question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>I am studying an example problem, concerning the very topic mentioned in the title. In this example problem, a car has a head-on collision with the wall; the initial and final velocity are known, as well as the mass. My question is, why does the car rebound off of the wall? Why doesn't the normal force of the wall reduce the car's velocity to zero, with the car remaining there, instead of reducing the car's velocity to zero, and then giving it a velocity in the opposite direction?</p> | g9168 | [
0.09938742220401764,
0.05776345357298851,
0.017100565135478973,
0.031100694090127945,
0.08464232087135315,
-0.0091315396130085,
0.06281592696905136,
0.05357916280627251,
-0.07514326274394989,
-0.07619137316942215,
-0.021371135488152504,
-0.029971245676279068,
0.0101227518171072,
0.03757602721452713,
0.04476376995444298,
0.0322975292801857,
0.01688656024634838,
-0.03494632616639137,
0.022772490978240967,
0.06425968557596207,
-0.02574985846877098,
0.021413203328847885,
0.00025881212786771357,
0.005455515813082457,
-0.003602990647777915,
0.00822027213871479,
0.003400788875296712,
-0.038968075066804886,
-0.008842900395393372,
0.012197651900351048,
0.02625761367380619,
-0.0032498971559107304,
0.01207638531923294,
-0.04553944617509842,
-0.015898171812295914,
0.03547314554452896,
0.015981318429112434,
-0.034457042813301086,
-0.0025786396581679583,
-0.0012145015643909574,
0.058856576681137085,
-0.030024506151676178,
0.03232596442103386,
-0.016472753137350082,
0.020761197432875633,
-0.005005220416933298,
0.010147931054234505,
-0.020854854956269264,
-0.023450253531336784,
0.014691348187625408,
-0.004652922507375479,
0.03053119033575058,
0.03055763989686966,
-0.0305363517254591,
0.013770043849945068,
-0.0039047428872436285,
0.06633805483579636,
0.00551907904446125,
0.017517857253551483,
0.016530340537428856,
-0.014547807164490223,
0.01683095283806324,
0.02457384020090103,
-0.0071939690969884396,
-0.024956632405519485,
-0.04629724472761154,
-0.04467371106147766,
0.050512898713350296,
0.014763971790671349,
-0.016428498551249504,
-0.024319201707839966,
0.032398734241724014,
-0.034773729741573334,
-0.026663970202207565,
-0.00952162779867649,
-0.03665945306420326,
0.02472580410540104,
-0.04334278032183647,
0.009472214616835117,
-0.00130073179025203,
-0.05844367295503616,
0.02777387574315071,
-0.012844732962548733,
0.036237552762031555,
-0.0033273259177803993,
0.06360609084367752,
0.011961127631366253,
0.009883477352559566,
-0.009256100282073021,
-0.013005519285798073,
0.027318978682160378,
-0.011176950298249722,
0.08474551141262054,
0.009895585477352142,
-0.031507741659879684,
-0.006810854654759169,
-0.051725827157497406,
0.039894089102745056,
0.047882597893476486,
0.00894930586218834,
-0.023432016372680664,
-0.030175991356372833,
0.02524118311703205,
0.01215060893446207,
-0.0038991165347397327,
0.022175855934619904,
0.033983517438173294,
0.05606976896524429,
0.00127713184338063,
-0.02176477201282978,
-0.009556914679706097,
-0.10173535346984863,
-0.0041435481980443,
-0.04583962634205818,
0.0031864503398537636,
-0.05182879790663719,
0.08737886697053909,
0.03854181244969368,
0.00583354476839304,
0.07007963955402374,
-0.07820838689804077,
0.009662938304245472,
-0.04612225666642189,
0.031140632927417755,
-0.03476313501596451,
-0.005496028810739517,
0.009044569917023182,
0.019887417554855347,
0.03332763910293579,
-0.019920680671930313,
0.031665313988924026,
0.036796923726797104,
0.018589191138744354,
0.016564346849918365,
0.01989714242517948,
0.02778720296919346,
-0.020607182756066322,
0.013337917625904083,
0.028697319328784943,
0.05573832988739014,
0.018058542162179947,
0.08185692876577377,
-0.003888476174324751,
0.012820955365896225,
-0.06130306050181389,
-0.0011761473724618554,
-0.020947899669408798,
0.032998498529195786,
0.02366573177278042,
0.019649000838398933,
-0.02176700532436371,
0.0015719832153990865,
-0.02670939825475216,
0.006352051626890898,
0.06098504364490509,
-0.028142819181084633,
0.05918188765645027,
-0.03907778859138489,
-0.04023633897304535,
0.010028130374848843,
0.062251076102256775,
-0.026014549657702446,
0.018884746357798576,
-0.03140590339899063,
-0.056746553629636765,
-0.014500905759632587,
-0.03866608440876007,
0.007534756790846586,
-0.01848534494638443,
-0.03536771237850189,
-0.051450058817863464,
-0.05076435208320618,
-0.02616926282644272,
0.09648117423057556,
-0.003980690147727728,
-0.016986627131700516,
0.03468022868037224,
-0.03491327539086342,
0.0013935603201389313,
-0.02415168657898903,
0.04337141662836075,
-0.0046621887013316154,
-0.005679535213857889,
0.012166662141680717,
0.09236729890108109,
0.008424322120845318,
0.04660208895802498,
0.08793479204177856,
-0.09186914563179016,
0.025514276698231697,
-0.009982725605368614,
-0.04937782138586044,
0.044405173510313034,
-0.02972235530614853,
-0.05935860425233841,
-0.011528669856488705,
-0.010116943158209324,
0.013258581049740314,
-0.035130325704813004,
0.018230874091386795,
-0.01226134691387415,
0.026729034259915352,
0.02728690765798092,
0.0045144688338041306,
-0.018123684450984,
-0.03853054717183113,
-0.008546845056116581,
0.03612818568944931,
0.03181590139865875,
-0.03812733665108681,
0.02654982917010784,
0.032153114676475525,
-0.05215736851096153,
0.0022169759031385183,
-0.02917841263115406,
-0.018913328647613525,
-0.018991246819496155,
0.06110655143857002,
0.03001408465206623,
-0.02462746389210224,
-0.029136866331100464,
0.023276755586266518,
-0.04696643352508545,
-0.048019520938396454,
-0.04800974205136299,
-0.022033903747797012,
-0.03424937650561333,
-0.036553699523210526,
-0.026433119550347328,
0.002973012626171112,
-0.0489492267370224,
0.016665834933519363,
0.017549505457282066,
-0.0014515171060338616,
0.015758926048874855,
-0.0027876710519194603,
0.07347403466701508,
0.0529232919216156,
0.01713862642645836,
0.019343838095664978,
-0.0009400516864843667,
-0.027714410796761513,
-0.006611548829823732,
-0.07614926248788834,
0.008545134216547012,
-0.06470538675785065,
-0.032164253294467926,
-0.028219012543559074,
0.039342425763607025,
-0.046992816030979156,
-0.020224666222929955,
0.03043207712471485,
-0.04412172734737396,
0.005715703591704369,
0.04580517113208771,
-0.032245490700006485,
-0.024155154824256897,
-0.012611784040927887,
-0.007047271355986595,
-0.022240981459617615,
-0.018312059342861176,
0.020604709163308144,
0.019240649417042732,
0.05639412999153137,
-0.05948425456881523,
0.04124587029218674,
-0.013432029634714127,
0.08728184551000595,
0.027592062950134277,
0.004524202551692724,
0.0011780454078689218,
0.041222646832466125,
0.004803623538464308,
0.0678141638636589,
-0.010684490203857422,
0.029256640002131462,
0.019924812018871307,
-0.07874389737844467,
0.001084635965526104,
0.04234650358557701,
0.0008742003119550645,
0.07427895814180374,
-0.04311474785208702,
-0.03222092241048813,
-0.033921606838703156,
-0.03393229469656944,
0.02892657369375229,
-0.025115499272942543,
-0.034870728850364685,
-0.012400303035974503,
-0.06980569660663605,
0.05099957808852196,
0.029785534366965294,
0.0035926394630223513,
0.0817229226231575,
0.06259973347187042,
0.014583378098905087,
0.007019109558314085,
-0.0564761608839035,
-0.03367765247821808,
-0.06866776198148727,
-0.013726389035582542,
-0.04126075655221939,
0.006859741639345884,
0.012717276811599731,
0.020808609202504158,
-0.008333000354468822,
0.011064455844461918,
-0.03416375815868378,
-0.004553608130663633,
0.0039949482306838036,
0.04878174513578415,
0.007523116189986467,
-0.016338802874088287,
-0.06403431296348572,
0.009097951464354992,
0.033275581896305084,
-0.015845807269215584,
-0.025219857692718506,
0.03641517832875252,
-0.06084500998258591,
-0.04665572568774223,
0.060367971658706665,
0.03657612204551697,
-0.0050118048675358295,
0.07499583810567856,
-0.04706821218132973,
0.0464545339345932,
0.023947754874825478,
-0.04488230496644974,
0.0381319560110569,
0.06655226647853851,
0.03804628551006317,
-0.03781742602586746,
-0.007069681771099567,
-0.01322657335549593,
0.0008126007160171866,
0.027384493499994278,
0.04572630301117897,
0.05321595445275307,
0.008651452139019966,
0.003060628892853856,
-0.0028638881631195545,
-0.047742825001478195,
0.050601113587617874,
0.09169241786003113,
0.04591815173625946,
-0.02687069959938526,
-0.013021839782595634,
-0.05351986363530159,
0.09139862656593323,
-0.02142159454524517,
0.04564903303980827,
-0.027477772906422615,
-0.029511287808418274,
0.008639147505164146,
-0.017736228182911873,
0.004079118836671114,
-0.030605385079979897,
0.01874830201268196,
0.0035706099588423967,
-0.022952143102884293,
-0.05671392008662224,
0.04818233102560043,
0.029213396832346916,
-0.03577307239174843,
0.006375654600560665,
0.06927398592233658,
-0.03371964395046234,
-0.06094401702284813,
0.04359395429491997,
-0.03047887049615383,
-0.01241756696254015,
0.006373169366270304,
-0.023386739194393158,
-0.04567690193653107,
0.007674639578908682,
0.03665884584188461,
0.018918590620160103,
0.011977880261838436,
0.07834096997976303,
-0.036925531923770905,
-0.04209069907665253,
-0.010017715394496918,
0.01362726278603077,
0.009044918231666088,
-0.07042872905731201,
-0.000696544477250427,
0.03813778609037399,
0.010103830136358738,
0.006263707764446735,
-0.004110211040824652,
0.045041706413030624,
0.006213458254933357,
0.05949004366993904,
0.02517322450876236,
0.0002343315863981843,
-0.050820574164390564,
-0.06058083474636078,
0.006219606380909681,
-0.014574968256056309,
0.046619415283203125,
0.02084825187921524,
0.016602108255028725,
0.034846704453229904,
-0.019183218479156494,
0.032208122313022614,
0.005234298296272755,
-0.012475105002522469,
-0.01086425967514515,
-0.005827850196510553,
-0.02818954735994339,
-0.04451911151409149,
-0.06017202138900757,
0.028267335146665573,
-0.028704505413770676,
-0.01712259277701378,
0.05824742838740349,
0.014710424467921257,
-0.016264380887150764,
-0.0022716866806149483,
0.0013940205099061131,
-0.034991852939128876,
0.0075400411151349545,
0.02478528954088688,
-0.004796725232154131,
0.006067897193133831,
0.005445660557597876,
-0.0024953526444733143,
-0.02452230453491211,
0.03410432115197182,
-0.014801292680203915,
-0.017267504706978798,
-0.025204850360751152,
-0.04118400439620018,
0.04610211402177811,
-0.0005228133522905409,
0.038396310061216354,
0.004703668411821127,
0.0038738518487662077,
-0.030357107520103455,
0.034622758626937866,
-0.031167790293693542,
0.019941598176956177,
-0.034810736775398254,
0.010507277213037014,
-0.027024779468774796,
-0.013074948452413082,
0.01857648231089115,
-0.02178790420293808,
-0.0278024822473526,
-0.00132694561034441,
-0.04003221169114113,
-0.039524536579847336,
-0.024055570363998413,
-0.037488583475351334,
-0.05351391062140465,
0.04472479969263077,
0.012328063137829304,
0.029747741296887398,
0.009264970198273659,
0.0238630473613739,
-0.034852445125579834,
0.021314388141036034,
-0.0326957069337368,
-0.058160413056612015,
0.02996049076318741,
0.018950188532471657,
-0.06546547263860703,
-0.016044648364186287,
-0.012782464735209942,
0.017437659204006195,
-0.020023111253976822,
-0.004812171682715416,
-0.03720049187541008,
-0.019999058917164803,
0.0013680410338565707,
0.03686116263270378,
0.03716578707098961,
-0.05757039785385132,
-0.019075967371463776,
0.02243046462535858,
-0.009965983219444752,
-0.020029183477163315,
-0.00571838952600956,
-0.017417211085557938,
-0.024812065064907074,
-0.038408614695072174,
0.013511348515748978,
-0.005468378774821758,
0.0028238960076123476,
-0.03071523830294609,
-0.044069379568099976,
-0.035830311477184296,
0.02207033708691597,
-0.049842484295368195,
-0.025667056441307068,
0.0016891919076442719,
-0.03336697444319725,
-0.0386962890625,
-0.10566593706607819,
-0.03286247327923775,
0.01410570926964283,
-0.01882384903728962,
-0.005247712600976229,
0.0678223967552185,
0.04111207649111748,
-0.015943516045808792,
-0.021443279460072517,
0.08811073750257492,
-0.02097941003739834,
0.01583353616297245,
0.11416930705308914,
-0.011810033582150936,
0.006053929217159748,
0.0031077214516699314,
0.013861168175935745,
-0.05654299259185791,
0.017609719187021255,
0.018358521163463593,
-0.00030021867132745683,
-0.04549260064959526,
0.005194104742258787,
-0.010067414492368698,
-0.07243885099887848,
0.03207893297076225,
0.011037925258278847,
-0.07977410405874252,
-0.07663176208734512,
0.06019102409482002,
0.0289210956543684,
-0.016010180115699768,
0.055577293038368225,
0.038024187088012695,
-0.07218507677316666,
-0.01457954291254282,
-0.01701190508902073,
-0.004454504232853651,
0.042171660810709,
-0.041696697473526,
-0.02807285450398922,
-0.031929563730955124,
0.0675375759601593,
0.08755556493997574,
0.0287147406488657,
0.01601739414036274,
-0.009437868371605873,
-0.015444478020071983,
-0.021259784698486328,
-0.05548946186900139,
-0.0925309807062149,
-0.015509197488427162,
-0.053281787782907486,
0.032602325081825256,
-0.02337951958179474,
-0.04248510301113129,
0.06465253233909607,
0.019963158294558525,
-0.016459397971630096,
-0.06902418285608292,
0.05847995728254318,
-0.0514720119535923,
0.03069743514060974,
-0.016064735129475594,
0.02464054524898529,
-0.006943352986127138,
-0.029395712539553642,
0.05354872718453407,
0.048759449273347855,
0.004047929309308529,
0.015052788890898228,
0.011146524921059608,
0.016763081774115562,
0.012325338087975979,
0.057690296322107315,
-0.0018159336177632213,
0.00829294417053461,
-0.048350121825933456,
-0.03497994691133499,
-0.008278736844658852,
0.02532384544610977,
0.010481064207851887,
0.02028702385723591,
-0.0894063338637352,
0.027859259396791458,
-0.025770917534828186,
-0.017987197265028954,
-0.03072138875722885,
0.05312035232782364,
0.010392354801297188,
-0.018521366640925407,
0.018864504992961884,
-0.0024998884182423353,
-0.05008275806903839,
-0.04314988851547241,
-0.0633532702922821,
-0.008170855231583118,
-0.00014821556396782398,
-0.015256511978805065,
-0.015843063592910767,
0.00894184596836567,
0.03670842945575714,
0.016711050644516945,
-0.00832041259855032,
0.031763456761837006,
0.048121143132448196,
0.03656517714262009,
0.023913778364658356,
0.006775428541004658,
0.016413424164056778,
0.0313900001347065,
0.05105970427393913,
-0.022339046001434326,
0.01847386173903942,
0.030656926333904266,
-0.010591059923171997,
-0.03848898783326149,
0.01753440871834755,
-0.04032820090651512,
-0.014023102819919586,
0.011181117966771126,
-0.06942269206047058,
0.034837618470191956,
-0.028454508632421494,
0.05081293731927872,
0.007029866799712181,
-0.08425438404083252,
0.02483290433883667,
0.07430948317050934,
0.02576819248497486,
0.009221302345395088,
0.001026795362122357,
-0.021022573113441467,
0.013689301908016205,
-0.05003516376018524,
0.04463972523808479,
-0.014030037447810173,
0.05805701017379761,
0.012026899494230747,
-0.0038846966344863176,
-0.004869693424552679,
0.028548486530780792,
-0.032841891050338745,
0.02203044295310974,
-0.08832234889268875,
0.0003938728477805853,
0.025818899273872375,
-0.011949911713600159,
-0.04885518178343773,
0.011346588842570782,
-0.0011856110068038106,
0.0019134526373818517,
-0.014461620710790157,
0.014492813497781754,
-0.0627145916223526,
0.016936222091317177,
-0.040304407477378845,
-0.01200381014496088,
0.052239302545785904,
0.0196359995752573,
-0.051487866789102554,
0.0062239086255431175,
0.01986744813621044,
0.0420994833111763,
0.015266244299709797,
0.0415787547826767,
0.02230009064078331,
-0.039110295474529266,
0.016420871019363403,
0.008243033662438393,
0.022394200786948204,
-0.06229211762547493,
0.006774734240025282,
0.006633254699409008,
0.044794246554374695,
0.058282677084207535,
0.006334167905151844,
0.008845875039696693,
0.01542416401207447,
-0.034293293952941895,
0.049782853573560715,
0.03572829067707062,
0.0029086831491440535,
-0.056941207498311996,
0.03840496391057968,
0.019474942237138748,
-0.01566564477980137,
0.08824674785137177,
0.00041416025487706065,
-0.027607105672359467,
-0.02792382426559925,
0.001348194433376193,
0.030377047136425972,
0.018978554755449295,
-0.051607660949230194,
-0.04266119748353958,
0.0029418235644698143,
0.06116786599159241,
-0.047090623527765274,
0.0003483808832243085,
-0.002507228637114167,
-0.016963161528110504,
0.013900082558393478,
0.02675589919090271,
-0.013884598389267921,
0.0075293672271072865,
-0.024176456034183502,
-0.05741581693291664,
-0.03719453513622284,
-0.037803586572408676,
-0.017295027151703835,
0.02179849147796631,
0.01357809454202652,
-0.009112181141972542,
-0.002716273069381714,
-0.016107313334941864,
0.00559990806505084,
0.06943455338478088,
0.03889150172472,
0.007911549881100655,
-0.001045644166879356,
-0.04887312650680542,
0.04771051183342934,
-0.09663722664117813,
-0.012072638608515263,
-0.005528278183192015,
-0.05884290486574173,
0.01997838169336319,
-0.0019124529790133238,
0.0449683703482151,
-0.03411007672548294,
0.011971289291977882,
0.020893538370728493,
0.001042054034769535,
0.013694286346435547,
-0.03833485394716263,
0.005225302651524544,
-0.007234878372400999,
-0.0248994380235672,
-0.015395971946418285,
-0.007996296510100365,
-0.023448599502444267,
0.028370870277285576,
-0.00638178875669837,
-0.00531966844573617,
-0.03758951649069786,
0.02139260247349739,
0.06560331583023071,
0.004939122591167688,
-0.0231543630361557,
0.0022381264716386795,
-0.0026854972820729017,
-0.052540842443704605,
0.00015836399688851088,
0.03488553687930107,
-0.04951096326112747,
-0.03212382271885872,
-0.01742521859705448,
-0.0010243681026622653,
-0.008394120261073112,
0.02330216020345688,
0.0007813607226125896,
0.019951604306697845,
-0.05498850345611572,
0.02473420836031437,
-0.02858256734907627,
-0.03152437135577202,
-0.017916269600391388
] |
<p>I was playing around with <a href="http://www.lpta.univ-montp2.fr/users/kneur/Suspect/">SuSpect</a> to generate some SUSY mass spectrums and I'm often encountering situations where I get a negative neutralino mass. </p>
<ol>
<li><p>What is the physical meaning of this negative mass I am getting? </p></li>
<li><p>Does this mean the parameters I am putting in is giving an unphysical spectrum?</p></li>
</ol> | g9169 | [
-0.010900437831878662,
0.021886933594942093,
0.0010466133244335651,
-0.07361546903848648,
0.0833125114440918,
0.06362947076559067,
-0.06139083206653595,
0.00858592800796032,
-0.04972999170422554,
-0.048698022961616516,
0.020355699583888054,
-0.026510115712881088,
0.05064932629466057,
0.004105500411242247,
-0.03547336161136627,
-0.06789640337228775,
0.14119422435760498,
-0.018383538350462914,
0.036927059292793274,
-0.0028673186898231506,
-0.06082089617848396,
0.04008932411670685,
-0.05817277356982231,
-0.05527595058083534,
-0.000320899038342759,
-0.015988552942872047,
0.052607063204050064,
0.05186201632022858,
0.03066447749733925,
-0.013482551090419292,
-0.03813622146844864,
-0.034789592027664185,
0.02066829428076744,
0.010879340581595898,
-0.08779127895832062,
-0.00985660683363676,
0.07276049256324768,
0.007819552905857563,
-0.02700704336166382,
0.004144101403653622,
0.0470283143222332,
0.01710698939859867,
0.01753661222755909,
-0.015574386343359947,
-0.015813099220395088,
0.03508468717336655,
-0.03465256839990616,
-0.021235650405287743,
-0.0162812490016222,
0.00029848929261788726,
0.008182305842638016,
-0.003631969913840294,
0.02687189169228077,
-0.0017510178731754422,
0.05082503706216812,
0.029062172397971153,
0.03312436863780022,
0.002516624052077532,
0.0370938815176487,
0.031980376690626144,
0.04346468672156334,
-0.013979078270494938,
0.03503692150115967,
-0.002895795274525881,
0.019842540845274925,
0.0012712556635960937,
-0.08669798821210861,
-0.007518269587308168,
0.0012716172495856881,
-0.024098429828882217,
-0.006765969563275576,
-0.0005795470788143575,
-0.006714208051562309,
-0.03291402757167816,
-0.004454901907593012,
0.04783126711845398,
-0.001857735333032906,
-0.0032904285471886396,
-0.01405146811157465,
-0.004603898618370295,
-0.062117308378219604,
-0.0028175392653793097,
-0.007570698391646147,
-0.01005349587649107,
0.05441956967115402,
0.010660515166819096,
-0.022709921002388,
0.023516736924648285,
-0.005959010683000088,
0.03573274239897728,
0.012408721260726452,
0.008257982321083546,
0.01924566738307476,
-0.016650723293423653,
-0.013818222098052502,
0.007546096108853817,
0.015178916044533253,
0.08914108574390411,
-0.058934155851602554,
-0.04173962399363518,
0.005788711365312338,
0.05500994250178337,
-0.00467345304787159,
-0.03986745327711105,
-0.006722766440361738,
0.05026448518037796,
-0.006269512698054314,
-0.037569090723991394,
0.019836803898215294,
-0.0047841244377195835,
-0.02185792289674282,
0.0065754735842347145,
-0.03942848742008209,
-0.03844767436385155,
-0.031807877123355865,
-0.05836772918701172,
0.03848888352513313,
-0.002028218936175108,
0.017514478415250778,
0.07309649884700775,
0.06932426989078522,
0.02513788267970085,
0.0076779271475970745,
0.0390942320227623,
-0.05229029431939125,
-0.05745178461074829,
0.03819046914577484,
0.005759797058999538,
0.03187144175171852,
-0.05726681277155876,
-0.0022851249668747187,
-0.03517292067408562,
-0.06623920053243637,
-0.041285060346126556,
0.042776256799697876,
-0.011445321142673492,
0.013444889336824417,
0.0023262053728103638,
-0.01586838625371456,
-0.010282637551426888,
0.034677427262067795,
-0.03337341919541359,
0.021638421341776848,
-0.04873731732368469,
0.011374358087778091,
-0.03698442503809929,
-0.05552912876009941,
-0.008714733645319939,
0.044366125017404556,
0.035331085324287415,
-0.022317107766866684,
0.05856464058160782,
0.03596412017941475,
-0.057350050657987595,
0.017698954790830612,
-0.003246638458222151,
0.01602867804467678,
0.05273512378334999,
-0.01681118831038475,
-0.05837666988372803,
0.059931643307209015,
-0.054537512362003326,
0.006524962373077869,
-0.016900092363357544,
-0.049729958176612854,
-0.015320532955229282,
0.015473684296011925,
-0.018125902861356735,
0.01826692558825016,
0.018315406516194344,
-0.05274998024106026,
0.013160298578441143,
-0.006608647760003805,
0.04026583209633827,
-0.006503070238977671,
0.06536097824573517,
0.013646199367940426,
-0.012347875162959099,
0.08192300796508789,
0.054609719663858414,
-0.039372529834508896,
-0.049856919795274734,
-0.008076152764260769,
-0.05352020263671875,
0.007054249290376902,
-0.04147140309214592,
0.011415193788707256,
0.07082481682300568,
-0.020628130063414574,
-0.0016392901306971908,
0.03342434763908386,
-0.018960876390337944,
0.003953380975872278,
0.0018048279453068972,
-0.04496466740965843,
-0.03320333734154701,
-0.02023381181061268,
-0.01996077410876751,
-0.035686321556568146,
-0.0244189091026783,
0.02897428348660469,
0.021977540105581284,
-0.0010612892219796777,
0.02513657882809639,
-0.004243324976414442,
-0.024714745581150055,
0.028783801943063736,
-0.01277641486376524,
0.031151913106441498,
0.004786649718880653,
-0.051956359297037125,
0.0018511353991925716,
0.05652216821908951,
-0.02229921892285347,
-0.030356284230947495,
0.004978110082447529,
-0.011783207766711712,
0.025471191853284836,
0.028271043673157692,
0.032653022557497025,
-0.03099561668932438,
0.027529016137123108,
0.01305555459111929,
0.03094075806438923,
-0.013714144937694073,
0.019797734916210175,
-0.04384290426969528,
-0.030935054644942284,
0.010131954215466976,
-0.05136178061366081,
-0.04424335062503815,
-0.046491917222738266,
0.08974761515855789,
0.01974031701683998,
0.027328111231327057,
0.017159834504127502,
0.027491454035043716,
-0.05642581358551979,
-0.00737760728225112,
-0.015166077762842178,
0.014705920591950417,
-0.043919630348682404,
-0.012363582849502563,
0.04703255742788315,
-0.014138787984848022,
-0.04245859384536743,
0.03372599184513092,
-0.018797600641846657,
-0.05877835676074028,
0.044994473457336426,
-0.040715135633945465,
0.03728097677230835,
0.004394103307276964,
0.0010862220078706741,
0.0036481779534369707,
-0.01195622980594635,
-0.045815080404281616,
0.05166563391685486,
-0.06487968564033508,
-0.01441525761038065,
0.06812548637390137,
-0.1034860908985138,
-0.01276341825723648,
-0.019260583445429802,
-0.05086522549390793,
-0.03091919608414173,
-0.0555964820086956,
-0.023403633385896683,
0.02743334323167801,
0.0368962436914444,
-0.009070664644241333,
0.04425882175564766,
0.06918009370565414,
-0.007888639345765114,
0.04766127094626427,
-0.014078558422625065,
-0.0302085243165493,
0.04469331353902817,
0.025224242359399796,
-0.03960316628217697,
0.03862094506621361,
0.0601729117333889,
-0.025235865265130997,
0.0110172713175416,
-0.0028886753134429455,
-0.011232735589146614,
-0.00043086695950478315,
-0.003419561078771949,
-0.08229891955852509,
0.0302467979490757,
0.014947283081710339,
-0.0006227580015547574,
0.0457950159907341,
0.0024720621295273304,
-0.004654170013964176,
0.036631736904382706,
0.05955624580383301,
-0.054829537868499756,
0.04289405420422554,
0.004643937572836876,
0.012145756743848324,
0.04601707682013512,
-0.024733848869800568,
-0.08789686113595963,
-0.01046308595687151,
-0.02533791959285736,
-0.03338675573468208,
0.029702207073569298,
0.009891523979604244,
-0.04012124240398407,
-0.07256549596786499,
0.009001166559755802,
0.07389691472053528,
-0.012360990978777409,
0.02260894514620304,
0.07033965736627579,
-0.05657372251152992,
-0.033500734716653824,
-0.03250157833099365,
-0.02670251950621605,
-0.055575110018253326,
-0.028064444661140442,
0.0480692982673645,
0.0030427402816712856,
0.059426628053188324,
0.014742106199264526,
0.029140492901206017,
0.03844435140490532,
0.01536654308438301,
-0.04626934975385666,
0.012940902262926102,
-0.03043317049741745,
-0.016285018995404243,
0.03365454822778702,
-0.03872017189860344,
0.0133103271946311,
-0.03709585219621658,
-0.021995482966303825,
0.047856129705905914,
0.04239736497402191,
-0.004494905937463045,
-0.03316027298569679,
-0.016320958733558655,
0.02363934926688671,
-0.037771545350551605,
0.021146759390830994,
-0.043836671859025955,
-0.05593637004494667,
0.031301725655794144,
-0.016122134402394295,
0.015256568789482117,
0.043134912848472595,
0.0025862003676593304,
-0.006556082051247358,
-0.009997139684855938,
0.03667718544602394,
-0.015710940584540367,
0.030844110995531082,
-0.023361753672361374,
0.07678506523370743,
0.018900297582149506,
-0.018203426152467728,
0.004278117790818214,
-0.0047929068095982075,
0.04118623584508896,
0.07934583723545074,
-0.04856877774000168,
0.0417853444814682,
0.002318838145583868,
0.009426291100680828,
-0.03397775813937187,
-0.037557121366262436,
0.029255680739879608,
-0.02929714322090149,
0.014584078453481197,
-0.038670387119054794,
-0.01458172407001257,
0.014974636025726795,
-0.010922174900770187,
0.036491576582193375,
0.037666428834199905,
-0.01588016375899315,
0.050357963889837265,
0.012797442264854908,
0.02981892228126526,
0.00516623817384243,
-0.05612926185131073,
0.048720136284828186,
-0.015158884227275848,
-0.06336093693971634,
0.013183943927288055,
-0.0274981539696455,
-0.03286724165081978,
-0.007274801842868328,
0.04376818239688873,
-0.01189185120165348,
0.004457890056073666,
-0.06339795887470245,
0.03626811504364014,
0.063927561044693,
-0.006162242032587528,
0.05731944367289543,
0.04689789563417435,
-0.01635011099278927,
-0.035797566175460815,
0.06601644307374954,
0.028978712856769562,
-0.015142216347157955,
0.06146911904215813,
-0.003933857195079327,
0.02650706097483635,
-0.025423990562558174,
-0.02317788638174534,
-0.05614081025123596,
0.021964963525533676,
0.06343546509742737,
0.016319802030920982,
-0.02156219258904457,
0.033518917858600616,
0.08519992977380753,
0.030144283547997475,
0.05550878494977951,
0.013717291876673698,
-0.02257385477423668,
-0.05649417266249657,
0.08219442516565323,
0.06584644317626953,
-0.0386224128305912,
-0.013782483525574207,
-0.023847080767154694,
0.056873295456171036,
-0.0016070444835349917,
0.03293785825371742,
0.062055375427007675,
-0.0223392266780138,
0.010976457968354225,
-0.07271648943424225,
0.028465725481510162,
-0.00041574751958251,
0.0643170028924942,
0.038024578243494034,
-0.04586824029684067,
-0.0067310454323887825,
-0.021470725536346436,
-0.03810679167509079,
-0.004193792585283518,
0.03179158270359039,
-0.002219432732090354,
-0.07288815081119537,
-0.010395570658147335,
0.0007187456358224154,
0.061915699392557144,
-0.051562029868364334,
-0.08103807270526886,
-0.017075786367058754,
0.04586523771286011,
-0.009579049423336983,
0.0753343477845192,
0.003617561189457774,
-0.008332368917763233,
-0.011599663645029068,
0.010290848091244698,
-0.03432173654437065,
-0.03087932989001274,
0.02099034935235977,
-0.004664720967411995,
-0.06874257326126099,
-0.012018636800348759,
-0.009452039375901222,
-0.042835783213377,
-0.012357192113995552,
0.0037109784316271544,
0.0005761248175986111,
-0.021877314895391464,
0.029949190095067024,
-0.011759068816900253,
-0.05054531618952751,
-0.05449973791837692,
-0.04430775344371796,
-0.01551950816065073,
0.03815772011876106,
0.03220360726118088,
0.036346692591905594,
-0.01107044517993927,
-0.03047020360827446,
0.056539371609687805,
-0.03635102137923241,
0.003581374417990446,
0.001185100874863565,
-0.049219027161598206,
-0.009623896330595016,
0.018359845504164696,
0.04213857650756836,
-0.008399632759392262,
-0.014274348504841328,
-0.009262891486287117,
0.03163571283221245,
0.016867930069565773,
-0.032818399369716644,
-0.00826888345181942,
-0.050451286137104034,
0.026544827967882156,
0.055564530193805695,
0.0449894554913044,
0.01119228359311819,
0.0259601641446352,
0.06888049840927124,
-0.022113794460892677,
0.0781678780913353,
-0.05222238600254059,
0.03720422089099884,
0.021488195285201073,
0.04537719115614891,
-0.021203212440013885,
-0.007705449592322111,
0.002394511364400387,
-0.04684273526072502,
0.03229306638240814,
-0.016486598178744316,
-0.004273355472832918,
-0.048627033829689026,
-0.00840063113719225,
0.009479675441980362,
-0.034177761524915695,
-0.014146607369184494,
-0.02448146604001522,
-0.00008546398748876527,
-0.009961098432540894,
0.0021782503463327885,
0.036858052015304565,
0.051309991627931595,
-0.028725560754537582,
0.11480063945055008,
-0.013901080004870892,
0.03129519894719124,
-0.015450367704033852,
0.008443733677268028,
0.03473007306456566,
-0.00830734334886074,
0.007069305516779423,
-0.014560747891664505,
-0.04933265596628189,
0.03380381315946579,
0.03113827295601368,
0.049507319927215576,
-0.03064723126590252,
0.07255302369594574,
0.044746845960617065,
0.016374612227082253,
-0.027506627142429352,
-0.03490006551146507,
0.018954910337924957,
0.03032558411359787,
0.005950296297669411,
0.04453891143202782,
-0.014111175201833248,
-0.008075760677456856,
0.003609995124861598,
-0.046817269176244736,
-0.0016573502216488123,
-0.028171515092253685,
0.0013763370225206017,
0.016002142801880836,
0.03934796154499054,
0.002714564325287938,
-0.044268298894166946,
0.001920152921229601,
-0.02313362807035446,
0.026826603338122368,
-0.009490219876170158,
0.004835832864046097,
0.021721044555306435,
0.031829215586185455,
-0.0031306070741266012,
-0.026996007189154625,
0.02482573315501213,
0.006351993419229984,
-0.017734205350279808,
-0.005451214499771595,
0.035198062658309937,
0.022190727293491364,
-0.009901315905153751,
0.022099191322922707,
-0.017134258523583412,
0.020855218172073364,
-0.00021788867888972163,
-0.02648448385298252,
-0.003604850033298135,
-0.003615142311900854,
-0.021185897290706635,
-0.011754720471799374,
-0.023395517840981483,
-0.024211425334215164,
-0.038256045430898666,
-0.020486127585172653,
0.015177465043962002,
-0.061969999223947525,
-0.05097891390323639,
-0.08313555270433426,
-0.036885134875774384,
0.05086546018719673,
0.01621527038514614,
-0.0007496991893276572,
0.01925668679177761,
-0.016281001269817352,
-0.03363057225942612,
-0.04552103951573372,
0.010840543545782566,
-0.07186707854270935,
0.018930967897176743,
-0.04963096231222153,
-0.01551531907171011,
-0.02316240221261978,
-0.020865656435489655,
0.022918272763490677,
-0.009400557726621628,
-0.004433971364051104,
0.054137520492076874,
-0.02176460064947605,
0.004510997328907251,
0.016114041209220886,
0.015599621459841728,
0.012036462314426899,
-0.02522134967148304,
0.01990969479084015,
0.01471644826233387,
0.0068976422771811485,
0.01099247857928276,
0.012829418294131756,
-0.02204836905002594,
0.0018375738291069865,
0.010493997484445572,
0.029303256422281265,
0.021285640075802803,
-0.031634312123060226,
0.008421777747571468,
0.004339069593697786,
0.08685843646526337,
0.13119667768478394,
-0.023112662136554718,
0.018033741042017937,
0.009549744427204132,
-0.05071616545319557,
-0.025921812281012535,
-0.05287293717265129,
0.042110465466976166,
-0.040996380150318146,
-0.013814615085721016,
-0.001821101875975728,
-0.023200538009405136,
-0.04750413820147514,
-0.03601573780179024,
0.005177253391593695,
0.05164923518896103,
-0.031230218708515167,
0.018684884533286095,
-0.00423154653981328,
-0.020875459536910057,
0.054951634258031845,
-0.059222061187028885,
-0.06932228803634644,
0.010858958587050438,
-0.015573397278785706,
-0.02832168899476528,
0.03599265590310097,
0.048884984105825424,
0.00932483933866024,
-0.06012512370944023,
0.008681265637278557,
-0.038993872702121735,
0.0017598712584003806,
-0.01572614535689354,
0.018118150532245636,
-0.03804972022771835,
-0.007878012023866177,
-0.005557129625231028,
-0.03894602879881859,
0.0019459502073004842,
-0.04751535877585411,
-0.01090454962104559,
-0.02052096091210842,
0.033682119101285934,
-0.006032957229763269,
0.029748929664492607,
-0.02155778929591179,
0.015369798988103867,
-0.04022374004125595,
-0.0017734247958287597,
0.02135881595313549,
-0.01122599933296442,
0.021661892533302307,
0.02920565754175186,
0.0351833701133728,
-0.04360470548272133,
-0.0455009751021862,
-0.03297065943479538,
-0.046491894870996475,
0.0420043058693409,
0.02479155920445919,
0.008101951330900192,
-0.0162765234708786,
0.03567252680659294,
-0.038455188274383545,
0.07016216963529587,
0.007162585388869047,
0.02206207625567913,
-0.0284400824457407,
-0.002259250031784177,
-0.017230696976184845,
0.0034424401819705963,
0.01886291429400444,
-0.03192580118775368,
-0.004709402099251747,
-0.005204080604016781,
0.003702737158164382,
-0.0028805804904550314,
0.030145272612571716,
0.015318157151341438,
-0.02119394764304161,
-0.01220591738820076,
-0.0010640589753165841,
0.04293518513441086,
0.02860739268362522,
0.011928681284189224,
-0.013898182660341263,
-0.04648580029606819,
-0.005101583898067474,
0.11276116222143173,
0.042767129838466644,
0.024489102885127068,
-0.06697162985801697,
0.02862703800201416,
-0.022524360567331314,
-0.025267532095313072,
-0.01213420182466507,
-0.006583813577890396,
0.010593806393444538,
0.021331707015633583,
0.02322525344789028,
0.02090964838862419,
-0.029336825013160706,
-0.027489161118865013,
-0.0028846412897109985,
-0.03168094903230667,
-0.00148183258716017,
-0.010883246548473835,
-0.08171715587377548,
0.010727609507739544,
0.021979251876473427,
-0.053113821893930435,
-0.008956437930464745,
-0.03137650713324547,
-0.0052261957898736,
0.09578531980514526,
-0.0017666271887719631,
-0.0906200036406517,
0.022203555330634117,
-0.046073831617832184,
0.05639299750328064,
-0.008038923144340515,
0.03655913844704628,
-0.03495611622929573,
0.0185715202242136,
0.027461852878332138,
-0.02702220343053341,
-0.040038738399744034,
0.013633192516863346,
-0.0016276614041998982
] |
<p>I'd like to calculate the distance between the Earth and an asteroid at a given date. Is this possible using the data from <a href="http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=433" rel="nofollow">JPL's small-body database</a>? Is there a better way?</p> | g9170 | [
0.03777741640806198,
0.020418837666511536,
0.00048188044456765056,
-0.041508425027132034,
-0.08700913935899734,
0.006486451253294945,
-0.024974029511213303,
-0.05425017699599266,
-0.05327969044446945,
-0.02384239435195923,
0.039371903985738754,
0.017947357147932053,
0.09341197460889816,
-0.04466932266950607,
0.00590854836627841,
-0.0029274793341755867,
0.07334102690219879,
-0.05787349492311478,
-0.04261483624577522,
0.07118075340986252,
0.1028604507446289,
-0.0012504014885053039,
-0.03662494570016861,
-0.017651904374361038,
0.013724367134273052,
-0.013889789581298828,
-0.0173586905002594,
0.046878986060619354,
-0.059839073568582535,
0.0448700487613678,
-0.04081333428621292,
-0.0024640837218612432,
0.04280246049165726,
0.0026625182945281267,
0.03993295505642891,
0.04255308210849762,
-0.01097098272293806,
-0.012560698203742504,
0.04545818641781807,
0.0010832709958776832,
-0.015765169635415077,
-0.024172501638531685,
0.03394268825650215,
-0.013993306085467339,
0.043152209371328354,
-0.06153861805796623,
-0.026648396626114845,
-0.05088557302951813,
0.04995567724108696,
-0.004306884948164225,
-0.028831683099269867,
0.056350480765104294,
0.0065471515990793705,
0.003954824060201645,
-0.010886981151998043,
-0.008874907158315182,
0.03997359424829483,
-0.0596640408039093,
-0.008574613370001316,
-0.03339981660246849,
-0.02571580372750759,
-0.044130224734544754,
-0.01272521447390318,
-0.004956090822815895,
0.044337984174489975,
0.05023452267050743,
-0.027681533247232437,
-0.03577829897403717,
-0.020229080691933632,
0.011323867365717888,
-0.017318325117230415,
0.033242058008909225,
-0.0012653062585741282,
-0.040012720972299576,
-0.07150205224752426,
-0.005769744515419006,
-0.02478313073515892,
0.015133555978536606,
0.046142902225255966,
0.03782762959599495,
-0.011073963716626167,
0.04565277323126793,
-0.008642715401947498,
-0.06462336331605911,
0.030965149402618408,
0.02689654938876629,
0.021284999325871468,
0.011409925296902657,
0.011139514856040478,
-0.0017294974531978369,
-0.02310333214700222,
0.04460282623767853,
0.009866124019026756,
-0.0018279466312378645,
0.03211021050810814,
0.007085199933499098,
-0.009320002049207687,
0.03246190771460533,
-0.02509240061044693,
0.044966328889131546,
-0.06051788851618767,
0.04177304357290268,
0.04965993016958237,
0.03857410326600075,
-0.006745803169906139,
-0.027797486633062363,
-0.009593268856406212,
-0.006324257701635361,
0.012868699617683887,
-0.04953271895647049,
-0.008270963095128536,
-0.0739576518535614,
0.035758085548877716,
-0.0184344332665205,
0.016457900404930115,
-0.036454781889915466,
-0.042191218584775925,
-0.022935109212994576,
-0.0359153226017952,
-0.010761282406747341,
-0.01381043903529644,
0.015779292210936546,
-0.0009424353484064341,
0.012781072407960892,
-0.057595402002334595,
-0.02946620248258114,
-0.01989988423883915,
0.006610344164073467,
0.04016052931547165,
-0.047346461564302444,
-0.07123670727014542,
-0.01197152677923441,
0.00848870538175106,
0.03528083488345146,
-0.02560778334736824,
-0.004827666096389294,
0.024846425279974937,
0.00729761365801096,
-0.04838277027010918,
0.0211041197180748,
0.0009763837442733347,
-0.030014051124453545,
0.0027916873805224895,
-0.0215266365557909,
-0.030380185693502426,
0.07331813126802444,
-0.05084838345646858,
0.049234163016080856,
0.001555616152472794,
0.049871791154146194,
0.0029109290335327387,
0.024753600358963013,
-0.004527952987700701,
0.04385286942124367,
0.01927340030670166,
0.028446711599826813,
-0.0007568798027932644,
0.040268998593091965,
-0.04111165180802345,
-0.042309537529945374,
0.014962553977966309,
0.019308194518089294,
0.05716283991932869,
-0.02594359964132309,
-0.035523850470781326,
0.048393361270427704,
0.03477516397833824,
-0.015397186391055584,
-0.03844030201435089,
-0.07770998030900955,
-0.02063988894224167,
-0.07093324512243271,
0.05787450820207596,
0.005178686697036028,
-0.010793100111186504,
0.028584880754351616,
0.003213900374248624,
0.010126909241080284,
-0.048872414976358414,
-0.006336131598800421,
0.03811553120613098,
-0.04742836952209473,
0.0441441684961319,
0.08287142217159271,
0.0014030152233317494,
-0.01296914741396904,
0.022191695868968964,
0.006654569413512945,
0.008496895432472229,
0.017221365123987198,
-0.04087436571717262,
-0.0843273401260376,
-0.0010843755444511771,
0.010227733291685581,
-0.0011867526918649673,
0.011538899503648281,
0.01775600202381611,
0.009001617319881916,
-0.030571073293685913,
-0.01075555570423603,
0.0008545006276108325,
0.08426067233085632,
0.010028085671365261,
0.002096319803968072,
0.06157156452536583,
-0.010879626497626305,
0.025097373872995377,
-0.029970955103635788,
-0.06389743089675903,
0.00008049595635384321,
-0.011428000405430794,
0.026194008067250252,
-0.003630776423960924,
0.002762066200375557,
-0.009232822805643082,
-0.0011689598904922605,
-0.038005802780389786,
0.04082348197698593,
-0.003727659350261092,
0.00992368534207344,
-0.01665947027504444,
0.00031438417499884963,
0.05586089938879013,
-0.05006108060479164,
0.06017903611063957,
0.029784156009554863,
0.03783673793077469,
0.06281755864620209,
0.01698358915746212,
-0.023635586723685265,
-0.017496971413493156,
-0.003938779700547457,
-0.022784771397709846,
-0.029259949922561646,
0.08724334836006165,
0.07998039573431015,
0.0489780493080616,
-0.02475920133292675,
-0.011992066167294979,
0.0826745480298996,
0.028986988589167595,
-0.10924038290977478,
0.0072846426628530025,
0.03126348555088043,
0.0764949694275856,
-0.0467132069170475,
0.024684621021151543,
0.02156226336956024,
-0.0018102227477356791,
0.011983489617705345,
0.006569971796125174,
0.03160671144723892,
-0.05180909112095833,
0.05722924321889877,
0.0012164231156930327,
-0.015492658130824566,
-0.06578810513019562,
-0.006019279360771179,
-0.01434340700507164,
-0.0224972665309906,
-0.0028519711922854185,
-0.027416246011853218,
0.03498407080769539,
0.043663252145051956,
0.02259351871907711,
-0.04019545391201973,
-0.05704854801297188,
-0.0013623666018247604,
-0.022374166175723076,
-0.058548420667648315,
-0.012686527334153652,
-0.014007559046149254,
0.08767670392990112,
0.013205258175730705,
-0.012793298810720444,
0.040460120886564255,
0.016467979177832603,
-0.038150854408741,
-0.02980288863182068,
-0.020548077300190926,
0.0341496579349041,
0.0033773882314562798,
0.023723913356661797,
0.05536583065986633,
0.015720590949058533,
-0.002523816656321287,
-0.012820744886994362,
0.02580631710588932,
0.04533565044403076,
-0.025088658556342125,
-0.04038197547197342,
-0.022798659279942513,
0.0129666393622756,
0.08022400736808777,
0.02920829877257347,
0.016901899129152298,
0.026738908141851425,
0.025379832834005356,
0.024235175922513008,
-0.009839284233748913,
0.004580442328006029,
-0.022672200575470924,
0.008709357120096684,
-0.0006558038876391947,
-0.013532121665775776,
-0.04209258779883385,
-0.029011759907007217,
-0.03515757992863655,
-0.03273855522274971,
-0.01871325448155403,
0.0020859583746641874,
0.009405944496393204,
0.01714853011071682,
0.04035041853785515,
-0.04281182959675789,
-0.010933583602309227,
-0.039299119263887405,
0.01812111958861351,
0.04250962659716606,
0.025363925844430923,
0.04170849546790123,
-0.07733523100614548,
-0.025568226352334023,
-0.006898726802319288,
-0.03795522451400757,
0.05861608311533928,
-0.04786425456404686,
0.01711648516356945,
-0.02478613704442978,
0.0011461410904303193,
-0.032579854130744934,
-0.02338865026831627,
-0.0033069229684770107,
0.004780981224030256,
-0.06792529672384262,
0.01022279728204012,
0.024485008791089058,
-0.009629445150494576,
-0.02156049758195877,
0.08808447420597076,
-0.03671390935778618,
0.004633802454918623,
-0.00904032215476036,
-0.03156663104891777,
-0.03483682498335838,
0.034224748611450195,
0.02456154115498066,
0.07651417702436447,
-0.02917318046092987,
-0.03597860783338547,
0.003493545576930046,
-0.0483560748398304,
0.014604872092604637,
-0.06586650758981705,
0.0403982438147068,
0.02938651479780674,
-0.032600581645965576,
0.021652067080140114,
0.033899083733558655,
-0.0010020207846537232,
0.04359979182481766,
0.046119190752506256,
0.018216567113995552,
-0.003715339582413435,
0.0022272642236202955,
-0.046121757477521896,
-0.018456382676959038,
0.019689342007040977,
0.05130918696522713,
-0.01396143063902855,
-0.017104176804423332,
-0.05727984383702278,
0.07826627045869827,
-0.010445748455822468,
0.06274747848510742,
-0.05136044695973396,
0.031502801924943924,
-0.025806818157434464,
-0.023131003603339195,
0.052327658981084824,
0.008078822866082191,
0.03675196319818497,
0.02173355594277382,
0.02226175367832184,
0.00690038176253438,
-0.042228780686855316,
-0.023830987513065338,
0.002277316991239786,
0.03633343428373337,
-0.05318363010883331,
0.004661857150495052,
-0.12988439202308655,
-0.02598153054714203,
0.02471735142171383,
0.047518085688352585,
0.015400807373225689,
-0.021574797108769417,
-0.008643313311040401,
-0.008441459387540817,
0.02797095477581024,
-0.014952922239899635,
0.02722869999706745,
0.025198843330144882,
0.048354655504226685,
-0.05572022870182991,
-0.008171993307769299,
0.018738579005002975,
-0.020480385050177574,
-0.05770193785429001,
-0.026031963527202606,
-0.04927483946084976,
-0.033077605068683624,
-0.06325468420982361,
-0.02067154087126255,
-0.008751116693019867,
-0.0015648591797798872,
-0.005862954072654247,
-0.015201546251773834,
0.027907753363251686,
0.036225493997335434,
-0.04040307179093361,
-0.0032789537217468023,
-0.0039856829680502415,
-0.05148767679929733,
-0.03857109323143959,
0.011919067241251469,
0.010103201493620872,
-0.017436182126402855,
0.03663893789052963,
0.055053289979696274,
0.035200975835323334,
0.0755729004740715,
0.02425200864672661,
0.07140182703733444,
-0.07132609933614731,
0.04033558815717697,
0.02511500008404255,
0.04889465495944023,
0.058158330619335175,
-0.09841364622116089,
-0.011995838023722172,
-0.014191287569701672,
0.11104343831539154,
0.004962234757840633,
-0.05876058340072632,
0.08463159203529358,
-0.05473287031054497,
-0.04199199005961418,
0.005914103239774704,
0.0050269486382603645,
0.03583519905805588,
-0.04552314057946205,
-0.035875894129276276,
0.039602573961019516,
-0.020625554025173187,
-0.012081803753972054,
-0.018844198435544968,
0.05893097072839737,
0.03506660833954811,
0.06402372568845749,
-0.009671671316027641,
0.022957531735301018,
0.039293453097343445,
0.0002593892568256706,
-0.0009155204170383513,
-0.03897619619965553,
-0.027424145489931107,
-0.043221425265073776,
0.026409579440951347,
-0.028115632012486458,
0.016661595553159714,
0.010601473972201347,
0.006144905462861061,
-0.005562282167375088,
-0.0492858923971653,
-0.00003444085450610146,
-0.01739196665585041,
-0.012221729382872581,
0.036911629140377045,
-0.01866571046411991,
-0.04223588481545448,
0.002170149702578783,
-0.01816164143383503,
0.020833171904087067,
0.0007869077962823212,
0.02490346133708954,
-0.03187983110547066,
-0.0008566042524762452,
-0.0030937877018004656,
0.05970241129398346,
-0.043024204671382904,
-0.03478280454874039,
0.017042728140950203,
-0.007987561635673046,
-0.03357549384236336,
-0.03555983677506447,
0.013157256878912449,
-0.03381982073187828,
-0.05617824196815491,
0.0031002021860331297,
-0.01839859038591385,
0.03260523080825806,
0.000796834472566843,
0.006413860712200403,
0.06273633986711502,
0.023576145991683006,
0.017812324687838554,
-0.0012450410285964608,
0.01703127659857273,
-0.009255178272724152,
0.02388508804142475,
-0.00914018228650093,
-0.010681682266294956,
-0.030741296708583832,
-0.020460350438952446,
0.010920831002295017,
0.03465815261006355,
0.046863920986652374,
-0.025980575010180473,
0.0064643314108252525,
0.03099244460463524,
0.0371430367231369,
0.06823913753032684,
0.03736688196659088,
-0.001449897768907249,
0.0033843040000647306,
-0.036421943455934525,
-0.024790873751044273,
-0.023776927962899208,
0.01960972510278225,
-0.026466934010386467,
-0.00698043592274189,
-0.0267157144844532,
-0.009950609877705574,
0.014790061861276627,
-0.006536761298775673,
-0.01591450534760952,
0.018782950937747955,
0.04874016344547272,
-0.11712291091680527,
-0.029467595741152763,
0.004465092904865742,
0.018981702625751495,
0.006921474356204271,
0.0021137655712664127,
-0.056085921823978424,
-0.023109853267669678,
0.03417891263961792,
-0.0013824492925778031,
0.008375318720936775,
0.03239603713154793,
-0.005801528226584196,
-0.008655023761093616,
-0.014989609830081463,
0.011581244878470898,
0.03289870172739029,
0.0018501955782994628,
0.028320187702775,
-0.01522727869451046,
-0.012757346965372562,
0.022390998899936676,
-0.035340551286935806,
-0.033010683953762054,
0.04286270961165428,
-0.07453809678554535,
-0.011039658449590206,
-0.011878096498548985,
-0.009622759185731411,
0.05790150538086891,
-0.050377968698740005,
-0.01967187039554119,
-0.0466424822807312,
-0.033647213131189346,
-0.023352855816483498,
-0.003929940517991781,
-0.004776285961270332,
0.006337189115583897,
-0.01905563473701477,
-0.013446604833006859,
0.027846621349453926,
-0.022441081702709198,
-0.023746946826577187,
-0.03592805936932564,
0.04662605747580528,
-0.05085497722029686,
0.03474542498588562,
-0.013823887333273888,
-0.025458788499236107,
0.0198079664260149,
-0.040157586336135864,
0.040804434567689896,
-0.021512947976589203,
-0.03204888105392456,
-0.021064937114715576,
-0.03351074084639549,
-0.053633857518434525,
-0.051624469459056854,
0.0354277603328228,
-0.018367527052760124,
0.068096823990345,
-0.021580073982477188,
0.01605622097849846,
0.04959976300597191,
0.05049661919474602,
-0.0010130623122677207,
-0.01849943771958351,
-0.038918059319257736,
0.0734606683254242,
0.04851134121417999,
-0.06552114337682724,
0.001497532706707716,
0.06893794238567352,
-0.04548046365380287,
0.05389796197414398,
0.0016372512327507138,
-0.053650230169296265,
-0.028628438711166382,
0.013336041942238808,
-0.029706358909606934,
0.028650814667344093,
0.025415470823645592,
0.015493521466851234,
-0.03738738223910332,
0.00682950671762228,
-0.009975548833608627,
0.02619953267276287,
-0.03866540640592575,
0.006126049440354109,
-0.01644490472972393,
-0.04017507657408714,
0.051691655069589615,
0.0062734466046094894,
0.023401781916618347,
0.012665159069001675,
0.02476196549832821,
0.04683566465973854,
-0.004193448927253485,
0.059491146355867386,
-0.008243138901889324,
0.03990589454770088,
0.011301161721348763,
-0.02507217600941658,
0.00037452956894412637,
0.04285465553402901,
-0.037214137613773346,
-0.026809800416231155,
0.029732543975114822,
0.059077560901641846,
-0.03333000838756561,
-0.00784924067556858,
0.07286180555820465,
-0.021978823468089104,
-0.0011003358522430062,
-0.0038638587575405836,
0.02425738424062729,
-0.0010581539245322347,
-0.00762720312923193,
-0.0177780669182539,
0.029065703973174095,
-0.012015998363494873,
0.023464825004339218,
-0.04186845198273659,
-0.007663381285965443,
-0.06663693487644196,
0.047364845871925354,
0.015148046426475048,
0.011312290094792843,
-0.01596938446164131,
-0.024338867515325546,
-0.022088056430220604,
-0.01572226919233799,
-0.005784547887742519,
-0.045664116740226746,
0.00545646995306015,
-0.0014332947321236134,
0.06789832562208176,
0.05211859568953514,
-0.011212592013180256,
-0.049334120005369186,
0.02355736307799816,
0.038246285170316696,
0.06400971114635468,
-0.030068546533584595,
0.03938523307442665,
-0.05115962773561478,
0.07807284593582153,
-0.0031302545685321093,
-0.005032438784837723,
0.08154004067182541,
-0.025777531787753105,
-0.028581952676177025,
0.02464054524898529,
-0.08900456875562668,
-0.05852440744638443,
-0.03178033232688904,
-0.07648022472858429,
-0.004597925115376711,
0.020365310832858086,
0.018102800473570824,
-0.03493974357843399,
0.002103196457028389,
0.009336897172033787,
0.04581215977668762,
-0.0278608500957489,
0.005777842830866575,
-0.013174722902476788,
-0.0006747783627361059,
0.008845035918056965,
-0.05411617457866669,
-0.005928355269134045,
0.03388609737157822,
0.004271917976438999,
-0.022340692579746246,
-0.004081479273736477,
-0.04175270348787308,
0.043191324919462204,
0.048392049968242645,
0.056513115763664246,
-0.026364635676145554,
0.03294368460774422,
-0.034197673201560974,
-0.01513767708092928,
0.05832592397928238,
-0.022853026166558266,
-0.023950520902872086,
0.0040507325902581215,
-0.046665970236063004,
0.009066064842045307,
0.031342457979917526,
-0.10187218338251114,
0.051527708768844604,
0.039621442556381226,
-0.016662197187542915,
-0.02016606368124485,
0.022381732240319252,
-0.006747680716216564,
-0.06357765942811966,
-0.0572524331510067,
-0.0009427457698620856,
0.07261088490486145,
-0.026348719373345375,
-0.017892764881253242,
-0.004039298743009567,
-0.029777823016047478,
-0.0036111369263380766,
-0.00688905268907547,
-0.010720673948526382,
0.0575106181204319,
0.03981483727693558,
-0.023215970024466515,
0.012295330874621868,
0.026498718187212944,
-0.03585997223854065,
0.03135440871119499,
-0.006943239830434322,
0.03794707730412483,
-0.014414780773222446,
-0.024102726951241493,
0.014301926828920841,
-0.010114459320902824,
-0.011004096828401089,
0.033920060843229294,
0.008405043743550777,
-0.007049018982797861,
0.011333957314491272,
-0.03364678844809532,
-0.002082578605040908,
-0.008139802142977715
] |
<p>This might be an incredibly naive question, but I'm wondering if there are a set of rules for "translating" between Standard Model and SUSY. For instance, if I want want to go from a Standard Model feynman diagram to a SUSY diagram, can one write down a set of rule including things like:</p>
<p>"replace quarks with the corresponding squark"</p>
<p>with the caveat of course that R-parity is conserved (so two SUSY particles at each vertex). Given the underlying symmetry between SM particles and their superpartners, it seems like there should be some type of correspondence between SM feynman rules and the SUSY feynman rules. It seems like it would be incredibly difficult to go through and learn a completely new set of interactions and rules for SUSY. Are there things that carry over from SM Feynman rules that can be used as rules of thumb for figuring out what are the allowed SUSY diagrams for a particular process?</p> | g9171 | [
0.029069917276501656,
0.026392115280032158,
0.020990146324038506,
-0.03071027621626854,
0.022346653044223785,
-0.043215200304985046,
-0.041090965270996094,
0.05545521527528763,
0.0045922319404780865,
-0.013698671013116837,
0.0028373305685818195,
-0.02184051275253296,
0.02200772613286972,
0.011186156421899796,
-0.008483227342367172,
0.03837275505065918,
0.021701792255043983,
-0.026385173201560974,
0.022069931030273438,
0.000182190808118321,
0.026554884389042854,
-0.010104130022227764,
0.024027811363339424,
-0.05161726474761963,
-0.07601616531610489,
-0.04638778418302536,
0.0030070007778704166,
-0.005686966702342033,
-0.03622213751077652,
-0.04952869936823845,
0.03554515913128853,
-0.03037399612367153,
0.0671345442533493,
-0.03918468952178955,
0.025433102622628212,
-0.051587339490652084,
0.04005800560116768,
-0.04386601969599724,
-0.003823103616014123,
0.05172105133533478,
0.02156948111951351,
-0.0018769275629892945,
-0.010887050069868565,
-0.021427258849143982,
-0.01763249561190605,
-0.008404678665101528,
-0.04306108504533768,
-0.02372366189956665,
-0.011154542677104473,
-0.0208708755671978,
0.04219997301697731,
0.012802667915821075,
0.035303451120853424,
0.013337459415197372,
0.01999123953282833,
0.006650776136666536,
0.041135888546705246,
-0.041612494736909866,
0.05399853736162186,
-0.010337271727621555,
-0.0062996032647788525,
-0.03192126005887985,
0.0063428436405956745,
0.06106549873948097,
0.05558755248785019,
0.04901092126965523,
-0.06201643869280815,
-0.02033292129635811,
0.016159644350409508,
0.03565153852105141,
0.011430909857153893,
0.003494259901344776,
0.038339462131261826,
-0.0037617082707583904,
-0.03382487967610359,
0.004997102078050375,
-0.02321024052798748,
-0.026788845658302307,
0.024204852059483528,
0.01633806712925434,
-0.06034477800130844,
-0.01796211674809456,
0.015339480713009834,
-0.014222845435142517,
-0.0048603881150484085,
0.009831405244767666,
-0.0554642528295517,
-0.014149150811135769,
-0.0379951186478138,
0.009818210266530514,
-0.03203905373811722,
-0.028043316677212715,
0.011524360626935959,
-0.00920518022030592,
-0.008138620294630527,
0.026848487555980682,
0.0031007605139166117,
-0.000510397891048342,
-0.013615532778203487,
0.0007683045696467161,
-0.06649089604616165,
0.0012170508271083236,
0.03552497550845146,
-0.008245084434747696,
-0.02130320481956005,
0.007034548092633486,
-0.010373166762292385,
0.041340023279190063,
0.056175168603658676,
-0.01934708096086979,
-0.012722203508019447,
-0.03339150920510292,
-0.01859397627413273,
0.021615080535411835,
-0.046864498406648636,
-0.06924322992563248,
0.04739120602607727,
-0.0024397538509219885,
0.0245626512914896,
0.035187967121601105,
-0.010959154926240444,
0.0006962782936170697,
-0.009570367634296417,
0.03632974624633789,
-0.0182498786598444,
-0.08120886981487274,
-0.03358209505677223,
0.05172482877969742,
0.019062824547290802,
0.02298087812960148,
0.0025622528046369553,
-0.032790910452604294,
-0.019745618104934692,
0.03420881927013397,
-0.04107212647795677,
0.02823774330317974,
0.06345094740390778,
0.0045366412959992886,
0.0838484838604927,
-0.12826526165008545,
-0.02944955602288246,
0.017194610089063644,
-0.06168944016098976,
-0.026215525344014168,
-0.03853965178132057,
-0.017470398917794228,
0.009800011292099953,
-0.0021024043671786785,
-0.06619627773761749,
0.04045688360929489,
0.02939356490969658,
0.04996155947446823,
0.014279220253229141,
-0.007264881394803524,
-0.014409334398806095,
-0.02983030304312706,
-0.008193650282919407,
0.000870494928676635,
0.011310737580060959,
-0.06441471725702286,
0.02706006169319153,
-0.0469929501414299,
-0.03483015298843384,
-0.00041465790127404034,
-0.04900502413511276,
-0.025455767288804054,
-0.033472221344709396,
-0.03599454089999199,
-0.02199247106909752,
-0.054089296609163284,
-0.0478261336684227,
0.00679832324385643,
-0.022325092926621437,
0.09050828963518143,
-0.01629042439162731,
0.055113255977630615,
-0.04849832504987717,
-0.004354637116193771,
0.0251340139657259,
-0.03268153965473175,
-0.06628291308879852,
-0.054915737360715866,
0.046497683972120285,
0.0012783780694007874,
-0.03590817004442215,
0.012532642111182213,
-0.060674045234918594,
0.0223739854991436,
0.04090392589569092,
0.005080017261207104,
-0.03397548571228981,
-0.0224277563393116,
0.0031140034552663565,
0.014694983139634132,
-0.01443981658667326,
-0.02984483540058136,
-0.02151394635438919,
-0.002075206721201539,
-0.0014040516689419746,
0.018957728520035744,
-0.04702981933951378,
0.037905655801296234,
0.04230928793549538,
-0.016596801578998566,
0.04641883075237274,
0.03886668011546135,
-0.021783340722322464,
0.013301758095622063,
0.060000497847795486,
-0.005879368633031845,
0.0014776347670704126,
0.020379703491926193,
0.03036898747086525,
-0.0578535720705986,
-0.001877629547379911,
0.012679323554039001,
-0.012427855283021927,
0.06569478660821915,
0.022250588983297348,
0.029566332697868347,
-0.05420524626970291,
-0.07487298548221588,
0.035002026706933975,
0.019156957045197487,
0.025463037192821503,
0.04805069789290428,
-0.01294048223644495,
0.02969038113951683,
0.024330217391252518,
0.028263689950108528,
-0.059829335659742355,
-0.00962129421532154,
-0.057818785309791565,
-0.07267612963914871,
0.0039038376417011023,
-0.02478311024606228,
0.003915217239409685,
-0.0008162230951711535,
0.053547851741313934,
-0.00537146907299757,
0.047365278005599976,
0.006219206843525171,
0.015078536234796047,
0.011701378040015697,
0.04886442422866821,
-0.028496894985437393,
0.037522125989198685,
0.047598160803318024,
-0.01541389524936676,
0.022115595638751984,
0.009933889843523502,
0.02723594754934311,
-0.008235365152359009,
-0.027407744899392128,
-0.004822714254260063,
-0.014341301284730434,
-0.019138997420668602,
0.04217775911092758,
0.009561554528772831,
-0.0013259687693789601,
0.029106220230460167,
-0.0013528765412047505,
-0.0336570180952549,
0.05221785604953766,
0.003172389231622219,
-0.03182803466916084,
-0.004678712226450443,
-0.011034428142011166,
0.006408983375877142,
0.014705444686114788,
-0.05785467103123665,
-0.021139491349458694,
0.01132114976644516,
-0.01857476681470871,
-0.0037029236555099487,
0.01689434051513672,
-0.011627111583948135,
-0.0017570839263498783,
0.029513824731111526,
0.001225637155584991,
0.0206343661993742,
-0.05595361441373825,
-0.03496404364705086,
0.01407109759747982,
0.0282583124935627,
-0.034730613231658936,
-0.011460202746093273,
-0.008166235871613026,
-0.046840932220220566,
0.04355303570628166,
-0.06938367336988449,
-0.022635402157902718,
0.009015207178890705,
0.03740246593952179,
-0.029148872941732407,
0.0058618392795324326,
-0.02796071395277977,
-0.014833628199994564,
-0.0005469255265779793,
0.05725148320198059,
-0.008533266372978687,
0.005098334047943354,
-0.052680544555187225,
0.07510945200920105,
0.056183964014053345,
0.031031979247927666,
-0.09488604217767715,
-0.01731434464454651,
0.03734596073627472,
-0.025578459724783897,
-0.00020470157323870808,
0.038833968341350555,
-0.024850476533174515,
0.026150396093726158,
-0.042417462915182114,
0.0006010495708324015,
0.035017162561416626,
0.04431964457035065,
0.06086645647883415,
0.0021202026400715113,
-0.03500249981880188,
-0.01299286913126707,
0.10355772078037262,
0.0031752365175634623,
0.042487747967243195,
0.042233776301145554,
-0.012430409900844097,
-0.006031858269125223,
-0.07444677501916885,
-0.0055163842625916,
0.014370321296155453,
0.009399314410984516,
0.02721213363111019,
-0.015454109758138657,
-0.09924545884132385,
0.01387329213321209,
-0.03934571519494057,
-0.04329913854598999,
0.027002999559044838,
-0.08044488728046417,
0.06457700580358505,
-0.01649821177124977,
-0.0073503125458955765,
0.014336992055177689,
0.003829289460554719,
-0.016253966838121414,
0.001106579089537263,
0.004861858673393726,
0.031768396496772766,
-0.07447579503059387,
0.000261014822172001,
0.06880287826061249,
0.06557352095842361,
0.017920782789587975,
-0.0273785088211298,
0.016160527244210243,
-0.014565475285053253,
0.012394574470818043,
-0.017851442098617554,
0.0007175217615440488,
-0.020770732313394547,
-0.015591120347380638,
-0.028180699795484543,
0.016798466444015503,
-0.03357045352458954,
0.09314100444316864,
-0.05551367625594139,
-0.016217827796936035,
0.05670306086540222,
0.002493728417903185,
-0.0392686165869236,
0.028656654059886932,
-0.044267695397138596,
0.02284199371933937,
-0.012140730395913124,
-0.027527563273906708,
0.0295766182243824,
0.03490636870265007,
-0.020330896601080894,
0.049576494842767715,
0.0005712974816560745,
0.06211217865347862,
-0.0426638200879097,
-0.03810606896877289,
0.05292915552854538,
0.027822455391287804,
-0.007786455564200878,
0.038427647203207016,
-0.059781111776828766,
0.04704037681221962,
0.017237242311239243,
-0.026394890621304512,
0.03089682199060917,
0.00785143207758665,
0.05600563436746597,
0.008316307328641415,
0.04676509648561478,
-0.0023891341406852007,
0.011028708890080452,
0.007875231094658375,
-0.059566106647253036,
0.02306288108229637,
-0.03834010288119316,
-0.05317286401987076,
-0.02934744954109192,
-0.04899183288216591,
-0.00009075495472643524,
0.013608023524284363,
0.039345186203718185,
0.025526205077767372,
0.013203650712966919,
0.010910849086940289,
0.05822910740971565,
0.002256837673485279,
-0.0009724564151838422,
0.014169427566230297,
-0.05626050755381584,
-0.05426061153411865,
-0.00043429312063381076,
-0.02210884541273117,
0.007529296446591616,
0.05420466512441635,
0.07090013474225998,
0.017713790759444237,
0.04321476072072983,
-0.07543069124221802,
0.03646637871861458,
-0.02725171111524105,
-0.008050534874200821,
-0.03477936238050461,
0.034682679921388626,
-0.016680505126714706,
-0.03994511812925339,
0.02720070816576481,
-0.05248437449336052,
-0.04294373467564583,
-0.013478154316544533,
-0.013632400892674923,
-0.0533549003303051,
0.05381466820836067,
0.044898949563503265,
-0.035577308386564255,
0.03691680729389191,
-0.0480586476624012,
0.009315543808043003,
0.023421980440616608,
-0.015271100215613842,
-0.008816041983664036,
-0.024096768349409103,
-0.03140818700194359,
-0.025286177173256874,
0.059341877698898315,
-0.026063986122608185,
-0.01897302269935608,
-0.02970070019364357,
-0.021467136219143867,
0.015009939670562744,
0.019157594069838524,
0.07978156208992004,
-0.04771793633699417,
-0.03268023952841759,
0.013229938223958015,
0.04934414103627205,
-0.00729925325140357,
-0.00039067724719643593,
0.061433419585227966,
-0.0671008750796318,
0.047929175198078156,
-0.02363262139260769,
-0.0031955030281096697,
-0.0004945409600622952,
-0.07892793416976929,
0.0532955564558506,
0.01883210428059101,
0.04467739537358284,
-0.01163340825587511,
-0.03282667696475983,
-0.062179870903491974,
0.031470492482185364,
-0.0029303445480763912,
-0.05637919902801514,
-0.009702513925731182,
0.033095624297857285,
-0.019436979666352272,
0.009740401059389114,
-0.006851485930383205,
0.008033937774598598,
-0.008371628820896149,
-0.02533876709640026,
-0.00789548922330141,
-0.02444755658507347,
-0.03296031430363655,
0.01570747047662735,
0.07393206655979156,
-0.026851149275898933,
-0.03226576745510101,
0.08845153450965881,
-0.025537630543112755,
-0.005495321471244097,
-0.02620621956884861,
0.0028060656040906906,
0.020957721397280693,
0.037935979664325714,
0.016364356502890587,
0.009369858540594578,
-0.009657309390604496,
0.024054069072008133,
-0.02658809907734394,
-0.06274206191301346,
-0.0011871057795360684,
0.0877758264541626,
0.0064635914750397205,
-0.014015567488968372,
0.030362434685230255,
-0.02819540537893772,
0.04804287105798721,
0.0006258980138227344,
0.060731492936611176,
-0.024545136839151382,
-0.05476435646414757,
0.029907267540693283,
0.03327902778983116,
-0.031843606382608414,
-0.03802359849214554,
-0.03106921724975109,
0.00266542611643672,
-0.07689287513494492,
0.05178946629166603,
0.09147076308727264,
0.0553438737988472,
0.037672895938158035,
-0.009279663674533367,
-0.029411477968096733,
0.08186584711074829,
0.030776312574744225,
-0.08218289166688919,
-0.057809844613075256,
-0.02106919139623642,
0.0218596700578928,
0.030480699613690376,
0.0010248878970742226,
-0.012045462615787983,
0.01922386884689331,
0.025085225701332092,
0.003429160686209798,
-0.013617663644254208,
0.005059041548520327,
0.03848728910088539,
-0.002788478508591652,
0.025322863832116127,
-0.0556860975921154,
-0.014781972393393517,
-0.021649915724992752,
-0.027190854772925377,
0.004134111572057009,
0.031931210309267044,
-0.0043294248171150684,
0.007534314878284931,
0.05451960116624832,
0.0210672989487648,
0.002417058916762471,
-0.007297502364963293,
0.057648368179798126,
0.001552049070596695,
-0.058289770036935806,
-0.045159999281167984,
-0.059553854167461395,
-0.03796093165874481,
0.09039603173732758,
0.08557231724262238,
0.027095520868897438,
-0.0018031372455880046,
0.026565400883555412,
0.02532217651605606,
-0.06459938734769821,
-0.010476439259946346,
-0.01752791926264763,
-0.004821669310331345,
0.007733580656349659,
-0.027924109250307083,
0.0450410321354866,
0.04666769132018089,
-0.03498685732483864,
-0.04272414371371269,
-0.05747859179973602,
0.05791988596320152,
-0.008895034901797771,
-0.02139090932905674,
0.005372876767069101,
0.07868880778551102,
-0.0023578540422022343,
-0.03122367151081562,
0.006657646037638187,
0.04151071608066559,
0.05855540558695793,
0.029624050483107567,
0.04849177598953247,
0.01096880342811346,
-0.0005532188806682825,
0.05923639237880707,
-0.022765951231122017,
-0.033538803458213806,
0.021603364497423172,
-0.020332632586359978,
0.013657431118190289,
0.08917036652565002,
-0.04908166453242302,
0.0660306066274643,
0.03685218095779419,
-0.012631809338927269,
0.01423573587089777,
-0.0500316396355629,
-0.0475047342479229,
-0.005414022598415613,
-0.004279159940779209,
-0.07125817239284515,
-0.023775730282068253,
0.0032815185841172934,
-0.0786266177892685,
-0.002906804671511054,
0.021189263090491295,
0.026018263772130013,
-0.026021938771009445,
-0.021261904388666153,
0.0007565857376903296,
0.024592556059360504,
0.002356212353333831,
0.041130490601062775,
0.02503950707614422,
-0.011456385254859924,
-0.028193462640047073,
0.0039536431431770325,
0.02158423326909542,
-0.009190748445689678,
0.01654062420129776,
0.0719357430934906,
-0.01876797154545784,
-0.006241826340556145,
-0.0022859738674014807,
0.007066345773637295,
0.026144497096538544,
0.010771716013550758,
0.027598142623901367,
0.01683798059821129,
0.011560704559087753,
-0.03331515192985535,
-0.03529192507266998,
0.01940883882343769,
-0.04229098558425903,
-0.0014275467256084085,
0.044813018292188644,
-0.006531901657581329,
-0.08898070454597473,
-0.03155679255723953,
-0.011421074159443378,
-0.00934866163879633,
-0.043173082172870636,
-0.0019192956387996674,
0.02860485017299652,
-0.039417821913957596,
0.05052375793457031,
-0.02647819183766842,
0.020382406190037727,
-0.0481402687728405,
0.021665243431925774,
-0.0031777271069586277,
-0.04267238825559616,
-0.008853841572999954,
0.02130160667002201,
-0.0533452071249485,
-0.043510813266038895,
-0.05715138837695122,
-0.03255508095026016,
0.011251186020672321,
0.056030914187431335,
-0.01927713118493557,
0.022234253585338593,
0.0410560742020607,
-0.013083434663712978,
-0.03905841335654259,
0.004667576402425766,
-0.06274914741516113,
-0.023705333471298218,
0.029956646263599396,
0.012028387747704983,
0.03389329835772514,
0.040539707988500595,
0.05596388131380081,
-0.012537161819636822,
0.015390104614198208,
-0.040656499564647675,
-0.018655546009540558,
-0.061030805110931396,
-0.00603510020300746,
-0.027683256193995476,
-0.037049148231744766,
0.005197206977754831,
0.043797269463539124,
-0.016528701409697533,
0.05415080115199089,
0.052396729588508606,
-0.01805051788687706,
-0.020620381459593773,
0.023638971149921417,
0.05895150825381279,
-0.006641893647611141,
-0.0492645688354969,
-0.047362010926008224,
0.010196304880082607,
-0.025436729192733765,
0.028054427355527878,
0.054760828614234924,
0.028040379285812378,
0.05762209743261337,
0.04311253875494003,
0.03456469252705574,
-0.002713418798521161,
-0.05069701746106148,
0.0844133049249649,
0.015305432491004467,
-0.027419330552220345,
0.01693897694349289,
-0.029849912971258163,
-0.01330115832388401,
0.036962252110242844,
-0.045610494911670685,
0.07182284444570541,
0.015626847743988037,
-0.03851325809955597,
0.00872291810810566,
0.06563965976238251,
-0.00919910054653883,
0.008324217051267624,
0.03457344323396683,
0.004820572212338448,
0.012246440164744854,
-0.011962390504777431,
-0.01814972795546055,
-0.069862961769104,
0.04162121191620827,
0.020496197044849396,
-0.0030642584897577763,
0.024907046929001808,
-0.017731759697198868,
-0.05341145768761635,
-0.05122110992670059,
-0.007469556760042906,
0.0081022335216403,
-0.02040509693324566,
-0.06247129291296005,
0.005059335380792618,
0.038742054253816605,
0.049096837639808655,
0.016277600079774857,
0.008961972780525684,
0.005012440960854292,
-0.038412876427173615,
0.015148497186601162,
0.0012619593180716038,
0.012242317199707031,
-0.021164726465940475,
0.03198628127574921,
-0.012440205551683903,
0.018409449607133865,
-0.009992562234401703,
0.02193666249513626,
-0.00985951628535986,
0.011675036512315273
] |
<p>I was attempting to do some calculations of apparent magnitude to help solidify my understanding of the topic, but have been running into some confusion.</p>
<p>According to <a href="http://en.wikipedia.org/wiki/Apparent_magnitude#Calculations" rel="nofollow">Wikipedia</a>, the apparent magnitude can be given as:</p>
<p>$m_x = -2.5\log_{10}(F_x/F^0_x)$</p>
<p>where $F_x$ is the observed flux and $F^0_x$ is a reference flux (in other words, this equation provides the <em>difference</em> of apparent magnitude between two observed values). Also, this is assuming that the same wavelength band is used in both flux measurements.</p>
<p><a href="http://en.wikipedia.org/wiki/Luminosity#Computing_between_brightness_and_luminosity" rel="nofollow">Flux</a>, in turn, can be calculated as:</p>
<p>$F = \frac{L}{A}$</p>
<p>where $L$ is the star's luminosity and $A$ is the flux density. Since stars act as point sources, this can be simplified to:</p>
<p>$F = \frac{L}{4\pi r^2}$</p>
<p>where $r$ is the distance to the star.</p>
<p>Since, historically, Vega has been used as the reference zero-point (having an apparent magnitude around 0.03), I tried doing a simple calculation to find out the apparent magnitude of Fomalhaut using the values for luminosity and distance given in Wikipedia for <a href="http://en.wikipedia.org/wiki/Vega" rel="nofollow">both</a> of <a href="http://en.wikipedia.org/wiki/Fomalhaut" rel="nofollow">them</a>.</p>
<p>First, the flux of Vega:</p>
<p>$F_{Vega} = \frac{37\,L_\odot}{4\pi (25.3\,ly)^2}$</p>
<p>$F_{Vega} = 4.5999\times 10^{-3}\,L_\odot/ly^2$</p>
<p>Next, the flux of Fomalhaut:</p>
<p>$F_{Fomalhaut} = \frac{17.66\,L_\odot}{4\pi (25\,ly)^2}$</p>
<p>$F_{Fomalhaut} = 2.2485\times 10^{-3}\,L_\odot/ly^2$</p>
<p>Now, to calculate the apparent magnitude:</p>
<p>$m_{Fomalhaut} = -2.5\log_{10}(\frac{2.2485\times 10^{-3}\,L_\odot/ly^2}{4.5999\times 10^{-3}\,L_\odot/ly^2})$</p>
<p>$m_{Fomalhaut} = 0.7777$</p>
<p>Huh?? Fomalhaut's apparent magnitude is supposed to be <strong>1.16</strong>. Even correcting for Vega's offset of 0.03, we still come up with <strong>0.8077</strong>. Why are the calculations failing? I don't think I've made a mistake in the mathematics. Am I using the wrong values?</p> | g9172 | [
-0.013298939913511276,
-0.04840618744492531,
0.00489838095381856,
-0.018368203192949295,
-0.012499669566750526,
0.040461815893650055,
0.06252812594175339,
0.004487954545766115,
-0.03955678641796112,
-0.02400060184299946,
0.016105663031339645,
0.05873452499508858,
0.07892893254756927,
0.0043832967057824135,
0.05061677098274231,
0.05269573628902435,
0.07663244754076004,
-0.006178352050483227,
0.05312595143914223,
0.014623105525970459,
-0.042149052023887634,
-0.012239104136824608,
-0.01293118018656969,
-0.01561691239476204,
-0.07855409383773804,
-0.010381396859884262,
-0.03770384564995766,
0.011629522778093815,
-0.03388827666640282,
-0.029480811208486557,
0.021952403709292412,
0.022395644336938858,
0.0898376926779747,
0.002656487515196204,
-0.025504255667328835,
0.039539884775877,
0.017438281327486038,
0.06272570788860321,
0.027127424255013466,
0.0009656660840846598,
0.03273141756653786,
0.02013924904167652,
0.05855056270956993,
0.0414523109793663,
-0.0763680562376976,
0.006705625914037228,
-0.06393904983997345,
-0.008430424146354198,
0.023130161687731743,
-0.00719783129170537,
0.028851700946688652,
-0.0035089675802737474,
0.04910662770271301,
-0.006853427272289991,
-0.003444552654400468,
0.037621136754751205,
0.011766801588237286,
-0.040601279586553574,
0.034186918288469315,
0.033421874046325684,
0.03134598210453987,
0.0025210052262991667,
-0.03225310891866684,
-0.007009744644165039,
-0.009715908206999302,
0.024175604805350304,
-0.029282109811902046,
0.022573363035917282,
-0.06770526617765427,
-0.019288916140794754,
-0.07492093741893768,
0.010071043856441975,
-0.03456293046474457,
0.016435150057077408,
-0.0851842388510704,
-0.005212203599512577,
-0.054435525089502335,
0.020951945334672928,
0.01663411781191826,
0.013515835627913475,
0.0206924956291914,
-0.013619812205433846,
0.02294999733567238,
0.07270904630422592,
0.04993760585784912,
-0.006958761718124151,
-0.026027685031294823,
0.01785086840391159,
0.03878879174590111,
-0.0035715114790946245,
-0.026203561574220657,
0.06821233779191971,
0.03697522357106209,
-0.06622278690338135,
-0.01812606304883957,
-0.012090775184333324,
0.0024152861442416906,
0.02211601473391056,
-0.009705073200166225,
0.05636415258049965,
0.00108806521166116,
0.049783315509557724,
0.011091668158769608,
0.04108601436018944,
0.039784025400877,
0.04149656370282173,
0.08166266977787018,
0.021217575296759605,
-0.04410121589899063,
-0.011338659562170506,
-0.08325216174125671,
-0.014533963054418564,
0.0608016736805439,
-0.046614184975624084,
-0.046330247074365616,
-0.04671734943985939,
0.04923810064792633,
-0.029084812849760056,
0.03481452539563179,
0.0360976867377758,
-0.0026885319966822863,
0.042276520282030106,
0.05663995072245598,
0.08823687583208084,
0.003994896076619625,
-0.05581637844443321,
0.009061343036592007,
-0.022744065150618553,
0.030613159760832787,
-0.024838758632540703,
-0.013155939988791943,
-0.013367275707423687,
-0.010809182189404964,
0.008086579851806164,
0.03209821507334709,
-0.008161303587257862,
0.013237315230071545,
-0.004856818355619907,
-0.02812173403799534,
0.06631207466125488,
-0.014654840342700481,
-0.019659580662846565,
0.01456311997026205,
-0.07064853608608246,
-0.017046969383955002,
0.015336280688643456,
-0.059237290173769,
-0.05723907798528671,
0.06778934597969055,
-0.01940929889678955,
0.05151212215423584,
0.09315507858991623,
0.009849811904132366,
0.01157337799668312,
-0.047450874000787735,
0.02458730712532997,
-0.0028550110291689634,
-0.026283638551831245,
-0.05246691778302193,
-0.0015749450540170074,
0.03383386507630348,
-0.027318863198161125,
0.06197906658053398,
-0.01899470016360283,
-0.005261143669486046,
0.03597317263484001,
0.040948860347270966,
-0.09050563722848892,
-0.04120438173413277,
0.0020837949123233557,
-0.011737380176782608,
0.013324247673153877,
0.07643250375986099,
-0.028487304225564003,
-0.02739238552749157,
0.006193175446242094,
0.07905974239110947,
0.00703055365011096,
-0.03929576277732849,
0.02999691106379032,
0.013506654649972916,
0.00016181408136617392,
-0.0018392516067251563,
-0.03380111977458,
0.003961533773690462,
-0.06150883436203003,
0.05475234612822533,
-0.013006608001887798,
-0.011918268166482449,
0.05883318930864334,
-0.02554265782237053,
0.022616099566221237,
0.004876714665442705,
0.05293027311563492,
0.008840013295412064,
-0.01941516436636448,
-0.020811118185520172,
-0.03816475346684456,
-0.02869972586631775,
0.0349888876080513,
0.0022685539443045855,
-0.011129588820040226,
-0.012223085388541222,
0.012281935662031174,
0.007077164016664028,
-0.0012040731962770224,
0.003777784528210759,
-0.015583688393235207,
-0.003761517582461238,
0.0342438742518425,
-0.07114366441965103,
-0.026574784889817238,
0.018227363005280495,
0.03505144640803337,
-0.021424848586320877,
0.027054226025938988,
-0.014118881896138191,
0.015874959528446198,
-0.04203538969159126,
0.012692540884017944,
0.0425904281437397,
-0.03478303924202919,
0.06601627916097641,
-0.06648888438940048,
-0.009502398781478405,
0.027190450578927994,
0.0031371749937534332,
-0.024787554517388344,
-0.005663715768605471,
0.039577171206474304,
-0.04064498469233513,
-0.011079962365329266,
-0.00855420995503664,
0.031251806765794754,
-0.016562480479478836,
0.008964006789028645,
-0.04829789698123932,
-0.006659028120338917,
0.029262691736221313,
0.03557107225060463,
0.04882838577032089,
-0.0422491692006588,
-0.07292817533016205,
0.06673075258731842,
0.023647382855415344,
0.0019506430253386497,
-0.015505820512771606,
-0.030584808439016342,
-0.039482928812503815,
0.01086494978517294,
-0.04166552796959877,
0.030246272683143616,
0.04482339322566986,
0.011435731314122677,
0.01209939830005169,
0.03251630440354347,
-0.02990591526031494,
-0.02183441072702408,
-0.05088113248348236,
0.06895537674427032,
-0.014059026725590229,
0.013160193338990211,
0.019204286858439445,
0.030400000512599945,
0.01740616373717785,
0.042470816522836685,
-0.005574476905167103,
0.039881668984889984,
-0.011766993440687656,
-0.0875621885061264,
0.05697900801897049,
-0.02281828783452511,
0.05748588219285011,
0.015673380345106125,
-0.02829757146537304,
0.09736930578947067,
-0.01615896448493004,
-0.0003255809424445033,
0.05073457211256027,
-0.005015627481043339,
0.012661664746701717,
-0.027098318561911583,
-0.037921592593193054,
0.004573069512844086,
-0.012713766656816006,
-0.07445468753576279,
-0.008175499737262726,
0.00642851646989584,
-0.017484962940216064,
-0.012758557684719563,
0.007258083205670118,
-0.006079788785427809,
-0.03028903901576996,
0.03240117430686951,
-0.03937925770878792,
0.005684285890311003,
0.03053140453994274,
0.07226195186376572,
-0.01940256357192993,
-0.014798903837800026,
0.0670861303806305,
-0.010268392972648144,
-0.057558681815862656,
0.013392101041972637,
0.04156273603439331,
0.02514204941689968,
-0.009802564978599548,
-0.027937009930610657,
-0.0035572184715420008,
0.009214679710566998,
0.00156527163926512,
-0.028963567689061165,
-0.017542360350489616,
-0.05318247899413109,
0.03879692777991295,
0.005569641478359699,
-0.020309749990701675,
0.01598290726542473,
-0.04636698216199875,
0.05667022615671158,
0.008933215402066708,
-0.04346127063035965,
-0.032199762761592865,
-0.004854987375438213,
0.06407371908426285,
-0.04367939382791519,
-0.035164907574653625,
-0.03169777989387512,
-0.016932757571339607,
-0.03778013959527016,
0.01933358795940876,
0.02359800599515438,
-0.05075908452272415,
-0.07396954298019409,
-0.02855484001338482,
-0.03352992981672287,
-0.02842325158417225,
0.048035088926553726,
-0.05047953501343727,
-0.0357619933784008,
-0.02498321607708931,
-0.01905765011906624,
-0.058185677975416183,
-0.057943195104599,
0.0164885725826025,
-0.013045385479927063,
-0.02882133424282074,
0.0005082938587293029,
-0.014668838120996952,
-0.03206070140004158,
-0.001573606044985354,
-0.02210671827197075,
-0.006211473140865564,
-0.013327463530004025,
-0.00734859611839056,
0.006359375547617674,
0.0029802729841321707,
-0.035016272217035294,
0.035233210772275925,
0.010024752467870712,
0.04586729034781456,
-0.015244248323142529,
-0.031099218875169754,
-0.0478353276848793,
0.043745480477809906,
-0.03822341561317444,
0.012303981930017471,
0.06337152421474457,
0.011699388734996319,
-0.018014514818787575,
-0.02299952134490013,
-0.04170794412493706,
-0.025321759283542633,
-0.053345609456300735,
0.05341751128435135,
-0.02524612471461296,
0.05397028848528862,
0.05176243931055069,
-0.042681045830249786,
0.09036210924386978,
0.05963287502527237,
0.02281797304749489,
-0.026205871254205704,
-0.018217891454696655,
0.02495528943836689,
-0.049007829278707504,
-0.02452736347913742,
0.010137737728655338,
0.02162562496960163,
-0.05379015952348709,
0.016324248164892197,
-0.03052470088005066,
-0.019509024918079376,
-0.006595049984753132,
-0.000449280661996454,
-0.04004942998290062,
0.038343559950590134,
0.03376369550824165,
0.011247966438531876,
0.05369427427649498,
0.03792230784893036,
-0.008077478967607021,
0.014283033087849617,
0.0406266413629055,
-0.002736056922003627,
-0.017837030813097954,
-0.0017515511717647314,
0.008746440522372723,
0.015757951885461807,
-0.00817343033850193,
-0.005952676758170128,
0.03272208943963051,
0.020301729440689087,
-0.0489807166159153,
-0.007581744808703661,
0.036875609308481216,
-0.016642525792121887,
-0.04680300131440163,
0.044349413365125656,
-0.011899775825440884,
-0.013613158836960793,
0.05788756161928177,
0.004826299846172333,
-0.09209845215082169,
0.028444357216358185,
0.07840552181005478,
0.034651875495910645,
-0.030556023120880127,
0.07071693986654282,
-0.007395349908620119,
0.044780295342206955,
0.04651784524321556,
0.004826944787055254,
0.053703662008047104,
-0.056607265025377274,
0.0886692926287651,
-0.0145411416888237,
0.10347924381494522,
0.04380502551794052,
0.009512055665254593,
0.017908012494444847,
-0.013477571308612823,
-0.012067850679159164,
-0.008798480033874512,
-0.030372142791748047,
0.04089660570025444,
-0.02064354717731476,
0.018283024430274963,
0.01755918376147747,
-0.03454367816448212,
0.013020534999668598,
-0.00995479803532362,
0.0494571179151535,
0.001304433448240161,
0.011983969248831272,
-0.01875741221010685,
-0.0015814213547855616,
0.022170500829815865,
-0.011395140551030636,
-0.02174345962703228,
-0.0059510888531804085,
0.016058245673775673,
-0.015882452949881554,
0.006804805248975754,
0.10558939725160599,
-0.03149391710758209,
-0.06796622276306152,
-0.010494210757315159,
0.018117830157279968,
-0.021845543757081032,
-0.029018277302384377,
-0.016562296077609062,
0.0264491718262434,
-0.0012668748386204243,
-0.029062261804938316,
-0.017152786254882812,
0.013860630802810192,
-0.00019258030806668103,
-0.008627761155366898,
0.01724252849817276,
-0.050649017095565796,
0.016295302659273148,
0.04355751723051071,
0.03513602912425995,
-0.012932069599628448,
0.10671326518058777,
0.006664401385933161,
-0.03515319153666496,
0.07960814982652664,
0.008264043368399143,
0.01754036173224449,
-0.04568296670913696,
0.028283078223466873,
-0.004415197763592005,
-0.002743114484474063,
-0.03480486199259758,
-0.021741187199950218,
-0.024014130234718323,
-0.020079219713807106,
0.0062944842502474785,
-0.05796981230378151,
0.06504113972187042,
-0.02992665208876133,
-0.005137019325047731,
0.022710857912898064,
0.02700076252222061,
0.027075957506895065,
-0.014078796841204166,
0.016337648034095764,
0.032016556710004807,
0.034723810851573944,
0.002380446530878544,
0.029589401558041573,
-0.02777709811925888,
-0.016754399985074997,
-0.019013449549674988,
0.021082501858472824,
0.004728693515062332,
0.013285317458212376,
-0.05299791321158409,
0.02643389068543911,
0.008497546426951885,
0.007685080170631409,
-0.044680025428533554,
0.008820884861052036,
-0.030933711677789688,
-0.03299207612872124,
-0.02803664281964302,
-0.04031984880566597,
-0.00572809437289834,
-0.06459568440914154,
0.06157004460692406,
-0.0024343361146748066,
-0.02873562090098858,
-0.019577031955122948,
0.044015154242515564,
-0.034911733120679855,
-0.036802154034376144,
0.01940244436264038,
-0.01921997033059597,
0.003636070294305682,
0.0290661733597517,
-0.04359973967075348,
0.008049916476011276,
-0.019993135705590248,
-0.012003292329609394,
0.0599961020052433,
0.02131504751741886,
0.0232181828469038,
-0.006097276229411364,
-0.017825471237301826,
0.02157364785671234,
0.0014917532680556178,
0.018987933173775673,
0.04400213807821274,
0.020901668816804886,
-0.0038263252936303616,
-0.026027174666523933,
-0.06147178262472153,
-0.028933823108673096,
0.03979555144906044,
0.030760399997234344,
-0.037887636572122574,
-0.021043770015239716,
0.0059708296321332455,
0.012293847277760506,
0.01532711461186409,
-0.017657814547419548,
0.006210052873939276,
-0.017716888338327408,
0.008068996481597424,
0.0004986863932572305,
0.03516622632741928,
-0.07465702295303345,
0.06575466692447662,
0.0832459032535553,
-0.023723769932985306,
-0.06006024777889252,
-0.03462515398859978,
-0.040182098746299744,
0.049425043165683746,
-0.0018057333072647452,
0.017000319436192513,
-0.018115025013685226,
-0.026154080405831337,
0.022181754931807518,
-0.06057843565940857,
-0.029280509799718857,
0.001632382394745946,
-0.06639423221349716,
0.034085508435964584,
-0.01828678697347641,
0.001893316744826734,
-0.06360944360494614,
-0.03713054582476616,
-0.05489868298172951,
-0.08131162822246552,
0.024098031222820282,
-0.06796540319919586,
-0.003902578726410866,
0.043204691261053085,
-0.004688977263867855,
0.046636782586574554,
-0.03244108334183693,
0.012951867654919624,
-0.04636430740356445,
-0.015966016799211502,
0.03464946895837784,
-0.021608831360936165,
0.01887999288737774,
-0.014891251921653748,
0.10216982662677765,
-0.0016572983004152775,
0.05116438493132591,
-0.021050261333584785,
-0.041256383061409,
-0.02773617021739483,
0.004329348914325237,
-0.00024721844238229096,
0.03942200541496277,
0.03738899156451225,
-0.06591495871543884,
0.017838120460510254,
-0.0043180580250918865,
0.03143592178821564,
0.06215729936957359,
0.020649509504437447,
-0.00559342373162508,
0.03891944885253906,
-0.027554497122764587,
0.014508586376905441,
-0.023097312077879906,
0.01915070414543152,
-0.010841763578355312,
0.060392189770936966,
0.015669826418161392,
-0.0010124749969691038,
0.010489528998732567,
0.005686124786734581,
0.006714716553688049,
-0.04166988655924797,
-0.0329882949590683,
0.034467171877622604,
0.008702922612428665,
0.03913050889968872,
0.01135912537574768,
-0.0410723052918911,
-0.013872805051505566,
-0.0539027601480484,
0.03705819696187973,
0.025718729943037033,
-0.04602472111582756,
0.0024255095049738884,
0.018964622169733047,
-0.02206869050860405,
0.012249970808625221,
-0.012975042685866356,
0.005267737433314323,
-0.0035278245341032743,
-0.005892586894333363,
0.02209562249481678,
-0.02945154905319214,
-0.012787820771336555,
-0.0012536552967503667,
-0.018035177141427994,
0.02043306827545166,
0.03634677082300186,
-0.040011655539274216,
-0.05034061148762703,
0.03586553782224655,
0.025024889037013054,
-0.016827013343572617,
-0.013342754915356636,
-0.03394046053290367,
0.01806381531059742,
-0.024075502529740334,
-0.010219261981546879,
0.007585134822875261,
0.008176890201866627,
-0.041311800479888916,
-0.0028514915611594915,
-0.004064036998897791,
-0.026674069464206696,
-0.013196839019656181,
-0.035582173615694046,
0.023666536435484886,
-0.050425104796886444,
-0.06285123527050018,
-0.016601966693997383,
-0.004577997140586376,
-0.024769915267825127,
-0.0327213816344738,
0.03113423101603985,
-0.0067349630407989025,
0.08014293760061264,
0.01093482505530119,
0.06381400674581528,
0.008256391622126102,
0.06322179734706879,
0.034247033298015594,
0.04348042234778404,
-0.049022722989320755,
0.0042728884145617485,
-0.0272405743598938,
-0.011043131351470947,
0.028186384588479996,
0.03925003483891487,
0.03899605572223663,
-0.0435897633433342,
-0.054177168756723404,
-0.015092447400093079,
-0.006926422473043203,
0.06943970173597336,
-0.03893427550792694,
0.029658209532499313,
-0.004006248898804188,
-0.03021600842475891,
0.01548620406538248,
-0.01136014610528946,
-0.01458502933382988,
-0.06776808947324753,
0.018924226984381676,
0.028377002105116844,
-0.023799965158104897,
-0.02750200219452381,
0.01829766295850277,
0.02201126329600811,
0.03183973580598831,
0.0012467904016375542,
-0.014543510973453522,
-0.03041832149028778,
0.001215228228829801,
-0.026850314810872078,
0.005977322813123465,
-0.07226767390966415,
-0.04794490337371826,
0.029721885919570923,
0.027471520006656647,
-0.0043637449853122234,
0.0360470749437809,
-0.06629610061645508,
-0.04277750477194786,
0.03737360239028931,
0.00021244733943603933,
-0.035414762794971466,
-0.029312465339899063,
0.00851519126445055,
0.010851561091840267,
-0.02641509473323822,
-0.052643198519945145,
-0.04312460497021675,
-0.0013086763210594654,
0.04717397689819336,
0.011730310507118702,
0.059240397065877914,
-0.04214740917086601,
-0.07295908033847809,
-0.03946831822395325,
0.005243497900664806,
-0.025200478732585907,
-0.025759929791092873,
-0.042398639023303986,
0.0018878956325352192,
0.0247949305921793,
-0.029386546462774277,
-0.06156471371650696,
-0.08285551518201828,
0.04006775841116905
] |
<p>When we first learn elementary geometrical optics, the first thing taught to us is the two broad divisions of the type of reflection.-Regular and Irregular or Diffused.<br>
The difference in cause for both of these is that in case of regular reflection an incoming ray is perfectly reflected in a specific direction but in diffused reflection, the reflected ray are diffused in several direction probably owing to minor irregularities of the surface. Hence the diffuse reflection does not form our image as a mirror does but instead produces general luminance. But then in case of multi-media-projectors or when we use a paper or a wall as a screen for real images, an otherwise diffuse surface (wall, paper, etc) produces an image which can be seen by us. Is this not only possible when the incoming rays are REGULARLY reflected on to our eyes? </p> | g9173 | [
-0.009909850545227528,
0.01586347259581089,
-0.003431465243920684,
-0.03224446251988411,
0.031238267198204994,
-0.0036993022076785564,
0.05907858908176422,
0.030118748545646667,
-0.027981627732515335,
-0.04298224300146103,
0.03223563730716705,
0.009759778156876564,
0.07789898663759232,
0.01893988624215126,
-0.004117462784051895,
-0.006989248562604189,
0.051825691014528275,
-0.03888192027807236,
0.0032042788807302713,
0.052760280668735504,
-0.03875597193837166,
0.018583258613944054,
0.04476045072078705,
-0.07681844383478165,
-0.0515735000371933,
0.0015946326311677694,
-0.002191325183957815,
-0.046514976769685745,
-0.057884566485881805,
-0.040968652814626694,
0.010013335384428501,
-0.002608911832794547,
-0.0023725470528006554,
-0.008710566908121109,
0.01391887478530407,
0.0038506328128278255,
0.007208243943750858,
0.04483739659190178,
0.03089529648423195,
0.009664880111813545,
-0.03995249420404434,
0.030127665027976036,
0.021363498643040657,
0.0022710920311510563,
-0.021687928587198257,
-0.017913641408085823,
-0.07670395076274872,
-0.03679225593805313,
0.000618445803411305,
-0.03887343779206276,
0.015347246080636978,
0.004375899210572243,
0.026985101401805878,
-0.02236773818731308,
-0.017597954720258713,
0.021442078053951263,
-0.061515942215919495,
0.009954017587006092,
0.08151848614215851,
-0.003275498514994979,
0.008021770976483822,
0.024875080212950706,
-0.0018282504752278328,
0.07864898443222046,
0.05773801729083061,
-0.02792859636247158,
-0.062329888343811035,
0.001055095694027841,
0.02277979999780655,
-0.06065211445093155,
0.03359019383788109,
-0.024153482168912888,
0.03725311532616615,
-0.03349972516298294,
0.00006030736039974727,
-0.049971889704465866,
0.042796824127435684,
-0.01658140867948532,
-0.027659904211759567,
0.029986292123794556,
0.03160012513399124,
-0.0354042686522007,
0.0014793851878494024,
-0.008997137658298016,
0.06844224780797958,
0.05550508201122284,
-0.028841741383075714,
-0.012002912349998951,
0.04158664494752884,
0.021151991561055183,
0.07076514512300491,
-0.029842518270015717,
0.05418650433421135,
0.09874238073825836,
0.012287989258766174,
-0.020806990563869476,
-0.008328977040946484,
0.026334788650274277,
-0.07184068113565445,
0.008077803999185562,
-0.06100353226065636,
-0.025703035295009613,
0.032843850553035736,
0.03198331966996193,
0.024679213762283325,
0.021514732390642166,
0.030833963304758072,
0.0007195608341135085,
-0.04690774157643318,
0.03477737680077553,
-0.06030181422829628,
-0.08345966786146164,
-0.07443294674158096,
-0.0004198712995275855,
0.02019384875893593,
-0.020014334470033646,
0.052795086055994034,
0.030552610754966736,
-0.009569118730723858,
0.13594068586826324,
-0.006283343303948641,
0.01221192441880703,
0.013592020608484745,
0.06069881096482277,
0.01713010109961033,
0.03346991166472435,
-0.009140162728726864,
-0.05656501278281212,
0.06758219748735428,
-0.0005549435736611485,
0.011186300776898861,
0.04359959438443184,
-0.037344224750995636,
0.01275614369660616,
0.04863903298974037,
0.08270633965730667,
0.036368049681186676,
-0.014322017319500446,
0.0334646962583065,
0.030606502667069435,
0.03762480616569519,
-0.02010010927915573,
-0.06885646283626556,
-0.04352707788348198,
-0.03409149870276451,
-0.021800074726343155,
-0.002101944060996175,
-0.006909143645316362,
0.015278864651918411,
0.001177429803647101,
-0.0005697158630937338,
0.031449440866708755,
0.026150399819016457,
0.02226361818611622,
-0.003072804305702448,
-0.0877302810549736,
-0.051635343581438065,
-0.02616758458316326,
-0.00514503987506032,
-0.014027654193341732,
0.05043032392859459,
-0.052263714373111725,
-0.08827703446149826,
-0.011514894664287567,
-0.05911964178085327,
-0.049050550907850266,
-0.006228941958397627,
-0.06547734141349792,
-0.015866795554757118,
-0.0630543977022171,
-0.011202066205441952,
0.10174745321273804,
-0.027671417221426964,
-0.004418093711137772,
0.010187963955104351,
0.022117335349321365,
0.04454827681183815,
-0.01020011305809021,
0.012702365405857563,
0.03832699730992317,
-0.08388020843267441,
0.027346299961209297,
-0.06677647680044174,
-0.10418379306793213,
0.039043255150318146,
-0.011468523181974888,
0.0062866248190402985,
-0.02925761230289936,
-0.009716367349028587,
0.035250741988420486,
0.011198731139302254,
0.012006526812911034,
0.0059066093526780605,
0.007348745130002499,
0.019149387255311012,
-0.008781294338405132,
0.04628780484199524,
0.010209708474576473,
-0.029703602194786072,
-0.006804984994232655,
-0.015706848353147507,
0.04078645631670952,
0.03554393723607063,
0.047438833862543106,
-0.021217530593276024,
0.03199649229645729,
0.011482413858175278,
0.01612686738371849,
0.010195789858698845,
-0.03981756046414375,
0.005026016850024462,
-0.0424966923892498,
-0.006715084426105022,
-0.0331631563603878,
-0.006003310438245535,
-0.009358321316540241,
-0.07583926618099213,
0.0016619237139821053,
0.010919071733951569,
0.021483592689037323,
0.014792114496231079,
0.028682531788945198,
0.0007295527029782534,
0.0020097556989639997,
-0.03487129509449005,
0.07130927592515945,
0.006845035590231419,
-0.00411986606195569,
-0.011642773635685444,
0.05392196401953697,
-0.05186444893479347,
-0.07003388553857803,
0.04077649489045143,
0.013793988153338432,
0.03312142565846443,
-0.034903790801763535,
-0.056671515107154846,
-0.022006850689649582,
0.04301798716187477,
0.006149367429316044,
0.04381844028830528,
-0.025740010663866997,
-0.04559478536248207,
-0.05476972460746765,
-0.03535352274775505,
-0.035782232880592346,
0.04922474920749664,
0.02634783834218979,
0.04265720024704933,
0.0261901393532753,
-0.0029029538854956627,
-0.035935115069150925,
0.011156203225255013,
-0.03522857278585434,
-0.01512126624584198,
-0.00992466788738966,
-0.005749957170337439,
-0.013911952264606953,
-0.008288746699690819,
0.006690330803394318,
0.012805487029254436,
-0.029972553253173828,
0.04643598943948746,
-0.005584887694567442,
-0.04364379122853279,
0.008694800548255444,
0.012201431207358837,
0.05949597805738449,
-0.005028125364333391,
0.04966912418603897,
0.036333996802568436,
0.06071918085217476,
0.030027898028492928,
0.014547093771398067,
-0.05584441125392914,
0.03182731568813324,
-0.02258584089577198,
-0.04999751225113869,
-0.014551113359630108,
0.004573986399918795,
-0.00180139543954283,
0.046069711446762085,
-0.03338715061545372,
-0.03814798966050148,
0.032761961221694946,
-0.009769129566848278,
0.04675066098570824,
0.03241895139217377,
-0.021582601591944695,
0.03082781285047531,
-0.110774464905262,
-0.04117092490196228,
0.015094086527824402,
-0.0033509309869259596,
-0.044958893209695816,
0.03320375457406044,
0.011641551740467548,
0.028708210214972496,
0.008830832317471504,
0.014903507195413113,
-0.0791921615600586,
0.012745842337608337,
0.023033257573843002,
0.01495339348912239,
0.01747402735054493,
-0.004084084182977676,
0.01890472136437893,
-0.03322412818670273,
0.04503044858574867,
-0.03560757637023926,
-0.01652238517999649,
0.03151821717619896,
-0.04267110675573349,
0.0898333415389061,
0.01818203739821911,
-0.02531929314136505,
0.02585620991885662,
0.016369575634598732,
0.017015691846609116,
0.0593804232776165,
-0.013552063144743443,
0.0507315918803215,
-0.03203180432319641,
-0.05558748543262482,
0.014043526723980904,
0.004883005283772945,
-0.0019404646009206772,
-0.00026131074992008507,
-0.0426035039126873,
-0.013748479075729847,
-0.014461852610111237,
0.006357547827064991,
-0.07492949813604355,
-0.01602858677506447,
0.026639424264431,
0.02545267343521118,
-0.05082044377923012,
-0.022462232038378716,
0.04858973249793053,
-0.033204637467861176,
0.06520029157400131,
-0.0018198605393990874,
-0.08453792333602905,
-0.04036906734108925,
0.05779889598488808,
-0.010650512762367725,
-0.04019956663250923,
-0.0012574270367622375,
-0.05128569155931473,
-0.009637819603085518,
0.04384656623005867,
0.017028339207172394,
0.059167999774217606,
-0.010456029325723648,
0.023546958342194557,
0.028406918048858643,
0.003963058348745108,
0.013491454534232616,
0.021020058542490005,
-0.035435374826192856,
0.0013851665426045656,
-0.019889114424586296,
-0.004358377773314714,
-0.0007056082249619067,
0.011249689385294914,
-0.020191075280308723,
0.0506078377366066,
0.030471129342913628,
-0.025385232642292976,
0.03813128545880318,
-0.01993558555841446,
-0.032597050070762634,
-0.02355385199189186,
0.0004287834162823856,
-0.024249501526355743,
0.01859048753976822,
-0.011683744378387928,
-0.016555048525333405,
-0.041211582720279694,
-0.021468427032232285,
-0.013650146313011646,
0.027670420706272125,
0.03507276996970177,
-0.016862599179148674,
0.006792121101170778,
0.03645015135407448,
-0.000404370337491855,
-0.02390611730515957,
0.05271788686513901,
-0.03865668922662735,
0.043345365673303604,
-0.001167632290162146,
-0.004911166615784168,
-0.008016158826649189,
-0.002859643427655101,
-0.020827220752835274,
0.04680561274290085,
-0.023873884230852127,
-0.028662513941526413,
-0.0008812433225102723,
0.014689875766634941,
0.031761277467012405,
0.013269539922475815,
0.020699944347143173,
-0.034419506788253784,
0.012008191086351871,
0.07102636247873306,
-0.011333288624882698,
0.002967085922136903,
-0.01625669002532959,
-0.022415615618228912,
-0.02384014241397381,
-0.022091245278716087,
-0.05795462429523468,
0.048452433198690414,
0.02538825012743473,
0.004861835390329361,
0.039213575422763824,
0.008144191466271877,
-0.005266877822577953,
-0.008941194973886013,
0.08133269846439362,
-0.040705230087041855,
0.0248060654848814,
0.014625045470893383,
0.0564449317753315,
0.044912680983543396,
-0.018762895837426186,
-0.02314956858754158,
-0.018389882519841194,
0.05650153383612633,
-0.001100642723031342,
-0.009667628444731236,
0.011693506501615047,
-0.015841025859117508,
-0.026870090514421463,
-0.02785634621977806,
0.07130192965269089,
0.03064790368080139,
0.0489061139523983,
0.06768098473548889,
-0.01994384452700615,
0.029122618958353996,
-0.022845374420285225,
0.00004926678957417607,
0.056930992752313614,
-0.03961767256259918,
0.006625826936215162,
0.022741854190826416,
0.04164169356226921,
-0.03428727015852928,
-0.027398154139518738,
0.004066443536430597,
-0.0374411977827549,
-0.010093070566654205,
0.004643305204808712,
-0.04389822855591774,
0.03558626398444176,
0.017271442338824272,
0.04687846451997757,
0.024687951430678368,
0.007000112906098366,
-0.003818643046543002,
0.0170325618237257,
0.010968397371470928,
-0.012349647469818592,
-0.04375738278031349,
0.0051357862539589405,
-0.0831267312169075,
-0.04038410633802414,
-0.00952205341309309,
0.07637359946966171,
0.049933817237615585,
0.01079937256872654,
-0.0109122758731246,
-0.00557053554803133,
-0.041929300874471664,
-0.030070461332798004,
-0.04421739652752876,
-0.012439531274139881,
-0.0024726795963943005,
-0.05157168582081795,
0.0177773330360651,
-0.029958153143525124,
-0.006941111292690039,
0.02655552141368389,
-0.022185999900102615,
0.010068606585264206,
-0.02514764294028282,
0.011897043325006962,
-0.018222223967313766,
-0.043801430612802505,
-0.008860290050506592,
-0.029495084658265114,
-0.010858039371669292,
-0.016870593652129173,
0.0573599636554718,
-0.018368734046816826,
-0.012275724671781063,
0.02352849394083023,
-0.046078987419605255,
0.003344322321936488,
0.009237293154001236,
-0.02896101400256157,
0.019889933988451958,
0.012310542166233063,
0.04642344266176224,
-0.08970210701227188,
-0.011580226942896843,
0.10669664293527603,
-0.004553928039968014,
-0.07370021939277649,
-0.012229039333760738,
0.01332616712898016,
0.025285344570875168,
-0.06541868299245834,
-0.03382806107401848,
0.06950309127569199,
-0.0014392690500244498,
-0.008110606111586094,
-0.0481930747628212,
-0.00982990488409996,
0.023342741653323174,
0.03001922369003296,
0.06361496448516846,
-0.016198555007576942,
-0.004209381062537432,
-0.035912856459617615,
0.05549568310379982,
0.0061233933083713055,
0.022155124694108963,
0.08469074964523315,
-0.0010501992655918002,
0.029833102598786354,
0.037508513778448105,
-0.06790285557508469,
-0.012818729504942894,
0.02444467879831791,
0.028118327260017395,
0.008670569397509098,
-0.053175244480371475,
0.01201583817601204,
0.03018193691968918,
0.03271741792559624,
0.07295113801956177,
0.007684771437197924,
-0.02663062885403633,
-0.0077264620922505856,
0.025065073743462563,
0.008385265246033669,
0.0032866972032934427,
0.015293224714696407,
-0.030913911759853363,
0.020407123491168022,
-0.009760947898030281,
0.025752348825335503,
-0.05946784093976021,
-0.006587632931768894,
-0.00028685995494015515,
-0.01100210566073656,
0.0664764940738678,
0.04739561676979065,
0.022252444177865982,
-0.06362272053956985,
-0.04687294736504555,
-0.06321686506271362,
-0.0024046674370765686,
-0.005385890137404203,
0.04885672405362129,
0.044889796525239944,
0.0043265544809401035,
-0.04579611122608185,
0.02361045777797699,
0.004717455245554447,
-0.0016581678064540029,
-0.03899640589952469,
0.02109691873192787,
-0.0015012338990345597,
-0.015611699782311916,
0.03098178282380104,
0.024855703115463257,
-0.004867632407695055,
0.0024560189340263605,
-0.042471837252378464,
0.0072496430948376656,
-0.031971633434295654,
-0.02458464726805687,
0.0005615117261186242,
0.009865210391581059,
-0.05226954445242882,
-0.06007467210292816,
-0.02145961858332157,
-0.015802638605237007,
-0.010183942504227161,
0.007060982286930084,
-0.04689184948801994,
0.005204145796597004,
0.037641145288944244,
-0.03217921778559685,
0.01829870045185089,
0.04271220415830612,
0.04593195021152496,
0.025547314435243607,
-0.06153718754649162,
0.04133131355047226,
0.03850013017654419,
-0.02499382011592388,
0.0018136915750801563,
0.003930903971195221,
0.018186934292316437,
0.04634026065468788,
0.0278281569480896,
-0.029638877138495445,
0.010807338170707226,
-0.03927118703722954,
-0.007087462116032839,
-0.04288586229085922,
-0.059942688792943954,
0.03337255120277405,
-0.07815773040056229,
0.022243576124310493,
-0.018405618146061897,
0.03792461380362511,
0.015795143321156502,
0.022494498640298843,
0.04171791300177574,
-0.05418461933732033,
-0.002033025724813342,
0.015385531820356846,
0.04065356031060219,
0.020774174481630325,
-0.06400416046380997,
0.02831936441361904,
0.02491355687379837,
0.014159017242491245,
0.02288350649178028,
-0.060125160962343216,
0.031156865879893303,
0.01676526665687561,
0.049234163016080856,
-0.020287010818719864,
0.02031984180212021,
0.04293637350201607,
0.011637288145720959,
-0.024321991950273514,
-0.011137440800666809,
-0.02371070720255375,
-0.02909419871866703,
-0.07847514003515244,
0.040500152856111526,
0.033182691782712936,
-0.013132764026522636,
0.0406268946826458,
-0.03552332520484924,
-0.03458431363105774,
0.039272092282772064,
0.03392498567700386,
-0.005403853952884674,
-0.022749053314328194,
-0.09929081797599792,
-0.01681923307478428,
-0.025773214176297188,
-0.062204524874687195,
-0.0445353239774704,
-0.036559153348207474,
-0.011813352815806866,
0.004368853289633989,
0.030994784086942673,
-0.04841526970267296,
0.0011288399109616876,
0.006517674308270216,
-0.055150799453258514,
-0.029351873323321342,
0.049633584916591644,
0.030271735042333603,
0.0035357738379389048,
0.01111582200974226,
-0.0019745524041354656,
-0.0005225777276791632,
-0.024311399087309837,
-0.007755025755614042,
0.04987131059169769,
0.007736885920166969,
0.026055768132209778,
-0.06982577592134476,
0.015534210950136185,
-0.0198633074760437,
0.01569204404950142,
0.012270689941942692,
-0.06762848049402237,
0.0000837031111586839,
-0.015316666103899479,
0.052639614790678024,
0.0299926046282053,
-0.003024943405762315,
-0.036767471581697464,
0.027553865686058998,
0.055273737758398056,
-0.0076807113364338875,
0.001908338163048029,
-0.04308415204286575,
0.006291624158620834,
-0.03865743800997734,
-0.027706801891326904,
0.03054114244878292,
-0.023881463333964348,
-0.007766051683574915,
0.01699325069785118,
0.03661109134554863,
-0.01949896104633808,
-0.012159602716565132,
0.018460405990481377,
-0.00027471414068713784,
0.05530393496155739,
-0.05839853733778,
-0.01373506709933281,
-0.022431809455156326,
0.013602809980511665,
-0.04435884207487106,
0.028132693842053413,
0.017170920968055725,
0.01630983129143715,
-0.020953364670276642,
-0.034029271453619,
-0.0015592646086588502,
0.018933916464447975,
0.0525657944381237,
-0.08540032804012299,
0.05145993456244469,
0.03683977201581001,
0.010699746198952198,
0.06703204661607742,
-0.0025424903724342585,
0.042005494236946106,
0.03802570700645447,
-0.00985799077898264,
0.0175175704061985,
-0.07418570667505264,
0.00042735139140859246,
-0.02339934930205345,
0.02470332384109497,
0.02530001290142536,
-0.00018297928909305483,
-0.046712856739759445,
-0.01753818802535534,
0.03744648024439812,
-0.025878464803099632,
-0.020508158951997757,
-0.007930432446300983,
-0.02877647988498211,
-0.052680227905511856,
0.05046211555600166,
0.029089482501149178,
-0.03362404927611351,
0.07340025901794434,
-0.05964764207601547,
0.02986682578921318,
0.02579435333609581,
0.03759714588522911,
-0.0013497616164386272,
-0.058548763394355774,
-0.038791388273239136,
-0.005331662017852068,
-0.022030046209692955,
0.005225964821875095,
-0.011201662942767143,
-0.03521685674786568,
-0.0032223069574683905
] |
<p>In his QFT book, Weinberg claims what follows (Vol I, pag. 144-145): given a (free) representation of the Poincaré group with generators $\bf P$ (spatial translations), $H_0$ (time translations), $\bf J$ (rotations), and ${\bf K}_0$ (boosts), one obtains another (interacting) reprentation by replacing $H_0$ and ${\bf K}_0$ with
$$
H = H_0 + \int \mathcal{H}({\bf x}, 0) d^3x \; \; \text{ and } \; \; {\bf K} = {\bf K}_0 - \int {\bf x} \mathcal{H}({\bf x}, 0) d^3x,
$$
respectively, where $\mathcal{H}(x)= \mathcal{H}({\bf x}, t)$ is a self-adjoint operator density which is covariant and causal, that is:
$$
U_0(\Lambda, a) \mathcal{H}(x) U_0(\Lambda, a)^{-1}= \mathcal{H}(\Lambda x + a)
\; \; \text{ and } \; \; [\mathcal{H}(x), \mathcal{H}(y )] = 0 \text{ for } (x - y)^2 \geq 0,
$$
where $U_0(\Lambda, a)$ is the free representation.</p>
<p>Weinberg provides only a partial proof of this claim. Does somebody know if this is a rigorous result, and where one can possibly find a complete/rigorous proof?</p> | g9174 | [
0.04045938700437546,
0.024154163897037506,
-0.0421491414308548,
-0.08341706544160843,
-0.02041185274720192,
-0.07478596270084381,
0.07293447852134705,
-0.02707456611096859,
0.00625207182019949,
0.050469476729631424,
-0.04971971735358238,
0.009517326951026917,
-0.02801719307899475,
0.007555861491709948,
-0.018852906301617622,
0.026581618934869766,
0.03070586547255516,
0.07626424729824066,
-0.009389190934598446,
-0.060865726321935654,
-0.025526827201247215,
0.01676422543823719,
-0.03454148396849632,
-0.0427829846739769,
0.051979634910821915,
-0.019720135256648064,
0.03852977976202965,
-0.03971819207072258,
-0.05472169071435928,
-0.03653327003121376,
0.06378761678934097,
0.04018811136484146,
-0.04359489306807518,
-0.055931851267814636,
-0.051306772977113724,
0.01287171058356762,
0.05227382481098175,
-0.019179536029696465,
0.016010386869311333,
0.03282216191291809,
0.01622869446873665,
0.005588284227997065,
0.07413866370916367,
-0.027820585295557976,
-0.03367212414741516,
0.026216857135295868,
-0.011315387673676014,
0.035661254078149796,
-0.02162003330886364,
-0.02792137674987316,
-0.0299729835242033,
0.025655774399638176,
0.011289766989648342,
-0.021916691213846207,
0.013710705563426018,
0.026159921661019325,
0.007851580157876015,
-0.03698347136378288,
-0.020889323204755783,
0.015085315331816673,
-0.06111013889312744,
0.012237466871738434,
-0.006405161693692207,
-0.01879686675965786,
0.06474021822214127,
-0.0033964526373893023,
-0.065150186419487,
-0.010080854408442974,
-0.030018141493201256,
-0.018016856163740158,
-0.023981578648090363,
-0.005726010538637638,
0.024482017382979393,
0.0641222819685936,
0.006363608408719301,
0.04528405889868736,
-0.01158280111849308,
0.011067201383411884,
0.03285873681306839,
-0.004105088766664267,
-0.059136759489774704,
-0.029907742515206337,
-0.00517933489754796,
-0.055619869381189346,
0.04335205256938934,
0.02462436631321907,
0.019272400066256523,
0.029940836131572723,
-0.023466283455491066,
0.029666313901543617,
0.035241007804870605,
-0.001766236498951912,
0.044385023415088654,
0.017282811924815178,
0.017368296161293983,
0.019603192806243896,
-0.02540290541946888,
0.031035011634230614,
-0.021911807358264923,
-0.024383865296840668,
-0.043756917119026184,
0.020798103883862495,
0.0037986324168741703,
-0.014017933048307896,
-0.024028126150369644,
-0.022499043494462967,
0.02035987563431263,
-0.021090392023324966,
-0.046059269458055496,
0.050136417150497437,
0.004144668113440275,
-0.02005886472761631,
0.051010798662900925,
-0.02773386426270008,
0.015377433970570564,
-0.021920274943113327,
0.029205290600657463,
-0.03373505547642708,
0.0014681899920105934,
0.07622630894184113,
-0.03954865783452988,
-0.0143381142988801,
0.00438724597916007,
0.08186839520931244,
0.03469402715563774,
-0.03539489954710007,
0.002603209111839533,
0.0050936355255544186,
-0.010740997269749641,
-0.021406713873147964,
-0.005267734173685312,
-0.03310638293623924,
-0.0033545142505317926,
0.088859423995018,
-0.0233287550508976,
0.0022533752489835024,
-0.0008796280599199235,
0.03309491276741028,
0.056894220411777496,
0.033025000244379044,
-0.028889188542962074,
-0.012290580198168755,
0.008304990828037262,
-0.016174262389540672,
0.005650434177368879,
-0.026423456147313118,
0.02495039626955986,
-0.0588233657181263,
0.02715633250772953,
-0.010322041809558868,
-0.0031409533694386482,
0.08995094895362854,
0.02764459140598774,
0.0038446744438260794,
0.045196227729320526,
-0.04803052917122841,
0.02610962837934494,
0.02013634331524372,
-0.00036828333395533264,
0.003500808496028185,
0.05936579033732414,
-0.011201230809092522,
0.06008383631706238,
-0.01538371667265892,
0.01634344272315502,
0.018616659566760063,
-0.032803960144519806,
-0.031756751239299774,
-0.04089636728167534,
-0.03260420635342598,
-0.05650630593299866,
0.04279230162501335,
-0.011159403249621391,
-0.001698281615972519,
0.025437694042921066,
-0.0455365814268589,
-0.06029174476861954,
0.01680385321378708,
-0.04782313108444214,
-0.0275143850594759,
-0.03882891684770584,
0.005638758186250925,
0.05078651383519173,
-0.011065098457038403,
0.013847981579601765,
0.02514374814927578,
-0.008298172615468502,
0.053692352026700974,
-0.02925073355436325,
-0.06026654690504074,
0.02642555721104145,
0.029563480988144875,
0.006716027390211821,
-0.0073937042616307735,
-0.022720355540513992,
0.06584201753139496,
0.014369720593094826,
-0.04752979055047035,
0.01932261697947979,
0.008325512520968914,
0.0013475713785737753,
0.0004195231886114925,
0.0479794517159462,
-0.0008986282628029585,
0.012650852091610432,
-0.01578514091670513,
-0.009391631931066513,
-0.010284312069416046,
0.0016039868351072073,
-0.05671519413590431,
-0.03773565962910652,
-0.05559726059436798,
0.01447535865008831,
0.03342190757393837,
-0.01871226727962494,
-0.09511961042881012,
-0.020621784031391144,
-0.020940711721777916,
-0.014405877329409122,
0.002627876354381442,
-0.0165077093988657,
-0.02397998608648777,
0.01793667860329151,
0.0006508240476250648,
-0.061551861464977264,
-0.002064381493255496,
0.025625476613640785,
-0.04516925662755966,
-0.06092961132526398,
0.07501112669706345,
-0.017567047849297523,
-0.042188432067632675,
-0.04471195861697197,
0.01639464497566223,
0.012836266309022903,
0.005453165620565414,
0.01932784914970398,
0.004461824893951416,
0.02314339019358158,
0.0929761454463005,
0.08420834690332413,
0.0030194802675396204,
-0.041637811809778214,
-0.013197473250329494,
0.0473378486931324,
0.005818106234073639,
0.03874945268034935,
-0.009101497009396553,
0.01768157258629799,
0.030931955203413963,
-0.02882569283246994,
0.010886523872613907,
-0.00446189334616065,
-0.009327013045549393,
0.006615451071411371,
0.03237716853618622,
-0.012802617624402046,
-0.014725697226822376,
-0.031033223494887352,
0.013692058622837067,
0.01603786274790764,
-0.0063905674032866955,
-0.02169712632894516,
-0.03089083358645439,
-0.020818958058953285,
-0.019155343994498253,
0.018707234412431717,
0.047443270683288574,
-0.04421692341566086,
-0.02905147150158882,
-0.06292808800935745,
0.022661669179797173,
-0.0009371205815114081,
0.0681881532073021,
-0.043936893343925476,
-0.0022299273405224085,
0.007202182896435261,
0.005763266235589981,
-0.02399986796081066,
-0.04696653038263321,
0.012376761063933372,
0.034844230860471725,
0.01439947821199894,
0.026062829419970512,
-0.004194760229438543,
0.0007154382765293121,
0.0367400087416172,
0.06046101823449135,
-0.008532265201210976,
0.025987911969423294,
0.030099943280220032,
0.040213923901319504,
0.025431010872125626,
0.06706748157739639,
-0.0020675661507993937,
0.06315583735704422,
-0.011239077895879745,
-0.062481705099344254,
0.03107231855392456,
0.027270684018731117,
-0.03537262603640556,
-0.04926997795701027,
0.060491979122161865,
0.0036298756022006273,
0.04694425314664841,
-0.08064941316843033,
-0.021543659269809723,
0.02391626499593258,
-0.04833846166729927,
0.009042034856975079,
-0.04893096536397934,
0.025285271927714348,
-0.04502756893634796,
-0.07380242645740509,
-0.00795402005314827,
0.013099247589707375,
0.024883991107344627,
0.00023262524337042123,
0.06338659673929214,
-0.042968858033418655,
0.0006700328667648137,
-0.017832065001130104,
0.03699525445699692,
-0.004224998410791159,
0.06526662409305573,
0.015932181850075722,
-0.07345685362815857,
-0.024205613881349564,
-0.03224663436412811,
-0.019000491127371788,
-0.025235718116164207,
0.014878416433930397,
0.09253384917974472,
-0.018170572817325592,
-0.05319047346711159,
-0.03794718533754349,
-0.03787386044859886,
0.025327051058411598,
0.012429694645106792,
-0.009320765733718872,
-0.031055347993969917,
-0.06187322363257408,
-0.049887292087078094,
0.01661466248333454,
-0.05909350886940956,
0.014193054288625717,
-0.014436475932598114,
-0.011968889273703098,
0.04760492220520973,
-0.013650793582201004,
-0.03360563516616821,
-0.02026624232530594,
0.023681076243519783,
-0.041349247097969055,
0.048492077738046646,
0.0038109077140688896,
0.04498027265071869,
-0.006091622170060873,
0.06104085221886635,
-0.005391859915107489,
-0.004296123515814543,
-0.017815396189689636,
-0.011534308083355427,
0.052234552800655365,
-0.0351254902780056,
0.014233026653528214,
0.024904731661081314,
0.03472191467881203,
-0.0015380129916593432,
0.024735592305660248,
-0.004905735608190298,
-0.016783645376563072,
0.003969226032495499,
0.01611696369946003,
-0.0029947981238365173,
-0.046420808881521225,
-0.007135166320949793,
-0.04159592464566231,
0.0034143212251365185,
-0.013739409856498241,
0.018367813900113106,
0.015448025427758694,
0.044099487364292145,
0.044720061123371124,
0.05768425762653351,
0.04551687836647034,
0.003133469959720969,
0.008307449519634247,
-0.006170411128550768,
0.008418988436460495,
0.005639233626425266,
0.032166581600904465,
0.05389801785349846,
0.029594505205750465,
0.0067168292589485645,
-0.06744194030761719,
0.02453298307955265,
0.00695395190268755,
-0.013612245209515095,
-0.019258743152022362,
-0.028206007555127144,
-0.07485178112983704,
-0.016393326222896576,
-0.002806722419336438,
0.02075299061834812,
-0.016763117164373398,
0.04124528542160988,
-0.030520161613821983,
0.023849371820688248,
-0.03445211797952652,
-0.03590429201722145,
-0.021542774513363838,
-0.007070478983223438,
-0.05861469358205795,
0.03608030825853348,
-0.011749343015253544,
0.018629180267453194,
-0.03938411548733711,
-0.030311377719044685,
0.003478541038930416,
-0.008452262729406357,
0.014479727484285831,
0.039331819862127304,
0.041388384997844696,
0.04300776124000549,
0.03547518327832222,
0.014344076626002789,
-0.002433421788737178,
-0.04363134875893593,
-0.05505134537816048,
0.04064935818314552,
0.02780919149518013,
0.020542657002806664,
0.03849362954497337,
-0.03971969708800316,
0.008475297130644321,
-0.05176360905170441,
0.07294727116823196,
-0.013865218497812748,
-0.025350257754325867,
0.017072025686502457,
0.005839143414050341,
0.01686890795826912,
-0.021694723516702652,
0.0019133231835439801,
0.08326631039381027,
0.005371586419641972,
-0.03888048976659775,
0.010642889887094498,
-0.018678097054362297,
0.004907278809696436,
0.007507910951972008,
0.07455047219991684,
-0.017516562715172768,
0.03188798204064369,
0.010110417380928993,
-0.02185681276023388,
0.021908970549702644,
0.013213902711868286,
-0.030688052996993065,
-0.036212217062711716,
0.015625087544322014,
0.049144718796014786,
0.0054285721853375435,
0.02008667215704918,
-0.0416998565196991,
-0.05212325230240822,
0.08434175699949265,
-0.03667416051030159,
-0.028433823958039284,
0.059592701494693756,
-0.005895001348108053,
0.020415224134922028,
-0.0415276437997818,
-0.019835056737065315,
0.010488579981029034,
0.0621287040412426,
-0.02087649330496788,
-0.04471251368522644,
-0.0340876579284668,
0.06981849670410156,
0.004243798553943634,
-0.0290777999907732,
-0.0348929800093174,
-0.03680744394659996,
0.047955624759197235,
-0.005523962434381247,
-0.03874724358320236,
-0.015190680511295795,
-0.046010784804821014,
0.03643620386719704,
-0.032501257956027985,
0.048806361854076385,
0.023564234375953674,
-0.013135590590536594,
0.015838973224163055,
0.02184576913714409,
-0.07580958306789398,
0.018463686108589172,
-0.04642850160598755,
-0.07109863311052322,
0.012939896434545517,
0.054610058665275574,
-0.015594885684549809,
0.01742926985025406,
0.03736671805381775,
0.06943210959434509,
0.027985602617263794,
-0.028372803702950478,
0.0422033928334713,
0.034204937517642975,
-0.015943119302392006,
0.007142921909689903,
0.03415563330054283,
0.01691099815070629,
0.0372469425201416,
-0.04147035628557205,
-0.027959030121564865,
-0.06124484911561012,
-0.09224232286214828,
0.02333034761250019,
0.024031350389122963,
-0.006288903299719095,
0.014595947228372097,
-0.007882791571319103,
0.05816301330924034,
-0.009699400514364243,
-0.10835906863212585,
-0.01209534052759409,
0.04130333662033081,
0.011671840213239193,
-0.03458620607852936,
0.055756598711013794,
-0.04371689632534981,
0.007985489442944527,
-0.051480527967214584,
0.03937302529811859,
-0.029238753020763397,
0.04525616765022278,
0.013373701833188534,
0.01170455850660801,
-0.06279289722442627,
-0.01926395855844021,
0.02319219708442688,
-0.023331308737397194,
0.04870201647281647,
-0.05584774166345596,
0.03271099552512169,
0.03766849637031555,
-0.0067235385067760944,
-0.03482668474316597,
0.025379115715622902,
-0.00920221209526062,
-0.05688704177737236,
-0.027066204696893692,
0.01114343386143446,
-0.011983739212155342,
0.023172365501523018,
-0.035233281552791595,
0.00894332118332386,
0.018734952434897423,
0.0034205340780317783,
-0.005015117581933737,
-0.016138384118676186,
-0.038336560130119324,
-0.018615856766700745,
0.0428224541246891,
0.043681979179382324,
0.04109853506088257,
0.03920309990644455,
-0.008342086337506771,
0.06642373651266098,
-0.0038759049493819475,
0.0075491685420274734,
0.007645366247743368,
0.014816215261816978,
0.058754462748765945,
-0.02034161426126957,
-0.07520350068807602,
-0.005118383094668388,
-0.05806887149810791,
0.015105161815881729,
-0.00857255607843399,
-0.008800397627055645,
-0.03414692357182503,
-0.02373524382710457,
-0.05640723556280136,
0.031265515834093094,
0.046483322978019714,
0.016708558425307274,
-0.027845006436109543,
0.031216343864798546,
-0.06065971031785011,
-0.037508755922317505,
-0.0033075069077312946,
0.00016017905727494508,
0.056922830641269684,
0.002172162989154458,
-0.07812593132257462,
-0.04898805916309357,
0.05096476152539253,
0.026687419041991234,
0.07660951465368271,
-0.03514588251709938,
0.010864479467272758,
0.01337988767772913,
-0.06286709010601044,
0.002874949714168906,
-0.004344044718891382,
-0.0015200321795418859,
-0.010244440287351608,
0.03737795725464821,
0.03854872286319733,
0.010556408204138279,
0.017847450450062752,
-0.014776200987398624,
0.050917211920022964,
0.01973266899585724,
0.0027541685849428177,
-0.0012144738575443625,
0.08839046955108643,
0.010359837673604488,
0.0015833295183256269,
-0.021680710837244987,
0.03917465731501579,
0.04501357674598694,
0.004447403363883495,
-0.03063143417239189,
0.05905008316040039,
0.005310803186148405,
0.050345148891210556,
-0.006295805796980858,
-0.09035556018352509,
0.02804366871714592,
-0.04967290163040161,
0.017307903617620468,
-0.0698089674115181,
0.04264751449227333,
0.032246265560388565,
0.02264929749071598,
-0.039541762322187424,
0.0857887789607048,
0.03287658095359802,
0.016453135758638382,
0.02913915552198887,
-0.053110796958208084,
0.045763049274683,
-0.04087824374437332,
-0.07157958298921585,
0.0447794571518898,
0.06079525128006935,
-0.005799737758934498,
0.021296249702572823,
-0.00991535373032093,
-0.10907237231731415,
-0.053474850952625275,
-0.017722060903906822,
0.004066243302077055,
-0.05593996122479439,
-0.008654490113258362,
-0.03917558863759041,
-0.013034549541771412,
-0.0236269049346447,
0.0034751093480736017,
-0.01925312913954258,
-0.004347453359514475,
0.009195034392178059,
0.037614721804857254,
0.04057614505290985,
0.020793180912733078,
0.03412635996937752,
0.014615777879953384,
-0.03158193081617355,
0.02985430136322975,
-0.002722345758229494,
-0.010914073325693607,
0.046665895730257034,
0.09346681833267212,
-0.008813257329165936,
-0.023704921826720238,
-0.013333220966160297,
0.04331924766302109,
-0.023185312747955322,
0.04311739280819893,
-0.03730250895023346,
-0.0011586104519665241,
0.054723288863897324,
-0.022609258070588112,
0.0021676875185221434,
0.03319449722766876,
0.00941751804202795,
-0.005157644860446453,
-0.02304663695394993,
-0.012797117233276367,
-0.032830461859703064,
0.001360868802294135,
0.020592309534549713,
0.03643854707479477,
-0.06802816689014435,
0.05312597379088402,
-0.023636214435100555,
0.005595528054982424,
-0.019065536558628082,
0.011090202257037163,
0.028417469933629036,
-0.006128217093646526,
-0.0009681446827016771,
-0.06245851144194603,
-0.012633503414690495,
-0.07023850828409195,
-0.03546594828367233,
0.012874118052423,
-0.015254723839461803,
-0.08955498039722443,
0.015785954892635345,
-0.023286152631044388,
-0.03279769793152809,
-0.03276361525058746,
0.03555640950798988,
-0.022386224940419197,
-0.03343547135591507,
0.02470816858112812,
0.0012078939471393824,
-0.04474558308720589,
0.02237514592707157,
-0.006277488078922033,
0.04251735657453537,
-0.030376717448234558,
-0.02215513028204441,
0.021482037380337715,
-0.02510290965437889,
-0.031322598457336426,
-0.03191259875893593,
0.06011781841516495,
0.014503316953778267,
-0.010536300018429756,
-0.04061310738325119,
0.021839577704668045,
0.05153448134660721,
0.03665156662464142,
-0.054706718772649765,
-0.060700252652168274,
0.06324243545532227,
-0.006260644644498825,
-0.017493141815066338,
-0.01314893364906311,
-0.013903262093663216,
0.0014406871050596237,
-0.006220551207661629,
-0.07715200632810593,
0.018866006284952164,
0.03090856969356537,
-0.017137950286269188,
0.02500160038471222,
0.01802883855998516,
-0.044124968349933624,
0.014127818867564201,
-0.007769882213324308,
0.04294199123978615,
0.018479371443390846,
-0.008109713904559612,
-0.01249014213681221,
0.03564893454313278,
0.024407846853137016,
-0.05759601294994354,
-0.03388155996799469,
0.043396417051553726,
0.053103409707546234
] |
<p>I study physics and am attending a course on quantum field theory. It is hard for me to draw connections from there to the old conventional theories.</p>
<p>In quantum field theory spin originates from the Dirac equation in the case of fermions. </p>
<p>I don't remember where it comes from in quantum mechanics. I just remember that there was the Stern Gerlach experiment where you shoot neutral spin 1/2 Ag atoms in. Is there also a electrically neutral elementary particle? If this is the case, how would this experiment look like in quantum field theory?
Of course I ask this for the lowest order, otherwise we would have to calculate an infinite number of Feynman graphs, won't we?</p> | g824 | [
0.038156092166900635,
-0.008575312793254852,
0.0028039440512657166,
-0.001804252271540463,
0.06926524639129639,
0.024221356958150864,
-0.007486487738788128,
0.03077668510377407,
0.03261278569698334,
-0.03729536384344101,
-0.018294306471943855,
0.017550012096762657,
0.018048647791147232,
-0.0020904710981994867,
-0.017170676961541176,
0.01912607252597809,
-0.0222953911870718,
-0.0016470997361466289,
-0.010361895896494389,
-0.009621910750865936,
0.028467398136854172,
0.0002198326837969944,
0.04193603992462158,
-0.06007508188486099,
0.00625195587053895,
-0.04318210855126381,
-0.049921851605176926,
-0.015028235502541065,
-0.01726716198027134,
-0.020412081852555275,
-0.014777242206037045,
-0.010410475544631481,
0.01523785199970007,
-0.024564232677221298,
-0.017981726676225662,
-0.06493715941905975,
0.028336284682154655,
0.09971727430820465,
-0.009463055059313774,
0.028027908876538277,
-0.025557145476341248,
-0.016538294032216072,
-0.018098175525665283,
-0.03916015848517418,
0.02129496820271015,
0.06725049018859863,
0.002051265211775899,
0.032875906676054,
-0.017795251682400703,
0.015243708156049252,
-0.08295861631631851,
0.028977924957871437,
0.035889897495508194,
0.018415119498968124,
-0.05707331374287605,
0.061349090188741684,
-0.001321308664046228,
-0.02025110460817814,
0.07319077104330063,
0.07013048976659775,
-0.012082403525710106,
0.001855360227636993,
0.009237922728061676,
0.01736558973789215,
0.04354087635874748,
-0.007721140049397945,
-0.04417748004198074,
0.02930978313088417,
0.03550717234611511,
0.0341545008122921,
-0.005480918101966381,
-0.10348030924797058,
0.0051838732324540615,
0.00282818591222167,
0.017542066052556038,
0.04917242377996445,
0.013451430946588516,
-0.01155037060379982,
0.027864716947078705,
-0.029403524473309517,
-0.06190589442849159,
-0.01800851710140705,
-0.04803326725959778,
-0.02338721789419651,
0.04558529704809189,
-0.01943925768136978,
-0.026564881205558777,
-0.012779449112713337,
0.01674746721982956,
0.05333776772022247,
0.0334780216217041,
0.03119429387152195,
0.05381651967763901,
-0.02091986872255802,
-0.030405424535274506,
-0.0054229083471000195,
-0.040616799145936966,
0.002490443643182516,
-0.04131319746375084,
-0.02995738573372364,
-0.0365787036716938,
-0.05876033008098602,
0.0664985254406929,
-0.027942411601543427,
-0.00859860423952341,
-0.013929490931332111,
0.05521988123655319,
-0.005929714068770409,
0.061781007796525955,
0.04994989186525345,
-0.01813700795173645,
0.001699973363429308,
-0.04958529770374298,
0.014127063564956188,
-0.013862219639122486,
0.008107279427349567,
0.037694480270147324,
-0.05423601344227791,
0.029258117079734802,
0.03165176510810852,
0.021800564602017403,
0.022316083312034607,
0.018898973241448402,
0.018632687628269196,
-0.03584977984428406,
-0.03156129643321037,
0.006715979892760515,
0.006161344703286886,
-0.005248042289167643,
0.01982627995312214,
-0.02464158646762371,
-0.04278058931231499,
0.01282164454460144,
-0.015214167535305023,
0.022535543888807297,
0.05268833786249161,
0.0024220894556492567,
0.0042079295963048935,
0.041885048151016235,
-0.010002357885241508,
0.022261343896389008,
-0.0834798663854599,
-0.008106902241706848,
-0.03389108553528786,
-0.00032375819864682853,
0.0014962805435061455,
0.060864657163619995,
-0.027231454849243164,
-0.039872050285339355,
0.03176277503371239,
0.013314438983798027,
0.052361082285642624,
0.04181525483727455,
0.003796866163611412,
0.023475732654333115,
-0.05121324211359024,
0.029934730380773544,
-0.08338835090398788,
0.0629250779747963,
-0.005991205107420683,
0.03362380713224411,
-0.030534842982888222,
-0.029347233474254608,
0.018824994564056396,
-0.05992351844906807,
-0.03851747512817383,
0.023944588378071785,
0.027980489656329155,
0.04261086881160736,
-0.0704178735613823,
-0.006332469172775745,
0.042195018380880356,
-0.027552751824259758,
0.029036592692136765,
0.0028698688838630915,
0.061227165162563324,
-0.072327621281147,
-0.04031243547797203,
0.036942675709724426,
0.015956254675984383,
-0.024228038266301155,
0.04819374904036522,
0.011287068016827106,
0.00143503921572119,
0.00014847393322270364,
-0.019110986962914467,
-0.028565051034092903,
0.04718473181128502,
-0.009936359710991383,
-0.054642025381326675,
-0.011567575857043266,
-0.012597916647791862,
-0.02376575395464897,
0.02283347211778164,
-0.0494050532579422,
-0.04500428959727287,
-0.012811480090022087,
-0.0564257875084877,
-0.008077211678028107,
0.04406428337097168,
0.036082394421100616,
0.08311948925256729,
-0.004705525003373623,
0.0007918188348412514,
0.028575971722602844,
-0.03332899510860443,
0.00284940074197948,
-0.019484154880046844,
0.10206034034490585,
-0.05274150148034096,
0.005160337779670954,
0.0723816305398941,
0.008875587023794651,
0.033602580428123474,
-0.04506051540374756,
0.0012950926320627332,
0.044557321816682816,
-0.0029963944107294083,
0.032182347029447556,
0.08506586402654648,
-0.009022681973874569,
-0.027299504727125168,
0.0367085225880146,
-0.007194321136921644,
-0.0009173234575428069,
0.012434424832463264,
0.014703050255775452,
-0.033653851598501205,
-0.057811107486486435,
0.001773257739841938,
-0.07543224841356277,
0.022344237193465233,
-0.01945420727133751,
-0.0410696417093277,
0.04499894380569458,
0.044557441025972366,
-0.0464291051030159,
-0.030966870486736298,
0.028578463941812515,
0.0025583533570170403,
-0.012194394133985043,
0.018755707889795303,
-0.023045051842927933,
0.02135598659515381,
0.020350614562630653,
-0.0037951867561787367,
0.0406305268406868,
0.007191206328570843,
-0.03254915773868561,
-0.00008730735135031864,
0.05408594384789467,
-0.002113308757543564,
-0.05446445196866989,
0.013870426453649998,
-0.018786495551466942,
-0.039329588413238525,
-0.035728439688682556,
0.04627450928092003,
-0.023090064525604248,
-0.07599618285894394,
0.022204233333468437,
-0.051540449261665344,
0.04003232344985008,
0.011422475799918175,
0.009488126263022423,
-0.00029357432504184544,
-0.0067865485325455666,
-0.0077857039868831635,
0.004914468619972467,
0.023317046463489532,
-0.07742145657539368,
0.07001286745071411,
-0.028798328712582588,
-0.05986124649643898,
-0.03398214280605316,
-0.07232611626386642,
0.01966807059943676,
0.02394230104982853,
0.011329674161970615,
-0.018711160868406296,
-0.03291034698486328,
-0.008690660819411278,
-0.06728330999612808,
0.0010228086030110717,
0.03488906845450401,
-0.02969682402908802,
0.00013969064457342029,
-0.042391885071992874,
-0.03212663158774376,
-0.018520373851060867,
-0.046890392899513245,
-0.0341053307056427,
0.08894219994544983,
0.02486715093255043,
0.010710709728300571,
-0.019166726619005203,
0.04016140475869179,
0.015387487597763538,
-0.0779319703578949,
0.11680768430233002,
-0.03721868246793747,
-0.05081295222043991,
-0.02985130064189434,
0.04855385050177574,
0.02049015276134014,
-0.006135978735983372,
-0.030194897204637527,
-0.047229036688804626,
-0.001982205081731081,
-0.02386881597340107,
-0.054877907037734985,
0.08297236263751984,
0.053323227912187576,
0.02885175682604313,
-0.057752154767513275,
-0.02504987083375454,
-0.023859834298491478,
0.04994078353047371,
0.058846693485975266,
-0.04820217192173004,
-0.031248433515429497,
-0.044930312782526016,
0.029917113482952118,
0.001138522638939321,
0.057344306260347366,
0.018129831179976463,
-0.024630198255181313,
0.019324157387018204,
-0.025068001821637154,
-0.045115191489458084,
-0.0003737797378562391,
0.0012049295473843813,
-0.025638338178396225,
0.026474935933947563,
-0.055227864533662796,
-0.038526877760887146,
-0.037922684103250504,
0.03724036365747452,
-0.017003370448946953,
0.008422370068728924,
-0.003069768426939845,
-0.028109518811106682,
-0.026252102106809616,
-0.01540274266153574,
-0.004261332098394632,
-0.03250596672296524,
-0.001038932241499424,
-0.02531406283378601,
0.02604060061275959,
0.01752513088285923,
-0.019769473001360893,
-0.00244024652056396,
0.018948687240481377,
0.03220399096608162,
0.007350017316639423,
-0.04633662849664688,
0.006374936085194349,
0.07722318917512894,
0.05515740066766739,
0.009122956544160843,
0.013942970894277096,
-0.02352835424244404,
0.03698214888572693,
-0.020087778568267822,
-0.036892808973789215,
-0.013467539101839066,
-0.04855624586343765,
0.0023706862702965736,
0.04857258498668671,
-0.05279633402824402,
-0.03559386730194092,
-0.011107640340924263,
0.021192077547311783,
0.016950596123933792,
-0.01595201902091503,
0.0031094655860215425,
0.029228268191218376,
0.1096382811665535,
-0.07580114901065826,
0.021089021116495132,
0.0008558427216485143,
0.04925035312771797,
0.04379558190703392,
0.05289394408464432,
-0.017025534063577652,
0.009947705082595348,
-0.023358477279543877,
0.03994905948638916,
-0.06471307575702667,
0.03803783655166626,
-0.01867242529988289,
0.01823458820581436,
-0.02206958830356598,
0.018082085996866226,
0.022721538320183754,
0.02110697329044342,
0.006396973505616188,
-0.026773009449243546,
0.009140588343143463,
0.030424274504184723,
-0.009001322090625763,
0.012345874682068825,
0.007040784694254398,
-0.02884219028055668,
-0.018742943182587624,
0.008242439478635788,
-0.012216915376484394,
-0.01731550320982933,
0.02228390797972679,
0.00554876122623682,
0.010694450698792934,
0.01449496392160654,
0.018524369224905968,
-0.01622776687145233,
0.04376188665628433,
-0.015205947682261467,
-0.0034646030981093645,
-0.006880856119096279,
-0.015161960385739803,
-0.044006552547216415,
0.04166274517774582,
0.06198519840836525,
0.06489814072847366,
-0.007050515152513981,
0.0010776956332847476,
0.028920911252498627,
0.011668060906231403,
0.07160691916942596,
-0.05815570801496506,
-0.01845167763531208,
-0.014466717839241028,
0.004753940273076296,
-0.056889571249485016,
0.0012599789770320058,
-0.06796175986528397,
0.014324074611067772,
-0.03468719869852066,
-0.046576887369155884,
-0.024266092106699944,
0.02519393153488636,
0.07128159701824188,
-0.022676508873701096,
0.02833353914320469,
-0.010408246889710426,
-0.006396865006536245,
0.04268066585063934,
-0.03613608330488205,
-0.027149077504873276,
-0.024813802912831306,
-0.03224065154790878,
0.03184518218040466,
0.06546998023986816,
-0.020382139831781387,
0.03861583024263382,
-0.024723362177610397,
0.003890994004905224,
-0.03468874841928482,
0.020235808566212654,
-0.005618713330477476,
0.02882802113890648,
-0.09620731323957443,
0.011336897499859333,
-0.046806175261735916,
-0.017552176490426064,
0.003720563370734453,
-0.02548292838037014,
-0.07410738617181778,
-0.03495268151164055,
-0.08442708104848862,
-0.02533554658293724,
0.012190906330943108,
-0.029451899230480194,
0.038989316672086716,
-0.002913581905886531,
-0.024711398407816887,
0.04391336068511009,
0.00655985064804554,
-0.02460244670510292,
-0.02798484079539776,
-0.05472688004374504,
-0.02351577952504158,
-0.0521569661796093,
-0.040796421468257904,
0.0034317222889512777,
0.011252250522375107,
0.006140890996903181,
-0.06308743357658386,
0.032566286623477936,
-0.010300494730472565,
-0.059897664934396744,
-0.028162559494376183,
-0.0386456698179245,
0.007173932157456875,
-0.009195046499371529,
0.020718563348054886,
-0.037832535803318024,
-0.04756762087345123,
-0.06606362015008926,
-0.0027249816339462996,
-0.00646521570160985,
-0.0408489964902401,
0.03491905704140663,
-0.0040341210551559925,
0.022809823974967003,
-0.009559153579175472,
0.053733278065919876,
0.0278755035251379,
-0.01937042362987995,
0.018681777641177177,
-0.010556361638009548,
0.017777033150196075,
-0.04867107793688774,
0.016129696741700172,
0.06051918491721153,
-0.006445186212658882,
0.03671129420399666,
-0.015084234066307545,
-0.042410001158714294,
0.034123796969652176,
-0.013576789759099483,
-0.003960955888032913,
0.02948542684316635,
0.01033255085349083,
-0.008238975889980793,
-0.0011321647325530648,
0.03221021965146065,
-0.05197698995471001,
0.010360042564570904,
0.025520794093608856,
0.03891858458518982,
0.009025449864566326,
0.01122685894370079,
0.033025942742824554,
0.030404621735215187,
0.04282822832465172,
-0.034363240003585815,
-0.006871956400573254,
0.015534612350165844,
0.02973095141351223,
0.02218783274292946,
-0.027725795283913612,
0.00808769091963768,
0.067393958568573,
0.03745635971426964,
-0.006773475091904402,
-0.0022454310674220324,
0.0011779703199863434,
-0.047641489654779434,
0.07010562717914581,
-0.05610044673085213,
-0.005013931542634964,
0.045634280890226364,
0.038169801235198975,
-0.001802640501409769,
-0.029170222580432892,
0.03233042359352112,
-0.053568560630083084,
-0.052944403141736984,
0.0011421270901337266,
0.015265015885233879,
0.03185524418950081,
-0.019077790901064873,
0.03786259517073631,
0.01202013622969389,
-0.010205353610217571,
0.03773001208901405,
0.0036489355843514204,
-0.0662166178226471,
0.06777802854776382,
-0.019347069784998894,
0.05823862925171852,
0.015406247228384018,
-0.021043935790657997,
0.05341847613453865,
0.05196341127157211,
-0.057626839727163315,
-0.01804651878774166,
0.011976893991231918,
-0.02367468550801277,
-0.02999306656420231,
0.011028279550373554,
0.006874146871268749,
0.0484551377594471,
-0.048667632043361664,
0.029739102348685265,
0.013831166550517082,
-0.03758178651332855,
0.03787608817219734,
0.009650777094066143,
0.04850168898701668,
-0.0691133514046669,
0.05514787882566452,
-0.05430293455719948,
-0.02812970243394375,
0.005518494639545679,
0.0016665050061419606,
0.04795815050601959,
-0.07892148941755295,
0.001699700835160911,
-0.00035242014564573765,
0.005223835818469524,
-0.005879727657884359,
0.016147706657648087,
0.06028040125966072,
0.0035240163560956717,
0.03574042394757271,
-0.00415450194850564,
0.028020063415169716,
0.009569401852786541,
0.005403047893196344,
-0.012900623492896557,
-0.01699143648147583,
-0.03473930433392525,
-0.02498074807226658,
-0.017290350049734116,
-0.02005237340927124,
0.054176270961761475,
0.0007312652305699885,
-0.03490392118692398,
0.03025287576019764,
0.00823273416608572,
0.010437794961035252,
-0.03728175535798073,
-0.049044400453567505,
0.052294690161943436,
-0.0024644823279231787,
0.019001290202140808,
0.04296174272894859,
0.033468812704086304,
-0.012547570280730724,
0.007447810377925634,
0.030089253559708595,
-0.002088855253532529,
0.01756245084106922,
-0.036499250680208206,
0.018831761553883553,
0.011714344844222069,
0.017499985173344612,
0.01680276356637478,
0.018449073657393456,
-0.018208790570497513,
0.004928034730255604,
0.02660166285932064,
0.011231662705540657,
-0.05810673162341118,
0.021296167746186256,
0.009467371739447117,
-0.016426337882876396,
-0.01500777993351221,
0.013001651503145695,
0.007564661093056202,
-0.026976168155670166,
0.01683146320283413,
0.013619008474051952,
0.007731139659881592,
-0.012147406116127968,
0.04886594042181969,
0.05110379680991173,
0.037391990423202515,
-0.06231516972184181,
-0.0394810251891613,
0.01064214576035738,
-0.006321008782833815,
-0.048216745257377625,
-0.05997800454497337,
-0.0118474792689085,
-0.037053659558296204,
-0.05166306346654892,
0.046907708048820496,
0.01255947444587946,
-0.02412727288901806,
-0.06830823421478271,
-0.03773863613605499,
-0.0010598939843475819,
-0.028482120484113693,
0.008295509032905102,
0.024602379649877548,
-0.015172814950346947,
0.0038364361971616745,
-0.02648564986884594,
-0.03097003698348999,
0.09728945046663284,
0.017191071063280106,
0.0055120536126196384,
-0.020935209468007088,
-0.0042527057230472565,
0.001710621640086174,
-0.026995228603482246,
0.017940787598490715,
0.0024590324610471725,
-0.0037217552307993174,
-0.039374493062496185,
0.03301448002457619,
-0.05275838449597359,
0.026233568787574768,
-0.03758883476257324,
-0.002443712204694748,
0.025945505127310753,
0.03642414137721062,
-0.0022320335265249014,
0.11740969121456146,
-0.022310545668005943,
0.008675058372318745,
0.010665812529623508,
0.04608026146888733,
-0.014620287343859673,
0.03990454226732254,
-0.023808253929018974,
-0.036574508994817734,
0.022655809298157692,
-0.009237761609256268,
0.05087120085954666,
0.04213671013712883,
0.10998917371034622,
0.005773608107119799,
-0.017807085067033768,
-0.021072523668408394,
-0.03139235079288483,
0.05784911662340164,
0.02366676926612854,
0.024140490218997,
0.008694254793226719,
-0.014008873142302036,
-0.0075453235767781734,
-0.025460395961999893,
-0.01678571105003357,
0.0015236916951835155,
0.016568174585700035,
0.08550610393285751,
0.05337586626410484,
0.05161576718091965,
0.012964592315256596,
-0.05721168592572212,
0.03520258888602257,
0.002950367983430624,
-0.005417863838374615,
-0.046759188175201416,
-0.000368955748854205,
0.005814320407807827,
-0.023478835821151733,
0.02486373297870159,
0.023088280111551285,
0.014876231551170349,
-0.023296259343624115,
-0.020283309742808342,
-0.015770481899380684,
-0.07273101806640625,
-0.009485898539423943,
0.05901491641998291,
0.006052026525139809,
-0.04212796315550804,
0.007152501959353685,
-0.018618173897266388,
0.05065047740936279,
0.0469372496008873,
-0.08970079571008682,
-0.007412141654640436,
0.06428792327642441,
0.01839078590273857,
0.043559104204177856,
0.0031135177705436945,
-0.05236758291721344,
0.0030452972277998924,
0.07349427044391632,
-0.08041399717330933,
-0.05918331444263458,
-0.01416839100420475,
0.03137259557843208
] |
<p>Non-unital completely positive (<a href="http://en.wikipedia.org/wiki/Choi%27s_theorem_on_completely_positive_maps" rel="nofollow">CP</a>) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily decreases its von Neumann entropy and, depending on how you define it, reduces its temperature.</p>
<p>Can a stronger connection be made between thermodynamics and CP maps? To what extent do non-unital CP maps reliably cool states that <em>aren't</em> infinite temperature?</p> | g9175 | [
0.004274540580809116,
-0.045434143394231796,
-0.018483461812138557,
-0.0002857011859305203,
0.024339403957128525,
0.011392198503017426,
0.003460927167907357,
0.03518971800804138,
0.021674927324056625,
-0.00503154844045639,
-0.006966363172978163,
-0.02924424409866333,
-0.022406412288546562,
-0.031789861619472504,
-0.05016021057963371,
-0.0001544589176774025,
0.027509069070219994,
0.026617463678121567,
0.02845808118581772,
0.05477055162191391,
-0.016976248472929,
0.02599932998418808,
0.08068862557411194,
-0.04147043451666832,
0.023132937029004097,
-0.03929642587900162,
0.009091711603105068,
-0.012435603886842728,
-0.04374321922659874,
-0.0023052513133734465,
0.0278454776853323,
0.01859358139336109,
0.01733323186635971,
-0.05347215011715889,
-0.044648587703704834,
-0.02632797323167324,
0.08326485008001328,
0.07583469897508621,
0.0493941493332386,
-0.016449883580207825,
0.013473971746861935,
0.04125823453068733,
0.021883031353354454,
-0.0225145872682333,
-0.024995217099785805,
0.01068794447928667,
-0.015630481764674187,
0.017494631931185722,
-0.04806007444858551,
0.010597184300422668,
-0.02870958298444748,
-0.019526351243257523,
0.015261707827448845,
0.007616117130964994,
0.021086303517222404,
0.00716767180711031,
-0.01703716814517975,
0.01747932657599449,
-0.028297914192080498,
0.023041240870952606,
0.04423316568136215,
-0.05707620084285736,
0.03501660004258156,
0.04403921589255333,
0.014296453446149826,
0.004722640383988619,
-0.004424753598868847,
-0.03315944969654083,
-0.020813144743442535,
0.0184517502784729,
-0.02575649321079254,
-0.04077032208442688,
-0.025260310620069504,
0.016567794606089592,
0.014501555822789669,
0.03518897667527199,
-0.01311484258621931,
-0.07926584035158157,
-0.010967956855893135,
-0.055550429970026016,
-0.06627066433429718,
-0.001145416172221303,
0.06091992184519768,
-0.03540172427892685,
0.025950556620955467,
0.015111546032130718,
0.014217764139175415,
0.007072478532791138,
-0.033427897840738297,
-0.004905147943645716,
-0.014445352368056774,
-0.011982403695583344,
0.05638132989406586,
0.011403425596654415,
0.04361771047115326,
0.05984208732843399,
0.07308301329612732,
-0.018331145867705345,
-0.027978412806987762,
-0.03917284682393074,
-0.007823491469025612,
0.0028762496076524258,
0.02586616575717926,
-0.017422467470169067,
-0.015863293781876564,
0.011006424203515053,
-0.010215232148766518,
-0.08173807710409164,
-0.04124370589852333,
0.041536521166563034,
-0.037302110344171524,
-0.002482271520420909,
-0.05561411380767822,
0.005168605595827103,
-0.055362045764923096,
0.007074739318341017,
0.006737481337040663,
-0.03431976959109306,
-0.029118260368704796,
0.0010878368047997355,
0.004581926856189966,
0.08633444458246231,
0.01821274124085903,
0.0293714739382267,
-0.005601269658654928,
0.0479370653629303,
-0.0012642821529880166,
-0.0578603595495224,
0.012631228193640709,
-0.029837699607014656,
0.024871520698070526,
0.04102597013115883,
-0.004199997987598181,
0.004562306217849255,
-0.008776932023465633,
-0.0018813817296177149,
0.048507899045944214,
0.024666402488946915,
0.023540977388620377,
0.04437657818198204,
-0.057503592222929,
-0.020972343161702156,
-0.020300908014178276,
0.036315519362688065,
0.0022859210148453712,
-0.016555272042751312,
-0.015898358076810837,
0.016667751595377922,
0.02383497916162014,
0.028045976534485817,
-0.014996128156781197,
0.012268707156181335,
0.03406643867492676,
-0.010525579564273357,
-0.04498196393251419,
0.006858511827886105,
0.016825838014483452,
-0.024366622790694237,
0.03867688030004501,
-0.042753592133522034,
-0.01566227711737156,
0.0443112850189209,
0.09475398063659668,
-0.04699253663420677,
-0.020527979359030724,
-0.028730714693665504,
0.005201639141887426,
-0.010807559825479984,
-0.0016248638276010752,
-0.05264938250184059,
-0.02409302443265915,
0.04759833961725235,
-0.04283978417515755,
0.01563265547156334,
0.009557296521961689,
-0.07233058661222458,
-0.033925946801900864,
0.03462838754057884,
0.0035345519427210093,
-0.07299820333719254,
-0.035834457725286484,
0.006121575832366943,
0.06940066814422607,
-0.012585901655256748,
0.02432793378829956,
0.03286297246813774,
-0.03847432881593704,
0.04333813115954399,
-0.07640573382377625,
0.033041227608919144,
-0.016417110338807106,
-0.03863208368420601,
0.0327671617269516,
0.0316510833799839,
-0.003411498386412859,
-0.05272897705435753,
-0.01809157058596611,
-0.01203879527747631,
-0.04882727190852165,
-0.029691118746995926,
0.009871896356344223,
-0.03609880805015564,
-0.04443324729800224,
-0.05851148068904877,
0.01738511398434639,
0.027228200808167458,
-0.015259751118719578,
-0.007899545133113861,
-0.002146148821339011,
-0.0016773594543337822,
0.0010268855839967728,
-0.05169650912284851,
-0.027414020150899887,
0.05575249344110489,
0.0011820427607744932,
-0.047329798340797424,
0.019428696483373642,
-0.0289224311709404,
0.007423047441989183,
0.006314732134342194,
-0.0278637558221817,
0.0903317928314209,
0.04191756993532181,
0.07484791427850723,
-0.02577504888176918,
0.03861705958843231,
-0.0453546866774559,
0.0011027917498722672,
-0.029469357803463936,
0.01019706204533577,
-0.028154848143458366,
0.04704307019710541,
0.046201471239328384,
-0.008959587663412094,
-0.03027554415166378,
0.06073155999183655,
0.04756864532828331,
0.0554269403219223,
-0.01805068552494049,
0.012926800176501274,
0.02734825760126114,
-0.04093695431947708,
-0.04278392717242241,
0.11750960350036621,
0.014294125139713287,
-0.01741642691195011,
-0.02476923167705536,
0.021069034934043884,
-0.02400260791182518,
0.04295029118657112,
-0.008649175986647606,
-0.01174936629831791,
-0.04585759714245796,
-0.0022174024488776922,
0.03686000034213066,
0.030915720388293266,
0.011165274307131767,
-0.01829979196190834,
-0.07593526691198349,
0.007396443281322718,
0.011845692992210388,
-0.04973435401916504,
-0.05185368284583092,
-0.07025608420372009,
-0.03136298060417175,
0.032580748200416565,
-0.011402823962271214,
-0.02394166588783264,
-0.05341187119483948,
0.03542131185531616,
0.003508959198370576,
0.052168045192956924,
0.012173746712505817,
0.04237217456102371,
-0.010615951381623745,
-0.02537318505346775,
-0.02278328314423561,
0.03804289922118187,
-0.0370839387178421,
-0.0753665342926979,
-0.04555400460958481,
0.0056109013967216015,
-0.037256430834531784,
-0.01792239397764206,
0.015542568638920784,
-0.057093922048807144,
-0.051630765199661255,
0.06933608651161194,
0.022424714639782906,
0.027214471250772476,
0.02076113596558571,
0.03286701813340187,
0.07035766541957855,
0.04981819912791252,
-0.05570047348737717,
0.020855354145169258,
0.03422175347805023,
-0.04896864295005798,
0.028572825714945793,
0.0020953803323209286,
0.05270921438932419,
0.004800420254468918,
0.003632280044257641,
0.017827268689870834,
0.06835106015205383,
0.013279369100928307,
-0.06367729604244232,
-0.05902128666639328,
0.018206022679805756,
-0.006508383434265852,
-0.020036090165376663,
0.025875922292470932,
-0.037233587354421616,
0.001268162508495152,
0.009584254585206509,
0.01374958548694849,
-0.027854472398757935,
0.02386792190372944,
-0.0038528977893292904,
-0.04034318029880524,
-0.011321434751152992,
-0.016695471480488777,
0.02573843114078045,
-0.03143303841352463,
0.04542144387960434,
-0.003220710437744856,
-0.0395391583442688,
-0.005075960885733366,
-0.029996193945407867,
-0.0048148855566978455,
0.022760991007089615,
-0.03624536842107773,
0.03531281650066376,
0.02043195441365242,
-0.06013178080320358,
-0.007541230879724026,
-0.04127415269613266,
-0.03357541188597679,
0.04602815955877304,
0.022999655455350876,
-0.026406442746520042,
-0.05022035539150238,
-0.03342645987868309,
-0.0005050408653914928,
0.0578932911157608,
0.029841430485248566,
-0.041781727224588394,
0.0062776352278888226,
0.017531810328364372,
0.009325830265879631,
0.002728711813688278,
-0.029689328745007515,
0.05556713789701462,
0.013196258805692196,
-0.0025708694010972977,
0.02965494990348816,
0.06411762535572052,
0.056614384055137634,
-0.015785658732056618,
0.037534020841121674,
-0.00528944144025445,
-0.008893422782421112,
0.05335990712046623,
-0.02749025821685791,
-0.010349425487220287,
0.07885205000638962,
-0.008088520728051662,
-0.013964726589620113,
0.005249139852821827,
-0.007652336731553078,
-0.009685778059065342,
-0.03735193610191345,
-0.028776120394468307,
-0.007667000871151686,
0.04622192308306694,
0.017129112035036087,
0.05171031132340431,
-0.008496621623635292,
-0.06255334615707397,
0.05301344394683838,
0.009736299514770508,
-0.0265179555863142,
0.06968078762292862,
-0.007648104336112738,
0.015895016491413116,
-0.018281107768416405,
-0.04726957157254219,
-0.00519527867436409,
0.0141659677028656,
-0.021743685007095337,
0.02216838300228119,
0.0004895373713225126,
-0.006216672249138355,
0.06735091656446457,
0.06193847954273224,
0.01979414001107216,
0.030108844861388206,
-0.01029631681740284,
0.013262082822620869,
0.03414876386523247,
0.02386925183236599,
-0.03364520147442818,
-0.015626536682248116,
-0.04188031330704689,
-0.026131587103009224,
-0.0766986757516861,
0.015053167939186096,
0.060534704476594925,
-0.019247179850935936,
-0.07719706743955612,
-0.006172966677695513,
-0.014098829589784145,
0.0149535508826375,
-0.029183899983763695,
0.06165977194905281,
-0.03223683685064316,
-0.007230220828205347,
-0.03902123495936394,
-0.008006292395293713,
0.044721487909555435,
-0.026970423758029938,
0.011693804524838924,
-0.004637895151972771,
0.06363557279109955,
0.010182579979300499,
-0.006706084590405226,
0.0554942823946476,
0.0046770693734288216,
-0.00244416412897408,
-0.049517564475536346,
0.03673737868666649,
0.015246381051838398,
-0.012049281038343906,
0.04926130920648575,
-0.032785262912511826,
0.03187570348381996,
-0.06072969362139702,
0.05338377133011818,
-0.055064961314201355,
0.0015345249557867646,
0.026134245097637177,
0.025965914130210876,
-0.01152377761900425,
0.051655806601047516,
-0.06622444093227386,
0.03411581739783287,
0.04394268989562988,
-0.013096224516630173,
-0.0729006975889206,
-0.04072056710720062,
-0.03695512190461159,
0.0544593445956707,
-0.03972413390874863,
-0.008690418675541878,
-0.015272039920091629,
-0.009804711677134037,
-0.0059424410574138165,
0.08985305577516556,
0.01994861476123333,
-0.003360217437148094,
0.0066633871756494045,
-0.04096889868378639,
0.07155649363994598,
-0.04013509303331375,
0.011768032796680927,
-0.003029777202755213,
-0.030199388042092323,
0.0575404018163681,
-0.061563797295093536,
-0.0020897870417684317,
0.042495597153902054,
0.10702061653137207,
0.02692418172955513,
0.05353053659200668,
-0.014083756133913994,
0.026978112757205963,
-0.009013468399643898,
-0.019952477887272835,
0.027293140068650246,
-0.038190681487321854,
0.02662443183362484,
0.02861635945737362,
-0.009387972764670849,
0.012240334413945675,
0.024263814091682434,
0.008042622357606888,
-0.01486464124172926,
0.03307453170418739,
-0.006518256850540638,
-0.024966562166810036,
0.030651211738586426,
0.04665682837367058,
0.060203664004802704,
0.042881209403276443,
-0.006644300650805235,
-0.038496196269989014,
-0.0769258588552475,
-0.06530418992042542,
-0.062498871237039566,
0.027784764766693115,
-0.11274309456348419,
0.01047887746244669,
0.02221600152552128,
0.007281045895069838,
-0.0175589919090271,
0.011567982845008373,
0.05910192430019379,
0.013566500507295132,
-0.04617355763912201,
0.012145108543336391,
-0.05577445030212402,
0.0311692226678133,
-0.02642909064888954,
0.007055996917188168,
-0.0049483743496239185,
0.03770282119512558,
-0.0766158476471901,
-0.10257546603679657,
-0.04342315346002579,
-0.07086507230997086,
0.025716979056596756,
-0.00537057826295495,
0.020844068378210068,
-0.03013165108859539,
0.031375110149383545,
0.059029046446084976,
-0.033739130944013596,
-0.030612312257289886,
0.0005774071905761957,
0.033026233315467834,
0.06125534698367119,
-0.006600172258913517,
0.032834820449352264,
-0.003462430089712143,
0.016368210315704346,
-0.029161453247070312,
0.006053722929209471,
0.04502031207084656,
0.04301729053258896,
0.04751800745725632,
0.04535473883152008,
-0.08125680685043335,
-0.0013628042070195079,
0.06448682397603989,
0.051332563161849976,
-0.03957035019993782,
-0.053451258689165115,
-0.024652549996972084,
-0.018096361309289932,
-0.03220372274518013,
-0.012259512208402157,
-0.009061876684427261,
0.008192128501832485,
-0.03487255424261093,
0.03645901381969452,
-0.03273874148726463,
0.04362158477306366,
-0.006013183388859034,
0.025113388895988464,
0.056236546486616135,
-0.0028621803503483534,
-0.02169756591320038,
0.08040791004896164,
0.05458764731884003,
0.03938677906990051,
-0.04788263514637947,
-0.06388650834560394,
-0.020234204828739166,
0.036271099001169205,
0.07500561326742172,
0.06369796395301819,
0.02250937931239605,
0.009637397713959217,
0.017315777018666267,
-0.00964183546602726,
-0.025521354749798775,
-0.05948985740542412,
-0.021349342539906502,
-0.020184913650155067,
-0.05005062744021416,
-0.03662734851241112,
-0.04111074283719063,
0.0257674902677536,
-0.021275168284773827,
-0.0034195375628769398,
0.002383313374593854,
-0.000008225564670283347,
0.01940777525305748,
0.04675442725419998,
0.060913000255823135,
-0.0127279506996274,
-0.05202744901180267,
-0.03825170174241066,
0.0555461049079895,
-0.009376535192131996,
-0.009012064896523952,
-0.021544180810451508,
-0.025958269834518433,
-0.024249274283647537,
-0.024463893845677376,
-0.008258271962404251,
-0.028138887137174606,
-0.005353888496756554,
-0.013054871931672096,
-0.006109174340963364,
0.075882688164711,
0.02601318620145321,
0.016633130609989166,
-0.036138929426670074,
0.031212078407406807,
0.011838589794933796,
0.01076796930283308,
-0.007687096484005451,
-0.02616794779896736,
0.029397813603281975,
-0.014449581503868103,
-0.014400197193026543,
0.042270727455616,
-0.02919360063970089,
0.005526476074010134,
-0.015826618298888206,
-0.006130035035312176,
0.004544243216514587,
0.010905958712100983,
-0.015588868409395218,
0.020267080515623093,
0.014443492516875267,
0.029201339930295944,
0.024065539240837097,
0.021768637001514435,
-0.005876543466001749,
0.021879874169826508,
-0.014726649038493633,
-0.042286328971385956,
-0.029258640483021736,
0.036737680435180664,
-0.025635816156864166,
-0.004913179203867912,
0.07297621667385101,
-0.025850865989923477,
-0.028306424617767334,
-0.0009650306892581284,
0.01736532896757126,
0.003479848150163889,
-0.005459794774651527,
-0.0160219669342041,
-0.019134873524308205,
0.009270510636270046,
-0.04959511384367943,
0.043650176376104355,
0.042431894689798355,
0.04677531495690346,
-0.08471229672431946,
0.025082485750317574,
-0.03268027678132057,
0.01848875731229782,
0.03711080551147461,
0.012612189166247845,
0.051986683160066605,
-0.004343363456428051,
0.06013784930109978,
-0.027553066611289978,
-0.002747539198026061,
0.04723425954580307,
0.022653961554169655,
0.0529826357960701,
-0.012335387989878654,
0.002611399395391345,
0.04139629378914833,
-0.07314997166395187,
0.029685568064451218,
0.019467853009700775,
0.0027249306440353394,
-0.04978738725185394,
0.0051383161917328835,
-0.009106045588850975,
-0.04694250971078873,
-0.009475830011069775,
-0.017841273918747902,
-0.013402857817709446,
0.03106261044740677,
-0.024161480367183685,
0.0287572480738163,
0.003201352432370186,
-0.02410300448536873,
0.019974282011389732,
-0.03322448208928108,
0.0027997251600027084,
-0.02411538176238537,
-0.01215252187103033,
-0.06724528223276138,
-0.027957892045378685,
0.01042994949966669,
0.07469442486763,
0.009824002161622047,
0.004108090419322252,
0.007239213213324547,
0.015440721996128559,
0.0015588676324114203,
-0.022730030119419098,
-0.01230629812926054,
0.0010931019205600023,
-0.0016151006566360593,
0.0008069857722148299,
0.008897844702005386,
-0.007432729005813599,
0.006451999768614769,
-0.02645971067249775,
-0.03611137345433235,
0.00020298105664551258,
-0.003982373513281345,
0.02645474672317505,
0.035600848495960236,
0.0076852221973240376,
-0.002195178298279643,
-0.11779934167861938,
-0.032022874802351,
-0.03011525608599186,
0.053079549223184586,
-0.0025870732497423887,
0.02251167595386505,
0.016885893419384956,
-0.05708037689328194,
-0.030581556260585785,
0.007462720386683941,
-0.029895031824707985,
-0.007095569744706154,
0.012575739994645119,
-0.00402107834815979,
0.029898619279265404,
-0.03336811810731888,
0.00292713544331491,
-0.04743589460849762,
-0.02519342489540577,
-0.06185765936970711,
-0.005262333899736404,
-0.004044046625494957,
-0.021193744614720345,
0.06139853969216347,
0.01921667903661728,
-0.07983923703432083,
-0.07749103754758835,
0.03566288203001022,
-0.05138399079442024,
0.02139616571366787,
0.009174819104373455,
-0.051115721464157104,
-0.03253311291337013,
-0.0065854270942509174,
-0.01797768473625183,
-0.021233290433883667,
0.054516032338142395,
-0.05803842842578888,
0.026911118999123573,
0.048351068049669266,
0.022272968664765358,
0.03838956356048584,
-0.0013541595544666052,
0.04434054717421532,
0.046735916286706924,
0.02346431277692318,
0.0087440712377429,
0.007696913555264473,
0.023967573419213295,
-0.061028651893138885,
-0.009905066341161728,
0.013421480543911457,
-0.010908701457083225
] |
<p>It is experimentally known that the equation of motion for a charge $e$ moving in a static electric field $\mathbf{E}$ is given by:</p>
<p>$$\frac{\mathrm{d}}{\mathrm{d}t} (\gamma m\mathbf{v}) = e\mathbf{E}$$</p>
<p>Is it possible to show this using just Newton's laws of motion for the proper frame of $e$, symmetry arguments, the Lorentz transformations and other additional principles?</p> | g9176 | [
0.018387913703918457,
0.029684418812394142,
-0.020412923768162727,
-0.02091403119266033,
0.11273173987865448,
0.006416230462491512,
0.04687393084168434,
-0.010390181094408035,
-0.01712334156036377,
0.04645813629031181,
-0.021295305341482162,
-0.006944676395505667,
0.030516386032104492,
-0.02247120626270771,
-0.020280323922634125,
-0.016341494396328926,
0.1275910884141922,
-0.02715536393225193,
-0.014191876165568829,
-0.0029422533698379993,
0.05286038666963577,
-0.004412231035530567,
0.03329199180006981,
-0.006979194935411215,
0.021412914618849754,
0.025214865803718567,
0.014287088066339493,
0.016934528946876526,
-0.02665659412741661,
-0.043541960418224335,
0.01651754230260849,
0.01847684569656849,
0.014170389622449875,
0.01221840362995863,
-0.04016568139195442,
-0.06315411627292633,
0.030462265014648438,
-0.012648108415305614,
0.05987146496772766,
0.006701536476612091,
-0.0008472899789921939,
0.008961093612015247,
-0.010497566312551498,
0.027403810992836952,
0.0501200295984745,
-0.025888558477163315,
0.002139181597158313,
0.0013048809487372637,
-0.07221898436546326,
0.005855953320860863,
-0.04298168793320656,
0.05149161443114281,
0.005578403361141682,
-0.050481926649808884,
-0.010767489671707153,
0.011339797638356686,
0.01143277995288372,
-0.01459265872836113,
0.056356098502874374,
0.03899917006492615,
-0.02348683774471283,
-0.014476357027888298,
0.01937791518867016,
-0.009623521938920021,
0.04319622740149498,
0.001177768805064261,
-0.07832610607147217,
-0.017059115692973137,
0.001794349169358611,
-0.004681416787207127,
0.0030480388086289167,
-0.041852861642837524,
-0.052770934998989105,
0.01996309868991375,
0.012516727671027184,
-0.00265239248983562,
0.0014360519126057625,
-0.030982712283730507,
-0.023668382316827774,
-0.05766405537724495,
-0.007139171939343214,
0.008694227784872055,
0.034201327711343765,
0.008958564139902592,
0.08049289882183075,
-0.04686720296740532,
0.05316150560975075,
0.05727417394518852,
0.0033324395772069693,
-0.05188039690256119,
-0.038284070789813995,
-0.010887202806770802,
0.06978611648082733,
0.03477558121085167,
0.004399497993290424,
-0.0326763354241848,
-0.04705461859703064,
0.08075449615716934,
-0.005419814959168434,
-0.04050660878419876,
-0.06557928025722504,
-0.009313578717410564,
-0.039921846240758896,
0.04221055656671524,
0.007184565998613834,
-0.017374031245708466,
0.005879053846001625,
0.0281143169850111,
0.0006267638527788222,
-0.02149796672165394,
0.0021335575729608536,
-0.02340201660990715,
-0.0005372124724090099,
-0.026930341497063637,
-0.05326901003718376,
-0.017280831933021545,
0.04267767071723938,
-0.032859791070222855,
-0.006127196364104748,
0.05568249151110649,
0.01601341925561428,
0.022830048575997353,
0.018420375883579254,
0.046974532306194305,
-0.02304041013121605,
0.0009610750712454319,
-0.014454558491706848,
0.02471536211669445,
0.03638627380132675,
0.0067094117403030396,
-0.00780510064214468,
0.0506797656416893,
0.006195968482643366,
-0.015518181957304478,
0.013544484041631222,
0.048988960683345795,
0.02823599986732006,
-0.0030420091934502125,
-0.02204289473593235,
-0.03300314396619797,
0.03878280892968178,
-0.033123552799224854,
0.04093426838517189,
0.0010294136591255665,
-0.024239545688033104,
0.0165109820663929,
-0.005864561069756746,
-0.008083023130893707,
0.04379546269774437,
0.04747200012207031,
-0.05450175330042839,
0.05592604726552963,
0.027117494493722916,
0.022878840565681458,
0.07777372747659683,
-0.06163143366575241,
0.060740694403648376,
-0.008990391157567501,
-0.0261540524661541,
-0.06818945705890656,
0.04134204238653183,
-0.03998138755559921,
0.025202453136444092,
-0.020445354282855988,
-0.03521161153912544,
-0.034173328429460526,
-0.020205695182085037,
0.043956223875284195,
0.015212484635412693,
-0.07848696410655975,
-0.08711271733045578,
-0.016363322734832764,
0.023460783064365387,
0.04916978254914284,
-0.02750190533697605,
0.04018275812268257,
-0.052678994834423065,
-0.04538966342806816,
-0.012669303454458714,
-0.015536163002252579,
-0.016736021265387535,
-0.020451011136174202,
0.04020408168435097,
-0.02134883962571621,
-0.049361102283000946,
0.019323648884892464,
-0.03104676678776741,
0.015528270043432713,
-0.03196414187550545,
0.014698210172355175,
-0.05503273382782936,
0.01977280154824257,
-0.030983425676822662,
0.03439942002296448,
-0.020939087495207787,
0.028629587963223457,
-0.04567874222993851,
-0.014916897751390934,
-0.046966686844825745,
-0.010497905313968658,
0.011606413871049881,
0.06689541041851044,
0.03899519145488739,
-0.02080322802066803,
0.021518917754292488,
-0.01586175337433815,
-0.02625218778848648,
-0.05368367210030556,
0.06518105417490005,
0.010160617530345917,
0.0385950468480587,
-0.03181954845786095,
-0.044241178780794144,
0.04120279476046562,
-0.009247026406228542,
-0.029957972466945648,
0.013150603510439396,
-0.013572501949965954,
-0.05772702768445015,
0.03790991008281708,
-0.08083958178758621,
0.008397374302148819,
0.016044221818447113,
0.035489410161972046,
-0.00946994498372078,
-0.04109865427017212,
-0.02023155428469181,
-0.028952473774552345,
-0.04738399013876915,
0.003678106004372239,
-0.04483068734407425,
0.06915935128927231,
-0.006488420534878969,
-0.015229280106723309,
0.06580367684364319,
0.05264248698949814,
-0.03491609916090965,
-0.03221707046031952,
0.04742914065718651,
-0.004870943259447813,
0.018126025795936584,
0.00297713209874928,
-0.010372160002589226,
-0.019560065120458603,
0.018554357811808586,
0.007991387508809566,
0.07644876837730408,
0.07713715732097626,
-0.0017998472321778536,
0.01754567213356495,
0.028472639620304108,
-0.04889319837093353,
0.00029113912023603916,
0.005757385399192572,
0.007804682943969965,
-0.03408920764923096,
-0.02935953065752983,
0.026879187673330307,
-0.010991539806127548,
0.0029768310487270355,
-0.04462515562772751,
-0.013936140574514866,
-0.02054930478334427,
0.05080645531415939,
-0.03201495110988617,
-0.001140139065682888,
-0.011666893027722836,
0.06838668882846832,
-0.021077891811728477,
-0.01161967497318983,
-0.0011252750409767032,
0.05090613290667534,
-0.02643054723739624,
-0.003180632134899497,
-0.037585701793432236,
-0.05038813129067421,
0.02146122232079506,
-0.039079952985048294,
-0.0010708948830142617,
-0.04168634116649628,
-0.01990189589560032,
-0.011567656882107258,
-0.024303430691361427,
0.009923123754560947,
0.030033273622393608,
-0.03619690239429474,
-0.02351701632142067,
-0.0421903021633625,
-0.010817214846611023,
0.030758175998926163,
-0.027340302243828773,
0.04435570165514946,
0.04913409426808357,
-0.026928694918751717,
-0.01971070095896721,
0.047821760177612305,
0.0026373688597232103,
-0.06014181300997734,
-0.0037148778792470694,
0.03218144178390503,
-0.008500764146447182,
0.01597709022462368,
-0.04442862421274185,
0.035923633724451065,
0.08146695792675018,
0.05724450200796127,
-0.0409439317882061,
-0.048528190702199936,
-0.0044107744470238686,
-0.018594518303871155,
-0.01877790316939354,
0.03258119523525238,
0.025827918201684952,
-0.0218784399330616,
-0.059106845408678055,
-0.028043318539857864,
0.02557665854692459,
0.0025331333745270967,
0.060483623296022415,
0.036986272782087326,
0.003828638233244419,
-0.04616512730717659,
-0.021289022639393806,
-0.03221484646201134,
0.07588046789169312,
0.0389254204928875,
-0.009293396025896072,
0.056752514094114304,
-0.029852217063307762,
-0.03252185508608818,
0.023711664602160454,
0.014302344992756844,
0.03748219460248947,
-0.02217455394566059,
0.0009380984120070934,
0.009447830729186535,
-0.016585953533649445,
0.06714048981666565,
0.02874833159148693,
-0.03309027478098869,
0.013203364796936512,
-0.027762316167354584,
-0.13139425218105316,
0.015515848062932491,
-0.03481179103255272,
-0.032380878925323486,
-0.02465898171067238,
-0.029196729883551598,
0.03153558075428009,
-0.008403673768043518,
-0.000518555985763669,
-0.0790322870016098,
-0.009048210456967354,
0.010213712230324745,
-0.020668072625994682,
-0.003919856622815132,
0.05915413051843643,
0.05556293949484825,
-0.01937689073383808,
0.007506930269300938,
0.00992919784039259,
0.0047273836098611355,
0.03442157059907913,
-0.015025224536657333,
0.01670403778553009,
0.017424648627638817,
-0.06196967512369156,
0.036795854568481445,
-0.027118122205138206,
-0.03974415734410286,
0.008023761212825775,
-0.05038429796695709,
0.011143390089273453,
-0.003967080265283585,
-0.006930089555680752,
-0.054408106952905655,
0.014035481959581375,
0.03560357540845871,
-0.06149701774120331,
0.044091541320085526,
0.02113800123333931,
0.019052062183618546,
0.0006459791911765933,
0.04012352600693703,
0.0019731754437088966,
-0.0005128771299496293,
-0.0010003217030316591,
0.04436653479933739,
0.03785547986626625,
0.0025393881369382143,
0.024149615317583084,
-0.044373493641614914,
-0.005758327431976795,
0.019889291375875473,
0.0026841526851058006,
-0.03681947663426399,
0.018223440274596214,
-0.0380672961473465,
-0.010723046027123928,
-0.029636763036251068,
0.024043677374720573,
0.0404452346265316,
0.007498933933675289,
0.023839490488171577,
-0.04816708341240883,
-0.008222510106861591,
0.06422418355941772,
-0.0465664304792881,
0.06073281541466713,
-0.04378359764814377,
-0.04192087799310684,
-0.018236955627799034,
-0.004437689669430256,
-0.035958025604486465,
0.012235087342560291,
0.0038717074785381556,
-0.015492255799472332,
-0.002668560016900301,
0.019708674401044846,
0.005111687816679478,
0.06192263588309288,
0.01837666518986225,
0.05240005627274513,
-0.028741924092173576,
-0.027943968772888184,
0.1089833527803421,
0.11333286017179489,
-0.002858220599591732,
-0.02218819595873356,
-0.009108318947255611,
-0.04537411406636238,
-0.0033146848436444998,
-0.02111239731311798,
0.03957926481962204,
-0.08276774734258652,
0.04394405707716942,
-0.03478282317519188,
0.06487099081277847,
-0.01866653375327587,
0.06522627174854279,
0.09814105927944183,
0.013772900216281414,
0.06014229729771614,
-0.032783232629299164,
-0.017718998715281487,
0.031052349135279655,
-0.01599726639688015,
-0.03469365835189819,
-0.005675612483173609,
-0.02743779867887497,
0.033030737191438675,
0.027807312086224556,
-0.01509767584502697,
0.05562947690486908,
0.018583308905363083,
-0.021805867552757263,
-0.047553982585668564,
-0.008637085556983948,
-0.038222022354602814,
0.010000583715736866,
-0.05136235058307648,
-0.017646435648202896,
0.04025822505354881,
0.04666360095143318,
0.0934520810842514,
-0.008667413145303726,
-0.02982051856815815,
-0.046354055404663086,
-0.04368791729211807,
0.0033282225485891104,
0.018185565248131752,
0.010151362977921963,
-0.011907266452908516,
-0.03310614079236984,
0.004225104581564665,
-0.030359286814928055,
-0.014910638332366943,
0.0113416388630867,
-0.04418155923485756,
-0.052146703004837036,
-0.01658286526799202,
-0.018192928284406662,
-0.0053655668161809444,
-0.00413981219753623,
-0.02428494393825531,
0.016212841495871544,
-0.04408186674118042,
0.08555451780557632,
-0.021226901561021805,
-0.04525335505604744,
-0.01100877020508051,
-0.009983506985008717,
-0.004533853847533464,
-0.02632073312997818,
0.009274967946112156,
0.11579907685518265,
-0.0446767695248127,
-0.013156717643141747,
-0.026589620858430862,
0.05024133622646332,
-0.04152679070830345,
-0.017339838668704033,
0.010394237004220486,
-0.01523798517882824,
0.03672848641872406,
0.03389563411474228,
0.05598875507712364,
0.0017783554503694177,
-0.07297877967357635,
0.03520213067531586,
0.009355190210044384,
0.04409662261605263,
-0.010969104245305061,
0.01597546972334385,
0.03097926825284958,
-0.016931768506765366,
-0.017812605947256088,
-0.035311080515384674,
-0.002631956245750189,
-0.057965993881225586,
0.05858461931347847,
-0.04308494180440903,
0.06202645227313042,
-0.032434988766908646,
-0.01746012642979622,
0.02129111811518669,
-0.03063243068754673,
-0.04394753277301788,
-0.011066443286836147,
0.013781171292066574,
-0.011796941980719566,
-0.044662363827228546,
0.040111590176820755,
0.024602672085165977,
-0.004406283609569073,
-0.046642836183309555,
0.02267364412546158,
-0.0029769649263471365,
0.013786809518933296,
0.011231622658669949,
-0.03023586794734001,
-0.08276020735502243,
0.06434430181980133,
0.02633582055568695,
-0.007128608878701925,
0.034432508051395416,
-0.034561384469270706,
0.016485774889588356,
0.04410381242632866,
-0.04063114523887634,
-0.032624874264001846,
0.038543231785297394,
-0.06206575408577919,
-0.023106850683689117,
-0.0227869413793087,
0.038399212062358856,
0.0045350599102675915,
-0.062455546110868454,
-0.030904363840818405,
0.020712846890091896,
0.008612441830337048,
0.03349222242832184,
0.027521049603819847,
0.04906347393989563,
-0.018342792987823486,
-0.02254648320376873,
0.051992010325193405,
-0.025522131472826004,
0.03708610683679581,
0.04203658923506737,
-0.015538579784333706,
0.04547350853681564,
0.006362448912113905,
0.04298658296465874,
0.0011401510564610362,
-0.0457892045378685,
0.008387274108827114,
-0.005782437510788441,
-0.09047560393810272,
0.00939231924712658,
0.0061693619936704636,
0.033283088356256485,
0.036626990884542465,
-0.026986368000507355,
-0.04243185371160507,
0.026297301054000854,
-0.0318969190120697,
0.015338697470724583,
-0.008520474657416344,
0.0008216962451115251,
-0.026880236342549324,
0.003680464345961809,
0.010314474813640118,
-0.012838423252105713,
-0.03204497694969177,
-0.001098519191145897,
0.028679147362709045,
-0.05303787440061569,
0.05374826118350029,
0.08776192367076874,
0.07394145429134369,
0.03389817476272583,
-0.024424560368061066,
-0.026315951719880104,
0.028934471309185028,
0.021770890802145004,
-0.03559013828635216,
0.01692424714565277,
0.00008514038927387446,
0.009206315502524376,
-0.020937753841280937,
-0.017058316618204117,
-0.02320719324052334,
-0.036405354738235474,
-0.021312186494469643,
0.016648883000016212,
0.011079932563006878,
0.02174919657409191,
0.013310328125953674,
-0.013557079248130322,
-0.004507176112383604,
-0.03151778131723404,
-0.011142210103571415,
-0.0039828685112297535,
0.04604678601026535,
0.031009675934910774,
-0.030280157923698425,
0.027545344084501266,
0.018077410757541656,
0.0056086573749780655,
0.01267943810671568,
-0.0007209712057374418,
-0.05148886516690254,
0.04502113536000252,
0.05091920495033264,
0.004144754260778427,
0.023234376683831215,
0.003836994990706444,
0.0070134117268025875,
0.05519937723875046,
-0.04490915685892105,
0.0396023727953434,
0.04099079221487045,
0.027623193338513374,
-0.09712444990873337,
-0.0056426371447741985,
0.032384950667619705,
-0.018065128475427628,
-0.0958326905965805,
0.03508076071739197,
0.04955941438674927,
-0.010205933824181557,
0.006851436570286751,
0.02525419555604458,
-0.0633930116891861,
-0.004259700421243906,
0.0344884879887104,
-0.0018894204404205084,
0.017816442996263504,
-0.058407340198755264,
0.01880418136715889,
-0.0064520337618887424,
0.026020294055342674,
-0.02987973764538765,
0.025401225313544273,
0.007273734547197819,
-0.026988975703716278,
-0.03282551467418671,
0.02276812493801117,
-0.024258065968751907,
0.03109460324048996,
0.0034359905403107405,
0.014120728708803654,
0.03321025148034096,
-0.03197777271270752,
-0.0335889533162117,
0.03366641327738762,
0.05013439059257507,
0.010490852408111095,
-0.030228886753320694,
-0.04160671681165695,
0.05347173660993576,
-0.014598791487514973,
0.04346010461449623,
-0.03396889194846153,
-0.02750484086573124,
0.007335236761718988,
0.01590024121105671,
-0.024652069434523582,
0.006627107039093971,
0.00004054109376738779,
-0.031622521579265594,
0.033041466027498245,
-0.006598860491067171,
-0.01867477037012577,
-0.002000171225517988,
0.01785038597881794,
-0.0035475182812660933,
0.029254261404275894,
-0.03840533271431923,
0.002621009713038802,
-0.027707574889063835,
-0.02335141785442829,
0.0034004554618149996,
-0.01036299392580986,
0.008028608746826649,
-0.03661733120679855,
-0.09392564743757248,
-0.04200795665383339,
0.03291567414999008,
0.04309988021850586,
0.002070993185043335,
0.0009604428778402507,
0.06399519741535187,
0.04143344238400459,
0.05621293932199478,
-0.026381799951195717,
0.06754444539546967,
0.034998904913663864,
-0.008271843194961548,
-0.02922300435602665,
0.006344993598759174,
-0.029086695984005928,
-0.036522723734378815,
-0.01057531125843525,
-0.012950364500284195,
-0.024639690294861794,
-0.016312576830387115,
0.05132698640227318,
-0.06856394559144974,
-0.03357624262571335,
-0.04764076694846153,
-0.003189046634361148,
0.031053967773914337,
-0.030233364552259445,
0.008453826420009136,
-0.0176993515342474,
-0.07728367298841476,
0.023196706548333168,
0.040894702076911926,
0.016808001324534416,
-0.041165340691804886,
-0.05067554861307144,
-0.058291926980018616,
-0.007469640579074621,
0.01272066030651331,
-0.002258279360830784,
0.024613237008452415,
0.004152234178036451,
0.018231380730867386,
0.050217706710100174,
0.002274861792102456,
-0.06567282974720001,
0.011431028135120869,
0.03245732560753822,
-0.002146913902834058,
-0.03017820045351982,
-0.026108257472515106,
0.05027246102690697,
0.050918951630592346,
-0.01466281432658434,
0.011636866256594658,
0.04467429593205452,
0.003349205246195197,
0.004289188887923956,
-0.08589495718479156,
-0.011307851411402225,
0.03754600137472153
] |
<p><strong>1.a</strong> In paragraph at <a href="http://en.wikipedia.org/wiki/Entropy#Relating_entropy_to_energy_usefulness">Wikipedia/Entropy</a> it is stated:</p>
<blockquote>
<p>This is because energy supplied at a <strong>high temperature (i.e. with low entropy)</strong>
tends to be more useful than the same amount of energy
available at room temperature</p>
</blockquote>
<p><strong>1.b</strong> But at <a href="http://www.nmsea.org/Curriculum/Primer/what_is_entropy.htm">What is Entropy?</a> there is:</p>
<blockquote>
<p>The higher the temperature of the gas, the faster the gas particles
are moving on average, so the wider the range of possible velocities
for the gas particles, and hence, the more uncertainty we have about
the velocity of any particular particle. <strong>Thus, higher temperature</strong>, as
well as greater volume, <strong>mean higher entropy</strong>.</p>
</blockquote>
<p><strong>2.a</strong> I was trying to obtain information on relation between entropy and work. Basically, if an external process modifies a system so that its entropy is reduced, then it is expected by me that work was done on the system and energy was contributed to it. I received good answers ( <a href="http://physics.stackexchange.com/questions/24134/connection-between-entropy-and-energy/24147">Connection between entropy and energy</a> ). However I feel that I was not properly understood.</p>
<p><strong>2.b</strong> In 1953 paper of L. Brillouin ("The Negentropy Principle of Information") wrote what I basically had in mind when I asked the question. I am not aware if the approach is correct and accepted. </p>
<blockquote>
<p>An isolated system contains negentropy if it reveals a possibility for
doing mechanical or electrical work. If the system is not at a uniform
temperature T, but consists of different parts at different
temperatures, it contains a certain amount of negentropy. This
negentropy can be used to obtain some mechanical work done by the
system, or it can be simply dissipated and lost by thermal conduction.
A difference in pressure between different parts of the system is
another case of negentropy. A difference of electrical potential
repre-sents another example. A tank of compressed gas in a room at
atmospheric pressure, a vacuum tank in a similar room, a charged
battery, any device that can produce high-grade energy (mechanical
work) or be degraded by some irreversible process (thermal
con-duction, electrical resistivity, friction, viscosity) is a source
of negentropy.</p>
</blockquote>
<p><strong>3.a</strong> There is often a contradict intuition about information entropy. Shannon approach sees maximum entropy as maximum uncertainty / information.</p>
<p><strong>3.b</strong> Joe Rosen in "The Symmetry Principle" states that maximum entropy is maximum symmetry – which means maximum redundancy, so minimum amount of information.</p>
<p><strong>4.</strong> Non-equilibrium thermodynamics – the branch is not mature and does not serve as a tool to solve issues like in 2.a, AFAIK.</p>
<p>I was seeing <a href="http://arxiv.org/abs/0707.3400">The Physics of Maxwell's demon and information</a> as very good guide through <strong>equilibrium</strong> (what about non-equilibrium?) thermodynamics, its connection with work and information. The authors did, however, when elaborating on entropy of a system in Brillouin's view, put an equal sign to it and Shannon entropy – which I think is contradict to Brillouin itself – who as I cited in 2.b stated that it is disequilibrium that allows system to work – meaning a complex, information-rich system (in other paragraph he also explicitly sates that negentropy is information). This conforms to Rosen 3.b.</p>
<p><strong>Are there other good compilations on entropy, information, maybe complexity science? Such that solve the contradictions, form compatible non-equilibrium foundation?</strong></p> | g9177 | [
0.01854432187974453,
-0.011149647645652294,
0.02542598731815815,
0.0007865871884860098,
0.03155433014035225,
-0.04176433011889458,
-0.0671270415186882,
-0.014188424684107304,
-0.048797037452459335,
0.04664340987801552,
0.005285743623971939,
-0.06396397203207016,
0.01149630919098854,
0.006599633023142815,
-0.008781896904110909,
0.003697725711390376,
0.08636748045682907,
0.016855621710419655,
0.028990333899855614,
0.023003818467259407,
-0.04194984585046768,
0.007182740606367588,
-0.007332480978220701,
-0.05924330651760101,
-0.035576581954956055,
-0.05092441290616989,
0.0011679697781801224,
-0.017328346148133278,
-0.05183449015021324,
-0.024230144917964935,
0.029500756412744522,
-0.022138318046927452,
0.04301910102367401,
-0.040128327906131744,
-0.04628235474228859,
0.005684682168066502,
0.06651981920003891,
0.049902670085430145,
0.025920458137989044,
0.005450393073260784,
-0.024239158257842064,
-0.02571370266377926,
0.016960524022579193,
-0.013954699970781803,
0.0063943564891815186,
0.062351781874895096,
-0.020288188010454178,
-0.050219759345054626,
-0.04356997460126877,
-0.024374453350901604,
0.01988868974149227,
0.05668843910098076,
0.05472642183303833,
0.022502092644572258,
0.061418209224939346,
-0.00898958183825016,
0.034384410828351974,
-0.00027616709121502936,
0.03427191078662872,
-0.021169513463974,
0.04713167995214462,
0.00510103115811944,
-0.017236247658729553,
0.0005599792930297554,
0.017255527898669243,
-0.004167845938354731,
0.0017703416524454951,
-0.0032131250482052565,
0.00947869848459959,
0.009476907551288605,
0.010559355840086937,
-0.011940433643758297,
-0.013226899318397045,
-0.02875717170536518,
0.02044430561363697,
0.002095201751217246,
0.07867518067359924,
-0.014768755063414574,
-0.027473844587802887,
-0.001663864590227604,
-0.009711435995995998,
-0.04140395298600197,
0.02322809025645256,
-0.013562778010964394,
0.07835186272859573,
-0.04317769408226013,
0.019559193402528763,
-0.02559783309698105,
0.026725444942712784,
0.02928069233894348,
-0.010647072456777096,
0.0017495080828666687,
0.11136910319328308,
0.005220541264861822,
-0.0006669738795608282,
0.06829863041639328,
-0.006940620485693216,
-0.01814400404691696,
0.018399681895971298,
0.0064107743091881275,
-0.007990975864231586,
-0.08029036968946457,
-0.010664686560630798,
-0.0066784098744392395,
-0.03244806453585625,
-0.0215800441801548,
-0.03418001905083656,
-0.07279779016971588,
-0.10974310338497162,
0.008540395647287369,
-0.019166510552167892,
-0.014465010724961758,
-0.05603250488638878,
-0.0010728167835623026,
0.013828469440340996,
-0.02749350108206272,
0.07709701359272003,
-0.03673553466796875,
-0.026993921026587486,
0.01818876340985298,
0.02990122139453888,
0.08664512634277344,
0.007444940507411957,
0.027427082881331444,
-0.020608626306056976,
-0.0012345259310677648,
0.02060946635901928,
-0.02578168548643589,
0.022912658751010895,
-0.04623090475797653,
0.003895390313118696,
-0.0046560801565647125,
-0.037770599126815796,
0.02158304676413536,
-0.006946857552975416,
-0.0015730547020211816,
0.011001156643033028,
-0.010282352566719055,
0.01767757534980774,
-0.016423344612121582,
-0.002135475166141987,
0.0029231132939457893,
-0.056753192096948624,
0.00272011780180037,
-0.05207529291510582,
0.0017654765397310257,
-0.07247935235500336,
0.010464389808475971,
0.0133389076218009,
0.0027998953592032194,
-0.013450653292238712,
0.031651608645915985,
-0.028322812169790268,
-0.06092580780386925,
0.022248681634664536,
-0.012002501636743546,
0.019065937027335167,
0.010496556758880615,
0.037155237048864365,
0.009884827770292759,
0.016547318547964096,
-0.044340696185827255,
0.0301812794059515,
0.00449049286544323,
-0.041453368961811066,
-0.005664361175149679,
0.03823840618133545,
-0.03711346164345741,
0.05369415134191513,
-0.026781711727380753,
-0.08907726407051086,
-0.026411104947328568,
0.0054531339555978775,
0.027521278709173203,
0.009688971564173698,
0.004775188863277435,
0.058249957859516144,
0.008445609360933304,
0.02718254365026951,
-0.07663891464471817,
-0.09466243535280228,
0.045387137681245804,
0.06291612982749939,
-0.03691405802965164,
-0.042782265692949295,
0.08612512052059174,
0.03027322329580784,
0.0485859252512455,
-0.09557195752859116,
-0.032969024032354355,
-0.02160470373928547,
0.0148908831179142,
-0.03461926802992821,
0.047675807029008865,
-0.017319073900580406,
0.00597229041159153,
0.00204431707970798,
-0.04746801778674126,
-0.05771351233124733,
-0.003981460817158222,
-0.05667052045464516,
0.043644584715366364,
-0.007534462492913008,
0.00367583055049181,
0.027870474383234978,
0.0680227279663086,
-0.03080795332789421,
0.034291431307792664,
0.0030129896476864815,
0.005446210969239473,
-0.009373484179377556,
-0.02649667300283909,
0.020474161952733994,
0.05626165121793747,
0.014299801550805569,
-0.07473143190145493,
-0.03075026534497738,
-0.01183384470641613,
0.018383977934718132,
0.0014066596049815416,
0.01975911669433117,
-0.034105945378541946,
0.03202374652028084,
0.023831043392419815,
-0.03656967356801033,
-0.022726040333509445,
-0.061286162585020065,
-0.037355680018663406,
-0.007970304228365421,
0.03759986534714699,
-0.0241206344217062,
0.06765588372945786,
0.0004009180120192468,
-0.010734038427472115,
0.004662279970943928,
0.033890631049871445,
0.03344433754682541,
-0.004226632881909609,
0.03438037261366844,
0.07497167587280273,
-0.001371189602650702,
-0.04796217009425163,
-0.041546400636434555,
0.035478625446558,
-0.006272901780903339,
-0.022793428972363472,
0.001786068081855774,
-0.06890727579593658,
0.012364676222205162,
0.002942972118034959,
-0.01209352258592844,
-0.01998000033199787,
-0.0229628998786211,
-0.051099106669425964,
-0.0053184982389211655,
0.033522021025419235,
0.02465633489191532,
0.018711742013692856,
-0.015794413164258003,
-0.028795301914215088,
0.059426359832286835,
-0.073004350066185,
-0.0015983800403773785,
0.038405079394578934,
-0.0229794941842556,
0.016282493248581886,
-0.04676680266857147,
-0.009713604114949703,
0.00011934281792491674,
-0.00792171061038971,
0.05673646554350853,
0.06245690956711769,
-0.04184173047542572,
0.02053465135395527,
-0.01024247519671917,
0.03082871250808239,
0.020923351868987083,
-0.0065686628222465515,
0.01407359167933464,
-0.03244868293404579,
-0.011308440938591957,
-0.008318756707012653,
-0.028114767745137215,
0.03370516747236252,
0.01561775803565979,
-0.028926139697432518,
-0.006625974550843239,
0.031209632754325867,
-0.027078382670879364,
0.03544548526406288,
0.038307707756757736,
-0.00030945788603276014,
0.008189020678400993,
0.022321846336126328,
-0.036523133516311646,
-0.005952704232186079,
-0.006857936270534992,
-0.04432995244860649,
0.013590735383331776,
-0.05529027804732323,
-0.006421404425054789,
-0.008524863980710506,
-0.01076431293040514,
0.05800633132457733,
0.04119538143277168,
0.033471956849098206,
-0.0784357339143753,
-0.029712514951825142,
0.005175911821424961,
0.006656911689788103,
-0.03730501979589462,
-0.042033158242702484,
0.01929161138832569,
0.02703312784433365,
-0.03390990197658539,
0.033716753125190735,
-0.007646325975656509,
-0.017694463953375816,
0.06486806273460388,
-0.00024719859356991947,
0.045677781105041504,
0.004895531106740236,
0.01797967590391636,
-0.07120051234960556,
0.04998999089002609,
0.04156319424510002,
-0.025813214480876923,
-0.0016841681208461523,
-0.08333452045917511,
-0.015829775482416153,
-0.031563013792037964,
-0.021419961005449295,
0.040773678570985794,
0.009342202916741371,
-0.07756567746400833,
-0.05818426236510277,
0.01690090261399746,
-0.0008591364021413028,
0.04506085440516472,
-0.02210870571434498,
0.04584193229675293,
-0.005202284082770348,
-0.024924417957663536,
0.008758272975683212,
-0.03249714896082878,
0.014612868428230286,
0.006707638967782259,
-0.014814523980021477,
-0.01740226149559021,
0.017269719392061234,
0.04472530633211136,
0.020245714113116264,
-0.01432852353900671,
0.026888782158493996,
-0.038835808634757996,
0.047321707010269165,
0.003500208491459489,
0.03029588796198368,
-0.006350500043481588,
-0.0018333387561142445,
-0.03951213136315346,
0.002734169829636812,
0.03834595903754234,
-0.004567738156765699,
-0.03432966023683548,
0.03832464665174484,
0.03228558972477913,
0.023282352834939957,
0.007413619663566351,
-0.02743942104279995,
-0.004845031071454287,
-0.036082424223423004,
-0.011379584670066833,
-0.008392563089728355,
0.08150862902402878,
0.0008243900374509394,
0.0535043366253376,
0.051073987036943436,
-0.03940269723534584,
0.035568803548812866,
0.07138147205114365,
-0.002670220099389553,
0.029573865234851837,
0.017271487042307854,
0.05470426008105278,
0.013190931640565395,
-0.03167054429650307,
0.029133977368474007,
-0.004201802425086498,
-0.06737182289361954,
-0.027605824172496796,
-0.012216263450682163,
-0.041866838932037354,
0.036904409527778625,
-0.003582674078643322,
-0.030281055718660355,
0.0389188714325428,
0.017852922901511192,
0.0345332995057106,
0.02082398533821106,
0.04096990078687668,
-0.044442951679229736,
0.032520849257707596,
0.049636662006378174,
-0.05878185108304024,
0.02361772395670414,
-0.016314277425408363,
-0.05341114103794098,
-0.004640783648937941,
-0.031295426189899445,
0.0005576686235144734,
-0.020346445962786674,
0.0022436778526753187,
-0.03814265877008438,
-0.02013387344777584,
-0.027488071471452713,
-0.02231404185295105,
-0.08671797066926956,
0.07453209161758423,
0.050555650144815445,
0.02018614672124386,
0.01763453520834446,
0.01483010035008192,
-0.009066554717719555,
-0.008219870738685131,
0.05409480258822441,
0.07421636581420898,
-0.0037112256977707148,
-0.03407156094908714,
-0.030734967440366745,
-0.006073522847145796,
0.014988838694989681,
0.005330844782292843,
-0.011261303909122944,
0.01374400407075882,
0.07991837710142136,
-0.046624213457107544,
0.009535624645650387,
0.025699783116579056,
0.044591017067432404,
0.023326484486460686,
0.001454459736123681,
0.061055850237607956,
-0.08422718197107315,
-0.00003612569344113581,
0.0376724936068058,
-0.030110124498605728,
0.01976122334599495,
-0.06797419488430023,
-0.030989723280072212,
-0.022041942924261093,
-0.011280999518930912,
-0.02944864146411419,
-0.005491018760949373,
-0.024735962972044945,
-0.008632834069430828,
-0.037801556289196014,
0.043581120669841766,
0.0028855791315436363,
0.005818433593958616,
-0.0310354121029377,
-0.030604341998696327,
0.023943983018398285,
0.02890613302588463,
0.032327521592378616,
0.04438144341111183,
-0.08230991661548615,
0.052553046494722366,
-0.05118570476770401,
-0.020920313894748688,
0.0366518497467041,
0.03949877247214317,
0.026546888053417206,
0.07574905455112457,
0.02312994748353958,
-0.0026136385276913643,
-0.007908331230282784,
-0.03488069027662277,
-0.01888171397149563,
0.04404360055923462,
-0.020679958164691925,
0.011674243025481701,
0.0241396427154541,
0.047474682331085205,
0.028327221050858498,
-0.010543097741901875,
-0.048823677003383636,
0.033577289432287216,
-0.015517249703407288,
-0.03128676488995552,
0.02827475592494011,
0.09365792572498322,
0.05390334501862526,
-0.008703057654201984,
-0.037052545696496964,
0.012044146656990051,
0.022447386756539345,
-0.04401040077209473,
-0.06185218691825867,
0.0007259944104589522,
-0.08316821604967117,
0.0019155505578964949,
-0.0406617596745491,
0.008035863749682903,
-0.015898119658231735,
-0.0039433385245501995,
0.011204845272004604,
0.03357062116265297,
-0.003173205303028226,
0.032944753766059875,
0.0343988873064518,
0.021465856581926346,
-0.014406557194888592,
0.031647827476263046,
0.027046607807278633,
-0.01757756806910038,
-0.0073832194320857525,
-0.010885138064622879,
-0.03893668204545975,
-0.06186056137084961,
0.06822702288627625,
0.03687665984034538,
0.06363813579082489,
-0.02419552579522133,
0.009128649719059467,
0.029158761724829674,
-0.043000228703022,
-0.028763949871063232,
0.02930297888815403,
0.02234482392668724,
0.009626376442611217,
0.04043528437614441,
0.038340285420417786,
0.02591067925095558,
-0.017222709953784943,
-0.04365314543247223,
-0.03719126433134079,
0.004103715997189283,
0.016399351879954338,
0.016470588743686676,
-0.0019343168241903186,
-0.011688387021422386,
0.022910451516509056,
0.04919002577662468,
-0.025894230231642723,
-0.04111303761601448,
-0.06686139106750488,
-0.03348512947559357,
0.01242995634675026,
-0.023568762466311455,
0.02448086254298687,
0.02171408012509346,
0.005300063639879227,
-0.06990350782871246,
-0.0018974656704813242,
-0.022413935512304306,
0.03667399287223816,
0.0050745741464197636,
-0.010552484542131424,
-0.012770617380738258,
0.023211030289530754,
0.03440836817026138,
0.0023860910441726446,
0.024933556094765663,
0.03292703628540039,
-0.05878431349992752,
-0.008931108750402927,
-0.01753372885286808,
-0.005112537182867527,
0.1319008320569992,
-0.0030360533855855465,
0.034705664962530136,
0.038048554211854935,
-0.0470610186457634,
0.028812699019908905,
-0.059561245143413544,
-0.06406984478235245,
-0.06406907737255096,
-0.057086993008852005,
-0.001845414750277996,
-0.04252634570002556,
-0.0638270378112793,
0.03753140568733215,
0.027222026139497757,
-0.04521558806300163,
0.047357507050037384,
-0.02820058912038803,
0.06453149020671844,
-0.004944020416587591,
-0.012407159432768822,
0.037724412977695465,
-0.027863603085279465,
-0.0024408837780356407,
0.00965441856533289,
-0.02498445473611355,
0.013507732190191746,
-0.038179896771907806,
-0.02745356224477291,
-0.06291192770004272,
0.022139787673950195,
-0.06619734317064285,
-0.0603630393743515,
0.000952838861849159,
-0.04641285911202431,
0.022805524989962578,
0.06515690684318542,
-0.014503524638712406,
0.056860554963350296,
-0.04748399555683136,
0.035478878766298294,
-0.05188770219683647,
0.06433793902397156,
-0.01080972608178854,
0.008231762796640396,
0.02829950861632824,
0.024763701483607292,
-0.043370865285396576,
0.009646437130868435,
-0.020113730803132057,
-0.02313200756907463,
-0.012775744311511517,
-0.003395721549168229,
0.04791001230478287,
-0.015183160081505775,
0.03806830942630768,
0.031868718564510345,
-0.029787331819534302,
-0.00206976430490613,
0.029986249282956123,
0.04074780270457268,
0.022679731249809265,
-0.00245106709189713,
0.03911089524626732,
0.05797739326953888,
-0.005057757720351219,
-0.03016217052936554,
-0.039278388023376465,
0.036610040813684464,
0.09605113416910172,
0.03164542466402054,
-0.02514718472957611,
-0.042043764144182205,
0.0026867876295000315,
0.001064610667526722,
-0.00751027837395668,
-0.048294078558683395,
0.003408267628401518,
0.03701985254883766,
-0.10233350843191147,
0.01357029564678669,
0.007868928834795952,
-0.0243111252784729,
-0.06414127349853516,
0.014771298505365849,
-0.03544931858778,
0.0731932744383812,
-0.037752941250801086,
0.0168980173766613,
0.0030943823512643576,
-0.0419473797082901,
0.025862140581011772,
-0.003382917493581772,
0.053516414016485214,
0.053530797362327576,
-0.0166942048817873,
0.06890136003494263,
-0.013542726635932922,
-0.03728281706571579,
-0.02944231405854225,
-0.053790368139743805,
0.01748369075357914,
-0.00027177282026968896,
-0.00273515610024333,
-0.007416104897856712,
-0.054338403046131134,
-0.001906525227241218,
0.03660045936703682,
-0.006556703709065914,
-0.001772885792888701,
0.011023573577404022,
-0.022236205637454987,
-0.02138466387987137,
-0.005105198826640844,
-0.014585614204406738,
-0.05774213373661041,
0.03693262115120888,
-0.0752594918012619,
0.08234748989343643,
0.03808697685599327,
-0.030157778412103653,
-0.02760348841547966,
-0.01591155305504799,
0.02485032193362713,
-0.010906756855547428,
-0.04628618061542511,
0.05139084532856941,
0.03587522357702255,
0.01189182884991169,
0.01839713379740715,
-0.07581374794244766,
0.0013402930926531553,
0.0066801453940570354,
-0.06098995730280876,
0.0015331038739532232,
0.009407687932252884,
-0.0005445840070024133,
0.01597968302667141,
0.007170282769948244,
-0.045354511588811874,
0.05545565485954285,
0.02061944454908371,
0.008983314037322998,
0.00795542262494564,
-0.038797225803136826,
0.005224527325481176,
-0.013735824264585972,
0.010408579371869564,
0.031434252858161926,
0.012453964911401272,
0.06065335497260094,
0.010347730480134487,
0.002582699991762638,
-0.06613024324178696,
-0.02825949527323246,
-0.04083210602402687,
-0.04937954619526863,
0.007375478278845549,
-0.03625376895070076,
0.030423803254961967,
0.010427417233586311,
0.0036363876424729824,
0.012065203860402107,
0.0021493060048669577,
-0.00400480255484581,
-0.002067642053589225,
0.040228743106126785,
0.023670092225074768,
0.00233336235396564,
0.00774768553674221,
0.006769952829927206,
0.03236093744635582,
-0.018652955070137978,
0.01497967541217804,
-0.008532668463885784,
-0.023689812049269676,
-0.08582998812198639,
-0.03758664429187775,
0.053889624774456024,
0.0371028333902359,
-0.029829153791069984,
-0.01981682889163494,
0.01012812927365303,
0.009583555161952972,
-0.03456273674964905,
0.047535307705402374,
-0.03749014437198639,
0.03763442113995552,
0.02244633249938488,
0.03851092606782913,
0.044062502682209015,
0.006548912730067968,
-0.02637507952749729,
-0.003274516435340047,
-0.00674052769318223,
0.03019081987440586,
0.022305181249976158,
0.027750583365559578,
-0.00931548047810793
] |
<p>I read a few times that a knot can reduce the strenght of a rope, but I can't understand why this happens. Can someone explain me what happens to a rope tied with a generic knot and stretched? Is there a way to calculate the reduction of resistance from the form of the knot?</p> | g9178 | [
0.007994615472853184,
-0.01656372658908367,
-0.029481153935194016,
-0.040978964418172836,
0.02458677999675274,
0.045976996421813965,
0.023972690105438232,
0.03684148192405701,
-0.05133729428052902,
0.015586229041218758,
-0.02795635536313057,
0.006434883456677198,
-0.021599523723125458,
-0.026581192389130592,
0.07839064300060272,
0.03230845555663109,
-0.0012943154433742166,
-0.0011280751787126064,
0.011950278654694557,
-0.03873996064066887,
-0.04508233070373535,
0.005387714598327875,
0.037603095173835754,
0.01580888405442238,
-0.07669680565595627,
-0.00406925892457366,
-0.03866998851299286,
0.057265255600214005,
-0.09409593790769577,
-0.039098646491765976,
0.033380888402462006,
0.026971278712153435,
0.054826945066452026,
-0.05106836557388306,
-0.006404723972082138,
0.004632252734154463,
0.02102755568921566,
0.033290497958660126,
-0.027824627235531807,
0.006630573887377977,
-0.013238419778645039,
-0.012947379611432552,
-0.0021859912667423487,
0.004718438256531954,
-0.0077016050927340984,
-0.047778140753507614,
0.005795682780444622,
0.030153287574648857,
0.04980979487299919,
-0.04406645521521568,
-0.026652725413441658,
0.010271448642015457,
-0.042549628764390945,
-0.040694709867239,
0.08980666846036911,
-0.0313127264380455,
0.011470086872577667,
-0.011072780936956406,
-0.0078809829428792,
-0.008562484756112099,
-0.008421940729022026,
-0.0425364151597023,
-0.0026778136380016804,
0.015790816396474838,
-0.002315506571903825,
-0.028420820832252502,
0.014339281246066093,
-0.04175673797726631,
0.01043055672198534,
0.07669337093830109,
0.014473549090325832,
-0.06650708615779877,
0.01013848464936018,
-0.03756339102983475,
0.019466308876872063,
-0.005906142760068178,
0.012319901026785374,
0.002607285976409912,
-0.07293790578842163,
0.030999094247817993,
-0.010312563739717007,
0.021643292158842087,
-0.06861649453639984,
0.03901778161525726,
-0.054478757083415985,
-0.03443429619073868,
0.03772008791565895,
0.03287719190120697,
-0.04162221401929855,
0.08814867585897446,
0.014158017933368683,
-0.0731210857629776,
0.11460743099451065,
-0.042313072830438614,
0.03515290841460228,
-0.02343401312828064,
-0.011196636594831944,
0.01973835565149784,
0.004019019193947315,
0.010442402213811874,
-0.027674313634634018,
0.015517580322921276,
0.005623423960059881,
-0.01883150078356266,
-0.059672169387340546,
0.013012556359171867,
0.04650835320353508,
0.0032336008735001087,
-0.010492758825421333,
-0.03177058696746826,
0.007646491285413504,
-0.029479261487722397,
-0.04305161163210869,
-0.016446035355329514,
0.027407487854361534,
-0.03915153443813324,
0.03746641427278519,
0.0031956983730196953,
0.027396459132432938,
-0.00823588389903307,
0.038552798330783844,
-0.0679156631231308,
0.003453340847045183,
0.02643958479166031,
0.02615666389465332,
0.01821618713438511,
0.028290320187807083,
0.031815558671951294,
-0.006720414850860834,
0.028969408944249153,
0.0397951602935791,
-0.05856122821569443,
-0.013789902441203594,
0.012238160707056522,
0.008689329959452152,
0.021726645529270172,
-0.030392076820135117,
0.013706116005778313,
0.06634773313999176,
0.004689147230237722,
-0.07296449691057205,
-0.01919868215918541,
-0.025111930444836617,
-0.02973836660385132,
-0.0334278829395771,
0.0015848578186705709,
0.03833109512925148,
0.0020679167937487364,
0.00531218945980072,
-0.019340109080076218,
0.03169194608926773,
0.011692347005009651,
-0.041406601667404175,
-0.017731908708810806,
0.032705046236515045,
0.04936014488339424,
0.013225499540567398,
-0.029005367308855057,
0.029000645503401756,
0.05430608242750168,
0.007726334035396576,
-0.017089007422327995,
-0.032002612948417664,
-0.0003585836966522038,
-0.07405582815408707,
0.012139884755015373,
-0.00500995758920908,
0.0019824234768748283,
-0.06359022855758667,
-0.026688706129789352,
0.030492618680000305,
-0.02774185873568058,
-0.0034006591886281967,
0.05957801267504692,
0.015981515869498253,
0.07463423162698746,
0.06275948882102966,
0.020044535398483276,
0.004626819398254156,
0.0034417021088302135,
-0.016918515786528587,
0.01692253164947033,
0.016866613179445267,
-0.07910952717065811,
0.019175294786691666,
0.05239783227443695,
0.0036509272176772356,
-0.009759975597262383,
-0.06376197934150696,
-0.06284444779157639,
-0.013204666785895824,
-0.03850517421960831,
0.019222509115934372,
0.00016217058873735368,
-0.016288315877318382,
-0.07482445240020752,
0.015537898056209087,
0.050104476511478424,
0.0027611730620265007,
0.025217382237315178,
-0.013125169090926647,
-0.03144329786300659,
0.02181384339928627,
-0.03272584453225136,
0.03938371315598488,
-0.0010095684556290507,
-0.014074260368943214,
0.00018232983711641282,
0.042323268949985504,
-0.014412273652851582,
0.04879928007721901,
0.03627604991197586,
0.05369330570101738,
-0.015000196173787117,
-0.007576090283691883,
-0.009830820374190807,
0.03169297054409981,
0.06784439831972122,
-0.024414675310254097,
-0.027690861374139786,
0.025599386543035507,
-0.01505771093070507,
-0.0022882255725562572,
-0.019984466955065727,
-0.012606596574187279,
-0.04031584784388542,
-0.041036199778318405,
-0.017205093055963516,
0.0049947453662753105,
-0.015764858573675156,
0.00971329864114523,
-0.013139520771801472,
-0.0625607818365097,
-0.0037954174913465977,
-0.012135503813624382,
0.027669595554471016,
-0.011094938032329082,
0.0036889459006488323,
0.02411484159529209,
-0.03782714530825615,
-0.0037987655960023403,
0.004907992668449879,
0.06493029743432999,
-0.011193826794624329,
0.047103364020586014,
0.005592904519289732,
0.04005350545048714,
0.02078910917043686,
-0.003327965270727873,
0.03909110650420189,
-0.0035759005695581436,
0.033030156046152115,
0.0005014898488298059,
0.03165863826870918,
-0.007993158884346485,
0.04505066201090813,
-0.026272989809513092,
0.012838741764426231,
-0.04546559602022171,
0.01787264458835125,
-0.011262288317084312,
0.06883423775434494,
-0.013293316587805748,
0.016316689550876617,
-0.10949616134166718,
0.020723754540085793,
0.009187853895127773,
-0.004453213419765234,
0.04747705161571503,
0.0167711079120636,
0.004058778751641512,
0.02789948508143425,
-0.03933056443929672,
-0.021977299824357033,
-0.0015846494352445006,
-0.03773720562458038,
0.025098133832216263,
0.010357186198234558,
-0.06004362180829048,
0.02863314189016819,
0.06707653403282166,
-0.05167752876877785,
-0.05331899970769882,
0.05556030198931694,
0.015260585583746433,
0.01275054831057787,
-0.03313504159450531,
-0.034962307661771774,
-0.04111828655004501,
-0.012649294920265675,
-0.003277108073234558,
0.015563968569040298,
0.027370911091566086,
0.008192963898181915,
0.025465575978159904,
0.02859339863061905,
-0.042408064007759094,
0.025349581614136696,
-0.013390674255788326,
0.015493426471948624,
-0.07633770257234573,
0.011885887943208218,
-0.023594748228788376,
0.023418275639414787,
0.01464658509939909,
0.07295677065849304,
0.0032114970963448286,
0.003996651154011488,
0.009220609441399574,
0.08312462270259857,
-0.08018742501735687,
0.023486997932195663,
0.016347570344805717,
-0.02968677505850792,
0.0035754914861172438,
-0.0029486592393368483,
0.054587315768003464,
0.0220918208360672,
0.019005365669727325,
0.000544356182217598,
0.03665608912706375,
-0.09872113913297653,
-0.03977120667695999,
0.01772512122988701,
-0.03137851133942604,
0.034891895949840546,
-0.062044668942689896,
0.015681514516472816,
-0.010562645271420479,
-0.028244495391845703,
0.00777048896998167,
-0.01664685644209385,
-0.03233519196510315,
-0.04353025555610657,
-0.0463038869202137,
-0.008110194467008114,
-0.04824945330619812,
0.022268999367952347,
-0.010717504657804966,
-0.019189292564988136,
-0.003968583419919014,
-0.03229914605617523,
-0.058399002999067307,
0.03416416794061661,
0.014322001487016678,
0.011141350492835045,
-0.003656375454738736,
-0.02409111149609089,
0.020201876759529114,
-0.051305897533893585,
0.07471820712089539,
0.009436948224902153,
0.04100840538740158,
-0.018445782363414764,
-0.0391911044716835,
0.06454604864120483,
-0.02017446607351303,
0.010628375224769115,
-0.0563981756567955,
-0.010474547743797302,
0.07251254469156265,
-0.03545821085572243,
0.030555550009012222,
0.03262968361377716,
-0.029498009011149406,
0.02752227708697319,
0.09471829980611801,
-0.02692526951432228,
-0.033449579030275345,
0.04612501338124275,
-0.03493370860815048,
-0.0076696728356182575,
-0.04494370147585869,
-0.03307964652776718,
-0.02390499785542488,
0.025534583255648613,
-0.025635601952672005,
0.0624697171151638,
0.013328637927770615,
0.04037858545780182,
0.043113697320222855,
-0.003282264806330204,
-0.04866521432995796,
-0.024409325793385506,
0.0053002187050879,
-0.04906473308801651,
-0.03859998285770416,
0.029143624007701874,
-0.015883557498455048,
0.014201575890183449,
-0.034236036241054535,
-0.0176809411495924,
-0.00529830576851964,
0.01354355551302433,
0.04015312343835831,
-0.012295244261622429,
-0.011170103214681149,
0.02732720412313938,
-0.02741357870399952,
0.024982206523418427,
0.0021422458812594414,
0.02971879579126835,
-0.044559236615896225,
0.0679645836353302,
0.049369145184755325,
-0.09472687542438507,
0.02236124873161316,
0.05280423164367676,
0.02679099515080452,
0.06291438639163971,
0.00929864589124918,
0.03708279877901077,
-0.00290019903331995,
-0.08058517426252365,
-0.02932778187096119,
-0.014823058620095253,
0.025233661755919456,
-0.0075780474580824375,
-0.07235034555196762,
-0.05107139050960541,
0.020866360515356064,
0.040536437183618546,
-0.0034626792185008526,
0.03944046422839165,
-0.0469311848282814,
0.012949840165674686,
-0.015105039812624454,
0.017778679728507996,
0.02552679367363453,
-0.006302813999354839,
0.025377996265888214,
0.03136606514453888,
-0.009988994337618351,
-0.014777532778680325,
-0.03588523715734482,
0.006977725774049759,
0.012263856828212738,
0.06400631368160248,
-0.009142246097326279,
0.01059881690889597,
0.016225354745984077,
0.04801120609045029,
0.0035585775040090084,
-0.01890053227543831,
-0.03908875957131386,
-0.03611273691058159,
-0.05996076390147209,
-0.005426749587059021,
-0.03646339103579521,
-0.014328207820653915,
-0.05813819542527199,
-0.02028309926390648,
0.03882407769560814,
-0.05385376513004303,
0.017962807789444923,
-0.06543780863285065,
0.018462570384144783,
-0.013464190997183323,
-0.00575299933552742,
0.021879469975829124,
-0.03099568374454975,
0.016881074756383896,
-0.06347446888685226,
-0.004948942922055721,
-0.020128173753619194,
0.018840910866856575,
0.025792241096496582,
0.011420803144574165,
-0.0037254313938319683,
0.05001001060009003,
0.03232955187559128,
-0.029219496995210648,
0.009011312387883663,
-0.009425142779946327,
0.022542839869856834,
-0.001763403881341219,
0.009208893403410912,
-0.004676962271332741,
0.03310035169124603,
-0.027549201622605324,
-0.0023887515999376774,
0.014179562218487263,
-0.06977005302906036,
-0.07370222359895706,
0.04336496442556381,
0.036298442631959915,
0.036527346819639206,
0.03685059770941734,
0.027062436565756798,
-0.00607969518750906,
0.017754679545760155,
0.005681335926055908,
-0.0001465598907088861,
0.02135205827653408,
-0.02566809393465519,
-0.01268057432025671,
0.01875377632677555,
0.0018673102604225278,
0.023107822984457016,
-0.026649078354239464,
-0.03290960565209389,
0.01696435734629631,
0.03555012494325638,
0.014810837805271149,
-0.048228222876787186,
0.042665693908929825,
-0.004343705251812935,
-0.00030497292755171657,
0.0016327424673363566,
0.05493026226758957,
0.014081286266446114,
-0.0008632864919491112,
-0.04189931973814964,
-0.015599585138261318,
0.05917227640748024,
-0.0010727507760748267,
-0.070370152592659,
-0.04629363492131233,
0.046355221420526505,
-0.0045735156163573265,
-0.005115191452205181,
-0.015782883390784264,
0.023042915388941765,
-0.03565061092376709,
0.028612548485398293,
0.043601181358098984,
-0.08657713234424591,
0.0472525916993618,
0.018045462667942047,
-0.00578735675662756,
-0.05787540227174759,
0.0032131210900843143,
0.037019915878772736,
0.018534785136580467,
0.020966455340385437,
0.028092309832572937,
-0.009152494370937347,
-0.004475954454392195,
0.004453160800039768,
-0.0022712782956659794,
0.004572704434394836,
-0.027347169816493988,
0.015775954350829124,
0.024878505617380142,
-0.04106656461954117,
-0.07806820422410965,
-0.04648122936487198,
-0.019858840852975845,
0.003938320092856884,
-0.016133150085806847,
-0.013211342506110668,
-0.04170243442058563,
-0.011232893913984299,
-0.0024952858220785856,
-0.04692484810948372,
0.024769863113760948,
0.04430430755019188,
-0.034977301955223083,
0.04238859564065933,
0.03980609029531479,
0.028325477614998817,
-0.005721852649003267,
-0.019083062186837196,
-0.004052548669278622,
0.05182842165231705,
-0.10100603103637695,
-0.008358180522918701,
0.02660614810883999,
0.07620910555124283,
0.05951238051056862,
0.005140268709510565,
-0.0375753790140152,
0.028397003188729286,
0.0049698795191943645,
0.0020201338920742273,
0.015595423988997936,
-0.06661788374185562,
-0.05162940174341202,
-0.010707921348512173,
-0.041330527514219284,
-0.006145786959677935,
0.0018688762793317437,
-0.04466962441802025,
-0.06010986864566803,
-0.01843896135687828,
-0.01869998127222061,
-0.027679603546857834,
-0.0627889484167099,
0.004133268259465694,
0.03420215845108032,
0.0039910911582410336,
0.0763210877776146,
-0.015935270115733147,
0.012425062246620655,
0.043111372739076614,
0.014424129389226437,
0.030839409679174423,
0.012461043894290924,
0.03164559230208397,
0.03948098421096802,
0.031729698181152344,
-0.05891464650630951,
0.11861854791641235,
-0.027349596843123436,
-0.006993251387029886,
0.0390666127204895,
0.06567168980836868,
-0.06312891840934753,
0.04559043049812317,
0.004444887395948172,
0.05602739006280899,
0.06503533571958542,
0.01664760522544384,
-0.003586751641705632,
0.0474315769970417,
-0.03338436409831047,
0.039493776857852936,
-0.0370352640748024,
0.029881538823246956,
-0.04420527070760727,
-0.031729813665151596,
-0.06893214583396912,
0.06397080421447754,
0.046874016523361206,
0.013258200138807297,
0.002260670531541109,
0.010791421867907047,
0.002045677276328206,
-0.009135788306593895,
-0.056686338037252426,
-0.04097035154700279,
0.02943907119333744,
-0.0529327429831028,
0.026930252090096474,
0.020323196426033974,
0.02717631682753563,
-0.021111957728862762,
0.009051783010363579,
0.032954391092061996,
0.08983398228883743,
0.035109274089336395,
-0.027796346694231033,
-0.006900701206177473,
-0.006014843005686998,
-0.03516421467065811,
-0.015684116631746292,
0.03799253702163696,
-0.054132867604494095,
-0.06965241581201553,
0.025886794552206993,
0.0382661372423172,
0.019696291536092758,
-0.0647798478603363,
0.05246013402938843,
0.011544768698513508,
-0.005667674820870161,
-0.06033770367503166,
-0.002713195513933897,
0.018938839435577393,
-0.017006956040859222,
-0.037107836455106735,
-0.012761530466377735,
-0.010312781669199467,
-0.0256899893283844,
0.038095809519290924,
0.05301337689161301,
0.09714201837778091,
-0.06560374796390533,
0.00900699570775032,
0.06652320921421051,
-0.02731812745332718,
-0.016969656571745872,
0.037043895572423935,
-0.020484767854213715,
0.006311514880508184,
-0.004629526287317276,
-0.040581151843070984,
0.002030739327892661,
-0.015454726293683052,
-0.014830735512077808,
-0.03258153796195984,
0.05475500226020813,
0.026733534410595894,
-0.050359029322862625,
-0.03498068079352379,
0.030757416039705276,
-0.0407835878431797,
0.008534309454262257,
-0.01435112114995718,
0.0044051711447536945,
0.046705856919288635,
0.025107048451900482,
-0.012132092379033566,
0.04999585077166557,
0.0408167690038681,
-0.0038336697034537792,
-0.042232681065797806,
-0.005921851843595505,
0.00011687359074130654,
-0.004407578147947788,
0.007091812789440155,
-0.03714599832892418,
0.007586942985653877,
-0.017730647698044777,
-0.014527762308716774,
0.012391339987516403,
-0.02457716315984726,
-0.05535702779889107,
-0.04895976558327675,
-0.061793986707925797,
0.012894567102193832,
0.045519065111875534,
-0.00904069747775793,
-0.019261660054326057,
-0.016050061210989952,
-0.0035906312987208366,
0.03395836427807808,
-0.05555816367268562,
0.01217446755617857,
-0.05972510948777199,
0.017590118572115898,
0.052557505667209625,
0.050182946026325226,
0.014154626056551933,
-0.051978711038827896,
-0.000889943796209991,
0.050447314977645874,
-0.03979899361729622,
-0.03467780351638794,
0.017312604933977127,
0.04132239148020744,
-0.03901561722159386,
0.05996200069785118,
-0.03309876099228859,
0.019428733736276627,
0.02840690314769745,
0.024522552266716957,
0.009165266528725624,
-0.00925382599234581,
0.07130182534456253,
0.0023602619767189026,
0.04165748134255409,
-0.06147950515151024,
0.026244597509503365,
0.014354377053678036,
-0.01862301491200924,
-0.03927377238869667,
0.026496538892388344,
0.02785194292664528,
-0.0030262931250035763,
0.032983969897031784,
-0.014424172230064869,
0.009878438897430897,
0.04620731994509697,
0.03512735292315483,
-0.01809345744550228,
-0.0798172876238823,
0.01393256988376379,
-0.04677422717213631,
-0.015604413114488125,
0.001545573235489428,
0.09375185519456863,
-0.048881568014621735,
-0.0015868537593632936,
-0.014121280051767826,
-0.025167355313897133,
-0.019876250997185707,
-0.0030168883968144655
] |
<p>First of all, does the expansion of spacetime solely cause the expansion of universe?</p>
<p>Secondly, if spacetime is the sole cause, do objects(matter with mass) themselves expand?</p>
<p>Thirdly, by spacetime expansion, does time also expand? (at least in general relativity)</p>
<p>Thanks.</p> | g56 | [
0.008330980315804482,
0.04067201167345047,
0.02485617808997631,
0.008920506574213505,
-0.010181421414017677,
0.08209781348705292,
-0.006099274381995201,
0.03300701826810837,
0.02364843524992466,
0.0026166385505348444,
0.029248258098959923,
-0.06733379513025284,
0.008353090845048428,
0.02894723415374756,
-0.06026868149638176,
-0.007243279833346605,
0.005859773606061935,
-0.02802334725856781,
0.017062505707144737,
0.058131780475378036,
-0.018550237640738487,
-0.02569088526070118,
0.030474593862891197,
-0.035052962601184845,
-0.020377343520522118,
0.015638859942555428,
0.042874354869127274,
-0.003793684532865882,
-0.018113382160663605,
-0.021290842443704605,
0.03859570249915123,
0.055580414831638336,
0.025397269055247307,
-0.014883168041706085,
0.03125857189297676,
-0.05682862922549248,
-0.02111113630235195,
-0.021813934668898582,
0.025347910821437836,
0.005878366995602846,
-0.051148347556591034,
-0.00016948349366430193,
0.013993876054883003,
0.0018744395347312093,
0.003172064432874322,
-0.01552337221801281,
-0.07863856852054596,
0.021772384643554688,
0.037936076521873474,
-0.015915751457214355,
-0.019971828907728195,
0.006075551267713308,
0.014570428058505058,
0.034271810203790665,
0.0020613649394363165,
0.058727141469717026,
0.00875190831720829,
-0.019329173490405083,
0.12948693335056305,
0.04453730210661888,
-0.05809688940644264,
0.015397852286696434,
0.06972303241491318,
0.013440155424177647,
-0.0019657823722809553,
0.02949495241045952,
-0.034150369465351105,
-0.044739387929439545,
0.05597729980945587,
-0.000531817611772567,
0.0702207013964653,
-0.0756530836224556,
-0.021038172766566277,
-0.06334906071424484,
-0.012855914421379566,
0.05315133556723595,
0.033263105899095535,
0.02221871353685856,
-0.0013553574681282043,
-0.01005044300109148,
-0.02746841497719288,
-0.028573740273714066,
-0.01200928632169962,
0.010344944894313812,
0.02315210923552513,
-0.05931203067302704,
-0.05532822012901306,
-0.0066878944635391235,
-0.02154373936355114,
0.005007640458643436,
0.009460820816457272,
0.013177936896681786,
0.026468632742762566,
0.029532337561249733,
0.003217792371287942,
-0.0120769077911973,
0.024303363636136055,
0.053936343640089035,
0.011828724294900894,
0.03849433362483978,
-0.05492192506790161,
0.01107493881136179,
0.040471237152814865,
-0.028589868918061256,
0.019466489553451538,
-0.003978087566792965,
0.008232521824538708,
-0.023833490908145905,
-0.0036147157661616802,
-0.028337763622403145,
-0.04528602957725525,
-0.037121426314115524,
0.002220320049673319,
0.005710448604077101,
-0.048014506697654724,
-0.036509834229946136,
0.017796814441680908,
0.01456926204264164,
0.005839832127094269,
0.025962838903069496,
-0.025498423725366592,
0.05548188462853432,
-0.012088866904377937,
0.031536754220724106,
-0.06886310875415802,
-0.029099194332957268,
0.000232918857363984,
-0.001953955739736557,
-0.036593466997146606,
0.0034448779188096523,
0.004430911038070917,
-0.008815149776637554,
0.003568910760805011,
0.014224988408386707,
-0.006340871565043926,
0.01625201664865017,
-0.007607550360262394,
-0.00022260387777350843,
-0.04687656834721565,
0.04205171763896942,
-0.010664132423698902,
-0.01138840802013874,
0.01523643173277378,
-0.009675677865743637,
0.006976772099733353,
-0.008298247121274471,
0.05299137905240059,
-0.002686913590878248,
-0.03249422088265419,
0.03083336539566517,
-0.02576899342238903,
0.0734984278678894,
-0.04067988321185112,
-0.04271658509969711,
0.05370718985795975,
0.055053722113370895,
-0.03792814910411835,
-0.038503967225551605,
0.031456977128982544,
-0.011297186836600304,
0.02522256411612034,
-0.01908215507864952,
0.004974482115358114,
0.020738879218697548,
0.006398369092494249,
0.05241264030337334,
-0.019200921058654785,
-0.042254697531461716,
-0.015905212610960007,
0.016817964613437653,
-0.002651490503922105,
-0.017747700214385986,
-0.04252762719988823,
0.04558810964226723,
-0.02601570449769497,
0.01713244430720806,
0.010881798341870308,
0.03098365105688572,
0.0052948142401874065,
0.01324678584933281,
-0.026098452508449554,
-0.07253724336624146,
-0.04411971941590309,
-0.048011962324380875,
-0.005894335452467203,
-0.0690707415342331,
0.012960106134414673,
0.018076270818710327,
-0.06640687584877014,
0.04489048942923546,
-0.022628838196396828,
-0.018794337287545204,
0.061547718942165375,
0.047273848205804825,
-0.0099400719627738,
-0.023705730214715004,
-0.019459214061498642,
0.03180446848273277,
-0.009865225292742252,
-0.022167352959513664,
-0.07629465311765671,
0.002724485006183386,
0.010262644849717617,
0.004019976127892733,
0.05034654214978218,
0.015118780545890331,
-0.021655147895216942,
-0.006065527908504009,
0.03616046532988548,
0.008003370836377144,
0.09236174076795578,
-0.007992308586835861,
0.023796139284968376,
-0.02875751256942749,
-0.028923729434609413,
-0.002065466484054923,
-0.061649616807699203,
0.005652446765452623,
0.01934874802827835,
-0.009019553661346436,
-0.009225144982337952,
0.05938749015331268,
-0.01842653751373291,
-0.05638944357633591,
-0.03255387395620346,
0.008222025819122791,
0.010946775786578655,
-0.03651861846446991,
0.030948445200920105,
-0.0020331856794655323,
-0.062369149178266525,
0.03555050864815712,
0.0366532988846302,
-0.009779388085007668,
0.05469168350100517,
-0.024558618664741516,
-0.01359772402793169,
0.014457020908594131,
0.005086333025246859,
-0.025671903043985367,
0.013920648023486137,
0.018465286120772362,
0.025883790105581284,
-0.04414644464850426,
0.054689615964889526,
-0.10168659687042236,
0.06931024044752121,
-0.07386226207017899,
-0.012504398822784424,
-0.0017936882795765996,
-0.04024236649274826,
-0.015927189961075783,
-0.04007960110902786,
0.0162432249635458,
-0.020347576588392258,
-0.030516164377331734,
0.01911027729511261,
0.08320490270853043,
-0.09469491988420486,
-0.03323885053396225,
0.0008608342031948268,
-0.004621793981641531,
-0.010161273181438446,
0.0392482690513134,
-0.0461525060236454,
-0.01286371424794197,
-0.02325158379971981,
-0.022749915719032288,
-0.010346822440624237,
-0.016439106315374374,
-0.045078445225954056,
0.01595265418291092,
-0.01713726297020912,
0.023935753852128983,
-0.027868017554283142,
0.04870786890387535,
0.05295610800385475,
0.01133202575147152,
0.012754020281136036,
-0.0761571079492569,
0.02830132655799389,
0.03911019116640091,
-0.09333202242851257,
-0.010330436751246452,
0.052778568118810654,
-0.021424956619739532,
-0.03434569388628006,
-0.04108181595802307,
0.013004975393414497,
-0.004679990001022816,
0.06256110966205597,
0.09437146782875061,
0.03906312584877014,
0.051089201122522354,
0.020679332315921783,
0.025356179103255272,
-0.009710428304970264,
0.001030188170261681,
0.0023769650142639875,
0.052220601588487625,
0.007988852448761463,
-0.04422464966773987,
0.022681379690766335,
-0.045481178909540176,
0.016634628176689148,
0.043664999306201935,
-0.011587277054786682,
-0.0014547526370733976,
0.02029355987906456,
-0.04365072399377823,
-0.017925262451171875,
0.0219020564109087,
0.004261771682649851,
0.067699134349823,
-0.03202182427048683,
0.013612399809062481,
0.007824517786502838,
-0.047889336943626404,
-0.02239920012652874,
-0.010890215635299683,
-0.009006291627883911,
-0.0017484471900388598,
-0.04121330380439758,
-0.025057705119252205,
0.03832778334617615,
-0.004178361035883427,
0.023760532960295677,
-0.03469978645443916,
-0.03048696182668209,
-0.001436716760508716,
-0.05094853416085243,
-0.06944955885410309,
0.04685761407017708,
0.014854857698082924,
-0.045979276299476624,
0.029075106605887413,
0.022058909758925438,
-0.04747282341122627,
-0.009397163987159729,
0.031050315126776695,
0.04291575402021408,
-0.01717519387602806,
-0.016853008419275284,
0.041251640766859055,
0.005422528833150864,
0.058636318892240524,
0.008055312559008598,
-0.04896562173962593,
0.05395324155688286,
0.004325877409428358,
0.02117936499416828,
-0.003983249422162771,
-0.004931972362101078,
0.05522961914539337,
0.0012821014970541,
0.023378193378448486,
0.005427742376923561,
0.05708440765738487,
-0.011070243082940578,
-0.062032684683799744,
-0.0185325276106596,
-0.03702573478221893,
0.01768512651324272,
0.05825863778591156,
0.001543742255307734,
0.04381459206342697,
0.0618574395775795,
-0.05970707908272743,
0.015947682783007622,
-0.004115432500839233,
0.07322145253419876,
0.02319873683154583,
-0.043497055768966675,
0.03324607387185097,
0.09104844927787781,
-0.017618298530578613,
-0.0031294976361095905,
0.03232792019844055,
-0.006520774681121111,
0.00954448152333498,
0.07096032053232193,
-0.006659702863544226,
0.023042580112814903,
0.05081021785736084,
-0.02746996283531189,
-0.0037226483691483736,
-0.09832201153039932,
-0.024532802402973175,
0.0011421773815527558,
-0.04601108282804489,
0.035384662449359894,
-0.039551544934511185,
-0.027497759088873863,
-0.07174310088157654,
0.007318426389247179,
-0.04583394154906273,
0.03289634361863136,
-0.012930796481668949,
0.08226003497838974,
0.02374289184808731,
0.008267284370958805,
0.10021732747554779,
0.036003973335027695,
0.0036197395529597998,
0.006590253673493862,
0.05881170183420181,
0.04099006950855255,
-0.06272637099027634,
0.0019430770771577954,
-0.0022200539242476225,
-0.02113027684390545,
0.055617135018110275,
-0.05035943165421486,
-0.01399467047303915,
0.0395437628030777,
-0.00423650024458766,
0.028735125437378883,
-0.06121302396059036,
0.001324380747973919,
0.008905635215342045,
0.001422406523488462,
-0.008520092815160751,
-0.02563752420246601,
0.015075651928782463,
-0.049915481358766556,
0.04864813759922981,
-0.017345670610666275,
-0.08579464256763458,
-0.01852959208190441,
0.04922559857368469,
-0.03436246141791344,
-0.01371187623590231,
0.02860168181359768,
0.06439261138439178,
-0.028079481795430183,
0.00013324794417712837,
-0.009083700366318226,
0.11814652383327484,
-0.02413804456591606,
-0.03897499665617943,
0.08367059379816055,
0.0458722785115242,
-0.012915108352899551,
0.02970689721405506,
0.03910519555211067,
0.01976134441792965,
-0.026591334491968155,
-0.04591325670480728,
-0.016065407544374466,
0.020831076428294182,
-0.05967904254794121,
0.0686274990439415,
0.0550743006169796,
-0.02614278346300125,
0.0023186076432466507,
0.040016524493694305,
0.021740466356277466,
0.009177661500871181,
0.036833178251981735,
0.017092160880565643,
-0.09093590825796127,
0.03198416158556938,
0.038289815187454224,
0.07060657441616058,
0.013979172334074974,
-0.05158621817827225,
-0.030024681240320206,
-0.001874154550023377,
-0.025629492476582527,
0.02936265990138054,
-0.03499428555369377,
0.0017154874512925744,
-0.02640177309513092,
-0.022482361644506454,
0.011074602603912354,
-0.010178369469940662,
-0.02959972620010376,
-0.033521197736263275,
-0.010213424451649189,
-0.0258711539208889,
0.021440740674734116,
-0.04601895064115524,
0.01299966312944889,
-0.020015159621834755,
0.0011849693255499005,
0.03779812529683113,
0.027115611359477043,
0.0564572736620903,
0.0909276232123375,
-0.05775481462478638,
0.014487114734947681,
0.0035851099528372288,
0.014581182040274143,
0.023582423105835915,
-0.03600367158651352,
0.04894036054611206,
-0.025924572721123695,
0.00958215817809105,
0.013716921210289001,
-0.004751742351800203,
0.041887007653713226,
0.003816037904471159,
0.030018625780940056,
0.042147379368543625,
-0.05449267476797104,
-0.010693976655602455,
-0.040845632553100586,
-0.02582361176609993,
-0.04798680171370506,
0.06488439440727234,
0.008566521108150482,
0.046543218195438385,
-0.0331440307199955,
0.008678511716425419,
0.000888484762981534,
-0.02767617255449295,
0.004008763004094362,
-0.017102815210819244,
0.0183451808989048,
-0.036226920783519745,
-0.04323584586381912,
0.011807739734649658,
0.0364915207028389,
0.008337332867085934,
0.04147174581885338,
0.037766724824905396,
0.00324136670678854,
-0.025305870920419693,
0.06165163218975067,
-0.019484909251332283,
0.01998809166252613,
0.008763181045651436,
0.03780164569616318,
-0.02476365864276886,
-0.02520710602402687,
-0.018386345356702805,
-0.02764393575489521,
0.021172035485506058,
0.04479144886136055,
0.0009647165425121784,
-0.044861264526844025,
-0.017997371032834053,
-0.02147367037832737,
0.0340215265750885,
-0.003616721834987402,
0.006569331046193838,
-0.0028352183289825916,
0.007995948195457458,
0.07383998483419418,
-0.022783435881137848,
-0.07021874189376831,
0.037450071424245834,
-0.007862396538257599,
-0.013101879507303238,
-0.05945608392357826,
0.053552620112895966,
-0.0029802019707858562,
-0.008621600456535816,
-0.02583550103008747,
-0.05601747706532478,
0.02464505098760128,
0.01773551106452942,
0.023712212219834328,
-0.07248063385486603,
-0.04766339808702469,
-0.02469167485833168,
0.04023752361536026,
-0.06195661798119545,
0.06137706711888313,
0.018426384776830673,
-0.013526679016649723,
0.0427391342818737,
-0.008411884307861328,
-0.08228487521409988,
0.012250304222106934,
0.04353112727403641,
0.0027033695951104164,
-0.062023114413022995,
-0.018785716965794563,
0.025943176820874214,
-0.005209240131080151,
-0.019201744347810745,
0.020077290013432503,
-0.03291545808315277,
-0.02730807103216648,
-0.009988668374717236,
-0.03815881162881851,
-0.002777275163680315,
0.02526342123746872,
-0.017833352088928223,
0.01763828843832016,
0.026464007794857025,
0.03634012117981911,
-0.08504198491573334,
-0.017879247665405273,
-0.002644374268129468,
-0.004420135635882616,
0.02853800356388092,
-0.004020841792225838,
0.012518561445176601,
0.012914176099002361,
0.05289437249302864,
0.0626009926199913,
0.021597109735012054,
0.0347176268696785,
-0.04539784416556358,
-0.07268267124891281,
0.002899120096117258,
0.03442471846938133,
-0.028490141034126282,
-0.011670585721731186,
-0.053726039826869965,
0.03683723136782646,
0.037785254418849945,
0.011743034236133099,
-0.06459781527519226,
0.012969844974577427,
-0.013718826696276665,
0.03411400690674782,
-0.03272630646824837,
0.04274822771549225,
-0.03584567829966545,
0.02698802761733532,
0.004207527730613947,
-0.03755611926317215,
-0.004076065961271524,
0.007290544919669628,
-0.0012865071184933186,
0.0242112185806036,
-0.013685589656233788,
-0.0028693308122456074,
0.03295327350497246,
-0.06980869174003601,
-0.011410553939640522,
-0.0030231038108468056,
0.045953359454870224,
0.04155094549059868,
-0.02826331928372383,
0.022451020777225494,
-0.010896638967096806,
0.03795900195837021,
-0.01144769974052906,
0.009278637357056141,
0.016143588349223137,
-0.08218076080083847,
-0.0004711360379587859,
0.017060711979866028,
0.021448861807584763,
-0.026225034147500992,
0.007536536548286676,
-0.0006865531322546303,
-0.007205716799944639,
-0.07098006457090378,
0.04253045469522476,
-0.01852971874177456,
-0.024360470473766327,
-0.06676404923200607,
-0.037354975938797,
0.016278712078928947,
-0.05091536417603493,
-0.06253398209810257,
-0.0022919331677258015,
-0.026427598670125008,
-0.002497678389772773,
-0.024226754903793335,
0.0500812828540802,
0.06685005128383636,
0.025605972856283188,
0.006872409023344517,
-0.02746661752462387,
-0.018667232245206833,
0.02104436233639717,
0.0211818628013134,
0.028579743579030037,
-0.012820268049836159,
-0.0601748563349247,
-0.09311839938163757,
-0.012156879529356956,
0.06266926974058151,
0.004874857142567635,
-0.03354666382074356,
0.014757419005036354,
-0.007780907209962606,
0.04824257269501686,
-0.006881037261337042,
0.0128641901537776,
0.02761922962963581,
-0.010616566985845566,
-0.029956070706248283,
-0.008174180053174496,
-0.036233991384506226,
0.004320398438721895,
-0.013202807866036892,
0.006671035196632147,
0.029633039608597755,
-0.025677207857370377,
0.050572752952575684,
0.030490173026919365,
-0.004294825717806816,
0.005253188777714968,
-0.08535443246364594,
-0.053113505244255066,
-0.02591490000486374,
-0.013782945461571217,
0.04173995181918144,
-0.024707552045583725,
-0.0018212847644463181,
0.03355743736028671,
-0.008977376855909824,
-0.00615293625742197,
0.0041772290132939816,
-0.01545353326946497,
-0.004821964539587498,
-0.041670218110084534,
0.004808759316802025,
-0.024700326845049858,
0.0072011686861515045,
-0.0016954781021922827,
-0.005746977403759956,
-0.03756909444928169,
0.002338106045499444,
-0.027487795799970627,
-0.04106978327035904,
-0.07105481624603271,
-0.04572940617799759,
0.01866838149726391,
0.016808373853564262,
-0.02822079136967659,
0.002357730409130454,
0.022081544622778893,
0.03883880749344826,
-0.06426873058080673,
-0.013611174188554287,
0.05574889853596687,
-0.003613566281273961,
0.061906613409519196,
0.03690897673368454,
-0.04334929212927818,
-0.038971029222011566,
0.024107178673148155,
-0.022660383954644203,
-0.027212513610720634,
-0.028425509110093117,
0.013292187824845314,
-0.03518182784318924,
-0.04275966063141823,
-0.024598028510808945,
0.06044093519449234,
0.030329180881381035,
0.03587392345070839,
-0.02689509280025959,
0.0500083789229393,
0.027421575039625168,
-0.010122446343302727,
0.0323367603123188,
-0.020113423466682434,
-0.054764311760663986,
-0.02527567185461521,
-0.032642804086208344,
0.01600085012614727,
0.04304834082722664,
0.033212725073099136,
0.009952127002179623,
-0.03591993823647499,
-0.015935491770505905,
0.013820655643939972,
-0.005102754104882479,
0.018792103976011276
] |
<p>A hydrogen atom is characterized by the wavefunction</p>
<p>$$\mid \psi \rangle =\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$</p>
<p>I want to know the possible outcomes and the probability for obtaining each outcome from measuring $E$, $L^2$, and $L_z$, while also calculating the expectation value of the energy expressed as some number times $E_1$ (for $E$), $\hbar^2$ (for $L^2$), and $\hbar$ (for $L_z$). I know the possible outcomes are the eigenvalues for the observable, but we didn't really go over any examples, and there are few examples of this sort in the textbook, so I don't know where to begin. For example, I know when we act $L^2$ on the system, we will get</p>
<p>$$ L^2\mid \psi\rangle=6\hbar^2\sqrt{\frac{2}{7}}\mid 4\,2\,1\rangle +2\hbar^2\sqrt{\frac{1}{7}}\mid 2 \,1\,\bar{1}\rangle+6\hbar^2\sqrt{\frac{4}{7}}\mid 3\,2\,0\rangle$$</p>
<p>However, what does this tell me about the possible outcomes? Would the probabilities for each outcome be the coefficient multiplying each successive term squared divided by the Pythagorean sum of the all three terms? How do I find the expectation value? Any help would be appreciated. </p> | g9179 | [
-0.06305408477783203,
0.020620042458176613,
-0.012262290343642235,
-0.03809940442442894,
0.02746519260108471,
-0.043891359120607376,
-0.005812821909785271,
0.030203936621546745,
-0.022201355546712875,
-0.021561266854405403,
-0.019688477739691734,
0.0014646545751020312,
0.006332622841000557,
0.020784670487046242,
0.031146693974733353,
-0.0285810474306345,
0.07129272073507309,
0.033495500683784485,
-0.06829357892274857,
-0.019756760448217392,
-0.01424817368388176,
0.020229941233992577,
-0.03272270783782005,
-0.043937407433986664,
0.01204004418104887,
-0.010058770887553692,
0.01441122405230999,
0.010966282337903976,
-0.07716342061758041,
-0.009073781780898571,
-0.013173566199839115,
0.005583994090557098,
0.06742572784423828,
-0.05661401152610779,
-0.03750906139612198,
0.04404647275805473,
0.108193539083004,
0.009427175857126713,
0.007062447257339954,
-0.052628595381975174,
-0.0092641431838274,
-0.02707006223499775,
0.013676263391971588,
-0.0378023199737072,
0.05180247128009796,
-0.0168590284883976,
0.0170846376568079,
0.014271283522248268,
0.009377404116094112,
0.0460410937666893,
0.04234271124005318,
0.03663529083132744,
0.08198485523462296,
0.0003658610221464187,
-0.001643445692025125,
0.053884509950876236,
-0.008339492604136467,
-0.043026410043239594,
0.05001791566610336,
0.052535127848386765,
0.02234833501279354,
-0.04260915517807007,
-0.01121695525944233,
-0.014752248302102089,
0.06402438879013062,
0.012796706520020962,
-0.021652190014719963,
0.016850892454385757,
-0.014178101904690266,
0.008088914677500725,
0.006382449995726347,
-0.0651722103357315,
0.002160056494176388,
-0.028653856366872787,
-0.020206835120916367,
0.004741515964269638,
0.01514443475753069,
0.01833682879805565,
0.008860727772116661,
0.053857170045375824,
-0.03391970321536064,
-0.06218045577406883,
0.0021301370579749346,
0.007579702418297529,
-0.03606671094894409,
0.01553935743868351,
-0.01398816704750061,
-0.029933517798781395,
-0.03993137180805206,
-0.010948466137051582,
0.0003142848436255008,
0.043191175907850266,
0.03413788974285126,
-0.012820107862353325,
-0.02425481751561165,
0.014539435505867004,
-0.06252381205558777,
0.023648619651794434,
-0.023324795067310333,
-0.0056045823730528355,
-0.028575967997312546,
0.007677519228309393,
0.05030259117484093,
-0.028141353279352188,
0.017598571255803108,
-0.021510343998670578,
0.0013176852371543646,
0.0008231042302213609,
0.009728184901177883,
-0.03709687292575836,
-0.02913740649819374,
0.03753958269953728,
-0.0024028923362493515,
-0.020758619531989098,
-0.028581978753209114,
-0.001504943473264575,
0.018595747649669647,
0.015133082866668701,
-0.03336647152900696,
0.066808320581913,
0.05825505778193474,
0.09020741283893585,
0.03651199862360954,
0.04895138740539551,
-0.031475186347961426,
-0.0006022746092639863,
-0.05896548181772232,
0.02639443799853325,
0.009397007524967194,
0.014487285166978836,
0.027499934658408165,
-0.015859710052609444,
-0.022915363311767578,
0.02272298000752926,
-0.034780386835336685,
0.026333754882216454,
0.019912468269467354,
0.044526513665914536,
-0.003553195623680949,
-0.028071343898773193,
0.06425121426582336,
-0.05090927705168724,
0.01533295027911663,
0.0011405053082853556,
-0.0074508413672447205,
-0.030479278415441513,
-0.01461082138121128,
-0.010285472497344017,
-0.028569161891937256,
-0.01472184993326664,
-0.04751397669315338,
0.058640819042921066,
-0.022927243262529373,
0.03357628360390663,
0.027511004358530045,
-0.014274809509515762,
-0.0074192616157233715,
-0.0009047014755196869,
-0.036193106323480606,
0.02639772556722164,
0.007702491246163845,
0.010738810524344444,
0.013647289015352726,
0.042662814259529114,
-0.04070129990577698,
0.0036882522981613874,
0.05454131215810776,
-0.054287973791360855,
0.03360232710838318,
-0.01868666335940361,
0.03220251202583313,
-0.029921188950538635,
-0.007510409224778414,
0.028589431196451187,
-0.019548797979950905,
0.07763181626796722,
0.02229217439889908,
-0.011415240354835987,
-0.03149142861366272,
0.036458827555179596,
0.009063820354640484,
-0.0023052587639540434,
0.06719085574150085,
-0.011696872301399708,
-0.017314812168478966,
-0.041670285165309906,
-0.016550377011299133,
0.027931254357099533,
-0.000661735306493938,
0.04936898127198219,
-0.019222507253289223,
0.01227177307009697,
-0.0054081035777926445,
0.0009138049208559096,
0.014833169989287853,
-0.012634865008294582,
0.006083877291530371,
-0.04468512907624245,
0.029489079490303993,
-0.006571673322468996,
0.022061951458454132,
0.020180679857730865,
0.03924299776554108,
0.02877594530582428,
0.07731011509895325,
-0.02755000814795494,
0.005071981810033321,
0.024506457149982452,
-0.014202723279595375,
0.0011988417245447636,
0.007007099222391844,
-0.06313080340623856,
-0.004619808867573738,
0.043662313371896744,
-0.005774686112999916,
0.05943115055561066,
0.046981148421764374,
-0.008215811103582382,
-0.0016301077557727695,
-0.021907862275838852,
0.005703876726329327,
-0.024995457381010056,
-0.033532656729221344,
0.002589303068816662,
-0.0018705427646636963,
0.06546387821435928,
-0.02634289860725403,
-0.05204933509230614,
-0.04557402431964874,
0.007852586917579174,
-0.03707322105765343,
0.008705978281795979,
0.0006677866913378239,
-0.04504802078008652,
0.008777557872235775,
0.08699888736009598,
-0.029829086735844612,
-0.028242748230695724,
0.053155362606048584,
-0.0007958885980769992,
-0.024245673790574074,
-0.009801738895475864,
-0.029875939711928368,
0.0003488569927867502,
0.03462615981698036,
-0.014574030414223671,
0.030932264402508736,
0.03186643123626709,
-0.0009300839737989008,
0.05200297012925148,
0.000672323047183454,
0.006407076492905617,
-0.06786265224218369,
0.016835853457450867,
-0.055444493889808655,
-0.02501947619020939,
-0.012813742272555828,
0.016279663890600204,
-0.004728330764919519,
-0.02232145331799984,
-0.045253023505210876,
0.00040453209658153355,
0.019371090456843376,
0.04881809651851654,
-0.053629279136657715,
-0.05769512057304382,
0.015582737512886524,
-0.07207838445901871,
-0.01987968198955059,
-0.013026786036789417,
-0.023531077429652214,
0.022939661517739296,
0.014924420975148678,
0.04090968519449234,
-0.04669583961367607,
-0.02624405547976494,
0.013377457857131958,
-0.03872423991560936,
0.03447316959500313,
-0.016309013590216637,
-0.07764456421136856,
-0.02486245147883892,
-0.0246102474629879,
0.06016850098967552,
0.01647811196744442,
-0.04931945726275444,
0.08097775280475616,
0.0365932323038578,
0.026400234550237656,
0.027389682829380035,
-0.024051692336797714,
0.013959677889943123,
0.015045689418911934,
0.021763596683740616,
-0.04000024497509003,
-0.018600204959511757,
0.05698549374938011,
-0.01710820384323597,
0.017668237909674644,
0.012667360715568066,
-0.040701184421777725,
-0.021282805129885674,
0.012237099930644035,
-0.014843062497675419,
-0.03614858165383339,
0.004089753609150648,
-0.055243197828531265,
0.01435339916497469,
0.051836784929037094,
-0.012397793121635914,
0.02104170247912407,
-0.018010620027780533,
-0.008619741536676884,
-0.044869404286146164,
-0.011835921555757523,
-0.016747497022151947,
-0.025514645501971245,
-0.00757586071267724,
-0.014554109424352646,
-0.007321862503886223,
0.002796522108837962,
-0.03812611848115921,
-0.031477488577365875,
-0.026364531368017197,
0.026728222146630287,
0.012438629753887653,
-0.06268522888422012,
0.00334255606867373,
-0.016905058175325394,
-0.011592723429203033,
0.02859029360115528,
0.047405045479536057,
-0.007118516601622105,
0.007157464046031237,
-0.03324568271636963,
-0.02420460246503353,
-0.021463993936777115,
0.014165882021188736,
0.016260623931884766,
0.00493751373142004,
0.01232261210680008,
-0.02274744026362896,
-0.0045135547406971455,
-0.01831204630434513,
0.013540641404688358,
-0.07878748327493668,
-0.036721259355545044,
-0.003896960522979498,
0.05071406438946724,
-0.04977100342512131,
-0.029266219586133957,
-0.06405351310968399,
0.040091048926115036,
0.0645129531621933,
0.06462924927473068,
0.0536651574075222,
0.023134466260671616,
-0.008975897915661335,
0.058713193982839584,
-0.02271156758069992,
-0.05099858343601227,
-0.0500018447637558,
0.0075984313152730465,
-0.003243645653128624,
-0.056206751614809036,
-0.04951146990060806,
-0.0056170448660850525,
0.09471212327480316,
-0.01173113752156496,
-0.028890563175082207,
0.016770286485552788,
-0.001761903753504157,
0.02452079951763153,
-0.007340742740780115,
0.005849264096468687,
-0.04484494775533676,
0.025561271235346794,
-0.02284407429397106,
-0.02547544427216053,
0.03919006139039993,
0.00948486477136612,
0.042548540979623795,
0.047498516738414764,
0.05256272479891777,
0.0033667301759123802,
-0.015385203994810581,
-0.0019994983449578285,
-0.01803944818675518,
-0.025243518874049187,
0.012021266855299473,
-0.04029460996389389,
-0.040831308811903,
-0.07104632258415222,
0.07566361129283905,
0.020203497260808945,
-0.039984483271837234,
0.04445350542664528,
-0.012706957757472992,
-0.09012358635663986,
0.06730394065380096,
-0.023036742582917213,
-0.010236392728984356,
0.029648557305336,
0.006650743540376425,
0.004693583585321903,
-0.02717304788529873,
0.0360066294670105,
-0.007455702405422926,
0.00958101823925972,
-0.0038642750587314367,
0.010106444358825684,
0.03391310200095177,
0.05744016915559769,
-0.05508984997868538,
-0.012003767304122448,
-0.0058084833435714245,
0.02572750672698021,
-0.09607148170471191,
-0.0392112135887146,
-0.0007628664607182145,
0.01798180118203163,
-0.016814598813652992,
0.0038021996151655912,
-0.012707341462373734,
0.025674806907773018,
0.008386094123125076,
0.0748668760061264,
0.005724107380956411,
0.0004665803862735629,
-0.03083672560751438,
0.008960846811532974,
-0.0476943701505661,
0.007478104904294014,
0.05487004294991493,
-0.07267798483371735,
-0.05063914507627487,
-0.03807396814227104,
0.008341718465089798,
-0.016810711473226547,
0.02030276134610176,
0.0063520679250359535,
0.020256370306015015,
-0.05906054750084877,
0.031609486788511276,
0.023720383644104004,
-0.014927886426448822,
-0.01426555123180151,
-0.08627256751060486,
0.04550933092832565,
0.026634439826011658,
-0.023888403549790382,
-0.028852561488747597,
-0.013645127415657043,
-0.005504918284714222,
-0.013236637227237225,
-0.029131203889846802,
-0.06110934913158417,
0.0034178642090409994,
0.03358716517686844,
0.03844757750630379,
-0.03313533961772919,
-0.02718404494225979,
-0.0072145164012908936,
-0.02425764501094818,
0.027320433408021927,
0.007390134502202272,
-0.08060438185930252,
0.03647109866142273,
-0.04492953047156334,
-0.023676522076129913,
0.011959929950535297,
-0.02664792165160179,
0.07558293640613556,
-0.06519588083028793,
-0.028750209137797356,
-0.05258593708276749,
-0.06307610124349594,
-0.05275467410683632,
0.02309301868081093,
-0.0030957194976508617,
-0.03250306844711304,
-0.007164971437305212,
0.026313375681638718,
0.05465322732925415,
-0.042502935975790024,
-0.02893376350402832,
-0.01895971968770027,
-0.05502230301499367,
0.00006147141539258882,
0.007244789972901344,
-0.0027343949768692255,
0.05748894438147545,
0.0462556816637516,
-0.01442856527864933,
0.026911549270153046,
-0.012595565058290958,
0.007767664268612862,
-0.04022170230746269,
-0.0018046157201752067,
0.06561043858528137,
-0.06692589819431305,
0.037844814360141754,
-0.037541233003139496,
0.016004644334316254,
0.025638163089752197,
0.027918292209506035,
0.1017342060804367,
-0.0007098824135027826,
0.019278081133961678,
0.011589474976062775,
-0.01263214461505413,
-0.02001032419502735,
0.007480246014893055,
0.031033730134367943,
0.008690967224538326,
0.011675745248794556,
-0.019487006589770317,
0.10280654579401016,
-0.07665855437517166,
0.02851133793592453,
0.05490175634622574,
0.026600057259202003,
0.041317738592624664,
-0.0689636617898941,
0.015273264609277248,
-0.00624593673273921,
-0.025423668324947357,
-0.018302014097571373,
-0.00951052363961935,
0.030957896262407303,
-0.004257532302290201,
0.04143647477030754,
0.009371801279485226,
0.027467088773846626,
0.05409662425518036,
0.004850714933127165,
-0.030987553298473358,
-0.010260077193379402,
0.022915069013834,
0.0130278579890728,
-0.007809699047356844,
-0.0066289110109210014,
-0.022176532074809074,
-0.02041524648666382,
-0.05879421532154083,
0.039513908326625824,
-0.01644536852836609,
0.005499660037457943,
0.03199603408575058,
0.02392972819507122,
-0.013835377991199493,
-0.05202040448784828,
-0.05251982808113098,
-0.054106567054986954,
0.019518304616212845,
0.055056702345609665,
0.04615986347198486,
-0.048865437507629395,
-0.015454770997166634,
0.06389366090297699,
0.06533581018447876,
0.0014827203704044223,
0.024990122765302658,
0.06402604281902313,
0.050574157387018204,
-0.029211074113845825,
-0.016573157161474228,
-0.03163967281579971,
0.029734695330262184,
0.05653977766633034,
0.009285302832722664,
-0.02428632602095604,
0.03952280804514885,
-0.011926678940653801,
0.05097534880042076,
0.02260465919971466,
0.03541504964232445,
-0.05327923595905304,
0.06210659444332123,
-0.00864460039883852,
-0.017411895096302032,
0.05741735175251961,
0.011894787661731243,
0.021300265565514565,
0.0009581365156918764,
0.08452573418617249,
0.006930307950824499,
-0.012107147835195065,
0.007455605547875166,
-0.021248264238238335,
0.011209093034267426,
-0.029143860563635826,
-0.027772678062319756,
-0.04613558575510979,
-0.03756023570895195,
0.06110313907265663,
0.02778409793972969,
-0.04957136884331703,
-0.03734201565384865,
0.03686978667974472,
0.022123269736766815,
-0.031116390600800514,
0.05461741238832474,
-0.09373361617326736,
0.023461293429136276,
0.048699624836444855,
-0.0709269642829895,
-0.016460783779621124,
-0.009717230685055256,
0.013434188440442085,
-0.016683334484696388,
0.011928957886993885,
0.01737613044679165,
-0.004296359606087208,
-0.03681987151503563,
-0.08165140450000763,
0.04342782124876976,
0.06602098792791367,
0.053706757724285126,
0.01575065776705742,
0.0725378692150116,
0.044255513697862625,
-0.010869227349758148,
-0.05259505659341812,
0.0510946586728096,
-0.008769244886934757,
-0.0048385378904640675,
-0.022118430584669113,
0.028105292469263077,
0.031938549131155014,
0.010909456759691238,
0.015093726105988026,
0.06198188289999962,
0.03712431713938713,
-0.03219626471400261,
0.038424380123615265,
-0.057542476803064346,
0.025776783004403114,
0.07296298444271088,
0.028835320845246315,
0.004686382599174976,
0.06945817917585373,
0.05119024217128754,
0.02328949049115181,
-0.07543934881687164,
0.006297110114246607,
0.06840385496616364,
-0.04477410018444061,
-0.10359279811382294,
-0.008376067504286766,
-0.031201811507344246,
-0.01582525670528412,
-0.01187178771942854,
0.005961773917078972,
-0.033879052847623825,
0.07149577140808105,
0.004812111146748066,
0.01738026924431324,
0.0203021802008152,
-0.02988448180258274,
-0.021890554577112198,
-0.05071749538183212,
-0.02666335180401802,
-0.014681837521493435,
-0.03433559089899063,
0.05492789298295975,
-0.017086559906601906,
-0.0648185983300209,
0.005728905089199543,
-0.052137333899736404,
-0.0013841635081917048,
-0.015533620491623878,
-0.0576334223151207,
-0.0034185515251010656,
-0.04657386615872383,
-0.024014605209231377,
0.012999243102967739,
0.04498876631259918,
-0.0026996692176908255,
-0.007914399728178978,
-0.006440082564949989,
0.0607328861951828,
-0.026496313512325287,
0.016293825581669807,
0.025584977120161057,
0.030174368992447853,
-0.07233212888240814,
-0.02739940583705902,
-0.001858020550571382,
0.051498450338840485,
-0.028699088841676712,
-0.02708958275616169,
-0.004551079589873552,
-0.03824185952544212,
0.01795521005988121,
-0.013983244076371193,
0.038938865065574646,
-0.019316432997584343,
0.015574304386973381,
0.024812001734972,
0.022228596732020378,
0.04987173527479172,
0.020453644916415215,
0.008009317331016064,
0.017982561141252518,
-0.007413339801132679,
0.006274022161960602,
-0.055658042430877686,
0.0340869277715683,
-0.0012987765949219465,
0.003989793825894594,
-0.01613314263522625,
-0.06412602961063385,
0.006094108801335096,
0.04826364666223526,
0.0017783029470592737,
-0.07509611546993256,
0.0005929054459556937,
0.0303940586745739,
-0.017559252679347992,
-0.04018178954720497,
0.01597723923623562,
0.001851048320531845,
0.014841096475720406,
0.00949664693325758,
-0.02764430269598961,
-0.01751917228102684,
0.023766251280903816,
-0.007115031126886606,
0.007766395341604948,
0.0007824968197382987,
-0.01752789504826069,
-0.043117422610521317,
0.043038930743932724,
-0.015378249809145927,
0.01162691880017519,
0.012972493655979633,
0.014564492739737034,
-0.013705993071198463,
0.016225524246692657,
-0.028540723025798798,
-0.03430301323533058,
0.01128293201327324,
-0.0018382305279374123,
0.031122157350182533,
-0.0219778660684824,
-0.07344427704811096,
0.020549295470118523,
0.11846098303794861,
-0.013998459093272686,
-0.03707237169146538,
0.032493866980075836,
0.013675312511622906,
0.06586325168609619,
0.04620427265763283,
-0.04228996858000755,
0.04543012008070946,
0.03576882928609848,
-0.02954065054655075,
0.0013678927207365632,
0.00018659218039829284,
-0.050689660012722015,
-0.07693681865930557,
-0.014447474852204323,
-0.07574823498725891,
0.014465817250311375,
0.0061866058968007565,
-0.0000772010680520907
] |
<p>If the earth left the solar system for some reason. Assuming its moving at the same velocity it's currently exhibiting. How long would it take for the atmosphere to freeze. Would we get methane clouds like Titan. Would there be an atmosphere or would it all be frozen on the ground? </p> | g918 | [
0.06543300300836563,
0.03993259742856026,
0.01539235282689333,
0.029889428988099098,
0.0021885994356125593,
0.004825432784855366,
0.0024547316133975983,
0.030463876202702522,
-0.054337020963430405,
-0.013023248873651028,
-0.004965346772223711,
0.020693710073828697,
0.01386083010584116,
0.004793691448867321,
0.03639579564332962,
0.03373722359538078,
-0.03349744901061058,
-0.04898151382803917,
-0.02157982438802719,
0.028921402990818024,
0.01477588340640068,
-0.030091440305113792,
0.022022848948836327,
-0.002064681611955166,
-0.008587525226175785,
0.002969911554828286,
0.03650118038058281,
-0.0057030306197702885,
-0.034065745770931244,
0.026202280074357986,
0.0317649282515049,
0.03137364983558655,
0.03028000332415104,
-0.0619315430521965,
-0.03324896842241287,
-0.05173243582248688,
0.05204915627837181,
0.06510312110185623,
0.0002059437829302624,
-0.08742962032556534,
0.12524546682834625,
-0.02498888596892357,
-0.019336232915520668,
0.01963222771883011,
0.044467926025390625,
-0.03474856913089752,
-0.0048174005933105946,
-0.026254335418343544,
0.015478027984499931,
-0.03838494047522545,
-0.0480685830116272,
0.03987954184412956,
-0.02309766598045826,
-0.018918341025710106,
-0.03652305155992508,
0.005700790323317051,
0.05805228278040886,
-0.025970177724957466,
0.0139033617451787,
-0.0007492875447496772,
-0.04747306555509567,
-0.03469070419669151,
0.038995370268821716,
-0.018217360600829124,
-0.009000609628856182,
0.013350161723792553,
-0.02399137243628502,
0.021369654685258865,
0.05400111526250839,
0.012347889132797718,
0.05801109969615936,
-0.01853492297232151,
-0.04379594698548317,
0.012317514978349209,
0.016053354367613792,
-0.005815555807203054,
-0.059326257556676865,
-0.0031714627984911203,
0.09389039129018784,
0.014144963584840298,
0.010855410248041153,
-0.017506061121821404,
0.008770176209509373,
0.010074884630739689,
0.009071777574717999,
-0.03610799089074135,
-0.04455702006816864,
-0.03197590634226799,
-0.05252021178603172,
0.01884802058339119,
-0.025363080203533173,
-0.04944782331585884,
-0.024975284934043884,
0.0007320854347199202,
-0.000367706612451002,
0.0288460124284029,
-0.01008831150829792,
0.07454565912485123,
0.013000966981053352,
-0.03983398526906967,
-0.03528349846601486,
-0.057167455554008484,
0.005106403026729822,
-0.03288592770695686,
0.07354675233364105,
0.022763416171073914,
0.0003167938848491758,
-0.031606629490852356,
0.018514283001422882,
-0.021272988989949226,
0.03746901825070381,
-0.024529987946152687,
0.002861864399164915,
0.05476465821266174,
0.003282801480963826,
-0.0013448386453092098,
0.00022882669873069972,
-0.059573154896497726,
0.05191794037818909,
0.0260663740336895,
0.046486519277095795,
0.05633791908621788,
-0.05490685999393463,
-0.023881103843450546,
-0.03138922154903412,
-0.012254893779754639,
0.01984008401632309,
-0.02239597775042057,
0.02079676277935505,
-0.005815756972879171,
-0.0036263561341911554,
0.020391492173075676,
-0.029644591733813286,
0.029853319749236107,
-0.017225289717316628,
-0.041426338255405426,
-0.024023640900850296,
-0.009794887155294418,
-0.048020120710134506,
0.016174379736185074,
0.05828244239091873,
0.02777731418609619,
0.009377178736031055,
0.03634979948401451,
-0.09185419231653214,
-0.001994273392483592,
-0.022582946345210075,
-0.007074387744069099,
0.027084076777100563,
0.010019953362643719,
-0.04454309493303299,
0.00908262562006712,
0.05959935113787651,
-0.005288580432534218,
0.017788581550121307,
-0.03941120207309723,
0.016823284327983856,
0.0613844096660614,
-0.007815849035978317,
-0.04990693926811218,
0.0376608781516552,
-0.021738165989518166,
0.04738515615463257,
0.013045010156929493,
-0.04221145063638687,
-0.0018485240871086717,
-0.03310515731573105,
-0.0013379055308178067,
0.04349203407764435,
-0.014172148890793324,
-0.02170838601887226,
0.02575862407684326,
0.0040197353810071945,
0.09527559578418732,
-0.01668667048215866,
0.02538539282977581,
0.047619808465242386,
0.02803744748234749,
-0.04928373917937279,
-0.004426370840519667,
0.06654727458953857,
-0.01657547615468502,
-0.041124098002910614,
0.00116518116556108,
0.037153150886297226,
-0.02160392329096794,
0.015639685094356537,
-0.051466405391693115,
-0.002759084105491638,
0.012126573361456394,
0.051837507635354996,
-0.017313096672296524,
0.002114189090207219,
0.0567704401910305,
0.02333172783255577,
-0.0496409572660923,
-0.028847217559814453,
-0.02366510033607483,
-0.019273223355412483,
-0.01140670571476221,
-0.006864109076559544,
0.023462751880288124,
0.025036757811903954,
-0.038177166134119034,
-0.007191820535808802,
-0.0032513663172721863,
-0.016210267320275307,
-0.030495185405015945,
0.023937728255987167,
-0.015512431040406227,
0.06417282670736313,
-0.021848587319254875,
0.00983445718884468,
0.04828774556517601,
-0.008403938263654709,
0.046386945992708206,
0.014662444591522217,
0.00006054169716662727,
0.01115147490054369,
0.020154079422354698,
-0.0351242758333683,
0.010997550562024117,
-0.02883944846689701,
-0.05673525482416153,
0.036301035434007645,
-0.044556692242622375,
-0.06234242767095566,
0.018300257623195648,
0.0030554740224033594,
0.03430595248937607,
0.04308521747589111,
0.0011089526815339923,
0.015017258934676647,
-0.002098826924338937,
-0.04859354346990585,
0.08423984050750732,
0.0014032324543222785,
-0.021579045802354813,
0.01798580400645733,
0.0154200354591012,
-0.0518723763525486,
0.02537793107330799,
-0.06560865789651871,
-0.007398362737149,
0.06004493311047554,
-0.08920014649629593,
0.059511758387088776,
0.035099539905786514,
-0.014380780048668385,
-0.007408798672258854,
0.027979381382465363,
-0.0057181185111403465,
-0.02570624276995659,
-0.02210773155093193,
-0.013033906929194927,
-0.03104027733206749,
-0.046472325921058655,
0.047010477632284164,
-0.01577574387192726,
-0.03323456272482872,
-0.013736395165324211,
-0.015707191079854965,
-0.0052168769761919975,
0.03262505307793617,
-0.09952108561992645,
-0.019158698618412018,
-0.008413787931203842,
0.024330860003829002,
0.0489434190094471,
-0.024821698665618896,
0.004320621024817228,
0.003389980411157012,
0.0032420221250504255,
0.04099130257964134,
-0.022769562900066376,
0.044931259006261826,
0.008947697468101978,
0.03467341139912605,
-0.0038214116357266903,
-0.03983550891280174,
0.026150183752179146,
-0.009535346180200577,
0.04604465141892433,
0.022722449153661728,
0.02062363363802433,
-0.04061286523938179,
-0.04265419393777847,
0.06278195232152939,
-0.07101936638355255,
0.010520142503082752,
-0.01514649111777544,
0.007396847940981388,
0.05834824964404106,
0.08481641113758087,
0.025869272649288177,
0.01912296563386917,
-0.02195182628929615,
0.02407226152718067,
-0.03687415271997452,
-0.019001251086592674,
0.015484089963138103,
-0.03153255209326744,
-0.0076807644218206406,
0.033864814788103104,
0.015107971616089344,
-0.017742054536938667,
-0.0275360606610775,
-0.014997701160609722,
-0.0010790711967274547,
-0.06989540904760361,
0.0567663237452507,
0.08428827673196793,
-0.036210525780916214,
0.06043850630521774,
-0.0258916188031435,
0.017576901242136955,
0.013934201560914516,
-0.004101983737200499,
0.07153181731700897,
-0.017825650051236153,
0.040189798921346664,
-0.04037328436970711,
0.003882983233779669,
0.014697534963488579,
0.004695381503552198,
0.04945092275738716,
-0.04922869801521301,
-0.03316712751984596,
-0.037426844239234924,
-0.006370042450726032,
0.00035896871122531593,
0.023992307484149933,
-0.012242285534739494,
0.0035405170638114214,
-0.0382501445710659,
-0.002480310620740056,
0.021907350048422813,
-0.02569310925900936,
0.015591578558087349,
0.013721306808292866,
0.04314444959163666,
0.029294326901435852,
-0.035674382001161575,
-0.005101248621940613,
-0.049519773572683334,
0.005225200206041336,
0.04344041272997856,
-0.05401694402098656,
-0.04006477817893028,
0.024269964545965195,
0.03073875419795513,
-0.030023859813809395,
0.0017720847390592098,
-0.0034430150408297777,
-0.046445462852716446,
0.04546408727765083,
0.011610804125666618,
-0.016096822917461395,
0.028717441484332085,
-0.04574546962976456,
-0.018583690747618675,
-0.04116333648562431,
0.016662010923027992,
0.015039187856018543,
-0.0031916582956910133,
-0.018082618713378906,
-0.050969209522008896,
-0.009588527493178844,
0.021387198939919472,
-0.007036442868411541,
-0.0075590768828988075,
0.023423131555318832,
-0.004101199097931385,
-0.02580568939447403,
0.05388181656599045,
-0.0617278628051281,
0.032913416624069214,
0.0162193663418293,
0.011399045586585999,
0.022563697770237923,
-0.009135439060628414,
-0.01842714473605156,
-0.019265474751591682,
-0.05519396811723709,
0.06479886919260025,
-0.04302438721060753,
-0.05281522125005722,
0.011700266972184181,
-0.02240821346640587,
-0.020555511116981506,
0.008807440288364887,
-0.04473215341567993,
0.010915650986135006,
-0.0037874432746320963,
0.005984799936413765,
-0.0016027099918574095,
0.04755615070462227,
0.04890214651823044,
0.027537954971194267,
-0.02120778150856495,
-0.004411260597407818,
0.005070841405540705,
0.005552068818360567,
-0.011909248307347298,
0.055785007774829865,
-0.0285456832498312,
0.007527241017669439,
-0.03844130411744118,
0.08163964003324509,
0.004851199220865965,
0.023402148857712746,
-0.0005692607373930514,
-0.02353757433593273,
0.019205693155527115,
0.04050976410508156,
-0.00413541728630662,
0.0014282366028055549,
-0.019386090338230133,
0.027194522321224213,
-0.020117247477173805,
-0.021578453481197357,
0.06447717547416687,
-0.0005173766403459013,
-0.024486565962433815,
0.010718867182731628,
0.02820693701505661,
0.06531742215156555,
-0.05339919030666351,
-0.05783262848854065,
0.029781591147184372,
0.02185329608619213,
-0.03469713404774666,
0.015079115517437458,
0.01921578124165535,
0.010444669984281063,
0.09036026895046234,
-0.007629006169736385,
-0.03986043855547905,
-0.006513471715152264,
0.05769672989845276,
0.02722521685063839,
0.020646153017878532,
0.08090179413557053,
0.02640216425061226,
-0.06662442535161972,
0.07805700600147247,
0.0702926442027092,
-0.06131112575531006,
0.03793738782405853,
-0.015793096274137497,
0.007178731262683868,
0.02108154073357582,
-0.07748939841985703,
0.07618452608585358,
-0.014988144859671593,
-0.04534740000963211,
-0.0030485664028674364,
0.04469570890069008,
0.006064147222787142,
0.10378820449113846,
-0.003850276116281748,
0.04535013809800148,
0.040351640433073044,
0.05455639585852623,
-0.0026230288203805685,
-0.05803729593753815,
-0.0037799205165356398,
-0.014365646988153458,
-0.014163539744913578,
0.035698533058166504,
-0.05066399648785591,
0.020991666242480278,
-0.015489804558455944,
0.0624467134475708,
-0.05399851128458977,
-0.009596303105354309,
-0.025068094953894615,
-0.02274387702345848,
0.06307487934827805,
0.013009512796998024,
-0.028058500960469246,
0.019066927954554558,
0.03358854725956917,
-0.005596152041107416,
0.017692014575004578,
-0.04649724066257477,
-0.07254649698734283,
-0.03237895667552948,
-0.0026401891373097897,
-0.038399457931518555,
-0.07986535131931305,
0.013423280790448189,
-0.0031809683423489332,
-0.052278537303209305,
0.0016974126920104027,
-0.02967829816043377,
-0.047857917845249176,
-0.07445613294839859,
-0.0033389595337212086,
-0.027351295575499535,
0.018658358603715897,
0.01763143017888069,
-0.020179826766252518,
-0.022821402177214622,
-0.01596735417842865,
0.03852982819080353,
-0.0334073044359684,
-0.004830443765968084,
0.034744661301374435,
-0.010588495060801506,
0.005884534679353237,
0.06849483400583267,
-0.021028952673077583,
0.07037929445505142,
0.02491537667810917,
-0.029878271743655205,
-0.04378412663936615,
0.009767850860953331,
-0.0013870790135115385,
-0.015159749425947666,
0.002028520219027996,
-0.031370244920253754,
0.02025752328336239,
0.02414991706609726,
-0.016758210957050323,
-0.020871596410870552,
-0.04801332578063011,
0.015801316127181053,
-0.0352768637239933,
0.014937314204871655,
0.002488528611138463,
-0.05273371934890747,
0.053668051958084106,
-0.027543092146515846,
0.05024086683988571,
-0.015903407707810402,
-0.036229442805051804,
0.04219849035143852,
0.09945770353078842,
-0.06498905271291733,
-0.0521882101893425,
-0.017978927120566368,
-0.026165975257754326,
0.016062023118138313,
0.009656885638833046,
0.018254466354846954,
-0.0023560526315122843,
0.08961793035268784,
0.05612032860517502,
-0.032975174486637115,
-0.03870503231883049,
-0.0051239910535514355,
-0.06058962270617485,
-0.04734202101826668,
-0.058209583163261414,
0.04411575570702553,
-0.023257741704583168,
-0.017710722982883453,
-0.017370104789733887,
0.017622480168938637,
0.043845515698194504,
0.016251837834715843,
0.03395385295152664,
-0.012546884827315807,
-0.04488234594464302,
-0.004299784544855356,
-0.03377309441566467,
-0.006813456770032644,
0.05553670600056648,
-0.0309695303440094,
0.05197570100426674,
-0.03267767280340195,
0.02102574333548546,
-0.023408126085996628,
-0.02289148047566414,
0.010471418499946594,
0.03455551341176033,
0.03766030818223953,
-0.02108633518218994,
-0.024111445993185043,
0.039642758667469025,
-0.013346978463232517,
0.04133393615484238,
-0.031355444341897964,
0.014809796586632729,
-0.008823983371257782,
0.017070550471544266,
-0.006633933167904615,
0.00997607596218586,
0.01329835131764412,
0.00705754617229104,
-0.04050546884536743,
-0.018619723618030548,
-0.03777552768588066,
-0.03917287662625313,
-0.0447949655354023,
-0.023736851289868355,
-0.06316256523132324,
0.02513989619910717,
0.05051307752728462,
0.02261260896921158,
0.05617690831422806,
0.04313170909881592,
-0.03717227280139923,
-0.01781057007610798,
0.04616405442357063,
0.028757473453879356,
0.07232616096735,
0.009273767471313477,
0.08846928924322128,
0.0010478232288733125,
-0.03998878225684166,
-0.01134525053203106,
-0.04688168317079544,
0.032249581068754196,
-0.000014565441233571619,
0.01885840855538845,
0.02938748709857464,
0.006673777010291815,
-0.014816892333328724,
-0.06487352401018143,
0.0027317304629832506,
-0.03269411250948906,
-0.04070485755801201,
-0.04250066354870796,
-0.010983255691826344,
-0.01935320720076561,
0.04405750706791878,
0.044729262590408325,
-0.019011422991752625,
0.07879730314016342,
-0.02228446863591671,
0.025228459388017654,
0.019758950918912888,
-0.00907494593411684,
-0.0063199144788086414,
0.01899907924234867,
-0.019176041707396507,
-0.04266505315899849,
-0.010955027304589748,
0.052423469722270966,
-0.06464491784572601,
-0.011196023784577847,
-0.034513648599386215,
-0.02171187289059162,
-0.03109705075621605,
0.026620840653777122,
-0.05693034827709198,
-0.018335195258259773,
-0.04007814824581146,
-0.0495612658560276,
-0.031689077615737915,
-0.03635445237159729,
0.002653091214597225,
-0.007248781155794859,
0.024439318105578423,
-0.025954384356737137,
0.01391390897333622,
-0.011215842328965664,
-0.06499137729406357,
0.014140965417027473,
-0.010746648535132408,
-0.004126931540668011,
0.052501142024993896,
0.05773478001356125,
0.04262929409742355,
0.036673299968242645,
-0.07551725953817368,
0.04208189994096756,
0.0002937357930932194,
-0.004683945327997208,
0.03422342985868454,
-0.01457719225436449,
0.021016528829932213,
-0.03946544602513313,
0.027892397716641426,
0.00450926972553134,
-0.05844670161604881,
0.011182255111634731,
-0.01419595442712307,
-0.044032786041498184,
0.007816369645297527,
-0.02530433051288128,
0.03749321028590202,
-0.025845356285572052,
0.02270537242293358,
0.02564438246190548,
0.019635578617453575,
0.007661864161491394,
-0.048133641481399536,
0.07122588157653809,
0.026008086279034615,
0.014166336506605148,
-0.05555308237671852,
-0.01762128435075283,
0.02941722609102726,
0.028822962194681168,
-0.07758132368326187,
0.04476642608642578,
-0.028203560039401054,
-0.06642957031726837,
0.021877000108361244,
0.07310641556978226,
0.02721911482512951,
-0.013422632589936256,
-0.03940587118268013,
-0.008593486621975899,
-0.014692525379359722,
-0.05402584746479988,
0.002221550326794386,
0.03827919811010361,
0.07219603657722473,
-0.01938033662736416,
0.0029357478488236666,
0.005438498221337795,
-0.023259365931153297,
0.019417675212025642,
0.028631364926695824,
0.008892323821783066,
-0.008329188451170921,
-0.050169289112091064,
-0.05101080983877182,
0.016090184450149536,
-0.011033996008336544,
-0.04661562293767929,
0.04675218462944031,
-0.02497146464884281,
-0.03967684507369995,
0.037811361253261566,
-0.08286315202713013,
-0.005429649259895086,
0.08800236880779266,
0.031118568032979965,
0.02682889811694622,
-0.05401579290628433,
0.012458049692213535,
0.014131938107311726,
-0.040553923696279526,
-0.010588747449219227,
0.015225470997393131,
-0.03184105455875397,
-0.0014038651715964079,
-0.02056296542286873,
-0.08053280413150787,
0.0660526230931282,
0.0109865702688694,
0.011164436116814613,
0.04233275353908539,
0.010671202093362808,
-0.0405535064637661,
-0.0006062634056434035,
-0.044911887496709824,
-0.01578298769891262,
0.00575642753392458,
-0.010623253881931305,
0.010777306742966175,
-0.023672347888350487,
0.01423588301986456,
-0.05829065665602684,
0.024427009746432304,
0.011182259768247604,
0.012914654798805714,
0.05669731646776199,
-0.017942218109965324,
0.017680946737527847,
-0.052299052476882935,
0.006607542745769024,
-0.010408003814518452
] |
<p>If we have a sphere which has $σ$ surface charge density and rotate it in axis z will this create current ? Is it possible without any potential difference ? </p> | g9180 | [
0.031682759523391724,
-0.002666920656338334,
0.005799693521112204,
0.0037135013844817877,
0.043378811329603195,
0.02622552402317524,
0.04486551135778427,
-0.035508375614881516,
0.018669577315449715,
0.04540558531880379,
0.00022808222274761647,
0.03640762344002724,
0.01667352207005024,
-0.014971956610679626,
0.004325497895479202,
0.01725505106151104,
-0.00869951955974102,
-0.012061991728842258,
-0.022898651659488678,
0.006106918677687645,
0.013615095056593418,
-0.08212292939424515,
0.035582296550273895,
-0.018106866627931595,
-0.006327438168227673,
0.010193431749939919,
-0.008820820599794388,
-0.0016156357014551759,
0.016627507284283638,
-0.009638067334890366,
0.03976207226514816,
0.02524048276245594,
0.013196158222854137,
0.04192488640546799,
-0.0382419191300869,
-0.0239967443048954,
0.008656557649374008,
-0.020476721227169037,
0.01549084484577179,
-0.05343152955174446,
-0.004063005559146404,
0.013479895889759064,
0.05603710934519768,
-0.012287060730159283,
0.04038378968834877,
-0.009314716793596745,
0.021301209926605225,
0.07195103913545609,
-0.0131449606269598,
-0.02244926430284977,
-0.03716675192117691,
0.011181852780282497,
0.03708253428339958,
-0.013124516233801842,
-0.040532127022743225,
-0.020989269018173218,
0.03599396347999573,
-0.037768278270959854,
0.01491324882954359,
0.04127120599150658,
-0.06729692965745926,
-0.011010124348104,
-0.02177673764526844,
0.02967197820544243,
0.01025691069662571,
-0.0199989415705204,
-0.04678155854344368,
0.00621733209118247,
-0.05191913619637489,
0.041924815624952316,
0.02027604915201664,
-0.02268444001674652,
-0.006978276651352644,
-0.05003158748149872,
-0.03929596021771431,
0.10413995385169983,
0.04288826510310173,
-0.021221721544861794,
0.030015375465154648,
-0.02443396858870983,
-0.020733455196022987,
-0.06229159235954285,
0.021827533841133118,
0.02033628709614277,
0.08820418268442154,
-0.04026992991566658,
-0.0014094120124354959,
-0.016106007620692253,
-0.015338465571403503,
-0.024369213730096817,
0.023914296180009842,
-0.035077791661024094,
0.017949284985661507,
-0.01786975935101509,
-0.024008734151721,
-0.03233063593506813,
-0.0028619817458093166,
0.016071852296590805,
-0.006585488095879555,
0.007852783426642418,
-0.037009913474321365,
-0.017466729506850243,
0.009088567458093166,
0.04149717837572098,
-0.03394119441509247,
0.03743640333414078,
-0.0049636936746537685,
-0.014143661595880985,
0.01756838709115982,
-0.0060677421279251575,
0.02423311211168766,
-0.04592704400420189,
0.020491978153586388,
0.05724658817052841,
-0.019956279546022415,
-0.0672810897231102,
0.062039609998464584,
-0.02886853739619255,
0.0028027910739183426,
0.06321068853139877,
-0.038658466190099716,
0.007038126699626446,
0.009072129614651203,
0.06038881465792656,
0.006218572147190571,
0.060119833797216415,
0.03818565234541893,
0.03512125089764595,
0.04162665829062462,
-0.03261454403400421,
-0.0003799626138061285,
0.02557280845940113,
-0.033375512808561325,
-0.0000761354312999174,
-0.02646145038306713,
-0.008798500522971153,
-0.046864379197359085,
-0.05407077446579933,
0.02200964093208313,
0.010113710537552834,
0.051140785217285156,
-0.03857529163360596,
0.03950852155685425,
-0.0551748089492321,
0.007973143830895424,
0.0053740511648356915,
-0.015874464064836502,
-0.03286894038319588,
0.0024582301266491413,
0.03613690286874771,
-0.013424333184957504,
0.02564501389861107,
0.04010362923145294,
-0.0170527882874012,
0.013126479461789131,
-0.03316507488489151,
0.04775744304060936,
0.004858007654547691,
0.09584902226924896,
-0.007287480868399143,
0.017444362863898277,
-0.025852356106042862,
0.011390822939574718,
-0.04269827529788017,
-0.013220341876149178,
-0.07612321525812149,
-0.008872426114976406,
-0.024219784885644913,
-0.036985334008932114,
-0.08569657057523727,
-0.002551487646996975,
-0.007195036858320236,
0.021185416728258133,
0.04664231091737747,
0.0075393179431557655,
-0.019026469439268112,
-0.10102460533380508,
0.001564825652167201,
0.07997650653123856,
0.059133611619472504,
-0.06093151122331619,
0.03447354957461357,
-0.013440038077533245,
0.0283407811075449,
0.009856535121798515,
0.06045152619481087,
-0.02716435119509697,
-0.017499400302767754,
-0.03395499661564827,
0.010031074285507202,
-0.07770480960607529,
-0.0018998010782524943,
-0.024602040648460388,
0.06172569468617439,
0.042534369975328445,
0.021239878609776497,
0.05995233729481697,
-0.04068829491734505,
-0.04454251378774643,
0.036689821630716324,
-0.033375084400177,
0.06496796756982803,
0.04494915530085564,
0.012804612517356873,
0.01162710227072239,
-0.019084017723798752,
-0.005064017605036497,
-0.077048160135746,
0.09115822613239288,
-0.02033715881407261,
0.06612589210271835,
0.01393086276948452,
-0.020538540557026863,
-0.03215062990784645,
-0.041947122663259506,
-0.01161158550530672,
-0.007244070526212454,
0.0404549203813076,
-0.024197936058044434,
0.003702219109982252,
-0.016314029693603516,
0.002243870170786977,
0.03840666636824608,
0.01200414914637804,
-0.03689192235469818,
0.029090089723467827,
0.005197163205593824,
-0.018521802499890327,
0.037499457597732544,
0.01446298137307167,
-0.00608748709782958,
-0.03826620429754257,
0.082872174680233,
0.018363388255238533,
-0.01776217482984066,
0.06582622230052948,
-0.038855262100696564,
0.04589400067925453,
-0.032555464655160904,
-0.05430329218506813,
-0.0016304169548675418,
-0.0016734735108911991,
-0.03376961499452591,
0.013374529778957367,
0.07486972212791443,
-0.012156859040260315,
0.0469641238451004,
0.07140115648508072,
0.02806122787296772,
0.03360524773597717,
0.09969169646501541,
-0.033842116594314575,
-0.02112462744116783,
0.04389861971139908,
-0.009498126804828644,
-0.019945213571190834,
-0.054802507162094116,
0.03142029792070389,
-0.005724250338971615,
-0.08024616539478302,
-0.056368421763181686,
-0.01933051086962223,
0.013873723335564137,
-0.0104063106700778,
-0.027188457548618317,
-0.0017540967091917992,
-0.05326797813177109,
-0.006747142877429724,
0.020065873861312866,
0.04458347707986832,
-0.027587998658418655,
0.05720456317067146,
0.04313573241233826,
0.09001974016427994,
-0.043202366679906845,
0.04242994636297226,
-0.013237027451395988,
0.010911409743130207,
0.024355197325348854,
-0.030388638377189636,
0.02990964986383915,
0.01264796033501625,
-0.05803206190466881,
0.07101936638355255,
0.009073910303413868,
-0.002030525356531143,
0.016539623960852623,
0.008290085010230541,
-0.048300713300704956,
-0.036815837025642395,
-0.019204897806048393,
0.03476449474692345,
0.10071175545454025,
-0.015147603116929531,
0.058272019028663635,
-0.006867448799312115,
0.025843171402812004,
-0.05720360204577446,
0.002802199451252818,
0.07490712404251099,
0.022175831720232964,
-0.024058859795331955,
-0.015409809537231922,
0.06136105954647064,
0.0432354137301445,
0.059159234166145325,
-0.05193250626325607,
-0.03333081677556038,
0.02525988593697548,
0.02445169910788536,
-0.051434315741062164,
0.05881591886281967,
0.02919182740151882,
-0.0013615451753139496,
-0.049130767583847046,
-0.0007464336813427508,
-0.03119022771716118,
-0.01122836209833622,
-0.0072812545113265514,
-0.0002272833080496639,
-0.03274055942893028,
0.02643171325325966,
-0.061371706426143646,
0.0017071337206289172,
0.04170389473438263,
0.06311244517564774,
-0.042991407215595245,
-0.021488120779395103,
-0.017378073185682297,
-0.020747201517224312,
-0.013815066777169704,
0.027804236859083176,
-0.0063658179715275764,
0.0007222650456242263,
-0.003982292488217354,
-0.013341210782527924,
-0.01134767010807991,
0.012017417699098587,
-0.003957526292651892,
0.04863836616277695,
-0.06897008419036865,
-0.06372898817062378,
-0.020012453198432922,
-0.0688411071896553,
-0.04740830883383751,
0.03352589160203934,
-0.047501690685749054,
-0.0394122339785099,
-0.019963933154940605,
-0.012819897383451462,
0.03563123568892479,
0.005627780687063932,
0.024950912222266197,
0.016785992309451103,
0.08697468042373657,
0.016422726213932037,
0.029859015718102455,
0.06516631692647934,
-0.003371771425008774,
-0.0096872728317976,
-0.01577860675752163,
-0.08255878835916519,
0.027986472472548485,
0.0011670173844322562,
0.015126323327422142,
0.01042595412582159,
-0.044558193534612656,
0.01866644062101841,
-0.022592347115278244,
-0.03823907673358917,
0.005195177160203457,
0.018158385530114174,
0.012571594677865505,
0.004360135644674301,
0.03895074501633644,
-0.041678063571453094,
-0.032108183950185776,
0.02108752168715,
-0.03496355190873146,
0.0071327174082398415,
0.024109337478876114,
-0.01933499611914158,
0.017961105331778526,
0.023090500384569168,
-0.025260530412197113,
0.05804567411541939,
0.005136228632181883,
0.016588790342211723,
-0.01024021115154028,
-0.008411348797380924,
-0.010482797399163246,
-0.003964894451200962,
0.027943799272179604,
-0.02724592760205269,
0.01923603005707264,
-0.04944121837615967,
-0.011917087249457836,
-0.0685524195432663,
-0.01959887146949768,
-0.02107723243534565,
0.04438357427716255,
0.034477245062589645,
-0.008154874667525291,
-0.01604127138853073,
0.043471645563840866,
-0.010768024250864983,
0.03273249417543411,
-0.057369545102119446,
-0.003091660561040044,
-0.0500996895134449,
0.03421173244714737,
0.001551200752146542,
0.01592339389026165,
-0.041911881417036057,
0.011228256858885288,
0.002796594751998782,
-0.043696992099285126,
0.006067379377782345,
0.011889975517988205,
0.011504452675580978,
-0.021443231031298637,
0.04523667320609093,
0.04554436728358269,
0.03242294490337372,
0.024365972727537155,
0.021570740267634392,
0.05713150277733803,
-0.04265362769365311,
-0.0064481403678655624,
-0.02130788564682007,
-0.029917551204562187,
0.061217013746500015,
-0.028174323961138725,
-0.04104221612215042,
-0.09827206283807755,
0.009799813851714134,
-0.03009970672428608,
-0.0009695224580354989,
-0.031599804759025574,
0.010100515559315681,
0.013399087823927402,
0.04243678227066994,
0.043474674224853516,
-0.07231103628873825,
0.021206609904766083,
0.07871682941913605,
-0.07255662977695465,
-0.030971307307481766,
-0.014797982759773731,
-0.013540550135076046,
-0.048637378960847855,
-0.03548429161310196,
-0.014550412073731422,
-0.0058181206695735455,
-0.03351525589823723,
0.04604890197515488,
-0.0367974191904068,
-0.00615596491843462,
-0.07248067110776901,
0.0435560941696167,
-0.032490286976099014,
-0.005773887038230896,
0.03542301058769226,
0.013296197168529034,
0.02354399487376213,
-0.04265259951353073,
-0.04833018407225609,
-0.003707129741087556,
-0.024337051436305046,
-0.03798259049654007,
-0.011533297598361969,
0.04778449609875679,
0.040234219282865524,
-0.00028604554245248437,
-0.025584733113646507,
0.012746116146445274,
0.061818718910217285,
-0.023611409589648247,
-0.04718749225139618,
-0.08576897531747818,
-0.08329631388187408,
0.015070571564137936,
0.00321200885809958,
0.017942799255251884,
0.009171963669359684,
0.062455326318740845,
-0.07341646403074265,
0.027076812461018562,
-0.009787780232727528,
-0.038001202046871185,
0.03724684193730354,
-0.0046529145911335945,
-0.038897935301065445,
-0.00426195515319705,
-0.0036634793505072594,
0.043261561542749405,
-0.029893817380070686,
-0.06678060442209244,
-0.06632477790117264,
0.053577765822410583,
0.046428631991147995,
-0.04419836774468422,
-0.014319314621388912,
0.03218180686235428,
-0.020091138780117035,
0.05919886752963066,
0.025970233604311943,
0.011318548582494259,
0.037320151925086975,
0.04728222265839577,
-0.046851638704538345,
-0.016673099249601364,
0.06510619819164276,
0.004446260631084442,
0.030667318031191826,
0.02576049603521824,
-0.053305305540561676,
-0.028444314375519753,
0.027098458260297775,
-0.0319271981716156,
0.0008358975173905492,
0.02542325295507908,
-0.022466903552412987,
-0.027315106242895126,
-0.005137571133673191,
-0.011107905767858028,
-0.06652316451072693,
0.002070841146633029,
0.08325885236263275,
0.04527651518583298,
0.0043903193436563015,
-0.0059430417604744434,
-0.010500555858016014,
-0.0683489590883255,
0.05129275470972061,
-0.02351818047463894,
-0.0032794924918562174,
0.037764694541692734,
-0.0006347814342007041,
0.007681418675929308,
-0.010322203859686852,
-0.037764161825180054,
0.046237602829933167,
0.0026648675557225943,
-0.019742514938116074,
-0.009180394932627678,
-0.05219769850373268,
-0.008962913416326046,
-0.01156663242727518,
0.012873649597167969,
-0.03373986855149269,
0.07642298191785812,
-0.04693005979061127,
0.005274535622447729,
-0.01773175410926342,
0.029785243794322014,
-0.04204578697681427,
-0.021229835227131844,
0.001102978247217834,
-0.02346060238778591,
0.017827870324254036,
-0.007070973049849272,
0.016660543158650398,
-0.035421863198280334,
-0.02425757236778736,
-0.04734627529978752,
-0.029118536040186882,
0.007837217301130295,
0.060111258178949356,
0.02783142402768135,
-0.05082651227712631,
-0.021488027647137642,
-0.0018600275507196784,
-0.031656570732593536,
0.02178931050002575,
-0.040024034678936005,
0.0012559950118884444,
0.04494281858205795,
-0.016226135194301605,
0.03907550871372223,
0.013990302570164204,
0.028369830921292305,
0.02573336474597454,
0.005142135079950094,
0.07569823414087296,
-0.005778700113296509,
0.02046973630785942,
-0.019732417538762093,
0.019775673747062683,
-0.05281317979097366,
-0.02864910662174225,
0.014328609220683575,
0.040705084800720215,
-0.052162401378154755,
-0.04388289153575897,
-0.036472223699092865,
0.002907918067649007,
0.010782177560031414,
0.03522561490535736,
-0.006371974945068359,
0.04129651561379433,
-0.011680152267217636,
0.01603650487959385,
0.04640563204884529,
0.011321439407765865,
-0.019670777022838593,
-0.00454357685521245,
0.05145569145679474,
-0.0019710836932063103,
-0.030709709972143173,
-0.05897809565067291,
-0.04944109544157982,
-0.021276697516441345,
-0.02233634889125824,
0.06142744421958923,
0.016652628779411316,
0.08281092345714569,
0.0003813511284533888,
0.005298721604049206,
-0.018287120386958122,
0.04918231442570686,
0.023459788411855698,
-0.02843886986374855,
-0.04564463347196579,
0.035724982619285583,
-0.0003282184188719839,
0.02094121463596821,
0.024885687977075577,
0.017428262159228325,
0.05297259986400604,
0.04311520606279373,
0.0059388428926467896,
0.003718959866091609,
-0.000737567082978785,
0.027388347312808037,
0.03348063305020332,
-0.003428868716582656,
0.017325380817055702,
0.010629472322762012,
-0.003960876725614071,
-0.004680589772760868,
0.0425688773393631,
0.03178790584206581,
0.014034834690392017,
-0.06227213889360428,
-0.05341663584113121,
0.013166944496333599,
-0.026331676170229912,
-0.053722452372312546,
0.020166631788015366,
0.04157612472772598,
-0.0165551844984293,
-0.016337348148226738,
0.019838711246848106,
-0.009382260031998158,
-0.02850916236639023,
0.05587349832057953,
0.022452695295214653,
0.005311606451869011,
-0.035674214363098145,
-0.0486169159412384,
0.00955757312476635,
0.0072395033203065395,
-0.0371038094162941,
-0.00989572424441576,
0.018043549731373787,
-0.04168098419904709,
0.02644655853509903,
0.024429762735962868,
-0.03248467668890953,
-0.04249090701341629,
0.002877224702388048,
-0.04209025204181671,
-0.010551433078944683,
-0.008490047417581081,
-0.007507029455155134,
0.051205042749643326,
0.020462270826101303,
-0.008664011023938656,
0.012812454253435135,
0.011452593840658665,
-0.007606571074575186,
-0.05751277133822441,
0.02798984944820404,
-0.03940489515662193,
-0.052003927528858185,
-0.06560572236776352,
-0.02039993554353714,
0.026942230761051178,
0.026295587420463562,
0.042531441897153854,
0.0262784194201231,
-0.030891044065356255,
0.04060199111700058,
-0.04846939072012901,
0.05916784703731537,
-0.019062446430325508,
0.06904088705778122,
0.03349601477384567,
0.01174523588269949,
0.013395761139690876,
0.002995546907186508,
0.01566941663622856,
0.004293583333492279,
0.01462974026799202,
-0.009852688759565353,
-0.07054530829191208,
0.0011778753250837326,
-0.021929379552602768,
0.016940684989094734,
0.022732486948370934,
0.015303662046790123,
-0.056147415190935135,
-0.024241218343377113,
0.04012968763709068,
0.007701943628489971,
0.007689944468438625,
0.021929718554019928,
0.019258970394730568,
0.04761911928653717,
-0.04275153949856758,
-0.0015926143387332559,
0.027071289718151093,
-0.0024259851779788733,
-0.05972221866250038,
-0.04305987432599068,
-0.046094778925180435,
0.02085738070309162,
0.0573902353644371,
0.0056165121495723724,
-0.0004738971474580467,
0.015160168521106243,
-0.016774915158748627,
-0.0053863623179495335,
-0.041021957993507385,
-0.008826025761663914,
-0.012840704061090946,
0.020043203607201576,
0.024478713050484657,
0.004883035086095333,
0.014074085280299187,
-0.03660563752055168,
0.04180917516350746,
-0.09352295100688934,
-0.015085997991263866,
0.05661676451563835,
0.002568258671090007,
0.037798911333084106,
0.05995979905128479,
0.022766297683119774,
0.014702496118843555,
0.0022269822657108307,
-0.0858757421374321,
-0.05978139489889145,
-0.03727184981107712,
-0.007418513298034668,
-0.01705368421971798,
0.023971203714609146,
-0.007352025713771582,
-0.00823750626295805,
-0.02529633790254593,
-0.02009703405201435,
0.012772932648658752,
0.040694743394851685,
0.0015693476889282465,
-0.09790650010108948,
0.006253035273402929,
-0.00624191015958786
] |
<p>I've been digging into emission spectra of different elements and found that such things as the Rydberg equation, Bohr's model, and quantum mechanics can only fully describe the single electron in the Hydrogen atom. How did we then make the leap to s,p,d,f shells of multi-electron atoms? How accurate is our analysis of these more complicated elements?</p>
<p>Rydberg Equation (side-note: Is this an empirical 'data-fitting' equation? What's the significance of that?)</p>
<p>$$\frac{1}{\lambda}=R_H\left( \frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$ </p>
<p>Hydrogen:
<img src="http://i.stack.imgur.com/9yWL5.jpg" alt="enter image description here"></p>
<p>Helium:
<img src="http://i.stack.imgur.com/EyQi5.jpg" alt="enter image description here"></p>
<p>Iron:
<img src="http://i.stack.imgur.com/Tx0Vp.jpg" alt="enter image description here"></p>
<p>Potassium:
<img src="http://i.stack.imgur.com/g23gw.jpg" alt="enter image description here"></p> | g9181 | [
-0.03955545648932457,
0.046776801347732544,
-0.017863599583506584,
0.01654048077762127,
0.02980075031518936,
0.010476281866431236,
-0.017868725582957268,
0.048467006534338,
-0.028405925258994102,
-0.02480187825858593,
-0.006914820056408644,
0.018967822194099426,
0.07793624699115753,
0.018200239166617393,
0.014037936925888062,
-0.06527610123157501,
0.017094561830163002,
0.004045288544148207,
0.03614602982997894,
-0.004526123404502869,
0.003903514239937067,
-0.011783426627516747,
-0.005322069860994816,
-0.038102153688669205,
0.004580316599458456,
0.016772514209151268,
0.006824089679867029,
-0.027331046760082245,
0.0011993872467428446,
0.021968983113765717,
0.013203135691583157,
-0.038598280400037766,
0.061514124274253845,
-0.03413258492946625,
-0.004788367077708244,
-0.032719239592552185,
0.037734802812337875,
0.02873079851269722,
-0.003338760929182172,
-0.019434945657849312,
-0.04571429640054703,
-0.02699795924127102,
0.0031275865621864796,
0.010228535160422325,
0.0068564945831894875,
-0.03689055144786835,
0.034217603504657745,
0.002293393248692155,
-0.023631196469068527,
0.02776784636080265,
0.013265011832118034,
0.07338204979896545,
0.03315814211964607,
0.05504930019378662,
-0.013995693065226078,
0.07394029200077057,
-0.013634265400469303,
-0.04682077094912529,
0.10184347629547119,
0.02776222489774227,
0.0005871538305655122,
0.021426323801279068,
-0.0044196052476763725,
-0.01236351951956749,
0.05351097881793976,
0.013171091675758362,
-0.02312491647899151,
0.004997260868549347,
0.006723709870129824,
-0.0366562083363533,
0.00925865676254034,
-0.025167401880025864,
-0.024310704320669174,
0.020681193098425865,
0.010664339177310467,
-0.0009538614540360868,
-0.013399552553892136,
-0.011633736081421375,
0.031060541048645973,
0.010921086184680462,
-0.0465560108423233,
-0.03895646706223488,
0.0027742229867726564,
0.0074971686117351055,
0.03446637839078903,
0.011759515851736069,
0.0026999199762940407,
0.0006383916479535401,
0.011172941885888577,
0.017939724028110504,
0.01261158287525177,
-0.006187539082020521,
-0.011014647781848907,
-0.08738930523395538,
-0.0004129410954192281,
0.013815043494105339,
-0.030819494277238846,
0.028997771441936493,
-0.030267959460616112,
-0.02401132322847843,
-0.011973608285188675,
-0.0024678008630871773,
-0.010769891552627087,
-0.0011985934106633067,
0.015046795830130577,
0.010467088781297207,
-0.035134486854076385,
0.002004866721108556,
0.06034670025110245,
0.00372240855358541,
-0.06450339406728745,
0.005137535277754068,
-0.03914814814925194,
-0.03025742806494236,
-0.008003388531506062,
0.0035193574149161577,
-0.012525695376098156,
-0.03409000113606453,
0.0020499920938163996,
0.04712018370628357,
0.004876097198575735,
-0.003993422724306583,
0.09418335556983948,
0.047837477177381516,
-0.02597332000732422,
-0.07159672677516937,
0.010348529554903507,
-0.011623518541455269,
0.022999867796897888,
-0.040950898081064224,
-0.015965528786182404,
-0.01413000002503395,
-0.01776611991226673,
-0.0003007928316947073,
0.04507354274392128,
0.03579292073845863,
-0.05807651951909065,
0.061603423207998276,
-0.0368911437690258,
-0.037387873977422714,
0.04624069109559059,
-0.02696560136973858,
-0.04658932238817215,
-0.08381272852420807,
-0.04116148501634598,
-0.03003181330859661,
-0.06839984655380249,
0.006257269531488419,
-0.017966557294130325,
0.03198561444878578,
0.011367457918822765,
0.007725253701210022,
0.07399265468120575,
0.008358104154467583,
-0.055212847888469696,
-0.07101907581090927,
0.0407191701233387,
-0.026247700676321983,
-0.014409318566322327,
0.001017533941194415,
-0.01031200960278511,
-0.024750834330916405,
0.015561746433377266,
0.007948527112603188,
0.03515344485640526,
0.018692314624786377,
0.002516712760552764,
-0.02814914472401142,
0.07490837574005127,
-0.03688027709722519,
0.01769096590578556,
-0.02765621803700924,
-0.015799419954419136,
-0.01799871027469635,
0.0027495548129081726,
0.04640134051442146,
0.08235523104667664,
-0.08938804268836975,
-0.014604000374674797,
0.03500693663954735,
0.055448971688747406,
0.04047870635986328,
0.021573279052972794,
-0.002137748757377267,
0.029383337125182152,
-0.014489229768514633,
-0.0922556072473526,
-0.01100509986281395,
0.04100652039051056,
-0.015317077748477459,
0.01144783478230238,
-0.010802941396832466,
0.09199865162372589,
-0.006073445547372103,
0.04402182623744011,
-0.0020358178298920393,
-0.035373710095882416,
-0.05789954215288162,
-0.00763415964320302,
-0.05199609324336052,
-0.01793542318046093,
0.012120943516492844,
-0.009893764741718769,
0.0413365513086319,
0.05951307341456413,
0.0212052371352911,
0.029090769588947296,
-0.010291370563209057,
0.022121096029877663,
-0.049472127109766006,
-0.02146347612142563,
0.008133675903081894,
-0.042401086539030075,
0.018312156200408936,
-0.005229623056948185,
0.02290479652583599,
-0.01733338087797165,
-0.04192632436752319,
0.007964682765305042,
-0.00736254220828414,
-0.0748620554804802,
-0.030464105308055878,
0.0323333814740181,
0.021173078566789627,
0.01510670967400074,
0.052281033247709274,
0.008716602809727192,
-0.012729751877486706,
-0.028300240635871887,
-0.010385462082922459,
-0.08570370078086853,
0.05279787257313728,
-0.038880959153175354,
-0.038640618324279785,
0.021028080955147743,
0.034318190068006516,
-0.017574260011315346,
-0.013409556820988655,
-0.03688707947731018,
0.003971406724303961,
0.016818363219499588,
-0.029743455350399017,
-0.047062452882528305,
-0.01763167604804039,
0.03349391371011734,
-0.002276803832501173,
0.04796984791755676,
0.002916092984378338,
-0.01287730410695076,
0.018884195014834404,
-0.03293626382946968,
-0.06894651055335999,
-0.0355803556740284,
0.019893767312169075,
-0.05134594812989235,
-0.0310758538544178,
0.003154227277263999,
0.05777612328529358,
-0.017127517610788345,
0.02733735553920269,
-0.007217559963464737,
0.00011384263052605093,
-0.01811458170413971,
0.043391551822423935,
-0.03999514877796173,
-0.03041902743279934,
-0.03273308277130127,
-0.027200423181056976,
0.015114310197532177,
-0.08856357634067535,
-0.05368822440505028,
0.024789873510599136,
-0.028640402480959892,
0.008382264524698257,
-0.03176019713282585,
-0.007060164585709572,
-0.03622504696249962,
0.0007094153552316129,
0.04526001960039139,
-0.02480360120534897,
-0.04713613539934158,
0.004166032187640667,
-0.02804124355316162,
0.017821891233325005,
-0.007412136998027563,
0.010837596841156483,
-0.001443434040993452,
0.008956793695688248,
0.022813230752944946,
0.058994781225919724,
-0.004524029325693846,
-0.010759612545371056,
0.02946329116821289,
0.049937814474105835,
-0.09183128923177719,
0.01686694473028183,
0.06318432837724686,
-0.01018615160137415,
0.010684936307370663,
0.03837613761425018,
-0.0269619170576334,
0.019060825929045677,
-0.024267757311463356,
0.0762522742152214,
0.05235392227768898,
-0.006999203935265541,
-0.03304945304989815,
-0.04651140049099922,
0.016402093693614006,
-0.04475853964686394,
-0.02770966663956642,
-0.00011981742136413231,
-0.018074406310915947,
0.05307791754603386,
-0.04348514974117279,
-0.03909961134195328,
-0.03238248825073242,
0.0553615465760231,
0.05168237164616585,
-0.020221415907144547,
-0.031290534883737564,
-0.05947500467300415,
0.019384972751140594,
-0.05356733128428459,
0.07837101817131042,
0.02376255951821804,
-0.036942459642887115,
-0.0923607274889946,
-0.03639404848217964,
-0.009939479641616344,
0.029429437592625618,
0.016362115740776062,
-0.01846545934677124,
0.06092233583331108,
-0.07551733404397964,
-0.010523252189159393,
-0.015025309287011623,
-0.0026742692571133375,
0.023723306134343147,
-0.007428969722241163,
-0.04857192561030388,
-0.06397990882396698,
0.012378779239952564,
0.032152820378541946,
-0.025399096310138702,
-0.01358632743358612,
-0.02506367489695549,
-0.015173233114182949,
0.028692109510302544,
-0.030696367844939232,
-0.024646257981657982,
0.053978435695171356,
0.010417434386909008,
0.03545629233121872,
-0.0026393753942102194,
0.04579169303178787,
0.03837034851312637,
0.003889016807079315,
0.046488042920827866,
0.033764567226171494,
-0.024474531412124634,
-0.040996089577674866,
0.0350218191742897,
0.03875292092561722,
-0.06146015599370003,
-0.037981968373060226,
-0.011634846217930317,
0.07302433252334595,
0.08347678929567337,
-0.047356151044368744,
-0.07827671617269516,
0.022358018904924393,
0.038945458829402924,
0.016822006553411484,
0.027931589633226395,
-0.022929083555936813,
-0.016715722158551216,
0.012509523890912533,
-0.004692927934229374,
0.043373897671699524,
-0.02082790620625019,
0.027142494916915894,
0.06517808139324188,
0.043134283274412155,
0.03133322298526764,
0.016070561483502388,
-0.02654087357223034,
-0.015022953040897846,
-0.056701526045799255,
0.023870889097452164,
0.008283828385174274,
0.005439965054392815,
-0.0439404658973217,
0.02476605400443077,
0.01475242804735899,
-0.036966267973184586,
0.08761308342218399,
-0.04267007112503052,
-0.0215524323284626,
0.1012636348605156,
-0.01623404771089554,
-0.06742642819881439,
-0.014515050686895847,
-0.0026326943188905716,
0.02598416805267334,
0.03929758071899414,
0.05113312974572182,
0.0008746792445890605,
0.01720902882516384,
-0.0463927797973156,
-0.006817348767071962,
-0.015034579671919346,
0.06348852068185806,
0.030175598338246346,
0.012843574397265911,
-0.002078764606267214,
0.005566008854657412,
-0.012060846202075481,
0.0021648884285241365,
-0.06342455744743347,
0.017543960362672806,
0.05409165844321251,
-0.004933093674480915,
0.004761574789881706,
0.05813809111714363,
0.041047874838113785,
0.038306813687086105,
-0.008456382900476456,
-0.00008679259190103039,
0.019144520163536072,
0.008479640819132328,
-0.035626742988824844,
0.03871205076575279,
0.04762705788016319,
-0.06394310295581818,
-0.005864755250513554,
-0.0485512875020504,
0.04141606390476227,
-0.031167887151241302,
0.0562594011425972,
0.06617052108049393,
0.01836339384317398,
0.00857018306851387,
0.04633765667676926,
0.03571653366088867,
-0.05053006485104561,
-0.06257698684930801,
0.0036825244314968586,
-0.03812352567911148,
0.015632521361112595,
-0.05107194185256958,
-0.003772718133404851,
-0.029013458639383316,
0.012518556788563728,
0.012838272377848625,
-0.02368178963661194,
-0.026342466473579407,
0.04642248526215553,
0.059367187321186066,
0.057839859277009964,
-0.05178961157798767,
-0.01218557357788086,
-0.016905363649129868,
0.03745846450328827,
0.014210189692676067,
-0.04888823255896568,
-0.04077600687742233,
0.036472104489803314,
-0.0907273218035698,
-0.01958218775689602,
0.0606047622859478,
0.009237022139132023,
0.025113314390182495,
-0.07113660871982574,
0.05326976254582405,
-0.08711738139390945,
0.004298788961023092,
-0.038557957857847214,
-0.01039400789886713,
-0.04976022243499756,
0.011733408086001873,
-0.01146011520177126,
0.027077630162239075,
0.07752477377653122,
-0.01484941691160202,
0.023148255422711372,
-0.013789916411042213,
0.02229941077530384,
-0.06083760783076286,
0.019474491477012634,
0.0003985685470979661,
0.030937623232603073,
-0.002031763084232807,
-0.03675778955221176,
0.011250672861933708,
0.05726994574069977,
0.03493387624621391,
-0.05422505363821983,
0.012768101878464222,
0.046013932675123215,
-0.06801345199346542,
0.08793649077415466,
0.02643303945660591,
-0.04078790172934532,
0.025300098583102226,
0.0559050478041172,
0.05980189889669418,
-0.050901152193546295,
0.01907460018992424,
-0.025790872052311897,
0.004476104862987995,
-0.04158114641904831,
-0.014993964694440365,
0.008684308268129826,
0.024075962603092194,
-0.028785979375243187,
-0.028520449995994568,
0.06017255038022995,
0.0038082979153841734,
-0.07371994853019714,
-0.007007255218923092,
0.004181165713816881,
0.017727026715874672,
0.002120537217706442,
0.056991804391145706,
0.02747769095003605,
-0.005446908995509148,
-0.03294886276125908,
-0.03303925320506096,
0.03131552040576935,
0.03031357191503048,
0.014349247328937054,
-0.009325172752141953,
0.03782149776816368,
0.04722043126821518,
0.0417889840900898,
-0.015073081478476524,
0.016919784247875214,
0.021999135613441467,
0.03718883544206619,
-0.012623834423720837,
0.036413416266441345,
0.0227533970028162,
0.058710623532533646,
-0.045331135392189026,
-0.02284705638885498,
0.03313960134983063,
0.04724757373332977,
-0.029839253053069115,
0.034094810485839844,
-0.0026734345592558384,
0.025772154331207275,
-0.00687998253852129,
-0.013051122426986694,
0.02782648243010044,
0.0017032725736498833,
0.007919196970760822,
-0.0521974191069603,
-0.004840398207306862,
0.0015520635060966015,
-0.037291381508111954,
0.004890372045338154,
0.05389966443181038,
0.010936437174677849,
0.02848808281123638,
0.01516793854534626,
-0.021539734676480293,
-0.021260077133774757,
-0.022684725001454353,
0.018664246425032616,
-0.03931441903114319,
0.01698085106909275,
0.031595855951309204,
-0.0046850224025547504,
0.03517124429345131,
0.0366642065346241,
0.001564555917866528,
-0.002480503637343645,
-0.020832985639572144,
-0.005898859351873398,
0.04119442030787468,
0.03634241968393326,
-0.014959235675632954,
0.013684457167983055,
0.0105070685967803,
0.07206600904464722,
0.013884840533137321,
0.03132031857967377,
0.0008178060525096953,
0.01349135022610426,
-0.020678525790572166,
0.008947267197072506,
0.05380253493785858,
-0.02743799053132534,
-0.03932845965027809,
-0.040202949196100235,
0.04798236861824989,
-0.056047119200229645,
-0.03317319229245186,
0.040435999631881714,
0.030789384618401527,
0.033191997557878494,
-0.01956137828528881,
-0.01380235981196165,
0.02483545057475567,
-0.020304467529058456,
-0.0350855216383934,
0.024022528901696205,
-0.02089761383831501,
-0.009344849735498428,
-0.03265171870589256,
-0.02799726091325283,
-0.0031936615705490112,
-0.01077026966959238,
-0.015320495702326298,
-0.06909360736608505,
0.06191706657409668,
0.07032415270805359,
0.014123218134045601,
0.040751680731773376,
0.018443595618009567,
-0.03573986515402794,
-0.008084469474852085,
-0.07083013653755188,
-0.006673020776361227,
0.06674303114414215,
-0.014581493102014065,
0.04301055520772934,
0.03484468162059784,
-0.002336045727133751,
-0.010015804320573807,
-0.017498845234513283,
0.03156198933720589,
0.05827520787715912,
-0.04331948608160019,
0.05128670111298561,
0.02860558219254017,
-0.033196769654750824,
-0.0076003773137927055,
0.04384523257613182,
-0.04678823798894882,
-0.005091068334877491,
0.0408233143389225,
0.02700771763920784,
-0.02902703918516636,
-0.03646794706583023,
0.03445828706026077,
-0.031895969063043594,
-0.08988429605960846,
-0.03721983730792999,
0.020216459408402443,
-0.021954229101538658,
-0.0632723942399025,
0.020766347646713257,
0.02546653337776661,
0.00048586539924144745,
-0.016066009178757668,
0.028455199673771858,
0.00990664679557085,
-0.07470965385437012,
-0.02055579423904419,
0.022883350029587746,
0.02282317727804184,
-0.01649298332631588,
0.031623635441064835,
0.0031067344825714827,
-0.015726398676633835,
-0.037596963346004486,
0.017438726499676704,
-0.03148337081074715,
-0.002874503843486309,
0.01468823105096817,
0.031207015737891197,
0.03492211923003197,
-0.04810328036546707,
0.013994400389492512,
-0.020590536296367645,
0.025483455508947372,
-0.0023468914441764355,
-0.048397358506917953,
-0.05475917086005211,
0.058768030256032944,
0.05099949985742569,
0.0012544328346848488,
-0.032800137996673584,
-0.051468972116708755,
-0.010453424416482449,
-0.04070083796977997,
-0.04137781262397766,
-0.026460113003849983,
0.01160688791424036,
-0.01846248470246792,
-0.017832687124609947,
-0.009186506271362305,
-0.05355062335729599,
0.006242294330149889,
-0.005597414914518595,
-0.005267091561108828,
0.052919674664735794,
0.03245675936341286,
0.022419743239879608,
0.022992193698883057,
0.03553178161382675,
-0.008462381549179554,
0.06123672425746918,
0.03579280152916908,
-0.03265409544110298,
-0.028129348531365395,
0.07356590032577515,
-0.013970481231808662,
-0.02136000618338585,
0.03385261446237564,
0.014949955977499485,
-0.012676786631345749,
0.055229976773262024,
-0.023712651804089546,
-0.024266377091407776,
0.04501637443900108,
-0.017732450738549232,
-0.01924215815961361,
-0.03396686911582947,
-0.03702545538544655,
0.01651693321764469,
-0.005727234296500683,
0.03764702379703522,
0.0019238847307860851,
-0.005162159446626902,
0.03028167597949505,
0.025577671825885773,
-0.00186168251093477,
-0.043809570372104645,
-0.004842853173613548,
-0.04339000582695007,
0.044774431735277176,
-0.06853696703910828,
0.018833745270967484,
0.032837092876434326,
0.006078597158193588,
0.0016586175188422203,
0.03322092816233635,
0.0056647188030183315,
-0.007786923553794622,
-0.01845119707286358,
-0.024775322526693344,
-0.08281229436397552,
-0.04604858532547951,
-0.1155562624335289,
-0.03183059021830559,
0.007142894435673952,
0.017154967412352562,
-0.03580966219305992,
0.02396007999777794,
-0.029777957126498222,
-0.0133269764482975,
0.04693128541111946,
-0.050124023109674454,
0.020966188982129097,
0.030648602172732353,
0.011622746475040913,
0.0651189386844635,
-0.01983065903186798,
0.01679484359920025,
-0.010158785618841648,
-0.005935944616794586,
-0.017116179689764977,
-0.06502490490674973,
-0.02937425673007965,
0.023311616852879524
] |
<p>At a very basic level I know that gravity isn't generated by mass but rather the <a href="https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor">stress-energy tensor</a> and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ is the source of gravity.</p>
<p>If the total energy of a particle contributes to the generation of a gravitational field, that seems to imply some strange things. For example, you could accelerate a particle like an electron to such a high velocity that it has enough momentum / kinetic energy to collapse into a black hole. An observer traveling with the electron would see an electron and stationary observers would see an arbitrarily massive black hole flying by. These observations seem to be contradictory. The same would be true of an extremely high energy photon.</p>
<p>Another consequence is that a stationary particle could appear to have so much mass that it could attract / deflect the trajectory of a rapidly moving observer. It seems odd that at low velocities you wouldn't even notice a stationary electron as you pass it by but at high velocities the gravitational field you observe could be significant enough to alter your path.</p>
<p>Am I correct that non-mass-energy generates a gravitational field? If it does, how are these strange observations like a particle looking like a black hole in one reference frame but not another reconciled?</p> | g112 | [
0.033588409423828125,
0.05586686730384827,
0.002957723569124937,
0.025953739881515503,
0.06725990027189255,
-0.0011802880326285958,
0.03438105434179306,
0.054189104586839676,
-0.04090006276965141,
-0.042173851281404495,
0.013316657394170761,
-0.014913144521415234,
0.04948379471898079,
-0.017160490155220032,
-0.03127776086330414,
0.0012261662632226944,
0.09584291279315948,
0.00050407147500664,
0.00917822401970625,
0.015979211777448654,
0.004746736027300358,
-0.013982835225760937,
0.04504181817173958,
-0.005011457949876785,
-0.04070227965712547,
0.025686513632535934,
0.04168175905942917,
-0.02660306729376316,
-0.029662776738405228,
-0.010718975216150284,
0.05897374078631401,
-0.005574912764132023,
0.03506726771593094,
-0.02040783129632473,
0.0065017626620829105,
0.01951536163687706,
0.05450865626335144,
0.0312771275639534,
0.0113492077216506,
0.014985890127718449,
-0.011390487663447857,
-0.058808133006095886,
-0.02268478088080883,
-0.03634481132030487,
-0.025984926149249077,
0.02932087332010269,
0.034605659544467926,
0.028920292854309082,
-0.004777288530021906,
-0.03740006685256958,
0.011118282563984394,
0.01543858740478754,
0.053885139524936676,
0.03361338749527931,
0.02874903380870819,
0.062314800918102264,
-0.009854723699390888,
0.021772243082523346,
0.04826652631163597,
0.0003770271723624319,
0.021071748808026314,
-0.030384115874767303,
0.005691806320101023,
0.044982992112636566,
0.005367905832827091,
-0.039942868053913116,
-0.05497519299387932,
0.0023635372053831816,
-0.015405560843646526,
0.02012701891362667,
0.028898054733872414,
-0.017438368871808052,
-0.031235821545124054,
0.018642932176589966,
0.023806193843483925,
-0.018929386511445045,
-0.008879385888576508,
0.0088929058983922,
-0.026966191828250885,
-0.04100984334945679,
0.03892647475004196,
-0.02285171113908291,
0.007507891859859228,
-0.0014315348817035556,
0.11600595712661743,
-0.0660032108426094,
-0.005210215225815773,
0.019377326592803,
-0.00624761451035738,
0.023857491090893745,
0.026568863540887833,
0.011358417570590973,
0.0930197462439537,
0.02593941241502762,
-0.05672820657491684,
-0.007351506967097521,
-0.03198504447937012,
0.08987963199615479,
-0.011584111489355564,
-0.016317345201969147,
-0.015407864935696125,
0.03320568799972534,
0.014734816737473011,
0.04037480056285858,
0.022590015083551407,
-0.0433720164000988,
-0.05775712430477142,
0.039659518748521805,
0.05225659906864166,
-0.00644549960270524,
-0.014079608023166656,
-0.01479149516671896,
0.013967414386570454,
-0.03594832494854927,
-0.08426866680383682,
-0.038785628974437714,
0.041298892349004745,
0.005334653425961733,
-0.0032873377203941345,
0.09672100096940994,
-0.0005002738907933235,
0.0069584473967552185,
-0.05424773320555687,
0.05016355589032173,
-0.03700323402881622,
-0.038619380444288254,
-0.0007783654727973044,
0.0024629575200378895,
0.030760621652007103,
-0.03252202644944191,
0.004337531980127096,
-0.05002683028578758,
-0.008236547000706196,
0.017990369349718094,
0.007273388095200062,
0.01173577643930912,
-0.0033352288883179426,
0.01627415418624878,
-0.041591595858335495,
0.04357084259390831,
-0.03457621484994888,
-0.029841072857379913,
-0.02568938583135605,
-0.047728098928928375,
-0.020945677533745766,
0.025555085390806198,
-0.01191393006592989,
-0.011212659068405628,
0.046856291592121124,
0.04938049614429474,
-0.00895218551158905,
0.02011091634631157,
-0.031977616250514984,
-0.036223214119672775,
0.07713627815246582,
0.03937568888068199,
-0.03083532303571701,
-0.0276452898979187,
-0.02982625924050808,
-0.0005547159817069769,
0.10033722221851349,
-0.058429352939128876,
0.08294574171304703,
0.018704917281866074,
-0.004666613414883614,
-0.02060912922024727,
0.024564417079091072,
-0.02498115971684456,
0.04928864911198616,
-0.0015669274143874645,
-0.036521222442388535,
-0.012286974117159843,
0.012432372197508812,
0.07724834233522415,
-0.0383828729391098,
-0.01609165221452713,
0.026589233428239822,
-0.005077224224805832,
0.05655257776379585,
-0.01859639212489128,
-0.023731468245387077,
-0.028346415609121323,
0.03602303937077522,
-0.06494128704071045,
0.040612488985061646,
-0.020930198952555656,
-0.0020457154605537653,
0.047775015234947205,
-0.05810340866446495,
0.07270421087741852,
-0.05888313427567482,
-0.010950821451842785,
0.01020677387714386,
0.06439369171857834,
-0.006254993379116058,
0.04330413043498993,
0.006528371013700962,
-0.005751100834459066,
-0.03473009169101715,
0.05270141735672951,
-0.036235954612493515,
0.01495908759534359,
-0.033798519521951675,
-0.022605419158935547,
0.017492761835455894,
0.015204684808850288,
-0.010441887192428112,
0.003452153643593192,
-0.0016389141092076898,
-0.06025463715195656,
0.02919699437916279,
-0.04969938471913338,
0.018326010555028915,
0.04462140053510666,
-0.007639216259121895,
0.03177597373723984,
-0.06402672827243805,
-0.010339869186282158,
0.010822959244251251,
-0.011701901443302631,
0.004612972028553486,
-0.02332199364900589,
0.0405077189207077,
-0.010119435377418995,
-0.02034803107380867,
0.039963554590940475,
-0.10401000082492828,
-0.08854123204946518,
-0.004805936012417078,
-0.013152720406651497,
-0.028865261003375053,
0.06550292670726776,
0.013180925510823727,
0.015490214340388775,
0.028212789446115494,
-0.01608167216181755,
0.01646864414215088,
-0.04138616472482681,
0.030601678416132927,
0.004300027620047331,
0.023098139092326164,
-0.048324499279260635,
-0.0247176606208086,
-0.06960279494524002,
0.02851296029984951,
-0.014553379267454147,
0.06527547538280487,
0.0038910210132598877,
0.016234248876571655,
-0.008463457226753235,
0.03409377485513687,
-0.04736639931797981,
-0.0385441780090332,
0.015305961482226849,
0.031807515770196915,
-0.037051741033792496,
-0.023097345605492592,
0.04741533845663071,
-0.07245530933141708,
-0.015451855026185513,
0.02428744174540043,
-0.00475268391892314,
-0.009840715676546097,
0.022446127608418465,
-0.04619689658284187,
-0.012869998812675476,
0.020856346935033798,
-0.04371793195605278,
-0.02430807799100876,
0.015105466358363628,
-0.04622787609696388,
0.01883169263601303,
0.03658507019281387,
0.04121912270784378,
-0.015679320320487022,
-0.01959952898323536,
-0.025531435385346413,
0.05894061550498009,
0.03792697191238403,
-0.03719993680715561,
-0.0431264229118824,
0.001888541504740715,
-0.03208335489034653,
0.009030594490468502,
0.032248906791210175,
-0.08040589094161987,
-0.024814141914248466,
-0.0440339595079422,
-0.0275935847312212,
-0.013267581351101398,
-0.010402509942650795,
0.005272228736430407,
0.019604282453656197,
0.05413901433348656,
-0.03133830428123474,
-0.016800550743937492,
-0.011115644127130508,
-0.001471244147978723,
-0.029436428099870682,
0.021221155300736427,
-0.0347515344619751,
-0.0047810738906264305,
0.004171879030764103,
0.04717370495200157,
-0.011675281450152397,
0.009989134036004543,
-0.06053602322936058,
-0.07552966475486755,
0.006944242399185896,
-0.006575155071914196,
-0.01872597075998783,
0.02388129197061062,
-0.016672197729349136,
0.05803978070616722,
-0.027698371559381485,
0.008960803039371967,
-0.021781668066978455,
-0.015941105782985687,
-0.021950436756014824,
-0.03439603000879288,
0.01084228977560997,
-0.0020661242306232452,
0.008741825819015503,
0.003454364137724042,
0.05198429524898529,
0.050261735916137695,
0.036577027291059494,
-0.015872517600655556,
-0.06828679144382477,
-0.037169188261032104,
0.019490428268909454,
-0.09244780242443085,
-0.0728997066617012,
0.04003407806158066,
-0.03110021911561489,
-0.03886357322335243,
-0.0007869717082940042,
-0.0006426811451092362,
0.09222947806119919,
0.012505793012678623,
0.032267238944768906,
0.04104525223374367,
-0.07427810877561569,
-0.0031672464683651924,
0.0019415916176512837,
0.0342734232544899,
-0.014865745790302753,
-0.04320120811462402,
0.008248044177889824,
-0.056413162499666214,
0.035991840064525604,
0.012166536413133144,
0.03802609071135521,
0.008689007721841335,
-0.006270904093980789,
-0.00713110389187932,
0.012463792227208614,
-0.003464293200522661,
-0.005176092963665724,
-0.011810654774308205,
-0.02797291800379753,
-0.00893257837742567,
0.04804309085011482,
0.040551744401454926,
-0.003868703730404377,
0.0022110100835561752,
-0.024751707911491394,
-0.022918086498975754,
0.033927686512470245,
-0.03520163521170616,
-0.007993505336344242,
-0.03351676091551781,
0.008363286033272743,
0.0006783040007576346,
-0.010904176160693169,
0.0015643315855413675,
0.08320330083370209,
-0.03667210415005684,
-0.018104754388332367,
-0.030345825478434563,
0.02443668805062771,
-0.009330827742815018,
0.040211305022239685,
-0.025926142930984497,
0.059162843972444534,
-0.007004069164395332,
-0.052426163107156754,
-0.022760439664125443,
0.029000544920563698,
-0.03188828006386757,
-0.013654613867402077,
-0.09039965271949768,
-0.010087736882269382,
-0.04681375250220299,
0.007887662388384342,
-0.012287057936191559,
0.02887873724102974,
-0.02144590951502323,
0.10924649983644485,
0.0142140444368124,
0.016580188646912575,
0.06383699923753738,
-0.010788160376250744,
0.015718290582299232,
0.0023316482547670603,
0.02860196679830551,
0.037182312458753586,
-0.05424986034631729,
-0.03876297175884247,
-0.04326741397380829,
0.061174437403678894,
0.01702258363366127,
0.0019838062580674887,
-0.0539061613380909,
-0.020190762355923653,
-0.011022836901247501,
-0.0032746242359280586,
0.010247435420751572,
0.04153119772672653,
0.024478750303387642,
0.045360635966062546,
-0.01826455257833004,
0.060237545520067215,
-0.014225362800061703,
-0.02990982122719288,
0.11139466613531113,
0.0009392105275765061,
-0.012475471943616867,
-0.09267174452543259,
0.0330866202712059,
0.055251944810152054,
0.0407329760491848,
0.00020298735762480646,
0.015774698927998543,
-0.022721074521541595,
0.05520755052566528,
-0.0015273792669177055,
0.010603945702314377,
0.00425148569047451,
0.0010665747104212642,
0.08526374399662018,
0.02780281752347946,
-0.00885410513728857,
-0.03694583475589752,
0.005206339526921511,
0.011898146010935307,
-0.057460419833660126,
-0.01775633729994297,
-0.05042046681046486,
-0.022240426391363144,
-0.012716532684862614,
-0.017446262761950493,
0.005743039306253195,
-0.02268032170832157,
0.035187896341085434,
-0.03416981175541878,
-0.05082952603697777,
0.029726732522249222,
-0.05111701041460037,
0.009998754598200321,
-0.09926940500736237,
-0.01212633028626442,
0.08087805658578873,
0.05948467552661896,
-0.039779502898454666,
-0.03570017218589783,
-0.06161556392908096,
-0.03777327761054039,
-0.020439008250832558,
-0.04289921373128891,
-0.07971435785293579,
0.04480203613638878,
-0.011670289561152458,
-0.024634424597024918,
0.012771137990057468,
0.002172961598262191,
-0.02933061495423317,
-0.014768225140869617,
-0.0028172058518975973,
-0.04582285135984421,
0.01182764396071434,
0.01237618550658226,
0.04574330523610115,
0.018898559734225273,
0.023783687502145767,
0.01675681583583355,
-0.04116155579686165,
0.0732957273721695,
0.011306117288768291,
-0.051833152770996094,
0.013828396797180176,
0.029182707890868187,
-0.007360740099102259,
-0.032162319868803024,
-0.004674449563026428,
0.012657662853598595,
0.05339338257908821,
-0.0076103247702121735,
-0.012031967751681805,
-0.002574721584096551,
-0.06646523624658585,
0.003051708685234189,
-0.01635526306927204,
0.02040373906493187,
0.027514392510056496,
0.0015049814246594906,
0.04046925902366638,
-0.030751043930649757,
0.060861460864543915,
0.04795989394187927,
-0.04586684703826904,
0.015561242587864399,
-0.04900895804166794,
0.01191397849470377,
0.027617743238806725,
-0.02680295519530773,
0.019833512604236603,
-0.021327434107661247,
-0.003584683407098055,
-0.004046736750751734,
0.07259626686573029,
-0.06817673146724701,
0.04518452286720276,
0.005825945176184177,
0.02018839865922928,
0.023204177618026733,
-0.034476906061172485,
0.014266341924667358,
0.01713022217154503,
0.05357946455478668,
0.038438864052295685,
-0.062070462852716446,
0.04733547940850258,
-0.008469303138554096,
-0.02424996718764305,
-0.03027443028986454,
0.030403289943933487,
0.003879375057294965,
0.027470622211694717,
-0.005908808670938015,
-0.02281487174332142,
-0.0615793839097023,
0.003938797861337662,
0.058599818497896194,
0.011653999797999859,
0.011245652101933956,
0.004455043468624353,
0.00523271132260561,
0.021398063749074936,
-0.0576065257191658,
-0.017315024510025978,
0.05397752672433853,
0.039886441081762314,
0.025338726118206978,
-0.012792197987437248,
0.030611325055360794,
-0.008627323433756828,
-0.020233670249581337,
-0.0686904713511467,
-0.07426036894321442,
0.016458500176668167,
0.025713186711072922,
0.026155032217502594,
-0.011298653669655323,
0.04833132401108742,
0.0270383358001709,
-0.014709815382957458,
-0.05540265142917633,
-0.014839716255664825,
0.011857680976390839,
0.03571682423353195,
0.06567314267158508,
0.013863922096788883,
-0.02543739229440689,
-0.011344227008521557,
0.022145966067910194,
0.00825820304453373,
0.026716485619544983,
-0.06372112035751343,
-0.028831960633397102,
0.0018706034170463681,
-0.03208667412400246,
0.033950578421354294,
-0.046939074993133545,
-0.02606618031859398,
0.005243133753538132,
-0.05431846156716347,
0.05781649425625801,
0.015867894515395164,
0.0038302186876535416,
-0.020742451772093773,
-0.004778882022947073,
0.009349708445370197,
0.0075583807192742825,
-0.044756922870874405,
-0.043885234743356705,
-0.015349783934652805,
-0.027754444628953934,
-0.009505300782620907,
-0.026638086885213852,
-0.014141809195280075,
0.04436196759343147,
0.019055595621466637,
-0.02953360229730606,
0.008081083185970783,
0.03678390756249428,
-0.059868380427360535,
-0.001019708113744855,
0.006555544212460518,
0.013183592818677425,
-0.011331554502248764,
0.012559536844491959,
0.006218593567609787,
0.016107389703392982,
-0.039222944527864456,
-0.012031483463943005,
-0.09482226520776749,
0.008123788982629776,
-0.020031051710247993,
-0.03608221188187599,
-0.005671448074281216,
0.0048352619633078575,
-0.0014255723217502236,
-0.049118369817733765,
0.04575636237859726,
0.02481558732688427,
-0.043317485600709915,
0.08630508184432983,
0.0780126079916954,
-0.02689794823527336,
-0.013529390096664429,
0.02432183176279068,
-0.05962144955992699,
0.028990156948566437,
-0.007117444183677435,
0.01745893619954586,
-0.03193230181932449,
0.048039842396974564,
0.061000943183898926,
-0.02628317102789879,
0.027087312191724777,
-0.017389411106705666,
0.02868230827152729,
0.002481939736753702,
-0.054524295032024384,
0.0500972755253315,
-0.008821512572467327,
0.037184711545705795,
-0.0409342423081398,
-0.025739235803484917,
-0.031273309141397476,
-0.06916950643062592,
0.007066820282489061,
0.007036228198558092,
-0.003150015836581588,
0.03722565993666649,
-0.019640624523162842,
0.006261097267270088,
0.029686132445931435,
-0.10060135275125504,
-0.027639521285891533,
0.04447087273001671,
-0.02119932696223259,
-0.002890079515054822,
0.011735697276890278,
0.03501946106553078,
-0.030392076820135117,
-0.04117272421717644,
-0.022466110065579414,
0.02482922375202179,
0.03284085914492607,
-0.04781732335686684,
-0.056074026972055435,
0.02536677196621895,
-0.05867009609937668,
-0.043658170849084854,
-0.027816204354166985,
0.024161767214536667,
0.00882915873080492,
0.02511785551905632,
0.0017675634007900953,
0.02589418552815914,
0.02379011921584606,
0.059305205941200256,
-0.01046599168330431,
-0.012350642122328281,
-0.03451354429125786,
0.052768830209970474,
-0.01989801414310932,
0.019291028380393982,
-0.05272874981164932,
0.012255262583494186,
0.03453193977475166,
0.020916782319545746,
-0.023121332749724388,
-0.024434061720967293,
0.04332296550273895,
0.027226200327277184,
0.05432348698377609,
-0.000013522668268706184,
-0.02530941367149353,
0.016689358279109,
-0.052839238196611404,
-0.02424239180982113,
0.03885454684495926,
0.032242801040410995,
0.057643625885248184,
-0.027617165818810463,
-0.04299016669392586,
0.019088445231318474,
0.02826664224267006,
-0.004031194839626551,
-0.04323970526456833,
-0.02331261709332466,
-0.021850096061825752,
-0.034502360969781876,
-0.016514645889401436,
0.04663529992103577,
-0.04081503301858902,
0.00969749316573143,
0.010888497345149517,
0.03906117007136345,
-0.009000633843243122,
-0.031035685911774635,
0.032816603779792786,
0.01657147705554962,
0.03208954259753227,
0.01834399253129959,
0.002233851468190551,
0.019546249881386757,
-0.045844610780477524,
-0.007274015340954065,
-0.004418655298650265,
-0.027124375104904175,
-0.020617051050066948,
0.01041070744395256,
0.03165126591920853,
0.010323493741452694,
0.0021826529409736395,
-0.020674290135502815,
0.03230646252632141,
-0.03815244510769844,
-0.007712843362241983,
-0.03784153237938881,
-0.0023986902087926865,
-0.0004828385717701167,
0.01917990855872631,
0.034893739968538284,
0.05572693049907684,
-0.010026293806731701,
0.038485653698444366,
0.02987755835056305,
-0.009564465843141079,
0.028465012088418007,
0.07426904886960983,
-0.07757798582315445,
-0.007017857860773802,
-0.006579073145985603,
-0.0701201930642128,
0.012047642841935158,
-0.005549798719584942,
-0.019318286329507828,
-0.012124618515372276,
-0.05104214325547218,
-0.039668358862400055,
-0.004870081786066294,
0.03657893091440201,
0.0413009449839592
] |
<p>In quantum electrodynamics, the classical Hamiltonian is obtained from the classical electromagnetic Lagrangian. Then the classical electric and magnetic fields are promoted to operators, as is the classical 4-vector potential $A_{\mu}$. The appropriate commutation relations are expected between the fields and their conjugate momenta.</p>
<p>Now, my question is, do the principles of quantum electrodynamics follow as a consequence of the fact that the charged particle producing the field is a quantum particle which must follow the principles of quantum mechanics?</p>
<p>Let me give a specific example. Consider a slow moving(for simplicity) free electron moving with a constant velocity initially.</p>
<p>Now, classically, the magnetic field at a point $P$ would be given by a function $\vec{B} = \vec{f}(\vec{r},\vec{x},\vec{p})$, where $\vec{r}$ is the position vector of the point at which the field is being 'measured' and $x$ and $p$ are the position and momenta of the charged particle evaluated at the retarded time.</p>
<p>Now, supposing I apply the principles of quantum mechanics to this electron and promote the above mentioned expression for the magnetic field at point $P$ to an operator by the usual quantum mechanical prescription. Would this prescription yield the correct values for the measured magnetic field at point $P$? Why? or Why not?</p>
<p>The bottom line of my entire question is whether the quantum field theory of an electron is a direct consequence of the fact that the particle producing the field is a quantum particle (and not a classical one) or does it involve much more than that?</p>
<p>EDIT: Thank you for your responses. I would also like to know if the above mentioned prescription for obtaining the magnetic field would yield accurate results for slow moving electrons(non-relativistic)?</p> | g9182 | [
0.0509641207754612,
-0.02536717616021633,
-0.011991756036877632,
-0.05087421089410782,
0.0802338495850563,
0.0183174517005682,
0.06493664532899857,
0.0034040005411952734,
0.0014524817233905196,
0.020469017326831818,
-0.025472594425082207,
0.030428236350417137,
-0.008829303085803986,
-0.006102049257606268,
-0.026909800246357918,
0.012982157059013844,
0.07972942292690277,
0.03207159414887428,
0.02776293084025383,
-0.0002845441922545433,
0.059222087264060974,
0.030975500121712685,
0.01933559961616993,
-0.01757696643471718,
-0.018728628754615784,
0.02827112190425396,
0.016332654282450676,
0.00011379625357221812,
0.04666357859969139,
0.0008860676898621023,
-0.014010661281645298,
-0.0016335932305082679,
0.03480026125907898,
-0.043687548488378525,
-0.01061246544122696,
-0.06570631265640259,
0.07012280076742172,
0.02690807543694973,
0.0017234787810593843,
-0.005397523287683725,
0.006505770608782768,
-0.02297423779964447,
0.007678843103349209,
0.010260378010571003,
0.03450154885649681,
-0.006145919673144817,
0.019012518227100372,
-0.030497169122099876,
-0.08513972163200378,
0.009129222482442856,
-0.00041001124191097915,
0.016605420038104057,
0.0328153632581234,
0.008330099284648895,
0.022575628012418747,
0.06196743622422218,
0.046791836619377136,
0.027790864929556847,
-0.004091238137334585,
0.037645258009433746,
0.03354863449931145,
0.028997346758842468,
0.027839604765176773,
-0.003969164565205574,
0.030779162421822548,
-0.019388355314731598,
-0.009879878722131252,
0.020664643496274948,
-0.033545736223459244,
0.036162834614515305,
-0.02307349257171154,
-0.11865964531898499,
-0.01419770810753107,
-0.020399142056703568,
0.025037135928869247,
0.036090172827243805,
0.008908959105610847,
-0.035717111080884933,
0.026884891092777252,
-0.056803423911333084,
-0.030321521684527397,
-0.04576409235596657,
0.01938578486442566,
0.024784406647086143,
0.06162630021572113,
-0.03142150118947029,
-0.001238485099747777,
0.01595117151737213,
0.052901491522789,
-0.0333833172917366,
0.00012458613491617143,
-0.02884938381612301,
0.03410091623663902,
0.03659269958734512,
-0.022158626466989517,
-0.05020862817764282,
-0.009510396048426628,
0.009364377707242966,
-0.031481705605983734,
0.014865100383758545,
-0.05677449330687523,
0.013399815186858177,
0.05387040972709656,
0.031488705426454544,
0.008632284589111805,
-0.04799147695302963,
0.06179778277873993,
0.018950795754790306,
0.040777888149023056,
-0.016157599166035652,
0.018951093778014183,
-0.04336133599281311,
0.006079495884478092,
-0.012142373248934746,
-0.09032510966062546,
-0.014269384555518627,
0.010448112152516842,
-0.01717485673725605,
-0.07186821103096008,
0.08197013288736343,
-0.00941943097859621,
0.0042818947695195675,
0.03178618475794792,
0.05534833297133446,
-0.03523578867316246,
0.012941821478307247,
-0.03831138089299202,
0.027057422325015068,
-0.018620077520608902,
0.03851401060819626,
-0.00550552224740386,
0.014762269333004951,
0.00018840072152670473,
0.049207597970962524,
-0.002225543837994337,
0.030113935470581055,
0.026749996468424797,
-0.0019214149797335267,
0.02034078538417816,
-0.01482551172375679,
0.05684898421168327,
-0.010825571604073048,
0.022249197587370872,
-0.05772044137120247,
-0.014989325776696205,
0.020417092368006706,
0.03462677448987961,
-0.04618426412343979,
0.048569776117801666,
0.06763732433319092,
-0.00725961709395051,
0.010709395632147789,
-0.013314916752278805,
0.03367943689227104,
0.05168582871556282,
0.03172619268298149,
0.008455498144030571,
0.007849523797631264,
0.004755225032567978,
-0.034174442291259766,
0.06287418305873871,
-0.02774631232023239,
0.04108720272779465,
0.03055804967880249,
0.01869232766330242,
-0.033663440495729446,
0.01755990833044052,
-0.03591679781675339,
0.015148581936955452,
-0.03273161128163338,
-0.02451545000076294,
0.019152583554387093,
-0.014042812399566174,
0.025757718831300735,
-0.021842358633875847,
0.052729032933712006,
-0.027506601065397263,
-0.0005398925859481096,
-0.03757694736123085,
-0.022556016221642494,
-0.050694167613983154,
-0.013407314196228981,
0.021842991933226585,
-0.026849782094359398,
-0.024569416418671608,
-0.015040291473269463,
-0.026154348626732826,
0.0616617314517498,
-0.04386281222105026,
-0.021535012871026993,
0.015433513559401035,
-0.02640531212091446,
-0.021893436089158058,
0.0356307178735733,
-0.04877734184265137,
-0.00017053524788934737,
-0.042321477085351944,
-0.048887286335229874,
-0.004862047731876373,
0.001362703274935484,
-0.018672732636332512,
0.0963374599814415,
0.016831913962960243,
-0.0028210440650582314,
0.02610657922923565,
-0.0023404008243232965,
-0.03861267492175102,
-0.01472395472228527,
0.045571643859148026,
-0.014623298309743404,
0.08497678488492966,
0.005006106570363045,
-0.026790784671902657,
0.012517357245087624,
-0.03961704298853874,
-0.08115021884441376,
-0.03604297712445259,
0.03674161806702614,
-0.016866719350218773,
0.0371270589530468,
-0.0786692425608635,
-0.03151943162083626,
0.05576138570904732,
-0.08133518695831299,
-0.03863295912742615,
0.013611841015517712,
-0.010184123180806637,
-0.022145727649331093,
-0.05413227900862694,
-0.00283653917722404,
-0.023218192160129547,
0.03125125169754028,
-0.03925159573554993,
-0.014022677205502987,
0.07490429282188416,
0.027997173368930817,
-0.026093631982803345,
-0.05314942076802254,
0.09705305844545364,
0.013854634948074818,
-0.012110559269785881,
0.019730886444449425,
0.008987260051071644,
-0.047773148864507675,
0.012475291267037392,
-0.046555034816265106,
0.06999009847640991,
-0.0044394670985639095,
-0.024052243679761887,
0.0015019540442153811,
0.023394068703055382,
-0.01239639613777399,
-0.03856777399778366,
0.010683894157409668,
0.049615636467933655,
-0.01081764791160822,
0.006902078166604042,
0.05485829338431358,
-0.005811368115246296,
-0.013423260301351547,
-0.010187214240431786,
0.06457178294658661,
-0.02430991269648075,
0.05082513019442558,
-0.0018668565899133682,
0.016803419217467308,
-0.01914513111114502,
0.06321796029806137,
0.013983462937176228,
-0.01671229489147663,
-0.06115645170211792,
0.027253320440649986,
0.005106783006340265,
-0.003023488214239478,
0.047909628599882126,
-0.04835336282849312,
-0.004659666214138269,
-0.021640053018927574,
0.01920253224670887,
-0.06891044229269028,
-0.010501970537006855,
-0.047670748084783554,
0.005033913999795914,
0.017690546810626984,
-0.025151679292321205,
-0.0540316104888916,
-0.026220671832561493,
-0.060282282531261444,
-0.018580466508865356,
0.028501473367214203,
-0.04304038733243942,
0.03407507762312889,
0.04339349642395973,
0.023074425756931305,
-0.044771257787942886,
-0.014216100797057152,
0.043657757341861725,
-0.021031493321061134,
-0.038951724767684937,
0.0629088506102562,
0.005796445999294519,
0.001983227673918009,
-0.04920575022697449,
0.036525215953588486,
0.07087289541959763,
0.030606132000684738,
-0.08015787601470947,
-0.0527426116168499,
0.014716651290655136,
-0.08608631789684296,
0.012249252758920193,
0.030032005161046982,
-0.040085140615701675,
0.0020035929046571255,
-0.03729642182588577,
-0.002743263728916645,
-0.017457053065299988,
0.016954798251390457,
0.07847639173269272,
0.020676571875810623,
-0.031842295080423355,
-0.0713893473148346,
-0.028965571895241737,
0.008721974678337574,
0.1111985594034195,
0.043414466083049774,
0.017508508637547493,
0.040071554481983185,
0.018708813935518265,
-0.005033532157540321,
0.01377005223184824,
-0.005169994663447142,
-0.009504650719463825,
0.030033079907298088,
-0.04325830936431885,
-0.015832388773560524,
0.04897911474108696,
0.001947601092979312,
0.024474289268255234,
0.007833272218704224,
0.012734541669487953,
-0.00435089785605669,
-0.08178508281707764,
0.026899108663201332,
0.007253605872392654,
-0.03550345450639725,
0.0012474990217015147,
-0.025185683742165565,
-0.03384864330291748,
-0.030874408781528473,
-0.014184749685227871,
-0.022630630061030388,
0.016775978729128838,
0.03174015134572983,
-0.043851397931575775,
0.007900923490524292,
0.06005408987402916,
0.01034212950617075,
0.009705343283712864,
-0.0037140094209462404,
-0.04301660507917404,
0.006066229194402695,
0.018546240404248238,
0.01667058654129505,
0.025197003036737442,
0.062398139387369156,
-0.016242943704128265,
0.006680329795926809,
0.04172205179929733,
-0.03168907016515732,
-0.04738783463835716,
-0.048800479620695114,
-0.019745921716094017,
0.06289349496364594,
-0.032162342220544815,
0.028949234634637833,
0.009994274005293846,
0.019375145435333252,
-0.09514516592025757,
-0.015407619066536427,
-0.012373363599181175,
0.06740301102399826,
-0.012227694503962994,
0.015314123593270779,
0.03253621235489845,
0.01231120340526104,
-0.0313696414232254,
0.03588467091321945,
-0.0021278318017721176,
-0.05101845785975456,
-0.03543554246425629,
-0.009870425797998905,
-0.016570860520005226,
0.027810579165816307,
0.017220759764313698,
0.04558182507753372,
0.024872994050383568,
-0.0383903905749321,
0.08107095211744308,
-0.03095763735473156,
-0.00693284859880805,
0.001226959633640945,
0.03669673204421997,
0.044939443469047546,
0.00764510128647089,
-0.05306313931941986,
0.07078608870506287,
-0.017057068645954132,
0.037096619606018066,
-0.06838317960500717,
-0.03255873918533325,
-0.05248524248600006,
-0.003975854720920324,
-0.017551060765981674,
-0.04219499230384827,
0.06160753220319748,
0.003992562647908926,
-0.05445897579193115,
0.00646737078204751,
-0.023222370073199272,
-0.010368366725742817,
0.00900998618453741,
0.07898633927106857,
-0.03814730420708656,
-0.03946805000305176,
0.08287110179662704,
0.052053362131118774,
-0.022638419643044472,
-0.04464024305343628,
-0.023325908929109573,
-0.013234343379735947,
0.02379080466926098,
0.018212687224149704,
-0.0027585334610193968,
-0.00901456642895937,
0.03346073627471924,
-0.09003379195928574,
0.030564097687602043,
0.03641263023018837,
-0.0004765073535963893,
0.04390504211187363,
0.0026629825588315725,
0.05841097608208656,
-0.025420309975743294,
-0.0759321004152298,
0.012247362174093723,
-0.0963912308216095,
0.00004961593003827147,
-0.025322655215859413,
-0.0700245201587677,
0.012493031099438667,
0.04859548807144165,
-0.02838253416121006,
0.011376296170055866,
-0.004235276952385902,
-0.06205638125538826,
-0.005727662239223719,
-0.06753924489021301,
0.002435321919620037,
-0.0032099366653710604,
-0.06009248271584511,
0.02468084916472435,
0.04294285550713539,
0.06025330722332001,
0.0246150940656662,
-0.010859774425625801,
-0.07812181115150452,
-0.012261273339390755,
-0.09669531881809235,
-0.04026446491479874,
0.016657255589962006,
-0.00016208762826863676,
-0.0019488092511892319,
-0.03500416874885559,
0.03316088020801544,
-0.030599182471632957,
0.008844339288771152,
-0.00398210808634758,
-0.01785586029291153,
-0.058290034532547,
0.004873007070273161,
-0.07488058507442474,
0.01106788869947195,
0.0032377305906265974,
-0.03906475007534027,
0.0021721755620092154,
-0.009836876764893532,
0.04142271727323532,
0.02632676064968109,
-0.04026256874203682,
0.06900125741958618,
0.00022488381364382803,
0.012293688952922821,
0.007932990789413452,
-0.0007906626560725272,
0.03474730625748634,
-0.012352046556770802,
0.008710023947060108,
-0.05116181820631027,
-0.02362830564379692,
-0.07911374419927597,
0.0102456733584404,
-0.027273908257484436,
0.05097479745745659,
-0.009274641051888466,
0.016719628125429153,
0.053959790617227554,
-0.044761624187231064,
-0.007725642062723637,
-0.053288403898477554,
0.01447601430118084,
0.004990788642317057,
0.02072603441774845,
0.013905776664614677,
0.020712392404675484,
0.033537570387125015,
-0.05386078357696533,
-0.00621518911793828,
0.007119753398001194,
-0.030221885070204735,
0.008318296633660793,
0.006012280471622944,
0.010632786899805069,
-0.04011671245098114,
0.011820463463664055,
0.009477240964770317,
-0.00407002167776227,
-0.009821838699281216,
0.00044646678725257516,
0.07788801193237305,
0.030049391090869904,
0.012510382570326328,
0.0482732392847538,
-0.014190887100994587,
-0.0024124300107359886,
-0.02853577770292759,
0.004574947524815798,
-0.029475754126906395,
-0.004165114369243383,
0.027422741055488586,
-0.00555614335462451,
-0.017889948561787605,
0.05286812782287598,
0.014056325890123844,
-0.014925244264304638,
0.0026181680150330067,
-0.03090687282383442,
0.034335508942604065,
0.042505573481321335,
-0.021076077595353127,
-0.03203678876161575,
0.007613913156092167,
-0.04320809617638588,
0.028688795864582062,
-0.025022590532898903,
0.036156319081783295,
-0.016742408275604248,
0.006703590974211693,
-0.040309127420186996,
-0.01217095647007227,
0.030978644266724586,
0.015706123784184456,
0.03071446157991886,
0.025016991421580315,
0.00009092605614569038,
0.036475829780101776,
0.04250076040625572,
-0.017504267394542694,
0.05298599600791931,
0.0448930487036705,
-0.010464445687830448,
0.04198789969086647,
0.01399522926658392,
0.00752310361713171,
0.016455939039587975,
0.03369370102882385,
-0.01354079507291317,
-0.03993184491991997,
-0.09641803801059723,
0.015643233433365822,
0.01690925657749176,
0.0010861821938306093,
-0.012323605827987194,
-0.06413672119379044,
-0.03766702115535736,
0.03346874937415123,
-0.012275324203073978,
0.020692627876996994,
0.008581179194152355,
0.08059459179639816,
0.0294868852943182,
0.0058751776814460754,
-0.021252097561955452,
0.046179406344890594,
-0.034076351672410965,
0.02002514898777008,
0.01709721051156521,
-0.05182572454214096,
-0.016469722613692284,
0.0749451220035553,
0.011254425160586834,
-0.016057560220360756,
-0.024150121957063675,
-0.03139050677418709,
0.01480918936431408,
0.04816555976867676,
-0.04312752187252045,
0.004824551288038492,
-0.0015263133682310581,
-0.04477587714791298,
0.009706440381705761,
-0.058584731072187424,
0.00014563264267053455,
0.008796891197562218,
-0.027174275368452072,
0.04785462096333504,
-0.012948105111718178,
0.05888175219297409,
-0.019241129979491234,
0.05516866594552994,
0.0005560140125453472,
0.008184828795492649,
-0.04821225255727768,
0.00031782727455720305,
-0.0023472944740206003,
0.050240784883499146,
-0.04414360597729683,
0.032416366040706635,
0.03613540530204773,
0.002084948355332017,
0.00612847413867712,
-0.01990278623998165,
-0.026763103902339935,
0.046683963388204575,
0.02567991055548191,
-0.04178806394338608,
0.035042904317379,
0.00948261097073555,
0.031468465924263,
0.019682154059410095,
-0.02596387453377247,
-0.005667232442647219,
0.03274998813867569,
-0.05433657765388489,
-0.08553088456392288,
-0.041196346282958984,
0.0038353109266608953,
0.051745932549238205,
-0.05143660306930542,
0.02670169435441494,
-0.004314928315579891,
0.005533609073609114,
-0.0072632646188139915,
0.002995908260345459,
0.03759823366999626,
-0.008667334914207458,
0.0304021704941988,
0.037666287273168564,
0.001782851992174983,
-0.05855606868863106,
-0.024407697841525078,
-0.03935430571436882,
-0.02588055655360222,
-0.04222298413515091,
0.009282552637159824,
-0.0077515216544270515,
-0.06136767566204071,
-0.03457511588931084,
-0.014182722195982933,
-0.020294757559895515,
0.01497096847742796,
-0.08450376242399216,
0.003598616225644946,
0.0525391660630703,
0.008285639807581902,
-0.014479122124612331,
0.006316601764410734,
0.07081132382154465,
-0.03545121103525162,
-0.003924978896975517,
-0.027057483792304993,
0.02543460577726364,
0.005981842987239361,
0.012690048664808273,
-0.047281499952077866,
-0.012784148566424847,
-0.06564661115407944,
-0.010132035240530968,
0.03391636535525322,
0.02421192079782486,
0.030445700511336327,
-0.055286020040512085,
0.005206618458032608,
-0.019480997696518898,
0.017104780301451683,
0.026723669841885567,
0.05568718537688255,
-0.013001660816371441,
0.027803590521216393,
0.016667263582348824,
-0.014341129921376705,
-0.019284389913082123,
-0.021761024370789528,
0.012974180281162262,
0.03757483512163162,
-0.021158624440431595,
0.023721283301711082,
-0.000437002454418689,
-0.08625662326812744,
0.06165888160467148,
0.006464812438935041,
0.01597530022263527,
0.02877381630241871,
-0.016707491129636765,
0.04147478565573692,
0.008126883767545223,
-0.0355115570127964,
0.06116454675793648,
-0.026778899133205414,
-0.009990707971155643,
0.008881228044629097,
0.010058050975203514,
-0.00604932801797986,
-0.05251344293355942,
0.04713143780827522,
0.020025501027703285,
0.005215974524617195,
-0.018369734287261963,
0.03193426877260208,
-0.040161944925785065,
0.013539795763790607,
-0.016951974481344223,
-0.03452353924512863,
-0.018631169572472572,
-0.0803898498415947,
-0.014162657782435417,
-0.01718057505786419,
-0.006609310861676931,
0.020067771896719933,
0.02405022270977497,
0.014888249337673187,
-0.048013076186180115,
-0.011999767273664474,
-0.0064336759969592094,
-0.03480149060487747,
0.005025211721658707,
0.03329094871878624,
0.049784816801548004,
0.013693321496248245,
0.04138193652033806,
-0.02820664644241333,
0.005652157589793205,
-0.05612189322710037,
0.009670891799032688,
0.052466705441474915,
-0.07059869170188904,
-0.00003969924000557512,
0.01648825593292713,
0.03862012177705765,
0.024478184059262276,
-0.006739635486155748,
-0.0557527095079422,
0.01748783141374588,
-0.028495443984866142,
-0.0782826617360115,
-0.015474585816264153,
-0.03627924993634224,
0.053842395544052124
] |
<ol>
<li><p>If gravity is the force of attraction between masses, does this force is an intrinsic property of every atoms? </p></li>
<li><p>Is there any possibility of some other particles within atom which is yet to be discovered? </p></li>
<li><p>Or is it simply a result of cosmic waves which created due to big bang?</p></li>
<li><p>Does anyone have any information regarding variations in gravitational force? </p></li>
<li><p>If its not there then is it simply be "something like plasma which entire universe in within its plume and huge masses simply accelerate the attraction"?</p></li>
</ol> | g9183 | [
0.027773981913924217,
0.0562080480158329,
-0.0020045004785060883,
-0.029530320316553116,
0.041543737053871155,
0.05312235280871391,
-0.030351029708981514,
-0.016975857317447662,
-0.07517819851636887,
-0.05058179423213005,
0.03717059642076492,
0.010500546544790268,
-0.017878422513604164,
-0.0012092005927115679,
0.018933091312646866,
0.012543772347271442,
0.08225548267364502,
-0.05944552272558212,
0.019752411171793938,
0.030071808025240898,
0.03591195493936539,
0.04487965628504753,
-0.0025904346257448196,
-0.0527622364461422,
-0.00006905010377522558,
0.026423102244734764,
0.020839715376496315,
-0.07188541442155838,
-0.03890589624643326,
-0.010217818431556225,
0.030916543677449226,
-0.046309635043144226,
0.008651490323245525,
-0.09526044130325317,
0.007761091459542513,
-0.016116725280880928,
-0.005626771133393049,
0.003712662262842059,
-0.015355370938777924,
0.028701717033982277,
-0.018775904551148415,
0.03233598917722702,
0.019146544858813286,
-0.024932431057095528,
0.01658245548605919,
0.025244509801268578,
-0.003109642071649432,
-0.014371613971889019,
0.028650179505348206,
-0.04199839383363724,
-0.03620216250419617,
0.0383480042219162,
0.007793292868882418,
0.01873396337032318,
-0.029415594413876534,
0.03163230046629906,
0.03418787568807602,
-0.007683302275836468,
0.04913025349378586,
0.022532185539603233,
0.004330059979110956,
0.03571290895342827,
0.03332459554076195,
-0.0042188651859760284,
0.015415622852742672,
-0.043854642659425735,
-0.07592187821865082,
0.018146375194191933,
0.004924514796584845,
-0.040325623005628586,
-0.0001252122165169567,
-0.04651227220892906,
-0.028979986906051636,
-0.008718264289200306,
-0.03561653196811676,
0.0414876788854599,
-0.017017165198922157,
0.048742301762104034,
-0.03586350008845329,
0.020327039062976837,
0.010091387666761875,
-0.03996913135051727,
0.029871752485632896,
0.007095428183674812,
0.04890210181474686,
-0.04593678191304207,
-0.057559896260499954,
-0.01596265658736229,
-0.007328891661018133,
0.013814718462526798,
0.020694207400083542,
0.014131919480860233,
0.013513699173927307,
0.005395262036472559,
-0.06368690729141235,
-0.02950313687324524,
0.012745937332510948,
0.0805368721485138,
-0.03384728357195854,
0.0048243398778140545,
0.007191322278231382,
0.03460365906357765,
0.014868884347379208,
0.02621307410299778,
0.051019974052906036,
-0.0036355778574943542,
0.0023605232127010822,
0.006546543445438147,
0.014365936629474163,
0.0031095861922949553,
0.014170807786285877,
-0.015674293041229248,
0.008627108298242092,
0.00937881413847208,
-0.06381666660308838,
-0.03437844663858414,
0.0507596880197525,
0.013533955439925194,
0.009189371019601822,
0.07833705842494965,
-0.018482614308595657,
0.011969071812927723,
0.007198850158601999,
-0.02425120212137699,
-0.030358122661709785,
-0.03489089757204056,
0.06433292478322983,
-0.005504765547811985,
-0.030309682711958885,
-0.07013984769582748,
0.03154655545949936,
0.015735557302832603,
-0.0076337638311088085,
-0.03178618103265762,
-0.025232892483472824,
-0.07096920162439346,
0.005934115499258041,
-0.008868762291967869,
-0.027708914130926132,
0.007470153737813234,
-0.023864133283495903,
-0.015181115828454494,
0.02565964125096798,
-0.028757084161043167,
0.025878095999360085,
0.05600651726126671,
-0.08059815317392349,
0.07008780539035797,
-0.003838701406493783,
0.0397595539689064,
-0.02436695247888565,
0.06989868730306625,
0.022226030007004738,
-0.043252959847450256,
-0.03491707518696785,
-0.03895018622279167,
-0.011742780916392803,
0.01762070134282112,
-0.03835436701774597,
-0.017994314432144165,
0.04381975904107094,
-0.0021031482610851526,
0.06506786495447159,
-0.00860167108476162,
0.04094275087118149,
0.03582964092493057,
0.022110803052783012,
0.025650249794125557,
0.01812489703297615,
0.008435524068772793,
-0.06308656930923462,
0.010025492869317532,
-0.028399283066391945,
0.05312646925449371,
0.06010082736611366,
-0.008780725300312042,
-0.0006884523318149149,
-0.061419639736413956,
0.01312183402478695,
-0.031142262741923332,
0.008520552888512611,
-0.06463128328323364,
0.0001397492305841297,
-0.002778866793960333,
-0.026928722858428955,
-0.023695793002843857,
0.0084329042583704,
0.0020576028618961573,
-0.007842736318707466,
0.024094466120004654,
-0.05499247461557388,
-0.018870562314987183,
0.016486331820487976,
0.002440460491925478,
0.06109875440597534,
-0.006225854158401489,
0.010265174321830273,
-0.017679234966635704,
0.01302944216877222,
0.0012176759773865342,
-0.016938341781497,
0.08316053450107574,
-0.0022181859239935875,
-0.0196065753698349,
0.043742015957832336,
0.010700739920139313,
0.03603275120258331,
0.026692749932408333,
0.06531441956758499,
-0.01268615573644638,
0.05501135438680649,
-0.038638051599264145,
0.046833209693431854,
-0.029791932553052902,
-0.026543376967310905,
0.034623585641384125,
-0.010547591373324394,
0.041023947298526764,
-0.005353410262614489,
0.03138415887951851,
-0.016320662572979927,
0.014095503836870193,
-0.02369159646332264,
0.01813727244734764,
-0.029441455379128456,
-0.05524161085486412,
-0.01590968295931816,
-0.008230508305132389,
0.02562122605741024,
0.06385644525289536,
-0.04038709029555321,
0.044906336814165115,
0.08908411860466003,
0.006588407326489687,
0.03189045935869217,
0.007911989465355873,
-0.016186978667974472,
-0.03419734910130501,
-0.019098151475191116,
-0.01973610557615757,
0.02857436053454876,
-0.05704263597726822,
-0.035520024597644806,
0.008706972002983093,
0.03968591243028641,
-0.06246552988886833,
0.011855767108500004,
0.021873734891414642,
0.014825875870883465,
0.013219153508543968,
0.01946789026260376,
-0.04731408506631851,
-0.06597119569778442,
0.016794804483652115,
0.013439720496535301,
-0.018458714708685875,
-0.029298434033989906,
0.043573781847953796,
-0.07629948854446411,
-0.05779736861586571,
0.026160679757595062,
-0.014909939840435982,
0.034297384321689606,
0.02577917091548443,
-0.06854597479104996,
-0.0021403951104730368,
-0.009352303110063076,
0.014246512204408646,
-0.052308909595012665,
-0.016123758628964424,
-0.027044184505939484,
0.042651768773794174,
-0.018650898709893227,
0.05640411749482155,
-0.064263254404068,
0.0685204565525055,
-0.05095613747835159,
-0.03660544380545616,
0.03439496457576752,
-0.0008671312243677676,
0.04688001051545143,
0.015314651653170586,
-0.07963444292545319,
-0.01857374608516693,
-0.0173537265509367,
0.011189784854650497,
-0.03651713207364082,
-0.019022276625037193,
0.00038276423583738506,
-0.016572557389736176,
-0.013869869522750378,
-0.008862272836267948,
0.06824159622192383,
0.01846577599644661,
-0.007699175737798214,
0.02409539185464382,
-0.012642157264053822,
0.04006727784872055,
-0.06486082822084427,
0.015590998344123363,
0.03714488819241524,
-0.06562723964452744,
-0.011028978042304516,
0.008902814239263535,
-0.0245959609746933,
0.0144478939473629,
-0.02601892314851284,
0.008933356031775475,
-0.04022775962948799,
-0.04109475016593933,
0.001837708055973053,
0.08722616732120514,
0.024319970980286598,
-0.005565157160162926,
-0.004973734263330698,
0.012161285616457462,
0.047156307846307755,
0.03578697144985199,
-0.005646703764796257,
-0.07026168704032898,
-0.03960399702191353,
-0.051523078233003616,
-0.016626136377453804,
-0.05497140437364578,
0.04430893808603287,
0.03836822882294655,
-0.02144221030175686,
-0.00930622685700655,
-0.06407597661018372,
-0.00842654425650835,
-0.021643951535224915,
-0.0696946457028389,
-0.05446788668632507,
0.017131976783275604,
-0.052818264812231064,
-0.03808729723095894,
0.02134070172905922,
-0.0356726311147213,
0.06191397085785866,
0.04484175518155098,
0.030019918456673622,
0.013945028185844421,
-0.059722959995269775,
-0.015399733558297157,
0.011422278359532356,
0.052562788128852844,
-0.014599029906094074,
-0.007378133479505777,
0.05364213511347771,
0.016996655613183975,
0.04394252225756645,
-0.03029140830039978,
0.05358666181564331,
-0.0027651770506054163,
0.044654861092567444,
-0.04773690924048424,
0.034431833773851395,
-0.02156355232000351,
-0.0152521301060915,
0.006580810993909836,
-0.04867321625351906,
-0.02520718425512314,
0.05904661864042282,
0.05616103112697601,
-0.019923623651266098,
-0.026560727506875992,
0.009826979599893093,
-0.05657670646905899,
0.011261845007538795,
-0.02436072565615177,
0.02608048915863037,
-0.018843434751033783,
0.004114776384085417,
-0.01563918963074684,
0.07947993278503418,
-0.07346495240926743,
0.04116246476769447,
0.0016142182284966111,
-0.020922062918543816,
-0.014103670604526997,
-0.006459868047386408,
0.026175539940595627,
0.020095746964216232,
0.05102495849132538,
0.01973840594291687,
-0.02867874875664711,
-0.06242894008755684,
-0.001034433371387422,
0.06858831644058228,
-0.07136344164609909,
-0.05707762390375137,
-0.031742386519908905,
-0.01564040407538414,
0.020180705934762955,
0.007161896210163832,
-0.004905544687062502,
0.019485624507069588,
-0.015072048641741276,
0.07663240283727646,
-0.0033390605822205544,
-0.01887306571006775,
0.06492050737142563,
-0.011051690205931664,
-0.00712675042450428,
0.024692891165614128,
0.05570165067911148,
0.06548961251974106,
0.012989707291126251,
0.029765546321868896,
-0.062345895916223526,
0.025037892162799835,
0.01652979478240013,
0.018827475607395172,
0.0061323088593780994,
-0.00737392483279109,
-0.03981342166662216,
-0.03954634070396423,
0.010055332444608212,
0.02382809668779373,
-0.019333675503730774,
0.02396770380437374,
0.060847971588373184,
0.0017577136168256402,
0.03343021124601364,
0.015752475708723068,
0.0810035839676857,
0.07155746966600418,
0.012477416545152664,
-0.013730542734265327,
-0.02282177284359932,
-0.018104877322912216,
0.014490445144474506,
0.05562828481197357,
0.04404202103614807,
-0.03419702127575874,
0.02202187478542328,
-0.022415004670619965,
-0.009230609983205795,
0.020025499165058136,
0.013753583654761314,
0.07991567254066467,
0.05103076621890068,
0.005758181679993868,
0.02530415542423725,
0.04765321686863899,
0.08839765936136246,
-0.06633003056049347,
-0.007108933757990599,
-0.04303126037120819,
-0.009261898696422577,
0.019822997972369194,
-0.04859231412410736,
-0.035052135586738586,
-0.014129837974905968,
-0.02418525144457817,
0.028265908360481262,
0.02400122582912445,
0.04388546198606491,
-0.02593979239463806,
-0.0036444072611629963,
-0.008413474075496197,
-0.029934750869870186,
0.012538264505565166,
0.062223758548498154,
0.0023443775717169046,
-0.044324129819869995,
-0.013510367833077908,
-0.04365898668766022,
-0.046423379331827164,
-0.016512801870703697,
0.03959644213318825,
0.02203192561864853,
0.06663519144058228,
-0.013749136589467525,
0.008188811130821705,
-0.05024653673171997,
0.012841683812439442,
-0.022615760564804077,
0.004764435812830925,
-0.042359981685876846,
-0.03766709193587303,
0.054361384361982346,
0.0000583194887440186,
0.020224129781126976,
-0.019118374213576317,
-0.035824134945869446,
-0.0192605871707201,
0.000591300253290683,
-0.021916454657912254,
-0.06228785589337349,
-0.007159478962421417,
-0.025358092039823532,
-0.009825523011386395,
-0.06589547544717789,
-0.01713067851960659,
0.00432708440348506,
-0.0522305890917778,
-0.009799826890230179,
0.02497691474854946,
0.01368645764887333,
0.021256757900118828,
0.036202967166900635,
0.00044642822467722,
-0.01570933312177658,
-0.00023541285190731287,
0.044925425201654434,
0.05317159742116928,
-0.010504573583602905,
-0.03042825125157833,
0.00807400792837143,
-0.05487223342061043,
0.030967408791184425,
-0.036801427602767944,
0.014601308852434158,
-0.034687820822000504,
0.0028398805297911167,
0.024449143558740616,
-0.0004594052443280816,
0.005709405522793531,
-0.01782510057091713,
-0.02565520815551281,
-0.04263683781027794,
0.0562606155872345,
0.03484337776899338,
0.02226288989186287,
0.020065177232027054,
0.012151298113167286,
0.04111596941947937,
0.00911012850701809,
0.0019380566664040089,
0.004658494144678116,
-0.02190534956753254,
0.06492612510919571,
-0.01747453399002552,
0.025480369105935097,
-0.0030655814334750175,
0.052315421402454376,
0.03987593203783035,
0.02076590619981289,
0.008894620463252068,
0.03571385517716408,
-0.060105156153440475,
-0.019885612651705742,
0.014812784269452095,
0.026547260582447052,
0.07584331184625626,
-0.017770247533917427,
0.018026156350970268,
0.05904189497232437,
-0.07514487951993942,
-0.00554646784439683,
0.03539545461535454,
0.01599236950278282,
0.04257576912641525,
-0.052457913756370544,
-0.01641865260899067,
0.0021598304156214,
-0.01306653581559658,
-0.04801299050450325,
-0.015696940943598747,
0.02105681784451008,
0.03238152340054512,
0.02755066752433777,
-0.06414370238780975,
0.015566006302833557,
-0.03386225923895836,
-0.013258812949061394,
-0.07788325846195221,
0.04012853279709816,
0.016825499013066292,
-0.011050318367779255,
0.041044626384973526,
-0.0326261967420578,
-0.014803995378315449,
0.058126676827669144,
-0.02097650244832039,
-0.010621474124491215,
-0.019807210192084312,
-0.026940448209643364,
0.005392272956669331,
0.06046556681394577,
-0.008377018384635448,
0.00464286282658577,
-0.04795803129673004,
-0.008291414938867092,
0.0016393217956647277,
-0.027425428852438927,
-0.02828877605497837,
0.017495576292276382,
-0.03129693120718002,
-0.02485276199877262,
-0.06142900511622429,
0.012447918765246868,
-0.034238725900650024,
-0.09756990522146225,
-0.006564653478562832,
0.022633757442235947,
-0.012144409120082855,
0.01691582426428795,
0.01283374335616827,
0.018595430999994278,
0.06138477101922035,
0.01692383363842964,
0.051335714757442474,
0.025661006569862366,
0.001220117905177176,
-0.010349726304411888,
-0.03992690145969391,
-0.02757195197045803,
0.0140300914645195,
-0.0014913651393726468,
-0.02606930024921894,
0.014430581592023373,
-0.046330492943525314,
0.013630591332912445,
-0.05966051667928696,
0.015611940063536167,
0.03910836577415466,
-0.03415348380804062,
-0.001549763954244554,
-0.008446644991636276,
-0.049288079142570496,
-0.0043755583465099335,
-0.024198124185204506,
0.00026656826958060265,
0.019083339720964432,
-0.06243523582816124,
0.08507263660430908,
0.024907726794481277,
0.013114923611283302,
0.01173090748488903,
-0.002825439441949129,
0.02285105548799038,
0.0164523683488369,
-0.03232013061642647,
0.0816953107714653,
-0.007789366412907839,
-0.01964329369366169,
0.05533929541707039,
-0.047097910195589066,
-0.0058760917745530605,
0.019121479243040085,
-0.021303610876202583,
-0.008472484536468983,
-0.08159353584051132,
0.029607871547341347,
0.034374337643384933,
-0.007318523712456226,
-0.0492265522480011,
-0.019861824810504913,
-0.05538589134812355,
0.009450963698327541,
0.028799228370189667,
0.028963226824998856,
-0.024797681719064713,
0.010530153289437294,
0.021021315827965736,
-0.03390878438949585,
-0.04973442852497101,
-0.09408291429281235,
-0.07055473327636719,
0.011759922839701176,
0.03384779766201973,
0.020749591290950775,
-0.024450039491057396,
0.0777832493185997,
-0.005543497856706381,
-0.06867446005344391,
-0.034966450184583664,
0.0144633324816823,
-0.012301134876906872,
-0.050051819533109665,
-0.012411758303642273,
-0.012417435646057129,
-0.0008610078366473317,
-0.00014792551519349217,
-0.05501504987478256,
-0.027534786611795425,
0.06393180042505264,
-0.019115934148430824,
-0.0000796845561126247,
0.1136825829744339,
-0.02217632532119751,
0.08656871318817139,
-0.06960634142160416,
0.03512401133775711,
-0.019338952377438545,
-0.004269795957952738,
-0.061554744839668274,
-0.0412827730178833,
-0.03288958966732025,
0.007240652106702328,
0.022697875276207924,
-0.03062920831143856,
-0.03582657128572464,
-0.05911554768681526,
0.009660017676651478,
0.030403990298509598,
-0.004732309840619564,
0.025382110849022865,
-0.024792850017547607,
-0.032076653093099594,
0.016798581928014755,
-0.03465387597680092,
0.04869635030627251,
0.005224543157964945,
-0.024300092831254005,
0.0046590231359004974,
-0.0625954270362854,
0.0698249563574791,
0.06086890399456024,
0.005966833792626858,
0.054996147751808167,
-0.01381508819758892,
0.024004265666007996,
0.04175397753715515,
-0.027284052222967148,
0.01172960177063942,
-0.0012259779032319784,
-0.002042988082394004,
0.05650017783045769,
-0.019248753786087036,
0.013509156182408333,
-0.03227894380688667,
-0.04465942084789276,
0.013078408315777779,
0.004803752992302179,
-0.027708588168025017,
-0.009666630066931248,
-0.013638069853186607,
0.0074238223023712635,
0.0332057848572731,
-0.0036680169869214296,
-0.039497509598731995,
-0.04158606752753258,
0.029192304238677025,
0.0616004653275013,
-0.06030980125069618,
0.022887688130140305,
0.0306235458701849,
0.011557439342141151,
-0.022338537499308586,
-0.0053034583106637,
-0.004173915833234787,
0.02472730353474617,
-0.035056568682193756,
-0.036179665476083755,
0.024150868877768517,
0.020036382600665092,
0.03427157178521156,
0.006216178182512522,
0.037370290607213974,
-0.04091230034828186,
0.03912094980478287,
0.009735350497066975,
-0.07301832735538483,
-0.000725438236258924,
0.081903375685215,
-0.013376982882618904,
-0.01714722067117691,
-0.01225065067410469,
0.0576988086104393,
0.026163766160607338,
-0.0045405300334095955,
0.002156253671273589,
0.02899022586643696,
-0.034245967864990234,
0.02092180959880352
] |
<p>In <a href="http://www.youtube.com/watch?v=EYPapE-3FRw" rel="nofollow">this video of Feynman discussing the scientific method</a>, starting at around eight minutes and 30 seconds, Feynman describes the proposition that space consists of a cubic lattice of points (as opposed to space being continuous). Feynman says "then we can prove that [the proposition] immediately is wrong," but he doesn't elaborate on the proof.</p>
<blockquote>
<p>My question is: What are the objection(s) to a cubic lattice universe that Feynman refers to in this video?</p>
</blockquote>
<p>I'm not looking for every possible objection to a cubic lattice universe. I'm wondering what in particular the (apparently immediate and obvious) objections are that made Feynman so dismissive of the idea.</p> | g114 | [
0.04992745444178581,
0.025856442749500275,
0.013491477817296982,
-0.021693453192710876,
0.02590671367943287,
0.03409634158015251,
0.019881168380379677,
-0.02530420571565628,
0.008125252090394497,
0.02426447905600071,
0.033365726470947266,
0.06276148557662964,
-0.04443066194653511,
0.05289054289460182,
-0.07497502863407135,
0.01437377743422985,
-0.039996691048145294,
-0.05284504219889641,
0.005303436424583197,
0.00683662248775363,
-0.002952833194285631,
-0.015195035375654697,
-0.017751848325133324,
-0.05084838718175888,
-0.028903299942612648,
-0.034798573702573776,
0.056707706302404404,
-0.07519084215164185,
0.03440820798277855,
-0.007370301987975836,
0.015623562969267368,
-0.019546056166291237,
0.050251662731170654,
-0.014383675530552864,
-0.025469927117228508,
-0.008674206212162971,
-0.022406673058867455,
-0.030709339305758476,
0.022860374301671982,
-0.0337391160428524,
-0.001960465917363763,
-0.04205937683582306,
-0.028684619814157486,
0.013704163022339344,
-0.010113888420164585,
0.008430037647485733,
-0.07447168231010437,
0.040635302662849426,
0.008886412717401981,
0.013048925437033176,
0.012662810273468494,
0.00692531606182456,
0.06169889494776726,
0.022345514968037605,
0.011009872891008854,
0.009376737289130688,
-0.034180521965026855,
0.007412724196910858,
0.09583090245723724,
-0.0017464281991124153,
-0.036020271480083466,
-0.006786765996366739,
0.028534242883324623,
0.0655079185962677,
0.07539456337690353,
0.011233237572014332,
-0.07735861837863922,
0.03499777987599373,
0.012784519232809544,
0.03189132362604141,
0.03688619285821915,
-0.0939445048570633,
-0.008080202154815197,
0.016506686806678772,
-0.03637702763080597,
0.04732653498649597,
0.006488206796348095,
0.01404245663434267,
0.06342531740665436,
-0.006694425828754902,
-0.07582413405179977,
-0.003961485810577869,
-0.007146226707845926,
-0.008118703030049801,
0.02918783202767372,
-0.02066662535071373,
-0.03366980701684952,
-0.029275620356202126,
-0.026664434000849724,
0.023251499980688095,
-0.005942658521234989,
0.006930962670594454,
0.06247464939951897,
-0.008255168795585632,
-0.060638781636953354,
-0.02066950313746929,
-0.052140556275844574,
0.00012310748570598662,
-0.0031619477085769176,
0.04585958644747734,
-0.1071452796459198,
-0.009502952918410301,
-0.032408419996500015,
-0.02216346189379692,
-0.041192471981048584,
-0.05593718960881233,
0.0030309786088764668,
0.04633655399084091,
-0.026668647304177284,
0.010516101494431496,
-0.03419336676597595,
0.007215427700430155,
-0.0723818689584732,
0.02994871325790882,
-0.05509151145815849,
-0.0013742436422035098,
0.07216671109199524,
-0.02947305329144001,
0.03922924026846886,
0.028600744903087616,
-0.015515360981225967,
0.02128368616104126,
0.029006849974393845,
-0.015552236698567867,
0.010056360624730587,
-0.00810274388641119,
-0.030515674501657486,
0.025263139978051186,
-0.008073602803051472,
-0.035297639667987823,
-0.01979680545628071,
0.05980631336569786,
-0.016274740919470787,
-0.02860841527581215,
-0.045451387763023376,
0.013604293577373028,
-0.005622671451419592,
-0.018219327554106712,
0.024010978639125824,
-0.014718192629516125,
0.01580280065536499,
0.015698080882430077,
0.059348542243242264,
-0.007496859412640333,
-0.011065300554037094,
-0.005873984657227993,
0.03915784880518913,
0.016500836238265038,
0.03126614913344383,
0.005236369092017412,
0.004568622913211584,
0.10170090198516846,
-0.006982228718698025,
-0.04322648048400879,
-0.000925615371670574,
0.024712080135941505,
0.07150428742170334,
0.015880392864346504,
0.0010284746531397104,
-0.02042049542069435,
0.05675634369254112,
0.028336472809314728,
0.00932635273784399,
0.01239929161965847,
-0.030615316703915596,
-0.0026751223485916853,
-0.008709347806870937,
-0.04496796056628227,
-0.00790458731353283,
-0.0007333391113206744,
-0.03966411575675011,
-0.003330235369503498,
-0.0007051869761198759,
0.08513416349887848,
0.02227427065372467,
0.05650147795677185,
-0.016132980585098267,
0.0034292584750801325,
0.026052476838231087,
0.004500166047364473,
0.002304304391145706,
0.02402617037296295,
0.013870587572455406,
0.03891553357243538,
0.0015753620536997914,
0.027429776266217232,
-0.04979805648326874,
0.024187736213207245,
-0.0028814361430704594,
-0.046793896704912186,
0.005979293957352638,
-0.07999914139509201,
-0.02948750928044319,
0.01555356290191412,
0.01646110974252224,
-0.007876534014940262,
0.013120371848344803,
-0.04195638373494148,
0.017276765778660774,
-0.025939064100384712,
0.02963460236787796,
-0.0020016587805002928,
0.03976200148463249,
0.026316877454519272,
0.023726122453808784,
0.035602372139692307,
-0.08033493906259537,
-0.005320670083165169,
0.008434257470071316,
0.07739491760730743,
0.05427934601902962,
0.009350193664431572,
-0.009299266152083874,
0.060907382518053055,
-0.03253766521811485,
0.009035347029566765,
-0.05855720862746239,
-0.001775462762452662,
-0.0018345516873523593,
0.034145914018154144,
-0.058603011071681976,
-0.05377062410116196,
-0.04433345049619675,
-0.03294086456298828,
0.023712025955319405,
-0.033987730741500854,
-0.023209601640701294,
-0.033382076770067215,
0.04387432336807251,
0.055888839066028595,
-0.032081540673971176,
-0.03858278691768646,
-0.05176541581749916,
-0.11672157049179077,
0.03973181173205376,
0.008262169547379017,
0.005030571483075619,
0.021700847893953323,
-0.05296134203672409,
0.014363333582878113,
-0.02668686769902706,
-0.01822197623550892,
-0.07656091451644897,
-0.007301490753889084,
-0.004861107096076012,
-0.06865167617797852,
0.032691627740859985,
-0.014238613657653332,
-0.010252109728753567,
-0.0063508134335279465,
0.021894292905926704,
-0.008017880842089653,
0.0035570000763982534,
0.02729339897632599,
0.05661797896027565,
0.04479699954390526,
0.02467094175517559,
0.08105925470590591,
-0.018462905660271645,
0.029734019190073013,
0.03586535528302193,
-0.07221914827823639,
0.027685679495334625,
0.011875559575855732,
-0.01565023697912693,
-0.027897048741579056,
-0.006994245573878288,
0.034686584025621414,
-0.025325218215584755,
-0.04974871128797531,
-0.01041533425450325,
0.05673445016145706,
-0.009098355658352375,
-0.007302027195692062,
-0.018908875063061714,
0.0048074424266815186,
-0.022633319720625877,
-0.01746358722448349,
0.08958443254232407,
-0.013737139292061329,
-0.026692822575569153,
0.030824853107333183,
-0.0804189071059227,
0.03116195648908615,
0.04971865192055702,
0.0007885887171141803,
-0.056632593274116516,
-0.01378050446510315,
-0.007846368476748466,
0.01291898638010025,
-0.03294965252280235,
0.007850655354559422,
0.004609401803463697,
-0.021686021238565445,
-0.016617316752672195,
-0.010962508618831635,
-0.0017758570611476898,
0.0030734469182789326,
0.017301926389336586,
0.041074324399232864,
-0.009136894717812538,
0.07468406111001968,
0.028479699045419693,
-0.04245495796203613,
0.03234472870826721,
0.02661304734647274,
-0.002897428348660469,
-0.05296308919787407,
-0.028579793870449066,
-0.05596369877457619,
0.04024498537182808,
0.06950898468494415,
0.012032256461679935,
-0.00019338449055794626,
-0.013656177558004856,
0.05510499328374863,
-0.007995925843715668,
0.04108591005206108,
0.06896746903657913,
-0.009639893658459187,
-0.012169867753982544,
0.05940776690840721,
-0.04571497067809105,
-0.01685212180018425,
0.09384025633335114,
0.017253249883651733,
-0.010233168490231037,
0.02057056687772274,
-0.036989856511354446,
0.00029606017051264644,
0.00004325443660491146,
-0.04577462002635002,
-0.036503586918115616,
-0.03728693723678589,
-0.0566861592233181,
-0.07600566744804382,
-0.0340299978852272,
0.012047532014548779,
0.03403143957257271,
-0.07589869946241379,
0.014887730590999126,
0.0696541890501976,
-0.0209394171833992,
0.01421188935637474,
-0.010138392448425293,
0.01969577558338642,
0.017731819301843643,
0.014928780496120453,
-0.008235126733779907,
-0.009860777296125889,
0.03022157773375511,
0.05078500136733055,
0.06666307896375656,
0.01118077989667654,
-0.02372458390891552,
0.02312580868601799,
-0.004174957517534494,
0.0005549857742153108,
0.07451280951499939,
-0.06766563653945923,
-0.018150031566619873,
0.02171042561531067,
0.04493936523795128,
0.006553743500262499,
-0.05063570290803909,
0.010369759984314442,
-0.03230717033147812,
0.04756748303771019,
-0.001633504987694323,
-0.011438803747296333,
0.014253605157136917,
-0.08138077706098557,
-0.015222376212477684,
-0.006761758588254452,
0.05086347833275795,
-0.038226962089538574,
-0.049570150673389435,
-0.026652714237570763,
-0.004710444249212742,
0.03830888494849205,
-0.018029283732175827,
0.06793031096458435,
0.036824144423007965,
-0.053763192147016525,
-0.027208922430872917,
0.007556584198027849,
-0.04477691277861595,
-0.0029757076408714056,
-0.04122812673449516,
-0.03424890339374542,
0.028170796111226082,
0.008251159451901913,
-0.04181021451950073,
0.008384408429265022,
-0.0220030564814806,
-0.007430920377373695,
-0.0026179540436714888,
0.05745721980929375,
0.009669343940913677,
0.039843183010816574,
0.05104467645287514,
-0.019119910895824432,
-0.00472198287025094,
-0.023720823228359222,
0.0016645120922476053,
-0.007858277298510075,
0.02403418906033039,
0.007167583331465721,
0.03281266614794731,
-0.006543265655636787,
0.009181114844977856,
0.004783288110047579,
-0.0006541898474097252,
-0.06365131586790085,
0.05359891802072525,
-0.013971655629575253,
-0.0242939293384552,
-0.05505343899130821,
0.046999700367450714,
-0.0211041159927845,
0.06534628570079803,
0.03517862409353256,
-0.013779789209365845,
-0.01467652153223753,
0.035829294472932816,
0.02412310615181923,
-0.04775375500321388,
-0.026268871501088142,
-0.028680426999926567,
0.021698566153645515,
0.022161968052387238,
0.05231134966015816,
-0.0062965466640889645,
0.05733734369277954,
0.017512407153844833,
-0.011692182160913944,
0.02549823559820652,
0.033193331211805344,
0.018995918333530426,
0.0486719124019146,
0.03431827947497368,
-0.059765830636024475,
0.02098798379302025,
-0.05806639418005943,
0.016840746626257896,
-0.008878539316356182,
-0.07526369392871857,
-0.006763404235243797,
-0.08468591421842575,
-0.01014377735555172,
0.021967023611068726,
0.011436616070568562,
-0.013966518454253674,
0.009669258259236813,
-0.05866986885666847,
-0.04435957595705986,
-0.036701321601867676,
0.04055764153599739,
0.026362664997577667,
0.060047246515750885,
-0.0032200650312006474,
-0.010055318474769592,
-0.02024073712527752,
0.06226496398448944,
0.08715996146202087,
0.07165222615003586,
-0.023905504494905472,
-0.010509068146348,
-0.011595421470701694,
-0.03173312172293663,
-0.004621522966772318,
-0.010577862150967121,
-0.004883260931819677,
0.031415730714797974,
0.0023969390895217657,
-0.007738317828625441,
-0.04919383302330971,
0.0029673846438527107,
-0.022333502769470215,
0.015715518966317177,
-0.0022805335465818644,
0.012355692684650421,
0.01180130522698164,
0.03149338811635971,
0.031421855092048645,
0.00131618429441005,
0.0002741393109317869,
0.03629199042916298,
-0.0018430255586281419,
-0.01762520894408226,
0.028865257278084755,
-0.011404348537325859,
0.04799831286072731,
0.03542023152112961,
-0.03214883804321289,
-0.014282801188528538,
-0.014480152167379856,
-0.06966768205165863,
-0.015201494097709656,
0.06638026982545853,
0.01993563026189804,
0.0024039377458393574,
0.027843020856380463,
-0.026170333847403526,
0.008853637613356113,
0.03565926104784012,
0.00298654125072062,
0.0009106285870075226,
-0.013843978755176067,
-0.04542587324976921,
0.006150893867015839,
0.03341967239975929,
0.014868617989122868,
0.08319427818059921,
0.03267771750688553,
-0.0380883626639843,
-0.0006684784893877804,
-0.08531782031059265,
-0.020712727680802345,
-0.05526736378669739,
0.022314423695206642,
0.02911890298128128,
0.038235653191804886,
-0.07900508493185043,
-0.015475861728191376,
-0.017224319279193878,
-0.02757524698972702,
-0.031049571931362152,
-0.024153536185622215,
0.03543483465909958,
-0.01392969861626625,
0.04674632102251053,
0.03739505261182785,
0.01700274460017681,
-0.05951303243637085,
0.009637127630412579,
-0.007648923434317112,
0.024278923869132996,
0.043090976774692535,
-0.019917096942663193,
0.004008975811302662,
-0.026859484612941742,
-0.00033727323170751333,
0.052795588970184326,
-0.013826316222548485,
0.03779365122318268,
-0.055668916553258896,
0.0297083780169487,
0.049674369394779205,
-0.035594288259744644,
-0.028827106580138206,
-0.006793561857193708,
-0.010343221016228199,
-0.024671770632267,
-0.012276628986001015,
0.0296203400939703,
-0.025626396760344505,
0.0019509921548888087,
-0.022602897137403488,
0.018567273393273354,
0.03423163294792175,
-0.000907476176507771,
0.004934969823807478,
-0.04679820314049721,
0.02097853645682335,
-0.032937273383140564,
-0.0213682409375906,
-0.005735026206821203,
0.01787901110947132,
-0.00850360095500946,
0.008089696057140827,
0.0366804413497448,
-0.030330277979373932,
0.027110448107123375,
-0.05314939469099045,
-0.027444778010249138,
-0.022342389449477196,
-0.007701091933995485,
-0.007125280797481537,
0.0013627209700644016,
-0.03887910395860672,
0.007599797565490007,
0.05839979276061058,
0.014067402109503746,
0.007356264628469944,
0.009298940189182758,
0.0014270322863012552,
0.042033057659864426,
0.021294623613357544,
-0.035353586077690125,
0.0017068153247237206,
0.0008838167996145785,
-0.03318054974079132,
-0.01928052119910717,
0.006523181218653917,
-0.0169413723051548,
0.00928986445069313,
-0.009478496387600899,
0.004276026971638203,
0.08143197745084763,
-0.016961270943284035,
0.030680479481816292,
0.016614707186818123,
-0.022320950403809547,
-0.01737765036523342,
0.050223205238580704,
0.014157076366245747,
-0.04445139318704605,
0.05376492068171501,
-0.054912980645895004,
0.02099962718784809,
0.054977137595415115,
0.0018959506414830685,
0.006836945656687021,
0.028742533177137375,
-0.03740467131137848,
-0.03744865953922272,
-0.053273461759090424,
-0.045482371002435684,
-0.05008948594331741,
0.016779964789748192,
0.007602434139698744,
0.00505700521171093,
0.00847149919718504,
0.05066268891096115,
0.03539065271615982,
-0.02835077978670597,
0.04862496256828308,
0.08957099169492722,
0.04223432391881943,
-0.017696628347039223,
-0.014695714227855206,
0.03622570261359215,
0.023243373259902,
-0.018875213339924812,
0.033901795744895935,
-0.042077891528606415,
-0.008227654732763767,
0.023440616205334663,
-0.03491448611021042,
-0.020543843507766724,
-0.01335518341511488,
0.008247507736086845,
-0.022077826783061028,
0.005965026561170816,
-0.034843191504478455,
-0.012544162571430206,
0.032723769545555115,
0.003325072582811117,
0.029409436509013176,
-0.022865986451506615,
-0.05527431145310402,
-0.002476511290296912,
-0.01686319150030613,
-0.0961381196975708,
0.03973253443837166,
-0.02742975763976574,
-0.015508238226175308,
0.0016743249725550413,
-0.10540737211704254,
-0.03898549824953079,
-0.019795138388872147,
-0.017136944457888603,
-0.006861717905849218,
-0.044470369815826416,
-0.01892591454088688,
-0.034070465713739395,
-0.046370334923267365,
-0.03738678619265556,
-0.03858919069170952,
0.027725564315915108,
-0.014673767611384392,
0.0040555731393396854,
0.0287807434797287,
0.02093692496418953,
-0.07305336743593216,
-0.013346120715141296,
0.025403667241334915,
0.05989174544811249,
0.0022429602686315775,
-0.028017288073897362,
0.03875022754073143,
-0.006494227331131697,
0.00428201025351882,
-0.015048915520310402,
-0.017458951100707054,
0.04774784669280052,
0.012322820723056793,
-0.01593007706105709,
-0.06720005720853806,
0.05737097188830376,
-0.013222478330135345,
-0.0016192946350201964,
-0.03480745106935501,
0.03187606856226921,
0.026494398713111877,
0.02907389961183071,
0.03072945587337017,
0.01664908044040203,
-0.06915242969989777,
-0.0027127997018396854,
-0.029853690415620804,
-0.06253264099359512,
0.03249688819050789,
0.021694375202059746,
0.00325318006798625,
0.07490827888250351,
0.016337864100933075,
-0.05368698760867119,
-0.004337647929787636,
0.05543290451169014,
0.07679971307516098,
-0.00032012935844250023,
0.01937584951519966,
0.05144764855504036,
0.022187357768416405,
-0.01467955857515335,
0.020991919562220573,
0.03302895650267601,
-0.026136569678783417,
-0.039053142070770264,
-0.011070630513131618,
-0.035771969705820084,
-0.04793001711368561,
-0.006291653960943222,
0.0009119738824665546,
0.0166500061750412,
-0.03768594190478325,
-0.07406992465257645,
-0.005752444267272949,
0.03566845506429672,
0.03701108321547508,
0.01375860720872879,
0.017674745991826057,
-0.05283600464463234,
0.009611347690224648,
-0.05144926905632019,
0.038927868008613586,
0.001463918830268085,
-0.009810719639062881,
-0.0475335456430912,
0.05579904466867447,
0.022631127387285233,
-0.01918628439307213,
0.0002997799892909825,
-0.05895445868372917,
-0.0890805646777153,
0.01876891776919365,
0.05895275995135307,
-0.010375901125371456,
-0.003914626315236092,
-0.00888355728238821,
0.023077886551618576,
0.04406450316309929,
0.04444756731390953,
-0.0539090670645237,
-0.08174079656600952,
-0.008882489986717701,
0.06829898059368134,
-0.004341870546340942,
-0.013758430257439613,
0.07048337161540985,
0.04440173879265785,
0.007517566904425621,
-0.04750579595565796,
0.026982028037309647,
-0.013868757523596287,
0.003916394431143999
] |
<p>Are there any theories out there that discuss the idea that space itself could be made out of particles?</p> | g302 | [
0.07114996016025543,
0.0327877514064312,
0.000762204232160002,
-0.042206089943647385,
-0.0021851686760783195,
0.0374474823474884,
-0.06309657543897629,
-0.0005456674261949956,
0.013999434188008308,
-0.022550366818904877,
0.06630177050828934,
-0.0119713693857193,
0.052661363035440445,
0.039907123893499374,
-0.06514682620763779,
-0.00024201770429499447,
0.03324798494577408,
0.026150507852435112,
-0.0047678337432444096,
0.04077853262424469,
0.004015425220131874,
-0.026383088901638985,
0.029926924034953117,
0.004027221817523241,
-0.09623033553361893,
-0.0007385067874565721,
0.002777234185487032,
-0.03136312589049339,
0.01990455575287342,
-0.007364789489656687,
0.0202798955142498,
-0.03396134451031685,
-0.06085043027997017,
-0.03946973755955696,
-0.0013852554839104414,
-0.07041876018047333,
0.0021874054800719023,
0.030842572450637817,
0.020708758383989334,
-0.007480625528842211,
-0.057567618787288666,
-0.07067044079303741,
-0.005798046011477709,
0.019188271835446358,
0.0015846970491111279,
0.010969912633299828,
0.01285856869071722,
0.05878765508532524,
-0.0039183394983410835,
-0.018498122692108154,
-0.04207952320575714,
0.048046957701444626,
0.036527104675769806,
-0.008008809760212898,
0.0176803357899189,
-0.01590568572282791,
0.0437922365963459,
-0.014714899472892284,
0.08228324353694916,
-0.00039854433271102607,
-0.025312038138508797,
0.06639911979436874,
-0.003818814642727375,
0.06112077832221985,
0.0164993517100811,
0.003273704554885626,
-0.036680225282907486,
0.022824153304100037,
0.08323422074317932,
-0.06016014888882637,
0.07151863723993301,
-0.005155656952410936,
0.005858355201780796,
-0.000746240490116179,
-0.037760570645332336,
0.05305379256606102,
-0.02699914760887623,
0.08600032329559326,
0.02987520955502987,
0.004215426277369261,
0.0200372152030468,
-0.015581713058054447,
-0.0034985970705747604,
-0.06973441690206528,
0.0851747915148735,
-0.03701098635792732,
-0.006993062328547239,
-0.034314870834350586,
-0.022722264751791954,
0.0009740342502482235,
-0.04915281757712364,
-0.012927155010402203,
0.009540921077132225,
-0.00946094375103712,
0.014420075342059135,
-0.024507157504558563,
0.013169398531317711,
0.039063386619091034,
-0.06975759565830231,
0.007751862984150648,
-0.04310939460992813,
0.002910115523263812,
0.008942156098783016,
0.0004562551330309361,
0.039683643728494644,
-0.00480277044698596,
0.001913377782329917,
-0.029611729085445404,
0.03358953446149826,
0.03638005256652832,
0.011429929174482822,
0.031784866005182266,
-0.02187962457537651,
0.03527679294347763,
0.041951734572649,
-0.04662556201219559,
0.080268993973732,
-0.06799014657735825,
0.040092065930366516,
0.05820479243993759,
-0.009187360294163227,
-0.05239550769329071,
-0.018450738862156868,
-0.026946788653731346,
-0.041576579213142395,
0.04031076282262802,
0.044849563390016556,
-0.025982476770877838,
-0.038723237812519073,
0.007324365433305502,
-0.010108208283782005,
-0.010336476378142834,
-0.023249447345733643,
-0.019169548526406288,
-0.03850238025188446,
-0.04015403240919113,
-0.031088126823306084,
-0.03817953169345856,
-0.015719300135970116,
0.018179673701524734,
0.009110505692660809,
-0.02261042408645153,
0.026614060625433922,
0.025780322030186653,
0.008529910817742348,
0.0005921300034970045,
-0.017855998128652573,
-0.002842631656676531,
-0.05015827342867851,
0.050391171127557755,
-0.0391678586602211,
0.07132045924663544,
0.009173315949738026,
-0.01596343331038952,
0.01731893979012966,
0.006360666826367378,
0.0034826104529201984,
0.05296147242188454,
0.002383375307545066,
0.012868799269199371,
0.022143101319670677,
-0.014659623615443707,
-0.0028706989251077175,
-0.03207673877477646,
-0.03927905857563019,
0.007743894122540951,
-0.04495707154273987,
0.005629648454487324,
-0.031959667801856995,
-0.02521989867091179,
-0.016444142907857895,
-0.017568740993738174,
-0.01501623634248972,
0.06313301622867584,
-0.006497172173112631,
0.0595315620303154,
-0.019453400745987892,
0.0047318958677351475,
0.01036153081804514,
0.015114524401724339,
0.03644668310880661,
-0.053118083626031876,
-0.00921652466058731,
-0.01952158287167549,
0.0656733363866806,
-0.006414287257939577,
-0.058455757796764374,
0.006809893064200878,
-0.058655690401792526,
0.03183912858366966,
-0.017077747732400894,
-0.001249187160283327,
0.03368312492966652,
0.013546895235776901,
0.05554012954235077,
0.003796500386670232,
0.05002378299832344,
-0.024990148842334747,
0.017793815582990646,
0.023173358291387558,
-0.0249000396579504,
0.05675528198480606,
0.039801497012376785,
0.03372611850500107,
0.04662945494055748,
-0.043733857572078705,
-0.045989226549863815,
0.0006851273356005549,
0.0041250851936638355,
0.04546339809894562,
0.06815174967050552,
-0.01999259740114212,
-0.005920650437474251,
0.02817581407725811,
-0.02176518738269806,
0.0017030463786795735,
-0.05254240706562996,
0.02435394562780857,
-0.033853642642498016,
0.024157339707016945,
-0.044109560549259186,
-0.04544162005186081,
0.002541894791647792,
0.0223582461476326,
0.013012003153562546,
-0.014012881554663181,
0.008625803515315056,
-0.02844078093767166,
-0.0038659628480672836,
0.03938332200050354,
-0.0595395565032959,
-0.001096553634852171,
0.006642528809607029,
-0.01067520771175623,
0.0010465283412486315,
0.04420125111937523,
-0.017467284575104713,
-0.03682921826839447,
0.01009366661310196,
0.0009449129574932158,
0.00854081753641367,
-0.03335341811180115,
-0.023004092276096344,
-0.0988432765007019,
0.05222558602690697,
-0.046257421374320984,
0.02645254321396351,
-0.03960205242037773,
-0.004905461799353361,
-0.03941699117422104,
-0.020328426733613014,
0.025086427107453346,
-0.03987845778465271,
-0.045043766498565674,
0.030721468850970268,
-0.009204561822116375,
0.015330692753195763,
0.08935187011957169,
-0.018681224435567856,
-0.08326384425163269,
0.029152886942029,
-0.04148818179965019,
-0.06410986185073853,
0.01730751432478428,
-0.013854090124368668,
-0.024356957525014877,
-0.032195400446653366,
0.05436689034104347,
-0.018530262634158134,
0.01723618619143963,
0.04599117487668991,
0.04220535233616829,
0.04146750271320343,
-0.025848757475614548,
-0.05030515417456627,
0.04194413498044014,
0.006078289821743965,
-0.02125498466193676,
0.029862355440855026,
-0.01180263701826334,
0.038028985261917114,
0.05767441168427467,
-0.06510865688323975,
0.01975370943546295,
-0.011999282985925674,
-0.05671507492661476,
-0.09138751775026321,
0.027696136385202408,
0.04439704492688179,
0.03951997682452202,
0.023649929091334343,
-0.02530491165816784,
0.028612373396754265,
-0.008571256883442402,
0.015001754276454449,
0.050635069608688354,
0.0123245008289814,
0.006785964127629995,
-0.004618355538696051,
0.0113510861992836,
0.017927590757608414,
-0.005635307636111975,
0.024625448510050774,
0.020125361159443855,
-0.0030239413026720285,
0.034771814942359924,
-0.03051835112273693,
-0.020723536610603333,
0.03556555137038231,
-0.07263382524251938,
-0.00047775215352885425,
0.0629630759358406,
0.015038980171084404,
0.06012643873691559,
-0.005897557362914085,
0.008215331472456455,
-0.01151271816343069,
-0.002426030347123742,
0.02449682727456093,
-0.029083436354994774,
0.015101665630936623,
0.020079726353287697,
0.03594803065061569,
-0.010962805710732937,
0.054175350815057755,
0.01669836789369583,
-0.045045580714941025,
-0.06221388280391693,
-0.028068823739886284,
0.01783381961286068,
-0.01133938878774643,
-0.02795492112636566,
0.020207729190587997,
-0.016120700165629387,
-0.057910192757844925,
-0.05551408603787422,
-0.025708753615617752,
0.0004551230522338301,
0.012784435413777828,
-0.029838722199201584,
-0.03338858112692833,
0.028063340112566948,
0.010324366390705109,
0.02458753064274788,
-0.005745913367718458,
0.06737163662910461,
0.04249130189418793,
-0.03465978056192398,
0.027141854166984558,
0.014805658720433712,
0.03378297761082649,
0.01901654712855816,
0.03622601926326752,
-0.008455519564449787,
0.030340250581502914,
0.050892747938632965,
0.036933980882167816,
0.03616476431488991,
0.03878295421600342,
-0.01639968901872635,
-0.011180250905454159,
-0.015896104276180267,
0.04716093838214874,
-0.026287944987416267,
0.006465797778218985,
0.009463324211537838,
-0.023873725906014442,
-0.03672010824084282,
0.0522313229739666,
0.004680980462580919,
-0.003971236292272806,
-0.007075270172208548,
-0.033773139119148254,
0.039439719170331955,
0.0588640458881855,
-0.02694067731499672,
0.013654803857207298,
-0.008161292411386967,
-0.059097666293382645,
-0.05411156266927719,
0.036135684698820114,
0.03911706805229187,
0.032934922724962234,
0.013996764086186886,
-0.01463585626333952,
0.03370187059044838,
-0.05459046736359596,
0.0021097331773489714,
-0.031228138133883476,
-0.0511673204600811,
0.02119406685233116,
-0.021042535081505775,
-0.0385780930519104,
-0.0864570140838623,
0.026469750329852104,
-0.032125260680913925,
-0.012943071313202381,
0.004627887159585953,
0.04891658574342728,
-0.025163445621728897,
0.02926257997751236,
0.05062161013484001,
-0.003397336695343256,
-0.07584551721811295,
0.023678969591856003,
0.014869431965053082,
0.03632144257426262,
-0.06632830947637558,
-0.07055722177028656,
-0.026076586917042732,
0.04823509231209755,
0.05045321583747864,
0.00747712142765522,
-0.023403842002153397,
-0.01849171333014965,
-0.012631360441446304,
-0.060011085122823715,
0.00459721265360713,
0.04443061724305153,
0.07220139354467392,
-0.009680553339421749,
0.0342542864382267,
-0.0003033030079677701,
0.027251867577433586,
0.06447374075651169,
0.018387818709015846,
-0.00803053192794323,
0.0047332243993878365,
-0.033771298825740814,
0.031196940690279007,
-0.04006510600447655,
0.0022526138927787542,
-0.06155141815543175,
0.02242005057632923,
0.01290098112076521,
-0.0263186227530241,
-0.06962020695209503,
0.018776610493659973,
-0.003422177629545331,
-0.003595584537833929,
0.051569487899541855,
-0.01942448318004608,
0.0584440715610981,
-0.02738727629184723,
0.06416263431310654,
0.05519353598356247,
-0.023435935378074646,
-0.00736079690977931,
-0.03150246664881706,
0.025579703971743584,
-0.00037244855775497854,
-0.03457247465848923,
-0.07324385643005371,
0.02164315991103649,
-0.04958759993314743,
0.037470415234565735,
-0.07560267299413681,
0.019396254792809486,
-0.012203609570860863,
0.036302097141742706,
-0.042226437479257584,
0.012907988391816616,
0.014221975579857826,
0.07491490244865417,
-0.0008920558029785752,
0.04405106231570244,
-0.05129417032003403,
-0.02790370211005211,
0.0038617150858044624,
-0.04451020807027817,
-0.015179121866822243,
0.018358130007982254,
0.002138433512300253,
0.0074757845140993595,
0.00865023210644722,
-0.016443222761154175,
-0.034064050763845444,
-0.003010230604559183,
-0.08205422759056091,
0.021166278049349785,
0.013607239350676537,
0.013390240259468555,
-0.0065822782926261425,
-0.03956017643213272,
-0.024708207696676254,
0.05416259542107582,
-0.07644958794116974,
0.0540941096842289,
-0.026706460863351822,
-0.028321553021669388,
-0.039303213357925415,
-0.038974322378635406,
-0.00014112752978689969,
0.0007380075985565782,
-0.06802662461996078,
-0.02128984034061432,
-0.058652613312006,
-0.03767578303813934,
-0.024336472153663635,
0.06324537098407745,
0.027736345306038857,
-0.030370762571692467,
0.023162508383393288,
-0.040817130357027054,
0.01510634459555149,
-0.028651529923081398,
0.018995536491274834,
-0.0013038042234256864,
-0.04821521043777466,
-0.046907179057598114,
0.0482223778963089,
0.038573335856199265,
-0.05136282369494438,
0.05058173090219498,
0.022759994491934776,
0.0533624142408371,
-0.03346909210085869,
0.0258706733584404,
0.04979470744729042,
-0.026108887046575546,
-0.007827294059097767,
-0.020363209769129753,
0.034200526773929596,
-0.0015580520266667008,
0.017947163432836533,
0.07956003397703171,
-0.08535493910312653,
-0.003390334080904722,
0.029297882691025734,
-0.03312204033136368,
0.017785925418138504,
-0.04505680873990059,
0.036404289305210114,
0.03284429758787155,
-0.01353751216083765,
-0.043377336114645004,
0.03078114613890648,
0.07277510315179825,
0.03725998103618622,
-0.008675681427121162,
-0.07017133384943008,
0.00029234986868686974,
-0.025292109698057175,
0.015700800344347954,
0.0077908760868012905,
0.030608220025897026,
-0.018329894170165062,
0.03773823752999306,
0.0654221624135971,
-0.09037027508020401,
0.001507278997451067,
-0.014120579697191715,
-0.01069340668618679,
-0.05131470784544945,
-0.022555887699127197,
0.02088678814470768,
0.03184846043586731,
-0.02246536687016487,
0.00789098534733057,
-0.03132336214184761,
0.008365631103515625,
0.0261420626193285,
0.009450561366975307,
0.031567949801683426,
-0.0796627476811409,
0.04193463549017906,
0.05165424570441246,
-0.03762011602520943,
0.017042221501469612,
-0.018299661576747894,
-0.03206745907664299,
0.09392652660608292,
-0.0017748442478477955,
-0.01705310307443142,
-0.048964764922857285,
-0.08068627119064331,
0.05981007218360901,
-0.04895702004432678,
-0.03592158854007721,
-0.00923596415668726,
0.092666856944561,
0.022809460759162903,
0.04807698354125023,
-0.021789126098155975,
-0.0856940895318985,
0.002597857965156436,
0.030660223215818405,
0.006044188980013132,
0.023945026099681854,
0.023386795073747635,
-0.014416497200727463,
-0.039684053510427475,
-0.01571173407137394,
-0.018024414777755737,
-0.022022152319550514,
0.02644733339548111,
0.036066871136426926,
-0.004231567028909922,
-0.036300767213106155,
0.04690280556678772,
-0.007417428772896528,
0.015468315221369267,
-0.052357591688632965,
0.0559939369559288,
0.02142210677266121,
0.01640894077718258,
-0.0577823780477047,
0.009474048390984535,
-0.018495917320251465,
0.03380545973777771,
-0.02063308283686638,
0.004229559097439051,
0.003301490331068635,
0.013847117312252522,
0.0078036487102508545,
-0.033493462949991226,
0.012766723521053791,
-0.010453334078192711,
-0.002296781400218606,
0.03831040859222412,
0.03706097602844238,
-0.012351163662970066,
-0.0603351816534996,
-0.026476005092263222,
0.01894388720393181,
0.0007873500580899417,
0.004729302134364843,
0.00482421088963747,
0.05094127357006073,
0.024620424956083298,
-0.006709991488605738,
-0.05091782286763191,
0.06478769332170486,
-0.002998423296958208,
-0.05747372284531593,
0.04103231430053711,
0.033526066690683365,
-0.021515870466828346,
-0.006421841215342283,
-0.030577637255191803,
-0.008553614839911461,
-0.04239797964692116,
0.016660936176776886,
-0.020464297384023666,
-0.05007144436240196,
-0.041671231389045715,
0.005415385123342276,
0.0017549905460327864,
0.007435136009007692,
-0.07013015449047089,
0.0075958180241286755,
-0.03883659467101097,
0.0035862706135958433,
-0.010945521295070648,
-0.010872142389416695,
0.0032669627107679844,
0.009614610113203526,
0.001763145555742085,
0.004813481587916613,
-0.07944700121879578,
-0.03164678439497948,
-0.014764867722988129,
0.04386789724230766,
-0.020861461758613586,
-0.03181811049580574,
0.01415304746478796,
-0.008131682872772217,
0.0067748576402664185,
-0.013742153532803059,
-0.06309868395328522,
0.005109768360853195,
0.008455795235931873,
-0.030066952109336853,
-0.0041543240658938885,
-0.0522429496049881,
-0.018773619085550308,
-0.018327385187149048,
0.04164629429578781,
0.02632014825940132,
0.054473478347063065,
0.049973536282777786,
0.08120348304510117,
-0.00362860644236207,
0.0438200980424881,
-0.0040583922527730465,
0.050219159573316574,
0.05048580840229988,
0.0010939603671431541,
-0.016093358397483826,
-0.015591099858283997,
-0.014441967941820621,
-0.006448649801313877,
-0.010767672210931778,
-0.07740940898656845,
-0.012518077157437801,
0.022522680461406708,
0.05930665507912636,
0.05402825027704239,
0.015129270032048225,
-0.0446162112057209,
-0.038462068885564804,
0.02435203269124031,
0.030177604407072067,
-0.07528345286846161,
0.0061760530807077885,
-0.05182701721787453,
0.027705708518624306,
0.02981295809149742,
-0.03564922511577606,
0.027884364128112793,
-0.003846770618110895,
0.06093266233801842,
0.01375716645270586,
0.024162951856851578,
0.012328562326729298,
-0.017695104703307152,
-0.02090437337756157,
0.02743513323366642,
0.01749517023563385,
0.060354068875312805,
-0.03817882761359215,
-0.004049879498779774,
-0.015417640097439289,
-0.007861021906137466,
0.04593673720955849,
0.01865951530635357,
0.043505579233169556,
-0.030414273962378502,
0.024322886019945145,
0.009933550842106342,
0.02487529069185257,
0.026531049981713295,
0.0015266812406480312,
-0.007814791053533554,
-0.04184839129447937,
0.000908514077309519,
-0.04386134445667267,
-0.05123909190297127,
0.010367875918745995,
-0.03305114433169365,
0.0036853638011962175,
-0.010478605516254902,
0.03148885816335678,
-0.027689853683114052,
-0.02654271386563778,
-0.010944858193397522,
-0.03653601184487343,
0.042361095547676086,
-0.010318752378225327,
0.02310369536280632,
0.01244518905878067,
0.03851756080985069,
0.00562590267509222,
0.0131978215649724,
0.06034683436155319,
-0.06579001992940903,
-0.05613139271736145,
0.05964396148920059,
0.0245413426309824,
-0.05275610834360123,
0.030649587512016296,
-0.01068046409636736,
0.03746650740504265,
-0.006479335483163595,
0.00042392470641061664,
0.00890281144529581,
0.035831961780786514,
0.015902437269687653
] |
<p>I can't find an answer of why the lowest temperature is -273.15ºC. Is it deduced theoretically or is it experimental?</p>
<p>An explanation is that when any gas volume tends to zero, the temperature will be -273.15ºC (Charles law). But shouldn't this number have some kind of error? And this would only apply to ideal gases.</p>
<p><img src="http://i.stack.imgur.com/LOk7j.jpg" alt="enter image description here"></p> | g9184 | [
0.07148756831884384,
-0.051653604954481125,
-0.006751292385160923,
-0.0060284133069217205,
0.030257519334554672,
0.019194604828953743,
-0.031137386336922646,
0.07119524478912354,
-0.02842172421514988,
-0.04533407464623451,
-0.013316546566784382,
0.0032351515255868435,
-0.0036359746009111404,
-0.00827722530812025,
0.008220059797167778,
0.023343954235315323,
0.043794095516204834,
-0.017400499433279037,
0.04947339743375778,
0.012003385461866856,
-0.0376085564494133,
-0.005595700815320015,
-0.005139494314789772,
-0.05869344249367714,
0.017120765522122383,
-0.04602111876010895,
-0.040243491530418396,
0.07396459579467773,
-0.044896166771650314,
0.003412429941818118,
0.017401259392499924,
0.002908749505877495,
0.017202403396368027,
-0.034127283841371536,
0.027106108143925667,
-0.0485646016895771,
0.010330337099730968,
0.0017132862703874707,
-0.007411052938550711,
-0.0313485749065876,
0.024134626612067223,
0.032469671219587326,
0.02234312705695629,
0.018511543050408363,
-0.04259302094578743,
0.04578155651688576,
-0.04429733380675316,
0.03150063008069992,
-0.0009112082188948989,
0.0060084811411798,
-0.002727896673604846,
0.021384811028838158,
0.021808341145515442,
-0.02431722730398178,
0.008041317574679852,
-0.03821970522403717,
-0.05359393730759621,
-0.017002763226628304,
0.030308440327644348,
0.024740489199757576,
0.032279741019010544,
-0.01578652858734131,
-0.00280487141571939,
-0.018276752904057503,
0.03154467046260834,
-0.02857917547225952,
-0.047444745898246765,
-0.002314675599336624,
0.05926536023616791,
0.03957298770546913,
0.0013487585820257664,
-0.04350867494940758,
-0.04428769648075104,
-0.03215494751930237,
-0.03973686322569847,
-0.005943522322922945,
0.013087166473269463,
-0.058433808386325836,
-0.014581182971596718,
-0.02411642298102379,
-0.053462397307157516,
-0.0010028303368017077,
0.004531825426965952,
0.005847102962434292,
-0.0016728509217500687,
-0.017707079648971558,
0.008062412030994892,
-0.022341694682836533,
-0.001619968214072287,
0.051497552543878555,
-0.049965422600507736,
0.07422401010990143,
0.1119590625166893,
-0.06628906726837158,
0.001430968171916902,
0.023021720349788666,
0.013812488876283169,
0.030654508620500565,
0.05553212761878967,
0.03086663968861103,
0.004780484363436699,
0.02656705491244793,
-0.01684163510799408,
-0.005960151087492704,
-0.043008510023355484,
0.026017464697360992,
-0.047784287482500076,
-0.00814479123800993,
-0.05009445920586586,
-0.009367775171995163,
-0.058074843138456345,
-0.046169232577085495,
-0.06931136548519135,
-0.03260284289717674,
0.01288921944797039,
0.026854829862713814,
0.0037240346428006887,
-0.026528412476181984,
0.03458291292190552,
0.045402806252241135,
0.03403177484869957,
0.06190037727355957,
-0.01482874434441328,
0.06621221452951431,
0.0018669841811060905,
-0.05750430375337601,
0.024362409487366676,
-0.024872979149222374,
0.009569942951202393,
-0.018799714744091034,
-0.01187458261847496,
0.026230067014694214,
-0.060136307030916214,
-0.03947392851114273,
0.03747568652033806,
-0.02592657133936882,
-0.004875257611274719,
0.04383348673582077,
-0.013216082006692886,
0.027020784094929695,
0.037683043628931046,
0.039781443774700165,
0.07172489911317825,
-0.0450366847217083,
-0.05280653014779091,
-0.04116404429078102,
-0.0866197869181633,
0.026098646223545074,
0.0745512917637825,
0.015079696662724018,
-0.02544519305229187,
0.013804431073367596,
0.0898134708404541,
-0.026013238355517387,
-0.04605371877551079,
-0.0367707721889019,
0.06966432929039001,
0.03770522400736809,
-0.003258787328377366,
-0.027115171775221825,
-0.0066927955485880375,
0.024792345240712166,
0.02421235665678978,
0.00004276906111044809,
-0.0657290518283844,
0.031723737716674805,
-0.041862547397613525,
0.03268527239561081,
0.011109046638011932,
-0.04250284284353256,
-0.05050089582800865,
0.004855602513998747,
-0.05815138667821884,
-0.006758602801710367,
-0.010123790241777897,
-0.013533681631088257,
0.037350501865148544,
0.02386854775249958,
-0.002680964069440961,
-0.09231917560100555,
0.027449658140540123,
-0.02386217564344406,
0.019767744466662407,
-0.06591244041919708,
-0.012339063920080662,
0.048727862536907196,
-0.01807182841002941,
-0.049982186406850815,
-0.05013253539800644,
-0.007046434562653303,
0.013218643143773079,
-0.004022296983748674,
-0.007160434033721685,
-0.04272863641381264,
0.004063798580318689,
-0.031445786356925964,
0.026568856090307236,
-0.011051971465349197,
-0.07450825721025467,
0.047511760145425797,
-0.037638500332832336,
0.020519157871603966,
0.021715393289923668,
-0.029845228418707848,
-0.03767884522676468,
-0.022748172283172607,
-0.012716330587863922,
-0.046875812113285065,
0.027525991201400757,
-0.009357144124805927,
-0.05758283659815788,
0.015192100778222084,
0.012770671397447586,
0.03213563561439514,
0.01334143616259098,
0.06356791406869888,
0.045771338045597076,
-0.003994415979832411,
-0.011464042589068413,
0.009275401942431927,
-0.02722271718084812,
0.03927355632185936,
0.0013369637308642268,
0.011104876175522804,
0.04141384735703468,
-0.050382569432258606,
-0.0429702028632164,
-0.028200799599289894,
0.03346911072731018,
-0.03666725754737854,
-0.01202393975108862,
0.0146722923964262,
-0.007900489494204521,
0.00043024495244026184,
0.004404175095260143,
0.04406280070543289,
0.014413726516067982,
-0.01610497198998928,
0.03040502592921257,
0.0802755355834961,
-0.02087731473147869,
-0.025699427351355553,
-0.04040779918432236,
0.08843781799077988,
0.023248903453350067,
0.004375453107059002,
-0.04059561714529991,
-0.013108834624290466,
0.021798044443130493,
-0.03034001588821411,
-0.0004559291701298207,
0.01484532281756401,
0.002693058457225561,
0.014326696284115314,
-0.043299589306116104,
0.022946780547499657,
-0.08579365164041519,
0.055866342037916183,
0.011516198515892029,
-0.09049241989850998,
0.06461716443300247,
-0.027753479778766632,
0.06062163785099983,
-0.00022783658641856164,
-0.03350866213440895,
0.004458279348909855,
-0.09392337501049042,
0.05655568465590477,
-0.0027512547094374895,
0.013786525465548038,
0.023156853392720222,
0.06673114001750946,
-0.007182273082435131,
0.03352786600589752,
-0.013783300295472145,
-0.027468541637063026,
0.023081099614501,
0.02790169045329094,
0.001528536668047309,
-0.036369726061820984,
-0.0032235817052423954,
0.01897873915731907,
-0.023717692121863365,
0.03976131230592728,
0.02826557494699955,
-0.026974422857165337,
-0.06913156807422638,
-0.0026914605405181646,
0.020425938069820404,
-0.06078970432281494,
0.0397854819893837,
0.059048715978860855,
0.0019098981283605099,
0.03332022204995155,
0.06440648436546326,
0.017905838787555695,
0.05321389064192772,
0.009167118929326534,
0.005003702826797962,
-0.03676491230726242,
-0.009716943837702274,
-0.039937056601047516,
-0.01990514062345028,
-0.017046641558408737,
-0.04287630319595337,
-0.011570212431252003,
-0.02151409350335598,
-0.002290760399773717,
-0.03399275988340378,
-0.0017424799734726548,
-0.0021381983533501625,
0.005313985049724579,
0.033388085663318634,
-0.012294929474592209,
-0.03444341942667961,
0.027684541419148445,
-0.045196592807769775,
-0.002122157718986273,
-0.013625171035528183,
0.03194734826683998,
-0.02117672935128212,
-0.03334100916981697,
-0.003422287991270423,
-0.04732412099838257,
0.008572311140596867,
0.003967838361859322,
-0.009558559395372868,
-0.06214297562837601,
-0.015646187588572502,
0.006544226314872503,
-0.010135959833860397,
-0.009963813237845898,
-0.040281977504491806,
0.007617725525051355,
-0.0050666178576648235,
-0.03468883037567139,
-0.07491902261972427,
0.02414011023938656,
0.03255966305732727,
0.035101547837257385,
-0.0016131250886246562,
-0.014453042298555374,
0.011914404109120369,
-0.004145815968513489,
0.036082759499549866,
0.0018883761949837208,
-0.024723444133996964,
0.05251026898622513,
-0.012133289128541946,
0.02798403799533844,
0.04207820072770119,
-0.06786910444498062,
0.0027972001116722822,
0.013814589008688927,
-0.008172441273927689,
0.03540210798382759,
-0.014603332616388798,
0.04517393186688423,
-0.022685887292027473,
-0.014721952378749847,
0.008667782880365849,
0.0011968001490458846,
0.036920215934515,
-0.00004615569923771545,
0.03338417038321495,
-0.0024046411272138357,
-0.05217408761382103,
0.047587815672159195,
0.06310717761516571,
-0.04007256403565407,
-0.05962381511926651,
-0.0329296812415123,
0.024491101503372192,
0.02005694806575775,
0.05322181060910225,
-0.042374853044748306,
0.029269017279148102,
0.02105080336332321,
-0.03211916238069534,
0.04329683259129524,
0.06234082579612732,
0.020440857857465744,
0.01635889522731304,
0.0018647083779796958,
0.004772764164954424,
-0.02384071983397007,
-0.05410017818212509,
-0.022680453956127167,
0.023156089708209038,
-0.10391159355640411,
-0.024524372071027756,
0.0460660383105278,
0.03383133187890053,
0.028112033382058144,
0.026703620329499245,
-0.006020994391292334,
0.028483211994171143,
0.0050531961023807526,
-0.08031769096851349,
-0.017893120646476746,
0.040633901953697205,
-0.02948993444442749,
0.05304732173681259,
0.02024288848042488,
0.0159787368029356,
0.032520510256290436,
0.0491107776761055,
-0.01322838943451643,
0.04632531851530075,
-0.014559934847056866,
0.029949694871902466,
-0.015210551209747791,
-0.03368194401264191,
-0.04422246664762497,
0.04872675985097885,
0.009281505830585957,
-0.008154037408530712,
-0.04174035042524338,
0.034787073731422424,
0.04031776264309883,
0.009501884691417217,
0.012242535129189491,
-0.03456886112689972,
-0.036975350230932236,
0.012959124520421028,
0.016955161467194557,
0.06715399026870728,
0.043748412281274796,
-0.014301368966698647,
-0.043528128415346146,
0.027456630021333694,
-0.05571688339114189,
-0.06716452538967133,
0.02876947447657585,
-0.006152102258056402,
0.02978319115936756,
0.03161441162228584,
0.04959867149591446,
0.029956908896565437,
0.07996567338705063,
0.021950645372271538,
0.013433016836643219,
0.025827983394265175,
-0.0010870092082768679,
-0.0617232508957386,
0.04460645467042923,
0.016847167164087296,
-0.05308252200484276,
0.005500924773514271,
-0.00005210923700360581,
0.05698069557547569,
0.013582009822130203,
-0.04553292691707611,
-0.040455907583236694,
-0.0064446646720170975,
-0.058923106640577316,
-0.07478545606136322,
0.11069952696561813,
-0.03367065265774727,
0.05911405012011528,
-0.07203162461519241,
-0.02184116281569004,
-0.017639385536313057,
0.03853074461221695,
0.058828532695770264,
0.011443771421909332,
0.013583730906248093,
0.004297780338674784,
0.015751052647829056,
0.020397426560521126,
-0.028723254799842834,
0.0635557472705841,
-0.010973621159791946,
0.028438378125429153,
-0.011936710216104984,
-0.025552913546562195,
0.04120006412267685,
-0.01841668039560318,
0.03563506901264191,
-0.03418393433094025,
0.010579871945083141,
0.03900335729122162,
-0.028365302830934525,
0.053508907556533813,
0.036004118621349335,
0.04241408035159111,
-0.07468237727880478,
-0.004299423191696405,
0.01831979490816593,
0.011853987351059914,
0.019021088257431984,
0.023332003504037857,
0.008486106991767883,
0.020619099959731102,
-0.022987235337495804,
-0.05692829191684723,
-0.00754424137994647,
0.0024463138543069363,
0.012789875268936157,
-0.003448499832302332,
-0.06359484046697617,
-0.005052289459854364,
-0.027513060718774796,
-0.019632820039987564,
-0.0036607326474040747,
-0.030658848583698273,
-0.011135941371321678,
-0.015700357034802437,
-0.0016017643501982093,
0.010864036157727242,
0.017705729231238365,
0.006238591857254505,
0.03127162531018257,
0.007210761308670044,
0.028063368052244186,
-0.018656117841601372,
0.00026342153432779014,
-0.017330868169665337,
-0.0006470626103691757,
-0.00830834824591875,
0.015427928417921066,
-0.027339832857251167,
0.01577177830040455,
-0.036247190088033676,
-0.0453786663711071,
0.013190621510148048,
-0.05454568564891815,
-0.0661558285355568,
-0.03634757176041603,
-0.018985284492373466,
-0.0548684261739254,
0.01893632672727108,
0.07499449700117111,
-0.006672065705060959,
0.001599104842171073,
0.0293350201100111,
-0.02465732954442501,
-0.015760177746415138,
0.06438411772251129,
-0.01847519353032112,
0.033838339149951935,
-0.037430208176374435,
-0.015041409991681576,
0.003011301625519991,
0.05204799026250839,
-0.015460047870874405,
-0.048252787441015244,
0.032116688787937164,
0.03457103669643402,
-0.019736649468541145,
0.006568721495568752,
0.01824532262980938,
-0.025529561564326286,
-0.033002376556396484,
0.032130345702171326,
-0.011843829415738583,
-0.011116833426058292,
0.03920960798859596,
0.00482091074809432,
0.03505757451057434,
0.021102221682667732,
0.06926101446151733,
0.030467525124549866,
0.07836876064538956,
-0.01684052124619484,
-0.060955945402383804,
-0.059888891875743866,
-0.012731066904962063,
0.02947426773607731,
0.025459423661231995,
0.0036483006551861763,
-0.015064607374370098,
-0.006518136244267225,
-0.01629932038486004,
0.05907665565609932,
-0.011346652172505856,
-0.038789309561252594,
-0.020949503406882286,
-0.017059694975614548,
0.022036274895071983,
0.008755616843700409,
-0.023450834676623344,
-0.006329155061393976,
-0.004068361595273018,
-0.032865915447473526,
0.039190419018268585,
-0.011119402013719082,
-0.02401573210954666,
-0.052057042717933655,
0.0005517344688996673,
0.02516958676278591,
0.0005519383121281862,
0.01004640944302082,
0.0014990827767178416,
0.030767811462283134,
-0.04831188544631004,
-0.034070566296577454,
-0.003514423267915845,
-0.05637271702289581,
-0.0064948974177241325,
0.05025031790137291,
0.04176720604300499,
0.008556741289794445,
-0.02135186456143856,
0.02720457874238491,
0.006967294495552778,
0.020062539726495743,
0.061152439564466476,
0.013720309361815453,
0.05184396356344223,
-0.04398581385612488,
0.06421752274036407,
-0.0006879334687255323,
-0.00950776319950819,
0.03835870325565338,
-0.07782334089279175,
0.0055706677958369255,
0.05317045375704765,
-0.032413266599178314,
0.020822126418352127,
-0.051672324538230896,
-0.0073305158875882626,
-0.03011581487953663,
0.0036425692960619926,
0.039407435804605484,
-0.002405816223472357,
-0.011121614836156368,
0.0599040761590004,
0.039964139461517334,
-0.04221588000655174,
0.023761646822094917,
-0.031294796615839005,
0.009579145349562168,
0.027706805616617203,
-0.018407290801405907,
-0.015756646171212196,
-0.0795450359582901,
-0.003894322318956256,
0.07844366878271103,
0.03458379954099655,
-0.00546203413978219,
-0.050457663834095,
0.007548663765192032,
-0.012040457688272,
-0.030408957973122597,
0.026608427986502647,
-0.01934838853776455,
-0.0452120415866375,
-0.036692213267087936,
-0.011736025102436543,
0.026364311575889587,
-0.019727488979697227,
-0.00538321677595377,
0.030769959092140198,
0.005458340048789978,
0.002614316064864397,
-0.014734773896634579,
-0.03404746204614639,
0.05433356389403343,
-0.01876693032681942,
-0.06097158044576645,
-0.008494662120938301,
0.034655891358852386,
0.038385871797800064,
0.026524342596530914,
0.03234117105603218,
0.041384391486644745,
-0.021823616698384285,
0.009470276534557343,
-0.133694589138031,
0.01783469319343567,
-0.021166661754250526,
-0.011847845278680325,
-0.07902030646800995,
0.02288161590695381,
0.05441867560148239,
-0.02156122215092182,
0.0020846726838499308,
0.04180249199271202,
0.05852940306067467,
0.015123377554118633,
0.0034577101469039917,
-0.0028416195418685675,
-0.09001962095499039,
-0.0227342676371336,
-0.0016818454023450613,
0.016986925154924393,
-0.017399931326508522,
0.008576048538088799,
-0.029448626562952995,
0.004547376185655594,
-0.037301626056432724,
0.054984401911497116,
-0.04032401368021965,
-0.04210061579942703,
0.03487573564052582,
0.032061733305454254,
-0.02250700071454048,
0.02099854126572609,
-0.053207878023386,
0.01823744736611843,
-0.041559018194675446,
-0.018005073070526123,
0.031550899147987366,
0.03870443254709244,
0.03604154288768768,
0.034689102321863174,
0.0617741197347641,
-0.08918366581201553,
-0.03419855609536171,
0.004361292347311974,
0.014944653958082199,
0.06610480695962906,
0.052720583975315094,
0.05945977196097374,
0.015386718325316906,
-0.03452576324343681,
-0.05654871463775635,
-0.007862979546189308,
-0.01642712578177452,
0.07759701460599899,
0.026096293702721596,
0.047635190188884735,
-0.042695704847574234,
-0.02172248624265194,
-0.02832070365548134,
-0.003338856855407357,
-0.010970566421747208,
0.025529546663165092,
-0.028409389778971672,
-0.021930083632469177,
0.09134500473737717,
-0.02503177709877491,
0.045588135719299316,
-0.04484604299068451,
0.06499770283699036,
0.029561173170804977,
0.012952554039657116,
0.028414612635970116,
0.052342820912599564,
0.012194235809147358,
0.040743544697761536,
0.0009382879361510277,
-0.02628222480416298,
0.021013766527175903,
-0.033819396048784256,
-0.05514365807175636,
0.049079373478889465,
0.019994260743260384,
-0.007757588289678097,
-0.011125468648970127,
-0.05037243291735649,
-0.02450895681977272,
0.023688677698373795,
-0.014181387610733509,
-0.054946206510066986,
0.005783524364233017,
-0.007482968270778656,
-0.021061018109321594,
0.01519698929041624,
-0.00977267511188984,
-0.020855292677879333,
0.03956728056073189,
0.0026371460407972336,
0.0070681022480130196,
0.015374330803751945,
-0.008589020930230618,
-0.03114168345928192
] |
<p>I know that
$A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$</p>
<p>But how can write $E_{[a} F_{bc]}$ like the above?</p>
<p>Can you provide a reference where this notational matter is discussed?</p> | g9185 | [
0.01511597540229559,
-0.019124656915664673,
-0.011163528077304363,
-0.0321730338037014,
0.08249576389789581,
-0.04061972349882126,
0.061914414167404175,
0.03622094541788101,
-0.033655691891908646,
-0.016772199422121048,
-0.0013289510970935225,
0.05108935013413429,
0.05330438166856766,
0.03452887758612633,
0.02848249487578869,
0.026443371549248695,
-0.006782743614166975,
0.004938939120620489,
0.047546837478876114,
-0.002827441319823265,
-0.0314212292432785,
0.01025831513106823,
0.012616277672350407,
0.0206614900380373,
0.04792019724845886,
-0.028058521449565887,
0.061140235513448715,
0.04146033525466919,
-0.04621654376387596,
-0.04574253782629967,
-0.0028336364775896072,
0.07376345992088318,
0.04767238348722458,
0.014807132072746754,
0.0041160560213029385,
-0.002494564512744546,
-0.03335701301693916,
0.06107531860470772,
0.013867739588022232,
-0.036674682050943375,
-0.01670719124376774,
0.028484506532549858,
-0.0466352216899395,
-0.005775305442512035,
-0.028244275599718094,
-0.03962722793221474,
-0.017976438626646996,
0.007245045620948076,
-0.05341881886124611,
-0.0029844308737665415,
0.05399370193481445,
0.05181526765227318,
0.05958406254649162,
-0.05395888909697533,
0.0076332841999828815,
0.026096131652593613,
0.010013710707426071,
-0.01532923523336649,
0.029147494584321976,
0.039915282279253006,
-0.04243270307779312,
-0.04218626767396927,
-0.023914607241749763,
0.018338441848754883,
0.024211367592215538,
0.03607538342475891,
-0.039831120520830154,
0.007554732263088226,
-0.024461187422275543,
-0.004766198806464672,
0.026148686185479164,
-0.07488227635622025,
0.036975324153900146,
0.004291780758649111,
-0.06576590240001678,
-0.019527284428477287,
-0.016216494143009186,
0.007464035879820585,
0.014107611030340195,
0.010834031738340855,
-0.009311839938163757,
-0.004508512560278177,
0.06565677374601364,
-0.014361637644469738,
-0.021977288648486137,
-0.012280776165425777,
-0.006086505018174648,
-0.009438890963792801,
-0.007068641483783722,
-0.037610992789268494,
-0.02948392555117607,
-0.037594884634017944,
-0.03657584637403488,
0.03816824406385422,
-0.002319537103176117,
-0.0670107901096344,
0.0035844561643898487,
0.0018690458964556456,
-0.055965762585401535,
-0.014144114218652248,
0.02364511974155903,
-0.016055777668952942,
0.0059193712659180164,
0.0015933875693008304,
-0.03736671060323715,
-0.04925241321325302,
0.05930129811167717,
-0.03120528906583786,
-0.017591940239071846,
-0.06514182686805725,
0.013499092310667038,
0.0023163475561887026,
-0.03991152346134186,
-0.07482890039682388,
-0.06144779175519943,
0.05048796534538269,
-0.008019058965146542,
-0.02986377663910389,
-0.04016822576522827,
0.025886306539177895,
-0.028388630598783493,
-0.05503233149647713,
0.03751228004693985,
0.019872207194566727,
-0.0218485239893198,
0.019847743213176727,
0.04326269030570984,
0.05701974406838417,
0.08607371896505356,
-0.04664098471403122,
0.0006328947492875159,
0.0025666439905762672,
0.09782259911298752,
-0.0389433316886425,
0.047538332641124725,
0.0699562206864357,
-0.005295215640217066,
0.017095834016799927,
-0.009171548299491405,
-0.025818195194005966,
-0.07669269293546677,
-0.03394870087504387,
0.0038996723014861345,
-0.039099372923374176,
-0.05491107702255249,
0.010781652294099331,
-0.04109501838684082,
-0.037445344030857086,
0.05189310386776924,
-0.0093107083812356,
-0.03166038170456886,
0.08641975373029709,
0.005866692867130041,
-0.0091940239071846,
0.029058633372187614,
0.04233246296644211,
0.06527572125196457,
-0.026819657534360886,
-0.05624211207032204,
0.00989118404686451,
0.028044167906045914,
0.02031787484884262,
-0.01080617681145668,
0.019992420449852943,
-0.05768095329403877,
0.00031414153636433184,
-0.078103207051754,
-0.04895779490470886,
-0.0565345361828804,
0.011735057458281517,
-0.004827788565307856,
0.05458616465330124,
0.009210721589624882,
0.049879997968673706,
0.050711739808321,
0.06552547961473465,
-0.03496643155813217,
0.007184051442891359,
0.03114227019250393,
0.017983146011829376,
-0.010581501759588718,
0.03132585436105728,
0.0035339640453457832,
0.07455158978700638,
0.017070025205612183,
0.006216251756995916,
0.006108958274126053,
0.013383629731833935,
0.038848765194416046,
-0.0035836503375321627,
-0.016104238107800484,
0.03131088241934776,
-0.008540717884898186,
0.04141666367650032,
-0.03141867369413376,
0.04257233813405037,
-0.06770969927310944,
-0.06206686422228813,
-0.011124926619231701,
0.03705279529094696,
0.01716603897511959,
0.02281535230576992,
0.022920524701476097,
-0.0007677729590795934,
0.009708263911306858,
0.01165835838764906,
-0.02729938179254532,
-0.012979209423065186,
-0.005907632876187563,
0.03198787197470665,
-0.029675692319869995,
-0.04313949868083,
0.0060752383433282375,
0.012552885338664055,
0.010403630323708057,
-0.03908376768231392,
0.00036613477277569473,
-0.005478429142385721,
-0.06368846446275711,
0.028748899698257446,
-0.017242394387722015,
0.018642619252204895,
-0.007009586319327354,
-0.03718077763915062,
-0.0291147343814373,
0.01129074301570654,
0.024234788492321968,
0.0384465754032135,
-0.004671158269047737,
-0.024766525253653526,
-0.10298056155443192,
0.0037257648073136806,
-0.04711008444428444,
-0.023067189380526543,
-0.04858320206403732,
-0.009291527792811394,
-0.02127521112561226,
0.008686007000505924,
0.014240292832255363,
0.03737140819430351,
-0.00915208738297224,
-0.006006534676998854,
-0.005000078584998846,
0.03628310188651085,
0.03149889409542084,
0.014365775510668755,
0.039948463439941406,
0.04662156105041504,
-0.018972167745232582,
0.02152879536151886,
-0.040430061519145966,
-0.05913488194346428,
-0.015618696808815002,
0.028067683801054955,
0.0037628302816301584,
-0.00901979673653841,
-0.03125563636422157,
-0.01915040798485279,
0.025220906361937523,
0.021500488743185997,
0.030472811311483383,
-0.021318381652235985,
0.02584950253367424,
0.010447490960359573,
-0.046574585139751434,
-0.011749298311769962,
-0.019424578174948692,
-0.0015864837914705276,
0.017023518681526184,
-0.00409981794655323,
-0.0014241994358599186,
-0.025408513844013214,
0.022619863972067833,
-0.005309250205755234,
-0.029288845136761665,
-0.04004096984863281,
0.025235570967197418,
-0.04215436056256294,
0.01288596075028181,
0.0010864025680348277,
-0.004427807871252298,
0.03775222972035408,
0.013655564747750759,
0.02570044994354248,
0.010658428072929382,
0.0108663784340024,
-0.03593812510371208,
0.08731310069561005,
-0.0031367356423288584,
-0.03553878143429756,
0.01710616424679756,
0.0052917273715138435,
0.00451745605096221,
-0.003362033748999238,
0.024768143892288208,
0.035877034068107605,
-0.008933758363127708,
0.011385808698832989,
0.006369184236973524,
0.0380714051425457,
-0.031413838267326355,
0.014740176498889923,
-0.010362704284489155,
-0.016228709369897842,
0.008436714299023151,
0.024202965199947357,
0.021360211074352264,
-0.05677783489227295,
0.03205062821507454,
-0.003665969241410494,
0.008269116282463074,
0.0147851025685668,
-0.0040274434722959995,
-0.020356332883238792,
-0.024413710460066795,
0.0022414790000766516,
0.045405782759189606,
0.023142952471971512,
0.015108131803572178,
-0.034963201731443405,
0.0067151812836527824,
-0.016781626269221306,
0.045482028275728226,
0.015127941034734249,
-0.007210865151137114,
-0.029535336419939995,
-0.031858179718256,
0.019448019564151764,
-0.011675169691443443,
-0.027095690369606018,
-0.008638071827590466,
-0.023770101368427277,
0.021225040778517723,
-0.055571652948856354,
-0.0008686297223903239,
-0.007319317199289799,
0.026627037674188614,
-0.0038493559695780277,
-0.0037757528480142355,
-0.015689417719841003,
0.010908667929470539,
0.011090336367487907,
0.029311630874872208,
0.004875312093645334,
-0.01834734156727791,
-0.026364581659436226,
0.01464015245437622,
0.026050375774502754,
0.007754229474812746,
-0.016100551933050156,
-0.05347038805484772,
-0.03598702698945999,
0.022025223821401596,
0.024301208555698395,
0.012763448990881443,
-0.037800583988428116,
0.04949478432536125,
-0.04188363626599312,
-0.008278938010334969,
-0.002377127530053258,
0.006748178042471409,
-0.01749369129538536,
0.04951977729797363,
0.09852391481399536,
0.027092115953564644,
-0.055541735142469406,
0.005479483865201473,
0.026692047715187073,
-0.015609231777489185,
0.06255491077899933,
0.02360052801668644,
-0.00962242390960455,
0.059953272342681885,
0.02212725579738617,
-0.015071387402713299,
-0.05037004500627518,
-0.04020974040031433,
0.01052937563508749,
0.01588011533021927,
0.01762191206216812,
-0.013343138620257378,
-0.04558255523443222,
0.021729862317442894,
-0.009620143100619316,
0.022359512746334076,
0.03489817678928375,
-0.011607886292040348,
0.028159016743302345,
0.07102753967046738,
-0.039460379630327225,
0.0015785867581143975,
-0.0017360911006107926,
-0.009068802930414677,
0.010163706727325916,
-0.011616615578532219,
-0.012566887773573399,
0.035909704864025116,
0.059429824352264404,
-0.0753447413444519,
0.048455994576215744,
-0.013348391279578209,
0.01985013298690319,
0.03965185955166817,
0.02967945672571659,
-0.012867103330790997,
-0.021870972588658333,
0.016918199136853218,
-0.044059716165065765,
0.02550658769905567,
-0.05651736631989479,
0.017821552231907845,
-0.05125018581748009,
0.007634694688022137,
-0.014165821485221386,
0.006194066256284714,
0.000958954740781337,
0.03225170075893402,
-0.023567743599414825,
0.08209621161222458,
0.01377169694751501,
0.036111246794462204,
-0.019685842096805573,
0.02381349727511406,
-0.06939361989498138,
0.07625529170036316,
0.01858513057231903,
0.010879610665142536,
-0.0006027675699442625,
0.04062293469905853,
0.054363418370485306,
-0.0284274872392416,
0.031242217868566513,
-0.044448088854551315,
0.02682451903820038,
-0.04932481795549393,
-0.017825670540332794,
-0.05622886121273041,
0.037212420254945755,
0.041896138340234756,
0.07126050442457199,
0.07983889430761337,
-0.07063192129135132,
-0.03879709169268608,
-0.016415419057011604,
0.06248260661959648,
0.004916489589959383,
-0.036101169884204865,
-0.03151330351829529,
0.05260862782597542,
0.008077225647866726,
-0.0005768559058196843,
0.027582507580518723,
0.05643301457166672,
-0.02497185580432415,
0.006471007596701384,
-0.008550540544092655,
-0.01912197284400463,
-0.03354386240243912,
0.02229556068778038,
-0.04453921318054199,
0.009079281240701675,
-0.02183261327445507,
-0.008757793344557285,
-0.03534839302301407,
-0.014883427880704403,
0.02898060902953148,
-0.003066480625420809,
-0.011184802278876305,
-0.008181633427739143,
-0.028007665649056435,
-0.011156374588608742,
0.02684483490884304,
-0.03397224470973015,
-0.040995217859745026,
0.06462337076663971,
0.0006898675346747041,
0.029593905434012413,
-0.0023990049958229065,
-0.058449797332286835,
-0.024185851216316223,
0.009421105496585369,
-0.08426133543252945,
-0.02558724209666252,
-0.028295598924160004,
-0.000030177663575159386,
-0.016249381005764008,
0.025118375197052956,
-0.05680035799741745,
-0.020959729328751564,
0.03624718263745308,
0.011270278133451939,
0.05647936835885048,
-0.0010962835513055325,
0.044483594596385956,
-0.02352191135287285,
-0.024468008428812027,
0.0852455273270607,
0.04249020665884018,
0.05786464363336563,
-0.039012495428323746,
-0.022319529205560684,
-0.017357701435685158,
-0.011745523661375046,
0.03020418994128704,
0.05010330304503441,
0.08814945071935654,
0.05151406675577164,
-0.03403957933187485,
-0.04893677309155464,
0.012854435481131077,
-0.03664823994040489,
-0.06612670421600342,
0.012391271069645882,
-0.007950134575366974,
0.012195445597171783,
0.04131960868835449,
-0.031075676903128624,
-0.032592643052339554,
-0.03634676709771156,
-0.05046388879418373,
0.0405476838350296,
-0.015828412026166916,
-0.03978780284523964,
-0.020386988297104836,
0.0057005626149475574,
-0.029691798612475395,
-0.04215244576334953,
-0.09038535505533218,
0.03674578666687012,
0.04909253865480423,
-0.06840688735246658,
-0.011380544863641262,
-0.02865677699446678,
0.015270747244358063,
0.034700244665145874,
-0.053904853761196136,
-0.027153372764587402,
-0.012581958435475826,
0.01335487887263298,
0.02460342086851597,
0.0027094711549580097,
0.04236910492181778,
-0.03971640393137932,
0.07225339114665985,
-0.03959237039089203,
0.010751978494226933,
-0.010326532647013664,
0.02114037610590458,
0.03771630674600601,
0.015972105786204338,
-0.024724291637539864,
-0.005098800640553236,
-0.03300374001264572,
-0.08192399144172668,
0.02976052463054657,
0.017910076305270195,
-0.031106820330023766,
-0.009898182936012745,
0.026680607348680496,
-0.020387839525938034,
-0.03618788719177246,
-0.033709824085235596,
-0.021658020094037056,
0.0013880468904972076,
-0.04121297225356102,
-0.04686436802148819,
0.027156410738825798,
0.07494227588176727,
-0.011778370477259159,
0.05974150821566582,
-0.01574092172086239,
0.006725891958922148,
-0.005082014482468367,
-0.027243053540587425,
0.02529047057032585,
0.040650881826877594,
0.009600111283361912,
-0.01386214792728424,
0.0338931679725647,
-0.014200902543962002,
-0.0037126236129552126,
0.02017802745103836,
0.039738595485687256,
0.03529874607920647,
-0.03250167518854141,
0.002278655767440796,
0.010763345286250114,
0.023066408932209015,
0.008542008697986603,
0.031981807202100754,
-0.03601173684000969,
-0.020458778366446495,
-0.03645196184515953,
0.07685110718011856,
-0.03241688013076782,
0.08149311691522598,
-0.041353579610586166,
0.06989424675703049,
0.03512078896164894,
0.00021132647816557437,
0.028249777853488922,
0.004625266417860985,
-0.014241053722798824,
-0.04068361595273018,
0.012453146278858185,
0.0658254474401474,
-0.023308854550123215,
0.0017691707471385598,
0.02056695893406868,
0.03142427280545235,
-0.018476100638508797,
-0.002270470606163144,
0.022634439170360565,
-0.019321566447615623,
-0.013177022337913513,
-0.06460357457399368,
-0.018585529178380966,
0.024105412885546684,
-0.019655916839838028,
0.01777099445462227,
0.030275970697402954,
-0.05377677455544472,
-0.03082970716059208,
-0.04745661839842796,
0.015003753826022148,
0.036160264164209366,
-0.022039160132408142,
0.01529172994196415,
0.059970512986183167,
-0.05426977202296257,
-0.02226843871176243,
0.004166540689766407,
-0.054462648928165436,
0.03833940252661705,
0.022851409390568733,
0.00667462358251214,
-0.07474623620510101,
0.054907139390707016,
-0.01933131366968155,
0.018497124314308167,
-0.07671128213405609,
0.06895442306995392,
0.021528031677007675,
0.06617572903633118,
-0.027384363114833832,
-0.0009411547798663378,
0.04913858324289322,
-0.027895711362361908,
-0.06176621466875076,
0.021146517246961594,
0.06071369722485542,
-0.0016521287616342306,
-0.009989270940423012,
0.027037953957915306,
-0.0757368952035904,
-0.03881477192044258,
0.042572952806949615,
0.020737305283546448,
-0.021523138508200645,
-0.046118106693029404,
0.01020779274404049,
0.01956426538527012,
0.024677857756614685,
-0.024186324328184128,
0.0345180369913578,
-0.010295478627085686,
0.03301442041993141,
-0.02316436357796192,
0.0365888848900795,
-0.028328027576208115,
0.01229099091142416,
-0.0377415306866169,
0.014611558988690376,
0.012417853809893131,
-0.0018224758096039295,
-0.006370471324771643,
0.008239204064011574,
0.03985190391540527,
-0.037346888333559036,
-0.03533471003174782,
0.03344329446554184,
-0.015473604202270508,
0.00017080434190575033,
-0.06305725127458572,
-0.03564886748790741,
0.04342498630285263,
-0.01696028746664524,
0.10130839794874191,
-0.008300840854644775,
0.03258683159947395,
0.025227714329957962,
0.004826176445931196,
0.05742519348859787,
-0.021747831255197525,
-0.0260169580578804,
-0.03878957778215408,
-0.013650537468492985,
-0.003788687288761139,
-0.05233513563871384,
-0.036256883293390274,
0.05266304686665535,
-0.010791267268359661,
0.04470082372426987,
-0.03782307729125023,
-0.022007549181580544,
-0.01852831430733204,
0.006889855954796076,
0.006084457039833069,
-0.03659246116876602,
-0.10959221422672272,
-0.012018476612865925,
-0.0029908542055636644,
0.017536908388137817,
-0.010153697803616524,
-0.020024411380290985,
-0.027445662766695023,
-0.029011517763137817,
0.06959599256515503,
-0.015322868712246418,
-0.01664259470999241,
-0.03565618023276329,
0.027514826506376266,
-0.034658756107091904,
-0.058714307844638824,
-0.042838204652071,
0.021033363416790962,
-0.01041727140545845,
0.008089941926300526,
-0.011046859435737133,
-0.01993667148053646,
-0.07202305644750595,
0.025236546993255615,
0.017193801701068878,
0.12787409126758575,
-0.06836207956075668,
-0.002261575311422348,
-0.016235271468758583,
-0.06824292242527008,
-0.011477628722786903,
0.033553753048181534,
-0.058645132929086685,
0.039247117936611176,
-0.03895677626132965,
-0.011384312994778156,
0.030813319608569145,
-0.006889748387038708,
-0.046320680528879166,
0.0043519483879208565,
0.04205947741866112,
-0.03933345526456833,
0.012573005631566048,
0.03473504260182381,
-0.029495015740394592,
0.010718152858316898,
0.08550944179296494,
0.039391227066516876,
0.04875366389751434,
0.05187394469976425,
0.014994250610470772,
-0.006477770395576954,
-0.02417677268385887,
0.07313597202301025,
-0.09815661609172821,
0.01806619204580784,
-0.0252551157027483,
-0.05548585578799248,
0.0349755696952343,
0.07463393360376358
] |
<p>Why do hurricane winds rotate? I know it´s about <a href="http://en.wikipedia.org/wiki/Coriolis_effect" rel="nofollow">Coriolis force</a> but how can I be quantitative? My problem is that I can´t imagine the direction velocity of wind and the angle with earth angular velocity rotation. Also, when can we explain other things like bathtubs, toilets.. using Coriolis? I mean when this force is relevant to explain the motion and the direction of rotation, CCW or CW(clock wise)?</p> | g9186 | [
0.04027469828724861,
0.04616441950201988,
-0.005113804712891579,
-0.025734003633260727,
0.06296876072883606,
0.022907797247171402,
0.0706404596567154,
0.00152792118024081,
-0.02472343109548092,
-0.039621833711862564,
-0.0076980674639344215,
0.010203194804489613,
0.04928482323884964,
0.020555362105369568,
0.04921014979481697,
-0.04510482773184776,
0.011651700362563133,
-0.0013018106110394,
0.07518327981233597,
0.03308635205030441,
0.020988773554563522,
-0.015567274764180183,
-0.004018331877887249,
-0.000758786394726485,
0.0034244495909661055,
-0.018298877403140068,
0.002119636395946145,
0.01638738065958023,
-0.03403349965810776,
-0.003331993008032441,
-0.018616998568177223,
0.028485821560025215,
0.025445764884352684,
-0.10536814481019974,
-0.02310778759419918,
-0.03287510201334953,
-0.03502830117940903,
-0.021866802126169205,
0.05068482458591461,
-0.006600428372621536,
-0.007927055470645428,
-0.005913169123232365,
0.04294295981526375,
0.041946399956941605,
-0.004783325362950563,
0.022057218477129936,
0.040389131754636765,
-0.02170610800385475,
-0.020393291488289833,
-0.04167832061648369,
-0.05964010953903198,
0.00484136026352644,
0.0292479507625103,
0.00628729397431016,
0.016520531848073006,
0.05666274204850197,
0.06957443058490753,
0.009829412214457989,
0.03911450877785683,
0.02700965479016304,
0.05114303156733513,
-0.012060149572789669,
0.00890394113957882,
0.059018585830926895,
0.030744310468435287,
-0.04157277196645737,
0.0015142873162403703,
0.0055587817914783955,
0.034716587513685226,
-0.005581224802881479,
0.02219962701201439,
-0.04533548653125763,
-0.007805088069289923,
-0.04155293479561806,
-0.02596195414662361,
0.036258019506931305,
0.0469837486743927,
-0.004525422118604183,
-0.024831498041749,
-0.01959138736128807,
0.012876499444246292,
-0.00878769252449274,
-0.013731183484196663,
0.028906140476465225,
0.0763453021645546,
0.019188914448022842,
0.029086627066135406,
0.027025366201996803,
0.06353149563074112,
-0.06130167841911316,
0.03299694508314133,
-0.095364049077034,
0.08757755160331726,
0.029026180505752563,
-0.05101814493536949,
-0.013921273872256279,
-0.07412302494049072,
0.062329042702913284,
0.00880172848701477,
0.05491844564676285,
-0.04337940365076065,
-0.0059127118438482285,
0.023696569725871086,
0.00523745222017169,
0.005941492039710283,
-0.004122740123420954,
0.014399693347513676,
0.07309560477733612,
-0.006205793935805559,
-0.01775781251490116,
-0.05619431287050247,
-0.010296684689819813,
-0.0023278119042515755,
0.03794840723276138,
-0.02400391176342964,
-0.04642697423696518,
0.08066758513450623,
-0.02575777657330036,
0.07496900856494904,
0.05405086651444435,
-0.00320825376547873,
0.03682820871472359,
-0.009684043936431408,
0.07864584773778915,
0.013959993608295918,
-0.034877851605415344,
0.04822692647576332,
-0.006919166073203087,
0.03053504042327404,
-0.04325992986559868,
0.04953252524137497,
0.01438536774367094,
-0.0013912842841818929,
0.030681591480970383,
0.03669062256813049,
0.01687682792544365,
-0.05466813966631889,
0.02880401909351349,
-0.00578331807628274,
0.0482785739004612,
0.007667656987905502,
-0.043354324996471405,
0.06835358589887619,
-0.00949031114578247,
-0.04724165424704552,
0.02703188732266426,
0.009781419299542904,
-0.016674647107720375,
0.08159472793340683,
0.01660839654505253,
-0.03893715888261795,
0.05432702973484993,
0.009956130757927895,
-0.022257613018155098,
0.01606743037700653,
-0.04517217352986336,
-0.026906875893473625,
-0.006201689597219229,
-0.019227847456932068,
0.03994789719581604,
0.09321317821741104,
-0.00407881336286664,
-0.01685313507914543,
0.03419261798262596,
-0.06204203888773918,
0.0009192528668791056,
-0.04514377936720848,
0.023368243128061295,
-0.02083301730453968,
-0.026760807260870934,
-0.053038064390420914,
-0.0050927987322211266,
0.033739931881427765,
0.021433379501104355,
-0.020237725228071213,
0.09438913315534592,
0.004181340802460909,
-0.027656814083456993,
-0.02142382599413395,
-0.020201193168759346,
-0.015731457620859146,
-0.0018141006585210562,
0.022746384143829346,
0.025370672345161438,
0.026836689561605453,
-0.014522560872137547,
0.0057330201379954815,
0.02872605249285698,
-0.07591874897480011,
0.0025822820607572794,
-0.0029321645852178335,
-0.02154117450118065,
-0.0312483012676239,
0.007599144242703915,
-0.007178585045039654,
0.002923853462561965,
-0.04139094799757004,
-0.014154208824038506,
-0.08666304498910904,
0.032438475638628006,
-0.03473405912518501,
-0.013860943727195263,
0.09418554604053497,
0.02327127195894718,
-0.06383778899908066,
0.03862995654344559,
0.02411055751144886,
0.007336575072258711,
0.01821022853255272,
0.03467880189418793,
-0.005340303760021925,
-0.014704035595059395,
-0.022980332374572754,
0.016488052904605865,
-0.016665449365973473,
-0.0027496081311255693,
-0.019625116139650345,
-0.006161985453218222,
-0.06369998306035995,
-0.004407939501106739,
-0.0041292873211205006,
-0.011560976505279541,
0.008222369477152824,
0.06562520563602448,
-0.026485569775104523,
0.004478692077100277,
-0.04993942379951477,
0.02528105117380619,
0.043676335364580154,
0.011935620568692684,
-0.04296217858791351,
-0.015436201356351376,
0.014961752109229565,
0.034428682178258896,
0.028274817392230034,
0.019682561978697777,
0.029230685904622078,
0.022596361115574837,
0.01944473758339882,
0.02450854703783989,
0.03919675201177597,
-0.033361922949552536,
0.04893701151013374,
-0.022812044247984886,
0.04289668798446655,
-0.01569429785013199,
0.06820519268512726,
-0.02153111808001995,
0.022109379991889,
0.05157873034477234,
0.024751825258135796,
-0.0666196197271347,
-0.043252404779195786,
-0.002468541031703353,
-0.014051368460059166,
0.010895727202296257,
-0.05305809900164604,
0.04380636662244797,
-0.0856938287615776,
0.021681683138012886,
0.019283967092633247,
-0.029622193425893784,
0.022027013823390007,
0.038449063897132874,
0.04354904964566231,
-0.020362792536616325,
-0.03642157465219498,
0.023195309564471245,
-0.019306795671582222,
-0.013820706866681576,
0.007373156026005745,
0.01246875524520874,
-0.00043616583570837975,
0.038427114486694336,
-0.05790507420897484,
0.007301525678485632,
0.016967663541436195,
-0.05589587241411209,
-0.043606195598840714,
0.025744374841451645,
0.034600887447595596,
-0.030395403504371643,
-0.02265540510416031,
0.0521707646548748,
-0.004688828717917204,
-0.022461965680122375,
-0.02178247831761837,
0.06766034662723541,
-0.0017996870446950197,
-0.024345213547348976,
-0.04667360335588455,
0.03746039420366287,
-0.015577148646116257,
-0.06202220171689987,
0.032307375222444534,
-0.0025799665600061417,
0.017882993444800377,
-0.015650702640414238,
0.01977851614356041,
0.021730922162532806,
0.025351379066705704,
-0.013088323175907135,
-0.003965282812714577,
0.015231707133352757,
-0.009244339540600777,
0.09074126929044724,
0.010798763483762741,
-0.08234471082687378,
-0.028421550989151,
0.02221984975039959,
-0.03053763322532177,
0.03370266407728195,
-0.07376494258642197,
0.0029463719110935926,
-0.08629559725522995,
0.014339555986225605,
-0.0142489243298769,
0.027201442047953606,
0.009524968452751637,
0.024315569549798965,
-0.024816792458295822,
-0.049036335200071335,
-0.013746962882578373,
-0.021544402465224266,
0.0019253295613452792,
0.046579234302043915,
0.0004967852728441358,
0.010894816368818283,
-0.004862308502197266,
-0.09447448700666428,
0.026530863717198372,
0.01835726574063301,
-0.016285061836242676,
-0.00926351360976696,
-0.0405900813639164,
0.022376760840415955,
-0.02303793467581272,
0.014970334246754646,
0.021914562210440636,
0.0006213744636625051,
-0.0038348136004060507,
-0.06673998385667801,
-0.04762034863233566,
-0.0500791072845459,
-0.055217500776052475,
0.04288223013281822,
0.04716198518872261,
-0.02439919114112854,
0.04731813073158264,
0.01390639878809452,
0.03969425708055496,
-0.010557660833001137,
-0.015035617165267467,
-0.010930909775197506,
0.024301201105117798,
0.03133029490709305,
0.05529448762536049,
0.031111247837543488,
-0.014326630160212517,
0.0371413491666317,
-0.024802668020129204,
0.001066535827703774,
-0.06545934826135635,
0.0043465797789394855,
0.026803115382790565,
0.06169644743204117,
0.0343024805188179,
0.039556242525577545,
-0.07750030606985092,
0.004373707342892885,
-0.017916645854711533,
-0.002178163267672062,
-0.018461793661117554,
-0.038818053901195526,
0.014511862769722939,
-0.02643856219947338,
0.02462289296090603,
0.041441693902015686,
0.0044566611759364605,
-0.024036657065153122,
0.02594190277159214,
-0.01206996664404869,
-0.00361750740557909,
0.03777991235256195,
0.02594611980021,
-0.04150940477848053,
-0.016155906021595,
0.009981231763958931,
-0.004570200107991695,
-0.10063362866640091,
0.04762705788016319,
-0.012414413504302502,
0.02027413435280323,
-0.038976188749074936,
0.025930775329470634,
-0.02756051905453205,
-0.013389570638537407,
0.032000478357076645,
-0.05000923573970795,
-0.0031249881722033024,
0.028161881491541862,
-0.0023213119711726904,
-0.01711052656173706,
0.052224770188331604,
-0.01484511699527502,
0.018602052703499794,
-0.027026275172829628,
-0.03529491648077965,
0.0005662557668983936,
-0.013554567471146584,
0.034112147986888885,
0.026899805292487144,
0.030159855261445045,
-0.07269570231437683,
0.04601658135652542,
0.05863553658127785,
-0.0246729776263237,
0.027699200436472893,
0.07470772415399551,
-0.01324815396219492,
0.0059053595177829266,
0.03471631184220314,
0.0480743944644928,
0.0009474748512730002,
-0.0456530824303627,
0.02171437442302704,
0.062008317559957504,
-0.0002759002964012325,
0.013152044266462326,
-0.04124843329191208,
-0.013698466122150421,
0.012662442401051521,
0.028776777908205986,
-0.03363081067800522,
0.011995329521596432,
-0.023159068077802658,
-0.012407764792442322,
0.031644728034734726,
0.016832152381539345,
0.013023623265326023,
0.00703470641747117,
0.049654968082904816,
0.015031570568680763,
-0.011403434909880161,
-0.02958599105477333,
0.0571836493909359,
0.07642418146133423,
-0.050408899784088135,
0.013751748017966747,
-0.058155257254838943,
-0.0433136485517025,
0.05555318668484688,
-0.03570947051048279,
-0.05417058244347572,
-0.00034818885615095496,
-0.0014637850690633059,
-0.02731459215283394,
0.008287569507956505,
-0.01116087380796671,
0.014929084107279778,
-0.057143326848745346,
0.002074185758829117,
-0.007239090278744698,
0.002485777949914336,
0.0067296396009624004,
-0.02516256459057331,
0.01268897857517004,
-0.04138513281941414,
-0.04477429762482643,
-0.03367825224995613,
-0.029924780130386353,
-0.014860237948596478,
-0.010070817545056343,
0.03966574743390083,
0.013107234612107277,
-0.006845841184258461,
0.029219133779406548,
-0.009777091443538666,
-0.029389429837465286,
-0.033715881407260895,
-0.004847611766308546,
0.030603867024183273,
0.0539696104824543,
0.05039205774664879,
-0.003047262318432331,
-0.08889838308095932,
0.0010008328827098012,
-0.015569190494716167,
0.04019380733370781,
-0.02631657011806965,
-0.04160111024975777,
0.019163867458701134,
0.033166855573654175,
-0.016111945733428,
-0.05024323984980583,
0.03865040838718414,
0.01243341900408268,
-0.05600409582257271,
0.00039069767808541656,
-0.03267870843410492,
-0.04184344410896301,
0.006656043231487274,
-0.04028617963194847,
0.040622979402542114,
0.017813557758927345,
0.016043487936258316,
0.03914664313197136,
0.001297559356316924,
-0.01027678232640028,
0.10212922096252441,
-0.025501634925603867,
-0.009625143371522427,
-0.04538557305932045,
0.0368863120675087,
0.09527185559272766,
-0.058211300522089005,
0.0033086214680224657,
-0.003158129518851638,
0.026345932856202126,
0.03609689697623253,
-0.04891514778137207,
0.0870232954621315,
-0.016253365203738213,
-0.03316330164670944,
-0.013173235580325127,
-0.027100613340735435,
-0.04803147912025452,
-0.02476063370704651,
-0.004313287790864706,
0.008676375262439251,
-0.05579498037695885,
0.0296517051756382,
0.00800209678709507,
0.03810186684131622,
0.01208208967000246,
-0.04076076298952103,
0.07041633874177933,
-0.036419566720724106,
0.0261605866253376,
0.0138434749096632,
-0.04483605921268463,
0.019078537821769714,
0.0454079769551754,
0.009789038449525833,
0.011723622679710388,
-0.0005234669079072773,
-0.014523427933454514,
-0.009038555435836315,
0.0562429204583168,
0.016628002747893333,
-0.042842645198106766,
0.0641477033495903,
0.07977800816297531,
-0.028131989762187004,
-0.026015806943178177,
0.015108831226825714,
-0.005585933569818735,
-0.03590652346611023,
-0.021617840975522995,
-0.05437121167778969,
0.03971949219703674,
0.010062946937978268,
0.020428277552127838,
-0.018990805372595787,
0.013610539957880974,
0.003936260472983122,
-0.010109479539096355,
0.008057200349867344,
0.06453482061624527,
0.09292934089899063,
-0.051649078726768494,
-0.1042899340391159,
-0.0589144192636013,
0.004248024895787239,
0.05146211385726929,
0.02794400416314602,
-0.00019587173301260918,
-0.03240275755524635,
-0.07197698205709457,
0.01685076765716076,
0.03732330724596977,
-0.04890527203679085,
0.03980902582406998,
-0.04207424074411392,
-0.0039161150343716145,
-0.0147473169490695,
-0.011996817775070667,
0.017909474670886993,
-0.020857837051153183,
-0.031241396442055702,
-0.03805824741721153,
0.02314014360308647,
-0.032051246613264084,
-0.035216737538576126,
-0.014789339154958725,
-0.06460873037576675,
-0.004834034480154514,
0.02157941646873951,
0.01323850080370903,
-0.07000994682312012,
-0.033694084733724594,
0.00879763811826706,
0.0317767933011055,
-0.01589876413345337,
0.021999871358275414,
-0.03690800070762634,
-0.037197843194007874,
-0.012667684815824032,
0.02454831264913082,
0.0022651096805930138,
-0.0007579862722195685,
0.03476261720061302,
0.05854453891515732,
0.003477682825177908,
-0.0039482032880187035,
-0.01717406138777733,
-0.034062452614307404,
0.009306726977229118,
-0.019694345071911812,
-0.010733113624155521,
0.020531807094812393,
-0.08127686381340027,
0.02257014438509941,
-0.03450436890125275,
0.032514993101358414,
0.03025416098535061,
-0.06846559047698975,
0.044659361243247986,
0.018357494845986366,
0.015151896513998508,
0.017442071810364723,
0.0054836212657392025,
-0.046543270349502563,
0.03084442764520645,
0.038767337799072266,
0.02739582769572735,
-0.04232750087976456,
0.05864344537258148,
0.018643448129296303,
0.04725492745637894,
0.01060356292873621,
0.07377221435308456,
0.004956437740474939,
-0.017826944589614868,
-0.01737746223807335,
-0.046716850250959396,
0.0000079722767623025,
-0.04809686169028282,
-0.020786600187420845,
-0.00569403450936079,
-0.00882556289434433,
-0.09551979601383209,
-0.004903011955320835,
0.003778011305257678,
-0.014339396730065346,
0.01905626244843006,
0.019267452880740166,
0.0007956193294376135,
-0.01256837509572506,
-0.013894911855459213,
-0.035444267094135284,
0.0413907989859581,
0.007730784360319376,
0.027075428515672684,
-0.02624749206006527,
0.0013950829161331058,
0.0110705541446805,
-0.00743891391903162,
0.020047426223754883,
-0.021141044795513153,
-0.006090883165597916,
-0.020915333181619644,
-0.0320015475153923,
-0.00527314655482769,
-0.01588127389550209,
-0.0024711345322430134,
-0.01758676953613758,
-0.03120923601090908,
0.0058951848186552525,
-0.027567051351070404,
-0.04632428660988808,
0.035804446786642075,
0.003254187759011984,
0.025997288525104523,
-0.03403836861252785,
0.01043954212218523,
0.021633509546518326,
-0.009218350984156132,
-0.013517189770936966,
-0.07820900529623032,
-0.007953816093504429,
0.05769987776875496,
-0.005801834166049957,
-0.033816859126091,
-0.022202178835868835,
0.007296529598534107,
0.06740342825651169,
-0.011694652959704399,
-0.014880864880979061,
-0.017298033460974693,
0.023035792633891106,
-0.04616812989115715,
0.03177248686552048,
-0.038541220128536224,
0.08730626851320267,
-0.0021482394076883793,
-0.06040490046143532,
-0.012510706670582294,
-0.06870394945144653,
-0.012987879104912281,
0.012539553456008434,
-0.02414741739630699,
0.030128486454486847,
-0.01680653914809227,
0.04465238004922867,
-0.008695747703313828,
0.037074968218803406,
0.009828411042690277,
-0.04238950461149216,
-0.0030202351044863462,
-0.09731884300708771,
-0.026178421452641487,
-0.004343864042311907,
-0.06541452556848526,
-0.030172865837812424,
-0.009473709389567375,
0.01538279838860035,
-0.05700809881091118,
-0.0011319669429212809,
-0.03140512481331825,
-0.0008918751846067607,
0.031289588660001755,
-0.028373580425977707,
-0.01823996566236019,
-0.03946303203701973,
0.023719126358628273,
-0.00800806563347578,
-0.06104932725429535,
0.001679342007264495,
0.007379710674285889,
0.03935536742210388,
0.006373557727783918,
-0.011988204903900623,
-0.03119812346994877,
-0.03091854229569435,
-0.006911789067089558,
-0.04355142265558243,
0.02864115498960018,
0.007057336624711752,
-0.021550623700022697,
0.034685783088207245,
0.08562028408050537,
-0.03463328257203102,
-0.0013496698811650276,
-0.031206240877509117,
-0.023965198546648026,
-0.01901334524154663,
-0.005547801963984966,
0.04955564811825752,
-0.03417293727397919,
0.036721136420965195,
0.017826305702328682,
0.04417222738265991,
-0.05591849982738495,
0.01781751587986946,
-0.048992820084095,
-0.051931124180555344,
-0.015921087935566902
] |
<p>I am looking for an introduction (textbook or paper, or if someone wouldn't mind writing a memo on it) to canonical quantum gravity, specifically the concept of minisuperspaces. I have been reading the paper of Wheeler (in Phys Review) but he doesn't speak about minisuperspaces, maybe they were not used/invented at the time.</p> | g9187 | [
0.035961784422397614,
0.05647481232881546,
0.024731511250138283,
-0.08597059547901154,
-0.08066242188215256,
0.03988387808203697,
0.044034622609615326,
-0.010646346025168896,
-0.027569012716412544,
-0.02126123569905758,
0.033280979841947556,
-0.03600853681564331,
0.026376161724328995,
0.009055252186954021,
0.01329649519175291,
-0.020714912563562393,
0.006030411925166845,
-0.004788912367075682,
0.061058420687913895,
-0.04546407610177994,
0.01712624356150627,
-0.012958449311554432,
-0.017925195395946503,
-0.04903028905391693,
-0.04497664049267769,
0.04590526595711708,
-0.0032802463974803686,
-0.07772847265005112,
0.046273402869701385,
0.01889169216156006,
-0.03704628348350525,
-0.024070531129837036,
-0.0024001740384846926,
-0.04563288390636444,
-0.03187023475766182,
-0.005357637070119381,
0.025400137528777122,
-0.009151511825621128,
-0.019095338881015778,
0.002378336153924465,
0.031074918806552887,
-0.06931766867637634,
-0.0016924687661230564,
-0.0513838492333889,
-0.008747071959078312,
0.027368787676095963,
-0.017422372475266457,
-0.03408733755350113,
-0.00034548109397292137,
0.020250549539923668,
-0.014529159292578697,
0.04600293189287186,
0.0014097815146669745,
0.0197424478828907,
0.008340977132320404,
-0.004498638678342104,
0.010217329487204552,
0.0009549955138936639,
0.0774107575416565,
0.017733756452798843,
0.030995165929198265,
0.01805424503982067,
0.010422535240650177,
0.03682046756148338,
0.0008741927449591458,
0.04038075730204582,
-0.0003824411251116544,
-0.07222317904233932,
0.05069727823138237,
-0.03759188577532768,
-0.0076806978322565556,
-0.025150038301944733,
0.018218155950307846,
0.02344590239226818,
0.01089502777904272,
0.023653365671634674,
-0.011165065690875053,
0.027745632454752922,
0.02186717465519905,
-0.03091990202665329,
-0.04002433642745018,
-0.026501404121518135,
0.04804098606109619,
-0.010042197071015835,
0.0635523572564125,
-0.0004563597613014281,
-0.05630109831690788,
-0.051031213253736496,
-0.013121514581143856,
-0.009713415987789631,
-0.03449244797229767,
0.0067476448602974415,
0.023415446281433105,
-0.03860948979854584,
-0.028744639828801155,
-0.012081763707101345,
0.015559280291199684,
-0.007658792193979025,
-0.05040162801742554,
0.008272678591310978,
0.00708375358954072,
0.013696842826902866,
0.0035940168891102076,
0.038511428982019424,
-0.021931879222393036,
0.012696908786892891,
-0.009297308512032032,
0.008431680500507355,
-0.019065868109464645,
0.021072570234537125,
-0.04866212233901024,
0.024140896275639534,
-0.056431401520967484,
-0.02612221986055374,
0.023471049964427948,
-0.020378353074193,
0.07999350875616074,
-0.014786873012781143,
0.04079722985625267,
0.06986487656831741,
-0.030849149450659752,
0.041911136358976364,
-0.007847650907933712,
0.013530201278626919,
-0.044817838817834854,
-0.010197369381785393,
-0.04665418714284897,
-0.03473864123225212,
0.024864375591278076,
-0.0014395165489986539,
0.02247457206249237,
-0.0015642521902918816,
-0.06992590427398682,
-0.010930231772363186,
-0.03345566242933273,
-0.0069432929158210754,
0.0007039784686639905,
-0.016857441514730453,
0.05917605757713318,
-0.0005405489937402308,
-0.005130348261445761,
-0.030436653643846512,
-0.018823256716132164,
0.01490768976509571,
0.06814093887805939,
-0.03933160379528999,
0.02269543521106243,
0.032509855926036835,
-0.020603066310286522,
0.02465604990720749,
0.01380402222275734,
0.04260442033410072,
-0.024506637826561928,
-0.034833550453186035,
-0.033884186297655106,
0.04008088633418083,
0.08271320164203644,
-0.04362790286540985,
0.029508737847208977,
-0.03131348267197609,
-0.014773721806704998,
0.002001425949856639,
-0.014188425615429878,
0.011222874745726585,
-0.054877541959285736,
0.04922086372971535,
0.02920999936759472,
-0.06319081783294678,
0.06551388651132584,
-0.05039617791771889,
0.034680698066949844,
-0.022849110886454582,
0.04125753417611122,
0.10016347467899323,
-0.018360134214162827,
0.07100928574800491,
0.045039448887109756,
-0.01211108174175024,
-0.03898022696375847,
-0.02333381399512291,
-0.008555907756090164,
-0.029628323391079903,
0.02073473110795021,
0.005621117539703846,
-0.033405851572752,
0.03944382444024086,
0.0233104657381773,
-0.000926460197661072,
0.014618804678320885,
0.0022266237065196037,
-0.0649268701672554,
-0.02199069783091545,
0.032738812267780304,
-0.00997875165194273,
0.03144669532775879,
-0.033159226179122925,
0.08027804642915726,
-0.036257535219192505,
-0.034350261092185974,
-0.006440804805606604,
-0.003358985763043165,
-0.0021739427465945482,
0.09295370429754257,
0.007808405440300703,
0.016684848815202713,
-0.02952304296195507,
0.04812731221318245,
-0.05690435692667961,
0.05412914603948593,
-0.0029343487694859505,
0.00306305312551558,
-0.014940540306270123,
0.05583062767982483,
0.009785312227904797,
-0.031604912132024765,
0.020435325801372528,
-0.05191256105899811,
0.023358594626188278,
0.0244631078094244,
0.025301024317741394,
0.015022160485386848,
0.0007082300144247711,
0.0358571782708168,
0.08059801161289215,
0.03650982305407524,
-0.032750822603702545,
0.007441771682351828,
-0.03420158475637436,
-0.003289811545982957,
-0.013495792634785175,
-0.16458676755428314,
0.004001014865934849,
-0.019343649968504906,
-0.028805172070860863,
0.016195064410567284,
0.04087042436003685,
0.02522779069840908,
-0.007196180522441864,
0.041736871004104614,
0.05609314516186714,
0.07621606439352036,
0.025994857773184776,
0.03890419378876686,
0.03419122099876404,
0.006482574623078108,
-0.03784715756773949,
-0.03181326016783714,
-0.04199646785855293,
0.000023574171791551635,
-0.028222890570759773,
0.004806123208254576,
-0.03832230716943741,
-0.03385075554251671,
-0.016090773046016693,
-0.00823869090527296,
0.048919811844825745,
-0.002435381291434169,
-0.028627909719944,
-0.06195855513215065,
-0.01230856403708458,
0.060897380113601685,
-0.04801478609442711,
-0.004346528090536594,
0.01910661719739437,
-0.004001268185675144,
-0.0523618683218956,
0.00588095560669899,
0.020259277895092964,
-0.03107891045510769,
0.0033729448914527893,
0.0056310719810426235,
0.10126665234565735,
-0.04050648957490921,
0.022887108847498894,
-0.007847120985388756,
0.01945648156106472,
-0.026508275419473648,
-0.014609599485993385,
-0.005096337292343378,
-0.005378653760999441,
-0.050667647272348404,
-0.03842464089393616,
-0.01519429124891758,
-0.006967371329665184,
0.007546750828623772,
-0.04932742938399315,
-0.049738869071006775,
0.06009600684046745,
-0.011987007223069668,
0.015841161832213402,
-0.0046225120313465595,
0.029506947845220566,
0.004489545244723558,
0.03439835458993912,
0.010339056141674519,
0.0213400200009346,
-0.051343005150556564,
0.04846135899424553,
-0.033156171441078186,
0.010640161111950874,
0.001356001477688551,
0.0213900376111269,
0.04896058514714241,
0.01469546277076006,
-0.06567425280809402,
0.005317467264831066,
-0.0052539329044520855,
-0.07367467135190964,
-0.042458172887563705,
0.00819842703640461,
-0.06078596040606499,
-0.008145916275680065,
0.0440795011818409,
0.07396239787340164,
-0.0444333590567112,
-0.025330036878585815,
-0.021852878853678703,
0.02616272307932377,
-0.014277712441980839,
-0.043484654277563095,
-0.020218033343553543,
-0.029751285910606384,
0.05333817005157471,
-0.05630430579185486,
0.06916435807943344,
0.10828081518411636,
-0.026948733255267143,
-0.0009435922256670892,
0.016857467591762543,
0.01753154955804348,
0.056221455335617065,
-0.062259458005428314,
-0.0032573016360402107,
0.016689829528331757,
-0.024843888357281685,
-0.0686243399977684,
-0.018139848485589027,
-0.02037527784705162,
-0.022983668372035027,
-0.017734305933117867,
0.030246824026107788,
0.031264692544937134,
0.01977670192718506,
-0.002926398301497102,
0.030995985493063927,
-0.005623700562864542,
0.04542509466409683,
0.03836178779602051,
-0.030617540702223778,
0.010153345763683319,
0.009427912533283234,
-0.03637716546654701,
0.041282668709754944,
-0.004461617674678564,
-0.010358799248933792,
0.07081206142902374,
0.008190817199647427,
0.012847641482949257,
0.05799947306513786,
0.0133713623508811,
-0.01614857278764248,
-0.01842012256383896,
0.009863648563623428,
0.028508778661489487,
0.002415925497189164,
-0.030229607596993446,
-0.023837141692638397,
-0.027132181450724602,
-0.06032469868659973,
0.02902732603251934,
-0.02876610867679119,
0.018298380076885223,
-0.002881352324038744,
0.000726094760466367,
0.008181112818419933,
-0.10979344695806503,
0.03190503641963005,
0.013973950408399105,
0.029916968196630478,
-0.027115995064377785,
-0.0358395017683506,
0.00020662635506596416,
0.05990484356880188,
-0.007218556012958288,
0.04667727276682854,
0.05232439935207367,
-0.023127514868974686,
-0.03518727421760559,
0.01759391278028488,
0.011274495162069798,
-0.0022888658568263054,
-0.03394985571503639,
-0.046971771866083145,
-0.008196833543479443,
-0.019086958840489388,
0.10766313970088959,
0.0004320776788517833,
-0.004301329609006643,
0.025120766833424568,
-0.00526276184245944,
-0.02381250448524952,
0.05111260339617729,
-0.02673710323870182,
0.017895782366394997,
-0.03605027124285698,
0.05040178820490837,
0.04520140960812569,
0.02889067307114601,
-0.03444892540574074,
0.003423531772568822,
0.05580602586269379,
-0.02440597489476204,
-0.029314637184143066,
-0.04015977308154106,
-0.0015896304976195097,
0.023205354809761047,
0.01962580718100071,
-0.025728939101099968,
0.06369413435459137,
0.0525704063475132,
0.0007373979315161705,
0.06495480984449387,
-0.0014114916557446122,
-0.008444856852293015,
-0.000023240660084411502,
0.03358251601457596,
-0.01023612730205059,
0.0282993633300066,
-0.006546585820615292,
-0.0016000630566850305,
0.005132400896400213,
0.005777579732239246,
-0.02481708489358425,
0.06646835058927536,
0.009613821282982826,
-0.03290826827287674,
-0.024822257459163666,
-0.02319476380944252,
-0.03531675413250923,
-0.03277279809117317,
0.10569626837968826,
0.002332106465473771,
-0.009878147393465042,
-0.021417446434497833,
-0.036529697477817535,
0.046063654124736786,
-0.018874825909733772,
0.01753811165690422,
-0.026589687913656235,
-0.03731667995452881,
0.04613115265965462,
0.0013733555097132921,
-0.017580365762114525,
-0.010669291950762272,
-0.0338735468685627,
-0.02304811216890812,
0.02437037043273449,
-0.015325840562582016,
0.05880625173449516,
0.04221915081143379,
0.018175849691033363,
0.017080549150705338,
-0.006497477646917105,
0.026745062321424484,
-0.03802333027124405,
-0.012952370569109917,
-0.10477447509765625,
0.024351727217435837,
0.00337519240565598,
-0.019144222140312195,
0.0024241486098617315,
-0.02245401032269001,
-0.024155328050255775,
0.0021048623602837324,
0.011670968495309353,
0.015621818602085114,
0.015300464816391468,
-0.05281875655055046,
-0.036443546414375305,
0.010301734320819378,
-0.002585609443485737,
-0.021953295916318893,
-0.016011595726013184,
0.03518499806523323,
0.03491801768541336,
-0.02732180990278721,
-0.0044839633628726006,
0.007281334139406681,
0.01665983721613884,
-0.0071027083322405815,
-0.03646356984972954,
-0.04213317856192589,
0.019276773557066917,
0.003911367617547512,
-0.059739768505096436,
-0.007841240614652634,
0.021959226578474045,
0.016578251495957375,
0.025312194600701332,
0.024816149845719337,
-0.011447230353951454,
0.05620589852333069,
-0.023378275334835052,
0.03828391805291176,
-0.01750105619430542,
0.00015140455798245966,
0.02521919086575508,
0.010069291107356548,
-0.05733099579811096,
0.055072247982025146,
0.002114210743457079,
0.07762226462364197,
-0.037891242653131485,
0.01207558810710907,
0.03679262101650238,
-0.05011080950498581,
0.001886746846139431,
-0.06905920803546906,
0.00043766028829850256,
0.02253568172454834,
-0.04366869479417801,
-0.06061872839927673,
0.008743805810809135,
0.020597975701093674,
0.053926557302474976,
0.03065633215010166,
-0.09669729322195053,
0.004331554286181927,
0.060993168503046036,
-0.0005098506808280945,
0.03438165783882141,
0.01711970567703247,
0.02353254146873951,
-0.022874046117067337,
-0.08020662516355515,
-0.00253593479283154,
0.037355758249759674,
0.059690024703741074,
0.06616519391536713,
-0.04703645780682564,
-0.1369008868932724,
-0.011996191926300526,
-0.05702409893274307,
-0.05170280486345291,
-0.025065794587135315,
-0.008792894892394543,
0.01956813596189022,
0.024905836209654808,
0.061117082834243774,
-0.00431798817589879,
-0.06661223620176315,
-0.028899170458316803,
0.044499725103378296,
0.029029617086052895,
-0.028855422511696815,
-0.005813427269458771,
-0.0347345732152462,
-0.05120642110705376,
-0.04893449693918228,
-0.006315369624644518,
0.014876492321491241,
0.02776975929737091,
0.012770142406225204,
0.010548275895416737,
-0.0650259479880333,
0.03278842195868492,
0.007294605020433664,
-0.06422367691993713,
0.036101438105106354,
0.0018866731552407146,
-0.03185174986720085,
0.014774019829928875,
0.016114993020892143,
0.004564693663269281,
-0.049613356590270996,
-0.004692289046943188,
0.02974851243197918,
-0.07011087238788605,
-0.05812178924679756,
-0.010078688152134418,
0.05462437495589256,
0.01612551137804985,
-0.00017935682262759656,
-0.023375192657113075,
-0.037987105548381805,
0.004869568161666393,
0.007436745800077915,
0.024116242304444313,
0.012949206866323948,
0.056596096605062485,
0.007854362949728966,
0.02227173000574112,
-0.0002573789097368717,
-0.03916199505329132,
0.009011363610625267,
-0.0072070821188390255,
0.05180911347270012,
0.006952233612537384,
-0.010323929600417614,
-0.01917700283229351,
0.010620765388011932,
0.045835815370082855,
-0.006774468347430229,
-0.0012717379722744226,
0.0010783373145386577,
0.06015649810433388,
-0.018485169857740402,
-0.007160776760429144,
0.02609163336455822,
0.021824900060892105,
0.002096017124131322,
0.0009266833658330142,
-0.027308925986289978,
-0.014397978782653809,
0.01752232387661934,
-0.08394035696983337,
0.02725980430841446,
-0.013898269273340702,
-0.011300645768642426,
-0.002029276918619871,
0.007997358217835426,
-0.000987992505542934,
0.04900618642568588,
0.015076469630002975,
0.0007265376043505967,
0.04038139805197716,
0.04803859815001488,
0.013365733437240124,
0.022167544811964035,
-0.027378633618354797,
-0.01650151051580906,
-0.04552134871482849,
0.08344034850597382,
0.003907194826751947,
-0.03811541199684143,
0.05028914287686348,
-0.06166638061404228,
-0.021067239344120026,
0.0527430884540081,
-0.02495289221405983,
0.04996350035071373,
-0.0405951552093029,
0.011319427751004696,
-0.0032191011123359203,
-0.04358880966901779,
0.0002589838986750692,
-0.01705823466181755,
0.044797006994485855,
0.0021047748159617186,
-0.017079714685678482,
0.038979463279247284,
-0.025234198197722435,
-0.019906282424926758,
-0.007998451590538025,
-0.09555143862962723,
0.0349387601017952,
0.03337173908948898,
-0.010563232004642487,
-0.019173720851540565,
-0.08667871356010437,
-0.04221661388874054,
0.0007239801343530416,
0.0013678300892934203,
0.03213749825954437,
-0.05107628181576729,
0.00800703652203083,
0.053062859922647476,
0.014956207945942879,
0.04021638259291649,
0.015526238828897476,
-0.034788504242897034,
-0.020006326958537102,
-0.05056353285908699,
0.0151324812322855,
0.0030023562721908092,
0.0015302790561690927,
0.022967640310525894,
0.014131096191704273,
0.05272833630442619,
0.008828436024487019,
0.03490433841943741,
-0.00047714717220515013,
-0.017730219289660454,
0.030683297663927078,
-0.02723846770823002,
-0.036364659667015076,
0.004676615819334984,
-0.0023163293953984976,
0.00964425504207611,
-0.034698840230703354,
0.00018558620649855584,
-0.07870656996965408,
-0.01477942243218422,
-0.04721042886376381,
0.028238549828529358,
-0.017537003383040428,
0.03993937745690346,
-0.01110219955444336,
-0.019223827868700027,
0.004019519779831171,
0.01521365437656641,
-0.05271756276488304,
-0.058912623673677444,
-0.010920369066298008,
0.025001851841807365,
-0.005964039824903011,
0.018524743616580963,
0.03408048674464226,
-0.0647926852107048,
-0.035963695496320724,
-0.01608666218817234,
0.02511323057115078,
0.021044455468654633,
0.014688071794807911,
0.04332282394170761,
-0.010484415106475353,
-0.0262531116604805,
0.036960091441869736,
0.06380835175514221,
-0.008628650568425655,
0.007507696747779846,
-0.0003248924040235579,
0.009550129994750023,
-0.05877896025776863,
-0.030638791620731354,
-0.04153108969330788,
-0.0023311807308346033,
0.0027225723024457693,
-0.004789066966623068,
0.0012479982106015086,
0.03005833737552166,
-0.0072632101364433765,
0.02531992644071579,
0.026123275980353355,
-0.0002733034489210695,
0.044169358909130096,
-0.0035776456352323294,
-0.1104586124420166,
0.09312838315963745,
0.02667052112519741,
-0.0006583922659046948,
0.008825667202472687,
0.014857405796647072,
0.01886240765452385,
-0.01396931055933237,
-0.0034686208236962557,
-0.043439578264951706,
-0.022437749430537224,
-0.02765659987926483,
-0.024263521656394005,
-0.0337868332862854,
0.036120325326919556,
0.05010126531124115,
0.02352740801870823,
0.04261639341711998,
-0.010301660746335983,
0.011008856818079948,
0.04103431478142738,
-0.007796041667461395,
-0.003994867671281099,
-0.041223134845495224,
0.0025404212065041065,
0.0870007798075676,
0.006872543133795261,
-0.050682663917541504,
-0.027333637699484825,
0.02906869165599346,
-0.007518158759921789
] |
<p>The circuit under consideration has two inductively coupled loops, one with a DC battery, inductor, and resistor in series. The other loop has two inductors, one inductively coupled to the first, the other not, and a resistor, all in series. </p>
<p>I would like to know the current in the top loop (the one without the battery) as a function of the given quantities after the battery is connected.</p>
<p>I tried adding the three inductors and using that value to find the bottom loop's current, then substituting that into the top loop to find d(phi)/dt and then current. This gives me the standard RL current expression for the bottom loop and an exponential decay model for the current in the top loop. This is counter-intuitive for me; I believed that the current in the top loop should start at zero, peak, and decay rather than start high and decay.</p>
<p>Thanks in advance.</p> | g9188 | [
-0.0026020740624517202,
-0.04619871452450752,
-0.009756983257830143,
-0.014352857135236263,
0.020703149959445,
-0.021545788273215294,
0.009674192406237125,
0.012933926656842232,
-0.035303764045238495,
0.0008140545105561614,
-0.0606020949780941,
0.056342851370573044,
-0.001817553536966443,
0.030074303969740868,
0.02469511702656746,
-0.0067121367901563644,
0.03694569319486618,
-0.03561544045805931,
0.05632207915186882,
-0.008318748325109482,
0.008130897767841816,
-0.027136534452438354,
-0.02528293803334236,
-0.029061317443847656,
-0.06111108511686325,
-0.04818486422300339,
-0.00021409864712040871,
0.03577413409948349,
-0.04774576425552368,
0.028434855863451958,
0.00017376475443597883,
0.006845343392342329,
0.09485271573066711,
-0.028857706114649773,
0.005140513181686401,
0.01636524312198162,
0.05747519060969353,
0.048782363533973694,
-0.022248217836022377,
0.017493339255452156,
0.013847359456121922,
-0.00935027189552784,
0.046103429049253464,
0.048205550760030746,
-0.03938588127493858,
-0.034650836139917374,
-0.03275062516331673,
0.06537187844514847,
-0.03691849857568741,
-0.03896505758166313,
0.0282804686576128,
0.07686516642570496,
-0.050741467624902725,
-0.017510339617729187,
-0.030297862365841866,
-0.012176433578133583,
0.010923972353339195,
-0.04760799556970596,
-0.01845402456820011,
0.046523746103048325,
0.015892311930656433,
-0.0047792731784284115,
0.019128989428281784,
0.008417429402470589,
0.037441741675138474,
0.023888207972049713,
0.04299831762909889,
-0.026457203552126884,
0.016961822286248207,
0.006980879697948694,
0.00792222935706377,
-0.03148192539811134,
-0.005178379360586405,
-0.039037756621837616,
0.012178635224699974,
0.021612955257296562,
0.06814303249120712,
-0.029337789863348007,
0.040979862213134766,
-0.02501031570136547,
-0.04539067670702934,
-0.0010506032267585397,
0.05714506283402443,
0.06505874544382095,
0.039687782526016235,
0.042278554290533066,
-0.01662040315568447,
-0.029070932418107986,
-0.01757943630218506,
0.028839852660894394,
0.02556736022233963,
0.04507661610841751,
0.04619014263153076,
-0.037968818098306656,
0.02970319241285324,
-0.04610642418265343,
-0.004493022337555885,
0.031042007729411125,
0.038670651614665985,
0.00037632029852829874,
0.02407624013721943,
-0.03323788568377495,
-0.017558710649609566,
-0.011814652942121029,
-0.025506144389510155,
0.012251075357198715,
0.04890032112598419,
-0.024770649150013924,
-0.0579567588865757,
-0.0012674067402258515,
-0.007004611659795046,
-0.07586240023374557,
-0.021939419209957123,
-0.025112099945545197,
-0.004423938225954771,
0.022215034812688828,
-0.014400096610188484,
-0.033049196004867554,
0.007199911866337061,
0.008148628287017345,
-0.03419968858361244,
0.003230446483939886,
0.012032246217131615,
0.05356280505657196,
-0.008251498453319073,
-0.019524838775396347,
-0.012305794283747673,
0.037975747138261795,
0.003044998971745372,
0.030965439975261688,
0.04111982136964798,
-0.009041901677846909,
0.002795706270262599,
0.038371626287698746,
0.04796982929110527,
0.01421444769948721,
0.0014488655142486095,
-0.010515435598790646,
-0.03933614119887352,
-0.026620756834745407,
-0.012543480843305588,
-0.026477549225091934,
-0.014687924645841122,
0.017225585877895355,
-0.0192379429936409,
0.06482566893100739,
-0.01329254824668169,
-0.024909304454922676,
0.017970921471714973,
-0.008193871937692165,
0.060628075152635574,
0.06184757128357887,
-0.044309765100479126,
-0.0028275265358388424,
-0.0013427615631371737,
0.022950155660510063,
0.06623154878616333,
0.016815366223454475,
-0.00959896668791771,
0.022607512772083282,
-0.06080516427755356,
-0.0014891944592818618,
-0.039680592715740204,
-0.01636531576514244,
-0.036176927387714386,
0.027651764452457428,
0.05896469205617905,
-0.07378432154655457,
-0.019798358902335167,
-0.04149739071726799,
-0.039131343364715576,
0.004780566319823265,
0.03623779118061066,
0.012594278901815414,
0.009966288693249226,
0.05916750058531761,
0.033705223351716995,
-0.01494679506868124,
0.012545788660645485,
0.006450933404266834,
0.012504726648330688,
-0.017558276653289795,
0.06043119356036186,
0.020296666771173477,
0.0057084085419774055,
0.01935497671365738,
-0.06110963225364685,
0.021876657381653786,
-0.051247790455818176,
-0.017847012728452682,
-0.06211302801966667,
0.020951727405190468,
0.04455816000699997,
0.02177526243031025,
-0.02883344143629074,
-0.0022494327276945114,
0.05229506269097328,
-0.07433877140283585,
0.025259124115109444,
0.014753292314708233,
0.03507927060127258,
-0.04871237277984619,
0.021202148869633675,
0.012630101293325424,
-0.024228675290942192,
0.037738047540187836,
-0.03869713097810745,
-0.01060163602232933,
-0.01758144237101078,
0.017787961289286613,
-0.08387427777051926,
-0.01662639155983925,
0.0018121477914974093,
0.006605425383895636,
-0.02754070982336998,
-0.054345469921827316,
0.013995463028550148,
0.05379629135131836,
-0.04436078295111656,
0.030957790091633797,
-0.014784303493797779,
-0.08162546902894974,
0.05706442520022392,
-0.0035508733708411455,
-0.003996503073722124,
-0.005371629726141691,
0.03431038558483124,
0.011824355460703373,
-0.049971453845500946,
-0.007523054722696543,
-0.04912489280104637,
0.023435749113559723,
-0.06745050847530365,
-0.046263109892606735,
0.008042043074965477,
0.05872062221169472,
0.050356633961200714,
-0.018364492803812027,
-0.0013510879362002015,
0.019904207438230515,
-0.06450678408145905,
0.04505070671439171,
0.047779347747564316,
0.05237039178609848,
0.03751664236187935,
-0.04612556844949722,
-0.0027127081993967295,
0.06311290711164474,
-0.022256333380937576,
0.02460651844739914,
0.006513360887765884,
0.003867922117933631,
-0.03489949554204941,
0.03126969188451767,
-0.024322260171175003,
-0.05461682006716728,
-0.01714283414185047,
-0.032911576330661774,
0.0004787214857060462,
-0.05902194604277611,
-0.022657057270407677,
-0.04099263995885849,
0.0016450044931843877,
0.04107273370027542,
-0.05181725323200226,
-0.03414203226566315,
0.01578104868531227,
-0.08066138625144958,
0.04615210369229317,
0.04054338485002518,
-0.060330767184495926,
0.02970234490931034,
0.02695421874523163,
-0.04754900559782982,
0.026773488149046898,
-0.034823108464479446,
0.03664262965321541,
-0.02077678218483925,
0.023964760825037956,
0.02107231877744198,
0.02785138599574566,
0.010554333217442036,
-0.007914278656244278,
0.05419981852173805,
0.03543546050786972,
-0.04607642441987991,
0.06698084622621536,
0.008172273635864258,
0.02163233980536461,
-0.0023323423229157925,
-0.01367033738642931,
-0.035460665822029114,
0.026145122945308685,
0.005184066016227007,
0.012451743707060814,
-0.022063342854380608,
0.04737568646669388,
-0.03244448080658913,
0.04409368708729744,
-0.0015973077388480306,
0.01940775290131569,
-0.07882361114025116,
0.032923225313425064,
-0.04899807274341583,
0.017964297905564308,
0.0071975658647716045,
0.012643511407077312,
0.0172580499202013,
0.009117502719163895,
0.05220084264874458,
-0.012154733762145042,
-0.03170908987522125,
0.019411833956837654,
-0.07489784061908722,
-0.013331609778106213,
-0.00629523815587163,
-0.011911381036043167,
-0.052240632474422455,
-0.005930440034717321,
-0.037129536271095276,
-0.015448080375790596,
-0.05969547480344772,
0.011034361086785793,
0.00550951948389411,
0.016267182305455208,
0.04650671407580376,
-0.021762076765298843,
-0.021700629964470863,
0.002595564117655158,
-0.019501833245158195,
-0.06308481097221375,
0.04934965819120407,
0.029205242171883583,
0.03357383608818054,
0.032363541424274445,
0.0002885515568777919,
0.012371562421321869,
0.015971481800079346,
0.018230848014354706,
-0.00026501549291424453,
0.037919335067272186,
-0.0021789006423205137,
-0.0014087827876210213,
0.012358610518276691,
0.005497039761394262,
-0.06820731610059738,
-0.039187245070934296,
0.07931283861398697,
0.03748541697859764,
-0.062167536467313766,
0.029838690534234047,
0.03638147935271263,
0.008345398120582104,
-0.010364246554672718,
-0.05028660595417023,
0.0801737830042839,
-0.010249754413962364,
0.04790858179330826,
0.004324659705162048,
0.02400756999850273,
0.0016686642775312066,
-0.038002658635377884,
-0.0012287196004763246,
0.024459244683384895,
0.021875428035855293,
-0.01455400325357914,
0.00451304716989398,
0.03781282156705856,
-0.019286664202809334,
-0.07046839594841003,
0.029309848323464394,
0.03605961799621582,
0.015283815562725067,
-0.02849358320236206,
0.009451753459870815,
-0.04162056744098663,
0.04974672570824623,
0.037110380828380585,
-0.07914948463439941,
0.06676881015300751,
0.00977395661175251,
-0.011256709694862366,
0.00794195756316185,
0.04318184778094292,
0.03232092782855034,
-0.006964753847569227,
0.0224163755774498,
0.026700356975197792,
-0.003705163486301899,
0.020394043996930122,
-0.037446342408657074,
0.03873300552368164,
0.03284730017185211,
-0.021406564861536026,
0.006476300302892923,
-0.0016545687103644013,
0.050573043525218964,
0.01932058110833168,
-0.02556132897734642,
-0.037159934639930725,
-0.027186652645468712,
0.037962764501571655,
0.019034726545214653,
0.03187747672200203,
0.04258770868182182,
0.017494652420282364,
0.008902270346879959,
-0.05460274592041969,
0.06270378082990646,
0.03199244290590286,
-0.07299485057592392,
0.00012472973321564496,
0.010722494684159756,
-0.010054945014417171,
-0.008977233432233334,
0.01564430445432663,
0.10100040584802628,
-0.0018949444638565183,
0.0700652003288269,
0.014472447335720062,
-0.03239680454134941,
-0.010987206362187862,
-0.015874706208705902,
-0.050292763859033585,
-0.0605601966381073,
0.0226909089833498,
0.015829935669898987,
0.007769814692437649,
0.024705348536372185,
0.0013863578205928206,
0.013010567985475063,
0.05552900955080986,
-0.03551914542913437,
0.023268550634384155,
-0.06355058401823044,
0.04222412034869194,
-0.015191894955933094,
0.03062620386481285,
-0.011907716281712055,
0.03968261927366257,
0.029689133167266846,
-0.022980164736509323,
-0.039334725588560104,
-0.0057085794396698475,
-0.004916434176266193,
0.025521472096443176,
-0.0887998640537262,
-0.02103675715625286,
0.0015505726914852858,
-0.01694125309586525,
-0.015098871663212776,
0.023784205317497253,
-0.04883802682161331,
-0.01682354137301445,
-0.034833114594221115,
0.030032670125365257,
0.054312776774168015,
-0.01486637070775032,
-0.015068256296217442,
0.024633269757032394,
-0.0732564777135849,
0.025013182312250137,
-0.03488218039274216,
-0.029911763966083527,
0.010489817708730698,
-0.031914692372083664,
-0.05423935130238533,
-0.0425480492413044,
-0.02907295897603035,
0.01561997551470995,
0.025399435311555862,
-0.0062385364435613155,
0.026867873966693878,
0.016752023249864578,
-0.011498542502522469,
-0.022954892367124557,
0.02382674068212509,
0.018893016502261162,
-0.0914546400308609,
0.011630895547568798,
-0.018912848085165024,
0.017964113503694534,
-0.046383753418922424,
0.005442716181278229,
-0.015132886357605457,
-0.04579024761915207,
-0.05465763807296753,
-0.02798357978463173,
0.018588148057460785,
0.0328199677169323,
0.014516553841531277,
0.08749766647815704,
0.08578140288591385,
-0.014391823671758175,
-0.015541070140898228,
0.029108872637152672,
0.006897196173667908,
-0.009895231574773788,
-0.017251484096050262,
0.061970554292201996,
-0.08348143100738525,
0.009834066964685917,
-0.02725238911807537,
0.052062489092350006,
-0.06735026836395264,
0.08891303092241287,
0.01720590330660343,
0.028921866789460182,
0.005617410410195589,
-0.02214599959552288,
0.020282287150621414,
0.007881054654717445,
-0.011747840791940689,
0.003145191352814436,
-0.0487222820520401,
0.028511973097920418,
-0.04899338632822037,
0.04626874998211861,
-0.030469708144664764,
0.03564271330833435,
0.07186730206012726,
0.02173740789294243,
0.0045297835022211075,
-0.02791779860854149,
0.0016830607783049345,
-0.03385937213897705,
-0.093907430768013,
0.013812189921736717,
0.08340601623058319,
-0.034795597195625305,
0.023921191692352295,
0.025880763307213783,
-0.0458114892244339,
-0.053156778216362,
-0.006018228828907013,
-0.02234748564660549,
0.03579454869031906,
-0.021619485691189766,
-0.03602198138833046,
0.03917103633284569,
0.020186707377433777,
0.06545663625001907,
0.033424824476242065,
0.05499982833862305,
-0.04712078720331192,
-0.0733284205198288,
-0.011276005767285824,
-0.039033904671669006,
-0.002509678713977337,
0.04273771494626999,
-0.007694953121244907,
-0.03673136606812477,
0.006757033057510853,
0.028640421107411385,
-0.008812790736556053,
-0.03692817687988281,
0.01788984425365925,
0.01579545997083187,
-0.04323418810963631,
0.017483152449131012,
0.0006175317103043199,
-0.021601602435112,
0.0024778826627880335,
0.06764193624258041,
0.014912464655935764,
-0.0325968861579895,
-0.012876240536570549,
0.026356568560004234,
0.017054131254553795,
-0.046618230640888214,
0.030311014503240585,
-0.05881916359066963,
-0.02359364740550518,
-0.015721948817372322,
0.05970237776637077,
0.010793600231409073,
-0.044208984822034836,
0.010167528875172138,
0.05007639899849892,
-0.03176461532711983,
-0.07015183568000793,
-0.02325443923473358,
0.035179462283849716,
-0.008059054613113403,
0.003954132087528706,
0.017600255087018013,
-0.011814250610768795,
-0.024057405069470406,
-0.01618177257478237,
0.03395944461226463,
0.03837541490793228,
0.00922386534512043,
-0.007809341885149479,
-0.041176557540893555,
0.040903490036726,
-0.029986806213855743,
0.022402312606573105,
0.014151356182992458,
0.05376369133591652,
0.03148793429136276,
-0.02028244361281395,
-0.041673850268125534,
0.011183304712176323,
-0.06119244918227196,
0.02370256744325161,
-0.023877155035734177,
0.04451841861009598,
0.019318217411637306,
-0.008645066060125828,
-0.0186094269156456,
-0.00036743353120982647,
0.005233255214989185,
-0.004948824644088745,
-0.004531276412308216,
0.008960457518696785,
0.002276418963447213,
0.02543482556939125,
0.0700988918542862,
0.0012119824532419443,
0.05997482314705849,
0.003870476968586445,
-0.01780305802822113,
-0.022238610312342644,
0.016592590138316154,
0.06469960510730743,
0.02413509227335453,
0.0011989057529717684,
0.0026231524534523487,
0.02705165185034275,
-0.010474979877471924,
-0.024910710752010345,
0.02069568820297718,
-0.03631039708852768,
-0.0031887951772660017,
0.06565050780773163,
0.04440205171704292,
0.007804573979228735,
0.0011992313666269183,
-0.02815530076622963,
0.011787671595811844,
0.028391441330313683,
-0.019105758517980576,
-0.050984662026166916,
0.047797057777643204,
-0.04572851210832596,
-0.10659319162368774,
0.10237003117799759,
0.03199444338679314,
-0.06490456312894821,
0.01569906808435917,
0.02544947899878025,
0.0348639152944088,
-0.040085069835186005,
0.01971130259335041,
0.00048060284461826086,
-0.001093945000320673,
0.034678637981414795,
0.028392991051077843,
0.0267250444740057,
-0.008161491714417934,
-0.009576858952641487,
-0.049588464200496674,
-0.018008822575211525,
-0.030591079965233803,
0.06461799889802933,
0.014962604269385338,
-0.027881188318133354,
-0.07300527393817902,
-0.0011400323128327727,
-0.05732778459787369,
-0.013907325454056263,
-0.07707270234823227,
-0.0050812093541026115,
0.024937687441706657,
-0.015636097639799118,
0.016155924648046494,
0.010725795291364193,
0.018800145015120506,
-0.04428624361753464,
-0.032111022621393204,
-0.017625557258725166,
-0.05000067129731178,
-0.030000943690538406,
-0.040391307324171066,
-0.014927646145224571,
0.07813021540641785,
0.005767143331468105,
-0.05809296667575836,
-0.03854412958025932,
0.030983857810497284,
-0.029971234500408173,
0.042241621762514114,
0.050970904529094696,
-0.03315774351358414,
-0.021068109199404716,
0.08580754697322845,
0.0006063321488909423,
-0.027539968490600586,
-0.024777963757514954,
0.00749439001083374,
0.048787303268909454,
0.012896477244794369,
0.03610473871231079,
-0.010535766370594501,
-0.03968266397714615,
-0.022456547245383263,
-0.05096142739057541,
-0.05170110613107681,
-0.022071903571486473,
0.025444036349654198,
-0.025783833116292953,
0.0381929948925972,
-0.02535557933151722,
-0.03359001502394676,
-0.021064691245555878,
0.019674120470881462,
-0.03008781000971794,
-0.046815793961286545,
-0.03109583631157875,
0.017407046630978584,
-0.07623634487390518,
-0.043443966656923294,
0.005131628829985857,
-0.0175950825214386,
-0.07155163586139679,
-0.04189814254641533,
-0.05372690409421921,
0.033019863069057465,
-0.005479616113007069,
-0.017909284681081772,
-0.02550242841243744,
0.0113524179905653,
-0.010850037448108196,
-0.018732260912656784,
0.021947994828224182,
0.03179573640227318,
0.03117021732032299,
0.015555063262581825,
0.028978722169995308,
0.02751835063099861,
-0.053237173706293106,
-0.07698263972997665,
0.00578530877828598,
-0.009310617111623287,
0.02206193096935749,
-0.028309136629104614,
0.024052035063505173,
0.0008754837908782065,
0.08504768460988998,
-0.07541032880544662,
-0.003173402976244688,
0.0209471695125103,
-0.037418048828840256,
-0.008529298938810825,
0.05175601691007614,
0.006921564228832722,
0.01455294992774725,
-0.01480775885283947,
-0.020836038514971733,
0.00678468169644475,
-0.030690407380461693,
-0.013156810775399208,
-0.039617281407117844,
0.018688203766942024,
0.07941994816064835,
-0.050177302211523056,
0.01620342768728733,
-0.03851652517914772
] |
<p>Let me create a very artificial experimental set up. Take a bathtub the size of Delaware and suspend it a mile above the ground. Fill it with water (though I'm not sure to what depth - and it might matter). Now pull the plug out.</p>
<p>The effect is that you have a waterfall with an endless supply of water, high above the ground, and, in my idealization, the stream of water is an arbitrarily thick, cylinder of water.</p>
<p>The question is, how fast does the water travel at the center of the waterfall? Obviously, I'm not looking for a numerical answer here, but I just want to understand the limits. Water at the edges of the waterfall are subject to wind resistance and will therefore quickly reach terminal velocity. But water at the center of the stream is removed from the effects of air resistence, so if the stream was thick enough and the waterfall high enough, would the center of the waterfall be unboundedly fast?</p> | g9189 | [
-0.012986698187887669,
0.0670504942536354,
-0.0017655168194323778,
-0.0019518756307661533,
-0.012093956582248211,
0.011595593765377998,
0.05408613011240959,
0.04363129660487175,
-0.045444387942552567,
-0.0014281350886449218,
-0.027283424511551857,
0.046610813587903976,
0.01968746818602085,
-0.007571052759885788,
-0.018196286633610725,
0.024444881826639175,
0.071286141872406,
0.004258827306330204,
0.06781543791294098,
-0.013727523386478424,
0.005203891545534134,
-0.03375933691859245,
-0.02896088734269142,
0.020481524989008904,
-0.009931028820574284,
-0.010073576122522354,
0.00994870439171791,
-0.019916590303182602,
-0.06330626457929611,
0.03037276118993759,
-0.0504511259496212,
0.0006022939924150705,
-0.026985235512256622,
-0.02275182493031025,
-0.05250882729887962,
0.019410358741879463,
-0.037160973995923996,
-0.01820908486843109,
-0.02971508540213108,
0.0050593893975019455,
0.011055299080908298,
0.01476257387548685,
-0.016963455826044083,
0.022133152931928635,
-0.04846980422735214,
0.002729238010942936,
0.034616079181432724,
0.002446847502142191,
-0.04862122982740402,
-0.029837267473340034,
0.0038677691482007504,
0.030529810115695,
-0.04122133180499077,
0.0388568714261055,
-0.05834202095866203,
0.028852520510554314,
-0.003715603845193982,
-0.009314526803791523,
-0.03080204874277115,
0.03720035031437874,
0.003806639462709427,
-0.021286433562636375,
-0.0011664857156574726,
-0.00012299048830755055,
0.05631915479898453,
-0.0015178940957412124,
-0.04163017123937607,
-0.006393695715814829,
0.02233266644179821,
0.021575817838311195,
0.03721800073981285,
-0.08633977174758911,
-0.04437025263905525,
-0.0623006746172905,
-0.009695880115032196,
0.0486098937690258,
-0.07620003074407578,
-0.02024083398282528,
0.03207198157906532,
-0.007353766821324825,
-0.03367244079709053,
0.017248405143618584,
-0.04602370038628578,
-0.004186525475233793,
0.031233588233590126,
0.023434344679117203,
0.009475039318203926,
-0.005674164742231369,
-0.01614447310566902,
0.0018917719135060906,
-0.051180627197027206,
-0.09225810319185257,
-0.002713983878493309,
-0.017955241724848747,
0.004080042243003845,
-0.032697778195142746,
-0.0021845423616468906,
0.07943665236234665,
-0.040809515863657,
0.03952439874410629,
-0.033373408019542694,
0.03408726677298546,
0.003214277094230056,
0.00221039867028594,
-0.08403695374727249,
-0.014099383726716042,
0.03760165348649025,
0.023039259016513824,
0.022004075348377228,
-0.014307798817753792,
-0.019761167466640472,
-0.055803168565034866,
-0.03613346070051193,
-0.006403569597750902,
-0.06716635823249817,
-0.0315600261092186,
-0.008886946365237236,
0.05440373346209526,
-0.05004686862230301,
0.02816559001803398,
0.02017952688038349,
0.06544508039951324,
0.010799730196595192,
0.09070403128862381,
0.005176804959774017,
0.010771029628813267,
-0.048068515956401825,
0.07567587494850159,
0.006782590411603451,
0.037357598543167114,
-0.007180897518992424,
-0.025950798764824867,
-0.006631040014326572,
0.013148041442036629,
0.061905235052108765,
0.029685305431485176,
-0.007990601472556591,
0.003524774219840765,
-0.0023781463969498873,
0.02666460908949375,
-0.02407780848443508,
-0.03928777948021889,
-0.004013529978692532,
-0.0007592501351609826,
-0.0813538208603859,
0.009171053767204285,
0.06086358055472374,
0.033975932747125626,
0.05456974729895592,
-0.043326832354068756,
-0.006937044207006693,
0.012876211665570736,
0.007209030445665121,
-0.0317862369120121,
-0.011201024055480957,
0.027910953387618065,
0.0041816155426204205,
-0.017111675813794136,
-0.004907622002065182,
-0.018998190760612488,
0.0015118062729015946,
-0.008086521178483963,
0.05487329512834549,
0.026514703407883644,
-0.07140560448169708,
0.034309882670640945,
0.0020923223346471786,
0.02529955469071865,
0.030009491369128227,
-0.02751517854630947,
-0.04760177060961723,
-0.017709171399474144,
0.020329149439930916,
0.03747468441724777,
-0.02072831057012081,
-0.03114933706820011,
0.05369099602103233,
-0.03992997482419014,
-0.020422037690877914,
-0.038370683789253235,
-0.04634897783398628,
-0.009233254939317703,
-0.020339513197541237,
-0.026753397658467293,
-0.009249391965568066,
0.03792506828904152,
0.04101979732513428,
0.013292905874550343,
-0.08374308049678802,
-0.046561773866415024,
0.01314741000533104,
0.025297490879893303,
0.011145394295454025,
0.049565624445676804,
-0.060803744941949844,
-0.025983799248933792,
0.03938249871134758,
-0.034798093140125275,
-0.021556226536631584,
-0.027474019676446915,
0.04393618553876877,
0.03145452216267586,
0.021621495485305786,
-0.012083043344318867,
0.018928293138742447,
-0.00195530173368752,
-0.021810779348015785,
0.018867723643779755,
-0.05664562061429024,
0.004897130187600851,
0.05267190933227539,
0.057470280677080154,
0.007680417504161596,
0.08724236488342285,
-0.02461223490536213,
-0.01642891950905323,
-0.023501940071582794,
0.004354707431048155,
0.015653321519494057,
0.005318211857229471,
0.03134888783097267,
0.011434908956289291,
-0.034618739038705826,
-0.01560452114790678,
-0.09049629420042038,
-0.031075244769454002,
-0.030491575598716736,
-0.04329982027411461,
0.018235765397548676,
0.008850240148603916,
0.02476692758500576,
0.03467525914311409,
0.008262999355793,
-0.039967652410268784,
0.014624645002186298,
0.015583625063300133,
0.022722188383340836,
0.02037951909005642,
-0.0015853127697482705,
-0.04619370773434639,
0.020354844629764557,
-0.0415973961353302,
-0.04812755808234215,
-0.006031733471900225,
-0.013226239010691643,
-0.03805055841803551,
0.00995618011802435,
-0.03729402273893356,
0.025815414264798164,
0.04268549382686615,
-0.023823140189051628,
-0.025534028187394142,
0.010761085897684097,
0.045204583555459976,
0.008381734602153301,
-0.0029108510352671146,
0.00839671678841114,
0.020627301186323166,
-0.05498515069484711,
-0.04318756237626076,
-0.0196771752089262,
0.0448886901140213,
0.03685273602604866,
0.0056153470650315285,
-0.0778634324669838,
0.002050960436463356,
-0.04715290293097496,
0.017188729718327522,
-0.008726068772375584,
0.02639085426926613,
-0.03576032072305679,
0.05578608810901642,
-0.013649937696754932,
0.07761639356613159,
-0.02469804510474205,
0.028834182769060135,
-0.009614981710910797,
-0.06673326343297958,
-0.024834364652633667,
0.04933548718690872,
-0.021621832624077797,
-0.0353161059319973,
0.01543212030082941,
0.023158477619290352,
0.006678735837340355,
-0.06977521628141403,
-0.006023582071065903,
0.07977667450904846,
-0.03669757395982742,
-0.011339252814650536,
-0.007515982259064913,
0.006621215958148241,
0.030695708468556404,
0.07694622129201889,
0.027152465656399727,
0.06760729849338531,
0.030470510944724083,
-0.04280434548854828,
-0.0008767636609263718,
0.0489678755402565,
-0.04096392169594765,
-0.025553232058882713,
0.01707346737384796,
0.016751959919929504,
-0.03735319897532463,
0.0063048056326806545,
-0.016768328845500946,
0.006298089865595102,
0.027384426444768906,
-0.017071016132831573,
0.040282849222421646,
0.01034272089600563,
-0.015437837690114975,
-0.038413155823946,
0.0010233181528747082,
0.013632972724735737,
0.0366867333650589,
-0.018670130521059036,
0.04493489861488342,
0.034478090703487396,
0.05108078941702843,
0.008020654320716858,
-0.03534170240163803,
0.06328695267438889,
0.046841077506542206,
0.009157147258520126,
-0.014142111875116825,
0.03001309372484684,
-0.06953981518745422,
-0.0652201697230339,
0.025987470522522926,
-0.0010589841986075044,
-0.025647057220339775,
-0.04113655537366867,
-0.008881471119821072,
-0.03254243731498718,
0.09316099435091019,
0.050301920622587204,
0.02946401946246624,
0.024522630497813225,
0.004671346861869097,
-0.013348909094929695,
-0.03478821739554405,
-0.021707966923713684,
0.02094334177672863,
-0.025621386244893074,
0.023051269352436066,
0.028877755627036095,
-0.019540904089808464,
0.07762860506772995,
0.04667101800441742,
-0.023180892691016197,
-0.044729430228471756,
-0.03674280643463135,
-0.01568499393761158,
0.019783025607466698,
0.051974277943372726,
0.04855998605489731,
-0.02055680938065052,
-0.04354596510529518,
0.03135761618614197,
0.010658368468284607,
0.040895652025938034,
0.009630161337554455,
-0.04536290094256401,
-0.003552559530362487,
0.0055708433501422405,
0.0018283360404893756,
-0.020387081429362297,
0.038777194917201996,
0.02384696900844574,
-0.034359466284513474,
-0.012670574709773064,
-0.00217916420660913,
0.011989339254796505,
-0.03825458884239197,
0.0482141338288784,
0.0548604279756546,
0.012665153481066227,
0.07847987860441208,
0.04010641947388649,
0.027068939059972763,
0.027006689459085464,
-0.02952517569065094,
-0.057508956640958786,
-0.025850066915154457,
-0.03144011273980141,
-0.03628139942884445,
0.06189892068505287,
-0.03401993587613106,
0.002988001797348261,
-0.02422463521361351,
0.017906639724969864,
-0.022687938064336777,
-0.002488602651283145,
0.06231428310275078,
0.016703611239790916,
-0.025012504309415817,
-0.10310324281454086,
-0.029837513342499733,
0.03380515053868294,
0.014359476044774055,
-0.031829942017793655,
0.06731338798999786,
-0.029444385319948196,
0.006674421019852161,
0.03293706104159355,
-0.019143342971801758,
-0.03915837034583092,
-0.02172086574137211,
0.02105521410703659,
-0.07521449029445648,
0.009710702113807201,
-0.05864184722304344,
-0.0014706607908010483,
0.03437206521630287,
-0.014025619253516197,
-0.00747134443372488,
-0.005606877151876688,
-0.020160863175988197,
0.0594727024435997,
-0.05794543772935867,
0.004702214617282152,
-0.0007452524732798338,
-0.004025373607873917,
-0.00907342042773962,
-0.009286785498261452,
-0.044832825660705566,
-0.04860329627990723,
-0.004897219594568014,
0.030083416029810905,
0.047857291996479034,
-0.03530746325850487,
0.05609985068440437,
0.007146364543586969,
0.04766719043254852,
0.004869641270488501,
0.03189660236239433,
0.057485632598400116,
0.03228943422436714,
0.014187400229275227,
0.029965417459607124,
0.04622293636202812,
0.03486928343772888,
-0.003932176623493433,
0.023009657859802246,
0.0014188442146405578,
-0.04294632747769356,
0.027596496045589447,
0.0008349631680175662,
-0.05658014118671417,
0.06033668667078018,
-0.01830240711569786,
-0.08076035231351852,
-0.023234281688928604,
0.009717768058180809,
-0.04668843373656273,
0.021176887676119804,
-0.029424458742141724,
0.0016655373619869351,
-0.0559484101831913,
0.012321602553129196,
-0.04463396593928337,
0.036370713263750076,
-0.03257383778691292,
-0.06451445072889328,
0.038271885365247726,
-0.02910926379263401,
-0.06811261922121048,
-0.05666371062397957,
0.05085691809654236,
0.02899213135242462,
0.05052750185132027,
0.10982470959424973,
-0.031268760561943054,
-0.009468131698668003,
0.017655840143561363,
0.029666533693671227,
0.05158773437142372,
-0.029155198484659195,
-0.0034344270825386047,
0.0004105163679923862,
-0.0010895398445427418,
-0.005113575141876936,
0.03792218118906021,
-0.04194781184196472,
-0.06982491165399551,
0.027786536142230034,
0.030661223456263542,
-0.06189313158392906,
-0.01464606449007988,
-0.012641462497413158,
-0.04042765125632286,
-0.0005537723191082478,
0.015665562823414803,
-0.05194294825196266,
0.04840767756104469,
0.0002738532202783972,
-0.001209959969855845,
0.0010105220135301352,
-0.02079533226788044,
0.034635111689567566,
0.007884123362600803,
0.006840402260422707,
0.008471852168440819,
0.06269081681966782,
0.013355286791920662,
-0.0010922736255452037,
-0.02095472440123558,
0.133525088429451,
-0.06189901381731033,
0.029141176491975784,
-0.027258405461907387,
-0.03480317071080208,
0.028944045305252075,
0.036360956728458405,
-0.028785351663827896,
-0.001334410160779953,
-0.01648370362818241,
0.05215084180235863,
0.07209771871566772,
0.020302943885326385,
0.0007029265980236232,
-0.004454150330275297,
-0.040923088788986206,
0.06791834533214569,
-0.08241502195596695,
0.006713733077049255,
-0.0029055317863821983,
0.04718732461333275,
-0.008066760376095772,
-0.010154406540095806,
-0.028850505128502846,
-0.022131118923425674,
-0.020459527149796486,
-0.001732982462272048,
0.027217090129852295,
-0.025824973359704018,
0.08321554958820343,
-0.02350345067679882,
-0.005718283820897341,
-0.007938511669635773,
0.025972964242100716,
0.08136557787656784,
-0.002605975838378072,
0.011108730919659138,
-0.00490180030465126,
-0.024411140009760857,
0.03274594992399216,
-0.005888897925615311,
-0.02492683008313179,
0.016434775665402412,
0.0033142706379294395,
0.043838679790496826,
0.046515677124261856,
0.0374593548476696,
-0.0069665489718317986,
0.006237258668988943,
0.0010855506407096982,
-0.05119100213050842,
0.006926395930349827,
0.041587233543395996,
0.02557128109037876,
0.000023333006538450718,
-0.012500543147325516,
-0.055420491844415665,
-0.04463198781013489,
0.018997572362422943,
0.03448091074824333,
0.06773010641336441,
0.0014430599985644221,
-0.03914244845509529,
0.04871531203389168,
-0.031205564737319946,
0.04363543540239334,
-0.009887234307825565,
0.01710537262260914,
0.018641311675310135,
-0.04851501062512398,
0.045507464557886124,
-0.08637280017137527,
-0.046872373670339584,
0.05629637837409973,
0.0017776400782167912,
0.012483363971114159,
0.018312454223632812,
-0.06656750291585922,
-0.0071303509175777435,
0.025988375768065453,
-0.037837088108062744,
0.002878985134884715,
-0.026519710198044777,
0.009698974899947643,
-0.027415338903665543,
0.03199922293424606,
-0.04609883576631546,
0.026601124554872513,
-0.018010733649134636,
-0.03205297887325287,
-0.008867491036653519,
0.049070052802562714,
-0.015571311116218567,
0.015893632546067238,
-0.01188612449914217,
0.018167607486248016,
-0.0026919615920633078,
0.011587549932301044,
-0.019430378451943398,
-0.019215013831853867,
-0.01580837182700634,
0.05771229788661003,
0.045199863612651825,
0.02149561606347561,
-0.04040510952472687,
-0.0944230705499649,
-0.02956271916627884,
-0.003926653880625963,
-0.03516869246959686,
0.03759078308939934,
0.008246486075222492,
0.043016280978918076,
-0.018613215535879135,
0.07417802512645721,
-0.04773220792412758,
0.03754619136452675,
0.02762187272310257,
-0.029084371402859688,
0.02289547584950924,
0.01748092658817768,
0.022278649732470512,
0.0427444688975811,
-0.00879374798387289,
-0.07825320214033127,
0.00041684319148771465,
0.006921051535755396,
0.021664757281541824,
-0.05756682530045509,
0.025304453447461128,
0.06692610681056976,
0.11565043032169342,
0.0024656946770846844,
0.01778520829975605,
-0.06546919047832489,
0.05850335210561752,
0.0028836005367338657,
0.004561455920338631,
0.039492830634117126,
0.0034217897336930037,
-0.011063896119594574,
-0.014874123968183994,
0.031297508627176285,
-0.03670911863446236,
0.009948608465492725,
0.033817142248153687,
-0.012084162794053555,
-0.033564671874046326,
0.0008285975200124085,
0.019699176773428917,
-0.026299338787794113,
-0.029684700071811676,
-0.01570766046643257,
0.03229598328471184,
0.01984081231057644,
-0.00702133821323514,
-0.018221769481897354,
0.05091004818677902,
0.04841875284910202,
0.024546686559915543,
-0.016622217372059822,
0.012443075887858868,
0.03458450362086296,
0.005303609650582075,
-0.027886969968676567,
0.04403824731707573,
0.03922487422823906,
-0.011861152946949005,
-0.00009485516784479842,
0.03606298565864563,
-0.024714943021535873,
-0.001009373925626278,
0.009307979606091976,
-0.011860464699566364,
0.02291976474225521,
-0.015559883788228035,
-0.054181136190891266,
0.002062021754682064,
-0.05104357749223709,
0.03892964869737625,
-0.005804417654871941,
-0.06405489891767502,
-0.024686554446816444,
0.06316617131233215,
-0.009527272544801235,
0.003713494399562478,
0.004669443238526583,
0.03575596585869789,
-0.025025086477398872,
-0.024829450994729996,
0.023524917662143707,
-0.034678585827350616,
0.037136781960725784,
-0.018091920763254166,
-0.027689959853887558,
0.03164143115282059,
0.009363466873764992,
0.04806101322174072,
-0.013601156882941723,
0.011077732779085636,
-0.04741370677947998,
0.016060680150985718,
-0.005930838640779257,
0.021677760407328606,
0.03134109824895859,
0.009216606616973877,
0.026508567854762077,
-0.0027662357315421104,
-0.031145349144935608,
-0.023568108677864075,
0.017484841868281364,
-0.04411894083023071,
-0.08432372659444809,
0.03469143435359001,
-0.02001306414604187,
-0.047918546944856644,
-0.011717552319169044,
0.024722253903746605,
-0.07888876646757126,
-0.026518071070313454,
-0.0046008252538740635,
-0.02691200189292431,
-0.036376599222421646,
-0.07113055884838104,
-0.002783952746540308,
-0.025703253224492073,
-0.031004605814814568,
-0.006206170655786991,
-0.008229768835008144,
-0.04682276025414467,
-0.04436811804771423,
-0.0457858070731163,
-0.033564817160367966,
-0.01784615032374859,
-0.027309851720929146,
-0.026820095255970955,
-0.017777660861611366,
0.0029371092095971107,
0.017513182014226913,
0.0063653988763689995,
0.02464837022125721,
-0.04696391150355339,
0.10312002897262573,
0.0073792776092886925,
0.04129491746425629,
0.03861735761165619,
0.010021946392953396,
-0.07627763599157333,
0.010141021572053432,
0.009419207461178303,
0.01119637954980135,
0.014595205895602703,
-0.05688369274139404,
-0.003146190196275711,
0.04818902909755707,
-0.030314240604639053,
-0.010913753882050514,
-0.021010344848036766,
-0.008085300214588642,
-0.013615275733172894
] |
<p>Will a plant grow faster when you would apply more upward gravitational force?</p>
<p>and/or</p>
<p>Will a plant grow slower when you would apply more downward gravitational force?</p> | g9190 | [
0.0678955540060997,
0.04815733805298805,
0.003608205122873187,
0.03414224833250046,
-0.0033685602247714996,
0.04695373773574829,
0.04763859510421753,
0.008693628944456577,
-0.06706152111291885,
-0.015985196456313133,
0.02523830346763134,
0.0004224454169161618,
0.018257547169923782,
0.020461417734622955,
0.0015238558407872915,
0.018603667616844177,
0.09876146912574768,
-0.055449146777391434,
0.02913232147693634,
0.006095931865274906,
-0.013800034299492836,
0.013508903793990612,
-0.0649968832731247,
-0.010554690845310688,
-0.0271161962300539,
0.050931233912706375,
-0.041034601628780365,
-0.03049531579017639,
-0.06529901176691055,
0.014467925764620304,
0.019789988175034523,
-0.002023611916229129,
0.00867602601647377,
-0.004092171788215637,
-0.030571863055229187,
-0.0005250372923910618,
0.012775984592735767,
-0.013305281288921833,
-0.016759144142270088,
-0.05857185646891594,
0.027833040803670883,
-0.046150919049978256,
0.02564527839422226,
-0.04267679154872894,
-0.01171970833092928,
-0.01032654196023941,
0.03969543054699898,
0.02625296823680401,
0.020556146278977394,
-0.0464729405939579,
-0.03911131992936134,
0.012083970941603184,
-0.02982925809919834,
-0.012695509940385818,
0.0037081516347825527,
0.0419946014881134,
0.053410883992910385,
-0.04466748237609863,
0.032815881073474884,
0.051854636520147324,
-0.01911921240389347,
0.0303685013204813,
0.0261423010379076,
-0.0014743265928700566,
0.03277165815234184,
0.029649723321199417,
0.01644800789654255,
-0.032094500958919525,
0.010009577497839928,
0.0002956879907287657,
0.003964296076446772,
-0.028103407472372055,
-0.025277715176343918,
-0.07527930289506912,
0.035560429096221924,
-0.018217815086245537,
0.033932462334632874,
-0.03039904683828354,
-0.003015937516465783,
0.02427319437265396,
0.003417596686631441,
-0.025441614910960197,
-0.001832597074098885,
0.0008753936272114515,
0.05972640588879585,
0.04231030493974686,
-0.003797305515035987,
-0.009146003052592278,
0.014723142609000206,
0.03267565742135048,
0.033775586634874344,
-0.03067384473979473,
0.07809559255838394,
0.01409858651459217,
-0.07068178802728653,
-0.007354688830673695,
0.0023548391181975603,
0.0269644595682621,
0.012630878016352654,
-0.029360083863139153,
-0.002550762379541993,
-0.025566035881638527,
0.04799705743789673,
-0.014424782246351242,
0.015418624505400658,
-0.04118150845170021,
0.04468999058008194,
-0.05394555255770683,
-0.07434538006782532,
-0.0194349717348814,
-0.016093553975224495,
-0.02315383404493332,
-0.00861847959458828,
-0.039047837257385254,
-0.024480408057570457,
-0.027595579624176025,
0.045832108706235886,
0.019086968153715134,
0.033186174929142,
0.006936944555491209,
0.023956716060638428,
0.06743811815977097,
-0.022451089695096016,
0.00965003203600645,
-0.0127254668623209,
0.0009085564524866641,
-0.028526511043310165,
0.013721492141485214,
-0.000633023853879422,
-0.0010178500087931752,
0.024676810950040817,
0.0014762717764824629,
-0.022307131439447403,
-0.009281972423195839,
-0.007257173769176006,
-0.02622612938284874,
-0.018923508003354073,
0.031206127256155014,
0.033094704151153564,
0.011119534261524677,
-0.016402430832386017,
-0.060378603637218475,
0.04059772565960884,
0.005216633435338736,
-0.02320622093975544,
0.02863132767379284,
0.05536900460720062,
0.05975467711687088,
-0.025265155360102654,
0.050128355622291565,
-0.02072598785161972,
0.004950472619384527,
0.025350423529744148,
-0.042241986840963364,
0.06682370603084564,
0.017973223701119423,
0.009207261726260185,
0.060903772711753845,
0.0779978483915329,
0.03757024183869362,
0.037863679230213165,
0.027912244200706482,
0.06177876144647598,
0.013696251437067986,
-0.018251661211252213,
0.01654662750661373,
0.023757776245474815,
-0.04443109408020973,
-0.0357857272028923,
0.015105225145816803,
-0.035928551107645035,
-0.043978236615657806,
0.04006747528910637,
0.01481564436107874,
0.03109055384993553,
0.0223844014108181,
0.061685722321271896,
-0.036932993680238724,
-0.028548793867230415,
0.017250893637537956,
0.017732292413711548,
-0.056698545813560486,
-0.01511741615831852,
-0.0028378695715218782,
0.012463664636015892,
-0.0328255221247673,
0.03181448206305504,
-0.02648286335170269,
-0.07541363686323166,
0.016138555482029915,
-0.03060149773955345,
0.01980716548860073,
0.00030086125480011106,
0.0536201186478138,
-0.02229519560933113,
-0.011231021955609322,
0.027429448440670967,
-0.006509588565677404,
-0.040230970829725266,
0.08269152045249939,
-0.03679228946566582,
0.06735844165086746,
0.06922361999750137,
-0.03305502235889435,
-0.041979480534791946,
-0.0372924730181694,
-0.04864541441202164,
0.026836765930056572,
0.055029451847076416,
-0.04998355358839035,
0.018802130594849586,
0.016198888421058655,
0.05309925973415375,
-0.0016289157792925835,
0.032440852373838425,
-0.014342025853693485,
0.0058310613967478275,
-0.0198696069419384,
-0.03871708735823631,
-0.00626128725707531,
-0.023824531584978104,
-0.017735715955495834,
0.03458651527762413,
0.021174689754843712,
-0.021161166951060295,
-0.06370880454778671,
0.00194518209900707,
-0.061921048909425735,
0.020330214872956276,
0.003326066769659519,
-0.03626053407788277,
0.04726865887641907,
0.014856459572911263,
-0.04614734649658203,
0.01667414791882038,
0.045438699424266815,
-0.008207535371184349,
0.024237647652626038,
0.0055506243370473385,
0.026854565367102623,
-0.012962192296981812,
-0.053751569241285324,
0.028358520939946175,
0.0017790126148611307,
0.03897284343838692,
-0.06249375641345978,
0.03541256859898567,
-0.006878357846289873,
-0.014983643777668476,
0.0038062790408730507,
0.06840697675943375,
0.06223120540380478,
-0.020527170971035957,
-0.017832452431321144,
-0.03942788764834404,
-0.03791676089167595,
-0.05604834482073784,
-0.016952237114310265,
-0.07633280009031296,
-0.009108642116189003,
0.03126280754804611,
-0.010672819800674915,
0.016735661774873734,
-0.017416201531887054,
-0.03254047781229019,
0.02693534456193447,
-0.053513918071985245,
-0.020503848791122437,
-0.001481174724176526,
0.04958676919341087,
-0.017180953174829483,
0.01873769983649254,
0.008979964070022106,
0.011592062190175056,
-0.05368321016430855,
-0.020678259432315826,
-0.002538127126172185,
0.02758808061480522,
-0.0022046349477022886,
-0.03892556577920914,
-0.05499425157904625,
-0.038640789687633514,
0.009032146073877811,
0.031057950109243393,
0.02834431454539299,
-0.04266076907515526,
-0.015460376627743244,
-0.04398598521947861,
-0.033726684749126434,
0.015180077403783798,
-0.04345507547259331,
0.03429196774959564,
0.05497850477695465,
0.04460073634982109,
0.004041718319058418,
0.023325523361563683,
-0.05045408755540848,
-0.04349668323993683,
-0.03673151135444641,
-0.012931394390761852,
0.01747041940689087,
0.00024692085571587086,
-0.00832483358681202,
0.033940769731998444,
-0.008697603829205036,
0.03866329789161682,
-0.05366990342736244,
-0.010431313887238503,
-0.0053219362162053585,
-0.036441318690776825,
-0.009703018702566624,
0.0777265876531601,
0.011799655854701996,
0.0354033000767231,
-0.07052935659885406,
-0.10317651182413101,
-0.03415204584598541,
0.02721875160932541,
-0.041495535522699356,
-0.017342792823910713,
0.0050914292223751545,
-0.0838194340467453,
-0.03426329419016838,
-0.019808193668723106,
-0.02074585296213627,
0.04589012637734413,
-0.019456524401903152,
0.045612722635269165,
0.01447877287864685,
-0.01372514571994543,
0.03557142987847328,
0.013561206869781017,
-0.01654600165784359,
0.04180106893181801,
-0.006131480913609266,
0.039570581167936325,
-0.017672820016741753,
0.01085908804088831,
0.00037098757456988096,
0.04817073047161102,
-0.023952772840857506,
0.013484046794474125,
-0.026774516329169273,
0.01871938817203045,
-0.009726760908961296,
0.06011511757969856,
0.009790968149900436,
0.02665446326136589,
-0.02222300134599209,
0.06264162808656693,
0.011943877674639225,
-0.06305532902479172,
0.0404546745121479,
0.004164591897279024,
0.03559473901987076,
-0.02106141857802868,
-0.015228142030537128,
-0.019360758364200592,
-0.07489511370658875,
-0.020682234317064285,
0.008186645805835724,
0.04218549281358719,
-0.033605001866817474,
0.08084563910961151,
-0.03430000692605972,
0.04400375485420227,
-0.015013005584478378,
0.06520285457372665,
-0.028853928670287132,
0.05057458579540253,
0.01821434497833252,
-0.018596908077597618,
0.018452484160661697,
-0.024604542180895805,
0.044263437390327454,
0.002693669870495796,
0.06533839553594589,
-0.08415534347295761,
0.03245599940419197,
-0.010880731046199799,
0.027352944016456604,
-0.03221294283866882,
-0.01426080334931612,
0.030584722757339478,
-0.015955984592437744,
0.024855421856045723,
-0.04969438910484314,
-0.04690534994006157,
0.03744039684534073,
-0.023863187059760094,
0.01852535270154476,
-0.00916317105293274,
-0.02815091609954834,
0.019944556057453156,
-0.0026671814266592264,
0.018991917371749878,
0.05331498757004738,
0.034272462129592896,
0.03772018849849701,
0.00042314152233302593,
-0.013428942300379276,
-0.017976323142647743,
-0.0226894523948431,
0.04977782070636749,
-0.05811678245663643,
0.018212387338280678,
0.03287067264318466,
0.026632819324731827,
-0.0710507482290268,
0.028878754004836082,
0.05372999235987663,
-0.030105700716376305,
0.007567450869828463,
-0.05316435545682907,
0.003162350272759795,
-0.06453508138656616,
0.008690468035638332,
0.039826519787311554,
-0.0033554439432919025,
0.0167057104408741,
0.03541630506515503,
0.05674874410033226,
0.02121376432478428,
-0.017568685114383698,
-0.002838526852428913,
0.04961910843849182,
0.03478618711233139,
-0.020946528762578964,
0.0018197564641013741,
0.010861958377063274,
0.019781630486249924,
0.03451921045780182,
0.013031752780079842,
-0.02831883169710636,
0.023224635049700737,
0.07258418947458267,
0.03585749492049217,
-0.00069281121250242,
0.03858426213264465,
0.024559015408158302,
0.010572691448032856,
0.040632396936416626,
-0.041904058307409286,
-0.016953615471720695,
0.02005404606461525,
0.10161272436380386,
0.002249519107863307,
-0.04089191183447838,
0.008129872381687164,
-0.029682707041502,
-0.004974387586116791,
0.012453648261725903,
0.005887558683753014,
-0.06997169554233551,
0.008492144756019115,
0.009979886934161186,
-0.01920454390347004,
0.02013949304819107,
-0.0004883430083282292,
0.002053576521575451,
-0.017963832244277,
0.01418793760240078,
0.030261756852269173,
-0.02795008197426796,
0.017652375623583794,
-0.03783201426267624,
-0.06522835046052933,
-0.007347125094383955,
-0.02729390189051628,
0.0696912482380867,
-0.039199985563755035,
-0.052662443369627,
0.009698956273496151,
0.08606787025928497,
-0.011814438737928867,
-0.016581937670707703,
-0.0037318095564842224,
0.013473589904606342,
0.0717068687081337,
-0.013267952017486095,
-0.02973318286240101,
0.01352741476148367,
0.013041181489825249,
-0.06193779036402702,
-0.01833447255194187,
0.0026625432074069977,
-0.020424067974090576,
0.00129492930136621,
0.03155374899506569,
-0.010840107686817646,
-0.009026682935655117,
-0.024148376658558846,
0.02011670358479023,
0.045344434678554535,
-0.05300847068428993,
0.006959155667573214,
-0.018345318734645844,
-0.03259886056184769,
0.027870317921042442,
-0.034617457538843155,
-0.0748535692691803,
-0.018704986199736595,
-0.010512858629226685,
-0.0004953279276378453,
-0.02546406164765358,
0.06332246214151382,
0.09651307016611099,
-0.0006839545094408095,
0.039113812148571014,
0.08132146298885345,
-0.0168090108782053,
0.03137209266424179,
0.014942127279937267,
0.00661340169608593,
0.0035435562022030354,
-0.0622350350022316,
0.019738512113690376,
0.06701115518808365,
-0.04318388178944588,
-0.03957158327102661,
0.08119283616542816,
-0.06996335089206696,
0.023505793884396553,
-0.07015124708414078,
0.05147664621472359,
0.0482185073196888,
-0.031989455223083496,
0.02057650312781334,
0.027569765225052834,
-0.02123011089861393,
0.02594558335840702,
0.03587881848216057,
0.012657944113016129,
-0.014243608340620995,
-0.015717964619398117,
0.03532160446047783,
0.07724586129188538,
0.05844773352146149,
0.03732924535870552,
-0.05182358995079994,
-0.0436897836625576,
-0.03580336645245552,
-0.010697176679968834,
0.016847098246216774,
-0.0038618380203843117,
-0.0270693339407444,
-0.044235505163669586,
0.011927688494324684,
0.014607123099267483,
-0.008446978405117989,
-0.0806792825460434,
-0.0323769673705101,
0.012039470486342907,
0.029971644282341003,
-0.04165972024202347,
0.024913394823670387,
-0.013762076385319233,
-0.02216319553554058,
0.038938675075769424,
-0.023487422615289688,
-0.006268767639994621,
-0.007281340193003416,
0.032438550144433975,
-0.06762649863958359,
0.03614583984017372,
-0.09189383685588837,
0.017917616292834282,
-0.0287428367882967,
0.057482458651065826,
0.044555455446243286,
-0.01700429432094097,
0.016766682267189026,
-0.01801386848092079,
0.015788286924362183,
0.015041673555970192,
-0.011368067003786564,
0.027116823941469193,
-0.025311242789030075,
-0.04479356110095978,
-0.03415900841355324,
-0.0016136805061250925,
0.013365554623305798,
-0.00040539909969083965,
-0.02081904374063015,
0.021455934271216393,
0.025926660746335983,
-0.05086027830839157,
0.038688573986291885,
0.04869001731276512,
-0.07403600960969925,
0.027616214007139206,
-0.044223956763744354,
-0.0142306387424469,
0.012481842190027237,
-0.03638007864356041,
-0.001776861841790378,
-0.028184007853269577,
0.027805225923657417,
0.003968271426856518,
-0.011127283796668053,
0.007128887809813023,
-0.008859436959028244,
0.11796469241380692,
-0.0466654971241951,
0.015124372206628323,
0.007227621972560883,
-0.03442125394940376,
0.02502693608403206,
0.04670516029000282,
-0.062170714139938354,
0.01692054606974125,
0.03807725012302399,
0.022229287773370743,
0.011345066130161285,
0.0011283563217148185,
0.02804909646511078,
0.0143285458907485,
-0.06281975656747818,
-0.0032247675117105246,
0.023026054725050926,
0.0038588931784033775,
-0.03978613018989563,
0.01863834448158741,
-0.10727567970752716,
0.02155110612511635,
-0.0342261977493763,
-0.010412907227873802,
-0.04319135099649429,
-0.02342257834970951,
-0.008977401070296764,
-0.013770262710750103,
-0.0424695648252964,
-0.03911690413951874,
0.029789771884679794,
0.040997449308633804,
0.021813740953803062,
0.03878692165017128,
0.025382883846759796,
-0.0037273301277309656,
0.003982284106314182,
0.011700177565217018,
0.06350161135196686,
-0.08580893278121948,
0.018905652686953545,
-0.002769970102235675,
0.05333763733506203,
0.01626872643828392,
-0.0033263403456658125,
0.002647110028192401,
-0.04515747353434563,
-0.07068711519241333,
-0.0082840071991086,
-0.037544675171375275,
-0.03183639794588089,
-0.019504103809595108,
0.07161855697631836,
-0.020764131098985672,
0.02211795374751091,
0.033898480236530304,
-0.0105705875903368,
0.021718524396419525,
-0.0300414077937603,
-0.01786153018474579,
0.02724914252758026,
-0.03847987577319145,
0.04066501930356026,
0.008514978922903538,
0.034922778606414795,
-0.05121748521924019,
0.059431057423353195,
0.031451303511857986,
-0.026544637978076935,
-0.026893362402915955,
0.02854837477207184,
0.00590449059382081,
-0.047923870384693146,
-0.05141507089138031,
-0.08735518157482147,
-0.03966064006090164,
-0.019914206117391586,
0.04043526202440262,
-0.036417730152606964,
0.029839765280485153,
-0.018148407340049744,
-0.041652921587228775,
-0.004668746143579483,
0.00967410858720541,
-0.024640457704663277,
0.0010529037099331617,
-0.04861680790781975,
-0.049561161547899246,
-0.0035530701279640198,
-0.03671744093298912,
0.02887587994337082,
-0.021933240815997124,
-0.022546174004673958,
-0.02093946561217308,
0.050953421741724014,
-0.06752102822065353,
-0.05072222277522087,
0.00022346490004565567,
0.03765280172228813,
0.005303055979311466,
-0.05228202044963837,
0.026236558333039284,
0.023370912298560143,
-0.02581615000963211,
0.05044584721326828,
-0.061520766466856,
-0.032273612916469574,
-0.002378700999543071,
0.02938983030617237,
-0.032428592443466187,
0.0069810329005122185,
0.02917618490755558,
0.006286752875894308,
-0.03469813987612724,
-0.027099451050162315,
-0.0029349401593208313,
-0.008747157640755177,
-0.03886145353317261,
-0.035647884011268616,
0.016711167991161346,
-0.08683121204376221,
-0.015158397145569324,
0.03577052429318428,
-0.005211378447711468,
-0.01632770523428917,
0.014017005451023579,
-0.03564760088920593,
0.003908135462552309,
-0.08329451829195023,
-0.004302640445530415,
0.007105214521288872,
-0.013621566817164421,
0.03302783519029617,
0.005297758616507053,
-0.0005789697752334177,
-0.017962636426091194,
0.006645191460847855,
-0.047242335975170135,
-0.025897126644849777,
-0.01157933659851551,
0.03162957727909088,
0.049222227185964584,
-0.006108450703322887,
-0.00851915217936039,
0.08812138438224792,
0.12909269332885742,
-0.042224086821079254,
0.02213914319872856,
0.043457068502902985,
-0.009604748338460922,
0.031147560104727745,
-0.01254227850586176,
0.013078249990940094,
0.02728283405303955,
-0.003945508506149054,
0.003962057642638683,
-0.02495371550321579,
-0.01109467912465334,
0.008311634883284569,
-0.020901808515191078,
-0.050463300198316574,
-0.023871924728155136,
-0.014523204416036606,
0.013400903902947903,
0.009504571557044983
] |
<p>I'm interested in a QFT model featuring a fermion derivative coupling like $XX^* \chi^*\gamma^\mu∂_\mu \psi$ where X is some other field operator.
Has anybody seen a paper containing something like this?
How would Feynman-Graphs for such an interaction look like?
Are derivatives of fermions ruled out by some consideration i am missing?</p> | g9191 | [
-0.00841621682047844,
0.04593083634972572,
0.004917722661048174,
-0.08533182740211487,
0.04171140864491463,
-0.04571639746427536,
-0.05222504585981369,
0.013103188946843147,
0.019924618303775787,
-0.009319202974438667,
0.0024385221768170595,
0.0061506773345172405,
0.012067699804902077,
0.00927842315286398,
-0.0101048294454813,
0.004891916643828154,
0.018601031973958015,
0.04920056462287903,
0.005021737888455391,
-0.037669502198696136,
-0.05526392161846161,
0.03451215848326683,
-0.018721602857112885,
-0.03375569358468056,
0.03207805007696152,
-0.030703511089086533,
0.013192928396165371,
-0.021049221977591515,
-0.016794009134173393,
-0.037031419575214386,
-0.0342710018157959,
0.01715122163295746,
0.03195669502019882,
-0.04521569982171059,
-0.049412697553634644,
0.005415093153715134,
0.04926088824868202,
0.005730919074267149,
0.037597887217998505,
0.0027062895242124796,
0.02603287436068058,
0.01140193548053503,
0.01398475468158722,
-0.021999241784214973,
-0.029515022411942482,
0.06373075395822525,
-0.003986082971096039,
0.059298884123563766,
-0.02132497914135456,
0.06518863141536713,
-0.026363682001829147,
0.03572121262550354,
0.03704017773270607,
-0.025362947955727577,
0.01374005526304245,
0.012536207213997841,
0.05450473725795746,
0.013219407759606838,
0.022085603326559067,
-0.021001853048801422,
-0.00009600963676348329,
-0.014013734646141529,
0.005502193700522184,
0.017020458355545998,
0.10428794473409653,
-0.007041068747639656,
-0.05757748708128929,
0.0020339067559689283,
0.0021391119807958603,
-0.0569523461163044,
-0.027088796719908714,
-0.003480840241536498,
0.006548939272761345,
0.06100328639149666,
0.0739857628941536,
0.01895921304821968,
-0.026365013793110847,
-0.04590007662773132,
0.022973736748099327,
0.001107513322494924,
-0.06799374520778656,
-0.010026732459664345,
0.012796531431376934,
0.006311386823654175,
0.041070252656936646,
-0.02346351370215416,
-0.04083683714270592,
-0.006069496739655733,
-0.009992491453886032,
-0.025383247062563896,
0.028904950246214867,
-0.05638076737523079,
-0.02968750335276127,
-0.020663278177380562,
0.0077307745814323425,
-0.006563789676874876,
-0.0196574367582798,
0.034810036420822144,
-0.039091840386390686,
-0.035604849457740784,
-0.0394422821700573,
0.05670259892940521,
0.04550228267908096,
-0.006942995358258486,
-0.08344395458698273,
-0.016601961106061935,
-0.029691433534026146,
0.03346264734864235,
0.03474307060241699,
0.06274435669183731,
-0.017824294045567513,
0.03945312276482582,
-0.00294516677968204,
-0.03420747444033623,
0.03694036230444908,
-0.059742335230112076,
-0.007474731188267469,
-0.009123384952545166,
-0.012825734913349152,
0.0429009273648262,
-0.037408631294965744,
-0.011413579806685448,
0.06457997113466263,
-0.011783234775066376,
-0.026427825912833214,
-0.06531663239002228,
-0.004565744660794735,
0.03733772039413452,
0.01253698579967022,
-0.01872844807803631,
0.07888834178447723,
-0.06423978507518768,
0.007202915381640196,
0.04156548157334328,
-0.012177815660834312,
0.045169927179813385,
-0.03526522219181061,
0.013463067822158337,
-0.0006900945445522666,
-0.011755052022635937,
-0.008985915221273899,
-0.0607757605612278,
-0.03590809181332588,
-0.01896809972822666,
0.008793811313807964,
0.00043122671195305884,
0.05261256918311119,
-0.0075029307045042515,
0.005152803845703602,
-0.005613464862108231,
0.037254348397254944,
0.0431157685816288,
-0.026237353682518005,
0.03338134288787842,
0.032863494008779526,
0.013374945148825645,
0.02802545391023159,
-0.0035619179252535105,
-0.05996958911418915,
-0.06986397504806519,
0.07215043902397156,
-0.0016839808085933328,
0.02190418541431427,
-0.0396234393119812,
0.001258738455362618,
-0.04434812068939209,
0.030189568176865578,
-0.05442333221435547,
-0.008926712907850742,
-0.0011204619659110904,
-0.05109096318483353,
0.03949369117617607,
0.02816222980618477,
0.0213164109736681,
0.007980434224009514,
0.042519617825746536,
-0.10859926789999008,
-0.025859886780381203,
0.022557374089956284,
0.03952901065349579,
0.0012029835488647223,
-0.014130603522062302,
0.027676809579133987,
-0.011497734114527702,
-0.01232242863625288,
-0.030314745381474495,
-0.02866997756063938,
-0.02258807048201561,
0.014820072799921036,
-0.008151140995323658,
-0.004069021437317133,
-0.030577659606933594,
0.023212125524878502,
-0.01895507425069809,
0.030567161738872528,
0.05530300736427307,
0.04055774211883545,
-0.07249180227518082,
-0.014815530739724636,
0.01610109955072403,
-0.03499097377061844,
0.03457972779870033,
0.07857432961463928,
-0.02211310900747776,
0.022264808416366577,
0.002873525023460388,
-0.05311140418052673,
0.012759084813296795,
0.04482768103480339,
-0.0286848284304142,
-0.0003658370696939528,
-0.05292593315243721,
0.08221150189638138,
0.06086663529276848,
0.031515225768089294,
-0.043830644339323044,
-0.004743499215692282,
0.002316742204129696,
0.01916598528623581,
0.017634857445955276,
0.07704422622919083,
-0.013056167401373386,
0.07554513961076736,
0.04936043545603752,
0.0066827405244112015,
-0.0003301903198007494,
-0.002930857939645648,
0.020736759528517723,
-0.018257854506373405,
0.020095856860280037,
-0.05828452110290527,
0.04526014253497124,
-0.022346246987581253,
-0.07394599914550781,
-0.03937143087387085,
0.021598678082227707,
-0.015021719969809055,
0.011676164343953133,
-0.004037629812955856,
0.043286655098199844,
0.015642942860722542,
0.022605223581194878,
-0.0618152841925621,
0.027962885797023773,
-0.020195189863443375,
0.022926324978470802,
-0.021211756393313408,
0.08186338096857071,
-0.01121602114289999,
0.009760349057614803,
0.06585019826889038,
0.0022416324354708195,
-0.032377295196056366,
0.04988141730427742,
-0.00972267147153616,
-0.004812703467905521,
0.0031888524536043406,
0.026346828788518906,
0.007211494259536266,
-0.037678252905607224,
0.009593351744115353,
0.009041505865752697,
0.025356028228998184,
0.020086564123630524,
0.021478304639458656,
-0.012531193904578686,
0.08968725055456161,
0.0009113684645853937,
-0.05202138051390648,
0.017938056960701942,
-0.01959451101720333,
0.056296125054359436,
-0.0018240208737552166,
0.04418225213885307,
0.00214030547067523,
-0.019406065344810486,
0.0021143867634236813,
0.016764070838689804,
-0.027263756841421127,
-0.049689728766679764,
0.007509907241910696,
-0.042840626090765,
-0.01706000044941902,
0.0053014312870800495,
0.043955471366643906,
-0.042409222573041916,
-0.011252405121922493,
0.00473650312051177,
0.025025125592947006,
0.020640239119529724,
-0.022130442783236504,
0.004984627943485975,
0.006824199575930834,
0.0012800541007891297,
-0.03661283478140831,
-0.030090022832155228,
0.02696361392736435,
-0.018032699823379517,
0.006767858285456896,
0.08114972710609436,
0.013555464334785938,
0.019713331013917923,
0.006415240932255983,
0.0907195508480072,
0.007807320915162563,
-0.05186149850487709,
-0.09782078117132187,
-0.02885737642645836,
-0.03662652522325516,
-0.03443306311964989,
-0.016689008101820946,
-0.026269173249602318,
-0.01206001453101635,
-0.03228669986128807,
-0.04682143032550812,
-0.009259995073080063,
-0.01844027079641819,
0.052198626101017,
0.04032687842845917,
0.010612623766064644,
0.0030936412513256073,
-0.05285769701004028,
0.02972809411585331,
-0.011847080662846565,
0.01940133236348629,
0.049828510731458664,
-0.04055946692824364,
0.027170279994606972,
-0.02022811770439148,
-0.015735870227217674,
0.049871739000082016,
-0.03920290246605873,
0.06552787125110626,
-0.032606761902570724,
-0.05539123713970184,
-0.021856456995010376,
-0.07617605477571487,
-0.01590513437986374,
0.01841866225004196,
-0.002519067609682679,
-0.034264616668224335,
-0.029389986768364906,
-0.015875698998570442,
-0.029093587771058083,
0.019692689180374146,
-0.0524597093462944,
-0.012756431475281715,
0.059556134045124054,
0.008195875212550163,
-0.031885065138339996,
-0.05699595436453819,
-0.026747863739728928,
0.01998613402247429,
-0.013707548379898071,
0.09655161201953888,
-0.042368967086076736,
-0.009830240160226822,
0.026210935786366463,
0.04291025549173355,
0.030944379046559334,
0.00010446604574099183,
0.0015527455834671855,
-0.017792632803320885,
0.02386186458170414,
-0.012423602864146233,
-0.04089224338531494,
-0.008948747999966145,
0.030824771150946617,
0.017119968309998512,
-0.02092937007546425,
0.026202142238616943,
0.04232430085539818,
0.019434841349720955,
0.0693298727273941,
-0.03988362103700638,
-0.02569815143942833,
-0.03028533235192299,
-0.025443613529205322,
0.013859941624104977,
-0.014551403932273388,
-0.028584927320480347,
0.04599769413471222,
-0.00034052913542836905,
0.05732991546392441,
0.07525129616260529,
0.00013681779091712087,
-0.017047924920916557,
0.00033382687252014875,
-0.021272791549563408,
0.022679591551423073,
0.0021562876645475626,
-0.0067658135667443275,
-0.003981894813477993,
0.04979933798313141,
-0.02315673977136612,
-0.041689202189445496,
0.05622459575533867,
-0.037164125591516495,
-0.03760869801044464,
0.041870828717947006,
0.005330600775778294,
-0.0406864732503891,
-0.0030014668591320515,
-0.04626331850886345,
-0.017909925431013107,
-0.04558023437857628,
-0.05317290499806404,
-0.03246132284402847,
0.04660171642899513,
-0.043348442763090134,
-0.01610085926949978,
-0.0020854128524661064,
0.010552920401096344,
-0.03462078049778938,
0.022240662947297096,
0.012317150831222534,
0.009984593838453293,
-0.039384208619594574,
-0.023224351927638054,
-0.013410384766757488,
0.04608753323554993,
-0.02733856812119484,
-0.0015341982943937182,
0.05442862585186958,
0.009076761081814766,
-0.005440355744212866,
0.03776298835873604,
0.01709422655403614,
-0.0123445400968194,
-0.08617676049470901,
0.01861685700714588,
0.005540200974792242,
-0.02626677416265011,
-0.0017750458791851997,
-0.0335736908018589,
0.024500861763954163,
-0.05150989070534706,
-0.06383191794157028,
-0.01514841802418232,
0.061920832842588425,
0.05488093942403793,
-0.03178000450134277,
0.015192640013992786,
-0.04590912535786629,
0.0087971780449152,
0.02497418038547039,
-0.06280022114515305,
-0.026738310232758522,
-0.021674755960702896,
-0.0366615429520607,
0.015045426785945892,
-0.03882807865738869,
-0.05727482959628105,
0.017266729846596718,
0.0250718854367733,
-0.05461523309350014,
-0.0016159849474206567,
0.0019414110574871302,
0.03139754757285118,
-0.04672588035464287,
-0.046144913882017136,
-0.048349201679229736,
0.024376414716243744,
-0.0027102092280983925,
-0.037245240062475204,
0.0027837567031383514,
-0.07002043724060059,
0.07236113399267197,
-0.01960190013051033,
0.032795775681734085,
-0.0037185896653681993,
0.016433410346508026,
0.07238921523094177,
0.002144987927749753,
0.028418637812137604,
0.03914620727300644,
-0.018599500879645348,
-0.012520916759967804,
0.00964000541716814,
-0.07137476652860641,
0.01724669151008129,
0.016912277787923813,
0.0029804722871631384,
-0.027804505079984665,
0.027012616395950317,
-0.06117396056652069,
0.01678219623863697,
0.015892187133431435,
0.0032465055119246244,
-0.11478814482688904,
0.04996354505419731,
0.023108432069420815,
0.03536616638302803,
0.010837544687092304,
-0.0004100002988707274,
0.008497679606080055,
0.0396302193403244,
-0.002398655517026782,
0.03907819464802742,
0.006439295131713152,
-0.0005266265361569822,
0.027781222015619278,
-0.051494136452674866,
-0.038621604442596436,
0.02639922872185707,
0.08469464629888535,
0.02964036539196968,
-0.0322311595082283,
0.005314890760928392,
0.039236024022102356,
-0.033724818378686905,
-0.010657519102096558,
0.05313803628087044,
0.019577262923121452,
-0.04739297553896904,
0.01493394747376442,
-0.04950495809316635,
-0.026776356622576714,
-0.030489357188344002,
-0.09233450144529343,
0.08518468588590622,
-0.016774630174040794,
-0.03737360239028931,
-0.03234432637691498,
0.0499977171421051,
0.003175147110596299,
-0.007693891413509846,
-0.026670794934034348,
-0.024834925308823586,
0.05412339046597481,
0.06162095442414284,
-0.008960995823144913,
0.016463620588183403,
0.07148781418800354,
-0.015369738452136517,
-0.004346442874521017,
0.06073838472366333,
0.0245915986597538,
0.060134027153253555,
0.02616875059902668,
0.01146511547267437,
-0.001430042553693056,
0.0461493544280529,
0.025878630578517914,
-0.02230500616133213,
-0.05331134423613548,
-0.03184023126959801,
0.038707856088876724,
-0.002293418161571026,
-0.03970479965209961,
0.01026176568120718,
-0.09453234076499939,
0.019884178414940834,
0.02839188650250435,
0.007463404443114996,
-0.022094590589404106,
0.003676793072372675,
-0.057978857308626175,
0.021157123148441315,
0.044176485389471054,
0.024858634918928146,
-0.0495048388838768,
0.034381203353405,
0.0056677935644984245,
-0.0038290894590318203,
-0.01118484977632761,
0.004549874924123287,
-0.0199907124042511,
0.04458940401673317,
0.0463668629527092,
0.015837442129850388,
0.033385489135980606,
0.00780013483017683,
0.03848668560385704,
-0.01083475723862648,
-0.02671634964644909,
0.05683698132634163,
-0.03049403429031372,
-0.002356945537030697,
-0.03550177812576294,
0.03707196190953255,
0.02033061720430851,
-0.015026348643004894,
-0.02953803911805153,
-0.0002984186285175383,
0.02097567729651928,
-0.0607837475836277,
0.017921485006809235,
0.017912283539772034,
0.05794224888086319,
-0.0040174610912799835,
0.03537943214178085,
-0.014575065113604069,
-0.020145868882536888,
0.05549432337284088,
0.0032954609487205744,
0.0016040867194533348,
-0.005537097342312336,
-0.013590462505817413,
-0.005700212437659502,
0.019282404333353043,
-0.0006058557773940265,
0.011994387954473495,
-0.010507120750844479,
0.03342800959944725,
0.04196479544043541,
0.0128696383908391,
0.03723978251218796,
0.03822801262140274,
-0.00919981487095356,
0.008394856937229633,
0.028087632730603218,
-0.021163294091820717,
0.012878107838332653,
0.02498042955994606,
-0.10160762071609497,
-0.031104445457458496,
0.001944757648743689,
-0.09272091090679169,
0.012986444868147373,
0.017504818737506866,
-0.0038948555011302233,
-0.0281031746417284,
-0.07409308850765228,
0.020499685779213905,
0.021122772246599197,
-0.002446515951305628,
-0.006587183102965355,
0.002812705934047699,
-0.03447524085640907,
0.0136565575376153,
0.0077995117753744125,
0.06567549705505371,
-0.031702734529972076,
-0.03794467821717262,
0.05178869515657425,
-0.06711819022893906,
0.011761226691305637,
0.04945710301399231,
0.055412888526916504,
-0.0038853890728205442,
0.028429601341485977,
0.02954280935227871,
0.004684018436819315,
0.03955717757344246,
0.007977902889251709,
0.05336253345012665,
-0.013560952618718147,
-0.08477316796779633,
0.012892939150333405,
0.050009433180093765,
0.026020513847470284,
-0.027118226513266563,
0.008468261919915676,
-0.0532296784222126,
-0.024706417694687843,
-0.008981225080788136,
0.025365928187966347,
0.0033931205980479717,
-0.04633500799536705,
-0.040073901414871216,
-0.03158086538314819,
-0.028749113902449608,
0.029139425605535507,
-0.0075935134664177895,
0.02176644094288349,
-0.014159802347421646,
0.004591388627886772,
0.00926860049366951,
0.009106867015361786,
-0.05129535123705864,
-0.07643397152423859,
-0.03310857340693474,
0.0358857661485672,
-0.01164305955171585,
-0.042239781469106674,
-0.016017109155654907,
0.05205836147069931,
-0.00222546118311584,
0.004544449970126152,
-0.04069735109806061,
0.026259398087859154,
0.01911091059446335,
-0.01643752120435238,
-0.050824351608753204,
-0.001610252889804542,
0.051461465656757355,
-0.001628813915885985,
0.02387319691479206,
0.029464716091752052,
-0.012851325795054436,
-0.02622772753238678,
-0.03735971450805664,
-0.06942471116781235,
-0.042036838829517365,
0.014364956878125668,
-0.011239822022616863,
0.04641708731651306,
0.029343605041503906,
0.10451752692461014,
0.07644616067409515,
-0.009069561958312988,
-0.05050690472126007,
-0.011363321915268898,
0.05285891517996788,
-0.03562339395284653,
0.02977890521287918,
-0.06760090589523315,
0.0034604789689183235,
-0.01617102138698101,
0.05275111272931099,
0.036933645606040955,
0.0121188685297966,
0.07681320607662201,
0.05303242802619934,
-0.0005689940298907459,
-0.04256121814250946,
-0.006110241636633873,
0.026259562000632286,
-0.010840610601007938,
-0.031176643446087837,
0.05431845784187317,
-0.027431050315499306,
-0.06327025592327118,
-0.001960338559001684,
-0.045296184718608856,
-0.056507620960474014,
0.019895773380994797,
0.007438797038048506,
0.054722629487514496,
0.014542520977556705,
-0.009283323772251606,
-0.06878242641687393,
0.02055799774825573,
-0.013435889035463333,
-0.012033162638545036,
-0.0646057277917862,
-0.03177648410201073,
0.005349672865122557,
-0.021482525393366814,
-0.0007839153986424208,
-0.006405204068869352,
0.02483336813747883,
-0.0009494054829701781,
0.04252001643180847,
-0.023371197283267975,
-0.010237235575914383,
-0.0439254492521286,
0.044794563204050064,
0.0018221222562715411,
-0.01351369358599186,
-0.030615955591201782,
-0.0005471027106977999,
0.004726838786154985,
0.021068183705210686,
-0.019956910982728004,
-0.055794890969991684,
0.04578433930873871,
0.03651184216141701,
0.023151123896241188,
-0.033011097460985184,
-0.03912726417183876,
-0.004588947631418705,
0.044906847178936005,
-0.015515490435063839,
0.01089432928711176,
0.032852381467819214,
-0.03163658455014229
] |
<p>Is there field theory which describe a second order phase transition without upper critical dimension ? Mermin-Wagner says something about lower critical dimension but nothing about upper dimension.</p> | g9192 | [
0.040455881506204605,
-0.03109479695558548,
0.025221316143870354,
0.019643526524305344,
-0.015617279335856438,
0.03749576583504677,
-0.023678692057728767,
0.010745386593043804,
-0.028932062909007072,
-0.024078011512756348,
-0.03648874908685684,
0.01686801388859749,
0.011742400005459785,
-0.02766926772892475,
0.006829910911619663,
-0.0007129746372811496,
-0.0006604704540222883,
-0.0017310872208327055,
0.014707345515489578,
-0.031362827867269516,
-0.015450999140739441,
-0.031946174800395966,
-0.008189707063138485,
-0.04772578179836273,
-0.01680823042988777,
0.021153662353754044,
0.055966250598430634,
-0.016316566616296768,
-0.026640240103006363,
-0.0068275947123765945,
0.03906293213367462,
0.017554383724927902,
0.044739942997694016,
-0.039372917264699936,
0.0008674705168232322,
0.026552679017186165,
0.045167695730924606,
0.07899128645658493,
-0.0020545385777950287,
0.027357270941138268,
0.006925034802407026,
0.03291171044111252,
0.015627050772309303,
-0.01984000951051712,
-0.020193610340356827,
0.03849174827337265,
-0.048908304423093796,
0.02090916968882084,
-0.05299100652337074,
0.0007425889489240944,
0.06279736757278442,
0.053550779819488525,
0.02936389669775963,
-0.038168925791978836,
-0.04761745035648346,
0.007553848437964916,
-0.02945425733923912,
0.016643786802887917,
0.08032902330160141,
0.0008174898102879524,
0.020102808251976967,
0.08230891078710556,
0.044036202132701874,
-0.012987485155463219,
-0.019343482330441475,
0.008956747129559517,
-0.034542761743068695,
-0.0779004693031311,
0.0230262391269207,
-0.044833261519670486,
-0.004090101458132267,
-0.0159606896340847,
-0.04292847216129303,
0.01896088756620884,
-0.008256257511675358,
0.031453974545001984,
-0.01663079857826233,
-0.044428396970033646,
0.005736565683037043,
-0.041252389550209045,
-0.05198794975876808,
0.008838390931487083,
0.00159623590297997,
0.006553266663104296,
0.06095346435904503,
0.004230800550431013,
0.031027553603053093,
0.002725080354139209,
0.013912535272538662,
-0.01713184453547001,
-0.002938369521871209,
0.05312930420041084,
-0.024028947576880455,
-0.057534873485565186,
0.030360253527760506,
0.06877674907445908,
-0.021695150062441826,
0.02115338109433651,
-0.003888146486133337,
-0.03155343607068062,
-0.03799370303750038,
0.06510313600301743,
0.04745398834347725,
-0.03725982457399368,
-0.00994470901787281,
-0.018366921693086624,
0.027392588555812836,
-0.009071150794625282,
0.03585107624530792,
0.027458511292934418,
-0.08659239113330841,
0.03090876154601574,
-0.0726124569773674,
0.009616130962967873,
-0.007593231275677681,
0.013195513747632504,
0.11702114343643188,
-0.08187957853078842,
0.03248767927289009,
-0.048632845282554626,
0.03857856243848801,
-0.05279378965497017,
0.08096282184123993,
0.011293575167655945,
-0.012667806819081306,
0.028113117441534996,
0.028975632041692734,
0.012936016544699669,
-0.0036074768286198378,
0.008389044553041458,
-0.018354063853621483,
0.026607763022184372,
0.03718525916337967,
0.017666015774011612,
0.06676878035068512,
0.010450197383761406,
-0.006140508688986301,
-0.00547070661559701,
0.020821066573262215,
0.019562093541026115,
-0.026738056913018227,
0.013903936371207237,
-0.02395516075193882,
0.01174276415258646,
-0.006797578185796738,
-0.03428247198462486,
0.05152245610952377,
0.0088528236374259,
-0.013708983547985554,
-0.021560266613960266,
-0.023688599467277527,
0.0274790171533823,
-0.0018022469012066722,
-0.03768442943692207,
-0.040160562843084335,
0.041799575090408325,
0.053810592740774155,
-0.0324050709605217,
0.0503314733505249,
-0.04102826490998268,
-0.016068561002612114,
-0.0017837142804637551,
0.010139589197933674,
0.04978915676474571,
-0.03821757063269615,
-0.07855129987001419,
-0.013269356451928616,
-0.012393465265631676,
-0.014632432721555233,
-0.01354222185909748,
0.01198688056319952,
-0.0018537521827965975,
0.05353828892111778,
0.10378880053758621,
0.006455420516431332,
0.015956535935401917,
-0.06325498223304749,
0.060125406831502914,
-0.0011454644845798612,
0.010511264204978943,
-0.0647517591714859,
-0.02544683963060379,
0.013420000672340393,
0.01406149286776781,
0.07766120135784149,
0.02622568979859352,
0.0069213006645441055,
0.07493907958269119,
0.012706221081316471,
-0.034107618033885956,
-0.08237794041633606,
0.0364387147128582,
0.01698559895157814,
-0.013845552690327168,
0.0018950850935652852,
0.04489372298121452,
0.02853512577712536,
-0.035370249301195145,
-0.03379553556442261,
0.030611677095294,
0.044289808720350266,
-0.0014856052584946156,
-0.06596887111663818,
-0.013202476315200329,
-0.06615043431520462,
0.06262261420488358,
-0.021003037691116333,
0.052321650087833405,
-0.03861171007156372,
-0.009814486838877201,
-0.01033919770270586,
-0.05774306133389473,
0.04345105588436127,
0.024178629741072655,
-0.07978596538305283,
0.03292415291070938,
0.008283768780529499,
0.01840084046125412,
-0.04067592695355415,
0.11022248864173889,
0.06413586437702179,
0.010282452218234539,
0.06232551112771034,
0.024937018752098083,
0.029693076387047768,
-0.0430009588599205,
0.00563404243439436,
0.04753750190138817,
0.0055724335834383965,
-0.04751332104206085,
-0.03477682173252106,
0.027591027319431305,
-0.02529754489660263,
-0.050956398248672485,
-0.0045493789948523045,
0.04895130544900894,
-0.03961576893925667,
-0.0366242453455925,
0.0733056515455246,
0.05406554788351059,
-0.003521074540913105,
0.00021397335513029248,
-0.031180385500192642,
-0.012486563995480537,
0.01969488151371479,
-0.018948404118418694,
0.04838030785322189,
0.009645462967455387,
-0.015763534232974052,
-0.00405431492254138,
-0.016104409471154213,
-0.007604988291859627,
-0.011756563559174538,
-0.0507839173078537,
-0.07737012207508087,
0.008948874659836292,
-0.0019839517772197723,
0.07543593645095825,
-0.07702901214361191,
-0.06267208606004715,
0.012310430407524109,
-0.03173897787928581,
0.0696222111582756,
0.016864508390426636,
-0.053790390491485596,
-0.024076921865344048,
-0.033428411930799484,
0.07248064130544662,
-0.022982226684689522,
0.005896355491131544,
-0.008235638961195946,
0.0736105889081955,
-0.0803954154253006,
0.022083252668380737,
-0.0031982881482690573,
0.0011963044526055455,
-0.014194297604262829,
-0.0071611120365560055,
0.044157590717077255,
0.0121749984100461,
-0.02514621801674366,
-0.013194368220865726,
0.0015334703493863344,
0.016886115074157715,
0.03027380257844925,
-0.008021255023777485,
-0.017932644113898277,
0.06185733526945114,
-0.03566789999604225,
-0.003909087739884853,
-0.02749466709792614,
0.01009984128177166,
-0.004027495626360178,
0.03500835597515106,
0.010662198998034,
-0.01914580538868904,
-0.0400262176990509,
-0.04234332963824272,
-0.033556804060935974,
0.003310492495074868,
0.005427636671811342,
-0.037722788751125336,
-0.01912885345518589,
-0.02231103926897049,
0.027802838012576103,
-0.011255951598286629,
-0.012196002528071404,
-0.07338415086269379,
-0.051804423332214355,
-0.037318840622901917,
0.0009838152909651399,
0.044787030667066574,
0.050083667039871216,
-0.00033623931813053787,
-0.054556313902139664,
-0.024297358468174934,
0.016039609909057617,
0.038942016661167145,
0.04023153334856033,
-0.04731825366616249,
-0.012456651777029037,
-0.03270464763045311,
0.014820240437984467,
-0.010967536829411983,
-0.016627956181764603,
0.04090075567364693,
-0.07907333225011826,
0.036829687654972076,
-0.02170913852751255,
0.002333942102268338,
0.010292190127074718,
0.005763065069913864,
0.03896165266633034,
0.007796760182827711,
-0.04257037490606308,
-0.018786640837788582,
-0.05931056663393974,
0.03343292698264122,
-0.0019802399910986423,
-0.008540482260286808,
-0.016470441594719887,
-0.021990470588207245,
0.03977988660335541,
0.04287637770175934,
0.006725102197378874,
-0.01906772330403328,
-0.029660675674676895,
-0.003693929873406887,
-0.027231676504015923,
-0.036426812410354614,
-0.006784784607589245,
-0.015665633603930473,
0.010923124849796295,
0.01992148905992508,
0.02174314670264721,
0.06043428182601929,
0.06147812679409981,
-0.02896745689213276,
0.04755983129143715,
-0.005144186317920685,
0.004123064689338207,
-0.034369342029094696,
0.015902433544397354,
0.0028258771635591984,
0.03573575243353844,
0.06136017292737961,
0.02427595481276512,
0.01375406514853239,
0.014123005792498589,
-0.01734321564435959,
0.07782768458127975,
-0.03485608473420143,
-0.018558498471975327,
-0.029430871829390526,
0.022883623838424683,
-0.014152399264276028,
-0.0035714968107640743,
0.004829491954296827,
-0.015110055916011333,
0.061975352466106415,
0.013311190530657768,
0.00954113993793726,
0.03954874724149704,
-0.011782251298427582,
-0.005908472463488579,
-0.02906334586441517,
-0.04938974231481552,
-0.046509530395269394,
-0.02226839028298855,
-0.02183298021554947,
-0.021473072469234467,
0.017908791080117226,
-0.0042772674933075905,
-0.06415059417486191,
0.02584977261722088,
-0.010603811591863632,
0.0032727892976254225,
0.02034175768494606,
-0.012907333672046661,
-0.02695986069738865,
0.022995343431830406,
-0.008429012261331081,
-0.023937026038765907,
-0.007031288463622332,
-0.023106258362531662,
-0.011191410943865776,
-0.00985563825815916,
0.03704404458403587,
-0.017539823427796364,
0.006829091347754002,
0.014520831406116486,
-0.012948831543326378,
-0.008659378625452518,
-0.06980536878108978,
0.01174444891512394,
-0.053005725145339966,
-0.020464425906538963,
-0.00026141287526115775,
0.038179002702236176,
0.015762409195303917,
0.052059490233659744,
0.016653962433338165,
-0.030372723937034607,
-0.020957274362444878,
-0.014427999965846539,
-0.011805043555796146,
-0.017659058794379234,
0.00685332715511322,
-0.04201653599739075,
0.05078525096178055,
0.01369128655642271,
0.047445278614759445,
-0.014677433297038078,
0.0015868034679442644,
-0.03177797421813011,
0.009961746633052826,
-0.0587606206536293,
0.011716742999851704,
-0.022592682391405106,
0.009274963289499283,
0.026165196672081947,
-0.023888254538178444,
0.009563117288053036,
0.03879363089799881,
-0.007929487153887749,
-0.01285853423178196,
0.03962109237909317,
-0.04174670949578285,
0.029949501156806946,
-0.0518299862742424,
0.002029213821515441,
0.0373820923268795,
-0.053245894610881805,
0.027745245024561882,
0.008746122010052204,
-0.06649159640073776,
-0.04851355776190758,
0.05997239798307419,
0.014814390800893307,
0.028387729078531265,
0.0017628967761993408,
-0.017842400819063187,
-0.03188329190015793,
-0.03106176294386387,
0.028924301266670227,
-0.0373443067073822,
-0.06153230741620064,
-0.033584076911211014,
-0.06922820955514908,
0.029065627604722977,
-0.0105859050527215,
0.03882719576358795,
0.006772254128009081,
-0.041258569806814194,
-0.00706773716956377,
0.02941727265715599,
0.003922053147107363,
0.02191266231238842,
0.03961217403411865,
0.011586463078856468,
0.040112413465976715,
-0.04227778688073158,
0.0457257442176342,
0.007466483395546675,
0.01671985164284706,
0.045243941247463226,
-0.05148008465766907,
-0.005040837451815605,
-0.013243221677839756,
-0.031449489295482635,
-0.02178724855184555,
0.03987046703696251,
-0.05222054943442345,
0.025368856266140938,
-0.012581500224769115,
0.0007320376462303102,
0.024971049278974533,
-0.05952553451061249,
-0.03184474632143974,
-0.04345015063881874,
-0.0832313522696495,
-0.02339337207376957,
0.0066785430535674095,
0.02428574487566948,
-0.03852835297584534,
0.017217790707945824,
0.04853427782654762,
0.05280667170882225,
-0.019023912027478218,
0.02249056100845337,
-0.008988126181066036,
-0.02160472236573696,
-0.015001933090388775,
0.04426347464323044,
0.03635797277092934,
-0.004661382641643286,
-0.00918673537671566,
0.00784211978316307,
-0.035403404384851456,
-0.05918842926621437,
0.03542792797088623,
0.009379971772432327,
0.0711226835846901,
-0.011102321557700634,
0.00043325379374437034,
0.07061044126749039,
-0.024055222049355507,
-0.03231408819556236,
0.034787971526384354,
0.03027494251728058,
0.012635663151741028,
-0.05351841449737549,
-0.0011130758794024587,
-0.024765439331531525,
0.02185020036995411,
-0.05060747265815735,
0.04327185079455376,
0.0445920005440712,
-0.03185819834470749,
0.02437468245625496,
-0.03336869180202484,
-0.0007270636269822717,
0.030876733362674713,
-0.01751822419464588,
0.022063910961151123,
0.03475017473101616,
-0.039352115243673325,
0.06019321456551552,
0.05466385930776596,
-0.022541755810379982,
-0.03574914112687111,
-0.03948572650551796,
-0.04079078882932663,
0.05418280139565468,
-0.016805825755000114,
0.018895555287599564,
0.029201170429587364,
-0.028644541278481483,
0.011095251888036728,
0.013426525518298149,
0.04768076911568642,
-0.016497299075126648,
0.020170213654637337,
-0.011272652074694633,
-0.025504324585199356,
-0.054738979786634445,
-0.018191302195191383,
0.03739350289106369,
0.01914037950336933,
-0.06022943928837776,
-0.002599462866783142,
0.08397969603538513,
0.04903869703412056,
0.07282698899507523,
0.013235440477728844,
-0.02742835320532322,
-0.015089466236531734,
-0.003879600204527378,
0.01688779704272747,
-0.03258134052157402,
-0.0011971795465797186,
0.06571163982152939,
0.05193459242582321,
-0.020549174398183823,
-0.035606738179922104,
-0.00052524299826473,
-0.002504669362679124,
-0.02768760174512863,
0.006882269401103258,
0.042626261711120605,
-0.023193657398223877,
0.0003293240733910352,
-0.022536711767315865,
-0.006500523071736097,
0.0783231258392334,
0.02217683382332325,
-0.04756753519177437,
-0.02288859151303768,
-0.03559991344809532,
0.08362554758787155,
0.033009957522153854,
-0.006158757489174604,
-0.03157559409737587,
0.07021894305944443,
0.021503552794456482,
0.08476593345403671,
0.013015414588153362,
0.03181575983762741,
0.05701310932636261,
0.046528421342372894,
0.0052744667045772076,
0.003442699322476983,
0.00268628285266459,
0.0042159478180110455,
-0.034712810069322586,
-0.007864436134696007,
0.05107354000210762,
0.008527723141014576,
-0.03334367647767067,
0.00035057455534115434,
0.03311934694647789,
-0.07365473359823227,
0.02340385690331459,
0.016589466482400894,
-0.017963571473956108,
0.00784861110150814,
-0.02220390923321247,
-0.02844584919512272,
0.046427249908447266,
0.011773746460676193,
-0.009087275713682175,
-0.008347324095666409,
0.04827917739748955,
0.007766958326101303,
0.009443392977118492,
-0.012119580060243607,
-0.07139120995998383,
-0.01135269831866026,
-0.01218631211668253,
-0.0237544197589159,
0.0066902488470077515,
0.012844022363424301,
0.0017840915825217962,
0.006214998196810484,
-0.04492494836449623,
0.019032780081033707,
0.0028819332364946604,
0.007411039434373379,
-0.06563713401556015,
0.0268513523042202,
0.06756507605314255,
-0.016019122675061226,
-0.03812506049871445,
-0.05577779561281204,
-0.042883288115262985,
0.026874493807554245,
0.07051577419042587,
0.053092289716005325,
-0.02125994674861431,
0.033146053552627563,
-0.013055121526122093,
0.05065818503499031,
0.01848101057112217,
0.00866751279681921,
-0.053646598011255264,
0.028482597321271896,
-0.005366185680031776,
-0.05175720900297165,
0.006977972574532032,
-0.05943414196372032,
-0.03979127109050751,
0.00933096744120121,
-0.05629756301641464,
-0.0017924342537298799,
0.03889108821749687,
-0.006920957006514072,
-0.010837123729288578,
0.050403937697410583,
0.03990739583969116,
-0.04078769311308861,
-0.013419495895504951,
-0.002802342874929309,
-0.013415804132819176,
-0.09126520901918411,
-0.019015146419405937,
0.05257844179868698,
0.050456225872039795,
0.021724946796894073,
-0.0012604710645973682,
-0.014959733001887798,
-0.020403912290930748,
-0.04788023605942726,
-0.005043624434620142,
-0.024357859045267105,
0.021974923089146614,
0.0021325903944671154,
-0.06132717430591583,
0.027454474940896034,
0.0055335755459964275,
0.003580917604267597,
-0.0029600488487631083,
-0.014189104549586773,
-0.11400438845157623,
0.007471782620996237,
-0.05267278477549553,
0.010155465453863144,
0.007339398376643658,
0.001426581060513854,
-0.05149771273136139,
0.0007884589140303433,
-0.003753217402845621,
0.12062408775091171,
-0.04048840329051018,
0.034182388335466385,
-0.00010526661935728043,
-0.015354050323367119,
-0.006150168366730213,
-0.025623885914683342,
0.043530888855457306,
-0.026568658649921417,
-0.01781332865357399,
-0.06207668408751488,
0.015093263238668442,
0.008647085167467594,
-0.0420159175992012,
-0.032647836953401566,
-0.05077000707387924,
-0.023311017081141472,
0.045554712414741516,
-0.0037477980367839336,
-0.013149450533092022,
-0.027202237397432327,
0.03830103948712349,
0.06433287262916565,
-0.07646504044532776,
0.07425018399953842,
-0.02698352374136448,
0.013514107093214989,
0.015413512475788593,
-0.10608139634132385,
0.0040955692529678345,
-0.00013267082977108657,
0.03331704065203667,
-0.03020932339131832,
0.014446193352341652,
-0.01925513707101345,
-0.04241334646940231,
0.006408431567251682,
0.009732341393828392,
0.011726396158337593,
-0.0753810927271843,
0.02426912821829319,
0.03635001182556152,
0.04297146573662758,
0.006951950490474701,
0.002403572201728821,
0.0009820954874157906,
0.0420047864317894,
0.010659735649824142,
-0.039184197783470154,
-0.010349215008318424,
-0.008088143542408943,
-0.03291379660367966,
0.018313629552721977,
0.012268646620213985,
-0.013701867312192917,
-0.012131799943745136,
0.05725273862481117
] |
<p>I'm a beginner in quantum mechanics, and I'm a bit confused about states and the probability to measure certain values. I would like to understand at least the following simplified situation:</p>
<p>Suppose the operator $S_z$ is measuring the spin in the $z$ direction of a free particle. Let $$\{e_s\},\quad s = -L, -L+1, \dots, L-1, L$$ be a basis of eigenstates for $S_z$, with $S_z(e_s) = s e_s$.</p>
<p>If at time $t<0$ the system is constantly in the pure state $P_{\psi}$, where $\psi$ is one basis vector, how can I compute the probability that the measuring the spin in the $z$ direction has result $-L/2$?</p> | g9193 | [
-0.007651747670024633,
0.028347056359052658,
-0.016454756259918213,
-0.035557493567466736,
0.0014177471166476607,
-0.011779804714024067,
0.08028176426887512,
0.053036801517009735,
0.033808402717113495,
-0.02984549105167389,
-0.030752811580896378,
-0.0013419481692835689,
0.0502779595553875,
-0.006131606176495552,
-0.009327671490609646,
-0.0054359957575798035,
0.06341716647148132,
0.026093970984220505,
-0.0016272036591544747,
-0.0004862730856984854,
-0.006813970394432545,
-0.03510075807571411,
-0.019766787067055702,
-0.07031816244125366,
0.08416061848402023,
-0.06772217899560928,
0.0065982649102807045,
-0.006941838655620813,
-0.002821974689140916,
0.004053008276969194,
-0.03191927447915077,
0.012089214287698269,
0.02045796997845173,
-0.025958795100450516,
0.013037176802754402,
-0.03696313127875328,
0.08621162921190262,
0.0442236065864563,
0.028487106785178185,
0.01373408455401659,
-0.006514751352369785,
-0.05789201334118843,
0.052634499967098236,
-0.03682779520750046,
0.045196469873189926,
0.03680508956313133,
0.02459910325706005,
0.008023160509765148,
-0.06848660111427307,
0.039700403809547424,
0.02476496249437332,
0.001550330314785242,
0.05586450919508934,
0.03399781137704849,
0.012970468029379845,
0.0280873104929924,
-0.009705038741230965,
-0.0013027118984609842,
0.009129577316343784,
0.07444498687982559,
0.03621475771069527,
-0.04865926504135132,
-0.008982667699456215,
-0.02551855705678463,
0.044944118708372116,
0.00048677288577891886,
-0.02590291202068329,
0.05177663266658783,
-0.04344503954052925,
0.06455355137586594,
-0.024386487901210785,
-0.06098227947950363,
0.040316395461559296,
-0.0027320212684571743,
-0.05073512718081474,
0.04115823656320572,
0.006910406984388828,
0.01106305606663227,
0.034560687839984894,
0.04277843236923218,
-0.027577431872487068,
-0.05445859953761101,
0.04424940049648285,
-0.06354502588510513,
0.025513488799333572,
0.039465341717004776,
-0.01802787184715271,
0.0015708401333540678,
-0.02651047147810459,
0.036329176276922226,
0.03718804568052292,
0.012986574321985245,
0.09613870084285736,
0.028727008029818535,
-0.0058570560067892075,
-0.05104048550128937,
-0.04391399398446083,
0.009321805089712143,
-0.043839458376169205,
-0.0009371661581099033,
-0.009714444167912006,
0.016537223011255264,
0.006603280548006296,
-0.037395451217889786,
-0.022581027820706367,
-0.03438346087932587,
-0.010662948712706566,
-0.0021599114406853914,
-0.026056718081235886,
-0.016370095312595367,
-0.00015152776904869825,
0.05897559970617294,
-0.015170491300523281,
0.00004805500429938547,
-0.06058730185031891,
0.0450795516371727,
0.08120141178369522,
0.020357567816972733,
-0.04830658435821533,
0.027039410546422005,
0.0016856816364452243,
0.057921528816223145,
0.018355313688516617,
0.0881856381893158,
-0.04308747127652168,
0.04378635436296463,
-0.01336597092449665,
-0.022244488820433617,
0.021419409662485123,
0.08123810589313507,
-0.00541679747402668,
-0.008304134011268616,
-0.006025817710906267,
0.009384541772305965,
-0.023631412535905838,
0.02403480000793934,
0.0261224452406168,
0.034476250410079956,
0.035431068390607834,
0.031113434582948685,
0.003093267558142543,
-0.05415128543972969,
0.013880530372262001,
-0.031230833381414413,
0.027598517015576363,
-0.025845929980278015,
0.03157133609056473,
-0.07999718189239502,
0.040781740099191666,
-0.005511526484042406,
0.01010904274880886,
0.04464064538478851,
-0.03218748793005943,
-0.05630234256386757,
0.03140297532081604,
-0.018598351627588272,
0.02461933344602585,
-0.015169437974691391,
0.00818561390042305,
0.0009397196699865162,
0.03697943687438965,
0.010641572065651417,
0.028557393699884415,
-0.004051453433930874,
-0.007236882578581572,
-0.016902949661016464,
0.008412973023951054,
-0.05606111139059067,
0.011841033585369587,
-0.05197947844862938,
-0.0030094331596046686,
-0.013709097169339657,
-0.006712043657898903,
0.004373203497380018,
-0.012324947863817215,
0.048791639506816864,
-0.03225335478782654,
0.004492885898798704,
0.05571230128407478,
0.01682281494140625,
-0.007715438958257437,
0.030824242159724236,
0.050775300711393356,
0.024695174768567085,
-0.035463783890008926,
-0.026464426890015602,
0.021842537447810173,
-0.011732778511941433,
-0.03528584539890289,
0.03178867697715759,
-0.018446480855345726,
-0.02905280888080597,
0.007746198680251837,
0.034766264259815216,
-0.037313513457775116,
-0.0324125774204731,
0.027342695742845535,
-0.09558961540460587,
-0.03507884219288826,
0.020234880968928337,
-0.022098474204540253,
-0.0011913160560652614,
-0.002088690409436822,
0.03260905668139458,
0.010234082117676735,
-0.06224307045340538,
0.02685278281569481,
0.008810008876025677,
-0.011953680776059628,
0.012492749840021133,
0.012146948836743832,
-0.006102227605879307,
-0.015555653721094131,
0.03455112501978874,
0.018329964950680733,
0.01710512675344944,
0.04308914393186569,
0.022558806464076042,
0.06826113164424896,
-0.0027658119797706604,
0.008540374226868153,
0.005776260048151016,
0.06374665349721909,
-0.012950642965734005,
-0.004260449670255184,
0.08418155461549759,
0.017685065045952797,
0.006041049957275391,
-0.040513988584280014,
0.05732238292694092,
-0.06175590306520462,
-0.05620824173092842,
-0.002069008070975542,
0.03814413398504257,
0.02544725500047207,
0.06699633598327637,
-0.006685846950858831,
0.05447760596871376,
0.007379576098173857,
-0.04418922960758209,
0.03431357815861702,
-0.022663256153464317,
0.013355428352952003,
0.025768889114260674,
0.02206432819366455,
-0.014779981225728989,
-0.008664682507514954,
0.019260747358202934,
-0.04781875014305115,
0.03162158280611038,
-0.014083468355238438,
-0.04051273688673973,
-0.02854856289923191,
0.046306122094392776,
-0.016415808349847794,
-0.035084083676338196,
0.029669474810361862,
-0.010827149264514446,
-0.04697592556476593,
-0.0037648500874638557,
0.0027515143156051636,
0.019656788557767868,
0.03367731347680092,
0.02995475009083748,
-0.008532850071787834,
-0.0211012102663517,
0.01092953234910965,
0.0012449638452380896,
-0.010116422548890114,
-0.0218381118029356,
-0.015230894088745117,
0.0686769112944603,
0.05190572887659073,
0.05310947448015213,
0.011867336928844452,
-0.06981511414051056,
0.008672687225043774,
0.008907090872526169,
-0.027320150285959244,
0.0024831050541251898,
-0.0925818458199501,
0.00803207978606224,
0.01552722230553627,
0.03897497430443764,
0.06287959218025208,
-0.027954714372754097,
0.05055604875087738,
-0.041249122470617294,
-0.02640102617442608,
-0.002740248804911971,
-0.022243069484829903,
0.041687220335006714,
0.007111795246601105,
-0.0014290979597717524,
-0.030712351202964783,
0.021862227469682693,
0.04613186791539192,
-0.0631709024310112,
0.009247669018805027,
0.11019802838563919,
-0.023890109732747078,
0.024175357073545456,
0.02554861456155777,
-0.05015762150287628,
0.06094443053007126,
-0.037276625633239746,
-0.04692915081977844,
-0.0041725956834852695,
-0.028816983103752136,
-0.044915102422237396,
-0.039819806814193726,
0.017794452607631683,
0.0006726205465383828,
-0.016056466847658157,
-0.0350237712264061,
0.04401588439941406,
-0.023307403549551964,
0.017938537523150444,
-0.0197967067360878,
-0.033494509756565094,
-0.0010829363018274307,
-0.016084818169474602,
0.023736609145998955,
-0.004762549884617329,
0.019294535741209984,
-0.06886327266693115,
-0.05749347060918808,
0.016678277403116226,
-0.032269515097141266,
0.02589854598045349,
0.04603685438632965,
0.03252559155225754,
-0.036138467490673065,
-0.0026803857181221247,
-0.06951097398996353,
-0.010561672039330006,
-0.03503922000527382,
-0.026329586282372475,
0.005748607683926821,
0.00604632031172514,
-0.07027120888233185,
-0.03117608092725277,
-0.03636211156845093,
-0.00030002646963112056,
-0.005491036456078291,
-0.037122536450624466,
-0.024469461292028427,
0.0036632525734603405,
-0.016960224136710167,
-0.026074234396219254,
-0.0006163377547636628,
0.011321188881993294,
0.01201125979423523,
0.0130890728905797,
-0.0029420352075248957,
0.04966971278190613,
-0.0016786267515271902,
0.012113968841731548,
0.02609184756875038,
0.02580276131629944,
0.015187475830316544,
-0.02703094482421875,
-0.04212469607591629,
-0.039677318185567856,
-0.01991393230855465,
-0.031605418771505356,
-0.002627225825563073,
0.02411239966750145,
0.08374886959791183,
-0.03814860060811043,
-0.01669543981552124,
0.019854974001646042,
0.05221167206764221,
0.027559777721762657,
-0.0076741441152989864,
-0.008750390261411667,
0.009502106346189976,
-0.022525299340486526,
-0.010190257802605629,
0.007684117648750544,
-0.008167754858732224,
0.022137753665447235,
0.019718369469046593,
-0.02779395319521427,
0.023404786363244057,
0.03362434729933739,
0.016603969037532806,
0.06394485384225845,
-0.012829525396227837,
-0.03988951817154884,
0.02276676893234253,
-0.0668969452381134,
-0.02402487024664879,
0.06813132017850876,
0.03219472989439964,
-0.002662565326318145,
0.03287550061941147,
-0.013624283485114574,
-0.007526757195591927,
0.04133639112114906,
0.008768086321651936,
-0.019440138712525368,
0.05276508629322052,
0.0022917459718883038,
-0.009991319850087166,
0.01749706082046032,
0.010644971393048763,
0.005167686380445957,
-0.00037153830635361373,
-0.008370505645871162,
-0.004392789211124182,
0.038207560777664185,
0.030244313180446625,
-0.03223278000950813,
-0.0005439121159724891,
0.01273054163902998,
0.024425335228443146,
-0.022733338177204132,
0.006463486235588789,
-0.013823830522596836,
-0.007595747709274292,
-0.03454556316137314,
0.07895147800445557,
-0.07395041733980179,
-0.030170295387506485,
0.024805165827274323,
0.021465495228767395,
0.018714968115091324,
-0.009170944802463055,
-0.02965855784714222,
0.03477505221962929,
0.0022277876269072294,
0.03818551078438759,
0.0223101656883955,
-0.08645659685134888,
-0.01663254015147686,
-0.025182440876960754,
0.0069706495851278305,
0.008477159775793552,
-0.005135045852512121,
-0.011362846940755844,
0.023347752168774605,
-0.009338433854281902,
-0.02546103484928608,
-0.062868632376194,
-0.014267029240727425,
-0.0019530379213392735,
-0.023346949368715286,
0.05857810750603676,
-0.05734048783779144,
-0.037509094923734665,
0.038909342139959335,
-0.053643252700567245,
-0.06121506541967392,
-0.018324773758649826,
-0.056011151522397995,
-0.044909022748470306,
0.03882116451859474,
0.031228629872202873,
0.03968994691967964,
-0.00004943898966303095,
-0.06395068764686584,
-0.05727195739746094,
-0.024263782426714897,
-0.056411612778902054,
0.01752929389476776,
-0.051160842180252075,
0.05687074735760689,
-0.08892016112804413,
-0.030189823359251022,
0.025688260793685913,
-0.03140635043382645,
0.06241390481591225,
0.013620791025459766,
0.001402400084771216,
0.04344068467617035,
-0.02093411609530449,
-0.015943923965096474,
0.008726497180759907,
-0.029369119554758072,
-0.02354908175766468,
-0.03116888739168644,
-0.02096595987677574,
-0.04059913009405136,
0.00754137709736824,
0.0027163950726389885,
-0.01246357336640358,
-0.08956946432590485,
0.018798978999257088,
-0.05913907289505005,
0.06743589043617249,
0.053301986306905746,
0.03960072249174118,
0.004726483020931482,
0.02134878747165203,
-0.0339055098593235,
-0.04506715387105942,
-0.04666867107152939,
-0.0051275696605443954,
0.013530902564525604,
-0.04702593386173248,
0.06467937678098679,
0.004184587858617306,
0.006683402694761753,
-0.010593741200864315,
-0.0037711095064878464,
0.028771687299013138,
-0.042351603507995605,
0.008931756019592285,
0.0031184812542051077,
-0.013445082120597363,
0.014695990830659866,
0.049186453223228455,
0.016933811828494072,
0.019164806231856346,
-0.06292888522148132,
-0.013975389301776886,
0.030956687405705452,
-0.032567158341407776,
0.012722558341920376,
0.022739753127098083,
-0.00863594375550747,
0.025607241317629814,
-0.052903927862644196,
-0.022953402251005173,
0.0019271137425675988,
-0.046290431171655655,
-0.007677916437387466,
-0.03211620822548866,
-0.035568881779909134,
0.032278481870889664,
0.01989833638072014,
0.008257882669568062,
0.015682440251111984,
0.010014939121901989,
-0.05547322332859039,
0.0005425856215879321,
-0.06330762803554535,
-0.0026203871238976717,
0.04337087273597717,
-0.003602065611630678,
-0.08584825694561005,
0.03906165063381195,
0.023201651871204376,
-0.05877402052283287,
0.00946501549333334,
0.03597930818796158,
-0.03882109373807907,
-0.029654577374458313,
-0.0023211275693029165,
-0.05653925985097885,
0.05014278367161751,
-0.03214266896247864,
-0.0651225745677948,
-0.028227021917700768,
0.024418944492936134,
-0.006448561325669289,
0.017821384593844414,
-0.03130722790956497,
0.011547542177140713,
0.06215713173151016,
-0.03353864327073097,
0.021556677296757698,
0.047880854457616806,
-0.026353850960731506,
0.02244468405842781,
-0.01715942844748497,
-0.021197360008955002,
0.0012948791263625026,
0.059426598250865936,
0.010646088048815727,
-0.01500888541340828,
-0.02578786574304104,
0.004956555552780628,
0.017716242000460625,
0.047050584107637405,
-0.050051722675561905,
-0.04842570424079895,
0.0029852662701159716,
-0.00277724233455956,
-0.061059609055519104,
0.03747287392616272,
0.007202661130577326,
0.029122961685061455,
0.012772551737725735,
0.09180575609207153,
-0.025908146053552628,
-0.05826308950781822,
0.004930349066853523,
0.0008661427418701351,
-0.01872260682284832,
-0.018151959404349327,
-0.05172853171825409,
0.013134952634572983,
-0.07191353291273117,
0.008056248538196087,
-0.03393661230802536,
-0.051476992666721344,
-0.015358742326498032,
-0.0038405947852879763,
0.03580113872885704,
-0.060900043696165085,
-0.003522368846461177,
-0.05949953570961952,
-0.052207302302122116,
0.08403807878494263,
0.010840731672942638,
-0.00801073294132948,
0.002794565400108695,
0.012631062418222427,
0.01822313480079174,
-0.04281831532716751,
0.003367107594385743,
0.043652281165122986,
0.0016214697388932109,
-0.05043737590312958,
0.05189162492752075,
0.04261104017496109,
-0.016611682251095772,
0.056736577302217484,
0.0746152326464653,
0.05635309964418411,
0.01693555898964405,
-0.03074187971651554,
0.08246978372335434,
0.038172196596860886,
-0.0064804162830114365,
-0.03956841304898262,
0.031714651733636856,
0.0038204332813620567,
0.02912089228630066,
-0.011381748132407665,
-0.020621392875909805,
0.02713804319500923,
-0.042196474969387054,
0.013025185093283653,
-0.038442377001047134,
0.04764091223478317,
0.04765056446194649,
0.0792870819568634,
-0.0006391283241100609,
0.05613813176751137,
0.04735235124826431,
-0.015553748235106468,
-0.0470278337597847,
0.004469496197998524,
0.028965558856725693,
0.020204342901706696,
-0.06157074123620987,
0.043894123286008835,
0.0072655826807022095,
-0.0215164665132761,
0.012816528789699078,
-0.022736521437764168,
0.019130082800984383,
0.013477551750838757,
0.08217985183000565,
0.007153662852942944,
0.04292502626776695,
-0.04641241580247879,
-0.04274187609553337,
-0.08071336895227432,
-0.021510470658540726,
-0.011771169491112232,
-0.027269575744867325,
0.06026357412338257,
-0.04141078516840935,
-0.030229177325963974,
0.048776887357234955,
-0.09874992072582245,
0.003976463805884123,
-0.01551909651607275,
-0.0991397574543953,
0.005481346044689417,
-0.002631915733218193,
-0.002494120504707098,
-0.00826980546116829,
0.053702495992183685,
-0.010053758509457111,
-0.016387391835451126,
-0.013332500122487545,
0.037584345787763596,
-0.04734485223889351,
-0.021931640803813934,
-0.04666340351104736,
0.022925343364477158,
-0.007472978439182043,
0.02046114020049572,
0.013936804607510567,
-0.010475549846887589,
0.022870682179927826,
0.0036359084770083427,
0.039034247398376465,
-0.027397826313972473,
-0.002555303741246462,
-0.052921321243047714,
0.06028427183628082,
0.053919605910778046,
0.029758131131529808,
-0.00579308345913887,
0.02267933078110218,
-0.04866938665509224,
0.017116768285632133,
0.04034590721130371,
0.08757015317678452,
-0.07125701010227203,
0.013259348459541798,
-0.02061503753066063,
-0.010189596563577652,
-0.01512010209262371,
-0.03082885779440403,
0.002776178764179349,
0.007907073013484478,
-0.01676853373646736,
-0.034725088626146317,
-0.021387584507465363,
-0.05182916671037674,
0.01710379123687744,
0.025468366220593452,
0.03428506851196289,
0.009744861163198948,
-0.03389916568994522,
0.0003408902557566762,
0.01338441763073206,
-0.005600146949291229,
-0.0360313355922699,
-0.00009431120997760445,
0.049452174454927444,
0.0448538213968277,
0.047273870557546616,
0.012931502424180508,
-0.009852311573922634,
-0.04336132854223251,
-0.004284018650650978,
0.007757475599646568,
0.0010576688218861818,
-0.009747270494699478,
-0.028308067470788956,
0.02222828008234501,
0.0071451133117079735,
-0.03148368373513222,
-0.05483030155301094,
0.027328962460160255,
0.01901577226817608,
-0.0073508224450051785,
0.0149656031280756,
-0.014485949650406837,
0.025940846651792526,
0.05236402899026871,
0.012627987191081047,
-0.040803708136081696,
0.020423099398612976,
-0.01979832910001278,
0.07124041020870209,
-0.004267667420208454,
-0.04425228387117386,
0.05105685070157051,
-0.04172263294458389,
0.006621953099966049,
-0.009552322328090668,
-0.03356420621275902,
-0.019913090392947197,
-0.05781369283795357,
0.01947193592786789,
-0.09097243845462799,
-0.052621226757764816,
-0.014619172550737858,
0.0847398042678833
] |
<p>Can anyone explain what metric signature is?</p>
<p>I have a basic knowledge regarding tensors, btw.</p>
<p>Also, how is it related to fundamental understanding of general relativity?</p>
<p>Thanks.</p> | g9194 | [
-0.029442807659506798,
0.05789006128907204,
0.00028933293651789427,
0.008642653003334999,
0.04042251408100128,
0.06054766848683357,
0.04724368825554848,
0.044998638331890106,
-0.017635367810726166,
-0.021839141845703125,
0.01604904606938362,
-0.04023673012852669,
0.09935527294874191,
-0.08833307772874832,
-0.013105681166052818,
-0.04764563590288162,
0.03430269658565521,
-0.0367383249104023,
0.08321310579776764,
-0.008466549217700958,
0.031552016735076904,
0.06169961765408516,
0.00936471950262785,
-0.053985800594091415,
-0.004316285252571106,
0.014758906327188015,
0.07517843693494797,
0.015000073239207268,
-0.0352756641805172,
-0.03716420754790306,
0.032921623438596725,
-0.019711177796125412,
0.06960903853178024,
-0.055084701627492905,
-0.01857307367026806,
-0.009083624929189682,
-0.0012786905281245708,
0.008707703091204166,
0.01795891858637333,
0.03012516163289547,
0.042805880308151245,
-0.017329420894384384,
-0.009713495150208473,
0.013657670468091965,
0.004405428189784288,
0.03284658119082451,
-0.0297763179987669,
-0.016053708270192146,
-0.03078317455947399,
0.01175594050437212,
-0.0049631246365606785,
0.03410661965608597,
0.004646125249564648,
0.028219865635037422,
0.03215508535504341,
0.037652503699064255,
0.02922842465341091,
-0.010968211106956005,
0.04452061653137207,
-0.009767886251211166,
-0.0060342224314808846,
0.009399962611496449,
-0.0035393983125686646,
0.028063684701919556,
-0.005183176603168249,
-0.04632528871297836,
-0.05825633555650711,
-0.06973496824502945,
0.0875474140048027,
0.011865677312016487,
0.08216474950313568,
-0.039606425911188126,
0.01642523519694805,
-0.015696503221988678,
0.024485787376761436,
0.010108517482876778,
0.056928277015686035,
0.01295429840683937,
0.031496819108724594,
-0.003007903229445219,
0.030369631946086884,
0.001780646271072328,
0.05676371976733208,
0.03889203071594238,
0.10875125974416733,
-0.00041682165465317667,
-0.07503566890954971,
0.010212606750428677,
-0.022818410769104958,
0.022798914462327957,
0.04219992458820343,
-0.05060163885354996,
0.03253606706857681,
-0.006067671347409487,
0.027493540197610855,
-0.03129693493247032,
-0.0034126059617847204,
-0.00836221780627966,
-0.0103842718526721,
-0.005958383437246084,
-0.0333281010389328,
0.012641278095543385,
0.013936342671513557,
-0.04932878538966179,
0.0188685841858387,
0.006485539022833109,
-0.02604586072266102,
0.0534089133143425,
0.010902512818574905,
-0.01574045978486538,
-0.028502177447080612,
0.014913278631865978,
-0.008764594793319702,
0.000708834093529731,
-0.09370259195566177,
-0.033546630293130875,
0.04227044805884361,
-0.01691208966076374,
-0.021580910310149193,
0.02473767288029194,
0.011861748993396759,
-0.005371137522161007,
-0.006096945144236088,
0.05211074277758598,
-0.06703374534845352,
-0.02524295449256897,
0.020931478589773178,
-0.04628623276948929,
-0.00024752208264544606,
-0.026289569213986397,
0.0665198415517807,
0.018616974353790283,
-0.01487711165100336,
-0.034211330115795135,
-0.026769163087010384,
0.027517303824424744,
0.030259374529123306,
0.003657942870631814,
-0.024142496287822723,
0.04692189395427704,
-0.03831401839852333,
0.020498137921094894,
0.046255700290203094,
-0.049186836928129196,
0.07181979715824127,
-0.009576641023159027,
0.01583273708820343,
0.023468591272830963,
0.006831709761172533,
-0.005749443080276251,
0.025719428434967995,
0.0882972776889801,
-0.03166849911212921,
-0.03836745023727417,
0.02187412418425083,
-0.033037181943655014,
-0.05213618651032448,
-0.040529895573854446,
-0.029209723696112633,
0.026861077174544334,
0.057413261383771896,
0.018134888261556625,
0.04795592650771141,
0.046029385179281235,
-0.053861379623413086,
0.02481617033481598,
0.009940900839865208,
-0.01146283932030201,
0.030714483931660652,
-0.029383907094597816,
-0.009497670456767082,
0.020301757380366325,
-0.017694897949695587,
0.06041707843542099,
-0.0037197801284492016,
-0.012838471680879593,
-0.01680307649075985,
-0.017618199810385704,
0.08568362146615982,
0.022774172946810722,
-0.035024989396333694,
-0.01828186959028244,
0.008442573249340057,
-0.028432754799723625,
-0.04779018461704254,
0.036676548421382904,
-0.0008113347575999796,
-0.043969832360744476,
-0.014464162290096283,
0.04566226527094841,
0.021341724321246147,
-0.023672420531511307,
0.005981547757983208,
0.06536617875099182,
0.037015948444604874,
-0.027784178033471107,
-0.006863940507173538,
-0.0044678617268800735,
-0.007763751316815615,
0.05160277709364891,
-0.037056006491184235,
-0.007382749114185572,
-0.008576680906116962,
0.04845818877220154,
-0.03293024003505707,
0.00800870731472969,
-0.010773362591862679,
-0.012595067732036114,
0.03694555163383484,
0.027833105996251106,
0.003201638348400593,
-0.06708592921495438,
0.05238840728998184,
0.001087858690880239,
0.013130931183695793,
-0.01836356520652771,
0.014937172643840313,
0.026317792013287544,
0.006533412262797356,
0.07148388773202896,
0.03401895612478256,
0.030631503090262413,
0.03396477922797203,
0.04332950338721275,
-0.05415741726756096,
-0.03350008279085159,
-0.002717007417231798,
0.024086762219667435,
0.021721018478274345,
0.021872976794838905,
-0.05124210938811302,
0.030626630410552025,
0.044523999094963074,
0.029382608830928802,
0.032564546912908554,
0.01641169935464859,
0.011995003558695316,
-0.07142653316259384,
0.010774271562695503,
0.02143935300409794,
-0.02135375142097473,
-0.031764909625053406,
0.024714045226573944,
0.009671819396317005,
0.007965528406202793,
0.0074583846144378185,
0.029767116531729698,
-0.043800804764032364,
0.0058925561606884,
-0.019604932516813278,
0.003584084799513221,
-0.033269137144088745,
-0.01976885087788105,
-0.04839615896344185,
0.0367979034781456,
0.05164644494652748,
0.015541608445346355,
0.014738774858415127,
-0.11242081224918365,
-0.04214251786470413,
0.03207842633128166,
-0.06286850571632385,
0.004726690240204334,
0.013088938780128956,
-0.02526770532131195,
-0.008513819426298141,
0.008047818206250668,
0.0496264323592186,
-0.035831745713949203,
-0.035214539617300034,
-0.025142589583992958,
0.03751315921545029,
-0.03774544596672058,
-0.026288174092769623,
-0.06508594006299973,
-0.024021046236157417,
-0.02325652725994587,
-0.047332290560007095,
-0.05572764575481415,
0.013730899430811405,
-0.029838576912879944,
-0.0019770858343690634,
-0.0718284472823143,
-0.01585414633154869,
0.030290037393569946,
-0.027496589347720146,
-0.019597690552473068,
0.0442860871553421,
-0.0067937239073216915,
0.04685046151280403,
0.007910257205367088,
0.02292114496231079,
-0.009556196630001068,
-0.053558047860860825,
0.01571044512093067,
0.050633374601602554,
0.00667171785607934,
0.00749789597466588,
-0.03473370522260666,
0.028466911986470222,
0.04345845803618431,
-0.0186318289488554,
0.026718825101852417,
-0.06953055411577225,
-0.0042166681960225105,
-0.06489251554012299,
-0.017854182049632072,
-0.014988936483860016,
-0.03674260526895523,
0.023002151399850845,
0.010326463729143143,
0.05681563913822174,
0.017946599051356316,
0.031088002026081085,
-0.009371906518936157,
0.0054458859376609325,
-0.038687996566295624,
0.03584489971399307,
-0.07984570413827896,
-0.01289636455476284,
-0.04117870330810547,
-0.03498705476522446,
-0.02074350230395794,
-0.006970883347094059,
0.07576873153448105,
-0.028267130255699158,
-0.04166542366147041,
-0.012165063992142677,
-0.02188032679259777,
0.01853354275226593,
0.008462217636406422,
-0.05063313618302345,
-0.04830712452530861,
0.03242645412683487,
-0.03992931917309761,
-0.033968910574913025,
-0.04537669196724892,
0.030081678181886673,
0.046919889748096466,
-0.03103708103299141,
0.06295766681432724,
0.006516452878713608,
-0.010739806108176708,
-0.03276265412569046,
-0.0028557972982525826,
0.03928402438759804,
0.07656921446323395,
-0.04054385423660278,
0.03976214677095413,
-0.03970053046941757,
0.018719900399446487,
0.016511904075741768,
0.031734175980091095,
-0.02908327989280224,
0.012092641554772854,
0.012131593190133572,
0.10535415261983871,
0.0321170873939991,
-0.0169652309268713,
-0.03686542436480522,
0.004648643080145121,
-0.009357578121125698,
0.0006799447000958025,
0.006852555088698864,
-0.01664750464260578,
-0.015801485627889633,
0.0423918291926384,
-0.03610383719205856,
-0.018686147406697273,
0.034395065158605576,
0.028523162007331848,
0.01847515068948269,
-0.03894410654902458,
0.07253514975309372,
-0.011895710602402687,
-0.010221574455499649,
0.015088321641087532,
0.0015414763474836946,
0.02353248931467533,
0.012834768742322922,
0.015539908781647682,
0.011103429831564426,
0.04340681806206703,
-0.019527161493897438,
0.0006626060931012034,
-0.032332491129636765,
-0.05680824816226959,
-0.01058365311473608,
0.03738361597061157,
-0.028469329699873924,
-0.03882018104195595,
-0.006858395878225565,
-0.06289476901292801,
-0.03754562884569168,
0.0061481669545173645,
-0.011604979634284973,
-0.0065981061197817326,
0.05669858306646347,
0.042729273438453674,
0.07434871047735214,
-0.03725981339812279,
0.04981574788689613,
0.01206214725971222,
0.0006049773073755205,
-0.0014430111041292548,
0.02892868034541607,
-0.007757930550724268,
-0.01682634837925434,
0.028165139257907867,
0.029857467859983444,
0.03232613578438759,
-0.0015358941163867712,
0.05982961505651474,
-0.0644197016954422,
0.08875852078199387,
0.05772470310330391,
-0.012010177597403526,
-0.020295100286602974,
-0.010443970561027527,
0.00602224376052618,
-0.014637159183621407,
0.05911905691027641,
0.0937260091304779,
0.0038673547096550465,
-0.013045601546764374,
0.04551904276013374,
0.038755688816308975,
0.004666681867092848,
-0.0339781679213047,
0.00242607737891376,
0.056863315403461456,
-0.03815191239118576,
-0.017896980047225952,
0.0001638200628804043,
-0.04606505483388901,
0.028124868869781494,
0.008074721321463585,
-0.02214530110359192,
-0.00581780169159174,
-0.01376701332628727,
0.10199873149394989,
0.01512444019317627,
-0.005186684895306826,
-0.02553781121969223,
-0.02427014335989952,
0.009047705680131912,
-0.035264741629362106,
0.00881784688681364,
-0.0650772824883461,
-0.0068234908394515514,
-0.034722793847322464,
-0.02396632730960846,
0.004777164198458195,
-0.0624346062541008,
0.02784760482609272,
0.022674178704619408,
0.0024848764296621084,
0.01348937302827835,
0.01851503923535347,
-0.01977122202515602,
-0.026191718876361847,
0.02967577613890171,
0.040660712867975235,
0.00421181321144104,
0.02760663814842701,
-0.07208314538002014,
-0.029137099161744118,
0.014518416486680508,
-0.012300565838813782,
0.002530655823647976,
-0.0040753851644694805,
-0.006266612559556961,
-0.009431159123778343,
-0.02665959671139717,
0.01755254901945591,
0.05242770537734032,
-0.039523858577013016,
-0.023510079830884933,
-0.00847992766648531,
-0.07635568082332611,
0.014851267449557781,
0.04641595482826233,
-0.00877105537801981,
-0.01570245623588562,
-0.015884937718510628,
0.002690328285098076,
-0.00887131504714489,
0.006091590039432049,
-0.011065042577683926,
0.010503501631319523,
0.026010863482952118,
0.012745514512062073,
0.03162834420800209,
0.026965104043483734,
-0.039867665618658066,
-0.015573574230074883,
0.02175488881766796,
-0.05812150239944458,
0.017260367050766945,
-0.030631449073553085,
-0.02654917910695076,
0.000942995073273778,
0.0851089283823967,
0.00540785351768136,
-0.0032101315446197987,
0.012069529853761196,
0.02227955125272274,
-0.008491374552249908,
0.003713046433404088,
0.09197143465280533,
-0.05740968883037567,
0.04237055033445358,
-0.04082734137773514,
-0.010921796783804893,
-0.027427982538938522,
-0.02408229559659958,
0.008802476339042187,
0.012529557570815086,
0.006168166641145945,
0.008404340595006943,
-0.07046318799257278,
-0.044227052479982376,
0.002363848267123103,
0.011866017244756222,
0.011565122753381729,
0.0008752981084398925,
-0.026974234730005264,
-0.004892565310001373,
0.04060835763812065,
0.024573545902967453,
-0.008938453160226345,
-0.030238930135965347,
0.054491542279720306,
0.006457126699388027,
0.06751910597085953,
-0.042862020432949066,
0.05712306872010231,
-0.02554912120103836,
0.06370037794113159,
0.002108910121023655,
-0.0453902930021286,
-0.019751179963350296,
-0.016657233238220215,
0.043678075075149536,
-0.006829456426203251,
-0.015350244008004665,
0.027246104553341866,
0.03150082379579544,
0.06724253296852112,
-0.08501061797142029,
-0.0185135118663311,
0.005656878929585218,
0.025364123284816742,
-0.024682801216840744,
-0.034549079835414886,
0.011749610304832458,
-0.002207063836976886,
-0.021511223167181015,
-0.06560561805963516,
0.0170834269374609,
0.03600915148854256,
0.024423327296972275,
-0.010657369159162045,
-0.017230188474059105,
0.00537861417979002,
-0.06600376963615417,
-0.03209996968507767,
-0.03246563673019409,
0.05797576531767845,
-0.0005437055951915681,
-0.017900286242365837,
0.04652106389403343,
-0.0013076263712719083,
-0.0251386109739542,
-0.03129909932613373,
0.011789812706410885,
0.01371802669018507,
0.012661224231123924,
-0.061075206845998764,
-0.033867642283439636,
0.02659311704337597,
0.05810534954071045,
0.06562447547912598,
-0.05679513141512871,
-0.03756172955036163,
-0.006961016915738583,
-0.03582124039530754,
-0.02952939085662365,
-0.005281191319227219,
0.0016012907726690173,
0.0205246489495039,
-0.025281930342316628,
-0.006825341377407312,
0.000531009747646749,
-0.07410641014575958,
-0.03616342321038246,
-0.009046118706464767,
0.10037752240896225,
0.006608407478779554,
-0.030241886153817177,
-0.052140962332487106,
0.042364295572042465,
0.031014520674943924,
0.002922331914305687,
0.008597036823630333,
-0.012168845161795616,
-0.026371143758296967,
-0.04970346763730049,
-0.05989626795053482,
0.018572578206658363,
-0.008757608011364937,
0.049183011054992676,
-0.0444822683930397,
0.01002664677798748,
-0.0014618698041886091,
-0.047418851405382156,
-0.03413182497024536,
0.010858065448701382,
-0.05420912429690361,
-0.03946142643690109,
0.02545308507978916,
0.01703738234937191,
0.02365673892199993,
0.01504862867295742,
-0.013014014810323715,
-0.027721993625164032,
-0.0036745574325323105,
0.039922237396240234,
-0.04003901779651642,
0.018427632749080658,
-0.05982901155948639,
-0.024836692959070206,
-0.031089164316654205,
0.0037312658969312906,
-0.04561711847782135,
-0.002839947585016489,
-0.02584429830312729,
0.024278711527585983,
0.09806966781616211,
-0.0002910116163548082,
0.0010462786303833127,
-0.0015897416742518544,
0.06636147201061249,
-0.044835202395915985,
-0.029580673202872276,
0.007499804720282555,
0.029313724488019943,
-0.014300929382443428,
-0.05420767143368721,
0.05028587952256203,
0.0012402100255712867,
-0.04669411852955818,
-0.018510721623897552,
0.06780919432640076,
-0.08201444149017334,
0.03668394312262535,
-0.03904043510556221,
0.02733222395181656,
0.006254585459828377,
-0.06433513760566711,
-0.04517929255962372,
0.022388940677046776,
-0.02766646258533001,
0.00887991487979889,
-0.02019033581018448,
0.019641026854515076,
0.04014163091778755,
-0.08013559132814407,
0.025514714419841766,
-0.013308051973581314,
-0.025695081800222397,
-0.023204481229186058,
-0.012134803459048271,
0.007780796382576227,
-0.018468869850039482,
0.014704151079058647,
-0.05945345014333725,
-0.013699263334274292,
0.01771279238164425,
-0.036202747374773026,
-0.03681020066142082,
0.07356777042150497,
0.012831594794988632,
0.014139099977910519,
-0.05387243628501892,
0.05834394320845604,
0.019868580624461174,
-0.0048535107634961605,
-0.007480798754841089,
-0.045781370252370834,
0.0011571652721613646,
-0.017079951241612434,
-0.0061320033855736256,
-0.00786825641989708,
0.03142143413424492,
-0.035175081342458725,
0.06310340017080307,
0.016672702506184578,
0.013126345351338387,
-0.01500603649765253,
-0.03559582307934761,
-0.008848104625940323,
-0.05874938890337944,
0.01888629049062729,
-0.0511438213288784,
-0.029899422079324722,
-0.030091729015111923,
-0.001440970110706985,
-0.011395911686122417,
-0.01106959953904152,
0.024081336334347725,
-0.06006673350930214,
0.04111737757921219,
0.011986138299107552,
-0.035491228103637695,
0.04856186732649803,
-0.023948052898049355,
-0.04809536784887314,
-0.0016695762751623988,
-0.03280588239431381,
0.011220866814255714,
0.007124267052859068,
0.03154890984296799,
-0.03546399623155594,
-0.0733485147356987,
0.017651060596108437,
0.00041473135934211314,
0.016947422176599503,
-0.004206632263958454,
-0.004800410009920597,
-0.008902732282876968,
0.020107660442590714,
-0.02617112174630165,
0.032855916768312454,
-0.043920136988162994,
0.10678429156541824,
0.03017151728272438,
-0.0229070782661438,
-0.0036731811705976725,
-0.014334834180772305,
0.04609706625342369,
-0.00423703296110034,
-0.045469533652067184,
-0.010033020749688148,
-0.008707260712981224,
-0.07963857799768448,
-0.02524919994175434,
0.012413936667144299,
-0.031503140926361084,
-0.0034813310485333204,
0.041635192930698395,
0.0673239603638649,
0.08797189593315125,
0.015759224072098732,
-0.04925069957971573,
-0.07499384135007858,
-0.011733757331967354,
0.03223169595003128,
0.03168623894453049,
-0.047675155103206635,
0.04629910737276077,
0.012527761980891228,
0.003622138872742653,
0.019749466329813004,
-0.025627655908465385,
0.023125411942601204,
-0.020789269357919693,
-0.010776817798614502
] |
<p>How do <a href="http://en.wikipedia.org/wiki/Stirling_engine" rel="nofollow">Stirling engines</a> work? I understand the heating and cooling of air, but how much faster (or more force, I'm not sure which to use) does the piston move per degree Celsius that the temperatures differ?</p> | g9195 | [
0.011460702866315842,
-0.005907785147428513,
-0.00579105457291007,
0.03292566165328026,
0.04419635981321335,
-0.043143466114997864,
0.051549945026636124,
0.03970452398061752,
-0.06582257151603699,
-0.03474651649594307,
0.0031878305599093437,
0.010104864835739136,
0.02467496506869793,
-0.014004131779074669,
0.0006604593363590539,
0.07617981731891632,
0.03676406666636467,
-0.010956725105643272,
0.03480910509824753,
0.08216576278209686,
0.01104249432682991,
0.035389550030231476,
-0.04811769351363182,
-0.02733009308576584,
0.024756664410233498,
-0.013579070568084717,
-0.07197262346744537,
-0.07881259173154831,
-0.04727675020694733,
-0.04244139418005943,
0.013421446084976196,
0.026282088831067085,
0.03138710558414459,
-0.026905599981546402,
-0.026306863874197006,
-0.0091005340218544,
0.03905455768108368,
-0.01467256061732769,
0.01275926548987627,
-0.008360099978744984,
-0.021141942590475082,
-0.030209548771381378,
0.050036653876304626,
0.021355992183089256,
0.03125470504164696,
-0.008788509294390678,
0.0045645274221897125,
-0.06310959160327911,
-0.06771885603666306,
0.028492389246821404,
0.05100422725081444,
-0.0032089967280626297,
-0.03728488087654114,
-0.003662850707769394,
-0.029614128172397614,
-0.028123175725340843,
0.004488487262278795,
0.0150405028834939,
0.03538622707128525,
0.02266261726617813,
-0.05705107003450394,
0.004402865655720234,
-0.0035089331213384867,
0.01580013521015644,
0.010492452420294285,
-0.01187141053378582,
0.015828827396035194,
-0.017418665811419487,
-0.0031844298355281353,
0.06077263504266739,
-0.048922646790742874,
-0.019679715856909752,
-0.0488571897149086,
-0.061151497066020966,
-0.009640790522098541,
-0.018924592062830925,
0.03603082895278931,
-0.0863637924194336,
0.020826280117034912,
-0.002198591595515609,
-0.022785374894738197,
-0.03763144463300705,
0.03649671748280525,
0.004043320659548044,
-0.001067181583493948,
-0.0006133103161118925,
-0.017187757417559624,
0.025551609694957733,
0.04001418873667717,
0.003866420825943351,
-0.053379274904727936,
0.08988673239946365,
0.08547819405794144,
0.041409995406866074,
0.022130630910396576,
0.018257368355989456,
-0.02998240664601326,
0.020593388006091118,
-0.03038666397333145,
-0.016976812854409218,
-0.021204154938459396,
-0.018670056015253067,
0.039509426802396774,
-0.002820797497406602,
-0.010568087920546532,
-0.02147100120782852,
-0.022303109988570213,
-0.020718004554510117,
-0.028200145810842514,
0.03862866386771202,
-0.035328928381204605,
0.00020194957323838025,
-0.048871736973524094,
0.01391354389488697,
-0.036333732306957245,
0.0051534175872802734,
-0.013037976808845997,
-0.00446747150272131,
0.007180939894169569,
-0.026455774903297424,
0.008342676796019077,
0.034787990152835846,
-0.00813005305826664,
0.05425756424665451,
0.03152722865343094,
0.012334322556853294,
0.037775907665491104,
-0.036702413111925125,
-0.04190707951784134,
-0.009027654305100441,
0.037818390876054764,
-0.008425626903772354,
-0.018506616353988647,
-0.02318243496119976,
0.005471230484545231,
0.0016779899597167969,
-0.032809704542160034,
0.046201154589653015,
-0.011265949346125126,
0.01605832204222679,
-0.013233297504484653,
-0.0077276527881622314,
-0.03245506435632706,
-0.012245310470461845,
-0.04148281365633011,
-0.017105085775256157,
-0.06285528093576431,
-0.014845290221273899,
0.015331720933318138,
0.048103217035532,
0.011690082028508186,
-0.013673367910087109,
0.07668575644493103,
-0.007403487339615822,
0.010799026116728783,
-0.004501907620579004,
0.011508087627589703,
0.04409944638609886,
0.02781861461699009,
0.008038630709052086,
0.026598960161209106,
-0.06634174287319183,
0.07707566767930984,
-0.0037540867924690247,
-0.08680196851491928,
0.047321617603302,
-0.039712417870759964,
0.0026238705031573772,
0.05282606929540634,
-0.0322408601641655,
-0.052053891122341156,
-0.03873152285814285,
-0.05076400563120842,
0.06408753991127014,
0.04282565787434578,
0.007766857277601957,
0.09261363744735718,
0.0036994183901697397,
-0.00267124455422163,
-0.02663823775947094,
-0.024979613721370697,
0.009284038096666336,
0.007053751964122057,
-0.059529222548007965,
0.01258880365639925,
0.05828210338950157,
0.028067179024219513,
-0.05681414529681206,
-0.08387566357851028,
0.03641989454627037,
-0.056518856436014175,
-0.06593432277441025,
0.05481184646487236,
0.00995758268982172,
-0.03868716210126877,
0.03851338103413582,
-0.04312809184193611,
-0.04471832886338234,
-0.05577123165130615,
0.019277624785900116,
0.02600700967013836,
0.006062640342861414,
0.025721751153469086,
-0.0373087152838707,
0.0325818732380867,
-0.030970346182584763,
0.014231666922569275,
0.011805914342403412,
0.007056419737637043,
-0.048392605036497116,
0.012549311853945255,
0.04402882233262062,
0.012537757866084576,
0.07222293317317963,
-0.007357518654316664,
0.0541236475110054,
-0.0037159326020628214,
-0.04277985170483589,
-0.029695259407162666,
-0.019835088402032852,
0.07742141932249069,
0.015556441619992256,
-0.004356037825345993,
-0.020495597273111343,
-0.030799368396401405,
-0.05088241398334503,
-0.0013654386857524514,
0.016901129856705666,
0.022544998675584793,
0.09690987318754196,
-0.030256321653723717,
0.004569951444864273,
0.025526035577058792,
-0.000737807946279645,
0.0160934180021286,
0.03577433526515961,
0.029960330575704575,
0.056652747094631195,
-0.002102511003613472,
0.10510385781526566,
0.04234456643462181,
-0.02048785611987114,
-0.06656895577907562,
0.006550883874297142,
0.005326432641595602,
-0.03674086183309555,
0.0101212989538908,
-0.02124445140361786,
-0.008865078911185265,
-0.012681663036346436,
0.004952819552272558,
0.00947926752269268,
-0.020830923691391945,
-0.001296407193876803,
-0.07102309912443161,
-0.0010453956201672554,
-0.07249963283538818,
-0.04595791548490524,
-0.027544016018509865,
0.037182923406362534,
0.0463201180100441,
0.03009806014597416,
0.015966646373271942,
-0.0037510038819164038,
-0.012582440860569477,
-0.04417387396097183,
-0.020393438637256622,
-0.0383564755320549,
0.016506202518939972,
0.014768647961318493,
-0.0298937875777483,
-0.014483379200100899,
0.006769389379769564,
-0.0345250703394413,
-0.04038473963737488,
-0.016828741878271103,
0.03205264359712601,
-0.023703593760728836,
0.025695092976093292,
-0.020288223400712013,
-0.001688207034021616,
-0.020982543006539345,
-0.03590231016278267,
-0.014772899448871613,
0.019313804805278778,
-0.02740337699651718,
-0.02612457051873207,
0.06515154987573624,
0.02696022391319275,
-0.05422690883278847,
-0.02135923132300377,
0.004799054004251957,
0.03924144431948662,
0.023971039801836014,
0.02379395067691803,
0.03678809478878975,
0.03542124107480049,
-0.041751012206077576,
-0.028196509927511215,
-0.0011227646609768271,
0.022892674431204796,
-0.050051894038915634,
-0.026659244671463966,
0.042975276708602905,
0.01921817660331726,
0.013265198096632957,
-0.07703321427106857,
-0.024677231907844543,
0.005034349393099546,
-0.03354009985923767,
-0.00580912409350276,
-0.016251036897301674,
-0.00021660600032191724,
-0.010225754231214523,
-0.011806086637079716,
-0.03150388225913048,
-0.08879154175519943,
-0.01598775014281273,
0.07530352473258972,
0.024111328646540642,
-0.009827956557273865,
-0.05930257588624954,
-0.0127969179302454,
-0.05009980499744415,
0.000490410253405571,
0.0694868192076683,
0.06754890084266663,
-0.00957686360925436,
-0.042231034487485886,
-0.01547244843095541,
0.021811053156852722,
0.04422251507639885,
-0.0640508309006691,
-0.04327408969402313,
-0.04374249652028084,
0.0350363664329052,
-0.012488589622080326,
0.03810793161392212,
0.008694369345903397,
-0.006041026208549738,
-0.007686053402721882,
0.007346686441451311,
0.011109610088169575,
0.059651996940374374,
0.016770144924521446,
0.010914416052401066,
0.00047667400212958455,
-0.0009157021413557231,
-0.01303244661539793,
0.01682239957153797,
0.09083326160907745,
-0.06088925525546074,
0.01499827578663826,
-0.0036348383873701096,
0.03158041834831238,
-0.0352412611246109,
-0.008935821242630482,
0.03494243696331978,
-0.016851143911480904,
0.002379101002588868,
0.028033766895532608,
0.016491331160068512,
-0.04530393332242966,
0.06476208567619324,
-0.037128474563360214,
-0.039616234600543976,
-0.029610974714159966,
0.041679296642541885,
0.03195638209581375,
-0.027648555114865303,
0.0015005228342488408,
0.010071777738630772,
-0.009818017482757568,
0.025795435532927513,
0.04236232489347458,
0.046696193516254425,
0.1287475973367691,
-0.009297957643866539,
-0.05192071199417114,
0.013296112418174744,
-0.045861054211854935,
0.03145291283726692,
-0.018609430640935898,
-0.0059606535360217094,
-0.011698482558131218,
-0.04010767489671707,
-0.02760140411555767,
-0.014948896132409573,
0.012076718732714653,
-0.06336239725351334,
-0.027113214135169983,
0.004228523932397366,
-0.050842974334955215,
0.029165564104914665,
0.0437556616961956,
0.019947240129113197,
0.03391939401626587,
-0.017523853108286858,
-0.022447070106863976,
-0.024326099082827568,
0.033087264746427536,
0.019917214289307594,
0.054465580731630325,
0.04323536902666092,
-0.05030031502246857,
-0.004842160269618034,
-0.001350305275991559,
0.01667618378996849,
0.001833406393416226,
0.0034379607532173395,
-0.06325536966323853,
0.051191240549087524,
0.06433441489934921,
-0.021749412640929222,
0.06535203754901886,
-0.023163923993706703,
-0.012735066935420036,
0.04668677598237991,
-0.01586254872381687,
0.03765750303864479,
-0.017337940633296967,
-0.02617836184799671,
-0.004062660038471222,
0.014111521653831005,
-0.019940288737416267,
0.030487844720482826,
0.02792033739387989,
-0.05601739510893822,
-0.011595038697123528,
-0.04618310183286667,
0.007794484030455351,
-0.04244838282465935,
0.015852490440011024,
0.013492335565388203,
0.01546753291040659,
0.05554374307394028,
0.014444042928516865,
0.06932124495506287,
0.01789732091128826,
0.043362051248550415,
0.0048546623438596725,
0.013631721027195454,
-0.00007680990529479459,
-0.016333909705281258,
0.03170676529407501,
0.013289030641317368,
-0.0021026460453867912,
-0.07156987488269806,
-0.0020590871572494507,
-0.04132332652807236,
-0.002347076078876853,
0.03676394745707512,
-0.06666364520788193,
0.018893582746386528,
0.01832800731062889,
0.029609855264425278,
0.003354397602379322,
0.059813231229782104,
-0.022551272064447403,
-0.019305793568491936,
-0.026622969657182693,
-0.03219182416796684,
-0.030979428440332413,
0.00430630287155509,
-0.036594144999980927,
-0.03072814829647541,
0.002616062294691801,
-0.011979158967733383,
-0.053593795746564865,
0.003588175168260932,
0.06273442506790161,
-0.02055170387029648,
-0.005548960994929075,
0.10028070211410522,
0.018912851810455322,
0.0039899274706840515,
0.05701645836234093,
-0.07105182111263275,
0.023413220420479774,
0.025841889902949333,
0.03405054286122322,
0.03592092543840408,
0.048893485218286514,
-0.001769208232872188,
0.052615538239479065,
-0.006906307768076658,
-0.03348977118730545,
0.0010733079398050904,
0.0012407675385475159,
0.04976267367601395,
-0.02928953804075718,
0.05603616312146187,
-0.04372505471110344,
-0.010261556133627892,
-0.022252853959798813,
0.015938736498355865,
0.04052858054637909,
0.033276330679655075,
0.00951616931706667,
0.027453478425741196,
-0.012673744931817055,
0.04653419181704521,
-0.049382880330085754,
-0.0006119529716670513,
-0.013211619108915329,
0.04012758284807205,
0.08511732518672943,
-0.014574914239346981,
0.03256874904036522,
0.035820454359054565,
-0.0005303198704496026,
0.03196964040398598,
0.0024368949234485626,
-0.013098501600325108,
0.036287903785705566,
-0.062158532440662384,
0.00737702427431941,
-0.0023657381534576416,
0.019582951441407204,
-0.05342889577150345,
0.059526897966861725,
-0.06598546355962753,
0.03674187883734703,
-0.0018597193993628025,
-0.09461720287799835,
-0.024118758738040924,
-0.03812287375330925,
-0.03348544239997864,
0.028872409835457802,
0.007636116351932287,
-0.02452518232166767,
-0.015391193330287933,
0.03879687562584877,
0.023611420765519142,
0.024662652984261513,
0.02313622273504734,
0.0054672942496836185,
-0.04333877936005592,
0.012858688831329346,
-0.03624831885099411,
0.0027264629025012255,
0.021339042112231255,
-0.009658106602728367,
0.05796106159687042,
0.0022103399969637394,
-0.033439427614212036,
-0.04470479488372803,
0.021958062425255775,
0.031995534896850586,
-0.006886928807944059,
0.0307961143553257,
0.03217077627778053,
0.009550461545586586,
0.014701061882078648,
0.04188919812440872,
0.022921057417988777,
0.05331248790025711,
-0.04666583240032196,
0.02615155652165413,
-0.0022820800077170134,
0.006313870660960674,
0.03436947241425514,
0.055272217839956284,
-0.0002915708173532039,
0.020832011476159096,
-0.03705041855573654,
-0.06165027245879173,
-0.007355575915426016,
0.03793298453092575,
0.06283857673406601,
0.04600543901324272,
-0.04911329597234726,
-0.03422039747238159,
-0.05245886743068695,
0.03842155262827873,
-0.07459471374750137,
-0.03721945732831955,
0.00044229315244592726,
-0.026402423158288002,
0.039810992777347565,
-0.01673157513141632,
0.011768103577196598,
-0.028109563514590263,
-0.007979919202625751,
0.037950050085783005,
-0.03289623185992241,
0.014650815166532993,
0.022013824433088303,
0.05516163632273674,
0.07413581758737564,
-0.024033399298787117,
-0.035662535578012466,
-0.004602708853781223,
-0.013625667430460453,
-0.01623842492699623,
-0.04876653477549553,
-0.020968196913599968,
0.03314631059765816,
0.013782368041574955,
0.0208900049328804,
0.03665269911289215,
0.03192596510052681,
0.0926448330283165,
-0.014009013772010803,
-0.017253030091524124,
0.041063092648983,
0.02867956832051277,
0.012380464002490044,
0.025362642481923103,
0.009141032584011555,
-0.04561164602637291,
0.034953001886606216,
0.05987551435828209,
-0.03459259495139122,
-0.006478625349700451,
-0.022115599364042282,
0.002930484712123871,
0.006812801584601402,
0.03162980079650879,
-0.03979258984327316,
0.01556596253067255,
-0.043758492916822433,
0.018859196454286575,
-0.07431499660015106,
0.015432010404765606,
0.019724717363715172,
-0.04135223850607872,
0.052834492176771164,
0.04316525533795357,
-0.01450429204851389,
0.04849497228860855,
-0.06507278233766556,
-0.035435501486063004,
0.033108994364738464,
-0.009417109191417694,
0.0038868149276822805,
-0.044071853160858154,
0.0489216148853302,
0.02513195388019085,
0.07291720807552338,
-0.0062596299685537815,
0.05085738003253937,
-0.038149867206811905,
0.061093904078006744,
-0.007409314159303904,
-0.023460613563656807,
-0.012130766175687313,
-0.013893158175051212,
-0.05119902640581131,
-0.0025818615686148405,
-0.056772228330373764,
-0.05800497904419899,
-0.09223712235689163,
0.026090333238244057,
-0.005317037459462881,
0.0434100367128849,
0.03900718688964844,
-0.05086451396346092,
-0.014321912080049515,
0.01981845125555992,
-0.005374121479690075,
-0.014016106724739075,
0.018642732873558998,
0.044939618557691574,
-0.005417470820248127,
0.060976818203926086,
-0.0686788409948349,
-0.012648334726691246,
0.03994257003068924,
0.006119913421571255,
-0.009739253669977188,
0.029440781101584435,
-0.016342299059033394,
-0.04564087092876434,
-0.022192541509866714,
0.014748044312000275,
-0.039913780987262726,
0.039015647023916245,
-0.012846147641539574,
-0.016582753509283066,
0.03439611941576004,
-0.07028301060199738,
0.02529704011976719,
-0.02042611688375473,
-0.049763161689043045,
-0.009992402978241444,
-0.008814449422061443,
0.029243160039186478,
0.06325771659612656,
-0.06287865340709686,
-0.0006690552108921111,
0.02760264091193676,
0.005727969575673342,
0.04975714907050133,
-0.051287904381752014,
0.012340480461716652,
-0.02821218967437744,
-0.0027460723649710417,
-0.033949702978134155,
0.021804727613925934,
-0.013087751343846321,
0.0027771631721407175,
0.05237278342247009,
0.03669861704111099,
0.02279510162770748,
-0.013832290656864643,
0.011682174168527126,
-0.020253712311387062,
-0.041649818420410156,
0.040704190731048584,
0.0037636589258909225,
-0.022356504574418068,
-0.02414737083017826,
-0.0371522456407547,
0.07644640654325485,
-0.02928265556693077,
-0.026773078367114067,
-0.01927248388528824,
-0.017583373934030533,
0.017376922070980072,
0.014927396550774574,
-0.004668545443564653,
-0.024033723399043083,
0.015166329219937325,
-0.00346335768699646,
0.00617498392239213,
-0.025228064507246017,
0.016439102590084076,
-0.007025113329291344,
0.004584297072142363,
-0.03053462505340576,
0.009777767583727837,
0.017267564311623573,
-0.02688206359744072,
-0.04891932010650635,
-0.011509519070386887,
0.037294160574674606,
0.016228066757321358,
0.012601043097674847,
0.011179406195878983,
0.004169519525021315,
-0.015757132321596146,
0.01570873148739338,
-0.04473286122083664,
-0.01944369450211525,
-0.05832275375723839,
-0.039500124752521515,
0.06152256950736046,
-0.0011943827848881483,
-0.026701657101511955,
0.06769850105047226,
0.003119475208222866,
-0.06445950269699097,
-0.0658755898475647,
-0.011812891811132431,
0.0003794755320996046,
-0.014075161889195442,
0.09682327508926392,
-0.009693029336631298,
-0.032623354345560074,
-0.023791052401065826,
-0.0034466907382011414,
-0.00744273466989398,
0.010094007477164268,
-0.042245395481586456,
-0.05443822592496872,
-0.044670578092336655,
-0.027904806658625603
] |
<p>So for a complex dielectric constant $\epsilon = \epsilon_a + i\epsilon_b$, the wave vector and index of refraction are related to it through $k = \frac{\omega}{c}n$ and $n = \sqrt{\frac{\mu \epsilon}{\mu_0 \epsilon_0}}$. According to Jackson, the real part of the dielectric is related to polarization and anomalous dispersion, while the imaginary part is associated with dissipation of energy into the medium.</p>
<p>If you write the wavevector as $k = \beta + i \alpha/2$ and plug it in the general wave formula (just in 1D right now) of $e^{ikr} = e^{-\alpha r/2}e^{i\beta r}$, the intensity drops as $e^{-\alpha r}$, so $\alpha$ is the attenuation constant, which tells you how quickly the wave dies out in the medium.</p>
<p>But, if you plug that form of $k$ into the above equations to solve for $\alpha$ and $\beta$ as a function of $\epsilon_a$ and $\epsilon_b$, you find that $\alpha$ and $\beta$ are both a function of both $\epsilon_a$ and $\epsilon_b$.</p>
<p>This is counterintuitive to me, because intuitively I'd think that the attenuation constant $\alpha$ would only be based on $\epsilon_b$, due to dissipation, and the same with $\beta$ and $\epsilon_a$.</p>
<p>Can anyone give a good physical explanation for this "mixing"?</p> | g9196 | [
0.013967575505375862,
-0.04815767705440521,
-0.005931482184678316,
-0.02855803817510605,
0.03749622404575348,
0.024356672540307045,
0.07456053793430328,
0.028334932401776314,
-0.02179814875125885,
0.02582796849310398,
-0.0339774563908577,
0.011729877442121506,
0.03226381167769432,
0.022674059495329857,
0.004112343769520521,
-0.04333950951695442,
0.06094186753034592,
0.03982016444206238,
0.003025958314538002,
-0.021045805886387825,
-0.03882576897740364,
-0.0013283394509926438,
0.004740624222904444,
-0.054303888231515884,
0.025927677750587463,
-0.003754501463845372,
0.04266061633825302,
0.005869915243238211,
-0.010197743773460388,
-0.03739042952656746,
0.04243665933609009,
-0.005181625485420227,
0.05226076394319534,
0.017211489379405975,
-0.025603704154491425,
0.021491428837180138,
0.024983936920762062,
0.076624296605587,
0.04901278018951416,
0.00583253288641572,
-0.029639892280101776,
0.009787864051759243,
-0.006474463269114494,
0.021342234686017036,
-0.022194266319274902,
-0.011454325169324875,
-0.05457927659153938,
0.0025988842826336622,
-0.028040897101163864,
-0.031223095953464508,
-0.005703847389668226,
-0.03174803778529167,
0.07286207377910614,
0.06147276610136032,
0.003822221187874675,
0.04484355077147484,
0.013959518633782864,
0.028225654736161232,
-0.010448453016579151,
0.0362568274140358,
0.034419119358062744,
-0.001490957336500287,
0.0038768555968999863,
0.01580669730901718,
0.061532195657491684,
-0.04041304066777229,
-0.024128824472427368,
-0.03600902482867241,
-0.010793630965054035,
0.0271889790892601,
-0.021702926605939865,
-0.05734119191765785,
0.0011789454147219658,
-0.05289063975214958,
-0.03256241977214813,
-0.03173806890845299,
-0.009016882628202438,
0.04715956747531891,
-0.009059350937604904,
0.015389266423881054,
-0.0029415490571409464,
0.02334696054458618,
0.033932529389858246,
-0.013628089800477028,
0.024518996477127075,
0.03131842985749245,
-0.001707949093542993,
-0.011770451441407204,
-0.033315934240818024,
-0.013436175882816315,
-0.012756701558828354,
-0.03897356614470482,
-0.005567352287471294,
0.005446449387818575,
0.0375635102391243,
-0.035416316241025925,
-0.02268741838634014,
0.052837226539850235,
-0.004248783923685551,
0.002324660075828433,
0.02367299236357212,
0.025032134726643562,
-0.015409312210977077,
0.038510266691446304,
-0.0412432961165905,
-0.010345354676246643,
0.012768463231623173,
-0.03231446444988251,
-0.01662071794271469,
0.03672819957137108,
-0.048673685640096664,
-0.04286661371588707,
-0.05183245241641998,
-0.05269631743431091,
-0.015660369768738747,
-0.026738854125142097,
-0.010869121178984642,
-0.047947436571121216,
0.018264802172780037,
-0.01279845368117094,
-0.0006281128735281527,
0.020963024348020554,
-0.009955770336091518,
0.06872008740901947,
-0.0066306558437645435,
0.060653820633888245,
0.06073594465851784,
0.011024918407201767,
0.04438195377588272,
-0.02288583107292652,
0.014283785596489906,
-0.05550110712647438,
-0.03715885803103447,
-0.005550098605453968,
-0.009937028400599957,
0.008366404101252556,
0.03791268542408943,
-0.0060045430436730385,
-0.0324130654335022,
0.07091759890317917,
0.010238893330097198,
-0.040761422365903854,
-0.012981059961020947,
-0.010177028365433216,
-0.05106385797262192,
0.08242334425449371,
-0.009832758456468582,
-0.053942397236824036,
0.05699256807565689,
-0.03279416635632515,
-0.00996861606836319,
0.058058422058820724,
0.02009451389312744,
-0.0024463534355163574,
-0.000079404613643419,
0.0035098064690828323,
0.02826021797955036,
-0.00928905326873064,
-0.013187373988330364,
0.021609514951705933,
0.03027769923210144,
-0.033554863184690475,
-0.0049813492223620415,
0.0508904755115509,
0.002604264533147216,
0.0180771816521883,
-0.013141905888915062,
-0.02562703751027584,
0.02172853797674179,
-0.051756396889686584,
-0.009597539901733398,
0.048455916345119476,
0.009280609898269176,
0.07035301625728607,
0.036397699266672134,
0.09377576410770416,
0.015466100536286831,
-0.011764059774577618,
-0.05446125939488411,
-0.02972031757235527,
-0.006946921348571777,
0.0439724437892437,
-0.01613294705748558,
-0.06596018373966217,
0.024865662679076195,
-0.007596239913254976,
0.00970306247472763,
0.010240613482892513,
-0.07107390463352203,
0.017574554309248924,
-0.005739605985581875,
-0.026378124952316284,
-0.0123166898265481,
0.06798487901687622,
-0.004634701181203127,
0.002098947297781706,
0.05305046588182449,
0.014584512449800968,
-0.03233524411916733,
0.011769989505410194,
-0.02518378756940365,
0.03896567225456238,
0.08159189671278,
-0.0039521027356386185,
0.014568316750228405,
0.038115244358778,
-0.013368173502385616,
0.06330902129411697,
-0.03545047342777252,
-0.0061493972316384315,
0.015139870345592499,
-0.052430037409067154,
0.01874641329050064,
0.02012844942510128,
-0.014474878087639809,
-0.014988803304731846,
0.00581930810585618,
-0.0010275231907144189,
-0.08378904312849045,
0.023956049233675003,
-0.08601686358451843,
0.04888416454195976,
-0.011262243613600731,
0.042119402438402176,
-0.04460083693265915,
-0.0015398225514218211,
-0.032048195600509644,
0.011087377555668354,
-0.04342087730765343,
-0.0007714122184552252,
-0.04830503091216087,
0.02201836369931698,
-0.01749884895980358,
0.017867425456643105,
0.00945646408945322,
0.01829668879508972,
-0.07834599912166595,
-0.06366757303476334,
-0.005837215110659599,
-0.008443656377494335,
-0.0193137526512146,
0.0037981162313371897,
-0.06348572671413422,
0.028509600088000298,
-0.007713573519140482,
0.019966429099440575,
0.0223207026720047,
-0.023124126717448235,
-0.06470583379268646,
0.006346691399812698,
-0.005057809874415398,
0.026950394734740257,
-0.01512908935546875,
-0.0013776415726169944,
0.019458523020148277,
-0.02048611268401146,
-0.02543068490922451,
0.04538539797067642,
-0.02672627381980419,
-0.010964380577206612,
-0.016608472913503647,
0.007079254370182753,
0.053601887077093124,
-0.02307290956377983,
-0.07652698457241058,
0.053129468113183975,
-0.0060075861401855946,
0.043756406754255295,
0.014323750510811806,
0.019848117604851723,
0.010190343484282494,
0.029589412733912468,
0.07065458595752716,
0.04613775387406349,
0.0032537232618778944,
0.028249794617295265,
-0.008476397022604942,
-0.05893375352025032,
0.05992310494184494,
-0.0701366439461708,
-0.058823149651288986,
0.021210551261901855,
-0.03977327048778534,
0.0478108786046505,
0.004999764263629913,
-0.04361523687839508,
0.04539890214800835,
0.05528441444039345,
-0.024074185639619827,
-0.008950159884989262,
-0.03720402345061302,
0.022221526131033897,
-0.04378358647227287,
0.009956744499504566,
-0.01918933540582657,
0.028665410354733467,
0.07417111098766327,
-0.06583661586046219,
-0.03125574439764023,
0.025625132024288177,
0.020018352195620537,
-0.028630482032895088,
-0.048051465302705765,
-0.03190458565950394,
-0.0010249561164528131,
0.04081090912222862,
-0.04895537346601486,
-0.047653138637542725,
0.00483065377920866,
0.02851230837404728,
0.013743074610829353,
0.008047818206250668,
-0.0007692489889450371,
0.060799989849328995,
-0.003933111671358347,
0.015719447284936905,
-0.00037939418689347804,
-0.05286319553852081,
0.042044006288051605,
0.00502043217420578,
-0.045390889048576355,
-0.025054369121789932,
-0.012576386332511902,
0.02015482261776924,
-0.001313274959102273,
-0.00378242414444685,
-0.04915889352560043,
0.04294624552130699,
-0.02697962149977684,
-0.008015037514269352,
-0.026179438456892967,
-0.06740368902683258,
0.0015947682550176978,
0.009002205915749073,
-0.05910288915038109,
-0.02902417816221714,
-0.03812558576464653,
0.04285239800810814,
-0.01582438312470913,
0.016164615750312805,
0.00850451085716486,
-0.0033335210755467415,
-0.05601375177502632,
-0.01127304881811142,
0.03351733833551407,
0.01807849295437336,
0.0289507694542408,
-0.03505523502826691,
0.0014530448243021965,
-0.012830255553126335,
0.0005154871032573283,
0.01713656447827816,
0.03310251608490944,
-0.04217536374926567,
-0.10771200805902481,
-0.017872191965579987,
0.05067965388298035,
-0.007279489189386368,
0.0345417819917202,
-0.027286795899271965,
0.06434853374958038,
-0.04279620572924614,
0.008066972717642784,
-0.08137616515159607,
-0.046888187527656555,
-0.021678980439901352,
0.032342758029699326,
0.08926977962255478,
-0.0712735578417778,
0.011807801201939583,
0.0053128949366509914,
0.009061142802238464,
-0.01987098716199398,
0.0407852865755558,
0.013924827799201012,
-0.014889374375343323,
-0.04433296620845795,
0.04001469537615776,
-0.042922526597976685,
0.05209658667445183,
0.02679308131337166,
0.012562406249344349,
0.050281040370464325,
0.056732263416051865,
0.04756515100598335,
-0.007822557352483273,
0.0008569691563025117,
0.005174661986529827,
0.035062409937381744,
-0.0359739325940609,
0.00994420237839222,
-0.0024389023892581463,
0.013987964950501919,
0.025753550231456757,
0.018315736204385757,
-0.061171095818281174,
-0.01991891674697399,
-0.01697920262813568,
0.0035054394975304604,
0.067497618496418,
0.0045265150256454945,
-0.013349832035601139,
-0.003509548958390951,
-0.0175112783908844,
0.07133793830871582,
0.014946261420845985,
0.05005982145667076,
-0.0053069498389959335,
0.025798188522458076,
-0.05744689330458641,
-0.002924134489148855,
0.008493661880493164,
-0.026842065155506134,
-0.12205517292022705,
0.027942227199673653,
0.03320712968707085,
0.04821925237774849,
-0.006949784234166145,
0.026550468057394028,
-0.025735333561897278,
0.00219365325756371,
0.04484175145626068,
-0.04014909639954567,
-0.007242156192660332,
0.030583104118704796,
-0.004617468919605017,
0.07901440560817719,
-0.019885452464222908,
-0.014541327953338623,
-0.028201023116707802,
-0.028518933802843094,
-0.01260312832891941,
-0.05280551686882973,
0.05676930025219917,
-0.030662959441542625,
0.02621961385011673,
-0.027836032211780548,
0.03785736858844757,
0.043909963220357895,
0.02019389159977436,
0.06370197981595993,
-0.05031244456768036,
-0.0023489079903811216,
-0.002804504707455635,
0.027436286211013794,
0.04135837033390999,
-0.042713891714811325,
-0.05957916006445885,
-0.008302105590701103,
-0.013016115874052048,
-0.04596341773867607,
0.03167537599802017,
0.016763146966695786,
-0.054988425225019455,
0.0006212531588971615,
-0.017407923936843872,
-0.003878807183355093,
0.08481930196285248,
0.009584754705429077,
-0.004692111164331436,
-0.06566756963729858,
-0.009934692643582821,
0.004880086053162813,
-0.013386020436882973,
0.030074991285800934,
-0.011671926826238632,
0.009602739475667477,
-0.006125005893409252,
-0.04975910857319832,
0.007316621020436287,
0.0021277577616274357,
0.053248148411512375,
0.04845566675066948,
0.021146120503544807,
0.02624695561826229,
-0.06375078111886978,
-0.05329826474189758,
-0.009105553850531578,
-0.072337806224823,
-0.04377616196870804,
0.008233370259404182,
-0.029343273490667343,
0.04389121010899544,
0.048035379499197006,
-0.017488177865743637,
-0.015214387327432632,
-0.028673067688941956,
0.004055782221257687,
-0.018870146945118904,
0.015047343447804451,
0.052204739302396774,
0.01781398430466652,
-0.01749517023563385,
-0.02213962748646736,
0.017258010804653168,
-0.04313959926366806,
0.05486493930220604,
-0.015052861534059048,
-0.02485298365354538,
0.015974432229995728,
-0.018323559314012527,
-0.06658392399549484,
-0.046824224293231964,
0.018009424209594727,
-0.029730668291449547,
0.030127407982945442,
0.046032585203647614,
-0.008210655301809311,
0.011378182098269463,
0.0896061435341835,
0.005643546115607023,
-0.02879476360976696,
0.028354443609714508,
-0.009806972928345203,
0.01570490375161171,
-0.020793920382857323,
-0.05401632562279701,
0.021976131945848465,
-0.04306364059448242,
0.015178018249571323,
0.037260688841342926,
0.020120279863476753,
-0.03924312815070152,
-0.03673112764954567,
0.016994507983326912,
0.022598229348659515,
-0.037140730768442154,
0.003280817298218608,
-0.008838927373290062,
-0.00673967320472002,
-0.009949769824743271,
0.03916606307029724,
0.0021826240699738264,
-0.025272507220506668,
0.014400282874703407,
-0.0678328350186348,
-0.007510465569794178,
-0.016077522188425064,
0.0026608200278133154,
-0.0042175049893558025,
-0.048396334052085876,
0.08933853358030319,
0.006140354089438915,
0.11261383444070816,
-0.027218949049711227,
0.018221188336610794,
0.008265932090580463,
-0.008697030134499073,
0.06072031706571579,
0.006378652062267065,
-0.020315902307629585,
-0.06382496654987335,
0.03941204398870468,
-0.04030952230095863,
-0.006967248395085335,
-0.0024254086893051863,
0.027552613988518715,
0.022153915837407112,
-0.0374235063791275,
-0.023171206936240196,
-0.019223421812057495,
0.005636503919959068,
-0.036790940910577774,
0.005245947744697332,
0.022088807076215744,
-0.08042743802070618,
0.05984478443861008,
0.031534042209386826,
0.03164123371243477,
-0.021155670285224915,
-0.023994198068976402,
-0.013726185075938702,
-0.01580720953643322,
0.008763330057263374,
0.0072831446304917336,
0.054165132343769073,
-0.0063186767511069775,
-0.015162747353315353,
0.0025913575664162636,
0.02076105959713459,
0.019294869154691696,
-0.006447461433708668,
0.026552405208349228,
0.01511450856924057,
-0.033041812479496,
-0.009147691540420055,
-0.07137375324964523,
-0.04336633160710335,
0.04185216501355171,
-0.07081441581249237,
-0.040875185281038284,
-0.044547222554683685,
-0.04690411686897278,
-0.04267742484807968,
-0.008422664366662502,
-0.018679967150092125,
0.07382013648748398,
0.0028303361032158136,
-0.012129249982535839,
-0.032575175166130066,
0.047714103013277054,
-0.0010996124474331737,
0.034166816622018814,
-0.014266015961766243,
-0.006162642035633326,
-0.05377010628581047,
0.023303447291254997,
-0.05968319997191429,
-0.0351034514605999,
0.02313016541302204,
0.054074037820100784,
0.03341100737452507,
0.016807949170470238,
0.007937348447740078,
-0.0187899861484766,
-0.09301263093948364,
-0.039164938032627106,
0.07696483284235,
0.005362215917557478,
0.039598967880010605,
-0.004437556024640799,
-0.06669110804796219,
0.033867932856082916,
-0.010533229447901249,
0.02464875765144825,
0.001112201134674251,
0.028821725398302078,
-0.032718416303396225,
0.019765036180615425,
-0.0009556081495247781,
0.03756561875343323,
0.05502432584762573,
0.020249124616384506,
0.03908342123031616,
0.02527005784213543,
0.015430881641805172,
-0.06583967059850693,
0.024420244619250298,
0.010670329444110394,
0.053081292659044266,
0.0356985479593277,
0.10874808579683304,
0.04298465698957443,
0.1014624685049057,
-0.0528859868645668,
0.06638553738594055,
0.05451225861907005,
-0.020047953352332115,
-0.05765474960207939,
-0.012090981937944889,
0.07063628733158112,
0.029536111280322075,
-0.03278941661119461,
-0.002865866757929325,
-0.06809882074594498,
-0.02853170596063137,
-0.011111043393611908,
0.005014494992792606,
0.008559361100196838,
-0.03799058124423027,
0.00776322977617383,
-0.0507398322224617,
-0.01616962067782879,
0.013375557027757168,
0.009213103912770748,
0.053449634462594986,
0.02827356569468975,
-0.06192794442176819,
0.03236311301589012,
-0.022040020674467087,
0.004367549438029528,
-0.011869954876601696,
0.0029788517858833075,
0.006569615565240383,
0.03295836225152016,
0.017185665667057037,
-0.009564372710883617,
-0.021784814074635506,
-0.02405528910458088,
0.0313464030623436,
0.041005510836839676,
0.03546300530433655,
0.02264062687754631,
-0.05548638105392456,
0.003607202088460326,
0.0752304419875145,
-0.06377781182527542,
0.03181297332048416,
0.03157787770032883,
0.025579776614904404,
-0.0013655158691108227,
-0.02988903783261776,
0.014253520406782627,
0.0553613007068634,
0.03537779301404953,
-0.03814025968313217,
0.008918305858969688,
0.02704373002052307,
-0.0008577433764003217,
-0.008485929109156132,
-0.04428529366850853,
-0.04049120098352432,
0.033530447632074356,
-0.002887321636080742,
-0.04855584725737572,
-0.0016565554542466998,
-0.025109244510531425,
-0.0708780586719513,
0.01245300192385912,
0.009582744911313057,
0.025988031178712845,
-0.020507756620645523,
0.03928773105144501,
-0.01490735448896885,
-0.02191627211868763,
0.04602254554629326,
-0.04031418636441231,
-0.0426877923309803,
-0.059767644852399826,
-0.03005220741033554,
-0.028012149035930634,
-0.01845000497996807,
0.032067377120256424,
-0.056229446083307266,
-0.007634475827217102,
-0.009544790722429752,
0.007743040099740028,
-0.03229551762342453,
0.007684024982154369,
0.030668463557958603,
-0.07000185549259186,
0.01870040036737919,
-0.07950180023908615,
0.0035829299595206976,
-0.009837847203016281,
0.00490556750446558,
0.004146247170865536,
-0.003378707217052579,
-0.018906377255916595,
0.0272362157702446,
-0.021546702831983566,
-0.04309943690896034,
-0.024180147796869278,
0.05092723295092583,
0.003053497290238738,
0.024218687787652016,
-0.005101582035422325,
0.028302250429987907,
0.0565871000289917,
-0.033339034765958786,
-0.04134803265333176,
-0.020639652386307716,
-0.016470711678266525,
0.00883461907505989,
0.07993967086076736,
-0.004180318210273981,
0.02074313536286354,
-0.024315375834703445,
0.02983146533370018,
-0.02867859974503517,
0.010126170702278614,
-0.05742447078227997,
-0.04074183106422424,
0.0502871610224247,
-0.03353061154484749,
-0.005285998340696096,
-0.0013642542762681842,
0.004104866646230221
] |
<p>What is the physics behind a normal human jump ?</p>
<p><img src="http://www.wired.com/images_blogs/wiredscience/2012/04/drawings_spring_12key_23.jpg" alt="a human jump"></p>
<p>when a normal human wants to jump.</p>
<ol>
<li>First, some energy is stored in their thighs and The elastic tendons Just like a spring.
In mechanics and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit</li>
</ol>
<p>$$F=-k.x$$
where
<strong>x</strong> is the displacement of the spring's end from its equilibrium position (a distance, in SI units: metres); <strong>F</strong> is the restoring force exerted by the spring on that end (in SI units: N or kg·m/s^2); and k is a constant called the rate or spring constant (in SI units: N/ m</p>
<p>what is human rate constant <strong>k</strong>?</p> | g9197 | [
0.07430762052536011,
0.07525008916854858,
-0.007490489166229963,
0.03467493876814842,
0.0010823698248714209,
0.026369929313659668,
0.024921279400587082,
0.020722031593322754,
-0.022970395162701607,
-0.05491923540830612,
-0.013090196065604687,
-0.02805417589843273,
-0.016210569068789482,
-0.06641573458909988,
0.0334477573633194,
0.0004427799431141466,
0.03307223320007324,
-0.04094766825437546,
0.04220489785075188,
0.012579343281686306,
-0.008107248693704605,
-0.003450150601565838,
-0.026821566745638847,
-0.05284878984093666,
0.0008664902416057885,
-0.011698117479681969,
-0.02777276374399662,
0.01234665047377348,
-0.04311223328113556,
-0.05389261618256569,
0.012604991905391216,
-0.06129508465528488,
0.04279950633645058,
-0.09403223544359207,
-0.0466325581073761,
0.03671684488654137,
0.0022752422373741865,
-0.008948159404098988,
0.030281949788331985,
-0.011108518578112125,
-0.0059537761844694614,
-0.056128934025764465,
-0.023474697023630142,
-0.01546436082571745,
0.0001691953366389498,
-0.005252163857221603,
-0.013193385675549507,
0.005364284850656986,
0.025361450389027596,
0.017323307693004608,
-0.06152556464076042,
0.04133079946041107,
-0.02065936103463173,
0.014525297097861767,
0.07017280161380768,
0.011428134515881538,
0.04738052561879158,
0.032014381140470505,
0.045047659426927567,
-0.0004311150696594268,
0.03064855746924877,
-0.017860978841781616,
0.03951168805360794,
-0.059887539595365524,
0.05970621854066849,
0.021403413265943527,
-0.01832512766122818,
0.025857070460915565,
0.028389906510710716,
0.013825829140841961,
-0.0035220810677856207,
-0.044196248054504395,
-0.04147955775260925,
-0.008578280918300152,
-0.052670709788799286,
0.003569653956219554,
-0.03515072166919708,
0.021919850260019302,
0.01959553174674511,
-0.0073684039525687695,
-0.03268229961395264,
0.023388324305415154,
-0.04295656085014343,
0.006633658893406391,
0.0486258901655674,
-0.01663036085665226,
-0.0031869837548583746,
0.0018930749502032995,
-0.026908598840236664,
0.0242166668176651,
0.053617171943187714,
0.011164724826812744,
0.1084425076842308,
0.01828899420797825,
-0.06458637118339539,
-0.05128169804811478,
-0.06442175060510635,
0.06650649011135101,
0.027970358729362488,
-0.05352800339460373,
-0.00433399947360158,
-0.029623327776789665,
0.015555731020867825,
-0.032500945031642914,
-0.022198999300599098,
0.0165622029453516,
0.023416107520461082,
0.030528675764799118,
-0.017171451821923256,
-0.006637219805270433,
0.0035507846623659134,
-0.00017111879424192011,
0.04275298863649368,
-0.005638916045427322,
-0.03452356532216072,
-0.05647318810224533,
0.0012260191142559052,
0.019887100905179977,
0.015911715105175972,
0.03203898295760155,
-0.008439825847744942,
0.040402479469776154,
0.06748676300048828,
0.02518249861896038,
-0.05511930212378502,
-0.07669533789157867,
0.011587467975914478,
0.007725391536951065,
-0.015538518317043781,
-0.015686940401792526,
0.003067736979573965,
0.01250290498137474,
-0.04031214118003845,
-0.010479596443474293,
0.005423404276371002,
0.06070103868842125,
0.034957677125930786,
-0.011630766093730927,
-0.028940200805664062,
0.02480398863554001,
-0.03528990596532822,
0.0013796634739264846,
0.030707068741321564,
-0.04968029260635376,
-0.03999539464712143,
0.0804765522480011,
-0.01248061191290617,
0.03698772192001343,
0.012621918693184853,
0.010053765028715134,
-0.0380408950150013,
0.049454718828201294,
0.015219702385365963,
-0.03148975968360901,
0.030018122866749763,
-0.016742048785090446,
0.03987208381295204,
0.0037742170970886946,
-0.03879362717270851,
0.08131079375743866,
0.04747188091278076,
-0.050913091748952866,
-0.033444520086050034,
0.04028838500380516,
-0.012243368662893772,
0.010154045186936855,
-0.0035239937715232372,
-0.018204297870397568,
0.06036150082945824,
-0.013991554267704487,
-0.06170084327459335,
-0.04793635383248329,
0.01806551218032837,
0.060274455696344376,
-0.0857415497303009,
-0.024286950007081032,
0.07050303369760513,
-0.05424207076430321,
-0.03770092502236366,
-0.07637669891119003,
-0.012168527580797672,
-0.025296641513705254,
0.028006844222545624,
-0.02126709185540676,
-0.03862113133072853,
0.021179160103201866,
0.06486152857542038,
0.01625491864979267,
0.02738167904317379,
-0.028618352487683296,
-0.0590759813785553,
-0.07056394964456558,
-0.027397144585847855,
0.020977569743990898,
-0.043466173112392426,
-0.03933991119265556,
0.04021262750029564,
0.051044680178165436,
-0.0034193280152976513,
0.025611838325858116,
0.0638982355594635,
-0.021932926028966904,
-0.009039623662829399,
-0.037609245628118515,
0.04734085500240326,
-0.0143732950091362,
0.01002658624202013,
-0.016133315861225128,
0.030691633000969887,
-0.0013547483831644058,
0.028867056593298912,
0.03399215638637543,
-0.04813903570175171,
0.07740417867898941,
0.024825746193528175,
-0.042595893144607544,
0.010258015245199203,
-0.046649567782878876,
0.021543089300394058,
-0.01873866654932499,
0.0053123594261705875,
-0.007447939831763506,
-0.013875761069357395,
-0.00665685860440135,
-0.025555294007062912,
-0.03300323709845543,
-0.05675782263278961,
-0.022451898083090782,
-0.0012892520753666759,
-0.01856907270848751,
-0.007588809356093407,
0.057899896055459976,
-0.0003989795804955065,
-0.007088481914252043,
-0.007990578189492226,
0.08230311423540115,
0.017425695434212685,
-0.013420705683529377,
0.0033462634310126305,
-0.031470898538827896,
0.05972405523061752,
-0.03548957780003548,
0.008969828486442566,
-0.05658353120088577,
-0.04893092066049576,
-0.015641435980796814,
0.0019513001898303628,
-0.0077033378183841705,
-0.002327254507690668,
-0.00850017461925745,
-0.015573868528008461,
-0.028929179534316063,
0.00419821310788393,
-0.004432321060448885,
0.002442738739773631,
-0.02725798264145851,
-0.04267438128590584,
-0.006635318044573069,
-0.07203787565231323,
-0.05847612023353577,
-0.01189557183533907,
-0.00655751395970583,
0.04487566277384758,
0.004101223312318325,
-0.09053695201873779,
-0.007580207660794258,
0.024767762050032616,
0.007695951033383608,
0.005321742966771126,
0.002225682605057955,
0.0018131471006199718,
0.06279508024454117,
-0.05684894323348999,
0.06909603625535965,
0.0436469204723835,
-0.0730479434132576,
-0.01924542896449566,
-0.034300919622182846,
-0.034841492772102356,
0.01135527528822422,
-0.036478642374277115,
0.02259703539311886,
0.004514461848884821,
-0.0138695128262043,
0.016816718503832817,
-0.05280372500419617,
0.03023422136902809,
-0.01653430052101612,
-0.06990686804056168,
-0.001466559013351798,
-0.027613090351223946,
0.017438003793358803,
0.020079804584383965,
-0.003365921787917614,
0.024171417579054832,
0.08220703154802322,
0.046626508235931396,
-0.020907210186123848,
-0.05944129824638367,
0.04519921913743019,
-0.04182415083050728,
-0.10738184303045273,
0.031144749373197556,
0.05484146624803543,
-0.030466187745332718,
0.05512445047497749,
0.00044840079499408603,
-0.033445823937654495,
0.01809047721326351,
0.06867881119251251,
0.005909282248467207,
0.01992637664079666,
0.03984775021672249,
0.013487283140420914,
-0.04830259084701538,
-0.02401355654001236,
0.019687702879309654,
0.02424647845327854,
0.011372343637049198,
-0.06251401454210281,
0.06068161875009537,
-0.056176211684942245,
0.017105262726545334,
0.003209322225302458,
0.007654909044504166,
0.0012140200706198812,
-0.04976416006684303,
0.0437430739402771,
-0.08828774839639664,
-0.038172606378793716,
-0.012584875337779522,
-0.027264472097158432,
-0.09112069755792618,
-0.02791413851082325,
-0.03509857878088951,
-0.04314554110169411,
-0.02167912945151329,
0.03811373561620712,
0.09039784967899323,
0.04299698770046234,
-0.02627347968518734,
-0.005976658780127764,
-0.06172087788581848,
-0.014305979013442993,
-0.010034018196165562,
0.0351659394800663,
0.027833016589283943,
-0.009233584627509117,
0.025646574795246124,
-0.04075755923986435,
0.031499918550252914,
-0.02118317410349846,
-0.011186211369931698,
-0.01708831451833248,
-0.015337604098021984,
0.01848548650741577,
0.04350582882761955,
0.007684287615120411,
-0.06484999507665634,
-0.027190955355763435,
0.03818514943122864,
-0.026315443217754364,
0.04496142640709877,
0.04883304610848427,
-0.03771975263953209,
-0.02890767902135849,
-0.031964629888534546,
0.10761282593011856,
-0.014046314172446728,
-0.037002623081207275,
-0.0016870575491338968,
-0.03270692005753517,
0.03976559266448021,
-0.016759265214204788,
-0.020090468227863312,
-0.011521329171955585,
-0.009164560586214066,
0.028180813416838646,
-0.04723522812128067,
-0.01928442157804966,
-0.005557361990213394,
0.06765682250261307,
-0.02909228391945362,
0.0053614666685462,
0.008092323318123817,
-0.0302349254488945,
0.0034931832924485207,
-0.012221003882586956,
0.047046612948179245,
-0.003026046324521303,
0.05546445772051811,
-0.05479509383440018,
-0.020374290645122528,
-0.0002818107604980469,
0.048196788877248764,
-0.0009411479695700109,
0.0015676136827096343,
0.009059576317667961,
-0.014832494780421257,
0.001886150217615068,
-0.003215352538973093,
0.05995292589068413,
-0.02055753953754902,
-0.0065159122459590435,
0.006057246122509241,
0.047871414572000504,
0.03402414917945862,
-0.0242408886551857,
0.06265199184417725,
-0.07744939625263214,
0.033357806503772736,
-0.02473525144159794,
-0.017406899482011795,
-0.04051486402750015,
0.03861217573285103,
-0.00037908850936219096,
0.045632582157850266,
-0.01624840684235096,
0.0008675740682519972,
0.0006316501530818641,
0.07978065311908722,
-0.001047152210958302,
0.04542345181107521,
-0.00954330712556839,
-0.008973202668130398,
0.037494778633117676,
0.03463468700647354,
-0.009105600416660309,
0.028157999739050865,
-0.039987679570913315,
-0.08731359243392944,
0.03205962851643562,
0.02283455990254879,
-0.010514870285987854,
-0.034500617533922195,
0.057845935225486755,
0.08074560016393661,
0.022961651906371117,
-0.07710147649049759,
0.03371802717447281,
0.036756731569767,
0.004643845371901989,
0.04664593189954758,
0.07137589901685715,
-0.06271184980869293,
0.03037373349070549,
-0.004752384498715401,
-0.06470348685979843,
-0.017092987895011902,
-0.009589683264493942,
0.01716630905866623,
-0.03459358587861061,
0.022347254678606987,
0.0031024739146232605,
-0.00892648845911026,
-0.004032603465020657,
-0.017171647399663925,
-0.005951868835836649,
0.006126927677541971,
0.003080465132370591,
-0.02458590269088745,
-0.010294164530932903,
0.022949790582060814,
0.01667426899075508,
-0.038545507937669754,
0.014225440099835396,
0.030164238065481186,
-0.05339610576629639,
0.00774321099743247,
0.04382703825831413,
0.04969828575849533,
0.0262114480137825,
0.029271388426423073,
0.018763337284326553,
0.04507279768586159,
0.019702564924955368,
0.062058813869953156,
0.0358925499022007,
0.014242749661207199,
-0.017928240820765495,
-0.03712686896324158,
0.006067739799618721,
-0.04028629884123802,
-0.0017421568045392632,
-0.012491094879806042,
-0.027606500312685966,
0.002032425021752715,
0.04318895563483238,
-0.004937940277159214,
0.023479856550693512,
0.056964218616485596,
-0.01124968659132719,
0.02799353003501892,
-0.02018037438392639,
0.02109535224735737,
0.04454255849123001,
-0.002059520222246647,
0.005180766806006432,
-0.005896538030356169,
-0.025013718754053116,
-0.07685055583715439,
-0.008081268519163132,
-0.03362265229225159,
0.0017853261670097709,
-0.03481049835681915,
0.032006822526454926,
-0.018318742513656616,
0.030677683651447296,
-0.01400035060942173,
0.024761630222201347,
-0.0006813944783061743,
0.04184054583311081,
0.016642844304442406,
-0.04329737648367882,
-0.04938353970646858,
0.01833217963576317,
0.013700797222554684,
-0.02986256405711174,
-0.01012900099158287,
-0.013491985388100147,
0.05108661204576492,
0.007202175911515951,
0.04157017171382904,
0.050084516406059265,
-0.008769250474870205,
0.02652709186077118,
0.006051022559404373,
-0.018193813040852547,
-0.02228260226547718,
0.05075465142726898,
0.005869756452739239,
0.030376892536878586,
0.034418970346450806,
-0.023839958012104034,
-0.03938973322510719,
-0.01307795662432909,
-0.04816567525267601,
0.0280791986733675,
-0.03497506305575371,
-0.043630894273519516,
-0.05920535698533058,
-0.005842703394591808,
0.034832537174224854,
0.05428539589047432,
-0.018161578103899956,
0.008051161654293537,
-0.030910516157746315,
-0.010740784928202629,
0.0004318007850088179,
-0.025887571275234222,
-0.026801925152540207,
-0.0010101471561938524,
-0.0043978639878332615,
0.04549615457653999,
0.005488748196512461,
0.030588658526539803,
0.002266929019242525,
-0.006801903247833252,
-0.053860608488321304,
0.01639440469443798,
0.019511202350258827,
0.060484204441308975,
0.01988578401505947,
0.012452160008251667,
0.08380240947008133,
-0.07154103368520737,
-0.013935808092355728,
-0.024965208023786545,
0.038199055939912796,
0.027788056060671806,
0.014602230861783028,
-0.009808272123336792,
0.04740562289953232,
0.05392074212431908,
-0.029805494472384453,
0.014685416594147682,
-0.05605275556445122,
-0.017995143309235573,
-0.07441109418869019,
-0.004249241203069687,
0.009000863879919052,
-0.03209087625145912,
-0.030836446210741997,
-0.06672753393650055,
-0.05651385709643364,
-0.0036579223815351725,
0.030064046382904053,
-0.023738674819469452,
0.03636683151125908,
-0.006214108318090439,
-0.04989485442638397,
0.000513724226038903,
-0.022513318806886673,
-0.020260939374566078,
-0.027372419834136963,
-0.031988564878702164,
0.020984366536140442,
-0.018123893067240715,
0.02732754871249199,
0.01918420009315014,
-0.0007524442044086754,
0.004520212300121784,
0.03479823097586632,
-0.03639136254787445,
0.020323101431131363,
0.0037672107573598623,
-0.023903194814920425,
0.028406281024217606,
-0.027596501633524895,
-0.0018293993780389428,
0.017485404387116432,
0.011097707785665989,
-0.028153231367468834,
0.008885042741894722,
-0.024421481415629387,
0.03201179578900337,
0.023911993950605392,
0.018048105761408806,
-0.013231245800852776,
0.02922588214278221,
-0.011922214180231094,
-0.036893345415592194,
0.049185797572135925,
0.0033306472469121218,
0.008249782957136631,
-0.030581984668970108,
-0.06265965104103088,
0.05395372584462166,
0.0006177057512104511,
0.011165115050971508,
-0.023809803649783134,
0.01961444690823555,
-0.035588692873716354,
0.07019250094890594,
-0.013693385757505894,
0.08702019602060318,
-0.06224863603711128,
-0.029576322063803673,
-0.01439556572586298,
0.053340207785367966,
-0.0012776737567037344,
0.019856097176671028,
0.021509088575839996,
0.017560409381985664,
-0.08438742905855179,
0.02529829554259777,
0.06674835830926895,
-0.029592914506793022,
-0.07630833983421326,
-0.02362057939171791,
0.014973994344472885,
-0.019672458991408348,
0.016790978610515594,
0.04909553378820419,
-0.012490439228713512,
0.040950555354356766,
0.0187226515263319,
0.012737320736050606,
0.04394923523068428,
-0.06833696365356445,
-0.002872062148526311,
0.048772335052490234,
0.07767068594694138,
-0.01587424986064434,
0.002294285222887993,
0.040176358073949814,
0.02616211585700512,
-0.0006684871623292565,
-0.015974698588252068,
0.030270278453826904,
0.026999644935131073,
-0.015300990082323551,
0.015049473382532597,
-0.001853294437751174,
-0.01781107299029827,
0.04475104436278343,
-0.0055284155532717705,
-0.001927463337779045,
0.01274392381310463,
-0.04605460539460182,
-0.03304317966103554,
0.020016390830278397,
-0.047900985926389694,
0.0002854378253687173,
-0.04367983341217041,
0.08298775553703308,
0.013562336564064026,
0.0036551421508193016,
0.025959482416510582,
0.029204832389950752,
-0.07709535211324692,
0.018971724435687065,
-0.008803533390164375,
-0.0062695941887795925,
0.006722703576087952,
-0.004677613731473684,
0.045604120939970016,
0.00992698222398758,
0.04349024221301079,
0.003684443421661854,
-0.009862668812274933,
0.036382440477609634,
0.01969964988529682,
0.04429488256573677,
0.0019175894558429718,
0.0290655680000782,
-0.049084145575761795,
-0.035631000995635986,
-0.028543155640363693,
-0.030208107084035873,
0.007799848914146423,
0.0038874635938555002,
0.0602833591401577,
0.06581393629312515,
-0.0034203401301056147,
0.021195778623223305,
0.032498277723789215,
0.0041557056829333305,
0.035754766315221786,
-0.04995400831103325,
0.01416128408163786,
-0.04126330837607384,
0.007126341573894024,
-0.003989098593592644,
-0.06378071010112762,
0.025053052231669426,
-0.06623847037553787,
0.00048148661153391004,
-0.04120291769504547,
0.020260505378246307,
-0.0247352197766304,
-0.0647476315498352,
0.0565304309129715,
-0.0008757555624470115,
-0.03336242958903313,
0.014066309668123722,
0.06974640488624573,
0.0014297629240900278,
-0.028625724837183952,
0.039312172681093216,
-0.022098954766988754,
-0.0026887033600360155,
0.001167410984635353,
-0.00950615480542183,
0.027431629598140717,
-0.019244767725467682,
-0.01893969438970089,
0.07555882632732391,
0.046200353652238846,
-0.017759954556822777,
0.029966460540890694,
-0.010909315198659897,
0.018538592383265495,
0.029445327818393707,
-0.00791461393237114,
-0.06371643394231796,
-0.022454196587204933,
0.04716609790921211,
0.02277643419802189,
-0.029154593124985695,
-0.07069116830825806,
-0.011901726014912128,
-0.004478651564568281,
-0.018793726339936256,
0.04298333451151848,
-0.002853398211300373,
-0.017142383381724358,
0.015902521088719368
] |
<p>I always thought that high voltage power lines would attract a lightning strike more than other structures in the same area. Turns out I was wrong. My neighbor's chimney got struck by lightning and it destroyed a lot of stuff (street lamps, wifi APs, small home electronics). We live very close to high voltage power lines - so, is my premise wrong? Do power lines not attract a lightning strike more that other objects?</p>
<p>Also, if a chimney isn't connected to the power grid (or am I wrong?), then how is it possible, that almost all of the street lamps don't work and other electronic devices were destroyed?</p> | g9198 | [
0.014227730222046375,
0.020401781424880028,
0.005756850820034742,
-0.020386865362524986,
0.06271957606077194,
-0.009996959008276463,
-0.04569805786013603,
0.02821734920144081,
0.0010818599257618189,
-0.06928562372922897,
-0.01544469129294157,
0.013877038843929768,
0.027934087440371513,
0.0332491360604763,
-0.04477085545659065,
-0.027917394414544106,
0.0982237234711647,
-0.004379031714051962,
0.03170895576477051,
0.030776653438806534,
-0.06287956237792969,
-0.03776372969150543,
0.02246255613863468,
-0.03890188783407211,
-0.0598347932100296,
-0.005436803214251995,
0.0451289638876915,
-0.040683597326278687,
0.010450621135532856,
-0.004087045323103666,
-0.09323715418577194,
-0.004417751915752888,
0.02888932079076767,
-0.05089752376079559,
-0.04568622261285782,
-0.013481912203133106,
0.01630936935544014,
-0.001970758894458413,
-0.004267201293259859,
0.016002420336008072,
-0.004756420385092497,
0.03715479373931885,
0.04255170002579689,
-0.03885120898485184,
0.0313289612531662,
0.03233733028173447,
-0.02679663896560669,
-0.0005010961904190481,
0.023339079692959785,
-0.0010486999526619911,
-0.03914259746670723,
-0.03865426033735275,
-0.025032779201865196,
0.013770452700555325,
0.04667680710554123,
-0.013395505025982857,
0.10393106937408447,
-0.037926383316516876,
0.04338531196117401,
0.01878075860440731,
0.029789112508296967,
0.04022343456745148,
0.03534712269902229,
0.0013400544412434101,
0.017166398465633392,
0.05907867103815079,
-0.11541859060525894,
-0.06451482325792313,
0.09999540448188782,
0.012250923551619053,
0.023326218128204346,
-0.020936956629157066,
-0.007970046252012253,
-0.05857330560684204,
0.019367003813385963,
0.02089393138885498,
0.004903555382043123,
-0.000186332079465501,
0.0062315515242516994,
0.06356816738843918,
0.020998483523726463,
-0.032064396888017654,
0.0004982394748367369,
0.03990299999713898,
0.03313468396663666,
0.028808636590838432,
0.0035364399664103985,
0.01809925213456154,
-0.006775624118745327,
-0.04314543306827545,
0.036457691341638565,
-0.008231054991483688,
0.0725187286734581,
0.0012567489175125957,
-0.04652110114693642,
0.01357453316450119,
-0.003376849228516221,
0.029079696163535118,
0.0016929262783378363,
-0.015152697451412678,
-0.045071449130773544,
-0.08131571114063263,
-0.000701247772667557,
-0.0068237935192883015,
-0.029411518946290016,
-0.027227733284235,
0.03485216200351715,
-0.024358374997973442,
-0.023414619266986847,
0.03287741541862488,
0.03952715918421745,
-0.03206121549010277,
-0.01946321316063404,
-0.07081862539052963,
-0.042409222573041916,
0.02309633046388626,
0.08196331560611725,
-0.02606351673603058,
0.027611494064331055,
0.06400952488183975,
0.044022537767887115,
-0.009588920511305332,
0.005386382807046175,
0.049837153404951096,
0.020898111164569855,
-0.026817824691534042,
0.028647273778915405,
0.016467975452542305,
0.06717152148485184,
-0.026892002671957016,
0.023720744997262955,
-0.0837404653429985,
-0.025751495733857155,
0.013131687417626381,
0.024676572531461716,
0.01259793434292078,
0.08485453575849533,
-0.030923349782824516,
0.04165774956345558,
0.02829587832093239,
-0.0028608909342437983,
0.029906921088695526,
0.02138230763375759,
-0.07300271093845367,
-0.0005475309444591403,
0.09466171264648438,
-0.05281977355480194,
0.01661665178835392,
-0.0423639640212059,
-0.006836575921624899,
0.001367752905935049,
0.04599230736494064,
0.006882351823151112,
-0.025617454200983047,
-0.04249914735555649,
-0.04933107644319534,
-0.011445200070738792,
0.013568967580795288,
-0.020660778507590294,
-0.03215194493532181,
0.012400207109749317,
-0.010026019997894764,
0.01579432375729084,
-0.026963403448462486,
0.05128572881221771,
-0.05715015158057213,
0.023982346057891846,
-0.018025590106844902,
-0.013251334428787231,
-0.0296378955245018,
-0.010714102536439896,
-0.0037625599652528763,
0.04115735739469528,
0.03257608041167259,
0.03729546442627907,
-0.058412469923496246,
0.029182735830545425,
-0.044632602483034134,
0.019328514114022255,
0.008905341848731041,
-0.006708682049065828,
-0.04508430138230324,
-0.02897486463189125,
0.014622124843299389,
0.03950676694512367,
0.025078091770410538,
-0.05035431683063507,
0.038437847048044205,
0.0006037710700184107,
0.02337646484375,
-0.05256228521466255,
-0.017860272899270058,
-0.0036410398315638304,
0.02474985085427761,
0.035357046872377396,
-0.022603904828429222,
-0.025660185143351555,
0.017556194216012955,
-0.05187920853495598,
-0.04998401179909706,
0.05113312229514122,
0.008942704647779465,
0.01704428717494011,
0.005042272619903088,
-0.055011775344610214,
0.06873158365488052,
-0.08413789421319962,
-0.026197655126452446,
0.0064653558656573296,
-0.07503987103700638,
-0.03494567796587944,
-0.06529200822114944,
-0.017154023051261902,
0.03713732585310936,
-0.01534281950443983,
-0.05533041059970856,
-0.06387206166982651,
-0.012690866366028786,
-0.04281166195869446,
-0.01572381518781185,
-0.007000776007771492,
-0.005853780545294285,
0.0326043926179409,
-0.02279314212501049,
0.023346807807683945,
0.026502935215830803,
0.02432597614824772,
-0.0032129830215126276,
0.021406780928373337,
-0.02445431798696518,
-0.028856921941041946,
0.044049907475709915,
0.002582665765658021,
-0.038093339651823044,
0.01008700393140316,
0.04542938619852066,
0.03331136703491211,
-0.016842415556311607,
-0.004214810207486153,
-0.053579095751047134,
-0.008418643847107887,
-0.047064781188964844,
0.06101108714938164,
0.0246035847812891,
0.06328094750642776,
-0.013670207932591438,
-0.010374248027801514,
0.012943247333168983,
-0.04494965448975563,
0.04774243012070656,
0.03213461488485336,
0.06888322532176971,
0.017237868160009384,
0.0014974133810028434,
-0.001716922502964735,
-0.023719942197203636,
0.011757051572203636,
0.03181363642215729,
-0.049395885318517685,
-0.04688500985503197,
-0.06376773864030838,
-0.008860104717314243,
0.02771482989192009,
-0.06738661974668503,
-0.025045834481716156,
0.05166954919695854,
-0.02290615253150463,
-0.04995236173272133,
-0.034873392432928085,
-0.07722914963960648,
-0.09265661984682083,
0.020226851105690002,
0.005700262263417244,
0.037369806319475174,
-0.007526830304414034,
-0.043666016310453415,
-0.0040206992998719215,
0.01804162561893463,
0.031001009047031403,
0.00281848874874413,
0.04596450552344322,
-0.026170024648308754,
-0.041317205876111984,
-0.06298066675662994,
0.03997503221035004,
-0.059899378567934036,
-0.04345054551959038,
-0.014664368703961372,
-0.06020214781165123,
0.004460764117538929,
-0.03505448251962662,
-0.07394825667142868,
-0.024306707084178925,
-0.04528051242232323,
0.0006824276060797274,
-0.010425430722534657,
0.0009814747609198093,
-0.018854688853025436,
-0.06315832585096359,
-0.011674781329929829,
-0.016785237938165665,
0.045168086886405945,
-0.025612104684114456,
-0.018165012821555138,
0.01128486730158329,
0.05152648314833641,
-0.020635079592466354,
-0.06504316627979279,
0.01462616864591837,
-0.02816719375550747,
0.021860362961888313,
0.06421269476413727,
-0.018954697996377945,
0.01652679033577442,
-0.016020871698856354,
0.027233218774199486,
0.04925987124443054,
0.0929064229130745,
-0.02109113708138466,
0.0610799714922905,
0.056525882333517075,
-0.020761637017130852,
-0.010093830525875092,
-0.010782251134514809,
-0.02060801349580288,
0.0002987106563523412,
-0.03461949899792671,
0.05070464313030243,
-0.004442998208105564,
-0.005255817901343107,
0.035800203680992126,
-0.005815505515784025,
-0.010825064964592457,
-0.03650130331516266,
-0.0313311405479908,
0.02812374010682106,
0.025628235191106796,
0.0037109116092324257,
0.0586545467376709,
0.021732240915298462,
0.030321188271045685,
-0.02225400134921074,
-0.07242360711097717,
-0.013307916931807995,
0.007134009152650833,
0.02951142005622387,
-0.04474770650267601,
0.0018930996302515268,
0.042780663818120956,
0.011847948655486107,
0.038576170802116394,
0.010608350858092308,
0.019089097157120705,
-0.01621134579181671,
-0.02833651378750801,
-0.023634659126400948,
0.010499321855604649,
0.004060518462210894,
0.012480516918003559,
0.06361596286296844,
-0.018872056156396866,
0.016566555947065353,
0.05628731846809387,
0.02528524212539196,
-0.035991571843624115,
0.015573352575302124,
-0.04450210928916931,
0.03112800046801567,
-0.03452562168240547,
0.031011611223220825,
0.026959307491779327,
0.02447352558374405,
-0.07374046742916107,
0.06809470802545547,
0.01351573970168829,
0.019979828968644142,
0.01843501441180706,
-0.01771940290927887,
0.0173182412981987,
0.0033602428156882524,
0.028236960992217064,
-0.021703394129872322,
-0.06539957970380783,
0.021373001858592033,
0.03362622112035751,
-0.06477046012878418,
-0.013706264086067677,
0.021913278847932816,
0.01505954097956419,
-0.017711251974105835,
-0.02915274165570736,
-0.022089477628469467,
-0.02794688008725643,
0.01106575783342123,
-0.008155794814229012,
-0.05375172197818756,
0.008981485851109028,
0.0005692190607078373,
0.04732387512922287,
0.017220474779605865,
0.04825654625892639,
0.01781131699681282,
0.010983290150761604,
0.009006706066429615,
0.07069473713636398,
-0.032929256558418274,
0.03888610377907753,
-0.005343293771147728,
-0.031579144299030304,
-0.04989384859800339,
-0.00003229295907658525,
0.0030894505325704813,
-0.03310859575867653,
-0.07627646625041962,
0.03110005147755146,
0.006865267176181078,
0.07712630182504654,
0.0435541532933712,
0.010859922505915165,
-0.005895812530070543,
0.06886687874794006,
-0.008231640793383121,
-0.04152078554034233,
-0.03387024253606796,
-0.02549935318529606,
0.0004549664445221424,
-0.0024396320804953575,
-0.03588077053427696,
-0.023968322202563286,
0.03834439441561699,
0.01523926667869091,
0.006999731529504061,
-0.0018266391707584262,
-0.03859970346093178,
0.02863215282559395,
0.016072260215878487,
0.02035001665353775,
0.06041211262345314,
0.02176997996866703,
0.016557469964027405,
0.09735266864299774,
-0.015310132876038551,
0.038232821971178055,
-0.00894883181899786,
0.04693600535392761,
-0.011269529350101948,
-0.014855957590043545,
0.03846729174256325,
-0.05607389286160469,
-0.011126456782221794,
-0.04068908840417862,
-0.03917432948946953,
0.017321133986115456,
-0.004331193398684263,
0.028344111517071724,
-0.003690632525831461,
0.04613548889756203,
0.010316376574337482,
0.01994839496910572,
0.02911604940891266,
-0.07569363713264465,
-0.08030528575181961,
-0.018991602584719658,
0.0020710427779704332,
0.055691543966531754,
0.040625207126140594,
-0.04604904353618622,
-0.05498575046658516,
-0.08617523312568665,
-0.022706881165504456,
0.04540807381272316,
0.05407610908150673,
0.007397993002086878,
-0.03889252245426178,
-0.0054766894318163395,
0.00896734744310379,
-0.019681265577673912,
0.01192350871860981,
-0.02091226540505886,
-0.0037402419839054346,
-0.02253333106637001,
-0.01858377642929554,
-0.0622120127081871,
-0.03212692588567734,
-0.008622800000011921,
-0.023329688236117363,
-0.01592046208679676,
0.052282966673374176,
0.03093617781996727,
-0.06785574555397034,
0.006270947866141796,
0.048810236155986786,
-0.0680587887763977,
0.014265542849898338,
0.007239204831421375,
-0.003003837773576379,
0.04689860716462135,
0.013149344362318516,
-0.019162947311997414,
0.011641987599432468,
0.002655462361872196,
-0.02264779806137085,
-0.033907391130924225,
-0.029576964676380157,
-0.028093652799725533,
0.0374152846634388,
0.06912202388048172,
-0.022279197350144386,
0.04121212661266327,
-0.031803544610738754,
0.0004001401539426297,
-0.00988465454429388,
-0.07200043648481369,
0.04634224995970726,
0.0025873035192489624,
-0.035098638385534286,
-0.07359256595373154,
0.009328778833150864,
-0.01569758914411068,
-0.02417365275323391,
0.022143583744764328,
-0.012478752061724663,
-0.019366616383194923,
-0.00956539623439312,
-0.023616699501872063,
-0.031084727495908737,
-0.010064728558063507,
0.005977315362542868,
-0.015300726518034935,
0.06318088620901108,
0.032622307538986206,
0.039627108722925186,
-0.055522311478853226,
0.018204158172011375,
0.006322305649518967,
0.030788524076342583,
0.009035687893629074,
-0.011387020349502563,
0.01837964355945587,
0.03877665102481842,
0.05182284861803055,
-0.02601081319153309,
0.03842351213097572,
0.028333593159914017,
0.04211544245481491,
-0.05187708139419556,
0.05419301986694336,
-0.00805633794516325,
0.026991475373506546,
0.03814077377319336,
0.016422627493739128,
0.10373643040657043,
0.01611848920583725,
0.031161945313215256,
-0.03939514234662056,
-0.009975564666092396,
0.0064323293045163155,
-0.010335151106119156,
0.016060709953308105,
-0.03488422930240631,
0.006330916192382574,
-0.02708781138062477,
-0.035914868116378784,
-0.06292904913425446,
0.061441127210855484,
-0.06275716423988342,
-0.010209299623966217,
-0.01227088738232851,
-0.013557489030063152,
0.07572648674249649,
0.08647370338439941,
-0.037767715752124786,
0.051649149507284164,
-0.05093903839588165,
-0.0395515151321888,
0.017159374430775642,
-0.022809457033872604,
0.030712516978383064,
0.010561199858784676,
-0.012877363711595535,
0.012969743460416794,
0.002442563185468316,
0.048976413905620575,
-0.028316471725702286,
-0.0010145580163225532,
0.011896554380655289,
0.019313788041472435,
0.009021648205816746,
0.03593102842569351,
0.00009005160973174497,
0.03195697441697121,
-0.028116723522543907,
-0.0007898109615780413,
-0.022182414308190346,
-0.03227018937468529,
-0.03407885879278183,
0.05353562906384468,
0.017060674726963043,
-0.06841622292995453,
-0.025072218850255013,
0.04303113371133804,
-0.025197502225637436,
0.02653082087635994,
-0.019768306985497475,
0.03442716598510742,
0.014640596695244312,
0.043273307383060455,
-0.034861255437135696,
-0.05258532613515854,
0.04528170824050903,
-0.0008633053512312472,
0.043505098670721054,
-0.015724917873740196,
0.06946729868650436,
-0.027829350903630257,
-0.041384436190128326,
-0.0437031053006649,
-0.022848231717944145,
-0.008623209781944752,
0.005434601102024317,
0.013405311852693558,
-0.02983315847814083,
-0.020364463329315186,
-0.0372934527695179,
-0.029464801773428917,
0.04620922729372978,
0.021992960944771767,
0.022877074778079987,
0.03839447721838951,
0.032300494611263275,
-0.0504947192966938,
-0.00005727354437112808,
0.016881491988897324,
-0.004294281359761953,
-0.029311588034033775,
0.04571632295846939,
0.01255321316421032,
0.003567370353266597,
0.008109131827950478,
-0.03165774047374725,
-0.018988097086548805,
0.02765507437288761,
-0.014028593897819519,
0.0024405766744166613,
0.03431006893515587,
-0.026522357016801834,
-0.040473151952028275,
0.0006325276917777956,
0.010165424086153507,
-0.02930353581905365,
0.017351852729916573,
0.04901031777262688,
0.0313035249710083,
0.0015843845903873444,
-0.028546223416924477,
-0.02997564524412155,
-0.022634927183389664,
0.02700044959783554,
0.017946181818842888,
-0.009853482246398926,
-0.019782641902565956,
0.03295375779271126,
-0.03464927151799202,
0.03333597630262375,
0.002103568287566304,
0.014121251180768013,
-0.016049742698669434,
-0.02568245865404606,
-0.005358113441616297,
0.0375598706305027,
0.02193981595337391,
-0.03876245394349098,
-0.02316240780055523,
-0.028306500986218452,
0.023445449769496918,
-0.003850189270451665,
-0.012680519372224808,
-0.015586788766086102,
0.0387619286775589,
-0.0165435578674078,
0.03574954345822334,
0.0038863986264914274,
0.0035949740558862686,
0.02811250276863575,
0.015144889242947102,
0.03917999193072319,
-0.03866691142320633,
0.007471785414963961,
0.011134385131299496,
-0.0380035936832428,
-0.04135747253894806,
-0.015294993296265602,
0.05892882123589516,
-0.05580223351716995,
-0.002744208322837949,
-0.018062060698866844,
0.06585664302110672,
-0.051493510603904724,
-0.007826438173651695,
-0.017409753054380417,
-0.0073781488463282585,
0.028690094128251076,
0.02301602251827717,
-0.02778320573270321,
0.07402952760457993,
0.03295888006687164,
0.00916450098156929,
-0.0390828475356102,
-0.05229141563177109,
0.03906265273690224,
0.01734926551580429,
0.04722951725125313,
0.03455139696598053,
0.009970398619771004,
-0.009481300599873066,
0.06398137658834457,
0.05751202255487442,
0.0074539585039019585,
-0.025144968181848526,
0.06470819562673569,
-0.035942982882261276,
0.02385333739221096,
0.007481724955141544,
0.0015077954158186913,
0.020576952025294304,
0.07385780662298203,
0.08892534673213959,
0.02508389949798584,
0.013845863752067089,
0.005631228908896446,
0.014784683473408222,
-0.02248876355588436,
0.010389463976025581,
-0.02785884402692318,
-0.04373491555452347,
0.0006871652440167964,
0.0443635955452919,
-0.009827096946537495,
-0.003079988993704319,
-0.03174838051199913,
0.03085913695394993,
0.03264886513352394,
-0.08574575930833817,
0.0018097471911460161,
-0.0026900030206888914,
-0.058142390102148056,
-0.013271034695208073,
0.0005185563932172954,
0.003898920025676489,
-0.012280896306037903,
-0.004744528327137232,
0.0342278890311718,
-0.0755995586514473,
-0.013650706969201565,
-0.028042061254382133,
-0.004259718116372824,
0.014775916002690792,
-0.012879987247288227,
0.014127315953373909,
0.028958691284060478,
-0.053428344428539276,
-0.015772279351949692,
-0.02931789867579937,
-0.01218422595411539,
0.02023317664861679,
-0.015693604946136475,
-0.002590914722532034,
-0.047263339161872864
] |
<p>This question follows on previous work on connections between (other) areas of physics and thermodynamics as in <a href="http://physics.stackexchange.com/q/115026/">here</a>, <a href="http://physics.stackexchange.com/q/114697/">here</a> and <a href="http://cs.stackexchange.com/q/26049/">even here</a>.</p>
<p><a href="http://en.wikipedia.org/wiki/Paul_Dirac" rel="nofollow">P. Dirac</a> (an electrical engineer initially) was one of the first to pose the possible existence of magnetic monopoles (<a href="http://users.physik.fu-berlin.de/~kleinert/files/dirac1931.pdf" rel="nofollow">original paper</a>)(for example as solenoids). This would allow more symmetric forms of certain equations (physicist fetish?). Anyway, this (a-)symmetry is also the starting point for possible connections to thermodynamical concepts.</p>
<blockquote>
<p>Is there any relation to the (non-) existence of <a href="http://en.wikipedia.org/wiki/Magnetic_monopole" rel="nofollow">magnetic
monopoles</a> and <a href="http://en.wikipedia.org/wiki/Second_law_of_thermodynamics" rel="nofollow">2nd
law</a>?</p>
<p>Would the possible existence of magnetic monopoles violate the 2nd
law, or does the 2nd law predict magnetic monopoles, or it is just
irrelevant (sth many physicists would not assume lightly)?</p>
</blockquote>
<p>Relevant physics areas include the intersection of materials magnetization and thermodynamics.</p>
<p>Relevant articles include <a href="http://www.nature.com/nphys/journal/v9/n6/full/nphys2611.html" rel="nofollow">this one</a> on <a href="http://en.wikipedia.org/wiki/Spin_ice" rel="nofollow">spin ice</a> and <a href="http://www.ncbi.nlm.nih.gov/pubmed/23443563" rel="nofollow">this one</a> on Brownian motion</p>
<p><strong>NOTE:</strong> have not actually read the articles as i do not have access, however mentioned as part of existing literature on the question's subject.</p>
<p>Relevant papers and outlines: <a href="http://www.int.washington.edu/talks/WorkShops/int_11_2c/People/Sondhi_S/sondhi.pdf" rel="nofollow">here</a>, <a href="http://arxiv.org/abs/1005.3557" rel="nofollow">here</a>, <a href="http://phys.org/news/2014-01-physicists-synthetic-magnetic-monopole-years.html" rel="nofollow">here</a> and <a href="http://arxiv.org/abs/0708.1783" rel="nofollow">an arxiv paper</a> by P. Davies on this issue (circa 2007)</p>
<p>UPDATE: An "unorthodox" critical view on mainstream mathematical physics (specifically <a href="http://milesmathis.com/yang.html" rel="nofollow">Yang-Mills theory</a>)</p> | g9199 | [
-0.0011914814822375774,
0.018289493396878242,
-0.004378859885036945,
-0.012024191208183765,
0.06787745654582977,
0.02234291285276413,
0.0022156971972435713,
0.0033396866638213396,
0.01126923318952322,
0.011188192293047905,
-0.03295044228434563,
-0.011320959776639938,
-0.0069506410509347916,
-0.02750561386346817,
-0.009950452484190464,
0.023426681756973267,
0.019273292273283005,
0.013849318958818913,
0.028263604268431664,
-0.027412494644522667,
-0.023214854300022125,
-0.012249876745045185,
0.0459032766520977,
-0.0751044824719429,
-0.044758934527635574,
0.016237597912549973,
0.0246575977653265,
-0.06213532015681267,
-0.03884617239236832,
-0.030621781945228577,
-0.007037718314677477,
-0.032323919236660004,
0.043471284210681915,
-0.08621308207511902,
-0.0342828668653965,
-0.032427165657281876,
0.04872380569577217,
0.037974681705236435,
-0.0031978385522961617,
-0.0012093879049643874,
-0.04629967361688614,
0.03708842769265175,
0.005718271713703871,
-0.014338544569909573,
0.01097386796027422,
-0.022088900208473206,
-0.01139653567224741,
0.014555216766893864,
-0.06986989080905914,
0.015305105596780777,
0.07219331711530685,
0.06293423473834991,
0.08722317218780518,
0.013752412050962448,
-0.0063834101893007755,
-0.020656943321228027,
0.01950034312903881,
-0.0524374321103096,
0.07178293168544769,
0.036579377949237823,
-0.021816596388816833,
0.05620517209172249,
-0.0014870360027998686,
0.03181277960538864,
0.056327901780605316,
-0.03235684707760811,
-0.0258388202637434,
-0.06287780404090881,
0.018318863585591316,
-0.008785700425505638,
0.05260120704770088,
0.0005686248186975718,
-0.01639954000711441,
-0.002808591350913048,
-0.011233694851398468,
0.03611186146736145,
0.11367359012365341,
-0.04210701957345009,
0.00947575457394123,
-0.014774162322282791,
-0.07063651829957962,
-0.0036350740119814873,
0.03857964649796486,
0.0051983194425702095,
0.05538052320480347,
-0.039659444242715836,
0.0058236694894731045,
0.009253553114831448,
-0.03660174831748009,
0.028219545260071754,
-0.04637553542852402,
0.024463970214128494,
0.027527667582035065,
-0.03830115124583244,
0.01696704514324665,
-0.017439499497413635,
0.09544888138771057,
0.03294142335653305,
-0.06877739727497101,
-0.0015566119691357017,
-0.018157292157411575,
-0.014218585565686226,
-0.0011310841655358672,
0.020260581746697426,
0.03118250146508217,
-0.036830320954322815,
0.08500128984451294,
-0.027374600991606712,
-0.015410877764225006,
0.03695738688111305,
-0.0015603118808940053,
0.00005763364606536925,
-0.05102173611521721,
0.050390373915433884,
-0.017794165760278702,
-0.01840793900191784,
0.0383562408387661,
-0.05581226199865341,
-0.0008383470703847706,
0.09572839736938477,
0.03444505110383034,
0.016820702701807022,
0.011766218580305576,
0.09682326018810272,
-0.007887800224125385,
0.0005562775186263025,
-0.017856653779745102,
-0.032856084406375885,
0.015598597005009651,
-0.06884778290987015,
-0.01203656755387783,
-0.034245822578668594,
-0.02787833660840988,
0.02021929994225502,
-0.01971341110765934,
0.037236567586660385,
-0.008085822686553001,
0.027824750170111656,
-0.026063574478030205,
-0.014834340661764145,
-0.010355820879340172,
-0.01262679137289524,
0.03325463831424713,
0.0028005391359329224,
-0.027188345789909363,
0.02533409371972084,
0.004811866208910942,
-0.02161821722984314,
0.00900784507393837,
0.07656759768724442,
0.005852122791111469,
0.046971727162599564,
0.006423162762075663,
0.0041551487520337105,
-0.026233050972223282,
0.021927352994680405,
-0.03427507355809212,
0.032836537808179855,
0.038821715861558914,
-0.04173051938414574,
0.001805021078325808,
-0.06107933819293976,
0.0004821809125132859,
0.03212442994117737,
-0.023394720628857613,
-0.028872234746813774,
0.05357450619339943,
0.0003204013919457793,
0.004287132062017918,
-0.04087183251976967,
-0.04581324756145477,
0.08227618038654327,
0.017156535759568214,
0.04656706005334854,
0.017645230516791344,
0.00469215726479888,
-0.08057320863008499,
-0.020413054153323174,
0.005243352148681879,
-0.045590419322252274,
-0.04768098145723343,
0.03353092074394226,
0.028895055875182152,
-0.014723684638738632,
-0.007591990288347006,
-0.023569824174046516,
0.013028650544583797,
0.04014835134148598,
-0.03557577729225159,
0.02515881508588791,
-0.06055033579468727,
0.024313876405358315,
0.00505475839599967,
0.056291498243808746,
-0.005476587917655706,
-0.05600452423095703,
-0.011476944200694561,
-0.011545772664248943,
-0.023244276642799377,
0.00662628747522831,
0.05922800302505493,
0.013461441732943058,
-0.012873439118266106,
-0.00939827598631382,
-0.010988779366016388,
0.029105104506015778,
0.019349761307239532,
0.0006849095225334167,
0.10194903612136841,
-0.017994871363043785,
-0.011029508896172047,
0.03319251909852028,
-0.02203386276960373,
-0.010175011120736599,
-0.02491001784801483,
-0.045569971203804016,
0.037084873765707016,
0.018853314220905304,
-0.07273726910352707,
0.0002253244601888582,
0.013201138004660606,
-0.010236645117402077,
-0.012171468697488308,
0.0017828085692599416,
-0.01415444165468216,
-0.030190296471118927,
-0.0451645627617836,
-0.04917566478252411,
-0.06363583356142044,
-0.010982916690409184,
-0.032322000712156296,
0.01063169538974762,
0.010248644277453423,
-0.04321446642279625,
0.046732351183891296,
0.06590809673070908,
0.020949365571141243,
-0.014984208159148693,
0.006815832108259201,
0.006961661856621504,
0.007337203714996576,
0.03577671945095062,
-0.0006530801183544099,
0.06104833260178566,
0.017299538478255272,
0.01928592100739479,
0.04806343466043472,
0.03483849763870239,
0.06786483526229858,
0.05148909613490105,
0.06856153905391693,
-0.014713585376739502,
-0.03413869068026543,
0.012944352813065052,
0.013769766315817833,
0.019613565877079964,
0.04895051568746567,
0.029953043907880783,
-0.0582626536488533,
-0.008059995248913765,
0.0337151437997818,
-0.025754448026418686,
-0.020782941952347755,
0.004111407324671745,
-0.02430560626089573,
0.003348172875121236,
-0.01935763657093048,
-0.01598096825182438,
0.014734713360667229,
-0.0016945557435974479,
-0.044452033936977386,
0.03764106705784798,
-0.02046489343047142,
0.009585867635905743,
0.01802212931215763,
0.02349678799510002,
0.029567470774054527,
-0.03042047657072544,
0.05523068457841873,
-0.05427969619631767,
-0.0017605260945856571,
-0.0008761028875596821,
0.003918824717402458,
0.005231557879596949,
0.026653939858078957,
-0.025507567450404167,
-0.05808776617050171,
0.00994481798261404,
-0.006292437668889761,
0.01082045678049326,
0.022956794127821922,
0.010122401639819145,
0.055386871099472046,
-0.01875484548509121,
-0.04334187135100365,
-0.0036070409696549177,
0.007682650350034237,
0.017328334972262383,
0.016136277467012405,
0.005047119688242674,
0.025138046592473984,
0.00006070237577660009,
-0.044222649186849594,
0.04229375720024109,
0.05823933333158493,
0.028394022956490517,
-0.07718762755393982,
-0.09109403192996979,
0.06549349427223206,
0.03683251515030861,
-0.0021056097466498613,
0.07698128372430801,
0.008635609410703182,
0.01935885287821293,
0.004984139930456877,
0.02546735666692257,
-0.05456351488828659,
0.041266098618507385,
0.0654112845659256,
-0.03915855288505554,
-0.012793152593076229,
0.010138117708265781,
0.009753596968948841,
-0.04901415482163429,
0.03602175414562225,
-0.016361329704523087,
-0.013048223219811916,
0.005999894812703133,
0.0226203091442585,
0.010448901914060116,
0.02315743826329708,
-0.012168779037892818,
0.0033326412085443735,
-0.03595532104372978,
-0.09725000709295273,
-0.022640027105808258,
0.014295095577836037,
-0.03167709708213806,
-0.03149527683854103,
-0.01788794994354248,
-0.004619678016752005,
-0.05290321260690689,
-0.007991875521838665,
0.012235261499881744,
0.005868295207619667,
0.03785419836640358,
-0.03303021937608719,
0.016776420176029205,
-0.0155201256275177,
-0.010599570348858833,
0.07207972556352615,
0.03481096401810646,
0.05106665566563606,
0.07582906633615494,
-0.022952543571591377,
0.024642659351229668,
0.05514195188879967,
0.010461577214300632,
0.0007058175397105515,
0.0018934473628178239,
-0.049299389123916626,
0.04137035086750984,
0.06865148991346359,
-0.0312969908118248,
0.007365526631474495,
0.0817522257566452,
-0.06489820033311844,
-0.014012543484568596,
0.011900567449629307,
-0.01669817790389061,
0.01989961788058281,
-0.011432097293436527,
-0.021562593057751656,
-0.021878957748413086,
0.0363541878759861,
0.06055411696434021,
0.02340404875576496,
0.020741291344165802,
-0.10010571777820587,
0.0452420599758625,
-0.011679809540510178,
0.004642661195248365,
0.06545710563659668,
0.06809011846780777,
0.015460960566997528,
-0.00993240438401699,
-0.039387308061122894,
0.021252568811178207,
-0.0004863338253926486,
-0.03724779933691025,
-0.052882760763168335,
0.05275042727589607,
-0.012022028677165508,
0.012257114052772522,
0.002104878891259432,
-0.0019445145735517144,
-0.05568550527095795,
-0.07341025769710541,
0.03153376653790474,
-0.0014190999791026115,
0.0245249904692173,
0.006501906551420689,
0.008868415839970112,
-0.028745532035827637,
-0.029017679393291473,
-0.0341433621942997,
0.05076386779546738,
-0.012178316712379456,
0.019332069903612137,
-0.046314798295497894,
-0.017052866518497467,
0.016768528148531914,
0.03964393585920334,
-0.029555339366197586,
0.027540991082787514,
-0.026850206777453423,
-0.012683283537626266,
-0.04779968783259392,
0.007034403271973133,
-0.014739744365215302,
0.01122601144015789,
-0.012121313251554966,
0.002059448743239045,
-0.04838814213871956,
-0.04403410479426384,
0.02538428269326687,
0.023766783997416496,
-0.06730807572603226,
-0.07867850363254547,
-0.05063442140817642,
-0.034344904124736786,
0.026977207511663437,
0.00034164669341407716,
-0.008426613174378872,
0.004554919432848692,
0.035062260925769806,
-0.022626714780926704,
0.02697755955159664,
-0.0041002933867275715,
0.024668870493769646,
0.033985428512096405,
0.03821196034550667,
0.05305619165301323,
0.0009129464742727578,
0.00996475387364626,
-0.022825228050351143,
-0.059744007885456085,
0.011316620744764805,
-0.04302029311656952,
0.0004468040424399078,
0.015193005092442036,
0.0379023477435112,
-0.029924888163805008,
0.020383216440677643,
-0.052099231630563736,
-0.02196383848786354,
-0.021905934438109398,
0.033884815871715546,
-0.00017151160864159465,
-0.020841317251324654,
0.006802219431847334,
-0.046483512967824936,
0.037340689450502396,
-0.05300987511873245,
0.0357850082218647,
0.005372591316699982,
0.02548583596944809,
-0.034055572003126144,
-0.0667487308382988,
-0.0901847556233406,
-0.028210585936903954,
0.04492660239338875,
0.018738750368356705,
0.04126386716961861,
0.03452629595994949,
0.015725484117865562,
0.0174898412078619,
-0.0208408422768116,
-0.03240315243601799,
-0.03541409969329834,
-0.04167115315794945,
0.045878857374191284,
-0.005415196530520916,
-0.02430831268429756,
0.04236670956015587,
0.0018570503452792764,
-0.015660008415579796,
0.0660712867975235,
-0.034785401076078415,
0.016268784180283546,
-0.033067796379327774,
0.029001997783780098,
-0.014978120103478432,
0.0005894222413189709,
-0.01646393910050392,
-0.010006708092987537,
-0.029799843207001686,
0.038741253316402435,
-0.04413741081953049,
0.02519890107214451,
-0.06405455619096756,
0.012469038367271423,
-0.008267940953373909,
-0.00654450710862875,
0.005848517641425133,
0.05262279510498047,
0.0692315325140953,
0.035822778940200806,
0.03889011591672897,
-0.0671134665608406,
0.010878810659050941,
-0.017453769221901894,
-0.02052890509366989,
0.021181343123316765,
0.040981683880090714,
0.07753308117389679,
-0.04185393080115318,
-0.03595898672938347,
0.00860658846795559,
-0.0891929566860199,
0.023024143651127815,
-0.009583122096955776,
0.0436612106859684,
-0.03069082461297512,
-0.06029464304447174,
0.01185481809079647,
-0.03033718466758728,
-0.041720833629369736,
0.014184614643454552,
0.08212029188871384,
-0.004939040169119835,
-0.0019885669462382793,
0.06031060218811035,
-0.000789735815487802,
-0.0024916809052228928,
-0.07977256923913956,
-0.027736935764551163,
-0.04696034640073776,
-0.006538082379847765,
0.020439129322767258,
0.04617498815059662,
-0.009494932368397713,
0.058349840342998505,
0.053240593522787094,
-0.01670750230550766,
-0.021137753501534462,
0.00425243005156517,
-0.06819925457239151,
0.03688279166817665,
-0.040898397564888,
-0.04069187492132187,
0.006843572482466698,
0.0059215533547103405,
0.01727581024169922,
0.022563105449080467,
0.02295403555035591,
-0.008205877617001534,
-0.04036276414990425,
0.03316676616668701,
-0.02657787688076496,
0.01511533372104168,
0.030832963064312935,
0.033191803842782974,
0.03399939835071564,
-0.056357480585575104,
-0.0026594330556690693,
0.05839664116501808,
-0.013491556979715824,
0.04776537045836449,
0.07561880350112915,
0.039228904992341995,
0.036927662789821625,
0.03501543402671814,
-0.015409340150654316,
0.006412571761757135,
-0.03310728818178177,
-0.021777832880616188,
-0.04173841327428818,
0.022624114528298378,
-0.010991054587066174,
0.023538971319794655,
0.039897482842206955,
0.043109916150569916,
-0.05082489177584648,
-0.01113731600344181,
0.05352858826518059,
-0.04345881938934326,
0.04054417461156845,
-0.028982672840356827,
-0.03191927820444107,
0.011094448156654835,
-0.04097171127796173,
-0.06299296766519547,
0.02084564045071602,
0.018180914223194122,
-0.07172103971242905,
-0.028415214270353317,
-0.002008038805797696,
-0.030749762430787086,
0.07776607573032379,
0.010255624540150166,
-0.01238747127354145,
-0.025648340582847595,
0.019645169377326965,
-0.011016113683581352,
0.02894533984363079,
-0.03359421715140343,
0.014275441877543926,
-0.004316343460232019,
0.0077122715301811695,
-0.04452923312783241,
0.004148608539253473,
-0.017278216779232025,
0.013914697803556919,
-0.006872368510812521,
-0.051688894629478455,
-0.051555126905441284,
0.010142787359654903,
-0.05252516269683838,
-0.005838886369019747,
-0.03348877280950546,
-0.02267622947692871,
-0.04387186840176582,
-0.05053494870662689,
0.009605194441974163,
-0.012180815450847149,
-0.020695043727755547,
0.051430877298116684,
0.06624165177345276,
0.04349861666560173,
-0.004355955868959427,
0.006473982706665993,
0.008479047566652298,
0.028132105246186256,
-0.007657196838408709,
0.017234502360224724,
-0.008152471855282784,
-0.05481383576989174,
0.05458233505487442,
-0.017120515927672386,
-0.08938751369714737,
0.02308490313589573,
0.04715803265571594,
0.023654816672205925,
0.002733121160417795,
-0.011596731841564178,
-0.016811033710837364,
0.04561617225408554,
-0.05233881622552872,
0.0017322162166237831,
-0.007140632718801498,
0.004946250468492508,
-0.027360927313566208,
-0.006394858006387949,
-0.0471312440931797,
-0.01654471829533577,
-0.0163252130150795,
-0.020337965339422226,
0.043476130813360214,
0.006322067696601152,
-0.01822984218597412,
0.021122604608535767,
0.0056040361523628235,
-0.04817377030849457,
-0.04546268284320831,
0.0335596427321434,
-0.006657897494733334,
-0.037973713129758835,
-0.014998313039541245,
-0.048394326120615005,
-0.026011843234300613,
-0.038626011461019516,
0.018001530319452286,
-0.010191124863922596,
-0.019284667447209358,
0.026486637070775032,
0.0030138231813907623,
-0.06589564681053162,
0.013720819726586342,
-0.007928261533379555,
0.04040087014436722,
-0.032066211104393005,
-0.01484686229377985,
-0.008755539543926716,
-0.005532866809517145,
0.03381500020623207,
-0.036244358867406845,
0.04989613592624664,
0.015001599676907063,
0.07529846578836441,
-0.013305596075952053,
-0.01652604341506958,
0.04201663285493851,
0.010062893852591515,
0.007304750382900238,
0.039212390780448914,
0.027982890605926514,
0.014125118963420391,
-0.0420512817800045,
-0.018753396347165108,
0.015171408653259277,
-0.0012474267277866602,
-0.06268807500600815,
-0.034929364919662476,
0.028517546132206917,
0.00097657588776201,
0.03126784786581993,
0.012980654835700989,
-0.07784995436668396,
0.06331927329301834,
-0.005964892450720072,
0.04599572718143463,
0.026696667075157166,
0.03163886070251465,
0.048525337129831314,
-0.0030243524815887213,
-0.0699056088924408,
-0.00350030860863626,
0.00722534442320466,
0.01324229035526514,
-0.06838947534561157,
-0.006306635681539774,
-0.04735919460654259,
-0.04786147549748421,
-0.05168365314602852,
-0.03020145185291767,
0.007226618006825447,
0.015655197203159332,
-0.02273898757994175,
-0.015281980857253075,
-0.00859110988676548,
0.027739306911826134,
-0.032703764736652374,
-0.02225419692695141,
-0.08557595312595367,
-0.012531436048448086,
0.007549619767814875,
-0.0350341796875,
0.040537215769290924,
-0.03699697181582451,
0.017239177599549294,
-0.012968955561518669,
0.07739245891571045,
-0.019939281046390533,
0.004280030727386475,
-0.001141166896559298,
-0.03892500326037407,
0.01862926036119461,
-0.01969347707927227,
0.0051298378966748714,
-0.048181720077991486,
0.006016850471496582,
-0.01899304799735546,
-0.04178225249052048,
0.07378604263067245,
-0.006176592782139778,
0.008568975143134594,
0.06813658773899078,
-0.016616441309452057,
0.037770096212625504,
-0.015653841197490692,
-0.001083679380826652,
0.011505447328090668,
0.05513465777039528,
-0.0674457773566246,
0.016863292083144188,
-0.04330684617161751,
0.040642544627189636
] |
<p>I'm aware of the so-called <a href="http://en.wikipedia.org/wiki/Refractive_index#Group_index" rel="nofollow">group index</a> but why is the phase velocity used in the <a href="http://en.wikipedia.org/wiki/Refractive_index#Definition" rel="nofollow">standard definition</a> of the index of refraction? What advantage does this offer?</p> | g9200 | [
0.007063641212880611,
0.024914106354117393,
-0.004979064222425222,
-0.02474231645464897,
0.036859914660453796,
-0.018888838589191437,
0.06589507311582565,
0.02283475361764431,
-0.03252900019288063,
-0.019387176260352135,
0.043946728110313416,
0.026765676215291023,
0.01496011670678854,
0.010693601332604885,
-0.022910643368959427,
-0.04258614778518677,
0.04424870386719704,
0.04397876560688019,
0.033341407775878906,
0.016307512298226357,
0.009358505718410015,
-0.021438902243971825,
-0.06438571214675903,
-0.023448482155799866,
0.06108124181628227,
0.02474704198539257,
0.008880624547600746,
-0.0911438912153244,
-0.09848751127719879,
-0.02187950164079666,
0.013171708211302757,
-0.0009928670478984714,
0.05893731117248535,
-0.044900696724653244,
0.029792165383696556,
-0.0013153937179595232,
0.02431858889758587,
0.018396662548184395,
0.024434300139546394,
0.00213443860411644,
0.0029099900275468826,
0.050240494310855865,
0.015723012387752533,
-0.006618880666792393,
0.050141509622335434,
0.002363580511882901,
-0.03138137608766556,
-0.052121348679065704,
-0.027069807052612305,
-0.014226991683244705,
0.04336925968527794,
0.030838092789053917,
0.00862698070704937,
0.027435610070824623,
0.05882015451788902,
0.006502203177660704,
-0.055701691657304764,
0.0517902635037899,
0.029224466532468796,
-0.008459650911390781,
-0.012093430384993553,
0.030310366302728653,
-0.003710607998073101,
0.023564152419567108,
0.012125469744205475,
-0.014293446205556393,
-0.015664368867874146,
-0.0001662709837546572,
0.0239413995295763,
-0.015350679866969585,
-0.024901028722524643,
-0.0014158482663333416,
-0.03752846270799637,
0.004828004166483879,
-0.07716170698404312,
0.0012591644190251827,
-0.029646581038832664,
-0.02396012842655182,
0.006756601855158806,
0.020584803074598312,
0.01921183615922928,
-0.051128629595041275,
-0.01448519341647625,
-0.03237537667155266,
0.020077545195817947,
0.06318942457437515,
0.030524948611855507,
-0.02215803973376751,
0.04706143960356712,
-0.004544593393802643,
0.016541633754968643,
-0.024616098031401634,
0.01798725314438343,
0.08098181337118149,
-0.006871511228382587,
0.06767115741968155,
-0.033336885273456573,
0.07509197294712067,
0.008052595891058445,
0.03586333245038986,
-0.012361540459096432,
0.006732818204909563,
-0.0036768855061382055,
-0.0008611304219812155,
0.041555024683475494,
-0.019422167912125587,
0.015060856938362122,
0.013114796951413155,
-0.017164820805191994,
0.02648327872157097,
-0.0575360469520092,
-0.0006120946491137147,
0.006166067440062761,
-0.009911012835800648,
-0.027555352076888084,
-0.03756265714764595,
0.059554215520620346,
-0.0093652019277215,
-0.008980082347989082,
0.022909672930836678,
0.009939177893102169,
0.010753304697573185,
0.013451782055199146,
0.10587918013334274,
-0.021876463666558266,
0.03814595192670822,
0.05806225538253784,
-0.03909085690975189,
0.038150206208229065,
-0.07524005323648453,
-0.03181006759405136,
-0.026505954563617706,
-0.021259211003780365,
-0.009623605757951736,
0.013023355975747108,
0.00823286548256874,
0.04292094707489014,
0.015274086967110634,
-0.05255187675356865,
0.03648843243718147,
-0.004680303391069174,
0.0006094794371165335,
-0.0027423682622611523,
-0.026955991983413696,
-0.0010161387035623193,
-0.010194947011768818,
-0.05995268002152443,
0.007579405792057514,
0.04933081567287445,
0.04843064025044441,
-0.043654534965753555,
0.06866350024938583,
0.02556169591844082,
0.022219249978661537,
-0.03293287381529808,
-0.04344373196363449,
0.022463634610176086,
0.01933136396110058,
-0.028413444757461548,
0.009518600068986416,
0.019763117656111717,
0.0026570186018943787,
0.007445597089827061,
0.006849899422377348,
-0.081024669110775,
-0.035735297948122025,
0.01820380426943302,
-0.01866021938621998,
-0.0029652821831405163,
-0.12608011066913605,
0.022910503670573235,
0.03073391318321228,
-0.005315650254487991,
0.04532076045870781,
-0.027474870905280113,
0.042329736053943634,
0.01753082312643528,
0.03619622066617012,
-0.020080016925930977,
0.05297687277197838,
-0.05634639412164688,
-0.029136603698134422,
0.022081391885876656,
-0.05249232426285744,
0.03445785120129585,
0.04135699197649956,
0.02783430553972721,
-0.04522993043065071,
-0.09927716851234436,
0.03761810436844826,
0.018003389239311218,
-0.05307355895638466,
-0.0351271852850914,
0.04830002412199974,
-0.025528768077492714,
-0.005642977077513933,
-0.034651171416044235,
-0.004194184206426144,
-0.13828855752944946,
0.04421677812933922,
-0.03694206476211548,
-0.005022648721933365,
0.01736828126013279,
0.006327158771455288,
-0.014392038807272911,
-0.024612460285425186,
0.00005552593938773498,
0.0573587603867054,
0.030128784477710724,
-0.016833288595080376,
0.03765236586332321,
0.022853756323456764,
0.03483371064066887,
-0.02150532603263855,
-0.010473129339516163,
0.028809402137994766,
0.0034433985128998756,
0.008662747219204903,
0.00033783979597501457,
0.028971517458558083,
-0.015218258835375309,
0.022220298647880554,
-0.01327265240252018,
0.016006315127015114,
-0.045665815472602844,
-0.04011296108365059,
-0.020076530054211617,
-0.002769656013697386,
0.021457212045788765,
0.012047852389514446,
-0.026528801769018173,
0.0014377767220139503,
-0.06129418686032295,
0.011599586345255375,
-0.006080397870391607,
0.028917420655488968,
0.03315218910574913,
0.030198389664292336,
-0.030500907450914383,
0.07897203415632248,
0.05866570398211479,
-0.05458555743098259,
-0.05192143842577934,
-0.040431149303913116,
-0.005621693097054958,
-0.0359746478497982,
0.034553658217191696,
-0.04667571559548378,
-0.002918252255767584,
0.03188346326351166,
-0.012847946025431156,
-0.004722756799310446,
0.004819471854716539,
-0.0335003100335598,
0.01106064859777689,
0.03989814966917038,
-0.04889737069606781,
0.037239108234643936,
-0.0649067685008049,
-0.019249852746725082,
0.009971524588763714,
0.004698548000305891,
0.02155882865190506,
-0.04870247468352318,
-0.020486755296587944,
0.019104434177279472,
0.010612028650939465,
0.0574670135974884,
0.00857422687113285,
-0.010442893952131271,
0.008094822987914085,
0.042118966579437256,
0.021410752087831497,
-0.03110647387802601,
-0.03513107821345329,
0.010195109061896801,
0.030449261888861656,
0.001418994041159749,
0.005213830154389143,
-0.014083486050367355,
-0.009400379844009876,
-0.02659001387655735,
-0.01756277121603489,
-0.0049819559790194035,
-0.005170351359993219,
0.016919951885938644,
0.035127248615026474,
0.04053475707769394,
-0.05239788815379143,
-0.04766474664211273,
-0.011107328347861767,
0.07593884319067001,
0.00518261082470417,
-0.004380508791655302,
0.04342960938811302,
-0.017643984407186508,
0.02301211841404438,
-0.017692802473902702,
0.016849495470523834,
0.021075807511806488,
-0.013857170939445496,
-0.001561453565955162,
-0.009145649150013924,
0.00930249784141779,
0.001061308546923101,
0.02977382019162178,
-0.011983036994934082,
-0.08179029077291489,
-0.04289809986948967,
0.004017968196421862,
0.039873767644166946,
0.062439750880002975,
0.0015629094559699297,
0.041643641889095306,
-0.011505667120218277,
0.020324591547250748,
-0.01884860172867775,
0.008353043347597122,
0.02607927843928337,
0.038023125380277634,
-0.015455145388841629,
-0.026414139196276665,
0.026014430448412895,
-0.008696756325662136,
-0.00782773271203041,
0.013217848725616932,
0.029606759548187256,
0.011580324731767178,
0.045090995728969574,
-0.028873471543192863,
-0.006305788643658161,
-0.007230485789477825,
-0.009826116263866425,
-0.003158795414492488,
-0.03352637588977814,
0.01408747024834156,
-0.015511778183281422,
0.023398254066705704,
0.025494854897260666,
-0.020670605823397636,
0.028481828048825264,
0.004208080470561981,
0.00046506949001923203,
0.0299137681722641,
0.0037066813092678785,
-0.026241904124617577,
0.003381249262019992,
0.05656138435006142,
-0.033715859055519104,
-0.027010532096028328,
0.0035261265002191067,
0.01623285748064518,
0.0019373790128156543,
-0.07036668807268143,
-0.05376851558685303,
0.0026504728011786938,
0.014299267902970314,
0.00048081090790219605,
0.04601050913333893,
-0.00040826635085977614,
0.02639482356607914,
0.03808043152093887,
-0.008600454777479172,
0.053982384502887726,
-0.0020852494053542614,
0.01861957460641861,
-0.0427013598382473,
0.07667176425457001,
-0.05672194063663483,
-0.03679643198847771,
-0.004773817490786314,
-0.06020496040582657,
-0.02601604163646698,
0.020287783816456795,
-0.04984745755791664,
0.05294407159090042,
0.007891206070780754,
-0.01798081211745739,
-0.06024312600493431,
0.0025785707402974367,
0.0058800033293664455,
-0.009641076438128948,
0.023701319471001625,
-0.0014585836324840784,
-0.0038312352262437344,
-0.08562467992305756,
-0.06848308444023132,
-0.03600431978702545,
0.0007825932116247714,
-0.07261442393064499,
0.005550422705709934,
-0.012580540962517262,
0.016349010169506073,
0.02698396146297455,
0.023609280586242676,
0.03752978891134262,
0.00746495695784688,
-0.03422587737441063,
-0.019192315638065338,
0.05571004003286362,
-0.0046100132167339325,
-0.058892738074064255,
0.004134212154895067,
0.028904596343636513,
0.010808432474732399,
0.012987364083528519,
0.04307409003376961,
-0.029419969767332077,
-0.02155604399740696,
-0.05307793244719505,
-0.045974891632795334,
0.06795291602611542,
0.0056311762891709805,
-0.036351095885038376,
0.04593576118350029,
0.09512891620397568,
0.04797428101301193,
-0.04207031801342964,
-0.02913138084113598,
0.034191153943538666,
-0.017325274646282196,
-0.0013547291746363044,
0.012544325552880764,
-0.06086144223809242,
-0.04092458635568619,
0.05227154120802879,
0.03818207606673241,
-0.018426619470119476,
-0.03640349954366684,
-0.05031539872288704,
0.037562884390354156,
0.053609102964401245,
0.02404533140361309,
0.0063627976924180984,
0.007615647744387388,
0.0033159092999994755,
-0.02819468267261982,
0.0705481544137001,
0.028721779584884644,
0.008091844618320465,
0.037551868706941605,
-0.01884027197957039,
-0.02638884261250496,
-0.0262928307056427,
-0.01832854375243187,
0.034629128873348236,
-0.014233085326850414,
-0.010492177680134773,
-0.10596095770597458,
0.0063814581371843815,
0.03010752983391285,
0.03453891724348068,
-0.03882410377264023,
0.0058687408454716206,
-0.0332556888461113,
0.0005306144594214857,
-0.05445476993918419,
-0.026206325739622116,
0.012463354505598545,
-0.0027243474032729864,
-0.11214538663625717,
0.05311029031872749,
-0.01722099632024765,
-0.05108897015452385,
0.06777267903089523,
0.01451091654598713,
0.004804594907909632,
-0.057533640414476395,
-0.0658479854464531,
-0.026057906448841095,
0.017921220511198044,
-0.06485765427350998,
0.003714001737535,
0.03474092110991478,
0.08138050138950348,
0.025559350848197937,
0.029233679175376892,
-0.005956277251243591,
-0.030021080747246742,
-0.03254516050219536,
-0.05010191351175308,
0.028153933584690094,
0.09257835149765015,
-0.028511852025985718,
0.05281723663210869,
-0.002737984759733081,
-0.07208926975727081,
0.011091072112321854,
-0.033848732709884644,
-0.0018471709918230772,
-0.021997470408678055,
-0.024415351450443268,
-0.021321648731827736,
-0.02358420379459858,
-0.013623910956084728,
-0.02771182917058468,
0.10061633586883545,
-0.012435967102646828,
-0.029495546594262123,
-0.04956074431538582,
-0.0708327367901802,
0.024480851367115974,
0.0396062470972538,
0.011414112523198128,
-0.005749245639890432,
0.0596543587744236,
0.06525185704231262,
-0.000434858346125111,
0.03821096941828728,
-0.003139980835840106,
0.022532645612955093,
-0.07169689238071442,
0.014563501812517643,
-0.04732932895421982,
0.03825410082936287,
0.008624574169516563,
0.023677842691540718,
-0.01859808713197708,
-0.019635826349258423,
-0.0400431789457798,
0.0024707098491489887,
-0.011200690641999245,
0.005595352966338396,
-0.015072480775415897,
0.013942585326731205,
-0.0434555858373642,
-0.06653585284948349,
-0.0038079090882092714,
0.01928211748600006,
0.017540423199534416,
0.0022494709119200706,
-0.04130721464753151,
0.11487693339586258,
0.0013883844949305058,
0.028833292424678802,
-0.0388810895383358,
0.01778894104063511,
-0.009686221368610859,
-0.000701849116012454,
-0.026516776531934738,
-0.12147506326436996,
0.054971445351839066,
-0.0007069298881106079,
0.051187820732593536,
0.011792332865297794,
-0.006295374594628811,
0.03132832422852516,
-0.04376840218901634,
-0.03453146293759346,
0.007406233809888363,
0.032088302075862885,
-0.028066759929060936,
0.07359285652637482,
-0.021915040910243988,
-0.012030739337205887,
0.025833746418356895,
0.022817613556981087,
0.010895074345171452,
-0.005525518208742142,
-0.032989103347063065,
0.04648671671748161,
0.034748345613479614,
-0.018914828076958656,
0.04060892388224602,
0.020309163257479668,
-0.030506674200296402,
0.015157502144575119,
0.050722625106573105,
0.008506818674504757,
0.005779240280389786,
-0.06128368154168129,
0.007425508927553892,
-0.017942221835255623,
0.005071680061519146,
-0.0013982849195599556,
0.03142225742340088,
-0.06558690965175629,
-0.04173126444220543,
-0.0297256987541914,
0.016601113602519035,
-0.02896149829030037,
-0.03255622088909149,
0.014862132258713245,
-0.008342576213181019,
-0.0067722550593316555,
-0.0648144781589508,
-0.0038399973418563604,
-0.012032472528517246,
0.04661806672811508,
0.02955303154885769,
-0.035495854914188385,
0.0015458917478099465,
-0.04191787540912628,
-0.022068368270993233,
-0.04648492485284805,
0.005069063510745764,
-0.03249529376626015,
0.06948147714138031,
-0.026664825156331062,
0.019609667360782623,
0.047802433371543884,
-0.048768043518066406,
0.049728259444236755,
0.004984525963664055,
0.05232783779501915,
0.017659831792116165,
0.0010566130513325334,
-0.004271689336746931,
0.04030919447541237,
0.015436896122992039,
-0.0188456904143095,
0.060233838856220245,
-0.004646968562155962,
0.006612113676965237,
-0.04667828977108002,
-0.000861291540786624,
-0.032741956412792206,
-0.0031789210624992847,
0.0048965588212013245,
-0.032582566142082214,
0.015664473176002502,
-0.08186414837837219,
0.012011097744107246,
0.02626761607825756,
0.05184631422162056,
0.013876610435545444,
-0.05296965688467026,
0.014363929629325867,
-0.017804009839892387,
0.0076509807258844376,
0.027354629710316658,
0.014935878105461597,
-0.011807015165686607,
0.018057353794574738,
-0.03184054046869278,
-0.005577013362199068,
-0.10292922705411911,
0.03275572881102562,
0.05597122758626938,
0.023287709802389145,
0.03413412347435951,
0.06590203940868378,
0.01967620477080345,
0.005881199147552252,
-0.043522585183382034,
-0.031063666567206383,
0.008633453398942947,
-0.007857320830225945,
-0.06740064173936844,
-0.04325688257813454,
-0.03827023506164551,
-0.027798673138022423,
-0.03796906769275665,
0.07463674992322922,
-0.01934744231402874,
0.058032989501953125,
-0.012301391921937466,
0.04450024291872978,
0.04554598778486252,
-0.014913561753928661,
-0.03477334603667259,
-0.004002812318503857,
0.015748340636491776,
-0.019980406388640404,
-0.025837482884526253,
0.012112122029066086,
-0.007914490066468716,
-0.026173586025834084,
0.03263542056083679,
0.01233946718275547,
0.0511496402323246,
0.06225193291902542,
0.0030180972535163164,
-0.0796390175819397,
0.020065056160092354,
-0.0064706322737038136,
-0.04067810997366905,
-0.01192912645637989,
-0.036445822566747665,
0.009719399735331535,
0.021578935906291008,
0.06083299219608307,
0.07930469512939453,
-0.008866913616657257,
-0.05934504047036171,
0.03609699383378029,
-0.03489435836672783,
0.04400304704904556,
0.095436230301857,
-0.003202492604032159,
0.03273696079850197,
-0.016187718138098717,
0.0016906745731830597,
-0.011463969945907593,
-0.015346894040703773,
-0.005772057455033064,
0.02118672989308834,
0.017779221758246422,
-0.033819280564785004,
0.006478502415120602,
-0.0010844115167856216,
-0.005265568383038044,
0.0019325425382703543,
0.0215152557939291,
0.06916436553001404,
0.004932538606226444,
0.014540853910148144,
0.008275283500552177,
-0.021750643849372864,
-0.014033248648047447,
-0.027206962928175926,
-0.035209935158491135,
0.040773794054985046,
0.009084288962185383,
-0.037985265254974365,
0.025071121752262115,
-0.014965451322495937,
0.01882641389966011,
-0.05709037557244301,
0.02803395688533783,
0.026085903868079185,
-0.07350718975067139,
0.028508896008133888,
-0.03429410234093666,
-0.038033150136470795,
0.0035113946069031954,
0.02016627788543701,
0.04149642586708069,
-0.021676862612366676,
-0.04581218585371971,
-0.004252259619534016,
-0.022201552987098694,
-0.0620880052447319,
0.04962056502699852,
-0.054099928587675095,
0.015942951664328575,
0.05436435714364052,
-0.01891562156379223,
-0.0030704308301210403,
0.07742450386285782,
0.03590044006705284,
-0.0017819113563746214,
0.026246869936585426,
-0.01366772223263979,
-0.01671423763036728,
-0.03083900362253189,
0.019356049597263336,
0.060210227966308594,
-0.02477436140179634,
-0.05194398760795593,
0.01972798816859722,
0.02630353346467018,
0.015554064884781837,
0.0042913225479424,
0.026182115077972412,
-0.022549428045749664,
0.008364899083971977,
-0.010513830929994583,
-0.015692222863435745,
-0.006435237359255552,
0.03977561742067337,
-0.0037143519148230553,
0.020797763019800186,
-0.016494369134306908,
-0.04840018227696419,
-0.04252536967396736,
-0.018524331972002983,
-0.009624352678656578
] |
<p>Sorry, since the question has been posed, but I insist that others posed not from this position.</p>
<p>Can any listener deduce whether we could measure, by analyzing electromagnetic disturbance, a particle$^1$ traveling faster than light? (or current measuring device, for the sake of assuming for questioning)</p>
<p>Studying to understand cosmic rays, inductance, and capture technologies by the artifacts of Tesla.. The name most studied by us uneducated electrical folk.</p>
<p>--</p>
<p>$^1$ For the 2011 OPERA neutrino experiment, see <a href="http://physics.stackexchange.com/q/14968/2451">this</a> Phys.SE post.</p> | g9201 | [
-0.03591861203312874,
0.039306625723838806,
0.011113807559013367,
-0.00002872064032999333,
0.06133250147104263,
0.01652533933520317,
0.01857569068670273,
0.043476659804582596,
0.004894129931926727,
0.006593951489776373,
0.029330138117074966,
0.05849099159240723,
0.03173636645078659,
0.028309017419815063,
-0.03710955008864403,
-0.0078050605952739716,
0.08220863342285156,
-0.004973473493009806,
0.04400114715099335,
0.04212774708867073,
0.07131752371788025,
0.01622045785188675,
-0.02672339789569378,
-0.04514247924089432,
0.02364673838019371,
-0.015401692129671574,
-0.008339832536876202,
-0.012585949152708054,
-0.03942706435918808,
-0.018988121300935745,
-0.015274563804268837,
-0.07005934417247772,
0.03533480688929558,
-0.025348860770463943,
-0.02677471563220024,
-0.04935130104422569,
0.0017690665554255247,
0.021983008831739426,
0.02544676698744297,
0.03332068771123886,
0.014163210988044739,
-0.0019311322830617428,
-0.008413249626755714,
-0.007733047474175692,
0.019536983221769333,
0.02611793391406536,
0.017166664823889732,
-0.009300779551267624,
0.0009246849804185331,
-0.05113256350159645,
-0.050829291343688965,
-0.01107043493539095,
0.06905491650104523,
0.08815748244524002,
-0.01311478205025196,
-0.013308098539710045,
0.02039269544184208,
-0.03920672833919525,
0.15263649821281433,
0.03767451271414757,
0.029824884608387947,
-0.037167277187108994,
0.01942867785692215,
-0.016535107046365738,
0.015670165419578552,
-0.013233616016805172,
-0.05014742538332939,
-0.0037376796826720238,
0.015570603311061859,
-0.044439010322093964,
0.06318704038858414,
-0.019545311108231544,
0.006015854887664318,
0.03492783010005951,
0.01951027475297451,
0.05296846851706505,
0.023844173178076744,
-0.0109397042542696,
0.002251910511404276,
0.016720477491617203,
-0.057684123516082764,
0.003398440545424819,
0.003023413708433509,
0.05816905200481415,
0.11047746986150742,
-0.05999748036265373,
-0.022411812096834183,
0.041211847215890884,
0.04854338988661766,
-0.009590484201908112,
0.006980690639466047,
-0.08935623615980148,
0.04067899286746979,
-0.026790305972099304,
0.04605880379676819,
-0.02159702777862549,
0.01987091265618801,
0.004430718254297972,
-0.011365711688995361,
-0.01299460232257843,
-0.011810217052698135,
-0.01713566854596138,
-0.06808175146579742,
-0.0004994233604520559,
0.009696437045931816,
0.006337060127407312,
-0.006626637652516365,
-0.046573348343372345,
-0.022042082622647285,
-0.025197161361575127,
0.028489241376519203,
-0.04992855712771416,
-0.011422188021242619,
-0.01572919636964798,
-0.019731920212507248,
-0.04883590340614319,
0.022658122703433037,
-0.008449964225292206,
-0.041919149458408356,
0.05175730213522911,
-0.011964850127696991,
0.020526081323623657,
-0.01448045950382948,
0.06413588672876358,
-0.08217854797840118,
0.042066581547260284,
0.0038587062153965235,
0.009946925565600395,
0.021677488461136818,
0.03815976902842522,
-0.09223033487796783,
-0.011475710198283195,
0.0168447382748127,
0.008214789442718029,
0.0033266933169215918,
0.011822468601167202,
0.061128370463848114,
-0.01631099358201027,
-0.03553255274891853,
0.0017548868199810386,
0.037062905728816986,
-0.027423642575740814,
0.02312801219522953,
-0.03142109140753746,
0.012390793301165104,
0.01667671464383602,
-0.01789160817861557,
0.018335651606321335,
-0.0028145681135356426,
0.03758807107806206,
0.024652568623423576,
0.03454677760601044,
-0.009858336299657822,
-0.055552758276462555,
0.04819115623831749,
0.003773517208173871,
0.02940686047077179,
0.03088177740573883,
-0.02234959788620472,
0.02427341416478157,
0.024356195703148842,
0.017004339024424553,
-0.03565225005149841,
0.04289116710424423,
0.015378337353467941,
-0.039742205291986465,
0.0455174557864666,
-0.017477290704846382,
0.019611654803156853,
-0.1056172102689743,
-0.08251511305570602,
-0.0069198585115373135,
0.04166867956519127,
0.0351809523999691,
0.009319577366113663,
0.06475090235471725,
0.0060984427109360695,
-0.051933031529188156,
-0.025099795311689377,
0.0031566324178129435,
-0.04084418714046478,
-0.017470983788371086,
-0.0240510031580925,
-0.04954691231250763,
-0.03702302277088165,
-0.0065579223446547985,
-0.07646305114030838,
-0.006910114083439112,
-0.016842542216181755,
-0.004502361174672842,
-0.013970192521810532,
-0.052088234573602676,
-0.02144959196448326,
0.026926716789603233,
-0.0012185340747237206,
-0.0323273204267025,
0.007076336070895195,
-0.023335931822657585,
-0.001195236574858427,
-0.0037567426916211843,
-0.005182958208024502,
0.05430047959089279,
0.08086702227592468,
-0.007381046190857887,
0.01596427522599697,
-0.062169864773750305,
-0.024606920778751373,
-0.03205159306526184,
0.010520240291953087,
-0.05907483026385307,
0.07049887627363205,
0.019326958805322647,
-0.018419282510876656,
0.009993268176913261,
-0.05810845270752907,
-0.052436161786317825,
0.015419135801494122,
-0.007162256632000208,
0.013122857548296452,
0.009356778115034103,
-0.05705063417553902,
0.007569137495011091,
0.04593559727072716,
-0.008066533133387566,
-0.05391841009259224,
-0.014183399267494678,
-0.03701057657599449,
-0.019683189690113068,
-0.028179088607430458,
0.00030445822631008923,
-0.10085617005825043,
0.08012829720973969,
-0.014283622615039349,
0.002190583385527134,
0.06237849220633507,
0.08510696142911911,
-0.008738329634070396,
-0.03991568088531494,
-0.0015935326227918267,
-0.0034713326022028923,
0.02090631239116192,
0.0019758797716349363,
-0.023669760674238205,
0.019556593149900436,
0.013190058059990406,
-0.037805311381816864,
-0.0281138326972723,
0.025087926536798477,
0.0017001081723719835,
-0.03002583049237728,
-0.023886732757091522,
0.024476774036884308,
0.022776907309889793,
0.0038910668808966875,
0.015036608092486858,
-0.0635606050491333,
0.031319648027420044,
0.054982855916023254,
-0.03467630594968796,
0.012019543908536434,
0.0060651120729744434,
0.0033900400158017874,
0.035638391971588135,
-0.02270263433456421,
0.050838809460401535,
-0.03429781273007393,
-0.03002438321709633,
0.015117483213543892,
-0.05670998618006706,
-0.02042890526354313,
-0.08952926844358444,
0.011896731331944466,
0.002978576347231865,
0.0021391131449490786,
-0.0020242822356522083,
-0.04001004993915558,
0.015530621632933617,
0.01212469395250082,
0.027464887127280235,
-0.019712021574378014,
-0.07271157205104828,
0.02630891092121601,
-0.05257304757833481,
-0.027667833492159843,
-0.0083263348788023,
-0.044014282524585724,
-0.04536299780011177,
-0.027333535254001617,
-0.02936043031513691,
0.007997239008545876,
-0.04930301755666733,
-0.05459979176521301,
0.019359616562724113,
-0.0045415498316287994,
-0.026334248483181,
0.025056278333067894,
0.028549404814839363,
-0.008454075083136559,
0.0447966642677784,
-0.010810481384396553,
0.08150149881839752,
-0.014266704209148884,
-0.008126589469611645,
-0.007989803329110146,
-0.0028351263608783484,
-0.0053987349383533,
0.00493563711643219,
0.0035485869739204645,
0.017133112996816635,
-0.024807097390294075,
-0.022028082981705666,
0.04793090745806694,
0.026425961405038834,
0.010589247569441795,
0.017920978367328644,
-0.02006671391427517,
0.008616513572633266,
0.029701897874474525,
0.011259758844971657,
0.0292141642421484,
0.05822214111685753,
-0.03527885675430298,
-0.01314566284418106,
-0.0003560448531061411,
0.03539325296878815,
-0.020624404773116112,
-0.015539119020104408,
0.08354794234037399,
-0.042991604655981064,
-0.029566539451479912,
-0.020226383581757545,
-0.05356714501976967,
0.0016148753929883242,
-0.013973121531307697,
0.00030658108880743384,
-0.02439712919294834,
0.02496938966214657,
0.06665747612714767,
0.06485111266374588,
0.037390027195215225,
-0.08515051007270813,
-0.017975470051169395,
-0.02335778810083866,
-0.005841380916535854,
0.0011500278487801552,
-0.021856708452105522,
-0.04568614810705185,
0.014820094220340252,
0.028337210416793823,
0.017275622114539146,
0.10908107459545135,
0.08349500596523285,
-0.016658032312989235,
-0.03865160420536995,
0.018930893391370773,
0.02767498604953289,
0.032599106431007385,
0.03578373044729233,
-0.018294434994459152,
-0.03203703090548515,
-0.00004398930832394399,
0.0027271301951259375,
0.042975664138793945,
-0.0075690122321248055,
-0.0198077242821455,
-0.0033047113101929426,
-0.030807293951511383,
0.10834424942731857,
-0.008524447679519653,
0.0001410401746397838,
-0.036745063960552216,
0.029076984152197838,
-0.062116749584674835,
0.021131759509444237,
0.023682203143835068,
-0.059952326118946075,
-0.0010232400381937623,
0.022187169641256332,
-0.0021716724149882793,
0.07439396530389786,
-0.020767537876963615,
0.07904574275016785,
0.019315915182232857,
-0.04271961748600006,
-0.003054792992770672,
0.03363988175988197,
-0.044837672263383865,
-0.012603562325239182,
-0.05296774581074715,
-0.0954165831208229,
-0.07575105130672455,
-0.000049619855417404324,
-0.038361188024282455,
0.04265216737985611,
0.027718592435121536,
-0.036370906978845596,
0.01330201979726553,
-0.05398348346352577,
0.025856900960206985,
0.05370832979679108,
0.012286152690649033,
0.017635973170399666,
0.03795372694730759,
0.009823042899370193,
-0.020907729864120483,
-0.002778091002255678,
0.007216071244329214,
-0.028468254953622818,
-0.03655713424086571,
0.00037719530519098043,
-0.06719686836004257,
-0.016699859872460365,
-0.057388849556446075,
-0.061140891164541245,
0.05134138464927673,
0.021334892138838768,
0.01746591366827488,
0.0009091028477996588,
0.09079059958457947,
-0.009521251544356346,
0.036450959742069244,
0.011612778529524803,
0.0131205590441823,
0.010975951328873634,
-0.051080372184515,
0.017990581691265106,
0.013003011234104633,
0.024603744968771935,
-0.0233429204672575,
-0.012251097708940506,
0.04689300060272217,
-0.0015853161457926035,
0.010180276818573475,
0.029109537601470947,
-0.01885419338941574,
0.050268784165382385,
-0.0011423979885876179,
0.05677630379796028,
0.05764510855078697,
0.03345697373151779,
0.053282879292964935,
-0.05618318170309067,
0.05520670861005783,
0.0033335997723042965,
-0.02119342051446438,
0.05296524614095688,
-0.048326753079891205,
0.007000909186899662,
-0.007022623438388109,
0.002642509527504444,
-0.04610852897167206,
-0.028216516599059105,
-0.05344777926802635,
-0.008643971756100655,
-0.014440502971410751,
-0.02928914874792099,
0.035951901227235794,
-0.0319884791970253,
0.05546503886580467,
0.013587918132543564,
-0.04730580002069473,
0.030337795615196228,
0.035343900322914124,
0.015936916694045067,
-0.011700385250151157,
-0.005448789335787296,
-0.06030396744608879,
-0.04660924896597862,
-0.08389121294021606,
-0.0007017124444246292,
-0.034500602632761,
-0.010394589975476265,
0.015285651199519634,
0.02201644890010357,
-0.0003623322118073702,
-0.02092023938894272,
-0.05517074838280678,
0.03407673165202141,
-0.09473933279514313,
-0.027211694046854973,
-0.03162767365574837,
0.007039704360067844,
-0.044830072671175,
-0.008102943189442158,
-0.02361399121582508,
0.017113622277975082,
-0.0846283808350563,
0.04826042801141739,
-0.024917766451835632,
-0.09293042868375778,
-0.013251636177301407,
0.01809081993997097,
0.040277961641550064,
-0.025737978518009186,
0.00008141972648445517,
-0.058695174753665924,
0.01790720596909523,
-0.03523377329111099,
-0.02283453941345215,
-0.03123997524380684,
0.00037131758290342987,
0.008922776207327843,
-0.01855684444308281,
0.03745325654745102,
-0.03673366457223892,
0.043442197144031525,
-0.0026807626709342003,
0.005276919808238745,
-0.01879022642970085,
0.01627945713698864,
-0.02997346967458725,
0.07960163801908493,
0.010425496846437454,
-0.0010499063646420836,
0.00853555928915739,
0.036446865648031235,
0.005535058211535215,
0.03616003692150116,
-0.023561151698231697,
-0.02950480580329895,
-0.008241127245128155,
0.007807598449289799,
0.02956579066812992,
0.004290378652513027,
0.01841941848397255,
0.007330377586185932,
0.00948664266616106,
0.007978714071214199,
0.021873872727155685,
0.028934679925441742,
0.06646707653999329,
-0.006306650582700968,
-0.016106395050883293,
-0.016881641000509262,
-0.00011033847113139927,
-0.012404777109622955,
0.04559412598609924,
-0.02971133217215538,
-0.031579047441482544,
0.022486243396997452,
-0.03643930330872536,
-0.003120315494015813,
0.06561741977930069,
0.06416250020265579,
0.06999850273132324,
-0.024049945175647736,
0.00811227597296238,
0.0009534066775813699,
0.015756292268633842,
-0.03280315920710564,
-0.01982547901570797,
-0.005687490571290255,
-0.011031475849449635,
0.03982210159301758,
-0.02729840762913227,
0.0165717676281929,
0.021580513566732407,
-0.02367902547121048,
-0.043370846658945084,
-0.045655377209186554,
-0.005284533370286226,
-0.006887026596814394,
0.06941799074411392,
-0.0027090373914688826,
0.029292942956089973,
-0.018975794315338135,
-0.007910593412816525,
-0.02515730820596218,
0.02811889536678791,
0.04164807125926018,
-0.018301939591765404,
-0.014916189946234226,
-0.002068483969196677,
-0.004128661472350359,
0.014704379253089428,
0.001775811892002821,
0.013567944057285786,
-0.0029263494070619345,
-0.043475985527038574,
-0.03120991215109825,
-0.0020839665085077286,
-0.0004601040855050087,
0.027240781113505363,
0.0008669698145240545,
0.040454644709825516,
0.04545154049992561,
-0.00440794974565506,
0.05018889158964157,
0.011333923786878586,
-0.005667916499078274,
0.0006411157664842904,
-0.02499028481543064,
0.03041551262140274,
-0.06232987344264984,
-0.07943525910377502,
0.0036486987955868244,
-0.044239263981580734,
-0.00932230707257986,
-0.019759543240070343,
0.0835273489356041,
-0.010501749813556671,
-0.0397232286632061,
-0.022265786305069923,
0.03013233281672001,
0.03038470819592476,
-0.003535205963999033,
0.013414575718343258,
0.015224769711494446,
0.026292571797966957,
-0.055476002395153046,
-0.00809564720839262,
0.017772814258933067,
-0.030256621539592743,
-0.03721163049340248,
-0.04495818167924881,
-0.02931337058544159,
0.0222309697419405,
-0.03911302983760834,
-0.012682952918112278,
0.055183812975883484,
0.016565745696425438,
0.00008960079867392778,
-0.012229458428919315,
0.002610559808090329,
-0.018625520169734955,
0.047668397426605225,
0.012560591101646423,
-0.007760603912174702,
0.011880660429596901,
0.0383303239941597,
-0.023465508595108986,
0.022186698392033577,
0.03584611415863037,
0.0029774403665214777,
0.024876266717910767,
0.028697719797492027,
0.06318990886211395,
0.000761688977945596,
0.04233519360423088,
0.02977324090898037,
0.01696765050292015,
0.012117882259190083,
-0.004080981016159058,
-0.016860684379935265,
-0.06106216460466385,
0.0240238755941391,
0.02857520803809166,
0.045156460255384445,
0.027277646586298943,
-0.0347946472465992,
0.010290682315826416,
0.014802172780036926,
0.013682969845831394,
-0.043869007378816605,
0.0271745752543211,
-0.022457169368863106,
0.022062135860323906,
0.018785424530506134,
0.049962013959884644,
-0.09610237926244736,
-0.044869646430015564,
-0.048143260180950165,
-0.006556560751050711,
0.025056852027773857,
0.018086755648255348,
-0.006479509174823761,
-0.05625000223517418,
-0.014513196423649788,
0.0038729982916265726,
-0.09843488037586212,
0.029844002798199654,
-0.045358821749687195,
0.012735038995742798,
-0.010998516343533993,
-0.01703074760735035,
-0.055341243743896484,
-0.01456840056926012,
-0.0023655532859265804,
0.007741908542811871,
0.01243127603083849,
0.02867870405316353,
-0.0009018236887641251,
0.04550538584589958,
0.017821364104747772,
-0.029002653434872627,
0.014284847304224968,
-0.060358159244060516,
-0.030302848666906357,
0.018992092460393906,
-0.05762896686792374,
-0.03297612816095352,
0.03261625021696091,
0.04345778375864029,
0.012296545319259167,
0.013455739244818687,
-0.01223566010594368,
-0.02086884342133999,
0.06246718019247055,
0.04513710364699364,
0.001053889631293714,
-0.027064364403486252,
0.024567218497395515,
0.02796473167836666,
-0.046893972903490067,
-0.0025382565800100565,
-0.03192218765616417,
0.0189837496727705,
-0.06586946547031403,
-0.06141190975904465,
0.05329078063368797,
-0.00335499900393188,
0.11251651495695114,
-0.04728076606988907,
0.05063960701227188,
0.012982686050236225,
0.004185870289802551,
0.030096745118498802,
-0.00553214643150568,
0.05969155579805374,
0.03517133370041847,
0.05663642659783363,
-0.006381599698215723,
-0.00490438099950552,
-0.0067459698766469955,
-0.004382345359772444,
-0.03283959627151489,
0.0021093343384563923,
0.06365560740232468,
0.008749804459512234,
-0.013131019659340382,
0.023230964317917824,
0.02542264387011528,
-0.015702180564403534,
-0.02041037194430828,
-0.08179249614477158,
0.06461677700281143,
0.03277267888188362,
0.02695724554359913,
-0.028794046491384506,
0.012452973984181881,
-0.02352900430560112,
-0.005967778153717518,
-0.03168570250272751,
-0.005650423001497984,
-0.02018505148589611,
-0.030574021860957146,
-0.006564635317772627,
0.017041493207216263,
-0.01565735600888729,
-0.03348918631672859,
0.005589121952652931,
0.00480263726785779,
-0.04332796856760979,
0.06405528634786606,
0.039592195302248,
-0.008221069350838661,
-0.0019388842629268765,
-0.02587563544511795,
0.02154766581952572,
-0.009236995130777359,
0.025276847183704376,
-0.026967579498887062,
0.007580892648547888,
0.0021104735787957907,
-0.034230589866638184,
-0.022866759449243546,
0.0319458469748497,
-0.03057212196290493
] |
<p>The limit of microscopes is 200nm, but apparently STED improves this according to this coverage of the Kavil prizes 2014 : </p>
<p><a href="http://www.photonics.com/Article.aspx?AID=56255" rel="nofollow">http://www.photonics.com/Article.aspx?AID=56255</a> </p>
<p>What is the current limit for microscopy ? </p> | g9202 | [
-0.013775446452200413,
0.04209931939840317,
0.006082799285650253,
0.010015351697802544,
-0.0005349348648451269,
-0.009980341419577599,
0.02904156781733036,
-0.030042989179491997,
0.005442833993583918,
0.029477009549736977,
0.0845927745103836,
0.019737092778086662,
0.023310638964176178,
-0.021609624847769737,
-0.020276915282011032,
-0.019505059346556664,
0.012599208392202854,
-0.008157090283930302,
-0.020403778180480003,
0.01778215914964676,
-0.04095352813601494,
-0.015173625200986862,
-0.026789316907525063,
-0.047078073024749756,
-0.006299925036728382,
0.08469820022583008,
-0.0006463655736297369,
0.0022035446017980576,
-0.01962682232260704,
0.051462553441524506,
0.06800482422113419,
-0.06566493958234787,
0.0051086475141346455,
0.014833862893283367,
0.029292752966284752,
-0.007933861576020718,
0.03793763741850853,
-0.03302349895238876,
0.01929069310426712,
-0.0030197626911103725,
0.03799723461270332,
-0.018403515219688416,
0.0035240384750068188,
-0.047650594264268875,
-0.012938937172293663,
-0.002974953269585967,
-0.0019917970057576895,
-0.046773511916399,
0.031205864623188972,
-0.09825444221496582,
-0.02394399791955948,
0.03857467323541641,
0.018759051337838173,
0.00760039733722806,
0.005727989599108696,
-0.014229733496904373,
-0.061950795352458954,
0.013420982286334038,
0.048360779881477356,
0.029253730550408363,
-0.010835668072104454,
-0.025560209527611732,
-0.02164197340607643,
-0.03400779142975807,
-0.00924644898623228,
-0.0004448551044333726,
-0.030224014073610306,
-0.058761630207300186,
0.03652806952595711,
0.020167740061879158,
0.031410135328769684,
0.004297398496419191,
-0.03371633589267731,
0.020185578614473343,
-0.031001921743154526,
-0.0005071797640994191,
0.005531946662813425,
0.011567523702979088,
-0.03598149120807648,
0.025468939915299416,
-0.06777350604534149,
-0.04213419929146767,
-0.052880480885505676,
-0.06088106334209442,
0.07099111378192902,
0.006128321867436171,
-0.03941408172249794,
0.035449665039777756,
0.02418210543692112,
0.06573892384767532,
0.03054741583764553,
0.04813431575894356,
-0.0003895880654454231,
0.039715345948934555,
0.023007091134786606,
-0.018147194758057594,
0.048956066370010376,
0.009815936908125877,
-0.010305509902536869,
0.01098852138966322,
0.08209553360939026,
-0.029337815940380096,
0.005084407515823841,
0.04432326927781105,
0.0018425011076033115,
0.0283907949924469,
0.018543727695941925,
-0.052454836666584015,
-0.035021450370550156,
-0.008224339224398136,
-0.0610525868833065,
0.01956617273390293,
-0.10179899632930756,
0.024504126980900764,
-0.05452959984540939,
-0.011816347017884254,
0.02908380515873432,
0.014570116065442562,
-0.02575983665883541,
0.03250668942928314,
0.03313269838690758,
-0.0008322872454300523,
0.053873129189014435,
-0.027220038697123528,
-0.03760889172554016,
0.04356856271624565,
0.027506530284881592,
-0.01079845055937767,
0.022551584988832474,
-0.006367743480950594,
-0.015783576294779778,
0.03606255725026131,
-0.023123471066355705,
0.015689339488744736,
0.03940030559897423,
0.015650374814867973,
-0.03006739541888237,
-0.008772811852395535,
-0.01835065521299839,
0.0020332939457148314,
-0.07780355960130692,
-0.05782218649983406,
0.03916773572564125,
0.03463345766067505,
0.01682901941239834,
-0.06045093759894371,
0.022687824442982674,
0.10555567592382431,
-0.0055266087874770164,
-0.009518950246274471,
-0.003472704440355301,
0.03245442360639572,
0.04213275760412216,
-0.054093681275844574,
-0.026956118643283844,
-0.030505290254950523,
0.014014802873134613,
0.013721023686230183,
-0.04281832277774811,
-0.014341319911181927,
-0.02530156634747982,
0.04110634699463844,
-0.03168373182415962,
-0.03134175017476082,
-0.05290338024497032,
-0.012364030815660954,
-0.0031221318058669567,
-0.027355153113603592,
0.014577625319361687,
-0.09550205618143082,
-0.04980571195483208,
0.02841658517718315,
0.0515945628285408,
-0.024729229509830475,
-0.01747041381895542,
0.007042568176984787,
-0.015827041119337082,
-0.02658802643418312,
-0.003236437449231744,
0.033923715353012085,
-0.004856577143073082,
-0.03636928275227547,
-0.030488789081573486,
-0.019702019169926643,
-0.026363158598542213,
0.014194604009389877,
0.037813443690538406,
-0.03500701114535332,
0.024087464436888695,
0.0042193857952952385,
-0.016750873997807503,
-0.008703574538230896,
-0.04970003664493561,
0.01967647485435009,
-0.022805023938417435,
0.017664127051830292,
0.06955397129058838,
-0.02282836101949215,
0.005363009870052338,
-0.031245732679963112,
0.005233715288341045,
0.047674138098955154,
0.011972183361649513,
0.004294703248888254,
0.07618981599807739,
-0.018197722733020782,
-0.04200616106390953,
0.03759020194411278,
0.026168448850512505,
-0.022405259311199188,
-0.039841193705797195,
0.04817773029208183,
-0.03041679970920086,
0.03050677478313446,
0.008649635128676891,
-0.048245739191770554,
0.022465692833065987,
0.013048009015619755,
0.01193226594477892,
0.014866345562040806,
0.034749895334243774,
0.02882583998143673,
-0.01762709766626358,
0.021476833149790764,
0.011902759782969952,
-0.00759604386985302,
0.026859862729907036,
-0.010405119508504868,
0.004129186738282442,
0.05314979329705238,
-0.07845398783683777,
-0.036643460392951965,
-0.013930127024650574,
-0.05701589956879616,
-0.001706679118797183,
-0.023041341453790665,
-0.020265407860279083,
0.00708740996196866,
-0.0629281997680664,
0.027972791343927383,
0.06766974925994873,
0.01186810526996851,
-0.06571695953607559,
0.012455553747713566,
-0.05579848960042,
-0.010855061002075672,
-0.02769038826227188,
-0.015371984802186489,
0.033829815685749054,
0.045221276581287384,
0.06577621400356293,
-0.005206206347793341,
0.05370992794632912,
0.037004392594099045,
-0.021330691874027252,
-0.02252192609012127,
-0.008715190924704075,
0.08240866661071777,
-0.07798430323600769,
0.0036651070695370436,
0.002793173538520932,
-0.0006010134820826352,
0.060687996447086334,
-0.0347212478518486,
0.021122368052601814,
0.014265251345932484,
-0.044211458414793015,
-0.03318566456437111,
0.0004417127347551286,
-0.008195404894649982,
0.015794647857546806,
0.046892695128917694,
-0.024277517572045326,
0.009487176313996315,
0.009696975350379944,
0.03858037292957306,
-0.017951592803001404,
0.02564011886715889,
0.0007616902585141361,
-0.09812746196985245,
-0.05689989775419235,
-0.04139731451869011,
-0.01768561266362667,
0.03477541729807854,
-0.01708933897316456,
-0.019366517663002014,
-0.009748894721269608,
-0.03747592866420746,
-0.01281743310391903,
0.038751501590013504,
-0.07236579805612564,
0.06043839082121849,
0.04872287064790726,
-0.008500473573803902,
0.003546470310539007,
0.011220035143196583,
0.018241163343191147,
-0.02974475733935833,
0.005232231691479683,
0.059511635452508926,
-0.041564155369997025,
-0.054445818066596985,
-0.0033490252681076527,
0.022061055526137352,
0.05320579931139946,
-0.02833480015397072,
-0.04245701804757118,
-0.039409805089235306,
0.0032241246663033962,
-0.005584374535828829,
0.029069188982248306,
0.012659529224038124,
-0.019326820969581604,
-0.0022193780168890953,
-0.03507128357887268,
0.0004759987350553274,
0.03693758323788643,
0.015741849318146706,
-0.032012809067964554,
0.03312397375702858,
-0.001389266806654632,
-0.017504217103123665,
-0.009288327768445015,
-0.04767614230513573,
0.011532742530107498,
0.016590431332588196,
0.020197508856654167,
-0.017263144254684448,
-0.05732859671115875,
0.0425136536359787,
0.04906515032052994,
0.0073758987709879875,
-0.03288501873612404,
0.02004747837781906,
0.016717011108994484,
0.005709797143936157,
-0.020159875974059105,
0.007493138778954744,
0.04556164890527725,
-0.022955920547246933,
-0.02684023417532444,
0.03942395746707916,
-0.06133764982223511,
-0.05897983908653259,
0.07272101193666458,
0.029199721291661263,
-0.08167470991611481,
0.009365323930978775,
-0.015038719400763512,
-0.02389291301369667,
0.013437877409160137,
0.03587079420685768,
0.005530918948352337,
-0.011348985135555267,
-0.017145298421382904,
0.06722831726074219,
0.01976964809000492,
0.06813252717256546,
0.04902402684092522,
-0.04569683223962784,
0.07338093221187592,
-0.008708612993359566,
0.035307709127664566,
-0.07397031038999557,
-0.0267234668135643,
-0.022670108824968338,
-0.004545517731457949,
0.05551540479063988,
0.034363240003585815,
-0.008860455825924873,
-0.05083073303103447,
-0.05562836676836014,
-0.015321043320000172,
0.04258785769343376,
-0.08317016065120697,
0.006966756656765938,
-0.03187855705618858,
0.021666843444108963,
-0.0031493688002228737,
0.015715189278125763,
-0.031529344618320465,
0.001014058361761272,
0.038632720708847046,
-0.06699977815151215,
-0.03788841888308525,
0.025920046493411064,
-0.026373887434601784,
-0.025499491021037102,
-0.06374930590391159,
-0.013411697931587696,
-0.042413581162691116,
0.0004909331328235567,
0.01064685732126236,
-0.004069558344781399,
-0.07023072987794876,
-0.01143549382686615,
0.023888129740953445,
0.0003428750205785036,
-0.0023456921335309744,
-0.020434489473700523,
0.084357850253582,
0.024344980716705322,
-0.046102896332740784,
0.005825370084494352,
0.013954101130366325,
0.012423871085047722,
-0.013870337046682835,
0.03282514214515686,
-0.00474562868475914,
-0.00784303992986679,
0.014549942687153816,
0.02312266081571579,
0.030123909935355186,
-0.007386218756437302,
0.07498221099376678,
-0.009165977127850056,
-0.04878490790724754,
-0.033685892820358276,
0.029580824077129364,
0.05751641094684601,
0.014596162363886833,
0.017047325149178505,
-0.03380361944437027,
0.014572687447071075,
0.018284043297171593,
0.02001717872917652,
-0.05127466097474098,
-0.02509087137877941,
-0.009553845971822739,
-0.06581737101078033,
0.019657742232084274,
-0.0018127313815057278,
-0.017848307266831398,
0.014582459814846516,
-0.010148383677005768,
0.044153135269880295,
-0.012861060909926891,
0.007535963319242001,
0.020751237869262695,
-0.005661124363541603,
0.00047172699123620987,
0.014237366616725922,
0.061457559466362,
0.009189176373183727,
0.009365340694785118,
0.02471649833023548,
0.023689022287726402,
-0.02762545272707939,
-0.02542962320148945,
0.025725385174155235,
-0.025192083790898323,
-0.024645596742630005,
0.005631216336041689,
-0.017955757677555084,
0.02324901707470417,
-0.03161480650305748,
-0.034777119755744934,
0.04658479243516922,
0.03943007439374924,
0.026692038401961327,
-0.03892718255519867,
0.049492839723825455,
-0.014141193591058254,
-0.0005696058506146073,
0.07091619074344635,
-0.00764349102973938,
-0.061877425760030746,
-0.037618238478899,
-0.05049619451165199,
-0.060046032071113586,
0.001612821826711297,
-0.022611897438764572,
0.036169350147247314,
0.05628172308206558,
-0.028369395062327385,
-0.02463141828775406,
0.031189104542136192,
-0.038818228989839554,
0.006749359890818596,
-0.05137830227613449,
-0.009587557055056095,
-0.018803466111421585,
-0.010059836320579052,
0.011312516406178474,
0.023987125605344772,
0.046426836401224136,
-0.046686600893735886,
0.029003961011767387,
-0.02452104166150093,
-0.06603654474020004,
-0.0009464529575780034,
0.045982103794813156,
-0.04412006959319115,
-0.01706368662416935,
-0.041445400565862656,
0.030713172629475594,
0.05838187411427498,
-0.040104106068611145,
-0.006095967721194029,
0.02076786756515503,
0.04885338991880417,
0.005936799105256796,
-0.04121873900294304,
-0.05679267644882202,
-0.030207298696041107,
0.05642688274383545,
-0.01075624581426382,
-0.05105084925889969,
-0.049183715134859085,
-0.011334125883877277,
0.007094566244632006,
-0.03878708556294441,
0.007089839782565832,
0.00924719963222742,
-0.019952258095145226,
-0.003448012052103877,
-0.007257284130901098,
0.021929336711764336,
-0.03313375636935234,
-0.07552272081375122,
-0.005345666315406561,
-0.05010354518890381,
0.04713992029428482,
-0.040753159672021866,
-0.0060975453816354275,
-0.024028293788433075,
-0.05084140971302986,
0.012635232880711555,
0.07301361858844757,
-0.010726838372647762,
0.02059750445187092,
-0.012198363430798054,
0.0024800098035484552,
-0.026531696319580078,
0.029864225536584854,
0.04459449648857117,
0.029050035402178764,
0.04098310321569443,
-0.026366181671619415,
-0.030768368393182755,
0.03973855823278427,
-0.017409656196832657,
0.021947598084807396,
0.07954247295856476,
0.08113060891628265,
-0.04478367790579796,
0.07405722886323929,
-0.048355668783187866,
0.0583699531853199,
-0.04708272963762283,
0.04470270499587059,
-0.010472975671291351,
0.004495071712881327,
0.011554544791579247,
0.010855688713490963,
0.020455999299883842,
0.005948315374553204,
-0.07056262344121933,
-0.032616496086120605,
0.021176407113671303,
0.04657604172825813,
0.01225136686116457,
-0.0037823303136974573,
-0.011558502912521362,
-0.04587240517139435,
-0.04754959046840668,
-0.04826795682311058,
-0.0003936951979994774,
0.004732921253889799,
0.012552674859762192,
0.017857816070318222,
-0.017547639086842537,
0.025511514395475388,
0.0035893891472369432,
0.05063549429178238,
0.03654218465089798,
0.0022228562738746405,
-0.0030191843397915363,
-0.037768781185150146,
-0.07570616900920868,
-0.0054518114775419235,
0.050718534737825394,
0.01234058290719986,
-0.021075580269098282,
-0.0000444496727141086,
0.02806592360138893,
0.023628361523151398,
0.008530063554644585,
0.09041880816221237,
-0.03658686950802803,
0.005461975932121277,
-0.08114667981863022,
0.0014324963558465242,
-0.012642666697502136,
0.004743206314742565,
-0.010470964014530182,
0.03428575396537781,
-0.0000535343679075595,
-0.04290463775396347,
0.08440098911523819,
0.05384163558483124,
0.009940964169800282,
0.0172836072742939,
0.02097746543586254,
0.03605135530233383,
0.03151382878422737,
-0.06667255610227585,
0.018246691673994064,
0.04587273672223091,
0.0011224793270230293,
-0.03149624168872833,
-0.050852950662374496,
-0.044524598866701126,
0.038334183394908905,
0.00547183770686388,
-0.033705856651067734,
0.0006866830517537892,
-0.020112130790948868,
-0.08326573669910431,
0.03153033182024956,
0.022284962236881256,
0.0031687060836702585,
-0.06944215297698975,
-0.01891007088124752,
-0.02699958346784115,
0.026149433106184006,
0.037839293479919434,
0.010748837143182755,
0.03987172618508339,
0.007333309389650822,
0.01943683624267578,
-0.012843893840909004,
-0.017320547252893448,
0.01093041431158781,
-0.010989408940076828,
0.03827908635139465,
-0.012664124369621277,
-0.04104907810688019,
0.030459458008408546,
0.024384239688515663,
0.0395323745906353,
-0.03783932700753212,
0.026487739756703377,
0.019976846873760223,
0.020188752561807632,
0.016406100243330002,
-0.008395924232900143,
0.07136703282594681,
0.0062486701644957066,
-0.02030051313340664,
0.030615614727139473,
-0.007184856105595827,
-0.08697745949029922,
0.030316755175590515,
-0.056015923619270325,
0.006455672904849052,
0.04655152186751366,
-0.011850422248244286,
0.08904216438531876,
-0.026993539184331894,
-0.019512055441737175,
0.0051847295835614204,
0.0006081922329030931,
-0.05472928658127785,
0.040306996554136276,
0.03007051721215248,
-0.014448505826294422,
-0.05128219723701477,
0.0114784836769104,
-0.0030191713012754917,
0.07406500726938248,
0.0115271657705307,
-0.014322510920464993,
-0.04694833979010582,
-0.006727644242346287,
0.014571883715689182,
0.011073540896177292,
0.012931454926729202,
-0.05449046194553375,
0.04269138723611832,
0.021748315542936325,
-0.012553082779049873,
0.07836513966321945,
-0.017987877130508423,
-0.007160451728850603,
-0.01629549078643322,
-0.0068350122310221195,
0.004587956238538027,
0.058680709451436996,
-0.00036326146801002324,
0.004817812703549862,
-0.01781204529106617,
-0.045074597001075745,
-0.006744343787431717,
0.0392368845641613,
0.018377790227532387,
0.00025424789055250585,
0.014276653528213501,
0.05589102953672409,
0.04040731489658356,
-0.0596277117729187,
0.002436742652207613,
0.02227182127535343,
0.018235884606838226,
-0.023391714319586754,
0.04548386484384537,
-0.02466433309018612,
-0.02209819108247757,
0.058657899498939514,
-0.0364309661090374,
-0.06893395632505417,
0.019559824839234352,
-0.00966904778033495,
0.006548565346747637,
0.055049218237400055,
0.017901215702295303,
0.01553705520927906,
-0.03987114876508713,
0.025814056396484375,
-0.006411115173250437,
-0.0032939801458269358,
0.020196979865431786,
-0.026546206325292587,
-0.01925434172153473,
-0.017409024760127068,
-0.01052254717797041,
0.08462641388177872,
-0.018113382160663605,
-0.01603962853550911,
-0.033247992396354675,
-0.028220003470778465,
0.039380110800266266,
-0.03987788408994675,
-0.01877487078309059,
-0.06229346990585327,
0.016443656757473946,
0.0676608607172966,
0.04547729715704918,
-0.03214229643344879,
-0.007027038838714361,
0.015401653945446014,
-0.013789098709821701,
-0.029328159987926483,
-0.0030136103741824627,
-0.006687906105071306,
0.0289924219250679,
-0.040632396936416626,
-0.08177796006202698,
0.0477815605700016,
0.05853350833058357,
-0.004072085488587618,
0.042244311422109604,
0.06341680139303207,
0.043246690183877945,
0.019583096727728844,
-0.08713690936565399,
0.0597115233540535,
-0.007659468799829483,
0.02951650135219097,
0.01813555508852005,
0.026894979178905487,
0.002088183304294944,
0.09324543923139572,
0.06971381604671478,
-0.020168786868453026,
-0.014871655032038689,
-0.03694586828351021,
-0.04289044067263603
] |
<p>I have searched the internet and have not found any actual test results.</p> | g9203 | [
0.013843074440956116,
-0.0020333584398031235,
0.024640250951051712,
-0.0011341103818267584,
0.013247686438262463,
0.006513661239296198,
-0.024415893480181694,
0.011493117548525333,
0.04009001702070236,
-0.03658147528767586,
-0.03666924312710762,
-0.03888406604528427,
-0.032560788094997406,
-0.0031547967810183764,
-0.04849880188703537,
-0.031560249626636505,
0.08338961005210876,
0.02023838646709919,
-0.03199167177081108,
0.050598666071891785,
0.039696719497442245,
0.002950250171124935,
-0.002378307282924652,
0.02177410013973713,
-0.019417526200413704,
-0.009719551540911198,
-0.07846373319625854,
0.07599609345197678,
-0.10178104043006897,
-0.0081892479211092,
0.006444153375923634,
-0.0030285210814327,
0.02469002455472946,
-0.033061131834983826,
-0.029236454516649246,
0.026478489860892296,
0.051643483340740204,
0.034564509987831116,
0.006517807487398386,
-0.006483001168817282,
-0.06958699971437454,
0.02254599891602993,
0.014585861004889011,
0.021635401993989944,
0.008251109160482883,
0.01895519345998764,
0.010941674932837486,
0.03704485669732094,
0.01302864495664835,
-0.07241551578044891,
-0.020995039492845535,
0.02857576124370098,
0.11240582168102264,
-0.0117409136146307,
-0.011727049015462399,
0.016253145411610603,
-0.03740113228559494,
0.015645457431674004,
0.007172256242483854,
0.012118062935769558,
0.026992186903953552,
0.007805393077433109,
0.023290950804948807,
-0.0009720282978378236,
0.029966026544570923,
-0.00877766776829958,
0.02375761605799198,
-0.04848216474056244,
-0.002174261724576354,
-0.008523862808942795,
0.010393444448709488,
-0.046619124710559845,
0.019495302811264992,
0.0163702592253685,
-0.07048419862985611,
-0.08401315659284592,
-0.014478941448032856,
0.01740262284874916,
-0.023109573870897293,
0.03343484178185463,
0.03343814238905907,
-0.0464928038418293,
-0.06252516806125641,
0.013557874597609043,
-0.0006958528538234532,
-0.039497315883636475,
0.006888092961162329,
-0.018722612410783768,
0.03289564698934555,
-0.01128035131841898,
0.016402894631028175,
0.04256454110145569,
-0.046402525156736374,
0.043139051645994186,
0.08962039649486542,
0.022730296477675438,
0.012475316412746906,
0.040313635021448135,
-0.020393144339323044,
-0.01577715016901493,
-0.0246238075196743,
0.053228165954351425,
0.030228694900870323,
-0.01940804533660412,
0.007081878371536732,
0.02327163703739643,
0.02328854613006115,
-0.05376853793859482,
0.00980814266949892,
0.013252370990812778,
-0.03436676412820816,
0.03764677420258522,
-0.03154882416129112,
-0.0060752686113119125,
0.06349610537290573,
-0.04213063418865204,
-0.025037545710802078,
0.017379503697156906,
-0.010886860080063343,
-0.039403051137924194,
0.06978065520524979,
0.05837540701031685,
0.0031322254799306393,
0.06891681253910065,
0.016903262585401535,
-0.023089906200766563,
0.022765886038541794,
-0.03654256835579872,
-0.007709397468715906,
0.03696705400943756,
-0.03201863914728165,
-0.002624219050630927,
0.013435589149594307,
-0.0323946587741375,
0.015370245091617107,
-0.04767609387636185,
0.0247658584266901,
0.012446066364645958,
-0.014893066138029099,
-0.041919153183698654,
-0.02862776629626751,
-0.024685952812433243,
0.042654313147068024,
0.031080972403287888,
0.045400287955999374,
-0.038702741265296936,
0.028100252151489258,
0.05296752601861954,
0.01823900267481804,
0.019331781193614006,
0.004286072216928005,
-0.046589165925979614,
0.037825603038072586,
0.010410073213279247,
-0.0551811158657074,
-0.027479825541377068,
-0.010074450634419918,
0.027531471103429794,
0.02251186966896057,
0.04609522596001625,
-0.009937899187207222,
-0.005919268354773521,
0.008041970431804657,
-0.015879902988672256,
-0.010567199438810349,
-0.04687468335032463,
-0.028621472418308258,
0.04823044314980507,
0.029051348567008972,
-0.038792915642261505,
-0.03731601685285568,
-0.005945551209151745,
0.020902805030345917,
0.04329083114862442,
-0.03482148051261902,
0.055255625396966934,
0.014248156920075417,
0.00885417778044939,
0.027444986626505852,
-0.0017638826975598931,
0.010177786462008953,
0.027498602867126465,
0.0006012314115650952,
-0.021681295707821846,
0.0051154145039618015,
-0.017070122063159943,
-0.025190912187099457,
0.015519509091973305,
-0.0008121636346913874,
-0.03706769272685051,
0.018969587981700897,
-0.012328408658504486,
-0.0026291438844054937,
-0.058365970849990845,
0.03600364923477173,
0.019025752320885658,
-0.006652836222201586,
-0.033184830099344254,
0.02094443142414093,
-0.012407181784510612,
0.03475829213857651,
0.07049445062875748,
0.002536770887672901,
0.025135386735200882,
-0.05840834602713585,
-0.14042185246944427,
0.015458974055945873,
-0.030901942402124405,
0.019882727414369583,
0.039830468595027924,
-0.014749592170119286,
-0.005578966811299324,
0.03285963833332062,
0.03347150236368179,
0.010566651821136475,
0.03144896775484085,
-0.018399091437458992,
0.017809202894568443,
-0.035396259278059006,
0.018611298874020576,
0.012209064327180386,
0.03692440688610077,
-0.04118126630783081,
-0.027721870690584183,
-0.018779946491122246,
0.013930571265518665,
0.034741904586553574,
-0.01945677399635315,
0.015842068940401077,
-0.0067010363563895226,
0.01666109263896942,
-0.051091667264699936,
0.041842471808195114,
-0.048356618732213974,
-0.03479546681046486,
0.042612746357917786,
0.0025297263637185097,
-0.030632611364126205,
-0.016874801367521286,
0.022137248888611794,
-0.04249320551753044,
-0.0431441105902195,
-0.013011354021728039,
0.07313216477632523,
0.04861479997634888,
-0.03213951364159584,
0.013808304443955421,
-0.0012635554885491729,
-0.013613687828183174,
0.06036366522312164,
0.005989281926304102,
0.09515953063964844,
0.0192197784781456,
0.03370523825287819,
-0.018772372975945473,
-0.006519383285194635,
0.009613852947950363,
-0.053219545632600784,
0.025431040674448013,
0.0015613860450685024,
-0.02466081827878952,
0.01084027998149395,
0.006516412831842899,
-0.006832474377006292,
-0.016284584999084473,
-0.06587473303079605,
-0.01804601401090622,
-0.0822564885020256,
0.017844080924987793,
0.051209744065999985,
0.051534149795770645,
-0.006660072598606348,
0.01910240575671196,
0.06875487416982651,
-0.018578743562102318,
-0.000028467426091083325,
-0.02100534364581108,
-0.008203485980629921,
0.027275394648313522,
-0.037061017006635666,
0.012665494345128536,
-0.03143588453531265,
0.009924594312906265,
0.03589252009987831,
-0.010797426104545593,
-0.006510757375508547,
-0.031097520142793655,
-0.01238210778683424,
0.005316757597029209,
0.015779880806803703,
-0.035528503358364105,
-0.020968234166502953,
0.06145298480987549,
0.007214815355837345,
-0.014890219084918499,
-0.01254371926188469,
0.0925324484705925,
-0.02014283277094364,
0.018425235524773598,
0.030805129557847977,
0.052181679755449295,
-0.010687431320548058,
-0.01427886076271534,
0.029386378824710846,
0.012105169706046581,
0.029015149921178818,
0.04263656586408615,
-0.0007270165951922536,
0.04364188015460968,
-0.0058464426547288895,
-0.02361632138490677,
0.037777941673994064,
0.07306176424026489,
-0.0212906114757061,
0.030795900151133537,
0.044067274779081345,
0.007744215428829193,
0.024393122643232346,
0.0307559072971344,
0.02560790255665779,
0.06067207455635071,
-0.0033839019015431404,
-0.02201424166560173,
0.013374904170632362,
-0.007388247177004814,
-0.04811928793787956,
0.004938831087201834,
0.0019681293051689863,
0.010090027004480362,
0.01778315380215645,
0.0008632858516648412,
0.06599145382642746,
0.0027801969554275274,
-0.01316164992749691,
-0.021319609135389328,
-0.005993244703859091,
-0.03823276236653328,
0.051844533532857895,
-0.029947102069854736,
-0.011611180379986763,
0.020365776494145393,
-0.03251788392663002,
-0.0010521644726395607,
0.024332115426659584,
-0.012728719040751457,
-0.00317854480817914,
-0.027698375284671783,
0.035227373242378235,
-0.002553267404437065,
0.021296430379152298,
0.043124448508024216,
-0.014324648305773735,
-0.03201615810394287,
-0.06272761523723602,
0.029832232743501663,
0.015036546625196934,
-0.016526076942682266,
0.014607878401875496,
-0.029452158138155937,
0.005084550473839045,
-0.006151480600237846,
0.008860244415700436,
0.05305284261703491,
-0.03297991678118706,
0.07958699762821198,
0.0923929214477539,
0.012728813104331493,
0.04916393384337425,
0.00248325290158391,
0.01620299555361271,
-0.017834894359111786,
0.03091154247522354,
0.07881505787372589,
0.049925267696380615,
0.033638812601566315,
0.028712473809719086,
-0.013183049857616425,
0.01430257223546505,
-0.04929198697209358,
0.01318648736923933,
0.07421500980854034,
-0.03323923051357269,
-0.014331272803246975,
0.005154752638190985,
0.014486650936305523,
-0.04613611847162247,
-0.010365428403019905,
-0.023319454863667488,
0.03921574354171753,
-0.0058665103279054165,
-0.020975539460778236,
-0.03116203099489212,
-0.08514152467250824,
0.028182292357087135,
-0.008372185751795769,
-0.09330525994300842,
0.034292370080947876,
0.032035209238529205,
-0.0688101127743721,
-0.04067421704530716,
-0.006800821051001549,
-0.0010066073155030608,
-0.000499399087857455,
0.02764715999364853,
-0.012350880540907383,
-0.013068058528006077,
-0.029983043670654297,
0.07605553418397903,
0.009518212638795376,
0.01957545429468155,
-0.0005203363834880292,
0.04932095855474472,
0.0322268009185791,
-0.020593205466866493,
-0.004804188851267099,
-0.006913441698998213,
0.02106008119881153,
-0.040620457381010056,
-0.02074664644896984,
-0.03361226245760918,
-0.03332674130797386,
0.023549307137727737,
-0.028479641303420067,
-0.007519764360040426,
-0.03430744633078575,
-0.004022801294922829,
-0.056094467639923096,
0.036246445029973984,
0.03780222684144974,
0.036358751356601715,
-0.024376150220632553,
-0.06988954544067383,
-0.038078416138887405,
0.019179588183760643,
0.0002954204101115465,
0.07299160212278366,
-0.03874057158827782,
0.02648974023759365,
0.010897628031671047,
0.03357769548892975,
-0.022135283797979355,
0.03123020939528942,
0.0014279845636337996,
0.07023604214191437,
0.028113435953855515,
0.09302739799022675,
-0.0008937397506088018,
-0.03163750097155571,
0.018741900101304054,
-0.03746096044778824,
0.009017542004585266,
0.00007815658318577334,
-0.046900782734155655,
-0.038399819284677505,
-0.031024187803268433,
0.011299417354166508,
-0.029141830280423164,
0.030502188950777054,
-0.02635267563164234,
0.04039639234542847,
-0.05617300420999527,
-0.044964343309402466,
0.04253840073943138,
0.012752903625369072,
0.02608003281056881,
0.025041095912456512,
-0.020906811580061913,
0.0116817532107234,
-0.015779046341776848,
-0.008431440219283104,
-0.03152650594711304,
-0.043080441653728485,
0.06934903562068939,
0.007408087607473135,
-0.01435176096856594,
0.0439826138317585,
-0.012390026822686195,
-0.008349021896719933,
-0.04084809124469757,
0.0502423495054245,
-0.0326138399541378,
0.019520435482263565,
-0.04708634316921234,
-0.025782879441976547,
0.02197706699371338,
0.01968109793961048,
-0.06584537774324417,
0.0449800007045269,
0.0898708775639534,
-0.055228907614946365,
0.019770070910453796,
0.020611828193068504,
-0.01017953734844923,
-0.08238295465707779,
-0.017833556979894638,
-0.05050445720553398,
-0.08686061203479767,
-0.0524819977581501,
-0.06564107537269592,
0.05747593939304352,
-0.0527949221432209,
-0.049462951719760895,
-0.003779667429625988,
0.050917934626340866,
-0.008107785135507584,
-0.026370108127593994,
0.02281518094241619,
0.011582511477172375,
-0.0931820496916771,
0.0035157075617462397,
-0.04909345880150795,
-0.032641179859638214,
0.005682427901774645,
0.019523251801729202,
-0.006418142933398485,
0.019780272617936134,
0.003909638151526451,
0.027716390788555145,
-0.046370040625333786,
-0.007656944915652275,
0.00014595375978387892,
-0.007371635641902685,
0.0137733593583107,
-0.03364485502243042,
0.018457738682627678,
0.002576075494289398,
-0.007327955681830645,
-0.04046656936407089,
0.05275093391537666,
-0.06265190988779068,
-0.03400197625160217,
0.010788698680698872,
0.05859585478901863,
-0.006832682527601719,
-0.006535044871270657,
-0.029574492946267128,
0.017988504841923714,
-0.001523145125247538,
-0.04490644484758377,
-0.03748953342437744,
-0.012814593501389027,
0.04762262850999832,
-0.008779400959610939,
-0.0148383853957057,
-0.020480968058109283,
0.06744875758886337,
-0.058203015476465225,
0.0023907674476504326,
-0.006048110779374838,
-0.06800803542137146,
0.008033357560634613,
0.001411916920915246,
-0.05120819807052612,
-0.014616052620112896,
0.029071243479847908,
0.006113502196967602,
0.040875695645809174,
-0.031167326495051384,
0.028401503339409828,
-0.00807367917150259,
0.052022784948349,
-0.010733972303569317,
-0.04968801885843277,
0.00019818304281216115,
0.014220648445189,
-0.013083520345389843,
-0.014807326719164848,
0.02035599946975708,
0.007302506826817989,
-0.07124880701303482,
-0.02852512151002884,
0.01860412023961544,
-0.001794574549421668,
-0.028336727991700172,
0.030652180314064026,
-0.02952253445982933,
0.01585301011800766,
-0.0002761695650406182,
0.021152684465050697,
-0.03993505984544754,
0.061787236481904984,
-0.018275916576385498,
-0.008917449973523617,
0.07279324531555176,
0.028272321447730064,
-0.0280549768358469,
0.032431647181510925,
0.03556891530752182,
-0.08443762362003326,
0.009219742380082607,
-0.01804792881011963,
0.03223656490445137,
-0.04787318408489227,
-0.03051164373755455,
-0.021486541256308556,
-0.02472078427672386,
-0.041891925036907196,
0.11032669246196747,
0.03187449276447296,
-0.013995085842907429,
-0.024577107280492783,
-0.04010118171572685,
-0.00783616490662098,
-0.05653438717126846,
-0.05387738719582558,
-0.040812861174345016,
0.013405350968241692,
0.03638160228729248,
-0.062456898391246796,
0.028554948046803474,
-0.08252579718828201,
0.03710569813847542,
0.02265310101211071,
0.007650486659258604,
-0.0076415883377194405,
-0.0061224340461194515,
0.020580440759658813,
0.005155580583959818,
0.048675742000341415,
-0.026351142674684525,
0.06542761623859406,
-0.04459591582417488,
0.0008093773503787816,
-0.050640691071748734,
0.020712528377771378,
-0.002964361570775509,
0.008149005472660065,
-0.002488869009539485,
-0.01280289888381958,
-0.056455209851264954,
-0.029970109462738037,
-0.03903736546635628,
-0.05110880360007286,
-0.051202982664108276,
-0.01374240592122078,
0.05304713174700737,
-0.0037512241397053003,
-0.01696242392063141,
0.08950980752706528,
0.014774414710700512,
0.01771635189652443,
0.02846452407538891,
-0.022010697051882744,
-0.0536482147872448,
-0.03784404695034027,
0.011533170007169247,
0.007762484718114138,
0.036889951676130295,
-0.025090904906392097,
-0.037337467074394226,
0.04300139099359512,
0.0037683884147554636,
0.00874923262745142,
0.01481303945183754,
-0.01790573075413704,
0.032796815037727356,
0.0620168074965477,
-0.008287610486149788,
-0.011964047327637672,
-0.06227409094572067,
0.013405789621174335,
-0.06252359598875046,
-0.02216007560491562,
0.00394916208460927,
-0.02937960997223854,
0.014881657436490059,
-0.033656973391771317,
-0.03380000963807106,
0.050496842712163925,
-0.06266234070062637,
0.037572313100099564,
0.061330415308475494,
-0.04002637043595314,
-0.003806854598224163,
0.01929023303091526,
0.03366316482424736,
0.016024621203541756,
0.035315725952386856,
-0.022145239636301994,
-0.005227688699960709,
-0.06251437216997147,
0.03729604184627533,
-0.01019962877035141,
0.009141883812844753,
0.03256336972117424,
-0.019266372546553612,
-0.10265910625457764,
-0.0742383673787117,
0.04555622115731239,
0.08889869600534439,
-0.014221549965441227,
0.016049876809120178,
0.006324356887489557,
-0.07215195149183273,
0.02633250318467617,
-0.04218655452132225,
-0.03596239537000656,
0.014778132550418377,
-0.02816081792116165,
0.026127783581614494,
0.001845993218012154,
0.04108940064907074,
-0.04138576239347458,
0.0235629603266716,
-0.05325610190629959,
0.016606267541646957,
-0.0014852533349767327,
0.008168398402631283,
-0.04077699035406113,
0.03806205093860626,
0.019491270184516907,
0.000911720038857311,
0.004552299156785011,
0.014080899767577648,
0.0240534245967865,
0.013083068653941154,
-0.06892240047454834,
0.01951153762638569,
-0.005883616860955954,
0.005453224293887615,
-0.009403880685567856,
-0.034809377044439316,
0.045444734394550323,
0.032665472477674484,
-0.05408772453665733,
-0.0047332122921943665,
0.011463652364909649,
0.047241341322660446,
0.00831054151058197,
0.023411305621266365,
-0.015894729644060135,
-0.02549489215016365,
0.008402897045016289,
-0.04328492656350136,
-0.04326019808650017,
0.0016439349856227636,
0.03852454945445061,
0.024048011749982834,
0.04489077627658844,
0.07714690268039703,
-0.01170351542532444,
-0.00827923696488142,
-0.0341326929628849,
0.0033935431856662035,
0.057280272245407104,
-0.026076793670654297,
0.05307905003428459,
0.044011086225509644,
0.021832764148712158,
0.022963499650359154,
-0.0013138713547959924,
0.036052484065294266,
-0.01117215771228075,
0.05714290216565132,
0.005036571063101292,
-0.005602295510470867,
-0.019783074036240578,
-0.0494401678442955,
0.06198563054203987,
-0.01888079009950161,
-0.01687898300588131,
-0.056338656693696976,
-0.015640443190932274,
0.01203759852796793,
-0.03454863652586937,
-0.05341674014925957,
0.017028074711561203,
-0.09873444586992264
] |
<p>While deriving lagrange's equation, for an infinitesimal displacement $\vec{dr}$, we express it using taylor series in terms of general coordinates as $\frac{\vec{dr}}{dq} \delta q$. Where $\frac{\vec{dr}}{dq}$ means derivative of $\vec{r}$. What does it mean?(this derivative term). What is the function whose derivative we are taking ?</p> | g9204 | [
0.07230836153030396,
-0.010771837085485458,
-0.007302758749574423,
-0.05469128489494324,
-0.004909745883196592,
0.046433400362730026,
0.06201387941837311,
0.03260335698723793,
-0.03702884539961815,
-0.05090762674808502,
-0.035915520042181015,
0.014112835749983788,
0.08143869787454605,
-0.019277431070804596,
0.02548942342400551,
0.0034920729231089354,
-0.012427751906216145,
0.017736991867423058,
-0.006391802337020636,
-0.013216708786785603,
-0.03923092782497406,
0.034821365028619766,
-0.0014987799804657698,
-0.022627606987953186,
0.07977159321308136,
-0.06170793995261192,
0.045083533972501755,
0.015075217932462692,
-0.07836046814918518,
0.001766106579452753,
-0.02031073346734047,
0.049465421587228775,
0.007797917816787958,
0.03991284221410751,
-0.04974043741822243,
-0.015415504574775696,
0.019473712891340256,
0.0024959633592516184,
0.057738807052373886,
-0.07249888777732849,
-0.024384744465351105,
0.018507592380046844,
0.018674666061997414,
0.025271225720643997,
0.020029671490192413,
0.0024409457109868526,
-0.05811947211623192,
-0.04131355509161949,
-0.000609781825914979,
0.01816231571137905,
0.012798665091395378,
0.020683404058218002,
0.004609227180480957,
-0.010007619857788086,
-0.02270524390041828,
0.027779322117567062,
0.06415815651416779,
-0.0051321168430149555,
-0.017267940565943718,
-0.0008946245070546865,
-0.015758421272039413,
-0.08752982318401337,
-0.03864632174372673,
-0.015516091138124466,
0.053744126111269,
-0.09029528498649597,
-0.03506749868392944,
-0.014202272519469261,
0.03756192699074745,
-0.04185202345252037,
0.054902467876672745,
-0.05298713967204094,
0.023511508479714394,
-0.019276084378361702,
-0.02368646301329136,
-0.047903873026371,
-0.004358465783298016,
0.00023321968910750002,
0.021846286952495575,
-0.0525188222527504,
0.004513263702392578,
0.010952906683087349,
0.02230299636721611,
0.06636445224285126,
0.09021206945180893,
0.015218831598758698,
0.007801476866006851,
0.07160557806491852,
-0.005560454912483692,
0.05666382238268852,
0.07026338577270508,
-0.005812061484903097,
0.0035017728805541992,
0.030194828286767006,
-0.059314221143722534,
-0.05690520629286766,
0.012475620955228806,
0.022315122187137604,
-0.014395731501281261,
-0.041126858443021774,
-0.010408787988126278,
-0.002401457168161869,
0.030527660623192787,
-0.001564720063470304,
0.06263609230518341,
0.008966685272753239,
0.014921891503036022,
0.009497950784862041,
0.04670433700084686,
-0.06363314390182495,
-0.009037494659423828,
0.0067224097438156605,
-0.022145861759781837,
-0.016953550279140472,
0.00674722483381629,
0.02233407087624073,
-0.018841955810785294,
-0.01977965235710144,
-0.06451128423213959,
0.06230642646551132,
-0.018887042999267578,
0.049548376351594925,
-0.0267769917845726,
0.06976237893104553,
-0.031199214980006218,
0.022356247529387474,
-0.026633575558662415,
0.01283207070082426,
0.05025045573711395,
0.046551063656806946,
-0.02415892668068409,
0.05283910408616066,
0.05205750837922096,
0.022794531658291817,
-0.04149140417575836,
0.0022910882253199816,
-0.008291253820061684,
-0.003221510909497738,
-0.02313902974128723,
0.025399671867489815,
-0.007177494000643492,
-0.03498269245028496,
-0.04067325219511986,
0.007330725900828838,
-0.019836729392409325,
0.010980026796460152,
-0.00838208757340908,
-0.03900955989956856,
-0.010637183673679829,
-0.06539919227361679,
0.04175437241792679,
-0.001603754353709519,
0.02099023573100567,
-0.006528682075440884,
0.057501792907714844,
-0.0224728062748909,
-0.01629246026277542,
0.029489057138562202,
-0.006230414845049381,
-0.009020352736115456,
0.01613682135939598,
0.02217060700058937,
0.020324165001511574,
0.06439325958490372,
-0.022869769483804703,
-0.0004313593963161111,
0.03866755589842796,
-0.05939348042011261,
-0.018684661015868187,
0.021717580035328865,
-0.03138705715537071,
0.03175860643386841,
-0.006272677797824144,
-0.0328948087990284,
-0.019023260101675987,
0.05743526667356491,
-0.03588046133518219,
0.006460968870669603,
-0.00813695415854454,
0.028408728539943695,
-0.0025387010537087917,
-0.0404256209731102,
0.010349414311349392,
-0.04714218154549599,
-0.0295643899589777,
-0.029607245698571205,
0.020523663610219955,
-0.04885492101311684,
0.028120940551161766,
0.05137491226196289,
-0.004914669785648584,
-0.01444223616272211,
0.025227531790733337,
0.03136684373021126,
-0.009529955685138702,
0.06244084611535072,
0.0035252594389021397,
-0.030705031007528305,
-0.03280128538608551,
0.03160681575536728,
-0.036054905503988266,
0.022072501480579376,
0.023114211857318878,
-0.01986178755760193,
-0.03555590659379959,
-0.015465130098164082,
-0.07210458070039749,
0.00457150349393487,
0.0031713549979031086,
0.0067475480027496815,
0.011414625681936741,
-0.09751886129379272,
0.013800600543618202,
0.019610363990068436,
-0.014010803773999214,
-0.06616891175508499,
0.019572991877794266,
0.01752658560872078,
0.00555852334946394,
-0.02711188979446888,
-0.019359232857823372,
0.0013527884148061275,
0.061187297105789185,
0.024549342691898346,
-0.02730555087327957,
0.05464113876223564,
0.0010837307199835777,
-0.010876397602260113,
-0.019404741004109383,
-0.016959819942712784,
-0.03738344833254814,
-0.06540004163980484,
0.01637747697532177,
0.00373157043941319,
0.026591628789901733,
0.023606613278388977,
-0.03445599973201752,
0.013378203846514225,
0.02570316009223461,
0.011537233367562294,
0.008850285783410072,
-0.0362095944583416,
-0.03423069790005684,
-0.01785910129547119,
0.03070026822388172,
0.04796174168586731,
0.0902915894985199,
0.05461854487657547,
-0.004868028685450554,
-0.04647711664438248,
-0.015059346333146095,
0.0095398323610425,
-0.019265510141849518,
-0.024124251678586006,
0.010496714152395725,
0.013841589912772179,
-0.02229630947113037,
-0.05030412599444389,
0.018241528421640396,
-0.08045724034309387,
-0.05903821811079979,
-0.009453235194087029,
0.018518885597586632,
0.014182982966303825,
-0.02175736241042614,
0.005421686917543411,
-0.018764059990644455,
-0.017393847927451134,
0.10263465344905853,
0.0033502064179629087,
0.03307479992508888,
0.0351184718310833,
0.07215245068073273,
0.03498057276010513,
-0.0022382275201380253,
-0.042358145117759705,
-0.01101772766560316,
-0.03463499993085861,
-0.020353319123387337,
-0.004809224512428045,
-0.010341566987335682,
-0.02914770133793354,
-0.0053108627907931805,
0.06936906278133392,
0.028986498713493347,
-0.018655287101864815,
0.011466328985989094,
0.03312908113002777,
-0.026574254035949707,
0.006751290988177061,
-0.009644268080592155,
-0.0010805133497342467,
-0.0030530737712979317,
-0.035227373242378235,
-0.04444922134280205,
0.05631543695926666,
-0.041326917707920074,
-0.02390802651643753,
0.06283806264400482,
0.004712543450295925,
0.002667047781869769,
-0.02556728944182396,
0.015174995176494122,
0.0018747352296486497,
-0.052103471010923386,
0.021969761699438095,
0.013534974306821823,
-0.0182048212736845,
-0.018932271748781204,
-0.023806501179933548,
0.004065565764904022,
-0.015074193477630615,
-0.002809171797707677,
-0.04038528725504875,
-0.019076094031333923,
0.01576012745499611,
0.02788861095905304,
-0.04383131116628647,
0.04920654743909836,
0.0440690815448761,
0.011736185289919376,
-0.07049722969532013,
-0.004479018971323967,
0.001358996843919158,
-0.019695045426487923,
0.00697858352214098,
-0.020884711295366287,
0.01810193620622158,
-0.04620223119854927,
-0.04056127741932869,
-0.040140990167856216,
-0.02310078591108322,
-0.031932175159454346,
-0.014714978635311127,
-0.03430239111185074,
0.009753385558724403,
-0.061888132244348526,
0.047252677381038666,
0.03713865950703621,
-0.030824819579720497,
-0.053162313997745514,
-0.013648970052599907,
-0.04268984496593475,
0.022015372291207314,
0.08718886971473694,
-0.047281406819820404,
0.030081970617175102,
0.10044699907302856,
0.03590817749500275,
0.030059222131967545,
-0.0034796239342540503,
-0.020210564136505127,
0.04553060606122017,
-0.0322076641023159,
-0.037232547998428345,
0.005075190216302872,
0.051759324967861176,
0.013563876040279865,
-0.05385696515440941,
0.005108772777020931,
0.03499932959675789,
-0.012555043213069439,
-0.08008544147014618,
0.049180299043655396,
0.006282537244260311,
0.0031145561952143908,
0.035236623138189316,
0.018228139728307724,
-0.10172869265079498,
-0.03359128162264824,
0.019250117242336273,
-0.019967282190918922,
0.008241417817771435,
0.024775777012109756,
0.055828314274549484,
-0.04753005504608154,
-0.02357681840658188,
0.016913389787077904,
-0.05405320227146149,
0.04136323183774948,
0.008406613953411579,
0.0473579503595829,
0.013370377011597157,
0.00704545620828867,
-0.00004286551848053932,
-0.006640848703682423,
0.008314584381878376,
0.032183095812797546,
0.04705675691366196,
-0.03900565579533577,
0.03132977336645126,
-0.011729068122804165,
0.02646542713046074,
-0.009957444854080677,
-0.0012643239460885525,
-0.039537619799375534,
0.006246930453926325,
0.0743054524064064,
-0.07738612592220306,
-0.01856495998799801,
-0.02137100324034691,
-0.02896641194820404,
0.043710529804229736,
0.011640086770057678,
-0.030062535777688026,
-0.0033774671610444784,
0.03723558411002159,
-0.039428938180208206,
0.048761822283267975,
-0.02629278600215912,
0.0025097306352108717,
-0.019615117460489273,
0.01746450364589691,
-0.023406993597745895,
0.056769877672195435,
-0.01154653262346983,
0.0306235458701849,
-0.0001176768055302091,
-0.017662756145000458,
0.01921837031841278,
0.034294888377189636,
-0.002615027828142047,
0.0390491709113121,
0.023574627935886383,
0.017093339934945107,
0.011415752582252026,
0.11476809531450272,
0.010793172754347324,
-0.009044867008924484,
-0.03528057783842087,
-0.025831313803792,
-0.012002332136034966,
0.0066602895967662334,
0.04404960200190544,
-0.0405375100672245,
0.026033900678157806,
0.011655466631054878,
0.02082492783665657,
-0.014249601401388645,
0.06224874034523964,
0.026054872199892998,
0.010599563829600811,
0.04185568541288376,
0.032890889793634415,
-0.007819663733243942,
0.030157368630170822,
0.055351898074150085,
-0.04085162281990051,
-0.0010983686661347747,
0.02893882803618908,
-0.0019172324100509286,
0.023427113890647888,
0.002947972621768713,
0.004750069230794907,
0.021280484274029732,
0.008051480166614056,
0.02429955266416073,
-0.10688568651676178,
-0.028714505955576897,
-0.023646319285035133,
-0.004183107055723667,
-0.06191222742199898,
-0.03360462561249733,
0.018701128661632538,
0.03371911868453026,
-0.0022657266817986965,
-0.04647156968712807,
0.042315781116485596,
-0.02467186376452446,
0.01598738692700863,
-0.03512755408883095,
0.01982886902987957,
0.009250674396753311,
-0.003196866950020194,
0.014543702825903893,
0.02590526081621647,
-0.013963624835014343,
-0.028370650485157967,
-0.04530176520347595,
-0.04111750051379204,
-0.01332406047731638,
-0.04272869974374771,
0.0017543036956340075,
-0.03664505481719971,
-0.025212638080120087,
-0.013170776888728142,
0.05395619571208954,
-0.0449020154774189,
0.006493573542684317,
0.0009242017986252904,
0.0534672774374485,
0.037912990897893906,
0.010261598974466324,
0.01281103678047657,
-0.062390152364969254,
0.008514744229614735,
0.028427083045244217,
0.005335479974746704,
0.0556534007191658,
0.0007524326210841537,
-0.049486953765153885,
0.012910187244415283,
0.007569733541458845,
-0.04000115022063255,
0.001652713748626411,
0.06528191268444061,
0.029546895995736122,
0.000323852407746017,
-0.03479459881782532,
0.01660061813890934,
0.011368290521204472,
0.023660864681005478,
0.015235524624586105,
-0.00554117513820529,
-0.01373413484543562,
-0.022946719080209732,
-0.04975133761763573,
0.0007445469964295626,
-0.06204000115394592,
-0.032170604914426804,
0.019070303067564964,
0.009948926977813244,
-0.011735878884792328,
-0.030643491074442863,
0.03776691481471062,
-0.0029795377049595118,
-0.016369903460144997,
-0.012919096276164055,
-0.03782886266708374,
0.025459477677941322,
0.03974195942282677,
0.09699556976556778,
0.06197056546807289,
-0.05152267962694168,
-0.010817824862897396,
-0.023517513647675514,
-0.026700755581259727,
-0.025013679638504982,
0.04613187536597252,
-0.02133180946111679,
-0.011800565756857395,
0.0006386672612279654,
0.0011490710312500596,
0.05573123320937157,
-0.06343851238489151,
0.02348434552550316,
-0.0008295464213006198,
-0.0019483715295791626,
0.004352821037173271,
-0.008931401185691357,
-0.02096445858478546,
0.03212752565741539,
0.0012865334283560514,
0.00044678934500552714,
-0.027963347733020782,
0.008440559729933739,
-0.0002530416240915656,
-0.007883116602897644,
-0.12326554208993912,
-0.0657527819275856,
-0.02441135048866272,
0.012624040246009827,
-0.01615915447473526,
0.00588142080232501,
-0.02686271071434021,
-0.036367952823638916,
0.032680943608284,
0.021332234144210815,
0.035750120878219604,
0.01167193055152893,
-0.010214748792350292,
0.030077306553721428,
0.01133732870221138,
0.04168006777763367,
0.08449746668338776,
0.022344602271914482,
-0.025312870740890503,
-0.0517963171005249,
-0.030282050371170044,
0.02141447551548481,
-0.006435966584831476,
-0.0229670237749815,
-0.00578908110037446,
-0.015356654301285744,
-0.09407024085521698,
0.009393827989697456,
0.013538355007767677,
-0.045130982995033264,
-0.008703387342393398,
0.09492011368274689,
0.05137007310986519,
0.016387315467000008,
0.018063127994537354,
0.025867938995361328,
0.06237515062093735,
-0.002053208649158478,
0.02920508198440075,
0.03305263817310333,
0.019959894940257072,
-0.028839057311415672,
0.03363198786973953,
0.050990521907806396,
-0.0009011654183268547,
0.038898177444934845,
-0.00814933143556118,
-0.06785807013511658,
-0.04144321009516716,
-0.020382778719067574,
-0.011551883071660995,
-0.0231177881360054,
0.08085499703884125,
0.021722501143813133,
0.0575786754488945,
0.023385465145111084,
0.040750399231910706,
-0.007746162824332714,
-0.043090637773275375,
0.04723530262708664,
-0.0493038035929203,
-0.0202300064265728,
0.03315600007772446,
0.005789360497146845,
-0.036508720368146896,
0.02355891652405262,
0.0004760438168887049,
0.03417406231164932,
-0.04678858816623688,
-0.0249633751809597,
-0.029567711055278778,
0.018441826105117798,
0.05957838147878647,
-0.010273825377225876,
-0.003879191353917122,
-0.004004664719104767,
-0.015720510855317116,
0.032038331031799316,
-0.03543724864721298,
0.028012709692120552,
0.004619290586560965,
0.043645843863487244,
-0.053047917783260345,
-0.0011824228568002582,
0.025217551738023758,
-0.010059511289000511,
-0.015682034194469452,
0.03178109601140022,
-0.023424819111824036,
-0.014832870103418827,
-0.08877214044332504,
-0.02448996528983116,
0.05144903063774109,
0.016051188111305237,
-0.026502029970288277,
0.032749153673648834,
0.035226065665483475,
0.004483836703002453,
-0.042887602001428604,
0.017106324434280396,
-0.05574280768632889,
-0.0346808023750782,
-0.0522795207798481,
-0.004672225099056959,
-0.0013710951898247004,
0.015666136518120766,
-0.006795396097004414,
0.05363280326128006,
0.018906647339463234,
0.013421900570392609,
-0.005154539365321398,
0.004808830097317696,
0.024794965982437134,
-0.030125731602311134,
0.05243721604347229,
-0.00572167057543993,
-0.015114194713532925,
0.024471521377563477,
-0.012805960141122341,
0.03192789480090141,
-0.032713912427425385,
0.035428378731012344,
-0.057923201471567154,
-0.026565957814455032,
0.024286435917019844,
-0.0789766013622284,
-0.07135439664125443,
-0.0351867750287056,
0.06077100709080696,
-0.015136794187128544,
-0.024545570835471153,
-0.01968635432422161,
-0.06264112889766693,
-0.01779365725815296,
-0.0525798536837101,
0.05447733402252197,
0.006576974876224995,
-0.02940833568572998,
0.006804239470511675,
0.034949708729982376,
-0.024379760026931763,
0.030813151970505714,
0.0017090452602133155,
-0.05172113701701164,
0.011679591611027718,
0.028276143595576286,
-0.01793762855231762,
-0.03219562768936157,
0.034915756434202194,
-0.02637559175491333,
0.016719786450266838,
0.01178640779107809,
0.061563994735479355,
-0.06634911149740219,
-0.0027770213782787323,
-0.05018956586718559,
-0.01027600560337305,
0.010646823793649673,
0.017224686220288277,
-0.013131790794432163,
-0.05192742496728897,
-0.05839357152581215,
0.08934351056814194,
0.05191030353307724,
0.02128838375210762,
-0.12904617190361023,
0.006544413510710001,
-0.006991229951381683,
-0.06028492748737335,
-0.09169717878103256,
0.020599685609340668,
-0.022553937509655952,
-0.04888526722788811,
0.05429019033908844,
-0.01654696837067604,
-0.015738576650619507,
-0.052596744149923325,
-0.00557626411318779,
-0.004083780571818352,
-0.015114902518689632,
0.04493420943617821,
0.06615088880062103,
0.014248416759073734,
-0.006943938322365284,
0.009823248721659184,
0.043472759425640106,
0.004550121258944273,
0.030699625611305237,
0.054357293993234634,
-0.0020060352981090546,
0.03137863799929619,
-0.04335504397749901,
0.05722919479012489,
0.0355616994202137,
0.014288384467363358,
-0.03649858385324478,
0.022045660763978958,
-0.055502500385046005,
0.017320258542895317,
-0.013822296634316444,
0.08230618387460709,
-0.016842614859342575,
-0.03783749043941498,
-0.003935390617698431,
0.009611374698579311,
0.005761327687650919,
0.014554818160831928,
-0.03760572895407677,
-0.010462013073265553,
0.006153639405965805
] |
<p>we are given a problem with spring with its own mass $m$. I am confused how to set up the
PE term in the Lagrangian.</p>
<p>Assume the spring has length of $L_{0}$ when it is laying on a table
horizontally. Now when we hold the spring upright and hang it vertically from
a pivot in the ceiling to make a pendulum, it will stretch a little due to its
own weight by $\frac{(m/3)g}{k}$ where $k$ is the spring constant. I use
$m/3$ there since that is the common factor used to generate an effective mass
used for a spring with its own weight.</p>
<p><a href="http://en.wikipedia.org/wiki/Effective_mass_%28spring-mass_system%29" rel="nofollow">http://en.wikipedia.org/wiki/Effective_mass_%28spring-mass_system%29</a></p>
<p>Hence now the length of the spring is $L_{0}+\frac{(m/3)g}{k}$ before we even
put the bob mass at the end of it. Should one use $L_{0}+\frac{(m/3)g}{k}$ as
the relaxed length of the spring or use $L_{0}?$</p>
<p>Will the PE for the spring be $\frac{1}{2}k\left( y-L_{0}\right) ^{2}$ or
$\frac{1}{2}k\left( y-(L_{0}+\frac{(m/3)g}{k})\right) ^{2}$? </p>
<p>Assuming one is measuring $y$ here from the ceiling where the spring is hanging from</p>
<pre><code> +---------
\ |
/ |
\ |
/ | y(t)
\ |
/ |
M V
</code></pre>
<p>Which term should be used for PE? </p>
<p>I know there will be additional PE term for the spring due to its own mass,
which is $-mg\frac{y}{2}\cos\theta$ </p>
<p>Hence total PE from the spring is</p>
<p>$PE=\frac{1}{2}k\left( y-L_{0}\right) ^{2}-mg\frac{y}{2}\cos\theta
-Mgy\cos\theta$</p>
<p>or</p>
<p>$PE=\frac{1}{2}k\left( y-(L_{0}+\frac{(m/3)g}{k})\right) ^{2}-mg\frac{y}
{2}\cos\theta-Mgy\cos\theta
$</p>
<p>where $\theta$ is angle of rotation of the spring pendulum.</p>
<p>not sure which to use.</p> | g9205 | [
0.08736927807331085,
0.005383688490837812,
0.027710480615496635,
-0.06250230222940445,
0.0002536668616812676,
0.028036661446094513,
0.05471131578087807,
0.008085319772362709,
-0.06503097712993622,
0.016111303120851517,
-0.038024164736270905,
0.037665173411369324,
-0.009321092627942562,
0.01615636982023716,
0.016223443672060966,
0.008615585044026375,
0.08269283920526505,
0.032752875238657,
0.04887427017092705,
0.011847703717648983,
-0.026615042239427567,
0.007506812456995249,
-0.008499457500874996,
-0.03263328596949577,
0.01866532303392887,
-0.00024250279238913208,
0.03777004033327103,
0.07262978702783585,
-0.045698028057813644,
-0.051260415464639664,
-0.022107847034931183,
0.04143922030925751,
0.018961220979690552,
-0.03125220537185669,
-0.03885803744196892,
-0.0017205391777679324,
0.030701380223035812,
0.07408620417118073,
-0.00276769557967782,
-0.006372136063873768,
0.01852830871939659,
-0.06913565844297409,
0.038647402077913284,
0.030886806547641754,
-0.0011875538621097803,
0.016605867072939873,
-0.01909382827579975,
0.020011484622955322,
-0.005229526199400425,
-0.004536682274192572,
-0.0026697965804487467,
0.041643060743808746,
0.006133942399173975,
-0.09403083473443985,
-0.0238653477281332,
0.06770111620426178,
0.01759280636906624,
0.0006067117210477591,
-0.004990445915609598,
0.04582758992910385,
0.015213831327855587,
-0.034579310566186905,
-0.0469353012740612,
-0.04800271615386009,
0.011737656779587269,
0.01851652003824711,
-0.012120501138269901,
0.000698122545145452,
-0.002399794990196824,
-0.018019743263721466,
-0.03252122178673744,
-0.05961909890174866,
0.041725777089595795,
-0.05658267065882683,
-0.021823016926646233,
-0.030029738321900368,
-0.03848722577095032,
0.0009757598745636642,
-0.0003189462295267731,
-0.06418871879577637,
-0.03250507265329361,
-0.02376159094274044,
-0.008004584349691868,
0.023985635489225388,
0.03902876004576683,
-0.03482916206121445,
-0.019456906244158745,
-0.0011874112533405423,
-0.039533842355012894,
0.007022232282906771,
0.002484501339495182,
-0.04795658960938454,
0.0232679583132267,
0.03290500491857529,
-0.03202249854803085,
-0.02477966621518135,
0.039831630885601044,
0.045000988990068436,
0.0066096545197069645,
-0.01964797079563141,
-0.034584641456604004,
0.04851093888282776,
-0.023822175338864326,
0.026064269244670868,
-0.046475350856781006,
0.039900653064250946,
0.039052437990903854,
-0.013931993395090103,
-0.062426820397377014,
-0.008949394337832928,
0.001858872827142477,
0.034402381628751755,
0.023019034415483475,
-0.040672965347766876,
-0.0861305370926857,
-0.023406200110912323,
0.10529828816652298,
0.014733030460774899,
0.03350605070590973,
-0.01229928806424141,
-0.010131200775504112,
0.019036484882235527,
0.06278800964355469,
0.04792475700378418,
-0.034877803176641464,
-0.0202601607888937,
-0.0035857080947607756,
0.006107480265200138,
0.04836772009730339,
-0.052508458495140076,
0.014373430982232094,
0.020256437361240387,
-0.027065459638834,
0.04124194756150246,
-0.0082724429666996,
0.026469457894563675,
0.006009043660014868,
0.0487651452422142,
-0.023989252746105194,
0.04415126144886017,
0.0010738642886281013,
-0.08185266703367233,
-0.008799383416771889,
-0.10773878544569016,
-0.004559020046144724,
0.06889833509922028,
-0.0013843990163877606,
-0.06539564579725266,
0.042636677622795105,
0.039706915616989136,
-0.005724430549889803,
0.05950130522251129,
-0.08263951539993286,
-0.009583402425050735,
0.034594617784023285,
-0.02743360958993435,
0.00011841272498713806,
-0.027773505076766014,
0.03580803424119949,
-0.003731382079422474,
0.01795828714966774,
-0.02407822385430336,
0.05583539232611656,
-0.0064992220140993595,
-0.06013023480772972,
0.058256860822439194,
-0.004590403754264116,
-0.0004011672572232783,
-0.07966063916683197,
-0.07636334002017975,
-0.05355211719870567,
-0.015176487155258656,
-0.006489153020083904,
0.019800154492259026,
-0.02690565027296543,
0.040452416986227036,
0.05809541419148445,
-0.029163816943764687,
0.03684963658452034,
0.03037063032388687,
-0.015853330492973328,
-0.058736614882946014,
0.008754365146160126,
0.013306813314557076,
-0.09189668297767639,
0.03632500022649765,
0.03850408270955086,
0.019614534452557564,
-0.02050163224339485,
-0.04275582730770111,
-0.026705922558903694,
-0.011450998485088348,
0.0005521231214515865,
0.08404950052499771,
-0.05207531154155731,
0.009584289975464344,
0.024378567934036255,
-0.038766950368881226,
-0.023514525964856148,
0.01579812914133072,
-0.02813064493238926,
-0.004697650205343962,
0.06778530031442642,
0.035011980682611465,
0.026687821373343468,
-0.013804638758301735,
-0.001887676538899541,
-0.023559153079986572,
0.018212884664535522,
0.010942668654024601,
0.010477210395038128,
-0.025138622149825096,
0.0494360513985157,
0.050840530544519424,
0.005480702966451645,
-0.0486050508916378,
0.005691985599696636,
0.02088811807334423,
0.004869077820330858,
0.011736053973436356,
-0.005670924670994282,
0.023063737899065018,
0.03415239229798317,
-0.014320083893835545,
-0.07966829091310501,
-0.009466413408517838,
0.023914089426398277,
0.018069393932819366,
0.00981734786182642,
0.005130067467689514,
-0.02384592778980732,
0.00485906982794404,
-0.024485407397150993,
0.043955009430646896,
0.008235957473516464,
0.01543626468628645,
-0.06502178311347961,
0.003506398294121027,
0.016372300684452057,
0.037041787058115005,
0.046512801200151443,
-0.026013769209384918,
-0.015714865177869797,
-0.03970974683761597,
0.029071997851133347,
0.006472396664321423,
0.0704244002699852,
0.026693398132920265,
-0.027267759665846825,
0.024441588670015335,
-0.052259352058172226,
-0.011119527742266655,
-0.06863226741552353,
0.03777533769607544,
-0.007779377046972513,
-0.03252178430557251,
-0.03217944875359535,
-0.013912606984376907,
-0.017308464273810387,
-0.012981771491467953,
0.01697181910276413,
-0.09622000902891159,
-0.011810895055532455,
0.039508696645498276,
-0.05687718093395233,
-0.01079517975449562,
-0.061457112431526184,
-0.06698101758956909,
0.07223521918058395,
0.03161342814564705,
0.008340691216289997,
0.06315477192401886,
0.07310573011636734,
0.06186840310692787,
-0.022887244820594788,
-0.015512042678892612,
0.02896842733025551,
-0.00837452057749033,
0.007359506096690893,
-0.004651520401239395,
0.052432432770729065,
-0.0207339059561491,
-0.010304778814315796,
0.04052969440817833,
0.06188267469406128,
-0.038639459758996964,
-0.008367059752345085,
0.017699813470244408,
-0.05571466311812401,
0.00024885180755518377,
0.022347787395119667,
0.037743549793958664,
0.004633117932826281,
-0.010065807960927486,
-0.01678617298603058,
0.07374535501003265,
-0.026136746630072594,
-0.017675764858722687,
-0.018970226868987083,
0.04228433594107628,
-0.006644961889833212,
-0.017741024494171143,
-0.017881199717521667,
-0.043773747980594635,
-0.010497044771909714,
0.014832185581326485,
0.0001532653986942023,
-0.016354260966181755,
0.037661194801330566,
-0.011328264139592648,
-0.055078018456697464,
0.02904531918466091,
0.07756159454584122,
-0.031161388382315636,
-0.0778951570391655,
-0.02281823754310608,
0.016627583652734756,
-0.031605567783117294,
-0.06547687947750092,
-0.06337355077266693,
0.01276381965726614,
-0.007419141475111246,
0.009495086967945099,
-0.04086088016629219,
-0.020890725776553154,
0.025989843532443047,
0.022231390699744225,
0.0022746899630874395,
-0.05185679346323013,
-0.0391569547355175,
-0.005781126208603382,
0.0065741329453885555,
0.01454322598874569,
-0.013630897738039494,
0.014712490141391754,
-0.03865230828523636,
0.005204859655350447,
0.004065580666065216,
0.026355091482400894,
0.04275209829211235,
-0.08444079756736755,
-0.01850917749106884,
-0.0748637467622757,
0.02400190569460392,
0.03701677918434143,
-0.038107313215732574,
-0.0012911061057820916,
0.019860506057739258,
0.040152657777071,
-0.035390209406614304,
-0.031976375728845596,
-0.018801867961883545,
-0.06202593073248863,
0.022038348019123077,
0.013248407281935215,
0.0017450533341616392,
0.028097765520215034,
0.041551657021045685,
-0.06928835809230804,
0.013994175009429455,
0.025980304926633835,
-0.02511751838028431,
-0.007010973058640957,
0.021199457347393036,
-0.0228099524974823,
0.04508493095636368,
-0.0029527342412620783,
0.07187137007713318,
0.0007489862036891282,
-0.020576024428009987,
0.0009377671522088349,
-0.02933351695537567,
0.012097274884581566,
-0.06615151464939117,
0.024783316999673843,
-0.033309515565633774,
0.03700442612171173,
0.024681465700268745,
-0.027586854994297028,
-0.012352004647254944,
-0.03923111781477928,
-0.03747819736599922,
-0.04145522788167,
0.011045021004974842,
-0.03033018857240677,
0.0030039430130273104,
-0.04109073430299759,
-0.0030742529779672623,
-0.005988213699311018,
-0.036856167018413544,
-0.018808070570230484,
-0.035848744213581085,
-0.050911881029605865,
0.047024864703416824,
0.05630482733249664,
0.0018122629262506962,
0.037642162293195724,
0.02290494181215763,
-0.00030880808481015265,
-0.003477361286059022,
-0.05369061604142189,
0.03146280720829964,
0.03711460530757904,
0.0160833653062582,
-0.03074973076581955,
0.05407843366265297,
0.04367421567440033,
-0.02879154495894909,
0.017513176426291466,
-0.017614835873246193,
-0.0028214312624186277,
-0.005883863195776939,
-0.013217191211879253,
-0.017294056713581085,
0.047625891864299774,
-0.044221967458724976,
0.02591850981116295,
0.0023682762403041124,
-0.04455797001719475,
-0.006568030454218388,
0.007306050509214401,
0.026633936911821365,
0.0315275602042675,
-0.07549482583999634,
-0.003900370793417096,
0.057786084711551666,
0.0006505466881208122,
-0.001267505926080048,
0.017546338960528374,
-0.034703709185123444,
-0.000574350415263325,
0.04258507862687111,
0.006415366195142269,
-0.04033404588699341,
-0.006886816583573818,
0.05743250995874405,
0.019740305840969086,
0.043158840388059616,
-0.011993472464382648,
0.04074947163462639,
-0.0034148700069636106,
0.037201471626758575,
-0.032568804919719696,
-0.0003859130956698209,
-0.010637002997100353,
-0.028741665184497833,
-0.013911410234868526,
-0.04206079617142677,
0.013471139594912529,
0.015992313623428345,
-0.026596710085868835,
-0.03552713617682457,
0.03302580490708351,
-0.012860381044447422,
0.03352940455079079,
0.03074350208044052,
-0.058165572583675385,
0.020507553592324257,
0.01725728251039982,
-0.03186991065740585,
0.00534334359690547,
-0.03630528971552849,
-0.024786019697785378,
0.012399367988109589,
0.018003012984991074,
-0.046294547617435455,
-0.00849968008697033,
-0.02096995897591114,
0.007926488295197487,
-0.007676098961383104,
0.03499576821923256,
-0.012170691974461079,
0.0033132287207990885,
-0.03654438629746437,
0.0126667944714427,
0.01558794267475605,
0.04007302597165108,
0.013291995041072369,
0.011227868497371674,
-0.05963369458913803,
-0.013775038532912731,
-0.05499653518199921,
-0.010613193735480309,
0.022702401503920555,
0.00949282106012106,
0.022393029183149338,
0.01830173470079899,
-0.07056130468845367,
0.0076255276799201965,
0.004863642156124115,
0.05829234421253204,
0.065871961414814,
-0.008745316416025162,
-0.003869285574182868,
0.02422184683382511,
-0.04631710797548294,
-0.020520418882369995,
0.0009890563087537885,
0.07170127332210541,
-0.006818834226578474,
-0.0035143534187227488,
0.059333834797143936,
-0.03221345320343971,
0.03461194038391113,
-0.03018195368349552,
0.027127372100949287,
-0.016768375411629677,
-0.0004999727243557572,
-0.01677035726606846,
0.02124752290546894,
0.016931600868701935,
0.00008663912740303203,
0.04812416434288025,
0.014922389760613441,
-0.025521816685795784,
-0.022471493110060692,
0.030149871483445168,
-0.020207924768328667,
-0.072564497590065,
-0.006189931184053421,
0.07915642112493515,
-0.007917981594800949,
-0.006068481132388115,
-0.06567846238613129,
0.027784718200564384,
0.02533336915075779,
-0.03763832896947861,
-0.022821933031082153,
-0.029623709619045258,
-0.0037472285330295563,
0.016006961464881897,
-0.02439078874886036,
-0.007975234650075436,
-0.008670702576637268,
-0.01491577085107565,
-0.010390952229499817,
-0.00916965026408434,
0.024114323779940605,
-0.005347942002117634,
-0.06339149177074432,
-0.0059692771174013615,
-0.08017143607139587,
0.0624157078564167,
0.0383329838514328,
-0.03488984704017639,
-0.00934538897126913,
0.02919478341937065,
-0.05519268289208412,
0.0662112608551979,
-0.0006773828063160181,
-0.034911468625068665,
0.09763675928115845,
-0.012160404585301876,
0.009498241357505322,
-0.014911928214132786,
0.07776477187871933,
0.027292631566524506,
-0.01090393029153347,
-0.0069030881859362125,
0.0469447486102581,
0.030804147943854332,
-0.02450687251985073,
0.03729163482785225,
-0.0007161837420426309,
0.009020448662340641,
0.004733453504741192,
-0.03409632295370102,
-0.05337722972035408,
0.010071635246276855,
0.024804318323731422,
-0.04346739500761032,
-0.010757485404610634,
-0.034826893359422684,
0.029109783470630646,
0.03081376478075981,
0.08828652650117874,
-0.0623941645026207,
-0.050212591886520386,
-0.026527080684900284,
0.015058670192956924,
-0.03165242820978165,
0.03358539193868637,
0.03457403928041458,
-0.01780308596789837,
-0.01070353388786316,
-0.001524364692158997,
-0.019861070439219475,
-0.0529857762157917,
0.002481789095327258,
-0.015368159860372543,
-0.017708737403154373,
0.00984302069991827,
-0.04373045638203621,
0.03599860519170761,
0.0030630663968622684,
0.0411481074988842,
-0.041908979415893555,
-0.04728500545024872,
-0.01350484136492014,
0.04452965781092644,
0.04864221066236496,
0.006010602228343487,
0.06955844908952713,
0.00267122033983469,
0.03041183389723301,
0.055048804730176926,
-0.05739888548851013,
0.05634600669145584,
-0.003892944660037756,
-0.016420630738139153,
0.015641095116734505,
0.004239622037857771,
0.04905521497130394,
-0.002194916596636176,
0.03257092460989952,
-0.012996690347790718,
-0.018861155956983566,
0.07951708883047104,
-0.018194111064076424,
0.01588616892695427,
0.017152970656752586,
0.009266972541809082,
0.04144318401813507,
-0.05688168853521347,
0.0021027964539825916,
0.01924685388803482,
-0.024701174348592758,
-0.03440886363387108,
0.0024655612651258707,
0.029916444793343544,
0.01373143307864666,
0.015063031576573849,
-0.0440935343503952,
0.0016694620717316866,
0.027260364964604378,
0.06618906557559967,
-0.018031293526291847,
0.08930669724941254,
0.07443253695964813,
0.05823495611548424,
-0.00850976537913084,
0.031922824680805206,
0.017175959423184395,
0.010394120588898659,
-0.047125931829214096,
-0.0183001309633255,
0.019071659073233604,
0.01333287637680769,
-0.052845776081085205,
-0.0028498568572103977,
-0.01886911876499653,
-0.02631380595266819,
-0.07219807058572769,
0.03531832993030548,
0.0463496595621109,
-0.041437432169914246,
0.04668479412794113,
-0.029415959492325783,
0.026368265971541405,
-0.03636127710342407,
-0.07649125158786774,
-0.010956753976643085,
0.0979674756526947,
0.0017327024834230542,
-0.012725068256258965,
0.07015024870634079,
-0.033488452434539795,
0.01509309932589531,
0.0021298322826623917,
0.04974722862243652,
-0.022337745875120163,
-0.03329922631382942,
-0.01738593727350235,
0.01644301228225231,
0.020081568509340286,
0.0234480369836092,
-0.0009391758940182626,
0.0076170917600393295,
-0.0406506210565567,
0.00865945778787136,
-0.001912128645926714,
-0.01907491870224476,
-0.06127636134624481,
0.009028991684317589,
0.03526468202471733,
0.03436664119362831,
-0.012952210381627083,
0.008210983127355576,
-0.015881946310400963,
-0.007591662462800741,
-0.007223199121654034,
0.06713299453258514,
0.0213292445987463,
0.037534020841121674,
-0.08505572378635406,
0.00071827502688393,
0.01284785382449627,
-0.010177072137594223,
0.06475815922021866,
0.027666961774230003,
0.05650163069367409,
-0.020018115639686584,
-0.01058993674814701,
0.04939703270792961,
0.061760593205690384,
-0.001305319368839264,
-0.0355587899684906,
0.051913511008024216,
-0.06251241266727448,
-0.006241203751415014,
0.013349010609090328,
0.021296687424182892,
0.007156400941312313,
0.03522152826189995,
0.008724352344870567,
0.029956931248307228,
-0.03146062418818474,
0.032243646681308746,
-0.0017059609526768327,
-0.03460574150085449,
-0.03251125290989876,
0.01425536721944809,
0.013147737830877304,
-0.1163899302482605,
-0.020923558622598648,
-0.03834238275885582,
-0.01072956807911396,
-0.006823217496275902,
-0.016905799508094788,
0.014780864119529724,
0.0023118380922824144,
-0.009376008063554764,
-0.015606663189828396,
0.01898440159857273,
-0.06041790544986725,
0.014520817436277866,
0.014787792228162289,
-0.05380800738930702,
0.0027171471156179905,
0.009407466277480125,
-0.037018027156591415,
-0.07526088505983353,
-0.005776218604296446,
-0.040840186178684235,
0.04286440834403038,
0.040657926350831985,
-0.03110748529434204,
0.042592499405145645,
0.0452435128390789,
-0.04883250966668129,
-0.027273768559098244,
0.043261852115392685,
-0.01922565884888172,
0.045667171478271484,
0.004449463449418545,
-0.05108703672885895,
0.02332625538110733,
0.023501640185713768,
-0.03091607615351677,
0.012202529236674309,
-0.03650593385100365,
-0.004332904238253832,
-0.0025280211120843887,
0.02435075305402279,
-0.03407680615782738,
-0.004254326224327087,
0.03978745639324188,
0.027848022058606148
] |
<p>Are the ions in a fluorescent lamps concentrated near the electrodes , and just the electrons move to the other electrode or the positive mercury ions move too?</p> | g9206 | [
-0.0015111814718693495,
0.03844887763261795,
-0.005472641438245773,
0.023481156677007675,
0.0725947692990303,
-0.007189145311713219,
0.028586266562342644,
-0.014209127984941006,
0.008144629187881947,
-0.012286663986742496,
-0.05657081678509712,
0.05834842845797539,
0.009968696162104607,
-0.028072817251086235,
0.00593891367316246,
-0.04078418388962746,
-0.005273452959954739,
-0.01795141026377678,
-0.008688087575137615,
0.04402356967329979,
-0.03152632340788841,
-0.007220293860882521,
-0.03145155310630798,
-0.040923528373241425,
-0.04128482565283775,
0.032374367117881775,
-0.046077657490968704,
-0.007746958173811436,
0.0018961549503728747,
-0.017876403406262398,
-0.018842825666069984,
-0.03502301126718521,
-0.016621174290776253,
-0.07047078758478165,
-0.021643906831741333,
-0.04820583760738373,
0.029541421681642532,
0.0278625451028347,
-0.024426503106951714,
0.012021021917462349,
0.05195086449384689,
0.050605256110429764,
0.07207036763429642,
-0.085006482899189,
0.04055138677358627,
-0.06261816620826721,
0.022916516289114952,
-0.032720357179641724,
0.0019136288901790977,
-0.04790659248828888,
-0.04331713914871216,
0.07625265419483185,
-0.06941674649715424,
-0.004596230573952198,
0.07022292912006378,
0.03459697216749191,
0.008240672759711742,
-0.05665234103798866,
0.05692742019891739,
0.037501852959394455,
0.09672708809375763,
-0.017571602016687393,
0.042411673814058304,
-0.02071147784590721,
0.014177665114402771,
0.02263694629073143,
-0.044498637318611145,
-0.006813500542193651,
0.014813518151640892,
0.0037498166784644127,
-0.019242212176322937,
0.034225545823574066,
-0.04098613187670708,
0.03491505980491638,
0.008942478336393833,
0.0353986881673336,
-0.015053744427859783,
-0.03211706131696701,
0.029612507671117783,
0.011005858890712261,
-0.04986731708049774,
-0.0718105211853981,
0.002045735251158476,
-0.04236898943781853,
0.025262601673603058,
0.03150028735399246,
-0.010430581867694855,
0.038065437227487564,
-0.07389964163303375,
-0.07973965257406235,
0.04890025407075882,
-0.05331549793481827,
0.06784947961568832,
-0.022053366526961327,
-0.05199466645717621,
0.014083276502788067,
-0.005027365870773792,
0.02458846941590309,
0.03193339705467224,
0.007327134720981121,
-0.0345749594271183,
-0.01807641051709652,
-0.012665440328419209,
-0.016249077394604683,
-0.024924535304307938,
-0.06309857219457626,
0.012886157259345055,
-0.02472013607621193,
0.012869484722614288,
-0.031300999224185944,
0.0012340330285951495,
-0.04053841531276703,
-0.06287644058465958,
-0.037148334085941315,
0.014670261181890965,
-0.002735268557444215,
0.052504416555166245,
-0.031402792781591415,
0.037818316370248795,
-0.027724487707018852,
0.0328136682510376,
0.08087070286273956,
0.012198394164443016,
-0.012543450109660625,
0.026635922491550446,
0.034486074000597,
0.030052701011300087,
0.022866694256663322,
-0.027179570868611336,
0.00007995166379259899,
0.03495798632502556,
-0.011838750913739204,
-0.051900289952754974,
0.022054344415664673,
-0.02103322558104992,
-0.03867579624056816,
0.05044279247522354,
0.04658493772149086,
-0.009992530569434166,
0.054642416536808014,
0.04422730579972267,
0.02114763855934143,
-0.0009839781560003757,
-0.06925366818904877,
0.009142640046775341,
0.001831458997912705,
0.021308481693267822,
0.038017481565475464,
0.10205859690904617,
0.018084725365042686,
0.0008096842793747783,
-0.0499863401055336,
0.033056072890758514,
-0.06720089167356491,
-0.005447633098810911,
-0.09463396668434143,
0.034175705164670944,
-0.018723415210843086,
0.013878075405955315,
0.008694454096257687,
0.0009915678529068828,
-0.07393210381269455,
0.049672145396471024,
-0.0031802314333617687,
-0.010641382075846195,
-0.011034416034817696,
0.0108631057664752,
0.017410913482308388,
0.0312923826277256,
0.016799580305814743,
0.0008061483968049288,
-0.024681733921170235,
-0.0007526923436671495,
0.0476229153573513,
0.061752524226903915,
0.05402696877717972,
-0.02200871892273426,
0.003603799967095256,
0.027323972433805466,
-0.03615978732705116,
-0.05483487248420715,
-0.04120985418558121,
-0.037673983722925186,
-0.07224210351705551,
0.0003046269412152469,
-0.017371980473399162,
-0.08676562458276749,
0.01271843072026968,
-0.0564972348511219,
0.010846973396837711,
0.04221136495471001,
0.018914517015218735,
0.06153688207268715,
0.009195303544402122,
-0.07061377912759781,
-0.04633702337741852,
-0.008509802632033825,
-0.04361843317747116,
-0.001159324892796576,
0.010351019911468029,
-0.013821985572576523,
-0.013231473974883556,
-0.02762305736541748,
0.01786426641047001,
0.05028095468878746,
0.014534729532897472,
-0.013860814273357391,
-0.0870145931839943,
0.017965108156204224,
0.004221729934215546,
-0.003941725008189678,
0.028138956055045128,
-0.0045686690136790276,
0.02587193250656128,
-0.02892444282770157,
-0.08249252289533615,
-0.023834798485040665,
0.010357324965298176,
0.028768666088581085,
0.009931993670761585,
-0.017786290496587753,
0.023271171376109123,
0.0053389244712889194,
-0.01454496942460537,
0.03308957815170288,
0.021499205380678177,
0.029820505529642105,
-0.002549959346652031,
-0.03599792718887329,
0.03262249007821083,
-0.029116161167621613,
-0.04376274347305298,
-0.04248586297035217,
-0.012360327877104282,
0.00010174015915254131,
0.07961907982826233,
-0.09124290943145752,
0.013517503626644611,
-0.02807619236409664,
-0.019269611686468124,
-0.06519133597612381,
-0.02759084850549698,
0.03245464712381363,
0.01940024644136429,
-0.03044937551021576,
0.03170855715870857,
0.042905569076538086,
0.06956452876329422,
0.013302894309163094,
0.06719529628753662,
0.044037334620952606,
-0.0022355043329298496,
0.06249580532312393,
0.039647314697504044,
-0.035078078508377075,
-0.033863749355077744,
-0.0018436878453940153,
0.010533355176448822,
0.02985292300581932,
-0.03617030009627342,
-0.020319728180766106,
-0.03422205522656441,
-0.013546847738325596,
0.011107160709798336,
-0.05009434372186661,
-0.035389430820941925,
0.005073264706879854,
-0.03233620151877403,
0.0453217588365078,
-0.06839247047901154,
0.0447058379650116,
0.03328068554401398,
-0.010544735938310623,
0.0018191789276897907,
-0.02267700619995594,
0.028795193880796432,
0.012007616460323334,
-0.04850611090660095,
0.039795927703380585,
-0.03559063747525215,
-0.03835102915763855,
0.027257245033979416,
-0.03662664815783501,
-0.027692900970578194,
-0.032828155905008316,
-0.001996214035898447,
0.016013609245419502,
0.01833120919764042,
0.010242357850074768,
0.030690990388393402,
-0.022277792915701866,
-0.05372193083167076,
0.0753820538520813,
-0.02100578136742115,
-0.03786863014101982,
0.013442452065646648,
0.026788940653204918,
-0.01876354217529297,
-0.0035503844264894724,
0.05491593852639198,
-0.013310753740370274,
0.008718939498066902,
-0.005394404754042625,
0.06068285182118416,
0.09383828938007355,
0.018066825345158577,
-0.022723698988556862,
-0.018068760633468628,
0.017553560435771942,
0.017709780484437943,
0.022747760638594627,
-0.01784270815551281,
0.01698623038828373,
0.04176345467567444,
0.004797704052180052,
-0.03449592366814613,
-0.03505473583936691,
0.03584466874599457,
0.013019663281738758,
0.024388520047068596,
0.005448448937386274,
-0.0509689599275589,
-0.012479500845074654,
-0.006368250586092472,
0.05655461922287941,
-0.04555477574467659,
0.04527638107538223,
-0.03649604693055153,
0.023162420839071274,
-0.02280132658779621,
-0.012010925449430943,
0.01819232851266861,
-0.009032320231199265,
-0.0247395858168602,
0.010558855719864368,
-0.05809073895215988,
0.015277016907930374,
0.027559662237763405,
0.012339836917817593,
0.024041784927248955,
0.009567424654960632,
-0.02483455464243889,
-0.05363965034484863,
-0.0443548783659935,
-0.013027715496718884,
-0.036912474781274796,
0.009019821882247925,
0.011109855026006699,
0.02589707262814045,
0.0023462416138499975,
0.023955972865223885,
0.05027920380234718,
-0.009757885709404945,
0.006310786120593548,
-0.05768784508109093,
-0.0632031112909317,
-0.024665020406246185,
0.008320845663547516,
-0.028255317360162735,
-0.026055186986923218,
-0.023145785555243492,
0.025988921523094177,
-0.0033532893285155296,
0.003331760410219431,
0.002760896924883127,
-0.048400480300188065,
-0.052922289818525314,
-0.000284416921203956,
0.05759961158037186,
-0.028402168303728104,
-0.023390481248497963,
0.015268074348568916,
0.04367984086275101,
0.004802640527486801,
0.041451677680015564,
-0.0015880382852628827,
-0.0017401449149474502,
-0.003235837910324335,
-0.03902517631649971,
0.04194130375981331,
-0.021384701132774353,
-0.046944960951805115,
-0.022758768871426582,
0.019516417756676674,
0.03180887922644615,
-0.023222660645842552,
0.013934017159044743,
0.00950058363378048,
-0.04306903854012489,
-0.07362306118011475,
-0.015580540522933006,
0.030115433037281036,
0.00004666931272367947,
-0.013804546557366848,
0.013477294705808163,
-0.007611124776303768,
0.02405017614364624,
0.04051664471626282,
0.00849438738077879,
0.02733169123530388,
0.013971512205898762,
-0.014820915646851063,
0.006190520711243153,
-0.018593372777104378,
-0.03742865473031998,
-0.02465955540537834,
-0.0064805541187524796,
-0.009152497164905071,
0.04512311890721321,
-0.014222774654626846,
-0.05519247055053711,
0.04156243056058884,
-0.027408676221966743,
0.026032177731394768,
0.007727166637778282,
0.0326608270406723,
0.013377991504967213,
-0.008289428427815437,
-0.008482815697789192,
0.0006015785620547831,
-0.00876428559422493,
0.077363520860672,
0.0643417164683342,
0.022720055654644966,
0.0077703725546598434,
0.0620945505797863,
0.048786602914333344,
0.02858603745698929,
0.011566678062081337,
-0.06279279291629791,
-0.02145695500075817,
0.0016169025329872966,
0.021628160029649734,
0.03219287469983101,
-0.004840256180614233,
0.06530596315860748,
-0.016612490639090538,
0.022874895483255386,
0.020093698054552078,
0.09266199916601181,
0.1119508296251297,
0.06404812633991241,
-0.04449167475104332,
0.05773665010929108,
-0.010187794454395771,
0.014780381694436073,
-0.055858444422483444,
0.010633248835802078,
0.021096745505928993,
-0.05039726197719574,
-0.008591895923018456,
0.040302447974681854,
-0.056126032024621964,
-0.015691950917243958,
0.05499034747481346,
-0.0037740333937108517,
0.005882412660866976,
0.04707722365856171,
0.01241705659776926,
0.03350207954645157,
0.0149388387799263,
-0.02807030826807022,
-0.009353693574666977,
0.018678713589906693,
0.08816669136285782,
-0.005436523351818323,
-0.007965548895299435,
-0.02570570819079876,
-0.08698847144842148,
-0.06408564746379852,
-0.04132052883505821,
0.05559395253658295,
0.05862056463956833,
0.01507552433758974,
0.030357345938682556,
-0.02999391034245491,
0.01914309896528721,
-0.009771197102963924,
-0.009396959096193314,
-0.016374289989471436,
-0.04576803743839264,
0.006844785995781422,
0.01731959730386734,
-0.03311588615179062,
-0.005269166082143784,
-0.04263460636138916,
-0.002935204654932022,
0.04693802073597908,
0.039569269865751266,
-0.0429750494658947,
0.008736371994018555,
0.025612087920308113,
0.012411002069711685,
0.016867278143763542,
-0.010563980787992477,
-0.03949825465679169,
-0.011620529927313328,
0.01378634199500084,
-0.003890283638611436,
0.037137601524591446,
0.012788288295269012,
-0.014874138869345188,
-0.040112920105457306,
-0.012500646524131298,
-0.002194152446463704,
0.03720192611217499,
0.020654868334531784,
-0.06576462835073471,
0.042486537247896194,
0.012713066302239895,
-0.037198297679424286,
-0.06231069192290306,
-0.05919383093714714,
0.03346901759505272,
0.05055425316095352,
-0.009813421405851841,
-0.07294636219739914,
0.03281175345182419,
-0.014548692852258682,
-0.009582411497831345,
-0.02058720774948597,
0.007665571756660938,
0.018700813874602318,
-0.011070090346038342,
0.07074560970067978,
-0.01637248881161213,
-0.04448191449046135,
0.04811723530292511,
0.05419764667749405,
0.025895938277244568,
0.06909812986850739,
0.052253834903240204,
0.04447532445192337,
-0.0006174847949296236,
0.02866724319756031,
-0.056537821888923645,
0.02013699896633625,
0.007983396761119366,
0.039711564779281616,
0.06840705126523972,
0.02306903526186943,
0.02602258138358593,
-0.022425277158617973,
0.09001307934522629,
-0.001844945247285068,
0.035595785826444626,
-0.015650557354092598,
0.0021008357871323824,
0.020236901938915253,
0.0005622311728075147,
-0.0032589067704975605,
0.026771893724799156,
-0.023211857303977013,
0.020898954942822456,
-0.04610336199402809,
0.04122861474752426,
0.005547007545828819,
-0.029753385111689568,
0.04510250687599182,
-0.0442047119140625,
0.038840606808662415,
0.012364942580461502,
-0.028595082461833954,
-0.022991880774497986,
0.05239809677004814,
-0.04000392556190491,
-0.030503401532769203,
0.04148609936237335,
0.03222506865859032,
0.05032246187329292,
0.0037090610712766647,
-0.057129912078380585,
0.00471584452316165,
-0.001715162885375321,
0.027806198224425316,
0.01767221838235855,
-0.04333964362740517,
0.0503099262714386,
-0.07528786361217499,
0.02770896814763546,
-0.0068503390066325665,
0.021987389773130417,
0.013455774635076523,
-0.0356316864490509,
-0.013666457496583462,
0.0028322262223809958,
0.016858160495758057,
0.0018383158603683114,
0.011220677755773067,
-0.06553930789232254,
-0.034358616918325424,
0.03338335081934929,
0.007820026017725468,
-0.0629502683877945,
-0.006168380379676819,
-0.01118674036115408,
-0.011228112503886223,
-0.021628938615322113,
0.006649107672274113,
-0.02594202198088169,
0.021821999922394753,
-0.008213236927986145,
-0.03750535845756531,
0.010348116979002953,
0.060072485357522964,
-0.07178183645009995,
0.01832982897758484,
0.10701467096805573,
-0.02767113968729973,
0.048878803849220276,
-0.0019333030795678496,
0.02956274151802063,
0.0357389934360981,
-0.05108874663710594,
-0.004649417940527201,
-0.018873924389481544,
-0.010231027379631996,
0.04011773690581322,
0.01717364974319935,
0.024286892265081406,
-0.013713845051825047,
-0.05000070109963417,
-0.042772430926561356,
0.006558156572282314,
0.026682347059249878,
0.05819205194711685,
0.01968848891556263,
-0.012455153279006481,
-0.06555631756782532,
0.002055318793281913,
0.023394882678985596,
0.026196526363492012,
-0.0015399025287479162,
-0.011891369707882404,
0.036225032061338425,
-0.020189113914966583,
0.04912523552775383,
-0.005175058264285326,
0.028344905003905296,
0.010594794526696205,
-0.051229819655418396,
0.0069981650449335575,
-0.008716018870472908,
-0.019336707890033722,
0.012880353257060051,
0.02011539600789547,
-0.016703488305211067,
-0.016091255471110344,
-0.01867036521434784,
0.05108356103301048,
0.007518101949244738,
-0.09791264683008194,
-0.02652589976787567,
0.03799000009894371,
0.02788812480866909,
0.036794763058423996,
-0.003178227227181196,
0.02451709471642971,
0.0003975418512709439,
-0.0077200536616146564,
-0.021064981818199158,
-0.044598538428545,
-0.018741171807050705,
0.049207452684640884,
-0.003629096085205674,
0.07151256501674652,
-0.01688171550631523,
-0.042690083384513855,
-0.06982515752315521,
-0.008507738821208477,
0.032389797270298004,
0.012229172512888908,
0.020517569035291672,
0.0011951422784477472,
0.06341547518968582,
0.05369867756962776,
-0.019803224131464958,
0.014699962921440601,
0.010612144134938717,
-0.06862185895442963,
-0.01685180887579918,
-0.025469398126006126,
0.007803109008818865,
-0.04306945949792862,
-0.03331504762172699,
-0.02735024504363537,
-0.023699849843978882,
-0.017262108623981476,
0.009632752276957035,
-0.023090483620762825,
0.04206622764468193,
-0.015929579734802246,
0.0038936836645007133,
0.0033794541377574205,
-0.0005707454401999712,
0.005540014244616032,
0.02711004950106144,
0.01297122985124588,
-0.0033588081132620573,
-0.0024202466011047363,
-0.005929217673838139,
-0.005525673273950815,
0.019914155825972557,
-0.009114492684602737,
0.018646784126758575,
0.011879348196089268,
-0.02253093756735325,
0.0067692045122385025,
0.011682860553264618,
-0.05267246440052986,
0.006132115609943867,
0.08086756616830826,
-0.02470766380429268,
0.007263240870088339,
0.03151528537273407,
-0.033282410353422165,
-0.04148908704519272,
-0.009914729744195938,
0.025877898558974266,
0.02093890681862831,
-0.02410942316055298,
0.02789766527712345,
0.032985933125019073,
-0.004119055345654488,
-0.05755958333611488,
0.01661968044936657,
0.03576575592160225,
0.014930970966815948,
-0.035076163709163666,
-0.0031781126745045185,
-0.0186440572142601,
-0.010644043795764446,
-0.06674306839704514,
0.007639855146408081,
-0.06762100756168365,
-0.0496373251080513,
0.042006488889455795,
-0.09045591205358505,
0.007549994625151157,
0.04532533884048462,
-0.0024943884927779436,
-0.12360826879739761,
-0.008582632057368755,
-0.023115504533052444,
-0.018990064039826393,
0.02931951731443405,
-0.0021623761858791113,
0.01035716850310564,
0.019811980426311493,
-0.007066429127007723,
-0.014883682131767273,
-0.006924112793058157,
-0.05133567377924919,
0.0048478893004357815,
0.0790126770734787,
-0.05661863833665848,
-0.023616131395101547,
0.032117463648319244,
0.02758372575044632,
0.021161329001188278,
-0.03474750369787216,
-0.03900134935975075,
-0.013504269532859325,
0.02389533445239067,
-0.025858186185359955,
-0.0021533805411309004,
-0.017839465290308,
-0.023850729689002037
] |
<p>An electron is orbiting two protons. With the Born-Oppenheimer approximation that the protons do not move, I'd write the Hamiltonian of the electron's movement as:</p>
<p>$$ \mathbf{H} = -\frac{\hbar^2}{2m}\nabla^2 + E_p$$</p>
<p>with</p>
<p>$$E_p = -\frac{e^2}{4\pi \epsilon_0}\left(\frac{1}{r_1}+\frac{1}{r_2}\right) $$</p>
<p>as the potential caused by the protons, with $r_1$ and $r_2$ denoting distances to the protons. Apparently it should be</p>
<p>$$E_p = -\frac{e^2}{4\pi \epsilon_0}\left(\frac{1}{r_1}+\frac{1}{r_2}-\frac{1}{r_0}\right), $$</p>
<p>where $r_0$ denotes the distance between the protons. How can that term be explained?</p> | g9207 | [
0.02327977865934372,
0.03066476806998253,
-0.02471798285841942,
0.025378301739692688,
0.099049873650074,
0.055137090384960175,
0.019082307815551758,
0.021833201870322227,
-0.04532647877931595,
-0.00990199763327837,
-0.0037829249631613493,
0.049223124980926514,
0.012586802244186401,
-0.0034764099400490522,
0.04277275502681732,
0.027069605886936188,
0.03826865926384926,
0.008387790061533451,
0.013451583683490753,
0.001227612141519785,
-0.007958940230309963,
0.010280270129442215,
0.0026523808483034372,
0.02614344283938408,
0.007552716881036758,
-0.04410460963845253,
-0.001754780882038176,
-0.016946645453572273,
-0.024108361452817917,
-0.012504239566624165,
0.0012588389217853546,
0.03058698959648609,
0.07933655381202698,
-0.06534891575574875,
-0.035884883254766464,
0.018794162198901176,
0.0845184475183487,
0.03133248910307884,
0.04373971372842789,
-0.06663398444652557,
-0.02855701372027397,
-0.08363015204668045,
0.00827645231038332,
-0.03460083156824112,
0.024432137608528137,
-0.018613750115036964,
-0.0195221658796072,
-0.011892960406839848,
0.016190055757761,
-0.019045596942305565,
-0.010984105989336967,
0.0734434500336647,
0.016774866729974747,
0.04657310992479324,
0.03867839276790619,
0.0030835196375846863,
0.022089239209890366,
0.01697203703224659,
0.08712943643331528,
0.06779593229293823,
0.06602448970079422,
-0.007788423448801041,
0.007494161371141672,
0.02633061818778515,
0.07612090557813644,
-0.018493009731173515,
-0.040526919066905975,
0.01916796900331974,
0.017313439399003983,
-0.04246756434440613,
0.013518797233700752,
-0.09032976627349854,
-0.05160199850797653,
-0.02691730670630932,
-0.041115131229162216,
0.013058370910584927,
0.006606299430131912,
-0.009828567504882812,
0.06357274204492569,
-0.009341991506516933,
-0.03629425913095474,
-0.008717465214431286,
0.006029881536960602,
0.030783463269472122,
0.09693365544080734,
0.03640167787671089,
0.013928735628724098,
0.013299821875989437,
-0.07548981159925461,
-0.051296163350343704,
-0.06747350841760635,
-0.088260218501091,
0.006923643872141838,
-0.03481941297650337,
0.03708625212311745,
-0.028535600751638412,
-0.0414421446621418,
0.026916401460766792,
-0.03235282376408577,
-0.0028082504868507385,
-0.04215060919523239,
0.03448101878166199,
0.007233707699924707,
-0.033884305506944656,
0.03865218907594681,
-0.006258124485611916,
0.05400810018181801,
-0.01190741453319788,
0.0723901242017746,
-0.02310887910425663,
-0.009646552614867687,
-0.0265208687633276,
0.0017151432111859322,
-0.030051978304982185,
-0.006052219774574041,
0.0207650326192379,
0.034212298691272736,
-0.018068406730890274,
0.019887078553438187,
0.022399140521883965,
0.010319814085960388,
0.00018881968571804464,
0.009628141298890114,
0.0836128368973732,
-0.03630227968096733,
0.03415694832801819,
-0.015940219163894653,
-0.02762608230113983,
0.044084060937166214,
0.020711833611130714,
0.0034970242995768785,
-0.022490449249744415,
0.011442933231592178,
0.009199869818985462,
0.0037254139315336943,
0.008480172604322433,
-0.023839835077524185,
0.012866202741861343,
-0.0009859877172857523,
0.01173878088593483,
0.014848361723124981,
-0.06920821964740753,
0.021762309595942497,
-0.07693488150835037,
-0.03254007548093796,
0.014346596784889698,
0.0161349568516016,
-0.03787441551685333,
0.03752143308520317,
0.02276802621781826,
-0.0020634003449231386,
0.08264801651239395,
-0.012955859303474426,
0.011376611888408661,
0.0571969673037529,
-0.03410322219133377,
0.048832450062036514,
0.013609647750854492,
-0.022960906848311424,
0.012882939539849758,
0.06930193305015564,
-0.025979679077863693,
0.009880157187581062,
0.01313288789242506,
-0.0666690245270729,
0.04043838381767273,
0.009533814154565334,
-0.0700291246175766,
-0.0020227597560733557,
-0.038296185433864594,
-0.018699709326028824,
-0.017545271664857864,
0.011231835000216961,
0.07351134717464447,
0.013774137012660503,
0.06095670163631439,
0.007465346250683069,
-0.011830410920083523,
-0.011020905338227749,
0.0464196540415287,
0.0108995595946908,
-0.016563942655920982,
0.027038415893912315,
0.011183305643498898,
-0.013755029067397118,
-0.017917703837156296,
-0.001262327074073255,
0.03897707909345627,
-0.023721320554614067,
-0.05307132005691528,
0.024997854605317116,
0.022519079968333244,
0.026331035420298576,
-0.004973297938704491,
-0.04976745322346687,
0.010969488881528378,
-0.0021807453595101833,
-0.09886869043111801,
0.008870743215084076,
-0.006537262815982103,
-0.018780531361699104,
0.011996457353234291,
0.06655353307723999,
-0.02504604123532772,
0.05787969380617142,
-0.013673710636794567,
-0.005707653239369392,
0.0010861994232982397,
0.0733708068728447,
0.0034005504567176104,
-0.038843777030706406,
0.0012865520548075438,
-0.030024340376257896,
0.03500298783183098,
0.011433511041104794,
-0.05484873801469803,
-0.019213473424315453,
0.031945209950208664,
-0.03976112976670265,
0.010933213867247105,
-0.04778628051280975,
-0.035558559000492096,
0.046944718807935715,
-0.038455333560705185,
-0.0015184043440967798,
0.026118474081158638,
-0.0015379918040707707,
0.011087740771472454,
-0.06277095526456833,
0.03287753090262413,
-0.0641501173377037,
0.002419580239802599,
-0.012811850756406784,
0.0080077750608325,
0.023210562765598297,
0.014600989408791065,
-0.009821574203670025,
-0.021739928051829338,
-0.004477505572140217,
-0.0020322133786976337,
0.006162989418953657,
-0.03358812630176544,
-0.024660589173436165,
-0.0010330924997106194,
0.07099828124046326,
0.029779696837067604,
0.0836055651307106,
0.02385326474905014,
-0.06334652751684189,
0.05790194123983383,
0.03360389545559883,
0.005369523540139198,
-0.07623590528964996,
0.004165355581790209,
-0.020965037867426872,
-0.04689231887459755,
-0.04828695207834244,
0.016250070184469223,
-0.03692200779914856,
-0.01974904164671898,
0.005048441234976053,
-0.02574697509407997,
-0.012563765048980713,
-0.007680198177695274,
-0.014473001472651958,
-0.03387710824608803,
-0.027881747111678123,
0.040563296526670456,
0.04762262850999832,
-0.034600138664245605,
-0.006688698194921017,
0.07082629203796387,
0.024872440844774246,
0.0534270703792572,
-0.02242843061685562,
-0.038768403232097626,
0.01209882739931345,
-0.02478339895606041,
0.04117507115006447,
0.02505592256784439,
-0.031042475253343582,
-0.016886258497834206,
-0.06412319093942642,
-0.008534152060747147,
0.010597349144518375,
-0.05642743408679962,
-0.000692862959112972,
0.029592471197247505,
-0.012947645038366318,
-0.04655788838863373,
-0.018720708787441254,
0.013460944406688213,
0.03817136585712433,
0.01586649753153324,
0.007830251939594746,
0.026067547500133514,
0.06427545100450516,
-0.0319693423807621,
-0.03191687911748886,
0.04186945781111717,
0.005050566513091326,
0.01697264052927494,
-0.022495117038488388,
0.01068015955388546,
0.015599838458001614,
0.0270970668643713,
-0.041955336928367615,
-0.06439776718616486,
-0.06916224211454391,
-0.0007116517517715693,
0.01415214966982603,
0.04478404298424721,
0.0025911482516676188,
0.010935395956039429,
0.025446094572544098,
-0.020520607009530067,
-0.05239544436335564,
-0.008885787799954414,
0.055350929498672485,
-0.013080954551696777,
-0.05722783878445625,
-0.07616186141967773,
-0.013296054676175117,
0.03224584832787514,
0.05140290781855583,
0.006104785017669201,
-0.09528157114982605,
0.009529371745884418,
-0.024220570921897888,
-0.0272817462682724,
0.017246922478079796,
-0.01574109122157097,
0.02722940966486931,
-0.048373568803071976,
-0.054908208549022675,
-0.004440770950168371,
0.04804623872041702,
0.0672382265329361,
0.023482536897063255,
0.0006055286503396928,
-0.061754241585731506,
-0.00276601011864841,
-0.05041532590985298,
0.016434501856565475,
-0.009305443614721298,
-0.03139736130833626,
-0.005139915272593498,
-0.023985840380191803,
0.014036115258932114,
-0.02715693973004818,
-0.02331867814064026,
0.012642125599086285,
0.05271380767226219,
0.04485500603914261,
-0.03616541624069214,
-0.02165919914841652,
-0.03204289823770523,
-0.017412548884749413,
0.007980707101523876,
0.024761179462075233,
-0.007441609166562557,
-0.03480661287903786,
-0.009951610118150711,
0.08919898420572281,
0.013575242832303047,
-0.06036260724067688,
-0.058011289685964584,
0.012017279863357544,
0.01803903467953205,
-0.04491210728883743,
-0.05138018727302551,
-0.05071938410401344,
0.027995634824037552,
-0.024652188643813133,
0.049217164516448975,
-0.02034304291009903,
-0.04116762429475784,
-0.0033769637811928988,
-0.090567946434021,
0.07301336526870728,
0.002586083486676216,
0.029867682605981827,
0.04467695578932762,
0.012536578811705112,
0.06730035692453384,
-0.0029145057778805494,
-0.0337582491338253,
-0.007464286405593157,
-0.025704966858029366,
0.005819123238325119,
0.021857410669326782,
-0.03913086652755737,
0.025921974331140518,
0.018993554636836052,
0.05607329308986664,
-0.05317017808556557,
0.04984698444604874,
-0.005469354800879955,
0.03148043900728226,
0.03803515061736107,
-0.007914724759757519,
-0.01589035987854004,
-0.02068324387073517,
-0.042908430099487305,
-0.00586325628682971,
-0.02203335054218769,
0.03266432508826256,
0.020505445078015327,
0.03358430042862892,
-0.0067331488244235516,
-0.01833270862698555,
0.07572901248931885,
0.020879510790109634,
-0.018448127433657646,
-0.026184769347310066,
-0.014032445847988129,
-0.022118592634797096,
-0.0018271799199283123,
-0.029003700241446495,
0.04913599044084549,
-0.03171364963054657,
0.007336495444178581,
0.03156551718711853,
-0.01512569934129715,
0.0052789561450481415,
0.047943633049726486,
-0.009067606180906296,
-0.0016751340590417385,
0.003913115244358778,
-0.033431489020586014,
-0.045611437410116196,
0.03961342200636864,
0.005555286072194576,
0.05145305022597313,
-0.03575834259390831,
0.042639344930648804,
-0.02360989898443222,
-0.012599796056747437,
-0.02617952600121498,
0.05236878991127014,
0.07447893917560577,
0.0015276327030733228,
0.010208413004875183,
0.06508004665374756,
-0.0027743105310946703,
0.023368114605545998,
-0.02095876820385456,
-0.09768124669790268,
0.01439875178039074,
-0.07346884906291962,
-0.019335662946105003,
0.007640690077096224,
0.0362534262239933,
0.025856036692857742,
0.015191032551229,
-0.057555150240659714,
-0.03762654587626457,
0.014198485761880875,
0.009469683282077312,
-0.007385818753391504,
-0.07790424674749374,
0.021851252764463425,
-0.005110127851366997,
-0.03537535294890404,
-0.011817715130746365,
0.005557740572839975,
-0.055114567279815674,
0.02071109414100647,
-0.03237154707312584,
0.01312186662107706,
0.00675374548882246,
-0.03977128490805626,
0.012005961500108242,
-0.014706398360431194,
0.0024403026327490807,
-0.022414689883589745,
-0.000019500870621413924,
-0.0004679163685068488,
-0.018144406378269196,
-0.040526133030653,
-0.03860998526215553,
-0.008191369473934174,
0.009466811083257198,
0.0410228930413723,
-0.037646859884262085,
0.006674664095044136,
0.006505938712507486,
-0.006530378479510546,
0.00333217135630548,
-0.020634228363633156,
0.027657825499773026,
0.025147493928670883,
-0.015635531395673752,
-0.010287596844136715,
0.02773711457848549,
-0.01079410407692194,
0.009550774469971657,
0.06327707320451736,
0.020751338452100754,
0.015602650120854378,
-0.0400020033121109,
0.010892110876739025,
-0.03242293372750282,
0.03655685856938362,
0.05185249075293541,
0.021202027797698975,
0.09036677330732346,
-0.04072878509759903,
0.019748881459236145,
-0.05747706815600395,
-0.013357610441744328,
-0.03274952620267868,
-0.0068910676054656506,
0.04111388698220253,
0.038405876606702805,
-0.004854676313698292,
-0.03931599110364914,
-0.007803177926689386,
-0.004384136293083429,
-0.009922369383275509,
0.06706677377223969,
-0.05092225223779678,
0.046719107776880264,
-0.03959454596042633,
0.043556660413742065,
-0.02307797037065029,
-0.018513448536396027,
0.008275055326521397,
-0.026877466589212418,
0.07222394645214081,
0.0045031048357486725,
-0.027366843074560165,
0.04782668128609657,
0.03635306656360626,
0.008111770264804363,
-0.02387300319969654,
-0.005515695549547672,
-0.014668845571577549,
0.018536124378442764,
-0.030695484951138496,
-0.014644138514995575,
-0.02855698950588703,
0.00023282822803594172,
0.108571358025074,
-0.038182616233825684,
0.06294439733028412,
-0.0558844618499279,
0.03819090873003006,
0.056424111127853394,
-0.013808495365083218,
-0.009645836427807808,
-0.03584883362054825,
-0.007214823272079229,
-0.06721294671297073,
0.026649540290236473,
0.0312543585896492,
0.035152971744537354,
-0.011641096323728561,
-0.01579689234495163,
-0.022157277911901474,
0.022186243906617165,
-0.023760085925459862,
0.015122123062610626,
0.061992097645998,
0.026059256866574287,
0.033025193959474564,
-0.004331684205681086,
0.03185466304421425,
0.031080737709999084,
0.006954490207135677,
-0.026107996702194214,
0.007209844421595335,
-0.0068985531106591225,
0.022696975618600845,
0.03264470770955086,
0.036860693246126175,
0.00219836737960577,
-0.013559856452047825,
-0.04805431514978409,
-0.021745238453149796,
-0.0027255110908299685,
0.024770142510533333,
0.009008626453578472,
-0.01614157296717167,
-0.030408931896090508,
0.05537532642483711,
-0.018010258674621582,
-0.04690556228160858,
0.11741847544908524,
0.018283257260918617,
-0.008019900880753994,
-0.03880079835653305,
-0.03056214191019535,
-0.04949638992547989,
-0.033757664263248444,
0.03877707198262215,
-0.012414856813848019,
-0.05308005213737488,
-0.0410601980984211,
0.04572169482707977,
0.031393323093652725,
0.013247278518974781,
0.005079461727291346,
0.03765370324254036,
0.0377221554517746,
0.049482472240924835,
-0.04573076590895653,
0.006600364111363888,
-0.0129825659096241,
0.03881468251347542,
-0.07203757762908936,
-0.012425349093973637,
0.026593593880534172,
-0.030961835756897926,
0.005434456747025251,
-0.021046938374638557,
0.026192856952548027,
0.06200241297483444,
-0.03353799879550934,
0.017490128055214882,
-0.009581192396581173,
-0.017696168273687363,
-0.03944040462374687,
-0.024909283965826035,
0.0414583683013916,
-0.016806982457637787,
-0.04925525560975075,
-0.010953706689178944,
0.008532044477760792,
0.009751531295478344,
0.03833114728331566,
-0.005087441299110651,
-0.043103281408548355,
0.03895740211009979,
0.008201953023672104,
0.034492138773202896,
-0.010533327236771584,
0.018200699239969254,
-0.015822261571884155,
0.014278565533459187,
0.0071652536280453205,
-0.00476857228204608,
0.046875737607479095,
-0.039648108184337616,
-0.07319629192352295,
-0.01119597814977169,
-0.0031160684302449226,
0.0004355484270490706,
-0.06719315052032471,
-0.014519316144287586,
-0.03013370744884014,
-0.004952200222760439,
-0.02606820873916149,
0.06396202743053436,
0.009120173752307892,
-0.05729927495121956,
-0.00681102741509676,
0.0042081777937710285,
-0.01835262030363083,
-0.03791925311088562,
-0.036146581172943115,
-0.05133191868662834,
0.00023277474974747747,
0.04238274320960045,
0.01127723976969719,
0.00026643427554517984,
-0.05458651855587959,
-0.028698040172457695,
0.0003268854634370655,
-0.0655578002333641,
0.004307249560952187,
-0.03760913759469986,
-0.0140173165127635,
0.06487365067005157,
-0.012816978618502617,
-0.003534118877723813,
0.06336239725351334,
0.0015961716417223215,
-0.0276307612657547,
-0.01757526583969593,
0.031100979074835777,
-0.010464277118444443,
0.01306545827537775,
0.003623567521572113,
-0.03187352046370506,
-0.0036507707554847,
-0.050779566168785095,
-0.011488827876746655,
-0.017571572214365005,
0.019264699891209602,
0.04064628854393959,
0.010347524657845497,
0.041145581752061844,
0.012351145036518574,
-0.02675940841436386,
0.03416558355093002,
-0.00025832801475189626,
0.02296406216919422,
0.032033953815698624,
0.011567788198590279,
0.039230041205883026,
-0.04548930004239082,
0.04819497838616371,
-0.001036741421557963,
0.049523141235113144,
-0.041483324021101,
0.05253559723496437,
-0.015177003107964993,
-0.03867717832326889,
-0.03878818079829216,
0.014930385164916515,
0.04337778314948082,
-0.003555932082235813,
0.001402702066116035,
0.040073201060295105,
-0.0062081096693873405,
0.04444064572453499,
0.04535148665308952,
0.008496183902025223,
0.004976789467036724,
-0.011850085109472275,
-0.02422432228922844,
0.029705984517931938,
-0.07786792516708374,
-0.026817992329597473,
-0.024525897577404976,
-0.012290066108107567,
-0.07765960693359375,
0.03270794451236725,
-0.00436750054359436,
-0.06670528650283813,
0.018152477219700813,
-0.028346093371510506,
0.0031982387881726027,
-0.09087050706148148,
-0.05278453603386879,
-0.04048287868499756,
-0.00020880936062894762,
0.0522499643266201,
0.01549588143825531,
-0.039808835834264755,
-0.0653819739818573,
0.01984487846493721,
-0.04030032455921173,
-0.028305858373641968,
-0.022656070068478584,
-0.015319500118494034,
0.01337386853992939,
0.07389520853757858,
0.028157439082860947,
0.017500894144177437,
0.04432382434606552,
-0.04739837348461151,
0.055878620594739914,
0.10136808454990387,
-0.02092656120657921,
-0.018231403082609177,
0.046263355761766434,
-0.012621725909411907,
0.03798030689358711,
-0.013348164036870003,
-0.0444251224398613,
-0.022211112082004547,
-0.008447522297501564,
-0.007952284999191761,
-0.040610626339912415,
0.0017726199002936482,
0.050419874489307404
] |
<p>I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. </p>
<ul>
<li><p>Does dimensional regularization see "all" kinds of divergences? </p>
<p>I mean - what does it <em>exactly</em> mean when one says that power law divergences and IR divergences disappear in the dimensional regularization. So is more regularization needed in general over and above dimensional regularization? </p></li>
<li><p>Does anything about the divergences get specially constrained if the theory is scale invariant? </p>
<p>I have often heard it being said that dimensional regularization "preserves" scale invariance. </p></li>
</ul> | g9208 | [
0.0475095696747303,
0.0203536469489336,
0.010471281595528126,
-0.026161473244428635,
0.02113872393965721,
0.022817004472017288,
-0.02079584077000618,
0.0021435068920254707,
-0.06415336579084396,
-0.0024959298316389322,
-0.01834174059331417,
-0.03086310438811779,
-0.03233404830098152,
0.036894604563713074,
-0.008686183020472527,
-0.042758360505104065,
0.04839342087507248,
-0.017162812873721123,
0.012863638810813427,
0.009763496927917004,
-0.03789558261632919,
0.004477168899029493,
0.03872472420334816,
0.021492505446076393,
-0.0031474619172513485,
-0.017275433987379074,
0.014912472106516361,
-0.019566195085644722,
-0.026034081354737282,
-0.07336818426847458,
0.08393976837396622,
0.006514790002256632,
0.058579765260219574,
-0.06892617046833038,
0.0041175102815032005,
0.021149786189198494,
0.056978099048137665,
0.06910708546638489,
0.033738113939762115,
0.027418503537774086,
0.004041503183543682,
0.036983128637075424,
0.019136199727654457,
0.02530527673661709,
-0.02969578467309475,
-0.02278505451977253,
-0.05692228302359581,
0.009186542592942715,
-0.023084722459316254,
0.04046858474612236,
0.02674449048936367,
0.03541018068790436,
0.035865943878889084,
-0.0031004580669105053,
-0.06213182583451271,
-0.02530672214925289,
-0.033468812704086304,
0.029170552268624306,
0.02447243221104145,
-0.05746585875749588,
0.018588626757264137,
0.01713109388947487,
-0.004702641628682613,
0.022150980308651924,
0.026301244273781776,
-0.056234534829854965,
-0.042306579649448395,
-0.00893058069050312,
0.032035887241363525,
-0.006448803469538689,
0.02109045535326004,
-0.01129027921706438,
-0.023884041234850883,
0.009252223186194897,
-0.05249149352312088,
0.010227273218333721,
0.04353123903274536,
-0.026785457506775856,
-0.059567663818597794,
0.02956436015665531,
-0.06646987795829773,
-0.02192603424191475,
-0.020765846595168114,
-0.006361823994666338,
0.077820785343647,
0.006714200135320425,
0.004041112959384918,
0.0064040482975542545,
-0.007440331391990185,
0.026660868898034096,
0.018680572509765625,
-0.05160138010978699,
-0.005573160480707884,
0.0445794053375721,
0.014397287741303444,
-0.004434761591255665,
0.024468254297971725,
0.0003080314490944147,
0.015493069775402546,
0.03330891579389572,
-0.005916202906519175,
0.05568202957510948,
-0.023827312514185905,
0.018283704295754433,
0.014814808964729309,
0.06772056221961975,
0.060849592089653015,
-0.02186395786702633,
0.0736512765288353,
-0.016626065596938133,
-0.07432287186384201,
-0.04446358606219292,
0.005731021054089069,
-0.012440313585102558,
0.007679925765842199,
0.014428517781198025,
0.06078896299004555,
-0.03691329061985016,
0.005554165691137314,
0.0077884262427687645,
0.07499468326568604,
-0.025770094245672226,
0.024721290916204453,
0.003708669450134039,
-0.0387326143682003,
0.028632869943976402,
0.0005745915696024895,
0.03226017579436302,
0.01162692904472351,
0.004046691581606865,
0.0258829053491354,
0.010292748920619488,
-0.05299036577343941,
-0.0197113286703825,
0.03662916272878647,
-0.01057493593543768,
-0.02006293646991253,
0.02068997360765934,
0.018564552068710327,
-0.0007467007380910218,
-0.05868199095129967,
0.052925944328308105,
0.017926326021552086,
-0.01166378241032362,
-0.029668834060430527,
-0.019669184461236,
0.006435135845094919,
-0.0044916244223713875,
0.004329356364905834,
0.0009732755133882165,
0.04094942286610603,
0.06013123691082001,
0.033050425350666046,
-0.0642838329076767,
0.00460027577355504,
0.05024610459804535,
0.019607961177825928,
0.003677110420539975,
0.08058660477399826,
-0.01815226674079895,
-0.026667216792702675,
0.04185769706964493,
0.048886753618717194,
-0.00037676337524317205,
0.006385609973222017,
-0.01828538067638874,
0.03485117852687836,
-0.014302299357950687,
-0.024236861616373062,
-0.017898909747600555,
-0.04489213228225708,
0.0734633058309555,
0.021487340331077576,
0.028858626261353493,
0.010171735659241676,
0.022395988926291466,
-0.05135686323046684,
-0.008090256713330746,
0.03360738232731819,
-0.0056711118668317795,
-0.0660625621676445,
-0.03993960842490196,
-0.0024291793815791607,
-0.07177893817424774,
0.05145474895834923,
0.009124083444476128,
0.026340913027524948,
-0.039318379014730453,
-0.0031165091786533594,
0.003192364238202572,
0.016385264694690704,
-0.009698303416371346,
-0.009754191152751446,
0.02044222690165043,
-0.00919936504215002,
-0.05057184770703316,
0.037949204444885254,
-0.013356855139136314,
-0.03444437310099602,
0.036647263914346695,
0.01569460518658161,
0.016801314428448677,
-0.044435083866119385,
0.0008155641262419522,
-0.03815970942378044,
0.04080949351191521,
-0.039264652878046036,
0.03324215114116669,
-0.01331029087305069,
-0.00962682906538248,
0.001510527334176004,
-0.03847997635602951,
0.011272352188825607,
-0.03209248557686806,
-0.015072126872837543,
0.02372617833316326,
-0.002887095557525754,
0.03384457528591156,
-0.05062919855117798,
0.0900278091430664,
0.01385748665779829,
-0.005081560462713242,
0.05365639179944992,
0.10665033012628555,
-0.06258908659219742,
0.026432981714606285,
-0.06196310743689537,
-0.010801966302096844,
-0.001717472798191011,
0.005202483851462603,
-0.05416620150208473,
-0.08789108693599701,
0.07914679497480392,
-0.013991679064929485,
-0.01867624558508396,
0.051436565816402435,
-0.023304829373955727,
-0.06304019689559937,
0.045627158135175705,
0.016322338953614235,
-0.012049559503793716,
0.010529975406825542,
0.010519806295633316,
0.017570815980434418,
0.027949368581175804,
0.03188024461269379,
0.033689409494400024,
-0.0010026927338913083,
-0.02610291913151741,
0.012029740028083324,
-0.010250120423734188,
0.0601455494761467,
-0.01767638698220253,
-0.007016147021204233,
-0.02111048251390457,
-0.04353288933634758,
0.09760836511850357,
0.03490174189209938,
0.007540184073150158,
-0.03669916093349457,
0.04444728046655655,
-0.003971894737333059,
-0.018786143511533737,
0.019308824092149734,
-0.029843522235751152,
0.03242219239473343,
0.09842102229595184,
0.016347799450159073,
-0.001437314786016941,
-0.008572246879339218,
0.011389021761715412,
0.052677758038043976,
-0.00007720584835624322,
0.04335730895400047,
0.043031055480241776,
0.022691085934638977,
0.00802464596927166,
-0.05494708940386772,
-0.02154669165611267,
-0.017366502434015274,
0.019995754584670067,
-0.0027424392756074667,
-0.053662367165088654,
0.011983457952737808,
0.03305375948548317,
-0.015354285016655922,
0.041258905082941055,
-0.008794687688350677,
-0.0014100116677582264,
0.03744226694107056,
-0.016009964048862457,
-0.04951205104589462,
-0.009715023450553417,
0.018016386777162552,
-0.011259992606937885,
0.004449580330401659,
-0.02100464515388012,
-0.09601650387048721,
-0.022221023216843605,
-0.02649223618209362,
-0.014814370311796665,
-0.0009134659776464105,
-0.04577358812093735,
0.009066160768270493,
0.0812586098909378,
-0.009200826287269592,
-0.048325616866350174,
0.016225693747401237,
-0.005753509234637022,
0.031021516770124435,
-0.0691128671169281,
0.06129565089941025,
-0.012750758789479733,
0.004586806986480951,
0.06345435976982117,
-0.00836953055113554,
0.014790235087275505,
0.0029619834385812283,
-0.004510694183409214,
-0.007973833940923214,
0.0018489437643438578,
-0.046586133539676666,
0.058944765478372574,
0.026298440992832184,
-0.035492513328790665,
0.051417212933301926,
-0.005327850114554167,
-0.02674376405775547,
-0.023396877571940422,
0.05762966349720955,
-0.018324393779039383,
-0.013597315177321434,
0.07407952100038528,
0.026465509086847305,
-0.0753609761595726,
-0.0418657623231411,
-0.07254999876022339,
-0.007006603758782148,
0.049643661826848984,
0.02688228152692318,
-0.010882152244448662,
-0.04624708369374275,
0.008437114767730236,
-0.03519565612077713,
0.01641934923827648,
-0.00580115569755435,
-0.0283608827739954,
-0.014419740065932274,
-0.04617568105459213,
-0.03508973494172096,
0.04960847273468971,
-0.01706658862531185,
0.05446956679224968,
-0.054770540446043015,
0.02306889183819294,
0.050682201981544495,
0.012567616067826748,
0.04563910514116287,
-0.028628651052713394,
-0.015465036034584045,
-0.013806367293000221,
-0.017391866073012352,
-0.0322003997862339,
0.0073024798184633255,
-0.02667810395359993,
0.010561130940914154,
0.045665428042411804,
-0.00114537647459656,
0.00372622930444777,
0.014712012372910976,
0.0590302012860775,
0.06322292238473892,
-0.040812138468027115,
-0.021185506135225296,
0.033472903072834015,
-0.011002451181411743,
0.040158119052648544,
0.056337397545576096,
-0.029405705630779266,
-0.003606976941227913,
0.04699274152517319,
0.04603622481226921,
-0.02786090224981308,
-0.002101561753079295,
0.0077639054507017136,
0.02434912882745266,
-0.05299864336848259,
0.006551912985742092,
0.007685261778533459,
-0.00618290388956666,
0.009627459570765495,
-0.019151628017425537,
0.0006934093544259667,
-0.012129746377468109,
0.02961741015315056,
-0.019556835293769836,
-0.013129384256899357,
0.007941213436424732,
-0.02373984456062317,
0.01591925509274006,
-0.009213442914187908,
-0.002661702688783407,
-0.024281738325953484,
0.03334956616163254,
-0.007611710112541914,
-0.022369185462594032,
-0.020571250468492508,
0.0011262212647125125,
0.011545354500412941,
0.010678587481379509,
-0.021805541589856148,
0.025452764704823494,
-0.037855591624975204,
-0.0606582835316658,
-0.02754216082394123,
-0.01838631182909012,
-0.007594962138682604,
-0.0034507529344409704,
0.023115569725632668,
-0.01277163252234459,
-0.022069217637181282,
0.009554916992783546,
-0.039899010211229324,
-0.010346704162657261,
0.007654957473278046,
0.03784290701150894,
0.057130683213472366,
-0.008935960941016674,
0.026438802480697632,
-0.016494588926434517,
0.07843824476003647,
-0.013743412680923939,
-0.058379169553518295,
-0.00013227119052316993,
-0.06209716945886612,
-0.013022235594689846,
-0.06015453115105629,
0.028914641588926315,
-0.07976708561182022,
0.01845024712383747,
0.013543367385864258,
0.007459571119397879,
0.06554263085126877,
0.021339839324355125,
-0.0681990459561348,
0.01830744370818138,
0.010836519300937653,
0.021243378520011902,
0.00026471007731743157,
0.007967881858348846,
0.005357050336897373,
0.03147512301802635,
-0.04080444574356079,
-0.019942373037338257,
-0.05709781125187874,
-0.03885019198060036,
0.0321909561753273,
0.052094753831624985,
0.0701996460556984,
0.01937834359705448,
-0.005946435499936342,
-0.022851910442113876,
-0.07008662819862366,
-0.04254942387342453,
0.045598406344652176,
-0.055926091969013214,
-0.0546865314245224,
0.018288813531398773,
-0.05156682804226875,
0.04727654159069061,
0.02242865227162838,
0.01675102859735489,
-0.010878379456698895,
0.025993382558226585,
-0.0319901667535305,
0.020429199561476707,
0.03222997114062309,
0.006169123575091362,
0.01585407368838787,
-0.03896142169833183,
-0.014016097411513329,
-0.059022072702646255,
0.04260335862636566,
0.018731147050857544,
-0.05438607186079025,
0.0040673427283763885,
-0.015133482404053211,
-0.04951063171029091,
-0.04682854562997818,
-0.03712756559252739,
-0.08296053856611252,
-0.008972542360424995,
0.030508602038025856,
0.05589572712779045,
-0.03363469988107681,
0.08185680955648422,
-0.015214627608656883,
-0.041154272854328156,
-0.03715338557958603,
-0.056188810616731644,
-0.006522289477288723,
-0.02884823828935623,
0.0906161367893219,
-0.03714953362941742,
-0.06297289580106735,
-0.00666812714189291,
0.11470744013786316,
0.009614501148462296,
0.038668081164360046,
-0.019405368715524673,
-0.0333537794649601,
0.054106228053569794,
-0.0395110659301281,
0.003064777934923768,
0.019314970821142197,
-0.04831364378333092,
-0.03514252230525017,
0.08093464374542236,
-0.000678112730383873,
-0.07407406717538834,
-0.0021347517613321543,
-0.05114711448550224,
0.06968335062265396,
-0.0543384850025177,
0.060768064111471176,
0.04281781613826752,
-0.012063128873705864,
-0.028587227687239647,
0.019508320838212967,
0.06600303947925568,
0.0753985270857811,
-0.012790282256901264,
-0.030052274465560913,
0.016659731045365334,
0.0013372614048421383,
0.0050057400949299335,
-0.004614380653947592,
0.03142913430929184,
-0.039809271693229675,
0.009693067520856857,
0.012865839526057243,
0.03474552184343338,
-0.031450774520635605,
-0.03453221172094345,
-0.012238341383635998,
-0.07272370159626007,
0.007592859677970409,
-0.025491446256637573,
0.013391729444265366,
-0.03645564615726471,
-0.04094530642032623,
0.002106092171743512,
-0.10370439291000366,
0.027446165680885315,
-0.07163090258836746,
0.011460479348897934,
0.00043895799899473786,
0.010615641251206398,
-0.03751382231712341,
0.013431135565042496,
-0.007528909016400576,
-0.015342445112764835,
0.035299092531204224,
-0.08634017407894135,
-0.054828301072120667,
-0.03928371146321297,
0.00618578027933836,
0.00589640811085701,
0.06318803876638412,
0.008402792736887932,
-0.00751526141539216,
0.01996331289410591,
0.045374490320682526,
0.010588680393993855,
0.022795982658863068,
-0.009258265607059002,
0.006311975885182619,
-0.10885895788669586,
0.004754525143653154,
-0.0232197605073452,
0.019148873165249825,
0.048818156123161316,
0.01491966936737299,
-0.055582195520401,
0.011729094199836254,
0.0005520061240531504,
-0.00590570317581296,
-0.03323574736714363,
0.038456931710243225,
0.005559912882745266,
0.0034226260613650084,
0.0046433256939053535,
0.03973077982664108,
-0.0010493302252143621,
-0.04451071470975876,
0.016467001289129257,
0.0007373620755970478,
0.031115662306547165,
-0.03264550119638443,
-0.03629445284605026,
0.025638027116656303,
-0.0005331987049430609,
0.024836894124746323,
-0.00828560534864664,
-0.037627529352903366,
0.04552540183067322,
-0.022398194298148155,
0.0013598604127764702,
-0.026733292266726494,
0.018360089510679245,
0.04412087798118591,
0.05314692482352257,
0.014258106239140034,
0.04177315533161163,
-0.020773012191057205,
0.012551807798445225,
-0.0644817128777504,
-0.039776116609573364,
-0.02025986649096012,
0.01550176553428173,
0.015573211014270782,
-0.03341228887438774,
0.005455686245113611,
0.06435783952474594,
0.04034173861145973,
0.016283437609672546,
0.005337197333574295,
0.02664746530354023,
0.037645868957042694,
-0.0238975677639246,
-0.06493845582008362,
-0.019728368148207664,
0.07047398388385773,
0.015257885679602623,
0.010763234458863735,
0.010706190019845963,
-0.06936856359243393,
0.058725908398628235,
-0.0015036787372082472,
-0.0016636979999020696,
-0.03206124156713486,
-0.009810992516577244,
0.024909256026148796,
-0.007586146704852581,
-0.015157876536250114,
0.02283310517668724,
0.015463342890143394,
-0.016487805172801018,
-0.04864262789487839,
-0.0425749309360981,
0.018011078238487244,
0.05215412750840187,
0.004562620539218187,
-0.06113189831376076,
0.00039551773807033896,
0.007825702428817749,
-0.04096760228276253,
0.039378948509693146,
-0.018368830904364586,
-0.052699413150548935,
0.012354725040495396,
0.004954786505550146,
0.013931096531450748,
-0.06613508611917496,
0.04524984955787659,
0.020534254610538483,
0.009338077157735825,
-0.0783831775188446,
-0.01172453910112381,
-0.02046862430870533,
0.009511749260127544,
-0.0694298967719078,
0.04520854726433754,
0.029515191912651062,
0.04914596304297447,
0.048501502722501755,
-0.050256237387657166,
0.04751348868012428,
-0.01914394274353981,
0.05849301815032959,
-0.0019822544418275356,
-0.010606694966554642,
-0.009197027422487736,
-0.07370571047067642,
-0.031741879880428314,
0.017992019653320312,
0.015459478832781315,
-0.05077368766069412,
-0.0715077742934227,
-0.034569744020700455,
-0.06542063504457474,
-0.025661922991275787,
0.011190081015229225,
0.028796635568141937,
0.0507180318236351,
0.0006044469773769379,
0.026224453002214432,
0.029664363712072372,
-0.004323492757976055,
0.019766634330153465,
-0.005240526981651783,
-0.009995942004024982,
0.006939941551536322,
-0.028651684522628784,
0.038241609930992126,
0.006382317747920752,
-0.020166760310530663,
-0.05360402166843414,
-0.05419633165001869,
0.0011500122491270304,
-0.031675904989242554,
-0.024837205186486244,
-0.01439534779638052,
-0.035454485565423965,
0.03128846362233162,
-0.0060101947747170925,
-0.021026577800512314,
-0.06331998854875565,
-0.030512599274516106,
-0.008240872994065285,
0.03779427707195282,
0.025539208203554153,
0.0015601502964273095,
-0.053034406155347824,
0.008433551527559757,
0.022575771436095238,
-0.013353420421481133,
-0.03751843050122261,
-0.017945444211363792,
0.004317081067711115,
0.026230378076434135,
0.05222759023308754,
-0.02182135544717312,
0.08216167241334915,
0.002783188596367836,
0.07989224791526794,
0.01813402585685253,
0.005167859606444836,
-0.06824854761362076,
-0.04888655245304108,
0.021369939669966698,
0.025456111878156662,
0.042710043489933014,
-0.015218517743051052,
-0.01523309014737606,
0.04013439267873764,
-0.022173099219799042,
-0.01973153091967106,
0.021394073963165283,
-0.013402811251580715,
-0.014584100805222988,
-0.004954962991178036,
-0.0049280268140137196,
0.022875502705574036,
0.009961417876183987,
0.05551667883992195,
0.006353576201945543,
0.024373644962906837,
-0.019325654953718185,
0.01687677763402462,
0.010433382354676723,
-0.00582877267152071,
0.031048284843564034,
0.01022898405790329,
-0.015327135100960732,
-0.02922523394227028,
-0.03791551664471626,
0.029070736840367317
] |
<p>Kinetic energy conservation in collision.</p>
<p>In any type of collision type of collision if we take the system to comprised of both bodies then the net external force is zero. So the work done by external force is also zero. By the relation $W=K_f-K_i$ as $W$ is zero hence kinetic energy is conserved. But this not the case. </p>
<p>Can you tell me what is the flaw in my argument? Some people say that the argument has neglected the fact that some kinetic energy is transformed into heat. But heat is created due to the interactions between bodies during collision which is thus an internal force and thus shouldn't affect kinetic energy. </p> | g9209 | [
0.07386822253465652,
0.006856946274638176,
0.01605260744690895,
0.02705938182771206,
0.03530687466263771,
0.025823388248682022,
0.020661689341068268,
0.04609903693199158,
-0.07162307947874069,
-0.02928799018263817,
0.04343733564019203,
-0.044880613684654236,
-0.03330785781145096,
0.015439186245203018,
-0.02610193006694317,
0.01623283512890339,
0.008902502246201038,
-0.023114291951060295,
-0.005137402098625898,
0.12347045540809631,
-0.07600059360265732,
-0.0072474125772714615,
-0.0593683160841465,
0.0013410666724666953,
-0.011029206216335297,
-0.00908883661031723,
0.078852079808712,
-0.027519339695572853,
-0.05930257961153984,
-0.07019845396280289,
0.09940700232982635,
0.04250236600637436,
0.010676272213459015,
-0.06335531175136566,
-0.0834498330950737,
-0.013899151235818863,
0.03231300786137581,
-0.019886067137122154,
-0.004666289314627647,
-0.0005779590574093163,
0.023547835648059845,
0.02840062975883484,
0.03939921408891678,
0.02848590351641178,
-0.01642177626490593,
-0.0034675223287194967,
-0.029899505898356438,
-0.01580512337386608,
-0.05023784190416336,
0.0558808371424675,
0.01263977587223053,
0.01467915903776884,
0.007678277790546417,
-0.015618853271007538,
0.05298387259244919,
-0.033437345176935196,
0.01126569788902998,
-0.02292262762784958,
0.004192582797259092,
0.014432131312787533,
0.021385353058576584,
-0.02248961105942726,
0.005541409831494093,
0.01024609711021185,
0.029836898669600487,
-0.08470719307661057,
-0.05005236342549324,
0.02823171205818653,
0.026249652728438377,
0.0058031147345900536,
-0.011447965167462826,
0.05695981904864311,
-0.026097793132066727,
0.012735113501548767,
0.02322753146290779,
0.012205291539430618,
0.0246998593211174,
0.005175077356398106,
0.01224564854055643,
0.004758324474096298,
-0.06593739241361618,
0.03437618911266327,
0.058832790702581406,
-0.006882164161652327,
0.043899912387132645,
0.016387369483709335,
-0.006333501543849707,
-0.006528689991682768,
-0.007130846381187439,
0.011013273149728775,
0.029345378279685974,
0.01587405428290367,
0.08836793154478073,
0.00996833760291338,
-0.027339767664670944,
0.022225286811590195,
-0.022996172308921814,
0.09228286147117615,
0.006004572845995426,
0.0033336076885461807,
-0.006337066181004047,
0.016761064529418945,
-0.00949688721448183,
0.0180459413677454,
0.07709746062755585,
-0.028619227930903435,
-0.0019001074833795428,
0.024282019585371017,
-0.032468751072883606,
-0.03846099227666855,
0.045572709292173386,
-0.0658993199467659,
-0.07611426711082458,
-0.030888281762599945,
-0.002306092530488968,
-0.06646765023469925,
0.04199274629354477,
-0.02983994036912918,
0.011258980259299278,
0.06514544039964676,
-0.004680284298956394,
0.008400775492191315,
-0.04134286940097809,
0.03601931780576706,
-0.0032479914370924234,
0.009723100811243057,
-0.00279574585147202,
-0.005391624756157398,
0.026638522744178772,
-0.04174521565437317,
-0.04920363798737526,
0.014252780005335808,
0.016510222107172012,
-0.019362298771739006,
0.024393271654844284,
0.06284875422716141,
-0.006293164566159248,
0.0062071834690868855,
-0.01785173825919628,
-0.008351713418960571,
0.0020313020795583725,
0.02045344188809395,
0.01138482429087162,
-0.08438694477081299,
-0.039068493992090225,
0.012738634832203388,
-0.042538393288850784,
-0.022698495537042618,
0.07099786400794983,
0.03748374432325363,
0.02191789448261261,
0.0484980046749115,
-0.04125532507896423,
-0.07136867940425873,
0.0032043643295764923,
-0.0300055630505085,
0.038321610540151596,
0.018678531050682068,
-0.01398918405175209,
0.0038739657029509544,
0.04263448342680931,
0.0005771081778220832,
0.09460301697254181,
-0.0381530299782753,
-0.032394006848335266,
-0.003247144864872098,
-0.04475778713822365,
-0.045101240277290344,
-0.008049402385950089,
-0.03537962958216667,
-0.07970450818538666,
-0.013877716846764088,
-0.028158018365502357,
0.026599425822496414,
-0.00034131010761484504,
-0.0077215987257659435,
-0.01064824964851141,
0.011196035891771317,
-0.052762482315301895,
0.02176179550588131,
-0.03265402093529701,
0.0035264156758785248,
0.019002141430974007,
-0.03231267258524895,
0.018543791025877,
0.02388538047671318,
0.010023725219070911,
0.10706352442502975,
-0.02192303165793419,
0.0013996328925713897,
-0.007131452672183514,
0.0036954276729375124,
-0.015564825385808945,
-0.05615862086415291,
0.010272013023495674,
0.0425071157515049,
-0.01463321503251791,
0.018960723653435707,
-0.03400525823235512,
-0.01174848061054945,
0.00005918677925365046,
0.0745043009519577,
-0.01619337685406208,
0.004528736229985952,
0.02460508979856968,
0.006651545409113169,
0.0017434514593333006,
0.000218829489313066,
-0.006681861821562052,
-0.041859354823827744,
0.020131465047597885,
0.006433533970266581,
-0.027994615957140923,
-0.005557452328503132,
0.027100486680865288,
0.017170105129480362,
-0.04911956936120987,
0.005257420241832733,
-0.023703476414084435,
-0.04264827072620392,
-0.054277949035167694,
0.02403896488249302,
0.018974656239151955,
-0.012640641070902348,
-0.08183686435222626,
-0.0525016263127327,
-0.035300593823194504,
-0.06006816774606705,
-0.017476139590144157,
0.040502969175577164,
-0.05099515616893768,
0.02528497576713562,
-0.00982428528368473,
-0.0018186357337981462,
0.044272828847169876,
0.03730408847332001,
0.020520957186818123,
0.039917659014463425,
0.008521969430148602,
0.06564196944236755,
0.042006805539131165,
-0.08259805291891098,
-0.038443997502326965,
0.008948653936386108,
0.07124397158622742,
-0.040037669241428375,
-0.0064344326965510845,
-0.0326383002102375,
-0.02554139494895935,
-0.031151048839092255,
0.012047390453517437,
0.03896409645676613,
-0.019041450694203377,
-0.020427312701940536,
0.01566636748611927,
-0.034396640956401825,
-0.019585425034165382,
0.03126117214560509,
-0.031678102910518646,
-0.02489611692726612,
0.04324023425579071,
-0.024324286729097366,
-0.04745497554540634,
0.03218473494052887,
-0.08403244614601135,
-0.010094250552356243,
-0.05584641546010971,
0.03267944976687431,
0.016289709135890007,
0.008767740800976753,
-0.029724348336458206,
0.060777995735406876,
-0.046125318855047226,
0.021566668525338173,
0.007619592361152172,
-0.03609157353639603,
-0.02478117309510708,
-0.059547144919633865,
0.030922992154955864,
-0.019187238067388535,
0.020785851404070854,
0.0380399189889431,
-0.02361377887427807,
0.010723660700023174,
0.02000831812620163,
-0.027389179915189743,
-0.03540755808353424,
-0.009283022955060005,
0.004742251709103584,
-0.05747663974761963,
-0.0012295737396925688,
0.06592573970556259,
0.01584266498684883,
-0.01811559684574604,
0.013410144485533237,
0.025773467496037483,
0.0537915974855423,
-0.041825853288173676,
-0.003648323705419898,
-0.008803262375295162,
0.010621168650686741,
-0.011665759608149529,
-0.011527078226208687,
0.03774905577301979,
0.03657437115907669,
0.0382690466940403,
-0.04342149570584297,
-0.08039090037345886,
0.00021115569688845426,
-0.013657367788255215,
0.029607253149151802,
0.04039526358246803,
-0.034672852605581284,
0.002615425968542695,
-0.04340965300798416,
0.006789599545300007,
-0.01831396482884884,
-0.06045849993824959,
0.0030302884988486767,
0.01718154549598694,
-0.009980550967156887,
-0.0008640567539259791,
0.021051347255706787,
-0.01392425037920475,
-0.020666785538196564,
0.02149348333477974,
-0.05256999656558037,
-0.027325937524437904,
0.052460312843322754,
0.0321386493742466,
-0.040715500712394714,
0.019243378192186356,
0.010094589553773403,
-0.03959786519408226,
-0.0066322567872703075,
-0.0460965521633625,
-0.03419650346040726,
-0.01766890473663807,
-0.01664051041007042,
0.06769642978906631,
0.009419852867722511,
0.0001935045002028346,
-0.0133168650791049,
0.0014582928270101547,
0.005634702742099762,
0.058756448328495026,
-0.0036725546233356,
-0.0007362687028944492,
-0.020215624943375587,
-0.05918744578957558,
0.049812883138656616,
-0.0015516056446358562,
0.005671869032084942,
-0.024707628414034843,
-0.045147787779569626,
0.0011847005225718021,
-0.026390140876173973,
0.042261648923158646,
-0.05754992365837097,
0.04790332168340683,
0.04181063920259476,
0.016096331179142,
0.038491055369377136,
-0.025718307122588158,
0.0061551909893751144,
0.022760463878512383,
-0.04192144423723221,
0.0008098867256194353,
0.007261891849339008,
-0.02732563205063343,
-0.030828967690467834,
-0.0008220762829296291,
-0.028326185420155525,
-0.023363972082734108,
0.10313063859939575,
-0.00780574232339859,
0.0979776382446289,
0.039207518100738525,
-0.03731214255094528,
0.04879366233944893,
0.08954691141843796,
0.010586018674075603,
-0.017076143994927406,
0.055921029299497604,
0.04655139893293381,
0.05920694023370743,
-0.01631668582558632,
0.04607149586081505,
0.024363014847040176,
0.005976754706352949,
0.0196949802339077,
-0.014035594649612904,
-0.007228843402117491,
-0.014518748968839645,
0.002376263728365302,
0.025367412716150284,
0.025036979466676712,
-0.042531371116638184,
0.03540811687707901,
-0.0061282021924853325,
-0.022638121619820595,
0.023101527243852615,
-0.013309113681316376,
-0.016736652702093124,
0.023503152653574944,
-0.0002800558868329972,
0.03393087908625603,
-0.018407747149467468,
-0.019166316837072372,
-0.040277134627103806,
0.026001427322626114,
-0.0047739408910274506,
-0.017112527042627335,
-0.039757829159498215,
-0.038247883319854736,
-0.060537587851285934,
-0.05257457494735718,
-0.014356441795825958,
0.08954145759344101,
-0.027910422533750534,
-0.008569487370550632,
0.02010139636695385,
-0.02371155098080635,
0.015148141421377659,
0.09436498582363129,
0.07083317637443542,
0.05010398477315903,
0.026967719197273254,
-0.03674563765525818,
-0.03300436958670616,
-0.007182933855801821,
0.007729439530521631,
-0.02027716673910618,
0.003580934600904584,
-0.0781363695859909,
0.028059111908078194,
-0.022965624928474426,
0.05608164146542549,
-0.005526105407625437,
0.0278329961001873,
0.058265119791030884,
0.03745799511671066,
-0.008464145474135876,
-0.009209707379341125,
0.035364359617233276,
0.060702208429574966,
0.005392759572714567,
-0.0451018400490284,
-0.03543645516037941,
-0.07004183530807495,
-0.018418628722429276,
-0.0011778813786804676,
-0.03176133334636688,
-0.0031011351384222507,
-0.02419450506567955,
0.010789007879793644,
-0.02295910008251667,
-0.033587951213121414,
-0.026728063821792603,
0.05941835418343544,
-0.03630400076508522,
0.05467981472611427,
0.010412936098873615,
0.014896929264068604,
0.001622880226932466,
0.03201727941632271,
-0.0030582239851355553,
0.03877537325024605,
-0.02524898387491703,
0.006458365824073553,
0.06144382804632187,
0.04931392893195152,
0.005316862836480141,
-0.007536339107900858,
0.009052454493939877,
0.03623452037572861,
0.0011951043270528316,
-0.008792872540652752,
0.017399825155735016,
0.00599757069721818,
0.029558608308434486,
0.0134209506213665,
0.02904576249420643,
0.022944366559386253,
0.0372951403260231,
0.026517057791352272,
-0.05713402479887009,
0.009411530569195747,
0.012790415436029434,
0.006902053952217102,
0.05910196527838707,
0.02205774374306202,
-0.017228636890649796,
-0.037280306220054626,
0.015592291951179504,
0.07728355377912521,
0.009104734286665916,
-0.040802642703056335,
0.003699122229591012,
-0.003965733572840691,
-0.05274336040019989,
-0.007921122945845127,
-0.0016968362033367157,
-0.033733490854501724,
0.04581320285797119,
0.06735281646251678,
0.08106180280447006,
-0.014278393238782883,
-0.0417499803006649,
0.026828715577721596,
-0.02225465513765812,
0.03272823616862297,
0.06024705991148949,
-0.0008561588474549353,
0.014523129910230637,
-0.00592298386618495,
0.05788172408938408,
-0.08291435986757278,
0.00006448036583606154,
-0.00038510854938067496,
0.05046195536851883,
0.012697805650532246,
0.030179988592863083,
0.016088390722870827,
-0.031854938715696335,
0.057243600487709045,
0.015430418774485588,
-0.033147018402814865,
-0.06926572322845459,
0.053991321474313736,
-0.0219037514179945,
-0.014063798822462559,
-0.0013753296807408333,
0.039660755544900894,
-0.08433795720338821,
-0.02629198506474495,
-0.034778937697410583,
0.011467965319752693,
0.001801088685169816,
0.0007473596488125622,
0.02935951203107834,
-0.06560251861810684,
0.005674910265952349,
0.009229118935763836,
-0.008960867300629616,
0.043831780552864075,
-0.0962318480014801,
-0.030195659026503563,
-0.04690845310688019,
-0.08361564576625824,
-0.006885737180709839,
0.044739942997694016,
0.026420503854751587,
-0.05417025089263916,
0.04755055904388428,
-0.014754049479961395,
0.04062066227197647,
0.002683273982256651,
-0.013346640393137932,
-0.0644548311829567,
-0.0010364009067416191,
0.07260466367006302,
-0.025922060012817383,
0.03422977402806282,
0.053292322903871536,
-0.0016449505928903818,
-0.04030032083392143,
0.014764606952667236,
0.028054339811205864,
-0.03357626497745514,
0.02454633265733719,
0.026416102424263954,
-0.024977751076221466,
0.009258427657186985,
0.047331303358078,
-0.04038097336888313,
-0.020349284633994102,
-0.02326946333050728,
-0.061667606234550476,
-0.05821770429611206,
0.03734542801976204,
-0.04334191977977753,
0.0062029664404690266,
-0.06674844026565552,
-0.001992791658267379,
0.016683541238307953,
-0.016867084428668022,
0.01003981102257967,
0.06111639365553856,
0.011479424312710762,
-0.009978380985558033,
0.006915183737874031,
0.008073601871728897,
0.04383851960301399,
-0.010820896364748478,
-0.01817849837243557,
-0.015470746904611588,
0.024339111521840096,
-0.022132080048322678,
0.03707636892795563,
-0.036647550761699677,
-0.020201969891786575,
0.021226992830634117,
-0.05891941860318184,
-0.02754242904484272,
0.022252649068832397,
-0.01948297582566738,
0.036984898149967194,
-0.015463347546756268,
0.012410377152264118,
-0.057514388114213943,
0.03186740726232529,
0.009847810491919518,
-0.02175055257976055,
-0.00437275180593133,
-0.014302088879048824,
-0.004847962409257889,
-0.0398792028427124,
-0.03677917644381523,
-0.056382302194833755,
0.010676475241780281,
-0.059372179210186005,
0.03958937153220177,
0.017071448266506195,
0.03432026132941246,
0.012511509470641613,
-0.10783116519451141,
0.0790620967745781,
0.07992785423994064,
-0.009143662638962269,
-0.02298750728368759,
0.0204042699187994,
-0.07175543904304504,
0.04671422764658928,
-0.029355287551879883,
0.013946795836091042,
0.024128884077072144,
-0.00036202254705131054,
0.03792827948927879,
-0.022893225774168968,
-0.011972863227128983,
-0.021431932225823402,
0.01983454078435898,
0.03503928333520889,
-0.06359589099884033,
0.015016821213066578,
0.02672201581299305,
-0.033550091087818146,
-0.05668508633971214,
0.013117232359945774,
-0.04526384547352791,
0.03197242692112923,
-0.012601037509739399,
-0.0074018496088683605,
-0.013198429718613625,
0.0010520671494305134,
-0.04070740565657616,
0.01907818764448166,
0.024044431746006012,
-0.014508181251585484,
0.028827166184782982,
-0.044823307543992996,
0.029134517535567284,
0.004328540526330471,
0.04476543143391609,
0.039477791637182236,
0.0019411321263760328,
-0.021438319236040115,
0.02133009023964405,
0.05926722660660744,
-0.00437060697004199,
-0.059626512229442596,
-0.029659079387784004,
-0.004337453283369541,
-0.019327392801642418,
0.028261233121156693,
0.032994579523801804,
-0.015304059721529484,
0.006609297823160887,
0.02781011536717415,
0.022869428619742393,
0.02223491668701172,
-0.027875162661075592,
0.0017763590440154076,
-0.011225852183997631,
0.019370734691619873,
-0.034585338085889816,
-0.027338670566678047,
0.01951146312057972,
0.0100700156763196,
-0.020066913217306137,
0.05413408949971199,
0.04250428453087807,
-0.033852364867925644,
-0.0113521134480834,
0.017618004232645035,
0.04343900457024574,
0.053414784371852875,
0.0017728285165503621,
0.011566615663468838,
0.007419543340802193,
-0.018191395327448845,
0.043956078588962555,
0.005255242809653282,
-0.02977067418396473,
0.052624255418777466,
0.007616893388330936,
-0.053641702979803085,
0.001478390535339713,
0.03829806298017502,
0.05834832042455673,
-0.015024946071207523,
0.038405269384384155,
-0.010175934992730618,
0.033533621579408646,
-0.0036302024964243174,
-0.0073701185174286366,
0.005939085967838764,
0.04163604602217674,
-0.04490729421377182,
0.041719742119312286,
-0.040672142058610916,
-0.014675208367407322,
-0.097453773021698,
-0.041532937437295914,
-0.00618572486564517,
0.018031589686870575,
-0.07184494286775589,
-0.029161361977458,
-0.01146814227104187,
-0.03178761154413223,
-0.02799048274755478,
-0.017795760184526443,
-0.0011218192521482706,
-0.004644338507205248,
-0.02211655117571354,
-0.009615259245038033,
-0.033650342375040054,
-0.03225196152925491,
0.034101929515600204,
-0.025896603241562843,
-0.021279357373714447,
-0.03669321909546852,
-0.013718950562179089,
-0.05186949297785759,
-0.040972720831632614,
0.018984170630574226,
0.022449757903814316,
0.019291458651423454,
0.03926290571689606,
0.04756806418299675,
-0.012799587100744247,
-0.06576454639434814,
0.01758723333477974,
0.015252061188220978,
-0.03500804305076599,
-0.003788156434893608,
0.0113593814894557,
-0.020564446225762367,
0.05149203538894653,
-0.015819374471902847,
0.012550144456326962,
-0.004279000218957663,
0.0018933676183223724,
0.025925371795892715,
-0.023105992004275322,
0.029409756883978844,
0.018657710403203964
] |
<p>I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$.</p>
<p>But in the former case, I had more measurements, so the error should be smaller. So would the error be 1 or rather $1/\sqrt{5}$ and $1/\sqrt{3}$ respectively?</p> | g9210 | [
-0.003492285730317235,
-0.0045230695977807045,
-0.012544575147330761,
-0.02430906519293785,
0.039237502962350845,
-0.02059774287045002,
0.00388238369487226,
-0.03777037188410759,
-0.008334419690072536,
0.015138976275920868,
-0.0456559881567955,
0.027192454785108566,
-0.04804185405373573,
0.044079799205064774,
0.0038846228271722794,
-0.0205765999853611,
0.05071378871798515,
-0.039495259523391724,
-0.008436227217316628,
0.03363978862762451,
-0.009003126062452793,
-0.022071314975619316,
-0.014919090084731579,
-0.05660008639097214,
0.09304583072662354,
-0.03170618787407875,
-0.034707292914390564,
0.013954782858490944,
-0.06426966935396194,
0.02720031514763832,
0.0037111793644726276,
-0.010479037649929523,
0.06661351770162582,
0.03347489610314369,
-0.02656647562980652,
-0.013583091087639332,
0.015375563874840736,
0.0024412646889686584,
0.10917437821626663,
-0.018045151606202126,
0.026038883253932,
-0.03088410571217537,
0.012009846977889538,
-0.026763370260596275,
0.03669752553105354,
0.02022942528128624,
0.012534852139651775,
0.025165840983390808,
0.07533172518014908,
0.0025202520191669464,
0.014040598645806313,
-0.026920340955257416,
0.049698714166879654,
0.0425875261425972,
0.00862239021807909,
-0.011667562648653984,
-0.017744572833180428,
-0.007464831694960594,
0.0389438159763813,
0.0702243372797966,
-0.009420186281204224,
-0.01864665374159813,
-0.009526034817099571,
-0.0374499075114727,
0.052153654396533966,
0.0737612396478653,
0.005529968999326229,
0.02085285075008869,
0.007958997040987015,
0.028961587697267532,
-0.010730015113949776,
-0.012956335209310055,
0.04788290709257126,
0.011163683608174324,
-0.025673342868685722,
0.03564413636922836,
0.010912282392382622,
-0.003307654056698084,
-0.027065906673669815,
0.03486033156514168,
-0.022796878591179848,
-0.03860017657279968,
0.0018910334911197424,
0.07210486382246017,
0.01332033146172762,
0.014498080126941204,
-0.020033622160553932,
-0.020275600254535675,
-0.047703806310892105,
0.03717944771051407,
0.008939252234995365,
-0.03633207827806473,
0.027096962556242943,
0.06559891253709793,
-0.05977201089262962,
-0.03713414818048477,
-0.02999032847583294,
0.021219899877905846,
0.018012655898928642,
0.04054873436689377,
-0.007761827670037746,
-0.0009931622771546245,
-0.0012777164811268449,
-0.03633160516619682,
-0.01525215432047844,
0.00730555597692728,
0.039184827357530594,
0.004878580570220947,
-0.05500161647796631,
-0.06929416209459305,
-0.039060328155756,
-0.01883622445166111,
-0.026687392964959145,
-0.03189495950937271,
-0.06206163763999939,
0.030354756861925125,
0.050426218658685684,
-0.04896783456206322,
-0.010128783993422985,
0.006486240774393082,
0.0016817064024508,
0.029819058254361153,
0.0820636972784996,
0.09334925562143326,
-0.002211512764915824,
0.016986748203635216,
-0.03158848360180855,
0.03478989377617836,
0.0314924493432045,
0.02760511264204979,
-0.027933718636631966,
-0.022873733192682266,
0.0009618056355975568,
-0.044334348291158676,
-0.03543560579419136,
0.03279070928692818,
0.010916649363934994,
0.016443468630313873,
-0.0012404732406139374,
-0.011751873418688774,
-0.02166951820254326,
0.016365431249141693,
0.05833511799573898,
-0.038942430168390274,
0.047170452773571014,
-0.016338756307959557,
-0.005995138082653284,
0.004777701571583748,
-0.09768716245889664,
0.01635029725730419,
0.017092404887080193,
0.019298579543828964,
-0.0029248830396682024,
0.061668653041124344,
-0.04570699483156204,
0.001476411591283977,
0.023912308737635612,
0.07643085718154907,
0.03959151729941368,
-0.010121753439307213,
-0.0029633454978466034,
0.012194187380373478,
0.02203148789703846,
0.0384477823972702,
-0.006439974065870047,
-0.01583767682313919,
-0.02429795451462269,
-0.058907732367515564,
-0.028903985396027565,
-0.04499181732535362,
0.01243210956454277,
0.009749649092555046,
0.03595210984349251,
-0.017176557332277298,
0.012864929623901844,
0.04743412882089615,
0.08828148990869522,
0.016817333176732063,
0.01616409607231617,
0.01230903621762991,
-0.0021138866432011127,
0.06290560215711594,
-0.01896950975060463,
-0.0558491051197052,
-0.026648536324501038,
-0.009629109874367714,
0.04086092859506607,
-0.09813990443944931,
-0.050563517957925797,
-0.009025247767567635,
-0.02919897250831127,
-0.024294378235936165,
0.0024889656342566013,
-0.0066784522496163845,
-0.012276793830096722,
-0.004554075188934803,
-0.01529103796929121,
-0.03979717567563057,
0.033624183386564255,
-0.004467339720577002,
0.032796189188957214,
0.0424601174890995,
0.06669901311397552,
-0.04354945942759514,
0.03942074999213219,
-0.015941383317112923,
-0.020050732418894768,
-0.05680718272924423,
0.02373974770307541,
-0.003071850398555398,
0.024810880422592163,
0.03371671587228775,
-0.010069427080452442,
-0.0030374263878911734,
0.01899334229528904,
-0.009203431196510792,
0.08100947737693787,
0.0010940507054328918,
0.04496420919895172,
-0.004530114121735096,
-0.0019521366339176893,
0.00015245014219544828,
0.0594649501144886,
-0.04721330478787422,
0.035699620842933655,
0.029838744550943375,
0.024212783202528954,
-0.038626376539468765,
0.006414259783923626,
0.008519928902387619,
-0.05661551281809807,
-0.07431701570749283,
0.044948071241378784,
-0.0011875687632709742,
0.015980344265699387,
0.048499803990125656,
0.019373280927538872,
-0.011934124864637852,
0.04131085053086281,
-0.004677141085267067,
0.028177179396152496,
0.00749974837526679,
-0.006327289622277021,
0.044597432017326355,
-0.008702175691723824,
0.006869607139378786,
-0.03165925294160843,
0.060875728726387024,
0.02102525718510151,
-0.002232162281870842,
-0.0066449991427361965,
0.049514226615428925,
0.018571173772215843,
-0.06370551139116287,
-0.0033319727517664433,
0.02219383791089058,
0.030359165742993355,
-0.014520742930471897,
-0.01833289861679077,
0.015563646331429482,
-0.07822350412607193,
0.014261762611567974,
-0.02011326141655445,
-0.0302767101675272,
0.060565829277038574,
-0.016818050295114517,
-0.00297616608440876,
0.02647031843662262,
0.009158880449831486,
-0.007374108768999577,
-0.014858202077448368,
0.04331791400909424,
0.01584520936012268,
0.0027150518726557493,
-0.004682493861764669,
-0.046663086861371994,
-0.04248039424419403,
-0.013256324455142021,
0.0684763565659523,
-0.06414346396923065,
-0.027004612609744072,
0.023413697257637978,
-0.07906876504421234,
0.01136161107569933,
0.06829952448606491,
0.014815226197242737,
0.06408050656318665,
-0.03908661752939224,
0.006644687615334988,
0.030596459284424782,
-0.014969032257795334,
0.002346936147660017,
0.004827582277357578,
-0.056277886033058167,
0.012262905947864056,
0.05564575269818306,
0.017391284927725792,
-0.053681500256061554,
0.061977021396160126,
0.00833780039101839,
-0.025802839547395706,
-0.00007191888289526105,
-0.03416714817285538,
-0.02875487133860588,
0.01833387464284897,
-0.025462500751018524,
0.018890181556344032,
-0.04132402688264847,
-0.03153600916266441,
-0.002769988030195236,
-0.0009690055740065873,
0.011710057035088539,
-0.0024435757659375668,
-0.024400744587183,
-0.024713536724448204,
-0.016658775508403778,
-0.004733030218631029,
0.024248454719781876,
-0.05369239300489426,
-0.0004913422162644565,
-0.026090839877724648,
-0.08105435967445374,
-0.02669540047645569,
-0.000976713839918375,
0.016704192385077477,
-0.010027902200818062,
-0.02446441352367401,
0.02491976134479046,
-0.015769798308610916,
-0.04971008375287056,
0.01695130206644535,
0.016371842473745346,
0.0004940477083437145,
-0.011702153831720352,
0.017402300611138344,
-0.045067910104990005,
-0.04218336567282677,
-0.01044156402349472,
0.018391959369182587,
0.030778905376791954,
-0.03799514099955559,
0.01776863820850849,
-0.03687025234103203,
-0.059986378997564316,
0.03437914699316025,
-0.018434330821037292,
0.02483474463224411,
0.06189432367682457,
0.009890211746096611,
-0.02684076316654682,
0.03680891543626785,
-0.024513885378837585,
-0.020036904141306877,
-0.02872350625693798,
0.00479779252782464,
0.06243421882390976,
0.03871696814894676,
0.06720535457134247,
-0.041623521596193314,
-0.04986785352230072,
0.0681900605559349,
-0.01579293981194496,
-0.05427253991365433,
0.03293178230524063,
-0.03116259165108204,
-0.06510233879089355,
0.0025902902707457542,
0.0588633231818676,
0.022883906960487366,
0.01059732586145401,
-0.021123744547367096,
0.019124895334243774,
0.04065006971359253,
0.005479114130139351,
0.02277633734047413,
-0.1122497022151947,
0.0031305623706430197,
-0.006639695726335049,
-0.002015771809965372,
0.009092384949326515,
0.04705503210425377,
0.021901721134781837,
-0.049694281071424484,
-0.03963172808289528,
-0.023276394233107567,
-0.020169448107481003,
0.0017930713947862387,
-0.03295646607875824,
-0.023761264979839325,
-0.030332442373037338,
-0.02294098772108555,
-0.042561277747154236,
-0.08396956324577332,
0.048676833510398865,
0.04002176597714424,
0.009701988659799099,
0.020725851878523827,
0.0004587006405927241,
-0.0353008434176445,
0.07256118953227997,
0.02299436554312706,
-0.020947439596056938,
0.0703309029340744,
-0.041435930877923965,
0.02425062283873558,
-0.008032753132283688,
0.058104176074266434,
0.07000456005334854,
-0.0042066751047968864,
0.03336640074849129,
-0.029496368020772934,
-0.010131346993148327,
-0.013827328570187092,
-0.05785642936825752,
0.05027322471141815,
0.043836481869220734,
-0.05375802516937256,
-0.037192292511463165,
-0.0270650964230299,
0.01969931088387966,
-0.02763638086616993,
-0.005172549746930599,
-0.047088585793972015,
-0.008260232396423817,
0.0004443918587639928,
-0.003105273237451911,
0.002422818448394537,
0.01456690113991499,
0.030921000987291336,
-0.04697933420538902,
0.019212855026125908,
0.012231639586389065,
0.0012040735455229878,
0.06843963265419006,
0.034334976226091385,
0.04482235014438629,
-0.00780489994212985,
0.011821931228041649,
0.018099768087267876,
-0.02000531367957592,
-0.0005723570357076824,
0.08506597578525543,
-0.06845979392528534,
-0.03902002424001694,
0.005883718840777874,
-0.03365928679704666,
0.012346869334578514,
0.005545874126255512,
-0.000018019616618403234,
0.02660404145717621,
-0.0378144346177578,
-0.012319302186369896,
-0.03474367782473564,
-0.027518564835190773,
-0.022871682420372963,
-0.05198952555656433,
0.01224223431199789,
0.03792198374867439,
-0.000517302833031863,
0.06223633512854576,
0.010277918539941311,
0.0125215332955122,
0.030903305858373642,
0.0364127978682518,
0.0008439449011348188,
0.002418982097879052,
-0.07561624050140381,
0.005235790740698576,
-0.035115309059619904,
0.006924312561750412,
-0.009146736934781075,
0.006406962405890226,
-0.006371249444782734,
0.01765647530555725,
0.010541548021137714,
-0.06050468981266022,
-0.022861385717988014,
0.04181230440735817,
-0.026855550706386566,
-0.030525291338562965,
0.023038916289806366,
-0.06446436047554016,
0.014749906025826931,
-0.009939699433743954,
-0.019835343584418297,
0.01625724323093891,
-0.0702759325504303,
-0.08252744376659393,
0.06686555594205856,
-0.008998766541481018,
0.07247866690158844,
0.019084779545664787,
0.0266107190400362,
0.022892167791724205,
-0.04002811387181282,
-0.0009585095685906708,
0.00010745038161985576,
-0.04032174125313759,
0.0029994298238307238,
0.0026985961012542248,
-0.021003825590014458,
0.0394350066781044,
-0.046819429844617844,
-0.033792752772569656,
-0.010817143134772778,
0.024235038086771965,
0.016253815963864326,
-0.034537751227617264,
-0.031900886446237564,
0.001872892607934773,
0.023327890783548355,
0.024783847853541374,
0.0648316815495491,
-0.014732500538229942,
-0.0013051124988123775,
0.006928746122866869,
0.032856255769729614,
-0.0021984742488712072,
-0.05816778540611267,
0.0019530176650732756,
0.06317726522684097,
0.006623364984989166,
-0.026567887514829636,
-0.06563398987054825,
0.02119767852127552,
-0.03401411324739456,
-0.018022360280156136,
-0.03136664256453514,
0.03240812197327614,
-0.007020586635917425,
0.047034263610839844,
0.021322427317500114,
0.005550737027078867,
0.00930883176624775,
0.029094042256474495,
-0.007333403918892145,
-0.07265622168779373,
-0.015966353937983513,
0.0409083254635334,
-0.02095860056579113,
-0.04287708178162575,
0.031366556882858276,
0.010370370000600815,
0.04248485714197159,
0.001868154387921095,
0.012416105717420578,
0.0048838090151548386,
-0.04284985363483429,
0.036767005920410156,
0.040430378168821335,
-0.006102771032601595,
0.023507224395871162,
-0.07812895625829697,
-0.01703624054789543,
-0.01155970711261034,
0.05132411792874336,
0.021519985049962997,
-0.014374450780451298,
-0.024688709527254105,
-0.0239715576171875,
0.005368767771869898,
-0.07048698514699936,
0.04150974377989769,
-0.0497652105987072,
-0.05406579375267029,
-0.09474971890449524,
0.017938680946826935,
-0.0003298691881354898,
0.013644464313983917,
0.05075693875551224,
-0.011885483749210835,
-0.018258657306432724,
-0.036071084439754486,
0.02867204137146473,
-0.0005664845812134445,
0.03101995401084423,
-0.006095514632761478,
-0.09284686297178268,
0.03554582595825195,
-0.02892131917178631,
-0.04169326275587082,
0.056989554315805435,
0.01510411873459816,
-0.028328845277428627,
0.02030007541179657,
0.10912973433732986,
0.06067319214344025,
0.0010482996003702283,
0.04137148708105087,
0.07327942550182343,
-0.047259584069252014,
-0.022670911625027657,
-0.03272968530654907,
0.0007152442703954875,
-0.04832072556018829,
-0.0035761946346610785,
0.0055161756463348866,
-0.05195320025086403,
-0.02220168523490429,
0.03836597874760628,
0.017201919108629227,
-0.02604272961616516,
0.07439542561769485,
-0.10436919331550598,
-0.04487455636262894,
0.08303724229335785,
0.00876557920128107,
0.035197023302316666,
0.0028486375231295824,
-0.027276379987597466,
0.027426864951848984,
0.03002178482711315,
0.0018015002133324742,
0.01967245526611805,
0.04697512835264206,
-0.0601702481508255,
-0.037193264812231064,
-0.029556499794125557,
-0.014649936929345131,
-0.023590629920363426,
0.04963856562972069,
-0.021272381767630577,
-0.019389020279049873,
-0.0022345285397022963,
-0.019056107848882675,
0.03185173496603966,
0.021701913326978683,
0.06039353460073471,
0.008503688499331474,
-0.022436844184994698,
0.012622443959116936,
-0.04315664619207382,
0.018731536343693733,
0.008554205298423767,
-0.026405898854136467,
0.043472226709127426,
-0.02162901684641838,
0.03802529349923134,
0.004862241446971893,
0.09556185454130173,
-0.012288450263440609,
0.019887305796146393,
0.030203942209482193,
-0.0011537440586835146,
-0.052177708595991135,
-0.0006950193201191723,
0.014970260672271252,
0.004291804041713476,
-0.049443963915109634,
0.03896521404385567,
-0.010500677861273289,
0.04013701155781746,
-0.002472582273185253,
-0.011632528156042099,
-0.00018994459242094308,
0.06457085907459259,
0.04487268999218941,
-0.012373680248856544,
0.013901755213737488,
-0.04311412572860718,
-0.0195170808583498,
-0.03395431116223335,
-0.02795250155031681,
0.024649810045957565,
-0.0012067941715940833,
0.06084504351019859,
-0.023591164499521255,
0.0022208832670003176,
-0.05989735946059227,
-0.07656761258840561,
0.04049170762300491,
-0.01664820685982704,
0.004503708798438311,
-0.038586199283599854,
0.0003059300361201167,
-0.00044711967348121107,
-0.02995328977704048,
0.0249380674213171,
-0.02546926587820053,
0.0006690082955174148,
0.039691489189863205,
-0.059032268822193146,
-0.028524650260806084,
0.001134671620093286,
-0.03238347917795181,
-0.011487392708659172,
-0.031184541061520576,
-0.041690390557050705,
0.04925956949591637,
0.018286775797605515,
-0.034228723496198654,
-0.03470023721456528,
0.023908067494630814,
-0.03773431107401848,
-0.03840755671262741,
0.010258412919938564,
0.07592527568340302,
0.012031110003590584,
0.014525225386023521,
-0.02539101056754589,
0.03218737244606018,
-0.042347777634859085,
0.04206632450222969,
0.006757475435733795,
0.03033740445971489,
0.0005251197726465762,
-0.06314752250909805,
-0.032497040927410126,
-0.03735851123929024,
-0.020829370245337486,
-0.03390286862850189,
-0.01192176528275013,
0.005539624020457268,
0.02869918942451477,
0.034171588718891144,
-0.019958309829235077,
-0.10225874930620193,
-0.06757457554340363,
0.011097830720245838,
-0.05880105495452881,
0.00278148683719337,
0.01168772391974926,
-0.003139997599646449,
-0.06923292577266693,
-0.052657268941402435,
-0.0539785698056221,
0.013652009889483452,
0.002536950632929802,
0.05663134902715683,
0.014150992035865784,
0.03185451403260231,
0.009474232792854309,
-0.030225375667214394,
-0.013200805522501469,
-0.04088876023888588,
-0.009239014238119125,
0.05202538147568703,
-0.0016353866085410118,
0.034072984009981155,
0.04148527607321739,
-0.0005176156992092729,
0.03584748134016991,
0.015068672597408295,
0.001611002953723073,
0.03800008073449135,
-0.05638923496007919,
0.04585515335202217,
0.03769918158650398,
-0.007615651469677687,
-0.04088432714343071,
0.012892233207821846,
0.01668648235499859,
0.055756211280822754,
0.023480331525206566,
-0.02577471174299717,
0.045279718935489655,
-0.005939288064837456,
0.035333022475242615,
-0.003049390157684684,
0.024829475209116936,
0.02528229169547558,
-0.013475569896399975,
-0.03744686767458916,
0.0211822297424078,
-0.0654056966304779,
-0.012915246188640594,
0.027072062715888023,
-0.04191060736775398
] |
<p>Does <a href="http://en.wikipedia.org/wiki/Chaos_theory">chaos theory</a> occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?</p> | g9211 | [
0.062021397054195404,
0.019093986600637436,
0.009046154096722603,
0.027274740859866142,
0.06850715726613998,
-0.026675930246710777,
-0.02408420294523239,
0.02106376923620701,
0.04933665320277214,
0.005410301964730024,
0.05884752422571182,
-0.02486429549753666,
0.0015971274115145206,
0.015516470186412334,
-0.0845654234290123,
0.004565751645714045,
0.03221698850393295,
0.08573992550373077,
0.03865513950586319,
0.04000465199351311,
-0.0397767573595047,
0.026418859139084816,
0.045989591628313065,
-0.03620164841413498,
0.010329789482057095,
0.03976728022098541,
0.020563717931509018,
-0.006797784008085728,
0.012465901672840118,
-0.0049082390032708645,
0.0687909945845604,
-0.012500742450356483,
0.0538322851061821,
-0.05387631058692932,
-0.006123578175902367,
0.014907044358551502,
0.03273513913154602,
-0.024073146283626556,
0.033731378614902496,
0.041208162903785706,
-0.02532261237502098,
0.012917493470013142,
-0.03147055208683014,
-0.02765277400612831,
-0.05384240671992302,
-0.045665450394153595,
-0.03085598163306713,
0.008567587472498417,
-0.04141340032219887,
0.0191580131649971,
0.06424155086278915,
0.044676754623651505,
0.06564508378505707,
-0.0001625720615265891,
0.04818734526634216,
-0.006359611637890339,
0.039125602692365646,
0.030456585809588432,
0.07025600224733353,
-0.02824070118367672,
-0.004539811983704567,
0.038270145654678345,
0.04549026116728783,
0.0357116274535656,
0.02893444150686264,
0.007117311470210552,
-0.02051377482712269,
-0.04385630786418915,
-0.012535963207483292,
-0.016341572627425194,
0.020463675260543823,
-0.047184184193611145,
-0.008240239694714546,
-0.00045098867849446833,
-0.02687113545835018,
0.04293416067957878,
-0.0048482175916433334,
-0.04555751010775566,
-0.002573142061010003,
-0.0049201324582099915,
-0.03515351563692093,
-0.011328606866300106,
0.037351589649915695,
-0.03957761079072952,
0.09078935533761978,
-0.05098859965801239,
-0.026594853028655052,
-0.006852245889604092,
-0.02768847346305847,
0.013112670741975307,
0.01779043674468994,
0.03791787102818489,
0.025863811373710632,
-0.0009605304221622646,
0.009622174315154552,
0.009563900530338287,
-0.005972716491669416,
0.04818693920969963,
-0.03631218150258064,
0.022037489339709282,
-0.04844679683446884,
-0.006809856742620468,
0.013034137897193432,
-0.04483718052506447,
0.015779612585902214,
-0.028148913756012917,
0.010142925195395947,
-0.035558003932237625,
0.010298610664904118,
0.011213889345526695,
-0.062237661331892014,
0.0035254755057394505,
0.0033085127361118793,
0.007858159020543098,
0.04620502144098282,
-0.028441453352570534,
0.012853775173425674,
-0.01539843250066042,
0.005559775047004223,
0.02565956488251686,
0.0019081805367022753,
0.015775198116898537,
0.046545013785362244,
0.00013040003250353038,
-0.04986366629600525,
0.03562113270163536,
0.039845649152994156,
0.013247991912066936,
0.020150449126958847,
-0.03850121051073074,
0.011926205828785896,
0.04301650822162628,
-0.025512291118502617,
0.0019630901515483856,
0.040589384734630585,
0.014180578291416168,
0.05168953165411949,
0.005681893322616816,
0.014254676178097725,
0.022316982969641685,
0.02923845686018467,
-0.014243395067751408,
0.03238805755972862,
-0.014706584624946117,
-0.0180845707654953,
-0.022610649466514587,
-0.0021776084322482347,
-0.02619902417063713,
-0.035005833953619,
0.016957944259047508,
-0.05273188650608063,
0.010534161701798439,
-0.006397252436727285,
-0.04185587167739868,
0.014902262948453426,
0.05772333964705467,
-0.04356563836336136,
0.03015788085758686,
-0.043817099183797836,
-0.052234239876270294,
0.018720397725701332,
-0.0038086751010268927,
0.07271581143140793,
-0.007537591736763716,
-0.023820262402296066,
-0.05707846209406853,
-0.050622716546058655,
-0.04719260334968567,
0.044443048536777496,
-0.022768743336200714,
-0.021294761449098587,
-0.02538071572780609,
-0.049380574375391006,
0.026829537004232407,
-0.03251274675130844,
0.04619302228093147,
-0.008651252835988998,
-0.015886740759015083,
-0.006048866081982851,
-0.0899343490600586,
-0.049578242003917694,
-0.04470745474100113,
0.04535963013768196,
-0.06794248521327972,
0.0066225165501236916,
0.04336497187614441,
0.019745392724871635,
0.009901179932057858,
-0.06891714781522751,
-0.00947463046759367,
-0.04688664898276329,
-0.03224983438849449,
0.010538171976804733,
-0.008018928579986095,
0.001949821598827839,
-0.011291316710412502,
-0.04716963693499565,
-0.03100184164941311,
0.003111892146989703,
0.01110212504863739,
0.07259582728147507,
0.03854778781533241,
-0.013697067275643349,
-0.026961086317896843,
-0.030882209539413452,
0.011797158978879452,
-0.07806361466646194,
0.028928227722644806,
0.005698042456060648,
0.0013361744349822402,
0.013364237733185291,
0.0036412908229976892,
0.025686679407954216,
0.038027144968509674,
-0.04005609452724457,
0.011273123323917389,
0.03396262228488922,
-0.022727331146597862,
0.02161031775176525,
0.04523881897330284,
0.06356748938560486,
0.0576806366443634,
-0.00020189964561723173,
-0.028987595811486244,
0.008385207504034042,
0.03063160739839077,
-0.04789244011044502,
-0.06882297992706299,
-0.017920823767781258,
0.011646322906017303,
-0.023645121604204178,
-0.012490016408264637,
0.03443052992224693,
-0.011797506362199783,
0.008499333634972572,
0.0540836937725544,
0.05156877636909485,
-0.04644046723842621,
0.047234028577804565,
-0.004010320175439119,
-0.02472727559506893,
-0.019118214026093483,
-0.01578148826956749,
0.023606164380908012,
-0.008863073773682117,
-0.03977549821138382,
-0.04281986877322197,
-0.03216519206762314,
-0.021045560017228127,
0.028457723557949066,
0.013120580464601517,
-0.08003942668437958,
-0.0513741560280323,
-0.03723110258579254,
0.003817137563601136,
0.018196668475866318,
0.043989550322294235,
0.008958852849900723,
-0.07451736181974411,
-0.04374060779809952,
0.01532959844917059,
-0.0026231505908071995,
0.013160447590053082,
0.004975736606866121,
-0.08347322046756744,
-0.03806068375706673,
0.03052511438727379,
0.0340292826294899,
-0.08801858127117157,
0.04205085337162018,
-0.03887803107500076,
0.014660056680440903,
-0.005952148232609034,
-0.02896287478506565,
-0.0032852482981979847,
0.025997189804911613,
0.0006286322604864836,
-0.01299226749688387,
0.008225928992033005,
-0.049708396196365356,
-0.05325266346335411,
0.027588199824094772,
-0.031009616330266,
0.01859170012176037,
-0.020755406469106674,
-0.0685623288154602,
-0.008971642702817917,
-0.021047910675406456,
-0.014216489158570766,
0.008172462694346905,
0.06886281073093414,
0.02721511200070381,
-0.014396806247532368,
0.07667393982410431,
-0.03156835213303566,
0.035401858389377594,
0.040532730519771576,
-0.05298710614442825,
0.02573949657380581,
0.05981067568063736,
0.012890669517219067,
-0.03273651748895645,
-0.024992452934384346,
0.05965287610888481,
0.05697926506400108,
0.03767538070678711,
0.012743726372718811,
-0.05736612528562546,
-0.01147062424570322,
-0.044620759785175323,
0.015622069127857685,
0.05977480113506317,
0.023771628737449646,
0.06981024891138077,
-0.03548863157629967,
0.0047227488830685616,
-0.004838204942643642,
-0.00677123386412859,
0.06582098454236984,
-0.028912479057908058,
-0.05138025060296059,
-0.041132278740406036,
0.029700126498937607,
-0.05547252669930458,
0.060479287058115005,
0.009200180880725384,
-0.024147827178239822,
-0.0091738011687994,
0.008245146833360195,
-0.018336720764636993,
-0.006121677812188864,
-0.08153214305639267,
0.005401921458542347,
0.011643251404166222,
-0.08191026002168655,
-0.02302333526313305,
0.004148968029767275,
-0.0005240176687948406,
0.03930717706680298,
0.042654141783714294,
0.012259401381015778,
0.014457903802394867,
0.004622744861990213,
-0.007068230304867029,
-0.022063856944441795,
0.035577114671468735,
0.002015162957832217,
0.029025008901953697,
0.022078651934862137,
-0.008623490110039711,
0.03414146974682808,
-0.06561203300952911,
0.03597823530435562,
-0.0017461222596466541,
-0.01117013767361641,
0.04205107316374779,
0.04734068736433983,
0.062145646661520004,
0.01840325817465782,
-0.0590699166059494,
-0.05197431519627571,
-0.03746823966503143,
0.04452415555715561,
0.028219901025295258,
0.03620607778429985,
0.08698521554470062,
0.008533449843525887,
-0.006026200018823147,
0.03993266075849533,
-0.026846908032894135,
0.017337091267108917,
0.015416856855154037,
0.015251376666128635,
-0.015083439648151398,
0.08163146674633026,
0.04084870591759682,
0.02488911896944046,
-0.0018460714491084218,
-0.04576423391699791,
-0.03685051575303078,
-0.012113318778574467,
-0.015420417301356792,
0.01697590947151184,
0.02409682795405388,
0.04823504015803337,
0.006374988704919815,
-0.02698010951280594,
0.005534082651138306,
0.012986505404114723,
-0.029510628432035446,
-0.018703782930970192,
0.010541582480072975,
0.01233955193310976,
0.016654914245009422,
-0.03750021383166313,
-0.025411712005734444,
0.03257172927260399,
-0.02349128946661949,
0.03732570260763168,
-0.014714261516928673,
0.028145482763648033,
-0.0571349672973156,
-0.05310296267271042,
0.02730162814259529,
0.04892000928521156,
0.017513401806354523,
0.037670593708753586,
-0.033165447413921356,
-0.027477746829390526,
0.00854579359292984,
0.026160119101405144,
-0.009979303926229477,
-0.02452259697020054,
-0.044422831386327744,
-0.03322862833738327,
-0.022200506180524826,
0.01327779795974493,
0.023619266226887703,
0.004233463201671839,
0.031162014231085777,
0.04846068099141121,
0.008445566520094872,
-0.020589767023921013,
0.02024589292705059,
-0.05253300815820694,
-0.014406653121113777,
0.0032159017864614725,
0.041780587285757065,
0.005062581039965153,
-0.02661159448325634,
-0.0026486299466341734,
-0.009651422500610352,
0.009938969276845455,
-0.0033066621981561184,
-0.03531072661280632,
-0.014370160177350044,
-0.029632439836859703,
0.04263712093234062,
0.05832313001155853,
-0.0075799860060215,
0.04453398287296295,
0.06997624039649963,
0.044569503515958786,
-0.004703393671661615,
-0.029121102765202522,
0.055610522627830505,
0.03277180343866348,
-0.050601813942193985,
-0.027722951024770737,
-0.02981160767376423,
-0.040864791721105576,
0.00927075557410717,
-0.03520090505480766,
0.01984417624771595,
-0.040258340537548065,
-0.015261500142514706,
-0.042825713753700256,
0.04699303209781647,
-0.005723475944250822,
0.05092013254761696,
-0.05799800530076027,
-0.05218438804149628,
0.0005850071320310235,
0.07255443930625916,
-0.05711745098233223,
0.018718088045716286,
-0.05459176376461983,
0.007194819860160351,
-0.07645825296640396,
-0.029886724427342415,
0.022224122658371925,
-0.0004276176041457802,
0.031100546941161156,
0.00029547110898420215,
0.018983112648129463,
-0.06177651137113571,
0.024396652355790138,
-0.01032365020364523,
-0.04300222545862198,
-0.07585608959197998,
0.03770771622657776,
-0.015899693593382835,
0.0457821786403656,
0.012002240866422653,
0.02812388353049755,
0.01186608150601387,
-0.003484337590634823,
0.044577401131391525,
-0.008044435642659664,
-0.03233722224831581,
0.00196362123824656,
0.05251790210604668,
-0.03918230161070824,
-0.03867654874920845,
-0.027957800775766373,
0.0371762290596962,
0.01201051939278841,
-0.04528755694627762,
-0.042585331946611404,
-0.022227341309189796,
-0.035204291343688965,
0.0012250327272340655,
-0.007631850428879261,
-0.015460547991096973,
-0.019069114699959755,
0.04322125390172005,
0.018420102074742317,
0.020313464105129242,
-0.05663837119936943,
-0.0020694176200777292,
0.0012762414989992976,
0.02279256097972393,
-0.05781308561563492,
0.051092322915792465,
0.036723244935274124,
0.031167836859822273,
-0.036385565996170044,
-0.013117489404976368,
-0.023922141641378403,
-0.05895739421248436,
0.026372702792286873,
-0.05958437919616699,
0.014274682849645615,
0.040153950452804565,
0.03755149990320206,
0.03278613090515137,
-0.018590392544865608,
0.003350789425894618,
-0.02683131955564022,
0.07846295088529587,
-0.0045164586044847965,
-0.023600758984684944,
0.08767900615930557,
0.02498435601592064,
-0.01123389694839716,
-0.0007646137964911759,
-0.02716236189007759,
0.05538938194513321,
0.0032513844780623913,
0.04623575136065483,
0.010938724502921104,
-0.02196594700217247,
0.022073114290833473,
0.002129961736500263,
0.014992732554674149,
0.05481710657477379,
0.005849478300660849,
-0.010059434920549393,
0.06780117750167847,
-0.041183359920978546,
-0.01953565701842308,
-0.004465265199542046,
-0.05100233107805252,
-0.06913203001022339,
-0.07535888254642487,
0.016834594309329987,
0.027405329048633575,
-0.020595775917172432,
-0.003989202901721001,
0.03719579428434372,
0.0017853305907920003,
0.007123381830751896,
0.06624685227870941,
-0.014755292795598507,
-0.07809081673622131,
0.03754203021526337,
0.015548383817076683,
-0.011777842417359352,
0.06413845717906952,
0.08255045115947723,
-0.0029916272033005953,
0.05797817185521126,
-0.009884308092296124,
0.005673049949109554,
0.06587319076061249,
-0.013868890702724457,
0.011199592612683773,
-0.08033586293458939,
-0.0631505474448204,
0.0044319950975477695,
-0.012841206975281239,
0.05415112152695656,
0.061138223856687546,
-0.0272251944988966,
-0.02960927225649357,
0.005453647579997778,
-0.009545663371682167,
0.04275038093328476,
-0.004754021298140287,
0.0548597052693367,
-0.015472052618861198,
0.023203620687127113,
-0.06657900661230087,
0.0198400616645813,
-0.05901879444718361,
0.008084507659077644,
0.02793547883629799,
0.024615773931145668,
-0.020546430721879005,
0.03129572793841362,
-0.04539630562067032,
-0.09981569647789001,
0.05367588251829147,
-0.008810969069600105,
-0.056943077594041824,
0.06583200395107269,
0.03346703201532364,
-0.04323712736368179,
-0.06228254362940788,
0.04880674183368683,
0.02839561179280281,
-0.019345471635460854,
0.04512561857700348,
-0.0022959739435464144,
-0.039509307593107224,
-0.06116507947444916,
0.002665138803422451,
0.009066147729754448,
-0.0015388327883556485,
0.020817620679736137,
0.044583503156900406,
-0.028161965310573578,
0.00024877366377040744,
0.00483733369037509,
0.04455932229757309,
-0.011159402318298817,
-0.07606977224349976,
0.03193405643105507,
0.05525647848844528,
0.004023849032819271,
-0.0018897189293056726,
-0.028023265302181244,
-0.0578947439789772,
0.03395332023501396,
-0.029980260878801346,
0.0342583991587162,
-0.0962027907371521,
-0.03938800096511841,
0.0357903353869915,
-0.016356006264686584,
-0.023030109703540802,
-0.028948664665222168,
0.07711424678564072,
0.00002871839933504816,
-0.010546364821493626,
0.03494841232895851,
0.006181001663208008,
-0.010404814966022968,
-0.022664733231067657,
0.00279806787148118,
0.00028826677589677274,
-0.04867497831583023,
-0.06176304817199707,
0.02098993957042694,
0.006156821735203266,
0.03393932431936264,
0.017448242753744125,
0.012933565303683281,
-0.03260594606399536,
-0.045358121395111084,
-0.04871455579996109,
-0.014514288865029812,
0.010032803751528263,
-0.02032790519297123,
0.005927496589720249,
0.06865090131759644,
-0.008326241746544838,
-0.014640799723565578,
-0.04683847725391388,
-0.005521682556718588,
0.017615683376789093,
-0.02108047530055046,
-0.038262542337179184,
-0.017582591623067856,
-0.02071893960237503,
-0.016433224081993103,
0.046175453811883926,
0.010954171419143677,
-0.012285761535167694,
0.009923302568495274,
0.020839810371398926,
-0.017875507473945618,
0.023630330339074135,
-0.002128831809386611,
-0.0162428580224514,
0.02056591771543026,
0.030153196305036545,
0.0245121568441391,
-0.045639071613550186,
0.004407691303640604,
0.029123740270733833,
-0.047306351363658905,
0.014113957062363625,
-0.05939352512359619,
0.06241246685385704,
0.002415795112028718,
0.05958438664674759,
-0.006478465162217617,
0.004747410304844379,
-0.010702608153223991,
-0.012968550436198711,
0.03616835176944733,
-0.04128856584429741,
0.0031486554071307182,
0.03825688734650612,
-0.038613609969615936,
0.06116246059536934,
-0.02502555586397648,
-0.06707489490509033,
0.04556724429130554,
-0.029770368710160255,
0.014364871196448803,
-0.012995150871574879,
0.0009160738554783165,
0.018089959397912025,
-0.024024629965424538,
-0.033580705523490906,
-0.008465331979095936,
0.0070203556679189205,
-0.029765013605356216,
-0.005406953860074282,
-0.011337241157889366,
-0.08035659790039062,
-0.03416961431503296,
-0.0330510213971138,
0.06610572338104248,
-0.005626088939607143,
-0.03738757222890854,
0.0016720402054488659,
-0.018663695082068443,
-0.04115385562181473,
0.004455534275621176,
-0.013116800226271152,
0.018114572390913963,
-0.02666415274143219,
-0.012926185503602028,
-0.0061068241484463215,
-0.01995095983147621,
0.043987371027469635,
-0.02090250328183174,
0.07708768546581268,
-0.04879036173224449,
0.06410709768533707,
-0.004867220763117075,
-0.0038731072563678026,
0.02946149744093418,
-0.021342437714338303,
-0.03560548275709152,
0.028993060812354088,
-0.01528218574821949,
-0.035598743706941605,
0.07701336592435837,
-0.00024784114793874323,
-0.012201406061649323,
0.09476005285978317,
0.01628156192600727,
-0.023603009060025215,
0.01854514703154564,
-0.004716761410236359,
0.004152519162744284,
-0.017724212259054184,
-0.0319737084209919,
-0.020680679008364677,
-0.03336885944008827,
-0.030335482209920883,
-0.028409413993358612,
-0.038893330842256546,
0.029625285416841507
] |
<p>Good evening,</p>
<p>I haven't had physics since year 7 and now I need to use elementary things in university. Since I lack a lot of basics I am now trying my best to fill these holes. Currently I am stuck at solving circuits and I hope one of you can help me with the following circuit. I've also attached an image at the bottom of the post (large image).</p>
<p>Given:<br>
$R_1 = 20\Omega$<br>
$R_2 = 100\Omega$<br>
$R_3 = 50\Omega$<br>
$R_6 = 100\Omega$<br>
$U_0 = 2V$<br>
$U_5 = 900mV$<br>
$U_6 = 1V$<br>
$I_5 = 10mA$<br>
$I_7 = 80mA$ </p>
<p>What needs to be calculated: $U_3, I_4, R_5, R_8, U_8, I_8$</p>
<p>My attempt on solving the circuit:</p>
<p>1) Since $U_5$ and $I_5$ are given we can use Ohm's law to calcualte $R_5 = 90\Omega$.<br>
2) Knowing $U_6$ we can use the Mesh-Current Method to determine $U_7 = 1V$.<br>
3) Again I used Ohm's law to calculate $I_7 = 80mA$ with $U_7 = 1V$ from 2)<br>
4) Ohm's law to determine $I_6 = 10mA$ since we have $U_6, R_6$ given.<br>
5) Now I used the Mesh-Current Method between $U_1, U_5 and U_6$. Since $U_1, U_2, U_3, U_4$ are parallel to each other I assumed that they must be equal (? not quite sure on this one). However this assumption lead to the following result for $U_1, U_2, U_3, U_4 = 100mV$.<br>
6) Knowing $R_1, R_2, R_3$ and now $U_1, U_2, U_3$ I calculated $I_1 = 5mA, I_2 = 1mA, I_3 = 2mA$ with Ohm's law.
7) Now this is the point where I am stuck at. I'm not sure if it is allowed to reduce the circuit to only a specific area. For Instance I reduced the circuit to the upper left corner to determine $I_4 = 2mA$ with the Branch-Current Method. Having that given allows me to easily calculate $R_4 = 50\Omega$ with the help of Ohm's law.
8) Knowing that $U_0 = 2V$ I used the Mesh-Current Method for the whole outer part of the circuit to calculate $U_8 = 1V$.
9) Using the Branch-Current Method I determined the value of $I_8 = 110mV$
10) Now I used Ohm's law to get the value of $R_8 = 9.09091\Omega$. </p>
<p>$U_3 = 100mV, I_4 = 2mA, R_5 = 90\Omega, R_8 = 9.09091\Omega, U_8 = 1V, I_8 = 110mV$</p>
<p>I somehow cannot attach any images yet so I hope it is okay if I post an outisde link:</p>
<p><a href="https://www.dropbox.com/s/bfj64pkm0kg36ht/01.jpg" rel="nofollow">https://www.dropbox.com/s/bfj64pkm0kg36ht/01.jpg</a> (link to the circuit, large file, same as shown below)</p>
<p><img src="http://i.stack.imgur.com/04zfe.png" alt="circuit"></p> | g9212 | [
-0.007264914456754923,
0.0029827174730598927,
-0.005113373510539532,
-0.010080569423735142,
0.029353905469179153,
-0.010838108137249947,
0.06132982298731804,
0.03262827545404434,
0.0038672112859785557,
0.002452295972034335,
-0.022894226014614105,
0.06826853007078171,
-0.024896446615457535,
0.07384683936834335,
0.01108204573392868,
0.021340932697057724,
-0.046865448355674744,
-0.0197837483137846,
0.03913689777255058,
-0.038678351789712906,
-0.024298032745718956,
0.053304523229599,
-0.0022033678833395243,
-0.01194204855710268,
-0.06695842742919922,
-0.09053346514701843,
-0.027365295216441154,
0.006064525339752436,
-0.10613842308521271,
-0.001282801036722958,
-0.05783756449818611,
-0.03859608992934227,
0.08681333065032959,
-0.006709663663059473,
-0.08304634690284729,
0.023536188527941704,
0.04235430806875229,
0.01803099364042282,
0.010450362227857113,
-0.005431947764009237,
-0.011197255924344063,
-0.04422405734658241,
0.03567056730389595,
0.045881859958171844,
-0.005297324154525995,
-0.050725582987070084,
-0.04203302413225174,
-0.054881077259778976,
-0.005246485583484173,
-0.023402554914355278,
-0.025512179359793663,
0.048963069915771484,
0.0391322486102581,
-0.028444640338420868,
-0.05365372821688652,
0.021701302379369736,
-0.0015702900709584355,
-0.04630739241838455,
0.07116647809743881,
0.060272347182035446,
-0.005656286142766476,
-0.017533177509903908,
0.02753201313316822,
-0.011083291843533516,
0.016764473170042038,
-0.0009635128662921488,
0.015863526612520218,
-0.01714615523815155,
-0.04392912983894348,
0.03450210392475128,
0.03141844645142555,
-0.08110968768596649,
-0.0032249356154352427,
-0.02774561010301113,
-0.0019537711050361395,
-0.005697963293641806,
0.01877077855169773,
0.03694906085729599,
0.05445580184459686,
0.006435884162783623,
-0.0007762650493532419,
-0.009546766057610512,
-0.011361435987055302,
0.06210797652602196,
0.027843138203024864,
-0.027393756434321404,
-0.035843681544065475,
0.01879023015499115,
-0.002558761043474078,
-0.014717310667037964,
-0.03834613040089607,
0.04709775745868683,
0.048434194177389145,
-0.04271342232823372,
0.0410970002412796,
-0.03447188064455986,
-0.018610524013638496,
0.04358341172337532,
0.010969104245305061,
-0.02442070096731186,
-0.04312170296907425,
-0.05461544916033745,
0.01204548217356205,
0.0040695383213460445,
-0.07707756757736206,
0.039694610983133316,
0.08477243036031723,
-0.0021857162937521935,
-0.02172628603875637,
0.01265698205679655,
-0.06472145020961761,
-0.07338099181652069,
-0.03533274680376053,
0.01304581668227911,
-0.020324580371379852,
-0.03797301650047302,
0.03857750818133354,
0.026466652750968933,
0.003204918932169676,
0.031930111348629,
-0.03476577624678612,
-0.01013200357556343,
0.042341332882642746,
0.022476881742477417,
0.052017390727996826,
-0.01800592802464962,
-0.02313627302646637,
0.0336872898042202,
0.039630260318517685,
0.020940130576491356,
-0.005821962375193834,
-0.05649459734559059,
-0.04039841145277023,
0.027914294973015785,
0.018869083374738693,
0.010880368761718273,
-0.02762606553733349,
-0.031031591817736626,
0.0064387512393295765,
-0.0008124654996208847,
-0.018885068595409393,
-0.016748765483498573,
-0.0034752292558550835,
-0.0202470812946558,
-0.011539562605321407,
0.0054549360647797585,
-0.006697909906506538,
-0.019882971420884132,
-0.016363022848963737,
0.0048341271467506886,
0.006322490517050028,
0.0599198155105114,
-0.05710206925868988,
0.04509912431240082,
-0.012365803122520447,
0.04083462804555893,
0.008819560520350933,
-0.03147553279995918,
0.010053030215203762,
-0.012412937358021736,
-0.03621649742126465,
0.05215046554803848,
-0.00675030704587698,
-0.0034126578830182552,
-0.05309862270951271,
-0.03398566320538521,
0.04595204070210457,
-0.0716271698474884,
-0.013697016052901745,
-0.03485376760363579,
-0.06613414734601974,
-0.037268370389938354,
0.0006020740256644785,
0.028765926137566566,
-0.021204087883234024,
0.016476716846227646,
0.06650571525096893,
-0.039794933050870895,
0.04577939584851265,
0.0397188775241375,
0.006574665196239948,
-0.002320426283404231,
0.01503076683729887,
0.013987891376018524,
-0.005859451834112406,
0.02963235229253769,
0.01038067601621151,
0.01470198668539524,
-0.05120692774653435,
-0.05062771961092949,
-0.05553938448429108,
-0.014176242053508759,
-0.01741851679980755,
0.017042281106114388,
-0.026384888216853142,
0.02255455031991005,
0.023710601031780243,
0.006617730017751455,
-0.033350586891174316,
-0.008806217461824417,
0.022498318925499916,
-0.010076342150568962,
0.022706398740410805,
-0.0046464442275464535,
0.06633129715919495,
0.03335734084248543,
0.01272776909172535,
-0.010002215392887592,
0.015889039263129234,
0.012379182502627373,
-0.034379396587610245,
-0.015643522143363953,
0.017290297895669937,
0.0410214401781559,
-0.018225055187940598,
-0.02034570463001728,
0.018025269731879234,
-0.04642299562692642,
-0.047723907977342606,
0.01612895354628563,
0.061151131987571716,
-0.02832738682627678,
0.05394163727760315,
-0.0648670494556427,
0.022287515923380852,
0.06186516210436821,
0.010930406861007214,
-0.013549038209021091,
-0.051802851259708405,
-0.014574938453733921,
-0.04342593625187874,
0.02795460820198059,
-0.029944032430648804,
-0.06432317942380905,
-0.01006025355309248,
0.006456117611378431,
0.0028162046801298857,
-0.004845624789595604,
-0.06981346756219864,
0.0009219905477948487,
-0.010302817448973656,
0.009714588522911072,
0.06574523448944092,
-0.014295870438218117,
0.03750143200159073,
-0.06704819202423096,
0.04387260228395462,
0.05769141763448715,
-0.05222224444150925,
0.037773214280605316,
0.050333090126514435,
0.01700015552341938,
-0.005096059758216143,
0.04909428954124451,
-0.0269886814057827,
-0.002120405901223421,
0.07487902045249939,
0.04077709838747978,
0.031900569796562195,
-0.0039619444869458675,
-0.06284182518720627,
-0.02108224667608738,
0.036935955286026,
0.04254419356584549,
-0.1234554871916771,
-0.028375914320349693,
-0.05484217032790184,
-0.06445526331663132,
0.05702795460820198,
-0.016999684274196625,
-0.019494004547595978,
0.041119225323200226,
-0.005768763832747936,
-0.0420035794377327,
0.020098116248846054,
-0.04141375795006752,
0.07402016967535019,
0.0023688403889536858,
0.007137366104871035,
0.053127262741327286,
0.034578658640384674,
-0.018193375319242477,
-0.08925934880971909,
0.022909434512257576,
0.022885072976350784,
-0.0396387055516243,
-0.0051775467582046986,
-0.021314287558197975,
0.02381545677781105,
0.0021760466042906046,
-0.004721252713352442,
-0.036041054874658585,
0.032497942447662354,
-0.01974228024482727,
0.03847735375165939,
0.039031967520713806,
0.04477144777774811,
-0.014299653470516205,
-0.00871530082076788,
0.030987653881311417,
-0.05360661447048187,
-0.04945651441812515,
0.016259295865893364,
-0.03631700575351715,
0.024216510355472565,
0.014362804591655731,
0.03922431170940399,
0.01130802370607853,
0.028329607099294662,
0.06949175894260406,
-0.01987691968679428,
0.007536807097494602,
0.024283966049551964,
-0.03877660259604454,
0.02577480487525463,
-0.0011282548075541854,
-0.02547382563352585,
-0.012115228921175003,
-0.016248775646090508,
0.0069890934973955154,
-0.03344030678272247,
-0.03418117016553879,
0.017336497083306313,
-0.003967946860939264,
-0.006141443736851215,
0.0782255232334137,
-0.04136925935745239,
-0.006566649302840233,
-0.007904589176177979,
-0.031837087124586105,
-0.05579947307705879,
-0.008023353293538094,
-0.018637949600815773,
0.04080049321055412,
-0.003995746374130249,
-0.08071229606866837,
-0.0062407758086919785,
0.021972309798002243,
0.03133862093091011,
-0.04409576579928398,
-0.01721823588013649,
-0.02089156210422516,
-0.025784187018871307,
-0.038353081792593,
0.0003187937836628407,
-0.03293507918715477,
-0.06150250881910324,
0.03613189607858658,
-0.017886405810713768,
-0.0316072516143322,
0.0785147175192833,
0.06498844921588898,
-0.00170383439399302,
0.0038890684954822063,
-0.007969995960593224,
0.01515156403183937,
-0.03183069825172424,
0.039732493460178375,
0.0032862068619579077,
0.013902461156249046,
-0.01107401680201292,
-0.055806152522563934,
0.009674015454947948,
0.06227986514568329,
0.018347451463341713,
-0.010985204949975014,
0.054803770035505295,
0.0036625517532229424,
-0.018866537138819695,
-0.0772005021572113,
0.002567739225924015,
-0.049056120216846466,
-0.003381866728886962,
0.007784930057823658,
-0.051443006843328476,
-0.019853290170431137,
0.02917500026524067,
0.06788326799869537,
-0.046694014221429825,
0.06430821120738983,
-0.02566865086555481,
0.0015184441581368446,
0.03919746354222298,
0.01754322089254856,
0.005394211038947105,
0.007691650651395321,
0.02400067448616028,
-0.007493285927921534,
0.008832688443362713,
0.00682199839502573,
-0.004461693111807108,
-0.025678090751171112,
-0.023387787863612175,
-0.004873128142207861,
-0.029755814000964165,
-0.05832034721970558,
0.00798740703612566,
0.021450823172926903,
-0.07668745517730713,
0.013150653801858425,
0.026664642617106438,
0.00872705690562725,
0.03833352029323578,
0.03611156344413757,
-0.009864210151135921,
-0.012251368723809719,
0.031385451555252075,
-0.008264163509011269,
0.07055842876434326,
0.011933489702641964,
-0.0025733814109116793,
0.032174356281757355,
0.009388788603246212,
-0.02758750133216381,
0.027982616797089577,
0.029293358325958252,
0.04393048211932182,
-0.02559470944106579,
0.01959957554936409,
0.024568447843194008,
0.020439935848116875,
0.03193364292383194,
-0.06746817380189896,
-0.05318809673190117,
-0.016315409913659096,
0.008531369268894196,
-0.0017405843827873468,
-0.026730787009000778,
0.06588610261678696,
0.02478037402033806,
-0.01991426758468151,
0.03365059196949005,
-0.09285975992679596,
-0.043888915330171585,
-0.08181730657815933,
0.03245624154806137,
-0.05963163077831268,
0.03280261531472206,
-0.011099709197878838,
0.04071175307035446,
0.046409375965595245,
0.026071272790431976,
-0.001544194994494319,
-0.013755526393651962,
-0.013509434647858143,
0.015069558285176754,
-0.08533088862895966,
-0.018743114545941353,
0.00905164796859026,
0.004551263991743326,
0.023062262684106827,
0.026977837085723877,
0.08827928453683853,
-0.02132469415664673,
-0.050174057483673096,
-0.026378605514764786,
0.006109719164669514,
0.0400458462536335,
0.031764548271894455,
0.09324078261852264,
-0.05959580838680267,
0.02646530419588089,
0.027853569015860558,
-0.01040085032582283,
0.05432724207639694,
-0.012872857972979546,
0.0021685452666133642,
-0.012703768908977509,
-0.012308456934988499,
-0.03396453708410263,
0.07074444741010666,
0.01973949559032917,
0.0026577268727123737,
0.012491517700254917,
-0.019515004009008408,
0.013186386786401272,
-0.0019881620537489653,
-0.018665187060832977,
-0.01764332316815853,
-0.01585013046860695,
-0.029892178252339363,
-0.031024189665913582,
-0.005087049212306738,
0.05716555193066597,
0.0033908619079738855,
-0.022158527746796608,
-0.007426440715789795,
0.022243399173021317,
-0.021475449204444885,
0.0224791057407856,
0.02631199359893799,
0.08089612424373627,
0.044496893882751465,
-0.008028115145862103,
0.0027315106708556414,
-0.05280953273177147,
0.04609545320272446,
0.0030655348673462868,
-0.06728751212358475,
0.01272626407444477,
-0.0494079627096653,
0.003147887298837304,
-0.04271455854177475,
-0.014216217212378979,
-0.022044626995921135,
0.0005598646239377558,
-0.05231797695159912,
0.01509113796055317,
0.02834872342646122,
-0.008013952523469925,
0.006767330225557089,
-0.000402981968363747,
0.027282150462269783,
0.03353525325655937,
0.011433804407715797,
-0.00848816242069006,
-0.07066423445940018,
0.0064670611172914505,
-0.04325953125953674,
-0.020624807104468346,
0.0864594429731369,
-0.04065249115228653,
0.0460486076772213,
0.01844784803688526,
-0.005695834290236235,
0.014198093675076962,
-0.03232681378722191,
-0.03488286957144737,
0.037453338503837585,
0.023851493373513222,
0.004446196369826794,
0.02369539998471737,
-0.018210243433713913,
-0.010554440319538116,
-0.014185532927513123,
0.014327902346849442,
0.017160002142190933,
-0.07368429750204086,
0.03509197384119034,
-0.012004544027149677,
0.042673222720623016,
0.06189446523785591,
0.04191706329584122,
-0.023769108578562737,
-0.014209496788680553,
-0.01962251402437687,
-0.01856311224400997,
-0.04791289195418358,
0.0013883172068744898,
-0.034049779176712036,
-0.04465697705745697,
0.009771790355443954,
-0.013451502658426762,
-0.02098984271287918,
0.017501112073659897,
-0.01508933212608099,
0.005551402922719717,
-0.039084162563085556,
-0.013074190355837345,
-0.002179058501496911,
0.08782337605953217,
-0.04429670050740242,
-0.037282370030879974,
-0.021990200504660606,
0.03132079541683197,
-0.02621878683567047,
-0.02031887322664261,
0.00973216351121664,
0.033977992832660675,
-0.03142719343304634,
0.017909813672304153,
-0.0603591613471508,
0.019326133653521538,
0.0020966914016753435,
0.058439046144485474,
0.0770377665758133,
0.019189292564988136,
0.024947205558419228,
0.048666100949048996,
0.049705058336257935,
-0.030427729710936546,
0.011630892753601074,
0.04724005609750748,
0.046117547899484634,
0.05396602675318718,
0.024801842868328094,
-0.034339502453804016,
-0.042784906923770905,
0.006768715567886829,
-0.02984214946627617,
0.007492818869650364,
0.05004303902387619,
0.008669402450323105,
0.00966694112867117,
0.04080989211797714,
0.002935370896011591,
0.004159245640039444,
-0.006118441000580788,
0.0023103486746549606,
0.0520474910736084,
0.02948596701025963,
-0.038098953664302826,
0.002505581360310316,
-0.021922554820775986,
0.017965923994779587,
0.041928332298994064,
-0.022494317963719368,
0.0019076525932177901,
-0.053609855473041534,
-0.008637949824333191,
0.037117697298526764,
0.017951609566807747,
-0.012823469936847687,
-0.009600845165550709,
0.012263242155313492,
-0.040191687643527985,
0.021452849730849266,
0.030699918046593666,
0.004218385089188814,
0.033926792442798615,
-0.012927536852657795,
0.05073912814259529,
-0.039490144699811935,
0.039319731295108795,
0.029057739302515984,
0.04113692790269852,
0.015815794467926025,
-0.00637041637673974,
0.06648775190114975,
-0.023334741592407227,
0.006337676662951708,
-0.04047202691435814,
-0.028932081535458565,
0.027394268661737442,
-0.007014886476099491,
0.04415733367204666,
0.013034187257289886,
0.0024533113464713097,
-0.013876564800739288,
0.1240396797657013,
0.009915483184158802,
-0.02479681186378002,
0.021267259493470192,
0.04129239171743393,
0.01034032367169857,
-0.06122256815433502,
0.05051523819565773,
0.03841300308704376,
-0.05202847719192505,
0.008720153011381626,
0.05065631493926048,
0.04627136141061783,
0.010948321782052517,
-0.0043120416812598705,
-0.013114540837705135,
-0.03740813583135605,
0.018178265541791916,
0.021647421643137932,
0.0566972941160202,
0.0011377001646906137,
0.0013951611472293735,
-0.039445020258426666,
0.015369090251624584,
0.0024806049186736345,
0.03524038568139076,
0.005425338167697191,
0.03831340745091438,
-0.026048127561807632,
0.00568147050216794,
-0.04403429478406906,
-0.023419013246893883,
-0.03210997208952904,
-0.01853589341044426,
0.040010929107666016,
0.013958306051790714,
0.003747004084289074,
0.010183777660131454,
0.04131436347961426,
-0.05280352756381035,
-0.038977574557065964,
0.017588797956705093,
-0.008924259804189205,
-0.07444823533296585,
-0.054778311401605606,
-0.017963403835892677,
0.02895139902830124,
-0.05829446762800217,
-0.044821739196777344,
0.05383419618010521,
0.02822832763195038,
0.040360987186431885,
0.05886591970920563,
-0.010934718884527683,
-0.017428956925868988,
-0.01693350449204445,
0.03214239329099655,
-0.01881759986281395,
0.009143582545220852,
0.0678369477391243,
-0.04076549410820007,
0.04511834308505058,
-0.014310726895928383,
0.00933700893074274,
0.011298619210720062,
-0.07770492881536484,
-0.0358552485704422,
-0.04688714072108269,
-0.023826878517866135,
-0.010701091960072517,
-0.02161739394068718,
0.029982762411236763,
0.04675577953457832,
-0.03678325563669205,
-0.0013439614558592439,
0.029472049325704575,
-0.023597262799739838,
-0.015695050358772278,
-0.00021247808763291687,
-0.01894443854689598,
0.03084016591310501,
-0.03869284689426422,
-0.026130642741918564,
-0.024287790060043335,
-0.0066637336276471615,
-0.01926686428487301,
0.055000871419906616,
0.015575365163385868,
0.011632469482719898,
-0.03533339500427246,
-0.03613370656967163,
-0.026761841028928757,
-0.06259716302156448,
0.0006190633866935968,
0.012701164931058884,
-0.011635784059762955,
-0.023494379594922066,
-0.04724745452404022,
-0.07064241915941238,
-0.005499669350683689,
0.034504540264606476,
0.0252187829464674,
-0.0851033478975296,
-0.022921958938241005,
0.008090201765298843,
0.014135852456092834,
-0.04253153130412102,
-0.06852490454912186,
0.030252769589424133,
0.04157603904604912,
0.023942794650793076,
-0.01211486104875803,
-0.005904027726501226,
-0.03000376746058464,
-0.056544408202171326,
0.02520722895860672,
-0.03717973828315735,
-0.01620378904044628,
0.04526200890541077,
0.03073045238852501,
0.018985847011208534,
-0.019369496032595634,
0.050617899745702744,
0.008507352322340012,
0.025747038424015045,
0.09692756831645966,
-0.012044054456055164,
0.006672011222690344,
-0.06480859965085983
] |
<p>Is there any dependence of the impurities ionization energy on temperature in silicon? I mean if there are any interactions between localized electron and phonons which leads to renormalization of electron binding energy.</p> | g9213 | [
0.07448060810565948,
0.04471734166145325,
0.03089667484164238,
0.0344298779964447,
-0.037370096892118454,
0.00044937219354324043,
-0.06614001095294952,
0.0420520044863224,
-0.016350504010915756,
0.05022037401795387,
-0.010554998181760311,
0.04400079697370529,
-0.05345539748668671,
-0.010952254757285118,
-0.046835314482450485,
0.003394109895452857,
0.10072728991508484,
-0.014848574995994568,
0.027716120705008507,
0.08031211793422699,
-0.06591196358203888,
-0.005535340867936611,
-0.043424732983112335,
-0.017756206914782524,
0.010853447020053864,
0.018903113901615143,
0.010069799609482288,
-0.022165119647979736,
-0.03250664100050926,
0.009320233948528767,
-0.02831427752971649,
0.02481831982731819,
0.031383614987134933,
0.006581294350326061,
-0.06289254873991013,
-0.029348447918891907,
0.007504100911319256,
-0.010945883579552174,
0.08326872438192368,
-0.048249609768390656,
-0.012192470021545887,
-0.007336967159062624,
0.09429880231618881,
0.00850699469447136,
-0.012357461266219616,
0.016726141795516014,
0.0031658909283578396,
0.007425343617796898,
-0.033652324229478836,
0.010771743021905422,
0.016133669763803482,
0.04354766011238098,
-0.013073106296360493,
0.050937097519636154,
0.0072571695782244205,
-0.010340345092117786,
-0.03657149896025658,
0.026396464556455612,
-0.010181674733757973,
0.07013381272554398,
0.0725388377904892,
0.04984979331493378,
-0.005036076530814171,
-0.005079993512481451,
0.029513565823435783,
-0.03264746442437172,
-0.03969406336545944,
0.029385875910520554,
-0.02227495238184929,
0.015385878272354603,
-0.004658750258386135,
-0.011531420052051544,
-0.0879700556397438,
0.00034996806061826646,
-0.06384892761707306,
-0.009829621762037277,
-0.031070727854967117,
-0.062214452773332596,
-0.0021914641838520765,
0.007300212047994137,
-0.029965927824378014,
-0.03387923911213875,
0.03279639035463333,
-0.02305227518081665,
0.01068010926246643,
-0.0423935241997242,
0.03091515600681305,
0.04820428043603897,
-0.054639123380184174,
0.05247560515999794,
-0.019757431000471115,
0.0033016910310834646,
0.05540971830487251,
-0.004141388460993767,
0.0008830017759464681,
0.02202540822327137,
-0.043395791202783585,
0.06993987411260605,
-0.011103138327598572,
-0.028969015926122665,
-0.03767499700188637,
-0.0012278619688004255,
0.08206827193498611,
0.01277556549757719,
-0.008618192747235298,
0.018277768045663834,
-0.03779364377260208,
-0.0678810253739357,
0.010757037438452244,
0.08397989720106125,
0.02520938590168953,
-0.0813707634806633,
0.041929055005311966,
0.006425124127417803,
-0.05858350172638893,
0.03332701697945595,
0.019451333209872246,
-0.03268200531601906,
0.04356839880347252,
0.009152761660516262,
0.033280692994594574,
0.03247270733118057,
-0.042206764221191406,
0.0027206542436033487,
0.009296699427068233,
0.02659776248037815,
0.019365431740880013,
-0.01597495749592781,
-0.046664897352457047,
-0.0038193969521671534,
-0.023255271837115288,
-0.03179644048213959,
-0.0062613594345748425,
-0.009518110193312168,
-0.011362948454916477,
-0.024919921532273293,
0.026376958936452866,
0.007148106582462788,
-0.05218685418367386,
-0.015185213647782803,
-0.03094654157757759,
0.03330744057893753,
0.004978363402187824,
-0.010642088018357754,
0.045900698751211166,
-0.07811751961708069,
-0.027209224179387093,
-0.0034733086358755827,
0.00005468711242428981,
0.07037492096424103,
-0.008004952222108841,
0.01144232228398323,
0.033750392496585846,
-0.04118708521127701,
-0.04313604533672333,
-0.0158156156539917,
0.023632420226931572,
0.03471050038933754,
0.0036831761244684458,
-0.0318228155374527,
-0.04022372141480446,
-0.0018240713980048895,
0.03212544694542885,
0.0008174162940122187,
-0.008132143877446651,
-0.041393522173166275,
0.021884826943278313,
0.030319059267640114,
-0.029548348858952522,
0.016834871843457222,
-0.03968726843595505,
-0.0063857706263661385,
0.014719124883413315,
0.03705282136797905,
0.013783950358629227,
-0.03961680456995964,
-0.009610900655388832,
0.01959625445306301,
0.05746559426188469,
-0.03205432370305061,
0.012263337150216103,
0.02792263776063919,
-0.05031104013323784,
-0.049619629979133606,
0.013243340887129307,
0.019269799813628197,
-0.02143564075231552,
0.013761200942099094,
-0.002942986087873578,
0.02978302165865898,
-0.031406667083501816,
-0.030445706099271774,
0.032170552760362625,
-0.05941997468471527,
-0.0035376090090721846,
-0.026065487414598465,
0.028147762641310692,
-0.05077112466096878,
-0.042510051280260086,
-0.01042097806930542,
-0.07337741553783417,
0.015770994126796722,
-0.04969285801053047,
-0.04977696016430855,
0.0512656643986702,
0.018305042758584023,
-0.014715699478983879,
-0.03756047785282135,
-0.04414370283484459,
0.00016907710232771933,
-0.033971305936574936,
0.00528007373213768,
0.026000695303082466,
0.07678382098674774,
0.04511761665344238,
0.024093544110655785,
0.023667756468057632,
0.0006704546394757926,
0.02384062670171261,
0.04986511543393135,
-0.019187744706869125,
-0.024598971009254456,
0.03430706262588501,
0.049569644033908844,
-0.027411004528403282,
0.014454987831413746,
-0.031220417469739914,
0.06211701035499573,
0.010391974821686745,
0.05331963673233986,
-0.07252495735883713,
0.0444544218480587,
-0.04615030065178871,
0.020691581070423126,
-0.012557607144117355,
0.022351259365677834,
-0.0573456697165966,
-0.04015589877963066,
0.002085896208882332,
0.0012063757749274373,
-0.03855299949645996,
0.024891497567296028,
-0.02941797487437725,
0.05860082060098648,
-0.011293052695691586,
-0.05641071870923042,
0.016818584874272346,
0.004956807941198349,
-0.0003609195991884917,
-0.08131130784749985,
-0.005161826498806477,
0.018752628937363625,
0.022091949358582497,
0.0433439239859581,
-0.02091543935239315,
-0.022392334416508675,
-0.03742113336920738,
-0.01453071366995573,
0.01800069957971573,
-0.02859540283679962,
0.014603983610868454,
0.009816000238060951,
-0.03556177020072937,
0.01260160468518734,
-0.029699187725782394,
-0.010360402055084705,
0.06498251855373383,
-0.010792452841997147,
-0.024798119440674782,
0.013899155892431736,
0.005408117081969976,
0.07934818416833878,
0.033344805240631104,
0.06198929250240326,
0.041622236371040344,
-0.02084270492196083,
0.015570317395031452,
0.027034342288970947,
0.0213331151753664,
-0.061663173139095306,
-0.04485257342457771,
-0.005725644528865814,
-0.040320299565792084,
-0.034011442214250565,
-0.012081852182745934,
-0.06604645401239395,
0.03743418678641319,
-0.04365312308073044,
0.02973289228975773,
-0.026886098086833954,
-0.051786720752716064,
-0.04330999404191971,
-0.0521584115922451,
0.006533099338412285,
0.03325106203556061,
-0.026247894391417503,
0.007717255037277937,
-0.030987393110990524,
-0.02045392617583275,
0.0630350410938263,
0.06092493236064911,
-0.03637595847249031,
-0.043446172028779984,
0.008092186413705349,
0.007867444306612015,
-0.028698494657874107,
-0.03569284826517105,
-0.044659726321697235,
0.0058648656122386456,
-0.03498285636305809,
0.0037650319281965494,
-0.006925596855580807,
0.01676294393837452,
0.025832217186689377,
-0.0294934269040823,
0.029967021197080612,
-0.08123982697725296,
0.0026380589697510004,
0.02834033966064453,
-0.03513490781188011,
-0.02276216261088848,
0.014639233238995075,
0.05901624634861946,
-0.04959087818861008,
0.005442420952022076,
0.02937520109117031,
0.020538637414574623,
-0.006769517902284861,
0.01636558771133423,
0.008427496999502182,
-0.012865033000707626,
0.006622316315770149,
-0.02601606212556362,
0.014262652024626732,
-0.01684730499982834,
-0.0009969117818400264,
-0.027311332523822784,
0.036698341369628906,
0.07767628133296967,
0.04112856462597847,
-0.006065011490136385,
0.048129986971616745,
-0.007903155870735645,
0.01783823035657406,
0.03468766435980797,
0.0793999433517456,
-0.0419832319021225,
0.007980196736752987,
0.009420051239430904,
0.020337413996458054,
0.05226504057645798,
-0.027885379269719124,
-0.0045730434358119965,
0.020217569544911385,
-0.023116694763302803,
0.03257307782769203,
-0.06937699764966965,
0.028744639828801155,
-0.051529888063669205,
-0.012489593587815762,
0.05952288582921028,
0.0010659504914656281,
-0.004544756840914488,
-0.09650762379169464,
-0.011827027425169945,
0.005568097345530987,
-0.048744942992925644,
0.00328176561743021,
0.06834489107131958,
-0.05860425531864166,
-0.02784033678472042,
0.012614507228136063,
-0.0028555262833833694,
0.048367034643888474,
-0.018168549984693527,
0.045839641243219376,
0.0020660676527768373,
0.000004473865828913404,
-0.014577523805201054,
-0.06318337470293045,
-0.07917945832014084,
-0.04190169647336006,
-0.04246839880943298,
0.024725595489144325,
0.06089334562420845,
-0.07344718277454376,
-0.034352414309978485,
0.02213267795741558,
-0.06735358387231827,
-0.05684112012386322,
0.01530747301876545,
-0.03016721084713936,
0.023754993453621864,
0.03481830656528473,
0.022144710645079613,
-0.04866338148713112,
0.023174164816737175,
-0.02029462717473507,
0.08556690812110901,
0.009641287848353386,
-0.017495110630989075,
0.03219549357891083,
0.09808763116598129,
-0.05274583026766777,
0.040797315537929535,
0.0398152731359005,
0.0821707621216774,
0.004913305398076773,
-0.06362875550985336,
-0.02581680193543434,
-0.03348229452967644,
0.060630060732364655,
-0.008531605824828148,
0.019078994169831276,
0.01728275790810585,
-0.006886511109769344,
-0.010523082688450813,
-0.021429393440485,
0.0008037716615945101,
-0.023712512105703354,
-0.008758127689361572,
0.044233229011297226,
-0.017345858737826347,
-0.03142830729484558,
-0.03230377659201622,
0.06868576258420944,
0.09349090605974197,
-0.025552505627274513,
-0.07116496562957764,
-0.01517847366631031,
0.005151190795004368,
0.019027290865778923,
0.016275817528367043,
-0.06411777436733246,
-0.010191702283918858,
0.02186567522585392,
-0.032164156436920166,
-0.025368770584464073,
-0.016413988545536995,
-0.0016896049492061138,
0.03426865115761757,
0.014287534169852734,
0.026534060016274452,
0.026289701461791992,
-0.05108596384525299,
-0.03853772208094597,
-0.031129995360970497,
-0.025325043126940727,
0.010439733974635601,
-0.027569236233830452,
0.04501516371965408,
0.020265430212020874,
-0.04621969163417816,
-0.03563675656914711,
0.02748963236808777,
0.013604575768113136,
-0.05201764032244682,
0.06940148770809174,
0.0004654661170206964,
0.00650792196393013,
-0.022418975830078125,
-0.06140972673892975,
0.009278587065637112,
0.07364200055599213,
-0.06240084022283554,
0.00014234129048418254,
0.010028531774878502,
-0.007988642901182175,
0.008748291060328484,
0.029775341972708702,
0.05016789585351944,
0.0012204729719087481,
0.02990332990884781,
0.032562900334596634,
0.03868219628930092,
-0.008783129043877125,
-0.023335646837949753,
-0.08507311344146729,
-0.009916967712342739,
-0.08881116658449173,
-0.0316166877746582,
-0.03174685314297676,
0.02150346152484417,
0.012534989975392818,
-0.01130614709109068,
-0.03216288983821869,
-0.054933059960603714,
0.01314191147685051,
0.016254881396889687,
-0.050317440181970596,
-0.009277443401515484,
0.013722224161028862,
0.04262120649218559,
0.015287482179701328,
0.020810458809137344,
0.007554651703685522,
0.05617903545498848,
0.03234178200364113,
-0.03511563315987587,
0.063324473798275,
0.0009573461138643324,
-0.05365956947207451,
-0.03665929287672043,
-0.0006644835812039673,
0.011150036007165909,
-0.04416454955935478,
0.06291108578443527,
-0.019247272983193398,
-0.02608456090092659,
0.005330863408744335,
0.0178085844963789,
0.04017464444041252,
0.008423766121268272,
-0.009019521065056324,
-0.0323522575199604,
0.007215178105980158,
0.01806081086397171,
0.0513380691409111,
0.01592225395143032,
-0.004866015166044235,
-0.01928778737783432,
-0.04270419478416443,
0.011968293227255344,
0.03932499140501022,
-0.025604359805583954,
-0.02375144697725773,
-0.02386794425547123,
-0.06461809575557709,
0.05988898128271103,
-0.05416467785835266,
0.07014958560466766,
0.007764033507555723,
0.0039056630339473486,
0.023412026464939117,
0.05527898296713829,
0.001462441054172814,
-0.018859107047319412,
0.011675774119794369,
-0.05521399527788162,
0.04306737706065178,
-0.01512027345597744,
0.0014990819618105888,
0.023678360506892204,
0.019391249865293503,
0.02262968383729458,
0.041397642344236374,
-0.04709162935614586,
0.05047042667865753,
-0.009514838457107544,
-0.01739802211523056,
0.008171848952770233,
-0.003363774623721838,
-0.020765947178006172,
-0.031163856387138367,
0.026577919721603394,
0.031078390777111053,
0.027874711900949478,
-0.043746232986450195,
-0.03707588091492653,
0.017032410949468613,
0.017391478642821312,
0.04932055249810219,
-0.026173384860157967,
0.02902357466518879,
0.010211939923465252,
-0.014410383068025112,
-0.022645942866802216,
0.0014233066467568278,
0.006000145338475704,
-0.0009298082441091537,
0.017445480450987816,
0.007385619450360537,
-0.011749891564249992,
-0.04432140290737152,
-0.014725246466696262,
-0.051664963364601135,
0.002945779589936137,
0.022293303161859512,
0.017234962433576584,
-0.0062601822428405285,
0.013252243399620056,
0.05683661252260208,
0.0119997663423419,
0.03060203231871128,
0.003032332519069314,
-0.03326248377561569,
-0.0029179782141000032,
0.025791309773921967,
0.05903447046875954,
-0.01056563388556242,
-0.012501980178058147,
-0.038677096366882324,
-0.003591333283111453,
0.01697978563606739,
-0.10279859602451324,
0.0066893757320940495,
0.003084462834522128,
-0.08051269501447678,
-0.052413854748010635,
0.03038278967142105,
0.03251747786998749,
-0.02109522931277752,
0.012528739869594574,
-0.004696657881140709,
0.014948942698538303,
-0.05836593359708786,
0.04158301278948784,
0.03119334578514099,
-0.0387326143682003,
0.0629383996129036,
-0.016344159841537476,
-0.01610233448445797,
0.05498706176877022,
-0.019116276875138283,
0.0010116163175553083,
-0.002133911242708564,
0.0268893763422966,
0.06559432297945023,
-0.0408102311193943,
-0.031215965747833252,
-0.0073879677802324295,
-0.0009528252412565053,
-0.049838289618492126,
0.003562417346984148,
-0.00036789989098906517,
0.049152523279190063,
-0.02545171044766903,
0.03563648834824562,
0.07406732439994812,
-0.08679381757974625,
-0.014366677962243557,
-0.009121937677264214,
0.020354753360152245,
0.036266352981328964,
0.02002357877790928,
0.009097600355744362,
-0.00047329571680165827,
-0.06314044445753098,
-0.06434562802314758,
0.04559401795268059,
0.0348985493183136,
-0.036303650587797165,
0.05079629644751549,
0.04157770797610283,
-0.013198139145970345,
0.02165769413113594,
-0.012087109498679638,
0.004356577526777983,
-0.004082999192178249,
-0.004347358364611864,
0.013126826845109463,
0.01496097631752491,
0.013938096351921558,
0.040596991777420044,
0.018933985382318497,
0.036633145064115524,
-0.027685148641467094,
-0.004563967231661081,
0.013433216139674187,
-0.008773318491876125,
-0.023291664198040962,
-0.0014827812556177378,
0.0003490517265163362,
0.03320783004164696,
0.027320560067892075,
0.05929539352655411,
-0.012866945005953312,
-0.04757324606180191,
0.03281988948583603,
0.019928138703107834,
-0.014276094734668732,
-0.02485022321343422,
-0.00035945544368587434,
-0.017880607396364212,
-0.011549072340130806,
0.02761889435350895,
-0.021661879494786263,
0.04278331995010376,
-0.06847476214170456,
-0.006027755793184042,
-0.013849498704075813,
-0.025671057403087616,
0.035415876656770706,
-0.04692960903048515,
-0.04688842222094536,
0.062070976942777634,
0.018848273903131485,
0.0013895194279029965,
-0.024214275181293488,
0.03148286044597626,
0.020762089639902115,
0.018171997740864754,
0.021172234788537025,
0.000009007590961118694,
-0.02148786187171936,
-0.02428758516907692,
0.040097177028656006,
0.03226509317755699,
0.032917823642492294,
0.03926821053028107,
0.08479750901460648,
0.05658414214849472,
0.04857906699180603,
-0.0245002843439579,
0.003919294569641352,
0.009792868047952652,
-0.009272079914808273,
0.005301171448081732,
-0.0538780614733696,
-0.004360554739832878,
0.09080856293439865,
-0.06225268915295601,
0.0038842440117150545,
-0.01921173930168152,
0.024391336366534233,
-0.040374040603637695,
0.00515004014596343,
-0.051011066883802414,
-0.03963764011859894,
0.06347377598285675,
0.04964224621653557,
0.018183570355176926,
0.06104088947176933,
0.0010641637491062284,
-0.021803174167871475,
-0.001844929764047265,
0.04457514360547066,
0.005695491097867489,
0.022554906085133553,
0.06152986362576485,
0.0009374541696161032,
0.0002400471712462604,
-0.011672724038362503,
-0.010747808031737804,
-0.04102278873324394,
0.0028520426712930202,
0.04085063189268112,
-0.05979486182332039,
0.03730951249599457,
-0.00497192470356822,
0.029580719769001007,
0.008751199580729008,
-0.008150149136781693,
-0.03407715633511543,
0.00963515229523182,
-0.0318322516977787,
0.0037777640391141176,
-0.0007304665050469339,
0.06360578536987305,
0.00684315012767911,
-0.0001651522470638156,
-0.028024256229400635,
-0.05642599239945412,
0.054777149111032486,
0.03204268962144852,
-0.038134388625621796,
-0.03720236197113991,
-0.021833691745996475,
0.006420394871383905,
-0.0393548347055912,
-0.029737155884504318,
-0.027150573208928108,
-0.027016736567020416,
-0.007916172035038471,
-0.02149694226682186,
-0.006053317803889513,
0.019397735595703125,
-0.032422833144664764
] |
<p>Liquid-gas transition critical point is believed to share the same universality class as the 3D Ising model.</p>
<p>We know that the liquid-gas transition is characterized by a phenomenon called critical opalescence that occurs at the critical point and which in short happens because the system becomes correlated at all length scales and thus scatters all frequency of the incident light, thus making the liquid-gas look opaque.</p>
<p><strong>Q</strong> : What is the analogous phenomenon of critical opalescence in a spin system ? Say one takes a material that may be described by a 3D Ising model and does neutron scattering with a broad range of neutron energy : At the critical magnetic ordering temperature, will he see critical opalescence of the neutrons, i.e a diffuse scattering of the neutrons at all wave-length at the critical temperature ?</p> | g9214 | [
0.03195309266448021,
0.04009171575307846,
0.021180907264351845,
0.0034499678295105696,
0.012845965102314949,
0.05947662889957428,
-0.06018182635307312,
0.0062379189766943455,
0.0036291801370680332,
0.012950764037668705,
0.03293821960687637,
0.01017663162201643,
-0.0010548216523602605,
-0.03581773489713669,
-0.02703101560473442,
0.022025883197784424,
0.029590273275971413,
0.004583464935421944,
-0.01619075983762741,
-0.006195619702339172,
-0.024473829194903374,
-0.04267570748925209,
0.009946421720087528,
-0.03242229297757149,
-0.05024678260087967,
0.046367596834897995,
-0.02038097009062767,
-0.06330085545778275,
0.022023554891347885,
-0.010134915821254253,
0.04042746126651764,
-0.017294971272349358,
-0.017922811210155487,
-0.06432775408029556,
0.007349280174821615,
-0.042514413595199585,
0.01454094797372818,
0.008717269636690617,
-0.028246751055121422,
0.004060904495418072,
0.019078506156802177,
0.041394561529159546,
0.054667770862579346,
-0.03616367280483246,
0.023405903950333595,
0.0552317276597023,
-0.06443382054567337,
0.010570392943918705,
-0.03369817137718201,
-0.04238935187458992,
0.004915620665997267,
0.07070579379796982,
0.006286423187702894,
0.006701820995658636,
0.01894845813512802,
0.049212515354156494,
-0.0438527874648571,
0.014818319119513035,
0.07073255628347397,
0.04824225977063179,
-0.020912615582346916,
0.07626570761203766,
-0.00822415854781866,
-0.05050981417298317,
0.07922215014696121,
-0.06508010625839233,
-0.07983065396547318,
0.05293465405702591,
0.01520581729710102,
-0.00523544754832983,
0.0065788221545517445,
-0.014607888646423817,
-0.006098930723965168,
-0.03743043541908264,
-0.0011474251514300704,
0.00398058770224452,
-0.027819430455565453,
-0.010117979720234871,
-0.060272108763456345,
0.008429201319813728,
-0.09752782434225082,
-0.004260365851223469,
-0.015305149368941784,
0.005377450026571751,
0.0014387486735358834,
0.050308842211961746,
0.02456234022974968,
0.0013664377620443702,
0.0001831802073866129,
0.028854839503765106,
0.05235818028450012,
-0.02063492313027382,
0.004362376872450113,
-0.024222860112786293,
0.010050884447991848,
0.0020141187123954296,
0.029903551563620567,
0.041402362287044525,
-0.02150135114789009,
0.01326235756278038,
-0.05544989928603172,
0.010280594229698181,
-0.01805252395570278,
-0.05486923083662987,
-0.014245357364416122,
0.020138636231422424,
0.022899670526385307,
0.032083332538604736,
0.028397949412465096,
0.03193832188844681,
-0.05557582899928093,
0.005158428568392992,
-0.08565249294042587,
0.052580878138542175,
-0.0124492347240448,
0.00029900274239480495,
0.047165192663669586,
0.040086135268211365,
0.048043154180049896,
0.026851007714867592,
0.11735942214727402,
0.004507238510996103,
0.04888336732983589,
0.06249440088868141,
0.005615437403321266,
-0.0006109243258833885,
0.04247020557522774,
0.051341794431209564,
-0.019074324518442154,
0.01286752987653017,
0.005670393817126751,
0.0008751137065701187,
-0.08559811860322952,
-0.009713629260659218,
0.0522911511361599,
0.03982021287083626,
0.07055678963661194,
-0.008122100494801998,
0.029590735211968422,
-0.03663947433233261,
-0.02277577854692936,
0.002534381579607725,
-0.053763922303915024,
-0.0372982993721962,
-0.03977924585342407,
-0.08575909584760666,
0.011366511695086956,
-0.007019237615168095,
-0.03507658466696739,
-0.02264910563826561,
0.0073572066612541676,
0.020649904385209084,
0.0007567155989818275,
-0.07597650587558746,
-0.022005202248692513,
-0.004782851319760084,
-0.01641462929546833,
-0.06389479339122772,
0.03607853502035141,
-0.05981605872511864,
0.0032497444190084934,
-0.010385038331151009,
0.020369580015540123,
0.019460497424006462,
-0.10018769651651382,
-0.05923043563961983,
0.02626946195960045,
0.0147135304287076,
0.048485126346349716,
0.0092790387570858,
-0.031707119196653366,
-0.0248959232121706,
0.036187849938869476,
0.03289301320910454,
0.009703715331852436,
-0.003411986166611314,
0.0596616268157959,
-0.026559950783848763,
0.011948291212320328,
-0.020622946321964264,
-0.013990460895001888,
-0.00480649946257472,
-0.014332654885947704,
0.015161685645580292,
-0.033393263816833496,
0.0784868448972702,
0.050912532955408096,
0.024986697360873222,
0.0021391266491264105,
-0.014297994785010815,
-0.038774777203798294,
0.03209145739674568,
0.005798568017780781,
0.013497939333319664,
0.004070608876645565,
-0.006351038347929716,
0.02806825377047062,
0.014424742199480534,
-0.04476988688111305,
-0.02780136466026306,
-0.009435834363102913,
0.007859311997890472,
-0.006890410557389259,
0.03588363528251648,
-0.014776366762816906,
-0.006206600461155176,
-0.007186987902969122,
0.08334321528673172,
0.028722021728754044,
0.0789109393954277,
-0.02279629372060299,
0.031917233020067215,
0.03606116399168968,
-0.01635126583278179,
-0.018255196511745453,
0.05950816720724106,
-0.03789518401026726,
0.028942406177520752,
0.04117623344063759,
0.061721790581941605,
-0.005676430184394121,
-0.00785429310053587,
0.0016520572826266289,
0.02814977616071701,
-0.05235991254448891,
-0.0435587614774704,
-0.04384828358888626,
-0.016682934015989304,
0.049942463636398315,
0.012694661505520344,
-0.04460825026035309,
-0.008482322096824646,
-0.03692878037691116,
-0.03172166272997856,
0.028670746833086014,
0.03205707669258118,
-0.056292884051799774,
-0.03291238844394684,
0.005632700398564339,
0.023462701588869095,
-0.03427474573254585,
-0.04706971347332001,
-0.06458491086959839,
0.0337865985929966,
0.03369572013616562,
-0.02018098719418049,
-0.024855181574821472,
-0.04594356566667557,
0.0023454243782907724,
-0.07069315016269684,
0.053024183958768845,
-0.014781475998461246,
-0.012519891373813152,
-0.04147617146372795,
-0.040767837315797806,
0.015213350765407085,
0.025248665362596512,
0.06540479511022568,
-0.04335523024201393,
-0.0006593875586986542,
-0.02399579808115959,
-0.01663448102772236,
0.015247044153511524,
-0.019314657896757126,
-0.022522231563925743,
0.01822713203728199,
-0.008841193281114101,
0.015749583020806313,
-0.04832596704363823,
0.02467023767530918,
0.016231030225753784,
0.044802721589803696,
-0.012833886779844761,
0.04988228529691696,
-0.018792161718010902,
0.009211596101522446,
-0.05727188289165497,
-0.004681825637817383,
0.055864106863737106,
-0.008775100111961365,
-0.050992947071790695,
-0.01228083111345768,
-0.027756202965974808,
-0.04194539040327072,
0.028906645253300667,
-0.02733745239675045,
0.016919102519750595,
-0.00892295129597187,
0.03518139198422432,
0.045461419969797134,
0.025144308805465698,
0.027933306992053986,
-0.00393748888745904,
-0.0013068618718534708,
-0.03322562575340271,
0.02256416343152523,
0.028192680329084396,
0.04002522677183151,
0.02607782743871212,
0.06138794124126434,
0.04458717629313469,
-0.040030330419540405,
-0.012885093688964844,
0.04836424067616463,
0.040633801370859146,
0.046683527529239655,
-0.03884055092930794,
-0.02693379484117031,
-0.016813037917017937,
0.01919022761285305,
-0.11177077889442444,
0.01607312634587288,
0.05618037283420563,
0.020371275022625923,
0.027070293202996254,
0.0414859801530838,
-0.0012146923691034317,
0.07771342992782593,
0.060508452355861664,
-0.06435194611549377,
-0.04967117682099342,
-0.02841096557676792,
0.02525469847023487,
-0.043418530374765396,
0.014806690625846386,
0.02439097687602043,
-0.056222882121801376,
-0.02859380654990673,
-0.060240525752305984,
0.06179778277873993,
-0.04151451960206032,
-0.027430633082985878,
0.0049058375880122185,
0.007742700167000294,
-0.07546934485435486,
0.031476836651563644,
-0.04558210447430611,
0.020889993757009506,
0.0012248510029166937,
0.050556398928165436,
0.023931430652737617,
-0.04682791978120804,
0.03317249193787575,
0.021975407376885414,
-0.018256351351737976,
-0.0103727076202631,
-0.057579509913921356,
-0.03119579143822193,
0.04001343250274658,
-0.022096337750554085,
0.01200066227465868,
0.010218673385679722,
0.04863826557993889,
0.0029588881880044937,
-0.03896859288215637,
-0.0025349678471684456,
0.05605026334524155,
-0.019003167748451233,
0.013181345537304878,
-0.0010033621219918132,
0.01782449521124363,
-0.06369595974683762,
0.0851682722568512,
0.003914239816367626,
-0.0022674030624330044,
0.013032619841396809,
0.020346378907561302,
0.04650746285915375,
0.05244810879230499,
-0.03760548308491707,
-0.012545133009552956,
-0.04809216782450676,
0.0012927140342071652,
-0.03104456141591072,
0.033542416989803314,
0.016588449478149414,
-0.08394377678632736,
0.010432390496134758,
-0.027665460482239723,
0.05279038846492767,
-0.001638196175917983,
-0.013057676143944263,
0.005403644870966673,
0.004740990698337555,
0.01769266091287136,
-0.013664573431015015,
-0.03249243646860123,
-0.13243432343006134,
-0.07516394555568695,
-0.0616220124065876,
0.040473002940416336,
-0.009630159474909306,
-0.00997559167444706,
0.0321292020380497,
0.052839163690805435,
0.002351221162825823,
-0.049724627286195755,
0.00779676204547286,
-0.02198873646557331,
0.027695709839463234,
-0.058034397661685944,
-0.004601047839969397,
-0.027184797450900078,
-0.012514160014688969,
0.042911943048238754,
-0.0329657606780529,
-0.005583321675658226,
-0.010327712632715702,
-0.004724821541458368,
0.005571587011218071,
0.03638416901230812,
-0.026956522837281227,
-0.03804972022771835,
0.03584473207592964,
-0.024276500567793846,
-0.04380561411380768,
-0.005787381902337074,
0.027364950627088547,
-0.038311395794153214,
-0.038342565298080444,
0.023470312356948853,
0.04384177550673485,
-0.010276120156049728,
0.009003235958516598,
-0.026474619284272194,
-0.018204960972070694,
0.02294108271598816,
0.01353582926094532,
-0.03642905503511429,
0.013950140215456486,
-0.031585052609443665,
0.01999083161354065,
0.022940196096897125,
0.026009786874055862,
-0.004197967704385519,
0.03721196949481964,
-0.08800005912780762,
-0.010938437655568123,
-0.0008485469734296203,
0.009993717074394226,
-0.002517306711524725,
0.01962997205555439,
0.003480961313471198,
-0.002963087521493435,
-0.000709228275809437,
0.02930315211415291,
0.01818288117647171,
-0.0031351852230727673,
-0.035134125500917435,
-0.0745992362499237,
-0.043089792132377625,
-0.0332956425845623,
-0.01556921936571598,
-0.029994230717420578,
0.007769908756017685,
-0.0397246852517128,
-0.050540804862976074,
0.03140490874648094,
-0.021822096779942513,
-0.025493038818240166,
0.019601251929998398,
-0.010994594544172287,
0.0019079431658610702,
-0.026168547570705414,
0.022254299372434616,
0.0036373580805957317,
0.030951613560318947,
-0.04338200390338898,
-0.021158238872885704,
-0.013358100317418575,
-0.0004607410228345543,
0.04085300490260124,
0.08454832434654236,
0.02038220688700676,
0.03840826079249382,
0.031947970390319824,
0.03692864999175072,
-0.011272045783698559,
0.05240876227617264,
-0.025782093405723572,
0.00239924737252295,
-0.026981540024280548,
0.10413840413093567,
-0.014773368835449219,
-0.049775611609220505,
0.016585584729909897,
0.011168831959366798,
-0.013259846717119217,
0.03292687609791756,
0.03257131204009056,
0.06072615087032318,
-0.03288884833455086,
0.007041767239570618,
0.041032902896404266,
0.0015421441057696939,
-0.0035385137889534235,
0.04778952896595001,
-0.07091144472360611,
-0.008921131491661072,
0.022108016535639763,
-0.014010805636644363,
0.0017450964078307152,
0.024560099467635155,
-0.0016997522907331586,
-0.039203956723213196,
0.09510434418916702,
-0.01998504437506199,
-0.060678623616695404,
0.06296592205762863,
0.016512390226125717,
-0.01997118443250656,
0.01671574078500271,
-0.031278643757104874,
0.04016244783997536,
0.04465963691473007,
-0.03305790200829506,
-0.007881134748458862,
-0.014584878459572792,
0.014005690813064575,
-0.0355638787150383,
-0.04916230961680412,
-0.022617483511567116,
-0.013838306069374084,
-0.013968020677566528,
-0.016338419169187546,
0.019367629662156105,
-0.005383700132369995,
-0.003438960760831833,
0.048372916877269745,
-0.007163637783378363,
0.05503788962960243,
0.025208530947566032,
0.020105957984924316,
-0.021245311945676804,
-0.01144526805728674,
0.015914330258965492,
-0.007811238989233971,
0.0486324317753315,
-0.0010891940910369158,
0.018048087134957314,
-0.07045961916446686,
0.010856112465262413,
-0.020235316827893257,
0.05626474320888519,
0.021023795008659363,
-0.01575440913438797,
-0.03272493928670883,
0.01969381608068943,
-0.006359525490552187,
-0.08982373774051666,
0.039314597845077515,
-0.04406513273715973,
-0.013415290042757988,
0.03703147545456886,
0.06386152654886246,
0.029305268079042435,
0.006048031151294708,
0.009556867182254791,
-0.01582738198339939,
0.014981409534811974,
0.04646509885787964,
-0.06247427687048912,
0.030318686738610268,
-0.04473855346441269,
-0.010445177555084229,
-0.043253447860479355,
-0.025397926568984985,
0.0033274278976023197,
-0.04365835711359978,
0.006608326453715563,
-0.008645949885249138,
0.012938139028847218,
-0.005670259706676006,
-0.0346812903881073,
0.025453437119722366,
-0.010369990952312946,
-0.00458716182038188,
0.010803765617311,
-0.031253471970558167,
0.001139834406785667,
0.026143919676542282,
0.0262801181524992,
0.04969291016459465,
0.04892561212182045,
0.006285456474870443,
-0.00040599500061944127,
0.0019722809083759785,
0.019897207617759705,
0.0008044829010032117,
-0.006016891449689865,
-0.013904518447816372,
0.0009656592737883329,
-0.03086884506046772,
-0.015940170735120773,
0.031137172132730484,
-0.00528422137722373,
-0.0376204252243042,
0.009709364734590054,
-0.11134308576583862,
0.009177368134260178,
-0.00827090721577406,
0.006371090188622475,
-0.020115582272410393,
0.008017740212380886,
-0.05956456437706947,
0.03857151046395302,
-0.01394408568739891,
-0.012636448256671429,
0.06281126290559769,
0.03467236086726189,
-0.0086978105828166,
0.06622684001922607,
-0.011556705459952354,
0.008881134912371635,
-0.0039671603590250015,
-0.048593346029520035,
0.05856112763285637,
-0.00942170899361372,
0.007522154599428177,
-0.03971303254365921,
0.03626740351319313,
-0.011965351179242134,
0.04698225110769272,
-0.04681511968374252,
0.005027113948017359,
-0.026039592921733856,
-0.034971933811903,
0.005810945760458708,
-0.02628903090953827,
0.02954121306538582,
-0.0025727427564561367,
0.031186645850539207,
0.017532071098685265,
0.0386238731443882,
0.0012329191667959094,
-0.020952142775058746,
-0.06334839761257172,
-0.06233053281903267,
0.05168002098798752,
0.003949742764234543,
0.0035683144815266132,
0.04434232786297798,
0.05884302034974098,
-0.023940924555063248,
-0.015115298330783844,
0.04361462593078613,
0.03954794630408287,
-0.03894567862153053,
-0.062444720417261124,
0.07676992565393448,
0.02883019857108593,
-0.07965860515832901,
-0.027600163593888283,
0.02498590387403965,
-0.001300301169976592,
0.02020873688161373,
0.03486037626862526,
0.05365291237831116,
0.03608997166156769,
0.02238498255610466,
-0.054773543030023575,
0.03064003773033619,
0.019069397822022438,
-0.028097962960600853,
-0.00736838486045599,
0.0034210504963994026,
0.03913988545536995,
-0.09037337452173233,
0.027718527242541313,
0.02667301520705223,
0.02077987790107727,
-0.02235795371234417,
-0.028036728501319885,
-0.004420985002070665,
0.024786457419395447,
-0.052750375121831894,
0.0010961933294311166,
0.019944917410612106,
0.08355677872896194,
-0.004407385364174843,
0.04335403814911842,
0.03556496277451515,
0.02301868237555027,
-0.04273514077067375,
-0.004896880127489567,
0.05232861638069153,
-0.015897488221526146,
0.07243330031633377,
0.01982874609529972,
-0.0014149632770568132,
-0.0106124896556139,
-0.01742822490632534,
0.055519092828035355,
-0.01244607474654913,
0.02158149890601635,
-0.011154541745781898,
0.021784083917737007,
-0.02800927311182022,
0.05604526028037071,
-0.009583478793501854,
0.016604365780949593,
0.00945139117538929,
-0.07608608156442642,
0.005295888055115938,
-0.053487349301576614,
0.012484034523367882,
0.03116864711046219,
-0.09480426460504532,
0.03126152604818344,
-0.08303748071193695,
0.03556343913078308,
0.034204453229904175,
0.029930921271443367,
0.018698014318943024,
0.03172186017036438,
0.016220320016145706,
-0.024142395704984665,
-0.02810283936560154,
-0.011785641312599182,
-0.0038520346861332655,
-0.010104505345225334,
-0.06485100835561752,
-0.007167569361627102,
0.00021640352497342974,
-0.05733413249254227,
-0.021424811333417892,
0.01853400282561779,
-0.018521064892411232,
-0.003932091407477856,
0.025096427649259567,
-0.010446022264659405,
0.021225880831480026,
-0.010653690434992313,
0.020873527973890305,
-0.013845960609614849,
0.004409783985465765,
-0.02791687101125717,
-0.029652250930666924,
-0.008367698639631271,
-0.016253039240837097,
-0.0039657349698245525,
-0.025235258042812347,
0.020474420860409737,
-0.0074247135780751705,
0.0204840749502182,
-0.016666043549776077,
-0.016612809151411057,
0.048345305025577545,
-0.007784693036228418,
0.01043709646910429,
-0.04057735577225685,
-0.05205637589097023,
0.07646297663450241,
0.003915696404874325,
0.030686061829328537,
-0.029944773763418198,
-0.02374115213751793,
0.02625751495361328,
-0.02733895741403103,
0.009908217005431652,
-0.08097768574953079,
0.003336407244205475,
-0.02499416470527649,
0.0009297310607507825,
-0.030280044302344322,
0.002881178865209222,
-0.02356054075062275,
0.04501011222600937
] |
<p>I really like to do research in physics and like to calculate to see what happen. However, I really find it hard to write a paper, to explain the results I obtained and to put them in order. One of the reasons is the lack of my vocabulary. </p>
<p>How do I write physics well? I think that writing physics is more dependent of an author's taste than writing mathematics is. Are there any good reference I can consult when writing? Or could you give me advice and tips on writing a paper? What do you take into account when you start writing a paper? What are your strategies on the process such as structuring the paper, writing a draft, polishing it, etc?</p>
<p>In addition, it is helpful to give me examples of great writing with the reason why you think it is good. Do you have specific recommendations?</p> | g9215 | [
0.029410459101200104,
0.06324445456266403,
0.03160329535603523,
0.0029485062696039677,
0.056879039853811264,
-0.040733855217695236,
-0.009791141375899315,
0.06288637220859528,
-0.013397174887359142,
0.003875213908031583,
0.0552794374525547,
-0.05120948329567909,
0.016994457691907883,
-0.006478558760136366,
-0.018601231276988983,
-0.015100548043847084,
0.040002837777137756,
0.018101535737514496,
0.01279241219162941,
0.033770833164453506,
0.04653390124440193,
0.0384155809879303,
0.02292777970433235,
-0.02534877322614193,
-0.08051951229572296,
-0.008266718126833439,
-0.0360390804708004,
-0.0530802421271801,
0.04010692611336708,
-0.04158579558134079,
0.05631642043590546,
-0.006641903892159462,
-0.05204872414469719,
0.0046982853673398495,
-0.012676930986344814,
-0.034481506794691086,
-0.03106238879263401,
0.02482578530907631,
-0.02064257487654686,
-0.01991715282201767,
0.047558728605508804,
-0.027866551652550697,
-0.008703186176717281,
-0.055310994386672974,
0.025477483868598938,
0.004406287334859371,
-0.030847610905766487,
-0.023703623563051224,
-0.05815727636218071,
0.04570048674941063,
-0.0114608034491539,
0.0764806717634201,
0.028051771223545074,
0.017808273434638977,
0.06132771819829941,
0.02691067010164261,
-0.000024010194465517998,
-0.005240613594651222,
0.06059054285287857,
-0.04931254684925079,
0.03893173858523369,
0.04516260325908661,
-0.05679283291101456,
-0.025330182164907455,
0.04073207825422287,
0.0026424829848110676,
-0.05048837140202522,
-0.017180003225803375,
-0.02123439870774746,
0.02837591990828514,
0.02572682499885559,
-0.02666275016963482,
0.019333546981215477,
-0.033668164163827896,
-0.0011512077180668712,
0.0135958855971694,
0.01614212431013584,
0.018485624343156815,
0.039470523595809937,
0.0512964203953743,
-0.015858199447393417,
0.023093266412615776,
0.05694571137428284,
-0.020540954545140266,
0.05014437809586525,
-0.014201403595507145,
-0.03706200048327446,
-0.06346062570810318,
0.020917925983667374,
-0.004843331407755613,
-0.0005404697731137276,
0.005606391001492739,
0.05366750434041023,
-0.021963000297546387,
-0.005943584721535444,
-0.02820846438407898,
-0.013244437985122204,
0.024701694026589394,
-0.0022001361940056086,
0.043306078761816025,
-0.05630117282271385,
0.007940787822008133,
0.002848090138286352,
-0.021038411185145378,
0.02583598531782627,
0.014673369005322456,
-0.0007947988342493773,
0.024400675669312477,
-0.024195170029997826,
0.012876424938440323,
-0.05883804336190224,
-0.0006790925981476903,
-0.0012123736087232828,
-0.05104288086295128,
-0.06443949043750763,
0.007460195571184158,
0.055333513766527176,
0.00863789301365614,
0.07261577993631363,
0.07909233123064041,
-0.006409600377082825,
0.04774143546819687,
-0.019456660374999046,
-0.04764001443982124,
-0.023383982479572296,
-0.029225217178463936,
0.025877155363559723,
-0.023320017382502556,
0.0031603157985955477,
0.027753105387091637,
0.026583759114146233,
-0.0665619894862175,
-0.045374795794487,
-0.0022232048213481903,
-0.020854854956269264,
0.12390799820423126,
0.01917840912938118,
0.04268726333975792,
0.014260128140449524,
-0.037711359560489655,
0.03984604403376579,
0.047144815325737,
0.022250119596719742,
-0.06334946304559708,
-0.037354785948991776,
0.05433841794729233,
-0.039249222725629807,
-0.04503205418586731,
0.020765917375683784,
-0.02752639539539814,
0.03780977427959442,
0.007426080759614706,
-0.04889136925339699,
-0.010491152293980122,
0.02437528595328331,
0.045847099274396896,
0.013945309445261955,
0.009276182390749454,
0.03106909617781639,
-0.008124997839331627,
0.0846257209777832,
0.011315545998513699,
-0.04444143921136856,
0.00183208251837641,
-0.013909120112657547,
-0.0024848838802427053,
0.0009243485983461142,
-0.029234595596790314,
-0.038873057812452316,
0.0228103157132864,
-0.029031546786427498,
-0.016282686963677406,
0.014469052664935589,
0.03722379356622696,
0.015177072025835514,
0.009455172345042229,
0.04027021303772926,
0.01770048774778843,
-0.016482021659612656,
-0.007314248010516167,
-0.0015553978737443686,
-0.03705085813999176,
0.0006482132012024522,
-0.022922318428754807,
-0.016337353736162186,
-0.011880260892212391,
0.04459807276725769,
0.07149526476860046,
-0.016989680007100105,
-0.013088307343423367,
0.01046724896878004,
0.0070071094669401646,
0.015607709996402264,
0.02664537914097309,
0.01567889004945755,
0.013028744608163834,
-0.020364511758089066,
-0.02173462137579918,
-0.03904997184872627,
0.047381944954395294,
-0.015406315214931965,
0.019980652257800102,
0.034778106957674026,
0.030969364568591118,
0.01880519650876522,
0.04917779937386513,
-0.02683561109006405,
-0.004984999541193247,
0.010100309737026691,
-0.0034427852369844913,
-0.0014424956170842052,
0.02790086716413498,
0.049872465431690216,
0.013537028804421425,
-0.015033923089504242,
0.01372179388999939,
-0.02738999016582966,
-0.07729234546422958,
-0.03376917541027069,
0.016944505274295807,
0.011966721154749393,
-0.06246938183903694,
0.008207658305764198,
0.06105417013168335,
-0.03271932899951935,
0.004666871391236782,
-0.07225867360830307,
-0.003307681530714035,
0.004711017943918705,
-0.07406920939683914,
-0.03143606334924698,
0.03165241330862045,
-0.03288428485393524,
-0.07747183740139008,
0.03323054313659668,
-0.01298928540199995,
0.016162270680069923,
-0.021549828350543976,
0.03952857106924057,
0.021794287487864494,
-0.048857130110263824,
-0.011430476792156696,
0.007048589643090963,
-0.024537401273846626,
-0.040878038853406906,
-0.04111388325691223,
0.029299091547727585,
0.008212395943701267,
-0.05182894691824913,
0.0021687878761440516,
0.06345529109239578,
-0.04080209508538246,
-0.005364925134927034,
-0.04002739116549492,
-0.014799880795180798,
-0.02605968713760376,
0.0023489498998969793,
0.029454918578267097,
0.0002561160072218627,
-0.012849012389779091,
0.03572556748986244,
-0.036924686282873154,
0.00567534239962697,
-0.018043378368020058,
-0.07198787480592728,
0.03032829985022545,
-0.09166596084833145,
-0.0054271942935884,
0.03337448090314865,
-0.012071196921169758,
0.013943590223789215,
-0.030577370896935463,
0.008911105804145336,
-0.040939897298812866,
0.009182971902191639,
-0.014115991070866585,
-0.010960126295685768,
-0.028820142149925232,
0.059441085904836655,
-0.051270999014377594,
0.03887917473912239,
-0.04293714463710785,
-0.02702959068119526,
0.01638614945113659,
0.031772635877132416,
-0.03929778188467026,
-0.017127802595496178,
-0.0031365712638944387,
-0.013244478963315487,
-0.03986387699842453,
0.005100342910736799,
-0.0019913758151233196,
0.01606525294482708,
-0.05036497861146927,
-0.0329241082072258,
0.11002709716558456,
0.0012374117504805326,
-0.05575865879654884,
-0.031623948365449905,
-0.004012721125036478,
-0.007848351262509823,
0.06340786814689636,
0.0343460813164711,
0.03984295204281807,
-0.005080833565443754,
0.042225468903779984,
0.012669309973716736,
0.05332128331065178,
-0.011353999376296997,
-0.03507590293884277,
0.040783174335956573,
0.042532894760370255,
0.03797927126288414,
-0.02698461338877678,
-0.0200782660394907,
0.038960814476013184,
0.03292366489768028,
0.014492571353912354,
0.04070402309298515,
-0.04688337817788124,
-0.024896109476685524,
-0.0011531226336956024,
0.12308180332183838,
-0.01831209287047386,
-0.008649674244225025,
0.016561804339289665,
0.004904395900666714,
-0.014726391062140465,
0.006631803698837757,
0.0046066781505942345,
-0.04819779470562935,
-0.008948775008320808,
-0.030895989388227463,
-0.05148296803236008,
-0.06470073759555817,
-0.028762562200427055,
0.05974772572517395,
-0.09386419504880905,
-0.0026496334467083216,
-0.031031686812639236,
0.016169851645827293,
-0.015544215217232704,
-0.030486254021525383,
-0.014418714679777622,
-0.011005519889295101,
-0.017371222376823425,
-0.020423203706741333,
0.05868453159928322,
0.011661558412015438,
-0.06118156388401985,
0.0451514795422554,
-0.014858146198093891,
0.042053304612636566,
-0.029848642647266388,
-0.008502479642629623,
-0.012662149034440517,
0.034281954169273376,
0.02966351807117462,
-0.05983548238873482,
0.02991410717368126,
-0.08021099865436554,
0.010557425208389759,
0.01108642853796482,
0.02395866997539997,
-0.04909958690404892,
0.03135759383440018,
-0.006492183078080416,
-0.01363949105143547,
-0.05669650807976723,
0.012448391877114773,
-0.013988465070724487,
0.025322958827018738,
0.034205250442028046,
-0.0003005470207426697,
-0.04019930213689804,
-0.04456980153918266,
-0.008601534180343151,
0.02386428788304329,
-0.06295634806156158,
-0.024355163797736168,
-0.0006729465676471591,
0.026663746684789658,
-0.016538282856345177,
-0.033952612429857254,
0.0607401505112648,
-0.028370628133416176,
-0.029651906341314316,
0.00322592630982399,
0.04399595782160759,
0.004704720806330442,
0.03182196617126465,
-0.009741832502186298,
-0.03508807346224785,
0.023138821125030518,
0.025399474427103996,
-0.031432971358299255,
0.03524519503116608,
0.08163969218730927,
-0.04956650361418724,
0.0159158818423748,
-0.04031701385974884,
0.020586276426911354,
0.014879613183438778,
0.02236931584775448,
0.008224979043006897,
-0.014675963670015335,
0.03378039598464966,
0.030009068548679352,
-0.06373312324285507,
-0.009427519515156746,
-0.022261539474129677,
0.03034653700888157,
0.02453320287168026,
-0.011041366495192051,
-0.012466227635741234,
0.01946459524333477,
-0.05976702272891998,
-0.04482724145054817,
0.04905698075890541,
-0.02672060765326023,
0.00966841634362936,
0.06914540380239487,
0.008595499210059643,
-0.03721609339118004,
0.013984612189233303,
-0.024541163817048073,
-0.007999910973012447,
-0.02111046575009823,
0.0522153414785862,
0.08993988484144211,
0.08401639759540558,
0.03880450502038002,
-0.009844828397035599,
-0.018894728273153305,
-0.012891918420791626,
-0.005212584976106882,
0.021682774648070335,
0.05213502049446106,
0.01020502857863903,
0.010402394458651543,
0.01673591509461403,
-0.004097950644791126,
-0.04235123097896576,
0.016227323561906815,
-0.042396869510412216,
0.030608663335442543,
-0.06890874356031418,
0.029835687950253487,
-0.02411210536956787,
-0.005880167707800865,
-0.02658967673778534,
-0.015428329817950726,
0.021244941279292107,
-0.0302549060434103,
-0.03418530896306038,
0.04736074060201645,
-0.0008925265865400434,
-0.023641634732484818,
0.03340211138129234,
-0.005529752001166344,
0.026208791881799698,
-0.005432466510683298,
-0.02988446317613125,
-0.014417865313589573,
-0.02873275987803936,
0.03735550493001938,
-0.020657533779740334,
-0.038996901363134384,
-0.03216389939188957,
-0.06061768904328346,
-0.056345805525779724,
0.0072666797786951065,
0.010650385171175003,
-0.016580691561102867,
0.04294325411319733,
0.05553092062473297,
0.004548891447484493,
-0.025114087387919426,
-0.0714607760310173,
0.04718846082687378,
0.042856037616729736,
0.02380644902586937,
0.011281606741249561,
-0.040797341614961624,
0.0247573833912611,
-0.0020788186229765415,
-0.02056456357240677,
0.0020968171302229166,
0.005892470479011536,
-0.06718842685222626,
-0.007692090701311827,
0.049088820815086365,
0.023525938391685486,
-0.026602033525705338,
-0.0930785983800888,
0.007618636824190617,
0.07780304551124573,
0.03764043003320694,
0.014791677705943584,
-0.0015429580816999078,
-0.027013393118977547,
0.005508841946721077,
-0.008715558797121048,
-0.0009549297392368317,
-0.01355294231325388,
-0.00884732324630022,
-0.024187032133340836,
-0.015441130846738815,
0.002692044945433736,
-0.01273425668478012,
0.05579675734043121,
0.02165558747947216,
-0.014249306172132492,
0.017153654247522354,
0.012251789681613445,
0.03377367928624153,
0.01669086143374443,
0.030607029795646667,
-0.028170885518193245,
0.04109053313732147,
0.002231375314295292,
-0.06902515143156052,
0.013473774306476116,
-0.0024787019938230515,
0.045059241354465485,
-0.028983060270547867,
-0.12897594273090363,
-0.041902318596839905,
0.018451057374477386,
-0.015422038733959198,
-0.02326478436589241,
-0.01717560924589634,
0.020628545433282852,
0.01426548883318901,
-0.0336650013923645,
-0.025595063343644142,
-0.016076862812042236,
-0.04741401970386505,
0.004558981396257877,
-0.001605816651135683,
-0.05987099930644035,
0.028988245874643326,
-0.016504976898431778,
0.05141356214880943,
0.04317968338727951,
-0.005960431415587664,
0.07524948567152023,
0.05811844766139984,
0.09517975151538849,
-0.035630322992801666,
-0.03124922327697277,
-0.01519065536558628,
-0.02450844645500183,
-0.020136559382081032,
0.02626829594373703,
0.011379603296518326,
0.02257731929421425,
-0.034021176397800446,
0.04979431629180908,
0.026952721178531647,
-0.07632067799568176,
-0.04836823791265488,
-0.04441532865166664,
-0.01857680082321167,
-0.030562425032258034,
0.002045372035354376,
-0.02483532764017582,
-0.060319915413856506,
-0.007912496104836464,
0.003756343387067318,
-0.007837940007448196,
0.002976411022245884,
-0.053433142602443695,
-0.004595796577632427,
-0.040482860058546066,
0.05447957664728165,
0.028645729646086693,
-0.019473491236567497,
-0.017389224842190742,
-0.020899856463074684,
0.020594066008925438,
0.07562302052974701,
0.050252798944711685,
-0.05867946147918701,
-0.04090852662920952,
0.004896790254861116,
0.0019436731236055493,
0.04183938354253769,
-0.053902458399534225,
-0.04230548068881035,
-0.048558082431554794,
0.004092404153198004,
-0.007210058625787497,
-0.024296240881085396,
0.00008831606101011857,
0.03261301666498184,
0.0689004436135292,
0.0009108245139941573,
-0.05378640815615654,
-0.0072039044462144375,
-0.021157415583729744,
-0.036947958171367645,
-0.019639194011688232,
-0.01591295562684536,
0.024173583835363388,
0.026511169970035553,
0.016020026057958603,
0.020679274573922157,
-0.01377737894654274,
-0.004623718559741974,
-0.06291285902261734,
0.043066587299108505,
0.020838676020503044,
0.025111161172389984,
-0.014476954005658627,
-0.018812110647559166,
0.03594216704368591,
0.03663179650902748,
0.054140105843544006,
-0.10310950875282288,
0.06357499957084656,
0.003170704934746027,
0.020981470122933388,
-0.05563824251294136,
0.028413569554686546,
0.019818797707557678,
-0.03921688720583916,
0.03321768343448639,
0.059391673654317856,
-0.06003166735172272,
0.01340538915246725,
-0.008201844990253448,
-0.021541794762015343,
0.08569023013114929,
0.019985400140285492,
0.010181848891079426,
0.0014602403389289975,
-0.04011179879307747,
0.016505597159266472,
0.03264729306101799,
-0.020897116512060165,
0.05172131583094597,
0.0030652014538645744,
-0.02438250742852688,
-0.056336674839258194,
-0.03422200679779053,
-0.015090450644493103,
-0.018832769244909286,
-0.030894659459590912,
0.05315713211894035,
0.06661713868379593,
-0.05559808760881424,
-0.018139459192752838,
0.02057134546339512,
0.03492657467722893,
0.055398128926754,
-0.00034943781793117523,
0.0160435289144516,
0.013874534517526627,
0.02755773812532425,
-0.009336205199360847,
0.013735386542975903,
0.0023553103674203157,
0.0030766665004193783,
-0.014134776778519154,
0.056809525936841965,
0.021131057292222977,
0.05135667696595192,
0.0435965396463871,
0.030709700658917427,
-0.0105238426476717,
-0.020484186708927155,
-0.04398023709654808,
0.04842532426118851,
0.0071136136539280415,
-0.007890935987234116,
-0.03949221596121788,
-0.001042853808030486,
-0.002925821114331484,
-0.03785274922847748,
-0.015573900192975998,
0.039228055626153946,
-0.03289804235100746,
0.016912756487727165,
-0.009417437948286533,
0.02714437060058117,
-0.06744693964719772,
0.06864570826292038,
0.02740412764251232,
0.04312126338481903,
-0.026677317917346954,
-0.05355595052242279,
0.0008144194143824279,
-0.0808488056063652,
-0.0043391818180680275,
-0.029554113745689392,
0.0905422568321228,
0.009156033396720886,
0.005004365928471088,
0.02191988192498684,
0.013740663416683674,
-0.02216518670320511,
0.029003532603383064,
-0.03511509299278259,
-0.02274811826646328,
-0.007580047007650137,
-0.0497441366314888,
0.02170301415026188,
-0.035265274345874786,
0.02883674018085003,
0.038019198924303055,
-0.03512166067957878,
0.02310236543416977,
-0.0037452606484293938,
-0.0013246092712506652,
0.06863442808389664,
-0.038194961845874786,
-0.013898353092372417,
-0.02143053151667118,
0.002703147241845727,
-0.06379877030849457,
0.027822744101285934,
0.0373593345284462,
-0.03322074934840202,
0.009020932018756866,
0.017444543540477753,
0.012011677958071232,
0.012251072563230991,
-0.054064054042100906,
0.03199879080057144,
0.036860767751932144,
0.043949373066425323,
-0.04500550776720047,
0.053380269557237625,
-0.004193881060928106,
-0.018790584057569504,
0.05752475559711456,
-0.04554636403918266,
0.00764273339882493,
-0.028554322198033333,
0.02332473360002041,
0.011421929113566875,
-0.021381083875894547,
-0.017525754868984222,
-0.01418020948767662,
-0.0642944797873497,
-0.03116275556385517,
0.04000584036111832,
0.032034359872341156,
-0.05417358875274658,
-0.012858047150075436,
0.06486303359270096,
-0.008965786546468735,
0.07611126452684402,
0.002141163684427738,
-0.021763034164905548,
0.03487025946378708,
0.05187680944800377,
-0.00676396070048213,
-0.011401978321373463,
0.04175376519560814,
0.027217349037528038,
0.009737911634147167,
0.00391923263669014,
-0.0584389828145504,
-0.004065071232616901,
0.031272049993276596,
-0.0023347120732069016
] |
<p>(for a more muddled version, see physics.stackexchange: <a href="http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable">http://physics.stackexchange.com/questions/14020/whats-with-mandelstams-argument-that-only-linear-regge-trajectories-are-stable</a>)</p>
<p>There is a 1974 argument of Mandelstam's that linear Regge trajectories implies stability, from "Dual-Resonance Models" from 1974, sciencedirect.com/science/article/pii/0370157374900349. Expand the Regge trajectory function $\alpha(s)$ in a dispersion relation with two subtractions:</p>
<p>$$ \alpha(s) = b + as + {1\over i\pi} \int_0^\infty {\mathrm{Im}(\alpha(s'))\over s-s'} ds'$$</p>
<p>The imaginary part of $\alpha(s)$ gives the decay of the string states, since where it hits an integer tells you where the poles are. So if the string resonances are exactly stable, then the imaginary part is zero, and the trajectory is linear.</p>
<p>This argument bugged me for these reasons:</p>
<ul>
<li>It seems to work just as well with two subtractions, three subtractions, etc. Can you conclude that exactly quadratic or exactly cubic Regge trajectories are also stable? What is a quadratic or cubic trajectory?</li>
<li>The Regge trajectory function appears in the exponent, so you have to take a log to extract it. Why is it clear that it has a representation like the above, without a cut contribution at negative s? </li>
<li>In string theory, the trajectories are linear when they are long-lived, but the trajectory function doesn't look as fundamental today. Is there a more modern formulation of this, which would tell you which string limits are non-interacting just from a condition on the spectrum?</li>
</ul>
<p>Mandelstam generously emailed me a short remark, saying essentially that the trajectory function imaginary part is a lifetime, and indeed this is obvious from the fact that it gives the position of the resonances, but I am still confused regarding the questions above.</p>
<p>Even a partial answer would be appreciated.</p> | g9216 | [
0.0016245036385953426,
-0.018355442211031914,
0.000608834729064256,
-0.046725474298000336,
0.0800279825925827,
0.036511171609163284,
0.03002738207578659,
-0.007305702660232782,
-0.00911529827862978,
-0.05334536358714104,
-0.011605276726186275,
-0.041202276945114136,
0.042995285242795944,
-0.010873806662857533,
-0.0370497889816761,
-0.04984886944293976,
0.05199098214507103,
0.01955394260585308,
0.05163770541548729,
-0.01568557508289814,
0.0020573048386722803,
-0.0016138132195919752,
0.043422210961580276,
0.003958826884627342,
0.010434769093990326,
-0.04131202772259712,
0.032712433487176895,
-0.028285011649131775,
-0.057141248136758804,
0.024906020611524582,
0.09388842433691025,
-0.024645837023854256,
0.06806428730487823,
0.054547809064388275,
-0.017984766513109207,
-0.042051639407873154,
0.0417119525372982,
-0.022387845441699028,
0.01638934016227722,
0.015498688444495201,
0.04681122303009033,
-0.05943845957517624,
0.022902052849531174,
-0.006753268651664257,
-0.024329112842679024,
0.0003166854730807245,
-0.033364225178956985,
-0.059243764728307724,
0.006844482850283384,
-0.015833085402846336,
-0.006885341834276915,
0.012940158136188984,
0.04504474252462387,
0.06688619405031204,
-0.0007758099818602204,
0.015741677954792976,
-0.01285732351243496,
0.018012281507253647,
-0.015957027673721313,
-0.0007316206465475261,
-0.00471554696559906,
-0.0205602515488863,
-0.005940887611359358,
0.02647658996284008,
-0.011693199165165424,
-0.040188588201999664,
-0.06923659890890121,
-0.03623069077730179,
0.015086101368069649,
-0.029349181801080704,
0.04742719978094101,
-0.07194000482559204,
-0.03628167137503624,
-0.037085555493831635,
-0.0012627857504412532,
0.01152329333126545,
0.03991641849279404,
-0.03507200628519058,
0.0040311263874173164,
0.027733737602829933,
-0.08075563609600067,
0.013171961531043053,
-0.0037776699755340815,
-0.05732615664601326,
0.03484887257218361,
0.015736103057861328,
0.05820964276790619,
0.01940273493528366,
-0.03992458060383797,
0.020144084468483925,
-0.043826326727867126,
0.020805170759558678,
0.03932029381394386,
-0.026021385565400124,
-0.0760631114244461,
0.015795517712831497,
-0.02135053649544716,
0.057091645896434784,
0.01951310597360134,
-0.0027139591984450817,
0.015501509420573711,
0.038976240903139114,
-0.009927211329340935,
0.03281744569540024,
0.002431977540254593,
0.005739125423133373,
0.0449584536254406,
-0.02343010902404785,
0.018649766221642494,
-0.05009172111749649,
-0.004599375184625387,
0.029729081317782402,
-0.04792173579335213,
-0.03216266632080078,
0.045020218938589096,
0.05109008401632309,
0.019541693851351738,
-0.05702969431877136,
0.03835813328623772,
0.058223895728588104,
0.08930416405200958,
0.029908958822488785,
0.0379980094730854,
0.016550730913877487,
-0.005594475194811821,
0.005985953379422426,
-0.008090800605714321,
0.05272139981389046,
0.055865783244371414,
-0.016384918242692947,
-0.035460229963064194,
0.024367252364754677,
0.006402747705578804,
0.016115957871079445,
-0.07217272371053696,
-0.009369523264467716,
-0.015663988888263702,
0.04299453645944595,
-0.02234152890741825,
0.03987322002649307,
0.014798798598349094,
-0.06620312482118607,
0.001602853648364544,
-0.012090783566236496,
0.021862929686903954,
0.03543354570865631,
-0.00001141288703365717,
-0.020256856456398964,
0.004274808336049318,
0.014497136697173119,
0.032095253467559814,
0.04247863218188286,
0.005518228746950626,
-0.016230884939432144,
-0.033573880791664124,
0.009430794045329094,
0.019841620698571205,
-0.04251665994524956,
-0.058228395879268646,
-0.0032201732974499464,
0.02397223189473152,
-0.06940686702728271,
-0.02180083654820919,
-0.003641348099336028,
-0.026791494339704514,
0.032027628272771835,
-0.006994782481342554,
-0.064728744328022,
-0.024441253393888474,
0.007268744520843029,
-0.01723705604672432,
-0.01277895737439394,
0.036482106894254684,
0.07920966297388077,
0.029869064688682556,
0.007005772087723017,
0.005613909102976322,
-0.031021321192383766,
0.026215635240077972,
0.005318555049598217,
-0.0011326257372274995,
0.010503287427127361,
-0.00842284131795168,
-0.057500049471855164,
0.023696700111031532,
0.007042943499982357,
0.014340467751026154,
0.010700393468141556,
-0.0477125458419323,
0.06356905400753021,
0.023142719641327858,
-0.014288508333265781,
0.00040091536357067525,
0.02062690444290638,
-0.008354066871106625,
-0.09480798989534378,
0.04439352825284004,
-0.0410507507622242,
-0.0065828911028802395,
0.03269274905323982,
0.05795478820800781,
0.0323743037879467,
-0.0121414540335536,
-0.07480331510305405,
0.01355037186294794,
-0.008895577862858772,
-0.005570129957050085,
0.021313581615686417,
-0.017730165272951126,
-0.0007747646886855364,
0.011288853362202644,
-0.022385168820619583,
0.034255944192409515,
-0.030404362827539444,
-0.008743242360651493,
-0.08600880950689316,
0.06806273013353348,
-0.0036704163067042828,
0.00823497399687767,
0.059755682945251465,
-0.0053560249507427216,
-0.016658727079629898,
-0.004691326525062323,
0.04879353567957878,
0.0041220118291676044,
-0.011132159270346165,
0.013046972453594208,
-0.00939794909209013,
-0.056974466890096664,
0.050364986062049866,
-0.052474573254585266,
-0.0408918671309948,
0.009207397699356079,
0.02733394131064415,
-0.0021167094819247723,
-0.013613956980407238,
0.03543616831302643,
-0.05043065920472145,
0.06410335004329681,
0.03865616023540497,
0.07530004531145096,
0.022655829787254333,
-0.0501570962369442,
0.07594475895166397,
0.07010496407747269,
-0.01628464087843895,
0.027238663285970688,
0.02153698168694973,
-0.007016064133495092,
-0.0033938316628336906,
0.04232955351471901,
0.028314124792814255,
0.003438927000388503,
-0.012474538758397102,
-0.025569681078195572,
-0.04417537897825241,
-0.024317676201462746,
0.06141756474971771,
-0.07012350857257843,
-0.01727111265063286,
0.023906584829092026,
0.055979955941438675,
-0.04224701225757599,
-0.01180629339069128,
-0.05685574188828468,
-0.041622910648584366,
-0.015319542959332466,
-0.005804105196148157,
-0.0705232247710228,
-0.03613196685910225,
-0.0645047202706337,
0.02327561378479004,
0.01934417523443699,
0.042953912168741226,
-0.0008458365919068456,
-0.0019273216603323817,
-0.016599206253886223,
0.021632758900523186,
0.01994832418859005,
-0.02149435132741928,
0.051876720041036606,
-0.013789812102913857,
-0.015908749774098396,
-0.006958717945963144,
-0.005098018329590559,
-0.03385152667760849,
0.06145583093166351,
0.07475201040506363,
0.02583257481455803,
0.009493200108408928,
-0.098557248711586,
-0.021502267569303513,
0.021407397463917732,
-0.02001854218542576,
-0.05411222577095032,
0.019553931429982185,
0.0022157991770654917,
-0.05865877494215965,
-0.003986699972301722,
-0.0192270427942276,
0.041726984083652496,
-0.04741348698735237,
-0.025146950036287308,
0.0276104174554348,
0.02274947613477707,
-0.013705318793654442,
-0.07316457480192184,
-0.051499947905540466,
-0.012624547816812992,
0.06390228122472763,
-0.010854247957468033,
0.04303942248225212,
0.00012844707816839218,
-0.014618994668126106,
0.03609703108668327,
0.020872289314866066,
-0.028110623359680176,
0.021067336201667786,
0.06543110311031342,
0.01751193031668663,
-0.009548570029437542,
-0.03263263404369354,
-0.03335949778556824,
0.014540301635861397,
0.014314386062324047,
-0.06271102279424667,
-0.07446693629026413,
0.0016881827032193542,
-0.03181210160255432,
0.009502721019089222,
0.0026698780711740255,
0.035384539514780045,
0.05206656828522682,
-0.04004901647567749,
0.006537649314850569,
-0.08057799190282822,
0.0046953014098107815,
0.014127255417406559,
0.03761976584792137,
0.024591943249106407,
0.026647960767149925,
-0.007001699414104223,
0.01982121728360653,
0.013830430805683136,
0.07330012321472168,
0.017035415396094322,
0.016694270074367523,
0.021332213655114174,
0.00813672598451376,
-0.03316236287355423,
-0.019334925338625908,
-0.05815847963094711,
-0.004054046701639891,
-0.0020689971279352903,
-0.012239287607371807,
0.03188082575798035,
0.013521597720682621,
0.05213325843214989,
0.01764584891498089,
-0.012473765760660172,
-0.07886248081922531,
-0.012062088586390018,
-0.04719855263829231,
-0.04500579461455345,
0.02776692435145378,
-0.007809110451489687,
0.0004402090853545815,
0.028804829344153404,
0.023596348240971565,
0.00873245857656002,
-0.035945646464824677,
0.03387396037578583,
-0.0209701806306839,
-0.036810968071222305,
0.014910915866494179,
-0.01389241311699152,
-0.03367163985967636,
-0.007157069630920887,
-0.03884641453623772,
0.07491198182106018,
0.06179528310894966,
-0.011637785471975803,
0.028467591851949692,
0.039608296006917953,
0.02407652884721756,
0.02711758390069008,
-0.029435807839035988,
0.031130461022257805,
-0.028955766931176186,
-0.02338900789618492,
0.005586184561252594,
-0.017944976687431335,
0.0057538291439414024,
-0.06167110800743103,
0.045299675315618515,
-0.016256950795650482,
-0.030084319412708282,
0.015787191689014435,
-0.013444177806377411,
0.025558292865753174,
-0.055811718106269836,
0.03504382446408272,
-0.0578201562166214,
0.008573831990361214,
0.039306070655584335,
0.05247833952307701,
0.013613232411444187,
0.013267810456454754,
-0.009960124269127846,
-0.045357368886470795,
-0.007509961724281311,
0.022677579894661903,
-0.03601788356900215,
-0.0443822517991066,
0.012597939930856228,
-0.03188861906528473,
-0.009903909638524055,
-0.07293365150690079,
-0.002621433464810252,
-0.03676317632198334,
0.07356078177690506,
0.0590595006942749,
-0.02862504869699478,
0.014733322896063328,
-0.029422247782349586,
0.017840059474110603,
0.026835771277546883,
-0.062246646732091904,
-0.002883270615711808,
-0.04621938243508339,
-0.008497298695147038,
-0.0005978109547868371,
0.04169097915291786,
0.04240262880921364,
-0.05218112841248512,
0.015436039306223392,
-0.043614160269498825,
-0.0027739955112338066,
0.04292876273393631,
0.009905776008963585,
0.0396377369761467,
0.02233009599149227,
0.03530560061335564,
0.037763651460409164,
-0.02128821425139904,
0.037870053201913834,
-0.0326555073261261,
-0.022362148389220238,
0.02780773676931858,
-0.03923378884792328,
-0.010077474638819695,
0.048404235392808914,
0.0015273902099579573,
-0.0357026681303978,
0.04274535924196243,
-0.05224239081144333,
0.0539761446416378,
0.0694483295083046,
0.04027709364891052,
0.000663372571580112,
0.024077830836176872,
-0.008851869963109493,
-0.012851233594119549,
0.0058106291107833385,
0.024698950350284576,
-0.023114966228604317,
0.0036054514348506927,
0.006858188658952713,
-0.012104013003408909,
-0.010280949994921684,
0.01835695281624794,
0.02740189991891384,
0.04144219681620598,
-0.045761093497276306,
-0.00036321120569482446,
-0.05040914565324783,
-0.034830886870622635,
-0.011936163529753685,
-0.04303360357880592,
-0.03031698800623417,
-0.01733502745628357,
-0.052505914121866226,
0.01551066618412733,
0.022906707599759102,
-0.01801013946533203,
0.005163762252777815,
0.03577699139714241,
-0.10318930447101593,
-0.02553274855017662,
0.04172554612159729,
0.034301698207855225,
-0.01197762694209814,
0.01639202982187271,
0.005357903894037008,
-0.037052154541015625,
-0.04081505164504051,
-0.03684519603848457,
-0.03624585270881653,
-0.02822435088455677,
-0.006555020809173584,
-0.06461020559072495,
0.017117707058787346,
0.030055779963731766,
0.0265204980969429,
-0.054386481642723083,
0.03743600472807884,
0.08829304575920105,
-0.05923181399703026,
-0.030195539817214012,
-0.011575651355087757,
0.044320471584796906,
0.0724998190999031,
-0.01655743084847927,
0.01956290192902088,
-0.005643729120492935,
-0.01491215918213129,
-0.009281573817133904,
0.017079880461096764,
-0.025669127702713013,
0.011654184199869633,
0.019824229180812836,
0.03902335837483406,
0.0032335452269762754,
-0.07563111186027527,
0.06481447070837021,
0.007355968467891216,
-0.011550607159733772,
-0.07018573582172394,
0.008585575968027115,
0.04994771629571915,
0.01090045366436243,
-0.032814741134643555,
-0.052090246230363846,
-0.04293868690729141,
-0.03155016526579857,
-0.038067035377025604,
-0.04478352889418602,
-0.03791411221027374,
0.00780428946018219,
-0.01611475646495819,
-0.020849091932177544,
-0.022932223975658417,
-0.011423756368458271,
0.07649964839220047,
0.023117879405617714,
-0.002539771841838956,
-0.021718468517065048,
0.011197991669178009,
-0.017621519044041634,
-0.05505019798874855,
-0.06643284857273102,
-0.03537878021597862,
-0.04213729500770569,
0.023721681907773018,
-0.01728999800980091,
0.03559703007340431,
-0.010089184157550335,
0.013659227639436722,
-0.029839258641004562,
0.04437656328082085,
-0.02089889906346798,
0.005499903578311205,
0.0316106453537941,
0.01804669015109539,
0.00813421793282032,
-0.0494823195040226,
-0.0056502921506762505,
0.01156593021005392,
-0.00040980783523991704,
0.0051924921572208405,
0.046411264687776566,
-0.03158445656299591,
0.019050179049372673,
0.05553041025996208,
-0.007234737742692232,
0.05113427713513374,
-0.06959988176822662,
-0.08365058898925781,
-0.018678009510040283,
-0.02312411181628704,
-0.05426311865448952,
-0.0028733580838888884,
0.043197017163038254,
0.03959649056196213,
-0.06045296788215637,
0.03720634803175926,
-0.0033453067298978567,
-0.04076077416539192,
0.0089949956163764,
-0.012557176873087883,
-0.025933196768164635,
0.028304142877459526,
-0.02761918492615223,
-0.0013888691319152713,
-0.011006348766386509,
-0.028092605993151665,
-0.0707465186715126,
0.019792836159467697,
-0.012673224322497845,
-0.05419896915555,
0.0013305569300428033,
0.048512835055589676,
0.06665782630443573,
-0.014834417961537838,
0.0009640782955102623,
0.053276028484106064,
0.05645548552274704,
0.0035768835805356503,
0.0069397022016346455,
0.05679915472865105,
-0.02519991807639599,
0.06672438234090805,
-0.006046990863978863,
0.041750602424144745,
0.045418839901685715,
-0.05377921462059021,
-0.06425169855356216,
0.07894034683704376,
0.0009836397366598248,
0.030779441818594933,
-0.014909425750374794,
-0.018627353012561798,
0.013934527523815632,
-0.03198372945189476,
0.0027905164752155542,
-0.014726730063557625,
0.002562416484579444,
0.018223408609628677,
0.02656817063689232,
-0.03612688556313515,
0.01830372028052807,
-0.004077554680407047,
0.034868933260440826,
0.010529108345508575,
0.037114787846803665,
0.0637379065155983,
-0.06689617037773132,
-0.007915147580206394,
0.02072344906628132,
-0.027508877217769623,
-0.032975006848573685,
0.039769984781742096,
0.04147236794233322,
0.01155945472419262,
-0.08671936392784119,
0.0006979459431022406,
0.04117603972554207,
-0.03559799864888191,
-0.030321944504976273,
0.022403601557016373,
0.023989062756299973,
0.003914660308510065,
-0.0285856481641531,
0.007596445735543966,
0.028651783242821693,
-0.02682630345225334,
-0.01752936840057373,
0.0210653655230999,
0.05798100680112839,
-0.014294696040451527,
-0.038478367030620575,
-0.01751907728612423,
-0.012146024964749813,
-0.059874288737773895,
0.05597654730081558,
0.008989688009023666,
-0.04562796279788017,
-0.043002381920814514,
0.017661625519394875,
0.013679386116564274,
-0.008046118542551994,
-0.03382287174463272,
0.019287671893835068,
-0.004347975831478834,
0.053417012095451355,
0.008437450043857098,
-0.02048163302242756,
-0.04491592198610306,
-0.03526177629828453,
0.05380265787243843,
0.02032299153506756,
-0.034575093537569046,
0.051014162600040436,
-0.04277896136045456,
0.0013608988374471664,
0.0046011582016944885,
-0.07379695773124695,
0.03232010081410408,
-0.03362784907221794,
-0.002039228565990925,
-0.006162835285067558,
0.07483425736427307,
0.05024952441453934,
-0.006810569670051336,
-0.007545682601630688,
0.005198874045163393,
-0.010889657773077488,
0.03373275324702263,
0.040782324969768524,
0.04140521213412285,
0.03381935507059097,
-0.0016177135985344648,
0.06351135671138763,
0.04728516563773155,
0.07551980018615723,
-0.002956272102892399,
-0.0002813509199768305,
-0.06966602802276611,
-0.05594025179743767,
-0.004164166748523712,
-0.059741947799921036,
0.052790723741054535,
0.0014793562004342675,
0.018511848524212837,
0.0360783226788044,
-0.016605332493782043,
0.034111782908439636,
0.02528686262667179,
-0.004342522006481886,
-0.0025132284499704838,
-0.015391851775348186,
-0.03495708480477333,
0.011130815371870995,
-0.023069798946380615,
-0.008822604082524776,
-0.04320875555276871,
0.03028346225619316,
-0.04027126729488373,
-0.03156069666147232,
-0.0016602238174527884,
-0.058689601719379425,
0.02262859418988228,
-0.014738962054252625,
0.0008165428880602121,
-0.070829838514328,
0.02159028686583042,
-0.05333225429058075,
0.007574174553155899,
-0.017723459750413895,
-0.006290598306804895,
-0.011534221470355988,
-0.021708976477384567,
0.019285263493657112,
-0.005484101362526417,
-0.06010274589061737,
0.013265243731439114,
0.02005249634385109,
-0.011559944599866867,
0.012339740991592407,
0.012546359561383724,
0.008295978419482708,
0.013976813293993473,
0.01008899137377739,
0.12373381853103638,
0.038210537284612656,
-0.0006494667613878846,
0.009133869782090187,
0.031706564128398895,
0.03789222240447998,
0.021668212488293648,
0.003980903886258602,
-0.010236276313662529,
0.056402940303087234,
0.02024410292506218,
-0.0006326767615973949,
-0.03545030578970909,
-0.04772306978702545,
0.027089722454547882
] |
<p>In his work on information processing in GPTs <a href="http://arxiv.org/abs/quant-ph/0508211">http://arxiv.org/abs/quant-ph/0508211</a> Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum theory, allowing for information processing capabilities not all of which occur in either the generalized no-signalling theory (GNST) or the generalized local theory (GLT). I'm wondering if this optimality is related to the symmetry of the associated polytope (of allowed states) in the theory, and in what exact manner. Any ideas?</p> | g9217 | [
-0.026205481961369514,
0.03337749093770981,
-0.010401595383882523,
0.00020326657977420837,
0.025207534432411194,
0.002112404443323612,
0.027790164574980736,
0.021978657692670822,
-0.04847867786884308,
0.018361913040280342,
0.0214023869484663,
-0.018581751734018326,
0.012680905871093273,
-0.014102810993790627,
-0.06344257295131683,
0.028354763984680176,
0.006655724253505468,
0.03348366543650627,
0.035305313766002655,
-0.001680060988292098,
0.012070641852915287,
-0.01691618002951145,
0.005041498690843582,
0.013543457724153996,
0.04756047949194908,
-0.010807466693222523,
0.05166001617908478,
-0.007125340402126312,
-0.033620089292526245,
-0.0033373951446264982,
0.03884878382086754,
-0.050691477954387665,
-0.0362745076417923,
-0.02104194089770317,
-0.014920435845851898,
-0.02353023737668991,
0.002639628713950515,
-0.016845719888806343,
0.00324174459092319,
0.017671585083007812,
0.03025239147245884,
0.037579767405986786,
-0.023245936259627342,
-0.038365285843610764,
-0.041485194116830826,
0.027196455746889114,
0.07075193524360657,
0.024866705760359764,
-0.024907901883125305,
-0.040823571383953094,
0.010626615025103092,
0.042383823543787,
0.017933493480086327,
-0.055657852441072464,
0.06017327681183815,
0.016591381281614304,
-0.022891845554113388,
0.04251577705144882,
-0.017734594643115997,
-0.03219018876552582,
0.034257978200912476,
0.008663037791848183,
-0.05517023429274559,
0.008083031512796879,
0.023619359359145164,
-0.03628302365541458,
-0.052191488444805145,
-0.046292539685964584,
-0.012555736117064953,
0.021603768691420555,
0.013844471424818039,
-0.015184340067207813,
-0.03248992934823036,
-0.012290007434785366,
0.01862885244190693,
-0.007989904843270779,
-0.019594475626945496,
0.02276957593858242,
0.0002972885558847338,
0.04008553922176361,
-0.057793281972408295,
-0.0027689586859196424,
0.021257631480693817,
-0.017534326761960983,
-0.029465004801750183,
0.022146722301840782,
0.06641120463609695,
-0.019488917663693428,
0.005561770871281624,
0.1026814728975296,
-0.018285034224390984,
-0.02312382496893406,
0.06632686406373978,
0.017285024747252464,
-0.00845253374427557,
0.07649499922990799,
-0.02054174244403839,
0.026631241664290428,
-0.00910431332886219,
0.002141836564987898,
0.005966848693788052,
-0.029864560812711716,
0.030591126531362534,
-0.021387465298175812,
0.001355704851448536,
-0.05199027433991432,
0.015286709181964397,
-0.07462748140096664,
-0.021720806136727333,
0.013620786368846893,
-0.023416360840201378,
0.01681932993233204,
0.0024956115521490574,
0.0225080493837595,
-0.04914618656039238,
-0.0034933616407215595,
0.0626932680606842,
-0.09674637764692307,
-0.046812478452920914,
-0.002827477641403675,
0.02125607617199421,
0.06855472177267075,
-0.09280595928430557,
0.05147998034954071,
-0.019582200795412064,
0.07283088564872742,
-0.012655091471970081,
0.012934139929711819,
-0.025639280676841736,
-0.04065743833780289,
-0.009216892533004284,
-0.03726208582520485,
0.050627805292606354,
0.11945825815200806,
0.007832570932805538,
0.02220088243484497,
0.013262082822620869,
0.012776118703186512,
0.01792789436876774,
-0.014453991316258907,
-0.04249270260334015,
-0.023719415068626404,
-0.06290917843580246,
0.004715586546808481,
0.02981681562960148,
-0.013843092136085033,
-0.0019065197557210922,
-0.015481754206120968,
-0.02122470922768116,
0.004845125135034323,
0.055307503789663315,
0.039709076285362244,
0.017229005694389343,
0.031113656237721443,
0.06490140408277512,
-0.03635357692837715,
0.053516048938035965,
0.0012498614378273487,
0.008482947014272213,
0.025404278188943863,
0.024635184556245804,
-0.010583375580608845,
-0.0548723004758358,
-0.0009664790122769773,
-0.09060842543840408,
-0.01792151853442192,
0.0047228154726326466,
-0.02630198746919632,
-0.007857703603804111,
-0.07579078525304794,
-0.0054979026317596436,
0.040255527943372726,
0.0004755745467264205,
0.02764420211315155,
0.008008641190826893,
0.05192694813013077,
-0.044980935752391815,
0.025393294170498848,
0.022661473602056503,
0.016522986814379692,
-0.02936919778585434,
-0.0318838432431221,
0.007384724449366331,
0.003394507337361574,
0.016948366537690163,
-0.00433339225128293,
-0.03908662870526314,
0.0017278633313253522,
0.014779537916183472,
0.01207675226032734,
0.01062004268169403,
0.028091970831155777,
-0.1001286432147026,
0.04777223616838455,
-0.058213330805301666,
-0.035543810576200485,
0.08262438327074051,
-0.0431840717792511,
-0.04274038225412369,
0.013608841225504875,
0.006157690659165382,
0.018116584047675133,
0.008615628816187382,
-0.002935817465186119,
0.00022525707026943564,
-0.024968311190605164,
-0.05002107471227646,
0.07076743990182877,
0.04329357296228409,
-0.052036285400390625,
0.030196206644177437,
-0.042067237198352814,
-0.012230072170495987,
0.012538563460111618,
0.0035421717911958694,
-0.04893002659082413,
0.01727396808564663,
0.015162506140768528,
0.043358854949474335,
-0.001490736729465425,
0.0037659157533198595,
0.03224671259522438,
-0.006346821319311857,
0.045056384056806564,
-0.056941840797662735,
0.003197592915967107,
0.010695233941078186,
0.003446667455136776,
-0.02693129889667034,
0.05254913493990898,
-0.06342699378728867,
-0.012861787341535091,
-0.05280127748847008,
-0.05564003065228462,
0.05293652415275574,
0.07660502940416336,
-0.02585757151246071,
-0.026520518586039543,
0.04419584944844246,
0.02737395092844963,
0.018612470477819443,
0.022821079939603806,
-0.05755474045872688,
0.00045384952682070434,
-0.03901926800608635,
-0.013709044083952904,
0.017567487433552742,
-0.0016275853849947453,
0.019154848530888557,
0.015386108309030533,
-0.04095226898789406,
-0.0017456009518355131,
0.012971034273505211,
-0.03441936522722244,
0.016119131818413734,
-0.05932493507862091,
0.07445493340492249,
-0.020335165783762932,
-0.02719939313828945,
-0.03121054358780384,
0.019177943468093872,
-0.041526276618242264,
0.01590370200574398,
-0.028087882325053215,
0.014369756914675236,
-0.017677394673228264,
0.00922884326428175,
-0.018460428342223167,
-0.07298272103071213,
0.043050337582826614,
0.009377037174999714,
0.0398186631500721,
-0.006397029850631952,
0.06493841856718063,
-0.006005794741213322,
0.00769443204626441,
-0.005291375797241926,
-0.014937794767320156,
-0.03655197098851204,
-0.010165814310312271,
-0.061082515865564346,
-0.07615874707698822,
-0.013921400532126427,
0.003389142220839858,
0.03158663213253021,
-0.01586320996284485,
0.03199971467256546,
0.0619409903883934,
0.004872702993452549,
0.07860055565834045,
0.036459919065237045,
0.010618084110319614,
0.03683137893676758,
0.05035198852419853,
-0.05806251987814903,
-0.017009377479553223,
0.010306354612112045,
-0.07941126078367233,
0.001591276377439499,
0.05613336339592934,
-0.027254022657871246,
-0.05502762272953987,
-0.02455076202750206,
0.01529513206332922,
0.015033682808279991,
-0.0720389112830162,
-0.052360039204359055,
-0.003673570230603218,
-0.052664898335933685,
0.0035495846532285213,
0.016785023733973503,
0.04837414622306824,
-0.005100869573652744,
-0.011567328125238419,
0.028149189427495003,
0.03001883439719677,
-0.020947668701410294,
-0.0005938529502600431,
-0.021561330184340477,
-0.053989384323358536,
-0.0050908769480884075,
0.035278160125017166,
0.03544510155916214,
-0.016599271446466446,
0.014619719237089157,
0.06356930732727051,
-0.04564318060874939,
0.009737029671669006,
0.013458679430186749,
-0.04673293977975845,
0.06181376054883003,
-0.008735492825508118,
0.013182119466364384,
-0.0182865709066391,
-0.04937499761581421,
-0.08500562608242035,
-0.003937923349440098,
-0.010125023312866688,
0.022260192781686783,
0.06102624908089638,
-0.03788040950894356,
-0.031566016376018524,
-0.05945225805044174,
-0.008909670636057854,
0.01945647969841957,
-0.01742248423397541,
-0.02057339809834957,
0.026401009410619736,
0.0019003006163984537,
0.014544487930834293,
-0.022672822698950768,
-0.015870576724410057,
-0.010440901853144169,
-0.0041451104916632175,
-0.017988137900829315,
0.04028894379734993,
-0.004174250178039074,
-0.0005147854099050164,
-0.00251043145544827,
0.0000927043438423425,
-0.0024086374323815107,
-0.011235316284000874,
-0.0034303765278309584,
0.004405846819281578,
-0.012448165565729141,
0.029708394780755043,
-0.023956798017024994,
-0.024139603599905968,
0.021858150139451027,
0.045529384166002274,
0.03172577917575836,
-0.0062727732583880424,
0.02665419690310955,
-0.05739419534802437,
0.052811577916145325,
-0.01990780606865883,
-0.0009457806008867919,
-0.020835034549236298,
-0.04652542993426323,
-0.02284357324242592,
0.035115573555231094,
-0.013914653100073338,
0.009359544143080711,
-0.0341908223927021,
0.0538201779127121,
0.054761406034231186,
-0.019179504364728928,
0.008937735110521317,
-0.032437942922115326,
-0.019570309668779373,
0.028842249885201454,
-0.05410749465227127,
0.005918390583246946,
0.011227923445403576,
-0.007937631569802761,
0.030879642814397812,
-0.030207978561520576,
0.026120372116565704,
0.002492480678483844,
0.03209014609456062,
0.016642216593027115,
-0.024292921647429466,
-0.053403329104185104,
-0.023638475686311722,
0.010101170279085636,
-0.021488213911652565,
-0.027274908497929573,
0.022713392972946167,
-0.013718596659600735,
-0.035129114985466,
-0.03808334097266197,
0.056681204587221146,
-0.040547747164964676,
-0.009654875844717026,
0.025694603100419044,
0.018424298614263535,
-0.051429927349090576,
-0.0864962786436081,
0.021663673222064972,
0.001479758182540536,
0.0030521575827151537,
0.04788792133331299,
0.031964775174856186,
-0.014432749710977077,
0.008424898609519005,
0.0022103835362941027,
0.03977696970105171,
0.01223504263907671,
0.007086205296218395,
-0.009713980369269848,
0.08847802132368088,
-0.00944305956363678,
0.05828256905078888,
0.011758144944906235,
-0.042883191257715225,
-0.0027651807758957148,
-0.06889144331216812,
0.0698041245341301,
0.01824757643043995,
-0.024161916226148605,
0.02959095500409603,
-0.015494137071073055,
-0.020801635459065437,
-0.03458477929234505,
0.008410794660449028,
0.02704835869371891,
-0.022815849632024765,
-0.005666396580636501,
0.011893079616129398,
-0.03370014205574989,
-0.02551552653312683,
-0.012272583320736885,
-0.008462133817374706,
-0.05549433454871178,
0.04110744595527649,
-0.005816389340907335,
-0.03172385320067406,
0.008712515234947205,
0.0668184831738472,
0.0311835166066885,
-0.00928234588354826,
0.014845792204141617,
-0.08075183629989624,
0.009031971916556358,
0.08743446320295334,
0.0383460596203804,
-0.060962334275245667,
0.03522636741399765,
-0.004391280468553305,
-0.049175556749105453,
0.0319858118891716,
-0.0007375678978860378,
0.046682532876729965,
0.03901504725217819,
-0.037944577634334564,
-0.023409951478242874,
-0.004028894938528538,
0.005003631580621004,
0.05649760738015175,
-0.0043656970374286175,
0.013834882527589798,
0.011884715408086777,
0.07883848994970322,
0.0418342687189579,
0.052656181156635284,
0.0015830809716135263,
0.019447414204478264,
-0.056085582822561264,
-0.01371052023023367,
-0.0271444171667099,
0.050658684223890305,
-0.013074962422251701,
0.008912231773138046,
0.002381704980507493,
0.010204337537288666,
-0.026280483230948448,
0.06627055257558823,
-0.008385621942579746,
-0.0564284510910511,
-0.024254053831100464,
-0.04627827927470207,
0.021371744573116302,
0.015741128474473953,
0.021497011184692383,
-0.018791723996400833,
0.02102769911289215,
0.0762561708688736,
-0.05589926615357399,
-0.012224427424371243,
0.0006471130764111876,
-0.027888257056474686,
-0.009291759692132473,
-0.03941547870635986,
0.021913953125476837,
-0.010691124945878983,
-0.023564642295241356,
-0.01849379576742649,
0.017998283728957176,
-0.06641964614391327,
-0.0035527783911675215,
-0.027202390134334564,
0.054432086646556854,
-0.0026027595158666372,
-0.0594705305993557,
0.019147809594869614,
0.025001686066389084,
-0.015141516923904419,
-0.010599800385534763,
-0.012735074386000633,
0.009082473814487457,
0.026211505755782127,
0.0344306156039238,
0.0359315387904644,
0.011595865711569786,
0.05136919021606445,
0.00046802370343357325,
-0.0419001579284668,
-0.04281551018357277,
0.03169397637248039,
0.048761334270238876,
-0.021942034363746643,
-0.02716958522796631,
-0.021289950236678123,
0.05579986795783043,
-0.01595432125031948,
-0.022842250764369965,
-0.07809057086706161,
-0.024879612028598785,
-0.03704199939966202,
-0.040098369121551514,
-0.006666446104645729,
-0.049216046929359436,
-0.008200399577617645,
-0.009433533996343613,
0.005628460086882114,
0.00017912623297888786,
0.0029129916802048683,
0.04029180854558945,
0.010874930769205093,
0.03544390946626663,
0.03242119401693344,
0.047208741307258606,
0.04187875613570213,
0.019200392067432404,
0.012547560036182404,
0.019427675753831863,
-0.018105488270521164,
-0.024544082581996918,
0.0019553368911147118,
0.03960566967725754,
-0.014729688875377178,
0.004248306155204773,
0.025122161954641342,
0.0856548324227333,
-0.01898336037993431,
0.0066292197443544865,
-0.010960998944938183,
-0.07344521582126617,
-0.011064293794333935,
0.07552802562713623,
-0.09033352881669998,
0.04797947406768799,
-0.009432726539671421,
-0.022877627983689308,
0.02689828909933567,
0.07196943461894989,
-0.07267976552248001,
-0.02953946217894554,
0.000048005604185163975,
0.07072596997022629,
-0.0005049476749263704,
-0.02423548325896263,
-0.043579645454883575,
0.042367443442344666,
0.06457049399614334,
-0.023930208757519722,
0.005740146618336439,
-0.11333830654621124,
-0.030651049688458443,
0.007898089475929737,
0.04866328090429306,
-0.03826640173792839,
0.05688660964369774,
0.003683397313579917,
-0.0005532802315428853,
0.0570034459233284,
-0.051916904747486115,
0.016605017706751823,
-0.05746981501579285,
0.00034205502015538514,
-0.0007256625103764236,
-0.011315085925161839,
0.03401409089565277,
-0.006023467518389225,
0.04368346184492111,
-0.053817588835954666,
0.008551339618861675,
-0.04190265014767647,
-0.015789993107318878,
0.030498754233121872,
0.03986199200153351,
-0.021152440458536148,
0.017095401883125305,
-0.004953883122652769,
0.07000113278627396,
0.08507489413022995,
-0.06451936811208725,
-0.03137850761413574,
0.000463405332993716,
0.02651769109070301,
0.055821195244789124,
0.029255850240588188,
0.02071050927042961,
0.05187395215034485,
0.0020697051659226418,
0.012788020074367523,
-0.04004192352294922,
0.011644287966191769,
0.03467259928584099,
-0.0006900497828610241,
-0.03283597528934479,
0.040951866656541824,
0.038365427404642105,
-0.015730515122413635,
0.06533724069595337,
0.02355237863957882,
0.055767159909009933,
-0.028907131403684616,
0.017613865435123444,
-0.000436318019637838,
-0.016437953338027,
-0.00611966522410512,
-0.038624994456768036,
-0.030485890805721283,
-0.04713005945086479,
-0.04031965136528015,
-0.027646007016301155,
-0.018169669434428215,
0.06511647254228592,
-0.007194924168288708,
-0.02234969101846218,
0.026875028386712074,
0.01647418923676014,
0.00280816201120615,
0.027734195813536644,
0.03917815163731575,
0.06887879967689514,
-0.051741838455200195,
-0.036032069474458694,
-0.06329493224620819,
-0.04839747026562691,
-0.016671758145093918,
0.01194467768073082,
0.023224767297506332,
0.07895086705684662,
-0.05797453224658966,
-0.04710925742983818,
-0.003223910229280591,
-0.04218999668955803,
0.0034654622431844473,
0.008846281096339226,
0.012587125413119793,
0.01102037075906992,
-0.016470355913043022,
-0.04630313068628311,
-0.030166367068886757,
-0.005150717217475176,
0.03720245882868767,
-0.03584570810198784,
0.006135148927569389,
0.0028771504294127226,
-0.04298373684287071,
0.03454082831740379,
0.030308641493320465,
0.006087043788284063,
0.009049451909959316,
-0.024295572191476822,
0.0005391715676523745,
-0.034067295491695404,
0.0023170229978859425,
0.03718655928969383,
-0.04295222833752632,
-0.04241938889026642,
0.0423186719417572,
0.028239842504262924,
-0.090519480407238,
0.05111518129706383,
-0.04916631802916527,
0.011885982006788254,
0.01422016229480505,
-0.014287834987044334,
0.03903660178184509,
-0.011815165169537067,
0.04353756457567215,
0.04924503341317177,
-0.0018477331614121795,
-0.06377899646759033,
0.008986697532236576,
0.018807800486683846,
0.05336650833487511,
-0.007422795984894037,
-0.02653302624821663,
-0.028636708855628967,
-0.015880022197961807,
0.007633749861270189,
-0.04802433028817177,
0.056061528623104095,
-0.052154265344142914,
0.005742634646594524,
0.06148211285471916,
-0.03359369933605194,
-0.03343018889427185,
-0.03982781246304512,
-0.015837984159588814,
-0.0360887348651886,
0.06196615844964981,
-0.013586340472102165,
-0.021443817764520645,
-0.019602172076702118,
-0.0005420841625891626,
0.012773643247783184,
-0.020961971953511238,
0.057213641703128815,
0.006433373782783747,
-0.019546501338481903,
-0.001488804235123098,
-0.05702368542551994,
-0.0028968516271561384,
0.007971455343067646,
-0.1166352853178978,
0.01238042302429676,
-0.02194281294941902,
-0.009631729684770107,
0.008659438230097294,
0.050836145877838135,
0.0513828843832016,
0.03362748771905899,
0.020306270569562912,
0.011105384677648544,
0.04811323434114456,
0.03840259835124016,
-0.009877059608697891,
0.0007243238505907357,
0.03879929706454277,
-0.049812037497758865,
0.015506254509091377,
0.02819267474114895,
0.004981265868991613
] |
<p>It always fascinate me that time is symmetrical classical physics while in life we all experience flow of time in only one direction. There is no preference direction of time in classical physics. The only exception being in thermodynamics where with the introduction of entropy, there is a prefer direction for the time axis. Physical systems evolve in the direction where the entropy increases (sorry for not being precise...) Personally, I have never truly accepted thermodynamics as a full theory as it never truly "explain" why entropy must increase. </p>
<p>But, in quantum theory, there seems to be a preferred direction for time too. And, this has nothing to do with entropy? The collapse of a wave function in a measurement seems to dictate a direction of time. Could this be a better explanation for the direction of time or maybe even for thermodynamics? (Ok, maybe not thermodynamics...)</p> | g303 | [
0.025709744542837143,
0.0046794358640909195,
-0.010500021278858185,
-0.019558968022465706,
0.05011843889951706,
0.04947774484753609,
0.02527703531086445,
-0.020559173077344894,
-0.011697312816977501,
-0.04025471210479736,
0.055618833750486374,
-0.026416635140776634,
0.008776790462434292,
0.050331100821495056,
-0.0029577529057860374,
-0.026384128257632256,
0.07547907531261444,
0.009864830411970615,
0.036574020981788635,
0.035551946610212326,
-0.054511550813913345,
-0.0193436611443758,
0.036999836564064026,
0.011815574020147324,
-0.01750616356730461,
-0.05181517079472542,
0.022912941873073578,
-0.053746238350868225,
0.024002131074666977,
0.020077131688594818,
0.00895778089761734,
0.045583441853523254,
0.016753796488046646,
-0.02697664126753807,
0.00887592975050211,
-0.07837014645338058,
-0.01888996548950672,
0.012386784888803959,
0.10112437605857849,
-0.016438009217381477,
0.0015459031565114856,
-0.05513106659054756,
0.009763775393366814,
-0.04339884594082832,
0.02216089516878128,
-0.020321397110819817,
-0.037563834339380264,
0.032811928540468216,
-0.011801455169916153,
-0.02297997660934925,
0.028780126944184303,
-0.0024181564804166555,
0.04152372479438782,
0.027442028746008873,
0.020885812118649483,
-0.004103832878172398,
-0.024146270006895065,
0.04769530147314072,
0.07389654219150543,
0.018875746056437492,
-0.003961619455367327,
0.025337664410471916,
-0.009309818968176842,
-0.02996956557035446,
0.05560174584388733,
-0.004458846058696508,
-0.021306687965989113,
-0.0454077385365963,
0.031282760202884674,
0.008363213390111923,
0.013904237188398838,
-0.08769743889570236,
-0.0024461790453642607,
0.010448812507092953,
0.06435345113277435,
0.06278228014707565,
0.00905404519289732,
-0.09531809389591217,
0.0022047830279916525,
-0.04316768795251846,
-0.04775852710008621,
-0.0039135306142270565,
0.017370957881212234,
-0.008688789792358875,
0.08515844494104385,
-0.0363328792154789,
0.04252456873655319,
-0.0011845988919958472,
-0.011126055382192135,
-0.002833547769114375,
-0.06445074081420898,
-0.03210565820336342,
0.10835932195186615,
0.01910221017897129,
-0.06367645412683487,
-0.034779999405145645,
-0.025491679087281227,
0.021883614361286163,
0.03541067987680435,
0.03549102321267128,
-0.034504346549510956,
-0.006853481754660606,
0.003868485800921917,
0.018772296607494354,
0.014554504305124283,
-0.06815849244594574,
-0.012723407708108425,
0.012556090019643307,
-0.07401817291975021,
-0.09261193871498108,
-0.023653803393244743,
0.007183423265814781,
-0.024276111274957657,
0.046949323266744614,
0.05161900445818901,
0.020191730931401253,
0.08378726989030838,
-0.06466863304376602,
0.006880626548081636,
0.04504146799445152,
-0.01228321436792612,
0.017102239653468132,
0.022792024537920952,
-0.008902295492589474,
-0.005550825968384743,
0.06022427976131439,
-0.040794238448143005,
-0.011852044612169266,
-0.0015635739546269178,
0.007410788908600807,
0.0027011181227862835,
0.024858122691512108,
-0.01444996241480112,
0.028951451182365417,
-0.010573447681963444,
0.01864563301205635,
-0.018702177330851555,
0.020668035373091698,
-0.02567572519183159,
0.0249957125633955,
0.019697537645697594,
-0.02254694327712059,
0.003107758006080985,
0.013434185646474361,
-0.013020457699894905,
-0.01017051748931408,
-0.03248070180416107,
-0.031405333429574966,
0.03971223905682564,
0.023108823224902153,
-0.013679626397788525,
0.06930622458457947,
-0.01477466244250536,
-0.04536886140704155,
-0.038435809314250946,
-0.016823511570692062,
0.0406634584069252,
0.011710581369698048,
-0.010096438229084015,
-0.002651376649737358,
0.0359196774661541,
0.05060894042253494,
-0.016786271706223488,
-0.02789466083049774,
-0.02212192304432392,
-0.00089793570805341,
0.0008060379768721759,
-0.043179456144571304,
0.022383106872439384,
-0.03652114421129227,
-0.017952851951122284,
-0.03240245208144188,
-0.06135431304574013,
0.058566439896821976,
-0.021715225651860237,
0.012146169319748878,
-0.027493903413414955,
0.06692305952310562,
0.02611621282994747,
0.004966556094586849,
-0.039642639458179474,
0.03183780610561371,
0.04431862384080887,
-0.032185375690460205,
-0.003374942811205983,
-0.02189137414097786,
0.022870492190122604,
0.050245434045791626,
-0.09388285875320435,
-0.05620240420103073,
0.030574815347790718,
-0.022582780569791794,
-0.07259821891784668,
0.07149945944547653,
0.01271848101168871,
-0.01943487487733364,
-0.011278503574430943,
-0.017307106405496597,
-0.09192004799842834,
0.053160347044467926,
-0.010445830412209034,
-0.009688069112598896,
0.027497978881001472,
0.011021438986063004,
-0.05135771632194519,
0.01228303276002407,
-0.013499943539500237,
0.02593844197690487,
0.042738109827041626,
-0.01451459713280201,
0.001762711675837636,
0.04976166412234306,
-0.022355182096362114,
-0.008700061589479446,
-0.023851724341511726,
-0.04358849674463272,
-0.009820331819355488,
0.009454004466533661,
-0.028233541175723076,
0.041665297001600266,
0.029463332146406174,
-0.02869388647377491,
0.0008569356286898255,
-0.011150415986776352,
-0.026933040469884872,
-0.02997446060180664,
-0.04359101504087448,
-0.08933217078447342,
-0.003938013222068548,
0.004308453761041164,
-0.07654359936714172,
0.06017225235700607,
0.06268042325973511,
0.03196397423744202,
0.04214664176106453,
0.06547846645116806,
-0.0015679372008889914,
-0.005093252751976252,
0.038244329392910004,
-0.025208499282598495,
-0.025508835911750793,
-0.032359715551137924,
-0.04672509804368019,
0.03325795382261276,
0.004135295283049345,
-0.0381266288459301,
-0.0001328479265794158,
-0.016655191779136658,
0.04076170548796654,
-0.028047628700733185,
0.04666973650455475,
-0.0186751876026392,
-0.03650513291358948,
-0.0656457245349884,
0.003542395541444421,
-0.016777705401182175,
-0.01741001568734646,
0.02879001945257187,
-0.10196781903505325,
-0.05779363214969635,
-0.029776576906442642,
-0.03755378723144531,
0.03019275702536106,
-0.0039926269091665745,
-0.01514146476984024,
0.015217716805636883,
-0.007735953666269779,
0.017245875671505928,
-0.04046615958213806,
-0.03289346396923065,
0.033128444105386734,
0.034084878861904144,
0.02575412020087242,
0.06262264400720596,
-0.03364367038011551,
-0.011276341043412685,
0.014371312223374844,
0.01388951763510704,
0.009533541277050972,
-0.0427577942609787,
-0.007154795806854963,
0.01902323216199875,
-0.04623846709728241,
0.0024516393896192312,
0.06541196256875992,
-0.05967035889625549,
0.04096667096018791,
-0.025651436299085617,
-0.0026841999497264624,
0.004767295904457569,
0.025113403797149658,
0.024847310036420822,
-0.047471631318330765,
-0.014281140640377998,
0.02314959466457367,
0.0011429653968662024,
0.05166584625840187,
-0.03329211845993996,
-0.02133810892701149,
0.04515406861901283,
-0.03555819392204285,
-0.024219276383519173,
0.012694819830358028,
0.01616380363702774,
0.00005624283949146047,
0.04355200007557869,
-0.08922704309225082,
-0.07664670795202255,
-0.029260339215397835,
0.023099899291992188,
0.05962679162621498,
0.04414667561650276,
-0.04248230531811714,
0.03218258544802666,
-0.03184613585472107,
-0.004910451825708151,
-0.09400081634521484,
0.021817510947585106,
0.021391376852989197,
-0.032706908881664276,
0.01383974775671959,
-0.008499103598296642,
0.032198354601860046,
-0.030209863558411598,
-0.011343625374138355,
-0.058203909546136856,
0.009268250316381454,
0.037797197699546814,
-0.05659358575940132,
-0.028539234772324562,
-0.021269988268613815,
-0.056151244789361954,
0.03554626554250717,
-0.015200200490653515,
-0.07184076309204102,
0.02935689501464367,
-0.013413975946605206,
-0.018901927396655083,
0.00418348191305995,
0.02585010416805744,
0.029578786343336105,
-0.008634165860712528,
-0.008102014660835266,
0.012798803858458996,
0.006145072635263205,
-0.01862192153930664,
-0.026227468624711037,
0.03172792121767998,
0.05283726006746292,
0.03416987508535385,
0.03377385810017586,
-0.012715146876871586,
-0.019231360405683517,
0.006493863649666309,
0.0009496410493738949,
0.030867302790284157,
0.03494804725050926,
0.08774465322494507,
0.039717018604278564,
-0.04738197848200798,
-0.061323340982198715,
0.0002975104143843055,
0.02510208636522293,
-0.019325997680425644,
0.006413882132619619,
0.04150491580367088,
-0.003879274008795619,
-0.0011277894955128431,
-0.033387959003448486,
-0.01656564697623253,
0.03459018096327782,
-0.017515571787953377,
0.0011114757508039474,
0.02525416575372219,
0.0773291140794754,
-0.045428015291690826,
0.010217011906206608,
0.047286707907915115,
-0.04996875673532486,
0.03175754100084305,
0.0007098565110936761,
-0.03937060385942459,
0.012614976614713669,
0.05676516890525818,
0.011983522213995457,
0.011900454759597778,
-0.07192453742027283,
-0.007607492618262768,
-0.05549248307943344,
-0.01474014762789011,
0.003269834676757455,
0.010523995384573936,
-0.01356973871588707,
-0.027382727712392807,
-0.04394397512078285,
0.03706718236207962,
0.040801163762807846,
0.022760245949029922,
-0.04922938346862793,
-0.007805108558386564,
0.021191125735640526,
-0.04090564697980881,
0.0012816943926736712,
0.005058335606008768,
0.02553016133606434,
0.01884063333272934,
0.00998080987483263,
-0.0435326062142849,
-0.06482338160276413,
-0.05860857293009758,
-0.0006883980240672827,
0.017885658890008926,
0.019206034019589424,
-0.029407380148768425,
0.06303512305021286,
-0.003006190061569214,
-0.026491036638617516,
-0.05040907487273216,
0.08730031549930573,
0.02343880757689476,
0.055250637233257294,
-0.0030625867657363415,
0.026964889839291573,
-0.004307767376303673,
-0.02431408315896988,
0.009382723830640316,
0.0831456109881401,
-0.027169013395905495,
-0.025143714621663094,
-0.016221456229686737,
0.01628831960260868,
0.022933676838874817,
0.04131629690527916,
0.014552757143974304,
0.019138537347316742,
0.023624245077371597,
-0.005223462823778391,
0.07157355546951294,
0.044880591332912445,
0.06896572560071945,
0.054151322692632675,
-0.019604824483394623,
-0.008541996590793133,
-0.033319856971502304,
-0.02607368677854538,
0.00721004419028759,
0.04942135512828827,
-0.03572157397866249,
-0.028699705377221107,
-0.04249291121959686,
-0.06551069021224976,
0.06158868968486786,
-0.017315573990345,
-0.0043846857734024525,
-0.04735778644680977,
-0.011553095653653145,
-0.04678230732679367,
0.04580991342663765,
0.03635382279753685,
0.0673605352640152,
-0.07301819324493408,
-0.03911010921001434,
0.009752350859344006,
0.030477456748485565,
-0.02482611872255802,
0.0029625927563756704,
0.010787363164126873,
0.03990178182721138,
-0.05992100387811661,
-0.0436641089618206,
-0.00940106064081192,
0.017137248069047928,
0.010152929462492466,
-0.006092678755521774,
-0.005018243100494146,
-0.003136424347758293,
-0.007299631834030151,
-0.040388088673353195,
0.010953759774565697,
-0.07100840657949448,
-0.01988457702100277,
-0.03162591531872749,
0.03425268828868866,
0.04775251820683479,
0.03386421129107475,
-0.02266869880259037,
-0.034936681389808655,
0.0006620418862439692,
0.03673867508769035,
-0.04220176860690117,
0.0016602218383923173,
0.02122831530869007,
0.035297393798828125,
-0.054025646299123764,
-0.02194833569228649,
0.005105850286781788,
-0.005298863165080547,
-0.03325488045811653,
0.0011080403346568346,
-0.07786153256893158,
-0.09250124543905258,
0.04335755482316017,
-0.03595340624451637,
0.007223031483590603,
-0.029053110629320145,
0.008796018548309803,
-0.0040048821829259396,
0.02454412169754505,
-0.09620543569326401,
0.025837760418653488,
0.03150279074907303,
0.001868956140242517,
0.018926143646240234,
0.014134137891232967,
0.0638008639216423,
-0.020762156695127487,
0.0000028025351639371365,
-0.026496266946196556,
0.07083016633987427,
-0.03220043331384659,
0.014259079471230507,
0.02408558689057827,
0.018871009349822998,
-0.0023882815148681402,
0.06692079454660416,
0.05373958498239517,
-0.08637537062168121,
-0.024584470316767693,
0.034811075776815414,
-0.02419104240834713,
-0.0015601053601130843,
0.01713690720498562,
0.04974614083766937,
0.007091976236552,
0.002039467915892601,
-0.024326298385858536,
-0.00371029251255095,
0.0415215827524662,
0.0021478519774973392,
-0.00748176034539938,
-0.020187629386782646,
0.014272700995206833,
-0.02035054750740528,
0.04382945969700813,
0.06925289332866669,
0.03328352048993111,
-0.0432576909661293,
-0.0282332431524992,
0.013600599020719528,
-0.019478145986795425,
-0.05124994367361069,
0.01642235368490219,
-0.05131320282816887,
0.009892928414046764,
-0.0034768222831189632,
-0.031983934342861176,
0.03944643959403038,
-0.03529516980051994,
-0.015476400032639503,
0.010889966040849686,
-0.01464200671762228,
0.03796534612774849,
0.033380914479494095,
0.033499326556921005,
0.0008589804638177156,
-0.03858790919184685,
0.05394219979643822,
-0.002002404537051916,
0.009369531646370888,
0.09591254591941833,
0.0038742166943848133,
-0.006959619000554085,
-0.009666385129094124,
0.03609868884086609,
0.032562505453825,
0.009148405864834785,
-0.0404544323682785,
-0.09121181815862656,
-0.027202453464269638,
-0.016024809330701828,
-0.016531936824321747,
-0.02550494112074375,
0.005969187244772911,
-0.03822087123990059,
-0.004680645652115345,
0.023547789081931114,
0.013660967350006104,
-0.0023325036745518446,
0.002287447452545166,
0.10011973977088928,
-0.02780613861978054,
-0.03419444337487221,
0.014806072227656841,
-0.01033883448690176,
-0.019647473469376564,
-0.005793706979602575,
0.00708151888102293,
0.017704365774989128,
-0.009743787348270416,
0.028792835772037506,
-0.06157585605978966,
-0.012308754958212376,
0.023002905771136284,
0.0006602140492759645,
0.05945340171456337,
0.040660977363586426,
0.013083862140774727,
0.043336279690265656,
0.03271112218499184,
0.006156386341899633,
0.012111170217394829,
0.026685256510972977,
0.0064911614172160625,
0.014222891069948673,
-0.022935252636671066,
-0.007038467098027468,
-0.02082289382815361,
0.015170428901910782,
-0.02232862450182438,
0.05539565905928612,
0.019903680309653282,
-0.010352011770009995,
0.004472690634429455,
0.014028113335371017,
0.05705871060490608,
0.02025909535586834,
-0.045632485300302505,
0.043208856135606766,
0.017944609746336937,
0.03770509734749794,
0.02721528895199299,
0.0037469174712896347,
-0.009894922375679016,
0.04719172418117523,
-0.016341116279363632,
-0.048337746411561966,
-0.06749866902828217,
-0.04584130272269249,
0.06523732841014862,
0.036310020834207535,
0.025009475648403168,
0.010737849399447441,
0.03850487992167473,
-0.013308095745742321,
-0.07173687219619751,
0.08835276961326599,
-0.013651594519615173,
0.03643633425235748,
-0.08037836104631424,
0.0013003950007259846,
0.023628495633602142,
-0.017610587179660797,
-0.020884307101368904,
-0.00401634955778718,
0.012787713669240475,
0.03454233705997467,
0.0024813595227897167,
-0.011315200477838516,
0.023726992309093475,
-0.048628564924001694,
-0.00718771992251277,
-0.007620106916874647,
0.02212377078831196,
0.05197333171963692,
-0.006115333642810583,
0.030357524752616882,
-0.0003123694041278213,
-0.03791464865207672,
-0.0004932120209559798,
-0.05975453928112984,
-0.015598735772073269,
-0.02167709358036518,
0.008568818680942059,
-0.03275347128510475,
-0.052555348724126816,
0.024291126057505608,
-0.030352264642715454,
-0.006007500924170017,
0.01196727342903614,
0.015369653701782227,
0.020129501819610596,
0.049368735402822495,
-0.003526005893945694,
-0.02283659391105175,
-0.0384216345846653,
0.03244217857718468,
0.006350170820951462,
-0.02250475063920021,
-0.03626203164458275,
0.03364592790603638,
-0.0484934039413929,
0.01462410669773817,
-0.056787870824337006,
-0.03569236770272255,
-0.012819443829357624,
0.018437419086694717,
0.10139908641576767,
-0.0012064401526004076,
-0.03252466768026352,
-0.013724859803915024,
0.019626637920737267,
-0.036440640687942505,
0.02561827376484871,
-0.0028932339046150446,
0.04263938218355179,
0.001188152120448649,
0.0498686283826828,
-0.017983222380280495,
-0.02434816211462021,
0.06317625194787979,
-0.02851860597729683,
0.015869265422225,
0.012638257816433907,
0.019443627446889877,
0.015171748585999012,
-0.017957620322704315,
-0.027192678302526474,
0.028712386265397072,
0.03719182685017586,
-0.019327437505126,
-0.007117052562534809,
-0.06464185565710068,
-0.0473693385720253,
-0.01576567068696022,
-0.03463159501552582,
0.007029591128230095,
-0.01265319436788559,
-0.07087795436382294,
-0.0009471740922890604,
-0.012840005569159985,
0.03964201733469963,
0.008546975441277027,
0.032547708600759506,
0.032003697007894516,
-0.027023402974009514,
0.056424420326948166,
-0.00804538931697607,
0.011883131228387356,
-0.03801824897527695,
-0.02426430583000183,
0.03371714428067207,
0.007278569974005222,
0.024134617298841476,
-0.007521442137658596,
-0.008340388536453247,
-0.07958078384399414,
-0.02413138374686241,
0.014928879216313362,
0.0479203425347805,
-0.023346098139882088,
0.009212428703904152,
0.032642997801303864,
0.008893897756934166,
-0.02902051992714405,
0.025853540748357773,
0.011417352594435215,
0.04434601962566376,
0.027697520330548286,
0.00009992525883717462,
-0.0019133153837174177,
0.02454504556953907,
-0.03472313657402992,
0.042581696063280106,
0.006717518903315067,
-0.023716997355222702,
0.024509776383638382,
-0.05975751951336861,
0.00784887932240963
] |
<p>Why do spinless fermions behave in the same way as weakly interacting bosons.</p> | g9218 | [
0.04320678859949112,
-0.03374040871858597,
0.031545720994472504,
-0.029894178733229637,
0.07812032103538513,
0.005042621865868568,
-0.003798878751695156,
0.03654581680893898,
0.025001520290970802,
-0.06131911277770996,
-0.030865902081131935,
0.036371488124132156,
-0.010740148834884167,
0.05771399289369583,
0.01942821592092514,
0.062413670122623444,
0.01034724060446024,
0.029507866129279137,
0.043968942016363144,
0.03809987008571625,
0.0010632878402248025,
-0.002626173896715045,
0.03380199149250984,
0.025343364104628563,
-0.03884812816977501,
-0.061983950436115265,
0.004883123561739922,
-0.0021790070459246635,
0.039115142077207565,
0.03720366954803467,
0.06817946583032608,
0.014329786412417889,
0.0391322486102581,
-0.035921599715948105,
0.01826559752225876,
-0.06024937331676483,
0.0930740088224411,
0.01523309201002121,
0.03884376212954521,
0.017839767038822174,
-0.023557964712381363,
-0.007091631647199392,
0.004064677748829126,
0.019712913781404495,
-0.017471397295594215,
0.012721776962280273,
0.03343268111348152,
0.004802269861102104,
-0.06751467287540436,
-0.027225930243730545,
-0.04355955496430397,
-0.02521182782948017,
-0.0021060958970338106,
0.03775526583194733,
0.03182701766490936,
-0.03506352752447128,
-0.006698500365018845,
-0.02231166511774063,
0.03936931490898132,
0.10495029389858246,
-0.017605144530534744,
-0.044092629104852676,
0.03498447686433792,
0.05580483376979828,
0.03188750147819519,
0.007037258706986904,
-0.015708019956946373,
0.01767325960099697,
0.05412726849317551,
0.001218794728629291,
-0.011672907508909702,
-0.023742517456412315,
-0.08120076358318329,
-0.038526058197021484,
0.018786609172821045,
0.04474854841828346,
-0.006430592853575945,
-0.032408710569143295,
-0.006615708116441965,
-0.0445600189268589,
-0.04720602184534073,
-0.07725793868303299,
-0.030278299003839493,
-0.015741854906082153,
0.06420907378196716,
-0.027577819302678108,
-0.018007351085543633,
-0.016949864104390144,
0.0014500413089990616,
0.02560713142156601,
0.03947274759411812,
-0.02603907324373722,
0.036116939038038254,
-0.03302488476037979,
-0.06526810675859451,
0.007404718082398176,
0.03252720460295677,
0.0077049401588737965,
-0.03637508302927017,
-0.06494186818599701,
-0.023024842143058777,
0.037483975291252136,
-0.011048863641917706,
-0.0038073475006967783,
0.005712849088013172,
-0.04716567322611809,
-0.015145688317716122,
0.029311683028936386,
0.007894263602793217,
-0.010045087896287441,
0.0025004076305776834,
0.014116931706666946,
-0.0012475424446165562,
0.008701981045305729,
-0.006854106672108173,
0.05238574743270874,
0.07911659777164459,
-0.034659694880247116,
0.07119965553283691,
0.035281337797641754,
-0.025099996477365494,
-0.033550847321748734,
0.007345262449234724,
0.019357191398739815,
-0.006351632531732321,
-0.05621952563524246,
0.036962393671274185,
-0.004183867014944553,
0.030205057933926582,
-0.02046123705804348,
-0.018396079540252686,
0.01808072067797184,
-0.012228377163410187,
0.0018905041506513953,
-0.018139617517590523,
0.06602198630571365,
-0.03018898516893387,
-0.031441934406757355,
0.04112965241074562,
0.008057982660830021,
-0.021878935396671295,
-0.030658207833766937,
0.010366187430918217,
-0.04309540614485741,
0.022060198709368706,
-0.027440179139375687,
0.007103686686605215,
-0.0527222715318203,
0.01684102788567543,
0.02567075937986374,
-0.001086032367311418,
0.05370150879025459,
0.02252935990691185,
0.00859109777957201,
-0.019645238295197487,
-0.012205509468913078,
0.08943277597427368,
-0.02966943010687828,
0.018315639346837997,
-0.01351820956915617,
0.03192930296063423,
-0.0279848575592041,
-0.002730461535975337,
-0.015550866723060608,
-0.08370411396026611,
-0.011047601699829102,
-0.0008843407267704606,
-0.03128010034561157,
0.009848549962043762,
-0.001049706363119185,
-0.05411999672651291,
-0.007500641513615847,
-0.05647154897451401,
0.07496589422225952,
0.03051506169140339,
0.03792104497551918,
-0.04178287088871002,
0.03850150480866432,
0.011827358044683933,
-0.01258306484669447,
-0.05605106055736542,
-0.01417478360235691,
0.007284512277692556,
-0.00547301210463047,
-0.008016112260520458,
0.029871584847569466,
-0.0014075422659516335,
0.009492522105574608,
0.006541167851537466,
-0.035825733095407486,
-0.002806225325912237,
-0.035224344581365585,
-0.009107565507292747,
0.008613869547843933,
-0.016282156109809875,
-0.016603639349341393,
-0.025495965033769608,
-0.02009967900812626,
-0.011302649043500423,
-0.0035917817149311304,
-0.027764927595853806,
-0.021743619814515114,
0.015523619018495083,
-0.011767352931201458,
-0.029533104971051216,
-0.036364831030368805,
0.0035735536366701126,
0.05801321566104889,
0.05845033377408981,
-0.020580343902111053,
0.000867231807205826,
0.03642961382865906,
-0.038703471422195435,
0.010068611241877079,
-0.03548770770430565,
0.025480428710579872,
-0.005678299814462662,
0.0002990387147292495,
-0.038939207792282104,
0.013279586099088192,
-0.020170612260699272,
-0.07558713853359222,
0.01910315454006195,
0.013741032220423222,
0.009126405231654644,
0.02244626358151436,
-0.050459831953048706,
0.0007575632771477103,
-0.005105909425765276,
0.0064152744598686695,
-0.011937274597585201,
-0.04151490703225136,
-0.028907760977745056,
0.00582131277769804,
-0.007587587460875511,
-0.01728784292936325,
0.01680161990225315,
0.007273024879395962,
0.00799794215708971,
0.025047143921256065,
0.008414740674197674,
0.010238749906420708,
-0.05811161920428276,
0.03791050240397453,
0.044701311737298965,
-0.0170050747692585,
-0.01645832322537899,
0.002249367767944932,
0.012773976661264896,
0.0252702459692955,
0.036305345594882965,
0.03651674464344978,
-0.03402600809931755,
0.0181749127805233,
-0.0066156103275716305,
0.022477058693766594,
-0.019587494432926178,
0.05850447714328766,
-0.053936004638671875,
-0.06248888000845909,
0.017979294061660767,
-0.028871964663267136,
0.0759156122803688,
0.04782111942768097,
0.008510676212608814,
0.022911474108695984,
0.016462573781609535,
0.012192923575639725,
0.006643264088779688,
0.025812692940235138,
-0.03196612745523453,
0.05359525978565216,
-0.02962041087448597,
-0.03673190996050835,
0.003135169390588999,
-0.003874007612466812,
-0.022661635652184486,
0.0647534430027008,
-0.0273119006305933,
-0.034950170665979385,
-0.0231898445636034,
-0.006832024082541466,
-0.0162072591483593,
-0.01718946546316147,
0.06189197674393654,
-0.05500781163573265,
-0.03572752699255943,
-0.05556989833712578,
-0.011891013011336327,
-0.03374943137168884,
-0.024201679974794388,
0.02463623136281967,
0.05056912824511528,
0.045228660106658936,
0.014910843223333359,
-0.006731398869305849,
-0.02539103850722313,
0.013418805785477161,
-0.04167093709111214,
0.09910143911838531,
0.012580376118421555,
-0.025706470012664795,
-0.00369567284360528,
-0.013204925693571568,
-0.02439568005502224,
-0.030959678813815117,
-0.05259883403778076,
-0.02142895571887493,
-0.10660695284605026,
-0.039465274661779404,
-0.04866744577884674,
0.03709055110812187,
0.006482260767370462,
0.04997136443853378,
-0.026729121804237366,
-0.013513533398509026,
-0.044666875153779984,
0.047064159065485,
0.0502813421189785,
-0.06300192326307297,
-0.0802876204252243,
0.019894873723387718,
0.011046817526221275,
-0.03862660378217697,
0.0015008468180894852,
-0.006013000383973122,
-0.004310060758143663,
-0.025504613295197487,
-0.04020201042294502,
0.05043413117527962,
-0.03299685940146446,
-0.004124618135392666,
0.008331897668540478,
-0.02709116041660309,
-0.0696808472275734,
-0.011854210868477821,
-0.044335223734378815,
0.03821450099349022,
-0.04141192510724068,
0.027843967080116272,
-0.01393346767872572,
-0.05201662331819534,
-0.06752970069646835,
0.03603670373558998,
-0.0428227037191391,
0.007713154889643192,
-0.01267183106392622,
-0.057371679693460464,
0.029627051204442978,
-0.0025261209812015295,
0.011724134907126427,
0.02998467907309532,
0.020555146038532257,
-0.027841705828905106,
0.006237601395696402,
-0.07337738573551178,
-0.00990372896194458,
0.02170293591916561,
0.07978112995624542,
0.0013742897426709533,
0.07379160076379776,
-0.00707740243524313,
-0.010619714856147766,
-0.010638347826898098,
-0.09020569175481796,
0.012547751888632774,
-0.00920451246201992,
-0.03879369795322418,
0.05258208140730858,
0.006059514824301004,
-0.009585665538907051,
-0.04796465486288071,
0.04288483411073685,
-0.011577339842915535,
0.030833708122372627,
-0.018104761838912964,
0.022578546777367592,
-0.026397868990898132,
-0.06052563339471817,
-0.02825246937572956,
0.062118347734212875,
-0.010044343769550323,
-0.007814568467438221,
0.06507192552089691,
0.0521533265709877,
0.052741676568984985,
0.019485486671328545,
0.034201014786958694,
-0.03072654828429222,
0.008970983326435089,
0.022163737565279007,
0.04704150930047035,
0.021547282114624977,
0.026090087369084358,
0.10111509263515472,
0.012412820011377335,
0.016541743651032448,
-0.02345232479274273,
0.014680512249469757,
0.04188064858317375,
-0.07131669670343399,
-0.013759504072368145,
-0.03187835216522217,
-0.035491943359375,
0.045392341911792755,
-0.010968751274049282,
-0.01230971235781908,
0.030350977554917336,
0.00568770244717598,
-0.01897730678319931,
-0.0023912680335342884,
0.08858678489923477,
0.03274580463767052,
-0.04432976245880127,
0.03926935791969299,
-0.017648110166192055,
0.015977436676621437,
-0.0009050329681485891,
-0.015196365304291248,
-0.03786879777908325,
0.03612819314002991,
-0.0003439781430643052,
-0.023934291675686836,
0.03100106306374073,
0.03241780027747154,
0.01588064804673195,
-0.024883687496185303,
0.03530823811888695,
-0.010517974384129047,
-0.029398996382951736,
-0.037584103643894196,
-0.011134841479361057,
-0.024488413706421852,
0.014213046990334988,
-0.06441386789083481,
-0.0018207067623734474,
-0.03573400154709816,
-0.005246056243777275,
0.056839145720005035,
0.09926673769950867,
-0.024454990401864052,
-0.03398739919066429,
-0.013759720139205456,
0.036389149725437164,
0.022871557623147964,
0.033746328204870224,
-0.04943499341607094,
-0.03349607437849045,
-0.01762404665350914,
-0.03036835975944996,
0.0014652492245659232,
0.018340658396482468,
-0.057416804134845734,
-0.0002133949164999649,
-0.0037021227180957794,
-0.021413305774331093,
-0.02823285013437271,
-0.019051875919103622,
0.04389021918177605,
-0.05754556134343147,
-0.04870209842920303,
0.001693706028163433,
-0.009227311238646507,
-0.016517439857125282,
-0.032660361379384995,
0.001288759522140026,
-0.03231952339410782,
-0.006936510559171438,
-0.04762917011976242,
-0.009833813644945621,
-0.007375423330813646,
0.0016138122882694006,
0.07235081493854523,
0.030523397028446198,
0.07185881584882736,
0.04033009335398674,
-0.0064851450733840466,
-0.03575446456670761,
0.02823195606470108,
0.0005136556574143469,
-0.020287781953811646,
-0.037455569952726364,
0.029962144792079926,
-0.03857268765568733,
-0.042528778314590454,
-0.008235414512455463,
-0.0004111249290872365,
0.018011583015322685,
0.0031090746633708477,
-0.014873876236379147,
0.020957324653863907,
-0.0039121368899941444,
-0.012097397819161415,
0.03572304919362068,
0.02931787446141243,
0.016635041683912277,
-0.01685776188969612,
-0.013404089957475662,
-0.01868310011923313,
0.04111608490347862,
-0.06116757541894913,
-0.03135586902499199,
-0.02338707447052002,
0.036228328943252563,
-0.013301619328558445,
0.05680079013109207,
0.08079949021339417,
-0.06310828030109406,
0.03012893721461296,
0.005639757961034775,
-0.0408889465034008,
-0.015221786685287952,
0.07012774050235748,
0.0632491409778595,
-0.07405070215463638,
0.03364727646112442,
0.01703060045838356,
0.026217147707939148,
-0.029606034979224205,
0.06054198741912842,
-0.014169251546263695,
0.009130267426371574,
-0.03176528960466385,
-0.012930705212056637,
0.024862147867679596,
-0.02540823630988598,
-0.012857401743531227,
0.005022694356739521,
-0.003186434041708708,
0.019273411482572556,
0.013385063968598843,
0.003830844769254327,
0.0843711793422699,
0.004578455816954374,
0.024302851408720016,
-0.034779392182826996,
0.014380439184606075,
0.012900494039058685,
-0.06400123983621597,
-0.036482684314250946,
0.02409639023244381,
-0.046393219381570816,
0.029550252482295036,
0.027432680130004883,
-0.0002181156596634537,
-0.02932218462228775,
-0.011262202635407448,
-0.02165338210761547,
0.02345733717083931,
-0.01463265996426344,
-0.05674297735095024,
0.09115596115589142,
-0.03250586986541748,
0.008169208653271198,
0.02728000096976757,
-0.027986299246549606,
0.005270959809422493,
0.015747034922242165,
0.06500859558582306,
-0.008460811339318752,
-0.0206482894718647,
-0.016327574849128723,
-0.018622159957885742,
0.07350175827741623,
0.0461711622774601,
0.021548908203840256,
-0.05088641494512558,
-0.010486423037946224,
0.004364609252661467,
0.013839184306561947,
-0.03412153199315071,
0.02837461791932583,
0.01931687630712986,
-0.010967431589961052,
-0.008440356701612473,
-0.019549435004591942,
-0.023676186800003052,
0.015030593611299992,
0.017243744805455208,
-0.016690878197550774,
0.04407547041773796,
0.029864568263292313,
0.024736011400818825,
-0.044629499316215515,
0.06411294639110565,
0.022328399121761322,
0.06350646167993546,
0.03592401370406151,
0.016380637884140015,
0.05872334539890289,
-0.005118993576616049,
0.04942021146416664,
-0.01641039177775383,
0.009480255655944347,
0.019279872998595238,
-0.013687320053577423,
-0.06652015447616577,
-0.04894992336630821,
-0.07483672350645065,
-0.09186195582151413,
0.008636045269668102,
0.0036315065808594227,
0.053752392530441284,
0.050636399537324905,
-0.01147201657295227,
0.024521498009562492,
-0.04493201524019241,
0.03183602914214134,
-0.029006456956267357,
0.08593915402889252,
-0.04990808293223381,
0.05724075436592102,
-0.011071007698774338,
-0.0536959245800972,
-0.005775495897978544,
-0.04319345951080322,
-0.01705939508974552,
-0.008615262806415558,
-0.035361114889383316,
-0.0006682836101390421,
-0.025546055287122726,
-0.06110638752579689,
-0.017341477796435356,
-0.10068488121032715,
0.04050735756754875,
0.021202437579631805,
0.005916124675422907,
0.020651670172810555,
0.0070886374451220036,
-0.01998095214366913,
-0.023802101612091064,
0.051612574607133865,
0.04488249123096466,
0.04456445574760437,
-0.03720308095216751,
-0.01407969556748867,
-0.06289910525083542,
-0.011098497547209263,
0.034164268523454666,
0.005906176753342152,
0.007292400114238262,
0.029254930093884468,
0.0033393504563719034,
0.06926624476909637,
-0.046569667756557465,
0.07847215980291367,
0.015780247747898102,
0.0005845949053764343,
-0.057184718549251556,
0.009538392536342144,
0.008961641229689121,
-0.031408537179231644,
0.0237776730209589,
0.005558543838560581,
-0.031023720279335976,
-0.0518859438598156,
-0.0019202176481485367,
0.046691276133060455,
0.07516857236623764,
0.00910133682191372,
-0.10628415644168854,
0.05433328077197075,
-0.04893698915839195,
-0.017793506383895874,
0.032139457762241364,
0.04239027202129364,
-0.004530915524810553,
0.023329325020313263,
0.053940415382385254,
0.005120422225445509,
-0.048794638365507126,
-0.036606766283512115,
-0.05412543565034866,
0.011721569113433361,
-0.02175641432404518,
-0.03605830296874046,
-0.018746957182884216,
-0.009160480462014675,
0.03380946069955826,
0.003151652868837118,
0.00589589960873127,
0.041844118386507034,
0.02179046906530857,
0.011852961964905262,
0.0033536325208842754,
0.06368560343980789,
0.03204594925045967,
0.03255079314112663,
0.0004561097885016352,
0.018928389996290207,
0.008330601267516613,
0.013162175193428993,
0.05308358371257782,
-0.010482178069651127,
-0.052014581859111786,
-0.005772600881755352,
-0.017391810193657875,
-0.010101997293531895,
-0.005998897831887007,
-0.013730691745877266,
0.03031444363296032,
0.01771502196788788,
-0.027023153379559517,
-0.030558675527572632,
0.07438260316848755,
0.01809513382613659,
0.008293251506984234,
-0.00930238887667656,
-0.06533680856227875,
-0.0040224879048764706,
0.026702508330345154,
0.017098775133490562,
0.04140284284949303,
0.06914807111024857,
0.007432436104863882,
0.01376955583691597,
0.011870334856212139,
-0.003031481057405472,
0.01686537079513073,
0.005702910479158163,
0.05397174507379532,
-0.08678773045539856,
-0.0317966528236866,
-0.014977199956774712,
-0.015697689726948738,
-0.044161438941955566,
0.030306821689009666,
0.00903240591287613,
0.057363033294677734,
0.06623375415802002,
-0.017170019447803497,
-0.010171595960855484,
-0.07762353122234344,
0.018824126571416855,
-0.04190194606781006,
0.02269131876528263,
0.017268503084778786,
0.03535778447985649,
-0.031991779804229736,
-0.04097754508256912,
0.01704266667366028,
0.003629491198807955,
-0.011201513931155205,
0.004977140109986067,
-0.029165685176849365,
0.011634648777544498,
-0.002321814652532339,
-0.05160025879740715,
0.05211513116955757,
-0.01893242634832859,
-0.039328157901763916,
0.013375447131693363,
0.001267152139917016,
0.10100223124027252,
0.017139771953225136,
-0.04954763874411583,
-0.026941275224089622,
0.028197458013892174,
-0.005878143943846226,
-0.0011789709096774459,
0.02320832572877407,
-0.015689199790358543,
-0.05301498994231224,
0.031488966196775436,
-0.05394949018955231,
-0.01495114155113697,
-0.02625175006687641,
0.034453894942998886
] |
<p>Would we all parish due to excessive heat? Or would that be only limited to the area near the impact while as the people on rest of the earth would die from other phenomenons such as mega earthquakes, volcanic activities, tsunamis etc. Does it matter where the impact is - if it landed in antarctica we would have massive floods but if it landed in the middle of eurasian continent, the effect would be different? </p> | g9219 | [
0.08480577915906906,
0.016532564535737038,
0.031412672251462936,
0.021863814443349838,
-0.011910277418792248,
0.050291940569877625,
-0.029981235042214394,
0.06264841556549072,
0.005844310857355595,
-0.051531821489334106,
0.05069708451628685,
-0.0004995398339815438,
0.04405480995774269,
0.00030802495894022286,
0.004964280407875776,
-0.015338186174631119,
0.025889672338962555,
0.00014811987057328224,
0.00568549195304513,
0.08157134056091309,
-0.08008456975221634,
-0.039124149829149246,
-0.004473671317100525,
0.0004804824711754918,
-0.08803404867649078,
-0.012005455791950226,
0.027687478810548782,
-0.015043954364955425,
-0.01838960126042366,
-0.013641740195453167,
0.0038870670832693577,
-0.02225428633391857,
-0.017627403140068054,
-0.0721634104847908,
-0.03751521185040474,
0.009788895957171917,
-0.057866159826517105,
-0.002916731871664524,
0.044930070638656616,
-0.006723129190504551,
-0.007970734499394894,
-0.03879501298069954,
-0.010142842307686806,
0.029845021665096283,
-0.0292894896119833,
0.00006011445293552242,
-0.032637931406497955,
-0.014756202697753906,
-0.003093068953603506,
-0.021184228360652924,
-0.034940917044878006,
-0.022498397156596184,
-0.029941672459244728,
0.011584077961742878,
0.046473558992147446,
0.013974432833492756,
0.04790021479129791,
0.02923514135181904,
0.0006182888755574822,
0.003673032857477665,
0.0082703260704875,
0.03837230056524277,
0.029912475496530533,
-0.00354769011028111,
-0.004543410148471594,
-0.02864678017795086,
-0.06111132726073265,
0.01749485544860363,
0.053278498351573944,
-0.0014141281135380268,
0.01878320798277855,
-0.031286537647247314,
-0.033014386892318726,
-0.06398947536945343,
-0.0006412753718905151,
0.0495319627225399,
0.008820910006761551,
0.02560480497777462,
0.05765506252646446,
0.006659356877207756,
-0.007688899524509907,
-0.003040340496227145,
0.0481005534529686,
-0.03417192026972771,
0.04501999169588089,
-0.08367033302783966,
0.020510312169790268,
-0.027999775484204292,
-0.022924110293388367,
-0.027093779295682907,
0.020795835182070732,
-0.014834376983344555,
0.045613765716552734,
0.049190688878297806,
0.01993432454764843,
-0.02632988430559635,
0.06203402951359749,
0.007744129281491041,
0.00695735914632678,
-0.022362936288118362,
-0.03555254265666008,
-0.029000798240303993,
0.032717909663915634,
-0.009979167021811008,
-0.012126456946134567,
-0.04078110307455063,
-0.011659260839223862,
-0.0010653886711224914,
0.01841099001467228,
-0.04906076565384865,
0.03786057233810425,
-0.04058527573943138,
-0.01276437472552061,
0.01970844715833664,
0.016476601362228394,
-0.0068227509036660194,
0.04211213439702988,
0.014323686249554157,
-0.034211236983537674,
0.07552063465118408,
0.016378045082092285,
-0.05012109875679016,
-0.015015549957752228,
0.0655563622713089,
-0.03484692424535751,
-0.02726837620139122,
-0.011521797627210617,
-0.006917320191860199,
0.041887037456035614,
-0.029715782031416893,
0.010850245133042336,
-0.013196004554629326,
0.003496861318126321,
0.05428359657526016,
0.04745256528258324,
-0.028914744034409523,
-0.03623482957482338,
0.030052945017814636,
0.01492596510797739,
0.029780641198158264,
-0.04013479873538017,
0.07414489984512329,
-0.027455521747469902,
0.030663635581731796,
-0.04335060715675354,
0.020333290100097656,
-0.030052218586206436,
0.0442073792219162,
-0.024212928488850594,
0.03932486101984978,
-0.004787800833582878,
-0.06632582098245621,
0.02411225438117981,
0.040006887167692184,
0.03139388933777809,
-0.00930930394679308,
-0.06400156766176224,
0.03971417248249054,
-0.02054744027554989,
-0.004767501726746559,
-0.02290867641568184,
0.013573088683187962,
-0.009319682605564594,
0.0037294647190719843,
-0.04903054237365723,
-0.007355295587331057,
0.024421248584985733,
-0.022171147167682648,
0.009277929551899433,
0.027695976197719574,
-0.01398635096848011,
-0.020555710420012474,
-0.04754435643553734,
-0.008270160295069218,
-0.019327696412801743,
0.000959535944275558,
0.00425599655136466,
0.0018772410694509745,
0.034985434263944626,
-0.025035278871655464,
0.01820429600775242,
-0.0490843839943409,
-0.012076129205524921,
-0.02781522460281849,
0.032950978726148605,
-0.023140519857406616,
0.0632488802075386,
0.03316990286111832,
-0.000976885436102748,
0.00382608431391418,
-0.02765139378607273,
-0.05812573805451393,
0.01617320254445076,
-0.022090189158916473,
0.01816936396062374,
-0.007787540089339018,
0.0010926993563771248,
0.0052178604528307915,
-0.041160836815834045,
0.020403055474162102,
0.010308334603905678,
0.032578058540821075,
0.04546010494232178,
-0.02444654516875744,
-0.019140193238854408,
0.04019368439912796,
-0.000018669566998141818,
0.01897509954869747,
0.015233851037919521,
-0.097282275557518,
0.01731608621776104,
-0.051163945347070694,
0.004002707079052925,
0.05314122140407562,
-0.019011368975043297,
-0.008087530732154846,
-0.05034257844090462,
0.013594870455563068,
-0.01630234345793724,
-0.01733555644750595,
0.02302371710538864,
0.056657176464796066,
-0.0877813994884491,
-0.003202718449756503,
0.022089054808020592,
0.026632260531187057,
-0.07285977900028229,
-0.05846255645155907,
0.012737350538372993,
-0.01525676716119051,
-0.027917765080928802,
0.011116600595414639,
0.023981226608157158,
-0.026901423931121826,
-0.0648730993270874,
0.001484678010456264,
0.01862342283129692,
-0.04801587387919426,
-0.005669696256518364,
0.03605025261640549,
-0.030682694166898727,
-0.05592488870024681,
0.05502210557460785,
-0.024550333619117737,
0.015315075404942036,
-0.07785818725824356,
-0.003667976474389434,
-0.00790950283408165,
0.015808340162038803,
-0.03216951712965965,
-0.03248493745923042,
-0.009704051539301872,
-0.06533531099557877,
-0.03527119383215904,
0.03846360743045807,
-0.04146278277039528,
-0.02555187977850437,
0.04246361181139946,
0.005599851254373789,
0.031601034104824066,
-0.03970450907945633,
0.0029374752193689346,
-0.004800836089998484,
0.012543966062366962,
-0.0572294257581234,
0.07917101681232452,
0.02778055891394615,
0.026492802426218987,
-0.010868498124182224,
0.004238007124513388,
0.011237808503210545,
0.012488561682403088,
-0.04450515657663345,
0.09163031727075577,
-0.009557169862091541,
-0.03464539349079132,
-0.021849192678928375,
-0.035635776817798615,
-0.001160468440502882,
-0.01796257309615612,
0.044978752732276917,
0.058247581124305725,
0.06145497038960457,
-0.03957463428378105,
0.02658851444721222,
-0.079483762383461,
0.004868140444159508,
0.06291648000478745,
0.02026176080107689,
0.0014954835642129183,
0.019551530480384827,
-0.04064558818936348,
0.02612527646124363,
0.010988464578986168,
0.04470845311880112,
0.057189907878637314,
-0.02998938411474228,
-0.03326881304383278,
-0.022902779281139374,
-0.02433292753994465,
0.05454500392079353,
-0.0360301174223423,
0.03256945312023163,
0.008870219811797142,
-0.06466636061668396,
-0.02156928926706314,
0.020416291430592537,
-0.027981197461485863,
-0.04464370384812355,
-0.05777691677212715,
-0.008798000402748585,
0.08071643859148026,
-0.012040072120726109,
0.06529834121465683,
-0.05502655357122421,
0.007841083221137524,
0.006755901966243982,
0.018910324200987816,
0.05538719519972801,
0.001663197297602892,
-0.018653767183423042,
-0.039136264473199844,
0.009263020008802414,
0.037193141877651215,
-0.0334930345416069,
0.07040777802467346,
-0.042809586971998215,
-0.00904444046318531,
-0.04527394101023674,
-0.00045919077820144594,
-0.03999870643019676,
-0.010969642549753189,
-0.03140553459525108,
0.0006495856214314699,
-0.06254985183477402,
0.017867829650640488,
0.029095511883497238,
0.007007436826825142,
0.03867041692137718,
0.07012751698493958,
0.01832907274365425,
-0.033701200038194656,
0.003962245304137468,
-0.0697539746761322,
-0.010359462350606918,
0.024159226566553116,
0.03039485029876232,
-0.024582067504525185,
-0.0048896800726652145,
0.016175050288438797,
0.06260894984006882,
-0.06964544951915741,
-0.025133341550827026,
0.01487225852906704,
0.021677223965525627,
0.03101036325097084,
0.045741792768239975,
-0.00019097051699645817,
-0.022942304611206055,
0.004490992520004511,
-0.018676789477467537,
0.0008524105069227517,
-0.011947819963097572,
-0.04291573166847229,
0.03929687291383743,
0.04007658362388611,
-0.020052507519721985,
-0.05534978210926056,
-0.030114108696579933,
0.03874598443508148,
0.06568729877471924,
0.016987571492791176,
-0.09006483107805252,
0.033561572432518005,
0.06296879053115845,
0.03818965330719948,
0.07722049206495285,
0.02726133167743683,
-0.05059130862355232,
-0.001554257469251752,
0.013482045382261276,
-0.052055563777685165,
0.04933072254061699,
-0.043898433446884155,
0.018043555319309235,
-0.019353292882442474,
-0.02488378994166851,
0.01302282977849245,
-0.05900751054286957,
-0.003825125051662326,
-0.004287075717002153,
-0.07123866677284241,
0.047229308634996414,
0.06783735752105713,
0.029736004769802094,
-0.007327888160943985,
0.017257219180464745,
0.01021744217723608,
0.032940153032541275,
0.0076179043389856815,
0.023414433002471924,
-0.02549484558403492,
0.07264082878828049,
-0.003325200639665127,
0.0006462549208663404,
-0.057921841740608215,
0.02922852523624897,
0.0005837707431055605,
-0.050223805010318756,
0.006182636134326458,
0.03654332458972931,
0.037254903465509415,
0.010824604891240597,
-0.06252370774745941,
0.060272201895713806,
0.06847109645605087,
0.007361130323261023,
0.014485176652669907,
0.006463790312409401,
0.022500401362776756,
0.041345592588186264,
-0.022427089512348175,
-0.02363375760614872,
-0.03840562328696251,
-0.006895459722727537,
-0.02034084126353264,
0.024165231734514236,
-0.05402156710624695,
0.016242317855358124,
0.019220519810914993,
-0.08533822745084763,
0.06504883617162704,
-0.030257893726229668,
0.045236825942993164,
0.044764239341020584,
-0.0010625736322253942,
-0.012998086400330067,
-0.07943444699048996,
0.04745076596736908,
-0.01948743872344494,
0.03709603101015091,
-0.010747566819190979,
-0.02474343217909336,
0.05929972976446152,
-0.017667576670646667,
0.10467388480901718,
0.06846010684967041,
-0.06270966678857803,
0.016180837526917458,
-0.04640292748808861,
-0.06957896798849106,
-0.03382956236600876,
-0.030028188601136208,
0.016400987282395363,
-0.013970126397907734,
-0.005264388397336006,
0.017610494047403336,
0.025285283103585243,
0.011951959691941738,
0.08170682191848755,
-0.05569232627749443,
-0.016526445746421814,
0.010089739225804806,
0.013163491152226925,
0.0014370472636073828,
-0.034398119896650314,
0.012356778606772423,
-0.028156504034996033,
-0.06134868040680885,
0.0331132635474205,
-0.002408432774245739,
0.02342095784842968,
-0.005465339869260788,
0.029712971299886703,
0.012543880380690098,
0.0637611448764801,
-0.03838207200169563,
-0.07463230937719345,
0.00395203148946166,
-0.07843223959207535,
0.009070903062820435,
-0.0371810719370842,
-0.020893899723887444,
-0.0005977653781883419,
-0.022586559876799583,
0.012679792940616608,
-0.058733802288770676,
0.007801095023751259,
0.024556996300816536,
-0.014960482716560364,
-0.005462272558361292,
0.004390344955027103,
-0.01014723815023899,
0.005994703620672226,
-0.026158297434449196,
-0.003294806694611907,
-0.0064712525345385075,
-0.02117263898253441,
0.01285533607006073,
-0.009084477089345455,
0.011983657255768776,
-0.004837956745177507,
0.02069159969687462,
0.017864562571048737,
-0.02437320351600647,
0.00417801970615983,
0.06508538126945496,
0.030466705560684204,
0.03885715454816818,
0.04806322231888771,
-0.034368958324193954,
0.020852889865636826,
-0.03275631368160248,
-0.019156809896230698,
0.024011489003896713,
0.04580744728446007,
0.008244226686656475,
0.025069858878850937,
0.013727117329835892,
-0.05056241527199745,
-0.010164128616452217,
-0.03810973837971687,
0.025934556499123573,
0.061659976840019226,
0.031098639592528343,
-0.04928424209356308,
-0.00360096525400877,
-0.07981479912996292,
-0.04581471160054207,
0.01310508418828249,
0.009263972751796246,
-0.016067277640104294,
0.028907766565680504,
0.03039606474339962,
0.0314827561378479,
-0.060026802122592926,
-0.026104632765054703,
0.03035983443260193,
0.12192714214324951,
-0.006613472942262888,
0.009053871035575867,
-0.037352077662944794,
0.05597392097115517,
0.037174757570028305,
-0.003264361759647727,
0.012007487937808037,
-0.007752234116196632,
0.027489934116601944,
0.0028962998185306787,
-0.008611558936536312,
0.007355306297540665,
0.05603143945336342,
0.02900136262178421,
0.01656750775873661,
-0.04975178465247154,
0.04372817650437355,
0.003231833456084132,
0.03842279314994812,
-0.010689213871955872,
-0.03420623391866684,
0.02218981832265854,
-0.013308195397257805,
-0.012254677712917328,
0.0008896373328752816,
-0.015964871272444725,
-0.007110923063009977,
-0.021550392732024193,
-0.048659276217222214,
0.040543362498283386,
-0.01796000450849533,
0.0674794390797615,
-0.07236670702695847,
0.0013345457846298814,
-0.08333524316549301,
0.02331923507153988,
0.01927707903087139,
0.023653069511055946,
-0.01804894022643566,
0.005825006403028965,
-0.007181752938777208,
0.022277820855379105,
-0.06004895269870758,
0.027335043996572495,
0.010329634882509708,
0.05125582590699196,
0.01157607976347208,
-0.020889250561594963,
0.052897993475198746,
0.07291704416275024,
0.04609350860118866,
-0.026376914232969284,
-0.02424103207886219,
-0.01419774442911148,
0.0281252171844244,
-0.045594651252031326,
-0.04846685379743576,
0.009005285799503326,
-0.025286689400672913,
-0.0398273803293705,
-0.01071484386920929,
0.0418967641890049,
-0.011231586337089539,
0.054197732359170914,
0.0005065807490609586,
-0.03085498698055744,
0.043899908661842346,
0.09269071370363235,
-0.0425027534365654,
0.028092918917536736,
0.0236322283744812,
0.010724388994276524,
0.03855995461344719,
-0.018532225862145424,
-0.013964403420686722,
0.02353813126683235,
-0.05413857102394104,
-0.05867466330528259,
-0.05272815003991127,
0.02913413755595684,
-0.010232101194560528,
-0.0295390784740448,
-0.011410239152610302,
-0.033512476831674576,
-0.01937434822320938,
-0.04708694666624069,
0.020104549825191498,
-0.034307606518268585,
0.0762215331196785,
0.037213101983070374,
0.014817126095294952,
0.019972780719399452,
0.013501843437552452,
0.017712045460939407,
0.019353322684764862,
0.0008230202365666628,
0.05242113023996353,
-0.005161445587873459,
-0.04457750543951988,
-0.0034907932858914137,
-0.01957201585173607,
-0.004188882652670145,
-0.013390757143497467,
-0.020223716273903847,
-0.017270369455218315,
-0.033798947930336,
-0.013409154489636421,
-0.003058176953345537,
-0.06129208207130432,
-0.010179213248193264,
-0.005622182972729206,
-0.03755631670355797,
-0.03781944513320923,
-0.0069986749440431595,
0.01572384685277939,
0.01529257744550705,
-0.010828590951859951,
-0.026634659618139267,
0.07793687283992767,
0.01816195622086525,
0.009217587299644947,
0.017658114433288574,
0.015116757713258266,
-0.035438086837530136,
0.059320442378520966,
0.004917413927614689,
0.018522804602980614,
0.045543868094682693,
-0.0938238725066185,
0.059496451169252396,
0.02282608114182949,
-0.03596247360110283,
-0.001907892874442041,
0.017127685248851776,
0.001481866231188178,
-0.04365453124046326,
-0.0037792904768139124,
0.00870103295892477,
-0.013803274370729923,
0.008045820519328117,
0.09422551095485687,
0.04595901444554329,
-0.04096164554357529,
-0.0037703372072428465,
-0.04789804667234421,
-0.0011226641945540905,
-0.043916504830121994,
0.028681933879852295,
0.08155251294374466,
0.02633887529373169,
-0.008140608668327332,
-0.010863307863473892,
0.01787608303129673,
0.011079640127718449,
-0.05768377333879471,
0.003675714833661914,
0.01021431665867567,
-0.007315695285797119,
-0.044015686959028244,
0.03069504350423813,
-0.039705414324998856,
-0.025059355422854424,
0.012913637794554234,
0.0937565267086029,
-0.039097171276807785,
0.05538197234272957,
0.027715926989912987,
-0.014540402218699455,
0.029827052727341652,
-0.017928648740053177,
-0.030581457540392876,
0.080723337829113,
0.05850960686802864,
0.05698307603597641,
0.042269229888916016,
0.0002286304661538452,
0.01920480839908123,
0.005986287258565426,
-0.04428612068295479,
-0.012453732080757618,
0.010565712116658688,
-0.027585383504629135,
-0.02102496474981308,
-0.03603625297546387,
-0.07405684143304825,
-0.015938948839902878,
0.03528520464897156,
-0.010482795536518097,
-0.07803650945425034,
0.029185986146330833,
-0.03041994385421276,
0.01818886585533619,
0.01433198619633913,
-0.007924268953502178,
0.02396419644355774,
0.01621289737522602,
0.028110982850193977,
0.010724828578531742,
-0.001093982602469623,
-0.01063640508800745,
-0.03405502438545227,
-0.0628310889005661,
-0.00881164614111185,
-0.010708344168961048,
0.016043037176132202,
-0.003886445192620158,
-0.006272721104323864,
0.0039925482124090195,
-0.037203557789325714,
-0.0051437076181173325,
-0.047317858785390854,
0.023984532803297043,
-0.02598615176975727,
-0.055012889206409454,
-0.012934062629938126,
0.0019021091284230351,
0.023166349157691002,
0.01128796860575676,
0.009547739289700985,
0.0056427898816764355,
-0.020755628123879433,
-0.003677473170682788,
-0.03650377690792084,
-0.0009708232246339321,
-0.014697152189910412,
0.03824231028556824,
-0.024640677496790886,
0.0005870396271348,
-0.0307733416557312
] |
<p>I would like to know the ballistic device characteristics and illustrations (if any) to understand how can we overcome the dependence of current on carrier mobility .</p> | g9220 | [
-0.012747468426823616,
-0.01117610838264227,
0.0072130803018808365,
0.040629755705595016,
0.08609993010759354,
0.012249908410012722,
0.027052367106080055,
-0.0336814746260643,
0.04027271270751953,
0.0071060326881706715,
-0.05713777616620064,
0.09454281628131866,
-0.01410928089171648,
0.03327365219593048,
0.036577291786670685,
-0.059463415294885635,
-0.0007396528380922973,
0.008117439225316048,
0.08102325350046158,
0.061492472887039185,
-0.004947238601744175,
0.03771166503429413,
-0.030812371522188187,
-0.0024349805898964405,
-0.00747338542714715,
0.016325747594237328,
0.047914355993270874,
-0.019062355160713196,
-0.03723732754588127,
-0.01775873452425003,
0.021607691422104836,
-0.06711719930171967,
-0.027260296046733856,
-0.022580046206712723,
-0.061510372906923294,
0.0059197889640927315,
-0.04291410371661186,
-0.03211361914873123,
-0.00398636981844902,
0.058467667549848557,
0.006512094289064407,
-0.06101759150624275,
-0.012538367882370949,
0.008010772988200188,
0.03139016032218933,
0.044011764228343964,
0.04626940190792084,
-0.069026418030262,
-0.006039488594979048,
-0.03241259604692459,
-0.09047496318817139,
0.01204624678939581,
0.031779445707798004,
-0.04277922585606575,
0.00009836887329583988,
-0.05057928338646889,
-0.06899632513523102,
0.052238862961530685,
-0.008310488425195217,
-0.08744222670793533,
-0.0583316832780838,
0.004667971283197403,
-0.02736794948577881,
0.015747059136629105,
0.03136265277862549,
-0.06508392095565796,
-0.0658014565706253,
-0.00519813084974885,
-0.017997970804572105,
0.03887660801410675,
0.02615385130047798,
-0.03258232772350311,
-0.07575775682926178,
-0.04568322375416756,
0.07118437439203262,
0.02049640752375126,
-0.020832479000091553,
-0.028821291401982307,
0.021670246496796608,
0.003181703621521592,
-0.015431279316544533,
-0.02204882726073265,
-0.012854620814323425,
-0.02752836048603058,
0.02348622865974903,
-0.02526162937283516,
0.01701114885509014,
0.04609997570514679,
0.05297422409057617,
-0.010480141267180443,
-0.014911091886460781,
0.028206253424286842,
0.02499988302588463,
0.014551873318850994,
0.04662717878818512,
0.0409817211329937,
-0.0006720913806930184,
0.025715649127960205,
0.022984515875577927,
-0.009732984006404877,
0.05234186723828316,
-0.04154072701931,
0.04913565143942833,
0.03418812155723572,
-0.047182679176330566,
0.034967854619026184,
0.032877303659915924,
-0.027074428275227547,
0.013704206794500351,
0.02091701701283455,
-0.03490506485104561,
-0.05705539137125015,
-0.04585779458284378,
0.018976572901010513,
0.04338480904698372,
0.005426500458270311,
-0.03282291814684868,
0.027614889666438103,
-0.04789222776889801,
0.013332964852452278,
0.0003999027539975941,
-0.002863015979528427,
-0.0509113110601902,
-0.06192084029316902,
0.004841737449169159,
0.027318378910422325,
-0.021046996116638184,
-0.00828136969357729,
-0.010909435339272022,
0.015049178153276443,
0.03716414421796799,
0.012810221873223782,
-0.010875695385038853,
0.021392060443758965,
-0.019016608595848083,
-0.017950115725398064,
0.0010797055438160896,
-0.05150682106614113,
-0.001484427833929658,
-0.010866514407098293,
0.02074306085705757,
-0.030161159113049507,
-0.005876859184354544,
0.03143201768398285,
0.04800582304596901,
-0.01026612427085638,
-0.03390328213572502,
-0.0010387577349320054,
0.04851623624563217,
0.05435224995017052,
0.03323705494403839,
0.03246453031897545,
-0.02885366417467594,
0.022959662601351738,
0.01373863685876131,
-0.014114759862422943,
0.13787566125392914,
0.011465547606348991,
0.0018299419898539782,
0.02037692628800869,
-0.034038349986076355,
-0.017223386093974113,
-0.016278522089123726,
0.05015096440911293,
-0.026225613430142403,
-0.04836103692650795,
-0.0029053830076009035,
0.05100560188293457,
0.05269409716129303,
-0.01653018593788147,
-0.045513372868299484,
-0.005465833004564047,
0.01850776933133602,
0.06740881502628326,
0.003519357880577445,
0.017153145745396614,
0.021564403548836708,
-0.03811492398381233,
0.03203609958291054,
-0.006495518609881401,
-0.058189403265714645,
0.023352917283773422,
-0.03005749173462391,
-0.008998827077448368,
-0.02267725206911564,
0.045680783689022064,
-0.02088436298072338,
0.029112983494997025,
0.014554155990481377,
-0.003268452128395438,
-0.028755901381373405,
-0.062101300805807114,
-0.06851357966661453,
-0.009657795540988445,
-0.026083409786224365,
-0.05612378939986229,
0.045153941959142685,
-0.0187761802226305,
0.05630749091506004,
-0.08400454372167587,
-0.03476281464099884,
0.02429603785276413,
0.059480730444192886,
0.02739335596561432,
0.07620315998792648,
-0.06105915084481239,
-0.025963563472032547,
0.010120396502315998,
0.009471744298934937,
0.016359444707632065,
0.008242408744990826,
-0.0012740861857309937,
0.0008526089950464666,
-0.014644411392509937,
0.0019492991268634796,
-0.036095112562179565,
-0.0222429521381855,
0.02507692389190197,
-0.011804729700088501,
-0.03405826538801193,
0.03654938563704491,
-0.0027484018355607986,
0.014877070672810078,
0.021028153598308563,
-0.06600531935691833,
0.01861617900431156,
0.012895775027573109,
0.021175595000386238,
0.0064969537779688835,
0.01558692753314972,
-0.05143681541085243,
-0.018427714705467224,
0.04114484786987305,
-0.010149502195417881,
0.041412658989429474,
0.03692218288779259,
0.060270942747592926,
-0.004593085031956434,
-0.028890687972307205,
0.031361065804958344,
0.027037890627980232,
-0.046447113156318665,
-0.008544939570128918,
0.018873240798711777,
0.007074642926454544,
-0.04866563901305199,
-0.015637902542948723,
0.06015220656991005,
0.00012023897579638287,
0.005085584707558155,
0.00579901272431016,
-0.0418163500726223,
-0.031478457152843475,
0.0185208972543478,
-0.03446067124605179,
-0.037959303706884384,
0.04348505660891533,
-0.00983268953859806,
0.0008328573312610388,
-0.029812151566147804,
-0.06152359023690224,
-0.022523779422044754,
-0.03277716040611267,
0.02225329726934433,
-0.017749354243278503,
0.02717193402349949,
0.021715005859732628,
-0.07152671366930008,
0.05023949593305588,
0.051431991159915924,
-0.017338646575808525,
0.02772579714655876,
0.013651549816131592,
-0.00868305191397667,
0.0017521589761599898,
0.0006716159405186772,
0.02302643656730652,
0.006641693413257599,
0.011190318502485752,
-0.0018544753547757864,
0.048437584191560745,
-0.022577065974473953,
-0.02442503720521927,
-0.009827923960983753,
-0.01575983688235283,
-0.03267043083906174,
0.027056138962507248,
0.007198008708655834,
0.022843031212687492,
-0.014113439247012138,
-0.007186484523117542,
-0.03312797099351883,
-0.016422582790255547,
0.0024249267298728228,
0.020566804334521294,
0.00013194992789067328,
0.0641765370965004,
-0.024873653426766396,
0.05214959755539894,
0.0019652063492685556,
0.024435941129922867,
-0.0038266764022409916,
0.026069844141602516,
-0.0018891976214945316,
-0.0314796157181263,
0.009425904601812363,
0.0005789371207356453,
-0.05588275194168091,
0.014558140188455582,
-0.021349482238292694,
-0.03697071596980095,
0.052033841609954834,
0.015057409182190895,
-0.005903318990021944,
-0.060918956995010376,
-0.019482232630252838,
-0.002530666533857584,
0.06268063932657242,
0.017616525292396545,
0.05284472182393074,
-0.023799581453204155,
-0.07389173656702042,
0.03883569315075874,
0.00017924525309354067,
0.025327133014798164,
0.056682195514440536,
0.015941955149173737,
0.007530610542744398,
0.05432813987135887,
0.00132231623865664,
0.04090859368443489,
0.04773817956447601,
0.03816362842917442,
-0.0005792467854917049,
-0.005242711398750544,
-0.03341403976082802,
0.03567119687795639,
0.08107171207666397,
-0.011778714135289192,
0.03530140593647957,
0.0027076920960098505,
-0.03529377281665802,
-0.052472054958343506,
-0.006776438094675541,
-0.057607557624578476,
-0.012278185226023197,
0.0038731563836336136,
0.007274530827999115,
0.015222862362861633,
-0.030478453263640404,
0.07287701964378357,
0.007938582450151443,
0.002142219804227352,
0.018382634967565536,
-0.041749585419893265,
0.02645086497068405,
-0.010026220232248306,
0.07139933109283447,
-0.030993347987532616,
0.05597879737615585,
-0.014257987029850483,
0.008635811507701874,
0.03634114935994148,
0.07651291787624359,
0.019081655889749527,
0.005601624492555857,
-0.007727690972387791,
0.037935927510261536,
0.016251593828201294,
-0.021833868697285652,
-0.050187848508358,
-0.04846314340829849,
-0.029808571562170982,
-0.008927073329687119,
0.00679938867688179,
0.05754702538251877,
0.009342878125607967,
0.008720873855054379,
-0.09151264280080795,
-0.007551995571702719,
-0.002779959701001644,
-0.03123818151652813,
0.03702158108353615,
0.03462955728173256,
-0.020269939675927162,
0.0035260918084532022,
-0.02793065458536148,
0.01890394277870655,
-0.08890879899263382,
-0.016780497506260872,
0.01462392695248127,
-0.019283894449472427,
-0.02382776513695717,
-0.027351561933755875,
0.02419745922088623,
-0.005231853574514389,
-0.012778060510754585,
-0.02645239420235157,
0.013686282560229301,
0.010904837399721146,
0.06046279892325401,
0.09468001127243042,
-0.007996480911970139,
-0.01775098778307438,
-0.007575862109661102,
-0.03729370981454849,
-0.01956300437450409,
-0.01660342328250408,
-0.020360656082630157,
-0.03306354582309723,
-0.03804420679807663,
-0.01941816881299019,
-0.06277760863304138,
0.0065408614464104176,
-0.008096644654870033,
0.020597385242581367,
0.01171417348086834,
0.049415770918130875,
-0.008059621788561344,
-0.050364166498184204,
0.008526132442057133,
0.027165215462446213,
0.013135126791894436,
-0.027670912444591522,
0.035059452056884766,
0.013084325939416885,
0.0363030843436718,
-0.017696425318717957,
0.057917963713407516,
0.08255276829004288,
-0.011651880107820034,
-0.05414268374443054,
-0.020630531013011932,
0.037845954298973083,
-0.001507230568677187,
0.020303776487708092,
0.02958577126264572,
0.021545857191085815,
0.01661098189651966,
0.05053582787513733,
0.028361540287733078,
-0.03925250843167305,
-0.04173903912305832,
-0.04592256247997284,
0.005061481613665819,
0.07787850499153137,
-0.07479225844144821,
0.009994993917644024,
0.041936345398426056,
0.025476515293121338,
0.006585231050848961,
-0.014166608452796936,
-0.03171657770872116,
-0.013775821775197983,
-0.033882927149534225,
0.037225838750600815,
-0.022562768310308456,
-0.07039520889520645,
0.06169779226183891,
-0.009435420855879784,
-0.05984625592827797,
0.03956922888755798,
0.007028885185718536,
0.02383510209619999,
-0.05381112918257713,
-0.037971481680870056,
0.0446520633995533,
-0.026226025074720383,
-0.04310113564133644,
0.0012942873872816563,
-0.05767640098929405,
0.019998472183942795,
0.004620365332812071,
0.05395085737109184,
-0.026866454631090164,
-0.05424235761165619,
0.05897380784153938,
-0.011156225576996803,
-0.023480098694562912,
-0.05866793915629387,
0.0019994154572486877,
0.018487468361854553,
-0.02709280326962471,
-0.038364194333553314,
-0.023635277524590492,
0.06211748346686363,
-0.03788348659873009,
0.018278636038303375,
-0.007297929842025042,
-0.03513208404183388,
0.06712283939123154,
0.030996279790997505,
-0.014562075957655907,
-0.017803549766540527,
-0.04829898104071617,
-0.033103421330451965,
0.08541189879179001,
0.07667585462331772,
-0.04270516708493233,
0.04271604120731354,
0.02364288829267025,
-0.06816615164279938,
0.028465840965509415,
0.05280213803052902,
-0.0172524806112051,
0.06686010211706161,
0.005730075761675835,
-0.013369051739573479,
-0.022865939885377884,
-0.04839761182665825,
-0.04028867185115814,
0.026194529607892036,
0.010550213046371937,
-0.044362589716911316,
-0.025136031210422516,
-0.03620230779051781,
-0.009741714224219322,
-0.0640251561999321,
-0.005193319637328386,
0.020505232736468315,
-0.008472763001918793,
-0.032009538263082504,
0.06285757571458817,
0.07459491491317749,
0.010937806218862534,
-0.010365840047597885,
-0.06074100732803345,
-0.01649448834359646,
0.025905320420861244,
-0.011468642391264439,
0.00552766490727663,
0.022541232407093048,
0.022531092166900635,
-0.058050818741321564,
-0.05978640168905258,
0.009314305149018764,
0.06277012825012207,
0.02695409767329693,
-0.048070427030324936,
-0.010641464032232761,
-0.017021290957927704,
0.007860803045332432,
0.030165499076247215,
0.018416665494441986,
0.049347344785928726,
-0.022726750001311302,
-0.02675957791507244,
0.00838320143520832,
0.0061089168302714825,
-0.04480447992682457,
-0.018289731815457344,
0.03378200903534889,
-0.02916995994746685,
-0.019871583208441734,
0.02533727139234543,
-0.030193893238902092,
0.02287430875003338,
-0.05607326328754425,
-0.007626306265592575,
-0.03202303498983383,
0.007721068803220987,
0.01263445895165205,
-0.020650262013077736,
0.027635173872113228,
0.08407637476921082,
-0.035606369376182556,
-0.027933431789278984,
0.07750916481018066,
0.08350622653961182,
0.027193473652005196,
-0.02253859117627144,
0.014297306537628174,
-0.05712364986538887,
0.003745418041944504,
0.03881216049194336,
0.0011729301186278462,
0.003302697092294693,
0.012838374823331833,
-0.00039705296512693167,
0.007098647765815258,
-0.006851419806480408,
0.04595537111163139,
-0.0013615228235721588,
0.007510947994887829,
0.014225121587514877,
0.01239823829382658,
0.0026546905282884836,
0.028830956667661667,
-0.06482424587011337,
0.021251637488603592,
-0.019803298637270927,
0.0453745536506176,
0.0738731250166893,
-0.050229448825120926,
-0.04456688463687897,
-0.027484383434057236,
0.004974187817424536,
-0.012546977959573269,
-0.006930193863809109,
0.008855357766151428,
0.053980350494384766,
-0.03556068241596222,
-0.04008720815181732,
0.0041980259120464325,
0.019121581688523293,
0.05127357318997383,
0.02179071120917797,
-0.0193789042532444,
0.011207877658307552,
0.0027028571348637342,
-0.036419108510017395,
-0.07472585886716843,
-0.020879898220300674,
-0.007257816847413778,
-0.041252490133047104,
-0.0012887733755633235,
-0.005345119629055262,
0.016524789854884148,
-0.018906619399785995,
0.06604745239019394,
0.02245107665657997,
0.016111280769109726,
-0.050597772002220154,
0.015381899662315845,
-0.039433203637599945,
0.016697848215699196,
0.033299483358860016,
0.04747004806995392,
-0.012827802449464798,
-0.00680802296847105,
-0.030176332220435143,
0.015503398142755032,
0.0451614186167717,
-0.0072686392813920975,
0.0378030464053154,
0.014067348092794418,
0.02175617776811123,
-0.007105645723640919,
0.010290524922311306,
-0.017258724197745323,
0.05935300141572952,
0.012582222931087017,
0.0021760358940809965,
0.04664397984743118,
-0.045287441462278366,
0.03725273162126541,
0.03142686188220978,
0.04084558039903641,
0.0188957080245018,
0.015619570389389992,
0.016538871452212334,
-0.0016295097302645445,
-0.06499742716550827,
-0.008853496052324772,
-0.00020011176820844412,
-0.006465638522058725,
0.0337175577878952,
-0.006654796190559864,
0.000389462715247646,
0.01817363128066063,
-0.03902193903923035,
-0.04333382844924927,
0.024073299020528793,
-0.01991605944931507,
-0.016883457079529762,
0.005234595388174057,
0.0023833303712308407,
-0.0378873385488987,
0.014395877718925476,
0.017398154363036156,
-0.031730566173791885,
-0.03854535147547722,
-0.03114633448421955,
0.020156152546405792,
-0.030703892931342125,
-0.09834283590316772,
-0.015935475006699562,
-0.007034512236714363,
-0.05431157350540161,
0.010807069018483162,
-0.004272879101336002,
-0.010336092673242092,
0.01629338040947914,
-0.01388232596218586,
-0.012045939452946186,
0.05330393463373184,
-0.06603556871414185,
-0.019782962277531624,
0.07915812730789185,
-0.036475785076618195,
0.06370329856872559,
-0.052374836057424545,
0.006338823586702347,
0.017217295244336128,
-0.030147355049848557,
-0.0314413420855999,
-0.04715171828866005,
0.06594536453485489,
0.00006432933150790632,
0.008866830728948116,
-0.021591667085886,
0.039762768894433975,
0.04202942177653313,
-0.0378398671746254,
0.04393262416124344,
0.010418609715998173,
-0.046697307378053665,
0.007112993858754635,
-0.02762560546398163,
0.03682459890842438,
-0.01696689985692501,
0.05534495413303375,
-0.014101244509220123,
-0.023269787430763245,
-0.023895390331745148,
0.004865981172770262,
0.04110599309206009,
-0.006190716754645109,
-0.00570062268525362,
0.05912979692220688,
0.07204193621873856,
0.06391084939241409,
0.03940346837043762,
-0.0008868923177942634,
0.004229186102747917,
-0.07954981178045273,
-0.0382271334528923,
0.0070177591405808926,
-0.004558693617582321,
-0.05932173132896423,
-0.030579103156924248,
-0.03546663001179695,
-0.0039266073144972324,
0.0002042441046796739,
-0.006286101881414652,
0.03466302156448364,
0.006814850959926844,
0.012104514054954052,
-0.0014318079920485616,
0.037814848124980927,
0.000451464467914775,
-0.023058326914906502,
-0.08116908371448517,
-0.04848035052418709,
-0.020104918628931046,
-0.008194332011044025,
0.0008912539924494922,
0.04243561252951622,
0.03925200551748276,
0.024096041917800903,
0.10117397457361221,
0.008593729697167873,
-0.07370169460773468,
-0.021989980712532997,
-0.0701390877366066,
-0.009830794297158718,
0.015545131638646126,
-0.008195674978196621,
0.057482194155454636,
0.01315933559089899,
0.001890536048449576,
-0.03605564311146736,
-0.03190763667225838,
-0.0009458934073336422,
-0.04213716834783554,
-0.05227664113044739,
-0.0034727263264358044,
-0.03863382339477539
] |
<p>I'm performing an experiment with a 2D <a href="http://en.wikipedia.org/wiki/Double_pendulum" rel="nofollow">double pendulum</a>, and in part of it I want to investigate the normal modes of the double pendulum, where the pendula are not of equal length or of equal mass. My question is - how will I actually know when I've successfully excited a normal mode? </p>
<p>I start by setting the initial angles to be in (roughly) the correct proportion to one another in order for the initial setup to be an eigenvector, but of course once I release the pendulum there is a slight 'jolt' which means I can't be sure the initial conditions were exactly an eigenvector (of course, realistically I'm only going to be closely approximating one). Then, once data is recorded I can generate a phase portrait with the computer, and the phase portrait I see when I get quite close to an eigenvector looks kind of like a tilted cylinder (sorry, don't know how to post a Matlab graph here). Is there a way to tell from this phase portrait (with the angles $\theta_1$ and $\theta_2$) whether I've hit a normal mode or not? Would appreciate some help.</p>
<p>(ie. if someone could post a picture of a phase portrait of the normal modes of a double pendulum, so that I know what I'm looking for, that would be very appreciated)</p> | g9221 | [
-0.018658462911844254,
0.032042089849710464,
0.01520849484950304,
-0.03397064283490181,
0.02352609857916832,
-0.02364259585738182,
0.09330461174249649,
-0.03298943117260933,
-0.01067072432488203,
0.009289449080824852,
-0.05239905044436455,
0.014711612835526466,
0.04324045404791832,
-0.005723700392991304,
0.03519028052687645,
-0.028608787804841995,
0.04092227667570114,
-0.017280858010053635,
0.09390727430582047,
-0.004435968119651079,
-0.017607009038329124,
0.036433145403862,
-0.03803616762161255,
0.010819940827786922,
0.0009459270513616502,
0.027468571439385414,
-0.018090423196554184,
0.022041143849492073,
-0.030387789011001587,
-0.033650681376457214,
-0.049928076565265656,
0.0004096240736544132,
0.012667872942984104,
0.006110561545938253,
-0.027301698923110962,
-0.0014365031383931637,
-0.020363913848996162,
0.06233048811554909,
-0.0311200600117445,
0.029101021587848663,
0.037801630795001984,
-0.06039096787571907,
-0.022529667243361473,
0.0023822635412216187,
0.024082399904727936,
0.050815001130104065,
0.028252944350242615,
-0.028711069375276566,
0.010529073886573315,
0.03482089191675186,
0.005634576082229614,
0.055899862200021744,
0.03521095588803291,
-0.03469032794237137,
-0.019949672743678093,
0.04676477611064911,
-0.011994287371635437,
0.024760659784078598,
0.06604345887899399,
-0.0014594679232686758,
0.0017633665120229125,
-0.02885805070400238,
0.03984516113996506,
0.01361259538680315,
-0.013925669714808464,
0.017406903207302094,
-0.03232424333691597,
-0.05962914973497391,
0.006372950505465269,
-0.028080282732844353,
-0.05001744255423546,
-0.019908877089619637,
0.04827180504798889,
-0.011865081265568733,
-0.0032875044271349907,
-0.01950567588210106,
0.029393507167696953,
-0.038381192833185196,
-0.0047136638313531876,
-0.013887680135667324,
0.029307985678315163,
0.030399814248085022,
-0.005015453789383173,
0.0043019321747124195,
0.0431978777050972,
0.04263467714190483,
-0.0523214116692543,
-0.011250454001128674,
-0.025281822308897972,
-0.009739585220813751,
0.07643988728523254,
-0.025553571060299873,
0.06889541447162628,
0.013566380366683006,
0.014252226799726486,
-0.026436304673552513,
-0.04328148812055588,
0.08524641394615173,
0.028566081076860428,
0.031148413196206093,
0.013190501369535923,
0.013337458483874798,
-0.04095358029007912,
-0.04577252268791199,
-0.05233396217226982,
0.03780404478311539,
0.018571708351373672,
-0.033545829355716705,
0.023253167048096657,
-0.043973252177238464,
-0.04824768751859665,
-0.0045059737749397755,
-0.039071109145879745,
-0.013106533326208591,
-0.06048832833766937,
-0.0652526319026947,
0.046929117292165756,
-0.018952751532197,
0.015131517313420773,
0.011132481507956982,
0.07590938359498978,
0.008404463529586792,
0.008602822199463844,
0.014072529040277004,
-0.012334112077951431,
0.006053368095308542,
-0.014558502472937107,
-0.006499100476503372,
0.07890746742486954,
0.03918195515871048,
-0.01336964126676321,
0.003417400876060128,
-0.005162753630429506,
0.041176531463861465,
0.052707936614751816,
0.024180078878998756,
-0.002387109911069274,
-0.013694990426301956,
-0.03376897796988487,
0.02534068189561367,
-0.03328634425997734,
-0.015236852690577507,
-0.03742313012480736,
-0.026160828769207,
0.0005025042337365448,
0.027995219454169273,
0.012847225181758404,
-0.013170196674764156,
0.033282987773418427,
0.06506902724504471,
-0.07850740849971771,
0.025525305420160294,
0.00642630597576499,
-0.024952357634902,
0.0031097251921892166,
-0.010241903364658356,
0.01283731497824192,
-0.05567336454987526,
0.021969368681311607,
0.045310020446777344,
0.060470905154943466,
-0.06524502485990524,
0.03361324593424797,
-0.004011849872767925,
0.026333928108215332,
-0.012407777830958366,
0.059831488877534866,
-0.08325791358947754,
0.013858232647180557,
-0.058222584426403046,
-0.014481507241725922,
-0.013302353210747242,
0.030982034280896187,
0.014647274278104305,
0.013715172186493874,
0.016672510653734207,
0.00026134212384931743,
-0.013323820196092129,
0.057699378579854965,
0.04781172424554825,
-0.04038545489311218,
0.03504510596394539,
-0.05573694407939911,
-0.03986416384577751,
0.009422996081411839,
-0.015493329614400864,
0.04103595390915871,
0.06515198200941086,
-0.030162323266267776,
0.009403763338923454,
0.05550574138760567,
-0.012961862608790398,
-0.015334616415202618,
-0.011886488646268845,
-0.01268591359257698,
-0.01608121581375599,
0.023753216490149498,
-0.023055164143443108,
-0.0510173961520195,
0.0308529119938612,
0.003125193528831005,
0.009530652314424515,
-0.011110899038612843,
0.04619506001472473,
-0.07484105974435806,
-0.007991044782102108,
0.0260397270321846,
-0.002455240348353982,
-0.023601079359650612,
0.0050802528858184814,
-0.031035786494612694,
0.03269749879837036,
-0.045819517225027084,
0.0756140723824501,
0.018266085535287857,
0.05566205829381943,
0.042515356093645096,
-0.03500392660498619,
0.0182794202119112,
-0.01627197675406933,
0.021363386884331703,
0.046047601848840714,
-0.023731190711259842,
-0.0353957824409008,
0.05812966451048851,
0.011698087677359581,
-0.05528967082500458,
0.04432741925120354,
-0.04388130456209183,
-0.003751704702153802,
-0.04190874099731445,
0.0077486708760261536,
0.03185886889696121,
-0.044425539672374725,
0.01300333347171545,
-0.005036343354731798,
-0.013245896436274052,
-0.005874523892998695,
0.016624463722109795,
-0.015638820827007294,
0.0396343357861042,
-0.023639705032110214,
-0.020618723705410957,
0.0072449990548193455,
-0.03742925450205803,
0.03044305555522442,
0.030110646039247513,
-0.006564234849065542,
0.024302449077367783,
0.05968388170003891,
-0.009275359101593494,
-0.004938595928251743,
-0.004923149943351746,
0.004834702238440514,
-0.055160075426101685,
0.023864511400461197,
-0.032876573503017426,
-0.01012833509594202,
-0.08495940268039703,
-0.04885614290833473,
-0.026266761124134064,
-0.0011535432422533631,
-0.02035466767847538,
0.032617148011922836,
-0.05511967092752457,
-0.04927057772874832,
0.008085492067039013,
0.011820410378277302,
-0.046924423426389694,
0.008293620310723782,
0.012391743250191212,
0.08482763916254044,
-0.047191422432661057,
0.01153339073061943,
-0.0005961229908280075,
0.007994715124368668,
0.024315504357218742,
-0.028423577547073364,
0.023266060277819633,
-0.02885311283171177,
-0.0320919007062912,
-0.007136135827749968,
-0.03997867554426193,
0.05799449235200882,
0.05988676846027374,
-0.014401528052985668,
-0.00659581646323204,
0.10643120110034943,
-0.044589243829250336,
0.029331088066101074,
-0.08982677012681961,
-0.0043422756716609,
-0.018646949902176857,
0.003149059135466814,
-0.03810780867934227,
-0.020020101219415665,
0.005301576107740402,
-0.02810472808778286,
0.021987246349453926,
0.017975177615880966,
-0.06302691251039505,
-0.005447666626423597,
-0.02080378122627735,
-0.005517010577023029,
-0.00791042111814022,
-0.06161787360906601,
-0.014932782389223576,
0.004184050485491753,
-0.01764569617807865,
-0.024150507524609566,
-0.0364188477396965,
-0.0091105280444026,
-0.008856415748596191,
0.035025205463171005,
-0.03069918416440487,
0.028390275314450264,
-0.043721601366996765,
0.04969215393066406,
-0.08533353358507156,
-0.013643249869346619,
-0.03290180116891861,
-0.026765873655676842,
0.0206689964979887,
0.04096625745296478,
-0.058303430676460266,
-0.03728658705949783,
0.03422917425632477,
-0.011775434017181396,
0.009925896301865578,
0.019216587767004967,
0.0753403753042221,
0.03465275466442108,
-0.05853944271802902,
-0.046977464109659195,
0.04070930555462837,
-0.015075016766786575,
-0.056229013949632645,
0.07031682878732681,
0.020808108150959015,
0.07144768536090851,
0.022967344149947166,
0.007309400476515293,
-0.03821203112602234,
-0.06318436563014984,
0.028115779161453247,
-0.06626935303211212,
-0.026643022894859314,
-0.02037881314754486,
0.001005797297693789,
-0.04566443711519241,
0.02838921546936035,
0.004938939120620489,
-0.006847149692475796,
-0.007867470383644104,
0.00031772145302966237,
0.00430363230407238,
0.0636611357331276,
-0.009562659077346325,
0.014025569893419743,
0.0007048435509204865,
0.01211631391197443,
-0.028772450983524323,
-0.013174306601285934,
-0.024990109726786613,
0.021116219460964203,
-0.08156458288431168,
-0.04089071974158287,
0.10658309608697891,
0.015045962296426296,
-0.032808225601911545,
0.010926288552582264,
-0.014810788445174694,
0.029182085767388344,
-0.01277683675289154,
0.008135865442454815,
0.0027246209792792797,
-0.027551431208848953,
0.005109434016048908,
-0.0012458375422284007,
0.08251435309648514,
-0.024284839630126953,
-0.0007986710406839848,
-0.0032855276949703693,
-0.003876894246786833,
-0.008338171988725662,
-0.009376703761518002,
0.025630995631217957,
0.045278094708919525,
0.11414828896522522,
-0.029253393411636353,
-0.0019424810307100415,
-0.036262016743421555,
-0.04302750900387764,
0.04405496269464493,
0.01638336107134819,
0.0019398718141019344,
0.02472238801419735,
0.05085337534546852,
-0.028855187818408012,
-0.00987947080284357,
-0.05496231094002724,
0.008159821853041649,
0.0089352335780859,
0.026415586471557617,
-0.05960305035114288,
-0.009954621084034443,
-0.001269722473807633,
0.020661229267716408,
0.011077583767473698,
-0.02306462824344635,
-0.008593144826591015,
-0.009563758037984371,
0.0015275297919288278,
-0.02927945740520954,
0.022705983370542526,
0.009785021655261517,
0.010683526284992695,
-0.032055169343948364,
0.007067569065839052,
-0.00231209397315979,
-0.009614026173949242,
0.062241081148386,
-0.04747198894619942,
-0.046121008694171906,
-0.05368785187602043,
0.07362257689237595,
0.05545802414417267,
0.012689576484262943,
0.01396778505295515,
-0.008482484146952629,
0.02386361174285412,
-0.057278525084257126,
-0.00817863829433918,
0.05513756722211838,
-0.07388115674257278,
0.020292062312364578,
-0.008369454182684422,
0.044102512300014496,
-0.03149090334773064,
0.0019972596783190966,
0.03416987881064415,
0.01258836779743433,
-0.03440408036112785,
-0.03902256488800049,
-0.02615341730415821,
-0.011943468824028969,
0.008941011503338814,
-0.03464633598923683,
-0.003714635269716382,
-0.031263623386621475,
-0.05796456336975098,
0.009769256226718426,
-0.04837373271584511,
-0.009698793292045593,
-0.007289151661098003,
0.013737154193222523,
0.025750698521733284,
0.08354835212230682,
-0.06360584497451782,
0.014101563021540642,
-0.003909499384462833,
-0.04709657281637192,
-0.013335741125047207,
-0.006060412619262934,
-0.01148283202201128,
-0.0420859269797802,
-0.056099049746990204,
-0.03732229769229889,
0.0019573986064642668,
-0.06163984164595604,
0.03067842312157154,
-0.06405118107795715,
0.0768471285700798,
-0.04954720661044121,
-0.032433316111564636,
-0.05999935418367386,
-0.008701424114406109,
0.031777020543813705,
0.014674471691250801,
-0.022413121536374092,
0.010938511230051517,
-0.00048372201854363084,
0.01956765726208687,
-0.028559941798448563,
0.043041884899139404,
-0.05540653318166733,
-0.029697200283408165,
0.0061702486127614975,
0.04356445372104645,
0.05000552907586098,
-0.009019582532346249,
0.008501407690346241,
-0.031325604766607285,
-0.08061493188142776,
0.06047368049621582,
0.0227306317538023,
0.03259051963686943,
-0.006415878888219595,
0.010602138005197048,
0.03746467083692551,
-0.06312480568885803,
0.08090038597583771,
0.012598459608852863,
0.02838798239827156,
-0.009881709702312946,
0.028508177027106285,
0.025956813246011734,
-0.026995105668902397,
-0.007486061658710241,
0.07278542965650558,
-0.008494662120938301,
0.0006042848690412939,
0.03492739424109459,
0.011894811876118183,
0.006920623127371073,
-0.012119059450924397,
-0.03197021782398224,
0.04250200837850571,
-0.045438479632139206,
-0.03502576798200607,
0.042712993919849396,
-0.03968794643878937,
0.04830280691385269,
-0.07028863579034805,
0.007048611529171467,
-0.012986431829631329,
0.012658021412789822,
0.024596838280558586,
0.0013953426387161016,
0.01979774236679077,
-0.01393736619502306,
0.032718267291784286,
-0.02113751508295536,
-0.005990542937070131,
0.0018741366220638156,
-0.014501267112791538,
0.047720763832330704,
0.010057036764919758,
-0.011644993908703327,
0.028505688533186913,
-0.022812750190496445,
-0.04192432016134262,
0.034031737595796585,
0.028553055599331856,
0.022590523585677147,
-0.0038492267485708,
0.025717725977301598,
-0.006667815614491701,
-0.01945566199719906,
0.00788404792547226,
-0.06871555745601654,
0.0035548051819205284,
0.018288172781467438,
0.044487833976745605,
-0.027867844328284264,
0.037938158959150314,
0.002132072113454342,
-0.025239376351237297,
-0.023001866415143013,
0.03101428598165512,
0.06890134513378143,
-0.007455545011907816,
0.07332789897918701,
0.036247268319129944,
-0.025104712694883347,
-0.005102450959384441,
-0.019170008599758148,
-0.0026474602054804564,
0.03430959954857826,
0.04927847906947136,
-0.05737267807126045,
-0.019217927008867264,
0.021150613203644753,
0.011225729249417782,
0.06262840330600739,
0.026042776182293892,
-0.042109619826078415,
0.029312973842024803,
0.0037054098211228848,
-0.019946303218603134,
-0.031716227531433105,
-0.008676079101860523,
0.012692445889115334,
0.03597845882177353,
0.026245256885886192,
0.04445061460137367,
0.02632889896631241,
-0.012234962545335293,
-0.0354616753757,
0.040531545877456665,
-0.04601481929421425,
-0.01344749890267849,
-0.03392241150140762,
-0.058004189282655716,
0.022761467844247818,
-0.008874957449734211,
-0.031595245003700256,
-0.00616667652502656,
-0.007872246205806732,
0.07714048773050308,
0.04817058518528938,
-0.0036948954220861197,
0.015395739115774632,
0.05633106082677841,
-0.03430230915546417,
-0.016927938908338547,
0.022565795108675957,
0.0018030527280643582,
-0.017130248248577118,
0.05076505243778229,
-0.018406996503472328,
-0.05187895521521568,
0.0031039707828313112,
0.02954273670911789,
-0.019514139741659164,
-0.04557087644934654,
0.01902097649872303,
-0.01195025909692049,
0.016301119700074196,
0.03899113088846207,
0.079836405813694,
-0.03669607266783714,
0.029337752610445023,
0.016495482996106148,
0.0006412024376913905,
0.04082993045449257,
-0.015770666301250458,
-0.0107791218906641,
0.1063256487250328,
0.0012581630144268274,
-0.006149509456008673,
-0.02565411850810051,
-0.0403357669711113,
0.014651298522949219,
-0.00968964584171772,
0.007657945156097412,
-0.04698198288679123,
0.07890371233224869,
0.030500467866659164,
0.03397640585899353,
0.04343881830573082,
0.0474683977663517,
-0.0012371866032481194,
-0.018239475786685944,
-0.062267255038022995,
-0.001929494901560247,
0.02260238490998745,
0.01879662089049816,
-0.023423096165060997,
-0.005983426701277494,
0.024416105821728706,
-0.01556122675538063,
0.01777573861181736,
0.04109644889831543,
0.005815862212330103,
0.09677426517009735,
0.08079120516777039,
-0.01563214138150215,
-0.02665950357913971,
0.015409904532134533,
-0.036888182163238525,
-0.015995997935533524,
-0.01971106417477131,
-0.07126908749341965,
-0.009850313887000084,
0.016372043639421463,
0.0014215128030627966,
0.0016680173575878143,
-0.019896453246474266,
0.005898264702409506,
-0.03939914330840111,
-0.04812835156917572,
-0.058758605271577835,
0.027555041015148163,
0.032093584537506104,
0.0004184239078313112,
-0.020997783169150352,
-0.0251848716288805,
-0.07708019018173218,
-0.011800743639469147,
0.04130557179450989,
0.036222320050001144,
-0.007806853391230106,
0.025000059977173805,
-0.015085932798683643,
0.035315729677677155,
-0.008831603452563286,
-0.04484958201646805,
-0.0628804862499237,
0.02012452855706215,
-0.04490705579519272,
0.07474642246961594,
0.021929943934082985,
-0.05595400184392929,
-0.05068749189376831,
0.010020939633250237,
0.017550110816955566,
0.0061283535324037075,
-0.02271713875234127,
-0.0016456671291962266,
0.028636593371629715,
-0.011457419954240322,
-0.0023096073418855667,
0.014184238389134407,
0.015886256471276283,
0.018346307799220085,
0.0290034469217062,
-0.023724624887108803,
-0.010956263169646263,
0.07749655097723007,
-0.03285008296370506,
0.028161752969026566,
-0.0058429003693163395,
0.05288494750857353,
0.006451096851378679,
0.03260534629225731,
-0.04551972821354866,
0.026301870122551918,
0.051226403564214706,
0.01174554880708456,
-0.17109987139701843,
0.035457637161016464,
-0.0025698887184262276,
0.001367516233585775,
0.0013312987284734845,
-0.03255286067724228,
-0.03328767418861389,
0.05763920769095421,
0.009993322193622589,
0.0020595393143594265,
0.026626985520124435,
-0.010715926997363567,
-0.0033558281138539314,
0.025695981457829475,
-0.06195349991321564,
-0.024388834834098816,
0.016764895990490913,
-0.041524406522512436,
0.04556770995259285,
0.015489134006202221,
-0.04560016840696335,
-0.04308212175965309,
0.019846981391310692,
-0.04814242199063301,
-0.007250551134347916,
0.04105590283870697,
0.0010571290040388703,
0.04601754620671272,
-0.002719893353059888,
0.007340703625231981,
-0.03151650354266167,
-0.010021746158599854,
-0.03560421243309975,
0.05450834333896637,
0.007810145150870085,
-0.06850581616163254,
-0.04525352641940117,
-0.016699783504009247,
-0.0018432510551065207,
-0.03957410156726837,
0.0018875014502555132,
0.03622914478182793,
0.005926423240453005,
-0.021956520155072212,
-0.06726137548685074,
-0.016219748184084892,
-0.012089474126696587,
-0.004397546872496605
] |
<p>Is light electromagnetic waves or quantum physical particle waves. Or are they the same?</p>
<p>Note: My question is specifically how electromagnetism plays into the quantum physics and the double slit experiment.</p> | g304 | [
0.021258044987916946,
0.020682252943515778,
0.0049230619333684444,
-0.00017680735618341714,
0.08962724357843399,
0.04907062277197838,
0.014278468675911427,
0.03057229146361351,
0.023541875183582306,
-0.047764621675014496,
0.02634810283780098,
0.01570439338684082,
0.03550686687231064,
0.03129616007208824,
-0.055218055844306946,
0.008973030373454094,
0.04658735170960426,
0.018723510205745697,
0.041006624698638916,
-0.0061974250711500645,
-0.019461803138256073,
0.024447336792945862,
-0.006764473859220743,
-0.06534720957279205,
-0.03878368064761162,
-0.0031081417109817266,
0.014430264011025429,
-0.04053322225809097,
0.008094283752143383,
0.00007309950888156891,
0.021654097363352776,
-0.031312860548496246,
0.04232335090637207,
-0.011179153807461262,
-0.029674850404262543,
-0.0765148252248764,
-0.004453849978744984,
0.05330915376543999,
-0.030436918139457703,
0.00471416674554348,
-0.0016336411936208606,
-0.033764153718948364,
-0.04136699438095093,
-0.027112584561109543,
0.03803635388612747,
-0.04749338701367378,
-0.04539801925420761,
0.008281489834189415,
-0.004237714223563671,
0.00271362392231822,
0.00632092822343111,
-0.008091376163065434,
0.03812389448285103,
0.11078904569149017,
0.08295805007219315,
0.022320475429296494,
-0.0013393048429861665,
-0.0016525619430467486,
0.13230633735656738,
0.05293240770697594,
0.02075999043881893,
0.004180725198239088,
0.021809643134474754,
0.0494624599814415,
-0.003329710103571415,
-0.027153491973876953,
-0.014888525940477848,
-0.012531724758446217,
0.0015679711941629648,
0.0047218636609613895,
0.009496533311903477,
-0.07974450290203094,
-0.021965645253658295,
-0.007270772010087967,
0.06672076135873795,
0.009255009703338146,
0.026979176327586174,
0.022532401606440544,
0.026145055890083313,
0.003161539090797305,
-0.028409196063876152,
-0.01007512491196394,
-0.057726286351680756,
0.027574773877859116,
0.028259774670004845,
-0.023571284487843513,
-0.06524147093296051,
-0.029153216630220413,
-0.018502643331885338,
-0.018459711223840714,
0.0478360690176487,
-0.024036584421992302,
0.07675488293170929,
0.02053750306367874,
0.00017377750191371888,
0.009589036926627159,
0.01194413099437952,
0.04051540419459343,
0.022656740620732307,
0.03886575996875763,
-0.02855045348405838,
-0.04082019627094269,
0.004929174203425646,
0.03216484189033508,
0.0221636351197958,
0.00933047290891409,
0.02721540443599224,
0.042353782802820206,
-0.017989223822951317,
0.04932159557938576,
-0.07533985376358032,
-0.011164323426783085,
-0.010140225291252136,
-0.0019339682767167687,
-0.0683813989162445,
-0.009275656193494797,
0.028294846415519714,
-0.024130215868353844,
0.013226370327174664,
0.05076155811548233,
0.05073392763733864,
0.03940007835626602,
-0.012254537083208561,
0.06515995413064957,
-0.006554254796355963,
0.006722964812070131,
-0.017825420945882797,
0.020511072129011154,
0.010986411944031715,
-0.004506327211856842,
0.025051511824131012,
-0.0018906502518802881,
0.015995750203728676,
0.017842743545770645,
-0.03439073637127876,
-0.03595539182424545,
0.05108798295259476,
-0.010900558903813362,
0.027769101783633232,
-0.02082771062850952,
-0.03839066997170448,
-0.022608742117881775,
0.02420973777770996,
-0.024622850120067596,
0.006113061681389809,
-0.018648266792297363,
0.008168904110789299,
0.026883404701948166,
-0.032400429248809814,
0.04689379781484604,
0.024714812636375427,
0.031088974326848984,
0.018018608912825584,
-0.03848591446876526,
-0.024357028305530548,
-0.03458358719944954,
0.04483552277088165,
-0.01967441663146019,
0.00023284055350814015,
0.05758100375533104,
0.09460997581481934,
0.016935735940933228,
0.006819441448897123,
0.04539380595088005,
0.02641637995839119,
-0.01385337021201849,
0.031649671494960785,
-0.028807945549488068,
0.02116379141807556,
-0.03146391361951828,
0.005736805964261293,
-0.00028306496096774936,
-0.018212242051959038,
0.0658893883228302,
0.0496116504073143,
0.10600024461746216,
-0.033769961446523666,
-0.010672183707356453,
0.010739745572209358,
-0.0003186824615113437,
-0.006547689903527498,
0.027877550572156906,
-0.0174960158765316,
-0.060130055993795395,
-0.026539161801338196,
-0.04236753284931183,
-0.057691607624292374,
0.013575323857367039,
-0.04810149967670441,
-0.03458799421787262,
-0.04535188898444176,
-0.04458431154489517,
-0.02540820650756359,
0.04002024978399277,
-0.016602100804448128,
-0.01781320758163929,
-0.00947848241776228,
0.04112634435296059,
-0.024541519582271576,
0.0038145934231579304,
-0.02308829128742218,
0.051374830305576324,
0.021477922797203064,
-0.028849445283412933,
0.026755083352327347,
0.04968805983662605,
-0.032180726528167725,
-0.051320988684892654,
0.036774035543203354,
-0.00520327128469944,
0.020964380353689194,
0.060302894562482834,
0.050423286855220795,
0.0114179952070117,
-0.0097264489158988,
-0.003443841589614749,
-0.020699946209788322,
0.006630871444940567,
-0.046530671417713165,
-0.00991007685661316,
-0.07359721511602402,
-0.012192112393677235,
0.027569619938731194,
-0.01832173764705658,
-0.006774099078029394,
0.0173894502222538,
-0.06500766426324844,
-0.009934586472809315,
-0.06524457037448883,
0.0314912311732769,
-0.051901206374168396,
0.02514185570180416,
-0.036278605461120605,
0.005138197913765907,
0.07582683861255646,
0.06332982331514359,
-0.0476064495742321,
0.019280366599559784,
0.05133005231618881,
-0.03788934648036957,
-0.017035432159900665,
0.014989563263952732,
-0.027463026344776154,
0.018303282558918,
0.021732233464717865,
-0.02397449128329754,
0.047863733023405075,
-0.003988185897469521,
-0.02840478904545307,
-0.020021745935082436,
0.07099044322967529,
-0.012384855188429356,
-0.019321661442518234,
-0.015284383669495583,
0.02036728709936142,
-0.02246694825589657,
0.00008285759395221248,
0.04216459020972252,
-0.08245118707418442,
-0.0020385198295116425,
0.027192851528525352,
0.000058575580624165013,
-0.03210964426398277,
0.005994758103042841,
0.01860879361629486,
-0.01939670369029045,
0.018885180354118347,
0.07057501375675201,
0.012341304682195187,
-0.028244748711586,
0.002809478435665369,
0.04516978934407234,
-0.005927004851400852,
-0.0801696702837944,
0.053282808512449265,
-0.07166584581136703,
-0.0172591432929039,
-0.057165224105119705,
0.05611545220017433,
-0.06639218330383301,
-0.027678262442350388,
0.01626979373395443,
-0.05410197004675865,
-0.004202569369226694,
0.025542456656694412,
-0.08676783740520477,
-0.011559155769646168,
-0.028560234233736992,
-0.02496168576180935,
0.028782380744814873,
-0.054095711559057236,
0.00573353935033083,
0.022900432348251343,
-0.021394355222582817,
-0.07575863599777222,
0.006875092163681984,
0.030035514384508133,
-0.0195442046970129,
-0.025648068636655807,
-0.0017950148321688175,
0.004191697109490633,
0.005313301924616098,
-0.025439830496907234,
0.053930722177028656,
0.0453079417347908,
0.048280034214258194,
-0.00961744412779808,
-0.029568996280431747,
-0.017932182177901268,
-0.014981365762650967,
-0.04933875426650047,
0.09572450816631317,
0.04113385081291199,
0.0494224838912487,
-0.059027049690485,
0.011881320737302303,
-0.043222445994615555,
0.03621147200465202,
0.03367217257618904,
-0.0061790961772203445,
-0.020954422652721405,
-0.006952967960387468,
0.00094446080038324,
-0.009099814109504223,
0.05605946481227875,
-0.02926858328282833,
0.06672760844230652,
-0.002326084766536951,
-0.03418136388063431,
0.014653689227998257,
-0.0443662628531456,
0.000012875933862233069,
-0.028979789465665817,
-0.007472890429198742,
0.012804199010133743,
-0.01821553148329258,
0.014830034226179123,
-0.002264982322230935,
0.025809913873672485,
0.0013166541466489434,
0.03476317226886749,
-0.03924212604761124,
-0.03639749810099602,
-0.007138262037187815,
-0.015137623995542526,
0.01579001359641552,
0.0032111071050167084,
-0.004192487336695194,
0.013880391605198383,
-0.007801221217960119,
0.02964496985077858,
0.004558933898806572,
-0.05797458440065384,
0.003216635435819626,
-0.0193728469312191,
-0.00898041669279337,
0.03970467299222946,
0.020597198978066444,
0.05805351212620735,
-0.023403653874993324,
-0.02097293920814991,
-0.05333734676241875,
-0.002667349763214588,
-0.04767119511961937,
-0.07217465341091156,
0.024087287485599518,
-0.017847204580903053,
-0.0033483279403299093,
-0.005642149597406387,
-0.029862472787499428,
-0.046093519777059555,
0.05953273922204971,
-0.03693327307701111,
0.02787143737077713,
-0.01852303557097912,
-0.001148891868069768,
-0.014345290139317513,
-0.022485800087451935,
-0.006841684225946665,
0.0356174036860466,
-0.05041917413473129,
0.07604733854532242,
0.05926348641514778,
0.04560821130871773,
0.028167102485895157,
-0.01510878186672926,
0.005748651456087828,
0.05130952224135399,
-0.034965209662914276,
-0.00469569256529212,
-0.03216344118118286,
0.021473640576004982,
-0.07281932234764099,
0.009284481406211853,
-0.00807944592088461,
-0.007042337208986282,
0.033149201422929764,
-0.056862637400627136,
0.04291224852204323,
0.020920835435390472,
0.0011252505937591195,
0.011116575449705124,
0.01068960689008236,
-0.004057351034134626,
-0.023128880187869072,
0.009679578244686127,
0.01751468889415264,
-0.03178281709551811,
-0.011845066212117672,
0.02557765319943428,
0.01149033848196268,
-0.005077881272882223,
-0.025612642988562584,
-0.05184311047196388,
0.016398146748542786,
0.02612912841141224,
0.014142029918730259,
-0.0046951486729085445,
-0.0026963648851960897,
-0.029485488310456276,
0.034046147018671036,
0.0471414178609848,
0.015486445277929306,
0.014887306839227676,
-0.03496892750263214,
0.05614244565367699,
0.0366545096039772,
0.009244604036211967,
-0.041865743696689606,
-0.03923030570149422,
-0.01240108534693718,
0.025681493803858757,
0.005848280619829893,
0.03554847091436386,
-0.06931659579277039,
0.055649060755968094,
-0.048750996589660645,
-0.022141888737678528,
0.03596093878149986,
0.00790382083505392,
0.0824299082159996,
-0.01465962640941143,
-0.03264649212360382,
0.006479136645793915,
-0.025139344856142998,
0.03784655034542084,
-0.00724215479567647,
-0.01976986601948738,
-0.03539775684475899,
-0.02386511117219925,
-0.01202928926795721,
0.035055629909038544,
-0.02971760369837284,
-0.018854567781090736,
-0.009349705651402473,
0.02476297877728939,
-0.006082132924348116,
0.01577981933951378,
0.039916448295116425,
0.030985292047262192,
-0.11437870562076569,
0.0012877493863925338,
0.0022606407292187214,
0.024891322478652,
0.01633596420288086,
-0.0225080456584692,
-0.05311460793018341,
-0.04559355601668358,
-0.08804618567228317,
0.009504103101789951,
-0.01529312040656805,
0.004809577949345112,
-0.0144159235060215,
-0.012069807387888432,
0.07714606821537018,
0.021694133058190346,
-0.06360755115747452,
-0.009062769822776318,
-0.023261938244104385,
-0.04568897932767868,
-0.0018164846114814281,
-0.046542782336473465,
0.015728268772363663,
0.0010125588160008192,
-0.07142571359872818,
-0.002212584251537919,
-0.018527736887335777,
0.08333037048578262,
-0.01605251431465149,
-0.0702294111251831,
0.007778707891702652,
-0.03763936832547188,
0.002774737309664488,
-0.016441622748970985,
0.003122412133961916,
-0.03192340210080147,
-0.030057061463594437,
0.008507826365530491,
0.011812150478363037,
-0.054507702589035034,
-0.0063891722820699215,
-0.012844747863709927,
-0.010116859339177608,
-0.015569431707262993,
-0.04056088253855705,
-0.0026024957187473774,
-0.023178787901997566,
-0.019749416038393974,
-0.00987031776458025,
0.004380838945508003,
-0.03389150649309158,
-0.010138584300875664,
-0.06896355748176575,
0.025555318221449852,
0.054776813834905624,
-0.007975309155881405,
0.00770821887999773,
0.04536687210202217,
0.016050415113568306,
-0.03752666711807251,
-0.005240653175860643,
0.025713616982102394,
0.06046205386519432,
-0.03265237808227539,
0.052121322602033615,
0.0041745444759726524,
-0.05290018022060394,
0.02486325614154339,
0.0705333948135376,
0.0049123819917440414,
0.04584117978811264,
0.06012208014726639,
0.044950492680072784,
0.05117511749267578,
-0.04976627603173256,
-0.05450630560517311,
0.02368437871336937,
-0.02188010886311531,
-0.012021612375974655,
0.050200942903757095,
-0.04163624346256256,
-0.01914346218109131,
0.035422712564468384,
0.06539665162563324,
0.043796736747026443,
-0.009494907222688198,
0.030597040429711342,
0.013458381406962872,
0.014253665693104267,
-0.013161629438400269,
-0.03434333950281143,
-0.04386076703667641,
0.004015335347503424,
-0.006076678168028593,
-0.04145989194512367,
0.031039608642458916,
-0.008253155276179314,
-0.04572942852973938,
0.0007615592912770808,
-0.0319388322532177,
0.05068154260516167,
0.03724382817745209,
-0.020651618018746376,
-0.027820143848657608,
0.03096770867705345,
0.012259937822818756,
0.008554252795875072,
-0.055751629173755646,
0.03406953066587448,
-0.021921489387750626,
-0.003058682195842266,
0.018428010866045952,
-0.0020356858149170876,
0.007894366979598999,
0.010618793778121471,
0.01965014450252056,
0.019201399758458138,
-0.05289098992943764,
-0.0958394706249237,
-0.049924079328775406,
0.047164253890514374,
0.06428277492523193,
0.000037522953789448366,
-0.01776977628469467,
-0.025111423805356026,
0.061759039759635925,
-0.031110435724258423,
0.03111616149544716,
0.027345838025212288,
0.02755270153284073,
-0.04783565551042557,
-0.004389297217130661,
-0.018729878589510918,
-0.005097777117043734,
-0.01703185774385929,
0.0015017656842246652,
0.023459454998373985,
-0.03967556357383728,
0.009023021906614304,
0.04353058710694313,
0.013151729479432106,
-0.024821877479553223,
-0.02124788798391819,
0.07434164732694626,
0.0741962194442749,
0.02072642184793949,
-0.005807085894048214,
-0.009571935050189495,
-0.00804946944117546,
0.014831069856882095,
-0.028909236192703247,
-0.003511664690449834,
-0.07969322055578232,
-0.03722668066620827,
-0.0278388112783432,
-0.0688772201538086,
-0.033730629831552505,
0.009835535660386086,
-0.0005206804489716887,
0.04267685115337372,
-0.033719297498464584,
-0.0610831081867218,
-0.045917000621557236,
-0.024205954745411873,
0.03007057122886181,
0.058964285999536514,
-0.0008690672693774104,
-0.020519889891147614,
0.05354940518736839,
-0.02795492671430111,
-0.010033991187810898,
0.000608458009082824,
0.04731324315071106,
0.0706120952963829,
-0.024612907320261,
-0.019923673942685127,
0.02232428267598152,
-0.0602186881005764,
-0.010072600096464157,
0.006902994122356176,
0.06592296063899994,
0.06597015261650085,
0.027631372213363647,
-0.016068708151578903,
-0.08742200583219528,
0.07738680392503738,
0.029863009229302406,
-0.053054820746183395,
-0.010306257754564285,
-0.011925261467695236,
-0.06547240167856216,
-0.06537946313619614,
-0.008067304268479347,
0.013779436238110065,
0.05023034289479256,
0.02591562457382679,
0.02130085974931717,
0.0063368529081344604,
-0.012955290265381336,
-0.07839822769165039,
-0.05551888421177864,
-0.0019160901429131627,
-0.040087733417749405,
0.007116544526070356,
0.008413827046751976,
0.017149759456515312,
-0.022951196879148483,
-0.07003720104694366,
0.01906248740851879,
-0.025353029370307922,
-0.04552137106657028,
-0.04939059540629387,
-0.03792805224657059,
0.03283538669347763,
0.004322037100791931,
-0.040777865797281265,
-0.03558718040585518,
0.04707235470414162,
-0.0002441735996399075,
-0.024414995685219765,
-0.04878468066453934,
0.04427376016974449,
0.032010357826948166,
-0.02064029686152935,
0.010976750403642654,
0.05824152007699013,
-0.03395085781812668,
-0.012726894579827785,
0.01756867952644825,
-0.010327992960810661,
0.0005452344776131213,
-0.019573349505662918,
-0.025787144899368286,
-0.008497364819049835,
-0.0033561810851097107,
-0.010869475081562996,
0.049455441534519196,
0.04133129492402077,
0.037863485515117645,
0.017618516460061073,
-0.009958031587302685,
0.025594661012291908,
-0.05613352358341217,
0.008757717907428741,
0.028403902426362038,
0.014718379825353622,
0.036211367696523666,
-0.0050246501341462135,
-0.028992190957069397,
0.015691522508859634,
0.016908474266529083,
0.022934440523386,
0.042233336716890335,
0.06353076547384262,
0.016082704067230225,
0.03862665593624115,
0.03390293940901756,
0.029516980051994324,
0.03909961134195328,
-0.01697380840778351,
0.04718242958188057,
-0.038396403193473816,
-0.05145200714468956,
0.004724395461380482,
-0.002960092620924115,
-0.013807134702801704,
0.01689562387764454,
-0.0211311224848032,
0.027348347008228302,
0.00588248623535037,
0.02207745611667633,
-0.009942063130438328,
-0.018938224762678146,
-0.020751673728227615,
-0.0325324647128582,
0.032237183302640915,
-0.0037537359166890383,
0.0554242804646492,
0.05520902946591377,
-0.015573455952107906,
0.07933420687913895,
-0.02855808287858963,
-0.030229244381189346,
-0.020176731050014496,
-0.044920917600393295,
-0.021686041727662086,
-0.020072875544428825,
0.024704914540052414,
0.02217276021838188,
0.010516701266169548,
-0.024771440774202347,
0.028571482747793198,
-0.061157576739788055,
0.10078135132789612,
0.043796878308057785,
-0.09614402055740356,
-0.029468532651662827,
0.0019116151379421353,
0.037650350481271744,
0.031291019171476364,
0.026592405512928963,
-0.007625495083630085,
-0.0184585340321064,
-0.0337144136428833,
-0.044616613537073135,
-0.00021723323152400553,
-0.00039104680763557553,
0.02481227181851864
] |
<p>Question: The melting point of copper is 1080 degrees Celsius and its heat of fusion is 200 kJ/kg. If a copper coin at this temperature is completely melted by the absorption of 2000 J of heat, what is the mass of the coin in kg?</p>
<hr>
<p>I am not sure which formula(s) to use. Is the melting point even needed in this particular problem with it's given information?</p>
<p>Thank you.</p> | g9222 | [
0.05303918197751045,
0.01667190156877041,
0.016420871019363403,
-0.040949009358882904,
0.010088917799293995,
-0.018799446523189545,
-0.009529680013656616,
0.05623944103717804,
-0.042206600308418274,
0.027445025742053986,
-0.07002638280391693,
0.03069360740482807,
-0.007280149031430483,
-0.03402384743094444,
0.027448488399386406,
-0.004985020961612463,
0.04855361580848694,
-0.000021592029952444136,
-0.015402517281472683,
0.0973135307431221,
-0.02701665088534355,
0.012155094183981419,
0.01754082553088665,
-0.017898892983794212,
-0.003632468404248357,
-0.03633931279182434,
0.000692592526320368,
0.03720834478735924,
-0.03118976578116417,
-0.003572576679289341,
-0.054036371409893036,
0.047819703817367554,
0.01433367095887661,
-0.03560558333992958,
-0.06248503550887108,
-0.03024481236934662,
0.06582391262054443,
0.015811486169695854,
0.023930400609970093,
-0.029771316796541214,
0.01378313172608614,
0.0029742021579295397,
0.04630688577890396,
0.02759777009487152,
0.024762656539678574,
0.05060654506087303,
0.02561495639383793,
-0.05961913242936134,
-0.008030097931623459,
-0.03916405513882637,
-0.00031918895547278225,
0.024931689724326134,
0.070198193192482,
-0.09939789772033691,
-0.07064781337976456,
0.049666889011859894,
0.023121926933526993,
-0.026570944115519524,
-0.03215417638421059,
0.011035270988941193,
0.058709267526865005,
-0.02133968658745289,
0.00299180974252522,
-0.1175321489572525,
0.03876624256372452,
0.0027275611646473408,
-0.026940805837512016,
0.03484155610203743,
-0.03263789787888527,
-0.0017707203514873981,
-0.02764648199081421,
0.021716490387916565,
-0.004826048389077187,
-0.05055835098028183,
-0.04833384230732918,
-0.09518468379974365,
0.05363331735134125,
0.021642789244651794,
0.020182954147458076,
-0.0054469602182507515,
-0.05761614069342613,
0.00985427014529705,
0.07165271788835526,
0.012966266833245754,
0.033180683851242065,
-0.025966400280594826,
-0.008596147410571575,
0.06748901307582855,
-0.029471484944224358,
0.039826568216085434,
0.0010417255107313395,
0.020932713523507118,
0.04295613244175911,
0.009945292957127094,
0.07598019391298294,
0.035511136054992676,
-0.0032333494164049625,
0.053848519921302795,
0.004057236015796661,
0.0532752126455307,
-0.04039934277534485,
-0.05395306646823883,
-0.02879190258681774,
0.003824537852779031,
-0.03304293379187584,
0.017801567912101746,
0.039175163954496384,
0.03661143407225609,
-0.031230229884386063,
-0.0030502101872116327,
-0.015219961293041706,
-0.01778768002986908,
-0.04433293268084526,
-0.02578597143292427,
-0.015849987044930458,
0.043986640870571136,
0.013875958509743214,
-0.005330199375748634,
0.027379801496863365,
0.01585746742784977,
0.032068923115730286,
-0.0027274442836642265,
0.009221557527780533,
0.0666937530040741,
0.009043920785188675,
-0.053069181740283966,
0.0027888084296137094,
0.043414633721113205,
0.07842990756034851,
-0.024266259744763374,
-0.03864319622516632,
0.08142969012260437,
0.014578205533325672,
-0.029309876263141632,
0.004004109650850296,
0.042308054864406586,
0.01396060548722744,
0.0754474401473999,
-0.02705134078860283,
0.010219953954219818,
0.038282353430986404,
0.005234006326645613,
0.004354565870016813,
-0.01076571550220251,
-0.06171153113245964,
-0.008023855276405811,
-0.05078733712434769,
-0.040866296738386154,
0.017846710979938507,
-0.010296736843883991,
0.014217979274690151,
0.057571880519390106,
0.02966959960758686,
-0.053013887256383896,
-0.023507509380578995,
-0.019984109327197075,
-0.015106315724551678,
-0.07043785601854324,
0.008563379757106304,
-0.023905767127871513,
0.017740221694111824,
0.006291689816862345,
-0.017368096858263016,
-0.024555737152695656,
-0.0299689881503582,
0.05732746794819832,
-0.05036521330475807,
-0.041662175208330154,
0.025323810055851936,
-0.031523559242486954,
-0.028047293424606323,
0.036066684871912,
-0.026811828836798668,
0.03090052865445614,
0.0023003967944532633,
0.05278925970196724,
0.06282732635736465,
0.03369543328881264,
0.04149339348077774,
-0.005616639740765095,
0.027511995285749435,
-0.02493938058614731,
0.06388046592473984,
-0.001879247254692018,
0.006064548157155514,
-0.012841318733990192,
0.10074003785848618,
-0.01036529615521431,
-0.028173692524433136,
0.007725073955953121,
-0.03717746213078499,
-0.012855649925768375,
0.009653978981077671,
-0.015520865097641945,
0.02423168160021305,
0.027137748897075653,
0.04633437842130661,
0.018588902428746223,
-0.08481121063232422,
0.021294893696904182,
0.06818810850381851,
0.039012592285871506,
-0.010150155983865261,
-0.007841859944164753,
0.0007813598494976759,
-0.015341452322900295,
-0.04073239490389824,
0.040982685983181,
0.01778225786983967,
0.0013216343941166997,
-0.025574374943971634,
-0.015980105847120285,
-0.006278846878558397,
0.047405172139406204,
-0.03374136984348297,
-0.005246084649115801,
0.02806197665631771,
0.04785848408937454,
-0.014724645763635635,
-0.02922632358968258,
0.005380913615226746,
0.0537143275141716,
-0.010387919843196869,
0.002385522937402129,
-0.013421694748103619,
-0.002194521715864539,
-0.03857261314988136,
-0.03671177476644516,
0.014735622331500053,
0.00986540038138628,
0.006788548547774553,
0.003573201596736908,
-0.003775637596845627,
-0.060733504593372345,
0.0218607559800148,
0.045899201184511185,
-0.052002113312482834,
0.023151740431785583,
0.0005558557459153235,
0.04882579296827316,
0.012126568704843521,
0.05806170031428337,
-0.07086849957704544,
-0.04411984980106354,
-0.02289840206503868,
-0.03753630816936493,
-0.006139982026070356,
-0.024259978905320168,
-0.010730216279625893,
0.044383566826581955,
-0.04884942248463631,
0.016818050295114517,
-0.026790903881192207,
-0.05129263177514076,
-0.006052961107343435,
-0.00006387801840901375,
-0.029836518689990044,
-0.004148260690271854,
-0.02866341732442379,
-0.01561448723077774,
0.04172484576702118,
-0.09742342680692673,
0.035266462713479996,
-0.015747714787721634,
-0.10314148664474487,
-0.03151550889015198,
-0.08546961098909378,
-0.07064375281333923,
0.03910228610038757,
0.030958622694015503,
-0.028796641156077385,
0.03163383901119232,
0.015229026786983013,
0.10016338527202606,
0.03920866921544075,
-0.028133369982242584,
0.008733250200748444,
-0.020656470209360123,
0.035900555551052094,
-0.05751743167638779,
-0.00247247819788754,
0.011746863834559917,
-0.042354099452495575,
0.039241861552000046,
-0.014209436252713203,
-0.04015560820698738,
-0.048168864101171494,
0.025340739637613297,
0.044128067791461945,
0.005226825829595327,
0.017383556813001633,
0.017819823697209358,
0.022529682144522667,
0.027852583676576614,
-0.020446958020329475,
0.044185612350702286,
0.07445517182350159,
-0.055892061442136765,
-0.06479639559984207,
-0.05707123503088951,
0.02866961620748043,
-0.03191128373146057,
-0.03754929080605507,
-0.001977229956537485,
0.04665350541472435,
0.10750046372413635,
0.015513738617300987,
-0.04254954680800438,
0.05454828962683678,
-0.07224669307470322,
-0.004454017151147127,
0.05254564806818962,
0.03718191012740135,
-0.0583752766251564,
-0.044120512902736664,
0.01817391999065876,
0.021522805094718933,
-0.030384743586182594,
0.05065574124455452,
-0.008392298594117165,
-0.023573044687509537,
-0.047129128128290176,
0.02330010011792183,
-0.022200478240847588,
0.01782435178756714,
0.016153449192643166,
0.01847532019019127,
-0.036039046943187714,
-0.022206565365195274,
-0.012934981845319271,
-0.03280868008732796,
0.04122726246714592,
-0.058217599987983704,
0.015817737206816673,
0.022516686469316483,
-0.01468319445848465,
0.019324183464050293,
-0.01000974141061306,
-0.020096294581890106,
0.04895014688372612,
0.023757275193929672,
-0.0025898306630551815,
-0.006178319454193115,
0.008731474168598652,
0.03901439905166626,
-0.02069971337914467,
0.009341882541775703,
0.009954988025128841,
0.007655235007405281,
-0.0378754623234272,
0.028161853551864624,
-0.02375011146068573,
-0.030532848089933395,
-0.018421541899442673,
-0.030084658414125443,
0.014781307429075241,
0.023760156705975533,
-0.0051088943146169186,
-0.04805253446102142,
0.03663744032382965,
0.046798933297395706,
-0.006631527561694384,
0.04537377506494522,
0.038888607174158096,
-0.013269403018057346,
-0.05422833561897278,
0.009148875251412392,
0.0018628374673426151,
-0.0028823462780565023,
-0.019222989678382874,
-0.04087898135185242,
-0.03146227449178696,
0.012557054869830608,
0.0017357136821374297,
0.0538058802485466,
-0.049740470945835114,
-0.028249302878975868,
0.047646645456552505,
-0.026030603796243668,
0.0564761757850647,
-0.021078094840049744,
-0.03442269191145897,
-0.0016708668554201722,
-0.008509484119713306,
0.01474582776427269,
0.0033695583697408438,
0.05839746072888374,
0.02084248512983322,
0.011267400346696377,
-0.046584151685237885,
0.038601912558078766,
-0.050346944481134415,
0.015691878274083138,
0.03226077929139137,
0.004251935984939337,
-0.01373144332319498,
0.012146571651101112,
-0.035134755074977875,
-0.023524209856987,
-0.04168550670146942,
0.04029851779341698,
-0.006502688396722078,
0.07639659196138382,
-0.023650208488106728,
0.006034891586750746,
0.015803106129169464,
-0.010032583959400654,
-0.09981086105108261,
0.06575236469507217,
-0.009933198802173138,
0.011820733547210693,
0.001157029066234827,
-0.021706879138946533,
-0.01381479948759079,
0.01186807919293642,
-0.032839350402355194,
-0.0028549092821776867,
-0.01549227349460125,
0.005972698796540499,
-0.03141641616821289,
-0.04393033683300018,
0.0033690438140183687,
-0.027618691325187683,
0.02708604373037815,
-0.04705207049846649,
0.024569734930992126,
0.07191233336925507,
-0.03079635091125965,
0.015653397887945175,
-0.03485819324851036,
0.06595971435308456,
-0.03198562562465668,
-0.013221660628914833,
0.011990942060947418,
-0.03341454267501831,
0.007534459233283997,
0.019992319867014885,
-0.02541130967438221,
-0.005370985716581345,
0.007264625746756792,
-0.008139567449688911,
-0.006074142642319202,
-0.04780545458197594,
0.04530992731451988,
-0.029902031645178795,
0.0022317233961075544,
0.024373695254325867,
-0.04677899554371834,
-0.051219191402196884,
-0.058186519891023636,
0.002086380962282419,
-0.002108559710904956,
-0.06746754795312881,
0.018753353506326675,
-0.017435478046536446,
0.03760955482721329,
-0.028831176459789276,
0.047682832926511765,
0.048934973776340485,
0.04643663763999939,
0.015270553529262543,
-0.00551071111112833,
-0.008578370325267315,
0.02391522377729416,
0.07000575214624405,
-0.054405104368925095,
0.009095094166696072,
-0.014277701266109943,
-0.0014150312636047602,
0.05559247359633446,
-0.01904270611703396,
-0.004126011859625578,
0.003978614695370197,
0.03664539009332657,
0.05225788801908493,
0.019711965695023537,
0.01508206594735384,
-0.025487473234534264,
0.02992166392505169,
-0.019608881324529648,
0.012886110693216324,
0.022682135924696922,
0.027469638735055923,
0.069716677069664,
0.012792661786079407,
0.03979650139808655,
-0.03681318461894989,
0.044604428112506866,
0.02360411547124386,
-0.07432635128498077,
0.01885239966213703,
0.015878519043326378,
0.057349905371665955,
0.003729047253727913,
0.0045904796570539474,
-0.022800981998443604,
-0.03696947172284126,
-0.048787422478199005,
0.06375769525766373,
0.03949100151658058,
0.01893964782357216,
0.010042396374046803,
0.014847340062260628,
0.028712468221783638,
0.008360577747225761,
-0.03192577138543129,
-0.02261270582675934,
0.016435883939266205,
0.02015097066760063,
-0.022014738991856575,
0.016279401257634163,
0.025943567976355553,
0.07100618630647659,
-0.009969656355679035,
-0.013554472476243973,
-0.020755987614393234,
-0.02906215377151966,
0.019357413053512573,
-0.005738051608204842,
0.010006420314311981,
0.013006716035306454,
-0.0033147516660392284,
0.009741692803800106,
0.02420421876013279,
0.020146306604146957,
-0.03521658852696419,
-0.027733340859413147,
-0.01947077363729477,
0.0509784109890461,
-0.03247276693582535,
0.047840364277362823,
0.008768247440457344,
0.008066815324127674,
0.009557044133543968,
-0.03858795017004013,
0.014921292662620544,
-0.04200379177927971,
0.0011832432355731726,
-0.01079554297029972,
-0.011561299674212933,
0.06506460160017014,
0.0038043896201997995,
0.008336460217833519,
0.028322335332632065,
-0.0393865741789341,
-0.005346318706870079,
0.015397865325212479,
-0.05297325178980827,
-0.01051535364240408,
-0.012246412225067616,
0.021925048902630806,
-0.008909326046705246,
0.023093331605196,
0.021655099466443062,
0.05394669994711876,
0.019361434504389763,
0.005685731768608093,
-0.012396403588354588,
0.010225365869700909,
-0.010929911397397518,
-0.002130123320966959,
-0.002993588335812092,
0.019343292340636253,
0.04602007567882538,
0.03824903815984726,
-0.09648159146308899,
-0.051726631820201874,
-0.07726754993200302,
0.07351937144994736,
-0.012951068580150604,
0.01542398240417242,
-0.0051571764051914215,
-0.03534277155995369,
-0.013451607897877693,
0.05737997218966484,
0.048221103847026825,
-0.029775844886898994,
-0.00964497122913599,
-0.008280937559902668,
0.001295840018428862,
0.01330029871314764,
0.03296557441353798,
-0.03469178080558777,
-0.02028508670628071,
-0.01778307557106018,
0.023940537124872208,
-0.01584228128194809,
0.05369526520371437,
-0.044625408947467804,
0.04928739741444588,
-0.015433707274496555,
-0.024144737049937248,
-0.001823014346882701,
-0.027954647317528725,
0.01578519493341446,
0.0018943294417113066,
-0.014862284995615482,
0.012255272828042507,
-0.0609075091779232,
-0.01304700504988432,
-0.005386829376220703,
0.0012387275928631425,
0.027350133284926414,
-0.039554301649332047,
0.007985885255038738,
-0.009962831623852253,
0.03062763623893261,
-0.010480117984116077,
-0.02915923111140728,
-0.034194059669971466,
0.02884599380195141,
0.028882326558232307,
0.013220702297985554,
0.006550305522978306,
-0.0496872253715992,
-0.009483173489570618,
0.006179735995829105,
0.02293071337044239,
-0.06018313020467758,
-0.01683109812438488,
0.03292645886540413,
-0.04778466373682022,
-0.00986833218485117,
-0.03217463567852974,
0.06925708055496216,
0.02576621249318123,
-0.05018039792776108,
0.04388997703790665,
0.038793474435806274,
-0.014734404161572456,
-0.003304267069324851,
0.013651086017489433,
-0.004209782462567091,
-0.02352502942085266,
-0.005015983246266842,
0.03953646495938301,
0.017942793667316437,
0.03554026409983635,
0.014454243704676628,
0.03186418116092682,
-0.042185258120298386,
-0.10753928869962692,
0.019563978537917137,
0.02077007293701172,
-0.031198840588331223,
0.015723010525107384,
0.01231320109218359,
0.018311694264411926,
-0.053404245525598526,
0.011258973740041256,
-0.03651350736618042,
-0.019359787926077843,
-0.05383977293968201,
0.000996860209852457,
-0.047652941197156906,
-0.006519147660583258,
0.01982354372739792,
0.038000915199518204,
0.0195950735360384,
0.006549118552356958,
-0.05543972924351692,
-0.030585085973143578,
-0.012324528768658638,
0.018304485827684402,
0.017731184139847755,
0.051564425230026245,
0.02273714356124401,
-0.004016001708805561,
-0.01616632379591465,
-0.0625406950712204,
0.0006403803708963096,
-0.056910328567028046,
-0.047319196164608,
-0.04432504251599312,
0.05706419423222542,
-0.019409773871302605,
0.01793338544666767,
-0.009935400448739529,
0.003685461124405265,
-0.010846263729035854,
-0.0421643927693367,
-0.007801747415214777,
-0.0011637386633083224,
-0.043345168232917786,
0.057810112833976746,
-0.010641546919941902,
0.011075621470808983,
0.009110304526984692,
0.07672577351331711,
0.052229635417461395,
-0.033559802919626236,
-0.026647206395864487,
0.04290337115526199,
0.002549043856561184,
-0.0016143516404554248,
0.02893863618373871,
0.037505634129047394,
0.03449749946594238,
0.03541843220591545,
0.010933881625533104,
0.011751224286854267,
-0.007218300364911556,
0.030488470569252968,
0.014957970008254051,
-0.038172848522663116,
0.02030966989696026,
0.0052170464769005775,
0.054561909288167953,
-0.015384411439299583,
0.008582793176174164,
0.08069778978824615,
0.028644906356930733,
0.05289563909173012,
-0.07065723836421967,
0.023852137848734856,
-0.03778263181447983,
-0.06815504282712936,
0.008369555696845055,
-0.026197979226708412,
-0.021610837429761887,
-0.0007601865218020976,
-0.0022408876102417707,
-0.0022817596327513456,
-0.07545139640569687,
0.018489554524421692,
-0.07246094197034836,
-0.02876727469265461,
0.0358818881213665,
-0.031731270253658295,
-0.03288322314620018,
0.015126803889870644,
0.027720093727111816,
-0.04421146214008331,
-0.02502496726810932,
0.03580450639128685,
-0.0216766856610775,
-0.0011659701121971011,
0.0017552117351442575,
-0.009707442484796047,
0.09216909855604172,
-0.05143418908119202,
-0.10241492837667465,
-0.017366666346788406,
-0.02120327018201351,
-0.017726870253682137,
-0.04584662616252899,
-0.06139202415943146,
0.08776628226041794,
0.0604696050286293,
-0.0465046688914299,
-0.04018271341919899,
0.013877639546990395,
-0.03805038705468178,
-0.049827102571725845,
0.013141314499080181,
-0.02551833540201187,
-0.009308195672929287,
0.018793538212776184,
-0.043040111660957336,
-0.013878234662115574,
-0.0060923038981854916,
-0.031162017956376076,
0.002917329780757427,
0.0526934415102005,
0.027117738500237465,
0.041811831295490265,
-0.012767338193953037,
-0.020533094182610512
] |
<p>How is the Lorenz gauge condition $\partial_\mu \overline{h}^{\mu \nu}=0$ equivalent to the <a href="http://en.wikipedia.org/wiki/Harmonic_coordinate_condition">harmonic gauge condition</a> $\Box x^\mu=0 $?</p> | g9223 | [
0.023037869483232498,
-0.04416560381650925,
-0.010950866155326366,
-0.02806001901626587,
-0.01599741540849209,
0.019036825746297836,
-0.0014160539722070098,
0.02757636085152626,
-0.03423268347978592,
-0.06310427188873291,
0.025141006335616112,
0.004230664577335119,
-0.04025166854262352,
0.02356933429837227,
0.038456473499536514,
0.008335014805197716,
0.03805972635746002,
0.046340059489011765,
0.006586885545402765,
-0.054413191974163055,
-0.04379771277308464,
0.058271415531635284,
0.022080527618527412,
-0.02016483247280121,
0.06725555658340454,
-0.04342978075146675,
0.024497495964169502,
-0.0397566482424736,
-0.0096643241122365,
-0.0411430224776268,
-0.006881985347718,
-0.046879950910806656,
0.08637617528438568,
0.028801534324884415,
-0.02524360828101635,
-0.01754620671272278,
0.078560009598732,
0.04377507418394089,
0.04947005584836006,
0.015896720811724663,
0.01572433114051819,
-0.009618581272661686,
-0.010623428970575333,
0.0027576263528317213,
-0.0398450531065464,
-0.005365613382309675,
-0.029638050124049187,
0.017472073435783386,
-0.018100619316101074,
0.03915470093488693,
-0.0007719299173913896,
-0.016542864963412285,
0.04686206206679344,
-0.05484209209680557,
0.004157900344580412,
0.04636278375983238,
-0.026537448167800903,
0.008986741304397583,
0.028137503191828728,
0.032304197549819946,
-0.02988811768591404,
0.03358874097466469,
0.022816943004727364,
0.01792772300541401,
0.022860998287796974,
0.010446327738463879,
-0.03487721458077431,
-0.04760207235813141,
-0.027291977778077126,
-0.008775358088314533,
-0.044288892298936844,
0.001279723714105785,
-0.05703241378068924,
0.012088747695088387,
0.007120335474610329,
0.038552843034267426,
-0.047423381358385086,
-0.035700466483831406,
0.007516073528677225,
-0.014049394056200981,
0.003828967222943902,
0.008429422974586487,
0.051477909088134766,
0.025694429874420166,
0.01532754022628069,
-0.025309883058071136,
0.042191363871097565,
-0.01045321673154831,
-0.02463885024189949,
0.026997284963726997,
0.008536788634955883,
-0.05135583132505417,
-0.03053698129951954,
0.03205788508057594,
0.05204081907868385,
0.04312204197049141,
0.018635163083672523,
0.014047042466700077,
-0.04094938188791275,
-0.0510849729180336,
-0.006819660775363445,
0.027789374813437462,
-0.006455636583268642,
0.022506901994347572,
-0.025392930954694748,
-0.007538459729403257,
0.015244275331497192,
0.03939999267458916,
0.042717065662145615,
0.02309650182723999,
-0.03197559714317322,
0.018985731527209282,
-0.0010444233193993568,
-0.042323000729084015,
-0.01991170644760132,
-0.02645660564303398,
0.05604102462530136,
0.01384658645838499,
-0.03702087327837944,
-0.006135114468634129,
0.00043469961383379996,
0.01752719283103943,
0.057061802595853806,
0.0375286266207695,
-0.03374336287379265,
0.03394707664847374,
-0.02536037005484104,
0.035210832953453064,
0.023051397874951363,
-0.03426015377044678,
0.02604062855243683,
-0.00013719314301852137,
0.0004488273407332599,
-0.01900319941341877,
-0.026490110903978348,
0.01315824780613184,
0.017295412719249725,
0.005340232513844967,
-0.014268692582845688,
-0.014176447875797749,
0.011299836449325085,
-0.04426676779985428,
-0.01652313955128193,
-0.06070194020867348,
0.04267111420631409,
0.01812654919922352,
0.021858934313058853,
-0.05620675906538963,
0.008279100991785526,
-0.005211336072534323,
-0.013287855312228203,
0.05932064354419708,
0.029888033866882324,
0.07054637372493744,
-0.04755331203341484,
0.005347957368940115,
0.00812510959804058,
-0.026518555358052254,
-0.005968442186713219,
0.0252549946308136,
-0.007967873476445675,
0.023820415139198303,
0.031626585870981216,
-0.005739275366067886,
0.00629751943051815,
-0.00975633505731821,
-0.04726612567901611,
-0.005308575462549925,
0.015047969296574593,
-0.053675662726163864,
-0.010262039490044117,
-0.031079528853297234,
0.013474217616021633,
0.013491258025169373,
0.0285098347812891,
0.07011259347200394,
0.015597612597048283,
-0.006743837613612413,
0.01399177499115467,
0.0058134375140070915,
0.02232048474252224,
-0.021506067365407944,
0.0018315789056941867,
-0.002913638949394226,
-0.04046172648668289,
0.03335564583539963,
0.03292907029390335,
-0.048399511724710464,
-0.012380745261907578,
0.02224123291671276,
0.014069672673940659,
-0.02115054428577423,
-0.008758427575230598,
0.009866726584732533,
0.05608321353793144,
0.0011728949612006545,
-0.010613992810249329,
0.0018937458517029881,
-0.04258112609386444,
0.02666633203625679,
-0.002318759448826313,
0.05980692431330681,
0.04646354168653488,
0.004866373725235462,
0.010365483351051807,
0.030739858746528625,
-0.020817488431930542,
0.038519300520420074,
0.0008542587165720761,
-0.0020855306647717953,
-0.02908763289451599,
-0.019096344709396362,
0.017372917383909225,
-0.014242490753531456,
-0.038194701075553894,
-0.03200613707304001,
0.02959183230996132,
0.013128252699971199,
-0.06503864377737045,
0.018278729170560837,
-0.009604125283658504,
-0.01864274963736534,
0.07349857687950134,
-0.013412469998002052,
-0.04442569240927696,
0.007684054784476757,
-0.012853780761361122,
0.021909845992922783,
0.05915433540940285,
0.004323201719671488,
0.09025011956691742,
-0.025110814720392227,
0.04446060582995415,
0.01854165829718113,
-0.06491469591856003,
0.025183681398630142,
-0.008758989162743092,
0.014122049324214458,
-0.013422282412648201,
-0.0216841958463192,
0.06677276641130447,
0.03355040401220322,
0.01644844003021717,
0.006008584052324295,
0.09129805862903595,
0.019820688292384148,
-0.0056702494621276855,
-0.03445320203900337,
-0.06703615933656693,
0.053191911429166794,
-0.0007125404081307352,
-0.0037220090162009,
0.09794384241104126,
0.004377233795821667,
0.009931176900863647,
-0.0394366979598999,
0.014318538829684258,
0.026177097111940384,
-0.0857321247458458,
-0.03545914962887764,
0.045637890696525574,
-0.011701968498528004,
0.013762690126895905,
0.018809113651514053,
-0.01967664621770382,
-0.010365910828113556,
0.057925887405872345,
0.03801856189966202,
-0.020802462473511696,
-0.06913972645998001,
0.03861379995942116,
0.03838847577571869,
0.03011135198175907,
0.06970319896936417,
-0.015064544044435024,
-0.04517734423279762,
-0.012102368287742138,
0.0636000782251358,
0.0042947037145495415,
-0.03228757157921791,
0.014044234529137611,
-0.0039679668843746185,
0.007387361954897642,
0.00784242246299982,
0.04285601153969765,
-0.0878622755408287,
-0.03241151198744774,
0.005248641595244408,
-0.0025860604364424944,
0.02458278089761734,
-0.014972250908613205,
0.03863534331321716,
-0.028154565021395683,
0.0040745544247329235,
-0.021972255781292915,
0.00023413354938384145,
0.021717309951782227,
-0.07950972020626068,
-0.02457769773900509,
0.021873222663998604,
-0.0011308520333841443,
-0.046729911118745804,
-0.02968556620180607,
-0.04678751155734062,
0.05888519063591957,
-0.0075712306424975395,
-0.014672563411295414,
-0.011598862707614899,
-0.06623679399490356,
-0.017089946195483208,
0.018362736329436302,
-0.026708286255598068,
0.0198861975222826,
0.03634047508239746,
-0.027183949947357178,
-0.015132217667996883,
-0.04500327259302139,
0.005949529353529215,
-0.05680868774652481,
-0.008443337865173817,
-0.034870389848947525,
-0.06281814724206924,
-0.014713442884385586,
0.022727882489562035,
0.0430937334895134,
-0.022015118971467018,
0.030287154018878937,
0.06813834607601166,
-0.062424398958683014,
0.017399054020643234,
0.04841843619942665,
-0.0005743629881180823,
0.006389614660292864,
0.032717958092689514,
0.020574375987052917,
-0.020922744646668434,
-0.13090980052947998,
0.03546636924147606,
0.030433032661676407,
-0.00734940730035305,
-0.016040800139307976,
0.012095567770302296,
-0.012859207578003407,
0.04710600525140762,
-0.00020690840028692037,
-0.0000524107672390528,
-0.014669130556285381,
0.004714067559689283,
0.04206860810518265,
0.031581100076436996,
-0.010921107605099678,
-0.010057925246655941,
0.022929247468709946,
0.008941486477851868,
0.01916344091296196,
-0.05300477519631386,
0.02857108600437641,
-0.015428570099174976,
0.04027334600687027,
0.06602507084608078,
0.06823676824569702,
-0.017875542864203453,
0.018346112221479416,
0.018903199583292007,
0.025046439841389656,
0.025319112464785576,
0.019453108310699463,
0.049919743090867996,
-0.018025344237685204,
0.030650516971945763,
-0.000005553639766731067,
-0.08958560228347778,
0.03126924857497215,
0.020905975252389908,
0.011304116807878017,
-0.09532921761274338,
0.08643806725740433,
-0.04301069304347038,
-0.004152128007262945,
0.07268945872783661,
0.03237553685903549,
0.020252445712685585,
0.011999544687569141,
-0.02554645948112011,
0.010662674903869629,
0.0027255816385149956,
-0.027482623234391212,
0.040419913828372955,
0.015770751982927322,
-0.024786638095974922,
-0.020719358697533607,
-0.06418193876743317,
-0.01806250773370266,
0.0036488957703113556,
-0.04689371585845947,
-0.0044466410763561726,
0.04597079008817673,
0.009266963228583336,
-0.01017081830650568,
-0.017497166991233826,
-0.010750673711299896,
0.02081911452114582,
-0.022802995517849922,
-0.0006742110708728433,
0.01852528750896454,
-0.022206827998161316,
0.0006433821399696171,
-0.02744545042514801,
0.03633178398013115,
-0.006308560725301504,
0.04660983383655548,
-0.024706540629267693,
-0.018588224425911903,
-0.03306352719664574,
0.03213370218873024,
0.013794784434139729,
-0.020811961963772774,
0.01663193479180336,
-0.050339676439762115,
-0.04566467925906181,
-0.023685060441493988,
0.01790166087448597,
0.029298411682248116,
-0.008566099219024181,
0.05281771346926689,
0.08393460512161255,
0.04063751921057701,
0.013188746757805347,
-0.002389746718108654,
-0.008392023853957653,
0.05209965631365776,
0.05477355793118477,
0.006684836000204086,
0.03986477106809616,
-0.07725151628255844,
-0.017850322648882866,
-0.09161054342985153,
0.0035433610901236534,
-0.03339496627449989,
0.03209241107106209,
0.058267876505851746,
0.03263264521956444,
0.01873716711997986,
0.0050501469522714615,
-0.05003124475479126,
0.006432951427996159,
-0.010750113055109978,
-0.048884790390729904,
-0.03324771672487259,
-0.1110052689909935,
-0.001961465459316969,
-0.004809877369552851,
-0.0025358961429446936,
-0.016985975205898285,
0.007769411895424128,
-0.022476699203252792,
-0.0039604040794074535,
0.038302697241306305,
-0.008550207130610943,
0.021085647866129875,
-0.030250288546085358,
-0.0731615200638771,
-0.0032783488277345896,
0.04934144392609596,
0.06717997044324875,
-0.0013963909586891532,
-0.05015356466174126,
-0.07776644080877304,
-0.04566648602485657,
0.04173027351498604,
0.035142987966537476,
-0.0029834257438778877,
0.06223335862159729,
-0.022229362279176712,
0.04417763277888298,
-0.006635255645960569,
-0.012098229490220547,
-0.010863235220313072,
-0.03207148611545563,
-0.0697222501039505,
-0.015421236865222454,
0.016063712537288666,
0.028573447838425636,
-0.003730728290975094,
-0.05135031417012215,
0.03712436556816101,
-0.027569584548473358,
0.008793574757874012,
0.011103400960564613,
-0.00006479013245552778,
-0.027488647028803825,
0.0004221574927214533,
0.06327389180660248,
0.016038626432418823,
-0.0037873995024710894,
-0.022487295791506767,
-0.04436280205845833,
-0.049231406301259995,
-0.01728072389960289,
-0.05912931263446808,
-0.03847883269190788,
-0.009474397636950016,
0.040184151381254196,
-0.022593602538108826,
0.0019248665776103735,
0.04653514549136162,
0.024931296706199646,
-0.02129911631345749,
-0.0278784167021513,
0.035790786147117615,
-0.018339036032557487,
0.01272671204060316,
0.07554768025875092,
0.0236891508102417,
0.02949437126517296,
0.02024506777524948,
0.0035655859392136335,
0.015521264635026455,
-0.04430932179093361,
-0.061491116881370544,
0.017791660502552986,
-0.04224457964301109,
-0.01997166872024536,
-0.06655795127153397,
0.03199029341340065,
0.06816138327121735,
-0.06383537501096725,
-0.02956457994878292,
-0.012799516320228577,
0.006269779521971941,
0.0048412149772048,
-0.006052704527974129,
0.04387453943490982,
-0.013655710965394974,
0.04478692635893822,
0.05118163675069809,
0.0025078183971345425,
-0.031514182686805725,
-0.011116201989352703,
0.05248536542057991,
0.025426864624023438,
-0.10296367853879929,
0.012155036441981792,
-0.003358957590535283,
0.007768457289785147,
-0.004242501687258482,
-0.008119246922433376,
0.012003601528704166,
-0.04444209113717079,
-0.04900175705552101,
-0.06547296792268753,
0.006299677304923534,
0.01738998293876648,
0.07327903807163239,
-0.015858009457588196,
-0.03558940812945366,
0.034765370190143585,
-0.04426725581288338,
-0.0506574772298336,
-0.02236148528754711,
0.009481209330260754,
0.0361911915242672,
-0.01886734552681446,
-0.008169424720108509,
0.03735913336277008,
0.01569337211549282,
0.004030228592455387,
-0.028651658445596695,
0.09654856473207474,
-0.03375806286931038,
-0.030542967841029167,
0.05134759098291397,
0.0638294667005539,
0.035614579916000366,
0.005509259179234505,
0.06828766316175461,
-0.011724173091351986,
-0.019515877589583397,
-0.020421532914042473,
0.04275735840201378,
0.010799743235111237,
0.022555381059646606,
-0.01756267249584198,
-0.07879837602376938,
0.0003193168085999787,
0.04829522222280502,
0.012391702271997929,
0.05379476770758629,
0.0783754512667656,
0.058752428740262985,
0.03884413093328476,
-0.048681311309337616,
-0.0009293741313740611,
0.01683371141552925,
0.010053758509457111,
0.060942914336919785,
0.02865091897547245,
0.0013084376696497202,
-0.014926222153007984,
0.024915849789977074,
0.04913744702935219,
-0.024919206276535988,
-0.001625923439860344,
-0.000181736919330433,
0.029638146981596947,
0.03979242965579033,
-0.029972320422530174,
-0.015368879772722721,
-0.06971623748540878,
-0.01893054135143757,
-0.012641391716897488,
0.00001919947135320399,
-0.01755138672888279,
-0.0065909624099731445,
0.06420855224132538,
-0.06692632287740707,
-0.008751901797950268,
-0.022710192948579788,
-0.025085879489779472,
-0.0072348034009337425,
0.01224946416914463,
0.010295158252120018,
-0.01441009622067213,
0.053333938121795654,
0.03637136518955231,
-0.010934688150882721,
0.017503580078482628,
0.024868184700608253,
-0.01801513321697712,
-0.04075107350945473,
0.06270908564329147,
0.00823679007589817,
-0.044259488582611084,
0.07058250159025192,
-0.0466097928583622,
-0.0659727230668068,
-0.05314214527606964,
0.02431855909526348,
0.06381755322217941,
0.05328281596302986,
0.004502362571656704,
0.030044935643672943,
0.047294981777668,
-0.041873764246702194,
-0.06692248582839966,
0.0017287139780819416,
0.017333125695586205,
-0.056937381625175476,
-0.11601956933736801,
-0.010745528154075146,
-0.023245278745889664,
-0.017034318298101425,
-0.038139987736940384,
-0.002612512093037367,
-0.07004230469465256,
-0.002974775619804859,
-0.001610281877219677,
0.04850729927420616,
-0.09605927020311356,
-0.04847778379917145,
0.015831362456083298,
0.04173501580953598,
0.03893448784947395,
0.01393923256546259,
-0.019913801923394203,
0.034634944051504135,
-0.015505089424550533,
-0.04211214557290077,
-0.011634492315351963,
-0.02796805277466774,
-0.06458210200071335,
-0.032070547342300415,
0.004167057108134031,
-0.022434242069721222,
0.019409550353884697,
-0.023641889914870262,
0.005795377306640148,
0.04908524081110954,
0.013249944895505905,
0.01814347691833973,
-0.00560088362544775,
-0.0034540893975645304,
-0.019036753103137016,
-0.007593933027237654,
-0.02246388979256153,
-0.06787456572055817,
-0.02356308326125145,
-0.02866947650909424,
0.08335528522729874,
-0.0024457883555442095,
-0.008334195241332054,
-0.0018363496055826545,
-0.00668700085952878,
-0.03350789472460747,
-0.024176308885216713,
-0.03697218745946884,
-0.04763581231236458,
0.05149742588400841,
0.015143025666475296,
-0.007003089878708124,
0.0002485970326233655,
0.008560612797737122,
-0.0025729918852448463,
0.03902524709701538,
0.03798340633511543,
0.008434990420937538,
0.023367220535874367,
-0.03444807603955269,
-0.031637124717235565,
0.004251077771186829,
0.05620672553777695,
0.04393327981233597,
-0.02492062933743,
-0.01190974097698927,
0.02765759825706482,
-0.004870889242738485,
0.040851227939128876,
0.0013413558481261134,
0.013630126602947712,
-0.08340200036764145,
-0.014717896468937397,
0.05290799215435982,
0.007076743524521589,
-0.03820377215743065,
0.002359760459512472,
0.006139324977993965,
-0.022230112925171852,
-0.014265855774283409,
-0.03276185691356659,
-0.050037261098623276,
-0.014117898419499397,
-0.03218642994761467,
-0.014338956214487553,
0.04436017945408821,
-0.0014443503459915519,
0.014384309761226177,
-0.035951174795627594,
0.015805641189217567,
-0.04014948382973671,
0.053185537457466125,
-0.01907873898744583,
-0.030510643497109413,
-0.022406093776226044,
-0.013326086103916168,
-0.04242332652211189,
0.003998566418886185,
-0.052151571959257126,
0.05025413632392883,
-0.005351103842258453,
-0.0026764371432363987,
-0.00924511719495058,
-0.011256306432187557,
-0.002109297551214695,
0.04162084683775902,
0.021869320422410965,
-0.13077576458454132,
0.04512190446257591,
0.025276588276028633,
0.06209009140729904,
-0.057228196412324905,
-0.022356627508997917,
0.027467116713523865,
-0.027316678315401077,
-0.007629200350493193,
-0.03363381326198578,
-0.049097076058387756,
-0.03662721440196037,
0.005680024158209562
] |
<p>How do the wave properties of an electron change with its motion? What about when it is stationary?</p> | g9224 | [
0.018138274550437927,
-0.010533949360251427,
0.0024060015566647053,
0.04966892674565315,
0.08124306797981262,
-0.004620432388037443,
0.0063027068972587585,
0.019185122102499008,
0.0024833837524056435,
0.018394192680716515,
-0.05223887786269188,
0.06612139940261841,
-0.010166853666305542,
0.012470707297325134,
0.004353545606136322,
-0.053445350378751755,
0.0608254075050354,
0.0026753563433885574,
-0.01801946759223938,
0.04963233694434166,
0.03619775176048279,
-0.004988168366253376,
0.00551558006554842,
-0.00538099417462945,
0.02446427382528782,
0.04890728369355202,
0.05617543309926987,
-0.014381246641278267,
0.03205127641558647,
0.010155516676604748,
0.009373601526021957,
0.027100082486867905,
0.05245506018400192,
-0.033815715461969376,
0.008569980971515179,
0.0054313973523676395,
0.06543537974357605,
-0.014113185927271843,
0.0608024001121521,
0.0004863032081630081,
-0.03251979127526283,
-0.05756209045648575,
-0.045954372733831406,
0.00926585216075182,
0.041949380189180374,
-0.048633966594934464,
0.024454321712255478,
-0.03593292832374573,
-0.05267488956451416,
-0.016979407519102097,
-0.038567349314689636,
0.05032307282090187,
0.017189176753163338,
-0.006585294846445322,
0.0020927265286445618,
0.03237897530198097,
-0.018456371501088142,
0.05437840148806572,
0.0985737293958664,
0.016905928030610085,
0.028955824673175812,
0.006041517481207848,
0.032956548035144806,
0.039752162992954254,
0.012127113528549671,
-0.040039870887994766,
0.0005526872701011598,
-0.005878269672393799,
-0.02121344767510891,
-0.007493178825825453,
0.022699782624840736,
-0.07982495427131653,
-0.08555059880018234,
-0.011047650128602982,
-0.0001503895764471963,
0.019671447575092316,
-0.00536971865221858,
-0.021915918216109276,
-0.031194977462291718,
-0.02479434944689274,
-0.039507150650024414,
-0.004458689130842686,
0.05977544188499451,
0.007550079841166735,
0.036329593509435654,
-0.021460160613059998,
0.013478979468345642,
0.018757544457912445,
0.00018232788715977222,
-0.05707234516739845,
0.01685064472258091,
-0.05576518177986145,
0.03988009691238403,
0.0814429447054863,
0.0011194951366633177,
-0.02765725366771221,
-0.05517914518713951,
0.035267554223537445,
0.020541662350296974,
-0.02216043882071972,
-0.026764458045363426,
-0.027409490197896957,
0.013916400261223316,
0.03006073273718357,
-0.006287002004683018,
-0.00992671586573124,
-0.03133136034011841,
-0.05246208608150482,
0.018433477729558945,
0.006055183708667755,
-0.006442452315241098,
-0.028116945177316666,
0.0004026806855108589,
-0.016375716775655746,
-0.05711989104747772,
-0.06272672861814499,
-0.011789345182478428,
0.005794966127723455,
0.010567947290837765,
0.010819328017532825,
0.02253633737564087,
0.007606565486639738,
-0.0166458897292614,
0.049177151173353195,
0.014547229744493961,
0.018848739564418793,
-0.018022792413830757,
-0.03757132217288017,
0.027289383113384247,
0.042148008942604065,
0.034891292452812195,
0.06992780417203903,
-0.05415147542953491,
0.04858938604593277,
0.03414679691195488,
0.022113105282187462,
0.023424463346600533,
0.023661501705646515,
0.0025475765578448772,
0.023914480581879616,
0.04444869980216026,
-0.03761793673038483,
0.013891330920159817,
-0.059664927423000336,
-0.02373979054391384,
-0.05560679733753204,
-0.004057447426021099,
0.012678590603172779,
0.06365261971950531,
-0.0069326539523899555,
-0.03425239026546478,
0.014888050965964794,
-0.0008863260154612362,
-0.04741240665316582,
0.057400014251470566,
-0.062274858355522156,
0.05963143706321716,
0.03781220689415932,
0.027299633249640465,
-0.022646915167570114,
0.03567115589976311,
-0.054591961205005646,
-0.012938068248331547,
0.039216842502355576,
-0.0765865370631218,
-0.0325973704457283,
-0.011486921459436417,
-0.00186744867824018,
0.02700101211667061,
-0.00391940725967288,
-0.026005903258919716,
-0.029788613319396973,
-0.04396330937743187,
0.03654026985168457,
-0.002580305328592658,
0.09238547831773758,
0.0033867759630084038,
-0.01785491220653057,
0.04371748864650726,
-0.04490695893764496,
-0.009739679284393787,
0.010751345194876194,
0.019539600238204002,
-0.05052298679947853,
0.029181646183133125,
0.049674902111291885,
-0.035133570432662964,
-0.03157078102231026,
-0.09952140599489212,
-0.027007129043340683,
0.004598475061357021,
-0.03819708898663521,
-0.0259038507938385,
0.011033156886696815,
-0.008197111077606678,
-0.025757092982530594,
-0.033422984182834625,
0.007222250569611788,
-0.06187408044934273,
-0.0683898776769638,
-0.0043236021883785725,
0.04442843794822693,
0.06313767284154892,
0.010557356290519238,
0.05000881478190422,
0.0005921376869082451,
0.027620457112789154,
-0.009065366350114346,
0.037394799292087555,
0.0018897892441600561,
0.0671863853931427,
0.022289443761110306,
-0.0368829183280468,
0.028399409726262093,
-0.01397753320634365,
0.061802562326192856,
-0.030649762600660324,
0.02192644774913788,
0.020263493061065674,
-0.0008111228817142546,
0.016679106280207634,
-0.008779688738286495,
-0.009620267897844315,
0.0689336359500885,
-0.015608538873493671,
0.009996872395277023,
-0.025570672005414963,
-0.003422507783398032,
0.020044438540935516,
0.04240847006440163,
-0.04879027605056763,
0.01688193902373314,
-0.02880692481994629,
0.015947766602039337,
0.035508688539266586,
0.003839109791442752,
-0.035826146602630615,
0.0038957083597779274,
0.04099781811237335,
-0.06331585347652435,
0.0043873777613043785,
0.03096032701432705,
-0.04224082827568054,
-0.046028293669223785,
0.02539915218949318,
-0.0010520858922973275,
0.06224451959133148,
0.02878861129283905,
-0.04231758788228035,
-0.0016076831379905343,
0.03484897315502167,
-0.014877423644065857,
-0.0658673495054245,
0.08318623900413513,
0.033950164914131165,
-0.058226536959409714,
-0.054884057492017746,
0.009444178082048893,
-0.014478476718068123,
-0.018892580643296242,
0.011340775527060032,
0.01201566681265831,
0.04481274634599686,
0.001978915184736252,
-0.014474771916866302,
-0.046440742909908295,
0.06235054135322571,
0.036084678024053574,
0.004940112121403217,
-0.03768746927380562,
0.010788069106638432,
0.0709950178861618,
0.008106641471385956,
0.052147626876831055,
-0.036187805235385895,
-0.01739995926618576,
0.02925662323832512,
-0.0250723734498024,
-0.0063370587304234505,
-0.06595201790332794,
-0.02047336846590042,
0.026272939518094063,
-0.08547884225845337,
0.03765229135751724,
0.020747536793351173,
-0.028410594910383224,
0.01915067806839943,
-0.024922460317611694,
-0.029942862689495087,
0.0025241710245609283,
-0.04456230625510216,
0.03883138298988342,
0.023283934220671654,
0.04197034612298012,
-0.06458123028278351,
-0.00981469452381134,
-0.010408813133835793,
-0.030961882323026657,
-0.022636935114860535,
0.0031144029926508665,
0.007500775158405304,
0.016884591430425644,
-0.05771532282233238,
0.0037355609238147736,
0.04142579063773155,
0.05410246551036835,
-0.009327314794063568,
-0.033193979412317276,
-0.0012540043098852038,
0.005463381297886372,
0.0013057412579655647,
0.03389701247215271,
-0.02967740222811699,
0.03579872101545334,
-0.008713613264262676,
-0.0030947260092943907,
-0.02589254267513752,
0.035674963146448135,
0.05471605062484741,
0.002124446677044034,
-0.06838492304086685,
-0.06775009632110596,
-0.006251535378396511,
-0.019572177901864052,
0.04157786816358566,
0.029617274180054665,
0.03405828773975372,
0.021372929215431213,
-0.05476396530866623,
-0.004693371243774891,
-0.003922936040908098,
0.026880059391260147,
-0.008668619208037853,
-0.03381475806236267,
0.05858805030584335,
-0.017041269689798355,
0.05091852694749832,
0.03344821557402611,
-0.00991375558078289,
0.018559250980615616,
0.015438934788107872,
-0.02585415728390217,
-0.10500713437795639,
0.03585968539118767,
-0.014539365656673908,
0.005202458240091801,
-0.02038544975221157,
-0.10857464373111725,
0.0379054881632328,
-0.0028521395288407803,
0.00979283545166254,
0.01771167293190956,
-0.017244650050997734,
0.014466988854110241,
-0.049098290503025055,
-0.021956514567136765,
0.002392074791714549,
-0.026518462225794792,
-0.0435841865837574,
-0.0037705309223383665,
-0.018583524972200394,
-0.09399352222681046,
-0.00044399654143489897,
0.018434206023812294,
-0.0008380948565900326,
0.02169661782681942,
-0.026914989575743675,
0.024060728028416634,
0.07375248521566391,
-0.04034199193120003,
-0.03222942352294922,
-0.04768478497862816,
-0.0010288197081536055,
0.02788359299302101,
-0.043851908296346664,
0.014316283166408539,
-0.040687624365091324,
0.04234909638762474,
-0.08550781011581421,
0.023506026715040207,
0.009844072163105011,
-0.022830182686448097,
0.03574008122086525,
-0.0057262093760073185,
-0.03014775924384594,
0.048231612890958786,
-0.010150863789021969,
0.037056054919958115,
0.004141066689044237,
0.0020298392046242952,
0.01770288124680519,
-0.03484062850475311,
0.04158680513501167,
-0.0461508072912693,
0.05173049122095108,
-0.06264999508857727,
0.03362796828150749,
-0.05477288365364075,
0.06039474532008171,
0.029266787692904472,
-0.014934908598661423,
0.04868605360388756,
-0.012261762283742428,
-0.04119342193007469,
0.022687537595629692,
0.012865987606346607,
0.04356350749731064,
-0.033784639090299606,
-0.03473998233675957,
-0.04035767540335655,
-0.046227097511291504,
0.03696326166391373,
-0.026891406625509262,
-0.054843463003635406,
-0.05763084068894386,
0.037343982607126236,
0.04541822150349617,
-0.04282459244132042,
-0.023538827896118164,
0.009846869856119156,
0.019728777930140495,
0.032162901014089584,
0.03483438864350319,
-0.001821822952479124,
-0.047831930220127106,
0.0718061700463295,
0.04405387490987778,
-0.01072804257273674,
0.0021075194235891104,
-0.04467674717307091,
-0.01779569312930107,
-0.017539914697408676,
0.05901336669921875,
0.04651644453406334,
-0.06216374784708023,
0.05130908638238907,
-0.014954070560634136,
-0.02721790224313736,
-0.025437956675887108,
-0.02107040211558342,
0.059189651161432266,
-0.008176349103450775,
0.006488470826297998,
-0.0013479709159582853,
-0.024050986394286156,
0.019167060032486916,
0.007102987263351679,
-0.040151141583919525,
0.010948379524052143,
-0.054167941212654114,
-0.04448631405830383,
0.05299561470746994,
-0.04025410860776901,
-0.0040894183330237865,
0.03851890563964844,
-0.03471193090081215,
-0.03637014701962471,
-0.0341360829770565,
-0.010756522417068481,
-0.06025156006217003,
-0.10125406831502914,
-0.0002500502159819007,
-0.008281515911221504,
0.008709999732673168,
-0.0039026939775794744,
-0.01064234972000122,
-0.005147313233464956,
-0.0158425010740757,
-0.036323558539152145,
0.04597068950533867,
0.05876270309090614,
-0.01907350681722164,
0.04027222841978073,
0.054281920194625854,
0.04460633918642998,
-0.035425662994384766,
0.024216530844569206,
0.003075012471526861,
-0.02087969146668911,
-0.05109650641679764,
0.016174620017409325,
-0.0176469124853611,
0.06347469985485077,
0.042511653155088425,
-0.04948711395263672,
-0.04580260068178177,
-0.025220060721039772,
0.053972192108631134,
0.01667141355574131,
-0.059668730944395065,
0.015502926893532276,
0.008485228754580021,
0.03011404722929001,
0.014542818069458008,
0.008241280913352966,
-0.03510841727256775,
0.0054216329008340836,
0.03618089109659195,
0.02875768207013607,
0.022394811734557152,
-0.009000102989375591,
0.0032931219320744276,
-0.004116669297218323,
0.002936192322522402,
0.0030091973021626472,
0.041197359561920166,
0.04306682199239731,
-0.038017045706510544,
-0.020509250462055206,
-0.006729656830430031,
0.012111904099583626,
0.0453275591135025,
-0.03334478661417961,
-0.003015692811459303,
0.026365183293819427,
-0.03787669539451599,
-0.04403778910636902,
-0.020541328936815262,
-0.06156732141971588,
0.03529772534966469,
0.00353896408341825,
0.003740397747606039,
0.10783383995294571,
-0.033490873873233795,
0.04614059627056122,
0.018168166279792786,
-0.05949394032359123,
-0.046535201370716095,
0.05119522288441658,
0.04674983769655228,
-0.003922603093087673,
-0.007203115615993738,
0.0636570155620575,
0.023979444056749344,
0.004984288476407528,
-0.024422969669103622,
0.02424948662519455,
0.025495612993836403,
-0.07296434044837952,
0.012503082863986492,
-0.006225628778338432,
-0.016545744612812996,
-0.019750215113162994,
0.07056944817304611,
-0.002579296240583062,
0.0011417652713134885,
0.00030922130099497736,
0.05178724601864815,
0.05065762624144554,
-0.02081318199634552,
-0.045859068632125854,
0.013756269589066505,
-0.00295413751155138,
-0.027064112946391106,
-0.027615321800112724,
0.0063149454072117805,
-0.00260380026884377,
-0.04879799485206604,
-0.03287119045853615,
-0.055767305195331573,
0.07124728709459305,
0.0493033267557621,
0.0267950426787138,
-0.03004160337150097,
0.07780111581087112,
-0.02782798558473587,
-0.004444887861609459,
0.026894964277744293,
0.039737336337566376,
0.023759374395012856,
0.006001562811434269,
0.034612614661455154,
-0.004830760415643454,
-0.08019303530454636,
-0.015824398025870323,
0.005343790631741285,
-0.01802515611052513,
-0.001443297485820949,
-0.09507560729980469,
-0.043748389929533005,
-0.020171571522951126,
0.01829579472541809,
-0.015635361894965172,
0.01585374027490616,
-0.027774067595601082,
0.02183513157069683,
0.00828724354505539,
0.02908322773873806,
0.0784907191991806,
0.03243904560804367,
-0.052227895706892014,
0.02855389192700386,
0.013878303579986095,
-0.012435992248356342,
0.008867138996720314,
0.037465427070856094,
-0.02435166761279106,
-0.015598579309880733,
0.009665641002357006,
-0.013132899068295956,
0.007712343707680702,
-0.0012752455659210682,
-0.007937818765640259,
0.020952925086021423,
-0.009249075315892696,
0.04938651621341705,
0.029599471017718315,
0.03437846153974533,
0.007863258942961693,
0.0030576137360185385,
-0.06791526079177856,
0.02499009482562542,
0.05854903161525726,
-0.053693074733018875,
-0.022786559537053108,
-0.008871160447597504,
0.001936720684170723,
0.039557863026857376,
0.008224617689847946,
-0.04008200392127037,
-0.03180468827486038,
-0.06148158386349678,
-0.023675398901104927,
0.031071752309799194,
0.005239441990852356,
-0.03585135191679001,
-0.029734155163168907,
-0.019555706530809402,
0.015510434284806252,
-0.07522425800561905,
0.021315816789865494,
0.04072095826268196,
-0.006036956328898668,
0.0805802196264267,
0.009131633676588535,
0.05815202742815018,
-0.016867078840732574,
0.008255913853645325,
0.00792199932038784,
-0.006092551629990339,
0.01724054664373398,
0.06627508997917175,
0.011659900657832623,
0.007086755707859993,
-0.06789107620716095,
0.02109937183558941,
0.03419031575322151,
-0.0508817657828331,
-0.042073048651218414,
-0.048720765858888626,
0.011571316048502922,
-0.02330712042748928,
-0.04056207463145256,
0.061150263994932175,
0.0017220883164554834,
0.000699625990819186,
-0.024363497272133827,
-0.04049428924918175,
0.00973091647028923,
-0.026381172239780426,
-0.014484092593193054,
-0.06836248189210892,
0.0023907648865133524,
0.008767416700720787,
0.03883163630962372,
0.04051915183663368,
-0.011078531853854656,
-0.06399901956319809,
0.005824527703225613,
0.010454243049025536,
-0.009954534471035004,
0.028808947652578354,
0.040311820805072784,
0.05689719319343567,
-0.005558621603995562,
0.022117583081126213,
-0.0387585386633873,
-0.000891116273123771,
-0.008273517712950706,
-0.021025750786066055,
0.012370944954454899,
0.02269141748547554,
0.07264700531959534,
-0.017199471592903137,
-0.03291371837258339,
-0.022516535595059395,
-0.027609283104538918,
0.011118077673017979,
0.03206363692879677,
-0.04234166070818901,
0.05534674599766731,
-0.02095341496169567,
0.03475688025355339,
-0.02790268138051033,
0.017953429371118546,
-0.03259069100022316,
-0.020398404449224472,
0.017830921337008476,
0.003319494891911745,
0.004242068622261286,
-0.02190173789858818,
-0.020385872572660446,
-0.00003396143074496649,
-0.002543970011174679,
0.06448943167924881,
-0.08399377018213272,
-0.03169263154268265,
-0.08092010021209717,
-0.04553164914250374,
-0.0023635742254555225,
0.00004429758701007813,
-0.012123283930122852,
0.03923749551177025,
-0.030349938198924065,
0.00981971062719822,
0.018840517848730087,
0.030840037390589714,
0.06251483410596848,
0.00869138352572918,
0.0547323115170002,
0.0010536496993154287,
-0.01590745523571968,
0.017860986292362213,
-0.004617319907993078,
0.02067074179649353,
-0.02872920036315918,
0.0035933153703808784,
0.01240637619048357,
0.0707598552107811,
0.0009480896987952292,
-0.05598942190408707,
0.04934369772672653,
-0.015473266132175922,
-0.019672244787216187,
-0.006598979700356722,
0.050342053174972534,
0.04127850383520126,
-0.019250864163041115,
0.03214249014854431,
0.0002509217301849276,
0.010872501879930496,
-0.006350184325128794,
-0.003943214192986488,
-0.006412684917449951,
-0.04744018614292145,
0.012739674188196659,
0.04597577825188637,
-0.005132089368999004,
0.014278164133429527,
-0.04291433095932007,
0.008207693696022034,
0.021567849442362785,
-0.04996047914028168,
-0.017010558396577835,
-0.04338560625910759,
-0.0014946633018553257,
-0.029237359762191772,
-0.03544827178120613,
0.02690267004072666,
-0.010457810014486313,
0.01762094534933567,
0.022078057751059532,
0.03630923107266426,
-0.03387526795268059,
-0.024608228355646133,
-0.0871429592370987,
-0.010226606391370296,
-0.03736501932144165
] |
<p>A student conducts an experiment to measure the motion of two unknown masses (A and B) along a smooth table. A constant force of 1 N was applied by means of a string connected by a falling weight. </p>
<p>A motion sensor recorded the position (measured from the start line) of each mass at regular time intervals as they slid along the table. The results displayed by the data logger are tabulated: </p>
<p><img src="http://i.stack.imgur.com/RDHr0.png" alt="enter image description here"></p>
<p>What would be the best way of describing the motion of both masses? Do you use acceleration? </p> | g9225 | [
0.04118506237864494,
0.02269257791340351,
-0.007389110513031483,
-0.024273794144392014,
0.05027968809008598,
-0.011651373468339443,
0.044213198125362396,
-0.004988706670701504,
-0.06971336156129837,
-0.016112590208649635,
-0.0018952896352857351,
0.011442909948527813,
0.02500363066792488,
0.049595292657613754,
0.00719175161793828,
0.00655130622908473,
0.08909045159816742,
-0.07341907918453217,
-0.011789623647928238,
0.020483285188674927,
0.07713287323713303,
0.07469158619642258,
-0.02124970033764839,
0.02027699165046215,
0.04002733901143074,
-0.023743469268083572,
-0.03239213302731514,
-0.005594656802713871,
-0.0325402207672596,
-0.03974360227584839,
0.0144810751080513,
-0.017783934250473976,
0.05094805732369423,
0.016254520043730736,
-0.008206897415220737,
-0.028682388365268707,
-0.0032473928295075893,
-0.0019734965171664953,
-0.04737366735935211,
-0.020714841783046722,
-0.024269862100481987,
-0.06690935045480728,
0.03697750344872475,
0.002471694489941001,
0.05433860048651695,
0.003623261349275708,
-0.017052918672561646,
-0.0676470398902893,
-0.0031866817735135555,
0.027891503646969795,
-0.026639534160494804,
0.025903934612870216,
0.016630016267299652,
-0.012796351686120033,
-0.026706906035542488,
0.07649005204439163,
-0.027107756584882736,
0.012165040709078312,
0.01087222620844841,
0.026717305183410645,
0.0041075474582612514,
-0.056907590478658676,
-0.0008479260141029954,
-0.11239024251699448,
0.04414793476462364,
0.05163870006799698,
-0.029889438301324844,
0.04321790859103203,
0.013500213623046875,
-0.010264158248901367,
-0.028979239985346794,
0.028378142043948174,
0.017595671117305756,
-0.02584252692759037,
-0.09278057515621185,
-0.016108371317386627,
-0.02991098165512085,
-0.052684515714645386,
0.007517283782362938,
0.022888749837875366,
-0.03476841747760773,
0.028625940904021263,
0.06498905271291733,
0.0134056331589818,
0.07410342246294022,
-0.012899830937385559,
0.012582020834088326,
0.023693155497312546,
-0.0056505585089325905,
0.02429104410111904,
0.03175392746925354,
-0.04683301970362663,
0.07561466842889786,
0.004749256186187267,
-0.02150588668882847,
-0.03903428837656975,
-0.035504408180713654,
0.10241144895553589,
0.009682845324277878,
0.00877183023840189,
0.009337452240288258,
0.03431979939341545,
-0.03265245258808136,
0.01091784331947565,
0.053466856479644775,
-0.038916803896427155,
0.007513246964663267,
-0.008553041145205498,
-0.018660521134734154,
-0.018856292590498924,
0.053239647299051285,
-0.047540027648210526,
-0.011317741125822067,
-0.07249019294977188,
-0.010270633734762669,
-0.060397129505872726,
0.04641883447766304,
0.04663516953587532,
-0.014674318954348564,
0.02819492295384407,
-0.031344007700681686,
0.030450083315372467,
0.004022072535008192,
0.06163853406906128,
-0.005383397918194532,
-0.028970271348953247,
0.00871698185801506,
0.03433246910572052,
0.011752530001103878,
-0.033604398369789124,
0.017817553132772446,
0.025080526247620583,
0.06055830419063568,
0.009920417331159115,
-0.029676787555217743,
0.014856983907520771,
0.0010259900009259582,
0.0018707442795857787,
-0.021826911717653275,
-0.01258549839258194,
0.021182427182793617,
-0.026938950642943382,
-0.030498506501317024,
-0.03470579907298088,
-0.04844158887863159,
0.04002216458320618,
-0.039892736822366714,
0.0026329029351472855,
0.05570464953780174,
0.0779368206858635,
0.008697017095983028,
0.032009951770305634,
-0.013209330849349499,
-0.014993545599281788,
0.032287098467350006,
-0.0021898013073951006,
0.08206069469451904,
0.004502466414123774,
-0.010874677449464798,
0.026177864521741867,
0.04796406999230385,
-0.030547212809324265,
0.012926790863275528,
0.0076492889784276485,
-0.01264215912669897,
-0.01609167829155922,
-0.004127380438148975,
-0.020138727501034737,
0.031647127121686935,
-0.048651814460754395,
-0.07388853281736374,
-0.05756214261054993,
0.034678395837545395,
0.050494883209466934,
-0.06517390161752701,
-0.027606653049588203,
0.006736970506608486,
-0.0075668832287192345,
0.03881477937102318,
0.0122098783031106,
0.04565832018852234,
-0.017398430034518242,
0.0011709814425557852,
-0.0222433153539896,
0.0022741048596799374,
-0.03128774091601372,
-0.003291314234957099,
0.02540670335292816,
-0.05781463161110878,
0.0004317130660638213,
-0.05055105686187744,
-0.10277992486953735,
-0.02283274382352829,
0.0309809111058712,
-0.05352834612131119,
0.005291627254337072,
0.05341780558228493,
-0.007501927670091391,
0.007908642292022705,
0.001203599851578474,
0.01194468792527914,
-0.001286233658902347,
-0.012664702720940113,
-0.02439880184829235,
0.0023422949016094208,
-0.019701456651091576,
0.014493615366518497,
0.009938761591911316,
-0.009515367448329926,
-0.012725337408483028,
0.045444559305906296,
0.07562398165464401,
-0.020516177639365196,
0.015451537445187569,
-0.004845624323934317,
-0.018318695947527885,
0.03272056579589844,
-0.01192681398242712,
0.054460395127534866,
-0.014207746833562851,
-0.010305975563824177,
-0.04917643964290619,
0.045547254383563995,
-0.011549734510481358,
-0.03163232281804085,
-0.04176630824804306,
-0.014372419565916061,
0.018674489110708237,
-0.04425932466983795,
0.007664097007364035,
-0.06452924758195877,
0.006565977819263935,
0.013914713636040688,
0.010813015513122082,
0.058349065482616425,
0.021830439567565918,
-0.022860748693346977,
0.059130337089300156,
0.0158027783036232,
-0.013715920969843864,
0.008052018471062183,
-0.05607954040169716,
0.015560074709355831,
-0.06869886815547943,
-0.017397211864590645,
-0.008862676098942757,
0.06635139882564545,
0.034751418977975845,
0.027337420731782913,
0.029850250110030174,
-0.035375699400901794,
-0.02390141785144806,
-0.0217939093708992,
0.002984433900564909,
0.03843996673822403,
-0.017677735537290573,
0.0051873489283025265,
-0.007113014347851276,
-0.01939440704882145,
0.02506300061941147,
0.0424514077603817,
-0.005547826178371906,
-0.032448943704366684,
0.02342366799712181,
-0.02429809607565403,
-0.0539800189435482,
-0.020715149119496346,
-0.023221224546432495,
0.02101774327456951,
-0.005745286121964455,
-0.018456805497407913,
-0.02982351742684841,
0.002343689324334264,
0.035092953592538834,
-0.01947459764778614,
-0.03312978148460388,
0.02425188012421131,
-0.038417182862758636,
-0.015714973211288452,
-0.0154215507209301,
-0.004836144857108593,
-0.02074771374464035,
-0.034789640456438065,
0.0009559269528836012,
0.024795208126306534,
0.01818937622010708,
0.0175023190677166,
-0.03486151993274689,
-0.03585801646113396,
0.02072472684085369,
-0.04696430638432503,
0.012652138248085976,
0.03393920138478279,
0.019115308299660683,
-0.02360575832426548,
0.1279268115758896,
0.0660020112991333,
-0.037888169288635254,
0.049229130148887634,
0.016519809141755104,
-0.03312249109148979,
-0.025801965966820717,
-0.0347939170897007,
0.013295071199536324,
-0.023291002959012985,
-0.030360491946339607,
0.012468223460018635,
-0.06599914282560349,
-0.00855119526386261,
-0.001451865304261446,
-0.01464841328561306,
-0.003857538104057312,
0.023800121620297432,
-0.009860976599156857,
-0.027847392484545708,
-0.021667929366230965,
-0.023131102323532104,
0.006580241955816746,
-0.016826441511511803,
-0.018053382635116577,
-0.029329441487789154,
-0.08379887044429779,
0.07348185777664185,
0.016245264559984207,
-0.041064780205488205,
0.06158359721302986,
0.027260590344667435,
0.04249388352036476,
-0.061300914734601974,
-0.06214853748679161,
-0.010340666398406029,
0.02207122929394245,
-0.041847191751003265,
-0.030558636412024498,
0.015843180939555168,
-0.03808435797691345,
0.05791863054037094,
-0.010395633056759834,
-0.012274272739887238,
0.04483465477824211,
-0.038934532552957535,
0.002072624396532774,
-0.027005381882190704,
-0.009557434357702732,
0.00519903376698494,
-0.0398578979074955,
0.03058195859193802,
-0.026114610955119133,
0.02489195019006729,
-0.06190232187509537,
0.03726358339190483,
-0.05033846199512482,
-0.006450768560171127,
0.016270410269498825,
-0.04569686949253082,
-0.0070863887667655945,
-0.004838427063077688,
-0.02489158697426319,
-0.07106047123670578,
0.010632327757775784,
0.022078054025769234,
0.03542846813797951,
-0.03199485316872597,
0.05187526345252991,
-0.036962661892175674,
-0.022131608799099922,
-0.05267633870244026,
0.09877531975507736,
-0.013089279644191265,
0.006473633926361799,
-0.016660254448652267,
-0.05772186070680618,
0.014787253923714161,
-0.052020568400621414,
0.005266755353659391,
-0.05247335508465767,
0.02409186214208603,
-0.0015101621393114328,
-0.011002576909959316,
0.06152119114995003,
0.03225739672780037,
-0.0045164464972913265,
-0.004350264091044664,
0.009571867063641548,
0.020915934816002846,
0.0018962621688842773,
-0.021784644573926926,
0.02990058995783329,
0.05439804866909981,
-0.02650311402976513,
0.050558723509311676,
-0.0707295686006546,
-0.048513419926166534,
0.014516337774693966,
0.031201880425214767,
0.004898239392787218,
0.007628328632563353,
0.021330660209059715,
0.037903349846601486,
-0.02013857662677765,
-0.052553415298461914,
0.0528905987739563,
-0.04700716212391853,
-0.017953960224986076,
-0.06594954431056976,
-0.007271719630807638,
0.014121346175670624,
-0.0159541554749012,
0.04441364109516144,
0.05421938747167587,
-0.00527165737003088,
-0.019991829991340637,
-0.01833435148000717,
-0.016050910577178,
0.003453675890341401,
0.019679948687553406,
0.017825817689299583,
0.06225164607167244,
-0.0630459114909172,
0.009971939027309418,
-0.03202839940786362,
0.10401304811239243,
-0.014643169939517975,
-0.0894513800740242,
-0.06783106178045273,
-0.00901798065751791,
0.02650921605527401,
0.023098882287740707,
0.03547988459467888,
0.015803126618266106,
0.002434635302051902,
0.004182022530585527,
0.05891738459467888,
0.06999962031841278,
-0.035235319286584854,
0.07829565554857254,
0.05337785929441452,
0.022451570257544518,
0.057462699711322784,
0.044275861233472824,
-0.0013694328954443336,
0.05637875571846962,
-0.0279952771961689,
0.020462799817323685,
-0.06280221045017242,
0.09382971376180649,
0.002871037693694234,
-0.06327313929796219,
0.004022287670522928,
-0.014581967145204544,
-0.0218687541782856,
0.023368023335933685,
-0.03141219541430473,
0.018096599727869034,
0.021743344143033028,
0.003190954215824604,
-0.00603403989225626,
0.06672355532646179,
-0.03194268047809601,
0.0018527284264564514,
0.020738087594509125,
0.03190310671925545,
-0.014907706528902054,
-0.04806772619485855,
-0.07605087757110596,
-0.04734530672430992,
-0.03071005642414093,
-0.03221729397773743,
0.0016228951280936599,
-0.0017806995892897248,
-0.0035789073444902897,
-0.033495791256427765,
-0.007348119746893644,
0.011578189209103584,
0.06171748414635658,
0.041433144360780716,
0.014478188008069992,
0.01012386567890644,
0.05540498346090317,
-0.01915949210524559,
-0.03611192852258682,
0.01836492493748665,
0.061856672167778015,
-0.05972536653280258,
0.009665320627391338,
-0.04426492378115654,
-0.021848898380994797,
0.002796898828819394,
0.06781996786594391,
0.023731814697384834,
0.026668956503272057,
0.03710302710533142,
-0.03399364650249481,
-0.051285408437252045,
-0.009040731005370617,
-0.01255017425864935,
-0.007043634541332722,
0.0017784889787435532,
0.004744359757751226,
0.0014664758928120136,
-0.07554920762777328,
0.05517304316163063,
0.07355566322803497,
0.03498801589012146,
-0.006235133856534958,
0.05059400573372841,
0.015836484730243683,
-0.02501937374472618,
0.009735790081322193,
0.060598280280828476,
-0.03153207525610924,
0.12305586785078049,
0.04930220916867256,
0.006267716642469168,
-0.03457222506403923,
0.03258334472775459,
0.09520435333251953,
0.01763632334768772,
-0.009635770693421364,
0.0024558808654546738,
0.08068732917308807,
-0.004126580897718668,
0.040093373507261276,
0.020329182967543602,
0.020805513486266136,
-0.011301339603960514,
-0.03195590525865555,
-0.0001286594633711502,
-0.04708771035075188,
-0.04279240220785141,
0.018995892256498337,
-0.048686154186725616,
0.014298749156296253,
-0.07177235186100006,
-0.018581697717308998,
-0.04538728669285774,
0.0175348948687315,
0.01051931269466877,
0.0021712775342166424,
-0.031435854732990265,
-0.10193139314651489,
-0.027348091825842857,
0.00017092929920181632,
0.028138697147369385,
0.004097327124327421,
-0.002548960503190756,
0.017017412930727005,
-0.036938492208719254,
0.0512147918343544,
-0.04545191302895546,
0.014212916605174541,
0.0006895102560520172,
-0.014718104153871536,
-0.012322253547608852,
0.019481966271996498,
0.012002179399132729,
0.004659024067223072,
-0.028139222413301468,
-0.03399594873189926,
0.0014986873138695955,
0.0029476084746420383,
-0.01670200191438198,
0.06099711358547211,
0.014367165043950081,
0.003465253859758377,
-0.04464050382375717,
0.014949138276278973,
-0.007073243148624897,
0.010697122663259506,
0.001074029365554452,
-0.013736002147197723,
-0.03975483030080795,
-0.01289178617298603,
0.02882610261440277,
0.0253582913428545,
0.042758673429489136,
-0.021665498614311218,
0.020478030666708946,
-0.045393090695142746,
-0.028518078848719597,
0.012008382007479668,
-0.0023014245089143515,
0.006369071081280708,
0.020753005519509315,
-0.021381942555308342,
-0.015705304220318794,
-0.005448382813483477,
-0.0228883009403944,
0.01341681182384491,
-0.0029270697850733995,
-0.034904222935438156,
0.00630896957591176,
-0.015792859718203545,
0.0011244009947404265,
-0.08181621134281158,
-0.012349848635494709,
-0.019550452008843422,
-0.03516395017504692,
-0.017860446125268936,
0.03369727358222008,
-0.03061591275036335,
0.01691243052482605,
0.05793382227420807,
-0.03935043886303902,
-0.012745962478220463,
-0.02677847445011139,
-0.007372377440333366,
-0.018628248944878578,
0.0010662440909072757,
-0.07976815849542618,
-0.04952245205640793,
0.011111988686025143,
0.005641459953039885,
0.05494171753525734,
0.012364598922431469,
0.0072860317304730415,
0.014751206152141094,
0.008930807001888752,
0.01026661042124033,
-0.015377308242022991,
0.0021455001551657915,
-0.01433541439473629,
0.027293970808386803,
-0.07111434638500214,
0.011958224698901176,
0.0070968992076814175,
-0.07712378352880478,
0.013543751090765,
0.004887830000370741,
0.005633590742945671,
-0.004783384967595339,
-0.0035626969765871763,
0.05060829222202301,
0.005924804601818323,
-0.019924970343708992,
0.12191767245531082,
0.019923308864235878,
0.07232522964477539,
0.0113846929743886,
0.034580640494823456,
0.03512051701545715,
0.042371414601802826,
-0.017024919390678406,
0.030419092625379562,
-0.023969870060682297,
-0.026209963485598564,
0.036061447113752365,
0.029256882146000862,
0.009481575340032578,
-0.02739715948700905,
-0.05945984274148941,
-0.031042668968439102,
-0.008956697769463062,
0.05567573755979538,
0.016169192269444466,
0.03929053992033005,
0.05440998449921608,
0.03875880688428879,
0.01931292749941349,
-0.025357315316796303,
-0.06288443505764008,
-0.04453860595822334,
0.004674182273447514,
-0.0633586123585701,
0.013504507020115852,
0.017143376171588898,
-0.0381256528198719,
0.016957053914666176,
-0.04111703112721443,
0.027815619483590126,
0.023336036130785942,
-0.025214137509465218,
0.02121024578809738,
0.031611256301403046,
0.014416269958019257,
0.0420459620654583,
-0.0034435929264873266,
-0.0482417494058609,
-0.06726621836423874,
-0.015943540260195732,
-0.018923718482255936,
-0.01755322515964508,
0.02166261523962021,
0.04700927063822746,
-0.0015217922627925873,
0.010949698276817799,
-0.024489495903253555,
0.04902012273669243,
-0.019870422780513763,
-0.04170907661318779,
-0.03223121538758278,
0.019021112471818924,
-0.01942179538309574,
-0.05349446460604668,
-0.01125763263553381,
-0.0229518823325634,
-0.04132920876145363,
0.04184224456548691,
0.014532635919749737,
0.02794911153614521,
-0.014644242823123932,
-0.00804965104907751,
0.03106870874762535,
0.07731102406978607,
-0.020386338233947754,
0.009038570336997509,
-0.014535890892148018,
-0.02084941789507866,
0.05948413163423538,
-0.00707774655893445,
-0.011655531823635101,
0.048826538026332855,
0.019518889486789703,
-0.020619234070181847,
0.0021776389330625534,
0.035819701850414276,
-0.06448285281658173,
0.009630574844777584,
0.02789870649576187,
0.011782735586166382,
0.026620732620358467,
0.005478318314999342,
0.02937687747180462,
-0.031219717115163803,
-0.0013646658044308424,
-0.048358526080846786,
-0.015809131786227226,
-0.006737398914992809,
-0.0005989359924569726,
-0.00879503320902586,
0.011444180272519588,
-0.01648697629570961,
-0.004901356529444456,
0.033508479595184326,
-0.03341548144817352,
-0.013570085167884827,
0.023088868707418442,
-0.006647475995123386,
-0.04579484835267067,
0.0545528270304203,
-0.02928578294813633,
-0.03958205133676529,
-0.03535514697432518,
0.028062017634510994,
0.043764710426330566,
-0.012563317082822323,
-0.02146880514919758,
0.04438606649637222,
0.05135493353009224,
-0.07139980792999268,
0.04676869884133339,
0.026852363720536232,
-0.07374148815870285,
0.02679974026978016,
-0.008817475289106369,
0.02781447395682335,
-0.007021259982138872,
-0.011498349718749523,
-0.0023814011365175247,
0.01820189319550991,
-0.026897037401795387,
0.0038984979037195444,
-0.049339499324560165,
-0.027541421353816986,
-0.01606789603829384,
-0.01870623044669628,
0.035219963639974594,
0.01630587689578533
] |
<p>When quantizing Yang-Mills theory, we introduce the ghosts as a way to gauge-fix the path integral and make sure that we "count" only one contribution from each gauge-orbit of the gauge field $A_\mu\,^a$, because physically only the orbits themselves correspond to distinct physical configurations whereas the motion within the gauge-orbit should not contribute to the path-integral.</p>
<p>How come we don't run into this problem when we quantize the Fermions, which also have gauge transformations, and also have a gauge orbit? Shouldn't we include a gauge-fixing term for the Fermions as well, or does the term introduced for the Boson fields already pick out the gauge orbit for the Fermions as well? How does this technically come to be?</p>
<p>So far I introduce a gauge fixing term into the Lagrangian as $$ 1 = \int d\left[\alpha\right]\det\left(\frac{\delta G\left[A_{\mu}\left[\alpha\right]\right]}{\delta\alpha}\right)\delta\left(G\left[A\left[\alpha\right]\right]\right) $$ where $\alpha(x)$ are the gauge functions, and $G[]$ is a functional which is non-zero only for a unique gauge-representative in each gauge-orbit, where we have the transformations as: $$ \begin{cases}
\psi_{c_{i}} & \mapsto\left(1+i\alpha^{a}t^{a}\right)_{c_{i}c_{j}}\psi_{c_{j}}+\mathcal{O}\left(\left(\alpha^{a}\right)^{2}\right)\\
A_{\mu}\,^{a} & \mapsto A_{\mu}\,^{a}+\frac{1}{g}D_{\mu}\,^{ab}\alpha^{b}+\mathcal{O}\left(\left(\alpha^{a}\right)^{2}\right)
\end{cases} $$</p> | g9226 | [
0.02026408351957798,
0.02051064558327198,
-0.013638395816087723,
-0.039124611765146255,
0.07093033194541931,
0.007330183405429125,
0.05201619118452072,
0.09716390073299408,
0.003025153884664178,
-0.02082987315952778,
-0.0032735744025558233,
0.020653223618865013,
-0.003907436970621347,
0.03721253201365471,
-0.04099828004837036,
0.014628984965384007,
-0.0009362585842609406,
-0.001415579579770565,
0.062181778252124786,
-0.0365600548684597,
0.020093509927392006,
0.03409017249941826,
0.016179116442799568,
-0.020914291962981224,
0.01637396402657032,
-0.03444835916161537,
0.10876218974590302,
-0.050975777208805084,
0.017697636038064957,
0.0461667962372303,
0.03761371970176697,
0.04036843404173851,
0.06318166106939316,
-0.010533644817769527,
0.01436697505414486,
-0.013467256911098957,
0.06346521526575089,
0.03403997793793678,
0.039818841964006424,
-0.009730788879096508,
-0.0073938979767262936,
-0.05340058356523514,
-0.006269967649132013,
-0.006696728989481926,
-0.04389984905719757,
0.014640961773693562,
0.016513077542185783,
-0.03609619662165642,
0.03263813257217407,
0.04312780871987343,
0.026975074782967567,
0.03303210809826851,
0.07940947264432907,
-0.008569793775677681,
0.003408722812309861,
0.051080912351608276,
0.04566152021288872,
0.02233809046447277,
-0.015984000638127327,
0.05678374320268631,
-0.005546923726797104,
-0.0474088229238987,
0.05127774551510811,
0.015052282251417637,
0.00991362426429987,
-0.014665600843727589,
0.0003189249546267092,
-0.001801125705242157,
-0.02663581818342209,
-0.018010949715971947,
-0.02305743098258972,
-0.008903414942324162,
0.011275386437773705,
0.055088337510824203,
0.021861115470528603,
0.037593476474285126,
0.005255470052361488,
0.03848164156079292,
-0.010755570605397224,
-0.07259984314441681,
-0.05373600497841835,
-0.057977937161922455,
0.023670829832553864,
0.01323013473302126,
0.07893606275320053,
0.0046470072120428085,
-0.015205087140202522,
-0.018614409491419792,
-0.022610127925872803,
0.0029176853131502867,
-0.04316875711083412,
-0.049077823758125305,
0.05645439773797989,
0.05921667441725731,
-0.0037261121906340122,
-0.003870835294947028,
0.013150433078408241,
0.0378434956073761,
0.004977304022759199,
-0.021320583298802376,
-0.07667265087366104,
0.05152720585465431,
-0.015173866413533688,
-0.021413380280137062,
-0.03761288523674011,
-0.023500243201851845,
0.005949199665337801,
0.018991654738783836,
0.05497834458947182,
-0.018856249749660492,
-0.032933060079813004,
0.04017027094960213,
0.00345946429297328,
-0.025292232632637024,
-0.041218310594558716,
0.03004664182662964,
0.052532657980918884,
-0.01042464841157198,
-0.05091958865523338,
0.03624095395207405,
0.006059892009943724,
-0.02850995771586895,
-0.024916909635066986,
0.015932675451040268,
0.00803124438971281,
0.003622933756560087,
-0.07400674372911453,
0.022753391414880753,
0.06517333537340164,
-0.017965074628591537,
0.020898330956697464,
0.02078600786626339,
0.018088847398757935,
0.0010532299056649208,
-0.016016211360692978,
-0.016475606709718704,
0.025610268115997314,
-0.004131400492042303,
-0.008937906473875046,
0.04778290167450905,
-0.03321551904082298,
-0.020454106852412224,
0.0043951706029474735,
0.005769317504018545,
-0.015331633388996124,
0.05031312257051468,
-0.012798324227333069,
-0.013424242846667767,
0.031117722392082214,
-0.03954295441508293,
0.001927911420352757,
0.06529546529054642,
-0.03706718608736992,
-0.01147117093205452,
0.05362879857420921,
-0.03257377818226814,
0.02043057605624199,
-0.017882462590932846,
-0.012809323146939278,
-0.05827207490801811,
0.0808812826871872,
0.0045327357947826385,
0.06018242985010147,
0.0020885830745100975,
-0.015253710560500622,
-0.016108941286802292,
0.042345061898231506,
-0.027304459363222122,
0.00779308844357729,
-0.025241147726774216,
0.02114832028746605,
-0.019377559423446655,
-0.020109297707676888,
0.03473030403256416,
0.02870970219373703,
0.07791703194379807,
-0.01543835736811161,
-0.006699744146317244,
-0.03582608699798584,
0.021926915273070335,
0.02860780991613865,
-0.013196263462305069,
0.004136144183576107,
-0.038867201656103134,
0.007327519357204437,
-0.043184179812669754,
-0.02816198393702507,
-0.042112670838832855,
-0.007765559479594231,
0.008843377232551575,
0.0054410588927567005,
-0.001955970423296094,
0.03483722731471062,
0.047062307596206665,
-0.0012364035937935114,
-0.004131844732910395,
0.027979761362075806,
-0.033266108483076096,
-0.028613662347197533,
-0.023282228037714958,
0.0014890525490045547,
0.039839934557676315,
0.030388422310352325,
-0.05824796482920647,
0.05837259069085121,
0.010496902279555798,
0.003958326764404774,
-0.006780944764614105,
-0.005145521834492683,
-0.03093348629772663,
0.016439393162727356,
-0.006684770341962576,
0.05800776928663254,
-0.05136459693312645,
-0.05836784467101097,
-0.011913083493709564,
0.021767232567071915,
-0.0030396361835300922,
-0.021650170907378197,
-0.04871039465069771,
0.025440530851483345,
0.015253134071826935,
0.05974737927317619,
0.017333954572677612,
-0.01003685500472784,
0.009498733095824718,
-0.02046968601644039,
0.00040459216688759625,
-0.027031106874346733,
0.03841862827539444,
-0.059002794325351715,
-0.001430876087397337,
-0.03932485356926918,
-0.025529740378260612,
0.008554521016776562,
-0.005041472148150206,
0.011217218823730946,
0.025371477007865906,
0.07452674210071564,
0.025200724601745605,
0.03302357718348503,
-0.004404589533805847,
0.008089995011687279,
-0.011683071032166481,
0.06997865438461304,
0.05370587855577469,
0.04380873218178749,
0.061652351170778275,
-0.06178443506360054,
0.06025306135416031,
0.008687466382980347,
-0.02085139788687229,
-0.030338900163769722,
-0.0004547767748590559,
0.015974128618836403,
-0.02594173140823841,
0.025670291855931282,
0.007449952885508537,
-0.028389986604452133,
0.02318127453327179,
0.027927275747060776,
-0.040268827229738235,
-0.0185126643627882,
0.04598401486873627,
-0.0289956983178854,
-0.01546849962323904,
-0.008293175138533115,
-0.004228238947689533,
-0.02749457210302353,
-0.007756853010505438,
-0.09465128183364868,
0.04184583202004433,
0.017212707549333572,
-0.032865971326828,
0.034491539001464844,
-0.027988258749246597,
-0.018688218668103218,
0.004646437708288431,
0.03717047721147537,
-0.019504228606820107,
-0.017640460282564163,
0.011676734313368797,
-0.0444810688495636,
0.014080281369388103,
-0.009769381955265999,
-0.06746359914541245,
-0.014166342094540596,
-0.015313755720853806,
0.0072550177574157715,
0.03926074877381325,
0.023027930408716202,
0.009274819865822792,
0.061928052455186844,
0.023408211767673492,
-0.04945773258805275,
-0.019703496247529984,
-0.013729813508689404,
0.005656592082232237,
-0.020926494151353836,
0.019138483330607414,
0.024382082745432854,
0.0592283196747303,
-0.02741541899740696,
0.044974323362112045,
0.03293754532933235,
-0.016576331108808517,
-0.05776503309607506,
-0.010328787378966808,
-0.012772020883858204,
-0.03386392444372177,
0.05036821961402893,
0.05012847110629082,
-0.04628980532288551,
-0.035936400294303894,
-0.013869336806237698,
-0.006861533969640732,
-0.014155115000903606,
-0.014985802583396435,
0.00012164837244199589,
0.00696879206225276,
-0.09269477427005768,
-0.011214549653232098,
-0.017654921859502792,
-0.040404707193374634,
0.02013680525124073,
0.020688017830252647,
-0.011367886327207088,
-0.019533002749085426,
0.045626115053892136,
0.019573833793401718,
0.019672950729727745,
-0.04310116916894913,
-0.05478883162140846,
-0.008812591433525085,
-0.03568435460329056,
-0.03409060835838318,
-0.025056084617972374,
-0.04520607739686966,
0.06244499981403351,
-0.011154933832585812,
-0.037299130111932755,
-0.02133006416261196,
-0.012159974314272404,
0.07135473191738129,
0.04644285514950752,
-0.03358805924654007,
0.011333417147397995,
0.05408772826194763,
0.03517676517367363,
-0.025279784575104713,
-0.019695037975907326,
-0.05001885071396828,
-0.0007113596657291055,
0.021352598443627357,
-0.041340313851833344,
-0.0166829414665699,
0.03276904299855232,
0.04502539336681366,
0.04734766483306885,
-0.03946373984217644,
0.007232019677758217,
-0.011711154133081436,
-0.02019590511918068,
-0.014791830442845821,
0.0025288749020546675,
-0.002076230011880398,
0.021528571844100952,
-0.008286122232675552,
0.02338654361665249,
-0.02596389129757881,
0.014046603813767433,
-0.031990550458431244,
-0.0158330537378788,
-0.05619757995009422,
-0.00942918285727501,
-0.03783800080418587,
0.01621164195239544,
-0.0005527888424694538,
-0.04339431971311569,
0.03159908205270767,
-0.03181624785065651,
0.05560290440917015,
0.0417497418820858,
0.026942046359181404,
0.03442764654755592,
0.05327611789107323,
-0.01581922546029091,
0.0068552810698747635,
-0.030262436717748642,
-0.028578132390975952,
-0.054910559207201004,
0.049461815506219864,
0.015294034034013748,
-0.0101996511220932,
0.030094075947999954,
-0.013948574662208557,
0.03919423371553421,
-0.043256066739559174,
0.005853345617651939,
0.044772472232580185,
0.00548325851559639,
-0.054297588765621185,
0.0019548661075532436,
-0.0372978039085865,
-0.012132304720580578,
-0.03841913864016533,
0.05006592348217964,
-0.00530518963932991,
0.035526398569345474,
-0.00680627441033721,
-0.05025758221745491,
0.003019743598997593,
0.05142364278435707,
-0.06311475485563278,
0.0008261172333732247,
-0.030044298619031906,
-0.009032504633069038,
-0.048013683408498764,
-0.002586452756077051,
-0.040487319231033325,
0.02820652164518833,
0.02881592884659767,
0.022452445700764656,
-0.02349019981920719,
-0.01738937385380268,
0.06764580309391022,
0.056805044412612915,
0.03620501235127449,
0.020342720672488213,
-0.05823856592178345,
0.02751726657152176,
0.06304734200239182,
0.02193569950759411,
0.009055751375854015,
-0.07496178150177002,
0.008381438441574574,
-0.0184894111007452,
0.03240254893898964,
0.0058559635654091835,
0.08025014400482178,
0.07625145465135574,
0.010760929435491562,
-0.015197829343378544,
-0.023121733218431473,
-0.01227579265832901,
0.014045936055481434,
-0.028104400262236595,
-0.06226620823144913,
-0.028199193999171257,
0.015249337069690228,
0.01058210153132677,
0.0431816503405571,
-0.044900186359882355,
-0.008800879120826721,
0.022976746782660484,
-0.054634157568216324,
0.01461969967931509,
0.010264848358929157,
0.009446891956031322,
-0.02886076830327511,
-0.07435202598571777,
-0.04709436371922493,
0.03340541943907738,
-0.002091942820698023,
0.008931312710046768,
-0.022529061883687973,
-0.07255369424819946,
0.03520358353853226,
-0.10071195662021637,
-0.03702906146645546,
0.02095532789826393,
0.03420175611972809,
0.010367480106651783,
-0.02477283775806427,
0.04958520457148552,
0.011501813307404518,
-0.00897989235818386,
-0.004981975071132183,
0.02434380166232586,
-0.04491197317838669,
-0.01157329510897398,
-0.04341405630111694,
0.055627427995204926,
0.026381930336356163,
-0.10421464592218399,
0.020559117197990417,
-0.04745567962527275,
-0.026148296892642975,
-0.027856577187776566,
-0.07618724554777145,
0.035328030586242676,
-0.032781168818473816,
0.018646370619535446,
-0.020660046488046646,
-0.000549438816960901,
-0.02385631762444973,
-0.04470307007431984,
0.054655514657497406,
0.0032459625508636236,
0.030017321929335594,
-0.011276835575699806,
0.052456971257925034,
-0.01746532879769802,
-0.057285748422145844,
-0.00033567630453035235,
0.0553581677377224,
0.03759213164448738,
0.019203992560505867,
0.012441432103514671,
-0.03313770890235901,
0.022926591336727142,
-0.0029615049716085196,
-0.0451146736741066,
-0.027993250638246536,
0.03874947875738144,
-0.0033396976068615913,
-0.022431910037994385,
-0.026453886181116104,
-0.05648670718073845,
-0.054263077676296234,
0.04222147539258003,
0.017677094787359238,
0.0039212689734995365,
-0.07124339789152145,
0.04483406990766525,
0.03472566977143288,
-0.051981352269649506,
-0.11930271238088608,
-0.008510743267834187,
0.013739239424467087,
0.01856904663145542,
-0.05921964719891548,
0.00669200299307704,
0.029228679835796356,
0.0005151219666004181,
-0.04018513858318329,
0.05436374247074127,
-0.056296296417713165,
0.02808442711830139,
0.01989397406578064,
0.002568451687693596,
0.0005073166685178876,
0.042282622307538986,
0.0029336470179259777,
-0.06576531380414963,
-0.05681540444493294,
0.03714951500296593,
-0.01514375675469637,
-0.049316827207803726,
-0.05447126179933548,
-0.07635503262281418,
-0.007721054367721081,
-0.018328865990042686,
-0.04632462188601494,
-0.07708295434713364,
0.0011341882636770606,
-0.0016814101254567504,
-0.00819542445242405,
-0.005848430562764406,
-0.010403498075902462,
0.003706425428390503,
-0.008386451750993729,
0.032697636634111404,
-0.0043204715475440025,
0.01692594401538372,
0.03570442646741867,
0.008162316866219044,
-0.0005665970966219902,
-0.010179092176258564,
0.0010082143126055598,
0.003751451149582863,
0.05671771243214607,
-0.016560502350330353,
-0.008527299389243126,
0.029628025367856026,
0.031318336725234985,
-0.04683024436235428,
-0.01762186922132969,
-0.05645502731204033,
-0.02418983168900013,
-0.03209098055958748,
0.006291700527071953,
0.03255219757556915,
-0.05883388593792915,
-0.040069956332445145,
0.07757452130317688,
-0.08252696692943573,
-0.038768693804740906,
0.03413991257548332,
0.04832567647099495,
-0.07073131203651428,
0.023294785991311073,
-0.009224689565598965,
-0.012598446570336819,
-0.012036067433655262,
0.048518478870391846,
-0.006939468905329704,
-0.024611368775367737,
-0.029309235513210297,
0.024289730936288834,
0.04809458181262016,
0.01936459168791771,
0.020381813868880272,
-0.00009029524517245591,
0.02104264311492443,
0.06267954409122467,
-0.04402627423405647,
-0.003326381789520383,
0.07722391933202744,
0.07399172335863113,
0.028927292674779892,
-0.0075880419462919235,
-0.037735335528850555,
0.022777440026402473,
0.006165004801005125,
-0.053048186004161835,
-0.04186168313026428,
0.07249443978071213,
-0.06124062463641167,
0.05064166709780693,
-0.014304280281066895,
0.020495720207691193,
-0.034635867923498154,
-0.03923347219824791,
0.012255169451236725,
0.019734010100364685,
0.002404378028586507,
-0.018872935324907303,
0.004319302272051573,
-0.03303780034184456,
-0.027397198602557182,
0.02159300446510315,
-0.06710832566022873,
-0.0010572844184935093,
-0.025218307971954346,
0.04496024549007416,
-0.044873714447021484,
0.016769537702202797,
0.018971992656588554,
-0.0007412604754790664,
-0.05467574670910835,
0.00003407871554372832,
0.033839400857686996,
-0.026863984763622284,
-0.042745191603899,
-0.009106624871492386,
0.01224607229232788,
-0.0071619912050664425,
-0.08398658782243729,
0.02459622547030449,
-0.02899065800011158,
0.011563015170395374,
-0.00938287004828453,
0.01586483232676983,
-0.04715605825185776,
0.021638503298163414,
-0.01275233831256628,
0.056382905691862106,
-0.008471404202282429,
-0.01532911229878664,
0.007679477799683809,
-0.07019726932048798,
-0.03374895825982094,
0.03902272507548332,
0.09957488626241684,
0.008410961367189884,
-0.02810853160917759,
-0.000446171936346218,
0.044308703392744064,
0.031115375459194183,
-0.023296812549233437,
0.03427286818623543,
-0.039375606924295425,
0.022644774988293648,
0.041058626025915146,
-0.008802075870335102,
-0.003127471311017871,
0.08728033304214478,
-0.03865852206945419,
0.0009072882821783423,
0.005923842545598745,
0.04833235964179039,
0.06926271319389343,
-0.013059008866548538,
-0.020593008026480675,
-0.020537782460451126,
0.022601526230573654,
-0.014695104211568832,
-0.004024106543511152,
-0.01741994544863701,
0.024258624762296677,
0.004872004501521587,
0.031715258955955505,
-0.0013225602451711893,
-0.043560661375522614,
0.02779977023601532,
0.05334548279643059,
0.027157282456755638,
0.08823053538799286,
0.01398987416177988,
0.043964698910713196,
-0.05570315569639206,
-0.030828183516860008,
-0.011759703978896141,
0.08748555183410645,
-0.023000042885541916,
-0.004662956576794386,
-0.0290057472884655,
-0.007670016027987003,
0.006544727832078934,
-0.0008889040327630937,
0.06340683251619339,
-0.0070673623122274876,
0.05460159853100777,
0.02864658832550049,
0.004118867218494415,
-0.04778040573000908,
0.029037024825811386,
0.03251095488667488,
0.007751654367893934,
0.025790607556700706,
-0.033668819814920425,
-0.06673040986061096,
-0.0010933867888525128,
0.05167123302817345,
-0.031568583101034164,
0.05103692039847374,
-0.07354343682527542,
0.033296097069978714,
-0.03363795578479767,
-0.06932780891656876,
0.007382436189800501,
-0.08962471038103104,
0.02589077316224575,
-0.04980703815817833,
0.009315870702266693,
-0.04556811973452568,
-0.06715099513530731,
-0.015831511467695236,
-0.021631605923175812,
0.002235943451523781,
-0.06624103337526321,
0.025858353823423386,
0.03637177124619484,
0.022697171196341515,
0.004499498289078474,
0.010100327432155609,
-0.00918312557041645,
0.0108494246378541,
0.03255040571093559,
0.03295011818408966,
0.01773071102797985,
-0.02046617679297924,
0.021133245900273323,
-0.013637389056384563,
-0.0038959258235991,
0.014017313718795776,
-0.03944840282201767,
0.01422052551060915,
0.05265716835856438,
0.02426893077790737,
-0.03800099715590477,
0.02588018774986267,
-0.003168501192703843,
-0.028126310557127,
-0.01838238164782524,
0.0331055149435997,
0.026866065338253975
] |
<p>I'm searching for references, articles and books, that discussed the geometrization of modern (and contemporary) physics, in a philosofical point of view. Something in the way that Michael Friedman did in "Space-time foundations theories" or Tian Yu Cao did in "The conceptual foundations and philosophical aspects of renormalization theory" or yet, what Roberto Torreti did in "Relativity and Geometry".</p> | g9227 | [
0.037901680916547775,
0.03537190705537796,
-0.005174135789275169,
-0.05150406435132027,
0.04318329319357872,
-0.004299423191696405,
-0.0011704264907166362,
-0.012194674462080002,
-0.021042736247181892,
0.021030936390161514,
0.07272593677043915,
-0.07895662635564804,
0.07699207216501236,
0.023046983405947685,
-0.04090843349695206,
-0.05446348339319229,
0.022217679768800735,
0.07408438622951508,
0.01754687912762165,
0.015554367564618587,
0.03885205462574959,
0.011766353622078896,
0.04564846679568291,
-0.030234823003411293,
-0.07697827368974686,
0.04048037901520729,
0.035848718136548996,
-0.04566105455160141,
0.004180265124887228,
-0.03823120892047882,
0.020211711525917053,
-0.014578924514353275,
-0.011267498135566711,
-0.0076959338039159775,
-0.03973117470741272,
-0.020263511687517166,
0.0254891999065876,
0.020483575761318207,
0.0026092471089214087,
-0.032172366976737976,
0.052796222269535065,
-0.0034110478591173887,
-0.03658231720328331,
-0.0014000440714880824,
-0.012600312009453773,
-0.02469235099852085,
-0.03247132897377014,
-0.013431462459266186,
-0.0072621493600308895,
0.032118819653987885,
-0.054282281547784805,
0.08282473683357239,
0.043868161737918854,
-0.055790599435567856,
0.006658487021923065,
0.0016437564045190811,
0.04465549811720848,
-0.0022887487430125475,
0.04475528001785278,
0.009769351221621037,
0.006698885932564735,
0.06991130858659744,
0.024362603202462196,
-0.006062734872102737,
0.03591928631067276,
0.03259746730327606,
-0.08442463725805283,
-0.04142991825938225,
-0.01900344155728817,
0.032815996557474136,
0.004221590235829353,
-0.043954964727163315,
0.014190924353897572,
0.005429571960121393,
-0.028829699382185936,
0.04070008918642998,
0.012820456176996231,
-0.020026810467243195,
0.020912475883960724,
-0.019207408651709557,
-0.04633155092597008,
0.01297637727111578,
0.02120768092572689,
-0.01648733578622341,
0.042937275022268295,
-0.034067459404468536,
0.03320299834012985,
0.017848460003733635,
-0.0007325217593461275,
-0.009305447340011597,
-0.03061726689338684,
-0.022906919941306114,
0.054787151515483856,
-0.028871342539787292,
-0.03245675936341286,
-0.0055242739617824554,
-0.024546528235077858,
0.008376971818506718,
-0.011288772337138653,
0.04941172152757645,
-0.08395721018314362,
0.01281716674566269,
0.014131706207990646,
0.015273835510015488,
0.014555525965988636,
0.0338769368827343,
0.023015053942799568,
-0.0011280425824224949,
0.022513289004564285,
0.02666538394987583,
-0.009329289197921753,
-0.005539138335734606,
-0.018622348085045815,
0.027109995484352112,
-0.058788418769836426,
-0.008351614698767662,
0.07111696153879166,
-0.06301617622375488,
-0.01942508853971958,
0.09287470579147339,
0.026188841089606285,
0.0387011282145977,
0.054188989102840424,
0.05689256638288498,
-0.006551550235599279,
0.0361398383975029,
-0.025021178647875786,
-0.03952430933713913,
-0.05814658850431442,
-0.00010246236342936754,
0.0547863207757473,
-0.06865426152944565,
-0.04841868579387665,
0.00352618214674294,
-0.04915822669863701,
0.011988312937319279,
0.015297770500183105,
-0.008285962045192719,
-0.02332114800810814,
-0.018262796103954315,
0.030210478231310844,
-0.0790424719452858,
0.02700408734381199,
-0.023541206493973732,
0.031183766201138496,
0.03108038567006588,
-0.030431173741817474,
-0.013799936510622501,
0.015083609148859978,
0.01410755980759859,
-0.012235183268785477,
0.03195423632860184,
-0.026544982567429543,
-0.012083430774509907,
-0.02735142968595028,
0.01358451321721077,
-0.023082589730620384,
-0.017348693683743477,
0.01604047603905201,
-0.03404104709625244,
-0.018576255068182945,
0.010968583635985851,
-0.05950815603137016,
0.0018495498225092888,
0.05157027021050453,
0.05384198576211929,
-0.009818436577916145,
-0.07869992405176163,
-0.015331858769059181,
-0.012166999280452728,
-0.055109813809394836,
-0.008089616894721985,
0.02073746919631958,
0.035907045006752014,
0.02471887692809105,
0.07148689031600952,
-0.01965133473277092,
0.0024195904843509197,
0.012078403495252132,
0.016870779916644096,
-0.0214009340852499,
-0.03092450089752674,
0.01672855205833912,
-0.008919622749090195,
-0.005621752701699734,
0.01578698866069317,
-0.018862944096326828,
-0.021329408511519432,
-0.05393913760781288,
0.03381520137190819,
0.004894144367426634,
0.016608411446213722,
0.019278541207313538,
0.065803661942482,
0.006912710145115852,
0.012171836569905281,
0.04684179276227951,
0.04081873223185539,
-0.0003426974581088871,
0.022607233375310898,
-0.007074612658470869,
0.025829453021287918,
0.08391958475112915,
0.005677616223692894,
0.016547780483961105,
-0.029968472197651863,
-0.022028064355254173,
-0.004133389797061682,
0.0010409612441435456,
0.032512862235307693,
-0.03460633009672165,
-0.049270518124103546,
0.050658173859119415,
-0.02902676910161972,
-0.0524526908993721,
-0.012259384617209435,
0.011730614118278027,
-0.021018346771597862,
-0.0030566328205168247,
0.06860847026109695,
0.0004495949251577258,
0.02017286978662014,
-0.0028363638557493687,
0.014409401454031467,
0.04738261178135872,
-0.08067282289266586,
0.0077889603562653065,
-0.04302971065044403,
0.030026450753211975,
-0.03067200444638729,
-0.07913564145565033,
0.011121038347482681,
-0.028262412175536156,
-0.015519099310040474,
0.062254276126623154,
0.015556937083601952,
-0.010214211419224739,
-0.022899257019162178,
0.03241153433918953,
-0.025452684611082077,
0.004130501765757799,
0.03403772413730621,
-0.009036539122462273,
-0.007906949147582054,
0.08343051373958588,
-0.10186431556940079,
0.07733582705259323,
-0.004571160767227411,
-0.06251323968172073,
-0.026907388120889664,
0.04044549912214279,
-0.03640054911375046,
-0.047552768141031265,
0.002048216061666608,
0.01806161366403103,
0.04559651017189026,
0.04980029538273811,
0.049031421542167664,
-0.06744485348463058,
-0.07970746606588364,
-0.012673408724367619,
-0.024703165516257286,
-0.04458903148770332,
0.03517080098390579,
-0.0118637066334486,
0.018122248351573944,
-0.013404939323663712,
0.008576435036957264,
-0.028701161965727806,
0.004476170055568218,
0.0695166066288948,
0.03152312710881233,
0.038720857352018356,
-0.007348170503973961,
-0.04000761732459068,
-0.03152833878993988,
0.020961131900548935,
-0.011701343581080437,
0.01074079517275095,
-0.022721225395798683,
0.038418207317590714,
-0.029470572248101234,
-0.0025241433177143335,
0.001299257972277701,
0.000011120777344331145,
-0.05539466440677643,
-0.006211951840668917,
0.024568624794483185,
0.015200501307845116,
0.014196554198861122,
0.013172419741749763,
0.008984462358057499,
-0.008912339806556702,
-0.022394821047782898,
-0.10477287322282791,
0.047369785606861115,
-0.02175302617251873,
0.016493581235408783,
0.024118697270751,
-0.052696291357278824,
-0.015236874110996723,
0.003800460835918784,
0.07582395523786545,
0.007485286332666874,
0.027444733306765556,
0.0050697424449026585,
0.007902749814093113,
-0.07330173254013062,
0.010960298590362072,
0.0022902803029865026,
-0.02276826836168766,
0.012542802840471268,
0.011875570751726627,
0.009197058156132698,
-0.00037016585702076554,
0.003766535548493266,
0.019760144874453545,
-0.018165305256843567,
0.008228246122598648,
-0.023224595934152603,
0.04226968437433243,
0.03228704631328583,
0.03602982684969902,
-0.03675759956240654,
0.036102544516325,
0.032371871173381805,
-0.02869531698524952,
-0.039947040379047394,
-0.032279904931783676,
0.0047119129449129105,
-0.014872470870614052,
-0.03679767996072769,
0.019279848784208298,
-0.050777412950992584,
-0.08454124629497528,
0.008816054090857506,
-0.004952904302626848,
0.004812860395759344,
0.040044575929641724,
-0.06773249804973602,
-0.028287790715694427,
-0.042162954807281494,
0.006730854976922274,
-0.02481756918132305,
-0.045805465430021286,
0.03506448492407799,
-0.008119659498333931,
0.011562061496078968,
0.024925731122493744,
-0.048534270375967026,
0.010719283483922482,
0.035284534096717834,
0.019093789160251617,
-0.03423917666077614,
-0.016981275752186775,
0.03674456477165222,
0.03979068621993065,
0.06819318234920502,
0.0382145419716835,
-0.04384981840848923,
-0.022832438349723816,
0.01252854522317648,
-0.022481534630060196,
-0.04607322812080383,
-0.008341282606124878,
0.04571333900094032,
0.042210400104522705,
-0.030461303889751434,
-0.07664316147565842,
-0.013780100271105766,
0.03195794299244881,
0.006173375062644482,
-0.028238190338015556,
-0.016742361709475517,
0.0012433779193088412,
0.00009661956573836505,
-0.01328450907021761,
0.02171982079744339,
-0.02513054944574833,
-0.01270193513482809,
0.027881883084774017,
0.005862808786332607,
0.0046078795567154884,
0.04949580132961273,
0.027978841215372086,
-0.0062235621735453606,
-0.025143546983599663,
-0.005841877311468124,
-0.021451007574796677,
-0.01863715797662735,
-0.022364584729075432,
-0.008816974237561226,
-0.018722165375947952,
-0.07722407579421997,
0.006734881084412336,
-0.0059361872263252735,
-0.01962912827730179,
0.01864033378660679,
-0.012460150755941868,
0.01926269941031933,
0.03104214556515217,
0.004344169050455093,
-0.011579212732613087,
0.02552151493728161,
0.018665671348571777,
0.005031445994973183,
0.02050923742353916,
-0.0451357401907444,
-0.005592552945017815,
-0.008510817773640156,
0.0030189678072929382,
-0.013257483020424843,
0.04997064918279648,
-0.047107670456171036,
0.03148360922932625,
0.04538340121507645,
-0.025948820635676384,
-0.08791182190179825,
0.055651064962148666,
0.008767148479819298,
0.000763625546824187,
0.05424655228853226,
-0.020902153104543686,
-0.05971542373299599,
0.015666993334889412,
0.024891739711165428,
0.0056547727435827255,
-0.01599997840821743,
-0.023321064189076424,
0.04904214292764664,
0.01877697929739952,
-0.05741269886493683,
-0.06571211665868759,
0.039927419275045395,
-0.06500351428985596,
-0.03293190151453018,
-0.06450894474983215,
0.03966853767633438,
0.05858368054032326,
-0.003945907577872276,
0.07474691420793533,
0.013668281026184559,
0.0042363181710243225,
-0.046875130385160446,
-0.007381639908999205,
0.03196003660559654,
-0.03485272452235222,
-0.015658212825655937,
-0.019337575882673264,
-0.017452051863074303,
0.006362807005643845,
0.01735076680779457,
0.040302522480487823,
0.03967161476612091,
-0.04139113426208496,
0.00429402245208621,
-0.04002268612384796,
-0.01692749746143818,
-0.008760920725762844,
-0.014514468610286713,
-0.02048879861831665,
-0.008706672117114067,
-0.02730243094265461,
0.06850162893533707,
-0.019757354632019997,
-0.0017107261810451746,
-0.09211329370737076,
0.018407579511404037,
-0.06291796267032623,
-0.01922541670501232,
-0.012128888629376888,
0.03454839438199997,
-0.023964788764715195,
-0.06505347043275833,
0.03476911783218384,
0.021282704547047615,
0.0006623287335969508,
-0.049959056079387665,
-0.001306990277953446,
-0.012640758417546749,
-0.039164941757917404,
0.02584671415388584,
0.005519927013665438,
-0.02408621832728386,
0.0331328883767128,
0.03626754879951477,
-0.05541936308145523,
0.003840393153950572,
-0.014027073979377747,
-0.007261890918016434,
0.0033155037090182304,
-0.09214584529399872,
0.05919433385133743,
-0.046169646084308624,
-0.04673362523317337,
0.010514786466956139,
-0.014365247450768948,
-0.013176683336496353,
-0.008777640759944916,
-0.009010580368340015,
-0.05050894245505333,
0.011905177496373653,
0.030846796929836273,
-0.008264833129942417,
0.03700747340917587,
0.012587731704115868,
0.0618390217423439,
0.005238593090325594,
-0.03318696469068527,
0.012906566262245178,
0.038593243807554245,
0.04534310847520828,
-0.013800212182104588,
0.02433166839182377,
0.06039559468626976,
-0.010572926141321659,
0.013363880105316639,
0.05161300301551819,
0.03590228781104088,
-0.06102876365184784,
-0.02777455747127533,
-0.028732290491461754,
0.013373869471251965,
-0.009328622370958328,
0.04846157133579254,
0.05938751995563507,
-0.029797270894050598,
-0.03960634395480156,
0.0649256482720375,
-0.010241031646728516,
-0.00873564276844263,
-0.01677502878010273,
0.008405069820582867,
0.0017645707121118903,
-0.008238790556788445,
-0.00048649380914866924,
-0.0015301606617867947,
0.013545878231525421,
0.07835758477449417,
-0.04923350736498833,
-0.04370474815368652,
0.02623954974114895,
0.024880116805434227,
-0.01600329391658306,
-0.02946810983121395,
0.03480393439531326,
0.028614196926355362,
0.0613282211124897,
0.042398110032081604,
-0.03010915033519268,
-0.03839350864291191,
-0.017107727006077766,
-0.0215302724391222,
-0.02676045335829258,
0.033195700496435165,
0.007347883656620979,
-0.023804765194654465,
-0.045476991683244705,
-0.08660778403282166,
-0.011101759038865566,
0.006344666238874197,
0.027402961626648903,
-0.01804896630346775,
0.0000017057841432688292,
-0.01550043374300003,
-0.035296954214572906,
0.08625813573598862,
-0.01867016777396202,
0.07871716469526291,
0.0016265573212876916,
0.03352022543549538,
-0.03601555526256561,
0.04499479755759239,
-0.024746470153331757,
-0.02683638036251068,
-0.007706008851528168,
0.01206291001290083,
-0.04985992982983589,
0.0023196088150143623,
-0.004741828888654709,
0.05473499000072479,
-0.016800515353679657,
0.036060430109500885,
-0.037853192538022995,
0.020549682900309563,
0.011192464269697666,
-0.021351756528019905,
0.015670331194996834,
-0.0681910365819931,
-0.01411087904125452,
0.007413864601403475,
0.026857422664761543,
-0.029677391052246094,
-0.021471723914146423,
-0.01573185995221138,
0.08999699354171753,
0.004373657517135143,
0.05414454638957977,
-0.03379925712943077,
0.059623491019010544,
-0.035109370946884155,
-0.00894877128303051,
0.03576460853219032,
-0.02814459055662155,
0.060203853994607925,
0.024894829839468002,
-0.030468881130218506,
-0.018231824040412903,
0.01948988437652588,
-0.010338748805224895,
0.03330185264348984,
0.06500115990638733,
-0.033276017755270004,
0.020914049819111824,
-0.049333807080984116,
-0.004941756837069988,
0.01906004548072815,
-0.0031338806729763746,
-0.021123545244336128,
-0.05856844410300255,
0.07240310311317444,
0.03500284254550934,
0.00016226716979872435,
0.0022097702603787184,
-0.02901572361588478,
-0.005720009561628103,
0.013937466777861118,
-0.02132311649620533,
0.05933326855301857,
-0.045899804681539536,
0.03605178743600845,
-0.025822805240750313,
0.08834695816040039,
0.020620016381144524,
-0.012964666821062565,
0.04728627949953079,
0.013382287696003914,
0.007656124420464039,
0.006887434981763363,
-0.009773485362529755,
0.02782963402569294,
-0.011977806687355042,
0.046143900603055954,
-0.04208381101489067,
-0.018377697095274925,
-0.04935586825013161,
-0.0495101623237133,
0.03337301313877106,
-0.01715666800737381,
0.0006219814531505108,
0.052127160131931305,
-0.06807930767536163,
0.009126468561589718,
0.017236214131116867,
-0.05073173716664314,
0.037275079637765884,
-0.041811831295490265,
0.034873511642217636,
0.008662665262818336,
-0.10303144156932831,
-0.0418003611266613,
0.040390051901340485,
0.06380210816860199,
-0.011799003928899765,
-0.09211248904466629,
0.08052375912666321,
-0.0014566712779924273,
-0.014744026586413383,
0.020828308537602425,
0.02896185778081417,
-0.027589721605181694,
-0.033875852823257446,
-0.0371134914457798,
-0.005134587176144123,
-0.07172556221485138,
-0.022549103945493698,
-0.011459563858807087,
0.01634087786078453,
0.010005838237702847,
0.02542959339916706,
0.057413481175899506,
0.06718914955854416,
0.01392742432653904,
-0.035607628524303436,
-0.053609449416399,
-0.014746312983334064,
0.00280706025660038,
0.004398218356072903,
0.002932704286649823,
0.026511818170547485,
0.022059286013245583,
-0.009430713951587677,
-0.0009771574987098575,
-0.034304097294807434,
0.01050669327378273,
-0.015147111378610134,
0.0506453700363636,
0.030314432457089424,
-0.002582595683634281,
-0.019123028963804245,
0.036688756197690964,
-0.01672252081334591,
-0.0150400809943676,
0.0015412679640576243,
0.04703657701611519,
-0.0516066811978817,
0.04038278013467789,
-0.030728831887245178,
0.021016433835029602,
0.03700092062354088,
-0.026803001761436462,
0.03911089152097702,
0.026257362216711044,
-0.027069760486483574,
0.026416851207613945,
0.04374420642852783,
-0.04949216544628143,
-0.02095346339046955,
0.007617420516908169,
-0.020845595747232437,
-0.021976755931973457,
-0.039147891104221344,
-0.008680435828864574,
-0.11286743730306625,
-0.00037835867260582745,
0.042117007076740265,
-0.05132794752717018,
-0.036490246653556824,
-0.025242814794182777,
0.019809920340776443,
0.006313884165138006,
-0.013034580275416374,
-0.021716898307204247,
0.05106101930141449,
-0.059489406645298004,
0.002739268820732832,
-0.018933407962322235,
-0.05258360505104065,
0.04258422553539276,
-0.040051937103271484,
0.0352468304336071,
-0.010355256497859955,
-0.014163044281303883,
0.03777485713362694,
0.011905180290341377,
0.007048710715025663,
-0.0123987328261137,
0.07072300463914871,
0.0412687286734581,
-0.033338382840156555,
-0.029489120468497276,
0.08866405487060547,
-0.014597090892493725,
0.017981380224227905,
-0.0040308572351932526,
-0.0366312675178051,
-0.018817288801074028,
-0.0059405164793133736,
0.06606031209230423,
0.040247827768325806,
0.06223979964852333,
-0.017897527664899826,
0.06998269259929657,
-0.007068471983075142,
-0.02778896503150463,
0.03141890838742256,
0.03376011550426483,
0.0356043241918087
] |
<p>I have a question that I can't seem to get my head around. I'm really rusty on my physics, but I'm sitting here trying to think this out, but I'm missing a really big part of the equation.</p>
<p>So lets say I have a turbine in space. It's purpose is to convert the energy given to it, in joules to watts. So I realize we will have friction, and we need to overturn the static friction before turning can be achieved. </p>
<p>I want the device to turn at a relatively high speed, therefore F > Ff. However, this will create a situation where the device will constantly accelerate, because there is F and not being apposed by friction, Fn = ma.</p>
<p>So here is my thought process for the situation.</p>
<p>Force needed to start turning...<br>
F = Fn - Ff<br>
Energy needed to start turning...<br>
W = Fd<br>
where...<br>
W = (KEf - KEi) where KEi = 0<br>
Therefore,<br>
a = F/m </p>
<p>Since there will always be force, and constant supply of energy, the device will accelerate to infinity, supplying infinite energy in watts?
I understand this to be fundamentally impossible... So where am I going wrong? I feel like this will be a facepalm moment, but I just can't seem to remember what I'm missing here.</p>
<p>Best Regards.</p> | g9228 | [
0.02632244862616062,
0.06035369634628296,
-0.005728390999138355,
0.029587984085083008,
0.04533398896455765,
-0.04295385628938675,
0.04807749390602112,
0.056246187537908554,
-0.09692343324422836,
-0.056422147899866104,
-0.011873727664351463,
0.008086565881967545,
0.019962718710303307,
-0.02454342693090439,
0.04778706282377243,
0.027197398245334625,
0.04363184794783592,
0.04029776155948639,
0.022117452695965767,
0.006958966143429279,
-0.003067268757149577,
-0.009143064729869366,
-0.03761344775557518,
-0.02784990519285202,
0.009346604347229004,
-0.04109710827469826,
0.008570282720029354,
-0.024813825264573097,
-0.016360828652977943,
-0.03373538330197334,
-0.0003697307547554374,
-0.005801232997328043,
-0.0001890682615339756,
0.01599166914820671,
-0.04500345140695572,
-0.049674730747938156,
0.05786985158920288,
-0.02185429260134697,
-0.004757799208164215,
-0.022766435518860817,
-0.01468663290143013,
-0.059170741587877274,
0.02601391263306141,
0.0235632061958313,
0.01909501850605011,
0.04692531377077103,
0.028824852779507637,
-0.031078573316335678,
-0.03883083164691925,
0.003308253362774849,
0.01917601004242897,
0.006483052391558886,
0.05176480859518051,
-0.007851368747651577,
0.024438265711069107,
0.04622028023004532,
0.0009323212434537709,
-0.04223048314452171,
0.017088115215301514,
0.04676182195544243,
-0.06245715543627739,
-0.018614618107676506,
0.006707931403070688,
-0.009890258312225342,
0.05703636631369591,
-0.0814325362443924,
0.017124826088547707,
0.019182229414582253,
0.01941448077559471,
-0.011956309899687767,
0.008908817544579506,
-0.016984591260552406,
0.04537632316350937,
-0.03389768302440643,
0.027756694704294205,
0.00019471360428724438,
0.00921675842255354,
0.003928715828806162,
-0.0026295429561287165,
0.00014723834465257823,
-0.02440151944756508,
0.04793977364897728,
0.06141253560781479,
-0.021014686673879623,
0.029510043561458588,
-0.004429294262081385,
-0.017596283927559853,
0.05300537869334221,
-0.00199994258582592,
-0.02955504134297371,
0.018701182678341866,
0.029736708849668503,
0.04536523297429085,
-0.017566615715622902,
-0.03224979341030121,
0.001925761578604579,
-0.034607093781232834,
0.0805324912071228,
-0.02260797843337059,
0.012387901544570923,
-0.013345696032047272,
-0.07163320481777191,
-0.0003092596016358584,
-0.014127973467111588,
0.03316739201545715,
-0.09016774594783783,
-0.028935423120856285,
0.02149580419063568,
0.050274211913347244,
-0.0040975296869874,
-0.013569089584052563,
0.0008292464772239327,
-0.014299655333161354,
-0.07737192511558533,
-0.01583436317741871,
-0.0039186133071780205,
0.016361715272068977,
0.08682069182395935,
-0.04098132252693176,
0.07109105587005615,
-0.028682943433523178,
-0.007600761018693447,
-0.08722467720508575,
0.04051399603486061,
-0.036714810878038406,
0.002363217296078801,
0.005295639391988516,
-0.01636872999370098,
0.019399311393499374,
0.0171110350638628,
-0.006635564845055342,
-0.009162915870547295,
-0.015331878326833248,
-0.027259087190032005,
0.015629282221198082,
0.07714822888374329,
-0.06198243051767349,
-0.006612527184188366,
0.03650931641459465,
0.07131574302911758,
-0.015236643142998219,
-0.09265610575675964,
0.010363033041357994,
0.014563673175871372,
-0.053252071142196655,
0.03632069751620293,
-0.03717157989740372,
-0.048537690192461014,
0.0821959525346756,
0.006509851198643446,
-0.023433521389961243,
0.07126440852880478,
-0.010852893814444542,
-0.010313685983419418,
0.10360793769359589,
0.008152464404702187,
0.10325898230075836,
0.005968005862087011,
0.003382617374882102,
-0.04727153852581978,
0.050403375178575516,
-0.01529579795897007,
0.04437226057052612,
-0.07571359723806381,
-0.10465829074382782,
-0.0005269494722597301,
-0.04813726618885994,
-0.016278386116027832,
-0.008063996210694313,
0.03600743040442467,
-0.07825961709022522,
-0.02717750519514084,
0.06727780401706696,
0.03332958370447159,
-0.0030596924480050802,
0.02665085531771183,
0.08096075803041458,
0.0039042585995048285,
0.022930312901735306,
0.023829640820622444,
0.008720620535314083,
-0.011186248622834682,
0.06917597353458405,
0.03524868190288544,
0.018748631700873375,
0.06272125244140625,
-0.0486893504858017,
0.0636746734380722,
-0.020464401692152023,
0.019490258768200874,
0.024760929867625237,
0.020849067717790604,
0.007085729856044054,
0.07550220191478729,
-0.03508661314845085,
0.04676683992147446,
-0.013001462444663048,
-0.07536657899618149,
-0.0017746187513694167,
-0.0651198998093605,
0.04651142284274101,
0.04516780003905296,
0.023772886022925377,
0.04363197833299637,
0.017242485657334328,
-0.023639321327209473,
-0.03008834645152092,
-0.00017966213636100292,
0.032786253839731216,
0.0001898193295346573,
0.032452549785375595,
0.041503407061100006,
-0.04842113330960274,
0.027777256444096565,
-0.037204958498477936,
-0.04095796123147011,
-0.035981275141239166,
-0.023348042741417885,
-0.007633028086274862,
-0.004062101244926453,
0.041470885276794434,
-0.007228194735944271,
0.052910707890987396,
0.020507125183939934,
-0.10879717022180557,
-0.028544342145323753,
-0.017007136717438698,
-0.08931334316730499,
-0.02361532859504223,
0.05257695913314819,
-0.03417302295565605,
-0.010739163495600224,
0.008147417567670345,
-0.04329656437039375,
0.02649300917983055,
0.030864542350172997,
0.005954775493592024,
0.07960450649261475,
-0.03465961292386055,
0.016545848920941353,
0.05505111813545227,
-0.028934143483638763,
-0.007738060317933559,
-0.07109180092811584,
-0.00034822215093299747,
-0.06903985887765884,
0.04650358855724335,
-0.05301054194569588,
0.021871529519557953,
0.001386110088787973,
-0.0033707686234265566,
-0.03782060742378235,
-0.018068134784698486,
0.028558604419231415,
-0.04223629832267761,
-0.04523085430264473,
-0.02262755110859871,
0.0017812344012781978,
-0.03810377046465874,
-0.03980342671275139,
0.012661765329539776,
0.024177562445402145,
0.013561119325459003,
0.05206330865621567,
-0.05578187108039856,
0.03202182427048683,
-0.027908941730856895,
-0.03536871075630188,
0.006947832182049751,
0.04624304920434952,
-0.009241677820682526,
0.00336853857152164,
0.020561737939715385,
0.042608484625816345,
0.0005170695367269218,
-0.027612295001745224,
0.006361068692058325,
-0.017590731382369995,
0.04417328163981438,
0.0446641705930233,
-0.024440307170152664,
-0.05878502130508423,
-0.016749486327171326,
0.06951910257339478,
-0.02314157225191593,
-0.030391180887818336,
-0.004679086618125439,
0.011477833613753319,
-0.05168858543038368,
0.028195904567837715,
-0.038636673241853714,
-0.012907715514302254,
0.03442402556538582,
-0.010008087381720543,
0.035031404346227646,
0.08031681180000305,
0.017537157982587814,
-0.00993354246020317,
-0.0017804126255214214,
0.01728000119328499,
0.029912032186985016,
-0.034269317984580994,
-0.030452469363808632,
0.013315352611243725,
-0.016470320522785187,
0.011517698876559734,
-0.02390395663678646,
-0.03802292421460152,
-0.0251312255859375,
0.002956872107461095,
-0.01984078623354435,
0.031566325575113297,
-0.009240184910595417,
-0.010766244493424892,
-0.030523069202899933,
-0.0076759629882872105,
0.018404146656394005,
-0.017495783045887947,
0.005884797312319279,
-0.017100004479289055,
-0.013922839425504208,
-0.03397229313850403,
0.025690827518701553,
0.007753018289804459,
0.004893659148365259,
0.06450606882572174,
-0.04660037159919739,
-0.0011505630100145936,
0.0052813817746937275,
-0.006921619176864624,
0.05397050827741623,
0.05060533806681633,
-0.025424914434552193,
-0.04681443050503731,
-0.023074405267834663,
-0.01557146105915308,
-0.04977663233876228,
0.041193969547748566,
0.02989688143134117,
0.04787100479006767,
0.0034305290319025517,
0.007185561116784811,
-0.06577449291944504,
0.023152176290750504,
-0.009872655384242535,
0.021069876849651337,
-0.03178972750902176,
0.002169051906093955,
-0.004054382909089327,
0.007782740518450737,
0.042061299085617065,
-0.061737265437841415,
-0.017730558291077614,
0.0022955648601055145,
0.042232006788253784,
0.005346729885786772,
0.02001376263797283,
0.03894166648387909,
-0.01168533880263567,
-0.033550046384334564,
0.03916537016630173,
-0.025593718513846397,
0.009846578352153301,
0.017914431169629097,
-0.0089143430814147,
0.0041193170472979546,
-0.063669852912426,
0.0197821706533432,
-0.034666694700717926,
-0.04173073172569275,
0.01151471957564354,
-0.10165783762931824,
-0.033633749932050705,
0.007576043717563152,
-0.019612949341535568,
-0.040548909455537796,
0.05417025834321976,
-0.022236982360482216,
0.0008256701403297484,
0.054602447897195816,
0.03155452758073807,
0.03565865010023117,
-0.022614939138293266,
0.028169622644782066,
0.0316619798541069,
0.055626630783081055,
-0.03900209069252014,
-0.0135417515411973,
0.07576361298561096,
-0.020476533100008965,
0.03458314761519432,
-0.0299026221036911,
0.0015971611719578505,
0.0074149551801383495,
-0.0021982144098728895,
0.012458751909434795,
0.02174445241689682,
-0.039703987538814545,
-0.000931927643250674,
-0.01138157770037651,
0.04215460643172264,
0.03999020904302597,
-0.008649460971355438,
0.0124796899035573,
-0.005914860870689154,
-0.013957993127405643,
0.03784656524658203,
-0.012144498527050018,
0.006377116311341524,
-0.03597395494580269,
0.008009127341210842,
0.007073992397636175,
-0.004508247599005699,
-0.06424077600240707,
-0.0027608806267380714,
-0.06148036941885948,
-0.000004361972514743684,
-0.01996610499918461,
0.045489128679037094,
-0.010557623580098152,
-0.03552455082535744,
0.013753166422247887,
-0.002914291573688388,
0.022532019764184952,
0.002080539707094431,
0.043845079839229584,
0.011436812579631805,
-0.037965014576911926,
-0.01329245138913393,
-0.05127561092376709,
0.02193792164325714,
0.018286896869540215,
0.0009038636344484985,
-0.0033827375154942274,
-0.03536747023463249,
0.058026090264320374,
-0.01557835377752781,
0.013002948835492134,
-0.002493560081347823,
0.07506421208381653,
0.032487764954566956,
0.02480044588446617,
0.0007712366641499102,
-0.01078382320702076,
-0.01173269934952259,
0.06287099421024323,
-0.04043116793036461,
-0.05263940244913101,
0.007029525935649872,
-0.036600515246391296,
-0.01006733812391758,
0.005653683561831713,
-0.0688052847981453,
-0.010397116653621197,
0.0027232894208282232,
-0.003979180473834276,
-0.04796304181218147,
-0.016085464507341385,
-0.003399255219846964,
0.034984998404979706,
-0.02518003061413765,
-0.01756281591951847,
-0.027790239080786705,
0.026608146727085114,
0.009707456454634666,
0.012264124117791653,
-0.0010936536127701402,
-0.04220997914671898,
-0.03451928123831749,
-0.039878830313682556,
0.04679961875081062,
-0.0055326903238892555,
0.010879937559366226,
0.10273250192403793,
-0.0037794853560626507,
0.03727177903056145,
-0.020184660330414772,
-0.021033329889178276,
-0.020441818982362747,
0.008902850560843945,
-0.0022115737665444613,
0.009375233203172684,
0.06444483995437622,
0.00590702285990119,
-0.00019083665392827243,
-0.0006313896737992764,
-0.05517791211605072,
0.029121126979589462,
0.04927869886159897,
0.016847357153892517,
0.028083445504307747,
0.07248422503471375,
-0.01091721374541521,
-0.060975331813097,
-0.027369946241378784,
0.051981087774038315,
0.013446027413010597,
-0.05537617579102516,
-0.03881765529513359,
0.027050284668803215,
-0.03859759494662285,
0.00007397196895908564,
-0.026834450662136078,
-0.011627214960753918,
0.015247429721057415,
0.043590255081653595,
0.06479833275079727,
-0.02776351384818554,
0.025099748745560646,
0.07439243048429489,
-0.03989250212907791,
0.07514826953411102,
0.041522540152072906,
0.05887949466705322,
0.050565674901008606,
0.014605219475924969,
-0.019856208935379982,
-0.039984967559576035,
-0.04050213098526001,
-0.053837936371564865,
0.07632183283567429,
-0.0013252506032586098,
-0.0032167951576411724,
-0.013264153152704239,
-0.020928461104631424,
0.036159712821245193,
-0.038385603576898575,
-0.007270564325153828,
-0.04468746483325958,
0.00599701376631856,
0.03513120859861374,
-0.015335708856582642,
-0.012747315689921379,
-0.024767117574810982,
-0.04321221634745598,
-0.0074016740545630455,
0.08289100974798203,
-0.02486276812851429,
0.0158756785094738,
-0.026461701840162277,
0.007079878356307745,
0.023376528173685074,
0.03079729527235031,
-0.051426175981760025,
-0.022683974355459213,
-0.007398431655019522,
0.004386762622743845,
-0.002474238397553563,
-0.015221170149743557,
-0.042396169155836105,
-0.022819884121418,
0.05076509341597557,
0.023853693157434464,
0.00027251034043729305,
0.022953102365136147,
0.003477826714515686,
0.021031560376286507,
-0.01939500868320465,
-0.0063249277882277966,
-0.07541798055171967,
0.05005628988146782,
0.01632303185760975,
0.01438503060489893,
0.02813512645661831,
0.062220245599746704,
-0.041956301778554916,
0.028690600767731667,
-0.0183562021702528,
0.04001753404736519,
0.08634958416223526,
0.05718366056680679,
0.03905470669269562,
-0.015299341641366482,
0.012523570097982883,
0.024274611845612526,
-0.020910965278744698,
-0.04183274507522583,
-0.02091248892247677,
0.0021343643311411142,
0.04365501552820206,
-0.03132417052984238,
-0.009764655493199825,
0.0075872610323131084,
-0.016051864251494408,
0.04287825897336006,
0.01383131928741932,
-0.04505471885204315,
0.0020204163156449795,
0.043738413602113724,
-0.019681690260767937,
-0.043086275458335876,
-0.004697820637375116,
0.051906049251556396,
-0.0014532600762322545,
-0.01979755237698555,
0.005764324683696032,
-0.0252991896122694,
-0.028287310153245926,
0.025402145460247993,
-0.03709280490875244,
-0.023061510175466537,
0.030248133465647697,
0.025510402396321297,
0.0026220607105642557,
0.015506438910961151,
0.017419729381799698,
-0.0014650661032646894,
0.01563451997935772,
0.03306131437420845,
0.008024471811950207,
-0.01216333918273449,
-0.019464781507849693,
0.012298911809921265,
-0.027932247146964073,
-0.013202454894781113,
0.029909992590546608,
0.025729941204190254,
0.011248483322560787,
0.01634945161640644,
-0.027492178604006767,
0.10124615579843521,
-0.00922568142414093,
0.02505861036479473,
-0.04430297762155533,
0.05512845143675804,
-0.009162915870547295,
-0.03372698277235031,
0.06262408196926117,
0.10973566770553589,
-0.018201449885964394,
0.023798003792762756,
-0.02304464392364025,
-0.05340290814638138,
0.06218980252742767,
0.0032334141433238983,
0.005894605536013842,
-0.03704480081796646,
-0.007039324380457401,
0.029638277366757393,
0.027746614068746567,
-0.06678830087184906,
0.05715474113821983,
-0.040398649871349335,
0.035923153162002563,
-0.015132169239223003,
-0.018877442926168442,
0.008373785763978958,
-0.03402547910809517,
0.007572959642857313,
-0.009060122072696686,
-0.04226880893111229,
-0.06743860244750977,
-0.016474926844239235,
-0.004763140343129635,
-0.057903438806533813,
0.058812979608774185,
-0.006554621737450361,
-0.023978479206562042,
0.037540990859270096,
0.004810152109712362,
0.03832007944583893,
-0.004431813023984432,
-0.025171618908643723,
0.005491386633366346,
-0.02938402257859707,
0.03088107891380787,
-0.014569303952157497,
0.03215431049466133,
0.047089818865060806,
-0.06227390840649605,
-0.020590508356690407,
-0.030738957226276398,
-0.04294121265411377,
-0.0038058217614889145,
0.011186426505446434,
-0.0014546409947797656,
-0.030310004949569702,
0.028116442263126373,
-0.022462382912635803,
-0.024935336783528328,
-0.022335972636938095,
-0.02485436387360096,
-0.04181470349431038,
-0.021517788991332054,
-0.019337810575962067,
-0.008101340383291245,
-0.07320137321949005,
0.038555048406124115,
-0.0008650756790302694,
0.004262098576873541,
-0.02540414407849312,
0.021307973191142082,
0.04372440278530121,
-0.03272109851241112,
-0.006342301610857248,
0.049422137439250946,
0.00007139472290873528,
0.004762269090861082,
-0.009828837588429451,
0.0005028030718676746,
0.07247855514287949,
-0.015125294215977192,
-0.027091946452856064,
0.03542807325720787,
-0.04852195829153061,
0.01974175125360489,
-0.019394997507333755,
-0.07816333323717117,
-0.011658810079097748,
0.010500197298824787,
0.003946353681385517,
-0.003400063142180443,
-0.045099008828401566,
-0.01409841701388359,
0.0384427048265934,
0.014839588664472103,
-0.011189525946974754,
0.014538148418068886,
-0.01225663535296917,
-0.030784979462623596,
-0.022284938022494316,
0.06898047775030136,
-0.030032262206077576,
-0.06916660070419312,
-0.0039361403323709965,
-0.04184546694159508,
-0.05242990329861641,
-0.04729339852929115,
-0.02016972377896309,
-0.026091672480106354,
-0.021071847528219223,
-0.020947260782122612,
0.03182428702712059,
0.027693022042512894,
-0.02201170101761818,
-0.023139644414186478,
0.024762198328971863,
-0.027086811140179634,
-0.07243639975786209,
0.035698600113391876,
-0.03428192064166069,
-0.03714365512132645,
-0.004141049925237894,
-0.0047194198705255985,
0.015567783266305923,
0.007701850030571222,
-0.0037796832621097565,
0.06277719140052795,
-0.007349466904997826,
0.046426016837358475,
0.05667496472597122,
0.02197476662695408,
-0.05951171740889549,
-0.0636981725692749,
0.050386812537908554,
-0.030448168516159058,
-0.019829027354717255,
0.05308564752340317,
-0.00012255643378011882,
0.015616931021213531,
-0.027692290022969246,
-0.018650837242603302,
-0.007122276350855827,
0.013165459036827087,
0.01304672658443451,
-0.059995852410793304,
-0.03116186335682869,
0.0006892479141242802
] |
<p>Why doesn't diamond show up in X-ray imaging? Diamond is the hardest substance ever known, and as we know, X-ray radiation is produced when a cathode ray of high frequency hits a very high atomic mass target. But I am amazed: why doesn't diamond show up in X-ray imaging?</p> | g9229 | [
0.03608730807900429,
0.0942053571343422,
0.04171617329120636,
-0.011622544378042221,
-0.004760459065437317,
0.019228998571634293,
-0.07810745388269424,
0.029006408527493477,
0.019218135625123978,
-0.010537895374000072,
0.060074109584093094,
0.050727467983961105,
0.01023745909333229,
-0.06941325217485428,
-0.05768756568431854,
0.04132559895515442,
-0.011595348827540874,
-0.04098496958613396,
0.03826272487640381,
0.052121352404356,
-0.015222017653286457,
-0.049514591693878174,
0.06006873771548271,
-0.03934447467327118,
-0.017309976741671562,
0.0474051870405674,
0.007209926377981901,
-0.04784485325217247,
-0.013988232240080833,
0.00474577909335494,
0.03365197032690048,
0.008270720951259136,
0.011841115541756153,
0.07961816340684891,
0.026400666683912277,
-0.08235511928796768,
-0.0076274145394563675,
0.03494374081492424,
0.019876375794410706,
0.03177088126540184,
-0.02009744942188263,
-0.027631014585494995,
-0.0010041053174063563,
-0.04705411195755005,
-0.04057293385267258,
0.026508942246437073,
0.01871214061975479,
0.007223856635391712,
0.028359636664390564,
-0.047121137380599976,
0.0050896392203867435,
0.0022743793670088053,
0.0726274847984314,
-0.016195310279726982,
0.0478176586329937,
-0.050356075167655945,
-0.012341304682195187,
0.031101685017347336,
0.033243995159864426,
-0.02125537022948265,
-0.015623243525624275,
-0.0001590929605299607,
0.0012620604829862714,
0.017504025250673294,
0.08224229514598846,
-0.02987849898636341,
-0.02442004904150963,
0.041260309517383575,
0.0328528918325901,
0.036922384053468704,
0.05946440249681473,
-0.06133805587887764,
-0.0075085521675646305,
0.006477752234786749,
0.016919124871492386,
-0.06626343727111816,
0.08761020749807358,
-0.015367933548986912,
-0.07434923946857452,
-0.02002529986202717,
0.06756970286369324,
-0.0023377486504614353,
0.0751870721578598,
0.007621580269187689,
0.04687761887907982,
0.022187698632478714,
0.003212067298591137,
0.02900988794863224,
0.0468246191740036,
0.05044029280543327,
0.06226343289017677,
0.03631003946065903,
-0.014293542131781578,
0.0449458509683609,
0.0038340934552252293,
-0.02982882410287857,
-0.029000231996178627,
0.04725077375769615,
-0.04765467345714569,
0.007682862225919962,
-0.01855023205280304,
-0.024561790749430656,
0.03466319665312767,
0.003848376916721463,
-0.029149910435080528,
0.014885970391333103,
-0.0356631763279438,
-0.01118061225861311,
-0.031110526993870735,
-0.023855850100517273,
-0.00687836529687047,
-0.00637578871101141,
-0.010108234360814095,
-0.011944456957280636,
0.014648927375674248,
0.025523770600557327,
0.06890324503183365,
-0.010450233705341816,
0.011509132571518421,
0.04234596714377403,
0.04531966522336006,
0.04202107712626457,
-0.006286340765655041,
-0.008352672681212425,
-0.04284754768013954,
-0.014859883114695549,
0.04339390620589256,
-0.02015133947134018,
0.025315003469586372,
-0.007734979968518019,
-0.042310524731874466,
0.053304754197597504,
0.0194262582808733,
0.03834602236747742,
0.03608354181051254,
0.03135591000318527,
-0.044650301337242126,
-0.014039781875908375,
0.030619032680988312,
-0.020320385694503784,
-0.02602585032582283,
0.043258700519800186,
-0.024202775210142136,
0.036236900836229324,
0.024844063445925713,
0.001912834239192307,
-0.03370232135057449,
0.0035442763473838568,
0.01377654355019331,
-0.018716134130954742,
0.061271294951438904,
0.03384684771299362,
0.06548509746789932,
-0.07533860951662064,
-0.01472687628120184,
0.00545797822996974,
0.02536914497613907,
-0.005507178138941526,
-0.02724675089120865,
-0.023005489259958267,
0.04679214581847191,
0.03737667202949524,
-0.052193161100149155,
-0.027662698179483414,
0.022345546633005142,
-0.026362700387835503,
0.011010272428393364,
-0.07869625091552734,
0.0064173550345003605,
0.05058247223496437,
0.001433352823369205,
-0.02459273301064968,
0.07883905619382858,
0.00021520770678762347,
-0.045910295099020004,
0.0037241580430418253,
0.020725563168525696,
-0.01391258928924799,
0.06548290699720383,
-0.05269280821084976,
-0.041024744510650635,
-0.052274979650974274,
-0.00802353210747242,
-0.04539194330573082,
-0.006749479565769434,
-0.0371626652777195,
0.047890521585941315,
-0.01095520704984665,
0.002435151720419526,
0.04718058183789253,
-0.04197654873132706,
-0.02945750020444393,
0.0362551249563694,
0.012328200973570347,
0.0494103766977787,
-0.018379630520939827,
-0.0030292647425085306,
-0.014288745820522308,
0.00827697105705738,
0.002097091870382428,
0.002585931681096554,
0.035761140286922455,
-0.04786847531795502,
0.017209328711032867,
0.0037372251972556114,
0.01030865777283907,
-0.045555174350738525,
0.04448641836643219,
0.0395333468914032,
-0.04799513891339302,
-0.02674475498497486,
0.016908692196011543,
-0.015369687229394913,
0.05076354742050171,
0.041457392275333405,
0.028793934732675552,
-0.04288263991475105,
-0.02477359212934971,
-0.036380406469106674,
-0.024879485368728638,
-0.04137297719717026,
-0.023358844220638275,
0.0006038905121386051,
-0.04527938365936279,
0.013685381971299648,
0.06598026305437088,
-0.02765144407749176,
0.03232482820749283,
0.03961256146430969,
-0.0019282415742054582,
0.00585593655705452,
-0.03012153133749962,
-0.030514679849147797,
0.027714503929018974,
0.014700627885758877,
-0.010804492980241776,
-0.023463517427444458,
-0.02962176688015461,
0.0020639952272176743,
-0.004901918116956949,
-0.07116186618804932,
-0.054621074348688126,
-0.02622847445309162,
0.008707436732947826,
0.005139561370015144,
-0.03060397319495678,
-0.026975080370903015,
-0.022999979555606842,
0.023191722109913826,
0.029469462111592293,
0.012558755464851856,
-0.018083637580275536,
-0.02789679542183876,
-0.04436993971467018,
0.01210359763354063,
-0.015693150460720062,
0.017597926780581474,
0.057394593954086304,
0.0030610181856900454,
-0.0454520545899868,
-0.04319368302822113,
-0.019942285493016243,
0.022519797086715698,
-0.05508819967508316,
-0.11164723336696625,
-0.03539063781499863,
0.00632502743974328,
-0.004549173638224602,
0.03254125267267227,
-0.022213587537407875,
-0.04069575294852257,
0.019388247281312943,
0.026917407289147377,
-0.030366970226168633,
-0.021521389484405518,
-0.03598817437887192,
-0.013466878794133663,
0.018067635595798492,
-0.033377714455127716,
0.015980927273631096,
-0.02800840139389038,
0.028602343052625656,
-0.06553594022989273,
-0.013831858523190022,
0.05413214489817619,
0.046665970236063004,
-0.030407505109906197,
-0.05156300961971283,
0.029971202835440636,
-0.00364522822201252,
-0.029023585841059685,
0.0024989049416035414,
-0.00845843181014061,
-0.016391519457101822,
-0.027336491271853447,
-0.024508275091648102,
0.08329928666353226,
-0.027832768857479095,
0.02746480517089367,
0.06183544546365738,
0.04453667625784874,
0.019075360149145126,
0.06566084176301956,
0.05004439502954483,
-0.01875656098127365,
-0.06626962125301361,
0.010301110334694386,
-0.03887287154793739,
-0.04389561712741852,
-0.014318235218524933,
0.040315523743629456,
0.010867591947317123,
0.001421767403371632,
0.056043051183223724,
-0.03327283635735512,
-0.03963150084018707,
0.023593895137310028,
-0.018002130091190338,
0.050651006400585175,
0.02510962262749672,
-0.012975314632058144,
0.044244375079870224,
0.001517956261523068,
-0.08658955246210098,
-0.03787238523364067,
0.024446386843919754,
-0.03857790306210518,
-0.06308304518461227,
0.018333252519369125,
-0.0010579581139609218,
0.044977787882089615,
0.04463398456573486,
-0.04737253114581108,
0.03430302068591118,
-0.07161097228527069,
0.00787282083183527,
-0.04723923280835152,
0.06711147725582123,
0.033725570887327194,
0.016245916485786438,
0.040894247591495514,
0.032426249235868454,
-0.11324242502450943,
-0.04849521815776825,
0.06447231024503708,
0.00819691363722086,
-0.029554463922977448,
-0.011049903929233551,
-0.026203013956546783,
0.019376682117581367,
0.03036613203585148,
0.026811642572283745,
0.019013047218322754,
0.009247667156159878,
-0.020419899374246597,
0.022458091378211975,
0.03259623423218727,
0.04385043680667877,
0.0033780355006456375,
-0.11486458033323288,
0.05649206042289734,
0.062236618250608444,
0.04794147610664368,
-0.06190098449587822,
-0.043396156281232834,
-0.01961303874850273,
0.012818421237170696,
-0.012117325328290462,
-0.005448136478662491,
0.005354745779186487,
-0.009153440594673157,
-0.018962599337100983,
0.030931951478123665,
0.05216841399669647,
0.04051712527871132,
-0.04573512449860573,
-0.01781388372182846,
0.03223835304379463,
-0.0636364296078682,
-0.008429445326328278,
-0.04138617217540741,
0.002741294912993908,
0.0001684012677287683,
-0.03988933563232422,
-0.010323978029191494,
-0.011972648091614246,
-0.022575395181775093,
0.013355529867112637,
-0.03835522010922432,
-0.028096389025449753,
0.0023246495984494686,
-0.017027057707309723,
-0.02549106627702713,
0.012672326527535915,
-0.08967939019203186,
-0.0241354089230299,
0.024614356458187103,
0.002079467521980405,
0.012004024349153042,
-0.026115382090210915,
0.014044894836843014,
0.010449622757732868,
-0.009199264459311962,
-0.04145418852567673,
0.056077443063259125,
0.03785541653633118,
0.004836515989154577,
-0.04223676770925522,
0.05459247902035713,
0.028891634196043015,
-0.03247763216495514,
-0.027913058176636696,
-0.032287295907735825,
0.00017461834067944437,
0.012913296930491924,
-0.011012312956154346,
-0.002828070893883705,
0.040752336382865906,
-0.018547752872109413,
0.021991726011037827,
0.026528414338827133,
-0.008559256792068481,
-0.012281716801226139,
0.0024878012482076883,
0.026001732796430588,
0.07889346778392792,
0.030646584928035736,
-0.00242354953661561,
-0.01416213158518076,
-0.00830541830509901,
0.012660078704357147,
0.008269120939075947,
-0.015358136035501957,
-0.01380087062716484,
0.002049008384346962,
-0.005820866208523512,
0.04161190986633301,
0.024866530671715736,
0.04161984845995903,
0.05155752971768379,
0.06374279409646988,
0.007435956038534641,
0.07573842257261276,
0.007298889569938183,
-0.04174487665295601,
0.010533737018704414,
-0.02239340916275978,
0.046041350811719894,
-0.04321000725030899,
0.0013709847116842866,
-0.011408360674977303,
-0.03585098683834076,
-0.020006956532597542,
-0.05040949955582619,
-0.004581536166369915,
-0.07160557806491852,
-0.0981280654668808,
-0.03960969299077988,
-0.03453480079770088,
0.13522019982337952,
-0.11644740402698517,
0.021519074216485023,
0.0007161654066294432,
0.016870388761162758,
0.01517008151859045,
-0.0029058242216706276,
-0.002107568085193634,
-0.053118746727705,
0.03408794850111008,
0.0702098160982132,
-0.008442643098533154,
-0.012819119729101658,
0.013460380956530571,
0.06015034392476082,
0.02888639084994793,
0.004313328303396702,
-0.032859936356544495,
-0.06356170028448105,
0.0003937559376936406,
-0.05677015706896782,
0.02218972146511078,
0.032708682119846344,
-0.023581458255648613,
0.009098977781832218,
-0.014474221505224705,
0.006417560391128063,
-0.048637352883815765,
0.07199183106422424,
-0.0074104610830545425,
-0.039035845547914505,
0.04523545131087303,
0.037596773356199265,
-0.0008357177721336484,
-0.03047926351428032,
-0.018734565004706383,
-0.02736295759677887,
0.045221757143735886,
-0.04987214878201485,
-0.030701102688908577,
0.021328074857592583,
-0.032810479402542114,
-0.04397759586572647,
-0.03204794600605965,
-0.045483607798814774,
0.014186134561896324,
0.0339508019387722,
0.009866155683994293,
-0.036436110734939575,
0.03965209797024727,
-0.020664619281888008,
-0.01727289706468582,
-0.024630043655633926,
-0.01275069173425436,
0.017148159444332123,
0.014435852877795696,
-0.01590687967836857,
-0.03191396966576576,
-0.03338995203375816,
-0.0002092476061079651,
-0.02038966305553913,
-0.016078541055321693,
-0.014282050542533398,
0.06151130422949791,
-0.028609925881028175,
0.03377111256122589,
-0.015694737434387207,
0.011310102418065071,
0.008105038665235043,
-0.004285658709704876,
0.02408229000866413,
0.025650568306446075,
0.002261712681502104,
0.017115836963057518,
-0.03774925321340561,
-0.05272035300731659,
-0.03580428287386894,
0.02123394049704075,
0.04587757587432861,
0.019898083060979843,
0.021068556234240532,
0.03193504735827446,
-0.016447745263576508,
0.05150619149208069,
0.04634688422083855,
-0.006984202656894922,
-0.021243372932076454,
0.007006966043263674,
-0.00913993176072836,
0.003923084586858749,
0.059963442385196686,
0.050176817923784256,
0.016487134620547295,
-0.01705784536898136,
0.00922068115323782,
-0.005726950708776712,
0.05403667688369751,
0.00560374092310667,
0.022785034030675888,
-0.022273557260632515,
-0.03571488335728645,
-0.012143661268055439,
0.033718377351760864,
-0.03957052528858185,
0.014872007071971893,
0.012234428897500038,
-0.06107926741242409,
0.008785939775407314,
0.009075596928596497,
0.0323585607111454,
0.015193603001534939,
-0.07957728207111359,
0.057297609746456146,
0.0613618828356266,
0.012468745931982994,
0.01597180962562561,
0.005202626343816519,
-0.0062696789391338825,
0.025421518832445145,
0.005843349266797304,
-0.0397660955786705,
-0.008363146334886551,
0.05567837134003639,
0.046012867242097855,
-0.023346778005361557,
0.007130876183509827,
-0.038690391927957535,
-0.05783906951546669,
-0.05347411707043648,
0.006978417281061411,
-0.04156343638896942,
0.013372236862778664,
-0.024269258603453636,
0.05228421464562416,
-0.001418511150404811,
-0.02255856990814209,
-0.06777331978082657,
-0.030163545161485672,
0.027813013643026352,
0.009481224231421947,
-0.04563404619693756,
0.01253112219274044,
-0.01155033428221941,
0.03638558089733124,
0.06279406696557999,
-0.006807251367717981,
-0.028616564348340034,
0.029367223381996155,
-0.06424926221370697,
0.011273208074271679,
0.038177020847797394,
-0.04053431749343872,
0.0759681910276413,
-0.05789633095264435,
0.03893183916807175,
-0.04804705083370209,
-0.052447360008955,
0.0011674434645101428,
-0.01756923273205757,
-0.015636887401342392,
-0.04576658457517624,
-0.043836187571287155,
0.05024952441453934,
0.017013994976878166,
-0.015455399639904499,
0.004881728906184435,
-0.038992393761873245,
-0.05450793355703354,
0.052208106964826584,
0.06981418281793594,
0.04009459540247917,
-0.028410963714122772,
-0.0001306027261307463,
0.00760316476225853,
0.02066182903945446,
-0.05204277113080025,
0.015084328129887581,
-0.025357995182275772,
-0.0014442665269598365,
-0.01642107218503952,
0.02235133945941925,
0.012697254307568073,
0.002940359991043806,
-0.015945984050631523,
-0.037963032722473145,
-0.01380977500230074,
0.03701821342110634,
-0.014532881788909435,
-0.02985631301999092,
-0.025838548317551613,
0.033284369856119156,
0.07508166879415512,
-0.010836600326001644,
0.027940087020397186,
-0.04543089494109154,
-0.01485197152942419,
-0.02175445854663849,
-0.012611961923539639,
-0.014068744145333767,
-0.020352637395262718,
0.004847483243793249,
-0.08060354739427567,
0.02894747070968151,
-0.10145678371191025,
-0.008884956128895283,
0.03660605102777481,
0.033070746809244156,
-0.028653260320425034,
-0.00704972492530942,
-0.005529245361685753,
0.032957762479782104,
-0.007558704353868961,
0.03031649813055992,
-0.003975098952651024,
-0.003963358700275421,
0.052188530564308167,
-0.031187785789370537,
0.0013342209858819842,
0.019166022539138794,
-0.02213856764137745,
0.025636693462729454,
0.010951201431453228,
0.06042734161019325,
0.0041513592004776,
-0.031498171389102936,
0.029783638194203377,
-0.027936575934290886,
-0.03843918815255165,
0.010263770818710327,
0.030101127922534943,
-0.00008639915176900104,
-0.010164524428546429,
-0.05652520805597305,
0.059530630707740784,
0.007462074048817158,
0.020580163225531578,
0.004865756258368492,
-0.025004027411341667,
-0.027342885732650757,
-0.01811755821108818,
-0.0015225321985781193,
-0.013436011038720608,
0.021875541657209396,
0.004943118896335363,
0.019541475921869278,
0.02319803647696972,
0.05210193991661072,
0.05022243782877922,
0.04330255091190338,
0.008904377929866314,
-0.027752099558711052,
-0.03623038902878761,
0.006248570512980223,
0.031003236770629883,
-0.05909857898950577,
0.03250453248620033,
0.03996693715453148,
-0.04985298588871956,
-0.0022064412478357553,
0.030644692480564117,
-0.01954927109181881,
0.025492755696177483,
0.06421263515949249,
-0.006987887900322676,
-0.014095463789999485,
0.0358908474445343,
-0.04859921336174011,
0.0010208220919594169,
-0.0335862822830677,
0.005466902162879705,
0.008611713536083698,
0.024971183389425278,
0.046753812581300735,
-0.01158206444233656,
-0.010651201009750366,
0.007233721204102039,
-0.0264474768191576,
-0.0035605612210929394,
0.0324036069214344,
-0.029880862683057785,
-0.005408545956015587,
-0.022237559780478477,
0.04220031574368477,
-0.01962839625775814,
-0.051056478172540665,
-0.015191700309515,
-0.02814527042210102,
0.024367135018110275,
0.0008779054041951895,
0.06058942899107933,
-0.0037322533316910267,
-0.04015978053212166,
-0.029591325670480728,
0.01018007192760706,
-0.0019642715342342854,
0.014268534258008003,
0.03444570675492287,
0.0315416194498539,
0.04543614387512207,
0.02948606386780739,
-0.08271672576665878,
-0.003436438739299774,
0.00009971250256057829,
0.0025697918608784676,
0.012482152320444584,
-0.015582533553242683,
-0.03565139323472977,
-0.05483200401067734,
-0.039681870490312576
] |
<p><a href="http://en.wikipedia.org/wiki/Particle_in_a_ring" rel="nofollow">Particle in ring</a> is a well-known example where a solution of the Schrodinger equation exists. My question is: In principle we also want that $\psi'(\theta) = \psi'(\theta + 2\pi)$. The thing is that this condition is never explicitly stated ( probably because it is fulfilled anyway, but in principle we would also need this condition, right?</p> | g9230 | [
0.00797525979578495,
0.03630422055721283,
0.0033343015238642693,
-0.02700134553015232,
0.09384340792894363,
-0.045075707137584686,
-0.0299520306289196,
0.03343970328569412,
-0.027737921103835106,
-0.001088064513169229,
0.002375946147367358,
0.045956384390592575,
-0.030756331980228424,
-0.008488007821142673,
-0.03546379879117012,
-0.005591127555817366,
0.0450139194726944,
-0.040813691914081573,
-0.00602355832234025,
0.02403132990002632,
-0.04266076907515526,
0.01619672030210495,
0.03725431486964226,
-0.014240754768252373,
0.075293630361557,
-0.042915333062410355,
0.048619553446769714,
-0.04597683995962143,
-0.020453019067645073,
-0.01832493767142296,
-0.014652447775006294,
0.004250208847224712,
0.043376605957746506,
-0.05627615004777908,
-0.01774195209145546,
-0.06670846045017242,
0.07608668506145477,
-0.007854257710278034,
0.007073941640555859,
-0.023233160376548767,
0.016653141006827354,
-0.02181769721210003,
0.011083613149821758,
-0.004161030985414982,
0.022180691361427307,
0.035166677087545395,
0.038998935371637344,
0.04743088781833649,
-0.0446484237909317,
0.01715671643614769,
-0.022947365418076515,
0.00481155002489686,
0.00826544500887394,
-0.006247275974601507,
-0.012874514795839787,
0.009485085494816303,
0.06926161795854568,
-0.03291007876396179,
0.0447685681283474,
0.06355766952037811,
-0.042235326021909714,
-0.01612822711467743,
0.059185273945331573,
-0.002694875467568636,
0.015274912118911743,
-0.028314797207713127,
-0.015138037502765656,
0.0000330595976265613,
-0.06518066674470901,
0.018235275521874428,
0.006980120670050383,
-0.07630326598882675,
0.04062138497829437,
-0.018688874319195747,
-0.014867297373712063,
0.03728200122714043,
-0.04172090068459511,
-0.04056919366121292,
0.04356257617473602,
0.05478553846478462,
-0.040374960750341415,
-0.008766626007854939,
0.0554063618183136,
-0.028380349278450012,
0.023398471996188164,
0.020351633429527283,
-0.00938425399363041,
-0.08349433541297913,
0.015391203574836254,
0.018902555108070374,
0.015000365674495697,
-0.0009818130638450384,
0.02521700970828533,
-0.024190301075577736,
0.026591211557388306,
-0.02588941715657711,
-0.05459802597761154,
0.061313651502132416,
-0.016306698322296143,
0.01991669274866581,
-0.025748198851943016,
-0.04396172985434532,
0.034288786351680756,
0.013368488289415836,
0.0371197871863842,
-0.04699377715587616,
-0.007014388684183359,
0.045203134417533875,
-0.0196895319968462,
0.0067949132062494755,
-0.0266562569886446,
-0.011783352121710777,
0.0033150706440210342,
-0.00018688304407987744,
-0.04563089832663536,
0.003437330247834325,
0.07428064197301865,
0.03998183831572533,
0.01640153117477894,
0.09357447922229767,
-0.024989549070596695,
-0.002113519236445427,
0.048765070736408234,
0.0790315642952919,
-0.02600468136370182,
0.02704812027513981,
0.012036914937198162,
-0.03409453481435776,
0.07042883336544037,
-0.052285872399806976,
0.0042107789777219296,
-0.018594156950712204,
0.008148886263370514,
0.054640594869852066,
-0.03982787951827049,
0.009472734294831753,
-0.043149806559085846,
-0.013761375099420547,
0.008253815583884716,
-0.006073569878935814,
0.005875115282833576,
-0.03879258781671524,
0.02186114713549614,
0.060587648302316666,
-0.07824742794036865,
-0.03671635314822197,
-0.01658768765628338,
-0.02256736531853676,
0.01716862991452217,
0.08409544825553894,
-0.08681698143482208,
0.03494764864444733,
-0.025730548426508904,
-0.019956232979893684,
0.05387076362967491,
-0.040186572819948196,
0.024408312514424324,
0.06808508932590485,
0.004937132354825735,
-0.01735718920826912,
0.04169277846813202,
0.00019393554248381406,
-0.03914850577712059,
0.01601581647992134,
-0.053195931017398834,
0.022408049553632736,
-0.01834559068083763,
-0.03910781443119049,
-0.04943064600229263,
-0.08199896663427353,
0.027444835752248764,
0.015426013618707657,
-0.011379698291420937,
0.03335797041654587,
0.012378962710499763,
0.06200239062309265,
-0.025885730981826782,
0.0054133590310812,
-0.001648984383791685,
0.02528074011206627,
-0.004580745939165354,
-0.043252937495708466,
0.03462069481611252,
-0.043222084641456604,
0.013391726650297642,
0.026285411790013313,
0.005392331629991531,
0.02071657031774521,
-0.03536374494433403,
0.03829922154545784,
0.007224022410809994,
0.020054886117577553,
0.04703467711806297,
0.058836400508880615,
0.035740796476602554,
0.005850060377269983,
0.02428177185356617,
-0.07354071736335754,
0.023726586252450943,
0.027779219672083855,
0.007327525410801172,
0.03832672908902168,
0.025943616405129433,
-0.020739896222949028,
0.020391657948493958,
-0.011110251769423485,
0.02061871811747551,
-0.03770848736166954,
0.0771322250366211,
-0.03812656179070473,
0.06132280454039574,
-0.06180274859070778,
-0.029760021716356277,
0.0006310695898719132,
-0.04196032136678696,
-0.04737156629562378,
0.03314119949936867,
-0.017414037138223648,
-0.06893332302570343,
0.021103816106915474,
0.0002798748027998954,
-0.049467671662569046,
0.012332076206803322,
-0.0008406684501096606,
0.04856488108634949,
0.004421827383339405,
-0.06297250837087631,
-0.04707292094826698,
-0.06905339658260345,
0.04070190340280533,
-0.017342662438750267,
-0.02602355368435383,
-0.056086648255586624,
-0.02696092426776886,
0.05796054005622864,
0.04409464821219444,
-0.006044080480933189,
0.010671940632164478,
0.06413640826940536,
0.02835593931376934,
0.0019160767551511526,
0.006432356778532267,
-0.023033861070871353,
0.03917619585990906,
-0.017366832122206688,
-0.016198767349123955,
-0.024781595915555954,
-0.020575301721692085,
-0.04626917466521263,
0.014697546139359474,
-0.0084275146946311,
-0.06522958725690842,
-0.0018910081125795841,
-0.04027433693408966,
-0.010373316705226898,
-0.04059291258454323,
0.017831580713391304,
0.018514428287744522,
-0.024030305445194244,
-0.01598549447953701,
0.015370097011327744,
-0.032045185565948486,
-0.016282279044389725,
0.0301523394882679,
-0.04188574105501175,
-0.016639122739434242,
-0.0013786072377115488,
-0.015069429762661457,
0.008256219327449799,
-0.005362635478377342,
-0.053935661911964417,
0.031317148357629776,
-0.02770056389272213,
0.014872151426970959,
-0.020118681713938713,
-0.024826176464557648,
0.03447960689663887,
0.0008410578011535108,
0.040490977466106415,
-0.014060300774872303,
0.021382706239819527,
-0.015206755138933659,
-0.03269462287425995,
0.11707721650600433,
0.010447833687067032,
-0.040957193821668625,
-0.0025354307144880295,
0.00031092626159079373,
0.042208991944789886,
0.01907763071358204,
0.002866571070626378,
0.04537155479192734,
0.009553450159728527,
0.03346148133277893,
-0.05078026279807091,
0.039623573422431946,
-0.0038230903446674347,
0.009285441599786282,
0.031153634190559387,
0.0606531947851181,
0.02123803272843361,
-0.030730046331882477,
-0.006713122129440308,
-0.0010067465482279658,
0.05063646286725998,
-0.0013836908619850874,
-0.06602348387241364,
-0.012579611502587795,
0.009976937435567379,
-0.007368213031440973,
-0.006934144999831915,
0.08667337894439697,
-0.02792445197701454,
0.03785821795463562,
-0.028911231085658073,
0.019328977912664413,
-0.03845342621207237,
-0.0114269545301795,
0.003388386918231845,
0.014885936863720417,
-0.04820556938648224,
-0.020071841776371002,
0.03499119356274605,
-0.04505744203925133,
0.02815823256969452,
-0.0035327801015228033,
-0.0961635485291481,
0.023029277101159096,
-0.024397119879722595,
-0.04916653409600258,
0.019296064972877502,
-0.008873491548001766,
0.0013960535870864987,
-0.050126511603593826,
-0.06619298458099365,
-0.05222100391983986,
-0.07981497049331665,
0.03404957801103592,
0.01774720288813114,
0.024189453572034836,
0.02712215669453144,
-0.05501098558306694,
-0.026454688981175423,
0.028268244117498398,
0.0006685006082989275,
0.010457323864102364,
-0.051943086087703705,
0.057402294129133224,
0.03745003789663315,
-0.00954375322908163,
0.025881482288241386,
-0.009234409779310226,
0.03200392797589302,
-0.02861887589097023,
0.0017217787681147456,
0.011699330061674118,
0.00761741166934371,
0.01762564852833748,
0.016364801675081253,
-0.052850786596536636,
0.009471828117966652,
-0.029032062739133835,
0.0361616425216198,
-0.026091698557138443,
0.0743272453546524,
-0.01697062887251377,
-0.017810389399528503,
0.01759963482618332,
0.019127527251839638,
-0.03730505704879761,
0.05975303053855896,
-0.009588679298758507,
0.0362028107047081,
0.022951209917664528,
0.08545438200235367,
-0.04789683222770691,
-0.03927309438586235,
0.02402711659669876,
-0.04352835938334465,
0.03053394891321659,
-0.051997508853673935,
0.011524118483066559,
-0.013193410821259022,
0.010520551353693008,
0.017299845814704895,
0.01592901349067688,
-0.013762216083705425,
0.06753960251808167,
0.0037323147989809513,
-0.0026901906821876764,
-0.004878498148173094,
0.014418277889490128,
-0.009303532540798187,
0.02790500968694687,
-0.038029108196496964,
0.026440653949975967,
0.03636766970157623,
-0.10794398188591003,
-0.046341922134160995,
0.005377467256039381,
0.0009832156356424093,
-0.025041675195097923,
0.0511835552752018,
-0.001983098452910781,
0.030176740139722824,
-0.03728833049535751,
0.03538096323609352,
-0.025959167629480362,
0.030353166162967682,
-0.012816870585083961,
-0.021639926359057426,
0.030768055468797684,
-0.005682663060724735,
0.009732555598020554,
0.043716270476579666,
-0.014161961153149605,
-0.0051553151570260525,
-0.0573747381567955,
0.014870046637952328,
0.01260627806186676,
-0.05276571214199066,
0.015118631534278393,
-0.011808118782937527,
-0.01725025847554207,
-0.00379865150898695,
0.06876322627067566,
0.022234851494431496,
0.04262745380401611,
-0.07009004056453705,
-0.05468842387199402,
0.0257104504853487,
-0.005351726897060871,
0.022992081940174103,
0.005662564188241959,
0.00820502731949091,
-0.009238610975444317,
-0.10916678607463837,
-0.03198028728365898,
-0.017009591683745384,
0.00263388198800385,
0.05836387723684311,
0.025825118646025658,
0.04420051723718643,
-0.04133261367678642,
-0.04275500401854515,
0.02142665721476078,
-0.051197152584791183,
0.0015045477775856853,
-0.015814244747161865,
-0.011609651148319244,
-0.004848466254770756,
0.005591756198555231,
-0.0033024318981915712,
-0.017328878864645958,
-0.018462583422660828,
-0.04022488743066788,
-0.033706627786159515,
-0.02048114687204361,
-0.03377387672662735,
0.07238621264696121,
-0.04072508215904236,
-0.024531656876206398,
-0.005863103084266186,
0.032944537699222565,
0.039058834314346313,
0.01283604372292757,
-0.06019818037748337,
-0.0165836401283741,
-0.045131150633096695,
-0.03795981779694557,
0.005998210981488228,
0.030630046501755714,
0.04118814319372177,
-0.021563448011875153,
0.04383586347103119,
-0.06952574849128723,
-0.04033484682440758,
-0.003443092107772827,
-0.03058641217648983,
-0.04694044217467308,
-0.02413988672196865,
0.041414715349674225,
0.005350757855921984,
0.038358815014362335,
0.024148840457201004,
0.015722420066595078,
-0.06273090839385986,
0.031224805861711502,
-0.011195826344192028,
-0.05973047763109207,
0.018197426572442055,
0.0783909261226654,
0.013552537187933922,
0.02053162269294262,
0.007413630839437246,
-0.042733319103717804,
0.020326320081949234,
-0.02898319810628891,
-0.0050719669088721275,
0.037081681191921234,
-0.019719252362847328,
0.0024619351606816053,
-0.002385456580668688,
0.010143440216779709,
-0.0038923390675336123,
0.058369845151901245,
0.07061601430177689,
0.04200080782175064,
0.004585713613778353,
-0.003849770873785019,
0.04676503688097,
-0.03135468065738678,
0.006089210510253906,
0.023099372163414955,
0.01844720169901848,
0.03391764312982559,
-0.033008161932229996,
0.018386945128440857,
-0.02790016680955887,
0.00033467859611846507,
0.024249764159321785,
0.012139835394918919,
0.0017346936510875821,
-0.0826178565621376,
-0.00355782313272357,
0.034575365483760834,
-0.06523152440786362,
-0.042559705674648285,
0.04858130216598511,
0.06415516138076782,
0.019130127504467964,
-0.07023512572050095,
-0.0032805411610752344,
0.058998849242925644,
0.06055869534611702,
-0.0682116374373436,
0.032404784113168716,
-0.014692774042487144,
-0.011209504678845406,
0.008095819503068924,
-0.004346730653196573,
-0.0004976916243322194,
0.08258523046970367,
0.02164839208126068,
0.01018083281815052,
0.0010687822941690683,
-0.007241768296808004,
0.06861807405948639,
-0.01776413805782795,
0.003426073584705591,
-0.02853807806968689,
-0.010339534841477871,
-0.021824555471539497,
0.011571874842047691,
0.006313621532171965,
-0.008985207416117191,
0.04219384491443634,
-0.00991759728640318,
-0.027995510026812553,
0.011794914491474628,
0.047750916332006454,
-0.0461466908454895,
-0.0031222037505358458,
0.0031277781818062067,
0.005899515002965927,
0.005261440761387348,
-0.012949998490512371,
0.0008964068838395178,
0.04600916802883148,
0.0053109885193407536,
-0.014542369171977043,
-0.008032490499317646,
-0.01704787276685238,
-0.013371936976909637,
0.03325240686535835,
-0.016232328489422798,
-0.059485405683517456,
-0.01252212654799223,
0.012584207579493523,
0.05692356079816818,
0.028108328580856323,
0.05771122872829437,
0.04519975930452347,
-0.06883548945188522,
0.04591832682490349,
0.013297708705067635,
-0.02333357185125351,
-0.0005916088121011853,
0.05949536710977554,
0.012777585536241531,
0.011531835421919823,
-0.04335746914148331,
-0.02359476312994957,
-0.0073342230170965195,
-0.006011568941175938,
0.02324378490447998,
0.007034709677100182,
-0.013199079781770706,
-0.021075602620840073,
0.06688741594552994,
0.04462862387299538,
-0.04707392305135727,
0.01837736740708351,
0.03468668460845947,
0.001315474626608193,
0.04341350495815277,
-0.014062109403312206,
0.0031750283669680357,
-0.0096211489289999,
0.019775206223130226,
-0.031154049560427666,
0.016659768298268318,
-0.016304148361086845,
-0.0302449781447649,
0.03639207035303116,
-0.08209424465894699,
0.06868362426757812,
0.05122120678424835,
-0.02995811216533184,
-0.027014022693037987,
0.030879251658916473,
-0.04170602932572365,
-0.006333889439702034,
0.01746956817805767,
0.058062177151441574,
-0.02363496460020542,
-0.01068299263715744,
0.04604407399892807,
0.09712778776884079,
-0.009618586860597134,
0.026917578652501106,
-0.02214037999510765,
-0.0352051742374897,
0.024317925795912743,
-0.03798942640423775,
0.01247632410377264,
-0.022904179990291595,
-0.033712100237607956,
0.019168643280863762,
0.015898125246167183,
0.024527721107006073,
0.03617601469159126,
0.0625338926911354,
-0.0010166859719902277,
-0.09367560595273972,
0.0005963154253549874,
0.09834306687116623,
0.01078801229596138,
-0.09968218207359314,
0.016769183799624443,
0.0777634009718895,
-0.004992874339222908,
-0.046119414269924164,
0.017959492281079292,
-0.022352978587150574,
-0.038212139159440994,
-0.006893658544868231,
-0.013959333300590515,
-0.038160793483257294,
-0.04424940049648285,
-0.025027845054864883,
-0.020649515092372894,
0.027932865545153618,
-0.017170557752251625,
-0.04253828153014183,
0.047627344727516174,
0.023125359788537025,
-0.0449586845934391,
0.033012133091688156,
-0.019971678033471107,
0.017834050580859184,
-0.027664730325341225,
-0.03943890705704689,
-0.013105074875056744,
-0.057088788598775864,
-0.009351701475679874,
0.04379875585436821,
0.026402462273836136,
-0.007756861858069897,
-0.018310485407710075,
-0.00469671655446291,
-0.02060624398291111,
0.0048470040783286095,
-0.01487962156534195,
-0.032722268253564835,
0.007022497709840536,
-0.014665817841887474,
-0.01671883463859558,
-0.04763141646981239,
0.04063388705253601,
0.01341995783150196,
0.048475924879312515,
0.028288261964917183,
-0.023261504247784615,
-0.0004985049599781632,
0.013532975688576698,
0.025365259498357773,
0.027827607467770576,
0.009996701963245869,
0.004983471240848303,
-0.008437564596533775,
-0.010365265421569347,
0.018612250685691833,
0.015455750748515129,
0.01400525588542223,
0.0014526421437039971,
-0.01329734642058611,
-0.0044743362814188,
-0.06635945290327072,
-0.006971126887947321,
-0.005333533510565758,
0.008331828750669956,
-0.0363612174987793,
0.002914265263825655,
0.0515718087553978,
0.036334313452243805,
-0.08100355416536331,
0.03511742874979973,
0.07269193977117538,
-0.015001105144619942,
0.01188373751938343,
0.026431161910295486,
-0.05672984570264816,
-0.06370876729488373,
0.001712947036139667,
-0.034051548689603806,
0.004005576949566603,
-0.0017337334575131536,
-0.018647709861397743,
0.0063005234114825726,
0.02730463072657585,
0.021839439868927002,
-0.04624687880277634,
0.027013318613171577,
0.00384219316765666,
-0.0402236208319664,
-0.03693408519029617,
-0.01460226159542799,
-0.011570719070732594,
0.003447827184572816,
0.0012588833924382925,
-0.04938676208257675,
-0.010832716710865498,
-0.018465112894773483,
-0.020624639466404915,
0.05687415227293968,
-0.012122979387640953,
-0.0034412071108818054,
0.018529590219259262,
0.01382763497531414,
-0.058553487062454224,
0.04134215787053108,
-0.02890334650874138,
0.0602964349091053,
0.06063634529709816,
-0.09008320420980453,
0.0326029509305954,
0.077127605676651,
-0.016725657507777214,
0.0012025815667584538,
0.016184555366635323,
-0.02322343923151493,
-0.01695908233523369,
0.01470184326171875,
-0.027891822159290314,
-0.04756778106093407,
-0.026560857892036438,
-0.05150974169373512
] |
<p>This year in college we"ve had a lot of quantum stuff thrown at us, and we"ve only been doing classical mechanics till last year. We"ve been introduced to Schrodinger"s equation, electron waves, what have you. This is my understanding(rather rudimentary) so far. When you solve Schrodinger"s equation for an atom, you get a set of wave functions(what are the inputs and outputs exactly in this function?). Each wave function can describe a maximum of 2 electrons. It was stated in one place that the wave function represents the amplitude of the electron wave, and its square gives the probability of finding the electron at a place.An orbital is a surface diagram that includes the regions where the electron described by a particular wave function is most likely to be found within the surface.
NOTE: I know the basic quantum formulae even though I may not understand what they mean.</p>
<p>Is my understanding right?(I realize I had forgotten to put this sentence when I first posted the question, and it would"ve seemed rather confusing as to what it was I actually wanted to know.)</p> | g9231 | [
-0.01830408163368702,
-0.002345251152291894,
-0.006170895881950855,
0.020973000675439835,
0.037009429186582565,
0.019861161708831787,
0.02228274568915367,
0.031093228608369827,
0.021556399762630463,
-0.0640098974108696,
-0.021649086847901344,
0.0342961810529232,
0.0816068947315216,
0.008802576921880245,
-0.0029024870600551367,
-0.03399953991174698,
0.043240632861852646,
-0.004601194988936186,
0.02497287280857563,
0.0033664691727608442,
0.035388268530368805,
0.03349972516298294,
-0.035544198006391525,
0.002998897572979331,
-0.04961172118782997,
0.015204684808850288,
0.0010644553694874048,
-0.007307636085897684,
-0.009760141372680664,
0.012146420776844025,
-0.02879314310848713,
0.008143780753016472,
0.0917523130774498,
-0.06518495082855225,
-0.034825198352336884,
-0.0007943243836052716,
0.045496102422475815,
0.008644966408610344,
0.0019787338096648455,
-0.018796490505337715,
-0.0050514498725533485,
-0.06060294061899185,
-0.010823567397892475,
-0.022557761520147324,
0.04783651977777481,
-0.02453339286148548,
-0.017305569723248482,
-0.054821159690618515,
0.013175715692341328,
-0.049880966544151306,
-0.005881447810679674,
0.047802772372961044,
0.06555820256471634,
-0.0002509468176867813,
-0.03210566192865372,
0.02991131879389286,
0.05223063379526138,
-0.009818293154239655,
0.08404630422592163,
0.055527299642562866,
0.06612750142812729,
0.03435005620121956,
0.016500214114785194,
0.019900282844901085,
0.0458376482129097,
0.03466242551803589,
0.0015409048646688461,
0.0020237741991877556,
-0.007178661413490772,
0.025184646248817444,
0.03480810672044754,
-0.11033249646425247,
0.00569757679477334,
-0.025958294048905373,
0.009948952123522758,
-0.0007530742441304028,
0.013909817673265934,
-0.027028806507587433,
0.020324675366282463,
0.03422428295016289,
-0.0049124304205179214,
-0.04797810688614845,
0.010371735319495201,
0.0030228705145418644,
0.0584055557847023,
0.057726383209228516,
-0.025325514376163483,
-0.030888639390468597,
-0.03895309194922447,
0.03424526005983353,
0.008815751411020756,
-0.0027410383336246014,
0.011007494293153286,
-0.02129306085407734,
-0.013647140935063362,
-0.02370590530335903,
-0.051226112991571426,
0.05021927133202553,
-0.01703759841620922,
0.049519337713718414,
-0.0648219957947731,
-0.02759164571762085,
0.06779816001653671,
-0.015097586438059807,
-0.002642915118485689,
0.0155379893258214,
-0.01854119636118412,
-0.010367794893682003,
0.05232566222548485,
0.02182803303003311,
-0.04086706414818764,
-0.0318974032998085,
0.01028747670352459,
0.0016965511022135615,
-0.07395514845848083,
0.008855988271534443,
0.019555198028683662,
-0.03749743849039078,
-0.015037372708320618,
0.05725792422890663,
0.010250244289636612,
0.03477868437767029,
0.03218847140669823,
0.014765624888241291,
0.03915711119771004,
0.04127493500709534,
-0.04319755360484123,
-0.029739635065197945,
0.06445764005184174,
0.009182466194033623,
0.0592026486992836,
0.005570027511566877,
-0.012779824435710907,
0.013052547350525856,
0.039084214717149734,
0.03210647031664848,
-0.011299383826553822,
-0.015125530771911144,
0.02209867164492607,
-0.02522718906402588,
0.025551561266183853,
-0.015642330050468445,
-0.024564530700445175,
-0.021592309698462486,
-0.02335270494222641,
-0.029407624155282974,
-0.044441837817430496,
0.01690111681818962,
-0.010036875493824482,
0.005641879979521036,
-0.0070860483683645725,
0.02581288293004036,
-0.026027558371424675,
-0.056841108947992325,
0.013531098142266273,
-0.0434129536151886,
0.004350885283201933,
-0.012756875716149807,
0.018678894266486168,
0.006272576283663511,
0.05646197870373726,
-0.004506692755967379,
0.0015004990855231881,
0.06311479955911636,
-0.05501969903707504,
-0.009554624557495117,
0.006261677946895361,
-0.09867676347494125,
0.0214533694088459,
-0.009220844134688377,
0.049524202942848206,
-0.016642123460769653,
-0.023754550144076347,
0.0015722644748166203,
-0.04909191653132439,
0.10127443075180054,
0.08163297921419144,
-0.006966455839574337,
0.05845789983868599,
0.05495954677462578,
0.0223570317029953,
0.021263528615236282,
0.0007231616182252765,
0.008679049089550972,
-0.020227860659360886,
-0.001524419873021543,
-0.02467724122107029,
0.009981118142604828,
-0.03368179872632027,
0.01858626864850521,
-0.02493743598461151,
-0.042337071150541306,
0.04969042167067528,
-0.007572846487164497,
0.0037542679347097874,
0.014618349261581898,
-0.004292502533644438,
-0.04329190030694008,
-0.032651979476213455,
-0.03437097743153572,
0.013075031340122223,
-0.013954946771264076,
-0.006444521714001894,
-0.013909795321524143,
0.046328600496053696,
0.03664514049887657,
0.01748201996088028,
0.0073618958704173565,
0.023435933515429497,
-0.011141513474285603,
0.04612071067094803,
-0.005519204307347536,
0.018000366166234016,
0.04115097224712372,
-0.019238391891121864,
-0.0014600332360714674,
-0.010786833241581917,
-0.013331918977200985,
-0.024589141830801964,
-0.028537467122077942,
0.024852771311998367,
-0.05593212693929672,
0.035500798374414444,
0.05560818314552307,
0.03372472897171974,
0.0666738972067833,
-0.03141862526535988,
-0.010895930230617523,
-0.029431568458676338,
0.07725880295038223,
-0.06558185070753098,
0.03724750876426697,
-0.03791309520602226,
-0.0381057932972908,
0.041761260479688644,
0.03357493877410889,
-0.010799312964081764,
-0.011609109118580818,
0.03916401043534279,
-0.008304962888360023,
0.0004105144180357456,
0.03208637237548828,
-0.033846236765384674,
-0.01647217757999897,
-0.008071144111454487,
-0.04919964075088501,
0.006781117990612984,
0.0038955819327384233,
-0.053525328636169434,
0.02415992133319378,
0.006068326532840729,
-0.03104747273027897,
-0.06084277853369713,
0.0003602227952796966,
0.002894357079640031,
-0.0317721925675869,
-0.08496637642383575,
0.022538883611559868,
-0.04743700101971626,
-0.035065509378910065,
-0.003728558775037527,
0.0446254201233387,
-0.020298969000577927,
0.03997647017240524,
-0.04530875012278557,
-0.056714024394750595,
-0.029982149600982666,
-0.032294515520334244,
0.01016975101083517,
-0.03855395317077637,
-0.013621976599097252,
0.122907355427742,
-0.0784921944141388,
0.01708098128437996,
-0.0021434687077999115,
-0.10578326880931854,
0.01093786209821701,
0.04442279413342476,
0.005576400086283684,
-0.04207991436123848,
0.0100943548604846,
0.005361562594771385,
-0.06675183773040771,
0.054101549088954926,
0.009719939902424812,
-0.041987378150224686,
0.05854044854640961,
0.04893775284290314,
0.03692694753408432,
0.011250614188611507,
-0.04033093526959419,
0.03461857885122299,
0.004614205099642277,
0.050383225083351135,
-0.07828866690397263,
0.004592072684317827,
0.0533820204436779,
-0.0031815350521355867,
-0.023522749543190002,
0.05437542870640755,
-0.06396358460187912,
-0.012575393542647362,
-0.0014449306763708591,
-0.025500578805804253,
0.027093788608908653,
0.05708533525466919,
-0.01660948432981968,
-0.01235266588628292,
-0.017781134694814682,
-0.02214176394045353,
-0.03983664512634277,
0.0631304457783699,
-0.016680769622325897,
-0.018964672461152077,
-0.0062355538830161095,
0.018526475876569748,
-0.04528539627790451,
0.009939671494066715,
0.0003945259377360344,
-0.08810444176197052,
-0.0815119668841362,
-0.04814715310931206,
-0.02468244731426239,
-0.014004077762365341,
0.043253131210803986,
0.048844724893569946,
-0.030157320201396942,
-0.0023266912903636694,
-0.029416808858513832,
-0.02452203631401062,
0.03853020444512367,
0.0008525672019459307,
-0.032170843333005905,
0.012931873090565205,
-0.002817312953993678,
-0.018816331401467323,
-0.006994071416556835,
0.01999516971409321,
0.033596936613321304,
0.008222541771829128,
0.0435970164835453,
-0.020814884454011917,
-0.012766541913151741,
-0.0007763848407194018,
0.02286066859960556,
-0.026652464643120766,
-0.0741131380200386,
0.011855937540531158,
0.019984792917966843,
-0.05376242846250534,
-0.019943412393331528,
0.004014136269688606,
0.016610203310847282,
0.04703259840607643,
-0.05186619609594345,
0.01110742799937725,
-0.0009976858273148537,
-0.003324655117467046,
0.030900711193680763,
0.0385480560362339,
-0.033695023506879807,
-0.008707651868462563,
0.011479252018034458,
0.04185232147574425,
-0.04635709896683693,
-0.07239272445440292,
-0.02970013953745365,
0.03946869447827339,
0.003810151247307658,
-0.08124817907810211,
-0.0380033478140831,
-0.01731744036078453,
0.030348753556609154,
0.051917169243097305,
0.005451461765915155,
-0.05951841175556183,
-0.06784310191869736,
0.014544720761477947,
-0.04825044423341751,
0.0049181911163032055,
-0.0264096911996603,
-0.001076498068869114,
0.07571960985660553,
0.05160325765609741,
0.04248775169253349,
-0.000608536007348448,
-0.014466839842498302,
0.016693562269210815,
0.031525127589702606,
-0.004589796531945467,
-0.02292482741177082,
-0.06425239890813828,
-0.026401448994874954,
0.05340071767568588,
0.0008442388498224318,
0.02026791125535965,
0.020008422434329987,
0.00020279487944208086,
-0.008937421254813671,
0.054239045828580856,
-0.01070652436465025,
-0.0074425265192985535,
-0.06863721460103989,
-0.0016229496104642749,
0.0036296232137829065,
0.0014928546734154224,
0.06023672968149185,
-0.03300704434514046,
-0.012365901842713356,
-0.04363482818007469,
-0.008153505623340607,
0.006241916678845882,
0.01525700930505991,
-0.031812336295843124,
-0.02764367125928402,
0.08266466856002808,
0.009110573679208755,
-0.060296911746263504,
-0.008009054698050022,
0.032369550317525864,
-0.002613228280097246,
0.06217707321047783,
0.03552660346031189,
-0.010303438641130924,
-0.03992285579442978,
-0.004559210501611233,
0.05533409118652344,
0.0061086732894182205,
-0.013316947035491467,
-0.040966324508190155,
-0.003793631913140416,
0.0366164967417717,
0.01419106125831604,
0.057346243411302567,
-0.07423103600740433,
0.00619936641305685,
-0.0328473336994648,
0.0149293327704072,
-0.014036282896995544,
-0.017904825508594513,
0.07520188391208649,
0.01314570289105177,
-0.005709420889616013,
0.034714024513959885,
0.047804031521081924,
-0.02036348171532154,
-0.024874312803149223,
-0.038009483367204666,
-0.04291416332125664,
-0.04828578233718872,
-0.036540497094392776,
0.038280338048934937,
0.04389188066124916,
-0.04586552456021309,
-0.019465869292616844,
-0.05389902740716934,
-0.023945720866322517,
-0.0017487177392467856,
0.021393584087491035,
0.027467135339975357,
-0.054070089012384415,
-0.010061211884021759,
0.005310386884957552,
0.0253874734044075,
0.0760815218091011,
-0.006277907639741898,
-0.0075750513933598995,
0.026537396013736725,
-0.10541458427906036,
-0.037059687077999115,
0.047832638025283813,
-0.01783803291618824,
0.06003572419285774,
-0.04103537276387215,
0.0253921989351511,
-0.027582501992583275,
-0.019959373399615288,
-0.013307572342455387,
-0.014597618021070957,
-0.03512809798121452,
-0.01114620827138424,
-0.022808507084846497,
0.0332646444439888,
0.0881163477897644,
-0.04912465810775757,
-0.019033310934901237,
-0.01465955562889576,
0.02198953554034233,
-0.004406431224197149,
0.0013775439001619816,
0.026692571118474007,
0.0028757075779139996,
0.02821999229490757,
-0.016986077651381493,
-0.010501190088689327,
-0.061732660979032516,
0.03393368050456047,
-0.013419942930340767,
-0.0001311746018473059,
0.030456040054559708,
-0.06476743519306183,
0.06103169173002243,
-0.009490431286394596,
0.01655724085867405,
-0.030956126749515533,
0.021536728367209435,
0.02130182459950447,
-0.05974575877189636,
0.031354278326034546,
0.014080450870096684,
0.030496664345264435,
-0.04002409055829048,
-0.05382676422595978,
0.0072522712871432304,
0.03994739055633545,
-0.01958157867193222,
-0.03779758885502815,
0.020377233624458313,
-0.039140600711107254,
0.07476281374692917,
0.010788370855152607,
0.0316992811858654,
-0.014953769743442535,
-0.05958781763911247,
0.020894858986139297,
0.027715496718883514,
-0.05367676541209221,
-0.021732091903686523,
0.06984616070985794,
0.07040812820196152,
-0.03693511337041855,
0.06495675444602966,
-0.015062600374221802,
0.033327531069517136,
0.009259974583983421,
0.008441366255283356,
-0.003797355806455016,
0.026037396863102913,
0.04998696222901344,
0.021598614752292633,
-0.043556369841098785,
0.06650684773921967,
-0.020082509145140648,
0.002581220120191574,
0.030726049095392227,
-0.030592264607548714,
-0.019178560003638268,
0.00947454385459423,
0.00875373650342226,
0.05702775716781616,
-0.01743144914507866,
0.012076139450073242,
0.004601288586854935,
-0.017916524782776833,
0.016275692731142044,
0.028068995103240013,
-0.022154834121465683,
0.009551032446324825,
-0.019806021824479103,
-0.045427266508340836,
0.07507296651601791,
0.05160626396536827,
0.0360550619661808,
0.023238230496644974,
0.03195811063051224,
0.03609997034072876,
-0.021189484745264053,
-0.008559711277484894,
0.0039596701972186565,
0.03726642206311226,
-0.02387806586921215,
-0.028812449425458908,
-0.016945799812674522,
0.022237436845898628,
0.022637302055954933,
0.031860481947660446,
-0.012303274124860764,
-0.028220925480127335,
-0.035662002861499786,
-0.04533468186855316,
-0.009989467449486256,
0.00030174924177117646,
-0.05108901858329773,
-0.00996978860348463,
-0.047230616211891174,
0.051992546766996384,
-0.0050791786052286625,
-0.05311691015958786,
0.05353246629238129,
0.01583177037537098,
-0.013967891223728657,
0.022989554330706596,
0.025861460715532303,
-0.003662648843601346,
-0.0028148458804935217,
-0.023333948105573654,
0.05937252566218376,
-0.022599410265684128,
-0.00104317138902843,
0.059417832642793655,
-0.01995725929737091,
-0.010167151689529419,
-0.02252076379954815,
0.01654568873345852,
0.0790046975016594,
0.030221911147236824,
0.016651738435029984,
-0.0162830650806427,
-0.033260613679885864,
-0.009277521632611752,
-0.0365869514644146,
-0.014938471838831902,
-0.018964942544698715,
-0.012940458953380585,
-0.015525964088737965,
-0.01576114073395729,
-0.008433896116912365,
0.056916847825050354,
0.014186063781380653,
-0.04037713259458542,
0.023152003064751625,
0.030562739819288254,
-0.01817287877202034,
0.02908460795879364,
0.037064943462610245,
0.001881931908428669,
0.014163662679493427,
-0.013740157708525658,
0.08888188749551773,
-0.03502735123038292,
0.030565975233912468,
-0.01688361167907715,
0.02809993550181389,
0.05944817513227463,
-0.007219717837870121,
0.021971069276332855,
-0.005803809966892004,
0.013197872787714005,
0.0066539207473397255,
0.05375545099377632,
-0.06229255348443985,
-0.01719122752547264,
0.04831479489803314,
0.03188645467162132,
-0.07125984132289886,
-0.05712512880563736,
0.03964768350124359,
-0.010987333953380585,
-0.06398674845695496,
-0.049718424677848816,
0.004666680935770273,
-0.001612760708667338,
-0.04023604840040207,
0.0025697213131934404,
0.01560278981924057,
-0.0027285253163427114,
0.04659717157483101,
0.05376727506518364,
-0.0026959434617310762,
-0.05070747807621956,
-0.01705537736415863,
-0.03823443502187729,
-0.007967552170157433,
-0.0077579692006111145,
-0.0012078591389581561,
0.055366404354572296,
-0.014042513445019722,
-0.028690364211797714,
-0.06310984492301941,
-0.0324661023914814,
-0.030003471300005913,
-0.040131207555532455,
-0.009484032168984413,
-0.0021475653629750013,
-0.023484041914343834,
0.04511626064777374,
-0.0016688823234289885,
0.0010663769207894802,
-0.03370770812034607,
-0.0242118239402771,
0.02187224291265011,
0.032332856208086014,
-0.01959061063826084,
-0.02741517871618271,
0.017459452152252197,
-0.042152442038059235,
-0.01416198443621397,
-0.007782065775245428,
-0.03444015979766846,
0.013938517309725285,
0.01425002608448267,
-0.018599651753902435,
-0.007509054150432348,
-0.044675711542367935,
-0.01903131604194641,
0.03851936385035515,
-0.025763150304555893,
0.05535414442420006,
0.08600612729787827,
0.013233051635324955,
0.021728862076997757,
-0.05805762857198715,
0.0003387319156900048,
-0.009073677472770214,
0.04926929250359535,
-0.007762912195175886,
0.02250964567065239,
-0.04359688237309456,
-0.0249487217515707,
-0.010725103318691254,
0.006305198650807142,
-0.026515502482652664,
0.03049503080546856,
-0.008726715110242367,
0.028113851323723793,
0.02619142085313797,
0.020320456475019455,
0.0860142931342125,
-0.028748346492648125,
0.004897004924714565,
0.05698991194367409,
0.048729874193668365,
0.033925727009773254,
-0.015819460153579712,
-0.008666370064020157,
0.026314930990338326,
0.017655344679951668,
-0.05211053788661957,
-0.010412481613457203,
-0.006512598600238562,
-0.009145176038146019,
-0.003587371902540326,
-0.020411480218172073,
0.02016683854162693,
-0.026911653578281403,
0.002595343394204974,
-0.013344657607376575,
0.0005672906991094351,
-0.010383808054029942,
0.05806995928287506,
0.05966934934258461,
-0.06849759817123413,
-0.007326023653149605,
-0.08390576392412186,
-0.07580606639385223,
-0.010358368046581745,
-0.017109278589487076,
-0.09841721504926682,
0.041825126856565475,
0.015093865804374218,
-0.02249700203537941,
0.018475277349352837,
-0.0035060052759945393,
0.042224619537591934,
0.027210131287574768,
-0.07741639018058777,
0.010301148518919945,
0.007906568236649036,
0.036661721765995026,
0.019856566563248634,
-0.013808961026370525,
0.0068352920934557915,
0.030659271404147148,
-0.0214616060256958,
-0.018640892580151558,
-0.07655160874128342,
-0.02530539035797119,
-0.03116626851260662
] |
<p>If I immerse a rod vertically in a liquid with a relative permittivity gradient (the permittivity decreases with depth), will the rod stretch (will the spacing of the atoms in the rod be affected by the varying permittivity)?</p> | g9232 | [
-0.019625244662165642,
0.03592262789607048,
0.010981268249452114,
-0.054217834025621414,
0.0010261227143928409,
0.05843720585107803,
0.05890002101659775,
0.01629171334207058,
-0.0021703937090933323,
0.0010083900997415185,
-0.02950018271803856,
0.06890510022640228,
-0.06346510350704193,
0.010280480608344078,
-0.013620666228234768,
0.019298328086733818,
0.024327458813786507,
-0.061675895005464554,
-0.0043927645310759544,
-0.025331126525998116,
-0.05871982499957085,
0.03416294604539871,
-0.04747217148542404,
0.007070257794111967,
-0.006773483008146286,
0.020522458478808403,
-0.01062816847115755,
-0.04830842837691307,
-0.05167952924966812,
0.02348724752664566,
-0.003382027382031083,
0.014892183244228363,
-0.0011595934629440308,
-0.04381948336958885,
0.035431843250989914,
-0.02722078748047352,
0.005453096237033606,
0.06767850369215012,
0.011364320293068886,
0.015099233947694302,
0.007083710748702288,
0.016656603664159775,
-0.0029551880434155464,
-0.07685220241546631,
0.02244485169649124,
-0.05942894145846367,
-0.04031321778893471,
-0.08593912422657013,
-0.0510900653898716,
-0.018136680126190186,
0.03684088587760925,
0.04852687194943428,
-0.025550968945026398,
-0.001625917386263609,
-0.005121266003698111,
-0.013444001786410809,
-0.06025173142552376,
0.03126475587487221,
0.03561067581176758,
0.05383206903934479,
0.016524825245141983,
0.0495922826230526,
-0.029354410246014595,
-0.016921527683734894,
0.01741967722773552,
-0.02329840697348118,
-0.06141497194766998,
-0.026166491210460663,
-0.03325435519218445,
0.029373208060860634,
0.0212248507887125,
-0.026656221598386765,
-0.06439784914255142,
-0.017936816439032555,
-0.0845324769616127,
0.008299274370074272,
-0.05944974347949028,
0.029958263039588928,
-0.013208596035838127,
-0.05269024521112442,
-0.08606159687042236,
0.004560020286589861,
0.01103174313902855,
0.00025879740132950246,
0.0491928793489933,
0.007540904451161623,
0.0023890440352261066,
-0.005247623194009066,
0.025704560801386833,
0.04316955432295799,
-0.03567548841238022,
-0.03345752879977226,
0.036852769553661346,
0.026808710768818855,
-0.008713165298104286,
-0.07578148692846298,
0.0319080576300621,
0.05419505760073662,
0.059324223548173904,
-0.044758401811122894,
-0.007768648210912943,
-0.01622634381055832,
0.02038426697254181,
0.008562036789953709,
-0.07984102517366409,
0.04365404322743416,
0.028295965865254402,
-0.00981028750538826,
0.04507216066122055,
-0.03581298142671585,
-0.00201350636780262,
-0.09497849643230438,
-0.03098425269126892,
0.054513975977897644,
-0.06978385895490646,
0.028696255758404732,
0.05644606798887253,
-0.03616580367088318,
-0.03929830715060234,
0.021652670577168465,
0.0512523278594017,
0.06806806474924088,
0.049560438841581345,
0.06946845352649689,
-0.03119468130171299,
0.061467673629522324,
-0.013493990525603294,
0.04295619577169418,
-0.04761708900332451,
-0.01201905682682991,
-0.010763742960989475,
0.014362212270498276,
-0.051634203642606735,
-0.04300486296415329,
-0.012538041919469833,
-0.08595288544893265,
0.004586296621710062,
-0.016510451212525368,
0.03731631115078926,
0.049131520092487335,
0.006613999605178833,
0.009452970698475838,
-0.0011899761157110333,
-0.014897488057613373,
-0.012838214635848999,
-0.07344278693199158,
-0.03574884310364723,
-0.006283330265432596,
0.025590786710381508,
-0.027579335495829582,
-0.0021408386528491974,
-0.00973503477871418,
-0.0018356078071519732,
-0.005457159131765366,
0.025896554812788963,
0.014136193320155144,
0.012177887372672558,
-0.010658737272024155,
0.07245940715074539,
0.018041836097836494,
0.006733996793627739,
0.004939241800457239,
0.004284415394067764,
-0.0030736008193343878,
-0.03846586495637894,
0.05434969812631607,
0.06025482714176178,
0.018356673419475555,
-0.018702909350395203,
-0.022232020273804665,
0.012117086909711361,
-0.02256227470934391,
-0.021488163620233536,
0.026603564620018005,
-0.0033841535914689302,
0.07278118282556534,
0.0014278236776590347,
-0.012035060673952103,
0.024217303842306137,
0.07812213897705078,
-0.04541909322142601,
0.005266539286822081,
-0.01002140250056982,
-0.06410667300224304,
0.018892671912908554,
0.019748708233237267,
-0.017590593546628952,
-0.031966619193553925,
-0.06511269509792328,
-0.019002428278326988,
0.04990191012620926,
-0.022407270967960358,
-0.03278150036931038,
0.0030632815323770046,
-0.046876102685928345,
-0.07579056173563004,
0.08481807261705399,
-0.033363912254571915,
-0.022587426006793976,
0.020730705931782722,
-0.038067471235990524,
0.009812512435019016,
0.026814281940460205,
0.01664145104587078,
0.03442716225981712,
0.029456494376063347,
-0.012850531376898289,
0.026747124269604683,
0.04602605104446411,
0.030176842585206032,
0.05434703454375267,
0.007436856627464294,
0.05523374304175377,
-0.012128857895731926,
0.049064259976148605,
-0.002342069987207651,
0.02823626436293125,
0.015488280914723873,
-0.034958526492118835,
0.04635828733444214,
0.037082452327013016,
0.00532836327329278,
-0.03020358458161354,
0.009168288670480251,
-0.034835685044527054,
-0.06799831241369247,
-0.009535787627100945,
0.002835626481100917,
0.0466797798871994,
0.008648949675261974,
-0.0022515300661325455,
-0.044507306069135666,
0.04303182289004326,
0.029611900448799133,
0.03260722756385803,
0.09753698855638504,
-0.03068048320710659,
-0.033686745911836624,
-0.024440493434667587,
-0.11098135262727737,
0.015618372708559036,
-0.025461243465542793,
0.0041714804247021675,
0.05695290118455887,
-0.0020320203620940447,
-0.020053017884492874,
-0.011669854633510113,
-0.0006760852411389351,
0.023061228916049004,
-0.0020448844879865646,
0.042293135076761246,
0.03339766338467598,
-0.014400187879800797,
0.07304592430591583,
-0.03571636602282524,
0.017415782436728477,
0.005070038139820099,
0.035591863095760345,
0.02315237559378147,
-0.04815235733985901,
-0.008427305147051811,
-0.006381751038134098,
-0.011398933827877045,
-0.003726232796907425,
-0.013532483018934727,
0.03721538931131363,
0.008354861289262772,
0.01705327443778515,
0.08683237433433533,
0.041096944361925125,
0.016723833978176117,
0.040063679218292236,
-0.011717143468558788,
0.037538666278123856,
0.023546749725937843,
0.04269637539982796,
0.041538793593645096,
-0.027013681828975677,
0.0010665818117558956,
-0.013254603371024132,
-0.012296345084905624,
-0.0014837445924058557,
0.002660076366737485,
0.012742361053824425,
0.03980868309736252,
-0.009650840424001217,
-0.0008308446849696338,
-0.004632945172488689,
-0.04533257707953453,
0.02651912532746792,
-0.04165753349661827,
0.00923086330294609,
0.03817848488688469,
0.035555705428123474,
-0.024557117372751236,
0.008666273206472397,
0.004635700024664402,
-0.04867749661207199,
0.010099947452545166,
0.0887494757771492,
-0.0386287197470665,
-0.0029471430461853743,
0.01729614846408367,
0.02763940766453743,
0.037833891808986664,
0.05397021770477295,
-0.062460917979478836,
0.014412148855626583,
0.023912644013762474,
0.0020525832660496235,
-0.12033902108669281,
0.030243797227740288,
0.0242942925542593,
0.023920299485325813,
-0.034328218549489975,
-0.025989780202507973,
0.025943215936422348,
0.0428411141037941,
-0.041549697518348694,
-0.04646945744752884,
-0.012318841181695461,
0.026075711473822594,
-0.006006487179547548,
0.007911733351647854,
0.0014785411767661572,
0.02009926550090313,
0.0072529069148004055,
-0.05861981585621834,
-0.057674262672662735,
0.0698864609003067,
-0.0344085618853569,
-0.028712302446365356,
0.04605424031615257,
0.01275347638875246,
0.014547544531524181,
-0.0268043614923954,
-0.04567786678671837,
0.05230383574962616,
-0.028443794697523117,
0.012851491570472717,
-0.0007966886623762548,
-0.028327247127890587,
0.014195118099451065,
0.01146688126027584,
0.01276285108178854,
0.012860103510320187,
-0.004493591841310263,
0.05983428284525871,
0.030533866956830025,
0.03904089704155922,
0.03508418798446655,
-0.025265581905841827,
-0.014122206717729568,
-0.008642519824206829,
-0.04215239733457565,
0.051180172711610794,
0.043471019715070724,
-0.048112209886312485,
-0.0009576864540576935,
-0.012058821506798267,
0.009185805916786194,
-0.09288369119167328,
-0.01655752956867218,
-0.00914179440587759,
-0.069522425532341,
0.05006994679570198,
0.03744235634803772,
0.001993637066334486,
-0.027725107967853546,
-0.019947784021496773,
-0.012691794894635677,
-0.006886910181492567,
-0.03090617246925831,
-0.012591340579092503,
0.02784581109881401,
-0.008275256492197514,
0.04365013539791107,
0.008945087902247906,
-0.06197337061166763,
0.006811027880758047,
-0.04862770065665245,
-0.026941780000925064,
0.002619798993691802,
0.007364511955529451,
-0.011686034500598907,
0.00959550030529499,
0.00698794424533844,
-0.01934381201863289,
-0.03252113237977028,
-0.034631043672561646,
-0.033895883709192276,
-0.026060407981276512,
-0.06009539216756821,
-0.030456537380814552,
0.02786431461572647,
-0.05288742855191231,
0.021513590589165688,
0.08998379111289978,
0.0540924035012722,
0.04160737618803978,
-0.015194282867014408,
0.0038886775728315115,
-0.0009081618045456707,
0.05839322507381439,
-0.016217006370425224,
-0.0187733955681324,
-0.003969034180045128,
0.03638084605336189,
-0.06975934654474258,
-0.00554670998826623,
0.004239179659634829,
-0.026820752769708633,
-0.050302617251873016,
-0.004635949153453112,
-0.002022200496867299,
0.018431684002280235,
0.020886633545160294,
-0.01709022931754589,
0.030515341088175774,
0.011360552161931992,
-0.008728459477424622,
0.09359472244977951,
-0.04619177058339119,
-0.03206124156713486,
0.018910015001893044,
0.001747480477206409,
0.037927452474832535,
-0.04616928845643997,
0.0439298115670681,
-0.006341105327010155,
-0.0202010627835989,
-0.020045744255185127,
0.001078871195204556,
-0.08578374236822128,
0.023101557046175003,
0.01350468210875988,
-0.05184826999902725,
-0.02083498425781727,
-0.004740802105516195,
0.043806932866573334,
-0.006722123362123966,
-0.03133165091276169,
-0.007813340984284878,
0.005531757604330778,
-0.0391450859606266,
0.039021387696266174,
-0.0362771674990654,
0.0003702233952935785,
0.017891976982355118,
0.03190825879573822,
-0.04205363616347313,
-0.0027900985442101955,
-0.007344591431319714,
-0.03206480294466019,
0.0030396301299333572,
-0.037056814879179,
-0.013117034919559956,
-0.008036327548325062,
0.02161586843430996,
-0.03147673234343529,
-0.019245199859142303,
0.05160035565495491,
-0.015393083915114403,
0.005599835887551308,
-0.05337823927402496,
-0.05217605084180832,
-0.005649616941809654,
-0.04154982417821884,
-0.001297025359235704,
-0.0012473551323637366,
0.05881136283278465,
0.010221914388239384,
0.02372204326093197,
0.012039651162922382,
0.0436878576874733,
-0.018867824226617813,
0.013660612516105175,
0.010678775608539581,
0.04734664782881737,
-0.055604059249162674,
-0.04485480114817619,
0.006397044751793146,
-0.004682866856455803,
-0.012627237476408482,
0.00008680766768520698,
0.016264120116829872,
-0.005591071210801601,
0.021965190768241882,
0.02327362261712551,
-0.02046292833983898,
-0.020234135910868645,
0.016518108546733856,
-0.042349155992269516,
0.04040100798010826,
-0.0183277390897274,
-0.04169926047325134,
-0.026606621220707893,
0.06402324885129929,
0.012051754631102085,
0.013083238154649734,
-0.021091578528285027,
0.03016861528158188,
0.03706821799278259,
-0.038561973720788956,
-0.025025129318237305,
0.07268460094928741,
-0.0009222087101079524,
0.029103409498929977,
0.012339266017079353,
0.024159284308552742,
-0.02357686683535576,
0.02911687083542347,
-0.004988392349332571,
-0.018030822277069092,
0.05223211273550987,
-0.07543405145406723,
-0.008304440416395664,
0.06365224719047546,
-0.07874082773923874,
0.0002773757150862366,
0.031819943338632584,
-0.010907018557190895,
-0.020085813477635384,
0.013557941652834415,
-0.035841651260852814,
0.06973247975111008,
-0.005060836672782898,
-0.04378441721200943,
0.014039522968232632,
0.020728416740894318,
0.022519176825881004,
0.08670035749673843,
0.032175470143556595,
-0.033367592841386795,
0.04276616871356964,
-0.005275600589811802,
-0.00842419546097517,
0.021830106154084206,
-0.010098363272845745,
0.01942019909620285,
-0.021308738738298416,
-0.023805633187294006,
0.0404122918844223,
0.0362277552485466,
-0.032038550823926926,
-0.0218642707914114,
-0.04420708119869232,
0.014059865847229958,
0.06232048571109772,
-0.028550012037158012,
0.011966833844780922,
-0.005629844032227993,
-0.08876390755176544,
0.089146189391613,
-0.0017872950993478298,
-0.026622265577316284,
-0.04426555708050728,
-0.056242864578962326,
0.0426497757434845,
0.013567344285547733,
0.05320415645837784,
-0.026843054220080376,
-0.0059263077564537525,
-0.08266552537679672,
0.005246308632194996,
-0.056200843304395676,
-0.0494564026594162,
0.0106031009927392,
0.06275628507137299,
-0.012685776688158512,
-0.019098130986094475,
-0.0543258935213089,
-0.025085223838686943,
0.00641676178202033,
0.042248811572790146,
0.02885902114212513,
-0.03631344437599182,
0.006582099944353104,
0.015992358326911926,
0.008891705423593521,
-0.009006009437143803,
-0.021184761077165604,
-0.008718564175069332,
0.029810918495059013,
0.0016996092163026333,
0.018086910247802734,
0.06798496842384338,
-0.02211029641330242,
0.0376632958650589,
-0.027650268748402596,
0.002898461651057005,
-0.005790395196527243,
0.04936865344643593,
0.020877450704574585,
0.022619137540459633,
0.010624222457408905,
-0.03344235196709633,
-0.03643239662051201,
0.03582419082522392,
0.11230849474668503,
0.06250523775815964,
0.02334326133131981,
-0.0065789301879704,
-0.04249294102191925,
0.012981492094695568,
0.02944023162126541,
-0.006784485187381506,
0.058261070400476456,
0.009231234900653362,
0.04754084721207619,
0.028270334005355835,
0.00683544110506773,
0.047082699835300446,
-0.021151356399059296,
0.027739042416214943,
-0.042383015155792236,
0.014112135395407677,
0.010769261047244072,
-0.009926465339958668,
0.06661579012870789,
-0.04057011753320694,
-0.04838840290904045,
-0.01716153882443905,
-0.0169218759983778,
-0.019854409620165825,
0.02996736206114292,
-0.030585557222366333,
-0.04215720295906067,
0.028899256139993668,
0.005044193007051945,
0.001574455527588725,
0.014752642251551151,
0.014069483615458012,
0.016649696975946426,
0.036378730088472366,
0.010614781640470028,
0.06825163960456848,
0.0015378810930997133,
0.004965599626302719,
0.0560850165784359,
0.04528706520795822,
-0.024039169773459435,
0.016552487388253212,
0.04199236258864403,
0.02372610755264759,
0.00438410509377718,
0.010780632495880127,
-0.01380788255482912,
-0.018453475087881088,
0.0752895399928093,
0.03441164270043373,
0.007819581776857376,
-0.06431443989276886,
0.018161725252866745,
0.010195287875831127,
0.042217157781124115,
-0.03558291494846344,
0.012675495818257332,
-0.030512815341353416,
-0.03521369770169258,
-0.06771709024906158,
-0.03651949390769005,
-0.001900420873425901,
-0.013018036261200905,
-0.007536467630416155,
0.0385526604950428,
0.024700414389371872,
-0.06420028209686279,
-0.009256260469555855,
0.019677333533763885,
0.002613540505990386,
-0.04356251284480095,
0.05147133022546768,
0.002394241513684392,
0.028588946908712387,
0.0014468544395640492,
-0.0421559102833271,
0.016267135739326477,
-0.014944547787308693,
-0.027410738170146942,
0.024344777688384056,
0.009281865321099758,
0.033450398594141006,
-0.05002199858427048,
-0.025941655039787292,
-0.011345728300511837,
-0.022162199020385742,
-0.08988209068775177,
0.05318831279873848,
-0.02246689237654209,
-0.03961557522416115,
0.006853477563709021,
-0.01920977793633938,
-0.002197555499151349,
0.07226645201444626,
-0.012895513325929642,
0.0035156661178916693,
0.041883911937475204,
-0.015145007520914078,
-0.007154709659516811,
-0.03263271227478981,
-0.03750880807638168,
-0.00193018966820091,
0.0012260429793968797,
0.003909197635948658,
-0.016061758622527122,
0.004397079814225435,
-0.014937273226678371,
-0.044609636068344116,
-0.0863342136144638,
0.014978308230638504,
0.04409882798790932,
0.00908905453979969,
-0.003286541672423482,
0.08434179425239563,
-0.037621330469846725,
-0.06524942070245743,
0.009992933832108974,
-0.012077007442712784,
-0.007911202497780323,
-0.026691140606999397,
0.002967296401038766,
0.04558193311095238,
-0.017550116404891014,
-0.04025983065366745,
-0.0514712855219841,
0.02848292887210846,
-0.04809785634279251,
0.0135119603946805,
-0.04312046617269516,
0.00933860894292593,
0.019367067143321037,
-0.013567578978836536,
-0.056096963584423065,
-0.009905075654387474,
0.0022951196879148483,
0.006500008516013622,
0.07556626200675964,
-0.00025315009406767786,
-0.005736444145441055,
-0.0015603280626237392,
0.006477907299995422,
-0.023592526093125343,
-0.03260023891925812,
0.05700512230396271,
0.051279883831739426,
-0.025711365044116974,
-0.003468274138867855,
0.031435612589120865,
-0.025753015652298927,
-0.06564956903457642,
-0.047175101935863495,
0.02456924319267273,
0.02303733490407467,
0.06396293640136719,
-0.02108512632548809,
-0.014915679581463337,
0.03232300654053688,
-0.005003878381103277,
-0.03492714464664459,
-0.038685157895088196,
-0.00610452750697732,
-0.006557645741850138,
-0.02130240388214588,
-0.03438049182295799,
0.032685406506061554,
-0.033713433891534805,
0.02155052311718464
] |
<p>There was some experiment that I read about some time back in which two particles (or the same particle, but split into two) were sent in opposite directions, but when something happened to one, it happened to the other at the same moment, as if they were the same particle.</p>
<p>I thought the word for this was "entrainment", but looking that up does not lead back to this experiment.</p>
<p>What is the term for this, assuming that I am not remembering something that never happened.</p> | g9233 | [
0.05208616331219673,
0.03827469050884247,
0.021851014345884323,
-0.06373826414346695,
0.07440223544836044,
0.021036386489868164,
0.006071185227483511,
0.039801765233278275,
-0.012198503129184246,
-0.021014926955103874,
-0.032287031412124634,
0.020413683727383614,
0.0002564790775068104,
-0.03144665062427521,
-0.04938393831253052,
-0.005469552706927061,
0.09949527680873871,
0.007568699773401022,
-0.027035744860768318,
0.056874360889196396,
-0.015140301547944546,
0.06307046860456467,
-0.037452902644872665,
-0.027745313942432404,
-0.03133491426706314,
-0.06897759437561035,
-0.062082137912511826,
-0.033966466784477234,
-0.03460036590695381,
-0.034535475075244904,
0.03799658268690109,
-0.043366000056266785,
0.04950399696826935,
-0.01802929677069187,
-0.025552773848176003,
-0.04575270041823387,
-0.021971987560391426,
-0.02648763358592987,
-0.0121671874076128,
0.016872353851795197,
0.07591944932937622,
-0.008717373013496399,
-0.03163545951247215,
-0.04982791468501091,
0.06909509003162384,
0.02608841098845005,
-0.017048673704266548,
-0.03542104363441467,
0.02436625212430954,
-0.024066489189863205,
-0.026890302076935768,
0.05403847619891167,
0.017538772895932198,
0.013428439386188984,
0.014711236581206322,
0.022392651066184044,
0.07338511943817139,
-0.0040465546771883965,
0.06223081424832344,
0.01485530100762844,
0.027758296579122543,
0.0068744271993637085,
0.02590089663863182,
-0.04117351025342941,
0.018926603719592094,
0.01775086671113968,
-0.05078500881791115,
0.033358972519636154,
0.02184925228357315,
-0.032077889889478683,
0.015100307762622833,
0.01262382697314024,
-0.020835811272263527,
0.02035493217408657,
0.010669845156371593,
-0.008973508141934872,
0.02191455289721489,
-0.021072179079055786,
0.005746763199567795,
0.002559392247349024,
-0.049793142825365067,
-0.01353103294968605,
-0.01563180796802044,
0.06681443750858307,
0.166781485080719,
0.021263692528009415,
-0.013699393719434738,
0.008133089169859886,
-0.06994099169969559,
-0.008680914528667927,
-0.036803096532821655,
-0.008561864495277405,
0.05155714973807335,
-0.017458565533161163,
-0.013644399121403694,
0.0035687144845724106,
0.0038181536365300417,
0.04609496891498566,
-0.023088492453098297,
0.02519640140235424,
-0.048139385879039764,
-0.005220015067607164,
0.05427617207169533,
-0.03158920258283615,
-0.005720816552639008,
0.022419853135943413,
0.026790492236614227,
-0.014461067505180836,
-0.03449821472167969,
-0.05236564949154854,
-0.03431036323308945,
0.022807100787758827,
-0.013774306513369083,
0.0008653674740344286,
0.005454935599118471,
-0.019173771142959595,
0.06057226285338402,
-0.008017503656446934,
-0.0032865137327462435,
-0.005528631154447794,
0.029831811785697937,
0.012909244745969772,
-0.03380186855792999,
0.06630001962184906,
-0.049136899411678314,
0.03720734268426895,
0.007116727530956268,
0.017352744936943054,
-0.016017168760299683,
-0.044633544981479645,
0.03282133489847183,
-0.02745729684829712,
0.03904831409454346,
0.0532839298248291,
-0.07193014025688171,
0.032023925334215164,
0.05216047167778015,
-0.014086593873798847,
0.011818932369351387,
-0.0053038038313388824,
-0.01729666069149971,
-0.043743692338466644,
-0.004692136310040951,
0.04753964766860008,
0.023637734353542328,
-0.005613704677671194,
-0.0026714603882282972,
0.004050532355904579,
-0.028574587777256966,
0.02497650869190693,
0.01412748172879219,
0.03727741912007332,
-0.00859813578426838,
0.0029209828935563564,
0.009903207421302795,
-0.045665349811315536,
-0.004746575374156237,
-0.015346686355769634,
0.012679066509008408,
0.0044302004389464855,
0.0631479024887085,
0.031859833747148514,
0.0024594608694314957,
0.0023213669192045927,
-0.043017975986003876,
0.04773630574345589,
0.024582481011748314,
-0.011712055653333664,
0.025868171826004982,
-0.04042641073465347,
-0.08551501482725143,
0.008366548456251621,
0.01912652514874935,
0.03304019942879677,
0.017573192715644836,
0.10188224911689758,
0.008799770846962929,
-0.02548602595925331,
0.001384331495501101,
0.028834402561187744,
-0.025468870997428894,
0.05887829512357712,
-0.04355136677622795,
-0.004714231472462416,
-0.058029770851135254,
-0.057447679340839386,
-0.054284896701574326,
0.01880193129181862,
-0.056397274136543274,
-0.018140651285648346,
-0.025794096291065216,
-0.05390579253435135,
-0.0014026592252776027,
-0.027127685025334358,
-0.0726672112941742,
-0.020025117322802544,
0.03998082876205444,
0.01818615198135376,
0.007446322124451399,
0.021841980516910553,
0.0022257338277995586,
0.03614610806107521,
0.02861844189465046,
0.01952669583261013,
-0.0192519910633564,
-0.046891700476408005,
-0.01856822520494461,
-0.0033543372992426157,
0.04511642083525658,
-0.005440177395939827,
0.013100100681185722,
0.007197072729468346,
0.03312324732542038,
-0.01974485069513321,
-0.0026562935672700405,
0.00833196472376585,
0.025720858946442604,
0.020871836692094803,
0.013639580458402634,
-0.02187846601009369,
-0.026873936876654625,
0.004914840683341026,
0.06453946977853775,
-0.059280138462781906,
0.005965282209217548,
-0.0018678337801247835,
0.04083817079663277,
-0.06421055644750595,
-0.030578024685382843,
0.04183812439441681,
-0.07909812033176422,
-0.014894167892634869,
-0.026217322796583176,
-0.026031415909528732,
0.06270716339349747,
0.04122601076960564,
-0.01751537062227726,
0.03201541677117348,
0.014256922528147697,
-0.025695720687508583,
-0.003999827429652214,
-0.0033496757969260216,
-0.08697929978370667,
0.004227750934660435,
-0.008693085983395576,
-0.007999151945114136,
0.027221256867051125,
-0.03582853451371193,
-0.0006056276615709066,
-0.017390839755535126,
0.01144231203943491,
0.006751215551048517,
-0.023955373093485832,
-0.03576236218214035,
0.010587728582322598,
-0.009187895804643631,
-0.008743725717067719,
-0.001834979630075395,
-0.07775601744651794,
-0.03520644083619118,
0.04540453106164932,
-0.03940679132938385,
0.048469360917806625,
-0.0327470526099205,
0.03953428566455841,
-0.0401509553194046,
0.04925714433193207,
0.05183853954076767,
0.010502705350518227,
0.003273691749200225,
-0.04414744675159454,
0.03297809511423111,
0.029204143211245537,
0.007358616683632135,
-0.023607496172189713,
-0.002548726974055171,
0.0027297239284962416,
-0.06685388088226318,
0.011598333716392517,
-0.01596091501414776,
0.01370304450392723,
0.022261904552578926,
0.003467547707259655,
0.06951930373907089,
0.013788054697215557,
-0.059699058532714844,
0.008206062018871307,
0.009978201240301132,
-0.0014432023745030165,
0.03223317861557007,
-0.05152308940887451,
-0.007531649898737669,
0.08819388598203659,
0.031228432431817055,
0.00590079789981246,
0.05030687525868416,
0.05511120706796646,
0.00032864834065549076,
-0.020976584404706955,
0.021886130794882774,
-0.038882847875356674,
-0.04312247782945633,
0.004474088549613953,
0.033702291548252106,
0.032476868480443954,
-0.04679720848798752,
-0.02584151364862919,
-0.017460288479924202,
-0.007361814379692078,
0.012576314620673656,
-0.06459799408912659,
0.002435010625049472,
0.011593498289585114,
0.04911534860730171,
-0.007101565599441528,
-0.0560544990003109,
0.006517831701785326,
0.042735129594802856,
0.028773659840226173,
-0.02735297754406929,
0.024181470274925232,
0.00004652959978557192,
0.03467020392417908,
0.050469204783439636,
0.0179684329777956,
0.01770421490073204,
-0.012181228958070278,
0.026290545240044594,
-0.0485454797744751,
-0.021184168756008148,
-0.022586382925510406,
0.01930258981883526,
0.010080186650156975,
-0.04017169028520584,
-0.004642683081328869,
-0.07475700229406357,
-0.01785091497004032,
0.017592137679457664,
0.019486187025904655,
0.045028991997241974,
0.08334098011255264,
0.016784153878688812,
0.013306326232850552,
0.008746929466724396,
0.024882514029741287,
0.05093850567936897,
0.0548953153192997,
0.028398556634783745,
0.021821508184075356,
0.06267198920249939,
0.040428973734378815,
0.04874745383858681,
-0.02848287858068943,
-0.022261610254645348,
-0.004052377305924892,
-0.050239335745573044,
0.03503410145640373,
-0.03350134566426277,
-0.0014974628575146198,
0.0182266216725111,
-0.013647833839058876,
-0.006668541580438614,
-0.03879532963037491,
0.012190470471978188,
-0.006263077724725008,
-0.07226701080799103,
-0.007075946312397718,
0.00946307834237814,
0.008751275949180126,
0.005147815681993961,
-0.012681730091571808,
0.010961229912936687,
-0.0380721241235733,
-0.01255104411393404,
-0.01619371771812439,
-0.024898188188672066,
0.05633481591939926,
0.03957418352365494,
-0.008342902176082134,
0.01645539328455925,
0.006295682396739721,
0.04255237802863121,
0.03679967299103737,
0.012492779642343521,
0.03037565015256405,
0.0031729992479085922,
0.004309181123971939,
0.026392320170998573,
-0.03668784350156784,
-0.019733259454369545,
0.056979283690452576,
0.009976046159863472,
-0.04214972257614136,
-0.042753253132104874,
0.03111061081290245,
0.006500886753201485,
-0.00532673392444849,
-0.035823944956064224,
0.05685504898428917,
-0.03782844915986061,
0.011046769097447395,
0.0028468079399317503,
-0.017739152535796165,
0.00655039818957448,
-0.0008314307196997106,
0.011767799034714699,
0.01572827622294426,
-0.01199290994554758,
-0.0450938381254673,
0.03539493680000305,
-0.026209579780697823,
0.04430778697133064,
-0.027004973962903023,
-0.01437894906848669,
0.008938992395997047,
-0.007135473657399416,
0.05144225060939789,
0.07541093230247498,
-0.013065317645668983,
0.045410942286252975,
-0.0334964394569397,
0.08011889457702637,
0.010592065751552582,
-0.039741046726703644,
0.012138769030570984,
0.013691111467778683,
-0.02063986472785473,
0.007877911441028118,
-0.03404901921749115,
-0.0197184719145298,
0.04222141578793526,
-0.022402310743927956,
-0.041905589401721954,
-0.02132168598473072,
-0.001228725304827094,
-0.0018666178220883012,
0.0013360839802771807,
0.019903291016817093,
0.018864333629608154,
0.09766452014446259,
0.06711865216493607,
0.008941836655139923,
0.0005392200546339154,
0.042854078114032745,
0.006677818950265646,
0.04816369339823723,
0.03172047436237335,
-0.04606778919696808,
0.022437116131186485,
-0.01695062592625618,
-0.022314900532364845,
0.05806939676403999,
-0.018235700204968452,
-0.026184244081377983,
0.004905685782432556,
-0.0013500043423846364,
-0.026305390521883965,
0.023210646584630013,
-0.042247287929058075,
0.027263425290584564,
-0.09681660681962967,
0.007092803250998259,
0.016603684052824974,
-0.007519094739109278,
-0.008842834271490574,
-0.01657351292669773,
-0.027746150270104408,
-0.05242756009101868,
-0.0676731988787651,
0.0007516623591072857,
-0.029284171760082245,
-0.004233367275446653,
-0.02381736785173416,
0.04079199954867363,
0.06317244470119476,
-0.001694209291599691,
0.010387462563812733,
-0.014235722832381725,
-0.011376083828508854,
-0.02858686074614525,
-0.02083691582083702,
-0.03641088306903839,
0.034752726554870605,
-0.04491500183939934,
0.018887843936681747,
0.05340476706624031,
-0.009525541216135025,
0.049175623804330826,
0.060164276510477066,
-0.04241089150309563,
-0.0006796853267587721,
-0.07233686000108719,
-0.026233719661831856,
-0.05759113281965256,
0.02822152152657509,
-0.05492100864648819,
-0.05900662764906883,
0.01719033718109131,
-0.002118336269631982,
-0.0016175978817045689,
-0.03179574012756348,
0.017435774207115173,
0.0015066936612129211,
0.006488011684268713,
0.04552040994167328,
0.01536712795495987,
-0.02325315959751606,
-0.003965364769101143,
-0.03872544318437576,
0.002586342627182603,
0.02121678553521633,
0.023531747981905937,
-0.02476600557565689,
0.042074207216501236,
-0.029049335047602654,
0.08634558320045471,
-0.010609759949147701,
-0.02523212693631649,
0.03489873558282852,
-0.032552823424339294,
-0.00662265857681632,
0.00463766697794199,
-0.037026144564151764,
0.073175810277462,
-0.04781275987625122,
-0.027220476418733597,
-0.04949108883738518,
0.05956270545721054,
-0.0005083167925477028,
0.03756694868206978,
0.032614413648843765,
-0.007082460448145866,
0.07159832864999771,
-0.03499032184481621,
-0.03330281004309654,
-0.0786103829741478,
-0.011995277367532253,
0.02880711294710636,
0.000044521693780552596,
-0.017557336017489433,
-0.04506904259324074,
-0.003658553119748831,
0.060362543910741806,
0.031571511179208755,
-0.05646130442619324,
0.06024770438671112,
-0.05179139971733093,
0.004916083067655563,
0.03278376907110214,
-0.013820243068039417,
0.04197888448834419,
-0.023455314338207245,
0.04081901162862778,
0.008851994760334492,
0.04078423231840134,
-0.001964754890650511,
-0.025494063273072243,
-0.03150664642453194,
-0.05634065344929695,
-0.038533687591552734,
-0.018550800159573555,
-0.015246951952576637,
0.04554526507854462,
-0.031213296577334404,
-0.0298923272639513,
-0.024489842355251312,
-0.013350514695048332,
0.002653684001415968,
0.02841038815677166,
0.026495376601815224,
0.022328274324536324,
-0.025199929252266884,
-0.0035299237351864576,
0.0005528309848159552,
0.03097023256123066,
0.023464879021048546,
-0.0013158851070329547,
-0.0070924293249845505,
-0.04384322091937065,
-0.011997339315712452,
-0.00507567310705781,
0.023461390286684036,
0.005284337792545557,
-0.024918876588344574,
-0.10540073364973068,
0.04143600910902023,
-0.07124406099319458,
0.04539080709218979,
0.05878962203860283,
0.01054370030760765,
-0.0322214812040329,
-0.03203877434134483,
-0.11338654160499573,
-0.056292954832315445,
-0.06168001517653465,
0.04321206361055374,
-0.02135271020233631,
0.04069658741354942,
0.0004615818033926189,
0.03425465524196625,
-0.06326304376125336,
-0.048113591969013214,
0.013597346842288971,
0.00011039318633265793,
-0.001007102313451469,
0.10847914218902588,
0.029753584414720535,
0.00027288158889859915,
0.018008936196565628,
0.012105535715818405,
-0.03889520838856697,
-0.04280756041407585,
-0.009435378946363926,
0.0006713540642522275,
-0.022179817780852318,
-0.022646427154541016,
-0.08044011145830154,
-0.030763564631342888,
-0.010199565440416336,
-0.0031249101739376783,
0.0048749856650829315,
-0.0012140596518293023,
0.00009055444388650358,
-0.03396134823560715,
0.010570892132818699,
0.04216417670249939,
-0.02903963252902031,
-0.003054535249248147,
0.03778964653611183,
0.021326908841729164,
-0.029715614393353462,
-0.0721232146024704,
-0.05176937207579613,
0.011392276734113693,
-0.006155646871775389,
-0.027303289622068405,
0.01577800326049328,
0.050112705677747726,
0.00924639031291008,
0.030062496662139893,
0.010051104240119457,
0.02978571318089962,
0.009223063476383686,
-0.01454963255673647,
-0.040552835911512375,
0.037167057394981384,
0.04685455560684204,
0.006236595567315817,
-0.014423169195652008,
-0.0663723424077034,
-0.046769991517066956,
0.006321300286799669,
-0.04335328936576843,
0.052925463765859604,
-0.01952952705323696,
0.005948422942310572,
0.07107052206993103,
0.03160356730222702,
0.014236231334507465,
-0.05832668021321297,
-0.06419289112091064,
-0.05936218053102493,
-0.02657022885978222,
0.04976479709148407,
-0.03712670877575874,
0.007505354005843401,
-0.03098336048424244,
-0.026494577527046204,
-0.014712780714035034,
-0.03715074434876442,
0.007424784824252129,
0.00712100462988019,
-0.0401911698281765,
-0.01711129955947399,
-0.05118339881300926,
-0.00621818145737052,
0.05089600011706352,
0.07976678758859634,
-0.027415502816438675,
-0.04767046496272087,
-0.027606751769781113,
-0.02585914172232151,
0.027716664597392082,
-0.00728721683844924,
-0.009929551742970943,
0.06020217388868332,
-0.05609734356403351,
0.03289351239800453,
-0.024396652355790138,
-0.025742653757333755,
-0.010946176014840603,
0.06028426066040993,
0.031919628381729126,
-0.025081386789679527,
-0.06098425015807152,
-0.009054677560925484,
0.08332978934049606,
0.060193032026290894,
-0.017262831330299377,
-0.036570265889167786,
0.013755659572780132,
0.02674628235399723,
0.0003911017847713083,
0.028282545506954193,
-0.03139946237206459,
-0.026826314628124237,
-0.00127940415404737,
0.0044646901078522205,
-0.011136270128190517,
-0.009444699622690678,
-0.06048839911818504,
0.03292786702513695,
0.04641485586762428,
0.07961217314004898,
-0.04754694178700447,
-0.022080179303884506,
-0.018165023997426033,
0.020116183906793594,
0.04050945118069649,
0.03734781593084335,
0.0083355363458395,
0.04430587217211723,
-0.00005636363130179234,
-0.036082711070775986,
-0.01670984923839569,
-0.0016486509703099728,
-0.0236662644892931,
0.03555631265044212,
0.055669162422418594,
0.0011918091913685203,
0.05899639055132866,
-0.030253209173679352,
-0.016641831025481224,
0.05225230008363724,
0.040621317923069,
-0.02291199006140232,
0.0029849472921341658,
0.049693554639816284,
0.005133552476763725,
-0.018976107239723206,
0.009514587000012398,
0.02644546516239643,
-0.05344204232096672,
-0.026779070496559143,
0.0011795080499723554,
-0.012847160920500755,
-0.02432429790496826,
0.024925515055656433,
-0.003339678281918168,
-0.07224802672863007,
-0.04059281945228577,
0.018030710518360138,
-0.011929168365895748,
0.07039099186658859,
0.08222929388284683,
-0.009987167082726955,
-0.014342660084366798,
0.01850471831858158,
-0.007579519879072905,
-0.06209011748433113,
-0.05703781545162201,
-0.02645811252295971,
0.015924790874123573,
-0.01766122691333294,
0.0010217834496870637,
0.0260453000664711,
0.015826385468244553,
0.007443106267601252
] |
<p>If I have a laser light incident on the double slit at an angle O < 90 what kind of interference pattern will I see? Will i see the same with less intensity or different pattern? </p> | g9234 | [
0.006932505406439304,
-0.010648717172443867,
0.01403507124632597,
-0.007924951612949371,
-0.033534612506628036,
0.03413200005888939,
0.03922386094927788,
0.024942319840192795,
0.010655420832335949,
-0.05475274473428726,
0.019975310191512108,
0.04988425597548485,
0.01463089045137167,
-0.00992084015160799,
-0.035329993814229965,
-0.014751161448657513,
0.029515862464904785,
-0.008328014053404331,
0.008321356028318405,
0.02856246754527092,
-0.02805289626121521,
0.018086079508066177,
-0.05770043283700943,
-0.05309789627790451,
0.0040230657905340195,
0.012795009650290012,
0.02417917363345623,
-0.0252868440002203,
-0.046314630657434464,
-0.01130866352468729,
0.008060201071202755,
-0.058819450438022614,
-0.006878389976918697,
-0.011129982769489288,
-0.06515958905220032,
-0.0016420630272477865,
0.050698213279247284,
0.017274964600801468,
0.01975991204380989,
0.015359455719590187,
-0.031755127012729645,
-0.030280040577054024,
-0.009611387737095356,
-0.043521732091903687,
-0.030870694667100906,
-0.0448310449719429,
0.015876106917858124,
0.022353561595082283,
0.014321244321763515,
0.004562012385576963,
-0.005269235465675592,
0.032633405178785324,
-0.026362739503383636,
-0.004778834991157055,
0.03731423616409302,
0.06890793889760971,
-0.05063147842884064,
0.012741055339574814,
0.058423805981874466,
0.006300547160208225,
-0.031736139208078384,
-0.0270161721855402,
-0.037254855036735535,
0.006266580894589424,
-0.0062680658884346485,
-0.010721856728196144,
-0.024029899388551712,
0.01691017486155033,
0.00563221937045455,
-0.018587762489914894,
-0.00010211861808784306,
-0.007023324724286795,
-0.03163375332951546,
-0.018975626677274704,
-0.031074469909071922,
0.0368732325732708,
0.0451861135661602,
0.03232424333691597,
-0.03796817734837532,
0.010623986832797527,
-0.03589913249015808,
-0.07257051765918732,
-0.037345584481954575,
-0.024638809263706207,
-0.013269264250993729,
0.010578209534287453,
-0.01897052489221096,
-0.023180868476629257,
0.03098289668560028,
0.013619138859212399,
0.0793987512588501,
0.007067494094371796,
0.054909612983465195,
0.01569245383143425,
0.008190812543034554,
0.049616385251283646,
-0.01142868772149086,
0.0032172526698559523,
0.014846216887235641,
0.030198529362678528,
0.009978962130844593,
-0.03559325262904167,
0.018760209903120995,
0.04392428323626518,
-0.014067373238503933,
-0.02544890157878399,
0.002490964252501726,
-0.030006613582372665,
-0.00020951256738044322,
0.027769679203629494,
-0.01715228520333767,
-0.025579316541552544,
-0.059471096843481064,
-0.014994491823017597,
0.00021532367100007832,
-0.02727551944553852,
0.064400315284729,
-0.01860065944492817,
0.04415171220898628,
0.03141377493739128,
0.09798089414834976,
-0.03230010345578194,
-0.021942077204585075,
0.044377997517585754,
0.02443121001124382,
0.05265934020280838,
0.009026787243783474,
0.02773934043943882,
0.02432239055633545,
-0.029092025011777878,
-0.02448248118162155,
0.038272012025117874,
-0.024445723742246628,
0.033563096076250076,
0.011313354596495628,
-0.031019942834973335,
0.013889167457818985,
-0.03764729201793671,
0.04547634720802307,
-0.048844221979379654,
0.027139892801642418,
0.0001385786454193294,
0.016104869544506073,
-0.01738293655216694,
-0.01411493495106697,
-0.05170496180653572,
-0.00267475051805377,
0.019895896315574646,
0.019656207412481308,
0.008555675856769085,
-0.012089964002370834,
0.033714357763528824,
0.007341589778661728,
-0.04243316501379013,
-0.03451959043741226,
-0.009989969432353973,
-0.0157645121216774,
-0.0066551812924444675,
0.004405274987220764,
0.03151315450668335,
0.02502080239355564,
-0.011914897710084915,
-0.0006061026942916214,
0.022260433062911034,
-0.01937226951122284,
0.02557418867945671,
0.06523797661066055,
-0.012717065401375294,
0.042567815631628036,
0.0014407975832000375,
-0.019674694165587425,
0.030328786000609398,
-0.0032401711214333773,
-0.04329697787761688,
0.0724690780043602,
0.07760204374790192,
0.015324086882174015,
0.006737600080668926,
0.05513233318924904,
0.035075604915618896,
-0.06582935899496078,
-0.001976963132619858,
-0.044690486043691635,
-0.10389918833971024,
-0.019742997363209724,
-0.031327273696660995,
0.03798607736825943,
-0.06555767357349396,
-0.04962018132209778,
0.01741301640868187,
0.028252344578504562,
-0.06840066611766815,
-0.04330849274992943,
0.027914926409721375,
-0.01940581575036049,
0.023201335221529007,
0.04317036271095276,
0.008983328938484192,
-0.06843738257884979,
0.010298376902937889,
0.00870069395750761,
0.043672606348991394,
0.013238420709967613,
0.03602563962340355,
-0.018688058480620384,
0.07496227324008942,
-0.0012388508766889572,
0.009274895302951336,
-0.03190309554338455,
-0.04037151113152504,
-0.023731499910354614,
0.044165726751089096,
0.02989480271935463,
0.051478177309036255,
0.007714863400906324,
0.04602789506316185,
0.01763106696307659,
0.010149254463613033,
-0.006031082011759281,
0.003227300476282835,
0.02563583105802536,
0.05232173204421997,
0.0017701508477330208,
-0.04183917120099068,
0.016832074150443077,
0.02121877856552601,
-0.06625957787036896,
-0.028195276856422424,
-0.03209775686264038,
0.050850801169872284,
-0.012026968412101269,
-0.04907245561480522,
0.02313297428190708,
-0.08729387074708939,
0.022632453590631485,
-0.013502677902579308,
-0.008214340545237064,
0.05989522114396095,
0.028200972825288773,
-0.0715227797627449,
0.020309217274188995,
0.011073407717049122,
-0.07009849697351456,
0.023923691362142563,
0.02510000951588154,
-0.01536644622683525,
-0.006104522850364447,
0.024906828999519348,
-0.05768598988652229,
-0.014065262861549854,
0.0020647956989705563,
0.06928298622369766,
-0.05442766472697258,
0.0003813373332377523,
-0.03263312578201294,
-0.01606643572449684,
0.012360084801912308,
-0.02452768199145794,
-0.06585933268070221,
0.010105847381055355,
-0.01247969176620245,
-0.02319825440645218,
0.019408833235502243,
-0.03866114467382431,
-0.030268525704741478,
-0.04241840913891792,
0.05956350266933441,
0.032214026898145676,
-0.0025075599551200867,
0.003254002658650279,
0.021082475781440735,
0.06600035727024078,
0.03484034165740013,
-0.02432587370276451,
0.06115370988845825,
0.04524993896484375,
-0.026354918256402016,
-0.0816398411989212,
0.018705768510699272,
-0.040925897657871246,
0.0059514353051781654,
0.0227534007281065,
-0.0016659782268106937,
0.02545430138707161,
0.02987922914326191,
-0.05947791785001755,
0.07630176842212677,
0.060339685529470444,
0.012203527614474297,
0.043681081384420395,
-0.03835994005203247,
0.009737872518599033,
-0.024067215621471405,
-0.010110857896506786,
-0.023489031940698624,
-0.045821644365787506,
0.005427268333733082,
0.018683532252907753,
0.012127285823225975,
-0.020171701908111572,
-0.03542269021272659,
-0.008330876007676125,
-0.046622004359960556,
-0.07436275482177734,
0.0488760769367218,
-0.038026582449674606,
-0.01386713981628418,
-0.021373135969042778,
0.02173912525177002,
0.03348877280950546,
-0.029607506468892097,
-0.005304529331624508,
0.051374487578868866,
0.0073903510347008705,
-0.0028036031872034073,
0.026642052456736565,
0.0019329895731061697,
-0.014615674503147602,
-0.005154512822628021,
0.08730700612068176,
0.00863597821444273,
0.04012371599674225,
0.019897500053048134,
0.009988168254494667,
-0.057917118072509766,
-0.034137625247240067,
0.0745365098118782,
-0.0007684787851758301,
0.0309448204934597,
0.051459286361932755,
0.016156423836946487,
-0.012999825179576874,
-0.08653365820646286,
0.015017395839095116,
0.046344541013240814,
0.0005766558460891247,
-0.022510187700390816,
-0.0015977915609255433,
-0.008110611699521542,
0.042468439787626266,
0.0671229138970375,
0.028387434780597687,
-0.02009063959121704,
-0.0760473757982254,
0.00019312223594170064,
-0.018222874030470848,
0.015334578230977058,
-0.00601721229031682,
-0.04103963077068329,
0.018085701391100883,
0.053748711943626404,
-0.021558614447712898,
-0.012594309635460377,
-0.064643993973732,
-0.043905869126319885,
-0.023465504869818687,
-0.004210494924336672,
0.06793791800737381,
0.026314038783311844,
-0.08403052389621735,
-0.01646484062075615,
-0.04542771726846695,
0.00007744089816696942,
-0.03818965703248978,
-0.051181551069021225,
-0.010642201639711857,
-0.02293197065591812,
-0.015188870951533318,
-0.00017384167585987598,
0.02738172374665737,
-0.06758895516395569,
-0.019347434863448143,
0.006417714059352875,
-0.030709130689501762,
-0.05713991820812225,
0.03584953397512436,
0.056394170969724655,
0.026121292263269424,
-0.03305613249540329,
0.053259916603565216,
-0.03833910822868347,
0.049137260764837265,
-0.031666435301303864,
0.004646512679755688,
-0.006317799910902977,
-0.003137021092697978,
0.0445425808429718,
-0.026261771097779274,
0.0617576539516449,
-0.053599003702402115,
0.035298291593790054,
-0.012377406470477581,
-0.054479748010635376,
0.029116813093423843,
0.023954296484589577,
-0.041981250047683716,
0.07242962718009949,
0.006879827938973904,
-0.030427489429712296,
-0.028776654973626137,
0.06954913586378098,
-0.03260055556893349,
0.004259371664375067,
-0.005622440949082375,
-0.05816429853439331,
-0.007281559985131025,
-0.007605824153870344,
0.015009207651019096,
-0.009320949204266071,
0.06496798992156982,
-0.005361241288483143,
-0.03213448449969292,
-0.013783431611955166,
-0.04355303570628166,
0.011140795424580574,
0.032603804022073746,
0.0484062135219574,
0.02809206396341324,
0.020400986075401306,
0.021793777123093605,
-0.008571889251470566,
0.046448227018117905,
0.026100274175405502,
0.021095488220453262,
0.005003196187317371,
-0.002690458670258522,
0.003912701271474361,
-0.043979380279779434,
-0.017286453396081924,
-0.07073312997817993,
0.013401951640844345,
-0.003609551815316081,
-0.07138381898403168,
-0.01010920014232397,
-0.046551045030355453,
0.030136190354824066,
0.0020909730810672045,
0.01637122593820095,
0.051446326076984406,
0.058933112770318985,
0.023008275777101517,
-0.028622688725590706,
-0.004725546110421419,
-0.00593801261857152,
0.022129597142338753,
0.03963464871048927,
0.030940532684326172,
-0.01114695705473423,
0.044796422123909,
-0.034453295171260834,
-0.06857708096504211,
-0.020016876980662346,
-0.00518566370010376,
-0.0324387364089489,
-0.04039464890956879,
-0.002208948601037264,
-0.0653218924999237,
0.045306332409381866,
0.034057486802339554,
0.0157318152487278,
-0.012489847838878632,
0.04761653393507004,
-0.001941422000527382,
-0.027645058929920197,
0.06387753784656525,
-0.03294183686375618,
-0.06557101011276245,
-0.04075570032000542,
-0.09761285781860352,
-0.060208145529031754,
0.015473180450499058,
0.0005259398021735251,
0.005312581080943346,
0.02696468122303486,
0.03738144040107727,
0.028791334480047226,
-0.07826203852891922,
0.01529679261147976,
0.005625789053738117,
-0.022708198055624962,
-0.057098403573036194,
-0.07050256431102753,
0.07050023972988129,
-0.0028343864250928164,
-0.023830529302358627,
-0.044975005090236664,
0.026591802015900612,
0.058232445269823074,
0.047285839915275574,
-0.024127895012497902,
-0.005619134288281202,
-0.024528300389647484,
-0.011631417088210583,
0.009701109491288662,
-0.030157841742038727,
0.02581610158085823,
0.04087322577834129,
-0.00037081909249536693,
0.03917856886982918,
0.05343282222747803,
-0.0020017430651932955,
0.01519760675728321,
-0.008201371878385544,
-0.019211040809750557,
-0.04410833492875099,
0.034059517085552216,
0.005799117032438517,
-0.0469665564596653,
0.0310671366751194,
0.04890860989689827,
-0.04007086157798767,
0.012090988457202911,
-0.01280110701918602,
-0.01838456466794014,
0.027702976018190384,
-0.0775771290063858,
0.0077403029426932335,
0.032549262046813965,
-0.022307079285383224,
-0.03281134366989136,
-0.0005656789289787412,
-0.039392437785863876,
0.017827993258833885,
-0.0010018444154411554,
0.0697324201464653,
-0.023832354694604874,
0.011641803197562695,
-0.01021064817905426,
-0.030965812504291534,
-0.008390780538320541,
0.007292168214917183,
0.04166516289114952,
-0.011433480307459831,
0.011722455732524395,
0.039970479905605316,
-0.036297544836997986,
0.04413169249892235,
0.00813070684671402,
-0.03554357588291168,
-0.029184410348534584,
-0.030995678156614304,
0.020234908908605576,
0.02417444996535778,
0.016119075939059258,
0.028824416920542717,
-0.028205502778291702,
-0.018177080899477005,
0.0041594733484089375,
-0.012164803221821785,
0.008550891652703285,
0.03504014387726784,
0.00944254919886589,
0.007729077711701393,
-0.010653766803443432,
-0.04373466223478317,
-0.01758468523621559,
-0.0013894347939640284,
0.01788431964814663,
0.05487682670354843,
-0.020101452246308327,
0.06334433704614639,
0.029325958341360092,
-0.029975460842251778,
0.0014601146103814244,
0.01815183460712433,
0.01288328692317009,
-0.028791863471269608,
-0.04839352145791054,
0.03746950998902321,
0.008731065317988396,
-0.04252735897898674,
0.021856587380170822,
-0.031388428062200546,
0.00446321489289403,
0.03798914700746536,
0.040678445249795914,
-0.033963609486818314,
-0.04510585963726044,
-0.023607049137353897,
0.004337453283369541,
0.0042722527869045734,
0.058971334248781204,
0.015135901980102062,
0.02729511633515358,
0.0324990376830101,
-0.012388309463858604,
-0.0392383374273777,
0.010356581769883633,
0.00905636791139841,
-0.020568441599607468,
-0.06980983912944794,
-0.020538894459605217,
0.058420050889253616,
0.03677874803543091,
0.008790233172476292,
0.0004247007891535759,
-0.03442814573645592,
0.04637598618865013,
0.04043139889836311,
0.04233941435813904,
0.018125982955098152,
-0.025535976514220238,
0.02292836271226406,
0.028354089707136154,
-0.006998816970735788,
0.01088427659124136,
0.01921677030622959,
-0.012464387342333794,
-0.04459376260638237,
0.03663948178291321,
0.058180563151836395,
0.0016289529157802463,
-0.0008186320192180574,
0.021542251110076904,
-0.06260818243026733,
-0.016680950298905373,
-0.05612894147634506,
-0.04564463719725609,
-0.019835958257317543,
-0.010961392894387245,
0.05550945922732353,
-0.08315683156251907,
-0.045817866921424866,
-0.016869377344846725,
-0.044972073286771774,
0.05010373145341873,
0.01870896853506565,
-0.0006215377943590283,
0.022794047370553017,
0.0025373748503625393,
-0.00260584382340312,
-0.037109363824129105,
0.036620546132326126,
0.005205012392252684,
0.005564105696976185,
0.0250141192227602,
-0.048530787229537964,
0.03989248350262642,
0.04201753810048103,
0.0640759989619255,
0.08952464163303375,
0.10248978435993195,
0.05231719836592674,
-0.05539051815867424,
-0.0015602600760757923,
0.049032215029001236,
-0.025257036089897156,
0.017402786761522293,
0.009167465381324291,
-0.016547776758670807,
-0.03375933691859245,
0.003713814541697502,
0.007486088667064905,
-0.011124899610877037,
0.014459659345448017,
0.05993938446044922,
0.009664575569331646,
0.04909275099635124,
0.001716159749776125,
-0.06195072457194328,
-0.062098413705825806,
0.021652942523360252,
-0.10756916552782059,
-0.045362938195466995,
0.05279705673456192,
0.03664248436689377,
0.06584692746400833,
-0.015802396461367607,
-0.07520250976085663,
0.00820866134017706,
-0.03353622928261757,
-0.10262475907802582,
-0.0095272371545434,
0.04841391742229462,
0.006231097970157862,
-0.04679425433278084,
-0.06022239103913307,
0.00444089574739337,
-0.006086597219109535,
0.0019098788034170866,
0.019049368798732758,
0.06553855538368225,
0.0254970695823431,
0.03133268654346466,
-0.04781261831521988,
0.009542157873511314,
-0.007494552526623011,
-0.03604249283671379,
0.014403214678168297,
-0.04092428460717201,
-0.01166797336190939,
0.011144325137138367,
-0.034971319139003754,
-0.06613324582576752,
-0.02937515266239643,
0.014774245209991932,
0.011475208215415478,
0.055506374686956406,
-0.017862606793642044,
0.01898455247282982,
0.002128311898559332,
0.08134373277425766,
-0.03982195258140564,
-0.0017703869380056858,
0.04490361735224724,
0.004392523318529129,
0.031462281942367554,
0.012752383016049862,
0.04306836798787117,
0.030811212956905365,
0.03714940324425697,
0.03150897100567818,
0.013509019277989864,
0.05635150149464607,
-0.0074347443878650665,
0.004725257400423288,
-0.04816380515694618,
0.008505367673933506,
-0.03364862874150276,
0.034823402762413025,
-0.04866866022348404,
-0.006057629361748695,
-0.007970425300300121,
0.03204888105392456,
0.0018934751860797405,
-0.004426466766744852,
0.03809801861643791,
0.04815567284822464,
0.0137953395023942,
0.03589693456888199,
-0.000953410635702312,
-0.03768598288297653,
-0.0712728276848793,
0.006300793029367924,
-0.07675247639417648,
-0.005292029585689306,
0.02580486610531807,
-0.008946318179368973,
0.03094935603439808,
0.019534718245267868,
0.060783255845308304,
-0.022603057324886322,
-0.03978574648499489,
-0.033842071890830994,
-0.006615560036152601,
0.0035843460354954004,
0.024880584329366684,
-0.04056317359209061,
0.027767155319452286,
0.006448227912187576,
0.02383023500442505,
0.005354507360607386,
-0.02812708541750908,
0.017385439947247505,
0.062386322766542435,
-0.019537853077054024,
-0.09567093849182129,
-0.03995903953909874,
-0.01426500640809536,
-0.06102998927235603,
0.06387989968061447,
-0.019292978569865227,
-0.0178263820707798,
-0.02838698960840702,
-0.03133183345198631,
0.010633190162479877,
0.015813099220395088,
-0.044680796563625336
] |
<p>Temperature is a measure of kinetic energy transferred to particles, henceforth, <a href="http://en.wikipedia.org/wiki/Outer_space#Environment" rel="nofollow">space</a> being vacuum, temperature cannot be measured.
But then, there is cosmic background radiation. It is the leftover heat from the Big Bang, but then heat in space doesn't make sense, how does this radiation, heat up space time when it technically cannot be heated up?
Moreover why is it referred to as heat when it is approximately just $2.5$ Kelvin, which is just above absolute zero?</p> | g9235 | [
0.06917769461870193,
0.004699124023318291,
-0.009239152073860168,
-0.013294563628733158,
-0.013340122066438198,
0.08289562165737152,
-0.008512793108820915,
0.077793650329113,
-0.048895999789237976,
-0.02941463142633438,
0.025501582771539688,
0.06179780513048172,
0.023839477449655533,
0.014816537499427795,
0.0012500104494392872,
-0.03583366051316261,
0.02943192422389984,
-0.0375463142991066,
0.07120519131422043,
0.028103454038500786,
0.016615722328424454,
-0.01613444648683071,
0.0008715092553757131,
-0.04250185936689377,
-0.03051762655377388,
-0.065894715487957,
0.019740425050258636,
0.0036781078670173883,
-0.023504605516791344,
-0.03850335255265236,
0.03501545637845993,
0.0604863278567791,
0.031078198924660683,
-0.015071597881615162,
0.008520000614225864,
-0.03481420874595642,
-0.0011138052213937044,
0.02373354882001877,
0.010109025053679943,
-0.04195275902748108,
-0.037054963409900665,
0.015478713437914848,
0.01750670000910759,
0.014745895750820637,
-0.011547302827239037,
0.08870839327573776,
-0.038911812007427216,
0.04775601625442505,
0.018762841820716858,
-0.0021241081412881613,
-0.02470238320529461,
-0.005228555761277676,
0.03323078155517578,
0.010315584018826485,
0.01973578706383705,
-0.05009275674819946,
-0.0048850467428565025,
-0.010384646244347095,
0.09679321199655533,
0.0458749383687973,
0.05505997687578201,
0.007749424781650305,
0.017048891633749008,
0.010386338457465172,
0.04442600533366203,
0.03744425252079964,
-0.018308406695723534,
0.018492689356207848,
-0.03195688873529434,
0.0004378647427074611,
0.03817315772175789,
-0.030119381844997406,
-0.0796903744339943,
-0.00034529875847510993,
-0.04283586144447327,
0.026448775082826614,
0.021609732881188393,
-0.020338378846645355,
0.0557849258184433,
0.013317110016942024,
-0.05869663134217262,
0.012211423367261887,
-0.032818254083395004,
-0.006988927721977234,
0.06339100003242493,
0.0018970746314153075,
-0.04338192194700241,
-0.02775522693991661,
-0.0026306065265089273,
0.025257345288991928,
0.011158178560435772,
0.03930984437465668,
0.09535083919763565,
0.012272869236767292,
0.023854542523622513,
-0.0029605221934616566,
-0.02853645384311676,
0.021548258140683174,
-0.033653613179922104,
-0.0214517954736948,
-0.010607060045003891,
-0.0104024363681674,
0.01205401960760355,
-0.016568662598729134,
0.04345141351222992,
-0.0000017537907979203737,
-0.03627835959196091,
0.00186818593647331,
-0.013568862341344357,
0.01938105747103691,
0.008795049041509628,
-0.016331568360328674,
-0.025088325142860413,
-0.051292888820171356,
-0.03472096472978592,
0.0002590083749964833,
0.04161529242992401,
-0.01710096374154091,
0.026042312383651733,
0.01734269969165325,
0.021032648161053658,
0.07642566412687302,
-0.04483906552195549,
0.015623885206878185,
-0.03498617559671402,
0.011144530028104782,
0.026832081377506256,
-0.05503231659531593,
-0.020575590431690216,
-0.01631481572985649,
-0.03298427537083626,
0.04110094904899597,
-0.05168735608458519,
0.005535372532904148,
0.020889589563012123,
-0.020524991676211357,
0.00876984279602766,
-0.008216719143092632,
-0.014839783310890198,
0.035330526530742645,
-0.026850122958421707,
-0.007228296250104904,
0.03323618695139885,
-0.013896822929382324,
-0.02820482663810253,
0.03668375313282013,
-0.01812567003071308,
0.042680878192186356,
0.05427232384681702,
0.011858087033033371,
0.021047962829470634,
0.10077233612537384,
0.031344130635261536,
-0.031760603189468384,
-0.00618349714204669,
-0.01532159186899662,
0.05984113737940788,
0.008270756341516972,
0.03294037654995918,
0.011627281084656715,
0.05279576778411865,
0.03788550943136215,
0.012562417425215244,
-0.0162501260638237,
-0.019630365073680878,
0.006095211021602154,
-0.07252457737922668,
-0.054100874811410904,
0.0024481057189404964,
-0.021858857944607735,
-0.06829022616147995,
-0.01423943042755127,
-0.009623573161661625,
-0.02377685345709324,
-0.01316269114613533,
0.05585094541311264,
0.04339861124753952,
0.09180960804224014,
-0.0027995251584798098,
-0.05097474902868271,
-0.013444130308926105,
-0.009957626461982727,
0.07206397503614426,
-0.0035047680139541626,
-0.027843069285154343,
0.006468276027590036,
-0.04840017855167389,
-0.053504928946495056,
0.017717400565743446,
0.0023207119666039944,
0.036142122000455856,
-0.06029901280999184,
0.02220490388572216,
0.020495470613241196,
0.051993537694215775,
-0.005562980193644762,
-0.0430806502699852,
-0.0029984652064740658,
-0.029381057247519493,
0.029272347688674927,
0.018893836066126823,
0.02662408910691738,
0.01309193391352892,
-0.03746723011136055,
0.0935962051153183,
0.023888399824500084,
-0.03546057268977165,
-0.049152523279190063,
-0.02607501484453678,
-0.01634778082370758,
0.017362510785460472,
-0.031688142567873,
0.0423654206097126,
-0.012654032558202744,
0.004804349038749933,
0.052874963730573654,
-0.04037574306130409,
-0.00948846060782671,
-0.023852281272411346,
-0.0014558987459167838,
-0.07167485356330872,
0.007525901775807142,
0.019770413637161255,
-0.01021294854581356,
-0.0021088209468871355,
-0.018840787932276726,
-0.09246106445789337,
-0.016194097697734833,
0.027113014832139015,
0.040476083755493164,
-0.06709460914134979,
0.01223061140626669,
-0.021890971809625626,
0.0004565380804706365,
0.057949598878622055,
-0.00453944830223918,
0.023036543279886246,
0.02534792758524418,
-0.017356084659695625,
0.05700013414025307,
-0.03523530066013336,
-0.009163121692836285,
-0.033486150205135345,
0.01550511084496975,
0.05408865958452225,
-0.04955179616808891,
0.008437029086053371,
-0.028350727632641792,
-0.022572951391339302,
-0.0570647232234478,
-0.021319227293133736,
-0.013122588396072388,
0.001977275125682354,
-0.04398898035287857,
0.005396441090852022,
-0.008452502079308033,
-0.052292048931121826,
0.05473892018198967,
-0.08767268806695938,
-0.05410999804735184,
0.0525498129427433,
-0.023870471864938736,
-0.0024123918265104294,
0.014252382330596447,
0.00048085529124364257,
-0.03315933421254158,
-0.044713616371154785,
0.07947441935539246,
-0.012219158932566643,
-0.011356419883668423,
-0.008404351770877838,
0.05301666632294655,
-0.00039589309017173946,
0.01733294129371643,
-0.01002089399844408,
0.03559761121869087,
0.0377633236348629,
-0.013355729170143604,
0.1040254756808281,
-0.05136279761791229,
0.04511146992444992,
0.02855338528752327,
-0.02883276902139187,
-0.017822081223130226,
-0.034959252923727036,
-0.06605075299739838,
-0.05644138902425766,
0.01370022352784872,
0.06642453372478485,
-0.07826551049947739,
0.023672915995121002,
-0.011324846185743809,
-0.006793731823563576,
0.01943019963800907,
0.008249756880104542,
-0.005213365890085697,
0.05368421971797943,
0.01800459250807762,
-0.019311636686325073,
-0.009027059189975262,
0.055606793612241745,
-0.04311944171786308,
0.008039827458560467,
-0.03364216908812523,
-0.013622471131384373,
0.0053343805484473705,
-0.04446683079004288,
-0.06570043414831161,
-0.07700866460800171,
0.012608562596142292,
0.06740851700305939,
0.005531421862542629,
-0.023688310757279396,
0.048023488372564316,
0.007050828076899052,
0.013341274112462997,
-0.05437212809920311,
-0.018814748153090477,
0.05412716418504715,
-0.0031873637344688177,
-0.004363498650491238,
0.02203521318733692,
-0.001853524474427104,
-0.02325892262160778,
-0.005299062933772802,
0.00013461799244396389,
-0.027150852605700493,
-0.057986024767160416,
-0.016855305060744286,
-0.012942712754011154,
-0.0039679910987615585,
-0.004474562592804432,
0.0015158758033066988,
-0.014053748920559883,
-0.032427601516246796,
-0.032794781029224396,
-0.02130444347858429,
0.013826289214193821,
0.02589595690369606,
0.05620945990085602,
0.00644790381193161,
0.0005951664061285555,
-0.04824747145175934,
0.06048781797289848,
-0.008669340051710606,
0.0778626874089241,
-0.01738194189965725,
-0.027104198932647705,
-0.032290980219841,
-0.009515559300780296,
0.05337997525930405,
0.027061207219958305,
0.01567724719643593,
0.0008178692078217864,
-0.07920453697443008,
0.04210948571562767,
0.0058050514198839664,
0.03150732070207596,
0.011450552381575108,
-0.028370458632707596,
0.05430462211370468,
0.025266846641898155,
0.04734667018055916,
-0.040764663368463516,
0.014023669064044952,
0.004724273458123207,
-0.003137113992124796,
-0.008049184456467628,
0.005691924598067999,
-0.019824353978037834,
0.0046109906397759914,
-0.03831646218895912,
-0.07017260789871216,
0.01671363227069378,
0.08306378871202469,
-0.04956435784697533,
-0.003453168785199523,
0.03447149693965912,
-0.03749791532754898,
0.013722378760576248,
-0.026279542595148087,
0.020054923370480537,
0.0367790162563324,
-0.0022581045050174,
0.051754508167505264,
0.007387652061879635,
-0.10148073732852936,
0.013326352462172508,
-0.021211709827184677,
-0.025437794625759125,
0.049056172370910645,
-0.017657915130257607,
0.011055940762162209,
-0.024296749383211136,
-0.006776886992156506,
-0.03328235074877739,
0.07470300048589706,
0.00519725913181901,
0.06211891770362854,
-0.0013465342344716191,
0.03316488862037659,
0.043184276670217514,
0.08025340735912323,
-0.028510598465800285,
0.023298026993870735,
-0.00938847754150629,
0.044273778796195984,
-0.034677665680646896,
-0.02601633034646511,
-0.017166513949632645,
0.004161055199801922,
-0.003358513116836548,
-0.009575607255101204,
-0.044086772948503494,
0.023108625784516335,
-0.0397581048309803,
-0.007701572496443987,
-0.04690990597009659,
0.035214863717556,
0.021705325692892075,
-0.0213366337120533,
0.0033393925987184048,
-0.021022947505116463,
-0.0036336423363536596,
-0.022568872198462486,
0.10718663781881332,
0.012840128503739834,
0.07338964939117432,
-0.006109942682087421,
0.008957409299910069,
0.014255031943321228,
0.021042661741375923,
-0.001717615406960249,
0.03987214341759682,
-0.01446093525737524,
0.03791506215929985,
-0.05559826269745827,
0.07743863016366959,
-0.010621029883623123,
-0.010799739509820938,
0.08048344403505325,
-0.019764648750424385,
0.010524281300604343,
0.034015901386737823,
-0.026378054171800613,
0.04396213963627815,
-0.005475355312228203,
-0.10008891671895981,
-0.05679803714156151,
-0.037450846284627914,
-0.005153584759682417,
0.02907143533229828,
-0.03050147369503975,
0.02480997145175934,
-0.01137821190059185,
-0.022120971232652664,
-0.004517356399446726,
-0.002846634015440941,
-0.00791676715016365,
0.052524976432323456,
-0.061377134174108505,
0.0008783534867689013,
0.05420594662427902,
0.006090276874601841,
0.029484109953045845,
-0.004346427507698536,
-0.019918939098715782,
-0.015813279896974564,
-0.024705437943339348,
0.040633220225572586,
0.024438777938485146,
0.03952263295650482,
0.021170172840356827,
0.021367967128753662,
-0.005539366975426674,
-0.011342156678438187,
0.03441525623202324,
-0.04354149103164673,
0.0015650313580408692,
-0.007264513056725264,
-0.0019179771188646555,
0.03582846000790596,
0.017685960978269577,
0.05543902516365051,
-0.03140779212117195,
0.0162272397428751,
-0.0823354497551918,
0.007599292788654566,
0.06032847613096237,
0.0016789183719083667,
0.04683839529752731,
0.02557307295501232,
0.03575145825743675,
0.024738477542996407,
0.007901279255747795,
0.036776185035705566,
-0.04792328551411629,
-0.017766956239938736,
0.025399193167686462,
-0.015396902337670326,
0.01135067455470562,
-0.005852439906448126,
-0.03848801553249359,
-0.026717064902186394,
-0.001565636252053082,
-0.01972782611846924,
0.04804572835564613,
-0.037464823573827744,
-0.02511047013103962,
0.041251011192798615,
-0.010451914742588997,
0.02184133790433407,
-0.028343381360173225,
-0.009738918393850327,
0.060966361314058304,
-0.02899479866027832,
0.01900383271276951,
-0.08444120734930038,
-0.0027840950060635805,
0.04424384608864784,
-0.03976587578654289,
0.04162102937698364,
0.06355635821819305,
0.0004389653622638434,
-0.01450391486287117,
-0.00021956559794489294,
-0.02566072717308998,
0.007713933940976858,
-0.007580502890050411,
0.03106273151934147,
-0.0062752957455813885,
0.045013152062892914,
0.01504170335829258,
0.05265519395470619,
-0.03685028851032257,
0.0074982657097280025,
-0.04792654141783714,
0.007682386785745621,
0.04109125956892967,
0.000619647849816829,
0.015192463994026184,
-0.06514386832714081,
-0.044187430292367935,
0.01034731324762106,
0.0658886730670929,
0.057678308337926865,
-0.0313362292945385,
-0.023006068542599678,
0.0020918266382068396,
-0.05727899819612503,
-0.011539792641997337,
-0.02164824679493904,
0.05986770987510681,
-0.07432856410741806,
0.006259542424231768,
-0.01609204150736332,
0.021395642310380936,
-0.0023852307349443436,
-0.0734110176563263,
-0.06119665876030922,
-0.04671960696578026,
0.016484998166561127,
0.03216471150517464,
0.022006861865520477,
0.023083439096808434,
-0.054279621690511703,
-0.019047897309064865,
-0.036120470613241196,
0.014116384088993073,
-0.002249526558443904,
-0.0259031243622303,
0.016247456893324852,
-0.01547322515398264,
-0.03889016807079315,
-0.0044611599296331406,
-0.04695780947804451,
-0.024873744696378708,
-0.03547033667564392,
-0.047316908836364746,
-0.028746172785758972,
0.040166135877370834,
0.015540014021098614,
0.018869221210479736,
-0.05350786820054054,
-0.013187400065362453,
0.019699763506650925,
-0.04029323533177376,
0.01259863656014204,
0.04535723105072975,
0.035878170281648636,
-0.0201092641800642,
-0.05662358179688454,
-0.014382879249751568,
0.016251804307103157,
-0.047832198441028595,
-0.005433561280369759,
-0.0478145033121109,
-0.0010412124684080482,
-0.03897520527243614,
-0.028329726308584213,
-0.04115230217576027,
-0.0248436126857996,
-0.030474571511149406,
-0.0013410741230472922,
0.04576128348708153,
-0.005057548172771931,
-0.03810269385576248,
0.019410472363233566,
0.03680442273616791,
0.0640021339058876,
-0.03517691791057587,
0.00046537083107978106,
0.020183051005005836,
0.00725968461483717,
-0.011592704802751541,
-0.049166496843099594,
-0.0029907182324677706,
-0.03519267961382866,
-0.01169040147215128,
-0.015461781062185764,
0.018893394619226456,
-0.028283176943659782,
0.017878148704767227,
0.02455170452594757,
0.044076066464185715,
0.004369677975773811,
-0.03869358077645302,
0.11441206932067871,
0.09102615714073181,
0.030849754810333252,
-0.02670389413833618,
0.01483070757240057,
-0.010767314583063126,
0.03544745221734047,
-0.018455302342772484,
0.005841466132551432,
-0.011633269488811493,
0.0001669052435318008,
-0.02495974861085415,
0.024225031957030296,
-0.03411213681101799,
-0.009356975555419922,
0.01469353400170803,
-0.008424229919910431,
-0.029081270098686218,
-0.016439316794276237,
-0.0027512963861227036,
-0.05006852373480797,
-0.024470239877700806,
-0.034753210842609406,
-0.06364654004573822,
-0.02639751508831978,
-0.012669802643358707,
-0.002939198398962617,
-0.012005058117210865,
0.010923259891569614,
-0.045778751373291016,
-0.0007455038139596581,
-0.0191974975168705,
-0.07720234245061874,
0.050229039043188095,
-0.044345587491989136,
-0.0091269975528121,
0.07169460505247116,
0.08586519211530685,
0.05722201615571976,
0.01824728026986122,
-0.013981238007545471,
0.05750162899494171,
-0.0872843936085701,
-0.02653324045240879,
0.008036009036004543,
-0.022892998531460762,
-0.03558200225234032,
0.007154625374823809,
-0.0419420562684536,
0.008877092972397804,
0.06754662096500397,
0.006333100143820047,
0.012854351662099361,
-0.019978661090135574,
0.020412243902683258,
0.003615956986322999,
0.018309755250811577,
-0.01995379850268364,
0.04135267063975334,
-0.008768567815423012,
0.013507360592484474,
0.033314649015665054,
-0.017050012946128845,
-0.02053646184504032,
0.02723097801208496,
-0.00665724603459239,
-0.024199824780225754,
0.016257822513580322,
-0.001197422738187015,
0.027908572927117348,
-0.0036868450697511435,
0.03305250033736229,
-0.06775306165218353,
0.024701805785298347,
-0.04030472785234451,
0.016349762678146362,
0.005977739579975605,
-0.0037289713509380817,
0.050474829971790314,
0.06246545538306236,
0.005249221809208393,
-0.05277904123067856,
0.0028205118142068386,
0.023747457191348076,
0.03721623495221138,
0.0780162587761879,
0.059476520866155624,
0.0023560263216495514,
-0.030413955450057983,
-0.036263056099414825,
-0.035513877868652344,
0.011676070280373096,
-0.07640152424573898,
0.017194954678416252,
-0.023645741865038872,
0.023544060066342354,
-0.020683856680989265,
0.01361791230738163,
0.02275034412741661,
-0.010307579301297665,
-0.07217638939619064,
0.024047235026955605,
-0.06597635895013809,
0.0032778510358184576,
0.06425255537033081,
-0.00035469475551508367,
-0.02436070330440998,
-0.07302535325288773,
0.021010033786296844,
0.01781042292714119,
-0.018602514639496803,
0.0527459941804409,
0.048280876129865646,
0.0014525504084303975,
0.01959378458559513,
-0.00417892262339592,
-0.03184746205806732,
-0.010082327760756016,
-0.060861196368932724,
-0.07675595581531525,
0.005348876118659973,
0.015250773169100285,
0.0008501885458827019,
0.012098565697669983,
0.033417899161577225,
-0.05099710822105408,
0.018638385459780693,
0.035810135304927826,
-0.008754981681704521,
0.003765441942960024,
-0.02123413048684597,
-0.02491358295083046,
0.002090195659548044,
0.004515634384006262,
0.029246056452393532,
-0.016947066411376,
-0.013263680972158909,
-0.0026422992814332247,
-0.049926284700632095,
-0.003007892519235611,
-0.009264886379241943
] |
<p>I have a uniform electric field $E$ projected from left to right and I placed an insulator or dielectric right in the middle of it. To the left of the insulator, the $E$ is the original $E$. Inside the insulator, there is an induced field and thus the net field is less than the original. What happen to the $E$ to the right of the insulator? Will it be the same as the original? If it does, then the $E$ will have to increase back? Why?</p> | g9236 | [
0.019964857026934624,
0.030718667432665825,
-0.0016006543301045895,
-0.02034900151193142,
0.04707317426800728,
0.01851905882358551,
0.026551803573966026,
0.06849155575037003,
-0.04498673975467682,
-0.055879395455121994,
-0.06625879555940628,
0.04260154440999031,
-0.050551097840070724,
-0.05072619393467903,
0.01479858998209238,
0.0067653958685696125,
0.05715453252196312,
-0.018112802878022194,
-0.0015287104761227965,
-0.012581167742609978,
-0.07115332037210464,
0.01843832992017269,
0.02289380505681038,
-0.026757873594760895,
0.003757594618946314,
-0.03815095126628876,
0.03784073889255524,
0.01464566309005022,
0.029934309422969818,
-0.0456477515399456,
0.04780847951769829,
0.0714908018708229,
0.034698210656642914,
-0.01587732322514057,
-0.05135616287589073,
0.011890781112015247,
0.0736161470413208,
0.07126268744468689,
-0.004476997070014477,
0.015110913664102554,
0.05077145993709564,
-0.004628881812095642,
0.036537375301122665,
-0.03240907937288284,
0.00044704426545649767,
-0.044875867664813995,
-0.014678114093840122,
0.019611742347478867,
0.02512037195265293,
-0.006103205494582653,
-0.06577442586421967,
-0.013569782488048077,
0.002777684247121215,
-0.011851366609334946,
0.02137434482574463,
0.03430123254656792,
-0.04286455363035202,
-0.06705620139837265,
0.02647913247346878,
0.04700873792171478,
-0.02575286477804184,
0.009591428562998772,
-0.007006379775702953,
0.002514778170734644,
-0.045591194182634354,
0.012363309971988201,
-0.04172958806157112,
0.04828444868326187,
-0.007757465820759535,
0.002736669033765793,
-0.05513639748096466,
0.054551947861909866,
-0.04598207771778107,
-0.02700384333729744,
-0.01816633716225624,
0.029412072151899338,
0.03703417629003525,
0.004037083126604557,
-0.01500733382999897,
0.0027889604680240154,
0.02005103789269924,
0.007251062896102667,
0.025837428867816925,
0.003024718491360545,
0.006128272507339716,
0.014825427904725075,
0.04848567023873329,
0.014506359584629536,
-0.023402197286486626,
0.004673992283642292,
0.05666666105389595,
0.0013736935798078775,
0.07696864008903503,
0.03641924262046814,
-0.021870283409953117,
-0.047555338591337204,
0.007401647046208382,
0.0275676641613245,
-0.00776776485145092,
-0.017373768612742424,
-0.030707912519574165,
-0.023455023765563965,
0.029114121571183205,
-0.041160423308610916,
-0.050839055329561234,
0.03510715439915657,
0.072146937251091,
0.025607554242014885,
-0.029497969895601273,
0.021730108186602592,
-0.00569287920370698,
-0.08469097316265106,
-0.05591118335723877,
-0.0369773805141449,
-0.043986059725284576,
0.00016737049736548215,
0.04561976343393326,
-0.005238495767116547,
-0.010419568046927452,
0.057976871728897095,
0.042143553495407104,
0.016112273558974266,
0.040219973772764206,
-0.024502670392394066,
-0.0053610350005328655,
0.04224715754389763,
-0.015102329663932323,
0.0291789211332798,
0.03697103634476662,
0.01162375882267952,
0.016059746965765953,
-0.0410396046936512,
-0.008926628157496452,
0.013326493091881275,
0.010967590846121311,
0.026175228878855705,
0.042202141135931015,
-0.005674824584275484,
0.0628410130739212,
0.02171504497528076,
0.012641433626413345,
-0.030141066759824753,
-0.009473971091210842,
-0.03453020378947258,
-0.010919328778982162,
0.045861516147851944,
0.05974794179201126,
-0.005400741472840309,
0.057455260306596756,
0.013269204646348953,
0.0012506804196164012,
0.03368153050541878,
-0.02888781763613224,
0.0012416787212714553,
0.011612716130912304,
-0.03947294503450394,
-0.0003611988795455545,
-0.02165934443473816,
0.048808272927999496,
-0.03839428722858429,
0.03682906925678253,
-0.005843184422701597,
0.042883895337581635,
0.05657946318387985,
-0.04329516366124153,
-0.0005432622856460512,
0.04004260152578354,
-0.020555999130010605,
0.02171800285577774,
-0.05127361789345741,
0.041329525411129,
0.015644513070583344,
0.0022304588928818703,
0.07882099598646164,
0.011715170927345753,
0.0865473672747612,
-0.02362528070807457,
-0.012997751124203205,
0.0640266090631485,
-0.022511076182127,
-0.055888619273900986,
0.04404796287417412,
0.022462930530309677,
-0.041181933134794235,
-0.026994111016392708,
-0.07478802651166916,
-0.042290836572647095,
0.057453811168670654,
-0.10879048705101013,
0.023474764078855515,
0.0062354798428714275,
0.027584243565797806,
-0.006695861462503672,
0.03615253418684006,
-0.00357579137198627,
0.022562982514500618,
0.024768177419900894,
-0.07514598965644836,
-0.014022424817085266,
-0.047007136046886444,
-0.07110024243593216,
-0.021290648728609085,
0.0580563060939312,
-0.0008918417152017355,
0.007149356417357922,
-0.02434796281158924,
-0.04876707121729851,
-0.04648389294743538,
0.04073375090956688,
-0.0079201003536582,
-0.02334928885102272,
0.016467833891510963,
0.0035494619514793158,
-0.00676968228071928,
-0.005225628614425659,
0.025599254295229912,
-0.020040396600961685,
-0.030760744586586952,
-0.015123377554118633,
-0.0006301800021901727,
-0.07325583696365356,
-0.011718865483999252,
0.06199866905808449,
-0.00009197932376991957,
-0.025956420227885246,
-0.06524727493524551,
0.0038135338108986616,
0.023246197029948235,
-0.045520707964897156,
0.0022968093398958445,
-0.02734561264514923,
0.039427291601896286,
-0.011371049098670483,
-0.010496228002011776,
0.020869309082627296,
-0.008158591575920582,
0.013125346973538399,
-0.04082554578781128,
0.02678757719695568,
-0.0704750269651413,
-0.027663154527544975,
0.018948746845126152,
0.028512893244624138,
0.031814053654670715,
-0.010796125046908855,
-0.022173786535859108,
0.07171722501516342,
-0.030191026628017426,
-0.013989278115332127,
0.056528616696596146,
-0.008123274892568588,
0.0013719919370487332,
0.003221321851015091,
-0.006115226540714502,
-0.02111823484301567,
0.0039382511749863625,
-0.05377025529742241,
0.06417397409677505,
0.026504285633563995,
-0.013143043965101242,
-0.0339556522667408,
0.0024230361450463533,
-0.00004834366700379178,
0.013170656748116016,
-0.028609130531549454,
0.03495510295033455,
0.035133324563503265,
-0.03924691677093506,
0.03925994783639908,
0.05915671959519386,
0.011239495128393173,
0.09023265540599823,
0.006166462786495686,
0.0397477000951767,
0.08680804818868637,
-0.007774608209729195,
0.008258570916950703,
-0.04977685213088989,
0.0014791283756494522,
-0.006839725188910961,
-0.023698370903730392,
-0.03266078233718872,
-0.0684102401137352,
0.028860589489340782,
-0.02766798995435238,
-0.0718890130519867,
0.013374272733926773,
-0.04059207811951637,
-0.05332737788558006,
0.0016860864125192165,
-0.053237345069646835,
-0.02449069917201996,
0.07463016360998154,
0.01744363270699978,
0.09283588081598282,
-0.02497297339141369,
0.011491312645375729,
-0.06368505209684372,
-0.03141250088810921,
0.018435588106513023,
-0.04637840762734413,
-0.01594213768839836,
0.010434065014123917,
-0.057881396263837814,
0.009265551343560219,
-0.03417152538895607,
-0.04841476306319237,
-0.06261132657527924,
0.04367745295166969,
0.007853778079152107,
-0.017550669610500336,
0.009398836642503738,
-0.03086221031844616,
0.006852196529507637,
-0.07047171890735626,
0.020787110552191734,
-0.009929773397743702,
0.024550769478082657,
-0.007080437615513802,
-0.04401580989360809,
-0.07166432589292526,
-0.00019326711480971426,
0.028192434459924698,
0.023701004683971405,
0.03981032595038414,
0.03175634145736694,
-0.032048217952251434,
0.05083741620182991,
-0.04998898133635521,
-0.040020547807216644,
-0.018869616091251373,
-0.02303309738636017,
-0.035086095333099365,
-0.04444503411650658,
0.06042489781975746,
0.019447701051831245,
0.014513492584228516,
0.07251737266778946,
0.032926756888628006,
0.047484830021858215,
-0.01756134442985058,
-0.01741199940443039,
-0.05469977483153343,
-0.059574104845523834,
0.009201915003359318,
-0.008102980442345142,
-0.015272194519639015,
-0.024680159986019135,
0.01820114068686962,
0.02826067991554737,
0.04700206220149994,
-0.025775497779250145,
0.004421246703714132,
-0.0020568494219332933,
-0.04533609747886658,
-0.01064081210643053,
-0.007707653567194939,
-0.03368007764220238,
0.02509736642241478,
0.007098505739122629,
0.019335094839334488,
-0.079963818192482,
-0.03437226638197899,
0.00790539849549532,
-0.056317489594221115,
0.011155486106872559,
0.005105485673993826,
0.036718979477882385,
-0.020927539095282555,
0.02564290538430214,
-0.05961799621582031,
0.02445077709853649,
-0.05004362016916275,
-0.003324330784380436,
-0.03613429516553879,
-0.05162260681390762,
0.013546007685363293,
0.012977182865142822,
-0.02532857283949852,
0.017411908134818077,
-0.00963631086051464,
-0.011640232056379318,
-0.008929707109928131,
-0.04537127912044525,
0.02272205986082554,
0.028139933943748474,
-0.013249018229544163,
0.027574634179472923,
0.00788121484220028,
-0.010368959046900272,
-0.01754564419388771,
-0.0028598071075975895,
0.002295241691172123,
0.018999656662344933,
0.006042641121894121,
0.02102871984243393,
-0.00040348898619413376,
-0.06257756799459457,
0.031152579933404922,
-0.04241069778800011,
0.001691145938821137,
-0.059269584715366364,
-0.014182043261826038,
-0.02730223536491394,
-0.027147123590111732,
-0.0068110572174191475,
0.0801226869225502,
-0.011390302330255508,
-0.008493340574204922,
-0.07737046480178833,
-0.03592919930815697,
-0.00550379091873765,
-0.024704692885279655,
-0.10249730199575424,
0.07492494583129883,
0.02995883859694004,
0.09124323725700378,
0.06515392661094666,
0.02269628457725048,
-0.029450874775648117,
0.027697285637259483,
-0.0009735478088259697,
0.04515528678894043,
-0.03283439204096794,
0.015208469703793526,
0.030127033591270447,
0.027326256036758423,
-0.03802856057882309,
0.020210083574056625,
-0.0028738072142004967,
-0.016485895961523056,
0.07218565046787262,
-0.04552922397851944,
-0.03537967801094055,
-0.03570236265659332,
0.004999539814889431,
-0.00949237123131752,
0.048720479011535645,
-0.012512445449829102,
0.04774516075849533,
0.08063865453004837,
-0.04691806063055992,
-0.019976438954472542,
-0.029271326959133148,
-0.03756801784038544,
0.01789095066487789,
-0.02976846508681774,
-0.012781314551830292,
-0.005709141027182341,
-0.012469657696783543,
0.0020646103657782078,
0.010102971456944942,
0.020950742065906525,
-0.026959072798490524,
0.029340209439396858,
-0.056021444499492645,
-0.04223274812102318,
0.013376826420426369,
-0.0023431596346199512,
-0.0168352872133255,
-0.03398696705698967,
0.024014675989747047,
-0.047267742455005646,
0.007657352834939957,
0.002359836595132947,
-0.039639949798583984,
-0.011022288352251053,
-0.018460996448993683,
-0.022445667535066605,
0.0013513315934687853,
0.05613616108894348,
0.020981423556804657,
0.018270792439579964,
0.008403361774981022,
0.07208023965358734,
0.028564348816871643,
0.011081351898610592,
-0.03338705375790596,
0.008334431797266006,
-0.06497272849082947,
-0.02569185197353363,
-0.07326076924800873,
0.025862058624625206,
0.0002665205392986536,
-0.02486041747033596,
0.006390511058270931,
-0.06016431748867035,
0.04154735431075096,
0.03773342818021774,
-0.03634722903370857,
0.046440962702035904,
0.004749474115669727,
0.029493095353245735,
0.0004959328798577189,
-0.037146054208278656,
0.0280306413769722,
0.0059850942343473434,
0.03577762842178345,
0.012858103029429913,
0.004295265767723322,
-0.04769827425479889,
0.025688042864203453,
-0.016957439482212067,
0.04588215425610542,
0.01437009871006012,
-0.009800354018807411,
-0.001639507943764329,
-0.02199799381196499,
-0.03842924162745476,
-0.02181238681077957,
-0.021060876548290253,
0.06215686351060867,
0.037548791617155075,
-0.01902042143046856,
0.032046493142843246,
-0.022539133206009865,
-0.05921569839119911,
0.016308918595314026,
0.00012723988038487732,
-0.005531837232410908,
0.0546993687748909,
-0.001082605100236833,
0.015022128820419312,
-0.040842555463314056,
0.056211814284324646,
0.008765725418925285,
-0.03375208005309105,
-0.024909691885113716,
0.03870738670229912,
0.010304342024028301,
0.0019600556697696447,
0.07796978205442429,
-0.011967936530709267,
-0.04633603245019913,
0.03870931267738342,
0.006730655208230019,
0.006623456720262766,
-0.03254152089357376,
0.04017668217420578,
0.008852862752974033,
0.0146738076582551,
-0.009358979761600494,
0.00854333583265543,
-0.0017350573325529695,
-0.08647412061691284,
0.015028100460767746,
-0.023012487217783928,
0.03269350901246071,
0.06967329978942871,
0.014854412525892258,
-0.026125172153115273,
0.010034523904323578,
-0.00447902362793684,
-0.003418742213398218,
0.04747813567519188,
0.02161306142807007,
-0.031044431030750275,
0.03571739420294762,
0.04481344297528267,
-0.05640853941440582,
0.04471501335501671,
-0.05812692642211914,
0.03950650990009308,
-0.004308030474931002,
0.02387869916856289,
-0.032837897539138794,
-0.003930862061679363,
0.002791881561279297,
0.08285236358642578,
0.021788571029901505,
0.023888252675533295,
-0.010263292118906975,
-0.01237549725919962,
0.012739349156618118,
-0.008088219910860062,
0.03199199587106705,
0.00016723046428523958,
-0.005306094419211149,
-0.0008904623682610691,
0.006570993922650814,
-0.03952324017882347,
-0.0023665642365813255,
0.02947736158967018,
-0.027390945702791214,
-0.0010885711526498199,
0.020097380504012108,
-0.06508824229240417,
-0.024504490196704865,
0.11601652204990387,
-0.018415147438645363,
-0.026267962530255318,
0.0062387906946241856,
0.03326735645532608,
0.04415816441178322,
-0.006362465675920248,
0.0323098823428154,
-0.040620721876621246,
-0.004143508151173592,
-0.0005647761281579733,
0.07330070436000824,
0.016480347141623497,
0.018506288528442383,
0.09100981056690216,
-0.049884237349033356,
-0.02979654259979725,
0.019371621310710907,
-0.008322699926793575,
0.0011082550045102835,
-0.05784900486469269,
-0.0038521066308021545,
0.009655974805355072,
-0.044745296239852905,
0.031992632895708084,
-0.01899966597557068,
-0.03630300983786583,
-0.022064952179789543,
-0.011315802112221718,
0.02439364232122898,
-0.01870565302670002,
-0.0029444571118801832,
-0.04745542258024216,
-0.07094736397266388,
-0.050297923386096954,
0.05721384659409523,
-0.03091919608414173,
0.06698096543550491,
-0.016375599429011345,
-0.049751706421375275,
0.03852733224630356,
-0.0026502993423491716,
-0.034110456705093384,
0.036598969250917435,
-0.1109292209148407,
0.028089459985494614,
0.028161749243736267,
0.016798242926597595,
0.038373369723558426,
0.04243665561079979,
0.039498984813690186,
0.01714295521378517,
-0.009395142085850239,
0.07315054535865784,
-0.023107361048460007,
0.009499155916273594,
-0.04156585782766342,
0.043153535574674606,
-0.004301943350583315,
0.01658540591597557,
-0.025682585313916206,
0.056496236473321915,
-0.01257776003330946,
0.026285069063305855,
-0.02051774598658085,
-0.017907651141285896,
-0.018703946843743324,
-0.013328575529158115,
0.02894367091357708,
0.021973520517349243,
0.015303496271371841,
-0.010710072703659534,
-0.054526880383491516,
-0.07681966572999954,
-0.03776704519987106,
0.05384290590882301,
0.0339655801653862,
-0.004408890847116709,
0.043625809252262115,
0.005357579793781042,
0.0016695555532351136,
-0.023490818217396736,
-0.026330411434173584,
-0.032108768820762634,
-0.018580032512545586,
0.014864831231534481,
-0.006590521894395351,
0.031482260674238205,
0.00512723671272397,
0.04715687036514282,
0.02523505501449108,
-0.021028827875852585,
-0.03122309036552906,
0.0685354620218277,
0.026009589433670044,
-0.05029841139912605,
-0.025997603312134743,
0.014167859219014645,
-0.013196568936109543,
-0.005278820637613535,
0.007770045194774866,
-0.02922150120139122,
0.01441809069365263,
0.017604246735572815,
0.023316586390137672,
0.05281366407871246,
-0.016262097284197807,
0.01232695672661066,
-0.02337847650051117,
0.040784966200590134,
0.004860094748437405,
-0.03813799098134041,
0.01841890439391136,
-0.02694767713546753,
-0.029234277084469795,
-0.0809418335556984,
0.031675953418016434,
0.00010814732377184555,
-0.029494350776076317,
0.0336061455309391,
-0.0234212689101696,
-0.0058320052921772,
0.03759046271443367,
-0.005354811903089285,
0.07585865259170532,
0.021673105657100677,
0.00997872557491064,
-0.028663333505392075,
-0.01612892560660839,
0.03018801659345627,
-0.020671190693974495,
0.011657520197331905,
-0.026408012956380844,
0.02176419086754322,
-0.03133548051118851,
-0.014491105452179909,
-0.028797248378396034,
0.022528667002916336,
-0.013317525386810303,
0.008850599639117718,
0.06920070201158524,
-0.03706205636262894,
-0.004171965643763542,
-0.017714614048600197,
-0.025163328275084496,
-0.025802282616496086,
-0.02054481953382492,
-0.002874784404411912,
-0.014006881974637508,
-0.0038561858236789703,
0.013142350129783154,
-0.05318652465939522,
-0.03028961457312107,
-0.046878665685653687,
-0.009812291711568832,
-0.030073268339037895,
-0.00988835096359253,
0.02915044128894806,
-0.016858739778399467,
0.04567566514015198,
0.05132089927792549,
-0.0612485334277153,
-0.030463071539998055,
-0.0532183013856411,
-0.04903503507375717,
0.050830524414777756,
0.10126291215419769,
-0.02051965333521366,
-0.029938071966171265,
0.021643290296196938,
0.024307822808623314,
0.008048344403505325,
-0.017742769792675972,
-0.02488822489976883,
-0.006512924563139677,
0.007291661109775305,
-0.0148692075163126,
0.0444815456867218,
0.049704715609550476,
0.06955781579017639
] |
<p>I have the following homework problem in theoretical electrodynamics:</p>
<blockquote>
<p>Show that the gauge invariant Lagrange density $\epsilon_{\mu\nu\alpha\beta} F^{\mu\nu} F^{\alpha\beta}$ can be written as a total divergence of a four-vector.</p>
</blockquote>
<p>This total divergence should be something like $\partial_\mu G^\mu$, right?</p>
<p>With
$$
\hat F^{\mu\nu} = \frac 12 \epsilon^{\mu\nu\alpha\beta} F_{\alpha\beta}
$$
I figured that I write this Lagrange density (I'll refer to it as $L_2$) could be written as:
$$
L_2 = 2 \hat F^{\mu\nu} F_{\mu\nu}
$$</p>
<p>I simplified this by using the matrix representations of each $F$ and got it down to:
$$
L_2 = -\frac 4c B_i E^i
$$</p>
<p>$B$ and $E$ can be expressed in Terms of $A$ like so:
$$
B_i = \epsilon_{ijk} \partial_j A^j
,\quad
E_i = -\partial_i A^0 -\partial_0 A^i
$$</p>
<p>How would I continue to find that four-vector $G$?</p> | g9237 | [
0.0682397186756134,
-0.005842628423124552,
-0.013492053374648094,
-0.10731355845928192,
0.07275030761957169,
0.009669874794781208,
0.05263663828372955,
0.028478238731622696,
-0.10988634824752808,
0.005017528310418129,
-0.01806160993874073,
-0.024618351832032204,
0.0035352285485714674,
0.0402364619076252,
0.0783129408955574,
0.0366797111928463,
0.04380862042307854,
-0.026358911767601967,
0.014534186571836472,
-0.037419795989990234,
-0.024151043966412544,
0.04400365799665451,
0.03345926105976105,
-0.01473418902605772,
0.04799101874232292,
-0.02144717052578926,
0.07555932551622391,
0.000571990036405623,
-0.04550180956721306,
-0.011969808489084244,
-0.0069479066878557205,
0.03851938247680664,
0.04424251616001129,
-0.013281702995300293,
-0.013765616342425346,
0.027843784540891647,
0.06141015142202377,
0.02723475731909275,
0.040636096149683,
-0.04490876570343971,
0.027182402089238167,
-0.04137719050049782,
-0.04151175916194916,
0.024042606353759766,
0.006783692166209221,
0.0033512196969240904,
-0.02788274735212326,
-0.0001875293382909149,
-0.04114146530628204,
0.05063672736287117,
0.062172845005989075,
0.04309333860874176,
0.04536619782447815,
-0.032272424548864365,
0.010895156301558018,
0.03150615096092224,
-0.0012607926037162542,
-0.011016342788934708,
0.022985566407442093,
0.021066797897219658,
0.02546391449868679,
-0.06843893975019455,
-0.012349690310657024,
-0.027884522452950478,
0.0470147505402565,
-0.024896124377846718,
-0.034650854766368866,
-0.0012337585212662816,
0.02063867449760437,
0.007671785075217485,
0.009455639868974686,
-0.027444573119282722,
0.02801503799855709,
-0.03513427823781967,
-0.04547978937625885,
0.006890816148370504,
0.017513783648610115,
-0.011702043935656548,
-0.022395607084035873,
-0.046723902225494385,
-0.05144733935594559,
-0.02499782294034958,
-0.0008524020086042583,
0.015552892349660397,
0.0990375280380249,
-0.05471978336572647,
-0.02441270276904106,
-0.007554040756076574,
-0.03528591990470886,
-0.05190788954496384,
-0.00882305484265089,
0.0014582222793251276,
-0.010190007276833057,
0.0285829808562994,
0.025275427848100662,
-0.021763315424323082,
0.006726599298417568,
0.021424803882837296,
-0.03372511267662048,
-0.04190632328391075,
0.016849562525749207,
0.07085014134645462,
0.02082788199186325,
0.0027219788171350956,
-0.031217079609632492,
0.022273216396570206,
0.03255245462059975,
-0.04311281070113182,
0.025389311835169792,
0.0001898616028483957,
-0.01340603455901146,
0.009369537234306335,
-0.03029816411435604,
-0.05976660177111626,
-0.05448615923523903,
0.013570294715464115,
0.06446006894111633,
-0.06238532438874245,
-0.07849866896867752,
0.04639787971973419,
-0.03247881308197975,
-0.03662765398621559,
0.018516046926379204,
0.04464311525225639,
0.03573961928486824,
0.06830902397632599,
-0.004720751661807299,
0.024111397564411163,
0.047659292817115784,
-0.013848699629306793,
0.010476119816303253,
0.030455278232693672,
0.02359575219452381,
0.016707556322216988,
0.019882168620824814,
0.030959803611040115,
-0.0552973635494709,
0.02808813378214836,
0.027521992102265358,
0.06875293701887131,
-0.017500370740890503,
-0.05809921771287918,
0.040143996477127075,
-0.030474785715341568,
0.0031078511383384466,
0.014620685949921608,
-0.07206884771585464,
-0.07731350511312485,
-0.004010395612567663,
-0.02554348297417164,
0.025172363966703415,
0.07824492454528809,
0.019423631951212883,
-0.005702665075659752,
0.018303027376532555,
0.022473404183983803,
0.05553506314754486,
0.006479218136519194,
-0.004797340836375952,
0.030763398855924606,
0.025471162050962448,
-0.047265298664569855,
0.03160989657044411,
0.022273696959018707,
-0.03587791323661804,
0.06996610760688782,
-0.004932888317853212,
-0.07950110733509064,
-0.0019338022684678435,
-0.06801167130470276,
-0.05915498360991478,
0.022302476689219475,
0.01787632331252098,
-0.008528502658009529,
0.004854636732488871,
0.04174421355128288,
-0.027860956266522408,
-0.04321157932281494,
0.0003218064666725695,
0.01868831180036068,
0.0016300675924867392,
-0.05035122111439705,
0.03837445378303528,
-0.01809941977262497,
-0.006296304054558277,
0.0035990485921502113,
0.044036805629730225,
0.022472109645605087,
0.029364297166466713,
0.00854955893009901,
0.029936207458376884,
0.013082511723041534,
-0.03823645040392876,
0.026129605248570442,
0.03234757483005524,
-0.015377329662442207,
0.03783885017037392,
-0.08800330758094788,
-0.006865719333291054,
0.04993678629398346,
0.017659591510891914,
0.04057873785495758,
0.03139664605259895,
-0.00016983177920337766,
-0.004615176934748888,
0.008718538098037243,
-0.06863176077604294,
-0.04115058481693268,
0.03484867140650749,
-0.0042474833317101,
0.015170471742749214,
-0.11671130359172821,
-0.01662028767168522,
0.04264094680547714,
-0.02456567995250225,
-0.062076348811388016,
0.02958345040678978,
0.0412759967148304,
-0.08976997435092926,
0.05948414281010628,
-0.0513591393828392,
-0.016150031238794327,
0.0019929292611777782,
0.05933212861418724,
0.005798041354864836,
0.06344185024499893,
0.01683587208390236,
-0.004762096796184778,
-0.01575564593076706,
-0.045528870075941086,
-0.044927019625902176,
-0.014147575944662094,
-0.0007308281492441893,
-0.016160886734724045,
0.02766011282801628,
0.05696152523159981,
-0.05345191806554794,
0.01521296612918377,
0.025998255237936974,
-0.04067334532737732,
0.01357774343341589,
0.010957164689898491,
0.011766847223043442,
0.005317768082022667,
0.03788170590996742,
0.02904784120619297,
0.027414897456765175,
0.01512173656374216,
-0.006841432303190231,
0.0029546343721449375,
-0.03206448256969452,
0.015788234770298004,
-0.009884066879749298,
0.04306928813457489,
0.006445929408073425,
-0.02934015914797783,
0.015309668146073818,
0.008280271664261818,
0.003785033244639635,
-0.009927556850016117,
-0.01396386418491602,
-0.07597854733467102,
0.02466697245836258,
0.0027737352065742016,
-0.10030148923397064,
0.030426081269979477,
0.007634061388671398,
-0.008158344775438309,
0.01177640724927187,
-0.009784706868231297,
-0.02653641812503338,
0.03514248505234718,
0.07435545325279236,
0.03474016487598419,
-0.04347946122288704,
0.0016547273844480515,
0.013474534265697002,
-0.048918865621089935,
0.012121438980102539,
-0.03181165084242821,
0.002886266214773059,
0.03945375233888626,
-0.0070097497664391994,
0.013264679349958897,
0.03149471804499626,
-0.12904426455497742,
0.0018362750997766852,
0.0033571398817002773,
0.016419464722275734,
-0.03001147136092186,
-0.025174863636493683,
0.004296940751373768,
0.03268292918801308,
-0.034966714680194855,
0.002689374377951026,
0.08220723271369934,
-0.041457563638687134,
-0.019729217514395714,
-0.008807008154690266,
-0.028851082548499107,
0.025134246796369553,
-0.006333591882139444,
-0.005993003025650978,
-0.04033224284648895,
0.05909864977002144,
-0.00841512717306614,
-0.040768712759017944,
0.024695435538887978,
0.011041611433029175,
-0.021479329094290733,
-0.022957818582654,
-0.04995260015130043,
0.032057661563158035,
-0.04384236037731171,
-0.03483894094824791,
-0.010592754930257797,
0.06266336888074875,
-0.03989429771900177,
0.07394836097955704,
-0.028435848653316498,
-0.003134913509711623,
-0.007636614143848419,
0.05419810861349106,
0.03875777870416641,
0.02971169725060463,
-0.0024078877177089453,
-0.022508440539240837,
0.004897087812423706,
-0.023898405954241753,
0.009844363667070866,
-0.038364823907613754,
-0.06743432581424713,
0.026915492489933968,
0.001755010336637497,
-0.006614349782466888,
0.011436278000473976,
-0.006952814292162657,
0.03040441684424877,
-0.0027475382667034864,
-0.022632170468568802,
-0.0938481017947197,
-0.061777982860803604,
-0.017997553572058678,
0.00809874664992094,
0.01890161819756031,
-0.0533338338136673,
-0.0033762482926249504,
0.0016603661933913827,
-0.005975242238491774,
0.03278360143303871,
-0.014184542000293732,
-0.0017227032221853733,
0.0546024926006794,
0.03457760438323021,
0.008653121069073677,
0.023803586140275,
0.03617329150438309,
-0.046855662018060684,
-0.004061710089445114,
0.01125330664217472,
0.024403348565101624,
-0.03171948716044426,
-0.005942678544670343,
-0.049163829535245895,
0.0004112485039513558,
0.033218756318092346,
0.01863470859825611,
0.02168649435043335,
0.03918885439634323,
0.01338982954621315,
0.08956076204776764,
0.020525885745882988,
-0.00469205342233181,
0.07181888818740845,
0.0008613245445303619,
-0.07813933491706848,
-0.00534463906660676,
0.0001290384097956121,
-0.053300581872463226,
0.021777166053652763,
0.037233732640743256,
-0.01553249079734087,
0.042123109102249146,
0.008308547548949718,
0.017850957810878754,
0.01892929896712303,
-0.003787130117416382,
-0.02449113503098488,
0.00038600864354521036,
-0.03282155096530914,
0.04550600424408913,
0.0007010144763626158,
-0.010360749438405037,
0.001808616449125111,
-0.0638008639216423,
-0.05764064937829971,
0.009641044773161411,
0.024315644055604935,
-0.0859261304140091,
0.07074571400880814,
-0.02616312727332115,
-0.0004975780029781163,
-0.0038920033257454634,
0.0217928234487772,
0.01102234236896038,
0.017954224720597267,
0.01827063597738743,
-0.010652423836290836,
0.07811281830072403,
-0.06251201033592224,
0.023550979793071747,
-0.011306500062346458,
0.005160953383892775,
-0.04610445350408554,
0.00609816238284111,
0.0036798513028770685,
-0.003015128429979086,
-0.045405711978673935,
0.05325683578848839,
-0.046660859137773514,
-0.005681648384779692,
-0.0014156659599393606,
-0.00947685819119215,
-0.03381631150841713,
0.04535391926765442,
0.0391215942800045,
0.032418590039014816,
0.056247808039188385,
-0.005933187901973724,
-0.005511156283318996,
-0.01294361986219883,
-0.016150861978530884,
-0.03331712633371353,
0.06691810488700867,
-0.0850074291229248,
0.006689282134175301,
-0.07099566608667374,
0.0007670150953345001,
-0.027386460453271866,
0.10097115486860275,
0.03317137062549591,
-0.07184267044067383,
0.026216469705104828,
-0.002575249643996358,
0.015485955402255058,
0.04708794504404068,
0.005046738311648369,
-0.027717234566807747,
0.05762697756290436,
0.07904800027608871,
-0.012595845386385918,
0.015392545610666275,
-0.02472398802638054,
0.026254668831825256,
-0.0009492444805800915,
-0.024359432980418205,
0.011551519855856895,
0.032596688717603683,
0.039217039942741394,
0.01371193490922451,
-0.012100381776690483,
-0.00027262596995569766,
-0.029130108654499054,
-0.014686285518109798,
0.07603490352630615,
-0.04295483976602554,
-0.02176664210855961,
0.060782305896282196,
-0.007373521104454994,
-0.047689661383628845,
-0.002990313107147813,
0.039913974702358246,
0.01891176775097847,
0.0019656207878142595,
-0.01718985289335251,
0.047373250126838684,
-0.021391823887825012,
0.020513201132416725,
-0.03638181835412979,
-0.02558852545917034,
-0.05075114220380783,
-0.04818424955010414,
-0.02540961094200611,
0.010542723350226879,
0.002864242997020483,
0.007661283016204834,
-0.005671082995831966,
-0.06350802630186081,
-0.03350280970335007,
-0.058328937739133835,
-0.005334173794835806,
0.008309143595397472,
0.014749429188668728,
0.03279588744044304,
-0.02350308746099472,
-0.010692531242966652,
0.049364615231752396,
0.0036226471420377493,
0.019412098452448845,
-0.01074098888784647,
-0.06255306303501129,
0.02392496168613434,
-0.012575898319482803,
-0.06909652054309845,
0.05489208549261093,
0.04722284898161888,
0.061451174318790436,
0.0034291527699679136,
-0.03587917611002922,
0.03894415125250816,
-0.012377879582345486,
0.0005696435109712183,
0.00824536569416523,
-0.024513477459549904,
0.006449317093938589,
-0.014971399679780006,
-0.05121973156929016,
0.030348869040608406,
-0.008297096937894821,
-0.06747732311487198,
0.03163586184382439,
-0.019698740914463997,
0.01496194489300251,
-0.04935842007398605,
0.0313061885535717,
-0.013613549992442131,
-0.06167532876133919,
-0.07206637412309647,
-0.006898659281432629,
0.020244071260094643,
0.018882011994719505,
-0.022861715406179428,
0.016647517681121826,
-0.06314076483249664,
0.03518553078174591,
-0.026730414479970932,
-0.04435405135154724,
-0.05510901287198067,
0.0008668002556078136,
0.024278711527585983,
0.010519140399992466,
-0.022059164941310883,
0.023169543594121933,
0.028233489021658897,
-0.020158004015684128,
-0.00047636358067393303,
-0.004623027052730322,
0.03456144407391548,
0.028686678037047386,
-0.021762875840067863,
-0.029377978295087814,
0.013046693988144398,
-0.006439057178795338,
-0.008436067961156368,
-0.03810267895460129,
-0.022071098908782005,
0.0062022763304412365,
0.06981941312551498,
-0.037217192351818085,
0.019627492874860764,
-0.003879174357280135,
-0.028305131942033768,
0.013602922670543194,
-0.0017137188697233796,
-0.04270629957318306,
-0.051221899688243866,
-0.005003073252737522,
-0.028676994144916534,
0.023710479959845543,
-0.006663009990006685,
0.014699333347380161,
0.027489684522151947,
0.01808641105890274,
0.053586430847644806,
0.0419251024723053,
0.021154318004846573,
0.0224794652312994,
-0.07963188737630844,
-0.009769934229552746,
-0.0008790185675024986,
-0.05386095494031906,
0.01573113724589348,
0.00831896997988224,
-0.019487330690026283,
-0.042011696845293045,
0.04803699627518654,
-0.04953203350305557,
-0.03897658735513687,
-0.06763792037963867,
0.0010976470075547695,
0.016000568866729736,
0.02627502754330635,
0.016035504639148712,
0.06594841182231903,
-0.01317478809505701,
0.04956357553601265,
0.019811667501926422,
-0.0008009104058146477,
-0.015024720691144466,
0.003921785857528448,
0.0734984502196312,
0.009838375262916088,
0.002871121745556593,
-0.01232452318072319,
0.020863261073827744,
0.011243483051657677,
-0.05022625997662544,
0.009045056998729706,
0.007485296577215195,
-0.03009502962231636,
0.014260869473218918,
-0.007430244702845812,
-0.003325031138956547,
0.019427936524152756,
0.023687416687607765,
0.017838401719927788,
0.040195610374212265,
0.07121054083108902,
-0.024311840534210205,
0.07551248371601105,
0.06167632341384888,
0.013093575835227966,
-0.053359705954790115,
-0.01903611049056053,
0.06121622398495674,
0.012097255326807499,
0.011276000179350376,
-0.02488129585981369,
0.054227668792009354,
0.0036182664334774017,
0.04036131128668785,
-0.02830866165459156,
0.018435124307870865,
0.002975459909066558,
0.03232374042272568,
0.05743061751127243,
-0.03531262278556824,
0.02950388938188553,
0.02582721784710884,
0.051483675837516785,
-0.013748903758823872,
0.000015178553439909592,
0.023189185187220573,
-0.026858391240239143,
0.00005282384154270403,
-0.01027884054929018,
-0.01785154454410076,
0.0028826354537159204,
-0.07387252897024155,
-0.012300733476877213,
0.04568742960691452,
0.031022759154438972,
-0.0400005578994751,
-0.002887067152187228,
-0.06156855821609497,
-0.008636021055281162,
0.014537682756781578,
0.010843326337635517,
0.012522732838988304,
-0.01832071878015995,
-0.012695668265223503,
-0.022047758102416992,
0.041693065315485,
-0.0269471388310194,
0.013269334100186825,
-0.001029103179462254,
-0.04478286951780319,
-0.03993278369307518,
0.021451380103826523,
-0.0688360333442688,
0.00008270569378510118,
-0.030537119135260582,
-0.03211976960301399,
0.06255478411912918,
0.008576489053666592,
0.009015760384500027,
-0.013296314515173435,
0.06305991113185883,
-0.06465185433626175,
0.01738007552921772,
-0.055948104709386826,
-0.008686274290084839,
-0.0159310270100832,
-0.02592008002102375,
-0.07319601625204086,
0.007271931041032076,
-0.038199931383132935,
0.009850948117673397,
0.020448921248316765,
0.022114980965852737,
-0.026441100984811783,
-0.02119697630405426,
0.017991678789258003,
-0.0026040885131806135,
-0.06007610261440277,
0.051524754613637924,
0.03435764089226723,
0.00602709362283349,
0.032611772418022156,
0.045947201550006866,
0.0024559060111641884,
0.010477855801582336,
0.001230525434948504,
-0.032702986150979996,
-0.009346365928649902,
0.011795971542596817,
-0.020712390542030334,
-0.016548173502087593,
-0.06741954386234283,
-0.012442663311958313,
-0.006075599230825901,
0.008407543413341045,
0.004964706487953663,
0.0007320910226553679,
0.06218496337532997,
-0.0028433804400265217,
-0.028429711237549782,
0.017179343849420547,
-0.027204325422644615,
-0.024678243324160576,
-0.009070652537047863,
-0.019230373203754425,
0.020025502890348434,
-0.03549155965447426,
-0.02637270651757717,
-0.03473395109176636,
-0.03582213073968887,
-0.011493387632071972,
0.03251996263861656,
-0.02035462111234665,
-0.0565401054918766,
0.011718862690031528,
-0.052687838673591614,
0.040713969618082047,
0.001890912652015686,
0.015490615740418434,
0.03608772158622742,
-0.025751842185854912,
0.0733981654047966,
0.016668517142534256,
-0.01713893748819828,
-0.05852409079670906,
0.00929115992039442,
0.02920735999941826,
0.02136375941336155,
0.009271564893424511,
-0.021333765238523483,
-0.02223990112543106,
0.03372654318809509,
-0.04074076563119888,
-0.004281746689230204,
0.011247157119214535,
-0.011808506213128567,
0.06664247810840607,
0.019469527527689934,
0.004343049600720406,
0.09532377868890762,
0.01514612976461649,
0.0487905889749527,
0.027360161766409874,
-0.026595527306199074,
-0.05198187008500099,
0.013037567026913166,
0.008466343395411968,
-0.028155900537967682,
-0.06800738722085953,
-0.005941835697740316,
-0.006975942756980658
] |
<p>Will a person on top of hill will age faster than one at sea level due to Time Dilation?</p> | g9238 | [
0.04932502284646034,
0.03607887402176857,
0.0012469356879591942,
0.026275020092725754,
-0.036592449992895126,
0.1087321788072586,
0.0467032715678215,
0.0007304248283617198,
0.031006980687379837,
-0.004166578873991966,
-0.013205421157181263,
-0.022174308076500893,
-0.014718325808644295,
0.00008388401329284534,
-0.006763571873307228,
-0.01283201389014721,
0.10777892917394638,
-0.05362321436405182,
-0.004766036756336689,
-0.017123956233263016,
-0.05191047117114067,
-0.017900651320815086,
-0.03493667021393776,
0.005423435475677252,
-0.05758005753159523,
-0.031878694891929626,
0.00047415902372449636,
0.03217155113816261,
-0.048914991319179535,
0.019516903907060623,
0.048797089606523514,
-0.05341281741857529,
-0.04184217378497124,
0.013089766725897789,
-0.03398432210087776,
-0.04884939640760422,
0.02348853088915348,
-0.03358158841729164,
0.025185249745845795,
-0.004839436616748571,
0.005618436727672815,
-0.01451703067868948,
0.02491307631134987,
-0.02678825519979,
-0.04048629477620125,
-0.016158344224095345,
-0.010774961672723293,
0.024982374161481857,
0.013227210380136967,
-0.015000652521848679,
-0.053855881094932556,
-0.01793154515326023,
-0.025271691381931305,
-0.009590859524905682,
-0.03074699454009533,
-0.002908403519541025,
0.011583983898162842,
0.011605501174926758,
-0.008625481277704239,
0.027632296085357666,
0.015999719500541687,
-0.04825032129883766,
-0.008486595004796982,
-0.010344866663217545,
0.08748894929885864,
0.039780981838703156,
-0.028704721480607986,
-0.00549027044326067,
0.08107922226190567,
-0.011455467902123928,
0.004123433493077755,
-0.020637689158320427,
-0.07193125784397125,
-0.0649883821606636,
-0.0368940569460392,
0.0413852222263813,
0.007198380772024393,
0.023141877725720406,
0.031000401824712753,
0.0588347427546978,
0.004168916959315538,
0.05294325202703476,
-0.04036875069141388,
-0.001572663546539843,
0.009474814869463444,
0.035259541124105453,
0.03507453203201294,
0.01639631949365139,
-0.0275232195854187,
0.05859200656414032,
-0.00868582259863615,
-0.045511528849601746,
0.07070266455411911,
0.029050301760435104,
-0.015980182215571404,
-0.029822053387761116,
0.03919478505849838,
0.08300156891345978,
-0.005452763754874468,
0.01706751622259617,
-0.06991337984800339,
-0.01888624206185341,
0.016320277005434036,
0.015492396429181099,
-0.02397323213517666,
-0.013800390064716339,
0.00581728108227253,
-0.021121414378285408,
-0.008390243165194988,
-0.02674342505633831,
0.007482300512492657,
-0.03188806772232056,
-0.015125609934329987,
0.019437268376350403,
-0.039331693202257156,
-0.024693723767995834,
-0.007641910575330257,
0.07430525124073029,
0.015827471390366554,
-0.02880781516432762,
0.055480871349573135,
0.009980721399188042,
-0.002112394431605935,
0.023173220455646515,
-0.0766948014497757,
0.03195451200008392,
-0.02283756248652935,
0.018459176644682884,
0.018589498475193977,
-0.02566913329064846,
-0.014589146710932255,
0.033194031566381454,
0.006661816965788603,
0.008822922594845295,
0.006326815579086542,
-0.013151361607015133,
-0.04114638641476631,
0.019007762894034386,
0.03215709701180458,
-0.030281584709882736,
0.003380528185516596,
-0.028169183060526848,
0.08255043625831604,
0.00014823469973634928,
-0.008400415070354939,
0.03080088645219803,
-0.02670135349035263,
0.02443525195121765,
-0.0033374980557709932,
0.019804034382104874,
-0.053232766687870026,
-0.016879094764590263,
0.029047507792711258,
-0.0028698418755084276,
0.03858484700322151,
0.06375082582235336,
-0.030641432851552963,
0.07160189747810364,
-0.018163254484534264,
0.06384436786174774,
-0.052005667239427567,
-0.006542256101965904,
-0.0020712297409772873,
0.03419363871216774,
-0.028866754844784737,
0.04161448031663895,
-0.023443490266799927,
-0.008276239037513733,
-0.03181624040007591,
-0.0280445609241724,
-0.0044181253761053085,
0.021566759794950485,
0.023432351648807526,
-0.01282672118395567,
0.03303162753582001,
-0.017315831035375595,
-0.03215108811855316,
-0.08223096281290054,
-0.08239778131246567,
-0.005948880687355995,
-0.02270185761153698,
-0.04784999042749405,
-0.04889952391386032,
-0.005310708656907082,
0.06030117720365524,
-0.0025338404811918736,
0.005201264750212431,
0.020285649225115776,
-0.04287174344062805,
-0.02770565077662468,
-0.01539645530283451,
-0.0271096620708704,
-0.044778693467378616,
0.03842124342918396,
-0.015334348194301128,
-0.03029867261648178,
0.0627482533454895,
-0.019201286137104034,
0.015170322731137276,
0.024318452924489975,
-0.034262046217918396,
-0.026808131486177444,
0.04142027720808983,
-0.04858619347214699,
-0.028741126880049706,
0.06127136945724487,
-0.0005330884014256299,
-0.0006170750712044537,
-0.015153775922954082,
-0.04194683954119682,
0.020240195095539093,
0.01708873175084591,
-0.009336888790130615,
-0.0023865867406129837,
-0.00597904110327363,
-0.015506532043218613,
-0.030660847201943398,
0.031675223261117935,
-0.012398838065564632,
-0.001408931682817638,
0.008723710663616657,
0.02338065579533577,
0.01638396456837654,
-0.0037390345241874456,
0.05900673195719719,
-0.09987474977970123,
-0.0025804482866078615,
-0.07775022089481354,
0.0039839535020291805,
-0.017763761803507805,
-0.0029416305478662252,
0.04231991618871689,
0.02366071566939354,
0.022984882816672325,
0.02093830518424511,
0.08013545721769333,
0.044143084436655045,
-0.021034536883234978,
0.0343916080892086,
-0.016929766163229942,
-0.003181916894391179,
-0.021383345127105713,
0.006193571258336306,
0.01837739534676075,
0.0525611937046051,
0.011645461432635784,
0.0027548230718821287,
-0.020556464791297913,
-0.024288902059197426,
0.031362567096948624,
0.005804792977869511,
-0.005081694107502699,
-0.01293890830129385,
0.011200846172869205,
0.00874262023717165,
-0.05033230036497116,
-0.030302412807941437,
-0.002687859581783414,
-0.04739999398589134,
-0.05977519601583481,
0.004352617543190718,
0.03332922235131264,
-0.02429772913455963,
-0.06505187600851059,
-0.018327437341213226,
0.024413401260972023,
0.009532293304800987,
0.04063860699534416,
0.008774739690124989,
0.020008495077490807,
0.03346533700823784,
0.03873259946703911,
0.002350876107811928,
0.08691488206386566,
-0.07194057106971741,
-0.01530301384627819,
-0.02531462348997593,
0.012827136553823948,
-0.005710134748369455,
0.016714680939912796,
-0.022376637905836105,
-0.05508695915341377,
0.005217387806624174,
0.06426410377025604,
0.018922025337815285,
-0.02662392519414425,
0.014205954037606716,
0.04493962973356247,
-0.01781187579035759,
0.048701051622629166,
0.0015288071008399129,
0.028865212574601173,
0.10215068608522415,
0.04241514950990677,
0.08032988011837006,
0.0750812366604805,
0.01726299338042736,
-0.0016472487477585673,
-0.032449252903461456,
0.01790347881615162,
0.02575099840760231,
-0.08395697921514511,
0.06707152724266052,
0.0513845756649971,
0.046716827899217606,
-0.010706156492233276,
-0.00894687045365572,
-0.0335325263440609,
0.04320189356803894,
-0.08132538199424744,
-0.022311683744192123,
0.016787610948085785,
-0.03304645046591759,
-0.024797242134809494,
0.005973513703793287,
0.011696584522724152,
-0.04108015447854996,
0.01866229623556137,
0.04498644918203354,
-0.022544367238879204,
-0.01982250064611435,
-0.02780020423233509,
-0.0774710550904274,
0.02947160042822361,
-0.047640565782785416,
-0.03499419614672661,
-0.012228033505380154,
0.029981710016727448,
-0.04451696574687958,
0.016922125592827797,
0.010913999751210213,
-0.014297833666205406,
0.010458412580192089,
-0.011029249988496304,
-0.04049355909228325,
-0.01876598782837391,
-0.005212957970798016,
0.027014151215553284,
0.03377314656972885,
-0.016755715012550354,
-0.03824269399046898,
0.03324763476848602,
-0.02155032567679882,
0.01648150570690632,
0.016716619953513145,
0.005596127361059189,
-0.014522396959364414,
-0.027726510539650917,
-0.06049896031618118,
0.00485238479450345,
0.01724994368851185,
-0.05908617004752159,
-0.013894777745008469,
-0.011140702292323112,
0.00836484506726265,
0.05395590513944626,
0.010997994802892208,
0.03595432639122009,
-0.016157327219843864,
-0.007221703417599201,
0.02790527045726776,
0.065498948097229,
0.04609515145421028,
0.0587240532040596,
-0.038749463856220245,
0.05366092175245285,
-0.04463633894920349,
0.07772187143564224,
0.046903226524591446,
0.00006792501517338678,
0.04220830276608467,
0.029475802555680275,
0.030097289010882378,
0.0022064053919166327,
0.030435359105467796,
0.049843765795230865,
0.02650391310453415,
-0.038436051458120346,
0.0023586649913340807,
-0.020729565992951393,
0.02769399806857109,
-0.042825184762477875,
-0.06548932194709778,
-0.02205931581556797,
-0.055450376123189926,
-0.061275914311409,
-0.02362968400120735,
-0.032579272985458374,
0.06013628467917442,
-0.04460866376757622,
0.04028989002108574,
-0.059153199195861816,
0.013827509246766567,
0.045138537883758545,
0.013570473529398441,
-0.003711935132741928,
0.024631153792142868,
0.015344688668847084,
-0.021572113037109375,
0.034745000302791595,
0.0036739225033670664,
0.06611014157533646,
-0.043822385370731354,
0.0662619024515152,
-0.04184431955218315,
0.018890080973505974,
0.01681574061512947,
-0.012703631073236465,
-0.060492098331451416,
-0.005512256175279617,
0.011891483329236507,
0.030235206708312035,
-0.03935978561639786,
-0.020387711003422737,
0.043413061648607254,
0.04887095093727112,
-0.013399889692664146,
-0.027087323367595673,
-0.007762924302369356,
0.049472980201244354,
-0.046491850167512894,
0.04031122103333473,
-0.02690926194190979,
-0.014314515516161919,
0.012968191877007484,
-0.018644997850060463,
0.01938805915415287,
0.011633145622909069,
-0.03698277100920677,
-0.0244275014847517,
0.030070006847381592,
0.03798678517341614,
-0.02065391279757023,
-0.08266318589448929,
0.0030577273573726416,
0.026440782472491264,
0.04774956777691841,
-0.007871013134717941,
-0.01917746104300022,
0.001226249965839088,
0.008230937644839287,
0.018848923966288567,
0.06328831613063812,
0.04186059534549713,
0.01506813708692789,
0.04329352453351021,
-0.09626160562038422,
-0.11678914725780487,
0.009915581904351711,
0.01855172961950302,
-0.004714245907962322,
0.02786058560013771,
0.007343437988311052,
-0.050717711448669434,
0.03915642201900482,
-0.02666291408240795,
0.008161978796124458,
-0.009169339202344418,
-0.013197735883295536,
0.04648878425359726,
-0.028194710612297058,
-0.023205099627375603,
0.06611615419387817,
-0.06747354567050934,
-0.07019910216331482,
-0.05076410248875618,
-0.05028584226965904,
-0.03652295470237732,
0.0016346242045983672,
0.013314475305378437,
-0.06160920858383179,
-0.07865685224533081,
0.04070436954498291,
0.04355539754033089,
-0.03448218107223511,
0.013799043372273445,
0.04529177024960518,
0.013156362809240818,
0.034963883459568024,
-0.05502032861113548,
-0.03349611908197403,
0.04786238446831703,
-0.019944146275520325,
-0.03558434173464775,
-0.03578057140111923,
0.038753874599933624,
-0.03412816300988197,
0.014951655641198158,
0.01767936535179615,
-0.027784200385212898,
0.0020637272391468287,
-0.04018966853618622,
-0.012458520010113716,
0.036192648112773895,
-0.01666630618274212,
-0.04771330952644348,
0.00932561419904232,
0.0691278949379921,
0.04763270542025566,
-0.021660784259438515,
-0.0031396588310599327,
-0.03365083411335945,
0.0035034669563174248,
-0.03275888413190842,
-0.002682645572349429,
-0.007366419304162264,
0.06927952915430069,
0.02067296952009201,
0.06829699128866196,
0.08310338109731674,
-0.0019349738722667098,
0.01404818706214428,
-0.002737370552495122,
0.016862772405147552,
0.01986432448029518,
-0.06328733265399933,
0.00598534382879734,
0.06385812908411026,
-0.00398346409201622,
-0.006321533117443323,
0.06331011652946472,
0.012280220165848732,
0.04120185971260071,
0.06433287262916565,
0.007977239787578583,
0.021216899156570435,
-0.038696594536304474,
-0.025966404005885124,
0.020639434456825256,
0.01959412358701229,
0.02855362743139267,
-0.05052017793059349,
0.00712962681427598,
-0.052750520408153534,
0.04801909998059273,
0.006250158883631229,
0.00853373110294342,
0.014355522580444813,
0.05733205005526543,
-0.009577151387929916,
-0.018755758181214333,
-0.05065717175602913,
0.02231363207101822,
0.03984531760215759,
0.003502819687128067,
-0.013968653976917267,
-0.11699927598237991,
0.028633594512939453,
0.06090838834643364,
0.028509045019745827,
0.013238306157290936,
0.01124910544604063,
0.05609137564897537,
0.021285105496644974,
-0.05266108363866806,
0.01899264007806778,
0.02644483745098114,
0.0115538714453578,
-0.010082601569592953,
-0.011235848069190979,
0.039945293217897415,
0.022435443475842476,
-0.03103008307516575,
0.022257091477513313,
-0.026616567745804787,
-0.03009982220828533,
-0.022126277908682823,
0.030862044543027878,
0.024843387305736542,
-0.039323002099990845,
0.03068586438894272,
-0.06873010098934174,
0.013991919346153736,
0.016195788979530334,
0.010884455405175686,
-0.0003912299871444702,
-0.021264953538775444,
-0.020907172933220863,
-0.0015842083375900984,
-0.014137569814920425,
-0.04759345203638077,
-0.029478009790182114,
0.0025172585155814886,
-0.0283984262496233,
-0.0053460258059203625,
-0.008004854433238506,
-0.0029494445770978928,
-0.04028796777129173,
0.009008578024804592,
0.03805585578083992,
0.003488332498818636,
-0.03276565670967102,
-0.0017770957201719284,
-0.010749558918178082,
-0.0587780736386776,
0.0039090304635465145,
-0.0072752367705106735,
0.01852954551577568,
-0.02360084094107151,
0.012419577687978745,
-0.004016082733869553,
-0.03535250574350357,
0.07798926532268524,
-0.017700400203466415,
0.0081853698939085,
0.013679679483175278,
-0.00899599026888609,
0.036621589213609695,
0.024915434420108795,
-0.07513830065727234,
0.05179528146982193,
0.02532687783241272,
0.030207665637135506,
0.03559993952512741,
-0.028378721326589584,
0.0035482875537127256,
0.004773826338350773,
0.004515386652201414,
-0.04084274172782898,
0.04153940826654434,
0.08163580298423767,
0.010321157984435558,
-0.007579941768199205,
-0.04734237492084503,
-0.0663183182477951,
-0.008812641724944115,
0.025269411504268646,
-0.0005896108341403306,
-0.007252618204802275,
0.013209600001573563,
0.05604270473122597,
-0.006224704906344414,
-0.013600085861980915,
0.032836467027664185,
0.021188365295529366,
0.00039293471490964293,
0.001384112169034779,
0.0011778628686442971,
-0.042203422635793686,
-0.002491279039531946,
0.0624987967312336,
0.026800423860549927,
-0.030411187559366226,
0.00024146870418917388,
0.008041514083743095,
0.010835535824298859,
0.028956398367881775,
0.031534235924482346,
-0.0313514806330204,
-0.04348425567150116,
0.02755853720009327,
0.04020733758807182,
-0.043033137917518616,
0.06449201703071594,
0.03661009669303894,
-0.05573931708931923,
-0.005370062310248613,
-0.057300910353660583,
0.02097971923649311,
0.031193813309073448,
-0.03009790927171707,
0.020916637033224106,
0.027479611337184906,
-0.019471313804388046,
-0.03722694516181946,
0.008954656310379505,
-0.014256165362894535,
-0.06969823688268661,
0.009284484200179577,
0.027810631319880486,
0.011763134971261024,
-0.05008070543408394,
-0.043616220355033875,
-0.0036572362296283245,
-0.038346562534570694,
0.0020119640976190567,
-0.06565946340560913,
-0.013882934115827084,
-0.016726847738027573,
0.07005089521408081,
0.027209768071770668,
-0.05520884692668915,
-0.032972194254398346,
-0.04595369100570679,
0.05129077658057213,
0.01219245046377182,
-0.01887623965740204,
-0.030278921127319336,
0.042983781546354294,
-0.010185728780925274,
0.004106292501091957,
0.0012546263169497252,
-0.02636357769370079,
0.015229814685881138,
0.015821166336536407,
0.008597449399530888,
0.043779242783784866,
-0.0031367121264338493,
0.038999587297439575,
-0.024839576333761215,
-0.01434006355702877,
0.02687446027994156,
0.03440066799521446,
-0.0007716083782725036,
0.007550523616373539,
-0.018181538209319115,
-0.04999596253037453,
0.0704113021492958,
-0.07515387237071991,
-0.02191389724612236,
0.011596481315791607,
0.03277258947491646,
-0.0023180705029517412,
0.04447835311293602,
0.015115723945200443,
-0.031086908653378487,
-0.0063305143266916275,
-0.04431993514299393,
-0.03610081598162651,
-0.03218069672584534,
-0.004876420367509127,
-0.030970057472586632,
0.017170768231153488,
-0.06438270211219788,
-0.027116496115922928,
0.005418821237981319,
0.002584257163107395,
0.0009718265500850976,
0.024756159633398056,
-0.06662669032812119,
-0.022593632340431213,
-0.0029334044083952904,
-0.030590038746595383,
-0.009088121354579926,
-0.022049617022275925,
-0.0015323968837037683,
0.017815088853240013,
0.006280951667577028,
-0.07747986912727356,
0.021416647359728813,
-0.06848516315221786,
0.05085410550236702,
0.007588726002722979,
0.03842335194349289,
-0.03268032521009445,
-0.02495482750236988,
0.02932501584291458,
0.009004932828247547,
0.03617356717586517,
-0.05004528537392616,
0.03322722762823105,
0.07024262100458145,
-0.031378746032714844,
0.00835560541599989,
-0.007564798463135958,
0.037086326628923416,
0.059051547199487686,
-0.045022182166576385,
0.013960848562419415,
-0.05849099159240723,
-0.0503188818693161,
-0.019922010600566864,
0.07132235914468765,
-0.02464052103459835,
-0.006468701176345348,
-0.02347031980752945,
0.003330700332298875,
-0.01966863125562668
] |
<p>I'm a first year graduate student in Mathematical Physics, and I am trying to generalise a certain method involving the so-called "Differential realizations" of certain algebras. The problem I'm having is that in papers <a href="http://arxiv.org/pdf/hep-th/9810074.pdf" rel="nofollow">here</a> (Page 8) and <a href="http://arxiv.org/pdf/hep-th/9804191.pdf" rel="nofollow">here</a> (Page 5-6), they express a certain type of algebra in terms of differential operators and I'm not sure how that is done. My goal is to see if such methods can be generalised to other algebras to test for a certain property called "Shape Invariance" which is mentioned in the latter paper. I'm wondering if anyone here has ever heard of differential realizations and has any idea how they can be derived for other algebras?</p> | g9239 | [
0.012141394428908825,
-0.060047540813684464,
0.0030112999957054853,
-0.026992959901690483,
0.04054926335811615,
0.021389447152614594,
0.052025213837623596,
0.029770106077194214,
-0.05420428887009621,
0.007037076633423567,
-0.05435996130108833,
0.0010895824525505304,
0.023123890161514282,
0.029708195477724075,
0.0059847705997526646,
-0.04193120077252388,
0.021786533296108246,
-0.05421948805451393,
0.008588442578911781,
-0.00016012346895877272,
0.014836406335234642,
0.05292367935180664,
-0.036027275025844574,
-0.006954113487154245,
0.04317135363817215,
-0.029535694047808647,
0.012261654250323772,
-0.04825880751013756,
-0.027929652482271194,
-0.003681437810882926,
-0.007810322567820549,
-0.009450012817978859,
0.06014033034443855,
0.0005689302342943847,
-0.03752429410815239,
0.01469652634114027,
0.07715942710638046,
0.03056458756327629,
0.017611293122172356,
-0.00601538410410285,
0.016121352091431618,
-0.03802412003278732,
-0.02029823698103428,
0.025973284617066383,
-0.02752835862338543,
-0.021474052220582962,
-0.007615972775965929,
0.01681036688387394,
0.013589556328952312,
-0.008510563522577286,
0.054621029645204544,
0.03324488550424576,
0.07186969369649887,
-0.1166943833231926,
-0.05980316177010536,
-0.00025036439183168113,
0.0012000356800854206,
0.006316459737718105,
0.04680204391479492,
-0.06851667910814285,
-0.05524076148867607,
0.0377180352807045,
0.012602468952536583,
0.020973503589630127,
0.0676310732960701,
-0.00154971145093441,
-0.03426055610179901,
-0.05948925390839577,
-0.04112836718559265,
-0.0032086821738630533,
-0.0068863253109157085,
0.02036909945309162,
0.039306554943323135,
-0.019078267738223076,
0.0037080564070492983,
-0.011666480451822281,
0.08674007654190063,
-0.012586280703544617,
-0.006375179626047611,
-0.01751650869846344,
-0.06684274226427078,
0.02480040304362774,
0.05953962355852127,
0.011947093531489372,
-0.007995471358299255,
0.03533939644694328,
0.03340991958975792,
0.012021258473396301,
0.033564940094947815,
0.0050938013009727,
0.027819178998470306,
0.040846168994903564,
0.023546479642391205,
0.03877265751361847,
-0.07942052185535431,
-0.020798655226826668,
-0.010945918038487434,
0.04529767856001854,
-0.03388255089521408,
0.009682385250926018,
-0.06208433955907822,
0.04072490707039833,
0.007236335426568985,
-0.005063295364379883,
0.03449488803744316,
-0.023767393082380295,
0.02492578886449337,
-0.02117658406496048,
-0.004210814833641052,
0.004985449369996786,
-0.026387197896838188,
-0.033899929374456406,
-0.06161901727318764,
0.04947628080844879,
-0.03243723511695862,
-0.008627302944660187,
-0.0012884479947388172,
-0.02739022485911846,
-0.04769860580563545,
0.022189049050211906,
0.03943705931305885,
0.01512343529611826,
-0.013645411469042301,
0.024689720943570137,
0.023604294285178185,
0.08483727276325226,
-0.044704701751470566,
-0.023794056847691536,
0.05448813736438751,
0.004422806669026613,
0.10003998875617981,
-0.043881770223379135,
0.010793890804052353,
0.03852564096450806,
-0.0205597672611475,
0.029110012575984,
-0.008809239603579044,
0.0436878427863121,
-0.0019551021978259087,
-0.005606818478554487,
-0.029159720987081528,
-0.030376119539141655,
-0.04825643450021744,
-0.004452829249203205,
0.06164907291531563,
0.006117162294685841,
0.030721284449100494,
-0.01615956611931324,
-0.04053748771548271,
0.049202244728803635,
0.00973776075989008,
0.08274924010038376,
0.05375839024782181,
-0.020002365112304688,
0.01612813025712967,
0.021184908226132393,
-0.008006521500647068,
-0.01257940474897623,
-0.012103285640478134,
-0.014152688905596733,
0.04954729601740837,
0.008984403684735298,
0.0006585913361050189,
-0.013296500779688358,
-0.0016189346788451076,
-0.021102339029312134,
0.010046575218439102,
-0.033176667988300323,
0.008241424337029457,
-0.07215481251478195,
-0.02008729986846447,
0.06522303074598312,
-0.0016081546200439334,
-0.01762690395116806,
0.04134613648056984,
0.052915528416633606,
-0.016016418114304543,
-0.04675513505935669,
0.025240402668714523,
0.043061718344688416,
-0.05864198878407478,
0.02945280633866787,
0.007455659098923206,
-0.01949666254222393,
0.07865197211503983,
0.018037371337413788,
0.05851757898926735,
-0.008221101015806198,
-0.08536747843027115,
-0.02452891133725643,
0.004245426971465349,
0.038584981113672256,
0.02692827582359314,
-0.0056664831936359406,
-0.007082734256982803,
0.03543047234416008,
0.07085896283388138,
-0.03064994141459465,
0.005495220888406038,
0.07446425408124924,
0.016866451129317284,
0.0879795104265213,
0.08123970031738281,
0.051430199295282364,
0.012838746421039104,
-0.018170883879065514,
-0.03066394291818142,
-0.02663157321512699,
0.06631715595722198,
0.00037693174090236425,
0.00371408648788929,
-0.05467523634433746,
0.01012892834842205,
-0.024998318403959274,
-0.008204384706914425,
0.03976862505078316,
0.0337752103805542,
-0.04824219271540642,
-0.022672070190310478,
-0.009216426871716976,
-0.00421910360455513,
-0.041308045387268066,
-0.04111363738775253,
0.020589187741279602,
-0.06805523484945297,
0.045220997184515,
-0.011828119866549969,
0.012049121782183647,
0.0006597891915589571,
-0.014572530053555965,
-0.028982212767004967,
0.026969803497195244,
-0.036517560482025146,
-0.08822014927864075,
0.059194061905145645,
-0.013556643389165401,
0.012865199707448483,
-0.03496728464961052,
0.0335419662296772,
0.053627610206604004,
-0.008432460017502308,
0.011361202225089073,
0.02861897461116314,
0.00626418087631464,
-0.0005525340675376356,
-0.0357501283288002,
0.030288320034742355,
0.029136911034584045,
0.031782329082489014,
0.028266044333577156,
-0.017150383442640305,
-0.04540109261870384,
-0.017708588391542435,
-0.03057302162051201,
0.006787111051380634,
0.0019986964762210846,
-0.030501924455165863,
0.009431731887161732,
0.048573125153779984,
0.0032217265106737614,
-0.03963936120271683,
0.00669498834758997,
-0.0192039143294096,
0.04217799752950668,
-0.05256057530641556,
-0.03820833936333656,
0.04421951249241829,
-0.04850894957780838,
-0.00083149567944929,
0.016431674361228943,
-0.016530796885490417,
0.024379823356866837,
0.015148892067372799,
-0.03258030116558075,
-0.015946971252560616,
-0.01073523424565792,
-0.02309148944914341,
-0.04587172716856003,
0.005447152070701122,
0.03261866047978401,
0.03479995205998421,
0.0024276161566376686,
-0.01377058681100607,
0.008260386064648628,
0.09600519388914108,
-0.005321017932146788,
0.005982541479170322,
-0.03381456434726715,
-0.001059398869983852,
0.003916861955076456,
0.012462325394153595,
0.015018654055893421,
-0.037989500910043716,
-0.02046499215066433,
-0.0646061971783638,
-0.0371234193444252,
-0.06813815236091614,
-0.03925536572933197,
-0.016403067857027054,
0.05116039514541626,
-0.0657796785235405,
-0.04930504038929939,
0.039917849004268646,
-0.05825008451938629,
0.048117853701114655,
0.048419639468193054,
-0.020266791805624962,
-0.024622082710266113,
0.031212935224175453,
-0.0019083194201812148,
-0.055302076041698456,
-0.010884558781981468,
-0.05311311036348343,
-0.0481477715075016,
0.009944419376552105,
0.009890440851449966,
-0.022912917658686638,
-0.0005082963034510612,
0.03599309176206589,
-0.026633912697434425,
0.013919724151492119,
-0.030565861612558365,
0.06986421346664429,
0.03184858337044716,
0.028278466314077377,
0.0032834764569997787,
-0.03488767892122269,
0.030411282554268837,
-0.034622181206941605,
-0.04405735805630684,
0.02492661029100418,
-0.013674748130142689,
-0.04236922040581703,
0.0010993831092491746,
-0.012084607034921646,
-0.04905402660369873,
-0.02179192192852497,
-0.0018624800723046064,
0.02445213869214058,
-0.052992645651102066,
-0.007999640889465809,
-0.03961705416440964,
-0.04520023986697197,
0.013126641511917114,
-0.03735528513789177,
-0.044762659817934036,
-0.06776479631662369,
0.060665398836135864,
-0.008317412808537483,
0.0061222584918141365,
0.015125368721783161,
-0.011418064124882221,
0.0740581750869751,
-0.05490834638476372,
0.02398662269115448,
-0.01515453215688467,
0.07423987239599228,
0.03181992843747139,
0.001933109830133617,
0.01456863060593605,
0.00040716418880037963,
-0.006072402466088533,
0.01721825636923313,
0.025899138301610947,
0.04092701897025108,
0.016223285347223282,
0.03073309175670147,
-0.015079719945788383,
-0.03190268203616142,
0.007781356107443571,
0.028487756848335266,
-0.044093742966651917,
0.01704854518175125,
0.0003559094911906868,
0.002535709412768483,
-0.059090904891490936,
-0.0045228321105241776,
0.054520923644304276,
-0.009771895594894886,
-0.02055453695356846,
-0.02012179233133793,
0.053667325526475906,
0.06163375824689865,
0.016500916332006454,
-0.015621872618794441,
0.01897730492055416,
-0.022444680333137512,
0.049624551087617874,
-0.017984135076403618,
-0.026654871180653572,
-0.0441150963306427,
0.010694650001823902,
0.001903712167404592,
0.029754284769296646,
-0.020617274567484856,
-0.0005310846026986837,
-0.008823870681226254,
-0.005172796081751585,
-0.051991406828165054,
0.04061971232295036,
-0.030596915632486343,
-0.014002269133925438,
0.07139673829078674,
-0.0033796909265220165,
-0.008891590870916843,
-0.05907939001917839,
0.01256366167217493,
-0.05719636008143425,
0.0023898642975836992,
0.0005484522553160787,
-0.057271067053079605,
0.02383926697075367,
0.03310086205601692,
0.01641959510743618,
-0.010574709624052048,
0.052698973566293716,
0.025434674695134163,
-0.020981188863515854,
0.018789436668157578,
0.0291108638048172,
0.061211515218019485,
0.05426746979355812,
0.007048087660223246,
0.012431596405804157,
0.021810639649629593,
0.0963670164346695,
0.02914452739059925,
0.025343019515275955,
0.017531050369143486,
-0.027475589886307716,
0.004603416193276644,
-0.025725191459059715,
0.020862195640802383,
0.04034117981791496,
-0.06660585850477219,
-0.0348951630294323,
-0.040650658309459686,
0.03502904623746872,
-0.015439567156136036,
0.01007746160030365,
0.04225553572177887,
-0.0020980185363441706,
0.005507665686309338,
-0.03268186375498772,
0.02074440009891987,
-0.0066287461668252945,
-0.02862446941435337,
-0.004694158677011728,
0.04307122901082039,
0.018376247957348824,
-0.05058098956942558,
0.0011383678065612912,
0.004151599016040564,
-0.020546160638332367,
-0.06157587096095085,
-0.006976184900850058,
-0.0037047001533210278,
0.06484221667051315,
-0.002178134862333536,
-0.01752927526831627,
0.0020101757254451513,
-0.01090283039957285,
-0.01794593594968319,
0.021516185253858566,
-0.0022970831487327814,
-0.027981743216514587,
-0.08742938190698624,
0.0212563406676054,
-0.017167698591947556,
-0.040782760828733444,
0.008008921518921852,
-0.036454543471336365,
0.010245263576507568,
0.021526802331209183,
0.039387430995702744,
-0.03299757465720177,
0.0012606348609551787,
0.00036825358984060585,
-0.054061077535152435,
-0.013659939169883728,
-0.042941220104694366,
-0.009196299128234386,
0.034390341490507126,
-0.019552376121282578,
0.00775571633130312,
0.05230753868818283,
-0.007674836553633213,
-0.0010828778613358736,
0.019092297181487083,
-0.0396149568259716,
-0.005963892675936222,
0.018305392935872078,
-0.006299838423728943,
0.0012573414715006948,
-0.02107382006943226,
0.021402819082140923,
-0.028409220278263092,
-0.013274677097797394,
-0.016913268715143204,
-0.02435176819562912,
-0.027363810688257217,
0.010222799144685268,
0.02388811483979225,
-0.009275115095078945,
0.031877461820840836,
0.00436402577906847,
0.06570738554000854,
-0.024909766390919685,
-0.0008387010893784463,
-0.026084054261446,
-0.012149455025792122,
0.04840851202607155,
0.02219584956765175,
0.05510246008634567,
-0.025097863748669624,
-0.01846069097518921,
-0.061758458614349365,
0.05277238413691521,
-0.03957170248031616,
-0.0989852324128151,
0.010985167697072029,
-0.04880755394697189,
0.03400786221027374,
-0.02988571859896183,
0.00027867770404554904,
-0.011801485903561115,
-0.045395080000162125,
-0.07642648369073868,
0.019479500129818916,
-0.00042215982102788985,
0.046710461378097534,
-0.023109130561351776,
0.021126125007867813,
-0.0113167529925704,
0.0029420775827020407,
-0.08526323735713959,
0.036181576550006866,
0.011358940042555332,
-0.02259943075478077,
-0.004777314607053995,
0.034632354974746704,
0.01915409415960312,
0.005824289284646511,
0.02135940082371235,
-0.0699596256017685,
-0.06147894635796547,
0.00964869000017643,
0.02926544100046158,
0.015920216217637062,
0.036537230014801025,
-0.07218487560749054,
-0.028923094272613525,
-0.04310595244169235,
-0.02210431918501854,
0.022101396694779396,
0.046277403831481934,
-0.05807269737124443,
-0.058479193598032,
-0.0010925312526524067,
0.027035364881157875,
0.017966026440262794,
0.04724245145916939,
0.023142507299780846,
-0.009250807575881481,
-0.05087742954492569,
-0.025988474488258362,
0.042433083057403564,
0.06150667741894722,
0.05432159826159477,
0.09056001901626587,
-0.010071036405861378,
0.011392757296562195,
0.022784678265452385,
-0.0539962500333786,
0.01744971238076687,
-0.05648425966501236,
0.06505733728408813,
-0.06105745583772659,
0.020711347460746765,
0.06322357058525085,
0.04833310469985008,
-0.020074233412742615,
-0.0015083078760653734,
0.007032257039099932,
-0.009089185856282711,
0.011159587651491165,
-0.006909258663654327,
0.029777953401207924,
-0.023037880659103394,
-0.0014716640580445528,
-0.006770595442503691,
0.05136052891612053,
-0.02569747157394886,
-0.013504430651664734,
0.008718575350940228,
-0.0600208044052124,
0.0005255895666778088,
0.07918541878461838,
-0.009969627484679222,
-0.03810684755444527,
-0.003107319353148341,
-0.02606816031038761,
0.07306638360023499,
0.008011812344193459,
-0.029260344803333282,
0.05820540711283684,
-0.05801469460129738,
-0.0003273116599302739,
0.010679925791919231,
0.005563472397625446,
-0.015843069180846214,
0.012260784395039082,
0.006322888657450676,
0.03834667056798935,
-0.008009975776076317,
-0.03700483217835426,
-0.015891971066594124,
-0.061425138264894485,
0.050271134823560715,
-0.05334402620792389,
-0.013056347146630287,
0.058044057339429855,
-0.001537563861347735,
-0.019870270043611526,
-0.01921856589615345,
0.07798109948635101,
-0.03816616162657738,
0.015011003240942955,
0.003778893733397126,
0.03998444974422455,
-0.023487143218517303,
-0.05253057926893234,
0.0004069028946105391,
0.022537657991051674,
0.00039700555498711765,
0.05838911607861519,
0.045132797211408615,
0.10739052295684814,
0.04386434331536293,
0.044381413608789444,
-0.025361593812704086,
0.04687012732028961,
0.007624532096087933,
-0.0012590376427397132,
0.005943481344729662,
-0.02071385085582733,
0.01802210509777069,
0.004414271097630262,
-0.04398708790540695,
0.02599128521978855,
0.04721738025546074,
-0.011773446574807167,
0.012785963714122772,
0.0009542218176648021,
-0.03168558329343796,
-0.017992669716477394,
0.06258062273263931,
-0.04474275931715965,
-0.0035298122093081474,
-0.047974634915590286,
-0.02484709396958351,
-0.04523417353630066,
0.01891867257654667,
0.0063208178617060184,
-0.022012833505868912,
-0.023731853812932968,
-0.022966792806982994,
-0.02775118127465248,
0.004389592912048101,
0.062282975763082504,
0.016755258664488792,
-0.0847514346241951,
0.0320756696164608,
0.02048465795814991,
-0.0038149456959217787,
-0.04076843708753586,
-0.008727062493562698,
0.05959099903702736,
-0.023082375526428223,
-0.038438837975263596,
0.009720438160002232,
0.04551739618182182,
-0.005942016374319792,
0.0071618263609707355,
-0.06780832260847092,
-0.03441590070724487,
0.01833515428006649,
-0.027817532420158386,
-0.023615801706910133,
-0.02912520244717598,
-0.05369510129094124,
0.007715989835560322,
0.07399579137563705,
-0.03070356883108616,
-0.022830938920378685,
-0.040230803191661835,
0.07472692430019379,
0.0758732408285141,
-0.009999571368098259,
-0.024618059396743774,
-0.042243968695402145,
-0.00704207131639123,
0.04084102064371109,
-0.024120116606354713,
0.0196552611887455,
-0.03896931931376457,
-0.04162128269672394,
0.0024097624700516462,
-0.017534693703055382,
0.006435138173401356,
0.0016541547374799848,
-0.007709763012826443,
-0.023846976459026337,
0.003366965800523758,
0.007094422820955515,
0.018045835196971893,
-0.06216978654265404,
-0.04864870384335518,
-0.0678715631365776,
-0.0054306150414049625,
0.030540017411112785,
0.013866315595805645,
-0.012001991271972656,
-0.06998835504055023,
0.017313364893198013,
-0.031328700482845306,
0.005726246628910303,
0.05818263068795204,
0.05042840912938118,
0.024752875789999962,
0.03665296733379364,
0.019628163427114487,
-0.023188747465610504,
0.050386618822813034,
0.0042625609785318375,
0.05705063045024872,
-0.006436262745410204,
-0.053564492613077164,
0.019827669486403465,
0.01763324812054634,
-0.04113402217626572,
-0.02962425723671913,
-0.0156130101531744,
-0.0335332415997982,
0.044045720249414444,
-0.02499569207429886,
0.018859559670090675,
0.05102452635765076,
-0.02780902199447155,
-0.06279110163450241,
-0.03683633729815483,
0.0022036866284906864,
-0.03342847898602486,
0.03514863923192024,
-0.038719017058610916,
0.0046327980235219,
0.012167074717581272,
0.03628868609666824,
0.013976620510220528,
0.0452512688934803,
-0.026275061070919037,
0.035378798842430115,
-0.0012878006091341376,
0.009678706526756287,
-0.07973116636276245,
-0.02025674842298031,
-0.04324468597769737,
0.020469684153795242
] |
<p>All know that Inflation may solve some of the problems of the Standard Model of Cosmology and today we suppose that the field responsible for that is the inflaton. The properties of the potential $V(\varphi)$ allow via the momentum-energy tensor to define a barotropic fluid for which $$p=-\rho$$ and when the slow-roll conditions $\epsilon\ll1$, $|\eta|\ll1$ are satisfied, this fluid with $w=-1$ has some sort of negative pressure or repulsive gravity that allow the expansion of Universe. So a scalar field may act like a cosmological constant $\Lambda$ giving some energy to the vacuum. Now seems that the Universe undergoes an epoch of "second inflation" with $$\ddot{a}>0.$$ My question is: why there is no exponential inflation like the old one if today the dominant fraction of the Universe budget is again a sort of cosmological constant $\Lambda$?
Maybe the two fluids are of completely different kind, or the behavior depends on the energy and temperature conditions or i am wrong something? </p> | g9240 | [
0.051936015486717224,
-0.04587900638580322,
0.011954288929700851,
0.011679433286190033,
0.0260920412838459,
0.03260175883769989,
-0.019076215103268623,
0.024765262380242348,
-0.08747587352991104,
-0.01585499756038189,
0.028001712635159492,
0.004467732738703489,
0.044057976454496384,
-0.003749737748876214,
0.021252134814858437,
0.024652209132909775,
0.022412791848182678,
-0.07616527378559113,
0.03579024598002434,
-0.040137164294719696,
0.003924319054931402,
0.022301893681287766,
0.040847744792699814,
-0.05594443157315254,
0.005759129766374826,
-0.010712964460253716,
0.018738532438874245,
0.005762105342000723,
-0.006786349695175886,
0.00005807081834063865,
0.08787983655929565,
0.01791803352534771,
0.043647900223731995,
-0.05199790745973587,
-0.008434507064521313,
-0.010667997412383556,
0.032319821417331696,
0.024096008390188217,
0.01763085648417473,
-0.028562482446432114,
0.016085147857666016,
0.01906760223209858,
0.02074107900261879,
0.062254685908555984,
-0.010133207775652409,
-0.008059697225689888,
-0.015201904810965061,
0.040017709136009216,
0.04935164749622345,
-0.11609570682048798,
0.002910782815888524,
0.017213191837072372,
-0.0226383525878191,
0.008981846272945404,
-0.05650941655039787,
0.006495620124042034,
0.027891645208001137,
0.02111465483903885,
0.01336356345564127,
0.0032585691660642624,
-0.029747888445854187,
-0.04428436607122421,
0.07111024856567383,
-0.02442447654902935,
0.013251757249236107,
0.0015676113544031978,
-0.022105460986495018,
-0.06384684145450592,
-0.003818071447312832,
-0.019305258989334106,
-0.0330013744533062,
0.002727602608501911,
-0.009742142632603645,
-0.024713680148124695,
-0.028637399896979332,
0.06577916443347931,
0.053124453872442245,
-0.05279841274023056,
-0.008638838306069374,
-0.037032004445791245,
0.017868313938379288,
-0.0012145389337092638,
0.019104087725281715,
0.0391390435397625,
0.031014984473586082,
-0.04188620299100876,
0.010567493736743927,
0.020294059067964554,
-0.02980671264231205,
-0.024515174329280853,
-0.001364381518214941,
-0.02838744781911373,
0.04762241989374161,
0.027231447398662567,
0.01877160556614399,
-0.015883801504969597,
-0.017032602801918983,
0.07721781730651855,
-0.022643903270363808,
0.018200164660811424,
-0.0024960096925497055,
0.03887663409113884,
0.1102399006485939,
0.006267722696065903,
0.0021719045471400023,
-0.008540874347090721,
0.04817700758576393,
-0.0241991076618433,
0.001495502539910376,
-0.039776239544153214,
0.008312239311635494,
-0.0071471151895821095,
-0.023456666618585587,
-0.043881725519895554,
-0.024654274806380272,
-0.01944383978843689,
0.03521239385008812,
-0.004106627311557531,
0.01839612051844597,
0.024140017107129097,
-0.04688014090061188,
-0.012289062142372131,
0.04401219263672829,
0.011274056509137154,
-0.025741657242178917,
-0.013080100528895855,
0.0345265194773674,
0.0005441744579002261,
0.005160217639058828,
-0.029537154361605644,
0.05108628422021866,
-0.0006294365739449859,
-0.02526998519897461,
-0.017236076295375824,
0.06417963653802872,
-0.02672472782433033,
-0.023053526878356934,
0.023744922131299973,
-0.0037645220290869474,
-0.00029732869006693363,
0.003091480815783143,
-0.06169532239437103,
0.013889756053686142,
-0.004358278587460518,
-0.01764804497361183,
0.038169313222169876,
0.02921193465590477,
-0.01685062050819397,
-0.02555265463888645,
0.003137636464089155,
-0.013529971241950989,
0.053423818200826645,
0.000777397130150348,
0.03542763367295265,
-0.05927664786577225,
0.03936506062746048,
0.0125019121915102,
0.013598437421023846,
-0.0031032483093440533,
-0.024250753223896027,
0.02110612764954567,
0.0026601129211485386,
0.02419394813477993,
0.0038348836824297905,
-0.008217088878154755,
0.03632379695773125,
-0.008137150667607784,
-0.05060926079750061,
-0.013865098357200623,
0.0028504214715212584,
-0.03987405076622963,
0.017477791756391525,
-0.011874695308506489,
-0.009403216652572155,
0.04942066967487335,
0.002006352413445711,
0.04027803987264633,
0.03046463243663311,
-0.04670031741261482,
-0.037610068917274475,
-0.022573551163077354,
-0.012652304023504257,
-0.017407020553946495,
0.012710840441286564,
0.05911719799041748,
0.009691757149994373,
0.013204751536250114,
0.04764384403824806,
-0.019166724756360054,
-0.0404326356947422,
0.02265501581132412,
0.031123165041208267,
0.02700725942850113,
-0.012005986645817757,
0.017085453495383263,
-0.0013614253839477897,
0.058905329555273056,
-0.06428617984056473,
-0.06919865310192108,
0.0047842212952673435,
-0.0005450643948279321,
0.0393901951611042,
0.06128809601068497,
-0.048687808215618134,
-0.03446260467171669,
0.03675636276602745,
-0.003087245859205723,
-0.010098863393068314,
0.048739902675151825,
-0.03574733808636665,
0.02110644057393074,
-0.08484609425067902,
0.004100360441952944,
-0.014064105227589607,
-0.013202274218201637,
-0.03569473326206207,
0.02453598380088806,
0.01280937995761633,
-0.0386064313352108,
0.031237244606018066,
-0.05196978524327278,
0.012508096173405647,
0.05427193641662598,
-0.02587532252073288,
0.003631936153396964,
-0.02352822758257389,
0.0052644009701907635,
0.005004556383937597,
0.013886572793126106,
0.026295926421880722,
-0.03359754756093025,
0.031139492988586426,
-0.01084523182362318,
0.03605605289340019,
0.0417114794254303,
-0.03090561553835869,
0.04163370281457901,
0.02750568464398384,
-0.0018904188182204962,
0.001240816549398005,
-0.010806165635585785,
0.025750523433089256,
-0.0304773710668087,
0.03156164661049843,
0.08961588144302368,
-0.07958181947469711,
-0.005484696011990309,
-0.012942265719175339,
-0.03784209117293358,
0.04923015087842941,
0.03063010983169079,
-0.05930954962968826,
-0.035855237394571304,
-0.010730583220720291,
-0.012600060552358627,
-0.045198697596788406,
0.027860786765813828,
0.025137457996606827,
-0.017223767936229706,
-0.02687445841729641,
0.05186982825398445,
0.008498309180140495,
0.026270033791661263,
0.0317542627453804,
-0.01565064676105976,
0.001140241278335452,
-0.057183075696229935,
0.031481239944696426,
-0.06693802028894424,
0.01055060513317585,
0.0028535572346299887,
0.007768341805785894,
0.0029987115412950516,
0.005561721511185169,
0.06816768646240234,
0.004836531355977058,
-0.015169400721788406,
-0.04164711385965347,
0.017300259321928024,
-0.04236878827214241,
0.006573024671524763,
-0.02787812240421772,
-0.002896893536671996,
-0.004688960500061512,
-0.017072347924113274,
-0.04334850609302521,
-0.030867794528603554,
0.009778640232980251,
0.017509041354060173,
0.018020182847976685,
0.04438157379627228,
0.02110711671411991,
-0.08914235234260559,
0.022264758124947548,
-0.017848318442702293,
-0.005294320173561573,
-0.003938205540180206,
-0.04636521637439728,
-0.04702514037489891,
-0.021409502252936363,
0.03704867139458656,
-0.07679594308137894,
0.008923718705773354,
-0.02609534002840519,
0.026396622881293297,
-0.05684974789619446,
-0.014185798354446888,
0.005730742588639259,
-0.04263456538319588,
-0.01988236978650093,
0.07346169650554657,
0.09102942049503326,
0.006079623941332102,
0.027669033035635948,
-0.04232284799218178,
0.033459458500146866,
-0.0033768590074032545,
-0.05748653784394264,
0.028112979605793953,
0.01057360041886568,
0.008738088421523571,
-0.05528760328888893,
0.019136685878038406,
0.020631790161132812,
0.011214146390557289,
0.054495085030794144,
-0.05552332103252411,
-0.047874100506305695,
-0.020629270002245903,
0.0014024407137185335,
0.016025586053729057,
-0.05835998058319092,
-0.020678313449025154,
0.014528735540807247,
0.0334039181470871,
0.0544385090470314,
-0.00500664534047246,
0.03150734677910805,
0.06820298731327057,
0.04639379680156708,
-0.05255192518234253,
0.03932482376694679,
-0.02411160059273243,
0.04938732087612152,
-0.022826163098216057,
0.021111436188220978,
-0.010907268151640892,
-0.009893964976072311,
0.029986558482050896,
0.01879824325442314,
0.07131484150886536,
0.002643964719027281,
0.07470779865980148,
-0.042391691356897354,
0.0053608897142112255,
0.015129944309592247,
0.061611924320459366,
-0.008678991347551346,
0.039599109441041946,
-0.04831811040639877,
-0.06499325484037399,
-0.07574557512998581,
0.01739557832479477,
0.052584726363420486,
-0.009927015751600266,
-0.032233159989118576,
0.0011750636622309685,
-0.03344282507896423,
-0.08472247421741486,
0.011664838530123234,
0.06716770678758621,
-0.014916427433490753,
0.002380331512540579,
0.019758302718400955,
0.007194208446890116,
-0.0807812437415123,
0.018973620608448982,
0.0022108075208961964,
-0.02143213339149952,
0.010569090023636818,
0.09233612567186356,
-0.04697909206151962,
-0.03556296229362488,
0.04880506545305252,
-0.0027520752046257257,
-0.011008447967469692,
-0.04107149690389633,
-0.0011564060114324093,
0.008461277931928635,
-0.11020632833242416,
0.026521163061261177,
0.014364281669259071,
0.02860819548368454,
0.025359323248267174,
0.0072156996466219425,
0.022929344326257706,
0.03660914674401283,
-0.05559391900897026,
-0.0005161684821359813,
-0.012478706426918507,
-0.01726950891315937,
-0.039188120514154434,
0.014353400096297264,
-0.019579516723752022,
-0.02181018330156803,
0.006044359412044287,
0.04334312304854393,
-0.0284759271889925,
0.03147115558385849,
-0.030280495062470436,
0.025856399908661842,
0.007989083416759968,
-0.018714478239417076,
-0.018856825307011604,
0.01815624162554741,
-0.027650021016597748,
0.08089547604322433,
-0.03762948885560036,
0.07103092223405838,
-0.0012101087486371398,
0.02578861638903618,
0.02154405042529106,
0.00991854164749384,
-0.012194941751658916,
-0.02557983063161373,
0.060219865292310715,
0.0457291454076767,
0.01849665492773056,
-0.07676706463098526,
0.003906808793544769,
0.04023163765668869,
0.006377164740115404,
0.005518838297575712,
0.027544405311346054,
0.002655724762007594,
0.02432727999985218,
-0.015545978210866451,
0.0033241265919059515,
-0.032393570989370346,
-0.0058907330967485905,
0.09853068739175797,
-0.051053378731012344,
0.01411343552172184,
-0.03154169023036957,
0.002177024958655238,
0.037795256823301315,
-0.011271864175796509,
-0.013842239044606686,
-0.006133239716291428,
-0.017272990196943283,
-0.02768649347126484,
-0.003845087718218565,
0.061915259808301926,
0.03258305788040161,
0.01763344183564186,
-0.00792703777551651,
-0.0018123891204595566,
-0.009763805195689201,
0.01739715039730072,
0.09180113673210144,
-0.0376155860722065,
-0.023275261744856834,
0.04584402218461037,
0.015374947339296341,
0.054766736924648285,
-0.03557240962982178,
-0.07331336289644241,
-0.04192918539047241,
-0.058661527931690216,
-0.025311723351478577,
0.0038556328509002924,
-0.03818435221910477,
-0.04111233353614807,
0.04248910769820213,
0.009108184836804867,
0.011398802511394024,
-0.015803303569555283,
-0.048340220004320145,
-0.0061870780773460865,
-0.03462434932589531,
0.013239553198218346,
-0.002967777196317911,
0.03918946161866188,
0.04395917057991028,
0.01166362501680851,
-0.03293507173657417,
-0.0582738034427166,
0.028442423790693283,
0.036864761263132095,
-0.0026845980901271105,
0.005190340802073479,
0.053417108952999115,
0.01732843928039074,
-0.021473480388522148,
-0.006448435131460428,
0.020975539460778236,
0.0043242378160357475,
0.016615070402622223,
0.017497286200523376,
-0.013390053994953632,
-0.03838598355650902,
-0.007295744493603706,
-0.08613725006580353,
0.009856866672635078,
0.013912570662796497,
0.01190959382802248,
0.004409903194755316,
0.02628224901854992,
-0.039213888347148895,
0.04651889204978943,
-0.01841944083571434,
-0.030142005532979965,
0.021314768120646477,
0.03905056416988373,
0.048713814467191696,
-0.06213098019361496,
0.016597241163253784,
-0.08680097758769989,
-0.008696538396179676,
-0.056902796030044556,
0.007035388145595789,
0.021709943190217018,
-0.007121684029698372,
0.040139686316251755,
0.06454131752252579,
0.024368897080421448,
0.007100939285010099,
-0.05813264101743698,
0.027570145204663277,
0.00795928854495287,
0.028091130778193474,
-0.02707502245903015,
-0.017691612243652344,
-0.05776573345065117,
0.08013930171728134,
-0.002014507306739688,
-0.0076032294891774654,
-0.0015943642938509583,
-0.0021041189320385456,
-0.03953099995851517,
0.02034672163426876,
-0.046005215495824814,
0.0038673034869134426,
-0.023201556876301765,
-0.025311961770057678,
0.007840851321816444,
-0.053960707038640976,
0.008190263994038105,
0.0103859081864357,
-0.08563030511140823,
-0.030311917886137962,
-0.010169927962124348,
0.03018820472061634,
0.06902036815881729,
-0.03766106814146042,
0.021806014701724052,
0.0487959049642086,
-0.017244257032871246,
-0.0053512356244027615,
-0.030248811468482018,
-0.016781525686383247,
0.017785293981432915,
0.014872333034873009,
0.0014982913853600621,
0.00104166055098176,
-0.02993251010775566,
0.07872836291790009,
-0.06905067712068558,
0.054960597306489944,
-0.003394190687686205,
0.008093947544693947,
0.04628729820251465,
0.06572818011045456,
-0.013513938523828983,
0.031519025564193726,
-0.007034918759018183,
-0.033199481666088104,
0.04467538371682167,
-0.014852517284452915,
-0.02281699888408184,
0.055401574820280075,
-0.029251057654619217,
0.03669234737753868,
-0.0897054374217987,
0.04304198920726776,
-0.05415261164307594,
-0.027301423251628876,
-0.060521986335515976,
0.014006366953253746,
0.012198914773762226,
-0.0261064525693655,
-0.009917928837239742,
-0.02779984660446644,
-0.07423702627420425,
-0.05340564623475075,
0.06896021217107773,
-0.03652326017618179,
-0.12864172458648682,
-0.055782660841941833,
-0.009202179498970509,
-0.005469996947795153,
-0.009803025051951408,
0.05670463666319847,
-0.05890222266316414,
-0.012197902426123619,
-0.003525238251313567,
0.017409948632121086,
0.06085120886564255,
0.02298593521118164,
0.04237972944974899,
-0.019132118672132492,
0.0065491292625665665,
-0.04084746539592743,
0.01398527529090643,
0.015048403292894363,
0.03548506274819374,
0.05964360758662224,
0.0332409143447876,
-0.03012472204864025,
-0.0037433146499097347,
0.025202490389347076,
0.00808532815426588,
0.006760689429938793,
-0.011984717100858688,
0.0019836805295199156,
0.007085451390594244,
-0.057623934000730515,
0.05159653350710869,
-0.015177889727056026,
0.00019227141456212848,
0.011716978624463081,
0.023896226659417152,
-0.005675412714481354,
0.024834109470248222,
-0.04174770042300224,
-0.040434904396533966,
-0.05174345150589943,
0.03236076235771179,
-0.06170377507805824,
-0.03174789622426033,
0.024405110627412796,
0.037504177540540695,
0.022033635526895523,
-0.017757315188646317,
-0.006599752232432365,
0.08819842338562012,
-0.014193213544785976,
0.027154866605997086,
-0.036737918853759766,
0.036652740091085434,
0.008443830534815788,
-0.005194623954594135,
0.030519230291247368,
-0.008774125948548317,
-0.04490096867084503,
0.0280672125518322,
0.004930584225803614,
-0.006446461658924818,
-0.0018118893494829535,
-0.024135835468769073,
-0.010342037305235863,
-0.018074514344334602,
-0.020797552540898323,
0.0382564552128315,
-0.019491733983159065,
-0.007328495848923922,
0.0489685945212841,
-0.1038629412651062,
0.08602503687143326,
-0.00039725060923956335,
0.008887693285942078,
-0.04334533214569092,
-0.06770578771829605,
-0.019020503386855125,
-0.0020699994638562202,
-0.017751028761267662,
-0.03301476314663887,
0.007430865429341793,
0.07303063571453094,
-0.0011255486169829965,
-0.008525819517672062,
0.006891443394124508,
0.040184374898672104,
0.008295819163322449,
-0.027348635718226433,
0.02521160989999771,
-0.0031409875955432653,
-0.011741709895431995,
0.0173632875084877,
-0.016688572242856026,
0.04713897034525871,
-0.005310290027409792,
0.024048257619142532,
-0.013846628367900848,
-0.04836707189679146,
0.0028768291231244802,
-0.020857328549027443,
-0.016332242637872696,
-0.03515889123082161,
0.00445495406165719,
0.02874576300382614,
-0.032785817980766296,
-0.058598797768354416,
0.000034277480153832585,
0.03397679328918457,
0.016911054030060768,
0.024401802569627762,
0.03770941123366356,
-0.06374207884073257,
0.016167400404810905,
0.02707432024180889,
-0.024494634941220284,
0.030161717906594276,
0.034248579293489456,
0.0696185901761055,
-0.010271027684211731,
-0.011389223858714104,
-0.06547614932060242,
-0.0033348535653203726,
-0.035769809037446976,
-0.03873572498559952,
-0.06782703846693039,
-0.008835218846797943,
-0.031125081703066826,
-0.00492496695369482,
0.0648142471909523,
-0.06049756705760956,
-0.03673689439892769,
-0.03464047610759735,
-0.017892854288220406,
-0.004665045998990536,
-0.06007883697748184,
0.040602196007966995,
-0.02626076526939869,
-0.01216159574687481,
0.014005154371261597,
0.07674364000558853,
0.043248500674963,
0.046451546251773834,
-0.021940838545560837,
-0.019846012815833092,
-0.04169695824384689,
0.032010242342948914,
0.03299674764275551,
0.020209498703479767,
-0.05991363525390625,
-0.0246603861451149,
-0.0010258326074108481,
0.06510429829359055,
0.0033784275874495506,
-0.013460572808980942,
-0.055597931146621704,
-0.023557109758257866,
-0.03880678117275238,
-0.012117980979382992,
-0.014062386937439442,
-0.006472037173807621,
0.0500560887157917,
-0.04105506092309952,
-0.030276618897914886,
-0.03519180044531822,
0.04375375807285309,
0.044376783072948456,
-0.008458315394818783,
0.03169139847159386,
0.010123108513653278,
0.024869374930858612,
0.042958445847034454
] |
<p>Ohm's Law tells us that $V = IR$. This implies that $I \propto \frac{1}{R}$. But, $R \propto l$, where l is the length of the conductor. This would mean that $I \propto \frac{1}{l}$. But this does not fit with the definition of current that says that current is the amount of charge $Q$ passing through a given point per unit time. Clearly, the amount of charge passing through a given point per second does not vary with the length of the conductor. How can this contradiction exist?</p> | g9241 | [
0.03795723244547844,
-0.004802128300070763,
-0.02783777564764023,
0.02405206300318241,
0.08608905225992203,
0.020960893481969833,
0.0421389564871788,
-0.02587495930492878,
-0.03633493930101395,
0.05005897581577301,
-0.024455754086375237,
0.030676256865262985,
-0.06701704114675522,
0.030339716002345085,
-0.01722436212003231,
-0.02182837389409542,
0.04935072734951973,
-0.008581169880926609,
0.0027194744907319546,
0.00862606056034565,
0.0002571989898569882,
-0.0438518226146698,
0.018661079928278923,
0.011457575485110283,
-0.02152939699590206,
-0.01200031116604805,
0.03467549756169319,
0.023970967158675194,
-0.04857373982667923,
-0.034946538507938385,
0.0071217939257621765,
-0.005288824904710054,
0.03707389160990715,
-0.017632367089390755,
-0.02627936564385891,
-0.045099902898073196,
0.018769795075058937,
0.017344623804092407,
0.08970559388399124,
-0.008858283050358295,
0.04401208460330963,
-0.007028909865766764,
0.06536714732646942,
-0.008271087892353535,
0.006581032183021307,
-0.03611541539430618,
-0.04561331868171692,
0.018931753933429718,
-0.03179868683218956,
-0.02886156551539898,
-0.006137515418231487,
0.053087018430233,
0.0034953858703374863,
-0.03865336999297142,
-0.019203919917345047,
-0.03125609830021858,
-0.026628021150827408,
-0.003105373354628682,
0.02152079902589321,
0.030091412365436554,
0.035783760249614716,
-0.012405949644744396,
0.009345713071525097,
0.041878972202539444,
0.011522259563207626,
-0.008880064822733402,
-0.03267623111605644,
-0.02166910655796528,
-0.011748461052775383,
0.05236266180872917,
-0.023167716339230537,
-0.06564601510763168,
-0.020791135728359222,
-0.03366765007376671,
0.006048153154551983,
0.024494178593158722,
0.03087240643799305,
0.013833495788276196,
0.03038482367992401,
-0.05263110250234604,
-0.0019693002104759216,
-0.03018316812813282,
-0.0037900633178651333,
0.07850657403469086,
0.06638184189796448,
-0.03721928596496582,
-0.0001434984733350575,
0.05614059418439865,
-0.0023153217043727636,
0.007563516031950712,
-0.043906696140766144,
-0.036925964057445526,
0.053975194692611694,
0.02147277258336544,
-0.04257112741470337,
-0.05732796713709831,
-0.04006443917751312,
0.0010620540706440806,
0.001779457670636475,
0.02474416047334671,
-0.021380439400672913,
-0.00416219886392355,
0.027372872456908226,
0.016377991065382957,
-0.05139937624335289,
0.05487379804253578,
0.009541299194097519,
0.016486063599586487,
-0.0233390424400568,
-0.06386395543813705,
-0.012090278789401054,
-0.056835856288671494,
-0.04491597041487694,
-0.01785622164607048,
-0.0003822879516519606,
-0.03924263268709183,
-0.00011507500312291086,
-0.003382817842066288,
-0.03628218546509743,
0.00904629286378622,
-0.05501703545451164,
-0.018093422055244446,
0.007503971457481384,
0.0496768094599247,
-0.04627596214413643,
0.04006604477763176,
-0.03103102557361126,
0.01986376941204071,
0.03280741721391678,
0.0124787837266922,
-0.03268808126449585,
-0.0021283847745507956,
-0.03930221498012543,
0.03226485475897789,
-0.00953133124858141,
-0.06074957549571991,
0.033346954733133316,
-0.04544607177376747,
-0.013788112439215183,
-0.014582096599042416,
0.011515740305185318,
-0.06231623515486717,
0.031596679240465164,
-0.09661223739385605,
-0.015443522483110428,
0.007798206061124802,
-0.010187809355556965,
-0.03997892886400223,
0.042411573231220245,
-0.036333370953798294,
0.009503626264631748,
0.09514696896076202,
0.010118450969457626,
0.0034041069447994232,
0.018122324720025063,
0.012503637932240963,
0.017152955755591393,
-0.0019039049511775374,
-0.01573239639401436,
-0.031888268887996674,
-0.009073298424482346,
0.002023285022005439,
-0.02779599092900753,
0.03835497796535492,
-0.03498392924666405,
-0.004447652492672205,
0.023879529908299446,
0.03698836639523506,
-0.015514951199293137,
-0.04300481081008911,
-0.024924859404563904,
-0.0023002694360911846,
0.04148925468325615,
0.03042653761804104,
0.03378763422369957,
0.008506936021149158,
-0.01601865142583847,
0.03257565200328827,
0.0378250889480114,
0.019115954637527466,
-0.07121230661869049,
-0.023183582350611687,
0.024154700338840485,
-0.046404432505369186,
-0.046447284519672394,
0.06938697397708893,
-0.05110481008887291,
-0.026804588735103607,
-0.055963434278964996,
0.005520474631339312,
-0.08004973083734512,
-0.02122621424496174,
-0.04818334802985191,
0.048925213515758514,
0.00710260309278965,
-0.012963115237653255,
0.01209702156484127,
-0.054662421345710754,
-0.007802410051226616,
-0.04015951231122017,
0.03882613778114319,
0.0032203844748437405,
0.08222148567438126,
0.015602811239659786,
0.03225177526473999,
-0.006335284560918808,
-0.0503711998462677,
-0.0012413142248988152,
0.05876738950610161,
0.025151558220386505,
0.036820076406002045,
-0.0026045453269034624,
0.009373913519084454,
0.0404638908803463,
-0.05165272206068039,
-0.09417620301246643,
-0.017088884487748146,
0.011029177345335484,
-0.03969519957900047,
-0.00866725668311119,
0.005849536973983049,
0.005582820624113083,
0.10373753309249878,
-0.037292562425136566,
-0.0431339405477047,
-0.013798766769468784,
0.017345977947115898,
-0.05639452859759331,
-0.06467420607805252,
0.0077626886777579784,
-0.021898824721574783,
0.01347278617322445,
-0.031158708035945892,
0.011693334206938744,
0.02118491753935814,
0.04962236434221268,
-0.02863476797938347,
-0.002517756074666977,
0.01373918168246746,
-0.01445639505982399,
-0.03764728084206581,
-0.06140298396348953,
-0.006577600259333849,
0.04788077995181084,
0.01928829401731491,
-0.00021513266256079078,
0.03207561373710632,
0.02436305209994316,
-0.06265614181756973,
-0.012207390740513802,
-0.006176623981446028,
0.03637252375483513,
0.01027891505509615,
0.04641437530517578,
-0.03257680684328079,
-0.024141492322087288,
0.016123365610837936,
0.03970345854759216,
0.020550278946757317,
-0.01851091906428337,
-0.029117096215486526,
0.0029371471609920263,
0.035941123962402344,
0.04101376235485077,
-0.05333971977233887,
-0.0017220216104760766,
-0.03279193118214607,
0.009708252735435963,
0.023645006120204926,
-0.019153311848640442,
-0.033636655658483505,
0.03202740103006363,
0.016179267317056656,
0.03273703157901764,
-0.0006211684667505324,
-0.057258639484643936,
-0.0007115153130143881,
-0.06171434372663498,
0.060213830322027206,
-0.01161307655274868,
0.03022831864655018,
0.005017541814595461,
-0.07914026826620102,
0.042255450040102005,
0.0576443187892437,
-0.04653564468026161,
0.02984107844531536,
0.012126453220844269,
-0.016745366156101227,
-0.006068042479455471,
-0.04088089242577553,
0.04275808110833168,
0.016544628888368607,
-0.04278487712144852,
0.01202279981225729,
0.013203351758420467,
0.036411087960004807,
-0.06375124305486679,
-0.02997327409684658,
0.02095475234091282,
0.02080303058028221,
-0.011793303303420544,
-0.022741181775927544,
0.05238579213619232,
0.0680784210562706,
0.029946761205792427,
-0.006169282365590334,
-0.08899887651205063,
0.016837654635310173,
-0.012174327857792377,
-0.00017763461801223457,
0.01595168188214302,
-0.005001092795282602,
-0.036356668919324875,
-0.03135167807340622,
-0.051291875541210175,
-0.0548207126557827,
0.04116382822394371,
-0.007425582502037287,
0.033375706523656845,
-0.015647923573851585,
-0.05425262078642845,
-0.017880987375974655,
0.012116880156099796,
0.004257220309227705,
-0.01545871514827013,
-0.05318116396665573,
-0.013027418404817581,
-0.04210498556494713,
0.02215634286403656,
-0.05501452460885048,
0.04133986681699753,
-0.00692262826487422,
-0.022612713277339935,
0.0539567694067955,
-0.05572204291820526,
0.009919374249875546,
0.05490078032016754,
0.023189373314380646,
0.03046189621090889,
-0.015675043687224388,
0.030363276600837708,
-0.03162793815135956,
-0.0008481144323013723,
0.03102325275540352,
0.014937832951545715,
-0.014268813654780388,
0.07035773247480392,
0.04978242143988609,
-0.005304743070155382,
0.045970331877470016,
0.009781381115317345,
0.00927517469972372,
-0.008679262362420559,
-0.026950357481837273,
0.03986794129014015,
-0.0036376190837472677,
0.113380566239357,
0.013013080693781376,
0.0003139857144560665,
0.08350496739149094,
-0.010254078544676304,
0.015133657492697239,
0.014535870403051376,
0.027450915426015854,
0.013723699375987053,
0.04142352566123009,
0.027699235826730728,
0.033521730452775955,
-0.057408276945352554,
-0.003749485593289137,
-0.07362198829650879,
0.029718471691012383,
0.032243385910987854,
0.09888521581888199,
-0.03501104190945625,
0.027629010379314423,
0.06625193357467651,
-0.003103745635598898,
0.10515087842941284,
0.021759795024991035,
0.03248124197125435,
-0.0005935402004979551,
-0.0344650000333786,
-0.03320358321070671,
0.023577282205224037,
-0.04620281606912613,
0.005661781411617994,
0.017335692420601845,
-0.04900011047720909,
-0.020399266853928566,
-0.02510683797299862,
-0.022301433607935905,
-0.03257595747709274,
-0.009317467920482159,
-0.06491069495677948,
-0.011398551054298878,
-0.006333931349217892,
-0.0034473480191081762,
0.022199416533112526,
0.01639777235686779,
0.01350205298513174,
0.011449300684034824,
-0.014176382683217525,
0.003289654618129134,
0.00579996220767498,
0.043718401342630386,
-0.026770589873194695,
0.05960974097251892,
-0.027898769825696945,
-0.11069422960281372,
0.0008903225534595549,
-0.009432362392544746,
-0.017849113792181015,
-0.017790373414754868,
0.013189566321671009,
0.013094629161059856,
-0.009988921694457531,
0.08315097540616989,
0.01818220689892769,
0.009274925105273724,
0.015946734696626663,
0.0009719221270643175,
-0.06526697427034378,
0.037797681987285614,
0.039773277938365936,
0.0478464737534523,
0.02738562785089016,
0.006226679310202599,
-0.009835162200033665,
-0.06787163019180298,
0.021162819117307663,
-0.02552197128534317,
-0.013313133269548416,
-0.052418146282434464,
0.024302147328853607,
0.008828604593873024,
0.07923561334609985,
-0.028770890086889267,
0.0691031664609909,
0.06538991630077362,
-0.0013652208726853132,
0.030944088473916054,
-0.024276157841086388,
0.009181283414363861,
-0.031112566590309143,
-0.058508869260549545,
0.007064745761454105,
-0.02290169894695282,
-0.03016476333141327,
-0.008158807642757893,
0.011074703186750412,
0.007785421796143055,
-0.028185926377773285,
-0.0022808986250311136,
-0.028715483844280243,
0.01974910870194435,
-0.026500072330236435,
0.025350121781229973,
-0.023791572079062462,
-0.024288786575198174,
-0.0005315585876815021,
-0.01570611260831356,
0.042610589414834976,
0.06570152938365936,
-0.00150076684076339,
0.014806774444878101,
-0.05271163955330849,
-0.00513808336108923,
0.0070331040769815445,
0.03498907759785652,
0.0479360893368721,
-0.04049837961792946,
0.019881190732121468,
0.04984843358397484,
-0.05660592392086983,
0.035279739648103714,
-0.012658923864364624,
-0.0794345960021019,
-0.050784915685653687,
-0.0325050912797451,
0.0012208402622491121,
-0.011582829058170319,
0.04162305220961571,
0.014534727670252323,
0.02624223753809929,
-0.007437475025653839,
0.04725266620516777,
-0.02579677663743496,
-0.023549361154437065,
0.02676192857325077,
0.07057751715183258,
0.01811046339571476,
0.053684916347265244,
-0.017264774069190025,
0.0827450305223465,
0.04199511930346489,
0.008464531041681767,
-0.0544874370098114,
0.02638646960258484,
-0.03896551579236984,
-0.0612560510635376,
0.04738214612007141,
0.046998266130685806,
-0.02358393929898739,
0.09239251166582108,
0.015491122379899025,
0.04238560423254967,
-0.06316124647855759,
-0.022475313395261765,
0.03388604521751404,
0.06344835460186005,
0.013100089505314827,
-0.002387247746810317,
0.02920340932905674,
0.015196193009614944,
-0.06971991062164307,
-0.015355194918811321,
-0.008950779214501381,
0.03252563625574112,
0.02399827539920807,
-0.016810422763228416,
0.056788261979818344,
-0.026260260492563248,
-0.025784924626350403,
0.03537020832300186,
-0.050169266760349274,
-0.06039627268910408,
0.055821340531110764,
0.03908373415470123,
0.026354489848017693,
0.001598196686245501,
-0.004217987880110741,
-0.07489786297082901,
-0.031008044257760048,
0.04089200869202614,
0.014758482575416565,
-0.04811035096645355,
0.0048301201313734055,
0.009490442462265491,
-0.009778662584722042,
0.04393058642745018,
0.030116867274045944,
0.022192735224962234,
-0.010008825920522213,
0.0062149399891495705,
-0.07430361956357956,
-0.05898566171526909,
0.041006021201610565,
-0.033982615917921066,
0.019328197464346886,
0.021981745958328247,
-0.03462658450007439,
-0.02306598238646984,
0.042983490973711014,
0.006497783586382866,
0.01558005716651678,
0.015287520363926888,
-0.07129964977502823,
-0.004929077345877886,
0.05305342748761177,
-0.019779102876782417,
-0.02012547478079796,
-0.003432233352214098,
0.05411200597882271,
-0.044456008821725845,
0.01628432795405388,
0.04952939599752426,
-0.01485132984817028,
0.027745766565203667,
0.04065316170454025,
-0.010737544856965542,
0.03223732113838196,
-0.040294401347637177,
0.007468224503099918,
0.04361424595117569,
-0.014914668165147305,
-0.08946805447340012,
0.0058901347219944,
-0.028039608150720596,
0.010439552366733551,
-0.08542898297309875,
-0.0013165374984964728,
0.02536499872803688,
-0.00206482270732522,
0.006255173124372959,
0.020714884623885155,
-0.025703128427267075,
0.03138795867562294,
0.024135461077094078,
-0.014975547790527344,
0.0029047480784356594,
-0.02067895047366619,
-0.030559116974473,
-0.007969996891915798,
-0.040008608251810074,
-0.034550741314888,
-0.060539186000823975,
0.013856579549610615,
0.049683280289173126,
0.04328156262636185,
0.01985287293791771,
0.0036951350048184395,
0.003964806906878948,
0.05103654786944389,
0.001103919930756092,
-0.008985794149339199,
0.03233794867992401,
0.00357072614133358,
0.032369859516620636,
0.009395844303071499,
0.021786265075206757,
-0.019623368978500366,
-0.003880326170474291,
0.015746375545859337,
0.03634344041347504,
-0.025197742506861687,
0.017476476728916168,
-0.05434257537126541,
0.05125853419303894,
0.02080559730529785,
0.03140178695321083,
-0.04139246419072151,
0.029857058078050613,
0.07919509708881378,
0.046386878937482834,
0.050550200045108795,
0.04589363932609558,
0.027985623106360435,
0.0028295263182371855,
-0.04003129526972771,
-0.015798749402165413,
-0.06473031640052795,
0.012691143900156021,
0.055231522768735886,
-0.031190240755677223,
-0.0039883083663880825,
-0.04013410955667496,
0.01185132097452879,
0.008215861395001411,
0.017535371705889702,
-0.017502231523394585,
0.013433357700705528,
0.025639725849032402,
-0.0636700764298439,
-0.040272101759910583,
0.03195561096072197,
0.0296504944562912,
-0.0601169690489769,
0.009285585023462772,
0.055875904858112335,
0.016082171350717545,
-0.03321097046136856,
0.0247846320271492,
-0.011891436763107777,
-0.025171887129545212,
-0.011760663241147995,
0.02758071757853031,
0.05356050282716751,
-0.03473993018269539,
-0.002632714109495282,
0.04797429218888283,
0.00187302113045007,
0.007906762883067131,
0.018249135464429855,
0.02344600297510624,
-0.017151622101664543,
-0.08729642629623413,
-0.013603711500763893,
-0.08531054854393005,
0.02457169070839882,
-0.044216446578502655,
0.06805580109357834,
-0.062165096402168274,
-0.009552109986543655,
0.0069120763801038265,
-0.030139155685901642,
0.05574149638414383,
0.026591932401061058,
0.011440419591963291,
0.020364783704280853,
-0.03490610048174858,
0.02248600497841835,
-0.004349308554083109,
-0.014125521294772625,
0.014205356128513813,
-0.0636507049202919,
-0.057950008660554886,
0.0066649531945586205,
0.02639779821038246,
0.01451709121465683,
-0.010419543832540512,
0.03765946999192238,
0.038566917181015015,
0.033602580428123474,
0.013286982662975788,
0.0472087599337101,
-0.0008702101185917854,
0.028230641037225723,
0.0022094242740422487,
0.037864670157432556,
-0.033037204295396805,
0.029619483277201653,
0.016797155141830444,
-0.01253425795584917,
0.023982925340533257,
0.009790278039872646,
-0.05039883777499199,
-0.05850652605295181,
-0.06643398851156235,
-0.006707101594656706,
0.0014209317741915584,
-0.001962651265785098,
-0.0263342447578907,
0.04435668885707855,
-0.023099400103092194,
-0.04090507701039314,
-0.006145586725324392,
0.010169880464673042,
-0.05227837711572647,
0.024154534563422203,
-0.02025493234395981,
-0.002173637505620718,
-0.05750768259167671,
-0.03488639369606972,
-0.02743402309715748,
0.015673382207751274,
0.005489561706781387,
-0.04891897737979889,
-0.010283018462359905,
0.003889460815116763,
0.00011844144319184124,
0.024528706446290016,
-0.0360189825296402,
-0.1039348840713501,
0.03941056877374649,
-0.0052813319489359856,
0.02658708579838276,
0.03521670401096344,
-0.012824962846934795,
0.0060480814427137375,
-0.02253720350563526,
-0.04027320072054863,
-0.012544993311166763,
-0.027557507157325745,
-0.025192992761731148,
-0.02016845904290676,
0.0034013877157121897,
0.06295294314622879,
-0.03203742206096649,
0.0011159623973071575,
0.03734844550490379,
-0.03501958027482033,
-0.0188093651086092,
0.04735899716615677,
0.0014835313195362687,
0.0019494539592415094,
0.001536377938464284,
-0.00571491988375783,
0.036412741988897324,
-0.026592768728733063,
-0.025524651631712914,
0.0032670435030013323,
-0.017049869522452354,
0.016001446172595024,
-0.03798755630850792,
-0.031783606857061386,
-0.01728391833603382
] |
<p>As our homework, we were asked to derive $P = I^2R$. </p>
<p>Now, I started off with the basic relation $P = \frac{W}{T}$. I was not able to think of anything from here, so I started plugging in random formulas from a purely algebraic point of view. </p>
<p>I tried the one for voltage $V = \frac{W}{q} \implies Vq = W$ and got $P = \frac{Vq}{T}$. And since $I = \frac{q}{T}$, $IT = q$, plugging this in we get $P = IV$. A simple application of Ohm's Law gives us the required equation. But, when I tried to get an intuitive grasp of what I'd just done, I found a few discrepancies:</p>
<ol>
<li><p>In the definition of voltage, $W$ refers to the energy an electron loses when it goes from the negative to the positive terminal. In the definition of power, $W$, refers to the total energy consumed by the appliances. How can you relate the two?</p></li>
<li><p>In the definition of current $T$, refers to the time taken by the electron to go from one terminal to the other, whereas, in power $T$ refers to the time for which the appliances run or the energy is supplied. How can these two be the same?</p></li>
</ol>
<p>Is my derivation incorrect? If not, then how would you counter the arguments I mentioned above?</p> | g9242 | [
0.034204304218292236,
-0.024063263088464737,
-0.04835604503750801,
-0.024831147864460945,
0.029105767607688904,
-0.04260958731174469,
0.02360532619059086,
-0.003744587767869234,
-0.06739325821399689,
0.006433554925024509,
-0.028797494247555733,
0.05219185724854469,
-0.001520826481282711,
0.052845295518636703,
0.009909850545227528,
-0.032546576112508774,
0.05694076791405678,
0.011546327732503414,
0.006998569704592228,
-0.02623371034860611,
-0.0031371554359793663,
-0.033277127891778946,
-0.04941253364086151,
-0.0029981019906699657,
0.002823369111865759,
-0.05856022983789444,
0.00011125270975753665,
0.0369509682059288,
-0.06287291646003723,
-0.0565309002995491,
0.004369126632809639,
0.016620079055428505,
0.06839282810688019,
-0.05459558963775635,
-0.07454810291528702,
0.03331755846738815,
0.06099475175142288,
0.02954707480967045,
0.027593012899160385,
-0.0028263991698622704,
-0.0368167981505394,
0.021820522844791412,
0.06260913610458374,
0.006689825560897589,
-0.0032126386649906635,
-0.019716091454029083,
-0.06695639342069626,
-0.0010687661124393344,
-0.01668461039662361,
-0.06385034322738647,
-0.010169482789933681,
0.026924889534711838,
0.02025483548641205,
-0.015290065668523312,
-0.006186638027429581,
-0.028964869678020477,
0.006792597472667694,
-0.029839396476745605,
0.016640905290842056,
0.05553451180458069,
0.004594461992383003,
0.013008929789066315,
0.014326557517051697,
0.03655200079083443,
0.0595361664891243,
-0.03419175371527672,
0.0082766218110919,
-0.014178833924233913,
-0.00345266773365438,
0.039989084005355835,
0.008036412298679352,
-0.060735106468200684,
-0.0013169931480661035,
-0.06418274343013763,
0.04458039253950119,
0.0026270675007253885,
0.06042387709021568,
-0.03499147295951843,
0.09059405326843262,
-0.00668535940349102,
-0.0223777424544096,
0.01840553805232048,
0.03674622252583504,
0.07219046354293823,
0.03862382844090462,
-0.0041575562208890915,
0.008370225317776203,
0.022532422095537186,
0.01377243921160698,
0.02829950861632824,
0.008276174776256084,
-0.010004867799580097,
0.058206986635923386,
0.0026910833548754454,
-0.028246009722352028,
-0.041107434779405594,
-0.013167318888008595,
0.016220251098275185,
-0.0008378187194466591,
0.015696093440055847,
0.044503822922706604,
-0.02197573520243168,
0.0040323566645383835,
-0.02509116195142269,
-0.0044773477129638195,
0.03634856268763542,
0.03191583231091499,
-0.01160407718271017,
0.016960712149739265,
-0.014054323546588421,
-0.02571977488696575,
-0.022953826934099197,
-0.04076625406742096,
-0.019802747294306755,
0.0071172211319208145,
-0.04003329575061798,
0.04057364910840988,
-0.026513537392020226,
-0.006566236261278391,
-0.002072017639875412,
-0.01512071117758751,
0.02526218257844448,
0.011786116287112236,
0.01455505657941103,
0.008780418895184994,
0.009861520491540432,
-0.036734845489263535,
0.0401906743645668,
0.052440859377384186,
0.03026370145380497,
0.00428432272747159,
-0.05268258973956108,
-0.029227618128061295,
0.03490886092185974,
0.023139426484704018,
-0.00233766483142972,
0.018185188993811607,
-0.03975846990942955,
0.01409382838755846,
0.018849676474928856,
0.003992944490164518,
-0.048142995685338974,
-0.03132572025060654,
-0.0461108535528183,
-0.0637689158320427,
0.03646945580840111,
-0.031604744493961334,
-0.05286424979567528,
0.08084453642368317,
0.00422185193747282,
-0.012884249910712242,
0.046030592173337936,
-0.02367069385945797,
-0.03784148022532463,
0.06203923374414444,
-0.04196600615978241,
0.02742728404700756,
-0.031937092542648315,
-0.018550299108028412,
-0.021959640085697174,
0.021952664479613304,
-0.03361216187477112,
0.03514743223786354,
-0.003165480215102434,
-0.005380745977163315,
-0.03357572853565216,
0.04553871974349022,
-0.023544952273368835,
-0.0004970217705704272,
-0.0478203110396862,
-0.030007226392626762,
-0.022699343040585518,
0.025648653507232666,
-0.025634165853261948,
0.026600884273648262,
0.0702090933918953,
-0.0005045334692113101,
-0.0015751429600641131,
0.014238028787076473,
0.048905208706855774,
-0.03560628741979599,
-0.023871567100286484,
0.007635957095772028,
-0.03189845755696297,
-0.021197756752371788,
0.00004494859240367077,
-0.03628174960613251,
0.027638642117381096,
-0.092006154358387,
-0.005615702830255032,
-0.040103599429130554,
0.02419886738061905,
-0.003437930950894952,
0.012859995476901531,
-0.07054980844259262,
0.05273912474513054,
-0.01252193097025156,
-0.017849257215857506,
-0.029099436476826668,
-0.0430617481470108,
0.03780380263924599,
-0.0036070069763809443,
0.030575597658753395,
0.04466128721833229,
0.04545814171433449,
0.028899449855089188,
-0.03921234980225563,
-0.043992847204208374,
0.038603805005550385,
0.019464218989014626,
-0.031029028818011284,
-0.005845380015671253,
0.008463057689368725,
0.04896095395088196,
-0.010544991120696068,
-0.09040394425392151,
-0.023099802434444427,
0.02164461277425289,
-0.06493920087814331,
-0.011975158005952835,
-0.012800517491996288,
-0.014117316342890263,
0.10215898603200912,
-0.02512349747121334,
-0.021810432896018028,
-0.004234324675053358,
0.011161061003804207,
-0.0535881444811821,
-0.10514332354068756,
-0.030264204367995262,
-0.05661633983254433,
0.01576690934598446,
-0.01378640253096819,
-0.021867044270038605,
0.033817823976278305,
0.02758411131799221,
-0.034344322979450226,
0.008838517591357231,
0.012974741868674755,
0.02043270878493786,
-0.0006600360502488911,
-0.01941324956715107,
0.012871704995632172,
0.03725353628396988,
-0.01680101826786995,
0.002188582206144929,
0.05865895003080368,
-0.0018315654015168548,
-0.05582248419523239,
-0.000696627888828516,
-0.04260548576712608,
0.018539385870099068,
-0.03788280487060547,
0.03013194352388382,
-0.03954845294356346,
-0.06888606399297714,
0.021315697580575943,
0.035218045115470886,
0.03180420398712158,
-0.01457384042441845,
-0.004961363971233368,
-0.06585043668746948,
-0.004264121409505606,
0.057471711188554764,
-0.02912052720785141,
-0.011147747747600079,
0.012678870931267738,
0.013943282887339592,
0.0494711771607399,
-0.04781508073210716,
-0.022371359169483185,
0.017556125298142433,
-0.02696257270872593,
0.00419196393340826,
0.03559592738747597,
-0.08258956670761108,
0.030532149598002434,
-0.03041832149028778,
0.07020553946495056,
-0.012342413887381554,
0.03322752192616463,
-0.00852500181645155,
-0.04338362440466881,
0.020502837374806404,
0.013549990020692348,
-0.05838176608085632,
0.026455553248524666,
0.029154790565371513,
-0.004600503481924534,
0.0025968013796955347,
-0.04424208030104637,
0.04817374795675278,
-0.01761472225189209,
-0.03176356479525566,
0.013497589156031609,
0.004020048771053553,
0.021214226260781288,
-0.05576937273144722,
-0.0488620288670063,
0.0014281756011769176,
-0.0006773817585781217,
0.0092975664883852,
-0.05280561372637749,
-0.0030754394829273224,
-0.0018153145210817456,
0.01610461249947548,
-0.028696967288851738,
-0.028101874515414238,
0.00019532180158421397,
0.02514977939426899,
-0.03257627412676811,
-0.011024786159396172,
0.03149378299713135,
-0.03067721799015999,
-0.016096722334623337,
-0.027085306122899055,
-0.04277091845870018,
-0.004571025725454092,
0.0041610002517700195,
0.018786655738949776,
-0.07608146965503693,
-0.018303290009498596,
-0.00011708549573086202,
0.0019017818849533796,
-0.02669602259993553,
-0.0014978789258748293,
-0.06821607053279877,
0.005194736644625664,
-0.028375884518027306,
-0.015964942052960396,
-0.034549079835414886,
-0.012590584345161915,
0.03427037224173546,
-0.03024861216545105,
0.020551329478621483,
-0.022635335102677345,
-0.0028255474753677845,
0.03493516147136688,
-0.018252212554216385,
0.03867881000041962,
-0.0046602534130215645,
0.02915734238922596,
-0.035660214722156525,
0.04123818129301071,
-0.004603820387274027,
-0.046573035418987274,
-0.06979446113109589,
0.06458557397127151,
0.03654765710234642,
-0.036105651408433914,
0.03669662028551102,
-0.015890328213572502,
0.021593298763036728,
0.032455723732709885,
-0.05138050764799118,
-0.018238818272948265,
-0.034809522330760956,
0.035663314163684845,
0.0022635722998529673,
0.04307780787348747,
-0.01517921220511198,
-0.04525037482380867,
0.05693140625953674,
0.015098128467798233,
-0.015529107302427292,
-0.008732059970498085,
-0.0056747435592114925,
0.07749509811401367,
-0.02098540961742401,
-0.060880351811647415,
0.027345016598701477,
-0.008369110524654388,
-0.04824712872505188,
0.04567079618573189,
0.05081189423799515,
-0.03565889969468117,
0.005987671669572592,
0.015526555478572845,
-0.05241435393691063,
0.12535761296749115,
0.011978981085121632,
-0.020898902788758278,
0.008828382007777691,
0.06556805968284607,
0.029024260118603706,
-0.02222852222621441,
-0.017894860357046127,
0.04815167561173439,
0.03868009150028229,
-0.06244903430342674,
-0.012458677403628826,
0.001401309622451663,
-0.012173191644251347,
-0.05431314930319786,
-0.024598149582743645,
-0.044579099863767624,
0.04158614203333855,
0.003479253500699997,
0.0021563651971518993,
0.06041480600833893,
-0.024697275832295418,
0.0006230012513697147,
0.0506105050444603,
0.0028958229813724756,
0.010026075877249241,
-0.0012818964896723628,
0.07408858835697174,
-0.04693618044257164,
0.06654328107833862,
-0.019639162346720695,
-0.07578818500041962,
-0.028994137421250343,
-0.0037048724479973316,
-0.04442641884088516,
-0.008911610580980778,
-0.03577795252203941,
0.06419771164655685,
-0.0272207148373127,
0.06863919645547867,
0.034654151648283005,
0.03010314516723156,
0.03488766774535179,
0.023691238835453987,
-0.057101909071207047,
0.02837173454463482,
0.036608897149562836,
0.03471275046467781,
0.003020002506673336,
-0.016008317470550537,
-0.02258160524070263,
0.025696249678730965,
0.03166429325938225,
-0.003459353931248188,
0.00182809354737401,
-0.014219967648386955,
0.04351058974862099,
-0.029504820704460144,
0.08865277469158173,
-0.026072312146425247,
0.07557787001132965,
0.0858558788895607,
-0.020542005077004433,
-0.000757733650971204,
0.019379638135433197,
0.0050721196457743645,
0.037504881620407104,
-0.01779978536069393,
-0.021288521587848663,
0.03225478157401085,
-0.011518802493810654,
-0.018597589805722237,
0.07794411480426788,
0.0522027388215065,
-0.02923871949315071,
0.07993099838495255,
-0.013174316845834255,
0.03338994085788727,
0.005590889137238264,
0.02899940125644207,
-0.015214438550174236,
-0.0687069222331047,
0.0022765514440834522,
-0.02311691641807556,
-0.007852640002965927,
0.022737642750144005,
-0.011331381276249886,
-0.022536998614668846,
-0.014871480874717236,
-0.05031444877386093,
-0.019208675250411034,
0.026418546214699745,
-0.0040535400621593,
-0.022319376468658447,
0.02310529537498951,
0.00784367322921753,
-0.0327310636639595,
0.04167748615145683,
-0.007932906039059162,
-0.07884512096643448,
-0.0031523320358246565,
-0.02559978887438774,
-0.016131799668073654,
-0.007418583147227764,
0.01438167691230774,
-0.0204660352319479,
0.010409372858703136,
-0.00945859495550394,
-0.002798205940052867,
0.01043388806283474,
-0.014907899312675,
-0.00411074236035347,
0.06569255143404007,
0.02528543397784233,
0.017382003366947174,
-0.02950439788401127,
0.08505835384130478,
0.02939213067293167,
0.048918988555669785,
-0.015166206285357475,
0.03035302273929119,
-0.039956968277692795,
0.046154968440532684,
-0.03343205526471138,
0.026743944734334946,
0.019224761053919792,
0.05203928425908089,
0.09156107157468796,
0.0029049979057163,
-0.03493746370077133,
0.03685293346643448,
0.03559301421046257,
0.03980241343379021,
0.0005306736566126347,
0.01261378824710846,
0.06954388320446014,
0.017943808808922768,
-0.08220910280942917,
-0.017261570319533348,
-0.018779652193188667,
-0.006366721820086241,
0.0647970512509346,
0.03228791430592537,
0.06821239739656448,
-0.05992415174841881,
-0.06163390725851059,
0.02425221912562847,
-0.06253640353679657,
-0.055144041776657104,
0.04484826698899269,
-0.0041456022299826145,
-0.0018032772932201624,
0.02654080279171467,
0.028537794947624207,
0.02308104932308197,
-0.034541886299848557,
0.01722348853945732,
-0.023364920169115067,
-0.0006435554823838174,
0.007230831775814295,
0.04027073085308075,
0.0014414164470508695,
-0.001054884516634047,
0.006005612667649984,
0.03350624069571495,
0.016481643542647362,
0.0048047625459730625,
-0.02522740699350834,
-0.03119940496981144,
0.0002189095102949068,
0.008796554990112782,
-0.04362378641963005,
0.011180909350514412,
0.027343135327100754,
0.011227516457438469,
0.05742545425891876,
-0.01395703200250864,
0.05048256367444992,
-0.0319937989115715,
-0.08148781210184097,
0.01986384578049183,
0.011680119670927525,
0.04335193708539009,
-0.001558234915137291,
0.006668462883681059,
0.06708890199661255,
-0.00441537844017148,
0.0312899611890316,
0.027234148234128952,
-0.03055248223245144,
0.08570366352796555,
0.09660518169403076,
0.018785152584314346,
0.03195017948746681,
-0.03274281695485115,
0.030100231990218163,
0.028384551405906677,
0.022146401926875114,
-0.02573191002011299,
0.01305864006280899,
-0.06954707950353622,
-0.017293421551585197,
-0.08695538341999054,
-0.0205129012465477,
-0.01095594558864832,
0.012830499559640884,
0.023986997082829475,
0.002292238175868988,
0.0004718751006294042,
0.07460284233093262,
-0.03814215213060379,
-0.0041733067482709885,
0.02812822535634041,
0.03166963905096054,
-0.019966574385762215,
0.0032629184424877167,
0.016728350892663002,
0.0010313739767298102,
-0.03005766123533249,
-0.011408666148781776,
0.016956791281700134,
0.009825739078223705,
0.04486362636089325,
-0.011980143375694752,
-0.030408604070544243,
0.06861268728971481,
0.0299335066229105,
-0.003453544806689024,
0.03176400810480118,
-0.03438938036561012,
0.002939807251095772,
-0.04032709449529648,
0.05341675132513046,
0.04693727567791939,
-0.00849037803709507,
0.006815844681113958,
-0.010035829618573189,
-0.022724689915776253,
0.07141093164682388,
0.015521900728344917,
0.025684699416160583,
0.02650044485926628,
-0.032110732048749924,
-0.015906380489468575,
0.03234206885099411,
0.06295415759086609,
0.06605783849954605,
-0.04136981815099716,
0.03445630893111229,
0.0014485000865533948,
-0.0026187074836343527,
-0.020978474989533424,
-0.052608322352170944,
-0.015912292525172234,
0.01579161547124386,
0.04366401955485344,
0.027265289798378944,
-0.035545118153095245,
0.016147155314683914,
0.0002445430727675557,
0.020634867250919342,
-0.015937797725200653,
-0.010259869508445263,
-0.015084763988852501,
0.010117853991687298,
-0.04556487873196602,
-0.019808411598205566,
0.033006224781274796,
-0.03036513365805149,
-0.040467072278261185,
0.025014067068696022,
0.021279247477650642,
0.04024573415517807,
-0.04314383491873741,
0.04294279217720032,
-0.041897308081388474,
-0.019229073077440262,
-0.017761265859007835,
-0.006420494988560677,
0.018468040972948074,
-0.016295721754431725,
0.03798174113035202,
-0.0068082730285823345,
-0.031793784350156784,
0.030049225315451622,
0.015610998496413231,
0.04503502696752548,
-0.06847913563251495,
-0.05962913855910301,
0.00994755420833826,
-0.04601582512259483,
-0.0005095307715237141,
-0.04960834980010986,
0.007167387288063765,
-0.015099627897143364,
-0.03141222521662712,
0.02935456857085228,
-0.014881505630910397,
0.038313210010528564,
-0.025571539998054504,
-0.001453596749342978,
-0.022622639313340187,
-0.05085430666804314,
-0.04676571115851402,
-0.007754312362521887,
-0.03572887182235718,
0.0050665345042943954,
-0.03962830454111099,
-0.07568108290433884,
-0.03777933493256569,
0.043766479939222336,
-0.021259909495711327,
-0.0255801472812891,
0.0742131918668747,
0.010325625538825989,
0.020161090418696404,
0.026951244100928307,
0.021251777186989784,
0.012614474631845951,
0.037769291549921036,
0.06821473687887192,
0.0680207759141922,
-0.024485526606440544,
0.006402641534805298,
-0.008540382608771324,
-0.006644843146204948,
0.015937529504299164,
-0.03299625962972641,
-0.042039841413497925,
-0.05328861251473427,
-0.035531189292669296,
-0.0000417807386838831,
0.015185953117907047,
-0.04214603453874588,
-0.012337732128798962,
0.04788092523813248,
0.01040811650454998,
0.022861210629343987,
0.029527200385928154,
-0.0040027303621172905,
-0.010974546894431114,
0.014398655854165554,
-0.01791282184422016,
-0.00007294114038813859,
-0.07427331060171127,
-0.011080298572778702,
0.010957692749798298,
0.0020567576866596937,
-0.03876946493983269,
-0.026284044608473778,
0.03835279121994972,
-0.08461480587720871,
-0.002553357742726803,
0.03128349035978317,
0.04538165032863617,
-0.04455943778157234,
0.022440876811742783,
0.03082207217812538,
0.012266021221876144,
0.022086622193455696,
0.01580553874373436,
-0.002342074178159237,
-0.04822474345564842,
-0.04798363149166107,
-0.03200988844037056,
-0.010665197856724262,
-0.014070883393287659,
0.002333110896870494,
0.017358433455228806,
0.019758692011237144,
-0.054148755967617035,
-0.030326049774885178,
0.01643580198287964,
-0.1161755621433258,
0.020763268694281578,
0.05716520920395851,
-0.04318588227033615,
-0.01592259109020233,
0.02633492648601532,
0.028123654425144196,
0.07903625071048737,
-0.04034127667546272,
-0.015543224290013313,
-0.040695060044527054,
-0.021143846213817596,
0.016925955191254616,
-0.07324130833148956,
-0.054331324994564056,
0.02457384765148163
] |
<p><img src="http://i.stack.imgur.com/H9uwm.jpg" alt="enter image description here"></p>
<p>If the above image is a cross section of a conductor, the field at the point shown is not zero. So the field inside a conductor is not zero at all points. </p>
<p>You could argue that the electrons would rearrange themselves so that the field inside is zero. But if that were true, all the positive charges would not be on the surface. For example, in the diagram above, the electron at the point shown, would move, leaving a charge in the centre.</p>
<p>What am I missing?</p>
<h1><em><strong>I am not looking for a proof that the field inside a conductor is zero. Please address the problem I discussed above.</em></strong></h1> | g9243 | [
0.020153995603322983,
0.020994089543819427,
-0.002195928478613496,
0.011180761270225048,
0.09211277961730957,
0.04591813683509827,
0.03842894360423088,
0.028782345354557037,
-0.01868782751262188,
-0.005732409190386534,
-0.028562186285853386,
0.03604524955153465,
-0.027678851038217545,
-0.035520218312740326,
-0.023996073752641678,
-0.011174638755619526,
0.031524766236543655,
-0.019152671098709106,
0.04156078025698662,
0.029253164306282997,
0.007296702824532986,
-0.02167297713458538,
0.027918606996536255,
-0.043393541127443314,
-0.03500312566757202,
-0.01206151768565178,
0.007942230440676212,
-0.017816001549363136,
-0.003259747289121151,
-0.05101318657398224,
0.017665190622210503,
0.06198250129818916,
0.03835150599479675,
-0.03684660419821739,
-0.049133382737636566,
-0.04428500682115555,
0.04964364320039749,
0.052177831530570984,
-0.027071284130215645,
0.03980260714888573,
0.0016278022667393088,
-0.029882924631237984,
0.03389396145939827,
-0.03355405107140541,
0.0240956898778677,
-0.010544228367507458,
0.0004548788710962981,
0.017793990671634674,
-0.015185586176812649,
-0.03200560063123703,
-0.051845449954271317,
0.015008923597633839,
0.055034566670656204,
-0.017699915915727615,
0.0320250578224659,
-0.002386388136073947,
-0.009308187291026115,
0.012052848003804684,
0.07844481617212296,
-0.003709824290126562,
-0.006861142348498106,
0.034419238567352295,
0.007953084073960781,
0.019949331879615784,
-0.011138818226754665,
0.054854415357112885,
-0.07118750363588333,
-0.009779991582036018,
-0.03391438350081444,
-0.014130373485386372,
-0.0062119499780237675,
-0.05696852132678032,
-0.07354997098445892,
-0.00524812052026391,
-0.040263496339321136,
0.05257273092865944,
-0.006839819252490997,
-0.01022592093795538,
0.05449296534061432,
-0.07991886883974075,
-0.06596330553293228,
-0.05024920776486397,
-0.027795419096946716,
0.048163723200559616,
0.05199539288878441,
0.012299302034080029,
0.05361214280128479,
-0.02162993513047695,
-0.020474262535572052,
-0.014257939532399178,
0.006406618747860193,
0.024912936612963676,
0.051028210669755936,
0.027966424822807312,
-0.03671067953109741,
-0.0684833899140358,
-0.02154272049665451,
0.035498443990945816,
-0.034755606204271317,
-0.017639489844441414,
-0.050300609320402145,
-0.0043407403863966465,
-0.024289987981319427,
0.06197508051991463,
-0.03246043995022774,
0.01914365030825138,
0.00720502994954586,
-0.028967831283807755,
0.016898425295948982,
0.012081538327038288,
0.01642400585114956,
-0.0530131496489048,
-0.07136579602956772,
-0.0003384954761713743,
0.024755481630563736,
0.014740933664143085,
0.10018640756607056,
-0.011371424421668053,
0.00045950894127599895,
0.02600347064435482,
-0.010466729290783405,
-0.0028390127699822187,
0.03608362376689911,
0.043320659548044205,
-0.008302146568894386,
0.001072091981768608,
-0.0407341867685318,
-0.01806429587304592,
0.036864567548036575,
0.01027456670999527,
-0.023999536409974098,
0.03933529555797577,
-0.03881293162703514,
0.026504507288336754,
0.025957025587558746,
-0.017489593476057053,
-0.0028258676175028086,
-0.07196301966905594,
-0.006699535995721817,
-0.005046950187534094,
0.03749487176537514,
0.017417525872588158,
-0.009899800643324852,
-0.035998713225126266,
0.07617032527923584,
-0.06742415577173233,
0.046170592308044434,
-0.00943305529654026,
0.06851201504468918,
0.02297113835811615,
0.02210480533540249,
0.0898272693157196,
-0.03233785927295685,
-0.03404136374592781,
0.003035502275452018,
-0.06827642768621445,
0.08073196560144424,
-0.024029096588492393,
0.01947643607854843,
-0.0599716380238533,
0.07881317287683487,
-0.003277020063251257,
0.010517207905650139,
-0.006349517498165369,
-0.02317913994193077,
-0.034924622625112534,
-0.013856715522706509,
-0.047233209013938904,
-0.020039213821291924,
-0.03254242241382599,
-0.022107388824224472,
0.009679779410362244,
0.026200352236628532,
0.04547179862856865,
-0.018090935423970222,
0.023434864357113838,
0.03843795880675316,
0.03539185971021652,
0.05928826704621315,
-0.01982729136943817,
-0.052127137780189514,
0.03457029163837433,
0.023393074050545692,
0.012292514555156231,
0.030291348695755005,
-0.04484875872731209,
-0.04400552064180374,
0.0836307555437088,
-0.042921263724565506,
-0.04788336902856827,
0.012973642908036709,
-0.009882545098662376,
-0.016473162919282913,
0.0003698257787618786,
-0.008570967242121696,
-0.015637407079339027,
0.02344745397567749,
-0.026075048372149467,
0.007427122909575701,
-0.050204113125801086,
0.03024127706885338,
0.005625684279948473,
0.02919551357626915,
0.03259221836924553,
0.018843060359358788,
-0.0682094469666481,
-0.015699347481131554,
-0.037939757108688354,
0.04765177518129349,
0.020541120320558548,
0.023549161851406097,
0.019758315756917,
-0.010286727920174599,
0.02827235497534275,
-0.008084136992692947,
-0.040626250207424164,
-0.05484427139163017,
-0.023882517591118813,
0.010235260240733624,
0.0010624501155689359,
-0.04312021657824516,
-0.021447569131851196,
0.021842574700713158,
-0.013490167446434498,
-0.02294139377772808,
0.03105897083878517,
0.037307750433683395,
-0.030713530257344246,
-0.07313820719718933,
0.00664295582100749,
-0.03431176394224167,
-0.014359720051288605,
-0.03482690453529358,
-0.02415022999048233,
0.030497441068291664,
0.0016939610941335559,
-0.060569822788238525,
0.00949519407004118,
-0.007775044068694115,
0.007916868664324284,
-0.041933901607990265,
-0.018932005390524864,
-0.023772114887833595,
-0.02224176749587059,
0.04280036687850952,
-0.05765005201101303,
0.03179293870925903,
-0.025736624374985695,
-0.014695445075631142,
0.02061139978468418,
0.04750155657529831,
0.013301926665008068,
0.02617923729121685,
0.04834960773587227,
-0.003926521632820368,
-0.051587581634521484,
-0.003285541431978345,
0.0331355556845665,
0.020562900230288506,
-0.0706462562084198,
-0.005661319009959698,
-0.012624594382941723,
-0.016514483839273453,
0.038850050419569016,
-0.09261094778776169,
-0.04956561699509621,
-0.07535848766565323,
-0.056475091725587845,
0.05436604842543602,
-0.00724665354937315,
-0.056358806788921356,
0.1032702699303627,
-0.0007880713674239814,
0.02998458594083786,
-0.00684930058196187,
-0.05568845197558403,
-0.008311509154736996,
0.0433928519487381,
0.023084424436092377,
0.033979058265686035,
0.09326893836259842,
0.044776905328035355,
-0.000872627308126539,
0.007702695671468973,
-0.017159590497612953,
-0.02241903729736805,
0.006527164485305548,
-0.02616714872419834,
-0.01843920163810253,
0.011044610291719437,
-0.002096073003485799,
-0.00005205800698604435,
0.10883238166570663,
-0.00682426430284977,
0.0027349272277206182,
0.003644370473921299,
0.07338988035917282,
-0.1022098958492279,
-0.024967731907963753,
0.0068441894836723804,
-0.016265705227851868,
0.04061374440789223,
-0.017567509785294533,
-0.0004848366370424628,
0.062341347336769104,
0.05040912330150604,
0.0021008814219385386,
-0.06360127031803131,
-0.008749947883188725,
-0.04283223673701286,
0.03630175068974495,
0.025974959135055542,
-0.003592230612412095,
-0.060351867228746414,
0.021158240735530853,
-0.013291258364915848,
-0.030845243483781815,
0.020639833062887192,
0.06403905153274536,
0.02635449357330799,
-0.04378361627459526,
-0.0022629867307841778,
0.022807227447628975,
0.011684013530611992,
0.07148131728172302,
0.054731275886297226,
-0.05035138130187988,
0.0453546978533268,
-0.06072743982076645,
0.02001064456999302,
0.0042472826316952705,
0.06396246701478958,
0.011944891884922981,
-0.027146173641085625,
0.03418266773223877,
-0.07402531057596207,
0.020559173077344894,
0.07751942425966263,
0.02261166088283062,
0.028116146102547646,
-0.00787119660526514,
-0.029966436326503754,
-0.07434690743684769,
-0.03227778896689415,
0.03842304274439812,
0.043379999697208405,
0.00977079663425684,
-0.043453022837638855,
0.009619282558560371,
-0.0638219565153122,
0.05801576003432274,
0.016812853515148163,
0.02119031548500061,
0.029963847249746323,
-0.032745540142059326,
0.012221245095133781,
-0.02832176350057125,
-0.012326262891292572,
-0.030009448528289795,
0.03310753405094147,
-0.025589700788259506,
-0.052596963942050934,
0.04687958210706711,
-0.023038482293486595,
-0.006392944138497114,
0.018527720123529434,
-0.03137309476733208,
0.05167757719755173,
0.0299955103546381,
-0.059763289988040924,
-0.0037697385996580124,
-0.05599992722272873,
-0.0370166078209877,
0.022421421483159065,
-0.004461952950805426,
-0.06281517446041107,
0.021893953904509544,
0.036131445318460464,
-0.0471988208591938,
0.03613327443599701,
0.0516154021024704,
0.005445575807243586,
-0.03606916964054108,
-0.015294152311980724,
-0.01607215404510498,
0.02965664118528366,
-0.03129330649971962,
-0.010756155475974083,
0.0037359336856752634,
-0.012350453995168209,
-0.001668931683525443,
0.05882394686341286,
0.012379783205688,
-0.006424855440855026,
-0.018600651994347572,
-0.008379954844713211,
0.03353395313024521,
-0.022516513243317604,
0.000507528253365308,
-0.006601074710488319,
0.05872678756713867,
0.033092599362134933,
-0.046481095254421234,
0.011992914602160454,
0.0024982525501400232,
-0.023084314540028572,
0.016996052116155624,
-0.03780576214194298,
-0.0059781745076179504,
-0.03414702042937279,
-0.005270701367408037,
0.0019985924009233713,
-0.03378687798976898,
-0.0648963674902916,
0.04086065664887428,
0.006436007563024759,
-0.00313067389652133,
0.008701026439666748,
0.013467369601130486,
-0.020314209163188934,
0.026929454877972603,
0.05733466520905495,
0.06985975801944733,
-0.02853025682270527,
0.014348104596138,
0.048168983310461044,
0.018603477627038956,
0.01849108189344406,
-0.0009800562402233481,
-0.037820614874362946,
-0.02025795355439186,
0.03135158494114876,
-0.04029056429862976,
0.0012644861126318574,
-0.06855099648237228,
0.06488758325576782,
-0.043609071522951126,
0.06641162931919098,
-0.0028801648877561092,
0.03806279972195625,
0.0618901327252388,
-0.022727960720658302,
0.05178003013134003,
0.026462366804480553,
-0.049874670803546906,
-0.00025977534824050963,
-0.06177789717912674,
-0.01063045859336853,
0.0032986984588205814,
-0.06608082354068756,
-0.07499242573976517,
0.024837184697389603,
-0.00578290456905961,
-0.0021434214431792498,
-0.027588006108999252,
-0.0408036969602108,
-0.04207049310207367,
-0.017003357410430908,
-0.04269547387957573,
0.021783359348773956,
0.006550875958055258,
-0.04990716651082039,
0.02721749059855938,
0.07386834174394608,
0.035054899752140045,
-0.0000865105030243285,
-0.03002101369202137,
-0.0357263907790184,
-0.00839156098663807,
-0.042091306298971176,
0.026994671672582626,
0.061496101319789886,
0.054712556302547455,
0.008434255607426167,
0.008094554767012596,
0.007705983240157366,
0.02424723282456398,
-0.030200133100152016,
-0.06370959430932999,
-0.03478693962097168,
-0.029071561992168427,
0.01728646457195282,
0.03157978877425194,
0.017323646694421768,
-0.018490182235836983,
0.02788088656961918,
-0.09333155304193497,
0.05166928470134735,
-0.0357314869761467,
-0.04818223416805267,
0.009987631812691689,
-0.020807430148124695,
0.021408261731266975,
-0.030383741483092308,
-0.03705118969082832,
-0.039878346025943756,
0.030749276280403137,
0.05631674453616142,
-0.05488697439432144,
0.01253409031778574,
-0.026549993082880974,
-0.011420653201639652,
-0.013659147545695305,
0.05813663825392723,
-0.013411173596978188,
0.027199357748031616,
-0.03751754015684128,
-0.029166948050260544,
0.010069346986711025,
-0.02913416177034378,
-0.023649616166949272,
0.006311723031103611,
0.024990355595946312,
0.009622601792216301,
0.05579062178730965,
-0.018434766680002213,
-0.08854787796735764,
-0.019138852134346962,
-0.04169287905097008,
0.025068234652280807,
0.050667181611061096,
0.005102611146867275,
-0.000008487209015584085,
-0.06789765506982803,
0.00807915162295103,
0.03218386694788933,
-0.04817020148038864,
-0.030727475881576538,
0.060068074613809586,
0.04315173253417015,
0.0307623203843832,
0.01316771563142538,
0.013754463754594326,
0.01988477259874344,
-0.016873247921466827,
-0.05071331188082695,
0.04632975906133652,
0.019281353801488876,
0.020989809185266495,
-0.011160952039062977,
0.04673443362116814,
-0.011034700088202953,
-0.005772933829575777,
0.045004043728113174,
-0.06475307792425156,
-0.0031356222461909056,
-0.08829943835735321,
-0.012706930749118328,
0.009804397821426392,
-0.025066619738936424,
0.03699824959039688,
0.037212107330560684,
-0.02727675437927246,
0.0004460966447368264,
0.002030268544331193,
-0.005528056062757969,
0.013074716553092003,
-0.02608638070523739,
-0.030810076743364334,
-0.05292358621954918,
0.06102859228849411,
0.0030801338143646717,
-0.01692020893096924,
0.026843994855880737,
0.009976337663829327,
0.01817336119711399,
-0.031096959486603737,
0.04686824232339859,
0.03713766485452652,
0.02055848389863968,
-0.017298758029937744,
0.05307277292013168,
0.020237091928720474,
0.006654035300016403,
-0.03501880541443825,
0.0132524985820055,
-0.028735492378473282,
0.010929185897111893,
-0.05548172816634178,
-0.029553372412919998,
0.0395633801817894,
0.0831824243068695,
0.057292256504297256,
-0.08059920370578766,
-0.0004309753130655736,
0.045920539647340775,
-0.0468720942735672,
-0.029767028987407684,
0.09625767171382904,
-0.002302085282281041,
-0.02870185300707817,
0.036715488880872726,
0.03283494710922241,
-0.025388194248080254,
0.007590777240693569,
-0.06081816926598549,
-0.0434085987508297,
0.013878321275115013,
-0.016176845878362656,
0.06008969992399216,
0.014191619120538235,
0.03561198711395264,
0.006627801340073347,
0.017849314957857132,
0.07869032025337219,
0.0351257286965847,
0.04128282889723778,
0.03538062050938606,
-0.023391475901007652,
-0.012792807072401047,
-0.009064560756087303,
0.03497541323304176,
0.033751800656318665,
-0.04754582792520523,
0.021446598693728447,
0.010371110402047634,
-0.02817748859524727,
0.038637273013591766,
-0.017494644969701767,
0.0035991016775369644,
0.03926590457558632,
-0.013739876449108124,
-0.04031777381896973,
0.03005461022257805,
0.012536569498479366,
0.0548701286315918,
-0.018410440534353256,
0.03192213922739029,
0.034261878579854965,
-0.02659325860440731,
-0.02752603590488434,
0.07821732014417648,
-0.01566174067556858,
0.006879033986479044,
0.026502598077058792,
0.00044648413313552737,
0.006362071260809898,
-0.02239535190165043,
-0.007878946140408516,
0.019005263224244118,
-0.062148306518793106,
0.014221658930182457,
0.02068968303501606,
-0.0006124248029664159,
-0.03817323222756386,
0.011157363653182983,
0.0022742096334695816,
0.00030781200621277094,
-0.05756340175867081,
0.0379800982773304,
0.04772055521607399,
0.0059489659033715725,
-0.01358828041702509,
-0.016719048842787743,
-0.019744228571653366,
-0.040323469787836075,
-0.016501188278198242,
0.005209576804190874,
-0.016657089814543724,
0.022258780896663666,
-0.03859725594520569,
-0.030171018093824387,
-0.005215100944042206,
-0.009713907726109028,
0.00038050313014537096,
0.046174585819244385,
-0.030970025807619095,
0.021511193364858627,
-0.028158828616142273,
-0.025718947872519493,
0.0051711429841816425,
-0.054690636694431305,
0.0202809888869524,
-0.019987890496850014,
0.020889824256300926,
0.006135066505521536,
0.05744371935725212,
0.03686561807990074,
0.031722068786621094,
0.013417748734354973,
0.012638309970498085,
0.0017170754726976156,
-0.02227942645549774,
-0.02915170043706894,
-0.00015901429287623614,
-0.04412198066711426,
-0.027789924293756485,
0.019861122593283653,
0.01734975166618824,
-0.03066542185842991,
0.07107526063919067,
0.02393467351794243,
-0.0020941197872161865,
-0.04062016308307648,
0.015949975699186325,
0.0632820874452591,
-0.02825297974050045,
0.017907744273543358,
0.035512372851371765,
-0.023985426872968674,
0.030939538031816483,
-0.015327597968280315,
-0.008458332158625126,
0.022365447133779526,
0.055284302681684494,
0.03191880136728287,
-0.014703878201544285,
-0.035393908619880676,
-0.0617847666144371,
0.0006805009325034916,
0.035208553075790405,
0.02577950805425644,
0.03573955222964287,
-0.025308510288596153,
0.052187733352184296,
0.006083499640226364,
-0.01620996929705143,
-0.0014660580782219768,
-0.005310250446200371,
0.018163561820983887,
-0.04897408187389374,
0.02404182031750679,
-0.009107173420488834,
0.017949553206562996,
-0.019646473228931427,
0.0036462435964494944,
0.03316964581608772,
0.04287979379296303,
0.03580394387245178,
-0.015927214175462723,
-0.03292163088917732,
0.0121353380382061,
-0.035191453993320465,
0.01133304089307785,
-0.03043234907090664,
-0.039681848138570786,
-0.003541493322700262,
-0.018871711567044258,
0.017439883202314377,
-0.04026405140757561,
0.005296776071190834,
-0.020756646990776062,
-0.0018259716453030705,
-0.06994650512933731,
-0.03895421326160431,
-0.009665273129940033,
-0.03255296126008034,
0.015580874867737293,
0.020639294758439064,
-0.007444292772561312,
0.0012332111364230514,
-0.0377037413418293,
-0.05136493220925331,
0.022623365744948387,
0.004081257618963718,
-0.06594794243574142,
0.016531309112906456,
-0.00511437701061368,
0.05113865062594414,
0.04186244681477547,
-0.01610914058983326,
-0.020563939586281776,
0.024019839242100716,
0.013068389147520065,
-0.019923601299524307,
-0.027551325038075447,
-0.028825512155890465,
-0.03200644254684448
] |
<p>Say I'm given the following Schrodinger equation</p>
<p>$$\frac{d^2u}{dx^2}+ \left[E - V(x)+ \frac{a}{x^2}\right]u(x) =0$$</p>
<p>Where $a \in \mathbb{R}$. What are the physical interpretations of this equation? I understand that it means the angular momentum is fixed, but are there any other implications associated with this?</p> | g9244 | [
0.0029122205451130867,
-0.02162453718483448,
-0.026162194088101387,
-0.058318525552749634,
0.0888286828994751,
0.029886582866311073,
0.035705722868442535,
0.03323689103126526,
0.015581514686346054,
-0.029268626123666763,
-0.011514761485159397,
-0.015495029278099537,
0.009888502769172192,
-0.01138246338814497,
0.03769546374678612,
0.03568489849567413,
0.040311988443136215,
-0.005896853748708963,
-0.030895166099071503,
-0.014233247376978397,
-0.06866579502820969,
0.031295087188482285,
-0.010285459458827972,
-0.04033450409770012,
0.010493460111320019,
-0.0397157222032547,
0.014408757910132408,
0.017783842980861664,
-0.029775509610772133,
-0.014117961749434471,
-0.01740327849984169,
-0.009722896851599216,
0.04600652679800987,
-0.04986903443932533,
-0.05953562632203102,
-0.048823826014995575,
0.03593645244836807,
0.008106992579996586,
0.08483199030160904,
-0.05109727010130882,
0.04900879040360451,
-0.018630292266607285,
-0.05092140659689903,
-0.012686141766607761,
-0.019020220264792442,
-0.0032034055329859257,
-0.04102417454123497,
0.0324757918715477,
0.00001146723752754042,
0.05048638954758644,
-0.02976694330573082,
0.027695225551724434,
0.03648204728960991,
0.003199196420609951,
0.024077629670500755,
0.05095108598470688,
0.056030385196208954,
0.005001102574169636,
0.07219627499580383,
0.0818670466542244,
0.02124354988336563,
-0.008427015505731106,
-0.020447026938199997,
-0.016273759305477142,
0.06736063212156296,
-0.04511844366788864,
-0.02068181149661541,
-0.0271161962300539,
0.0377916544675827,
-0.03945533558726311,
0.03344626724720001,
-0.10119649767875671,
-0.03755085542798042,
-0.0424489825963974,
-0.028584470972418785,
-0.014827604405581951,
-0.00334377633407712,
-0.03591718152165413,
-0.00970936007797718,
-0.03643620014190674,
-0.03720226138830185,
-0.024353530257940292,
0.05114838480949402,
-0.044999316334724426,
0.047398872673511505,
-0.01373097114264965,
0.014776275493204594,
0.024431243538856506,
-0.013299863785505295,
0.040548957884311676,
0.00494585745036602,
-0.0635439082980156,
-0.020172368735074997,
-0.05034187436103821,
-0.020250502973794937,
-0.05625846982002258,
-0.04688384383916855,
0.06127442792057991,
-0.003742848290130496,
0.02777320332825184,
-0.07538875192403793,
0.023123877122998238,
0.023714037612080574,
0.019732095301151276,
0.014723485335707664,
0.014114025980234146,
-0.00803904328495264,
0.053525809198617935,
0.014296630397439003,
-0.058953091502189636,
-0.03252221643924713,
0.005096716340631247,
-0.01038119476288557,
0.00013670035696122795,
-0.0185881108045578,
-0.07448532432317734,
0.01397709921002388,
-0.0221734456717968,
-0.01439595129340887,
0.08291667699813843,
0.04236884042620659,
0.07031723856925964,
-0.0007471103454008698,
0.07787276059389114,
-0.009715639054775238,
-0.02235163375735283,
-0.046216391026973724,
-0.009703096933662891,
0.06035735085606575,
0.007748452015221119,
0.0379626601934433,
-0.06949570029973984,
0.009691111743450165,
0.03508240357041359,
0.048291679471731186,
0.06979335844516754,
-0.04258999973535538,
0.009587510488927364,
-0.01747916266322136,
0.004036740865558386,
0.03656504303216934,
-0.023463452234864235,
-0.019431455060839653,
0.02734605222940445,
-0.06236972287297249,
-0.011442005634307861,
-0.016248786821961403,
-0.042513929307460785,
0.022297557443380356,
-0.014321384951472282,
-0.07934743165969849,
0.05893632024526596,
-0.03032362088561058,
-0.03960508108139038,
0.03948935493826866,
-0.004185548052191734,
0.019166115671396255,
-0.02198641747236252,
0.006651080679148436,
-0.015073824673891068,
0.09515301883220673,
0.03339405730366707,
0.012150879018008709,
0.034673500806093216,
-0.07515181601047516,
0.011170715093612671,
0.03171083331108093,
-0.05623047053813934,
-0.02461809106171131,
-0.022968288511037827,
-0.0141303651034832,
0.06015659496188164,
-0.008791903033852577,
0.037062160670757294,
0.0006343469140119851,
0.10339342057704926,
-0.02712276205420494,
-0.05857904255390167,
0.007305953651666641,
0.04090290144085884,
-0.010545320808887482,
-0.010268071666359901,
0.053760409355163574,
-0.030292313545942307,
0.0017513965722173452,
-0.012915556319057941,
-0.006689147092401981,
0.06901497393846512,
-0.03933187574148178,
0.006698958110064268,
0.018943896517157555,
0.010302391834557056,
0.018552683293819427,
0.11616355925798416,
-0.02669530361890793,
-0.025346174836158752,
-0.0342225506901741,
-0.03141861408948898,
-0.03716706112027168,
0.06113649159669876,
-0.0035044027026742697,
0.022443246096372604,
0.06677547842264175,
0.01804974116384983,
0.057538773864507675,
-0.022497259080410004,
0.019334344193339348,
-0.015042919665575027,
0.033713940531015396,
0.020484233275055885,
0.05366729572415352,
-0.018054019659757614,
-0.013512799516320229,
0.0017878636717796326,
-0.04814731702208519,
-0.019993048161268234,
0.034955669194459915,
0.0004980918020009995,
-0.052733778953552246,
0.050653014332056046,
-0.04680218547582626,
-0.042045217007398605,
0.002280426910147071,
0.006281101610511541,
-0.022957656532526016,
0.004641052335500717,
-0.08821336925029755,
-0.021509043872356415,
-0.025253605097532272,
0.03790251538157463,
-0.0026032275054603815,
0.028426865115761757,
0.01374865509569645,
0.001967787276953459,
0.02144169621169567,
0.040215834975242615,
-0.016513802111148834,
-0.02351662889122963,
0.05828234180808067,
-0.020455120131373405,
0.029009107500314713,
-0.002275284146890044,
-0.07691055536270142,
-0.0041852109134197235,
0.037523187696933746,
0.10850154608488083,
0.0703057050704956,
-0.019691526889801025,
0.012812035158276558,
0.05710099637508392,
0.012306428514420986,
-0.011138622649013996,
-0.039689358323812485,
0.001235264353454113,
-0.048329856246709824,
-0.049111057072877884,
-0.029883647337555885,
0.041406355798244476,
-0.06318139284849167,
-0.022007042542099953,
-0.0637212023139,
-0.009669019840657711,
-0.019452063366770744,
0.03266153484582901,
-0.005728417541831732,
0.050604019314050674,
-0.023889169096946716,
0.07160661369562149,
0.05952245369553566,
-0.0039018839597702026,
0.026827335357666016,
0.0630665048956871,
-0.03760647773742676,
0.048136062920093536,
0.028005965054035187,
-0.06744769960641861,
0.023150023072957993,
-0.03688965365290642,
-0.0015825385926291347,
-0.048596810549497604,
0.007345736958086491,
0.05856843665242195,
-0.03550559654831886,
0.08174483478069305,
0.04113738611340523,
-0.013699068687856197,
-0.02075020968914032,
0.04203416779637337,
0.006484498269855976,
0.02094872295856476,
-0.005544559098780155,
0.0013583141844719648,
0.06220518797636032,
-0.029269592836499214,
-0.00045265964581631124,
0.05426643788814545,
0.024655768647789955,
0.005868205800652504,
0.005510580725967884,
0.055427055805921555,
-0.018343565985560417,
0.0150980856269598,
-0.04975058138370514,
0.00729532353579998,
0.00758922565728426,
0.02834523841738701,
-0.055685579776763916,
0.006451629102230072,
-0.02701549232006073,
-0.023529216647148132,
-0.0543837696313858,
0.05086967349052429,
-0.013429315760731697,
-0.028346514329314232,
-0.05823277309536934,
0.0048620314337313175,
-0.056592121720314026,
0.010260101407766342,
-0.013856116682291031,
-0.03350646793842316,
-0.04938355088233948,
-0.06610618531703949,
0.012335040606558323,
-0.02306104451417923,
0.017849363386631012,
0.016385335475206375,
-0.05286979675292969,
-0.0007065118406899273,
-0.019078830257058144,
-0.006455398164689541,
0.022234896197915077,
0.01505072321742773,
-0.011815221980214119,
-0.0073898364789783955,
-0.052883051335811615,
0.01868470013141632,
-0.058733630925416946,
0.0570925697684288,
0.04222438856959343,
-0.015424290671944618,
0.038288820534944534,
-0.03894484043121338,
-0.02245916798710823,
0.044913530349731445,
0.04064793884754181,
-0.011861530132591724,
-0.02428467944264412,
0.009205728769302368,
0.03605973720550537,
-0.009278267621994019,
-0.03458256646990776,
0.0030788949225097895,
-0.0063177780248224735,
0.006461939308792353,
0.0011304488871246576,
0.03183865547180176,
0.02388540655374527,
0.04814334958791733,
-0.042634736746549606,
0.03062068484723568,
0.0008269270765595138,
-0.03191551938652992,
-0.0051022665575146675,
0.049737196415662766,
-0.018865425139665604,
-0.00368238496594131,
-0.011051148176193237,
0.02408204972743988,
-0.014630153775215149,
-0.016901426017284393,
-0.037384796887636185,
-0.027318064123392105,
-0.0050387633964419365,
0.030961016193032265,
-0.016068831086158752,
-0.007625380530953407,
-0.011499268934130669,
-0.006188054569065571,
-0.05805930867791176,
0.01574106141924858,
0.009123782627284527,
0.04908187687397003,
-0.0026909904554486275,
0.06172386556863785,
-0.019964348524808884,
-0.032258011400699615,
-0.025664368644356728,
0.049101658165454865,
-0.0015564295463263988,
-0.020542040467262268,
0.028845319524407387,
-0.02877454087138176,
-0.03492613509297371,
0.06053789705038071,
-0.00021568663942161947,
-0.010010088793933392,
-0.00977378711104393,
-0.03340855613350868,
-0.03386838361620903,
0.021759208291769028,
-0.021049678325653076,
-0.020580319687724113,
-0.015518772415816784,
-0.048175930976867676,
0.0021248608827590942,
0.05009356886148453,
0.04496893659234047,
-0.018017660826444626,
0.02584502100944519,
-0.044883325695991516,
-0.02154204063117504,
0.0036357108037918806,
0.013097019866108894,
-0.05781233310699463,
-0.02942749671638012,
0.026202654466032982,
-0.0010088299168273807,
-0.04506223648786545,
0.007923063822090626,
0.01932486705482006,
0.051074784249067307,
0.025972459465265274,
0.059238944202661514,
-0.01836216263473034,
0.002619590610265732,
-0.004990552086383104,
0.08418846875429153,
0.00812713336199522,
-0.021316835656762123,
0.02325398288667202,
0.0047995829954743385,
0.026159361004829407,
-0.023290270939469337,
-0.004236578941345215,
-0.023045776411890984,
0.04380340129137039,
-0.021505940705537796,
0.009028103202581406,
-0.036425139755010605,
0.1015675812959671,
0.08911310881376266,
-0.035101085901260376,
0.030034532770514488,
-0.010554345324635506,
0.00530932005494833,
0.03733990341424942,
-0.011257228441536427,
-0.04507724195718765,
0.009824797511100769,
-0.014029381796717644,
-0.021723084151744843,
0.03949585184454918,
-0.0020142672583460808,
-0.04808337613940239,
0.02562686614692211,
-0.04944818466901779,
-0.06013030558824539,
0.03489205241203308,
0.0005182077875360847,
-0.043096885085105896,
-0.0528007410466671,
-0.00832490622997284,
-0.009430739097297192,
-0.05054955556988716,
0.030778294429183006,
-0.03343290090560913,
-0.020506655797362328,
-0.016530819237232208,
-0.08104197680950165,
-0.02831375040113926,
0.008070181123912334,
-0.04450302571058273,
0.017268957570195198,
0.005063132848590612,
0.029092084616422653,
-0.032766714692115784,
-0.021763479337096214,
-0.011889098212122917,
0.047095078974962234,
-0.060812681913375854,
0.01169564388692379,
0.0018851874629035592,
0.009363510645925999,
0.012413940392434597,
-0.04782109707593918,
-0.009201057255268097,
-0.06132207065820694,
-0.010630707256495953,
0.010191526263952255,
-0.0004140256205573678,
0.09802365303039551,
0.05967661738395691,
-0.010183787904679775,
-0.011444264091551304,
-0.023450057953596115,
0.06715166568756104,
-0.026220407336950302,
-0.003926798235625029,
0.031344301998615265,
-0.001309497863985598,
-0.012669811025261879,
-0.02659866027534008,
0.05992148816585541,
0.03377453237771988,
0.007133763749152422,
0.07486823946237564,
0.057607799768447876,
-0.014871224761009216,
0.030225493013858795,
-0.0009112266707234085,
-0.013118947856128216,
-0.0170141514390707,
0.009208297356963158,
0.029079552739858627,
0.007709351368248463,
-0.007047499995678663,
-0.04666484519839287,
-0.019081255421042442,
-0.0008350817370228469,
-0.007484653498977423,
0.0014701313339173794,
-0.0296823401004076,
0.019502820447087288,
-0.04527004808187485,
0.042908795177936554,
-0.04513198137283325,
-0.025355104357004166,
-0.026604440063238144,
0.0035848491825163364,
0.08913174271583557,
0.011068873107433319,
-0.02284151129424572,
0.08346956223249435,
0.019835948944091797,
0.010209483094513416,
-0.04009376838803291,
-0.029060596600174904,
-0.01769363507628441,
0.054730337113142014,
0.022108400240540504,
-0.0002557419065851718,
0.0019921029452234507,
0.02961157262325287,
0.0443652905523777,
-0.06406592577695847,
-0.011798137798905373,
-0.0063774180598556995,
0.04188226908445358,
0.053527072072029114,
-0.03133821859955788,
-0.03278560936450958,
-0.013843719847500324,
-0.035954177379608154,
-0.07595166563987732,
0.03494097292423248,
-0.028206363320350647,
-0.008848742581903934,
0.020310835912823677,
-0.000755739863961935,
-0.02230152301490307,
0.036520421504974365,
-0.0056627485901117325,
0.02077568508684635,
0.015873190015554428,
0.007772968616336584,
-0.036477528512477875,
0.04957437515258789,
0.005473644472658634,
0.03150760382413864,
0.0031388539355248213,
-0.057367321103811264,
0.03844011574983597,
0.016090942546725273,
0.0255306214094162,
0.017700981348752975,
0.02130119688808918,
-0.025281846523284912,
-0.005883678328245878,
0.0029962242115288973,
-0.008465677499771118,
-0.0029361017514020205,
-0.01756744645535946,
0.07969730347394943,
0.031112633645534515,
0.0017192160012200475,
-0.001691169454716146,
-0.023788901045918465,
-0.0087458286434412,
0.04000941663980484,
-0.006779900286346674,
-0.035941194742918015,
0.026941891759634018,
-0.007792796473950148,
-0.03283698856830597,
-0.009602248668670654,
-0.010635481216013432,
0.021707579493522644,
-0.04086419567465782,
-0.05435836687684059,
0.020868251100182533,
0.06952589005231857,
0.035523198544979095,
-0.010239290073513985,
0.04459601640701294,
0.017411360517144203,
-0.027272583916783333,
-0.041794680058956146,
-0.030389660969376564,
-0.04192506521940231,
0.03345463052392006,
-0.0074738613329827785,
0.03389580920338631,
-0.006234530825167894,
0.020085357129573822,
-0.04280761629343033,
-0.00154434097930789,
0.0042890398763120174,
0.04763046279549599,
0.00537859695032239,
-0.06721320748329163,
0.024019399657845497,
0.014089430682361126,
0.006150590721517801,
-0.0194284375756979,
0.02048419415950775,
0.013934907503426075,
0.0064356084913015366,
0.03414078429341316,
0.0514826774597168,
0.032246183604002,
0.0050723194144666195,
0.03333215042948723,
0.006881011184304953,
0.0037573170848190784,
-0.001936417887918651,
0.0050450596027076244,
0.005635973531752825,
-0.0041149272583425045,
0.08497432619333267,
0.04902077838778496,
0.023091524839401245,
0.046842362731695175,
0.03450364992022514,
-0.03312426805496216,
-0.06729241460561752,
-0.013271755538880825,
0.007029328029602766,
-0.034008510410785675,
-0.08349546045064926,
-0.009640427306294441,
-0.0033649445977061987,
-0.026730883866548538,
0.0038676541298627853,
0.043784309178590775,
-0.05671434476971626,
-0.044358640909194946,
-0.02182712033390999,
0.05866208299994469,
0.02358859032392502,
-0.04918400198221207,
-0.019075289368629456,
-0.008997155353426933,
-0.017489705234766006,
0.006970908958464861,
-0.027806254103779793,
-0.006042072549462318,
0.010630903765559196,
-0.0474766306579113,
0.028400234878063202,
-0.03664174675941467,
-0.012158035300672054,
0.012496859766542912,
-0.0310139749199152,
-0.009255383163690567,
-0.02698505111038685,
0.029577743262052536,
-0.017441587522625923,
-0.0011051830369979143,
-0.05775878578424454,
0.0010425410000607371,
0.023947931826114655,
0.024970706552267075,
0.05268507078289986,
-0.008252951316535473,
-0.0685390904545784,
0.030098333954811096,
0.0019394571427255869,
-0.015946388244628906,
-0.022636301815509796,
0.04270043596625328,
0.031102683395147324,
0.05779152363538742,
0.07684367150068283,
0.005039256066083908,
-0.020372509956359863,
-0.0519314706325531,
-0.015288213267922401,
0.05683629587292671,
-0.004341296385973692,
-0.024463677778840065,
0.019295912235975266,
-0.034986961632966995,
0.029266495257616043,
-0.010076320730149746,
0.03011178784072399,
0.010810012929141521,
0.010693651624023914,
-0.007844976149499416,
-0.01127938274294138,
-0.02999061718583107,
0.02236188016831875,
-0.08348684757947922,
0.019406475126743317,
-0.000677559815812856,
0.040588341653347015,
-0.0012422377476468682,
-0.04645039886236191,
0.06061868742108345,
0.02444959059357643,
0.01427757740020752,
-0.03688967600464821,
0.00614537950605154,
-0.010724173858761787,
-0.08328131586313248,
-0.031567007303237915,
-0.01389332115650177,
-0.06548501551151276,
0.01441284827888012,
0.0042070806957781315,
0.013605453073978424,
0.00017409876454621553,
0.026822946965694427,
-0.0025785265024751425,
0.04913901537656784,
-0.029406046494841576,
0.0035875842440873384,
-0.003972119651734829,
0.009391910396516323,
-0.047161899507045746,
0.013534612953662872,
-0.007836898788809776,
-0.07990475744009018,
0.004823420196771622,
-0.019063323736190796,
-0.045310087502002716,
-0.03678495064377785,
-0.017913028597831726,
0.012779957614839077,
0.025696685537695885,
-0.006414204835891724,
0.029751483350992203,
0.02149384282529354,
-0.030014773830771446,
0.009537679143249989,
0.01964801549911499,
-0.06442610919475555,
-0.013418508693575859,
0.00783829391002655,
0.04435890167951584,
0.017063667997717857,
0.040293868631124496,
0.01834365352988243,
-0.03395691514015198,
-0.017290452495217323,
0.011636313982307911,
-0.09552549570798874,
-0.042301055043935776,
0.03038858436048031
] |
<p>This is a question triggered by <a href="http://physics.stackexchange.com/questions/93124/divergent-series">this post</a></p>
<p><a href="http://en.wikipedia.org/wiki/Madelung_constant" rel="nofollow">Madelung's constant</a> is defined to the coefficient of electrostatic potential energy in a ionic crystal. In the example of $NaCl$,
\begin{equation}
M = \sum_{ijk}{}^{'}\frac{(-1)^{i+j+k}}{\sqrt{i^2+j^2+k^2}}
\end{equation}
is conditionally convergent. </p>
<blockquote>
<p><em>Since this sum is conditionally convergent it is not suitable as definition of Madelung's constant unless the order of summation is also specified. There are two "obvious" methods of summing this series, by expanding cubes or expanding spheres. The latter, though devoid of a meaningful physical interpretation (there are no spherical crystals) is rather popular because of its simplicity. Thus, the following expansion is often found in the literature:[2]</em>
$$ M = -6 +12/ \sqrt{2} -8/ \sqrt{3} +6/2 - 24/ \sqrt{5} + \dotsb = -1.74756\dots. $$
<em>However, this is wrong as this series diverges as was shown by Emersleben in 1951.[3][4] The summation over expanding cubes converges to the correct value. An unambiguous mathematical definition is given by Borwein, Borwein and Taylor by means of analytic continuation of an absolutely convergent series.</em></p>
</blockquote>
<p>I have the following questions.</p>
<p>1) Expanding sphere leads to a divergent series. OK, what if I make a perfect spherical sample of $NaCl$, will the experimentally measured Madelung's constant to be infinity?</p>
<p>(<strong>EDIT</strong>: I maybe have some misunderstanding of divergence: it could be the case that the series is bounded but don't have a definite limit. So is the series for expanding sphere bounded? and if there is no definite limit, what's the experimentally measured value for a perfect spherical crystal?)</p>
<p>2) What physical principle dictates the order of summation? or why does finite number obtained by analytic continuation should be consistent with the observed value?</p>
<p>3) What is the role of charge neutrality here? I ever programed to compute Madelung's constant using the fractional charge idea((assign $\frac{1}{8}$ charge to the corner, $\frac{1}{4}$ to the edge, $\frac{1}{2}$ to the face ), which makes the expanding cube charge neutral. Does that mean charge neutrality is one of conditions that <em>must</em> be enforced? or it is just for the sake of computational efficiency?</p> | g9245 | [
0.04245155304670334,
0.0762326642870903,
0.014614846557378769,
-0.07407357543706894,
-0.006166571285575628,
0.008179260417819023,
0.025112340226769447,
-0.0011336180614307523,
-0.001911903265863657,
0.02373836748301983,
-0.03880884125828743,
0.030649226158857346,
0.02568618580698967,
0.0032687182538211346,
-0.044710922986269,
-0.00024172170378733426,
0.008096931502223015,
-0.0777360275387764,
-0.03319239988923073,
0.07018506526947021,
0.021260254085063934,
-0.0006266533746384084,
0.0254720076918602,
-0.03409016877412796,
-0.025952283293008804,
0.0054189423099160194,
0.05528338998556137,
0.004520583897829056,
-0.005703394766896963,
-0.040159545838832855,
0.03819752484560013,
-0.009352540597319603,
0.006655652076005936,
-0.007310085464268923,
-0.02479386329650879,
0.037681180983781815,
0.03903451934456825,
0.03333153948187828,
0.038097381591796875,
-0.01787135936319828,
-0.02627422660589218,
0.015482451766729355,
0.002043158048763871,
0.06004418432712555,
-0.04272666946053505,
-0.06697726994752884,
0.007030334323644638,
-0.01924469694495201,
0.053366564214229584,
-0.010508205741643906,
-0.04771171882748604,
0.050690896809101105,
0.05292762815952301,
-0.07000923901796341,
-0.013528943061828613,
0.08099217712879181,
-0.006738422438502312,
0.03857359662652016,
0.04206950590014458,
0.06834562122821808,
0.09130033105611801,
-0.034148793667554855,
0.01784006506204605,
-0.005589744541794062,
0.06086016818881035,
-0.021768515929579735,
-0.024501388892531395,
0.05329066514968872,
-0.020342595875263214,
-0.00007824570639058948,
-0.0022236055228859186,
-0.07781639695167542,
-0.05358284339308739,
-0.008907100185751915,
-0.006051391828805208,
0.0017259767046198249,
0.09495559334754944,
0.010466177947819233,
0.045336950570344925,
-0.02556353621184826,
-0.03810711205005646,
-0.04160595312714577,
0.031362950801849365,
-0.01321952510625124,
0.08532754331827164,
-0.030341019853949547,
-0.001588030019775033,
-0.008851245976984501,
-0.02345529943704605,
0.008626130409538746,
-0.013852457515895367,
-0.05233190581202507,
-0.005567091051489115,
-0.01327111478894949,
-0.0322754792869091,
-0.02138715423643589,
0.06235339865088463,
-0.014891676604747772,
0.042800042778253555,
0.0036976137198507786,
-0.02414446696639061,
-0.013455499894917011,
0.025851799175143242,
0.03525948524475098,
0.014791457913815975,
0.022856133058667183,
0.022133074700832367,
-0.016999708488583565,
0.03610384091734886,
-0.04505489766597748,
-0.011003471910953522,
-0.001230177702382207,
-0.05009831488132477,
-0.06466908007860184,
-0.08412020653486252,
-0.007010702043771744,
0.06949906796216965,
0.04001431167125702,
-0.02836107276380062,
0.0024394893553107977,
-0.009748554788529873,
0.06364981830120087,
0.05432726815342903,
0.01873970590531826,
-0.04257705807685852,
0.0317804180085659,
0.08071916550397873,
-0.005654837936162949,
-0.03518298640847206,
-0.05207956209778786,
0.021914144977927208,
0.003176175756379962,
-0.017472179606556892,
0.010415461845695972,
-0.004306410904973745,
0.012834625318646431,
-0.015634479001164436,
0.018367217853665352,
0.01464870385825634,
0.031021161004900932,
-0.07594112306833267,
-0.09163416922092438,
0.0016390267992392182,
0.010585568845272064,
-0.0019091381691396236,
0.01284390315413475,
-0.003988610580563545,
-0.026377813890576363,
0.01726720668375492,
0.028465501964092255,
0.021244412288069725,
0.053554534912109375,
0.015134265646338463,
-0.021565204486250877,
-0.015272246673703194,
0.03305596858263016,
0.09969780594110489,
0.008927523158490658,
0.05445884168148041,
0.00006123957427917048,
-0.013719087466597557,
0.00018878102127928287,
-0.07167600840330124,
0.04139522463083267,
-0.04132793843746185,
-0.0024252256844192743,
0.0071948617696762085,
-0.001366238109767437,
0.05342760682106018,
-0.10289721935987473,
0.00048146641347557306,
0.004815671592950821,
-0.027228953316807747,
0.014277595095336437,
0.031229477375745773,
0.048339348286390305,
0.014138828963041306,
-0.00876232422888279,
0.0439179390668869,
-0.020084934309124947,
-0.06874363124370575,
-0.006739715114235878,
0.03504415601491928,
-0.007667801808565855,
-0.03336421027779579,
0.018040994182229042,
0.009273642674088478,
-0.009874573908746243,
0.02096627652645111,
0.017440028488636017,
-0.009500416927039623,
0.04350477084517479,
-0.04770619794726372,
0.08068922162055969,
0.01322846207767725,
-0.0012799659743905067,
0.056186381727457047,
-0.028490576893091202,
-0.026298534125089645,
-0.009998360648751259,
-0.00692123593762517,
0.08187288045883179,
-0.026065519079566002,
0.026412710547447205,
0.018032196909189224,
0.04256200045347214,
-0.030459079891443253,
-0.04651962220668793,
0.03385404124855995,
0.016121627762913704,
-0.0273685734719038,
0.007475831545889378,
-0.06057720258831978,
-0.004463297314941883,
0.029178906232118607,
0.00880331452935934,
0.000027998106816085055,
0.01264551654458046,
-0.026668155565857887,
0.039565276354551315,
-0.06602093577384949,
0.04444218799471855,
-0.013248372822999954,
-0.020402994006872177,
0.003853204194456339,
-0.0193968303501606,
0.004032415803521872,
-0.012675168924033642,
-0.0035385864321142435,
-0.020963987335562706,
-0.08259687572717667,
-0.021123453974723816,
0.03919665142893791,
-0.00635925168171525,
0.05183132365345955,
0.03860435634851456,
-0.08671550452709198,
0.026003407314419746,
0.02308006025850773,
-0.028626080602407455,
0.017340760678052902,
-0.03892086446285248,
-0.01381014660000801,
-0.002015317091718316,
0.0037539987824857235,
-0.046361733227968216,
0.003423381829634309,
-0.008650369942188263,
0.012129627168178558,
0.0069009121507406235,
0.03803807497024536,
-0.03265058249235153,
0.03433074802160263,
0.05208923667669296,
-0.01230060588568449,
-0.0004888471448794007,
0.03629079461097717,
0.025250887498259544,
0.03115762025117874,
-0.046654149889945984,
-0.006763512268662453,
-0.013625680468976498,
0.027166306972503662,
-0.016463588923215866,
-0.04602380841970444,
0.01220784429460764,
-0.04526901990175247,
0.04949920251965523,
0.03934010863304138,
-0.03541373461484909,
0.0005873641930520535,
0.044548150151968,
0.11889582127332687,
0.039126019924879074,
-0.043120257556438446,
0.012613791972398758,
0.021948687732219696,
-0.01862727850675583,
0.027683138847351074,
-0.027685752138495445,
-0.05766397714614868,
-0.01751622185111046,
-0.03159041330218315,
0.06041571497917175,
-0.0042805178090929985,
-0.011561368592083454,
0.0682525485754013,
-0.03807301074266434,
0.016037490218877792,
0.011245502158999443,
0.004319494590163231,
0.018847990781068802,
0.02848343551158905,
0.03494346886873245,
-0.017961211502552032,
-0.01593816466629505,
-0.01814887300133705,
-0.040996331721544266,
0.01596025563776493,
0.054547395557165146,
0.019966749474406242,
-0.04191472381353378,
-0.019847866147756577,
0.0648784413933754,
0.018912460654973984,
0.07063734531402588,
-0.00949543621391058,
-0.05194687470793724,
-0.0015589965041726828,
0.040572766214609146,
-0.07401199638843536,
-0.002532471437007189,
0.021408800035715103,
0.043820057064294815,
-0.02003675326704979,
0.03733423352241516,
-0.017953194677829742,
0.01610686257481575,
0.013208289630711079,
-0.024139007553458214,
-0.02525242604315281,
0.014698685146868229,
0.02525923401117325,
0.05849287658929825,
0.0070936656557023525,
0.0038569574244320393,
-0.03783513978123665,
-0.030798805877566338,
-0.04260812699794769,
0.033768221735954285,
-0.000889913528226316,
0.020930595695972443,
0.04813634604215622,
0.009908056817948818,
0.0021183921489864588,
-0.08195324242115021,
-0.03335467725992203,
-0.016393044963479042,
0.052224405109882355,
0.02208571508526802,
-0.05517447739839554,
-0.026672901585698128,
-0.022205466404557228,
-0.03178158402442932,
-0.03313184157013893,
-0.02726220339536667,
-0.07210592925548553,
-0.024675630033016205,
-0.018769055604934692,
0.017522307112812996,
0.0304380115121603,
0.02472803182899952,
0.00876277033239603,
0.041834261268377304,
0.039313606917858124,
-0.001088721677660942,
-0.01070769689977169,
0.060850925743579865,
-0.04910794645547867,
-0.04468095675110817,
0.04666508734226227,
-0.02504529245197773,
0.0075211916118860245,
-0.021099375560879707,
-0.007895155809819698,
-0.00947158969938755,
0.017640016973018646,
0.08385168015956879,
0.046271152794361115,
-0.04222602769732475,
0.04138726368546486,
-0.0209795068949461,
0.021845940500497818,
0.01767812855541706,
0.04636755958199501,
-0.012530685402452946,
-0.010714804753661156,
0.0658162385225296,
-0.05897103250026703,
0.030049415305256844,
0.06412696838378906,
0.013331742957234383,
0.028834646567702293,
-0.02028759755194187,
-0.07388638705015182,
0.020297136157751083,
-0.017781736329197884,
-0.0021491514053195715,
0.005290147382766008,
-0.04124898836016655,
0.0569453127682209,
-0.01429592166095972,
-0.0543198399245739,
0.0009219225030392408,
-0.0016050920821726322,
-0.024353988468647003,
-0.037595368921756744,
-0.012932803481817245,
-0.007431294769048691,
0.009282484650611877,
0.06530912965536118,
-0.010917343199253082,
-0.030743146315217018,
-0.03757674992084503,
-0.001145777991041541,
-0.03891473263502121,
0.05953628197312355,
-0.023245569318532944,
0.018296338617801666,
-0.07270441949367523,
0.03064008615911007,
0.028675418347120285,
-0.023617960512638092,
-0.07490354031324387,
0.035809412598609924,
-0.044093452394008636,
0.018399421125650406,
-0.019303906708955765,
0.004758681636303663,
-0.004700516816228628,
-0.016588998958468437,
0.00355198560282588,
-0.04192531108856201,
-0.024425722658634186,
0.02960255928337574,
0.06591445952653885,
-0.00641561159864068,
-0.025601482018828392,
-0.03862714767456055,
-0.020022403448820114,
-0.02769562415778637,
0.052158597856760025,
0.029277721419930458,
-0.007138564717024565,
-0.050891440361738205,
0.026799794286489487,
-0.0232663843780756,
0.028926311060786247,
-0.049284156411886215,
0.018234800547361374,
0.056954849511384964,
0.02242361754179001,
0.07778122276067734,
0.026885850355029106,
0.02059115096926689,
-0.032431188970804214,
-0.061158765107393265,
-0.009146660566329956,
0.07016903907060623,
0.01766059175133705,
-0.02391958050429821,
0.04934334754943848,
0.040274232625961304,
-0.014661871828138828,
0.006574195344001055,
0.0008636935381218791,
-0.004856233950704336,
-0.0007957892958074808,
-0.03980642184615135,
-0.008035849779844284,
0.011870212852954865,
-0.0358237586915493,
-0.017834139987826347,
-0.03088562935590744,
0.03188268840312958,
0.026948489248752594,
-0.03651510924100876,
-0.05673719942569733,
0.007019709330052137,
-0.022686634212732315,
-0.013954502530395985,
0.03667259216308594,
0.08565888553857803,
-0.008552605286240578,
-0.00969939399510622,
-0.06347334384918213,
-0.0035022194497287273,
-0.025695238262414932,
-0.011844458989799023,
-0.033986881375312805,
-0.03218730539083481,
0.00012046619667671621,
-0.030628258362412453,
0.04540545493364334,
0.02212340198457241,
0.0027460562996566296,
-0.0173660721629858,
-0.044105734676122665,
-0.0031682648696005344,
-0.0012294851476326585,
0.01733320951461792,
-0.052006181329488754,
0.03815470635890961,
0.0385107696056366,
-0.01112284604460001,
0.04600653797388077,
0.0012433649972081184,
0.008675328455865383,
0.07037681341171265,
0.012412124313414097,
-0.016349710524082184,
0.011279069818556309,
-0.06625022739171982,
0.016844814643263817,
-0.03342533856630325,
-0.009740499779582024,
0.06145239993929863,
-0.020635567605495453,
0.026226533576846123,
-0.012218561954796314,
-0.016842719167470932,
0.0004070153518114239,
0.013826156035065651,
0.02603640779852867,
0.0658627599477768,
-0.007958689704537392,
-0.06279496103525162,
-0.040075890719890594,
-0.10660415887832642,
-0.005229267757385969,
0.006255033891648054,
0.011400442570447922,
0.0319133922457695,
-0.0013621647376567125,
0.03715666010975838,
-0.03174727037549019,
-0.007762107998132706,
-0.04064224660396576,
0.017220022156834602,
0.033690232783555984,
0.0003509963280521333,
0.058514609932899475,
-0.03342287614941597,
-0.025605367496609688,
-0.004239992238581181,
0.005358392372727394,
-0.05490439385175705,
-0.00867074728012085,
0.022682929411530495,
0.012999013066291809,
0.001206914777867496,
0.016821131110191345,
-0.010010303929448128,
0.06355917453765869,
-0.057932108640670776,
0.007489901967346668,
-0.00768205476924777,
0.024958640336990356,
0.0606815367937088,
-0.03201257437467575,
-0.040844157338142395,
-0.015781361609697342,
-0.02360112965106964,
-0.016091888770461082,
0.05846855044364929,
0.0331895686686039,
0.019728360697627068,
-0.0172955971211195,
-0.04380727559328079,
-0.06641258299350739,
-0.0042976574040949345,
-0.022595107555389404,
-0.017763342708349228,
0.00898378249257803,
0.008626461960375309,
-0.10338859260082245,
0.0531671941280365,
0.009517630562186241,
0.008107203058898449,
0.03483346104621887,
0.0011212535900995135,
0.05883871391415596,
0.020123273134231567,
-0.020978396758437157,
0.04875987023115158,
0.03024127706885338,
-0.03893139585852623,
-0.02871963195502758,
0.026147861033678055,
-0.005570331122726202,
-0.04335309565067291,
0.020125022158026695,
-0.004174601752310991,
-0.0004602612170856446,
-0.004225658718496561,
0.029678866267204285,
-0.007612070068717003,
-0.000993334106169641,
0.004955420270562172,
-0.05735005810856819,
-0.003827895037829876,
-0.013588573783636093,
0.06077538803219795,
-0.00770625751465559,
0.009583035483956337,
-0.04196693375706673,
-0.0021177383605390787,
-0.02420908212661743,
0.02990209497511387,
-0.04587334394454956,
-0.0017003221437335014,
0.036548711359500885,
-0.013862216845154762,
-0.009321662597358227,
-0.018742963671684265,
-0.019067976623773575,
-0.01980515569448471,
0.014037320390343666,
0.007120255846530199,
0.0038550987374037504,
-0.032021235674619675,
0.018433164805173874,
0.029225388541817665,
-0.025005435571074486,
0.0004669087938964367,
-0.028758637607097626,
0.009150009602308273,
-0.019455408677458763,
-0.05505016818642616,
-0.03200988098978996,
0.012145851738750935,
-0.0047167884185910225,
-0.01332075148820877,
-0.021464727818965912,
0.05548427626490593,
0.04771995171904564,
-0.017490321770310402,
0.027161583304405212,
-0.0008421748061664402,
0.047729115933179855,
0.020161127671599388,
0.003524009371176362,
-0.053679343312978745,
0.05074978247284889,
0.02301238663494587,
0.033896997570991516,
-0.027910279110074043,
0.007031172048300505,
0.012451513670384884,
-0.010677331127226353,
-0.07226055860519409,
0.0354173369705677,
0.07143022865056992,
0.019888892769813538,
-0.05077945068478584,
0.07513979822397232,
0.01673411950469017,
-0.0013370333472266793,
-0.06658519059419632,
0.019692469388246536,
0.04206088185310364,
-0.025854459032416344,
-0.034972287714481354,
0.06054837256669998,
-0.06041976809501648,
0.037073809653520584,
0.008820676244795322,
0.047648679465055466,
0.06366395205259323,
0.0014764935476705432,
-0.04226020723581314,
0.038132987916469574,
0.0027930717915296555,
-0.04031359404325485,
-0.022259380668401718,
0.006520685274153948,
-0.007255865726619959,
-0.05245131254196167,
0.023424945771694183,
-0.10476754605770111,
0.05343254655599594,
0.015539503656327724,
0.014068400487303734,
0.056004930287599564,
0.043157681822776794,
0.020180469378829002,
-0.03477519378066063,
-0.009176191873848438,
-0.018528902903199196,
0.01575571484863758,
-0.005135448649525642,
0.005390909034758806,
-0.002357528079301119,
-0.014753073453903198,
-0.0176253505051136,
0.015132573433220387,
-0.05956490337848663,
-0.009638592600822449,
0.0029835656750947237,
-0.0274006687104702,
0.012261495925486088,
0.011277646757662296,
0.014401273801922798,
0.016717998310923576,
0.0012145244982093573,
-0.023372186347842216,
0.02189398743212223,
0.008146598003804684,
-0.006811333820223808,
-0.03370934724807739,
-0.008811219595372677,
-0.04655715078115463,
-0.04640146717429161,
-0.07820983231067657,
0.008192047476768494,
-0.016297634690999985,
-0.02672920562326908,
0.011008516885340214,
0.01048315316438675,
-0.04849104583263397,
-0.015016413293778896,
-0.026774302124977112,
-0.014894871972501278,
-0.03303688392043114,
0.03709663823246956,
-0.006110682152211666,
0.019963707774877548,
-0.012209937907755375,
0.04051579162478447,
0.030186397954821587,
-0.03954741358757019,
-0.007568972185254097,
0.008312026038765907,
-0.039407189935445786,
-0.04070631414651871,
-0.03924975171685219,
-0.0410638153553009,
0.02098233997821808,
-0.024640316143631935,
0.037243425846099854,
-0.002688669366762042,
-0.012240100651979446,
-0.027967864647507668,
0.02335454523563385,
-0.03184106945991516,
-0.010848747566342354,
0.029534971341490746,
-0.06259729713201523,
0.018164116889238358,
-0.017745697870850563,
0.012548335827887058,
-0.020802054554224014,
-0.0033252479042857885,
-0.07955480366945267,
-0.0049179294146597385,
-0.00916136521846056,
-0.13194015622138977,
0.07093280553817749,
0.10138817131519318,
0.015234877355396748,
-0.02960941381752491,
-0.025270897895097733,
0.02228129282593727,
0.004617778584361076,
0.00900582317262888,
0.012341056950390339,
-0.01640975847840309,
0.04260433837771416,
0.05091305449604988,
-0.0224279947578907,
-0.03515790402889252,
-0.039627715945243835,
0.03138870745897293,
0.047667719423770905,
-0.01865203306078911,
-0.058104049414396286,
-0.014395782724022865,
-0.010467492043972015
] |
<p>While studying reflection through a plane mirror, I have been told that when the object is real the image will be virtual and <strong>the image will be real while the object is virtual</strong>.</p>
<p>What are virtual objects? Do they really exist in nature? </p> | g209 | [
-0.006993402726948261,
0.034387391060590744,
0.01518979761749506,
-0.03030960075557232,
0.05758930370211601,
0.0669914036989212,
-0.018182039260864258,
0.030646776780486107,
-0.002663414226844907,
-0.023767394945025444,
-0.03917372226715088,
0.011187943629920483,
0.022569146007299423,
0.012166532687842846,
-0.060748785734176636,
-0.022602679207921028,
0.03595432639122009,
-0.03912988677620888,
0.019430045038461685,
-0.00895669311285019,
-0.016661595553159714,
-0.0268610380589962,
0.02116699144244194,
-0.03476044163107872,
-0.04009665176272392,
0.019942495971918106,
-0.03664041683077812,
0.014912031590938568,
-0.007727233227342367,
-0.025604212656617165,
0.048506513237953186,
-0.03206027299165726,
0.06409339606761932,
-0.035812754184007645,
0.01938352920114994,
0.0187687985599041,
-0.0029356323648244143,
0.07865744829177856,
0.06231500208377838,
-0.007552301045507193,
-0.06206236034631729,
-0.006900000385940075,
0.02051173895597458,
-0.014036879874765873,
-0.013086722232401371,
0.022849323228001595,
-0.005063656717538834,
-0.024672379717230797,
0.04294448718428612,
-0.04976362735033035,
-0.0006580848130397499,
0.012377317063510418,
0.0034398511052131653,
-0.014512560330331326,
0.050939880311489105,
-0.0035776360891759396,
0.03257575258612633,
0.0014865314587950706,
0.0155556108802557,
-0.050868939608335495,
0.01878870464861393,
0.012108891271054745,
0.009462582878768444,
0.04886704310774803,
0.09758782386779785,
0.0055110580287873745,
-0.08988123387098312,
-0.00807217974215746,
0.026845095679163933,
0.011661014519631863,
0.015583097003400326,
-0.017616961151361465,
0.0004172051267232746,
-0.03463112190365791,
0.02979530207812786,
0.0013746790355071425,
0.054187092930078506,
-0.06577838957309723,
0.0038615234661847353,
0.044760726392269135,
0.04943244904279709,
0.015472650527954102,
-0.03245146572589874,
0.010402168147265911,
0.06362797319889069,
-0.02025732584297657,
-0.0072469222359359264,
-0.01143590547144413,
0.045840851962566376,
0.017212528735399246,
0.018479831516742706,
-0.05260980874300003,
0.018684500828385353,
0.03248298168182373,
-0.01096495520323515,
-0.0044693597592413425,
-0.017211180180311203,
0.03100733272731304,
-0.03383501246571541,
0.04108459874987602,
-0.02939702197909355,
-0.029448850080370903,
0.018097730353474617,
-0.018688591197133064,
0.01255635917186737,
0.023998230695724487,
0.023649701848626137,
0.02696148119866848,
-0.040667951107025146,
-0.03112412616610527,
-0.013399549759924412,
-0.045599035918712616,
-0.06673698127269745,
-0.0042162793688476086,
-0.016388308256864548,
-0.011549113318324089,
0.033912599086761475,
-0.010289669036865234,
0.009299569763243198,
0.09659229964017868,
0.06441560387611389,
-0.00689740153029561,
-0.004628646187484264,
0.07056135684251785,
0.014629651792347431,
-0.03563851863145828,
0.06800527125597,
-0.053907833993434906,
0.019905833527445793,
-0.006709768902510405,
-0.036452438682317734,
0.02942638471722603,
-0.043542999774217606,
-0.01775282621383667,
0.009581907652318478,
0.010942790657281876,
0.007944452576339245,
-0.10151892900466919,
0.0568099245429039,
-0.019777949899435043,
-0.0038201066199690104,
-0.012142352759838104,
-0.028464099392294884,
-0.03953416272997856,
-0.023705855011940002,
-0.08016768842935562,
0.07556576281785965,
0.02985817939043045,
-0.019828587770462036,
-0.023573217913508415,
-0.016265379264950752,
0.09888997673988342,
-0.014731237664818764,
-0.03924047201871872,
-0.06326169520616531,
-0.05195542424917221,
0.03338653966784477,
-0.01119838934391737,
0.04492751136422157,
-0.0017062301049008965,
0.07714244723320007,
-0.007996411062777042,
-0.025644052773714066,
-0.008327001705765724,
-0.029966801404953003,
-0.06074830889701843,
0.012310243211686611,
-0.05419110134243965,
0.04633332043886185,
0.00664479099214077,
-0.028046542778611183,
-0.006381716579198837,
0.021824676543474197,
0.020600244402885437,
-0.022387856617569923,
-0.005344757344573736,
-0.02330988273024559,
-0.0310883317142725,
0.08326185494661331,
0.04021487757563591,
-0.022055426612496376,
-0.061925794929265976,
-0.029925759881734848,
-0.008039886131882668,
0.0037393264938145876,
-0.010284090414643288,
-0.03545175865292549,
-0.014837810769677162,
-0.055422015488147736,
0.03631658852100372,
-0.062428560107946396,
-0.05974305048584938,
0.06334087252616882,
0.002479898976162076,
-0.0009774661157280207,
-0.025825506076216698,
0.030515428632497787,
-0.014680180698633194,
-0.06718271970748901,
0.026514841243624687,
0.02270791493356228,
0.019303975626826286,
0.03363834321498871,
0.03415238857269287,
-0.052628736943006516,
-0.014164529740810394,
0.0035332473926246166,
-0.03641323000192642,
-0.054695673286914825,
-0.018753446638584137,
0.10030827671289444,
0.013110673986375332,
0.01819770596921444,
-0.04013979807496071,
-0.01916835643351078,
0.02493327483534813,
-0.05261894688010216,
-0.028698690235614777,
-0.0224982388317585,
0.018695630133152008,
0.04062514752149582,
-0.004449554719030857,
0.04056595638394356,
-0.039842478930950165,
-0.007322144228965044,
0.015516970306634903,
-0.019024141132831573,
-0.021809473633766174,
0.05510064586997032,
-0.0059143174439668655,
-0.024818625301122665,
-0.0435260534286499,
0.08803343027830124,
0.0023462793324142694,
0.02540067955851555,
0.046867623925209045,
-0.03098667785525322,
0.03737828508019447,
0.019747069105505943,
-0.019039813429117203,
0.050356701016426086,
-0.03702474385499954,
0.013001514598727226,
-0.026645643636584282,
0.01943320222198963,
-0.015919728204607964,
0.026648640632629395,
-0.004762659315019846,
0.06505388021469116,
0.0151883065700531,
-0.015729671344161034,
-0.013157638721168041,
-0.011490910314023495,
0.032581619918346405,
-0.05775143578648567,
0.030925363302230835,
0.011085481382906437,
-0.01095400471240282,
-0.0038614929653704166,
0.00720351142808795,
-0.007031118962913752,
0.027642030268907547,
0.012054447084665298,
0.034931033849716187,
0.00142050557769835,
-0.01759193278849125,
-0.06251690536737442,
0.013753105886280537,
0.03316068649291992,
0.014579509384930134,
-0.06434554606676102,
0.04966401308774948,
-0.01755518466234207,
-0.04218405857682228,
0.01395840011537075,
0.017151229083538055,
-0.02652612514793873,
0.013100077398121357,
-0.007185306865721941,
0.007406629156321287,
-0.004518059082329273,
0.04522441327571869,
-0.05849337577819824,
-0.03667528182268143,
-0.007059577852487564,
-0.03049500845372677,
-0.0134692108258605,
0.02757389470934868,
-0.02776814065873623,
-0.015528799965977669,
-0.05904802680015564,
-0.004129255190491676,
0.030781401321291924,
-0.028012145310640335,
-0.0730590894818306,
-0.014727672562003136,
0.07046603411436081,
-0.003484101267531514,
0.04848559573292732,
0.04276018962264061,
-0.0016810346860438585,
0.02930334582924843,
0.02144467644393444,
-0.005016666371375322,
0.06622625887393951,
0.0009700487134978175,
0.03026401810348034,
0.01781114935874939,
-0.01265897136181593,
-0.011110336519777775,
-0.038345299661159515,
-0.002019754843786359,
-0.04606741666793823,
0.007502177730202675,
0.02120543085038662,
0.054466113448143005,
-0.09616637229919434,
0.06774585694074631,
-0.002095530042424798,
-0.037101320922374725,
-0.012616496533155441,
-0.019307978451251984,
-0.017641276121139526,
0.02391168847680092,
0.04203303903341293,
-0.0013175866333767772,
-0.033237967640161514,
-0.002849463140591979,
0.03336881473660469,
0.00526410574093461,
0.00965413823723793,
-0.00583260552957654,
-0.02805173024535179,
-0.014123421162366867,
-0.05837908387184143,
-0.005086973309516907,
-0.06288541108369827,
-0.0008389470749534667,
0.029622754082083702,
-0.004493949469178915,
0.02768283151090145,
-0.02954687736928463,
0.005908132530748844,
-0.038362711668014526,
0.08844028413295746,
0.0279123205691576,
-0.07250279188156128,
-0.012544040568172932,
0.006288500968366861,
0.0069734943099319935,
0.05259060859680176,
0.015416973270475864,
0.049251168966293335,
-0.05555528402328491,
-0.0018993509002029896,
0.027198299765586853,
-0.008325926959514618,
0.014334284700453281,
-0.03037656471133232,
-0.03538142517209053,
0.01978091150522232,
0.0007392980623990297,
0.06889020651578903,
-0.04288041964173317,
-0.012178827077150345,
-0.0030085307080298662,
0.029788531363010406,
0.006870581302791834,
0.040333718061447144,
0.07168355584144592,
0.006476730573922396,
0.004992990288883448,
-0.05476979538798332,
0.014036347158253193,
-0.006547787692397833,
0.01737472414970398,
0.008378703147172928,
0.014265602454543114,
-0.05005500093102455,
-0.01127681601792574,
0.046111829578876495,
0.03500301018357277,
0.05241715535521507,
0.0621538981795311,
-0.011423105373978615,
0.008391364477574825,
-0.04187849536538124,
-0.04224197566509247,
0.022879691794514656,
-0.04466218501329422,
0.041298191994428635,
-0.0017929886234924197,
-0.07970484346151352,
-0.007023275829851627,
0.02401464246213436,
-0.05372901260852814,
0.014199087396264076,
-0.012941095046699047,
-0.03071531094610691,
-0.03460557013750076,
-0.02335619553923607,
0.09144039452075958,
-0.035490814596414566,
-0.0114399753510952,
-0.005128148477524519,
0.0037563228979706764,
0.0047785141505301,
0.03129047155380249,
-0.04679989442229271,
-0.037869732826948166,
-0.041579749435186386,
-0.00421734107658267,
0.029737234115600586,
-0.09312890470027924,
-0.01269510667771101,
0.0333840511739254,
-0.006929922383278608,
0.043239694088697433,
0.040183912962675095,
-0.021675284951925278,
-0.0010017277672886848,
0.06801150739192963,
0.018100935965776443,
0.007738940417766571,
-0.01123987976461649,
0.016448240727186203,
-0.005154955200850964,
0.02800055593252182,
-0.021464567631483078,
0.005533967167139053,
0.04949432611465454,
-0.040774308145046234,
0.02731804922223091,
-0.00592759158462286,
0.0013978967908769846,
0.06031229346990585,
0.023222994059324265,
-0.01270690280944109,
0.001775110955350101,
0.010819385759532452,
0.03417321294546127,
0.024370571598410606,
0.10867888480424881,
0.0048537240363657475,
0.019207239151000977,
0.0063362387008965015,
-0.02462436817586422,
0.01853775605559349,
0.0013111132429912686,
-0.009274104610085487,
-0.0517662949860096,
0.047895386815071106,
-0.009569126181304455,
-0.06422938406467438,
0.025937778875231743,
-0.001679620356298983,
-0.0005013947375118732,
-0.006925526075065136,
-0.03478750213980675,
-0.03525696322321892,
-0.03755561262369156,
0.011187947355210781,
0.006464303936809301,
0.05233991518616676,
0.006342358887195587,
0.008861258625984192,
-0.04266757890582085,
-0.038017090409994125,
-0.020748097449541092,
-0.005874131340533495,
-0.04025264084339142,
0.03181116655468941,
0.04698774963617325,
0.052699703723192215,
0.038092758506536484,
0.023463290184736252,
-0.01526348665356636,
-0.04664646461606026,
0.029229745268821716,
-0.03816409409046173,
-0.01705704815685749,
-0.005372875370085239,
0.00854096282273531,
-0.01980239525437355,
-0.04971221089363098,
0.00773993507027626,
-0.04006170853972435,
0.06077338755130768,
-0.018358105793595314,
0.03269259259104729,
0.018940750509500504,
-0.03218523785471916,
-0.0172652006149292,
0.0017294423887506127,
0.024216659367084503,
-0.027240781113505363,
-0.011931700631976128,
-0.007828295230865479,
-0.03770044073462486,
0.06006640940904617,
-0.015428191050887108,
-0.03498087823390961,
-0.005622028838843107,
-0.0035783175844699144,
-0.010744042694568634,
0.061050619930028915,
0.06420113146305084,
-0.07275533676147461,
0.00778618548065424,
0.05473935976624489,
0.08257884532213211,
-0.05678001418709755,
-0.028605833649635315,
0.03466436266899109,
0.019223390147089958,
-0.029400266706943512,
-0.0005512405768968165,
0.04990636929869652,
-0.05515509843826294,
0.01701514981687069,
-0.011108103208243847,
-0.006996553391218185,
0.053456034511327744,
0.007392816711217165,
-0.0011395709589123726,
0.0218794122338295,
0.016415491700172424,
-0.035850416868925095,
0.08384228497743607,
0.015736235305666924,
0.023142173886299133,
0.004881236702203751,
-0.041219040751457214,
0.01546146534383297,
-0.024056777358055115,
-0.006055508274585009,
0.010969460941851139,
0.008987769484519958,
0.008139310404658318,
0.01687517948448658,
-0.03681989386677742,
0.011278683319687843,
-0.000048035650252131745,
0.061020318418741226,
0.0076997969299554825,
-0.010338588617742062,
0.01283425372093916,
0.022775566205382347,
0.0844888910651207,
0.04874234274029732,
-0.031830478459596634,
0.012444619089365005,
-0.0749427080154419,
0.026737714186310768,
0.07015395164489746,
0.02001233957707882,
-0.04175342991948128,
0.00040478617302142084,
-0.01568208821117878,
-0.058407124131917953,
-0.00737030291929841,
0.06282038241624832,
-0.046805061399936676,
-0.0486237108707428,
-0.03619522601366043,
-0.029440898448228836,
0.04350331425666809,
-0.005223819054663181,
0.005407652817666531,
-0.04656415432691574,
-0.07857037335634232,
0.06304717808961868,
0.05166669189929962,
-0.008578415028750896,
0.06608516722917557,
0.020583128556609154,
-0.032692618668079376,
-0.011565839871764183,
-0.04230437055230141,
0.024785730987787247,
0.04514802247285843,
-0.04881546273827553,
0.00730940094217658,
-0.00016309467901010066,
-0.012300673872232437,
-0.05281076952815056,
0.02179410122334957,
-0.046340711414813995,
-0.002462649019435048,
-0.021728791296482086,
0.032794684171676636,
0.06158682331442833,
-0.032878391444683075,
-0.054755598306655884,
0.0368085540831089,
-0.05862366780638695,
0.033239398151636124,
0.04185387119650841,
-0.06137702986598015,
0.03299052268266678,
0.029206791892647743,
-0.008129721507430077,
-0.014992951415479183,
-0.010214832611382008,
-0.004027377814054489,
0.02265351265668869,
-0.027687406167387962,
-0.004086995963007212,
-0.007271855138242245,
0.013580970466136932,
0.029133787378668785,
0.017767978832125664,
0.010674470104277134,
0.04659254476428032,
-0.014560580253601074,
-0.038100503385066986,
-0.00627505499869585,
-0.0594107024371624,
0.004364029038697481,
-0.015156429260969162,
-0.016540808603167534,
-0.0654909536242485,
0.03074951283633709,
-0.009453758597373962,
0.07919298112392426,
0.02427600882947445,
-0.02455407939851284,
0.04457636550068855,
0.0740530788898468,
0.09219182282686234,
-0.021322371438145638,
-0.036949194967746735,
-0.017557678744196892,
0.04774722456932068,
0.028305940330028534,
0.0450727716088295,
-0.05500885471701622,
0.046641755849123,
0.025554126128554344,
-0.016093524172902107,
0.008435322903096676,
-0.027220649644732475,
0.01714693382382393,
-0.014800344593822956,
-0.011197764426469803,
-0.004261805675923824,
-0.022175438702106476,
-0.03480453044176102,
-0.060965944081544876,
-0.03775792196393013,
0.05674978345632553,
-0.010306447744369507,
0.04329715296626091,
-0.06358686834573746,
-0.07715430110692978,
0.01770184561610222,
-0.012472339905798435,
-0.044856730848550797,
-0.03394649922847748,
-0.06424953043460846,
-0.05828876420855522,
0.00428767642006278,
-0.0701170340180397,
-0.061444949358701706,
0.013171463273465633,
0.013557661324739456,
-0.036353111267089844,
-0.035550348460674286,
-0.02352438122034073,
-0.017278021201491356,
-0.03344668447971344,
-0.053077008575201035,
-0.00017108993779402226,
-0.02400583028793335,
0.023940695449709892,
-0.027145640924572945,
-0.03560639172792435,
0.02162199839949608,
0.028368541970849037,
0.03299356624484062,
0.010744736529886723,
0.12567906081676483,
0.02066672220826149,
0.007767209317535162,
-0.032026201486587524,
-0.020746413618326187,
-0.008460329845547676,
-0.000429895386332646,
0.008041911758482456,
-0.058214522898197174,
-0.011032283306121826,
-0.00970828253775835,
-0.03256014361977577,
-0.0065604764968156815,
-0.007628952153027058,
-0.052369374781847,
0.004317155107855797,
0.001888936385512352,
0.02567082643508911,
-0.02181307226419449,
0.0016594050684943795,
0.04659649357199669,
0.015940451994538307,
0.015160879120230675,
-0.017866628244519234,
0.013935824856162071,
0.009809352457523346,
0.03259718790650368,
0.036736663430929184,
0.007733056787401438,
-0.0186880212277174,
0.02666982263326645,
0.08110727369785309,
-0.028191544115543365,
0.02227027900516987,
-0.05238332226872444,
-0.02384583093225956,
0.053057342767715454,
-0.01803247444331646,
0.026624757796525955,
-0.003152077319100499,
-0.03390688821673393,
0.0024235628079622984,
-0.02300061285495758,
0.007629163097590208,
0.0074270060285925865,
0.02528681978583336,
-0.04857635870575905,
-0.0060369521379470825,
0.02465950883924961,
0.0018786615692079067,
0.000248470256337896,
-0.03553410619497299,
0.047640297561883926,
-0.00784357264637947,
0.011831643059849739,
-0.019091833382844925,
-0.004028265364468098,
-0.012441441416740417,
0.002607508096843958,
0.07076181471347809,
-0.013811239041388035,
-0.009574927389621735,
-0.042657118290662766,
-0.025587227195501328,
-0.02436842955648899,
-0.02496916800737381,
-0.015224942937493324,
-0.01496194303035736,
-0.0006124520441517234,
-0.037337254732847214,
0.05095123127102852,
0.022680502384901047,
0.07355164736509323,
0.023001084104180336,
-0.05235172435641289,
0.002118696691468358,
0.03416608273983002,
0.06200147047638893,
0.0254602562636137,
-0.027492692694067955,
-0.0030357169453054667,
0.02017415128648281,
0.01993296667933464,
0.012157151475548744,
-0.07881046086549759,
-0.049711503088474274,
0.009446073323488235
] |
<p>If $|\psi \rangle$ represents a wavefunction through a column matrix and $\langle \psi |$ represents the dual vector in a row matrix and $|\psi \rangle \langle \psi | = \rho $ is the probability density of the wavefunction collapse to a particular value in $\mathbb{R}$ by a measurement, and matter is also a wave (DeBroglie), how does one represent matter by using Dirac notations - how about anti-matter? Would there be something similar to $\langle \psi |\psi \rangle = n \in \mathbb{R} $ ?</p>
<p>I apologize if the question is quite ignorant, i.e. Dirac's equations don't relate matter/anti-matter, it just seems they should - and I would like to know how ;)</p>
<p>Thanks,</p>
<p>Brian</p> | g9246 | [
0.012807147577404976,
-0.04633102938532829,
-0.020699208602309227,
-0.07237061858177185,
0.09172292798757553,
0.010306023992598057,
0.05449128523468971,
0.0192196574062109,
-0.09411370754241943,
-0.03173915296792984,
0.0053383540362119675,
-0.014743371866643429,
0.06093144044280052,
0.05928551033139229,
0.03662780672311783,
0.03778744861483574,
0.02140148915350437,
-0.019863829016685486,
0.006226577330380678,
0.0013474088627845049,
-0.021335327997803688,
0.001795712043531239,
0.016449522227048874,
-0.05489658564329147,
0.024726539850234985,
-0.01254346501082182,
0.01846807636320591,
-0.04979196935892105,
-0.019392099231481552,
0.02610304020345211,
0.005013061221688986,
0.028172247111797333,
-0.01081726886332035,
-0.04852282255887985,
-0.0039802310056984425,
0.014134189113974571,
0.024975275620818138,
0.051648881286382675,
0.014281152747571468,
-0.0002684206410776824,
-0.0392620675265789,
-0.03144564852118492,
0.025850072503089905,
-0.046922218054533005,
-0.00906230229884386,
0.05010644719004631,
-0.05303360894322395,
0.0038828083779662848,
-0.054123274981975555,
0.01584535837173462,
0.012408473528921604,
0.01188085600733757,
0.01013261266052723,
0.042490385472774506,
-0.02483559213578701,
0.06098957359790802,
0.013137594796717167,
-0.04599494859576225,
0.09062589704990387,
0.061279330402612686,
0.008669580332934856,
-0.004483662545681,
-0.02787138521671295,
-0.0062376041896641254,
0.07215207070112228,
0.01562913879752159,
-0.036780234426259995,
0.013122206553816795,
0.003948844037950039,
-0.009019403718411922,
0.026612965390086174,
-0.037421200424432755,
0.037898071110248566,
-0.05069999769330025,
-0.03831346333026886,
0.005649215076118708,
0.04427701607346535,
-0.009598868899047375,
0.024220962077379227,
-0.01121649332344532,
-0.06979890167713165,
-0.029717659577727318,
0.09742185473442078,
0.008708392269909382,
0.056405000388622284,
0.027705581858754158,
0.0373251847922802,
0.04246460273861885,
-0.005807570181787014,
0.0442306324839592,
-0.019112609326839447,
-0.041822150349617004,
0.05003086477518082,
0.012567969970405102,
-0.03524014726281166,
-0.032926712185144424,
-0.06361129879951477,
-0.024076862260699272,
-0.04299941286444664,
-0.00940279383212328,
0.030302586033940315,
-0.017315173521637917,
0.045768480747938156,
-0.015425656922161579,
-0.019891219213604927,
-0.006642460357397795,
0.015096736140549183,
-0.01937173120677471,
0.013956834562122822,
-0.006297936663031578,
-0.056474719196558,
0.007860287092626095,
-0.07938781380653381,
0.0076600671745836735,
-0.02475656196475029,
-0.06906931102275848,
0.05135585367679596,
-0.08893396705389023,
-0.032507870346307755,
0.09457318484783173,
-0.012266047298908234,
0.06344955414533615,
0.05417902022600174,
0.021037274971604347,
0.0013313895324245095,
-0.005561708472669125,
-0.002933648880571127,
0.060122013092041016,
0.03591614216566086,
-0.025829168036580086,
0.09217891097068787,
-0.004676605574786663,
-0.018026448786258698,
0.010687862522900105,
0.02689126506447792,
0.029511047527194023,
-0.053436972200870514,
0.0775010883808136,
-0.026404347270727158,
-0.018650975078344345,
0.03814174607396126,
-0.025888172909617424,
0.007202520035207272,
0.014998985454440117,
-0.039561737328767776,
-0.0469026155769825,
-0.02540181390941143,
-0.034573156386613846,
-0.0160994790494442,
0.001320510869845748,
0.0020888904109597206,
0.06420523673295975,
-0.042997393757104874,
-0.06424813717603683,
0.04690035805106163,
0.06260678172111511,
0.04894643649458885,
-0.05584469810128212,
-0.05757054686546326,
0.030882153660058975,
0.045421626418828964,
0.02497880347073078,
-0.01163471955806017,
0.046227701008319855,
-0.04586612433195114,
-0.041441235691308975,
-0.0053246202878654,
0.010829897597432137,
0.009032622911036015,
-0.033297665417194366,
-0.023072456941008568,
-0.006487038917839527,
-0.007323825266212225,
0.021816719323396683,
0.04894466698169708,
0.03948241472244263,
-0.057660918682813644,
0.002934404881671071,
0.04066243767738342,
-0.024276679381728172,
-0.011694380082190037,
0.03342263400554657,
0.04283482953906059,
-0.022926105186343193,
0.02431490644812584,
0.002702421508729458,
0.06918857991695404,
0.032261691987514496,
-0.07538347691297531,
0.012854140251874924,
-0.04957408085465431,
-0.04526619240641594,
-0.06062765792012215,
0.008940810337662697,
0.0337626188993454,
-0.03400667384266853,
0.012297269888222218,
-0.026214556768536568,
-0.005427854135632515,
0.07793167233467102,
0.016820503398776054,
0.02799241803586483,
0.02949376218020916,
-0.013138373382389545,
0.02187139168381691,
0.04551812633872032,
-0.02757965214550495,
-0.015301190316677094,
0.052347008138895035,
-0.023569617420434952,
0.04331934452056885,
-0.02364937961101532,
0.021666044369339943,
-0.025674069300293922,
-0.031209472566843033,
0.010771543718874454,
0.016554854810237885,
-0.01632026396691799,
-0.016350332647562027,
0.055026374757289886,
-0.09209997206926346,
-0.05978795140981674,
-0.02450699917972088,
-0.001001488883048296,
0.040443021804094315,
0.012551859952509403,
-0.0041087013669312,
-0.01213129237294197,
0.006001289933919907,
-0.01734425500035286,
-0.04629012569785118,
0.03947940468788147,
-0.003490639617666602,
-0.00913330540060997,
-0.0027838638052344322,
0.06614866852760315,
0.016432661563158035,
0.0075496044009923935,
0.02587273344397545,
-0.029430145397782326,
-0.017915163189172745,
0.0006949438247829676,
-0.031000075861811638,
0.04745372384786606,
0.00042630836833268404,
0.009748433716595173,
0.014065486378967762,
0.0001503367820987478,
-0.033834803849458694,
0.0248031634837389,
-0.03170674294233322,
0.0189573485404253,
-0.045834776014089584,
0.0052302535623312,
0.015367181040346622,
-0.007547605782747269,
-0.03811296448111534,
0.02661265805363655,
-0.02098141238093376,
0.005475197918713093,
0.06345809251070023,
0.043307866901159286,
0.002549856435507536,
0.026153074577450752,
-0.037605103105306625,
0.032171010971069336,
-0.025137891992926598,
0.05666940659284592,
0.02123146876692772,
0.01861533708870411,
0.02837156131863594,
0.06597590446472168,
0.014183624647557735,
-0.02546120062470436,
0.028800439089536667,
-0.012232362292706966,
-0.010670226067304611,
-0.06102576106786728,
0.039065901190042496,
-0.0822698175907135,
-0.06536268442869186,
0.006162509322166443,
-0.029932864010334015,
-0.014134947210550308,
0.051392193883657455,
-0.08074088394641876,
0.03937231004238129,
0.006508670747280121,
0.008287801407277584,
-0.023184580728411674,
-0.011068662628531456,
0.048663295805454254,
-0.007759219966828823,
0.025288905948400497,
-0.03435540199279785,
-0.007234511431306601,
0.04130382835865021,
-0.020290203392505646,
0.01548959780484438,
0.025119096040725708,
-0.06460030376911163,
-0.012469179928302765,
-0.006340459920465946,
-0.01387035008519888,
0.024695251137018204,
0.09674178808927536,
-0.07644632458686829,
-0.02137393318116665,
-0.03379910811781883,
-0.021274162456393242,
-0.01335056871175766,
0.029771672561764717,
-0.02506379224359989,
-0.030957447364926338,
-0.03164783865213394,
-0.021665260195732117,
0.013760695233941078,
-0.007322777062654495,
0.021031569689512253,
0.02215195633471012,
-0.03988746553659439,
-0.04790240898728371,
0.06970734149217606,
-0.03679756447672844,
-0.005016970448195934,
-0.027826685458421707,
-0.06908499449491501,
0.05791611596941948,
-0.06226735934615135,
-0.042844295501708984,
0.012517058290541172,
-0.04167772829532623,
0.08823662996292114,
0.04962437227368355,
-0.07427822053432465,
0.04978996142745018,
-0.03203662857413292,
-0.010120643302798271,
-0.011982394382357597,
0.03045828826725483,
-0.0028447862714529037,
-0.02165577933192253,
0.008702155202627182,
-0.01411701925098896,
-0.017482446506619453,
0.017900964245200157,
0.008148293010890484,
-0.0017713923007249832,
0.015346926636993885,
-0.03141061216592789,
-0.0530691035091877,
-0.016790999099612236,
0.0931587964296341,
-0.009362277574837208,
-0.013173060491681099,
-0.043675169348716736,
0.07657037675380707,
0.0359841026365757,
0.05025361105799675,
-0.0010693715885281563,
-0.0518941730260849,
-0.013601288199424744,
0.006183868274092674,
-0.008911900222301483,
0.009937934577465057,
-0.04470989480614662,
0.03211667388677597,
0.002420980017632246,
-0.014071357436478138,
-0.023722337558865547,
0.05774009972810745,
0.015753168612718582,
0.005632453132420778,
0.008352968841791153,
-0.026391496881842613,
-0.045266155153512955,
-0.011373678222298622,
-0.01607605442404747,
-0.007255658973008394,
0.06587973982095718,
-0.03502339497208595,
0.0009969848906621337,
0.07997187972068787,
-0.02961656264960766,
-0.030451636761426926,
0.00445130281150341,
-0.008361849933862686,
0.013313613831996918,
-0.004635476041585207,
-0.012349877506494522,
-0.022753898054361343,
-0.04665497690439224,
-0.04214557260274887,
0.00013255866360850632,
0.029723674058914185,
-0.02065189555287361,
0.005498175043612719,
-0.0005963400471955538,
-0.05695480480790138,
0.06848118454217911,
-0.014797893352806568,
0.02028878591954708,
0.02663307636976242,
-0.005271547473967075,
0.019597897306084633,
0.001491860835812986,
0.026167279109358788,
-0.03604774922132492,
0.01696610078215599,
0.011567359790205956,
-0.012757454998791218,
-0.059314798563718796,
0.030296895653009415,
-0.05540907382965088,
0.008976125158369541,
-0.0009005190804600716,
0.05861331894993782,
-0.036692261695861816,
-0.009519408456981182,
0.046900831162929535,
0.023160601034760475,
0.05673154070973396,
0.01623592898249626,
0.008548195473849773,
-0.0404723696410656,
-0.01571357622742653,
0.05544513463973999,
-0.004707938525825739,
-0.010067427530884743,
-0.0211784690618515,
-0.028632184490561485,
-0.05767674371600151,
-0.006055094767361879,
0.07327266782522202,
-0.07439783960580826,
0.005985390394926071,
-0.05682223290205002,
0.031238682568073273,
0.012150721624493599,
0.038543060421943665,
0.01899036020040512,
0.0036056938115507364,
0.010450475849211216,
-0.051629871129989624,
-0.01779758743941784,
0.03737536817789078,
-0.010487781837582588,
-0.030532531440258026,
-0.03331636264920235,
-0.012716787867248058,
-0.039256155490875244,
0.04087596386671066,
-0.0035127082373946905,
-0.06431339681148529,
0.019049011170864105,
0.012345429509878159,
0.009225061163306236,
0.04488787800073624,
0.02751021832227707,
-0.02484336867928505,
-0.04570343717932701,
0.00020567950559780002,
-0.033832188695669174,
-0.03020201064646244,
0.0009962276089936495,
-0.01973913237452507,
-0.06250399351119995,
-0.030983826145529747,
-0.008634565398097038,
-0.015931744128465652,
-0.001693596364930272,
-0.01990147866308689,
-0.02249971404671669,
-0.06581253558397293,
-0.01401962898671627,
0.0299286600202322,
-0.013119402341544628,
0.0016010366380214691,
-0.06961598992347717,
-0.05914365500211716,
-0.016428593546152115,
0.03929966315627098,
0.05216733366250992,
0.0027078676503151655,
0.03253595903515816,
0.013164449483156204,
-0.0030730708967894316,
-0.01696491241455078,
-0.05150611698627472,
-0.0007882359204813838,
-0.0012136383447796106,
0.03767791762948036,
-0.026488250121474266,
0.024000009521842003,
0.043195392936468124,
0.005422516260296106,
0.03777305781841278,
0.004928933456540108,
-0.028200047090649605,
0.008831220678985119,
0.0241079181432724,
-0.0069060735404491425,
0.009839072823524475,
0.051649995148181915,
-0.0004358756705187261,
0.02940308302640915,
0.05090450122952461,
0.025334550067782402,
-0.01746263913810253,
0.026923557743430138,
0.03361358866095543,
0.020013652741909027,
0.051331400871276855,
0.016714945435523987,
-0.040393829345703125,
-0.005915918853133917,
-0.039703287184238434,
0.010045390576124191,
-0.013514053076505661,
-0.07397273182868958,
0.00885995477437973,
-0.02898949570953846,
0.03166244924068451,
-0.017051082104444504,
-0.02044764719903469,
-0.03680257871747017,
0.0019512048456817865,
-0.050201963633298874,
0.016547424718737602,
-0.013014770112931728,
0.020329132676124573,
-0.026569629088044167,
0.006714885123074055,
-0.018664000555872917,
-0.0007450947887264192,
-0.04354483634233475,
0.013427745550870895,
0.013683130033314228,
0.050567228347063065,
0.02142184041440487,
-0.017176635563373566,
-0.007908436469733715,
0.05699251592159271,
0.08589641004800797,
-0.04642662778496742,
0.01598329283297062,
-0.006515204440802336,
-0.03291769698262215,
0.0007113457540981472,
-0.009778987616300583,
-0.019669992849230766,
-0.048826541751623154,
-0.031019430607557297,
0.013673239387571812,
0.016087079420685768,
0.01308064628392458,
0.018552465364336967,
-0.07644584029912949,
-0.04297889024019241,
0.048533909022808075,
-0.022098984569311142,
-0.027718404307961464,
0.03336256742477417,
0.08329132199287415,
-0.01142384298145771,
-0.0034925970248878,
0.0023862053640186787,
-0.028293604031205177,
0.021321749314665794,
-0.022881457582116127,
-0.01693280041217804,
-0.00875837728381157,
-0.006696891039609909,
-0.019308453425765038,
0.049486976116895676,
0.014538975432515144,
0.037647731602191925,
-0.05815872550010681,
0.033289454877376556,
-0.01874379999935627,
0.045003391802310944,
-0.029223451390862465,
0.01974395103752613,
-0.017394276335835457,
-0.05617170408368111,
-0.0474887415766716,
-0.012710951268672943,
-0.019468512386083603,
0.016071273013949394,
0.038901135325431824,
-0.03262941911816597,
-0.03760765492916107,
-0.041769277304410934,
0.01944141276180744,
-0.029469918459653854,
0.03737198933959007,
-0.03506479039788246,
-0.0397660955786705,
0.02583835832774639,
0.02800777554512024,
0.040152426809072495,
0.0040967524982988834,
0.07062365114688873,
-0.03575888276100159,
0.030695490539073944,
0.012575165368616581,
-0.05060071125626564,
-0.03186231851577759,
-0.003641319228336215,
-0.012883523479104042,
0.014134262688457966,
-0.0003718101652339101,
-0.004173635505139828,
0.0640399381518364,
0.039994385093450546,
-0.08162569254636765,
-0.004812238272279501,
0.025692427530884743,
-0.06204620748758316,
0.015870049595832825,
0.020389210432767868,
0.021216830238699913,
-0.016519645228981972,
-0.0722399353981018,
0.051196370273828506,
0.03365601971745491,
0.00488243019208312,
0.02463790774345398,
0.04334734380245209,
0.019887568429112434,
0.010569347999989986,
-0.013910372741520405,
0.0210401713848114,
-0.015381239354610443,
-0.029650472104549408,
0.05861303210258484,
-0.0743403211236,
-0.001734734047204256,
0.07402035593986511,
0.032536786049604416,
-0.006519534159451723,
0.04384598881006241,
0.07469747215509415,
0.005603523459285498,
-0.036277491599321365,
-0.0019324946915730834,
0.046787068247795105,
-0.03235899284482002,
-0.08521421253681183,
0.004539940506219864,
0.04391530156135559,
-0.027669137343764305,
-0.04788058251142502,
0.052674174308776855,
-0.05793345719575882,
0.016422510147094727,
0.08803515136241913,
0.06977087259292603,
0.012667239643633366,
-0.0349709577858448,
-0.005022068042308092,
-0.05930614098906517,
-0.03240139037370682,
-0.04850940778851509,
0.017661696299910545,
0.008983545936644077,
-0.03457833454012871,
-0.041029129177331924,
0.05931428074836731,
-0.009026876650750637,
0.0000197077988559613,
-0.01770634949207306,
-0.040036942809820175,
-0.03808002546429634,
-0.0116083063185215,
-0.026403671130537987,
0.00843008328229189,
-0.005080037750303745,
-0.030207358300685883,
-0.024632982909679413,
0.018777238205075264,
-0.011939984746277332,
0.015131917782127857,
-0.021101120859384537,
0.009271383285522461,
0.020978983491659164,
0.07524630427360535,
0.027580732479691505,
-0.021581031382083893,
-0.0030468665063381195,
0.029508914798498154,
-0.04090812802314758,
0.019936559721827507,
-0.0050441427156329155,
-0.04060395807027817,
-0.0010577089851722121,
0.06620597094297409,
0.035874515771865845,
0.014956202358007431,
0.020116247236728668,
0.039005059748888016,
0.025473149493336678,
-0.01209617406129837,
0.023412130773067474,
0.03395342454314232,
0.0002907986054196954,
0.01885349117219448,
-0.03287091851234436,
-0.036227501928806305,
-0.027136782184243202,
0.0028571593575179577,
0.02267633005976677,
-0.020613214001059532,
0.05400499328970909,
0.0071356529369950294,
-0.01985800825059414,
-0.04640704393386841,
-0.002248857170343399,
0.021780388429760933,
-0.001603397075086832,
-0.053046636283397675,
-0.030782954767346382,
-0.05860308185219765,
-0.026977913454174995,
0.054342254996299744,
-0.03890561684966087,
-0.053094878792762756,
0.03038850799202919,
-0.018844300881028175,
0.039477117359638214,
-0.052838679403066635,
0.027950990945100784,
-0.024042079225182533,
0.059369444847106934,
-0.01286887563765049,
0.017824437469244003,
0.005466038826853037,
-0.013181445188820362,
0.054267872124910355,
0.02836054190993309,
-0.04621987044811249,
-0.013802658766508102,
-0.034036796540021896,
0.05786268413066864,
0.012914438731968403,
-0.02930656261742115,
0.01770172081887722,
0.014508500695228577,
0.06499616801738739,
0.007396492175757885,
0.01648543030023575,
0.06556743383407593,
0.00894270371645689,
0.032929301261901855,
0.05709078907966614,
-0.04230030998587608,
0.013330981135368347,
-0.005663247779011726,
0.02116536907851696,
0.011274603195488453,
0.020008424296975136,
-0.04223044216632843,
-0.010276651941239834,
-0.005675141233950853,
-0.019648050889372826,
-0.005268380045890808,
-0.04770728200674057,
0.028578592464327812
] |
<p>Suppose we havean uniform slender rod of dimensions : $L$( length) and $A$( cross sectional area). Now at different points on the rod we apply different forces. So, in this situation how are we expected to find the elongation in the rod?</p>
<p>I tried in 2 different ways:</p>
<ul>
<li>I considered each part and found the elongation for each part, and then added them up.</li>
<li>I considered cumulative segments, that is: from part A to B then from part A to C ( hence taking the forces at junction B as internal force and not taking them into account) and then adding them up.</li>
</ul>
<p>My question is, as these two processes yield different results, which is the correct method and why? Also if anyone has a better method, please share it with me.</p>
<p>The type of the question can be found in Timoshenko & Young : Elements of Strengths of Materials, Exercise 1.2 figure A.</p> | g9247 | [
0.0744522213935852,
-0.010371382348239422,
-0.002357771620154381,
-0.041209060698747635,
0.020614754408597946,
-0.00690388074144721,
0.042340170592069626,
0.027876438573002815,
-0.02727477252483368,
-0.006735258735716343,
0.05042693018913269,
-0.029983075335621834,
0.020710274577140808,
0.009219015017151833,
0.06095103174448013,
-0.006303485482931137,
0.07578941434621811,
-0.06471053510904312,
0.03128615394234657,
0.025049062445759773,
-0.010623600333929062,
0.04319271445274353,
0.016164293512701988,
-0.011401212774217129,
0.0023101039696484804,
-0.011937208473682404,
0.010261495597660542,
0.023449018597602844,
-0.04781150072813034,
-0.03248310461640358,
0.023604197427630424,
0.01913362741470337,
0.025201113894581795,
-0.05531550198793411,
-0.01007091999053955,
-0.02397054247558117,
0.055643945932388306,
0.042945124208927155,
-0.016895243898034096,
-0.012455690652132034,
-0.00016237788076978177,
-0.048485167324543,
0.03693035617470741,
0.004060002509504557,
0.005138218868523836,
-0.06735160946846008,
-0.033816248178482056,
-0.012704494409263134,
-0.014683459885418415,
0.004202257376164198,
-0.007678994443267584,
0.031004594638943672,
0.01887967623770237,
-0.060502789914608,
0.04740513861179352,
0.07814068347215652,
-0.011190877296030521,
-0.04752868786454201,
0.05505342409014702,
-0.0016814750852063298,
0.048365745693445206,
-0.014673520810902119,
0.0218657236546278,
-0.007759407162666321,
0.01587938331067562,
-0.0040677073411643505,
-0.0042652166448533535,
0.03501937910914421,
-0.013771763071417809,
-0.0019916826859116554,
-0.014122928492724895,
-0.07643120735883713,
0.024366917088627815,
-0.05510225519537926,
-0.0760759711265564,
-0.008532164618372917,
-0.022636577486991882,
0.0408918522298336,
-0.038863200694322586,
-0.034633275121450424,
-0.041450612246990204,
-0.01213318482041359,
0.027181601151823997,
-0.0001733640965539962,
0.02410348691046238,
0.0671391412615776,
0.018670981749892235,
0.04807107150554657,
-0.002417610725387931,
0.02858073078095913,
-0.0017217665445059538,
0.031341541558504105,
0.0417981781065464,
0.0511791929602623,
-0.060231633484363556,
-0.053713973611593246,
0.006325643043965101,
0.04426155239343643,
0.029809998348355293,
0.04290022328495979,
0.007578484248369932,
0.006961960811167955,
-0.009353348053991795,
-0.007751289289444685,
-0.040640994906425476,
-0.012617035768926144,
0.018462056294083595,
-0.051875390112400055,
-0.03544631227850914,
0.010246364399790764,
-0.0719313696026802,
-0.030292989686131477,
-0.03504008427262306,
-0.014482485130429268,
0.014894824475049973,
0.02892778441309929,
0.06697648018598557,
0.016758037731051445,
0.01704527996480465,
0.030836407095193863,
0.008139288984239101,
-0.013207091018557549,
0.03654693812131882,
0.0732429102063179,
-0.0011481347028166056,
-0.033195339143276215,
-0.033337969332933426,
0.02787274681031704,
0.001895056921057403,
-0.026336506009101868,
0.05050521716475487,
-0.00978455413132906,
0.04777713865041733,
-0.019087372347712517,
0.08059544861316681,
-0.02832459844648838,
-0.032267384231090546,
-0.003522726707160473,
0.012948057614266872,
0.03356938436627388,
-0.026203492656350136,
-0.03557766228914261,
-0.01779375970363617,
-0.01215561293065548,
-0.006154769100248814,
-0.011752384714782238,
-0.02704421430826187,
-0.030443662777543068,
-0.022779343649744987,
0.001846164814196527,
-0.008841976523399353,
0.049660854041576385,
0.00628448324277997,
-0.0604093074798584,
-0.013303766027092934,
0.009031426161527634,
0.038693301379680634,
-0.05365496873855591,
0.009404513984918594,
0.0027367749717086554,
-0.0006206972757354379,
-0.0157878790050745,
0.028090819716453552,
-0.005360271781682968,
-0.03474191948771477,
0.04311253875494003,
-0.021308179944753647,
-0.020805884152650833,
0.057835906744003296,
-0.014584563672542572,
0.009464454837143421,
-0.03215587139129639,
0.021560486406087875,
0.020662767812609673,
0.006413223221898079,
0.1069425418972969,
0.08908961713314056,
-0.0690523013472557,
0.0016277877148240805,
-0.023497961461544037,
-0.024288000538945198,
-0.0032951892353594303,
0.024409616366028786,
0.0196492038667202,
0.0199710913002491,
-0.008253220468759537,
0.10715653747320175,
0.06225451081991196,
-0.02460215985774994,
0.013947876170277596,
-0.02663583680987358,
0.03677972033619881,
-0.04569244012236595,
0.040990520268678665,
-0.02469930611550808,
-0.02026095613837242,
0.0897955447435379,
-0.1118544265627861,
-0.016138287261128426,
-0.026299284771084785,
-0.03141088783740997,
0.04517926648259163,
-0.005019757896661758,
0.04106075316667557,
0.000486013334011659,
0.016721323132514954,
-0.047716476023197174,
-0.03917911648750305,
0.012124534696340561,
0.013500995934009552,
-0.009572516195476055,
0.003954555839300156,
-0.033951740711927414,
0.03112386353313923,
-0.02066163904964924,
-0.03197597712278366,
-0.0027051246725022793,
0.005619903095066547,
-0.01115132961422205,
0.012949788942933083,
-0.026860807090997696,
-0.03075944259762764,
-0.023729082196950912,
-0.0018023591255769134,
-0.0021255239844322205,
-0.024619225412607193,
0.055586159229278564,
0.020433567464351654,
-0.01212289184331894,
-0.013253774493932724,
-0.08981816470623016,
-0.028919463977217674,
-0.028785988688468933,
0.013315761461853981,
0.030018683522939682,
-0.0004494077293202281,
-0.041373904794454575,
0.018522746860980988,
-0.059337664395570755,
0.03430066630244255,
0.03793991729617119,
-0.02358776144683361,
-0.008814173750579357,
-0.04470011219382286,
0.019986532628536224,
-0.05166500061750412,
0.06465666741132736,
-0.06324895471334457,
0.03308659791946411,
0.059875987470149994,
-0.0179063118994236,
0.043792854994535446,
0.034895461052656174,
0.03709094971418381,
0.0146103510633111,
0.004032082390040159,
-0.028854727745056152,
0.05309201404452324,
0.011839408427476883,
-0.05402038246393204,
0.007476127240806818,
0.046883709728717804,
0.004437869414687157,
0.0440097376704216,
-0.0882222130894661,
-0.01383869256824255,
-0.0636347308754921,
-0.10252703726291656,
0.013846025802195072,
0.016390858218073845,
-0.07975368946790695,
0.004096734803169966,
0.0018284906400367618,
0.003711278550326824,
0.0031532852444797754,
-0.03703220188617706,
0.03668546304106712,
0.014948948286473751,
0.03662781044840813,
0.017283672466874123,
0.039648473262786865,
-0.00261624320410192,
0.00857946090400219,
0.05420776456594467,
0.02726857177913189,
-0.004505098331719637,
0.05001647397875786,
-0.02210831642150879,
-0.02083391137421131,
0.02094775252044201,
-0.033595334738492966,
-0.022181343287229538,
0.030695278197526932,
-0.04575686156749725,
0.051653072237968445,
0.010939392261207104,
-0.002957404125481844,
-0.10382705181837082,
-0.028671611100435257,
-0.025242814794182777,
-0.04072090610861778,
-0.002705377759411931,
-0.006380515638738871,
0.005309221334755421,
0.05898340791463852,
0.04501716420054436,
-0.05020752176642418,
-0.04479476064443588,
0.039073556661605835,
-0.07623693346977234,
-0.004344126209616661,
0.0026689853984862566,
0.05260607972741127,
-0.015263584442436695,
-0.03875774145126343,
-0.029650771990418434,
0.05402359738945961,
0.027029700577259064,
0.026775121688842773,
-0.01673775166273117,
-0.018516385927796364,
-0.021231021732091904,
0.06030859425663948,
0.017392031848430634,
-0.028417112305760384,
0.016238605603575706,
0.02952803671360016,
0.012145069427788258,
-0.020900141447782516,
0.059788838028907776,
-0.057041678577661514,
0.054324693977832794,
-0.010950724594295025,
0.010795839130878448,
-0.03238268569111824,
-0.05086223781108856,
-0.07628198713064194,
-0.0046007647179067135,
0.055250272154808044,
0.0521540530025959,
-0.0017344895750284195,
-0.0005590547225438058,
-0.03652091324329376,
0.014625860378146172,
-0.0054140579886734486,
-0.018849123269319534,
0.034020017832517624,
0.07734820991754532,
0.0016129108844324946,
0.0020598217379301786,
0.007648833096027374,
0.019127409905195236,
-0.03400351479649544,
0.023657510057091713,
0.021201850846409798,
0.039109013974666595,
0.01977853663265705,
0.010706441476941109,
0.002365048974752426,
-0.04059239476919174,
0.042917169630527496,
-0.04586658999323845,
0.003179417457431555,
-0.009016038849949837,
-0.0333840437233448,
0.025174757465720177,
0.07061818987131119,
0.04953305795788765,
0.018490975722670555,
-0.04791964963078499,
0.01696755550801754,
-0.027631811797618866,
-0.03562004864215851,
-0.029772333800792694,
0.016227375715970993,
-0.010261124931275845,
0.032331615686416626,
-0.01818135939538479,
0.006413089577108622,
0.02171199582517147,
0.047718338668346405,
0.0711207166314125,
-0.0022229833994060755,
0.011624055914580822,
-0.06394647806882858,
0.013613186776638031,
-0.027972254902124405,
0.003965659998357296,
0.012699265964329243,
-0.05748903006315231,
0.011683248914778233,
-0.021968934684991837,
-0.0849117711186409,
-0.019216066226363182,
0.02390611171722412,
-0.007490586955100298,
0.09806784987449646,
-0.009617647156119347,
-0.005337450187653303,
-0.007613922469317913,
0.0015017795376479626,
0.026801202446222305,
-0.007224254310131073,
0.03850720822811127,
-0.008865111507475376,
0.00007780400483170524,
-0.022598449140787125,
-0.054285746067762375,
-0.000486809469293803,
-0.007224800065159798,
0.014468043111264706,
-0.019247347488999367,
0.021886790171265602,
-0.05216487497091293,
0.05130736529827118,
-0.05655999854207039,
0.04045308381319046,
-0.03232749179005623,
-0.03081372193992138,
-0.0047582583501935005,
0.009066447615623474,
0.03969920799136162,
-0.0918709859251976,
-0.014631999656558037,
0.02133530005812645,
0.06355928629636765,
-0.017372548580169678,
0.035138774663209915,
0.0675273984670639,
-0.06394722312688828,
-0.04304252937436104,
0.022377273067831993,
0.001544967875815928,
-0.021270303055644035,
-0.04486585408449173,
-0.0070510064251720905,
-0.012188692577183247,
0.040540050715208054,
0.0020640536677092314,
0.062401171773672104,
-0.056972239166498184,
0.024618392810225487,
0.007210989948362112,
0.014715980738401413,
-0.012985143810510635,
0.03654506802558899,
-0.06113330274820328,
-0.034786444157361984,
-0.04060684144496918,
-0.03325589373707771,
-0.026208363473415375,
0.009855838492512703,
0.03716457635164261,
-0.054505202919244766,
0.01864917017519474,
-0.005480839870870113,
-0.024112829938530922,
0.027469174936413765,
0.021656593307852745,
0.0009313072077929974,
-0.0063512977212667465,
-0.00483468035236001,
-0.04585302248597145,
-0.0022075034212321043,
-0.024525674059987068,
0.001503431936725974,
-0.03933253511786461,
-0.04050063714385033,
-0.031523074954748154,
0.017798084765672684,
0.04683015123009682,
0.018709035590291023,
0.07142519950866699,
-0.01026980672031641,
-0.014205140061676502,
-0.01848643831908703,
0.003599654883146286,
-0.0064986711367964745,
0.004969614092260599,
-0.01845535635948181,
-0.06827103346586227,
-0.02382039465010166,
-0.028487548232078552,
-0.05313694104552269,
0.053961414843797684,
0.012257290072739124,
-0.005179538391530514,
-0.013433285988867283,
0.03216826543211937,
0.07003675401210785,
0.013963676989078522,
0.03789496421813965,
0.012818761169910431,
0.021711528301239014,
-0.018558533862233162,
-0.010335090570151806,
0.005291556939482689,
-0.034177765250205994,
-0.016588490456342697,
0.005443735513836145,
-0.011255964636802673,
0.015689484775066376,
-0.06283286213874817,
0.05066916346549988,
-0.014596772380173206,
0.04509039968252182,
0.09699657559394836,
0.003696140833199024,
-0.0047989292070269585,
0.0030428655445575714,
-0.00157436344306916,
0.05473834648728371,
0.01674169860780239,
-0.061743296682834625,
0.0035896506160497665,
-0.0018536449642851949,
0.0017716371221467853,
0.058199357241392136,
-0.009573100134730339,
-0.015378718264400959,
0.11433760076761246,
0.05580262839794159,
-0.01787685789167881,
-0.0413377583026886,
0.010628982447087765,
0.018903004005551338,
-0.06445252150297165,
0.0018404371803626418,
0.02893167734146118,
-0.011483117938041687,
0.025341002270579338,
-0.01851530559360981,
-0.006256752647459507,
0.00017799431225284934,
-0.032415200024843216,
-0.007648492697626352,
0.01446439977735281,
-0.02308548428118229,
-0.0004133092297706753,
-0.05162718519568443,
0.016910012811422348,
-0.02082611434161663,
0.01857195794582367,
0.04764747619628906,
-0.05887166038155556,
-0.02982107363641262,
0.009298563003540039,
-0.05735815316438675,
0.02975628897547722,
0.0456424355506897,
-0.007981794886291027,
-0.00475905928760767,
0.009117458015680313,
0.02661571279168129,
-0.02839156985282898,
0.010238826274871826,
0.02645997889339924,
-0.05446022003889084,
0.01867472007870674,
-0.021380048245191574,
0.03194032236933708,
-0.07735072821378708,
-0.003408222459256649,
0.003118604188784957,
0.012828927487134933,
-0.061391379684209824,
-0.06590934097766876,
0.00852676760405302,
0.0162565428763628,
0.0766453817486763,
0.04808971285820007,
-0.06474252790212631,
0.018250610679388046,
0.016823913902044296,
-0.007669398095458746,
0.012766150757670403,
-0.02648293226957321,
0.028909437358379364,
-0.011149909347295761,
0.0344601534307003,
-0.031924281269311905,
0.030128447338938713,
-0.04972093552350998,
0.025816291570663452,
-0.00357248866930604,
0.09190577268600464,
-0.019040176644921303,
-0.061242636293172836,
-0.018059100955724716,
-0.027824316173791885,
-0.031885210424661636,
0.03208357095718384,
-0.0005744090885855258,
0.019671758636832237,
-0.03417203575372696,
-0.00044434264418669045,
-0.022052766755223274,
0.014643778093159199,
0.037360552698373795,
0.06836014986038208,
-0.013700681738555431,
0.086704321205616,
0.07142142206430435,
-0.014037651009857655,
0.0485243983566761,
-0.018865348771214485,
0.013422354124486446,
-0.01918768510222435,
0.04164531081914902,
-0.008994616568088531,
0.029278451576828957,
0.012015909887850285,
-0.009415856562554836,
-0.013699449598789215,
0.06550933420658112,
-0.00926661305129528,
0.015744300559163094,
-0.031867604702711105,
0.017623620107769966,
0.00708661787211895,
0.026777813211083412,
-0.033255450427532196,
0.02838050201535225,
-0.02908307872712612,
0.01464421208947897,
0.11057989299297333,
-0.10172875225543976,
-0.06603920459747314,
-0.012465878389775753,
-0.06460046023130417,
0.013024313375353813,
-0.027269914746284485,
-0.021598871797323227,
0.04099738225340843,
-0.02653079852461815,
0.049324240535497665,
0.024737685918807983,
0.01632576622068882,
0.0334390327334404,
0.06257797032594681,
-0.011261353269219398,
0.021282659843564034,
0.010230734944343567,
0.049464236944913864,
-0.06169183924794197,
-0.03336013853549957,
-0.0007792141404934227,
0.01525968313217163,
-0.03584517166018486,
0.01661047339439392,
0.04740780591964722,
-0.03929908573627472,
-0.03794895485043526,
0.025694429874420166,
0.00333849317394197,
0.037882670760154724,
-0.022556573152542114,
-0.05551629140973091,
0.04953053221106529,
0.003614658722653985,
-0.051416054368019104,
0.02459014020860195,
-0.01147775910794735,
0.018923036754131317,
-0.018953939899802208,
0.04167862609028816,
-0.028018629178404808,
0.01220629457384348,
-0.05787544324994087,
-0.03651373088359833,
0.0689888745546341,
0.017836282029747963,
0.0011551285861060023,
0.07102358341217041,
0.05447734519839287,
-0.01772555336356163,
-0.023543504998087883,
-0.046824414283037186,
-0.024514270946383476,
-0.012520515359938145,
0.03245285153388977,
0.03945476934313774,
-0.02122034877538681,
-0.04024216905236244,
-0.025346916168928146,
0.021551210433244705,
-0.016389619559049606,
-0.0179602038115263,
0.005491901654750109,
-0.017505895346403122,
0.014258281327784061,
0.04407128319144249,
-0.009981431066989899,
0.03172777593135834,
-0.028206676244735718,
-0.012552140280604362,
-0.017887864261865616,
0.0010783527977764606,
-0.020099833607673645,
0.058614570647478104,
-0.04565860331058502,
-0.044372349977493286,
-0.0008722993079572916,
-0.022844893857836723,
-0.004645370412617922,
-0.02086968719959259,
-0.055622607469558716,
-0.031230922788381577,
-0.005536729469895363,
-0.01187929417937994,
0.0012043151073157787,
0.03641157224774361,
-0.01757199317216873,
0.021468408405780792,
0.014824528247117996,
-0.01518949493765831,
-0.02324081026017666,
-0.006017798557877541,
0.0656052753329277,
0.036586225032806396,
-0.023206910118460655,
-0.01050369068980217,
-0.018073229119181633,
-0.02839965932071209,
-0.02909320592880249,
-0.044689420610666275,
0.03808113560080528,
0.003079740097746253,
-0.005759870633482933,
0.042379189282655716,
0.0009084161720238626,
-0.10186252743005753,
-0.018614478409290314,
-0.013395196758210659,
0.028790105134248734,
-0.013074926100671291,
-0.0005999312270432711,
-0.04201028123497963,
0.00544425705447793,
-0.014195623807609081,
-0.05317998304963112,
-0.02778858132660389,
-0.027601443231105804,
-0.013361283577978611,
-0.015274443663656712,
-0.0015722817042842507,
-0.04518129676580429,
0.07514545321464539,
0.010742751881480217,
0.028594311326742172,
-0.020914226770401,
0.03594272583723068,
-0.00958932563662529,
0.019657820463180542,
-0.011141368187963963,
-0.03328154608607292,
-0.004026603419333696,
-0.006933088880032301,
-0.015701042488217354,
0.020463645458221436,
0.014231936074793339,
0.06930970400571823,
-0.03681599348783493,
-0.016302309930324554,
-0.002135458169505,
-0.0035037000197917223,
-0.021304016932845116,
-0.009216547943651676
] |
<p>In Rindler's book: Relativity, Special, General and Cosmological, is stated on page 40 that the Relativity Principle (RP), when applied to just one Inertial Frame (IF), guarantees the homogeneity and isotropy of tha IF. By inertial frame Rindler means an ideal infinity extended rigid body moving freely in a world without gravity. This is distinct from an inertial coordinate system, that should be understood as an IF plus, in it, a choice of standard coordinates $x$, $y$, $z$ and $t$.
As he says, the RP concerns inertial coordinate systems: the laws of physics are invariant under a change of inertial coordinate systems.</p>
<p>I can't understand why this imply homogeneity and isotropy of an IF. If I suppose the existence of an special direction in some inertial reference frame, I could imagine some physical law governig the propagation of some signal (it can be light if you want, but it's not necessary), and if by measuring the velocity of this signal in two different directions and I get two different results, this would violate the isotropy of the IF and at the same time I could write the physical law in an invariant way under coordinate changes inside de IF (sure, it would depend on the special direction) and this would be in accordance with the RP as stated above. What is wrong with my reasoning?</p> | g9248 | [
-0.008161446079611778,
0.04947885125875473,
-0.01655711606144905,
0.02159956470131874,
0.06972005218267441,
0.05235211178660393,
0.026930995285511017,
0.028430240228772163,
-0.03333606570959091,
0.010848481208086014,
0.02107713371515274,
-0.021007731556892395,
-0.04467887431383133,
-0.0008239432936534286,
0.00200214353390038,
-0.02340983971953392,
0.0815485268831253,
-0.010209708474576473,
0.04692799970507622,
-0.004444766324013472,
0.028188129886984825,
0.03618296608328819,
-0.026851261034607887,
-0.023481572046875954,
0.04221014678478241,
0.0026732643600553274,
0.06398588418960571,
-0.073947973549366,
-0.06832770258188248,
0.006949034985154867,
0.03715827316045761,
0.005684588570147753,
0.04444149136543274,
-0.04210694134235382,
0.046005334705114365,
-0.02502056024968624,
0.05897369980812073,
0.03154822811484337,
0.030278192833065987,
0.040148984640836716,
0.01877373829483986,
0.012722859159111977,
-0.00202092994004488,
-0.026471924036741257,
-0.00010213130008196458,
0.027834037318825722,
-0.012891675345599651,
0.006557689048349857,
-0.02924342267215252,
-0.0049810633063316345,
-0.009202595800161362,
0.03614034876227379,
0.004329323768615723,
0.0007834056741558015,
0.005266477819532156,
0.04959162697196007,
0.008420019410550594,
-0.007243953179568052,
0.009521769359707832,
0.04204493388533592,
-0.016980884596705437,
0.0031686860602349043,
0.017484700307250023,
0.01853969693183899,
0.013278995640575886,
0.017864512279629707,
-0.029759444296360016,
-0.02138962224125862,
0.03118455782532692,
0.025354912504553795,
0.027061911299824715,
-0.03217943012714386,
0.014326099306344986,
0.013596848584711552,
-0.06245582178235054,
0.031060243025422096,
0.036386698484420776,
0.007309402339160442,
-0.019681891426444054,
0.02219454012811184,
-0.012691191397607327,
-0.04251784831285477,
0.06876330822706223,
0.03925691545009613,
0.04631141945719719,
-0.0007233577780425549,
0.03923484683036804,
0.011565400287508965,
-0.01910192146897316,
0.009525769390165806,
-0.023985156789422035,
-0.0066831596195697784,
0.08314412832260132,
0.025125188753008842,
-0.0316329263150692,
-0.0278122927993536,
-0.04332055523991585,
0.027121564373373985,
0.02316853031516075,
0.003384206211194396,
-0.05858532711863518,
0.01416640542447567,
-0.0032769953832030296,
-0.011934119276702404,
0.04361005872488022,
-0.04343731701374054,
0.058985937386751175,
0.04987476393580437,
-0.0563209131360054,
-0.10626310110092163,
-0.012456879951059818,
-0.023123210296034813,
0.022391825914382935,
-0.04730838164687157,
-0.032979611307382584,
0.008666238747537136,
0.10492844134569168,
-0.01025255024433136,
0.012300613336265087,
0.037439003586769104,
0.0032112891785800457,
0.00473049096763134,
0.02202659845352173,
0.12837402522563934,
-0.027876047417521477,
-0.003606086364015937,
-0.010167509317398071,
-0.016672778874635696,
0.04093259945511818,
-0.031397223472595215,
0.03780931979417801,
-0.0027609593234956264,
-0.005433593410998583,
-0.016392087563872337,
-0.05303551256656647,
-0.011407081037759781,
0.05946827679872513,
0.011759939603507519,
0.002611397998407483,
-0.024748994037508965,
-0.041581716388463974,
-0.0025859735906124115,
-0.003974911756813526,
-0.008087138645350933,
-0.03836803883314133,
0.03669693320989609,
0.03687399625778198,
0.0017519259126856923,
0.038736216723918915,
-0.0039435336366295815,
-0.018509766086935997,
0.13649477064609528,
-0.01814253069460392,
0.014706249348819256,
0.03820151835680008,
0.01753493770956993,
0.017370574176311493,
0.016103383153676987,
-0.022871363908052444,
-0.02374516800045967,
0.06298776715993881,
0.039434678852558136,
0.009372550994157791,
0.018362829461693764,
-0.04903719201683998,
0.08558851480484009,
-0.024717943742871284,
-0.051157716661691666,
-0.018367817625403404,
-0.06364381313323975,
-0.08325907588005066,
0.04167769104242325,
-0.021130019798874855,
-0.0004813026753254235,
0.038250990211963654,
0.012323097325861454,
-0.028706436976790428,
0.01234044786542654,
0.055061448365449905,
-0.028352953493595123,
-0.05854257568717003,
-0.015272492542862892,
0.020849402993917465,
-0.05180893465876579,
-0.04537313058972359,
-0.008406640030443668,
0.022730275988578796,
-0.0579582042992115,
-0.04071873798966408,
-0.014117402955889702,
-0.009586738422513008,
-0.0036364898551255465,
-0.023402748629450798,
0.02555060386657715,
-0.02777913399040699,
0.00948837585747242,
0.00818355567753315,
0.01823439635336399,
-0.029866211116313934,
0.06543104350566864,
-0.031836025416851044,
0.018305579200387,
0.01290277112275362,
0.037289611995220184,
-0.04096784070134163,
-0.05951990932226181,
-0.03296413645148277,
0.03695755824446678,
0.019443051889538765,
0.02957984432578087,
0.021920539438724518,
-0.04822098836302757,
0.013482630252838135,
-0.013507777824997902,
-0.008813388645648956,
-0.039765864610672,
0.043882470577955246,
-0.007766722235828638,
-0.02169695869088173,
-0.0054596164263784885,
-0.02318555675446987,
-0.007018526084721088,
0.0205024853348732,
0.04705129563808441,
-0.015973027795553207,
-0.06545032560825348,
-0.08850599080324173,
-0.04118138924241066,
0.02621568739414215,
0.0416141003370285,
0.016899440437555313,
-0.004561872221529484,
-0.0018825562437996268,
0.008983897045254707,
0.03589196130633354,
0.006028969772160053,
0.03210021182894707,
0.0036704635713249445,
0.031764350831508636,
-0.0013112758751958609,
0.0031184502877295017,
0.009103566408157349,
0.007178908679634333,
-0.017071740701794624,
-0.015298943035304546,
-0.0059561352245509624,
0.033942267298698425,
-0.02500392682850361,
-0.033053815364837646,
0.05126246437430382,
0.0015271580778062344,
-0.011880079284310341,
-0.03716420382261276,
-0.03529147803783417,
0.02574324794113636,
0.04362303391098976,
0.0005080592818558216,
0.020165665075182915,
-0.0873335674405098,
-0.029416358098387718,
-0.0059546432457864285,
-0.032266564667224884,
-0.014205961488187313,
0.008941099978983402,
-0.07572770863771439,
0.07102205604314804,
0.028713159263134003,
0.04756787791848183,
0.015402885153889656,
-0.03496907651424408,
-0.005191744305193424,
0.0413469634950161,
0.0037651043385267258,
0.05823975428938866,
-0.0022812136448919773,
0.06466645747423172,
-0.027456682175397873,
-0.06671380251646042,
-0.007124206982553005,
0.0007269216584973037,
-0.014990474097430706,
0.025014515966176987,
-0.03513012453913689,
-0.04289405420422554,
0.06893043220043182,
0.013420626521110535,
0.008715252391994,
0.011547866277396679,
-0.01822427287697792,
-0.01188722811639309,
-0.012140793725848198,
-0.002093262504786253,
0.019331203773617744,
-0.01412865798920393,
-0.01224966999143362,
0.013206754811108112,
-0.07188336551189423,
-0.03007056936621666,
-0.0580272302031517,
0.0530615858733654,
0.022931456565856934,
0.005500216502696276,
0.061689965426921844,
0.04264456778764725,
-0.0128110870718956,
0.007968634366989136,
-0.0654170885682106,
-0.017147906124591827,
-0.04342251643538475,
0.029977580532431602,
0.002318698214367032,
0.015590249560773373,
-0.02125178836286068,
-0.008936651051044464,
-0.022301459684967995,
0.033525194972753525,
-0.029905932024121284,
-0.011119883507490158,
-0.01670089364051819,
0.021363068372011185,
-0.053555551916360855,
-0.011206971481442451,
0.011960036121308804,
-0.04588945582509041,
0.0832916796207428,
0.012611934915184975,
-0.024026263505220413,
-0.019090525805950165,
-0.03417905047535896,
-0.005875652655959129,
-0.007254231721162796,
0.02376480959355831,
-0.019435979425907135,
0.028223849833011627,
-0.048169124871492386,
0.004644959699362516,
0.002495094435289502,
-0.011520798318088055,
0.06640332192182541,
0.023742729797959328,
0.07066571712493896,
-0.042648229748010635,
-0.07745680958032608,
0.055581070482730865,
-0.04512869939208031,
0.0031332988291978836,
0.07679060101509094,
-0.016726726666092873,
0.04293924570083618,
0.017930522561073303,
0.022688407450914383,
0.01649811863899231,
0.01583699882030487,
-0.03937612846493721,
-0.05425423011183739,
0.02858877368271351,
0.039620671421289444,
0.06143499165773392,
-0.028807131573557854,
-0.04552919790148735,
0.024867404252290726,
0.018391123041510582,
-0.016076013445854187,
-0.010274743661284447,
0.008623333647847176,
0.05111561715602875,
0.025059418752789497,
-0.030735528096556664,
-0.03647550567984581,
-0.020569313317537308,
0.0035472605377435684,
-0.029846418648958206,
0.017565269023180008,
-0.017651857808232307,
0.008034178987145424,
-0.058049388229846954,
0.070381298661232,
0.014967464841902256,
-0.030580196529626846,
-0.01709171012043953,
0.04725150018930435,
0.026042094454169273,
-0.035627663135528564,
0.025837523862719536,
0.03826943039894104,
0.023961694911122322,
-0.02432875521481037,
0.018417758867144585,
0.008331159129738808,
0.023518627509474754,
-0.005314103327691555,
-0.030634446069598198,
-0.031130829825997353,
-0.03621911257505417,
0.036126501858234406,
-0.005572458263486624,
0.002501515671610832,
0.01180986873805523,
0.00845634751021862,
0.011210242286324501,
0.023041943088173866,
-0.030767785385251045,
-0.0035480333026498556,
0.01537249144166708,
-0.020779723301529884,
0.0068828086368739605,
0.02643170952796936,
-0.028808195143938065,
0.0639377310872078,
0.03339018300175667,
0.0330817773938179,
0.008047452196478844,
0.04844653233885765,
-0.039340145885944366,
0.0774376392364502,
0.020380087196826935,
0.04802113026380539,
-0.06858296692371368,
0.012306490913033485,
-0.006446246523410082,
-0.012139221653342247,
0.021854998543858528,
0.05864715203642845,
-0.05623955279588699,
0.018446195870637894,
0.09039807319641113,
0.04113154113292694,
-0.05199111998081207,
0.005488323513418436,
-0.011683404445648193,
0.02179845981299877,
0.033848024904727936,
0.020944863557815552,
-0.007667979225516319,
-0.06120050698518753,
0.026413163170218468,
0.008625717833638191,
0.025458265095949173,
0.02799481339752674,
0.0020976532250642776,
-0.008078177459537983,
-0.0369238406419754,
-0.00038432746077887714,
-0.04499423876404762,
-0.035422392189502716,
0.07930943369865417,
0.035962942987680435,
-0.04893273860216141,
-0.03488479554653168,
-0.027957584708929062,
0.017170734703540802,
0.03398674353957176,
-0.005721077788621187,
0.023490475490689278,
-0.0025886751245707273,
-0.017846403643488884,
-0.07860226184129715,
0.008073496632277966,
0.016196226701140404,
0.029084695503115654,
-0.030130110681056976,
-0.047972846776247025,
0.01961355097591877,
-0.00019852905825246125,
-0.010375918820500374,
0.010907277464866638,
-0.098017618060112,
0.006149064749479294,
-0.09827511757612228,
-0.0009579375036992133,
0.01516734529286623,
0.007974617183208466,
-0.05247369036078453,
-0.017957041040062904,
0.06697627156972885,
-0.011522567830979824,
0.016391409561038017,
-0.007074874360114336,
-0.026276007294654846,
-0.05761876329779625,
-0.08667180687189102,
0.0005919055547565222,
0.05342964082956314,
0.050083279609680176,
0.061457645148038864,
-0.016446415334939957,
-0.03839307278394699,
0.051833514124155045,
-0.04117952287197113,
-0.05682368203997612,
0.03730907663702965,
-0.05756811052560806,
0.03489142283797264,
-0.032906822860240936,
0.027183979749679565,
-0.01625070907175541,
-0.019066089764237404,
-0.0438409261405468,
-0.05408018082380295,
-0.04904880002140999,
-0.05032266676425934,
-0.004730943124741316,
0.03464771807193756,
-0.0027443065773695707,
0.000510096549987793,
0.004812072496861219,
0.08135056495666504,
0.04449046403169632,
-0.0357956625521183,
0.007403253111988306,
0.06291044503450394,
0.025077681988477707,
-0.04806537181138992,
-0.014772121794521809,
0.030999381095170975,
-0.012409745715558529,
-0.01781020127236843,
-0.0036474382504820824,
0.014152392745018005,
-0.08097930252552032,
-0.0032926960848271847,
-0.007439794018864632,
0.022278456017374992,
-0.021635189652442932,
-0.018584037199616432,
0.044599778950214386,
-0.009400364011526108,
-0.025324231013655663,
-0.013899597339332104,
0.020499739795923233,
-0.032127607613801956,
0.00849101971834898,
0.008466784842312336,
-0.03691316768527031,
0.015475811436772346,
-0.05027174577116966,
0.011090870015323162,
-0.017452843487262726,
0.034792542457580566,
-0.0074848574586212635,
-0.025301402434706688,
-0.008493050001561642,
0.013732546009123325,
0.040715962648391724,
-0.06012802943587303,
0.04227862134575844,
-0.06795717030763626,
-0.00013105127436574548,
0.00942616630345583,
-0.049956366419792175,
-0.05982246994972229,
0.02701243944466114,
0.01843693107366562,
0.0007145078270696104,
-0.03858616575598717,
0.050774622708559036,
0.03795415535569191,
-0.021633591502904892,
-0.013768368400633335,
-0.01667073182761669,
0.030274193733930588,
-0.02442629262804985,
0.024376776069402695,
0.019449690356850624,
-0.03787495195865631,
-0.05058268830180168,
0.03908009082078934,
-0.0751565545797348,
0.059119999408721924,
0.02785824052989483,
-0.03342953324317932,
0.020868735387921333,
-0.020674604922533035,
0.016019294038414955,
0.017266858369112015,
0.02173127979040146,
-0.048387955874204636,
-0.008871227502822876,
-0.03911440819501877,
-0.015091614797711372,
0.004352344200015068,
0.008089332841336727,
0.026292704045772552,
-0.04030369222164154,
-0.09123864024877548,
0.018774520605802536,
-0.019305216148495674,
-0.05384020507335663,
-0.009793698787689209,
0.02532697468996048,
0.016949612647294998,
-0.017770329490303993,
-0.029587840661406517,
0.0016135743353515863,
-0.09997805953025818,
-0.017699550837278366,
-0.0235667172819376,
-0.05094027891755104,
-0.024074949324131012,
-0.036730654537677765,
0.01847035624086857,
0.014840980060398579,
0.07023636996746063,
-0.04592350870370865,
-0.05545983463525772,
0.006671085488051176,
-0.055798258632421494,
-0.03537587821483612,
0.042307671159505844,
-0.0014894723426550627,
-0.026729149743914604,
0.03444608300924301,
-0.006634633522480726,
-0.01847766526043415,
0.008169349282979965,
0.0028746132738888264,
-0.057482000440359116,
-0.0018806307343766093,
-0.0012836274690926075,
-0.03880486264824867,
0.047750625759363174,
0.008937199600040913,
0.03133779764175415,
0.025296686217188835,
0.03740719333291054,
0.01585872285068035,
-0.06887221336364746,
0.05930893123149872,
0.02616659365594387,
0.02278652787208557,
0.012222410179674625,
-0.03676934912800789,
-0.07588553428649902,
0.02252049185335636,
-0.011336431838572025,
-0.044628407806158066,
0.0031376637052744627,
0.010235876776278019,
0.046764686703681946,
0.003492094576358795,
-0.0015782220289111137,
0.04724876955151558,
0.028261855244636536,
0.02323601022362709,
-0.06301264464855194,
-0.030466673895716667,
0.05705733969807625,
-0.04194115102291107,
-0.07266594469547272,
0.026249023154377937,
-0.018172740936279297,
-0.003780650207772851,
-0.018171563744544983,
0.05079404264688492,
-0.028892848640680313,
-0.030400313436985016,
-0.022441856563091278,
0.008064416237175465,
0.03187407925724983,
-0.08681274205446243,
-0.03560223802924156,
-0.0036364742554724216,
-0.009086440317332745,
0.00696062995120883,
-0.02163732424378395,
0.03751949965953827,
0.01663518324494362,
-0.0672249123454094,
-0.0066802711226046085,
0.019266193732619286,
0.02293441630899906,
0.022159956395626068,
0.025291908532381058,
0.033933624625205994,
0.026275573298335075,
-0.010752593167126179,
0.011553258635103703,
0.013296444900333881,
0.0184622909873724,
0.01138350460678339,
0.004126289393752813,
0.08544059842824936,
-0.025161216035485268,
0.0193173848092556,
-0.01040694396942854,
0.0190361887216568,
-0.009618623182177544,
-0.04192356392741203,
-0.024670882150530815,
-0.05729169771075249,
-0.025499293580651283,
0.017803486436605453,
-0.03625517338514328,
-0.02072928473353386,
-0.06749621033668518,
0.02527312934398651,
0.0800028070807457,
0.061262305825948715,
-0.039165545254945755,
-0.04267735406756401,
0.0029701287858188152,
0.011292915791273117,
-0.012552033178508282,
0.02878298982977867,
0.08811967819929123,
-0.053363777697086334,
0.0068399724550545216,
-0.02774152345955372,
-0.007694347761571407,
0.0018401837442070246,
0.004549557808786631,
0.03991708159446716,
0.024327905848622322,
-0.00887540727853775,
-0.012377495877444744,
0.04392419010400772,
-0.04427287355065346,
-0.011426824145019054,
0.0002171273372368887,
-0.03426840156316757,
-0.04286131635308266,
-0.017250290140509605,
-0.0028184130787849426,
-0.04432877153158188,
0.009953261353075504,
-0.011592978611588478,
0.03329877555370331,
-0.05565459653735161,
0.03615298494696617,
-0.033877789974212646,
0.007444632705301046,
0.008294384926557541,
-0.06800633668899536,
0.007696396205574274,
0.027346238493919373,
0.07341968268156052,
0.03445771709084511,
-0.05901633948087692,
-0.00710585992783308,
0.03701424598693848,
0.043967850506305695,
-0.035807304084300995,
0.004902753513306379,
0.022066893056035042,
-0.0503963939845562,
-0.035428695380687714,
0.01987517438828945,
-0.023932117968797684,
-0.005434792954474688,
0.006034846417605877,
-0.06472686678171158,
0.06608537584543228,
0.0106923533603549,
0.008283617906272411,
0.04314097389578819,
-0.011507172137498856,
0.006192463915795088,
-0.04433595389127731,
0.025903521105647087,
0.04414273053407669,
0.026363378390669823,
0.023022964596748352,
0.011923560872673988,
-0.012189294211566448,
-0.03152421861886978,
0.010989541187882423,
0.00604839576408267,
0.02607836201786995
] |
<p>Doppler redshift of distant galaxies gave first hint that the universe is expanding. I am curious to know how this redshift is actually measured and interpreted from observation. Suppose I observe some visible line say red with wavelength \lambda_1. This is not enough to tell that this line is redshifted, i.e., the original line emitted from that galaxy had a smaller wavelength. How do I know the value of that particular line when it was emitted from that galaxy? It appears that mere observation of a line is not enough. So how do we proceed?</p> | g9249 | [
0.008115721866488457,
0.011428617872297764,
-0.002293142257258296,
-0.06113026663661003,
0.049896273761987686,
0.00971640832722187,
-0.027188505977392197,
0.012440995313227177,
0.007369611412286758,
-0.10225747525691986,
-0.0010713539086282253,
0.01722765900194645,
0.09309814870357513,
0.05964834243059158,
0.062045179307460785,
-0.04213932529091835,
0.04317683354020119,
-0.07324319332838058,
0.06759613752365112,
-0.021803949028253555,
-0.0006837643450126052,
-0.004297655075788498,
0.020244263112545013,
-0.037123844027519226,
-0.0671849250793457,
-0.013901112601161003,
-0.007643087767064571,
-0.004755833186209202,
-0.017789626494050026,
-0.03026467189192772,
-0.013058331795036793,
-0.026301460340619087,
0.06264831125736237,
0.029736200347542763,
0.01413754839450121,
0.015902750194072723,
0.02340126968920231,
0.017031630501151085,
0.030155515298247337,
-0.0027076255064457655,
-0.004511985462158918,
0.02079964615404606,
0.006231553386896849,
0.0028895766008645296,
0.051980819553136826,
0.010270637460052967,
0.006734486203640699,
0.015139690600335598,
0.05916627123951912,
-0.005633242428302765,
-0.042542099952697754,
0.013873827643692493,
-0.0209549218416214,
0.1106310486793518,
-0.03315779194235802,
0.0377848781645298,
0.023971522226929665,
-0.0587582066655159,
0.07342599332332611,
-0.02111918106675148,
0.0026015336625277996,
-0.01824260503053665,
0.01764773577451706,
-0.047086331993341446,
0.03409940376877785,
0.03742637112736702,
0.000545051007065922,
-0.01637479104101658,
-0.001941381604410708,
-0.005876251962035894,
-0.00402096239849925,
-0.05377021059393883,
-0.04636605456471443,
-0.014703118242323399,
-0.054992061108350754,
0.022563692182302475,
-0.02590966783463955,
-0.03430420532822609,
-0.047983743250370026,
0.014267697930335999,
0.01595667190849781,
-0.015707002952694893,
-0.013906057924032211,
0.05184114724397659,
0.05806256830692291,
0.00657190615311265,
-0.021023323759436607,
0.0401630699634552,
0.052076976746320724,
0.012652149423956871,
0.028803179040551186,
0.017563899978995323,
0.05373711138963699,
-0.055648788809776306,
0.03847873583436012,
-0.03381062299013138,
-0.05448468029499054,
0.018935244530439377,
-0.011398152448236942,
-0.03552224859595299,
-0.01745738461613655,
0.04176529496908188,
0.00806461088359356,
-0.06907864660024643,
0.06565757095813751,
-0.011937771923840046,
0.016495605930685997,
0.006730399094521999,
0.006644012872129679,
-0.08451960235834122,
0.006703933700919151,
-0.08852964639663696,
-0.004602756351232529,
-0.03125341981649399,
-0.05226234346628189,
-0.009930819272994995,
0.026113921776413918,
0.06936611980199814,
0.04737189784646034,
0.043117739260196686,
-0.009773175232112408,
0.02490350790321827,
0.030614133924245834,
0.02181863784790039,
0.027334101498126984,
0.022922061383724213,
-0.00997256301343441,
-0.06560847163200378,
0.035491473972797394,
0.016782615333795547,
-0.006795146502554417,
0.03934121131896973,
0.0381472110748291,
0.015279299579560757,
0.003648134181275964,
0.006518229842185974,
0.034345030784606934,
0.015002449043095112,
-0.027125677093863487,
0.04112255573272705,
0.06247697398066521,
-0.03905448690056801,
0.06746134907007217,
-0.06734225153923035,
-0.008037248626351357,
-0.008729278109967709,
-0.0060770586133003235,
-0.01575331948697567,
0.07515383511781693,
-0.009340066462755203,
-0.008649672381579876,
0.031892068684101105,
-0.013896770775318146,
0.01414414681494236,
-0.04464128240942955,
-0.0309737715870142,
-0.00340430811047554,
-0.020461447536945343,
-0.03714173659682274,
0.019700560718774796,
0.05533811077475548,
-0.0030772602185606956,
-0.03308878839015961,
0.043309733271598816,
0.008028187789022923,
-0.0040040514431893826,
0.008230146951973438,
-0.06660373508930206,
0.04725964739918709,
-0.03974585980176926,
-0.00036443129647523165,
0.008648009970784187,
0.019844844937324524,
-0.016980845481157303,
-0.01802149973809719,
0.07512705773115158,
0.079084113240242,
-0.01335005834698677,
-0.045812781900167465,
0.06365359574556351,
-0.03916940838098526,
-0.0692426934838295,
0.01638609915971756,
-0.010018697939813137,
0.001533718197606504,
-0.01717374101281166,
-0.02093999832868576,
-0.09092845767736435,
0.013094713911414146,
0.04248901456594467,
-0.020860640332102776,
-0.002820056863129139,
0.04744856432080269,
0.019640464335680008,
-0.022708307951688766,
-0.010684332810342312,
-0.014406123198568821,
-0.019932622089982033,
-0.0339774452149868,
0.0003418164560571313,
0.018252769485116005,
0.00781124085187912,
-0.012935278937220573,
0.0005122965667396784,
-0.008695797063410282,
-0.008826332166790962,
-0.012563011609017849,
-0.012764031067490578,
0.03199378028512001,
-0.018138617277145386,
0.00814184918999672,
-0.02167533151805401,
-0.014592328108847141,
-0.016841303557157516,
-0.035920318216085434,
0.06398680806159973,
-0.015521314926445484,
0.016155308112502098,
0.01553317066282034,
0.031463731080293655,
0.010789390653371811,
-0.000991437816992402,
0.07855367660522461,
-0.03508475795388222,
0.04896850883960724,
-0.04789779707789421,
-0.05426454916596413,
0.03776276484131813,
0.055020201951265335,
0.021190283820033073,
-0.027291331440210342,
0.007453644182533026,
-0.016659198328852654,
-0.0048160008154809475,
-0.008968868292868137,
-0.016604945063591003,
-0.012944054789841175,
-0.011836780235171318,
0.00989533867686987,
0.05877117067575455,
0.007659986615180969,
-0.057353898882865906,
-0.033735401928424835,
0.05072028934955597,
0.02963000163435936,
-0.008328738622367382,
0.028545185923576355,
-0.008471062406897545,
-0.03609707951545715,
-0.016359465196728706,
0.05782371014356613,
0.01579906791448593,
0.0700046718120575,
-0.036502741277217865,
-0.06758901476860046,
-0.0054002427496016026,
0.013140327297151089,
0.0787067785859108,
-0.06001593545079231,
-0.017560070380568504,
-0.013948489911854267,
-0.05269552394747734,
0.0560029074549675,
-0.010161575861275196,
0.04911346733570099,
0.0029796443413943052,
-0.022608011960983276,
0.02726263552904129,
-0.041162483394145966,
-0.07846958935260773,
0.032846491783857346,
0.017207801342010498,
-0.018961619585752487,
0.03170265629887581,
-0.009997854009270668,
0.06146864593029022,
0.018267948180437088,
0.008810344152152538,
0.039817970246076584,
0.009646095335483551,
-0.04291517287492752,
-0.03348112106323242,
-0.09126192331314087,
0.0319453626871109,
0.007820647209882736,
-0.052135858684778214,
0.00816616415977478,
-0.0158780999481678,
0.036114420741796494,
-0.027899065986275673,
-0.012193577364087105,
0.027633829042315483,
-0.0357067696750164,
0.037393733859062195,
-0.028592294082045555,
0.022898156195878983,
0.05068054050207138,
0.050190269947052,
0.03723470866680145,
-0.0012928753858432174,
0.026043632999062538,
-0.07343354821205139,
-0.02263023518025875,
-0.04981297254562378,
0.03260665759444237,
0.01703803427517414,
0.013436567969620228,
-0.03386484459042549,
0.015268436633050442,
-0.02002756856381893,
-0.022907942533493042,
-0.00425525289028883,
0.02050923742353916,
0.0009213574812747538,
-0.007580919656902552,
0.015927806496620178,
-0.023773154243826866,
0.008646811358630657,
-0.03800171986222267,
0.05328068137168884,
0.04315463826060295,
-0.03896411135792732,
-0.08361206948757172,
-0.052136220037937164,
0.029666831716895103,
-0.023956099525094032,
0.007999843917787075,
-0.0512811504304409,
-0.030744405463337898,
0.016609398648142815,
0.00421084463596344,
0.006593951489776373,
-0.07190681993961334,
-0.03915984556078911,
-0.02112290821969509,
-0.008220217190682888,
-0.039227962493896484,
-0.008410768583416939,
0.03695046529173851,
-0.0018792286282405257,
-0.042751945555210114,
-0.020041676238179207,
-0.03800532966852188,
-0.0019209461752325296,
0.01888667233288288,
-0.02806774154305458,
0.011366342194378376,
0.0391211099922657,
-0.015821333974599838,
-0.055312130600214005,
0.039501726627349854,
-0.0003291280590929091,
-0.013107861392199993,
-0.03302980959415436,
0.009563326835632324,
0.036457352340221405,
0.058123085647821426,
-0.0019879464525729418,
-0.014708470553159714,
0.028735190629959106,
0.05618181452155113,
0.0017813700251281261,
-0.035049524158239365,
-0.008110752329230309,
0.028199555352330208,
-0.016701245680451393,
0.00797448493540287,
0.016438450664281845,
0.026462947949767113,
0.02349422685801983,
-0.01041950099170208,
-0.053179945796728134,
-0.03164464607834816,
0.06694889813661575,
-0.02471623197197914,
-0.005096058826893568,
0.03827216476202011,
0.003018850227817893,
-0.014891372062265873,
0.06640802323818207,
0.017572928220033646,
0.03132688254117966,
-0.002485299715772271,
-0.016939200460910797,
0.017314089462161064,
-0.006867371033877134,
-0.02233186922967434,
-0.04382678493857384,
0.025415796786546707,
-0.02610938437283039,
0.004003575071692467,
-0.04872317612171173,
-0.006347558461129665,
0.003431870136409998,
0.023094123229384422,
-0.0434943251311779,
-0.004338455852121115,
0.03728225827217102,
0.046701475977897644,
0.01626051776111126,
-0.031022951006889343,
0.020231567323207855,
0.007686987519264221,
0.028438836336135864,
-0.039625074714422226,
-0.022678878158330917,
0.018908752128481865,
-0.005969330668449402,
0.01924954354763031,
0.020061388611793518,
-0.05470246076583862,
-0.01935386098921299,
0.0019419578602537513,
-0.1111844852566719,
-0.024133456870913506,
-0.0002532436337787658,
0.07044753432273865,
-0.09856367856264114,
0.0050458223558962345,
0.040729131549596786,
0.018541738390922546,
0.020342569798231125,
0.004780394025146961,
-0.01646585576236248,
-0.06215950474143028,
0.051699478179216385,
-0.008069832809269428,
-0.014803952537477016,
-0.007622846402227879,
0.002737282542511821,
-0.010866504162549973,
-0.017306488007307053,
0.04405480623245239,
0.0679878443479538,
-0.03907688334584236,
0.016792235895991325,
0.012864910997450352,
0.07115236669778824,
-0.04548546299338341,
-0.00024979995214380324,
0.04036547616124153,
-0.042496129870414734,
-0.04908576235175133,
0.018009081482887268,
0.004412450827658176,
0.068354032933712,
-0.06307800114154816,
0.013766449876129627,
-0.045662570744752884,
-0.04412063956260681,
-0.0412198081612587,
0.008545727469027042,
-0.062418416142463684,
0.04776011407375336,
0.03604760393500328,
-0.06344516575336456,
-0.007817025296390057,
-0.0014317837776616216,
0.029502201825380325,
0.04474630579352379,
-0.006071188487112522,
0.01812686026096344,
0.015364391729235649,
-0.008088840171694756,
0.012032130733132362,
-0.017760055139660835,
-0.018893305212259293,
-0.049757424741983414,
0.024637095630168915,
0.09295990318059921,
-0.06822120398283005,
-0.02394365519285202,
0.01757342927157879,
-0.01105918176472187,
0.0061116768047213554,
0.013136819005012512,
-0.0322146937251091,
0.0056013609282672405,
0.028853213414549828,
-0.036092955619096756,
-0.008725729770958424,
-0.008652113378047943,
0.048482198268175125,
-0.021930068731307983,
-0.03172338008880615,
0.034839242696762085,
-0.0075404769740998745,
0.018207810819149017,
-0.013186193071305752,
0.022127611562609673,
0.02577309124171734,
0.02705117128789425,
0.01125918235629797,
0.038754165172576904,
-0.05585271865129471,
0.01685093156993389,
-0.01745389774441719,
-0.022257817909121513,
-0.0026455300394445658,
-0.05052880942821503,
-0.030611535534262657,
0.08063157647848129,
0.00785033218562603,
0.030880434438586235,
0.005922175943851471,
-0.005761784967035055,
-0.006186207756400108,
-0.0702190026640892,
-0.0013319130521267653,
-0.017280355095863342,
-0.0808945968747139,
0.0011512237833812833,
0.00485850777477026,
-0.016410009935498238,
0.09484344720840454,
-0.07047636806964874,
-0.02701864019036293,
0.033420950174331665,
0.017605576664209366,
-0.014530127868056297,
-0.04878764972090721,
0.0032593272626399994,
0.017778804525732994,
-0.04692566394805908,
0.0330866277217865,
-0.025918003171682358,
0.005471155978739262,
0.04673590138554573,
0.02146853134036064,
-0.07473021745681763,
0.05787843093276024,
0.010485305450856686,
-0.017306160181760788,
-0.011094955727458,
0.0737510621547699,
0.04284920170903206,
0.00474832346662879,
0.013960914686322212,
-0.053043466061353683,
-0.015635792165994644,
-0.021780891343951225,
0.03732062131166458,
-0.0032047200947999954,
0.009832045994699001,
-0.03212631121277809,
-0.001846119062975049,
-0.0273296982049942,
0.04916687309741974,
0.09124889224767685,
-0.0224035382270813,
-0.014116944745182991,
-0.010990907438099384,
-0.010762438178062439,
0.04394169896841049,
-0.024982351809740067,
-0.014257642440497875,
0.07266847044229507,
-0.06277431547641754,
-0.007173496764153242,
-0.03338858112692833,
-0.01614219695329666,
-0.01408825721591711,
0.02023325301706791,
-0.004214165266603231,
-0.010920064523816109,
-0.012658793479204178,
0.03762069717049599,
-0.04600924625992775,
0.04216315597295761,
0.027311084792017937,
-0.07804684340953827,
-0.037213727831840515,
0.009598909877240658,
0.02119304984807968,
-0.008369171060621738,
0.05263969674706459,
0.019357897341251373,
0.019744647666811943,
-0.02139088325202465,
-0.0180857852101326,
0.006156029179692268,
0.021615341305732727,
0.06570937484502792,
0.01720399223268032,
-0.03783728554844856,
0.052711304277181625,
0.03136133402585983,
0.05581682175397873,
0.029388543218374252,
0.020594747737050056,
0.03377179056406021,
0.008160552941262722,
-0.006474753376096487,
-0.06163695827126503,
-0.026108622550964355,
-0.09878014773130417,
-0.016348369419574738,
-0.026026709005236626,
-0.04712781310081482,
0.03550506755709648,
0.015478700399398804,
-0.03933468088507652,
0.03727685287594795,
-0.05976469814777374,
0.020581046119332314,
-0.07704021036624908,
-0.023758098483085632,
-0.016218947246670723,
0.06361758708953857,
-0.025187164545059204,
0.009205621667206287,
0.013988061808049679,
0.028390659019351006,
0.0427207387983799,
0.02815031260251999,
-0.014015822671353817,
0.0563187301158905,
-0.05202803760766983,
-0.030138861387968063,
-0.012838706374168396,
0.06513868272304535,
-0.01734139584004879,
0.033843424171209335,
0.013089572079479694,
-0.007429586723446846,
0.046727150678634644,
-0.0018364405259490013,
-0.05231761932373047,
0.005672244820743799,
0.03515508770942688,
-0.03689153119921684,
0.0556824617087841,
-0.0025896925944834948,
0.008808175101876259,
-0.0008410080918110907,
0.0007923231460154057,
-0.008306747302412987,
0.02760661207139492,
0.01638624258339405,
0.02705935202538967,
0.06277083605527878,
-0.021622352302074432,
0.053300466388463974,
-0.045795850455760956,
-0.06430276483297348,
0.010189982131123543,
0.029239147901535034,
0.04861706495285034,
-0.04272133857011795,
-0.016042053699493408,
-0.062203776091337204,
-0.053775448352098465,
0.000156632813741453,
0.016681337729096413,
-0.01979510486125946,
0.050187524408102036,
0.014646290801465511,
0.0031787774059921503,
-0.02027813531458378,
-0.06964370608329773,
-0.02601158432662487,
-0.03865134343504906,
-0.054717499762773514,
0.020939001813530922,
0.023842664435505867,
0.03605213761329651,
0.05731571465730667,
-0.005305321887135506,
-0.017951007932424545,
-0.03380315378308296,
-0.002546275733038783,
-0.020939603447914124,
0.006167024374008179,
-0.0002603227330837399,
-0.002966307569295168,
-0.037080854177474976,
-0.049984246492385864,
0.027661528438329697,
0.04892260208725929,
-0.03726625815033913,
-0.05213874578475952,
0.06511371582746506,
0.029849130660295486,
0.023838059976696968,
-0.015755290165543556,
0.03193765506148338,
-0.07294618338346481,
-0.01383680384606123,
-0.027026310563087463,
-0.02136898599565029,
-0.06002773344516754,
-0.03698926419019699,
-0.015235853381454945,
-0.08561541140079498,
-0.009930637665092945,
-0.025857364758849144,
0.014581427909433842,
0.02184419333934784,
0.020124340429902077,
-0.015527955256402493,
-0.020339900627732277,
-0.0025856909342110157,
-0.018342044204473495,
0.004639543127268553,
0.02317689172923565,
-0.011713924817740917,
-0.01926773227751255,
0.00691080279648304,
-0.03014797531068325,
-0.00886605866253376,
0.030257344245910645,
-0.000511008023750037,
0.08379096537828445,
0.014774873852729797,
-0.011786564253270626,
-0.003845018334686756,
-0.012440009973943233,
0.0031552265863865614,
0.029039617627859116,
0.027345556765794754,
0.02875150553882122,
-0.005142015404999256,
0.011715673841536045,
-0.04413904622197151,
-0.010040190070867538,
0.010411117225885391,
0.01877572014927864,
0.037444889545440674,
0.0043501779437065125,
-0.024745143949985504,
-0.025771599262952805,
0.034917235374450684,
0.050315018743276596,
-0.007240497041493654,
-0.07573942840099335,
0.04116680473089218,
0.025612741708755493,
0.01703163981437683,
-0.03190957009792328,
-0.008851739577949047,
0.002018043538555503,
0.013640742748975754,
-0.014180708676576614,
0.02413003146648407,
0.038465581834316254,
-0.05765267834067345,
0.003726610681042075,
0.04682811349630356,
0.052294742316007614,
-0.00405516754835844,
0.041387975215911865,
0.07908593118190765,
0.011796751990914345,
0.013596651144325733,
0.0015824547735974193,
-0.028841540217399597,
-0.04726969078183174,
-0.01646643504500389,
-0.05410682037472725,
-0.08408006280660629,
0.030206935480237007,
-0.009190833196043968,
-0.009428823366761208,
0.024926558136940002,
-0.021092897281050682,
-0.013126472011208534,
-0.012621847912669182,
0.016723986715078354
] |
<p>In the canonical quantization of fields, CCR is postulated as (for scalar boson field ):
$$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$
in analogy with the ordinary QM commutation relation:
$$[x_i,p_j]=i\delta_{ij}\qquad\qquad(2)$$
However, using (2) we could demo the continuum feature of the spectrum of $x_i$, while (1) raises the issue of $\delta(0)$ for the searching of spectrum of $\phi(x)$, so what would be its spectrum? <br><br>
I guess that the configure space in QFT is the set of all functions of $x$ in $R^3$, so the QFT version of $\langle x'|x\rangle=\delta(x'-x)$ would be $\langle f(x)|g(x)\rangle=\delta[f(x),g(x)]$, <br>but what does $\delta[f(x),g(x)]$ mean?<br><br> If you will say it means $\int Dg(x) F[g(x)]\delta[f(x),g(x)]=F[f(x)]$, then how is the measure $Dg(x)$ defined?<br><br>
And what is the cardinality of the set $\{g(x)\}$? Is the state space of QFT a separable Hilbert sapce also? Then are field operators well defined on this space?</p>
<p>Actually if you choose to quantize in an $L^3$ box, many issues will not emerge, but many symmetries cannot be studied in this approximation, such as translation and rotation, so that would not be the standard route, <br>so I wonder how the rigor is preserved in the formalism in the whole space rather than in a box or cylinder model?<br>
<br>
I'm now beginning learning QFT, and know little about the mathematical formulation of QFT, so please help me with these conceptual issues.</p> | g9250 | [
-0.0026896547060459852,
-0.007104129996150732,
-0.02302754670381546,
-0.04081650450825691,
0.07135673612356186,
-0.011809827759861946,
0.05546111240983009,
0.0037030621897429228,
-0.019668010994791985,
-0.07466477900743484,
-0.05499434843659401,
-0.009296439588069916,
-0.027012532576918602,
-0.006154550705105066,
0.014004534110426903,
-0.039335064589977264,
-0.01374669186770916,
0.04751911759376526,
0.0303057748824358,
-0.0832834243774414,
-0.0337773822247982,
0.015294704586267471,
0.0010205148719251156,
-0.01566237583756447,
0.018999086692929268,
-0.0018612323328852654,
0.04416586831212044,
0.035802602767944336,
0.008224080316722393,
-0.03032049536705017,
0.00009757273801369593,
0.07476963102817535,
0.03758114203810692,
0.01332091074436903,
0.028840752318501472,
-0.048474229872226715,
0.057488132268190384,
0.03963537514209747,
0.03636323660612106,
-0.04402006417512894,
-0.02103564701974392,
-0.029140964150428772,
0.036371249705553055,
-0.006814070511609316,
-0.01910380646586418,
0.005372944753617048,
0.03628058359026909,
-0.02907998487353325,
-0.023516172543168068,
0.008475810289382935,
-0.036921996623277664,
0.04689107835292816,
0.034597378224134445,
0.01409144140779972,
0.021685408428311348,
0.07364083081483841,
-0.002583911409601569,
0.0031761727295815945,
0.018706930801272392,
-0.04444146901369095,
0.002505002310499549,
-0.026093794032931328,
0.01785598322749138,
0.016559245064854622,
0.03218424320220947,
-0.010108289308845997,
-0.004592107143253088,
-0.0019138811621814966,
-0.032475195825099945,
-0.03483396768569946,
0.024652473628520966,
-0.04332996904850006,
0.0465967170894146,
0.06591589748859406,
-0.06083070486783981,
-0.014560886658728123,
-0.03090931661427021,
-0.007661676499992609,
0.0031047947704792023,
-0.014063157141208649,
-0.05304506793618202,
-0.04007148742675781,
0.007200734224170446,
0.03630565479397774,
0.04357969015836716,
0.03340925648808479,
0.005070272367447615,
0.002806826028972864,
0.013897598721086979,
0.014434175565838814,
-0.041628431528806686,
-0.0759492963552475,
0.042621538043022156,
0.05730300769209862,
0.0053189960308372974,
-0.017355799674987793,
0.0015423576114699244,
0.03231953829526901,
-0.0038963330443948507,
0.000036468307371251285,
-0.041855331510305405,
0.07495475560426712,
0.02679368481040001,
0.006296887528151274,
-0.08035426586866379,
0.03234754130244255,
0.064161516726017,
-0.018030449748039246,
-0.014503817074000835,
0.040225353091955185,
-0.07252741605043411,
0.0452515110373497,
-0.01492131594568491,
-0.023447198793292046,
-0.01961415261030197,
-0.015795273706316948,
0.023540671914815903,
-0.022933896631002426,
0.02246716246008873,
0.05713518708944321,
0.012170414440333843,
-0.0004971877788193524,
0.06475557386875153,
0.004709388129413128,
0.009936117567121983,
-0.002744572702795267,
-0.07149524241685867,
-0.0010870402911677957,
0.0754452794790268,
-0.0025670998729765415,
0.02313552051782608,
-0.008958924561738968,
-0.04290546476840973,
0.08615104109048843,
0.00146752898581326,
-0.013166065327823162,
-0.0121382474899292,
0.006842610891908407,
0.001096634310670197,
-0.01958037167787552,
-0.022194597870111465,
0.03408204764127731,
-0.036697499454021454,
-0.010620239190757275,
0.04116953909397125,
-0.028522223234176636,
0.02372431568801403,
-0.0415068194270134,
0.00723234424367547,
0.012179585173726082,
0.04171909764409065,
0.08389637619256973,
-0.006372412666678429,
-0.014949380420148373,
0.044693443924188614,
0.031957048922777176,
0.059955842792987823,
-0.008233277127146721,
-0.013064924627542496,
-0.052183471620082855,
0.03448593243956566,
0.011585342697799206,
-0.027252867817878723,
0.016859160736203194,
-0.006808117497712374,
-0.05140237137675285,
0.03854355961084366,
-0.056015584617853165,
0.036873068660497665,
-0.02955769933760166,
0.012853670865297318,
0.03768943250179291,
0.020374108105897903,
0.005121076945215464,
-0.026376958936452866,
0.03855835273861885,
-0.00854280311614275,
-0.03352067247033119,
-0.023973843082785606,
0.03374536707997322,
-0.04501408711075783,
0.03167625889182091,
-0.023602722212672234,
-0.023212766274809837,
0.005751763004809618,
0.011277138255536556,
-0.00022660761896986514,
-0.06101135537028313,
-0.02194988541305065,
0.05947896093130112,
0.013498736545443535,
0.02105158567428589,
0.01066605094820261,
0.021354353055357933,
0.010718791745603085,
0.02524295449256897,
-0.0023757631424814463,
-0.05523323640227318,
-0.020309271290898323,
-0.06206797808408737,
0.0038338624872267246,
-0.0015846629394218326,
0.05215301737189293,
0.04214775189757347,
0.021524181589484215,
0.008365306071937084,
0.020161457359790802,
0.029565567150712013,
0.017985258251428604,
0.036826327443122864,
-0.014611199498176575,
-0.03581628575921059,
-0.018368864431977272,
0.022939909249544144,
0.022790003567934036,
-0.009937763214111328,
-0.008293603546917439,
0.02544071152806282,
-0.01641993038356304,
0.010421223938465118,
-0.002578000072389841,
-0.03320663794875145,
0.08920943737030029,
0.0561823770403862,
-0.02313445508480072,
0.06769006699323654,
0.0017352290451526642,
0.0238453708589077,
-0.018854981288313866,
0.02238394133746624,
-0.048951439559459686,
0.004237520974129438,
-0.0595877431333065,
-0.009117631241679192,
-0.0005100186099298298,
0.07845038175582886,
-0.036257095634937286,
-0.03952767699956894,
0.04723865166306496,
0.10631722211837769,
0.06375649571418762,
0.03663028031587601,
-0.027712929993867874,
0.029195070266723633,
0.02114894427359104,
0.02403148077428341,
0.04790087789297104,
0.06449484825134277,
-0.06220720708370209,
-0.001224277075380087,
-0.03798039257526398,
0.006175687536597252,
-0.0056737796403467655,
-0.013871824368834496,
-0.017967861145734787,
0.0008483793935738504,
0.02952243946492672,
-0.026919981464743614,
-0.021003691479563713,
0.007762049790471792,
0.01577075570821762,
-0.0873405709862709,
-0.05888841673731804,
0.02035214565694332,
-0.05882468447089195,
-0.054526276886463165,
0.007532760500907898,
0.032683223485946655,
-0.052314016968011856,
-0.009351536631584167,
-0.05412565916776657,
-0.02963278256356716,
0.03593582287430763,
0.014409047551453114,
-0.03333621099591255,
-0.033440001308918,
-0.05807029455900192,
-0.002797800814732909,
-0.013167884200811386,
-0.03212829306721687,
-0.008196032606065273,
-0.021268442273139954,
-0.024444954469799995,
0.04075317457318306,
-0.0014445086708292365,
-0.017173273488879204,
-0.024789243936538696,
0.018794827163219452,
0.003070053644478321,
-0.002349164802581072,
-0.005394438281655312,
0.0024503476452082396,
-0.02423284575343132,
-0.004331050906330347,
-0.050678543746471405,
0.051967259496450424,
-0.02252430096268654,
-0.028539851307868958,
0.02553173340857029,
0.07919833809137344,
0.0062826815992593765,
0.009616860188543797,
0.016143012791872025,
0.01497157197445631,
-0.0187432449311018,
-0.0636170506477356,
-0.03835120424628258,
-0.0059274728409945965,
-0.019396578893065453,
-0.02395899035036564,
-0.03991379588842392,
-0.0069542271085083485,
-0.0764782726764679,
-0.03567543253302574,
0.0016806076746433973,
-0.04601218178868294,
-0.020794671028852463,
0.036104533821344376,
-0.0035872829612344503,
-0.030786706134676933,
0.011924994178116322,
-0.06213831529021263,
0.019904617220163345,
-0.009248558431863785,
0.0671514943242073,
0.06514274328947067,
-0.04550093039870262,
0.0023517946247011423,
0.007048656698316336,
-0.05535569414496422,
0.014984211884438992,
0.0008047500159591436,
0.005961504299193621,
0.0011932728812098503,
-0.06899432092905045,
-0.01107870601117611,
-0.062628373503685,
-0.014976326376199722,
0.05331907793879509,
-0.009937185794115067,
0.018271466717123985,
-0.023299159482121468,
-0.029267681762576103,
0.028042444959282875,
0.003145951544865966,
0.005500318482518196,
0.022131668403744698,
-0.0010742112062871456,
0.04256870970129967,
-0.01717446744441986,
-0.08327309042215347,
-0.03913446515798569,
-0.007919339463114738,
0.005044306628406048,
-0.007513524033129215,
0.05748901516199112,
0.015048532746732235,
0.007020329125225544,
0.033063385635614395,
-0.017187034711241722,
-0.018841765820980072,
-0.047064945101737976,
-0.004492849111557007,
0.04410569742321968,
0.0013315875548869371,
-0.006681005470454693,
0.008977158926427364,
-0.030039532110095024,
0.00039140149601735175,
0.037251170724630356,
0.031530432403087616,
-0.026976095512509346,
0.017775852233171463,
0.002102998550981283,
0.017808588221669197,
-0.07074430584907532,
0.007599195931106806,
-0.07026267051696777,
0.007199218031018972,
-0.019582344219088554,
-0.011540019884705544,
0.03820420429110527,
0.06470264494419098,
0.025739649310708046,
0.035842444747686386,
0.01053518895059824,
-0.0052376422099769115,
-0.00036134858964942396,
-0.0242164246737957,
0.03157370537519455,
0.022188380360603333,
-0.06467700749635696,
-0.014284058474004269,
-0.020303741097450256,
0.011824844405055046,
-0.0017114157089963555,
-0.012601516209542751,
0.007235804572701454,
-0.06160160154104233,
0.003971346653997898,
0.005734194535762072,
-0.03644823282957077,
0.02245965041220188,
-0.028382061049342155,
-0.04651276767253876,
-0.0407126285135746,
-0.01591404154896736,
-0.029255200177431107,
0.014779884368181229,
-0.0264726672321558,
-0.007825431413948536,
0.0016816670540720224,
-0.0326501838862896,
-0.04631100967526436,
0.01345400046557188,
0.026111729443073273,
0.04620274528861046,
-0.03184155374765396,
-0.021563507616519928,
-0.02986178547143936,
0.009557920508086681,
-0.024401456117630005,
0.005582244135439396,
-0.012422142550349236,
0.06686370074748993,
0.07198191434144974,
0.036244455724954605,
0.00033101419103331864,
0.01503697969019413,
-0.027225442230701447,
0.06815367192029953,
0.01040681079030037,
0.019594499841332436,
0.07429143041372299,
-0.048413436859846115,
0.020360080525279045,
-0.09373290091753006,
0.00413185590878129,
-0.04620194435119629,
0.01922772452235222,
0.0500464141368866,
-0.01515024434775114,
-0.02258276753127575,
-0.043000925332307816,
-0.06163899227976799,
0.006404179148375988,
-0.03354255110025406,
0.004168063867837191,
-0.03319529816508293,
-0.08422334492206573,
0.00423373794183135,
0.028111109510064125,
-0.039373788982629776,
0.012009852565824986,
0.011400745250284672,
-0.06890200078487396,
0.004763632547110319,
-0.03251985087990761,
0.04554156959056854,
0.010874451138079166,
-0.0375249944627285,
-0.00038557773223146796,
-0.025685232132673264,
0.008139238692820072,
0.03987777233123779,
0.03717244416475296,
-0.1061861589550972,
-0.010570986196398735,
-0.03858937323093414,
-0.010089782997965813,
0.07407177984714508,
-0.027614613994956017,
0.04887020215392113,
-0.060274261981248856,
0.01348765566945076,
0.0011149945203214884,
0.036910150200128555,
-0.014436534605920315,
-0.0245500635355711,
-0.03187454119324684,
0.025156738236546516,
0.01672830618917942,
0.05219169333577156,
0.018397260457277298,
0.009147986769676208,
-0.0014016428031027317,
0.061916548758745193,
-0.029942557215690613,
-0.04513337463140488,
-0.0072104972787201405,
0.030317271128296852,
0.06781993061304092,
0.06036083772778511,
0.042385946959257126,
0.024171695113182068,
0.023475660011172295,
-0.0036056810058653355,
-0.014244930818676949,
-0.005033143796026707,
0.016094764694571495,
-0.0029853153973817825,
0.038320545107126236,
0.028298068791627884,
0.03074968419969082,
-0.04820411279797554,
0.06211429089307785,
0.08573130518198013,
0.04378389194607735,
-0.04067488759756088,
0.022110750898718834,
0.013882017694413662,
0.00806330144405365,
-0.017175570130348206,
0.03394458070397377,
0.020235266536474228,
-0.03456379473209381,
-0.03873400390148163,
-0.06354658305644989,
-0.05906577780842781,
-0.02952677756547928,
-0.004649170208722353,
0.03813587501645088,
0.01876397617161274,
-0.023840406909585,
-0.0053993347100913525,
0.06437378376722336,
-0.021812256425619125,
-0.06878414750099182,
-0.04810992255806923,
0.04331929609179497,
0.048470865935087204,
0.025400757789611816,
0.029008815065026283,
-0.006904853042215109,
0.003342196810990572,
-0.008369062095880508,
0.01385156624019146,
0.0042182100005447865,
0.021441364660859108,
0.05340397357940674,
-0.03874540701508522,
-0.017550554126501083,
0.0005564144812524319,
0.00039967530756257474,
0.011020462960004807,
0.025178248062729836,
-0.01953229308128357,
0.043878283351659775,
-0.011427780613303185,
-0.049250099807977676,
-0.022523874416947365,
-0.08255036920309067,
0.001642440096475184,
-0.004703632555902004,
0.0312923789024353,
0.031845301389694214,
0.00821689609438181,
-0.035106878727674484,
-0.04352109879255295,
0.009440448135137558,
-0.0069789704866707325,
0.004595858044922352,
-0.026841597631573677,
-0.09271469712257385,
0.05451358109712601,
0.028401469811797142,
0.036058615893125534,
0.010561181232333183,
0.04936271905899048,
0.008346432819962502,
-0.04878965765237808,
0.008130155503749847,
0.02876218780875206,
0.015641316771507263,
-0.007124796509742737,
0.03201841935515404,
-0.03154333308339119,
-0.036800626665353775,
-0.07789380848407745,
-0.026938283815979958,
0.06584518402814865,
0.003762900596484542,
0.008552233688533306,
-0.06812231242656708,
-0.014549827203154564,
0.1073421910405159,
0.020961079746484756,
-0.04135166108608246,
0.03981921449303627,
0.036539655178785324,
-0.04547698423266411,
0.03833422809839249,
-0.003733949037268758,
0.021229850128293037,
-0.005808757618069649,
0.06778561323881149,
0.02027614787220955,
0.015490848571062088,
-0.04272010549902916,
-0.060343045741319656,
0.040356047451496124,
0.05169745534658432,
0.05500121787190437,
-0.059009719640016556,
0.03757476434111595,
0.05232207477092743,
-0.04331885278224945,
-0.044312648475170135,
0.004262340720742941,
0.01201710756868124,
0.006065065972507,
-0.01609133742749691,
0.02691241167485714,
0.02070903405547142,
0.0009032952948473394,
-0.0001937706401804462,
0.006516672670841217,
0.05356033146381378,
-0.021445976570248604,
0.08841013163328171,
0.017407257109880447,
-0.028033103793859482,
0.03602401167154312,
-0.029572714120149612,
0.03966226801276207,
0.06815283745527267,
0.002693832153454423,
0.01604432985186577,
0.014298588037490845,
-0.008863489143550396,
-0.009123772382736206,
0.003373577492311597,
0.05074625834822655,
-0.029054932296276093,
-0.001215178519487381,
-0.01418627891689539,
-0.08850875496864319,
-0.0017812547739595175,
0.024426527321338654,
-0.00966336764395237,
-0.023162251338362694,
0.07139726728200912,
0.0768207386136055,
-0.0761195495724678,
-0.02150728367269039,
-0.00015745297423563898,
0.044240985065698624,
-0.01762113906443119,
-0.05625806003808975,
0.008979996666312218,
0.022935759276151657,
0.0477009192109108,
-0.025571390986442566,
-0.04466124251484871,
0.0045496015809476376,
0.016356095671653748,
0.08091829717159271,
-0.008394264616072178,
-0.06625788658857346,
-0.03989963233470917,
-0.018442446365952492,
-0.03387913852930069,
-0.10584881156682968,
0.030116844922304153,
-0.017491072416305542,
0.016414830461144447,
0.03591764345765114,
-0.005934695713222027,
0.027065152302384377,
-0.0366705060005188,
0.024027522653341293,
-0.014137960970401764,
-0.018147818744182587,
0.01191734429448843,
-0.043441396206617355,
-0.01645202375948429,
0.018422545865178108,
0.0782008096575737,
-0.005077321548014879,
-0.02014000527560711,
-0.0017379430355504155,
0.06978026777505875,
0.011908495798707008,
0.006877051666378975,
-0.04103482514619827,
0.013252069242298603,
0.007295951247215271,
-0.027841318398714066,
0.013709619641304016,
-0.027420440688729286,
-0.01776994578540325,
-0.04273275285959244,
0.009546524845063686,
-0.027447514235973358,
0.01577102765440941,
0.030777093023061752,
0.0522003099322319,
0.013420877046883106,
0.04536300525069237,
0.06626062840223312,
0.048008568584918976,
-0.03280891850590706,
-0.03586956486105919,
-0.031571295112371445,
0.03015446849167347,
-0.04450571537017822,
-0.006135748699307442,
-0.040106918662786484,
-0.07142233848571777,
-0.002440645359456539,
0.003850537585094571,
0.003863588673993945,
-0.0070121982134878635,
-0.015236003324389458,
0.05467265471816063,
0.0019053672440350056,
-0.020454254001379013,
0.03210525959730148,
-0.015430309809744358,
-0.01768634095788002,
0.005947099067270756,
0.00026926700957119465,
0.0031929202377796173,
-0.020908910781145096,
0.013459273613989353,
-0.009738952852785587,
-0.026318654417991638,
-0.06963617354631424,
-0.0034770118072628975,
0.03360560163855553,
-0.06656789779663086,
-0.008850387297570705,
-0.04048877954483032,
-0.025600392371416092,
-0.008881848305463791,
0.072476327419281,
-0.006150091532617807,
-0.01831609569489956,
0.014509578235447407,
0.016294263303279877,
-0.032511476427316666,
0.03170187398791313,
0.02118947170674801,
0.008889664895832539,
-0.019604483619332314,
-0.02804875187575817,
-0.012395728379487991,
-0.044243160635232925,
0.019969772547483444,
-0.010704405605793,
-0.03199155628681183,
-0.0336897149682045,
-0.029454300180077553,
0.061315976083278656,
0.004107313230633736,
-0.02928720973432064,
0.07795283198356628,
0.051345739513635635,
0.055056940764188766,
0.00680240523070097,
-0.02046971209347248,
-0.020968180149793625,
-0.027076177299022675,
0.022593602538108826,
-0.06790377199649811,
0.01200241781771183,
0.0006588259129785001,
0.025276828557252884
] |
<p>Can anyone explain the process required to make a Hadamard gate that acts on 1st, 2nd and 3rd qbits?</p>
<p>For Hgates acting on the first qubit i realise the matrix is $H=\begin{pmatrix} 1&1\\1&-1\end{pmatrix}$, but I am unsure how to formulate such a gate. As to acting on the second qubit I have read this <a href="http://en.wikipedia.org/wiki/Hadamard_transform" rel="nofollow">web page 1 </a>but I am not really sure if it is correct, because it is just a 4x4 matrix without any zeroes. I found this $\begin{pmatrix} 1 & 1 \\-1 & 1 \end{pmatrix} $ on another website which will obviously have zeroes when it is multiplied by $I$. Simply can anyone explain how Hadarmd gates can be formulated and built to n qubits? </p> | g9251 | [
0.028901834040880203,
0.04511600360274315,
-0.02127872221171856,
-0.060971371829509735,
0.027634277939796448,
-0.031624339520931244,
-0.019918279722332954,
-0.016590630635619164,
-0.0504625141620636,
0.008548512123525143,
-0.017575601115822792,
0.07306884229183197,
-0.04658626765012741,
-0.02335476689040661,
0.004811164923012257,
0.09184049814939499,
0.053296927362680435,
0.07155730575323105,
0.010726327076554298,
-0.013707160949707031,
-0.04118473082780838,
0.014861945994198322,
-0.04761476814746857,
-0.03030884638428688,
-0.009354449808597565,
-0.07626587152481079,
-0.02461867779493332,
-0.004282623995095491,
-0.08097605407238007,
0.003112255595624447,
-0.014668986201286316,
0.018604658544063568,
0.036482084542512894,
-0.045561183243989944,
0.045691996812820435,
0.01653379760682583,
0.028756888583302498,
-0.006934511009603739,
-0.03615345433354378,
0.007352036889642477,
-0.06090104579925537,
-0.044971369206905365,
-0.0022418093867599964,
0.0504852831363678,
-0.044223785400390625,
0.011734969913959503,
0.04085762798786163,
0.022322792559862137,
-0.0019800937734544277,
0.011180493980646133,
0.008576835505664349,
0.01581788994371891,
0.02472272887825966,
-0.04787507280707359,
-0.013933886773884296,
0.04612220823764801,
-0.04381290823221207,
0.01441598404198885,
0.03073989599943161,
0.012018511071801186,
-0.016930101439356804,
-0.06262398511171341,
0.031807225197553635,
0.016610343009233475,
0.05479535087943077,
0.004191057290881872,
0.024062011390924454,
0.056707561016082764,
-0.018977975472807884,
0.0944419652223587,
-0.05825842544436455,
-0.01907191053032875,
0.06035884842276573,
0.04711311310529709,
0.08741641044616699,
0.0026461174711585045,
0.056195810437202454,
-0.007232517935335636,
0.008222224190831184,
0.03288622573018074,
-0.005324988160282373,
-0.017666226252913475,
0.0492485836148262,
-0.012836520560085773,
0.027200818061828613,
0.04107476770877838,
-0.0015620093327015638,
-0.07992897927761078,
0.025853125378489494,
-0.0008062506094574928,
-0.0011544607114046812,
0.019613439217209816,
0.02707134373486042,
0.06196730583906174,
-0.05037277564406395,
-0.05139349773526192,
-0.013143717311322689,
0.042885780334472656,
0.03735221549868584,
-0.002464592456817627,
-0.01476056408137083,
0.013822764158248901,
0.017480384558439255,
-0.015877917408943176,
-0.027008268982172012,
0.0052316333167254925,
-0.015149705111980438,
-0.005055979825556278,
0.02252921089529991,
0.041929617524147034,
-0.056933436542749405,
-0.011847353540360928,
-0.02061457931995392,
-0.037138931453228,
-0.0006299730157479644,
0.03131738305091858,
0.042084701359272,
-0.007043532095849514,
-0.0033718408085405827,
0.051421891897916794,
0.0023077549412846565,
-0.05509033799171448,
0.016825322061777115,
0.01689828559756279,
0.03161703422665596,
-0.0064587583765387535,
-0.04522532969713211,
0.057511020451784134,
0.034523818641901016,
0.029731811955571175,
0.04263383895158768,
-0.022847549989819527,
0.04728695750236511,
0.0026836919132620096,
-0.028795922175049782,
0.03465817868709564,
0.037535544484853745,
0.025342535227537155,
-0.016822824254631996,
-0.0151642682030797,
-0.03089265339076519,
-0.049212947487831116,
-0.024835534393787384,
-0.01109880581498146,
0.024265043437480927,
0.0012307577999308705,
0.07006407529115677,
0.014054910279810429,
-0.0021792377810925245,
0.009377109818160534,
0.01138539332896471,
0.09277526289224625,
0.01866152696311474,
0.06164151430130005,
-0.03076918050646782,
-0.014398805797100067,
0.055491384118795395,
0.02955162152647972,
-0.0442814901471138,
-0.011965891346335411,
0.030454149469733238,
-0.010028540156781673,
0.005919968243688345,
-0.02773677371442318,
-0.029321899637579918,
-0.022353241220116615,
0.03659311681985855,
-0.021125679835677147,
0.01680506207048893,
-0.05860119313001633,
0.014318323694169521,
-0.02238786593079567,
-0.04309641569852829,
0.007722679525613785,
-0.00977349653840065,
0.017974084243178368,
-0.018025407567620277,
0.0487186498939991,
0.052435118705034256,
-0.005516891833394766,
-0.043763838708400726,
0.010551068931818008,
-0.022814199328422546,
0.05388503894209862,
-0.004670597147196531,
-0.01974247209727764,
0.05601569637656212,
0.029420625418424606,
-0.038009971380233765,
0.0013489918783307076,
-0.031376369297504425,
0.05927836149930954,
0.019558675587177277,
-0.008272331207990646,
0.021383410319685936,
0.04155252128839493,
0.08538760989904404,
-0.05051480978727341,
0.01986212469637394,
-0.012150018475949764,
0.028591228649020195,
0.011937050148844719,
0.007065816316753626,
-0.002588412258774042,
0.029938530176877975,
0.0458696186542511,
0.06480395048856735,
0.01993059553205967,
-0.023241912946105003,
0.022391898557543755,
-0.036843910813331604,
0.02882552333176136,
0.0050490968860685825,
0.06604611128568649,
0.013502637855708599,
-0.01859194226562977,
0.0050500547513365746,
-0.022813215851783752,
0.03205941244959831,
-0.0367872454226017,
-0.05943608656525612,
-0.032708585262298584,
0.005860735662281513,
0.02698940970003605,
-0.05500444397330284,
0.07211371511220932,
0.01466275006532669,
-0.03199146315455437,
-0.026923205703496933,
0.058028336614370346,
-0.008079677820205688,
-0.0015812608180567622,
-0.07982967048883438,
-0.04379195719957352,
0.0031772328075021505,
-0.01599610410630703,
-0.029979323968291283,
-0.0055163027718663216,
0.025049617514014244,
0.07247178256511688,
0.07134618610143661,
0.0006093255360610783,
0.004510480910539627,
-0.020931847393512726,
0.015151792205870152,
-0.06551772356033325,
0.03077203594148159,
0.03138208016753197,
-0.0461224801838398,
0.0470307283103466,
-0.05115381255745888,
-0.057506222277879715,
-0.02705690637230873,
-0.04151163250207901,
-0.024939002469182014,
0.009126270189881325,
0.031048620119690895,
-0.042824577540159225,
-0.00245459727011621,
-0.038048576563596725,
0.009201283566653728,
0.009206200018525124,
-0.04054686054587364,
-0.027780110016465187,
-0.021947264671325684,
-0.015074558556079865,
-0.024056149646639824,
0.04715448617935181,
0.04040689021348953,
-0.029243124648928642,
-0.028435131534934044,
0.017838604748249054,
0.008158979937434196,
0.002489987760782242,
-0.03359447792172432,
-0.06059233471751213,
0.0016510802088305354,
0.04506276920437813,
0.0222461074590683,
0.04258637875318527,
-0.023968679830431938,
-0.027654817327857018,
-0.0699549987912178,
-0.019610222429037094,
0.0072334203869104385,
-0.05729389190673828,
0.036749087274074554,
-0.03690880537033081,
-0.03439711779356003,
0.03666175529360771,
-0.05962631478905678,
0.013722246512770653,
-0.00725775258615613,
-0.047416478395462036,
-0.03248366713523865,
-0.027379654347896576,
-0.04338528588414192,
-0.027115561068058014,
-0.016302786767482758,
0.07856447249650955,
-0.0692809596657753,
-0.007495858706533909,
-0.008936582133173943,
-0.020624937489628792,
0.046746548265218735,
-0.005659590475261211,
0.004273922182619572,
-0.013408144935965538,
-0.0759878158569336,
0.010374503210186958,
0.014435462653636932,
0.017490550875663757,
0.02716851979494095,
-0.021400513127446175,
0.015337313525378704,
0.007073359098285437,
0.02578284963965416,
0.010534489527344704,
0.019734732806682587,
0.045070067048072815,
-0.046544257551431656,
-0.046425286680459976,
0.019050445407629013,
0.015833847224712372,
0.08437313139438629,
0.04123426228761673,
-0.017198171466588974,
0.021588977426290512,
-0.025229496881365776,
-0.04882087931036949,
0.008423014543950558,
0.04293224215507507,
0.041888002306222916,
0.026633623987436295,
0.00477505661547184,
-0.09521181881427765,
0.010426713153719902,
-0.006615079939365387,
-0.0466424822807312,
-0.0008555311942473054,
-0.007828719913959503,
-0.05104369297623634,
0.004368098918348551,
-0.0032875395845621824,
0.010556709952652454,
-0.0464952327311039,
0.05988413840532303,
0.0620814748108387,
-0.010718919336795807,
-0.03697953373193741,
-0.008069922216236591,
-0.03458670154213905,
0.01793188415467739,
0.04499611258506775,
0.014318324625492096,
0.04456251487135887,
-0.0366310216486454,
0.05588316544890404,
0.023864146322011948,
0.0028766074683517218,
-0.038248296827077866,
-0.012058291584253311,
-0.013465876691043377,
0.05223803594708443,
0.014146358706057072,
-0.021236160770058632,
-0.0273581575602293,
-0.010876089334487915,
-0.006705532316118479,
-0.04742817580699921,
0.05810611695051193,
-0.006726650986820459,
0.03861066699028015,
-0.03626353666186333,
-0.04657851532101631,
-0.05092998221516609,
-0.017586644738912582,
-0.04950478672981262,
0.032522447407245636,
0.05158108472824097,
-0.04372577741742134,
0.048721183091402054,
0.07268603891134262,
-0.016273045912384987,
0.004210814833641052,
0.0029075397178530693,
-0.0371338315308094,
-0.042510777711868286,
-0.0029694978147745132,
-0.03000979870557785,
-0.0056674666702747345,
-0.016476135700941086,
0.0009243387612514198,
-0.01908617839217186,
-0.009676176123321056,
-0.0037018819712102413,
0.0298157911747694,
-0.039271030575037,
-0.04620717093348503,
0.01413804292678833,
-0.015455464832484722,
0.06185377389192581,
-0.0046502393670380116,
-0.05543202906847,
-0.017119644209742546,
-0.0728965774178505,
0.027278952300548553,
-0.004297935403883457,
0.05583512410521507,
0.009854476898908615,
-0.018547963351011276,
-0.049128271639347076,
0.026391372084617615,
-0.015891633927822113,
0.050555694848299026,
0.04268309846520424,
0.020017914474010468,
0.03511354699730873,
-0.0648384541273117,
-0.05307917669415474,
-0.000593647244386375,
0.03901302441954613,
0.03129894658923149,
0.01997273601591587,
0.053572505712509155,
0.02143002860248089,
-0.000623077794443816,
-0.011983823031187057,
0.053000498563051224,
0.021811865270137787,
0.009238649159669876,
0.011032301001250744,
0.032524473965168,
0.014855027198791504,
-0.011711466126143932,
-0.048582613468170166,
-0.042378272861242294,
0.04933501034975052,
0.009699178859591484,
-0.03790348023176193,
0.03982500731945038,
0.054387167096138,
-0.05382006615400314,
-0.0013148492434993386,
-0.004164837300777435,
0.04341711476445198,
-0.02209446020424366,
-0.020492274314165115,
-0.018153274431824684,
-0.0018516628770157695,
0.029443493112921715,
0.008657730184495449,
0.0021235791500657797,
-0.06664692610502243,
0.0029244173783808947,
0.029698718339204788,
-0.05679070204496384,
0.039210472255945206,
0.045627765357494354,
0.04994860291481018,
-0.06642258912324905,
-0.03594285249710083,
-0.042657990008592606,
0.011610168032348156,
-0.004089432768523693,
0.015302433632314205,
-0.04784548282623291,
0.031101416796445847,
-0.007397034205496311,
0.003964526113122702,
0.012593896128237247,
0.015884267166256905,
-0.05717651546001434,
-0.011377464979887009,
-0.012025679461658001,
-0.012608705088496208,
0.002326236106455326,
-0.015430234372615814,
0.009214384481310844,
-0.03665829822421074,
-0.018872743472456932,
0.030338792130351067,
0.027588292956352234,
0.026407701894640923,
0.005033590365201235,
-0.02388690784573555,
-0.0027919288258999586,
-0.08113908767700195,
0.03704571723937988,
-0.038618844002485275,
0.0051355017349123955,
0.05374240502715111,
0.04173557832837105,
0.017038529738783836,
0.00516535947099328,
-0.0418412983417511,
0.02547799050807953,
-0.029282262548804283,
-0.025884050875902176,
-0.00020513760682661086,
-0.06424423307180405,
0.0008475988870486617,
-0.05727807432413101,
0.012430631555616856,
0.0016291250940412283,
0.03805529326200485,
0.05669892206788063,
-0.027346152812242508,
-0.019055990502238274,
-0.008563189767301083,
-0.030126772820949554,
0.018871886655688286,
-0.008342046290636063,
-0.013964025303721428,
0.02650720439851284,
0.06389812380075455,
0.056194767355918884,
-0.037728775292634964,
-0.052752479910850525,
0.038506049662828445,
0.025580735877156258,
-0.04432455450296402,
0.03622465580701828,
-0.05172637850046158,
-0.00035733848926611245,
-0.02477775327861309,
0.013193106278777122,
-0.04947393015027046,
-0.02438645251095295,
0.046877361834049225,
-0.012485979124903679,
-0.0004590815515257418,
-0.0425817146897316,
0.026255590841174126,
-0.007925122044980526,
-0.019300835207104683,
0.007675859611481428,
-0.015981929376721382,
0.04477962106466293,
0.03711509332060814,
-0.015611470676958561,
-0.038417354226112366,
0.040321338921785355,
0.05636107549071312,
-0.06618423014879227,
-0.06900802999734879,
-0.01173626258969307,
-0.028398241847753525,
-0.001075467560440302,
-0.01823219656944275,
0.015292699448764324,
-0.0512462817132473,
-0.015074126422405243,
-0.0037251031026244164,
-0.005695725325495005,
0.021350737661123276,
-0.01519995741546154,
-0.02005339227616787,
0.0810379609465599,
-0.046728428453207016,
0.021583784371614456,
-0.0007379485759884119,
-0.02634579688310623,
-0.002382903825491667,
-0.003806192195042968,
-0.028973326086997986,
0.0006784764700569212,
0.04099177196621895,
0.06753826141357422,
0.07349172234535217,
0.04945053532719612,
-0.06273667514324188,
-0.0428219735622406,
0.0003869296924676746,
0.014751903712749481,
0.038139309734106064,
0.022121699526906013,
-0.01698494330048561,
0.0021020553540438414,
0.024678530171513557,
0.037968263030052185,
0.05956445634365082,
-0.005651997867971659,
-0.022817248478531837,
0.028132997453212738,
0.048342470079660416,
-0.004953677766025066,
-0.02829563058912754,
-0.02689974755048752,
0.03721567243337631,
-0.05044308677315712,
-0.009467892348766327,
-0.06374190002679825,
-0.053286243230104446,
-0.005651875864714384,
0.02578621543943882,
0.0571109764277935,
0.02289062924683094,
0.0042051468044519424,
-0.06314967572689056,
-0.04305320605635643,
-0.017435377463698387,
-0.024294214323163033,
-0.02147803269326687,
-0.00143600651063025,
0.05004337802529335,
0.013976408168673515,
-0.03567085415124893,
0.003775175893679261,
0.037981390953063965,
0.008823144249618053,
0.012185133993625641,
-0.05921570211648941,
-0.018950138241052628,
0.06530054658651352,
-0.053243488073349,
-0.025260569527745247,
-0.010225150734186172,
0.005653965286910534,
-0.004868367221206427,
0.005234470125287771,
0.01220941822975874,
-0.04865242540836334,
-0.052541766315698624,
0.06749050319194794,
0.051718492060899734,
0.020703481510281563,
-0.011273033916950226,
0.02834295481443405,
0.0013515891041606665,
0.017271604388952255,
-0.03580702468752861,
0.02563503012061119,
0.054339706897735596,
0.01605360582470894,
0.01414940133690834,
-0.0693238228559494,
0.05151035264134407,
-0.010028935968875885,
0.029714297503232956,
0.03616710379719734,
0.035411424934864044,
0.011606236919760704,
-0.009704952128231525,
0.031844694167375565,
0.008720084093511105,
-0.03651677444577217,
0.02011771872639656,
-0.07365713268518448,
0.05643552541732788,
0.027869662269949913,
-0.004866246599704027,
-0.010432641953229904,
0.04506603628396988,
-0.037274908274412155,
0.03607897460460663,
-0.008614878170192242,
0.006104547996073961,
0.010360666550695896,
-0.03055548295378685,
-0.03530734032392502,
-0.03922227770090103,
-0.026379231363534927,
0.03785882517695427,
0.054492924362421036,
0.06134966388344765,
0.05351192131638527,
0.04366094619035721,
0.022517813369631767,
-0.0270397886633873,
-0.05121922865509987,
-0.05703059211373329,
-0.02819148078560829,
0.03636721894145012,
0.0002692095877137035,
-0.02652778849005699,
0.015141455456614494,
0.13049712777137756,
-0.042842622846364975,
-0.003962404560297728,
-0.008036105893552303,
0.013902702368795872,
-0.07108628749847412,
-0.037619564682245255,
0.03927825391292572,
0.01689760759472847,
-0.01633920893073082,
-0.011676649563014507,
-0.06307478249073029,
0.0005688591045327485,
0.0462450310587883,
-0.09709357470273972,
-0.033413346856832504,
0.021990865468978882,
-0.06543372571468353,
0.01607208326458931,
0.048933159559965134,
0.021442390978336334,
-0.010429348796606064,
0.036430295556783676,
-0.014214731752872467,
-0.0338839516043663,
0.026029491797089577,
0.050172559916973114,
0.029484352096915245,
-0.015155382454395294,
-0.03687727823853493,
0.04056016728281975,
-0.008148941211402416,
-0.012187092565000057,
-0.0323110930621624,
0.04002565145492554,
-0.009917262010276318,
-0.0023840824142098427,
0.022268258035182953,
-0.01963205635547638,
-0.006156628020107746,
0.012781082652509212,
0.023579636588692665,
-0.007807204965502024,
0.039787959307432175,
0.003571451874449849,
-0.036108214408159256,
-0.004401564598083496,
-0.027637062594294548,
-0.0486142598092556,
0.008964036591351032,
0.02006465569138527,
-0.01462758518755436,
-0.030371271073818207,
-0.005820124875754118,
-0.02860054187476635,
-0.03702973201870918,
0.0489472895860672,
0.05233052745461464,
0.004106640350073576,
-0.02941732108592987,
-0.07527107745409012,
0.01168160792440176,
0.024122662842273712,
-0.03581877425312996,
-0.0051567209884524345,
-0.0025776145048439503,
-0.01627236232161522,
0.03450372442603111,
-0.024536335840821266,
-0.030816271901130676,
0.038231927901506424,
0.038045454770326614,
-0.055692534893751144,
-0.022555967792868614,
-0.03448983281850815,
0.044724367558956146,
-0.010599256493151188,
0.036103688180446625,
-0.03761369735002518,
-0.049567267298698425,
0.08224537968635559,
0.0392775796353817,
-0.03202097490429878,
-0.006221762392669916,
-0.05341910198330879,
-0.04180928319692612,
-0.018014339730143547,
-0.04558997601270676,
-0.04448806494474411,
0.01370889600366354,
-0.050087716430425644
] |
<p><img src="http://i.stack.imgur.com/jHugn.png" alt="enter image description here"></p>
<p>The electric field in a wire is parallel to the wire's surface (it is always pointing "to the front"). If the electric field did not point in this direction, surface charges would build up and change the electric field to make it point the correct way.</p>
<p>In the above diagram the electric field vectors are pointing the wrong direction, but there will be no charge build up, since the current flowing into the junction is same as the current flowing out. So in this scenario how would the surface charges rearrange to make the electric field point in the correct direction?</p> | g9252 | [
0.05193200707435608,
-0.02263517491519451,
-0.011370204389095306,
0.012507778592407703,
0.07830751687288284,
0.04381208494305611,
0.04421368986368179,
0.01583387330174446,
-0.0532827228307724,
-0.015256288461387157,
-0.03423560783267021,
0.0418107695877552,
-0.009596272371709347,
0.004059655591845512,
0.016358496621251106,
0.02985222265124321,
0.032657328993082047,
0.0030020959675312042,
0.01934351958334446,
0.029775848612189293,
0.04109310731291771,
-0.027299020439386368,
0.026141436770558357,
-0.005930633749812841,
-0.04163644462823868,
-0.067801833152771,
0.003957739565521479,
0.013292485848069191,
0.006482251919806004,
-0.0773824155330658,
0.004069724585860968,
0.05452859029173851,
-0.013445882126688957,
-0.005275486968457699,
-0.0630531907081604,
-0.049071453511714935,
-0.010556298308074474,
0.027295062318444252,
-0.0000020821462385356426,
0.0008449307060800493,
0.02886449359357357,
-0.04194001853466034,
0.04549672082066536,
-0.02364201471209526,
0.011071482673287392,
-0.03112821839749813,
-0.003042449476197362,
0.021468814462423325,
0.014614139683544636,
-0.02040722593665123,
-0.024434395134449005,
0.005120600573718548,
-0.00186984206084162,
-0.0030565622728317976,
0.018250152468681335,
0.03689076006412506,
0.0055001527070999146,
-0.02246786653995514,
0.04557153582572937,
0.05030856281518936,
-0.01804235577583313,
0.011061669327318668,
-0.0013793943217024207,
-0.0097886947914958,
-0.031049462035298347,
-0.024450358003377914,
-0.05517822131514549,
0.010541954077780247,
-0.038380708545446396,
0.026880599558353424,
0.010183746926486492,
-0.030642973259091377,
-0.012925849296152592,
-0.01694691926240921,
-0.06228393688797951,
-0.016051527112722397,
-0.009298483841121197,
-0.047936033457517624,
0.013033230789005756,
-0.047291867434978485,
-0.02423284947872162,
-0.030172720551490784,
-0.019514331594109535,
0.019190501421689987,
0.0640764981508255,
-0.015818651765584946,
0.026879524812102318,
-0.021556880325078964,
-0.032046593725681305,
-0.04624330997467041,
-0.03600325807929039,
0.05045720934867859,
0.07220128923654556,
0.04201667755842209,
-0.0814346894621849,
-0.11791249364614487,
-0.03986819460988045,
0.029782917350530624,
-0.019674479961395264,
-0.020708978176116943,
-0.0791875571012497,
-0.020556151866912842,
0.02031472884118557,
0.05201068893074989,
-0.059167418628931046,
0.013766558840870857,
0.04729690030217171,
0.019024493172764778,
0.008449372835457325,
-0.03189608454704285,
-0.021918265148997307,
-0.08959370106458664,
-0.051982127130031586,
0.026789428666234016,
0.03548046573996544,
-0.008098124526441097,
0.07561731338500977,
-0.02554434910416603,
0.032686762511730194,
0.03602677211165428,
-0.013302118517458439,
-0.033191584050655365,
0.012874397449195385,
0.013566747307777405,
0.025532573461532593,
0.03046872466802597,
-0.027392279356718063,
-0.003418378531932831,
0.04200202599167824,
0.003950723446905613,
0.019554484635591507,
0.006718373391777277,
0.0191202312707901,
-0.001525280880741775,
0.0012867009500041604,
-0.021696867421269417,
0.011580786667764187,
-0.019907256588339806,
0.034464310854673386,
-0.020255880430340767,
0.09651312977075577,
-0.03589200600981712,
0.041731446981430054,
-0.04756541550159454,
0.01908700168132782,
-0.039709337055683136,
0.02968575805425644,
-0.03146527335047722,
0.06562300771474838,
0.005379640497267246,
0.018303565680980682,
0.04447613283991814,
-0.007722307927906513,
-0.03296655789017677,
0.005244155880063772,
-0.004752445966005325,
0.06405770033597946,
-0.013453913852572441,
0.08406230062246323,
-0.08989717066287994,
0.0598103366792202,
-0.05084144324064255,
0.007903947494924068,
-0.006529816891998053,
0.017561625689268112,
-0.04017975553870201,
0.0023266077041625977,
-0.016063986346125603,
0.0009184492519125342,
-0.046018652617931366,
-0.012857193127274513,
0.005284549668431282,
0.01547200232744217,
0.05575556680560112,
0.016323471441864967,
0.06976369768381119,
-0.008270235732197762,
0.037756990641355515,
0.03852219879627228,
0.018611036241054535,
-0.026897674426436424,
0.020399034023284912,
0.04744753986597061,
0.028028635308146477,
-0.012945382855832577,
-0.04509414732456207,
-0.0717415139079094,
0.030457312241196632,
-0.04280952736735344,
-0.014494013972580433,
-0.006716278847306967,
0.006453145761042833,
-0.07477264851331711,
0.053635336458683014,
-0.01370229572057724,
0.002660224912688136,
0.0033692175056785345,
-0.03706630691885948,
-0.013864281587302685,
-0.03568824380636215,
-0.026901787146925926,
0.009520932100713253,
-0.002855096710845828,
0.07811993360519409,
-0.03270937502384186,
-0.06170983612537384,
-0.017407862469553947,
-0.03541141003370285,
0.06554296612739563,
0.00036246146191842854,
0.006154262460768223,
0.048011742532253265,
-0.006290058139711618,
0.016108239069581032,
-0.0027388178277760744,
0.005198915954679251,
-0.0009075616835616529,
-0.03054683655500412,
-0.028164120391011238,
-0.03702876716852188,
-0.07469480484724045,
-0.03754676878452301,
0.022626366466283798,
0.012558799237012863,
-0.02322964183986187,
0.010250110179185867,
0.03544827923178673,
-0.03643827885389328,
-0.032168708741664886,
0.014793824404478073,
0.005530265625566244,
-0.015282397158443928,
-0.014067649841308594,
-0.004458023235201836,
0.014122379012405872,
0.051022518426179886,
-0.04967094212770462,
0.05133362486958504,
-0.028755800798535347,
-0.04962553083896637,
-0.033313654363155365,
-0.049018021672964096,
0.04228072613477707,
-0.0012666427064687014,
0.03497542813420296,
-0.01572534255683422,
0.12324322760105133,
-0.010003033094108105,
-0.05951155722141266,
0.07429445534944534,
0.09993118792772293,
0.03275658190250397,
0.027975384145975113,
0.03351351618766785,
-0.009604239836335182,
-0.04848534241318703,
0.03638840466737747,
0.052032772451639175,
-0.016629958525300026,
-0.06899724155664444,
-0.02789992094039917,
-0.03252459689974785,
-0.016177140176296234,
0.020151132717728615,
-0.023971304297447205,
0.002094724914059043,
-0.04012656584382057,
-0.024991029873490334,
0.017734473571181297,
0.005602708552032709,
0.02291526272892952,
0.04156409204006195,
0.08649010956287384,
0.01581544242799282,
-0.002093757037073374,
-0.028815727680921555,
0.027001870796084404,
-0.0016364308539777994,
-0.005161820445209742,
0.028667805716395378,
0.004738000687211752,
0.07067429274320602,
-0.008392812684178352,
0.01720583811402321,
0.017189303413033485,
-0.020591815933585167,
0.019947383552789688,
-0.06036376953125,
-0.022482283413410187,
0.030613869428634644,
-0.07024739682674408,
-0.017369378358125687,
0.04029926657676697,
-0.04793843999505043,
0.04575267806649208,
-0.013629129156470299,
0.04955611005425453,
-0.06889761984348297,
-0.03450793772935867,
0.048766814172267914,
-0.03900402784347534,
0.009826035238802433,
-0.04542361944913864,
-0.035813815891742706,
0.05666472390294075,
0.061518169939517975,
-0.011795633472502232,
-0.053419142961502075,
0.04010840505361557,
-0.01785755529999733,
0.03153642266988754,
0.021266896277666092,
0.01712639257311821,
-0.047218021005392075,
0.004814105108380318,
-0.028780497610569,
-0.025011427700519562,
0.02600831165909767,
0.06403964757919312,
0.043977491557598114,
-0.06393427401781082,
0.010520268231630325,
0.004630101379007101,
0.01796751096844673,
0.056363657116889954,
0.07837546616792679,
0.015604979358613491,
0.058660976588726044,
-0.034124381840229034,
0.01129508763551712,
-0.012202324345707893,
0.0574798546731472,
0.01074964925646782,
-0.027437089011073112,
0.03130412474274635,
0.025328153744339943,
0.04022210091352463,
0.07405729591846466,
-0.000506065203808248,
0.039540212601423264,
0.025153428316116333,
-0.01567358896136284,
-0.02781534381210804,
-0.08403204381465912,
-0.016259239986538887,
0.02263585478067398,
0.03741756081581116,
0.006076544523239136,
-0.006727576721459627,
-0.02261042222380638,
0.06230476498603821,
-0.003277849406003952,
-0.009547203779220581,
0.04329545050859451,
0.010491592809557915,
-0.003903117263689637,
-0.0399923250079155,
0.028239598497748375,
-0.036202285438776016,
0.017773229628801346,
-0.0350952111184597,
-0.06154824048280716,
0.007314396556466818,
-0.013532300479710102,
-0.028074467554688454,
0.03482995554804802,
-0.013768552802503109,
0.043310102075338364,
-0.007066410034894943,
-0.0911678746342659,
0.009868061169981956,
-0.010510618798434734,
-0.01704743318259716,
0.020935621112585068,
-0.0724935233592987,
-0.018657444044947624,
0.05215577036142349,
0.03594717010855675,
-0.0023611236829310656,
0.007943917065858841,
-0.026763685047626495,
-0.006634891964495182,
-0.05850734934210777,
-0.01859235391020775,
0.009979422204196453,
0.06308118253946304,
0.0005437618237920105,
-0.015253782272338867,
0.040512219071388245,
0.04089541733264923,
0.015068387612700462,
0.027154991403222084,
0.023877117782831192,
-0.038234103471040726,
0.013822425156831741,
-0.005422812886536121,
-0.012715999968349934,
0.012988698668777943,
-0.03749050572514534,
-0.009118538349866867,
0.07190695405006409,
0.021060235798358917,
-0.061923470348119736,
0.0028974672313779593,
-0.001055311062373221,
-0.026239050552248955,
0.013096926733851433,
-0.027552124112844467,
0.006331000477075577,
0.020685050636529922,
0.0012812959030270576,
-0.017181426286697388,
0.04317356273531914,
-0.07240135222673416,
0.031102461740374565,
0.02077599987387657,
0.029781509190797806,
0.03509404882788658,
0.010345542803406715,
-0.014588853344321251,
0.013489589095115662,
0.0036583878099918365,
0.12191935628652573,
-0.01826675422489643,
0.016728805378079414,
0.03136932849884033,
0.05812441185116768,
-0.05724240839481354,
0.011370642110705376,
-0.018622322008013725,
-0.04069138690829277,
0.08110278099775314,
-0.04169931262731552,
-0.032163724303245544,
-0.0824049785733223,
0.015577991493046284,
-0.0053076548501849174,
0.03790069371461868,
0.005182298831641674,
0.051314279437065125,
0.04026325047016144,
0.03144194185733795,
-0.011310161091387272,
-0.024389805272221565,
-0.03680523857474327,
0.024786019697785378,
-0.07835939526557922,
-0.006819696165621281,
-0.0033439313992857933,
-0.0750155970454216,
-0.05050123110413551,
0.04180433228611946,
-0.006992905866354704,
-0.0026047895662486553,
-0.007005126215517521,
-0.06118481978774071,
-0.05339052155613899,
0.018364056944847107,
-0.0032811560668051243,
0.02091563679277897,
-0.019043168053030968,
-0.04009641334414482,
-0.01394522376358509,
-0.017267439514398575,
0.03735170513391495,
0.0025380002334713936,
0.02721279487013817,
-0.0801331102848053,
-0.03706303611397743,
-0.01812984049320221,
-0.0019099637866020203,
0.044729121029376984,
-0.01360191311687231,
0.06277001649141312,
0.01413056906312704,
0.0045264544896781445,
0.035349953919649124,
-0.023908430710434914,
-0.07558778673410416,
-0.024431057274341583,
-0.07186803221702576,
-0.027747370302677155,
0.03884662315249443,
0.02575916238129139,
-0.03478328883647919,
0.007308006286621094,
-0.008698681369423866,
0.0020699219312518835,
0.01916835457086563,
-0.0028712309431284666,
0.01536827813833952,
0.018352694809436798,
0.015065906569361687,
0.007626403588801622,
0.0031568827107548714,
-0.008238676004111767,
-0.006584673188626766,
0.05961364880204201,
-0.007213191129267216,
-0.0014488842571154237,
-0.012385962530970573,
-0.005712150130420923,
-0.03900749608874321,
-0.013027063570916653,
-0.024866586551070213,
0.025509526953101158,
-0.010222653858363628,
-0.01763063855469227,
-0.0039740330539643764,
-0.025527380406856537,
-0.027485378086566925,
-0.009435108862817287,
0.04524786397814751,
-0.041882216930389404,
0.05180220678448677,
-0.0192965567111969,
-0.06725339591503143,
0.00039068571641109884,
-0.009641746990382671,
-0.006650528404861689,
0.05485657602548599,
-0.03297426179051399,
-0.041677720844745636,
-0.08324785530567169,
-0.012581420131027699,
0.012795697897672653,
-0.09848301857709885,
0.0009880452416837215,
0.05108393728733063,
-0.008616434410214424,
-0.02193262428045273,
0.05259381979703903,
0.004737790673971176,
0.02030336670577526,
0.025629356503486633,
-0.030872756615281105,
0.05491127446293831,
0.003660746617242694,
0.013721290044486523,
0.02117014117538929,
0.01364368386566639,
-0.013324262574315071,
-0.005108918994665146,
0.020566992461681366,
-0.024949226528406143,
-0.027571862563490868,
-0.06398672610521317,
0.01187780499458313,
0.0022099269554018974,
-0.04497559368610382,
-0.003533522831276059,
0.05786432325839996,
-0.04128168150782585,
0.01732996106147766,
-0.00009603601938579232,
-0.03962511569261551,
0.029067106544971466,
-0.020601442083716393,
-0.0471932627260685,
-0.050055187195539474,
0.058137331157922745,
0.017855899408459663,
0.011167344637215137,
0.0326710045337677,
0.01792660728096962,
0.017022166401147842,
-0.024092454463243484,
0.02157454751431942,
0.051542021334171295,
0.01685486175119877,
-0.014396129176020622,
-0.04512149468064308,
-0.017664052546024323,
0.0021535803098231554,
-0.0015194426523521543,
0.01361064612865448,
-0.059936054050922394,
0.034139588475227356,
-0.04592307284474373,
0.020260967314243317,
-0.004125890322029591,
0.06947213411331177,
0.016229283064603806,
-0.061732564121484756,
0.00850172434002161,
0.022050723433494568,
-0.04009995982050896,
-0.034096911549568176,
0.0467095673084259,
-0.007824798114597797,
-0.02252276800572872,
0.02904246747493744,
0.0469135120511055,
0.011463696137070656,
-0.04289720207452774,
-0.001919890521094203,
-0.028292838484048843,
0.09892772883176804,
-0.013304661959409714,
0.055220089852809906,
-0.026380348950624466,
0.01295756921172142,
-0.004133095033466816,
0.021243354305624962,
0.05114787817001343,
0.052051205188035965,
0.040949899703264236,
0.0690593346953392,
0.029772870242595673,
-0.005346916150301695,
0.008765565231442451,
-0.04206046834588051,
-0.041724130511283875,
-0.02663937769830227,
0.04589870944619179,
0.07434874027967453,
-0.03751339390873909,
-0.0011118800612166524,
-0.02822769805788994,
0.03751550242304802,
0.03343325853347778,
0.009877941571176052,
-0.028090568259358406,
0.02633698843419552,
0.022084852680563927,
-0.032619405537843704,
-0.04677513614296913,
-0.023193249478936195,
0.030519118532538414,
0.0021763022523373365,
-0.006785695441067219,
-0.002572435885667801,
-0.037721309810876846,
0.04081796482205391,
0.04699031263589859,
-0.008063182234764099,
0.0153102558106184,
-0.015304911881685257,
0.004501241724938154,
0.03259962797164917,
-0.02951752208173275,
0.05520403012633324,
-0.0361705906689167,
0.02679615467786789,
0.01368043664842844,
-0.040887996554374695,
-0.04699855297803879,
0.01414333377033472,
-0.013548529706895351,
0.02372250147163868,
0.027922648936510086,
-0.021244589239358902,
-0.0381229892373085,
0.023257778957486153,
-0.009882990270853043,
0.022950123995542526,
0.011542366817593575,
0.013489912264049053,
0.030303582549095154,
0.023109037429094315,
-0.04937079921364784,
-0.009034084156155586,
-0.000998734962195158,
-0.01045032124966383,
0.04928962141275406,
0.001125544891692698,
-0.004136867355555296,
0.009133650921285152,
-0.010157392360270023,
0.013512752950191498,
-0.0216277576982975,
-0.05632432550191879,
0.03883722797036171,
-0.010263990610837936,
-0.00791771151125431,
-0.011544119566679,
0.07362468540668488,
0.03846265748143196,
-0.036914292722940445,
0.006547942291945219,
0.011982827447354794,
0.05208931490778923,
-0.01903190277516842,
-0.02816273644566536,
-0.011663760989904404,
-0.03448772430419922,
-0.010809299536049366,
0.09264425933361053,
-0.04983534663915634,
-0.015287397429347038,
0.01961836963891983,
0.041793037205934525,
-0.07496561855077744,
0.00211475882679224,
-0.010371255688369274,
0.10315617173910141,
0.0019301699940115213,
0.010755536146461964,
0.04465074464678764,
-0.009442894719541073,
0.023019874468445778,
-0.0015666885301470757,
0.018895646557211876,
-0.0019739284180104733,
-0.010354569181799889,
-0.013387867249548435,
-0.044929612427949905,
0.013890807516872883,
-0.002419800031930208,
-0.005635080859065056,
-0.01465331856161356,
0.033253997564315796,
0.03217924013733864,
0.014494831673800945,
0.032207831740379333,
0.009340333752334118,
-0.027580121532082558,
0.0008377667400054634,
0.0014104620786383748,
0.010670725256204605,
-0.05448435992002487,
0.027308855205774307,
-0.002028146293014288,
0.024843184277415276,
0.000501176982652396,
-0.009084371849894524,
-0.0008810376166366041,
0.0465618334710598,
-0.0019870279356837273,
-0.041562873870134354,
-0.0026480986271053553,
-0.00025210549938492477,
-0.0010771694360300899,
0.044048044830560684,
-0.00308937462978065,
-0.02717537432909012,
0.0010236904490739107,
-0.051200609654188156,
0.036358971148729324,
-0.055568765848875046,
-0.0014045964926481247,
-0.046860214322805405,
0.010144286789000034,
-0.06337453424930573,
-0.009025241248309612,
-0.01862877979874611,
-0.019546419382095337,
0.06592602282762527,
0.03633539751172066,
0.0044537503272295,
0.03435281291604042,
-0.04874342307448387,
-0.038222406059503555,
-0.03144712373614311,
0.009559476748108864,
0.020789867267012596,
-0.0032188002951443195,
-0.01682870276272297,
0.0016924355877563357,
-0.016691118478775024,
-0.05008680373430252,
-0.026639970019459724,
-0.01639123260974884,
-0.010737106204032898,
-0.02434593066573143,
-0.06581424176692963,
-0.08901036530733109,
-0.012091124430298805
] |
<p>A black hole engulfs the matter nearby, how does it store the mass inside? We know that matter is composed of particles, does a black hole store the mass in massive particles? Or can we assume that it's composed of extremal black holes? what are theories about it?</p>
<p>EDIT:
I checked out <a href="http://physics.stackexchange.com/questions/35150/black-holes-are-in-which-state-of-matter">Black-holes are in which state of matter?</a>
it doesn't provide a definite answer.</p> | g9253 | [
0.02228531613945961,
-0.025288142263889313,
0.011851616203784943,
-0.018232641741633415,
0.03970048576593399,
0.03310326114296913,
-0.010699203237891197,
0.04466623812913895,
0.009518898092210293,
-0.004417838528752327,
0.023381320759654045,
-0.0064065768383443356,
0.034292712807655334,
-0.015463817864656448,
-0.04212535545229912,
0.005602779798209667,
0.030200909823179245,
0.01956963539123535,
-0.01129592303186655,
0.004898461978882551,
-0.010612852871418,
-0.04839341342449188,
0.036929644644260406,
0.016603438183665276,
-0.006144253071397543,
0.044798288494348526,
0.024746211245656013,
-0.008489048108458519,
0.02460790053009987,
0.01911799982190132,
0.010183222591876984,
-0.058210328221321106,
-0.013176161795854568,
0.0012088727671653032,
0.041604530066251755,
-0.04021666944026947,
-0.03479193523526192,
-0.04525115340948105,
-0.015565500594675541,
-0.01283420529216528,
0.05411383509635925,
-0.062309347093105316,
-0.015989840030670166,
-0.024385575205087662,
-0.036573950201272964,
0.016418103128671646,
0.00983462668955326,
-0.015868263319134712,
0.006197446957230568,
-0.016287202015519142,
-0.011155324056744576,
0.013707579113543034,
0.05758582055568695,
0.046675220131874084,
0.030321920290589333,
-0.0037519976031035185,
0.053746193647384644,
0.022500136867165565,
0.05109826475381851,
-0.00525509612634778,
-0.0024799108505249023,
0.0032081580720841885,
0.009448125027120113,
0.010151203721761703,
0.023115120828151703,
-0.03561302646994591,
-0.0876145139336586,
0.03942861035466194,
0.005959019064903259,
0.02361414022743702,
0.03208446875214577,
0.011965136043727398,
0.02713840641081333,
-0.08714502304792404,
-0.03236466273665428,
0.038688089698553085,
0.006643741857260466,
0.06284400820732117,
0.03320826217532158,
0.029645923525094986,
-0.003012332133948803,
0.02785736508667469,
0.09711634367704391,
-0.03884098306298256,
0.04461652785539627,
0.0248777586966753,
-0.04194456338882446,
0.004672170616686344,
0.0042395745404064655,
0.041665975004434586,
0.019878234714269638,
-0.005979995708912611,
0.06387714296579361,
0.012902466580271721,
0.008419021032750607,
0.029385637491941452,
-0.007686140947043896,
0.03006312996149063,
-0.0442180335521698,
-0.0032719785813242197,
-0.013033551163971424,
-0.025835048407316208,
-0.00447234557941556,
-0.05102213844656944,
0.0576336570084095,
0.034570902585983276,
0.024294191971421242,
0.03331782668828964,
-0.02546943537890911,
0.06939487904310226,
0.007337228860706091,
-0.07679827511310577,
0.0050681233406066895,
-0.007158545311540365,
-0.09010086953639984,
0.061540283262729645,
0.04108467698097229,
0.04280370473861694,
0.01818772405385971,
0.04199983552098274,
0.014301891438663006,
0.07936277985572815,
-0.0015820114640519023,
-0.026507176458835602,
0.025528177618980408,
-0.0647854283452034,
-0.0028169541619718075,
-0.04577549174427986,
-0.05055607482790947,
0.04759320616722107,
0.012283003889024258,
-0.006031433120369911,
-0.0009213587618432939,
-0.01673726923763752,
-0.05616915598511696,
0.027276404201984406,
0.012478097341954708,
0.027368389070034027,
-0.05732055753469467,
-0.03816278278827667,
-0.016013002023100853,
0.021422604098916054,
0.01234324462711811,
0.041632030159235,
0.01093033142387867,
-0.007598501164466143,
-0.04641741141676903,
-0.04338979348540306,
-0.006246441975235939,
-0.011350356973707676,
0.04107823595404625,
0.04330475628376007,
-0.02640565298497677,
-0.029559170827269554,
0.01800145022571087,
0.019050369039177895,
0.05341217666864395,
0.03056194819509983,
0.0026315043214708567,
0.03693711757659912,
0.05618933215737343,
-0.04880430921912193,
-0.010730509646236897,
0.07341605424880981,
-0.02439676597714424,
-0.009110487066209316,
-0.004577610641717911,
-0.035985786467790604,
0.018950598314404488,
-0.016177671030163765,
-0.025909533724188805,
0.032137587666511536,
-0.009820520877838135,
0.10597836971282959,
0.00943391490727663,
-0.008985597640275955,
0.006842370145022869,
-0.02954239770770073,
0.025579774752259254,
-0.010679668746888638,
0.05544590950012207,
-0.02001609466969967,
-0.011779898777604103,
-0.016446223482489586,
-0.004212861880660057,
-0.03194603696465492,
0.03281431272625923,
0.05247974768280983,
0.029510241001844406,
0.03411399945616722,
-0.06440994143486023,
0.010427278466522694,
0.03686549887061119,
0.0768013596534729,
0.03649546951055527,
-0.001961503643542528,
0.025574568659067154,
-0.05709408223628998,
0.027056220918893814,
0.012683608569204807,
0.0039267814718186855,
-0.01171711552888155,
-0.012044372968375683,
0.014566432684659958,
0.038436997681856155,
0.055841151624917984,
-0.011953490786254406,
0.0008443623664788902,
0.02289743162691593,
-0.0001491874863859266,
0.021292109042406082,
-0.032754138112068176,
0.014047807082533836,
-0.002357081277295947,
-0.013185452669858932,
0.06819896399974823,
-0.055584318935871124,
0.015108277089893818,
0.02086877077817917,
-0.02470693551003933,
-0.02587987296283245,
-0.06552837789058685,
0.002905437024310231,
-0.06213061511516571,
0.002135042566806078,
0.027835862711071968,
-0.0819883868098259,
-0.010801206342875957,
0.02173355408012867,
0.033318061381578445,
-0.05213376507163048,
0.04234783723950386,
0.02237641252577305,
0.012187913991510868,
0.03872042894363403,
0.04348260164260864,
0.0036568145733326674,
-0.02085776999592781,
-0.0142957903444767,
0.0071618156507611275,
0.03512527421116829,
0.014061602763831615,
-0.009440467692911625,
-0.007756885606795549,
0.004947518464177847,
-0.04739672690629959,
0.017917465418577194,
-0.03375818952918053,
0.019420146942138672,
0.05699758604168892,
0.00665236497297883,
-0.016185490414500237,
0.036890141665935516,
-0.027948647737503052,
0.035718679428100586,
-0.02772735059261322,
0.028338465839624405,
0.035628609359264374,
-0.040258608758449554,
-0.036431580781936646,
0.0334479957818985,
-0.01974092796444893,
-0.02088969200849533,
0.014665506780147552,
-0.057096682488918304,
-0.030618788674473763,
-0.061310045421123505,
0.009410507045686245,
0.014848710037767887,
0.06425104290246964,
0.008846806362271309,
0.00031533086439594626,
0.022100485861301422,
-0.03245119750499725,
0.020486904308199883,
0.006398641970008612,
-0.060463111847639084,
-0.024887463077902794,
0.09100356698036194,
-0.013573972508311272,
-0.03878818079829216,
0.03306342661380768,
-0.060361944139003754,
0.013142213225364685,
0.012768608517944813,
-0.05446392670273781,
-0.056640975177288055,
0.020657790824770927,
-0.0008120809798128903,
-0.07089109718799591,
0.016072308644652367,
-0.025133559480309486,
0.025255339220166206,
0.008683349005877972,
0.027131550014019012,
0.08062592893838882,
0.0006295116036199033,
-0.01747327670454979,
-0.03207802772521973,
-0.004550341982394457,
-0.01928480714559555,
-0.007981820032000542,
0.034695301204919815,
-0.034042488783597946,
-0.0016051807906478643,
0.0934918224811554,
0.01852210983633995,
-0.016616782173514366,
0.0001226116728503257,
-0.06647784262895584,
0.0004824977950192988,
-0.011132465675473213,
0.0010901789646595716,
0.051061924546957016,
-0.010224349796772003,
0.006639402359724045,
-0.00969509594142437,
0.0510239340364933,
-0.005087845493108034,
-0.052438631653785706,
-0.02040627971291542,
0.058675799518823624,
0.031438980251550674,
-0.04546096920967102,
0.01532925758510828,
-0.0007969935541041195,
-0.01096623670309782,
-0.054673586040735245,
-0.0533180795609951,
-0.008984280750155449,
0.012612497434020042,
-0.035355210304260254,
-0.07274846732616425,
0.013761771842837334,
-0.00022530255955643952,
-0.01870342716574669,
-0.01221256423741579,
-0.030638515949249268,
0.08000043034553528,
-0.0653187558054924,
0.0779728963971138,
-0.057015009224414825,
0.011662001721560955,
0.012190849520266056,
-0.02763340063393116,
0.011514938436448574,
0.0021465830504894257,
-0.0631621927022934,
0.02708551287651062,
-0.004189825151115656,
-0.023941105231642723,
-0.007301374804228544,
0.014209127984941006,
-0.03157244622707367,
-0.011905990540981293,
-0.00945291481912136,
0.0002972120710182935,
0.010892033576965332,
0.032395072281360626,
0.018452107906341553,
0.014634180814027786,
-0.05306699872016907,
0.040606580674648285,
-0.054568737745285034,
-0.02904415875673294,
-0.026367470622062683,
0.001211844035424292,
-0.10355141758918762,
0.005810345523059368,
0.026356471702456474,
-0.018909038975834846,
0.00964795146137476,
0.0024754758924245834,
0.05110994353890419,
0.03393840044736862,
-0.06931806355714798,
0.04391302168369293,
0.03606467321515083,
-0.018892435356974602,
-0.07717453688383102,
0.02104335092008114,
0.035161007195711136,
-0.002264917129650712,
-0.02196333184838295,
-0.014549294486641884,
0.0066931056790053844,
-0.006660475395619869,
0.0019072084687650204,
-0.019098520278930664,
-0.052333731204271317,
0.02163917012512684,
-0.06714531034231186,
-0.020158521831035614,
-0.07774796336889267,
0.0063523356802761555,
0.040102507919073105,
-0.03038640506565571,
-0.01615745574235916,
0.05959785357117653,
-0.0411263145506382,
0.06558476388454437,
0.0574609749019146,
0.0013803759356960654,
-0.020881278440356255,
0.041899025440216064,
0.014029274694621563,
-0.004452497698366642,
-0.051833946257829666,
-0.03104071505367756,
-0.05618899315595627,
0.04669786989688873,
0.02888353168964386,
-0.01906104013323784,
-0.004150422289967537,
0.004749282728880644,
-0.019161533564329147,
-0.0017367072869092226,
-0.012345980852842331,
0.010132557712495327,
0.02117796614766121,
0.021785637363791466,
-0.04392831400036812,
-0.025391198694705963,
0.028175655752420425,
0.010083494707942009,
-0.01977633312344551,
-0.014451536349952221,
0.07369732856750488,
-0.01979289948940277,
0.05642028898000717,
0.015807844698429108,
-0.04041521996259689,
-0.008164317347109318,
0.052831776440143585,
-0.05683160573244095,
0.0359499491751194,
-0.052340567111968994,
-0.015750639140605927,
0.01801677979528904,
0.006471424829214811,
0.030836455523967743,
-0.009594690054655075,
-0.055648323148489,
-0.014751012437045574,
0.0012373268837109208,
0.006202815566211939,
0.050385963171720505,
0.08212991058826447,
-0.023660317063331604,
-0.021274475380778313,
-0.057674940675497055,
-0.049506109207868576,
-0.061207015067338943,
-0.12163284420967102,
-0.013998732902109623,
0.0540519617497921,
-0.02819412387907505,
0.046786341816186905,
0.004195313435047865,
0.01928272284567356,
-0.09761245548725128,
-0.03588861599564552,
0.04211368411779404,
0.04904233291745186,
-0.020719872787594795,
-0.01469563227146864,
0.012780500575900078,
-0.05112401023507118,
0.011704291217029095,
0.026700790971517563,
-0.027703166007995605,
0.020625652745366096,
0.0347185879945755,
-0.0033826131839305162,
0.03555202856659889,
0.029899626970291138,
-0.04198332130908966,
-0.06416771560907364,
-0.02671940252184868,
-0.021081581711769104,
0.01796591468155384,
0.006177682429552078,
0.053221527487039566,
0.0015910001238808036,
0.017626497894525528,
0.024350054562091827,
-0.02147189900279045,
0.03868618980050087,
-0.061108965426683426,
-0.006740871351212263,
-0.0003543070051819086,
0.013715929351747036,
-0.019431332126259804,
0.03212246671319008,
0.001730447867885232,
-0.028141312301158905,
-0.008305731229484081,
-0.008954056538641453,
-0.00011935750808333978,
0.007601115852594376,
0.0279142614454031,
-0.01578475534915924,
0.008573481813073158,
0.02718530036509037,
0.012718664482235909,
0.06464748084545135,
-0.02414361760020256,
-0.020896466448903084,
0.010520250536501408,
-0.01699923165142536,
-0.00006466811464633793,
0.045822568237781525,
-0.042518697679042816,
0.0143455034121871,
0.04203835874795914,
-0.046079039573669434,
-0.006836684886366129,
0.04796978458762169,
0.025561261922121048,
0.00043250969611108303,
-0.053208496421575546,
-0.01741957664489746,
0.022558659315109253,
0.07795384526252747,
0.00028094390290789306,
-0.002023755107074976,
-0.02572091855108738,
-0.016600914299488068,
0.007541753351688385,
0.040643543004989624,
0.00487698195502162,
-0.0501563735306263,
-0.0021571547258645296,
-0.020802227780222893,
-0.006257176864892244,
-0.007256132550537586,
0.00727631151676178,
0.005605460610240698,
0.07871341705322266,
-0.005213683005422354,
-0.01725229062139988,
-0.06672101467847824,
-0.009338430128991604,
0.06380987167358398,
0.05925985053181648,
-0.004680108744651079,
-0.05554898828268051,
0.024131787940859795,
0.04353593662381172,
-0.01872006058692932,
-0.06776122003793716,
0.0398535393178463,
-0.012570836581289768,
0.009399604052305222,
0.037064436823129654,
0.02610737644135952,
-0.0033600074239075184,
-0.0303568784147501,
-0.06735546886920929,
-0.07104863971471786,
-0.03335541859269142,
0.03355295956134796,
-0.019553599879145622,
-0.009071551263332367,
0.006841203197836876,
-0.0179896242916584,
0.015995511785149574,
-0.04828163981437683,
0.06619108468294144,
-0.044981688261032104,
-0.0220627561211586,
0.006191975902765989,
0.034395840018987656,
0.013139407150447369,
0.003626215038821101,
-0.011612211354076862,
-0.03140539675951004,
0.052981555461883545,
0.062097083777189255,
-0.014913887716829777,
0.06748344004154205,
-0.06550316512584686,
0.10177074372768402,
-0.06614109873771667,
-0.0011993262451142073,
0.02230670489370823,
0.005548868328332901,
0.04599456861615181,
0.02727692201733589,
0.044039107859134674,
0.031232496723532677,
0.0298078041523695,
0.014101888984441757,
-0.03404555469751358,
-0.03881860896945,
0.01745496317744255,
0.0004088534915354103,
-0.01815415918827057,
-0.005937377922236919,
-0.07778006047010422,
0.005671468563377857,
0.028729703277349472,
0.010935048572719097,
-0.00977363158017397,
0.01293224934488535,
0.019226860255002975,
-0.04368014261126518,
-0.023446252569556236,
-0.029561607167124748,
0.011733131483197212,
0.00495288847014308,
0.0029249018989503384,
-0.04841373860836029,
-0.0038644259329885244,
-0.010681848973035812,
-0.020852167159318924,
-0.016933510079979897,
0.0010070776334032416,
-0.02137642726302147,
-0.025481384247541428,
-0.021560505032539368,
0.025420263409614563,
0.005692248698323965,
-0.012577632442116737,
0.009746775031089783,
0.07680340111255646,
-0.015340695157647133,
0.06368788331747055,
0.08797360211610794,
0.011987109668552876,
0.04104319587349892,
0.023535775020718575,
0.051228150725364685,
-0.03372715041041374,
0.004051053896546364,
0.026542697101831436,
0.002753611421212554,
-0.0012671785661950707,
-0.019517747685313225,
-0.017864754423499107,
-0.015984592959284782,
-0.07464263588190079,
-0.0012986473739147186,
0.08632394671440125,
-0.06665169447660446,
0.01943102292716503,
0.006047472357749939,
0.05502615496516228,
-0.015244174748659134,
-0.03497134521603584,
-0.0033072391524910927,
-0.03154290094971657,
-0.061418529599905014,
0.0004781638563144952,
-0.011409800499677658,
-0.016033533960580826,
-0.027595626190304756,
-0.028162499889731407,
0.0633045881986618,
-0.08308056741952896,
-0.07565496116876602,
-0.0028154654428362846,
-0.00594789395108819,
-0.008869264274835587,
0.009309754706919193,
0.02896643988788128,
0.061224546283483505,
-0.04745287075638771,
0.004279560875147581,
-0.05618129298090935,
-0.011755741201341152,
-0.052923981100320816,
-0.06239130720496178,
-0.042502015829086304,
-0.05922060087323189,
-0.07801485061645508,
0.004635279066860676,
0.05034191906452179,
0.016743911430239677,
0.05340711772441864,
0.0196430254727602,
0.03881163150072098,
0.02612367458641529,
0.051018957048654556,
0.0007643825956620276,
0.020214995369315147,
-0.02780262380838394,
0.07905137538909912,
-0.009763160720467567,
0.012032109312713146,
0.014946922659873962,
0.016921915113925934,
-0.014674670994281769,
-0.03225484862923622,
0.0053872535936534405,
0.022943958640098572,
0.02308695763349533,
0.0022097912151366472,
-0.01182729471474886,
-0.06797871738672256,
-0.035726167261600494,
-0.020366402342915535,
0.04221262410283089,
-0.07573168724775314,
0.054338160902261734,
-0.013943417929112911,
-0.02230255678296089,
0.01710931584239006,
-0.047059595584869385,
0.015915291383862495,
0.019553568214178085,
-0.017115620896220207,
0.01017443835735321,
-0.026772677898406982,
-0.0030401018448174,
-0.061248231679201126,
-0.005206479225307703,
-0.04991252347826958,
-0.03797551617026329,
-0.042041439563035965,
-0.028252393007278442,
0.06901684403419495,
0.011244640685617924,
-0.023075127974152565,
-0.023993702605366707,
-0.026012461632490158,
0.061568163335323334,
0.05592814087867737,
-0.053696971386671066,
-0.03444930538535118,
-0.061178673058748245,
0.02470458298921585,
-0.012356964871287346,
0.006249940022826195,
-0.02361709251999855,
-0.015612106770277023,
0.027155231684446335,
0.022998549044132233,
-0.014022059738636017,
-0.003476672573015094,
0.011239448562264442,
-0.048062294721603394,
-0.007140059024095535,
-0.034765806049108505,
-0.022123990580439568,
-0.020113319158554077,
0.005552628077566624,
0.02219466306269169,
0.06265952438116074,
0.001056510373018682,
0.06286663562059402,
-0.0024857069365680218,
0.010532118380069733,
0.010045057162642479,
-0.00860070250928402,
-0.06110772117972374,
-0.003917552065104246,
-0.008370193652808666,
-0.013927827589213848,
0.04453778639435768,
-0.02534668520092964,
0.01839972287416458,
0.016072971746325493,
-0.020105969160795212,
0.016703369095921516,
0.006127967964857817,
0.022296680137515068,
-0.029801201075315475
] |
<p>If the Alice sends to Bob an q-bit $\alpha\left|\mathbf{0}\right> + \beta\left|\mathbf{1}\right>$ in quantum key exchange (such as BB84) it is assumed that Eve cannot copy the state (due to no cloning theorem) and attempts to read the state requires guessing the base which would allow to detect interception.</p>
<p>However if the Eve put $\left|\mathbf{1}\right>$ through C-Not gate than the state would be:</p>
<p>$$\phi_0 = (\alpha\left|\mathbf{0}\right> + \beta\left|\mathbf{1}\right>)\otimes\left|\mathbf{1}\right>$$
$$\phi_1 = \alpha\left|\mathbf{00}\right> + \beta\left|\mathbf{11}\right>$$</p>
<p>Now Eve can store her q-bit somewhere and send the 'original' one to Bob. Since the base disclosure is on public channel she can measure her q-bit in correct base (the state would be collapsed but it shouldn't matter).</p>
<p>Why then quantum entanglement doesn't break quantum cryptography?</p>
<p><strong>Edit:</strong> To clarify what I understand (I haven't read the text about density matrices).</p>
<p>Alice sends to Bob two qubits - $\left|\mathbf{0}\right>$ and $\left|\mathbf{+}\right>$. Let's assume they are not discarded then in first case after Eve entangle it's qubit with sent qubit the state in case one:</p>
<p>$$\phi_{\left|\mathbf{0}\right>} = \left(\begin{array}{rrrr} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)\left(\begin{array}{r} 0 \\ 1 \\ 0 \\ 0\end{array}\right) = \left(\begin{array}{r} 1 \\ 0 \\ 0 \\ 0\end{array}\right) = \left|\mathbf{00}\right>$$</p>
<p>Now the only possible value read by Bob is $\mathbf{0}$ assuming he guessed base. Eve can then overhear the disclosure of bases and measure the reduced state on previously stored entangled qubit.</p>
<p>In second case:</p>
<p>$$\phi_{\left|\mathbf{+}\right>} = \left(\begin{array}{rrrr} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right)\frac{1}{\sqrt{2}}\left(\begin{array}{r} 0 \\ 1 \\ 0 \\ 1\end{array}\right) = \frac{1}{\sqrt{2}}\left(\begin{array}{r} 1 \\ 0 \\ 0 \\ 1\end{array}\right) = \left|\mathbf{++}\right>$$</p>
<p>Assuming that the Bob guessed the base correctly the Eve would also measured $\mathbf{+}$ in similar way as previously. If Bob didn't guessed it correctly Eve can discard particular qubit.</p>
<p>Now if quantum cryptography works:</p>
<ul>
<li>For some reasons the entanglement is forbidden (if yes - what is the difference between sending qubit and processing it inside quantum computer?)</li>
<li>Reduction of state by Bob does not happen in a way I think (possibly due to not knowing the density matrix).</li>
</ul> | g9254 | [
-0.009302069433033466,
0.02262747660279274,
0.0064400373958051205,
-0.059737928211688995,
0.025358691811561584,
0.03041967749595642,
0.055094920098781586,
-0.014781590551137924,
0.014564815908670425,
0.010495839640498161,
-0.030160194262862206,
0.06124049425125122,
-0.03456445038318634,
0.007573086302727461,
-0.014820625074207783,
0.0533423088490963,
0.1201784685254097,
-0.023018188774585724,
0.06779395788908005,
-0.00647900952026248,
-0.05458708852529526,
0.04809032380580902,
-0.0744038075208664,
-0.018811315298080444,
-0.022255394607782364,
-0.07879266887903214,
-0.01718701608479023,
0.005299723707139492,
-0.03275056555867195,
-0.007848300971090794,
0.017279664054512978,
-0.036191362887620926,
0.031750891357660294,
-0.10126467049121857,
-0.03470984473824501,
-0.013116217218339443,
0.0017919389065355062,
-0.04446083679795265,
-0.06282538920640945,
-0.0011232756078243256,
0.0007897800533100963,
-0.01600121147930622,
-0.020110057666897774,
-0.010758164338767529,
-0.028474049642682076,
0.006786630488932133,
0.05862972140312195,
-0.033991072326898575,
0.04649464786052704,
-0.05781855061650276,
-0.00011639270815066993,
0.005831127054989338,
0.061713915318250656,
0.019572477787733078,
0.07161835581064224,
0.09208150207996368,
0.015109052881598473,
0.0013567613204941154,
0.011806393973529339,
-0.06953422725200653,
0.002885775873437524,
-0.1024005115032196,
0.02830513007938862,
0.016024639829993248,
0.04740254580974579,
0.026467658579349518,
-0.06196334585547447,
0.039460599422454834,
-0.03496187552809715,
0.014296195469796658,
-0.027492711320519447,
-0.0687059834599495,
-0.04862629622220993,
-0.03479235619306564,
0.0711701363325119,
0.061161402612924576,
0.04906361177563667,
-0.038624122738838196,
0.022732378914952278,
0.0678909495472908,
-0.025350678712129593,
-0.015369169414043427,
0.037871576845645905,
0.022527121007442474,
0.06280618160963058,
0.046929411590099335,
-0.011777258478105068,
0.013010529801249504,
0.019009023904800415,
0.008513080887496471,
-0.0189363956451416,
-0.08317762613296509,
0.02781386859714985,
0.012724085710942745,
-0.015766233205795288,
-0.02900167554616928,
0.011896668933331966,
0.02087259665131569,
0.001714872196316719,
0.03647158294916153,
-0.00747518427670002,
-0.002514032181352377,
0.02578684687614441,
-0.023645665496587753,
-0.03503039851784706,
-0.007968079298734665,
0.02694409154355526,
-0.017540374770760536,
-0.04184545949101448,
0.05002348870038986,
-0.006794839631766081,
-0.044696468859910965,
-0.039857883006334305,
-0.015386907383799553,
-0.01351314876228571,
-0.014480853453278542,
0.05646394193172455,
-0.026781706139445305,
-0.03657553717494011,
-0.00030413197237066925,
-0.03320208936929703,
0.001164515153504908,
0.04539242759346962,
-0.029896732419729233,
-0.03960145264863968,
-0.0070623061619699,
-0.0033382675610482693,
0.03661492094397545,
0.04430072754621506,
-0.0177515409886837,
0.010454867035150528,
0.04964626953005791,
0.012034665793180466,
0.07972344011068344,
-0.003965623676776886,
-0.007618188392370939,
0.0059201354160904884,
0.044092413038015366,
0.038742512464523315,
-0.05788196995854378,
-0.04592665284872055,
0.0562121607363224,
0.018812354654073715,
-0.009525755420327187,
-0.009671639651060104,
-0.009832332842051983,
0.021622750908136368,
0.015844065696001053,
-0.00037367831100709736,
0.0428515262901783,
-0.0012863578740507364,
-0.0025373492389917374,
-0.04432729631662369,
0.031937528401613235,
-0.013821507804095745,
0.06814257800579071,
0.08112083375453949,
-0.032042089849710464,
-0.008303836919367313,
0.04092220589518547,
0.0671464055776596,
0.02008620835840702,
-0.03484582528471947,
-0.010485398583114147,
-0.016342297196388245,
0.027214564383029938,
-0.009085134603083134,
-0.049641773104667664,
0.018827376887202263,
-0.05447845906019211,
-0.04247819259762764,
0.025992294773459435,
-0.023423731327056885,
0.04850829020142555,
-0.019168851897120476,
0.08842664211988449,
-0.05077270418405533,
-0.012497362680733204,
0.07934601604938507,
0.03071342036128044,
-0.012632794678211212,
0.0029069308657199144,
0.01620856113731861,
0.01064098160713911,
-0.027830732986330986,
-0.011632639914751053,
0.015348372049629688,
-0.0001139064333983697,
-0.017366740852594376,
-0.03832041099667549,
-0.06357695162296295,
-0.046534232795238495,
-0.0036727236583828926,
0.013835784047842026,
0.01291339285671711,
0.006185587029904127,
0.008593278005719185,
-0.01690785028040409,
-0.026046816259622574,
0.062092896550893784,
0.00974931288510561,
0.03888711333274841,
-0.0035449170973151922,
-0.026574762538075447,
-0.00035710816155187786,
0.0060057551600039005,
-0.01031361985951662,
0.02627071924507618,
-0.0180249884724617,
-0.012746402062475681,
0.026208847761154175,
-0.014222417958080769,
-0.008753808215260506,
0.012945106253027916,
0.035990241914987564,
-0.010289746336638927,
0.056896086782217026,
0.04300317540764809,
-0.014542190358042717,
0.02443135529756546,
-0.009616074152290821,
-0.004149779211729765,
0.037783972918987274,
-0.05103963613510132,
-0.046345774084329605,
0.04073696210980415,
0.0014967827592045069,
-0.04728901386260986,
-0.03094259276986122,
0.033833619207143784,
-0.03836546838283539,
-0.03283781185746193,
-0.07249131798744202,
0.005760690197348595,
0.01398725900799036,
0.0489872470498085,
-0.015508994460105896,
0.02699289098381996,
-0.023454660549759865,
-0.006824044976383448,
0.037478458136320114,
0.02228381857275963,
-0.04708600789308548,
0.019293731078505516,
0.023702174425125122,
0.01779276505112648,
-0.03918466344475746,
-0.03584934026002884,
-0.008096653036773205,
0.0200670063495636,
-0.010606052353978157,
-0.02086843177676201,
-0.03364089876413345,
-0.010144401341676712,
0.0014447515131905675,
-0.026345517486333847,
0.02420720085501671,
-0.0033481826540082693,
-0.04528048262000084,
-0.05292010307312012,
-0.05491681769490242,
-0.023074138909578323,
-0.03973795473575592,
-0.003208794863894582,
0.0021634281147271395,
0.0020739303436130285,
-0.025433499366044998,
0.04380979388952255,
0.005553408060222864,
0.032968033105134964,
-0.05284329876303673,
0.0798153281211853,
-0.013588753528892994,
0.03041352704167366,
0.0183026734739542,
-0.01123187318444252,
-0.03982749953866005,
-0.010028568096458912,
0.00039663491770625114,
-0.015737945213913918,
-0.07720395922660828,
0.026056814938783646,
-0.0710989460349083,
0.0036540539003908634,
0.017995687201619148,
-0.023510241881012917,
-0.033225249499082565,
0.006210531573742628,
0.055343497544527054,
-0.00895956065505743,
-0.018629448488354683,
0.0070835864171385765,
0.033523544669151306,
-0.014288886450231075,
-0.004530942067503929,
0.023653583601117134,
-0.028176095336675644,
-0.007602836471050978,
0.029654262587428093,
0.036322545260190964,
-0.04139568656682968,
0.026768239215016365,
-0.01699063368141651,
0.022650087252259254,
0.04837504029273987,
0.014396741054952145,
-0.04756568744778633,
0.0683080181479454,
-0.0383894219994545,
0.012256421148777008,
-0.02308240532875061,
-0.015982937067747116,
-0.003370942547917366,
-0.06761422008275986,
-0.0007777512073516846,
-0.06308340281248093,
-0.00910631287842989,
0.013893697410821915,
0.05835718289017677,
-0.0113444272428751,
-0.02646169438958168,
0.005118876695632935,
-0.010473357513546944,
-0.0029842862859368324,
0.06045191362500191,
0.032976772636175156,
-0.08708629757165909,
0.09099989384412766,
-0.04218709468841553,
-0.06236523017287254,
0.03931998834013939,
0.02120257541537285,
0.06485063582658768,
0.01606157049536705,
-0.05982355773448944,
-0.08024029433727264,
-0.01253065001219511,
0.04778371378779411,
0.004808602388948202,
0.020094458013772964,
-0.006495174486190081,
-0.02620760351419449,
0.03202340379357338,
0.021859699860215187,
0.054591789841651917,
-0.015210616402328014,
0.0363151952624321,
0.012521407566964626,
0.012740734964609146,
0.03224018216133118,
0.015248404815793037,
0.02387908287346363,
-0.01187912467867136,
-0.015551668591797352,
-0.025210650637745857,
0.057586055248975754,
-0.05221916362643242,
0.037907421588897705,
0.04617885872721672,
-0.00556268822401762,
0.049934469163417816,
-0.034636490046978,
0.05410885810852051,
-0.02323400229215622,
0.017958182841539383,
0.030319303274154663,
0.015920192003250122,
0.002166144549846649,
-0.010966120287775993,
0.039240870624780655,
-0.024894176051020622,
-0.02825515903532505,
0.049391523003578186,
0.007902565412223339,
-0.0011567787732928991,
-0.0521702878177166,
0.02812543697655201,
-0.009819797240197659,
0.006858943961560726,
0.016261029988527298,
0.03831753134727478,
-0.008783465251326561,
0.014264254830777645,
-0.010491844266653061,
0.029401207342743874,
-0.01331847719848156,
-0.017928602173924446,
-0.014876505360007286,
-0.025606650859117508,
0.007124551106244326,
0.016202537342905998,
-0.0189274400472641,
-0.029241163283586502,
0.00471915677189827,
0.030887767672538757,
0.018257969990372658,
0.010492886416614056,
-0.021613717079162598,
-0.07586271315813065,
0.055149756371974945,
-0.07101553678512573,
-0.0029082477558404207,
-0.026746956631541252,
-0.04221896082162857,
0.008766913786530495,
-0.04251624271273613,
-0.00796154048293829,
0.008364569395780563,
0.005222941283136606,
-0.04133252799510956,
-0.007927368395030499,
-0.0012566274963319302,
-0.0662352442741394,
-0.026202848181128502,
-0.017128052189946175,
-0.011836397461593151,
0.04678351432085037,
0.030817797407507896,
-0.02742483653128147,
-0.010300955735147,
0.020485587418079376,
0.033725664019584656,
0.0360688716173172,
0.04320797696709633,
0.025754068046808243,
0.019557099789381027,
0.015046008862555027,
0.001122753252275288,
0.08708303421735764,
-0.03869129717350006,
0.0535920225083828,
0.017915887758135796,
0.004444529768079519,
-0.003992391284555197,
-0.04128676652908325,
-0.04084789752960205,
-0.08740340173244476,
0.027441857382655144,
0.005215188954025507,
-0.016452744603157043,
0.060301125049591064,
-0.019099948927760124,
-0.01689300127327442,
0.00856307428330183,
0.056240908801555634,
0.04478384181857109,
-0.01280249748378992,
0.005476261489093304,
-0.00858918484300375,
-0.03103732317686081,
0.010031650774180889,
0.004891689401119947,
0.03413897752761841,
-0.03425074741244316,
-0.017625512555241585,
0.017758406698703766,
-0.006750043015927076,
0.0031513916328549385,
0.01521451398730278,
0.10231810063123703,
-0.032749347388744354,
0.031023792922496796,
-0.019386710599064827,
0.03194564953446388,
-0.023955632001161575,
-0.017866335809230804,
-0.05366411432623863,
0.02407464012503624,
-0.008207877166569233,
0.004168644081801176,
-0.044077951461076736,
-0.01180803868919611,
0.05453725904226303,
0.040745317935943604,
-0.015447966754436493,
0.05977907404303551,
-0.024343974888324738,
-0.008054452948272228,
-0.010897542349994183,
-0.037279125303030014,
0.02411755546927452,
0.018881289288401604,
0.0038281104061752558,
0.034652046859264374,
-0.012164087034761906,
0.05563352257013321,
0.0047259870916605,
-0.05034762993454933,
-0.009940746240317822,
-0.03753814846277237,
0.07955140620470047,
0.015121118165552616,
0.040328022092580795,
0.006262489128857851,
-0.0061848401091992855,
-0.043680619448423386,
0.005950195714831352,
-0.006831958424299955,
-0.021067969501018524,
0.01726243831217289,
-0.015736596658825874,
0.017836570739746094,
0.0044028121046721935,
0.05886588990688324,
-0.02275780215859413,
0.01968003436923027,
0.03568301722407341,
0.05098056048154831,
-0.056612446904182434,
-0.02281760424375534,
-0.013698079623281956,
-0.017069250345230103,
-0.038990020751953125,
-0.06881475448608398,
0.0001743464672472328,
0.008550718426704407,
-0.08591792732477188,
-0.04989888146519661,
-0.011807030066847801,
-0.039452943950891495,
-0.01108899898827076,
0.048700980842113495,
0.026790175586938858,
0.00574538204818964,
0.015726104378700256,
-0.034097544848918915,
-0.03516183793544769,
-0.05983695760369301,
-0.0034506137017160654,
-0.005082498304545879,
0.0332169272005558,
0.03655488044023514,
0.005620554555207491,
0.007385656237602234,
0.03942595049738884,
-0.010700640268623829,
0.005348152946680784,
-0.004551905672997236,
0.03485105559229851,
0.037937045097351074,
0.03285745531320572,
-0.04786083102226257,
-0.007874911651015282,
0.056142862886190414,
-0.016004178673028946,
-0.05214569717645645,
-0.07593518495559692,
-0.023537153378129005,
-0.008828884921967983,
-0.03348836302757263,
-0.021295279264450073,
-0.0036016074009239674,
-0.08473662286996841,
0.025200022384524345,
0.034786514937877655,
-0.009032540954649448,
0.002538793720304966,
-0.006506843958050013,
0.0029795358423143625,
-0.002286505186930299,
-0.011195042170584202,
0.014686930924654007,
0.05559530109167099,
0.026741473004221916,
0.008711040019989014,
-0.03202169016003609,
-0.006112807895988226,
-0.0031360879074782133,
0.027711302042007446,
0.031145349144935608,
-0.014274702407419682,
-0.007805142551660538,
-0.043696388602256775,
-0.005928404629230499,
0.02456844225525856,
0.03802819550037384,
-0.08110759407281876,
-0.04619951918721199,
-0.007173669524490833,
-0.01484539546072483,
-0.012095754034817219,
0.03592229261994362,
0.012692015618085861,
0.0444299653172493,
0.028119657188653946,
0.04518992826342583,
-0.058028485625982285,
0.00809653103351593,
0.04602769389748573,
-0.04353618621826172,
-0.07922887802124023,
0.032743725925683975,
0.01147904247045517,
-0.04180014878511429,
-0.028577012941241264,
0.019570358097553253,
-0.0016608709702268243,
-0.04617564007639885,
-0.021897567436099052,
-0.03587505593895912,
-0.02424275316298008,
-0.029505128040909767,
0.04386700689792633,
-0.04803697392344475,
-0.010865394957363605,
0.03419988974928856,
-0.026307720690965652,
-0.026515204459428787,
0.02383768931031227,
0.017269287258386612,
-0.023775408044457436,
0.008374370634555817,
0.005396786145865917,
-0.009812049567699432,
0.024508638307452202,
-0.05803468078374863,
0.023893194273114204,
0.03114737942814827,
-0.05854042246937752,
0.02373245358467102,
0.02688603289425373,
0.015788692981004715,
-0.026065651327371597,
-0.027415210381150246,
0.020237896591424942,
0.08732067048549652,
-0.011761141940951347,
0.010226625949144363,
0.0838865414261818,
0.019459640607237816,
0.03592623025178909,
0.01309211179614067,
-0.004318838473409414,
-0.020383458584547043,
-0.02677510492503643,
0.013656828552484512,
-0.04809536039829254,
0.07098571956157684,
0.025834478437900543,
-0.018360447138547897,
0.04372559115290642,
0.054754920303821564,
-0.009222014807164669,
0.01851668395102024,
-0.08418626338243484,
0.05691724270582199,
-0.0051823146641254425,
0.03626903519034386,
-0.0781228169798851,
0.06321455538272858,
0.010580606758594513,
0.06175150349736214,
-0.06927899271249771,
-0.01692335307598114,
-0.015077590011060238,
-0.0061993845738470554,
0.07537749409675598,
0.0786762461066246,
0.0007186598959378898,
-0.057086031883955,
-0.03133682534098625,
-0.08925261348485947,
0.022726308554410934,
0.0013297486584633589,
0.07913146913051605,
-0.025831276550889015,
0.017663711681962013,
-0.040205031633377075,
-0.034810870885849,
-0.03448685258626938,
-0.018705731257796288,
-0.07533933967351913,
-0.023828843608498573,
-0.013158795423805714,
0.07743209600448608,
-0.028355039656162262,
0.07490482181310654,
0.0038825427182018757,
-0.07678341865539551,
-0.011481656692922115,
0.0050263116136193275,
0.03178912773728371,
-0.022257719188928604,
0.01744110882282257,
0.00027425281587056816,
0.04066090285778046,
-0.027180159464478493,
0.020721908658742905,
0.011267360299825668,
-0.003216144163161516,
-0.0014626323245465755,
0.006127332337200642,
0.02517053484916687,
0.039358217269182205,
-0.025445736944675446,
0.05991864949464798,
0.020398356020450592,
0.014607139863073826,
0.03444904834032059,
0.04236634820699692,
0.002548126270994544,
0.0020747510716319084,
0.03311929479241371,
0.004005809780210257,
0.026538832113146782,
-0.02713910862803459,
0.0012699824292212725,
0.03467385098338127,
-0.016346869990229607,
-0.017104847356677055,
0.0039789313450455666,
0.009868435561656952,
0.017041727900505066,
-0.006525934673845768,
0.0394287072122097,
-0.00158686691429466,
-0.006976348347961903,
0.05546598881483078,
0.05956496670842171,
-0.0019180414965376258,
0.0048731244169175625,
-0.015423987060785294,
-0.06349002569913864,
0.0027417736127972603,
0.00025838369037956,
-0.0031067924574017525,
0.01022697426378727,
0.022916670888662338,
-0.020676692947745323,
-0.03566981106996536,
-0.02702641859650612,
-0.004084999673068523,
-0.01745392009615898,
-0.026330439373850822,
0.0291808620095253,
-0.0007175566861405969,
-0.022705357521772385,
0.01597789116203785,
-0.032922327518463135,
0.01088165957480669,
-0.041707269847393036,
0.05744286999106407,
0.00008066987356869504,
-0.017666364088654518,
-0.012152576819062233,
-0.09177343547344208,
-0.09067127108573914,
-0.011433805339038372,
0.026960283517837524,
-0.06390444189310074,
0.005440859589725733,
-0.08690502494573593,
-0.04883859306573868,
0.041568268090486526,
0.005391453858464956,
0.001331062987446785,
-0.012473012320697308,
0.0001990213932003826,
0.028086373582482338,
-0.010463841259479523,
-0.026315776631236076,
0.0011454279301688075,
-0.04374435544013977,
0.0016672284109517932,
-0.056652411818504333,
-0.035164084285497665,
0.029259830713272095,
0.039849042892456055
] |
<p>I know there are theories (or postulates) that hold that our Universe could be a simulation. I was wondering, if Special Relativity states that two events which are not causally linked can be judged to have happened simultaneously or not, depending on the reference frame of the observer, can someone (or something) simulating the Universe reproduce this effect (if one observer says that two events were simultaneous, and the other disagrees, and they are both equally justified in their claims, what would the simulator conclude regarding their simultaneity)? </p> | g9255 | [
0.0617162361741066,
-0.009494000114500523,
0.030719682574272156,
0.0011878228979185224,
0.01102188415825367,
0.02466833032667637,
0.002533466089516878,
0.06403888761997223,
0.03709530830383301,
-0.062047045677900314,
0.030343344435095787,
-0.03107640892267227,
0.027814744040369987,
0.02191624790430069,
-0.05173041298985481,
-0.031323689967393875,
0.0319296158850193,
-0.03879217430949211,
-0.03936668485403061,
0.028423972427845,
0.025060124695301056,
-0.002909462433308363,
0.04704929515719414,
-0.027216246351599693,
-0.006795247085392475,
-0.0009283402469009161,
0.021525662392377853,
-0.055839765816926956,
-0.05146148055791855,
0.012523483484983444,
0.021401729434728622,
-0.004516066517680883,
0.007663337513804436,
-0.00863337516784668,
0.02893243357539177,
-0.03269950672984123,
-0.014928998425602913,
-0.02360503189265728,
-0.004833007697016001,
-0.028210027143359184,
-0.0009704613476060331,
0.02746809646487236,
0.010037346743047237,
-0.07875732332468033,
0.02370605058968067,
-0.008425429463386536,
0.044213198125362396,
0.0372779481112957,
0.04902731627225876,
-0.025580937042832375,
-0.016414102166891098,
0.050483208149671555,
0.033403199166059494,
0.021413199603557587,
0.03693700581789017,
0.012426086701452732,
0.017017370089888573,
0.05819743871688843,
0.05178606137633324,
0.014327342621982098,
-0.02232395112514496,
0.014316730201244354,
0.057550784200429916,
0.013738617300987244,
-0.0008584988536313176,
0.04181315749883652,
-0.03631821647286415,
-0.013644853606820107,
-0.0058443667367100716,
-0.04479967802762985,
0.03138573840260506,
0.002439803909510374,
-0.02887272834777832,
0.0021484496537595987,
-0.00812740158289671,
0.05872795730829239,
0.01886146143078804,
-0.0085818562656641,
-0.007628863211721182,
0.036273520439863205,
-0.03313910961151123,
-0.02376529946923256,
0.005465534050017595,
0.032244615256786346,
0.027591807767748833,
-0.0517544262111187,
-0.00661578681319952,
-0.020796388387680054,
-0.04737154766917229,
0.006823871284723282,
0.03500497341156006,
-0.015828942880034447,
0.06316868215799332,
0.040676869451999664,
-0.024751655757427216,
0.02767920307815075,
-0.08419293165206909,
0.04589083790779114,
0.05206378921866417,
0.012320672161877155,
-0.09696315228939056,
0.03659180551767349,
0.048051077872514725,
-0.05287686362862587,
0.0010494027519598603,
-0.030277976766228676,
-0.02224721759557724,
0.0611196905374527,
0.005268205888569355,
-0.06269051134586334,
-0.038195688277482986,
-0.08099214732646942,
-0.011518503539264202,
0.015471819788217545,
-0.03656512871384621,
-0.06664206087589264,
0.05024031177163124,
-0.031136969104409218,
-0.023341447114944458,
0.03810515254735947,
-0.033326998353004456,
0.03075389564037323,
-0.054521963000297546,
0.07128778100013733,
-0.05092940479516983,
0.01271227840334177,
-0.019145341590046883,
0.0708821639418602,
0.0013024506624788046,
-0.01056976430118084,
0.012527219951152802,
-0.022180018946528435,
0.018419530242681503,
0.06380540132522583,
-0.02959272265434265,
-0.019752057269215584,
0.0495903342962265,
-0.046245213598012924,
-0.0025656705256551504,
0.04132631793618202,
0.04034196957945824,
0.03346657752990723,
-0.05420510843396187,
-0.022833582013845444,
0.01935313642024994,
-0.004084868356585503,
-0.015503553673624992,
0.034857407212257385,
-0.05107312276959419,
0.02585485391318798,
0.0318649485707283,
0.06125674396753311,
-0.011054071597754955,
-0.029959456995129585,
0.012259816750884056,
0.01718945801258087,
-0.06127897650003433,
-0.010471420362591743,
-0.01277163065969944,
-0.02621721662580967,
0.08076208084821701,
-0.04595622792840004,
0.038293588906526566,
-0.009722842834889889,
-0.027171600610017776,
0.056402537971735,
-0.006397062446922064,
-0.06416260451078415,
-0.02427130937576294,
-0.06082024425268173,
-0.019271010532975197,
0.0014932024059817195,
-0.027147982269525528,
0.0391056090593338,
0.06491675227880478,
-0.004657544661313295,
-0.02161887101829052,
-0.015508397482335567,
-0.03763639181852341,
0.008097571320831776,
-0.047773901373147964,
0.014357183128595352,
-0.062113869935274124,
-0.0599541999399662,
0.04926237836480141,
-0.03724757954478264,
-0.006607874296605587,
-0.00303704384714365,
-0.013653052970767021,
-0.0028795688413083553,
-0.022205447778105736,
-0.032476432621479034,
0.017647597938776016,
-0.019445868209004402,
-0.024063626304268837,
-0.03257708624005318,
0.02596294693648815,
0.00024654666776768863,
0.032384905964136124,
0.03745396435260773,
-0.011886531487107277,
0.03811557963490486,
0.026480883359909058,
-0.011815465055406094,
0.00897361058741808,
-0.01201830804347992,
0.0012985168723389506,
-0.006674582604318857,
-0.012901069596409798,
-0.04455559328198433,
0.017825577408075333,
-0.03166208788752556,
0.01004309207201004,
-0.035685084760189056,
-0.029210010543465614,
0.01896732486784458,
0.005081457085907459,
0.02474147267639637,
-0.028641778975725174,
0.021238332614302635,
-0.004554171115159988,
-0.004163325298577547,
0.0167749784886837,
-0.010994290933012962,
-0.027136096730828285,
-0.0074149081483483315,
-0.03408968076109886,
0.005124520510435104,
0.02175682969391346,
0.02474350482225418,
-0.015308002941310406,
0.0007525446126237512,
0.026942342519760132,
-0.03345564380288124,
0.04636077582836151,
0.05691361427307129,
0.017200220376253128,
-0.0050430609844625,
-0.0007672893698327243,
-0.01625371165573597,
0.0010163473198190331,
0.007077359594404697,
-0.027816511690616608,
0.0008521438576281071,
0.06216377764940262,
-0.05808819830417633,
0.0978274792432785,
-0.015225231647491455,
0.061389341950416565,
-0.008121678605675697,
-0.026373254135251045,
-0.018698206171393394,
-0.04741782695055008,
0.00861895177513361,
0.01606636866927147,
-0.01927020587027073,
0.012030038982629776,
0.06487903743982315,
-0.04893406480550766,
-0.014061547815799713,
0.036714330315589905,
-0.07012727856636047,
0.05575614050030708,
0.02444585971534252,
0.005029184278100729,
-0.020243370905518532,
0.009055436588823795,
-0.010680705308914185,
-0.07440519332885742,
-0.01174879539757967,
-0.013413123786449432,
-0.0195861104875803,
-0.004678014665842056,
0.06376262754201889,
0.005527219269424677,
0.0431971438229084,
-0.0045232814736664295,
-0.016140954568982124,
0.03234821930527687,
-0.017790550366044044,
-0.020713509991765022,
0.04594926908612251,
-0.006378161255270243,
0.005742775741964579,
0.04697169363498688,
-0.04142065718770027,
-0.025320513173937798,
-0.06398401409387589,
0.011773628182709217,
0.04857859015464783,
-0.022267207503318787,
0.03782177343964577,
-0.013450396247208118,
0.0895974338054657,
-0.06656386703252792,
0.057044852524995804,
-0.037775710225105286,
-0.02015254832804203,
-0.014467265456914902,
0.03381853923201561,
0.009000095538794994,
0.00023770489497110248,
0.004254790022969246,
0.03258146718144417,
-0.012367594987154007,
-0.0048993732780218124,
-0.07314283400774002,
0.029982389882206917,
0.031637463718652725,
-0.06316941976547241,
-0.028580138459801674,
0.05492185428738594,
0.019270578399300575,
-0.013080690056085587,
-0.03729837015271187,
0.060001783072948456,
0.0058763897977769375,
0.006410766858607531,
-0.03580152988433838,
0.003952854312956333,
0.005380780436098576,
0.03154909610748291,
-0.0705176591873169,
0.02022400312125683,
0.013056937605142593,
0.046437475830316544,
-0.004568012431263924,
-0.04330221563577652,
-0.04972928762435913,
0.0026562174316495657,
-0.006794410292059183,
-0.04603284224867821,
-0.05935393646359444,
0.013351080007851124,
0.03000868298113346,
0.023736460134387016,
-0.02041643299162388,
-0.024370217695832253,
0.053268659859895706,
0.059195663779973984,
0.05595080554485321,
0.014432177878916264,
-0.009112263098359108,
0.015047525987029076,
-0.013779852539300919,
0.08931590616703033,
0.006865372881293297,
0.022105447947978973,
0.02473016269505024,
-0.014657549560070038,
0.07746154069900513,
0.01629032753407955,
0.004338772036135197,
-0.023784464225172997,
0.031068716198205948,
0.0340275876224041,
0.06236783042550087,
-0.013110981322824955,
-0.00553366681560874,
-0.025185592472553253,
0.014708188362419605,
-0.0031283486168831587,
-0.04029884934425354,
0.0008709786343388259,
0.03446630761027336,
0.034767188131809235,
0.003814903786405921,
0.009502645581960678,
0.013856248930096626,
0.03022249974310398,
0.004101572558283806,
0.04052671417593956,
-0.03598518669605255,
0.0008936665835790336,
0.04380439594388008,
-0.03768782317638397,
0.07388027757406235,
0.008182908408343792,
0.0099608413875103,
0.048779286444187164,
0.036495309323072433,
0.07607346028089523,
0.0365678034722805,
0.053391627967357635,
0.05537481978535652,
-0.025599978864192963,
0.03913617134094238,
-0.009355263784527779,
0.01050649769604206,
-0.07866287231445312,
0.04805706441402435,
-0.04044882580637932,
-0.05600593239068985,
-0.026940898969769478,
0.0653495341539383,
0.011753963306546211,
-0.00021734173060394824,
-0.05667014420032501,
0.04672061279416084,
0.0039398204535245895,
-0.006026203278452158,
-0.03207072988152504,
-0.007341204676777124,
-0.047485530376434326,
-0.056099794805049896,
0.014371450990438461,
0.0032712470274418592,
-0.04450177773833275,
-0.05963728949427605,
0.0034424203913658857,
0.03440461680293083,
0.05936649441719055,
0.00021854751685168594,
-0.044046614319086075,
0.015448587946593761,
0.020624011754989624,
-0.00850037019699812,
0.015452124178409576,
0.03116745315492153,
0.058392483741045,
0.02652171067893505,
0.06338095664978027,
0.041163112968206406,
0.008705485612154007,
0.028097424656152725,
0.0013705006567761302,
0.023987526074051857,
-0.014449921436607838,
-0.047878384590148926,
-0.011986251920461655,
0.011585330590605736,
0.016257328912615776,
0.030691439285874367,
0.04841567203402519,
-0.021192532032728195,
0.018894510343670845,
0.013593543320894241,
0.03322923928499222,
0.017189932987093925,
0.019651835784316063,
-0.014422104693949223,
-0.03262538090348244,
0.031259164214134216,
-0.018267158418893814,
-0.007412835024297237,
0.08268143236637115,
-0.05347944796085358,
-0.05092499777674675,
-0.05247779190540314,
-0.05877968296408653,
-0.07773035764694214,
0.027826452627778053,
-0.056951653212308884,
-0.014614231884479523,
-0.004522309172898531,
0.021132435649633408,
-0.009359813295304775,
0.041151516139507294,
-0.03629888966679573,
0.019472608342766762,
-0.020860113203525543,
0.00529442960396409,
0.06502193212509155,
0.01088418997824192,
-0.005858834367245436,
-0.027437826618552208,
-0.05833309888839722,
-0.028791697695851326,
-0.037302326411008835,
-0.006968718487769365,
-0.02679280750453472,
-0.06001875922083855,
0.008080272004008293,
-0.0020439247600734234,
0.006046645808964968,
-0.06893304735422134,
-0.04447408393025398,
-0.016391383484005928,
-0.007571734022349119,
0.00966443307697773,
-0.008430855348706245,
-0.015918372198939323,
0.006824797950685024,
-0.012031259946525097,
0.06189918518066406,
0.010494188405573368,
-0.008974502794444561,
0.005510821472853422,
0.022455234080553055,
-0.012329128570854664,
-0.000774659332819283,
-0.02083677239716053,
0.04118930175900459,
-0.026138167828321457,
-0.016961010172963142,
-0.021608484908938408,
0.009071605280041695,
0.001453258330002427,
-0.018590172752738,
0.015319314785301685,
-0.0158008374273777,
0.04608066380023956,
0.08802052587270737,
-0.032537925988435745,
-0.03963751345872879,
0.02873830869793892,
-0.016476429998874664,
0.009923633188009262,
-0.049309685826301575,
0.07068274915218353,
-0.03010677918791771,
0.04147689789533615,
-0.029954474419355392,
0.00542791560292244,
0.010067366994917393,
-0.0436466820538044,
0.03398003429174423,
-0.07496654987335205,
0.01587505266070366,
-0.10259214788675308,
0.002359206322580576,
-0.0017089868197217584,
0.03560582920908928,
0.014735544100403786,
-0.027439603582024574,
-0.05115622654557228,
-0.004345252178609371,
-0.00235133059322834,
0.02692565694451332,
-0.016461044549942017,
-0.007350805215537548,
0.045681826770305634,
0.006859521381556988,
-0.0172540545463562,
0.024749064818024635,
-0.022873137146234512,
0.008922609500586987,
-0.013374380767345428,
0.00984717532992363,
0.040268585085868835,
-0.03407031670212746,
-0.032069943845272064,
0.03734278306365013,
0.037427108734846115,
-0.01452277135103941,
-0.002061977284029126,
-0.02418345957994461,
0.0656050518155098,
0.073678158223629,
-0.052293919026851654,
-0.04757383465766907,
0.03702918067574501,
-0.010724371299147606,
0.04199157655239105,
0.02712375484406948,
0.06691233068704605,
-0.005491307470947504,
0.0040694335475564,
0.03772517666220665,
-0.01722043938934803,
-0.023284653201699257,
0.020505711436271667,
0.03713386505842209,
-0.02624255232512951,
-0.0804431363940239,
-0.0348224863409996,
-0.014056496322154999,
-0.0451795794069767,
0.010622082278132439,
-0.007814387790858746,
0.01637469232082367,
-0.02304493449628353,
-0.004213659558445215,
-0.03920463100075722,
-0.05631354823708534,
-0.0218464694917202,
0.020209912210702896,
0.02595207467675209,
-0.013602575287222862,
-0.015583306550979614,
-0.01393972523510456,
-0.036010049283504486,
0.03562868759036064,
0.0092700757086277,
-0.008910640142858028,
-0.014118002727627754,
-0.028380058705806732,
0.017842411994934082,
-0.038215652108192444,
0.05456932261586189,
0.023593347519636154,
0.005726994946599007,
-0.03777415305376053,
-0.04033804312348366,
-0.0006021347362548113,
-0.061977747827768326,
0.03051774576306343,
0.0026643702294677496,
-0.030703047290444374,
0.08711696416139603,
-0.022585080936551094,
-0.0365973599255085,
0.04880387708544731,
-0.05096359923481941,
-0.008986571803689003,
0.0532618872821331,
-0.050506964325904846,
0.01711977832019329,
0.05514126271009445,
-0.011907367035746574,
-0.020120149478316307,
-0.02736485004425049,
-0.018356073647737503,
0.03562082722783089,
-0.05326974019408226,
-0.012965027242898941,
-0.0008314703009091318,
-0.08210809528827667,
0.0003960900357924402,
-0.06275320798158646,
0.05251133069396019,
0.04052172973752022,
0.011216717772185802,
0.01655992865562439,
-0.01774372160434723,
0.028389427810907364,
-0.046268291771411896,
0.021955177187919617,
0.0761653333902359,
0.0500151552259922,
-0.007305127568542957,
-0.016698701307177544,
-0.0037992282304912806,
-0.0046950774267315865,
-0.014849299564957619,
0.08257493376731873,
0.01179596409201622,
0.04232945665717125,
-0.004028992727398872,
-0.00781805720180273,
0.012849131599068642,
0.04797222837805748,
0.00778987817466259,
0.025187356397509575,
0.008524837903678417,
-0.06709443032741547,
0.04445401579141617,
-0.0160738043487072,
-0.047343660145998,
0.007529519498348236,
-0.03772755712270737,
-0.01315021887421608,
-0.00995403341948986,
0.03726766258478165,
-0.06758429855108261,
0.013412263244390488,
-0.046267468482255936,
0.03943665698170662,
-0.004275818355381489,
-0.06315290182828903,
-0.07603354007005692,
-0.01813865825533867,
-0.0795714482665062,
-0.037969499826431274,
-0.02957714907824993,
0.01892702654004097,
0.014846878126263618,
-0.06707163900136948,
-0.014391412027180195,
0.012682286091148853,
0.037568192929029465,
-0.02650333382189274,
-0.03861195594072342,
0.014546852558851242,
-0.030131671577692032,
-0.08599840849637985,
-0.0171901136636734,
0.03076801635324955,
0.032758478075265884,
-0.011308967135846615,
-0.030951805412769318,
0.05186877027153969,
0.04566090181469917,
0.043091196566820145,
-0.04038820415735245,
0.03652022406458855,
0.08575837314128876,
-0.04513351246714592,
-0.05047440156340599,
-0.056012727320194244,
0.01437735091894865,
0.0025349524803459644,
-0.014204258099198341,
0.015031646937131882,
0.0031625365372747183,
-0.003847467480227351,
0.024822698906064034,
0.0399000309407711,
-0.02154700830578804,
-0.04269695654511452,
-0.05475616827607155,
0.05555713549256325,
-0.05366601422429085,
0.013244342990219593,
0.0004352790710981935,
-0.04825151339173317,
-0.02611844427883625,
0.016759946942329407,
-0.024270253255963326,
-0.007029206492006779,
0.017538197338581085,
0.01395957451313734,
-0.03313180059194565,
0.023125968873500824,
-0.06472373753786087,
-0.04813147336244583,
-0.049483925104141235,
-0.030085748061537743,
0.08305944502353668,
-0.009955089539289474,
-0.010120370425283909,
0.0063371979631483555,
-0.022191980853676796,
-0.0038862607907503843,
0.030883681029081345,
0.039227019995450974,
0.01738189347088337,
-0.024607941508293152,
-0.038748741149902344,
0.021473320201039314,
0.06190584599971771,
0.059041570872068405,
-0.026479989290237427,
0.039351169019937515,
-0.03678353875875473,
0.03585134446620941,
-0.00325869326479733,
0.00828471127897501,
-0.05794836953282356,
0.0036952286027371883,
0.02392588183283806,
-0.01666262559592724,
0.0058017936535179615,
-0.015262254513800144,
0.05374329164624214,
-0.03722649812698364,
-0.018216151744127274,
0.007023519370704889,
0.007455113809555769,
0.007982983253896236,
-0.05011645331978798,
0.009745691902935505,
-0.029893670231103897,
0.013436976820230484,
0.06784822791814804,
0.0002644596970640123,
-0.06585829704999924,
0.0033817000221461058,
0.015904802829027176,
0.03367501124739647,
-0.039898358285427094,
0.007916741073131561,
-0.020170969888567924,
-0.047162916511297226,
-0.03822759911417961,
-0.02931184321641922,
0.044363636523485184,
0.08730487525463104
] |
<p>What sort of no-slip zone is in place when liquid water flows from a faucet through air at room temperature? Does the water drag a layer of air molecules along with it?</p> | g9256 | [
0.003686979878693819,
0.015248360112309456,
-0.026393989101052284,
0.02479533664882183,
-0.015506494790315628,
0.05362742766737938,
0.06619957089424133,
-0.037207454442977905,
-0.044275108724832535,
-0.07373980432748795,
-0.02278495766222477,
-0.03520077094435692,
-0.03868900239467621,
0.05707206949591637,
-0.028649142012000084,
0.036954499781131744,
0.002605726942420006,
0.0030272500589489937,
0.058095645159482956,
-0.012991253286600113,
-0.02395029179751873,
-0.025782005861401558,
-0.02491753362119198,
-0.015153233893215656,
-0.023925112560391426,
-0.04917679727077484,
0.013034988194704056,
-0.041242584586143494,
0.015559372492134571,
-0.025490116328001022,
0.029232297092676163,
0.03540195897221565,
-0.00355341169051826,
-0.06860587745904922,
-0.0056264144368469715,
-0.01989743486046791,
0.034885600209236145,
-0.004423683509230614,
0.015119677409529686,
-0.056022852659225464,
0.031752441078424454,
0.04818812012672424,
-0.014361700043082237,
0.053064990788698196,
0.0164567269384861,
0.01648177206516266,
-0.016169629991054535,
-0.018719833344221115,
-0.06536595523357391,
0.02664458006620407,
0.02368347905576229,
0.013738433830440044,
-0.03903687372803688,
0.021571779623627663,
-0.09125959873199463,
-0.02130219340324402,
0.008233060128986835,
0.01114249974489212,
0.05449320748448372,
0.02735498547554016,
0.0037261268589645624,
0.017894020304083824,
-0.010646642185747623,
0.008379433304071426,
0.03218700736761093,
0.01953001692891121,
-0.05760125815868378,
-0.016548072919249535,
0.007380484603345394,
0.013516619801521301,
-0.05078959837555885,
-0.005113576073199511,
0.005861872807145119,
-0.041033923625946045,
-0.01888742484152317,
-0.04599887505173683,
-0.083314448595047,
-0.027042118832468987,
0.0686546191573143,
-0.02820407785475254,
0.019499141722917557,
0.01510521862655878,
0.028439192101359367,
-0.01808510348200798,
0.061215855181217194,
-0.00003456492777331732,
-0.012539790011942387,
-0.043874792754650116,
-0.0027670564595609903,
0.00200002733618021,
-0.008825148455798626,
-0.036947816610336304,
-0.0165301151573658,
0.004494656343013048,
0.0005334282759577036,
0.02507813833653927,
0.03662693873047829,
0.0022133723832666874,
0.03470814228057861,
-0.010591494850814342,
-0.038122039288282394,
0.005083536263555288,
0.02759389765560627,
-0.015264453366398811,
0.011449423618614674,
-0.012313015758991241,
-0.00029020849615335464,
-0.0017102020792663097,
0.001186777837574482,
0.03266989439725876,
-0.02554859220981598,
-0.003142081666737795,
-0.06578145176172256,
0.037874918431043625,
0.026212560012936592,
0.005365945864468813,
0.03038693591952324,
0.06261906027793884,
-0.036651916801929474,
0.05589829757809639,
0.03936679661273956,
0.03414135053753853,
0.06137949228286743,
0.03534012287855148,
0.0015557712176814675,
-0.008306515403091908,
-0.01462590228766203,
0.045578669756650925,
-0.0015484970062971115,
0.012789291329681873,
-0.010875764302909374,
0.009831119328737259,
-0.0014863669639453292,
-0.015330093912780285,
-0.008444328792393208,
-0.02208348922431469,
-0.00527971051633358,
-0.020947733893990517,
0.02003338374197483,
-0.026680896058678627,
0.11551935970783234,
0.0007493139710277319,
0.020361151546239853,
0.020918328315019608,
-0.015782391652464867,
-0.07554303854703903,
-0.004964920692145824,
0.02746068872511387,
0.029835252091288567,
-0.05699493736028671,
-0.023373525589704514,
-0.0007500969804823399,
0.016106804832816124,
-0.026876453310251236,
-0.01139096263796091,
-0.024681104347109795,
0.02729346789419651,
-0.03212304040789604,
0.06440377980470657,
0.03619096800684929,
-0.005734659731388092,
-0.029026905074715614,
0.03067741170525551,
-0.026091886684298515,
-0.10002215206623077,
-0.03773697093129158,
-0.018618011847138405,
0.04085640609264374,
0.05604954808950424,
0.0032442761585116386,
-0.046851228922605515,
-0.022438302636146545,
-0.04440481588244438,
0.026115786284208298,
0.009909912943840027,
-0.0037710792385041714,
0.021158507093787193,
0.032287564128637314,
0.060139235109090805,
-0.0196014866232872,
0.03025912493467331,
0.030868133530020714,
-0.012142188847064972,
-0.046029817312955856,
-0.009902909398078918,
0.05567910894751549,
-0.05754615738987923,
-0.00911498349159956,
-0.00395239656791091,
0.006724185310304165,
0.056614432483911514,
-0.08331765979528427,
0.02362864464521408,
0.05590251833200455,
-0.028118858113884926,
0.023567592725157738,
-0.013419180177152157,
-0.07268766313791275,
-0.04570642486214638,
0.001982731046155095,
0.043391432613134384,
-0.0755661129951477,
0.026240088045597076,
0.0035620026756078005,
0.068723164498806,
0.05479464679956436,
0.0032708735670894384,
-0.008909194730222225,
0.02622300013899803,
0.013282623142004013,
0.005741036031395197,
0.049430787563323975,
0.03962066397070885,
-0.015784846618771553,
0.005922601092606783,
0.01299132127314806,
-0.06460431218147278,
0.007026949431747198,
-0.013559042476117611,
0.0273207388818264,
0.026992298662662506,
-0.005909543950110674,
-0.03635489195585251,
0.06842660903930664,
-0.02080043964087963,
-0.053988728672266006,
-0.027411773800849915,
-0.023053038865327835,
-0.014463960193097591,
0.02297573909163475,
-0.04100240021944046,
-0.01566644199192524,
0.003872332163155079,
-0.01097521185874939,
0.015098840929567814,
-0.00014252218534238636,
-0.010055405087769032,
0.0005989292985759676,
0.04556865990161896,
-0.02023749239742756,
-0.022658277302980423,
-0.019730128347873688,
-0.11280935257673264,
-0.015286541543900967,
-0.004746802616864443,
0.03096035122871399,
-0.007334766909480095,
-0.07531750202178955,
0.0070261708460748196,
-0.003035171888768673,
0.03281361609697342,
-0.04680567979812622,
0.032493434846401215,
0.06877397000789642,
-0.048643749207258224,
0.005036118905991316,
-0.010693363845348358,
-0.026476439088582993,
0.0017676973948255181,
-0.02657165750861168,
0.00540098687633872,
-0.07145939767360687,
-0.02174490876495838,
-0.0047552515752613544,
-0.013541698455810547,
0.02072116546332836,
-0.05967245623469353,
0.05857004597783089,
0.03352805972099304,
0.056005336344242096,
0.04274805635213852,
-0.019333798438310623,
-0.017735064029693604,
0.022169575095176697,
-0.017381826415657997,
-0.018100230023264885,
0.03139566630125046,
-0.000876080768648535,
-0.00001020958643493941,
0.019047632813453674,
0.003520749509334564,
0.0007654897053726017,
-0.026784542948007584,
0.004535914398729801,
0.008243567310273647,
-0.07051146775484085,
0.007748716976493597,
0.048958614468574524,
-0.0253725778311491,
0.001312031876295805,
0.0235229954123497,
-0.0049219150096178055,
0.031625423580408096,
0.06167168542742729,
0.024929536506533623,
-0.0110930185765028,
0.046870384365320206,
0.013266172260046005,
0.010152430273592472,
0.008913224563002586,
0.01236341055482626,
-0.01443526055663824,
0.003828135086223483,
0.03023376874625683,
-0.0014267702354118228,
-0.032024502754211426,
-0.03684833645820618,
-0.06367509067058563,
-0.014186529442667961,
-0.028175273910164833,
0.030796540901064873,
0.03961266577243805,
-0.01446615718305111,
0.05708274990320206,
-0.011729255318641663,
0.02449127286672592,
-0.016957685351371765,
0.017904585227370262,
0.04375655949115753,
0.06465857475996017,
0.008290008641779423,
-0.01814841479063034,
0.031647488474845886,
0.050442155450582504,
0.019668901339173317,
0.002784443786367774,
0.04207750782370567,
0.021242666989564896,
-0.062474850565195084,
-0.022348200902342796,
0.004140922799706459,
-0.009798125363886356,
-0.015122026205062866,
-0.05065331608057022,
-0.004632077645510435,
0.012458991259336472,
0.023576591163873672,
0.03613175079226494,
0.056623708456754684,
-0.0250653475522995,
-0.027609391137957573,
-0.02309669554233551,
0.037960655987262726,
-0.027482695877552032,
0.03394356369972229,
-0.030919091776013374,
0.04491151496767998,
0.017793629318475723,
-0.009605486877262592,
0.04227215796709061,
0.06403789669275284,
-0.051440346986055374,
-0.009325483813881874,
-0.04147554934024811,
0.004166185390204191,
0.02690286934375763,
-0.0013847813243046403,
0.03019076958298683,
-0.007069066166877747,
-0.01978960633277893,
-0.014403576031327248,
-0.06568188220262527,
0.020377546548843384,
0.08132967352867126,
-0.026631031185388565,
0.0086869727820158,
-0.007328032981604338,
0.06507247686386108,
-0.01332380622625351,
0.009425368160009384,
-0.023226290941238403,
0.00871484074741602,
-0.03009357489645481,
0.044310759752988815,
0.03449336439371109,
-0.025293104350566864,
0.009198140352964401,
0.0035198088735342026,
-0.04841012880206108,
0.044702328741550446,
0.05502438172698021,
-0.00032725397613830864,
-0.02473573200404644,
-0.005299975164234638,
0.0014591787476092577,
-0.0018977082800120115,
-0.06407450139522552,
0.003087191376835108,
0.0098137641325593,
-0.05288456007838249,
-0.014399792067706585,
0.07325909286737442,
0.03302156925201416,
-0.03594882786273956,
0.010238319635391235,
0.025223122909665108,
0.035541221499443054,
0.07332666963338852,
-0.07647104561328888,
0.008930621668696404,
0.03371065482497215,
0.00911397859454155,
-0.0858498215675354,
-0.018939312547445297,
0.032919447869062424,
0.034310393035411835,
-0.0003654485335573554,
-0.005934343207627535,
-0.008046619594097137,
-0.022519933059811592,
-0.002268821932375431,
-0.01485458668321371,
-0.06791998445987701,
-0.019866954535245895,
-0.04519287869334221,
-0.013756501488387585,
-0.048433564603328705,
0.017282985150814056,
0.02407480590045452,
-0.008654887787997723,
-0.0009148959070444107,
0.04982462525367737,
-0.02329176478087902,
0.02447659522294998,
0.0030859075486660004,
-0.014031071215867996,
0.08039635419845581,
0.035387203097343445,
-0.028309671208262444,
-0.01640447787940502,
-0.06741171330213547,
-0.053685080260038376,
-0.04993702098727226,
0.03404935821890831,
0.08939462900161743,
0.03544580191373825,
0.003187884809449315,
-0.03963174298405647,
0.025438183918595314,
0.04624655470252037,
-0.02334633283317089,
0.001332942396402359,
0.004349317867308855,
0.029577307403087616,
-0.05346572771668434,
0.09838847815990448,
0.046707700937986374,
-0.029384935274720192,
0.05287827551364899,
-0.005082566291093826,
-0.08637344837188721,
0.05270881578326225,
-0.018315041437745094,
0.012577862478792667,
-0.05485565587878227,
0.018562108278274536,
-0.02665085718035698,
-0.030215110629796982,
-0.030518565326929092,
0.03502194583415985,
0.027185359969735146,
-0.02197844721376896,
-0.06245289370417595,
0.0010114993201568723,
-0.034015413373708725,
-0.049725037068128586,
0.0324864462018013,
-0.0370367206633091,
-0.03387555480003357,
-0.005950910970568657,
0.03489590063691139,
0.0009730738820508122,
0.003184870583936572,
0.11176910996437073,
0.0733131617307663,
0.01755688153207302,
0.03183195739984512,
0.02525569498538971,
0.029187839478254318,
-0.04222247749567032,
-0.02022709883749485,
0.04430081322789192,
0.029721733182668686,
0.062455594539642334,
-0.00439724326133728,
-0.009049927815794945,
-0.021059714257717133,
0.062152281403541565,
0.019650213420391083,
-0.02519639953970909,
-0.0052408319897949696,
0.03172452747821808,
-0.052682261914014816,
-0.051208771765232086,
-0.09515593945980072,
-0.01785544492304325,
0.008446882478892803,
0.03242727741599083,
0.04551363363862038,
-0.011475182138383389,
-0.03454282134771347,
0.0205144714564085,
0.062007639557123184,
-0.008738475851714611,
0.03392603620886803,
0.054379865527153015,
0.012256389483809471,
-0.030782800167798996,
-0.04595020040869713,
0.06994600594043732,
-0.015260453335940838,
-0.021237574517726898,
-0.027651479467749596,
0.04425513371825218,
0.07506775110960007,
-0.015434900298714638,
-0.009635715745389462,
-0.017885390669107437,
-0.03171350806951523,
0.05286693200469017,
0.01673879101872444,
0.009568028151988983,
-0.05045444518327713,
-0.004800218157470226,
-0.02813221886754036,
-0.009231801144778728,
-0.008122998289763927,
0.00038386331289075315,
-0.012681752443313599,
0.04701967164874077,
0.028133060783147812,
0.000545627495739609,
0.024841632694005966,
0.012353996746242046,
0.03827308118343353,
-0.0580781027674675,
-0.015409760177135468,
-0.03323977813124657,
0.07161039113998413,
0.014144737273454666,
-0.03030768223106861,
-0.008860679343342781,
0.0145812276750803,
0.03441940248012543,
-0.0002581103763077408,
0.0349305085837841,
0.008214344270527363,
0.033123794943094254,
-0.007060004398226738,
-0.02880891226232052,
-0.007493792101740837,
0.017887119203805923,
-0.03524645417928696,
0.07311945408582687,
0.023152397945523262,
-0.0027372136246412992,
0.020084913820028305,
-0.019232628867030144,
-0.003737659426406026,
0.0010303464950993657,
0.05384727194905281,
-0.01653684861958027,
0.046229615807533264,
0.0064180996268987656,
0.056552208960056305,
-0.008577956818044186,
-0.06826743483543396,
0.024668937548995018,
-0.010425977408885956,
0.060185834765434265,
-0.022231725975871086,
-0.013857834041118622,
-0.0010086966212838888,
-0.05608072876930237,
-0.007899072952568531,
0.019390258938074112,
-0.068443663418293,
-0.027607984840869904,
0.019168859347701073,
0.02727750688791275,
0.04861459136009216,
-0.010583111084997654,
-0.05600108578801155,
-0.036912187933921814,
0.02168365754187107,
0.006772984284907579,
-0.02548270858824253,
0.013528368435800076,
0.029717495664954185,
0.03429931402206421,
-0.06438427418470383,
0.0015790336765348911,
0.007245203014463186,
-0.007279666606336832,
0.011720655485987663,
-0.019634561613202095,
0.016668980941176414,
0.01561045739799738,
0.014485012739896774,
0.05232461541891098,
-0.039660029113292694,
0.06615310907363892,
0.025760093703866005,
-0.061078332364559174,
-0.011236780323088169,
0.022352835163474083,
0.021641315892338753,
0.02778233028948307,
0.03485387563705444,
0.021823741495609283,
-0.009028283879160881,
0.023736106231808662,
0.06484897434711456,
-0.04012127220630646,
0.043892987072467804,
-0.07735689729452133,
0.00427996926009655,
-0.056559544056653976,
-0.045819878578186035,
0.009917929768562317,
0.02241560071706772,
-0.0521748885512352,
-0.01634790189564228,
-0.03383858501911163,
-0.02150016836822033,
0.020729348063468933,
-0.05045267939567566,
0.049134399741888046,
0.006158149801194668,
0.009028214029967785,
0.03305422514677048,
0.006700693164020777,
-0.02786727249622345,
0.002908630296587944,
0.003726216498762369,
0.010735097341239452,
-0.08740239590406418,
-0.0009761035325936973,
0.07405349612236023,
0.020359361544251442,
0.03410238400101662,
0.011704868637025356,
0.0006063993205316365,
0.002083137631416321,
-0.0036463493015617132,
-0.029044998809695244,
-0.051855266094207764,
-0.01184424664825201,
-0.0191452968865633,
-0.041942473500967026,
-0.0369006022810936,
-0.07674793154001236,
-0.026499586179852486,
0.05418892577290535,
0.02414770983159542,
0.009538446553051472,
-0.030973654240369797,
0.024537911638617516,
-0.07493403553962708,
-0.058327846229076385,
-0.023368317633867264,
-0.005001717247068882,
0.01569513790309429,
0.031965892761945724,
0.034168776124715805,
0.037957847118377686,
-0.01056548859924078,
-0.010443395003676414,
0.048480574041604996,
-0.037825338542461395,
0.00030520930886268616,
-0.047537729144096375,
0.02836393564939499,
-0.0028174773324280977,
-0.015590588562190533,
0.03662053123116493,
0.016113201156258583,
0.03726626932621002,
-0.005181358195841312,
-0.011838190257549286,
0.045750293880701065,
0.026457257568836212,
0.05646030604839325,
-0.017034295946359634,
-0.0069527714513242245,
-0.017911061644554138,
-0.021914485841989517,
-0.03479522466659546,
-0.009165831841528416,
-0.08804981410503387,
0.025721825659275055,
0.057679180055856705,
-0.056731462478637695,
-0.03305765613913536,
-0.036430321633815765,
0.03884078562259674,
0.003990506753325462,
-0.1042509526014328,
-0.032895732671022415,
-0.025487763807177544,
-0.0020807385444641113,
0.015314243733882904,
-0.029509570449590683,
0.024727096781134605,
0.006147731561213732,
0.0110649224370718,
-0.019158456474542618,
-0.02906382828950882,
-0.006288692355155945,
-0.04624364152550697,
-0.038611020892858505,
0.05342693254351616,
0.004348072689026594,
-0.027130763977766037,
0.10307086259126663,
-0.004184153862297535,
-0.04195356369018555,
0.0248824805021286,
-0.009392226114869118,
0.02007952518761158,
-0.06196267902851105,
-0.031707387417554855,
-0.05691169202327728,
0.0006963614141568542,
-0.028307370841503143,
0.020041566342115402,
-0.016923584043979645,
0.02022765390574932,
-0.04739069193601608,
-0.025467101484537125,
-0.022757504135370255,
0.008438576012849808,
-0.016707904636859894,
-0.04141556844115257,
-0.06171977519989014,
0.01576686091721058,
0.025800857692956924,
0.053301338106393814,
0.028453126549720764,
-0.04662808030843735,
0.021658580750226974,
0.04611029475927353,
0.036123864352703094,
-0.0015084723709151149,
0.02290407195687294,
-0.013252794742584229,
0.017705030739307404,
0.017907852306962013,
0.016853857785463333,
-0.05356985330581665,
0.05723167955875397,
-0.0035839711781591177,
0.03595142066478729,
-0.069182388484478,
0.03925379738211632,
-0.06049998477101326,
-0.08040989190340042,
0.05592777952551842,
-0.0024234126321971416,
-0.009039541706442833,
-0.04297835752367973,
-0.08224161714315414,
0.004721462726593018,
0.02732192352414131,
0.021484242752194405,
-0.016183286905288696,
-0.023305336013436317,
-0.016468564048409462
] |
<p>Is there a way to see that <a href="http://en.wikipedia.org/wiki/Bertrand%27s_theorem" rel="nofollow">Bertrand's theorem</a> is true intuitively. I mean without getting into too much mathematics ?</p> | g9257 | [
-0.005530521273612976,
0.06827393174171448,
-0.0028848773799836636,
-0.06653895229101181,
0.010698004625737667,
-0.03881455212831497,
0.010602525435388088,
-0.01124502718448639,
-0.024276571348309517,
0.005614296533167362,
0.001948605407960713,
0.034363746643066406,
0.028610818088054657,
0.07014824450016022,
-0.06798704713582993,
0.0004211696214042604,
0.0314464271068573,
-0.03377236798405647,
0.12380395829677582,
-0.013708256185054779,
0.06345092505216599,
0.02768060192465782,
0.029743904247879982,
-0.023388639092445374,
-0.05365503579378128,
-0.002802482107654214,
-0.03529614582657814,
0.005940871313214302,
-0.02875298075377941,
-0.036936454474925995,
0.02788509801030159,
-0.03358246013522148,
0.049732986837625504,
-0.011075077578425407,
0.0067398808896541595,
-0.032239072024822235,
0.07826016843318939,
0.05724600702524185,
0.022741902619600296,
-0.011417217552661896,
-0.026263093575835228,
0.0607588030397892,
0.03735817223787308,
-0.0011310601839795709,
-0.03849676623940468,
0.010605164803564548,
-0.029947711154818535,
0.02422165870666504,
-0.035954706370830536,
0.0029997604433447123,
0.01889451965689659,
0.026997549459338188,
-0.01869117096066475,
0.02562364749610424,
0.007864476181566715,
-0.029077883809804916,
0.05263226479291916,
0.001305340207181871,
0.09152597934007645,
-0.03982769697904587,
0.0018122122855857015,
0.010246071964502335,
0.00041094215703196824,
0.049647387117147446,
-0.01641564629971981,
0.032478347420692444,
0.0175482090562582,
-0.05785191431641579,
-0.019161904230713844,
-0.009907626546919346,
-0.0691417008638382,
-0.013234155252575874,
-0.015497012063860893,
-0.013994547538459301,
-0.02239050716161728,
0.03629210591316223,
0.005515843164175749,
0.027165722101926804,
0.006443937309086323,
0.05806471034884453,
-0.039910413324832916,
0.023336896672844887,
0.004785836674273014,
-0.027784589678049088,
0.0004845276416745037,
-0.03575492277741432,
0.01590828411281109,
-0.06157323718070984,
0.06226283684372902,
-0.03846229612827301,
0.030143341049551964,
0.02681521326303482,
0.037979479879140854,
0.02642727643251419,
0.035396602004766464,
-0.006988743785768747,
0.00936620868742466,
0.02593434974551201,
-0.008480858989059925,
-0.040968094021081924,
-0.06167612224817276,
0.049181632697582245,
-0.0666038990020752,
-0.05225883796811104,
0.038573332130908966,
-0.010189143940806389,
0.025363704189658165,
0.0001739523868309334,
-0.01969132386147976,
-0.01208476535975933,
-0.04067708179354668,
-0.062057457864284515,
-0.04292954131960869,
0.07036937028169632,
-0.018802575767040253,
-0.002097528660669923,
-0.0038907343987375498,
0.019616181030869484,
-0.031238140538334846,
0.05830786004662514,
0.002420500386506319,
0.035679515451192856,
0.07629991322755814,
0.09743907302618027,
-0.0034433368127793074,
0.08359327167272568,
-0.007400504779070616,
0.005917540285736322,
0.01487347949296236,
-0.013725335709750652,
0.05405356362462044,
-0.017352083697915077,
0.05797508731484413,
0.006624236702919006,
-0.018913177773356438,
0.013000444509088993,
0.009119458496570587,
0.0486651249229908,
-0.021408120170235634,
-0.006771677173674107,
-0.041951097548007965,
-0.045606378465890884,
-0.009539400227367878,
-0.018449576571583748,
0.022687064483761787,
-0.06017421931028366,
-0.00740490248426795,
0.04104581102728844,
-0.016988130286335945,
0.05027610436081886,
-0.05708404257893562,
0.03878571465611458,
0.044471025466918945,
0.01768331788480282,
0.0010138327488675714,
-0.007156125269830227,
0.013080606237053871,
-0.01402504276484251,
0.0010456019081175327,
-0.020129000768065453,
0.045411814004182816,
0.014130916446447372,
0.009942831471562386,
-0.02888995222747326,
-0.03873366117477417,
-0.004407383501529694,
-0.03512831777334213,
-0.021592268720269203,
-0.056587327271699905,
-0.008838164620101452,
-0.028850972652435303,
0.04441537335515022,
0.004546982701867819,
0.009635776281356812,
-0.007130900863558054,
0.03179996460676193,
-0.06285365670919418,
0.03166792541742325,
0.034321948885917664,
-0.02721991389989853,
0.010112706571817398,
-0.015017352998256683,
0.04364009574055672,
0.017788536846637726,
0.009814240038394928,
0.04250820353627205,
-0.027172604575753212,
0.0017618114361539483,
-0.023566588759422302,
0.027716655284166336,
-0.05371680110692978,
0.01962258480489254,
-0.015288565307855606,
0.05292808637022972,
0.044311534613370895,
0.013984635472297668,
-0.01309966016560793,
-0.022643350064754486,
-0.007488312665373087,
-0.004124614875763655,
0.05976693704724312,
0.009470573626458645,
0.060540083795785904,
-0.0017526635201647878,
-0.06628910452127457,
-0.018475010991096497,
0.0030675563029944897,
0.008963187225162983,
-0.032695669680833817,
-0.0035853583831340075,
0.06646423786878586,
-0.03415995463728905,
0.005716396030038595,
0.017364520579576492,
-0.010457104071974754,
0.03745105862617493,
-0.03302201256155968,
0.006184105295687914,
-0.01812528260052204,
-0.005397980101406574,
-0.01590035855770111,
0.0330246165394783,
-0.010946464724838734,
-0.013754433952271938,
0.009960183873772621,
0.06305118650197983,
-0.009391698986291885,
-0.057499296963214874,
0.04084346815943718,
0.04779931530356407,
-0.05023821070790291,
-0.076961949467659,
-0.019664341583848,
0.0034519743639975786,
0.0445113331079483,
0.05205847695469856,
0.02528439648449421,
0.00023527888697572052,
0.02732900343835354,
0.06329791247844696,
-0.02070736140012741,
-0.06152625009417534,
-0.033918533474206924,
0.05268242582678795,
-0.01633799448609352,
-0.07634704560041428,
0.038414642214775085,
0.004863151349127293,
0.04307851940393448,
-0.005054319277405739,
0.012164329178631306,
-0.009134220890700817,
0.029030516743659973,
0.015804197639226913,
0.015741264447569847,
0.05538656562566757,
-0.0006048564100638032,
-0.010244589298963547,
0.002378727775067091,
0.04757518321275711,
-0.012664126232266426,
-0.03231257200241089,
0.01547328196465969,
0.04548240825533867,
-0.01294378750026226,
-0.01738712377846241,
-0.00968634057790041,
0.009737796150147915,
-0.025211183354258537,
-0.0030252893920987844,
0.009215704165399075,
0.03331876918673515,
-0.0002660428872331977,
-0.01044858992099762,
-0.0468490906059742,
0.013016650453209877,
-0.022884177044034004,
0.013668741099536419,
-0.027399618178606033,
0.002362349536269903,
-0.031416550278663635,
-0.00889183022081852,
-0.055854566395282745,
0.051835834980010986,
-0.009292537346482277,
0.03081073984503746,
-0.058074627071619034,
0.028050245717167854,
-0.051699668169021606,
0.007086215075105429,
0.008096111007034779,
-0.003425652626901865,
0.03700776770710945,
0.023190565407276154,
-0.07872749865055084,
-0.006715712137520313,
0.020875992253422737,
0.024315306916832924,
0.03240443766117096,
0.033452123403549194,
0.02884877659380436,
0.00024331703025382012,
-0.003800809383392334,
-0.05245625972747803,
0.05260230973362923,
-0.0182796698063612,
0.03604217618703842,
-0.04153454676270485,
0.04030798375606537,
-0.04169147089123726,
-0.011947527527809143,
0.03877851739525795,
0.050935640931129456,
0.019225165247917175,
0.02182392217218876,
0.02544035203754902,
0.030329138040542603,
0.024411924183368683,
0.06019007787108421,
-0.027409112080931664,
-0.011825596913695335,
-0.0323922373354435,
-0.031586021184921265,
-0.06923360377550125,
0.042651258409023285,
-0.04585576802492142,
-0.022752000018954277,
0.007331050932407379,
0.01995081827044487,
-0.0394425205886364,
0.034417830407619476,
0.02884073741734028,
-0.020252127200365067,
-0.0776141807436943,
-0.009461654350161552,
-0.02497989684343338,
-0.035406503826379776,
0.018567224964499474,
0.04283888265490532,
0.0015673597808927298,
0.018461083993315697,
-0.030083784833550453,
-0.015625031664967537,
0.03658401593565941,
-0.04629926756024361,
-0.002769849030300975,
-0.01574312336742878,
0.07396939396858215,
0.05060987174510956,
0.0038387326058000326,
-0.009857739321887493,
-0.05626824498176575,
0.02957775630056858,
-0.02437136135995388,
0.010272602550685406,
0.023625453934073448,
-0.0002834860351867974,
0.022252585738897324,
-0.026293186470866203,
-0.021822785958647728,
0.06059609353542328,
-0.05570481717586517,
-0.02383602038025856,
0.017590312287211418,
0.04475719854235649,
0.07128020375967026,
-0.024498827755451202,
0.06825509667396545,
-0.012199671007692814,
-0.06059907004237175,
-0.03710344806313515,
-0.06172284483909607,
0.03660016134381294,
0.020190145820379257,
0.0649167001247406,
-0.04342994466423988,
0.01599140092730522,
0.031642209738492966,
0.030646203085780144,
0.019363215193152428,
0.016163980588316917,
0.04108484834432602,
0.032420381903648376,
-0.024614684283733368,
0.05559585615992546,
-0.032049380242824554,
-0.07935617864131927,
-0.06724708527326584,
0.031486086547374725,
0.04431653395295143,
0.013342099264264107,
0.02303280681371689,
-0.012955017387866974,
0.05014980956912041,
-0.012995881959795952,
0.01836376264691353,
-0.013686064630746841,
0.006440500728785992,
-0.03397512808442116,
0.037563640624284744,
-0.012904368340969086,
0.009430725127458572,
-0.04261048138141632,
0.02083965763449669,
-0.012143674306571484,
0.01391649805009365,
0.03708625212311745,
-0.010969950817525387,
0.0013840137980878353,
-0.022157080471515656,
-0.027907032519578934,
-0.03555751219391823,
0.04085245728492737,
0.02863769233226776,
-0.00021552805264946073,
0.043936826288700104,
-0.0018645082600414753,
-0.09807394444942474,
-0.010279574431478977,
0.008110595867037773,
-0.017350969836115837,
0.004818662069737911,
-0.06058473885059357,
-0.044192805886268616,
-0.08001860976219177,
0.06834641844034195,
-0.0061998493038117886,
0.0546751469373703,
0.010696186684072018,
0.007022039033472538,
-0.032005440443754196,
0.026446273550391197,
-0.015523003414273262,
0.00580864492803812,
-0.0826028436422348,
-0.006855844520032406,
-0.0068562645465135574,
0.10615667700767517,
-0.026472751051187515,
0.009557395242154598,
0.04490949213504791,
0.007909179665148258,
-0.04397016391158104,
-0.051854949444532394,
-0.013212517835199833,
0.030124370008707047,
0.04052295163273811,
0.016231568530201912,
0.0030732122249901295,
-0.017289478331804276,
-0.050290193408727646,
-0.0058976043947041035,
-0.04425472021102905,
0.01830647885799408,
0.0017257012659683824,
0.011195071041584015,
-0.021265164017677307,
0.005001327954232693,
-0.04605396091938019,
0.01173524372279644,
-0.04554120823740959,
-0.016014602035284042,
0.021396443247795105,
0.04102841392159462,
-0.00894962903112173,
0.012309771031141281,
-0.08312562853097916,
0.010537204332649708,
0.04494011029601097,
-0.01053731981664896,
0.013134454376995564,
-0.00611279159784317,
-0.008690005168318748,
-0.04834560304880142,
-0.06492986530065536,
-0.05160064622759819,
0.013414026238024235,
0.01622990518808365,
-0.08757376670837402,
-0.02281123772263527,
-0.03023982048034668,
0.052144430577754974,
0.02339947409927845,
-0.050037264823913574,
0.05906129628419876,
0.058896105736494064,
-0.0020788207184523344,
0.014158439822494984,
0.010639466345310211,
-0.03334950655698776,
0.03235374018549919,
0.005542125552892685,
0.03057107701897621,
-0.04412718862295151,
-0.09246379137039185,
-0.08500320464372635,
0.01917331852018833,
-0.007956272922456264,
0.007838067598640919,
-0.004319691099226475,
-0.08285729587078094,
-0.002075191820040345,
0.012112834490835667,
0.06885124742984772,
-0.0075995903462171555,
0.02454266883432865,
-0.0011200264561921358,
-0.027056852355599403,
-0.0020416653715074062,
0.0846232920885086,
0.018937580287456512,
-0.009599545039236546,
-0.045613788068294525,
-0.013933778740465641,
0.05695727467536926,
0.023090770468115807,
0.002935499418526888,
0.008510188199579716,
-0.03818919509649277,
0.015463068149983883,
0.020234718918800354,
0.058040551841259,
-0.00976499542593956,
-0.007033765781670809,
-0.009165124036371708,
-0.06601963937282562,
-0.04127604514360428,
-0.06375960260629654,
-0.06796108186244965,
-0.013018428348004818,
-0.006204167380928993,
-0.02128179930150509,
0.026435738429427147,
0.022055471315979958,
0.01984393410384655,
0.024736806750297546,
0.08880191296339035,
-0.0004499095375649631,
0.014569982886314392,
-0.04546843096613884,
0.016986258327960968,
0.036352794617414474,
0.01298544555902481,
0.04823613539338112,
-0.021331114694476128,
-0.003253164468333125,
-0.024351321160793304,
0.004336145240813494,
0.061938412487506866,
-0.04185282066464424,
0.002488761441782117,
0.008348091505467892,
-0.029546860605478287,
0.0046233837492764,
-0.007568127941340208,
0.06152133271098137,
-0.004095228388905525,
0.009965159930288792,
-0.012460581958293915,
-0.02644149214029312,
0.023775150999426842,
-0.013885816559195518,
-0.010189071297645569,
-0.020335426554083824,
-0.042476046830415726,
-0.03893548622727394,
-0.020438892766833305,
0.06535189598798752,
0.05751807242631912,
0.019474340602755547,
0.01286502368748188,
-0.06308670341968536,
-0.024411195889115334,
-0.004893140867352486,
0.004817315377295017,
-0.003981341607868671,
-0.07638759911060333,
-0.007342811208218336,
0.037692777812480927,
-0.01833268813788891,
-0.04666729271411896,
0.00018492418166715652,
0.05839415639638901,
0.029878811910748482,
0.010335405357182026,
0.03418479114770889,
-0.0493210144340992,
0.03372982516884804,
-0.0017978682881221175,
-0.015098516829311848,
0.009528662078082561,
0.010399317368865013,
-0.03731093183159828,
-0.019877096638083458,
0.006018397863954306,
0.008900020271539688,
-0.014979113824665546,
0.034247346222400665,
0.07372809946537018,
0.04185841977596283,
-0.0035094255581498146,
-0.021415356546640396,
0.04861870035529137,
-0.02174212969839573,
0.0011512493947520852,
0.040411870926618576,
0.04407431557774544,
0.013626493513584137,
0.0017922380939126015,
-0.022517908364534378,
-0.013942766934633255,
0.07917943596839905,
-0.01639094576239586,
0.04347336292266846,
-0.04106450080871582,
-0.05874628573656082,
-0.08826106041669846,
-0.08590631932020187,
-0.03013947419822216,
-0.022540006786584854,
0.027022143825888634,
-0.04154793173074722,
-0.028238678351044655,
0.03732571750879288,
0.01084569189697504,
0.07545638084411621,
-0.027866536751389503,
0.010474921204149723,
0.056654829531908035,
-0.028659597039222717,
0.012541623786091805,
-0.03693549707531929,
-0.033730991184711456,
0.027761584147810936,
0.04109318554401398,
-0.05321578308939934,
0.0016692461213096976,
-0.016354037448763847,
0.026700789108872414,
0.024618275463581085,
-0.06119832769036293,
0.03300630673766136,
0.05475154146552086,
0.016323786228895187,
-0.026685478165745735,
-0.0662323459982872,
-0.010042491368949413,
-0.0041609457693994045,
-0.062429625540971756,
0.023841524496674538,
0.05810697749257088,
-0.010365316644310951,
-0.002548417542129755,
-0.00628944905474782,
-0.009314055554568768,
0.05244743824005127,
-0.011495731770992279,
-0.03445804864168167,
-0.01168600469827652,
-0.06689365953207016,
-0.032750677317380905,
0.029813889414072037,
-0.009835268370807171,
-0.05843941494822502,
-0.007506487425416708,
0.020776836201548576,
0.0070084016770124435,
-0.040536437183618546,
-0.03919602185487747,
-0.029462510719895363,
-0.0023232214152812958,
-0.04681159555912018,
0.021162696182727814,
-0.008672337979078293,
0.011129002086818218,
-0.02800709754228592,
0.026149092242121696,
-0.003176846308633685,
-0.027463296428322792,
-0.028862038627266884,
0.0363222137093544,
-0.03873852267861366,
-0.004435465671122074,
-0.0012059890432283282,
-0.0024825374130159616,
0.03231053426861763,
-0.024130698293447495,
-0.01219311822205782,
0.002085182350128889,
0.0020204598549753428,
-0.04989645630121231,
0.026748301461338997,
0.048765916377305984,
-0.059822872281074524,
0.05961082503199577,
-0.02027120254933834,
0.02351207658648491,
-0.008847539313137531,
-0.030806656926870346,
0.010121310129761696,
0.006056624930351973,
-0.004813584499061108,
-0.03714502230286598,
-0.028380071744322777,
-0.06867892295122147,
-0.030892156064510345,
0.031238427385687828,
0.016464605927467346,
-0.08691997081041336,
0.0024225995875895023,
0.007651763968169689,
0.03034638613462448,
-0.022547265514731407,
0.04956992343068123,
0.049074430018663406,
-0.029033372178673744,
0.019367216154932976,
-0.02426038309931755,
0.0148578230291605,
0.015444113872945309,
-0.03377503901720047,
-0.026044201105833054,
-0.016911203041672707,
-0.025995660573244095,
-0.08272317051887512,
0.06875995546579361,
-0.04098382219672203,
0.060681574046611786,
-0.057275839149951935,
0.025974225252866745,
0.01206157635897398,
0.008752663619816303,
0.030810009688138962,
0.05615251138806343,
-0.04153050109744072,
0.03014702908694744,
-0.005038921721279621,
-0.003771598218008876,
0.004279701039195061,
-0.010560301132500172,
-0.020844820886850357,
0.056552063673734665,
0.02145400457084179,
-0.057851675897836685,
0.01123548112809658,
-0.006237815599888563,
-0.030505647882819176,
0.03299982100725174,
0.029712898656725883,
-0.007580294273793697,
-0.01438132207840681,
0.0875231921672821,
0.005894225090742111,
-0.00934738852083683,
0.017651615664362907,
-0.01418699137866497,
-0.01918795332312584,
-0.011193300597369671,
0.023113109171390533,
0.006415600888431072,
0.009526995941996574,
-0.016070395708084106,
-0.03861914575099945,
0.03245734050869942,
-0.0515889897942543,
-0.04493893310427666,
-0.02212395705282688,
-0.0368613675236702
] |
<p><code>Person A</code> and <code>Person B</code> are same person (theortically). They both weigh 800N. They both can vertically
lift 1000N. They want to check something out.</p>
<p><code>G -> Gravity; N -> "Normal"; M -> Muscular active</code></p>
<p><code>R -> Netto; 1 -> Person A; 2 -> Person B</code></p>
<p>$F_{g1} = 800N$</p>
<p>$F_{g2} = 800N$</p>
<p>$F_{m1} = 0N$</p>
<p>$F_{m2} = 0N$</p>
<p>$F_{n1} = F_{g1} - F_{m2} = 800N$</p>
<p>$F_{n2} = F_{g2} - F_{m1}= 800N$</p>
<p>$F_{r1} = F_{g1} - F_{n1} - F{m2} = 0N$ (no move)</p>
<p>$F_{r2} = F_{g2} - F_{n2} - F{m1} = 0N$ (no move)</p>
<ul>
<li><code>Person A</code> grabs <code>Person B</code> with both hands shirt of <code>Person B</code> in region of a bit lower than collarbone (like "tough" guys do on films).</li>
<li><code>Person A</code> lifts <code>Person B</code> with 1000N in air, about 135 degrees relative to his torso.</li>
</ul>
<p>$F_{g1} = 800N$</p>
<p>$F_{g2} = 800N$</p>
<p>$F_{m1} = 800N$</p>
<p>$F_{m2} = 0N$</p>
<p>$F_{n1} = F_{g1} + F_{g2} = 1600N$</p>
<p>$F_{n2} = F_{g2} - F_{m1} = 0N$</p>
<p>$F_{r1} = F_{g1} - F_{n1} - F{m2} = 0N$ (no move; on ground)</p>
<p>$F_{r2} = F_{g2} - F_{n2} - F{m1} = 0N$ (no move; in air)</p>
<ul>
<li>Seems till now, perfectly understandable and normal to me. In my perception of physics.</li>
<li><code>Person B</code> grabs <code>Person A</code> with both hands whatever of <code>Person A</code> in region of whatever. By whatever I mean, somewhere on body that person is still able to pull <code>Person A</code> in air.</li>
<li><code>Person B</code> lifts(?) <code>Person A</code> with 1000N in air(?), about 135 degrees relative to his torso.</li>
<li>This is when I lose it. Following rules, are total non-sense and also cause why I write this.</li>
</ul>
<p>$F_{g1} = 800N$</p>
<p>$F_{g2} = 800N$</p>
<p>$F_{m1} = 800N$</p>
<p>$F_{m2} = 800N$</p>
<p>$F_{n1} = F_{g1} - F_{m2} = 0N$</p>
<p>$F_{n2} = F_{g2} - F_{m1} = 0N$</p>
<p>$F_{r1} = F_{g1} - F_{n1} - F_{m2} = 0N$ ("floating")</p>
<p>$F_{r2} = F_{g2} - F_{n2} - F_{m1} = 0N$ ("floating")</p>
<p>"My brain", that gummy moisten tube in my head filled with baloney, tells me that first gravity and muscle force count. Then the normal one. This would cause $F_{r_{both}} = 0N$. They both have effect of being "freed" from effect of "normal" force. As <code>Person 2</code> was when he/she was in air, being lifted by <code>Person 1</code>. But it's impossible. There is still gravity pulling them to earth. And at this point. There is "floating" going on and explaining this with "Normal force" would make it even worse because both of them separately will be either flying or falling through ground.</p>
<p>@edit - When <code>Person A</code> will pull <code>Person B</code> up. <code>Person B</code>'s attitude would decrease till on feet. What then?</p>
<p>As if, if they normally stay on ground turning to tomatoes because of pulling each other up. What happens to that all the force they put in it? This 1600N.</p>
<p>"Definables": T-Shirt is untearable, won't fall off and does not hurt body at all. Both of them stay right on their feet. Please explain as plain as possible. I am really really really low with my knowledge. Relatively to you, I am idiot. I'm sorry for grammar.</p>
<p><strong>Question:</strong> What happens to <code>Person 1</code> and <code>Person 2</code>? Could you explain forces influencing their bodies, please?</p>
<p>If you are about to think "Goddammit, you're so stupid, answer is so obvious!" keep in mind I am teenager (17) without real physics knowledge. Answer may just lay around my point of view/knowledge/logic. In place of getting offensive try to explain where I made my mistake so it won't happen again :).</p> | g9258 | [
0.04191043600440025,
0.015690501779317856,
-0.005682831630110741,
0.00355913327075541,
0.04120046645402908,
0.05754799768328667,
0.054207414388656616,
0.0014316242886707187,
-0.0264830831438303,
-0.02257341332733631,
0.008260191418230534,
0.03365187719464302,
-0.03719467297196388,
-0.023989291861653328,
0.05082064867019653,
0.05937455594539642,
0.032249122858047485,
-0.053982462733983994,
0.021389402449131012,
-0.0245799720287323,
-0.02100912481546402,
0.049245599657297134,
0.010536646470427513,
-0.038094595074653625,
-0.07520484924316406,
-0.0788639709353447,
-0.0006182275246828794,
0.03352194279432297,
-0.06493277102708817,
-0.029945803806185722,
-0.03497986122965813,
-0.016261663287878036,
-0.018962804228067398,
-0.12710712850093842,
-0.08588910102844238,
-0.052844274789094925,
0.04627818986773491,
-0.04619719833135605,
-0.011986645869910717,
0.03205415979027748,
-0.01903051696717739,
-0.04448018595576286,
-0.03444116190075874,
-0.02418140135705471,
-0.010187532752752304,
0.025708718225359917,
0.004666081629693508,
-0.03825069218873978,
-0.008483842946588993,
-0.02532980404794216,
-0.008113375864923,
0.00424059946089983,
0.01377816777676344,
-0.019021205604076385,
-0.024549076333642006,
-0.0036543705500662327,
0.041089486330747604,
-0.019864801317453384,
0.037873685359954834,
0.011907831765711308,
-0.013821983709931374,
-0.002749107079580426,
0.015409108251333237,
-0.01725020632147789,
-0.0035538203082978725,
0.025300003588199615,
-0.06510011106729507,
0.017835043370723724,
-0.005976871587336063,
-0.016497060656547546,
-0.009785369969904423,
-0.08120501041412354,
-0.03110184334218502,
-0.02823500894010067,
-0.08595620840787888,
0.007394773419946432,
-0.01903516612946987,
0.003229239024221897,
0.07148031145334244,
0.05713864415884018,
-0.023791193962097168,
-0.0018295793561264873,
-0.017402175813913345,
0.07091550529003143,
0.03803544491529465,
-0.025990920141339302,
0.00011383304808987305,
0.03300794959068298,
-0.06796306371688843,
0.09014187008142471,
0.0553886778652668,
-0.016870127990841866,
0.07083755731582642,
0.10855481773614883,
-0.06511300057172775,
-0.032047338783741,
0.04717828705906868,
0.035579752177000046,
-0.009637940675020218,
-0.037234533578157425,
-0.007046910002827644,
0.009861823171377182,
0.009664551354944706,
0.004843396600335836,
-0.04022866487503052,
-0.00013625422434415668,
0.09925411641597748,
0.061901092529296875,
-0.031295206397771835,
-0.02957598678767681,
-0.04621751233935356,
0.018707899376749992,
-0.02967989444732666,
-0.04664038121700287,
0.003481881460174918,
-0.08128231018781662,
0.016009896993637085,
0.009457421489059925,
-0.0238910261541605,
-0.023409957066178322,
0.009202401153743267,
0.009665114805102348,
0.051966290920972824,
0.0388728603720665,
-0.010331791825592518,
-0.05634419992566109,
0.012782643549144268,
0.026777073740959167,
0.02670004963874817,
-0.06607138365507126,
0.006324851419776678,
-0.014242331497371197,
0.03018088825047016,
-0.025332661345601082,
-0.027029620483517647,
0.011097710579633713,
-0.02037797123193741,
-0.0068544019013643265,
0.003540951758623123,
-0.04293821379542351,
-0.006398194469511509,
-0.020298104733228683,
-0.0062212347984313965,
-0.010221933014690876,
0.02323180064558983,
-0.01207594946026802,
-0.007857187651097775,
0.04369569197297096,
0.02719414047896862,
-0.011479295790195465,
0.017629172652959824,
0.07928866147994995,
0.016516070812940598,
-0.007940579205751419,
0.027708057314157486,
0.003192329313606024,
0.05387657508254051,
0.03320566564798355,
0.0044982233084738255,
0.03975050151348114,
0.04742431640625,
0.0408397875726223,
0.022310586646199226,
0.013661395758390427,
-0.06781703978776932,
0.024020276963710785,
-0.007903797551989555,
-0.031786683946847916,
0.02146310918033123,
0.002241158625110984,
-0.1057741791009903,
-0.012443398125469685,
-0.017810868099331856,
0.07283110916614532,
-0.0017529480392113328,
0.06596437841653824,
0.05234783515334129,
-0.05748012289404869,
0.0256006121635437,
-0.03089742921292782,
-0.031375765800476074,
0.016245799139142036,
0.02849198505282402,
0.007210799027234316,
-0.036303866654634476,
0.0020761408377438784,
-0.008709211833775043,
0.08463764935731888,
-0.05241958051919937,
-0.023216301575303078,
-0.060534920543432236,
-0.02920224890112877,
-0.02123849466443062,
0.021265577524900436,
-0.0541066937148571,
-0.00021600647596642375,
0.006009779870510101,
0.028395630419254303,
0.0021684940438717604,
0.057874392718076706,
0.011291030794382095,
-0.06689125299453735,
0.03250664472579956,
-0.03537905216217041,
-0.030354518443346024,
-0.014015965163707733,
0.023813942447304726,
0.01113106869161129,
0.007146970368921757,
-0.06522670388221741,
0.005549877416342497,
-0.030369436368346214,
-0.0007971089798957109,
0.021253423765301704,
0.023835821077227592,
-0.03627239912748337,
-0.05601818487048149,
-0.018926052376627922,
-0.05598733201622963,
-0.039744723588228226,
0.06698925793170929,
-0.015026826411485672,
0.037848517298698425,
-0.024256424978375435,
-0.022524673491716385,
-0.03148048743605614,
-0.002692848676815629,
-0.00992591679096222,
-0.015158812515437603,
-0.009532495401799679,
-0.04248260334134102,
0.015149220824241638,
0.0363585501909256,
0.011049063876271248,
-0.016752006486058235,
0.00906285922974348,
0.02314528450369835,
0.05404387414455414,
0.005826652981340885,
-0.01792784593999386,
0.020916983485221863,
-0.015760930255055428,
0.0040990086272358894,
0.013090121559798717,
0.035556502640247345,
0.012623194605112076,
0.009900959208607674,
0.0266201663762331,
-0.0027273616287857294,
0.044699788093566895,
-0.021160457283258438,
-0.013325473293662071,
-0.07390068471431732,
0.030893858522176743,
0.005126729607582092,
0.026338687166571617,
-0.03580249473452568,
-0.004215053282678127,
-0.005836008582264185,
-0.0095540601760149,
-0.01670745573937893,
-0.01312042586505413,
-0.011134321801364422,
0.04892750456929207,
-0.11590968072414398,
0.014389149844646454,
-0.021664384752511978,
-0.01643463596701622,
0.009873643517494202,
-0.028688423335552216,
-0.02954801544547081,
0.016950463876128197,
0.031066084280610085,
0.020655550062656403,
-0.02568884752690792,
-0.021470967680215836,
0.01244764681905508,
-0.03619997203350067,
-0.0014042288530617952,
0.027894053608179092,
-0.0029525049030780792,
0.02737649716436863,
-0.033843036741018295,
0.006329881027340889,
0.044224683195352554,
-0.009788074530661106,
-0.019436782225966454,
-0.022453755140304565,
-0.032844044268131256,
0.003010170068591833,
0.02294818125665188,
0.015096662566065788,
0.06450536102056503,
-0.013647551648318768,
0.015539014711976051,
0.03360195830464363,
-0.02323177270591259,
-0.057160235941410065,
-0.08598600327968597,
0.013068410567939281,
0.004018029198050499,
-0.027737010270357132,
0.054146721959114075,
0.07294300943613052,
0.025205006822943687,
-0.021149320527911186,
-0.04251446574926376,
-0.051397617906332016,
0.008609781973063946,
0.0011210396187379956,
0.010022435337305069,
0.05764920637011528,
-0.028261354193091393,
-0.01798664592206478,
0.022897226735949516,
0.0015017726691439748,
-0.012336242944002151,
0.0018916361732408404,
-0.056684527546167374,
-0.061364129185676575,
0.002088467590510845,
-0.027972757816314697,
0.008973815478384495,
0.023222051560878754,
0.028684483841061592,
0.04390786215662956,
-0.06034409999847412,
0.03077765740454197,
-0.021509062498807907,
-0.05768321827054024,
0.005663288291543722,
0.021249303594231606,
-0.013812416233122349,
-0.06778610497713089,
-0.03765114024281502,
-0.013539466075599194,
0.018097469583153725,
0.008032705634832382,
0.057792432606220245,
0.012598127126693726,
0.003695056773722172,
0.02239307202398777,
-0.037467919290065765,
-0.05626947060227394,
0.03689368814229965,
0.05261686444282532,
0.023647617548704147,
0.01880919560790062,
-0.036138009279966354,
0.023778345435857773,
0.022530866786837578,
-0.03093058057129383,
0.019598117098212242,
-0.05961226299405098,
0.014532315544784069,
-0.011192793026566505,
0.012402373366057873,
-0.017876965925097466,
-0.058848969638347626,
-0.027894310653209686,
0.0063591888174414635,
0.03395385295152664,
-0.03533852845430374,
0.05406469479203224,
0.027122970670461655,
-0.006392881739884615,
-0.015722285956144333,
0.07860196381807327,
-0.04309574142098427,
-0.028677180409431458,
-0.009017536416649818,
-0.007324207108467817,
-0.010280059650540352,
-0.02939262054860592,
0.004035012796521187,
-0.03624691069126129,
0.0853683352470398,
-0.052788782864809036,
-0.008440511301159859,
0.04052986577153206,
0.07015523314476013,
0.0021684090606868267,
-0.026397306472063065,
0.02437870018184185,
0.05603880062699318,
0.023138443008065224,
-0.0035794524010270834,
0.05593658238649368,
0.08500975370407104,
0.011710469610989094,
0.024339331313967705,
-0.051621731370687485,
-0.01642773300409317,
-0.012348570860922337,
0.056660402566194534,
0.003948693163692951,
0.02959216572344303,
0.04478980600833893,
0.036422085016965866,
0.004284340888261795,
-0.05156903341412544,
0.05044672265648842,
-0.0006970414542593062,
-0.007850350812077522,
-0.0657009482383728,
-0.003117407439276576,
-0.008821272291243076,
0.009822871536016464,
0.007760329637676477,
-0.00870535895228386,
0.04072589799761772,
0.03219212591648102,
-0.011338603682816029,
-0.07684136182069778,
0.0030210635159164667,
0.011784885078668594,
0.017916155979037285,
0.04089190810918808,
0.020505506545305252,
0.015074937604367733,
0.052306439727544785,
0.08259597420692444,
-0.010958210565149784,
-0.029850129038095474,
0.051455307751894,
0.052484773099422455,
0.035236895084381104,
0.02607276849448681,
0.058001577854156494,
-0.032853465527296066,
-0.007875173352658749,
0.04643721133470535,
0.011638978496193886,
0.013692687265574932,
-0.019300241023302078,
0.0606328621506691,
-0.004753853194415569,
0.036609239876270294,
0.03609893471002579,
0.06992508471012115,
0.0486137755215168,
-0.012298230081796646,
-0.04711967706680298,
-0.015957122668623924,
0.04016204550862312,
0.026073232293128967,
0.0025483753997832537,
-0.02967795915901661,
0.004839097615331411,
-0.0018196753226220608,
-0.028427546843886375,
0.0029497139621526003,
0.03528314828872681,
-0.05373515188694,
-0.0031680858228355646,
-0.007769179996103048,
0.041530780494213104,
-0.027480069547891617,
-0.031837478280067444,
-0.0316336490213871,
-0.038456644862890244,
-0.028434747830033302,
-0.016437387093901634,
-0.02190285176038742,
-0.03712503984570503,
0.024274585768580437,
-0.04140392318367958,
0.00233587552793324,
0.005758510436862707,
-0.012075898237526417,
-0.0007089502760209143,
-0.012442564591765404,
0.02157585881650448,
0.031149305403232574,
-0.012389319948852062,
0.0452321358025074,
0.044811882078647614,
0.0003079970774706453,
0.05113888159394264,
0.0012508967192843556,
-0.010482200421392918,
0.02273602783679962,
0.006354714278131723,
-0.004436127841472626,
-0.044459737837314606,
-0.0034549436531960964,
0.0166885145008564,
0.027629580348730087,
0.04572111740708351,
0.022337010130286217,
0.007682700641453266,
-0.029652930796146393,
-0.003061115276068449,
0.0025916793383657932,
-0.08645305782556534,
-0.014680695720016956,
-0.03476332873106003,
0.0471380241215229,
-0.017923587933182716,
-0.031910188496112823,
-0.057700302451848984,
0.059661298990249634,
0.0316581130027771,
-0.0068654147908091545,
-0.022502778097987175,
0.011420011520385742,
0.013724643737077713,
0.012008038349449635,
0.0017454567132517695,
0.06197310984134674,
-0.06494457274675369,
-0.00721382163465023,
0.04777767136693001,
0.005041168071329594,
-0.012625932693481445,
0.01446065679192543,
0.055937834084033966,
-0.021648475900292397,
-0.021780146285891533,
0.004065897315740585,
0.10553725808858871,
-0.01931471936404705,
0.04606811702251434,
0.037995871156454086,
-0.027075491845607758,
0.034962572157382965,
-0.03610880300402641,
0.0017832788871601224,
-0.01230041403323412,
0.07420860975980759,
0.05123437941074371,
0.008098410442471504,
0.012525337748229504,
-0.02760569378733635,
0.010106482543051243,
-0.04691317304968834,
0.02458464540541172,
-0.037076447159051895,
0.05259672552347183,
-0.029334448277950287,
0.040788304060697556,
0.02201015315949917,
-0.04197832942008972,
0.05096767097711563,
-0.06947380304336548,
0.01661137491464615,
-0.023552872240543365,
-0.060757383704185486,
0.04242883622646332,
0.0010149702429771423,
-0.05526953935623169,
0.030837124213576317,
0.012064524926245213,
0.02342662401497364,
0.051803138107061386,
-0.03234216198325157,
-0.06340305507183075,
-0.029079245403409004,
-0.02180284820497036,
0.012659024447202682,
0.05389551445841789,
-0.0015434625092893839,
0.03357519209384918,
-0.013774076476693153,
0.03847619518637657,
-0.05727991461753845,
-0.0351933017373085,
-0.013996204361319542,
0.021625198423862457,
0.046935565769672394,
0.037250664085149765,
0.02036050520837307,
-0.01887042261660099,
0.026122640818357468,
0.004365091677755117,
0.040163490921258926,
-0.040182605385780334,
-0.0047605144791305065,
0.009278276935219765,
-0.02540517970919609,
-0.0069456095807254314,
-0.0024311868473887444,
-0.025527523830533028,
-0.044500164687633514,
-0.04359683766961098,
0.07502385973930359,
-0.04686374217271805,
-0.034231919795274734,
0.017063047736883163,
-0.025582926347851753,
-0.05887971818447113,
-0.03234782814979553,
-0.00545552559196949,
-0.02771764062345028,
-0.06058607995510101,
-0.031005488708615303,
0.0197298564016819,
-0.0008251460967585444,
-0.03178243339061737,
0.04134509712457657,
0.03150089457631111,
0.04522634297609329,
0.031241169199347496,
-0.010735804215073586,
0.0022999539505690336,
0.04214556887745857,
-0.027298761531710625,
0.0051172832027077675,
-0.004742917139083147,
-0.011324833147227764,
-0.05687835440039635,
0.004926338791847229,
0.013523358851671219,
-0.011217392049729824,
0.04295378550887108,
-0.05833686143159866,
0.01325412467122078,
0.017460955306887627,
-0.025484828278422356,
-0.02533097192645073,
-0.022374607622623444,
-0.05452798679471016,
0.028747806325554848,
-0.03855465352535248,
0.027751803398132324,
-0.005793094169348478,
-0.03927494212985039,
0.046030376106500626,
0.008467499166727066,
0.03271003067493439,
-0.02014562301337719,
-0.02242637239396572,
-0.006112791132181883,
0.04916843771934509,
-0.003420152934268117,
0.05730845779180527,
-0.04454857483506203,
0.052060745656490326,
0.04295635595917702,
0.018268803134560585,
0.028234360739588737,
0.061683397740125656,
-0.028484787791967392,
-0.007026385515928268,
-0.009179653599858284,
-0.020395085215568542,
0.013560134917497635,
0.021716659888625145,
-0.034616779536008835,
0.011490127071738243,
0.009619652293622494,
-0.04752477630972862,
-0.020731918513774872,
0.05419527739286423,
-0.030944904312491417,
0.04205325245857239,
-0.0016631719190627337,
-0.045839883387088776,
-0.021015899255871773,
-0.06858497858047485,
-0.048505548387765884,
-0.019336024299263954,
0.026148473843932152,
0.049008458852767944,
-0.03255331143736839,
0.048066720366477966,
-0.008033880032598972,
-0.031839776784181595,
-0.013701400719583035,
0.005961664952337742,
-0.0005348489503376186,
-0.027778008952736855,
-0.016665512695908546,
-0.0001162211992777884,
-0.009059512987732887,
0.025234989821910858,
-0.008850683458149433,
-0.03274357318878174,
-0.011487462557852268,
-0.0646100714802742,
0.029187409207224846,
0.01108363177627325,
0.01751088537275791,
0.018045688048005104,
0.005793044343590736,
0.024507246911525726,
0.02004808560013771,
0.016771970316767693,
0.0019404692575335503,
-0.007678090129047632,
-0.012648066505789757,
0.0414888933300972,
-0.0456094928085804,
0.0358586385846138,
-0.04836311191320419,
0.005652779713273048,
-0.014312125742435455,
0.08599969744682312,
0.06957343220710754,
0.023998428136110306,
0.011671483516693115,
-0.01785719022154808,
-0.045058444142341614,
0.01761014573276043,
0.0006703793769702315,
0.0024884112644940615,
-0.009463267400860786,
0.0049097235314548016,
-0.023362338542938232,
-0.042061638087034225,
-0.008054926991462708,
0.010472175665199757,
0.05744015425443649,
0.023683249950408936,
0.028735799714922905,
0.02471974492073059,
-0.0027081065345555544,
0.04521458223462105,
-0.02064434438943863,
0.016505710780620575,
0.014985631220042706,
-0.016659723594784737,
-0.010612604208290577,
-0.0615505613386631,
-0.09166465699672699,
0.03695903345942497,
0.021691245958209038,
0.005033687688410282,
0.005718566942960024,
-0.018913771957159042,
-0.0502178929746151,
-0.044901296496391296,
-0.06610013544559479,
-0.028729988262057304,
0.04081627354025841,
0.0354657880961895,
-0.022860895842313766,
-0.03504609316587448,
-0.06037219613790512,
-0.0037409167271107435,
-0.04362643137574196,
0.02262740582227707,
0.003133967285975814,
0.03709103912115097,
0.018584677949547768,
0.0145254572853446,
-0.0552564412355423,
0.06526945531368256,
0.010014798492193222,
-0.021586716175079346,
0.028404098004102707,
-0.00582417007535696,
-0.0584212951362133,
0.04391573742032051,
0.014224848710000515,
0.009314372204244137,
-0.04988962784409523,
0.03525037318468094,
0.08468643575906754,
-0.06076415628194809,
-0.056869663298130035,
-0.04107178747653961,
-0.031417082995176315,
-0.022519424557685852,
-0.003012701403349638,
0.03177176043391228,
-0.03569193184375763,
0.08738891035318375
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.