496601,
-0.0114776361733675,
0.05563661456108093,
-0.015501494519412518,
0.027526089921593666,
0.016609998419880867,
-0.07180733233690262,
-0.02159261889755726,
-0.015135085210204124,
0.030441801995038986,
0.0006728923763148487,
-0.019549783319234848,
0.035085637122392654,
0.007924538105726242,
0.019466182217001915,
-0.0015632353024557233,
-0.017952000722289085,
0.023029277101159096,
0.01994035392999649,
0.047566868364810944,
0.016260070726275444,
0.028738588094711304,
0.05647655948996544,
-0.012906034477055073,
-0.0030516288243234158,
0.025063911452889442,
-0.018584327772259712,
-0.0642700269818306,
-0.0035698567517101765,
-0.008764445781707764,
0.015584408305585384,
0.018727563321590424,
-0.06110657379031181,
0.043473485857248306,
0.06569809466600418,
-0.06819221377372742,
0.012902756221592426,
-0.06814298033714294,
0.009157070890069008,
-0.022645510733127594,
-0.011730737052857876,
0.0013476831372827291,
0.05406945198774338,
0.0068749631755054,
0.05219950154423714,
0.01731289178133011,
0.01584635116159916,
-0.0027045742608606815,
2.912220509188046e-7,
-0.020129479467868805,
0.040818795561790466,
0.017502209171652794,
0.025333968922495842,
0.07026729732751846,
-0.020790059119462967,
-0.04461740702390671,
0.024229062721133232,
-0.040542006492614746,
0.009129447862505913,
-0.019786279648542404,
0.008613193407654762,
0.009284907020628452,
0.041570376604795456,
0.017019813880324364,
-0.0031271171756088734,
0.02154865674674511,
0.0186074860394001,
0.02351822517812252,
-0.004959228914231062,
0.005616495385766029,
-0.017974717542529106,
0.019093481823801994,
-0.0655275359749794,
-0.0029006111435592175,
-0.012811892665922642,
-0.011043528094887733,
0.00996880978345871,
-0.0035616757813841105,
0.02244088239967823,
0.03865372762084007,
-0.010127420537173748,
0.002499786438420415,
-0.031184764578938484,
-0.0013345329789444804,
0.029698461294174194,
-0.007673186250030994,
-0.008915179409086704,
0.014822948724031448,
0.0063561368733644485,
-0.004120573867112398,
-0.013748309575021267,
-0.021021375432610512,
-0.013784809969365597,
-0.06292102485895157,
-0.03120122291147709,
0.026132361963391304,
0.00800883024930954,
-0.029197964817285538,
-0.04772119224071503,
-0.017126504331827164,
-0.009124142117798328,
0.029152218252420425,
0.045330364257097244,
-0.007605273276567459,
-0.051605235785245895,
-0.009898388758301735,
-0.08235406875610352,
0.04638942331075668,
0.03921142965555191,
-0.01678609848022461,
-0.042038630694150925,
-0.008965183980762959,
0.00449714157730341,
0.026089519262313843,
0.04770784452557564,
0.0016547994455322623,
0.00542105920612812,
0.0430058054625988,
-0.023113450035452843,
0.03401685133576393,
-0.03877439349889755,
-0.016991496086120605,
-0.024266036227345467,
0.038680221885442734,
0.03084261529147625,
0.010084602981805801,
-0.02026413194835186,
0.026187168434262276,
0.055833734571933746,
-0.047455381602048874,
-0.011528277769684792,
-0.006193292327225208,
-0.05128005892038345,
0.03773227334022522,
0.008352062664926052,
-0.04818081483244896,
0.0971556305885315,
-0.0008168848580680788,
-0.005258850287646055,
0.03535088524222374,
-0.0002942223218269646,
-0.01658720336854458,
0.040497735142707825,
-0.03329719975590706,
-0.020648621022701263,
-0.027408141642808914,
0.00022817392891738564,
0.06870979070663452,
-0.05263721942901611,
-0.0033798799850046635,
0.04366206377744675,
-0.015536419115960598,
-0.021518399938941002,
0.02965262532234192,
0.043522100895643234,
0.01791400834918022,
0.01888279803097248,
0.029892051592469215,
0.02355819381773472,
-0.003686340292915702,
-0.023882512003183365,
0.055359672755002975,
0.008967862464487553,
-0.004940977320075035,
-0.0151059590280056,
0.020176729187369347,
-0.012894835323095322,
0.0166954156011343,
0.041688304394483566,
0.0457121767103672,
-0.011177555657923222,
-0.04477298632264137,
0.00486639142036438,
0.002424366306513548,
0.0018709226278588176,
-0.0009639263735152781,
-0.020761093124747276,
0.056692879647016525,
-0.0063859387300908566,
-0.03454924374818802,
-0.014348275028169155,
0.02764085680246353,
-0.01970953494310379,
0.003824772546067834,
0.011150198057293892,
0.0016866989899426699,
0.004623891320079565,
-0.028364721685647964,
-0.02443738654255867,
-0.0009834134252741933,
0.024321548640727997,
-0.03339703008532524,
0.023180346935987473,
-0.004478382412344217,
0.01458332221955061,
-0.027424141764640808,
0.002143249614164233,
-0.02576092630624771,
0.004433314315974712,
0.017773432657122612,
0.026657534763216972,
0.016292229294776917,
-0.029063887894153595,
0.04180467501282692,
-0.030348725616931915,
0.05665590614080429,
-0.03201324865221977,
0.019394733011722565,
-0.004573446698486805,
-0.0017249403754249215,
0.032112281769514084,
-0.005335463676601648
] |
<p>Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? </p>
<p>Why can it be 0 when spin and linear momentum are parallel?</p>
<p>Like in the example of a scalar field at rest decaying into an electron and a positron via interaction $\frac{1}{2}g\phi \bar{\Psi}\Psi $ </p>
<p>If spin is along x axis and three-momenta is along z axis, decay rate will be 0 if two spins are opposite because orbital momentum is not 0 after decaying.</p>
| 463 |
[
-0.05072866752743721,
-0.010100571438670158,
-0.03127524256706238,
-0.005869769491255283,
0.049456652253866196,
-0.004021968226879835,
-0.07705006003379822,
-0.002631671493873,
0.0370529480278492,
-0.03246241807937622,
0.01239729207009077,
0.015081219375133514,
0.04523519426584244,
0.009740709327161312,
0.01592409797012806,
0.005737541243433952,
-0.00025011220714077353,
-0.0007710212958045304,
-0.02348422445356846,
-0.017132587730884552,
-0.011262153275310993,
0.03878891095519066,
0.028723224997520447,
0.031865525990724564,
-0.003478792030364275,
0.014945494011044502,
0.013432580977678299,
0.022150585427880287,
0.028110165148973465,
0.055480487644672394,
-0.028011983260512352,
-0.024771450087428093,
0.022147197276353836,
0.05415525287389755,
0.023414725437760353,
0.0004102306847926229,
-0.007330391556024551,
-0.03549456596374512,
-0.005875799339264631,
0.036126695573329926,
-0.036547381430864334,
-0.028926681727170944,
-0.06116399168968201,
0.07565847784280777,
-0.018519116565585136,
0.000593748118262738,
0.019592856988310814,
0.0008217687718570232,
0.07010797411203384,
-0.04852722957730293,
0.03800058364868164,
-0.027367442846298218,
0.044576846063137054,
0.007272644899785519,
0.010009832680225372,
0.0002050380571745336,
0.08291567116975784,
0.09045909345149994,
0.01356102991849184,
-0.03361430764198303,
-0.03210519254207611,
0.0017012604512274265,
0.004213215317577124,
-0.00974472425878048,
-0.029790757223963737,
0.027289267629384995,
0.028444994240999222,
-0.005765063222497702,
0.02599017322063446,
0.0021677541080862284,
0.020080912858247757,
0.02640683948993683,
0.02031753584742546,
-0.03125212341547012,
0.002553741680458188,
-0.010226014070212841,
0.016181187704205513,
0.007733273785561323,
0.023973552510142326,
0.01607390306890011,
0.003840659512206912,
-0.009243542328476906,
0.02883201651275158,
-0.0004187586600892246,
0.00589173287153244,
0.0037429900839924812,
0.07216282933950424,
0.012718871235847473,
-0.008908513002097607,
0.0366990864276886,
0.016556821763515472,
0.02866067923605442,
-0.0002399954100837931,
-0.006295965984463692,
-0.037929780781269073,
0.04418288171291351,
-0.00858987495303154,
0.049258001148700714,
0.014382138848304749,
-0.013867785222828388,
-0.01739511825144291,
-0.04048049822449684,
-0.010204317979514599,
0.06233258917927742,
0.019003722816705704,
0.01567847467958927,
-0.027666788548231125,
0.030254734680056572,
-0.05459654703736305,
-0.032284993678331375,
0.012007351964712143,
0.013140258379280567,
-0.010340438224375248,
0.00013076989853288978,
-0.034919437021017075,
-0.00010942079097731039,
0.007403964176774025,
-0.01752321980893612,
0.026894042268395424,
0.04665660858154297,
0.03167307749390602,
-0.007337785325944424,
-0.013634496368467808,
-0.0384831577539444,
-0.08735114336013794,
0.005439273547381163,
0.033843785524368286,
-0.005367358680814505,
-0.08749907463788986,
0.004849383607506752,
0.015854693949222565,
-0.011575421318411827,
0.00397796044126153,
-0.0015109808882698417,
0.009574930183589458,
-0.02385319024324417,
-0.12524524331092834,
-0.023082923144102097,
0.01468772441148758,
-0.06639565527439117,
-0.0031201255042105913,
-0.0854615718126297,
-0.03350827470421791,
0.04140491783618927,
0.08352939784526825,
-0.04979850351810455,
-0.013176994398236275,
-0.019574839621782303,
0.018491923809051514,
-0.014815111644566059,
-0.0007537910714745522,
0.009687379002571106,
-0.013466157019138336,
-0.06062156707048416,
-0.012976769357919693,
-0.04115782305598259,
-0.004649598617106676,
0.017816724255681038,
-0.006367177702486515,
0.006123549770563841,
0.05034558102488518,
-0.04641320928931236,
0.025276798754930496,
0.015832388773560524,
-0.010603532195091248,
-0.06338690221309662,
0.06552141904830933,
-0.0023040769156068563,
0.01943087764084339,
0.04295124113559723,
-0.011581966653466225,
0.04185595363378525,
-0.010708724148571491,
0.06315647065639496,
0.05031127110123634,
-0.05674399435520172,
-0.02096741646528244,
-0.03365006670355797,
-0.004557381849735975,
-0.021732965484261513,
-0.05412619188427925,
-0.04220951348543167,
-0.012581896036863327,
0.018887899816036224,
-0.012139245867729187,
0.04039091616868973,
-0.0024338937364518642,
0.010153254494071007,
-0.003651299746707082,
-0.02211105264723301,
0.010357151739299297,
-0.08386098593473434,
0.04589270427823067,
0.03644388169050217,
-0.02481888234615326,
0.05477549880743027,
0.02936122938990593,
0.0279983039945364,
-0.021287826821208,
-0.04801902920007706,
-0.0038789615500718355,
0.04408418759703636,
-0.01818474568426609,
0.008321108296513557,
0.05226505175232887,
0.058965034782886505,
0.045480772852897644,
0.00559932179749012,
0.02802548184990883,
-0.017487280070781708,
-0.03138056769967079,
0.0022993660531938076,
0.0414142981171608,
0.014294978231191635,
0.021905595436692238,
0.008344939909875393,
-0.004396836739033461,
0.01192088145762682,
-0.007825888693332672,
0.04876019433140755,
-0.033760979771614075,
0.0573410801589489,
0.06533881276845932,
-0.013988357037305832,
0.02479582652449608,
0.03437486290931702,
-0.00013678036339115351,
0.013713719323277473,
-0.007841582410037518,
-0.03931433707475662,
-0.012267906218767166,
0.0069567300379276276,
0.039506103843450546,
0.03650394827127457,
-0.046654604375362396,
0.018476931378245354,
0.02337915264070034,
0.03763241693377495,
0.015025687403976917,
0.03806992247700691,
-0.03979514166712761,
-0.057591550052165985,
0.000733286957256496,
0.005747620016336441,
0.007687363773584366,
0.010928656905889511,
0.056769128888845444,
-0.005968342535197735,
0.023449569940567017,
0.03804348036646843,
-0.046242307871580124,
0.0343194454908371,
0.03414726257324219,
-0.02795795165002346,
-0.002025937894359231,
-0.03105008974671364,
0.027624813839793205,
0.002956454176455736,
0.019039025530219078,
0.03082108125090599,
-0.00020504070562310517,
-0.0004633436328731477,
-0.014841112308204174,
0.004942244850099087,
0.015371826477348804,
-0.015358882024884224,
-0.02428065799176693,
-0.008320179767906666,
0.0043657757341861725,
-0.004384302068501711,
-0.027998417615890503,
-0.030588435009121895,
0.0033397930674254894,
-0.01613546349108219,
-0.004377682693302631,
0.059605710208415985,
0.011857475154101849,
0.02705548331141472,
-0.0009596890304237604,
-0.03700092062354088,
0.0319448858499527,
0.0015705778496339917,
0.01834205351769924,
0.01818515732884407,
-0.0465061217546463,
0.03202976658940315,
-0.0491989441215992,
-0.014955342747271061,
0.010531151667237282,
-0.0056983535178005695,
0.04178594797849655,
0.024072811007499695,
0.009251361712813377,
-0.07500983774662018,
-0.06245401129126549,
-0.024273794144392014,
-0.004648099187761545,
0.0031893912237137556,
-0.005063876509666443,
0.06548037379980087,
-0.02429729513823986,
-0.02976994588971138,
0.0022590733133256435,
-0.027495011687278748,
-0.058151789009571075,
0.00579805625602603,
0.007516718469560146,
0.02463749796152115,
-0.03733466565608978,
0.012949611991643906,
0.010640397667884827,
-0.05199402943253517,
-0.014392218552529812,
-0.0627356544137001,
-0.0014918058877810836,
0.00690926518291235,
0.02206134796142578,
-0.014922616071999073,
0.00018735698540695012,
-0.040443871170282364,
0.07382699847221375,
0.02209066040813923,
-0.0032460952643305063,
-0.006702406331896782,
0.005467346869409084,
-0.02548154816031456,
-0.05565580353140831,
0.007873253896832466,
-0.0034932908602058887,
0.005510128103196621,
0.040572088211774826,
0.000649533758405596,
0.02323503978550434,
0.0006767975864931941,
0.0357341505587101,
-0.005750996991991997,
0.015572481788694859,
-0.006435104180127382,
-0.013242392800748348,
0.039284806698560715,
0.006059582810848951,
-0.01896720938384533,
-0.016849759966135025,
0.045117367058992386,
0.0018192566931247711,
-0.03729540482163429,
-0.06094637140631676,
0.060373786836862564,
0.0015127878868952394,
0.04295976087450981,
0.01928611472249031,
0.04966800659894943,
0.027182769030332565,
-0.0073148650117218494,
0.0063791838474571705,
0.011629733256995678,
0.04380425810813904,
-0.010218947194516659,
0.019177261739969254,
0.023636899888515472,
-0.002648866269737482,
-0.009447421878576279,
-0.018685510382056236,
-0.025461729615926743,
-0.008095327764749527,
-0.0009667252888903022,
-0.028895655646920204,
-0.042453061789274216,
0.041564326733350754,
0.03365320339798927,
-0.011641162447631359,
-0.04078901931643486,
-0.009282086975872517,
-0.03042840026319027,
-0.04124670848250389,
0.047178152948617935,
0.009221251122653484,
0.044047534465789795,
0.04286116734147072,
0.05591849237680435,
0.035437170416116714,
0.003991079982370138,
-0.017474014312028885,
-0.0013234305661171675,
-0.07785994559526443,
0.005825716070830822,
-0.031105609610676765,
-0.026734542101621628,
-0.0032460722140967846,
-0.007096077315509319,
-0.022223761305212975,
-0.015322745777666569,
-0.02331002615392208,
-0.05295759066939354,
-0.03234224393963814,
-0.021963881328701973,
0.02902616560459137,
-0.013887015171349049,
0.004842597059905529,
-0.0327608622610569,
0.048084575682878494,
0.011644543148577213,
-0.029027367010712624,
0.03545347973704338,
0.05154241994023323,
-0.042326413094997406,
-0.021178461611270905,
-0.04053870216012001,
0.024218490347266197,
-0.016893543303012848,
0.019771171733736992,
0.06224328279495239,
-0.0020137394312769175,
-0.019638003781437874,
-0.0018233753507956862,
0.03604152798652649,
0.07020201534032822,
0.018620647490024567,
-0.0040753064677119255,
-0.01583409681916237,
-0.03687630966305733,
-0.005373369436711073,
0.0020383759401738644,
0.05804581940174103,
0.01619066670536995,
0.016975151374936104,
0.0010814876295626163,
0.029667623341083527,
0.00979856587946415,
0.029100719839334488,
0.03779894486069679,
0.024587947875261307,
0.0045290421694517136,
-0.0320294126868248,
-0.0021410423796623945,
0.0050027016550302505,
-0.014034862630069256,
0.003447915194556117,
-0.017172060906887054,
-0.03484337776899338,
-0.03378070890903473,
-0.013426253572106361,
0.01942583918571472,
-0.007898455485701561,
-0.002591797150671482,
-0.014438007958233356,
0.006652415730059147,
-0.00032475090119987726,
0.006988517474383116,
-0.007620073854923248,
0.059248894453048706,
0.0478532537817955,
0.023432951420545578,
0.007992702536284924,
-0.024843741208314896,
0.01362608652561903,
0.009126446209847927,
0.05005001276731491,
0.007159711793065071,
-0.0346403606235981,
0.007109382655471563,
-0.020822426304221153,
0.056552886962890625,
-0.04784592613577843,
0.050023626536130905,
-0.0032702318858355284,
0.008889546617865562,
-0.01358279399573803,
-0.060035474598407745,
-0.048747994005680084,
0.04227720946073532,
-0.027715930715203285,
-0.018445326015353203,
-0.052803341299295425,
-0.003741374472156167,
-0.031004631891846657,
0.028304439038038254,
-0.007286165375262499,
0.0261844415217638,
0.00973447971045971,
0.024579115211963654,
-0.005319821182638407,
0.04112447053194046,
0.0010142710525542498,
-0.10964249819517136,
0.0033918346744030714,
-0.018043605610728264,
-0.024389738216996193,
0.05896126106381416,
-0.049968164414167404,
-0.06937704235315323,
0.012175926007330418,
0.005937608890235424,
-0.0006087651127018034,
0.020486902445554733,
-0.05723359435796738,
0.027653193101286888,
0.020568281412124634,
0.006730233319103718,
0.06712546944618225,
0.03079203888773918,
-0.017333632335066795,
-0.047836191952228546,
-0.0387464240193367,
0.037793152034282684,
-0.029739199206233025,
0.01941470243036747,
-0.03622886911034584,
0.02835090458393097,
0.005335806403309107,
0.07616139948368073,
-0.05120290070772171,
0.017936017364263535,
0.018340149894356728,
-0.006900519598275423,
-0.023199275135993958,
0.017962569370865822,
-0.00593967642635107,
-0.012079450301826,
-0.020481986925005913,
-0.05099556967616081,
-0.04159969463944435,
0.004219511989504099,
0.013909954577684402,
-0.04993370175361633,
-0.004425054881721735,
0.03640218451619148,
0.008304084651172161,
0.016039883717894554,
-0.030384022742509842,
0.02724989503622055,
-0.020924484357237816,
-0.05391446873545647,
-0.024479946121573448,
-0.016382798552513123,
-0.01933363266289234,
0.030673757195472717,
-0.00464653829112649,
-0.0029768587555736303,
0.0163583904504776,
-0.0028332832735031843,
0.021520579233765602,
-0.042993348091840744,
-0.03240809217095375,
0.001733947079628706,
0.009425049647688866,
-0.08182861655950546,
-0.034988392144441605,
-0.0022286369930952787,
0.011006548069417477,
0.019319280982017517,
-0.026259396225214005,
-0.005940771196037531,
-0.014232807792723179,
-0.04595689848065376,
-0.010074011981487274,
0.035760968923568726,
-0.056488603353500366,
-0.010552223771810532,
-0.0045885746367275715,
-0.00953787099570036,
0.0390421599149704,
-0.034322500228881836,
-0.04706214368343353,
-0.006113914772868156,
-0.039163704961538315,
0.01128917932510376,
-0.008131478913128376,
0.08067472279071808,
-0.006198258604854345,
-0.059100355952978134,
0.01050715520977974,
-0.042596686631441116,
0.02174694836139679,
-0.008014963008463383,
-0.010814941488206387,
0.005423252936452627,
-0.007592793554067612,
0.02236602082848549,
0.021479012444615364,
0.0046265264973044395,
0.004545804113149643,
0.057041727006435394,
0.018223252147436142,
-0.0238798838108778,
-0.026158075779676437,
-0.041163261979818344,
0.010809599421918392,
0.009865299798548222,
0.01243615336716175,
-0.013348456472158432,
0.06260081380605698,
-0.00036956334952265024,
0.01093454658985138,
-0.030892938375473022,
0.008691641502082348,
-0.014569245278835297,
-0.013555055484175682,
0.029059365391731262,
0.004460352938622236,
0.008254743181169033,
-0.008670381270349026,
-0.01099314820021391,
-0.009385563433170319,
0.014477650634944439,
0.062155600637197495,
-0.017747173085808754,
0.03930528089404106,
0.02602277509868145,
0.0028537639882415533,
-0.04124099388718605,
-0.03600255027413368,
-0.0017929233144968748,
0.024410977959632874,
0.004072641022503376,
0.0401504784822464,
-0.03873715177178383,
0.015069309622049332,
0.05142240971326828,
0.05579923838376999,
-0.012111492455005646,
0.024485481902956963,
0.04405782371759415,
0.003181107109412551,
0.034903109073638916,
0.03502847999334335,
-0.05543287470936775,
0.04522155225276947,
-0.029554150998592377,
0.026072850450873375,
0.024936247617006302,
-0.016246004030108452,
0.02603507600724697,
0.0497719831764698,
0.002522506285458803,
-0.04492134973406792,
-0.005082402378320694,
-0.04696483910083771,
0.006406377535313368,
0.03262786567211151,
0.020106241106987,
-0.023395700380206108,
0.017189836129546165,
0.0542166531085968,
0.027760770171880722,
0.028731543570756912,
-0.002721555298194289,
-0.040015947073698044,
-0.014786919578909874,
-0.015612718649208546,
-0.021091369912028313,
0.04841499775648117,
-0.016454601660370827,
-0.003161147003993392,
0.014249772764742374,
-0.008225832134485245,
0.02461276203393936,
-0.003318136790767312,
0.015514287166297436,
-0.04687798023223877,
0.050485894083976746,
0.030962642282247543,
0.011419222690165043,
0.008989694528281689,
0.010324684903025627,
0.12485149502754211,
0.05294394865632057,
0.006820943206548691,
-0.07690694183111191,
0.0030470837373286486,
-0.005895123817026615,
-0.004759361036121845,
-0.04061853140592575,
0.021769220009446144,
0.0038846663665026426,
0.018674209713935852,
-0.015695588663220406,
0.05744832381606102,
0.013770418241620064,
-0.03687099739909172,
0.022396573796868324,
-0.0693131685256958,
-0.04723195731639862,
-0.04066011682152748,
0.023913834244012833,
-0.014270907267928123,
-0.011480877175927162,
-0.050897080451250076,
0.02341284602880478,
-0.04028940200805664,
0.021432220935821533,
-0.01724213734269142,
-0.024129191413521767,
0.040714167058467865,
-0.029314350336790085,
-0.0688212662935257,
0.0032274897675961256,
0.05075082555413246,
-0.0205850712954998,
-0.06226800009608269,
0.033497512340545654,
0.03489932790398598,
-0.0005974942469038069,
0.054086390882730484,
0.06150754913687706,
-0.015700357034802437,
0.031991273164749146,
0.04082351550459862,
-0.005771965254098177,
-0.04570280760526657,
-0.01929471455514431,
-0.050074201077222824,
0.09092892706394196,
-0.021682070568203926,
-0.011203735135495663,
-0.015610834583640099,
-0.027362581342458725,
0.0028057130984961987,
-0.03195275738835335,
-0.017601627856492996,
-0.02086576819419861,
0.010684030130505562,
-0.008429308421909809,
-0.004140760749578476,
-0.006049970164895058,
0.018044644966721535,
0.022608527913689613,
0.01384479459375143,
0.01930133067071438,
-0.0011111440835520625,
0.015444074757397175,
-0.019714925438165665,
0.05000324919819832,
0.002469140337780118,
0.01161368191242218,
-0.0035574377980083227,
-0.0037027013022452593,
-0.02638157643377781,
0.014734439551830292,
0.05185960605740547,
0.004759275354444981,
0.05645047873258591,
0.013319982215762138,
-0.00970354676246643,
-0.01693608984351158,
-0.06677881628274918,
0.0322769470512867,
-0.0039266436360776424,
-0.013435769826173782,
0.0065752300433814526,
0.014600537717342377,
0.02912425808608532,
0.043876782059669495,
-0.029383955523371696,
-0.0069044772535562515,
0.007321502547711134,
0.044670138508081436,
0.022578567266464233,
-0.005531023722141981,
-0.0687420442700386,
0.002423530910164118,
-0.01326738204807043,
-0.013977117836475372,
-0.030435720458626747,
0.0019441732438281178,
0.04585402086377144,
0.031582437455654144,
0.00031703931745141745,
0.012526117265224457,
-0.00019752103253267705,
-0.018735133111476898,
0.05719539523124695,
-0.016705583781003952,
0.03898361697793007,
0.05146413296461105,
0.011099465191364288,
-0.018945129588246346,
-0.03370531648397446,
-0.00223473459482193,
-0.002982241567224264,
0.03610491380095482,
-0.016329491510987282,
-0.027528896927833557,
-0.017884084954857826,
-0.01904727891087532,
0.05770329758524895,
-0.026774484664201736,
-0.020099159330129623,
-0.03682044893503189,
0.0392347052693367,
0.008933953009545803,
-0.031462494283914566,
-0.01926145702600479,
0.041043490171432495,
0.02481234446167946,
-0.015667365863919258,
0.00757132051512599,
0.019850561395287514,
-0.0021664872765541077,
0.011864674277603626,
0.04128391295671463,
-0.0010336642153561115,
0.032748423516750336,
0.022270074114203453,
-0.02743488922715187,
0.04304584488272667,
-0.009456007741391659,
-0.06305325776338577,
0.036665309220552444,
-0.012346077710390091,
-0.0016447037924081087,
0.020885052159428596,
-0.02460390143096447,
-0.02428697608411312,
0.02749100886285305,
-0.021390041336417198,
-0.013421471230685711,
0.01941497065126896,
-0.01597927138209343,
-0.00569598563015461,
-0.0013376338174566627,
0.0009825031738728285,
-0.009286697022616863,
-0.04479629173874855,
-0.006921075284481049,
0.0004609330208040774,
-0.011925077997148037,
0.030336497351527214,
-0.028463562950491905,
0.015785442665219307,
0.007483998313546181,
0.022440139204263687,
0.004514905158430338,
0.01593993604183197,
0.029980475082993507,
-0.025634976103901863,
0.04328243061900139,
0.019388629123568535,
0.00972645916044712,
-0.09913219511508942,
0.004387428984045982,
-0.028594788163900375,
0.003323990385979414,
0.038500066846609116,
-0.04945989325642586,
-0.014170621521770954,
0.028339840471744537,
-0.06665750592947006,
0.011615651659667492,
-0.004308256320655346,
-0.03397149220108986,
-0.013075101189315319,
-0.01814846135675907,
-0.032011281698942184,
0.053652916103601456,
-0.006068582180887461,
0.0384436771273613,
0.02000826969742775,
0.003942560404539108,
-0.006152364891022444,
-0.019618608057498932,
-0.03205927833914757,
0.008401771076023579,
-0.05005040019750595,
0.014732906594872475,
0.056640204042196274,
0.0006817116518504918,
-0.03318311646580696,
0.04343655705451965,
-0.007192067801952362,
-0.02188926562666893,
-0.021216705441474915,
0.028741346672177315,
-0.03691476583480835,
0.016032060608267784,
0.008807091973721981,
0.017026539891958237,
-0.02063729241490364,
-0.014339668676257133,
0.03448627516627312,
0.023984041064977646,
-0.044949449598789215,
0.019876861944794655,
0.0044060200452804565,
-0.04590250924229622,
-0.04723652824759483,
0.020534276962280273,
-0.013783508911728859,
-0.04241267591714859,
0.005507984198629856,
0.002467706333845854,
0.02281232364475727,
-0.031194360926747322,
0.007546997629106045,
-0.026470955461263657,
-0.004826390650123358,
0.024885617196559906,
0.013097994960844517,
0.007386109326034784,
-0.00909819733351469,
-0.013444558717310429,
-0.022326428443193436,
0.015733318403363228,
0.002922377083450556,
0.006870033219456673,
-0.04977576062083244,
0.008267844095826149,
-0.004317280370742083,
-0.009213832207024097,
-0.0020759757608175278,
-0.038832493126392365,
-0.04373599961400032,
0.05160951986908913,
-0.007458494510501623,
-0.00016222865087911487,
-0.01426243782043457,
-0.009727517142891884,
-0.02040863037109375,
-0.06266504526138306,
0.0263336431235075,
0.0034977071918547153,
0.006028271280229092,
-0.044826485216617584,
-0.0032770135439932346,
-0.02149180695414543,
0.0057369195856153965,
0.04186444357037544,
0.005402788519859314,
-0.016342127695679665,
0.00976896658539772,
0.0035422220826148987,
0.010685679502785206,
-0.025713756680488586,
0.019020410254597664,
0.0048416052013635635,
-0.016145853325724602,
0.012668571434915066,
-0.02351042814552784,
-0.039327818900346756,
0.015009446069598198,
0.011032520793378353,
0.015733592212200165,
-0.003365028416737914,
0.02768787182867527,
-0.04229617863893509,
0.052479106932878494,
-0.007904772646725178,
0.00296658743172884,
0.05856935307383537,
0.03314874693751335,
0.027412155643105507,
0.043643973767757416,
-0.010851173661649227,
-0.03555526211857796,
0.022747786715626717,
-0.0519724078476429,
0.004743464291095734,
-0.05121826007962227,
-0.02098500356078148,
0.052248913794755936,
-0.010991166345775127,
-0.0029218760319054127,
0.05119021236896515,
-0.054865993559360504,
-0.0011205446207895875,
0.02419174648821354,
-0.026259809732437134,
0.03913281485438347,
0.016917923465371132,
0.020620744675397873,
0.009854765608906746,
0.007606002036482096,
0.023559249937534332,
0.024476421996951103,
-0.014261635951697826,
0.008226350881159306,
0.008463852107524872,
0.034850139170885086,
-0.037729185074567795,
0.023003200069069862,
0.02140043117105961,
0.04564866051077843,
-0.02006452903151512,
-0.0015681146178394556,
0.02638479508459568,
-0.006498157512396574,
-0.001110578770749271,
0.0328994020819664,
-0.021650614216923714,
0.059382397681474686,
-0.0326056107878685,
0.015992876142263412,
-0.02688342146575451,
-0.00034503781353123486,
-0.010879491455852985,
0.020413469523191452,
0.037789106369018555,
0.05799909681081772,
-0.015002849511802197,
-0.02936043031513691,
-0.016729146242141724,
-0.0302853025496006,
0.031015442684292793,
-0.0265717264264822,
-0.007865948602557182,
0.006025476381182671,
-0.03634492680430412,
0.00929147470742464,
-0.014540120027959347,
-0.032039668411016464,
-0.028617041185498238,
-0.011257882229983807,
0.00051478500245139,
0.04005458950996399,
-0.03593827784061432,
0.007261123973876238,
-0.01572447270154953,
0.027381032705307007,
-0.04287883639335632,
-0.008010323159396648,
-0.01672722026705742,
0.011891106143593788,
-0.01469196006655693,
0.005192430689930916
] |
<p>I'm in a mechanical physics class, and I'm having a hard time understanding what the quantity of work represents. How can I understand it conceptually?</p>
| 380 |
[
-0.013769703917205334,
-0.006371872033923864,
-0.0119375204667449,
-0.03245745226740837,
0.050225768238306046,
0.015269643627107143,
-0.027234569191932678,
-0.01852087676525116,
-0.040157780051231384,
0.001044961274601519,
0.020488716661930084,
0.0660381093621254,
0.027373718097805977,
-0.008824402466416359,
0.02292986959218979,
0.0158377718180418,
-0.0025742286816239357,
-0.03876829519867897,
-0.0021383254788815975,
-0.002730285283178091,
-0.009016747586429119,
-0.0024675962049514055,
0.0027275981847196817,
0.0015322441468015313,
-0.018884453922510147,
0.011138591915369034,
0.04033077880740166,
-0.012102099135518074,
0.031621064990758896,
0.038654934614896774,
0.007231949828565121,
-0.0002743881777860224,
0.0011774332961067557,
0.03762288764119148,
0.020688677206635475,
0.007276852149516344,
-0.032172273844480515,
-0.014090693555772305,
-0.027944037690758705,
0.04260123893618584,
-0.040780916810035706,
0.004533990751951933,
0.004306231625378132,
0.03528938442468643,
-0.05529389902949333,
0.02688121609389782,
-0.00952843390405178,
-0.01201894972473383,
0.038769643753767014,
-0.057381462305784225,
0.07591059803962708,
0.009550461545586586,
0.05280739814043045,
0.022666601464152336,
-0.012969624251127243,
0.02093004807829857,
0.08144164830446243,
0.055843375623226166,
-0.013134034350514412,
-0.0512964129447937,
-0.04751226678490639,
0.011968451552093029,
-0.02275189757347107,
-0.033695317804813385,
0.023090947419404984,
0.03597467020153999,
-0.01110819075256586,
-0.022855302318930626,
0.07201237231492996,
0.023269180208444595,
0.03761181980371475,
0.04100631922483444,
0.05052921548485756,
-0.030085407197475433,
0.00101290678139776,
-0.04918716475367546,
0.043989039957523346,
0.0008960176492109895,
0.026743212714791298,
0.048301756381988525,
-0.020812619477510452,
0.005976901855319738,
0.04654836654663086,
0.07236573100090027,
-0.01053757406771183,
-0.006339253857731819,
0.07581048458814621,
0.01782551035284996,
0.043461523950099945,
0.018426263704895973,
0.01729469746351242,
-0.002645251341164112,
0.02418125979602337,
0.016006236895918846,
-0.005975819658488035,
0.023313574492931366,
-0.019662706181406975,
0.03268564119935036,
0.027234584093093872,
-0.02335016056895256,
0.024399863556027412,
-0.025531139224767685,
0.019585618749260902,
0.05607593432068825,
0.005759775172919035,
-0.005512568634003401,
-0.01886717602610588,
0.028497302904725075,
0.009324946440756321,
0.0008104394655674696,
-0.02145429700613022,
0.007946322672069073,
0.008225327357649803,
0.0073524354957044125,
-0.007757721934467554,
0.005745193921029568,
0.0039404467679560184,
-0.02428208664059639,
0.04263196140527725,
0.04576703533530235,
0.028885478153824806,
-0.03953869268298149,
0.055452536791563034,
-0.019237564876675606,
-0.04109090939164162,
0.03213317692279816,
0.02403608337044716,
-0.04009988531470299,
-0.016481701284646988,
0.04171586036682129,
-0.012409932911396027,
-0.020170634612441063,
-0.0165066197514534,
0.000031742802093504,
0.022600779309868813,
-0.02633172832429409,
-0.06420722603797913,
-0.057637769728899,
0.04111417755484581,
0.0049601709470152855,
-0.0447450689971447,
-0.0694667398929596,
0.0030537520069628954,
0.017534783110022545,
0.055248409509658813,
0.004883878864347935,
-0.003985975868999958,
-0.006350234150886536,
0.03522993251681328,
0.0008073737262748182,
0.0033584863413125277,
-0.004762726835906506,
0.0020463557448238134,
-0.029673337936401367,
0.04740534722805023,
-0.0581999272108078,
-0.0002845928829628974,
0.030237501487135887,
0.00018626228848006576,
-0.05915039777755737,
0.03008231520652771,
-0.027807040140032768,
-0.025450190529227257,
0.030693579465150833,
-0.02404283545911312,
-0.017918601632118225,
0.07052430510520935,
0.008141990751028061,
0.011256953701376915,
0.05239279195666313,
0.02540602907538414,
0.008274165913462639,
0.013454203493893147,
0.0680747702717781,
0.03542143478989601,
-0.022462228313088417,
-0.023959947749972343,
-0.02767733857035637,
0.01527096051722765,
0.005872952751815319,
-0.03657184913754463,
-0.06014172360301018,
0.00988916028290987,
0.022093845531344414,
-0.011744231916964054,
0.04525338113307953,
0.005310884211212397,
-0.00900284480303526,
-0.024437008425593376,
-0.011248171329498291,
-0.027380838990211487,
-0.06775332242250443,
0.03025699593126774,
-0.027873268350958824,
-0.007898383773863316,
0.013360428623855114,
-0.0034698841627687216,
0.030816804617643356,
-0.06553327292203903,
-0.03470287844538689,
-0.005236542783677578,
0.0436699278652668,
0.005631730426102877,
-0.002133266068994999,
0.005022008903324604,
0.04250619187951088,
0.03811471164226532,
0.04187658056616783,
0.04696925729513168,
-0.017973357811570168,
-0.011396368965506554,
0.005809609778225422,
-0.0140280956402421,
0.010523435659706593,
0.026752207428216934,
-0.006116098258644342,
-0.0069345287047326565,
-0.025681786239147186,
-0.0013101755175739527,
0.05112165957689285,
-0.010059058666229248,
0.0747280940413475,
0.05241667851805687,
-0.00532374856993556,
-0.03014889918267727,
0.042611014097929,
-0.030275858938694,
-0.00006651315197814256,
-0.019705435261130333,
-0.016393857076764107,
-0.0011499131796881557,
0.011615847237408161,
0.03629273548722267,
0.023383455350995064,
-0.00906267948448658,
-0.016860736533999443,
0.027566591277718544,
0.03912799432873726,
0.032002076506614685,
0.023354994133114815,
-0.04733135551214218,
-0.01563943177461624,
0.026706984266638756,
0.007447985466569662,
0.003009291598573327,
0.03894553333520889,
0.035388294607400894,
0.06951203942298889,
0.01916874200105667,
-0.0014597298577427864,
-0.029126392677426338,
0.053210727870464325,
-0.018981005996465683,
0.022718625143170357,
0.02041822113096714,
-0.02887386828660965,
0.0237977746874094,
-0.018326155841350555,
0.028063833713531494,
0.024161992594599724,
-0.019723840057849884,
0.021929733455181122,
-0.028344586491584778,
-0.018422048538923264,
0.005063339602202177,
-0.008756984956562519,
-0.005011773202568293,
-0.008797231130301952,
0.027393968775868416,
-0.00016677736130077392,
0.01814996637403965,
-0.0015067404601722956,
-0.03296331688761711,
-0.013268199749290943,
-0.023732002824544907,
0.006290877237915993,
0.008110202848911285,
0.049674421548843384,
-0.03657267987728119,
-0.0324789434671402,
-0.0021058719139546156,
-0.04679958149790764,
0.01478792354464531,
-0.02920108288526535,
-0.04409436509013176,
0.01604999601840973,
0.00013742463488597423,
-0.029819468036293983,
0.05743631720542908,
-0.029179932549595833,
-0.009500843472778797,
0.023196391761302948,
-0.03154739364981651,
-0.013930713757872581,
0.00983430165797472,
-0.02427911013364792,
0.02433289773762226,
-0.00622453773394227,
0.026601100340485573,
0.045517802238464355,
-0.07812146097421646,
-0.04944374039769173,
0.014414168894290924,
-0.03939274698495865,
-0.057730190455913544,
-0.025993065908551216,
-0.008532936684787273,
0.014547215774655342,
-0.026938358321785927,
0.017378080636262894,
0.014189695939421654,
-0.0786241665482521,
-0.016400983557105064,
-0.03599162772297859,
-0.04705823212862015,
-0.009300644509494305,
-0.014392307959496975,
0.023301512002944946,
-0.027855470776557922,
-0.07168719917535782,
0.06483478844165802,
-0.01535810437053442,
-0.04563915729522705,
-0.006968282628804445,
-0.005426277872174978,
0.010872420854866505,
-0.005346484947949648,
0.03285415843129158,
0.044505223631858826,
-0.028115829452872276,
0.03403742238879204,
0.013258064165711403,
0.028146229684352875,
0.02338549867272377,
0.03703968599438667,
-0.019878070801496506,
-0.016545960679650307,
-0.01826832816004753,
0.0007238946272991598,
0.014917400665581226,
0.0032526555005460978,
-0.03567915037274361,
0.061544764786958694,
-0.0032563519198447466,
0.02320469543337822,
0.005211599171161652,
-0.024830855429172516,
0.04748356714844704,
0.01435366366058588,
0.017412135377526283,
-0.05671952664852142,
0.049650512635707855,
-0.0163224246352911,
0.0035807425156235695,
0.004580566193908453,
-0.015966616570949554,
0.026417069137096405,
-0.025865281000733376,
-0.016831083223223686,
0.02814619243144989,
0.011230502277612686,
-0.019825519993901253,
-0.02364538237452507,
-0.018745863810181618,
-0.006604191847145557,
-0.0077665396966040134,
0.0005764574743807316,
-0.01498387660831213,
0.03138254955410957,
0.018858905881643295,
0.025005662813782692,
0.014397690072655678,
-0.04242590814828873,
0.00937182828783989,
-0.06751617044210434,
-0.03031516820192337,
0.022367537021636963,
0.01720581389963627,
0.006013863254338503,
0.06923690438270569,
0.016188353300094604,
0.01108334120362997,
0.028955893591046333,
-0.03214535117149353,
-0.05395776033401489,
0.04860631749033928,
-0.013244451954960823,
-0.010772363282740116,
0.0014729229733347893,
-0.015772776678204536,
-0.008263886906206608,
-0.06099643558263779,
-0.036609720438718796,
-0.0018551928224042058,
0.00908023864030838,
-0.05098380893468857,
0.0024325514677911997,
-0.00980076938867569,
-0.019884129986166954,
-0.00864456221461296,
0.006091144401580095,
0.03729686141014099,
-0.010153612121939659,
0.013915890827775002,
0.05461737513542175,
-0.025262190029025078,
-0.008695593103766441,
0.003276097821071744,
-0.01690843515098095,
0.006661639083176851,
0.008041654713451862,
0.007022622041404247,
0.027989864349365234,
-0.005102504510432482,
0.029261814430356026,
0.013657004572451115,
0.020282192155718803,
0.024278540164232254,
-0.02678750827908516,
-0.047468770295381546,
-0.03602440282702446,
-0.00010441012273076922,
0.005898591130971909,
0.04123193025588989,
-0.01087900996208191,
0.022535433992743492,
0.02145208977162838,
-0.00935998372733593,
-0.04597515985369682,
0.029284104704856873,
0.055466532707214355,
0.03340105339884758,
-0.05086906626820564,
-0.07437514513731003,
-0.006448758766055107,
-0.039862506091594696,
0.0071986666880548,
0.007860038429498672,
0.0017300420440733433,
-0.03324621543288231,
0.007092383690178394,
0.005406724754720926,
-0.030633987858891487,
-0.023473532870411873,
-0.01937042362987995,
-0.027837524190545082,
0.00836698804050684,
0.02679482102394104,
-0.01047307625412941,
0.03128133341670036,
0.05227445065975189,
0.029346946626901627,
0.013095250353217125,
-0.028366219252347946,
-0.10068512707948685,
-0.028853880241513252,
0.02533971518278122,
-0.00048543571028858423,
-0.03406623378396034,
0.0072200181894004345,
0.027005022391676903,
-0.015570730902254581,
0.0706636980175972,
-0.04827496409416199,
0.03727353364229202,
-0.035059425979852676,
0.02135601080954075,
-0.015253860503435135,
-0.002907597227022052,
-0.03216860815882683,
0.044054146856069565,
-0.0035400036722421646,
0.037899941205978394,
0.008516240864992142,
0.026348302140831947,
-0.013726613484323025,
0.011524037458002567,
0.015706803649663925,
0.030683306977152824,
0.009877919219434261,
-0.017122572287917137,
0.011377432383596897,
0.05621183663606644,
-0.016410335898399353,
-0.05673385038971901,
-0.013934632763266563,
-0.008903623558580875,
-0.009388335980474949,
0.005708633456379175,
-0.03804594278335571,
-0.04783863574266434,
0.022285128012299538,
-0.003262854414060712,
0.0014033422339707613,
-0.035917576402425766,
-0.06592846661806107,
0.035983629524707794,
0.048133235424757004,
0.015212357975542545,
0.049745090305805206,
0.02047516591846943,
-0.05857494845986366,
0.014188566245138645,
-0.035998545587062836,
0.044336188584566116,
0.006627488881349564,
-0.003295794827863574,
-0.04091477766633034,
0.0005897883675061166,
-0.017507603392004967,
0.04493967816233635,
-0.0214894600212574,
0.022421186789870262,
-0.0337522029876709,
-0.03908202052116394,
-0.04404535889625549,
0.02133811078965664,
0.05169079452753067,
-0.03881554305553436,
0.006560591049492359,
0.007200389169156551,
0.013372392393648624,
-0.020263953134417534,
-0.017887309193611145,
0.026163069531321526,
-0.01449549663811922,
0.016607802361249924,
0.01175260916352272,
0.01926933228969574,
-0.025261441245675087,
-0.014247596263885498,
0.04652434587478638,
-0.038215506821870804,
0.05175111070275307,
-0.019637975841760635,
-0.0037562204524874687,
-0.019008515402674675,
-0.07380392402410507,
-0.05685601383447647,
0.004664964973926544,
-0.019946489483118057,
0.04212162271142006,
-0.023527417331933975,
0.015189321711659431,
0.005528523586690426,
0.007835102267563343,
-0.041061729192733765,
-0.045036107301712036,
0.021430859342217445,
0.023359423503279686,
0.008836107328534126,
0.014681660570204258,
0.017979200929403305,
0.0010274451924487948,
-0.05765843391418457,
0.01624147593975067,
0.04549442604184151,
-0.030383219942450523,
-0.0034348508343100548,
-0.004651455674320459,
-0.007116253487765789,
0.04328478127717972,
0.005551699083298445,
-0.04425539821386337,
0.0006758351810276508,
-0.0015587334055453539,
-0.04412877932190895,
0.014394665136933327,
0.020949792116880417,
-0.03186824545264244,
-0.0060125840827822685,
0.008211135864257812,
0.0009130995604209602,
0.0505899079144001,
-0.04152205213904381,
0.007223049644380808,
0.023907992988824844,
0.025348857045173645,
-0.006607657764106989,
-0.029979266226291656,
0.056587811559438705,
0.015133107081055641,
0.059122901409864426,
0.007486224640160799,
-0.0006195572204887867,
-0.034336283802986145,
-0.05095990374684334,
0.029324593022465706,
0.019052952527999878,
-0.006870944052934647,
0.0029010907746851444,
0.05167717486619949,
-0.024719173088669777,
-0.008231556974351406,
0.0000544843751413282,
-0.020405305549502373,
-0.009792868979275227,
-0.003424794878810644,
0.026703517884016037,
0.020975889638066292,
-0.0022925178054720163,
-0.052812717854976654,
-0.009853385388851166,
-0.021908987313508987,
-0.008252572268247604,
0.057111769914627075,
-0.038737691938877106,
0.06630133092403412,
0.017608599737286568,
-0.0290398970246315,
0.04482781141996384,
0.0012270738370716572,
-0.02256941981613636,
0.019995544105768204,
0.01853284426033497,
0.016870267689228058,
-0.014126758091151714,
-0.019565409049391747,
0.04984458535909653,
0.02074284292757511,
-0.012221298180520535,
-0.003964062314480543,
0.034585993736982346,
0.015335211530327797,
-0.010903796181082726,
-0.005854095797985792,
-0.05472559109330177,
0.038861922919750214,
-0.009320753626525402,
0.039705123752355576,
-0.030885806307196617,
0.00070250837597996,
0.054205868393182755,
0.0011108922772109509,
0.0007414913852699101,
-0.02424616552889347,
-0.009400548413395882,
-0.05202827602624893,
-0.004368259571492672,
0.008631153963506222,
-0.031098520383238792,
0.000575309619307518,
0.002417696872726083,
-0.0005434618215076625,
-0.007494315505027771,
0.030085358768701553,
-0.005465303082019091,
-0.054037220776081085,
-0.03725999593734741,
-0.02919536828994751,
-0.05334222689270973,
0.021807454526424408,
0.007664123084396124,
-0.040668077766895294,
0.0321771465241909,
-0.013635179027915001,
0.004249406047165394,
-0.029048919677734375,
0.011409536935389042,
-0.027735253795981407,
0.06108568608760834,
0.017253385856747627,
0.03933347016572952,
0.007858908735215664,
-0.003306485014036298,
0.08900437504053116,
0.06344359368085861,
0.02636817842721939,
-0.03422153741121292,
0.03076266124844551,
-0.046159740537405014,
-0.022320277988910675,
-0.011671729385852814,
0.04190748929977417,
-0.0023974578361958265,
0.028816943988204002,
0.004042739514261484,
0.02611389011144638,
-0.005575946532189846,
0.017332708463072777,
0.06585679948329926,
-0.025075038895010948,
-0.029801366850733757,
0.015781665220856667,
0.03444649651646614,
-0.0007461897330358624,
0.023975485935807228,
-0.0470644049346447,
-0.008550400845706463,
-0.04276534914970398,
-0.02423073537647724,
0.005436753388494253,
-0.05106693133711815,
0.048996880650520325,
0.0036676116287708282,
-0.011540352366864681,
0.016172289848327637,
-0.0022523438092321157,
-0.017011160030961037,
-0.025673793628811836,
0.026232026517391205,
0.038825929164886475,
0.01446941215544939,
-0.004323365166783333,
0.006099754478782415,
-0.007238906342536211,
0.0002278751926496625,
-0.013227533549070358,
-0.012409227900207043,
-0.038535475730895996,
0.0023682585451751947,
-0.020135818049311638,
0.03393421694636345,
-0.0126816900447011,
0.057526808232069016,
0.006640252657234669,
-0.01113183330744505,
-0.03970499709248543,
-0.054669443517923355,
-0.00850836094468832,
-0.0038536996580660343,
0.015624294057488441,
-0.012824644334614277,
-0.0392792634665966,
-0.03267936035990715,
-0.009812159463763237,
-0.02255283296108246,
0.032095540314912796,
0.013024230487644672,
-0.011145397089421749,
0.02456345036625862,
-0.001376257510855794,
0.028046131134033203,
-0.05627385154366493,
-0.0390281118452549,
0.010737904347479343,
-0.014981239102780819,
-0.020782001316547394,
-0.00039478365215472877,
0.018721869215369225,
0.011229163035750389,
0.00036800449015572667,
-0.007167196366935968,
-0.014585701748728752,
-0.02742566540837288,
-0.042176514863967896,
0.04999003931879997,
0.003680703230202198,
-0.023789415135979652,
-0.02272992581129074,
0.02313871495425701,
0.03480924665927887,
0.04569999873638153,
0.014165004715323448,
0.04941941797733307,
-0.007640557829290628,
-0.019202029332518578,
0.02519509755074978,
-0.015563294291496277,
-0.013778191059827805,
0.04496033489704132,
-0.03760071098804474,
-0.00997254904359579,
0.012656229548156261,
0.031020401045680046,
0.03228369727730751,
-0.025704003870487213,
-0.004812616854906082,
0.029010657221078873,
-0.01602778211236,
-0.00010038897016784176,
0.024692023172974586,
-0.06033632159233093,
-0.032276712357997894,
0.012651053257286549,
-0.004490576218813658,
-0.05880100280046463,
-0.027555763721466064,
-0.05668320134282112,
0.00499472813680768,
-0.019124383106827736,
0.07028782367706299,
-0.012430788949131966,
0.014729426242411137,
0.006998383440077305,
0.033176906406879425,
-0.053267356008291245,
0.006339859217405319,
-0.06239403411746025,
0.011442949995398521,
0.039652008563280106,
-0.0004000951594207436,
-0.015665430575609207,
0.032309211790561676,
0.00724375993013382,
-0.022572685033082962,
0.011038203723728657,
0.013128629885613918,
0.014902963303029537,
-0.008952770382165909,
0.0294854287058115,
-0.03450733423233032,
0.0541863888502121,
-0.02636285498738289,
-0.02974904328584671,
0.05497715622186661,
-0.04738150164484978,
-0.025636645033955574,
0.037579137831926346,
-0.019993972033262253,
0.05017833039164543,
0.024047676473855972,
-0.03220139816403389,
-0.044911399483680725,
0.03518642112612724,
-0.0593203641474247,
0.006509304512292147,
-0.027670158073306084,
-0.009727053344249725,
-0.03225405141711235,
-0.03014172613620758,
0.015925144776701927,
-0.0011688361410051584,
-0.0043966262601315975,
0.0032426915131509304,
0.03999542444944382,
-0.00594634423032403,
-0.017887931317090988,
0.025533676147460938,
0.0023998827673494816,
0.015880919992923737,
0.039518091827631,
-0.0010488666594028473,
0.023733248934149742,
0.028377680107951164,
-0.04759553074836731,
0.05225126072764397,
-0.003069982398301363,
-0.001994816120713949,
-0.10981374979019165,
-0.008765515871345997,
-0.028276972472667694,
-0.02406073361635208,
0.03720754384994507,
-0.03165707737207413,
0.020192695781588554,
0.012007220648229122,
-0.05702066794037819,
0.039508938789367676,
-0.05883193388581276,
-0.038422610610723495,
0.008603349328041077,
-0.017580417916178703,
0.016501229256391525,
0.05794128030538559,
0.03285536170005798,
0.05597381666302681,
0.016945945098996162,
0.009617562405765057,
-0.008796115405857563,
-0.0467836931347847,
0.01559809222817421,
0.0449334941804409,
-0.014416398480534554,
0.0011162383016198874,
0.0464792437851429,
-0.016848528757691383,
-0.03221562132239342,
0.03170648217201233,
-0.041002701967954636,
0.035384610295295715,
-0.007602262310683727,
0.03260907530784607,
-0.011661750264465809,
0.06711909919977188,
-0.007570873014628887,
-0.022136643528938293,
-0.03254387155175209,
-0.000706973485648632,
0.01459177490323782,
0.01777961291372776,
-0.009962084703147411,
0.005323376972228289,
0.033291611820459366,
-0.018823372200131416,
-0.026593273505568504,
0.04129554703831673,
-0.021421795710921288,
0.0006420722347684205,
0.0191750917583704,
0.0029918530490249395,
0.01749333180487156,
-0.043222010135650635,
0.020403767004609108,
-0.033101946115493774,
-0.02007361501455307,
0.02020784467458725,
0.008946701884269714,
-0.014102206565439701,
0.0010902367066591978,
0.01308941189199686,
-0.009832125157117844,
0.010203241370618343,
0.005908409599214792,
-0.03478184714913368,
-0.07825635373592377,
0.017159009352326393,
0.02283330075442791,
-0.04016755893826485,
-0.000663932238239795,
-0.032834671437740326,
-0.03080611303448677,
0.025490988045930862,
0.04346831887960434,
-0.0022289312910288572,
0.0010066962568089366,
-0.05709009990096092,
-0.045676089823246,
-0.09197647869586945,
0.04678099602460861,
0.008611206896603107,
-0.01870488002896309,
-0.06510864943265915,
-0.02673683874309063,
0.005233862902969122,
0.019732806831598282,
0.04791821166872978,
-0.015892213210463524,
-0.043911486864089966,
0.004494234453886747,
-0.008361920714378357,
0.013166258111596107,
-0.0240620244294405,
0.02121713198721409,
-0.012108562514185905,
-0.03261980041861534,
-0.02197354845702648,
-0.001238698372617364,
-0.03485546633601189,
-0.008089757524430752,
0.032591626048088074,
-0.021920114755630493,
0.017417898401618004,
-0.016686758026480675,
-0.005307009443640709,
0.04919284209609032,
0.0053810011595487595,
-0.025797948241233826,
0.04537895694375038,
-0.013406037352979183,
0.034761276096105576,
0.03309682384133339,
-0.0290034431964159,
-0.0627790167927742,
0.034584544599056244,
-0.01574355736374855,
0.027157949283719063,
-0.002448845887556672,
-0.009185447357594967,
0.06708396226167679,
-0.06739311665296555,
-0.021310580894351006,
0.0567031055688858,
-0.008973684161901474,
-0.000515663530677557,
0.04025253653526306,
0.0877327248454094,
0.03493010997772217,
-0.02372288703918457,
0.009184274822473526,
-0.014374393969774246,
-0.007826307788491249,
0.018665630370378494,
0.041987884789705276,
0.038621652871370316,
0.01395381148904562,
0.021476224064826965,
0.026781894266605377,
-0.022779498249292374,
0.010786239057779312,
0.015996422618627548,
0.0368933267891407,
-0.05101188272237778,
-0.040225107222795486,
-0.027943268418312073,
-0.027649283409118652,
0.018187325447797775,
0.023873042315244675,
-0.005785123910754919,
0.0965207889676094,
-0.0174443107098341,
-0.002499327529221773,
-0.029785556718707085,
0.003790559945628047,
0.0020345745142549276,
-0.05649919807910919,
0.046739362180233,
0.06855043023824692,
0.0047674356028437614,
-0.01090301014482975,
-0.012797528877854347,
0.021207820624113083,
0.03553227707743645,
-0.017509818077087402,
0.031285498291254044,
0.004875579848885536,
-0.027274757623672485,
-0.050839148461818695,
-0.004040291532874107,
-0.06304525583982468,
-0.01681152544915676,
0.06262214481830597,
0.053150903433561325,
0.002659708959981799,
0.03832889720797539,
-0.03719114884734154,
-0.004341403488069773,
0.02772572450339794,
-0.05846310034394264,
0.0027498709969222546,
-0.02444123476743698,
0.048831213265657425,
0.024064721539616585,
-0.0072278608568012714
] |
<p>On <a href="http://en.wikipedia.org/wiki/Ampere" rel="nofollow">Wikipedia</a> it says: </p>
<blockquote>
<p>This force is used in the formal definition of the ampere, which states that it is "the constant current that will produce an attractive force of $2 × 10–7$ newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum."</p>
</blockquote>
<p>In reference to the definition of an Ampere, why was $2 × 10–7$ chosen?</p>
| 9,405 |
[
-0.020859962329268456,
-0.0049199629575014114,
-0.009015713818371296,
-0.016609594225883484,
0.03137309476733208,
-0.01152239739894867,
-0.02006022445857525,
-0.003256812458857894,
-0.018840564414858818,
-0.020281383767724037,
0.01759565807878971,
0.045573264360427856,
0.08388733863830566,
0.003493768163025379,
0.02897973731160164,
0.015914512798190117,
0.016632307320833206,
-0.006358304526656866,
0.002083203289657831,
-0.031616903841495514,
0.002409338252618909,
0.03189004957675934,
-0.02977530099451542,
0.03427503630518913,
-0.008889215998351574,
0.03690372407436371,
0.04216494783759117,
-0.007587597239762545,
0.04224921390414238,
0.041791677474975586,
0.013390958309173584,
-0.03278099000453949,
0.04677999019622803,
-0.009314795024693012,
0.02761145681142807,
-0.005638315342366695,
-0.005431509111076593,
-0.024748167023062706,
0.006815407890826464,
0.02229713462293148,
-0.004755330737680197,
-0.011356501840054989,
-0.00022675961372442544,
0.03155885264277458,
-0.03886732459068298,
0.018516279757022858,
0.010877843014895916,
-0.02099817804992199,
0.023777177557349205,
-0.04220185428857803,
0.04938650131225586,
0.022419285029172897,
0.04317691549658775,
0.02561834827065468,
-0.02935328707098961,
-0.028887789696455002,
0.05419578775763512,
0.045255519449710846,
-0.029668699949979782,
-0.06107537820935249,
-0.008228381164371967,
-0.005822198931127787,
-0.035334620624780655,
-0.030840275809168816,
-0.00861347932368517,
0.04047316685318947,
-0.0034819748252630234,
-0.013166905380785465,
0.02482145093381405,
0.007069156970828772,
0.02681991085410118,
0.02437921054661274,
-0.0025716039817780256,
-0.009114637970924377,
-0.0049399519339203835,
-0.013372809626162052,
0.020863646641373634,
0.003062895266339183,
0.03788186237215996,
0.03469664976000786,
-0.03310341387987137,
-0.011044844053685665,
0.0664006918668747,
0.03554799407720566,
0.022037966176867485,
-0.010599433444440365,
0.05701541155576706,
-0.01765318401157856,
0.015876883640885353,
0.02076626755297184,
0.008807591162621975,
0.04186328500509262,
-0.006176796276122332,
0.005619524512439966,
0.021928707137703896,
0.019286222755908966,
-0.005155479535460472,
0.050965528935194016,
0.02635703794658184,
-0.034683357924222946,
0.02216273918747902,
0.01420414075255394,
0.026182018220424652,
0.07292020320892334,
0.006969991605728865,
-0.035158924758434296,
-0.003148921299725771,
0.012719775550067425,
-0.024511370807886124,
0.0055227396078407764,
-0.049312345683574677,
0.03984653577208519,
-0.010868181474506855,
-0.009668334387242794,
0.0032161131966859102,
-0.043397206813097,
0.030749211087822914,
0.023298731073737144,
0.09090724587440491,
0.05634848028421402,
0.036995235830545425,
-0.032584358006715775,
0.009520439431071281,
-0.04489050433039665,
-0.035280440002679825,
0.015512403100728989,
0.027598200365900993,
-0.004670442081987858,
0.006108028814196587,
0.019552081823349,
0.002880251035094261,
-0.011332385241985321,
-0.04860662668943405,
0.02380390278995037,
0.04685332998633385,
0.0022172504104673862,
-0.08537939935922623,
-0.07763013243675232,
0.023029981181025505,
-0.020749006420373917,
-0.015851452946662903,
-0.0690729171037674,
0.022443529218435287,
0.024077072739601135,
0.055467020720243454,
-0.007189956493675709,
0.0005347520927898586,
0.004168502055108547,
0.02413768880069256,
-0.006567107047885656,
0.0033765160478651524,
-0.03989263251423836,
0.01992025598883629,
-0.0164702907204628,
-0.024990074336528778,
-0.06639058887958527,
0.025353657081723213,
0.05093497037887573,
0.008876817300915718,
-0.030205996707081795,
0.07304038852453232,
-0.0372212752699852,
-0.03123927116394043,
0.010847494006156921,
0.005707328207790852,
-0.017585011199116707,
0.06049160286784172,
0.03274579346179962,
-0.029121102765202522,
0.06630586832761765,
0.005994100123643875,
0.05780386924743652,
0.036776915192604065,
-0.014173848554491997,
0.03894265368580818,
-0.025677038356661797,
0.010623374953866005,
-0.04384201765060425,
0.021893037483096123,
0.02168862894177437,
-0.04630591347813606,
-0.05057600885629654,
-0.0006097524892538786,
0.005934054031968117,
-0.003086535260081291,
0.044392913579940796,
0.006118326913565397,
-0.0009364401921629906,
-0.0034015618730336428,
-0.03884459286928177,
-0.025185586884617805,
-0.05736932158470154,
0.048405151814222336,
-0.003820306621491909,
-0.017855092883110046,
0.009582486934959888,
-0.007442947942763567,
0.01912052184343338,
-0.04115945100784302,
-0.012731330469250679,
0.015480889938771725,
0.0112672233954072,
-0.00045855093048885465,
-0.019848816096782684,
0.009827762842178345,
0.016732996329665184,
0.030890123918652534,
0.011665252037346363,
0.04110385477542877,
0.01110581774264574,
-0.027788544073700905,
0.03675928711891174,
-0.026733191683888435,
0.04511255770921707,
0.03073711134493351,
-0.004268762189894915,
-0.020269114524126053,
-0.010911659337580204,
-0.009221676737070084,
0.10250140726566315,
-0.006135713774710894,
0.07275412976741791,
0.02533627301454544,
0.040738508105278015,
0.009419690817594528,
0.04378564655780792,
0.0013458916218951344,
0.005054644774645567,
-0.022824980318546295,
-0.03645668551325798,
-0.08528093248605728,
0.0033818352967500687,
0.06024906784296036,
0.04649538919329643,
-0.041744768619537354,
0.004381511826068163,
0.022450704127550125,
0.03583776205778122,
0.032786089926958084,
0.03527224436402321,
-0.041349656879901886,
-0.0505773089826107,
0.03397773951292038,
0.023618478327989578,
-0.0017750412225723267,
0.03264712914824486,
0.050979193300008774,
0.03130223602056503,
0.02233511209487915,
0.03466615453362465,
-0.016514595597982407,
0.06451249122619629,
-0.008844681084156036,
0.030360443517565727,
0.010944337584078312,
-0.020289920270442963,
0.03786395862698555,
-0.04430916905403137,
0.03055753745138645,
0.019874241203069687,
0.028890755027532578,
0.011545506305992603,
-0.007428954821079969,
0.0015538823790848255,
-0.005416870582848787,
-0.038295846432447433,
-0.040218550711870193,
-0.02910645492374897,
0.01715942472219467,
-0.03517841920256615,
-0.008297503925859928,
-0.04151693359017372,
0.021362708881497383,
-0.02621700055897236,
-0.026746127754449844,
-0.0220054779201746,
0.017187654972076416,
0.0543556734919548,
-0.014633141458034515,
-0.02229336090385914,
-0.003662511007860303,
-0.06180974096059799,
0.02368248999118805,
0.0064695957116782665,
0.014441786333918571,
0.010903719812631607,
-0.02413901314139366,
-0.028880354017019272,
0.06449640542268753,
-0.009474722668528557,
0.018566731363534927,
0.009093300439417362,
-0.009506694041192532,
-0.038448989391326904,
0.01738036796450615,
-0.03095879592001438,
0.031087301671504974,
-0.006421178579330444,
-0.025173617526888847,
0.04299941658973694,
-0.01506814919412136,
-0.012180247344076633,
0.02635231614112854,
-0.049145039170980453,
-0.033537279814481735,
-0.014263682067394257,
-0.008800404146313667,
0.031486015766859055,
-0.030387215316295624,
0.038828201591968536,
0.004997361451387405,
-0.021105404943227768,
0.00932042021304369,
-0.039848167449235916,
-0.0325947143137455,
0.0004502474330365658,
-0.047347135841846466,
0.05489230528473854,
-0.018967997282743454,
-0.049388542771339417,
0.06951121240854263,
0.022648954764008522,
-0.018436208367347717,
-0.015008235350251198,
-0.00661558797582984,
-0.02267398312687874,
-0.05293826013803482,
-0.010129918344318867,
0.06407830119132996,
-0.007219755556434393,
0.025884315371513367,
0.023855557665228844,
0.0356299988925457,
0.021414319053292274,
0.014036650769412518,
-0.01532045379281044,
-0.001680321409367025,
-0.01082555577158928,
-0.028910981491208076,
0.05066804587841034,
0.019968021661043167,
-0.023289673030376434,
0.021053452044725418,
-0.008566305972635746,
0.036977771669626236,
-0.0004458624462131411,
-0.028272297233343124,
0.04214044287800789,
-0.002405396895483136,
0.010306871496140957,
-0.031501684337854385,
0.025215743109583855,
-0.006224432028830051,
-0.04282870888710022,
0.005952619947493076,
0.03224599361419678,
0.028010807931423187,
-0.06513236463069916,
-0.04291481152176857,
0.018251469358801842,
0.013596604578197002,
-0.016192249953746796,
-0.03508419543504715,
0.009127400815486908,
0.0010407691588625312,
0.03042990155518055,
-0.011405402794480324,
-0.02717929519712925,
-0.021649768576025963,
0.03744965046644211,
0.022874854505062103,
0.018419474363327026,
-0.03098548948764801,
-0.009558438323438168,
-0.07121498882770538,
-0.013435798697173595,
-0.0016038190806284547,
0.053571682423353195,
-0.018533259630203247,
0.048650991171598434,
0.014266650192439556,
0.014312398619949818,
-0.005517284851521254,
0.012050040997564793,
-0.09736426174640656,
0.02914326637983322,
-0.059380561113357544,
-0.03754795342683792,
-0.005394375883042812,
-0.037594206631183624,
-0.028438391163945198,
0.011454860679805279,
-0.014018924906849861,
-0.03950701653957367,
-0.009988473728299141,
-0.031874362379312515,
0.013034387491643429,
-0.02250169776380062,
-0.012609323486685753,
-0.033501915633678436,
0.03459294140338898,
0.03608504682779312,
-0.03346667438745499,
0.01856062561273575,
0.020903995260596275,
-0.0014159593265503645,
-0.028735972940921783,
-0.011150063946843147,
-0.02695479802787304,
0.0330403670668602,
0.005768404342234135,
0.022749826312065125,
0.010052839294075966,
-0.027726657688617706,
0.005630929954349995,
-0.0029980710241943598,
0.04603508114814758,
0.04596986621618271,
0.004211598075926304,
-0.04641077667474747,
-0.060537371784448624,
0.006563073489814997,
-0.00792626105248928,
0.04579925909638405,
-0.0001452377618988976,
0.021023839712142944,
0.03640647232532501,
0.002683511935174465,
-0.004398038145154715,
0.022320877760648727,
0.015368298627436161,
-0.00200718198902905,
-0.03101387433707714,
-0.06573937833309174,
0.04025835171341896,
-0.0323684960603714,
0.011974334716796875,
0.018446985632181168,
-0.006966732442378998,
-0.043916404247283936,
-0.022782934829592705,
0.027211414650082588,
0.005407107528299093,
-0.03613179177045822,
0.031051967293024063,
0.003963964991271496,
0.014369210228323936,
-0.005601991433650255,
-0.010361135937273502,
-0.010955987498164177,
0.037443093955516815,
0.032930102199316025,
0.007789354305714369,
-0.04167027026414871,
-0.0857718214392662,
0.0043803853914141655,
0.01067566778510809,
0.04037053883075714,
-0.009075218811631203,
-0.04161711037158966,
-0.05175000801682472,
0.004104604013264179,
0.02205185405910015,
-0.055058397352695465,
0.025148237124085426,
-0.0553288497030735,
0.012191307730972767,
-0.002133583649992943,
-0.03511292487382889,
-0.005167980212718248,
0.017441824078559875,
-0.00380027387291193,
0.015763523057103157,
-0.02826281078159809,
-0.015298946760594845,
0.028472602367401123,
0.00540489237755537,
0.05183830112218857,
0.04822078347206116,
0.005930480547249317,
-0.0037744948640465736,
-0.013002653606235981,
-0.013675080612301826,
-0.03715052083134651,
-0.05862127244472504,
-0.015453220345079899,
-0.001938165514729917,
0.013176515698432922,
-0.0012716584606096148,
-0.03973838686943054,
-0.05452108755707741,
0.0031174214091151953,
0.0032508487347513437,
0.0075353397987782955,
0.011307261884212494,
-0.014763634651899338,
0.048188500106334686,
0.06851043552160263,
0.0034770171623677015,
0.08425333350896835,
0.033050134778022766,
-0.05042970925569534,
0.005700450856238604,
-0.039610356092453,
0.01541185099631548,
0.00035997721715830266,
-0.015542716719210148,
-0.03481052443385124,
0.03201055899262428,
-0.06462117284536362,
0.05903691425919533,
-0.0014393212040886283,
0.0100698908790946,
-0.034837156534194946,
-0.03417593240737915,
-0.02098924107849598,
0.04424947127699852,
0.003736951155588031,
0.0038767806254327297,
0.0011130277998745441,
0.03213753178715706,
-0.004205796867609024,
-0.026472605764865875,
0.027677973732352257,
0.015705550089478493,
0.024009356275200844,
0.02834939770400524,
0.0023580484557896852,
0.02797776460647583,
0.009645569138228893,
-0.028933243826031685,
0.04844719544053078,
-0.049279533326625824,
0.06310219317674637,
-0.0007205044967122376,
-0.005837025120854378,
-0.015940193086862564,
-0.06457587331533432,
-0.09438024461269379,
0.012051691301167011,
-0.013014443218708038,
0.06207403168082237,
-0.046303946524858475,
0.04129792004823685,
0.03237159550189972,
0.05123782530426979,
-0.03291909396648407,
-0.029847633093595505,
0.050748471170663834,
0.011378154158592224,
0.010490655899047852,
0.04412603750824928,
-0.015510734170675278,
-0.011838091537356377,
-0.047923311591148376,
-0.01315621193498373,
0.07108484208583832,
-0.02952297404408455,
-0.03737577423453331,
-0.012953363358974457,
0.026087315753102303,
0.052463386207818985,
0.01582866720855236,
-0.014448813162744045,
-0.006377313751727343,
-0.04795381799340248,
0.010095017962157726,
0.012807514518499374,
0.07069821655750275,
-0.03662807121872902,
-0.037460021674633026,
-0.009526059962809086,
-0.006643456406891346,
0.031945426017045975,
-0.008948021568357944,
-0.0043248445726931095,
0.04728759452700615,
-0.004356323275715113,
-0.016289403662085533,
0.006204166449606419,
0.013307824730873108,
-0.005863187834620476,
0.02126346528530121,
-0.00478536169975996,
-0.01093119103461504,
-0.04613468796014786,
-0.028900546953082085,
0.006714615970849991,
0.015374095179140568,
-0.002846411196514964,
-0.02480107732117176,
0.040398020297288895,
-0.026700494810938835,
0.001453549601137638,
0.019312411546707153,
-0.0014048012671992183,
0.04784925654530525,
0.0074235848151147366,
0.008602505549788475,
-0.002470264909788966,
0.010056895203888416,
-0.026234831660985947,
-0.01576177217066288,
0.0039211162365973,
0.02639855444431305,
0.05636623874306679,
-0.03624310716986656,
0.06517573446035385,
0.013278632424771786,
-0.03904147073626518,
-0.001460360363125801,
-0.005860483273863792,
-0.013133450411260128,
-0.012885205447673798,
0.036316655576229095,
-0.007649173494428396,
-0.012057154439389706,
0.020499631762504578,
0.009629792533814907,
0.010354509577155113,
0.009776106104254723,
-0.038892246782779694,
0.021731719374656677,
0.03464903682470322,
-0.010593093000352383,
-0.019783873111009598,
-0.020093075931072235,
0.035636283457279205,
0.0007894723094068468,
0.03314322978258133,
0.018770897760987282,
-0.05162809416651726,
0.02361181564629078,
-0.05804581567645073,
-0.012856876477599144,
-0.03291664272546768,
-0.008092562668025494,
-0.03248576819896698,
0.0007718880078755319,
0.024673180654644966,
-0.002132917521521449,
0.016365906223654747,
0.01652088202536106,
0.015305428765714169,
0.02224556915462017,
0.030672607943415642,
0.021450594067573547,
-0.030188336968421936,
0.010607131756842136,
-0.06255078315734863,
-0.04865878075361252,
0.02246122620999813,
-0.02049640379846096,
-0.09211912006139755,
0.014083605259656906,
-0.03171823173761368,
0.025016266852617264,
0.04428894817829132,
0.013506567105650902,
-0.03221740201115608,
0.09965082257986069,
-0.028832746669650078,
-0.00277488911524415,
-0.04507943242788315,
-0.01525346003472805,
0.10549289733171463,
0.029141848906874657,
0.0035103228874504566,
-0.07578092068433762,
0.02761063352227211,
-0.04255727678537369,
-0.024200232699513435,
-0.03157161548733711,
-0.014537721872329712,
-0.040530040860176086,
0.014934002421796322,
0.02609609067440033,
0.039187513291835785,
0.0010560061782598495,
0.011386037804186344,
0.06303434818983078,
-0.021848546341061592,
-0.025033414363861084,
0.02419291064143181,
0.019847895950078964,
-0.015591312199831009,
0.03587823361158371,
-0.040723178535699844,
0.010461278259754181,
-0.01936081051826477,
0.006281042005866766,
-0.041610416024923325,
-0.011214714497327805,
0.020414575934410095,
0.005108639597892761,
-0.0356476865708828,
-0.001128580654039979,
0.0044867172837257385,
-0.022218244150280952,
-0.04449500888586044,
-0.0005692200502380729,
0.01405880507081747,
-0.013865762390196323,
0.0028769916389137506,
0.014955539256334305,
0.011104477569460869,
0.00007382188778137788,
0.007269322406500578,
0.0009594156290404499,
-0.06396549195051193,
-0.014593488536775112,
-0.018113402649760246,
0.026503941044211388,
0.005487218964844942,
-0.00317562953568995,
0.03216642886400223,
0.03531045466661453,
-0.013676108792424202,
-0.04768195003271103,
-0.04878758266568184,
-0.029401548206806183,
0.040782902389764786,
-0.03576289117336273,
-0.03203888610005379,
-0.042933911085128784,
0.0297896359115839,
-0.028153151273727417,
0.032655537128448486,
0.0033346156124025583,
0.017847655341029167,
0.0076997531577944756,
0.027012482285499573,
-0.0020168148912489414,
-0.01885906793177128,
-0.025505492463707924,
-0.02760298177599907,
-0.04048275947570801,
-0.08199561387300491,
-0.02080395817756653,
-0.005025423597544432,
0.03183181583881378,
0.03149883821606636,
-0.022614918649196625,
0.0005284223589114845,
-0.03180938959121704,
-0.05378331243991852,
0.04773498699069023,
-0.004031820688396692,
-0.010412137024104595,
0.0007532851304858923,
0.0025645068380981684,
-0.005418351851403713,
0.009439322166144848,
-0.010959286242723465,
-0.006662352010607719,
0.014778206124901772,
-0.004795040003955364,
0.02388223446905613,
-0.02662842348217964,
-0.01641388051211834,
-0.002982521429657936,
-0.021115271374583244,
-0.012041711248457432,
0.015465554781258106,
0.016961118206381798,
0.020610999315977097,
-0.001991508062928915,
0.005578348413109779,
0.019990315660834312,
-0.03745957091450691,
0.010928831063210964,
0.01413924340158701,
-0.012649819254875183,
0.012026186101138592,
0.011434151791036129,
-0.0052222819067537785,
-0.04471868649125099,
-0.011738949455320835,
-0.05052284151315689,
0.014761417172849178,
0.00856140349060297,
0.03159283846616745,
-0.03617153689265251,
0.017288057133555412,
-0.04054219648241997,
-0.014164467342197895,
-0.056942764669656754,
-0.018443778157234192,
-0.04859217628836632,
-0.038714516907930374,
-0.012976501137018204,
0.01317660789936781,
-0.03925016522407532,
0.04321703314781189,
-0.030649760738015175,
-0.018086619675159454,
0.02149883657693863,
-0.0015385254519060254,
-0.026653768494725227,
-0.022009501233696938,
0.0063749998807907104,
-0.017597487196326256,
0.05297348275780678,
-0.02980109490454197,
-0.037484943866729736,
0.03944205120205879,
-0.03296855092048645,
-0.01403204258531332,
0.032598551362752914,
-0.0032908516004681587,
0.022605780512094498,
0.0427049919962883,
-0.001237318734638393,
-0.0025935336016118526,
0.04013637453317642,
-0.03222382813692093,
0.004050842486321926,
-0.013028990477323532,
-0.023575354367494583,
0.00452781654894352,
-0.021586308255791664,
-0.008144546300172806,
-0.0018161388579756021,
0.028519997373223305,
0.03039599023759365,
0.04069676622748375,
0.006160551682114601,
-0.033063143491744995,
0.00921789463609457,
0.02679133415222168,
0.025705289095640182,
0.026995280757546425,
0.033246852457523346,
-0.0033662233036011457,
0.05165903642773628,
-0.042756225913763046,
0.04127783328294754,
0.0030709723941981792,
-0.025859717279672623,
-0.08606229722499847,
-0.02301202528178692,
-0.03147275745868683,
0.02756301686167717,
0.02782047539949417,
-0.038029659539461136,
0.03003506176173687,
0.0033892737701535225,
-0.052772920578718185,
-0.007965856231749058,
-0.014558574184775352,
-0.03395776450634003,
0.013827282004058361,
-0.041467808187007904,
0.008738460950553417,
0.03537411615252495,
0.019907107576727867,
0.029170585796236992,
0.026182852685451508,
-0.020244592800736427,
-0.005000416189432144,
-0.04142572358250618,
-0.01605638675391674,
0.051242344081401825,
-0.034211721271276474,
0.008921952918171883,
0.027279816567897797,
0.01428069919347763,
-0.023171178996562958,
0.07871980965137482,
0.004351969342678785,
-0.00724043371155858,
-0.008253519423305988,
0.023578139021992683,
0.0030455479864031076,
0.05682794749736786,
0.014058557339012623,
-0.012775246053934097,
-0.024155838415026665,
0.03473872318863869,
0.018819626420736313,
0.019815679639577866,
0.029884135350584984,
-0.010363598354160786,
0.03937844932079315,
-0.013402601704001427,
-0.018076825886964798,
0.041095100343227386,
-0.021253742277622223,
0.007843969389796257,
0.04291848465800285,
0.0147061413154006,
0.008832286112010479,
-0.05131619796156883,
0.0009070883388631046,
-0.024533532559871674,
-0.021919121965765953,
0.06242724135518074,
-0.04161308705806732,
-0.0035499511286616325,
0.021171104162931442,
0.002957384567707777,
0.0037510027177631855,
0.046414148062467575,
0.028105439618229866,
-0.0014657048741355538,
-0.06078628450632095,
-0.020113589242100716,
0.011912336573004723,
-0.023928070440888405,
0.04412092640995979,
-0.0301516093313694,
-0.02190040983259678,
0.026639746502041817,
0.026959802955389023,
0.002859547035768628,
-0.016888249665498734,
-0.04819248989224434,
0.00588013231754303,
-0.05079358443617821,
0.03135697916150093,
0.006741173565387726,
-0.010504474863409996,
-0.03458622470498085,
-0.046486083418130875,
0.009064995683729649,
0.021503016352653503,
0.052560288459062576,
0.0013099039206281304,
-0.030296381562948227,
-0.006709020119160414,
0.008882892318069935,
0.004624611232429743,
-0.019201455637812614,
0.008739395067095757,
0.028515048325061798,
-0.03281175345182419,
-0.007275434210896492,
-0.0025677871890366077,
0.006458523217588663,
0.030213868245482445,
0.020075954496860504,
0.009885701350867748,
-0.0005406779237091541,
-0.018025662750005722,
-0.036834899336099625,
0.047928400337696075,
0.01841052994132042,
-0.013458264991641045,
0.049786780029535294,
-0.011261587031185627,
0.03129225969314575,
-0.032124582678079605,
-0.012047534808516502,
-0.02526024356484413,
-0.03760804608464241,
-0.032682690769433975,
0.024356957525014877,
-0.024166887626051903,
-0.0011780379572883248,
0.05088209733366966,
-0.031446702778339386,
-0.013943418860435486,
0.0617397166788578,
-0.0388505756855011,
-0.032529547810554504,
0.032953545451164246,
0.005214600823819637,
0.049811262637376785,
-0.003996084909886122,
0.04068083316087723,
-0.014380151405930519,
-0.006973084527999163,
-0.02768709324300289,
0.027962829917669296,
0.06246589869260788,
-0.0059285094030201435,
-0.022057343274354935,
0.06789794564247131,
0.0057229273952543736,
0.009308569133281708,
0.017261598259210587,
0.020591886714100838,
-0.019150612875819206,
-0.049725331366062164,
-0.004309170879423618,
-0.02960069850087166,
0.005802537314593792,
0.0012044431641697884,
-0.01732955314218998,
0.1181180328130722,
0.003002281067892909,
0.038882363587617874,
0.023889800533652306,
-0.002420830773189664,
0.007255546748638153,
0.019379539415240288,
-0.008671795949339867,
-0.0067817447707057,
-0.013710866682231426,
-0.012624971568584442,
-0.005317692179232836,
0.0018686497351154685,
0.014910387806594372,
-0.0195609237998724,
0.010533309541642666,
0.010551666840910912,
-0.012935412116348743,
-0.06981399655342102,
0.031090669333934784,
-0.005920869298279285,
-0.00790153443813324,
0.06806491315364838,
0.01813727430999279,
0.009129785932600498,
-0.009496350772678852,
0.009572845883667469,
-0.0129106929525733,
0.05364816263318062,
-0.0811878889799118,
-0.033270616084337234,
-0.02400774322450161,
-0.002045565750449896,
0.014831979759037495,
0.0033489384222775698
] |
<p>Let's say </p>
<ul>
<li><p>the cylinder has a diameter equal to its height of $25\;\mathrm{cm}$</p></li>
<li><p>the cylinder is sealed at the top and filled with sand</p></li>
<li><p>the cylinder is also buried in the sand at sea at a depth of $10\;\mathrm{m}$ with only its top exposed</p></li>
<li><p>the top has a handle for you to pull on</p></li>
<li><p>the cylinder's weight is negligible ($0.0\;\mathrm{kg}$)</p></li>
</ul>
<p>How much force is needed to pull it out (excluding friction)? </p>
<p>I just need the formulas to figure out how big of a cylinder I need to anchor a buoy. Precision is up to you.</p>
<p>Please correct my computations if they are wrong.</p>
<p>Assuming the density of wet sand is $1920\;\mathrm{kg\;m^{-3}}$:</p>
<ul>
<li><p>Volume of cylinder $= \pi r^2 h = 3.1416 \times 0.015625\;\mathrm{m^2} \times 0.25\;\mathrm{m} \approx 0.012272\;\mathrm{m^3}$</p></li>
<li><p>Mass of sand in cylinder $= 0.012272\;\mathrm{m^3} \times 1920\;\mathrm{kg\;m^{-3}} = 23.56\;\mathrm{kg}$</p></li>
<li><p>Weight of sand in cylinder $= 23.56\;\mathrm{kg} \times 9.8\;\mathrm{m\;s^{-2}} = 231\;\mathrm{N}$</p>
<hr></li>
<li><p>Water pressure at $10\;\mathrm{m}$ depth $= 2\;\mathrm{atm} = 200000\;\mathrm{N\;m^{-2}}$</p></li>
<li><p>Surface area of top of cylinder $= \pi r^2 = 3.1416 \times (0.125\;\mathrm{m})^2 = 0.049\;\mathrm{m^2}$</p></li>
<li><p>Pressure force on top of cylinder $= 0.049\;\mathrm{m^2} \times 200000\;\mathrm{N\;m^{-2}} = 9800\;\mathrm{N}$</p>
<hr></li>
<li><p>Total force $= 231\;\mathrm{N} + 9800\;\mathrm{N} = 10031\;\mathrm{N}$</p></li>
</ul>
<p>Edit: Converted to newtons ($\mathrm{N}$). Thanks @KvdLingen!</p>
<p>Note: This is not homework. I'm a freediver. I am literally thinking of burying a plastic cylinder into a patch of sand at a $10\;\mathrm{m}$ depth. At the top of the cylinder, a one way check valve will be attached to let water get out when burying and a release valve so I can pull it out. I will attach to the "handle" a rope and a buoy to the other end of the rope. The cylinder will serve as a temporary anchor. A real anchor can be easily pulled up by vertical forces when there are waves acting on the buoy. An anchor can also damage corals in dive sites--thus having a need to secure it in a patch of sand. </p>
<p>I've seen this technique used in construction of underwater tunnels and oil rigs to fix the structure in place. It is called a vacuum-anchor (e.g. Troll A platform). I want to apply it in a smaller scale.</p>
| 9,406 |
[
-0.03618249669671059,
-0.0008687184890732169,
0.005007903091609478,
-0.0011673775734379888,
0.05361650511622429,
-0.029880627989768982,
-0.012707510963082314,
-0.02073885314166546,
-0.0008112135110422969,
-0.04608670249581337,
0.030498474836349487,
0.08365709334611893,
0.0331696979701519,
0.03991701081395149,
0.030122879892587662,
0.013009103015065193,
-0.007961374707520008,
-0.05360519513487816,
0.03609485179185867,
0.0015496137784793973,
-0.0010641959961503744,
0.013864435255527496,
-0.01443934440612793,
-0.00305123976431787,
0.00659132469445467,
0.008904267102479935,
0.057543836534023285,
-0.0415693074464798,
0.021298721432685852,
0.06812825053930283,
-0.009217704646289349,
-0.03196791559457779,
0.02845362387597561,
0.0626622661948204,
0.009241491556167603,
0.03188677877187729,
-0.028668466955423355,
-0.02277328632771969,
-0.023478010669350624,
0.038000743836164474,
-0.008489735424518585,
0.011530670337378979,
-0.003312060609459877,
0.03620927035808563,
-0.006133829243481159,
0.05207229405641556,
-0.037781886756420135,
-0.03715582937002182,
0.021811846643686295,
-0.04202660545706749,
0.03701205924153328,
0.007960664108395576,
0.03062778152525425,
0.02281147986650467,
-0.010767031461000443,
-0.04366543889045715,
0.048771146684885025,
0.05406907945871353,
0.007586292456835508,
-0.060095179826021194,
0.03190220147371292,
-0.004675847943872213,
-0.03671640157699585,
-0.07570619881153107,
0.015262588858604431,
0.0005566453328356147,
-0.022556815296411514,
0.005244901403784752,
0.007415636442601681,
-0.015068935230374336,
0.01107728946954012,
-0.021965766325592995,
0.030960245057940483,
-0.031302258372306824,
-0.014116753824055195,
-0.0183747336268425,
-0.04187561944127083,
0.009753523394465446,
-0.0025664507411420345,
0.057263944298028946,
-0.008633038029074669,
0.013608384877443314,
0.04355600103735924,
0.0561557374894619,
0.05305804684758186,
-0.041963208466768265,
0.05162070691585541,
0.031626153737306595,
0.030200911685824394,
-0.020723899826407433,
0.0013290946371853352,
0.003916033077985048,
0.004749739076942205,
-0.004513839725404978,
0.008314580656588078,
0.04237537458539009,
0.016027210280299187,
0.0070249950513243675,
-0.009252809919416904,
-0.003937314264476299,
-0.009696705266833305,
-0.02774842455983162,
0.028431475162506104,
0.0957443043589592,
-0.005604594945907593,
-0.015549163334071636,
-0.028344986960291862,
0.03180944547057152,
-0.01671103574335575,
-0.031383443623781204,
0.006329057738184929,
0.04258892312645912,
-0.01693671941757202,
-0.03945162892341614,
-0.06390015035867691,
-0.03396275267004967,
0.01116372924298048,
-0.032237350940704346,
0.029655274003744125,
0.011761520057916641,
0.045007456094026566,
-0.02338036336004734,
-0.0008916612714529037,
-0.0800483226776123,
-0.08203529566526413,
0.012611381709575653,
0.02554023452103138,
-0.0423014797270298,
-0.03918743133544922,
0.04412947967648506,
0.010765056125819683,
-0.015324526466429234,
0.0017526759766042233,
0.002964561805129051,
0.03169552981853485,
-0.009453468956053257,
-0.10621341317892075,
-0.0673762708902359,
0.03008226491510868,
0.024244703352451324,
-0.007720560301095247,
-0.04504917934536934,
0.03777756541967392,
0.038328468799591064,
0.04645344987511635,
0.008417986333370209,
0.024339621886610985,
0.017996950075030327,
0.027367549017071724,
-0.01423605252057314,
-0.030003154650330544,
0.007017166819423437,
0.02466818317770958,
-0.029383108019828796,
-0.037090003490448,
-0.09829740971326828,
-0.00798114761710167,
-0.011422775685787201,
0.018122423440217972,
-0.02762570045888424,
0.042724885046482086,
-0.0037695749197155237,
-0.017349522560834885,
-0.009124098345637321,
-0.014548041857779026,
-0.04203090816736221,
0.06219629943370819,
-0.003125283634290099,
0.0036237204913049936,
0.060855090618133545,
0.01174952182918787,
-0.009361089207231998,
-0.009619300253689289,
-0.0075440118089318275,
0.048395682126283646,
-0.04413862153887749,
0.017730291932821274,
-0.039962396025657654,
0.0052601308561861515,
0.024885443970561028,
-0.06614518910646439,
-0.04512698948383331,
-0.017579270526766777,
0.0022831056267023087,
0.03813823685050011,
0.028469402343034744,
0.017328476533293724,
-0.040445100516080856,
-0.0024788971059024334,
-0.0457485057413578,
0.04078641161322594,
-0.0337379015982151,
0.041957441717386246,
0.013703315518796444,
0.03491981327533722,
0.0012775713112205267,
-0.034604039043188095,
0.006228913087397814,
-0.023870134726166725,
-0.00006505343480966985,
0.0053945379331707954,
0.01980636827647686,
0.010807851329445839,
-0.017366493120789528,
0.010680061765015125,
0.0361769013106823,
0.03841697424650192,
-0.00450750719755888,
0.0037846993654966354,
-0.02834615483880043,
0.00048514496302232146,
0.0027215471491217613,
-0.030607666820287704,
-0.015142811462283134,
0.0200990978628397,
-0.006405384745448828,
0.03457576781511307,
-0.014081510715186596,
0.031030550599098206,
0.02353516034781933,
-0.011235810816287994,
0.07461906224489212,
0.055756576359272,
0.038498468697071075,
0.048090819269418716,
-0.020762277767062187,
-0.025244668126106262,
0.04730740934610367,
0.0018907844787463546,
0.018432579934597015,
-0.06869387626647949,
-0.006325765047222376,
0.023302273824810982,
0.04827108234167099,
-0.02656065672636032,
0.010334969498217106,
0.0355590358376503,
0.032262012362480164,
0.026419105008244514,
0.00103874655906111,
-0.012197713367640972,
-0.010046410374343395,
0.01444434467703104,
0.03514067828655243,
-0.03425052762031555,
0.008465313352644444,
0.005332679953426123,
0.02404041588306427,
0.03730318695306778,
-0.012460808269679546,
-0.02064603567123413,
0.02353169396519661,
0.016617463901638985,
-0.009454754181206226,
-0.013959787786006927,
-0.002670935820788145,
0.05351501330733299,
-0.03814620152115822,
-0.017364967614412308,
0.014555319212377071,
0.0029304116033017635,
-0.0015464355237782001,
-0.01535845547914505,
0.0030239911284297705,
0.011525167152285576,
0.0038485194090753794,
0.010929820127785206,
-0.03747868910431862,
0.03379732742905617,
0.004004132933914661,
-0.024877965450286865,
-0.02729339338839054,
0.007264219224452972,
-0.027508148923516273,
0.007026643492281437,
0.03252805396914482,
-0.019267475232481956,
0.05635682865977287,
-0.021466201171278954,
-0.010454592294991016,
-0.0033580060116946697,
0.03286563605070114,
-0.015821116045117378,
-0.021681873127818108,
-0.03100946731865406,
-0.0030193631537258625,
-0.0006526980432681739,
-0.023916713893413544,
0.0611700564622879,
-0.00798495952039957,
-0.033784180879592896,
0.018433615565299988,
0.007294921670109034,
-0.03303274139761925,
-0.0076845264993608,
-0.005765486974269152,
0.009372707456350327,
-0.04204602912068367,
0.005453216377645731,
0.05435396730899811,
0.02357345260679722,
-0.02977539412677288,
0.04367827996611595,
-0.058860160410404205,
-0.028420140966773033,
-0.020864367485046387,
0.006359275430440903,
-0.025128161534667015,
-0.05073798447847366,
0.027015630155801773,
-0.03227933123707771,
0.018874770030379295,
0.006009084638208151,
-0.06412613391876221,
-0.004338539205491543,
-0.009655231609940529,
-0.005920721217989922,
0.049161504954099655,
-0.020013755187392235,
-0.027893435209989548,
0.11497693508863449,
0.014586618170142174,
-0.020831678062677383,
0.004180664196610451,
0.00006526683864649385,
0.00033022224670276046,
-0.019791943952441216,
0.013060287572443485,
0.02424205280840397,
-0.023996056988835335,
0.031666651368141174,
-0.012307015247642994,
-0.004771172534674406,
0.03172234073281288,
0.054598525166511536,
0.03566812723875046,
0.022127550095319748,
0.010516615584492683,
0.007762919645756483,
0.08361701667308807,
0.0019233743660151958,
-0.02059568651020527,
0.045454733073711395,
-0.014251364395022392,
0.03575082868337631,
0.01831083744764328,
-0.04087118059396744,
0.03980106860399246,
0.014738887548446655,
-0.004740098025649786,
-0.014405873604118824,
0.011524486355483532,
-0.004670952912420034,
-0.021197259426116943,
0.003929648082703352,
-0.040049731731414795,
0.0424276702105999,
0.007152496371418238,
-0.0334717333316803,
0.03819655254483223,
0.08086764812469482,
0.004591049626469612,
-0.022652674466371536,
0.0010050125420093536,
0.00799562968313694,
0.011737002991139889,
-0.013310492038726807,
-0.014184064231812954,
0.0020403233356773853,
0.02743564173579216,
0.011304677464067936,
-0.007922939956188202,
-0.010870281606912613,
-0.013545578345656395,
-0.07999219000339508,
-0.04852702468633652,
-0.019369984045624733,
0.06613723933696747,
0.011313093826174736,
0.011662018485367298,
-0.0002764724486041814,
-0.020930124446749687,
0.04119972884654999,
0.03007587417960167,
-0.06321978569030762,
0.0042386543937027454,
0.006157666444778442,
-0.01444648951292038,
0.03232418745756149,
-0.022890770807862282,
-0.005337178707122803,
-0.02612515725195408,
0.017564445734024048,
0.01925651542842388,
0.011982378549873829,
-0.03607309237122536,
0.05714654549956322,
0.0016479970654472709,
-0.01919395849108696,
0.02317972667515278,
0.04636131972074509,
0.01128217950463295,
-0.009397558867931366,
0.04627710208296776,
0.003053647466003895,
-0.04102606326341629,
-0.009132366627454758,
0.021987007930874825,
-0.024331828579306602,
0.009726356714963913,
0.016265645623207092,
-0.018573183566331863,
0.014792060479521751,
-0.023674599826335907,
-0.017355654388666153,
-0.022999586537480354,
0.007043465506285429,
0.013715187087655067,
0.013653723523020744,
-0.03901519998908043,
-0.0372064970433712,
-0.0017257705330848694,
0.015447740443050861,
0.04855826869606972,
-0.023177558556199074,
-0.023485194891691208,
0.019268523901700974,
-0.0412425696849823,
0.000507748918607831,
0.026720331981778145,
0.0118132084608078,
0.013552306219935417,
-0.028187481686472893,
-0.030055515468120575,
-0.007782481145113707,
-0.044437799602746964,
-0.00427474407479167,
-0.011522629298269749,
0.026352306827902794,
-0.013072624802589417,
-0.018521850928664207,
0.05921759083867073,
0.01825890503823757,
-0.02010674774646759,
0.05025458708405495,
0.01981123350560665,
0.041479356586933136,
-0.01966176927089691,
0.02311626635491848,
0.033591967076063156,
0.03439169004559517,
0.031167468056082726,
0.007222739513963461,
0.003750405041500926,
-0.054014455527067184,
-0.04331109672784805,
0.025403061881661415,
0.030436920002102852,
-0.015298978425562382,
-0.016798006370663643,
-0.0791996419429779,
-0.033076636493206024,
0.04420046880841255,
-0.04167444258928299,
0.0006996504380367696,
-0.029030147939920425,
0.017612578347325325,
-0.002675545634701848,
-0.04557681828737259,
-0.05695822089910507,
-0.017054593190550804,
-0.026371289044618607,
0.054508574306964874,
-0.021365733817219734,
0.011272327043116093,
0.018461154773831367,
0.05356970429420471,
0.05169770494103432,
0.05485709011554718,
0.010593399405479431,
-0.011164180003106594,
-0.015849746763706207,
-0.018427712842822075,
-0.015561835840344429,
-0.044804517179727554,
-0.00686160521581769,
-0.03380131348967552,
-0.0002615121193230152,
0.021199746057391167,
-0.047631435096263885,
-0.04953721910715103,
0.011355736292898655,
0.02626141719520092,
-0.006570551544427872,
0.008371676318347454,
-0.03229539841413498,
0.005854798015207052,
0.030378293246030807,
-0.012747912667691708,
0.04365486651659012,
0.010569239035248756,
-0.0212017223238945,
0.011475250124931335,
-0.0571625754237175,
-0.020448574796319008,
-0.0038222200237214565,
-0.030952487140893936,
-0.056980714201927185,
0.026679951697587967,
-0.03725738078355789,
0.03970658406615257,
0.019120721146464348,
0.0014750423142686486,
-0.00168372574262321,
-0.03179287165403366,
-0.007129735313355923,
0.014620095491409302,
0.014105555601418018,
0.005854007788002491,
0.023550767451524734,
0.013077340088784695,
0.024215154349803925,
-0.04621993377804756,
-0.00482097128406167,
0.011516368947923183,
0.02167818322777748,
-0.0090333865955472,
-0.00840149074792862,
0.0032820519991219044,
-0.01000383123755455,
0.021553000435233116,
0.007822904735803604,
-0.05975177884101868,
0.056071892380714417,
-0.051759399473667145,
0.02094174548983574,
-0.00373258488252759,
-0.025221005082130432,
0.0004780645249411464,
0.004182474687695503,
-0.01422515232115984,
0.01994268037378788,
-0.028446711599826813,
-0.00971348024904728,
0.04783335700631142,
0.026187773793935776,
0.01110893301665783,
-0.023621363565325737,
0.017399100586771965,
0.004211345687508583,
-0.027082717046141624,
-0.025690756738185883,
-0.011181632988154888,
-0.007927589118480682,
-0.049784108996391296,
-0.014177827164530754,
0.07487650960683823,
-0.0593130961060524,
0.007412765175104141,
-0.0008154757670126855,
0.025673504918813705,
0.0628063827753067,
-0.02003597654402256,
0.01624768041074276,
-0.004181708209216595,
-0.04227027669548988,
-0.018082914873957634,
-0.011770352721214294,
0.018615197390317917,
-0.026354854926466942,
-0.051414694637060165,
-0.002318538958206773,
-0.005911420099437237,
0.026982301846146584,
-0.007994364015758038,
0.008262685500085354,
0.0018932067323476076,
0.035614799708127975,
-0.03060031123459339,
0.004974984098225832,
0.043559059500694275,
0.024352136999368668,
0.01966523751616478,
-0.02893848903477192,
0.021845199167728424,
-0.03719029203057289,
-0.026220113039016724,
0.03182055056095123,
-0.014880052767693996,
0.004863379057496786,
-0.013679629191756248,
0.07709255069494247,
-0.016606047749519348,
0.0018118028528988361,
0.006862045265734196,
-0.007808552589267492,
0.020513072609901428,
0.027573226019740105,
-0.012391213327646255,
0.029758689925074577,
0.006128298584371805,
-0.012873794883489609,
-0.030176645144820213,
-0.045059897005558014,
0.005802287254482508,
0.041264574974775314,
-0.0019994473550468683,
0.04233701154589653,
0.03220624104142189,
0.01522410474717617,
0.06017361581325531,
-0.019451839849352837,
-0.0018795960349962115,
-0.010507189668715,
0.00836077518761158,
0.044613100588321686,
-0.008388486690819263,
-0.01468952652066946,
0.05969710275530815,
0.03435296565294266,
0.002107064938172698,
-0.006964236032217741,
0.005198689643293619,
0.019594978541135788,
-0.005670820362865925,
-0.058085598051548004,
-0.03601133078336716,
0.04061758145689964,
-0.02239604853093624,
0.023574765771627426,
-0.009272044524550438,
-0.019332053139805794,
0.030602790415287018,
0.02548033930361271,
0.01388427335768938,
-0.03696010634303093,
-0.0060980007983744144,
-0.023663895204663277,
-0.004509510938078165,
0.03467779606580734,
-0.0032577617093920708,
-0.016015691682696342,
0.04529757425189018,
0.013442883267998695,
-0.016206348314881325,
0.02237396314740181,
-0.03398258984088898,
-0.05585668236017227,
-0.009870802983641624,
-0.0030649006366729736,
-0.06433302909135818,
0.05264721438288689,
0.012133399024605751,
-0.03983141854405403,
0.057500019669532776,
-0.030210396274924278,
0.014808530919253826,
0.04122132062911987,
-0.006411121226847172,
-0.011773496866226196,
0.08332816511392593,
-0.03603599593043327,
-0.0326654277741909,
-0.03756985068321228,
-0.015743520110845566,
0.15201731026172638,
0.04713106527924538,
0.02793426252901554,
-0.0013057573232799768,
0.003967107739299536,
-0.032635677605867386,
-0.002410637680441141,
-0.04655756801366806,
-0.00555435148999095,
-0.02288876101374626,
-0.007768785580992699,
0.023998957127332687,
0.047126833349466324,
-0.056486453860998154,
-0.025957584381103516,
0.005000323988497257,
-0.03942690044641495,
-0.01856233738362789,
-0.012863279320299625,
0.009247291833162308,
-0.02901059202849865,
0.0036755444016307592,
-0.00876727607101202,
0.04380090907216072,
-0.015037077479064465,
-0.005367044359445572,
-0.06157698482275009,
-0.03363656625151634,
0.03851081803441048,
-0.02045714110136032,
-0.09241263568401337,
0.017347296699881554,
-0.03197326883673668,
-0.039057109504938126,
-0.006335150916129351,
0.02623017318546772,
-0.0012297088978812099,
-0.03526657447218895,
-0.017280368134379387,
0.019197851419448853,
-0.002086079213768244,
0.03508627787232399,
-0.002872819546610117,
0.02502857893705368,
-0.07611223310232162,
-0.01651940681040287,
-0.05489544942975044,
0.06254793703556061,
-0.01758698932826519,
-0.030548719689249992,
-0.009812499396502972,
0.03264324367046356,
0.007910910993814468,
-0.0006044506444595754,
0.010530275292694569,
0.016865549609065056,
0.042004503309726715,
-0.0010518168564885855,
-0.031411588191986084,
0.01784881018102169,
0.033201318234205246,
0.0376439243555069,
0.011212443001568317,
0.021640589460730553,
-0.010170317254960537,
-0.023378755897283554,
0.00333092431537807,
0.058012090623378754,
0.012653243727982044,
0.0043617174960672855,
-0.04355131834745407,
-0.009381169453263283,
-0.01869027316570282,
0.015886442735791206,
-0.01507063489407301,
0.011733650229871273,
0.0631648525595665,
-0.009669780731201172,
-0.010485434904694557,
-0.042580440640449524,
-0.08495888859033585,
0.06799361854791641,
-0.04629778489470482,
-0.045659370720386505,
-0.06859153509140015,
-0.04932262748479843,
-0.006549586541950703,
0.049615535885095596,
0.05342024937272072,
0.0071403165347874165,
0.014563295058906078,
0.02912932261824608,
0.019151946529746056,
-0.026708202436566353,
-0.031037937849760056,
-0.0065935952588915825,
0.00409723399206996,
0.015560932457447052,
-0.01804284006357193,
-0.017400598153471947,
0.04660527780652046,
0.005585187114775181,
-0.017453674226999283,
0.03775109723210335,
-0.023246189579367638,
-0.029662074521183968,
0.007288835942745209,
0.006403318140655756,
-0.015391897410154343,
0.0449417419731617,
0.015455220825970173,
-0.04983339458703995,
0.006251553073525429,
-0.03216705471277237,
-0.006997853517532349,
-0.01545854564756155,
-0.009822389110922813,
-0.015121093951165676,
0.026125606149435043,
-0.04210476577281952,
-0.0035930194426327944,
-0.004019031301140785,
-0.010481351986527443,
-0.04717414081096649,
-0.03761625289916992,
0.00993885938078165,
0.0001864786900114268,
-0.0422777459025383,
-0.005709052551537752,
-0.04642967879772186,
-0.0066321128979325294,
-0.0009072319371625781,
-0.050001807510852814,
-0.01975839212536812,
-0.0070544457994401455,
-0.008243385702371597,
0.015660036355257034,
0.01051576342433691,
-0.02031659334897995,
-0.040407806634902954,
0.014666150324046612,
-0.007596968673169613,
-0.009461944922804832,
0.014490531757473946,
0.031814947724342346,
0.06327153742313385,
0.025936421006917953,
-0.003918948117643595,
-0.042488809674978256,
0.05740402638912201,
0.0017984268488362432,
-0.028978053480386734,
-0.03209458664059639,
-0.05181879550218582,
0.022825142368674278,
-0.007733974140137434,
0.031242242082953453,
-0.010513514280319214,
-0.019271008670330048,
0.004415667150169611,
0.023020699620246887,
0.04043969884514809,
-0.0017178957350552082,
0.02518884465098381,
0.015357697382569313,
-0.008007362484931946,
0.006571329664438963,
-0.017974073067307472,
0.015577016398310661,
0.031551022082567215,
-0.026979325339198112,
0.031790558248758316,
0.04556130990386009,
0.012912681326270103,
-0.10138989239931107,
-0.0022343227174133062,
0.012903807684779167,
0.028934502974152565,
0.05385536700487137,
-0.07348070293664932,
-0.007250906899571419,
0.0267157144844532,
-0.03278322145342827,
0.004412089940160513,
-0.047356147319078445,
0.01158873364329338,
-0.0470452755689621,
-0.0010226351441815495,
0.026318106800317764,
0.030561527237296104,
-0.014808766543865204,
0.028784828260540962,
0.021960722282528877,
0.05660904943943024,
-0.02283979207277298,
-0.030921809375286102,
0.03144356608390808,
0.05874384567141533,
-0.01455537136644125,
-0.004024059511721134,
0.06575871258974075,
-0.012298207730054855,
-0.011091433465480804,
0.024573570117354393,
-0.019412124529480934,
0.011488827876746655,
-0.021903812885284424,
0.014342790469527245,
-0.002111218636855483,
0.04144611954689026,
0.029735729098320007,
0.03992568701505661,
-0.018394438549876213,
0.048487499356269836,
0.004167267121374607,
-0.011384964920580387,
-0.017900364473462105,
-0.003937378991395235,
0.015168382786214352,
-0.03977978974580765,
-0.022325411438941956,
0.03738784044981003,
-0.03987329825758934,
0.06476353853940964,
0.014407585375010967,
-0.035152774304151535,
0.001421096851117909,
-0.026679018512368202,
-0.02689959667623043,
-0.016303544864058495,
0.010078160092234612,
0.033683039247989655,
-0.024704597890377045,
-0.016580970957875252,
0.0027042205911129713,
0.03075558878481388,
-0.0076619950123131275,
-0.0039910366758704185,
-0.01761128008365631,
-0.01842149719595909,
-0.05252109095454216,
0.0027525541372597218,
0.02527604252099991,
-0.015161784365773201,
-0.0018321969546377659,
0.005954339634627104,
-0.03013034537434578,
0.03170651197433472,
0.021882545202970505,
0.02349538542330265,
0.026333585381507874,
0.011288759298622608,
-0.005403037182986736,
-0.059997837990522385,
0.027155155315995216,
0.02937912382185459,
-0.05141231790184975,
-0.04360919073224068,
-0.05368714779615402,
0.01735185645520687,
0.0252164788544178,
0.047777533531188965,
-0.019350191578269005,
-0.042869728058576584,
-0.04252278059720993,
-0.02754264883697033,
-0.023092467337846756,
-0.022918416187167168,
0.032514121383428574,
0.04518311470746994,
-0.0143644530326128,
-0.007851998321712017,
0.012045812793076038,
0.021892758086323738,
-0.02354070171713829,
0.03573666885495186,
-0.02580857090651989,
0.02550339885056019,
0.005529210902750492,
-0.0054376753978431225,
0.005011591594666243,
-0.0008169914945028722,
0.003310534870252013,
0.07202249765396118,
-0.002636500634253025,
-0.0018884442979469895,
0.011096133850514889,
-0.03157753497362137,
-0.031889986246824265,
0.03401045873761177,
-0.021337095648050308,
-0.009800827130675316,
0.013189432211220264,
-0.014659262262284756,
0.03589930012822151,
-0.033315736800432205,
-0.004912130534648895,
0.01585475169122219,
-0.0027306803967803717,
-0.046560149639844894,
0.016671208664774895,
0.037376485764980316,
0.05419819802045822,
-0.05667615681886673,
0.04264429584145546,
0.014239138923585415,
-0.052033595740795135,
0.03944513574242592,
0.013828536495566368,
0.04303085058927536,
-0.02668117918074131,
-0.00047479706699959934,
0.0473116859793663,
0.01232372410595417,
0.03270309418439865,
0.025795819237828255,
0.016050605103373528,
0.0014403422828763723,
-0.030609572306275368,
0.020771194249391556,
-0.026098482310771942,
-0.018540121614933014,
0.00590472761541605,
-0.0020284235943108797,
0.056258998811244965,
-0.006487877108156681,
-0.005331630352884531,
-0.016043763607740402,
0.0020301868207752705,
0.0077734533697366714,
0.028986450284719467,
-0.02237655781209469,
0.019203783944249153,
0.003495879005640745,
0.003622664837166667,
-0.012615643441677094,
0.011529683135449886,
0.05091533064842224,
0.011190759018063545,
0.010698970407247543,
0.025526100769639015,
0.041241202503442764,
-0.04858403280377388,
-0.03277233988046646,
0.017022646963596344,
-0.03442821651697159,
0.05405944585800171,
0.03163949400186539,
0.007196935825049877,
-0.0030641977209597826,
-0.0063336812891066074,
0.009813078679144382,
0.04744942858815193,
-0.036661066114902496,
-0.02506287954747677,
-0.014801610261201859,
0.003617360955104232,
-0.009544873610138893,
-0.01751503348350525
] |
<p>There's a common QnA which has amused and inspired many kids:</p>
<blockquote>
<p><strong>There are billions of Stars in the sky. If we combine lights received from all stars, wouldn't it beat Sun? Why is night dark really?</strong><br>
It's because speed of light is finite and lights from most of stars are in the way to the Earth.</p>
</blockquote>
<p>My Question: If universe didn't expand faster than light in any point of time, would our nights brighter like day?</p>
<p>Common sense says, Yes. But, unfortunately, universe is full of common sense busters. Is there anything else which can affect this?</p>
<p>Note: I am talking about visible light only. I know, night is already bright in other wavelengths.</p>
<p><strong>Update:</strong><br>
I am clarifying the behavior setup of universe in If clause:</p>
<ul>
<li><p>Universe expansion speed is calculated classically with Super Cluster Red Shift. No GR globally separated reference frame glitch here.</p></li>
<li><p>Universe is expanding today, but not accelerating. Similar to original Hubble's discovery except Inflation shouldn't accelerate universe to faster than light.</p></li>
</ul>
<p>My common sense reasoning:</p>
<ul>
<li><p>After universe became transparent to light, all luminous objects should continuously illuminate possible position of Earth until their death. As universe is young, death probability should be low.</p></li>
<li><p>Till the time of birth of Earth and till today, light from most of slightly younger stars should reach Earth for continuous illumination.</p></li>
</ul>
<p>This is the reasoning of my common sense.</p>
<p>If I am still not clear, let me know.</p>
| 9,407 |
[
-0.015969181433320045,
-0.0663239061832428,
0.03308786079287529,
-0.0013258855324238539,
0.05492034927010536,
0.0025007615331560373,
-0.01858975738286972,
-0.06225848197937012,
-0.0020605335012078285,
-0.0508328452706337,
0.026728808879852295,
0.06464547663927078,
0.01760617457330227,
0.0202789269387722,
0.025487175211310387,
0.01632658950984478,
0.005156189668923616,
-0.03326818719506264,
-0.01930508203804493,
-0.040174201130867004,
0.03437211364507675,
0.03835708275437355,
0.02718847244977951,
0.014871982857584953,
-0.029503483325242996,
0.03936535492539406,
0.025017209351062775,
0.01665477827191353,
0.00038737853174097836,
0.068526491522789,
-0.005368970334529877,
-0.020292500033974648,
0.013956456445157528,
0.0338967889547348,
0.011355392634868622,
-0.023430056869983673,
-0.007325110957026482,
-0.0032209379132837057,
0.006041650660336018,
-0.010105594992637634,
-0.02468496933579445,
-0.010410024784505367,
-0.00601431867107749,
0.05297461524605751,
-0.01069121528416872,
0.037405651062726974,
0.015210135839879513,
0.012381182983517647,
0.07435940206050873,
-0.029410775750875473,
0.04715825989842415,
-0.036569125950336456,
0.005491416901350021,
0.04842427000403404,
-0.02626514434814453,
-0.025353070348501205,
0.05785781517624855,
0.07202670723199844,
0.005427914671599865,
-0.0331236869096756,
-0.034293871372938156,
-0.014106363989412785,
0.006228545680642128,
-0.028236014768481255,
0.008584558963775635,
0.02681402862071991,
-0.029909631237387657,
0.030238132923841476,
0.004971110727638006,
-0.002190187107771635,
0.014710784889757633,
0.003019008319824934,
0.04386128857731819,
-0.005547329317778349,
0.006332234479486942,
-0.037374403327703476,
0.01907235011458397,
0.009999743662774563,
0.035661809146404266,
0.05024055764079094,
-0.02214176021516323,
-0.003915563225746155,
0.044412292540073395,
0.041635554283857346,
0.018561922013759613,
0.01939525455236435,
0.051059506833553314,
-0.005324115045368671,
0.016374770551919937,
0.04189353063702583,
-0.01916624791920185,
0.0073054488748312,
0.048454686999320984,
0.013594956137239933,
-0.013326464220881462,
0.06692089885473251,
-0.0017356148455291986,
0.006422256585210562,
-0.0033911028876900673,
-0.02177472971379757,
-0.0010273550869897008,
-0.01245311088860035,
0.01949022337794304,
0.07337604463100433,
0.007474934216588736,
-0.03291188180446625,
-0.05454440787434578,
0.00932825356721878,
-0.03271998092532158,
-0.003062008647248149,
-0.045805756002664566,
0.004299664869904518,
0.037040844559669495,
0.00919386651366949,
-0.011146440170705318,
-0.09602449089288712,
0.016855726018548012,
-0.046813011169433594,
0.06271228939294815,
0.0564582385122776,
0.04483027011156082,
0.019236823543906212,
0.030257264152169228,
-0.028519535437226295,
-0.022733259946107864,
-0.00292326882481575,
0.013971440494060516,
-0.032910291105508804,
-0.031099805608391762,
0.03176161274313927,
-0.013035379350185394,
-0.018897438421845436,
-0.016239602118730545,
-0.021801544353365898,
0.05908522382378578,
-0.005310582462698221,
-0.07954253256320953,
-0.031356193125247955,
0.06753470003604889,
0.01861228235065937,
-0.02107006311416626,
-0.07117563486099243,
0.017690300941467285,
0.005883566103875637,
0.10457125306129456,
0.01909167692065239,
-0.004060657694935799,
-0.004570601508021355,
0.04331745207309723,
0.01020055916160345,
-0.051928259432315826,
-0.016236571595072746,
0.014262835495173931,
-0.03357652574777603,
0.006141431163996458,
-0.08778126537799835,
0.00548239890486002,
0.015938103199005127,
-0.028914134949445724,
-0.010098766535520554,
0.03397277742624283,
-0.033201560378074646,
-0.006760860793292522,
-0.022087574005126953,
0.00023218095884658396,
-0.05104988068342209,
0.07854517549276352,
0.023934783414006233,
-0.009910176508128643,
0.05988068878650665,
-0.02530805394053459,
0.01373770646750927,
0.011608998291194439,
-0.011876899749040604,
0.011718659661710262,
-0.049863461405038834,
-0.002965950407087803,
-0.03366110101342201,
0.018818875774741173,
-0.0021775588393211365,
-0.0012900084257125854,
0.01797444373369217,
-0.05253947526216507,
-0.029953330755233765,
0.04172703996300697,
0.03284621238708496,
-0.006397715769708157,
0.030666137114167213,
0.025533625856041908,
-0.02218244969844818,
0.002731623128056526,
-0.07554153352975845,
-0.012716768309473991,
0.028715742751955986,
-0.0025132803712040186,
-0.016727624461054802,
0.008120827376842499,
0.032320719212293625,
0.002772275125607848,
-0.0017754570581018925,
-0.0062688784673810005,
0.030694354325532913,
-0.004783429205417633,
-0.00911655556410551,
0.023003123700618744,
0.06019734963774681,
0.037659499794244766,
-0.023428112268447876,
-0.025233633816242218,
-0.021130498498678207,
-0.03318000212311745,
0.04654720798134804,
-0.008814834989607334,
0.007851330563426018,
-0.011133906431496143,
0.03679576516151428,
0.05468466132879257,
0.024639859795570374,
-0.010752088390290737,
0.022947972640395164,
-0.02815825305879116,
0.041930973529815674,
0.022340694442391396,
-0.022066500037908554,
0.025511503219604492,
0.043368566781282425,
-0.01499650813639164,
-0.005448381882160902,
0.02451052889227867,
0.006872205063700676,
-0.06460800766944885,
-0.017306551337242126,
0.02172281965613365,
-0.002853560261428356,
-0.026533937081694603,
0.04187266528606415,
0.05881355702877045,
0.0410706102848053,
0.00839533656835556,
0.03205900266766548,
-0.017732126638293266,
-0.05728120356798172,
-0.008472928777337074,
0.014663717709481716,
0.02132982388138771,
0.01982193998992443,
0.0022144359536468983,
0.007462731562554836,
0.04166340455412865,
-0.019293200224637985,
-0.018830738961696625,
0.011793396435678005,
0.026676146313548088,
0.02963913604617119,
-0.004766284488141537,
-0.021922878921031952,
0.015539933927357197,
-0.010272166691720486,
0.024689478799700737,
0.025852568447589874,
-0.010195111855864525,
-0.009078113362193108,
-0.07483010739088058,
-0.026063043624162674,
-0.02659512497484684,
0.007914461195468903,
-0.06626944988965988,
-0.012879383750259876,
0.026507485657930374,
-0.021348221227526665,
0.005553986877202988,
-0.012093842960894108,
-0.0026809354312717915,
-0.059873197227716446,
-0.02459869161248207,
0.023775536566972733,
0.014730139635503292,
0.0012170657282695174,
-0.08108381927013397,
-0.034319180995225906,
0.0002664091298356652,
0.02237081713974476,
-0.011961954645812511,
0.01613526977598667,
-0.032963868230581284,
0.04687857627868652,
-0.011270339600741863,
-0.05505026504397392,
0.04310853034257889,
0.0072619859129190445,
0.022974492982029915,
0.04912256821990013,
-0.011796830222010612,
-0.03209974989295006,
0.005409464240074158,
-0.04641072824597359,
-0.011578419245779514,
-0.043797191232442856,
-0.03595200181007385,
0.07256478071212769,
-0.034580331295728683,
-0.054113298654556274,
-0.011169363744556904,
-0.04767190292477608,
-0.03226129338145256,
0.020273886620998383,
0.02025693655014038,
-0.002296163933351636,
-0.03541254624724388,
0.029262270778417587,
-0.045232661068439484,
-0.018710361793637276,
-0.0017700734315440059,
-0.060994431376457214,
-0.06307016313076019,
0.030607003718614578,
0.02207491174340248,
0.07039603590965271,
0.014001232571899891,
0.006472650449723005,
0.009000366553664207,
0.06508447229862213,
0.002027238020673394,
-0.051526084542274475,
0.008864379487931728,
0.023679612204432487,
-0.016158606857061386,
0.0190353374928236,
-0.012748115696012974,
-0.004150523338466883,
-0.0007577541982755065,
0.046620819717645645,
0.028393367305397987,
0.018274886533617973,
0.0324929840862751,
-0.0021309128496795893,
-0.007633255794644356,
-0.0033063776791095734,
0.026257233694195747,
0.023472871631383896,
0.005202591884881258,
-0.027269558981060982,
0.011595845222473145,
-0.009262778796255589,
0.031721703708171844,
0.009383649565279484,
-0.045936647802591324,
0.06170450523495674,
0.031356897205114365,
0.01588146947324276,
-0.03596515953540802,
0.035291291773319244,
0.019666926935315132,
0.0002219447196694091,
-0.03230297192931175,
0.017543604597449303,
0.040796615183353424,
0.03473164513707161,
0.03496856614947319,
-0.024955686181783676,
0.028000349178910255,
-0.015274020843207836,
-0.03726402297616005,
0.008680297993123531,
-0.0008457597577944398,
0.04006024822592735,
-0.04390358552336693,
-0.007544948253780603,
0.0705363005399704,
0.04978488013148308,
-0.021466366946697235,
-0.01534713339060545,
-0.04019715264439583,
-0.006497497670352459,
-0.04728549346327782,
-0.01056402362883091,
-0.05609455332159996,
0.026769522577524185,
-0.004778225906193256,
0.022167908027768135,
0.021912360563874245,
0.0036875533405691385,
0.019293494522571564,
-0.003798417281359434,
-0.07333477586507797,
0.00851034838706255,
-0.04185018688440323,
-0.036630429327487946,
-0.015944022685289383,
-0.017308048903942108,
-0.035478416830301285,
-0.019784046337008476,
0.008010349236428738,
-0.04328547418117523,
0.008039182052016258,
-0.031270477920770645,
0.0013379361480474472,
-0.038473114371299744,
-0.06530309468507767,
0.011740212328732014,
0.0026607487816363573,
0.04615233466029167,
-0.005763634108006954,
0.03226488456130028,
0.02869649976491928,
-0.021146178245544434,
-0.013758243061602116,
-0.027034087106585503,
0.00530301034450531,
0.010576090775430202,
0.004021297208964825,
0.03455623239278793,
0.01646910235285759,
-0.04898909851908684,
-0.005619337782263756,
0.036578383296728134,
-0.021743187680840492,
0.0002600738371256739,
-0.012713327072560787,
-0.029209675267338753,
-0.00965473335236311,
-0.032059039920568466,
-0.018480127677321434,
0.037095651030540466,
-0.011141386814415455,
0.022938553243875504,
0.04057380184531212,
0.01169300265610218,
0.01583554781973362,
0.014990243129432201,
0.06995002925395966,
-0.046649228781461716,
-0.014646644704043865,
-0.01759512722492218,
-0.023934097960591316,
-0.04135062173008919,
0.007333032321184874,
0.02495986595749855,
0.0029156506061553955,
-0.00478778500109911,
0.003773273667320609,
0.00005543944280361757,
0.01981569267809391,
0.007941236719489098,
0.027803992852568626,
-0.013875222764909267,
0.012801584787666798,
0.01328508835285902,
0.023901600390672684,
-0.006023574620485306,
0.03176577389240265,
0.031008077785372734,
-0.011728870682418346,
-0.009064319543540478,
-0.05799899622797966,
-0.003937345929443836,
0.041938889771699905,
0.05142296478152275,
0.010196751914918423,
-0.003107544267550111,
-0.06914941221475601,
-0.020463237538933754,
-0.01531632337719202,
-0.027710242196917534,
0.041247207671403885,
0.0069678244180977345,
-0.018855653703212738,
-0.004372398369014263,
-0.03780806437134743,
-0.004922962281852961,
0.01126125268638134,
-0.030731728300452232,
0.014888844452798367,
0.01944737695157528,
0.0139662129804492,
-0.03914899379014969,
0.002896656980738044,
0.01105369534343481,
0.0401114746928215,
-0.025292277336120605,
-0.01203486230224371,
-0.002633261727169156,
-0.019460732117295265,
-0.036250244826078415,
-0.0751546323299408,
0.02429315447807312,
-0.018746230751276016,
-0.061164166778326035,
0.05723113194108009,
-0.028368111699819565,
-0.019175436347723007,
0.026202358305454254,
-0.0008863782277330756,
-0.050676293671131134,
0.005057872273027897,
-0.05518060550093651,
0.0026813256554305553,
0.03399839252233505,
0.02444252371788025,
0.0027663996443152428,
0.02592766284942627,
-0.007499001454561949,
0.05540930852293968,
-0.00913256499916315,
0.019831331446766853,
-0.05174820497632027,
0.02499164640903473,
0.008806031197309494,
-0.03344523906707764,
-0.026725556701421738,
0.03905247896909714,
-0.018112163990736008,
-0.014004799537360668,
0.01311455201357603,
-0.02344391494989395,
0.008891510777175426,
0.03824344277381897,
0.007325060199946165,
0.045913759618997574,
-0.027653295546770096,
0.008942396380007267,
0.005952854175120592,
-0.017651064321398735,
0.05377136543393135,
0.018842235207557678,
-0.013963322155177593,
0.00990423932671547,
0.019183402881026268,
0.026728779077529907,
0.006236011162400246,
0.019131788983941078,
0.01394024770706892,
-0.04275473207235336,
0.0508081391453743,
0.03309299424290657,
0.0069284141063690186,
0.018694687634706497,
-0.043125879019498825,
-0.03391430154442787,
0.010026604868471622,
-0.027283040806651115,
0.018542606383562088,
-0.024732442572712898,
-0.020485110580921173,
0.009239286184310913,
0.011038601398468018,
-0.07483351230621338,
-0.0008330025593750179,
-0.010126381181180477,
0.03423430025577545,
0.0014733420684933662,
-0.0316508524119854,
-0.006783874239772558,
-0.047158271074295044,
-0.010310920886695385,
0.004053487908095121,
0.011977605521678925,
0.022707248106598854,
-0.0033236537128686905,
-0.0012212889268994331,
0.02080773375928402,
0.0423409678041935,
-0.03985964134335518,
0.0014586820034310222,
-0.02983943000435829,
-0.01928117871284485,
-0.0037890798412263393,
-0.010966384783387184,
0.06734512001276016,
-0.0237294789403677,
-0.05333898961544037,
-0.03565824404358864,
-0.025590209290385246,
-0.003213493386283517,
-0.03189190477132797,
-0.019776619970798492,
0.038099344819784164,
0.0013032485730946064,
-0.01633276790380478,
-0.03473976254463196,
0.05103595182299614,
-0.025005651637911797,
0.00608679186552763,
0.0022082615178078413,
0.012557032518088818,
-0.008009749464690685,
-0.07410558313131332,
0.0352044515311718,
0.0017503616400063038,
0.015484550036489964,
0.0011989575577899814,
0.0437568761408329,
0.006026426795870066,
-0.04638979956507683,
0.029386691749095917,
-0.0005649212398566306,
0.01693589985370636,
-0.0032535367645323277,
0.004643666557967663,
-0.009383182972669601,
-0.05472557991743088,
-0.0039370134472846985,
-0.01507639605551958,
-0.02742846868932247,
-0.018750062212347984,
0.07588750869035721,
-0.007995929569005966,
0.01731334626674652,
-0.014430155977606773,
-0.019433949142694473,
-0.021647777408361435,
-0.04937085881829262,
0.011024507693946362,
0.005656982306391001,
-0.006035692524164915,
0.01651352271437645,
-0.02501261979341507,
0.004303352907299995,
0.028858063742518425,
0.04632887989282608,
-0.005763554479926825,
0.01876346580684185,
0.048622164875268936,
0.02332335151731968,
0.003787874011322856,
-0.028506141155958176,
-0.026994377374649048,
0.033138979226350784,
-0.03767816349864006,
0.008336354047060013,
0.007643505930900574,
-0.01770644821226597,
0.04255583509802818,
-0.0027163659688085318,
-0.016804290935397148,
0.011736789718270302,
-0.022008519619703293,
-0.04832233488559723,
-0.029209831729531288,
0.022187814116477966,
0.024687543511390686,
0.010120624676346779,
-0.015622853301465511,
-0.0002686053921934217,
0.022424446418881416,
0.034883785992860794,
-0.022801076993346214,
-0.0589405857026577,
-0.06331779807806015,
-0.03573644533753395,
-0.007649000734090805,
0.04753163084387779,
0.03333640471100807,
-0.04475264996290207,
0.015361386351287365,
-0.009234234690666199,
0.005431396886706352,
0.029158147051930428,
0.03573371469974518,
0.005976224318146706,
0.043098632246255875,
-0.005229352507740259,
0.021723128855228424,
-0.013874853029847145,
0.0171501561999321,
0.1360245943069458,
0.042186710983514786,
0.02316548489034176,
-0.048033829778432846,
0.009017284959554672,
-0.023242222145199776,
0.007941042073071003,
-0.017253288999199867,
0.02165590599179268,
-0.020018581300973892,
0.011365199461579323,
0.02219417504966259,
0.09016155451536179,
0.03200852870941162,
-0.04619848355650902,
0.0024229439441114664,
-0.03921938315033913,
-0.023190675303339958,
-0.0034541760105639696,
0.03689155727624893,
0.02026452124118805,
0.020382486283779144,
-0.03853832185268402,
0.010872851125895977,
-0.016509471461176872,
-0.015358073636889458,
-0.04244613274931908,
-0.023548167198896408,
-0.005246911197900772,
-0.010186644271016121,
-0.06410745531320572,
0.01375657320022583,
-0.00840100646018982,
-0.0565674863755703,
-0.027292758226394653,
-0.011307674460113049,
0.05801671743392944,
-0.002271698322147131,
0.014316130429506302,
0.05704350769519806,
0.045597512274980545,
0.012747097760438919,
0.010011624544858932,
0.03765854239463806,
-0.01615668460726738,
-0.007497236132621765,
-0.008794324472546577,
0.04289231821894646,
-0.03501037508249283,
-0.006370852701365948,
0.004735533148050308,
0.0036697103641927242,
-0.013721145689487457,
-0.0456824004650116,
0.04102319851517677,
0.05079583078622818,
0.02749168500304222,
0.039494987577199936,
-0.024663472548127174,
-0.022927168756723404,
0.002478410489857197,
0.03826650604605675,
0.031658291816711426,
-0.023683318868279457,
0.03287426009774208,
0.012518730014562607,
-0.03054291196167469,
0.0737302228808403,
-0.010052639991044998,
0.012991519644856453,
-0.03915674611926079,
0.015333572402596474,
-0.035021934658288956,
-0.022968046367168427,
0.015563811175525188,
0.023202311247587204,
0.0026294891722500324,
-0.0022511600982397795,
0.03218534216284752,
-0.03283632919192314,
-0.04341873526573181,
0.025004317983984947,
-0.0004526884586084634,
-0.031588707119226456,
-0.018458470702171326,
-0.0170199703425169,
0.008893810212612152,
0.005713246762752533,
-0.012806333601474762,
0.007924436591565609,
-0.01755904033780098,
0.0701008141040802,
-0.0022782590240240097,
-0.024912696331739426,
0.01014159806072712,
-0.025242533534765244,
-0.014203259721398354,
-0.006982871331274509,
-0.03376757726073265,
0.03240683674812317,
0.015106572769582272,
-0.007909092120826244,
0.010412306524813175,
0.02716134674847126,
-0.024463867768645287,
0.015070189721882343,
-0.0001479195198044181,
-0.008896056562662125,
0.008158184587955475,
0.0329580120742321,
0.05089498683810234,
0.002243177965283394,
-0.05305847153067589,
0.0036724298261106014,
-0.018237190321087837,
-0.017361033707857132,
-0.03516663983464241,
-0.04414694756269455,
0.015949197113513947,
-0.008788407780230045,
0.012042575515806675,
-0.07152093201875687,
0.028586076572537422,
-0.03377436101436615,
-0.0032638381235301495,
0.017750900238752365,
-0.0495954230427742,
-0.00987123791128397,
0.039896637201309204,
-0.030999761074781418,
-0.012636314146220684,
-0.0010439747711643577,
-0.009053139016032219,
-0.022672178223729134,
-0.006049496121704578,
0.01437273621559143,
-0.010980016551911831,
0.017603682354092598,
0.003656945889815688,
-0.040006719529628754,
-0.005591085646301508,
-0.01252821460366249,
-0.06832320988178253,
0.01515889260917902,
-0.026276035234332085,
0.052070412784814835,
0.0002308487892150879,
0.01710500381886959,
-0.035735469311475754,
0.06973430514335632,
-0.0464477576315403,
-0.039327505975961685,
0.03247572481632233,
-0.0016532402951270342,
0.03802800551056862,
0.019475167617201805,
-0.0012335212668403983,
0.004640204831957817,
-0.017696086317300797,
0.03491883724927902,
0.025464432314038277,
-0.020731568336486816,
-0.002548502990975976,
0.017217976972460747,
-0.030642526224255562,
-0.02280115708708763,
0.01092496421188116,
-0.011333628557622433,
0.023359648883342743,
0.03149828314781189,
-0.03030812181532383,
0.053499676287174225,
0.005096741020679474,
-0.016249243170022964,
-0.09375779330730438,
0.02760300226509571,
0.005712749436497688,
-0.014306874945759773,
0.050280239433050156,
-0.03187965974211693,
0.037932783365249634,
0.0045358301140367985,
-0.07100096344947815,
0.07547012716531754,
-0.013640192337334156,
-0.025090523064136505,
-0.04510975256562233,
0.032356083393096924,
0.023363593965768814,
0.032130640000104904,
0.0459161214530468,
0.026054896414279938,
-0.009118029847741127,
0.0010820633033290505,
0.001207978930324316,
-0.011451703496277332,
0.008669264614582062,
0.021464120596647263,
0.003824244486168027,
0.010914650745689869,
0.06663542985916138,
-0.005816809367388487,
0.01613949052989483,
0.0044858418405056,
0.05402204394340515,
0.01986459642648697,
-0.016212118789553642,
-0.02771010994911194,
-0.026919540017843246,
0.001532040536403656,
0.02993842400610447,
0.011780788190662861,
-0.0130123570561409,
0.04025118425488472,
0.03075927309691906,
0.012600220739841461,
0.0029110333416610956,
-0.0009949780069291592,
0.00910754781216383,
-0.03803016245365143,
-0.033194612711668015,
-0.008429712615907192,
0.027522005140781403,
0.04339426010847092,
0.03615614399313927,
0.015329517424106598,
-0.014952396973967552,
0.007090410683304071,
-0.006126512307673693,
-0.03152088075876236,
0.005247780587524176,
0.020591212436556816,
0.019603652879595757,
0.00039447605377063155,
-0.003045467659831047,
-0.024296794086694717,
-0.025336962193250656,
-0.05084249749779701,
-0.010173802264034748,
0.018089883029460907,
-0.02325035072863102,
0.004377900157123804,
0.011565868742763996,
0.018945155665278435,
0.008443146012723446,
-0.029853932559490204,
-0.026076510548591614,
0.03657972440123558,
0.010381900705397129,
0.018400276079773903,
0.02360563911497593,
-0.023812128230929375,
-0.009607362560927868,
-0.05151233822107315,
-0.007727437652647495,
-0.021927600726485252,
0.03489433228969574,
-0.07266469299793243,
-0.029046056792140007,
-0.006856711581349373,
0.004226401913911104,
0.06322538107633591,
-0.0024100274313241243,
-0.01451908890157938,
0.0020484314300119877,
0.004951619077473879,
0.028902774676680565,
-0.07343102991580963,
0.03819333761930466,
-0.02214895188808441,
-0.010709783993661404,
-0.011686766520142555,
-0.001886538346298039,
-0.030441537499427795,
-0.004946916364133358,
0.03503907844424248,
0.005865645129233599,
0.029964132234454155,
0.0140873733907938,
-0.01984812319278717,
0.03053917922079563,
-0.01664089411497116,
0.003207884496077895,
0.056557461619377136,
0.0030210078693926334,
-0.022868728265166283,
0.05397835373878479,
0.015324601903557777,
-0.05394304171204567,
0.03623436018824577,
-0.035283174365758896,
-0.05169939622282982,
0.010848366655409336,
-0.01403980515897274,
-0.03234747052192688,
-0.05421235412359238,
-0.030056508257985115,
0.050623491406440735,
-0.013052240945398808,
-0.03635475039482117,
0.023580504581332207,
-0.026342647150158882,
0.08045708388090134,
-0.005841701757162809,
0.026667572557926178,
0.0010751179652288556,
-0.001822066493332386,
-0.004670191090553999,
0.006640865467488766,
0.014883485622704029,
-0.018308771774172783,
0.06812432408332825,
0.032896704971790314,
0.03450275957584381,
0.012210696935653687,
0.007856645621359348,
0.060395851731300354,
-0.04080094397068024,
-0.0027574459090828896,
0.014404891058802605,
0.0365324541926384,
0.008458230644464493,
0.028693947941064835,
0.03251813352108002,
0.0673086941242218,
-0.014501185156404972,
0.04669807478785515,
0.010708313435316086,
-0.022966448217630386,
-0.05828872323036194,
0.0452473908662796,
-0.03121643140912056,
0.01989944837987423,
-0.005716667044907808,
-0.005928146652877331,
-0.025952691212296486,
-0.021255269646644592,
0.027194155380129814,
-0.023845480754971504,
-0.01070992648601532,
-0.014517979696393013,
-0.02286044880747795,
0.03276064991950989,
0.004278500564396381,
0.009418352507054806,
-0.011549626477062702,
0.053361035883426666,
0.018801992759108543,
0.008656096644699574,
-0.0286425594240427,
-0.0222769808024168,
-0.004096515942364931,
0.04903437942266464,
-0.0855020061135292,
-0.022034214809536934,
-0.03423913195729256,
0.012075770646333694,
-0.030729467049241066,
-0.059643834829330444
] |
<p>I have a reptil UVB lamp in my room, and a de-humidifier that uses a UV lamp to clean the air passing through it. Honestly since I got it working (the lamp was dead at first) my room is mold free. </p>
<p>I just read that UV air purifiers were banned, and although the dehumidifier model is not in the ban notice, I wonder whether the addition of both the lamps could be too much ozone in my room.</p>
<p>I got the lamp specs and the gov page stating a safe level of ozone should be under 0.050 ppm, but I don't know how to calculate the ozone generation by those devices.</p>
<p>Could anyone calculate it for me? </p>
<p>Reptisun 5.0 UVB lamp: <a href="http://zoomed.com/Library//ProductDBFiles/EPREP1109_ReptileLighting.pdf" rel="nofollow">http://zoomed.com/Library//ProductDBFiles/EPREP1109_ReptileLighting.pdf</a></p>
<p>Gov page about ozone generators ban:
<a href="http://www.arb.ca.gov/research/indoor/o3g-list.htm" rel="nofollow">http://www.arb.ca.gov/research/indoor/o3g-list.htm</a></p>
<p>Extra link about required/safe levels, if you wonder (please fix the link. I couldn't post more than two)
www [remove this space] landesbioscience [dot] com/pdf/01ReichrathHolick.pdf</p>
<p>The dehumidifier description is www [dot] sunpentown [dot] com/sdmidewitiuv.html</p>
<p>Thanks.</p>
| 9,408 |
[
-0.01082522887736559,
-0.03139562904834747,
0.01564960367977619,
-0.027254894375801086,
0.03468736261129379,
-0.03584921732544899,
-0.03160297870635986,
-0.02110113389790058,
-0.00405689375475049,
-0.06942868232727051,
0.05619111657142639,
0.06471554189920425,
0.048580143600702286,
0.040803033858537674,
-0.0044379704631865025,
-0.0310607198625803,
0.015244539827108383,
0.025255687534809113,
0.027414295822381973,
-0.01905798725783825,
-0.021682631224393845,
-0.012310780584812164,
-0.0008890977478586137,
0.01580353081226349,
-0.06122574210166931,
0.017584707587957382,
0.06688242405653,
0.012758851982653141,
-0.028506170958280563,
0.015939190983772278,
-0.02666059508919716,
-0.009570359252393246,
0.02182718738913536,
-0.025348907336592674,
0.003574951086193323,
0.007090717554092407,
-0.01484924741089344,
-0.021166346967220306,
-0.01329507865011692,
0.034125372767448425,
0.010021686553955078,
0.0006264031981118023,
0.00043108389945700765,
0.023810148239135742,
-0.009141404181718826,
-0.011366371065378189,
-0.016323408111929893,
0.012901351787149906,
0.031102946028113365,
-0.07942113280296326,
0.06835993379354477,
0.005418514832854271,
0.029154431074857712,
0.020656118169426918,
-0.02160380780696869,
0.008662165142595768,
0.06558114290237427,
0.06346464902162552,
-0.007086194586008787,
-0.04012743756175041,
-0.01621895283460617,
-0.0011485996656119823,
-0.039526890963315964,
-0.003461935091763735,
-0.028469178825616837,
0.012298572808504105,
-0.004075761418789625,
-0.002692814916372299,
0.04790636897087097,
-0.0032813569996505976,
0.07802590727806091,
-0.0040306649170815945,
0.0074015045538544655,
-0.017933417111635208,
0.017976226285099983,
-0.012401514686644077,
0.012133018113672733,
0.028503650799393654,
0.013434932567179203,
0.017215842381119728,
-0.030751561746001244,
0.0015691057778894901,
0.0008874473860487342,
0.011102816089987755,
0.035962723195552826,
-0.01914648897945881,
0.10166109353303909,
-0.023025143891572952,
-0.01769889146089554,
0.006026711314916611,
0.026155447587370872,
0.024372564628720284,
0.045178987085819244,
0.01759105734527111,
-0.0006909634103067219,
0.028701182454824448,
-0.007230399176478386,
0.08082793653011322,
-0.039479196071624756,
0.013112193904817104,
0.009446509182453156,
0.03590540587902069,
0.0514741949737072,
0.02648969367146492,
-0.05846380442380905,
-0.038937464356422424,
-0.00528042484074831,
-0.01000518724322319,
0.026810219511389732,
-0.02555214986205101,
-0.047692153602838516,
-0.00824601761996746,
-0.02892487868666649,
-0.034500252455472946,
0.0015613933792337775,
-0.002084990730509162,
0.025041688233613968,
0.016986742615699768,
0.05846453830599785,
0.022648885846138,
0.042877160012722015,
-0.015303067862987518,
0.0209750197827816,
-0.06119847297668457,
-0.07992701977491379,
-0.004548327997326851,
0.003949796315282583,
0.006237446330487728,
-0.043874356895685196,
0.02906518615782261,
-0.011015710420906544,
0.006950388662517071,
0.016722794622182846,
-0.026561236009001732,
0.04908854141831398,
-0.031450241804122925,
-0.06860353797674179,
-0.044741224497556686,
0.05011167749762535,
0.012785914354026318,
0.010588563978672028,
-0.06997567415237427,
-0.01699932850897312,
-0.029713628813624382,
0.043275944888591766,
0.027871672064065933,
-0.005946620367467403,
-0.01790292002260685,
0.04800882935523987,
-0.008805333636701107,
-0.016484996303915977,
0.033936090767383575,
0.0009636348113417625,
-0.01356633473187685,
-0.0007390262326225638,
-0.10022664070129395,
0.04008925333619118,
0.05703664943575859,
0.029093820601701736,
-0.008160562254488468,
0.05744074285030365,
-0.005448685027658939,
-0.012177057564258575,
-0.034866541624069214,
-0.021069012582302094,
-0.04877005144953728,
0.04993889480829239,
-0.02738199196755886,
0.0027218316681683064,
0.015035659074783325,
-0.03245486319065094,
0.026170913130044937,
-0.005396081600338221,
-0.01767709106206894,
0.043442972004413605,
-0.009919834323227406,
0.011656742542982101,
-0.050903789699077606,
0.05452820286154747,
0.010499733500182629,
-0.0430697500705719,
0.02632461115717888,
0.013325645588338375,
-0.026748092845082283,
0.011928677558898926,
0.00018411943165119737,
-0.020799100399017334,
-0.016591809689998627,
0.016130059957504272,
-0.053862567991018295,
-0.059532348066568375,
-0.07851719111204147,
-0.0069045741111040115,
-0.024944860488176346,
-0.011306921020150185,
0.010161194950342178,
0.0014128232141956687,
0.057615868747234344,
-0.005515871569514275,
-0.0162242129445076,
-0.02864912338554859,
0.021432366222143173,
0.03847634419798851,
0.011710605584084988,
0.017164168879389763,
0.051661793142557144,
0.05983162298798561,
-0.03487849235534668,
0.051638562232255936,
-0.010472157038748264,
-0.011538587510585785,
-0.030155466869473457,
-0.013458034954965115,
-0.0064437538385391235,
-0.005982846952974796,
0.02062385156750679,
0.015731899067759514,
-0.03541027382016182,
-0.006655635312199593,
0.019848745316267014,
-0.0094919977709651,
0.05367615446448326,
0.08106070756912231,
0.01258176937699318,
0.00554802268743515,
0.00984521396458149,
0.01963135413825512,
-0.0021294832695275545,
0.021061500534415245,
-0.009810363873839378,
-0.018933039158582687,
0.009796956554055214,
0.06762630492448807,
-0.010308547876775265,
0.0020619670394808054,
0.013448379002511501,
0.02051497995853424,
-0.004177255090326071,
0.027154510840773582,
0.04862622171640396,
-0.006332192569971085,
-0.02089393325150013,
0.015510483644902706,
0.05185392126441002,
0.03830021992325783,
0.04416993260383606,
0.015489368699491024,
0.009952960535883904,
0.025858119130134583,
-0.012336221523582935,
-0.005831349175423384,
0.05885801464319229,
0.03280743211507797,
0.004510917235165834,
0.013916156254708767,
0.0017296017613261938,
0.07453984767198563,
-0.027043435722589493,
0.034602127969264984,
0.0243790652602911,
-0.009327447041869164,
0.01997538097202778,
0.0002000767271965742,
-0.027864281088113785,
0.013318561017513275,
0.03357831761240959,
-0.03872169554233551,
0.004502183757722378,
0.011837136931717396,
-0.05269479379057884,
-0.008463973179459572,
-0.047299906611442566,
-0.006185651291161776,
-0.040219228714704514,
-0.015651002526283264,
0.005798622965812683,
0.0028263810090720654,
0.029334720224142075,
-0.02591150440275669,
-0.025823703035712242,
-0.036167409271001816,
-0.038180239498615265,
-0.00967872142791748,
0.006945598870515823,
0.006925398018211126,
0.007525329943746328,
-0.000981074059382081,
-0.016461478546261787,
0.01922096125781536,
0.00392931280657649,
-0.020251525565981865,
0.03404197096824646,
0.010184441693127155,
-0.04123447462916374,
-0.04370943084359169,
0.013863690197467804,
0.010169179178774357,
-0.0168970488011837,
-0.03883953392505646,
-0.0073106903582811356,
-0.002466508187353611,
-0.007376580499112606,
0.028334984555840492,
-0.02945246919989586,
-0.019878869876265526,
-0.01156257838010788,
-0.009831656701862812,
0.024110138416290283,
-0.02058826945722103,
-0.024379603564739227,
0.018225915729999542,
-0.03239841014146805,
-0.00990708265453577,
-0.03852537274360657,
-0.06144006550312042,
0.04511066526174545,
0.036969128996133804,
0.03774046525359154,
0.018981993198394775,
-0.06416886299848557,
0.06783866137266159,
0.02078232355415821,
-0.05728713423013687,
-0.03528967499732971,
-0.01681639440357685,
-0.033024635165929794,
-0.07242630422115326,
-0.018887953832745552,
0.059718433767557144,
0.01124326791614294,
0.040330830961465836,
0.01646609418094158,
0.008143030107021332,
0.018340691924095154,
0.01688169315457344,
0.004694804549217224,
0.00033904059091582894,
0.0024214135482907295,
-0.03646291047334671,
0.06709389388561249,
0.00700049614533782,
0.010084783658385277,
-0.01922413893043995,
-0.012168552726507187,
0.03735911473631859,
0.05614394694566727,
-0.06016764044761658,
0.012388053350150585,
0.04269193485379219,
0.030748918652534485,
-0.049863990396261215,
0.020443689078092575,
0.03435186296701431,
-0.012454421259462833,
-0.016513006761670113,
0.003524262923747301,
0.07017269730567932,
-0.012865488417446613,
-0.024700485169887543,
0.05701762065291405,
0.07166758179664612,
-0.010560840368270874,
-0.035188913345336914,
-0.020010698586702347,
0.006666718516498804,
-0.011830651201307774,
0.029917823150753975,
-0.01163430791348219,
0.04794033616781235,
0.019861040636897087,
0.01016527134925127,
-0.006019045598804951,
-0.04333210363984108,
0.007469637785106897,
-0.03517591208219528,
0.026407357305288315,
0.0003078972513321787,
0.05445512384176254,
-0.007337342016398907,
0.03726730868220329,
-0.044648557901382446,
-0.054494574666023254,
0.01510614063590765,
-0.025394968688488007,
-0.05428469181060791,
0.06912123411893845,
0.0029058160725980997,
0.007334711030125618,
-0.00568646565079689,
-0.012762467376887798,
0.001927851582877338,
0.025897083804011345,
-0.029737742617726326,
-0.02878456562757492,
0.004852434154599905,
-0.0440172515809536,
0.0052122375927865505,
-0.01207529753446579,
-0.028992513194680214,
-0.003065666416659951,
0.03621590882539749,
-0.02593090943992138,
-0.013157728128135204,
0.034189507365226746,
0.02735977992415428,
-0.05169004574418068,
0.002983659505844116,
-0.05123526602983475,
0.013845512643456459,
-0.015575977973639965,
0.026519298553466797,
0.03634687140583992,
-0.003304071957245469,
-0.0034074026625603437,
-0.022104619070887566,
-0.008971687406301498,
-0.0007162821129895747,
-0.003356470260769129,
0.0032057182397693396,
-0.07123268395662308,
-0.029074836522340775,
-0.04471774399280548,
0.014750606380403042,
0.03100699745118618,
-0.017292862758040428,
0.0514245331287384,
0.01208497118204832,
-0.029352238401770592,
-0.015146814286708832,
0.017820483073592186,
0.03082791343331337,
-0.04682277888059616,
0.01611459255218506,
-0.020432552322745323,
-0.022743914276361465,
-0.0030006126035004854,
-0.002676858101040125,
0.012825722806155682,
0.02475319243967533,
-0.04674369469285011,
-0.04962005093693733,
0.015793804079294205,
0.0028505376540124416,
-0.01476078387349844,
0.03647313639521599,
0.0015847890172153711,
-0.007524760905653238,
-0.028073662891983986,
-0.02768537402153015,
-0.005354233551770449,
0.011150969192385674,
0.03435676172375679,
0.023369790986180305,
0.008054113946855068,
-0.10052064061164856,
0.0010418406454846263,
0.06711352616548538,
0.03898762911558151,
-0.0006607588147744536,
0.006491050124168396,
-0.05790623277425766,
-0.015921682119369507,
0.024824565276503563,
-0.017824804410338402,
0.0017839273205026984,
-0.028411222621798515,
0.02023386023938656,
-0.009814751334488392,
-0.03360667824745178,
0.01069044228643179,
-0.008220076560974121,
0.021401843056082726,
0.03374876081943512,
-0.0010378786828368902,
-0.038167648017406464,
0.005919651128351688,
0.03721276670694351,
0.01731147989630699,
0.07243414223194122,
-0.009175523184239864,
-0.0346897654235363,
0.034954920411109924,
-0.0034620575606822968,
-0.0280623696744442,
-0.04159674048423767,
-0.026218470185995102,
0.02626904658973217,
0.0028863197658210993,
0.07444386184215546,
-0.011744419112801552,
-0.0007259960402734578,
0.019286544993519783,
0.0070468285121023655,
-0.022077452391386032,
-0.033714696764945984,
-0.06017440930008888,
0.04531475156545639,
0.01486201025545597,
0.01062620896846056,
0.027361150830984116,
0.030817752704024315,
0.014114324003458023,
0.0223521888256073,
-0.040046099573373795,
0.05819882079958916,
-0.03576292470097542,
-0.030852770432829857,
-0.028115618973970413,
-0.0263659730553627,
-0.015158100984990597,
0.07169142365455627,
0.017137737944722176,
0.035447441041469574,
-0.023814750835299492,
-0.01824014075100422,
0.039657026529312134,
0.019785182550549507,
-0.017346614971756935,
-0.020065614953637123,
-0.013451853767037392,
0.05999596416950226,
-0.0027268670964986086,
-0.0023763910867273808,
0.020493635907769203,
-0.062185559421777725,
0.00840659812092781,
0.032459013164043427,
-0.03505944088101387,
0.02410963736474514,
-0.028601277619600296,
0.014766904525458813,
-0.03714768961071968,
0.003589187515899539,
0.0399431474506855,
0.00450120959430933,
0.04698739945888519,
0.0019447653321549296,
-0.0474567674100399,
-0.02519354596734047,
0.01880117505788803,
0.006369265727698803,
0.0411156490445137,
-0.02458200789988041,
0.07346760481595993,
0.007964755408465862,
-0.016301944851875305,
-0.009899108670651913,
-0.016600660979747772,
-0.004948734305799007,
0.0287439227104187,
-0.03959278017282486,
-0.0553118996322155,
-0.016748938709497452,
-0.02706771343946457,
-0.036848340183496475,
-0.02310907654464245,
0.050302810966968536,
-0.04941007122397423,
0.007977589033544064,
0.03424680978059769,
0.0010853533167392015,
0.08184631168842316,
-0.027981556951999664,
-0.01340180542320013,
0.000897195830475539,
-0.015759779140353203,
-0.02306489460170269,
0.020673740655183792,
-0.004015481565147638,
-0.03181314840912819,
-0.04983164370059967,
0.018704980611801147,
0.014905604533851147,
0.06328479200601578,
-0.029743246734142303,
-0.002628793939948082,
0.03096134029328823,
0.015408377163112164,
0.0010694043012335896,
-0.005079133901745081,
0.054980725049972534,
-0.016818109899759293,
0.016323400661349297,
0.02171310782432556,
0.04233501851558685,
-0.050025954842567444,
0.004649457521736622,
-0.016781240701675415,
0.0005133901140652597,
0.03144891932606697,
0.011494500562548637,
0.0727447122335434,
-0.033940307796001434,
0.022287866100668907,
0.012352466583251953,
-0.06541819125413895,
0.05756533890962601,
-0.03306395187973976,
0.03312230110168457,
0.004650915041565895,
0.008859822526574135,
-0.02958131767809391,
-0.05487607419490814,
-0.06786012649536133,
-0.04581569880247116,
0.051673226058483124,
-0.00155194744002074,
-0.008824177086353302,
-0.012837149202823639,
0.005367421545088291,
0.006906466092914343,
-0.028429526835680008,
0.005391721148043871,
0.03538454324007034,
0.03612373769283295,
0.024343380704522133,
0.004194845911115408,
0.015018713660538197,
0.003993306774646044,
0.013790401630103588,
0.03789154812693596,
0.012203716672956944,
0.05095015466213226,
0.013672503642737865,
0.025572961196303368,
-0.022740276530385017,
-0.0014678409788757563,
0.06544523686170578,
-0.03407289832830429,
0.03141151741147041,
-0.008619138039648533,
-0.01792757399380207,
0.05111762881278992,
-0.03496387228369713,
-0.04020289331674576,
-0.04219791665673256,
-0.03964695334434509,
-0.064341239631176,
0.021425364539027214,
-0.010212014429271221,
-0.012603893876075745,
-0.004040874075144529,
0.018644053488969803,
0.042905330657958984,
0.028378525748848915,
0.026476874947547913,
-0.051691532135009766,
-0.060027964413166046,
-0.00446392223238945,
-0.009505494497716427,
-0.02965661510825157,
0.02167593501508236,
-0.012861978262662888,
-0.024852938950061798,
0.0009375089430250227,
-0.05172451585531235,
0.002095517236739397,
-0.023203272372484207,
0.03207360953092575,
0.04923181235790253,
0.058825504034757614,
-0.002266055904328823,
0.018872063606977463,
-0.02832944318652153,
0.03880349546670914,
0.13594384491443634,
0.013703853823244572,
0.0012174999574199319,
-0.057237934321165085,
-0.03555417060852051,
0.04947718605399132,
0.01590464822947979,
-0.0032285163179039955,
0.0179977435618639,
-0.0312826968729496,
-0.005638309754431248,
0.037266455590724945,
0.025189857929944992,
0.004761842079460621,
0.03574903681874275,
0.03182888776063919,
0.006699699442833662,
-0.03754067048430443,
0.02334849163889885,
0.0015793050406500697,
-0.03415236622095108,
-0.006541769951581955,
-0.008226828649640083,
-0.008476552553474903,
-0.00892934575676918,
0.007490222342312336,
-0.015996187925338745,
-0.02398061566054821,
0.046557847410440445,
0.014049040153622627,
-0.016884561628103256,
0.006290110759437084,
0.008261224254965782,
0.021280422806739807,
-0.03412806615233421,
-0.03291228041052818,
0.04268519952893257,
-0.02222489006817341,
0.002303545596078038,
0.05041375011205673,
0.02338232658803463,
-0.00719906110316515,
-0.004307655617594719,
0.034507036209106445,
-0.04921438544988632,
0.00545684015378356,
0.015264422632753849,
-0.01095908135175705,
-0.006388488691300154,
0.03407817333936691,
0.005781387444585562,
0.027441542595624924,
-0.006441639736294746,
-0.052515968680381775,
-0.04231410473585129,
-0.007628357503563166,
0.04120127856731415,
-0.037810660898685455,
-0.003690082114189863,
-0.02564084157347679,
0.026425473392009735,
-0.005870323162525892,
0.02493480034172535,
0.0022980414796620607,
0.010698332451283932,
-0.013758678920567036,
-0.036061882972717285,
0.04159998148679733,
-0.03267412260174751,
0.005692478734999895,
-0.02546839974820614,
0.003041829215362668,
-0.006165451370179653,
0.009131325408816338,
-0.011613032780587673,
0.021963762119412422,
0.030263682827353477,
0.00612609600648284,
-0.0025473919231444597,
-0.008353684097528458,
-0.07260341942310333,
0.02124227024614811,
0.0014623884344473481,
-0.07936681061983109,
-0.0024498701095581055,
-0.006574552971869707,
0.017561620101332664,
0.020849477499723434,
0.01218621339648962,
0.043258730322122574,
0.025252731516957283,
0.015703745186328888,
0.01594584248960018,
-0.03932327404618263,
0.002272801473736763,
0.04637451469898224,
-0.0037067458033561707,
-0.012983113527297974,
-0.022637387737631798,
0.04830845445394516,
-0.011564837768673897,
0.014383099041879177,
0.010611205361783504,
0.022518878802657127,
-0.04116786643862724,
-0.005155286286026239,
-0.014150633476674557,
-0.03731965646147728,
0.02075505629181862,
-0.010415077209472656,
-0.026029448956251144,
-0.011640939861536026,
-0.009609178639948368,
-0.05899251624941826,
-0.025858106091618538,
-0.0167350172996521,
-0.032115429639816284,
-0.024222835898399353,
0.030628079548478127,
-0.012739082798361778,
0.01236106175929308,
-0.00653008371591568,
-0.05260225012898445,
-0.02087051048874855,
0.013667196966707706,
-0.009566191583871841,
0.00867144949734211,
-0.0007638483075425029,
0.0465766079723835,
-0.010276040062308311,
-0.027776870876550674,
0.028320513665676117,
0.05279569700360298,
-0.005220215301960707,
-0.032027386128902435,
-0.002758470829576254,
-0.018848203122615814,
0.08079700171947479,
-0.027668511494994164,
-0.006918813567608595,
0.04905162379145622,
-0.027560178190469742,
-0.028675027191638947,
0.016278160735964775,
-0.01573142409324646,
0.007194972597062588,
0.03232872486114502,
-0.01652604155242443,
0.02241259627044201,
0.05647594854235649,
-0.026910284534096718,
0.03462637588381767,
-0.04890529811382294,
-0.012162945233285427,
0.02683347277343273,
0.04457087814807892,
-0.028063615784049034,
-0.02883981354534626,
0.005046171136200428,
0.03859275206923485,
0.03895742446184158,
0.007201062515377998,
0.0050468165427446365,
-0.03921393305063248,
-0.04317757487297058,
0.008917449042201042,
0.0038854959420859814,
0.014120357111096382,
-0.024616917595267296,
0.03917867690324783,
-0.006449964828789234,
0.03236152604222298,
-0.02020883746445179,
-0.020940151065587997,
-0.09813933819532394,
-0.015233267098665237,
0.004781628493219614,
0.01969047449529171,
0.01075527910143137,
-0.02920682169497013,
0.03181074187159538,
0.005800298880785704,
-0.0440404936671257,
-0.020106354728341103,
-0.0003910020168405026,
0.016714386641979218,
-0.03424272686243057,
0.022935308516025543,
-0.014692348428070545,
-0.0012921355664730072,
0.0021157939918339252,
0.04362199828028679,
-0.009340513497591019,
-0.0028374900575727224,
-0.025495419278740883,
-0.0574195496737957,
0.009209198877215385,
0.0198956485837698,
0.0016392284305766225,
-0.023337792605161667,
0.026034913957118988,
-0.05532045662403107,
0.018725154921412468,
0.03079131431877613,
-0.013865982182323933,
0.01789485104382038,
-0.0059190853498876095,
0.038616981357336044,
-0.015403826721012592,
0.017799153923988342,
0.05190788581967354,
0.03089490532875061,
-0.0607718788087368,
-0.004537427797913551,
0.015022856183350086,
0.007578285411000252,
0.0067658270709216595,
0.007129767909646034,
0.02942708507180214,
0.013930018991231918,
-0.02566768415272236,
0.0639977753162384,
-0.0340927317738533,
-0.039722807705402374,
0.015594790689647198,
0.011539001949131489,
0.004202059470117092,
-0.060560841113328934,
-0.009015996940433979,
-0.05888389050960541,
0.01130562275648117,
0.03016652539372444,
-0.01336709875613451,
0.009984220378100872,
-0.013576063327491283,
-0.0009834886295720935,
-0.03042277880012989,
0.0189510527998209,
0.0016310575883835554,
0.002616320503875613,
-0.049873314797878265,
0.014478027820587158,
-0.03177342936396599,
-0.006579506676644087,
-0.002833420177921653,
-0.02258181944489479,
-0.024691805243492126,
0.0008607913623563945,
-0.0416250079870224,
-0.014102356508374214,
0.018298085778951645,
-0.005734880920499563,
-0.005504582077264786,
-0.014020035974681377,
0.02609073370695114,
0.018740154802799225,
0.01651667058467865,
-0.08502951264381409,
-0.021080348640680313,
0.009344490244984627,
0.056972935795784,
0.02491438388824463,
-0.004011969547718763,
-0.01709851808845997,
-0.014889688231050968,
0.004978729411959648,
0.020130785182118416,
-0.025314312428236008,
0.008067584596574306,
0.06393590569496155,
-0.05478675290942192,
0.021523909643292427,
-0.014498455449938774,
-0.013853938318789005,
0.003978119697421789,
0.041364409029483795,
-0.019781598821282387,
0.025719165802001953,
-0.01568124257028103,
-0.01392494235187769,
0.01028314046561718,
-0.00026882553356699646,
-0.03126244246959686,
0.05767048895359039,
-0.021441912278532982,
0.02008575014770031,
0.029713453724980354,
-0.018590737134218216,
-0.016142891719937325,
0.0451306477189064,
-0.023536985740065575,
0.024666287004947662,
0.0022622267715632915,
-0.023449482396245003,
0.03833429515361786,
-0.043349750339984894,
0.018246622756123543,
-0.018082313239574432,
-0.028875304386019707,
0.02267407439649105,
0.04051252081990242,
0.003512677503749728,
-0.013453916646540165,
0.007209014147520065,
0.02710903435945511,
0.0192111749202013,
-0.0037520986516028643,
-0.019782286137342453,
0.057376522570848465,
0.01544403936713934,
-0.01765979267656803,
-0.01813969761133194,
0.009123277850449085,
0.013377254828810692,
0.059275005012750626,
0.025568969547748566,
0.05961306020617485,
0.013186239637434483,
-0.004007330164313316,
-0.004568324889987707,
0.03114074468612671,
-0.05411466956138611,
0.030132267624139786,
-0.03603948652744293,
0.03956027701497078,
0.013171086087822914,
0.013394409790635109,
-0.056510090827941895,
-0.042096301913261414,
-0.01772760972380638,
0.01645161211490631,
0.008452826179564,
0.028114698827266693,
0.008422920480370522,
-0.0018572605913504958,
-0.009067712351679802,
-0.012627193704247475,
0.0027242787182331085,
-0.04036372900009155,
0.03513619303703308,
-0.010467248037457466,
0.0071192774921655655,
-0.020621202886104584,
-0.02369510754942894,
0.028028039261698723,
-0.002652697265148163,
-0.002777470974251628,
0.03895954787731171,
-0.02420419082045555,
0.012316735461354256,
-0.026872390881180763,
0.005236619617789984,
0.04406779259443283,
-0.041044626384973526,
-0.011801081709563732,
-0.0005817174096591771,
-0.022686000913381577,
-0.008208413608372211,
-0.03144587576389313
] |
<p>In the Peltier effect, we consider charge carriers being able to carry heat. As for electrons or ions, this attitude makes sense, since external electric potential drives particles with mass in a direction and effectively transfers heat from one point of material to another.</p>
<p>But for holes, this situation is only virtual, holes moving in a direction is only reformulation of the fact that the electron making up the hole environment are traveling opposite direction. I just cannot grasp the concept that the holes can indeed carry heat.</p>
<p>I know one can argue that the holes have effective mass, but effective mass is only a measure of how much can you accelerate / decelerate the electron (or hole) in a crystal field.</p>
<p>Can you help me out please?</p>
| 9,409 |
[
0.020497720688581467,
-0.02699880674481392,
0.016321247443556786,
-0.020871611312031746,
-0.01414226833730936,
-0.0027420346159487963,
0.004206178244203329,
0.021976899355649948,
-0.04386159032583237,
0.03087182156741619,
0.027614735066890717,
-0.014146318659186363,
0.051053695380687714,
-0.001329250168055296,
-0.030717166140675545,
0.020197929814457893,
-0.035386696457862854,
-0.036316320300102234,
-0.022773321717977524,
-0.035100534558296204,
-0.01804100163280964,
0.05610640347003937,
-0.033498309552669525,
-0.009635746479034424,
-0.03792911395430565,
0.025191491469740868,
0.017707180231809616,
0.001989328069612384,
0.019343681633472443,
0.033558715134859085,
-0.013407943770289421,
-0.03675106540322304,
0.029836582019925117,
-0.01936478167772293,
-0.00018658755288925022,
-0.0013231507036834955,
-0.03186758607625961,
-0.005645295139402151,
0.0017209273064509034,
0.018553774803876877,
-0.002723305718973279,
-0.018577711656689644,
-0.0149344177916646,
0.029085367918014526,
0.028630463406443596,
-0.006799163296818733,
0.021309318020939827,
-0.0017587702022865415,
0.033298373222351074,
-0.06098135560750961,
0.04967458173632622,
-0.04020831361413002,
0.04680861532688141,
0.009486278519034386,
0.0013560405932366848,
0.007120008580386639,
0.055101197212934494,
0.0713241919875145,
-0.0064247683621943,
-0.02609274722635746,
0.00012545663048513234,
0.024024533107876778,
-0.03219526261091232,
-0.053725309669971466,
-0.00037123914808034897,
-0.013237888924777508,
0.017106613144278526,
-0.011981923133134842,
0.03959169238805771,
0.0052764625288546085,
0.05162464454770088,
-0.008450157940387726,
0.02152288146317005,
0.012884136289358139,
0.032580163329839706,
-0.01477237232029438,
0.010339505039155483,
0.025412116199731827,
0.033304061740636826,
0.02975260280072689,
-0.04598723724484444,
0.0014813413145020604,
0.030508778989315033,
0.04981964826583862,
0.019415702670812607,
-0.024551721289753914,
0.04357541352510452,
-0.018387727439403534,
0.030311889946460724,
0.03425978869199753,
-0.003642614698037505,
-0.0030083367601037025,
-0.002119554439559579,
-0.0008272162522189319,
-0.021811503916978836,
-0.01913519762456417,
0.01146085374057293,
0.033374760299921036,
0.017702167853713036,
0.01442129909992218,
-0.0014056727522984147,
0.007734776474535465,
0.029248325154185295,
0.09973765909671783,
-0.009925123304128647,
-0.041894618421792984,
-0.020639494061470032,
0.018675902858376503,
0.034374307841062546,
0.006236135959625244,
-0.06047365814447403,
0.0012776381336152554,
-0.019787635654211044,
-0.02733963169157505,
0.026989242061972618,
-0.030851123854517937,
0.007227471563965082,
-0.029755542054772377,
0.0031741918064653873,
0.033474355936050415,
0.020665664225816727,
-0.013671849854290485,
0.017482463270425797,
-0.03656715154647827,
-0.08800534904003143,
0.00919050071388483,
0.05606505647301674,
-0.016776949167251587,
-0.003914928529411554,
0.008881035260856152,
0.0216868594288826,
-0.003859833348542452,
0.019721558317542076,
-0.02035890333354473,
0.018652476370334625,
-0.01715942658483982,
-0.08823166787624359,
-0.04862668737769127,
0.07543151825666428,
-0.02526479959487915,
0.0034352694638073444,
-0.06380551308393478,
-0.006139302626252174,
0.03306597098708153,
0.07711552083492279,
-0.022060992196202278,
0.009466376155614853,
-0.035845380276441574,
0.049008555710315704,
0.0018150311661884189,
-0.002671301132068038,
-0.046145036816596985,
-0.007026731502264738,
-0.01247035339474678,
0.01637701876461506,
-0.05846336483955383,
0.04077407345175743,
0.005833440460264683,
-0.014528403989970684,
-0.04135126620531082,
0.060975249856710434,
-0.0385715588927269,
0.0027256368193775415,
0.011552955023944378,
-0.03798290714621544,
-0.021534623578190804,
0.06016736105084419,
-0.024796931073069572,
0.008301619440317154,
0.03241422399878502,
0.022208239883184433,
0.029185060411691666,
0.020156996324658394,
0.02200387604534626,
0.036025866866111755,
-0.028919994831085205,
-0.006290065124630928,
-0.03369905799627304,
0.00926059577614069,
0.012239820323884487,
-0.06360536068677902,
-0.0636676698923111,
0.014435121789574623,
-0.019598476588726044,
-0.006460270844399929,
0.008688589558005333,
0.004401573911309242,
-0.02774292789399624,
-0.009992252103984356,
-0.015107830055058002,
-0.008190234191715717,
-0.09251637756824493,
0.026616517454385757,
0.011810792610049248,
0.016150254756212234,
0.005502589978277683,
0.010675346478819847,
0.010854111053049564,
-0.031980961561203,
-0.04425814747810364,
-0.023346422240138054,
0.0015411089407280087,
-0.02026817947626114,
-0.011055882088840008,
0.0264026690274477,
0.01968294382095337,
0.017813917249441147,
-0.020502040162682533,
0.018151158466935158,
-0.0032869891729205847,
0.009777362458407879,
0.00079003581777215,
-0.04751403257250786,
0.02126556821167469,
0.025096381083130836,
-0.024760384112596512,
-0.012613310478627682,
-0.0033629853278398514,
-0.01696663349866867,
0.05102114751935005,
0.021478237584233284,
0.07949765771627426,
0.0011773406295105815,
0.0022016246803104877,
-0.028107287362217903,
0.034652020782232285,
-0.03218914568424225,
-0.004358998499810696,
-0.013027406297624111,
-0.03777211159467697,
-0.04650011286139488,
0.008110103197395802,
0.028067896142601967,
0.012182656675577164,
-0.04232829436659813,
0.016938231885433197,
0.04069463908672333,
0.02163430117070675,
0.048223335295915604,
0.040147002786397934,
-0.027281412854790688,
0.00461981538683176,
0.05109594389796257,
-0.013803173787891865,
0.007894417271018028,
0.0010452857241034508,
0.08136122673749924,
-0.008373879827558994,
-0.0037284065037965775,
-0.013276025652885437,
-0.014302605763077736,
0.0468292310833931,
0.027952058240771294,
0.02901918813586235,
-0.004561492707580328,
-0.040272027254104614,
-0.006002505775541067,
-0.005080099683254957,
0.03306012228131294,
0.015504240058362484,
0.025912560522556305,
0.02925567887723446,
-0.06760422140359879,
-0.01388456579297781,
0.01597079634666443,
0.01166482176631689,
0.027379395440220833,
-0.004565619397908449,
0.01973811909556389,
-0.04198940470814705,
0.03291885554790497,
-0.0247197262942791,
0.007053840905427933,
-0.0037872984539717436,
-0.0016508674016222358,
0.022122254595160484,
-0.010657311417162418,
0.034860074520111084,
-0.0358530730009079,
-0.022633330896496773,
-0.03840991109609604,
-0.033712904900312424,
0.036961816251277924,
0.03804217651486397,
-0.03111763298511505,
0.01314899418503046,
-0.013995557092130184,
-0.039693012833595276,
0.030825745314359665,
-0.0014184756437316537,
-0.03896166756749153,
-0.006630065385252237,
-0.024939751252532005,
-0.007640833966434002,
0.027053093537688255,
-0.017106350511312485,
-0.010415199212729931,
-0.025998134166002274,
0.012064722366631031,
0.05470329150557518,
-0.05420354753732681,
-0.03533646836876869,
0.01146948803216219,
-0.013704746961593628,
-0.022773027420043945,
0.03168429434299469,
-0.06358306854963303,
0.007251867558807135,
-0.01845468021929264,
0.02490750513970852,
0.04532657563686371,
-0.031409841030836105,
0.007859897799789906,
-0.05061120167374611,
-0.0380132719874382,
0.046332888305187225,
-0.022652238607406616,
-0.014272293075919151,
-0.02103125862777233,
-0.021871479228138924,
0.06572166085243225,
0.0506332665681839,
-0.03175906464457512,
0.018157413229346275,
-0.04425719380378723,
-0.025248482823371887,
-0.030413929373025894,
0.02360338158905506,
0.053586214780807495,
-0.007426512893289328,
-0.004821207839995623,
0.03242092952132225,
0.055593233555555344,
-0.00542726693674922,
-0.018548063933849335,
-0.02037729322910309,
-0.024717984721064568,
0.01741405576467514,
-0.016041046008467674,
0.0424012616276741,
0.0150727154687047,
-0.0362994521856308,
0.020736142992973328,
-0.003308578860014677,
0.012351453304290771,
0.024351298809051514,
-0.08860122412443161,
0.04215617850422859,
0.007483248133212328,
0.019840188324451447,
-0.037364307790994644,
0.053045883774757385,
0.008924259804189205,
-0.006031080149114132,
0.0035961633548140526,
0.005479416809976101,
0.0319763720035553,
-0.02401946857571602,
0.015582248568534851,
-0.010409241542220116,
0.04733189940452576,
-0.009104813449084759,
-0.006390995811671019,
0.008648484013974667,
-0.009316402487456799,
0.009327834472060204,
0.014028162695467472,
-0.001041000708937645,
0.04337345063686371,
0.0353672169148922,
0.0709121897816658,
0.010324621573090553,
-0.019099470227956772,
-0.04005590081214905,
-0.06349726766347885,
0.0027153994888067245,
0.030788833275437355,
0.06423826515674591,
0.02026371844112873,
0.015799803659319878,
0.04114655405282974,
0.033185213804244995,
0.023691385984420776,
-0.014016789384186268,
-0.06994321197271347,
0.00489560654386878,
0.009906419552862644,
-0.02974841557443142,
-0.01917809247970581,
-0.030376601964235306,
-0.0005721720517612994,
-0.033777620643377304,
-0.06399881094694138,
-0.011574204079806805,
0.006826120428740978,
-0.047825612127780914,
0.014307858422398567,
-0.02490447647869587,
-0.03934536501765251,
-0.04198808968067169,
0.03006884828209877,
0.04284219443798065,
-0.06197535991668701,
0.01063250470906496,
0.042462583631277084,
-0.04568050429224968,
0.01773298904299736,
-0.0267358236014843,
0.031046027317643166,
0.020933017134666443,
0.006791180931031704,
0.003390898695215583,
0.006564867217093706,
-0.02563834749162197,
-0.0026763645000755787,
0.052022237330675125,
0.03576525300741196,
0.00770198879763484,
-0.018200624734163284,
-0.007626209873706102,
-0.01877504773437977,
-0.009788163006305695,
0.0004466540995053947,
0.08151581883430481,
-0.0038678189739584923,
0.007332592271268368,
0.03663572296500206,
0.02275669202208519,
-0.019775185734033585,
-0.003366439836099744,
0.007945574820041656,
0.018753323704004288,
-0.026662392541766167,
-0.06482374668121338,
-0.0009734096238389611,
-0.0033388761803507805,
0.00833629909902811,
0.050918497145175934,
-0.006451769731938839,
-0.015360613353550434,
0.0022911576088517904,
-0.014168293215334415,
-0.0066890413872897625,
-0.031480442732572556,
-0.007992874830961227,
-0.011679054237902164,
0.052886251360177994,
-0.022329945117235184,
-0.0003034875262528658,
0.005538128782063723,
0.028514496982097626,
0.006856535095721483,
0.014192286878824234,
-0.028825508430600166,
-0.06452744454145432,
-0.001518488279543817,
0.055797554552555084,
0.04641095548868179,
0.0066094971261918545,
-0.001462490065023303,
-0.026088885962963104,
0.003452843287959695,
0.005365204066038132,
-0.002047101268544793,
0.014914575032889843,
-0.015474776737391949,
-0.0027735289186239243,
-0.038428500294685364,
0.0005627555656246841,
-0.03118179179728031,
0.028670229017734528,
-0.027863459661602974,
0.0003412558580748737,
-0.03404168412089348,
-0.02227536030113697,
-0.01462837215512991,
-0.0023965006694197655,
0.05288612097501755,
0.06064506992697716,
-0.003587582381442189,
0.04496346041560173,
0.0548192523419857,
-0.0161664430052042,
-0.027480095624923706,
-0.09623947739601135,
0.008825160562992096,
0.014070930890738964,
0.014324797317385674,
0.03923037275671959,
-0.0416385643184185,
-0.028378723189234734,
0.02071176841855049,
-0.018802912905812263,
-0.01320435106754303,
-0.051956500858068466,
-0.060231007635593414,
0.03980392962694168,
-0.005489607807248831,
0.01246633194386959,
0.06601814925670624,
0.008751162327826023,
-0.0479251891374588,
0.0008525318698957562,
-0.04562082514166832,
0.014390675351023674,
-0.027439497411251068,
0.022053135558962822,
-0.04577910900115967,
0.02533782459795475,
0.005827693268656731,
0.05276961624622345,
-0.005956900306046009,
0.0042654299177229404,
-0.020534226670861244,
-0.041973959654569626,
-0.027895497158169746,
-0.029409805312752724,
-0.025496622547507286,
0.014713198877871037,
-0.03216808661818504,
0.016319219022989273,
0.01544900145381689,
-0.01925056055188179,
0.017405947670340538,
0.007146432530134916,
-0.01249286625534296,
0.04257773980498314,
-0.010539471171796322,
0.011255498044192791,
0.005125622730702162,
-0.026570819318294525,
-0.012772753834724426,
-0.04453627020120621,
0.04954444244503975,
0.006071886979043484,
-0.0224751103669405,
0.02382943220436573,
-0.05956675484776497,
0.007477974984794855,
0.02414393424987793,
0.01122309174388647,
0.014992623589932919,
-0.04178648442029953,
0.049804359674453735,
0.027828048914670944,
0.018957672640681267,
-0.08020702749490738,
-0.03603516146540642,
0.0072021326050162315,
-0.006231612525880337,
-0.05164915323257446,
-0.03139026090502739,
-0.032114140689373016,
-0.03204978257417679,
-0.020321834832429886,
0.055562980473041534,
0.021314719691872597,
-0.004788885358721018,
0.026213575154542923,
0.05703575536608696,
0.04992014169692993,
0.05131341516971588,
0.015684280544519424,
-0.03943117335438728,
0.014190757647156715,
0.002936133649200201,
-0.017841409891843796,
0.03324916213750839,
0.03430257737636566,
-0.019374612718820572,
-0.006808483973145485,
0.00006012068115524016,
0.01496211253106594,
0.05664384365081787,
0.015554933808743954,
-0.014627992175519466,
0.013569328933954239,
0.04463732987642288,
-0.029274629428982735,
-0.03298170492053032,
0.01600808836519718,
0.03783884271979332,
0.038447305560112,
-0.013146008364856243,
0.00007025870581855997,
-0.023488027974963188,
-0.015679936856031418,
0.019530989229679108,
0.012962022796273232,
0.0019103579688817263,
0.02333115227520466,
0.056147344410419464,
-0.036175914108753204,
0.015803683549165726,
0.008106772787868977,
-0.0053108567371964455,
0.0277276448905468,
-0.0165146142244339,
-0.004265033174306154,
-0.039599739015102386,
-0.0007820168975740671,
-0.023495104163885117,
0.00841018557548523,
-0.04346241056919098,
0.012254550121724606,
0.06743219494819641,
-0.004763546399772167,
0.04137640818953514,
0.003088707569986582,
-0.013414506800472736,
0.009143814444541931,
-0.021074943244457245,
-0.0318048931658268,
0.03524554520845413,
-0.01766072027385235,
0.008214866742491722,
-0.026491597294807434,
-0.00837643537670374,
0.02721170336008072,
0.056115202605724335,
-0.03191602602601051,
0.05702952295541763,
0.037896186113357544,
0.010035212151706219,
0.0125890439376235,
-0.0011845682747662067,
-0.025416599586606026,
0.05005510523915291,
-0.018739767372608185,
0.026944158598780632,
-0.02236040309071541,
-0.0072962213307619095,
0.06465944647789001,
0.0005399090587161481,
-0.0021443876903504133,
-0.017983943223953247,
-0.07362430542707443,
-0.0311911441385746,
-0.004336978774517775,
-0.014439844526350498,
0.05589989945292473,
0.014360720291733742,
-0.014266490004956722,
0.019833391532301903,
0.0014619013527408242,
-0.02864893339574337,
0.026120129972696304,
-0.025539088994264603,
-0.01420800294727087,
-0.02083776891231537,
-0.038503196090459824,
0.022974343970417976,
-0.010157902725040913,
-0.030448181554675102,
0.014082618057727814,
-0.04268166422843933,
0.019027702510356903,
0.008565619587898254,
0.03562284633517265,
0.006828781217336655,
0.06221844628453255,
0.004255404230207205,
0.011793329380452633,
-0.03750858083367348,
0.017776496708393097,
0.1292540729045868,
0.013287780806422234,
0.02142386883497238,
-0.061859626322984695,
-0.030609959736466408,
-0.012985452078282833,
0.013377681374549866,
-0.022040661424398422,
0.018443766981363297,
-0.06532415747642517,
0.05821554362773895,
0.027207886800169945,
0.07754767686128616,
0.0024724991526454687,
0.005166781600564718,
0.02796879969537258,
-0.02061682939529419,
-0.019249556586146355,
0.03893688693642616,
-0.003812390612438321,
-0.017609532922506332,
0.006834584753960371,
-0.04797990247607231,
-0.002018020721152425,
-0.02840973250567913,
0.00863634143024683,
-0.013116614893078804,
-0.03555981069803238,
0.033054132014513016,
0.01800244115293026,
-0.06425892561674118,
-0.01029097381979227,
0.021540015935897827,
-0.015805287286639214,
-0.023212818428874016,
-0.018761105835437775,
0.03454199805855751,
-0.029874438419938087,
0.04108653590083122,
0.03277447074651718,
0.025840990245342255,
-0.00991736724972725,
0.04384845867753029,
0.01230711955577135,
-0.047581009566783905,
-0.001789818168617785,
-0.016218330711126328,
-0.000954007264226675,
-0.010311651043593884,
-0.03198637440800667,
0.010159958153963089,
-0.02769405208528042,
0.009543721564114094,
-0.041405193507671356,
-0.008450102061033249,
-0.026373382657766342,
0.024687042459845543,
0.00055611168500036,
-0.008222891017794609,
-0.0351053811609745,
0.019503740593791008,
-0.0004803327319677919,
-0.0033952922094613314,
-0.0001925957330968231,
-0.00336442980915308,
0.0068196868523955345,
-0.030457936227321625,
0.03992767259478569,
-0.008030863478779793,
-0.03476519510149956,
-0.026265569031238556,
-0.029641136527061462,
-0.03356325626373291,
-0.02322908118367195,
-0.004670605529099703,
0.018439944833517075,
0.018611449748277664,
0.019389066845178604,
0.007427953649312258,
0.017392488196492195,
-0.07817701995372772,
-0.013412272557616234,
-0.008085421286523342,
-0.010268940590322018,
-0.004047302529215813,
-0.0005538846598938107,
0.040787965059280396,
0.03270898386836052,
-0.015084363520145416,
-0.015512045472860336,
0.009973682463169098,
0.006417531054466963,
0.023210717365145683,
-0.05294603109359741,
-0.04777929559350014,
0.017556019127368927,
-0.03776479884982109,
-0.001749043702147901,
0.029353739693760872,
-0.0037587874103337526,
-0.0013451235136017203,
-0.023039573803544044,
0.006715024821460247,
0.004787876270711422,
-0.03121999278664589,
0.009362403303384781,
0.014344656839966774,
-0.004107346758246422,
-0.012215320020914078,
0.023045307025313377,
-0.017216568812727928,
-0.014451159164309502,
-0.048315759748220444,
-0.0338052399456501,
-0.00483328104019165,
-0.008731579408049583,
0.05750930309295654,
-0.028100894764065742,
0.023057539016008377,
-0.02808583714067936,
0.01475317683070898,
-0.061447009444236755,
-0.00004399723184178583,
-0.041724756360054016,
-0.012021955102682114,
0.039420466870069504,
0.03509392589330673,
-0.03473024442791939,
0.047239746898412704,
-0.06646570563316345,
0.0014591285726055503,
0.05630951002240181,
0.02235746942460537,
-0.019555509090423584,
-0.019996773451566696,
0.023796608671545982,
-0.019037052989006042,
0.053756460547447205,
0.0014373759040609002,
-0.017801465466618538,
0.0480610728263855,
-0.006975839845836163,
-0.022286158055067062,
-0.0017111171036958694,
-0.017493056133389473,
0.02305259369313717,
-0.0008877141517587006,
0.02015131525695324,
-0.0034997814800590277,
0.056861843913793564,
-0.017439041286706924,
-0.029294967651367188,
-0.007892667315900326,
-0.0664004385471344,
0.0035247220657765865,
-0.009066484868526459,
0.016199739649891853,
-0.03911273553967476,
-0.002486464334651828,
0.056076858192682266,
0.029807787388563156,
-0.0033092419616878033,
-0.017819829285144806,
-0.024244293570518494,
-0.005390993785113096,
0.0052222260273993015,
0.04261229559779167,
0.006174904759973288,
0.0062674772925674915,
0.04164969176054001,
0.00392632931470871,
0.028720663860440254,
0.022969108074903488,
0.028087997809052467,
-0.11381270736455917,
-0.01878937892615795,
-0.016639469191432,
0.03374670445919037,
0.004187007434666157,
-0.058091942220926285,
0.026404866948723793,
-0.015553820878267288,
-0.0509943813085556,
0.036575235426425934,
-0.010008181445300579,
-0.012081543914973736,
-0.052217479795217514,
0.022393977269530296,
-0.00657964963465929,
0.02427581697702408,
0.03402950242161751,
0.057475537061691284,
-0.027089901268482208,
0.020401161164045334,
-0.021226709708571434,
-0.020786352455615997,
-0.04176560044288635,
0.02707524783909321,
0.012012514285743237,
0.008556010201573372,
0.07264646142721176,
-0.012220078147947788,
0.02422330342233181,
0.0054739294573664665,
-0.004323586821556091,
-0.00885398406535387,
0.03902800753712654,
0.00817223358899355,
0.017394041642546654,
0.06926217675209045,
0.013783890753984451,
-0.012399207800626755,
-0.023293891921639442,
0.005262791644781828,
0.029233237728476524,
0.021574873477220535,
0.007991082966327667,
-0.0005854583578184247,
0.010878806002438068,
-0.019338589161634445,
0.006197075359523296,
0.031994692981243134,
-0.041451312601566315,
-0.033222682774066925,
0.017213307321071625,
0.016033394262194633,
0.03912489116191864,
-0.01192739699035883,
0.027732815593481064,
-0.05498479679226875,
-0.023426927626132965,
0.029918860644102097,
-0.003960355184972286,
0.03847311809659004,
0.015391673892736435,
0.028209997341036797,
0.028437895700335503,
0.015563135035336018,
0.014766521751880646,
0.020883072167634964,
-0.0197587963193655,
0.01174884382635355,
0.0016254099318757653,
-0.002149050822481513,
-0.02031695283949375,
-0.05630521476268768,
-0.03798411041498184,
0.042219024151563644,
0.0032376954331994057,
0.04430652782320976,
-0.013000630773603916,
-0.049967437982559204,
-0.005921428091824055,
-0.04157068580389023,
0.012921992689371109,
-0.0031317458488047123,
0.007550832349807024,
-0.03970244899392128,
-0.04353383183479309,
0.03139069303870201,
0.05966183915734291,
0.0792521983385086,
-0.00034865018096752465,
-0.015326176770031452,
0.048514995723962784,
-0.04533767327666283,
0.039747174829244614,
-0.06610145419836044,
0.0004234701918903738,
-0.02303512766957283,
-0.036416128277778625,
0.01694459840655327,
-0.008961695246398449,
-0.05623470991849899,
0.021773425862193108,
0.05868513137102127,
-0.020917983725667,
-0.015728387981653214,
-0.011522594839334488,
-0.03642614558339119,
0.06516053527593613,
0.04308218136429787,
-0.0023107235319912434,
0.08045294135808945,
-0.013309270143508911,
0.018357830122113228,
0.019223647192120552,
-0.02854161150753498,
-0.03289593756198883,
0.00926171988248825,
-0.02571806311607361,
-0.005423891358077526,
0.0027470579370856285,
-0.03914349898695946,
0.030045155435800552,
-0.05616801977157593,
-0.009039540775120258,
0.02728370763361454,
-0.06354714184999466,
-0.027148237451910973,
0.041459303349256516,
0.009139140136539936,
0.033537548035383224,
-0.03482389077544212,
0.04604673013091087,
-0.04747840389609337,
-0.013055936433374882,
-0.0349959060549736,
0.048172011971473694,
0.01449947152286768,
-0.02705506607890129,
0.02584277279675007,
0.019305571913719177,
0.01164877600967884,
-0.010167879052460194,
0.02643534354865551,
0.03291893005371094,
-0.03083925135433674,
-0.01699763536453247,
0.06571716070175171,
-0.008288227021694183,
0.009381940588355064,
0.02601771242916584,
0.00587513716891408,
0.10521119087934494,
0.0012467717751860619,
0.0018047899939119816,
-0.0348043218255043,
0.000035128829040331766,
-0.00813954696059227,
0.019587598741054535,
0.019604038447141647,
0.040132004767656326,
-0.0205928236246109,
0.0008098669932223856,
-0.01012875884771347,
-0.0030703002121299505,
0.004421779420226812,
-0.04902069643139839,
0.002730662003159523,
0.00047160551184788346,
-0.011371836997568607,
0.009765821509063244,
0.011061135679483414,
-0.004817812237888575,
0.0323878675699234,
0.025427818298339844,
0.04838085547089577,
-0.01007634773850441,
0.044970352202653885,
-0.019055604934692383,
0.0015136095462366939,
0.03371936455368996,
-0.07036425173282623,
0.024440305307507515,
-0.03955154865980148,
0.036803148686885834,
-0.004542212001979351,
-0.027195464819669724
] |
<p>I read in several papers that for a Harmonic Oscillator Hamiltonian in the time dependent Schrödinger equation a Gaussian wave packet remains Gaussian.</p>
<p>Unfortunately I could not find any proof for this statement and trying to verify it myself I did not succeed. If I make a general ansatz with a spherically symmetric Gaussian wave packet with time dependent width and time and space dependent phase
$$ \psi(t,\vec x) = (\pi a(t)^2)^{-3/4} \exp\left(-\frac{x^2}{2 a(t)^2} + i \phi(t,\vec x)\right)$$
and insert it into the Schrödinger equation
$$ i \dot{\psi}(t,\vec x) = -\frac{1}{2m} \Delta\psi(t,\vec x) + \frac{k}{2} x^2 \psi(t,\vec x) $$
I get relatively complicated differential equations involving first time derivatives of a and $\phi$ as well as first and second order spatial derivatives of $\phi$. I failed to solve those equations or even show that a solution exists.</p>
<p>Is there an easy way to show this?</p>
<p>Is there any reference where this is shown?</p>
<p>Which are the solutions for $a(t)$ and $\phi(t,\vec x)$ for a Gaussian (given initial conditions $a(0) = \sigma$ and $\phi(0,\vec x)=0$)?</p>
| 9,410 |
[
0.0016040646005421877,
-0.02328091487288475,
0.02164001762866974,
0.004262147471308708,
0.03223671019077301,
-0.028876235708594322,
-0.06517406553030014,
-0.05403261259198189,
0.0031266757287085056,
-0.03454241529107094,
0.019210459664463997,
0.02913866750895977,
0.04739253968000412,
0.007240453269332647,
0.026617709547281265,
0.011453328654170036,
-0.012629574164748192,
-0.033836811780929565,
-0.03662411496043205,
-0.026179051026701927,
-0.0020530589390546083,
0.03775912523269653,
-0.004541686270385981,
-0.022445375099778175,
-0.03505924716591835,
0.01811305619776249,
0.0107211759313941,
0.01710743084549904,
-0.011480160988867283,
0.08096298575401306,
-0.015987038612365723,
-0.011543751694262028,
0.004396274220198393,
0.05788497254252434,
0.03438311815261841,
0.007972913794219494,
-0.051139626652002335,
-0.05188702046871185,
0.011883128434419632,
0.008696330711245537,
-0.031755801290273666,
-0.02398708090186119,
0.005053036380559206,
0.06332515180110931,
-0.0011944855796173215,
0.0032903074752539396,
0.011103270575404167,
-0.011284667067229748,
0.055457498878240585,
-0.05151790753006935,
0.06997831165790558,
-0.004175225272774696,
0.035274628549814224,
-0.007088006474077702,
0.021295689046382904,
-0.005537198856472969,
0.060677725821733475,
0.06454005837440491,
-0.019768759608268738,
-0.05020459368824959,
0.028797464445233345,
-0.02318280190229416,
0.015119400806725025,
-0.021324776113033295,
-0.03350489214062691,
-0.0322597399353981,
-0.007952718064188957,
-0.05337222293019295,
0.014166738837957382,
-0.03769627586007118,
0.014653002843260765,
0.00021442837896756828,
0.035023901611566544,
-0.027856478467583656,
0.0035369480028748512,
-0.003138544037938118,
-0.00605309521779418,
0.00682087941095233,
0.03597927466034889,
0.0022203149273991585,
0.0028706835582852364,
0.02006424032151699,
-0.012506941333413124,
0.010406400077044964,
-0.02677794359624386,
0.020960209891200066,
0.07794623076915741,
-0.005464325193315744,
0.03113229013979435,
0.05907769873738289,
-0.020145803689956665,
0.04160027205944061,
0.05409730225801468,
-0.03672876954078674,
-0.017942756414413452,
0.03904007375240326,
0.016398746520280838,
0.04449533298611641,
0.008563624694943428,
-0.021273449063301086,
0.009452019818127155,
-0.038887880742549896,
0.02008442021906376,
0.08891751617193222,
-0.021158039569854736,
-0.009664718061685562,
-0.03742145746946335,
0.020235834643244743,
-0.021712344139814377,
-0.044539544731378555,
-0.0645982101559639,
0.012088535353541374,
0.010298781096935272,
0.00765548599883914,
0.00491247046738863,
-0.022109413519501686,
-0.005101144313812256,
-0.01095511857420206,
0.027808886021375656,
0.09583871066570282,
0.04719967022538185,
-0.041054755449295044,
0.02229374833405018,
-0.022480687126517296,
-0.06040171533823013,
0.0022969155106693506,
0.03289017081260681,
0.01612107641994953,
-0.04204162210226059,
0.01677102968096733,
0.0010336979757994413,
-0.012228862382471561,
0.01746869832277298,
-0.006527825724333525,
0.013672148808836937,
-0.04512555152177811,
-0.1225505843758583,
-0.04916207119822502,
0.02635497786104679,
-0.017718251794576645,
-0.004796265624463558,
-0.0948377475142479,
0.0021940376609563828,
0.026402512565255165,
0.07482848316431046,
-0.0373530387878418,
-0.0004884775262326002,
0.011229272000491619,
0.06998380273580551,
0.03198866918683052,
-0.020563747733831406,
-0.014688354916870594,
0.0020050869788974524,
-0.039929892867803574,
-0.008069846779108047,
-0.04748111218214035,
0.028214868158102036,
0.018465356901288033,
0.012629513628780842,
-0.01260763593018055,
0.09489976614713669,
-0.008056635968387127,
-0.0034180181100964546,
-0.009642626158893108,
0.025633016601204872,
-0.03603934496641159,
0.09791360795497894,
0.02061581052839756,
-0.006987792905420065,
0.00717204762622714,
0.009541261941194534,
0.02817310020327568,
-0.020548710599541664,
0.013059882447123528,
-0.004566963762044907,
-0.050849929451942444,
-0.014057706110179424,
-0.01241666916757822,
-0.005138216074556112,
0.018934862688183784,
0.0033370794262737036,
-0.011222325265407562,
-0.026398133486509323,
0.009134093299508095,
-0.0007180693792179227,
0.05704842507839203,
0.02255096659064293,
0.035844795405864716,
-0.028117535635828972,
-0.0654122456908226,
0.0063598002307116985,
-0.06994355469942093,
0.058238547295331955,
0.016895465552806854,
-0.03552278131246567,
0.07769834995269775,
0.027726316824555397,
0.002734775422140956,
0.008114227093756199,
-0.058489035815000534,
-0.005226916633546352,
0.02339295856654644,
-0.009187980554997921,
-0.04809432104229927,
0.04019962623715401,
0.04177150875329971,
0.02792021818459034,
-0.0005850104498676956,
0.03668824955821037,
-0.0022859738674014807,
-0.02146976813673973,
-0.0076898797415196896,
-0.0004158410883974284,
0.041524577885866165,
-0.005924738943576813,
-0.014180049300193787,
-0.032818280160427094,
0.00890705082565546,
-0.008842263370752335,
0.03623455762863159,
-0.060843538492918015,
0.055950962007045746,
0.08103813976049423,
-0.0003695828199852258,
-0.009548753499984741,
0.050063058733940125,
0.015388713218271732,
0.02112971991300583,
-0.010149871930480003,
-0.04104659706354141,
-0.028462514281272888,
0.013453608378767967,
0.01945706643164158,
0.04194110631942749,
-0.026593660935759544,
-0.003040920477360487,
0.013912543654441833,
0.04004114866256714,
0.06495340913534164,
0.0281812883913517,
-0.0015259619103744626,
-0.046690259128808975,
0.03273643180727959,
-0.0005420612287707627,
-0.011980275623500347,
0.009429272264242172,
0.055335503071546555,
-0.014711219817399979,
-0.001699317479506135,
0.007432259619235992,
-0.002775606233626604,
0.009591014124453068,
-0.03345518186688423,
-0.01670220121741295,
0.0014065159484744072,
-0.03130974993109703,
0.023622719570994377,
-0.00882211234420538,
0.027410537004470825,
0.021850289776921272,
-0.014732523821294308,
-0.01186019740998745,
-0.039664048701524734,
-0.013528553768992424,
0.03585601598024368,
-0.050663210451602936,
-0.03909623250365257,
-0.010562588460743427,
0.01036881748586893,
-0.036550458520650864,
-0.006490163970738649,
0.00887005403637886,
0.02214258909225464,
-0.025965161621570587,
-0.0038801783230155706,
0.027826031669974327,
0.027476489543914795,
0.023031800985336304,
-0.017802830785512924,
-0.028783705085515976,
0.028163868933916092,
-0.008445117622613907,
0.02076803334057331,
0.023826630786061287,
-0.02665170095860958,
0.04714171215891838,
-0.022709930315613747,
-0.021150236949324608,
0.05749111622571945,
-0.024744734168052673,
0.010256286710500717,
-0.020113220438361168,
-0.006211380939930677,
-0.051619041711091995,
0.016964327543973923,
-0.018162952736020088,
-0.01319816242903471,
-0.0441812239587307,
0.031460780650377274,
0.01307020802050829,
-0.015605472028255463,
-0.019387515261769295,
0.05599408224225044,
0.009627890773117542,
-0.026718614622950554,
-0.009994424879550934,
-0.009721309877932072,
0.03794682025909424,
-0.029035020619630814,
0.051452070474624634,
0.01916465535759926,
-0.01679087057709694,
-0.012525547295808792,
-0.0411597304046154,
-0.03407192975282669,
0.039802320301532745,
0.0017866023117676377,
0.039299700409173965,
-0.011495607905089855,
-0.011889997869729996,
0.07672029733657837,
0.03805406764149666,
-0.005319308955222368,
-0.0018367230659350753,
0.02086675353348255,
-0.008451253175735474,
0.02067403681576252,
-0.001041076728142798,
0.009387882426381111,
-0.021514320746064186,
0.057915039360523224,
0.013177100569009781,
0.024532346054911613,
0.03347663953900337,
0.028867339715361595,
-0.020884642377495766,
0.016723860055208206,
-0.013826451264321804,
0.024561172351241112,
0.03971334546804428,
0.013373092748224735,
-0.005231063347309828,
0.00851588323712349,
0.019898420199751854,
-0.0007701982976868749,
0.0060173687525093555,
-0.049859095364809036,
0.041655026376247406,
-0.014149640686810017,
-0.0089057432487607,
-0.018062274903059006,
0.024498671293258667,
0.013504116795957088,
0.0050445860251784325,
-0.023141732439398766,
0.027036353945732117,
0.022396596148610115,
-0.013601921498775482,
0.027917414903640747,
0.04371294379234314,
-0.00008213205001084134,
-0.00822141021490097,
-0.035366978496313095,
0.009730442427098751,
-0.00843261182308197,
0.05745093896985054,
-0.024913448840379715,
-0.06554540246725082,
0.022637566551566124,
0.014583922922611237,
0.015368593856692314,
-0.028327740728855133,
-0.03531445190310478,
-0.013303159736096859,
-0.055102989077568054,
0.0338185578584671,
-0.013350746594369411,
0.03952304273843765,
0.023286709561944008,
0.06921615451574326,
0.01801265962421894,
0.04308788850903511,
0.025655942037701607,
0.02757054753601551,
-0.025748424232006073,
0.001475493423640728,
-0.026919914409518242,
-0.0006215519388206303,
0.0033917429391294718,
-0.007840020582079887,
0.004629401955753565,
-0.0075543662533164024,
-0.01742628589272499,
-0.007057843264192343,
-0.003141935681924224,
-0.0457727275788784,
-0.01118965819478035,
-0.019343256950378418,
-0.04708929732441902,
-0.03065677545964718,
0.02249966561794281,
-0.005585139151662588,
0.021631067618727684,
0.01693781465291977,
0.07132947444915771,
-0.02356916107237339,
0.023662880063056946,
-0.03678969666361809,
0.0004636442754417658,
0.007937404327094555,
0.014291836880147457,
0.06762083619832993,
0.017541782930493355,
0.0019805466290563345,
-0.0024836149532347918,
-0.0002945421147160232,
0.05902707576751709,
-0.024548731744289398,
0.009763700887560844,
0.021757226437330246,
-0.02516310289502144,
-0.01796059124171734,
0.0017948220483958721,
0.04273119196295738,
0.032954420894384384,
-0.007235571276396513,
0.008714154362678528,
-0.0176527239382267,
0.003555757226422429,
0.06779950857162476,
-0.005949367303401232,
0.005438884720206261,
0.001563053927384317,
-0.027115844190120697,
-0.013646955601871014,
-0.023951372131705284,
-0.009594927541911602,
-0.005095486994832754,
-0.01268266886472702,
0.001368759898468852,
0.009264379739761353,
-0.009714947082102299,
0.038939252495765686,
0.02425612509250641,
-0.052210379391908646,
-0.032005585730075836,
0.0025513586588203907,
-0.0022183202672749758,
0.00013852135452907532,
-0.009784365072846413,
0.02371710166335106,
0.026601744815707207,
0.017901761457324028,
0.028913483023643494,
-0.06111593544483185,
-0.033153973519802094,
0.012652019970119,
0.014793268404901028,
0.041856080293655396,
-0.016507145017385483,
-0.03528550639748573,
-0.016456222161650658,
0.03350979462265968,
0.016533799469470978,
0.05198197066783905,
0.012052427977323532,
-0.0297575443983078,
-0.01800432987511158,
-0.05210326611995697,
-0.0153083186596632,
-0.016517648473381996,
-0.03435327485203743,
-0.015552946366369724,
-0.029806658625602722,
-0.019215932115912437,
-0.017816342413425446,
-0.002265150658786297,
0.0011615401599556208,
0.08822726458311081,
0.012084217742085457,
-0.03179188817739487,
-0.015091092325747013,
0.019735019654035568,
-0.031503718346357346,
-0.09014937281608582,
-0.005473497323691845,
-0.00850464217364788,
-0.01754186674952507,
0.049240246415138245,
-0.05707412213087082,
-0.015900377184152603,
0.03132147341966629,
0.04210266098380089,
-0.057990662753582,
0.028269875794649124,
-0.028199758380651474,
0.017083408311009407,
-0.007315751165151596,
0.015624658204615116,
0.042717862874269485,
0.07040750235319138,
0.0008233372354879975,
-0.0346498116850853,
-0.014098543673753738,
0.06075601279735565,
-0.027831468731164932,
0.00676692696288228,
-0.03152616322040558,
0.017461586743593216,
-0.03504987061023712,
0.056275881826877594,
-0.011496063321828842,
0.011432286351919174,
0.022592993453145027,
-0.0300824586302042,
0.025760527700185776,
0.012190630659461021,
-0.02734445594251156,
0.04200465977191925,
-0.012035621330142021,
0.019234664738178253,
0.00549061456695199,
-0.01808825694024563,
-0.03022265061736107,
-0.018450584262609482,
-0.009686250239610672,
0.04616702347993851,
-0.001759509788826108,
0.049394018948078156,
-0.0270586758852005,
-0.02204137109220028,
-0.0029900867957621813,
-0.07032560557126999,
0.026644740253686905,
0.00928665790706873,
-0.005004727281630039,
0.028481734916567802,
-0.066627137362957,
-0.02003263309597969,
0.010721636936068535,
0.0025293882936239243,
0.02772929146885872,
-0.029024630784988403,
-0.003910150844603777,
0.020723814144730568,
0.03614618629217148,
-0.10565809905529022,
-0.03896065428853035,
-0.01301162876188755,
-0.01191677711904049,
-0.028780654072761536,
-0.03375929221510887,
0.027955664321780205,
-0.041962116956710815,
-0.018635952845215797,
0.016574913635849953,
0.021992100402712822,
0.013951276428997517,
-0.016030894592404366,
0.010113921016454697,
0.03985470160841942,
0.01926679164171219,
-0.012073799967765808,
0.00681816041469574,
0.005513614509254694,
-0.023779606446623802,
-0.005763526540249586,
0.02345666103065014,
0.06091814860701561,
-0.012971311807632446,
-0.020632391795516014,
-0.0017713025445118546,
-0.03330821916460991,
0.026016179472208023,
0.00985571276396513,
-0.06547896564006805,
0.015090257860720158,
0.01857537031173706,
0.024293676018714905,
-0.02297423966228962,
-0.011752093210816383,
-0.043568797409534454,
0.014810924418270588,
0.02427494153380394,
-0.02361074648797512,
-0.04368256777524948,
-0.030501337721943855,
0.021472429856657982,
-0.01031976193189621,
-0.031579989939928055,
0.029896780848503113,
0.08246000111103058,
0.007786693517118692,
0.028001870959997177,
0.026344485580921173,
0.03040176071226597,
0.009240439161658287,
-0.010654313489794731,
-0.0067339930683374405,
-0.0012813596986234188,
-0.004076262935996056,
-0.03104541264474392,
-0.04004431515932083,
-0.024343501776456833,
0.027347397059202194,
0.05850415304303169,
-0.02926662005484104,
0.06230779364705086,
0.03171628713607788,
0.01887006126344204,
-0.027110695838928223,
-0.011304977349936962,
-0.005297988653182983,
-0.0015920851146802306,
-0.021455513313412666,
0.04307788237929344,
-0.033202748745679855,
0.0030780204106122255,
0.040738724172115326,
0.02985203266143799,
-0.030833963304758072,
0.00639647850766778,
0.004058288875967264,
0.005012383684515953,
0.020881593227386475,
-0.0019157235510647297,
-0.017979806289076805,
0.02411160059273243,
-0.006264416966587305,
0.053620949387550354,
-0.009841524064540863,
-0.038456983864307404,
0.004309695679694414,
0.012191024608910084,
0.02028137631714344,
-0.01806020550429821,
-0.001955862622708082,
-0.04451439529657364,
0.03094557486474514,
0.0077303145080804825,
-0.02221105247735977,
0.02494070492684841,
0.04774058237671852,
0.025477316230535507,
0.008448404259979725,
0.024914491921663284,
-0.02035122737288475,
-0.052568573504686356,
-0.02525433525443077,
-0.045760564506053925,
-0.05964000150561333,
0.01967138797044754,
0.02383621223270893,
-0.04987030103802681,
0.02200128510594368,
-0.028591236099600792,
0.02690974622964859,
0.019507993012666702,
0.0106517868116498,
0.0076241265051066875,
0.08876391500234604,
0.00622254004701972,
0.008064712397754192,
-0.0006331208860501647,
0.0316232331097126,
0.09032601118087769,
0.063469797372818,
0.02804630994796753,
-0.06269542127847672,
0.017568403854966164,
-0.030163321644067764,
0.003138747299090028,
-0.04759739339351654,
0.025438394397497177,
-0.023942619562149048,
-0.026612164452672005,
-0.035975344479084015,
0.05839567631483078,
0.011348827742040157,
-0.000009841843166213948,
0.04504138603806496,
-0.059832170605659485,
-0.046916164457798004,
0.015507597476243973,
-0.014598993584513664,
0.02388029173016548,
0.00936186220496893,
-0.021535726264119148,
0.04664875566959381,
-0.043701499700546265,
-0.008983292616903782,
-0.034447427839040756,
-0.05183282494544983,
0.013815682381391525,
-0.023046310991048813,
-0.028563186526298523,
0.014348055236041546,
0.01504732295870781,
-0.012758912518620491,
-0.03033733367919922,
0.01408355962485075,
0.023396236822009087,
-0.027184056118130684,
0.028124017640948296,
0.03984437137842178,
0.011508770287036896,
0.017522994428873062,
0.02542969025671482,
0.02112211100757122,
-0.022008206695318222,
-0.020646044984459877,
-0.019748011603951454,
0.08105876296758652,
-0.02832059934735298,
-0.025652043521404266,
0.006500698626041412,
-0.013896829448640347,
-0.016075920313596725,
-0.07761544734239578,
-0.026418762281537056,
-0.021043267101049423,
0.045613329857587814,
-0.00704594049602747,
0.005434585269540548,
-0.02540932409465313,
-0.011330398730933666,
0.010710448026657104,
0.026604842394590378,
-0.017963213846087456,
-0.0012310458114370704,
0.011687684804201126,
-0.033119626343250275,
0.013567370362579823,
-0.017922883853316307,
-0.02801676094532013,
-0.0022857999429106712,
-0.024595918133854866,
-0.06407906115055084,
-0.056924235075712204,
0.03856425732374191,
0.00026885440456680954,
0.03386376425623894,
-0.004895532038062811,
-0.009284292347729206,
-0.019852640107274055,
-0.090772844851017,
-0.0078738359734416,
-0.020094361156225204,
-0.0062990086153149605,
0.03435969352722168,
-0.008135082200169563,
0.04412449523806572,
0.03519055247306824,
-0.026556408032774925,
0.008637992665171623,
-0.004983705002814531,
0.03311523050069809,
0.028284383937716484,
-0.02477280981838703,
-0.0190925020724535,
0.03624498471617699,
-0.006242513190954924,
0.00859297439455986,
-0.021571988239884377,
0.011486922390758991,
0.01121568400412798,
0.030729176476597786,
-0.002433023415505886,
0.04076889529824257,
-0.03840463608503342,
-0.03891029208898544,
0.016109392046928406,
-0.004546085838228464,
-0.0022332400549203157,
0.04004597291350365,
0.056929152458906174,
-0.02887795679271221,
-0.03450673818588257,
-0.029707424342632294,
0.013920999132096767,
0.010745780542492867,
-0.030716724693775177,
-0.026295144110918045,
0.007666889578104019,
-0.0057136365212500095,
0.008872007019817829,
-0.026190945878624916,
-0.006992649752646685,
-0.04076991230249405,
0.007661501411348581,
-0.014322318136692047,
-0.0012158943573012948,
0.009730859659612179,
0.022450421005487442,
-0.010872741229832172,
-0.03578450530767441,
0.04312201961874962,
0.034145504236221313,
-0.004461236298084259,
0.04086519405245781,
0.02047831192612648,
0.012217141687870026,
0.04211781919002533,
0.015458147041499615,
-0.03216679021716118,
-0.006139346864074469,
-0.06619720160961151,
-0.012531994841992855,
0.023230191320180893,
-0.0223735049366951,
0.010422739200294018,
0.0011695013381540775,
-0.015802495181560516,
0.01045320089906454,
0.04380733147263527,
0.006239029578864574,
0.007731636520475149,
0.0004912563017569482,
-0.04469437524676323,
0.003066928591579199,
-0.02116459794342518,
0.0060112630017101765,
-0.017242558300495148,
0.0014379458734765649,
0.020713642239570618,
0.02677951008081436,
-0.007359164301306009,
-0.0019086991669610143,
0.008169129490852356,
-0.010157099924981594,
0.03590105101466179,
0.03229105472564697,
-0.00853650365024805,
0.023997429758310318,
0.054698165506124496,
-0.005161060020327568,
0.04190453141927719,
0.01660636067390442,
0.04409702867269516,
-0.09087390452623367,
0.009282522834837437,
0.012164577841758728,
0.036829862743616104,
0.034006938338279724,
-0.030847245827317238,
-0.005458337254822254,
0.04038973152637482,
-0.06685327738523483,
0.015049375593662262,
-0.014540896750986576,
0.03693412244319916,
-0.0005499007529579103,
0.02060323767364025,
-0.04936322569847107,
0.048837631940841675,
0.01953585259616375,
0.04536798223853111,
0.023976555094122887,
0.0407136008143425,
-0.021662527695298195,
-0.03998386859893799,
0.00216298783197999,
0.03118065558373928,
0.044794533401727676,
-0.017545346170663834,
0.05385376513004303,
-0.020516175776720047,
-0.012728300876915455,
0.027355685830116272,
-0.023360740393400192,
-0.04745658114552498,
-0.021798409521579742,
0.032219450920820236,
-0.01471251342445612,
0.0071153780445456505,
0.012038055807352066,
0.015133652836084366,
0.030800312757492065,
0.01734929159283638,
-0.0014720021281391382,
0.0018345954595133662,
-0.01681421883404255,
-0.017598791047930717,
0.013105189427733421,
-0.013438578695058823,
-0.04495163634419441,
0.05159817636013031,
-0.00018564602942205966,
-0.006916321348398924,
-0.011647951789200306,
-0.023124298080801964,
0.01547674834728241,
0.017392728477716446,
0.022611239925026894,
-0.035167790949344635,
-0.025727244094014168,
-0.016913412138819695,
0.017018036916851997,
-0.017061440274119377,
0.016990449279546738,
-0.04667462781071663,
-0.051391106098890305,
0.037219271063804626,
-0.01481785997748375,
-0.021135814487934113,
-0.03688153624534607,
-0.003691971069201827,
-0.014919730834662914,
-0.023649532347917557,
-0.017846563830971718,
0.001202102517709136,
-0.027795707806944847,
0.05324183404445648,
0.00912042148411274,
0.005543491803109646,
-0.040375106036663055,
-0.013877627439796925,
-0.01239603292196989,
-0.0664643868803978,
0.010100733488798141,
0.04708556458353996,
-0.027202559635043144,
-0.03581122308969498,
-0.03409016132354736,
-0.01576772890985012,
0.03953017294406891,
0.04319203644990921,
-0.04627673327922821,
-0.005327511113137007,
0.04430041462182999,
-0.020204676315188408,
-0.03023604303598404,
-0.03508166968822479,
0.004921888466924429,
-0.01245790347456932,
-0.022537067532539368,
0.0024573788978159428,
0.021307094022631645,
-0.03344269096851349,
0.033427461981773376,
-0.012983357533812523,
0.00776148634031415,
0.010663357563316822,
-0.0008348841802217066,
-0.051722824573516846,
0.04776882752776146,
0.031449757516384125,
-0.020304463803768158,
0.06795020401477814,
-0.016080215573310852,
0.013104012235999107,
0.026362933218479156,
-0.018786655738949776,
-0.05591057613492012,
0.0047403257340192795,
-0.03474658727645874,
-0.03854537010192871,
-0.010651825927197933,
-0.024242017418146133,
-0.001387318130582571,
-0.03666051849722862,
-0.013614657334983349,
0.024874748662114143,
-0.0209650918841362,
-0.037701450288295746,
0.04823404178023338,
0.013769600540399551,
0.038643188774585724,
0.02329917624592781,
-0.026028092950582504,
0.0068116262555122375,
0.017363348975777626,
-0.0024468135088682175,
0.05554095283150673,
0.003219613339751959,
0.012943441979587078,
0.025226004421710968,
-0.001600409159436822,
-0.030032940208911896,
0.012200461700558662,
-0.015579366125166416,
0.015388192608952522,
-0.02293846197426319,
0.005887794308364391,
0.04842781648039818,
-0.025416389107704163,
-0.03555378317832947,
0.004018654581159353,
-0.019288688898086548,
0.0403246246278286,
-0.023173626512289047,
0.00008304240327561274,
-0.01041114330291748,
-0.001163738896138966,
-0.015044135972857475,
0.023200776427984238,
0.04119006544351578,
0.03140558302402496,
-0.042717427015304565,
-0.01814204268157482,
-0.013414459303021431,
0.012953021563589573,
0.004720636643469334,
-0.05663517862558365,
-0.0040566930547356606,
0.0030478877015411854,
-0.010281353257596493,
0.008933719247579575,
-0.013251678086817265,
0.02649250067770481,
-0.02322053723037243,
-0.004775725770741701,
0.0063416664488613605,
0.01856592483818531,
-0.013113819062709808,
0.017263716086745262,
-0.050067879259586334,
0.10815075784921646,
-0.07716096192598343,
0.013827926479279995,
0.003497854107990861,
0.009797632694244385,
-0.04991926997900009,
0.023507321253418922
] |
<p>Try this:</p>
<p>Make a cup of tea, add sugar, and stir it. </p>
<p>Now add some milk, while it's still spinning.</p>
<p>What I noticed is that the milk appears to move around a lot quicker in the middle of the cup of tea, than the outside. </p>
<p>This seems to be the opposite of what happens on a vinyl, though it's the same as what happens with planets orbiting the sun. </p>
<p>What's the explanation here?</p>
| 9,411 |
[
0.01173598226159811,
-0.014533584006130695,
-0.00649324432015419,
-0.011336480267345905,
0.014753004536032677,
-0.015011121518909931,
-0.010484428144991398,
0.0331493504345417,
-0.02254130318760872,
-0.0073206666857004166,
-0.019674377515912056,
0.06983227282762527,
0.06147051975131035,
0.050875864923000336,
0.014113066717982292,
0.011297461576759815,
0.010372661054134369,
-0.015944212675094604,
-0.019764378666877747,
-0.0531441792845726,
-0.0171551164239645,
0.0011135448003187776,
-0.004063318017870188,
-0.005386548116803169,
-0.014714838936924934,
0.029242461547255516,
0.028227856382727623,
-0.003172526368871331,
0.026842139661312103,
0.03145027160644531,
0.0018700296059250832,
-0.01742972992360592,
-0.021977504715323448,
0.014465603046119213,
0.0635373666882515,
-0.007848754525184631,
-0.035605646669864655,
-0.030471814796328545,
0.010708577930927277,
0.01500975526869297,
-0.023472577333450317,
0.021887484937906265,
-0.031207473948597908,
0.01622641459107399,
-0.005267191678285599,
0.04054594039916992,
-0.007833721116185188,
0.029329512268304825,
0.07832962274551392,
-0.045321449637413025,
0.06668058782815933,
-0.016154449433088303,
-0.021378763020038605,
0.03647250682115555,
0.012831627391278744,
0.012706071138381958,
0.07336318492889404,
0.06331171840429306,
-0.023523984476923943,
-0.030397146940231323,
-0.004077231977134943,
-0.03377871587872505,
-0.04448658600449562,
-0.03645307570695877,
-0.015705671161413193,
0.002054596086964011,
0.016762247309088707,
-0.0017807884141802788,
0.020999478176236153,
0.043545305728912354,
0.0078662671148777,
0.014943946152925491,
0.057359375059604645,
-0.02434050850570202,
-0.0024173075798898935,
-0.05393888056278229,
0.0054092914797365665,
0.012132980860769749,
0.02837662398815155,
0.03194386512041092,
-0.002140196505934,
-0.019170518964529037,
-0.0006710003945045173,
0.026596490293741226,
0.029740851372480392,
-0.03162618726491928,
0.04233349859714508,
-0.012444532476365566,
-0.011434861458837986,
0.060360539704561234,
0.0050511788576841354,
0.008364737033843994,
0.04653778299689293,
0.024354320019483566,
-0.03164425864815712,
0.03631066530942917,
0.014485138468444347,
0.04299190267920494,
0.03843486309051514,
-0.018225030973553658,
-0.019865604117512703,
-0.010973092168569565,
0.03079373575747013,
0.08271559327840805,
0.03316028416156769,
-0.03309943899512291,
-0.03203136473894119,
0.02666490152478218,
-0.0074319858103990555,
0.016717804595828056,
-0.06298188865184784,
-0.026436544954776764,
0.011426376178860664,
-0.019513368606567383,
0.0034575588069856167,
-0.01534315850585699,
-0.026403004303574562,
-0.015416564419865608,
0.021254802122712135,
0.0654919371008873,
0.016594842076301575,
-0.05152011290192604,
-0.002869904739782214,
-0.04721871763467789,
-0.03586839884519577,
0.05719788372516632,
0.009684553369879723,
-0.03376879543066025,
-0.01890694908797741,
0.00579583877697587,
0.018769942224025726,
-0.030359413474798203,
0.010519343428313732,
-0.033787257969379425,
0.03491124510765076,
0.019371913745999336,
-0.11273764073848724,
-0.04214790090918541,
0.053739994764328,
0.01915794238448143,
-0.03444870188832283,
-0.05371208116412163,
0.008390395902097225,
0.002192908665165305,
0.08598064631223679,
0.0007648871978744864,
-0.013158628717064857,
-0.03132786229252815,
0.048117294907569885,
0.0011034675408154726,
-0.01178257167339325,
0.008621461689472198,
-0.029851216822862625,
-0.060488343238830566,
0.011798201128840446,
-0.05270053818821907,
0.0019847627263516188,
0.044193025678396225,
-0.002995682181790471,
-0.005637792404741049,
0.01493623573333025,
-0.06791692227125168,
0.023427680134773254,
0.006070997100323439,
0.0043076034635305405,
-0.05816012620925903,
0.06415580958127975,
0.018274830654263496,
0.012034636922180653,
0.005444298963993788,
-0.01609198749065399,
0.0518176332116127,
-0.007319864351302385,
0.000152853928739205,
0.01739615574479103,
0.0069485134445130825,
-0.007270376663655043,
0.03475296124815941,
0.01775556430220604,
0.012306435033679008,
-0.027873685583472252,
-0.035535939037799835,
-0.021443603560328484,
0.02795150689780712,
0.01907319761812687,
0.06576652079820633,
-0.010930727235972881,
-0.0012548462254926562,
-0.005935973022133112,
-0.05331834778189659,
-0.025309424847364426,
-0.04744444414973259,
0.005261799320578575,
-0.025162309408187866,
-0.028023188933730125,
0.013388628140091896,
0.05413713678717613,
0.017901843413710594,
-0.012344200164079666,
0.00656242435798049,
-0.005416291765868664,
0.025105658918619156,
0.003971613012254238,
0.00672692758962512,
0.004227610770612955,
0.05914105474948883,
0.004189923871308565,
-0.044796958565711975,
-0.016585849225521088,
-0.008938160724937916,
0.004326510243117809,
0.031138833612203598,
-0.00957738608121872,
0.009402901865541935,
-0.004534573759883642,
-0.025004582479596138,
0.02101854607462883,
0.03479420766234398,
0.0033388242591172457,
0.021268920972943306,
-0.007485128473490477,
0.0557231530547142,
0.0634114071726799,
-0.03655964136123657,
0.04979585111141205,
-0.002765560057014227,
0.013612249866127968,
0.024291876703500748,
0.0312361977994442,
-0.044396720826625824,
-0.036801330745220184,
-0.04344362020492554,
0.032875750213861465,
0.014989163726568222,
-0.01232459768652916,
0.007599990349262953,
0.03841809183359146,
0.03821565955877304,
0.018002597615122795,
0.003762671956792474,
0.009101483039557934,
-0.03564388304948807,
0.006919636391103268,
-0.015600064769387245,
0.022373413667082787,
0.00003071924948017113,
0.03493465855717659,
-0.010179176926612854,
0.034208379685878754,
0.010756310075521469,
-0.03421446681022644,
0.004764947574585676,
0.025703299790620804,
0.03951685503125191,
-0.0022522720973938704,
-0.03445732593536377,
0.0004936988116241992,
-0.03152434527873993,
-0.007895918563008308,
0.03478770703077316,
0.020586801692843437,
0.04548284783959389,
-0.038905251771211624,
0.001856568269431591,
-0.017712930217385292,
0.0010608574375510216,
0.01202031597495079,
-0.00344322482123971,
0.05170314386487007,
-0.006887160707265139,
0.009684588760137558,
-0.0029210527427494526,
0.0010266058379784226,
0.012408195994794369,
0.0103377690538764,
0.03124840371310711,
0.029991840943694115,
0.02751919813454151,
-0.010578124783933163,
-0.00034485539072193205,
-0.01254461333155632,
-0.0033501130528748035,
-0.007503873202949762,
0.012256019748747349,
-0.03237006440758705,
0.03431416675448418,
-0.029843982309103012,
-0.02202034741640091,
0.005470206495374441,
0.005694919731467962,
-0.004629961680620909,
-0.02255934104323387,
-0.017734289169311523,
-0.08653035014867783,
-0.02104726992547512,
-0.00421690009534359,
0.011432879604399204,
-0.05809745937585831,
0.006891620345413685,
0.05875282362103462,
0.04533364623785019,
-0.03849620744585991,
0.022440718486905098,
-0.04757209122180939,
-0.04630354791879654,
0.014922820962965488,
0.011092917993664742,
0.03515830263495445,
-0.05513257160782814,
0.006172914989292622,
0.0183509923517704,
0.006653050426393747,
-0.014589286409318447,
-0.049521949142217636,
-0.021586572751402855,
-0.009134269319474697,
-0.03960516303777695,
0.06946320086717606,
-0.02214689552783966,
-0.015698708593845367,
0.08205793797969818,
0.05701534450054169,
-0.030565408989787102,
-0.02237551286816597,
-0.030283857136964798,
-0.02188180945813656,
-0.07349547743797302,
0.03167520463466644,
0.07772354781627655,
-0.046198468655347824,
0.017815999686717987,
0.03473955765366554,
0.048626236617565155,
0.0038075053598731756,
0.007824206724762917,
-0.01949312351644039,
0.01958005130290985,
-0.0010142795508727431,
-0.038263313472270966,
0.052906084805727005,
0.03987380489706993,
-0.015568078495562077,
0.014922886155545712,
-0.026986442506313324,
0.04299928620457649,
0.028402604162693024,
-0.06986459344625473,
0.06295386701822281,
-0.03649309277534485,
-0.01377099473029375,
-0.011027492582798004,
0.034495264291763306,
0.010462835431098938,
-0.008035609498620033,
-0.022827373817563057,
0.03456563130021095,
0.046859268099069595,
0.027631061151623726,
-0.015218254178762436,
0.0440220832824707,
0.018629146739840508,
-0.013307870365679264,
0.0008029228774830699,
-0.008934354409575462,
-0.02386397495865822,
0.026246413588523865,
-0.05570054426789284,
-0.017623435705900192,
0.049328260123729706,
0.030508099123835564,
-0.026283511891961098,
0.004704680759459734,
-0.05076395347714424,
-0.02443445473909378,
-0.06343888491392136,
-0.009238318540155888,
-0.02412596344947815,
0.02986804209649563,
0.020109539851546288,
0.06554580479860306,
0.008413775824010372,
-0.018030203878879547,
0.012759638018906116,
-0.027125924825668335,
-0.07920544594526291,
0.024220727384090424,
0.010692738927900791,
-0.023553328588604927,
-0.025401948019862175,
-0.031006677076220512,
-0.004590801894664764,
-0.03930382430553436,
-0.000947121880017221,
-0.041832324117422104,
-0.017826231196522713,
-0.044813502579927444,
0.020925533026456833,
0.008049862459301949,
-0.033589690923690796,
-0.028903895989060402,
0.02275262586772442,
0.026907045394182205,
0.004957272671163082,
-0.0006165658123791218,
0.027199769392609596,
-0.0666898787021637,
0.0132981538772583,
-0.007453524973243475,
-0.031930383294820786,
-0.019209321588277817,
0.019409896805882454,
0.02157987467944622,
-0.05032757297158241,
-0.04085550829768181,
0.008568715304136276,
0.020489681512117386,
0.04289236664772034,
-0.018553324043750763,
-0.04764474928379059,
-0.03794907033443451,
-0.02501387521624565,
-0.01738649047911167,
0.012452343478798866,
0.047163236886262894,
0.01563488133251667,
0.019703108817338943,
0.026288645341992378,
-0.0035286657512187958,
0.01545798685401678,
0.04081418737769127,
0.045330364257097244,
-0.012057885527610779,
-0.017353462055325508,
-0.07822141796350479,
-0.03953399509191513,
0.007257934659719467,
-0.008081753738224506,
0.018293222412467003,
0.00634702667593956,
0.011629131622612476,
-0.03342686593532562,
-0.006198279093950987,
-0.0348055362701416,
-0.008512974716722965,
-0.01670880801975727,
-0.05263490974903107,
-0.016849853098392487,
-0.0006848791381344199,
0.012151992879807949,
-0.0035985384602099657,
0.04144229367375374,
0.01940750516951084,
0.016598865389823914,
-0.028784262016415596,
-0.10475492477416992,
-0.0046849241480231285,
0.03481114283204079,
0.016126763075590134,
-0.023998094722628593,
-0.0062377979047596455,
-0.0570419542491436,
-0.011538201943039894,
0.01999736577272415,
-0.040003836154937744,
0.04947967827320099,
-0.0346890352666378,
-0.05612075701355934,
-0.01530721690505743,
-0.02167907916009426,
-0.01947593130171299,
0.024896793067455292,
-0.03308247774839401,
0.012518496252596378,
-0.022937998175621033,
-0.017907094210386276,
-0.03286246210336685,
0.015350875444710255,
0.004422924481332302,
0.011283349245786667,
-0.01732545904815197,
0.03006667271256447,
0.004071047995239496,
0.0023570519406348467,
-0.036249373108148575,
-0.05876868963241577,
0.023199865594506264,
-0.019570495933294296,
0.0010769936488941312,
0.0139995152130723,
-0.02063058875501156,
-0.0504806749522686,
0.004035180900245905,
0.017633747309446335,
0.009715142659842968,
-0.03032422438263893,
-0.017298299819231033,
0.008334765210747719,
-0.0028287109453231096,
0.003694790881127119,
0.015935176983475685,
0.045498162508010864,
-0.044547561556100845,
-0.0210099034011364,
0.03971000760793686,
0.017794691026210785,
-0.012051284313201904,
0.02820860967040062,
-0.009091787971556187,
0.01847357489168644,
-0.037094343453645706,
0.046054501086473465,
0.005547808017581701,
0.04392988979816437,
-0.013543570414185524,
-0.02564924769103527,
-0.018243951722979546,
0.03205520287156105,
-0.005365898832678795,
-0.029835954308509827,
-0.01774909533560276,
-0.015936223790049553,
0.03202183544635773,
0.012132961302995682,
0.036955758929252625,
0.01738906092941761,
0.01832728087902069,
0.037190183997154236,
0.007133627776056528,
0.026792021468281746,
-0.050676871091127396,
-0.009329055435955524,
-0.03111402690410614,
-0.023178325966000557,
0.030533529818058014,
-0.017348766326904297,
0.005284855607897043,
0.025017138570547104,
-0.020901281386613846,
-0.013607440516352654,
0.013152169063687325,
-0.06793127208948135,
0.020211532711982727,
-0.011330694891512394,
0.019404852762818336,
0.02409517392516136,
0.015396283939480782,
-0.023790959268808365,
-0.059532295912504196,
0.050525497645139694,
0.038865312933921814,
-0.005020711570978165,
-0.023147447034716606,
-0.02536414936184883,
-0.021932676434516907,
0.0025801011361181736,
0.031208010390400887,
0.03795962780714035,
-0.026157157495617867,
-0.012953139841556549,
0.04599075764417648,
-0.005236865021288395,
0.08797051012516022,
0.005367931444197893,
-0.033656347543001175,
0.0198220182210207,
-0.0009129573008976877,
-0.032974064350128174,
-0.01922159269452095,
0.030731497332453728,
-0.05170254409313202,
-0.048032961785793304,
0.00475460197776556,
0.017829760909080505,
0.023363422602415085,
0.001090278965421021,
-0.020872335880994797,
0.019206354394555092,
-0.00809828843921423,
-0.010483408346772194,
-0.044436898082494736,
0.03676387667655945,
0.036872681230306625,
-0.026207176968455315,
0.007500865031033754,
0.001614525681361556,
0.006643381435424089,
-0.045308224856853485,
0.01815718784928322,
-0.0008421677630394697,
-0.02367532253265381,
0.004857446998357773,
0.06959447264671326,
0.0024375796783715487,
0.008108909241855145,
0.0190232302993536,
-0.06287810951471329,
0.008993919938802719,
0.02131432108581066,
-0.0005650544189848006,
-0.0029966807924211025,
0.010425295680761337,
-0.022205252200365067,
0.022409632802009583,
-0.007520564831793308,
-0.01025378704071045,
0.0427279993891716,
0.010634313337504864,
0.05979600176215172,
0.03477957099676132,
0.002019372070208192,
-0.030990418046712875,
0.0018490179209038615,
-0.014711330644786358,
-0.0003600846976041794,
-0.005095347296446562,
0.03822741284966469,
-0.018485944718122482,
-0.02756151556968689,
0.04064873978495598,
0.06224047392606735,
-0.013633528724312782,
0.003014615271240473,
0.03952939063310623,
0.007063005119562149,
0.027788428589701653,
-0.008254113607108593,
-0.034970615059137344,
0.029710469767451286,
-0.04580894857645035,
0.050106775015592575,
-0.00593326473608613,
0.0014819807838648558,
0.04119846597313881,
0.03240622580051422,
0.007298700511455536,
-0.05810423195362091,
0.004226180259138346,
-0.07701367139816284,
-0.01052910927683115,
0.011048514395952225,
-0.006114322226494551,
0.02503465861082077,
-0.035916589200496674,
0.04917905852198601,
0.014547303318977356,
-0.03243718668818474,
-0.014244153164327145,
-0.06386428326368332,
-0.0017219216097146273,
0.0043565803207457066,
-0.02163204364478588,
0.06034143269062042,
-0.010981346480548382,
-0.043675221502780914,
0.007071770261973143,
-0.02850249595940113,
0.028290823101997375,
0.02948322892189026,
0.0033636256121098995,
-0.032054025679826736,
0.07282322645187378,
0.0025363625027239323,
-0.006094439420849085,
-0.014866620302200317,
0.03571978211402893,
0.14016342163085938,
0.003632527543231845,
0.0002871695614885539,
-0.02273605577647686,
0.010883396491408348,
-0.008308554999530315,
0.030011029914021492,
-0.0017879713559523225,
0.01751156896352768,
-0.020459139719605446,
0.006629976909607649,
0.012271997518837452,
0.09747523069381714,
0.04801435396075249,
0.020602986216545105,
0.013874656520783901,
-0.03242982551455498,
0.007447238080203533,
-0.0010669099865481257,
0.004917582031339407,
-0.014910432510077953,
0.017650049179792404,
-0.056673552840948105,
-0.017980562523007393,
-0.041381120681762695,
0.03271611034870148,
-0.014199080877006054,
-0.04818027466535568,
-0.013155657798051834,
0.04056686535477638,
-0.03463571518659592,
0.040027979761362076,
-0.03026098944246769,
-0.008129357360303402,
-0.038674406707286835,
0.052482061088085175,
0.03428028151392937,
0.004099390469491482,
0.006282854825258255,
0.03160266578197479,
0.00712544983252883,
0.02136269025504589,
0.03072400391101837,
0.00926985777914524,
-0.039061788469552994,
0.011043225415050983,
-0.03347363695502281,
0.02706308476626873,
0.003269858192652464,
-0.025426698848605156,
-0.021583402529358864,
-0.005721868947148323,
-0.013511301949620247,
-0.03180399537086487,
0.004282309673726559,
0.01697295531630516,
-0.02933761104941368,
0.006859008222818375,
-0.00249756989069283,
0.012286677025258541,
0.0031601269729435444,
0.021948322653770447,
0.02506270818412304,
0.002517474815249443,
0.02778138592839241,
0.0028487422969192266,
0.02431846596300602,
0.04061983898282051,
-0.018767546862363815,
-0.013166042044758797,
0.001548741478472948,
-0.007747793570160866,
-0.05112007260322571,
0.02683252841234207,
0.01578615978360176,
0.01814996264874935,
-0.019498644396662712,
-0.011723033152520657,
-0.01686432585120201,
-0.03231063485145569,
-0.01924384944140911,
0.04626307636499405,
-0.00911236647516489,
-0.013348840177059174,
-0.022766562178730965,
-0.013928978703916073,
0.048034340143203735,
0.01362663134932518,
-0.03799493983387947,
-0.009026668034493923,
-0.0010191829642280936,
0.06947833299636841,
-0.008533699437975883,
-0.00045590908848680556,
0.010119803249835968,
0.0053788828663527966,
-0.02008483186364174,
-0.01776283048093319,
-0.016246372833848,
0.04830467328429222,
0.029439223930239677,
-0.03426602855324745,
0.021600740030407906,
0.010501926764845848,
-0.026314765214920044,
0.017850585281848907,
0.041218824684619904,
-0.005385941360145807,
-0.03631279245018959,
0.015929069370031357,
-0.027453070506453514,
-0.033586230129003525,
-0.02811993658542633,
0.006660693325102329,
-0.03168608993291855,
-0.05557128041982651,
0.04921729490160942,
0.0003669330617412925,
0.033483896404504776,
-0.05000890791416168,
0.018489759415388107,
-0.049373749643564224,
0.0034080741461366415,
-0.09800498187541962,
-0.002461964963003993,
0.035130515694618225,
0.024343611672520638,
-0.0057280343025922775,
0.03793874755501747,
-0.033566683530807495,
0.0065148272551596165,
-0.026920923963189125,
-0.010916512459516525,
0.0032442575320601463,
-0.004815835040062666,
0.05206731706857681,
-0.014624863862991333,
0.003887644037604332,
-0.06019777059555054,
-0.06693437695503235,
0.024844158440828323,
-0.016922084614634514,
-0.051221851259469986,
-0.014349677599966526,
-0.01765834167599678,
0.024706464260816574,
0.021605590358376503,
-0.019435329362750053,
0.022141916677355766,
0.07560639083385468,
-0.03224655240774155,
-0.033194515854120255,
-0.02140107750892639,
-0.021099306643009186,
0.017734048888087273,
-0.008390930481255054,
0.04204536974430084,
-0.016306187957525253,
-0.010452608577907085,
0.023674260824918747,
0.02768031135201454,
-0.014940590597689152,
0.0118173249065876,
-0.05384265258908272,
-0.02619827911257744,
0.0090835802257061,
-0.016838761046528816,
0.037229686975479126,
0.02445366233587265,
0.020151222124695778,
-0.03501136228442192,
0.023295771330595016,
0.02819792740046978,
-0.016597265377640724,
-0.0900302305817604,
-0.01876097358763218,
-0.02019871212542057,
-0.01147508155554533,
0.00944958720356226,
-0.06407469511032104,
-0.012245546095073223,
0.008361248299479485,
-0.09046334773302078,
0.03607707470655441,
-0.021697398275136948,
-0.02730688825249672,
-0.06365274637937546,
0.022860603407025337,
-0.018840156495571136,
0.06289871037006378,
0.043387819081544876,
0.025844674557447433,
0.016537273302674294,
0.011376738548278809,
-0.018159503117203712,
-0.008789443410933018,
0.009299518540501595,
0.04136890918016434,
-0.007917714305222034,
0.009076595306396484,
0.03880607709288597,
-0.02942338027060032,
-0.05088302493095398,
0.01952270418405533,
-0.04034581035375595,
0.05594980716705322,
-0.042539991438388824,
-0.02381427027285099,
0.0008528050384484231,
0.0014173454837873578,
0.015567116439342499,
0.02567376010119915,
-0.008763520047068596,
0.041405584663152695,
0.037229400128126144,
0.028293156996369362,
-0.003461382118985057,
0.020316479727625847,
0.013766048476099968,
-0.0080458614975214,
-0.00028233983903191984,
0.007357629481703043,
-0.013302933424711227,
0.023832540959119797,
0.04445381462574005,
0.03100861981511116,
0.008856370113790035,
-0.03047596663236618,
0.021328819915652275,
-0.048578739166259766,
0.008264798671007156,
0.03434646502137184,
0.020156431943178177,
-0.03303047642111778,
0.017187627032399178,
0.02767096273601055,
0.02623690664768219,
-0.003839955199509859,
0.019844261929392815,
-0.008154086768627167,
-0.027502862736582756,
-0.015219409950077534,
0.0009420537389814854,
0.0019097820622846484,
-0.0019177509238943458,
0.0033407616429030895,
-0.0327523909509182,
0.00969415158033371,
0.0466422513127327,
0.03803398087620735,
-0.004284159280359745,
-0.029736118391156197,
0.00001607802914804779,
-0.0500481016933918,
-0.000051783550588879734,
-0.012814706191420555,
-0.005609753075987101,
-0.020195195451378822,
-0.019220814108848572,
0.0023470933083444834,
0.02513270266354084,
0.07623305916786194,
0.03213313966989517,
0.0027068613562732935,
0.018553396686911583,
-0.040932368487119675,
0.018333477899432182,
-0.028348693624138832,
-0.009280393831431866,
-0.014773343689739704,
-0.008647953160107136,
0.0734294205904007,
-0.025297563523054123,
-0.04787702485918999,
0.016615763306617737,
0.05137660726904869,
-0.03203294798731804,
0.04827988147735596,
0.033776260912418365,
-0.025000309571623802,
0.042613089084625244,
0.007588683161884546,
0.027457764372229576,
0.08515410870313644,
0.025544894859194756,
0.005329151172190905,
0.017695672810077667,
-0.008573951199650764,
-0.05640198662877083,
0.03566654399037361,
-0.03885038197040558,
0.004223619122058153,
-0.052578508853912354,
-0.028775829821825027,
-0.011766774579882622,
-0.0039942702278494835,
0.010391599498689175,
0.008418099954724312,
-0.012549063190817833,
0.005859500262886286,
0.004025778733193874,
0.01773085817694664,
0.022631580010056496,
0.011915569193661213,
-0.008622098714113235,
-0.008142489939928055,
-0.002393661765381694,
-0.005164458882063627,
0.05003046989440918,
0.038139864802360535,
0.020817922428250313,
0.010550237260758877,
0.02088990807533264,
0.022507065907120705,
0.021753443405032158,
0.0011714543215930462,
0.0121003407984972,
0.05033278092741966,
-0.008202330209314823,
0.02038232795894146,
-0.026334496214985847,
0.0060450551100075245,
0.023471836000680923,
0.0024394916836172342,
0.06290478259325027,
-0.04885794594883919,
0.006008091848343611,
-0.014920548535883427,
0.011384046636521816,
-0.010503692552447319,
0.0029086130671203136,
-0.0026070824824273586,
-0.023878687992691994,
-0.02962430566549301,
-0.0365060456097126,
-0.04481882601976395,
-0.004732862114906311,
0.012527091428637505,
-0.025912296026945114,
0.014860800467431545,
-0.02501227892935276,
-0.010300492867827415,
0.02760871686041355,
0.020121093839406967,
-0.005793809425085783,
-0.0035987587179988623,
0.03981202095746994,
0.03415302932262421,
-0.0085672028362751,
-0.009140298701822758,
-0.011129066348075867,
-0.008494950830936432,
0.06896234303712845,
-0.07141655683517456,
-0.05948719009757042,
-0.013289818540215492,
0.06154659390449524,
-0.01691759005188942,
-0.020342065021395683
] |
<p>I want to write $F^{\mu \nu}F_{\mu \nu}$ in terms of $F_{\mu \nu}F^{\mu \nu}$. How to do it?</p>
| 9,412 |
[
-0.018380027264356613,
0.009187287651002407,
-0.015637531876564026,
-0.03793279826641083,
0.029166938737034798,
0.054833535104990005,
-0.0016061064088717103,
-0.008470323868095875,
0.009196633473038673,
-0.025601372122764587,
0.059545524418354034,
0.023374129086732864,
0.09786023199558258,
0.0018352176994085312,
0.02234152890741825,
-0.008383626118302345,
-0.04735131189227104,
0.003953513689339161,
-0.02897302620112896,
-0.0481894351541996,
-0.005549785681068897,
0.03309190273284912,
-0.02220902405679226,
0.01265235710889101,
0.008951107040047646,
0.06474035233259201,
0.04334401711821556,
0.015428072772920132,
-0.003553485032171011,
0.045573148876428604,
0.0003540405596140772,
-0.045306846499443054,
0.005831010639667511,
0.028198760002851486,
-0.02768268622457981,
0.02242918685078621,
0.011796844191849232,
0.0011845426633954048,
-0.01413643453270197,
-0.013612505979835987,
-0.03554757684469223,
-0.024039030075073242,
0.013378249481320381,
0.03891656547784805,
-0.027764374390244484,
0.03772604465484619,
0.0019524138187989593,
0.010510685853660107,
0.04699786379933357,
-0.03784073516726494,
0.10324017703533173,
0.039176516234874725,
0.046963002532720566,
0.0667918249964714,
-0.0369671992957592,
0.007911327295005322,
0.06463371962308884,
0.07782427966594696,
0.03090071864426136,
-0.04669184237718582,
-0.030604274943470955,
-0.05579438433051109,
0.005020293407142162,
-0.010181247256696224,
-0.004303750582039356,
0.03162425756454468,
-0.02064576931297779,
0.008430435322225094,
0.013160874135792255,
-0.016743335872888565,
-0.03925495222210884,
0.00262162066064775,
0.06630223989486694,
-0.05034308880567551,
0.03601228445768356,
-0.03125526010990143,
0.020936783403158188,
-0.0004051137366332114,
0.037041179835796356,
0.007799483370035887,
-0.024458622559905052,
0.04452717304229736,
0.055802877992391586,
-0.0344809927046299,
-0.020569832995533943,
-0.032709743827581406,
0.032902542501688004,
-0.006848372984677553,
0.03222501277923584,
0.02456372231245041,
0.017177274450659752,
-0.0014169947244226933,
0.06817749887704849,
0.003943285904824734,
-0.02676902525126934,
0.01157564576715231,
-0.00842767022550106,
-0.0074258060194551945,
-0.0005707067321054637,
-0.030713174492120743,
-0.010574139654636383,
-0.03294801712036133,
0.02005334198474884,
0.047825295478105545,
-0.004661325365304947,
0.009553655982017517,
-0.018115922808647156,
-0.008445767685770988,
-0.02282404899597168,
-0.009890977293252945,
-0.007759716361761093,
0.010330419056117535,
-0.04479456692934036,
0.016536273062229156,
0.018687458708882332,
-0.046721767634153366,
0.0013664016732946038,
-0.004979873076081276,
0.05832178518176079,
0.07119381427764893,
0.03237076476216316,
-0.016286557540297508,
0.04074181616306305,
-0.01663738116621971,
-0.07517758011817932,
0.024666041135787964,
0.03945627063512802,
-0.0017207851633429527,
-0.05607094615697861,
0.02590307593345642,
0.01699686422944069,
-0.018436158075928688,
-0.03005770780146122,
-0.021766390651464462,
-0.01776241883635521,
-0.0150148281827569,
-0.06479774415493011,
-0.040416039526462555,
0.036261726170778275,
-0.029035892337560654,
-0.015936775133013725,
-0.08840833604335785,
0.029772229492664337,
0.04068553447723389,
0.11182097345590591,
0.04818183556199074,
-0.00452479999512434,
0.008200200274586678,
0.028991473838686943,
-0.023230018094182014,
0.014283851720392704,
-0.03657270967960358,
0.008640674874186516,
-0.02782907895743847,
-0.009387798607349396,
-0.025348886847496033,
0.011184519156813622,
0.0286009069532156,
-0.01261634100228548,
-0.0024376576766371727,
0.10974963009357452,
-0.0007299046264961362,
0.006723938975483179,
0.01754022389650345,
-0.017228424549102783,
-0.041708070784807205,
0.06405356526374817,
0.010471576824784279,
0.02699321322143078,
0.025150496512651443,
0.013201776891946793,
0.013635765761137009,
-0.009368712082505226,
0.04269391670823097,
0.08084449172019958,
-0.03926539421081543,
0.004533858969807625,
-0.03187870979309082,
0.0059670619666576385,
-0.00704685365781188,
-0.005039655603468418,
-0.05292456969618797,
0.0032199802808463573,
-0.0016704696463420987,
-0.004507814068347216,
0.00812101922929287,
0.023928875103592873,
0.01221458800137043,
0.02603083662688732,
-0.06566249579191208,
-0.010794349014759064,
-0.052617497742176056,
0.022724099457263947,
-0.012294684536755085,
-0.03129813075065613,
0.0003333949134685099,
0.02915685437619686,
0.03566865995526314,
-0.02231857366859913,
-0.057274747639894485,
-0.013066898100078106,
-0.013706971891224384,
0.007505052722990513,
-0.005416505970060825,
-0.0011727889068424702,
0.022643575444817543,
0.057962872087955475,
0.018396377563476562,
0.05211850255727768,
-0.03199676424264908,
-0.0024315733462572098,
-0.004838025663048029,
-0.004775785841047764,
0.022024787962436676,
-0.03608134388923645,
0.018891269341111183,
0.023835940286517143,
0.0014017659705132246,
-0.01632065139710903,
0.028223074972629547,
-0.011999099515378475,
0.011972839944064617,
0.06938622146844864,
0.05486111342906952,
0.025655413046479225,
0.03855187073349953,
0.0024076795671135187,
0.020823661237955093,
0.006116076838225126,
-0.03544285520911217,
-0.03618110716342926,
-0.0024057808332145214,
0.0073251123540103436,
0.009456450119614601,
-0.011292047798633575,
-0.0003935960994567722,
0.0418158657848835,
0.02460375428199768,
0.06547148525714874,
0.06860918551683426,
-0.03542036563158035,
-0.03274832293391228,
-0.01974906399846077,
0.012723994441330433,
0.03441080078482628,
0.008069402538239956,
0.02036115899682045,
0.03717545047402382,
0.019316416233778,
-0.01570337451994419,
-0.0052516465075314045,
0.06420420110225677,
-0.03767526149749756,
-0.024305710569024086,
0.025564374402165413,
-0.044805362820625305,
0.0076670474372804165,
-0.03662196919322014,
0.01008655596524477,
0.03231487050652504,
-0.023167360574007034,
-0.0008519837283529341,
-0.02464650571346283,
-0.015653185546398163,
0.0017110274638980627,
0.020106568932533264,
-0.009516561403870583,
-0.027440214529633522,
0.038358334451913834,
-0.036772724241018295,
0.015492101199924946,
-0.004285972565412521,
-0.002440306358039379,
-0.009787693619728088,
-0.012372455559670925,
-0.0018222879152745008,
-0.0032940732780843973,
0.0049859583377838135,
0.005288766231387854,
-0.03209126740694046,
0.020464321598410606,
-0.02065560221672058,
0.029050787910819054,
-0.007649260573089123,
-0.016362318769097328,
0.002514704829081893,
-0.017616065219044685,
-0.036149896681308746,
-0.008919556625187397,
0.014541438780725002,
-0.0024724588729441166,
0.00654672272503376,
0.006770151201635599,
-0.07240530848503113,
-0.011775139719247818,
-0.007144646719098091,
0.001536873052828014,
-0.010144613683223724,
0.022761911153793335,
0.04252943396568298,
0.032769251614809036,
-0.04126774147152901,
-0.04982929676771164,
-0.009700932539999485,
-0.0357406847178936,
-0.042079754173755646,
-0.0003654785396065563,
0.026036538183689117,
-0.024723893031477928,
0.04348016902804375,
0.014813141897320747,
-0.045061443001031876,
0.007872811518609524,
-0.06035517901182175,
-0.023542774841189384,
-0.012639021500945091,
-0.0016261187847703695,
0.028224939480423927,
-0.0026210779324173927,
-0.03139226511120796,
0.0530744232237339,
0.029980376362800598,
-0.020087245851755142,
-0.022429831326007843,
0.01403263583779335,
0.023301420733332634,
-0.09534034132957458,
-0.03410053253173828,
-0.005569775588810444,
-0.030334696173667908,
-0.0032645333558321,
0.06586819887161255,
-0.03436392918229103,
0.053864385932683945,
0.04763033986091614,
0.005063182674348354,
-0.011097019538283348,
-0.03175974637269974,
-0.004079457838088274,
0.036324597895145416,
-0.033441584557294846,
0.004647145979106426,
0.02468160167336464,
0.003159318584948778,
0.01725849136710167,
0.03431826829910278,
-0.013584968633949757,
0.037316471338272095,
0.03552371263504028,
-0.014148685149848461,
-0.06262950599193573,
0.035472359508275986,
-0.011637927033007145,
-0.03352978080511093,
0.00006194441812112927,
0.041010208427906036,
0.04431848227977753,
-0.0524258017539978,
0.008334183134138584,
0.06317543238401413,
0.044891953468322754,
-0.02169252187013626,
-0.045488350093364716,
-0.03216646984219551,
-0.0026403276715427637,
0.026367252692580223,
-0.0401361808180809,
0.004167040344327688,
0.01616004668176174,
0.01709512434899807,
0.029538149014115334,
-0.01009347103536129,
0.009015001356601715,
-0.0005790612194687128,
-0.05074590444564819,
-0.014186614193022251,
0.007232728414237499,
0.05355313792824745,
0.016860470175743103,
0.03848181292414665,
0.013770529069006443,
0.020479105412960052,
0.0016504591330885887,
-0.011179393157362938,
-0.09114424884319305,
0.05407058075070381,
-0.012509859167039394,
-0.013173731043934822,
0.004261138383299112,
-0.028842607513070107,
-0.018643466755747795,
-0.014442568644881248,
-0.055124085396528244,
-0.030484674498438835,
-0.02264607697725296,
-0.02134607918560505,
0.01368660293519497,
-0.04090079292654991,
-0.058787159621715546,
0.0065464056096971035,
0.06247621774673462,
0.06552241742610931,
-0.012309569865465164,
0.007143767084926367,
0.02258087322115898,
-0.010510521940886974,
-0.011919713579118252,
-0.03739398345351219,
0.044151533395051956,
0.0034573932643979788,
0.012921919114887714,
0.02496887370944023,
0.06673382222652435,
-0.02879096381366253,
0.03781133517622948,
0.0194375142455101,
0.041207581758499146,
0.04035087302327156,
-0.03126717358827591,
-0.0356484018266201,
-0.03846113383769989,
-0.010081346146762371,
0.004061988554894924,
0.06161174178123474,
0.0027928664349019527,
-0.006372982636094093,
0.048823289573192596,
0.006688535679131746,
-0.014512295834720135,
0.053771406412124634,
0.06523297727108002,
-0.0009530604584142566,
-0.04573100805282593,
-0.03645972162485123,
-0.006990416906774044,
0.004763925913721323,
0.015113288536667824,
-0.004294999875128269,
0.018157048150897026,
-0.0026357693132013083,
-0.012774433940649033,
-0.009327893145382404,
-0.014911472797393799,
-0.013224547728896141,
0.008696288801729679,
-0.00647733872756362,
-0.033092740923166275,
-0.016333939507603645,
-0.00448608910664916,
0.01620345376431942,
0.07725346088409424,
0.010981474071741104,
0.01817280799150467,
0.017835505306720734,
-0.06848478317260742,
-0.0020443133544176817,
0.015255093574523926,
0.007490048184990883,
0.01789172925055027,
0.004494329448789358,
-0.045624278485774994,
0.004379121121019125,
0.05952073261141777,
-0.016261380165815353,
0.06516605615615845,
0.0065687233582139015,
0.025559287518262863,
0.0029067981522530317,
0.009905768558382988,
-0.01736718788743019,
0.06688951700925827,
-0.041281674057245255,
0.018983272835612297,
-0.036696817725896835,
0.012729988433420658,
-0.03776900842785835,
0.004289965610951185,
0.004273741506040096,
0.03873131424188614,
0.005589478649199009,
-0.006766160484403372,
0.0063797477632761,
0.04158654063940048,
-0.0016134660691022873,
-0.06435392796993256,
0.030734408646821976,
0.009830201976001263,
-0.009330370463430882,
0.005137700121849775,
-0.014669985510408878,
-0.03108767420053482,
0.037239015102386475,
-0.0006190795102156699,
-0.0018237042240798473,
0.01782003603875637,
-0.043969638645648956,
0.0696142390370369,
0.03153788298368454,
0.003497655736282468,
0.06669557094573975,
0.01929520256817341,
0.023509979248046875,
0.04002595692873001,
-0.06677987426519394,
0.017090467736124992,
-0.03555644676089287,
0.0101372255012393,
-0.012512940913438797,
0.03055974468588829,
-0.02909831330180168,
0.0185321606695652,
-0.046098582446575165,
0.0488668791949749,
0.00853749644011259,
-0.021329646930098534,
-0.028887808322906494,
-0.005014771595597267,
-0.0011913469061255455,
-0.02695036493241787,
0.033369030803442,
0.024790262803435326,
-0.005618756636977196,
0.003366730874404311,
0.029418235644698143,
-0.006405708380043507,
0.008768442086875439,
-0.001630062935873866,
-0.02510915882885456,
0.0353400893509388,
-0.0022272251080721617,
-0.02689361199736595,
0.01760256476700306,
-0.03198742866516113,
0.03487870842218399,
-0.035832442343235016,
0.01465682778507471,
0.01326923817396164,
-0.05570517107844353,
-0.03718788921833038,
0.025263410061597824,
0.007671932689845562,
0.0035253772512078285,
-0.050518590956926346,
0.015498533844947815,
0.04403295740485191,
-0.03077779710292816,
-0.05142413079738617,
-0.037981852889060974,
0.020152246579527855,
-0.018626755103468895,
0.028700068593025208,
-0.04129767417907715,
0.006155704613775015,
-0.027028728276491165,
-0.027920758351683617,
-0.02146007865667343,
0.03518456220626831,
0.009146535769104958,
-0.02238507755100727,
0.0038262978196144104,
0.016009535640478134,
0.07520925998687744,
0.0007095246110111475,
-0.01070401817560196,
0.01177246868610382,
0.01279472280293703,
-0.017977653071284294,
0.011609961278736591,
0.019580582156777382,
-0.010318724438548088,
-0.0009374803630635142,
0.006364964880049229,
-0.020462816581130028,
0.021849708631634712,
0.012821977026760578,
0.0067074778489768505,
0.021593453362584114,
0.039860982447862625,
0.03123430348932743,
-0.008691059425473213,
0.00810198113322258,
-0.008050081320106983,
0.0302162803709507,
-0.04460083320736885,
-0.0026435600593686104,
0.016057416796684265,
-0.019404936581850052,
0.005546981003135443,
-0.03330501168966293,
0.03952452167868614,
0.00644534220919013,
0.062323398888111115,
-0.008437169715762138,
-0.016529008746147156,
0.029500091448426247,
0.012990147806704044,
-0.0011600699508562684,
0.0056916940957307816,
0.02056700363755226,
-0.022073816508054733,
0.011861828155815601,
-0.03727151080965996,
-0.003360817674547434,
-0.021067116409540176,
0.004710654728114605,
0.07703623175621033,
-0.023197442293167114,
0.0445941761136055,
0.02138020657002926,
0.01673186384141445,
0.032689422369003296,
-0.004292632918804884,
-0.0374227799475193,
0.018524160608649254,
-0.00462452182546258,
0.07344874739646912,
-0.026867525652050972,
0.02131488360464573,
0.030228838324546814,
0.046895138919353485,
-0.0453827828168869,
0.04773032292723656,
-0.013348449021577835,
0.019137004390358925,
0.004544678144156933,
-0.009958808310329914,
-0.037070970982313156,
0.031575072556734085,
-0.0619991235435009,
0.007080772425979376,
-0.02903786301612854,
-0.005450614262372255,
0.013952876441180706,
0.012819935567677021,
-0.011539334431290627,
0.0003146499511785805,
-0.019720623269677162,
-0.04345106706023216,
0.0016025406075641513,
0.03533036261796951,
0.0037833743263036013,
0.03632085770368576,
-0.011749413795769215,
0.08120014518499374,
-0.031974293291568756,
0.0216275192797184,
-0.02781902812421322,
-0.00520789809525013,
-0.033710822463035583,
-0.06252991408109665,
-0.059200871735811234,
0.07117967307567596,
-0.03406054154038429,
-0.011774524115025997,
0.009794443845748901,
0.011760705150663853,
-0.006476689130067825,
-0.0038634652737528086,
-0.0037749179173260927,
-0.008219672366976738,
0.04760029539465904,
0.010904268361628056,
0.03168656304478645,
-0.009598716162145138,
0.01995094306766987,
0.11214587837457657,
0.028128918260335922,
0.038860321044921875,
-0.06495731323957443,
0.014578286558389664,
-0.034417297691106796,
-0.0034190048463642597,
-0.03798176720738411,
0.03172881528735161,
-0.01990285888314247,
-0.024889936670660973,
-0.009518267586827278,
0.07020951807498932,
-0.009951259940862656,
-0.01261426042765379,
0.019349604845046997,
-0.034491896629333496,
-0.019378522410988808,
0.020529508590698242,
-0.002663361607119441,
0.009544276632368565,
-0.0038988105952739716,
-0.05831839144229889,
-0.008534331806004047,
-0.00022973635350354016,
-0.0072965556755661964,
-0.022770749405026436,
0.007325866259634495,
0.014917442575097084,
0.010720751248300076,
-0.041193585842847824,
0.005605639424175024,
0.02523479238152504,
0.029531074687838554,
0.024650685489177704,
0.026732709258794785,
0.023952029645442963,
-0.03798260912299156,
0.009691737592220306,
0.04915311560034752,
0.028212854638695717,
0.01692637987434864,
-0.0025143749080598354,
-0.010026853531599045,
-0.030772190541028976,
0.01643526181578636,
-0.04881046339869499,
0.0317705012857914,
-0.005230156239122152,
-0.010583137162029743,
-0.007554654031991959,
0.04279882460832596,
0.015127049759030342,
-0.03307512775063515,
0.023084409534931183,
0.04190424457192421,
0.0331350602209568,
-0.027878182008862495,
-0.00656743673607707,
0.014826114289462566,
0.011927437037229538,
0.012626268900930882,
0.027058066800236702,
-0.0006788030732423067,
-0.023203948512673378,
0.015221797861158848,
0.0030244432855397463,
-0.025431843474507332,
-0.020175745710730553,
-0.036943670362234116,
-0.004612339660525322,
0.004944715183228254,
-0.026925159618258476,
-0.044326137751340866,
-0.007364868652075529,
0.0018554296111688018,
0.024288492277264595,
-0.000694645510520786,
0.017496634274721146,
-0.0046342420391738415,
-0.05455314368009567,
0.0323045440018177,
0.004774180240929127,
-0.014013836160302162,
0.005558990407735109,
-0.020446261391043663,
0.026557117700576782,
0.02094481699168682,
-0.0005540989222936332,
-0.02368284948170185,
-0.007927410304546356,
0.0008557618129998446,
0.07002174109220505,
-0.0349561832845211,
-0.05287580564618111,
0.03074146807193756,
-0.0057017006911337376,
-0.008326202630996704,
-0.04125409945845604,
0.02880740351974964,
0.04210282862186432,
-0.008546325378119946,
0.006125799845904112,
0.0831589624285698,
0.0033228991087526083,
-0.028257019817829132,
0.005949984770268202,
-0.003944905009120703,
0.015739811584353447,
0.011083259247243404,
-0.025725707411766052,
-0.003388486336916685,
-0.009401296265423298,
-0.017104752361774445,
-0.008431682363152504,
0.025749586522579193,
0.0076077040284872055,
-0.03671623021364212,
0.012449022382497787,
-0.034672513604164124,
0.0009940946474671364,
0.015029104426503181,
-0.021813426166772842,
-0.04504531994462013,
-0.014379041269421577,
0.013677726499736309,
-0.04183327034115791,
-0.02553984522819519,
0.027155933901667595,
-0.03309289738535881,
-0.014811305329203606,
0.05490809306502342,
0.013779064640402794,
-0.007202660199254751,
-0.01899624802172184,
0.009879420511424541,
-0.015773991122841835,
0.04782147333025932,
0.01671941764652729,
0.013374611735343933,
0.007432670332491398,
-0.030476678162813187,
-0.03013732098042965,
0.02424556016921997,
0.03615301102399826,
0.06800668686628342,
0.017478523775935173,
-0.012902281247079372,
-0.026017548516392708,
0.061852119863033295,
-0.05532839894294739,
-0.0013092213775962591,
-0.02307330071926117,
-0.0060140532441437244,
-0.010032519698143005,
-0.032098688185214996,
-0.011624783277511597,
-0.012324236333370209,
0.013704982586205006,
-0.02193765714764595,
0.006474086083471775,
-0.01980423927307129,
-0.04829353094100952,
-0.0015271357260644436,
-0.006547741126269102,
0.0171032827347517,
-0.01534743420779705,
0.024264095351099968,
0.0054937866516411304,
0.02864147536456585,
-0.04048464447259903,
0.0094406483694911,
0.0009367938037030399,
0.00415263744071126,
-0.09909050911664963,
-0.05790144205093384,
0.02770555205643177,
0.01646142452955246,
0.06586645543575287,
-0.043031543493270874,
0.0045740120112895966,
-0.033486898988485336,
-0.016678079962730408,
-0.03827572613954544,
-0.02088066004216671,
0.0059637404046952724,
0.006608213763684034,
-0.027105212211608887,
-0.008559727109968662,
0.04801098257303238,
0.005656746216118336,
0.013194710947573185,
-0.017941493541002274,
-0.009549833834171295,
-0.02250896394252777,
-0.029173098504543304,
-0.014820465818047523,
-0.00797270517796278,
-0.004790556151419878,
-0.07508295774459839,
0.05641581490635872,
-0.004194860812276602,
-0.051432427018880844,
0.010530523024499416,
-0.024377629160881042,
-0.0198887437582016,
0.012580099515616894,
0.03749748319387436,
0.05044145509600639,
0.018555931746959686,
-0.020274894312024117,
-0.011965230107307434,
-0.008977553807199001,
-0.0037179177161306143,
0.030818428844213486,
0.0284041129052639,
-0.04091876745223999,
-0.02616899274289608,
0.02605190873146057,
-0.021922413259744644,
-0.03872612118721008,
0.023747660219669342,
-0.02332758530974388,
-0.0166936032474041,
-0.029954299330711365,
-0.05127698928117752,
0.017999546602368355,
-0.024392927065491676,
0.02738574892282486,
-0.03191725164651871,
0.012995918281376362,
0.012775778770446777,
-0.004420807119458914,
0.00869316328316927,
0.00980071909725666,
0.023572439327836037,
-0.03214718773961067,
-0.004000215325504541,
0.007967846468091011,
-0.029997307807207108,
-0.02642492949962616,
-0.03320591524243355,
0.019749680534005165,
-0.0026798949111253023,
-0.007656204979866743,
-0.04902876541018486,
-0.06895888596773148,
0.006384212523698807,
-0.005600645672529936,
0.01912453956902027,
-0.014117198996245861,
-0.04181637614965439,
0.03009396232664585,
-0.04797749221324921,
-0.007818150334060192,
0.03606933727860451,
-0.001282515819184482,
-0.0040263463743031025,
0.0018373654456809163,
-0.007978081703186035,
0.03752632439136505,
0.06268803775310516,
-0.006975145079195499,
-0.04386644437909126,
-0.023146184161305428,
0.042524710297584534,
0.049085941165685654,
-0.0597674734890461,
0.009844883345067501,
-0.007626444101333618,
-0.0067220875062048435,
0.009215597994625568,
0.0036021654959768057,
-0.03848448395729065,
0.03086286038160324,
0.014370922930538654,
-0.0120634650811553,
-0.04986776039004326,
-0.0008358954219147563,
-0.03177830949425697,
0.009750197641551495,
-0.006943889893591404,
-0.03140044957399368,
0.03311983495950699,
0.0216347835958004,
0.020213047042489052,
0.03453756496310234,
-0.0032840885687619448,
-0.05586618930101395,
-0.0021966597996652126,
-0.0832490622997284,
-0.028560422360897064,
-0.01887386292219162,
-0.004810073412954807,
0.009788915514945984,
-0.06286242604255676,
-0.005365179385989904,
0.052608076483011246,
-0.0571734644472599,
-0.017741691321134567,
0.053939320147037506,
0.038273558020591736,
0.0069170156493783,
0.037053342908620834,
-0.010269206017255783,
-0.021829113364219666,
-0.023682788014411926,
0.010124911554157734,
0.009320876561105251,
0.03029588982462883,
-0.017649367451667786,
0.007567747961729765,
0.02883276715874672,
-0.040387529879808426,
0.006221521645784378,
0.007149951066821814,
0.042930543422698975,
-0.02815263904631138,
-0.013171542435884476,
-0.0036505088210105896,
0.0004590061726048589,
0.01745159737765789,
0.005715087987482548,
-0.034291744232177734,
0.04895094782114029,
-0.03566503897309303,
0.04208645969629288,
-0.050088148564100266,
0.0011404312681406736,
-0.04217036813497543,
0.009174139238893986,
0.04888657480478287,
0.053805794566869736,
-0.042780183255672455,
0.01353144645690918,
-0.008915391750633717,
-0.0328737236559391,
-0.009620174765586853,
-0.04970032349228859,
-0.027147704735398293,
0.024480335414409637,
-0.024657199159264565,
-0.010153952054679394,
-0.012875991873443127,
-0.02015417441725731,
-0.0242571122944355,
0.026091216132044792,
0.001236087060533464,
0.0043742964044213295,
0.014216944575309753,
-0.008890435099601746,
-0.027530454099178314,
0.038395125418901443,
-0.04341232031583786,
-0.03120797872543335,
-0.049080975353717804,
0.028203142806887627,
-0.001340129179880023,
0.011673634871840477
] |
<p>$\newcommand{\bra}[1]{\left\langle#1\right|}$
$\newcommand{\ket}[1]{\left|#1\right\rangle}$
Suppose I have a beam splitter that will either reflect a photon by 45 degrees, or will allow the photon to pass directly through.</p>
<p>If I send a single photon state through, that is, $\ket{1}_{initial}$, we have:</p>
<p>$\ket{1}_{initial} = \frac{1}{\sqrt{2}}(\ket{0}_a\ket{1}_b + i\ket{1}_a\ket{0}_b)$</p>
<p>where $a$ and $b$ represent the paths that pass straight through, and the reflecting paths respectively.</p>
<p>Now suppose instead of sending through a single photon, the initial state is two photons, that is, $\ket{2}_{initial}$. Classically I would suspect the state to look something like this:</p>
<p>$\ket{2}_{initial} \propto (\ket{0}_a\ket{2}_b + \ket{2}_a\ket{0}_b + 2\ket{1}_a\ket{1}_b$)</p>
<p>I have the factor of 2 in front of the $\ket{1}_a\ket{1}_b$ state because classically you could have the first photon passing through and the second photon reflecting, or vice-versa. Is this still correct for quantum mechanics, where photons are indistinguishable?</p>
<p>Also, could you please show how to derive result that I have simply guessed for two photons (given the 1 photon case in the first equation)?</p>
| 9,413 |
[
0.011736201122403145,
-0.017417356371879578,
-0.014764362946152687,
-0.012033727020025253,
0.032870855182409286,
-0.009833895601332188,
-0.0033577014692127705,
-0.039736077189445496,
0.024000700563192368,
-0.003575478680431843,
0.06734063476324081,
0.024298083037137985,
0.029338276013731956,
0.02011157013475895,
0.013222378678619862,
0.0032695909030735493,
-0.0036401660181581974,
-0.006729879882186651,
0.0017013776814565063,
-0.044852979481220245,
-0.005572962574660778,
0.030219173058867455,
0.034091103821992874,
-0.012353245168924332,
-0.03169650584459305,
0.03731293976306915,
-0.008767594583332539,
0.010226082988083363,
0.0015910703223198652,
0.048198506236076355,
0.03696509078145027,
-0.03150347247719765,
0.0020891567692160606,
0.04891432076692581,
-0.028265535831451416,
-0.01668252982199192,
-0.03655894100666046,
-0.05903174728155136,
-0.004059838596731424,
-0.004548607859760523,
-0.04607084393501282,
-0.019885225221514702,
-0.043599653989076614,
0.03403755649924278,
0.002858395455405116,
-0.010585461743175983,
-0.017944548279047012,
-0.0023638964630663395,
0.03771084547042847,
-0.053550105541944504,
0.08627574890851974,
0.017173169180750847,
0.05956399440765381,
-0.006623921450227499,
-0.04814284294843674,
-0.0338699109852314,
0.060501232743263245,
0.09074609726667404,
-0.01070214994251728,
-0.01932584121823311,
-0.024259353056550026,
-0.02833363600075245,
-0.024565141648054123,
0.004026062786579132,
-0.045253872871398926,
0.00596587173640728,
-0.01778372749686241,
-0.04022582247853279,
0.034509047865867615,
-0.033230010420084,
0.020503297448158264,
-0.019387003034353256,
0.06089257821440697,
-0.04037504643201828,
0.0011119410628452897,
-0.001175139332190156,
0.009033620357513428,
0.03796956315636635,
0.02969605103135109,
0.02596135437488556,
-0.018094101920723915,
-0.004303967114537954,
0.014189123176038265,
0.03901822492480278,
0.008153999224305153,
-0.01787519082427025,
0.06270524859428406,
-0.017828719690442085,
0.018863551318645477,
0.010676552541553974,
-0.02696535550057888,
0.03823181241750717,
0.022302787750959396,
0.0006606069509871304,
-0.003963614348322153,
0.05453205853700638,
0.011503246612846851,
0.06759502738714218,
-0.005338371265679598,
-0.030230320990085602,
-0.007789168506860733,
-0.015315864235162735,
0.026728812605142593,
0.07825576514005661,
-0.029301021248102188,
0.014005286619067192,
-0.03321681544184685,
0.0435168631374836,
-0.02633873000741005,
-0.01626547984778881,
-0.03384239226579666,
0.033372972160577774,
-0.0225847065448761,
0.0046742078848183155,
0.03324752673506737,
-0.0597151555120945,
-0.005249746143817902,
-0.021248046308755875,
0.051259368658065796,
0.07704034447669983,
0.052377618849277496,
-0.021807486191391945,
0.024255169555544853,
-0.04520094394683838,
-0.03669704124331474,
0.005533566698431969,
0.039827242493629456,
-0.0042339228093624115,
-0.05280313640832901,
0.02020256780087948,
0.002115726238116622,
-0.009793375618755817,
-0.009326455183327198,
-0.008153688162565231,
-0.019573189318180084,
-0.0587555468082428,
-0.12548261880874634,
-0.07257962226867676,
0.027886882424354553,
-0.03053944557905197,
-0.02630661427974701,
-0.06811977177858353,
0.049608245491981506,
0.0508381649851799,
0.12083393335342407,
-0.02578362263739109,
0.028114836663007736,
0.01312324684113264,
0.03589347377419472,
0.01733725517988205,
-0.04691029712557793,
-0.004441839177161455,
-0.0063019925728440285,
-0.017391351982951164,
0.01351369172334671,
-0.028547706082463264,
0.012757319957017899,
0.05659159645438194,
-0.013727270066738129,
-0.027881821617484093,
0.06348521262407303,
-0.040090397000312805,
0.018658321350812912,
0.04916594177484512,
-0.011181925423443317,
-0.031807128340005875,
0.10523629933595657,
0.06021023541688919,
-0.0000034665151815715944,
0.03951634094119072,
0.003926335833966732,
-0.009360709227621555,
-0.02520940452814102,
-0.00671409722417593,
0.0062073296867311,
-0.03544684499502182,
-0.01402167696505785,
0.001609442988410592,
0.008588992059230804,
-0.019218822941184044,
-0.011798123829066753,
-0.044018834829330444,
-0.018649732694029808,
0.011242027394473553,
-0.0016688161995261908,
0.011170181445777416,
-0.0019504361553117633,
-0.004830886144191027,
-0.023164262995123863,
-0.03648817539215088,
-0.0007837946759536862,
-0.05491459742188454,
0.022125694900751114,
0.03314821794629097,
-0.01882755011320114,
0.03815189003944397,
0.015557131730020046,
0.030700940638780594,
-0.0001436098391423002,
-0.034562256187200546,
-0.037079133093357086,
-0.004046904854476452,
0.0013626704458147287,
-0.003019860479980707,
0.024738458916544914,
0.06910118460655212,
0.0468616746366024,
0.026648620143532753,
0.04124855250120163,
-0.027595505118370056,
-0.008276776410639286,
0.00172235572244972,
-0.012491537258028984,
0.04918520897626877,
-0.016485346481204033,
0.02215110883116722,
-0.013789776712656021,
-0.013853399083018303,
-0.02764926105737686,
0.017310263589024544,
-0.0726795643568039,
0.053431253880262375,
0.04054444283246994,
0.01438194140791893,
-0.008592931553721428,
0.03552962467074394,
0.01603848673403263,
0.013732951134443283,
-0.01321334671229124,
-0.06757265329360962,
-0.03788936883211136,
-0.01597491465508938,
0.03190943971276283,
0.004398474935442209,
-0.04083967208862305,
0.03327897563576698,
0.01855829544365406,
0.022625772282481194,
0.0279706884175539,
0.021889643743634224,
-0.04804236814379692,
-0.021779529750347137,
0.030473196879029274,
0.021024679765105247,
-0.02125496044754982,
0.018846921622753143,
0.005834606476128101,
-0.01762344501912594,
0.014162315055727959,
0.007432570215314627,
-0.027875708416104317,
-0.009218018501996994,
-0.03588346019387245,
0.021308116614818573,
0.0008670707466080785,
-0.033503543585538864,
0.02777239680290222,
-0.0044870092533528805,
0.014392510987818241,
0.03012913465499878,
-0.010080035775899887,
-0.018052635714411736,
-0.013700698502361774,
-0.0067595383152365685,
-0.012077192775905132,
-0.009372057393193245,
-0.010544609278440475,
-0.013125409372150898,
0.026923339813947678,
-0.028102364391088486,
0.006963742896914482,
-0.03327568620443344,
0.0006635168101638556,
-0.02940106950700283,
-0.035003989934921265,
0.006883764173835516,
0.016265377402305603,
0.018466532230377197,
-0.06490115076303482,
-0.03062852844595909,
-0.0014425404369831085,
-0.01181788370013237,
0.029101012274622917,
-0.022545889019966125,
-0.04670895263552666,
0.03780768811702728,
-0.03954116255044937,
0.005235216114670038,
0.051288895308971405,
-0.015269914641976357,
-0.011609602719545364,
-0.009436194784939289,
-0.03466155007481575,
-0.07548493146896362,
-0.03672299534082413,
-0.034371327608823776,
0.007005259394645691,
-0.02709437534213066,
-0.03552570566534996,
0.04767276346683502,
0.01190260611474514,
-0.04022657126188278,
-0.030294861644506454,
-0.02073981612920761,
-0.047149330377578735,
-0.019289107993245125,
-0.04045047238469124,
0.02178162708878517,
-0.02952541783452034,
0.0213000550866127,
0.0316845141351223,
-0.047535307705402374,
0.02099119871854782,
-0.06798619776964188,
-0.038739293813705444,
0.03914988040924072,
0.007803406100720167,
0.021499525755643845,
0.0233390424400568,
-0.02736409567296505,
0.06937173753976822,
0.035451002418994904,
-0.00901236105710268,
-0.0005271407426334918,
0.008345810696482658,
0.003365779295563698,
-0.03308962285518646,
0.000948647502809763,
0.016313083469867706,
-0.014446132816374302,
0.05786352977156639,
0.03065279684960842,
0.0002703833451960236,
0.05946340411901474,
0.016480356454849243,
-0.004482385702431202,
0.007345303893089294,
0.010361718945205212,
-0.013876914978027344,
0.01871630921959877,
0.03057604655623436,
-0.02588888816535473,
0.0054976558312773705,
0.0007113225292414427,
-0.019331295043230057,
-0.015233066864311695,
-0.03461931645870209,
0.060783371329307556,
0.008060870692133904,
0.026033371686935425,
-0.024657152593135834,
0.03943997994065285,
-0.009083381853997707,
0.012838728725910187,
-0.000049994625442195684,
0.02140946313738823,
0.02995063178241253,
-0.043360669165849686,
-0.0005075182998552918,
0.033213041722774506,
0.018132852390408516,
0.007428217213600874,
-0.03272000700235367,
0.027188951149582863,
-0.014992981217801571,
0.023325981572270393,
0.02388475462794304,
-0.03219710290431976,
0.03838428854942322,
0.020423749461770058,
0.04508950561285019,
-0.013915373012423515,
-0.021903641521930695,
-0.02398427575826645,
-0.03266765922307968,
0.019259124994277954,
0.00575430179014802,
0.053870148956775665,
-0.0023862801026552916,
0.03372519835829735,
0.038802940398454666,
0.022185076028108597,
-0.008729886263608932,
-0.015185646712779999,
-0.06694456189870834,
0.01675470359623432,
-0.005596486385911703,
-0.028215622529387474,
0.007019359152764082,
-0.012554410845041275,
-0.011200659908354282,
-0.05156426504254341,
-0.0703895092010498,
0.0012661342043429613,
-0.024449340999126434,
-0.0343121737241745,
0.008780493400990963,
-0.04704483970999718,
-0.046292390674352646,
-0.01872912421822548,
0.009284468367695808,
0.02559315599501133,
-0.021411173045635223,
0.01095182728022337,
0.06205626204609871,
-0.051618367433547974,
0.028620198369026184,
-0.03833744302392006,
0.017589466646313667,
0.018279429525136948,
0.03596194088459015,
0.07402810454368591,
0.018924739211797714,
0.010035119019448757,
0.01770518161356449,
-0.01871049962937832,
0.016014304012060165,
-0.00019735400564968586,
-0.0362045057117939,
-0.0058035338297486305,
-0.018965795636177063,
0.00500441575422883,
-0.03771736100316048,
0.053633224219083786,
0.007210662588477135,
-0.006894102785736322,
0.030639981850981712,
0.04063161090016365,
-0.007600586395710707,
0.01763349212706089,
0.07131000608205795,
0.002208961406722665,
-0.012069634161889553,
-0.04341559484601021,
-0.004690933972597122,
-0.021043479442596436,
-0.004114256240427494,
0.006154737435281277,
-0.014094643294811249,
-0.013646891340613365,
0.008568108081817627,
0.020480617880821228,
0.026637854054570198,
0.007473439909517765,
0.0034334163647145033,
-0.014478793367743492,
-0.003914790228009224,
0.01852659322321415,
-0.016351468861103058,
-0.012539047747850418,
0.03569013625383377,
0.014974243938922882,
0.0032921377569437027,
0.011818287894129753,
-0.05929069221019745,
-0.006778737995773554,
0.009210889227688313,
0.016057603061199188,
-0.010404801927506924,
-0.025478385388851166,
-0.03405786678195,
-0.037205666303634644,
0.03102952614426613,
0.004691555630415678,
0.06708987057209015,
-0.01715805009007454,
-0.03420650586485863,
-0.0024475902318954468,
-0.025975802913308144,
-0.02013389766216278,
0.0453290119767189,
0.020430561155080795,
0.028408819809556007,
0.017085036262869835,
-0.03511587902903557,
-0.014413726516067982,
-0.008656412363052368,
0.0009426307515241206,
0.07048960030078888,
-0.03924725949764252,
-0.02421959489583969,
0.0015846199821680784,
0.03765655681490898,
-0.020561883226037025,
-0.07638464123010635,
0.028784049674868584,
0.014773493632674217,
-0.022630436345934868,
0.03513812646269798,
-0.04631144553422928,
-0.02403935231268406,
0.03981352597475052,
0.021695803850889206,
0.012853399850428104,
0.01704457588493824,
-0.02069750614464283,
0.04392705112695694,
-0.0006768772145733237,
0.004662659950554371,
0.06893675774335861,
0.02229325659573078,
-0.000639874255284667,
0.0009414103114977479,
-0.02054218389093876,
0.06509938091039658,
-0.00919989962130785,
-0.001954240957275033,
-0.028707435354590416,
0.030269650742411613,
-0.036839935928583145,
0.07982435822486877,
-0.012273228727281094,
0.008996385149657726,
0.006259423680603504,
-0.04688774049282074,
0.014313951134681702,
0.03461490571498871,
-0.03974832966923714,
0.017915215343236923,
-0.03804483264684677,
0.05397091060876846,
0.002907984424382448,
-0.018978742882609367,
0.004982126411050558,
-0.018030105158686638,
0.027927909046411514,
0.01359967328608036,
-0.004111812449991703,
0.05739206448197365,
-0.02345746010541916,
-0.021372955292463303,
0.019590996205806732,
-0.05298705771565437,
0.04070001840591431,
-0.0026172164361923933,
0.01724006049335003,
0.010231372900307178,
-0.04898182675242424,
-0.03694978728890419,
0.019861575216054916,
0.002431044355034828,
0.016301177442073822,
-0.04854421690106392,
0.004416514188051224,
0.014891823753714561,
-0.02480711229145527,
-0.07404754310846329,
-0.06349380314350128,
0.015852060168981552,
-0.0030323921237140894,
0.006852404680103064,
-0.03586624562740326,
0.02375873737037182,
-0.02009955234825611,
-0.02794673852622509,
-0.02558647282421589,
0.04641178995370865,
-0.013498672284185886,
-0.029650550335645676,
0.013360537588596344,
0.03189690411090851,
0.009634318761527538,
0.02095573954284191,
-0.009569552727043629,
-0.003759263549000025,
-0.016226986423134804,
-0.02094523049890995,
0.033345069736242294,
0.05881767347455025,
-0.03390964865684509,
-0.07839281857013702,
-0.040136631578207016,
0.019278990104794502,
0.05108727142214775,
-0.023424364626407623,
-0.012763338163495064,
-0.0015134980203583837,
0.018262825906276703,
0.002841331996023655,
0.01786479353904724,
-0.010658430866897106,
0.018461721017956734,
0.013850584626197815,
0.01395667064934969,
-0.007978844456374645,
-0.015971515327692032,
-0.041245777159929276,
0.03182150423526764,
0.010956566780805588,
0.008113209158182144,
-0.007783566601574421,
0.048079267144203186,
0.010684349574148655,
0.006639824248850346,
0.044735584408044815,
-0.004591166041791439,
0.0003845837782137096,
-0.0006895668338984251,
-0.010113414376974106,
0.021919332444667816,
-0.017993168905377388,
-0.014536217786371708,
-0.012739165686070919,
-0.037116844207048416,
0.0138577651232481,
0.07919805496931076,
-0.00997152179479599,
0.04123779758810997,
0.018681464716792107,
0.007153387647122145,
-0.011346309445798397,
-0.014613548293709755,
-0.016064608469605446,
-0.010027483105659485,
-0.001964208437129855,
0.04199197515845299,
-0.054120514541864395,
0.008609971962869167,
0.013946878723800182,
0.05629337206482887,
0.026250818744301796,
0.01795431785285473,
0.04045763984322548,
0.015723802149295807,
0.017132999375462532,
-0.005311928223818541,
-0.02637821063399315,
0.04011646285653114,
-0.02932741865515709,
0.0004790991952177137,
-0.019498903304338455,
-0.02592385932803154,
0.05081028863787651,
0.0073189763352274895,
0.013459650799632072,
-0.03706994280219078,
-0.008542709052562714,
-0.04996084049344063,
0.0135306091979146,
0.003201940329745412,
0.009941001422703266,
0.04664968326687813,
0.020590847358107567,
0.031452078372240067,
0.008296540006995201,
0.02655782178044319,
-0.018288521096110344,
-0.0442228727042675,
-0.06047166883945465,
-0.04823971167206764,
-0.04478776454925537,
0.05987141653895378,
-0.017141355201601982,
-0.0015468058409169316,
0.031612955033779144,
-0.03816380351781845,
0.017887379974126816,
0.03047066740691662,
0.055236462503671646,
-0.004712884314358234,
0.05230420082807541,
-0.006761668715626001,
0.019353583455085754,
-0.0002095887321047485,
-0.0018385769799351692,
0.09146515280008316,
0.06801638007164001,
0.026606356725096703,
-0.05927758663892746,
0.028948763385415077,
-0.02134900912642479,
0.01179137360304594,
-0.016590943560004234,
0.02861432544887066,
-0.022105494514107704,
0.0031434246338903904,
-0.0014481507241725922,
0.032949622720479965,
0.02930454909801483,
0.00340075115673244,
0.01718439906835556,
-0.06004415452480316,
-0.05916425213217735,
0.0238456130027771,
0.02177361585199833,
0.015827510505914688,
0.017643341794610023,
-0.0019290933851152658,
-0.0052196127362549305,
-0.029710235074162483,
0.022022627294063568,
-0.010791980661451817,
-0.006865206174552441,
0.01266509760171175,
0.001908385194838047,
0.025454845279455185,
0.01143516693264246,
0.0209379643201828,
-0.02496335469186306,
-0.006443822756409645,
0.019386792555451393,
0.042154710739851,
-0.023392684757709503,
0.04393741860985756,
0.019314181059598923,
0.034587353467941284,
-0.0026998238172382116,
0.04815535619854927,
0.0056693051010370255,
-0.046111542731523514,
-0.010198052041232586,
-0.0012053364189341664,
0.06012660637497902,
-0.024892035871744156,
-0.0015006514731794596,
-0.02591845393180847,
-0.03345706686377525,
0.039868634194135666,
-0.05759524181485176,
-0.017035605385899544,
0.017829008400440216,
0.01790696755051613,
-0.03226480633020401,
0.008226984180510044,
0.007511170115321875,
0.009401833638548851,
0.007673065643757582,
0.009116810746490955,
-0.023029973730444908,
-0.0019014326389878988,
0.002369968919083476,
0.012898710556328297,
0.024864694103598595,
-0.0006555755971930921,
-0.015269807539880276,
-0.0332023948431015,
-0.023547980934381485,
-0.05963481217622757,
-0.03436155617237091,
0.03892304375767708,
0.01675717532634735,
0.0358874537050724,
-0.02192772552371025,
-0.013308428227901459,
0.004134513437747955,
-0.06990139931440353,
-0.016219519078731537,
-0.007343036588281393,
-0.017498953267931938,
0.008736309595406055,
0.019883323460817337,
0.020765751600265503,
0.049819160252809525,
-0.015209688805043697,
-0.025014150887727737,
0.04875214397907257,
0.012123286724090576,
0.06239122152328491,
-0.03446869179606438,
-0.016782144084572792,
0.01750981993973255,
0.005571650341153145,
-0.018566373735666275,
-0.061601560562849045,
0.031475137919187546,
-0.000027685255190590397,
0.02008194290101528,
-0.001978339161723852,
0.030547190457582474,
-0.056848250329494476,
-0.017381951212882996,
0.0014977670507505536,
-0.03831588104367256,
0.003098792629316449,
0.022507065907120705,
0.042270731180906296,
-0.006246068049222231,
-0.017271677032113075,
0.0037054189015179873,
-0.0033293322194367647,
0.02200472727417946,
-0.020256144925951958,
-0.04424884915351868,
-0.037552498281002045,
-0.017662305384874344,
-0.02749214880168438,
-0.04573136568069458,
-0.019658653065562248,
0.0039228638634085655,
0.008532118052244186,
-0.018813006579875946,
0.0023436867631971836,
-0.01698356680572033,
0.0613594651222229,
0.012983113527297974,
-0.023888621479272842,
0.031865574419498444,
0.06423827260732651,
0.0004957880009897053,
-0.01574615016579628,
0.02701530046761036,
0.008459066972136497,
0.06520187109708786,
-0.0066717020235955715,
-0.018849236890673637,
0.026494521647691727,
-0.03191225975751877,
-0.012559548020362854,
0.04482320696115494,
0.021672340109944344,
0.04296170920133591,
0.04825722426176071,
-0.014095722697675228,
-0.012084166519343853,
0.04644087702035904,
0.004505031276494265,
-0.0032300082966685295,
-0.011560041457414627,
-0.029527073726058006,
0.001131234923377633,
-0.034164659678936005,
0.002345450920984149,
0.012575278989970684,
-0.022823793813586235,
0.021121470257639885,
-0.013464614748954773,
-0.0029098906088620424,
0.028746627271175385,
-0.025387726724147797,
0.010929147712886333,
0.01118712779134512,
0.037750374525785446,
-0.01131779607385397,
-0.007403487805277109,
0.07650081813335419,
-0.006992053706198931,
0.024549178779125214,
0.03432483226060867,
0.029421817511320114,
-0.09131289273500443,
-0.0023223317693918943,
0.003481964347884059,
0.016587765887379646,
0.03175627067685127,
-0.042641423642635345,
0.04048408940434456,
0.04370800778269768,
-0.05379308760166168,
0.014864291064441204,
-0.005895889364182949,
-0.010136701166629791,
-0.04238859936594963,
0.009993326850235462,
-0.05609583109617233,
0.06051025539636612,
-0.005148034077137709,
0.03926575556397438,
0.020629683509469032,
-0.008565696887671947,
0.0070825074799358845,
-0.0404445044696331,
-0.009300490841269493,
-0.012697070837020874,
-0.026572663336992264,
-0.006150466855615377,
0.07465353608131409,
0.0024346276186406612,
-0.022674761712551117,
0.026452679187059402,
-0.04442021995782852,
0.00867384485900402,
-0.0027905888855457306,
0.010231743566691875,
0.02954283356666565,
0.026253562420606613,
-0.018228139728307724,
-0.013774605467915535,
-0.02168596349656582,
-0.00210088724270463,
0.04112619534134865,
0.005420766305178404,
-0.014442653395235538,
-0.02749827317893505,
0.014946987852454185,
-0.0386832132935524,
-0.07005937397480011,
0.01213920395821333,
-0.0046760160475969315,
-0.01798216439783573,
0.012263736687600613,
0.00724073825404048,
0.015447711572051048,
-0.04924287647008896,
0.023119082674384117,
-0.06610272079706192,
-0.015941817313432693,
0.008452113717794418,
0.0012149991234764457,
-0.012090655043721199,
0.01451150793582201,
-0.0369415320456028,
-0.04624038562178612,
0.041121311485767365,
0.002800042973831296,
-0.007802311331033707,
-0.05542103946208954,
-0.050644565373659134,
0.017052920535206795,
0.012698587030172348,
0.007864461280405521,
-0.041646555066108704,
-0.0425075888633728,
0.03408677503466606,
-0.02245078980922699,
0.034452032297849655,
0.010296371765434742,
-0.01214214600622654,
-0.07097265869379044,
-0.07311360538005829,
0.02525937184691429,
0.033587999641895294,
-0.00790178868919611,
-0.041924621909856796,
-0.014918338507413864,
-0.04924582690000534,
0.0276485662907362,
0.0797065794467926,
0.0055571612901985645,
-0.018514063209295273,
0.007306190673261881,
0.028075851500034332,
0.018404211848974228,
-0.03229445964097977,
0.0015443075681105256,
-0.0145399309694767,
-0.0143800163641572,
-0.02504449523985386,
0.002824479714035988,
-0.01834140345454216,
0.024572081863880157,
-0.003658918896690011,
0.0008995791431516409,
-0.019215237349271774,
0.0019227920565754175,
-0.017990654334425926,
0.045160941779613495,
-0.023031126707792282,
0.013675656169652939,
0.07399813830852509,
-0.01941610686480999,
0.024439729750156403,
0.038786888122558594,
-0.047137510031461716,
-0.05918356031179428,
0.0024829653557389975,
-0.029817484319210052,
-0.002544068032875657,
-0.0172196626663208,
0.004184370394796133,
0.03036469779908657,
-0.040217284113168716,
-0.004255170002579689,
0.014761812053620815,
-0.0228662621229887,
0.014715549536049366,
0.015992362052202225,
-0.020379185676574707,
0.06456027179956436,
0.020200654864311218,
0.02879614569246769,
0.027606766670942307,
0.002812987193465233,
0.0026248511858284473,
0.05432647466659546,
0.016127515584230423,
0.01460090558975935,
0.02686096914112568,
0.021203529089689255,
-0.03351331129670143,
0.0036012823693454266,
0.004861864261329174,
0.006917680613696575,
-0.01884601265192032,
-0.010496612638235092,
0.018445689231157303,
-0.0003770450712181628,
-0.03312968090176582,
-0.025241337716579437,
-0.014535868540406227,
0.06127439811825752,
-0.015642434358596802,
0.03527325391769409,
-0.004158264026045799,
0.02269202657043934,
0.0055901650339365005,
0.016595931723713875,
0.043695200234651566,
0.03719545528292656,
0.0074352058582007885,
-0.015432048588991165,
-0.028266942128539085,
-0.014095781370997429,
-0.007205118425190449,
-0.04633742570877075,
0.003922083880752325,
0.0035459594801068306,
-0.021239327266812325,
-0.0016889522084966302,
-0.0292061660438776,
0.035954393446445465,
-0.038315560668706894,
0.008260158821940422,
0.043780118227005005,
0.011041021905839443,
-0.006410335656255484,
-0.005201708525419235,
-0.00011042875848943368,
0.08563259989023209,
-0.04142753407359123,
-0.016645444557070732,
-0.026446733623743057,
0.020921973511576653,
-0.0311186071485281,
-0.0010407638037577271
] |
<p>I know that the components of stress energy tensor are: energy density, energy flux, momentum density and momentum flux.</p>
<p>But can I explicitly calculate the form of stress energy tensor in any complicated situation? </p>
<p>Or explicit form is known only for few systems? How do I do it?</p>
| 9,414 |
[
-0.03293660283088684,
0.04106714949011803,
-0.025111563503742218,
-0.03840913996100426,
0.04060421139001846,
0.011947661638259888,
-0.048720262944698334,
-0.009284992702305317,
-0.008476733230054379,
-0.021564114838838577,
0.03270195797085762,
-0.0031636166386306286,
0.0418132022023201,
0.02996198460459709,
0.025921765714883804,
-0.03600480407476425,
0.017596004530787468,
0.006506850011646748,
-0.005766275804489851,
-0.05138514190912247,
-0.009305783547461033,
-0.02966129221022129,
-0.024053577333688736,
-0.01734997145831585,
-0.00884801521897316,
0.04338369145989418,
0.036796413362026215,
-0.014200333505868912,
0.03480009734630585,
0.031168133020401,
-0.018529245629906654,
-0.01567576639354229,
0.00042209867388010025,
0.01834902912378311,
0.009579217992722988,
-0.004162273835390806,
-0.06165271997451782,
-0.03983849659562111,
-0.014555324800312519,
0.0015393032226711512,
-0.014829769730567932,
0.01932954415678978,
0.00032106434809975326,
0.037636127322912216,
-0.02175493724644184,
0.03647270053625107,
0.001503056031651795,
-0.029149675741791725,
0.007049325853586197,
-0.054151713848114014,
0.0799483209848404,
-0.0030481263529509306,
0.07363603264093399,
0.016551189124584198,
-0.031719058752059937,
-0.012204430997371674,
0.04701380431652069,
0.06462810933589935,
-0.009638329967856407,
-0.041065432131290436,
-0.012447744607925415,
0.025773722678422928,
-0.03749685361981392,
-0.06171824038028717,
0.002855636179447174,
0.03544753044843674,
-0.004698201548308134,
-0.035960402339696884,
0.05281083285808563,
-0.00560831418260932,
0.005787720903754234,
-0.008136930875480175,
0.03241076320409775,
-0.024220997467637062,
0.0014906771248206496,
-0.010941955260932446,
0.04433417692780495,
-0.007448629476130009,
0.02610734850168228,
0.06133037433028221,
-0.010271885432302952,
0.022408992052078247,
0.037635572254657745,
0.047862231731414795,
0.0020152146462351084,
-0.010657058097422123,
0.055622681975364685,
0.01524315308779478,
0.007803207263350487,
0.01399035844951868,
0.021819785237312317,
0.014429798349738121,
-0.002572804456576705,
0.0026937758084386587,
-0.026091894134879112,
0.012181493453681469,
-0.005206587724387646,
0.052645422518253326,
0.0022151395678520203,
-0.021696265786886215,
0.007055542431771755,
-0.022622952237725258,
0.00838546548038721,
0.07306081056594849,
-0.007103072013705969,
0.00447870371863246,
-0.04971473664045334,
0.005296983290463686,
-0.023942824453115463,
-0.001101779518648982,
0.00043781849672086537,
-0.013046873733401299,
-0.01783854328095913,
-0.005245558451861143,
0.014342506416141987,
-0.020505772903561592,
-0.0070767938159406185,
-0.012563800439238548,
0.0069946423172950745,
0.08379825949668884,
0.031920675188302994,
-0.0247592031955719,
0.025154903531074524,
0.00039676661253906786,
-0.07059472054243088,
0.024229204282164574,
0.05671472102403641,
-0.027527479454874992,
-0.049034327268600464,
0.027410011738538742,
0.012271721847355366,
-0.027082456275820732,
0.001024005701765418,
0.005855384282767773,
0.01518101803958416,
-0.026093853637576103,
-0.10125396400690079,
-0.0801878571510315,
0.0283912792801857,
-0.022746259346604347,
-0.022376656532287598,
-0.07939530909061432,
0.008462921716272831,
0.0656193420290947,
0.045029014348983765,
0.006968091707676649,
-0.002845282666385174,
0.031718961894512177,
0.035828955471515656,
-0.01791124977171421,
-0.03165030851960182,
-0.012025858275592327,
-0.03410635516047478,
-0.03071012906730175,
0.02048501744866371,
-0.06683208048343658,
0.017737727612257004,
0.02913042902946472,
-0.02610715478658676,
0.007746068295091391,
0.05054036155343056,
-0.02150426059961319,
-0.00896945409476757,
0.03073306567966938,
-0.019852377474308014,
-0.018576642498373985,
0.062407657504081726,
-0.007993924431502819,
0.016103923320770264,
0.02139732986688614,
-0.0063115740194916725,
-0.046960677951574326,
-0.03078763373196125,
0.03153578191995621,
0.065897636115551,
-0.049353089183568954,
0.007701568305492401,
-0.003036038251593709,
0.0023027826100587845,
0.010652031749486923,
-0.03711734712123871,
-0.03397461026906967,
0.0029905468691140413,
0.010996799916028976,
0.004299578722566366,
0.04619288817048073,
-0.0002239206078229472,
-0.024524014443159103,
-0.00834226980805397,
-0.04031567648053169,
-0.02686869353055954,
-0.014238005504012108,
0.031153349205851555,
-0.045153867453336716,
-0.007358476985245943,
0.01483936607837677,
-0.0022873654961586,
0.02396143414080143,
-0.05123192071914673,
-0.017036836594343185,
0.0002724376099649817,
0.022686230018734932,
0.007080595009028912,
-0.016208088025450706,
0.010195995680987835,
-0.017180711030960083,
0.028260162100195885,
0.028384769335389137,
0.03112916462123394,
-0.02353401482105255,
-0.02386554330587387,
0.03840262442827225,
-0.05270601809024811,
0.02957446500658989,
0.008548070676624775,
-0.04773978143930435,
-0.00009419254638487473,
0.0060525075532495975,
0.04274845868349075,
0.002404007827863097,
-0.039463188499212265,
0.05238305777311325,
0.07195838540792465,
0.02292036823928356,
0.010880421847105026,
0.02198813669383526,
0.009667937643826008,
0.017987186089158058,
0.005025533493608236,
-0.00775942811742425,
-0.040882695466279984,
-0.013511798344552517,
0.027349557727575302,
0.02947213314473629,
-0.07982245832681656,
0.014789976179599762,
0.038163211196660995,
0.00434906268492341,
0.05966930463910103,
0.047035928815603256,
-0.019804075360298157,
-0.03774981573224068,
0.0318739227950573,
0.055745601654052734,
0.012662081979215145,
0.02099558524787426,
0.0008283510687761009,
0.0383753627538681,
-0.01040966808795929,
-0.014200435020029545,
-0.003985440358519554,
0.04479226469993591,
-0.013818005099892616,
-0.00744863785803318,
0.012551993131637573,
-0.046098340302705765,
0.047941360622644424,
-0.022965487092733383,
0.06338079273700714,
0.05498061701655388,
-0.019948633387684822,
0.002666088053956628,
0.012626717798411846,
-0.009497532621026039,
0.013169695623219013,
0.024379635229706764,
-0.003428259864449501,
-0.026046978309750557,
0.032848212867975235,
-0.017922427505254745,
0.013714379630982876,
-0.010918935760855675,
-0.009940898977220058,
-0.022230420261621475,
-0.020748673006892204,
0.032422054558992386,
-0.027641136199235916,
0.02438502199947834,
-0.0011912609916180372,
-0.009816251695156097,
0.021830081939697266,
-0.02675064653158188,
-0.01657070219516754,
-0.013704434968531132,
-0.05849391967058182,
0.011698907241225243,
-0.02677108719944954,
-0.0562547892332077,
0.040083616971969604,
-0.028492797166109085,
-0.01528111007064581,
0.02671906352043152,
-0.011684228666126728,
-0.049749862402677536,
-0.006762603297829628,
-0.0005591901135630906,
0.001611183281056583,
-0.024794716387987137,
-0.0021515130065381527,
0.06607300043106079,
-0.04444941133260727,
-0.032528676092624664,
-0.01439971849322319,
-0.00495592225342989,
-0.055201731622219086,
-0.016481120139360428,
-0.028330961242318153,
0.013934088870882988,
-0.0026076410431414843,
0.048674292862415314,
0.030484819784760475,
-0.07683639973402023,
0.015398621559143066,
-0.04535841569304466,
-0.03506731986999512,
0.01614423468708992,
0.009448391385376453,
0.04862993583083153,
0.014494718052446842,
-0.07670669257640839,
0.08149021863937378,
-0.007478184532374144,
-0.07634461671113968,
0.0045314147137105465,
-0.02671201340854168,
0.016267739236354828,
-0.0325113944709301,
-0.019220707938075066,
-0.0017189333448186517,
-0.010268609039485455,
0.010356814600527287,
0.023539217188954353,
0.023217175155878067,
0.03185374662280083,
0.03920929506421089,
-0.027214830741286278,
0.005533861927688122,
0.02685343660414219,
0.00004430134140420705,
0.04243887960910797,
0.00960510689765215,
-0.022819604724645615,
0.003371951635926962,
-0.010713500902056694,
0.02843472547829151,
0.010541597381234169,
-0.030839163810014725,
0.03787599503993988,
-0.004334520548582077,
-0.0191173292696476,
-0.0617009736597538,
0.034374870359897614,
0.008891427889466286,
-0.007197287864983082,
0.024901490658521652,
0.0493423156440258,
0.01389299239963293,
-0.014149045571684837,
0.024138130247592926,
0.018920887261629105,
0.044575709849596024,
-0.020313026383519173,
-0.04607751965522766,
0.031680718064308167,
-0.02135022170841694,
0.04813503846526146,
-0.01810070127248764,
-0.0057905204594135284,
0.025275666266679764,
0.03198561072349548,
0.037479598075151443,
0.010698402300477028,
-0.024823132902383804,
0.0542866513133049,
-0.03854101896286011,
-0.018440568819642067,
0.018267514184117317,
0.05239251255989075,
-0.0011525462614372373,
0.07836215943098068,
0.000235046332818456,
0.0019114547176286578,
0.0708962082862854,
-0.004067340865731239,
-0.07435304671525955,
0.020079514011740685,
-0.017258208245038986,
-0.005908193998038769,
0.010823884978890419,
-0.002046247012913227,
0.01570987142622471,
-0.06340275704860687,
-0.012793544679880142,
-0.003930211067199707,
0.01687292940914631,
-0.04917868226766586,
0.03521396219730377,
-0.02445971593260765,
-0.021592529490590096,
-0.00251463963650167,
0.03472522646188736,
0.024279722943902016,
-0.037134502083063126,
-0.009296946227550507,
0.06903598457574844,
-0.008955429308116436,
-0.004521139897406101,
-0.013846910558640957,
0.013973040506243706,
-0.0029993264470249414,
0.04506496712565422,
0.031087838113307953,
0.01876250095665455,
0.003961759619414806,
0.01076455507427454,
0.020666595548391342,
0.03908278048038483,
0.003699138294905424,
-0.016157472506165504,
-0.03219826519489288,
-0.0006632116273976862,
-0.005313283763825893,
0.0056541054509580135,
0.05283894017338753,
-0.00898072961717844,
0.014330375008285046,
0.00591048039495945,
0.025494322180747986,
-0.04989975690841675,
0.04988580197095871,
0.06455126404762268,
0.002339933766052127,
-0.03632734343409538,
-0.07353030890226364,
0.03209225833415985,
-0.01624843291938305,
-0.0007099687936715782,
-0.006430303677916527,
0.016850430518388748,
-0.06463926285505295,
0.0450720489025116,
-0.005851601716130972,
0.01382826454937458,
-0.0008473544730804861,
0.025468774139881134,
0.027971137315034866,
0.014173724688589573,
0.025604626163840294,
-0.0021042139269411564,
0.03140392526984215,
0.036345306783914566,
0.03747297823429108,
0.014516645111143589,
-0.00296855834312737,
-0.07357002794742584,
0.012482011690735817,
0.012796992436051369,
0.024088121950626373,
-0.004236016888171434,
-0.010501588694751263,
-0.0293158870190382,
-0.04462327063083649,
0.05913916230201721,
-0.006870330777019262,
0.03368696570396423,
-0.026204293593764305,
0.013982227072119713,
0.01148996502161026,
-0.0096372589468956,
-0.02591705694794655,
0.07522128522396088,
-0.03348639979958534,
0.019699176773428917,
-0.02988937497138977,
0.009731309488415718,
0.0179819967597723,
0.0011246477952226996,
0.001541224541142583,
0.009549996815621853,
0.018704410642385483,
-0.03228708729147911,
-0.038097649812698364,
0.0511397048830986,
-0.03040745109319687,
-0.07050890475511551,
-0.028679635375738144,
0.01305731013417244,
0.0036108873318880796,
-0.0004397636221256107,
-0.021060526371002197,
-0.028992321342229843,
0.026292363181710243,
0.011975886300206184,
0.015295019373297691,
0.01347601879388094,
-0.011227887123823166,
0.05115644261240959,
0.03499460220336914,
-0.014437464065849781,
0.07022501528263092,
0.024886300787329674,
-0.04529760405421257,
0.0009516380378045142,
-0.026027094572782516,
-0.012029774487018585,
-0.044824179261922836,
0.027972474694252014,
-0.015559742227196693,
0.04016425088047981,
-0.04189464822411537,
0.0340067557990551,
-0.029141604900360107,
0.051448673009872437,
0.028011037036776543,
-0.02252790704369545,
-0.00413775909692049,
0.03405894339084625,
0.0033678526524454355,
-0.03120703250169754,
-0.0037188411224633455,
0.023630397394299507,
-0.008206482045352459,
-0.03284795582294464,
0.006074029020965099,
0.043941594660282135,
0.007581221405416727,
0.021390795707702637,
-0.0016457631718367338,
0.018424002453684807,
-0.019970333203673363,
-0.056434232741594315,
0.05238333344459534,
-0.06003668159246445,
0.056899700313806534,
-0.031229600310325623,
0.01253563817590475,
0.011047362349927425,
-0.03011312149465084,
-0.01397790014743805,
0.01663690246641636,
-0.005574643146246672,
0.04714291915297508,
-0.017303040251135826,
0.021727830171585083,
0.014872102998197079,
0.03589281812310219,
-0.0511491596698761,
-0.012073185294866562,
0.030701424926519394,
0.010149660520255566,
-0.015607102774083614,
-0.03423590958118439,
0.005551610607653856,
-0.02112841233611107,
-0.04817542806267738,
0.00040896437712945044,
0.06400399655103683,
-0.026664476841688156,
-0.014039585366845131,
-0.0181221105158329,
0.0030420429538935423,
0.023437945172190666,
0.01616394892334938,
0.022522097453475,
0.05202377215027809,
0.005388891324400902,
-0.008817837573587894,
-0.024687858298420906,
0.05303659290075302,
-0.019607016816735268,
-0.0020950199104845524,
-0.004908245522528887,
0.010566795244812965,
0.03557342290878296,
-0.002348804846405983,
0.04311661049723625,
0.024162186309695244,
0.01948278769850731,
-0.0324166864156723,
-0.029178561642766,
0.04091135412454605,
-0.008537082932889462,
0.04272584244608879,
-0.01567402295768261,
-0.017046313732862473,
-0.05500926822423935,
-0.03612878918647766,
0.005624623969197273,
0.005033649038523436,
0.021565882489085197,
-0.02334560453891754,
0.07676029205322266,
0.007109066005796194,
-0.007206099107861519,
0.014626983553171158,
-0.009956340305507183,
0.00018577669106889516,
0.03130004182457924,
0.02881731651723385,
0.03206963464617729,
0.00313712190836668,
-0.032517384737730026,
-0.02639819122850895,
-0.03396746888756752,
-0.014005930162966251,
0.07718603312969208,
-0.05897760018706322,
0.04232003539800644,
0.0049242000095546246,
0.018288366496562958,
0.020401008427143097,
0.00673514511436224,
-0.03849438950419426,
0.0012320504756644368,
-0.0007351229432970285,
0.07396628707647324,
-0.020034413784742355,
-0.018891261890530586,
0.014654021710157394,
0.028575513511896133,
-0.04891572520136833,
0.04872714728116989,
-0.016421442851424217,
0.004783130716532469,
-0.000843218294903636,
-0.030767172574996948,
-0.035359274595975876,
0.009947720915079117,
-0.022581037133932114,
0.03676526993513107,
-0.008518553338944912,
0.001098493579775095,
0.05093982070684433,
0.018544910475611687,
0.000988213112577796,
-0.025171194225549698,
-0.010959728620946407,
-0.0271878894418478,
0.05432005971670151,
-0.001513982773758471,
-0.022212758660316467,
-0.02706298604607582,
0.03619571402668953,
0.01300223357975483,
-0.0049272864125669,
0.024265743792057037,
-0.0038253171369433403,
-0.05399737507104874,
-0.03922329470515251,
-0.024178706109523773,
-0.061758022755384445,
0.030463311821222305,
0.015393855981528759,
-0.02417033351957798,
0.011841954663395882,
-0.016572196036577225,
0.04742889106273651,
-0.0008576506515964866,
0.012790811248123646,
0.013133615255355835,
0.08049535751342773,
-0.026418836787343025,
0.029398690909147263,
-0.004134779330343008,
0.01325185690075159,
0.13741885125637054,
0.06588640064001083,
0.020001523196697235,
-0.06121967360377312,
0.009165034629404545,
-0.018420832231640816,
-0.017710482701659203,
-0.024310097098350525,
0.04988843575119972,
0.0021985648199915886,
0.006678383331745863,
-0.006997489836066961,
0.06156013160943985,
-0.025513973087072372,
-0.027829520404338837,
0.033775169402360916,
-0.05077637359499931,
-0.029951782897114754,
-0.003946936689317226,
0.02671956643462181,
-0.05570729076862335,
0.010045741684734821,
-0.005018632858991623,
0.010516861453652382,
-0.022880787029862404,
0.027226828038692474,
-0.05070722475647926,
-0.059747710824012756,
0.011054697446525097,
-0.013340308330953121,
-0.036667127162218094,
-0.003191830823197961,
-0.010834882035851479,
-0.006947283633053303,
-0.027440469712018967,
0.0020467997528612614,
0.04072286933660507,
-0.0011011200258508325,
0.037102002650499344,
0.010639779269695282,
-0.016525855287909508,
-0.002495516324415803,
0.010136191733181477,
0.006522538606077433,
-0.023478638380765915,
0.005037909373641014,
-0.03670634329319,
0.04177465662360191,
0.014299836941063404,
0.009975098073482513,
-0.0033350596204400063,
-0.020163824781775475,
0.005452639423310757,
-0.025531573221087456,
-0.024504348635673523,
-0.004684706684201956,
0.01708444207906723,
-0.02228538878262043,
-0.029139695689082146,
-0.03641519695520401,
-0.0032719671726226807,
0.04186197370290756,
0.029907815158367157,
-0.005367168691009283,
0.011878038756549358,
0.017059417441487312,
-0.006344473455101252,
0.04545402154326439,
-0.03300362452864647,
-0.017070109024643898,
-0.0647355169057846,
-0.03223836421966553,
-0.028360741212964058,
-0.01235338393598795,
0.024923961609601974,
-0.006998646073043346,
-0.009670894593000412,
0.00994203519076109,
-0.01349524687975645,
-0.01493031531572342,
-0.042842838913202286,
0.03357650339603424,
-0.022684985771775246,
-0.053984541445970535,
-0.0014613103121519089,
0.02058584615588188,
0.015563101507723331,
0.0721365362405777,
-0.008313411846756935,
-0.011113720946013927,
0.003692355938255787,
-0.024458007887005806,
0.049149397760629654,
-0.003096420783549547,
-0.039822373539209366,
-0.010187972337007523,
-0.013831301592290401,
0.012030265294015408,
-0.010173516348004341,
0.007189560681581497,
0.04318694770336151,
0.008667564019560814,
-0.00239140959456563,
0.03374548628926277,
-0.006990710739046335,
0.00016164446424227208,
0.017237387597560883,
-0.0075341141782701015,
-0.004984897095710039,
0.006709045730531216,
0.0034977528266608715,
-0.021055517718195915,
0.002169397659599781,
-0.0379498265683651,
-0.05026103928685188,
-0.02045511268079281,
0.03616500273346901,
-0.01761133410036564,
-0.015750719234347343,
-0.029120223596692085,
0.023995162919163704,
-0.04169711098074913,
0.011855415999889374,
-0.006759120151400566,
0.004692896269261837,
0.012895329855382442,
-0.0291602723300457,
-0.04800817742943764,
0.022373178973793983,
-0.01898397132754326,
0.004491239786148071,
0.0316111221909523,
0.00670322822406888,
-0.019003894180059433,
0.009887629188597202,
0.04144393280148506,
-0.02259749546647072,
0.06014394015073776,
0.010016296058893204,
-0.04164804145693779,
0.005064515862613916,
-0.051722537726163864,
-0.018903516232967377,
0.04699517786502838,
0.0031857017893344164,
0.04130587726831436,
0.02409275993704796,
-0.005575782619416714,
-0.003131746780127287,
0.04791601002216339,
-0.0037432394456118345,
-0.005704998038709164,
-0.017646798864006996,
-0.04028095677495003,
-0.036457981914281845,
-0.03275453299283981,
0.03966035693883896,
-0.017192576080560684,
-0.01852286420762539,
0.015211757272481918,
-0.0023709756787866354,
0.022973351180553436,
-0.011626831255853176,
0.03512654826045036,
0.014326667413115501,
0.0050301337614655495,
0.029101261869072914,
-0.013098446652293205,
0.03566531091928482,
0.05678509175777435,
-0.016120508313179016,
-0.006850033532828093,
0.020462805405259132,
-0.0047599319368600845,
-0.05980835109949112,
-0.023898951709270477,
-0.026941576972603798,
-0.003040578216314316,
0.018875235691666603,
-0.06635218113660812,
0.06580445915460587,
0.035406842827796936,
-0.03939952328801155,
0.021040553227066994,
-0.021590987220406532,
-0.02746039628982544,
0.00021943870524410158,
0.002831035293638706,
-0.03512122482061386,
0.06285617500543594,
0.049022216349840164,
0.03573499619960785,
0.007606872823089361,
0.0037492208648473024,
0.02286389097571373,
-0.0028319908306002617,
-0.01581159606575966,
0.027056369930505753,
-0.010411810129880905,
-0.043260250240564346,
0.08813589811325073,
-0.01625678688287735,
-0.03461587056517601,
0.0010966570116579533,
-0.00470045767724514,
-0.008801004849374294,
0.013810848817229271,
0.025881633162498474,
-0.021553557366132736,
0.029121218249201775,
0.007143803406506777,
-0.05071910098195076,
-0.0008775860187597573,
0.03774061053991318,
0.004770957864820957,
0.006930560804903507,
-0.04275219142436981,
-0.0019598931539803743,
0.004906374029815197,
-0.017504597082734108,
-0.02841109037399292,
0.08561428636312485,
-0.04128541797399521,
-0.04427632316946983,
-0.007719838060438633,
-0.05744890123605728,
0.0291585735976696,
-0.01331327948719263,
0.011250047013163567,
-0.0629369467496872,
0.005558360368013382,
0.018997125327587128,
0.002386605367064476,
-0.007007656153291464,
0.024723345413804054,
-0.006306127179414034,
-0.04200708866119385,
0.013698258437216282,
-0.011030732654035091,
-0.041684865951538086,
-0.07280229777097702,
0.011900200508534908,
0.01087637897580862,
-0.04133134335279465,
-0.025599393993616104,
-0.04135419428348541,
-0.02808370068669319,
0.036396365612745285,
0.031347911804914474,
0.029280859977006912,
0.02746165543794632,
-0.03691612556576729,
-0.0307613592594862,
-0.0776410698890686,
0.004989915993064642,
-0.0026309844106435776,
-0.0351695716381073,
-0.014305676333606243,
-0.009818166494369507,
-0.014277029782533646,
0.018792301416397095,
0.047449350357055664,
-0.017894331365823746,
0.0006498986622318625,
0.01531521137803793,
0.02179550752043724,
0.002123454585671425,
-0.0739482045173645,
-0.022907709702849388,
-0.007884982042014599,
-0.01857953704893589,
0.005762818269431591,
-0.015220985747873783,
-0.009027292020618916,
0.006689758971333504,
0.025888431817293167,
0.014585128054022789,
0.011176319792866707,
0.003187110647559166,
-0.010533305816352367,
0.04104092717170715,
-0.024476172402501106,
-0.01082572527229786,
0.0587897002696991,
-0.027718186378479004,
0.012614188715815544,
0.04171903058886528,
-0.05110606923699379,
-0.00028436057618819177,
-0.010007273405790329,
-0.03622577339410782,
0.018514057621359825,
-0.01859370991587639,
-0.018951771780848503,
0.06695424020290375,
-0.06994553655385971,
0.0026908779982477427,
0.05726559832692146,
-0.05666513368487358,
0.02483556419610977,
0.033615339547395706,
0.026529574766755104,
0.03626711666584015,
-0.018570512533187866,
0.0176137275993824,
0.01272873766720295,
-0.004711522255092859,
0.02872293069958687,
0.002982116537168622,
0.03056575171649456,
-0.01662828028202057,
0.019298115745186806,
-0.009751438163220882,
-0.06402625888586044,
0.006750340107828379,
0.010646437294781208,
-0.008578437380492687,
-0.020081177353858948,
-0.026698589324951172,
0.024180209264159203,
-0.0031685354188084602,
0.019457126036286354,
-0.01853235624730587,
-0.03640155866742134,
0.05928114056587219,
-0.009823460131883621,
-0.009349845349788666,
-0.04004690423607826,
0.02305220253765583,
-0.03917335718870163,
0.013087806291878223,
0.014791848137974739,
0.03675507381558418,
0.025204485282301903,
0.010136198252439499,
-0.0217818021774292,
0.0006122412160038948,
0.008251089602708817,
-0.052356984466314316,
0.004421360325068235,
0.005362238734960556,
0.006109907291829586,
0.006454020738601685,
-0.030148018151521683,
-0.04303533211350441,
-0.04421107843518257,
0.014466404914855957,
0.008671051822602749,
0.01911672204732895,
0.020281445235013962,
0.019324980676174164,
-0.03175615146756172,
0.07235700637102127,
-0.0453450046479702,
0.002668372355401516,
-0.006218039430677891,
0.021922357380390167,
-0.010982937179505825,
-0.015052204951643944
] |
<p>As far as I know Coulomb's law only works for point charges but what if there are not any point charges? For example, let's imagine there are three rectangles with different sizes. First one is 50 cm, second one is 30 cm and last one ise 10 cm. The distance between first and second triangle is 10 cm and the distance between the second and third rectangle is also 10 cm. If their centers are collinear what is the net force acting on second ractangle? Should I calculate it by think their centers as a point charge? I searched for it but couldn't find a clear answer.</p>
<p><a href="https://docs.google.com/file/d/0B01xsQRugsj8d0QyOGpWREJZZUE" rel="nofollow">Here</a> is the picture of the problem for those who couldn't understand from my explanation.</p>
<p><img src="http://i.stack.imgur.com/OGsDC.png" alt="Charges"></p>
| 9,415 |
[
-0.032390087842941284,
-0.0006645061075687408,
-0.01750377006828785,
-0.01093380805104971,
0.05125338211655617,
-0.0012280585942789912,
-0.03665948286652565,
-0.01075844094157219,
0.03820318356156349,
-0.02788054198026657,
0.06689095497131348,
0.033183563500642776,
0.05740770697593689,
0.01971256546676159,
0.016103701665997505,
0.01498298067599535,
-0.02603655681014061,
-0.021470947191119194,
0.0034609304275363684,
-0.052892960608005524,
-0.026251502335071564,
0.03349582105875015,
0.029722444713115692,
0.01673545502126217,
-0.011359304189682007,
0.03147674351930618,
0.01604776829481125,
-0.01855083368718624,
0.015089413151144981,
0.03376323729753494,
-0.024170387536287308,
-0.03205337002873421,
0.02920398861169815,
0.027439389377832413,
0.012891865335404873,
-0.005610794294625521,
-0.02292335033416748,
-0.002663056366145611,
-0.039660170674324036,
0.030228206887841225,
-0.009752282872796059,
-0.013693716377019882,
0.0036024379078298807,
0.03950260952115059,
-0.043791141360998154,
0.013668015599250793,
-0.011003166437149048,
-0.054070208221673965,
0.05277986824512482,
-0.057787150144577026,
0.08253650367259979,
0.04665030911564827,
0.05323589965701103,
0.04477044194936752,
-0.007464515045285225,
-0.02502530813217163,
0.06138543412089348,
0.03554186969995499,
0.014178114011883736,
-0.017182793468236923,
-0.01734999381005764,
-0.0040434859693050385,
0.012655275873839855,
-0.05131717026233673,
-0.04107705131173134,
0.04825785011053085,
-0.017289210110902786,
-0.011133075691759586,
0.01733546145260334,
0.008965453132987022,
0.0014312209095805883,
0.009581456892192364,
0.019093617796897888,
-0.01710308901965618,
0.00803885143250227,
-0.023245247080922127,
0.01070739421993494,
-0.02382296696305275,
0.05258643999695778,
0.02113799750804901,
-0.054684948176145554,
0.013467904180288315,
0.014761739410459995,
0.047486767172813416,
0.023617325350642204,
-0.04867343232035637,
0.07181291282176971,
-0.006762074306607246,
0.02052805759012699,
-0.012099881656467915,
-0.029504140838980675,
-0.02178831584751606,
0.04202088341116905,
0.0028230869211256504,
0.007349771913141012,
0.030357742682099342,
-0.026536477729678154,
0.053705982863903046,
0.026680082082748413,
-0.009919321164488792,
0.008794358000159264,
-0.01950015127658844,
0.00049184839008376,
0.06897374987602234,
-0.002194278175011277,
-0.00816895067691803,
-0.0348719023168087,
0.03755407780408859,
-0.02423950843513012,
-0.020333148539066315,
-0.04897481948137283,
0.02550315484404564,
-0.007811175659298897,
0.009780160151422024,
0.02481118030846119,
-0.017779860645532608,
0.01966351643204689,
0.009801913052797318,
0.030833955854177475,
0.030346155166625977,
0.02609303966164589,
-0.037132784724235535,
0.04764588922262192,
-0.03013615310192108,
-0.04980884864926338,
0.0019492552382871509,
-0.012389236129820347,
-0.010177439078688622,
-0.0388818196952343,
0.031047087162733078,
-0.008075900375843048,
-0.004151159897446632,
-0.02955096960067749,
0.0165331419557333,
0.03902845457196236,
-0.018427444621920586,
-0.07357867807149887,
-0.040523871779441833,
0.029418842867016792,
-0.031595900654792786,
-0.007439241744577885,
-0.06766627728939056,
-0.002455130685120821,
0.006139033939689398,
0.029563574120402336,
-0.007610974367707968,
-0.03505157679319382,
0.006590475793927908,
0.04178160801529884,
-0.02899353578686714,
-0.004593329969793558,
0.003701096633449197,
-0.019633492454886436,
-0.014540184289216995,
-0.005717012099921703,
-0.07314621657133102,
0.03326873481273651,
0.008785475045442581,
0.02527909353375435,
-0.03194133937358856,
0.021741308271884918,
-0.013484494760632515,
-0.0012606807285919785,
-0.004676483571529388,
0.0021875554230064154,
-0.05014115571975708,
0.10170911997556686,
0.016501400619745255,
-0.017692705616354942,
0.05562575161457062,
-0.004685381893068552,
0.05173378065228462,
0.0007880827761255205,
0.021945051848888397,
0.0587911382317543,
-0.010688853450119495,
-0.008880582638084888,
-0.02732800506055355,
0.016728373244404793,
0.028211776167154312,
-0.04746304452419281,
-0.031474512070417404,
-0.007349729537963867,
0.021741926670074463,
0.0038185787852853537,
0.052017536014318466,
-0.021405665203928947,
-0.015997277572751045,
-0.024394415318965912,
0.007965861819684505,
0.0011049809399992228,
-0.0941799134016037,
0.07678454369306564,
0.014913497492671013,
-0.020442776381969452,
0.014828739687800407,
-0.008464268408715725,
0.013307454064488411,
-0.023565012961626053,
-0.05975990742444992,
-0.018140096217393875,
0.06170227751135826,
-0.008269802667200565,
-0.019756492227315903,
0.047341153025627136,
0.024278493598103523,
0.04440473020076752,
0.002604805864393711,
0.04625021293759346,
0.019319137558341026,
0.0052655963227152824,
0.0056262509897351265,
-0.030420970171689987,
0.03263237327337265,
0.011028294451534748,
-0.017179002985358238,
0.0068215676583349705,
0.02862970158457756,
-0.01234458852559328,
0.0718051865696907,
-0.005266998894512653,
0.09780487418174744,
0.042847707867622375,
0.002207790035754442,
0.006478490307927132,
0.015627233311533928,
-0.019280878826975822,
0.010397188365459442,
-0.0013767275959253311,
-0.03743550181388855,
-0.0703485831618309,
-0.010141582228243351,
-0.012423311360180378,
0.02018243819475174,
-0.03355710208415985,
-0.03276209160685539,
0.0409863218665123,
0.01550310105085373,
0.030601732432842255,
-0.002713201567530632,
-0.0019981483928859234,
-0.011746861971914768,
0.02201332524418831,
0.05377964675426483,
-0.02072623185813427,
-0.010533301159739494,
0.038253411650657654,
0.024134960025548935,
0.04093991219997406,
-0.021473625674843788,
-0.03471573069691658,
0.03892216831445694,
-0.019033700227737427,
0.033492907881736755,
0.007057846989482641,
-0.018967272713780403,
0.056681834161281586,
-0.0027485161554068327,
0.03388125076889992,
0.020046990364789963,
0.0009404183947481215,
-0.03496742621064186,
-0.022229930385947227,
0.01036916859447956,
0.022355420514941216,
-0.004839124623686075,
-0.02765525132417679,
-0.03138419985771179,
-0.0013221463887020946,
-0.0335436686873436,
0.0033216134179383516,
0.02767215669155121,
-0.029636351391673088,
-0.03334391862154007,
-0.0029669590294361115,
0.007083099335432053,
0.025189993903040886,
0.05965191870927811,
-0.013111944310367107,
-0.005690311081707478,
-0.009280516766011715,
-0.00874832458794117,
-0.025281719863414764,
0.028587039560079575,
-0.02488419972360134,
-0.0005463885026983917,
-0.04901649057865143,
-0.022239873185753822,
0.04345327615737915,
0.0036090577486902475,
0.01801975443959236,
0.04735400900244713,
-0.018409868702292442,
-0.059336014091968536,
0.012716978788375854,
-0.03712007403373718,
0.04592190682888031,
-0.04422357678413391,
-0.012174881994724274,
0.04278390482068062,
-0.008901010267436504,
-0.03074951283633709,
0.016807232052087784,
-0.02987515926361084,
-0.07536599040031433,
-0.009099413640797138,
0.009001856669783592,
-0.0033570413943380117,
-0.04165196791291237,
0.001946016913279891,
0.01928848773241043,
-0.03404189273715019,
-0.019021261483430862,
-0.04600018262863159,
-0.021861298009753227,
0.0028914620634168386,
-0.0076126111671328545,
0.03631729260087013,
-0.029115738347172737,
-0.08721976727247238,
0.05630803108215332,
-0.011027032509446144,
-0.014746908098459244,
0.029777836054563522,
-0.02608545683324337,
-0.02926664985716343,
-0.01107355672866106,
0.016003334894776344,
0.025365665555000305,
-0.042252007871866226,
-0.029424989596009254,
-0.005791491828858852,
0.02808026596903801,
0.04655865952372551,
-0.016815759241580963,
0.029144171625375748,
0.010029563680291176,
0.028176240622997284,
0.006183392368257046,
0.08173239231109619,
0.029599061235785484,
-0.03419429808855057,
-0.012146818451583385,
0.008930839598178864,
0.0384463295340538,
0.03571478649973869,
-0.04155367612838745,
0.044794075191020966,
-0.023432765156030655,
0.015124878846108913,
0.011711440980434418,
0.027340808883309364,
0.052336957305669785,
-0.030852867290377617,
0.006759258918464184,
0.04966546967625618,
0.048577681183815,
-0.012160059995949268,
-0.04623101279139519,
0.05015530437231064,
0.05416599288582802,
-0.004179822281002998,
-0.03436467796564102,
-0.0031470218673348427,
0.00262218015268445,
0.016362488269805908,
0.007143715396523476,
-0.012951482087373734,
0.02017507329583168,
0.016916651278734207,
-0.000976490555331111,
0.016727885231375694,
-0.020919783040881157,
0.0011928942985832691,
-0.08150965720415115,
-0.003954421728849411,
0.007945431396365166,
0.06860646605491638,
0.017557403072714806,
0.03745722025632858,
0.022129815071821213,
0.008272717706859112,
0.026265613734722137,
-0.006305845454335213,
-0.04744423180818558,
0.02642146311700344,
-0.012660807929933071,
-0.0299395639449358,
-0.016659758985042572,
-0.027919163927435875,
-0.03827721253037453,
0.010557212866842747,
0.01161053404211998,
-0.02120804227888584,
0.005323945544660091,
-0.026458358392119408,
0.019756527617573738,
-0.035556502640247345,
-0.007510138209909201,
0.0070952195674180984,
0.0535384826362133,
0.003212756710126996,
-0.06688433885574341,
0.025189846754074097,
0.04802977293729782,
-0.03176821768283844,
0.004579881671816111,
-0.022138549014925957,
-0.02871610037982464,
0.023425396531820297,
0.004996966570615768,
-0.001457540551200509,
-0.0013366679195314646,
0.021660955622792244,
-0.006852881982922554,
-0.00475987559184432,
0.05753906071186066,
0.02834383025765419,
-0.005274455063045025,
-0.024812735617160797,
-0.07194115966558456,
-0.006271644029766321,
-0.027238767594099045,
0.07213634997606277,
-0.0013771450612694025,
-0.010084814392030239,
-0.007896403782069683,
0.005405927076935768,
0.020286865532398224,
0.029080528765916824,
0.04258009418845177,
0.07913492619991302,
-0.03336864337325096,
-0.03892895206809044,
-0.013760360889136791,
-0.027703100815415382,
0.010322335176169872,
0.023366857320070267,
-0.024166490882635117,
-0.027229977771639824,
-0.0016297792317345738,
0.06832963973283768,
0.0007232067873701453,
-0.009958959184587002,
0.005524084437638521,
-0.007422678638249636,
0.011183354072272778,
-0.035671573132276535,
-0.00963504333049059,
0.035851988941431046,
0.00029557320522144437,
0.022029906511306763,
-0.02557198889553547,
-0.022928599268198013,
-0.057450130581855774,
0.01072630938142538,
0.037447739392519,
0.001050880877301097,
-0.03288249671459198,
-0.013015721924602985,
-0.045978743582963943,
-0.004651600029319525,
0.04673462361097336,
-0.048415668308734894,
0.006841529626399279,
0.0021812052000313997,
0.009088332764804363,
0.01616097055375576,
-0.04496712237596512,
-0.057166263461112976,
0.022381465882062912,
-0.041244201362133026,
0.03938025236129761,
-0.025357769802212715,
0.008218050934374332,
0.04497843608260155,
0.017678694799542427,
0.036836035549640656,
0.06037500873208046,
0.01924992725253105,
-0.0032956451177597046,
-0.007250535301864147,
0.03594466671347618,
0.00879176240414381,
-0.06419453769922256,
0.02159423939883709,
-0.0018480427097529173,
-0.0014848265564069152,
0.03740191087126732,
-0.022108880802989006,
-0.03042415902018547,
-0.019095925614237785,
-0.018929019570350647,
0.006694391369819641,
0.009717918001115322,
-0.009382694959640503,
0.06107845902442932,
0.0401165746152401,
-0.03695250675082207,
0.012499107047915459,
0.008792530745267868,
-0.030503306537866592,
-0.054695773869752884,
-0.006773323751986027,
0.0466555655002594,
-0.0021209123078733683,
-0.008312237448990345,
-0.03847743198275566,
0.016126371920108795,
-0.019504835829138756,
0.02184499241411686,
-0.03362616151571274,
0.03795597702264786,
-0.02096562273800373,
-0.019606567919254303,
0.02258586883544922,
0.02210446260869503,
0.010860506445169449,
0.03934627026319504,
-0.03260919451713562,
0.020609429106116295,
0.0209958553314209,
-0.028302012011408806,
0.006161126773804426,
-0.001427750918082893,
-0.0021766016725450754,
0.007187816314399242,
0.007887511514127254,
-0.03630158305168152,
-0.02290933020412922,
0.008899426087737083,
-0.025686360895633698,
-0.06283779442310333,
0.05481650307774544,
-0.019692519679665565,
-0.006815995089709759,
0.007300911005586386,
-0.025360893458127975,
-0.04947550222277641,
0.04771682620048523,
-0.01070418767631054,
0.05869657173752785,
-0.03668925538659096,
0.023788340389728546,
-0.004306575749069452,
-0.0033487912733107805,
-0.031348589807748795,
-0.039906132966279984,
0.009555775672197342,
0.025319982320070267,
0.008439329452812672,
-0.006766023579984903,
-0.031927529722452164,
-0.005255674943327904,
-0.05653120577335358,
0.011544154025614262,
0.06845162063837051,
-0.029085980728268623,
-0.02986273728311062,
0.007548750843852758,
-0.020667899399995804,
0.059927940368652344,
-0.02461358718574047,
-0.007789181545376778,
0.003992625046521425,
-0.05350247025489807,
-0.0035842466168105602,
-0.0033706435933709145,
0.03156037628650665,
0.006188173778355122,
-0.03295966237783432,
-0.020863734185695648,
-0.020020224153995514,
0.06291300803422928,
-0.05017080157995224,
0.00990548636764288,
0.027643902227282524,
0.021526053547859192,
-0.03428127244114876,
-0.0103218425065279,
0.03367825224995613,
0.034738559275865555,
0.008114490658044815,
-0.012255292385816574,
0.017377028241753578,
-0.053646817803382874,
-0.03194683790206909,
0.024310074746608734,
0.0016480007907375693,
0.01049493532627821,
-0.018080303445458412,
0.08508487045764923,
-0.045290570706129074,
0.01628873310983181,
0.002831251360476017,
0.025997769087553024,
0.03637304902076721,
-0.03216022253036499,
-0.0100584477186203,
-0.01269419863820076,
0.023013941943645477,
-0.024629121646285057,
0.00664236256852746,
-0.03352225199341774,
0.04966792091727257,
0.07968150079250336,
-0.027190113440155983,
0.042997248470783234,
0.010065507143735886,
0.0007116370834410191,
-0.01780398003757,
-0.006936159450560808,
-0.019947703927755356,
-0.03263275325298309,
0.024452833458781242,
-0.0015137537848204374,
-0.044952671974897385,
0.015648240223526955,
0.06811410188674927,
0.040620360523462296,
0.023454075679183006,
0.010373905301094055,
0.024263471364974976,
-0.009720086120069027,
0.00023781220079399645,
0.00232704053632915,
-0.03943018242716789,
0.03522038832306862,
-0.022657865658402443,
0.018010668456554413,
-0.0005259487661533058,
-0.056890688836574554,
0.023392168805003166,
0.004038013517856598,
-0.00024466789909638464,
-0.022147702053189278,
-0.022973330691456795,
-0.02386852540075779,
0.053012914955616,
0.006471292115747929,
0.0023009362630546093,
-0.060570280998945236,
-0.005414722487330437,
0.00672729080542922,
0.0011527782771736383,
0.01826382614672184,
-0.030184512957930565,
-0.06865482032299042,
-0.043461401015520096,
-0.03620249032974243,
0.008604143746197224,
0.013843188062310219,
0.013306250795722008,
-0.049099765717983246,
0.058427970856428146,
-0.0017684061313048005,
0.047195207327604294,
0.023733314126729965,
0.016620919108390808,
-0.04826045408844948,
0.07809431105852127,
0.0320749469101429,
0.01488441601395607,
0.0017936148215085268,
0.0017168959602713585,
0.1271020472049713,
-0.026563424617052078,
-0.007334449328482151,
-0.04489884153008461,
0.016642022877931595,
-0.0053860945627093315,
-0.010005592368543148,
-0.03803642839193344,
0.008451581001281738,
-0.009946765378117561,
0.012982972897589207,
0.0025037257000803947,
0.018093431368470192,
-0.0013447778765112162,
0.007059955969452858,
0.04485716670751572,
-0.022424928843975067,
-0.08681632578372955,
-0.008055057376623154,
0.0038566270377486944,
0.004977392498403788,
-0.0037838490679860115,
-0.036581847816705704,
0.047438349574804306,
-0.0497184582054615,
0.0007657624664716423,
-0.052082858979701996,
0.011595246382057667,
0.015044276602566242,
0.022222772240638733,
-0.052983708679676056,
0.018798870965838432,
0.007684436626732349,
-0.03221069276332855,
-0.06820496171712875,
0.05042076110839844,
0.021085305139422417,
-0.015187930315732956,
0.0213825274258852,
0.013539270497858524,
-0.011412844061851501,
0.008438847959041595,
-0.0017419916111975908,
0.009805324487388134,
-0.03674522414803505,
-0.025790948420763016,
-0.020603550598025322,
0.05045900493860245,
-0.0202235858887434,
0.014888801611959934,
-0.0002641475875861943,
0.020816216245293617,
0.022478913888335228,
-0.04307272285223007,
-0.0020969060715287924,
-0.036602459847927094,
0.0027476537507027388,
0.0011689026141539216,
-0.008120243437588215,
-0.03560727834701538,
0.058244816958904266,
-0.010049623437225819,
0.020133651793003082,
-0.008259644731879234,
0.014203377068042755,
0.007204113528132439,
0.0011143662268295884,
0.08305371552705765,
-0.027599552646279335,
-0.001608399790711701,
-0.004364935681223869,
-0.041534122079610825,
-0.02846473641693592,
-0.02933485060930252,
0.021037381142377853,
0.06252063065767288,
0.006074147764593363,
-0.007163143251091242,
-0.01546873152256012,
-0.021529100835323334,
-0.0679539144039154,
0.012118911370635033,
-0.005819747690111399,
0.02647443301975727,
-0.028338072821497917,
-0.011717754416167736,
0.026162365451455116,
0.07010159641504288,
0.0023163550067692995,
-0.014700192026793957,
0.0046282378025352955,
0.025235911831259727,
0.019593093544244766,
-0.005948269739747047,
-0.02326228655874729,
-0.007787185255438089,
-0.024767642840743065,
0.0049866437911987305,
-0.009393099695444107,
0.011621463112533092,
0.014390735886991024,
0.017321664839982986,
0.009016109630465508,
0.027530914172530174,
-0.017938032746315002,
0.018791627138853073,
0.0033701201900839806,
-0.01772347278892994,
0.014741679653525352,
0.017352843657135963,
0.0037502781488001347,
-0.037084728479385376,
0.01675316132605076,
-0.011519404128193855,
0.013827698305249214,
0.018707485869526863,
0.0539461225271225,
-0.021457234397530556,
-0.03860919177532196,
-0.009549536742269993,
-0.012158130295574665,
-0.008550332859158516,
-0.018386736512184143,
-0.05423721671104431,
0.009729091078042984,
0.014228111132979393,
-0.014669010415673256,
-0.040040768682956696,
0.01471659541130066,
-0.01868291012942791,
0.02296433411538601,
0.04516136273741722,
-0.003906125435605645,
-0.008428661152720451,
-0.04720582813024521,
0.011842767708003521,
-0.015329920686781406,
0.06879384070634842,
-0.014344774186611176,
-0.02332349866628647,
0.026263609528541565,
-0.015518109314143658,
-0.0254006739705801,
0.018238935619592667,
-0.03573985397815704,
0.04150214046239853,
-0.011441404931247234,
0.02790755219757557,
-0.009697251953184605,
0.06739263981580734,
-0.011923052370548248,
-0.022852586582303047,
-0.01829218491911888,
-0.0322546511888504,
0.014837902970612049,
-0.032718125730752945,
0.018858056515455246,
-0.01938544027507305,
0.023528438061475754,
0.04611974582076073,
0.0017853789031505585,
0.004495111294090748,
-0.017744211480021477,
0.028409749269485474,
0.0009269691072404385,
-0.017267674207687378,
0.017753923311829567,
0.03111165016889572,
-0.020137185230851173,
0.05739076808094978,
-0.02287551388144493,
0.03020511567592621,
0.0009666154510341585,
0.02021799050271511,
-0.11529246717691422,
-0.00034484168281778693,
0.02098722569644451,
-0.022867251187562943,
0.04849690943956375,
-0.05600912123918533,
-0.012966342270374298,
0.01220702938735485,
-0.09384036064147949,
0.009112599305808544,
0.00017965557344723493,
-0.028834963217377663,
-0.012351996265351772,
-0.004694752395153046,
0.011193935759365559,
0.05244756117463112,
-0.006657047662883997,
0.06808528304100037,
0.03677208349108696,
0.007373325061053038,
-0.004249433055520058,
-0.04453094303607941,
-0.02104831673204899,
0.015694759786128998,
0.00803706981241703,
0.0006691277958452702,
0.008910560049116611,
-0.03217523917555809,
-0.0005043653072789311,
0.045703575015068054,
-0.05323738977313042,
-0.03267489746212959,
-0.02563043311238289,
0.03904743492603302,
-0.011817822232842445,
0.05178287252783775,
0.0205965805798769,
0.007161539047956467,
0.010346627794206142,
0.013906351290643215,
-0.011875560507178307,
0.0035515648778527975,
-0.006568253971636295,
-0.012154142372310162,
0.04665231704711914,
-0.0398574136197567,
-0.047307275235652924,
0.018379108980298042,
0.015809984877705574,
-0.022387562319636345,
-0.0018237337935715914,
0.02061128057539463,
0.03942941501736641,
-0.018000183627009392,
-0.011113384738564491,
-0.03405974060297012,
0.012533992528915405,
0.04800856113433838,
0.0005744987865909934,
-0.031746260821819305,
-0.009823382832109928,
-0.024202624335885048,
-0.005967788398265839,
-0.02158091589808464,
0.010933992452919483,
0.013802269473671913,
-0.08745142817497253,
-0.0151442252099514,
0.000244692200794816,
-0.02096155844628811,
-0.006192140281200409,
-0.033903397619724274,
-0.031690821051597595,
0.06554830819368362,
0.016774293035268784,
0.007830590941011906,
0.017263036221265793,
-0.007540928665548563,
-0.02337838150560856,
-0.05375141277909279,
0.00650144275277853,
0.006826635915786028,
-0.020252486690878868,
-0.04124036058783531,
-0.03263809159398079,
0.0012158062309026718,
0.007965798489749432,
0.05743365362286568,
0.006770570762455463,
0.003428526222705841,
0.014444595202803612,
-0.031026970595121384,
-0.030664896592497826,
-0.050223927944898605,
-0.02142617292702198,
0.024324890226125717,
-0.002096270676702261,
0.004037884064018726,
0.01504102349281311,
-0.00033406110014766455,
0.00042680997285060585,
0.0019218613160774112,
-0.0009077100548893213,
-0.023322951048612595,
-0.041643787175416946,
-0.03797637298703194,
0.02067294903099537,
0.018397659063339233,
0.010647299699485302,
0.08088197559118271,
0.015711480751633644,
0.023646652698516846,
-0.008668025024235249,
-0.01214570552110672,
-0.012210781686007977,
0.002816850319504738,
-0.061635468155145645,
0.008446207270026207,
-0.02509233169257641,
-0.02624335326254368,
0.04986172541975975,
-0.049910977482795715,
-0.03017440065741539,
0.04255131632089615,
-0.05128215253353119,
0.00048147744382731616,
0.043292637914419174,
0.002226709621027112,
0.04439987614750862,
-0.01517194788902998,
0.0036508827470242977,
0.01370872464030981,
0.0008849785081110895,
-0.011898727156221867,
0.009622577577829361,
0.0070677949115633965,
0.0025276776868849993,
-0.027729738503694534,
0.042840249836444855,
0.0027444642037153244,
-0.01232100185006857,
-0.008035515435039997,
0.04241801053285599,
0.03292546793818474,
-0.022426538169384003,
-0.007667364552617073,
-0.009390074759721756,
0.03876960650086403,
0.03010888397693634,
0.0011212610406801105,
0.06657979637384415,
-0.0371771976351738,
0.018190661445260048,
0.010022781789302826,
-0.01978415623307228,
0.009868374094367027,
0.023530082777142525,
0.02384767308831215,
0.04028899222612381,
-0.03943759948015213,
-0.04410763457417488,
-0.010210522450506687,
-0.01228093821555376,
0.03811468556523323,
-0.0001758341386448592,
0.050384122878313065,
0.0009853901574388146,
0.04237473011016846,
-0.0004928434500470757,
-0.028643783181905746,
-0.010115368291735649,
0.0013540810905396938,
0.03697540983557701,
0.024657726287841797,
0.027541499584913254,
0.00792897678911686,
0.03890913724899292,
-0.014303615316748619,
0.04915701970458031,
-0.033526480197906494,
-0.04391567409038544,
-0.014251130633056164,
-0.015209873206913471,
0.004173391032963991,
0.0017671131063252687
] |
<p>Firstly, I understand what the Doppler effect is when it comes to sound or light waves.</p>
<p>From everything that I've read, we are told that the universe is constantly expanding since the all the radiation we observed is red-shifted.
Assuming we are observing a distant galaxy/start that is moving away from us, the EMR waves incident on us from that galaxy is red shifted.
My question is:</p>
<p>how do we know that the light is red shifted? When you measure its wavelength you are given just ONE value Λ, right? How does one know what its original wavelength was to begin with? Its only after we know both the values (the actual wavelength when it was emitted and the wavelength that we measure hear on earth) that we can claim that the galaxy/star is moving away. </p>
<p>I always assumed that one would observe both the wavelength of the photons and the energy and there is some sort of disparity there that tells us the light is red-shifted. But that does not make sense since one usually determines the wavelength based on the energy of the photon......I am confused here. Any answer will be appreciated. Thanks.</p>
| 9,416 |
[
-0.011971605010330677,
-0.010086072608828545,
0.019428467378020287,
-0.037617772817611694,
0.0512651726603508,
0.02835814096033573,
-0.003190082497894764,
-0.03773575648665428,
-0.015284547582268715,
-0.00770152360200882,
0.008952541276812553,
0.031371843069791794,
0.03042479418218136,
0.011210257187485695,
0.03148864582180977,
-0.001135188271291554,
-0.004795411601662636,
0.011648965999484062,
-0.007809898816049099,
-0.032315850257873535,
0.008745812810957432,
0.012591094709932804,
0.011224440298974514,
0.013106307946145535,
-0.04742366075515747,
0.010580508969724178,
0.03401041030883789,
0.04699671268463135,
0.028094002977013588,
0.05547507479786873,
0.019556105136871338,
-0.03033657930791378,
-0.012444328516721725,
0.05387437343597412,
0.016133610159158707,
-0.007939109578728676,
-0.044740576297044754,
-0.002298520179465413,
-0.01970302127301693,
0.009559276513755322,
-0.0704934373497963,
-0.00840854737907648,
0.027949906885623932,
0.05208780989050865,
-0.035937655717134476,
-0.03267389163374901,
-0.010365181602537632,
-0.007685110904276371,
0.0649537742137909,
-0.013856773264706135,
0.08708584308624268,
-0.03745390847325325,
0.03722443804144859,
0.02328507974743843,
0.005289171356707811,
0.039874106645584106,
0.090021513402462,
0.07191380113363266,
-0.02817365527153015,
-0.021592501550912857,
-0.010841448791325092,
0.0014887124998494983,
-0.0029628972988575697,
-0.019220661371946335,
-0.025521067902445793,
-0.0003937126602977514,
-0.016215691342949867,
0.0049519105814397335,
0.0364738367497921,
0.016807464882731438,
0.007091178558766842,
0.00909389927983284,
0.020458614453673363,
-0.030338706448674202,
0.01664634980261326,
-0.04648325592279434,
0.0019061490893363953,
0.01894143968820572,
0.04992544278502464,
0.04641489312052727,
-0.0164012610912323,
0.007170120254158974,
0.0248185433447361,
0.03669149428606033,
0.014530288055539131,
-0.008568291552364826,
0.07220524549484253,
0.006327735260128975,
-0.010591994971036911,
0.01483065914362669,
0.011820263229310513,
0.02217595838010311,
0.005423457827419043,
-0.027506664395332336,
-0.037866633385419846,
0.04807048663496971,
-0.01514350064098835,
0.05505954846739769,
-0.005542986560612917,
-0.03586560860276222,
0.040116842836141586,
0.015671733766794205,
0.02646302618086338,
0.033676374703645706,
-0.037166301161050797,
-0.019969824701547623,
-0.05925194174051285,
0.027644457295536995,
-0.027992086485028267,
-0.029302027076482773,
-0.02015259675681591,
0.002341259503737092,
0.0055418130941689014,
0.008729194290935993,
0.018373718485236168,
-0.03690686449408531,
0.004974829964339733,
-0.00692663574591279,
0.06925410032272339,
0.08177847415208817,
0.021445970982313156,
-0.027593940496444702,
0.0188469048589468,
0.006483605597168207,
-0.03528573736548424,
0.017278499901294708,
0.021492158994078636,
0.000007662237294425722,
-0.03923746570944786,
0.04929180070757866,
-0.02436305396258831,
-0.03656911104917526,
0.015265015885233879,
-0.006804733537137508,
0.021109003573656082,
0.0031743627041578293,
-0.13140703737735748,
-0.06215011328458786,
0.006008191034197807,
-0.014971275813877583,
-0.006182582583278418,
-0.07140407711267471,
-0.006679496727883816,
0.017704587429761887,
0.0912182405591011,
-0.0034234444610774517,
0.0026581266429275274,
-0.024771681055426598,
0.03495229780673981,
-0.01173948310315609,
-0.028529483824968338,
-0.040038347244262695,
-0.026090268045663834,
-0.03324398770928383,
-0.005344046279788017,
-0.055787719786167145,
-0.0376751683652401,
0.028421541675925255,
-0.03410506993532181,
-0.026831530034542084,
0.05465296283364296,
0.0017942906124517322,
-0.037218958139419556,
0.00398436700925231,
-0.0007726913318037987,
-0.020410146564245224,
0.1061304360628128,
0.03485755994915962,
-0.03235593065619469,
0.036664754152297974,
0.015081285499036312,
0.027727607637643814,
0.004669457208365202,
0.017654167488217354,
0.0220926683396101,
-0.04174019396305084,
-0.034918494522571564,
-0.030402690172195435,
0.02101076766848564,
-0.002512999577447772,
-0.026272471994161606,
-0.028378743678331375,
0.00830025877803564,
-0.020095668733119965,
0.035466913133859634,
0.038292672485113144,
0.017740027979016304,
0.001147006987594068,
0.006541397888213396,
-0.05050055682659149,
-0.00035389658296480775,
-0.025103149935603142,
0.024699801579117775,
-0.003703625639900565,
-0.012247167527675629,
-0.023924998939037323,
0.032022953033447266,
0.01763088069856167,
-0.005962378345429897,
-0.025708336383104324,
0.01889742910861969,
0.02378278784453869,
-0.002820829628035426,
0.00471405079588294,
0.025633053854107857,
0.056888751685619354,
0.03349960595369339,
0.019598010927438736,
-0.005664010066539049,
-0.02239977940917015,
-0.026159105822443962,
0.0337485745549202,
-0.009746485389769077,
0.002962644211947918,
-0.015044687315821648,
0.011647875420749187,
-0.021031372249126434,
0.01156668458133936,
0.04242108017206192,
0.0203129593282938,
-0.026514429599046707,
0.034357950091362,
0.0005558141274377704,
-0.010490312241017818,
0.004275387153029442,
0.04288959503173828,
-0.02257719077169895,
0.007602747064083815,
-0.015548989176750183,
-0.03105650655925274,
-0.06675509363412857,
-0.0029591808561235666,
0.012920131906867027,
-0.007613248657435179,
0.0004300989967305213,
0.014716780744493008,
0.01866278238594532,
0.04752470925450325,
0.029422398656606674,
0.05078969895839691,
-0.03764242306351662,
-0.05738170072436333,
-0.029661130160093307,
0.03550885617733002,
-0.009217983111739159,
0.013373774476349354,
0.031893305480480194,
0.006620345637202263,
0.03837694227695465,
-0.017448849976062775,
0.00180855265352875,
0.0378122515976429,
-0.008458549156785011,
0.010710611008107662,
-0.003209595335647464,
-0.035170599818229675,
0.0023556132800877094,
-0.01783566176891327,
0.022672368213534355,
0.009602722711861134,
-0.032929427921772,
-0.00664288317784667,
-0.05092093348503113,
0.01127762719988823,
-0.012542182579636574,
-0.022861933335661888,
-0.04973454028367996,
-0.003833392634987831,
0.014705570414662361,
-0.0419619046151638,
0.034940868616104126,
-0.009645204059779644,
-0.0035176274832338095,
-0.03675045818090439,
-0.022760862484574318,
0.026410792022943497,
0.012045186012983322,
0.02051992155611515,
-0.04751274362206459,
-0.04968080297112465,
0.023284688591957092,
-0.04463224858045578,
0.020843565464019775,
0.01354413852095604,
-0.019874321296811104,
0.021385733038187027,
-0.001789290108717978,
-0.032605815678834915,
0.0473213866353035,
-0.003730425611138344,
0.021888267248868942,
0.03545242175459862,
0.016223877668380737,
-0.0704423189163208,
-0.01430443860590458,
-0.01670568250119686,
0.0017268075607717037,
0.00021927320631220937,
-0.011884113773703575,
0.07437209784984589,
-0.0409829281270504,
-0.03431961312890053,
0.01222688052803278,
-0.06474118679761887,
-0.024299688637256622,
-0.018843477591872215,
-0.0004328182840254158,
0.0016334124375134706,
-0.048636242747306824,
0.0388774573802948,
0.00819058995693922,
-0.05328145995736122,
-0.0012544337660074234,
-0.021606216207146645,
-0.06786928325891495,
0.0437333807349205,
0.0011150251375511289,
0.03549058735370636,
-0.009378280490636826,
-0.01878538355231285,
0.04527437314391136,
0.027104776352643967,
-0.02726183645427227,
-0.02013898268342018,
0.04966277629137039,
-0.02194145694375038,
-0.024589354172348976,
0.018429310992360115,
0.030805496498942375,
-0.015183689072728157,
0.045377619564533234,
0.02185477688908577,
0.026975367218255997,
0.015541525557637215,
0.04841548576951027,
-0.014951705932617188,
0.01386435516178608,
-0.016207369044423103,
0.00950532965362072,
0.04841622710227966,
0.02812863141298294,
-0.04412388801574707,
0.021750962361693382,
0.004647404421120882,
0.037880126386880875,
0.013643192127346992,
-0.018737925216555595,
0.027484526857733727,
0.00785427913069725,
-0.008959224447607994,
-0.06082108989357948,
-0.00450741034001112,
0.025244709104299545,
0.011739125475287437,
-0.0029431318398565054,
0.017076492309570312,
0.015019726008176804,
0.023467203602194786,
-0.020639663562178612,
0.043162137269973755,
0.02609056606888771,
0.002337775891646743,
-0.013604354113340378,
-0.0007914598099887371,
-0.032563209533691406,
0.03927144035696983,
-0.03671399876475334,
-0.02926267683506012,
0.07182202488183975,
0.026190580800175667,
-0.003834519535303116,
-0.020316410809755325,
-0.04747610166668892,
0.0008087722817435861,
-0.029678355902433395,
-0.007614701054990292,
0.044897228479385376,
0.03326892480254173,
0.0233538169413805,
0.09275851398706436,
0.03680988773703575,
0.019461456686258316,
0.019672321155667305,
-0.0136331208050251,
-0.08800700306892395,
0.019021572545170784,
-0.03306472674012184,
-0.034197643399238586,
-0.008355867117643356,
-0.008767993189394474,
-0.03093821182847023,
-0.05500750243663788,
-0.01967182755470276,
-0.025400785729289055,
-0.037524737417697906,
-0.04584386944770813,
0.02745817042887211,
-0.01824665442109108,
-0.045305222272872925,
-0.040435198694467545,
0.03778349980711937,
0.05004957318305969,
0.018959926441311836,
0.024788731709122658,
0.048968616873025894,
-0.014313078485429287,
-0.0048652333207428455,
0.005161141976714134,
-0.006040080450475216,
0.010490374639630318,
0.04576949030160904,
0.06648825109004974,
0.0316707007586956,
-0.033010341227054596,
0.006331271957606077,
0.030799439176917076,
0.025186285376548767,
-0.009896132163703442,
-0.0169704370200634,
-0.021941645070910454,
-0.005248652771115303,
-0.006168384570628405,
-0.02710396610200405,
0.06325706094503403,
-0.0011031774338334799,
0.0182541161775589,
0.02459186688065529,
0.01810363680124283,
-0.03579775243997574,
0.04584452137351036,
0.0629400834441185,
-0.037690699100494385,
-0.0045541757717728615,
-0.04362763464450836,
0.02039109542965889,
-0.035582784563302994,
-0.02121857739984989,
-0.010148532688617706,
0.013549772091209888,
-0.013098008930683136,
0.011384773068130016,
0.005938179325312376,
0.014907661825418472,
0.012634293176233768,
-0.030385524034500122,
0.00441566901281476,
-0.001210599672049284,
-0.013929422944784164,
-0.002230287529528141,
-0.0015343778068199754,
0.052078165113925934,
0.04064305126667023,
-0.009447905234992504,
-0.0013833061093464494,
-0.07248064875602722,
0.005814888048917055,
-0.011210907250642776,
0.02052554301917553,
-0.006238509435206652,
0.01403836440294981,
-0.05032689869403839,
-0.02713906206190586,
0.035112813115119934,
-0.033895909786224365,
0.04454679787158966,
-0.007474239449948072,
-0.02188739739358425,
-0.0028783793095499277,
0.003793541109189391,
-0.020422380417585373,
0.02167699672281742,
-0.011183703318238258,
-0.02015610784292221,
-0.018806837499141693,
0.0022185826674103737,
-0.05021388456225395,
-0.016657238826155663,
0.015894390642642975,
0.05278903990983963,
-0.009826227091252804,
-0.004182862117886543,
-0.021395243704319,
0.013898390345275402,
0.016869796440005302,
-0.06126430258154869,
0.009058264084160328,
0.0006566426600329578,
-0.0066953254863619804,
0.040291186422109604,
-0.012163032777607441,
-0.041842635720968246,
0.007791209500283003,
0.018463416025042534,
-0.00818292424082756,
0.00026511584292165935,
-0.042144279927015305,
0.0331144817173481,
0.00026910725864581764,
0.0063685760833323,
0.06485558301210403,
0.03268418088555336,
0.015610339120030403,
0.029974201694130898,
0.0070663862861692905,
0.029278911650180817,
-0.05605724826455116,
0.014400860294699669,
0.013254339806735516,
0.018985692411661148,
-0.005647496320307255,
0.07917304337024689,
-0.008002158254384995,
-0.009146182797849178,
0.03340500593185425,
-0.012948825024068356,
-0.004490697756409645,
0.042189821600914,
-0.020478971302509308,
0.021157389506697655,
-0.006783613003790379,
0.007813015021383762,
-0.04352277144789696,
-0.015407626517117023,
0.023390375077724457,
0.03826609626412392,
-0.03735153004527092,
0.010733012109994888,
-0.004274736624211073,
0.037966400384902954,
-0.0053862170316278934,
0.014783370308578014,
0.03737794607877731,
-0.03322910889983177,
0.00974676851183176,
-0.011767874471843243,
0.04294315725564957,
-0.008281317539513111,
-0.0650036558508873,
-0.0490327849984169,
0.0027655151207000017,
-0.03493007645010948,
0.028961125761270523,
-0.05052017420530319,
0.02382797561585903,
0.02496703900396824,
0.006349264178425074,
-0.09854287654161453,
-0.019761547446250916,
0.021388700231909752,
0.021380817517638206,
-0.019210083410143852,
0.003061657538637519,
0.00934677105396986,
-0.043686382472515106,
0.001330694416537881,
-0.03023918718099594,
0.03202241659164429,
0.015316476114094257,
-0.020546000450849533,
0.006998759228736162,
0.005542382597923279,
0.030089247971773148,
-0.03565198928117752,
-0.014388645067811012,
-0.002829692093655467,
0.003069494850933552,
-0.024607514962553978,
0.010389503091573715,
0.06073509156703949,
-0.0103965038433671,
-0.048122864216566086,
-0.02396576851606369,
-0.009889720007777214,
-0.008840263821184635,
-0.04505770653486252,
-0.014884697273373604,
0.02304767817258835,
0.025814514607191086,
0.011392001993954182,
-0.00461363373324275,
0.030074728652834892,
-0.026052633300423622,
0.02402053214609623,
0.0027062816079705954,
-0.03289329260587692,
-0.025612320750951767,
-0.04724096134305,
0.011734575033187866,
0.019631363451480865,
0.05059591308236122,
0.0012882986338809133,
0.05836356803774834,
0.015316399745643139,
-0.012301749549806118,
0.02081388421356678,
0.002357513876631856,
-0.006031593773514032,
-0.040055595338344574,
0.019400620833039284,
-0.004931193310767412,
-0.007254328113049269,
-0.037576090544462204,
-0.008910875767469406,
-0.03561098501086235,
0.007190398406237364,
0.0776701495051384,
-0.020372513681650162,
0.08739612996578217,
0.006965500768274069,
0.002998980227857828,
-0.00936188641935587,
-0.019426727667450905,
-0.015992991626262665,
-0.021635238081216812,
-0.04082805663347244,
0.0024562629405409098,
-0.036107711493968964,
-0.008395879529416561,
0.0015237164916470647,
0.039354752749204636,
0.02013169415295124,
0.027463575825095177,
0.03493422642350197,
0.04116971418261528,
0.03900250419974327,
-0.012982703745365143,
-0.028024470433592796,
0.010123403742909431,
-0.027606265619397163,
0.0059756445698440075,
0.031470052897930145,
0.00921947043389082,
0.04052197188138962,
0.01219039224088192,
0.009808642789721489,
-0.028952153399586678,
0.005916260182857513,
-0.07069608569145203,
0.0010997907957062125,
-0.005198613274842501,
0.019798947498202324,
0.017904050648212433,
-0.02021857351064682,
0.010003815405070782,
0.022117067128419876,
0.024704739451408386,
-0.002566153649240732,
-0.06485197693109512,
-0.056708451360464096,
-0.025769544765353203,
-0.022499000653624535,
0.08200064301490784,
0.005737875588238239,
-0.051289357244968414,
-0.019520793110132217,
-0.008787433616816998,
0.011741559021174908,
0.019440874457359314,
0.016609525308012962,
-0.024563655257225037,
0.07812155783176422,
-0.015929430723190308,
0.03232262283563614,
-0.00844662357121706,
0.037800632417201996,
0.09196748584508896,
0.060031790286302567,
0.003232182702049613,
-0.04753798618912697,
0.024025171995162964,
-0.04298130050301552,
0.01678311824798584,
-0.03939448297023773,
0.020243557170033455,
-0.024093035608530045,
0.05491314455866814,
0.0014057742664590478,
0.05550695210695267,
0.036511801183223724,
-0.02156820148229599,
0.03768916428089142,
-0.04362080618739128,
-0.04008592665195465,
0.04379801079630852,
0.02386745996773243,
0.005015315022319555,
0.02279151976108551,
-0.03467496111989021,
0.005658537149429321,
-0.03725695610046387,
-0.015505552291870117,
-0.001007370068691671,
-0.06276403367519379,
0.0038201126735657454,
-0.009447530843317509,
-0.05545257404446602,
0.009324261918663979,
0.006222838070243597,
-0.012197708711028099,
-0.03997080773115158,
0.026111368089914322,
0.07181830704212189,
-0.02240864373743534,
0.032106559723615646,
0.00277643371373415,
0.017601894214749336,
-0.0024401850532740355,
-0.001332134590484202,
0.02150622196495533,
-0.0002973394875880331,
-0.019199199974536896,
-0.020817963406443596,
0.058579057455062866,
-0.010646545328199863,
-0.007456377614289522,
-0.0018421881832182407,
0.023352930322289467,
-0.03874732553958893,
-0.09082484990358353,
0.0037729328032583,
0.024896306917071342,
0.014923461712896824,
-0.0184753630310297,
-0.023233754560351372,
-0.015658710151910782,
-0.008962580934166908,
0.014841475524008274,
0.024198396131396294,
-0.00970965065062046,
0.005656631197780371,
-0.009787232615053654,
-0.037193663418293,
0.06871219724416733,
-0.007264977786689997,
-0.03350404277443886,
0.004223039373755455,
0.004111852031201124,
-0.06183253601193428,
0.01996742933988571,
0.03815797343850136,
0.04148205742239952,
-0.001958235399797559,
0.005285690538585186,
0.00107373867649585,
-0.029367227107286453,
-0.07857459783554077,
0.021402914077043533,
-0.004951447248458862,
-0.053851693868637085,
-0.009540308266878128,
0.006531514227390289,
0.042569663375616074,
0.015888409689068794,
0.012417125515639782,
0.006201544776558876,
0.005570037756115198,
-0.0024891432840377092,
0.04115085303783417,
-0.02121218666434288,
-0.007720258552581072,
0.03633473813533783,
-0.0022372358944267035,
-0.038030337542295456,
-0.046242665499448776,
0.026339365169405937,
0.008074237033724785,
0.004131150897592306,
0.0028078421019017696,
0.015919825062155724,
-0.04388601705431938,
-0.01067742146551609,
-0.02229269966483116,
-0.0020098707173019648,
0.004735223483294249,
-0.02847178652882576,
0.010256407782435417,
-0.03169456124305725,
-0.026738930493593216,
-0.039519984275102615,
-0.004709863569587469,
-0.017183098942041397,
-0.01804248057305813,
-0.02835126221179962,
0.03404729813337326,
-0.029759172350168228,
0.007799721788614988,
-0.04366074874997139,
0.004956059157848358,
-0.04324112460017204,
0.013955987989902496,
-0.03221562132239342,
-0.025887418538331985,
-0.008907603099942207,
0.038223013281822205,
-0.051491934806108475,
-0.06899537146091461,
0.030882494524121284,
0.021007539704442024,
-0.0007411029073409736,
0.01883920654654503,
0.02144145593047142,
-0.016054479405283928,
0.021597253158688545,
-0.012436546385288239,
-0.039823032915592194,
0.014160621911287308,
-0.06096380949020386,
-0.03987337276339531,
0.04156188666820526,
-0.006096566095948219,
0.04489010199904442,
0.006738452240824699,
0.006760530639439821,
-0.0066553098149597645,
0.03684328868985176,
-0.004854382947087288,
0.0009467789786867797,
-0.0030820847023278475,
-0.024467473849654198,
0.017344309017062187,
0.019412674009799957,
0.013333032839000225,
-0.001712109660729766,
-0.004790274892002344,
0.0428498312830925,
0.020014505833387375,
0.004165160935372114,
0.02892666682600975,
-0.012863807380199432,
-0.027065632864832878,
0.008629449643194675,
0.028760934248566628,
-0.0024419878609478474,
0.0351753868162632,
0.06632087379693985,
-0.04800114408135414,
0.04204513505101204,
0.02233533374965191,
-0.025663521140813828,
-0.10770036280155182,
0.013212763704359531,
0.004396757576614618,
0.008888613432645798,
0.027731724083423615,
-0.05119844526052475,
0.01819593273103237,
0.030222268775105476,
-0.0384582057595253,
0.03333126753568649,
-0.042429521679878235,
0.005906037520617247,
-0.015481868758797646,
0.02967752330005169,
-0.021824048832058907,
0.047791432589292526,
0.08189493417739868,
0.06386881321668625,
0.0014326542150229216,
0.0023699786979705095,
-0.005192233715206385,
-0.0062225391156971455,
-0.008603736758232117,
0.0259011872112751,
0.02662629261612892,
0.0076665193773806095,
0.04429808259010315,
-0.013916654512286186,
-0.00342162000015378,
0.04760075360536575,
-0.011742944829165936,
0.054012399166822433,
-0.010475467890501022,
-0.007851947098970413,
0.007923612371087074,
-0.014532117173075676,
0.006706046871840954,
-0.018800964578986168,
-0.034946948289871216,
0.054416172206401825,
0.026730313897132874,
0.011088903993368149,
-0.005609144456684589,
-0.03691671043634415,
0.020719729363918304,
-0.08228335529565811,
-0.0069584171287715435,
0.0415642075240612,
0.018215561285614967,
0.011263757944107056,
0.031577806919813156,
0.028020579367876053,
-0.005667857825756073,
-0.02104359306395054,
0.01672288216650486,
-0.04783748835325241,
-0.03683038055896759,
-0.007501397281885147,
0.03546962887048721,
-0.025422820821404457,
-0.00944280531257391,
-0.014559810981154442,
-0.018208719789981842,
0.01104012317955494,
-0.02501141093671322,
0.004798046313226223,
-0.04326841980218887,
-0.003331952728331089,
0.0018743948312476277,
-0.0330515094101429,
0.016421904787421227,
-0.01225673221051693,
-0.05259875953197479,
0.038592629134655,
0.010246292687952518,
0.007495993748307228,
-0.010983583517372608,
-0.03757166862487793,
-0.026919089257717133,
-0.07508597522974014,
0.029875535517930984,
0.04608914256095886,
0.011961174197494984,
-0.05025434494018555,
-0.03726915642619133,
-0.021223479881882668,
-0.0002483203134033829,
0.08149371296167374,
0.005281822755932808,
-0.034276705235242844,
0.009116907604038715,
-0.01269527804106474,
0.010830731131136417,
-0.04129643738269806,
-0.008418688550591469,
0.0009000914869830012,
-0.0250032190233469,
-0.04666917771100998,
-0.0008800938376225531,
-0.025417553260922432,
0.007089240476489067,
0.006333484780043364,
-0.008510763756930828,
0.057345084846019745,
-0.005847788415849209,
-0.03945323824882507,
0.03134980797767639,
0.011626529507339,
-0.0026713726110756397,
0.035969916731119156,
-0.011429793201386929,
0.0015649732667952776,
0.042587943375110626,
-0.011086897924542427,
-0.060209404677152634,
0.04180179908871651,
-0.01948736608028412,
-0.0013120764633640647,
0.018535567447543144,
0.031132841482758522,
0.03536774218082428,
-0.023200588300824165,
-0.018523085862398148,
0.04829958453774452,
-0.04662712663412094,
-0.022822508588433266,
0.0569475032389164,
0.007277213502675295,
-0.0014587024925276637,
0.008456246927380562,
-0.004931873641908169,
0.021932680159807205,
0.000479030713904649,
0.0015107512008398771,
0.05619320273399353,
0.025428738445043564,
0.00785091333091259,
0.058866098523139954,
0.026785898953676224,
-0.006407528184354305,
-0.014831681735813618,
-0.015276051126420498,
0.03094378486275673,
-0.056312445551157,
0.004787762649357319,
-0.020484309643507004,
-0.014995694160461426,
-0.01478428766131401,
0.05564674362540245,
-0.029549647122621536,
0.08472726494073868,
-0.03814958408474922,
0.0300377756357193,
0.02728290855884552,
-0.020216913893818855,
-0.011600816622376442,
0.015162074007093906,
0.0006966042565181851,
0.0063919927924871445,
0.022743694484233856,
0.019815368577837944,
-0.0371820405125618,
0.007195493206381798,
0.018358811736106873,
-0.034157026559114456,
0.0005957569228485227,
-0.0068134828470647335,
-0.04550723358988762,
-0.006494096480309963,
0.020061274990439415,
-0.027785880491137505,
-0.005859252065420151,
0.036808278411626816,
0.027585022151470184,
0.028967512771487236,
0.014733408577740192,
0.0012228034902364016,
-0.03874470293521881,
0.014638872817158699,
-0.05952947959303856,
-0.004407375119626522,
-0.019823063164949417,
0.03124145232141018,
-0.00788060575723648,
-0.007695601787418127
] |
<p>As far as I know, a magnetic field can only be produced by a moving electric charge, or from a particle's spin (this is how a permanent magnet works, all the spins are in the same direction)</p>
<p>What is strength and direction of the magnetic field of a stationary electron at the origin with spin oriented straight up? I suspect a function of cylindrical coordinates is most convenient.</p>
| 9,417 |
[
-0.024689890444278717,
0.0036788666620850563,
0.010286243632435799,
-0.04922358691692352,
0.053379498422145844,
-0.020709538832306862,
-0.01921149156987667,
0.011450465768575668,
0.010861710645258427,
-0.03797122463583946,
0.0418626070022583,
0.030685782432556152,
0.07239605486392975,
0.03491456061601639,
0.013832204043865204,
0.013381928205490112,
0.005894141271710396,
-0.02419610135257244,
-0.023328451439738274,
-0.033094462007284164,
0.007968530058860779,
0.020094649866223335,
-0.004859583452343941,
0.026662765070796013,
-0.0227919053286314,
0.005014266353100538,
0.03239155933260918,
0.043320197612047195,
0.015034510754048824,
0.048260774463415146,
-0.02719951421022415,
-0.03167376294732094,
0.021008670330047607,
0.03386196866631508,
0.04382939264178276,
-0.029211902990937233,
-0.02152077853679657,
-0.058630138635635376,
-0.032826293259859085,
0.014925885014235973,
-0.0518500842154026,
-0.012693881057202816,
-0.0175333134829998,
0.06793489307165146,
-0.005705198738723993,
0.006700119934976101,
-0.0005785432877019048,
-0.021202029660344124,
0.0689689964056015,
-0.07232043892145157,
0.05597633123397827,
-0.03939718008041382,
0.05304192751646042,
-0.029442930594086647,
0.00825023278594017,
-0.023204172030091286,
0.0834643766283989,
0.021956752985715866,
0.01509323064237833,
-0.05669502913951874,
-0.028071897104382515,
-0.003558539319783449,
-0.006088972557336092,
-0.04319213703274727,
-0.054571498185396194,
0.020377984270453453,
0.011069172993302345,
-0.01027953065931797,
0.04618322104215622,
-0.01841166615486145,
0.02226145751774311,
0.0332285612821579,
0.036053743213415146,
-0.020303254947066307,
-0.010791642591357231,
-0.04078875109553337,
0.03623344376683235,
0.00010098546044901013,
0.00983111560344696,
0.011005223728716373,
-0.04130196198821068,
0.00023707853688392788,
0.046014998108148575,
0.05624911189079285,
-0.005331743508577347,
0.006967382971197367,
0.054084692150354385,
-0.008599672466516495,
0.02802303433418274,
0.04139390587806702,
-0.0006962416227906942,
0.020173652097582817,
0.038637034595012665,
-0.03922382369637489,
-0.04167970269918442,
0.011687159538269043,
0.0032103746198117733,
0.033853769302368164,
0.026529865339398384,
-0.018211964517831802,
0.03460196405649185,
-0.005664965137839317,
-0.016660800203680992,
0.07851240038871765,
0.03488469496369362,
-0.024600869044661522,
0.013459092937409878,
0.025662507861852646,
-0.025527948513627052,
-0.025346318259835243,
-0.014751364476978779,
0.030896788462996483,
0.006522066425532103,
-0.01834711618721485,
0.009119994938373566,
-0.019878046587109566,
0.02790660597383976,
-0.03498731926083565,
0.03332453966140747,
0.06597153842449188,
0.013369717635214329,
-0.041907213628292084,
0.009466364048421383,
-0.03351663053035736,
-0.050771359354257584,
-0.02614377811551094,
0.03818872570991516,
0.020657353103160858,
-0.021369071677327156,
0.02255961112678051,
-0.0021547863725572824,
-0.022084852680563927,
0.02517172321677208,
-0.009287943132221699,
0.040205102413892746,
-0.027760250493884087,
-0.09194598346948624,
-0.05157937854528427,
0.01980048231780529,
-0.025947509333491325,
0.011673083528876305,
-0.06314457207918167,
-0.03012409619987011,
0.028119979426264763,
0.06291466951370239,
-0.02981436997652054,
0.03337297588586807,
-0.020443083718419075,
0.05372410640120506,
0.0076155709102749825,
-0.016481276601552963,
-0.018931105732917786,
-0.01855654828250408,
-0.04769198223948479,
-0.02035124972462654,
-0.03984740376472473,
0.014583675190806389,
0.016531389206647873,
-0.010039225220680237,
-0.028582599014043808,
0.06741917133331299,
-0.03203422203660011,
0.02086714468896389,
-0.0006615511956624687,
-0.027025654911994934,
-0.030634647235274315,
0.07977808266878128,
0.02630601078271866,
-0.005149466916918755,
0.05053214356303215,
-0.012923749163746834,
0.00818598736077547,
0.02277112565934658,
-0.01211211085319519,
0.02969525381922722,
-0.051152169704437256,
-0.055056698620319366,
-0.03359733894467354,
0.059828974306583405,
0.035400837659835815,
-0.04337923228740692,
-0.027721470221877098,
-0.013478915207087994,
0.0048603033646941185,
0.003233610885217786,
0.05047617852687836,
-0.011931674554944038,
-0.004347584210336208,
-0.03709010034799576,
-0.05110067501664162,
0.02249438688158989,
-0.044206924736499786,
0.03287409245967865,
-0.02268616110086441,
-0.001611727406270802,
0.047059450298547745,
0.017078502103686333,
0.02381356619298458,
-0.05027959868311882,
-0.06521032005548477,
0.006512652616947889,
0.015669817104935646,
-0.03275775536894798,
0.0033595357090234756,
0.0027007253374904394,
0.03922487422823906,
0.021722862496972084,
0.030929500237107277,
0.045077186077833176,
-0.01562359556555748,
-0.023290004581212997,
0.012625346891582012,
-0.04211450740695,
0.01753723807632923,
0.05357906222343445,
0.006296918727457523,
-0.01729126274585724,
-0.007553074508905411,
0.007181680761277676,
0.021434416994452477,
-0.012068177573382854,
0.11416080594062805,
0.03597593680024147,
0.005592609755694866,
0.02773735485970974,
0.036282267421483994,
0.027970479801297188,
-0.009443449787795544,
0.009265061467885971,
-0.03673368692398071,
-0.04679986461997032,
0.01403565239161253,
0.060598909854888916,
-0.010600738227367401,
-0.07573291659355164,
0.029534457251429558,
0.008335678838193417,
0.03396645188331604,
0.008504758588969707,
0.03824653476476669,
-0.06450845301151276,
-0.027252092957496643,
0.008370734751224518,
0.0032822852954268456,
-0.020838648080825806,
0.011711419560015202,
0.06169526278972626,
0.016431253403425217,
0.0005583717720583081,
0.040507517755031586,
-0.047945424914360046,
0.05318153277039528,
-0.02489747479557991,
-0.021514808759093285,
0.016489695757627487,
-0.0698675811290741,
0.047333475202322006,
-0.05157947167754173,
0.02291962504386902,
-0.005144237540662289,
-0.03691662475466728,
0.016375457867980003,
0.0008496460504829884,
0.0033933259546756744,
0.015301206149160862,
-0.024131493642926216,
-0.0038885571993887424,
-0.010229011997580528,
0.030993545427918434,
-0.03673173859715462,
-0.024078235030174255,
-0.010813605040311813,
0.0038152935449033976,
0.015578058548271656,
0.006177250295877457,
0.05091550201177597,
0.024126850068569183,
0.018891891464591026,
0.013278014957904816,
-0.034518394619226456,
0.0012426201719790697,
-0.04672108590602875,
0.030991602689027786,
0.04297623038291931,
-0.04556100815534592,
0.013300474733114243,
-0.027370799332857132,
-0.02140064537525177,
0.04483950883150101,
-0.0031221534591168165,
0.011436684988439083,
0.004587553907185793,
-0.001889505423605442,
-0.044034693390131,
-0.021335991099476814,
-0.04340660572052002,
0.04396722465753555,
-0.03707398101687431,
0.003175472840666771,
0.04870974272489548,
-0.029823943972587585,
0.0026075628120452166,
0.03364702686667442,
-0.01951846107840538,
-0.03764018416404724,
0.0024617144372314215,
0.014653720892965794,
0.03057490475475788,
-0.03386557102203369,
0.044268783181905746,
0.02918459288775921,
-0.04414578154683113,
-0.0151506457477808,
-0.04029248654842377,
-0.02669612690806389,
0.025105291977524757,
-0.021954597905278206,
0.011455555446445942,
-0.015040322206914425,
-0.057655613869428635,
0.06066977605223656,
0.009215342812240124,
-0.046536482870578766,
-0.029837211593985558,
-0.02308940887451172,
-0.03567005693912506,
-0.03649256378412247,
-0.02294366993010044,
0.03151901066303253,
0.0217797439545393,
0.028010118752717972,
0.035690002143383026,
0.024619311094284058,
-0.01440709363669157,
0.014812183566391468,
-0.007337565068155527,
0.03417591005563736,
-0.01819835975766182,
-0.010643103159964085,
0.04342111945152283,
0.010434257797896862,
-0.024305755272507668,
0.020505119115114212,
0.017952242866158485,
0.03629382699728012,
-0.013237387873232365,
-0.017287015914916992,
0.031155597418546677,
0.001839563949033618,
0.02305605448782444,
-0.020598525181412697,
0.02697819657623768,
-0.03989963233470917,
0.017002059146761894,
-0.00501773739233613,
-0.00366480671800673,
0.0001491787697887048,
-0.03326993063092232,
-0.012751237489283085,
0.048639338463544846,
0.021130328997969627,
-0.03980488330125809,
-0.034719787538051605,
0.010528506711125374,
0.00319510861299932,
0.014490059576928616,
-0.033917855471372604,
-0.03353137895464897,
0.03641567751765251,
0.026391062885522842,
0.023099711164832115,
0.029559440910816193,
-0.027801796793937683,
-0.005090953316539526,
-0.06551256775856018,
0.028819061815738678,
0.01924172416329384,
0.04691976681351662,
0.02618882805109024,
0.0457700677216053,
0.0515604168176651,
-0.009349609725177288,
0.00570704834535718,
0.006069337949156761,
-0.07102630287408829,
0.02810760587453842,
-0.023644955828785896,
0.00004960892329108901,
-0.013462089002132416,
-0.005174616817384958,
-0.012581560760736465,
-0.056887250393629074,
-0.005742162466049194,
-0.020749272778630257,
-0.015002947300672531,
-0.05145378038287163,
0.04347457364201546,
-0.044717758893966675,
-0.031610939651727676,
-0.0402049720287323,
0.05316644161939621,
0.030515413731336594,
-0.04612451791763306,
0.009716760367155075,
0.02235783264040947,
-0.031706396490335464,
0.011617185547947884,
-0.02018393948674202,
0.024508878588676453,
0.009276929311454296,
0.018367288634181023,
0.03724673390388489,
-0.015005539171397686,
-0.006772687193006277,
-0.010910730808973312,
-0.005185258109122515,
0.04493914172053337,
0.029837626963853836,
0.006805619690567255,
-0.03432293236255646,
-0.03851170837879181,
0.01602339930832386,
-0.021586870774626732,
0.042573392391204834,
-0.018458396196365356,
-0.0015693377936258912,
0.05693407356739044,
0.004392491653561592,
-0.01319913100451231,
0.020237309858202934,
0.06237494572997093,
0.0197428148239851,
-0.027158457785844803,
-0.03913816437125206,
0.038107626140117645,
-0.02193506620824337,
0.000617506040725857,
-0.004713751375675201,
-0.029462482780218124,
-0.046179983764886856,
-0.004542834125459194,
0.028370913118124008,
-0.0027116660494357347,
-0.013372392393648624,
0.018482660874724388,
-0.020291553810238838,
0.042156483978033066,
0.0072731999680399895,
0.002015455160290003,
0.004935808014124632,
0.020187893882393837,
0.032005466520786285,
0.04179692640900612,
-0.03637561947107315,
-0.06846485286951065,
-0.008044830523431301,
0.01770004816353321,
0.03135517239570618,
0.02294818125665188,
-0.02262907475233078,
-0.05709290876984596,
0.015627723187208176,
0.05299011990427971,
-0.04691805690526962,
0.02987620234489441,
0.004498313181102276,
-0.015607558190822601,
-0.026855507865548134,
-0.015506780706346035,
-0.08177987486124039,
0.039532702416181564,
-0.0196981281042099,
0.0312734879553318,
-0.039020270109176636,
0.017236314713954926,
-0.027582846581935883,
0.024113260209560394,
0.014739924110472202,
0.019463947042822838,
0.04673624411225319,
0.0048261783085763454,
0.0025123227387666702,
0.015043817460536957,
0.008572425693273544,
-0.09397786110639572,
-0.009380234405398369,
0.011309700086712837,
-0.011784317903220654,
0.028647098690271378,
-0.020414557307958603,
-0.03313078731298447,
-0.000233671220485121,
-0.03729712590575218,
0.017242522910237312,
0.037047114223241806,
-0.027295319363474846,
0.054789137095212936,
0.004126615822315216,
0.0038773040287196636,
0.06779985874891281,
0.011958345770835876,
-0.02025436796247959,
-0.007458189036697149,
-0.02020346187055111,
0.028755584731698036,
0.0015254825120791793,
0.003146747127175331,
-0.02047049067914486,
0.0228731669485569,
-0.027307560667395592,
0.05625737085938454,
-0.03134291246533394,
0.01234639436006546,
0.0021164065692573786,
-0.03135742247104645,
-0.029365167021751404,
0.023590361699461937,
-0.014148607850074768,
-0.0391576811671257,
0.002074300544336438,
0.00469786673784256,
-0.024053670465946198,
-0.04087711498141289,
0.0068060243502259254,
-0.005519847851246595,
0.01266222633421421,
0.030495598912239075,
-0.03645743057131767,
-0.0022230870090425014,
-0.020954325795173645,
-0.010487973690032959,
-0.0026095097418874502,
-0.046363718807697296,
0.06206398457288742,
-0.025280456990003586,
-0.01460198499262333,
0.005600393749773502,
-0.056138645857572556,
-0.03073835000395775,
0.014496738091111183,
0.0071827806532382965,
0.017513005062937737,
-0.040315236896276474,
-0.027986671775579453,
-0.012671750970184803,
-0.0031864121556282043,
-0.07139522582292557,
-0.07645902782678604,
0.0032810510601848364,
0.016861237585544586,
0.0114282900467515,
0.0018115745624527335,
0.007131911348551512,
-0.0006082591717131436,
-0.03659887984395027,
0.021202493458986282,
0.054116979241371155,
-0.02196526527404785,
-0.01186232827603817,
0.006494674365967512,
-0.01676868088543415,
0.024595167487859726,
0.004428632091730833,
-0.027323702350258827,
0.023913726210594177,
-0.006102086044847965,
0.019357241690158844,
0.019908972084522247,
0.03813595697283745,
-0.011743256822228432,
-0.04758891090750694,
-0.011803949251770973,
0.027728436514735222,
0.04270376265048981,
-0.0023004685062915087,
-0.02842104807496071,
0.052889298647642136,
0.0120381535962224,
-0.04357250779867172,
-0.022721020504832268,
0.019646530970931053,
0.007449829485267401,
0.009652928449213505,
-0.01848660036921501,
0.004312701523303986,
-0.029965180903673172,
-0.03638656437397003,
0.018316717818379402,
0.015204375609755516,
0.022556297481060028,
0.002862556604668498,
0.05128420144319534,
0.015303881838917732,
-0.008979546837508678,
0.03705064579844475,
0.008496219292283058,
0.014754975214600563,
0.005480450112372637,
0.015945468097925186,
-0.012888375669717789,
-0.017212670296430588,
-0.03545740246772766,
-0.012752830050885677,
0.007491382770240307,
0.017672749236226082,
0.035859912633895874,
0.013503783382475376,
0.050106778740882874,
0.03498929738998413,
0.035575974732637405,
-0.04393790289759636,
0.005055725574493408,
-0.017847644165158272,
-0.010460840538144112,
-0.006150506436824799,
0.0394325815141201,
-0.01644076593220234,
0.01348321232944727,
0.035948365926742554,
0.0666000097990036,
-0.02595778927206993,
0.005649791099131107,
0.021916771307587624,
0.0050436281599104404,
0.04891956225037575,
0.005469552241265774,
-0.05286223068833351,
0.04748507961630821,
-0.0046218750067055225,
0.04160540550947189,
0.018363626673817635,
-0.021202296018600464,
0.056336659938097,
-0.024065710604190826,
0.014805939048528671,
-0.00616737874224782,
-0.01852313056588173,
-0.03585037216544151,
-0.01527127530425787,
0.048863429576158524,
-0.004972328897565603,
-0.02667853981256485,
0.033562030643224716,
0.008676263503730297,
-0.006394923664629459,
-0.001088446588255465,
0.0019349628128111362,
-0.04032336547970772,
-0.013514821417629719,
-0.031800527125597,
-0.04521847516298294,
0.05942481756210327,
-0.006478873081505299,
-0.00805641245096922,
0.03297891467809677,
-0.019111718982458115,
0.01735542342066765,
0.02902265451848507,
0.0326647087931633,
-0.002810285659506917,
0.0783853754401207,
-0.016834449023008347,
-0.022127771750092506,
-0.025446996092796326,
0.004136481322348118,
0.11367837339639664,
0.04033876210451126,
0.024119576439261436,
-0.07009004056453705,
0.01614241488277912,
-0.04117457941174507,
0.02310166507959366,
-0.009166599251329899,
0.02831839956343174,
-0.044253453612327576,
0.024382837116718292,
0.013389733619987965,
0.05295969545841217,
-0.005438004154711962,
0.03559659421443939,
0.03785756975412369,
-0.04101211950182915,
-0.029801419004797935,
0.0007697519031353295,
0.049604497849941254,
0.01047949492931366,
0.004466852638870478,
-0.02669479511678219,
0.02587268128991127,
-0.08327046036720276,
0.0005266324151307344,
-0.020863134413957596,
-0.05447554960846901,
0.033584315329790115,
-0.02221003733575344,
-0.04813853278756142,
-0.004863392561674118,
-0.015037870034575462,
-0.008065322414040565,
-0.0668567568063736,
0.000018213570001535118,
0.039355844259262085,
0.0006407362525351346,
0.03462548926472664,
0.003027915256097913,
0.02780863083899021,
0.017795048654079437,
0.005342866759747267,
0.014643378555774689,
-0.0247283224016428,
-0.010875757783651352,
-0.04299923777580261,
0.032666441053152084,
0.003301785560324788,
0.024616368114948273,
0.019211240112781525,
0.02675485983490944,
0.014822898432612419,
-0.03169698268175125,
-0.01247252058237791,
-0.03323779255151749,
0.024230439215898514,
-0.007221417501568794,
-0.001811224385164678,
-0.014200948178768158,
0.07278481870889664,
-0.0061931186355650425,
-0.0026759838219732046,
-0.023440958932042122,
0.000413746340200305,
0.01607825979590416,
-0.01712588220834732,
0.0674709677696228,
0.016316121444106102,
-0.04888775199651718,
-0.02747456170618534,
-0.05279470235109329,
-0.043304093182086945,
0.04262515529990196,
0.030506320297718048,
0.007842778228223324,
0.024308636784553528,
-0.019011162221431732,
0.008161124773323536,
0.05245008319616318,
-0.053205911070108414,
0.021485112607479095,
-0.02232787013053894,
-0.008168228901922703,
0.010316336527466774,
0.027379505336284637,
0.04244839772582054,
0.03478211909532547,
-0.01595056988298893,
0.03310874477028847,
-0.007235454395413399,
-0.015249744057655334,
0.009705310687422752,
-0.03985049948096275,
-0.023340629413723946,
0.01822495274245739,
-0.02778320014476776,
-0.00007847196684451774,
-0.035956092178821564,
0.011158558540046215,
0.03743287920951843,
0.015245936810970306,
-0.017296096310019493,
0.031131697818636894,
-0.012099204584956169,
0.009132199920713902,
0.013489012606441975,
-0.033750053495168686,
-0.03549918159842491,
0.010773849673569202,
-0.031465090811252594,
-0.05723084881901741,
-0.04263012483716011,
-0.019234124571084976,
0.0010707087349146605,
-0.010964114218950272,
0.04833969846367836,
-0.030062299221754074,
0.01534969825297594,
0.019716555252671242,
-0.007682039402425289,
-0.033763520419597626,
0.019046969711780548,
-0.007306973449885845,
0.013160394504666328,
0.030078887939453125,
0.007299966178834438,
-0.020573610439896584,
0.028677329421043396,
-0.007557617966085672,
-0.014625621028244495,
0.00048752661678008735,
0.011516941711306572,
0.01140496227890253,
0.02115294337272644,
0.00014155458484310657,
0.02251119539141655,
0.03936521336436272,
0.007981298491358757,
0.0020548005122691393,
-0.000260105705820024,
-0.04228353872895241,
-0.05059085413813591,
0.022255050018429756,
-0.021563902497291565,
0.02407083660364151,
0.04081583395600319,
0.01094278134405613,
-0.004126155748963356,
0.04261419177055359,
0.004967367742210627,
-0.00797672662883997,
0.008871431462466717,
-0.02825239673256874,
0.02502373978495598,
-0.02920091710984707,
0.00885218009352684,
-0.003740272717550397,
-0.01723683439195156,
0.03615806624293327,
0.015985874459147453,
-0.009499986656010151,
0.0029362263157963753,
-0.005450127646327019,
0.01761079579591751,
-0.03930649906396866,
0.056455016136169434,
-0.038450807332992554,
0.0412275530397892,
0.052346110343933105,
-0.046256422996520996,
-0.0008570576319471002,
0.008824476972222328,
0.021084913983941078,
-0.08560264855623245,
-0.012719186022877693,
-0.014939225278794765,
-0.025416769087314606,
0.022884586825966835,
-0.053966667503118515,
-0.01175146084278822,
0.0576818622648716,
-0.09178084880113602,
-0.0038642433937639,
-0.019180884584784508,
-0.02049555629491806,
-0.014772177673876286,
-0.03357567638158798,
-0.007867488078773022,
0.05067703500390053,
0.02447451837360859,
0.09509247541427612,
0.0212557315826416,
0.007836505770683289,
-0.025564614683389664,
-0.03786832466721535,
-0.03507998213171959,
0.05083967745304108,
0.005403511691838503,
-0.0006167667452245951,
0.047382716089487076,
-0.012769771739840508,
-0.007606727536767721,
0.03785865008831024,
-0.007113713771104813,
0.019072212278842926,
-0.011944674886763096,
0.013829841278493404,
0.018124207854270935,
0.026323644444346428,
-0.020968737080693245,
-0.004064114298671484,
-0.003291188972070813,
-0.0017826426774263382,
0.027372298762202263,
0.02137579210102558,
-0.008643466979265213,
0.00073596480069682,
-0.0031130239367485046,
-0.03277080878615379,
-0.0022217310033738613,
0.06145819276571274,
-0.053492724895477295,
-0.027492422610521317,
-0.01936611905694008,
0.02088998071849346,
0.03173451870679855,
-0.01259566843509674,
0.023661402985453606,
-0.05622256174683571,
-0.018507076427340508,
-0.007034223526716232,
-0.013064947910606861,
0.0066969930194318295,
0.023697443306446075,
-0.020033136010169983,
-0.027003474533557892,
0.012054668739438057,
-0.0076026213355362415,
-0.002435591071844101,
-0.05489085242152214,
0.024817176163196564,
0.030639290809631348,
-0.005063722841441631,
0.039731480181217194,
-0.03786516934633255,
-0.018636927008628845,
-0.0017337467288598418,
0.0321674570441246,
0.017274072393774986,
0.0025362318847328424,
-0.053609199821949005,
0.011616217903792858,
-0.04914841800928116,
0.059595756232738495,
0.01916385255753994,
-0.00786164402961731,
-0.017349565401673317,
-0.08054064214229584,
0.0031415552366524935,
0.032681550830602646,
0.04705530405044556,
-0.020674610510468483,
-0.026165027171373367,
0.04280475154519081,
-0.029668228700757027,
0.006471247412264347,
-0.06273645907640457,
-0.012681892141699791,
-0.012563100084662437,
-0.02210688218474388,
0.0009109623497352004,
-0.01765785738825798,
-0.01664682663977146,
0.0354762077331543,
0.010535430163145065,
0.02412017062306404,
0.017330467700958252,
-0.014937118627130985,
-0.06607571989297867,
0.028221897780895233,
0.019390739500522614,
-0.03506527096033096,
0.04211947321891785,
-0.0027359509840607643,
-0.00008351825090358034,
0.021014079451560974,
-0.028548115864396095,
-0.015802918002009392,
-0.007344238460063934,
-0.01981424354016781,
0.007044889032840729,
-0.015079842880368233,
0.004236117471009493,
0.06786150485277176,
-0.01707378588616848,
0.0015424737939611077,
0.045483894646167755,
-0.048325393348932266,
0.0020153974182903767,
0.032327860593795776,
0.007301932200789452,
0.020230969414114952,
-0.030958838760852814,
0.012629075907170773,
0.01818987727165222,
0.007853611372411251,
0.011607716791331768,
0.027773767709732056,
0.020665962249040604,
0.01668085716664791,
0.014245690777897835,
0.04232349619269371,
-0.0323713943362236,
0.006826503202319145,
-0.002635239390656352,
0.023679563775658607,
-0.029385488480329514,
-0.013898362405598164,
0.019468599930405617,
-0.028950702399015427,
0.01129714772105217,
0.00530264712870121,
-0.02028164081275463,
0.08048797398805618,
0.0021398342214524746,
0.007459465879946947,
-0.006401393096894026,
0.024044184014201164,
0.015787513926625252,
0.004033240024000406,
0.0050796885043382645,
0.0415324829518795,
-0.006231974344700575,
-0.01724150776863098,
0.005056148394942284,
-0.0047544147819280624,
0.0592736080288887,
-0.05064346268773079,
0.012009544298052788,
0.011818910017609596,
-0.0032984688878059387,
-0.05106797814369202,
-0.007295670919120312,
-0.05805051699280739,
-0.02425692044198513,
0.018601303920149803,
0.019016703590750694,
0.015072613023221493,
-0.00808773934841156,
-0.0017787421820685267,
-0.024333475157618523,
0.04542399197816849,
-0.05962703377008438,
-0.015476210974156857,
-0.039460983127355576,
0.029737060889601707,
-0.01821528933942318,
0.016004249453544617
] |
<p>I have two solid objects. Each of them has an arbitary complex surface, which is discribed by set of vertices. The aim is to describe their interaction, result of which is the change in trajectory of one of them.</p>
<p>Example: one object (M1) is stable and fixed. The second object (M2) moves along some certain axis and has, for example, one degree of freedom perpindicular to the motion axis. In some moment M2 touches M1. Because of the degree of freedom, M2 changes its trajectory from line to some curve, the form of which depends on the form of two interacted objects.</p>
<p>So, how it can be described in formulas? Of course, there can be up to 6 degrees of freedom.</p>
| 9,418 |
[
0.010209144093096256,
-0.02228289283812046,
-0.027802005410194397,
-0.01162270549684763,
0.012852901592850685,
0.0235185194760561,
-0.015460909344255924,
-0.0077956439927220345,
0.019778113812208176,
-0.030013475567102432,
0.03574378788471222,
0.019660435616970062,
0.02686385065317154,
0.033953242003917694,
0.02205020561814308,
-0.008125421591103077,
-0.013743299059569836,
-0.010036652907729149,
-0.010387198999524117,
-0.029119903221726418,
0.0026703784242272377,
-0.015533000230789185,
0.03453581780195236,
-0.010276331566274166,
0.014849254861474037,
0.021394774317741394,
0.011404315941035748,
-0.06379835307598114,
0.007761185523122549,
0.06450631469488144,
-0.03804837539792061,
-0.037692394107580185,
0.007418913301080465,
0.020396456122398376,
0.026862042024731636,
0.0031621581874787807,
-0.05028080940246582,
-0.0518263578414917,
-0.0014331161510199308,
0.03021647036075592,
-0.061987608671188354,
-0.035382676869630814,
-0.03090449422597885,
0.08669973164796829,
-0.024119317531585693,
-0.017026301473379135,
-0.028587007895112038,
-0.010112916119396687,
0.06034637615084648,
-0.061568018049001694,
0.07721393555402756,
-0.03009931743144989,
0.07779981940984726,
0.01753600686788559,
-0.00341015518642962,
0.005819166079163551,
0.034696176648139954,
0.04215042665600777,
0.002142413053661585,
-0.03990936279296875,
-0.01804894581437111,
-0.022306863218545914,
0.011851312592625618,
-0.049569983035326004,
-0.048312243074178696,
0.02953529916703701,
-0.034356918185949326,
-0.02591206505894661,
0.026311421766877174,
0.007708745542913675,
0.003732985118404031,
0.009435327723622322,
0.05342024937272072,
-0.018188174813985825,
0.042946506291627884,
-0.016588689759373665,
0.039134420454502106,
0.030186209827661514,
0.0012000909773632884,
0.04463580623269081,
-0.01398304384201765,
0.018774470314383507,
0.04080585390329361,
0.0037206080742180347,
-0.0055938540026545525,
-0.051201194524765015,
0.06269779056310654,
0.023233693093061447,
0.01651185005903244,
-0.010271022096276283,
0.0036984875332564116,
-0.00040380944847129285,
0.05890694260597229,
0.011044513434171677,
-0.03178970888257027,
-0.018319621682167053,
0.03751462325453758,
0.0340559147298336,
-0.009712032042443752,
-0.006135587114840746,
-0.019849421456456184,
-0.053093019872903824,
-0.004262219183146954,
0.06775975972414017,
-0.0035658718552440405,
0.02215140126645565,
-0.030004845932126045,
-0.028670188039541245,
-0.0025461791083216667,
-0.028031734749674797,
0.04789598658680916,
0.005856194533407688,
0.016115956008434296,
0.02720225416123867,
-0.005475309677422047,
-0.012202613987028599,
-0.03689224645495415,
0.0029184462036937475,
0.022959887981414795,
0.04062069579958916,
0.05211266502737999,
-0.055310219526290894,
-0.002366019878536463,
-0.03868461027741432,
-0.05646730586886406,
-0.01260425802320242,
0.038806427270174026,
-0.011901668272912502,
-0.03920261189341545,
0.011974770575761795,
-0.010984323918819427,
-0.01499798521399498,
-0.010882865637540817,
-0.0016261035343632102,
-0.009431867860257626,
0.009194796904921532,
-0.09094557166099548,
-0.053480491042137146,
0.01590696908533573,
-0.009452374652028084,
-0.0008782312506809831,
-0.040094174444675446,
0.03488830476999283,
0.06836813688278198,
0.09013862162828445,
-0.021263988688588142,
-0.017655840143561363,
0.056392643600702286,
0.026311032474040985,
-0.03936144709587097,
-0.006619710009545088,
-0.0391739197075367,
-0.008383099921047688,
-0.034388065338134766,
-0.00319028552621603,
-0.03314981237053871,
0.033270034939050674,
0.07053177803754807,
0.004365377128124237,
0.0035252722445875406,
0.03509499132633209,
-0.020809050649404526,
-0.013691816478967667,
0.03607730194926262,
0.016967657953500748,
-0.05083584040403366,
0.06670632213354111,
0.012767844833433628,
0.01976611837744713,
0.04251200705766678,
0.016410930082201958,
0.024431169033050537,
-0.0012468224158510566,
0.03529376536607742,
0.04325419291853905,
0.022526035085320473,
-0.02547553926706314,
0.006917341612279415,
-0.05833915248513222,
-0.016369149088859558,
-0.031566884368658066,
-0.05007702857255936,
-0.02183166891336441,
0.012907257303595543,
-0.000007748548341623973,
0.031233690679073334,
0.008419432677328587,
0.02238943986594677,
-0.007069694809615612,
-0.026583172380924225,
-0.02270517498254776,
-0.06887896358966827,
0.05432089418172836,
-0.02195071615278721,
-0.030437346547842026,
0.031311169266700745,
0.003499658778309822,
-0.01681198738515377,
-0.0018129039090126753,
-0.046206675469875336,
-0.02341998927295208,
0.007266436703503132,
0.006725745741277933,
-0.016103923320770264,
0.00037636078195646405,
0.05690986290574074,
0.04782455414533615,
-0.010032658465206623,
0.045772191137075424,
-0.026866208761930466,
-0.014794046990573406,
-0.015101240016520023,
0.01348037738353014,
0.003648313693702221,
0.025303734466433525,
-0.025299353525042534,
-0.011734865605831146,
-0.01763651706278324,
-0.023355208337306976,
0.04652134329080582,
-0.0405355803668499,
0.07418105751276016,
0.09860071539878845,
0.022311165928840637,
0.014631091617047787,
0.041489146649837494,
0.0007436788873746991,
0.0038035009056329727,
0.0039231921546161175,
-0.04978950321674347,
-0.014394751749932766,
-0.03822152689099312,
0.014843745157122612,
0.0866120457649231,
-0.04396739602088928,
-0.01665729284286499,
0.05477910488843918,
0.02639433555305004,
0.02241375297307968,
0.028155850246548653,
0.0027694383170455694,
-0.026288840919733047,
0.06357265263795853,
-0.021927429363131523,
0.0314301960170269,
0.005218925885856152,
-0.03269995003938675,
0.050077952444553375,
0.004041294101625681,
0.002411777386441827,
-0.027028197422623634,
0.042576007544994354,
0.00478613656014204,
-0.014410282485187054,
0.010783247649669647,
-0.00683788163587451,
0.03202568739652634,
-0.014458498917520046,
-0.01605297066271305,
0.022021714597940445,
-0.0036111732479184866,
-0.042733751237392426,
-0.02251092717051506,
0.00911368615925312,
0.04235069826245308,
-0.015574926510453224,
-0.01169995591044426,
-0.03574464097619057,
0.018809346482157707,
-0.014011325314640999,
0.02407602034509182,
0.02814839780330658,
-0.03292924165725708,
-0.006344386376440525,
0.011911469511687756,
0.014922669157385826,
0.031230377033352852,
0.03203976899385452,
-0.0027323421090841293,
-0.04244112968444824,
0.008896717801690102,
-0.016264721751213074,
-0.01669500768184662,
0.03240593522787094,
-0.06930238753557205,
0.041685521602630615,
-0.011848896741867065,
-0.038530025631189346,
0.05974293127655983,
-0.005575876217335463,
-0.03161519765853882,
0.04577087238430977,
0.013167529366910458,
-0.07685866206884384,
-0.051203083246946335,
-0.012548180297017097,
-0.005715461913496256,
-0.049293868243694305,
-0.006241898518055677,
0.022771142423152924,
-0.0041659241542220116,
-0.029420124366879463,
0.0023149445187300444,
0.015004873275756836,
-0.04038027673959732,
-0.012319963425397873,
-0.008095570839941502,
0.024271124973893166,
0.0021315221674740314,
-0.017906678840517998,
0.011755410581827164,
-0.017702952027320862,
-0.010491898283362389,
-0.09065551310777664,
-0.024105260148644447,
0.024781327694654465,
-0.029681827872991562,
0.03417316451668739,
-0.01692441664636135,
-0.016812525689601898,
0.07950783520936966,
-0.0421609990298748,
-0.05647074803709984,
-0.0038419642951339483,
0.008295292034745216,
-0.0035649577621370554,
-0.018081681802868843,
0.012560836970806122,
0.028827304020524025,
-0.03012259490787983,
0.018073612824082375,
0.01595490239560604,
-0.03150201216340065,
0.031734250485897064,
-0.02501346357166767,
0.014827148988842964,
-0.0022818513680249453,
0.012533966451883316,
-0.014535783790051937,
0.0278314258903265,
0.015177291817963123,
-0.023072360083460808,
0.023008864372968674,
0.012544381432235241,
-0.0019800772424787283,
0.03425472602248192,
-0.04946035519242287,
0.02935330756008625,
-0.0008583804010413587,
0.001931308303028345,
0.00922325998544693,
0.044657181948423386,
0.016538133844733238,
-0.04258384183049202,
-0.020766356959939003,
0.06444856524467468,
0.05628436431288719,
-0.025459175929427147,
0.014149338006973267,
0.049782201647758484,
0.0370345413684845,
-0.016705244779586792,
-0.05053772032260895,
0.00588966254144907,
-0.0013818404404446483,
0.023356204852461815,
-0.03933568671345711,
-0.04072050377726555,
0.022746151313185692,
-0.006975490599870682,
-0.0008447570144198835,
-0.005206647329032421,
-0.013221120461821556,
-0.009732100181281567,
-0.044730838388204575,
-0.01975666545331478,
-0.010046044364571571,
0.04395395144820213,
-0.005321076139807701,
0.03784608468413353,
-0.030945435166358948,
-0.009893705137073994,
0.02724502794444561,
0.0008173613459803164,
-0.08336161822080612,
0.04241113364696503,
-0.023772289976477623,
-0.00171469000633806,
0.005897530820220709,
-0.00995350256562233,
0.016154050827026367,
-0.03791641816496849,
-0.016882797703146935,
-0.015639852732419968,
-0.00956028699874878,
-0.05794340372085571,
-0.010893342085182667,
-0.051598962396383286,
-0.03767584636807442,
0.009848230518400669,
0.04254915565252304,
0.037498388439416885,
-0.02759893424808979,
0.0022398503497242928,
0.035472869873046875,
-0.05496999993920326,
0.003688662312924862,
-0.052730001509189606,
-0.023050103336572647,
-0.016504798084497452,
0.029025940224528313,
0.006831440143287182,
0.0401427261531353,
0.020890774205327034,
0.04363589361310005,
-0.014608125202357769,
0.05669421702623367,
0.018174193799495697,
0.006640988402068615,
-0.005788298789411783,
-0.08628727495670319,
0.0030053777154535055,
-0.01520969532430172,
0.07180935144424438,
-0.011768489144742489,
-0.021005980670452118,
0.02534119039773941,
0.009295138530433178,
-0.02765728160738945,
0.04189836233854294,
0.033331237733364105,
0.056305304169654846,
-0.00818780530244112,
-0.037294674664735794,
-0.011362058110535145,
0.008564574643969536,
-0.007755009923130274,
0.02836727350950241,
-0.005432066507637501,
-0.0173637717962265,
-0.006049645598977804,
-0.004201481118798256,
0.0037661665119230747,
-0.020366180688142776,
-0.031126005575060844,
-0.030340256169438362,
0.00674662459641695,
-0.01342085376381874,
-0.0005114973173476756,
0.00003442725210334174,
0.03850575536489487,
0.015433134511113167,
-0.00030662136850878596,
-0.01953933946788311,
-0.05422814190387726,
-0.022837208583950996,
0.06268970668315887,
0.011720488779246807,
-0.0077459681779146194,
-0.0008943715365603566,
-0.009530184790492058,
0.0036756168119609356,
0.060263294726610184,
0.003318097908049822,
0.037629902362823486,
-0.0029183882288634777,
0.012267543002963066,
-0.01713888719677925,
0.009935349225997925,
-0.04648975655436516,
0.033566880971193314,
0.000455398578196764,
0.024789731949567795,
-0.033418990671634674,
-0.01726074516773224,
0.013124175369739532,
0.04019578918814659,
0.03447755053639412,
0.05519115552306175,
0.021909087896347046,
-0.027950165793299675,
0.01713419333100319,
-0.007510793395340443,
-0.02804153971374035,
-0.07718322426080704,
0.028366638347506523,
0.011585819534957409,
0.013401897624135017,
0.060907166451215744,
-0.05010636895895004,
0.00809222087264061,
0.0006599953630939126,
0.003430779790505767,
0.03531722351908684,
-0.010387738235294819,
0.011434686370193958,
0.058659471571445465,
0.05668170005083084,
-0.022732190787792206,
0.017580701038241386,
0.017558302730321884,
-0.012399070896208286,
-0.04620954021811485,
0.04117077216506004,
0.02878718636929989,
0.018909048289060593,
-0.0162796713411808,
-0.02913784794509411,
0.005187689792364836,
-0.061316635459661484,
0.03902586176991463,
-0.0141221284866333,
0.029936181381344795,
-0.0525808185338974,
0.005588556174188852,
-0.06005236878991127,
0.01608090288937092,
-0.014838634990155697,
-0.004963127430528402,
0.00886157900094986,
0.012049325741827488,
0.027111351490020752,
-0.010837876237928867,
0.004855586215853691,
-0.048597030341625214,
-0.03508112207055092,
0.02096201665699482,
-0.00009060173033503816,
0.024066880345344543,
-0.0565333254635334,
-0.027278965339064598,
-0.031222762539982796,
-0.06465286016464233,
0.015251214616000652,
-0.01131370197981596,
0.027684403583407402,
0.043183136731386185,
-0.06835324317216873,
-0.015122860670089722,
-0.017467886209487915,
0.015130875632166862,
0.011194481514394283,
-0.02860480360686779,
-0.0028617617208510637,
0.0037213824689388275,
-0.013646405190229416,
-0.062434855848550797,
-0.06660004705190659,
0.015830090269446373,
0.015046434476971626,
-0.013032005168497562,
-0.00851307064294815,
0.002019874518737197,
-0.024293143302202225,
-0.036491505801677704,
0.022123344242572784,
0.031406961381435394,
-0.046208906918764114,
0.002236432395875454,
0.05349375680088997,
0.0006999968900345266,
0.053899090737104416,
0.01680484227836132,
0.021601853892207146,
0.005476535297930241,
-0.014683005400002003,
0.005897799972444773,
0.028427965939044952,
0.040008295327425,
-0.0004366670036688447,
-0.037684228271245956,
-0.01906522735953331,
-0.0008857272332534194,
0.04964115098118782,
0.0033853205386549234,
0.03333403915166855,
0.01659362018108368,
0.015864107757806778,
0.005375924054533243,
-0.020859962329268456,
-0.015248357318341732,
-0.0027468991465866566,
0.02429567277431488,
0.007294042501598597,
0.008992377668619156,
-0.010546494275331497,
-0.04944605380296707,
0.013352316804230213,
-0.0024566748179495335,
-0.028551863506436348,
0.019794749096035957,
0.057928506284952164,
-0.009819909930229187,
-0.02162718027830124,
0.006010370794683695,
0.010873706080019474,
0.03573335334658623,
-0.02509918622672558,
-0.015963997691869736,
0.024760697036981583,
0.017594020813703537,
-0.046654678881168365,
-0.02150716260075569,
-0.03977888450026512,
0.02096865326166153,
0.041600026190280914,
-0.042258597910404205,
0.049880363047122955,
0.035041693598032,
0.020494135096669197,
-0.006601881701499224,
0.013072894886136055,
-0.012308898381888866,
-0.013465658761560917,
0.013520491309463978,
0.053339146077632904,
-0.03813191130757332,
0.012924437411129475,
0.0415351502597332,
0.021317893639206886,
-0.0574747771024704,
0.036986399441957474,
-0.015064865350723267,
0.0015042915474623442,
0.00015366863226518035,
0.014161716215312481,
-0.006464559119194746,
0.07119914144277573,
-0.035780567675828934,
0.05800088122487068,
-0.015574698336422443,
0.0014582098228856921,
0.011225966736674309,
0.059138569980859756,
0.023014403879642487,
-0.026867784559726715,
-0.023783069103956223,
-0.030276065692305565,
0.04308094084262848,
0.007740393280982971,
-0.01656019315123558,
0.0070627909153699875,
0.006303234025835991,
0.024709483608603477,
-0.025270583108067513,
-0.0024716099724173546,
-0.005334476940333843,
-0.05203007534146309,
0.0123193534091115,
-0.04775416478514671,
-0.04658041521906853,
0.03920136019587517,
0.029081398621201515,
0.014235054142773151,
0.026832422241568565,
0.00008506161975674331,
-0.005151856224983931,
0.021113598719239235,
0.030575022101402283,
-0.04289408400654793,
0.07319900393486023,
-0.03108893521130085,
0.01795884780585766,
-0.010897462256252766,
-0.0022681632544845343,
0.12812216579914093,
0.01685686595737934,
-0.014491486363112926,
-0.049089740961790085,
0.029010171070694923,
0.01297533418983221,
-0.004985638428479433,
-0.04418816789984703,
0.011671125888824463,
0.021078994497656822,
-0.013290501199662685,
0.004817758221179247,
0.0240937527269125,
0.03755362704396248,
0.007363670505583286,
0.0237132515758276,
-0.05862686410546303,
-0.027124468237161636,
-0.003269617911428213,
-0.026405056938529015,
-0.02721191570162773,
0.03241227567195892,
-0.012263710610568523,
-0.03297141566872597,
-0.046591758728027344,
-0.019010882824659348,
-0.01121639646589756,
-0.020226044580340385,
0.06716465204954147,
0.03925014287233353,
-0.045438457280397415,
0.023960933089256287,
0.03354296088218689,
0.00005890282409382053,
0.013750195503234863,
0.022165220230817795,
0.025528790429234505,
-0.020376009866595268,
0.015689924359321594,
0.05502273142337799,
0.018880341202020645,
-0.011852799914777279,
-0.010660319589078426,
-0.020530709996819496,
-0.0759909451007843,
-0.034663956612348557,
-0.06585799157619476,
0.027765706181526184,
0.0039514596574008465,
0.013724589720368385,
-0.01337389089167118,
-0.026136580854654312,
0.023814667016267776,
-0.03267848119139671,
-0.008847578428685665,
-0.017611751332879066,
0.014520231634378433,
-0.06812909245491028,
0.006601072382181883,
-0.020497115328907967,
0.04457209259271622,
0.015345564112067223,
0.01782216690480709,
0.0316370353102684,
-0.00944888312369585,
0.0017694723792374134,
0.0026638128329068422,
0.052558738738298416,
-0.019018525257706642,
-0.0058861905708909035,
-0.023394938558340073,
-0.004407149739563465,
-0.0031641435343772173,
-0.02412460558116436,
-0.01090798620134592,
0.02577979490160942,
-0.027202384546399117,
-0.005230076611042023,
-0.011686192825436592,
-0.019857294857501984,
-0.03374439477920532,
0.003025317331776023,
-0.004488639999181032,
-0.004490458406507969,
-0.04006273299455643,
-0.012152919545769691,
0.07029642909765244,
-0.0015804680297151208,
-0.026870030909776688,
-0.02302350476384163,
-0.042414840310811996,
0.014392416924238205,
0.023405257612466812,
-0.013608771376311779,
-0.02446630410850048,
0.026715999469161034,
-0.025671476498246193,
0.014134861528873444,
-0.017639385536313057,
0.0578509084880352,
0.009033415466547012,
-0.010389362461864948,
-0.01683243364095688,
0.050372038036584854,
-0.0037509880494326353,
0.03380405530333519,
0.013799711130559444,
0.004230552818626165,
-0.02105034701526165,
0.016121145337820053,
0.024324292317032814,
-0.016626810654997826,
0.00005896336733712815,
-0.01504430826753378,
-0.02757268399000168,
0.025364715605974197,
0.01869756542146206,
-0.03010794334113598,
0.010459842160344124,
0.0033938507549464703,
0.008801537565886974,
-0.0007485933601856232,
0.012636846862733364,
-0.04946520924568176,
0.014595850370824337,
0.0561867356300354,
-0.004239500965923071,
-0.004658587276935577,
-0.0005394751206040382,
-0.019028138369321823,
-0.020389536395668983,
0.02876090630888939,
0.03462829440832138,
0.01633496955037117,
-0.0199026670306921,
0.015182282775640488,
-0.03535417467355728,
0.04114317521452904,
-0.01747991517186165,
-0.032750338315963745,
0.011533919721841812,
-0.04486757144331932,
-0.007829816080629826,
0.033165182918310165,
-0.01720137894153595,
0.05081901326775551,
0.019636079668998718,
-0.02322968654334545,
0.026133082807064056,
0.015821823850274086,
-0.03239560127258301,
0.0032063310500234365,
-0.0009173394646495581,
-0.03318050131201744,
-0.05019240081310272,
-0.02235349453985691,
0.036465857177972794,
-0.024172384291887283,
-0.030020900070667267,
-0.008226267993450165,
0.019196121022105217,
0.0020840654615312815,
-0.02599763311445713,
0.010178379714488983,
0.01180626917630434,
0.02081115171313286,
0.03427984192967415,
0.0040412964299321175,
0.09370764344930649,
0.030211642384529114,
-0.028418703004717827,
-0.024509912356734276,
0.03612262010574341,
0.011020522564649582,
-0.07205072790384293,
-0.024827362969517708,
0.024260468780994415,
0.015301323495805264,
0.07864579558372498,
-0.05528855323791504,
0.03160550817847252,
0.009585880674421787,
-0.04899611324071884,
-0.016487764194607735,
-0.0324753038585186,
0.009319289587438107,
-0.022613342851400375,
-0.021687472239136696,
0.0029809686820954084,
0.07723920047283173,
-0.00635324465110898,
0.03692794591188431,
0.036317307502031326,
0.011205070652067661,
-0.025440899655222893,
0.013379178941249847,
0.010151322931051254,
-0.0019101791549474,
-0.02974475920200348,
-0.042857617139816284,
0.044586099684238434,
-0.02173348143696785,
-0.021712828427553177,
0.017868319526314735,
-0.036166056990623474,
-0.0043579102493822575,
0.0030135964043438435,
0.0049248323775827885,
-0.0058926986530423164,
0.009456395171582699,
0.0015263727400451899,
-0.011013397946953773,
-0.034776587039232254,
0.0036538513377308846,
-0.01009594276547432,
0.021325720474123955,
-0.0025131842121481895,
0.00520606804639101,
-0.017537932842969894,
-0.04543473944067955,
0.0008268321398645639,
0.024234948679804802,
-0.0039369030855596066,
-0.014985287562012672,
-0.0657372772693634,
-0.008345987647771835,
0.02374814823269844,
-0.038604266941547394,
-0.004367353394627571,
-0.02447170577943325,
0.008193876594305038,
0.029573798179626465,
0.014961568638682365,
0.019611775875091553,
-0.0033561151940375566,
-0.004048875533044338,
-0.003399823559448123,
0.02139417827129364,
0.018532769754529,
-0.006394804921001196,
-0.04018765315413475,
-0.015611536800861359,
0.013187866657972336,
-0.007293213624507189,
0.010206064209342003,
-0.020996885374188423,
-0.017618678510189056,
-0.005666438955813646,
0.0004705546307377517,
0.03652573004364967,
-0.024218065664172173,
-0.03546036779880524,
-0.014016586355865002,
-0.06299033761024475,
0.019970552995800972,
0.028292810544371605,
-0.01275916863232851,
-0.039071131497621536,
0.023034414276480675,
0.03087003342807293,
0.0009729526937007904,
0.04766670987010002,
-0.03520559147000313,
-0.01594037190079689,
-0.018705889582633972,
0.021876661106944084,
0.026137132197618484,
-0.018459776416420937,
-0.023996902629733086,
-0.006937233731150627,
0.006219701375812292,
0.004971847403794527,
-0.015544818714261055,
0.028096524998545647,
0.027888426557183266,
-0.0041040279902517796,
-0.01154432725161314,
0.036669738590717316,
0.021061226725578308,
-0.07854484021663666,
-0.006866728886961937,
0.0181446336209774,
-0.0013070963323116302,
0.082760289311409,
-0.014496151357889175,
0.03750888258218765,
0.017091382294893265,
-0.021005285903811455,
-0.0038367605302482843,
0.024056652560830116,
-0.056000396609306335,
-0.026364285498857498,
-0.030570348724722862,
-0.01963995024561882,
0.007546446286141872,
-0.08840610086917877,
-0.02872825600206852,
-0.0021864105947315693,
-0.036246851086616516,
-0.024541504681110382,
0.040628038346767426,
0.027987312525510788,
0.052647389471530914,
0.013303745537996292,
0.03446904569864273,
0.024912988767027855,
-0.009984120726585388,
0.018767718225717545,
0.003134021768346429,
0.027622494846582413,
0.004389200359582901,
-0.026347691193223,
0.04350138455629349,
-0.012066216208040714,
0.025519128888845444,
0.01849634014070034,
0.03900882229208946,
0.05832717567682266,
0.014679043553769588,
0.0029655518010258675,
-0.0011537210084497929,
0.008183658123016357,
0.045370474457740784,
-0.000969516288023442,
0.05725470557808876,
-0.03923337534070015,
-0.010681982152163982,
-0.029392514377832413,
0.027830109000205994,
-0.016675345599651337,
0.01689416728913784,
0.04413891211152077,
0.04081929847598076,
0.017615461722016335,
0.0034711218904703856,
0.009234842844307423,
-0.03395526483654976,
0.023723673075437546,
0.012621365487575531,
0.025300445035099983,
-0.003690407145768404,
0.009587466716766357,
0.008682123385369778,
-0.012544157914817333,
-0.020610874518752098,
-0.045709818601608276,
0.0605277493596077,
0.04355626180768013,
0.05178966373205185,
-0.020669855177402496,
0.017912225797772408,
-0.05411004647612572,
0.043708354234695435,
-0.07609642297029495,
-0.013919565826654434,
0.0014216041890904307,
0.0528738833963871,
-0.009673510678112507,
0.01388187613338232
] |
<p>I have read that the pressure in a water barometer at the top of the water column is around 0.5 psi and at such low pressures water should boil at around ~26°C (Room temperature). <a href="http://www.engineeringtoolbox.com/boiling-point-water-d_926.html" rel="nofollow">[1]</a> <a href="http://www.thermospokenhere.com/wp/02_tsh/B160___water_barometer/water_barometer.html" rel="nofollow">[2]</a></p>
<p><img src="http://www.thermospokenhere.com/wp/02_tsh/B160___water_barometer/water_barometer.png" alt="Water barometer"></p>
<p>How come the water in the column near the surface doesn't boil?</p>
| 9,419 |
[
-0.01963087171316147,
-0.005509138107299805,
-0.01928750053048134,
0.0013408170780166984,
0.021493621170520782,
-0.029240215197205544,
-0.049811951816082,
-0.010907009243965149,
0.0060670278035104275,
-0.036143042147159576,
0.035497963428497314,
0.07817164063453674,
0.02767976000905037,
0.012906421907246113,
0.037984173744916916,
0.010303761810064316,
-0.003913231194019318,
-0.041266780346632004,
-0.018428096547722816,
0.0007818662561476231,
-0.0049053700640797615,
0.029953721910715103,
-0.004143152851611376,
-0.0021735031623393297,
-0.019124113023281097,
-0.0021944749169051647,
0.03552452102303505,
0.01098246593028307,
0.032155878841876984,
0.04820307716727257,
0.0021755530033260584,
-0.030481526628136635,
-0.010976026766002178,
0.0031925588846206665,
0.03429730609059334,
-0.008211543783545494,
-0.020504042506217957,
-0.029002562165260315,
-0.04311928153038025,
0.013145570643246174,
-0.013172004371881485,
-0.03251810371875763,
-0.006834554020315409,
0.019347721710801125,
-0.02775229699909687,
-0.017434990033507347,
0.009005512110888958,
-0.020634792745113373,
0.03486616909503937,
-0.07522216439247131,
-0.0016306124161928892,
0.028103817254304886,
0.059624459594488144,
0.050646502524614334,
0.005034036468714476,
0.022277647629380226,
0.09428492933511734,
0.07590066641569138,
-0.04962560907006264,
-0.036694761365652084,
-0.003468520473688841,
-0.030056530609726906,
-0.033970028162002563,
-0.014672715216875076,
-0.03784565627574921,
0.034609392285346985,
-0.0018600743496790528,
-0.022967280820012093,
0.007756628096103668,
0.00991822686046362,
0.01230933889746666,
-0.007067882921546698,
0.022747885435819626,
-0.023133888840675354,
0.01901867985725403,
-0.0300399512052536,
0.011332344263792038,
0.0187915600836277,
0.007282669190317392,
0.06837570667266846,
0.010732997208833694,
0.03217906132340431,
0.022970566526055336,
0.008488100953400135,
0.009387608617544174,
-0.011006600223481655,
0.05742989853024483,
-0.0048132287338376045,
0.0003497065627016127,
0.048981864005327225,
-0.0060076541267335415,
0.025057697668671608,
-0.01738119125366211,
0.028194444254040718,
0.028126895427703857,
0.022102633491158485,
-0.007291588466614485,
0.06726168841123581,
-0.0028591312002390623,
-0.04128079488873482,
0.02636575698852539,
-0.0030693267472088337,
0.03686016425490379,
0.08301537483930588,
0.0096864253282547,
-0.04002896323800087,
-0.040123336017131805,
-0.0007955475011840463,
0.020222818478941917,
-0.027814462780952454,
-0.010488759726285934,
-0.02539665997028351,
-0.001552450587041676,
-0.050089966505765915,
0.01024781633168459,
-0.02934434451162815,
0.020034724846482277,
-0.03783102706074715,
0.04339560121297836,
0.002325519220903516,
0.020728211849927902,
-0.004995252471417189,
0.0008443842525593936,
-0.04823680967092514,
-0.06203286722302437,
0.03530534356832504,
-0.029005208984017372,
-0.028555046766996384,
-0.018327608704566956,
0.01597905158996582,
-0.023850660771131516,
-0.0030830970499664545,
0.019602401182055473,
-0.013050142675638199,
0.06691396236419678,
-0.019020847976207733,
-0.11882605403661728,
-0.04580330848693848,
0.0448627732694149,
-0.012222210876643658,
-0.037654366344213486,
-0.0821467787027359,
0.020009933039546013,
0.03498195856809616,
0.055223286151885986,
-0.009891938418149948,
0.011311840265989304,
-0.045438528060913086,
0.0050386772491037846,
0.003949325066059828,
-0.003956513479351997,
-0.014939959160983562,
0.013237293809652328,
-0.0417049378156662,
0.008583915419876575,
-0.08116164058446884,
0.017885364592075348,
0.030832793563604355,
0.0003432642261032015,
-0.010396912693977356,
0.03333810716867447,
-0.005667445249855518,
0.01388593204319477,
-0.007479752879589796,
-0.002724764170125127,
-0.04887228086590767,
0.06869334727525711,
-0.009985106997191906,
0.00872560404241085,
0.03305483236908913,
-0.003546557854861021,
0.016125507652759552,
-0.04931895062327385,
0.023172348737716675,
0.04550697281956673,
-0.016183461993932724,
-0.0030587075743824244,
-0.021345719695091248,
0.06082240119576454,
0.037782106548547745,
-0.050827473402023315,
0.013483445160090923,
0.0011426483979448676,
0.007678821682929993,
0.006531969644129276,
0.058384619653224945,
-0.028114663437008858,
-0.022462202236056328,
-0.005673057399690151,
-0.059728868305683136,
-0.012287369929254055,
-0.032527320086956024,
0.014641949906945229,
0.004670064430683851,
0.03080447018146515,
0.01183120347559452,
0.020452454686164856,
0.04163833335042,
-0.0254351869225502,
-0.025595037266612053,
0.001534627634100616,
0.023949315771460533,
0.033798396587371826,
-0.0003001276054419577,
0.04178299009799957,
0.021801339462399483,
0.0698774978518486,
-0.0015064447652548552,
0.004931646399199963,
-0.037952084094285965,
-0.02443360537290573,
0.0018173600547015667,
-0.027432462200522423,
-0.00839502364397049,
-0.0039057694375514984,
-0.021533263847231865,
0.021943140774965286,
0.006922340486198664,
-0.008536363020539284,
0.028698796406388283,
-0.014989746734499931,
0.08287494629621506,
0.009171070531010628,
0.011486360803246498,
0.002809071447700262,
0.008960426785051823,
0.02860858291387558,
-0.013683991506695747,
-0.002903894754126668,
-0.008769460953772068,
-0.0473787859082222,
0.01587679050862789,
0.025485171005129814,
0.01637977361679077,
-0.024328451603651047,
0.0036999944131821394,
0.008823462761938572,
0.046046528965234756,
0.01546346303075552,
0.00047904232633300126,
-0.01000792533159256,
-0.006904290523380041,
0.009639989584684372,
0.040022145956754684,
0.01777898520231247,
0.017970111221075058,
0.036600567400455475,
0.04403622820973396,
0.04493081942200661,
-0.04483320564031601,
-0.00725993188098073,
0.028371984139084816,
-0.021472260355949402,
0.02817239612340927,
-0.023806454613804817,
0.0038591695483773947,
0.046038899570703506,
-0.02960880845785141,
-0.008330902084708214,
-0.034428391605615616,
0.02607199363410473,
0.025539517402648926,
-0.04518971964716911,
-0.022031402215361595,
0.0003801590937655419,
0.031021233648061752,
-0.03691655397415161,
-0.009446796029806137,
0.016191447153687477,
-0.017432408407330513,
0.008468515239655972,
-0.06916501373052597,
0.008119706995785236,
-0.04222189262509346,
-0.010911654680967331,
0.049620095640420914,
0.0014259022427722812,
0.07562290877103806,
-0.06915432959794998,
-0.04259871691465378,
-0.0027399128302931786,
-0.017633410170674324,
-0.018620412796735764,
0.008780000731348991,
-0.023099295794963837,
-0.0077979788184165955,
-0.006514636799693108,
0.009291618131101131,
0.046831704676151276,
-0.008392281830310822,
0.009750131517648697,
-0.008752320893108845,
-0.002970890374854207,
-0.025172417983412743,
-0.0008784167584963143,
-0.025414522737264633,
-0.016505764797329903,
-0.0048052784986793995,
-0.012676915153861046,
0.049262359738349915,
-0.022950422018766403,
-0.012357152067124844,
0.04401963949203491,
-0.06966310739517212,
-0.05659859627485275,
-0.00436980277299881,
0.012562704272568226,
-0.0023457875940948725,
-0.037503354251384735,
0.027204284444451332,
0.02068924345076084,
-0.0852079764008522,
-0.004642417188733816,
-0.040727391839027405,
-0.04629337787628174,
0.01319540198892355,
0.008003028109669685,
0.03816181421279907,
0.008571268990635872,
-0.031849946826696396,
0.036260709166526794,
-0.00038266685442067683,
-0.06175438314676285,
-0.014553342945873737,
-0.025682739913463593,
-0.022539079189300537,
-0.049164947122335434,
-0.008270937949419022,
0.07471662014722824,
-0.033404164016246796,
0.018521366640925407,
0.02807735465466976,
0.03254897519946098,
0.044326573610305786,
0.01053067296743393,
0.022607319056987762,
-0.0187024287879467,
0.030967142432928085,
0.017802754417061806,
0.02660987339913845,
-0.02959933876991272,
0.0004820517497137189,
0.0027778809890151024,
-0.023473527282476425,
0.03171450272202492,
0.03427295386791229,
-0.025446807965636253,
0.06466859579086304,
-0.025607554242014885,
0.006597294006496668,
-0.06202050298452377,
0.014528247527778149,
-0.016212966293096542,
0.014610442332923412,
0.01901644468307495,
0.017545467242598534,
0.05568912625312805,
-0.0028160596266388893,
-0.025879787281155586,
0.059183016419410706,
0.061946041882038116,
-0.014332628808915615,
-0.024866845458745956,
0.031484149396419525,
-0.035497959703207016,
0.004660923965275288,
0.00997384823858738,
0.006189178675413132,
0.08158312737941742,
0.012540379539132118,
0.004534803796559572,
-0.0019439122406765819,
-0.022357599809765816,
0.006184449419379234,
-0.04918120056390762,
-0.01547469012439251,
-0.003665030701085925,
0.05085137486457825,
-0.007681849412620068,
0.04586371034383774,
0.03520117327570915,
0.03211042284965515,
0.01430642232298851,
0.01430255826562643,
-0.03879489749670029,
0.013470178470015526,
-0.03264591470360756,
-0.009753595106303692,
-0.0022158799692988396,
-0.02364257723093033,
-0.02070716954767704,
0.012171435169875622,
0.0005795120960101485,
-0.009728865697979927,
0.03063901886343956,
-0.0505523718893528,
0.023327810689806938,
0.021046103909611702,
0.0022886532824486494,
-0.04044157266616821,
0.017624402418732643,
0.01463725883513689,
-0.01781585067510605,
0.022826528176665306,
0.02091923914849758,
-0.009082078002393246,
0.009532264433801174,
-0.015381664969027042,
0.015583639033138752,
0.019595099613070488,
0.018104951828718185,
0.036680594086647034,
0.009628782980144024,
-0.015086538158357143,
-0.03410036489367485,
0.017406567931175232,
0.018961172550916672,
-0.014814060181379318,
0.018138140439987183,
-0.0013883979991078377,
-0.03826690465211868,
-0.0030303536914288998,
0.035980403423309326,
0.028488626703619957,
-0.05030245706439018,
0.021886514499783516,
-0.0159685667604208,
-0.04504138231277466,
0.005274897441267967,
0.048348747193813324,
0.0444745272397995,
0.0024544044863432646,
0.012788415886461735,
-0.04683026671409607,
-0.03390277922153473,
-0.08037103712558746,
-0.008963736705482006,
0.01790466532111168,
0.008865254931151867,
-0.014419888146221638,
-0.01772814430296421,
0.03933540731668472,
-0.028890687972307205,
0.013093316927552223,
-0.0013328405329957604,
0.006998751312494278,
0.042454205453395844,
-0.01610397733747959,
-0.013506815768778324,
0.026183823123574257,
0.018906716257333755,
0.02053089067339897,
-0.0028581665828824043,
-0.027706217020750046,
-0.0499286949634552,
-0.04634374752640724,
0.022864198312163353,
0.03345527499914169,
0.009923337958753109,
-0.0018824530998244882,
-0.08559530973434448,
-0.016281146556138992,
0.07658854871988297,
-0.031266409903764725,
0.01858595199882984,
-0.016387121751904488,
0.0037423991598188877,
-0.030071282759308815,
-0.021957313641905785,
0.01332344301044941,
-0.022302918136119843,
-0.0034153168089687824,
0.042054373770952225,
-0.03467123955488205,
-0.013673454523086548,
-0.03891408443450928,
0.014625725336372852,
-0.00525060435757041,
0.0399823933839798,
0.005524931009858847,
0.02259742096066475,
-0.0009190468699671328,
0.01302049309015274,
0.004990921821445227,
-0.05011344328522682,
-0.007526712492108345,
-0.03019597753882408,
0.04115509241819382,
0.04051235318183899,
-0.044837262481451035,
-0.06264952570199966,
0.030406611040234566,
0.0021913056261837482,
0.001347400713711977,
-0.017589883878827095,
-0.021280279383063316,
0.014587686397135258,
0.017568351700901985,
-0.013417593203485012,
0.03808365389704704,
0.027798857539892197,
-0.016952408477663994,
-0.0258015226572752,
-0.05700407922267914,
0.02485082484781742,
-0.043881673365831375,
-0.0358157642185688,
-0.01917218789458275,
-0.010845296084880829,
-0.021307168528437614,
0.04035832732915878,
-0.008935770019888878,
-0.0032055950723588467,
-0.017759913578629494,
-0.03366689383983612,
-0.004075490869581699,
0.0018707511480897665,
0.03548703342676163,
0.0003601407224778086,
0.010618581436574459,
0.03163764253258705,
-0.009146402589976788,
-0.034735020250082016,
0.0365370474755764,
-0.018748674541711807,
-0.008860389702022076,
-0.0077873533591628075,
-0.028407705947756767,
0.020753398537635803,
-0.004320841282606125,
-0.0033974051475524902,
0.019612552598118782,
-0.06078705936670303,
0.02260197512805462,
-0.03473610058426857,
0.0011602783342823386,
0.020561451092362404,
-0.06119528040289879,
-0.012340903282165527,
0.009189974516630173,
-0.003951842896640301,
0.03928680717945099,
-0.051858678460121155,
0.044544488191604614,
0.05057559907436371,
0.025456208735704422,
-0.05323720723390579,
-0.06282515078783035,
0.055303774774074554,
0.03344423696398735,
0.003080274211242795,
-0.018230997025966644,
-0.002634654985740781,
-0.02005009725689888,
-0.017089933156967163,
-0.00444106524810195,
0.02773093990981579,
-0.00681152893230319,
-0.03280024603009224,
0.03237093240022659,
-0.0005635943380184472,
0.0815117135643959,
-0.03090539202094078,
-0.024401359260082245,
0.05059485882520676,
-0.03621039539575577,
-0.04062550887465477,
-0.008516930043697357,
0.05059046298265457,
-0.030595246702432632,
-0.017024019733071327,
0.002766020130366087,
0.00011930943583138287,
0.03906763717532158,
-0.02032485418021679,
0.00531427888199687,
-0.00024385855067521334,
0.026253359392285347,
0.01461403351277113,
-0.03842204064130783,
0.050406314432621,
0.03675146773457527,
0.011101961135864258,
0.004529627505689859,
-0.03241819143295288,
-0.04047605022788048,
-0.023448683321475983,
0.011647242121398449,
-0.023448823019862175,
0.0063400715589523315,
-0.02381906285881996,
0.06951435655355453,
0.026807839050889015,
-0.019976545125246048,
0.005392478778958321,
-0.04159271717071533,
-0.004328398499637842,
0.05347080156207085,
-0.028170939534902573,
0.015256385318934917,
0.04127532243728638,
-0.03283992037177086,
-0.05499069020152092,
-0.02632272057235241,
0.004196543712168932,
0.058212459087371826,
0.004676162265241146,
0.07042275369167328,
0.020108643919229507,
-0.02415734902024269,
0.03723056614398956,
-0.021543430164456367,
-0.022694706916809082,
0.02525855228304863,
-0.0016389592783525586,
0.011869611218571663,
-0.025752566754817963,
0.02925027534365654,
0.012981015257537365,
0.041674405336380005,
-0.002009263029322028,
0.02713910862803459,
0.06075876206159592,
0.019569531083106995,
-0.009409329853951931,
-0.002909573959186673,
-0.0507328137755394,
0.043109871447086334,
-0.02744314819574356,
0.034049440175294876,
0.006912915501743555,
-0.003985733259469271,
0.03143526613712311,
-0.014522067271173,
-0.01241668313741684,
-0.0810801088809967,
-0.004882437642663717,
-0.01603884808719158,
-0.01021631807088852,
-0.0051257130689918995,
0.0034481219481676817,
-0.021637270227074623,
0.021436544135212898,
-0.01238378044217825,
0.013089853338897228,
0.008641619235277176,
-0.010981762781739235,
-0.03906700015068054,
-0.014520818367600441,
0.0035713333636522293,
-0.04952934384346008,
0.05492004007101059,
0.02153099700808525,
-0.037336286157369614,
0.01938680186867714,
-0.04609296843409538,
0.00841981079429388,
-0.012213431298732758,
0.0008226428180932999,
-0.013692987151443958,
0.037666913121938705,
0.005561354104429483,
0.01214993093162775,
0.019840558990836143,
0.0022145379334688187,
0.11331304907798767,
0.047926053404808044,
0.011720770969986916,
-0.08139926940202713,
0.02688624896109104,
0.0027151501271873713,
0.010883753187954426,
-0.023044636473059654,
-0.023932302370667458,
-0.009967474266886711,
0.03447381779551506,
0.009289517998695374,
0.08408607542514801,
-0.01629592478275299,
0.023776603862643242,
0.03291231766343117,
-0.05903147906064987,
-0.01081438921391964,
-0.002643376588821411,
0.00979045033454895,
-0.045070160180330276,
0.024954333901405334,
-0.03021380864083767,
0.03246460482478142,
-0.017663218080997467,
-0.014172176830470562,
-0.010375802405178547,
0.011713476851582527,
0.01592808961868286,
0.005332678556442261,
-0.06864669173955917,
-0.004894041921943426,
-0.02276027947664261,
-0.03736282140016556,
-0.04445642605423927,
0.02559847943484783,
0.03858081251382828,
-0.005217461381107569,
0.005992603953927755,
-0.0070877461694180965,
0.003123028902336955,
0.016627417877316475,
0.004379719495773315,
0.03712863475084305,
-0.04200388118624687,
-0.004823348019272089,
-0.01576242968440056,
0.03606611117720604,
-0.012557361274957657,
-0.033571913838386536,
-0.008544864133000374,
-0.0003241205122321844,
-0.0007755534606985748,
-0.024300752207636833,
-0.031274449080228806,
-0.016065001487731934,
0.0407579243183136,
-0.015294648706912994,
-0.06818410009145737,
-0.02779492177069187,
0.031437113881111145,
-0.035056013613939285,
0.0038406916428357363,
0.023050455376505852,
0.01423743087798357,
-0.040794871747493744,
-0.002766967285424471,
0.03150339424610138,
-0.0073990472592413425,
0.021926747635006905,
-0.015387055464088917,
-0.008463523350656033,
-0.04723430052399635,
-0.02643405646085739,
0.02045358344912529,
0.017582112923264503,
0.06171882152557373,
0.0335041806101799,
-0.005530397407710552,
-0.0026878651697188616,
-0.03393265977501869,
0.05138668417930603,
-0.03550763428211212,
-0.021877827122807503,
-0.06010422855615616,
-0.006009596399962902,
-0.00035276272683404386,
0.053328339010477066,
-0.0018634849693626165,
0.009472508914768696,
0.016637682914733887,
0.007956298068165779,
0.03931650519371033,
-0.020554380491375923,
-0.040540844202041626,
0.0263033676892519,
-0.028351133689284325,
-0.00808346550911665,
0.01826665922999382,
0.03445285186171532,
0.039622701704502106,
0.013907957822084427,
0.016330767422914505,
0.003630391787737608,
-0.03686704486608505,
-0.03431755676865578,
0.010821857489645481,
-0.01526002585887909,
-0.0014622765593230724,
0.006540440954267979,
-0.007073881104588509,
-0.005444963928312063,
-0.027088018134236336,
-0.035682860761880875,
0.0175229012966156,
0.012109601870179176,
0.04432911425828934,
-0.030395619571208954,
0.00018365371215622872,
-0.012521998956799507,
0.005201890133321285,
-0.041365958750247955,
-0.017723437398672104,
-0.08539415895938873,
-0.03383791819214821,
0.010930748656392097,
0.015312932431697845,
-0.05496793985366821,
0.055221717804670334,
-0.03718177601695061,
-0.005299309268593788,
0.04345265403389931,
0.039532337337732315,
0.006220541894435883,
0.010234538465738297,
0.03134749457240105,
-0.0027697267942130566,
0.041089627891778946,
-0.03321600705385208,
-0.03882850334048271,
0.07102515548467636,
-0.023688584566116333,
-0.03325900062918663,
0.020542072132229805,
-0.018882185220718384,
0.0051137967966496944,
0.046197835355997086,
-0.008099974133074284,
-0.0057283807545900345,
0.08021137863397598,
-0.028226301074028015,
0.019508972764015198,
-0.018403466790914536,
0.012096037156879902,
0.033323194831609726,
0.013685312122106552,
0.0043710037134587765,
-0.024301476776599884,
-0.002616959623992443,
0.04649118334054947,
0.060878120362758636,
0.014155144803225994,
0.0015053660608828068,
-0.001848870888352394,
0.009582619182765484,
0.0474504753947258,
0.04332071542739868,
0.014636743813753128,
0.010642786510288715,
0.04591246321797371,
-0.054353225976228714,
0.06862792372703552,
-0.013287998735904694,
0.00013567873975262046,
-0.09983718395233154,
0.006335523910820484,
-0.020285053178668022,
-0.007813710719347,
0.03076871670782566,
-0.025018008425831795,
-0.02920062653720379,
0.045138850808143616,
-0.07068847864866257,
-0.02791309915482998,
-0.01045632641762495,
-0.021035410463809967,
-0.014493807218968868,
-0.017751481384038925,
-0.010983528569340706,
0.0864931270480156,
0.009555170312523842,
0.04739029332995415,
0.0348246730864048,
0.02373112365603447,
0.007770462427288294,
-0.019121158868074417,
-0.005767460446804762,
0.043966539204120636,
-0.004352969583123922,
0.005081242881715298,
0.05545096471905708,
-0.021517882123589516,
-0.014231687411665916,
0.006780159194022417,
-0.04847178980708122,
0.014482729136943817,
0.013247529976069927,
0.022390278056263924,
-0.020025214180350304,
0.035879041999578476,
0.011879269964993,
-0.008808385580778122,
-0.011431491002440453,
0.047866299748420715,
0.05105103552341461,
0.008685875684022903,
-0.006555936299264431,
-0.00614361185580492,
-0.00038090519956313074,
-0.03654436394572258,
-0.050909366458654404,
-0.0036207081284374,
-0.01869247481226921,
0.02540169283747673,
0.026101158931851387,
-0.0020309456158429384,
0.01967809721827507,
-0.03530709818005562,
-0.027297090739011765,
-0.05156790837645531,
0.009554138407111168,
0.05169243738055229,
0.02644583396613598,
-0.010501626878976822,
0.008095989003777504,
0.01944822259247303,
-0.03168758377432823,
-0.0031655849888920784,
0.020162217319011688,
-0.032484810799360275,
-0.043844301253557205,
-0.018673865124583244,
0.033223554491996765,
-0.030149998143315315,
-0.004515869542956352,
-0.017420602962374687,
-0.007134242448955774,
0.060193706303834915,
0.002032520482316613,
0.016951996833086014,
0.0037090997211635113,
-0.030370263382792473,
-0.05206238850951195,
-0.05119204893708229,
0.04819957911968231,
-0.028546243906021118,
0.020174192264676094,
-0.03722566366195679,
-0.027858741581439972,
-0.0014167223125696182,
0.01055140607059002,
0.05817418545484543,
0.004005139693617821,
0.0014340438647195697,
-0.007235122844576836,
0.009505811147391796,
-0.007471194490790367,
-0.037614088505506516,
0.024870669469237328,
0.025949250906705856,
-0.03049657493829727,
0.03957164287567139,
-0.038381870836019516,
-0.006195155903697014,
-0.006072366610169411,
0.020983610302209854,
-0.012409696355462074,
0.006437796633690596,
-0.0009216730250045657,
-0.0026731102261692286,
0.02745126374065876,
-0.0023214411921799183,
-0.014208206906914711,
0.07728983461856842,
-0.01211597304791212,
0.006747374776750803,
0.04664401710033417,
0.010540944524109364,
-0.031164461746811867,
0.06352725625038147,
-0.004578267224133015,
0.022232385352253914,
-0.0032334441784769297,
0.021047167479991913,
-0.02442687749862671,
-0.05101373791694641,
0.029523393139243126,
0.008183026686310768,
-0.011299392208456993,
-0.00961248017847538,
0.046913303434848785,
-0.02287846989929676,
0.0111854774877429,
-0.014834091067314148,
0.009547998197376728,
0.007349791936576366,
0.022014781832695007,
0.012983821332454681,
0.05704670026898384,
0.055922240018844604,
-0.02568751387298107,
0.017369654029607773,
0.031770288944244385,
-0.004302679095417261,
0.03828956186771393,
0.02767062745988369,
0.00601978600025177,
-0.006473395973443985,
-0.06118444725871086,
0.004217363893985748,
-0.000650177476927638,
-0.0001841438643168658,
0.013791567645967007,
-0.009035919792950153,
0.08518465608358383,
-0.017994092777371407,
-0.004860184621065855,
-0.03134223446249962,
0.009697826579213142,
0.013499092310667038,
0.01755911484360695,
-0.0013407355872914195,
0.024029256775975227,
-0.04570107161998749,
-0.0164845772087574,
0.013474272564053535,
0.010597208514809608,
0.003425661940127611,
-0.000085432046034839,
0.026530733332037926,
-0.038796983659267426,
0.024303218349814415,
-0.06077992171049118,
0.007384024560451508,
-0.009268711321055889,
-0.009919412434101105,
0.03427815064787865,
0.028485087677836418,
0.006740727927535772,
0.04742392152547836,
-0.04270406812429428,
-0.007213111501187086,
0.03134651482105255,
-0.084312304854393,
-0.010821403004229069,
-0.007521410938352346,
-0.0028195942286401987,
-0.006167426705360413,
-0.05884247273206711
] |
<p>Wikipedia: "Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero."</p>
<p>Is it possible to annihilate a quark-antiquark pair if the antiquark has a color different from the quark?</p>
<p>Eg.: Will red up and anti-green anti-up annihilate? And if so, what is the product?</p>
| 9,420 |
[
-0.0019867715891450644,
-0.039251770824193954,
-0.001317685702815652,
-0.00707527669146657,
0.05008618161082268,
0.01114638615399599,
-0.046677783131599426,
0.017361531034111977,
0.0018806548323482275,
-0.0018338157096877694,
0.008115085773169994,
0.005635532550513744,
0.047794874757528305,
0.006005013827234507,
0.0030535697005689144,
0.023829668760299683,
-0.013145865872502327,
-0.04243423789739609,
0.004356237128376961,
0.006293474696576595,
0.022488731890916824,
0.0007242650026455522,
0.018002135679125786,
0.0021076102275401354,
-0.011942597106099129,
0.051457371562719345,
0.046713560819625854,
-0.017391787841916084,
0.01647101156413555,
0.05264846608042717,
0.00987011194229126,
-0.048115819692611694,
0.05655600130558014,
0.03959554806351662,
0.03387322276830673,
0.01662510447204113,
0.0030491941142827272,
-0.04911481589078903,
-0.04479378089308739,
-0.002522876486182213,
-0.013873845338821411,
-0.04074253514409065,
0.016524426639080048,
0.03983522206544876,
-0.045671530067920685,
0.00031783321173861623,
-0.013740019872784615,
-0.03600449115037918,
0.04023941606283188,
-0.07109448313713074,
0.036734439432621,
0.04503534361720085,
0.03680236637592316,
-0.004661677870899439,
0.006909902673214674,
-0.007547373417764902,
0.06285072863101959,
0.06376565992832184,
0.015192074701189995,
-0.03012467920780182,
0.002972629154101014,
0.011330610141158104,
0.012909390963613987,
-0.014322975650429726,
-0.05667505040764809,
0.0327468179166317,
0.026935787871479988,
-0.003490314120426774,
-0.010985690169036388,
-0.019003069028258324,
0.016304099932312965,
0.02287249267101288,
0.03183608502149582,
-0.01798124797642231,
-0.010255948640406132,
-0.03910137712955475,
0.012189759872853756,
0.029946833848953247,
0.014046086929738522,
0.06655388325452805,
-0.007830624468624592,
0.027477575466036797,
-0.01005520485341549,
0.008879310451447964,
0.013411306776106358,
-0.01660696603357792,
0.05701857805252075,
0.006612951401621103,
-0.023908114060759544,
0.012696915306150913,
0.011810633353888988,
0.008376380428671837,
0.030361032113432884,
0.012954060919582844,
-0.02114959992468357,
0.03059818036854267,
0.0008825765107758343,
0.050457701086997986,
-0.014453605748713017,
-0.02380944974720478,
0.012036300264298916,
-0.0039497134275734425,
0.0251784548163414,
0.04280873388051987,
0.002403665566816926,
-0.023488907143473625,
-0.02677813544869423,
0.033116281032562256,
0.0110359201207757,
0.021600088104605675,
-0.02503977343440056,
0.0014083682326599956,
-0.0009242052328772843,
-0.05635545775294304,
0.004444593098014593,
-0.017858222126960754,
-0.020980671048164368,
-0.008534823544323444,
0.07583601772785187,
0.04665283486247063,
0.0474654920399189,
-0.003221043385565281,
0.005483435932546854,
-0.025835612788796425,
-0.014812958426773548,
-0.022197293117642403,
0.0035885318648070097,
-0.0077126966789364815,
-0.02932446077466011,
0.039968572556972504,
0.003813045797869563,
-0.02654903754591942,
0.007393592037260532,
-0.02834291011095047,
0.012809290550649166,
-0.04202505573630333,
-0.09216862171888351,
-0.08374012261629105,
0.01945648156106472,
-0.03781767934560776,
-0.02892647683620453,
-0.032439764589071274,
-0.009526362642645836,
0.003075835993513465,
0.06659575551748276,
-0.03735301271080971,
-0.011719916015863419,
-0.006306787487119436,
0.00020586849132087082,
0.04037541523575783,
0.009541490115225315,
-0.05079140514135361,
0.0011634790571406484,
-0.05885760486125946,
0.018181374296545982,
-0.06736186891794205,
0.026352066546678543,
0.037585753947496414,
0.014323737472295761,
0.0007145761046558619,
0.06888600438833237,
-0.015227037481963634,
-0.00024616511655040085,
0.04828499257564545,
-0.024972274899482727,
-0.03151700645685196,
0.07570941746234894,
0.022821364924311638,
-0.0524863637983799,
0.02398448809981346,
0.012810601852834225,
0.023394886404275894,
0.026576237753033638,
0.03113776445388794,
0.047397322952747345,
-0.002135809510946274,
-0.016053950414061546,
-0.04174956679344177,
0.04030933231115341,
-0.02203889936208725,
-0.03992268443107605,
-0.04052785038948059,
-0.01944783516228199,
0.016415990889072418,
0.04360329732298851,
0.04291237145662308,
-0.006353385746479034,
-0.013241642154753208,
0.027581343427300453,
-0.057811636477708817,
-0.014399688690900803,
-0.06561325490474701,
0.02559238113462925,
0.03673769161105156,
-0.006565030664205551,
0.03537093102931976,
0.06714281439781189,
0.01951814629137516,
-0.046777479350566864,
-0.028260277584195137,
-0.0037052761763334274,
0.0262133926153183,
0.0009150160476565361,
-0.010909118689596653,
0.009927662089467049,
0.061779119074344635,
0.045833177864551544,
-0.026212230324745178,
0.053550705313682556,
-0.049625273793935776,
-0.045072782784700394,
-0.01165329571813345,
-0.007563885301351547,
0.014706800691783428,
-0.006866992451250553,
0.007433888036757708,
0.01826036348938942,
0.023392871022224426,
0.008267408236861229,
0.01862933300435543,
-0.01074695773422718,
0.045443274080753326,
-0.005884031765162945,
-0.009959226474165916,
-0.023333894088864326,
0.021522976458072662,
0.05557018145918846,
0.023664018139243126,
-0.015037234872579575,
-0.005670176353305578,
-0.023571059107780457,
-0.01000701542943716,
0.013753599487245083,
0.02680804207921028,
-0.028140293434262276,
0.03740857169032097,
0.0003340782131999731,
0.032984815537929535,
0.010068971663713455,
0.002767810830846429,
-0.022719545289874077,
-0.021328968927264214,
-0.011202431283891201,
0.005196438170969486,
-0.02120341546833515,
0.00522087886929512,
0.04083621874451637,
-0.023175489157438278,
-0.0072718127630651,
-0.00776520324870944,
-0.04593968763947487,
0.01238421443849802,
-0.0012958687730133533,
0.006821389310061932,
-0.022670377045869827,
-0.06791727989912033,
0.01651456579566002,
-0.039832837879657745,
0.04280632361769676,
-0.008727991953492165,
-0.01636671833693981,
-0.01863892935216427,
0.008426015265285969,
-0.01612848788499832,
-0.05236012488603592,
-0.02940423972904682,
-0.019852766767144203,
0.00530273886397481,
0.011269976384937763,
-0.03427795693278313,
0.0016354741528630257,
-0.011028899811208248,
0.0022365357726812363,
-0.04093068465590477,
0.007245728280395269,
0.03477718308568001,
0.007688671350479126,
0.0470547117292881,
-0.03175791725516319,
-0.036220699548721313,
0.02879101224243641,
-0.032484184950590134,
0.045023515820503235,
0.06342823803424835,
-0.028017064556479454,
0.03392970561981201,
-0.07817690819501877,
-0.0464615672826767,
0.0006508783553726971,
-0.029228689149022102,
0.008837796747684479,
0.03475326672196388,
-0.050819966942071915,
-0.04402526468038559,
-0.005974092520773411,
-0.049801893532276154,
0.00502041494473815,
-0.05776862055063248,
0.030802201479673386,
0.014180428348481655,
-0.002563734073191881,
-0.044923827052116394,
-0.03277458995580673,
-0.06429456174373627,
-0.053960055112838745,
0.010534802451729774,
-0.017281536012887955,
0.06373746693134308,
-0.027355458587408066,
0.0027807739097625017,
0.053032610565423965,
-0.05800720304250717,
0.0006357083329930902,
-0.05183137580752373,
-0.046184953302145004,
0.011418779380619526,
0.025860203430056572,
0.015622632578015327,
0.012695711106061935,
-0.01756208948791027,
0.06059715151786804,
0.01779746823012829,
-0.037007275968790054,
-0.0008687766967341304,
0.0035387668758630753,
-0.017830027267336845,
-0.018085965886712074,
0.02101203054189682,
0.022020619362592697,
0.005844450555741787,
0.039511848241090775,
0.0029168270993977785,
0.050869375467300415,
0.03393201529979706,
0.02123558148741722,
-0.06105555593967438,
0.0023192591033875942,
0.0363091379404068,
0.0206589475274086,
0.024276455864310265,
-0.000024493379896739498,
-0.016181642189621925,
0.025136861950159073,
0.02300143800675869,
0.03771410137414932,
-0.016612164676189423,
-0.006633239798247814,
0.07040505856275558,
0.020181791856884956,
0.049156609922647476,
-0.025470441207289696,
0.054645638912916183,
-0.011786042712628841,
0.002817280124872923,
0.023522060364484787,
0.0063117677345871925,
0.028316140174865723,
-0.029474491253495216,
0.022620564326643944,
0.031122900545597076,
0.044358592480421066,
-0.028352539986371994,
-0.03022233210504055,
0.004530160687863827,
-0.018017055466771126,
0.02468082867562771,
-0.017300590872764587,
0.015099809505045414,
0.02797386422753334,
0.02204500325024128,
0.007585178595036268,
0.020700478926301003,
-0.002274611499160528,
-0.003287862055003643,
-0.08252502232789993,
-0.02641516551375389,
-0.00808208528906107,
0.034201882779598236,
0.0166594497859478,
0.07624614238739014,
0.005281456280499697,
0.0031277944799512625,
0.010342344641685486,
-0.02846280299127102,
-0.10452330112457275,
0.009700717404484749,
-0.019276967272162437,
-0.016946373507380486,
-0.0010014359140768647,
-0.057719651609659195,
0.0028487250674515963,
-0.03226029872894287,
-0.053751878440380096,
-0.009819891303777695,
-0.0028282843995839357,
-0.011011638678610325,
0.02705594152212143,
-0.040736664086580276,
-0.04569343104958534,
0.007301876321434975,
0.01739318296313286,
0.04732165485620499,
-0.013292859308421612,
0.02068992331624031,
0.029960419982671738,
-0.05728013440966606,
-0.0015533101977780461,
-0.024195564910769463,
0.03724336996674538,
0.016991479322314262,
0.03144712746143341,
0.05423293635249138,
0.054586317390203476,
-0.05764986574649811,
-0.005750394891947508,
0.02374785766005516,
0.05427630618214607,
0.0002072118950309232,
0.006850826554000378,
-0.0036177344154566526,
-0.049304790794849396,
-0.023365087807178497,
-0.028801007196307182,
0.04120969399809837,
-0.028892992064356804,
-0.010599188506603241,
0.030198993161320686,
0.03492139279842377,
-0.01835009828209877,
0.04189971461892128,
0.11081497371196747,
0.008136977441608906,
-0.008751151151955128,
-0.010853919200599194,
0.00351306376978755,
-0.004158892203122377,
-0.008734813891351223,
-0.007847368717193604,
-0.005240150261670351,
-0.02903507649898529,
0.023916134610772133,
0.012859191745519638,
0.05019204318523407,
-0.026288853958249092,
-0.006697279866784811,
-0.039329808205366135,
-0.00810543168336153,
-0.01672934740781784,
0.007425788789987564,
-0.01718953624367714,
0.056270524859428406,
0.014382981695234776,
0.014994803816080093,
-0.017343781888484955,
-0.06285252422094345,
-0.005458869505673647,
0.034867532551288605,
0.06664212793111801,
0.007922369986772537,
-0.02030002512037754,
-0.07961542159318924,
-0.0331169031560421,
0.06678558140993118,
-0.011351541616022587,
-0.000894412281922996,
0.002204295713454485,
-0.028392625972628593,
-0.01519987266510725,
0.02207941748201847,
-0.0015821275301277637,
0.0775008574128151,
-0.01772410236299038,
-0.02322392165660858,
-0.005829151254147291,
0.004846513271331787,
-0.02819950319826603,
0.032753389328718185,
0.05421450734138489,
0.026597045361995697,
-0.013712447136640549,
0.028013231232762337,
0.024663083255290985,
-0.011059697717428207,
0.007436653133481741,
-0.08988717198371887,
0.014242597855627537,
-0.0014070909237489104,
-0.015624706633388996,
0.062152910977602005,
-0.011262452229857445,
-0.010136273689568043,
0.009125671349465847,
0.00855674035847187,
0.0048299022018909454,
0.003253527916967869,
-0.06506083160638809,
0.022603653371334076,
0.02427751012146473,
-0.021544096991419792,
0.043736763298511505,
0.03123440220952034,
-0.01886988803744316,
-0.00231859995983541,
-0.05068719759583473,
0.039242424070835114,
-0.013897042721509933,
0.004040968604385853,
-0.010866825468838215,
0.0007802908075973392,
0.003644015174359083,
0.025344397872686386,
-0.03655581548810005,
0.03727464750409126,
-0.0006356691592372954,
-0.0443260557949543,
-0.012321066111326218,
-0.022597402334213257,
0.01231204904615879,
0.012146622873842716,
0.010057386942207813,
0.017787083983421326,
-0.018907951191067696,
-0.015599013306200504,
0.029278412461280823,
-0.006392322480678558,
-0.005618709605187178,
-0.008568283170461655,
-0.005648748949170113,
0.03523234650492668,
-0.027029694989323616,
-0.013978315517306328,
-0.002233236562460661,
0.005336219910532236,
0.016185235232114792,
-0.016141274943947792,
0.006996199022978544,
0.012482409365475178,
-0.03538878634572029,
-0.050459738820791245,
-0.0047961389645934105,
-0.036865267902612686,
-0.006721170619130135,
-0.05550255998969078,
0.08400370925664902,
0.035814519971609116,
-0.015492559410631657,
-0.08369940519332886,
-0.04210067167878151,
0.013136095367372036,
0.01673908717930317,
-0.004913070239126682,
-0.020258966833353043,
-0.01087399385869503,
0.0019371003145352006,
0.021102868020534515,
0.0010082477238029242,
0.0683356374502182,
-0.04067885875701904,
-0.03627771511673927,
0.004567292053252459,
-0.0008777024922892451,
0.015367328189313412,
0.007418707013130188,
-0.009448951110243797,
-0.00876410398632288,
0.0056554707698524,
0.012861231341958046,
0.032378580421209335,
0.04341775178909302,
-0.022564588114619255,
-0.05604875087738037,
0.003177307778969407,
-0.014150602743029594,
0.019517777487635612,
-0.028728816658258438,
0.010658875107765198,
-0.0041162241250276566,
0.03808332979679108,
0.014814266003668308,
0.01722501777112484,
0.018740054219961166,
-0.009097646921873093,
0.013070262968540192,
0.011378672905266285,
-0.020594105124473572,
-0.01691983826458454,
-0.029359977692365646,
0.02417081966996193,
0.006863259710371494,
-0.010061345063149929,
0.00018322651158086956,
0.06290771067142487,
-0.0008496041991747916,
-0.03310596942901611,
0.00752698490396142,
-0.0364488922059536,
0.014329572208225727,
-0.049610793590545654,
-0.005993145518004894,
-0.00005862898251507431,
0.008376754820346832,
0.0020170172210782766,
-0.023487638682127,
-0.025085942819714546,
-0.021341338753700256,
0.023990977555513382,
-0.04120016098022461,
0.05084669962525368,
0.0013391583925113082,
0.03383397310972214,
-0.01671556569635868,
-0.04455690085887909,
0.009416686370968819,
-0.00040838815039023757,
0.016694825142621994,
0.022533545270562172,
-0.0004234164662193507,
0.014281539246439934,
0.005437468644231558,
0.07411918044090271,
0.006449219770729542,
-0.00451698387041688,
0.030147505924105644,
0.007147703319787979,
0.03229159489274025,
0.003953528590500355,
-0.04560406133532524,
0.028392354026436806,
-0.0593801885843277,
-0.004325058311223984,
-0.0006907634669914842,
-0.0616859570145607,
0.03640865162014961,
-0.009222437627613544,
0.02282531000673771,
-0.010743892751634121,
-0.04217176511883736,
-0.028538549318909645,
0.03265540301799774,
0.018288809806108475,
0.042991481721401215,
0.0030320780351758003,
0.006066175643354654,
0.019004208967089653,
0.02214607037603855,
0.02052352763712406,
-0.033405788242816925,
-0.08492026478052139,
-0.04133051633834839,
-0.04573862999677658,
-0.03473593667149544,
0.03074781969189644,
-0.029907094314694405,
-0.001479020225815475,
0.008086087182164192,
-0.015455936081707478,
0.04634804278612137,
-0.030625903978943825,
0.015430465340614319,
-0.02893233485519886,
0.009735975414514542,
-0.015186583623290062,
0.04751265048980713,
0.00012826824968215078,
0.02572745829820633,
0.11441534757614136,
0.024499032646417618,
0.01119931135326624,
-0.0649920329451561,
0.004461176227778196,
-0.013139677233994007,
-0.015548043884336948,
-0.022549210116267204,
0.024328332394361496,
-0.015775619074702263,
0.02497841976583004,
0.0035255809780210257,
0.0686919167637825,
0.024375086650252342,
-0.03000740148127079,
0.050322748720645905,
-0.030001439154148102,
-0.057579975575208664,
-0.004353129770606756,
0.027710050344467163,
-0.018437504768371582,
0.007660828065127134,
-0.05472930893301964,
0.0017112658824771643,
-0.014241899363696575,
0.0046402704901993275,
-0.020048314705491066,
-0.021612420678138733,
0.01984586752951145,
0.038326118141412735,
-0.023172792047262192,
0.03409520164132118,
0.017715999856591225,
0.012117850594222546,
-0.024859292432665825,
0.011136663146317005,
0.03478381037712097,
-0.030254997313022614,
0.03296590596437454,
0.018943019211292267,
0.061200086027383804,
-0.014413661323487759,
-0.006851529236882925,
0.011804317124187946,
-0.07230272889137268,
-0.003368642646819353,
-0.010432546027004719,
0.03023754432797432,
-0.04523507505655289,
-0.01430240087211132,
-0.011032924987375736,
-0.003813693067058921,
0.02009604312479496,
-0.053203046321868896,
-0.0330977663397789,
-0.0024161189794540405,
0.021999463438987732,
0.0007352535612881184,
0.001176227000541985,
0.0046397484838962555,
0.029143206775188446,
-0.022037360817193985,
0.021758705377578735,
-0.006067351903766394,
-0.005554228089749813,
0.01183890737593174,
-0.0023844148963689804,
0.018461700528860092,
0.0064003197476267815,
-0.03333088010549545,
-0.033273063600063324,
0.0165410153567791,
-0.012910538353025913,
-0.018364008516073227,
0.015178295783698559,
0.04120764508843422,
0.037910133600234985,
0.022672351449728012,
-0.0002211339888162911,
-0.019953100010752678,
-0.04070878028869629,
0.03882600739598274,
-0.03839843347668648,
-0.012284031137824059,
-0.0037781076971441507,
-0.018272656947374344,
0.05030046030879021,
0.025859611108899117,
-0.017939120531082153,
-0.007769093848764896,
-0.004595148377120495,
0.04714447632431984,
0.02766554430127144,
0.018364109098911285,
0.015578048303723335,
-0.005356718320399523,
-0.042109012603759766,
-0.006074215285480022,
-0.04373830184340477,
0.03211309388279915,
0.02950347401201725,
0.02103465050458908,
-0.005717921536415815,
0.011241422034800053,
0.006589227821677923,
-0.036518894135951996,
0.021135909482836723,
-0.016716931015253067,
0.002205800963565707,
0.007515643257647753,
0.03628110885620117,
-0.007317532319575548,
-0.03874044865369797,
0.008425558917224407,
-0.0066217961721122265,
-0.003466218477115035,
0.023372869938611984,
-0.02952917292714119,
-0.012016741558909416,
-0.017705541104078293,
0.013290497474372387,
-0.010094212368130684,
-0.011285302229225636,
-0.03791724145412445,
-0.013033307157456875,
-0.01995507813990116,
-0.009488151408731937,
0.007112585008144379,
0.031608015298843384,
-0.0029748352244496346,
-0.012616091407835484,
0.012789063155651093,
0.03842993825674057,
-0.010002633556723595,
-0.0036778694484382868,
0.022778363898396492,
0.013571259565651417,
0.05871368572115898,
0.014590517617762089,
-0.03378342464566231,
0.07064949721097946,
-0.02661009319126606,
-0.04204539209604263,
0.03324861451983452,
-0.017894016578793526,
0.032223645597696304,
0.020717624574899673,
-0.03594310209155083,
-0.046629346907138824,
0.04488285630941391,
-0.011342746205627918,
-0.016204381361603737,
0.0024300075601786375,
-0.016799509525299072,
-0.0423605814576149,
-0.010268736630678177,
-0.02948707342147827,
0.007275145035237074,
-0.022235436365008354,
0.011697696521878242,
0.029325729236006737,
-0.014091704040765762,
0.03808503970503807,
-0.024765437468886375,
0.00886028166860342,
0.032994285225868225,
0.017383376136422157,
-0.019418643787503242,
-0.028915420174598694,
0.020729778334498405,
0.006703290622681379,
0.06314142048358917,
-0.0031384530011564493,
-0.013188792392611504,
-0.11045657098293304,
-0.0030180937610566616,
0.04183552414178848,
-0.00895692314952612,
-0.018382102251052856,
-0.0654834657907486,
0.0221354141831398,
0.04509400576353073,
-0.08473317325115204,
0.054827768355607986,
-0.06194223091006279,
-0.06685590744018555,
-0.025129012763500214,
0.03162477910518646,
-0.008006757125258446,
0.04342007264494896,
0.030801570042967796,
0.02289576642215252,
0.011388399638235569,
-0.0015798989916220307,
-0.020996587350964546,
-0.03620164096355438,
-0.005681747104972601,
-0.014268800616264343,
0.006466791965067387,
-0.015972601249814034,
0.04468166083097458,
-0.03152811899781227,
0.008985377848148346,
-0.0017524672439321876,
-0.05351971462368965,
-0.0295461006462574,
-0.012430932372808456,
0.025361694395542145,
0.02163325622677803,
0.030540665611624718,
-0.005749035160988569,
0.03715230152010918,
-0.016041189432144165,
0.008237095549702644,
0.030877595767378807,
0.0272524394094944,
-0.022154346108436584,
0.03215164691209793,
0.004734274465590715,
0.0033685762900859118,
-0.031949691474437714,
0.04137187451124191,
-0.010364193469285965,
-0.03168362006545067,
0.006162350531667471,
0.025489408522844315,
-0.0036947682965546846,
-0.008774942718446255,
-0.00767182232812047,
-0.028089916333556175,
0.011271286755800247,
-0.016495976597070694,
-0.0040696063078939915,
0.017526263371109962,
0.007182949688285589,
-0.02064591273665428,
-0.005018419586122036,
0.023814862594008446,
0.0019997330382466316,
0.023661533370614052,
-0.004352960269898176,
0.001918432884849608,
0.004063248634338379,
0.04748601093888283,
0.008743789978325367,
-0.06516209244728088,
-0.020752327516674995,
0.011339564807713032,
-0.014445474371314049,
0.04974466562271118,
-0.014718275517225266,
-0.056302979588508606,
-0.008791554719209671,
-0.052154913544654846,
0.02567620947957039,
0.03338134288787842,
0.0537305623292923,
-0.029987864196300507,
0.002247592667117715,
0.0056748539209365845,
0.021397382020950317,
0.04277192801237106,
-0.0049842968583106995,
-0.03693923354148865,
0.009199758060276508,
0.0008044113637879491,
0.023996051400899887,
0.034268900752067566,
-0.0010247345780953765,
0.002443722216412425,
-0.026208434253931046,
-0.02623961679637432,
0.03256543353199959,
-0.022949330508708954,
0.040605176240205765,
0.02697388082742691,
-0.007663415279239416,
-0.021503441035747528,
0.022584587335586548,
-0.06413914263248444,
0.08533479273319244,
-0.009815630502998829,
0.023244231939315796,
0.07764778286218643,
-0.0018952075624838471,
0.05096372216939926,
0.014060183428227901,
-0.024524874985218048,
-0.06685689091682434,
0.0016028735553845763,
-0.023197568953037262,
-0.011021528393030167,
0.010209866799414158,
-0.027771538123488426,
0.037631288170814514,
-0.03999845311045647,
0.03279371187090874,
0.056131817400455475,
-0.011380125768482685,
-0.034616462886333466,
0.04470709711313248,
0.05486549437046051,
0.04379289597272873,
-0.02886394038796425,
0.002335792873054743,
0.01859959401190281,
0.032936785370111465,
0.006737336050719023,
0.030582010746002197,
-0.007543886546045542,
0.043924480676651,
0.022052502259612083,
-0.0007805300992913544,
0.013267201371490955,
-0.012180461548268795,
0.018961455672979355,
0.009313144721090794,
0.006955876015126705,
0.01314439158886671,
0.01442581508308649,
-0.022480841726064682,
0.07707449048757553,
0.024461375549435616,
-0.03200932964682579,
0.08623024821281433,
-0.06339563429355621,
0.03240816295146942,
-0.03137129172682762,
0.018686339259147644,
-0.028343865647912025,
-0.023306231945753098,
-0.003931540995836258,
0.031021492555737495,
-0.024160832166671753,
-0.049897633492946625,
-0.012076682411134243,
0.02443113923072815,
0.02542589046061039,
-0.05688474327325821,
0.0152923334389925,
0.008615396916866302,
-0.005153400357812643,
-0.02238972671329975,
-0.007413747254759073,
-0.03976402431726456,
-0.003301437944173813,
0.007386974524706602,
0.03554627299308777,
0.0027331686578691006,
0.011791210621595383,
-0.01980075053870678,
-0.028737500309944153,
0.013922739773988724,
-0.018921108916401863,
-0.031418781727552414,
-0.016636161133646965,
0.0243474580347538,
-0.03718973696231842,
-0.013080846518278122
] |
<p>As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for solitons in nonlinear wave equation? </p>
| 9,421 |
[
-0.01158294640481472,
-0.00004333847755333409,
-0.003343120915815234,
-0.026592878624796867,
0.04386672005057335,
0.014398551546037197,
-0.05237125605344772,
-0.04459092393517494,
0.0275861993432045,
-0.03135029226541519,
0.04817879945039749,
0.003160968655720353,
0.02940950356423855,
0.007181758526712656,
0.01861041598021984,
0.008780967444181442,
-0.034754909574985504,
-0.006200931500643492,
-0.03538971766829491,
0.0071391090750694275,
-0.028313152492046356,
0.017237603664398193,
-0.016463235020637512,
-0.00619114562869072,
-0.01925082691013813,
0.00043231173185631633,
0.01600167527794838,
0.02974308840930462,
0.05823567137122154,
0.030485544353723526,
-0.014211301691830158,
-0.01936120167374611,
0.010400316677987576,
0.0494084469974041,
0.01076189149171114,
-0.013947072438895702,
-0.041010234504938126,
-0.049182821065187454,
-0.016087079420685768,
-0.004145781043916941,
0.006421301513910294,
-0.0635792687535286,
0.0005110943457111716,
0.013348301872611046,
-0.04597112536430359,
0.01345872599631548,
0.022756585851311684,
-0.019018081948161125,
0.015796106308698654,
-0.09035313874483109,
0.032510630786418915,
-0.010213890112936497,
0.053009044378995895,
-0.025032788515090942,
0.015997081995010376,
0.023816991597414017,
0.07604941725730896,
0.038760993629693985,
-0.042797528207302094,
-0.06423427909612656,
-0.021498603746294975,
0.04589133709669113,
0.004487941507250071,
-0.03405439108610153,
-0.030128145590424538,
0.05466644465923309,
0.004952661693096161,
-0.013621695339679718,
0.017219703644514084,
-0.03193283453583717,
-0.037134818732738495,
0.0026927406433969736,
0.02780398353934288,
-0.030943721532821655,
0.01086991373449564,
-0.007630562875419855,
-0.011600946076214314,
-0.02069157548248768,
0.03392573818564415,
0.03686440736055374,
0.03827774524688721,
0.03122520260512829,
0.012300646863877773,
0.0006066703936085105,
0.012493136338889599,
-0.03495394065976143,
0.06454356759786606,
-0.007569512352347374,
0.01811993680894375,
0.01099331770092249,
0.0012466678163036704,
0.00965037476271391,
0.03826400637626648,
0.002375520532950759,
-0.013877867721021175,
0.0036123842000961304,
0.025614216923713684,
0.04543875902891159,
0.03185177594423294,
-0.03667085990309715,
0.008517269045114517,
-0.028191905468702316,
0.043249547481536865,
0.06753697246313095,
-0.009902962483465672,
-0.016070730984210968,
-0.051487673074007034,
0.021944230422377586,
-0.04532350227236748,
-0.015132525935769081,
-0.01925458200275898,
0.005067638121545315,
0.006620727013796568,
0.015575287863612175,
0.03813019394874573,
0.031332675367593765,
0.020076775923371315,
-0.04156923666596413,
0.022078603506088257,
0.07341384142637253,
0.024594426155090332,
-0.0228341706097126,
0.05720677599310875,
-0.029589418321847916,
-0.07313986867666245,
0.00011203149915672839,
0.03793373331427574,
-0.012565474025905132,
-0.0501825325191021,
0.005829849746078253,
-0.013304847292602062,
-0.003444201312959194,
0.022523313760757446,
0.006509921979159117,
0.0665382370352745,
-0.013685387559235096,
-0.11524496227502823,
-0.06764505058526993,
0.030009163543581963,
0.006018113344907761,
-0.03142818808555603,
-0.0593530610203743,
0.0036796568892896175,
0.04492034390568733,
0.08020810782909393,
-0.019608933478593826,
0.006216344423592091,
0.025644058361649513,
0.040783826261758804,
0.023368487134575844,
-0.008580533787608147,
-0.025236548855900764,
0.02436174638569355,
-0.05841943249106407,
0.02820170484483242,
-0.07506093382835388,
0.000045461511035682634,
0.009741492569446564,
0.011356995441019535,
-0.038928963243961334,
0.07782519608736038,
-0.02047993801534176,
0.005465872120112181,
0.02410595491528511,
-0.011127645149827003,
-0.030164163559675217,
0.09455952048301697,
-0.042532216757535934,
0.0583060085773468,
0.04379192739725113,
-0.019797595217823982,
0.017419498413801193,
0.017163172364234924,
0.02979007177054882,
0.002702102530747652,
-0.03528424724936485,
-0.029262050986289978,
0.018851807340979576,
-0.009347825311124325,
0.026164738461375237,
-0.028917841613292694,
-0.038175903260707855,
0.027971211820840836,
0.03430115431547165,
-0.012368825264275074,
0.051766812801361084,
0.0025456566363573074,
-0.04821804165840149,
0.006939225364476442,
-0.06453438848257065,
0.02304273098707199,
-0.05257300287485123,
0.05367887392640114,
0.008642901666462421,
0.006997383199632168,
0.027233313769102097,
0.023679465055465698,
0.0012074136175215244,
-0.04404555261135101,
0.011619710363447666,
-0.01043123658746481,
0.07626279443502426,
-0.004946554079651833,
-0.03039547987282276,
0.02757863700389862,
0.03688444942235947,
-0.008923816494643688,
-0.010100547224283218,
0.05956466495990753,
-0.014148163609206676,
-0.015782123431563377,
0.008881605230271816,
-0.025213100016117096,
0.028774309903383255,
-0.011287940666079521,
0.0011505072470754385,
0.014608976431190968,
-0.013266261667013168,
-0.02686597779393196,
0.04878385365009308,
-0.03835500031709671,
0.05469808727502823,
0.054174572229385376,
0.019995061680674553,
-0.0011800136417150497,
0.02166644297540188,
-0.01271846704185009,
0.022000068798661232,
0.030641786754131317,
-0.0348682627081871,
-0.03734640032052994,
0.0022807742934674025,
0.03251895681023598,
0.048564523458480835,
-0.026302753016352654,
0.025038553401827812,
0.014685066416859627,
0.03859434649348259,
0.05312133580446243,
0.03931465372443199,
-0.005559626966714859,
-0.005295375362038612,
0.04557408392429352,
0.02735409326851368,
0.014474927447736263,
-0.000341215287335217,
0.04321860522031784,
0.025574063882231712,
0.009091543965041637,
-0.057731494307518005,
-0.028438787907361984,
0.041078466922044754,
-0.011830346658825874,
0.02784634754061699,
0.018138183280825615,
-0.03191682696342468,
0.000991182285360992,
-0.05050962045788765,
0.0023816486354917288,
0.007238366641104221,
-0.002666962333023548,
0.00701226107776165,
-0.0017703495686873794,
-0.0041036345064640045,
0.017014505341649055,
0.013723624870181084,
-0.00012085151684004813,
-0.016644630581140518,
0.020491823554039,
-0.03480600565671921,
-0.0036371478345245123,
-0.013216424733400345,
-0.035553157329559326,
-0.012809423729777336,
0.0000804791779955849,
0.049014631658792496,
0.013220774941146374,
0.02478480339050293,
-0.016733936965465546,
-0.03641456738114357,
0.01796346716582775,
-0.03433860465884209,
-0.011062130331993103,
0.002620635088533163,
-0.033712394535541534,
0.032614815980196,
-0.038537364453077316,
-0.017308522015810013,
0.031600963324308395,
-0.020584184676408768,
0.04969693720340729,
-0.005801340565085411,
-0.047658711671829224,
-0.04364936426281929,
-0.044942740350961685,
-0.02824956364929676,
0.03473500907421112,
0.012274658307433128,
0.00576638663187623,
0.06379860639572144,
-0.0007351213716901839,
-0.0332193560898304,
0.003269942244514823,
-0.009584112092852592,
-0.036592088639736176,
-0.03276972472667694,
-0.0028776272665709257,
0.050436217337846756,
-0.06433778256177902,
0.018322257325053215,
0.019154474139213562,
-0.07259375602006912,
0.021604230627417564,
-0.051766183227300644,
-0.05968933552503586,
0.00495978444814682,
0.003998896572738886,
0.02866189181804657,
0.013946407474577427,
-0.040298547595739365,
0.06803035736083984,
0.017612794414162636,
-0.015056037344038486,
-0.03390715271234512,
0.009900358505547047,
-0.025065874680876732,
0.006805294193327427,
0.011388126760721207,
0.02828766219317913,
0.0072290292009711266,
0.005560173187404871,
0.034550122916698456,
0.02407354861497879,
0.050275251269340515,
0.042821548879146576,
-0.025732945650815964,
-0.016416821628808975,
0.004432361572980881,
-0.002023818902671337,
0.0196037907153368,
0.01358109898865223,
-0.04105191305279732,
0.019475916400551796,
0.014969300478696823,
-0.01911901868879795,
0.017566587775945663,
-0.01950506493449211,
0.030522355809807777,
0.009152280166745186,
0.019028374925255775,
-0.003869334701448679,
0.03359295055270195,
0.018658708781003952,
0.004662822932004929,
-0.012367906048893929,
0.0015330977039411664,
0.0393710620701313,
-0.008265846408903599,
-0.0030192742124199867,
-0.0065921894274652,
0.020263532176613808,
-0.05163274332880974,
-0.014008117839694023,
-0.009944808669388294,
-0.012841875664889812,
0.025299888104200363,
0.012318072840571404,
-0.012243328616023064,
0.07167273014783859,
0.01986226998269558,
0.00498576182872057,
-0.0388190932571888,
-0.03216458112001419,
-0.015853850170969963,
-0.045619938522577286,
-0.020015113055706024,
-0.0019518781919032335,
0.06707418709993362,
0.015524184331297874,
0.06266211718320847,
0.029512761160731316,
0.03479957953095436,
0.028054244816303253,
-0.001989484764635563,
-0.07563665509223938,
-0.0077240657992661,
-0.0560612715780735,
-0.03419443964958191,
-0.02471761219203472,
0.005818071775138378,
-0.03613591194152832,
0.028878921642899513,
-0.01596558652818203,
-0.014714480377733707,
-0.023457461968064308,
-0.06841419637203217,
0.016626091673970222,
-0.03129185363650322,
-0.026515934616327286,
-0.03266444802284241,
0.012903960421681404,
0.030095160007476807,
0.01226167194545269,
-0.014374983496963978,
0.04238930344581604,
-0.0037882444448769093,
-0.0020470251329243183,
0.010550269857048988,
-0.00997877772897482,
0.02210209332406521,
0.032144248485565186,
0.004999589640647173,
0.030177932232618332,
-0.020525028929114342,
0.0036243884824216366,
0.042602524161338806,
0.03925158828496933,
-0.006155115552246571,
0.00754951499402523,
0.0010592800099402666,
-0.025169331580400467,
0.0020434425678104162,
-0.010274183936417103,
0.04851001873612404,
0.03237508609890938,
-0.0045464192517101765,
0.020254217088222504,
-0.021276384592056274,
-0.032253921031951904,
0.029716474935412407,
0.026807334274053574,
0.026904867962002754,
-0.027229266241192818,
-0.044564180076122284,
-0.013343961909413338,
-0.04147491976618767,
0.01671260967850685,
-0.0018044405151158571,
-0.03238473832607269,
-0.018982432782649994,
0.039804112166166306,
0.030969731509685516,
-0.030404554679989815,
-0.00498921936377883,
-0.03155255317687988,
0.004515916109085083,
0.007750141434371471,
-0.0120136933401227,
-0.0018233644077554345,
0.0002743916993495077,
0.05164326727390289,
0.012136301957070827,
-0.0057411943562328815,
-0.03031104989349842,
-0.07646447420120239,
0.011182294227182865,
0.028885794803500175,
0.0043752253986895084,
-0.006177226547151804,
-0.005078469403088093,
-0.05084610730409622,
-0.04475788027048111,
0.032762207090854645,
-0.02640286087989807,
0.023450477048754692,
-0.001045598997734487,
-0.023603321984410286,
-0.0201897993683815,
0.0014967861352488399,
0.01962600089609623,
0.056623440235853195,
0.009990458376705647,
0.014612392522394657,
-0.0403590202331543,
0.035943880677223206,
-0.0031510756816715,
0.05165954306721687,
-0.028339769691228867,
0.08653203397989273,
0.007695200387388468,
0.010483152233064175,
-0.00445588119328022,
0.012904235161840916,
-0.04441351443529129,
-0.05614299699664116,
-0.008550244383513927,
0.013322253711521626,
-0.01732097938656807,
0.044339366257190704,
-0.022775007411837578,
-0.06049271300435066,
0.0025236380752176046,
0.03348924219608307,
0.02547474205493927,
-0.019164297729730606,
-0.03906309977173805,
0.020438997074961662,
0.03114825114607811,
-0.0032101699616760015,
0.04079168662428856,
0.029640939086675644,
-0.04560885205864906,
-0.03236554563045502,
-0.03378453105688095,
0.01952226087450981,
-0.03526405245065689,
-0.022944364696741104,
-0.016722848638892174,
0.008673127740621567,
-0.03989497572183609,
0.09408711642026901,
-0.025324618443846703,
0.00033026107121258974,
-0.01181675586849451,
-0.016201265156269073,
-0.031782761216163635,
0.03669862449169159,
0.042419686913490295,
-0.02995198220014572,
-0.020967673510313034,
0.018726767972111702,
0.036402370780706406,
-0.030538326129317284,
-0.01937699504196644,
-0.020253237336874008,
0.03117581270635128,
0.07636716216802597,
0.021568549796938896,
0.003283001249656081,
-0.05605177953839302,
-0.020711779594421387,
0.05497484654188156,
-0.029961230233311653,
0.012782774865627289,
0.009237609803676605,
-0.024352578446269035,
0.04015381261706352,
-0.057482700794935226,
0.005983108654618263,
-0.02831992134451866,
-0.002434150315821171,
0.03011339344084263,
-0.04939523711800575,
0.055202666670084,
0.04773841053247452,
0.01001181360334158,
-0.09749560803174973,
-0.06555260717868805,
0.015924550592899323,
-0.016229353845119476,
-0.022447150200605392,
-0.011346704326570034,
0.044185321778059006,
-0.03695526719093323,
-0.0037127051036804914,
-0.018997441977262497,
0.04944344237446785,
-0.02102985978126526,
-0.016908492892980576,
-0.0005540347192436457,
0.033200062811374664,
0.046096816658973694,
0.01960902288556099,
-0.0448974184691906,
0.009631752967834473,
-0.021852636709809303,
0.033160846680402756,
0.004722265992313623,
0.04978561773896217,
-0.01986381597816944,
-0.016239752992987633,
-0.027556579560041428,
-0.038653064519166946,
0.021864930167794228,
-0.010341412387788296,
0.0055615827441215515,
0.039579395204782486,
0.014623126946389675,
-0.024052251130342484,
-0.02075854316353798,
-0.008219893090426922,
-0.023390447720885277,
0.02827868051826954,
0.005688355769962072,
-0.019548116251826286,
0.0016072673024609685,
-0.028378387913107872,
0.03736460208892822,
-0.004873799160122871,
-0.033097632229328156,
-0.0038297113496810198,
0.04325256869196892,
-0.034291185438632965,
-0.0012358380481600761,
-0.011278611607849598,
-0.008701590821146965,
0.021037176251411438,
-0.018195414915680885,
-0.017216676846146584,
0.012007949873805046,
0.0356871671974659,
-0.029414819553494453,
-0.025440754368901253,
-0.018336057662963867,
0.03529118373990059,
0.04935282841324806,
-0.020131073892116547,
0.04441295191645622,
0.009469341486692429,
0.007574873976409435,
0.003429761854931712,
-0.02401912957429886,
0.013410720974206924,
0.010436377488076687,
-0.0047830855473876,
0.024054933339357376,
-0.013608815148472786,
0.007372832391411066,
0.014163530431687832,
0.03448181226849556,
0.007753691170364618,
0.01476428285241127,
0.01616583950817585,
0.02166249230504036,
-0.015776878222823143,
0.01581314578652382,
-0.041860152035951614,
0.03717077150940895,
-0.05167991667985916,
0.02322421595454216,
0.03110937401652336,
-0.01153484731912613,
0.03491898253560066,
-0.005294152535498142,
0.0023858933709561825,
-0.0303973201662302,
0.025524109601974487,
-0.005498567130416632,
0.021942878141999245,
0.019123738631606102,
0.03343922272324562,
0.023530321195721626,
0.010022394359111786,
0.023535531014204025,
0.019023332744836807,
0.014756714925169945,
0.011659457348287106,
-0.09450765699148178,
-0.03286230191588402,
-0.03812035918235779,
-0.04648881405591965,
0.023505238816142082,
0.041667383164167404,
-0.039459940046072006,
-0.005271908827126026,
-0.029590658843517303,
0.01768607273697853,
0.008422681130468845,
0.01933804340660572,
-0.024590227752923965,
0.04044504091143608,
0.00844951905310154,
0.020123247057199478,
0.005213434807956219,
0.021389689296483994,
0.11235988140106201,
0.05371646583080292,
0.007581207435578108,
-0.0750635638833046,
0.004329127259552479,
0.0018703792011365294,
-0.007018831092864275,
-0.023136381059885025,
0.019073106348514557,
0.021625980734825134,
0.03262336924672127,
0.00191751797683537,
0.05484462156891823,
0.0002259542525280267,
0.03750859573483467,
0.04123606160283089,
-0.052308157086372375,
-0.07991760969161987,
0.03350159153342247,
-0.006959420628845692,
-0.0013024151558056474,
0.00800983514636755,
-0.01433503907173872,
0.05626826733350754,
-0.004133814480155706,
-0.01449523027986288,
-0.04679087921977043,
-0.03052043356001377,
0.06158054620027542,
-0.013965463265776634,
-0.03603295609354973,
-0.031039582565426826,
0.02317342534661293,
-0.013075446709990501,
-0.04278424754738808,
0.024218019098043442,
0.0008444339619018137,
-0.01821993850171566,
0.031090615317225456,
-0.003007864346727729,
-0.008160955272614956,
-0.03971440717577934,
0.007970291189849377,
-0.004839588422328234,
-0.02878032997250557,
0.011343609541654587,
-0.00783416349440813,
0.021371377632021904,
0.005802531726658344,
0.03286762535572052,
0.00045824225526303053,
0.005634595640003681,
-0.012482643127441406,
-0.02334042452275753,
-0.0232456736266613,
0.0026110108010470867,
0.03493364527821541,
-0.0281066931784153,
-0.007359177339822054,
-0.039620593190193176,
-0.0258383397012949,
0.014131707139313221,
0.02840961329638958,
0.0014440317172557116,
-0.013661563396453857,
0.028719309717416763,
-0.00032436908804811537,
0.0032822301145642996,
-0.010571642778813839,
-0.006563894916325808,
-0.04542836174368858,
0.0059349313378334045,
-0.020443012937903404,
-0.025179531425237656,
0.020313257351517677,
0.02032056264579296,
0.019930534064769745,
0.02851797454059124,
-0.025957193225622177,
0.003006927901878953,
-0.0766533687710762,
0.058741725981235504,
0.0026393781881779432,
-0.01723022758960724,
-0.026229314506053925,
0.05234381929039955,
0.043961506336927414,
0.043159596621990204,
0.0014986739261075854,
0.025958752259612083,
-0.03273146227002144,
0.013686694204807281,
-0.0006655710167251527,
-0.02320999652147293,
-0.02521110512316227,
0.00880634505301714,
0.0009533597622066736,
0.028167717158794403,
-0.004159433301538229,
0.0005697681335732341,
0.034758880734443665,
0.0194032434374094,
-0.00019722920842468739,
0.0634806752204895,
-0.029817966744303703,
-0.00905568990856409,
0.021042022854089737,
-0.0333423875272274,
0.00993791501969099,
0.026788605377078056,
0.031609877943992615,
-0.033868495374917984,
-0.0407559834420681,
-0.020014945417642593,
0.005221489816904068,
0.02733798138797283,
-0.01428233366459608,
-0.009546764194965363,
-0.01567056030035019,
-0.00897188764065504,
0.03911397233605385,
-0.07663864642381668,
-0.048510368913412094,
-0.03468037396669388,
0.016959767788648605,
-0.01302172802388668,
-0.02584715560078621,
-0.011728528887033463,
0.00020112624042667449,
-0.013765585608780384,
-0.0042511411011219025,
-0.0015469322679564357,
0.04020366072654724,
-0.01473361998796463,
0.03238112851977348,
0.027827925980091095,
-0.013650769367814064,
0.03515356406569481,
-0.01350758783519268,
-0.05569169297814369,
0.014160600490868092,
-0.030417976900935173,
-0.04600878432393074,
0.032977160066366196,
0.013851369731128216,
0.013006228022277355,
0.034536212682724,
0.004268590826541185,
-0.006442385725677013,
0.02594953589141369,
-0.037885937839746475,
-0.0057674674317240715,
-0.010542770847678185,
-0.03366585075855255,
-0.022511189803481102,
0.0015842417487874627,
-0.006352683529257774,
-0.005981594789773226,
-0.028706256300210953,
0.025188561528921127,
0.04827095940709114,
0.02412603236734867,
-0.016084780916571617,
0.024792291224002838,
-0.004182434640824795,
0.046984005719423294,
-0.005643452517688274,
-0.005251064896583557,
0.049594614654779434,
0.056435372680425644,
-0.021105708554387093,
0.02093329466879368,
-0.011814625933766365,
0.0021600923500955105,
-0.09733553975820541,
-0.01679517887532711,
0.01743055135011673,
0.014047044329345226,
0.04687387868762016,
-0.022302892059087753,
0.02761826664209366,
0.00747712841257453,
-0.04888669028878212,
0.021517666056752205,
-0.025060126557946205,
-0.018647216260433197,
-0.005687696859240532,
0.000491009617689997,
-0.03916202858090401,
0.07276077568531036,
0.0509149543941021,
0.014980512671172619,
-0.0030814867932349443,
-0.000988393323495984,
-0.007340479642152786,
0.03964472934603691,
-0.0206952765583992,
0.03450945392251015,
-0.004607853479683399,
-0.008456001058220863,
0.06866041570901871,
0.019757011905312538,
-0.04874156787991524,
0.003676170948892832,
-0.027163339778780937,
-0.028180940076708794,
0.021700682118535042,
0.024720562621951103,
-0.018213795498013496,
0.039868712425231934,
0.04667305573821068,
-0.018664436414837837,
-0.03746936470270157,
0.02439102716743946,
0.00901282113045454,
0.033426351845264435,
0.019550316035747528,
-0.007099073845893145,
-0.0022773705422878265,
-0.045721281319856644,
-0.03342393785715103,
0.023052314296364784,
-0.017023416236042976,
-0.032698921859264374,
-0.012689000926911831,
-0.021703580394387245,
-0.001403172966092825,
-0.0007514262688346207,
-0.008738979697227478,
-0.02415940910577774,
-0.004048400558531284,
-0.0070289368741214275,
0.020200340077280998,
0.010250653140246868,
0.0472748763859272,
-0.013357839547097683,
-0.06595931947231293,
0.025854961946606636,
0.02705749310553074,
-0.007480151019990444,
-0.045002780854701996,
0.01757512427866459,
-0.001932094688527286,
-0.0006305269198492169,
0.0013992232270538807,
-0.002991312649101019,
-0.0007259715348482132,
0.03773462772369385,
0.0014733144780620933,
0.0000499267152918037,
0.020287219434976578,
-0.04863835498690605,
-0.04804477468132973,
-0.06344010680913925,
0.08220457285642624,
-0.00965111143887043,
-0.035526636987924576,
-0.047599781304597855,
0.00815783254802227,
-0.04448628053069115,
0.01984887383878231,
0.042678967118263245,
-0.01924293301999569,
0.005291003733873367,
0.04072782024741173,
-0.008032592013478279,
0.007614792324602604,
-0.01065953727811575,
-0.04304289072751999,
-0.006322313565760851,
-0.010093431919813156,
-0.022787777706980705,
0.016201714053750038,
-0.046931810677051544,
0.026034658774733543,
0.027830131351947784,
-0.012734485790133476,
0.025452202185988426,
0.005438871681690216,
-0.021791011095046997,
0.01894315332174301,
0.042478714138269424,
-0.0355745293200016,
0.07382446527481079,
-0.032240867614746094,
0.03020995296537876,
0.0049461317248642445,
-0.01937117613852024,
-0.049413807690143585,
0.021542442962527275,
-0.05058920383453369,
0.007940389215946198,
0.01109785120934248,
-0.019444093108177185,
0.05090940743684769,
-0.0453408844769001,
-0.036643136292696,
0.03740055486559868,
-0.03967457637190819,
-0.0028863311745226383,
0.042011573910713196,
0.01172429695725441,
-0.027237648144364357,
-0.004004748072475195,
0.018332164734601974,
0.007621887605637312,
0.004804999101907015,
-0.014286467805504799,
0.043929677456617355,
-0.012824097648262978,
0.014076664112508297,
0.002200074726715684,
-0.009740964509546757,
-0.007191396784037352,
0.020903902128338814,
0.010751678608357906,
0.030431920662522316,
-0.01883252151310444,
-0.00712191266939044,
0.035302091389894485,
-0.035474009811878204,
0.0035920708905905485,
0.02673177421092987,
-0.02783767320215702,
0.06328212469816208,
-0.023610113188624382,
0.03882366791367531,
-0.018142031505703926,
-0.02129048854112625,
-0.02826911024749279,
-0.019563840702176094,
0.01931741274893284,
0.029196245595812798,
-0.009451988153159618,
0.020545639097690582,
0.013748339377343655,
0.00498233875259757,
0.06485433131456375,
-0.06265860050916672,
0.01649891398847103,
-0.019755277782678604,
-0.0224550049751997,
-0.014922430738806725,
-0.023930946364998817,
-0.06618466228246689,
0.011823289096355438,
0.016740862280130386,
-0.002279294654726982,
0.0030991381499916315,
0.00006154232687549666,
-0.04639647901058197,
-0.03962392359972,
0.06375382095575333,
-0.054772596806287766,
0.009904728271067142,
-0.004810764454305172,
-0.008936352096498013,
-0.012015610933303833,
-0.004641065839678049
] |
<p>I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really illuminating in some aspects, I still feel that regardless of how hard I try there is something with relativity that prevents me form doing anything but the simplest questions. I was trying to pinpoint my problem and I think that a big part of it is velocity addition. </p>
<p>I understand that the Galilean transformation would predict the $$V_{A}=V_{B}-V_{rel}$$ provided that A and B are two frames of reference. I also understand that we need to use the Lorentz transformation to get the velocity transformation in relativity;
$$
\begin{pmatrix}
c \Delta T_A \\
\Delta x_A\\
\end{pmatrix} \begin{pmatrix}
\gamma & \gamma \beta \\
\gamma \beta & \gamma\\
\end{pmatrix} = \begin{pmatrix}
c \Delta T_B \\
\Delta x_B\\
\end{pmatrix}
$$</p>
<p>Transforming the velocity u measured in frame to frame B; </p>
<p>$$u = \dfrac{\Delta x_A}{\Delta t_A} = \dfrac{v_B + u_{rel}}{1+\dfrac{v_B u_{rel}}{c^2}}$$</p>
<p>But as far as I understand we could equally reverse the frames A and B and simply transform the other way around which means we need the inverse of the transformation matrix; \begin{pmatrix}
\gamma & - \gamma \beta \\
- \gamma \beta & \gamma\\
\end{pmatrix}</p>
<p>This will yield the formula; </p>
<p>$$u = \dfrac{\Delta x_B}{\Delta t_B} = \dfrac{v_A - u_{rel}}{1-\dfrac{v_A u_{rel}}{c^2}}$$. </p>
<p>However since the naming of frames is arbitrary, how do I know which of the two formula to use, the one with the all plus and the all minus signs. I have tried to look on the internet for the explanation of this, but I could not find anything. Also provided that I know which equation to use how, do I use it what is the sign convention for the velocities? </p>
<p>Thank you very much for all the help and sorry for the long post </p>
<p>P.S. I would be also very grateful if someone could point me to some good and simple resources on relativistic dynamics especially collisions. Thanks again. </p>
| 9,422 |
[
0.009996166452765465,
0.002114747418090701,
0.000057325240049976856,
0.006774991285055876,
0.06368137896060944,
0.014178131707012653,
-0.03173407167196274,
-0.008451172150671482,
0.020763661712408066,
-0.004906048998236656,
0.019410444423556328,
0.0114166010171175,
0.06999077647924423,
0.0073340279050171375,
0.024422399699687958,
0.00667260168120265,
-0.004024434369057417,
-0.021549109369516373,
-0.03895050287246704,
-0.04304640740156174,
0.038429271429777145,
0.009725362993776798,
0.03603982552886009,
-0.005211297422647476,
-0.016313601285219193,
0.05563672259449959,
0.010225792415440083,
-0.007401835173368454,
-0.04127722233533859,
0.05726126208901405,
-0.011986156925559044,
-0.02825692854821682,
0.03225284814834595,
-0.010976412333548069,
0.005873194895684719,
0.03217855840921402,
-0.04359780251979828,
-0.018215855583548546,
0.002777624875307083,
0.019639156758785248,
-0.040218040347099304,
0.004063735716044903,
-0.045238662511110306,
0.06240014731884003,
-0.008009197190403938,
0.016205180436372757,
0.0032935047056525946,
0.015570545569062233,
0.03892708569765091,
-0.005311102140694857,
0.09110290557146072,
0.015433693304657936,
0.03908075764775276,
-0.004108952824026346,
-0.01878906413912773,
-0.02148604951798916,
0.09090327471494675,
0.07081054151058197,
0.018737565726041794,
-0.04519288241863251,
0.03551076725125313,
-0.009697502478957176,
-0.027969693765044212,
-0.024031465873122215,
0.0023625001776963472,
0.041912708431482315,
-0.01925393007695675,
0.03840836137533188,
0.006309452001005411,
-0.040661487728357315,
0.03881895914673805,
-0.031031502410769463,
0.024219976738095284,
-0.007210982497781515,
0.023661496117711067,
-0.05156022310256958,
-0.009707902558147907,
0.03591032698750496,
0.023973839357495308,
0.05147109180688858,
-0.0054337759502232075,
0.019949018955230713,
0.033351410180330276,
0.005076984409242868,
-0.027212196961045265,
-0.02821454219520092,
0.025667205452919006,
0.006702519487589598,
-0.004249969031661749,
0.05235147476196289,
-0.02438666857779026,
0.025407955050468445,
-0.01588057167828083,
0.002175785368308425,
-0.013262269087135792,
0.05439145863056183,
-0.006796291097998619,
0.03653077781200409,
0.003205470507964492,
-0.04168574512004852,
-0.024157118052244186,
-0.011930787935853004,
0.005659318063408136,
0.11073679476976395,
-0.00567253353074193,
-0.02306387946009636,
-0.016802573576569557,
0.01974712871015072,
-0.014731735922396183,
-0.0549335703253746,
-0.042909033596515656,
0.017484936863183975,
-0.03759024664759636,
0.01621227338910103,
0.01580505259335041,
-0.03039138950407505,
-0.0052318572998046875,
-0.019900409504771233,
0.07036712020635605,
0.02272723615169525,
0.05020482838153839,
-0.024823756888508797,
0.024743512272834778,
0.016936063766479492,
-0.04982210323214531,
0.005815255455672741,
0.018831977620720863,
0.004388971719890833,
0.01348746195435524,
-0.017417464405298233,
0.007990757934749126,
-0.036673687398433685,
0.03754447028040886,
0.01674613356590271,
0.022941939532756805,
-0.002420796314254403,
-0.12260837852954865,
-0.07861393690109253,
0.07633528858423233,
0.016618818044662476,
0.0031358343549072742,
-0.08875129371881485,
0.022805074229836464,
0.033351682126522064,
0.09911391884088516,
0.0165726225823164,
0.024850979447364807,
0.030318202450871468,
0.024935411289334297,
0.010990838520228863,
-0.008004405535757542,
0.0201224684715271,
-0.02303430810570717,
-0.03220198675990105,
0.0062645599246025085,
-0.0480489581823349,
0.009388783946633339,
0.016951410099864006,
-0.023340683430433273,
0.03694016858935356,
0.06498967856168747,
0.016569657251238823,
-0.0006546993972733617,
0.03163819760084152,
-0.0018718696665018797,
-0.022533806040883064,
0.06035977974534035,
-0.005874279886484146,
-0.0244285948574543,
0.047875817865133286,
-0.024850523099303246,
0.001793024130165577,
-0.02663932740688324,
0.014692074619233608,
0.05832239240407944,
-0.0021979412995278835,
-0.04140940308570862,
0.02064485102891922,
-0.02200363203883171,
-0.021795568987727165,
-0.03389321267604828,
-0.0536019392311573,
-0.021417858079075813,
-0.009778863750398159,
0.04002630338072777,
0.06025950610637665,
0.036610525101423264,
0.03475923091173172,
-0.010102028958499432,
-0.010199612006545067,
-0.0027657297905534506,
-0.05562206730246544,
-0.004551413469016552,
0.007325747516006231,
0.007240877486765385,
0.04613368585705757,
-0.025232534855604172,
0.006385330576449633,
-0.012456333264708519,
-0.02861512452363968,
0.008317426778376102,
0.04460329934954643,
0.01435902900993824,
-0.013950757682323456,
0.03549065440893173,
0.021306633949279785,
0.08917536586523056,
-0.004658122081309557,
-0.009266373701393604,
-0.00363988452591002,
0.029448144137859344,
-0.015706652775406837,
-0.0076094078831374645,
0.033425223082304,
-0.016184654086828232,
0.011130218394100666,
0.01390718761831522,
-0.011710812337696552,
-0.012784374877810478,
0.01376340165734291,
-0.026760976761579514,
0.0734003409743309,
0.031916096806526184,
-0.0025143760722130537,
-0.005957915913313627,
0.08318585902452469,
0.03323381766676903,
0.04955841228365898,
0.0016677340026944876,
-0.024442950263619423,
-0.01234984491020441,
0.004676412791013718,
0.021716035902500153,
0.02843284048140049,
-0.048280682414770126,
-0.0026681567542254925,
0.015907831490039825,
0.023131845518946648,
-0.006480147130787373,
0.031644854694604874,
0.012137096375226974,
-0.07953973114490509,
0.01536845974624157,
-0.027278386056423187,
0.02167878858745098,
0.011853761039674282,
0.01573253981769085,
-0.006030450575053692,
0.017710013315081596,
-0.03206352889537811,
-0.0137183154001832,
0.019418710842728615,
0.0016386661445721984,
0.001350560924038291,
0.020906854420900345,
0.004152344539761543,
0.0672684907913208,
0.022768659517169,
0.0659305527806282,
0.03776191174983978,
-0.015945255756378174,
-0.010809006169438362,
-0.00779413478448987,
0.015325760468840599,
0.023166216909885406,
-0.007270053494721651,
0.0115400655195117,
-0.0012466972693800926,
0.015509444288909435,
-0.056276459246873856,
0.015828538686037064,
-0.01770666614174843,
-0.043378282338380814,
-0.010538064874708652,
-0.04042082279920578,
-0.016064424067735672,
0.04200753942131996,
0.028405699878931046,
-0.02833137847483158,
0.005998449400067329,
-0.0012249939609318972,
0.008360081352293491,
-0.003167550079524517,
0.013517067767679691,
-0.044156838208436966,
0.05368620529770851,
-0.03849022462964058,
0.010932913050055504,
0.012818578630685806,
0.009858889505267143,
0.011726714670658112,
-0.003173297271132469,
-0.02837604098021984,
-0.10122024267911911,
-0.062036290764808655,
-0.006726553663611412,
-0.02376156859099865,
-0.039471033960580826,
0.017132047563791275,
0.04287610575556755,
0.0024273660965263844,
-0.07185124605894089,
-0.020480526611208916,
-0.03744596987962723,
-0.06053544580936432,
-0.026910945773124695,
0.013570151291787624,
0.015561745502054691,
-0.029556935653090477,
0.044631730765104294,
0.0015946788480505347,
-0.01795792207121849,
0.018269803375005722,
-0.029718894511461258,
0.008417734876275063,
0.023614296689629555,
0.04641888290643692,
0.04464733228087425,
0.04598642885684967,
-0.024203425273299217,
0.07051591575145721,
0.0066393050365149975,
-0.004189750179648399,
-0.022637411952018738,
0.03336483612656593,
0.015460259281098843,
-0.04818199574947357,
0.02565704844892025,
0.04280973970890045,
-0.014069982804358006,
0.0284795630723238,
-0.015281288884580135,
0.03207212686538696,
0.042038071900606155,
0.03629417344927788,
0.003283617552369833,
0.005887344945222139,
0.007582949940115213,
0.023087982088327408,
0.03678189590573311,
0.01506380457431078,
0.004379855003207922,
0.023486539721488953,
0.007306703832000494,
0.03992711380124092,
0.012709965929389,
-0.05060190334916115,
0.029851628467440605,
0.013825005851686,
-0.021478649228811264,
-0.004662264604121447,
0.010216706432402134,
0.006836045067757368,
-0.018610574305057526,
0.012543370015919209,
0.01313632633537054,
0.02045983076095581,
-0.007297779433429241,
0.027830049395561218,
0.04547974839806557,
0.03382522612810135,
0.009277313947677612,
-0.038076285272836685,
0.01300404779613018,
-0.007158348802477121,
0.038580767810344696,
-0.03874671831727028,
0.017983298748731613,
0.057928670197725296,
0.05405186489224434,
-0.016551848500967026,
0.013409064151346684,
-0.05466654524207115,
-0.008909204043447971,
-0.030245156958699226,
-0.007489501498639584,
-0.03216727823019028,
0.054260823875665665,
0.00029573735082522035,
0.035641759634017944,
0.013141557574272156,
0.006267194170504808,
0.004397138487547636,
-0.012842118740081787,
-0.0640423372387886,
0.04324132949113846,
-0.03377661854028702,
-0.006764022633433342,
-0.02691909484565258,
0.009444842115044594,
0.04024357348680496,
-0.036647263914346695,
-0.02735769748687744,
-0.027885906398296356,
-0.0192643441259861,
-0.08279236406087875,
0.02795211598277092,
-0.02746289223432541,
-0.039615046232938766,
-0.02977336384356022,
0.006401782389730215,
0.05487825721502304,
-0.03784087672829628,
-0.010640932247042656,
0.04163026437163353,
-0.028729800134897232,
-0.0020213276147842407,
-0.03403298929333687,
-0.0005223109619691968,
0.0369192436337471,
-0.00265855947509408,
0.0016267625615000725,
0.021893098950386047,
-0.036963336169719696,
0.0103653809055686,
0.0344688817858696,
-0.0019318151753395796,
-0.008675901219248772,
-0.01728406921029091,
-0.08145585656166077,
-0.02808607742190361,
-0.002638832665979862,
-0.008292151615023613,
0.08221515268087387,
-0.000965454033575952,
0.028242236003279686,
0.03708161786198616,
0.01991632953286171,
0.007493502460420132,
0.019712945446372032,
0.028162052854895592,
-0.01871870830655098,
-0.0014323110226541758,
-0.021587569266557693,
-0.031852301210165024,
-0.01787356100976467,
-0.04494253918528557,
0.03653058409690857,
-0.00905389990657568,
-0.045541368424892426,
-0.028749193996191025,
0.04695301130414009,
0.026623550802469254,
-0.014398309402167797,
0.014936022460460663,
-0.008160379715263844,
-0.010227498598396778,
0.039282187819480896,
-0.04198990389704704,
-0.016836173832416534,
0.006467202678322792,
0.05589434877038002,
-0.002680028323084116,
0.03105931356549263,
-0.06419122219085693,
-0.03439779207110405,
0.01746046356856823,
0.03144887089729309,
-0.014848124235868454,
-0.019183695316314697,
-0.03380202874541283,
-0.048487477004528046,
0.039513442665338516,
-0.04001406580209732,
0.046783868223428726,
0.009834892116487026,
0.0016536228358745575,
-0.04634179547429085,
-0.055742114782333374,
-0.03961372748017311,
0.01859094202518463,
-0.045465581119060516,
-0.015023773536086082,
-0.015569762326776981,
0.005164872854948044,
-0.007375007960945368,
-0.005940904375165701,
0.01069412287324667,
0.04473871737718582,
-0.008158169686794281,
-0.023714765906333923,
0.008384753949940205,
0.0528893768787384,
-0.05367451533675194,
-0.10536619275808334,
0.012852702289819717,
0.014850493520498276,
-0.011872795410454273,
0.015029008500277996,
-0.027327846735715866,
-0.040015388280153275,
0.054612696170806885,
0.00832920242100954,
0.01626919023692608,
0.01965348981320858,
-0.05291521176695824,
0.02866496331989765,
0.016878554597496986,
-0.007357688155025244,
0.04438844695687294,
0.01638307422399521,
-0.04316626861691475,
-0.012943587265908718,
-0.010698119178414345,
-0.014124867506325245,
-0.03935550898313522,
0.008067145943641663,
-0.014597846195101738,
-0.002109541092067957,
-0.005715770181268454,
0.04935126751661301,
-0.03013782948255539,
0.01977553963661194,
0.011072899214923382,
-0.03549030423164368,
-0.010155265219509602,
0.019619157537817955,
-0.03043641522526741,
0.029741523787379265,
-0.018700353801250458,
-0.025664441287517548,
0.013247149996459484,
-0.044047947973012924,
0.017845313996076584,
0.017134062945842743,
-0.019059965386986732,
0.04303043708205223,
-0.040937311947345734,
-0.006808873265981674,
0.019697781652212143,
-0.02762746624648571,
-0.0009469952783547342,
-0.03250972554087639,
0.03909233212471008,
-0.0064927274361252785,
-0.013962038792669773,
0.024127058684825897,
0.013308200053870678,
-0.047003649175167084,
0.022397832944989204,
-0.036892857402563095,
-0.005357349291443825,
-0.056565023958683014,
-0.017092067748308182,
0.023460891097784042,
0.023307107388973236,
-0.0454108789563179,
-0.04259687662124634,
0.016004491597414017,
-0.0217394158244133,
-0.03098548762500286,
-0.04990633949637413,
0.007767217233777046,
-0.017648879438638687,
-0.024407412856817245,
0.005248477216809988,
0.06674864888191223,
-0.024761777371168137,
-0.012529062107205391,
-0.0007315501570701599,
0.02557140775024891,
0.027734361588954926,
-0.0452968068420887,
0.0009784457506611943,
0.003773690899834037,
-0.012518237344920635,
0.00579708581790328,
0.00856050569564104,
0.04405946284532547,
-0.011372897773981094,
-0.032783184200525284,
-0.024799587205052376,
0.010318538174033165,
0.00142396439332515,
-0.019002355635166168,
-0.013125577010214329,
0.03896554931998253,
0.01229562982916832,
-0.007286762818694115,
-0.038292501121759415,
-0.014107413589954376,
0.033028047531843185,
0.029623791575431824,
0.012936529703438282,
0.0021981385070830584,
-0.029542487114667892,
-0.023607594892382622,
0.027881965041160583,
-0.018280087038874626,
-0.02152334712445736,
-0.02313964068889618,
0.03477112576365471,
-0.019994789734482765,
0.018407242372632027,
0.021046463400125504,
-0.0061376821249723434,
0.025916632264852524,
-0.009224574081599712,
0.019683001562952995,
0.03315352648496628,
-0.02738858200609684,
-0.05374469608068466,
-0.015307559631764889,
-0.02994862198829651,
0.007579415570944548,
0.07681140303611755,
0.0049290889874100685,
0.01708034612238407,
0.00970922689884901,
0.008183781988918781,
-0.009359064511954784,
-0.009563816711306572,
-0.020265420898795128,
0.00577143020927906,
0.005011385772377253,
0.03577904403209686,
-0.02711813896894455,
-0.06295288354158401,
0.013809621334075928,
0.020750664174556732,
-0.029429465532302856,
-0.008824882097542286,
0.03234001621603966,
0.02091008424758911,
-0.02332661859691143,
0.00986364297568798,
-0.03472979739308357,
0.02848995476961136,
-0.010068877600133419,
0.005648686550557613,
-0.000860988104250282,
0.00771601777523756,
0.06375458836555481,
0.03448125347495079,
0.028972584754228592,
-0.03758307918906212,
-0.02622206322848797,
-0.06019364297389984,
0.000055234220781130716,
0.021425869315862656,
0.029279492795467377,
0.012952475808560848,
-0.025982161983847618,
0.0513845719397068,
-0.016027601435780525,
0.042821772396564484,
-0.03597164526581764,
-0.04749836027622223,
-0.014833421446383,
-0.05169880762696266,
-0.030531948432326317,
0.07368006557226181,
0.006208337843418121,
-0.012179958634078503,
-0.0062357718124985695,
-0.015264520421624184,
0.032653313130140305,
0.018915122374892235,
0.03616610914468765,
-0.024785125628113747,
0.060881923884153366,
0.00013593821495305747,
-0.018183231353759766,
-0.0020176495891064405,
0.02134641632437706,
0.11591797322034836,
0.027678055688738823,
0.009917061775922775,
-0.05391912907361984,
0.0285139512270689,
-0.0031632890459150076,
0.01989281363785267,
-0.039981409907341,
0.04496770724654198,
-0.02652791701257229,
-0.022011416032910347,
-0.005511486902832985,
0.03283976390957832,
0.0030032782815396786,
-0.037499211728572845,
0.037909943610429764,
-0.06281161308288574,
-0.014981556683778763,
0.032658230513334274,
-0.00060737767489627,
-0.020975178107619286,
0.009372514672577381,
0.002466660225763917,
0.02211984060704708,
-0.03201023116707802,
-0.01894492842257023,
-0.04842328652739525,
-0.02846866473555565,
0.007264230865985155,
-0.00939902663230896,
-0.017239056527614594,
0.04782651737332344,
0.03610699251294136,
-0.013218470849096775,
-0.02979283779859543,
0.0008074771030806005,
0.015331767499446869,
-0.007169520482420921,
0.041927073150873184,
0.009033913724124432,
-0.006856991443783045,
0.05006490275263786,
0.024803046137094498,
0.018330635502934456,
-0.04116839915513992,
0.023654570803046227,
-0.006065762601792812,
0.0770922601222992,
-0.034202560782432556,
0.011609741486608982,
0.009970076382160187,
-0.008692340925335884,
-0.00024205939553212374,
-0.08658884465694427,
0.002482274081557989,
0.01583005301654339,
0.019027579575777054,
0.027028601616621017,
-0.002853651065379381,
-0.021929964423179626,
0.05312100425362587,
0.010260825045406818,
0.02996012382209301,
-0.006531579419970512,
-0.027439335361123085,
-0.02421865612268448,
0.007562418933957815,
0.0669088363647461,
-0.02704486809670925,
-0.014742810279130936,
-0.011621075682342052,
0.007955756038427353,
-0.0016542271478101611,
-0.029448995366692543,
0.02461678721010685,
0.009231002070009708,
0.007018305826932192,
-0.015504498034715652,
0.00841264147311449,
-0.05100441351532936,
-0.08561579138040543,
0.0018203902291134,
-0.0016134838806465268,
0.010637626051902771,
-0.004388806410133839,
0.03392219915986061,
0.026181399822235107,
0.057358115911483765,
-0.03637625649571419,
-0.019639600068330765,
0.04215439036488533,
0.005195460747927427,
0.05302188917994499,
-0.00018809612083714455,
-0.013874946162104607,
-0.007438983302563429,
0.015335897915065289,
-0.002900504507124424,
-0.05147081986069679,
0.007641972508281469,
0.057317331433296204,
0.011996036395430565,
-0.024373119696974754,
0.012902877293527126,
-0.016471536830067635,
-0.019470755010843277,
0.02970803529024124,
-0.026156317442655563,
0.011862928979098797,
0.0005253494018688798,
0.03951013460755348,
-0.01470055989921093,
0.016035959124565125,
-0.00752366054803133,
0.012516320683062077,
-0.024841008707880974,
-0.002948812674731016,
-0.019814301282167435,
0.006581348367035389,
-0.030034944415092468,
0.008698691613972187,
-0.056328896433115005,
-0.008555526845157146,
0.0028929677791893482,
0.034656111150979996,
-0.01744581013917923,
-0.021189868450164795,
-0.05134948343038559,
0.05023379996418953,
-0.012496527284383774,
-0.00955086201429367,
0.0030854553915560246,
0.04432108625769615,
-0.0003800984413828701,
-0.053117334842681885,
-0.003598569892346859,
-0.012544427998363972,
-0.008454883471131325,
-0.0016417799051851034,
-0.034271374344825745,
0.044567182660102844,
-0.0017504766583442688,
-0.003049081191420555,
0.053866349160671234,
0.011927030049264431,
0.024570811539888382,
0.018967270851135254,
-0.03709538280963898,
-0.020962219685316086,
0.07664202898740768,
-0.02184051275253296,
0.017160505056381226,
-0.03166821971535683,
-0.04023757949471474,
0.010196215473115444,
-0.023898977786302567,
0.04359636828303337,
-0.004933961201459169,
0.01203061081469059,
0.027071775868535042,
0.005734419450163841,
-0.034774161875247955,
0.019749142229557037,
-0.007921639829874039,
-0.01386785227805376,
0.0006888828938826919,
0.04074651002883911,
0.0010392331751063466,
0.024749016389250755,
0.04380645975470543,
-0.014832922257483006,
0.026007913053035736,
0.036367449909448624,
0.01474755723029375,
-0.09842327982187271,
-0.02365490049123764,
0.02914714254438877,
-0.003279097145423293,
0.05419991537928581,
-0.051223549991846085,
0.021024849265813828,
0.047462865710258484,
-0.044458676129579544,
-0.005374599248170853,
-0.04952041432261467,
-0.026718933135271072,
0.001106570940464735,
-0.0285029374063015,
-0.037841904908418655,
0.04211917147040367,
0.018805736675858498,
0.021051103249192238,
0.013766670599579811,
0.018735192716121674,
-0.022552436217665672,
-0.06864126026630402,
-0.024746635928750038,
0.015725601464509964,
-0.006488284096121788,
0.0011001438833773136,
0.04556485265493393,
-0.03259273245930672,
-0.024184949696063995,
0.04634733498096466,
0.006946653127670288,
0.03085377626121044,
-0.01686408556997776,
0.03888487070798874,
0.004801255185157061,
0.029914595186710358,
0.050730038434267044,
0.00006459494034061208,
-0.00921919010579586,
-0.009387172758579254,
0.04951584339141846,
0.026205915957689285,
-0.030437560752034187,
-0.033763542771339417,
-0.006825947668403387,
-0.027558734640479088,
-0.019117344170808792,
-0.01035595964640379,
-0.028265608474612236,
-0.01114972960203886,
-0.01331852376461029,
0.018413767218589783,
-0.003254680195823312,
-0.0332682728767395,
-0.0023200209252536297,
-0.06720877438783646,
-0.006661158986389637,
0.04391360282897949,
-0.003522878047078848,
0.026848990470170975,
-0.01170446164906025,
-0.0092573007568717,
-0.023765798658132553,
0.0240160059183836,
-0.019555946812033653,
-0.015378167852759361,
-0.03471831977367401,
-0.03281806781888008,
0.03645014017820358,
-0.020807508379220963,
-0.007585049606859684,
-0.02886645495891571,
-0.02712302841246128,
0.026012951508164406,
0.019810205325484276,
0.008687814697623253,
-0.04528534784913063,
0.0014454140327870846,
0.01478063128888607,
-0.05747056379914284,
0.021037617698311806,
-0.002424785168841481,
-0.04576801508665085,
-0.014372174628078938,
0.0027323788963258266,
-0.006104884669184685,
0.0059006353840231895,
0.07139434665441513,
-0.02480725198984146,
0.014354961924254894,
0.04160456359386444,
-0.009984740056097507,
0.009393220767378807,
-0.026626965031027794,
-0.02018083445727825,
-0.03049498051404953,
-0.046690165996551514,
0.00235962076112628,
-0.007171337492763996,
-0.01122776884585619,
0.027738675475120544,
-0.007775977719575167,
-0.04168563708662987,
0.018357854336500168,
0.0264741163700819,
-0.04242581129074097,
0.02302440255880356,
-0.00574646657332778,
-0.030645621940493584,
0.03394969552755356,
0.030284136533737183,
0.01980668120086193,
0.022505464032292366,
-0.05640322342514992,
-0.036052267998456955,
-0.010991367511451244,
-0.013921963982284069,
-0.02090861089527607,
-0.02043001912534237,
-0.03297187387943268,
0.013403176330029964,
-0.06470084190368652,
0.0052051180973649025,
0.060869235545396805,
-0.04588353633880615,
0.02653641626238823,
0.04313104599714279,
-0.02048804610967636,
0.0268565583974123,
0.0012397468090057373,
0.013966509141027927,
0.024555005133152008,
-0.009531080722808838,
0.008665689267218113,
0.003727404633536935,
0.01402701623737812,
0.022390935570001602,
-0.033600058406591415,
0.06932331621646881,
-0.012143708765506744,
0.011022175662219524,
-0.01947348192334175,
0.003541072830557823,
-0.004693802446126938,
0.02047809399664402,
0.0009287074790336192,
-0.029809990897774696,
0.006410279776901007,
0.020775089040398598,
-0.009183823131024837,
0.062359768897295,
-0.033942174166440964,
0.02293950691819191,
-0.004034565761685371,
0.01261876616626978,
-0.0068342010490596294,
0.020526912063360214,
0.022400449961423874,
0.028514502570033073,
-0.01758347451686859,
-0.007006633095443249,
-0.03198232501745224,
-0.030207520350813866,
-0.006464092526584864,
-0.026178626343607903,
-0.01436202134937048,
0.005692664068192244,
-0.0030851196497678757,
0.018306508660316467,
-0.00596790062263608,
-0.024284306913614273,
-0.05451154708862305,
0.026644596830010414,
0.009746089577674866,
0.00740312272682786,
-0.022511715069413185,
-0.03269941359758377,
0.014684372581541538,
0.04169254004955292,
-0.016943233087658882,
-0.0463220477104187,
0.0009717668872326612,
0.015312191098928452,
-0.03612077236175537,
-0.00927827786654234
] |
<p>I'm just looking to set up a free body diagram for this scenario and I'm having a bit of trouble understanding what's going on. The problem states, "A rectangular block of mass $m_1$ lies on top of a (larger) rectangular block of mass $m_2$, which lies on a horizontal plane without friction. Between the two blocks there is a viscous force with magnitude $F=kv$, where v is their relative speed, which opposes their relative motion. At time t = 0 the larger block is at rest, while the smaller block moves in the horizontal x direction with initial speed $v_0$."</p>
<p>My interpretation is that in between the blocks there is some fluid that when the smaller block moves, that fluid opposes the block's motion. Also, since the lower block is on top of a frictionless surface it will move as well and eventually reach the same velocity as the smaller block. Am I correct in that interpretation? So then the forces acting on the smaller block are $F_{net}=F-kv$. I'm not sure how to do the larger block. Any help is appreciated.</p>
| 9,423 |
[
0.003304883139207959,
-0.03471779450774193,
-0.067348413169384,
0.0286552757024765,
0.029526857659220695,
-0.01341337151825428,
0.012588227167725563,
-0.0004224309523124248,
0.01837802492082119,
-0.02075934037566185,
0.02765989676117897,
0.048252400010824203,
0.04933663830161095,
-0.020216863602399826,
0.04331161081790924,
0.023914536461234093,
-0.029886649921536446,
-0.037500739097595215,
0.03120897337794304,
-0.03619970381259918,
-0.03336087986826897,
0.00040394801180809736,
0.08185388892889023,
0.0028498144820332527,
-0.027995813637971878,
0.05065537244081497,
0.014105520211160183,
-0.04041171446442604,
0.011327560059726238,
0.02768833562731743,
-0.01084178313612938,
-0.039329659193754196,
-0.032371778041124344,
-0.0005855840281583369,
-0.018579214811325073,
0.032081764191389084,
-0.049389857798814774,
-0.018523363396525383,
0.012580262497067451,
0.03042248636484146,
-0.026095861569046974,
-0.012222588993608952,
-0.029032491147518158,
0.03723684698343277,
-0.03937234729528427,
0.001863272162154317,
0.03134216368198395,
-0.02509317547082901,
0.058852046728134155,
-0.04290269687771797,
0.07399041950702667,
0.012140873819589615,
0.10052799433469772,
0.04957057535648346,
-0.018639536574482918,
-0.0008238012087531388,
0.07372361421585083,
0.09194064140319824,
0.010417409241199493,
-0.03540583699941635,
-0.021715110167860985,
-0.03704821318387985,
-0.055815327912569046,
-0.014792212285101414,
-0.017349200323224068,
0.04382910206913948,
-0.07095064222812653,
-0.00618141982704401,
0.012736713513731956,
0.006989447399973869,
0.00882252212613821,
-0.010686134919524193,
0.05768314376473427,
-0.028108319267630577,
0.002727361163124442,
-0.014248707331717014,
0.009612685069441795,
0.022162185981869698,
0.004266624804586172,
0.015345167368650436,
-0.03673078492283821,
0.02282199263572693,
0.03408602252602577,
0.05099256709218025,
0.0018675331957638264,
-0.012621574103832245,
0.05943230912089348,
0.026047084480524063,
0.03180282562971115,
0.036593854427337646,
-0.02752683125436306,
0.010538449510931969,
0.019668586552143097,
-0.006361787673085928,
-0.0027738919015973806,
-0.015458750538527966,
0.0014906900469213724,
0.047255855053663254,
0.019538868218660355,
0.006766381207853556,
-0.00807885080575943,
-0.03232068195939064,
0.0013724458403885365,
0.058021530508995056,
-0.006119127850979567,
0.009678049944341183,
-0.056280601769685745,
0.04263334348797798,
0.013106592930853367,
-0.007349632680416107,
-0.02810102514922619,
0.015661217272281647,
-0.021065693348646164,
-0.00324175669811666,
-0.01868773251771927,
-0.03380558639764786,
0.02580126002430916,
0.008233388885855675,
0.034627288579940796,
0.013669238425791264,
0.054749127477407455,
-0.022060854360461235,
0.06653258949518204,
0.005785481072962284,
-0.07806815952062607,
0.010711311362683773,
0.006116563454270363,
-0.023177478462457657,
-0.028146810829639435,
0.05520341172814369,
0.012166005559265614,
-0.02069621905684471,
-0.011471238918602467,
-0.009601511061191559,
0.04391484335064888,
-0.023349348455667496,
-0.06392235308885574,
-0.06401258707046509,
0.05195041373372078,
-0.027193639427423477,
-0.004809644538909197,
-0.07401669025421143,
-0.03414492309093475,
0.023722799494862556,
0.09126873314380646,
-0.03610239923000336,
-0.004527613054960966,
-0.0010354935657233,
0.024063752964138985,
-0.015774965286254883,
0.0025206664577126503,
-0.030006475746631622,
0.0007952847518026829,
-0.038887254893779755,
-0.02374439686536789,
-0.05941638723015785,
0.01478435005992651,
0.02740108035504818,
-0.02974328026175499,
-0.01086164265871048,
0.03484147787094116,
-0.009655804373323917,
0.01558057963848114,
0.015476376749575138,
-0.021717101335525513,
-0.026753248646855354,
0.07456275820732117,
0.011685812845826149,
0.0043181441724300385,
0.047046441584825516,
0.059146951884031296,
0.014133408665657043,
0.001892397296614945,
0.04559386149048805,
0.0416070930659771,
0.006196098402142525,
-0.011696071363985538,
0.013089558109641075,
-0.0012325769057497382,
-0.010287170298397541,
-0.007341449614614248,
-0.045784734189510345,
-0.015013650059700012,
-0.028848841786384583,
0.014800230041146278,
0.040435850620269775,
-0.004724547732621431,
0.013193563558161259,
-0.008017085492610931,
-0.04258435219526291,
-0.02966409921646118,
-0.0879080519080162,
0.04408980533480644,
-0.020905902609229088,
0.006707470398396254,
0.012774701230227947,
-0.0008113848161883652,
0.0304200891405344,
-0.05671124905347824,
-0.05194889008998871,
0.00975845381617546,
0.04175266623497009,
0.012070437893271446,
0.0009615817107260227,
0.025511600077152252,
0.0263509638607502,
0.021156474947929382,
0.011056899093091488,
-0.011072401888668537,
-0.028546644374728203,
-0.0050348564982414246,
0.006660067476332188,
-0.013698199763894081,
0.004374746233224869,
-0.005032446701079607,
0.017593294382095337,
-0.0024184221401810646,
0.008031761273741722,
0.017058467492461205,
0.005010215099900961,
-0.04707733541727066,
0.09026583284139633,
0.06358037889003754,
0.028830453753471375,
-0.008842913433909416,
0.04264869913458824,
0.024888144806027412,
0.008723068051040173,
0.012194464914500713,
-0.040530070662498474,
-0.05150841176509857,
-0.0014008545549586415,
-0.0047239442355930805,
0.021190641447901726,
-0.013047020882368088,
0.01901182346045971,
0.030727406963706017,
0.019098365679383278,
0.025873582810163498,
-0.0050551388412714005,
0.01462398562580347,
0.003442950313910842,
0.00487765297293663,
0.03875504806637764,
-0.022359374910593033,
0.0076740216463804245,
0.030924882739782333,
0.06414139270782471,
0.02106393873691559,
-0.007417288608849049,
-0.01678740605711937,
0.03813859075307846,
0.001269963919185102,
0.03392539918422699,
0.0022349192295223475,
-0.02948467619717121,
0.02723808027803898,
-0.00443488173186779,
0.014026696793735027,
0.04418535903096199,
0.008603858761489391,
0.005721383728086948,
-0.04114145040512085,
0.00016031971608754247,
0.030031070113182068,
-0.013664597645401955,
-0.00782235898077488,
-0.00605399115011096,
0.03590882942080498,
-0.0387730598449707,
0.0355796255171299,
-0.024731772020459175,
-0.04021846130490303,
-0.01767786778509617,
0.004661929793655872,
-0.009946011006832123,
0.006453304085880518,
0.04987679049372673,
-0.012731270864605904,
-0.0065177022479474545,
-0.002837556414306164,
-0.03252314776182175,
-0.003495834767818451,
0.0005171115044504404,
-0.05594424903392792,
0.02319948747754097,
-0.06558012962341309,
-0.013185585848987103,
0.04658126458525658,
0.020551785826683044,
-0.02272314392030239,
0.03459527716040611,
-0.02962239645421505,
-0.04797884449362755,
-0.027971472591161728,
-0.03127549588680267,
-0.013067989610135555,
-0.01666676066815853,
0.04002287611365318,
0.040675364434719086,
-0.003248385386541486,
-0.016075287014245987,
0.013221239671111107,
-0.0693436935544014,
-0.02908722311258316,
-0.014435084536671638,
-0.0008139208657667041,
0.011621744371950626,
-0.005879443138837814,
0.017379790544509888,
0.03714274242520332,
-0.02759818732738495,
-0.00258451490662992,
-0.029978519305586815,
-0.06011617183685303,
0.003212815383449197,
-0.012786325998604298,
0.056318093091249466,
-0.009243519976735115,
-0.02710387110710144,
0.07331207394599915,
0.008791584521532059,
0.014601658098399639,
-0.009835903532803059,
-0.007362190168350935,
-0.011781860142946243,
-0.057106610387563705,
0.04252844303846359,
0.0030931185465306044,
-0.008071697317063808,
0.011525638401508331,
0.035936933010816574,
0.0023980257101356983,
0.046467386186122894,
-0.015777893364429474,
0.0058805872686207294,
0.019907481968402863,
0.039053741842508316,
0.006784803234040737,
0.03697659447789192,
0.009852633811533451,
-0.013716340996325016,
0.023860571905970573,
-0.02258075773715973,
0.04599772021174431,
0.0022754750680178404,
-0.05448319390416145,
0.05262035131454468,
-0.017308901995420456,
-0.00010417406156193465,
0.00022888380044605583,
0.04604335129261017,
-0.003181620268151164,
0.01011480763554573,
0.012723039835691452,
0.02362285926938057,
0.056231461465358734,
-0.019321149215102196,
-0.0037137207109481096,
0.048169687390327454,
0.008097612299025059,
-0.02268405072391033,
-0.04066469147801399,
-0.01721457950770855,
0.015575406141579151,
0.04875100776553154,
-0.007423359900712967,
0.004993831738829613,
0.01802557148039341,
-0.009685797616839409,
0.05322530120611191,
0.02331102080643177,
-0.03127342835068703,
0.005679761990904808,
-0.038958530873060226,
-0.012758307158946991,
0.037047047168016434,
0.046925581991672516,
-0.042124297469854355,
0.029565736651420593,
-0.000862768676597625,
0.01660589873790741,
0.014967632479965687,
0.02371792681515217,
-0.05486217513680458,
0.031348660588264465,
-0.041308529675006866,
-0.007103410549461842,
0.016709083691239357,
0.001024893019348383,
0.017494238913059235,
-0.0339144729077816,
-0.015291019342839718,
0.013227710500359535,
0.006304534152150154,
-0.07481931149959564,
-0.009610628709197044,
-0.03564192354679108,
-0.017805032432079315,
0.022563396021723747,
0.002021755324676633,
0.032408662140369415,
-0.04507937282323837,
0.04594437777996063,
0.04041360318660736,
-0.023374350741505623,
-0.01300628948956728,
-0.004880048334598541,
-0.020889146253466606,
0.04361360892653465,
-0.01973075233399868,
0.028301211073994637,
0.025737734511494637,
-0.022953303530812263,
0.009310252964496613,
-0.004233866930007935,
0.06168687343597412,
0.015276472084224224,
-0.0001715371327009052,
-0.007955559529364109,
-0.05951372906565666,
-0.023596659302711487,
-0.01076954323798418,
0.0606217235326767,
0.00216621533036232,
-0.01655150204896927,
0.026898248121142387,
0.014063444919884205,
-0.016472307965159416,
0.07315011322498322,
0.037132371217012405,
0.03140741214156151,
-0.009934764355421066,
-0.043866585940122604,
-0.015110903419554234,
-0.036434356123209,
-0.018290024250745773,
0.03646363317966461,
-0.015492487698793411,
-0.033232901245355606,
-0.020236171782016754,
0.017917528748512268,
0.03710589557886124,
0.009977676905691624,
0.0020772994030267,
-0.02397654950618744,
0.010477316565811634,
-0.024798143655061722,
0.010043364949524403,
-0.005087254568934441,
0.011808034032583237,
0.008108122274279594,
-0.018514467403292656,
0.03173694759607315,
-0.07371606677770615,
-0.03238910809159279,
0.01973702199757099,
0.023192819207906723,
-0.006238394416868687,
0.0032876094337552786,
-0.05291835591197014,
-0.00883028469979763,
0.046944644302129745,
-0.015933139249682426,
0.03740173578262329,
0.00006206709804246202,
0.011605661362409592,
-0.018643148243427277,
0.004323975183069706,
0.006284569390118122,
-0.022105641663074493,
-0.01665703020989895,
0.028731336817145348,
0.005328064784407616,
0.013298559002578259,
0.03544780984520912,
-0.004255157429724932,
0.03804445266723633,
0.05305921286344528,
-0.0045307413674890995,
-0.04146311804652214,
-0.0007698642439208925,
0.014968904666602612,
-0.04467953369021416,
-0.06375382095575333,
-0.0015963350888341665,
-0.02719886228442192,
-0.027287263423204422,
0.0036288497503846884,
-0.020985107868909836,
-0.0530490018427372,
0.04616081342101097,
0.0013798216823488474,
-0.01419434417039156,
0.00003060989547520876,
-0.0025538725312799215,
0.05226762965321541,
0.04331153258681297,
-0.028601346537470818,
0.028689667582511902,
0.056453827768564224,
-0.016883745789527893,
-0.030733870342373848,
0.008808296173810959,
0.035289887338876724,
0.0011820485815405846,
0.006013712380081415,
-0.05691518262028694,
-0.002016426995396614,
-0.019808977842330933,
0.01913045533001423,
-0.006751425098627806,
0.039413902908563614,
-0.004984692670404911,
-0.04897913336753845,
-0.0064768800511956215,
0.05359826236963272,
0.017606163397431374,
0.008233897387981415,
0.027210576459765434,
-0.007028581108897924,
0.0017716477159410715,
-0.03874984383583069,
0.008618858642876148,
-0.009586440399289131,
0.006352278869599104,
0.028356028720736504,
0.00982105452567339,
0.004816461820155382,
-0.013481847941875458,
-0.0547269806265831,
-0.0007615778595209122,
-0.05460537597537041,
0.03127886354923248,
-0.0028081692289561033,
0.023970473557710648,
0.01672004722058773,
-0.06980932503938675,
0.02188747003674507,
0.026464058086276054,
0.004760009702295065,
0.007788493297994137,
-0.01352538913488388,
0.01558369304984808,
0.054708536714315414,
0.012112659402191639,
-0.07005182653665543,
-0.03968276083469391,
0.027530141174793243,
0.02210650034248829,
-0.03328825905919075,
-0.05143330991268158,
-0.0013649796601384878,
-0.003677142783999443,
-0.03986656665802002,
0.007699659094214439,
0.06859941780567169,
-0.021854430437088013,
-0.033123936504125595,
0.038940854370594025,
0.0028807169292122126,
0.04824785888195038,
-0.009471752680838108,
-0.008813831023871899,
-0.004039733670651913,
-0.02687627077102661,
-0.03502464294433594,
0.0007901721401140094,
0.06703269481658936,
-0.017589062452316284,
0.012202546931803226,
-0.021325910463929176,
0.025829732418060303,
0.05689827725291252,
-0.008079160936176777,
0.013987775892019272,
0.027262387797236443,
0.04118683189153671,
0.0021529518999159336,
-0.04014365375041962,
0.017757218331098557,
0.0015117027796804905,
0.03935733437538147,
0.02388649806380272,
0.003951603081077337,
0.00028307142201811075,
-0.08312027901411057,
0.02146555297076702,
-0.02702256664633751,
0.005348169710487127,
-0.000514975399710238,
0.10541106015443802,
-0.030177397653460503,
0.01575380377471447,
0.009806190617382526,
-0.02142755500972271,
0.03972892090678215,
0.009759364649653435,
-0.008930254727602005,
0.013385376892983913,
0.02126138098537922,
-0.027841364964842796,
-0.0233274195343256,
-0.04326676204800606,
0.020615804940462112,
0.09763608127832413,
-0.07325748354196548,
0.06912487745285034,
0.016915667802095413,
-0.017514461651444435,
0.044679105281829834,
-0.0010581966489553452,
-0.0026835936587303877,
-0.01142368745058775,
0.001327082864008844,
0.022392088547348976,
-0.03334784507751465,
-0.004439544398337603,
0.022039562463760376,
0.04250885173678398,
0.010977613739669323,
-0.011009695008397102,
0.02358211949467659,
-0.003832021960988641,
0.025034397840499878,
0.02314068004488945,
-0.041242409497499466,
0.038736071437597275,
-0.007190704345703125,
0.06816883385181427,
-0.016636991873383522,
-0.019891100004315376,
0.0677180364727974,
0.02683628350496292,
0.014005000703036785,
-0.05371813103556633,
-0.00876106321811676,
-0.030334599316120148,
0.035155922174453735,
-0.0030613199342042208,
0.03505156934261322,
-0.0009882363956421614,
0.019199244678020477,
0.02329918183386326,
0.03182248771190643,
0.001555699622258544,
-0.031633082777261734,
-0.0516095794737339,
-0.04626023769378662,
-0.008271779865026474,
-0.009578230790793896,
0.05267753824591637,
0.024437453597784042,
-0.016407346352934837,
0.040541134774684906,
-0.016049349680542946,
0.013178598135709763,
-0.014711963944137096,
0.009118358604609966,
-0.017184853553771973,
0.08352705091238022,
-0.03277471661567688,
0.018127424642443657,
-0.03520152345299721,
0.002903945744037628,
0.08530055731534958,
0.04412709176540375,
0.019580457359552383,
-0.04405459016561508,
0.01595618948340416,
-0.029294203966856003,
-0.032543085515499115,
-0.03537525609135628,
0.03685727342963219,
0.004850273486226797,
0.001001647673547268,
0.00026498112129047513,
0.04052311182022095,
-0.002773789456114173,
0.005227338057011366,
0.0376523993909359,
-0.032748766243457794,
-0.05486280471086502,
-0.017223697155714035,
0.0028167320415377617,
-0.017905907705426216,
0.007172528654336929,
-0.032128170132637024,
0.04795652627944946,
-0.003383666044101119,
-0.018948042765259743,
-0.04613259807229042,
-0.033176764845848083,
0.04908283054828644,
0.018876545131206512,
-0.06806404888629913,
0.03862081468105316,
-0.006359854247421026,
-0.037381917238235474,
-0.041943129152059555,
0.041423358023166656,
-0.022481834515929222,
-0.023845044896006584,
0.0415005125105381,
0.03708823770284653,
-0.004905391950160265,
0.010654639452695847,
0.013650544919073582,
-0.03909601271152496,
-0.044599585235118866,
0.017293795943260193,
-0.04075539484620094,
0.03939952701330185,
-0.007915289141237736,
0.010681848041713238,
0.013003145344555378,
0.01181972585618496,
-0.0017635483527556062,
-0.044257622212171555,
0.0077272444032132626,
-0.005046421196311712,
0.053345900028944016,
0.002136384602636099,
0.01139739342033863,
0.0019825308118015528,
0.047037456184625626,
-0.009625475853681564,
-0.025921905413269997,
0.033514514565467834,
-0.016023902222514153,
0.015487002208828926,
-0.0178975909948349,
0.06193853169679642,
-0.018946604803204536,
-0.013968195766210556,
-0.02557450160384178,
0.004711253102868795,
-0.04527631774544716,
-0.031159991398453712,
0.016615111380815506,
0.06673189997673035,
0.01299163419753313,
-0.01066279225051403,
-0.05014880374073982,
-0.03994688019156456,
-0.061505287885665894,
0.0275766272097826,
-0.03986447677016258,
0.0031373410020023584,
-0.034937534481287,
-0.019711902365088463,
0.04402768239378929,
0.02794625423848629,
-0.03093448467552662,
0.0009258378995582461,
0.003815615549683571,
0.040314916521310806,
0.018471568822860718,
-0.02401682734489441,
-0.03888566046953201,
-0.025495024397969246,
-0.013391943648457527,
0.005320453550666571,
-0.02870594523847103,
0.023868411779403687,
0.025577738881111145,
-0.01376146450638771,
-0.0049642715603113174,
0.028095697984099388,
0.012653146870434284,
-0.0018910455983132124,
0.006278729997575283,
-0.03430509194731712,
-0.00118603790178895,
0.02710641734302044,
-0.004570034798234701,
-0.009568877518177032,
-0.03586899861693382,
-0.02127734199166298,
-0.008927335031330585,
-0.00203434145078063,
0.03559805825352669,
-0.03610137477517128,
0.0010007607052102685,
-0.031204642727971077,
0.031549472361803055,
-0.005259259603917599,
-0.03180651739239693,
-0.04851813614368439,
-0.03767179697751999,
0.02325722761452198,
0.015051550231873989,
-0.04427499324083328,
0.0033356870990246534,
-0.0250014066696167,
0.020556924864649773,
-0.02111685648560524,
-0.005251029506325722,
-0.01762077584862709,
0.0018396866507828236,
0.024928314611315727,
-0.017906393855810165,
0.05465688556432724,
-0.025893209502100945,
-0.014834191650152206,
0.041056908667087555,
-0.014118995517492294,
-0.033691875636577606,
0.011329281143844128,
0.037278108298778534,
0.03285907208919525,
-0.023147396743297577,
-0.026257650926709175,
-0.03288467228412628,
0.06814861297607422,
-0.03471720963716507,
-0.003558490425348282,
0.002446169964969158,
-0.05419369041919708,
-0.04723667353391647,
-0.03868824243545532,
-0.005745677277445793,
-0.00843583233654499,
0.022687431424856186,
0.0027686087414622307,
0.02489713951945305,
-0.02770569734275341,
-0.05284889042377472,
-0.019368041306734085,
0.005892940331250429,
0.0030863783322274685,
0.019287029281258583,
0.0017036204226315022,
0.021013299003243446,
0.02739887684583664,
-0.0065515306778252125,
0.011733029969036579,
0.014638877473771572,
-0.009629734791815281,
-0.09719222784042358,
-0.0062061697244644165,
0.0010362484026700258,
0.017921628430485725,
0.027965709567070007,
-0.0798724815249443,
-0.03515738993883133,
0.056292470544576645,
-0.02002285234630108,
-0.016284359619021416,
-0.036393970251083374,
-0.0179930217564106,
0.009838459081947803,
-0.03418372571468353,
0.01863509975373745,
0.03597287833690643,
-0.005905066151171923,
0.004876898601651192,
0.03081377036869526,
0.012395023368299007,
-0.02535504288971424,
-0.0033825465943664312,
0.00310944439843297,
0.0012531251413747668,
0.01744917966425419,
-0.020204726606607437,
0.025871310383081436,
0.006200833711773157,
-0.03561653941869736,
0.03960714489221573,
-0.016839567571878433,
-0.00919522624462843,
-0.00898221880197525,
0.020571192726492882,
-0.03943701460957527,
0.020968113094568253,
0.005697515327483416,
0.014950767159461975,
0.015301127918064594,
0.027491969987750053,
0.0018169813556596637,
0.032443221658468246,
-0.01106354407966137,
0.0006431122892536223,
0.02278086356818676,
-0.06850290298461914,
0.004507079254835844,
0.0003591591084841639,
-0.029747365042567253,
0.017369838431477547,
-0.006029313895851374,
-0.01972249522805214,
0.052155960351228714,
-0.02721584588289261,
-0.007928007282316685,
-0.02561129443347454,
-0.029398160055279732,
0.06539775431156158,
-0.010122616775333881,
-0.01347268931567669,
0.029050059616565704,
0.02040669694542885,
-0.012094018049538136,
-0.010383550077676773,
-0.01191167626529932,
-0.010332092642784119,
-0.0682661384344101,
-0.07254339754581451,
-0.015577869489789009,
-0.03541964665055275,
-0.05575984716415405,
-0.039052095264196396,
-0.04698154330253601,
0.029505355283617973,
0.0038849017582833767,
0.025782359763979912,
0.0016875221626833081,
-0.047529347240924835,
-0.011537079699337482,
-0.03284069895744324,
0.014321738854050636,
-0.0008989687194116414,
-0.04106104001402855,
-0.00730468612164259,
-0.012114163488149643,
0.03203730285167694,
-0.010690607130527496,
0.052215151488780975,
0.000011755534615076613,
0.006831206846982241,
0.014838394708931446,
0.004085436463356018,
0.007674220949411392,
-0.018395831808447838,
-0.0016536192269995809,
-0.020459063351154327,
-0.013101606629788876,
0.05362636595964432,
-0.0019515795866027474,
-0.0012538186274468899,
-0.001933362102136016,
0.019425101578235626,
-0.00800864864140749,
0.019527070224285126,
-0.007635067217051983,
-0.013238641433417797,
0.001905413344502449,
0.01086106151342392,
-0.010139280930161476,
0.07014700025320053,
-0.022947050631046295,
0.00691231107339263,
0.03197958692908287,
-0.039122894406318665,
-0.07234995812177658,
0.01565312221646309,
-0.055456094443798065,
0.0039210510440170765,
-0.017769640311598778,
-0.03412755951285362,
0.0034851047676056623,
-0.0662652924656868,
-0.013812401331961155,
0.002393071074038744,
-0.03619645535945892,
0.011491723358631134,
0.052395351231098175,
0.06982363015413284,
0.0055193305015563965,
-0.05062815546989441,
0.024117223918437958,
-0.001484827371314168,
-0.00594373932108283,
0.02683330699801445,
0.016727576032280922,
0.037949852645397186,
-0.0069962372072041035,
-0.009315939620137215,
0.023724716156721115,
-0.0031200414523482323,
0.02851075865328312,
0.010353093966841698,
0.016266783699393272,
0.021747663617134094,
-0.045580871403217316,
-0.007279437035322189,
0.02787022851407528,
-0.005454102996736765,
0.00287231313996017,
0.002244585193693638,
0.04098081216216087,
-0.016631823033094406,
0.01866736076772213,
-0.010042673908174038,
-0.03037988394498825,
0.0011819109786301851,
0.003331511514261365,
0.03598978370428085,
0.021951600909233093,
-0.048507895320653915,
-0.015042455866932869,
0.017603570595383644,
-0.032941121608018875,
0.018569404259324074,
0.006608191877603531,
0.010006352327764034,
-0.0007023985381238163,
0.009023099206387997,
-0.014147660695016384,
-0.011793432757258415,
-0.007635446731001139,
-0.015102339908480644,
0.05081356316804886,
0.06897757947444916,
-0.013679269701242447,
-0.002721219090744853,
0.010720346122980118,
-0.03641720488667488,
0.022531190887093544,
-0.09001782536506653,
-0.0283760167658329,
-0.02044316753745079,
0.04002707451581955,
0.0419779047369957,
0.025969523936510086
] |
<p>Let's say we somehow speed up the moon's rotation. (I'm thinking about a big asteroid smashing into it, but I'm open to better ideas.) Here are some questions:</p>
<p>How fast could we get the moon to spin before gravity stopped holding it together? (An answer in revolutions per minute would be nice.) </p>
<p>At half that speed, what would the consequences be on the moon, on space missions to the moon, and here on earth? </p>
<p>How many asteroids would it take to get it to spin at that speed?</p>
| 9,424 |
[
-0.05050940811634064,
-0.007775633595883846,
-0.029362984001636505,
-0.04278936609625816,
0.040737446397542953,
-0.011162119917571545,
-0.03902297094464302,
-0.025911295786499977,
0.014434238895773888,
-0.021353829652071,
0.01786854863166809,
0.08889364451169968,
0.022168023511767387,
0.026019779965281487,
-0.003633363638073206,
0.01279327180236578,
-0.012110662646591663,
-0.027657538652420044,
-0.009153746999800205,
0.00021890870993956923,
0.011605346575379372,
-0.029993191361427307,
0.018858885392546654,
0.012528001330792904,
-0.014705287292599678,
0.019984785467386246,
0.07153314352035522,
-0.016028350219130516,
0.022794660180807114,
0.027676425874233246,
0.039094243198633194,
-0.003742455504834652,
0.05149510130286217,
0.029071208089590073,
0.015256136655807495,
0.016778381541371346,
-0.024198519065976143,
0.001499385223723948,
0.0037817475385963917,
0.037358880043029785,
-0.039968106895685196,
0.0010977266356348991,
0.005065629258751869,
0.026465917006134987,
-0.011744536459445953,
0.024487251415848732,
-0.00664438446983695,
-0.04683961719274521,
0.027277663350105286,
-0.06985247880220413,
0.07609158754348755,
-0.00695442408323288,
0.01873275823891163,
0.02200191095471382,
0.005150686018168926,
-0.016356240957975388,
0.08613058179616928,
0.08074428886175156,
-0.014810723252594471,
-0.03744136169552803,
-0.039872635155916214,
-0.02292581833899021,
0.0007536471239291131,
-0.027324439957737923,
-0.011493075639009476,
0.04583001509308815,
-0.06009151041507721,
0.009409062564373016,
0.03216630592942238,
-0.011321848258376122,
0.02984166331589222,
0.019432909786701202,
0.02985442988574505,
-0.029658490791916847,
-0.01641944982111454,
-0.0637674555182457,
0.030985822901129723,
-0.0052954936400055885,
0.009281810373067856,
0.06583335250616074,
-0.030795618891716003,
0.009048042818903923,
0.0584377646446228,
0.03667940944433212,
0.027310697361826897,
0.01950782723724842,
0.06938418000936508,
0.022051474079489708,
0.02429935149848461,
0.02497766725718975,
0.0015519448788836598,
-0.01810198277235031,
0.011704024858772755,
-0.02688533067703247,
-0.02658442221581936,
0.04060336574912071,
-0.019398191943764687,
0.07335777580738068,
0.016430525109171867,
0.0005080527043901384,
0.02312663570046425,
0.01921800523996353,
0.007209586910903454,
0.05093048885464668,
-0.0029221565928310156,
0.004628950729966164,
-0.027233069762587547,
-0.008030853234231472,
-0.0070524816401302814,
-0.04101746901869774,
-0.021452080458402634,
-0.0059600332751870155,
-0.01576683484017849,
-0.023304957896471024,
-0.004609982017427683,
0.011925335973501205,
0.020458782091736794,
-0.0338057205080986,
0.03082095831632614,
0.06013021245598793,
0.04364771395921707,
0.007631209213286638,
0.013241472654044628,
-0.02825653925538063,
-0.01074305921792984,
0.01712484285235405,
0.01633327640593052,
-0.03361867368221283,
-0.007651481311768293,
-0.010806064121425152,
-0.01296431664377451,
-0.029742969200015068,
-0.022049443796277046,
-0.03274998068809509,
0.05543476343154907,
-0.01342078484594822,
-0.06551361829042435,
-0.06157734617590904,
0.048885125666856766,
0.006381286308169365,
-0.038289763033390045,
-0.081617072224617,
0.02830733358860016,
-0.029803810641169548,
0.05561690405011177,
0.017577635124325752,
-0.0006272626342251897,
0.008844799362123013,
0.03521731123328209,
0.010426800698041916,
-0.04371090605854988,
0.0017702096374705434,
0.0436728373169899,
-0.03707374259829521,
-0.003465088317170739,
-0.08478888869285583,
0.011443562805652618,
0.03563389182090759,
-0.010409611277282238,
-0.03697532042860985,
0.010694739408791065,
-0.026202687993645668,
0.02841143123805523,
0.009262938983738422,
-0.002529930090531707,
-0.025958875194191933,
0.08006776124238968,
0.030769094824790955,
-0.016997026279568672,
0.013100499287247658,
0.03367135673761368,
0.03821100294589996,
0.01830877549946308,
-0.010101769119501114,
0.04656005650758743,
-0.04671240970492363,
-0.0062128412537276745,
-0.030515355989336967,
-0.010936945676803589,
-0.026951884850859642,
-0.003845374332740903,
-0.034471940249204636,
0.0059196497313678265,
0.0007269162451848388,
0.01841564290225506,
0.05311945453286171,
0.012242457829415798,
-0.007875311188399792,
-0.006297130137681961,
-0.024194911122322083,
0.014879165217280388,
-0.063875213265419,
0.024412820115685463,
0.008948569186031818,
-0.000889122427906841,
0.012923182919621468,
0.026503322646021843,
0.04814111068844795,
-0.021897785365581512,
-0.0172929298132658,
0.026041969656944275,
0.044455986469984055,
-0.00022072771389503032,
-0.022826597094535828,
0.006314645987004042,
0.08142682164907455,
0.010131170973181725,
-0.03511693328619003,
-0.004003574140369892,
0.018782686442136765,
-0.00910757202655077,
-0.021214254200458527,
-0.012977573089301586,
-0.004832316655665636,
0.01005262229591608,
0.03664054721593857,
0.06889503449201584,
0.013707337900996208,
0.02066328562796116,
-0.005233405157923698,
-0.0015566878719255328,
0.1349327713251114,
0.030620941892266273,
-0.03721456602215767,
0.052535030990839005,
0.02631421945989132,
0.02952801063656807,
-0.019673842936754227,
0.01789742521941662,
-0.02909453585743904,
-0.031081421300768852,
-0.005390041507780552,
-0.004047165624797344,
0.009697948582470417,
-0.027946781367063522,
0.03756793960928917,
0.06332947313785553,
0.029196158051490784,
0.040718525648117065,
0.0045222449116408825,
-0.02037515863776207,
-0.013042343780398369,
-0.014415438286960125,
-0.015932025387883186,
-0.025119489058852196,
0.013500867411494255,
0.021724378690123558,
0.02731989696621895,
-0.016204431653022766,
0.005396298132836819,
-0.020954344421625137,
0.05027085915207863,
0.026833215728402138,
-0.025964679196476936,
0.021128244698047638,
-0.035159580409526825,
0.05642538145184517,
-0.028577230870723724,
-0.005676699336618185,
0.026781903579831123,
-0.0019247237360104918,
0.0160299614071846,
-0.05342027544975281,
-0.009224065579473972,
-0.02421344257891178,
0.028407637029886246,
0.030322274193167686,
-0.011736547574400902,
0.04208297282457352,
-0.03885529935359955,
0.011005421169102192,
-0.00034740613773465157,
-0.009866544976830482,
-0.032171983271837234,
-0.01521770004183054,
0.03335176780819893,
0.012071371078491211,
0.043729282915592194,
-0.002350829541683197,
-0.0288582444190979,
0.02890852838754654,
-0.05198521539568901,
-0.013158014975488186,
-0.007329833228141069,
-0.06888120621442795,
0.019807223230600357,
-0.0007466923561878502,
-0.010854996740818024,
0.04306553676724434,
-0.007228311616927385,
0.02945649065077305,
0.012224607169628143,
-0.011751544661819935,
-0.038507454097270966,
0.001045106677338481,
-0.038618821650743484,
0.011519324034452438,
-0.03659790754318237,
0.007601034827530384,
0.03954743966460228,
-0.013356698676943779,
-0.003012941451743245,
0.016230303794145584,
-0.03712531551718712,
-0.029044989496469498,
-0.009602038189768791,
0.02986263670027256,
0.017125315964221954,
-0.038209013640880585,
-0.028192756697535515,
-0.013473670929670334,
-0.051580946892499924,
0.015325241722166538,
-0.03583161532878876,
-0.049111075699329376,
0.008013986051082611,
-0.024422550573945045,
0.04462934285402298,
-0.004679340869188309,
-0.04327321797609329,
0.07806396484375,
0.026324819773435593,
-0.012808351777493954,
-0.04836784675717354,
-0.0030477773398160934,
0.003758877282962203,
-0.0560496523976326,
0.013943947851657867,
0.029404722154140472,
-0.011427581310272217,
-0.0038785042706876993,
0.013038490898907185,
0.019675178453326225,
0.018094031140208244,
0.02292858622968197,
-0.00805101078003645,
-0.004919921513646841,
0.010679804719984531,
0.020572366192936897,
-0.000973004789557308,
0.030533727258443832,
-0.024134714156389236,
0.057524144649505615,
-0.021217213943600655,
0.05218906328082085,
0.017285984009504318,
-0.06887432187795639,
0.03645259514451027,
0.014227575622498989,
-0.01728525385260582,
0.012807261198759079,
0.03219303488731384,
-0.015638845041394234,
0.01144277025014162,
0.002662959275767207,
0.014274721033871174,
0.051468685269355774,
0.014448651112616062,
0.004690537229180336,
0.022861279547214508,
0.04378075897693634,
-0.012914247810840607,
-0.02101421356201172,
-0.04609094187617302,
0.0005226623034104705,
0.028209084644913673,
-0.037935320287942886,
-0.012751354835927486,
0.02828703448176384,
0.023516224697232246,
0.03503096476197243,
-0.033162470906972885,
-0.022621558979153633,
0.000554119236767292,
-0.07753999531269073,
0.013896606862545013,
-0.03233814984560013,
0.027397947385907173,
0.006197810173034668,
0.04323640465736389,
0.04081643745303154,
0.012912049889564514,
0.011858444660902023,
0.007980914786458015,
-0.08339284360408783,
0.048162639141082764,
-0.05764855816960335,
-0.03547443076968193,
0.010005145333707333,
0.04453296586871147,
-0.006132455542683601,
-0.027376091107726097,
-0.030873514711856842,
-0.04509403929114342,
-0.020331013947725296,
-0.030573587864637375,
0.027714984491467476,
-0.013013441115617752,
-0.007469624280929565,
0.0026590467896312475,
0.07682356983423233,
0.04485200345516205,
-0.001420518266968429,
0.03239273279905319,
0.005719583947211504,
-0.0316484272480011,
0.0181963462382555,
0.00966308731585741,
-0.006528870202600956,
-0.0560467392206192,
0.032379306852817535,
-0.003565190825611353,
0.011179539375007153,
-0.009365471079945564,
-0.0028978039044886827,
0.0001326243218500167,
0.023011215031147003,
0.024892617017030716,
0.023377107456326485,
-0.04262036830186844,
-0.04502275958657265,
0.02389431744813919,
-0.028394905850291252,
0.03448948636651039,
-0.012578794732689857,
-0.02135504223406315,
0.022467955946922302,
-0.013925098814070225,
-0.010457471944391727,
0.028679627925157547,
0.06867049634456635,
0.009460165165364742,
-0.01700623705983162,
-0.05512341856956482,
-0.04634234309196472,
-0.006961948703974485,
-0.020688079297542572,
-0.005326069891452789,
-0.021933570504188538,
-0.04825710877776146,
0.01746922731399536,
-0.003920640330761671,
-0.01468710694462061,
-0.01018430758267641,
0.01787564903497696,
-0.010316582396626472,
0.05621645972132683,
0.01629798486828804,
-0.0007448464166373014,
0.007084613665938377,
0.03656267747282982,
0.04789471626281738,
-0.008225244469940662,
-0.0025354349054396152,
-0.05443252995610237,
-0.005828441586345434,
0.012255312874913216,
0.0472094900906086,
-0.015388274565339088,
-0.01667811907827854,
-0.07865697890520096,
-0.033484917134046555,
0.046640995889902115,
-0.043159544467926025,
0.038867998868227005,
0.0021335084456950426,
0.025553297251462936,
-0.01941249519586563,
-0.008710614405572414,
-0.020958319306373596,
0.018883125856518745,
0.003657823195680976,
0.05302036926150322,
-0.016822053119540215,
-0.010906309820711613,
-0.01630348525941372,
0.020952457562088966,
0.06786727905273438,
0.03803996369242668,
0.027355007827281952,
0.024928774684667587,
0.008975899778306484,
-0.01939338631927967,
-0.02078019455075264,
-0.08615124225616455,
0.015350418165326118,
-0.00035105348797515035,
-0.04607820883393288,
0.04863492399454117,
-0.04180542752146721,
-0.043454285711050034,
0.041977282613515854,
0.019051212817430496,
-0.010741089470684528,
-0.0005772801232524216,
-0.047745976597070694,
0.0029373052529990673,
0.05097546428442001,
0.030500248074531555,
-0.0011315452866256237,
0.018681373447179794,
-0.030179137364029884,
0.01068164687603712,
-0.03690608963370323,
0.023997914046049118,
-0.04680776223540306,
-0.006606631446629763,
0.015635976567864418,
-0.0064909798093140125,
-0.04400274157524109,
0.03627397119998932,
0.006162781268358231,
0.03326558321714401,
0.012795491144061089,
-0.020558342337608337,
-0.02429458498954773,
0.008389556780457497,
0.029807891696691513,
-0.016323979943990707,
0.014839603565633297,
0.019798414781689644,
0.0011597186094149947,
-0.006631964817643166,
0.02872919663786888,
0.00004334128971095197,
-0.005831720307469368,
0.03680117055773735,
-0.02558848075568676,
-0.02721145562827587,
-0.026115233078598976,
-0.019738852977752686,
-0.005909758619964123,
-0.024561570957303047,
0.07310271263122559,
-0.026676909998059273,
-0.0017645159969106317,
0.04910111427307129,
-0.046157367527484894,
-0.0017909485613927245,
0.005028050858527422,
-0.017205191776156425,
0.03362917900085449,
-0.04774211347103119,
0.034831199795007706,
0.0296475887298584,
0.008598588407039642,
-0.04608049616217613,
-0.024512222036719322,
0.05964062735438347,
-0.007477245293557644,
-0.023236433044075966,
-0.01448119431734085,
0.007978571578860283,
-0.0470714345574379,
-0.04000530019402504,
0.00008568268094677478,
0.05808412283658981,
-0.04595302790403366,
-0.0028379533905535936,
0.043106984347105026,
-0.017737312242388725,
0.07550840079784393,
-0.006522235460579395,
-0.058521512895822525,
0.01236315630376339,
-0.030038608238101006,
-0.008956310339272022,
-0.036756910383701324,
0.08187280595302582,
-0.05115136876702309,
-0.025975264608860016,
-0.024581655859947205,
-0.028954943642020226,
0.004999935626983643,
-0.0023317434825003147,
0.007883630692958832,
0.03918375447392464,
0.03173259645700455,
0.00907253846526146,
-0.004434647504240274,
0.05625364929437637,
-0.0066738915629684925,
0.03734257444739342,
-0.008521504700183868,
0.017878735437989235,
-0.0309310182929039,
-0.04783542826771736,
0.026137175038456917,
0.013352574780583382,
0.021693242713809013,
-0.0038364005740731955,
0.040999047458171844,
0.0018501010490581393,
-0.02702721208333969,
0.021628515794873238,
-0.01152412872761488,
0.03197102248668671,
0.011220652610063553,
-0.03127511963248253,
-0.010007942095398903,
-0.024755412712693214,
-0.03599774092435837,
-0.06051186844706535,
0.01501699909567833,
-0.02757364884018898,
0.07780273258686066,
-0.06484807282686234,
0.033085357397794724,
-0.007753139361739159,
0.04382770508527756,
-0.031484492123126984,
-0.015877805650234222,
-0.004023589659482241,
0.030582740902900696,
0.012243169359862804,
-0.006524821277707815,
-0.0009112699190154672,
0.016773074865341187,
0.01631573960185051,
0.046749867498874664,
0.004621620289981365,
0.046982526779174805,
0.048454027622938156,
-0.020282039418816566,
0.04386270046234131,
-0.015201958827674389,
-0.02972310222685337,
0.018145810812711716,
-0.019363123923540115,
0.052696678787469864,
-0.00038800924085080624,
0.0038752108812332153,
0.05826381593942642,
0.008761062286794186,
0.0005341231008060277,
-0.014468317851424217,
0.002728666877374053,
-0.04899120703339577,
-0.02573845535516739,
0.012913900427520275,
-0.003615219844505191,
-0.0014411323936656117,
-0.011577514000236988,
0.027739787474274635,
-0.015079256147146225,
-0.006874751299619675,
-0.03509089723229408,
-0.06650099158287048,
-0.026444874703884125,
-0.04493644833564758,
-0.054852552711963654,
0.049661990255117416,
0.03395305201411247,
-0.018728727474808693,
0.02164153754711151,
-0.014808683656156063,
0.005467727780342102,
-0.005429849028587341,
0.04198156297206879,
-0.027881506830453873,
0.08763958513736725,
-0.009412656538188457,
0.0034556665923446417,
-0.028518809005618095,
0.003638424212113023,
0.10042256861925125,
0.04617132991552353,
0.01569024845957756,
-0.025971807539463043,
0.016071578487753868,
-0.025288226082921028,
0.00212105386890471,
-0.02681076154112816,
-0.023396145552396774,
0.014037459157407284,
0.011524217203259468,
0.010924960486590862,
0.02933676913380623,
-0.012959291227161884,
-0.009388069622218609,
0.03377463296055794,
-0.006086524110287428,
-0.004298361949622631,
-0.009041405282914639,
0.013323526829481125,
0.005304732359945774,
0.01987498812377453,
-0.03336315229535103,
0.018451685085892677,
-0.044554371386766434,
-0.031204011291265488,
-0.05430391803383827,
-0.03308641165494919,
0.015392925590276718,
0.0016557322815060616,
-0.055625591427087784,
0.012824521400034428,
0.006541870068758726,
-0.04603741690516472,
-0.041254863142967224,
0.04020700603723526,
0.011637700721621513,
-0.0022971979342401028,
0.0021747008431702852,
0.02609260194003582,
0.004483891651034355,
0.026434682309627533,
-0.009889425709843636,
0.023806488141417503,
-0.06446268409490585,
-0.005035539623349905,
-0.03556100279092789,
0.03707672283053398,
0.000759341346565634,
0.012498028576374054,
0.0031019554007798433,
0.011677445843815804,
-0.00693506607785821,
-0.03603820502758026,
0.005843480583280325,
0.009449059143662453,
0.03278823569417,
-0.00003823545193881728,
-0.015658395364880562,
-0.00390209280885756,
0.01223793625831604,
-0.0027535115368664265,
0.038948919624090195,
-0.017084110528230667,
0.01649683341383934,
-0.027925856411457062,
-0.01357995718717575,
0.02441929280757904,
-0.04223249852657318,
-0.03982619568705559,
-0.0388074591755867,
-0.008225140161812305,
-0.03278660401701927,
0.03697036951780319,
0.045835286378860474,
0.014111767522990704,
0.015140284784138203,
0.013597996905446053,
-0.018507085740566254,
-0.024752017110586166,
-0.0002132637018803507,
0.07075200229883194,
0.005001473240554333,
-0.009964813478291035,
-0.034862663596868515,
-0.0231171865016222,
0.06359969824552536,
-0.010103873908519745,
-0.028747502714395523,
-0.00704243965446949,
-0.03602726384997368,
0.014388544484972954,
0.03535652160644531,
-0.02176300808787346,
-0.01573074236512184,
0.019690314307808876,
0.0071983328089118,
0.01646317169070244,
-0.014852168969810009,
0.06313284486532211,
0.028032436966896057,
-0.04292039945721626,
0.011914816685020924,
0.01699146255850792,
-0.00677325576543808,
0.016751032322645187,
0.04627092182636261,
-0.017186306416988373,
-0.04993108659982681,
0.018681900575757027,
-0.009438279084861279,
-0.015591013245284557,
-0.019243869930505753,
-0.05326739326119423,
-0.02896573394536972,
-0.005364390555769205,
0.027391716837882996,
-0.03740936145186424,
0.06796133518218994,
-0.019425423815846443,
0.024607207626104355,
-0.03307531774044037,
0.046108901500701904,
-0.04083731397986412,
0.014293599873781204,
-0.005179972387850285,
-0.02478494495153427,
0.025962434709072113,
0.0362764410674572,
-0.010611145757138729,
-0.036186978220939636,
0.009812911041080952,
0.004604442045092583,
0.016278022900223732,
0.023958304896950722,
0.006583600305020809,
-0.016375401988625526,
0.05015910044312477,
-0.035005178302526474,
-0.00775738013908267,
0.03599138930439949,
-0.036532141268253326,
-0.03220495954155922,
0.023899324238300323,
-0.04478776082396507,
0.05241716280579567,
-0.008575180545449257,
-0.023755621165037155,
-0.030354203656315804,
0.056315839290618896,
-0.04922281205654144,
-0.017702754586935043,
0.01568693295121193,
-0.011692441999912262,
-0.04043116047978401,
0.0049705179408192635,
0.021902963519096375,
-0.060963671654462814,
0.010568814352154732,
0.03552016243338585,
0.025116393342614174,
-0.05746834725141525,
0.02810017205774784,
-0.020296776667237282,
-0.019189992919564247,
0.012752052396535873,
0.0006534581771120429,
-0.010946188122034073,
0.019222775474190712,
0.014463430270552635,
-0.02813672460615635,
0.052525706589221954,
0.01071036234498024,
-0.027362927794456482,
-0.069206602871418,
0.012464835308492184,
-0.004204224329441786,
-0.027765857055783272,
0.06002016365528107,
-0.03826677426695824,
-0.008651981130242348,
0.052150726318359375,
-0.07276857644319534,
0.02156412973999977,
-0.056818753480911255,
-0.0076384348794817924,
-0.04789119213819504,
0.01159914955496788,
0.0035996860824525356,
0.0027419154066592455,
0.010772127658128738,
0.015555359423160553,
-0.0021643161308020353,
0.014696137048304081,
-0.01859387196600437,
-0.017911415547132492,
0.03948212414979935,
0.013564828783273697,
-0.0056563145481050014,
0.03295028209686279,
0.06298665702342987,
-0.035731829702854156,
-0.011400670744478703,
0.012906760908663273,
0.006509875413030386,
0.0644252598285675,
-0.021700754761695862,
-0.012969393283128738,
-0.0075263711623847485,
0.012123649939894676,
0.01771034300327301,
-0.012371423654258251,
-0.008487332612276077,
0.03992074355483055,
0.0011278814636170864,
0.04542246088385582,
-0.007661125157028437,
0.0042077829129993916,
0.0085267573595047,
-0.040404219180345535,
0.007109569851309061,
-0.012698192149400711,
0.001171899028122425,
0.023294765502214432,
0.024557365104556084,
0.006151719484478235,
0.02992754802107811,
-0.021455682814121246,
-0.0016186997527256608,
-0.00507281394675374,
0.0026399341877549887,
-0.0033664500806480646,
-0.029155610129237175,
-0.0049569252878427505,
0.04658978059887886,
-0.02559838443994522,
0.003315324429422617,
-0.01731339655816555,
-0.03863411396741867,
-0.008473356254398823,
-0.07029902189970016,
0.0029284690972417593,
0.017830532044172287,
0.0009709722944535315,
-0.027858488261699677,
-0.00955176167190075,
0.014662902802228928,
0.03305190056562424,
0.013424431905150414,
0.02416721172630787,
0.01059735007584095,
-0.05721870809793472,
-0.014389418065547943,
-0.04058034345507622,
-0.005685233511030674,
0.008877886459231377,
0.008483568206429482,
-0.01958356983959675,
-0.04312986880540848,
-0.011840946972370148,
-0.012492833659052849,
0.04513176158070564,
0.007417706307023764,
0.009350736625492573,
0.02763199247419834,
-0.03775547817349434,
0.004125963430851698,
-0.07376185804605484,
-0.019914230331778526,
-0.022373611107468605,
-0.030658645555377007,
0.00906843226402998,
-0.042933981865644455,
-0.025174207985401154,
-0.019256185740232468,
0.040792543441057205,
0.025611180812120438,
0.0008764102822169662,
0.03220485895872116,
-0.00781258475035429,
0.04731379821896553,
0.010478634387254715,
-0.009081165306270123,
0.0678003653883934,
0.004444545134902,
-0.00229400722309947,
0.0008509490289725363,
-0.006057584658265114,
-0.054768726229667664,
0.02404746599495411,
-0.04745907709002495,
-0.00009315917122876272,
-0.021130064502358437,
-0.032997939735651016,
0.03783467411994934,
-0.03457590937614441,
0.03562392294406891,
0.032200805842876434,
-0.03819195553660393,
0.022947238758206367,
0.00917033664882183,
0.02240711636841297,
0.03969370946288109,
-0.05408287048339844,
0.006001556757837534,
0.021813513711094856,
-0.02409224584698677,
-0.02258966863155365,
0.017110301181674004,
0.014825541526079178,
0.012032642960548401,
-0.0077826762571930885,
0.025307778269052505,
0.025120368227362633,
0.0035271449014544487,
0.03437800705432892,
0.04244113340973854,
-0.035607852041721344,
-0.061870601028203964,
0.01582122966647148,
-0.015277544036507607,
0.015523875132203102,
0.05933938920497894,
-0.005928131751716137,
0.05940316244959831,
0.024570249021053314,
0.01095561683177948,
-0.00014059375098440796,
-0.016621069982647896,
-0.03425123915076256,
-0.009900149889290333,
-0.036900054663419724,
0.029900383204221725,
-0.009929499588906765,
-0.002824993571266532,
0.006507134065032005,
0.015504509210586548,
0.046154677867889404,
-0.01932171732187271,
0.03135329857468605,
-0.006601662375032902,
0.01735176518559456,
-0.014838488772511482,
-0.04448157921433449,
-0.04969533160328865,
-0.026126986369490623,
0.04565396159887314,
0.012164605781435966,
0.0037789628840982914,
-0.01128863263875246,
-0.029193872585892677,
-0.019915932789444923,
0.04979972541332245,
-0.051712337881326675,
-0.030430682003498077,
-0.03509696573019028,
0.02217862568795681,
-0.032579369843006134,
-0.02213742770254612
] |
<p>Imagine an arbitrary object with center of mass at the red dot in the picture, rotational inertia from the point of the hanging: <strong>I</strong>, hanging from a fixed point, what is the energy required to start moving at constant angular velocity of $\ ω=ω_0 $ the object within a small amount of time $\ t=t_1$, from position A to Position B (angle=θ Rads), if gravity all this time is against our motion.
<img src="http://i.stack.imgur.com/bmC3S.png" alt="enter image description here"><br>
i believe we need to exert a torque which will result the needed velocity in the given time, and then a torque which will cancel out the torque of gravity so we can keep the constant angular velocity. After these we will need to stop our body which means we should exert the necessary force against the motion, considering the "help of gravity" so we can stop the body in a small amount of time again. So we have a function of Torque, and we will integrate Torque•dΘ from Theta=0 to Theta=θ rads. Is that correct? If yes, can you help with formulation?</p>
<p>suppose no air friction and axis friction, the body starts and ends at rest</p>
| 9,425 |
[
-0.029675230383872986,
-0.016482489183545113,
-0.0034837403800338507,
0.014750988222658634,
0.00949561782181263,
-0.007662350311875343,
-0.05885423347353935,
-0.03235691413283348,
-0.0021581253968179226,
-0.040338221937417984,
-0.0029755530413240194,
0.050316549837589264,
0.04557735472917557,
0.03467404469847679,
0.021743347868323326,
-0.04140850901603699,
-0.018472732976078987,
-0.03540709614753723,
-0.00806914921849966,
-0.03388518840074539,
0.0078729297965765,
0.0015432111686095595,
0.0021863155998289585,
-0.003354754764586687,
-0.025532159954309464,
0.01838609389960766,
0.034971024841070175,
-0.021382251754403114,
-0.024429334327578545,
0.07506471127271652,
-0.03741712495684624,
-0.012816344387829304,
-0.0021753639448434114,
0.010136788710951805,
0.012013408355414867,
0.03793557360768318,
-0.07464619725942612,
-0.0285200048238039,
0.004624189343303442,
0.04559929668903351,
-0.022180305793881416,
-0.029203202575445175,
-0.060481492429971695,
0.04856892675161362,
-0.02590327337384224,
0.026000607758760452,
0.0014166170731186867,
0.007923146709799767,
0.06881647557020187,
-0.0447714664041996,
0.06695735454559326,
0.000010199256394116674,
0.05494634434580803,
-0.01153324544429779,
-0.012194730341434479,
-0.032244693487882614,
0.06851651519536972,
0.030654415488243103,
-0.04067938029766083,
-0.04738345369696617,
-0.02232467383146286,
-0.03073267824947834,
-0.014777122065424919,
-0.012395230121910572,
0.023702112957835197,
-0.02439473569393158,
-0.003076396184042096,
0.01438015978783369,
0.041484519839286804,
0.009801440872251987,
0.04112967103719711,
0.0036075704265385866,
0.03132115304470062,
-0.013699449598789215,
-0.004641984589397907,
0.0065528531558811665,
0.01891210675239563,
0.005291737616062164,
0.029792074114084244,
0.03840450569987297,
-0.00704837404191494,
-0.0166873000562191,
0.07957828789949417,
0.07797051966190338,
0.00962600577622652,
0.026438260450959206,
0.05755463242530823,
0.011140870861709118,
0.01179987657815218,
0.03807998448610306,
0.03440369293093681,
0.0027782327961176634,
0.0049013798125088215,
0.00587832136079669,
-0.013467076234519482,
0.056312378495931625,
0.014788401313126087,
0.03463933989405632,
0.018390586599707603,
-0.018361644819378853,
-0.004591092467308044,
-0.035220667719841,
0.03495962545275688,
0.040468163788318634,
0.010531597770750523,
-0.006119999568909407,
-0.014385748654603958,
-0.007997050881385803,
-0.009022637270390987,
-0.021991273388266563,
-0.044751860201358795,
0.022475579753518105,
-0.02043907158076763,
-0.03472726792097092,
-0.024570204317569733,
0.0023378245532512665,
-0.0202402975410223,
-0.012549882754683495,
0.02156980335712433,
0.01933838613331318,
0.03402832895517349,
0.0008870488964021206,
0.033860690891742706,
-0.037459660321474075,
-0.031114671379327774,
0.02336539886891842,
0.040665436536073685,
-0.030599281191825867,
-0.053795259445905685,
0.0115232914686203,
0.020111121237277985,
-0.037924934178590775,
-0.01016590092331171,
0.017597222700715065,
0.08105482161045074,
0.007024859078228474,
-0.07482478767633438,
-0.03730211406946182,
0.02869246155023575,
-0.01799244061112404,
-0.018076803535223007,
-0.06410635262727737,
-0.00016384816262871027,
0.013679529540240765,
0.0638199895620346,
-0.012036211788654327,
0.0002749733976088464,
-0.004992741625756025,
0.0035458924248814583,
-0.016759589314460754,
-0.03486427292227745,
-0.016915474086999893,
0.026665952056646347,
-0.04312228411436081,
-0.029432451352477074,
-0.06581178307533264,
0.05148865282535553,
0.04311797022819519,
0.01974828913807869,
-0.04496853053569794,
0.012625278905034065,
-0.04114626348018646,
0.020567916333675385,
0.019579103216528893,
-0.014358698390424252,
-0.03454045206308365,
0.07937155663967133,
0.010251929052174091,
0.007796204648911953,
0.028741471469402313,
0.030512254685163498,
0.03423624858260155,
-0.008053699508309364,
0.011021606624126434,
0.01987594924867153,
-0.052220992743968964,
-0.022404341027140617,
-0.03471360728144646,
-0.005232350435107946,
0.006359847728163004,
-0.03292420133948326,
-0.04078911989927292,
0.015832271426916122,
-0.050112590193748474,
-0.009414504282176495,
0.08075983077287674,
-0.0030807636212557554,
0.001952178543433547,
-0.03382905200123787,
0.007048401981592178,
0.038385502994060516,
-0.076701819896698,
0.03442529961466789,
-0.022939257323741913,
-0.010404729284346104,
0.012024728581309319,
0.029359422624111176,
0.01008671149611473,
-0.025397932156920433,
0.0023097265511751175,
-0.015051351860165596,
0.01644432730972767,
0.0020404972601681948,
-0.01495342142879963,
0.018551310524344444,
0.06790128350257874,
0.043984852731227875,
0.037029072642326355,
0.014788240194320679,
-0.004284421913325787,
-0.033519089221954346,
-0.02796701341867447,
-0.05592399090528488,
0.05209505558013916,
0.04918600991368294,
0.03060794621706009,
0.03018132969737053,
-0.016447242349386215,
-0.008171865716576576,
0.025334525853395462,
0.021270224824547768,
0.07170750200748444,
0.035680390894412994,
0.01676524616777897,
0.01774311438202858,
0.06921637058258057,
0.01921503059566021,
-0.00857237447053194,
0.004727640189230442,
-0.05614616721868515,
0.0004298536223359406,
0.011043848469853401,
0.021708352491259575,
0.034871917217969894,
-0.06132002919912338,
0.02707674354314804,
0.04002446308732033,
0.030962688848376274,
0.037068452686071396,
0.03637097403407097,
-0.0053067333064973354,
-0.015110515989363194,
0.036030739545822144,
-0.001028495142236352,
-0.02011208049952984,
0.034983422607183456,
-0.00023905523994471878,
0.03307832032442093,
-0.01189968828111887,
0.026862071827054024,
-0.019740700721740723,
0.035027433186769485,
0.028846556320786476,
0.008115560747683048,
-0.009920352138578892,
-0.023949503898620605,
0.04453345388174057,
-0.023218387737870216,
0.052172835916280746,
0.022879764437675476,
0.010554932989180088,
0.015035196207463741,
-0.03713687136769295,
-0.023741304874420166,
0.008944086730480194,
0.0033978938590735197,
0.006221537012606859,
0.001500812009908259,
0.037303779274225235,
-0.010899104177951813,
-0.005078317131847143,
-0.027697280049324036,
-0.015542515553534031,
-0.0074607739225029945,
0.005908841732889414,
0.010535547509789467,
0.034319523721933365,
0.03599349409341812,
-0.0186582263559103,
-0.02529742196202278,
-0.017935339361429214,
-0.02910139225423336,
-0.017940957099199295,
0.047111526131629944,
-0.05546046048402786,
0.007366473320871592,
-0.027125008404254913,
-0.016242438927292824,
0.06239955127239227,
-0.0022363036405295134,
-0.004413502756506205,
0.043933555483818054,
-0.0014211769448593259,
-0.051856376230716705,
-0.008785092271864414,
-0.017303088679909706,
-0.026859283447265625,
-0.02882731519639492,
-0.022644545882940292,
0.035487834364175797,
-0.0086329011246562,
0.0034484677016735077,
0.052789703011512756,
-0.06272928416728973,
-0.048301372677087784,
-0.00009850424248725176,
0.028403744101524353,
0.05178070440888405,
-0.025609074160456657,
0.019283436238765717,
-0.008149503730237484,
-0.030947864055633545,
0.010053170844912529,
-0.0721772313117981,
-0.023631803691387177,
0.008420630358159542,
0.014771969988942146,
0.05395551770925522,
0.013613415881991386,
-0.04362357780337334,
0.08646859228610992,
0.017210615798830986,
-0.037129323929548264,
-0.03465614840388298,
-0.011115266010165215,
-0.0030862013809382915,
-0.050137657672166824,
-0.04267949238419533,
0.001975606894120574,
-0.03557189181447029,
-0.010347694158554077,
0.029624003916978836,
-0.03911422938108444,
0.06251908093690872,
0.007470287848263979,
0.007374264765530825,
0.007260360289365053,
0.027837717905640602,
0.008429985493421555,
0.04760491102933884,
0.008334933780133724,
0.007903925143182278,
-0.01556946150958538,
-0.01927284337580204,
0.04013895243406296,
-0.006602086126804352,
-0.08376273512840271,
0.03530128300189972,
-0.022296439856290817,
-0.0005806023254990578,
0.022428514435887337,
0.06434375792741776,
0.0107695572078228,
-0.03606095537543297,
0.013011576607823372,
0.03128116577863693,
0.06299833953380585,
-0.009241622872650623,
-0.011503245681524277,
0.036112647503614426,
0.04507233947515488,
-0.016117192804813385,
-0.03685248643159866,
0.007643823511898518,
0.007273382041603327,
0.04245881736278534,
-0.02882039174437523,
-0.0024899484124034643,
0.009856989607214928,
0.020607350394129753,
0.03584066033363342,
0.013535158708691597,
-0.03596127778291702,
-0.012056490406394005,
-0.06333250552415848,
0.007444562390446663,
-0.002251091180369258,
0.057378966361284256,
0.002967480570077896,
0.0425616018474102,
0.031368281692266464,
0.03466961160302162,
0.023082196712493896,
0.029285140335559845,
-0.0953562930226326,
0.04464145749807358,
-0.049139078706502914,
-0.03154581040143967,
0.050897903740406036,
0.017828337848186493,
-0.008302389644086361,
-0.01598811149597168,
0.000156725975102745,
-0.019526991993188858,
-0.008462980389595032,
-0.033617254346609116,
0.008955330587923527,
-0.02735424041748047,
-0.012928616255521774,
0.007464689668267965,
0.016027014702558517,
0.025559669360518456,
-0.02376396581530571,
0.03290644660592079,
0.07761363685131073,
-0.031947217881679535,
0.04036707058548927,
-0.019139079377055168,
-0.016960643231868744,
-0.00727922422811389,
-0.009053235873579979,
0.041524000465869904,
0.030482642352581024,
0.021710220724344254,
-0.004172223620116711,
-0.0001932983286678791,
0.056973252445459366,
0.011807470582425594,
0.022688286378979683,
-0.025529872626066208,
-0.0695769414305687,
-0.025128016248345375,
0.02349053882062435,
0.05658179521560669,
-0.02282380685210228,
-0.02052435837686062,
0.028507521376013756,
-0.004356552381068468,
-0.010854054242372513,
0.026624197140336037,
0.06791683286428452,
0.04633074626326561,
-0.011457055807113647,
-0.05290032550692558,
-0.04726916179060936,
-0.009554587304592133,
-0.03383023664355278,
-0.0008786729304119945,
-0.004568480420857668,
-0.036708004772663116,
-0.00197864742949605,
0.015387934632599354,
0.018537553027272224,
0.02225353568792343,
0.022613773122429848,
-0.0326705165207386,
0.02932300791144371,
-0.026113249361515045,
-0.021919162943959236,
0.008051031269133091,
0.01741839200258255,
0.03572729229927063,
-0.005662884097546339,
0.018875323235988617,
-0.0538138821721077,
-0.03799153491854668,
0.019501473754644394,
0.05680025368928909,
0.02460082620382309,
0.001174716278910637,
-0.0639701560139656,
-0.04656359925866127,
0.037643250077962875,
-0.014594257809221745,
0.07023333758115768,
-0.04404812306165695,
-0.01698635332286358,
-0.005125673022121191,
-0.05550745874643326,
-0.02203943207859993,
0.006907238624989986,
-0.012475566007196903,
0.013546206057071686,
-0.013325302861630917,
-0.015159421600401402,
0.02590532973408699,
0.006956520490348339,
-0.0019540353678166866,
0.0068785990588366985,
0.012338935397565365,
-0.021285342052578926,
0.0030786381103098392,
0.02971000410616398,
-0.00490461615845561,
-0.07258886843919754,
-0.03265027329325676,
-0.017180003225803375,
-0.06248278170824051,
0.022372858598828316,
-0.04748474434018135,
-0.03217801824212074,
0.031137265264987946,
-0.0074399844743311405,
0.023027226328849792,
0.03752734884619713,
-0.03698297590017319,
0.05174529552459717,
0.038641564548015594,
-0.007551261689513922,
0.03039136715233326,
0.06641075015068054,
-0.03132586553692818,
0.008835047483444214,
-0.027318617329001427,
0.004529773723334074,
0.015816697850823402,
-0.021605288609862328,
-0.06632321327924728,
0.01735294982790947,
-0.03827154263854027,
0.03535722568631172,
0.008969366550445557,
-0.004571306053549051,
-0.010423258878290653,
-0.022448530420660973,
-0.008825692348182201,
0.05429520830512047,
0.028779268264770508,
-0.032117944210767746,
-0.00912894494831562,
0.03950529173016548,
-0.0019408478401601315,
0.003164781956002116,
-0.023444024845957756,
-0.02391260303556919,
0.016025638207793236,
0.04828811064362526,
-0.010638240724802017,
0.01580779254436493,
-0.03137471526861191,
-0.02126700058579445,
-0.006458390038460493,
-0.0814758911728859,
0.04604122415184975,
-0.03019997850060463,
0.0017344431253150105,
0.027401061728596687,
-0.05428292974829674,
-0.041688013821840286,
-0.011217411607503891,
0.008858979679644108,
-0.00023723734193481505,
-0.03655629977583885,
0.02907811850309372,
-0.000505842559505254,
0.005776906386017799,
-0.03276945278048515,
-0.05140141770243645,
0.01393240038305521,
0.0029473116155713797,
-0.006439658347517252,
-0.030606674030423164,
0.01893819309771061,
-0.027156537398695946,
-0.039433449506759644,
-0.015771351754665375,
0.021902332082390785,
-0.03788285329937935,
0.03129798173904419,
-0.00232507660984993,
0.025447063148021698,
0.02429194375872612,
-0.00881998986005783,
-0.010691211558878422,
0.032050590962171555,
-0.037246715277433395,
-0.0171132143586874,
0.00865662470459938,
0.05805099010467529,
-0.036668892949819565,
-0.028074294328689575,
-0.0049813310615718365,
0.006640575360506773,
0.020727548748254776,
0.031247297301888466,
0.0011106283636763692,
0.039800774306058884,
-0.009987836703658104,
0.018233172595500946,
0.005044084042310715,
0.04311363771557808,
0.011304601095616817,
0.032409410923719406,
0.034252576529979706,
-0.0025472671259194613,
-0.026767924427986145,
-0.041047487407922745,
0.02864491194486618,
-0.022259289398789406,
0.01721995696425438,
-0.007965370081365108,
0.05892210081219673,
-0.02501322142779827,
0.0033616614528000355,
0.023501722142100334,
-0.0013734680833294988,
0.046904902905225754,
-0.012042445130646229,
-0.039623089134693146,
0.06192643195390701,
-0.026144320145249367,
-0.04579002410173416,
-0.03248876333236694,
-0.02803950384259224,
-0.0027806456200778484,
0.02544482983648777,
-0.012040247209370136,
0.055961284786462784,
0.015118448063731194,
0.018451126292347908,
-0.017004266381263733,
0.00965021550655365,
0.00600718567147851,
-0.02686348743736744,
0.027882222086191177,
0.013046235777437687,
-0.012700363993644714,
0.008346004411578178,
0.04953216761350632,
0.037760961800813675,
-0.018808191642165184,
0.033604785799980164,
0.0370040126144886,
-0.01804860681295395,
0.023969506844878197,
0.00820199679583311,
-0.014406727626919746,
0.007890394888818264,
0.006026851013302803,
0.08952528238296509,
-0.02319849655032158,
-0.053274236619472504,
0.01379027683287859,
0.034219078719615936,
0.038454584777355194,
-0.03771736100316048,
0.014600329101085663,
-0.059770576655864716,
0.010893505997955799,
0.023978130891919136,
-0.011583676561713219,
-0.00029597949469462037,
-0.008152077905833721,
0.030422713607549667,
0.0019086997490376234,
0.030562227591872215,
-0.03780878707766533,
-0.00984391663223505,
-0.003522278042510152,
-0.03663197159767151,
-0.07245118916034698,
0.04952941834926605,
0.005853168200701475,
-0.006499673705548048,
0.034984830766916275,
-0.012679179199039936,
0.01726050116121769,
-0.0020404511597007513,
0.037505365908145905,
-0.017468541860580444,
0.10647471994161606,
-0.028235837817192078,
0.015069715678691864,
-0.013530734926462173,
0.012896205298602581,
0.11931756883859634,
0.03809163719415665,
-0.020469095557928085,
-0.010670684278011322,
0.000289955671178177,
0.003838806413114071,
0.00427244184538722,
-0.03263213112950325,
0.0017996984533965588,
0.0045842663384974,
0.009275466203689575,
-0.003450713586062193,
0.04046735167503357,
-0.042689643800258636,
-0.03647712618112564,
0.03191642835736275,
-0.04448064789175987,
-0.029332194477319717,
-0.005940049421042204,
-0.0010739247081801295,
0.013898669742047787,
-0.023107564076781273,
-0.004018872044980526,
0.029288744553923607,
-0.011814330704510212,
-0.018484707921743393,
0.015151957049965858,
-0.03542717173695564,
0.023531001061201096,
-0.034620728343725204,
-0.06351874768733978,
0.0182343777269125,
0.007674685213714838,
-0.02553923986852169,
-0.02565165050327778,
0.030726123601198196,
0.0009408273035660386,
-0.0004948284476995468,
0.02566409297287464,
0.050794485956430435,
0.010819563642144203,
0.01603216491639614,
0.02065042406320572,
-0.023152580484747887,
0.0028639109805226326,
-0.025894764810800552,
-0.03271494805812836,
0.035182513296604156,
-0.015968700870871544,
0.0354505255818367,
0.024751251563429832,
-0.03227756917476654,
0.0072145527228713036,
-0.045244552195072174,
-0.0049200807698071,
-0.046090610325336456,
0.011906562373042107,
-0.02690037339925766,
-0.011379851959645748,
-0.022123098373413086,
-0.006690229754894972,
0.0303746797144413,
0.026382843032479286,
-0.011140787042677402,
-0.02656007744371891,
0.009379837661981583,
0.0003457536513451487,
0.07848672568798065,
-0.010299577377736568,
0.0025351427029818296,
-0.01757483370602131,
-0.024392539635300636,
-0.001709708827547729,
0.0037894693668931723,
-0.0034498402383178473,
0.011949998326599598,
-0.0034062808845192194,
-0.008630211465060711,
0.010455925017595291,
-0.049210015684366226,
-0.036473218351602554,
0.028561655431985855,
-0.0219487976282835,
-0.034569330513477325,
-0.01589411124587059,
0.005830741953104734,
0.012874693609774113,
0.03792409971356392,
-0.00600375235080719,
0.010251914151012897,
0.008334940299391747,
0.03299699351191521,
0.03654027357697487,
-0.031506869941949844,
-0.04422643035650253,
-0.0006050057709217072,
0.011854034848511219,
0.022458670660853386,
0.009207605384290218,
0.021651670336723328,
0.011304683052003384,
0.00767604261636734,
-0.016079306602478027,
0.016225362196564674,
-0.015539618209004402,
0.004598867613822222,
0.008595692925155163,
-0.0317482128739357,
-0.03158150613307953,
0.02768048457801342,
-0.019833000376820564,
-0.052236564457416534,
0.02641681768000126,
-0.027002710849046707,
0.0212894044816494,
-0.028656022623181343,
0.004405714105814695,
-0.027462894096970558,
0.03063652105629444,
-0.03258281946182251,
0.02909783273935318,
-0.041805751621723175,
0.03815843164920807,
-0.017999567091464996,
0.02053365297615528,
0.006707813125103712,
0.0035260100848972797,
-0.031922709196805954,
0.03972739353775978,
0.00046776814269833267,
-0.012944310903549194,
-0.020962093025445938,
0.013055901974439621,
-0.012686877511441708,
-0.006438407581299543,
0.01865110546350479,
-0.016911637037992477,
0.04610225185751915,
-0.007922790944576263,
-0.05241651087999344,
-0.004095037467777729,
-0.025419970974326134,
-0.021918360143899918,
0.03997951000928879,
-0.0029028160497546196,
0.022613734006881714,
0.017774412408471107,
-0.0702873170375824,
0.003189442213624716,
0.034441303461790085,
-0.01644582487642765,
-0.02886103466153145,
0.002470407634973526,
-0.015197823755443096,
-0.04855428263545036,
-0.02920864149928093,
0.023512670770287514,
-0.03099614754319191,
0.0051458729431033134,
0.0206068716943264,
0.02256406471133232,
-0.034495364874601364,
-0.019475121051073074,
0.03100571036338806,
0.015458997339010239,
-0.02778257615864277,
0.023850610479712486,
0.028051316738128662,
0.02185298316180706,
0.05899418517947197,
-0.03279322013258934,
0.0017389986896887422,
-0.009959214366972446,
0.01846906915307045,
-0.10234128683805466,
0.00809953361749649,
-0.0002145927574019879,
0.0025976747274398804,
0.04119158908724785,
-0.04628361761569977,
-0.009148282930254936,
0.026945462450385094,
-0.0620681457221508,
-0.019133836030960083,
-0.031332649290561676,
0.02826535329222679,
-0.010110310278832912,
-0.011896784417331219,
0.025375748053193092,
0.010483448393642902,
-0.005534463096410036,
0.03533518314361572,
0.0037959814071655273,
0.010468042455613613,
-0.009934778325259686,
-0.04857388511300087,
0.03986457362771034,
0.04982283338904381,
-0.019740063697099686,
-0.03863486647605896,
0.09664736688137054,
-0.029827844351530075,
-0.021658938378095627,
0.018642760813236237,
-0.02076386660337448,
0.015586030669510365,
-0.006967464927583933,
0.02558690495789051,
-0.04852278530597687,
0.03508317470550537,
0.00699373334646225,
0.004584736656397581,
-0.007468053605407476,
0.023168759420514107,
0.029822025448083878,
0.0027033474761992693,
-0.07328681647777557,
-0.0018610601546242833,
0.009729819372296333,
-0.04083980247378349,
-0.05674005672335625,
0.02211918868124485,
-0.0482853539288044,
0.004402876831591129,
0.02161041833460331,
0.000678824435453862,
-0.01054033637046814,
-0.03146423399448395,
-0.05804184079170227,
-0.04290139302611351,
0.017739102244377136,
0.024922821670770645,
-0.05137394368648529,
0.01634569652378559,
-0.0053786421194672585,
0.005003646481782198,
-0.01379939541220665,
0.026145227253437042,
-0.004310016520321369,
-0.056550655514001846,
-0.05072035267949104,
0.011272973380982876,
-0.001716728787869215,
-0.002492354018613696,
-0.02327185682952404,
-0.023855319246649742,
0.002189098158851266,
0.018787434324622154,
0.026850920170545578,
0.023619331419467926,
0.019610809162259102,
-0.008013197220861912,
-0.036331869661808014,
-0.057655904442071915,
0.03443554416298866,
-0.015432007610797882,
-0.020866824313998222,
-0.014787147752940655,
-0.02378980815410614,
0.0017896420322358608,
-0.002810779260471463,
0.03972840681672096,
-0.029795698821544647,
-0.03232574090361595,
0.05732709541916847,
-0.011152719147503376,
-0.00873066857457161,
-0.006406459491699934,
0.007921102456748486,
-0.024710601195693016,
-0.023034416139125824,
0.031171085312962532,
0.010668337345123291,
0.004172967281192541,
-0.0048330435529351234,
0.005461565684527159,
-0.013434719294309616,
0.030217746272683144,
-0.005309865809977055,
-0.03869852051138878,
0.0154993562027812,
0.015732984989881516,
-0.010474353097379208,
0.07379165291786194,
-0.0008834584150463343,
0.013807041570544243,
0.020305760204792023,
-0.05447114631533623,
-0.026595760136842728,
0.06983129680156708,
-0.0423932783305645,
-0.004256941843777895,
-0.0241878479719162,
-0.038136184215545654,
0.010028529912233353,
-0.08056459575891495,
-0.01771494373679161,
0.04001832753419876,
-0.0029293226543813944,
0.004661206156015396,
-0.0005107671022415161,
0.009016241878271103,
0.04348209500312805,
-0.0194390919059515,
0.03402165696024895,
0.04081115871667862,
-0.00955726858228445,
0.0073267254047095776,
0.017216484993696213,
0.018881140276789665,
-0.014042251743376255,
0.00637683505192399,
0.018509773537516594,
0.00847287941724062,
0.03489435464143753,
0.0024476549588143826,
0.048012591898441315,
-0.004589863587170839,
-0.04264410212635994,
-0.01372565794736147,
0.005259288474917412,
-0.028205974027514458,
0.035631075501441956,
-0.021392159163951874,
0.05526592582464218,
-0.0011452684411779046,
0.0012906292686238885,
0.006045414134860039,
-0.002402850892394781,
-0.03753333166241646,
-0.009797682985663414,
0.030805537477135658,
0.02875572256743908,
-0.025397179648280144,
-0.013526612892746925,
-0.010130676440894604,
0.01135687530040741,
0.026938417926430702,
0.00536392442882061,
0.024416105821728706,
0.03071456588804722,
-0.01302273664623499,
-0.00521245039999485,
-0.035063840448856354,
-0.03566437587141991,
-0.05740153789520264,
0.03745533153414726,
0.03581726923584938,
0.042138226330280304,
-0.016036279499530792,
0.012780847027897835,
0.0017077387310564518,
0.07403233647346497,
-0.05187085270881653,
0.003472529351711273,
0.024500392377376556,
0.011996898800134659,
-0.01938519813120365,
-0.007396915461868048
] |
<p>My textbook states that "Ideally, we would like to have measurements of pressure versus altitude over the specific range for the specific conditions (temperature, reference pressure) for which the pressure is to be determined. However, this type of information is usually not available. Thus, a "standard atmosphere" has been determined that can be used in the design of aircraft..."</p>
<p>"The standard atmosphere is an idealized representation of mean conditions in the earth's atmosphere"</p>
<p>My question is, why can't we determine how pressure varies with altitude. Say we want to know the pressure at 1000 m. Why can't we measure the pressure at 1000 m for different temperatures?</p>
| 9,426 |
[
-0.04243505001068115,
-0.004054464865475893,
-0.01760076731443405,
0.0021210433915257454,
0.04442249611020088,
0.0005006493302062154,
-0.013530601747334003,
-0.02630111575126648,
0.011500497348606586,
-0.019531909376382828,
0.04221058264374733,
0.06333829462528229,
0.0464613251388073,
0.003636411391198635,
0.002000940963625908,
-0.007463224697858095,
-0.027396326884627342,
0.015159252099692822,
-0.005960702896118164,
-0.010443403385579586,
-0.03472263738512993,
0.024219481274485588,
0.003381321905180812,
-0.006653802935034037,
-0.005862624384462833,
0.01689840853214264,
0.021073898300528526,
-0.011931449174880981,
0.05053209140896797,
0.04683658853173256,
-0.028624337166547775,
-0.002843966707587242,
0.0225090142339468,
0.023134328424930573,
0.04434443637728691,
-0.003674374893307686,
-0.01896830089390278,
-0.00021014201047364622,
-0.030730513855814934,
0.057076506316661835,
-0.02498544007539749,
-0.01656777784228325,
0.023128114640712738,
0.004000616259872913,
-0.0356934480369091,
0.03901536762714386,
0.030016019940376282,
-0.02649421989917755,
0.018493007868528366,
-0.06809309870004654,
0.021917229518294334,
-0.027923526242375374,
0.0362042672932148,
0.0893123671412468,
-0.005365587305277586,
0.008253302425146103,
0.0697527751326561,
0.06451742351055145,
-0.02030850388109684,
-0.035726457834243774,
-0.02084098942577839,
-0.006614771205931902,
0.0037832988891750574,
0.010480399243533611,
-0.01939108781516552,
-0.0009504107874818146,
-0.00460740365087986,
-0.014522534795105457,
0.037987299263477325,
-0.015317931771278381,
0.01768137887120247,
0.027307745069265366,
-0.009737263433635235,
-0.037638772279024124,
0.03987520560622215,
-0.028015632182359695,
0.014914101921021938,
0.01791728101670742,
0.07911281287670135,
0.0498880110681057,
0.009567671455442905,
0.017814407125115395,
0.024414490908384323,
0.008906451985239983,
-0.0004207562014926225,
0.01030133105814457,
0.07578804343938828,
-0.004116628784686327,
-0.02048812061548233,
0.04444238916039467,
0.034879546612501144,
0.0028152114246040583,
0.008858981542289257,
-0.010825011879205704,
0.01075313612818718,
0.018237818032503128,
-0.035159554332494736,
0.05448625609278679,
-0.009601225145161152,
-0.04098520055413246,
0.029205255210399628,
-0.0064329057931900024,
0.02479216828942299,
0.027254696935415268,
0.007744218222796917,
-0.009943845681846142,
-0.02164331264793873,
0.012452992610633373,
0.026951726526021957,
0.002829316072165966,
-0.023406794294714928,
0.00194786605425179,
-0.013687998987734318,
-0.007540376391261816,
0.021421827375888824,
0.015536397695541382,
0.03215046226978302,
-0.022192561998963356,
0.024878904223442078,
0.03506135568022728,
0.056400321424007416,
0.0046711754985153675,
0.007079365663230419,
-0.0011140310671180487,
-0.06198570132255554,
0.044082894921302795,
-0.001778503879904747,
0.006086822133511305,
-0.02520223706960678,
0.011903458274900913,
-0.010144926607608795,
-0.01617751456797123,
0.015262953005731106,
0.010379476472735405,
0.06217622384428978,
-0.024370376020669937,
-0.11081381142139435,
-0.06448692828416824,
0.009614813141524792,
0.03550425171852112,
-0.02872360683977604,
-0.05404232442378998,
0.021431462839245796,
0.015271230600774288,
0.032154954969882965,
0.0011634054826572537,
0.030843030661344528,
-0.026269426569342613,
0.010787789709866047,
0.01779995486140251,
0.00041875234455801547,
-0.013374404050409794,
0.0095075573772192,
-0.06502430886030197,
-0.009892421774566174,
-0.07950563728809357,
-0.011915450915694237,
-0.006572435609996319,
-0.02658982202410698,
-0.027310973033308983,
0.030637722462415695,
-0.011680659838020802,
-0.018044808879494667,
-0.02139781415462494,
0.019269730895757675,
-0.012011071667075157,
0.0729137435555458,
0.003664843738079071,
-0.010183081030845642,
0.03040592558681965,
0.007277383469045162,
0.02688400074839592,
-0.030043939128518105,
-0.0002256944280816242,
0.06528540700674057,
-0.011869438923895359,
-0.00946437194943428,
-0.03817298263311386,
0.017066672444343567,
0.016684208065271378,
-0.03602802753448486,
-0.0051954067312181,
0.02305537648499012,
0.028524501249194145,
-0.000955871248152107,
0.053429149091243744,
0.003740045242011547,
0.005450723227113485,
0.01753585785627365,
-0.05687827616930008,
-0.02392386458814144,
-0.057595882564783096,
0.025775030255317688,
-0.021375281736254692,
0.003290936117991805,
0.03318934142589569,
-0.008539529517292976,
0.01992795057594776,
-0.06337399780750275,
-0.03892533853650093,
0.010331953875720501,
0.0018128158990293741,
0.05083015188574791,
-0.008711655624210835,
0.05044730380177498,
0.049429696053266525,
0.05460312217473984,
0.008385731838643551,
0.002966185100376606,
-0.013524016365408897,
-0.056980013847351074,
-0.008273412473499775,
-0.06940795481204987,
-0.0030961534939706326,
0.037931058555841446,
-0.00737675279378891,
-0.0024512603413313627,
0.027657797560095787,
-0.007870552130043507,
0.03888192027807236,
-0.010200693272054195,
0.07734184712171555,
0.04214292764663696,
-0.0037741707637906075,
0.016162920743227005,
0.04267392307519913,
0.03336706385016441,
-0.002241093199700117,
0.008505177684128284,
-0.03789092227816582,
-0.035111088305711746,
-0.02239828370511532,
0.0028419536538422108,
0.00351742678321898,
-0.047846436500549316,
0.0004640660772565752,
0.04765160754323006,
0.03400088846683502,
0.035352401435375214,
0.03421862795948982,
0.030695384368300438,
-0.04751759395003319,
0.027180928736925125,
0.017855456098914146,
0.037070631980895996,
0.044171787798404694,
0.023895472288131714,
0.03370383009314537,
0.020766424015164375,
-0.016009513288736343,
-0.01819068193435669,
0.053654223680496216,
-0.009744898416101933,
0.03871434926986694,
0.013312606140971184,
0.012740926817059517,
0.015431324020028114,
-0.04222842678427696,
0.02975141629576683,
0.024616647511720657,
-0.023980360478162766,
-0.0033820555545389652,
-0.005561725702136755,
-0.012034733779728413,
0.014947711490094662,
0.03086761198937893,
-0.005899988114833832,
0.014575397595763206,
0.01595889776945114,
-0.061490513384342194,
0.020914703607559204,
-0.04793759435415268,
-0.006812277715653181,
-0.05527908727526665,
-0.02701708674430847,
0.04031439125537872,
0.0012658530613407493,
0.026427431032061577,
0.020940370857715607,
-0.04936641827225685,
-0.018158061429858208,
-0.05128459632396698,
0.007958545349538326,
0.004382401239126921,
-0.008087745867669582,
-0.005324403755366802,
-0.021720588207244873,
-0.03758305311203003,
0.01186694111675024,
-0.027573909610509872,
0.006225230637937784,
0.007393863517791033,
-0.035367269068956375,
-0.03537143021821976,
0.0070966025814414024,
-0.03799090161919594,
-0.03486742451786995,
0.015875253826379776,
-0.03493179380893707,
0.05123316869139671,
-0.035621967166662216,
-0.015510644763708115,
0.05024771764874458,
-0.0675453469157219,
-0.032460398972034454,
-0.04882105439901352,
-0.012238279916346073,
0.003139202482998371,
-0.04350480064749718,
0.020212646573781967,
0.04102156683802605,
-0.05257298797369003,
-0.05056246742606163,
-0.019864698871970177,
-0.056266866624355316,
-0.007528885267674923,
0.009197100065648556,
0.0326516330242157,
-0.005370328202843666,
-0.025080954656004906,
0.08396197855472565,
-0.005524512846022844,
-0.03791376203298569,
-0.03016000986099243,
0.001937664463184774,
-0.026790712028741837,
-0.03998576104640961,
0.007234765682369471,
0.012316933833062649,
-0.0269053652882576,
-0.0022499372716993093,
0.022507671266794205,
0.032939162105321884,
0.0279721450060606,
0.044887859374284744,
-0.015387170016765594,
-0.02555333822965622,
-0.013532931916415691,
0.024127954617142677,
0.09945815056562424,
0.00196017324924469,
-0.0249036718159914,
-0.015816137194633484,
-0.014089243486523628,
0.03562231361865997,
0.022588636726140976,
-0.04983118548989296,
0.045948777347803116,
-0.013013140298426151,
0.00929895881563425,
-0.0572848841547966,
0.013845616951584816,
-0.009017019532620907,
0.0007469627889804542,
0.017095452174544334,
0.02918620966374874,
0.02311367355287075,
-0.009095080196857452,
-0.05759643390774727,
0.051591575145721436,
0.07059412449598312,
-0.030315887182950974,
-0.01653333753347397,
0.03622667118906975,
-0.012070124968886375,
0.030195172876119614,
-0.02424117736518383,
-0.051871877163648605,
0.033840764313936234,
0.05970711261034012,
0.02172391302883625,
0.0015663520898669958,
-0.04890584200620651,
0.02844768762588501,
-0.05510501191020012,
-0.03057543933391571,
-0.005968356970697641,
0.06303336471319199,
-0.009012043476104736,
0.0753631666302681,
0.021870220080018044,
0.018409861251711845,
0.02341555804014206,
0.007856323383748531,
-0.08410809934139252,
0.013540488667786121,
-0.05176218971610069,
-0.037189386785030365,
-0.0015493930550292134,
-0.012469543144106865,
-0.015105605125427246,
-0.0430932454764843,
-0.007321590557694435,
-0.023584721609950066,
0.004754312336444855,
-0.043030668050050735,
-0.00479194475337863,
-0.017043432220816612,
-0.024076804518699646,
-0.045152366161346436,
0.05483390390872955,
0.02088017761707306,
-0.011289823800325394,
0.053680673241615295,
0.05924775451421738,
-0.02111591212451458,
-0.03148613125085831,
-0.027192221954464912,
0.012516956776380539,
0.00588529696688056,
0.044357772916555405,
0.0008513106731697917,
0.014671146869659424,
-0.02332197315990925,
0.016972960904240608,
0.027737068012356758,
0.04734766483306885,
-0.026368333026766777,
0.030058177188038826,
-0.011962362565100193,
-0.023450152948498726,
-0.008390584960579872,
0.03584451600909233,
-0.005335663445293903,
-0.006947504822164774,
0.008885784074664116,
0.012155886739492416,
-0.0048976787365973,
-0.031716398894786835,
0.05690213292837143,
0.017939874902367592,
-0.039811909198760986,
0.014962585642933846,
-0.020113440230488777,
-0.0241409819573164,
-0.07201188802719116,
-0.024533018469810486,
0.02817254327237606,
-0.0025397713761776686,
-0.024788927286863327,
-0.02340596914291382,
0.035806212574243546,
-0.0030604430940002203,
-0.00933844968676567,
-0.0072860377840697765,
0.01989097148180008,
0.003367261029779911,
-0.005232121795415878,
-0.015466298907995224,
0.005936770234256983,
0.01033808570355177,
0.016610097140073776,
-0.0029743267223238945,
-0.022752072662115097,
-0.08531810343265533,
-0.03211599960923195,
0.0003763109561987221,
0.008761931210756302,
-0.0012228311970829964,
0.001590900239534676,
-0.027337122708559036,
-0.025338182225823402,
0.045461371541023254,
0.004671153612434864,
0.030644578859210014,
-0.03770795837044716,
0.029207903891801834,
0.0007327714702114463,
-0.007311329245567322,
-0.007156915497034788,
0.01112894807010889,
0.026981795206665993,
-0.02139688841998577,
-0.014902702532708645,
0.02848449908196926,
-0.007033258676528931,
-0.005756308324635029,
0.01690167561173439,
0.05903782323002815,
0.01077182311564684,
-0.0005460038082674146,
0.014150614850223064,
0.0027755037881433964,
-0.0333719402551651,
-0.05403265357017517,
-0.03440123796463013,
-0.004301800858229399,
0.05120076239109039,
0.02640947885811329,
0.0034160662908107042,
-0.08960498124361038,
0.029130632057785988,
-0.02576443925499916,
-0.02080974355340004,
-0.0011325256200507283,
-0.004649674519896507,
0.051512476056814194,
0.03675379976630211,
0.005733209196478128,
0.03557491675019264,
0.019910333678126335,
0.012149328365921974,
0.014770814217627048,
-0.03367113694548607,
0.03338504955172539,
-0.05629552900791168,
-0.04389985278248787,
-0.022107863798737526,
0.007573979906737804,
-0.011565112508833408,
0.04577946290373802,
-0.012222860008478165,
0.014893583953380585,
-0.023228667676448822,
-0.06145267188549042,
0.014257403090596199,
0.007651017513126135,
0.024477412924170494,
0.01126811932772398,
-0.010163916274905205,
0.010548918507993221,
0.014339692890644073,
-0.03932516649365425,
-0.005494344048202038,
0.015703395009040833,
0.007902150973677635,
-0.01268936600536108,
-0.01527415867894888,
0.013835788704454899,
-0.05257349833846092,
-0.016057772561907768,
0.04106444865465164,
-0.04635770618915558,
0.06418301165103912,
-0.0072587342001497746,
0.03326902166008949,
0.04574619606137276,
-0.0409267321228981,
-0.04945210739970207,
0.02156601846218109,
-0.0186934731900692,
0.039390187710523605,
-0.039478689432144165,
0.013253862038254738,
-0.0036404388956725597,
0.0015393858775496483,
-0.05594027787446976,
-0.031446970999240875,
0.04021332040429115,
0.014759883284568787,
-0.006066692527383566,
-0.03413248434662819,
-0.01366502232849598,
-0.0008593663806095719,
-0.008199218660593033,
-0.012886740267276764,
0.04169438034296036,
0.0019485483644530177,
-0.06314796954393387,
-0.0018468499183654785,
0.020891454070806503,
0.05202754959464073,
-0.01945854350924492,
-0.018687518313527107,
0.0007997936336323619,
0.009782345965504646,
-0.018030360341072083,
-0.028978196904063225,
0.015537218190729618,
-0.017114505171775818,
-0.03373108431696892,
-0.003836026880890131,
-0.019855374470353127,
0.019854029640555382,
-0.03823898732662201,
0.03527946397662163,
0.022808484733104706,
-0.012461293488740921,
0.02313043549656868,
-0.019919436424970627,
0.036368776112794876,
-0.010382939130067825,
0.016813306137919426,
-0.031105639412999153,
0.0002402515965513885,
-0.025875704362988472,
-0.013447131961584091,
0.01755543239414692,
0.00519513338804245,
-0.0013569151051342487,
0.0007301036966964602,
0.062165267765522,
0.029086299240589142,
-0.028602106496691704,
0.006966635584831238,
-0.011141112074255943,
-0.005657630041241646,
0.030766701325774193,
-0.020910728722810745,
0.055755071341991425,
0.04163680970668793,
-0.01506990659981966,
-0.02444792538881302,
-0.024232663214206696,
0.012304620817303658,
0.07418790459632874,
0.013220964930951595,
0.08287500590085983,
0.014037667773663998,
-0.005823352374136448,
0.013833694159984589,
-0.038401536643505096,
-0.025109149515628815,
0.006164650898426771,
-0.003377970540896058,
0.02940865233540535,
-0.0014227788196876645,
0.011060532182455063,
0.009611571207642555,
0.019167451187968254,
0.004796833731234074,
0.012970774434506893,
0.027761287987232208,
0.03757452592253685,
0.018273426219820976,
0.009105520322918892,
-0.048405274748802185,
0.08721919357776642,
-0.029868032783269882,
0.011040477082133293,
0.002831911901012063,
0.017401712015271187,
0.025450656190514565,
0.0012542677577584982,
0.0036608048249036074,
-0.06750287860631943,
0.0014955061487853527,
-0.027957733720541,
0.018440047279000282,
0.002888862509280443,
-0.012872324325144291,
0.034425146877765656,
0.004646298475563526,
0.01983718015253544,
-0.040470898151397705,
-0.014238192699849606,
-0.013604726642370224,
-0.026475919410586357,
-0.04978161305189133,
-0.019897179678082466,
-0.055115241557359695,
0.04510503262281418,
-0.025659959763288498,
-0.05082981288433075,
0.011907917447388172,
-0.00600758520886302,
0.016604041680693626,
-0.0029063448309898376,
0.011322674341499805,
-0.010195757262408733,
0.05499862879514694,
0.008306678384542465,
-0.0007717263652011752,
-0.0029103709384799004,
0.0455959178507328,
0.10607224702835083,
0.02630631811916828,
0.02701312117278576,
-0.04596152529120445,
0.013090035878121853,
-0.014052515849471092,
0.00653590215370059,
-0.027719825506210327,
0.043836016207933426,
0.018513208255171776,
0.011235099285840988,
0.0071473438292741776,
0.05097135156393051,
-0.005754720885306597,
-0.005659517832100391,
0.06924690306186676,
-0.02929980307817459,
-0.00031702680280432105,
-0.002649494679644704,
0.007774502970278263,
-0.028334615752100945,
0.024528900161385536,
-0.007086208090186119,
0.0515211783349514,
-0.04019726440310478,
-0.002901931758970022,
-0.011712195351719856,
-0.0279517974704504,
0.017318105325102806,
0.00850463006645441,
-0.04530194401741028,
0.011275691911578178,
0.038466423749923706,
-0.00545226177200675,
-0.0643293634057045,
0.013573014177381992,
-0.0019668147433549166,
-0.006940871011465788,
-0.002301324624568224,
0.036183882504701614,
0.0062139881774783134,
-0.0022608779836446047,
-0.022768331691622734,
0.0018538349540904164,
-0.028732089325785637,
-0.04167959839105606,
-0.008221473544836044,
0.02867833897471428,
0.0007740071159787476,
-0.038220662623643875,
-0.00495996093377471,
0.011237701401114464,
-0.02315135858952999,
-0.05065720155835152,
-0.02100127376616001,
-0.019383667036890984,
0.02027207240462303,
-0.03005947545170784,
-0.05744253098964691,
-0.01115114800632,
0.013449038378894329,
0.010018286295235157,
0.01497085951268673,
-0.0043413578532636166,
0.008736694231629372,
-0.019951434805989265,
-0.035083796828985214,
0.027366062626242638,
-0.027484504505991936,
0.0023065507411956787,
-0.012334000319242477,
-0.0006829497870057821,
-0.04229586198925972,
-0.030469467863440514,
0.03242484852671623,
0.02389155887067318,
0.04290256276726723,
0.04422726482152939,
-0.018478261306881905,
0.009928782470524311,
0.001888303435407579,
0.034993547946214676,
-0.003246201667934656,
-0.04390466585755348,
-0.0015420453855767846,
-0.008427053689956665,
-0.004565560258924961,
0.07018932700157166,
0.0209860447794199,
-0.01837417110800743,
0.035797953605651855,
0.011050279252231121,
0.025562696158885956,
-0.051912643015384674,
-0.04724038019776344,
0.03658905625343323,
-0.060808874666690826,
0.04115648940205574,
0.03374461457133293,
0.05892961099743843,
0.04154684394598007,
0.02747965045273304,
-0.013667775318026543,
0.026209458708763123,
-0.02533337101340294,
0.022409703582525253,
0.016454046592116356,
-0.028687266632914543,
0.029849708080291748,
-0.017337383702397346,
0.017858151346445084,
-0.033377259969711304,
0.0065961177460849285,
-0.04427763447165489,
0.015933450311422348,
-0.010826077312231064,
-0.02204751968383789,
0.015482249669730663,
0.053622983396053314,
-0.007935631088912487,
-0.007062533404678106,
-0.06005669757723808,
0.0025317163672298193,
-0.05429632589221001,
0.010823624208569527,
-0.01560267899185419,
-0.02308279275894165,
-0.013962243683636189,
0.003950637299567461,
-0.07594124972820282,
-0.007682444527745247,
0.04021372273564339,
0.031732045114040375,
-0.008585863746702671,
-0.011972224339842796,
-0.01769026555120945,
0.01341373659670353,
0.054913684725761414,
-0.06044862046837807,
-0.013328314758837223,
0.038832005113363266,
-0.010608578100800514,
-0.05401482805609703,
0.03213601931929588,
0.021028030663728714,
0.03954073414206505,
0.05059792101383209,
-0.009777146391570568,
-0.04847777262330055,
0.0321200005710125,
-0.00625061197206378,
0.006480639800429344,
-0.02681184746325016,
0.010056738741695881,
0.01358706597238779,
0.008247699588537216,
0.00011018903023796156,
-0.04106050729751587,
0.005459983833134174,
0.015856590121984482,
0.015152858570218086,
0.011974481865763664,
-0.003960897214710712,
0.010673904791474342,
-0.006567773409187794,
0.022278498858213425,
0.016985690221190453,
0.01792254112660885,
0.02506849728524685,
0.039108432829380035,
-0.04807598888874054,
0.03471873328089714,
0.018867792561650276,
0.002238909015432,
-0.09454844892024994,
-0.011591022834181786,
-0.007365045137703419,
0.008436593227088451,
0.025089049711823463,
-0.006631174590438604,
-0.00037530329427681863,
0.04172321408987045,
-0.07339706271886826,
-0.0322306752204895,
-0.034182507544755936,
-0.025857439264655113,
-0.02632165141403675,
-0.005676231812685728,
0.015774274244904518,
0.052269283682107925,
0.04523921012878418,
0.009788124822080135,
0.0061931791715323925,
-0.012330207042396069,
0.041315946727991104,
-0.006756734102964401,
-0.01738770306110382,
-0.018406376242637634,
-0.008731314912438393,
-0.007555454969406128,
0.03954227268695831,
-0.02838858589529991,
-0.025708874687552452,
0.03372998163104057,
-0.014420329593122005,
0.01720319874584675,
-0.009328057989478111,
-0.008016044273972511,
-0.029637936502695084,
0.032857079058885574,
0.018969755619764328,
-0.010718990117311478,
-0.031683698296546936,
0.009520909748971462,
0.01591814123094082,
0.010101057589054108,
-0.004020948428660631,
-0.009057167917490005,
0.010492376983165741,
-0.037072401493787766,
-0.045925721526145935,
0.030794290825724602,
-0.010959966108202934,
-0.030680153518915176,
0.03589513897895813,
0.03104839287698269,
-0.010517815127968788,
-0.038563527166843414,
-0.012637780979275703,
-0.04268854856491089,
0.02574882097542286,
0.0279396865516901,
0.029862703755497932,
-0.022714942693710327,
0.0062364935874938965,
-0.01127039734274149,
-0.01696740835905075,
0.04820392653346062,
0.02019413933157921,
-0.045066170394420624,
-0.03383418917655945,
-0.02074449695646763,
-0.02240932732820511,
-0.048242997378110886,
-0.01193877961486578,
-0.027092624455690384,
-0.03468798100948334,
0.006357206031680107,
0.0018213213188573718,
0.010074052959680557,
-0.035014599561691284,
-0.046891581267118454,
-0.011592846363782883,
-0.06266672164201736,
0.06852633506059647,
-0.019561437889933586,
0.015375485643744469,
-0.0535789430141449,
-0.018774937838315964,
-0.03183705359697342,
0.024871118366718292,
0.05018443241715431,
0.041574977338314056,
-0.0037586812395602465,
0.004252159036695957,
-0.004110031295567751,
-0.0026802795473486185,
-0.01875440590083599,
0.026804549619555473,
0.04288192838430405,
-0.05400107800960541,
0.022980598732829094,
-0.03486715257167816,
-0.0060185519978404045,
0.0179966501891613,
0.05219919607043266,
-0.03224436566233635,
0.039025962352752686,
0.03098217397928238,
-0.0023662527091801167,
0.03172149881720543,
0.013280937448143959,
-0.023721469566226006,
0.043189648538827896,
-0.0012008873745799065,
-0.0029627785552293062,
0.029552914202213287,
0.011922754347324371,
-0.04316457733511925,
0.04226001352071762,
-0.016913115978240967,
-0.03922010585665703,
-0.022431444376707077,
0.03049902617931366,
0.007381128612905741,
-0.05114078149199486,
0.007598708383738995,
0.03583414852619171,
-0.04779796302318573,
-0.019640905782580376,
0.07112792879343033,
0.02945956215262413,
0.025525683537125587,
-0.04991171881556511,
0.006404343992471695,
0.017140790820121765,
-0.022430498152971268,
0.022164776921272278,
0.03132963925600052,
0.07270637154579163,
0.0021785071585327387,
0.014160328544676304,
0.031655218452215195,
-0.0044199214316904545,
0.0065915584564208984,
0.0534861721098423,
0.06887699663639069,
-0.02748185396194458,
-0.06176302954554558,
-0.012126147747039795,
-0.013428756035864353,
0.017870929092168808,
0.027694277465343475,
-0.005232515744864941,
0.06063586845993996,
-0.015792379155755043,
-0.016056828200817108,
-0.046102505177259445,
0.017240939661860466,
-0.03755444288253784,
0.011924413032829762,
0.008833412081003189,
0.01899031177163124,
-0.0049230135045945644,
0.004739024676382542,
0.009210284799337387,
0.01805180124938488,
0.024115974083542824,
-0.018962472677230835,
0.019772229716181755,
-0.0403425395488739,
-0.03363598510622978,
-0.03537972271442413,
0.005715967155992985,
-0.03300674632191658,
0.015920991078019142,
0.052332788705825806,
0.040031809359788895,
0.052066296339035034,
0.027514532208442688,
-0.03881445899605751,
-0.04229895398020744,
0.03245330974459648,
-0.08778701722621918,
-0.036627549678087234,
-0.009515075944364071,
0.03064245730638504,
-0.009591035544872284,
-0.026874655857682228
] |
<p>Could you please, explain to me the logic of the folllowing process as you would do to your 8 y/o sister:</p>
<blockquote>
<p>Ubiquitousness and stability of atoms relies on their binding energy,
which means that an atom has a lower energy than an unbound system of
the nucleus and electrons. Where the temperature is much higher than
ionization potential, the matter exists in the form of plasma – a gas
of positively-charged ions and electrons. When the temperature drops
below the ionization potential, atoms become statistically favorable.</p>
</blockquote>
<p>Source: <a href="http://en.wikipedia.org/wiki/Atom" rel="nofollow">wiki</a></p>
<p>How that that binding energy can be explained in plain English? Is it somewhat intrinsic to atoms, with each kind having its own level of binding energy? I understand that this can be translated in the language of closed systems using terms as Gnatt energy (G), etc. - but how?</p>
| 9,427 |
[
-0.052480973303318024,
-0.06914257258176804,
0.031887952238321304,
-0.04951713606715202,
-0.0014799030032008886,
-0.004668417386710644,
-0.03714936971664429,
-0.011991268955171108,
0.034799251705408096,
-0.0260629840195179,
0.03959757834672928,
0.02461392804980278,
0.028532834723591805,
-0.013115855865180492,
0.011175902560353279,
0.00859019160270691,
0.013773107901215553,
-0.07224313914775848,
0.013470344245433807,
-0.025504495948553085,
0.01403413712978363,
-0.005064745899289846,
-0.057650528848171234,
0.012306688353419304,
-0.024685554206371307,
0.03767893463373184,
0.011430284939706326,
-0.031845077872276306,
0.03945121169090271,
0.03814041614532471,
-0.009844397194683552,
0.0036024462897330523,
0.02812081202864647,
-0.003327546175569296,
0.037683840841054916,
0.014179234392940998,
-0.03869910165667534,
0.0008801986114121974,
-0.015560995787382126,
0.023511404171586037,
-0.03800802305340767,
-0.027971334755420685,
-0.03463650122284889,
0.00221151951700449,
-0.034151963889598846,
-0.024195628240704536,
0.003289937973022461,
-0.00773478951305151,
0.05147261545062065,
-0.03604338690638542,
0.021612057462334633,
-0.00016056500317063183,
0.038555681705474854,
0.02652248553931713,
-0.011025152169167995,
-0.008389148861169815,
0.07446739822626114,
0.06430023163557053,
-0.02130042016506195,
-0.023203304037451744,
-0.044901374727487564,
0.0006133353454060853,
-0.03141798451542854,
0.023554731160402298,
0.015131896361708641,
-0.00689880782738328,
0.009915442205965519,
-0.05991964787244797,
0.014561336487531662,
0.025145607069134712,
0.005519289989024401,
0.022152267396450043,
0.06387706845998764,
-0.004444401245564222,
0.041415441781282425,
-0.01010988000780344,
0.038040801882743835,
0.018460072576999664,
0.03349091485142708,
0.03187980502843857,
-0.02088606357574463,
-0.0003119746979791671,
0.023292643949389458,
0.045012351125478745,
-0.018285226076841354,
-0.052274588495492935,
0.055666372179985046,
-0.026949577033519745,
0.03623935580253601,
0.07463032752275467,
-0.0242364052683115,
-0.005185123533010483,
0.03350241482257843,
0.028267154470086098,
-0.04954627901315689,
0.002649543574079871,
0.0365457721054554,
0.05897648632526398,
-0.0019994480535387993,
0.04686938598752022,
0.027761269360780716,
-0.02234167605638504,
0.011753706261515617,
0.06932716816663742,
0.0014070479664951563,
-0.009424332529306412,
-0.036104608327150345,
0.02297895774245262,
-0.012430082075297832,
0.03608798235654831,
-0.0284121073782444,
-0.00046939568710513413,
0.013989867642521858,
-0.030217690393328667,
0.0032028919085860252,
-0.0298758652061224,
0.012961054220795631,
0.021717986091971397,
0.06515765190124512,
0.019477328285574913,
0.0004032118013128638,
-0.008158640004694462,
0.03160380572080612,
0.006905412767082453,
-0.046259939670562744,
0.0155331427231431,
0.023871032521128654,
-0.03947848081588745,
-0.027303602546453476,
0.02111249417066574,
-0.030866555869579315,
-0.0067955562844872475,
-0.005326190497726202,
-0.004718675743788481,
0.017955712974071503,
-0.017409062013030052,
-0.09411277621984482,
-0.04378753527998924,
0.04804956540465355,
0.00432675052434206,
0.006166310515254736,
-0.10645320266485214,
0.010061574168503284,
-0.0005392266903072596,
0.04162762314081192,
0.01901588961482048,
-0.04289977625012398,
-0.019749438390135765,
0.0030966298654675484,
0.026154272258281708,
-0.011708848178386688,
-0.01166568510234356,
-0.0048444014973938465,
-0.04883894696831703,
-0.026317456737160683,
-0.09052148461341858,
0.054990801960229874,
0.02025807835161686,
-0.024151355028152466,
0.007128496188670397,
0.03762076050043106,
-0.032335150986909866,
-0.011591787450015545,
0.0032037454657256603,
0.011550014838576317,
-0.03772753104567528,
0.08578481525182724,
0.018540076911449432,
-0.004857016261667013,
0.07356689125299454,
0.008760396391153336,
0.024073351174592972,
-0.013359185308218002,
0.03806636855006218,
0.001939169829711318,
-0.031101562082767487,
0.002453551162034273,
-0.05807530879974365,
0.00514252157881856,
0.002973860129714012,
0.003521493636071682,
-0.026605620980262756,
-0.003817111486569047,
-0.006117559969425201,
0.0006819919217377901,
-0.005104536190629005,
0.013161156326532364,
-0.007103174924850464,
-0.009742731228470802,
-0.035322465002536774,
-0.0052075679413974285,
-0.08612867444753647,
0.023175355046987534,
-0.022786034271121025,
-0.0009899871656671166,
0.040194202214479446,
-0.0003833744558505714,
-0.0029435548931360245,
-0.036021750420331955,
-0.03888789564371109,
-0.022867729887366295,
0.029596827924251556,
-0.014251459389925003,
-0.02180437184870243,
0.02214771881699562,
0.09500686079263687,
0.008791711181402206,
-0.014249876141548157,
0.020459027960896492,
-0.04336407780647278,
-0.017505507916212082,
-0.03139964118599892,
0.012076372280716896,
0.03603445366024971,
0.054851070046424866,
-0.0008968270267359912,
0.024651944637298584,
-0.019064556807279587,
0.027254225686192513,
0.01274893805384636,
-0.027688121423125267,
0.037061143666505814,
0.031139373779296875,
0.021548187360167503,
0.025021687150001526,
0.04428253322839737,
-0.011017624288797379,
0.02186605893075466,
0.012434588745236397,
-0.030576027929782867,
-0.03720570728182793,
-0.03907829895615578,
0.019194772467017174,
0.03853605315089226,
-0.029392100870609283,
0.020525725558400154,
0.00716736912727356,
0.03396730124950409,
0.048047419637441635,
-0.007027337793260813,
-0.025143347680568695,
0.0059752631932497025,
0.03814924135804176,
-0.023026658222079277,
0.01311782281845808,
0.015318457037210464,
-0.00010050945274997503,
0.01627826876938343,
0.012299321591854095,
0.004182946868240833,
-0.006346350070089102,
0.023159055039286613,
0.047792721539735794,
0.01609247550368309,
-0.010355737991631031,
-0.040941983461380005,
0.04310932382941246,
-0.020088519901037216,
0.04908121004700661,
0.07025747746229172,
-0.023488586768507957,
-0.0035148963797837496,
-0.04487123340368271,
-0.01841672509908676,
0.022402843460440636,
0.015389564447104931,
-0.012521831318736076,
0.012825456447899342,
0.01970396190881729,
-0.02976433001458645,
0.01940736174583435,
0.01204241719096899,
-0.011202311143279076,
-0.02406172640621662,
0.01431260909885168,
0.013569524511694908,
0.016852032393217087,
-0.020975980907678604,
-0.023538127541542053,
-0.032889850437641144,
-0.018882697448134422,
-0.03579568490386009,
0.008246042765676975,
0.031705621629953384,
-0.023990938439965248,
-0.01933751441538334,
-0.009028542786836624,
0.0004249360063113272,
0.05444394424557686,
-0.023085514083504677,
0.009093483909964561,
-0.006749439984560013,
0.00856428686529398,
-0.016763634979724884,
0.008477971889078617,
-0.008509693667292595,
-0.05519607663154602,
-0.005508221220225096,
0.03658086434006691,
0.042976099997758865,
0.0006899465224705637,
-0.007753520738333464,
0.020596958696842194,
-0.05327809974551201,
-0.03091234341263771,
-0.023698946461081505,
-0.04418513923883438,
0.023030586540699005,
-0.0091392295435071,
0.04161207005381584,
0.04091254621744156,
-0.048130426555871964,
-0.0067841485142707825,
-0.04324148967862129,
-0.01754646562039852,
0.00511401891708374,
0.0029293966945260763,
0.03626863658428192,
0.01839999482035637,
-0.0379725880920887,
0.05236928537487984,
0.0004931666189804673,
-0.014999092556536198,
-0.004977676086127758,
-0.0008276630542241037,
-0.006689927540719509,
-0.008325391449034214,
0.01782119646668434,
0.04511847347021103,
0.009282284416258335,
-0.016114475205540657,
0.033766523003578186,
0.07079264521598816,
0.034360893070697784,
0.0071379439905285835,
-0.03123283199965954,
0.02740260399878025,
-0.00009785560541786253,
0.00570386927574873,
0.00720285065472126,
0.017945701256394386,
0.014112120494246483,
-0.0002653616538736969,
0.00671862019225955,
0.03837896138429642,
0.05398669093847275,
-0.06084449961781502,
0.02773376554250717,
0.02827530913054943,
-0.02043471857905388,
-0.045359332114458084,
0.02360183373093605,
-0.010504471138119698,
-0.06399717926979065,
0.009281959384679794,
-0.0027324524708092213,
0.03903014957904816,
-0.013500283472239971,
-0.024944288656115532,
0.025390619412064552,
0.05160985141992569,
-0.0031250957399606705,
-0.016002202406525612,
0.01207294687628746,
-0.03138232231140137,
0.021951807662844658,
-0.04086792841553688,
-0.011338597163558006,
0.006758706644177437,
0.003915805369615555,
0.008128807879984379,
-0.02822043187916279,
-0.06059956178069115,
-0.004834817722439766,
-0.06564249098300934,
-0.023846790194511414,
-0.02784476801753044,
0.04505091533064842,
-0.01673615723848343,
0.04026557132601738,
0.01790272444486618,
0.07419927418231964,
0.024370601400732994,
-0.02843799814581871,
-0.07811419665813446,
0.029060712084174156,
-0.026111561805009842,
-0.013003540225327015,
-0.035514507442712784,
0.03990146145224571,
-0.028707532212138176,
-0.013645644299685955,
-0.01540926843881607,
0.0032939868979156017,
0.022328242659568787,
-0.012921798042953014,
-0.03071620501577854,
-0.02392788976430893,
-0.03212988004088402,
-0.03696025535464287,
0.07401018589735031,
0.04887634888291359,
-0.02608601003885269,
0.03515196591615677,
0.021894773468375206,
-0.006852853111922741,
-0.04577222093939781,
-0.04137582331895828,
-0.0011769533157348633,
0.04197688400745392,
0.027952048927545547,
0.015063050203025341,
0.0027065330650657415,
-0.008012931793928146,
-0.03977235034108162,
0.028331508859992027,
0.02684503234922886,
0.0076759993098676205,
-0.005576102063059807,
0.0002495156950317323,
-0.043355945497751236,
-0.046287957578897476,
0.02627846784889698,
0.051909226924180984,
-0.020937878638505936,
0.05689823254942894,
-0.02544609270989895,
0.0017106715822592378,
-0.023041969165205956,
0.06280200928449631,
0.03248686343431473,
-0.01072146836668253,
-0.030196338891983032,
-0.01813552714884281,
0.02378338761627674,
-0.059227339923381805,
0.03024708665907383,
0.016086703166365623,
-0.0005924096331000328,
-0.021556830033659935,
-0.010827155783772469,
-0.022675026208162308,
0.052585385739803314,
-0.022702977061271667,
-0.018025364726781845,
-0.05622316524386406,
0.02792118676006794,
-0.030631931498646736,
0.0010345712071284652,
0.04231545329093933,
0.02094443514943123,
0.012120525352656841,
0.006848481483757496,
0.0032926611602306366,
-0.05733819305896759,
0.019163861870765686,
0.016884123906493187,
0.040822479873895645,
0.015389087609946728,
-0.004501014482229948,
-0.0485890693962574,
-0.026140840724110603,
0.0076566822826862335,
-0.04144779592752457,
0.010833526961505413,
-0.02951829694211483,
0.01189463958144188,
0.0006628934061154723,
-0.041310153901576996,
0.027027834206819534,
0.008807165548205376,
0.015619223937392235,
0.02234114520251751,
0.003197364741936326,
-0.007438254076987505,
0.00012259191134944558,
-0.0015964210033416748,
-0.01232125423848629,
0.049363911151885986,
-0.03575475513935089,
-0.02687845192849636,
0.015803014859557152,
-0.0020420937798917294,
-0.018701007589697838,
-0.08841907978057861,
-0.009719124995172024,
-0.01772398315370083,
-0.027204841375350952,
0.04497862607240677,
-0.027780631557106972,
-0.04590693861246109,
0.0044508567079901695,
0.0212534312158823,
-0.0003384342708159238,
-0.00573103129863739,
-0.024695271626114845,
0.08200068026781082,
0.020337551832199097,
-0.03344710171222687,
0.052623651921749115,
0.002190687693655491,
-0.04280563443899155,
-0.002592931967228651,
-0.03206195309758186,
0.023845117539167404,
-0.0681377723813057,
0.0016465159133076668,
-0.027867039665579796,
0.015792755410075188,
-0.0021883186418563128,
0.034806326031684875,
0.023631397634744644,
-0.007651600055396557,
-0.023621508851647377,
-0.05339553579688072,
0.016677048057317734,
-0.010456396266818047,
-0.013819682411849499,
-0.010130525566637516,
-0.022765936329960823,
0.0318833664059639,
-0.020782561972737312,
-0.018955526873469353,
0.030475497245788574,
-0.04000985249876976,
-0.009134138002991676,
0.0016858313465490937,
-0.009282665327191353,
0.017430901527404785,
-0.016935329884290695,
-0.016183774918317795,
0.034751471132040024,
-0.04464586079120636,
0.046974752098321915,
0.0025573265738785267,
0.01207499485462904,
0.006367665249854326,
-0.02463344670832157,
0.006620585452765226,
0.0014358644839376211,
-0.012027202174067497,
0.030194958671927452,
-0.00954335555434227,
0.04121469706296921,
-0.015339039266109467,
0.007234865799546242,
-0.05195354297757149,
-0.040220681577920914,
-0.0024945810437202454,
-0.015438484027981758,
-0.04683448001742363,
-0.03703032433986664,
-0.007177675608545542,
-0.04913340508937836,
-0.012594697065651417,
-0.019268816336989403,
0.014232857152819633,
-0.023527946323156357,
0.012405113317072392,
0.03774768114089966,
0.014445471577346325,
0.0738556757569313,
-0.01703064702451229,
-0.030448852106928825,
0.029210856184363365,
-0.025812361389398575,
0.006932631600648165,
0.0011351065477356315,
0.02110418863594532,
-0.01806012913584709,
-0.029899640008807182,
0.01597575843334198,
0.02189224772155285,
0.031187789514660835,
0.003165610833093524,
-0.025718437507748604,
0.04015230014920235,
0.02803402580320835,
0.018150275573134422,
-0.03446508198976517,
0.0016086520627140999,
-0.010419734753668308,
0.03317033872008324,
0.008064880967140198,
0.0023729829117655754,
-0.003049807623028755,
-0.014952698722481728,
0.04632069543004036,
0.01568099856376648,
0.016339479014277458,
0.04374200850725174,
0.061101771891117096,
-0.0005856198840774596,
0.006684957072138786,
0.03962494060397148,
-0.03082609735429287,
0.05604567751288414,
0.018421411514282227,
-0.015544528141617775,
-0.01188794244080782,
0.002260088687762618,
-0.05205006152391434,
-0.03220246732234955,
-0.06783623993396759,
0.029294589534401894,
0.01714383251965046,
-0.03485369682312012,
0.05937231332063675,
-0.029585810378193855,
-0.021029772236943245,
-0.0028575006872415543,
-0.06524885445833206,
0.006771659478545189,
0.004948205314576626,
0.009251817129552364,
0.0022413181141018867,
-0.002897067228332162,
0.01605195552110672,
0.014685692265629768,
0.08686265349388123,
-0.040630366653203964,
0.005616758484393358,
0.051725249737501144,
0.0293827336281538,
0.005565965082496405,
-0.042372819036245346,
-0.02547501027584076,
0.08020109683275223,
-0.05811316519975662,
0.04113627225160599,
0.007269422523677349,
0.017381904646754265,
0.046898238360881805,
-0.014920178800821304,
0.02358115091919899,
-0.03757218271493912,
-0.022658681496977806,
-0.025880947709083557,
0.0367022268474102,
0.03232400864362717,
-0.018287183716893196,
0.02590790018439293,
0.00606991071254015,
0.015962880104780197,
-0.00004181613985565491,
-0.01777982898056507,
-0.01619255356490612,
-0.02820628695189953,
-0.005598121788352728,
-0.058362528681755066,
-0.06105212867259979,
0.014548752456903458,
-0.029209310188889503,
-0.024935360997915268,
0.012446618638932705,
0.0006045715999789536,
0.020303264260292053,
0.01969989202916622,
0.04654073342680931,
0.0016891893465071917,
0.09868697822093964,
0.01281413808465004,
-0.01109092403203249,
0.0036821134854108095,
0.033311691135168076,
0.13715985417366028,
0.054533451795578,
-0.015726637095212936,
-0.048068005591630936,
-0.013405879028141499,
-0.019812367856502533,
0.0058860862627625465,
-0.0018293464090675116,
0.006027760449796915,
0.004028151743113995,
0.019928794354200363,
0.035814426839351654,
0.062278613448143005,
0.020130449905991554,
0.0542401559650898,
0.07137589156627655,
-0.03526679426431656,
-0.008343142457306385,
0.0059181335382163525,
-0.02817949652671814,
-0.0031719673424959183,
-0.0007367322104983032,
-0.02501017600297928,
-0.012604202143847942,
0.007693868596106768,
0.03392469510436058,
-0.01550830528140068,
0.006905287969857454,
0.05456332862377167,
-0.002675084164366126,
-0.03180849552154541,
0.0361139141023159,
0.02104930579662323,
0.02082277275621891,
-0.01020044181495905,
-0.02325226366519928,
0.02117075026035309,
-0.01532022561877966,
-0.0006795694353058934,
0.010847877711057663,
0.02219460904598236,
0.004904057830572128,
-0.01689763180911541,
0.010215497575700283,
0.012355407699942589,
-0.027278995141386986,
-0.026322223246097565,
0.036097005009651184,
-0.03347040340304375,
-0.015240072272717953,
0.002219036454334855,
0.040623877197504044,
-0.007505340501666069,
-0.03990059718489647,
-0.014621174894273281,
0.001972714439034462,
0.01821781136095524,
-0.02779303677380085,
-0.0050975605845451355,
-0.04096320644021034,
0.02082897536456585,
-0.023706037551164627,
-0.012605865485966206,
0.009034370072185993,
0.020937206223607063,
0.03776957467198372,
-0.03641417250037193,
0.0011706469813361764,
0.003828450571745634,
0.016137709841132164,
-0.011065336875617504,
0.01906110905110836,
-0.039240770041942596,
-0.026209574192762375,
0.0008570318459533155,
0.015921279788017273,
0.056264881044626236,
0.014323129318654537,
0.0064437598921358585,
-0.029736073687672615,
-0.031101929023861885,
0.05089251324534416,
0.013351531699299812,
-0.0379413440823555,
-0.0016435222933068871,
-0.013183360919356346,
-0.010991753078997135,
0.024030542001128197,
-0.019202860072255135,
0.030288631096482277,
0.012572775594890118,
0.024033334106206894,
-0.017132190987467766,
-0.020460503175854683,
-0.0603332445025444,
0.03277210146188736,
-0.016193052753806114,
-0.008378871716558933,
0.02568935975432396,
0.04280812293291092,
-0.0260093305259943,
-0.0029367711395025253,
0.04244116693735123,
0.03918187692761421,
-0.01766299270093441,
0.013160831294953823,
0.014681321568787098,
-0.005511974450200796,
-0.005386381410062313,
0.015850910916924477,
-0.060461316257715225,
0.012623696587979794,
-0.033954400569200516,
-0.004684928804636002,
-0.015107721090316772,
0.013516450300812721,
0.025757065042853355,
-0.021017925813794136,
0.03766271844506264,
-0.02546183206140995,
0.011390508152544498,
-0.020068461075425148,
-0.005346634425222874,
-0.03826306387782097,
0.01730433665215969,
0.025872305035591125,
-0.034251753240823746,
0.018054546788334846,
0.018155880272388458,
-0.03350631892681122,
-0.02236357517540455,
0.05365849658846855,
-0.004711979068815708,
-0.003196675330400467,
-0.006575784645974636,
-0.004641381092369556,
-0.027123477309942245,
0.03532304987311363,
-0.021106764674186707,
-0.03854367136955261,
0.00955591257661581,
-0.03526555746793747,
-0.07597041875123978,
-0.0211979690939188,
0.005492826923727989,
0.011937366798520088,
0.03954276442527771,
0.02243279665708542,
-0.024131201207637787,
0.08392468839883804,
-0.006639199797064066,
-0.018073206767439842,
0.026647347956895828,
0.001587140141054988,
-0.00417215283960104,
0.04192193225026131,
0.013657248578965664,
-0.042341962456703186,
0.007448370568454266,
0.02595553919672966,
0.03896428644657135,
-0.035013582557439804,
0.004772522486746311,
-0.02066842094063759,
-0.005370371509343386,
-0.030564401298761368,
0.0288039930164814,
0.05147365853190422,
0.02312479168176651,
0.05698294937610626,
-0.0031894147396087646,
0.006652574520558119,
-0.01881047897040844,
-0.023844020441174507,
-0.07453359663486481,
-0.0041300347074866295,
-0.007830888032913208,
-0.0540735088288784,
0.006587319541722536,
-0.024326952174305916,
0.022897332906723022,
-0.01475413516163826,
-0.06226813793182373,
-0.03476772457361221,
-0.002208990277722478,
-0.007249696645885706,
-0.04707123339176178,
0.00858159177005291,
-0.0487615205347538,
0.054520588368177414,
-0.013305301778018475,
-0.003961741458624601,
-0.005416567903012037,
0.02735571749508381,
-0.011123481206595898,
-0.024996135383844376,
-0.01588457264006138,
0.07055946439504623,
0.012258184142410755,
-0.005924078170210123,
0.0589609257876873,
-0.04536077007651329,
0.010603190399706364,
0.011789252981543541,
-0.019380871206521988,
-0.022228887304663658,
-0.015043618157505989,
-0.002468752209097147,
-0.015589730814099312,
0.02620106004178524,
-0.015033012256026268,
-0.0012606086675077677,
-0.01598319411277771,
0.04354047030210495,
0.03129367530345917,
0.039872054010629654,
0.005193894729018211,
-0.031247539445757866,
0.05805513262748718,
-0.025163894519209862,
-0.03857886418700218,
0.04112574830651283,
0.002325502224266529,
0.03938772529363632,
0.04751528799533844,
-0.025911029428243637,
0.031596094369888306,
-0.0015931532252579927,
-0.05619591474533081,
-0.03263391554355621,
0.01108542364090681,
0.017626456916332245,
0.042293645441532135,
0.006400494370609522,
-0.024047773331403732,
-0.03254858776926994,
0.005225726403295994,
-0.0014178575947880745,
0.03282150998711586,
-0.003358715446665883,
0.014762542210519314,
-0.003656398504972458,
0.007921998389065266,
0.006654159165918827,
-0.01502335537225008,
-0.03233110159635544,
-0.0439959391951561,
0.018868939951062202,
-0.013076270930469036,
0.020088400691747665,
-0.006818846799433231,
-0.055209897458553314,
0.0033309736754745245,
-0.040916576981544495,
0.018471907824277878,
-0.033443111926317215,
0.021362489089369774,
-0.04586759954690933,
0.007972863502800465,
0.009976295754313469,
0.037711385637521744,
0.02672712504863739,
-0.0011175638064742088,
-0.006601450964808464,
-0.006144532468169928,
-0.027656499296426773,
0.01851394586265087,
-0.05419308692216873,
-0.004118917975574732,
0.0034428713843226433,
0.015881087630987167,
0.01635720767080784,
-0.010788711719214916,
-0.03781362995505333,
-0.006701567675918341,
0.03581400588154793,
0.027351226657629013,
-0.009574552066624165,
-0.008643178269267082,
-0.028177611529827118,
0.016570890322327614,
0.019542153924703598,
-0.008408411405980587,
0.09339930862188339,
-0.03949838876724243,
-0.02204655297100544,
0.02671937271952629,
-0.017384374514222145,
-0.028786959126591682,
0.049849722534418106,
-0.06473273038864136,
0.049740079790353775,
-0.044602714478969574,
-0.047904469072818756,
0.00404060585424304,
-0.06647874414920807,
0.016884179785847664,
0.026418134570121765,
-0.03834545984864235,
-0.024584447965025902,
0.03634478896856308,
0.051998645067214966,
0.03216627612709999,
-0.06712222844362259,
0.011352724395692348,
-0.018344085663557053,
-0.010740889236330986,
0.0049379803240299225,
0.07244870066642761,
0.036313608288764954,
0.007464755792170763,
0.08255676180124283,
-0.02871767058968544,
0.025637678802013397,
0.023391596972942352,
0.020398728549480438,
0.032812755554914474,
-0.01039708498865366,
-0.034175023436546326,
0.02358883246779442,
0.016820106655359268,
0.04663027077913284,
0.03426559641957283,
-0.015835857018828392,
0.06727464497089386,
-0.04825884848833084,
-0.03753473237156868,
0.006549909710884094,
0.02691359631717205,
-0.05017780885100365,
0.01583290472626686,
0.025411095470190048,
0.057882022112607956,
0.008234160020947456,
0.011735599488019943,
-0.038583483546972275,
0.017341721802949905,
0.025109894573688507,
-0.03343500196933746,
0.01589229330420494,
-0.02902260050177574,
-0.006114184390753508,
0.020145857706665993,
0.017550915479660034,
-0.03701658174395561,
0.0035731352400034666,
0.004741101525723934,
-0.006320437882095575,
0.018358523026108742,
-0.008199023082852364,
0.006468839943408966,
-0.012308260425925255,
0.059800781309604645,
-0.017977312207221985,
-0.00889561790972948,
-0.027479784563183784,
-0.011273587122559547,
-0.033295296132564545,
-0.03569682314991951
] |
<p>Last night, a rather strange noise woke me up around 5 am. It was like if a normal thunder sound had been fed to a reverb/delay box. As I was getting back to sleep afterwards, I could hear the sound of rain.</p>
<p>As I have been producing acid house tracks the whole day (it's just a hobby), using quite a lot of delays here and there, i'm rather skeptical of myself. Yet it seems I was woken up by a reverbed thunder sound (the reverbed part of the sound didn,t last longer than 5 seconds).</p>
<p>As I live under high-tension lines, I'm wondering : if lightning falls on them, can it produce the kind of resonating metallic sound I heard last night ?</p>
| 9,428 |
[
-0.034954335540533066,
-0.025195321068167686,
-0.02995326928794384,
-0.02423623576760292,
0.0194320697337389,
-0.014746008440852165,
-0.03304634615778923,
0.00038010344724170864,
0.05286606773734093,
-0.034284815192222595,
0.021597320213913918,
0.050145380198955536,
0.02987801469862461,
0.05912679433822632,
-0.0018770145252346992,
0.0022973178420215845,
0.016168616712093353,
0.0020189275965094566,
0.02270362712442875,
-0.07037190347909927,
-0.010137347504496574,
0.03430875763297081,
0.005697490647435188,
-0.014532255940139294,
-0.047193970531225204,
0.021162856370210648,
0.01739928126335144,
-0.014594449661672115,
0.008955495432019234,
-0.019377069547772408,
-0.01889136992394924,
-0.06461284309625626,
-0.020636538043618202,
0.010705770924687386,
0.08626307547092438,
0.007906711660325527,
-0.009585884399712086,
-0.031413499265909195,
-0.038039617240428925,
0.006762141827493906,
0.03989404812455177,
-0.02150128223001957,
0.00659581134095788,
0.00846357923001051,
-0.04938450828194618,
-0.010998698882758617,
-0.013896540738642216,
-0.04991946741938591,
0.03929353877902031,
-0.06601440906524658,
0.03304378688335419,
-0.009686436504125595,
-0.023463917896151543,
0.03445718437433243,
0.01624184474349022,
0.004117313772439957,
0.058858878910541534,
0.061245147138834,
-0.018221592530608177,
-0.04464400187134743,
0.03976663202047348,
-0.01591862365603447,
-0.03475068882107735,
0.0004180859832558781,
-0.0392143577337265,
0.010132193565368652,
0.004615818150341511,
-0.02137991040945053,
0.03198205307126045,
0.014676607213914394,
-0.0014598113484680653,
-0.014301645569503307,
0.016842147335410118,
0.008497838862240314,
-0.01462741382420063,
-0.002662187907844782,
0.0059515321627259254,
-0.014823777601122856,
0.018940718844532967,
0.06387856602668762,
-0.007905269972980022,
0.00606701010838151,
-0.017949411645531654,
0.019294120371341705,
0.022461004555225372,
-0.015682319179177284,
0.0624672994017601,
-0.018101362511515617,
-0.024985183030366898,
-0.00711070466786623,
-0.005356618203222752,
0.007316554896533489,
-0.02412557601928711,
0.019954174757003784,
-0.01804550737142563,
-0.040103230625391006,
0.012481046840548515,
0.04144980385899544,
0.003667447017505765,
-0.002480823313817382,
-0.008657394908368587,
0.004052735865116119,
0.02847142145037651,
0.04188409820199013,
-0.0023882384411990643,
-0.029755985364317894,
-0.0010004867799580097,
0.004600472282618284,
-0.035350311547517776,
0.004235066939145327,
-0.0331813283264637,
0.007340413052588701,
0.006591248791664839,
-0.0212849248200655,
-0.027845734730362892,
-0.026719938963651657,
0.03704024851322174,
-0.01090395636856556,
0.06395121663808823,
0.0372682623565197,
0.022002439945936203,
-0.018973039463162422,
0.04426271840929985,
-0.03311778977513313,
-0.040659237653017044,
-0.01740802265703678,
-0.0025590481236577034,
-0.0241016186773777,
-0.029150821268558502,
0.03226224333047867,
-0.005331834778189659,
-0.02866724133491516,
-0.005433035083115101,
-0.0002809476281981915,
0.07050871104001999,
-0.016650939360260963,
-0.10841524600982666,
-0.04594165086746216,
0.01305681187659502,
0.011854948475956917,
0.0014906558208167553,
-0.060953620821237564,
0.0099946279078722,
0.007797125726938248,
0.016669122502207756,
-0.0012530580861493945,
0.021538028493523598,
-0.024246279150247574,
0.00981549546122551,
0.049824248999357224,
-0.016255751252174377,
-0.03513065725564957,
-0.01305166631937027,
-0.04214545711874962,
0.022882910445332527,
-0.02793031558394432,
0.022443784400820732,
0.005218162201344967,
0.04201178997755051,
-0.016964387148618698,
0.0035413478035479784,
-0.04176141321659088,
-0.007464283611625433,
0.07254538685083389,
-0.010781717486679554,
-0.020153269171714783,
0.06107878312468529,
0.015086905099451542,
-0.0010584242409095168,
0.024566881358623505,
0.028990233317017555,
0.04128211364150047,
0.06192895397543907,
0.013855662196874619,
0.04065150022506714,
-0.06252576410770416,
-0.004600805230438709,
-0.04995964840054512,
0.023718228563666344,
-0.025443533435463905,
0.007417323999106884,
-0.0004319595464039594,
0.021073777228593826,
0.012911085039377213,
0.021636148914694786,
0.020538201555609703,
-0.015641357749700546,
-0.058945994824171066,
0.022152522578835487,
0.01607692241668701,
0.03492854908108711,
-0.017883406952023506,
0.044602904468774796,
-0.022795073688030243,
0.03681899607181549,
-0.03874952346086502,
0.0016939108027145267,
0.06343506276607513,
-0.06000373885035515,
0.0023606023751199245,
0.02721794880926609,
-0.01785646378993988,
0.014938930980861187,
-0.0278857983648777,
-0.030300281941890717,
0.024559732526540756,
-0.0168201494961977,
-0.007849558256566525,
0.025171510875225067,
-0.02886633388698101,
-0.008292214013636112,
-0.003206411376595497,
-0.009724633768200874,
-0.002872771816328168,
-0.014892775565385818,
-0.007925591431558132,
0.06389240175485611,
0.0034030075185000896,
0.0030809498857706785,
0.018971052020788193,
0.005577143747359514,
0.056101176887750626,
0.07160215079784393,
0.007428299635648727,
0.0028444307390600443,
0.0215403251349926,
0.018746016547083855,
-0.02338917925953865,
-0.031138058751821518,
0.002532048150897026,
-0.07747039943933487,
-0.015472321771085262,
0.0949728935956955,
-0.005563626531511545,
-0.0032734195701777935,
0.03974509239196777,
0.04518844932317734,
0.047458216547966,
0.05316590890288353,
0.028334910050034523,
0.03454827889800072,
-0.023020923137664795,
0.014495259150862694,
0.03152238950133324,
0.0363958477973938,
0.01887761428952217,
0.03610849007964134,
0.004866905510425568,
0.018978407606482506,
-0.0789075493812561,
0.0019761270377784967,
0.013862472958862782,
-0.02454928122460842,
0.007541785016655922,
-0.012351547367870808,
-0.033479440957307816,
0.009358554147183895,
-0.027206627652049065,
0.041888728737831116,
-0.004847671836614609,
0.025918997824192047,
0.01711788773536682,
-0.021728672087192535,
-0.009152417071163654,
0.008733750320971012,
-0.006106651853770018,
-0.04998168721795082,
-0.045199472457170486,
0.05034572258591652,
-0.03319055214524269,
-0.01994461938738823,
0.016489680856466293,
-0.021312516182661057,
-0.0015134351560845971,
0.004611173644661903,
0.01467550452798605,
0.010770002380013466,
0.02277643233537674,
-0.010922779329121113,
-0.05550604313611984,
0.002516854787245393,
-0.03442982956767082,
-0.0007319715223275125,
-0.006107000168412924,
-0.02604806423187256,
0.01659492217004299,
-0.017924761399626732,
-0.021237220615148544,
0.06214750558137894,
-0.017490174621343613,
-0.028640728443861008,
-0.0283065102994442,
-0.02651033364236355,
-0.027241412550210953,
0.009015105664730072,
-0.02386978268623352,
0.00003487600770313293,
-0.03714003413915634,
-0.03994770720601082,
0.011937336064875126,
0.007560981437563896,
0.005216850899159908,
0.00024856271920725703,
-0.020149417221546173,
0.016743900254368782,
0.00352722080424428,
-0.01014125719666481,
0.0035607998725026846,
-0.0037687052972614765,
0.013407273218035698,
0.03072943352162838,
-0.02588428184390068,
-0.0312894731760025,
-0.030524447560310364,
-0.05662047863006592,
-0.01910155452787876,
-0.015389661304652691,
0.04677015542984009,
0.015520854853093624,
-0.07141853123903275,
0.027559254318475723,
0.027908118441700935,
-0.024877339601516724,
0.026759102940559387,
-0.03755616396665573,
-0.005644695367664099,
-0.037918638437986374,
-0.00328739732503891,
0.03682506084442139,
-0.03292983025312424,
0.028194135054945946,
0.04682702571153641,
-0.02604924514889717,
0.04704345762729645,
-0.001458676066249609,
-0.04294910281896591,
0.030045609921216965,
0.0022942745126783848,
0.01119841169565916,
0.03967883437871933,
0.04074949026107788,
-0.01641853153705597,
-0.020762361586093903,
-0.03515850380063057,
0.014290955848991871,
0.03992890194058418,
-0.0412634052336216,
0.021522659808397293,
-0.010450288653373718,
0.027200646698474884,
-0.052719809114933014,
-0.0011496386723592877,
0.0028020930476486683,
-0.02174116112291813,
-0.03780515864491463,
0.03202733024954796,
0.05295901000499725,
0.007362066768109798,
0.018683679401874542,
0.00870458222925663,
0.047126926481723785,
-0.01912369392812252,
-0.05306032672524452,
0.023480981588363647,
0.011330223642289639,
0.015505782328546047,
0.01212332397699356,
0.00509173097088933,
0.01706935465335846,
-0.05195675417780876,
0.04484505206346512,
0.030457336455583572,
-0.06680496037006378,
0.015092186629772186,
-0.0725729912519455,
0.028165219351649284,
0.025401409715414047,
0.01600871980190277,
-0.012449458241462708,
0.09490300714969635,
0.0010165798012167215,
0.002785236109048128,
0.01709597371518612,
-0.026563910767436028,
-0.07810650020837784,
-0.00018240597273688763,
-0.023032639175653458,
-0.006386162247508764,
-0.013451945967972279,
-0.0020107103046029806,
-0.03276931867003441,
-0.0025215328205376863,
-0.033890750259160995,
-0.03264375030994415,
-0.026653826236724854,
-0.07706129550933838,
0.0036711646243929863,
-0.03429068997502327,
-0.030365481972694397,
-0.0035926979035139084,
-0.0158494021743536,
0.03658067807555199,
0.0114952577278018,
0.004095107316970825,
-0.00693175382912159,
0.006528196390718222,
-0.027926232665777206,
-0.028284838423132896,
-0.018605314195156097,
-0.0392146110534668,
0.02777436375617981,
0.01931959018111229,
-0.011918610893189907,
-0.009143213741481304,
0.017834383994340897,
0.012601759284734726,
0.03612866997718811,
0.0068681975826621056,
-0.0032592262141406536,
-0.01897907815873623,
-0.04069330170750618,
-0.006477758754044771,
0.018252549692988396,
0.029360579326748848,
0.01682436838746071,
0.021220536902546883,
-0.02468101866543293,
-0.028948523104190826,
-0.004767785780131817,
-0.010032220743596554,
0.02852710522711277,
0.010332153178751469,
-0.001610685489140451,
-0.06148746609687805,
-0.0318245068192482,
-0.023213785141706467,
0.0009093608241528273,
-0.01701430045068264,
0.003415796672925353,
0.008913680911064148,
0.011017239652574062,
0.01092640683054924,
0.00883322861045599,
0.02036060392856598,
0.035171329975128174,
-0.03373676538467407,
-0.0075833797454833984,
0.0018138844752684236,
0.018736492842435837,
-0.0063713314011693,
0.030273251235485077,
0.007211162708699703,
0.009985136799514294,
-0.04567020758986473,
-0.11908063292503357,
0.004107068758457899,
0.044192325323820114,
0.06125999242067337,
-0.04826989024877548,
0.01506460178643465,
-0.04551631584763527,
-0.025187792256474495,
0.038536787033081055,
-0.0014136150712147355,
0.026809535920619965,
0.009103955700993538,
0.008426581509411335,
-0.005320856347680092,
-0.03340410441160202,
0.004648147150874138,
0.03613261133432388,
0.027550457045435905,
0.03642527759075165,
0.011026354506611824,
-0.058834969997406006,
0.02013160102069378,
0.05638575181365013,
0.02974136918783188,
0.0551186203956604,
0.005930105224251747,
0.0009462313028052449,
-0.07162325829267502,
-0.0009183927322737873,
0.012914726510643959,
-0.042880069464445114,
0.00484585203230381,
-0.01004382036626339,
-0.03279034048318863,
0.05826058238744736,
0.002044310327619314,
-0.04567303508520126,
0.03695974126458168,
-0.004916451871395111,
0.0036502063740044832,
-0.0027141710743308067,
-0.0009114986751228571,
0.0209419634193182,
0.046478647738695145,
0.022623654454946518,
0.03108626790344715,
0.008228071965277195,
-0.020133351907134056,
0.020933914929628372,
0.03809915855526924,
0.019755443558096886,
-0.024121562018990517,
0.037417344748973846,
-0.011535651981830597,
0.029426615685224533,
-0.046320151537656784,
0.04715372622013092,
0.004565899260342121,
0.010527288541197777,
-0.0010731527581810951,
-0.0024082206655293703,
-0.019660737365484238,
0.043371450155973434,
0.0005932553322054446,
-0.0031865143682807684,
-0.05524531006813049,
0.02764381840825081,
-0.007926654070615768,
-0.01247461885213852,
-0.03596863895654678,
-0.03143499419093132,
0.03908072039484978,
0.042925380170345306,
-0.028638459742069244,
-0.020796913653612137,
-0.03109428472816944,
-0.025721566751599312,
0.03844452276825905,
-0.05072438716888428,
0.07606901228427887,
0.0022428210359066725,
-0.008882465772330761,
0.059719666838645935,
-0.022204797714948654,
0.06033184379339218,
0.007284224033355713,
-0.03997842222452164,
0.03310977667570114,
-0.07299420237541199,
0.03352058306336403,
-0.016924558207392693,
0.0275677852332592,
-0.06621204316616058,
-0.04961572587490082,
0.05536012351512909,
0.046938374638557434,
-0.049851421266794205,
-0.034137044101953506,
-0.03544355556368828,
-0.007665670942515135,
-0.010913812555372715,
0.006234175059944391,
0.023559127002954483,
-0.0267648808658123,
-0.00012629585398826748,
0.048015810549259186,
-0.0042901975102722645,
0.0668383464217186,
-0.019903801381587982,
0.0008110365597531199,
0.044639721512794495,
-0.07082033902406693,
0.0016583808464929461,
-0.031231261789798737,
-0.00964132696390152,
-0.033582840114831924,
-0.011887767352163792,
-0.016767168417572975,
0.004215020686388016,
0.05335186421871185,
-0.03657298907637596,
0.03501530736684799,
-0.0009609258268028498,
0.02368495985865593,
0.009707557037472725,
-0.014117580838501453,
0.03436116501688957,
0.004528461489826441,
-0.008895063772797585,
-0.02072576992213726,
-0.027027882635593414,
-0.009486000053584576,
-0.013603122904896736,
0.02587937004864216,
0.013268837705254555,
0.00706989411264658,
0.0038732439279556274,
0.07140418142080307,
-0.028109367936849594,
-0.03963988646864891,
0.029879221692681313,
-0.06510491669178009,
0.040409721434116364,
-0.021735653281211853,
0.009386422112584114,
0.03644993156194687,
-0.015529847703874111,
-0.045978862792253494,
-0.042694441974163055,
0.024103745818138123,
-0.024588987231254578,
0.06400882452726364,
-0.017491618171334267,
0.009493617340922356,
0.004521157592535019,
-0.006352660246193409,
-0.02951051853597164,
0.0033444371074438095,
-0.0013598809018731117,
0.010402652435004711,
-0.030466517433524132,
0.027481483295559883,
-0.022822370752692223,
0.05212056264281273,
-0.000430431857239455,
0.019789768382906914,
-0.005407838150858879,
0.0240897499024868,
0.012560000643134117,
0.016938384622335434,
0.04096890240907669,
0.02049713023006916,
-0.048051755875349045,
0.017407791689038277,
-0.07002288103103638,
0.019890008494257927,
0.03763769567012787,
0.036481115967035294,
0.05332999303936958,
0.04130876436829567,
0.012775284238159657,
-0.03989296779036522,
-0.012526395730674267,
-0.023172833025455475,
0.008401806466281414,
0.004809847567230463,
0.013998410664498806,
0.013042844831943512,
0.02042367495596409,
-0.008916318416595459,
0.0040260301902890205,
0.006513554137200117,
0.00973058957606554,
-0.03610401973128319,
0.011087043210864067,
-0.0005304042133502662,
-0.028117533773183823,
0.08559729158878326,
-0.021627238020300865,
0.016034990549087524,
0.041613511741161346,
-0.02611866034567356,
0.05637321248650551,
-0.004891982302069664,
0.011881223879754543,
0.04304211586713791,
0.06048373878002167,
0.004053598735481501,
0.033985480666160583,
-0.007576530799269676,
0.027066798880696297,
0.13408291339874268,
0.04956505447626114,
0.044583987444639206,
0.0036095285322517157,
-0.00675194151699543,
-0.03573467954993248,
0.0055438438430428505,
0.012403302825987339,
-0.017865881323814392,
-0.03189615160226822,
0.012628411874175072,
0.03500368446111679,
0.025674810633063316,
-0.021179411560297012,
0.010215750895440578,
0.0648861825466156,
-0.012450050562620163,
-0.011161216534674168,
-0.012672376818954945,
0.011457675136625767,
0.008611594326794147,
0.009047896601259708,
-0.08651772141456604,
0.010057931765913963,
0.00023166507889982313,
0.01619962975382805,
-0.04157845675945282,
-0.032667212188243866,
0.03214619681239128,
-0.015791065990924835,
-0.021463947370648384,
-0.00693571288138628,
0.03523449972271919,
0.002509291283786297,
-0.011986433528363705,
0.036780066788196564,
0.051369186490774155,
0.022990422323346138,
0.008012203499674797,
0.032056547701358795,
0.04126917943358421,
-0.03441542387008667,
-0.014138350263237953,
0.013749789446592331,
-0.0385039858520031,
-0.009771919809281826,
-0.006461445242166519,
-0.016821198165416718,
-0.010215014219284058,
0.010043649934232235,
-0.022088222205638885,
0.0015426360769197345,
0.05384104326367378,
-0.020158493891358376,
-0.03146493062376976,
0.00022211216855794191,
0.0007602382102049887,
-0.007194400765001774,
-0.03501935675740242,
-0.02033153362572193,
0.041341811418533325,
0.043837904930114746,
-0.00953647494316101,
0.041522350162267685,
0.011419456452131271,
0.002708169398829341,
0.03439393639564514,
0.05841108039021492,
0.010215898975729942,
-0.007493634708225727,
-0.06283461302518845,
0.014108356088399887,
-0.012156538665294647,
-0.03553739935159683,
-0.0021045785397291183,
0.03666013106703758,
0.008428639732301235,
0.02355552650988102,
-0.029600929468870163,
-0.0041881138458848,
-0.01931251399219036,
0.03415414318442345,
-0.014826006256043911,
0.005780618172138929,
0.0033099367283284664,
0.01356931496411562,
0.01887453906238079,
-0.0022658344823867083,
0.003144419752061367,
0.014131295494735241,
0.03347775712609291,
0.08293788880109787,
0.023985279724001884,
-0.0368715263903141,
0.008518703281879425,
-0.016599973663687706,
-0.01850622519850731,
0.02444102056324482,
0.020291555672883987,
0.04133453220129013,
-0.008505437523126602,
-0.006484081503003836,
0.025817180052399635,
0.019121862947940826,
-0.035796187818050385,
-0.017009472474455833,
-0.014514632523059845,
-0.05173003673553467,
-0.015877334401011467,
-0.014948121272027493,
0.034596361219882965,
-0.01603090390563011,
-0.00837919395416975,
-0.0025655056815594435,
0.02171732485294342,
-0.03565296530723572,
-0.013917868956923485,
-0.03861905634403229,
-0.0031410169322043657,
0.018629876896739006,
0.004286047536879778,
-0.00944094080477953,
0.0084886709228158,
-0.005919583607465029,
-0.011903730221092701,
0.017746098339557648,
0.010730135254561901,
-0.011502171866595745,
0.03968775272369385,
-0.046958860009908676,
-0.011026102118194103,
0.00576474703848362,
0.01995004341006279,
-0.009320398792624474,
-0.006173584144562483,
0.023255206644535065,
-0.02291245386004448,
0.04326186329126358,
-0.04186570644378662,
-0.05135650187730789,
0.05145047605037689,
-0.024334127083420753,
-0.046242255717515945,
0.048939257860183716,
-0.028391841799020767,
0.02676066942512989,
0.024857565760612488,
0.006374246906489134,
0.011757614091038704,
0.06889081001281738,
0.016933079808950424,
0.012845370918512344,
-0.008061112836003304,
0.007671022787690163,
0.026254242286086082,
0.036206748336553574,
-0.0030928743071854115,
-0.04603448137640953,
0.002734615933150053,
0.025678297504782677,
0.039909813553094864,
-0.0006649565184488893,
0.017691677436232567,
0.02632187493145466,
-0.04845058545470238,
0.0036350502632558346,
0.015770254656672478,
0.010573861189186573,
0.01818060874938965,
0.04343028739094734,
-0.03562392294406891,
0.005894580855965614,
0.0018497644923627377,
-0.0353962704539299,
-0.09635625779628754,
0.004327361937612295,
0.01995861530303955,
-0.0124910157173872,
0.0000247056559601333,
-0.011576691642403603,
0.03321440517902374,
0.01971159502863884,
-0.06466580927371979,
-0.039479080587625504,
-0.011192983947694302,
-0.08635611087083817,
-0.024402694776654243,
0.0322682224214077,
-0.020348185673356056,
-0.01398939173668623,
-0.025036074221134186,
0.04811549931764603,
0.038078952580690384,
0.06066957861185074,
-0.023746153339743614,
-0.005937426351010799,
-0.010094464756548405,
0.03855767101049423,
0.028019774705171585,
0.012904257513582706,
0.08868829160928726,
-0.07823418825864792,
0.0038452232256531715,
0.02320004068315029,
0.005942607764154673,
0.03197038546204567,
-0.027694670483469963,
0.005319421645253897,
0.007065278943628073,
0.008525642566382885,
-0.0015286655398085713,
-0.011360831558704376,
-0.009607866406440735,
-0.00029977253871038556,
0.010929828509688377,
0.022731300443410873,
-0.024825243279337883,
-0.0201131422072649,
-0.04049773886799812,
-0.001865782425738871,
-0.01596818119287491,
0.02906441129744053,
-0.042310360819101334,
0.02183147333562374,
-0.0059713092632591724,
0.04407648369669914,
-0.020590102300047874,
0.010107663460075855,
-0.02419150434434414,
-0.011632243171334267,
-0.00907956250011921,
0.046554986387491226,
-0.007755920756608248,
-0.004300036933273077,
0.03852255269885063,
-0.019411150366067886,
-0.020739199593663216,
-0.016063958406448364,
0.0049882810562849045,
-0.06711193174123764,
-0.05611028894782066,
-0.032763246446847916,
-0.04072524234652519,
0.046467192471027374,
0.011288518086075783,
-0.004388606175780296,
-0.0299310814589262,
0.015015576034784317,
0.029287969693541527,
0.031308699399232864,
0.012273457832634449,
-0.060463398694992065,
-0.009286477230489254,
-0.05979953333735466,
0.05815097689628601,
-0.025945816189050674,
-0.03512771427631378,
-0.07029121369123459,
-0.03953828290104866,
0.013270859606564045,
0.005910271778702736,
0.0698932632803917,
-0.028505656868219376,
-0.0032573516946285963,
0.023332074284553528,
-0.015678782016038895,
0.028364384546875954,
-0.03422941267490387,
0.004277277272194624,
0.05436152219772339,
-0.005337837617844343,
-0.0036974563263356686,
-0.04069230705499649,
-0.010196998715400696,
0.03429274260997772,
0.05517769232392311,
0.01693243719637394,
0.02306770160794258,
-0.0318482369184494,
-0.02150811441242695,
0.027645567432045937,
0.013755511492490768,
0.00525763351470232,
0.08189454674720764,
-0.028041891753673553,
-0.01011029351502657,
-0.027087803930044174,
-0.04368036612868309,
-0.0580923929810524,
0.06825342774391174,
-0.011332044377923012,
0.0330001525580883,
-0.007202190812677145,
-0.020178206264972687,
0.03682882711291313,
-0.036361757665872574,
-0.014530545100569725,
0.018602026626467705,
-0.018633397296071053,
-0.003293393412604928,
0.04610774293541908,
-0.058538757264614105,
0.001300052390433848,
0.0020783422514796257,
0.01676972024142742,
0.022340824827551842,
0.005904001649469137,
-0.03775409236550331,
0.010708246380090714,
0.037774331867694855,
-0.02678864635527134,
0.014886568300426006,
0.02958577498793602,
-0.011049699038267136,
0.006784677039831877,
0.00781982485204935,
0.006771607790142298,
-0.013970847241580486,
-0.0016200911486521363,
0.019462950527668,
-0.009104866534471512,
-0.0026400811038911343,
0.002925492124632001,
-0.024040229618549347,
0.07912704348564148,
0.0016773695824667811,
0.00822010263800621,
-0.03141637519001961,
0.0015005078166723251,
0.0036140033043920994,
0.01742793619632721,
0.005030062980949879,
-0.016870424151420593,
-0.009062185883522034,
0.018533855676651,
-0.037431903183460236,
-0.01488528586924076,
0.021875977516174316,
-0.04578683525323868,
0.00044858810724690557,
-0.03147924318909645,
0.02874959632754326,
0.016576601192355156,
-0.004875004757195711,
-0.03404148668050766,
-0.018941501155495644,
0.033951714634895325,
-0.021050840616226196,
0.0035406409297138453,
-0.01702558435499668,
0.009181697852909565,
0.006687399465590715,
0.033129919320344925,
-0.05261291190981865,
-0.00636162469163537,
-0.010539871640503407,
0.005441133864223957,
0.02027662843465805,
-0.015018756501376629
] |
<p>I would like to know, how measurements of the speed of light are conducted these days, especially in the context of the invariance of $c$.</p>
<p>Do all the methods involve mirrors to redirect the photons back to the place where they were emitted from?</p>
<p>If not, could somebody, please, describe the method briefly?</p>
<p>Again, what I am chiefly interested in are attempts to test the invariance, like the <a href="https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment" rel="nofollow">Michelson-Morley experiment</a>.</p>
| 9,429 |
[
-0.016552021726965904,
-0.0020009302534163,
-0.04130705073475838,
-0.04708221182227135,
0.0829894170165062,
0.007521160412579775,
-0.019950514659285545,
-0.023514719679951668,
-0.0059653110802173615,
0.008816146291792393,
0.029343683272600174,
0.07791709899902344,
0.037725917994976044,
0.006872805766761303,
0.02642536349594593,
-0.013904173858463764,
-0.007216959726065397,
0.02459292858839035,
-0.004581415560096502,
-0.03195425495505333,
0.009874558076262474,
0.010358495637774467,
0.03604263439774513,
0.016420401632785797,
-0.04087073728442192,
0.006930569186806679,
-0.01426760945469141,
-0.0030052210204303265,
-0.008904453366994858,
0.03359134867787361,
-0.027012823149561882,
-0.028167514130473137,
-0.013538883067667484,
0.00950383860617876,
-0.002677012700587511,
-0.0016640955582261086,
-0.001918391790241003,
-0.06306235492229462,
0.02489388734102249,
0.03542659804224968,
-0.060238663107156754,
-0.0362238846719265,
-0.05172327160835266,
0.029444405809044838,
0.007803746499121189,
-0.011519036255776882,
-0.03512456640601158,
-0.008306380361318588,
0.037698328495025635,
-0.07817378640174866,
0.07591095566749573,
-0.005867807660251856,
-0.014817418530583382,
-0.014011380262672901,
-0.011033797636628151,
-0.006820137612521648,
0.09618818014860153,
0.04482613131403923,
-0.014395556412637234,
-0.03651304170489311,
-0.005825426429510117,
-0.01687120459973812,
0.009731501340866089,
-0.020264161750674248,
-0.02807830460369587,
0.021195685490965843,
-0.010887352749705315,
-0.013926935382187366,
0.03903979808092117,
-0.0026490341406315565,
0.00668576592579484,
0.020090995356440544,
0.03247562795877457,
0.03174036741256714,
-0.010395118966698647,
-0.03488118201494217,
0.009945925325155258,
0.03217269480228424,
0.03470005840063095,
0.04398687556385994,
-0.0003556221490725875,
-0.0007260314887389541,
0.016170842573046684,
0.021786311641335487,
-0.010830039158463478,
-0.02433733269572258,
0.08036761730909348,
-0.0009227599948644638,
-0.021957693621516228,
0.024653909727931023,
0.0046014925464987755,
-0.025075677782297134,
-0.003414374543353915,
0.007913033477962017,
-0.027383623644709587,
0.02223465032875538,
-0.007885019294917583,
0.06084904447197914,
-0.004973417613655329,
-0.029832977801561356,
-0.008823144249618053,
0.026577826589345932,
0.003176430007442832,
0.06065629422664642,
-0.020828887820243835,
-0.004278833512216806,
-0.012692954391241074,
0.01676253229379654,
-0.02302505634725094,
0.005155328661203384,
-0.04158587381243706,
0.022812632843852043,
0.010367642156779766,
0.04550336301326752,
0.024258598685264587,
-0.02832253836095333,
-0.004756160546094179,
-0.04826090857386589,
0.0982995554804802,
0.04128231480717659,
0.004981903359293938,
-0.008784948848187923,
-0.012540365569293499,
-0.0074089402332901955,
-0.03634948283433914,
0.00614054873585701,
0.011375145986676216,
-0.0022983108647167683,
-0.02430419810116291,
0.014557985588908195,
0.0290779247879982,
-0.03530300408601761,
0.005922897718846798,
0.0028388493228703737,
0.004142394755035639,
-0.013667643070220947,
-0.1473313570022583,
-0.08637779206037521,
0.06681929528713226,
0.023646052926778793,
-0.00980191770941019,
-0.06578688323497772,
0.018591171130537987,
0.030398551374673843,
0.07167863100767136,
-0.008251460269093513,
0.009631799533963203,
-0.004763869568705559,
0.020252158865332603,
-0.0018266813131049275,
0.005786582827568054,
-0.03925136849284172,
0.03297930210828781,
-0.005921742878854275,
0.007617657072842121,
-0.07086662203073502,
0.023550812155008316,
0.0385986790060997,
-0.012167846783995628,
-0.019012844190001488,
0.0614212229847908,
-0.0020435252226889133,
-0.002960201585665345,
0.009235233068466187,
-0.0017512229969725013,
-0.015371999703347683,
0.0853140726685524,
0.030385039746761322,
-0.0008216873393394053,
0.00842851959168911,
0.004900122527033091,
0.03574295714497566,
0.007221543695777655,
-0.02477281540632248,
0.04270310699939728,
-0.03416748717427254,
-0.016716862097382545,
0.03288733586668968,
0.018490009009838104,
-0.0017316004959866405,
-0.008072140626609325,
-0.0058950092643499374,
0.024855168536305428,
-0.007698482368141413,
0.03518471494317055,
0.061799224466085434,
-0.041292157024145126,
0.02690061181783676,
0.014570431783795357,
-0.04675494134426117,
0.013236970640718937,
-0.035113271325826645,
0.008211057633161545,
0.02172565646469593,
0.008535967208445072,
0.014221464283764362,
-0.0004397515149321407,
-0.012661384418606758,
-0.015494098886847496,
-0.055372629314661026,
0.01610962487757206,
0.05904555320739746,
0.004703009966760874,
0.005841454956680536,
0.013696260750293732,
0.03680264949798584,
0.05788725987076759,
0.006535051856189966,
-0.006989435292780399,
-0.011967111378908157,
-0.03263337165117264,
0.01148176658898592,
-0.02916617877781391,
-0.008093351498246193,
0.001629108446650207,
0.032969772815704346,
0.00905230175703764,
0.0213472880423069,
0.005059770308434963,
0.026683753356337547,
-0.00008508101018378511,
0.06430474668741226,
0.006696784868836403,
0.009934723377227783,
0.030643492937088013,
0.03220447525382042,
-0.022596171125769615,
0.02497861720621586,
0.03150290250778198,
-0.03075012005865574,
-0.056240372359752655,
-0.04188024252653122,
0.016701361164450645,
-0.005187543574720621,
-0.058758899569511414,
0.0025169241707772017,
0.011747937649488449,
0.040614157915115356,
0.026876522228121758,
-0.010350990109145641,
-0.044794417917728424,
-0.08297773450613022,
0.0158613920211792,
0.029969507828354836,
0.0010458651231601834,
0.03785830736160278,
0.009587811306118965,
-0.004929110407829285,
0.003704081755131483,
0.009468114003539085,
0.020256921648979187,
0.0034538002219051123,
-0.02075832709670067,
-0.018508344888687134,
-0.016301825642585754,
-0.02674025669693947,
0.0356549508869648,
-0.011417335830628872,
0.019042370840907097,
0.03895252197980881,
0.02340572513639927,
0.043543752282857895,
-0.04486880451440811,
-0.0001568289881106466,
0.013726294972002506,
-0.016894759610295296,
-0.02441772259771824,
-0.035105083137750626,
0.022510338574647903,
-0.020702198147773743,
0.06382511556148529,
-0.04936757683753967,
0.003140482120215893,
-0.025705017149448395,
-0.007133173756301403,
0.0011819609208032489,
-0.006500540766865015,
0.016475215554237366,
-0.026799995452165604,
-0.03847234696149826,
0.011812930926680565,
-0.048687271773815155,
0.023153075948357582,
0.028726711869239807,
-0.01661590114235878,
0.044554758816957474,
-0.02980346791446209,
-0.027318984270095825,
0.01563858799636364,
-0.023486429825425148,
0.03431687876582146,
0.060614559799432755,
0.023632951080799103,
-0.08016206324100494,
-0.005490753799676895,
0.006400818005204201,
-0.03253835439682007,
-0.02265525422990322,
0.03669196739792824,
0.03636784106492996,
0.011361297219991684,
-0.03889201208949089,
-0.0040437085554003716,
-0.045566312968730927,
-0.034831397235393524,
-0.018966425210237503,
-0.034527018666267395,
0.0019840144086629152,
-0.06284686923027039,
0.037080664187669754,
0.041885241866111755,
-0.06088775768876076,
0.016871746629476547,
-0.02361917309463024,
-0.03405090421438217,
0.03762108460068703,
-0.00037374484236352146,
0.03521047905087471,
0.0038983868435025215,
-0.019812947139143944,
0.0495164655148983,
0.05082184821367264,
-0.031444795429706573,
-0.041874486953020096,
0.01839316077530384,
-0.004695966839790344,
-0.05580732598900795,
-0.008444446139037609,
0.020150883123278618,
-0.029371781274676323,
-0.0010452312417328358,
0.013812175020575523,
0.00768099632114172,
0.009488771669566631,
0.02533091977238655,
0.009157671593129635,
0.007843747735023499,
-0.013605277985334396,
0.009035635739564896,
0.04832213371992111,
0.03605404868721962,
-0.03879395127296448,
-0.02545289508998394,
0.026371173560619354,
0.03462829440832138,
0.030158989131450653,
-0.048715345561504364,
0.026939349249005318,
0.015890810638666153,
-0.0057467068545520306,
-0.026367634534835815,
0.0035243553575128317,
0.004122365266084671,
0.020790869370102882,
0.02124871127307415,
0.018001222983002663,
0.004836256615817547,
-0.0022536597680300474,
0.0033549522049725056,
0.01699998788535595,
0.0312358271330595,
0.002161419717594981,
-0.021480590105056763,
0.009435992687940598,
-0.0076137324795126915,
0.044032350182533264,
-0.0384061373770237,
-0.024681372568011284,
0.06681569665670395,
0.0473945289850235,
-0.0006377126555889845,
-0.02851698361337185,
-0.02020270749926567,
-0.0060270181857049465,
-0.037921175360679626,
0.008069773204624653,
-0.0015281460946425796,
0.03478600084781647,
0.009135422296822071,
0.030075399205088615,
0.03090032935142517,
0.003476941492408514,
-0.010205533355474472,
-0.022266358137130737,
-0.09659267961978912,
0.02181381732225418,
-0.058147333562374115,
-0.011908228509128094,
-0.04079758748412132,
-0.005245804786682129,
0.00824685301631689,
-0.02246670238673687,
0.012714220210909843,
-0.036006294190883636,
-0.00033663661452010274,
-0.036039598286151886,
0.011227923445403576,
-0.013272854499518871,
-0.04897039756178856,
-0.02795388735830784,
0.028757160529494286,
0.025671962648630142,
-0.03725122660398483,
-0.003931678831577301,
0.013458095490932465,
-0.03392115607857704,
-0.02057792618870735,
-0.008619960397481918,
0.012204473838210106,
0.023544328287243843,
0.03012082725763321,
0.050950415432453156,
0.003450782736763358,
-0.036463312804698944,
0.02998586744070053,
0.04087924584746361,
0.03982612118124962,
-0.001995474100112915,
-0.011716379784047604,
-0.039831459522247314,
-0.03859424218535423,
-0.01985078677535057,
-0.006663748063147068,
0.054356854408979416,
-0.007605411112308502,
0.0014833403984084725,
0.021520299836993217,
0.0180495735257864,
-0.010921101085841656,
0.042093273252248764,
0.0430540107190609,
-0.02913271076977253,
0.0028272958006709814,
-0.03205663710832596,
-0.011909225955605507,
0.004880663473159075,
-0.0032953068148344755,
0.020844977349042892,
0.016610657796263695,
0.0017517366213724017,
-0.017862988635897636,
0.025476401671767235,
0.034693967550992966,
0.004921764601022005,
0.01027548685669899,
-0.00754947355017066,
0.002822916256263852,
0.025702351704239845,
0.019770987331867218,
-0.020194699987769127,
0.03780776634812355,
0.04390830546617508,
0.006000443361699581,
-0.0021460363641381264,
-0.04721885919570923,
0.010143172927200794,
0.007628323510289192,
0.0139544066041708,
-0.017482364550232887,
-0.006661422550678253,
-0.07031244039535522,
0.029232241213321686,
0.016067301854491234,
-0.029209526255726814,
0.033714212477207184,
-0.024140289053320885,
-0.008280698210000992,
-0.0259091854095459,
0.009265701286494732,
-0.012273202650249004,
0.0185454823076725,
0.01440835278481245,
-0.037032101303339005,
-0.014902583323419094,
0.00015421411080751568,
-0.026105498895049095,
-0.010031563229858875,
0.0255105160176754,
0.03771102428436279,
-0.007978416047990322,
0.006409364752471447,
0.01724313385784626,
0.03855769708752632,
-0.035491038113832474,
-0.06578562408685684,
-0.012057752348482609,
0.02108202874660492,
-0.007784061133861542,
0.06967668980360031,
-0.009464094415307045,
-0.07693036645650864,
0.044892143458127975,
-0.00970629882067442,
-0.018648860976099968,
0.031138671562075615,
-0.05110931396484375,
0.020917339250445366,
0.010401367209851742,
-0.016054652631282806,
0.07459032535552979,
0.058771029114723206,
-0.012465395033359528,
-0.0035009323619306087,
0.033648330718278885,
0.04288933798670769,
-0.018830401822924614,
-0.03987922519445419,
-0.011764949187636375,
-0.002889735624194145,
-0.024855997413396835,
0.05530477315187454,
-0.006715030875056982,
0.012560737319290638,
-0.00962311401963234,
-0.030314192175865173,
-0.018191611394286156,
0.04091950133442879,
0.010436810553073883,
0.0021460005082190037,
-0.003401507157832384,
0.019478049129247665,
-0.011066210456192493,
-0.046550121158361435,
0.02097565308213234,
0.017197540029883385,
0.013146388344466686,
-0.0063795605674386024,
-0.003418411361053586,
0.010081366635859013,
-0.03192175179719925,
-0.011382642202079296,
0.027991756796836853,
-0.009598123840987682,
0.04410723224282265,
-0.0036932004150003195,
0.01165552344173193,
0.014874027110636234,
-0.049831654876470566,
-0.04250501096248627,
0.014129405841231346,
-0.03532513603568077,
0.03138597309589386,
-0.08840920776128769,
0.018058713525533676,
0.00013094357564114034,
0.01780754141509533,
-0.06688006967306137,
-0.03764045983552933,
0.038633886724710464,
-0.020751703530550003,
0.0012090376112610102,
-0.02985166385769844,
-0.0009906543418765068,
-0.002826499054208398,
-0.03890830650925636,
-0.050229355692863464,
0.046048346906900406,
-0.022813839837908745,
-0.00003029228355444502,
-0.016567545011639595,
-0.009039969183504581,
0.04960352182388306,
-0.02641398087143898,
-0.027886364609003067,
-0.011114637367427349,
-0.019198888912796974,
-0.013100367039442062,
0.004554577171802521,
0.02825155481696129,
-0.015722066164016724,
-0.0575595423579216,
-0.04793144762516022,
0.02531275525689125,
-0.009416745975613594,
-0.021440686658024788,
0.0012466363841667771,
0.04317464306950569,
0.00009841001883614808,
-0.028915386646986008,
-0.004049400333315134,
0.004721290897578001,
0.007787575013935566,
0.030935395509004593,
-0.0045053292997181416,
-0.0052153621800243855,
-0.007673209998756647,
-0.04628303274512291,
0.04847927391529083,
0.009676316753029823,
0.01608346775174141,
-0.03936835750937462,
0.03176920861005783,
-0.017355643212795258,
-0.02844640240073204,
-0.0005630888044834137,
0.0022476736921817064,
-0.0041680000722408295,
-0.012382254004478455,
0.025654850527644157,
0.020052090287208557,
-0.020790541544556618,
-0.028024611994624138,
-0.04150990769267082,
-0.019588174298405647,
-0.018921304494142532,
0.071903295814991,
0.019225269556045532,
0.061365265399217606,
0.029514839872717857,
-0.009858756326138973,
-0.011243128217756748,
-0.013177001848816872,
-0.039580125361680984,
0.02270558476448059,
0.017465446144342422,
0.01962686888873577,
-0.014697950333356857,
0.0022823670879006386,
0.03967282921075821,
0.016777275130152702,
0.006223348435014486,
-0.002997409552335739,
0.028038401156663895,
0.04829004779458046,
0.021709926426410675,
-0.019132208079099655,
-0.005841611884534359,
0.01900475285947323,
-0.027261387556791306,
0.027343034744262695,
-0.008059023879468441,
-0.008561898022890091,
0.032354261726140976,
-0.006641887594014406,
0.041174937039613724,
-0.045457880944013596,
-0.009146547876298428,
-0.054137665778398514,
-0.009022615849971771,
0.007046968676149845,
0.013275123201310635,
-0.027439886704087257,
-0.02297295816242695,
0.02747570350766182,
0.014641820453107357,
0.021770410239696503,
-0.0264026690274477,
-0.07168498635292053,
-0.041881781071424484,
-0.0052580623887479305,
-0.022756755352020264,
0.08005727082490921,
-0.0107301976531744,
0.00719935679808259,
-0.009761369787156582,
-0.023824773728847504,
0.02337762340903282,
0.03197881579399109,
0.04889144375920296,
-0.016820501536130905,
0.05600450932979584,
-0.028310248628258705,
0.010862009599804878,
-0.022835150361061096,
0.0020397223997861147,
0.08866897970438004,
0.032230645418167114,
0.017624659463763237,
-0.07321617752313614,
0.0501040481030941,
-0.028085917234420776,
0.03142976015806198,
-0.04477745294570923,
0.027329113334417343,
-0.003105195239186287,
0.048964012414216995,
0.026612889021635056,
0.03436051309108734,
0.008236939087510109,
-0.0029209686908870935,
0.052590709179639816,
-0.017800385132431984,
-0.02355288714170456,
0.029433194547891617,
0.03969613090157509,
-0.0038415512535721064,
0.04141984134912491,
-0.0027811257168650627,
0.017624232918024063,
-0.012999647296965122,
-0.03613370284438133,
-0.010312953032553196,
-0.043681010603904724,
-0.010322727262973785,
-0.0037218669895082712,
-0.045520003885030746,
0.015964791178703308,
0.007805868983268738,
-0.04224129393696785,
-0.0791252925992012,
0.002533496357500553,
0.01685614138841629,
0.007143068127334118,
0.03519267588853836,
0.05882018432021141,
0.007110175676643848,
-0.008136937394738197,
0.027964981272816658,
0.0016728598857298493,
-0.046110861003398895,
-0.007173181511461735,
-0.0016913049621507525,
0.05944504588842392,
-0.033014699816703796,
-0.013543225824832916,
-0.015256600454449654,
-0.00495173642411828,
0.02389492280781269,
-0.04877796396613121,
-0.0021913480013608932,
0.010577963665127754,
0.014672445133328438,
-0.030894052237272263,
0.01524418592453003,
-0.017295951023697853,
0.02754848822951317,
-0.00045948318438604474,
0.020771421492099762,
-0.031226323917508125,
-0.00010520183423068374,
-0.029293833300471306,
-0.022992946207523346,
0.007929668761789799,
0.0004967161221429706,
-0.025692220777273178,
-0.009305236861109734,
-0.014876004308462143,
-0.021874183788895607,
-0.000652199552860111,
0.042304202914237976,
0.011190284974873066,
-0.002576919039711356,
-0.001129618496634066,
0.005445259157568216,
-0.027607625350356102,
-0.08690658956766129,
0.0050007980316877365,
-0.07382840663194656,
-0.024653270840644836,
-0.026431186124682426,
-0.017209181562066078,
0.05615135282278061,
0.01773909479379654,
-0.000928025518078357,
0.007148606702685356,
0.019285274669528008,
0.010099965147674084,
0.02472749724984169,
-0.025474850088357925,
-0.010391263291239738,
-0.008584306575357914,
0.0025695099029690027,
-0.034826457500457764,
-0.05501328408718109,
0.03110494464635849,
0.06421250104904175,
-0.01608247309923172,
0.011341136880218983,
-0.0060647097416222095,
-0.014050786383450031,
0.002204155083745718,
0.023247038945555687,
-0.03725697845220566,
0.008860561065375805,
-0.027624525129795074,
0.0558621883392334,
-0.02335215173661709,
-0.027965722605586052,
-0.05724160000681877,
0.029962044209241867,
-0.013033532537519932,
-0.01359750796109438,
-0.009094471111893654,
0.021051013842225075,
-0.021078336983919144,
0.025315511971712112,
-0.051106490194797516,
0.009217835031449795,
0.014934880658984184,
0.01464548334479332,
-0.014134957455098629,
-0.020659206435084343,
-0.01319892518222332,
0.045016735792160034,
0.0050601414404809475,
-0.02456197701394558,
0.030974753201007843,
0.041324105113744736,
0.009872793219983578,
0.006427004002034664,
0.015006840229034424,
0.027359794825315475,
0.007187655661255121,
-0.021078547462821007,
-0.027143394574522972,
0.057245444506406784,
-0.013289191760122776,
-0.04991648718714714,
0.0827518105506897,
-0.03963145613670349,
0.008599764667451382,
0.021768182516098022,
-0.016349738463759422,
0.011653991416096687,
0.02058207057416439,
-0.009662938304245472,
-0.0005262966151349247,
-0.01346332672983408,
-0.01739903911948204,
0.041822824627161026,
0.03648354113101959,
0.05278586968779564,
-0.056206297129392624,
-0.025099340826272964,
0.05838267132639885,
0.02515905722975731,
-0.02257660962641239,
0.0638081431388855,
-0.008408291265368462,
-0.03166910260915756,
0.009317616932094097,
0.024501033127307892,
-0.00751070398837328,
0.026100434362888336,
0.07807589322328568,
-0.04820461943745613,
0.03755754604935646,
-0.006535582710057497,
0.013634329661726952,
-0.09770025312900543,
-0.004293723031878471,
-0.00015920441364869475,
0.03412199765443802,
0.05359064042568207,
-0.05874061584472656,
0.03239413723349571,
0.04679136350750923,
-0.06354617327451706,
0.021080613136291504,
-0.023389697074890137,
-0.06629887223243713,
-0.029057474806904793,
-0.020450923591852188,
0.0011797721963375807,
0.057269688695669174,
-0.001954752951860428,
0.021862659603357315,
0.024290556088089943,
0.01645657978951931,
-0.04801235720515251,
-0.018357165157794952,
0.0031154444441199303,
-0.0011368198320269585,
0.03292092680931091,
-0.009885542094707489,
0.07136920839548111,
-0.00417608255520463,
-0.020875101909041405,
0.03986163064837456,
0.02404702454805374,
0.0426899790763855,
-0.019541025161743164,
0.00465229619294405,
0.012817470356822014,
0.01449466124176979,
0.01629275269806385,
-0.018357953056693077,
-0.022089630365371704,
0.012672554701566696,
0.005514226388186216,
0.024981636554002762,
0.01176127977669239,
-0.010154763236641884,
0.012522373348474503,
-0.0840383768081665,
-0.0262414813041687,
0.012966407462954521,
-0.010854656808078289,
-0.026666728779673576,
0.03128823637962341,
-0.0035851486027240753,
0.009459208697080612,
-0.01809457689523697,
-0.03099001757800579,
-0.0795140340924263,
-0.009561842307448387,
0.02308046445250511,
-0.008220921270549297,
-0.0017143557779490948,
-0.0077225156128406525,
-0.01371962670236826,
-0.009376058354973793,
0.046187758445739746,
-0.020618030801415443,
-0.0032455988693982363,
-0.051572930067777634,
-0.024206729605793953,
0.03145872801542282,
-0.0040723844431340694,
0.029114779084920883,
-0.01685504801571369,
-0.007826721295714378,
0.04087081179022789,
0.02182142250239849,
-0.010885873809456825,
-0.04769167676568031,
-0.011885607615113258,
-0.03072543442249298,
-0.02776065282523632,
0.0339440256357193,
0.006389907095581293,
0.02280520461499691,
-0.024255378171801567,
-0.0065539525821805,
-0.03047400899231434,
-0.017328089103102684,
0.07544887810945511,
-0.022701503708958626,
-0.011073676869273186,
-0.0014986013993620872,
0.010426556691527367,
-0.0143542205914855,
-0.08553602546453476,
0.0018677199259400368,
-0.02449548989534378,
-0.038550715893507004,
-0.042360059916973114,
-0.025208069011569023,
-0.006163270212709904,
0.002295650774613023,
-0.0035562377888709307,
0.00990285538136959,
0.0633423775434494,
-0.014372473582625389,
-0.04075104743242264,
0.03814278170466423,
0.01935606449842453,
-0.011761714704334736,
0.03155818581581116,
0.009342016652226448,
0.050822582095861435,
0.0603487528860569,
-0.028036659583449364,
-0.05995781347155571,
0.003880484029650688,
0.000645156716927886,
-0.011417387053370476,
-0.028615012764930725,
0.008349642157554626,
0.016294676810503006,
-0.04226323962211609,
0.019015183672308922,
0.04293427988886833,
-0.027553584426641464,
-0.014054710976779461,
0.08528392761945724,
0.014585490338504314,
0.012160874903202057,
0.030220411717891693,
0.04687910154461861,
0.031038209795951843,
-0.0047760154120624065,
-0.009907271713018417,
0.061093688011169434,
0.04111834615468979,
-0.003356095403432846,
0.05800991505384445,
0.04609685018658638,
-0.0014215847477316856,
0.038880664855241776,
-0.014589360915124416,
0.04058528319001198,
-0.021474838256835938,
0.018238354474306107,
0.026195522397756577,
-0.037923168390989304,
0.00034913173294626176,
0.023364590480923653,
-0.025029905140399933,
0.08788543194532394,
-0.05257222056388855,
0.011748487129807472,
0.010968559421598911,
-0.006386479362845421,
0.0036924786400049925,
-0.016016891226172447,
-0.002296395832672715,
0.04145655035972595,
-0.0094213355332613,
0.039756711572408676,
-0.02057618461549282,
0.00219963351264596,
0.03022698685526848,
-0.03480665758252144,
0.020020075142383575,
-0.006007225718349218,
-0.021544938907027245,
0.008088193833827972,
-0.03321874141693115,
-0.030552173033356667,
-0.032744236290454865,
-0.01925974152982235,
0.00733065465465188,
0.023589149117469788,
0.007898134179413319,
0.020214436575770378,
-0.011278843507170677,
0.04195551574230194,
-0.04420650750398636,
0.0006039341096766293,
0.010488014668226242,
0.02812947891652584,
-0.03844018280506134,
0.001280514756217599
] |
<p>I have a problem understanding how to deal with the chemical potential when two thermodynamic systems are in contact. For simplicity, let us consider $T=0\ K$. We have a system that is composed of two parts - I and II - where I occupies a space of fixed volume and II occupies the remaining space (essentially going to infinity in all directions). Both parts are initially filled with a crystal that is made up of a finite number of atomic types $i$. This is an equilibrium configuration (1). Now, I apply a long-range displacement field that originates in part I. If the boundary between parts I and II is permeable for the matter, some atoms move across this boundary. Here, part II can be thought of as a reservoir for the matter. The system eventually settles into another equilibrium (2), where the number of atoms $n_i$ in the part I is different from the above, i.e. there is nonzero </p>
<p>$$\Delta n_i=n_i^{(2)}-n_i^{(1)}\ .$$</p>
<p>The free energy difference between the two equilibrium states of part I is then</p>
<p>$$\Delta F \equiv F^{(2)}-F^{(1)} = V\sum_{ij}\sigma_{ij}\Delta\epsilon_{ij}+\sum_i\mu_i\Delta n_i\ .$$ </p>
<p>In each of the two configurations (1) and (2), the parts I and II are in contact equilibrium, which means that $\mu_i^{I(1)}=\mu_i^{II(1)}$ and $\mu_i^{I(2)}=\mu_i^{II(2)}$, where the number in the bracket refers to the configuration. So, we have two chemical potentials for each $i$, one corresponding to configuration (1) and the other (generally different) for the configuration (2). Moreover, the particles move into I from the immediate neighborhood of the boundary I-II, which implies that $\mu_i$ should correspond to the atoms in the part II that are close to this boundary. However, how am I to understand a single $\mu_i$ in the equation above? </p>
| 9,430 |
[
0.00033414430799894035,
-0.013380423188209534,
0.02689381316304207,
0.003980275709182024,
0.010907747782766819,
-0.023886000737547874,
0.013129553757607937,
0.008715961128473282,
-0.007856602780520916,
-0.015749000012874603,
0.023412367329001427,
-0.012956997379660606,
0.04204978421330452,
-0.02237721160054207,
0.017835045233368874,
0.01772310957312584,
0.0014147673500701785,
-0.0029914898332208395,
-0.007351978216320276,
-0.0055361646227538586,
0.012249349616467953,
0.02859044075012207,
0.020211612805724144,
-0.011839082464575768,
-0.0662599578499794,
0.06436219066381454,
-0.03848326951265335,
-0.06341816484928131,
-0.02236342616379261,
0.047172803431749344,
0.0008372964803129435,
-0.021445313468575478,
0.017459673807024956,
-0.02011154778301716,
-0.02311752736568451,
0.02159201353788376,
0.002709337742999196,
-0.017416533082723618,
-0.030387872830033302,
0.01801237463951111,
-0.0797671228647232,
0.008627617731690407,
-0.01594642922282219,
0.008472898975014687,
-0.0031026366632431746,
0.014720533043146133,
-0.00012583810894284397,
-0.02015603519976139,
0.006821167189627886,
-0.040392179042100906,
0.01683158054947853,
0.02441568858921528,
0.05891023948788643,
0.04198213294148445,
-0.014361384324729443,
-0.015680376440286636,
0.032422859221696854,
0.07301034033298492,
0.004515430890023708,
-0.04020576924085617,
-0.042268525809049606,
-0.032091930508613586,
-0.000009883633538265713,
-0.013599250465631485,
-0.016811929643154144,
0.02492702007293701,
-0.022103333845734596,
-0.04255327582359314,
-0.005287868902087212,
-0.0025645256973803043,
0.010195531882345676,
-0.028941411525011063,
0.01517176628112793,
-0.028330733999609947,
0.0376724936068058,
0.0386367067694664,
0.01174322422593832,
0.040324434638023376,
0.006460065953433514,
0.02517727017402649,
-0.028563013300299644,
0.021080348640680313,
0.027324756607413292,
0.0268410574644804,
0.009788136929273605,
-0.024242915213108063,
0.04118000715970993,
0.0007481339853256941,
0.011910048313438892,
0.031110066920518875,
-0.0033588018268346786,
0.028310878202319145,
0.046820372343063354,
-0.015593933872878551,
-0.016762379556894302,
0.032279640436172485,
0.008136185817420483,
0.029305415228009224,
-0.008436220698058605,
-0.03246661275625229,
-0.04415097087621689,
-0.0390639528632164,
0.02558887004852295,
0.06175344064831734,
0.0046159084886312485,
-0.014635777100920677,
-0.038275450468063354,
-0.0002671830006875098,
-0.010334298014640808,
-0.006939402315765619,
-0.030664261430501938,
0.005629485473036766,
0.0011497164377942681,
-0.0027914855163544416,
-0.012243802659213543,
0.0001101996676879935,
-0.042092978954315186,
-0.005383568815886974,
0.01737278327345848,
0.06961284577846527,
0.045840367674827576,
-0.043565455824136734,
0.004442343953996897,
0.005486571695655584,
-0.10314445197582245,
-0.007773017510771751,
0.0534292571246624,
-0.017885440960526466,
-0.022799288854002953,
-0.00969643797725439,
0.040036171674728394,
0.033669982105493546,
-0.008970988914370537,
0.001503534964285791,
-0.010004295967519283,
-0.010899795219302177,
-0.07619383931159973,
-0.03350567817687988,
0.0543614886701107,
-0.034896768629550934,
-0.05979055538773537,
-0.08535617589950562,
-0.03483118116855621,
0.06378693133592606,
0.07899188250303268,
-0.016676561906933784,
-0.020563630387187004,
-0.00306136766448617,
0.05351823940873146,
0.03299206495285034,
-0.031856514513492584,
-0.03631551191210747,
-0.020235005766153336,
0.008848185651004314,
-0.012883623130619526,
-0.042388904839754105,
0.04326381906867027,
0.06124377250671387,
0.03807295858860016,
0.034234821796417236,
0.03558127209544182,
-0.005241993349045515,
-0.01642780750989914,
0.004711172543466091,
-0.022863678634166718,
-0.01423685159534216,
0.036502331495285034,
0.011702002957463264,
0.03256090730428696,
0.027439676225185394,
0.024747740477323532,
0.003154089907184243,
-0.025121664628386497,
0.04964332655072212,
0.02178015001118183,
-0.016817064955830574,
0.025184569880366325,
-0.03524932637810707,
-0.016067955642938614,
0.017230277881026268,
0.0001094595791073516,
-0.019287658855319023,
-0.02971973642706871,
0.006110612768679857,
0.0364106111228466,
0.038249362260103226,
0.008712613955140114,
0.006751798093318939,
-0.021000761538743973,
-0.0760522112250328,
-0.0285653043538332,
-0.056564006954431534,
-0.011850682087242603,
-0.0037730042822659016,
-0.028281794860959053,
0.08363573253154755,
-0.002437009708955884,
-0.0017533908830955625,
0.007588782347738743,
-0.04291898384690285,
-0.019311394542455673,
0.020520031452178955,
0.007161384914070368,
0.000015566482034046203,
0.0312357135117054,
0.0722186341881752,
0.05989454314112663,
0.043351419270038605,
0.043724797666072845,
-0.010478120297193527,
-0.036733683198690414,
0.020068027079105377,
-0.020611578598618507,
0.04915887489914894,
0.038111116737127304,
-0.021387368440628052,
-0.04662745073437691,
0.03512289747595787,
0.018223723396658897,
0.033151738345623016,
-0.02146756462752819,
0.04314906522631645,
0.0868024155497551,
0.02160835452377796,
-0.03145923838019371,
0.06601417064666748,
-0.014940316788852215,
0.028026627376675606,
-0.0287761352956295,
-0.022970911115407944,
-0.03253567963838577,
-0.02175210788846016,
0.03756937012076378,
0.08478657901287079,
-0.038601353764534,
-0.031120385974645615,
-0.005227063316851854,
0.018203746527433395,
0.02348678931593895,
0.01166566926985979,
-0.015744950622320175,
-0.041400790214538574,
0.05759536102414131,
-0.03248748928308487,
0.007834111340343952,
-0.033330559730529785,
0.023713666945695877,
0.013689002953469753,
0.033708665519952774,
-0.059786029160022736,
-0.027147313579916954,
0.011796277016401291,
0.01758812554180622,
-0.029079494997859,
-0.021685058251023293,
0.0046647703275084496,
0.012695254758000374,
0.013879370875656605,
0.011251378804445267,
0.02873717062175274,
-0.011395272798836231,
0.022982008755207062,
-0.06902051717042923,
0.005583717953413725,
0.02938605658710003,
-0.0017163996817544103,
0.019013311713933945,
-0.007551276590675116,
0.013415711000561714,
-0.04563535749912262,
-0.0013307412154972553,
0.004260505083948374,
0.03178919479250908,
0.02404121123254299,
-0.0012643481604754925,
-0.0022144087124615908,
0.021167870610952377,
0.0009431858779862523,
-0.008469853550195694,
-0.0014756100717931986,
0.011752182617783546,
0.003278292715549469,
0.034934524446725845,
0.04428920894861221,
-0.04494934156537056,
-0.01847647689282894,
-0.03311691805720329,
-0.031202616170048714,
0.019033988937735558,
0.017414910718798637,
-0.017831886187195778,
-0.017785819247364998,
-0.01908491738140583,
-0.04249314218759537,
-0.03288833051919937,
-0.0006326757720671594,
-0.009985644370317459,
-0.02938999980688095,
0.02879592962563038,
0.04340745136141777,
-0.0112417908385396,
-0.10186071693897247,
0.0034905255306512117,
-0.029391903430223465,
-0.05078226327896118,
-0.005101823713630438,
-0.03274169936776161,
0.03351224213838577,
-0.027962684631347656,
0.035542093217372894,
0.057171039283275604,
-0.038567401468753815,
-0.004385228268802166,
-0.04943818971514702,
-0.038499295711517334,
0.01107294112443924,
-0.03805376961827278,
0.05020947381854057,
-0.0038552868645638227,
-0.05713922530412674,
0.07699287682771683,
-0.01140831969678402,
-0.00805604550987482,
0.015454632230103016,
-0.012134267948567867,
0.02329978719353676,
-0.008470294997096062,
0.006754845846444368,
0.043595802038908005,
0.007857595570385456,
0.04875767230987549,
0.0061217681504786015,
0.05651680380105972,
0.05170692130923271,
-0.016582585871219635,
-0.007717455737292767,
0.01362951286137104,
0.006943689659237862,
-0.021444153040647507,
0.048106320202350616,
-0.006071200128644705,
0.03266938403248787,
0.04346134141087532,
-0.009371301159262657,
0.011444270610809326,
0.05432731285691261,
-0.07806126773357391,
0.06144493445754051,
0.018396370112895966,
-0.010567575693130493,
-0.0654640793800354,
0.0665881484746933,
0.012497560121119022,
-0.04314490780234337,
0.009131801314651966,
0.014197234995663166,
0.07715334743261337,
-0.04403191804885864,
-0.004835278261452913,
0.026370104402303696,
0.031833600252866745,
-0.02487104758620262,
-0.03516748175024986,
0.013212548568844795,
-0.0027825296856462955,
0.02085244283080101,
-0.010046864859759808,
-0.011991501785814762,
0.010795308277010918,
0.004231705795973539,
0.01996060647070408,
-0.03545656055212021,
-0.0013316830154508352,
-0.019085321575403214,
-0.05311115086078644,
-0.010740370489656925,
-0.010959092527627945,
0.031028568744659424,
-0.028405873104929924,
0.03411499038338661,
-0.010932945646345615,
-0.019499173387885094,
0.0010130966547876596,
-0.010954868979752064,
-0.07145745307207108,
0.030454464256763458,
0.021853158250451088,
0.0005495572695508599,
0.006961622275412083,
-0.010071602649986744,
0.022261792793869972,
-0.020486515015363693,
0.030125780031085014,
0.009356827475130558,
0.030414456501603127,
-0.04840785264968872,
-0.002852704608812928,
-0.04665730893611908,
-0.011271975934505463,
-0.01461691502481699,
0.056636061519384384,
0.0681954100728035,
-0.018605414777994156,
0.0024747950956225395,
0.02849970944225788,
-0.027583694085478783,
0.014654101803898811,
-0.003417754778638482,
0.015223256312310696,
0.014754816889762878,
0.016329066827893257,
0.03718594089150429,
0.018375741317868233,
0.027048898860812187,
0.0005333152948878706,
0.029327256605029106,
0.02776036225259304,
0.018816377967596054,
-0.013865405693650246,
0.040332235395908356,
-0.054137635976076126,
-0.04238533228635788,
-0.03163669630885124,
0.0817924216389656,
0.0025292541831731796,
0.041130390018224716,
0.01966724917292595,
0.02173493802547455,
-0.010997219011187553,
0.06064741313457489,
0.03197690472006798,
0.014830130152404308,
-0.020650714635849,
-0.0391683466732502,
-0.030474528670310974,
-0.038762085139751434,
0.018270978704094887,
0.0011919108219444752,
0.00835935678333044,
-0.034726984798908234,
-0.005165149457752705,
-0.0010559749789536,
0.02573641762137413,
-0.0451933853328228,
0.002691297559067607,
-0.01778571680188179,
0.01365608163177967,
-0.00024688313715159893,
0.01246650516986847,
0.006723994389176369,
-0.03232336789369583,
0.02178971655666828,
-0.029387587681412697,
0.035185761749744415,
-0.06305737048387527,
-0.0473395511507988,
0.04663123935461044,
0.01254801545292139,
-0.0034244991838932037,
0.047653842717409134,
-0.03810873255133629,
-0.03325745835900307,
0.02153758704662323,
-0.0020758938044309616,
0.03315068781375885,
-0.011671069078147411,
-0.010822282172739506,
-0.012077952735126019,
-0.0776895135641098,
-0.037027791142463684,
0.0033018565736711025,
-0.0038274521939456463,
0.01896415464580059,
-0.029879946261644363,
0.0027005167212337255,
-0.008345630019903183,
-0.004066668916493654,
0.0050927018746733665,
0.04815901443362236,
-0.036262597888708115,
-0.02653227187693119,
0.02965240739285946,
0.009645876474678516,
-0.024369413033127785,
-0.0777871236205101,
0.004655078984797001,
-0.02467344142496586,
0.0271309781819582,
0.012057680636644363,
-0.039085496217012405,
-0.06919541209936142,
0.0660053938627243,
0.0035141853149980307,
-0.03400241956114769,
0.004849718883633614,
0.017220109701156616,
0.08839479833841324,
0.040626559406518936,
-0.006035221740603447,
0.04512271657586098,
0.039087925106287,
0.000025235471184714697,
0.031036194413900375,
-0.039093077182769775,
0.010785505175590515,
-0.0010074080200865865,
-0.0012005808530375361,
-0.05327463895082474,
0.03814644366502762,
-0.008259703405201435,
0.03796366974711418,
-0.010510310530662537,
0.04164855554699898,
0.009544546715915203,
-0.023140354081988335,
0.016907846555113792,
0.009791034273803234,
0.005657789297401905,
0.0038643144071102142,
0.028576849028468132,
0.025943303480744362,
0.04973789304494858,
0.008950984105467796,
-0.010255623608827591,
-0.01672358438372612,
0.009391424246132374,
0.02613532729446888,
-0.02318265661597252,
0.014867113903164864,
-0.02300441823899746,
-0.0262345802038908,
0.0006897667772136629,
-0.03786449879407883,
0.025520673021674156,
-0.00008861863170750439,
0.010710950009524822,
0.003373841056600213,
-0.02122182957828045,
-0.023950185626745224,
0.01504762377589941,
-0.010598350316286087,
0.02007061429321766,
-0.012495560571551323,
0.020376741886138916,
0.048305463045835495,
0.0012090603122487664,
-0.08402977138757706,
-0.009506814181804657,
0.015559901483356953,
-0.02030733786523342,
-0.0727953314781189,
-0.04126559570431709,
-0.009936492890119553,
0.026225093752145767,
-0.022276297211647034,
0.043534308671951294,
0.0408608540892601,
-0.012393509037792683,
-0.014018739573657513,
0.03505149111151695,
0.04905268922448158,
0.03897886723279953,
-0.019259754568338394,
-0.010144071653485298,
0.013261870481073856,
-0.011875439435243607,
-0.001095859450288117,
0.01330874115228653,
0.01689179427921772,
-0.04022042080760002,
-0.011219226755201817,
0.021849840879440308,
-0.007185050286352634,
0.03178099915385246,
-0.016551366075873375,
-0.030220117419958115,
0.0032607244793325663,
-0.005847543943673372,
-0.01493449229747057,
0.0043753390200436115,
-0.035697679966688156,
-0.0025436915457248688,
0.03629478067159653,
0.021596619859337807,
0.023434296250343323,
-0.009287545457482338,
0.0025829654186964035,
-0.00893736444413662,
-0.016101375222206116,
-0.0024873632937669754,
0.02134072221815586,
0.06968539953231812,
-0.022183246910572052,
0.0002553577651269734,
-0.004777655936777592,
0.010395280085504055,
0.05587155744433403,
-0.009542068466544151,
0.002979230135679245,
0.00972718931734562,
0.02147054672241211,
-0.023360474035143852,
-0.012099582701921463,
-0.05702865868806839,
0.05313262715935707,
0.05249488726258278,
-0.039906587451696396,
0.022611254826188087,
0.004130174405872822,
0.01693722791969776,
0.013276125304400921,
-0.010494752787053585,
-0.013248015195131302,
0.026344332844018936,
-0.0386095829308033,
0.005618731956928968,
-0.05353391543030739,
-0.03935969993472099,
0.056314412504434586,
-0.012748047709465027,
-0.05836651474237442,
0.006662104744464159,
0.016083702445030212,
0.021526457741856575,
0.0031194081529974937,
-0.02979317493736744,
0.00047918528434820473,
0.06055391579866409,
-0.033346060663461685,
0.03495312109589577,
0.005810762755572796,
-0.038530170917510986,
0.02006148360669613,
0.03868560120463371,
0.04096880927681923,
-0.04953836277127266,
-0.04556909576058388,
0.0016188195440918207,
0.03261217474937439,
0.002353052841499448,
0.02650105021893978,
0.058946456760168076,
-0.014459931291639805,
0.01738414168357849,
0.021740615367889404,
-0.017283715307712555,
-0.013650180771946907,
-0.04160791635513306,
0.009733105078339577,
-0.01042994111776352,
-0.05554945766925812,
0.003081331728026271,
-0.022631343454122543,
-0.02965380996465683,
0.021055204793810844,
-0.00009072157990885898,
0.0059132445603609085,
0.03888377547264099,
-0.02269160933792591,
-0.013132965192198753,
0.051172442734241486,
-0.009342332370579243,
0.06945446133613586,
-0.02756328321993351,
0.006869046948850155,
0.14735251665115356,
0.04368584230542183,
0.008071358315646648,
-0.014753062278032303,
0.014310001395642757,
0.008171512745320797,
-0.0272047221660614,
-0.029371842741966248,
0.0257712509483099,
0.028235360980033875,
-0.01969437673687935,
-0.03773125261068344,
0.03256436809897423,
-0.019823512062430382,
0.01603579707443714,
0.013365959748625755,
-0.04528028890490532,
-0.018512282520532608,
-0.0040433029644191265,
-0.03204965218901634,
-0.0269596129655838,
-0.004087398760020733,
0.004536335356533527,
-0.004059473518282175,
-0.017436210066080093,
0.043346256017684937,
-0.01914266124367714,
-0.02016555145382881,
0.022900911048054695,
0.026513321325182915,
-0.025942670181393623,
0.00013233459321781993,
-0.01368796732276678,
-0.011629290878772736,
0.0061597260646522045,
0.02825900726020336,
0.025583509355783463,
-0.02738853357732296,
0.019314846023917198,
0.010974422097206116,
-0.01279271300882101,
0.009429464116692543,
0.025409607216715813,
0.01784433238208294,
-0.022796617820858955,
-0.010424437932670116,
-0.031054139137268066,
0.043454285711050034,
-0.018329020589590073,
-0.024953361600637436,
0.020577454939484596,
-0.03357861563563347,
0.00412874948233366,
-0.018933022394776344,
-0.03171037510037422,
-0.004479589406400919,
0.04639332741498947,
-0.0032316430006176233,
-0.0051880148239433765,
-0.009101830422878265,
0.060490597039461136,
0.011605249717831612,
0.006983784027397633,
-0.018467914313077927,
-0.020078236237168312,
-0.021383723244071007,
0.03111778199672699,
0.02083558216691017,
0.028221603482961655,
0.011588810943067074,
-0.03512640669941902,
0.0292850062251091,
-0.05208093300461769,
-0.04614225775003433,
-0.016516609117388725,
0.02643929049372673,
0.0534144788980484,
0.002150680171325803,
-0.028069570660591125,
-0.00949719175696373,
-0.05163901299238205,
-0.010171031579375267,
-0.038854457437992096,
-0.018582675606012344,
-0.032658666372299194,
-0.004958196543157101,
-0.012425814755260944,
0.04936627671122551,
-0.04074939340353012,
0.004993019625544548,
0.02070494554936886,
0.0334167554974556,
0.026372266933321953,
-0.03324219211935997,
-0.06798329204320908,
-0.02483697235584259,
-0.006678924895823002,
0.032027579843997955,
0.01264368835836649,
0.012967041693627834,
0.02158370055258274,
0.016917118802666664,
0.014084543101489544,
0.024768754839897156,
-0.025794561952352524,
0.008778962306678295,
0.006626305636018515,
0.023863883689045906,
-0.021938567981123924,
0.037376418709754944,
0.02339046634733677,
0.0052187214605510235,
-0.02050279825925827,
0.0033738603815436363,
-0.03291410580277443,
0.04702851176261902,
0.015124049037694931,
-0.04913148656487465,
-0.014848131686449051,
-0.02851172164082527,
0.043284136801958084,
0.03259385749697685,
-0.05162885785102844,
-0.04682285711169243,
-0.007824434898793697,
0.0042749741114676,
0.043961163610219955,
-0.02440200001001358,
-0.010045423172414303,
-0.0528978630900383,
0.0014819508651271462,
0.03326926752924919,
0.060861606150865555,
0.02420164830982685,
-0.022416412830352783,
0.027028599753975868,
-0.008324112743139267,
0.023871777579188347,
-0.02958805300295353,
-0.040745966136455536,
0.02433697134256363,
-0.004842271097004414,
-0.0759565532207489,
-0.02048299089074135,
-0.013897884637117386,
0.047810059040784836,
0.005059499759227037,
0.007155938073992729,
-0.033530231565237045,
0.04308297857642174,
-0.050887331366539,
0.03482266515493393,
-0.023064110428094864,
0.005367032717913389,
-0.04717083275318146,
-0.06522393971681595,
0.025958044454455376,
0.007891856133937836,
0.028603889048099518,
-0.005601934157311916,
0.030611205846071243,
-0.04301982372999191,
-0.04084373638033867,
0.007292747963219881,
-0.059657201170921326,
0.011039101518690586,
-0.0037953995633870363,
0.013282881118357182,
0.0016788047505542636,
0.01407196931540966,
0.015795515850186348,
0.03152846544981003,
0.007675249595195055,
0.012110932730138302,
-0.06646599620580673,
-0.027886029332876205,
0.006104581989347935,
0.021005649119615555,
0.03766482695937157,
-0.02167072705924511,
-0.02835667133331299,
0.018170658499002457,
-0.0547015406191349,
-0.0013562458334490657,
-0.03617247939109802,
0.013376506976783276,
0.0019132673041895032,
-0.020307524129748344,
-0.0398852564394474,
0.025929177179932594,
0.04964060336351395,
0.04154764488339424,
-0.0019410254899412394,
0.027438344433903694,
-0.034884121268987656,
-0.037368398159742355,
0.0089813731610775,
-0.0048608602955937386,
-0.019452828913927078,
-0.04242418333888054,
0.03696458786725998,
0.012717762030661106,
-0.012347903102636337,
-0.013753366656601429,
-0.005481093656271696,
-0.055565863847732544,
0.026342108845710754,
0.012882153503596783,
-0.00669540511444211,
0.04027598351240158,
-0.04293593019247055,
0.013548924587666988,
0.013528259471058846,
0.0004952609888277948,
-0.010977800004184246,
-0.014863166026771069,
-0.021052200347185135,
-0.01884353905916214,
0.04571908712387085,
-0.014370022341609001,
-0.013756999745965004,
0.05690756067633629,
-0.02420739457011223,
0.0013883857754990458,
0.011516316793859005,
0.02392490580677986,
0.04345300793647766,
-0.02694488875567913,
-0.021275121718645096,
-0.01933358795940876,
0.030247194692492485,
0.03166770190000534,
0.031272582709789276,
0.00021611728880088776,
0.03212409093976021,
-0.020325476303696632,
-0.029321156442165375,
0.02521222084760666,
0.008933627977967262,
-0.054932963103055954,
-0.03973282128572464,
-0.03497360646724701,
-0.04439308121800423,
-0.029598766937851906,
-0.03068692423403263,
-0.020845135673880577,
-0.04936074838042259,
0.027282029390335083,
0.008280660025775433,
0.03688393905758858,
-0.03396286070346832,
-0.044429611414670944,
-0.02007579430937767,
-0.0709393247961998,
-0.00078752008266747,
0.0016841647448018193,
-0.003199093509465456,
0.002121445257216692,
-0.028884289786219597,
-0.02754395641386509,
0.03027609921991825,
0.04793987423181534,
0.012673013843595982,
-0.018233809620141983,
-0.0304977186024189,
-0.00169689382892102,
0.06946456432342529,
-0.029890408739447594,
-0.02123825065791607,
-0.0019187364960089326,
-0.013837866485118866,
0.031101437285542488,
0.01664523221552372,
0.017694681882858276,
0.015461412258446217,
0.013427004218101501,
-0.03622431308031082,
-0.014348256401717663,
0.00951614510267973,
-0.021150611340999603,
0.021977361291646957,
-0.01109577901661396,
0.012565708719193935,
0.05029059201478958,
0.0006773454952053726,
0.03639409318566322,
-0.0005730928387492895,
-0.014770165085792542,
-0.03922071307897568,
-0.004123721271753311,
-0.04264718294143677,
-0.010110930539667606,
-0.02261756733059883,
-0.006541924085468054,
0.04146343469619751,
-0.02196383848786354,
0.02482159435749054,
0.028026824817061424,
-0.034085240215063095,
-0.06600650399923325,
0.05851968377828598,
0.028678961098194122,
0.025754820555448532,
0.02016701176762581,
0.04577169194817543,
-0.026376429945230484,
0.011667555198073387,
0.033980127424001694,
0.03754285350441933,
0.055633772164583206,
-0.000007802459549566265,
-0.0006173280416987836,
0.025217901915311813,
-0.027719547972083092,
-0.012295709922909737,
-0.010965993627905846,
-0.012241729535162449,
0.013092285953462124,
-0.01796264946460724,
0.03458428755402565,
0.005201009567826986,
-0.008151033893227577,
0.02553633227944374,
0.000166236815857701,
0.07812417298555374,
-0.009616325609385967,
0.016251640394330025,
-0.03797798231244087,
0.02476452849805355,
-0.005773037672042847,
-0.012403060682117939,
0.012617492116987705,
0.01758415624499321,
-0.03425773233175278,
0.01011727750301361,
-0.017848404124379158,
0.020955421030521393,
0.003727597650140524,
-0.06204385310411453,
0.02518373355269432,
0.05453253164887428,
0.018170153722167015,
-0.04401180148124695,
0.009062125347554684,
-0.045695193111896515,
-0.04128890857100487,
0.002371592912822962,
0.06523919850587845,
0.02082238905131817,
0.004061044193804264,
0.015398244373500347,
-0.005704437382519245,
0.04580194503068924,
-0.010963017120957375,
0.005460234824568033,
0.00100714061409235,
0.0071426574140787125,
-0.00017885385022964329,
0.00220002350397408
] |
<blockquote>
<p>Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$.</p>
</blockquote>
<p>Where $P=-i\hbar \nabla$.</p>
<p>Here's what I've gotten: $$T_\epsilon\Psi(\mathbf r)= e^{i \mathbf{\epsilon} P/ \hbar}\Psi(\mathbf r)=\sum^\infty_{n=0} \frac{(i\epsilon \cdot (-i\hbar \nabla)/\hbar)^n}{n!} \Psi(\mathbf r)=\sum^\infty_{n=0} \frac{(\mathbf \epsilon \cdot \nabla)^n}{n!}\Psi(\mathbf r)= \Psi(\mathbf r) + (\epsilon \cdot \nabla) \Psi(\mathbf r) + \frac{(\epsilon \cdot \nabla)^2 \Psi(\mathbf r)}{2} + \cdots$$</p>
<p>This looks somewhat like a Taylor expansion of $\Psi(\mathbf r)$, but it's different than I've seen before -- I've never seen it in terms of a directional derivative. Can you confirm if this is the Taylor expansion of $\Psi(\mathbf r + \mathbf \epsilon)$? Or if not, what I should be getting when expanding $e^{i \mathbf{\epsilon} P/ \hbar}\Psi(\mathbf r)$? </p>
| 9,431 |
[
0.008244187571108341,
-0.040549490600824356,
0.009177806787192822,
-0.023646213114261627,
0.06142556294798851,
-0.0022458364255726337,
0.020167730748653412,
0.012559686787426472,
0.01843537949025631,
-0.03367024287581444,
-0.008605677634477615,
0.034806251525878906,
0.0762341171503067,
-0.013465209864079952,
-0.0004250332131050527,
0.042406242340803146,
-0.038108743727207184,
0.04787788540124893,
0.02020718902349472,
-0.002089050132781267,
-0.006115900818258524,
0.03311025723814964,
-0.0038068690337240696,
0.03609325736761093,
-0.033540792763233185,
0.017808303236961365,
-0.017433758825063705,
0.00783719401806593,
0.010581978596746922,
0.04800640419125557,
-0.005020586308091879,
-0.020097622647881508,
0.026644615456461906,
0.030277812853455544,
-0.00129368482157588,
0.01008105929940939,
-0.06121869757771492,
-0.01696191541850567,
-0.019661281257867813,
-0.0037522055208683014,
-0.03640826418995857,
-0.04386298358440399,
0.014147629030048847,
0.050828684121370316,
-0.051260411739349365,
0.0004260371788404882,
-0.016395552083849907,
-0.006625515874475241,
0.05374160036444664,
-0.05370573326945305,
0.054580479860305786,
0.012133440934121609,
0.032262302935123444,
0.032636020332574844,
-0.022498829290270805,
0.009502758271992207,
0.06771598756313324,
0.050804778933525085,
0.018325451761484146,
-0.03721325099468231,
-0.009012005291879177,
-0.02237623929977417,
0.003499722806736827,
-0.0033057352993637323,
-0.030501749366521835,
-0.011725897900760174,
0.022027933970093727,
-0.0014925658470019698,
0.005561071913689375,
-0.031023461371660233,
0.018283933401107788,
-0.0018574638525024056,
0.021332036703824997,
-0.042275574058294296,
0.006625894457101822,
0.0006457801791839302,
0.011155488900840282,
0.022653808817267418,
0.04453260451555252,
0.018433112651109695,
0.014765874482691288,
0.0070250993594527245,
0.027227208018302917,
0.03526122868061066,
0.05187484622001648,
0.032039400190114975,
0.05882598087191582,
-0.011012709699571133,
0.005642099771648645,
-0.005333034787327051,
0.002577003324404359,
0.001739283325150609,
0.0060692657716572285,
-0.016399389132857323,
-0.032541245222091675,
0.01981106773018837,
0.0054526799358427525,
-0.007142664398998022,
0.013294702395796776,
-0.042872022837400436,
-0.03294878080487251,
-0.03283784165978432,
-0.050996698439121246,
0.0175748523324728,
0.011695574969053268,
-0.013009046204388142,
-0.02624502405524254,
-0.006651118863373995,
-0.04227627068758011,
-0.026822058483958244,
-0.059965237975120544,
0.004753000568598509,
-0.030344178900122643,
-0.009638383984565735,
-0.05481167510151863,
-0.06865713000297546,
-0.010628030635416508,
0.014944006688892841,
0.048886191099882126,
0.08301514387130737,
0.0575241893529892,
0.01578047312796116,
-0.001552347675897181,
-0.015868814662098885,
-0.06525959819555283,
0.023062685504555702,
0.03467167541384697,
-0.0472525879740715,
-0.07013578712940216,
0.023736894130706787,
0.04696394503116608,
0.017956536263227463,
-0.012835696339607239,
-0.006237771362066269,
0.00445678411051631,
-0.019241532310843468,
-0.0998418852686882,
-0.02120795100927353,
0.006385753396898508,
-0.0341573990881443,
0.00928470678627491,
-0.04630444943904877,
-0.018574733287096024,
0.04447373002767563,
0.12490057945251465,
0.009580533020198345,
0.027209628373384476,
-0.024289675056934357,
0.01615152694284916,
-0.011195988394320011,
-0.014145664870738983,
-0.07434029877185822,
-0.02738100290298462,
-0.053755179047584534,
-0.000135229536681436,
-0.07600633054971695,
0.004627587273716927,
0.01447622012346983,
-0.004106066655367613,
0.02857265993952751,
0.11543762683868408,
-0.004745696671307087,
0.00419281842187047,
0.014764619059860706,
-0.017201021313667297,
-0.02716626040637493,
0.0887608453631401,
0.014173350296914577,
0.01696801744401455,
0.03754333034157753,
-0.0003203399246558547,
0.023962674662470818,
0.0317126102745533,
0.03019890934228897,
0.038836460560560226,
-0.09136388450860977,
-0.023746496066451073,
-0.04453354328870773,
0.00021245652169454843,
0.005089538637548685,
-0.035463809967041016,
-0.03777730464935303,
-0.02640603668987751,
-0.019429977983236313,
0.00871303677558899,
0.018569739535450935,
0.013981548137962818,
-0.019867055118083954,
-0.024722671136260033,
-0.03872189298272133,
0.05255547910928726,
-0.0034029879607260227,
0.009578637778759003,
-0.013900545425713062,
-0.010979064740240574,
0.0475207082927227,
-0.008929233998060226,
0.043884679675102234,
0.014541697688400745,
-0.05788017809391022,
0.008219875395298004,
0.03177212178707123,
0.037391841411590576,
-0.009556896053254604,
0.03621552139520645,
0.025045374408364296,
0.03646363317966461,
0.02832917496562004,
0.02770564705133438,
-0.025762055069208145,
-0.014301981776952744,
0.02854962646961212,
-0.011352015659213066,
0.029737433418631554,
0.014022071845829487,
-0.038008082658052444,
0.015818828716874123,
-0.003933362662792206,
-0.027671480551362038,
0.027504393830895424,
-0.043359387665987015,
0.0650707334280014,
0.05523093044757843,
0.037541162222623825,
-0.007389361504465342,
0.004527589771896601,
0.020629866048693657,
0.04737083241343498,
-0.017423434183001518,
-0.046520065516233444,
-0.037462107837200165,
0.006388425827026367,
0.039224475622177124,
0.01857149600982666,
-0.050093162804841995,
0.012596998363733292,
0.017426257953047752,
0.03461373597383499,
0.04852497577667236,
0.05039282515645027,
-0.0367557592689991,
-0.02353076823055744,
0.01272510178387165,
0.008086311630904675,
0.015866218134760857,
-0.008256128989160061,
0.06637594848871231,
0.0030421919655054808,
0.09260664135217667,
0.010161365382373333,
-0.009033501148223877,
0.030180802568793297,
-0.017923826351761818,
0.016396289691329002,
0.022408153861761093,
-0.035655729472637177,
0.025565534830093384,
-0.052902936935424805,
-0.009378433227539062,
0.045826107263565063,
-0.026464782655239105,
0.02495206519961357,
-0.04198407381772995,
0.0043349904008209705,
0.0063655017875134945,
-0.016838429495692253,
-0.013025723397731781,
-0.021035879850387573,
0.017862040549516678,
-0.038502685725688934,
-0.012261083349585533,
0.006101949606090784,
0.0021134447306394577,
-0.008260232396423817,
-0.00041630121995694935,
0.051950372755527496,
0.024560725316405296,
0.0056818388402462006,
0.004779898561537266,
-0.010235371999442577,
0.017693735659122467,
0.006869493052363396,
0.014463669620454311,
-0.009009328670799732,
-0.09168440848588943,
0.01854558102786541,
-0.046301670372486115,
-0.009682012721896172,
0.034939657896757126,
-0.0025080956984311342,
-0.007259814068675041,
-0.005978946574032307,
-0.008032607845962048,
-0.05144352465867996,
-0.013592179864645004,
-0.03947222977876663,
0.045700203627347946,
-0.0510190948843956,
-0.016181346029043198,
0.04014251381158829,
-0.05875120684504509,
-0.017541998997330666,
0.007238590158522129,
-0.014724226668477058,
-0.01664343662559986,
-0.00804439652711153,
-0.0047362190671265125,
-0.005873410031199455,
-0.018260309472680092,
0.030606666579842567,
0.0158072616904974,
-0.03786162659525871,
-0.020205294713377953,
-0.07661018520593643,
-0.0479588508605957,
0.00003815482705249451,
0.05539483204483986,
0.034991320222616196,
0.0041216891258955,
-0.018084080889821053,
0.07670386135578156,
0.010091514326632023,
-0.0569077804684639,
-0.0032832191791385412,
-0.007887459360063076,
0.009724179282784462,
-0.02558339573442936,
0.004829198122024536,
0.029507726430892944,
0.016975924372673035,
0.026088614016771317,
-0.015940286219120026,
0.02871066704392433,
0.014900106005370617,
-0.005600140430033207,
-0.014433656819164753,
0.03346564248204231,
-0.03579769656062126,
-0.012904874980449677,
0.05431252345442772,
-0.015271526761353016,
-0.01656457781791687,
-0.0046736556105315685,
0.009261914528906345,
0.014318197965621948,
0.014819317497313023,
-0.008714836090803146,
0.03639107570052147,
0.02416270785033703,
0.006678846664726734,
-0.01687057688832283,
0.05500704422593117,
-0.030831389129161835,
-0.018370680510997772,
-0.02634274959564209,
0.026878077536821365,
0.041523221880197525,
-0.034532491117715836,
0.050217144191265106,
0.0050591821782290936,
0.01974223554134369,
-0.046244315803050995,
-0.02012528106570244,
-0.026406683027744293,
0.021104387938976288,
0.05032670497894287,
-0.013408183120191097,
-0.032807882875204086,
0.03967568278312683,
0.03302708640694618,
0.0021540322341024876,
-0.017041657119989395,
0.0067101758904755116,
0.009372355416417122,
-0.02715301886200905,
0.03429630771279335,
0.000399938493501395,
0.062418121844530106,
-0.009424196556210518,
0.03681463375687599,
-0.0021983387414366007,
0.020727654919028282,
0.0451233945786953,
0.009626159444451332,
-0.012434962205588818,
-0.0023910696618258953,
0.0042464854195714,
-0.0300213024020195,
0.0015214212471619248,
-0.014392957091331482,
0.01244798582047224,
-0.03754980489611626,
0.002973909955471754,
-0.023573536425828934,
-0.03787088394165039,
-0.01730410009622574,
0.02996167168021202,
-0.056048598140478134,
-0.026027366518974304,
0.012916399165987968,
0.010454598814249039,
0.0371769517660141,
0.0014701910549774766,
-0.004214118234813213,
0.028363274410367012,
-0.012233573012053967,
-0.0089217284694314,
0.009572621434926987,
0.006835885811597109,
0.03795323148369789,
0.04363221302628517,
0.0412900373339653,
0.0014308339450508356,
0.009322754107415676,
0.010885978117585182,
-0.002261530142277479,
0.056299272924661636,
0.005792999640107155,
-0.0029539328534156084,
-0.018756624311208725,
-0.03174617141485214,
-0.00619536405429244,
0.0029255207628011703,
0.07214000076055527,
0.02935759164392948,
0.011964636854827404,
0.020808374509215355,
0.025736192241311073,
-0.01471757609397173,
0.025554653257131577,
0.029366079717874527,
-0.02169487439095974,
0.013737696222960949,
-0.07126364856958389,
0.0325653962790966,
-0.008987274952232838,
-0.011207125149667263,
-0.014916174113750458,
-0.023169849067926407,
-0.021977240219712257,
-0.007972131483256817,
0.010140405036509037,
0.014845640398561954,
-0.0014128576731309295,
-0.009645683690905571,
0.015871090814471245,
0.025366153568029404,
-0.015623916871845722,
0.021284040063619614,
0.00896422378718853,
0.03740391507744789,
0.04209594428539276,
0.0027044680900871754,
-0.0318681001663208,
-0.05215708538889885,
0.030792560428380966,
-0.0004389927489683032,
0.009617545641958714,
-0.007065440993756056,
0.011782009154558182,
-0.019338304176926613,
-0.027164775878190994,
0.05321309342980385,
-0.009388954378664494,
0.04672197625041008,
0.001456660684198141,
-0.001405623508617282,
0.027635008096694946,
-0.03334767743945122,
-0.04739287868142128,
-0.009811359457671642,
-0.018239395692944527,
-0.01647643931210041,
-0.023869462311267853,
-0.00841429177671671,
-0.039703115820884705,
-0.010234944522380829,
0.021755732595920563,
0.053858593106269836,
0.0008773599984124303,
-0.04840058088302612,
-0.012642983347177505,
0.010783457197248936,
-0.018956826999783516,
-0.06481491774320602,
0.0004294223908800632,
-0.0038149887695908546,
-0.008761800825595856,
0.03525608405470848,
-0.01990431733429432,
-0.059992920607328415,
0.050884537398815155,
0.007957030087709427,
-0.047321174293756485,
0.012735467404127121,
-0.038912706077098846,
0.05809184908866882,
0.03644292429089546,
0.01321830041706562,
0.07533708959817886,
0.0810692310333252,
0.014363705180585384,
0.03051634132862091,
-0.02926311269402504,
0.013601874001324177,
0.015839887782931328,
0.01621983014047146,
-0.0215311162173748,
0.006100773811340332,
-0.01705835945904255,
0.034638114273548126,
-0.030667418614029884,
-0.0028745026793330908,
-0.007867658510804176,
-0.04267038032412529,
0.005332710221409798,
0.0033492837101221085,
-0.03568854555487633,
-0.04032568261027336,
0.03498460724949837,
0.025615083053708076,
0.0328485369682312,
-0.012776593677699566,
-0.004550965502858162,
-0.007087877951562405,
0.03835836797952652,
0.05759081244468689,
0.004100924823433161,
0.018073180690407753,
0.00961851142346859,
0.005338017828762531,
0.020632807165384293,
-0.06853652000427246,
-0.02584768645465374,
0.001334535307250917,
-0.010704328306019306,
0.009692704305052757,
-0.005405988544225693,
-0.0019229709869250655,
-0.007291411515325308,
0.004661199636757374,
-0.017232904210686684,
-0.050983402878046036,
-0.017272068187594414,
0.024963729083538055,
-0.012612818740308285,
-0.06199105456471443,
-0.028554005548357964,
0.04077805206179619,
0.008031358011066914,
-0.016998572275042534,
-0.030959144234657288,
-0.0029240017756819725,
-0.027725208550691605,
0.006616996135562658,
0.018770573660731316,
0.025912616401910782,
0.013201011344790459,
-0.005074857734143734,
0.027111565694212914,
-0.004868245683610439,
0.05225308611989021,
0.013761603273451328,
-0.008931340649724007,
-0.00681172264739871,
-0.019106894731521606,
-0.018968932330608368,
0.0018395206425338984,
0.07058630883693695,
0.0014057044172659516,
-0.010769662447273731,
-0.038703955709934235,
0.0030299238860607147,
0.016230031847953796,
-0.012120485305786133,
-0.038452766835689545,
0.009766288101673126,
0.00893269944936037,
0.0057735866867005825,
-0.03632492199540138,
-0.043892454355955124,
-0.016871703788638115,
0.015378043055534363,
-0.01020742580294609,
0.007965479046106339,
-0.02327193133533001,
-0.04585973173379898,
-0.010997855104506016,
0.015702849254012108,
0.03984030708670616,
-0.0029218215495347977,
0.02947923168540001,
-0.027573050931096077,
0.016524169594049454,
0.020481746643781662,
-0.007681593298912048,
0.002125595463439822,
-0.0016425136709585786,
-0.012653819285333157,
-0.010350104421377182,
0.004126737825572491,
-0.002991369226947427,
-0.028006661683321,
-0.046462517231702805,
0.0420997180044651,
0.05198034644126892,
-0.001580839161761105,
0.038399387151002884,
0.02375815622508526,
-0.0201782938092947,
-0.03623197600245476,
0.01025354117155075,
-0.03914262354373932,
0.02273796871304512,
-0.006946095265448093,
0.01586843840777874,
-0.01772882416844368,
0.009061831049621105,
-0.00589724350720644,
0.04686141759157181,
-0.03346091881394386,
-0.004999701865017414,
0.007982459850609303,
0.03466970846056938,
0.01647784374654293,
0.00898199062794447,
-0.0057264817878603935,
0.05633233115077019,
-0.0010165091371163726,
0.032422956079244614,
0.024787431582808495,
-0.013489175587892532,
0.020364971831440926,
0.037970349192619324,
0.006202891003340483,
-0.015706079080700874,
-0.007229394745081663,
-0.018386701121926308,
-0.016802357509732246,
0.021911635994911194,
0.0037885589990764856,
0.01712346076965332,
-0.0013395558344200253,
0.025500431656837463,
0.030199429020285606,
0.010893283411860466,
-0.026781568303704262,
-0.03874938562512398,
0.010439054109156132,
-0.032697707414627075,
-0.028178580105304718,
0.035768087953329086,
-0.005104982294142246,
0.001457001082599163,
0.005171432159841061,
0.0004500506038311869,
0.01951577700674534,
0.014153525233268738,
-0.009960558265447617,
0.010178458876907825,
0.0791831836104393,
0.009667924605309963,
-0.024448510259389877,
-0.005210889503359795,
-0.009524727240204811,
0.11678127199411392,
0.06816958636045456,
0.03041703626513481,
-0.05606059357523918,
0.01474238932132721,
-0.025678785517811775,
0.0017264779889956117,
-0.06406370550394058,
0.0028403042815625668,
-0.0015302725369110703,
0.006612291093915701,
0.0017979382537305355,
0.09354157745838165,
0.0020103997085243464,
-0.026665398851037025,
0.02344347909092903,
-0.032729703933000565,
-0.026856178417801857,
0.04284849762916565,
-0.0006519019952975214,
0.005816662684082985,
-0.017352033406496048,
-0.06009954586625099,
0.016323180869221687,
-0.051572468131780624,
0.024298159405589104,
-0.04162859171628952,
-0.024478908628225327,
0.003455920610576868,
-0.00423435727134347,
-0.050824012607336044,
-0.03298021852970123,
-0.006647932343184948,
0.021396813914179802,
0.0019689241889864206,
0.04362437501549721,
0.045139048248529434,
-0.027685090899467468,
0.052721407264471054,
0.029353633522987366,
0.04792197048664093,
0.022359881550073624,
0.016356544569134712,
0.006556300446391106,
-0.03955075144767761,
-0.013381565921008587,
-0.02038610726594925,
0.04882269725203514,
-0.0004516480548772961,
0.009480650536715984,
0.0039416165091097355,
-0.005188023205846548,
0.03246140107512474,
-0.04343782365322113,
-0.028792593628168106,
-0.02278743125498295,
0.01840808428823948,
0.007783158216625452,
0.0021060346625745296,
-0.04797247797250748,
0.011432770639657974,
0.021248696371912956,
0.01118389517068863,
-0.004408835433423519,
-0.021123263984918594,
0.015171008184552193,
-0.011370154097676277,
0.05369824171066284,
0.010347096249461174,
-0.03299447149038315,
-0.016091814264655113,
-0.0435325913131237,
-0.058754872530698776,
-0.0090265404433012,
-0.02494327537715435,
-0.004390736576169729,
0.02308756858110428,
-0.017703216522932053,
-0.03410455957055092,
-0.022985262796282768,
-0.06833838671445847,
-0.000711193832103163,
-0.014304143376648426,
-0.003996843472123146,
0.007348161656409502,
-0.018646247684955597,
0.02579694613814354,
0.008484506979584694,
-0.028347928076982498,
-0.004529925063252449,
-0.009231334552168846,
0.046245377510786057,
0.041553933173418045,
-0.041260726749897,
-0.055680014193058014,
-0.011803987435996532,
-0.01789025589823723,
0.021281206980347633,
0.0074888258241117,
-0.0005712080746889114,
0.012415435165166855,
0.00906863622367382,
-0.01468465942889452,
-0.02844100072979927,
-0.047329582273960114,
-0.011461494490504265,
0.019991658627986908,
-0.03297720104455948,
0.020670544356107712,
0.023147020488977432,
-0.00879181083291769,
-0.06033262982964516,
0.018435703590512276,
-0.018751397728919983,
0.037213295698165894,
-0.0034469205420464277,
0.019448360428214073,
-0.041869960725307465,
-0.0397573746740818,
-0.025492247194051743,
0.017540084198117256,
-0.024998260661959648,
-0.004053414799273014,
-0.07642091065645218,
0.014097273349761963,
0.004765769001096487,
0.016523675993084908,
-0.020347103476524353,
0.0435803048312664,
-0.04228292778134346,
-0.06219838187098503,
0.06262979656457901,
0.033786628395318985,
-0.005324635189026594,
-0.004733762238174677,
0.025248991325497627,
0.010511673055589199,
0.025154603645205498,
0.0012692033778876066,
-0.03936579078435898,
0.07812649756669998,
-0.029894264414906502,
-0.05948740988969803,
0.013447091914713383,
0.0406610332429409,
0.03137220814824104,
-0.005993641912937164,
-0.013286440633237362,
-0.022473733872175217,
0.04360926151275635,
-0.003947368357330561,
0.004004484973847866,
0.015607385896146297,
-0.06343083083629608,
-0.005668449215590954,
-0.062177978456020355,
0.0343240387737751,
0.002588900737464428,
-0.006449579726904631,
0.01617472432553768,
0.015423987992107868,
-0.01794493943452835,
0.007071887608617544,
0.021106617525219917,
-0.021994156762957573,
0.0098832156509161,
0.008932176046073437,
-0.01778898574411869,
0.02535228617489338,
0.03188362345099449,
-0.033122461289167404,
0.004289776552468538,
-0.014613108709454536,
0.024843279272317886,
-0.10977604240179062,
-0.018545500934123993,
-0.015314828604459763,
-0.0036794329062104225,
0.01961013674736023,
-0.05711480975151062,
0.05125293508172035,
0.002081286394968629,
-0.026572242379188538,
0.032618794590234756,
-0.04085325077176094,
0.0028699461836367846,
-0.015075881965458393,
0.023991504684090614,
-0.0056852721609175205,
0.026866603642702103,
0.03245468810200691,
0.05191228911280632,
0.025506149977445602,
0.004517751280218363,
-0.01695431023836136,
0.015430782921612263,
-0.03594742342829704,
0.040440887212753296,
0.019974473863840103,
-0.04051364213228226,
0.06491906940937042,
-0.005356175824999809,
-0.022090235725045204,
-0.008912191726267338,
-0.007870064117014408,
-0.036393046379089355,
-0.028725847601890564,
0.001226805499754846,
0.04791203513741493,
0.04026317596435547,
-0.007540340535342693,
-0.01138143241405487,
-0.018466833978891373,
-0.02880886197090149,
0.042605187743902206,
-0.0008640186861157417,
-0.005523203406482935,
-0.026729855686426163,
0.021133646368980408,
0.0010132574243471026,
-0.030257554724812508,
0.0377536341547966,
-0.020222123712301254,
0.015744639560580254,
0.00897787231951952,
-0.022828448563814163,
0.00566869368776679,
-0.013128581456840038,
0.05453202500939369,
-0.02861802466213703,
-0.008991007693111897,
-0.007663564756512642,
0.021112553775310516,
-0.05026978999376297,
0.008666840381920338,
-0.011461219750344753,
-0.07543525099754333,
0.020142339169979095,
0.017978087067604065,
-0.007377761881798506,
-0.022152256220579147,
0.02612215094268322,
-0.0015684831887483597,
0.01772816851735115,
-0.005539179313927889,
-0.04210681468248367,
-0.07279782742261887,
0.014319394715130329,
0.017686372622847557,
0.030660489574074745,
0.010822863318026066,
-0.010741868987679482,
-0.02965513989329338,
-0.067879319190979,
0.03873530030250549,
0.034664008766412735,
-0.033250078558921814,
-0.01176124345511198,
-0.012798139825463295,
-0.002444735262542963,
0.011721458286046982,
0.06501006335020065,
0.0001893859007395804,
-0.045251332223415375,
0.01175849512219429,
0.012392471544444561,
0.014142447151243687,
-0.07852638512849808,
-0.012318604625761509,
0.025452205911278725,
-0.000876995618455112,
-0.006900500506162643,
-0.0070698680356144905,
-0.01640993356704712,
0.03354005515575409,
0.0034765286836773157,
0.021143630146980286,
0.0328066349029541,
-0.013412189669907093,
-0.06350920349359512,
0.05055403336882591,
-0.038028012961149216,
-0.024287192150950432,
0.07294740527868271,
-0.008993719704449177,
0.011933498084545135,
0.012748106382787228,
-0.0325082391500473,
-0.01204098854213953,
-0.011388585902750492,
-0.014708348549902439,
-0.005245451349765062,
-0.011634573340415955,
-0.009671459905803204,
0.03494371846318245,
-0.026657411828637123,
-0.011705933138728142,
0.03583027794957161,
-0.019124504178762436,
-0.020302163437008858,
0.0639992356300354,
0.007249624002724886,
0.0012284228578209877,
0.021636009216308594,
0.033784523606300354,
0.010224717669188976,
0.017781555652618408,
0.012032349593937397,
0.05720304697751999,
0.03429080918431282,
0.022264204919338226,
0.03667030856013298,
0.035087864845991135,
-0.038218408823013306,
0.050295449793338776,
-0.013990795239806175,
-0.01023750938475132,
-0.043800752609968185,
-0.03835003823041916,
0.0218606349080801,
-0.012209142558276653,
0.028563814237713814,
0.03852412849664688,
-0.018106548115611076,
0.07539615035057068,
-0.0035320681054145098,
0.044536832720041275,
0.013590398244559765,
0.03021087683737278,
-0.010383054614067078,
0.02488025277853012,
0.0258956141769886,
0.01980351097881794,
-0.013954658061265945,
-0.0005594626418314874,
-0.009506250731647015,
-0.04739391431212425,
-0.03347036987543106,
-0.07993963360786438,
-0.013238497078418732,
0.028926430270075798,
-0.031736988574266434,
-0.028924372047185898,
-0.005370852071791887,
-0.044201213866472244,
-0.04747484624385834,
-0.0024258168414235115,
0.04836137965321541,
0.02133750356733799,
-0.015567234717309475,
-0.013489658012986183,
-0.008379874750971794,
0.06303274631500244,
-0.08487707376480103,
0.019399462267756462,
0.0023189072962850332,
0.021653100848197937,
-0.0021619172766804695,
-0.010640318505465984
] |
<p>I have a big confusion. There is a question in my book which basically says that a ball is tied to a string and rotated. and it asks me to tell whether the following statement is true of false. Direction of radial acceleration MAY remain the same.
This statement is true.
Please explain to me a case where this is possible. i thought that this is only when an object moves straight and in circular motion radial acceleration is towards the centre.</p>
| 9,432 |
[
-0.06718655675649643,
-0.014603707939386368,
-0.022058429196476936,
-0.0011551615316420794,
0.013473852537572384,
0.010296164080500603,
-0.012380757369101048,
0.010153506882488728,
0.027567818760871887,
-0.02202673628926277,
0.019729143008589745,
0.02997967228293419,
0.052272699773311615,
0.03439246118068695,
0.04979953169822693,
0.01900521107017994,
-0.021161053329706192,
-0.009878365322947502,
0.0117019172757864,
-0.012202396988868713,
0.009314198046922684,
-0.0082181291654706,
0.0018822387792170048,
-0.0066308449022471905,
0.010639773681759834,
0.018570221960544586,
0.0287605132907629,
-0.004909238778054714,
0.01828787475824356,
0.04264887422323227,
-0.01122036762535572,
0.0024944618344306946,
0.0032433236483484507,
0.056423015892505646,
0.025877254083752632,
0.012867460958659649,
-0.04603317752480507,
-0.018579168245196342,
-0.02594495750963688,
0.010795509442687035,
-0.028208956122398376,
-0.01313953846693039,
-0.008855004794895649,
0.10298333317041397,
-0.020893877372145653,
0.027972396463155746,
0.0002573881938587874,
0.016658667474985123,
0.07441825419664383,
-0.0357089526951313,
0.07691273093223572,
-0.05774909630417824,
0.018146546557545662,
0.01960575394332409,
0.012439875863492489,
-0.00032177710090763867,
0.08280869573354721,
0.04394599422812462,
-0.01374233141541481,
-0.050377801060676575,
-0.007949166931211948,
-0.036567121744155884,
-0.005575810093432665,
-0.03685598075389862,
-0.037825342267751694,
-0.006402087397873402,
-0.010719734244048595,
-0.012727828696370125,
0.03066866099834442,
-0.015277916565537453,
-0.032359905540943146,
0.013253129087388515,
0.028977731242775917,
-0.011600330471992493,
-0.005538972560316324,
-0.018978159874677658,
0.03724471852183342,
0.0056660291738808155,
0.006392220966517925,
0.03746943920850754,
-0.0175599567592144,
-0.020620550960302353,
0.06417237222194672,
0.059056300669908524,
0.025040047243237495,
-0.022815072908997536,
0.016272244974970818,
0.005352639593183994,
0.025266528129577637,
0.024267788976430893,
0.028492456302046776,
-0.0352986678481102,
-0.005099395290017128,
-0.026871219277381897,
-0.014143088832497597,
0.03308190777897835,
-0.004764363635331392,
0.06204621121287346,
-0.011860900558531284,
-0.030376698821783066,
0.0016351821832358837,
-0.024889571592211723,
0.03591986745595932,
0.04673371464014053,
0.026622824370861053,
-0.02561258338391781,
-0.01705673709511757,
0.017426015809178352,
-0.015819182619452477,
-0.025868454948067665,
-0.038768380880355835,
0.012812009081244469,
-0.028309613466262817,
0.002302887849509716,
0.03140408545732498,
-0.004752541426569223,
-0.027227647602558136,
0.01694604754447937,
0.04759303480386734,
0.03422524780035019,
0.06203325092792511,
-0.029415613040328026,
0.009273841977119446,
-0.024953724816441536,
0.004612281918525696,
-0.004034601617604494,
0.02927345037460327,
-0.03974270448088646,
-0.01777932606637478,
0.036832377314567566,
0.014113016426563263,
-0.020234936848282814,
-0.009555770084261894,
0.0008768971310928464,
0.06638830155134201,
-0.019967375323176384,
-0.11167076975107193,
-0.027209481224417686,
0.056622739881277084,
0.023074589669704437,
-0.01263058464974165,
-0.05706839635968208,
0.017560163512825966,
0.014878720976412296,
0.09033046662807465,
-0.026353411376476288,
0.018739033490419388,
0.035783134400844574,
0.028433984145522118,
0.017125867307186127,
-0.001127412891946733,
-0.04045924171805382,
0.003416201565414667,
-0.06471484154462814,
-0.012760373763740063,
-0.06180896237492561,
0.01652216911315918,
-0.0013809753581881523,
0.009769362397491932,
-0.07120590656995773,
0.03233174607157707,
-0.042140278965234756,
0.025210188701748848,
0.008324332535266876,
-0.015095533803105354,
-0.002865418093279004,
0.06820955872535706,
0.01553276740014553,
-0.04912513121962547,
0.02896137535572052,
0.023371798917651176,
0.04835333675146103,
0.005332166329026222,
0.011286510154604912,
0.04891326650977135,
-0.06867020577192307,
-0.015051291324198246,
0.00009147662058239803,
0.007478130515664816,
-0.007885941304266453,
-0.03534526005387306,
-0.019117029383778572,
-0.0006961276521906257,
0.016735190525650978,
-0.015762614086270332,
0.06927725672721863,
0.017560187727212906,
0.0165867879986763,
-0.014843198470771313,
-0.017176756635308266,
0.04920361191034317,
-0.055061519145965576,
0.03854137659072876,
-0.024741526693105698,
-0.01137922890484333,
-0.0002797913330141455,
0.04336189478635788,
0.028591491281986237,
-0.038880739361047745,
0.0024103957694023848,
-0.005505167879164219,
0.019571566954255104,
-0.02484898269176483,
-0.0383031889796257,
0.006553366780281067,
0.0450558066368103,
0.04608883708715439,
0.0072265551425516605,
-0.009711549617350101,
-0.014050531201064587,
-0.00942593440413475,
0.0011523327557370067,
-0.0031775652896612883,
0.012407860718667507,
0.022982174530625343,
0.0003852777590509504,
0.02687053754925728,
0.006856114603579044,
-0.011884958483278751,
0.03219648078083992,
-0.02956858091056347,
0.05788212642073631,
0.028959112241864204,
-0.027488674968481064,
0.025784717872738838,
0.017259720712900162,
0.009575936943292618,
-0.012545125558972359,
0.02232571877539158,
-0.05597946047782898,
-0.04984375461935997,
0.03719622641801834,
0.012729465961456299,
0.030874885618686676,
-0.051965706050395966,
0.014597628265619278,
0.05371258407831192,
0.03988667204976082,
0.0017645873595029116,
0.03702368214726448,
-0.01529462169855833,
-0.048580702394247055,
0.023330094292759895,
0.020657140761613846,
-0.01640157587826252,
-0.019728077575564384,
0.013991443440318108,
0.0067412774078547955,
0.029407229274511337,
0.040205005556344986,
-0.018127698451280594,
0.024840472266077995,
0.00200084806419909,
0.005112477112561464,
0.04536672309041023,
-0.051226500421762466,
0.027750998735427856,
-0.031416818499565125,
0.0329328291118145,
0.03745759651064873,
0.009127594530582428,
-0.001973653445020318,
-0.018411846831440926,
0.02178826369345188,
0.003981098998337984,
0.006419206038117409,
-0.02997680939733982,
-0.01641516387462616,
0.02021666243672371,
-0.02992181107401848,
-0.03642702475190163,
-0.000646876753307879,
0.013296850025653839,
-0.018169306218624115,
0.012904155999422073,
0.03153246268630028,
0.012809954583644867,
0.017028432339429855,
0.008918591775000095,
0.0025435620918869972,
-0.02638270892202854,
-0.04765177518129349,
-0.02691807597875595,
0.012732427567243576,
-0.06590329855680466,
0.03527435287833214,
0.0050377920269966125,
-0.028156759217381477,
0.031414974480867386,
-0.014867210760712624,
0.006338912528008223,
0.06692532449960709,
-0.0042999242432415485,
-0.0519523024559021,
-0.011025108397006989,
-0.027434654533863068,
0.008303056471049786,
-0.0670439824461937,
-0.015233599580824375,
0.06545611470937729,
0.030201327055692673,
0.02372434362769127,
0.02769564278423786,
-0.06600596755743027,
-0.05614299327135086,
0.012845179997384548,
-0.010915104299783707,
0.05315303057432175,
-0.0025972973089665174,
0.01714387908577919,
0.0010916393948718905,
-0.012937847524881363,
-0.012343569658696651,
-0.03284287452697754,
-0.03661134093999863,
0.02243993617594242,
0.00824777688831091,
0.03165443241596222,
0.0031153259333223104,
-0.029478490352630615,
0.06029585748910904,
0.03578964248299599,
-0.04715905338525772,
-0.02805170789361,
-0.004537976812571287,
-0.019480295479297638,
-0.046976786106824875,
-0.009831361472606659,
0.003730291035026312,
-0.012487350031733513,
0.014895059168338776,
0.060457371175289154,
0.01356697827577591,
0.00659369770437479,
0.004362261854112148,
0.01271023415029049,
-0.013545685447752476,
0.0374036468565464,
0.0008425267296843231,
0.02189578115940094,
0.007107648532837629,
-0.020755596458911896,
-0.023066729307174683,
0.005459724925458431,
0.03222603350877762,
-0.002835043240338564,
-0.04501880705356598,
0.04762660712003708,
-0.03853248804807663,
0.0011579698184505105,
0.0057275015860795975,
0.05490625277161598,
0.01364368200302124,
0.014119106344878674,
-0.012058159336447716,
0.011434229090809822,
0.029090480878949165,
-0.021859005093574524,
0.023110659793019295,
0.02779885195195675,
0.00996521208435297,
0.0029009405989199877,
-0.04022352024912834,
0.014264159835875034,
0.02053743600845337,
0.09030120074748993,
-0.05561217665672302,
-0.04188143461942673,
0.0213464442640543,
0.009683781303465366,
-0.004824540577828884,
0.02317316085100174,
-0.05210605263710022,
0.026217995211482048,
-0.05345369502902031,
0.02326369285583496,
-0.0404667891561985,
0.021697310730814934,
-0.00139627477619797,
0.04215044900774956,
0.06115276366472244,
0.006533293519169092,
-0.0010399563470855355,
0.02713644504547119,
-0.07980574667453766,
0.018127216026186943,
-0.05909615382552147,
0.0074936277233064175,
-0.010729328729212284,
-0.00624059746041894,
-0.038171663880348206,
-0.042434342205524445,
-0.0077043091878294945,
-0.011780926026403904,
-0.029002347961068153,
-0.05396382510662079,
0.020614221692085266,
-0.03266751766204834,
-0.03239390254020691,
-0.002041578758507967,
0.04494340717792511,
0.00619161082431674,
-0.028510071337223053,
0.07597649842500687,
0.038130782544612885,
-0.015157783403992653,
0.01092266570776701,
-0.036425452679395676,
0.0039171213284134865,
0.028230294585227966,
0.030089640989899635,
0.05320505052804947,
0.017224431037902832,
0.004754148423671722,
0.012483872473239899,
0.04240971431136131,
0.022704320028424263,
-0.004596293903887272,
-0.030463706701993942,
-0.0266578309237957,
-0.0561063215136528,
-0.01862432435154915,
-0.024592027068138123,
0.06050102040171623,
0.03597103804349899,
-0.0179879330098629,
0.07270114123821259,
0.00006726196443196386,
-0.01571245864033699,
0.0004508497950155288,
0.05028928816318512,
0.02845909632742405,
-0.010798163712024689,
-0.03855356574058533,
0.006640282459557056,
-0.01635449379682541,
-0.020417150110006332,
0.019576966762542725,
-0.03123052977025509,
-0.02004544995725155,
0.0010420348262414336,
0.03345109522342682,
0.02211962826550007,
-0.0014447118155658245,
0.017341647297143936,
-0.03463588282465935,
0.044000789523124695,
0.006635880097746849,
0.01581639237701893,
0.03805581480264664,
0.022239666432142258,
0.00930063147097826,
0.02833816409111023,
-0.04082392901182175,
-0.02865472435951233,
-0.006150406785309315,
0.023588217794895172,
0.01984107680618763,
-0.03357375040650368,
-0.007751902565360069,
-0.031169343739748,
-0.017084820196032524,
0.028783658519387245,
-0.03829009458422661,
0.0460439994931221,
-0.03241163492202759,
0.008096391335129738,
0.0036577358841896057,
-0.04036644846200943,
-0.050472404807806015,
-0.008962123654782772,
-0.031693458557128906,
-0.0000548079187865369,
-0.009845188818871975,
0.00133473239839077,
-0.010329136624932289,
-0.024097226560115814,
0.020757198333740234,
0.008390829898416996,
-0.0018596600275486708,
-0.004994913004338741,
-0.001172789721749723,
0.036725062876939774,
-0.012547051534056664,
-0.07761022448539734,
0.019149433821439743,
0.015164104290306568,
0.009181949310004711,
0.02229727990925312,
-0.029755596071481705,
-0.010727319866418839,
0.005507897585630417,
-0.024921396747231483,
-0.0009667158010415733,
0.03214365616440773,
-0.02700098045170307,
0.011304068379104137,
0.00405017239972949,
-0.027815962210297585,
0.04768892005085945,
0.023824945092201233,
0.02125380001962185,
-0.042690787464380264,
-0.01968909427523613,
0.015679657459259033,
-0.03924205154180527,
0.014795858412981033,
-0.020690003409981728,
0.031423281878232956,
0.005669752601534128,
0.020937126129865646,
0.00915222242474556,
0.003765620058402419,
0.007894016802310944,
-0.02168438769876957,
-0.02167031355202198,
0.05133805051445961,
0.02430438995361328,
-0.008346117101609707,
-0.003946234937757254,
0.006202620454132557,
-0.030540473759174347,
-0.043419789522886276,
-0.012039040215313435,
-0.009597172029316425,
-0.03748251870274544,
0.030479619279503822,
-0.0037707879673689604,
0.03438783064484596,
-0.007615089416503906,
-0.035387519747018814,
-0.03329874947667122,
-0.07419277727603912,
0.0523541085422039,
-0.009672028943896294,
-0.02174965664744377,
0.04171998053789139,
-0.04928819462656975,
-0.02732706256210804,
-0.009202929213643074,
-0.0042298599146306515,
0.011807726696133614,
-0.045139558613300323,
0.02002505399286747,
-0.0012106526410207152,
0.014395051635801792,
-0.038417309522628784,
-0.06679156422615051,
0.025327473878860474,
0.009563012048602104,
-0.022644080221652985,
-0.003499135375022888,
-0.016080422326922417,
-0.0293179489672184,
-0.030965272337198257,
-0.027472777292132378,
0.03543991222977638,
-0.018930058926343918,
-0.0009547101799398661,
0.029109042137861252,
-0.02263387106359005,
0.07360511273145676,
-0.0028462812770158052,
-0.02643636427819729,
-0.00982974935323,
-0.01840663142502308,
0.023859599605202675,
-0.030882297083735466,
0.09008035808801651,
-0.00883021205663681,
-0.026237405836582184,
-0.02319626323878765,
-0.004163695499300957,
0.05983731150627136,
0.005205274093896151,
-0.02822871506214142,
0.023250436410307884,
0.018139932304620743,
-0.016960453242063522,
-0.015924252569675446,
-0.010683147236704826,
-0.031923338770866394,
0.030431391671299934,
0.009170066565275192,
0.006601458415389061,
-0.04188058525323868,
-0.0436740480363369,
0.016011357307434082,
0.03600247949361801,
-0.0005965203163214028,
0.035185083746910095,
0.0851656049489975,
-0.010643812827765942,
-0.009754180908203125,
-0.012087595649063587,
0.005779279861599207,
0.017058303579688072,
-0.005324395839124918,
-0.022349633276462555,
-0.009617344476282597,
0.015568957664072514,
-0.0377536416053772,
-0.02736826241016388,
0.010578058660030365,
0.03667285665869713,
0.08512021601200104,
-0.0015595019795000553,
0.07478800415992737,
0.03278839960694313,
0.033840421587228775,
-0.010970063507556915,
-0.00840669497847557,
0.00966637022793293,
-0.04024254158139229,
-0.0041344547644257545,
0.03239205852150917,
-0.05455884709954262,
0.005147992633283138,
0.02899998612701893,
0.05470753461122513,
-0.0040405141189694405,
-0.0033627492375671864,
0.03480161726474762,
-0.024250896647572517,
0.009389274753630161,
0.048485830426216125,
-0.03804994001984596,
-0.006810275372117758,
-0.013304325751960278,
0.08804943412542343,
-0.004344603046774864,
-0.000016634006897220388,
0.03699670359492302,
-0.0019556914921849966,
0.028891712427139282,
-0.05344701558351517,
-0.01604183204472065,
-0.01633017510175705,
0.007506272755563259,
-0.004187463317066431,
0.010980005376040936,
-0.02801523171365261,
0.0029828448314219713,
0.04166561737656593,
0.00014074706996325403,
0.035313401371240616,
-0.05534738302230835,
-0.03939433768391609,
-0.03490535169839859,
-0.040461909025907516,
-0.00934729352593422,
0.02740343287587166,
0.028421133756637573,
-0.029541129246354103,
0.01261781807988882,
-0.00009148443496087566,
0.013962752185761929,
0.05268893018364906,
0.05309886857867241,
0.0016962309600785375,
0.08182894438505173,
-0.011731117963790894,
0.027976341545581818,
-0.02668345533311367,
0.00808906089514494,
0.09367426484823227,
0.027780473232269287,
-0.0010373592376708984,
-0.03158639743924141,
0.02609986811876297,
-0.020515093579888344,
0.014101289212703705,
-0.03923042491078377,
0.03389817103743553,
0.0076702130027115345,
0.01477731205523014,
0.04567554593086243,
0.073974609375,
-0.02220224402844906,
-0.0289243683218956,
0.057895250618457794,
-0.04307519271969795,
-0.04550981521606445,
-0.03363170474767685,
-0.008186853490769863,
0.012743720784783363,
0.029150011017918587,
-0.03769297152757645,
0.02050248719751835,
-0.043535903096199036,
-0.04410862922668457,
-0.013950947672128677,
-0.03341085463762283,
0.027113011106848717,
0.015582334250211716,
-0.0406869575381279,
-0.005992532707750797,
0.020074034109711647,
-0.04216731712222099,
-0.0831390842795372,
-0.01421782560646534,
0.01814897358417511,
-0.03770066052675247,
0.02844179794192314,
0.013374892063438892,
0.030469108372926712,
0.055827658623456955,
0.02508452907204628,
0.028850290924310684,
-0.043456267565488815,
0.01466076634824276,
-0.027590632438659668,
0.027556288987398148,
-0.0033940179273486137,
0.029868993908166885,
-0.004620973952114582,
0.013249943032860756,
0.00265593477524817,
-0.09018972516059875,
-0.006351994350552559,
-0.010308448225259781,
0.009237764403223991,
-0.007694403640925884,
0.004630701616406441,
-0.04520157724618912,
-0.0013518260093405843,
0.006438476033508778,
0.014176836237311363,
0.006825976073741913,
0.0015060697915032506,
0.008606813848018646,
-0.003941627219319344,
0.0720883384346962,
-0.054995063692331314,
-0.029514620080590248,
-0.01320927869528532,
-0.02024994231760502,
-0.01466822624206543,
0.027622943744063377,
0.020665010437369347,
0.012742981314659119,
0.0149707505479455,
-0.003875572932884097,
0.013605832122266293,
0.003809974528849125,
-0.03455536067485809,
-0.007246059365570545,
-0.01871323212981224,
-0.032697346061468124,
-0.011964038014411926,
0.013992161490023136,
0.052565086632966995,
0.03731822595000267,
-0.02872302010655403,
0.00675768218934536,
-0.02458002045750618,
0.01100351195782423,
0.041403573006391525,
-0.024750329554080963,
-0.029731761664152145,
-0.004070894327014685,
-0.06969160586595535,
0.0013975995825603604,
-0.017799565568566322,
0.04074975848197937,
0.06848467886447906,
0.021238461136817932,
-0.020612116903066635,
0.007130143232643604,
-0.008135517127811909,
0.007837999612092972,
0.009715425781905651,
-0.033558886498212814,
0.013361970894038677,
0.04479799047112465,
-0.010566346347332,
-0.06531897932291031,
-0.025664769113063812,
-0.014224328100681305,
-0.014215093106031418,
0.01139807514846325,
-0.006602840032428503,
-0.01725439541041851,
0.013060648925602436,
-0.03141500800848007,
0.0028177557978779078,
-0.047841787338256836,
0.014168520458042622,
-0.08986452966928482,
-0.03666761890053749,
0.03714800626039505,
-0.032933931797742844,
0.0023130662739276886,
0.014360916800796986,
-0.021431267261505127,
-0.012621925212442875,
0.026670170947909355,
0.01296674832701683,
0.014401826076209545,
-0.013586662709712982,
0.015280785039067268,
-0.0004518803034443408,
0.05406983196735382,
-0.02499748393893242,
-0.0517459511756897,
0.0356513075530529,
-0.013527477160096169,
-0.018783442676067352,
0.044898055493831635,
-0.01839376799762249,
0.031770702451467514,
-0.004195611458271742,
-0.017231635749340057,
0.0017916631186380982,
0.051598407328128815,
-0.002277100458741188,
-0.0004777280264534056,
0.019482098519802094,
-0.05334765091538429,
0.0035740418825298548,
-0.007725186180323362,
-0.0019975232426077127,
-0.011978674679994583,
-0.03165103867650032,
0.04586467891931534,
0.043852780014276505,
-0.009720670990645885,
-0.014640378765761852,
0.00786969531327486,
0.028929227963089943,
-0.024046767503023148,
0.05167485028505325,
0.010274598374962807,
0.0382414311170578,
0.04784439131617546,
-0.05073245242238045,
0.022543886676430702,
0.013111044652760029,
-0.01070400606840849,
-0.06369097530841827,
-0.007070627063512802,
0.014673979952931404,
-0.013687249273061752,
-0.016010256484150887,
-0.0410483293235302,
0.0054182130843400955,
0.03058239258825779,
-0.08000358194112778,
0.008302166126668453,
-0.046030670404434204,
-0.0029449728317558765,
-0.03484202176332474,
-0.031798191368579865,
-0.00452363071963191,
0.029200533404946327,
0.026143506169319153,
0.039952948689460754,
0.0005883110570721328,
-0.022872399538755417,
-0.01568644307553768,
0.009143338538706303,
-0.0004524273972492665,
0.055487025529146194,
-0.0039268983528018,
0.01987348310649395,
0.054117441177368164,
-0.021253300830721855,
-0.04154607653617859,
0.0042373198084533215,
-0.04149400442838669,
0.006883830297738314,
0.01917455904185772,
-0.011288432404398918,
0.0019335022661834955,
0.007475128397345543,
-0.020843248814344406,
0.018733730539679527,
-0.02452212944626808,
0.005668713245540857,
0.025900352746248245,
0.02834773063659668,
-0.054224710911512375,
-0.02513117529451847,
-0.014227192848920822,
-0.07865695655345917,
-0.025597479194402695,
0.023917358368635178,
-0.03840557858347893,
-0.008197346702218056,
-0.020277081057429314,
0.0001220577978529036,
-0.002990205306559801,
-0.0016235978109762073,
0.005991966463625431,
-0.030567288398742676,
-0.006641798187047243,
0.025969920679926872,
0.0030340137891471386,
-0.011695930734276772,
0.013935977593064308,
0.015368916094303131,
-0.01737387664616108,
0.013743896037340164,
0.005407937802374363,
-0.007283170707523823,
-0.03299623355269432,
0.009352030232548714,
0.017220206558704376,
-0.03767994046211243,
-0.021213894709944725,
-0.05593154579401016,
0.03511912375688553,
0.04838531091809273,
0.05652468279004097,
0.0008882465772330761,
0.030257824808359146,
-0.02341717667877674,
-0.03181563690304756,
-0.09477056562900543,
0.04182950034737587,
0.03308923542499542,
-0.042335622012615204,
-0.03405006602406502,
-0.0029205703176558018,
-0.0008141340222209692,
0.012167484499514103,
0.028017841279506683,
-0.027672458440065384,
-0.024787815287709236,
0.0289032943546772,
-0.016655221581459045,
0.002266947878524661,
-0.0245829951018095,
0.002658918732777238,
-0.018787657842040062,
-0.02758180908858776,
-0.009328478947281837,
-0.029843151569366455,
-0.043352771550416946,
0.013491027057170868,
-0.014039908535778522,
0.002049860078841448,
0.056582387536764145,
-0.012249380350112915,
-0.03517496958374977,
0.016265515238046646,
0.04238802567124367,
0.00995849259197712,
0.09020864963531494,
0.002416160423308611,
-0.022880226373672485,
0.01885344833135605,
-0.017842136323451996,
-0.010856885462999344,
0.07051399350166321,
-0.04167161136865616,
-0.00406760536134243,
-0.02155245468020439,
-0.0006270124576985836,
0.03632359579205513,
-0.025971904397010803,
-0.009608084335923195,
0.036293115466833115,
-0.023833733052015305,
-0.02046641707420349,
0.02998231165111065,
0.017089340835809708,
0.011975564993917942,
-0.024856898933649063,
0.0005702779744751751,
0.03917330130934715,
-0.005675075110048056,
0.0044568199664354324,
0.020899873226881027,
0.003945708740502596,
0.019990092143416405,
-0.006115698721259832,
0.04001187905669212,
-0.02782265469431877,
0.03818009793758392,
-0.01699785515666008,
0.05491536483168602,
-0.03631792962551117,
0.02049415186047554,
-0.020873816683888435,
-0.029733292758464813,
-0.005928292870521545,
0.019621610641479492,
-0.014962495304644108,
0.015135176479816437,
-0.033583153039216995,
0.002884570974856615,
0.052048247307538986,
-0.020129898563027382,
-0.0016541556688025594,
0.0192665234208107,
0.015239855274558067,
-0.01638142205774784,
0.024466153234243393,
-0.03389107063412666,
0.005763460882008076,
-0.014923284761607647,
0.045471880584955215,
0.008938482962548733,
-0.005869119893759489,
0.009140565991401672,
-0.010953690856695175,
-0.035143207758665085,
0.0027620787732303143,
-0.028596442192792892,
0.016253279522061348,
0.0343337245285511,
0.01809752732515335,
0.02473406121134758,
-0.01557969581335783,
0.008903163485229015,
-0.017081700265407562,
0.09392829239368439,
-0.07521090656518936,
-0.04273603856563568,
-0.018568402156233788,
0.026345113292336464,
0.00013228757597971708,
0.010372438468039036
] |
<p>I had a doubt on what kind of transformations can be applied to qubits. I understand that
the transformations need to be reversible , but they also have to preserve the norm thats why
the transformations need to be unitary as $U^{\dagger}U=I$.<br><br>
But then I was reading the paper 'Quantum Mechanics Near closed Timelike Lines , by D.Deutsch'.In it he has applied a transformation give by<br></p>
<p>$|x\rangle |y\rangle \Rightarrow |x\rangle |y \vee f(x)\rangle$ , where $\vee$ stands for XOR and $x,y \in \{0,1\}^{n}$ and $f:\{0,1\}^{n} \rightarrow \{0,1\}^{n}$ <br><br></p>
<p>Now I can see that that the transformation is reversible ( apply twice and get the same thing ) but it is not unitary , am I missing something ?</p>
| 9,433 |
[
0.005824971478432417,
-0.018149185925722122,
0.006631034426391125,
-0.018214058130979538,
0.01906561478972435,
0.0053613255731761456,
-0.04046018049120903,
-0.03912852331995964,
0.004739048890769482,
-0.028725646436214447,
0.05111876130104065,
0.01857202872633934,
0.060246024280786514,
-0.01860048621892929,
0.0006385510787367821,
0.015527377836406231,
-0.04087929055094719,
-0.0019292584620416164,
-0.03286939859390259,
-0.024359669536352158,
-0.011166100390255451,
0.04034492373466492,
0.03683393821120262,
-0.0035545811988413334,
0.010840179398655891,
0.03090919554233551,
-0.009103330783545971,
0.03330282121896744,
0.0417940691113472,
0.08963947743177414,
-0.01526365615427494,
-0.07336430996656418,
-0.027055617421865463,
0.01782941445708275,
-0.02796715870499611,
-0.004824871197342873,
-0.03138634189963341,
-0.05255134776234627,
-0.0037153619341552258,
0.00389019213616848,
-0.016684388741850853,
-0.027395889163017273,
-0.02555435337126255,
0.07528411597013474,
0.004422536585479975,
0.03640057146549225,
-0.005255954340100288,
-0.008890778757631779,
0.027790529653429985,
-0.0333339162170887,
0.11440892517566681,
-0.006372819188982248,
0.005953315645456314,
0.0042909421026706696,
0.00938312616199255,
0.002517918823286891,
0.08312120288610458,
0.046801917254924774,
-0.024064429104328156,
-0.026398254558444023,
-0.003482396947219968,
-0.028017261996865273,
-0.007543214596807957,
0.008461606688797474,
-0.028111351653933525,
0.008550967089831829,
-0.006056745070964098,
0.0002532683138269931,
0.010981290601193905,
-0.015024857595562935,
0.022485490888357162,
-0.002191545208916068,
0.05106320604681969,
-0.06304663419723511,
-0.025783756747841835,
-0.010470942594110966,
0.0017590896459296346,
0.024129437282681465,
0.01752101629972458,
0.048019889742136,
-0.00221682945266366,
0.03036353550851345,
0.015394018031656742,
-0.0019886805675923824,
-0.04507388547062874,
-0.013841044157743454,
0.060589276254177094,
-0.014033143408596516,
0.01202014647424221,
0.03743060678243637,
0.017143305391073227,
0.014735271222889423,
0.04271737113595009,
-0.007839339785277843,
-0.015166902914643288,
0.028943579643964767,
0.021259594708681107,
0.017429500818252563,
-0.0372786819934845,
-0.0138059351593256,
-0.009531237185001373,
-0.03101188689470291,
-0.005001929588615894,
0.04596756398677826,
-0.018756456673145294,
0.02920624613761902,
-0.008201596327126026,
0.04119938239455223,
-0.010816934518516064,
-0.02758634462952614,
-0.06120612472295761,
-0.0000017630976572036161,
-0.05570060759782791,
0.019058892503380775,
0.019715571776032448,
-0.01259850338101387,
0.013323135673999786,
0.009649808518588543,
0.04104483127593994,
0.06710761785507202,
0.044578079134225845,
-0.008905326016247272,
0.018504923209547997,
-0.04938102141022682,
-0.06558558344841003,
0.05414772406220436,
0.03537137806415558,
0.05836481228470802,
-0.033203624188899994,
0.0319051556289196,
-0.013113030232489109,
-0.007709784898906946,
0.00498762633651495,
0.01650712825357914,
0.04744641110301018,
-0.01605626754462719,
-0.13134631514549255,
-0.06967414170503616,
0.031062345951795578,
-0.020528173074126244,
0.020663704723119736,
-0.09223271161317825,
0.06174223870038986,
0.03197623789310455,
0.06848649680614471,
0.02880227006971836,
0.024586550891399384,
0.02742348425090313,
-0.007124889176338911,
0.023240678012371063,
0.02203299105167389,
-0.005243856459856033,
-0.006684225983917713,
-0.04393324255943298,
0.0054613505490124226,
-0.015053206123411655,
0.058460693806409836,
0.04657944291830063,
-0.03473864495754242,
-0.028605222702026367,
0.08007057011127472,
-0.038682349026203156,
0.0069120535627007484,
0.004086717497557402,
-0.013748349621891975,
-0.03061133623123169,
0.09247586876153946,
0.0034369705244898796,
0.013915790244936943,
0.03205934539437294,
-0.005793537013232708,
0.01768333837389946,
0.0014509446918964386,
0.03740309551358223,
0.02551531419157982,
-0.01196957379579544,
-0.02238629385828972,
-0.03291695564985275,
-0.0012077896390110254,
-0.004873259924352169,
-0.006320643704384565,
-0.02279702201485634,
-0.022328229621052742,
-0.006605012807995081,
-0.031096283346414566,
0.01679195649921894,
0.013637681491672993,
-0.0032021598890423775,
-0.02206835150718689,
-0.0669032633304596,
0.006195578724145889,
-0.050539277493953705,
0.03695483133196831,
0.020240992307662964,
0.00041780798346735537,
0.03391747549176216,
0.011922317557036877,
0.01120805460959673,
-0.020179621875286102,
-0.026728494092822075,
-0.02377367950975895,
-0.0060491664335131645,
-0.011461381800472736,
-0.00520982826128602,
0.02332613617181778,
0.03828844428062439,
0.028864465653896332,
0.012124436907470226,
0.04351641610264778,
-0.023400751873850822,
0.0023555748630315065,
-0.010628808289766312,
0.00817448366433382,
0.031441446393728256,
-0.00492478720843792,
-0.007895833812654018,
0.03583007678389549,
-0.018770640715956688,
-0.012388722971081734,
-0.0037296703085303307,
-0.03979551047086716,
0.05689819157123566,
0.019870681688189507,
-0.02646295726299286,
-0.005141288973391056,
0.0609138160943985,
0.03760525956749916,
0.012937083840370178,
0.012544075027108192,
-0.05924639478325844,
-0.024295266717672348,
0.03026384487748146,
-0.01589052937924862,
0.03456834331154823,
-0.04159628599882126,
0.037783633917570114,
0.020052829757332802,
0.022966336458921432,
0.027023641392588615,
-0.02445901744067669,
-0.019842298701405525,
-0.03650832921266556,
0.00675432151183486,
-0.01223940309137106,
0.007896522991359234,
-0.014723771251738071,
-0.009348046965897083,
-0.009639290161430836,
0.012457220815122128,
0.003598666051402688,
-0.026974381878972054,
0.04132337495684624,
-0.02778473310172558,
0.012962233275175095,
0.0037893331609666348,
-0.014302855357527733,
-0.012288031168282032,
-0.01417618989944458,
0.010564165189862251,
0.011976957321166992,
0.012753370217978954,
-0.0270081739872694,
-0.017633330076932907,
-0.023274708539247513,
0.020801398903131485,
-0.004477489739656448,
-0.025121303275227547,
0.0010604424169287086,
0.02509419061243534,
-0.03805108368396759,
0.03076767548918724,
-0.03620395064353943,
-0.012674733065068722,
-0.02905092015862465,
-0.02826583944261074,
0.03743213787674904,
0.022730344906449318,
0.008832897990942001,
-0.07228988409042358,
-0.007062424905598164,
-0.0006003829184919596,
-0.006640179082751274,
0.017758872359991074,
0.01837940141558647,
-0.02472350001335144,
0.06259890645742416,
-0.06137755513191223,
0.014342737384140491,
0.009088567458093166,
-0.02780298702418804,
0.032828036695718765,
0.0054280757904052734,
-0.03912811353802681,
-0.07717641443014145,
-0.030193738639354706,
-0.06756565719842911,
0.012987523339688778,
-0.01880212128162384,
-0.0157379899173975,
0.054310694336891174,
-0.016499454155564308,
-0.00812279712408781,
-0.025976115837693214,
0.003938457928597927,
-0.023916928097605705,
-0.027020640671253204,
0.005627860315144062,
0.022580277174711227,
-0.018765753135085106,
0.04222957789897919,
0.017233069986104965,
-0.03554941713809967,
-0.011438772082328796,
-0.016377493739128113,
-0.05816083773970604,
0.008735906332731247,
0.00691687036305666,
0.021746864542365074,
0.03141398727893829,
0.0004878095642197877,
0.06912942975759506,
0.01706911250948906,
-0.057608891278505325,
-0.054835762828588486,
0.019448356702923775,
0.008956377394497395,
-0.03517298772931099,
0.0032667608465999365,
0.04848799109458923,
-0.009964210912585258,
0.03602784499526024,
0.002093131421133876,
0.017433280125260353,
0.06590180844068527,
0.001488330541178584,
-0.042162369936704636,
0.03843023627996445,
0.007207188755273819,
-0.002094384515658021,
0.046193066984415054,
-0.030355898663401604,
-0.04542188346385956,
0.006292922887951136,
0.017735449597239494,
0.02396896295249462,
-0.004296659491956234,
-0.026348281651735306,
0.06153686344623566,
0.026546353474259377,
-0.012223402038216591,
0.005653291940689087,
0.04828159883618355,
-0.022332509979605675,
0.017028050497174263,
-0.003323311684653163,
0.019363796338438988,
0.020077060908079147,
-0.04788501188158989,
0.044792573899030685,
0.004749403800815344,
0.028151651844382286,
-0.019108077511191368,
0.00511083472520113,
-0.002436244860291481,
-0.014212669804692268,
0.05741414427757263,
-0.03697030618786812,
-0.05490127205848694,
0.02466842345893383,
0.02060343511402607,
0.021618207916617393,
0.0067053670063614845,
-0.02067727968096733,
-0.01257409993559122,
0.015607362613081932,
0.019381510093808174,
0.023813435807824135,
0.0699303150177002,
0.040798164904117584,
0.039833247661590576,
0.025159349665045738,
-0.0012058054562658072,
-0.016042297706007957,
-0.02333652414381504,
-0.05613955110311508,
0.03230784833431244,
-0.023667987436056137,
-0.005424208473414183,
-0.007784619461745024,
-0.01872866414487362,
0.026216406375169754,
-0.022165192291140556,
-0.007405958138406277,
-0.0072327968664467335,
-0.03007236309349537,
-0.07852374017238617,
-0.006818287540227175,
-0.028272388502955437,
-0.031077153980731964,
-0.002221946604549885,
0.0499550886452198,
0.0476265512406826,
-0.04273796081542969,
0.03168214485049248,
0.0042360695078969,
-0.05851896479725838,
0.010445203632116318,
0.005998141132295132,
0.012194640934467316,
0.03822777047753334,
0.0138084152713418,
0.016451619565486908,
0.01628652587532997,
-0.00006202677468536422,
-0.015721216797828674,
0.000534242601133883,
0.04592256247997284,
0.0018227886175736785,
-0.030607353895902634,
-0.024692853912711143,
-0.04291810095310211,
-0.009039233438670635,
0.027466997504234314,
0.07833779603242874,
0.023325147107243538,
0.03064023330807686,
0.039133284240961075,
0.019610321149230003,
-0.05806778743863106,
0.02030976489186287,
0.037339288741350174,
-0.007940225303173065,
-0.008014800027012825,
-0.030245328322052956,
-0.0016787366475909948,
0.011945032514631748,
0.010547084733843803,
0.0211386326700449,
-0.03279608115553856,
-0.04305146634578705,
-0.0007631193147972226,
0.027401568368077278,
0.031249692663550377,
-0.018310589715838432,
-0.023843027651309967,
0.010262100957334042,
-0.01597929373383522,
0.0031533215660601854,
-0.004268655087798834,
0.010115440003573895,
0.021074604243040085,
0.026914458721876144,
0.029696865007281303,
0.022816047072410583,
-0.01661420240998268,
-0.02683207578957081,
0.045367367565631866,
0.06432195007801056,
0.018225889652967453,
0.015335386618971825,
-0.024840280413627625,
-0.04859945550560951,
0.03180443122982979,
-0.033153388649225235,
0.053712330758571625,
0.022043609991669655,
-0.03485441580414772,
-0.017407342791557312,
-0.03415559232234955,
-0.005776377860456705,
0.021626710891723633,
0.01564894989132881,
0.03177659958600998,
-0.006959669291973114,
-0.009366116486489773,
-0.024924669414758682,
-0.020984748378396034,
-0.017617985606193542,
0.04723995178937912,
-0.01609189808368683,
0.03554041311144829,
0.025994611904025078,
0.04539769887924194,
-0.01875273883342743,
-0.09223713725805283,
0.016800224781036377,
0.019938591867685318,
0.019563093781471252,
0.05660298839211464,
-0.008363976143300533,
-0.07037287205457687,
0.0374460406601429,
-0.016957469284534454,
0.008841906674206257,
0.032007601112127304,
-0.021471796557307243,
0.05855627730488777,
0.009466060437262058,
0.013430087827146053,
0.02563609555363655,
0.02164345607161522,
0.02338440530002117,
-0.030263904482126236,
-0.022136330604553223,
0.028299324214458466,
-0.06737259030342102,
0.017681151628494263,
-0.023064596578478813,
-0.007016384042799473,
-0.015545395202934742,
0.05474717170000076,
-0.033647701144218445,
0.00374201824888587,
-0.004040906205773354,
-0.012053283862769604,
-0.02851478010416031,
0.01953762024641037,
-0.004424261394888163,
0.010072232224047184,
-0.04346819221973419,
0.007708111312240362,
-0.007829096168279648,
-0.014880770817399025,
0.019494380801916122,
-0.03792555257678032,
0.0009835159871727228,
0.04968079924583435,
-0.032616619020700455,
0.022202810272574425,
0.010201234370470047,
-0.03703539818525314,
-0.022366710007190704,
-0.08234535902738571,
0.026077505201101303,
-0.0250855665653944,
-0.02488250471651554,
0.011524737812578678,
-0.029170682653784752,
-0.02235393039882183,
-0.003150991164147854,
-0.00046636429033242166,
-0.013515254482626915,
-0.06507638096809387,
0.009833874180912971,
0.017404841259121895,
0.0298475231975317,
-0.08576860278844833,
-0.06517912447452545,
0.023445622995495796,
-0.01591009646654129,
-0.017725640907883644,
-0.024635808542370796,
0.025724241510033607,
0.008470633998513222,
-0.02042287215590477,
-0.0362655334174633,
0.047308094799518585,
-0.02353946678340435,
0.0007091543520800769,
0.0023270186502486467,
0.026063302531838417,
0.0336705818772316,
-0.014967954717576504,
-0.024755174294114113,
0.022019226104021072,
-0.020011255517601967,
0.012577833607792854,
0.016409724950790405,
0.03349330648779869,
-0.04122514650225639,
-0.02289022132754326,
-0.01708957739174366,
0.0031716544181108475,
0.017255889251828194,
-0.012538659386336803,
0.014781341888010502,
0.03396019712090492,
0.021324874833226204,
0.015347200445830822,
0.007042587734758854,
-0.0005230994429439306,
0.006578915752470493,
0.006998369935899973,
0.009965757839381695,
-0.024537837132811546,
-0.01274490263313055,
-0.047068651765584946,
0.03832761570811272,
-0.010088352486491203,
0.02252233400940895,
0.015893951058387756,
0.06743893027305603,
-0.014174001291394234,
-0.018491249531507492,
0.029237767681479454,
-0.06055925413966179,
0.01955549418926239,
-0.026005802676081657,
-0.011995095759630203,
-0.011600973084568977,
-0.0029930020682513714,
-0.047275360673666,
-0.03443249687552452,
-0.03858284279704094,
0.018964141607284546,
0.08113172650337219,
-0.002090539550408721,
0.03240620344877243,
0.048020295798778534,
0.010460175573825836,
-0.015459433197975159,
-0.027040250599384308,
-0.03236505016684532,
0.010202907025814056,
-0.007063874509185553,
0.018746376037597656,
-0.02864961326122284,
-0.022829603403806686,
0.0032770156394690275,
0.04877939820289612,
-0.01859406754374504,
0.026460519060492516,
0.01048192847520113,
0.041927020996809006,
0.020575689151883125,
-0.005304274149239063,
-0.042508598417043686,
0.023181632161140442,
-0.04535478726029396,
0.029039975255727768,
0.009796499274671078,
-0.009744646027684212,
0.036145664751529694,
0.030872194096446037,
0.05531250312924385,
-0.00945498701184988,
-0.04589902609586716,
-0.05859488248825073,
-0.0049296654760837555,
-0.002575031714513898,
0.01576811447739601,
-0.005522890016436577,
0.011038816533982754,
0.05229203402996063,
0.02618013508617878,
0.00809107068926096,
-0.007631674874573946,
-0.026260774582624435,
0.011658231727778912,
-0.018946168944239616,
-0.036910802125930786,
0.035891804844141006,
-0.016544902697205544,
-0.018379563465714455,
0.008673755452036858,
-0.03980078175663948,
0.016146140173077583,
0.0015221211360767484,
0.03940603882074356,
-0.031004516407847404,
0.06181894615292549,
0.020476896315813065,
0.03117893636226654,
-0.007046897429972887,
0.012318463996052742,
0.09703890234231949,
0.052882030606269836,
0.009482143446803093,
-0.06572343409061432,
-0.02370142564177513,
-0.009079504758119583,
0.0022952721919864416,
0.00016427751688752323,
0.017980676144361496,
0.017174510285258293,
0.00910950731486082,
-0.015884943306446075,
0.04548380523920059,
0.02553437650203705,
-0.03615855425596237,
0.050946786999702454,
-0.03041803278028965,
-0.04159526899456978,
0.021201971918344498,
0.018233826383948326,
0.0017899846425279975,
-0.0176383126527071,
-0.051149625331163406,
-0.007069824263453484,
-0.03480910137295723,
-0.023221932351589203,
-0.02235543355345726,
-0.008531824685633183,
0.03476255387067795,
0.03700698912143707,
0.00046669176663272083,
-0.014384121634066105,
-0.008650200441479683,
-0.021907368674874306,
-0.03794856742024422,
0.03364555910229683,
-0.0022698305547237396,
-0.009881715290248394,
0.020374711602926254,
0.06204087287187576,
0.02700825408101082,
0.01529682893306017,
0.03341546654701233,
-0.04315617308020592,
-0.041782647371292114,
0.0024685258977115154,
-0.03688940778374672,
0.04690513759851456,
-0.013868720270693302,
-0.0025063587818294764,
0.018370233476161957,
0.00003159831976518035,
0.002782630966976285,
-0.060998380184173584,
-0.0040034824050962925,
0.02100001648068428,
0.007098364643752575,
0.02456534095108509,
-0.012243266217410564,
0.0026285441126674414,
0.020023096352815628,
0.009161903522908688,
0.03414316102862358,
-0.002715702634304762,
-0.0049555422738194466,
0.0033504795283079147,
0.0114187803119421,
0.015611812472343445,
-0.0009279425721615553,
0.01687079295516014,
-0.04266640171408653,
-0.012964947149157524,
-0.034030139446258545,
-0.04192885383963585,
0.04053011164069176,
-0.007114812731742859,
0.03067139908671379,
-0.006002150010317564,
-0.015759948641061783,
-0.009452708065509796,
-0.10962437838315964,
0.02077300287783146,
-0.006379447411745787,
-0.02175794541835785,
0.004310101270675659,
0.0056406245566904545,
0.04232881963253021,
0.06263861060142517,
-0.006535339634865522,
-0.031599145382642746,
0.021613452583551407,
-0.02177903614938259,
0.06033679097890854,
-0.01171842496842146,
-0.02933628298342228,
0.013473893515765667,
-0.030369991436600685,
0.009169070050120354,
-0.037059661000967026,
0.0028645650018006563,
0.035799574106931686,
-0.017916440963745117,
-0.024435291066765785,
0.05308527499437332,
-0.013256622478365898,
-0.008604180067777634,
-0.019442666321992874,
-0.03164410591125488,
0.026181792840361595,
0.024263979867100716,
0.02067204751074314,
-0.02559327706694603,
-0.048015058040618896,
-0.002375143114477396,
0.002012824174016714,
0.004264505114406347,
-0.0133245550096035,
-0.02317204885184765,
-0.02115088328719139,
0.0018866462633013725,
0.054213739931583405,
0.006026877090334892,
-0.002876925515010953,
-0.01242497656494379,
0.026355566456913948,
0.004385550040751696,
0.005879630800336599,
-0.018572727218270302,
0.034016549587249756,
0.024216270074248314,
-0.020619338378310204,
0.022730056196451187,
0.05424819514155388,
-0.012351930141448975,
-0.0011596080148592591,
0.0008625479531474411,
0.02015100046992302,
0.03490941971540451,
-0.019015951082110405,
-0.04356338828802109,
0.03679827228188515,
-0.052594587206840515,
-0.006481654942035675,
0.06339800357818604,
-0.002367848064750433,
0.007184525951743126,
0.04031703993678093,
0.02184407413005829,
-0.02838077023625374,
0.03754834085702896,
-0.004254434257745743,
-0.001838933676481247,
0.014814222231507301,
-0.031019536778330803,
0.024297766387462616,
-0.008025716990232468,
-0.015389574691653252,
-0.015052616596221924,
-0.008424323052167892,
0.007867412641644478,
0.03384101018309593,
0.008491954766213894,
0.0004712285881396383,
-0.028478674590587616,
0.018442360684275627,
0.054676175117492676,
0.04942722246050835,
-0.00973320472985506,
0.026643458753824234,
0.049495503306388855,
-0.04972698912024498,
0.009850253351032734,
0.018326934427022934,
0.013030863367021084,
-0.09041393548250198,
-0.019729070365428925,
0.02592889778316021,
0.024433325976133347,
0.012616481631994247,
-0.0570235438644886,
-0.001111657707951963,
0.014691394753754139,
-0.06278273463249207,
-0.005223060492426157,
-0.04833132028579712,
-0.02428535372018814,
-0.007995174266397953,
0.03811497241258621,
-0.03808151185512543,
0.060213394463062286,
-0.001962022390216589,
0.012552398256957531,
-0.006944022607058287,
0.014015032909810543,
-0.004378266166895628,
-0.04972129687666893,
-0.02342071384191513,
0.0263480544090271,
-0.02157556638121605,
-0.00806836411356926,
0.03487834706902504,
-0.03373066335916519,
-0.05130442604422569,
0.033427074551582336,
-0.022365069016814232,
-0.011739879846572876,
-0.022053634747862816,
0.0108084911480546,
0.04416033625602722,
0.0032729050144553185,
0.0323544442653656,
-0.028573524206876755,
0.017318619415163994,
-0.001535810180939734,
0.019536631181836128,
0.004413393791764975,
-0.008083189837634563,
-0.031657278537750244,
0.03130446374416351,
-0.032804880291223526,
-0.028614675626158714,
0.0023566014133393764,
-0.0027534395921975374,
0.0061853849329054356,
0.007283855229616165,
0.004524771124124527,
0.0078026833944022655,
-0.017267324030399323,
0.04192904755473137,
-0.049694497138261795,
-0.026916053146123886,
0.018648745492100716,
0.005635636392980814,
0.01522899977862835,
0.005786525085568428,
0.00251975585706532,
-0.05140653997659683,
0.05274217203259468,
-0.004984752740710974,
-0.014783973805606365,
-0.06792289763689041,
-0.015332427807152271,
0.020935310050845146,
0.0035248538479208946,
0.004908333532512188,
-0.044717952609062195,
-0.04635429009795189,
-0.011416413821280003,
-0.012722019106149673,
0.019479304552078247,
-0.03945856913924217,
-0.01432053092867136,
-0.046028364449739456,
-0.02935379184782505,
0.025370564311742783,
0.015964562073349953,
-0.005401864182204008,
-0.03834673389792442,
-0.038631368428468704,
-0.013828940689563751,
0.03048861213028431,
0.0603206604719162,
-0.011338990181684494,
-0.00329544092528522,
0.015183650888502598,
0.005334377754479647,
0.04758482798933983,
-0.02183959260582924,
-0.013523138128221035,
-0.04998914152383804,
0.010229813866317272,
0.0031613246537745,
-0.00934714637696743,
-0.06131463497877121,
0.024911800399422646,
0.038885101675987244,
-0.01907472126185894,
-0.015002920292317867,
-0.0030372319743037224,
-0.04266781359910965,
0.039635688066482544,
0.01070398185402155,
0.034239254891872406,
0.07943723350763321,
0.02093466743826866,
0.028813190758228302,
0.024908069521188736,
-0.028369059786200523,
-0.06449107825756073,
-0.0004933790187351406,
-0.029587917029857635,
-0.014852083288133144,
-0.0042481133714318275,
-0.017821108922362328,
0.052878238260746,
-0.015519941225647926,
-0.007802923675626516,
0.03346149995923042,
-0.05404255539178848,
0.016945360228419304,
0.05606989189982414,
0.007879240438342094,
0.02084646373987198,
0.006913554389029741,
0.024990303441882133,
-0.005886638071388006,
0.0027038862463086843,
0.038735538721084595,
0.038709450513124466,
0.02302703820168972,
0.0038298293948173523,
0.03013937920331955,
0.04643774777650833,
-0.02399219200015068,
0.037247441709041595,
-0.003438294166699052,
0.037725456058979034,
-0.03262103721499443,
0.013762146234512329,
0.03614015132188797,
-0.033173322677612305,
-0.027035072445869446,
0.015376592054963112,
-0.0362093411386013,
0.06690242886543274,
-0.03861016035079956,
0.023746665567159653,
-0.0344189777970314,
-0.025854939594864845,
-0.027041206136345863,
0.028952449560165405,
0.05394965410232544,
0.055857717990875244,
-0.07085341215133667,
-0.013359216041862965,
-0.05651191622018814,
-0.02813629060983658,
0.004483036231249571,
-0.036655452102422714,
-0.03343326598405838,
0.004685943480581045,
0.004401280079036951,
-0.004137174226343632,
-0.03575856238603592,
-0.022987812757492065,
-0.02219962328672409,
-0.0053279101848602295,
0.030356060713529587,
0.02327367477118969,
-0.007609871681779623,
0.029261525720357895,
-0.021492773666977882,
0.0510268472135067,
-0.05802755430340767,
-0.010346490889787674,
-0.028594529256224632,
0.04444617033004761,
0.03973668813705444,
-0.0085178567096591
] |
<p>While reading Polchinski's Chapter 1, I encountered the following on page 24,</p>
<p>"For example, the $(D-1)$ dimensional vector representation of $SO(D-1)$ breaks up into an invariant and a $(D-2)$-vector under the $SO(D-2)$ acting on the transverse directions, $$ \vec{v} = (v^1, 0, 0, \dots) + (0. v^2, v^2, \dots, v^{D-1}) $$ </p>
<p>Thus, if a massive particle is in the vector representation of $SO(D-1)$, we will see a scalar and a vector when we look at the transformation properties under $S0(D-2)$. This idea extends to any representation : one can always reconstruct the full $SO(D-1)$ spin representation from the behaviour under $SO(D-2)$. " </p>
<p>I can show that the second excited states which is given by, $$ \alpha_{-1}^i \alpha_{-1}^j |0\rangle \bigoplus \alpha_{-2}^i |0\rangle $$ where $i,j$ runs from $\{2,D-1\}$ and treating them symmetric, the no. of excited states would be $\dfrac{(D+1)(D-2)}{2}$ which matches with the dimensions of a traceless symmetric irrep of $SO(D-1)$. </p>
<p>My question is how can we be sure by just matching numbers, and what does this Physically mean and is there a mechanism to do this consistently ? What does this business of "reconstructing $SO(D-1)$ representation from $SO(D-2)$" mean ? </p>
<p>I know a little bit about group theory like, Cartan Matrices, Dynkin Diagrams and Young Tableaux method for SU(N) theory, so it is fine if someone could give me a good reference. A precise answer would ofcourse be great :). </p>
| 9,434 |
[
-0.020413769409060478,
-0.02314787730574608,
-0.008940636180341244,
-0.04259176179766655,
0.05342958867549896,
0.009432013146579266,
-0.03830781206488609,
-0.005302916280925274,
0.030721034854650497,
-0.08394818753004074,
0.022952977567911148,
-0.013508584350347519,
0.056441426277160645,
0.025319673120975494,
0.010408518835902214,
0.01505396980792284,
0.006417492404580116,
-0.03881480544805527,
-0.0020635314285755157,
-0.00956833828240633,
0.021402548998594284,
0.038094982504844666,
0.018873941153287888,
-0.00620941212400794,
-0.003876686794683337,
0.052528996020555496,
0.017170820385217667,
0.019595978781580925,
-0.01273643784224987,
0.023937245830893517,
0.004635668825358152,
-0.035261183977127075,
-0.023308344185352325,
0.023494375869631767,
-0.02831038273870945,
0.0064132907427847385,
0.03150913119316101,
-0.04033525660634041,
0.02597861737012863,
0.01064844336360693,
-0.03935698792338371,
-0.0005629642400890589,
-0.05126846954226494,
0.024668535217642784,
0.004232895560562611,
0.03383300080895424,
-0.010287079960107803,
-0.00993883516639471,
0.044313881546258926,
-0.05608747899532318,
0.0582161545753479,
0.017780877649784088,
0.02709386497735977,
-0.010842422023415565,
0.0162039827555418,
-0.021938329562544823,
0.05102890357375145,
0.054234933108091354,
0.029240364208817482,
-0.04787987098097801,
-0.04975883290171623,
-0.02133139781653881,
0.022394631057977676,
0.01892031356692314,
-0.008720722049474716,
0.0007015583105385303,
0.009111356921494007,
-0.03375685214996338,
0.024963773787021637,
-0.01531684398651123,
0.005180473905056715,
0.013248909264802933,
0.030110549181699753,
-0.018279194831848145,
0.026419207453727722,
-0.0027297884225845337,
0.011723464354872704,
-0.0016292664222419262,
0.020246820524334908,
0.015571704134345055,
-0.034540243446826935,
0.016381917521357536,
-0.0055551775731146336,
0.015855954959988594,
0.011837492696940899,
-0.03679738938808441,
0.050176866352558136,
0.007230819668620825,
-0.0013031462440267205,
0.04513535648584366,
0.0018774010241031647,
-0.006725416984409094,
0.04804433509707451,
0.001641943003050983,
-0.058705151081085205,
-0.015409394167363644,
0.014959468506276608,
0.06530046463012695,
-0.04613048583269119,
-0.0025659629609435797,
-0.024496007710695267,
-0.016478125005960464,
-0.012655545026063919,
0.06776399165391922,
-0.0042708092369139194,
0.02181278169155121,
-0.030552128329873085,
-0.004329366143792868,
0.002692960435524583,
-0.040117040276527405,
-0.045496873557567596,
-0.0025887403171509504,
-0.010324915871024132,
-0.008053443394601345,
-0.010362274013459682,
-0.006715896539390087,
-0.012648564763367176,
0.02916761115193367,
0.05806373059749603,
0.07534732669591904,
0.013074559159576893,
0.04350171238183975,
0.0002476910303812474,
-0.04661887511610985,
-0.07717883586883545,
0.026509735733270645,
0.06303776800632477,
0.0018788687884807587,
-0.04356808960437775,
0.024478165432810783,
0.07812859117984772,
0.011575520038604736,
0.001209167530760169,
0.0008786329417489469,
0.03005126118659973,
0.008088549599051476,
-0.08616422116756439,
-0.03986898064613342,
0.03039487637579441,
-0.0164575707167387,
0.0060092792846262455,
-0.067608542740345,
-0.0002797058841679245,
0.05953846871852875,
0.06253208220005035,
-0.02838708646595478,
0.018149560317397118,
-0.00803661160171032,
0.011945228092372417,
0.027716917917132378,
0.003590337699279189,
-0.01971231773495674,
-0.006411978043615818,
-0.04912439361214638,
-0.048029571771621704,
-0.024665256962180138,
0.07730471342802048,
0.03489701449871063,
0.0017110686749219894,
-0.034078359603881836,
0.09958554059267044,
-0.012571504339575768,
-0.002110973931849003,
0.03966708108782768,
0.006864992436021566,
-0.008333127945661545,
0.08622761815786362,
0.003962602932006121,
-0.004484076052904129,
0.025056879967451096,
-0.02805124595761299,
0.053614068776369095,
0.021900374442338943,
0.031168658286333084,
0.03411059454083443,
-0.011196639388799667,
-0.05606415122747421,
-0.01738758198916912,
-0.012482251040637493,
-0.017563672736287117,
-0.014437107369303703,
-0.0323198176920414,
-0.005673589650541544,
0.025598321110010147,
-0.0014507374726235867,
0.02423088625073433,
0.021131010726094246,
0.011072760447859764,
-0.002869504503905773,
-0.051359742879867554,
-0.014976351521909237,
-0.0034077379386872053,
-0.004068606998771429,
0.013624345883727074,
-0.056542400270700455,
0.037016596645116806,
-0.008296284824609756,
0.02070857584476471,
0.030613932758569717,
-0.026587503030896187,
-0.017544012516736984,
-0.004430136177688837,
0.035813022404909134,
-0.030223019421100616,
0.021226245909929276,
0.028288645669817924,
0.050780121237039566,
0.016648735851049423,
0.024480657652020454,
-0.009486382827162743,
-0.005559857003390789,
-0.02118232659995556,
0.007294060662388802,
0.0027164893690496683,
0.021230854094028473,
0.01974274404346943,
-0.024373004212975502,
0.01331098098307848,
0.013965080492198467,
0.013739991933107376,
-0.004924642853438854,
0.05145367980003357,
0.043427545577287674,
0.035579755902290344,
-0.01169841829687357,
0.008964943699538708,
0.004962199367582798,
-0.00098616408649832,
-0.002483762102201581,
-0.03558725118637085,
-0.03931208327412605,
-0.035757824778556824,
0.010723797604441643,
0.018757915124297142,
-0.028994426131248474,
-0.015353703871369362,
0.025309421122074127,
0.045016758143901825,
0.003015592461451888,
-0.00463122921064496,
-0.02775495871901512,
-0.003541651414707303,
0.015583569183945656,
0.01124447863548994,
0.015656637027859688,
0.03013339452445507,
-0.008221231400966644,
0.030693883076310158,
0.01594657078385353,
0.008767547085881233,
-0.009969742968678474,
0.06162731349468231,
-0.039508502930402756,
0.014277776703238487,
0.007150625344365835,
-0.03577340394258499,
0.04537519812583923,
0.014106168411672115,
0.017520539462566376,
0.0759834572672844,
-0.036833882331848145,
-0.011150719597935677,
-0.02614481933414936,
-0.0014604809693992138,
0.010595211759209633,
-0.012330496683716774,
-0.03397367149591446,
-0.02046218141913414,
0.010073860175907612,
-0.02890915609896183,
0.01818966679275036,
-0.013290714472532272,
-0.051180798560380936,
0.008220602758228779,
0.007646153215318918,
0.03255467116832733,
0.015351761132478714,
0.021197646856307983,
-0.04219496250152588,
0.024130363017320633,
0.01065966859459877,
-0.01580098271369934,
0.05652356892824173,
0.07510107755661011,
-0.0495336651802063,
0.00034866173518821597,
-0.10094467550516129,
-0.042740415781736374,
0.023152334615588188,
-0.002364180749282241,
0.0003733291814569384,
0.009074312634766102,
-0.0021945941261947155,
-0.0734880268573761,
-0.043428387492895126,
0.002346813678741455,
0.009147848933935165,
-0.04811432957649231,
-0.02881450392305851,
0.029372410848736763,
0.023837625980377197,
-0.03085278905928135,
0.011035502888262272,
-0.016549237072467804,
-0.017145780846476555,
-0.012401942163705826,
-0.01766253635287285,
0.019632386043667793,
-0.023879457265138626,
0.06247429922223091,
0.038326576352119446,
-0.015327303670346737,
-0.010987120680510998,
-0.04130172356963158,
-0.046334996819496155,
-0.0034309569746255875,
0.05449887365102768,
0.02096457965672016,
0.008782421238720417,
-0.040738023817539215,
0.06054769083857536,
-0.016267452389001846,
-0.038194768130779266,
-0.017059357836842537,
0.02524169534444809,
-0.02708481065928936,
-0.009677312336862087,
0.005014700815081596,
0.027382636442780495,
0.03671607747673988,
0.025493694469332695,
0.029224682599306107,
0.048250824213027954,
0.014911818318068981,
-0.025578921660780907,
-0.05625685304403305,
0.03838489204645157,
0.016198642551898956,
0.006649252958595753,
0.030216772109270096,
-0.04310224577784538,
-0.029561104252934456,
0.003107822732999921,
0.02862887643277645,
0.03795458376407623,
0.03124765306711197,
-0.022107897326350212,
0.06596311181783676,
-0.012814238667488098,
0.005697884131222963,
0.0051413592882454395,
0.03058161959052086,
-0.012485718354582787,
-0.04871023818850517,
0.0003365747397765517,
0.015659479424357414,
0.025128396227955818,
-0.03402441367506981,
-0.011329283937811852,
0.026204295456409454,
0.006665670312941074,
-0.02965719625353813,
-0.005140326451510191,
-0.03678907826542854,
-0.008968261070549488,
0.0020778956823050976,
-0.032385192811489105,
-0.016656773164868355,
0.027465341612696648,
0.04139547422528267,
0.04260775074362755,
-0.011025694198906422,
-0.002557126572355628,
0.031689129769802094,
-0.035506635904312134,
0.009020215831696987,
-0.0250998567789793,
0.03470374271273613,
-0.01520700752735138,
0.04973923787474632,
0.048212021589279175,
0.03154177963733673,
-0.01716780476272106,
0.003339138114824891,
-0.07291620969772339,
-0.013732009567320347,
-0.03425190970301628,
0.03658250719308853,
-0.026508953422307968,
-0.0019146216800436378,
0.013523357920348644,
-0.012257740832865238,
-0.05884174630045891,
0.004348506685346365,
-0.020164718851447105,
-0.04982691630721092,
0.02428329549729824,
-0.0649634525179863,
-0.031288351863622665,
-0.047562126070261,
0.06231911852955818,
0.03985017538070679,
-0.07027597725391388,
-0.021182434633374214,
0.021489614620804787,
-0.029748424887657166,
0.032918527722358704,
-0.03910126909613609,
0.015622688457369804,
0.01441493071615696,
0.020333439111709595,
0.043279070407152176,
0.02516513131558895,
-0.018131405115127563,
-0.0444888174533844,
-0.012316551059484482,
0.06611627340316772,
0.026281798258423805,
-0.01259399950504303,
-0.012458798475563526,
-0.03916385397315025,
-0.010593743994832039,
-0.004966503940522671,
0.04667041823267937,
0.014045781455934048,
0.0037895820569247007,
0.04247068986296654,
-0.0026535335928201675,
-0.03592903912067413,
0.04501465708017349,
0.08041875809431076,
-0.008742861449718475,
0.0002898300881497562,
-0.04869386926293373,
-0.014711503870785236,
-0.02356852777302265,
-0.006195883732289076,
0.004660285543650389,
-0.019636206328868866,
-0.0008099106489680707,
0.002491976600140333,
0.023636629804968834,
0.01271006464958191,
-0.027495868504047394,
0.0034563185181468725,
-0.007757867220789194,
0.021268852055072784,
0.013852919451892376,
0.010565731674432755,
0.002292790450155735,
0.0031226726714521646,
0.011802669614553452,
0.023627234622836113,
0.0037139023188501596,
-0.06643686443567276,
-0.01651688478887081,
0.007236588280647993,
0.03811425343155861,
-0.0003003596793860197,
-0.005322389770299196,
-0.05483437702059746,
-0.005952680949121714,
0.06785014271736145,
-0.029710739850997925,
0.011261447332799435,
-0.005406463053077459,
-0.06962072849273682,
-0.043561648577451706,
-0.013007539324462414,
-0.03352586552500725,
0.028285400941967964,
-0.008786456659436226,
0.011143721640110016,
-0.027264142408967018,
-0.007352359127253294,
-0.04787297174334526,
0.011456807143986225,
0.002963034901767969,
0.01349571067839861,
0.0452408641576767,
0.03188057616353035,
-0.0063126180320978165,
0.046727318316698074,
-0.05427445098757744,
-0.06061335653066635,
-0.0023513594642281532,
0.020611915737390518,
0.010324493981897831,
0.0443049818277359,
-0.04796574264764786,
-0.06061933934688568,
0.03408756107091904,
0.005044220015406609,
0.025877973064780235,
0.0074600884690880775,
-0.056561220437288284,
0.04604591429233551,
0.011229298077523708,
-0.03531958907842636,
0.020915716886520386,
0.02017507329583168,
0.003135481383651495,
-0.015269838273525238,
-0.006955322809517384,
0.0069246371276676655,
-0.001227054512128234,
0.011589506641030312,
-0.041314080357551575,
0.03047003038227558,
-0.04966909438371658,
0.06976047158241272,
-0.015930097550153732,
0.011522297747433186,
0.033703334629535675,
-0.02419951558113098,
-0.010575633496046066,
0.0716642513871193,
-0.003142321715131402,
-0.0190754234790802,
0.00039160967571660876,
0.06978991627693176,
0.022370805963873863,
-0.015381842851638794,
0.0197394210845232,
-0.027560018002986908,
0.00469185458496213,
0.008399762213230133,
-0.01546879205852747,
0.025490524247288704,
-0.03711845353245735,
-0.024699801579117775,
0.042009931057691574,
-0.027235880494117737,
0.04607805982232094,
-0.026586471125483513,
-0.02819133549928665,
-0.005999304354190826,
-0.03771086037158966,
-0.025937722995877266,
0.02118915505707264,
-0.011529717594385147,
0.002226463984698057,
-0.025079134851694107,
0.0022361765149980783,
0.05296623706817627,
0.000009259802936867345,
-0.08951273560523987,
-0.02312355302274227,
0.025546789169311523,
0.01165858469903469,
-0.042879149317741394,
-0.029262948781251907,
0.0023225604090839624,
0.015106456354260445,
-0.022866344079375267,
-0.01469439547508955,
0.035182975232601166,
-0.00744207389652729,
-0.01736271195113659,
0.006458473391830921,
0.05774884298443794,
0.02015373297035694,
-0.029118608683347702,
-0.003048405982553959,
0.0026221361476927996,
-0.00640060706064105,
0.02518252283334732,
-0.000057782042858889326,
0.04437697306275368,
-0.015113483183085918,
-0.008990977890789509,
-0.04384571313858032,
0.02836143970489502,
0.019495850428938866,
-0.018321171402931213,
-0.020931648090481758,
-0.007519369013607502,
-0.000606259738560766,
0.03711751475930214,
-0.017027880996465683,
-0.029246902093291283,
-0.00040925247594714165,
0.02935865893959999,
0.000321720726788044,
0.0016385093331336975,
-0.007525910157710314,
-0.009934844449162483,
0.007166644092649221,
-0.007843283005058765,
0.028570054098963737,
0.017389530315995216,
0.04684002697467804,
-0.006528255995362997,
0.026780111715197563,
0.02866474725306034,
-0.011198224499821663,
-0.004986755549907684,
0.024480825290083885,
0.030807260423898697,
0.00042048891191370785,
0.0134063009172678,
-0.022727904841303825,
-0.051251091063022614,
-0.05546635016798973,
0.02660094015300274,
0.05298934876918793,
0.02405117079615593,
-0.010759454220533371,
0.0004340112500358373,
-0.004611737560480833,
0.007119326386600733,
-0.03164249658584595,
-0.01880449615418911,
-0.024525480344891548,
-0.012509643100202084,
0.05336719751358032,
-0.04639941453933716,
-0.02165881358087063,
0.012944811023771763,
0.052049942314624786,
-0.021013768389821053,
0.01659691333770752,
0.03897691145539284,
-0.01739850454032421,
0.027333607897162437,
-0.02963503636419773,
-0.025250090286135674,
0.06393313407897949,
-0.00545252300798893,
-0.0008516223751939833,
0.02017958089709282,
0.016566578298807144,
0.012159273028373718,
0.024797948077321053,
0.06047379970550537,
-0.027916543185710907,
-0.05248740315437317,
-0.07034318149089813,
0.049659423530101776,
0.026962220668792725,
0.004415188450366259,
0.012998778373003006,
0.006566483527421951,
0.01476622000336647,
0.007162724621593952,
0.0048813968896865845,
0.0021671452559530735,
-0.030717408284544945,
-0.02070680260658264,
-0.040810324251651764,
-0.04860295355319977,
0.09389738738536835,
-0.07568453252315521,
-0.013747920282185078,
-0.004243405070155859,
-0.014380566775798798,
-0.007520660758018494,
-0.01990046352148056,
0.03588876500725746,
-0.028068900108337402,
0.04000908136367798,
-0.018679823726415634,
0.01836204342544079,
0.0034811559598892927,
-0.006218175869435072,
0.1161893829703331,
0.06380698829889297,
0.005336858332157135,
-0.04731208086013794,
0.002955663949251175,
-0.0005953863728791475,
0.0033028610050678253,
-0.006326525472104549,
0.028341662138700485,
0.017674395814538002,
-0.0108150290325284,
-0.04281468316912651,
0.06388047337532043,
-0.02024126797914505,
0.04072779044508934,
0.02617540955543518,
-0.04868214577436447,
-0.04659975320100784,
0.015081117860972881,
0.038696181029081345,
-0.03407197818160057,
-0.0027219641488045454,
-0.022032784298062325,
-0.0015011293580755591,
0.02066556178033352,
0.0035237830597907305,
-0.02970005013048649,
-0.006779765244573355,
0.02723623812198639,
0.020393244922161102,
-0.03744189068675041,
0.02694866806268692,
-0.012902544811367989,
0.027124878019094467,
-0.03406243026256561,
0.04425781965255737,
0.028049765154719353,
-0.001823572558350861,
0.03126409277319908,
0.03419807180762291,
-0.007210305891931057,
-0.01149452943354845,
0.0165609922260046,
-0.029045291244983673,
-0.007922365330159664,
-0.04515662416815758,
-0.011086469516158104,
0.07924996316432953,
-0.04381781071424484,
-0.039717093110084534,
0.005188814830034971,
-0.014550496824085712,
0.017853526398539543,
-0.060024697333574295,
-0.016663216054439545,
-0.006119092460721731,
0.017195777967572212,
-0.04220487177371979,
0.018029818311333656,
-0.021680787205696106,
-0.007412171922624111,
-0.0006166964303702116,
0.021633245050907135,
-0.011331634595990181,
-0.028694983571767807,
-0.001753376331180334,
0.01698300614953041,
0.06217935308814049,
0.020525142550468445,
0.012892150320112705,
-0.01652348041534424,
-0.006223120726644993,
-0.03540065884590149,
-0.030636709183454514,
0.020138146355748177,
0.010589946992695332,
0.04150232672691345,
-0.022282173857092857,
-0.02705495059490204,
-0.01903868280351162,
-0.04417170211672783,
-0.004798559471964836,
-0.016741672530770302,
-0.04127892479300499,
0.001050469814799726,
0.002873640274628997,
0.023837918415665627,
0.058519624173641205,
-0.03650844469666481,
0.030620574951171875,
-0.011930851265788078,
0.05336281657218933,
0.024684641510248184,
-0.055476151406764984,
-0.019476154819130898,
-0.009731394238770008,
-0.03710610046982765,
-0.016101626679301262,
-0.033431604504585266,
0.019414668902754784,
0.01754339411854744,
-0.015463503077626228,
-0.0069860792718827724,
0.05741637200117111,
-0.0036184010095894337,
0.0009237977210432291,
0.020006733015179634,
-0.0504021979868412,
0.02183433063328266,
0.007677064277231693,
-0.0024288534186780453,
-0.047840286046266556,
-0.010046927258372307,
-0.014462894760072231,
-0.020587243139743805,
-0.013324329629540443,
0.0029614754021167755,
-0.04266280308365822,
-0.027463149279356003,
-0.04640212282538414,
0.01293174922466278,
0.0005407050484791398,
-0.04077159985899925,
-0.04108895733952522,
0.011944739148020744,
-0.02986738830804825,
0.011669817380607128,
0.011068083345890045,
0.024796821177005768,
0.0029336377047002316,
-0.03591802716255188,
0.028729168698191643,
0.04655826836824417,
-0.011696143075823784,
-0.016064239665865898,
-0.004694662522524595,
-0.016363462433218956,
0.04205804318189621,
-0.02020242251455784,
-0.060334887355566025,
0.023003194481134415,
-0.005725562106817961,
-0.007932550273835659,
0.06687954068183899,
0.013230900280177593,
0.021095270290970802,
0.02229428105056286,
-0.008067220449447632,
0.00219918810762465,
0.025363368913531303,
-0.036496851593256,
-0.02125043421983719,
0.0025204892735928297,
-0.054740648716688156,
-0.014662799425423145,
-0.02088717371225357,
0.0032252012751996517,
0.01851527951657772,
-0.02482074685394764,
0.02921411581337452,
-0.005816089920699596,
-0.004943836014717817,
-0.015593321062624454,
-0.001613345113582909,
0.0030426334124058485,
0.07342735677957535,
0.019350655376911163,
0.016335923224687576,
-0.02304827608168125,
0.03445114940404892,
-0.030814165249466896,
0.020032139495015144,
-0.01323030050843954,
-0.007142636459320784,
-0.0540386401116848,
-0.0033933373633772135,
-0.009037274867296219,
0.017483089119195938,
0.033037252724170685,
-0.03472999483346939,
-0.003891465486958623,
0.03832927346229553,
-0.06816856563091278,
0.02010950818657875,
-0.06875794380903244,
0.008977387100458145,
-0.018141239881515503,
-0.01902926154434681,
-0.043635983020067215,
0.05857517197728157,
0.034393418580293655,
0.02325514145195484,
0.0018077237764373422,
0.0018352895276620984,
-0.02197013609111309,
-0.05199302360415459,
-0.047458160668611526,
0.026038633659482002,
0.001930135884322226,
-0.0191339123994112,
0.07246209681034088,
0.000042884203139692545,
-0.031469836831092834,
0.02165728434920311,
-0.006604934111237526,
0.022279899567365646,
-0.017277922481298447,
0.004090685397386551,
0.004615196958184242,
0.03218580782413483,
0.02212371863424778,
0.04407047852873802,
0.00010595812636893243,
-0.023782966658473015,
0.0158296637237072,
0.0051855603232979774,
0.007900498807430267,
0.019279511645436287,
0.010373230092227459,
-0.03994405269622803,
0.00712999515235424,
0.039451271295547485,
-0.025475675240159035,
-0.03659980744123459,
-0.0048872921615839005,
-0.0053323376923799515,
0.02166336216032505,
-0.0067793335765600204,
0.045536935329437256,
-0.03445924073457718,
-0.007580566685646772,
0.012047164142131805,
0.027583280578255653,
0.03296753391623497,
0.03908131271600723,
-0.005173032637685537,
-0.0497857965528965,
0.04476238042116165,
0.011560069397091866,
-0.03841652348637581,
-0.05077551305294037,
-0.018745025619864464,
0.0191972516477108,
0.05019303783774376,
0.01883655972778797,
-0.046358201652765274,
-0.04087070748209953,
0.015826810151338577,
0.005059052258729935,
0.040735479444265366,
-0.02149786241352558,
-0.058833442628383636,
-0.022225243970751762,
-0.030076738446950912,
0.06926005333662033,
0.029384970664978027,
-0.02651270106434822,
-0.003798249177634716,
0.01996403932571411,
0.010255553759634495,
0.015079510398209095,
0.03708440065383911,
0.024988047778606415,
-0.04251909628510475,
0.03511858731508255,
0.013167236000299454,
0.03405417501926422,
0.006144838873296976,
-0.0007582965772598982,
0.0005280216573737562,
-0.0019020970212295651,
-0.013853310607373714,
0.0159846730530262,
-0.026429908350110054,
0.02241496741771698,
0.013747443445026875,
-0.0032730000093579292,
0.02482922002673149,
0.005528084002435207,
-0.06556516885757446,
0.046107035130262375,
-0.012017847038805485,
-0.001293396344408393,
0.07841616868972778,
0.006042432505637407,
-0.0029533698689192533,
0.01649921014904976,
-0.033490411937236786,
-0.04500976949930191,
0.04564538225531578,
-0.022305689752101898,
-0.034195128828287125,
0.002011755481362343,
-0.006370509508997202,
0.04031645506620407,
-0.022303998470306396,
0.02497723698616028,
0.03533308953046799,
-0.018005484715104103,
-0.016729725524783134,
0.0666227787733078,
0.005646992474794388,
-0.0080347815528512,
0.04951530694961548,
0.01982748508453369,
0.06564385443925858,
-0.03260073810815811,
0.0362822562456131,
0.06199757382273674,
0.042110174894332886,
0.04647810012102127,
-0.013949431478977203,
0.01524579431861639,
0.004002085421234369,
0.003559650620445609,
0.027025075629353523,
0.025681788101792336,
-0.031703073531389236,
-0.0019149725558236241,
0.031054161489009857,
-0.02602466754615307,
-0.0011250184616073966,
0.0001519176148576662,
-0.034925173968076706,
0.049887046217918396,
-0.03656943514943123,
0.0063891359604895115,
-0.06141922250390053,
0.008248783648014069,
-0.01953122764825821,
-0.02067422680556774,
0.0001653442595852539,
0.04931392893195152,
-0.03076784871518612,
-0.029408270493149757,
-0.049042947590351105,
-0.01585754193365574,
0.045853737741708755,
-0.04973697289824486,
-0.008265165612101555,
0.009233084507286549,
-0.010139300487935543,
-0.012205837294459343,
-0.001615604618564248,
-0.03621532395482063,
0.0007268015178851783,
0.05422225221991539,
0.024895330891013145,
0.002675507217645645,
0.005930952727794647,
-0.03877297416329384,
-0.0177568718791008,
0.03598826006054878,
-0.052305541932582855,
-0.03205213323235512,
-0.021924925968050957,
0.013467430137097836,
-0.019581807777285576,
-0.008652493357658386
] |
<p>I'm doing a research internship in attosecond physics right now, and one of the really important things in the field is the description of a propagating laser pulse as the combination of a slowly (or not) varying envelope and a carrier frequency.</p>
<p>I was wondering, is this envelope-carrier description completely general, i.e. does it apply to any arbitrary solution of the wave equation? In my waves course we learned briefly about beats and derived the whole envelope-carrier description for a system consisting of 2 sinusoids, but what about in general?</p>
<p>One of the reasons I am confused is because if I consider the general solution to the wave equation using a superposition of sines and cosines (i.e. Fourier series), then I can imagine constructing a Gaussian pulse. This obviously won't have a carrier frequency attached to it.</p>
<p>So basically, when is this envelope-carrier description valid?</p>
<p>If anyone could clear things up, that would be greatly appreciated.</p>
| 9,435 |
[
-0.002117816125974059,
-0.019261423498392105,
0.009615054354071617,
-0.039461277425289154,
0.02061654068529606,
-0.016941988840699196,
-0.04916141554713249,
-0.046925656497478485,
-0.025315457955002785,
-0.017345484346151352,
0.03717916086316109,
0.025971362367272377,
0.05836087465286255,
0.0055300211533904076,
0.0034261958207935095,
0.01981070451438427,
-0.008458754979074001,
-0.016359634697437286,
-0.057188622653484344,
-0.01673089899122715,
0.002031635493040085,
0.03106011636555195,
-0.01583300158381462,
-0.02512337826192379,
-0.028721492737531662,
0.03809375688433647,
0.02557995170354843,
-0.0003141412162221968,
0.03663314878940582,
0.02731109783053398,
-0.012788068503141403,
-0.02046566642820835,
-0.0034106350503861904,
0.042257532477378845,
0.056583765894174576,
0.015606231056153774,
-0.06624341011047363,
-0.063350148499012,
0.009669971652328968,
0.03023534268140793,
-0.04152959585189819,
0.009480963461101055,
-0.0006193706067278981,
0.009496575221419334,
-0.030533114448189735,
0.018319156020879745,
-0.003709422657266259,
-0.011979890055954456,
0.046675197780132294,
-0.07342972606420517,
0.07484956085681915,
-0.006119434256106615,
0.04606624320149422,
0.00271650985814631,
-0.01177291851490736,
-0.002355423290282488,
0.10390443354845047,
0.024697307497262955,
0.016874117776751518,
-0.038083188235759735,
0.00404772674664855,
0.016857603564858437,
-0.011693783104419708,
-0.03131033480167389,
-0.0022757654078304768,
0.003427758114412427,
0.015381105244159698,
-0.03210114687681198,
0.002415368100628257,
-0.025136176496744156,
-0.0013427832163870335,
-0.015724195167422295,
0.03455378860235214,
-0.06761360913515091,
-0.008155095390975475,
-0.02297523245215416,
0.01181388646364212,
0.004452065099030733,
0.019625550135970116,
0.0328962504863739,
-0.03343775123357773,
0.005265531595796347,
-0.024078818038105965,
0.017093433067202568,
0.02172146551311016,
-0.018504666164517403,
0.05740085616707802,
-0.027427971363067627,
0.0008970669587142766,
0.030721189454197884,
-0.01069580391049385,
0.04244373366236687,
0.025612182915210724,
-0.028559610247612,
-0.017857052385807037,
0.03125249221920967,
0.009538067504763603,
0.06966701149940491,
0.021794261410832405,
-0.023005038499832153,
-0.0035377521999180317,
-0.03944876417517662,
-0.004558134358376265,
0.08326489478349686,
-0.027683692052960396,
0.005494510754942894,
-0.027607763186097145,
0.027812449261546135,
-0.038464609533548355,
-0.02040480636060238,
-0.027349911630153656,
0.02186875231564045,
0.013975278474390507,
0.05084690451622009,
0.0029846597462892532,
-0.006199851632118225,
0.029677536338567734,
-0.011685577221214771,
0.04780096933245659,
0.10491815209388733,
0.049986474215984344,
-0.057285331189632416,
0.047247882932424545,
-0.004043232649564743,
-0.021702101454138756,
0.002082954626530409,
-0.004800281021744013,
0.022779429331421852,
-0.03282197564840317,
0.00427789194509387,
0.01868259534239769,
-0.052857257425785065,
0.004409183282405138,
0.008468497544527054,
-0.0007605290156789124,
-0.07687372714281082,
-0.1301575005054474,
-0.027556365355849266,
-0.02773848921060562,
-0.0323173813521862,
-0.016008129343390465,
-0.0805826485157013,
0.015706464648246765,
-0.0012901306618005037,
0.05874943360686302,
-0.029309270903468132,
0.018079724162817,
0.013935543596744537,
0.026727713644504547,
0.007332919631153345,
-0.009604168124496937,
-0.030779991298913956,
0.0022575068287551403,
-0.0570213720202446,
-0.006311492994427681,
-0.06067841500043869,
0.032525673508644104,
0.01868141070008278,
0.012983810156583786,
0.018323421478271484,
0.04828518629074097,
-0.012842745520174503,
-0.0355382077395916,
0.018924403935670853,
0.019199341535568237,
-0.043873488903045654,
0.09154107421636581,
0.01174467895179987,
0.039670296013355255,
0.04831960052251816,
-0.016323328018188477,
0.011059886775910854,
-0.01215849258005619,
0.014622597955167294,
0.005433663260191679,
-0.0642181932926178,
0.013238289393484592,
-0.0026906009297817945,
0.007591398898512125,
-0.007565031759440899,
0.00794624537229538,
-0.03518788889050484,
0.018080249428749084,
-0.005422565154731274,
0.00815634522587061,
0.035084281116724014,
0.01738792099058628,
0.016826001927256584,
-0.010092690587043762,
-0.07754423469305038,
0.031435608863830566,
-0.014715347439050674,
0.06093795970082283,
0.03131929412484169,
-0.018326912075281143,
0.028849102556705475,
-0.011798201128840446,
0.017239177599549294,
0.02501683309674263,
-0.03527853265404701,
-0.022491514682769775,
0.040508072823286057,
-0.016967277973890305,
-0.037767332047224045,
0.043107252568006516,
0.05244619399309158,
0.0027644748333841562,
-0.026035530492663383,
0.052343837916851044,
-0.011650308035314083,
-0.013780733570456505,
0.0064283814281225204,
-0.008893770165741444,
0.055643584579229355,
0.004284349270164967,
0.02423001267015934,
-0.007303157821297646,
-0.009193132631480694,
-0.016008375212550163,
0.03385044261813164,
-0.04373603314161301,
0.07080602645874023,
0.05654894560575485,
-0.009489498101174831,
0.0003434326790738851,
0.050997041165828705,
0.007806791458278894,
0.005100178066641092,
0.03915829584002495,
-0.06868096441030502,
-0.014640958048403263,
0.03674883767962456,
0.055908605456352234,
0.04329134151339531,
-0.039241012185811996,
0.023434298112988472,
0.038500476628541946,
0.04041115939617157,
0.06727776676416397,
0.04714982584118843,
0.014323634095489979,
-0.01654857024550438,
0.03415725380182266,
-0.01212221384048462,
0.01717579923570156,
0.019507890567183495,
0.043724145740270615,
0.005420125555247068,
0.0030013760551810265,
0.01904621161520481,
-0.042079538106918335,
0.040866829454898834,
-0.019551612436771393,
-0.000519267690833658,
-0.012868006713688374,
-0.010531216859817505,
0.009130974300205708,
-0.07035822421312332,
0.06411800533533096,
0.026553567498922348,
-0.025194715708494186,
-0.01876549981534481,
-0.02342671900987625,
-0.02218380942940712,
0.016660816967487335,
-0.03153323009610176,
-0.01758408173918724,
-0.026712436228990555,
0.013398462906479836,
-0.021019861102104187,
0.002250129356980324,
0.0001762554602464661,
-0.012025836855173111,
-0.015195523388683796,
-0.04150885343551636,
0.045854873955249786,
0.0040663061663508415,
0.013121039606630802,
-0.05580531805753708,
-0.05032823979854584,
0.015458675101399422,
-0.019267283380031586,
0.04141727834939957,
0.01128987967967987,
-0.010108502581715584,
0.02323770895600319,
-0.014521914534270763,
-0.05146339535713196,
0.04873711243271828,
-0.040506791323423386,
-0.005081649869680405,
-0.01707780547440052,
-0.04765703156590462,
-0.05814160779118538,
0.0038187133613973856,
0.004746720194816589,
0.020357489585876465,
-0.02666361629962921,
0.02036423608660698,
0.06376755982637405,
-0.007972493767738342,
-0.021936018019914627,
0.007511141709983349,
0.0028434537816792727,
-0.03496386483311653,
-0.0023118366952985525,
-0.02367161586880684,
0.03497268259525299,
-0.0663972869515419,
0.049675267189741135,
0.012752542272210121,
-0.05634962394833565,
-0.008519256487488747,
-0.02206874080002308,
-0.05686753988265991,
0.008460073731839657,
-0.004800344817340374,
0.04882035776972771,
0.004476874601095915,
-0.02657998353242874,
0.08783774077892303,
0.025775820016860962,
-0.02264087088406086,
0.001691023469902575,
0.023663733154535294,
0.00823864247649908,
-0.014474540948867798,
0.033069804310798645,
0.019208218902349472,
-0.033852387219667435,
0.014009454287588596,
-0.011924919672310352,
0.005206285510212183,
0.06608951836824417,
0.027908459305763245,
-0.01485053077340126,
0.00323845143429935,
0.0015948653453961015,
0.004522330593317747,
0.015431472100317478,
0.027422606945037842,
-0.03387623280286789,
0.03341761603951454,
-0.015075838193297386,
0.010890057310461998,
0.026192886754870415,
-0.027425112202763557,
0.017762798815965652,
0.0006735640345141292,
-0.021372532472014427,
-0.023141318932175636,
0.02639441005885601,
-0.01098009292036295,
-0.012593853287398815,
-0.05163442716002464,
0.04090157151222229,
0.009846115484833717,
-0.0211448036134243,
0.007977987639605999,
0.036705635488033295,
0.046931423246860504,
-0.026676194742321968,
-0.0003784216532949358,
0.02028348669409752,
-0.018007557839155197,
0.030320219695568085,
-0.029185431078076363,
-0.04865184798836708,
0.0465230718255043,
0.0035828480031341314,
0.02674855664372444,
-0.011152999475598335,
-0.029567565768957138,
-0.008013324812054634,
-0.06948529183864594,
-0.008560135960578918,
0.00810177344828844,
0.031830500811338425,
0.004669514950364828,
0.10631044209003448,
0.025128081440925598,
0.04814706742763519,
0.030174074694514275,
0.026564383879303932,
-0.07501982897520065,
-0.003283541416749358,
-0.00780717097222805,
-0.031137241050601006,
-0.022791648283600807,
-0.0042684851214289665,
0.02154955454170704,
0.014254889450967312,
-0.0400870218873024,
-0.04372110217809677,
-0.015722857788205147,
-0.020122533664107323,
0.03255298733711243,
-0.020241333171725273,
-0.06446079909801483,
-0.023373520001769066,
0.03952920809388161,
0.0029416964389383793,
0.002894456498324871,
0.037380240857601166,
0.018146095797419548,
-0.022231878712773323,
0.007369723170995712,
0.01837432198226452,
0.004629996605217457,
-0.018976682797074318,
0.008733851835131645,
0.03204786777496338,
0.043139223009347916,
0.01283134613186121,
0.03918834403157234,
0.021150588989257812,
0.08795276284217834,
0.015637094154953957,
-0.02859554812312126,
0.008034581318497658,
-0.01986398920416832,
0.00600819056853652,
0.01337908674031496,
0.050104837864637375,
0.022658977657556534,
-0.03395357355475426,
0.017884910106658936,
0.009184086695313454,
0.02531866356730461,
0.06239430978894234,
0.02398655377328396,
-0.034779369831085205,
-0.016544895246624947,
-0.04529213905334473,
0.020997600629925728,
-0.014959256164729595,
-0.0002475933579262346,
-0.011627819389104843,
-0.009666915982961655,
0.011206778697669506,
0.01479289960116148,
-0.010948474518954754,
-0.009932405315339565,
0.00702306441962719,
-0.019655436277389526,
-0.03417833894491196,
-0.026561042293906212,
0.014200781472027302,
-0.0038489096332341433,
-0.00463300384581089,
0.021519334986805916,
0.013204292394220829,
0.031788457185029984,
0.009385354816913605,
-0.05445559695363045,
0.00841998029500246,
0.020360488444566727,
0.0319882333278656,
-0.009831514209508896,
-0.011697071604430676,
-0.06581084430217743,
-0.03474593907594681,
-0.001837317831814289,
0.0020416092593222857,
0.0510128028690815,
0.007573504466563463,
-0.025006452575325966,
-0.008948619477450848,
0.012636548839509487,
-0.017418697476387024,
0.006349052768200636,
-0.021175099536776543,
0.0020657344721257687,
-0.017270641401410103,
-0.00008499823888996616,
0.040060289204120636,
0.03338492289185524,
0.017644133418798447,
0.05283477529883385,
-0.02204381301999092,
-0.048013169318437576,
0.004935506731271744,
0.02808651700615883,
0.021828917786478996,
-0.05304230749607086,
-0.028489544987678528,
0.019145339727401733,
0.025438344106078148,
0.034872546792030334,
-0.02041083201766014,
-0.04658004269003868,
0.028357243165373802,
0.03503724932670593,
0.006195113994181156,
0.008658703416585922,
-0.014348519966006279,
0.040035806596279144,
0.000851580174639821,
0.011981395073235035,
0.019801758229732513,
0.05728139355778694,
-0.03055126778781414,
-0.006621712353080511,
-0.027012452483177185,
0.05065126717090607,
-0.028060007840394974,
0.01761479489505291,
-0.023724252358078957,
0.00042384391417726874,
-0.03529437631368637,
0.08152566850185394,
-0.0034701854456216097,
0.0016285580350086093,
0.012814194895327091,
-0.012513818219304085,
0.01754642091691494,
0.017450036481022835,
-0.05110356584191322,
0.022775966674089432,
-0.028486493974924088,
0.039700016379356384,
-0.012608407065272331,
-0.012178773991763592,
-0.014866966754198074,
-0.0095511544495821,
0.03576131910085678,
0.04724116995930672,
0.02844277396798134,
0.01989368163049221,
-0.042406342923641205,
-0.02000182494521141,
0.01272829994559288,
-0.05992875248193741,
0.07730468362569809,
-0.007639641407877207,
0.03860078006982803,
0.013328098691999912,
-0.04666532576084137,
-0.029513368383049965,
0.000037739759136456996,
-0.033607225865125656,
0.08523702621459961,
-0.048579879105091095,
0.0037664829287678003,
0.009906456805765629,
-0.0008529474143870175,
-0.06655264645814896,
-0.061006270349025726,
0.03967408463358879,
-0.005946193356066942,
-0.010328179225325584,
-0.014560419134795666,
0.03475818410515785,
-0.029578741639852524,
-0.005116371437907219,
0.02574554830789566,
0.044252924621105194,
-0.017733408138155937,
-0.03209441527724266,
0.004441631492227316,
0.014394895173609257,
0.03448820486664772,
0.013367542065680027,
-0.032422054558992386,
0.02194826863706112,
0.0033305485267192125,
0.016567884013056755,
0.004893288481980562,
0.028506377711892128,
-0.02853231690824032,
-0.019426437094807625,
-0.03110526315867901,
-0.01848961040377617,
0.01442816574126482,
-0.02643955498933792,
-0.027200084179639816,
0.025036800652742386,
0.003380049020051956,
0.010130970738828182,
-0.021955344825983047,
0.01061243936419487,
-0.018528206273913383,
-0.00395241379737854,
-0.023581551387906075,
-0.013530554249882698,
-0.03476731479167938,
-0.04250822588801384,
0.016356689855456352,
0.016130145639181137,
-0.003036493668332696,
0.02601267211139202,
0.03191543370485306,
-0.013052149675786495,
0.02251891791820526,
-0.009310010820627213,
-0.011168199591338634,
0.021418515592813492,
-0.006248971447348595,
0.014331305399537086,
0.0163322314620018,
0.0037699323147535324,
-0.015834350138902664,
-0.02961822599172592,
-0.043193522840738297,
0.002992762951180339,
0.0736561045050621,
-0.007577214390039444,
0.0034569124691188335,
0.03407749906182289,
0.006963610649108887,
-0.004563210532069206,
-0.0038170742336660624,
0.03291661664843559,
0.0028560764621943235,
-0.004685744643211365,
0.03242864832282066,
-0.03998913615942001,
-0.018678687512874603,
0.014345825649797916,
0.03391933813691139,
-0.0076801287941634655,
-0.012803779914975166,
-0.001258044969290495,
0.03229442983865738,
0.013355711475014687,
0.0047196149826049805,
-0.02837359718978405,
0.06684620678424835,
-0.028817638754844666,
0.038749974220991135,
-0.002344445325434208,
-0.008192184381186962,
0.016834288835525513,
0.016736704856157303,
0.009475808590650558,
-0.03772461414337158,
-0.0052468557842075825,
-0.025978537276387215,
0.04199625179171562,
0.016529357060790062,
0.023595163598656654,
0.0418655164539814,
-0.01980455592274666,
0.058693062514066696,
0.03242659941315651,
0.017205288633704185,
-0.011948826722800732,
-0.04270433634519577,
-0.002407127059996128,
-0.05082472786307335,
-0.02793112024664879,
0.023060809820890427,
0.013455862179398537,
0.0073842210695147514,
-0.008387601003050804,
-0.03912890702486038,
0.020919103175401688,
0.038655370473861694,
0.01157150324434042,
-0.00626784423366189,
0.09657663851976395,
-0.013315120711922646,
-0.002953166840597987,
-0.03262500837445259,
0.018335040658712387,
0.11155830323696136,
0.04791070148348808,
0.025861088186502457,
-0.04603883624076843,
0.023600848391652107,
-0.049478743225336075,
0.014980987645685673,
-0.02553938888013363,
0.008880372159183025,
-0.011680311523377895,
-0.02631472609937191,
0.0010141272796317935,
0.05049906298518181,
-0.0007421383634209633,
0.016242114827036858,
0.023068200796842575,
-0.04305530712008476,
-0.0030135924462229013,
0.02931910566985607,
-0.007562985643744469,
0.0026728615630418062,
0.03510800749063492,
0.0023667628411203623,
0.004321059677749872,
-0.018135689198970795,
-0.023114535957574844,
-0.019056547433137894,
-0.02546401508152485,
0.034336529672145844,
-0.008318803273141384,
-0.004507224541157484,
-0.001023859716951847,
0.012326776050031185,
-0.0035186659079045057,
-0.016616694629192352,
0.016977757215499878,
0.03479127958416939,
-0.021451450884342194,
0.0064532277174293995,
0.01280736830085516,
-0.003970268648117781,
0.016073474660515785,
0.02812257967889309,
0.007268440444022417,
-0.04106387495994568,
-0.012786106206476688,
-0.03837724030017853,
0.024826887995004654,
0.027433080598711967,
-0.004413844086229801,
-0.001397176762111485,
0.010461914353072643,
0.028023185208439827,
-0.06965386122465134,
0.005007167346775532,
-0.013640444725751877,
0.036885637789964676,
-0.029268011450767517,
-0.029260609298944473,
-0.010451361536979675,
0.014735690318048,
0.027321573346853256,
0.028812319040298462,
-0.008117464371025562,
0.004337336868047714,
0.00008779419295024127,
-0.02357448823750019,
0.022353332489728928,
0.021895838901400566,
-0.04313062131404877,
0.007571516092866659,
-0.0024946434423327446,
-0.05367952957749367,
-0.06268400698900223,
0.028378915041685104,
-0.0059584625996649265,
0.03283585608005524,
0.02772672474384308,
0.012465940788388252,
-0.020871663466095924,
-0.09861321747303009,
0.039028652012348175,
0.02316318452358246,
-0.045864589512348175,
0.03532659634947777,
-0.03416947275400162,
0.03416748344898224,
0.021737543866038322,
-0.022941216826438904,
0.07541124522686005,
-0.018911894410848618,
0.041269153356552124,
0.051063161343336105,
-0.05820636451244354,
-0.004444642458111048,
0.010168744251132011,
-0.001721136155538261,
-0.018528858199715614,
-0.013316734693944454,
0.022809192538261414,
0.0001383799099130556,
0.024316618219017982,
-0.0342218391597271,
0.05799575522542,
-0.05852841958403587,
-0.03845391795039177,
-0.02740316651761532,
0.010056582279503345,
0.03433682769536972,
0.022984221577644348,
0.04804693162441254,
-0.044910967350006104,
-0.017492182552814484,
-0.012974690645933151,
0.007309602107852697,
0.014138610102236271,
-0.005734181497246027,
-0.020879924297332764,
0.03731454908847809,
0.010372806340456009,
-0.017570333555340767,
-0.01686316542327404,
-0.030553672462701797,
0.004011445213109255,
0.049206752330064774,
-0.011689950712025166,
-0.03488799184560776,
-0.01145130954682827,
0.02070687711238861,
-0.037134800106287,
-0.039782844483852386,
0.032506272196769714,
0.013445996679365635,
-0.034231096506118774,
0.008770599029958248,
0.014993919059634209,
-0.022470766678452492,
0.01045837253332138,
-0.028092864900827408,
-0.025214269757270813,
0.0017669755034148693,
-0.043275099247694016,
-0.03320882469415665,
0.019152289256453514,
0.006857977714389563,
0.011314747855067253,
0.023599911481142044,
-0.0002176205161958933,
-0.00418059341609478,
0.03145570680499077,
0.001024857978336513,
0.012033950537443161,
0.003676522755995393,
-0.006094781681895256,
0.01085938885807991,
0.003500202903524041,
-0.010220703668892384,
0.01478994358330965,
0.0005715283332392573,
0.03848080709576607,
0.031237320974469185,
-0.04204005002975464,
0.02071458473801613,
-0.009823967702686787,
-0.04171166568994522,
0.01990121230483055,
-0.0080778943374753,
-0.011387286707758904,
0.029328979551792145,
0.001470377785153687,
0.04301433265209198,
0.024857185781002045,
0.01068905834108591,
0.023493146523833275,
-0.1041596308350563,
-0.0012097336584702134,
0.009688871912658215,
0.0329388789832592,
0.03176366910338402,
-0.02426506206393242,
-0.003120805835351348,
0.022619951516389847,
-0.05082818865776062,
0.04739382490515709,
-0.004740387201309204,
-0.013661970384418964,
-0.03323034569621086,
0.022641487419605255,
-0.04869351536035538,
0.014813150279223919,
0.011297482065856457,
0.006895324215292931,
-0.0021640812046825886,
-0.002134534763172269,
0.015683351084589958,
-0.022361312061548233,
-0.011507833376526833,
-0.013085758313536644,
0.021776512265205383,
0.011264950037002563,
0.04944619536399841,
0.00441404664888978,
-0.039033740758895874,
0.015606250613927841,
-0.009796635247766972,
-0.004128756932914257,
-0.0030097556300461292,
0.05251980572938919,
0.009155936539173126,
0.014612589962780476,
0.02973104640841484,
-0.01640552654862404,
0.017694391310214996,
0.02289487048983574,
0.01053777989000082,
0.02122911624610424,
-0.012013989500701427,
-0.018758336082100868,
0.01172493863850832,
-0.024460742250084877,
-0.035606060177087784,
0.039382822811603546,
-0.011940998025238514,
-0.015159075148403645,
0.006422361824661493,
-0.006914481986314058,
0.018870875239372253,
0.02156774513423443,
0.014236042276024818,
-0.06677690148353577,
-0.02703217975795269,
-0.0059181032702326775,
-0.002486651064828038,
-0.019930968061089516,
-0.0035922464448958635,
-0.046483114361763,
-0.059209249913692474,
0.03987833112478256,
-0.0010696499375626445,
-0.007964556105434895,
-0.04448409378528595,
-0.025324728339910507,
-0.0004950099973939359,
-0.01092838030308485,
0.012762049213051796,
-0.0014759680489078164,
0.005318063776940107,
0.041326019912958145,
0.015911448746919632,
0.009018993005156517,
-0.011360653676092625,
-0.04050217196345329,
-0.025678062811493874,
-0.04187387600541115,
0.02402385137975216,
-0.007406892254948616,
0.012971810065209866,
-0.03910655528306961,
-0.04272513836622238,
0.009519302286207676,
0.054599981755018234,
0.050157543271780014,
-0.024278007447719574,
-0.0005432702018879354,
0.043260183185338974,
-0.05107340216636658,
-0.017330139875411987,
-0.02807709015905857,
-0.020922008901834488,
-0.003813705174252391,
-0.007318687159568071,
-0.02558859996497631,
-0.022083323448896408,
-0.07183738797903061,
0.01966938190162182,
0.0039306520484387875,
0.01959436759352684,
0.03700551390647888,
-0.036909446120262146,
-0.05295094475150108,
0.04241735488176346,
0.039422933012247086,
-0.023272952064871788,
0.033625200390815735,
-0.006413015071302652,
0.006930018309503794,
0.009842370636761189,
-0.04956091567873955,
-0.08812782913446426,
-0.004747500643134117,
-0.031644511967897415,
-0.009166449308395386,
-0.008267471566796303,
0.010397392325103283,
0.033776238560676575,
-0.059490032494068146,
-0.01164554338902235,
0.0020118888933211565,
-0.05245955288410187,
-0.03024165891110897,
0.07875651121139526,
-0.010903330519795418,
0.008833874948322773,
0.0014901101822033525,
0.022609388455748558,
-0.008156306110322475,
0.006476231850683689,
-0.018126726150512695,
0.006392566952854395,
0.031091906130313873,
0.006920904386788607,
0.01932159811258316,
-0.00647975318133831,
-0.012922982685267925,
-0.005667866673320532,
0.0000900641898624599,
0.032795801758766174,
-0.024917850270867348,
-0.0011459722882136703,
0.013346973806619644,
-0.018831079825758934,
-0.04357009381055832,
0.05186918377876282,
-0.00045833043986931443,
0.05416721850633621,
-0.020961865782737732,
-0.02180970273911953,
-0.02265416830778122,
0.010913638398051262,
-0.03403610363602638,
-0.0020126185845583677,
0.01926341839134693,
0.017276199534535408,
-0.01895119994878769,
0.01895379275083542,
-0.045208703726530075,
-0.028970036655664444,
0.047712672501802444,
-0.10807774215936661,
-0.002488006604835391,
-0.029484650120139122,
-0.012346817180514336,
-0.012483843602240086,
0.00337228924036026,
-0.03684449940919876,
-0.00205695116892457,
-0.013244918547570705,
0.0016377904685214162,
-0.022349528968334198,
-0.015680477023124695,
0.012705136090517044,
-0.006839035078883171,
0.0630451962351799,
-0.08000527322292328,
0.018259750679135323,
-0.0009504056652076542,
0.05539768189191818,
-0.0044700209982693195,
-0.006028078030794859
] |
<p>Different kinds of white light have a different spectrum.</p>
<p>Light from a white LED will have blue at the peak intensity while white light from a CFL or something else will have a different looking spectrum.</p>
<p>I dont understand how this works. Shouldn't pure white light have a unique spectrum no matter what?</p>
<p><img src="http://i.stack.imgur.com/qwkQ8.png" alt="White LED Spectrum"></p>
<p>Thats white LED spectrum</p>
| 9,436 |
[
-0.0585239976644516,
-0.020140020176768303,
-0.0023920536041259766,
-0.018100520595908165,
0.06382689625024796,
-0.001913101295940578,
-0.016970453783869743,
-0.039062462747097015,
0.02561403624713421,
-0.03431989625096321,
0.014176960103213787,
0.0322163961827755,
0.007975415326654911,
0.03222847357392311,
0.036455992609262466,
0.01514002401381731,
0.012560426257550716,
0.01070477720350027,
-0.017798446118831635,
-0.011815919540822506,
-0.03386404365301132,
0.007350065279752016,
-0.012112407013773918,
-0.00031970578129403293,
-0.050754379481077194,
0.021969405934214592,
0.046260859817266464,
0.02379673346877098,
0.057039231061935425,
0.026848189532756805,
-0.019118236377835274,
-0.010649251751601696,
-0.012520890682935715,
0.02595939300954342,
0.027430357411503792,
-0.002928295638412237,
-0.03522937372326851,
-0.015579710714519024,
0.003086221870034933,
0.032445523887872696,
-0.01547066867351532,
-0.006423987913876772,
-0.0027281860820949078,
0.030961837619543076,
-0.03961407020688057,
0.014085779897868633,
-0.005973860155791044,
-0.027868712320923805,
0.03356839716434479,
-0.06787997484207153,
0.08648666739463806,
-0.026987820863723755,
0.060483723878860474,
0.037890370935201645,
-0.007892218418419361,
0.03557268902659416,
0.06395769119262695,
0.054407622665166855,
-0.016392262652516365,
-0.035070210695266724,
0.00004238281326252036,
-0.000757203612010926,
0.005249627400189638,
-0.00852120853960514,
-0.04182906821370125,
0.026785850524902344,
0.002323164837434888,
-0.015421036630868912,
-0.008965646848082542,
0.011441589333117008,
0.017927443608641624,
0.03335419297218323,
0.0341402143239975,
-0.03992165997624397,
0.0046603004448115826,
-0.05952981859445572,
0.021654408425092697,
0.05935012176632881,
0.04863550513982773,
0.009049387648701668,
-0.008950434625148773,
-0.007310485001653433,
-0.040417350828647614,
-0.0012326784199103713,
0.012136615812778473,
-0.008108771406114101,
0.07107093930244446,
-0.013152030296623707,
0.004317129962146282,
0.026766154915094376,
0.014118117280304432,
0.025486735627055168,
0.036131761968135834,
0.035617366433143616,
0.00009402992145624012,
0.03645802289247513,
-0.019393624737858772,
0.008468679152429104,
-0.0037876898422837257,
-0.03515147045254707,
0.042800113558769226,
-0.03560623154044151,
0.04992978274822235,
0.039436377584934235,
-0.045837100595235825,
-0.031792525202035904,
-0.008208374492824078,
0.007002839352935553,
0.017861947417259216,
0.013028734363615513,
-0.01649591512978077,
-0.009403470903635025,
0.026179179549217224,
-0.007777141872793436,
-0.016749659553170204,
-0.009003031998872757,
-0.01749294251203537,
0.004872483666986227,
0.04544465243816376,
0.06148429214954376,
-0.00316515751183033,
-0.02672327309846878,
0.013358802534639835,
-0.022327622398734093,
-0.0541616715490818,
-0.00806735921651125,
-0.020793689414858818,
0.02635948918759823,
-0.049113720655441284,
0.017191613093018532,
-0.015337263233959675,
-0.011666076257824898,
0.014933011494576931,
-0.005546754226088524,
0.00433453731238842,
-0.026112817227840424,
-0.09340836852788925,
-0.053117554634809494,
0.012184933759272099,
-0.005983480252325535,
0.0010028666583821177,
-0.06466624140739441,
0.040942300111055374,
0.0007110324804671109,
0.07589346915483475,
0.004464203026145697,
-0.0042593167163431644,
0.0025602434761822224,
-0.005169977899640799,
-0.00531803909689188,
-0.002838114043697715,
-0.021955035626888275,
0.022456584498286247,
-0.03512199968099594,
0.03271930664777756,
-0.08508520573377609,
-0.0006235382170416415,
0.012113499455153942,
0.0023170465137809515,
-0.018034858629107475,
0.021413613110780716,
-0.007306610234081745,
-0.002103107748553157,
0.013041235506534576,
0.024792660027742386,
-0.03560655936598778,
0.06749340891838074,
0.019302571192383766,
0.000610997318290174,
0.02252943441271782,
-0.03967488557100296,
0.014117920771241188,
-0.010478143580257893,
0.04112180694937706,
0.03028305247426033,
-0.009656599722802639,
-0.03239458054304123,
-0.006650314666330814,
0.06303711980581284,
-0.012786118313670158,
-0.06367772817611694,
-0.03734174370765686,
-0.005406315438449383,
0.039070963859558105,
0.024072660133242607,
0.03819982707500458,
0.0020581181161105633,
0.006496138870716095,
0.014782220125198364,
-0.0595988892018795,
0.0015020542778074741,
-0.041631024330854416,
0.012628251686692238,
-0.01194148138165474,
-0.03519396856427193,
-0.0068999044597148895,
0.007228004280477762,
0.027904050424695015,
-0.0007172316545620561,
-0.018504533916711807,
-0.02439142018556595,
0.04067441076040268,
0.002406865358352661,
-0.03175043687224388,
0.019386157393455505,
0.02771627902984619,
0.015538724139332771,
-0.013855158351361752,
0.026513606309890747,
-0.030799945816397667,
-0.03347324952483177,
0.02700742706656456,
-0.03551089018583298,
0.018575439229607582,
-0.02289097011089325,
0.011545156128704548,
0.01729712076485157,
0.012915494851768017,
-0.016015276312828064,
0.04981996864080429,
-0.0093080410733819,
0.04166292026638985,
0.030211031436920166,
-0.05645569786429405,
0.005976559594273567,
0.003458531806245446,
-0.00531240738928318,
0.017442354932427406,
-0.008419462479650974,
-0.04664800316095352,
-0.06183113530278206,
0.015828046947717667,
0.02057800441980362,
-0.00531026441603899,
-0.039761967957019806,
0.0009480995940975845,
0.008141908794641495,
0.035160984843969345,
0.028220729902386665,
0.028135865926742554,
-0.009065762162208557,
-0.01933201774954796,
0.0051659755408763885,
0.03516403213143349,
0.020173704251646996,
0.02974627912044525,
0.016905562952160835,
0.007719938177615404,
0.06472532451152802,
-0.041204482316970825,
-0.016341397538781166,
0.06276104599237442,
-0.037736449390649796,
-0.016577469184994698,
-0.008324956521391869,
-0.020519457757472992,
0.043267782777547836,
-0.021630441769957542,
0.03502621129155159,
0.014468775130808353,
-0.026298170909285545,
-0.006251044105738401,
-0.020663540810346603,
-0.019567636772990227,
0.014599530026316643,
0.02267405018210411,
-0.040162064135074615,
0.015204592607915401,
0.004773184657096863,
0.005242679268121719,
0.032465022057294846,
-0.029918977990746498,
-0.01539786159992218,
-0.05817000940442085,
0.004369418136775494,
0.03444869443774223,
0.010150539688766003,
0.02301364578306675,
-0.09116986393928528,
-0.06456667184829712,
-0.016235625371336937,
-0.04692033305764198,
-0.00023704962222836912,
-0.02185659669339657,
-0.03438365459442139,
0.01537905354052782,
-0.04382597282528877,
-0.018223585560917854,
0.0005641835741698742,
-0.014385745860636234,
-0.012212560512125492,
0.021553125232458115,
-0.0116488141939044,
-0.04920751228928566,
-0.011846780776977539,
-0.0252403374761343,
0.06117969751358032,
-0.013590031303465366,
-0.025552110746502876,
0.047378700226545334,
-0.01842627115547657,
-0.06616220623254776,
-0.0010435291333124042,
-0.08358066529035568,
-0.03957502543926239,
-0.0024137997534126043,
-0.02153843641281128,
0.047851450741291046,
-0.031084425747394562,
0.017373496666550636,
0.0032222489826381207,
-0.04131323844194412,
0.010220211930572987,
-0.02706991508603096,
-0.03888591378927231,
-0.004943558480590582,
-0.005183348432183266,
0.061002202332019806,
0.010612857528030872,
0.015487179160118103,
0.037425797432661057,
0.0439816452562809,
-0.0000032603470572212245,
-0.05671478807926178,
-0.037579670548439026,
-0.030144911259412766,
-0.0687035620212555,
0.015384839847683907,
0.056708142161369324,
-0.03563805669546127,
0.0024680292699486017,
0.022952621802687645,
0.020327866077423096,
0.044319894164800644,
0.0142636364325881,
-0.028441166505217552,
0.033537283539772034,
0.0038661963772028685,
-0.010125971399247646,
0.03399112820625305,
0.012120362371206284,
-0.03239274397492409,
-0.01905934140086174,
0.030622432008385658,
0.035698674619197845,
0.012389174662530422,
-0.017371291294693947,
0.0735127404332161,
0.018975289538502693,
0.021948296576738358,
-0.06952719390392303,
0.028269881382584572,
0.017587700858712196,
0.019606338813900948,
-0.01684839278459549,
0.019385984167456627,
0.02174670435488224,
-0.0009508469374850392,
0.01683029532432556,
0.0522017702460289,
0.017808159813284874,
-0.025459548458456993,
-0.024228449910879135,
0.02032649889588356,
-0.015483192168176174,
0.008615679107606411,
0.013587509281933308,
-0.03509603813290596,
0.06865276396274567,
0.031540460884571075,
0.05846835672855377,
-0.017177365720272064,
-0.019642777740955353,
-0.01957768388092518,
-0.07889954000711441,
0.009954147040843964,
0.0028362583834677935,
0.0618537962436676,
0.012441202998161316,
0.07706607133150101,
0.04325484111905098,
-0.0004621658008545637,
0.027895353734493256,
0.002294698962941766,
-0.09114418923854828,
0.03957519680261612,
0.0032651126384735107,
0.001027619931846857,
-0.052847277373075485,
-0.051865529268980026,
-0.021477069705724716,
-0.024043506011366844,
-0.03050237149000168,
0.005539909470826387,
-0.0026734403800219297,
-0.03258842974901199,
0.01342017948627472,
0.011696659959852695,
-0.0344095416367054,
-0.029023729264736176,
0.019520461559295654,
0.007001926191151142,
0.024342242628335953,
0.009939562529325485,
0.02089412324130535,
-0.027510467916727066,
0.037254881113767624,
-0.01951487548649311,
0.01542735006660223,
0.03870920464396477,
0.028610842302441597,
0.02917887642979622,
0.0761587917804718,
-0.031188270077109337,
-0.010551831685006618,
0.005931916180998087,
0.01923714205622673,
0.0359262079000473,
-0.021570386365056038,
-0.017536617815494537,
-0.042369745671749115,
0.006792911794036627,
0.022486550733447075,
0.02370128221809864,
-0.021587219089269638,
0.006676666438579559,
0.025311583653092384,
-0.018831536173820496,
-0.033780064433813095,
0.006787202320992947,
0.025560276582837105,
-0.01798149012029171,
-0.024819722399115562,
-0.014856662601232529,
0.011430271901190281,
-0.020714247599244118,
0.033484525978565216,
-0.008782236836850643,
0.008938548155128956,
-0.022912384942173958,
0.007258658763021231,
0.011327706277370453,
0.010273778811097145,
-0.01621267944574356,
-0.026176130399107933,
-0.018704155460000038,
-0.005812791176140308,
-0.011522209271788597,
-0.02124754525721073,
-0.01159458328038454,
0.037305451929569244,
0.008689279668033123,
0.0026347108650952578,
-0.009219693951308727,
-0.075852170586586,
-0.00843103788793087,
0.02481456659734249,
0.014141442254185677,
-0.0037475372664630413,
-0.03703003376722336,
-0.05982867255806923,
0.004401308484375477,
-0.008135912008583546,
-0.010415242053568363,
0.04838615655899048,
-0.00796748697757721,
0.02268725447356701,
-0.013042674399912357,
0.000015598548998241313,
-0.0065477583557367325,
0.033599305897951126,
0.018380427733063698,
0.014663396403193474,
-0.020185546949505806,
-0.010295138694345951,
-0.02225111797451973,
0.01603059470653534,
0.0497242771089077,
0.05551793798804283,
-0.04310045391321182,
-0.00672881817445159,
0.018013866618275642,
0.025873050093650818,
-0.004146557301282883,
-0.06034421920776367,
-0.005234628915786743,
0.03244908154010773,
0.010991639457643032,
0.03541278466582298,
-0.04752887785434723,
-0.08373839408159256,
0.026845477521419525,
0.05456898361444473,
-0.017348119989037514,
-0.0026152990758419037,
-0.03829532489180565,
0.03212897107005119,
0.032120462507009506,
0.012959577143192291,
0.047152288258075714,
0.04577206075191498,
-0.05806484445929527,
-0.010457541793584824,
-0.026499181985855103,
0.0734034925699234,
-0.05011984333395958,
-0.010557702742516994,
-0.014442375861108303,
0.007392295636236668,
-0.03491649776697159,
0.060237523168325424,
0.003118968103080988,
-0.0025033822748810053,
-0.0036403716076165438,
-0.051184140145778656,
-0.0006823467556387186,
0.0487886443734169,
-0.005261510144919157,
-0.005917077884078026,
-0.026921246200799942,
0.010857607237994671,
-0.002421091077849269,
0.03152056038379669,
0.028920920565724373,
-0.010167323052883148,
-0.029140131548047066,
0.03607902675867081,
0.03649681806564331,
0.0448998361825943,
-0.03760908544063568,
0.008594542741775513,
-0.012956997379660606,
-0.02555725909769535,
0.03476443514227867,
0.02060280553996563,
0.04561774060130119,
0.0316641740500927,
-0.06755170226097107,
-0.02905033342540264,
0.008091669529676437,
-0.01729302480816841,
0.004199828486889601,
-0.0285736583173275,
0.04378233477473259,
0.02153090573847294,
-0.017410967499017715,
-0.06271481513977051,
-0.029781945049762726,
0.00023732830595690757,
0.040563467890024185,
-0.014796124771237373,
-0.016991890966892242,
0.012471502646803856,
0.006361900828778744,
-0.011340301483869553,
-0.0002677343727555126,
-0.005245497450232506,
-0.014885992743074894,
-0.0027396120131015778,
0.04991983622312546,
-0.01746268942952156,
0.027270054444670677,
0.01325170136988163,
-0.007526600267738104,
-0.04066935554146767,
-0.030686048790812492,
-0.03530179336667061,
0.009316042996942997,
0.05543587729334831,
-0.028086068108677864,
-0.0471806600689888,
0.003307572565972805,
0.012493444606661797,
0.07005718350410461,
-0.03095002844929695,
-0.02545730583369732,
-0.005588906817138195,
0.043862614780664444,
-0.0585935115814209,
-0.04053535312414169,
0.001307261292822659,
0.01116220373660326,
0.012001984752714634,
0.009123142808675766,
-0.024016622453927994,
-0.040111739188432693,
-0.04331478103995323,
-0.009635237976908684,
0.0027012855280190706,
0.007180052809417248,
-0.002417725743725896,
0.05889423191547394,
-0.0538969486951828,
-0.0035619314294308424,
-0.010748693719506264,
-0.021594975143671036,
0.02664010226726532,
-0.013606784865260124,
0.02139633148908615,
0.034091878682374954,
0.031462088227272034,
0.003964333329349756,
-0.01358027197420597,
-0.03452884033322334,
-0.014814178459346294,
0.0332491397857666,
0.006363665219396353,
0.05276784300804138,
0.04170427843928337,
-0.02970944158732891,
-0.003809806890785694,
-0.035226672887802124,
-0.016887392848730087,
-0.016620103269815445,
-0.003971797879785299,
0.029919736087322235,
0.001018829527311027,
-0.031594958156347275,
0.010997272096574306,
0.038991544395685196,
0.024892615154385567,
0.018595267087221146,
0.08480437099933624,
0.006435812916606665,
-0.023367827758193016,
0.012932646088302135,
-0.05337195470929146,
0.038464661687612534,
0.002027289941906929,
0.023073600605130196,
0.034838054329156876,
0.01662115380167961,
0.04745703190565109,
-0.006206858437508345,
-0.0058225346729159355,
-0.055040255188941956,
0.015577602200210094,
-0.05084270238876343,
0.04401553049683571,
0.014487511478364468,
0.026253078132867813,
0.01196590531617403,
0.000940099882427603,
0.004236889071762562,
0.016978900879621506,
0.020166469737887383,
-0.028164727613329887,
-0.059908926486968994,
-0.04542018100619316,
-0.035734623670578,
-0.01270526833832264,
0.027937788516283035,
-0.022104019299149513,
-0.035030875355005264,
0.014433218166232109,
-0.057481344789266586,
0.0218687541782856,
0.004191568586975336,
0.03426341712474823,
0.0037813696544617414,
0.00420825369656086,
0.0203721821308136,
0.05850106477737427,
0.003172844648361206,
-0.0005407482385635376,
0.11374977231025696,
0.03976878896355629,
-0.01097667496651411,
-0.08562009781599045,
-0.01122397743165493,
-0.012592977844178677,
0.01022594515234232,
-0.0014889294980093837,
0.02884565107524395,
-0.02137087844312191,
0.049557141959667206,
-0.001967235468327999,
0.0367637500166893,
0.026740850880742073,
-0.003602684708312154,
0.024292252957820892,
-0.022929497063159943,
-0.04250139370560646,
0.020488770678639412,
0.02614927664399147,
-0.02681110054254532,
0.03767916187644005,
-0.055446770042181015,
0.015183812938630581,
-0.016568472608923912,
-0.00289861555211246,
-0.027054617181420326,
-0.02110845223069191,
0.033561963587999344,
-0.004858867265284061,
-0.014702067710459232,
0.00543011911213398,
0.04842180386185646,
-0.017887942492961884,
-0.037406232208013535,
0.042151834815740585,
0.047116950154304504,
-0.007013856433331966,
0.03041056916117668,
0.00627490459010005,
0.04525100067257881,
-0.0343608483672142,
0.005187361966818571,
-0.0001206842134706676,
-0.023525623604655266,
0.0019897064194083214,
-0.055350467562675476,
0.026122931391000748,
-0.0057210735976696014,
0.004141239915043116,
-0.026084478944540024,
0.02681710571050644,
-0.003687969408929348,
-0.058676596730947495,
0.03210582956671715,
0.011073960922658443,
0.010886842384934425,
-0.045931246131658554,
-0.007218953222036362,
-0.0793377235531807,
-0.005858306307345629,
-0.00593101279810071,
0.015254095196723938,
-0.011551011353731155,
0.009050006046891212,
0.015775693580508232,
-0.006954873446375132,
0.016622133553028107,
0.026055049151182175,
-0.019097179174423218,
0.023962322622537613,
-0.024724643677473068,
-0.026996783912181854,
-0.059573762118816376,
0.015802234411239624,
0.015199720859527588,
0.020142052322626114,
-0.005748641211539507,
-0.02345782145857811,
-0.02415475621819496,
-0.07984456419944763,
0.038834985345602036,
0.03555892035365105,
-0.012994148768484592,
0.0030869359616190195,
-0.008839452639222145,
0.0349983349442482,
0.046574532985687256,
0.0310744047164917,
0.04218494892120361,
0.00806796457618475,
0.01113309245556593,
0.051158398389816284,
-0.025665534660220146,
-0.0005742081557400525,
0.050038907676935196,
-0.0026060231029987335,
0.023214146494865417,
-0.00828800443559885,
0.018198754638433456,
-0.0013910609995946288,
0.013475990854203701,
0.010891634970903397,
-0.0010635562939569354,
-0.06230122223496437,
-0.014453976415097713,
-0.03921066224575043,
-0.024922868236899376,
0.01446539256721735,
0.013370796106755733,
0.004333739168941975,
0.006273753009736538,
-0.0732208862900734,
-0.009720335714519024,
0.0018565300852060318,
0.03254808858036995,
0.01867312751710415,
0.0022277547977864742,
0.007749258540570736,
0.012838993221521378,
0.01851288415491581,
-0.038040582090616226,
-0.037534575909376144,
-0.05146990343928337,
0.008483797311782837,
0.01721816137433052,
0.0018295993795618415,
-0.016498636454343796,
0.025510413572192192,
-0.003007512539625168,
-0.0015482252929359674,
0.048348020762205124,
0.06541025638580322,
-0.0017753065330907702,
-0.01061368826776743,
0.02846405655145645,
-0.00657585309818387,
0.06224627420306206,
-0.009118836373090744,
-0.0072161913849413395,
0.04158458113670349,
-0.010573280043900013,
-0.015099206939339638,
0.018894042819738388,
-0.02797381766140461,
0.03312571719288826,
0.012575770728290081,
0.0034801859874278307,
0.021919630467891693,
0.05260583013296127,
0.00982013437896967,
-0.024340273812413216,
0.00765186594799161,
-0.00878234300762415,
0.03463280200958252,
0.024781543761491776,
-0.006753891706466675,
0.00672494200989604,
0.000989485764876008,
0.05222412943840027,
0.005719701759517193,
0.016030162572860718,
-0.0198685135692358,
-0.023570571094751358,
0.01458424236625433,
0.03150707855820656,
0.03940463438630104,
0.013008031994104385,
0.003388131968677044,
0.015416023321449757,
0.0007459799526259303,
0.02645612508058548,
-0.023455927148461342,
-0.012989737093448639,
-0.09164635092020035,
0.00228219386190176,
-0.0017388237174600363,
-0.014968863688409328,
0.009318239986896515,
-0.04721304029226303,
0.026196179911494255,
0.03675014525651932,
-0.0960063487291336,
-0.010870779864490032,
0.0036407732404768467,
-0.0012310175225138664,
-0.020736444741487503,
0.04092780500650406,
-0.03350992873311043,
0.0367148257791996,
0.04974755272269249,
0.04997298866510391,
0.026216808706521988,
0.007906773127615452,
-0.023137688636779785,
0.010331228375434875,
-0.013079922646284103,
0.030251676216721535,
-0.00839171465486288,
-0.032510921359062195,
0.04328875243663788,
-0.023197881877422333,
-0.017417114228010178,
0.006509213708341122,
-0.007467690855264664,
0.004511658567935228,
-0.011619862169027328,
0.02624140866100788,
0.01795540750026703,
-0.03541973978281021,
0.017886638641357422,
-0.010539282113313675,
-0.03627690672874451,
0.012213582172989845,
0.05505872890353203,
0.040338777005672455,
0.013290227390825748,
-0.009491306729614735,
0.01683145761489868,
-0.0552673414349556,
-0.039684493094682693,
0.034849703311920166,
-0.025268224999308586,
-0.0018855617381632328,
0.003679297398775816,
0.03181513026356697,
0.007428836077451706,
-0.03676803410053253,
-0.0032677275594323874,
-0.06559965759515762,
0.0006827282486483455,
0.00872055534273386,
0.0216950885951519,
0.015901008620858192,
-0.022706208750605583,
-0.030117584392428398,
-0.04598970711231232,
0.046806465834379196,
0.025016121566295624,
-0.022380447015166283,
0.0025203204713761806,
0.0038788113743066788,
0.023522043600678444,
0.017457613721489906,
0.020668363198637962,
0.008821861818432808,
-0.07230159640312195,
0.0016640805406495929,
-0.009085685946047306,
-0.015722740441560745,
0.0010525897378101945,
-0.06873542815446854,
-0.04948407784104347,
-0.0464889332652092,
0.054959844797849655,
-0.004215552471578121,
-0.05673658475279808,
-0.06746141612529755,
-0.030563335865736008,
-0.011102898977696896,
0.06809025257825851,
0.05390862748026848,
0.00526810297742486,
-0.026478316634893417,
-0.0010637488448992372,
0.03779258579015732,
0.047305718064308167,
-0.03534051030874252,
0.03945762291550636,
0.027212494984269142,
-0.008026229217648506,
-0.026183800771832466,
0.013349196873605251,
-0.03353835269808769,
0.03165252506732941,
0.028144322335720062,
-0.013271206989884377,
-0.011740942485630512,
-0.02316068857908249,
-0.028016937896609306,
0.052389562129974365,
-0.043156735599040985,
-0.03696135804057121,
0.0682872012257576,
-0.028286051005125046,
0.008645487949252129,
0.03000960312783718,
-0.014382991939783096,
-0.035977061837911606,
0.016898777335882187,
-0.023939790204167366,
0.012956192716956139,
0.00242213299497962,
0.013392562977969646,
0.06412698328495026,
-0.056502584367990494,
0.00021062871383037418,
-0.007074575871229172,
-0.021233543753623962,
-0.030671481043100357,
0.07630006223917007,
0.009984288364648819,
0.024730855599045753,
0.011111567728221416,
0.014211281202733517,
-0.03174702078104019,
0.004490620922297239,
0.007230993825942278,
0.02907080203294754,
-0.007907104678452015,
0.016361234709620476,
0.051016706973314285,
0.021152814850211143,
0.019588733091950417,
0.015517977066338062,
-0.01928490214049816,
0.037445735186338425,
-0.05014966055750847,
-0.015348131768405437,
0.005438680294901133,
0.011155810207128525,
0.028569748625159264,
0.017648611217737198,
-0.03010646253824234,
0.05931549519300461,
-0.033149220049381256,
0.022667763754725456,
-0.018099842593073845,
0.016048431396484375,
-0.04805463179945946,
0.01052361074835062,
-0.00584645988419652,
0.024924004450440407,
0.009012352675199509,
-0.017014864832162857,
-0.04092564061284065,
0.0024642394855618477,
0.05578291043639183,
-0.046440932899713516,
0.046045947819948196,
0.012662017717957497,
-0.030668677762150764,
0.007931921631097794,
0.00961746834218502,
0.013902572914958,
-0.00480941915884614,
-0.013901644386351109,
0.036435093730688095,
0.005712639074772596,
-0.011002587154507637,
-0.012443327344954014,
-0.036222945898771286,
0.02894723415374756,
-0.06917449086904526,
-0.0009574322612024844,
0.00867419969290495,
-0.01733255200088024,
-0.0277851689606905,
-0.024771593511104584
] |
<p>To account for parity violation the weak interaction matrix element is written in the form</p>
<p>$$
M \propto \sum_{i} C_i (\bar u_p O_i u_n) (\bar u_e O_i (1 + {{C'_i}\over{C_i}}\gamma^5)u_\nu)
$$</p>
<p>Why does time reversal invariance imply that the $C_i$ coefficients must be real?</p>
<p>I was thinking that maybe it might be related to some kind of hermiticity condition, in order to have $|M_{if}|=|M_{fi}|$. Am I on the right path?</p>
| 9,437 |
[
0.013002211228013039,
-0.026077747344970703,
-0.020876970142126083,
0.002830721205100417,
0.06514398008584976,
0.06857553869485855,
-0.033833302557468414,
-0.014109519310295582,
0.016966426745057106,
-0.023458832874894142,
0.03939605504274368,
-0.004429985303431749,
0.047587037086486816,
0.039908066391944885,
0.008958261460065842,
0.030659135431051254,
-0.011412562802433968,
-0.008830488659441471,
-0.01503042783588171,
-0.009437484666705132,
-0.005567953456193209,
0.04338402673602104,
0.011250359006226063,
0.011821046471595764,
-0.010240655392408371,
0.04693603515625,
0.0009316540672443807,
0.032804399728775024,
-0.0025429425295442343,
0.07758709043264389,
-0.014755366370081902,
-0.046390682458877563,
-0.002708116313442588,
-0.006857100408524275,
0.03650061413645744,
0.001454726792871952,
-0.0253809355199337,
-0.06438814848661423,
0.02517954260110855,
0.02042056806385517,
-0.01918800361454487,
-0.041926052421331406,
-0.0353434793651104,
0.03850991651415825,
0.01137046329677105,
-0.007342139724642038,
-0.019353246316313744,
0.003053575986996293,
0.054900042712688446,
-0.06026919186115265,
0.07631069421768188,
-0.039475005120038986,
0.04385014995932579,
0.004079378210008144,
-0.013336713425815105,
-0.027036849409341812,
0.07915319502353668,
0.05460194870829582,
0.020124318078160286,
-0.042822107672691345,
0.0158839114010334,
-0.006804808508604765,
0.01778780110180378,
-0.001482160878367722,
-0.01606929302215576,
0.030809512361884117,
-0.006710845977067947,
0.0031611595768481493,
-0.016966819763183594,
-0.016660016030073166,
0.017165768891572952,
-0.023028194904327393,
0.03190010040998459,
-0.03136720508337021,
-0.011328080669045448,
-0.028216291218996048,
0.011110696010291576,
0.007776783779263496,
0.03248990327119827,
0.028699196875095367,
0.02215219847857952,
0.039036549627780914,
0.011669610626995564,
0.0406465083360672,
-0.04014413058757782,
-0.00710313068702817,
0.030446479097008705,
0.005308077204972506,
-0.009066004306077957,
0.027622967958450317,
0.01224606204777956,
0.001900015282444656,
0.025642642751336098,
0.010431964881718159,
-0.03689037263393402,
0.006721758749336004,
0.01202818937599659,
0.04420416057109833,
0.009748280979692936,
0.0210307277739048,
-0.02639767900109291,
0.012093584053218365,
0.0028915617149323225,
0.06746228784322739,
-0.01402637455612421,
0.0015467196935787797,
-0.025985153391957283,
0.03521022945642471,
0.01586233824491501,
-0.011927731335163116,
-0.03238628804683685,
-0.03248971700668335,
-0.036254432052373886,
-0.005560004152357578,
0.03950090706348419,
-0.04294779524207115,
-0.023331979289650917,
-0.01269199326634407,
0.07399620115756989,
0.0808437168598175,
0.020145433023571968,
-0.020795388147234917,
0.04281172901391983,
-0.049838002771139145,
-0.07008516788482666,
-0.007116670720279217,
0.03359606862068176,
0.002319679595530033,
-0.030258027836680412,
0.017311954870820045,
0.03627237305045128,
-0.040238428860902786,
-0.0020489380694925785,
-0.02766525000333786,
0.05712088942527771,
-0.009864632040262222,
-0.1588619500398636,
-0.08577388525009155,
0.010352800600230694,
-0.0005311917630024254,
-0.030925936996936798,
-0.0790218859910965,
0.0017490104073658586,
0.0333121232688427,
0.08536756038665771,
-0.033880848437547684,
0.02138369344174862,
0.006928849965333939,
0.010027850978076458,
0.023706642910838127,
-0.011206748895347118,
-0.014148164540529251,
-0.02513851411640644,
-0.03878957778215408,
-0.020628497004508972,
-0.08253447711467743,
0.0008432280155830085,
0.012421232648193836,
0.00009031131048686802,
0.0015453187515959144,
0.06542110443115234,
-0.0030047555919736624,
0.03370191156864166,
0.0055964854545891285,
-0.052151165902614594,
-0.036378540098667145,
0.06024777516722679,
0.020194949582219124,
0.019778164103627205,
0.03872863948345184,
-0.013483375310897827,
-0.003913723863661289,
-1.684175714444791e-7,
0.03321094438433647,
0.03892022371292114,
-0.055161915719509125,
-0.04045746475458145,
-0.0018815022194758058,
-0.0199874397367239,
-0.010780499316751957,
-0.0494074709713459,
-0.03831135481595993,
-0.024580467492341995,
0.010777520015835762,
0.015464821830391884,
0.03350922465324402,
-0.03671371564269066,
0.003668825840577483,
0.012233172543346882,
-0.0349360853433609,
-0.03102826699614525,
-0.04679621756076813,
-0.014447618275880814,
0.01274873223155737,
-0.024553848430514336,
0.030234534293413162,
0.010285597294569016,
0.02168564312160015,
0.007009655702859163,
-0.03499463200569153,
-0.0274924598634243,
0.015330569818615913,
0.02135404944419861,
0.004629889503121376,
0.02922874130308628,
0.016559941694140434,
0.03784722462296486,
0.005441144574433565,
0.027218572795391083,
-0.0036518583074212074,
-0.018139054998755455,
-0.002877801191061735,
-0.0188418161123991,
0.03884170949459076,
0.018192538991570473,
-0.0012037238338962197,
0.02024834044277668,
-0.04378426447510719,
0.010302522219717503,
0.016156639903783798,
-0.017901724204421043,
0.07062217593193054,
0.030722452327609062,
0.028726084157824516,
0.010523831471800804,
0.048391371965408325,
0.01771054044365883,
0.02918136864900589,
-0.0023163154255598783,
-0.028389254584908485,
-0.029561053961515427,
-0.016111193224787712,
0.0064172218553721905,
0.053902775049209595,
-0.02734694443643093,
0.05332847312092781,
0.009310638532042503,
0.05491446331143379,
0.002592458389699459,
0.01030768547207117,
-0.001160867395810783,
-0.06513822078704834,
0.024514809250831604,
-0.005909794941544533,
-0.01877095364034176,
0.02049500122666359,
0.009793626144528389,
-0.03322942182421684,
0.032661501318216324,
-0.03306988254189491,
0.006870538927614689,
0.0001092757738661021,
-0.0053103272803127766,
-0.009051693603396416,
-0.01888222247362137,
-0.06683522462844849,
0.05142178386449814,
-0.00550438929349184,
0.06796543300151825,
0.015157838352024555,
-0.010304201394319534,
0.008682270534336567,
-0.010706756263971329,
-0.04228273034095764,
-0.011670689098536968,
-0.026127053424715996,
-0.02276379056274891,
-0.02433670684695244,
0.02981654182076454,
-0.04533630609512329,
0.038315027952194214,
-0.0390029102563858,
0.023094840347766876,
-0.01254488155245781,
-0.056326575577259064,
0.04018520191311836,
0.015483533032238483,
0.018173206597566605,
-0.016428261995315552,
-0.018192963674664497,
-0.011546960100531578,
-0.02786123938858509,
0.03860502317547798,
0.03459449112415314,
-0.049666423350572586,
0.036216359585523605,
-0.05332228168845177,
0.04136621952056885,
0.0006822869763709605,
0.03565872460603714,
-0.01920825056731701,
0.0370132252573967,
-0.01218558568507433,
-0.08170782029628754,
-0.05937269702553749,
-0.02135501056909561,
0.013369602151215076,
-0.01985684037208557,
-0.014162317849695683,
0.06576330959796906,
0.0037010563537478447,
0.002951362170279026,
-0.014671619050204754,
-0.03866611421108246,
-0.030002696439623833,
-0.019193340092897415,
-0.011783457361161709,
0.02610005810856819,
-0.03320086747407913,
0.031887710094451904,
0.023410024121403694,
-0.032175254076719284,
0.0315898172557354,
-0.05326300114393234,
-0.051539331674575806,
0.007006165571510792,
-0.000022849058950669132,
0.030922070145606995,
0.03933364525437355,
-0.044246602803468704,
0.11705461889505386,
0.03571099042892456,
-0.01135979127138853,
-0.03566474840044975,
-0.0223531574010849,
-0.03024005889892578,
-0.07347206771373749,
0.03203216567635536,
0.012096388265490532,
-0.012642176821827888,
0.05081633850932121,
0.024507932364940643,
0.039462484419345856,
0.012350596487522125,
0.008284099400043488,
-0.01785823330283165,
-0.010587363503873348,
-0.020849768072366714,
-0.02980564534664154,
0.05330587923526764,
-0.011827691458165646,
-0.014556809328496456,
-0.03004147671163082,
-0.004365883767604828,
0.0048515573143959045,
0.0035393459256738424,
-0.046342529356479645,
0.02491951175034046,
-0.018490329384803772,
0.04614609479904175,
-0.036374833434820175,
0.059900373220443726,
-0.024988388642668724,
-0.024152372032403946,
-0.00986481737345457,
0.03196532279253006,
0.02633979730308056,
-0.06820090860128403,
0.012197906151413918,
0.01288909837603569,
0.035167571157217026,
0.00112809834536165,
-0.032721150666475296,
0.016297563910484314,
-0.04893781244754791,
0.01061664056032896,
-0.04210160672664642,
-0.017597129568457603,
0.04592030867934227,
0.015327071771025658,
0.01714378595352173,
-0.02527974173426628,
-0.046296924352645874,
-0.025060130283236504,
-0.004755297210067511,
0.03901810944080353,
-0.005224197171628475,
0.07505088299512863,
0.0022373301908373833,
0.024803897365927696,
0.019140783697366714,
-0.04261040687561035,
0.012865278869867325,
-0.015566022135317326,
-0.035739269107580185,
0.05569703131914139,
-0.0015265588881447911,
-0.008090478368103504,
0.005263097118586302,
-0.03714806213974953,
0.011658408679068089,
-0.02497073821723461,
0.007810487877577543,
-0.013163371942937374,
-0.011460219509899616,
-0.038737960159778595,
0.01705978624522686,
-0.04785346984863281,
-0.010690485127270222,
-0.006474567577242851,
0.02100956067442894,
0.0429719053208828,
-0.02185654640197754,
0.007573735900223255,
0.019024567678570747,
-0.03084219992160797,
-0.00567308533936739,
-0.025305574759840965,
0.029257996007800102,
0.018104813992977142,
0.014436908066272736,
0.06495622545480728,
0.017916103824973106,
-0.02331039495766163,
-0.01222614198923111,
0.007433275226503611,
0.034301191568374634,
0.03313194587826729,
0.014583648182451725,
0.002173809800297022,
-0.020106613636016846,
-0.002141524339094758,
0.04401913657784462,
0.053954143077135086,
0.03885496035218239,
0.006024898961186409,
0.027581095695495605,
0.040711015462875366,
-0.03681741654872894,
0.03262097388505936,
0.045836228877305984,
0.01953924633562565,
0.010315372608602047,
-0.08356399089097977,
-0.0063640885055065155,
0.01958058774471283,
-0.005553330760449171,
0.0016588338185101748,
-0.009572855196893215,
-0.04330834001302719,
-0.009866416454315186,
0.006831748876720667,
0.01781468652188778,
-0.012713962234556675,
0.015343068167567253,
-0.004828407429158688,
-0.0011004561092704535,
-0.0039793141186237335,
-0.011848708614706993,
0.00967054907232523,
0.048761799931526184,
0.0367453433573246,
0.03360125049948692,
0.011506443843245506,
-0.0550222210586071,
-0.018841462209820747,
0.02432646043598652,
0.03586026653647423,
0.00743717048317194,
-0.03069158084690571,
-0.04470661282539368,
-0.008551618084311485,
0.035759150981903076,
-0.024208594113588333,
0.08993835002183914,
0.009137026034295559,
-0.0029394072480499744,
0.005755014717578888,
-0.027509242296218872,
-0.03283897414803505,
0.05066171661019325,
0.02204762026667595,
0.03955298662185669,
-0.035453490912914276,
-0.007648293394595385,
-0.0449567474424839,
-0.0037384030874818563,
0.020251311361789703,
0.0414305254817009,
-0.026155848056077957,
0.03431309014558792,
0.03147614374756813,
0.030114876106381416,
-0.005332936532795429,
-0.08921599388122559,
0.03611141815781593,
-0.0018910166108980775,
0.017099160701036453,
0.040191665291786194,
-0.021593164652585983,
-0.018956337124109268,
-0.012624629773199558,
0.03377724066376686,
0.02388571761548519,
-0.02435319311916828,
-0.042023856192827225,
0.03540943190455437,
0.00599542586132884,
-0.02899923361837864,
0.05424340441823006,
0.04245147854089737,
-0.0024431440979242325,
0.023471226915717125,
-0.036055825650691986,
0.0027447070460766554,
-0.024308184161782265,
0.03721391037106514,
-0.0456952303647995,
0.01010049507021904,
0.016126470640301704,
0.027991782873868942,
-0.006728661246597767,
0.029607106000185013,
-0.00027681063511408865,
-0.009089499711990356,
-0.04820377752184868,
0.057736266404390335,
-0.02189592830836773,
-0.02827743999660015,
0.009665966033935547,
0.005051244981586933,
-0.006533628795295954,
-0.026792248710989952,
0.04405439645051956,
-0.03613969683647156,
-0.024424999952316284,
0.030459297820925713,
0.0292209442704916,
0.004198964219540358,
0.018176035955548286,
-0.044962842017412186,
-0.02844303660094738,
-0.0314023420214653,
0.0033658118918538094,
-0.011300398968160152,
0.023829061537981033,
-0.00067763717379421,
-0.03336867690086365,
0.015532896853983402,
0.026870999485254288,
-0.04103053733706474,
0.03216582536697388,
-0.05400193855166435,
0.02107669599354267,
0.0067703695967793465,
0.004762526601552963,
-0.06737799942493439,
-0.05401737615466118,
0.0036798010114580393,
0.010998966172337532,
-0.055846668779850006,
-0.009123345836997032,
-0.02729182504117489,
-0.004201275296509266,
-0.038294028490781784,
-0.006200285628437996,
0.0692644938826561,
-0.03888082504272461,
-0.010892530903220177,
0.05217355489730835,
0.005338982213288546,
0.0651264637708664,
-0.033713966608047485,
-0.0024605183862149715,
0.03947119042277336,
-0.02740892767906189,
-0.02440381981432438,
-0.004249932710081339,
0.04910670593380928,
-0.01897241175174713,
-0.050139255821704865,
-0.009583968669176102,
0.02587713673710823,
0.006863993592560291,
0.028265496715903282,
0.010474101640284061,
0.02422141097486019,
-0.04516338184475899,
0.007741113193333149,
-0.04411645978689194,
0.004147922620177269,
0.036261726170778275,
0.03845387324690819,
0.016432369127869606,
-0.01608790084719658,
-0.028364554047584534,
-0.015409310348331928,
0.06297849863767624,
-0.010443227365612984,
0.0013431889237836003,
0.024282585829496384,
0.03651333972811699,
-0.019752198830246925,
-0.008817804045975208,
0.049388691782951355,
-0.028491437435150146,
0.01902654394507408,
0.007761053275316954,
0.0028843898326158524,
0.010690429247915745,
0.0004226397431921214,
-0.05897596478462219,
0.011719198897480965,
-0.023103905841708183,
0.07653167098760605,
0.044805802404880524,
0.006072223652154207,
0.017950814217329025,
0.015154716558754444,
-0.016981055960059166,
-0.024905670434236526,
0.00584576278924942,
-0.050440914928913116,
0.013190026395022869,
0.01845286227762699,
-0.004305168054997921,
-0.04012560099363327,
-0.024674467742443085,
0.01347366813570261,
0.032316360622644424,
-0.022467317059636116,
0.006641135085374117,
0.047512903809547424,
0.005360711831599474,
0.0044735088013112545,
0.01875193603336811,
-0.026270747184753418,
0.03403658792376518,
-0.030732717365026474,
-0.004674843512475491,
0.02690039947628975,
0.018219439312815666,
0.0542503260076046,
0.02939983643591404,
0.020899871364235878,
-0.04825654625892639,
-0.00970817543566227,
-0.04829730466008186,
0.00237547536380589,
0.05407101660966873,
-0.01734466664493084,
0.008381400257349014,
-0.019349846988916397,
0.04937371239066124,
0.0065542045049369335,
0.00033540872391313314,
-0.008618407882750034,
-0.057020314037799835,
-0.03385686129331589,
-0.019852669909596443,
-0.032472796738147736,
0.04335980489850044,
-0.042335301637649536,
0.012844651006162167,
-0.019327539950609207,
-0.027876444160938263,
-0.011163802817463875,
0.03584082052111626,
0.03332856670022011,
-0.022105921059846878,
0.03126765787601471,
0.0010190188186243176,
-0.0009428355842828751,
-0.0071017127484083176,
-0.007327042520046234,
0.12081684172153473,
0.02572893537580967,
-0.011692269705235958,
-0.05856688320636749,
0.03614669665694237,
-0.019108066335320473,
0.022709542885422707,
-0.021727535873651505,
0.030946670100092888,
0.002081689890474081,
-0.019135797396302223,
0.013661468401551247,
0.047946371138095856,
0.02162082865834236,
0.021918846294283867,
0.046561069786548615,
-0.047197386622428894,
-0.04388671740889549,
0.029000936076045036,
0.032000940293073654,
-0.024847837164998055,
-0.02765566296875477,
-0.005675927735865116,
0.0018944430630654097,
-0.007096749730408192,
-0.027024315670132637,
0.026206037029623985,
-0.02530018612742424,
0.015339036472141743,
0.006213863845914602,
-0.03162736818194389,
-0.00006478933210019022,
-0.004186281003057957,
0.013433057814836502,
-0.0413973368704319,
0.016725244000554085,
0.014700979925692081,
0.0029609696939587593,
0.054844778031110764,
0.012983358465135098,
-0.012018071487545967,
-0.010860241018235683,
0.03289838135242462,
0.005489460192620754,
-0.03271561488509178,
-0.010643239133059978,
-0.009785063564777374,
0.04397046938538551,
-0.013937330804765224,
-0.01921733282506466,
-0.007182688917964697,
0.00728264357894659,
0.012406179681420326,
-0.060663025826215744,
-0.006164241582155228,
0.020813997834920883,
0.015384024009108543,
-0.04704584926366806,
0.009046000428497791,
-0.017048530280590057,
0.005662445444613695,
0.02657533995807171,
0.020259758457541466,
-0.018721994012594223,
-0.02688707411289215,
-0.006940975785255432,
-0.030070262029767036,
0.02537510357797146,
0.025982577353715897,
-0.01808955892920494,
-0.03488179296255112,
-0.012129469774663448,
-0.02882983908057213,
-0.03158600255846977,
0.03124176152050495,
0.010793606750667095,
0.02753756009042263,
-0.011123580858111382,
0.00298391655087471,
-0.014674711041152477,
-0.05409977585077286,
0.02779829502105713,
-0.034452058374881744,
-0.05260837823152542,
-0.011403377167880535,
-0.044686924666166306,
-0.0031584494281560183,
0.05895887315273285,
-0.05691669508814812,
-0.00703476881608367,
0.004127344116568565,
0.0348823256790638,
0.03010088950395584,
-0.008464603684842587,
-0.02468382567167282,
0.011564407497644424,
-0.0135721480473876,
-0.002049121307209134,
-0.013031095266342163,
-0.013911056332290173,
0.03448595851659775,
-0.011226149275898933,
0.02099006250500679,
0.01678984984755516,
-0.03773868456482887,
-0.03368926793336868,
0.021795550361275673,
-0.026605332270264626,
-0.0048743044026196,
0.02419663965702057,
-0.01651422493159771,
-0.015256136655807495,
-0.04275303706526756,
-0.030474171042442322,
-0.026703521609306335,
0.014661982655525208,
0.0078124054707586765,
-0.01801874302327633,
-0.012329920195043087,
-0.02218322642147541,
0.024879785254597664,
-0.015563441440463066,
-0.0204638559371233,
-0.03450280800461769,
0.025479156523942947,
-0.012566336430609226,
-0.008163385093212128,
-0.03518640249967575,
0.0075123002752661705,
-0.015695026144385338,
-0.0056577278301119804,
0.026957301422953606,
0.020680731162428856,
-0.03878515958786011,
-0.02014283835887909,
0.012559649534523487,
0.024349847808480263,
0.017396192997694016,
-0.012851853854954243,
-0.03161820396780968,
0.03693500533699989,
-0.033523570746183395,
-0.05865141376852989,
0.05173011124134064,
-0.017684871330857277,
0.021858057007193565,
0.013050013221800327,
-0.0035172891803085804,
0.005861902609467506,
0.04326712712645531,
-0.025608135387301445,
0.02437029778957367,
-0.01120251789689064,
0.031032077968120575,
0.018976965919137,
-0.027806244790554047,
-0.008520867675542831,
-0.0062523470260202885,
-0.00794809777289629,
-0.006888325791805983,
-0.018286483362317085,
0.0022588027641177177,
0.01875070482492447,
-0.05484379082918167,
0.023379581049084663,
0.007355866022408009,
0.02881077490746975,
0.01776992157101631,
-0.03516312316060066,
0.02344518154859543,
-0.03583955392241478,
0.029975948855280876,
-0.000018699338397709653,
0.0009844800224527717,
-0.08003273606300354,
-0.030485428869724274,
0.008422470651566982,
0.010520865209400654,
0.037683892995119095,
-0.06284908205270767,
0.041889488697052,
0.02029675431549549,
-0.033323630690574646,
0.016191456466913223,
-0.024244464933872223,
-0.03638086095452309,
-0.019758103415369987,
-0.0017461947863921523,
-0.01663912460207939,
0.03454788774251938,
0.01722545549273491,
0.0034230074379593134,
0.02236783318221569,
0.010660863481462002,
-0.0001899365015560761,
-0.03702704608440399,
-0.024680854752659798,
0.00027140218298882246,
-0.002000798936933279,
-0.02862715907394886,
0.10186557471752167,
-0.008876889944076538,
-0.029802117496728897,
0.03324434533715248,
-0.005268740002065897,
0.00956615712493658,
-0.013035391457378864,
0.05108034610748291,
-0.015373548492789268,
0.028328800573945045,
0.02054418995976448,
-0.03623814508318901,
0.019808854907751083,
0.02876565232872963,
0.004216999281197786,
0.016101671382784843,
-0.014250264503061771,
0.014113958925008774,
-0.020228492096066475,
-0.04172923415899277,
-0.027342045679688454,
0.011324414983391762,
-0.0033211619593203068,
-0.03110974282026291,
-0.017301876097917557,
0.012279882095754147,
-0.010355865582823753,
-0.02230914868414402,
0.02000533603131771,
-0.05211280658841133,
0.0044017368927598,
0.026700828224420547,
0.022315140813589096,
0.01369095966219902,
-0.006499425042420626,
0.0017516411608085036,
-0.05179091915488243,
0.048444852232933044,
0.01580909825861454,
-0.0035572671331465244,
-0.038620106875896454,
-0.03618665784597397,
0.05284116044640541,
0.01468448992818594,
-0.012310082092881203,
-0.018768751993775368,
-0.03560469672083855,
0.018969068303704262,
0.01638440601527691,
-0.0017890356248244643,
-0.03278019279241562,
-0.018808851018548012,
0.005476684775203466,
-0.04835718870162964,
0.0031522223725914955,
0.021463913843035698,
0.020006978884339333,
0.02380065806210041,
-0.011760963127017021,
-0.02736743725836277,
0.0004873966099694371,
0.05033762380480766,
0.017923757433891296,
-0.07211195677518845,
0.035650450736284256,
-0.006264048162847757,
-0.01172530185431242,
-0.024085063487291336,
0.007531360723078251,
0.0034325215965509415,
-0.010210860520601273,
0.028382882475852966,
-0.003290358930826187,
-0.025622114539146423,
0.04344986751675606,
-0.005477456841617823,
0.007467183750122786,
0.016784705221652985,
-0.0012973047560080886,
-0.055647578090429306,
0.045194562524557114,
0.01027524285018444,
0.01646130345761776,
0.06795848160982132,
0.009171194396913052,
0.050331201404333115,
0.015721702948212624,
-0.05419507622718811,
-0.04280044138431549,
0.000900154875125736,
-0.022478526458144188,
-0.01460077241063118,
-0.027836225926876068,
0.028332777321338654,
0.03908753767609596,
-0.044662971049547195,
0.040424562990665436,
0.045837074518203735,
-0.017024759203195572,
-0.022795692086219788,
0.01758064515888691,
0.04263698682188988,
0.029724622145295143,
0.029090313240885735,
0.058256424963474274,
0.0022477805614471436,
-0.0006704757106490433,
0.059548597782850266,
0.04771892726421356,
0.01749773509800434,
0.00025050484691746533,
0.025905665010213852,
0.005801975727081299,
-0.011704821139574051,
0.031060734763741493,
-0.022289272397756577,
0.06043020263314247,
-0.022045670077204704,
0.007919558323919773,
0.034669581800699234,
-0.0224442258477211,
0.006163872312754393,
0.008525312878191471,
-0.009859987534582615,
0.062340132892131805,
-0.040458809584379196,
0.019264955073595047,
-0.013802939094603062,
0.022376134991645813,
-0.012269527651369572,
0.027933955192565918,
0.04011409729719162,
0.04595271870493889,
-0.005930471234023571,
0.004092326387763023,
-0.0362495593726635,
-0.012633935548365116,
0.00966597255319357,
-0.07547147572040558,
-0.02521572820842266,
0.03621253743767738,
-0.015965953469276428,
-0.0038042126689106226,
-0.022424241527915,
-0.03201819583773613,
-0.030667558312416077,
-0.007879034616053104,
0.032355520874261856,
0.027618611231446266,
-0.01473764143884182,
-0.026689110323786736,
0.0038803010247647762,
0.03170982003211975,
-0.009268294088542461,
0.01802545040845871,
-0.015770968049764633,
0.02972363494336605,
-0.020292622968554497,
0.023678919300436974
] |
<p>What is the rigorous definition of the <a href="http://en.wikipedia.org/wiki/Aufbau_principle" rel="nofollow">Aufbau principle</a> and the mathematical model used for its description? </p>
<p>From Wikipedia, we have that the principle postulates a hypothetical process in which an atom is "built up" by progressively adding electrons. For modeling the postulate, we use the Madelung rule, Pauli exclusion and "if two same energy orbitals are available, choose the less occupied one)". So, $n+\ell$ ordering with constraints. And I also know that the Aufbau principle has its exceptions.</p>
| 9,438 |
[
-0.03740342706441879,
-0.03949913755059242,
0.011943655088543892,
-0.03926665708422661,
0.006153492256999016,
-0.021021315827965736,
-0.04764997214078903,
0.000029718961741309613,
0.017978359013795853,
-0.03943127021193504,
0.06910885870456696,
0.01598495803773403,
0.05779314786195755,
0.02081342600286007,
0.005637947469949722,
0.015224327333271503,
0.019265979528427124,
-0.05098652094602585,
-0.020119396969676018,
-0.01004823762923479,
-0.009814138524234295,
0.015028944239020348,
0.010101748630404472,
-0.030445866286754608,
-0.019225282594561577,
-0.0006135281873866916,
0.02007090114057064,
0.007093110587447882,
0.019901586696505547,
0.06973689794540405,
0.01375367771834135,
-0.027865201234817505,
0.054791409522295,
0.0004049114650115371,
0.03768986091017723,
0.00437532365322113,
0.0035703484900295734,
-0.030517717823386192,
0.00830263551324606,
0.022832009941339493,
-0.024714555591344833,
-0.030208468437194824,
-0.024241255596280098,
0.026318272575736046,
-0.0024724267423152924,
0.01655440777540207,
0.013401154428720474,
-0.012881838716566563,
0.02955525740981102,
-0.0523037351667881,
0.06392939388751984,
0.00807652436196804,
0.04420032352209091,
0.00609565619379282,
0.006717268377542496,
-0.02689790166914463,
0.06139261648058891,
0.0580991767346859,
0.00297012971714139,
-0.03715096414089203,
-0.033492788672447205,
-0.05499113351106644,
0.0015922896564006805,
0.009766338393092155,
-0.025184715166687965,
0.05530126020312309,
0.0018599005416035652,
-0.0042677768506109715,
0.01362374983727932,
0.019282493740320206,
-0.012832658365368843,
-0.01916712522506714,
0.041436366736888885,
-0.013154731132090092,
0.013812507502734661,
-0.020600099116563797,
0.040719155222177505,
-0.002680764067918062,
0.010883376002311707,
0.05087316408753395,
-0.014034895226359367,
0.0354834608733654,
0.01053563691675663,
0.01862580142915249,
-0.008874250575900078,
-0.030148176476359367,
0.08447752892971039,
-0.016842886805534363,
0.039057351648807526,
0.029091257601976395,
-0.022816898301243782,
0.027693534269928932,
0.02301912009716034,
-0.03603971377015114,
-0.02187683805823326,
0.030784348025918007,
-0.013297192752361298,
0.059617068618535995,
-0.008272632025182247,
-0.014134805649518967,
0.035953085869550705,
-0.028184011578559875,
0.024684354662895203,
0.05803990736603737,
0.007976819761097431,
-0.02674938179552555,
-0.03803962841629982,
0.04278404265642166,
0.004244612064212561,
0.015615771524608135,
-0.008902297355234623,
0.04416477680206299,
0.005062456242740154,
0.006148896645754576,
0.006152137648314238,
0.016932621598243713,
0.01264648325741291,
-0.0001511681330157444,
0.05311451479792595,
0.04846220090985298,
0.04943256452679634,
-0.012633753009140491,
0.039514873176813126,
-0.001732903067022562,
-0.0641939714550972,
-0.011314230039715767,
-0.0004070268478244543,
-0.014682385139167309,
-0.003909487277269363,
0.04295559599995613,
-0.005344638135284185,
-0.06352297961711884,
0.02978847362101078,
0.0423215851187706,
0.04609035328030586,
-0.002853541634976864,
-0.11516249924898148,
-0.05121448263525963,
0.05891106277704239,
-0.022250045090913773,
0.003729112446308136,
-0.07985184341669083,
0.021823950111865997,
0.0028206584975123405,
0.09621065109968185,
0.021642029285430908,
-0.00944901816546917,
-0.003823332255706191,
0.02663225680589676,
0.023404506966471672,
-0.009319054894149303,
-0.011102004908025265,
0.029659975320100784,
-0.03949884697794914,
-0.04541834071278572,
-0.08240118622779846,
0.05886268988251686,
0.04464327171444893,
0.0035880336072295904,
-0.046013087034225464,
0.0704161673784256,
-0.009710166603326797,
-0.013853590935468674,
0.0073476145043969154,
0.025473354384303093,
-0.024576034396886826,
0.036922622472047806,
0.01012310478836298,
-0.005771105643361807,
0.07187387347221375,
0.017814433202147484,
0.02955370582640171,
-0.02316191978752613,
0.04320241138339043,
0.02156023308634758,
-0.040324389934539795,
-0.020820777863264084,
-0.04899453744292259,
0.01354373898357153,
0.029660120606422424,
-0.052313677966594696,
-0.010554316453635693,
0.02643720619380474,
0.032984986901283264,
-0.01046911533921957,
-0.005242144223302603,
-0.008224854245781898,
0.015666916966438293,
0.011999128386378288,
-0.03155767545104027,
0.005353310611099005,
-0.08356467634439468,
0.02766057848930359,
-0.014176551252603531,
-0.016439158469438553,
0.04493575915694237,
-0.003451091703027487,
-0.0026968223974108696,
-0.019326789304614067,
-0.030340805649757385,
-0.02328907698392868,
0.007016252260655165,
0.007136206142604351,
-0.0029941746033728123,
0.025202181190252304,
0.057645078748464584,
0.04163835197687149,
0.018060356378555298,
0.05946928262710571,
-0.030626613646745682,
-0.0015762810362502933,
0.001828994369134307,
-0.0012080518063157797,
0.014683922752737999,
0.03176604583859444,
-0.00400527473539114,
-0.00824378989636898,
-0.040690045803785324,
0.013998930342495441,
0.0666530430316925,
-0.012791519053280354,
0.0691889077425003,
0.027828631922602654,
0.032083507627248764,
0.035953156650066376,
0.04902155324816704,
-0.0028722193092107773,
-0.01209601853042841,
0.0059548113495111465,
-0.06128601357340813,
-0.010676784440875053,
-0.02835898846387863,
0.03142883628606796,
0.04549098387360573,
-0.038085419684648514,
0.0008011438767425716,
-0.01578809693455696,
0.03548450022935867,
0.045830562710762024,
0.050888270139694214,
-0.06208963319659233,
-0.03007298894226551,
0.02788485214114189,
0.011925259605050087,
0.01924232207238674,
0.02208663895726204,
0.01383295375853777,
0.025083934888243675,
0.022946065291762352,
0.0025256762746721506,
-0.03422711789608002,
0.03260505944490433,
-0.0017252778634428978,
-0.021260777488350868,
-0.024071993306279182,
-0.017467381432652473,
0.01748695969581604,
-0.022038282826542854,
0.03290928155183792,
0.019994059577584267,
-0.030686281621456146,
0.025113388895988464,
-0.055358387529850006,
-0.01569216325879097,
0.020344063639640808,
-0.010017000138759613,
-0.03808707371354103,
-0.02214016392827034,
-0.0005930475890636444,
-0.00235412223264575,
-0.016927065327763557,
-0.05372846499085426,
-0.011339333839714527,
-0.020987140014767647,
0.007969820871949196,
0.0029139567632228136,
-0.0002114648959832266,
0.01921384036540985,
-0.02645353600382805,
-0.027724716812372208,
-0.055814895778894424,
-0.06821814179420471,
0.05250353738665581,
0.020056534558534622,
-0.042337268590927124,
-0.012674086727201939,
-0.013450962491333485,
-0.00743003049865365,
0.07923319935798645,
-0.014323144219815731,
0.024241197854280472,
-0.00841096043586731,
-0.0031061330810189247,
-0.028232969343662262,
-0.004433600697666407,
-0.017090706154704094,
-0.005637120455503464,
-0.0019045023946091533,
-0.024903560057282448,
0.042925745248794556,
-0.031336791813373566,
-0.025027554482221603,
0.029099706560373306,
-0.0206631887704134,
-0.044853996485471725,
-0.006727679166942835,
-0.01890309527516365,
0.027606673538684845,
-0.021338604390621185,
0.02985878475010395,
0.04573240876197815,
-0.06776505708694458,
-0.01028987392783165,
-0.03036108799278736,
-0.06696727871894836,
0.021519631147384644,
-0.0840538963675499,
0.01641610823571682,
0.010595015250146389,
-0.03645701706409454,
0.08132071793079376,
0.019176367670297623,
-0.015329253859817982,
-0.030062023550271988,
-0.019578076899051666,
0.02781173214316368,
0.004609263967722654,
0.009348798543214798,
0.045721761882305145,
0.012349054217338562,
0.04237956553697586,
0.019385239109396935,
0.027594977989792824,
0.06064685434103012,
0.021711699664592743,
-0.006243763025850058,
0.0022209808230400085,
-0.002041093772277236,
-0.005687489174306393,
0.018381576985120773,
0.010411715134978294,
-0.026638273149728775,
0.047169990837574005,
-0.013711224310100079,
0.035652630031108856,
0.018792781978845596,
-0.04382767155766487,
0.020032161846756935,
0.0003485022753011435,
-0.017426401376724243,
-0.02754431590437889,
0.044810835272073746,
-0.012350921519100666,
-0.03836573287844658,
0.006086873821914196,
0.01893351413309574,
0.008624503389000893,
-0.02633376233279705,
-0.026196707040071487,
0.015361480414867401,
0.01272489596158266,
-0.0493958480656147,
-0.0009711466846056283,
0.008290375582873821,
-0.017783232033252716,
-0.0035344392526894808,
-0.02186400443315506,
-0.008664588443934917,
0.03852052241563797,
0.004690427333116531,
0.0187427569180727,
-0.004683471750468016,
-0.044799525290727615,
-0.029218392446637154,
-0.07518524676561356,
0.0077699339017271996,
0.008267192170023918,
0.0705292671918869,
-0.006916956976056099,
0.06123464182019234,
0.013665281236171722,
-0.00017721416952554137,
0.02048048935830593,
-0.015634510666131973,
-0.08224263042211533,
0.023644184693694115,
-0.006716195028275251,
0.02755110338330269,
0.00874828640371561,
-0.009662270545959473,
-0.02385592833161354,
-0.047279998660087585,
-0.05863187834620476,
-0.0518806129693985,
0.03387065976858139,
-0.04343094676733017,
0.011013297364115715,
-0.05405285581946373,
0.0009200319764204323,
-0.030533738434314728,
0.03708045184612274,
0.04456291347742081,
-0.05306314677000046,
0.002403764985501766,
0.04514368250966072,
-0.03142978996038437,
-0.0192104484885931,
-0.01785106584429741,
0.02637280896306038,
0.011545680463314056,
0.012392310425639153,
0.023057660087943077,
0.03538691624999046,
-0.018933242186903954,
-0.026257239282131195,
-0.026565734297037125,
0.0658966451883316,
0.04214635118842125,
0.02385198324918747,
-0.018949588760733604,
-0.02416880615055561,
-0.005088866222649813,
0.0033932693768292665,
0.01912841387093067,
-0.017514783889055252,
0.03883255645632744,
0.055715397000312805,
-0.011554170399904251,
-0.023358937352895737,
0.0361577644944191,
0.05537426099181175,
0.035788390785455704,
-0.008506538346409798,
-0.019391369074583054,
-0.003928499296307564,
-0.006285157520323992,
0.012279897928237915,
0.018824061378836632,
-0.0478803776204586,
-0.021492190659046173,
0.02197016030550003,
-0.006252815015614033,
0.005545959807932377,
-0.021757356822490692,
-0.02386535331606865,
-0.016076253727078438,
0.014773492701351643,
0.0024601013865321875,
-0.021368367597460747,
0.00915288832038641,
-0.0034216674976050854,
0.05159464851021767,
0.05229334905743599,
0.0047090803273022175,
-0.06402964144945145,
0.021067488938570023,
0.026643401011824608,
0.026696277782320976,
-0.02018037810921669,
0.04140462353825569,
-0.04418793320655823,
-0.01686478778719902,
0.03163919225335121,
-0.01650671288371086,
0.03699503466486931,
-0.041594598442316055,
0.01424564328044653,
-0.023479480296373367,
-0.03881854563951492,
0.002127064624801278,
0.01521093025803566,
-0.02158878929913044,
0.014371776953339577,
-0.016270330175757408,
0.004203652963042259,
-0.011531772091984749,
0.004931105766445398,
0.03156896308064461,
0.03531425818800926,
-0.0039050562772899866,
0.005212235264480114,
0.005598203744739294,
0.02956012263894081,
-0.028402915224432945,
-0.07370851933956146,
-0.003289527725428343,
0.012479403056204319,
-0.012730186805129051,
0.010813235305249691,
-0.03377775847911835,
-0.030519036576151848,
0.000790860562119633,
0.007614480797201395,
-0.029689863324165344,
0.007177331484854221,
-0.018577048555016518,
0.0974198654294014,
0.059861332178115845,
-0.021886790171265602,
0.052000321447849274,
0.042713843286037445,
-0.007827885448932648,
-0.001118044601753354,
-0.02522553876042366,
0.03206818178296089,
-0.017471127212047577,
0.015977637842297554,
-0.056105971336364746,
0.010056308470666409,
-0.04670213535428047,
0.04613357037305832,
0.003136495826765895,
-0.022925840690732002,
-0.010424976237118244,
-0.04500114172697067,
-0.030810434371232986,
-0.0034313511569052935,
-0.0056338259018957615,
0.00020991590281482786,
-0.03207053616642952,
0.040066976100206375,
0.013452224433422089,
-0.02639675885438919,
0.03733942657709122,
-0.032904066145420074,
0.011446249671280384,
-0.012910806573927402,
-0.004754728637635708,
0.029910730198025703,
-0.02115047536790371,
-0.029866481199860573,
-0.0015709151048213243,
-0.02858758345246315,
0.05911850929260254,
-0.008308874443173409,
0.0033598497975617647,
-0.028579868376255035,
-0.04947345703840256,
-0.006288350559771061,
0.0029343441128730774,
-0.014625669457018375,
0.024751203134655952,
-0.006771102547645569,
0.04494025930762291,
-0.008968105539679527,
0.00007193478086264804,
-0.08499730378389359,
-0.04760872945189476,
0.012669351883232594,
-0.020546024665236473,
-0.016199754551053047,
-0.036877963691949844,
-0.009326041676104069,
-0.012144961394369602,
-0.0383983813226223,
0.007964334450662136,
0.05569428950548172,
-0.045792948454618454,
-0.029637843370437622,
0.042854759842157364,
0.00442171934992075,
0.04687674343585968,
-0.014234366826713085,
-0.042350538074970245,
0.0009466803749091923,
-0.00827254168689251,
0.025415677577257156,
0.004867343232035637,
0.00882208812981844,
-0.0197762344032526,
-0.015361730009317398,
-0.016639938578009605,
0.0013921152567490935,
0.028307346627116203,
-0.024242786690592766,
-0.05786243826150894,
-0.003810629015788436,
-0.0009223029483109713,
-0.010433340445160866,
-0.03577983006834984,
-0.00786880124360323,
-0.034931231290102005,
0.04598657414317131,
0.03320110961794853,
0.002763408701866865,
-0.011960464529693127,
-0.06173918396234512,
0.0009675772744230926,
-0.007403824012726545,
0.0015383462887257338,
0.015208867378532887,
0.04659245163202286,
0.004674150142818689,
-0.007947315461933613,
0.03803964704275131,
-0.04493607580661774,
0.03852993994951248,
-0.0093307513743639,
0.007250935770571232,
0.018751734867691994,
-0.006414402276277542,
-0.03796114772558212,
-0.028343984857201576,
-0.04209224879741669,
0.009037166833877563,
0.031071234494447708,
-0.04613699018955231,
0.04104098677635193,
0.030617717653512955,
0.007972989231348038,
-0.002041260711848736,
0.001880365191027522,
0.008949285373091698,
0.01616564951837063,
-0.001348688150756061,
0.0451861172914505,
-0.0285940058529377,
-0.012541365809738636,
0.07197210937738419,
0.06802348792552948,
-0.02294914238154888,
0.021569613367319107,
0.011155033484101295,
0.005730140022933483,
-0.012120641767978668,
-0.0023902705870568752,
-0.029220126569271088,
0.037604618817567825,
-0.020095866173505783,
0.010088047944009304,
0.0190103892236948,
-0.0177253857254982,
0.027665061876177788,
-0.007776498328894377,
0.03540502116084099,
-0.04260750859975815,
-0.03504708409309387,
-0.014496798627078533,
0.005720870103687048,
0.013660052791237831,
-0.007707604672759771,
0.012899602763354778,
-0.012473883107304573,
-0.0043754721991717815,
0.012649737298488617,
0.022742241621017456,
0.00031179646612145007,
-0.026264306157827377,
0.023267565295100212,
-0.04734417423605919,
-0.06625529378652573,
-0.010382422246038914,
-0.003919582813978195,
-0.04729529097676277,
-0.02465140074491501,
0.004278825595974922,
0.004339226987212896,
0.022486994042992592,
0.05094439908862114,
0.014948779717087746,
0.09786128252744675,
-0.00044883470400236547,
0.028646335005760193,
0.0059691681526601315,
0.01988564059138298,
0.12010874599218369,
0.049853190779685974,
0.0210347268730402,
-0.07360703498125076,
0.011523297987878323,
0.01762252487242222,
-0.022271692752838135,
0.003853824455291033,
0.002696405630558729,
-0.0006376648670993745,
0.006796804256737232,
-0.0021525428164750338,
0.023764770478010178,
-0.019550269469618797,
0.021569538861513138,
0.05162930488586426,
-0.08245152980089188,
-0.03597378730773926,
-0.004681631922721863,
0.005348133854568005,
0.009670523926615715,
0.005933469161391258,
-0.029354779049754143,
-0.027382617816329002,
-0.0009940997697412968,
-0.008651955984532833,
-0.017529452219605446,
-0.03633279725909233,
0.04773577302694321,
0.02567223086953163,
-0.011759424582123756,
-0.008945872075855732,
-0.01858207955956459,
-0.02175702154636383,
-0.012859798036515713,
-0.003640132723376155,
0.007237104699015617,
-0.022976219654083252,
0.024627551436424255,
0.0366063229739666,
0.03816751018166542,
-0.004814515821635723,
-0.01087024062871933,
0.024602917954325676,
-0.03008461184799671,
0.00004531442391453311,
0.01101653277873993,
0.009013650007545948,
-0.05525953322649002,
-0.0016623387346044183,
-0.0018260516226291656,
-0.01414706464856863,
0.029728619381785393,
-0.027585597708821297,
-0.022329792380332947,
0.010309217497706413,
0.007594730705022812,
0.010569058358669281,
-0.05654263496398926,
-0.031884368509054184,
0.013695384375751019,
-0.036745429039001465,
0.0009696712950244546,
0.01216164231300354,
-0.04378906637430191,
0.03247590363025665,
-0.0007220289553515613,
-0.001113547128625214,
-0.004890982061624527,
-0.01546346116811037,
-0.07506342977285385,
-0.009965790435671806,
-0.02721712738275528,
-0.04031120240688324,
0.03790142759680748,
0.0010412365663796663,
0.06554578989744186,
-0.009854847565293312,
0.0037295252550393343,
-0.008396629244089127,
-0.048166800290346146,
0.02359098568558693,
-0.012473543174564838,
-0.03867450729012489,
-0.03578966483473778,
-0.0004883268848061562,
0.017368409782648087,
0.04227495566010475,
-0.020078321918845177,
0.027868002653121948,
0.023881662636995316,
0.014018107205629349,
-0.010700962506234646,
-0.01877465657889843,
-0.004158700816333294,
0.004445771686732769,
-0.025362912565469742,
-0.005358932074159384,
0.005690844729542732,
0.042301762849092484,
0.04071743041276932,
-0.0028831001836806536,
0.0012243679957464337,
0.05171448364853859,
-0.026410406455397606,
0.021310457959771156,
-0.002384133404120803,
-0.008516022004187107,
0.0022973285522311926,
0.011894305236637592,
0.011353462003171444,
-0.052401795983314514,
-0.008613805286586285,
-0.017901144921779633,
-0.006597474217414856,
0.01681196317076683,
0.017242200672626495,
-0.022150656208395958,
0.027594441547989845,
0.001163196167908609,
0.0080996323376894,
-0.03176581859588623,
-0.01760249026119709,
-0.015700168907642365,
0.020877668634057045,
0.026444416493177414,
0.007755551487207413,
-0.03613172098994255,
0.02555994503200054,
0.00670065451413393,
-0.06302458047866821,
0.013033166527748108,
0.05212622135877609,
-0.008618605323135853,
0.012724068947136402,
-0.0046277521178126335,
-0.02798490785062313,
0.05548303574323654,
-0.010601412504911423,
-0.018041986972093582,
-0.00627675699070096,
-0.04144459590315819,
-0.041374169290065765,
0.011274025775492191,
-0.04182036966085434,
-0.015436938963830471,
0.030670825392007828,
0.00400090916082263,
-0.013954801484942436,
0.026158377528190613,
-0.004604507237672806,
-0.0005741565837524831,
-0.001222669263370335,
0.009121570736169815,
-0.02828977443277836,
-0.026613282039761543,
-0.03208070993423462,
0.004673905670642853,
-0.008990975096821785,
0.018787123262882233,
0.07482226192951202,
-0.009478628635406494,
0.0024304958060383797,
0.006787335965782404,
-0.020606109872460365,
0.005293678492307663,
0.019319305196404457,
-0.008881743997335434,
0.003615885740146041,
0.03756796568632126,
-0.00810963474214077,
0.060440219938755035,
0.0006744026904925704,
-0.002154956804588437,
-0.062212128192186356,
-0.0024431408382952213,
0.028872130438685417,
-0.017474574968218803,
0.0037591438740491867,
-0.009235220961272717,
0.019167950376868248,
0.03394593670964241,
-0.03871163725852966,
0.0012904693139716983,
-0.01577749475836754,
0.0018685676623135805,
-0.05018218979239464,
-0.022822843864560127,
-0.03325630724430084,
0.040644194930791855,
-0.015065302141010761,
0.07844426482915878,
0.04268386960029602,
0.027711309492588043,
-0.02951606921851635,
-0.0876493901014328,
-0.015193544328212738,
0.0056731547228991985,
-0.024043910205364227,
-0.017087547108530998,
0.07487901300191879,
0.007573762908577919,
-0.03388284891843796,
0.04268081486225128,
-0.012089962139725685,
-0.005632488522678614,
0.004532454535365105,
0.03238407522439957,
-0.017006395384669304,
0.04554636776447296,
0.0023516600485891104,
0.004614363890141249,
0.014825355261564255,
0.03418150916695595,
0.021200530230998993,
0.027819517999887466,
0.029971102252602577,
0.01134856604039669,
0.017346259206533432,
-0.00877058133482933,
-0.059656281024217606,
0.04158585146069527,
0.049041748046875,
-0.0004843318893108517,
0.009808545932173729,
-0.005723231937736273,
0.023643111810088158,
-0.01645801030099392,
0.006537961307913065,
-0.0078032310120761395,
-0.018705250695347786,
0.014932338148355484,
0.0055071162059903145,
-0.01009791623800993,
0.010622655041515827,
-0.03935050964355469,
-0.037020038813352585,
0.024709222838282585,
0.00031813004170544446,
-0.034040845930576324,
-0.057680971920490265,
-0.00726547185331583,
0.008726440370082855,
-0.008971530944108963,
-0.026153968647122383,
-0.03216118738055229,
-0.038108132779598236,
0.030794134363532066,
0.0018608653917908669,
-0.01969097927212715,
-0.006390701048076153,
-0.08297112584114075,
-0.005772352684289217,
-0.049762651324272156,
0.06577543169260025,
-0.0385943204164505,
0.04233870282769203,
-0.028285643085837364,
-0.0010420369217172265,
0.022964725270867348,
0.012959630228579044,
0.05077367648482323,
-0.0014111242489889264,
-0.031910527497529984,
-0.010404704138636589,
0.011890452355146408,
0.02182452194392681,
-0.03585480898618698,
0.017383024096488953,
0.020758377388119698,
-0.011015164665877819,
-0.011926814913749695,
-0.013449474237859249,
-0.040202267467975616,
0.032844893634319305,
0.037857092916965485,
0.0032683920580893755,
-0.016101328656077385,
-0.002687017433345318,
-0.037361085414886475,
0.04941445589065552,
0.022900225594639778,
-0.007682702969759703,
0.07044205814599991,
-0.035145994275808334,
0.029358450323343277,
0.023570897057652473,
-0.026939865201711655,
-0.06306397169828415,
0.02899906598031521,
-0.024738557636737823,
0.005977969616651535,
-0.010288327001035213,
-1.3186765457362526e-8,
0.035559359937906265,
-0.027534019201993942,
-0.014495997689664364,
0.01097883377224207,
-0.011888392269611359,
-0.032700832933187485,
0.0318184457719326,
0.03832479566335678,
0.09023240208625793,
-0.023210637271404266,
-0.00931762158870697,
-0.012184813618659973,
0.0004816419677808881,
-0.014430558308959007,
0.03990130126476288,
0.03340889513492584,
-0.03195856139063835,
0.042897626757621765,
0.017002206295728683,
0.008346613496541977,
0.0008179478463716805,
0.017808828502893448,
0.021289749071002007,
-0.01430325023829937,
-0.012011207640171051,
0.020305488258600235,
-0.004039374180138111,
0.03164609894156456,
0.03473740443587303,
-0.011440199799835682,
0.0988648310303688,
-0.015057387761771679,
0.024069299921393394,
0.006012825295329094,
0.03396876901388168,
-0.016641026362776756,
-0.0340917743742466,
0.0038611884228885174,
0.05270245298743248,
-0.03653442859649658,
-0.007701171096414328,
0.0014851975720375776,
0.02231465093791485,
0.028045007959008217,
-0.019425388425588608,
0.05819467082619667,
-0.008626247756183147,
-0.013454264961183071,
-0.009487170726060867,
-0.003488113870844245,
-0.046859972178936005,
-0.014894049614667892,
0.030020911246538162,
0.030489156022667885,
-0.003266141517087817,
0.021611325442790985,
0.005155311897397041,
-0.02886970341205597,
0.05288659781217575,
-0.06472959369421005,
-0.00315332249738276,
-0.049767374992370605,
0.015970895066857338,
-0.05535471439361572,
-0.019409330561757088
] |
<p>To put it bluntly, weather is described by the Navier-Stokes equation, which in turn exhibits turbulence, so eventually predictions will become unreliable.</p>
<p>I am interested in a derivation of the time-scale where weather predictions become unreliable. Let us call this the critical time-scale for weather on Earth.</p>
<p>We could estimate this time-scale if we knew some critical length and velocity scales. Since weather basically lives on an $S^2$ with radius of the Earth we seem to have a natural candidate for the critical length scale.</p>
<p>So I assume that the relevant length scale is the radius of the Earth (about 6400km) and the relevant velocity scale some typical speed of wind (say, 25m/s, but frankly, I am taking this number out of, well, thin air). Then I get a typical time-scale of $2.6\cdot 10^5$s, which is roughly three days.</p>
<p>The result three days seems not completely unreasonable, but I would like to see an actual derivation.</p>
<p>Does anyone know how to obtain a more accurate and reliable estimate of the critical time-scale for weather on Earth?</p>
| 9,439 |
[
-0.03675752133131027,
-0.01757446862757206,
-0.008901146240532398,
-0.0157918781042099,
0.05628565698862076,
-0.009703769348561764,
-0.02379085123538971,
-0.02309350110590458,
0.024087194353342056,
-0.03535063937306404,
0.03060491383075714,
0.059357255697250366,
0.02590484730899334,
0.02451767586171627,
-0.00719209760427475,
0.017932206392288208,
-0.022428104653954506,
-0.0010856847511604428,
0.0003347806341480464,
-0.028020018711686134,
0.006226879544556141,
0.025585485622286797,
0.0014034612104296684,
0.002233413513749838,
-0.038610655814409256,
-0.013188107870519161,
0.014135069213807583,
0.014658543281257153,
0.023293225094676018,
0.031028587371110916,
-0.01323156338185072,
0.004894983489066362,
0.028558501973748207,
0.03991835564374924,
0.04920772463083267,
0.040403250604867935,
-0.03405630961060524,
-0.02178313210606575,
-0.03420701622962952,
-0.002707730745896697,
-0.039955984801054,
0.008088452741503716,
-0.0006927056820131838,
0.0013440623879432678,
-0.035181138664484024,
0.008451568894088268,
0.010654482990503311,
-0.027850890532135963,
0.051560595631599426,
-0.061411064118146896,
0.06495383381843567,
-0.004278890788555145,
0.025590060278773308,
0.012695366516709328,
-0.017184263095259666,
-0.03663521632552147,
0.0820227637887001,
0.055922817438840866,
0.01854535937309265,
-0.023366764187812805,
-0.010354830883443356,
-0.003331131301820278,
0.00211266428232193,
-0.02256842330098152,
-0.011031784117221832,
0.05170750990509987,
-0.02194581739604473,
-0.0068403324112296104,
0.00885247252881527,
-0.012342450208961964,
-0.006497211288660765,
-0.016200846061110497,
0.03191186115145683,
0.04567784070968628,
0.025981774553656578,
-0.007800174877047539,
0.01123983133584261,
0.004571226425468922,
0.026975417509675026,
0.05280962958931923,
-0.00946721713989973,
0.036253973841667175,
-0.000926402339246124,
-0.003336799331009388,
0.002960170852020383,
-0.00810769572854042,
0.07668616622686386,
-0.025498006492853165,
-0.0011284071952104568,
0.046754542738199234,
-0.027449600398540497,
-0.001972791738808155,
0.012233122251927853,
-0.016063956543803215,
-0.0059553347527980804,
0.038432322442531586,
0.01586838997900486,
0.008434750139713287,
0.006949020083993673,
0.0000795906744315289,
-0.00987053383141756,
-0.05385126918554306,
0.010501304641366005,
0.060619231313467026,
0.023738708347082138,
-0.028380196541547775,
-0.055827151983976364,
-0.02917906828224659,
-0.0434613898396492,
-0.05112550035119057,
0.01063599158078432,
0.0066928560845553875,
-0.010220236144959927,
0.0014504528371617198,
-0.027828723192214966,
-0.004092470742762089,
0.029523320496082306,
-0.05019822716712952,
0.04308348521590233,
0.018413618206977844,
0.03194337338209152,
0.01063711941242218,
0.0008861224632710218,
-0.032584886997938156,
-0.05480652302503586,
0.044478196650743484,
0.027885518968105316,
-0.03437769412994385,
-0.009233620949089527,
0.010212783701717854,
-0.007622437085956335,
-0.013658835552632809,
-0.007031636778265238,
-0.04083972051739693,
0.012396221980452538,
-0.024533214047551155,
-0.13033679127693176,
-0.03875299170613289,
0.028690721839666367,
0.010625050403177738,
0.004912700038403273,
-0.05305555835366249,
0.009977733716368675,
0.013482638634741306,
0.05487144738435745,
-0.017609471455216408,
0.03751286491751671,
-0.010442239232361317,
0.051478154957294464,
-0.025207433849573135,
-0.05467234179377556,
0.005410052835941315,
0.006548080127686262,
-0.02769356593489647,
-0.010612329468131065,
-0.044627126306295395,
0.04377901926636696,
0.06506270170211792,
0.03857904300093651,
-0.009402663446962833,
0.019332103431224823,
-0.008694003336131573,
-0.008554463274776936,
0.0014381686924025416,
0.0235060453414917,
-0.031609825789928436,
0.06491394340991974,
0.03457292169332504,
0.029036512598395348,
0.03769192844629288,
0.019595259800553322,
0.002330624032765627,
0.02102435566484928,
0.017773088067770004,
0.101578488945961,
0.010254151187837124,
0.03194553032517433,
-0.0018344561103731394,
-0.02020847797393799,
0.005499182268977165,
-0.02533242478966713,
0.006173055153340101,
-0.011251512914896011,
0.00007686082972213626,
0.007980706170201302,
0.049239397048950195,
-0.039321932941675186,
-0.0015953551046550274,
-0.0004406892985571176,
-0.08188287913799286,
-0.016123471781611443,
-0.06339962780475616,
0.012547845020890236,
-0.00847358163446188,
-0.0020827646367251873,
0.029080849140882492,
-0.029141882434487343,
0.03953853249549866,
0.011771849356591702,
-0.04030328616499901,
-0.014187575317919254,
0.051331423223018646,
0.045965950936079025,
-0.01297261193394661,
0.02742108702659607,
0.0626683309674263,
0.029991986230015755,
0.006803619209676981,
0.03213486820459366,
0.0074284872971475124,
-0.06256748735904694,
-0.019190337508916855,
-0.0364253930747509,
0.03661361336708069,
-0.02349027246236801,
-0.03246726095676422,
0.048143625259399414,
-0.01443086750805378,
0.018561745062470436,
-0.023764261975884438,
-0.023983322083950043,
0.043396513909101486,
0.03822169452905655,
0.014548968523740768,
0.021304402500391006,
0.039469361305236816,
0.03142445161938667,
-0.03736327588558197,
-0.028646815568208694,
-0.026247287169098854,
-0.04295805096626282,
-0.018215108662843704,
0.0507412850856781,
0.061080317944288254,
-0.0007779097650200129,
0.00400335481390357,
0.047402944415807724,
0.037294626235961914,
0.04635963216423988,
0.02320125885307789,
0.017195802181959152,
-0.00013144097465556115,
0.003329414175823331,
-0.010081976652145386,
0.04440409317612648,
-0.009792675264179707,
0.020216962322592735,
0.0236208513379097,
-0.00004383640771266073,
-0.05196278542280197,
-0.031833309680223465,
0.007340722717344761,
-0.019460393115878105,
-0.0127149298787117,
-0.023142805323004723,
-0.016089223325252533,
0.05480150133371353,
-0.02132192999124527,
-0.016726886853575706,
0.024659622460603714,
0.0009446877520531416,
0.04990909621119499,
-0.02989177405834198,
-0.04053005203604698,
0.06438960134983063,
0.00938597321510315,
-0.002424560021609068,
-0.03232170268893242,
0.025006037205457687,
-0.024030586704611778,
-0.0163437370210886,
0.0012694646138697863,
-0.016320783644914627,
-0.014735400676727295,
0.0018276858609169722,
0.014453492127358913,
0.023707300424575806,
-0.0040182811208069324,
0.03557564318180084,
-0.051757391542196274,
0.0398942232131958,
-0.005189906340092421,
-0.008665453642606735,
0.01113368384540081,
-0.016287364065647125,
0.004776738118380308,
0.017048990353941917,
-0.036118969321250916,
0.06247018277645111,
-0.030208604410290718,
0.00243399734608829,
-0.016067801043391228,
-0.008308978751301765,
-0.05108625814318657,
0.012990853749215603,
-0.042936790734529495,
0.0001382845512125641,
-0.018735850229859352,
-0.02414335496723652,
0.07506735622882843,
-0.029677987098693848,
-0.04631509631872177,
0.04625895991921425,
-0.0285548847168684,
-0.045099660754203796,
-0.02144950069487095,
0.03100450150668621,
0.004008603282272816,
-0.06332357972860336,
0.01940082386136055,
0.007864649407565594,
-0.027578916400671005,
-0.016047783195972443,
-0.02305511385202408,
-0.07757336646318436,
0.0006465539336204529,
-0.013001995161175728,
0.08181831240653992,
-0.024846481159329414,
-0.046247128397226334,
0.07058346271514893,
0.019276762381196022,
0.0052348049357533455,
0.01148089300841093,
0.021615780889987946,
-0.012935592792928219,
-0.021678166463971138,
-0.012960678897798061,
0.02012394182384014,
0.01058132853358984,
0.006363261956721544,
0.015352966263890266,
0.02650212123990059,
0.018021129071712494,
-0.008873124606907368,
-0.006335049401968718,
0.010164984501898289,
-0.01176665909588337,
0.01976105570793152,
0.028136830776929855,
0.015956616029143333,
-0.024762822315096855,
-0.000031957195460563526,
-0.02573428861796856,
0.040018480271101,
0.013272558338940144,
-0.08997789025306702,
0.02937966398894787,
-0.02318396419286728,
-0.0036920804996043444,
-0.03681528940796852,
-0.004787375684827566,
-0.03761807829141617,
-0.01971861720085144,
-0.007660823408514261,
0.009783496148884296,
0.03168943151831627,
0.037976957857608795,
-0.0027552505489438772,
0.04815293103456497,
0.10492653399705887,
0.00798497349023819,
-0.05393466353416443,
-0.019550833851099014,
-0.00006481439777417108,
0.04182497039437294,
-0.0009378187824040651,
0.006710787303745747,
0.04321640357375145,
0.007294698152691126,
-0.00007331909000640735,
-0.01714872010052204,
-0.02724331058561802,
0.023273492231965065,
-0.05161033570766449,
-0.0009914906695485115,
-0.055763524025678635,
0.035520289093256,
-0.004167351871728897,
0.025700975209474564,
0.013137942180037498,
0.0020521748811006546,
0.020893413573503494,
0.03179047256708145,
-0.08481597900390625,
0.027677088975906372,
-0.02248866856098175,
-0.039218563586473465,
-0.027831047773361206,
0.025548351928591728,
0.004934415686875582,
-0.015639018267393112,
0.01574360392987728,
-0.016576863825321198,
0.02055460214614868,
-0.04622577503323555,
-0.007882315665483475,
-0.012242838740348816,
-0.05160706117749214,
-0.03467267006635666,
0.018990298733115196,
0.05759764090180397,
-0.018757455050945282,
0.02480166032910347,
0.03842276334762573,
-0.0012723046820610762,
-0.05010738968849182,
-0.026689454913139343,
-0.003025239799171686,
0.0018114210106432438,
0.010296391323208809,
0.010457771830260754,
-0.009136125445365906,
-0.03789251670241356,
0.031062858179211617,
-0.005185267422348261,
-0.0012197982287034392,
-0.0019647786393761635,
0.03769303485751152,
-0.030708298087120056,
-0.032887984067201614,
0.0028511614073067904,
0.06955479830503464,
-0.003599924733862281,
0.004904703702777624,
0.0020915695931762457,
0.017367323860526085,
-0.011421144008636475,
-0.02376025915145874,
0.055080048739910126,
0.009875071235001087,
-0.03654605150222778,
0.0006812933715991676,
-0.04659987613558769,
-0.011441629379987717,
-0.03702745959162712,
-0.0066413902677595615,
0.007583583705127239,
0.03513025864958763,
0.021108713001012802,
-0.027279464527964592,
0.0384952612221241,
-0.036320559680461884,
-0.0031019840389490128,
0.029158757999539375,
0.03713837265968323,
0.032277315855026245,
0.01019446924328804,
0.014436522498726845,
0.0055932821705937386,
0.04461098834872246,
0.023928988724946976,
0.04850821569561958,
0.013313950970768929,
-0.05502839386463165,
-0.010828719474375248,
0.02880696766078472,
0.013932927511632442,
-0.020833933725953102,
-0.01363434735685587,
-0.06535735726356506,
-0.02525719627737999,
0.03522457182407379,
-0.01093137077987194,
0.04390207678079605,
0.006026489194482565,
-0.012646895833313465,
0.004834469873458147,
-0.04366372153162956,
-0.022436724975705147,
0.007012331858277321,
0.012719761580228806,
0.03649785369634628,
-0.009210523217916489,
-0.005101462826132774,
-0.0218962412327528,
0.028174936771392822,
0.02890438586473465,
0.033291611820459366,
0.03028496913611889,
-0.0016979383071884513,
-0.03685718774795532,
-0.05776764452457428,
-0.021506141871213913,
-0.06977172940969467,
-0.019478756934404373,
0.016652526333928108,
-0.018942540511488914,
0.02535466104745865,
-0.03993932157754898,
-0.0560690201818943,
0.03422830253839493,
0.024198101833462715,
0.003529217327013612,
-0.0005616790149360895,
-0.054082684218883514,
0.04724457114934921,
0.006889029871672392,
0.015122298151254654,
0.018079912289977074,
0.028804320842027664,
0.0007491885335184634,
-0.012108063325285912,
0.011497328989207745,
0.026776358485221863,
-0.020431749522686005,
0.010310009121894836,
-0.005266634281724691,
-0.019428418949246407,
-0.033804476261138916,
0.061828579753637314,
-0.016452966257929802,
0.022219261154532433,
-0.01658737100660801,
-0.03663221746683121,
-0.023225829005241394,
-0.01399337686598301,
0.01633010245859623,
-0.027090957388281822,
-0.008937934413552284,
0.031702253967523575,
0.0369834378361702,
-0.004990152083337307,
0.005311055574566126,
0.008143585175275803,
0.04052469879388809,
0.026613421738147736,
-0.024245677515864372,
-0.03992179036140442,
-0.026003096252679825,
-0.0024076607078313828,
0.006976304575800896,
-0.04396963119506836,
0.06516984105110168,
-0.03779245913028717,
-0.019740216434001923,
0.02747090719640255,
-0.026934074237942696,
0.00036160630406811833,
0.02738243341445923,
0.013798350468277931,
0.057766251266002655,
-0.04104810580611229,
-0.0494510792195797,
0.0283840149641037,
0.009094464592635632,
-0.062231600284576416,
-0.01011023111641407,
0.0493292361497879,
0.02921314537525177,
-0.031155133619904518,
-0.0373845212161541,
-0.000898779951967299,
-0.02790975384414196,
-0.04696004465222359,
-0.021704036742448807,
0.056717388331890106,
-0.010765713639557362,
-0.03536819666624069,
-0.03880345821380615,
0.05197977274656296,
0.05882197991013527,
-0.04595417156815529,
0.024101559072732925,
0.03491007536649704,
-0.029662635177373886,
-0.022372668609023094,
-0.030157065019011497,
0.08155592530965805,
-0.024036534130573273,
-0.007600767537951469,
-0.005703314207494259,
-0.035834863781929016,
0.01273171417415142,
-0.01457201223820448,
-0.00632070004940033,
0.02067330665886402,
0.008754221722483635,
-0.0012852008221670985,
0.01347530446946621,
0.020916571840643883,
0.028597233816981316,
0.021327681839466095,
-0.040144745260477066,
-0.025692157447338104,
-0.007120136171579361,
-0.0004173866182100028,
0.01824878342449665,
0.010604835115373135,
-0.005048627499490976,
0.011927819810807705,
0.029129810631275177,
0.025853967294096947,
-0.03339267522096634,
0.014785056002438068,
-0.029745720326900482,
0.024774007499217987,
0.04941169172525406,
-0.002367181470617652,
0.0483892448246479,
0.018740182742476463,
-0.025382457301020622,
-0.04702156409621239,
-0.038447655737400055,
0.002296924591064453,
0.06836824119091034,
-0.046466752886772156,
0.015744369477033615,
0.0009329608292318881,
0.016210075467824936,
-0.010253142565488815,
-0.03531405329704285,
0.0005460022948682308,
0.0010972961317747831,
0.03022712469100952,
0.05867438763380051,
-0.015427201054990292,
0.010543129406869411,
0.002229887992143631,
0.024119844660162926,
0.02119283750653267,
0.014394029043614864,
0.010190581902861595,
-0.008419801481068134,
0.013533004559576511,
-0.05261695757508278,
-0.05722840502858162,
0.04809991642832756,
-0.029760735109448433,
0.024607626721262932,
0.053176987916231155,
0.026432041078805923,
0.021937167271971703,
0.023978132754564285,
-0.024888131767511368,
-0.033920202404260635,
-0.02873634360730648,
-0.05187472328543663,
-0.013251060619950294,
-0.0005181593587622046,
-0.018102146685123444,
0.028834043070673943,
0.006304977927356958,
0.02481285110116005,
0.0022429993841797113,
0.006830431055277586,
0.0029160163830965757,
-0.027559863403439522,
0.01267936173826456,
-0.03536035865545273,
-0.04786718636751175,
0.05772240832448006,
0.030290959402918816,
-0.03344045579433441,
-0.0024332294706255198,
-0.013997909612953663,
0.03190091624855995,
0.0034079302567988634,
0.00793438870459795,
-0.020911909639835358,
0.06901253014802933,
0.02451140619814396,
-0.02754087559878826,
-0.027917565777897835,
0.030101127922534943,
0.112381212413311,
0.0416317842900753,
0.016397006809711456,
-0.0409843884408474,
0.060717348009347916,
-0.026455853134393692,
0.005377078428864479,
-0.0661286860704422,
0.006795788649469614,
-0.008022045716643333,
-0.009325303137302399,
0.029663944616913795,
0.04362686723470688,
0.010452168062329292,
-0.0203565564006567,
0.05508868023753166,
-0.052416808903217316,
-0.002913205185905099,
-0.01655353046953678,
0.005545186344534159,
0.005237733945250511,
-0.012584835290908813,
-0.018710395321249962,
0.05561389401555061,
-0.03910026699304581,
0.0029920507222414017,
-0.006628183647990227,
0.006835270207375288,
0.011610276997089386,
-0.021610721945762634,
-0.04861858859658241,
0.012983765453100204,
0.020772477611899376,
-0.024864336475729942,
-0.009134514257311821,
-0.004516441375017166,
0.00302474619820714,
-0.012164980173110962,
0.04753120616078377,
0.043357331305742264,
-0.002548736985772848,
0.025187965482473373,
0.01572110876441002,
0.03854808956384659,
-0.031071754172444344,
-0.04835150018334389,
-0.04522593691945076,
0.023482898250222206,
0.0017793026054278016,
0.0052400738932192326,
0.0020664269104599953,
-0.01530908141285181,
0.007989072240889072,
-0.020507123321294785,
0.015650462359189987,
-0.015295165590941906,
0.047651395201683044,
-0.04564095288515091,
-0.03026231750845909,
-0.008678339421749115,
0.02098225988447666,
0.015119313262403011,
0.0107802115380764,
0.05026257410645485,
-0.0063543859869241714,
-0.028998075053095818,
0.018473248928785324,
0.049175042659044266,
-0.000588520138990134,
-0.011621791869401932,
-0.02878698520362377,
-0.027501920238137245,
-0.02449708804488182,
0.007242053281515837,
0.031264085322618484,
0.007739234250038862,
0.04840603843331337,
0.0057190158404409885,
-0.01855158992111683,
-0.04705321416258812,
-0.04349903389811516,
0.0326056107878685,
-0.005260168574750423,
-0.019806690514087677,
-0.03528217598795891,
-0.0065166843123734,
-0.013708597980439663,
0.028384950011968613,
0.00722393998876214,
0.0016323933377861977,
-0.0218255165964365,
0.050966162234544754,
0.030431659892201424,
-0.027029061689972878,
0.017792144790291786,
0.010525661520659924,
-0.015465415082871914,
0.02062426321208477,
0.032706085592508316,
0.04698628932237625,
0.027441566810011864,
-0.004882401786744595,
0.013472792692482471,
0.045095864683389664,
-0.014919031411409378,
-0.01270813774317503,
0.05443247780203819,
-0.03311777487397194,
0.012803416699171066,
0.005579158663749695,
-0.02301800064742565,
-0.009066778235137463,
-0.035567186772823334,
-0.039130788296461105,
-0.006335841957479715,
0.008137867785990238,
-0.017670029774308205,
-0.032045427709817886,
0.027891047298908234,
0.01115800254046917,
0.0033325047697871923,
-0.04291389882564545,
0.0004174749774392694,
-0.033553533256053925,
0.025573736056685448,
-0.03440750017762184,
-0.037739671766757965,
0.008316612802445889,
0.0397021658718586,
-0.04970068857073784,
-0.01732896827161312,
0.03136635944247246,
-0.005523602943867445,
0.011655344627797604,
-0.030544530600309372,
-0.035228431224823,
0.007856846787035465,
0.055641014128923416,
-0.03126782178878784,
-0.0599493645131588,
0.04041345790028572,
-0.04163806885480881,
-0.06141594052314758,
0.07159699499607086,
-0.005807917099446058,
0.029111875221133232,
0.027829863131046295,
-0.009201444685459137,
-0.012838125228881836,
0.0769236832857132,
0.006476119626313448,
0.01017471682280302,
-0.024876581504940987,
0.013615009374916553,
-0.008435814641416073,
-0.006078762002289295,
0.035803403705358505,
-0.039762742817401886,
0.007375234272330999,
0.010132868774235249,
0.04069619998335838,
-0.019256379455327988,
0.019590673968195915,
0.03176165744662285,
-0.03833749145269394,
0.025489088147878647,
-0.006443963386118412,
0.022163912653923035,
0.019486714154481888,
0.06656380742788315,
-0.040498822927474976,
0.010189223103225231,
-0.007649938575923443,
-0.020819514989852905,
-0.13233546912670135,
0.031106065958738327,
0.021187175065279007,
0.0297478549182415,
0.010250567458570004,
-0.059849295765161514,
0.003010307904332876,
0.00920838862657547,
-0.03973491117358208,
-0.012551506981253624,
-0.049610432237386703,
0.01071368157863617,
-0.03563399612903595,
-0.02080274373292923,
-0.030718104913830757,
0.0323600247502327,
0.038567185401916504,
0.006033188663423061,
0.012872938998043537,
0.04724777117371559,
-0.03614998236298561,
-0.028531299903988838,
0.016485439613461494,
0.02700847201049328,
0.003912705462425947,
-0.03312884271144867,
0.03465690836310387,
-0.021277690306305885,
0.003074318403378129,
0.0416148379445076,
-0.04093525558710098,
0.034578293561935425,
-0.0379934124648571,
0.013829422183334827,
-0.003720428328961134,
0.011968819424510002,
0.027071792632341385,
-0.017517808824777603,
0.042076706886291504,
0.028523556888103485,
-0.004209224600344896,
0.025137653574347496,
-0.022572070360183716,
-0.024512499570846558,
0.002754309680312872,
-0.0307550560683012,
-0.05315903201699257,
0.04123106226325035,
-0.008005877956748009,
0.008938096463680267,
0.027635138481855392,
0.007563407067209482,
0.014202013611793518,
-0.009621856734156609,
0.01926623284816742,
-0.033654846251010895,
-0.02692251279950142,
0.026303043588995934,
0.025094565004110336,
-0.052388206124305725,
0.019708938896656036,
-0.046875983476638794,
-0.03771277517080307,
0.029619378969073296,
-0.02581772394478321,
-0.006161882542073727,
-0.03997952863574028,
-0.028476646170020103,
-0.002319084480404854,
0.002454666420817375,
-0.02392193116247654,
0.005660325288772583,
-0.01572805643081665,
0.038656387478113174,
0.002701675286516547,
0.038810838013887405,
-0.00871600303798914,
-0.04141901433467865,
-0.009499148465692997,
-0.07113511860370636,
0.027411382645368576,
0.005580649245530367,
0.03280951455235481,
-0.05078183487057686,
-0.04598337411880493,
0.0012001523282378912,
0.004546497482806444,
0.0571468211710453,
-0.009659474715590477,
0.0017774697626009583,
0.015089336782693863,
0.02880684845149517,
0.0033052617218345404,
-0.07222314178943634,
-0.03168194368481636,
-0.02004464901983738,
-0.00655027199536562,
-0.02339990809559822,
-0.0531732551753521,
0.023546239361166954,
-0.019235270097851753,
0.018022945150732994,
0.03605595976114273,
0.02198193222284317,
0.031877610832452774,
-0.02175098843872547,
0.03300165385007858,
0.018627455458045006,
-0.01672547310590744,
0.05497626215219498,
-0.010296002961695194,
0.0029228355269879103,
0.006193752866238356,
-0.013420667499303818,
-0.03262670338153839,
0.04417695105075836,
-0.04441296309232712,
-0.005835164338350296,
0.008755872026085854,
-0.028512772172689438,
0.030788414180278778,
-0.04742242023348808,
-0.020373215898871422,
0.01430223137140274,
0.014128074049949646,
0.02011755295097828,
0.018957503139972687,
0.00014365922834258527,
0.027626952156424522,
-0.012606128118932247,
-0.02969590201973915,
0.05503634363412857,
0.006859140004962683,
-0.020223820582032204,
0.012148432433605194,
0.06826042383909225,
-0.011935669928789139,
0.013459322042763233,
0.00727118318900466,
-0.01925426907837391,
0.036542586982250214,
0.023611852899193764,
0.03828053176403046,
-0.019288241863250732,
-0.049685999751091,
0.021881576627492905,
-0.011354341171681881,
-0.010280723683536053,
0.013240458443760872,
-0.002942048478871584,
0.04486139118671417,
0.036036670207977295,
0.0022790117654949427,
-0.015082087367773056,
-0.001594681409187615,
-0.050677042454481125,
0.03137022629380226,
-0.020833710208535194,
0.02586853876709938,
-0.0248037651181221,
0.02697187103331089,
0.01648649014532566,
0.00864616222679615,
0.011366899125277996,
-0.03241559863090515,
0.02747557871043682,
-0.005928565748035908,
0.014851030893623829,
-0.015203366987407207,
-0.023677151650190353,
-0.023596102371811867,
-0.028274523094296455,
0.01962953619658947,
0.004176190122961998,
0.028731530532240868,
0.013176029548048973,
0.017011204734444618,
0.00829838216304779,
0.058833543211221695,
-0.09199833869934082,
-0.0035935493651777506,
-0.035884417593479156,
0.034659627825021744,
-0.010495628230273724,
-0.039419982582330704
] |
<p>I've only learned about to use kinematics equation when solving projectile problems but today i came across the following equations. where does they come from?</p>
<ul>
<li>Distance travelled</li>
<li>Time of flight</li>
<li>Angle of reach</li>
</ul>
| 9,440 |
[
-0.00658009946346283,
-0.03147030249238014,
-0.022951193153858185,
0.001178676844574511,
0.033767685294151306,
0.0038656145334243774,
-0.018462421372532845,
0.014059673063457012,
0.030766524374485016,
-0.02323988452553749,
-0.011513225734233856,
0.036965757608413696,
0.049418315291404724,
0.006447226274758577,
0.05407743901014328,
0.014911714009940624,
-0.009972845204174519,
0.0161427091807127,
0.01592123694717884,
-0.05701163783669472,
0.02114877849817276,
-0.014446842484176159,
0.01890522986650467,
0.0004353766271378845,
0.012410402297973633,
0.04543726518750191,
0.007502677850425243,
0.0013801302993670106,
0.016706928610801697,
0.028020966798067093,
0.0334896557033062,
-0.02382447011768818,
0.01668708026409149,
-0.012163251638412476,
-0.020265523344278336,
-0.013180050998926163,
0.0034015134442597628,
-0.02401665598154068,
-0.025965461507439613,
0.009725009091198444,
-0.052071891725063324,
-0.012817868031561375,
-0.0071074883453547955,
0.04830409958958626,
-0.028646480292081833,
0.03721938282251358,
-0.025318415835499763,
-0.01873420923948288,
0.061488647013902664,
-0.03912508115172386,
0.06734706461429596,
0.005076762288808823,
0.05203790217638016,
-0.0036550313234329224,
0.00352486502379179,
0.0359715037047863,
0.08303852379322052,
0.0352168008685112,
-0.047800492495298386,
-0.054017502814531326,
-0.00819527730345726,
-0.02808224782347679,
0.008408251218497753,
0.0012789705069735646,
-0.010258975438773632,
0.026009809225797653,
-0.00818124320358038,
-0.03517921641469002,
0.005319972988218069,
-0.03862811252474785,
0.0022317057009786367,
0.023753736168146133,
0.04391716420650482,
-0.005079388618469238,
0.013574843294918537,
-0.027248850092291832,
0.007525833323597908,
-0.024881111457943916,
0.039825841784477234,
0.06465376913547516,
-0.024931158870458603,
0.03929759934544563,
0.04092399775981903,
-0.0023535755462944508,
-0.007479912135750055,
-0.023396240547299385,
0.06262484192848206,
0.019087933003902435,
0.022748643532395363,
0.009403815492987633,
0.0012136055156588554,
0.020616114139556885,
0.025093473494052887,
-0.016884030774235725,
0.019176101312041283,
0.040782298892736435,
-0.003588186576962471,
0.06678874045610428,
0.02188771404325962,
-0.02900746650993824,
0.029398398473858833,
-0.04823020100593567,
-0.008206924423575401,
0.07286980748176575,
0.0009303816477768123,
-0.01744934543967247,
-0.030160406604409218,
0.03670283034443855,
-0.04437902942299843,
0.0028727015014737844,
-0.039262719452381134,
0.03593027591705322,
-0.003269374603405595,
0.02256721258163452,
-0.029482387006282806,
-0.021285133436322212,
0.019574852660298347,
-0.01499849557876587,
0.04316220432519913,
0.041616715490818024,
0.04486963897943497,
-0.02294352650642395,
0.028556883335113525,
0.020700844004750252,
-0.04636386036872864,
0.020896565169095993,
0.0267083328217268,
-0.0529249869287014,
-0.008669604547321796,
0.015094446949660778,
-0.01709415391087532,
-0.03572120890021324,
0.012657870538532734,
0.04296279698610306,
-0.005280929617583752,
0.023775732144713402,
-0.09793514758348465,
-0.051945190876722336,
0.017596809193491936,
0.012376612052321434,
-0.03329584002494812,
-0.08311827480792999,
0.04714414104819298,
0.010543801821768284,
0.06965841352939606,
-0.014892651699483395,
0.00016355965635739267,
-0.009550239890813828,
0.00695703225210309,
-0.035142816603183746,
0.009701826609671116,
-0.01704341359436512,
-0.013237321749329567,
-0.023062387481331825,
0.009877650067210197,
-0.07178011536598206,
0.008945921435952187,
0.0036565170157700777,
-0.0038033020682632923,
-0.024996299296617508,
0.07911990582942963,
-0.0060364436358213425,
-0.0440087616443634,
0.008163684979081154,
-0.0034695472568273544,
-0.027219124138355255,
0.07336900383234024,
0.019595332443714142,
-0.019508639350533485,
0.05674009397625923,
0.03142227977514267,
0.049037981778383255,
0.0009024972678162158,
-0.00007777262362651527,
0.02386656031012535,
-0.012052628211677074,
-0.030979234725236893,
-0.001592211308889091,
-0.041259050369262695,
0.013129164464771748,
-0.044247984886169434,
-0.04690025746822357,
0.029830792918801308,
0.004709940403699875,
0.023811865597963333,
0.06338081508874893,
-0.0006184109370224178,
0.01113791111856699,
0.014418194070458412,
-0.0069945091381669044,
0.013001770712435246,
-0.0827140137553215,
0.037354592233896255,
-0.02387799136340618,
0.03004470281302929,
0.03465212136507034,
0.026977721601724625,
0.006770567502826452,
-0.0025785157922655344,
0.008018751628696918,
-0.06312959641218185,
0.030860867351293564,
-0.0013448991812765598,
0.002495949389412999,
0.010923330672085285,
0.06268082559108734,
0.056286443024873734,
0.03394985571503639,
0.02123682200908661,
-0.047363586723804474,
0.01344373170286417,
-0.01778402365744114,
-0.01784035935997963,
0.01717354916036129,
-0.005135825835168362,
-0.026124324649572372,
0.004832996521145105,
-0.004349789582192898,
-0.022111225873231888,
0.01851610466837883,
-0.024820499122142792,
0.07902345061302185,
0.03525774925947189,
0.02419823408126831,
-0.006380219478160143,
0.07596111297607422,
-0.006307059898972511,
0.02736639603972435,
0.011960719712078571,
-0.03756047412753105,
-0.016869790852069855,
-0.05357467755675316,
0.013981182128190994,
-0.0036440042313188314,
-0.03580830246210098,
-0.004712742753326893,
0.026356400921940804,
0.0019560533110052347,
0.01938222534954548,
0.031079215928912163,
-0.010277723893523216,
-0.044589605182409286,
0.0023443554528057575,
0.017812363803386688,
-0.03591082617640495,
-0.008682056330144405,
0.01221289113163948,
0.030035624280571938,
-0.012952595949172974,
0.02764817513525486,
-0.026614172384142876,
0.016400586813688278,
0.017292063683271408,
0.004319828003644943,
0.016945820301771164,
-0.05321861431002617,
0.04911143705248833,
-0.0085342051461339,
0.026302248239517212,
0.03889761492609978,
0.017881369218230247,
-0.003669793251901865,
0.019555529579520226,
0.007490314543247223,
0.03210899606347084,
-0.003834452712908387,
-0.0029132666531950235,
0.0018078044522553682,
0.033948514610528946,
-0.05013725906610489,
0.03003808483481407,
-0.025232337415218353,
-0.062292203307151794,
-0.02964627929031849,
0.0016736260149627924,
-0.007366201840341091,
0.07105372846126556,
0.006831351201981306,
0.011028088629245758,
-0.026950571686029434,
-0.01731867901980877,
-0.022718150168657303,
-0.026365848258137703,
0.013551725074648857,
-0.034015264362096786,
0.0454055480659008,
-0.03533494472503662,
-0.03502284735441208,
0.06393535435199738,
-0.0035660641733556986,
0.013537506572902203,
0.011482005938887596,
-0.03496579825878143,
-0.05204704776406288,
-0.037874843925237656,
0.001199647900648415,
0.023595135658979416,
-0.0042995912954211235,
0.01798425428569317,
0.030501937493681908,
-0.02731325663626194,
-0.003123979549854994,
0.03296307474374771,
-0.07518424093723297,
-0.0461236946284771,
-0.050661955028772354,
0.006616175174713135,
0.02689971588551998,
-0.00305246002972126,
0.017845191061496735,
0.0182243250310421,
-0.052090566605329514,
-0.019255448132753372,
-0.05373309180140495,
-0.03735605627298355,
0.01503273006528616,
0.012058179825544357,
0.03427081182599068,
-0.010822377167642117,
-0.0038604051806032658,
0.09196317195892334,
0.026323352009058,
-0.059533365070819855,
-0.005077420733869076,
-0.009172288700938225,
-0.004180038347840309,
-0.0066216797567903996,
-0.000515004969201982,
0.01831013523042202,
-0.02422114834189415,
0.022596700116991997,
-0.017187481746077538,
0.02002417854964733,
0.05505802109837532,
-0.006002108100801706,
0.030762063339352608,
-0.05107849836349487,
0.0006601610803045332,
-0.043448176234960556,
0.04185308516025543,
0.004871589131653309,
-0.03624330088496208,
0.030740560963749886,
0.008548867888748646,
0.06893032044172287,
0.011231155134737492,
-0.05507568642497063,
0.027773810550570488,
0.0026018458884209394,
-0.025965694338083267,
-0.00618678517639637,
0.03198682516813278,
-0.012039871886372566,
-0.030857427045702934,
-0.0163781326264143,
0.06320331990718842,
0.05021905153989792,
-0.03129751607775688,
0.001256951130926609,
-0.010526200756430626,
0.014956826344132423,
-0.021317994222044945,
-0.012053631246089935,
-0.025007586926221848,
-0.011433618143200874,
0.03678036108613014,
-0.005975472275167704,
-0.01118647400289774,
0.029273133724927902,
-0.01025998592376709,
0.0051417225040495396,
0.011986766010522842,
-0.03153344243764877,
0.014018436893820763,
-0.05170779302716255,
-0.00028875970747321844,
-0.03557344153523445,
0.02045757696032524,
-0.007368044462054968,
0.08478894084692001,
-0.004821922164410353,
0.009224667213857174,
0.03396569937467575,
-0.01636463962495327,
-0.07396436482667923,
0.03963930532336235,
-0.06452476978302002,
-0.06095050275325775,
-0.03304917365312576,
-0.0010054187150672078,
0.0003086065116804093,
-0.03915688395500183,
-0.01815088465809822,
-0.01876954361796379,
-0.029513439163565636,
-0.03703846409916878,
0.013138805516064167,
-0.020895956084132195,
-0.03840482607483864,
0.02039249986410141,
0.012566301971673965,
0.027062872424721718,
-0.033030733466148376,
0.010305180214345455,
0.05370624363422394,
-0.0071195391938090324,
-0.03885572776198387,
-0.04372521862387657,
-0.012706328183412552,
-0.009815053083002567,
0.00778651749715209,
0.016954807564616203,
0.00024140415189322084,
0.0028736344538629055,
0.02157723717391491,
-0.024828143417835236,
0.07646840065717697,
0.006023104302585125,
-0.012366133742034435,
-0.043126460164785385,
-0.06832892447710037,
0.015712205320596695,
0.021772976964712143,
0.044016554951667786,
0.0027866559103131294,
0.01823759451508522,
0.02735479734838009,
0.01776241883635521,
-0.0047882250510156155,
0.03488045930862427,
0.03214811533689499,
0.023880640044808388,
0.005427990574389696,
-0.03895413130521774,
0.021187162026762962,
-0.01284512598067522,
-0.009526802226901054,
0.017093101516366005,
0.0008904181304387748,
0.0019908114336431026,
0.0332721583545208,
0.048903778195381165,
-0.0063401744700968266,
-0.02871006540954113,
0.020679768174886703,
-0.009586804546415806,
-0.005448182579129934,
-0.014183059334754944,
-0.0014850725419819355,
0.012722622603178024,
0.023728670552372932,
0.0396072082221508,
-0.022744614630937576,
0.02566443756222725,
-0.06704267859458923,
-0.0034667043946683407,
0.0261988528072834,
0.008352485485374928,
-0.030818358063697815,
0.0036947419866919518,
-0.03505874425172806,
-0.04148642718791962,
0.043667033314704895,
0.011103366501629353,
0.06139932572841644,
-0.0028131455183029175,
-0.013275036588311195,
-0.003975562751293182,
-0.0073533267714083195,
-0.03426569327712059,
0.016219135373830795,
0.005151052493602037,
-0.0010515530593693256,
-0.03380643203854561,
0.03984759375452995,
0.017889078706502914,
0.0372312031686306,
0.015126284211874008,
0.05883130058646202,
0.02372264489531517,
-0.008969352580606937,
-0.004506498575210571,
-0.01618601754307747,
-0.02537688985466957,
-0.036852285265922546,
-0.011543004773557186,
0.0164636317640543,
0.04077401012182236,
0.011238048784434795,
-0.046469662338495255,
-0.01713777333498001,
0.005586162209510803,
0.007656163536012173,
0.00040136888856068254,
-0.012539763934910297,
-0.05656639114022255,
-0.019002145156264305,
0.05013909935951233,
-0.04590338096022606,
0.036341097205877304,
0.03666945919394493,
-0.018669769167900085,
-0.01459660567343235,
-0.011600903235375881,
0.032384470105171204,
0.027575870975852013,
-0.024682654067873955,
-0.05070038512349129,
0.01630985736846924,
-0.018685856834053993,
0.06213544309139252,
-0.012912226840853691,
0.0073752268217504025,
-0.02731744945049286,
-0.03775613754987717,
-0.04316779598593712,
0.03902088850736618,
0.04977789521217346,
-0.0049631851725280285,
0.009579408913850784,
-0.00586474034935236,
0.011320333927869797,
-0.011672133579850197,
0.030959906056523323,
0.009761592373251915,
0.003521924838423729,
0.014164681546390057,
0.020453231409192085,
0.007866793312132359,
-0.03622177988290787,
-0.029408594593405724,
0.04346226155757904,
-0.05217953398823738,
0.04115249589085579,
-0.007250466849654913,
-0.05194280669093132,
0.04174685850739479,
-0.06422153860330582,
-0.08289561420679092,
0.006704743020236492,
-0.012127605266869068,
0.03602583706378937,
-0.03212839365005493,
0.008794867433607578,
-0.018195779994130135,
0.02615400031208992,
-0.025546323508024216,
-0.028746817260980606,
0.030614247545599937,
-0.010882220230996609,
-0.05133708938956261,
-0.003046893747523427,
-0.01565767265856266,
-0.025753671303391457,
-0.03407353162765503,
0.05310323089361191,
0.06596525758504868,
-0.01879524253308773,
-0.041790690273046494,
0.015172547660768032,
0.0015653690788894892,
0.04815687984228134,
0.043497178703546524,
0.009326823055744171,
0.018062902614474297,
-0.01712167076766491,
0.026832913979887962,
0.014549311250448227,
0.09190661460161209,
-0.0034908466041088104,
0.00791325606405735,
-0.018329497426748276,
-0.013124012388288975,
0.03173806145787239,
-0.06469305604696274,
0.030438560992479324,
-0.019026346504688263,
0.002313246252015233,
-0.029827656224370003,
-0.013769821263849735,
0.04372287541627884,
-0.0017257629660889506,
0.006968616042286158,
-0.00476707611232996,
0.015138556249439716,
-0.028993675485253334,
0.026773452758789062,
0.05130631476640701,
-0.008197907358407974,
0.048949334770441055,
-0.0164166372269392,
0.028521697968244553,
-0.008008213713765144,
0.00878879427909851,
0.03614901751279831,
0.022851916030049324,
0.04124661162495613,
-0.009748438373208046,
-0.013110756874084473,
0.02584206499159336,
0.03678208217024803,
-0.019671889021992683,
-0.0030200143810361624,
-0.042903557419776917,
0.018124055117368698,
0.08355960994958878,
-0.0391232967376709,
0.08945367485284805,
0.006966596469283104,
0.0016440030885860324,
0.02560652233660221,
0.006012678612023592,
-0.029362741857767105,
0.00019957803306169808,
0.01948728784918785,
0.04078129306435585,
-0.03906358778476715,
-0.006352713331580162,
0.0016740931896492839,
0.005449018441140652,
-0.029910864308476448,
-0.03555350750684738,
-0.014955922961235046,
-0.02398770861327648,
-0.017221875488758087,
0.00030853250063955784,
-0.014984732493758202,
0.04088412597775459,
-0.006846156436949968,
0.026592491194605827,
-0.008430657908320427,
-0.012585058808326721,
0.05075567588210106,
0.006866304203867912,
-0.02341965213418007,
-0.06089392304420471,
0.02702919766306877,
-0.025052057579159737,
-0.01915730908513069,
-0.0003039254806935787,
-0.00440253596752882,
-0.01370773185044527,
0.018434705212712288,
0.05420897901058197,
-0.007402411662042141,
0.028316857293248177,
-0.014433327130973339,
-0.020439891144633293,
-0.023884154856204987,
-0.044326119124889374,
-0.027545202523469925,
0.00655059190467,
-0.01897214725613594,
-0.02112543024122715,
-0.011231675744056702,
0.01821887120604515,
0.008966411463916302,
-0.008184338919818401,
-0.007191004231572151,
-0.05756634473800659,
0.07927083224058151,
-0.01229557953774929,
-0.03826021030545235,
-0.014512785710394382,
-0.007428648415952921,
0.1193246990442276,
0.01286303624510765,
-0.02142244763672352,
-0.046332865953445435,
0.02759278379380703,
0.0021202063653618097,
0.0031034976709634066,
-0.01985330507159233,
0.03643381968140602,
0.0105310482904315,
0.016647202894091606,
0.021651212126016617,
0.0029623291920870543,
0.009290642105042934,
0.026171838864684105,
0.04517943784594536,
-0.02850506082177162,
-0.053246233612298965,
-0.00011331489076837897,
-0.017939377576112747,
0.0026905378326773643,
0.01168933603912592,
-0.006843176204711199,
0.04284880310297012,
-0.027748635038733482,
-0.01400845218449831,
-0.005914869252592325,
-0.0576346293091774,
0.006261722184717655,
0.010481969453394413,
-0.02808350697159767,
0.0225111935287714,
0.04606394097208977,
0.000236963591305539,
-0.025458011776208878,
0.03249384090304375,
0.023052038624882698,
-0.026764564216136932,
0.007016594987362623,
0.04012477397918701,
0.030867794528603554,
0.002586019691079855,
-0.00883256271481514,
0.005764128640294075,
-0.04401484131813049,
0.0017656598938629031,
-0.04411103203892708,
0.018628636375069618,
-0.023899126797914505,
0.028154289349913597,
-0.054393600672483444,
0.001881900243461132,
0.006527885794639587,
-0.06596960127353668,
-0.005010240711271763,
0.03664848953485489,
0.006941601168364286,
-0.036620453000068665,
0.014727286994457245,
-0.05902988836169243,
-0.015332558192312717,
0.004371958319097757,
0.01855386421084404,
0.024320928379893303,
0.04585723578929901,
0.016321051865816116,
-0.017468586564064026,
0.044974345713853836,
-0.03981539234519005,
-0.03077097050845623,
-0.028643859550356865,
0.0006831705686636269,
-0.02838090807199478,
-0.014198820106685162,
0.026842856779694557,
0.037449032068252563,
-0.02247864566743374,
0.035357922315597534,
-0.0035501786042004824,
-0.04692111909389496,
-0.08518790453672409,
0.03386930003762245,
-0.021866803988814354,
-0.004839002620428801,
-0.05297720432281494,
-0.010746406391263008,
0.0032089503947645426,
0.04952944815158844,
-0.004348958842456341,
0.027050506323575974,
-0.040191709995269775,
0.02857835404574871,
0.021809399127960205,
-0.03410087153315544,
-0.008577198721468449,
0.050618015229701996,
-0.018274812027812004,
0.010083822533488274,
-0.04203014448285103,
0.06394676119089127,
0.044868696480989456,
0.008371565490961075,
0.007968614809215069,
0.017080899327993393,
-0.02946019545197487,
0.0003573372378014028,
0.011243052780628204,
-0.01873822696506977,
0.020406179130077362,
0.0031934340950101614,
0.008009624667465687,
-0.02465062588453293,
0.0041226111352443695,
0.002793198451399803,
-0.0398910827934742,
0.001946220058016479,
0.004809015430510044,
-0.026799583807587624,
0.0055076139979064465,
-0.06834059953689575,
0.027479322627186775,
-0.02563730999827385,
0.03126491978764534,
-0.03840632736682892,
-0.0012033481616526842,
-0.029893388971686363,
-0.017124054953455925,
-0.012505723163485527,
0.010515592060983181,
-0.02921248972415924,
-0.0029789055697619915,
0.034297216683626175,
0.0005849782610312104,
-0.003512026509270072,
-0.034189946949481964,
0.012357966974377632,
-0.03678811341524124,
0.024869706481695175,
-0.014327919110655785,
-0.00423441780731082,
-0.005156280472874641,
-0.01660747267305851,
-0.053986094892024994,
0.028869688510894775,
-0.010747158899903297,
0.05052107945084572,
0.030210966244339943,
-0.013289445079863071,
0.013068660162389278,
0.06935543566942215,
-0.043348148465156555,
-0.01697036437690258,
0.001450695563107729,
-0.03912689536809921,
0.02625717595219612,
-0.03228669613599777,
0.004246437456458807,
-0.010337362065911293,
-0.004104260820895433,
-0.0025039012543857098,
0.002423283876851201,
-0.0291777141392231,
0.01789049431681633,
0.028538957238197327,
0.0026134690269827843,
-0.005595094058662653,
0.006365029141306877,
-0.0013839136809110641,
0.0336502343416214,
0.030674606561660767,
0.004548812285065651,
0.030015023425221443,
0.05703091248869896,
0.03595289587974548,
-0.0650414302945137,
0.042211487889289856,
-0.010025779716670513,
-0.005498467944562435,
0.056529056280851364,
-0.06100635230541229,
0.008210106752812862,
0.0459415577352047,
-0.04233253002166748,
0.014362553134560585,
-0.03819069266319275,
-0.005872479639947414,
-0.005021481309086084,
-0.027610689401626587,
0.0481196828186512,
0.06332750618457794,
0.020806673914194107,
-0.00860175583511591,
0.04373258352279663,
0.02446935512125492,
-0.0025746687315404415,
-0.048879750072956085,
0.002176586538553238,
0.014605375938117504,
-0.007715543732047081,
0.001352836610749364,
0.054884880781173706,
-0.02527359500527382,
-0.011530815623700619,
0.03549886494874954,
-0.0018265534890815616,
0.014971401542425156,
-0.008624153211712837,
0.016434023156762123,
0.025449100881814957,
0.010321224108338356,
0.009471249766647816,
-0.010139520280063152,
-0.014078386127948761,
0.0027718814089894295,
-0.023100603371858597,
0.018774723634123802,
0.007922464050352573,
-0.009540348313748837,
-0.0013941990910097957,
-0.0180798526853323,
-0.05571487173438072,
0.02786240726709366,
-0.005169813055545092,
-0.027153028175234795,
0.033174555748701096,
0.004688809160143137,
-0.013906360603868961,
-0.04816009849309921,
-0.02116716466844082,
-0.036906901746988297,
0.010648933239281178,
0.03842518478631973,
-0.03671101853251457,
-0.019747639074921608,
0.05315255746245384,
-0.024369996041059494,
-0.019584717229008675,
0.0009629526175558567,
-0.010299875400960445,
-0.02081836760044098,
-0.05479509010910988,
0.030483761802315712,
0.03545798361301422,
0.008108647540211678,
-0.020158378407359123,
-0.0002632135583553463,
-0.03077174723148346,
0.0148210683837533,
0.0026051062159240246,
-0.016952548176050186,
0.020294126123189926,
-0.028004836291074753,
-0.01872257888317108,
-0.055538661777973175,
0.06137067824602127,
-0.0070313275791704655,
-0.034504473209381104,
-0.06057927384972572,
-0.027480725198984146,
0.02271883189678192,
0.013968735001981258,
0.06512749195098877,
-0.031624745577573776,
-0.009918881580233574,
0.003429216565564275,
0.007396449334919453,
-0.010936347767710686,
-0.03445037454366684,
-0.015179947949945927,
0.006726930383592844,
-0.007768550422042608,
-0.009562390856444836,
-0.01949269510805607,
-0.027800297364592552,
0.028418494388461113,
0.0008361529908142984,
-0.005065594334155321,
0.024154791608452797,
-0.002174432622268796,
-0.048296622931957245,
-0.0016203932464122772,
0.045507919043302536,
-0.020975714549422264,
0.07282741367816925,
-0.005067114252597094,
0.039044108241796494,
0.011809323914349079,
-0.025549864396452904,
-0.02216016873717308,
0.023318180814385414,
-0.009374123997986317,
-0.030843498185276985,
-0.04209880903363228,
-0.02184179611504078,
0.04413440823554993,
-0.06802909076213837,
-0.022434620186686516,
0.04105546325445175,
-0.01504733320325613,
-0.016965515911579132,
0.05377397686243057,
0.04732956364750862,
0.043658602982759476,
-0.036314718425273895,
0.041489046066999435,
0.01925802044570446,
-0.045868683606386185,
0.0014046764699742198,
0.06642540544271469,
0.043204355984926224,
-0.014811903238296509,
-0.041012804955244064,
0.01227565947920084,
0.010319842956960201,
0.018462583422660828,
0.023230301216244698,
0.06425604224205017,
-0.04182468727231026,
-0.0172419436275959,
-0.023265404626727104,
-0.05681299790740013,
0.000684996775817126,
0.027089882642030716,
-0.038546107709407806,
0.06563033163547516,
-0.040905606001615524,
0.014018531888723373,
-0.02223302237689495,
0.045306719839572906,
-0.008640781044960022,
-0.011207867413759232,
-0.022723140195012093,
0.0007425245712511241,
0.000048652156692696735,
0.008438220247626305,
-0.006466118153184652,
0.010117138735949993,
0.01515832357108593,
0.007963676005601883,
0.025960130617022514,
0.02410849928855896,
0.022544916719198227,
-0.023943612352013588,
-0.02821444906294346,
-0.016771376132965088,
0.0104227839037776,
0.03733766824007034,
0.039681337773799896,
0.016335228458046913,
-0.022988682612776756,
-0.018155455589294434,
-0.02217118814587593,
0.03835495561361313,
-0.0693008229136467,
-0.0232305396348238,
-0.016701122745871544,
0.04267871752381325,
-0.019555632025003433,
-0.010445459745824337
] |
<p>The damping of a spring is calculated with:</p>
<p>$$[\zeta] = \frac{[c]}{\sqrt{[m][k]}}$$</p>
<p>Where c is the 'viscous damping coefficient' of the spring, according to Wikipedia. m is the mass, k is the spring constant, and zeta is the damping ratio.</p>
<p>How is the value of c calculated though? Is it a constant for the air through which the spring is moving or does it depend on the spring itself?</p>
<p>What data is required to calculate it and how can it be done?</p>
<p>I'm just looking at the oscillation of a spring vertically, and I have data for its decreasing amplitude, and the velocity of the spring at all points. </p>
<p>I have the value of the damping ratio, and I'm trying to find the value of 'c' in order to prove the above equation in an investigation.</p>
<p>There is almost no information about this online.</p>
| 9,441 |
[
-0.005501916166394949,
-0.026059910655021667,
-0.0024519176222383976,
-0.025696590542793274,
0.01692732237279415,
-0.009646667167544365,
-0.016371645033359528,
-0.026577981188893318,
-0.016389621421694756,
-0.039955198764801025,
-0.002997863804921508,
0.06290290504693985,
0.037061482667922974,
0.039517901837825775,
-0.003028067061677575,
-0.024614211171865463,
-0.006617829669266939,
0.0076727415435016155,
-0.020805496722459793,
-0.07400241494178772,
-0.0012891469523310661,
0.01693461462855339,
-0.0149199478328228,
-0.01799427717924118,
-0.021049903705716133,
0.04042321816086769,
0.03229572996497154,
0.011899166740477085,
-0.0018162158085033298,
0.015885762870311737,
-0.05731428414583206,
-0.0043078758753836155,
0.007086208555847406,
0.02296537160873413,
0.025927910581231117,
0.018156811594963074,
-0.05168885737657547,
-0.008776556700468063,
-0.030130138620734215,
0.07971862703561783,
-0.02299877628684044,
-0.029680488631129265,
0.002925387816503644,
0.02424871176481247,
-0.007978269830346107,
-0.007574419490993023,
0.03041260503232479,
-0.03202569857239723,
0.04071148857474327,
-0.0617220439016819,
0.0525369867682457,
0.019552338868379593,
0.0029180266428738832,
0.029666421934962273,
0.005413868930190802,
-0.03176289051771164,
0.059688083827495575,
0.030227215960621834,
-0.013026471249759197,
-0.060462113469839096,
0.030158715322613716,
-0.02181377448141575,
-0.026462845504283905,
-0.020569605752825737,
-0.01696871593594551,
0.02626606822013855,
-0.008008787408471107,
-0.019657321274280548,
0.06631653755903244,
-0.005283455830067396,
0.008527779951691628,
-0.002930998569354415,
0.06506915390491486,
-0.025435779243707657,
-0.004279260989278555,
-0.03854009881615639,
-0.013344204984605312,
0.07068781554698944,
0.0626232698559761,
0.02021024376153946,
-0.02163524739444256,
-0.0012696520425379276,
0.021961776539683342,
0.010795661248266697,
-0.011704767122864723,
-0.01460673101246357,
0.07375548779964447,
0.028682829812169075,
0.020862720906734467,
-0.014342010021209717,
0.023187309503555298,
0.015548985451459885,
-0.0015939247095957398,
-0.04122636839747429,
0.002980149118229747,
0.012948006391525269,
-0.02021707594394684,
0.03894282877445221,
0.006315546575933695,
-0.03392735868692398,
-0.017694076523184776,
-0.008636241778731346,
-0.008578229695558548,
0.07168243080377579,
0.003933555446565151,
0.002887735143303871,
0.014917321503162384,
-0.023220453411340714,
-0.0411435030400753,
-0.02845047228038311,
-0.05648846924304962,
-0.02220381610095501,
-0.019345136359333992,
0.0012392525095492601,
-0.0009681846131570637,
0.010110896080732346,
-0.012502702884376049,
-0.014324304647743702,
0.05231817066669464,
0.016229776665568352,
0.03625081852078438,
-0.033983755856752396,
0.02494095265865326,
-0.021190660074353218,
-0.0736490786075592,
0.030400976538658142,
0.015468483790755272,
-0.013018573634326458,
-0.04158096760511398,
0.020935531705617905,
0.013730530627071857,
-0.03165557608008385,
-0.009050633758306503,
0.025973275303840637,
0.008008558303117752,
0.0035302743781358004,
-0.09756802022457123,
-0.06384558230638504,
0.04533623903989792,
-0.009718798100948334,
-0.00830957293510437,
-0.10795868188142776,
0.005255655851215124,
0.05482325330376625,
0.08426399528980255,
0.02662159502506256,
0.006670407950878143,
0.0011498794192448258,
0.007921886630356312,
0.03810517117381096,
-0.0006507569923996925,
-0.0503101572394371,
0.019972695037722588,
-0.015008814632892609,
0.0027821147814393044,
-0.005584320053458214,
0.016322657465934753,
0.02843041531741619,
0.020153209567070007,
-0.0038662864826619625,
0.05414384976029396,
-0.0191865935921669,
-0.0013727276818826795,
0.028037313371896744,
-0.004317414481192827,
-0.06529146432876587,
0.03285816311836243,
-0.0016474516596645117,
0.03194958344101906,
-0.01659735105931759,
-0.004736721515655518,
-0.015565717592835426,
0.007373587694019079,
-0.012168488465249538,
0.060685623437166214,
-0.04246114566922188,
0.0023500139359384775,
-0.04034887254238129,
0.014384984038770199,
0.0029632423538714647,
-0.053491637110710144,
-0.03253382444381714,
0.008997561410069466,
0.023762356489896774,
0.011206217110157013,
0.046425171196460724,
0.01684209518134594,
0.028746576979756355,
0.029168562963604927,
-0.02490338124334812,
-0.03940839692950249,
-0.01977911964058876,
0.022932393476366997,
-0.03690308704972267,
-0.008232345804572105,
0.026181381195783615,
0.0238087996840477,
0.018784761428833008,
-0.03498285263776779,
-0.031050067394971848,
0.018729306757450104,
-0.00039328899583779275,
0.0008051593904383481,
-0.019120270386338234,
0.02993737906217575,
0.035693805664777756,
0.02595142275094986,
0.007200794294476509,
0.016266558319330215,
-0.0017409769352525473,
-0.028941232711076736,
-0.02278473787009716,
-0.05520301312208176,
0.02780797891318798,
0.005807402078062296,
0.010763062164187431,
0.02877918630838394,
-0.03732554242014885,
0.023006729781627655,
0.017606329172849655,
-0.009726074524223804,
0.07852091640233994,
0.1009758785367012,
0.01938466727733612,
0.017376413568854332,
0.025216450914740562,
-0.01790362223982811,
0.01169666275382042,
-0.015492281876504421,
0.019033722579479218,
-0.0617188885807991,
-0.027031753212213516,
0.03896314278244972,
0.016039693728089333,
-0.03481648489832878,
-0.02320718951523304,
0.0370696559548378,
0.02546684630215168,
0.045269619673490524,
0.018691066652536392,
0.005199024453759193,
-0.07754690945148468,
0.005066902842372656,
0.02431384101510048,
0.0059304614551365376,
0.027890520170331,
0.03354732319712639,
0.012109773233532906,
0.061544694006443024,
-0.04356234148144722,
0.007959436625242233,
0.05117553472518921,
-0.005559396930038929,
0.02760118804872036,
0.0035814668517559767,
-0.019983401522040367,
0.022977106273174286,
-0.020723741501569748,
0.053561385720968246,
-0.00425994535908103,
-0.0032808310352265835,
0.02909703366458416,
0.00958632305264473,
0.014118782244622707,
0.01668567955493927,
-0.010964974761009216,
-0.06230748072266579,
-0.014183184131979942,
0.025028685107827187,
-0.05469656363129616,
0.008191218599677086,
-0.017191974446177483,
-0.023940591141581535,
-0.009049622341990471,
-0.012935850769281387,
0.04083534702658653,
0.0036683036014437675,
0.016181031242012978,
-0.019253132864832878,
-0.03633079305291176,
0.018885862082242966,
-0.04338771849870682,
0.0026216430123895407,
0.02297309786081314,
-0.014070911332964897,
0.022547787055373192,
0.00788190495222807,
-0.04087034612894058,
0.0010885101510211825,
-0.0008392540621571243,
0.0063204714097082615,
0.02149190567433834,
0.017822975292801857,
-0.04725361987948418,
-0.01964471861720085,
0.0012683598324656487,
-0.010765804909169674,
-0.04686341807246208,
0.015608616173267365,
0.029735583811998367,
0.002860755193978548,
-0.009810065850615501,
0.04353169724345207,
-0.026603620499372482,
-0.04418358951807022,
-0.04705001786351204,
-0.0036732470616698265,
0.05586683750152588,
-0.06381598860025406,
-0.008058656007051468,
0.027573704719543457,
-0.0017233733087778091,
0.007320235949009657,
-0.04546165093779564,
-0.0495692640542984,
0.011102710850536823,
-0.011160125955939293,
0.07009474188089371,
0.046190083026885986,
-0.03266046196222305,
0.10466914623975754,
0.021587001159787178,
-0.010928673669695854,
-0.010619519278407097,
-0.0020866557024419308,
-0.02211749739944935,
-0.024767844006419182,
-0.04736393690109253,
0.05079561471939087,
-0.021306535229086876,
0.009101017378270626,
0.017961077392101288,
0.006706472020596266,
0.050111666321754456,
0.014945750124752522,
0.013554861769080162,
0.011096268892288208,
-0.00835789181292057,
-0.008902819827198982,
0.06533348560333252,
0.013142801821231842,
0.004695776384323835,
0.0143227968364954,
0.007607500534504652,
0.027010761201381683,
0.03168454393744469,
-0.07105454057455063,
0.016385190188884735,
0.013024120591580868,
-0.01880156621336937,
-0.03824038803577423,
0.024529138579964638,
0.013198263011872768,
-0.01382624451071024,
-0.0022633003536611795,
-0.004949549678713083,
0.015768200159072876,
0.014860721305012703,
-0.002626517554745078,
0.03283586725592613,
0.055083267390728,
0.01661333255469799,
-0.06380953639745712,
-0.014469566754996777,
-0.004819732159376144,
0.01307574100792408,
-0.03691988065838814,
-0.03071371652185917,
0.0009568679379299283,
0.025425365194678307,
0.026279233396053314,
0.0020556366071105003,
-0.07815022021532059,
0.005046003498136997,
-0.03382902964949608,
-0.04339548200368881,
0.006289173848927021,
0.051240768283605576,
0.005509883165359497,
0.08587437123060226,
0.01271416712552309,
0.01289411447942257,
0.05465637892484665,
0.012638699263334274,
-0.062186941504478455,
0.031052354723215103,
-0.043139152228832245,
-0.017392156645655632,
0.0009850984206423163,
-0.025110695511102676,
0.03319121524691582,
0.007322137244045734,
-0.00962845329195261,
0.012189590372145176,
0.0040467772632837296,
-0.04537561908364296,
0.012895137071609497,
-0.029758933931589127,
0.0004637230304069817,
-0.027667950838804245,
0.034535281360149384,
0.04493212327361107,
-0.031035471707582474,
0.026979196816682816,
0.07250258326530457,
-0.0022934924345463514,
-0.024978870525956154,
-0.030181776732206345,
-0.013241994194686413,
0.00583735853433609,
-0.003382437862455845,
0.03528386726975441,
-0.029213620349764824,
-0.019410591572523117,
0.002348463051021099,
0.0017328945687040687,
0.04821150377392769,
0.013387506827712059,
-0.0036889170296490192,
-0.035127315670251846,
-0.035340480506420135,
0.003950679209083319,
0.0032575251534581184,
0.027485299855470657,
-0.02973731979727745,
0.008163354359567165,
0.027757955715060234,
-0.023063741624355316,
-0.009016063064336777,
0.05005549266934395,
0.021040409803390503,
0.007508212700486183,
-0.009880859404802322,
-0.06357922405004501,
0.007444937713444233,
-0.020740309730172157,
-0.017350275069475174,
0.006043534725904465,
0.02363397926092148,
-0.010168978944420815,
0.012257620692253113,
0.022489171475172043,
-0.0048232171684503555,
-0.008499899879097939,
0.014969845302402973,
-0.008815120905637741,
0.038911353796720505,
-0.002636765828356147,
-0.05118522793054581,
0.018185624852776527,
0.016614623367786407,
0.06958471983671188,
0.03602287545800209,
-0.015201210975646973,
-0.07910739630460739,
-0.03801114484667778,
0.015328914858400822,
0.023893488571047783,
-0.022338125854730606,
-0.014039294794201851,
-0.04520915448665619,
-0.011742831207811832,
0.03628052398562431,
-0.026590533554553986,
0.04864068701863289,
0.02014133892953396,
0.03719503805041313,
-0.03561093658208847,
-0.033549997955560684,
-0.004210304003208876,
0.03178224340081215,
-0.02364283800125122,
-0.024747490882873535,
-0.028998490422964096,
-0.01795014925301075,
0.001502344268374145,
0.01824181340634823,
-0.006506918929517269,
0.0521714985370636,
0.011591344140470028,
-0.007418377324938774,
-0.013168455101549625,
-0.03933770954608917,
-0.02519761025905609,
-0.06269706040620804,
-0.010579225607216358,
-0.00025712884962558746,
0.012064371258020401,
0.01715325377881527,
-0.011098858900368214,
-0.020206434652209282,
0.046510543674230576,
0.039814725518226624,
-0.017183523625135422,
-0.011286206543445587,
-0.053461868315935135,
0.02336767502129078,
0.02121281623840332,
0.010906005278229713,
0.06913017481565475,
0.053619056940078735,
-0.031673215329647064,
0.025431109592318535,
0.022745508700609207,
0.005056244321167469,
-0.0173714067786932,
0.009787352755665779,
-0.01783882826566696,
0.03259864076972008,
-0.04187516123056412,
0.037666238844394684,
0.007628687657415867,
0.03478897362947464,
-0.027501210570335388,
-0.014017025008797646,
-0.03635150194168091,
0.011663395911455154,
0.012210560031235218,
0.024206139147281647,
0.025643201544880867,
0.009136407636106014,
0.022539345547556877,
-0.00701001426205039,
0.010519240982830524,
0.0005683919880539179,
-0.010043105110526085,
0.006721039302647114,
-0.03712404519319534,
-0.02274504117667675,
-0.020145950838923454,
-0.0043397871777415276,
0.021251816302537918,
-0.02916717529296875,
0.06988448649644852,
-0.00995976384729147,
0.00024111363745760173,
0.01698140986263752,
-0.03510704264044762,
-0.04526318982243538,
0.01707010343670845,
-0.008290968835353851,
0.04691718518733978,
-0.07339964807033539,
0.009167404845356941,
0.019215267151594162,
0.03798920288681984,
-0.032856520265340805,
-0.029231179505586624,
0.03520951047539711,
0.01773393154144287,
-0.00979998055845499,
-0.029425224289298058,
-0.018908005207777023,
0.0048176501877605915,
-0.03362033888697624,
0.057123396545648575,
0.01768227107822895,
0.004821441136300564,
0.012138115242123604,
0.0009782923152670264,
0.032638538628816605,
0.026791494339704514,
0.008860775269567966,
0.014849813655018806,
-0.006091437768191099,
-0.0277053602039814,
-0.03731684759259224,
0.032995034009218216,
0.08023903518915176,
-0.020999127998948097,
0.0009741451358422637,
-0.009060372598469257,
0.018399709835648537,
0.011440560221672058,
0.007059560623019934,
-0.03388740122318268,
0.020679766312241554,
0.02007811702787876,
0.03229137137532234,
-0.05054572597146034,
0.012318865396082401,
0.03147684410214424,
0.044486213475465775,
-0.006040008272975683,
-0.0072198170237243176,
-0.040076062083244324,
-0.04286663979291916,
0.012158897705376148,
0.03332968428730965,
0.0040666162967681885,
-0.014380321837961674,
0.06634839624166489,
-0.053666260093450546,
-0.012379745952785015,
-0.0016438773600384593,
0.008797567337751389,
0.02757570706307888,
-0.00434942776337266,
0.023037759587168694,
0.013706991448998451,
0.006482348777353764,
-0.012104596942663193,
-0.016302073374390602,
-0.056588251143693924,
-0.0010714905802160501,
0.0727851539850235,
-0.010443725623190403,
0.060513611882925034,
0.05324719101190567,
-0.010812990367412567,
0.01986408419907093,
-0.0019115160685032606,
-0.03727496787905693,
-0.012228409759700298,
-0.009404398500919342,
0.026228729635477066,
-0.027530228719115257,
0.00030615617288276553,
0.017930839210748672,
0.0189996175467968,
-0.04410337284207344,
-0.02301800437271595,
0.02282535471022129,
0.0331721231341362,
0.01309618353843689,
-0.017698928713798523,
0.00792003609240055,
0.025383321568369865,
0.009459652937948704,
0.07275916635990143,
0.0022983835078775883,
-0.013298454694449902,
0.029493534937500954,
0.04059482365846634,
-0.00566475884988904,
-0.052599769085645676,
0.025285707786679268,
-0.02602791041135788,
0.016119491308927536,
0.02368844300508499,
-0.01332489401102066,
0.025017905980348587,
0.023294441401958466,
0.02881431020796299,
-0.0111991623416543,
0.03884221613407135,
0.001214457442983985,
0.009764278307557106,
-0.013608104549348354,
-0.04356294497847557,
-0.05113137885928154,
0.03444092348217964,
0.005450931377708912,
-0.05795314162969589,
0.048785462975502014,
-0.02395857311785221,
0.04119115322828293,
0.019923757761716843,
0.027309590950608253,
-0.016618791967630386,
0.0863587036728859,
-0.02257736772298813,
-0.015375918708741665,
-0.02855949103832245,
0.03899897634983063,
0.1294897049665451,
0.03614012151956558,
0.0019207143923267722,
-0.04129648953676224,
0.0032099527306854725,
0.00858167465776205,
0.02114265039563179,
-0.05301244556903839,
0.002753734588623047,
0.0011030937312170863,
0.0038507336284965277,
0.029010223224759102,
0.06222912296652794,
-0.05100131779909134,
-0.019914161413908005,
0.04515952989459038,
0.0010613114573061466,
-0.029303792864084244,
0.003257578471675515,
-0.016382139176130295,
-0.03746530041098595,
-0.00026091348263435066,
-0.00459411833435297,
0.030928272753953934,
-0.018782608211040497,
-0.04279813915491104,
-0.032811570912599564,
-0.04498562961816788,
-0.005553907714784145,
-0.05100807175040245,
-0.04347475618124008,
-0.012086761184036732,
0.028406178578734398,
-0.010980421677231789,
-0.04822227358818054,
0.01973523385822773,
0.05116384103894234,
0.01265658251941204,
0.025353461503982544,
0.08005549013614655,
-0.005147943738847971,
-0.014558583498001099,
-0.03497934341430664,
0.014886139892041683,
-0.03445082902908325,
-0.02619524858891964,
-0.07005691528320312,
0.023931456729769707,
0.011795206926763058,
-0.005279656033962965,
-0.005151535850018263,
0.037111762911081314,
0.018159927800297737,
-0.02733280509710312,
0.0013538538478314877,
-0.011029317043721676,
0.033929187804460526,
-0.09331966191530228,
-0.015572483651340008,
-0.0010399423772469163,
-0.020737119019031525,
0.022127823904156685,
0.0009483672911301255,
-0.011883178725838661,
-0.04853515699505806,
-0.043660614639520645,
-0.005184167996048927,
0.016411270946264267,
-0.02399718016386032,
-0.021038146689534187,
0.004390188492834568,
-0.019165223464369774,
-0.027119692414999008,
-0.0015351212350651622,
-0.01576194353401661,
0.0403219498693943,
0.04381546005606651,
-0.025311388075351715,
-0.012714032083749771,
-0.017740199342370033,
-0.06012023985385895,
0.04627827927470207,
0.012670720927417278,
0.021921245381236076,
-0.05452205240726471,
-0.04366983100771904,
-0.00875056628137827,
0.03661930188536644,
-0.03678936883807182,
0.011130983941257,
-0.029382530599832535,
0.01345252338796854,
0.041770752519369125,
-0.031437862664461136,
-0.004727396182715893,
0.016004124656319618,
-0.05903754383325577,
0.0290323868393898,
-0.011005747132003307,
0.07754920423030853,
0.04048269987106323,
0.0425511971116066,
0.011302218772470951,
0.01208404079079628,
-0.049875110387802124,
0.008050879463553429,
0.015071780420839787,
-0.02406155690550804,
-0.0004580993845593184,
0.010731708258390427,
-0.0021070903167128563,
-0.01703345775604248,
-0.02593010850250721,
-0.0437391996383667,
0.006515734363347292,
-0.011638252064585686,
0.015067391097545624,
-0.04901770502328873,
0.024969222024083138,
-0.04321538656949997,
-0.02442564070224762,
-0.07394479960203171,
0.0034561820793896914,
-0.021614765748381615,
-0.0072343661449849606,
0.014021418057382107,
0.01739145629107952,
-0.031083734706044197,
-0.009160686284303665,
-0.021494979038834572,
-0.0024477681145071983,
-0.013657533563673496,
0.003939267713576555,
0.023718789219856262,
-0.03187229484319687,
0.018854625523090363,
-0.024491962045431137,
0.024882720783352852,
0.001345859025605023,
-0.06122276932001114,
0.059687621891498566,
-0.01255714800208807,
-0.04541366547346115,
0.013908971101045609,
0.0016968584386631846,
0.012154039926826954,
0.029139040037989616,
-0.0143769895657897,
0.010312732309103012,
0.041632894426584244,
-0.014131484553217888,
0.0015792049234732985,
-0.0392322838306427,
-0.016667131334543228,
0.005828894674777985,
-0.012318556196987629,
0.00663295853883028,
-0.05297929421067238,
0.013012346811592579,
0.0141923101618886,
0.04133019223809242,
0.0037108995020389557,
0.016873404383659363,
0.015945641323924065,
-0.024122219532728195,
-0.013814462348818779,
0.047978706657886505,
0.056981708854436874,
0.02405528351664543,
0.051195159554481506,
-0.0017276983708143234,
0.01533763948827982,
0.025862088426947594,
0.0059952461160719395,
-0.12179594486951828,
0.007155980449169874,
-0.029451748356223106,
0.017551535740494728,
0.010515382513403893,
-0.0251122135668993,
0.030389076098799706,
0.013592584058642387,
-0.032473400235176086,
-0.018166618421673775,
-0.029924536123871803,
0.00900218915194273,
-0.028833815827965736,
-0.014188353903591633,
0.026770729571580887,
0.06582484394311905,
0.040930017828941345,
0.00473965797573328,
0.012194106355309486,
-0.009449906647205353,
-0.005287839099764824,
0.014207377098500729,
0.032367028295993805,
0.0005068486789241433,
-0.006844178773462772,
-0.015597834251821041,
0.044685717672109604,
-0.015073394402861595,
-0.015175949782133102,
0.024361025542020798,
-0.006921289023011923,
0.01793455146253109,
-0.013904331251978874,
0.01888965256512165,
-0.005690716672688723,
0.044756196439266205,
0.023045683279633522,
-0.004979947116225958,
-0.026598023250699043,
-0.005035023204982281,
0.0187506265938282,
0.007854674011468887,
-0.016749529168009758,
0.0019309415947645903,
0.014766327105462551,
-0.024724898859858513,
-0.03732924535870552,
0.017068738117814064,
-0.06040066480636597,
0.013490197248756886,
-0.011716565117239952,
-0.03255702182650566,
-0.0062496052123606205,
0.011568838730454445,
0.018655600026249886,
-0.002134364563971758,
0.0343417264521122,
0.047574207186698914,
-0.007943402975797653,
-0.0008602788439020514,
-0.015035425312817097,
0.014169851318001747,
-0.025426562875509262,
-0.015252922661602497,
0.0057451664470136166,
-0.008468682877719402,
-0.06954488158226013,
-0.052669741213321686,
0.004916115198284388,
0.003192095784470439,
-0.020470768213272095,
-0.007522674277424812,
-0.03204610198736191,
0.03908846154808998,
0.05092247202992439,
0.030001837760210037,
-0.013162357732653618,
-0.027369417250156403,
0.005040109623223543,
-0.055593714118003845,
0.03134360909461975,
0.0030413339845836163,
-0.03980452939867973,
-0.0209969449788332,
-0.021792344748973846,
0.010570173151791096,
0.019722290337085724,
0.06141060218214989,
-0.02487504482269287,
-0.0248042531311512,
0.0031854116823524237,
-0.0016603244002908468,
-0.0037900833413004875,
-0.043062251061201096,
-0.015909520909190178,
-0.021909523755311966,
-0.04623735696077347,
0.007645470555871725,
-0.006814359687268734,
0.007292945869266987,
0.008626176975667477,
0.01868009753525257,
0.0025176743511110544,
0.054563216865062714,
-0.004564716015011072,
-0.036472387611866,
0.0290371123701334,
0.011534568853676319,
-0.02893330715596676,
0.07639272511005402,
0.012440558522939682,
-0.009882938116788864,
0.02673708274960518,
-0.022286318242549896,
-0.061723459511995316,
0.039250921458005905,
-0.028953252360224724,
-0.012933547608554363,
0.0029243486933410168,
-0.03015139512717724,
0.005049934610724449,
-0.05142875388264656,
-0.006825126241892576,
0.042923711240291595,
-0.058776646852493286,
-0.033620357513427734,
0.0282522514462471,
0.0054403566755354404,
0.04523538798093796,
0.03985116630792618,
0.055858731269836426,
0.02610236220061779,
-0.039859335869550705,
0.002561120083555579,
0.02018868923187256,
0.027979476377367973,
-0.02544485591351986,
-0.007620017509907484,
0.01902713067829609,
-0.011330317705869675,
0.03357495367527008,
0.001548864645883441,
-0.015683244913816452,
-0.021447962149977684,
-0.04990424960851669,
0.023012202233076096,
-0.02443856932222843,
-0.008118480443954468,
0.04938381165266037,
-0.020531730726361275,
0.10434197634458542,
-0.01468006893992424,
-0.002434214111417532,
-0.009099406190216541,
0.015479544177651405,
-0.02363826334476471,
0.006630877032876015,
0.028171589598059654,
0.01564265973865986,
0.0007581064710393548,
0.03148600459098816,
-0.006058423314243555,
-0.012423612177371979,
0.005761877633631229,
-0.038202330470085144,
0.010646425187587738,
0.011449710465967655,
-0.0022520378697663546,
-0.006140556186437607,
-0.02246803790330887,
-0.03996859863400459,
-0.011787200346589088,
0.07304366677999496,
-0.0005242798360995948,
-0.020874643698334694,
0.008802766911685467,
-0.017365068197250366,
0.0014245425118133426,
0.04639724642038345,
-0.027124356478452682,
-0.0119833555072546,
-0.020618723705410957,
0.02679290436208248,
0.006769256200641394,
0.001495101721957326
] |
<p>As the only way String theory can respect the principles of quantum mechanics and Special theory of relativity, by formulating it in hypothetical nine dimensional space.
You could use string compactification for d number of non compact direction, all it requires to have d non compact direction is to choose an appropriate compact space of dimension (9-d).</p>
<p>The question arises here, Then Why our Universe is in Three dimensional space?</p>
| 9,442 |
[
-0.0030251587741076946,
-0.023762669414281845,
0.03308040276169777,
-0.0579499788582325,
0.035872187465429306,
0.008353744633495808,
-0.042533282190561295,
-0.02175098843872547,
0.005457848310470581,
-0.037677474319934845,
0.014865114353597164,
-0.010882841423153877,
0.02847035601735115,
0.03475675731897354,
0.014740877784788609,
0.03142847493290901,
0.015489690005779266,
-0.009200138039886951,
-0.02953045442700386,
-0.03669080138206482,
0.03901010379195213,
0.0178578719496727,
-0.010545982047915459,
0.03603038564324379,
-0.008601677604019642,
0.00281114992685616,
0.0465436689555645,
0.021572494879364967,
0.02964441105723381,
0.03140847012400627,
-0.002051505260169506,
-0.006470408756285906,
0.011939401738345623,
0.06336744874715805,
0.000882340595126152,
-0.03166141360998154,
-0.013268210925161839,
0.005666003096848726,
0.005684583447873592,
-0.014211002737283707,
0.001862211269326508,
-0.024303022772073746,
-0.004966666456311941,
0.05323996767401695,
-0.0244583822786808,
0.0542798712849617,
0.0026490245945751667,
-0.03725416585803032,
0.05175958573818207,
-0.06706387549638748,
0.06103682518005371,
-0.027653995901346207,
0.030657893046736717,
-0.018920140340924263,
-0.0003735846548806876,
-0.01164756529033184,
0.0847812294960022,
0.07821691781282425,
-0.002553385216742754,
-0.031007051467895508,
-0.03423832356929779,
-0.01429933961480856,
0.052092280238866806,
-0.007171292789280415,
-0.01768770068883896,
0.039907872676849365,
-0.009278497658669949,
0.004905510228127241,
-0.004859578795731068,
-0.0076019312255084515,
-0.024776672944426537,
0.007184671238064766,
0.02933765947818756,
-0.014523860067129135,
0.01534133031964302,
-0.008582794107496738,
0.03360309079289436,
-0.005990379024296999,
0.038377270102500916,
0.028476543724536896,
0.0002916641824413091,
-0.034089040011167526,
0.018796397373080254,
0.029670432209968567,
0.01794436387717724,
-0.010148383677005768,
0.03993092104792595,
-0.018184857442975044,
-0.028034381568431854,
0.05773970112204552,
0.005743097048252821,
0.01129234954714775,
0.04836870729923248,
0.0009008838678710163,
-0.005103183910250664,
0.038033660501241684,
0.02520415000617504,
0.023625684902071953,
-0.01475877407938242,
-0.02158542536199093,
0.004922950640320778,
-0.00903614517301321,
0.03901216387748718,
0.05398049205541611,
0.026074381545186043,
0.01364484615623951,
-0.06888843327760696,
0.04084005951881409,
-0.047815386205911636,
0.008968053385615349,
-0.03944002464413643,
0.015528528951108456,
-0.005260884296149015,
-0.0018498272402212024,
0.017791148275136948,
-0.016347691416740417,
0.020198022946715355,
-0.01666892319917679,
0.04073288291692734,
0.09774048626422882,
0.014911391772329807,
-0.013879622332751751,
0.006654726807028055,
0.009221364744007587,
-0.06936081498861313,
-0.011844038963317871,
0.029492469504475594,
0.005914740264415741,
-0.0109053710475564,
0.023698296397924423,
0.01950034871697426,
-0.027527887374162674,
0.03788653761148453,
-0.0021641291677951813,
0.070403091609478,
-0.004586094990372658,
-0.10517669469118118,
-0.05241579934954643,
0.057541411370038986,
-0.004429125692695379,
-0.007391077466309071,
-0.06844758242368698,
0.010683543048799038,
0.052373725920915604,
0.08748967200517654,
-0.011895093135535717,
0.0008145160390995443,
0.03159087151288986,
0.02702915668487549,
-0.007122863084077835,
-0.0439189188182354,
0.00008100923878373578,
-0.0054802317172288895,
-0.054002199321985245,
-0.008998224511742592,
-0.052471037954092026,
0.028057768940925598,
0.028845250606536865,
-0.0008100594859570265,
-0.05925838649272919,
0.049063585698604584,
-0.04220553860068321,
-0.0025469667743891478,
0.004085944965481758,
-0.02767479047179222,
-0.011871080845594406,
0.06915653496980667,
0.02193434350192547,
-0.018057100474834442,
0.017245041206479073,
-0.02059118077158928,
0.01340491697192192,
0.020473994314670563,
0.05687032639980316,
-0.0007563959807157516,
-0.04893071949481964,
-0.014512564055621624,
0.0018835501978173852,
0.02315392531454563,
-0.038860954344272614,
-0.03768125921487808,
-0.019765788689255714,
-0.0019050902919843793,
0.01023272518068552,
-0.006370937917381525,
0.044942013919353485,
-0.03295348212122917,
-0.023344574496150017,
0.0003886222548317164,
-0.04486566781997681,
-0.005617909599095583,
-0.05126357823610306,
0.018314579501748085,
0.0240413099527359,
-0.009331158362329006,
-0.0024630220141261816,
0.006792058236896992,
0.0011844105320051312,
-0.04005613550543785,
-0.012480990961194038,
-0.020495321601629257,
0.04572271928191185,
-0.011339999735355377,
-0.015311447903513908,
0.021139508113265038,
0.03948958218097687,
0.03399985283613205,
-0.05381365492939949,
0.007130364887416363,
0.008775684982538223,
-0.018309177830815315,
0.028271514922380447,
-0.0260910764336586,
-0.009724265895783901,
-0.01790686883032322,
0.004929134156554937,
0.03235265612602234,
0.007102519739419222,
-0.013523360714316368,
0.06585050374269485,
-0.035117823630571365,
0.06553034484386444,
0.03024979680776596,
0.0009742867550812662,
0.010695664212107658,
0.009874598123133183,
-0.046191222965717316,
0.0175087358802557,
0.022485166788101196,
-0.028890974819660187,
-0.046808499842882156,
0.00002596436570456717,
0.02138582058250904,
0.044105831533670425,
-0.030713748186826706,
0.010783804580569267,
0.01582980342209339,
0.050241488963365555,
0.02821403183043003,
0.042615074664354324,
-0.026725895702838898,
-0.01931680738925934,
-0.020149944350123405,
-0.020661592483520508,
0.03765340894460678,
0.015962723642587662,
0.008652305230498314,
0.03704307973384857,
0.00333698489703238,
-0.017072858288884163,
-0.03363848850131035,
0.03851468861103058,
-0.011210283264517784,
0.018866760656237602,
0.041659869253635406,
-0.04575974494218826,
0.02357444167137146,
-0.031964823603630066,
0.01736762747168541,
0.03481065109372139,
-0.005694114603102207,
0.02484775148332119,
-0.009400430135428905,
-0.012406479567289352,
0.030580129474401474,
0.06190140172839165,
0.004121539182960987,
-0.03356130048632622,
0.04335137456655502,
-0.03385850042104721,
-0.018740737810730934,
-0.019481563940644264,
0.019818589091300964,
-0.01816137693822384,
0.012475701980292797,
0.07085394114255905,
-0.00789543054997921,
0.03024933859705925,
-0.017437951639294624,
-0.0239702295511961,
0.003850014181807637,
-0.012355896644294262,
-0.023445656523108482,
-0.0018203873187303543,
-0.05292947217822075,
0.0218951553106308,
-0.011190074495971203,
-0.04249172657728195,
0.024448556825518608,
-0.007286666426807642,
0.03476719185709953,
0.0003633734304457903,
-0.02235117182135582,
-0.03417322039604187,
-0.019696908071637154,
-0.01590903475880623,
0.034622516483068466,
0.016441505402326584,
-0.007761793211102486,
0.05515063554048538,
-0.004203637130558491,
-0.003170870477333665,
-0.009778250940144062,
-0.026557259261608124,
-0.07996741682291031,
0.0069936830550432205,
0.006740406155586243,
0.004236593376845121,
-0.04760057479143143,
0.04313642904162407,
0.0018129824893549085,
-0.05996863171458244,
0.004881064873188734,
-0.04576732590794563,
-0.0452408567070961,
0.021895401179790497,
0.006782963871955872,
0.062141574919223785,
-0.009125236421823502,
-0.05459349974989891,
0.05058521777391434,
0.05072908475995064,
-0.05706397816538811,
0.005186844151467085,
-0.003847578540444374,
-0.04865177348256111,
-0.019776901230216026,
0.03644110634922981,
0.006395232398062944,
-0.008851353079080582,
0.013220291584730148,
0.04893000051379204,
0.047267619520425797,
0.016723111271858215,
-0.02673456072807312,
-0.03076067566871643,
-0.008662823587656021,
0.016283253207802773,
0.05782786384224892,
0.01476377248764038,
-0.012768527492880821,
-0.04712887108325958,
-0.006259345915168524,
-0.013987882062792778,
-0.005243251565843821,
-0.0026660114526748657,
-0.05564543977379799,
0.03645128011703491,
0.01277242973446846,
0.045901745557785034,
-0.01353383343666792,
-0.007808585185557604,
-0.0037010994274169207,
-0.015141461044549942,
0.01882578618824482,
0.021381456404924393,
0.008848142810165882,
-0.0017773599829524755,
0.02339543029665947,
-0.02587359957396984,
0.0194895900785923,
-0.038791269063949585,
-0.030762599781155586,
0.013102058321237564,
0.002266585361212492,
0.030393391847610474,
-0.027459891512989998,
-0.015297960489988327,
0.04177356883883476,
0.03843843564391136,
0.02799702249467373,
0.013628587126731873,
-0.041175201535224915,
0.0157764945179224,
-0.0369856022298336,
-0.022283358499407768,
0.005095853470265865,
0.024008329957723618,
-0.010690713301301003,
0.02825753390789032,
0.03991376608610153,
0.009042007848620415,
0.0035820710472762585,
-0.026829948648810387,
-0.09016472846269608,
-0.03959298133850098,
-0.048010386526584625,
0.017664946615695953,
-0.0005659058806486428,
-0.016534097492694855,
-0.04300587996840477,
-0.021327780559659004,
-0.004174722358584404,
0.006559670902788639,
-0.031955536454916,
-0.09495911002159119,
-0.007866308093070984,
-0.038736630231142044,
-0.028902577236294746,
-0.029192540794610977,
0.0627165287733078,
0.05968255177140236,
-0.009022827260196209,
-0.008945366367697716,
0.04965049773454666,
-0.048555344343185425,
-0.046351928263902664,
0.0021288541611284018,
0.01806923933327198,
0.021571991965174675,
0.02932005375623703,
0.008336186408996582,
0.013105913065373898,
-0.012159168720245361,
0.0007217354141175747,
0.00856820773333311,
0.01778077892959118,
-0.015758592635393143,
-0.008986400440335274,
-0.012293237261474133,
-0.04061238095164299,
-0.01031241100281477,
0.0007746259798295796,
0.04685744643211365,
0.038268495351076126,
-0.0132578294724226,
0.06012522056698799,
0.011942893266677856,
-0.04092569649219513,
0.018127555027604103,
0.04279547929763794,
-0.0070564234629273415,
-0.05057061091065407,
-0.040230751037597656,
-0.029297979548573494,
-0.034608855843544006,
-0.01492579560726881,
0.001937225228175521,
-0.0037522276397794485,
-0.05216992273926735,
0.01239008642733097,
0.019280804321169853,
-0.018584689125418663,
-0.041716527193784714,
0.004153986927121878,
0.006974606774747372,
0.034255851060152054,
-0.011868917383253574,
0.023656146600842476,
-0.009570175781846046,
0.0385262593626976,
-0.010848917067050934,
-0.0029302046168595552,
-0.0500570647418499,
-0.056401465088129044,
0.009090803563594818,
-0.003420304274186492,
0.031526438891887665,
0.016798634082078934,
-0.03366145119071007,
-0.07453154772520065,
-0.05240993574261665,
0.029224703088402748,
-0.05379248410463333,
0.028255682438611984,
-0.041989073157310486,
-0.020700734108686447,
-0.017386585474014282,
0.010886600241065025,
-0.004213242791593075,
0.024081898853182793,
-0.006277143955230713,
0.019543686881661415,
-0.010649331845343113,
0.0019728525076061487,
-0.0256876852363348,
0.019960008561611176,
0.035355985164642334,
0.007148782256990671,
0.006941514555364847,
0.03356879949569702,
-0.009861961007118225,
0.042773857712745667,
-0.036893658339977264,
-0.03407002612948418,
0.015168692916631699,
0.03396156057715416,
-0.0006892214878462255,
0.04144608601927757,
-0.03931020200252533,
-0.01770123466849327,
-0.01124528981745243,
-0.0032820829655975103,
0.007781638763844967,
0.02272603288292885,
-0.013287721201777458,
0.0023125705774873495,
0.003836852964013815,
-0.019135210663080215,
0.010174045339226723,
0.011373662389814854,
-0.015761932358145714,
-0.01330555696040392,
-0.04141857475042343,
0.03756348416209221,
-0.02989150583744049,
0.03324148803949356,
-0.03750704601407051,
-0.005188395734876394,
-0.036401115357875824,
0.041594065725803375,
-0.01237498875707388,
-0.026195723563432693,
-0.004484015982598066,
-0.02116091549396515,
-0.05257230997085571,
-0.023573562502861023,
0.028727974742650986,
0.012466596439480782,
0.008748740889132023,
-0.0014405272668227553,
0.011698197573423386,
-0.004881399217993021,
0.008371895179152489,
0.02010153792798519,
0.012998104095458984,
0.02779393270611763,
0.0026742075569927692,
0.01913061924278736,
-0.009704758413136005,
-0.007476393599063158,
0.04367979243397713,
-0.05893506854772568,
0.009271347895264626,
-0.017700165510177612,
-0.014508268795907497,
0.0025024553760886192,
-0.08626808226108551,
-0.027952732518315315,
-0.019434969872236252,
-0.013644100166857243,
0.040144581347703934,
-0.050324637442827225,
0.02231724187731743,
0.02046460285782814,
0.03545871376991272,
-0.08968470990657806,
-0.009637572802603245,
-0.009399186819791794,
0.02507346123456955,
0.015004911459982395,
-0.01951606757938862,
0.013195523992180824,
-0.045037321746349335,
-0.01656176894903183,
-0.04091150313615799,
0.05304163694381714,
-0.003910550381988287,
-0.009861028753221035,
0.04290828853845596,
0.01467119250446558,
0.024868177250027657,
0.003836043644696474,
0.000022651935069006868,
-0.0005710870609618723,
0.004551170859485865,
0.039002180099487305,
-0.048486605286598206,
0.04135765880346298,
-0.01160280592739582,
-0.04135588929057121,
-0.010506927035748959,
-0.011993414722383022,
0.01589868776500225,
-0.01868739165365696,
0.011027771979570389,
-0.012601515278220177,
-0.0005361369112506509,
-0.009042762219905853,
-0.021973703056573868,
0.018416769802570343,
-0.025171823799610138,
-0.0008696584263816476,
-0.038513924926519394,
-0.0032013976015150547,
-0.04320351034402847,
-0.03170575201511383,
0.004899815656244755,
0.0021579773165285587,
-0.01782979443669319,
-0.006397235672920942,
0.02972513809800148,
0.04717627540230751,
-0.021866556257009506,
0.014273959212005138,
-0.0014621671289205551,
-0.012625977396965027,
-0.005263581406325102,
-0.007611029781401157,
0.026981020346283913,
0.022886620834469795,
0.002667803782969713,
-0.05247946456074715,
-0.030237654224038124,
0.07210447639226913,
0.0465913861989975,
-0.020016547292470932,
0.04779178649187088,
0.03755475580692291,
-0.03210035338997841,
-0.016866713762283325,
-0.028588781133294106,
-0.03264037147164345,
0.0011152609949931502,
0.02391187846660614,
0.030842453241348267,
-0.005953061860054731,
0.02295011840760708,
0.03576128929853439,
0.03917345032095909,
-0.02360451966524124,
0.04799038544297218,
0.038590122014284134,
0.005253122188150883,
0.027013180777430534,
-0.005362931173294783,
-0.04153236374258995,
0.07829401642084122,
-0.027705781161785126,
0.017892757430672646,
0.051629625260829926,
-0.00117867614608258,
0.015506762079894543,
-0.02006652019917965,
-0.030523113906383514,
-0.004749766550958157,
-0.007974575273692608,
-0.053131915628910065,
0.01626548357307911,
0.03984340652823448,
0.04181726276874542,
0.012157844379544258,
0.015560644678771496,
0.03145182132720947,
0.024149078875780106,
0.024273745715618134,
0.03270746022462845,
-0.04667499661445618,
-0.023178238421678543,
-0.035087138414382935,
-0.02529727667570114,
0.07496848702430725,
0.03437022492289543,
-0.02066350169479847,
-0.004225762560963631,
-0.02106723189353943,
0.015199163928627968,
0.01567061059176922,
0.04244779422879219,
-0.02922009490430355,
0.07290609180927277,
0.012137177400290966,
0.03236481174826622,
-0.02383279800415039,
0.02459249086678028,
0.1308286339044571,
0.06370507180690765,
0.01443649735301733,
-0.059173814952373505,
0.030517766252160072,
-0.03472839668393135,
-0.0040107169188559055,
-0.049447789788246155,
0.04232469201087952,
0.022079378366470337,
0.053466156125068665,
-0.022151507437229156,
0.054247695952653885,
0.0020737757440656424,
-0.023825202137231827,
0.04637722298502922,
-0.04561745747923851,
-0.07226183265447617,
0.009740074165165424,
0.016298256814479828,
0.014650585129857063,
-0.008033902384340763,
-0.05992854759097099,
0.01686381734907627,
-0.008941767737269402,
0.0024602399207651615,
0.0004240412381477654,
-0.008022570982575417,
0.02061879262328148,
-0.004926624707877636,
-0.042286016047000885,
-0.013140865601599216,
-0.020110903307795525,
-0.042227812111377716,
-0.0972309410572052,
-0.0029762417543679476,
0.015106655657291412,
-0.027615545317530632,
0.007326084189116955,
0.03069543093442917,
0.0202510803937912,
0.0012875695247203112,
-0.03189743682742119,
0.018826056271791458,
-0.05217978358268738,
-0.011145644821226597,
-0.023906487971544266,
0.016213955357670784,
-0.012873698957264423,
-0.010065577924251556,
-0.003968141973018646,
0.03006993979215622,
0.03081880882382393,
-0.043877728283405304,
-0.006489716935902834,
0.007965008728206158,
0.0368792749941349,
-0.020250394940376282,
-0.02094733901321888,
-0.012250479310750961,
-0.0124406972900033,
-0.01098328921943903,
0.041571035981178284,
-0.031654518097639084,
0.009151820093393326,
0.021350665017962456,
0.018432607874274254,
0.0157740730792284,
-0.018409639596939087,
0.0045396010391414165,
-0.05703523010015488,
0.01898324489593506,
-0.047902029007673264,
-0.0037679942324757576,
0.047471411526203156,
0.049316566437482834,
0.02231764607131481,
0.011823490262031555,
0.0047055077739059925,
0.006566069554537535,
-0.0022320300340652466,
0.015710050240159035,
-0.03218122199177742,
-0.011182937771081924,
-0.004139087628573179,
-0.01278705708682537,
-0.003329906612634659,
0.029533619061112404,
-0.027691014111042023,
0.00006482437311206013,
-0.029515838250517845,
-0.007470547221601009,
0.027680160477757454,
-0.02793988771736622,
-0.007578026968985796,
-0.030112717300653458,
-0.03598908334970474,
-0.0016958385240286589,
0.006375249940901995,
0.028697911649942398,
0.016397658735513687,
-0.02088664472103119,
0.011809991672635078,
0.08244314789772034,
-0.04075879231095314,
-0.017849041149020195,
0.015956517308950424,
-0.033854369074106216,
0.03220592066645622,
0.0443350113928318,
0.016190964728593826,
-0.03948085382580757,
-0.0321241095662117,
-0.0010087067494168878,
0.019571833312511444,
0.029776372015476227,
0.015972323715686798,
-0.056736767292022705,
0.015998007729649544,
-0.010119480080902576,
0.0073552438989281654,
-0.08145232498645782,
0.008829375728964806,
-0.044965121895074844,
0.03981871157884598,
-0.03215208649635315,
-0.001170032424852252,
0.00741921178996563,
0.011275804601609707,
-0.04948517680168152,
-0.029813552275300026,
0.010605717077851295,
0.013714892789721489,
-0.021924788132309914,
0.01456450019031763,
-0.00004345049092080444,
0.016814660280942917,
0.01955413445830345,
-0.022252822294831276,
-0.017187096178531647,
0.022801732644438744,
-0.06203436851501465,
-0.06344128400087357,
0.025890540331602097,
-0.02698430046439171,
0.01678401045501232,
0.03359027951955795,
-0.0002664622734300792,
-0.01879127137362957,
0.044879574328660965,
-0.02197045087814331,
-0.00524667976424098,
0.05672271549701691,
-0.025833291932940483,
-0.004779496230185032,
-0.026129188016057014,
-0.0009093633852899075,
0.01342123281210661,
-0.021787067875266075,
0.020162558183073997,
0.034402213990688324,
0.036141928285360336,
-0.0003773093339987099,
0.025578698143363,
-0.017157427966594696,
0.00440636184066534,
0.032381050288677216,
-0.016525866463780403,
-0.015468738041818142,
0.051597561687231064,
-0.06733617186546326,
0.032595474272966385,
0.028597557917237282,
-0.017674483358860016,
-0.0788520947098732,
0.00016782285820227116,
0.016960395500063896,
0.010819054208695889,
0.02442130632698536,
-0.04201669245958328,
0.023948367685079575,
0.034217339009046555,
-0.058415334671735764,
0.07866901904344559,
-0.023429835215210915,
-0.013661818578839302,
-0.03878781571984291,
-0.01688227988779545,
-0.03081119805574417,
0.08881788700819016,
0.05140174552798271,
0.029956139624118805,
0.005174433346837759,
-0.002584011759608984,
-0.0033259750343859196,
-0.019001252949237823,
-0.02592339552938938,
0.0334867499768734,
-0.021050557494163513,
0.003205778542906046,
0.030213112011551857,
-0.005509925540536642,
-0.03648056089878082,
0.037077270448207855,
0.014554143883287907,
0.008526903577148914,
0.01452441792935133,
-0.013501675799489021,
0.005418707616627216,
-0.0044567761942744255,
0.04473210126161575,
-0.03837507218122482,
-0.0015009965281933546,
0.0148782292380929,
0.030756115913391113,
-0.0009148357785306871,
0.029480144381523132,
0.004140497650951147,
-0.0034925914369523525,
-0.058924026787281036,
0.02277875319123268,
0.03273056820034981,
-0.012900575995445251,
0.03478105366230011,
0.007769367657601833,
-0.011283480562269688,
-0.002388393972069025,
-0.01657671108841896,
-0.05259096249938011,
-0.07307618856430054,
0.0019163100514560938,
0.01256751548498869,
0.017973778769373894,
0.0064124735072255135,
0.018076488748192787,
0.00783445592969656,
-0.06589656323194504,
0.008292282931506634,
0.020382050424814224,
0.02762594260275364,
-0.028288837522268295,
0.009438715875148773,
0.01281303446739912,
0.011997796595096588,
0.01232091337442398,
-0.04568789154291153,
-0.009626520797610283,
0.056194644421339035,
-0.005907826125621796,
0.02774016186594963,
0.0008903888519853354,
-0.05615619570016861,
-0.015678344294428825,
-0.06948180496692657,
0.045826587826013565,
0.017600426450371742,
-0.011225571855902672,
-0.05312376469373703,
0.0010053528239950538,
-0.015875840559601784,
0.02063506282866001,
0.019980311393737793,
-0.004088755697011948,
-0.026992078870534897,
-0.002856523497030139,
0.0056667509488761425,
0.011152905412018299,
-0.0170647781342268,
-0.02999044768512249,
0.0038499736692756414,
-0.04712701961398125,
-0.0009935398120433092,
-0.0026957131922245026,
-0.019139859825372696,
0.005245190113782883,
0.007655320223420858,
-0.008556135930120945,
0.032199256122112274,
0.02003045566380024,
-0.06027466058731079,
0.010525892488658428,
-0.021333882585167885,
-0.01024192851036787,
0.056967176496982574,
-0.009791446849703789,
-0.0062182070687413216,
0.027756022289395332,
-0.011606083251535892,
0.015831345692276955,
-0.0057442751713097095,
-0.025310097262263298,
0.013697304762899876,
-0.026492368429899216,
0.0047393785789608955,
0.06073052063584328,
-0.02542686089873314,
-0.03058139607310295,
0.06077743321657181,
-0.015262466855347157,
0.011079971678555012,
0.06023627147078514,
0.010887939482927322,
0.036057863384485245,
-0.009266930632293224,
0.002177473856136203,
0.05434982478618622,
0.006689030677080154,
0.013989303261041641,
0.03464698791503906,
0.012632596306502819,
-0.01025845855474472,
0.024188602343201637,
0.029452677816152573,
-0.011503750458359718,
0.035621095448732376,
0.027649808675050735,
0.06577466428279877,
-0.011734150350093842,
0.015379518270492554,
0.0026825147215276957,
-0.019340315833687782,
0.036084555089473724,
0.01762380823493004,
-0.015925874933600426,
0.08939239382743835,
0.010627159848809242,
-0.010694018565118313,
0.017915770411491394,
-0.0061295474879443645,
-0.05685296282172203,
0.01566985808312893,
0.00007075120811350644,
0.05021897330880165,
-0.00528167188167572,
0.0011911912588402629,
0.018082039430737495,
0.02608487196266651,
0.0476832278072834,
-0.01648663729429245,
-0.028189729899168015,
-0.027088694274425507,
-0.030277447775006294,
0.0039060800336301327,
0.0011444187257438898,
0.010655436664819717,
-0.016663551330566406,
0.03699113801121712,
0.031968239694833755,
0.05545304715633392,
-0.04269004240632057,
0.015682626515626907,
-0.01799195632338524,
0.04768002778291702,
-0.03230247646570206,
-0.02492346242070198,
-0.04072602838277817,
0.017215002328157425,
-0.01131154503673315,
-0.02759280800819397
] |
<p>Suppose that the atmosphere is composed of 21% $O_2$ and 78% $Kr$ (instead of $N_2$). Since the density of $Kr$ is greater than the density of $O_2$, the lower atmosphere (where we live) should be deprived of $O_2$. Am I right? I know that diffusion has a role here, but is there a temperature where diffusion can't overcome the fact that $O_2$ should be in the upper atmosphere?</p>
| 9,443 |
[
-0.013877829536795616,
-0.007601368241012096,
-0.012330957688391209,
-0.0015816533705219626,
0.025053774937987328,
-0.030135316774249077,
-0.047966375946998596,
-0.04166626185178757,
0.01207610685378313,
-0.05354974418878555,
0.027797823771834373,
0.0316501185297966,
0.07786842435598373,
-0.005873192101716995,
-0.007459184620529413,
-0.030908768996596336,
-0.025110416114330292,
-0.0101981982588768,
0.012146125547587872,
0.005067489575594664,
-0.01590564474463463,
0.008155194111168385,
0.0063256071880459785,
0.0018717589555308223,
-0.040920060127973557,
0.04772099107503891,
-0.0027190588880330324,
-0.009395040571689606,
0.020992077887058258,
0.014507745392620564,
0.004717973992228508,
-0.01195690967142582,
0.0183428768068552,
0.046888306736946106,
0.02954573929309845,
0.02616189233958721,
-0.01286239642649889,
0.0016604856355115771,
-0.03436630219221115,
0.03274783492088318,
-0.05801592394709587,
-0.039808232337236404,
0.014838099479675293,
-0.03145664557814598,
0.011908999644219875,
0.022110706195235252,
0.060858383774757385,
-0.029703712090849876,
0.07228507846593857,
-0.053911905735731125,
0.03506787121295929,
-0.0024754400365054607,
0.012712025083601475,
0.08031949400901794,
-0.02902662381529808,
-0.012260341085493565,
0.11243042349815369,
0.1111661046743393,
0.030532432720065117,
0.03684373199939728,
-0.029713505879044533,
-0.025661248713731766,
-0.034619856625795364,
0.016518913209438324,
-0.016474515199661255,
0.032603904604911804,
-0.02366749756038189,
-0.016613690182566643,
0.021558385342359543,
0.027911225333809853,
-0.0028824859764426947,
0.017109982669353485,
-0.007338524796068668,
-0.014390972442924976,
0.02916683442890644,
0.00974124576896429,
0.05372430756688118,
-0.008877303451299667,
0.028614215552806854,
0.016601787880063057,
-0.018210550770163536,
0.014170839451253414,
0.040780045092105865,
0.003615002613514662,
-0.02229844592511654,
0.029228223487734795,
0.08134787529706955,
-0.022489149123430252,
0.001138159423135221,
0.02816961146891117,
-0.006630368996411562,
0.02025657519698143,
0.02700527384877205,
0.00887815561145544,
0.020370816811919212,
0.026109660044312477,
-0.002626023953780532,
0.026979457587003708,
-0.03517594188451767,
-0.005327949300408363,
-0.022615524008870125,
-0.0041096690110862255,
0.04206756129860878,
0.08285900950431824,
0.03080657310783863,
-0.01844099350273609,
-0.0753789097070694,
-0.000933849427383393,
-0.009100211784243584,
-0.01700301095843315,
-0.0422188974916935,
0.02396446093916893,
-0.017271416261792183,
-0.04306793957948685,
0.02390599250793457,
-0.0015786190051585436,
-0.01627442054450512,
-0.0367811843752861,
0.024303916841745377,
0.04940146952867508,
0.04320021718740463,
0.033993229269981384,
0.02276051789522171,
-0.009410292841494083,
-0.07105112075805664,
0.06367643922567368,
0.01915060356259346,
0.007852568291127682,
-0.01619480922818184,
0.005094542633742094,
-0.03491123020648956,
-0.04074561595916748,
0.02414325624704361,
-0.002997556235641241,
0.06067435443401337,
-0.019042961299419403,
-0.0827968418598175,
-0.04291597008705139,
0.024739354848861694,
-0.020488223060965538,
0.009496166370809078,
-0.05560982599854469,
-0.01948629505932331,
0.018154649063944817,
0.048338524997234344,
0.01748756691813469,
-0.008003904484212399,
-0.024936914443969727,
0.03666667640209198,
-0.0017929746536538005,
-0.03199665620923042,
-0.01067029032856226,
0.014166276901960373,
-0.05355991795659065,
-0.0015748081495985389,
-0.08008488267660141,
0.04089968651533127,
0.02473326213657856,
0.05105765908956528,
-0.018580498173832893,
0.03499835357069969,
-0.013214703649282455,
-0.026594923809170723,
0.0015365300932899117,
0.01290440559387207,
-0.016811946406960487,
0.06284844875335693,
0.033482812345027924,
0.037384387105703354,
0.013596751727163792,
0.032935719937086105,
0.029885470867156982,
0.0027787962462753057,
0.033594515174627304,
0.05300438404083252,
-0.024929147213697433,
0.013194229453802109,
-0.032807692885398865,
-0.010005996562540531,
0.011294945143163204,
-0.04101109877228737,
0.010738401673734188,
-0.003150427248328924,
-0.008047646842896938,
0.015457013621926308,
0.04020011052489281,
0.016267288476228714,
-0.02199946716427803,
0.021385079249739647,
-0.04958266764879227,
0.004130887798964977,
-0.028294172137975693,
0.007926183752715588,
0.0005867786821909249,
-0.03665800765156746,
0.012204925529658794,
0.01390928030014038,
0.06286943703889847,
-0.029481763020157814,
-0.03850724548101425,
0.014386664144694805,
-0.012454912066459656,
0.0049610198475420475,
-0.003392221871763468,
0.0391961894929409,
0.06843510270118713,
0.027718128636479378,
-0.020207524299621582,
0.05443144589662552,
-0.0388827845454216,
-0.02559593692421913,
-0.03557150065898895,
-0.02465352602303028,
0.030276823788881302,
-0.012557882815599442,
-0.016986824572086334,
0.012139732018113136,
0.015469091944396496,
0.006126087158918381,
0.023435555398464203,
-0.023435121402144432,
0.08499684929847717,
0.07119861245155334,
0.03806174546480179,
-0.006741777993738651,
0.04381801560521126,
0.031548112630844116,
0.019263582304120064,
-0.01244379859417677,
-0.05498385801911354,
-0.011923493817448616,
-0.021875670179724693,
0.07807240635156631,
-0.010582546703517437,
-0.07247699797153473,
0.030035097151994705,
0.004773102700710297,
0.05520572140812874,
0.0545111745595932,
0.0038409193512052298,
0.011516151949763298,
-0.01017056591808796,
0.004393980372697115,
0.009702842682600021,
0.029842538759112358,
0.012013819068670273,
0.022750845178961754,
0.018739847466349602,
0.03304733335971832,
-0.03738635778427124,
-0.024256257340312004,
-0.008034691214561462,
0.02368856407701969,
0.046000003814697266,
-0.016043342649936676,
0.0031626473646610975,
0.02955903485417366,
-0.029665235430002213,
0.043048977851867676,
0.042020924389362335,
-0.007109839469194412,
0.04388023167848587,
0.01215046551078558,
-0.02543344907462597,
0.008572950959205627,
0.048375047743320465,
-0.008736365474760532,
-0.002825771691277623,
0.030456792563199997,
-0.03517874330282211,
0.010702048428356647,
-0.022671036422252655,
0.018654024228453636,
-0.011803500354290009,
0.010684879496693611,
0.04835454002022743,
-0.010747170075774193,
-0.020978786051273346,
0.00899050384759903,
-0.027701985090970993,
-0.0636867880821228,
-0.036070894449949265,
-0.030316246673464775,
0.03058283030986786,
-0.02449079602956772,
0.02343650907278061,
0.0002691853733267635,
-0.028328819200396538,
0.030187612399458885,
-0.007421575952321291,
-0.020648637786507607,
-0.015538971871137619,
-0.04976072907447815,
-0.045756202191114426,
-0.006739610806107521,
-0.03055352345108986,
-0.012297909706830978,
-0.01745542511343956,
-0.0030342862010002136,
0.06436260044574738,
-0.03239724412560463,
-0.014588059857487679,
-0.0031507888343185186,
-0.06267055869102478,
-0.059564147144556046,
-0.028643596917390823,
0.00735172163695097,
0.022335663437843323,
-0.03586800396442413,
0.03200085461139679,
0.04950788617134094,
-0.037641432136297226,
-0.0175500325858593,
-0.03238708898425102,
-0.0642085075378418,
0.031601905822753906,
-0.024231620132923126,
0.025067351758480072,
-0.025557495653629303,
-0.036975424736738205,
0.056562621146440506,
0.04005086421966553,
0.015800321474671364,
0.006932944059371948,
-0.02201934903860092,
-0.019911685958504677,
-0.021701646968722343,
0.017818262800574303,
0.015494144521653652,
-0.001254639821127057,
0.023228077217936516,
0.027968332171440125,
0.02211216278374195,
0.029205983504652977,
-0.013858838006854057,
-0.03656947612762451,
0.03228802978992462,
0.009909573942422867,
0.003318648785352707,
0.062102172523736954,
-0.004604035522788763,
-0.028519252315163612,
0.0089777372777462,
-0.013730203732848167,
0.06175948679447174,
0.06522513180971146,
-0.060582235455513,
0.01808355562388897,
-0.01223378349095583,
0.014438235200941563,
-0.053003158420324326,
0.022409942001104355,
0.029111506417393684,
-0.0031096383463591337,
0.0019073716830462217,
0.013794712722301483,
0.0321890152990818,
-0.005367793142795563,
-0.006820557173341513,
0.037811122834682465,
0.04857933893799782,
-0.03458740562200546,
-0.03456534072756767,
0.026263661682605743,
-0.02966957725584507,
0.010627925395965576,
0.04303930699825287,
-0.007818727754056454,
0.018968183547258377,
0.02263883873820305,
0.017237607389688492,
-0.027035534381866455,
-0.05751355364918709,
0.037112001329660416,
-0.07260119169950485,
-0.016170037910342216,
0.0229823999106884,
0.043393444269895554,
-0.0396089106798172,
0.03376886993646622,
-0.01305350661277771,
0.010433217510581017,
0.015648752450942993,
0.026387766003608704,
-0.06872163712978363,
0.013087774626910686,
-0.014869741164147854,
-0.04143455624580383,
-0.0011750961421057582,
-0.022183183580636978,
-0.01833960972726345,
-0.03484158217906952,
-0.018923049792647362,
-0.0016162190586328506,
0.011205951683223248,
-0.0466163270175457,
-0.010513128712773323,
-0.032271403819322586,
-0.0301115233451128,
-0.028461886569857597,
0.016456156969070435,
0.020588796585798264,
-0.029185865074396133,
0.030150292441248894,
0.05730109661817551,
-0.013301799073815346,
-0.024090277031064034,
-0.03591219708323479,
0.025683568790555,
0.0034831291995942593,
0.0023059388622641563,
0.001353808562271297,
-0.01095813699066639,
-0.03850365802645683,
0.0024090672377496958,
0.01644187606871128,
0.05918661132454872,
-0.017222939059138298,
0.016654174774885178,
-0.015149151906371117,
-0.04248455539345741,
-0.04684997722506523,
0.019228920340538025,
0.025141902267932892,
-0.036836378276348114,
0.02571602538228035,
0.014403244480490685,
-0.022740235552191734,
0.010148676112294197,
-0.008099401369690895,
0.04874755069613457,
-0.011299898847937584,
-0.010388118214905262,
-0.015586277469992638,
-0.054706450551748276,
-0.043500866740942,
0.021639280021190643,
-0.0014326447853818536,
-0.02126244269311428,
-0.01626744121313095,
-0.02337387576699257,
0.016301210969686508,
0.03375193476676941,
-0.009695894084870815,
0.0013542857486754656,
0.02884000726044178,
0.012081989087164402,
-0.03226136043667793,
-0.014943446032702923,
0.009607141837477684,
-0.025901665911078453,
0.024434290826320648,
0.001886372803710401,
0.04589220508933067,
-0.09224124997854233,
0.006314507219940424,
0.037108294665813446,
0.02413814142346382,
0.004532997030764818,
0.021250290796160698,
-0.08287955075502396,
-0.002169414423406124,
0.06929752230644226,
0.0023200889118015766,
0.04022930935025215,
-0.00031512283021584153,
-0.02411169558763504,
0.038735561072826385,
-0.04787477105855942,
0.03968627750873566,
0.0010066974209621549,
0.027940042316913605,
-0.017303606495261192,
0.014674392528831959,
0.018051713705062866,
-0.00104938552249223,
0.011452733539044857,
0.053295016288757324,
0.054341692477464676,
0.02627635933458805,
-0.03438301011919975,
-0.019989870488643646,
-0.01097822841256857,
-0.03155836835503578,
-0.03670339658856392,
-0.03825458139181137,
0.026402877643704414,
-0.028480326756834984,
0.04819726571440697,
-0.013683224096894264,
-0.04308578744530678,
0.03835825249552727,
0.01587662287056446,
-0.01611297018826008,
-0.020574484020471573,
-0.004379861522465944,
0.0624297596514225,
0.03695144131779671,
-0.000634057738352567,
0.053299568593502045,
0.04234779253602028,
0.0141905527561903,
0.043374765664339066,
-0.05741402506828308,
0.027030615136027336,
-0.05043184384703636,
0.004765210673213005,
-0.019994812086224556,
-0.018227705731987953,
0.026852380484342575,
0.033853452652692795,
0.013466975651681423,
0.013656548224389553,
-0.005641716532409191,
-0.0495980829000473,
0.0430084690451622,
0.008182147517800331,
0.009646102786064148,
0.011907757259905338,
-0.010034237056970596,
0.023352177813649178,
-0.018429992720484734,
-0.0034413214307278395,
0.022800927981734276,
0.005130093544721603,
-0.004652711097151041,
-0.013782903552055359,
-0.019139647483825684,
-0.0011312100104987621,
-0.030878322198987007,
0.008834903128445148,
-0.0192890502512455,
-0.009225488640367985,
0.038997355848550797,
-0.02347736805677414,
-0.025195840746164322,
0.013781973160803318,
-0.04605098068714142,
-0.003904963843524456,
0.024380523711442947,
0.0009731121244840324,
0.04362128674983978,
-0.01797395385801792,
0.020616650581359863,
0.01284924615174532,
0.018684132024645805,
-0.13047990202903748,
-0.01866825856268406,
0.013869775459170341,
0.013934138230979443,
-0.005085418466478586,
-0.052303049713373184,
-0.023502416908740997,
-0.018925856798887253,
-0.03803929686546326,
0.008557183668017387,
0.06458273530006409,
0.006791599560528994,
-0.029394913464784622,
-0.013805604539811611,
0.03314170986413956,
0.05617545172572136,
-0.026695935055613518,
-0.006943065207451582,
-0.005881862714886665,
-0.00501462584361434,
-0.003890021238476038,
-0.011215145699679852,
0.024505391716957092,
-0.03094780631363392,
-0.011391186155378819,
-0.02509246952831745,
-0.032185617834329605,
0.0224912129342556,
-0.01708552986383438,
-0.06457771360874176,
0.06275186687707901,
0.014264370314776897,
0.013137641362845898,
-0.031561464071273804,
0.03700355067849159,
-0.02944362722337246,
0.01525859534740448,
-0.03281553089618683,
0.031320247799158096,
-0.032054562121629715,
-0.01218917965888977,
0.0008213439723476768,
0.009865287691354752,
0.004600942600518465,
0.004929531831294298,
0.11024853587150574,
-0.023142468184232712,
-0.01687614992260933,
0.019583508372306824,
-0.00819355808198452,
0.037070345133543015,
0.008041419088840485,
-0.022173915058374405,
0.04501761496067047,
0.012300618924200535,
-0.031844038516283035,
-0.0550452321767807,
-0.05319798365235329,
0.00004885220914729871,
0.05297795310616493,
-0.07313354313373566,
0.0017989391926676035,
0.015274434350430965,
-0.007895084097981453,
0.043447960168123245,
-0.03505552187561989,
-0.012207134626805782,
0.03805416449904442,
-0.03630542755126953,
0.015213378705084324,
0.025628576055169106,
0.00960729643702507,
0.02861538901925087,
0.050626080483198166,
0.015907585620880127,
0.0156715027987957,
0.0071544162929058075,
0.026631757616996765,
-0.007745504844933748,
-0.001109137898311019,
-0.03347422555088997,
0.027332715690135956,
-0.041549183428287506,
0.05196104198694229,
0.006634167395532131,
-0.012842335738241673,
0.05870624631643295,
0.009623334743082523,
-0.003329468658193946,
-0.030444910749793053,
-0.05119955167174339,
-0.023232286795973778,
0.007140829227864742,
-0.03262894228100777,
0.01282740943133831,
0.03155248239636421,
-0.004338221158832312,
0.0753505676984787,
0.011121822521090508,
-0.00034307478927075863,
-0.028862785547971725,
-0.029698586091399193,
-0.013436955399811268,
0.011508991941809654,
-0.023941554129123688,
0.011417709290981293,
-0.02753949910402298,
-0.06024135276675224,
0.011105077341198921,
-0.008206553757190704,
0.002679147059097886,
0.026072902604937553,
0.022966504096984863,
0.031333908438682556,
0.06346087902784348,
0.005621384829282761,
0.02113490179181099,
-0.005265573970973492,
0.0334697850048542,
0.10949882119894028,
0.06231968477368355,
0.015513834543526173,
-0.04032522067427635,
-0.022176815196871758,
-0.013315660879015923,
-0.03425174951553345,
-0.04139312356710434,
0.001277986099012196,
-0.009317117743194103,
0.004109622444957495,
0.02845194935798645,
0.053683627396821976,
-0.004129179287701845,
-0.00969894789159298,
0.03151679411530495,
-0.037153586745262146,
-0.011559231206774712,
0.014897978864610195,
-0.012478104792535305,
-0.005290831904858351,
0.0015011625364422798,
-0.05208761990070343,
0.03907610848546028,
-0.01428102608770132,
0.011302893981337547,
-0.0447157621383667,
-0.009080521762371063,
0.021916452795267105,
-0.021021651104092598,
-0.04148300737142563,
0.004157313145697117,
0.014134662225842476,
-0.025264836847782135,
-0.034644000232219696,
-0.03499261662364006,
-0.007764947600662708,
-0.04033615067601204,
0.017916394397616386,
0.02084910310804844,
0.030521728098392487,
0.02761763520538807,
0.007293056696653366,
0.037572991102933884,
-0.010415662080049515,
0.014270263724029064,
-0.008999241515994072,
0.01695851981639862,
-0.04076923057436943,
-0.010865913704037666,
0.030538201332092285,
0.019645286723971367,
-0.028777599334716797,
-0.02830815128982067,
0.0020009528379887342,
-0.005023627076297998,
0.04822733625769615,
-0.007368937134742737,
-0.027983224019408226,
-0.03439478203654289,
-0.0011182348243892193,
0.0316697359085083,
-0.015307288616895676,
-0.019220059737563133,
0.006568719167262316,
-0.009493258781731129,
0.002029688097536564,
0.04833880066871643,
-0.004786711651831865,
-0.020867226645350456,
-0.03857852891087532,
0.04018561914563179,
-0.03523300960659981,
-0.004739625845104456,
0.013997097499668598,
0.020038072019815445,
0.06170224770903587,
0.029436806216835976,
-0.02765776216983795,
-0.036530669778585434,
-0.05497168377041817,
0.015519209206104279,
0.0060864901170134544,
-0.037480082362890244,
-0.02482343465089798,
-0.016426032409071922,
-0.04690851643681526,
0.021331800147891045,
0.0005545750609599054,
0.01248024683445692,
0.017159247770905495,
0.03280038386583328,
0.01349202822893858,
-0.0728345662355423,
-0.034669630229473114,
-0.026857785880565643,
-0.05413006618618965,
-0.005873799789696932,
0.0006947786896489561,
0.04595396667718887,
-0.00032299364102073014,
-0.007680116221308708,
-0.01699034869670868,
0.0369843989610672,
-0.051112595945596695,
0.022286994382739067,
-0.010539638809859753,
-0.03804580494761467,
0.000031388037314172834,
0.002212150488048792,
-0.006168188061565161,
-0.01019332930445671,
-0.021058818325400352,
-0.03480803593993187,
0.005103781819343567,
-0.011210473254323006,
-0.02015618234872818,
-0.0010633229976519942,
0.011798298917710781,
-0.011182606220245361,
0.007121790666133165,
-0.018582407385110855,
0.006475257687270641,
-0.058837465941905975,
-0.002483643824234605,
-0.0015489127254113555,
0.006974625401198864,
-0.0054619391448795795,
0.04088504984974861,
-0.021178945899009705,
0.01652117446064949,
0.019382664933800697,
0.03465423360466957,
0.006017464678734541,
-0.008144580759108067,
0.002341879764571786,
0.005492411553859711,
0.06120879948139191,
-0.06597992032766342,
-0.014031680300831795,
0.03376568481326103,
-0.0011857154313474894,
-0.08233896642923355,
-0.006449481938034296,
-0.020308857783675194,
0.03498176857829094,
0.011704198084771633,
0.015379219315946102,
-0.05530141294002533,
0.08506113290786743,
0.006621816195547581,
0.014519410207867622,
0.0008055237703956664,
-0.003648898331448436,
0.005206016823649406,
-0.031725723296403885,
-0.007826784625649452,
-0.005966749507933855,
-0.010456779040396214,
0.02444796822965145,
0.024506080895662308,
-0.015962617471814156,
0.02233763411641121,
-0.015052268281579018,
-0.028858255594968796,
0.0034534966107457876,
-0.0017126451712101698,
0.0008181019802577794,
0.02553916536271572,
0.044906135648489,
-0.021556857973337173,
0.006258130539208651,
0.05209172144532204,
-0.02363460510969162,
-0.09819994121789932,
-0.01441575400531292,
0.03614417836070061,
-0.0016937474720180035,
0.015862658619880676,
-0.04172760993242264,
0.021558798849582672,
0.044800009578466415,
-0.05054313689470291,
-0.021085862070322037,
-0.02111743576824665,
-0.014973782934248447,
-0.04430248960852623,
-0.01579526625573635,
-0.03797030448913574,
0.006216481793671846,
0.022696079686284065,
0.05213379114866257,
-0.014671145007014275,
0.04063898324966431,
0.01437732856720686,
-0.033212706446647644,
-0.004883434623479843,
-0.011645752005279064,
0.011445190757513046,
-0.01364908181130886,
0.04302319511771202,
-0.009323248639702797,
0.010470007546246052,
0.041985224932432175,
-0.027084413915872574,
0.006682427600026131,
-0.01630588248372078,
-0.015146761201322079,
-0.019637564197182655,
0.03053302876651287,
0.0026109761092811823,
0.005101426970213652,
-0.008275652304291725,
0.02299807220697403,
-0.018605461344122887,
-0.006364569999277592,
-0.03460913151502609,
-0.0010009336983785033,
0.04549199715256691,
-0.03269634023308754,
-0.04006420448422432,
0.03004373237490654,
-0.0017877042992040515,
0.01132130529731512,
0.03565981239080429,
0.013798419386148453,
0.010810963809490204,
-0.01253697369247675,
-0.02664347179234028,
-0.0314759723842144,
-0.005808818619698286,
-0.0009726086282171309,
-0.014081710949540138,
-0.03362568840384483,
-0.028312068432569504,
-0.009041241370141506,
-0.00634228577837348,
0.031171299517154694,
0.014286911115050316,
0.013139369897544384,
-0.03391892835497856,
-0.024145247414708138,
-0.03346933797001839,
-0.02247411198914051,
-0.009351854212582111,
-0.02816421166062355,
-0.042813997715711594,
0.04218459874391556,
-0.0004877976607531309,
0.017078807577490807,
-0.014532787725329399,
-0.04151962324976921,
-0.018282296136021614,
-0.05323263257741928,
0.006333719938993454,
-0.03834239020943642,
0.022590428590774536,
-0.035441335290670395,
-0.0039853681810200214,
-0.006724563892930746,
0.0070487153716385365,
0.03677232936024666,
0.048574045300483704,
0.03629831224679947,
0.016862915828824043,
-0.010680045001208782,
0.0274190716445446,
-0.044312234967947006,
0.07417762279510498,
0.033327698707580566,
-0.033937565982341766,
-0.0013518176274374127,
-0.02180681936442852,
-0.030949655920267105,
-0.008001814596354961,
0.023938581347465515,
0.017687544226646423,
0.0007635439978912473,
0.03246905654668808,
0.01611555553972721,
0.04355776309967041,
0.00647146487608552,
-0.005213900003582239,
0.036512818187475204,
-0.028429927304387093,
-0.013596131466329098,
0.022450588643550873,
-0.009110772982239723,
-0.05109728127717972,
0.031553156673908234,
-0.018354780972003937,
-0.023567112162709236,
-0.012507891282439232,
-0.0053229196928441525,
0.007188888266682625,
-0.017934603616595268,
-0.01434904895722866,
0.05000309646129608,
-0.0545266754925251,
0.01497554499655962,
0.028232896700501442,
0.02233569324016571,
0.04508643597364426,
-0.0015829686308279634,
-0.004494211636483669,
0.024293741211295128,
0.013828976079821587,
-0.012418722733855247,
0.034330662339925766,
0.04060777649283409,
-0.017793184146285057,
0.010306457988917828,
-0.018597513437271118,
0.008634894154965878,
0.03592405095696449,
0.016240844503045082,
0.022867437452077866,
-0.02663298323750496,
-0.010108593851327896,
0.03471614420413971,
0.03963303565979004,
0.0019384935731068254,
0.00008377624180866405,
-0.0007744177710264921,
0.048486582934856415,
-0.007889697328209877,
0.021231763064861298,
-0.04966239631175995,
0.01724875159561634,
-0.012628997676074505,
0.03430664539337158,
0.030905194580554962,
-0.008457549847662449,
-0.01465553417801857,
0.020278843119740486,
-0.010621181689202785,
0.008145472034811974,
0.02405153028666973,
-0.026134658604860306,
0.026149338111281395,
-0.04465726763010025,
-0.0387735515832901,
-0.01660342700779438,
0.029428835958242416,
-0.023981967940926552,
-0.019316405057907104,
0.011139988899230957,
0.0374978706240654,
0.03562923148274422,
0.00574899697676301,
-0.020664218813180923,
-0.005564987659454346,
0.04837040230631828,
-0.06884817034006119,
-0.019674183800816536,
-0.025598354637622833,
0.012031997554004192,
-0.03496886044740677,
-0.02830359898507595
] |
<p>I found this <a href="http://www.matweb.com/search/datasheet.aspx?matguid=638937fc52ca4683bc0c3f18f54f5a24" rel="nofollow">link where it described steel with UTS at 5200 MPa (755kpsi)</a>, is this the strongest steel or just a typo because value is seemed to be unreal?</p>
| 9,444 |
[
-0.0201142355799675,
-0.06112143397331238,
-0.03358302265405655,
-0.028700312599539757,
0.05887964740395546,
0.03956412896513939,
-0.05194869264960289,
-0.0626121535897255,
0.009000685065984726,
-0.05169552564620972,
0.05600832402706146,
0.06969127058982849,
0.02466205693781376,
0.03635126352310181,
-0.02454095147550106,
0.007921567186713219,
0.0120383957400918,
-0.006103558465838432,
-0.008753578178584576,
-0.034364040940999985,
0.006108216475695372,
-0.01821264438331127,
-0.021506275981664658,
0.02858416922390461,
-0.013301127590239048,
0.030701348558068275,
-0.002280679764226079,
0.010346844792366028,
0.03003481775522232,
0.006515558809041977,
-0.03032376617193222,
-0.04583926498889923,
0.022507350891828537,
-0.012619883753359318,
0.05912075191736221,
0.010161877609789371,
-0.04174298793077469,
-0.06307076662778854,
-0.019492166116833687,
0.04877063259482384,
0.02790246531367302,
-0.016020415350794792,
0.0038771647959947586,
0.04227304458618164,
-0.000028967755497433245,
0.03378641605377197,
0.0096463393419981,
-0.011407044716179371,
0.017841804772615433,
-0.04209025204181671,
0.03231094032526016,
-0.025746392086148262,
0.05668044090270996,
-0.0034420553129166365,
-0.002270442433655262,
0.01433661300688982,
0.04028506204485893,
0.05538042634725571,
0.00663580559194088,
-0.05403754860162735,
0.019794344902038574,
0.009815093129873276,
-0.00626984192058444,
-0.016736365854740143,
-0.00842292420566082,
0.08395925164222717,
-0.0323590524494648,
-0.035384368151426315,
0.019832255318760872,
0.002735752612352371,
-0.0013526290422305465,
0.015439098700881004,
0.022089224308729172,
-0.008589928038418293,
-0.0031257544178515673,
-0.05033658444881439,
0.021197650581598282,
0.02040153183043003,
0.007590858265757561,
0.05093177780508995,
-0.024415070191025734,
0.04681392014026642,
0.015521274879574776,
0.024977508932352066,
0.028809795156121254,
-0.0013970915460959077,
0.061705026775598526,
0.02905641496181488,
0.02084466814994812,
0.04975259304046631,
-0.018562283366918564,
0.007463227491825819,
0.032608985900878906,
0.0130960363894701,
-0.002772618317976594,
-0.053332407027482986,
0.0006607326795347035,
0.061179570853710175,
-0.023013440892100334,
-0.00899386778473854,
0.032452262938022614,
-0.015969600528478622,
0.012033014558255672,
0.0748547911643982,
0.03908202797174454,
-0.036739759147167206,
0.005506066605448723,
0.0018250471912324429,
0.009529266506433487,
0.020849833264946938,
-0.06288418173789978,
-0.01083721686154604,
-0.011936250142753124,
0.009953114204108715,
0.002134531270712614,
-0.05778719112277031,
0.0028518219478428364,
0.02682238072156906,
0.011961781419813633,
0.007905391976237297,
0.013944095931947231,
-0.02463074028491974,
0.037991855293512344,
-0.03406849503517151,
-0.06011470407247543,
0.051018793135881424,
0.02350989729166031,
0.009092706255614758,
-0.020373238250613213,
0.04830101504921913,
-0.030884554609656334,
0.0036919007543474436,
0.017675403505563736,
-0.012859762646257877,
0.05200415477156639,
-0.030882200226187706,
-0.11585067212581635,
-0.08490140736103058,
0.06013340502977371,
-0.002697342075407505,
-0.033119622617959976,
-0.06723204255104065,
0.006691354792565107,
0.05321764945983887,
0.053656965494155884,
0.013378770090639591,
0.029319601133465767,
-0.021032556891441345,
0.007482312619686127,
0.01958315446972847,
-0.03319906070828438,
-0.02041320502758026,
0.011014253832399845,
-0.05033763125538826,
0.03248074650764465,
-0.054441362619400024,
-0.009917382150888443,
0.007398391608148813,
-0.004150854889303446,
-0.04321705922484398,
0.008481292985379696,
-0.02161857672035694,
0.01088345143944025,
-0.008461691439151764,
-0.036462560296058655,
-0.005386668723076582,
0.07497376203536987,
-0.03577795997262001,
0.028178207576274872,
0.04365856572985649,
0.011988824233412743,
-0.0005855413037352264,
0.03368170186877251,
-0.006791766732931137,
0.029715055599808693,
-0.031428851187229156,
-0.013310268521308899,
-0.04010411724448204,
0.012177846394479275,
0.009161374531686306,
-0.050002675503492355,
-0.027181364595890045,
-0.04854840785264969,
0.037495870143175125,
0.015299945138394833,
0.05438968911767006,
0.004999098833650351,
-0.008617130108177662,
0.023717712610960007,
-0.05865347757935524,
-0.03520562872290611,
0.005996765103191137,
0.03931400179862976,
-0.010566442273557186,
0.0000618631747784093,
0.004984485451132059,
-0.03151317313313484,
0.008480390533804893,
-0.028574779629707336,
0.01799633540213108,
0.023282771930098534,
0.019452638924121857,
0.025970809161663055,
0.003593854373320937,
0.023855216801166534,
0.03379537910223007,
0.00808791909366846,
-0.014389255084097385,
0.01319324504584074,
-0.023541301488876343,
0.00001534030889160931,
0.02943984419107437,
-0.0022738859988749027,
-0.004152442328631878,
-0.012999161146581173,
-0.04082249850034714,
0.024048514664173126,
-0.017819266766309738,
-0.0002092588401865214,
-0.01972077786922455,
-0.02459205500781536,
0.08961065858602524,
0.006463414989411831,
0.00990055501461029,
-0.01618349552154541,
0.014521750621497631,
-0.009575989097356796,
0.04212349280714989,
0.002062771003693342,
0.03882316127419472,
-0.06032460555434227,
0.02225414291024208,
0.04796101897954941,
0.03975609317421913,
-0.07213965803384781,
0.00042922477587126195,
0.010195056907832623,
-0.016653746366500854,
0.03740741312503815,
-0.0017539691179990768,
-0.04708335921168327,
-0.04453517869114876,
0.05620542913675308,
0.021238282322883606,
0.03864952549338341,
0.04777853563427925,
-0.0025371902156621218,
0.04573027417063713,
0.027316782623529434,
-0.03714725002646446,
0.016782283782958984,
0.03305048868060112,
-0.0298541858792305,
0.0163500364869833,
0.007032373454421759,
-0.04192180931568146,
0.042326875030994415,
-0.04073715582489967,
0.021241407841444016,
0.03713766112923622,
0.014402927830815315,
0.009714280255138874,
-0.04226062819361687,
-0.014211306348443031,
0.01890670694410801,
-0.00850851833820343,
-0.006186744663864374,
-0.04360603541135788,
0.016412869095802307,
-0.04444317892193794,
0.00530915567651391,
-0.02571033127605915,
0.029853826388716698,
-0.024427881464362144,
-0.021308232098817825,
0.01928003318607807,
-0.002504001371562481,
0.02454238571226597,
-0.02276078797876835,
0.011623913422226906,
-0.007223252672702074,
-0.03453400731086731,
-0.012146258726716042,
-0.004451297223567963,
-0.07376187294721603,
0.01454098429530859,
0.012439925223588943,
-0.03777303174138069,
0.03448333963751793,
0.021761387586593628,
-0.0501675046980381,
0.04446601867675781,
0.0002451397303957492,
-0.023215042427182198,
-0.013810357078909874,
0.0038715864066034555,
0.03258194401860237,
-0.007955358363687992,
0.007955055683851242,
0.0027451233472675085,
-0.015537429600954056,
-0.005052315071225166,
0.012288510799407959,
-0.03692449629306793,
-0.0063173542730510235,
-0.010281320661306381,
-0.010159672237932682,
0.02223055437207222,
-0.01226535253226757,
0.04878174886107445,
0.052722569555044174,
-0.029548656195402145,
0.006260840222239494,
-0.013577657751739025,
-0.013221140019595623,
0.0344703271985054,
-0.03139572590589523,
0.04193103313446045,
-0.011630117893218994,
-0.049710940569639206,
0.057135649025440216,
-0.0014867221470922232,
-0.06780005991458893,
-0.04068294167518616,
0.00524377403780818,
0.008309189230203629,
-0.03158556669950485,
0.023824656382203102,
0.010332424193620682,
-0.002129865810275078,
-0.0015418275725096464,
-0.019663365557789803,
0.04460405185818672,
0.06518686562776566,
-0.003659400623291731,
-0.003718259045854211,
0.0027186055667698383,
-0.023571237921714783,
-0.00657690828666091,
0.03884086012840271,
0.029121240600943565,
-0.028680747374892235,
0.023118585348129272,
0.0011983693111687899,
0.03698759898543358,
0.04223862290382385,
-0.0226389579474926,
0.05617471784353256,
0.03866523876786232,
0.024480000138282776,
-0.06119098141789436,
0.02204759232699871,
-0.02984345518052578,
-0.035998862236738205,
-0.0219598188996315,
0.04011965170502663,
0.01183632854372263,
0.010090416297316551,
-0.015535447746515274,
0.02622498944401741,
-0.00522608170285821,
0.020281946286559105,
0.010273434221744537,
-0.0019510792335495353,
-0.008573301136493683,
0.019646650180220604,
0.0005028212908655405,
-0.030445262789726257,
0.06159490719437599,
0.011144964024424553,
0.04943355545401573,
0.03141174092888832,
0.00480440491810441,
0.003292548004537821,
-0.06920146197080612,
-0.01632826402783394,
-0.029895707964897156,
0.03402414172887802,
0.01027920562773943,
0.028698764741420746,
0.02801324427127838,
0.004701780155301094,
0.007815063931047916,
-0.007239244878292084,
-0.07941196858882904,
0.009802468121051788,
-0.03221159800887108,
-0.020956648513674736,
-0.011694406159222126,
-0.07365463674068451,
-0.058022208511829376,
-0.03343651443719864,
-0.014680813997983932,
0.016675269231200218,
-0.00020568854233715683,
-0.06757231801748276,
0.013481952250003815,
0.013228016905486584,
0.022967716678977013,
0.004093679133802652,
-0.0008997726836241782,
0.0039833649061620235,
-0.012827759608626366,
0.013044806197285652,
0.009072499349713326,
-0.03233901411294937,
-0.0016774891410022974,
-0.013193679973483086,
0.048069149255752563,
0.03375823795795441,
0.03555930778384209,
-0.004391215741634369,
0.028750283643603325,
0.007262413389980793,
-0.022285975515842438,
-0.009676981717348099,
0.050853367894887924,
0.04393833503127098,
-0.003552062436938286,
-0.054410532116889954,
-0.007250157184898853,
-0.00794137455523014,
0.018243826925754547,
0.024420365691184998,
-0.005582453683018684,
0.004554675426334143,
0.008456145413219929,
-0.019170142710208893,
-0.02671610750257969,
0.0360381081700325,
0.03864717856049538,
-0.0016218021046370268,
0.006485348101705313,
-0.061496030539274216,
-0.04820450022816658,
-0.04265589639544487,
-0.04792463406920433,
0.0259667057543993,
0.05586995556950569,
-0.02534669265151024,
0.019107641652226448,
0.027020860463380814,
0.019998060539364815,
-0.036670077592134476,
0.03750012442469597,
0.007724865805357695,
-0.013115709647536278,
-0.010046789422631264,
-0.017632482573390007,
0.004001733381301165,
0.028838125988841057,
0.05469319596886635,
0.026507331058382988,
-0.0074077206663787365,
-0.06667917966842651,
-0.010972538031637669,
0.025358716025948524,
0.051407791674137115,
-0.03298754617571831,
0.0015599075704813004,
-0.0020988218020647764,
-0.010048487223684788,
0.016176801174879074,
-0.015494736842811108,
0.07561065256595612,
-0.00672556646168232,
-0.007556273136287928,
-0.010890590026974678,
-0.010739306919276714,
-0.0011881627142429352,
-0.02858157642185688,
0.008725298568606377,
0.04311178997159004,
-0.02483164146542549,
0.011631178669631481,
0.026903467252850533,
-0.002833019709214568,
0.0020868307910859585,
0.01649286411702633,
-0.03038090653717518,
-0.015933280810713768,
-0.0031372623052448034,
0.061776235699653625,
-0.030626744031906128,
-0.06727384775876999,
-0.014753245748579502,
-0.024658450856804848,
-0.0044547501020133495,
-0.01621335558593273,
-0.024354038760066032,
-0.027949610725045204,
0.07473720610141754,
0.034245751798152924,
0.010505392216145992,
-0.007622986100614071,
-0.020481975749135017,
0.05713636428117752,
0.025706110522150993,
-0.021222533658146858,
0.01888193190097809,
0.03871626779437065,
0.0016139608342200518,
-0.01577475480735302,
-0.021086435765028,
0.055974140763282776,
-0.045953087508678436,
-0.02577248401939869,
-0.017898177728056908,
0.040779754519462585,
-0.029469791799783707,
0.007322746329009533,
-0.00859076902270317,
0.045929763466119766,
-0.041375257074832916,
-0.02171594463288784,
0.018035726621747017,
0.009047354571521282,
0.0006558269960805774,
-0.0046675619669258595,
-0.04990200698375702,
0.01120880525559187,
-0.030401650816202164,
-0.033563677221536636,
-0.04279864579439163,
-0.01741662621498108,
0.022014033049345016,
0.03766418993473053,
0.0006517329020425677,
0.01680399477481842,
-0.01707446202635765,
-0.03753897175192833,
0.027315780520439148,
-0.02263331227004528,
0.059528060257434845,
-0.014190591871738434,
0.023228894919157028,
0.03284303471446037,
-0.030250435695052147,
0.01515424344688654,
0.03316715732216835,
0.02623419277369976,
0.03395535424351692,
-0.07021268457174301,
0.08114184439182281,
-0.012774101458489895,
0.025907002389431,
-0.03080110251903534,
-0.06656625121831894,
0.0531328059732914,
0.028566721826791763,
-0.03384563699364662,
-0.014296463690698147,
0.006781286559998989,
0.006853591650724411,
-0.01045353151857853,
-0.009358449839055538,
0.04224640503525734,
0.00030509757925756276,
-0.010848802514374256,
0.01415958534926176,
-0.021878479048609734,
0.061748769134283066,
0.006136783864349127,
-0.01619323343038559,
0.014516950584948063,
0.017751865088939667,
-0.006255350075662136,
-0.012017006054520607,
0.026873094961047173,
-0.01223325077444315,
0.016875535249710083,
0.008261836133897305,
0.008363844826817513,
0.06127764284610748,
0.004914841614663601,
0.03280577436089516,
0.024509118869900703,
0.024600759148597717,
-0.0030010610353201628,
-0.011590206995606422,
0.03806855157017708,
-0.0012867652112618089,
-0.012367418967187405,
0.005392757244408131,
0.0004046644316986203,
0.0015575714642181993,
-0.0012141451006755233,
-0.007642450276762247,
-0.013091481290757656,
0.008269847370684147,
-0.01510102953761816,
0.07148928195238113,
-0.010135121643543243,
0.01619151420891285,
-0.046570904552936554,
-0.060560692101716995,
0.012876988388597965,
0.03281619772315025,
0.039240870624780655,
-0.008451413363218307,
-0.02922217734158039,
-0.018344677984714508,
-0.02344687096774578,
-0.03495977073907852,
0.0368877574801445,
0.06843635439872742,
-0.015166142955422401,
0.015942594036459923,
0.03674696385860443,
-0.041455429047346115,
0.01899801939725876,
-0.016945622861385345,
-0.03449174389243126,
0.01455921120941639,
-0.01727556250989437,
0.018775589764118195,
0.00037209325819276273,
0.0043884627521038055,
0.019457271322607994,
0.015923308208584785,
0.014964019879698753,
-0.03117929957807064,
0.020590679720044136,
-0.0022709565237164497,
0.01901404745876789,
-0.031878940761089325,
-0.041389383375644684,
0.06896603107452393,
-0.009846491739153862,
0.019542507827281952,
0.006956758908927441,
0.018671246245503426,
0.037459228187799454,
0.003037784481421113,
0.04064999148249626,
-0.05245330557227135,
-0.03138110041618347,
-0.024146515876054764,
0.021280866116285324,
0.01813732460141182,
-0.017666153609752655,
-0.014151383191347122,
0.02574111521244049,
0.024831833317875862,
0.025698741897940636,
0.03838033601641655,
-0.03808772563934326,
-0.056965939700603485,
0.02905656024813652,
-0.030314037576317787,
-0.029748842120170593,
0.0197715125977993,
0.020636696368455887,
-0.02398640103638172,
0.028512952849268913,
-0.02792692743241787,
-0.008719589561223984,
-0.0330020897090435,
0.05010443553328514,
0.028748292475938797,
0.0790177658200264,
-0.027880964800715446,
0.0602167546749115,
0.008530518971383572,
0.011500304564833641,
0.12519018352031708,
0.029141655191779137,
0.027490317821502686,
-0.026050478219985962,
0.024208955466747284,
0.005263135302811861,
-0.015428277663886547,
0.007171637378633022,
-0.02615758404135704,
-0.005080802831798792,
0.00728919031098485,
0.04839197173714638,
0.042054709047079086,
0.011956916190683842,
0.04334811121225357,
0.032316215336322784,
-0.011900771409273148,
0.012949036434292793,
0.020666230469942093,
0.01686529442667961,
0.0226867888122797,
-0.040260110050439835,
-0.03437194973230362,
0.01704900898039341,
0.016360238194465637,
-0.04289001598954201,
-0.02583211474120617,
-0.030178358778357506,
0.04890558496117592,
0.03707973659038544,
-0.002710445085540414,
-0.024252356961369514,
-0.0038810973055660725,
0.04339848458766937,
-0.06001448258757591,
-0.026951104402542114,
0.014076542109251022,
-0.001665653777308762,
0.023703934624791145,
0.0010611622128635645,
0.026805447414517403,
0.00460516894236207,
0.02737601287662983,
0.02453779987990856,
-0.03186516463756561,
0.012514562346041203,
-0.023962536826729774,
-0.02988159842789173,
-0.0038111815229058266,
-0.003514588577672839,
0.029057050123810768,
0.007168823853135109,
0.012217032723128796,
-0.029885360971093178,
-0.056581560522317886,
-0.012159264646470547,
0.023619042709469795,
-0.0038543471600860357,
-0.05185757204890251,
-0.04127857834100723,
0.030951419845223427,
0.0033158273436129093,
-0.01643902063369751,
0.006040798034518957,
-0.02761918492615223,
0.03638656437397003,
-0.00829146709293127,
0.032269954681396484,
-0.011957901529967785,
-0.018984587863087654,
-0.0067202565260231495,
-0.008948487229645252,
-0.027682244777679443,
-0.02068663015961647,
0.004452730994671583,
0.013441921211779118,
0.028950506821274757,
0.02168397419154644,
0.0010332510573789477,
-0.03660587593913078,
-0.05688014253973961,
0.036908406764268875,
-0.029514264315366745,
-0.010993743315339088,
-0.025551529601216316,
0.001359948655590415,
0.013205747120082378,
0.021679768338799477,
-0.03229841589927673,
0.024503955617547035,
-0.01915118098258972,
0.0007890055421739817,
0.007100838236510754,
-0.056058116257190704,
-0.00996148306876421,
-0.0032829991541802883,
-0.055533792823553085,
0.02312856912612915,
0.028881510719656944,
0.036582816392183304,
0.047690872102975845,
-0.0025531775318086147,
0.011662296019494534,
0.009933516383171082,
-0.022014658898115158,
-0.015462558716535568,
0.00007808811642462388,
-0.037276145070791245,
-0.002526561263948679,
-0.014107524417340755,
0.013592136092483997,
-0.013940863311290741,
-0.02391868084669113,
-0.026915637776255608,
-0.07745419442653656,
-0.0004775344277732074,
0.03069986402988434,
-0.019738145172595978,
0.026897531002759933,
-0.02328874170780182,
-0.03213043883442879,
-0.00782242976129055,
-0.02315787971019745,
-0.0036188133526593447,
-0.03785817697644234,
0.04389490559697151,
0.021889984607696533,
-0.048576731234788895,
0.004111793823540211,
0.007147977594286203,
0.02069307118654251,
-0.005604085978120565,
0.006158838514238596,
-0.00719304196536541,
-0.036849331110715866,
0.027318347245454788,
0.01030360721051693,
0.051156964153051376,
-0.028365666046738625,
0.01046775933355093,
0.01219752337783575,
-0.00914955884218216,
-0.029866918921470642,
0.056403499096632004,
-0.02281692624092102,
-0.0065283807925879955,
-0.023120902478694916,
0.021339667961001396,
-0.020809100940823555,
0.07797528058290482,
-0.024241596460342407,
0.02990671992301941,
0.035403717309236526,
-0.007759431377053261,
0.025645511224865913,
0.027592629194259644,
-0.047492124140262604,
0.019665876403450966,
-0.021766841411590576,
0.03805449232459068,
0.0015588653041049838,
0.02633097767829895,
0.006658733356744051,
-0.009213319979608059,
0.0051217772997915745,
-0.0064039272256195545,
0.034630946815013885,
-0.005436642095446587,
0.04196939617395401,
0.025838255882263184,
-0.008399349637329578,
0.009775745682418346,
0.0008215759880840778,
-0.01487460546195507,
-0.08125118911266327,
-0.012443621642887592,
-0.023875346407294273,
-0.02159304730594158,
0.02503933571279049,
-0.04661254584789276,
0.04360781982541084,
0.02908368781208992,
-0.04815724492073059,
-0.009491203352808952,
-0.03340467810630798,
-0.05814516916871071,
-0.06015143543481827,
-0.0508369579911232,
-0.008800317533314228,
0.03671037033200264,
-0.014876852743327618,
0.009711562655866146,
0.03454350680112839,
0.03168422356247902,
-0.04857013747096062,
-0.0008660139283165336,
-0.005372174549847841,
0.026820940896868706,
0.0066377995535731316,
-0.01566549763083458,
0.03937738016247749,
-0.031313225626945496,
-0.06474895030260086,
0.030176039785146713,
-0.0551600381731987,
-0.000051385886763455346,
-0.018735913559794426,
0.02290913462638855,
-0.004068436566740274,
0.043069224804639816,
0.027174441143870354,
-0.0192685816437006,
-0.005812535528093576,
-0.022270577028393745,
-0.021332215517759323,
0.028030699118971825,
0.006726137828081846,
-0.0018772582989186049,
0.002161250216886401,
-0.009162578731775284,
-0.01519168820232153,
0.018657952547073364,
-0.02513451687991619,
-0.007098023314028978,
0.003472817363217473,
-0.014239553362131119,
0.031179284676909447,
-0.04539579898118973,
-0.013151769526302814,
-0.02988281473517418,
0.005409957841038704,
0.028435731306672096,
-0.016684608533978462,
0.002201787196099758,
0.014690798707306385,
-0.011920531280338764,
-0.0236173365265131,
0.015718957409262657,
0.0026734196580946445,
-0.04284968227148056,
-0.038759637624025345,
-0.026674684137105942,
0.020388489589095116,
-0.041680023074150085,
-0.022206798195838928,
0.00692729651927948,
-0.009837441146373749,
0.05204983800649643,
0.08124300092458725,
-0.005699264816939831,
0.05604797229170799,
-0.001335197128355503,
0.00391393294557929,
-0.0751844272017479,
0.027672845870256424,
-0.007699810434132814,
-0.024380458518862724,
0.003665575524792075,
-0.03550778701901436,
0.05087912827730179,
0.004318401217460632,
0.037076640874147415,
-0.030074067413806915,
0.005829318892210722,
0.02095496840775013,
-0.008145701140165329,
-0.009419684298336506,
-0.038195401430130005,
0.02487114816904068,
0.006231842562556267,
-0.06366247683763504,
-0.014522486366331577,
-0.01288063358515501,
0.013902693055570126,
0.025528306141495705,
0.024677276611328125,
-0.013807474635541439,
-0.011957306414842606,
-0.010601506568491459,
0.01591268926858902,
0.02789492718875408,
-0.017059803009033203,
-0.0374918095767498,
0.09887737035751343,
0.0005666006472893059,
-0.019220218062400818,
-0.013564564287662506,
0.004991919733583927,
-0.03594451770186424,
0.004762100987136364,
-0.0186047051101923,
0.017115455120801926,
0.00022201355022843927,
-0.00798626895993948,
0.03162218630313873,
-0.08070720732212067,
0.0030840348917990923,
0.053711023181676865,
-0.04810713976621628,
-0.020744139328598976,
0.045257568359375,
0.009997798129916191,
0.01987001672387123,
0.022536154836416245,
0.04535181075334549,
-0.0198788084089756,
-0.05817202106118202,
-0.0084632383659482,
0.025901146233081818,
0.02081693708896637,
0.024258127436041832,
-0.013050786219537258,
0.04574095457792282,
-0.05585407465696335,
-0.006583848502486944,
0.015419850125908852,
0.027927624061703682,
-0.04928965866565704,
-0.018095621839165688,
-0.009678798727691174,
-0.03705456480383873,
0.02703162468969822,
0.03582535311579704,
-0.02277342788875103,
0.07091176509857178,
-0.050919242203235626,
-0.023860909044742584,
-0.055226054042577744,
0.02291777729988098,
0.02118445187807083,
-0.02331637218594551,
0.05682918429374695,
-0.00001746307680150494,
-0.01983059197664261,
-0.009348358027637005,
0.02461237832903862,
0.024556515738368034,
0.039304204285144806,
-0.03741239756345749,
-0.011275863274931908,
-0.05191681161522865,
0.017228316515684128,
-0.029224930331110954,
-0.010915599763393402,
-0.01036702748388052,
0.030352693051099777,
0.02554558403789997,
-0.012623623013496399,
-0.016587719321250916,
-0.03728293254971504,
-0.014896738342940807,
-0.014389736577868462,
0.019481239840388298,
-0.07058341056108475,
0.025321371853351593,
-0.028437277302145958,
0.028359798714518547,
-0.06038464233279228,
-0.012351998127996922
] |
<p>My question concerns the following definition</p>
<blockquote>
<p><strong>Definition:</strong> The <em>timelike</em> (resp. null) <em>generic condition</em> in GR is fulfilled if
$$u_{[\alpha} R_{\rho]\mu \nu [\sigma}u_{\beta]}u^\mu u^\nu \ne 0$$
at some point of each timelike (resp. null) geodesic with tangent vector $\vec u$. ($R_{\rho \mu \nu \sigma}$ is the Riemann curvature tensor.)</p>
</blockquote>
<p>It is written in many places that this is the right condition to impose if one wants to assume that every freely falling (or light) particle encounters some form of matter or radiation in its history (or something to that effect).</p>
<p>But I don't understand, why the particular tensor $u_{[\alpha} R_{\rho]\mu \nu [\sigma}u_{\beta]}u^\mu u^\nu \ne 0$ is the right thing to look at in this context. For example, why don't we assume that $R_{\rho\mu\nu\sigma}u^\mu u^\nu \ne 0$ at some point? Or maybe that $R_{\mu \nu}u^\mu u^\nu \ne 0$, or perhaps that $G_{\mu \nu} u^\mu u^\nu \ne 0$?</p>
<p>I'm guessing that the last two condition could be too weak to derive the singularity theorems we want, so that something stronger must be assumed.
But the expression $u_{[\alpha} R_{\rho]\mu \nu [\sigma}u_{\beta]}u^\mu u^\nu \ne 0$ really looks a bit strange to me (i.e. I don't understand its significance). Could someone explain to me why this is the right condition to impose? </p>
<p>Thanks!</p>
| 9,445 |
[
-0.03145298734307289,
-0.031108494848012924,
0.029758261516690254,
-0.058687105774879456,
0.025645485147833824,
0.039958368986845016,
-0.028711779043078423,
-0.028355924412608147,
-0.022802632302045822,
-0.04289978742599487,
0.020224090665578842,
-0.0035987969022244215,
0.0592401884496212,
0.014752227813005447,
0.039067186415195465,
0.002934283809736371,
-0.021618114784359932,
-0.010130654089152813,
-0.03254655376076698,
-0.061649125069379807,
0.03210216760635376,
0.055649738758802414,
-0.019528644159436226,
0.01908198744058609,
0.01203646045178175,
0.011279414407908916,
0.0003397157706785947,
0.01756930537521839,
-0.010152043774724007,
0.04292986914515495,
-0.04265714809298515,
-0.001160909770987928,
-0.046937014907598495,
-0.011303693056106567,
0.016165079548954964,
0.023111866787075996,
-0.029176846146583557,
-0.00531113101169467,
-0.028842883184552193,
0.001108180615119636,
-0.01956949010491371,
-0.024547498673200607,
-0.012364133261144161,
0.0497756190598011,
-0.05580886825919151,
0.020979061722755432,
0.04371330887079239,
0.010417716577649117,
0.03563537076115608,
-0.03652121499180794,
0.05260148644447327,
0.002837973413988948,
0.04180785268545151,
0.011383297853171825,
0.0000929635571083054,
-0.025855740532279015,
0.05605318769812584,
0.06610891968011856,
-0.029854105785489082,
-0.04337158799171448,
-0.008157252334058285,
0.0010622953996062279,
0.0017330991104245186,
-0.013736563734710217,
-0.0035224235616624355,
0.05870192497968674,
0.004197334870696068,
0.014240949414670467,
0.038817085325717926,
-0.03534706309437752,
-0.006175311282277107,
-0.049186985939741135,
-0.00946821365505457,
0.029244625940918922,
-0.0027119102887809277,
0.003263557329773903,
-0.01168035063892603,
-0.012556008994579315,
0.051697809249162674,
0.012152628973126411,
-0.01589610055088997,
0.026514694094657898,
0.03854449465870857,
0.0023721964098513126,
-0.014185153879225254,
0.001625416916795075,
0.07699935883283615,
-0.025144262239336967,
0.022216621786355972,
0.0201118104159832,
0.006503755692392588,
-0.018443915992975235,
0.006248190999031067,
-0.0049038114957511425,
-0.04998926818370819,
0.014556070789694786,
0.0026268032379448414,
0.0036153653636574745,
-0.0214368999004364,
-0.008983222767710686,
-0.01699332520365715,
-0.03451073169708252,
0.0058541144244372845,
0.06547443568706512,
0.021533994004130363,
-0.01630355417728424,
-0.06306236982345581,
-0.011944510973989964,
-0.02500213496387005,
-0.04495779052376747,
-0.045852310955524445,
0.016457101330161095,
-0.046378668397665024,
-0.015480528585612774,
0.002333397278562188,
-0.02287299558520317,
0.026569249108433723,
-0.01060541719198227,
0.060041673481464386,
0.06637486070394516,
0.06253741681575775,
0.011116335168480873,
0.024127481505274773,
-0.03030778467655182,
-0.08432648330926895,
0.03656243160367012,
0.05777391791343689,
-0.0020262855105102062,
-0.032190658152103424,
-0.0041110580787062645,
0.019566483795642853,
0.022694354876875877,
-0.0008768586558289826,
0.02467491663992405,
0.04445540904998779,
-0.04346034303307533,
-0.07736474275588989,
-0.049230869859457016,
0.028978386893868446,
0.016086604446172714,
-0.013821221888065338,
-0.04585733637213707,
0.0031815827824175358,
0.02644106186926365,
0.08358974009752274,
-0.010973702184855938,
0.0475742481648922,
0.013560814782977104,
0.02193809673190117,
0.0129281897097826,
-0.0214487724006176,
0.006527964491397142,
-0.02122812718153,
-0.017605148255825043,
-0.025630973279476166,
-0.08005217462778091,
0.01357253547757864,
0.017507309094071388,
-0.0009861192665994167,
-0.00048768898705020547,
0.0960337221622467,
-0.000208480836590752,
0.032618939876556396,
0.026921000331640244,
-0.03379342705011368,
-0.02263716235756874,
0.09340175986289978,
0.044448066502809525,
0.04322946444153786,
0.04616478085517883,
0.048006802797317505,
0.05680014193058014,
0.003894709749147296,
0.0477030873298645,
0.03464847803115845,
-0.042398180812597275,
-0.010006626136600971,
0.024703452363610268,
-0.017079155892133713,
0.016170520335435867,
-0.043703388422727585,
0.008011030964553356,
-0.03093697316944599,
-0.018316693603992462,
-0.012389821000397205,
0.0443534180521965,
-0.00008552240615244955,
-0.009668809361755848,
-0.00041559358942322433,
-0.028928641229867935,
0.017833108082413673,
-0.04246099293231964,
0.004075734410434961,
0.010707457549870014,
-0.025721976533532143,
0.01708034798502922,
-0.009625840000808239,
-0.008065014146268368,
-0.01676117815077305,
-0.026265418156981468,
-0.01264273002743721,
0.04018689692020416,
-0.0017307617235928774,
-0.025522977113723755,
0.009285819716751575,
0.012881191447377205,
0.011573083698749542,
0.030495282262563705,
0.029703756794333458,
0.008709770627319813,
-0.017378591001033783,
0.022450454533100128,
0.020627576857805252,
0.020967604592442513,
0.028765132650732994,
0.037391092628240585,
0.00793424528092146,
-0.020238438621163368,
-0.01838728040456772,
0.018331145867705345,
-0.05346505716443062,
0.02944314107298851,
0.04370436072349548,
0.021064886823296547,
0.000114129223220516,
0.06358484923839569,
0.01669587381184101,
0.0167511235922575,
-0.010439612902700901,
-0.028050513938069344,
-0.014127111993730068,
0.016464777290821075,
0.02975386753678322,
0.04506683722138405,
-0.029800627380609512,
0.035759467631578445,
0.013659557327628136,
0.03994857147336006,
-0.0302981398999691,
0.024348638951778412,
0.007910767570137978,
-0.051011260598897934,
0.03240804001688957,
0.0011151727521792054,
0.016837410628795624,
-0.014689267612993717,
0.003149272408336401,
-0.005125068593770266,
0.01579246111214161,
-0.03580382093787193,
-0.0074607739225029945,
0.05368220433592796,
-0.015516230836510658,
-0.009257124736905098,
0.01453067921102047,
0.001112612197175622,
0.02956067956984043,
-0.005123873706907034,
0.03744684159755707,
0.0606292225420475,
-0.00099062395747751,
-0.028299426659941673,
-0.061793453991413116,
-0.031253982335329056,
0.040844179689884186,
0.0205718744546175,
0.016848212108016014,
-0.02574829012155533,
0.021323829889297485,
-0.06444413214921951,
-0.021940046921372414,
-0.02174234762787819,
-0.03585048392415047,
-0.01939125917851925,
0.005828761495649815,
0.035626448690891266,
0.007026858627796173,
0.016390589997172356,
-0.0464116632938385,
-0.023353511467576027,
0.0030948540661484003,
0.017168372869491577,
-0.005397452507168055,
0.0591152086853981,
-0.050056662410497665,
0.03120153211057186,
-0.02602800913155079,
-0.0004668832989409566,
0.05668078735470772,
0.003983996342867613,
0.0036680849734693766,
0.02772429771721363,
-0.018313799053430557,
-0.039128921926021576,
-0.047127850353717804,
-0.017766671255230904,
-0.0041864546947181225,
-0.013774107210338116,
-0.0207169558852911,
0.043966785073280334,
0.0007033894071355462,
-0.042160339653491974,
0.03009878657758236,
-0.037605270743370056,
-0.06736040860414505,
-0.005369673017412424,
0.010044504888355732,
-0.00130756595171988,
-0.03940169885754585,
0.05239841714501381,
0.044243648648262024,
-0.04789089784026146,
-0.020735539495944977,
-0.029245518147945404,
-0.056824516505002975,
0.026160530745983124,
-0.03217172995209694,
0.025181831791996956,
0.042003288865089417,
-0.057387832552194595,
0.06413747370243073,
0.02386154793202877,
-0.020321398973464966,
-0.053206413984298706,
0.018992654979228973,
-0.017180321738123894,
-0.026124095544219017,
-0.02427457645535469,
-0.012056936509907246,
0.012098968960344791,
0.005491337738931179,
0.041595276445150375,
0.05343356356024742,
0.0031743331346660852,
0.039788100868463516,
-0.010804384015500546,
-0.007146686781197786,
0.010857051238417625,
-0.01631360501050949,
0.015806734561920166,
0.03195358067750931,
0.028154730796813965,
0.0030014277435839176,
-0.020517798140645027,
0.03512811288237572,
0.037967704236507416,
-0.04461212083697319,
0.022136516869068146,
0.0062434496358036995,
0.0034068298991769552,
0.01781132072210312,
0.028574174270033836,
-0.027284318581223488,
-0.033783335238695145,
-0.014730948954820633,
-0.002070704475045204,
0.0457579530775547,
-0.04370848089456558,
-0.01279598567634821,
0.021267328411340714,
0.01143256388604641,
-0.03034706972539425,
-0.017994247376918793,
-0.015173940919339657,
-0.021264037117362022,
0.02426277846097946,
-0.007787104230374098,
0.02751029096543789,
0.04634473845362663,
0.02897624857723713,
0.0352768748998642,
-0.005923642311245203,
-0.04233307018876076,
-0.04532591253519058,
-0.04272550344467163,
0.03473363816738129,
0.0014325242955237627,
0.045771583914756775,
-0.01097103115171194,
0.021615514531731606,
0.0576692596077919,
0.011848332360386848,
0.003694705432280898,
-0.012279038317501545,
-0.07991229742765427,
0.014451557770371437,
-0.03345067799091339,
-0.033361952751874924,
0.01124608889222145,
0.0008247445803135633,
-0.013970483094453812,
-0.029158713296055794,
-0.017679434269666672,
-0.01521373726427555,
0.015887701883912086,
-0.05491046607494354,
0.006364984903484583,
-0.048363253474235535,
-0.055097829550504684,
-0.0076085906475782394,
0.0360739566385746,
0.03221483901143074,
-0.005891967564821243,
-0.011003266088664532,
0.015635665506124496,
-0.009634017013013363,
0.011703495867550373,
-0.0042485687881708145,
0.030038172379136086,
-0.012937589548528194,
-0.007215452380478382,
0.02726343832910061,
0.010688715614378452,
0.0020133364014327526,
0.009106729179620743,
0.049301184713840485,
0.051993876695632935,
-0.013336744159460068,
0.0016198778757825494,
-0.013709820806980133,
-0.051744624972343445,
-0.01983785070478916,
-0.00046715937787666917,
0.06919689476490021,
0.04342355579137802,
-0.04104132950305939,
0.01446213386952877,
-0.0036433921195566654,
0.00926152616739273,
0.04006548970937729,
0.06097281724214554,
-0.01640160009264946,
-0.024670472368597984,
-0.05156534165143967,
-0.01571926474571228,
-0.01008143462240696,
0.01969384402036667,
0.020089969038963318,
-0.009472083300352097,
-0.05736679211258888,
0.0005801471997983754,
-0.009045801125466824,
-0.012625297531485558,
-0.01837659254670143,
-0.008355376310646534,
0.03342423215508461,
0.0059923748485744,
0.015305133536458015,
-0.018660468980669975,
0.0018541499739512801,
0.04755999892950058,
0.06334978342056274,
0.015442882664501667,
0.004644028376787901,
-0.020828355103731155,
0.001429992844350636,
0.03593264892697334,
-0.006651651579886675,
0.009310852736234665,
-0.03291623294353485,
-0.060507651418447495,
0.0004132864996790886,
0.03517748415470123,
-0.008155276998877525,
0.03431234508752823,
0.008566795848309994,
0.015706632286310196,
-0.0035176014062017202,
-0.041467275470495224,
-0.011892256326973438,
0.03787295147776604,
0.011729453690350056,
0.013922149315476418,
-0.02814018726348877,
0.009642492979764938,
-0.009454555809497833,
0.005271678324788809,
-0.010364089161157608,
0.040058817714452744,
0.02225448191165924,
-0.019794370979070663,
0.008643770590424538,
0.019235264509916306,
-0.02454645372927189,
-0.09512216597795486,
-0.01925589144229889,
0.006949845235794783,
-0.003744169371202588,
0.03318164125084877,
-0.017637640237808228,
-0.029845673590898514,
0.03455350548028946,
0.023820072412490845,
0.0028736544772982597,
0.04204120859503746,
-0.039677299559116364,
0.02086501382291317,
0.03293224051594734,
0.007784243673086166,
0.0368766225874424,
0.013244402594864368,
0.03261556848883629,
0.008653120137751102,
-0.048298612236976624,
0.033574823290109634,
-0.05513247475028038,
0.0036416982766240835,
-0.03707651421427727,
-0.003766425186768174,
-0.029985060915350914,
0.027547912672162056,
-0.031725313514471054,
0.01085177157074213,
0.04847051575779915,
-0.05397781357169151,
-0.00310942973010242,
0.03504246100783348,
0.02865549549460411,
-0.00893309060484171,
0.02127857320010662,
0.034153711050748825,
-0.040491923689842224,
0.030928554013371468,
0.025932805612683296,
0.0006830685306340456,
0.000533499289304018,
0.06076406314969063,
0.0010848715901374817,
0.019963253289461136,
0.01723208837211132,
-0.018350213766098022,
0.0154741071164608,
-0.04988355189561844,
0.04759911447763443,
-0.0034809827338904142,
-0.010334194637835026,
0.028328295797109604,
-0.003915573004633188,
0.018560079857707024,
-0.02003076672554016,
-0.034978948533535004,
0.039283934980630875,
-0.0735255777835846,
0.013876756653189659,
0.04318315163254738,
0.0021460263524204493,
-0.09245533496141434,
-0.03347267955541611,
0.048432931303977966,
-0.003673939034342766,
-0.014102390967309475,
-0.009259046986699104,
0.03583899512887001,
-0.049726590514183044,
-0.018770325928926468,
-0.025574341416358948,
0.06636890023946762,
0.01229126751422882,
-0.042615193873643875,
-0.0007913503213785589,
0.09562786668539047,
0.04083804041147232,
-0.048510611057281494,
0.006107137072831392,
0.031208107247948647,
0.0070741381496191025,
0.009403601288795471,
-0.006634518038481474,
0.05730125680565834,
0.003002067096531391,
-0.0387427844107151,
-0.034103550016880035,
-0.02684159390628338,
-0.018286921083927155,
0.002344895852729678,
0.01026456244289875,
0.033770523965358734,
0.011886619962751865,
-0.009585070423781872,
-0.032101068645715714,
0.011253423057496548,
-0.011152215301990509,
0.008699740283191204,
-0.02204989269375801,
0.009075864218175411,
-0.0018041599541902542,
-0.05149751156568527,
0.07227736711502075,
-0.047209419310092926,
0.022605828940868378,
-0.0009486099006608129,
0.0341719351708889,
-0.0011571601498872042,
-0.01854042522609234,
-0.009095520712435246,
-0.02119339071214199,
0.021096261218190193,
0.014005640521645546,
-0.004427709151059389,
0.028716983273625374,
-0.024834753945469856,
-0.04027467966079712,
-0.011567799374461174,
-0.045319121330976486,
0.05461609363555908,
0.09449467062950134,
-0.023419352248311043,
0.03524794429540634,
-0.0031723163556307554,
-0.049698736518621445,
-0.015579206869006157,
-0.042398497462272644,
-0.01966155506670475,
-0.008874773979187012,
0.0026453121099621058,
0.02217211201786995,
-0.018923187628388405,
-0.021581005305051804,
0.01941971480846405,
0.028161076828837395,
-0.026644760742783546,
0.03442348539829254,
0.019554389640688896,
0.022350287064909935,
0.017797254025936127,
-0.030571334064006805,
-0.027560286223888397,
0.050834592431783676,
-0.0478086844086647,
0.030229413881897926,
0.022676169872283936,
-0.01263949554413557,
0.0016163717955350876,
0.02915225736796856,
0.05108356103301048,
-0.020685818046331406,
-0.0006517949514091015,
-0.04345697909593582,
0.011325827799737453,
0.025310857221484184,
-0.030891675502061844,
-0.017486462369561195,
-0.00409010611474514,
0.038958143442869186,
-0.0034026633948087692,
0.030059801414608955,
0.02161088027060032,
-0.06497618556022644,
-0.017315572127699852,
-0.05021471902728081,
-0.03273792937397957,
0.05717843770980835,
0.010083417408168316,
-0.004522927571088076,
0.005995011888444424,
-0.01675289496779442,
-0.003782752202823758,
0.042897094041109085,
0.044653888791799545,
-0.010073590092360973,
0.04256346449255943,
0.02565460279583931,
0.0004810122773051262,
-0.019156619906425476,
-0.03742913529276848,
0.11759372055530548,
0.06527362018823624,
0.007893597707152367,
-0.032121431082487106,
-0.0020941137336194515,
-0.019104227423667908,
0.017119457945227623,
-0.05351920798420906,
0.05885300785303116,
-0.009261155501008034,
0.018431076779961586,
0.00640104990452528,
0.04628758877515793,
-0.004371805116534233,
-0.009427073411643505,
0.02851119451224804,
-0.06116499751806259,
-0.026167500764131546,
-0.0006286456482484937,
0.021837148815393448,
0.008834397420287132,
0.007939565926790237,
-0.02121022716164589,
0.022629177197813988,
0.008771034888923168,
0.0031596594490110874,
-0.0074263219721615314,
-0.012704557739198208,
0.000673428934533149,
-0.017229078337550163,
-0.03908872231841087,
0.01027300301939249,
0.0071074203588068485,
0.004914821591228247,
-0.020144015550613403,
-0.014870441518723965,
0.0054268562234938145,
-0.03498157113790512,
0.03217403218150139,
0.014525242149829865,
-0.019986195489764214,
-0.010247540660202503,
0.022830745205283165,
0.028243759647011757,
-0.00731352623552084,
-0.00008917110972106457,
-0.012062429450452328,
0.06617075204849243,
-0.04229570925235748,
-0.005647594109177589,
0.008470941334962845,
-0.0072879428043961525,
0.000027815549401566386,
-0.05768170952796936,
-0.0013153698528185487,
-0.02233177237212658,
0.00743156997486949,
0.0185000691562891,
-0.0069991000927984715,
0.026441039517521858,
0.0148936090990901,
0.02521923929452896,
0.03402617573738098,
-0.01632259041070938,
-0.02084636315703392,
0.0039175087586045265,
-0.03436475992202759,
0.035469383001327515,
-0.0307646244764328,
0.01021567452698946,
-0.014982584863901138,
-0.0022292404901236296,
-0.058779265731573105,
-0.02177129127085209,
0.027695557102560997,
-0.0033858385868370533,
0.053419165313243866,
-0.008929218165576458,
0.02858809009194374,
-0.014697486534714699,
-0.0638868510723114,
0.035484429448843,
-0.027332652360200882,
-0.042979784309864044,
-0.05098220705986023,
0.005691693164408207,
-0.0077559384517371655,
0.04645700752735138,
-0.01746179535984993,
-0.037662506103515625,
-0.01507494319230318,
0.03871937468647957,
-0.0048674955032765865,
-0.025792120024561882,
-0.062260791659355164,
0.004420539364218712,
-0.004516362678259611,
0.004540241323411465,
-0.021410688757896423,
-0.031952887773513794,
0.014301257207989693,
0.012753788381814957,
0.0036026062443852425,
0.05726759508252144,
0.0007146354764699936,
-0.01366578321903944,
0.019376488402485847,
-0.007687725592404604,
0.02913089655339718,
0.03776312246918678,
0.0012229963904246688,
-0.04705008864402771,
-0.013219641521573067,
-0.01923424005508423,
-0.012979907914996147,
-0.008288543671369553,
-0.007050319109112024,
-0.015288660302758217,
0.02790861204266548,
-0.0028863216284662485,
0.005541928578168154,
-0.035054322332143784,
0.0037390810903161764,
-0.04261121526360512,
0.038996659219264984,
-0.006794822867959738,
-0.03143822401762009,
-0.01192342210561037,
0.01993439719080925,
0.013242128305137157,
-0.06663531810045242,
0.010983859188854694,
0.031278692185878754,
-0.02268940769135952,
0.023937776684761047,
0.030240023508667946,
-0.009400743059813976,
0.04741629958152771,
0.014490442350506783,
-0.021389203146100044,
0.002210004022344947,
-0.038136716932058334,
-0.05130991339683533,
0.018033774569630623,
0.03584814444184303,
0.0017890508752316236,
-0.0013167767319828272,
-0.013654188252985477,
-0.014518502168357372,
0.06910007447004318,
-0.015060867182910442,
-0.0186334028840065,
-0.01682356372475624,
-0.03632209822535515,
-0.048677608370780945,
-0.015067381784319878,
0.04854067042469978,
0.00430747726932168,
0.01287241280078888,
0.016478421166539192,
0.00806136429309845,
-0.03825097158551216,
-0.021799668669700623,
0.004818592686206102,
-0.009518146514892578,
0.006491135340183973,
0.01153472252190113,
0.03016253560781479,
0.02938006818294525,
0.058717548847198486,
-0.07621926814317703,
0.02302706055343151,
0.01110944151878357,
0.0021624930668622255,
-0.0892297774553299,
-0.026846982538700104,
0.040978167206048965,
0.015371954999864101,
0.06140872463583946,
-0.04609568789601326,
0.03669533133506775,
0.015959199517965317,
-0.01769753359258175,
-0.019837675616145134,
-0.024432681500911713,
0.013167664408683777,
-0.01610187254846096,
-0.00537308631464839,
-0.032498862594366074,
0.05149329453706741,
0.03759341686964035,
0.023868652060627937,
-0.012942609377205372,
-0.012900126166641712,
-0.024248840287327766,
-0.04555504769086838,
-0.02973075956106186,
0.04763403162360191,
-0.02103140577673912,
-0.029168175533413887,
0.09574248641729355,
0.013898800127208233,
-0.05203443020582199,
0.009137379005551338,
0.007157344836741686,
-0.0065693981014192104,
0.015174864791333675,
0.04280979186296463,
0.01742328703403473,
0.003177221165969968,
0.04465135186910629,
-0.009077676571905613,
-0.0041392166167497635,
0.0074143134988844395,
-0.010250379331409931,
0.016383051872253418,
0.013526729308068752,
-0.01542688813060522,
-0.016494277864694595,
-0.04190590977668762,
-0.023572726175189018,
0.004264262970536947,
-0.030243823304772377,
-0.049387749284505844,
0.004728073254227638,
0.02176564559340477,
0.005919193848967552,
-0.024769926443696022,
0.024782732129096985,
-0.019504791125655174,
0.013552050106227398,
0.044079650193452835,
0.016352035105228424,
0.013623781502246857,
0.030755355954170227,
-0.029385540634393692,
-0.04351735860109329,
-0.006120732985436916,
-0.013146376237273216,
-0.011993658728897572,
-0.06215273216366768,
0.00004899712803307921,
-0.03022882714867592,
-0.014357141219079494,
-0.009466814808547497,
-0.02298877201974392,
-0.03398139774799347,
0.02687142603099346,
0.02596292831003666,
0.013616044074296951,
-0.0064044673927128315,
-0.018991641700267792,
-0.011790706776082516,
-0.06898542493581772,
0.017172202467918396,
-0.0108186025172472,
0.019404130056500435,
-0.019015783444046974,
-0.023973658680915833,
-0.019957641139626503,
0.03987725451588631,
0.05182301625609398,
-0.02502327412366867,
-0.014812246896326542,
0.04855848476290703,
0.031850654631853104,
0.009495706297457218,
-0.009601305238902569,
0.03396960720419884,
0.03144827485084534,
-0.02606075070798397,
0.016129568219184875,
0.0009354216745123267,
0.015567712485790253,
0.02446700818836689,
0.023912426084280014,
-0.027947813272476196,
0.03147308900952339,
0.011829613707959652,
-0.018337611109018326,
0.04862320423126221,
0.029712481424212456,
-0.017136558890342712,
0.025627467781305313,
0.0006602069479413331,
0.04528190568089485,
0.015200474299490452,
-0.005945687182247639,
-0.05133744701743126,
0.024209048599004745,
0.003050009021535516,
-0.0806535854935646,
-0.027945736423134804,
-0.0070351348258554935,
0.02118113823235035,
-0.04335343465209007,
-0.012108652852475643,
0.03056981973350048,
-0.05356526002287865,
-0.021979808807373047,
0.01855447143316269,
0.006765470374375582,
0.04215694218873978,
0.014825248159468174,
-0.011508521623909473,
0.023531043902039528,
-0.030464407056570053,
0.019436078146100044,
0.04233477637171745,
0.04137706756591797,
0.0010259205009788275,
-0.0009123487398028374,
0.031371500343084335,
-0.0295509472489357,
-0.030326470732688904,
-0.007157751824706793,
0.04398993030190468,
-0.019765658304095268,
-0.02888168953359127,
0.02930109202861786,
-0.01773756928741932,
-0.01787937805056572,
0.00992908701300621,
-0.006230177357792854,
0.09311357885599136,
-0.024640943855047226,
0.004102368373423815,
-0.009247981011867523,
-0.028578026220202446,
-0.00932985171675682,
0.06699776649475098,
0.024056309834122658,
0.06391493231058121,
-0.007920586504042149,
0.0025393678806722164,
-0.02885308861732483,
-0.0418764129281044,
0.04499008506536484,
-0.02819094993174076,
-0.024486390873789787,
0.02234480157494545,
-0.020755408331751823,
-0.0013693697983399034,
-0.03384719043970108,
-0.02671053633093834,
-0.01879534311592579,
-0.0005034070927649736,
-0.008426843211054802,
0.017773080617189407,
-0.037979207932949066,
-0.018237095326185226,
-0.06645794212818146,
0.025277813896536827,
-0.06475425511598587,
0.010416178032755852,
-0.028507370501756668,
0.018954051658511162,
-0.029723035171628,
0.024396849796175957
] |
<p>I came across the word "absorption grating" in a review article. I googled it tried to find out what it means but couldn't. Could you explain it to me? </p>
| 9,446 |
[
-0.03642153739929199,
-0.02541842870414257,
-0.00611394876614213,
-0.027522588148713112,
0.026020975783467293,
0.02022184245288372,
0.004139470402151346,
-0.016641348600387573,
0.01242362055927515,
-0.05871853604912758,
0.05447384715080261,
0.037709642201662064,
0.04939896613359451,
0.010592632927000523,
-0.007098108995705843,
0.00441392045468092,
-0.003775332123041153,
-0.0024586813524365425,
-0.007137920241802931,
-0.03141670301556587,
-0.028358574956655502,
0.019704576581716537,
-0.003447527065873146,
0.007037984672933817,
-0.013853236101567745,
0.028270011767745018,
0.02656089887022972,
0.006769909523427486,
0.050892069935798645,
0.017322227358818054,
-0.03529408201575279,
0.023576298728585243,
-0.023055139929056168,
0.022316766902804375,
0.01655784621834755,
-0.021590543910861015,
-0.016676312312483788,
-0.02141338586807251,
-0.04524028301239014,
0.00978374108672142,
-0.01740257814526558,
-0.008717956952750683,
-0.020795762538909912,
0.04792962968349457,
-0.012726763263344765,
-0.021431397646665573,
-0.0007658965769223869,
-0.06517727673053741,
0.01846524141728878,
-0.06831689924001694,
0.06962686032056808,
-0.015956487506628036,
0.043088365346193314,
0.022370390594005585,
-0.016927625983953476,
0.04518235847353935,
0.06765523552894592,
0.09198010712862015,
-0.04281410947442055,
-0.05145792290568352,
-0.019155701622366905,
0.003096546744927764,
-0.023631570860743523,
-0.014617454260587692,
-0.029779892414808273,
0.030807605013251305,
0.029649430885910988,
-0.04231081157922745,
0.07470255345106125,
0.04685182496905327,
-0.015695566311478615,
0.002390878275036812,
0.038872119039297104,
0.007407213095575571,
-0.02826719544827938,
-0.06351780891418457,
-0.0065195742063224316,
0.030513586476445198,
0.04224833846092224,
0.024574555456638336,
0.011656601913273335,
0.018162185326218605,
-0.029578033834695816,
0.006855195853859186,
-0.03392219915986061,
-0.007439711596816778,
0.08780942857265472,
-0.023371808230876923,
0.018127575516700745,
0.019598180428147316,
-0.03078479692339897,
0.0337834358215332,
0.009844697080552578,
0.032305434346199036,
-0.029799235984683037,
-0.0023762702476233244,
-0.011478516273200512,
0.0524037629365921,
-0.007178238593041897,
-0.03793366625905037,
0.016199393197894096,
0.0038836682215332985,
0.03110123611986637,
0.06367126107215881,
-0.011137190274894238,
-0.03330925852060318,
-0.0416262187063694,
0.04837702587246895,
0.01123142521828413,
0.009542967192828655,
-0.033379826694726944,
-0.028099440038204193,
0.02105068229138851,
-0.00505788391456008,
0.029031746089458466,
0.013115487061440945,
0.013424650765955448,
0.03502389416098595,
0.02346642315387726,
0.10609594732522964,
0.029499869793653488,
-0.016101719811558723,
0.02618170529603958,
0.024399127811193466,
-0.10064690560102463,
0.04011521488428116,
0.015254685655236244,
0.006278499495238066,
-0.05030667036771774,
0.028982704505324364,
-0.013188785873353481,
-0.027126029133796692,
0.014155331067740917,
-0.0056142061948776245,
0.006969983223825693,
-0.023083116859197617,
-0.08858885616064072,
-0.059165600687265396,
0.04099154472351074,
-0.005184180568903685,
0.011162047274410725,
-0.05565904080867767,
-0.007230027113109827,
0.008398321457207203,
0.07405044883489609,
0.048101756721735,
0.009994572028517723,
-0.0025160424411296844,
0.014112317934632301,
0.04738100245594978,
-0.024863217025995255,
-0.030445318669080734,
0.007498133461922407,
-0.04241674020886421,
0.01204704586416483,
-0.05719708651304245,
0.011582487262785435,
0.049219030886888504,
-0.029454275965690613,
-0.028717266395688057,
0.03724946454167366,
-0.017989404499530792,
-0.0016988572897389531,
0.01673181727528572,
-0.02737814001739025,
-0.0384783037006855,
0.05795156955718994,
0.012144018895924091,
0.0014122157590463758,
0.042156461626291275,
0.026875128969550133,
0.02864825911819935,
-0.0016426952788606286,
0.04881959408521652,
-0.01023449283093214,
0.010046180337667465,
0.00611543282866478,
0.00353818666189909,
0.006043889559805393,
0.010173100046813488,
-0.013984509743750095,
-0.03338483348488808,
0.04250789433717728,
0.03724411502480507,
0.002099924022331834,
0.040169209241867065,
-0.01379720214754343,
-0.03608426824212074,
0.016192423179745674,
-0.05315840616822243,
0.031462181359529495,
-0.03529816120862961,
0.03024730272591114,
-0.014391491189599037,
-0.0009226335678249598,
0.010856945998966694,
0.000465211778646335,
-0.02983170934021473,
-0.02746717818081379,
-0.054522570222616196,
-0.008596814237535,
-0.039107099175453186,
0.013209493830800056,
-0.032353442162275314,
0.013721675612032413,
0.06411665678024292,
0.014319557696580887,
0.0064604212529957294,
0.06469777226448059,
-0.049704134464263916,
-0.009055438451468945,
0.00981720257550478,
0.004013175144791603,
0.043305668979883194,
-0.040478724986314774,
-0.011349047534167767,
0.002829338423907757,
-0.006266226060688496,
-0.008473668247461319,
0.029070505872368813,
-0.060219597071409225,
0.04256386682391167,
0.033862534910440445,
0.013453096151351929,
-0.005516510456800461,
0.03312103450298309,
-0.02062707208096981,
-0.008584610186517239,
-0.0024513360112905502,
-0.03386690467596054,
-0.04171905294060707,
0.010543613694608212,
0.06223123520612717,
0.022704653441905975,
-0.050105445086956024,
0.0040973275899887085,
-0.013903288170695305,
0.05626395717263222,
0.06054992601275444,
0.0248543843626976,
-0.005345589481294155,
-0.0006355370278470218,
0.025309061631560326,
-0.013941250741481781,
-0.008745023049414158,
0.021733321249485016,
0.03274792805314064,
0.03533884137868881,
0.04184542968869209,
-0.023661429062485695,
-0.021929096430540085,
0.053598251193761826,
-0.023266403004527092,
0.03082847408950329,
-0.00480999518185854,
-0.01953413337469101,
-0.010692672803997993,
-0.07190412282943726,
0.021067213267087936,
0.034050095826387405,
0.0015273184981197119,
0.012912549078464508,
-0.029854871332645416,
-0.00878586433827877,
-0.002460977528244257,
0.017171325162053108,
-0.02804887294769287,
-0.0014840085059404373,
0.03489132225513458,
-0.03427403047680855,
0.004055136814713478,
-0.04150135815143585,
0.021759290248155594,
-0.02835122123360634,
-0.00855884701013565,
0.020540457218885422,
0.017632421106100082,
0.05286195129156113,
-0.0352209210395813,
-0.036938294768333435,
-0.012296386994421482,
-0.029550926759839058,
0.016937240958213806,
-0.03336239978671074,
-0.02447420172393322,
-0.00642459886148572,
-0.025047529488801956,
-0.03956135734915733,
0.0664195716381073,
-0.0566692091524601,
-0.06254574656486511,
-0.012450926005840302,
-0.04332542419433594,
-0.02670752815902233,
-0.01110133808106184,
0.0010713926749303937,
0.00815654918551445,
-0.04214414954185486,
-0.019197827205061913,
0.031192360445857048,
-0.024927381426095963,
-0.006162631791085005,
-0.00569853326305747,
-0.02925705537199974,
-0.009583874605596066,
0.0007494009914807975,
-0.018241550773382187,
0.026975957676768303,
-0.04059218987822533,
0.02572893165051937,
0.027724964544177055,
-0.04169289395213127,
0.03607286512851715,
-0.0324423611164093,
-0.02654760330915451,
0.034818775951862335,
-0.0008026605355553329,
0.052823230624198914,
-0.013568326830863953,
0.008038781583309174,
0.06759823113679886,
0.015693996101617813,
0.0005600942531600595,
-0.007963509298861027,
-0.014431651681661606,
0.01203606091439724,
-0.009623739868402481,
0.023336350917816162,
0.0390441007912159,
0.021195627748966217,
0.038979947566986084,
-0.010413977317512035,
-0.014252042397856712,
0.08160238713026047,
-0.0018177839228883386,
-0.026173919439315796,
0.0004993703332729638,
-0.03512270376086235,
-0.004764759913086891,
0.008561110123991966,
0.022817464545369148,
-0.05514414235949516,
0.030944516882300377,
0.010150007903575897,
0.02331528067588806,
0.01890961453318596,
-0.03793634846806526,
0.06968976557254791,
0.010346153751015663,
-0.010094162076711655,
0.003487208392471075,
0.059050388634204865,
0.0017261006869375706,
-0.00027360275271348655,
-0.0020516773220151663,
0.02176075242459774,
0.03552050516009331,
-0.007409083191305399,
-0.006505192257463932,
0.04596574604511261,
0.0466972291469574,
-0.019176060333848,
0.029782915487885475,
-0.015029926784336567,
-0.002037421567365527,
-0.015708040446043015,
-0.012239268980920315,
-0.02206570655107498,
0.06695885956287384,
0.039195477962493896,
0.024140814319252968,
-0.002247285097837448,
-0.02762056700885296,
-0.013278907164931297,
-0.045220449566841125,
0.02461315132677555,
0.05098286271095276,
0.04485071077942848,
-0.0010848055826500058,
0.03030109591782093,
0.03851912170648575,
0.01619795523583889,
0.03590245917439461,
0.006686402950435877,
-0.07390580326318741,
-0.0031105035450309515,
-0.024884812533855438,
-0.016161693260073662,
-0.01184613723307848,
-0.026369687169790268,
-0.007313732523471117,
-0.00960270781069994,
-0.03633696585893631,
-0.006136216223239899,
0.025265425443649292,
-0.04094506427645683,
0.021601885557174683,
0.026441166177392006,
0.006234035361558199,
-0.023310767486691475,
0.0014342372305691242,
0.024608805775642395,
0.013467458076775074,
0.017749564722180367,
0.014144966378808022,
-0.030755052343010902,
0.018394704908132553,
-0.02699405699968338,
0.005031179636716843,
0.048508644104003906,
0.030439898371696472,
0.03529629856348038,
0.0386064313352108,
0.0076280138455331326,
-0.0007895748713053763,
0.003047721926122904,
0.0606192946434021,
0.0011429410660639405,
-0.04449860006570816,
-0.01823587901890278,
-0.028858890756964684,
-0.012393809854984283,
-0.017863977700471878,
0.03590269386768341,
-0.033680323511362076,
0.008411453105509281,
0.01404538843780756,
0.014573146589100361,
-0.04613036289811134,
0.020866943523287773,
0.0157039575278759,
0.056667644530534744,
-0.017605695873498917,
-0.032280754297971725,
-0.017190564423799515,
-0.028127504512667656,
0.023076292127370834,
0.018422706052660942,
0.0038826321251690388,
-0.018438613042235374,
0.027717530727386475,
0.020931052044034004,
0.004802183713763952,
-0.016696015372872353,
-0.04280586540699005,
-0.008501535281538963,
-0.01872902363538742,
-0.01177290454506874,
-0.00014357315376400948,
-0.008196256123483181,
0.06491754204034805,
0.052659112960100174,
0.008545747958123684,
-0.0025961699429899454,
-0.11128506809473038,
0.03099208138883114,
0.03458159416913986,
0.0043737138621509075,
0.0019389211665838957,
0.0036403732374310493,
-0.002142681274563074,
0.01607949286699295,
-0.0029013960156589746,
-0.015391004271805286,
0.04177045077085495,
-0.03365808725357056,
0.01467745378613472,
-0.022669924423098564,
-0.0006651973817497492,
0.026809902861714363,
0.022126326337456703,
0.015181411989033222,
0.00842528697103262,
-0.001119463937357068,
-0.013752639293670654,
-0.03376736491918564,
-0.012620649300515652,
-0.024900395423173904,
0.029475199058651924,
-0.020581698045134544,
-0.03396276384592056,
0.011803330853581429,
0.05880344286561012,
-0.03855083882808685,
-0.06336460262537003,
-0.035163018852472305,
0.044576410204172134,
-0.03211898356676102,
0.05951164290308952,
-0.02156989276409149,
-0.031154382973909378,
0.022267166525125504,
0.025707760825753212,
-0.036078471690416336,
-0.0342223159968853,
-0.014194220304489136,
0.028587862849235535,
0.02956925705075264,
0.0022512581199407578,
0.08160094916820526,
0.0043323771096765995,
-0.028232675045728683,
0.016787774860858917,
0.008069760166108608,
0.050592318177223206,
-0.03625544160604477,
-0.002872719429433346,
0.0018198114121332765,
0.0071345726028084755,
-0.05842700973153114,
0.055166929960250854,
-0.013372390531003475,
0.0031878394074738026,
-0.010657287202775478,
-0.06526162475347519,
-0.02932511642575264,
0.023942748084664345,
-0.019161393865942955,
-0.0035156665835529566,
-0.006097320932894945,
0.022384842857718468,
0.004532575607299805,
0.004105887375771999,
0.01250892411917448,
-0.02061653509736061,
0.020318564027547836,
0.04370173439383507,
0.03616026043891907,
0.010787636041641235,
-0.09035907685756683,
-0.033602215349674225,
0.03435885161161423,
-0.0255599208176136,
0.0711144506931305,
-0.035162877291440964,
0.03193807229399681,
0.002557208528742194,
-0.08474984765052795,
-0.04964805021882057,
0.004452448803931475,
-0.026408597826957703,
0.0406653992831707,
-0.045730069279670715,
0.05826636031270027,
0.018572324886918068,
0.0020802696235477924,
-0.0657699704170227,
-0.024267207831144333,
0.04695575311779976,
0.04800938814878464,
-0.03169872984290123,
-0.029042275622487068,
-0.003357149660587311,
-0.021659983322024345,
-0.0673660933971405,
0.010585815645754337,
0.0039355577901005745,
-0.029959075152873993,
0.01056878361850977,
0.012275236658751965,
-0.0048394398763775826,
0.05544726923108101,
0.007650870364159346,
-0.019757770001888275,
0.0006818139809183776,
-0.04100195690989494,
-0.016566699370741844,
0.014133188873529434,
0.0037233561743050814,
-0.03255228325724602,
-0.017225483432412148,
-0.041715435683727264,
0.009694711305201054,
0.04667375236749649,
-0.024257492274045944,
-0.008896075189113617,
0.009802456945180893,
0.002018823754042387,
-0.01507323794066906,
-0.004562161862850189,
0.01660767011344433,
-0.016618598252534866,
0.024911606684327126,
0.0024083785247057676,
-0.00493131298571825,
0.004593773745000362,
-0.01069558970630169,
0.055552493780851364,
0.016264569014310837,
0.02087927982211113,
-0.003321578726172447,
0.11563394218683243,
-0.01767813414335251,
0.033915985375642776,
-0.020795125514268875,
-0.03183168172836304,
0.02752811834216118,
0.011856789700686932,
0.036213576793670654,
0.023864621296525,
-0.00760144367814064,
-0.0173625648021698,
-0.045432500541210175,
-0.018225960433483124,
-0.01398482546210289,
0.043551258742809296,
-0.07657667249441147,
0.056669894605875015,
0.031050723046064377,
-0.04319804534316063,
-0.007905624806880951,
-0.03017682023346424,
0.00373732578009367,
0.021331433206796646,
-0.02211667411029339,
0.04547252133488655,
0.000013907364518672694,
-0.015810679644346237,
-0.002099015051499009,
0.06571268290281296,
-0.0015569827519357204,
0.036541420966386795,
0.020113518461585045,
0.06147119402885437,
-0.0013811178505420685,
-0.010776601731777191,
-0.04967454820871353,
0.05700548738241196,
-0.051091600209474564,
0.015545675531029701,
-0.010398141108453274,
-0.007583565078675747,
0.03623349592089653,
-0.015177621506154537,
0.008893010206520557,
-0.05276697129011154,
-0.0019403574988245964,
-0.030927827581763268,
0.0050672204233706,
0.012072662822902203,
-0.011411230079829693,
0.03716663271188736,
-0.02258933149278164,
-0.004197826609015465,
0.014195882715284824,
0.010053776204586029,
0.01514960452914238,
-0.05514615774154663,
-0.020129015669226646,
-0.05608765408396721,
-0.019894113764166832,
0.0180132444947958,
-0.010412333533167839,
-0.03037329390645027,
0.00380337773822248,
-0.010184136219322681,
0.020184310153126717,
0.030092753469944,
-0.00998769048601389,
-0.016392579302191734,
0.04943372309207916,
-0.008301680907607079,
0.043530434370040894,
0.054830402135849,
-0.004646295681595802,
0.1254671812057495,
0.06562495976686478,
0.01669102907180786,
-0.06510160118341446,
-0.03542472794651985,
-0.020738573744893074,
-0.00560154439881444,
0.0012384691508486867,
0.006207678932696581,
-0.026825489476323128,
0.03524666279554367,
0.021268213167786598,
0.027076756581664085,
0.014801411889493465,
-0.008974727243185043,
0.012600226327776909,
-0.0557696595788002,
-0.0065726288594305515,
0.06284520775079727,
-0.0026297415606677532,
-0.013064615428447723,
0.015606182627379894,
-0.07012873142957687,
0.013487416319549084,
0.019704319536685944,
-0.012998517602682114,
-0.026681475341320038,
-0.04803195968270302,
0.013566642068326473,
0.010808791033923626,
-0.03037453070282936,
-0.019493795931339264,
-0.037979960441589355,
-0.017427634447813034,
-0.02379615046083927,
0.014259510673582554,
0.03841410577297211,
0.011039625853300095,
-0.017214400693774223,
0.011433659121394157,
-0.006902798544615507,
-0.0074755046516656876,
0.024346094578504562,
0.027364786714315414,
-0.01838819310069084,
-0.022786669433116913,
0.019932202994823456,
0.0060278624296188354,
-0.03431897610425949,
-0.02552359737455845,
-0.002000143751502037,
-0.010904735885560513,
-0.0029631538782268763,
-0.03971036896109581,
0.017942246049642563,
0.01497458666563034,
-0.0035457946360111237,
-0.029110565781593323,
-0.0353592149913311,
0.005855892784893513,
0.007375573739409447,
0.005218354053795338,
0.018768081441521645,
0.0005017181392759085,
0.01265199389308691,
0.05175275355577469,
-0.011873496696352959,
0.028422905132174492,
0.012923864647746086,
-0.03320905566215515,
-0.019191307947039604,
0.021261947229504585,
-0.012264457531273365,
-0.043053727596998215,
-0.03320932388305664,
0.016525235027074814,
0.013285430148243904,
0.007862494327127934,
-0.029211722314357758,
-0.013404157012701035,
-0.04922974854707718,
0.051757827401161194,
-0.026144113391637802,
-0.012955717742443085,
-0.041196126490831375,
-0.002432119334116578,
0.03883489966392517,
0.007376239635050297,
-0.01096270326524973,
0.032955896109342575,
-0.010442809201776981,
0.020421769469976425,
0.01750483363866806,
0.000540840090252459,
-0.04911338537931442,
0.03936048597097397,
-0.016675248742103577,
-0.008986199274659157,
0.036689382046461105,
0.05901636555790901,
0.003975503612309694,
-0.002877322258427739,
0.012838256545364857,
0.01886172965168953,
-0.03740254417061806,
-0.0034976291935890913,
-0.01722566969692707,
-0.023116527125239372,
-0.009771337732672691,
-0.0003311579639557749,
-0.015818918123841286,
-0.03791775926947594,
-0.010063079185783863,
-0.03114517778158188,
-0.031061014160513878,
0.024227440357208252,
0.04259367659687996,
0.015683531761169434,
0.02700522355735302,
-0.0026933173649013042,
0.00737585686147213,
-0.008988498710095882,
-0.008858339861035347,
-0.053448449820280075,
-0.004346692003309727,
-0.013174128718674183,
0.0036154098343104124,
-0.025594795122742653,
0.012745482847094536,
-0.010460952296853065,
-0.03109094314277172,
0.01860138401389122,
0.03336644172668457,
0.004792692139744759,
0.046387165784835815,
0.03259250521659851,
-0.026667006313800812,
0.05016619339585304,
-0.009332599118351936,
-0.013281034305691719,
0.04819737374782562,
-0.04435039684176445,
-0.01306165475398302,
0.010162369348108768,
-0.026182707399129868,
0.03857554495334625,
0.016603967174887657,
-0.005422862246632576,
-0.011485429480671883,
0.020238880068063736,
-0.0043036118149757385,
-0.050631195306777954,
-0.02300785481929779,
-0.014117452315986156,
0.004455037415027618,
-0.01409207284450531,
-0.01394613552838564,
-0.01631619781255722,
-0.008884148672223091,
0.022725889459252357,
0.013658453710377216,
0.016104191541671753,
-0.005594289395958185,
-0.012867776677012444,
-0.01759873889386654,
-0.0008166370680555701,
-0.007736779283732176,
-0.02204837091267109,
0.01299099251627922,
0.03145214915275574,
-0.0382443405687809,
0.03557530790567398,
0.008557561784982681,
0.006065632216632366,
-0.1002923995256424,
0.014156844466924667,
-0.006032960955053568,
0.00011306110536679626,
0.05208767578005791,
-0.053599219769239426,
0.047754209488630295,
-0.00019812860409729183,
-0.046112366020679474,
-0.0002284627698827535,
-0.019471274688839912,
-0.051602862775325775,
-0.051518797874450684,
0.03592483699321747,
-0.010411516763269901,
0.0015133788110688329,
0.019597835838794708,
0.011998568661510944,
-0.018909325823187828,
0.022523777559399605,
-0.03135073184967041,
-0.02322280965745449,
0.030628245323896408,
0.0029293824918568134,
-0.05316510796546936,
0.003240381134673953,
0.07056175917387009,
0.01544423121958971,
-0.030153866857290268,
0.032368093729019165,
-0.018844561651349068,
0.018210671842098236,
0.03706393018364906,
0.004969034343957901,
0.003957276698201895,
0.014303912408649921,
-0.0032407345715910196,
-0.013201842084527016,
-0.046250130981206894,
0.011652856133878231,
0.015256522223353386,
0.024519534781575203,
0.030153416097164154,
-0.004639090038836002,
0.0022114089224487543,
-0.042862530797719955,
-0.03618500754237175,
0.018174560740590096,
-0.0052711316384375095,
-0.008168371394276619,
0.010264779441058636,
-0.009894177317619324,
0.01526589971035719,
-0.034362539649009705,
-0.013128007762134075,
-0.06551101803779602,
-0.017378920689225197,
-0.0029501409735530615,
0.008868065662682056,
-0.045083411037921906,
0.023049581795930862,
-0.04258793219923973,
-0.05919254198670387,
0.007679000496864319,
0.03289157897233963,
-0.010042107664048672,
-0.0014762419741600752,
-0.018224691972136497,
-0.007792837917804718,
-0.015463538467884064,
-0.008269774727523327,
0.022515911608934402,
-0.031748466193675995,
0.013252866454422474,
-0.009779905900359154,
-0.005677273031324148,
0.04804563894867897,
-0.049625642597675323,
-0.004008852876722813,
-0.035415876656770706,
0.07271009683609009,
-0.018056735396385193,
-0.0440732017159462,
-0.02620098553597927,
-0.01882370375096798,
-0.018735144287347794,
0.06563723832368851,
0.05188251659274101,
-0.02903980202972889,
-0.020430754870176315,
-0.0021332961041480303,
0.0027405626606196165,
0.01792040280997753,
-0.028441663831472397,
0.029566461220383644,
0.01814441941678524,
-0.04442361369729042,
-0.03927799314260483,
-0.010233860462903976,
-0.020126881077885628,
-0.0002841489331331104,
0.016943782567977905,
0.016718190163373947,
0.039186831563711166,
-0.020485758781433105,
-0.001532881404273212,
0.057389240711927414,
0.01550342794507742,
-0.013318834826350212,
0.04469618573784828,
-0.013000872917473316,
-0.007460159249603748,
0.026399284601211548,
0.020995311439037323,
-0.059190332889556885,
0.02110426127910614,
-0.026779187843203545,
0.019292080774903297,
0.011323430575430393,
-0.01067650131881237,
0.03186803311109543,
-0.024867495521903038,
-0.006477059330791235,
0.017043184489011765,
-0.05540874972939491,
0.0034539371263235807,
0.07344097644090652,
0.01677468791604042,
0.037234432995319366,
0.01139848679304123,
-0.004204446449875832,
-0.022554313763976097,
-0.028524044901132584,
-0.03937534987926483,
0.05987770855426788,
0.0037794567178934813,
0.03757862001657486,
0.04987006261944771,
0.025740204378962517,
0.008490530773997307,
0.018150586634874344,
0.015286660753190517,
0.00424316106364131,
-0.030948109924793243,
-0.005395377520471811,
-0.004121198784559965,
-0.013436877168715,
0.012769518420100212,
0.03596537932753563,
-0.005147181451320648,
0.07256361842155457,
-0.05145527049899101,
0.005526264663785696,
-0.0210115984082222,
0.00003524701969581656,
-0.008752333000302315,
0.012912764213979244,
0.04774263873696327,
0.041727446019649506,
-0.0031425682827830315,
-0.007600617129355669,
-0.027824072167277336,
0.0014224631013348699,
-0.013319602236151695,
-0.015028802677989006,
0.05844064801931381,
-0.006523153744637966,
-0.015285393223166466,
0.004364016931504011,
-0.005241293925791979,
0.010770312510430813,
-0.005256094038486481,
-0.017684072256088257,
0.019272854551672935,
-0.01019980013370514,
0.052788373082876205,
-0.005084832198917866,
-0.01900334283709526,
0.057418882846832275,
-0.09120002388954163,
0.006668465211987495,
-0.014531120657920837,
0.008919843472540379,
-0.017352918162941933,
-0.004945841152220964
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.